Handbook of Optical Sensing of Glucose in Biological Fluids and Tissues (Series in Medical Physics and Biomedical Engineering)

Handbook of Optical Sensing of Glucose in Biological Fluids and Tissues

© 2009 by Taylor & Francis Group, LLC

Series in Medical Physics and Biomedical Engineering Series Editors: John  G Webster, E Russell Ritenour, Slavik Tabakov, and Kwan-Hoong Ng Other recent books in the series: A Introduction to Radiation Protection in Medicine Jamie V. Trapp and Tomas Kron (Eds) A Practical Approach to Medical Image Processing Elizabeth Berry Biomolecular Action of Ionizing Radiation Shirley Lehnert An Introduction to Rehabilitation Engineering R A Cooper, H Ohnabe, and D A Hobson The Physics of Modern Brachytherapy for Oncology D Baltas, N Zamboglou, and L Sakelliou Electrical Impedance Tomography D Holder (Ed) Contemporary IMRT S Webb The Physical Measurement of Bone C M Langton and C F Njeh (Eds) Therapeutic Applications of Monte Carlo Calculations in Nuclear Medicine H Zaidi and G Sgouros (Eds) Minimally Invasive Medical Technology J G Webster (Ed) Intensity-Modulated Radiation Therapy S Webb Physics for Diagnostic Radiology, Second Edition P Dendy and B Heaton Achieving Quality in Brachytherapy B R Thomadsen Medical Physics and Biomedical Engineering B H Brown, R H Smallwood, D C Barber, P V Lawford, and D R Hose Monte Carlo Calculations in Nuclear Medicine M Ljungberg, S-E Strand, and M A King (Eds) © 2009 by Taylor & Francis Group, LLC

Series in Medical Physics and Biomedical Engineering

Handbook of Optical Sensing of Glucose in Biological Fluids and Tissues

Edited by

Valery V. Tuchin

Saratov State University and Institute of Precise Mechanics and Control of RAS Russia

Boca Raton London New York

CRC Press is an imprint of the Taylor & Francis Group, an informa business

A TA Y L O R & F R A N C I S B O O K

© 2009 by Taylor & Francis Group, LLC

CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487‑2742 © 2009 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed in the United States of America on acid‑free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number‑13: 978‑1‑58488‑974‑8 (Hardcover) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, trans‑ mitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright. com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978‑750‑8400. CCC is a not‑for‑profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging‑in‑Publication Data Handbook of optical sensing of glucose in biological fluids and tissues / editor, Valery V. Tuchin. p. ; cm. ‑‑ (Series in medical physics and biomedical engineering) Includes bibliographical references and index. ISBN 978‑1‑58488‑974‑8 (hardback : alk. paper) 1. Blood sugar monitoring‑‑Handbooks, manuals, etc. 2. Near infrared spectroscopy‑‑Handbooks, manuals, etc. 3. Diagnosis, Noninvasive‑‑Handbooks, manuals, etc. I. Tuchin, V. V. (Valerii Viktorovich) II. Series. [DNLM: 1. Blood Glucose‑‑analysis. 2. Biosensing Techniques‑‑instrumentation. 3. Blood Glucose Self‑Monitoring‑‑instrumentation. 4. Blood Glucose Self‑Monitoring‑‑methods. 5. Optics. 6. Spectrum Analysis‑‑methods. 7. Tomography, Optical‑‑methods. QY 470 H236 2008] RC660.H363 2008 572’.565‑‑dc22 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com

© 2009 by Taylor & Francis Group, LLC

2008014799

Contents

Preface List of Contributors 1

2

xvii xxvii

Glucose: Physiological Norm and Pathology Lidia I. Malinova and Tatyana P. Denisova 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 Goal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2 Terms and definitions . . . . . . . . . . . . . . . . . . . . . 1.2 System of Blood Glucose Level Regulation and Carbohydrate Metabolism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Glucose transporters . . . . . . . . . . . . . . . . . . . . . 1.2.2 Pathways of glucose concentration change: glucose distribution and concentrations in human organism . . . . . . . . . 1.2.3 Regulation of glucose metabolism: main pathways and processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.4 Insulin: the key hormone of glucose metabolism . . . . . . 1.2.5 Endothelium and glucose metabolism . . . . . . . . . . . . 1.3 Glucose and Carbohydrate Metabolism Violations . . . . . . . . . 1.3.1 Diabetes mellitus: glucose — victim or culprit? . . . . . . . 1.3.2 Atherosclerosis and coronary artery disease: glucose’s place in pathogenesis . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Blood Glucose Level Monitoring in Clinical Practice . . . . . . . . 1.4.1 Glucose level regulation system tests: clinical and experimental use . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.2 Clinical value of blood glucose level measurements . . . . . 1.4.3 Current state of the problem: unsolved questions . . . . . . 1.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Commercial Biosensors for Diabetes Vasiliki Fragkou and Anthony P.F. Turner 2.1 Introduction . . . . . . . . . . . . . . . . . 2.2 Diabetes Mellitus . . . . . . . . . . . . . . 2.2.1 Type I diabetes . . . . . . . . . . . 2.2.2 Type II diabetes . . . . . . . . . . 2.2.3 Gestational diabetes . . . . . . . . . 2.2.4 Incidence - A major world problem

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Handbook of Optical Sensing of Glucose 2.2.5 Treatments . . . . . . . . . . . . . . . . . . . . Home Urine/Blood Glucose Monitoring . . . . . . . . . 2.3.1 Urine glucose monitoring . . . . . . . . . . . . . 2.3.2 Blood glucose monitoring . . . . . . . . . . . . 2.4 Glucose Meters . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Colorimetric strips . . . . . . . . . . . . . . . . 2.4.2 Ames Reflectance Meter . . . . . . . . . . . . . 2.5 Glucose Biosensors . . . . . . . . . . . . . . . . . . . . 2.5.1 The Clark enzyme electrode . . . . . . . . . . . 2.5.2 Yellow Springs Instrument . . . . . . . . . . . . 2.5.3 Mediated biosensors . . . . . . . . . . . . . . . 2.6 Current Commercial Home Blood Glucose Monitoring . 2.6.1 General principles . . . . . . . . . . . . . . . . 2.6.2 Commercial aspects . . . . . . . . . . . . . . . . 2.7 Integrated Devices . . . . . . . . . . . . . . . . . . . . 2.8 Alternative Glucose Monitors . . . . . . . . . . . . . . 2.8.1 Minimally invasive testing . . . . . . . . . . . . 2.8.2 Continuous Glucose Monitoring System [36, 37] 2.9 Challenges and Hurdles Facing Glucose Biosensors . . . 2.10 Future Perspectives & Conclusions . . . . . . . . . . . 2.3

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Monte Carlo Simulation of Light Propagation in Human Tissues and Noninvasive Glucose Sensing Alexander V. Bykov, Mikhail Yu. Kirillin and Alexander V. Priezzhev 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Effect of Glucose on Optical Parameters of Particulate Media . . . 3.3 Principles of the Monte Carlo Technique . . . . . . . . . . . . . . 3.3.1 Basics of the Monte Carlo method . . . . . . . . . . . . . . 3.3.2 Monte Carlo algorithm . . . . . . . . . . . . . . . . . . . . 3.4 Modeling of Glucose Sensing with OCT . . . . . . . . . . . . . . . 3.4.1 Principles of OCT . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Simulation of the OCT A-scan . . . . . . . . . . . . . . . . 3.4.3 Comparison of simulated and experimental results . . . . . 3.5 Modeling of Glucose Sensing with Spatial Resolved Reflectometry 3.5.1 Multilayer biotissue phantom and its optical properties for Monte Carlo simulation . . . . . . . . . . . . . . . . . . . . 3.5.2 SRR-signal . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.3 Relative sensitivity of SRR . . . . . . . . . . . . . . . . . . 3.5.4 Scattering maps . . . . . . . . . . . . . . . . . . . . . . . 3.5.5 Dependence of SRR-signal on glucose concentration . . . . 3.6 Modeling of Glucose Sensing with Time Domain Technique . . . . 3.6.1 Output time-of-flight signal . . . . . . . . . . . . . . . . . . 3.6.2 Relative sensitivity of the TOF signals to glucose concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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66 67 68 68 69 72 72 73 75 77 77 78 80 81 81 83 84 85

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Modeling of Glucose Sensing with Frequency Domain Technique . 3.7.1 Principles of frequency domain technique . . . . . . . . . . 3.7.2 Simulation of frequency domain signals . . . . . . . . . . . 3.7.3 Analysis of glucose sensing potentialities of the frequency domain technique . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vii 86 86 88 89 90

Statistical Analysis for Glucose Prediction in Blood Samples by Infrared Spectroscopy 97 Gilwon Yoon 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Selection of Optimal Wavelength Region Based on the First Loading Vector Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Optimal wavelength region in the mid infrared . . . . . . . 4.2.2 Optimal wavelength region in the near infrared . . . . . . . 4.3 Minimization of Hemoglobin Interference . . . . . . . . . . . . . . 4.3.1 Hemoglobin influence in the mid infrared region . . . . . . 4.3.2 Hemoglobin influence in the near infrared region . . . . . . 4.4 Independent Component Analysis without Calibration Process . . . 4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

98 100 100 102 105 106 106 108 111

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Near-Infrared Reflection Spectroscopy for Noninvasive Monitoring of Glucose — Established and Novel Strategies for Multivariate Calibration 115 H.Michael Heise, Peter Lampen and Ralf Marbach 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 5.2 Experimental Design and Methods . . . . . . . . . . . . . . . . . . 118 5.2.1 Patients and calibration design . . . . . . . . . . . . . . . . 118 5.2.2 Reference measurements and calibration method . . . . . . 119 5.2.3 Experiments and spectroscopic data . . . . . . . . . . . . . 120 5.3 Results Obtained by Conventional Calibration and Discussion . . . 124 5.4 Advantages of the “Science-Based” Calibration Method . . . . . . 132 5.5 Theory and Background . . . . . . . . . . . . . . . . . . . . . . . 133 5.6 Specificity of Response . . . . . . . . . . . . . . . . . . . . . . . . 136 5.7 Illustration of the Science-Based Calibration Method . . . . . . . . 141 5.7.1 Outlook for the novel calibration method . . . . . . . . . . 150 5.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

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Characterizing the Influence of Acute Hyperglycaemia on Cerebral Hemodynamics by Optical Imaging 157 Qingming Luo, Zhen Wang, Weihua Luo and Pengcheng Li 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 6.2 Optical Imaging Techniques of Functional Brain . . . . . . . . . . 159 6.2.1 Laser speckle imaging . . . . . . . . . . . . . . . . . . . . 159

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6.3

6.4

6.2.2 Intrinsic optical signal imaging . . . . . . . . . . . . . . . . Influence of Acute Hyperglycaemia on CBF and SD in Rat Cortex . 6.3.1 Long-term monitoring the influence of glucose upon CBF in rat cortex . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Optical imaging of hemodynamic response during cortical spreading depression in the normal or acute hyperglycemic rat cortex . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

162 164 164

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Near-Infrared Thermo-Optical Response of the Localized Reflectance of Diabetic and Non-Diabetic Human Skin 181 Omar S. Khalil 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 7.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 184 7.3 Temperature Dependence of µa and µs′ of Individual’s Skin . . . . . 185 7.4 Temperature Modulation of µa and µs′ of Skin Over Prolonged Interaction Between the Optical Probe and Skin . . . . . . . . . . . . . 190 7.5 Dependence of Thermo-Optical Response of Localized Reflectance of Human Skin on Diabetic State . . . . . . . . . . . . . . . . . . 192 7.6 Test for Diabetic State . . . . . . . . . . . . . . . . . . . . . . . . 193 7.7 Biological Noise and Glucose Determinations . . . . . . . . . . . . 194 7.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

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In Vivo Nondestructive Measurement of Blood Glucose by Near-Infrared Diffuse-Reflectance Spectroscopy 205 Yukihiro Ozaki, Hideyuki Shinzawa, Katsuhiko Maruo, Yi Ping Du and Sumaporn Kasemsumran 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 8.2 Importance of NIR In Vivo Monitoring of Blood Glucose . . . . . . 207 8.3 The NIR System for Noninvasive Blood Glucose Assay . . . . . . 208 8.3.1 Outline of the NIR instrument . . . . . . . . . . . . . . . . 209 8.3.2 Spectral measurements . . . . . . . . . . . . . . . . . . . . 210 8.4 NIR Spectra of Human Skin and Built of Calibration Models . . . . 210 8.4.1 NIR spectra of human skin . . . . . . . . . . . . . . . . . . 210 8.4.2 Calibration models . . . . . . . . . . . . . . . . . . . . . . 211 8.4.3 Blood glucose assay . . . . . . . . . . . . . . . . . . . . . 211 8.4.4 The regression coefficient characteristics . . . . . . . . . . . 214 8.4.5 The prediction of blood glucose content . . . . . . . . . . . 214 8.5 New Chemometrics Algorithms for Wavelength Interval Selection and Sample Selection and Their Applications to In Vivo Near-Infrared Spectroscopic Determination of Blood Glucose . . . . . . . . . . . 217 8.5.1 Moving window partial least squares regression (MWPLSR) 219 8.5.2 Changeable size moving window partial least squares (CSMWPLS) and searching combination moving window partial least squares (SCMWPLS) . . . . . . . . . . . . . . . . . . . . . 221

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8.5.3

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Application of MWPLSR and SCMWPLS to noninvasive blood glucose assay with NIR spectroscopy . . . . . . . . . . . . 222 Multi-Objective Genetic Algorithm-Based Sample Selection for Partial Least Squares Model Building . . . . . . . . . . . . . . . . . . 226 8.6.1 Multi-objective genetic algorithm . . . . . . . . . . . . . . 226 8.6.2 Sample selection by multi-objective GA in PLS . . . . . . . 227 8.6.3 Applications of multi-objective GA to NIR spectra of human skin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 Region Orthogonal Signal Correction (ROSC) and Its Application to In Vivo NIR Spectra of Human Skin . . . . . . . . . . . . . . . . . 231

Glucose Correlation with Light Scattering Patterns Ilya Fine 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1.1 Clinical need for blood glucose measurement . . . . . . . . 9.1.2 Current art of noninvasive blood measurements . . . . . . . 9.1.3 Red blood cells aggregation phenomena . . . . . . . . . . . 9.1.4 Shear forces and blood viscosity . . . . . . . . . . . . . . . 9.1.5 Clinical relevance of RBC aggregation . . . . . . . . . . . 9.1.6 Measurement of RBC aggregation . . . . . . . . . . . . . . 9.2 Principles of Occlusion Spectroscopy . . . . . . . . . . . . . . . . 9.2.1 Aggregation assisted optical signal in vivo . . . . . . . . . . 9.2.2 The occlusion spectroscopy system . . . . . . . . . . . . . 9.3 Spectro-Kinetic Features of Aggregation Assisted Signal . . . . . . 9.3.1 The parametric slope . . . . . . . . . . . . . . . . . . . . . 9.3.2 Structure of parametric slope in vivo . . . . . . . . . . . . . 9.3.3 In vitro measurement of POS signal . . . . . . . . . . . . . 9.4 Refractive Index of RBC as a Function of Blood Glucose . . . . . . 9.4.1 Mismatch of refractive index . . . . . . . . . . . . . . . . . 9.4.2 Mismatch of refractive index as a function of glucose . . . . 9.5 Parametric Slope as a Function of BG . . . . . . . . . . . . . . . . 9.5.1 Time dependent optical parameters . . . . . . . . . . . . . . 9.5.2 General expression for the PS . . . . . . . . . . . . . . . . 9.6 PS Glucose Dependence for Single RBCs and Small Aggregates . . 9.6.1 RBC scattering pattern . . . . . . . . . . . . . . . . . . . . 9.6.2 PS for Mie scattering approximation . . . . . . . . . . . . . 9.6.3 PSV as a function of glucose . . . . . . . . . . . . . . . . . 9.6.4 PSS as function of blood plasma glucose for small aggregates 9.7 PSS in the Framework of WKB Model . . . . . . . . . . . . . . . 9.7.1 WKB approximation . . . . . . . . . . . . . . . . . . . . . 9.7.2 Expression for the K-function . . . . . . . . . . . . . . . . 9.7.3 Critical wavelength . . . . . . . . . . . . . . . . . . . . . . 9.7.4 Effect of glucose on the light transmission for very long aggregates . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

10 Challenges and Countermeasures in NIR Noninvasive Blood Glucose Monitoring 281 Kexin Xu and Ruikang K. Wang 10.1 The Principles and Issues on the Measurement of Blood Glucose Using Near-Infrared Spectroscopy . . . . . . . . . . . . . . . . . . 10.1.1 The principle of blood glucose measurement using near infrared spectroscopy . . . . . . . . . . . . . . . . . . . . . . 10.1.2 Noninvasive glucose measurement by diffuse reflectance spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1.3 The main questions of noninvasive glucose measurement by NIR spectroscopy . . . . . . . . . . . . . . . . . . . . . . 10.2 Factors of Influencing the Measuring Precision of Glucose Monitor 10.2.1 The relationship between measuring precision and instrumental precision . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.2 An effective calibration method to improve the measuring precision of glucose concentration . . . . . . . . . . . . . . 10.2.3 The influence of sample complexity on measuring precision 10.2.4 The optimal pathlength method to improve the measuring precision of glucose concentration . . . . . . . . . . . . . . 10.2.5 Precision analysis of the glucose concentration measurement by diffuse reflectance spectroscopy from dermis layer . . . . 10.3 Noninvasive Glucose Measurement and Human-Spectrometer Interface Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1 The influence of measurement site and position . . . . . . . 10.3.2 The influence of contact pressure . . . . . . . . . . . . . . . 10.3.3 The measuring conditions reproducible system (MCRS) and human glucose sensing experiments . . . . . . . . . . . . . 10.4 Challenges and Solutions in In Vivo Noninvasive Blood Glucose Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.1 The influence of the time dependent variations from physiological background on the glucose measurement . . . . . . . 10.4.2 The floating-reference method solution . . . . . . . . . . . 10.4.3 The preliminary experimental validation of the floating-reference method . . . . . . . . . . . . . . . . . . . . . . . . 10.4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Fluorescence-Based Glucose Biosensors

282 282 283 286 287 288 289 290 293 295 297 297 299 304 307 307 309 312 315 319

Gerard L. Cot`e, M. McShane and M.V. Pishko 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 11.2 Historical Review of Fluorescence-Based Glucose Assays . . . . . 321 11.3 Issues Involved with In Vivo Glucose Monitoring Using Fluorescent Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321

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Table of Contents 11.4 Fluorescence-Based Glucose-Binding Protein Assays . . . . . . . . 11.4.1 Concanavalin A-based approaches . . . . . . . . . . . . . . 11.4.2 Engineered glucose-binding proteins . . . . . . . . . . . . . 11.5 Fluorescence Resonance Energy Transfer Systems for Glucose Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.5.1 Single-molecule RET systems using dual-labeled engineered proteins . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.6 Enzyme-Based Glucose Sensors . . . . . . . . . . . . . . . . . . . 11.6.1 Apo-glucose oxidase . . . . . . . . . . . . . . . . . . . . . 11.7 Boronic Acid Derivatives . . . . . . . . . . . . . . . . . . . . . . 11.8 Summary and Concluding Remarks . . . . . . . . . . . . . . . . . 12 Quantitative Biological Raman Spectroscopy Wei-Chuan Shih, Kate L. Bechtel and Michael S. Feld 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 12.1.1 Introduction to Raman spectroscopy . . . . . . . . 12.2 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2.1 Semi-quantitative implementation . . . . . . . . . 12.2.2 Univariate implementation . . . . . . . . . . . . . 12.2.3 Multivariate implementation . . . . . . . . . . . . 12.3 Quantitative Considerations for Raman Spectroscopy . . . 12.3.1 Considerations for multivariate calibration models 12.3.2 Fundamental and practical limits . . . . . . . . . . 12.3.3 Chance or spurious correlation . . . . . . . . . . . 12.3.4 Spectral evidence of the analyte of interest . . . . . 12.3.5 Minimum detection limit . . . . . . . . . . . . . . 12.4 Biological Considerations for Raman Spectroscopy . . . . 12.4.1 Using near infrared radiation . . . . . . . . . . . . 12.4.2 Background signal in biological Raman spectra . . 12.4.3 Heterogeneities in human skin . . . . . . . . . . . 12.5 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . 12.5.1 Excitation light source . . . . . . . . . . . . . . . 12.5.2 Light delivery, collection, and transport . . . . . . 12.5.3 Spectrograph and detector . . . . . . . . . . . . . 12.6 Data Pre-Processing . . . . . . . . . . . . . . . . . . . . 12.6.1 Image curvature correction . . . . . . . . . . . . . 12.6.2 Spectral range selection . . . . . . . . . . . . . . . 12.6.3 Cosmic ray removal . . . . . . . . . . . . . . . . . 12.6.4 Background subtraction . . . . . . . . . . . . . . . 12.6.5 Random noise rejection and suppression . . . . . . 12.6.6 White light correction and wavelength calibration . 12.6.7 Wavelength selection . . . . . . . . . . . . . . . . 12.7 In Vitro and In Vivo Studies . . . . . . . . . . . . . . . . 12.7.1 Model validation protocol and summary statistics .

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Handbook of Optical Sensing of Glucose 12.7.2 Blood serum . . . . . . . . . . . . . . . . . . . . . . . . . 12.7.3 Whole blood . . . . . . . . . . . . . . . . . . . . . . . . . 12.7.4 Human study . . . . . . . . . . . . . . . . . . . . . . . . . 12.8 Toward Prospective Application . . . . . . . . . . . . . . . . . . . 12.8.1 Analyte-specific information extraction using hybrid calibration methods . . . . . . . . . . . . . . . . . . . . . . . . . 12.8.2 Hybrid linear analysis (HLA) . . . . . . . . . . . . . . . . . 12.8.3 Constrained regularization (CR) . . . . . . . . . . . . . . . 12.8.4 Sampling volume correction using intrinsic Raman spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.8.5 Corrections based on photon migration theory . . . . . . . . 12.8.6 Intrinsic Raman spectroscopy (IRS) . . . . . . . . . . . . . 12.8.7 Other considerations and future directions . . . . . . . . . . 12.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

372 373 373 374 374 375 375 377 377 378 379 380

13 Tear Fluid Photonic Crystal Contact Lens Noninvasive Glucose Sensors 387 Sanford A. Asher and Justin T. Baca 13.1 Importance of Glucose Monitoring in Diabetes Management 13.2 Eye Tear Film . . . . . . . . . . . . . . . . . . . . . . . . 13.3 Glucose in Tear Fluid . . . . . . . . . . . . . . . . . . . . . 13.3.1 Tear fluid glucose transport . . . . . . . . . . . . . 13.3.2 Tear glucose in diabetic subjects . . . . . . . . . . . 13.4 Previously Reported Tear Fluid Glucose Concentrations . . 13.4.1 Previous measurements of tears in extracted tear fluid 13.4.2 Mechanical tear fluid stimulation . . . . . . . . . . . 13.4.3 Chemical and non-contact tear fluid stimulation . . . 13.4.4 Non-stimulated tear fluid . . . . . . . . . . . . . . . 13.5 Recent Tear Fluid Glucose Determinations . . . . . . . . . 13.6 In Situ Tear Glucose Measurements . . . . . . . . . . . . . 13.7 Photonic Crystal Glucose Sensors . . . . . . . . . . . . . . 13.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . .

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14 Pulsed Photoacoustic Techniques and Glucose Determination in Human Blood and Tissue 419 Risto Myllyl¨a, Zuomin Zhao and Matti Kinnunen 14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2 Theoretical Aspects of PA Techniques Used in Glucose Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2.1 Cylindrical PA source in a weakly absorbing liquid . . . . . 14.2.2 Plane PA source in strongly absorbing and scattering tissues 14.2.3 Spherical PA source . . . . . . . . . . . . . . . . . . . . . . 14.3 Optical Sources and Detectors . . . . . . . . . . . . . . . . . . . . 14.3.1 Optical sources . . . . . . . . . . . . . . . . . . . . . . . . 14.3.2 PA detectors . . . . . . . . . . . . . . . . . . . . . . . . . .

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Table of Contents 14.4 PA Glucose Determination . . . . . . . . . . . 14.4.1 In vitro glucose studies . . . . . . . . . . 14.4.2 In vivo noninvasive glucose determination 14.5 Problems and Future Perspectives . . . . . . . .

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15 A Noninvasive Glucose Sensor Based on Polarimetric Measurements Through the Aqueous Humor of the Eye 457 Gerard L. Cot`e and Brent D. Cameron 15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.2 Theory of Polarized Light for Detecting Chemical Compounds . . . 15.3 The Anterior Chamber of the Eye as a Site for Polarimetric Glucose Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.3.1 Why use the eye? . . . . . . . . . . . . . . . . . . . . . . . 15.3.2 The anatomy and physiology of the eye toward glucose monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.3.3 Corneal curvature and birefringence . . . . . . . . . . . . . 15.4 Polarimetric Glucose Monitoring Using a Single Wavelength . . . . 15.5 Measurement of Optical Rotatory Dispersion of Aqueous Humor Analytes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.6 Corneal Birefringence Simulation and Experimental Measurement . 15.7 Dual Wavelength (Multi-Spectral) Polarimetric Glucose Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.8 Concluding Remarks Regarding the Use of Polarization for Glucose Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

458 458 462 462 463 465 469 470 475 480 481

16 Noninvasive Measurements of Glucose in the Human Body Using Polarimetry and Brewster-Reflection Off of the Eye Lens 487 Luigi Rovati and Rafat R. Ansari 16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488 16.2 Basic Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489 16.3 Anatomy and Properties of the Human Eye of Interest for Polarimetric Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 490 16.3.1 Polarization effects in the eye’s anterior chamber . . . . . . 490 16.3.2 The Navarro eye model . . . . . . . . . . . . . . . . . . . 491 16.4 Optical Access to the Aqueous: Tangential Path and Brewster Scheme Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493 16.4.1 Tangential path approach . . . . . . . . . . . . . . . . . . . 493 16.4.2 Brewster scheme . . . . . . . . . . . . . . . . . . . . . . . 493 16.5 Glucose Sensor Based on the Brewster Scheme . . . . . . . . . . . 498 16.5.1 Working principle . . . . . . . . . . . . . . . . . . . . . . . 498 16.5.2 Angle detection unit . . . . . . . . . . . . . . . . . . . . . 499 16.5.3 Experimental set-up . . . . . . . . . . . . . . . . . . . . . . 500 16.6 Performance of the Glucose Sensor Based on the Brewster Scheme 501 16.6.1 Theoretical analysis . . . . . . . . . . . . . . . . . . . . . 502

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Handbook of Optical Sensing of Glucose 16.6.2 In vitro experiments . . . . . . . . . . . . . . . . . . . . . . 516 16.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523

17 Toward Noninvasive Glucose Sensing Using Polarization Analysis of Multiply Scattered Light 527 Michael F. G. Wood, Nirmalya Ghosh, Xinxin Guo and I. Alex Vitkin 17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 528 17.2 Polarimetry in Turbid Media: Experimental Platform for Sensitive Polarization Measurements in the Presence of Large Depolarized Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530 17.3 Polarimetry in Turbid Media: Accurate Forward Modeling Using the Monte Carlo Approach . . . . . . . . . . . . . . . . . . . . . . . . 536 17.4 Tackling the Inverse Problem: Polar Decomposition of the Lumped Mueller Matrix to Extract Individual Polarization Contributions . . 540 17.5 Monte Carlo Modeling Results for Measurement Geometry, Optical Pathlength, Detection Depth, and Sampling Volume Quantification . 547 17.6 Combining Intensity and Polarization Information via Spectroscopic Turbid Polarimetry with Chemometric Analysis . . . . . . . . . . . 553 17.7 Concluding Remarks on the Prospect of Glucose Detection in Optically Thick Scattering Tissues with Polarized Light . . . . . . . . . 558 18 Noninvasive Monitoring of Glucose Concentration with Optical Coherence Tomography 563 Rinat O. Esenaliev and Donald S. Prough 18.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564 18.2 Noninvasive Optical Techniques for Glucose Monitoring . . . . . . 566 18.3 Optical Coherence Tomography . . . . . . . . . . . . . . . . . . . 567 18.4 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 569 18.5 Studies in Tissue Phantoms . . . . . . . . . . . . . . . . . . . . . 570 18.6 Animal Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571 18.7 Specificity Studies . . . . . . . . . . . . . . . . . . . . . . . . . . 572 18.8 Clinical Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574 18.9 Mechanisms of Glucose-Induced Changes in Optical Properties of Tissue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576 18.10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578 19 Measurement of Glucose Diffusion Coefficients in Human Tissues Alexey N. Bashkatov, Elina A. Genina and Valery V. Tuchin 19.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.2 Spectroscopic Methods . . . . . . . . . . . . . . . . . . . . . . 19.3 Photoacoustic Technique . . . . . . . . . . . . . . . . . . . . . 19.4 Use of Radioactive Labels for Detecting Matter Flux . . . . . . 19.5 Light Scattering Measurements . . . . . . . . . . . . . . . . .

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19.5.1 Spectrophotometry . . . . . . . . . . . . . . . . . . . . . . 600 19.5.2 OCT and interferometry . . . . . . . . . . . . . . . . . . . 610 19.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 612 20 Monitoring of Glucose Diffusion in Epithelial Tissues with Optical Coherence Tomography 623 Kirill V. Larin and Valery V. Tuchin 20.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624 20.2 Basic Theories of Glucose-Induced Changes of Tissue Optical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 627 20.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . 630 20.3.1 Materials and methods . . . . . . . . . . . . . . . . . . . . 630 20.3.2 Quantification of molecular diffusion in ocular tissues (cornea and sclera) in vitro . . . . . . . . . . . . . . . . . . . . . . 632 20.3.3 Quantification of glucose diffusion in skin in vitro . . . . . . 636 20.3.4 Quantification of glucose diffusion in skin in vivo . . . . . . 637 20.3.5 Quantification of glucose diffusion in healthy and diseased aortas in vitro . . . . . . . . . . . . . . . . . . . . . . . . . 637 20.3.6 Comparative studies for assessment of molecular diffusion with OCT and histology . . . . . . . . . . . . . . . . . . . 640 20.3.7 Assessment of optical clearing of ocular tissues with OCT . 642 20.3.8 Depth-resolved assessment of glucose diffusion in tissues . . 643 21 Glucose-Induced Optical Clearing Effects in Tissues and Blood Elina A. Genina, Alexey N. Bashkatov and Valery V. Tuchin 21.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Structure and Optical Properties of Fibrous Tissues and Blood . . . 21.2.1 Structure, physical and optical properties of fibrous tissues . 21.2.2 Structure, physical and optical properties of skin . . . . . . 21.2.3 Optical model of fibrous tissue . . . . . . . . . . . . . . . . 21.2.4 Structure, physical and optical properties of blood . . . . . . 21.2.5 Optical model of blood . . . . . . . . . . . . . . . . . . . . 21.3 Glucose-Induced Optical Clearing Effects in Tissues . . . . . . . . 21.3.1 Mechanisms of optical immersion clearing . . . . . . . . . 21.3.2 Optical clearing of fibrous tissues . . . . . . . . . . . . . . 21.3.3 Optical clearing of skin . . . . . . . . . . . . . . . . . . . . 21.4 Glucose-Induced Optical Clearing Effects in Blood and Cellular Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4.1 Optical clearing of blood . . . . . . . . . . . . . . . . . . . 21.4.2 Time-domain and frequency-domain measurements . . . . . 21.4.3 Experimental results . . . . . . . . . . . . . . . . . . . . . 21.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Preface

Approximately 17 million people in the USA (6% of the population) and 140 million people worldwide (this number is expected to rise to almost 300 million by the year 2025) suffer from diabetes mellitus. Currently, there are a few dozen commercialized devices for detecting blood glucose levels [1]. However, most of them are invasive. The development of a noninvasive method would considerably improve the quality of life for diabetic patients, facilitate their compliance for glucose monitoring, and reduce complications and mortality associated with this disease. Noninvasive and continuous monitoring of glucose concentration in blood and tissues is one of the most challenging and exciting applications of optics in medicine. The major difficulty in the development of a clinical application of optical noninvasive blood glucose sensors is associated with the very low signal produced by glucose molecules. This results in low sensitivity and specificity of glucose monitoring by optical methods and needs a lot of effort to overcome this difficulty. A wide range of optical technologies have been designed in attempts to develop robust noninvasive methods for glucose sensing. The methods include infrared absorption; near-infrared scattering; Raman, fluorescent, and thermal gradient spectroscopies; as well as polarimetric, polarization heterodyning, photonic crystal, optoacoustic, optothermal, and optical coherence tomography (OCT) techniques [1-31]. For example, the polarimetric quantification of glucose is based on the phenomenon of optical rotatory dispersion, whereby a chiral molecule in an aqueous solution rotates the plane of linearly polarized light passing through the solution. The angle of rotation depends linearly on the concentration of the chiral species, the path length through the sample, and the molecule specific rotation. However, a polarization sensitive optical technique makes it difficult to measure in vivo glucose concentration in blood through the skin because of the strong light scattering that causes light depolarization. For this reason, the anterior chamber of the eye has been suggested as a site well suited for polarimetric measurements, since scattering in the eye is generally very low compared to that in other tissues, and a high correlation exists between the glucose in the blood and in the aqueous humor. The high accuracy of anterior eye chamber measurements is also due to the low concentration of optically active aqueous proteins within the aqueous humor. On the other hand, the concept of noninvasive blood glucose sensing using the scattering properties of blood and tissues as an alternative to spectral absorption and polarization methods for monitoring of physiological glucose concentrations in diabetic patients has been under intensive discussion for the last decade. Many of the considered effects, such as changing of the size, refractive index, packing, and ag-

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gregation of RBC under glucose variation, are important for glucose monitoring in diabetic patients. Indeed, at physiological concentrations of glucose, ranging from 40 to 400 mg/dl, the role of some of the effects may be modified, and some other effects, such as glucose penetration inside the RBC and the followed hemoglobin glycation, may be important [30-32]. Noninvasive determination of glucose was attempted using light scattering of skin tissue components measured by a spatially-resolved diffuse reflectance or NIR frequency-domain reflectance techniques. Both approaches are based on a change in glucose concentration, which affects the refractive index mismatch between the interstitial fluid and tissue fibers, and hence reduces scattering coefficient. A glucose clamp experiment showed that reduced scattering coefficient measured in the visible range qualitatively tracked changes in blood glucose concentration in the volunteer with diabetes who was studied. The so-called occlusion spectroscopy is an approach that is based on light scattering from RBCs. This method suggests a controlled occlusion of finger blood vessels to slow blood flow in order to provide the shear forces of blood flow to be minimal and, thus, to allow RBCs to aggregate. Change in light scattering upon occlusion should be measured. Occlusion does not affect the rest of the tissue components, while scattering properties of aggregated RBCs differ from those of the nonaggregated ones and from the rest of the tissue. Change in glucose concentration affects refractive index of blood plasma, and hence affects blood light scattering at occlusion due to the refractive index match/mismatch between aggregates and plasma. Occlusion spectroscopy differs from that of spatially-resolved reflectance and frequencydomain measurements in that it proposes measurements of glucose in blood rather than in the interstitial fluid. Recently, the OCT technique has been proposed for noninvasive assessment of glucose concentration in tissues.High resolution of the OCT technique may allow high sensitivity, accuracy, and specificity of glucose concentration monitoring due to precise measurements of glucose-induced changes in the tissue optical properties from the layer of interest (dermis). Unlike diffuse reflectance method, OCT allows provision of depth-resolved qualitative and quantitative information about tissue optical properties of the three major layers of human skin: dead keratinized layer of squames (stratum corneum of epidermis); prickle cells layer (epidermis); and connective tissue of dermis. Dermis is the only layer of the skin containing a developed blood microvessel network. Since glucose concentration in the interstitial fluid is closely related to the blood glucose concentration, one can expect glucose-induced changes in the OCT signal detected from the dermis area of the skin. Two methods of OCT-based measurement and monitoring of tissue glucose concentration were proposed: 1) monitoring of the tissue scattering coefficient as a function of blood glucose concentration using conventional OCT; and 2) measurement of glucose-induced changes in the refractive index using novel polarization maintaining fiber-based dual channel phase-sensitive optical low-coherence reflectometer (PS-OLCR). In monitoring and determining chemical traces, the time-resolved OA technique and other optothermal techniques may be used in noninvasive monitoring of glucose. In the low scattering mode when aqueous glucose solutions were irradiated by NIR

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laser pulses at wavelengths that corresponded to NIR absorption of glucose (1.0–1.8 µ m), OA signal generation was assumed to be due to initial light absorption by the glucose molecules. A linear relationship between the OA signal and glucose concentration was found. It was also shown that the OA signal tracks changes in glucose concentration in human measurements. No specific advantages of OA spectroscopy over an NIR measurement of glucose are expected in this case. Another approach for OA glucose detection is based on the glucose property to change scattering parameters of tissues. The OA signal from the tissue depth is defined by optical attenuation, which is related to changes in the refractive index of the medium induced by changes in glucose concentration. Decreasing scattering increases the energy density in the OA sound source and induces higher OA signals. OA temporal profiles induced by laser pulses in in vivo tissues demonstrated that a 1 mM increase in glucose concentration resulted in up to a 5% decrease of effective optical attenuation. Measurement of glucose concentration and its diffusivity within the tissue is of widespread interest not only in the health care of diabetics, an automatic noninvasive monitoring of glucose concentration, it is also important for controlling growing cell cultures in tissue engineering, primarily for the production of implantable in vitro tissues and organs, as well as for controlling tissue optical properties [33-38]. At present only a few overview papers and sections in book chapters describing methods and techniques of optical glucose sensing and its influence on optical properties of tissues and blood are available. The recent book, edited by Geddes and Lakowicz [14], is devoted to glucose sensing using fluorescence spectroscopic method. No separate book, where various optical approaches are overviewed and discussed, could be found in literature. The lack of such a book makes it difficult to get a complete view of the field, since the information on optical glucose sensing and impact is spread over numerous publications in journals of physical, chemical, biophysical and biomedical specialization. Thus, a book that summarizes and analyzes new trends and perspectives of noninvasive glucose sensing and its impact on tissue optical properties seems to be needed and useful. The unique features of this book, which is a collection of 21 chapters written by world-recognized experts in the field, are the following: 1) for the first time in one book different noninvasive optical methods and techniques of glucose sensing are overviewed and analyzed; 2) the presence of chapters on basic research containing the updated results on coherent and polarization properties of light scattered by tissues and biological fluids containing glucose on physiological and hyperphysiological levels that allow for understanding optical techniques of glucose sensing and impact on tissue and blood optical properties; 3) discussion of the most recent prospective glucose-sensing methods based on light scattering, coherent-domain, polarization-sensitive, optoacoustic, and photonic crystal measurements; 4) new optical techniques for glucose diffusion coefficient measurements in human tissues; and 5) a description of glucose-induced optical clearing effects in tissue and blood. The book opens with a chapter that reviews data on glucose metabolism in physiological norm and pathology, shows the role of glucose in pathogenesis of diabetes mellitus and atherosclerosis, and describes problems of glucose sensing in clinical

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practice. The second chapter gives an introduction into commercial biosensors and the science behind their functionality. Chapter 3 describes the Monte Carlo method for statistical simulation of photons travelling in highly scattering tissues influenced by glucose. This chapter gives a theoretical background for a few basic optical techniques for glucose sensing, such as OCT, time-of-flight, spatial resolved reflectometry, frequency domain, and polarization sensitive. Two chapters, 4 and 5, describe methods that improve the accuracy of glucose prediction based on infrared absorption spectroscopy, such as a partial least squares regression loading vector analysis method; the method of minimization of spectral interference by other components; independent component analysis eliminating the calibration process; and the novel multivariate calibration method, the so-called “science based calibration” for estimating key performance parameters of multivariate spectrometric assays. Chapter 6 presents recent studies on the influence of acute hyperglycaemia on cerebral blood flow and spreading depression in rat cerebral cortex performed by the novel optical imaging techniques for investigating the cerebral hemodynamics, such as intrinsic optical signal imaging and laser speckle imaging. The correlation between diabetes and thermo-optical response of human skin is discussed in chapter 7. Both light absorption and scattering properties of human skin affected by temperature modulation and glucose concentration change are considered. Some systematic errors of the method, arising due to the contact between the skin and the measuring probe that causes changes in skin hydration and partial occlusion, are analyzed. In chapter 8 monitoring of glucose in skin by NIR diffusereflectance spectroscopy is provided. A fiber optical probe design enables selective optical signals from dermis tissue and reduces the interference noise arising from the stratum corneum. Authors carry out the partial least squares regression analysis for the NIR data and build calibration models for each subject individually. They are also developing new chemometrics algorithms and data pretreatment methods that are useful for blood glucose assays. Chapter 9 demonstrates correlation of glucose concentration with light scattering patterns. The author examines the light scattering related approach, the so-called “occlusion spectroscopy,” where light scattering fluctuations are associated with the red blood cells aggregation process which is triggered by artificial blood flow cessation and glucose concentration in blood. Due to the multiple-scattering in tissues that amplifies significantly scatter alterations, increased sensitivity to the changes in glucose concentration of blood plasma is found. NIR noninvasive blood glucose monitoring is discussed in chapter 10, regarding both methodological and instrumental implementations. The preliminary in vitro study of the suggested floating-reference method indicates the effect of the technique on improvement of the specificity of glucose signal extraction with the promising prospects for solving the interference caused by the variations of human physiological background. Fluorescence-based glucose biosensors are discussed in chapter 11, where the general requirements for using fluorescence spectroscopy for in vivo glucose monitoring are presented. Various fluorescence phenomena, glucose receptors, assays for glu-

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cose using these receptors, as well as the materials and methods for interfacing measurement instrumentation with receptors for construction of biosensors, are analyzed in this chapter. Chapter 12 discusses the application of quantitative Raman spectroscopy to biological tissue, in particular to glucose studies in blood serum, whole blood, and human subjects. Two new techniques, constrained regularization (CR) and intrinsic Raman spectroscopy (IRS), which are shown to significantly improve measurement accuracy, are presented. A photonic crystal contact lens sensor for the noninvasive determination of glucose in tear fluid is described in chapter 13. The drawbacks and advantages of tear fluid glucose studies in diabetic subjects are discussed. The authors present new measurements of tear glucose concentrations by using a method designed to avoid tear stimulation. On the basis of these results and recent studies on monitoring of tear glucose concentrations in situ by using contact lens-based sensing devices, the authors concluded that in vivo tear glucose sensing has a future. Chapter 14 gives an introduction into pulsed photoacoustic (PA) technique in its application to chemical trace measurement, including glucose determination in human blood and tissue. Discussion of in vitro studies of glucose determination in water, tissue phantoms, tissues, and blood, as well as in vivo studies of animals and human subjects, is presented. Major problems of PA glucose sensing are summarized together with discussion of future perspectives of the method. Three chapters, 15, 16, and 17, are devoted to discussion of problems and prospects of polarimetric glucose sensing in transparent (low scattering) and turbid (strongly scattering) tissues. In chapter 15, the reader will find a description of a noninvasive glucose sensor based on polarimetric measurements through the aqueous humor of the eye. The fundamentals of optical polarimetry and optical rotatory dispersion as a technique for monitoring chiral molecules are also presented. Sources of errors of optical measurements in the eye that include time lag between the blood and aqueous humor, corneal birefringence, and motion artefacts are analyzed. A multi-wavelength system having good prospects for in vivo measurements is described. In chapter 16 a new optical concept for measuring glucose concentration in the aqueous humor is discussed. The concept is based on reflecting the incident circularly polarized light from the ocular lens at the Brewster angle and by detecting and analyzing the linearly polarized light as it traverses through the eye’s anterior chamber. Chapter 17 shows prospects of noninvasive glucose sensing using polarization analysis of multiply scattered light. In this chapter a variety of experimental and theoretical tools of turbid polarimetry are described. Chapters 18 and 20 propose using a high-resolution optical technique, optical coherence tomography (OCT), for noninvasive, continuous, and accurate monitoring of blood glucose physiological concentration as well as for measurement of the diffusion of glucose and other related analytes in tissues. Major achievements in the development of this technique for noninvasive glucose monitoring from idea to successful clinical studies are presented in chapter 18. A description of recent progress made on developing a noninvasive molecular diffusion biosensor based on the OCT technique can be found in chapter 20. Due to the capability of the OCT technique

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for depth-resolved imaging of tissues with high in-depth resolution, glucose diffusion could be quantified not only as a function of time but also as a function of depth. Chapter 19 reviews the main experimental methods used for in vitro and in vivo measurements of glucose diffusion coefficients in human tissues, such as spectroscopic, photoacoustic, radioactive labeling, light scattering, including spectrophotometry, interferometry, and OCT. The last chapter (21) summarizes recent results on tissue and blood optical clearing effects induced by the action of glucose solutions. The refractive index concept as a main mechanism of optical clearing is discussed. Optical clearing properties of fibrous (eye sclera, skin dermis, and dura mater) and cell-structured tissues (liver, skin epidermis) are analyzed in the framework of tissue spectrophotometry, timeresolved, fluorescence, and polarization measurements, as well as usage of confocal microscopy, two-photon excitation imaging, and OCT. Results of in vitro, ex vivo, and in vivo studies of a variety of human and animal tissues and blood are presented. The audience at which this book is aimed is researchers, postgraduate and undergraduate students, laser engineers, biomedical engineers, and physicians who are interested in designing and applying noninvasive optical methods and instruments for glucose sensing and tissue optical clearing using glucose. Because of the large amount of basic research on light interactions with tissues and blood presented in the book it should be useful for a broad audience including students and physicians. Investigators who are strongly involved in the field will find updated results in any area discussed in the book. Physicians and biomedical engineers will be interested in clinical applications of designed techniques and instruments, which are described in some chapters. Optical engineers could be interested in the book, because their acquaintance with new fields of light applications can stimulate new ideas of optical instrumentation designing. This book represents a valuable contribution by well-known experts in the field of biomedical optics and biophotonics with their particular interest to the problem of glucose sensing and impact. The contributors are drawn from Russia, USA, UK, South Korea, Finland, Germany, China, Japan, Israel, Italy, and Canada. I greatly appreciate the cooperation and contributions of all authors of the book, who have done great work on preparation of their chapters. It should be mentioned that this book presents results of international collaborations and exchanges of ideas among all research groups participating in the book project. I would like to thank all those authors and publishers who freely granted permissions to reproduce their copyrighted works. I am grateful to Dr John Navas, senior editor, Physics, of Taylor & Francis/CRC Press, for his valuable suggestions and help on preparation of the manuscript and to Professor Vladimir L. Derbov, Saratov State University, for preparation of the camera-ready manuscript and help in technical editing of the book. I greatly appreciate the cooperation, contributions, and support of all my colleagues from the Optics and Biomedical Physics Division and Research-Educational Institute of Optics and Biophotonics of Physics Department of Saratov State University and the Institute of Precise Mechanics and Control of the Russian Academy of Science.

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Last, but not least, I express my gratitude to my family, especially to my wife Natalia and grandchildren Dasha, Zhenya, and Stepa, for their indispensable support, understanding, and patience during my writing and editing of the book. Valery V. Tuchin July 2008 Saratov, Russia

References [1] J.D. Newman and A.P.F. Turner, “Home blood glucose biosensors: a commercial perspective,” Biosens. Bioelectr., vol. 20, 2005, pp. 2435–2453. [2] O. Khalil, “Noninvasive glucose measurement technologies: an update from 1999 to the dawn of the new Millenium,” Diabetes Technol. Ther., vol. 6, no. 5, 2004, pp. 660–697. [3] R.J. McNichols and G.L. Cot´e, “Optical glucose sensing in biological fluids: an overview,” J. Biomed. Opt., vol. 5, no.1, 2000, pp. 5–16. [4] K.J. Jeon, I. D. Hwang, S. Hahn, and G. Yoon, ”Comparison between transmittance and reflectance measurements in glucose determination using near infrared spectroscopy,” J. Biomed. Opt., vol. 11, 2006, 014022. [5] Bo-Yan Li, S. Kasemsumran, Y. Hu, Yi-Z. Liang, and Y. Ozaki, “Comparison of performance of partial least squares regression, secured principal component regression, and modified secured principal regression for determination of human serum albumin, γ -globulin, and glucose in buffer solutions and in vivo blood glucose quantification by near-infrared spectroscopy,” Anal. Bioanal. Chem., vol. 387, 2007, pp. 603–611. [6] H.M. Heise, “In vivo assay of glucose,” in Encyclopedia of Analytical Chemistry - Instrumentation and Applications, R.A. Meyers (ed.), Wiley, Chichester, 2000, Vol. I, pp. 56–83. [7] R. Marbach, “A new method for multivariate calibration,” J. Near Infrared Spectrosc., vol. 13, 2005, pp. 241–254. [8] J.S. Maier, S.A. Walker, S. Fantini, M.A. Franceschini, and E. Gratton, “Possible correlation between blood glucose concentration and the reduced scattering coefficient of tissues in the near infrared,” Opt. Lett., vol. 19, 1994, pp. 2062–2064. [9] M. Kohl, M. Cope, M. Essenpreis, and D. B¨ocker, “Influence of glucose concentration on light scattering in tissue-simulating phantoms,” Opt. Lett., vol. 19, 1994, pp. 2170–2172.

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[10] J.T. Bruulsema, J.E. Hayward, T.J. Farrell, M.S. Patterson, L. Heinemann, M. Berger, T. Koschinsky, J. Sandahal-Christiansen, H. Orskov, M. Essenpreis, G. Schmelzeisen-Redeker, and D. B¨ocker, “Correlation between blood glucose concentration in diabetics and noninvasively measured tissue optical scattering coefficient,” Opt. Lett., vol. 22, no. 3, 1997, pp. 190–192. [11] M. Kohl, M. Essenpreis, and M. Cope, “The influence of glucose concentration upon the transport of light in tissue-simulating phantoms,” Phys. Med. Biol., vol. 40, 1995, pp. 1267–1287. [12] L.D. Shvartsman and I. Fine, “Optical transmission of blood: effect of erythrocyte aggregation,” IEEE Trans. Biomed. Eng., vol. 50, 2003, pp. 1026– 1033. [13] O. Cohen, I. Fine, E. Monashkin, and A. Karasik, “Glucose correlation with light scattering patterns—a novel method for noninvasive glucose measurements,” Diabet. Technol. Ther., vol. 5, 2003, pp. 11–17. [14] C.D. Geddes and J.R. Lakowicz (eds.), Topics in Fluorescence Spectroscopy, vol. 11, Glucose Sensing, Springer, New York, 2006. [15] A.M.K. Enejder, T.G. Scecina, J. Oh, M. Hunter, W.-C. Shih, S. Sasic, G.L. Horowitz, and M. S. Feld, ”Raman spectroscopy for noninvasive glucose measurements,” J. Biomed. Opt., vol. 10, 2005, 031114. [16] M. Ren, M.A. Arnold, “Comparison of multivariate calibration models for glucose, urea, and lactate from near-infrared and Raman spectra,” Anal. Bioanal. Chem., vol. 387, 2007, pp. 879–888. [17] J.S. Baba, B.D. Cameron, S. Theru, and G.L. Cot´e, ”The effect of temperature, pH, and corneal birefringence on polarimetric glucose monitoring in the eye,” J. Biomed. Opt., vol. 7, 2002, pp. 321–328. [18] R.R. Ansari, S. Boeckle, and L. Rovati, “New optical scheme for a polarimetric-based glucose sensor,” J. Biomed. Opt., vol. 9, 2004, pp.1 03– 115. [19] X. Guo, M.F.G. Wood, and I.A. Vitkin, “Stokes polarimetry in multiply scattering chiral media: effects of experimental geometry,” Appl. Opt., vol. 46, 2007, pp. 4491–4500. [20] C. Chou, C.Y. Han, W.C. Kuo, Y.C. Huang, C.M. Feng, and J.C. Shyu, “Noninvasive glucose monitoring in vivo with an optical heterodyne polarimeter,” Appl. Opt., vol. 37, no.16, 1998, pp. 3553–3557. [21] V.L. Alexeev, S. Das, D.N. Finegold, and S.A. Asher, “Photonic crystal glucose-sensing material for noninvasive monitoring of glucose in tear fluid,” Clin. Chem., vol. 50, 2004, pp. 2353–2360. [22] H.A. MacKenzie, H.S. Ashton, S. Spiers, Y. Shen, S.S. Freeborn, J. Hannigan, J. Lindberg, and P. Rae, “Advances in photoacoustic noninvasive glucose testing,” Clin. Chem., vol. 45, 1999, pp. 1587–1595.

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[23] M. Kinnunen and R. Myllyl¨a, “Effect of glucose on photoacoustic signals at the wavelength of 1064 and 532 nm in pig blood and Intralipid,” J. Phys. D: Appl. Phys., vol. 38, 2005, pp. 2654–2661. [24] Glucon, Inc.: http://www.glucon.com/ [25] Y. Shen, Z. Lu, S. Spiers, H.A. MacKenzie, H.S. Ashton, J. Hannigan, S.S. Freeborn, and J. Lindberg, “Measurement of the optical absorption coefficient of a liquid by use of a time-resolved photoacoustic technique,” Appl. Opt., vol. 39, 2000, pp. 4007–4012. [26] R.O. Esenaliev, K.V. Larin, I.V. Larina, and M. Motamedi, “Noninvasive monitoring of glucose concentration with optical coherence tomography,” Opt. Let., vol. 26, no. 13, 2001, pp. 992–994. [27] K.V. Larin, M.S. Eledrisi, M. Motamedi, R.O. Esenaliev, “Noninvasive blood glucose monitoring with optical coherence tomography: a pilot study in human subjects,” Diabetes Care, vol. 25, no. 12, 2002, pp. 2263–2267. [28] K.V. Larin, M. Motamedi, T.V. Ashitkov, and R.O. Esenaliev, “Specificity of noninvasive blood glucose sensing using optical coherence tomography technique: a pilot study,” Phys. Med. Biol., vol. 48, 2003, pp. 1371–1390. [29] C.D. Malchoff, K. Shoukri, J.I. Landau, and J.M. Buchert, “A novel noninvasive blood glucose monitor,” Diabet. Care, vol. 25, 2002, pp. 2268–2275. [30] G. Mazarevica, T. Freivalds, and A. Jurka, “Properties of erythrocyte light refraction in diabetic patients,” J. Biomed. Opt., vol. 7, no. 2, 2002, pp. 244– 247. [31] V.V. Tuchin, R.K. Wang, E.I. Galanzha, N.A. Lakodina, and A.V. Solovieva, “Monitoring of glycated hemoglobin in a whole blood by refractive index measurement with OCT, Conference Program CLEO/QELS, Baltimore, June 1–6, 2003, p. 120. [32] A.K. Amerov, J. Chen, G.W. Small, and M.A. Arnold, “The influence of glucose upon the transport of light through whole blood,” Proc. SPIE 5330, 2004, pp. 101–111. [33] J. Qu and B.C. Wilson, “Monte Carlo modeling studies of the effect of physiological factors and other analytes on the determination of glucose concentration in vivo by near infrared optical absorption and scattering measurements,” J. Biomed. Opt., vol. 2, no. 3, 1997, pp. 319–325. [34] V.V. Tuchin, “Coherent optical techniques for the analysis of tissue structure and dynamics,” J. Biomed. Opt., vol. 4, 1999, pp. 106–124. [35] V.V. Tuchin, “Optical clearing of tissue and blood using immersion method,” J. Phys. D: Appl. Phys., vol. 38, 2005, pp. 2497–2518. [36] V.V. Tuchin, Optical Clearing in Tissues and Blood, SPIE Press, Bellingham, WA, 2005.

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[37] A.N. Bashkatov, E.A. Genina, Yu.P. Sinichkin, V.I. Kochubey, N.A. Lakodina, and V.V. Tuchin, “Glucose and manitol diffusion in human dura mater,“ Biophys. J., vol. 79, 2003, pp. 3310–3318. [38] M.G. Ghosn, V.V. Tuchin, and K.V. Larin, “Non-destructive quantification of analytes diffusion in cornea and sclera by using optical coherence tomography,” Invest. Ophthal. Vis. Sci., vol. 48, 2007, pp. 2726–2733.

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List of Contributors Rafat R. Ansari NASA Glenn Research Center, Cleveland, OH 44135, USA Sanford A. Asher Department of Chemistry, University of Pittsburgh, Pittsburgh, PA 15260, USA Justin T. Baca Department of Chemistry, University of Pittsburgh, Pittsburgh, PA 15260, USA Alexey N. Bashkatov Institute of Optics and Biophotonics, Saratov State University, Saratov, 410012, Russia Kate L. Bechtel George R. Harrison Spectroscopy Laboratory Massachusetts Institute of Technology, Cambridge, MA 02139, USA Alexander V. Bykov Physics Department and International Laser Center, M.V. Lomonosov Moscow State University, Moscow, Russia, and Department of Technology, University of Oulu, Oulu, Finland Brent D. Cameron Texas A&M University, Department of Biomedical Engineering, College Station, TX 77843, USA Gerard L. Cot`e Department of Biomedical Engineering, Texas A&M University, College Station, TX 77843, USA

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Tatyana P. Denisova Saratov State Medical University Saratov, Russia Yi Ping Du Research and Analysis Center, East China University of Science and Technology, Shanghai 200237, China Rinat O. Esenaliev Laboratory for Optical Sensing and Monitoring, Center for Biomedical Engineeering, Department of Neuroscience and Cell Biology, and Department of Anesthesiology, The University of Texas Medical Branch, Galveston, TX 77555-0456, USA Michael S. Feld George R. Harrison Spectroscopy Laboratory Massachusetts Institute of Technology, Cambridge, MA 02139, USA Ilya Fine Elfi-Tech Ltd., Science Park, Rehovot, Israel Vasiliki Fragkou Cranfield Health, Cranfield University, Silsoe, MK45 4D, UK Elina A. Genina Institute of Optics and Biophotonics, Saratov State University, Saratov, 410012, Russia Nirmalya Ghosh Division of Biophysics and Bioimaging, Ontario Cancer Institute and Department of Medical Biophysics, University of Toronto Toronto, Ontario, Canada Xinxin Guo Division of Biophysics and Bioimaging, Ontario Cancer Institute and Department of Medical Biophysics, University of Toronto Toronto, Ontario, Canada H. Michael Heise ISAS - Institute for Analytical Sciences at the Technical University of Dortmund, Dortmund, 44139, Germany

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Sumaporn Kasemsumran Nondestructive Quality Evaluation Unit, Kasetsart Agricultural and Agro-Industrial Product Improvement Institute (KAPI), Kasetsart University, Bangkok 10900, Thailand Omar S. Khalil Pharos Biomedical Research, Chicago, IL, USA Matti Kinnunen Department of Electrical and Information Engineering, University of Oulu, Oulu, Finland Mikhail Yu. Kirillin Physics Department and International Laser Center, M.V. Lomonosov Moscow State University, Moscow, Russia, and Department of Technology, University of Oulu, Oulu, Finland Peter Lampen ISAS - Institute for Analytical Sciences at the Technical University of Dortmund, Dortmund, 44139, Germany Kirill V. Larin Biomedical Engineering Program, University of Houston, Houston, TX 77204, USA; Institute of Optics and Biophotonics, Saratov State University, Saratov, 410012, Russia Pengcheng Li Britton Chance Center for Biomedical Photonics, Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, PR China Qingming Luo Britton Chance Center for Biomedical Photonics, Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, PR China Weihua Luo Britton Chance Center for Biomedical Photonics, Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, PR China

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Lidia I. Malinova Saratov Research Institute of Cardiology Saratov, Russia Ralf Marbach VTT Optical Instruments Centre, Oulu, Finland Katsuhiko Maruo Advanced Technologies Development Laboratory, Matsushita Electric Works Ltd., Kadoma, Osaka 571-8686, Japan M. McShane Department of Biomedical Engineering, Texas A&M University, College Station, TX 77843, USA Risto Myllyl¨a Department of Electrical and Information Engineering, University of Oulu, Oulu, Finland Yukihiro Ozaki Department of Chemistry, School of Science and Technology, Kwansei-Gakuin University, Sanda 669-1337, Japan M.V. Pishko Department of Chemical Engineering, Texas A&M University, College Station, TX 77843, USA Alexander V. Priezzhev Physics Department and International Laser Center, M.V. Lomonosov Moscow State University, Moscow, Russia, and Department of Technology, University of Oulu, Oulu, Finland Donald S. Prough Department of Anesthesiology, The University of Texas Medical Branch, Galveston, TX 77555-0591, USA Luigi Rovati Department of Information Engineering, University of Modena and Reggio Emilia, Modena, 41100 Italy

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Wei-Chuan Shih George R. Harrison Spectroscopy Laboratory Massachusetts Institute of Technology, Cambridge, MA 02139, USA Hideyuki Shinzawa Department of Chemistry, School of Science and Technology, Kwansei-Gakuin University, Sanda 669-1337, Japan Valery V. Tuchin Institute of Optics and Biophotonics, Saratov State University, Saratov, 410012, Russia, Institute of Precise Mechanics and Control of RAS, Saratov 410056, Russia Anthony P.F. Turner Cranfield Health, Cranfield University, Silsoe, MK45 4D, UK I. Alex Vitkin Division of Biophysics and Bioimaging, Ontario Cancer Institute and Department of Medical Biophysics, University of Toronto Toronto, Ontario, Canada Ruikang Wang Department of Biomedical Engineering, Oregon Health & Science University Portland, OR 97239, USA Zhen Wang Britton Chance Center for Biomedical Photonics, Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, PR China Michael F. G. Wood Division of Biophysics and Bioimaging, Ontario Cancer Institute and Department of Medical Biophysics, University of Toronto Toronto, Ontario, Canada Kexin Xu College of Precision Instrument and Opto-Electronics Engineering, Tianjin University, Tianjin 300072, P.R. China

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Gilwon Yoon Seoul National University of Technology Nowon-gu Kongneung-dong Seoul, Korea Zuomin Zhao Department of Electrical and Information Engineering, University of Oulu, Oulu, Finland

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1 Glucose: Physiological Norm and Pathology

Lidia I. Malinova Saratov Research Institute of Cardiology, Saratov, Russia Tatyana P. Denisova Saratov State Medical University, Saratov, Russia 1.1 1.2 1.3 1.4 1.5 1.6

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . System of Blood Glucose Level Regulation and Carbohydrate Metabolism . Glucose and Carbohydrate Metabolism Violations . . . . . . . . . . . . . . . . . . . . . . . . . Blood Glucose Level Monitoring in Clinical Practice . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 4 14 21 24 25 26

In the present chapter the physiology and clinical applications of glucose metabolism are going to be discussed. Glucose is one of the central substances in human life supporting processes. Glucose distribution and concentration in blood, interstitial fluid, and tissues, kinetics and mechanisms of transcapillary glucose transport, kinetics and metabolism of glucose transport via its transporters into cells, detailed mechanisms of glucose level influence upon clinical course and prognosis in pathology are still in the area of uncertainty. Morbidity and mortality via diabetes mellitus and atherosclerosis are still increasing, enhancing attention of clinicians and biophysics to the problem of glucose sensing and impact. The purpose of this chapter is to review the data on glucose metabolism in physiological norm and pathology, the role of glucose in pathogenesis of diabetes mellitus and atherosclerosis and the glucose sensing in clinical practice. The described problems form three parts of the chapter. Key words: glucose, metabolism, diabetes mellitus, atherosclerosis, glucose level monitoring.

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1.1 Introduction 1.1.1 Goal Health and happiness of a human being were the main aim and a golden dream for scientists over the centuries. Attempts to reach this top resulted in thorough investigating of human physiology and pathology. Unfortunately unsolved problems are prevailing over solved ones even (especially!) nowadays. The 21st century meets us with an explosion in frequency of such a merciless disease as insulin dependent and non-insulin dependent diabetes mellitus. Coronary atherosclerosis becomes more “young” and a frequent form of pathology. The elderly population significantly increases in many countries all over the world. All listed above problems are overlapping. One of possible “joins” is well known and still a mysterious compound — glucose. Further investigations in this area are impossible without improvement of scientific research instruments. The ongoing discussions on the state-of-the-art of glucose sensors, the most prospective glucose-sensing methods, new optical techniques for glucose diffusion coefficient measurements, and glucose-induced optical clearing effects in tissues and blood demand clear understanding of glucose metabolism, distribution and concentrations in human organism compartments. So, the present chapter is dedicated to the problem of glucose’s role in life supporting processes both under physiological norm conditions and in pathology. We’ll review the most actual concepts on glucose transport, metabolic pathways and crosses, main glucose level regulation mechanisms in practically healthy persons and in patients with diabetes mellitus and coronary heart disease. Another point of interest to discuss in this chapter is clinical applications of glucose sensing and main problems in that field. Thus, the main goal of the present part is to form physiological and clinical grounds of the handbook, to reveal the urgency of cooperation of clinicians and physicists in the described area.

1.1.2 Terms and definitions Glucose, a monosaccharide, is the central carbohydrate in human physiology. The ´ ), which means “sweet.” There name comes from the Greek word “glykys” (γλ υκ υς are two optical isomers of glucose, D- and L-glucose (Fig. 1.1), and both of them are optically active with the opposite chirality (Fig. 1.2). However, only D-glucose is involved in human metabolism. The mirror-image of the molecule, L-glucose, is present in food but cannot be used by mammalian cells [1]. Hereinafter the term “glucose” will mean its biological active isoform (D-isoform). The central place of glucose in human metabolism is caused by its plural functions. Glucose is the transport form of carbohydrate, and important fuel for stoking metabolic energy in all human cells. Glucose is participating in a large amount of biochemical reactions modulating metabolic profile both at physiological norm and in pathology. Glucose role is critical in the production of proteins and in lipid

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FIGURE 1.1: D and L isoforms of glucose.

FIGURE 1.2: Polarimetry in study of carbohydrate: (A) - polarization planes of both linear polarizers placed before (polarizer) and after (analyzer) measuring cell with water are collinear; water is optically nonactive medium. Thus, polarized light freely passes through the analyzer (bright field of view); (B) - D- or L-glucose isoforms rotate the plane of light polarization; thus, polarized light is attenuated by the analyzer that is in parallel with the polarizer plane (darken field of view); (C) rotation of analyzer plane allows one to make field of view bright; measured polarizer rotation angle is equal to glucose rotation angle α .

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metabolism. According to metabolic theory glucose metabolism is involved in aging processes. Blood glucose level is a parameter of a high predictive value in such disorders as diabetes mellitus, coronary heart disease and arterial hypertension. Details are going to be discussed in other parts of the chapter.

1.2 System of Blood Glucose Level Regulation and Carbohydrate Metabolism Glucose metabolism presents a complex net of biological substances interaction. The result of these interactions is a relatively constant blood glucose level. The last one does not belong to strict biological constants. It means that blood glucose level may vary in the physiological range. All biological agents influencing upon carbohydrate metabolism, humans’ feed behavior and the very glucose concentration (as the result) form the functional system of blood glucose level regulation. Plural possible disorders in this system are nearly connected and form the pathophysiology sense of several forms of the internal pathology. Let’s consider glucose metabolism in norm. The initial step in glucose metabolism is the hexose transport across the cell membrane down a normally large concentration gradient from extracellular fluid to cytoplasm. This process is carried out by a family of glucose transport proteins.

1.2.1 Glucose transporters There are two categories of glucose transporters: Na+ dependent (SGLT) and Na+ independent (GLUT). SGLT glucose transport is coupled to Na+ transport and permits the glucose to cross the cell membrane against its concentration gradient. When the loss of glucose from isolated intestinal epithelial cells is prevented by blocking GLUTs, the cell can concentrate glucose, taken via its SGLT. The main location of SGLTs is the brush border of intestinal and proximal renal tubular cells. SGLT-1 cycles between the interior and the plasma membrane [2]. GLUTs are distributed widely in human organisms, although varying in density of localization. Each transport protein spans the plasma membrane 12 times and both its amino and carboxy termini are located within the cytoplasm. Glucose molecules move across a cell membrane via GLUT in the direction of glucose concentration gradient. There may be energy barriers in GLUTs that glucose molecules must overcome in connection with one or more association-dissociation steps. To date, 13 functional mammalian facilitated hexose carriers (GLUTs) have been detected in mammals. They were divided into three classes according to the sequence similarities. Class I GLUTs include the high-affinity binding proteins GLUT1, GLUT3, and GLUT4 and the lower-affinity transporter GLUT2. Class II transporters includes GLUT5, GLUT7, GLUT9, and GLUT11 or myoinositol transporter (HMIT1).

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Transporters of this class have a very low affinity for glucose and preferentially transport fructose, and thus they are not discussed in this review. Class III transporters comprise four novel GLUTs, GLUT6, GLUT8, GLUT10, and GLUT12 [3]. The GLUT1 transporter is expressed constitutively and is responsible for the low level of basal glucose uptake alone or in company with other GLUT isoforms. This transporter expression is increased by fasting and decreased by glycemia. GLUT1 is located mainly in pancreatic β -cells. GLUT2 is expressed by hepatic and renal tubular cells that transfer glucose level out of the cell into extracellular fluid and plasma and by small intestinal epithelial cells that transport glucose from the gut lumen into the plasma. GLUT2 is also present in insulin secreting cells of the pancreatic islets, where it maintains a virtual equilibrium between the glucose concentrations in the extracellular liquid and cytoplasm. GLUT3 is a high affinity glucose transporter expressed in neurons and the placenta. GLUT4 is the major glucose transporter in insulin sensitive cells, in which insulin increases the glucose uptake. The GLUT4 transporter is expressed exclusively in cardiac and skeletal muscle and adipose tissue. In skeletal muscle there may be no GLUT4 in the plasma membrane in the basal state. GLUT4 and possibly GLUT1 in the plasma membrane exist in at least two stable configurations, and they can change them, and, because of that, change their ability to transport glucose in response to predominantly insulin concentration. GLUT7 has been localized at hepatocyte endoplasmic reticulum. GLUT7 transports newly produced glucose out of endoplasmic reticulum lumen into cytoplasm, from which it leaves the cell via GLUT2. Less is known about the Class III transporter proteins. They exhibit tissue- and cell-specific expression patterns and demonstrate preferential transport of glucose similar to class I transporters. GLUT6 (previously named GLUT9) is predominantly expressed in spleen, leukocytes, and brain [4]. In humans, GLUT8 (previously named GLUTX1) is predominantly found in insulin-sensitive tissues such as muscle, fat, and liver, as well as in testis, and is inhibited by fructose [5]. GLUT10 is predominantly expressed in insulin-sensitive tissues (liver, muscle, and pancreas), but is also found in lung, brain, placenta, and kidney [6]. GLUT12 is predominantly expressed in skeletal muscle, heart, fat, and prostate. In the absence of insulin, this receptor is found in a perinuclear location [7]. To date, there are no known human or animal diseases associated with alterations in either protein structure or expression of the class III transporters.

1.2.2 Pathways of glucose concentration change: glucose distribution and concentrations in human organism Plasma glucose concentration is a result of balance between glucose entering the circulation and glucose removal from the circulation. Basal plasma glucose level is tightly regulated around 80 mg/dl (4.5 µ mol/L), with a range of 60 to 110 mg/dl [8]. There are three main blood glucose sources: intestinal absorption during the meal, glycogenolysis, and gluconeogenesis (Fig. 1.3). The first one component is predominantly determined by the digestive tract function, i.e., the rate of gastric emptying. Two peptides decrease the rate of gastric emptying: glucagon-like polypeptide-1

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FIGURE 1.3: Glucose fate in human organism. Comments are in the text.

(GLP-1) [9, 10] and amylin [11]. Other sources of circulating glucose are derived chiefly from hepatic processes: glycogenolysis (the breakdown of glycogen), and gluconeogenesis (the formation of glucose primarily from lactate and amino acids during the fasting state). Glycogenolysis and gluconeogenesis are united in terms of endogenous glucose production (EGP). EGP by the splanchnic bed is about 0.62 mmol min−1 on 1.73 m2 (body surface)−1 [12], by the kidney 0.07 mmol min−1 on 1.73 m2 (body surface)−1, and total production 0.69 mmol min−1 on 1.73 m2 (body surface)−1 [13]. EGP is partly under the control of glucagon [14]. Glucagon is a key catabolic hormone secreted from pancreatic α -cells. Described by Roger Unger in the 1950s, glucagon was characterized as opposing the effects of insulin. Glucagon facilitates glycogenolysis during the first 8-12 hours of fasting and thus promotes glucose appearance in the circulation. Over longer periods of fasting, glucose is produced by gluconeogenesis primarily in the liver. In the presence of constant basal insulin concentrations TGP is regulated by rapid and reciprocal changes in glucose within the physiological range [15]. Glucose disappearance is the result of its consumption and use by peripheral tissues (Fig. 1.3). Approximately 55% of glucose use results from terminal oxidation. Another 20% results from glycolysis; the resulting lactate then returns to the liver for resynthesis into glucose (Cori cycle). Reuptake by the liver and other splanchnic tissues accounts for the remaining 25% of glucose use. Glucose uptake by skeletal muscle would be 0.12 mmol min−1 [17], by heart 0.08 mmol min−1 [16] per 1.73 m2 (body surface)−1, and the total glucose uptake with brain tissue participation will be ∼ 90% of the reported glucose production. At real conditions glucose is not oxidized completely. The circulating pool of glucose in one hour of fasting is only slightly

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FIGURE 1.4: Glucose turnover: the balance of glycogen. Comments are in the text.

larger than the liver output. This concentration is hardly sufficient to maintain brain oxidation for several hours in absence of any other glucose sources. Hepatic uptake and use of circulating lactate account for more than half the glucose supplied by gluconeogenesis. The remainder is largely accounted for by amino acids, especially alanine. Glycolysis in muscle, red blood cells, white blood cells, and a few other tissues provides main lactate supply of these processes (Fig. 1.4). The amino acids precursors come from proteolysis of muscle. The only amino acids precursors increase does not result in the “explosion” of gluconeogenesis rate. The necessary enzymes must be upregulated by hormonal modulation or by hepatic autoregulation responses to the failing glucose level. Glycolysis, oxidation, and storage as glycogen are the main but not the only pathways of glucose metabolism. The pentose phosphate pathway or hexose monophosphate chunt is active in several tissues. When glucose concentrations are high, the enzyme aldose reductase reduces glucose to sorbitol, which can subsequently be oxidized to fructose (polyol pathway). The major products of glycolysis, lactate and piruvate, circulate at average concentrations of 0.7 and 0.07 mM, respectively. This 10:1 ratio of lactate to piruvate ordinarily prevails as long as oxygen is plentiful. Oxidation of glucose uptake by the beating heart accounts for only 35% of observed O2 uptake [15]. Unlike skeletal muscle, the heart takes up lactate and can use it as substrate for oxidation. This still leaves most of the O2 uptake to be accounted for by FFA [16]. In fact little or none of the glucose taken up by muscle in the basal state is stored as glycogen [17], a fact demonstrated by nuclear magnetic resonance spectroscopy [18].

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FIGURE 1.5: Simplified scheme of blood glucose level regulation. Comments are in the text.

1.2.3 Regulation of glucose metabolism: main pathways and processes Regulation of glucose metabolism is still in the area of uncertainty. One of the accepted hypotheses still of current importance is the food and famine hypothesis, which considers effects of meals and periods between them on blood glucose concentration and glucose uptake and output [19]. The hypothesis deals with three time periods: prandial and immediate postprandial, delayed postprandial, and remote postprandial periods. During these periods the reciprocal relations between glucoregulatory hormones have taken place. Glucoregulatory hormones include insulin, glucagon, amylin, GLP-1, glucosedependent insulinotropic peptide (GIP), epinephrine, cortisol, and growth hormone. Of these, insulin and amylin are derived from the β -cells, glucagon from the α -cells of the pancreas, and GLP-1 and GIP from the L-cells of the intestine (Fig. 1.5). Amylin is a neuroendocrine hormone expressed and secreted with insulin as a response to nutrient stimuli [20–23]. In healthy adults, fasting plasma amylin concentrations range from 4 to 8 pmol/l rising as high as 25 pmol/l postprandially. In diabetic patients, amylin is deficient (IDDM) or impaired (NIDDM) [24, 25]. Amylin’s main task is to prevent an abnormal rise in glucose concentrations via two main mechanisms: suppression of postprandial glucagon secretion [26], and inhibition of the rate of gastric emptying [27]. GIP stimulates insulin secretion and regulates fat metabolism, but does not inhibit glucagon secretion or gastric emptying [28]. GLP-1 stimulates insulin secretion in the pancreas [29, 30]. Artificial infusion of GLP-1 results in decrease of postprandial glucose as well as fasting blood glucose concentrations. GLP-1 helps to regulate

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gastric emptying and gastric acid secretion [31]. GH “violates” insulin-stimulated glucose uptake. Froesch with coauthors described that IGF-I has an “insulin-sparing” effect. IGF-I is lipolytic and enhances GH in its prevention of protein catabolism [32]. Exposure to increasing concentrations of beta-adrenergic agonists and glucagon in the intermediate and late postprandial period causes glycogenolysis and gluconeogenesis. The basal state is a quite late postprandial period in which glucose metabolic quasi-stability is maintained. Most of glucose use (about 70%) in the basal state is independent of insulin for insulin and GH blood levels are at their lowest concentration of the 24-h period [33, 34]. In a subject in the basal state, glucose turnover is about 2 mg/kg/min (11 µ mol/kg/min), and a slow decline of blood glucose concentration, by less than 1% per hour, has taken place. The next period is a prandial state. Glucose in the gut is absorbed mainly in the jejunum and ileum, by two routes: transcellular and paracellular. The paracellular route includes absorption across the tight junction between enterocytes and lateral clefts between cells. The transcellular route is via SGLT and GLUT-2. An increase in dietary carbohydrate increases glucose absorption from small intestinal segments via an unknown path that leads to an increase in the number of SGLT in the brushborder membrane [35, 36]. High concentration of glucose in the gut lumen also increases paracellular glucose transport possibly by a cascade of signals from brushborder SGLT [37]. Translocation through GLUT-2 in the basolateral membrane is increased by hyperglycemia within 30 min [38]. When an individual ingests glucose after overnight fasting, a significant proportion of the load is assimilated by peripheral tissues, mainly muscle, and the rest by the splanchnic tissues, mainly liver. Only from 20% to 30% of a glucose load is oxidized during 3 to 5 hours required to its absorption from the gastrointestinal tract. The remaining glucose is stored as glycogen, partly in liver. Glucose initially stored as muscle glycogen can later be transferred to the liver by undergoing glycolysis to lactate, which is released into the circulation. The lactate is then taken up by the liver, rebuilt into glucose, and stored as glycogen in that organ. During the period of peak absorption of exogenous glucose, hepatic output of the sugar is largely unnecessary and is greatly reduced from the basal levels. Hyperglycemia declines as glucose is transferred from interstitial fluid into cells. There are two components to this increased glucose uptake: an insulin-dependent and an insulin-independent component [39, 40]. Increased glucose uptake has to occur with hyperglycemia, without intervention of hormones due to glucose concentration gradient and GLUTs saturation degree. There are only two tissues that do not increase glucose uptake in response only to increased glucose delivery: brain and, in humans, skeletal muscle [41]. 1.2.3.1 Free fatty acids role in glucose metabolism regulation Glucose metabolism is interlaced with lipid metabolism pathways, i.e., free fatty acids (FFA). Randle et al. [42] based on the animal model proposed that circulating FFA led to increased FFA uptake, followed by t decreased glucose oxidation, and

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the citrate inhibition of phosphofructokinase, thereby blocking glycolysis [43]. This process was considered to proceed independently of any hormonal control. Support of Randle’s hypothesis in humans comes from input-output studies of legs in healthy young adults with analyses of biopsied muscle and euglycemic insulin clamps [44]. When FFA concentration was kept constant during hyperinsulinemia there was less glucose uptake, less glycogen store, reduced leg respiratory quotient, and reduced muscle pyruvate dehydrogenase activity. The major factor in insulin’s indirect suppression of EGP is decreased plasma FFA concentration, due to the antilipolytic effect of insulin on adipose tissue. There is experimental evidence that increased peripheral insulin concentration causes a small decrease in hepatic uptake of gluconeogenic substrate, prevented by fatty acid infusion [45]. Whether most of insulin induced suppression is direct or indirect is disputable. Bergman’s group [46] had shown it was indirect, whereas Cherrington lab [45] calculates that most of the effect is directly on the liver via the hepatic insulin receptor. 1.2.3.2 Physical activity and glucose metabolism Glucose metabolism intensity is the result of the physical activity degree in the individual. Muscle glucose uptake during or immediately after muscle exercise increased at least in part due to increased plasma membrane GLUT4 [47]. Exercise has been reported to increase sensitivity to insulin. Some researchers had shown that there is a factor in serum, probably a protein, which interacts with exercise to increase glucose [48]. There are no reports of an acute effect of physical activity on adipocyte glucose uptake and plasma membrane GLUT density [49]. 1.2.3.3 Oxygen and glucose metabolism Another factor to be a modulator of glucose metabolism is hypoxia. It has been known at least since 1958 that hypoxia stimulates glucose uptake by skeletal muscle [42]. Lasting hypoxia causes an inhibition of oxidative phosphorylation leading to significant increases in glucose transport. Hypoxia increases blood-brain barrier transport of glucose and binding of cytochalasin B to GLUT1 in cerebral microvessels [50]. Hypoxia also modulates glucose transport in human fetal and bovine aortic endothelial cells [51]. Hypoxia activates glucose transport during several hours. This process is associated with an increased expression of GLUT1 protein and mRNA. In some researchers’ opinion fat oxidative metabolism might serve an important signal for adaptive responses in endothelial cells to hypoxia [51]. In the absence of glucose, coronary microvascular endotheial cells become markedly sensitive to hypoxia [52].

1.2.4 Insulin: the key hormone of glucose metabolism Insulin is a key anabolic hormone (Fig. 1.6), which exerts its actions through binding to specific receptors present mainly on fat, liver, and muscle cells. Insulin takes part in postprandial glucose level control in three ways. The first one, insulin, promotes glucose uptake by insulin-sensitive peripheral tissues, primarily skeletal

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FIGURE 1.6: Anabolic role of insulin. Comments are in text.

muscle. Then insulin stimulates glycogenesis in liver and simultaneously inhibits glucagon secretion from pancreatic α -cells and ends endogenous glucose production by liver. Insulin action is carefully regulated by circulating glucose concentrations. Insulin is not secreted at all if the blood glucose concentration is ≤ 3.3 mmol/l. The secretion of insulin occurs in two phases: an initial rapid release of preformed insulin, and increased insulin synthesis and release. Long-term release of insulin occurs if glucose concentrations remain high [53, 54]. With glucose concentration decrease plasma insulin concentration continues to fall to the upper range of normal basal and then falls slowly during the intermediate and late postprandial period. During the rising and peak portions of the blood insulin concentration curve, blood levels of GH decrease, even to immeasurably small concentrations. GH, glucagon, betaadrenergic agonists, and cortisol are released into the circulation at some point on the downlimb of falling blood glucose concentration (∼ 1.6 mM below the subject’s basal level or less) [55]. These agents act to prevent insulin-induced hypoglycemia [53]. When hyperinsulinemia becomes sufficiently high, the insulin-receptor complex in insulin sensitive cells (adipocytes, myocardiocytes, and skeletal muscle cells) initiates a transduction chain that results in translocation of intracellular vesicles to fuse with the plasma membrane. While glucose is the most potent stimulus of insulin, other factors stimulate insulin secretion. These additional stimuli of insulin secretion and release include increased plasma concentrations of some amino acids, especially arginine, leucine, and lysine; GLP-1 and GIP released from the gut following a meal; and parasympathetic stimulation via the vagus nerve. The first stimuli for insulin release from pancreatic β -cells are a family of peptides, incretins, GLP-

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1, glucagon, vasoactive intestinal peptide, and pituitary adenylate cyclase-activating peptide. Incretins are released into the circulation in response to carbohydrate and long-chain fatty acids in the gut. Insulin decreases or prevents net release of glucose from the liver, and perhaps the kidney, by two mechanisms, direct and indirect. Direct effects of insulin on liver and kidney are exerted by way of insulin actions on the insulin receptor, initiating transduction cascades that lead to increased glycogen synthase activity and decreased glycogenolysis [56]. Increased systemic insulin concentration, in the estimated absence of increased portal venous insulin concentration, suppressed hepatic glucose output [57]. The phenomenon was confirmed and demonstrated convincingly in humans by a series of reports mainly from the laboratories of Giacca [58], Bergman [46], and Cherrington [59]. A contributory factor is insulin inhibition of glucagon release from the pancreas. Insulin stimulates much greater multiples of increase in skeletal muscle glucose uptake in the intact subject than in excised muscle or its membrane fractions. 1.2.4.1 Nonglycemical insulin activities Blood glucose level changes, associated with plasma insulin concentration increase and decrease. Besides its glycemic properties discussed above insulin possesses several nonglycemical ones. For instance, insulin can increase blood flow in skeletal muscle, and whether this increased flow is an additional cause of increased glucose uptake is controversial [60]. Baron et al. have a series of reports that insulin, administered by continuous intravenous infusion for hours, increases leg blood flow [61, 62]. Deussen studied heterogeneity of blood flow and glucose uptake in the dog heart and concluded that variations in local blood flow cannot explain the differences in local glucose uptake [63]. Insulin stimulates nitric oxide (NO) synthase in vascular endothelium [64, 65] and therefore is capable of vasodilating. One of the possible mechanisms is stimulation of NO synthase in endothelium. The more obvious this fact becomes in the light of experiments demonstrated that administration of N-monomethyl-L-arginine, a competitive inhibitor of NO synthase, prevents increased blood flow otherwise seen with intravenous insulin after several hours. This fact remains disputable due to some experiments in which researchers could not detect an insulin effect on the relative dispersion of blood flow [66, 67]. A NO synthase (NOS) inhibitor decreased basal and exercise-stimulated glucose uptake but had no effect on insulin-stimulated glucose uptake. Addition of the NO donor, Na nitroprusside, increased basal glucose uptake; this effect was additive to the effects of submaximal and maximal insulin concentrations [68]. A role for NO as a modulator of glucose transport in skeletal muscle has been documented, with GLUT4 implicated in the four- to fivefold increase in basal glucose transport mediated by sodium nitroprusside [69]. In contrast, myocardial glucose uptake is increased in the presence of NO syntetase inhibitor L-NAME and in preparation isolated from eNOS knok-out mice, suggesting that NO may in some vascular beds down regulate glucose uptake via cGMP-dependent mechanism [70]. The role NO plays in physiological insulin secretion has been controversial. The evidence that

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exogenous NO stimulates insulin secretion and that endogenous NO production occurs and is involved in the regulation of insulin release was received in animal model experiments. Applied NO is able to exert an insulinotropic effect, and implicated endogenously produced NO in the physiological regulation of insulin release. When the insulin concentration is high and glucagon and epinephrine concentrations are low, hepatic and renal glycogenolysis and gluconeogenesis cease. Whereas in the basal state little or none of skeletal muscle glucose uptake can be accounted for by glycogen deposition, in response to insulin ≤70% of glucose uptake is accounted for by an increase in muscle glycogen [71, 72].

1.2.5 Endothelium and glucose metabolism Endothelium, the internal vessel layer, may be defined as a special organ with powerful synthetic activity. Endothelial functional state determines one of the main life supporting processes in human organism - tissue perfusion. Glucose is actively metabolized in endothelial cells [73] and sustains anaerobic and aerobic metabolism [52, 74]. In the presence of 5 mM D-glucose, catabolism of aminoacids, palmitate, and lactate is reduced significantly. In experimental rat models it was shown that, in coronary microvascular endothelial cells, < 98% of incorporated glucose is metabolized to lactate [74]. At physiological glucose levels in microvascular endothelial cells almost all of the energy obtained from glucose metabolism obtained from catabolism of glucose is generated glycolytically. At lower glucose concentration (∼1 mM), the oxidation of glucose via Krebs cycle is higher. Thus oxidative metabolism of glucose is inhibited at physiological concentrations of glucose, demonstrating that endothelial cells express the Grabtree effect (i.e., an inhibitory effect of glucose on mitochondrial respiration). Endothelial cells are of high glycolitic activity [75, 76]. The effects of elevated glucose level on endothelial cell are often specific [77-79]. Elevated glucose also increases the generation of superoxide anions known to react with NO to form peroxinitrite, which upon decomposition generates a strong oxidant with reactivity similar to hydroxyl radicals [80]. Human endothelial cells exposed to hyperglycemia (established diabetes mellitus) are more sensitive to reactive oxygen species, since intracellular levels of glutathione, vitamin E, superoxide dismutase, catalase, and ascorbic acid are reduced significantly [81, 82]. Transport of glucose analogs has been characterized in cultured endothelial cells isolated from bovine aorta and a bovine aortic endothelial cell line GM7373 [51, 77, 83, 84]. The absence of GLUT isoforms in pulmonary endothelial cells suggests that pulmonary vessels may have a low requirement of glucose. Bradikinin apparently stimulates glucose uptake by the coronary microcirculation of the rat isolated perfused heart [85]. In cultured coronary microvascular endothelial cells, activation of H1 receptors by histamine stimulates glucose transport (∼ 10–50%), reaching a maximum after 5 min of histamine application. GLUT1 mRNA and protein was detected in these microvascular cells, suggesting that acute stimulation of glucose transport by histamine may involve modulation of GLUT1 expression and/or activity. Endothelial dysfunction has been implicated in the pathogenesis of diabetic vascular disorders such as di-

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abetic retinopathy. The study of Schmetterer and colleagues indicated that either NO-syntase activity was increased or NO sensitivity was decreased in patients with IDDM and supported the concept of an involvement of the L-arginine-NO system in the pathophysiology of diabetic retinopathy [86]. Capillary endothelial cells are thought to limit the transport of insulin from the vascular to the interstitial space, resulting in attenuated hormonal action at target sites. It was shown that capillary endothelial cells affect the transcapillary transport of insulin by slowing the transfer to interstitium. Insulin is transported by a bidirectional convective transport rather than by a saturable receptor-mediated mechanism. Endothelium-derived NO is without effect on transcapilary insulin transport in rat heart model [87].

1.3 Glucose and Carbohydrate Metabolism Violations Carbohydrate metabolism violations are very common in clinical practice. They have taken place in such widespread internal pathologies, as diabetes mellitus, coronary heart disease, and arterial hypertension. In this review we’ll focus only on the part of the problem — the role of glucose in pathogenesis and clinical course of diabetes mellitus (reference carbohydrate metabolism disorder) and coronary heart disease (patients whose carbohydrate metabolic state contribution on disease pathogenesis are still controversial).

1.3.1 Diabetes mellitus: glucose — victim or culprit? Diabetes mellitus (DM) is impaired insulin secretion and variable degrees of peripheral insulin resistance leading to hyperglycemia. There are two main categories of diabetes mellitus (DM). Type 1 (Insulin Dependent Diabetes Mellitus - IDDM) and type 2 (Non Insulin Dependent Diabetes Mellitus - NIDDM) differ one from another by etiology, several pathogenesis pathways, and clinical course. In the sequel we will focus our attention predominantly on NIDDM. Glucose concentration measurement is the major diagnostic criterion of diabetes (Table 1.1). The pathophysiology of NIDDM includes impairments in both insulin action and insulin secretion [88–90]. In insulin-resistant conditions, glucose clearance in response to insulin decreases. The most conclusive evidence for defective insulin sensitivity in type 2 diabetes comes from euglycemic hyperinsulinemic clamp studies, in which total body glucose clearance is shown to be reduced in NIDDM patients compared with age and weight-matched controls [91]. Alterations in insulin “physiology” are not the only component in DM pathogenesis. R.H. Unger was the first to describe the diabetic state as a “bi-hormonal” disease characterized by insulin deficiency and glucagon excess [92]. He further speculated that a therapy targeting the correction of glucagon excess would offer an important advancement in the treat-

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TABLE 1.1: Glucose concentrations as diagnostic criteria of diabetes Test FPG OGTT

Normal IGR DM <100 (<5.6) 100–125 (5.6–6.9) ≥126 (≥7) <140 (<7.7) 140–199 (7.7–11.0) ≥200 (≥11.1

FPG = fasting plasma glucose; OGTT = oral glucose tolerance test, 2 h glucose level. All values refer to glucose levels in mg/dL (mmol/L).

ment of diabetes. In humans, insulin secretion increases with progressive insulin resistance [93]. Failure of pancreatic β -cells to compensate for insulin resistance is critical in the NIDDM pathogenesis of type 2 diabetes [94]. Factors limiting the ability of β -cells to respond to an increasing of glucose level include glucotoxicity and lipotoxicity [95, 96]. In addition, reduced insulin secretion could be mediated in part by abnormal glucose metabolism of β -cells where it is associated to insulin biosynthesis and secretion [97]. Besides, β -cells, as it was recently shown, are an insulin-responsive tissue [98, 99]. This fact also demonstrates a potential link between peripheral insulin resistance and β -cells failure, hyperglycemia, and β -cells functional insufficiency. Whole body glucose clearance is due to both insulin-dependent and insulin-independent mechanisms. Insulin-independent clearance depends on the ability of plasma glucose to influence its own clearance by a mass action effect [100–103]. In addition, glucose regulates activity of the enzymes involved its own metabolism, such as AMP-activated protein kinase (AMPK) [104]. For obvious reasons glucose metabolism is under rapt attention during all study history of diabetes mellitus [105]. Speaking about blood glucose level increase in patients with DM we faced two situations: acute and chronic elevated glucose level. Acute hyperglycemia with subsequent insulin concentration increase exerts a direct inhibitory effect on glucose production and a stimulatory effect on glucose uptake [106]. Patients with NIDDM exhibit preprandial hyperglycemia and excessive postprandial hyperglycemia. The preprandial hyperglycemia is due to impaired suppression of EGP via elevation of plasma glucose and/or insulin concentrations as well as impaired glucose uptake in peripheral tissues [88], and defect of splanchnic glucose uptake [106]. For individuals with diabetes in the fasting state, plasma glucose is derived from glycogenolysis and gluconeogenesis under the direction of glucagon. Exogenous insulin influences the rate of peripheral glucose disappearance and, because of its deficiency in the portal circulation, does not properly regulate the degree to which hepatic gluconeogenesis and glycogenolysis occur. For individuals with diabetes in the fed state, exogenous insulin is ineffective in suppressing glucagon secretion through the physiological paracrine route, resulting in elevated hepatic glucose production. As a result, the appearance of glucose in the circulation exceeds the rate of glucose disappearance. The net effect is postprandial hyperglycemia.

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1.3.1.1 Glucose toxicity Recently, it has become clear that chronic hyperglycemia is not only a marker of disease or poor metabolic control but plays a harmful role. Chronic hyperglycemia regulates both insulin secretion and action and via this mechanism provokes pathologic metabolic effects, which have been referred to as “glucose toxicity” [107–111]. Chronic hyperglycemia per se has been proposed as an independent factor in the development of insulin resistance in skeletal muscle and adipose tissue and in the reduction of the ability of pancreatic β -cells to respond to an acute glycemic challenge in type 2 diabetes [109, 112, 113]. The maintenance of normoglycemia for 72 h by treatment with insulin restored the normal effectiveness of glucose to suppress EGP in poorly controlled diabetic subjects [114]. Chronic hyperglycemia impairs glucose- and/or insulin-induced dissociation of glucokinase (GK) from GK regulatory protein that is responsible, at least partly, for the impaired response of hepatic glucose flux to elevated glucose and/or insulin [115]. These results suggested a role for glucose toxicity in the development of impaired insulin-mediated suppression of net hepatic glucose production (NHGP) in diabetes. There is a point of view that glucose toxicity can be defined as nonphysiological and potentially irreversible β -cell damage caused by chronic exposure to hyperglycemia [116]. In its initial stages, this damage is characterized by defective insulin gene expression [117, 118]. Next stage is cellular refractoriness to glucose stimulation. β -cell functional exhaustion refers to depletion of β -cell insulin stores, so that insulin secretion is impossible, even after β -cells resensitization to glucose. Glucose toxicity might also affect other important steps on the way from insulin gene expression to insulin release into the blood. Discussible candidates are translational rates change in insulin synthesis, suppression of glucokinase gene expression, mitochondrial function decrease, exocytotic mechanisms violation, and accelerated apoptosis [119–121]. 1.3.1.2 Free fatty acids NIDDM in humans is frequently associated with obesity and hyperlipidemia as well as hyperglycemia. There is ample evidence that fatty acids (FA) become toxic when present at elevated concentrations for prolonged periods of time [122]. Adverse effects of chronic exposure of the β -cell to elevated FA concentrations include decreased glucose-induced insulin secretion [123, 124], impaired insulin gene expression [125], and increased apoptosis [126, 127]. Among the mechanisms by which FA impair β -cell function there are decreased glucose oxidation [123], lipid-derived intracytosolic metabolites action [127], and hypothesis, initially proposed by Prentki and Corkey (1996) [128] and developed by Robertson with colleagues [117]. They postulate that in the presence of physiological glucose concentrations, excessive FAs are readily disposed of through mitochondrial β -oxidation. In contrast, when both fatty acids and glucose are elevated, accumulation of metabolites derived from fatty acid esterification impairs β -cell function. This data also can be considered as another side of glucose toxicity.

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1.3.1.3 Diabetes mellitus complications and glucose Years of poorly controlled hyperglycemia lead to multiple, primarily vascular complications that affect small (microvascular) and/or large (macrovascular) vessels. In common the mechanisms by which vascular disease develops include glycosylation of serum and tissue proteins with formation of advanced glycation end products; superoxide production; activation of protein kinase C, a signaling molecule that increases vascular permeability and causes endothelial dysfunction; accelerated hexosamine biosynthetic and polyol pathways leading to sorbitol accumulation within tissues; hypertension and dyslipidemias that commonly accompany DM; arterial microthromboses; and pro-inflammatory and prothrombotic effects of hyperglycemia and hyperinsulinemia that impair vascular autoregulation. Among vascular complications of DM the major ones are diabetic retinopathy and cataract, diabetic nephropathy, neuropathy, and macrovascular disease. Chronic supraphysiological glucose concentration results in increased expression of basement membrane components in retinal pericytes and endothelial cells [129], DNA damage in endothelial cells, accumulation of advanced glycosilation end products [130], increased matrix synthesis by mesangail cells [131], abnormal release of prostanoids, protein kinase C activation [132], and plural shifts in haemostasis system. The endothelial lining of blood vessels provides a barrier for the exchange of the nutrients. Endothelial cell activity is involved in the local control of vascular homeostasis. Endothelium-dependent vascular relaxation is markedly impaired in diseases such as diabetes mellitus, atherosclerosis, and hypertension. High levels of plasminogen activator inhibitor type 1 (PAI 1) have been consistently associated with increased insulin concentrations and decreased insulin sensitivity [133, 134]. Several recent studies have demonstrated that apoptosis of pancreatic β -cells is induced as a consequence of NIDDM, release of cytokines and free fatty acids from adipocytes, and hyperglycemia [123, 135, 136]. Glucokinase (GCK), or hexokinase IV, is a well-known member of the mammalian hexokinase family that catalyzes the initial step of glucose metabolism in several metabolic pathways [137]. Won-Ho Kim with colleagues demonstrates that β -cell apoptosis from exposure to chronic high glucose occurs in relation to lowered GCK expression and reduced association with mitochondria [138]. Described biochemical alterations base structural and functional abnormalities, such as capillary basement membrane thickening, microaneurysms, capillary occlusion, increased glomerular filtration rate, proteinuria, thrombosis and rheological disorders, which form the sense of upper counted complications. Immune dysfunction is another major complication and develops from the direct effects of hyperglycemia on cellular immunity. Diabetes and atherosclerosis have been proposed to be influenced by immune and autoimmune mechanisms. Initially, active chronic inflammatory disease was found to lead to peripheral insulin resistance [139]. The next step was determination of association between circulating insulin and white blood cell count and C-reactive protein (CRP) in patients with angina pectoris [139]. More recently, chronic subclinical inflammation has been proposed

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as a part of the insulin resistance syndrome [140]. To date, one of the most accepted hypotheses is triggering of the inflammatory cascade that leads to insulin resistance and atherosclerosis [141, 142]. A common incriminated antigen in both disorders is the heat shock protein (HSP)60/65. In the numerous papers of Harats group it was shown that the accelerated atherosclerotic process was associated with heightened immune response to HSP 65 and a shift to a TH1 cytokine profile [143].

1.3.2 Atherosclerosis and coronary artery disease: glucose’s place in pathogenesis Coronary artery disease involves impairment of blood flow through the coronary arteries, most commonly by atheromas. Usually, CAD is due to subintimal deposition of atheromas in large and medium-sized coronary arteries. Occasionally, an atheromatous plaque ruptures or splits. Reasons are unclear but probably relate to an inflammatory process that softens the plaque. Rupture exposes thrombogenic material, which activates platelets and the coagulation cascade, resulting in an acute thrombus and ischemia. In arteries with atheroma, the atheroma may cause local hypercontractility; proposed mechanisms include loss of sensitivity to intrinsic vasodilators (e.g., acetylcholine) and increased production of vasoconstrictors (e.g., angiotensin II, endothelin, leukotrienes, serotonin, thromboxane) in the area of the atheroma. Recurrent spasm may damage the intima, leading to atheroma formation. Among proved risk factors for CAD there are carbohydrate violations and DM. High blood levels of triglycerides and insulin (reflecting insulin resistance) may be risk factors, but data are less clear [144]. 1.3.2.1 Hyperglycemia and atherogenesis Currently hyperglycemia influence upon atheroma formation comes to generalized endothelial dysfunction and oxidative stress explosion [145, 146]. Summarizing numerous clinical and experimental trials data three main mechanisms of hyperglycemia influence upon atherogenesis have been posed: 1) biomolecules dysfunction due to conformational changes, enzyme activity modulation, receptor affinity decrease, and some other molecular abnormalities reached via nonenzymatic proteins and lipid glycosylation; 2) oxidative stress; 3) proteinkinase C activation with further going violations in growth factors expression. It is important to note that all these mechanism are united in a single pathological net influencing upon each other and overlapping [147]. Oxidative stress under hyperglycemia conditions in aggregate with nonenzymatic glycosylation enhancing promotes monocyte-endothelial interaction, one of the trigger mechanisms of atherosclerotic lesions formation [148]. Initially circulating lipids are exposed to oxidative stress agents. As it was shown in works of S. Cushing et al. [149] and T. Rajavashisth et al. [150], monocytes more “willingly” consume oxidated low density lipoproteins and due to this secrete several chemo attractants into the blood stream, their level increasing induces local monocytes attraction and adhesion to endothelium provoking complex leukocyte-

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endotheliocytes interaction [149, 150]. Quin with colleagues were the first to show present mechanism in the in vitro model [151]. Inside the vessel wall the monocytes start to accumulate lipids and transform into foam cells producing inflammatory cytokines. Endotheliocytes due to inflammatory cytokine stimuli increase production of adhesion molecules such as ELAM-1, ICAM-1, and VCAM-1. All these substances increase monocytes adhesiveness to endothelium and penetration into vessel media closing the vicious circle. Besides hyperglycemia via increase of glycosilated metabolites concentration leads towards their accumulation in plasma and vessel wall (proved in patients with NIDDM) [130, 152]. Glycosilates enhance human T lymphoblasts attraction to endotheliocytes [153] thus promoting T lymphoblasts growth in the atherosclerotic plaque. The described mechanism is one possibility to provoke the initial atheroma formation during chronic hyperglycemia and specify its cells content. Hyperglycemia inhibits NO synthesis and modifies blood flow characteristics with increase of endothelial mechanical traumatisation probability. Another component of vascular disfunction is nearly connected induced by chronic hyperglycemia insulin resistance. We’ve already mentioned that insulin signaling through the phosphatidylinositol 3-kinase pathway takes part in NO production in endothelium [154–156]. Associated with IR disruption of this signaling pathway violates NO production and contributes to endothelium disfunction onset. Increase in asymmetric dimethylarginine concentration (ADMA - an endogenous and competitive inhibitor of NOS) as it was shown in Cooke’s review is associated with endothelial dysfunction and increased risk of CVD [157]. Stuhlinger et al. have demonstrated that plasma ADMA concentrations are positively correlated with impairment of insulin-mediated glucose metabolism in subjects with the metabolic syndrome, independent of hypertension [158]. An essential cofactor for the catalytic activity of eNOS tetrahydrobioproterin (BH4) is depleted via excessive oxidation [159] and insulin resistance metabolic shifts. IR can diminish the activity of the enzyme that produces BH4 in human coronary arteries with resultant BH4 depletion and endothelial dysfunction, which is reversed by BH4 administration. BH4 “failure” causes eNOS to uncouple and NO production decreases. Chronic hyperglycemia in not less than 69% of patients that caused specific lipid metabolism disorders [148] was initially studied in diabetic subjects with NIDDM, and because of that called diabetic dislipidemia. Diabetic dislipidemia include hypertriglyceridimia, increase in concentration of minor dense low density lipoproteins (LDL), and increase of high density lipoproteins (HDL). This lipid triad presence is a special type of atherogenic dislipidemia and enhances atherogenesis independently from total cholesterol and total LDL fraction [160–162]. Several reports show strong correlation within intensity of diabetic dislipidemia, hypertruglyceridemia first of all, and insulin concentration, and IR [161–164]. On the other hand hyperinsulinemia and IR besides lipid metabolism disorders are independent risk factors of coronary heart disease (CHD) [165, 166]. Shinozaki with colleagues proved significant interaction between IR and coronary atherosclerotic lesion value in patient with CHD proved by angiography [165]. As it was previously discussed one of the possible

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mechanisms of IR is insulin receptors violation (total amount decrease) caused by chronic high glucose concentration. Such interaction closes another vicious circle. 1.3.2.2 Haemostasis and rheology modifications and glucose Hyperinsulinemia and IR influence upon atherosclerosis partly mediates by modification of haemostasis system [167]. What is the main culprit of endothelial disfunction onset and progression: hyperglycemia or hyperinsulinemia? The question is still unsolved, but Carli with colleagues postulates the key role of hyperglycemia in endothelial disfunction development via oxidative stress and proteinkinase C activation [168]. Athesclerotic plaque type predominantly determines the clinical course of coronary heart disease. Hyperglycemia, IR, and hyperinsulinemia cause extended endothelial lesion, lipid metabolism disorders, and initiate oxidative stress. This combination provokes a cascade of violations in coagulation and fibrinolysis and results in appearance of “soft” atherosclerotic plaques, in which cell and interstitial structure promotes its destabilization cap rupture. One of the most mysterious types of hypeglycemia is the posprandial one, blood glucose level increases within two hours after meal or glucose tolerance test baseline point. One of the results of a seven year trial that included 30000 volunteers in USA and Europe was establishing that blood glucose level two hours after standard carbohydrate load was a more sensitive predictor of cardiovascular mortality than fasting glucose concentration. Two hours postprandial hyperglycemia allow a researcher to reveal patients with high cardiovascular mortality risk. This data prove the necessity of oral glucose tolerance test as a screening method in patients with coronary heart disease (Diabetes Epidemiology: Collaborative Analysis of Diagnostic Criteria in Europe (DECODE), 1999). Both acute and chronic hyperglycemia influence upon blood cell, especially erythrocytes, membrane structure, and functional abilities [169, 170]. Haemoglobin glycation modifies its oxygen capacity. Erythrocytes’ cell membrane proteins’ glycation leads to their structural and functional changes [171]. Glycated haemoglobin increase intracellular viscosity of erythrocytes, modify their mechanical rigidity, and influence upon NO metabolism [172]. Such modulation in blood cells’ properties provokes rheology changes and aggravates endothelial function closing another vicious circle. Summarizing the present data we can conclude that glucose metabolism violations are nearly connected with coronary heart disease pathogenesis (Fig. 1.7), and blood glucose concentration as a discrete parameter and continuous glucose monitoring are important components of a patient with CHD investigation.

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FIGURE 1.7: Simplified scheme of glucose level influence upon atherogenesis.

1.4 Blood Glucose Level Monitoring in Clinical Practice 1.4.1 Glucose level regulation system tests: clinical and experimental use Several laboratory and functional tests were proposed to judge upon functional state of blood glucose level regulation system [173–176]. All of them can be divided into two large groups. The first one includes direct detection of any system component concentration in an interesting human organism compartment. Among such components glucose, insulin, C-peptide, glucagons, amylin, all contrainsulin hormones, glycation products, and others can be measured. According to the aims and purposes of the study glucose, for example, can be measured in all biological fluids: blood, plasma, serum, intestinal liquid, cerebrospinal fluid, sinovial liquid, saliva, semen, and others. Moreover glucose concentration can be measured in different blood vessels regions. In common clinical practice but in order to standardize glucose determination (ESC and EASD guidelines) the primary specimen in clinical laboratory investigations is blood plasma. Accuracy of measurement also is determined by study design; in clinical practice glucose level is measured to within 0.1 mg/dL or mmol/L. Since many equipment use either whole blood or venous or capillary blood threshold for these methods are also detected. Actually there are several equations that allow investigators to convert whole blood plasma, capillary blood, and serum glucose level to plasma glucose level. For example: plasma glucose level (mmol/L) = 0.55+1.119× whole blood glucose (mmol/L) [176]. Glycated haemoglobin (HbA1C ) is useful in a clinical practice parameter of metabo-

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lic control. It is an integrated summary of circadian blood glucose during the preceding 6-8 weeks (the lifespan of erythrocytes). In general, FPG, PPG, and especially mean plasma glucose (MPG) concentrations, defined by the average of multiple measurements of glucose taken throughout the day, are highly correlated with HbA1C . It provides a mean value but does not reveal any information on the extent and frequency of blood glucose level excursions. HbA1C has never been recommended as a diagnostic test for diabetes [176]. The second group of tests includes so-called functional tests, which illustrate metabolic interactions really existing in human organism within components of blood glucose level regulation system. Up to now thousands of such tests have been developed. The primary principle of these tests is to change (the more often increase) concentration of the selected participant of a studied functional system and monitor other selected parameters concentration (the system answer). Such participants may be glucose itself (all types of glucose loading tests), insulin (so-called glucose clamp tests) and theoretically any other component according to the clinical situation or purpose of the study. Glucose loading tests or glucose tolerance tests also can be divided into oral and intravenous glucose tolerance tests according to the chosen way of glucose concentration increase, all with its own benefits and limitations in use. For example, oral glucose tolerance test results significantly depend on gastrointestinal tract functional state; intravenous glucose tolerance test is an invasive procedure. Up to now several protocols of glucose loading tests have been developed.

1.4.2 Clinical value of blood glucose level measurements As it was discussed above blood glucose level is a parameter strongly recommended to detect in patients with CHD and DM and in persons with coronary risk factors presence. Results from the Diabetes Care and Complications Trial show that tight blood glucose control significantly reduces the long-term complications of diabetes mellitus (1993) [173]. Self-monitoring blood glucose control (SMBG) presents itself to be a very important component of therapy in patients with DM, although it is still a matter of debate, for it possesses several limitations in clinical use. For example, a trial involving 3567 patients with NIDDM had shown that SMBG can have an important role in improving metabolic control if it is an integral part of a wider educational strategy devoted to the promotion of patient autonomy [174].

1.4.3 Current state of the problem: unsolved questions One of the most precise methods of glucose level measurement is based on the obtaining of a blood sample and furthergoing biochemical test (several modifications). In fact despite important outcomes in this scientific area several clinical problems are still unsolved. The main ones are development of a noninvasive blood glucose level technique and continuous glucose level monitoring (CGM). Widespread types of glucometers used in patient self control of glycemia are based on the same biochemical tests and it is necessary to prick a finger to withdraw a blood drop. Multiple finger pricks are undesirable in many cases, especially in diabetic pa-

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tients. The pain and inconvenience of self-testing, along with the fear and danger of hypoglycaemia, has led to patient acceptance of a tight control regimen, despite the clear long-term advantages. Difficulties in comparing the results and the possibility of frequent glucose measuring severe complications underline the urgency of a safe and effective noninvasive glucose sensing technique development. Guy et al. demonstrated a noninvasive method to transport glucose through the skin using low-level electrical current [175]. To provide a quantitative measurement, the flux of glucose extracted across the skin must correlate with serum glucose in a predictive manner. The results of a study by Tamada with colleagues presented a quantitative relationship between serum and transdermally extracted glucose in diabetics [177]. Recently, several methods of noninvasive blood glucose testing were proposed. The most available in clinical practice techniques are based on near infrared spectroscopy, light scattering methods, and photoacoustic spectroscopy [178]. Near infrared spectroscopy is the most studied noninvasive technology [179, 180]. The precision, however, is presently not good enough to use this technology clinically via unpredictable spectral variations that are not related to glucose, blood flow, temperature, light scattering, overlapping absorption by non-glucose metabolites, and a particularly strong absorption by water in the near infrared region, and movement artefact caused by changes in the alignment of the instrumentation [178]. Another noninvasive glucose sensing technology is based on changes in light scattering in the tissues [181]. Refractive index increase of the plasma and interstitial fluid as glucose concentration increases lowers the scattering coefficient by about 1% for each 5 mmol/l change. Temperature, tissue hydration, and probe alignment also make immediate clinical application difficult. Photoacoustic spectroscopy is based on the fact that pulsed infrared light is absorbed by glucose molecules and produces an ultrasound wave that is detectable at the skin surface by a piezoelectric microphone [182]. Some available in clinical practice devices measure glucose transcutaneously, but their use has been limited by skin irritation and erratic readings; better technology may soon make near-continuous readings with such devices feasible. Continuous glucose monitoring provides information about direction, magnitude, duration, frequency, and causes of fluctuations in blood glucose levels throughout the day and facilitates the optimal treatment strategy for the patient, i.e., diabetic one. Continuous glucose monitoring can express the frequency and severity of hypoglycemic episodes much more rapidly and clearly than common biochemical glucose testing does. Besides, the capability of expressing the mean blood glucose value in new ways is also an important outcome of CGM. The currently available in clinical practice systems for continuous glucose monitoring measure blood glucose either through continuous measurement of interstitial fluid (ISF) or with the noninvasive method of applying electromagnetic radiation through the skin to blood vessels in the body. The technologies for bringing a sensor into contact with ISF include inserting an indwelling sensor subcutaneously to measure ISF in situ or harvesting this fluid by various mechanisms that compromise the skin barrier and deliver the fluid to an external sensor [183]. These ISF measurement

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technologies are defined as minimally invasive because they compromise the skin barrier but do not puncture any blood vessels. Results are available to the patient in real time or retrospectively. Currently available CGMs can present problems in use [184]. First of all is the lack of accuracy for each single data point compared with the accuracy of simultaneous intermittent blood glucose measurements, especially in the hypoglycemic range [185]. A minimally invasive CGM can be associated with side effects related to chronic ISF harvesting. Skin irritation complicates the use of several devices for CGM. Most currently available continuous blood glucose monitors do not actually measure the glucose concentration within whole blood, but within the ISF. It was proved that equilibration between shifting blood and interstitial fluid glucose levels may lag [185]. It is unknown whether sensor site selection can minimize this phenomena or the lag due difference between arterial and skin capillary blood glucose levels at sites other than the fingertip. Unfortunately up to now there is an insufficient number of randomized, controlled trials of CGM devices, in which a statistically significant decrease in diabetic complications or HbA1C levels were shown as the result of long-term blood glucose control [187–192]. The specificity of blood glucose level dynamics may result in alignment of hyperglycemic and hypoglycemic spikes during long-term CGM. Continuous glucose monitoring can distinguish the two exposures, but long-term markers cannot stratify time spent above and below a particular target.

1.5 Conclusion Summarizing all previous data it can be concluded that functional system of regulation of blood glucose level not only reflects plural metabolism violations in human organism, but per se actively participates in pathogenesis. Present review demonstrates only fragments of a significant progress in its role study. Despite fulfilled significant scientific research work in this area there are a lot of blanks, problems to solve both in fundamental and practical branches of medicine. Recent answers on puzzling questions mostly are limited via technical and methodological imperfections. Figuratively we are still at the beginning of the way, thorny and hard, and only productive cooperation of scientists (partly illustrated in this book) may bring success.

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1.6 Glossary Antibody – an immunoglobulin molecule that reacts with a specific antigen that induced its synthesis. Antigen – any substance, almost always a protein, not normally present in the body which when introduced to the body stimulates a specific immune response and the production of antibodies. Apoptosis – programmed cell death; fragmentation of the cell into membranebound particles that are eliminated by phagocytosis; from the Greek for “falling off.” Coagulate – to cause to clot or become clotted; to convert a fluid or substance in solution into a solid or a gel. Elderly population – totality of individuals of 60 years old and older. Free fatty acids – Fatty acids can be bound or attached to other molecules, such as in triglycerides or phospholipids. When they are not attached to other molecules, they are known as “free” fatty acids. Gluconeogenesis – the generation of glucose from non-sugar carbon and glucogenic amino acids. Glycogenolysis – the catabolism of glycogen by removal of a glucose monomer and addition of phosphate to produce glucose-1-phosphate. Glycolysis – Embden-Meyerhof pathway, cytoplasmic anaerobic phase of carbohydrate combustion. Hypoxia – reduced supply of oxygen to tissues (below physiologic levels) despite normal blood perfusion. Idiopathic – occurring without known cause. Ketosis – an accelerated production of ketoacids, which occurs when carbohydrate intake is low or when fasting is prolonged beyond the usual overnight period. Metabolism – the sum of all the chemical processes involved in producing energy from endogenous and exogenous sources, synthesizing and degrading structural and functional tissue components and disposing of resultant waste products. Morbidity – the condition of being diseased or sick; the ‘sick’ rate, i.e., the ratio of sick to well persons in a community. Mortality – the quality of being mortal or alive; the ‘death’ rate, i.e., the number of people dying in a given population. Necrosis – the morphological changes indicative of cell death caused by progressive enzymatic degradation. Pathognomonic – characteristic or indicative of a disease; denoting symptoms or findings specific for a given disease and not found in any other condition. Perfusion – complicated process of transport of oxygen and nutrient from blood vessels to internal organs, tissues, etc. Prognosis – a forecast of the course and probable outcome of a disorder.

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References [1] T.M. Devlin (ed.), Textbook of biochemistry with clinical correlations. 6th edition, Wiley-Liss, N.Y., 2006. [2] R.P. Ferraris, and J. M. Diamond, “Use of phlorizin binding to demonstrate induction of intestinal glucose transporters,” J. Membr. Biol., vol. 94, 1986, pp. 77–82. [3] H.G. Joost, G.I. Bell, J.D. Best, et al., “Nomenclature of the GLUT/SLC2A family of sugar/polyol transport facilitators,” Am. J. Physiol. Endocrinol. Metab., vol. 282, 2002, pp. E974–E976. [4] H. Doege, A. Bocianski, A. Scheepers, et al., “Characterization of human glucose transporter (GLUT) 11 (encoded by SLC2A11), a novel sugar-transport facilitator specifically expressed in heart and skeletal muscle,” Biochem. J., vol. 359, 2001, pp. 443–449. [5] M. Ibberson, M. Uldry, and B. Thorens, “GLUTX1, a novel mammalian glucose transporter expressed in the central nervous system and insulin-sensitive tissues,” J. Biol. Chem. vol.275, 2000, pp. 4607–4612. [6] P.A. Dawson, J.C. Mychaleckyj, S.C. Fossey, et al., “Sequence and functional analysis of GLUT10: a glucose transporter in the type 2 diabetes-linked region of chromosome 20q12–13.1,” Mol. Genet. Metab., vol. 74, 2001, pp. 186–199. [7] S. Rogers, M.L. Macheda, S.E. Docherty, et al., “Identification of a novel glucose transporter-like protein-GLUT-12,” Am. J. Physiol. Endocrinol. Metab., vol. 282, 2002, pp. E733–E738. [8] K. Zierler, and M. Kenneth, “Whole body glucose metabolism,” Am.J. Physiol., vol. 276, 1999, pp. E409–E426. [9] A. Wettergren, B. Schjoldager, P.E. Mortensen, et al., “Truncated GLP-1 (proglucagon 78 107-amide) inhibits gastric and pancreatic functions in man,” Dig. Dis. Sci., vol. 38, 1993, pp. 665–673. [10] D.J. Drucker, “Glucagon-like peptides,” Diabetes, vol. l47, 1998, pp. 159– 169. [11] A.A. Young, B. Gedulin, W. Vine, et al., “Gastric emptying is accelerated in diabetic BB rats and is slowed by subcutaneous injections of amylin,” Diabetologia, vol. 38, 1995, pp. 642–648. [12] A.R. Natali, R. Bonadonna, D. Santoro, et al., “Insulin resistance and vasodilation in hypertension. Studies with adenosine,” J. Clin. Invest., vol. 94, 1994, pp. 1570–1576.

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[26] B.R. Gedulin, T.J. Rink, and A.A. Young, “Dose-response for glucagonostatic effect of amylin in rats,” Metabolism, vol. 46, 1997, pp. 67–70. [27] M. Samson, L.A. Szarka, M. Camilleri, et al., “Pramlintide, an amylin analog, selectively delays gastric emptying: potential role of vagal inhibition,” Am. J. Physiol., vol. 278, 2000, pp. G946–G951. [28] T. Vilsboll, T. Krarup, C.F. Deacon, et al., “Reduced postprandial concentrations of intact biologically active glucagon-like peptide 1 in type 2 diabetic patients,” Diabetes, vol. 50, 2001, pp. 609–613. [29] M.A. Nauck, J.J. Holst, B. Willms, and W. Schmiegel, “Glucagon-like peptide 1 (GLP-1) as a new therapeutic approach for type 2 diabetes,” Exp. Clin. Endocrinol. Diabetes, vol 105, 1997, pp. 187–195. [30] R. Perfetti, and P. Merkel, “Glucagon-like peptide-1: a major regulator of pancreatic beta-cell function,” Eur. J. Endocrinol., vol. 143, 2000, pp. 717– 725. [31] D.J. Drucker, “Minireview: the glucagon-like peptides,” Endocrinology, vol. 142, 2001, pp. 521–527. [32] A.H. Mehboob, O. Schmitz, and E.R. Froesch, “Growth hormone, insulin, and insulin-like growth factor 1: revisiting the food and famine theory,” News Physiol. Sci., vol. 10, 1995, pp. 81–86. [33] M.F. Dallman, A.M. Strack, S.F. Akana, et al., “Feast and famine: critical role of glucocorticoids with insulin in daily energy flow,” Front. Neuroendocrinol., vol.14, 1993, pp. 303–347. [34] O. Hother-Nielsen, and H. Beck-Nielsen, “On the determination of basal glucose production rate in patients with type 2 (non-insulin-dependent) diabetes mellitus using primed-continuous 3H-glucose infusion,” Diabetologia, 33, 1990, pp. 603–610. [35] R.P. Ferraris, and J. Diamond, “Regulation of intestinal sugar transport,” Physiol. Rev., vol. 77, 1997, pp. 257–301. [36] W.H. Karasov, and J. M. Diamond, “Adaptive regulation of sugar and amino acid transport by vertebrate intestine,” Am. J. Physiol., vol. 245 (Gastrointest. Liver Physiol. 8), 1983, pp. G443–G462. [37] D.J. Philpott, J.D. Butzner, and J.B. Meddings, “Regulation of intestinal glucose transport,” Can. J. Physiol. Pharmacol., vol.70, 1992, pp. 1201–1207. [38] C.I. Cheeseman, and D. D. Maenz, “Rapid regulation of D-glucose transport in basolateral membrane of rat jejunum,” Am. J. Physiol., vol. 256 (Gastrointest. Liver Physiol. 19), 1989, pp. G878–G883. [39] A.D. Baron, G. Brechtel, P. Wallace, and S.V. Edelman, “Rates and tissue sites of non-insulin- and insulin-mediated glucose uptake in humans,” Am. J. Physiol. (Endocrinol. Metab. 18), vol. 255, 1988, pp. E769–E774.

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[92] S.L. Aronoff, K. Berkowitz, B. Sheiner, and L. Want, “Glucose metabolism and regulation: beyond insulin and glucagon,” Diabetes Spectrum, vol. 17, 2004, pp. 183–190. [93] S.E. Kahn, R.L. Prigeon, D.K. McCulloch, et al., “Quantification of the relationship between insulin sensitivity and ß-cell function in human subjects. Evidence for a hyperbolic function,” Diabetes, vol. 42, 1993, pp. 1663–1672. [94] C. Weyer, C. Bogardus, D.M. Mott, and R.E. Pratley, “The natural history of insulin secretory dysfunction and insulin resistance in the pathogenesis of type 2 diabetes mellitus,” J. Clin. Invest., vol. 104, 1999, pp. 787–794. [95] V. Poitout, and R.P. Robertson, “Minireview: secondary ß-cell failure in type 2 diabetes–a convergence of glucotoxicity and lipotoxicity,” Endocrinology, vol. 143, 2002, pp. 339–342. [96] C. Bernard-Kargar, and A. Ktorza, “Endocrine pancreas plasticity under physiological and pathological conditions,” Diabetes, vol. 50(Suppl 1), 2001, pp. S30–S35. [97] B. Leibiger, T. Moede, T. Schwarz, et al., “Short-term regulation of insulin gene transcription by glucose,” Proc. Natl. Acad. Sci. USA, vol. 95, 1998, pp. 9307–9312. [98] R.N. Kulkarni, J.C. Bruning, J.N. Winnay, et al., “Tissue-specific knockout of the insulin receptor in pancreatic ß cells creates an insulin secretory defect similar to that in type 2 diabetes,” Cell, vol. 96, 1999, pp. 329–339. [99] B. Leibiger, I.B. Leibiger, T. Moede et al., “Selective insulin signaling through A and B insulin receptors regulates transcription of insulin and glucokinase genes in pancreatic ß cells,” Mol. Cell., vol. 7, 2001, pp. 559–570. [100] A.D. Cherrington, P.E. Williams, and M.S. Harris, “Relationship between the plasma glucose level and glucose uptake in the conscious dog,” Metabolism, vol. 27, 1978, pp. 787–791. [101] R.N. Bergman, “Lilly lecture 1989. Toward physiological understanding of glucose tolerance. Minimal-model approach,” Diabetes, vol. 38, 1989, pp. 1512–1527. [102] M. Ader, T.C. Ni, R.N. Bergman, “Glucose effectiveness assessed under dynamic and steady state conditions. Comparability of uptake versus production components,” J. Clin. Invest., vol. 99, 1997, pp. 1187–1199. [103] S. Del Prato, A. Riccio, S. Vigili de Kreutzenberg, et al., “Basal plasma insulin levels exert a qualitative but not quantitative effect on glucose-mediated glucose uptake,” Am. J. Physiol., vol. 268, 1995, pp. E1089–E1095. [104] S.I. Itani, A.K. Saha, T.G. Kurowski, et al., “Glucose autoregulates its uptake in skeletal muscle: involvement of AMP-activated protein kinase,” Diabetes, vol. 52, 2003, pp. 1635–1640.

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[105] C. Bouch´e, S. Serdy, C.R. Kahn, and A.B. Goldfine, “The cellular fate of glucose and its relevance in type 2 diabetes,” Endocrine Reviews, vol. 25, 2004, pp. 807–830. [106] P.J. Campbell, L.J. Mandarino, and J.E. Gerich, “Quantification of the relative impairment in actions of insulin on hepatic glucose production and peripheral glucose uptake in non-insulin-dependent diabetes mellitus,” Metabolism, vol. 37, 1988, pp. 15–21. [107] A. Basu, R. Basu, P. Shah, et al., “Effects of type 2 diabetes on the ability of insulin and glucose to regulate splanchnic and muscle glucose metabolism: evidence for a defect in hepatic glucokinase activity,” Diabetes, vol. 49, 2000. pp. 272–283. [108] R.H. Unger, and S. Grundy, “Hyperglycaemia as an inducer as well as a consequence of impaired islet cell function and insulin resistance: implications for the management of diabetes,” Diabetologia, vol. 28, 1985, pp. 119–121. [109] L. Rossetti, A. Giaccari, and R.A. De Fronzo, “Glucose toxicity,” Diabetes Care, vol 13, 1990, pp. 610–630. [110] H. Yki-Jarvinen, “Glucose toxicity,” Endocrine Rev., vol. 13, 1992, pp. 415– 431. [111] H. Yki-Jarvinen, “Acute and chronic effects of hyperglycaemia on glucose metabolism,” Diabetologia, vol. 33, 1990, pp. 579–585. [112] J.L. Leahy, S. Bonner-Weir, and G.C. Weir, “ß-Cell dysfunction induced by chronic hyperglycemia: current ideas on mechanism of impaired glucoseinduced insulin secretion,” Diabetes Care, vol. 15, 1992, pp. 442–455. [113] B.B. Kahn, G.I. Shulman, R.A. De Fronzo, et al., “Normalization of blood glucose in diabetic rats with phlorizin treatment reverses insulin-resistant glucose transport in adipose cells without restoring glucose transporter gene expression,” J. Clin. Invest., vol. 87, 1991, pp. 561–570. [114] M. Hawkins, I. Gabriely, R. Wozniak, et al., “Glycemic control determines hepatic and peripheral glucose effectiveness in type 2 diabetic subjects,” Diabetes, vol. 51, 2002, pp. 2179–2189. [115] Y. Fujimoto, T.P. Torres, E.P. Donahue, and M. Shiota, “Glucose toxicity is responsible for the development of impaired regulation of endogenous glucose production and hepatic glucokinase in Zucker diabetic fatty rats,” Diabetes, vol. 55, 2006, pp. 2479–2490. [116] R.P. Robertson, J. Harmon, P.O. Tran et al., “Glucose toxicity in ß-cells: type 2 diabetes, good radicals gone bad, and the glutathione connection,” Diabetes, vol. 52, 2003, pp. 581–587. [117] R.P. Robertson, J. Harmon, P.O. Tran, and V. Poitout, “ß-cell glucose toxicity, lipotoxicity, and chronic oxidative stress in type 2 diabetes,” Diabetes, vol. 53, 2004, pp. S119–S124.

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[118] R.P. Robertson, Y. Tanaka, G. Sacchi, et al., “Glucose toxicity of the ß-cell: cellular and molecular mechanisms,” In Diabetes Mellitus, D. LeRoith, J.M. Olefsky, S. Taylor (eds.), New York, Lippincott Williams & Wilkins, 2000, pp. 125 –132. [119] Y. Kajimoto, T. Matsuoka, H. Kaneto, et al., “Induction of glycation suppresses glucokinase gene expression in HIT-T15 cells,” Diabetologia, vol. 42, 1999, pp. 1417 –1424. [120] P. Maechler, L. Jornot, and C.B. Wollheim, “Hydrogen peroxide alters mitochondrial activation and insulin secretion in pancreatic beta cells,” J. Biol. Chem., vol. 274, 1999, pp. 27905 –27913. [121] A.E. Butler, J. Janson, S. Bonner-Weir, et al., “ß-Cell deficit and increased ß-cell apoptosis in humans with type-2 diabetes mellitus,” Diabetes, vol. 52, 2003, pp. 102 –110. [122] J.D. McGarry, and R.L. Dobbins, “Fatty acids, lipotoxicity and insulin secretion,” Diabetologia, vol. 42, 1999, pp. 128 –138. [123] Y.P. Zhou, and V.E. Grill, “Long-term exposure of rat pancreatic islets to fatty acids inhibits glucose-induced insulin secretion and biosynthesis through a glucose fatty acid cycle,” J. Clin. Invest., vol. 93, 1994, pp. 870–876. [124] T.M. Mason, T. Goh, V. Tchipashvili, et al., “Prolonged elevation of plasma free fatty acids desensitizes the insulin secretory response to glucose in vivo in rats,” Diabetes, vol. 48, 1999, pp. 524–530. [125] I. Briaud, J.S. Harmon, C.L. Kelpe et al., “Lipotoxicity of the pancreatic ß-cell is associated with glucose-dependent esterification of fatty acids into neutral lipids,” Diabetes, vol. 50, 2001, pp. 315–321. [126] M. Shimabukuro, Y.T. Zhou, M. Levi, and R.H. Unger, “Fatty acid-induced ß-cell apoptosis: a link between obesity and diabetes,” Proc. Natl. Acad. Sci. USA, vol. 95, 1998, pp. 2498–2502. [127] V. Poitout, “Lipid partitioning in the pancreatic ß-cell: physiologic and pathophysiologic implications,” Curr. Opin. Endocrinol. Diabetes, vol. 9, 2002, pp. 152–159. [128] M. Prentki, and B.E. Corkey, “Are the ß-cell signaling molecules malonylCoA and cystolic long-chain acyl-CoA implicated in multiple tissue defects of obesity and NIDDM?” Diabetes, vol. 45, 1996, pp. 273–283. [129] G. Pugliese, “Glucose-induced metabolic imbalances in the pathogenesis of diabetic vascular disease,” Diabetes Metab. Rev., vol. 7, 1991, pp. 35–59. [130] M. Brownlee, A. Cerami, and H. Vlassara, “Advanced glycosylation end products in tissue and the biochemical basis of diabetic end products in tissue and the biochemical basis of diabetic complications,” N. Engl. J. Med., vol. 318, 1988, pp. 1315–1321.

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[131] T. Deckert, B. Feldt-Rasmussen, K. Borch-Johnsen, et al., “Albuminuria reflects widespread vascular damage. The Steno hypothesis,” Diabetologia, vol. 32, 1989, pp. 219–226. [132] B. Tesfamariam, M.L. Brown, and R.A. Cohen, “Elevated glucose impairs endothelium-dependent relaxation by activating protein impairs endotheliumdependent relaxation by activating protein kinase C,” J. Clin. Invest., vol. 87, 1991, pp. 1643–1648. [133] P. van Loon, C. Kluft, J.K. Radder, et al., “The cardiovascular risk factor plasminogen activator inhibitor type 1 is related to insulin resistance,” Metabolism, vol. 42, 1993, pp. 945–949. [134] R. Festa, D’Agostino, L. Mykkanen, et al., “Relative contribution of insulin and its precursors to fibrinogen and PAI-1 in a large population with different states of glucose tolerance,” Aterioscler. Thromb. Vasc. Biol., vol. 19, 1999, pp. 562–568. [135] M. Cnop, J.C. Hannaert, A. Hoorens, et al., “Inverse relationship between cytotoxicity of free fatty acids in pancreatic islet cells and cellular triglyceride accumulation,” Diabetes, vol. 50, 2001, pp. 1771–1777. [136] E. Gurgul, S. Lortz, M. Tiedge, et al., “Mitochondrial catalase overexpression protects insulin-producing cells against toxicity of reactive oxygen species and proinflammatory cytokines,” Diabetes, vol. 53, 2004, pp. 2271–2280. [137] C. Postic, M. Shiota, and M.A. Magnuson, “Cell-specific roles of glucokinase in glucose homeostasis,” Recent Prog. Horm. Res., vol. 56, 2001, pp. 195– 217. [138] W.-H. Kim, J.W. Lee, Y.H. Suh, et al., “Exposure to chronic high glucose induces ß-cell apoptosis through decreased interaction of glucokinase with mitochondria. Downregulation of glucokinase in pancreatic ß-cells,” Diabetes, vol. 54, 2005, pp. 2602–2611. [139] K.L. Svenson, T. Pollare, H. Lithell, and R. Hallgren, “Impaired glucose handling in active rheumatoid arthritis: relationship to peripheral insulin resistance,” Metabolism, vol. 37, 1988, pp. 125–130. [140] I. Juhan-Vague, S.G. Thompson, and J. Jespersen, “Involvement of the hemostatic system in the insulin resistance syndrome. A study of 1500 patients with angina pectoris. The ECAT Angina Pectoris Study Group,” Arterioscler. Thromb., vol. 13, 1993, pp. 1865–1873. [141] R. Festa, D’Agostino, G. Howard, et al., “Chronic subclinical inflammation as part of the insulin resistance syndrome: the Insulin Resistance Atherosclerosis Study (IRAS),” Circulation, vol. 102, 2000, pp. 42–47. [142] J.M. Fern´andez-Real, and W. Ricart, “Insulin resistance and chronic cardiovascular inflammatory syndrome,” Endocrine Reviews, vol. 24 (3), 2003, pp. 278–301.

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[143] P. Keren, J. George, H. Levkovitz, et al., “Effect of hyperglycemia and hyperlipidemia on atherosclerosis in LDL receptor-deficient mice: establishment of a combined model and assosiation with shock protein 65 immunity,” Diabetes, vol. 49, 2000, pp. 1064–1069. [144] V. Fonseca, C. Desouza, S. Asnani, and I. Jialal, “Nontraditional risk factors for cardiovascular disease in diabetes,” Endocrine Reviews, vol. 25, 2004, pp. 153–175. [145] J.A. Beckman, M.A. Creager M.A., and P. Libby, “Diabetes and atherosclerosis: epidemiology, pathophysiology, and management,” JAMA, vol. 287, 2002, pp. 2570–2581. [146] A. Ceriello, “Hyperglycaemia: the bridge between non-enzymatic glycation and oxidative stress in the pathogenesis of diabetic complications,” Diabetes Nutrition and Metabolism, vol. 12, 1999, pp. 42–47. [147] D. Aronson, and E.J. Rayfield, “How hyperglycemia promotes atherosclerosis: molecular mechanisms,” Cardiovascular Diabetology, N 1, 2002. Available at http://www.cardiab.com/content/1/1/1. [148] P.T. Shih, M.J. Elices, F.J. Fang, et al., “Minimally modified low-density lipoprotein induces monocyte adhesion to endothelial connecting segment-1 by activating b1 integrin,” J. Clin. Invest., vol. 103, 1999, pp. 613–625. [149] S.D. Cushing, J.A. Berliner, A.J. Valente, et al., “Minimally modified low density lipoprotein induces monocyte chemotactic protein 1 in human endothelial cells and smooth muscle cells,” Proc. Natl. Acad. Sci. USA, vol. 87, 1990, pp. 5134–5138. [150] T.B. Rajavashisth, A. Andalibi, M.C. Territo, et al., “Induction of endothelial cell expression of granulocyte and macrophage colony-stimulating factors by modified low-density lipoproteins,” Nature, vol. 344, 1990, pp. 254–257. [151] M.T. Quinn, S. Parthasarathy, L.G. Fong, and D. Steinberg, “Oxidatively modified low density lipoproteins: a potential role in recruitment and retention of monocyte/macrophages during atherogenesis,” Proc. Natl. Acad. Sci. USA, vol. 84, 1987, pp. 2995–2998. [152] J.W. Baynes, “Role of oxidative stress in development of complications in diabetes,” Diabetes, vol. 40, 1991, pp. 405–412. [153] A.M. Schmidt, O. Hori, J.X. Chen, et al., “Advanced glycation end products interacting with their endothelial receptor induce expression of vascular cell adhesion molecule-1 (VCAM-1) in cultured human endothelial cells and in mice. A potential mechanism for the accelerated vasculopathy of diabetes,” J. Clin. Invest., vol. 96, 1995, pp. 1395–1403. [154] G. Zeng, F.H. Nystrom, L.V. Ravichandran, et al., ”Roles for insulin receptor, PI3-kinase, and Akt in insulin-signaling pathways related to production of

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Handbook of Optical Sensing of Glucose nitric oxide in human vascular endothelial cells,” Circulation, vol. 101, 2000, pp. 1539–1545.

[155] M. Montagnani, I. Golovchenko, I. Kim, et al., “Inhibition of phosphatidylinositol 3-kinase enhances mitogenic actions of insulin in endothelial cells,” J. Biol. Chem., vol. 277, 2002, pp. 1794–1799. [156] K. Kuboki, Z.Y. Jiang, N. Takahara, et al., “Regulation of endothelial constitutive nitric oxide synthase gene expression in endothelial cells and in vivo: a specific vascular action of insulin,” Circulation, vol. 101, 2000, pp. 676–681. [157] J.P. Cooke, “Does ADMA cause endothelial dysfunction?” Arterioscler. Thromb. Vasc. Biol., vol. 20, 2000, pp. 2032–2037. [158] M.C. Stuhlinger, F. Abbasi, J.W. Chu, et al., “Relationship between insulin resistance and an endogenous nitric oxide synthase inhibitor,” JAMA, vol. 287, 2002, pp. 1420–1426. [159] Z.S. Katusic, “Vascular endothelial dysfunction: does tetrahydrobiopterin play a role?” Am. J. Physiol., vol. 281, 2001, pp. H981–H986. [160] M. Gotto, “Introduction,” Am. J. Cardiol., vol. 88 (Supp 11), 1998, pp. 1–2. [161] Y. Homma, H. Ozawa, T. Kobayashi, et al. “Effects of simvastatin on plasma lipoprotein subfractions, cholesterol esterification rate, and cholesteryl ester transfer protein in type II hyperlipoproteinemia,” Atherosclerosis, vol. 114 (Is. 2), 1995, pp. 223–234. [162] H.R. Superko, R.M. Krauss, and C. Di Ricco, “Effect of fluvastatin on lowdensity lipoprotein peak particle diameter,” Am. J. Cardiol., vol. 80, 1997. pp. 78–81. [163] G. Howard, D.H. O’Leary, D. Zaccaro, et al., “Insulin sensitivity and atherosclerosis,” Circulation, vol. 93, 1996, pp. 1809–1817. [164] T.K. Nordt, H. Sawa, S. Fujii, and B.E. Sobel, “Induction of plasminogen activator inhibitor type-1 (PAI-1) by proinsulin and insulin in vivo,” Circulation, vol. 91, 1995, pp. 764–770. [165] K. Shinozaki, M. Suzuki, M. Ikebuchi, et al., “Demonstration of insulin resistance in coronary artery disease documented with angiography,” Diabetes Care, vol. 19, 1996, pp. 1–7. [166] T.A. Welborn and K. Wearne, “Coronary heart disease incidence and cardiovascular mortality in Busselton with reference to glucose and insulin concentrations,” Diabetes Care, vol. 2, 1979, pp. 154–160. [167] W.B. Kannel, R.D. Abbot, D.D. Savage, et al., “Epidemiologic features of chronic atrial fibrillation: the Framingham Study,” NEJM, vol. 306, 1982, pp. 1018–1022.

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[168] M.F. Di Carli, J. Janisse, G. Grunberger, and J. Ager , “Role of chronic hyperglycemia in the pathogenesis of coronary microvascular dysfunction in diabetes,” J. Am. Coll. Cardiol., vol. 41, 2003, pp. 1387–1393. [169] L.I. Malinova, G.V. Simonenko, T. P. Denisova, et al., “Suspension properties of whole blood and its components under glucose influence studied in patients with acute coronary syndrome,” Proc. SPIE 5330, 2004, pp. 200–207. [170] L.I. Malinova, T.P. Denisova, G.V. Simonenko, et al., “Effect of high concentrations of glucose on physiological parameters of erythrocytes in patients with ischemic heart disease,” Kardiologia, vol. 44, 2004, pp. 24–27. [171] M. Brownlee, “Glycation and diabetic complications,” Diabetes Care, vol. 43, 1993, pp. 836–841. [172] P.E. James, D.Lang, T. Tufnell-Barret, et al., “Vasorelaxation by red blood cells and impairment in diabetes,” Circ. Res., vol. 94, 2004, pp. 976–987. [173] “The Diabetes Control and Complications Trial Research Group. The effect of intensive treatment of diabetes on the development and progression of longterm complications in insulin-dependent diabetes mellitus. 1993,” New. Engl. J. Med., vol. 329, 1993, pp. 977–1036. [174] M. Franciosi, F. Pellegrini, G. De Berardis et al., “The impact of blood glucose self-monitoring on metabolic control and quality of life in type 2 diabetic patients: an urgent need for better educational strategies,” Diabetes Care, vol. 24 (11), 2001, pp. 1870–1877. [175] P. Glikfeld, R.S. Hinz, and R.H. Guy, “Noninvasive sampling of biological fluids by iontophoresis,” Pharmac. Res., vol. 6, 1989, pp. 988–990. [176] “Guidelines on diabetes, pre-diabetes, and cardiovascular diseases: full text,” European Heart Journal, doi:10.1093/eurheartj/ehl261 [177] J.A. Tamada, N.J. Bohannon, and R.O. Potts, ”Measurement of glucose in diabetic subjects using noninvasive transdermal extraction,” Nat Med., vol. 1(11), 1995, pp. 1198–201. [178] J. Pickup, L. McCartney, O. Rolinski, and D. Birch, “In vivo glucose sensing for diabetes management: progress towards non-invasive monitoring,” BMJ, vol. 319, 1999, pp. 1289. [179] M.A. Arnold, “Non-invasive glucose monitoring,” Curr. Opin. Biotechnol., vol. 7, 1996, pp. 46–49. [180] M.R. Robinson, R.P. Eaton, D.M. Haaland, et al., “Non-invasive glucose monitoring in diabetic patients: a preliminary evaluation,” Clin. Chem. vol. 38, 1992, pp. 1618–1622. [181] L. Heinemann and G. Schmelzeise Redeker, “Non-invasive continuous glucose monitoring in type 1 diabetic patients with optical glucose sensors,” Diabetologia, vol. 41, 1998, pp. 848–854.

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[182] G.B. Christison and H.A. MacKenzie, “Laser photoacoustic determination of physiological glucose concentrations in human blood,” Med. Biol. Comput., vol. 31, 1993, pp. 284–290. [183] C. Choleau, J.C. Klein, G. Reach, et al., “Calibration of a subcutaneous amperometric glucose sensor. Part 1. Effect of measurement uncertainties on the determination of sensor sensitivity and background current,” Biosens. Bioelectron., vol. 17, 2002, pp. 641–646. [184] D.C. Klonoff, “Continuous glucose monitoring. Roadmap for 21st century diabetes therapy,” Diabetes Care, vol. 28, 2005, pp. 1231–1239. [185] D.C. Klonoff, “The need for separate performance goals for glucose sensors in the hypoglycemic, normoglycemic, and hyperglycemic ranges,” Diabetes Care, vol. 27, 2004, pp. 834–836. [186] E. Kulcu, J.A. Tamada, G. Reach, et al., “Physiological differences between interstitial glucose and blood glucose measured in human subjects,” Diabetes Care, vol. 26, 2003, pp. 2405–2409. [187] D.E. Goldstein, R.R. Little, R.A. Lorenz, et al., “Tests of glycemia in diabetes,” Diabetes Care, vol. 18, 1995, pp. 896–909. [188] H.P. Chase, M.D. Roberts, C. Wightman, et al., “Use of the GlucoWatch Biographer in children with type 1 diabetes,” Pediatrics, vol. 111, 2003, pp.790– 794. [189] H.P. Chase, L.M. Kim, S.L. Owen, et al., “Continuous subcutaneous glucose monitoring in children with type 1 diabetes,” Pediatrics, vol. 107, 2001, pp. 222–226. [190] C.P. Vidal-Rios, M. Subira, and A. Novials, “The continuous glucose monitoring system is useful for detecting unrecognized hypoglycemias in patients with type 1 and type 2 diabetes but is not better than frequent capillary glucose measurements for improving metabolic control,” Diabetes Care, vol. 26, 2003, pp.1153–1157. [191] J. Ludvigsson and R. Hanas, “Continuous subcutaneous glucose monitoring improved metabolic control in pediatric patients with type 1 diabetes: a controlled crossover study,” Pediatrics, vol. 111, 2001, pp. 933–938. [192] R. Tanenberg, B. Bode, W. Lane, et al., “Use of the continuous glucose monitoring system to guide therapy in patients with insulin-treated diabetes: a randomized controlled trial,” Mayo Clin. Proc., vol. 79, 2004, pp. 1521–1526.

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2 Commercial Biosensors for Diabetes Vasiliki Fragkou and Anthony P.F. Turner Cranfield Health, Cranfield University, Silsoe, MK45 4D, UK

2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Diabetes Mellitus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Home Urine/Blood Glucose Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glucose Meters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glucose Biosensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Current Commercial Home Blood Glucose Monitoring . . . . . . . . . . . . . . . . . . . . Integrated Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alternative Glucose Monitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Challenges and Hurdles Facing Glucose Biosensors . . . . . . . . . . . . . . . . . . . . . . . Future Perspectives & Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

42 43 46 47 47 50 54 56 59 61 62

Diabetes is a metabolic disorder, which occurs either because of a lack of insulin or because of the presence of factors that oppose the action of insulin. There is currently no cure for diabetes and the control of elevated blood glucose levels, without causing abnormally low levels, is the major goal in treating diabetes. Reasonable control is now relatively easily achieved with a blood glucose meter/glucose biosensor. Currently, there are more than 40 commercialized devices for detecting blood glucose levels. As a result of intense competition, companies have resorted to a strategy where existing technology has been pragmatically optimized to meet commercial objectives, such as small size and fast response time. As a consequence of this continual development, commercial practice often differs from the theoretical papers appearing in the literature. This chapter will focus on commercial biosensors and the underlying science behind their functionality.

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2.1 Introduction Diabetes is a metabolic disorder characterized by the presence of an excess of glucose in the blood and tissues of the body [1]. Diabetes is a chronic condition that without treatment can have very serious consequences. The health implications of diabetes are astounding, since this disease is very widespread, increasing in incidence and associated with morbidity and mortality. Over time, diabetes can lead to blindness, kidney failure and nerve damage. Diabetes is also an important factor in accelerating hardening and narrowing of the arteries (atherosclerosis) leading to strokes, coronary heart disease and other blood vessel diseases [2]. The care and management of diabetes involves many costs. It has been characterized as one of the largest therapeutic segments of global pharmaceutical sales. The annual direct healthcare costs of diabetes worldwide, for people in the 20–79 age bracket, are estimated to be at least 153 billion international dollars and may be as much as 286 billion. If predictions of diabetes prevalence are fulfilled, total direct healthcare expenditure on diabetes worldwide will be between 213 billion and 396 billion international dollars in 2025 [3]. It should be noted that a person with diabetes incurs medical costs that are two to five times higher than a person without diabetes. These medical costs include medical visits, the likelihood of the diabetic being admitted to a hospital and the purchase of supplies and medications. There is currently no cure for diabetes and the control of elevated blood glucose levels, without causing abnormally low levels, is the major goal in treating diabetes. Reasonable control is now relatively easily achieved in most cases with a blood glucose meter/glucose biosensor and the invention of this technology was one of the most important steps in managing diabetes, since it facilitates intensive therapy that reduces the risk of long-term complications. In comparison with conventional methods of glucose testing, glucose biosensors provide a rapid and easy method of testing blood glucose levels. This is one of the major reasons that the glucose biosensors occupy 85% of the current world market for biosensors, which is estimated to be worth over $ 6.9 billion [4]. Currently, there are more than 40 commercialized devices for detecting blood glucose levels. Four multinational companies dominate the biosensor industry: Roche Diagnostics, LifeScan, Abbott (now owned by GE) and Bayer. As a result of intense competition, companies have resorted to a strategy, where existing technology has been pragmatically optimized to meet commercial objectives, such as small size and fast response time and consequently, over the years, we have moved away from the theoretical understanding of the operation of these devices. This chapter will focus on commercial biosensors and the underlying science behind their current functionality.

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2.2 Diabetes Mellitus Diabetes Mellitus (Diabetes) is characterized by the presence of excess of glucose in the blood and tissues of the body. It is a metabolic disorder in which the pancreas underproduces or does not produce insulin. Insulin is a hormone produced by the pancreas that is needed by cells of the body in order to use glucose, the major source of energy for the human body. There are three main types of diabetes: Type I diabetes, Type II diabetes and Gestational diabetes [5].

2.2.1 Type I diabetes Type I diabetes was previously known as insulin-dependant diabetes and affects approximately 10% of all people with diabetes. It is rare in the first nine months of life and has peak incidences at twelve and between twenty to thirty-five years old [6]. It is due to the destruction of β -cells in the pancreatic islets of Langerhans with resulting loss of insulin production and finally in hyperglycemia. The process of islets destruction probably begins very early in life and is known to start several years before the clinical onset of diabetes. Clinically a person with this disorder presents a number of symptoms, including: polydipsia (increased thirst), which is an attempt to compensate for fluid loss; polyuria (frequent passage of urine), which is due to the presence of excess glucose in the urine; muscle cramps, which are due to electrolyte disturbances because of the fluid loss; weight loss due to the lack of insulin and consequently to the break-down of proteins and fat despite increased appetite; blurred vision due to the excess accumulation of glucose in the eye lenses; nausea, vomiting and abdominal pain [1].

2.2.2 Type II diabetes Type II diabetes, previously known as non-insulin dependent diabetes, affects approximately 90% of all people with diabetes and is usually found in middle aged or older patients. Type II diabetes is due to a combination of disorders with differing progression and outlook. This combination of disorders includes resistance to the action of insulin in peripherical tissues such as muscle and fat cells, the failure of the insulin secreting cells of the pancreas to produce sufficient insulin and the failure of insulin to inhibit the production of glucose in the liver. Symptoms of people with type II diabetes include: polydipsia, polyuria, increased appetite, fatigue, erectile dysfunction and frequent or slow-healing infections [1].

2.2.3 Gestational diabetes Gestational diabetes is a condition that occurs during pregnancy. During pregnancy, the placenta provides the baby with nourishment and also produces a number of hormones that interfere with the body’s usual response to insulin (insulin resis-

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tance). Most pregnant women do not suffer from gestational diabetes, because the pancreas works to produce extra quantities of insulin in order to compensate for insulin resistance. However, when a woman’s pancreas cannot produce enough extra insulin, blood levels of glucose stay abnormally high, and the woman is considered to have gestational diabetes. Gestational diabetes affects two to four percent of all pregnancies with an increased risk of developing diabetes for both mother and child [7].

2.2.4 Incidence - A major world problem Diabetes is a major world health problem. It is estimated that the number of diabetics worldwide is 171 million and approximately 4 million deaths each year are caused by diabetes (9% of deaths worldwide). Several studies on the prevalence of diabetes have shown that the above figure of 171 million is projected to rise to 366 million by 2030 [8]. These studies usually include data on diabetes prevalence according to age, sex and region. The prevalence of diabetes is higher in men than women despite the fact that at the moment there is, worldwide, a significantly higher amount of women suffering from diabetes. The same study also demonstrated that the most important demographic change to diabetes prevalence worldwide appears to be the increase in the proportion of people below the age of sixty-five years [9] (Fig. 2.1).

Estimated number of people with diabetes by age group 200 150 2000

100

2030

50 0 20-44

45-64 Age

65+

FIGURE 2.1: Estimated number (in millions) of people with diabetes by age group [Adapted from ref. 9]

Diabetes was once considered to be a disease afflicting wealthy countries. Nowadays, it is affecting low income and developing countries. In the future the largest proportional and absolute increase will occur in developing countries, where the prevalence will rise from 4.2% to 5.6% [3]. By 2025, the adult diabetic population is expected to double in India to about 73 million and in China to 46 million. At the same time, diabetes prevalence is expected to increase to 2.8% of the adult population in Africa and 7.2% in South and Central America. The European Region,

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with 48 million and the Western Pacific Region, with 43 million, currently have the highest number of people with diabetes. However the prevalence rate of the Western Pacific Region at 3.1% is significantly lower than the 7.9% in the North American Region and 7.8% in the European Region [10] (Fig. 2.2).

Estimated prevalence of diabetes in selected countries by 2025

Prevalence %

12.00% 10.00% 8.00% 6.00% 4.00% 2.00% 0.00%

t... n n n n n as ion E gio gio gio gio gio g Re Re Re Re Re Re dle d c n n n n a i i a a a if ic ia ric ric pe ac dM As Afr an me me st O uro nP r a A A n H E e l E a t W a O s rth ne ntr uth We No WH rra Ce So O O ite d H H d O W W an Me WH rn uth So ste a O 2003 E O WH WH 2025 Countries

FIGURE 2.2: Estimated prevalence of diabetes in selected countries by 2025 [Adapted from ref. 10]

It is worthy of note that by 2010, cases of Type 2 diabetes are projected to rise 111%, from 62 million to 132 million, and in mainland China alone, the increase over the next 10 years is predicted to be 35–36 million. In general, worldwide, Type 2 diabetes clearly predominates, but several reports clarify that the 4.3 million cases of Type I diabetes are expected to increase to 5.3 million cases by 2010 [10].

2.2.5 Treatments Diabetes is a chronic condition that without treatment can have very serious consequences. The overall health implications of diabetes are astounding. The disease is associated with morbidity and mortality and studies have shown that persons diagnosed with diabetes before the age of forty tend to present a life decrease, which for men amounts to 12 years and for women to 19 years [2]. The goal of diabetic therapy is to control blood glucose levels and prevent the complications of diabetes. Type I diabetes is treated with insulin, exercise and a diabetic diet. Type II diabetes is first

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treated with weight reduction, a diabetic diet and exercise. When these measures fail to control the elevated blood sugars, oral medications are used. In cases that oral medication are still insufficient, insulin medications are considered. It is worthy to note that it is necessary not only to treat the diabetes, but to monitor the effects of treatment on blood glucose levels to avoid overtreatment or undertreatment of the diabetes [11].

2.3 Home Urine/Blood Glucose Monitoring Urine and blood glucose self monitoring are the two primary methods used by the person with diabetes to monitor their diabetes control.

2.3.1 Urine glucose monitoring Urine glucose monitoring [12] is a viable, cost-effective way of monitoring diabetes control, but has a number of limitations and is not a substitute for blood glucose monitoring [13]. There are two types of urine glucose tests which rely on a chemical reaction that produces a color change. The tests use either tablets or strips. Generally, the test strip or tablet is placed in urine and the resulting color change is matched against a colour chart provided by the manufacturer, which shows the different colors produced by different levels of glucose. The first type, the copper reduction test, uses cupric sulfate. In the presence of glucose, cupric sulfate, which is blue, changes to cuprous oxide, which is green to orange. The second type of urine glucose test, called the glucose oxidase test, uses the chemical toluidine and the enzyme glucose oxidase. Glucose oxidase converts the glucose in urine to gluconic acid and hydrogen peroxide. The interaction of the hydrogen peroxide with the toluidine causes a change in color. The main limitations of this kind of test are firstly the fact that the cupric sulfate and the glucose oxidase can react with substances other than glucose in the urine, like aspirin, penicillin, vitamin C and cephalosporin-type antibiotics and lead to false positive results and secondly it cannot distinguish between low and normal blood glucose levels or high and very high blood glucose levels. However, urine glucose monitoring is particularly helpful in persons at low risk of hypoglycemia and whose blood glucose levels are not too high and generally stable [3].

2.3.2 Blood glucose monitoring Blood glucose monitoring [14, 15] is achieved in several ways. The traditional method of testing the blood glucose involves pricking the finger with a lancet (a small, sharp needle), putting a drop of blood on a test strip and then placing the strip into a meter that displays the blood glucose level. Meters vary in features, readability, portability, speed, size and cost. Some of the most recent developed meters allow the patient to test sites other than the fingertip, including sites such as the upper arm,

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forearm, base of the thumb and thigh. However, testing at alternative sites may give results that are different from the blood glucose levels obtained from the fingertip [16].

2.4 Glucose Meters Before focusing on glucose biosensors, it is important to have a quick look at the past in order to get a broader understanding of their importance.

2.4.1 Colorimetric strips Ames, a division of Miles Laboratories, developed and introduced in 1965 a product called Dextrostix. These were paper strips to which a drop of blood was added and timed for one minute. A blue colour developed, which was interpreted by comparing it to a colour chart, which indicated an approximation of the blood glucose level. People who were following this procedure on a regular basis frequently got to read Dextrostix strips very well. But for most people, because of the limited usage, the interpretation was not always successful [17].

2.4.2 Ames Reflectance Meter The solution came with the development of the Ames Reflectance Meter in 1971, by Anton H. Clemens. The device was able to read and interpret the Dextrostix strips. In more detail the Ames Reflectance Meter was a light meter that read reflected light. This reflected light was sent to a photoelectric cell and a read out was given. Although the instrument was more able to read the minor changes in the reflection of the darkness and lightness of the shade of blue, adding a certain degree of interpretation accuracy, it was very expensive, heavy, required connection to an electrical outlet for power and, most importantly, it needed a prescription. It is worth noting, however, that this instrument was a success and was the forerunner of a great variety of other products [18].

2.5 Glucose Biosensors 2.5.1 The Clark enzyme electrode Prof. Leyland Clark Jr. was immortalized by his invention of the Clark oxygen electrode in 1956 (Fig 2.3).

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Glucose optical sensing and impact Connections to amplifier Epoxy seal Silver wire coated with AgCl

Hole to add 100 mM KCL electrolyte

Plexiglass cylinder O2-permeable memberane, held in place with O-ring in groove

Pt wire melted to give bead at end, sealed in glass, ground down to expose flat surface

FIGURE 2.3: Clark oxygen electrode [4] A few years later, in 1962 at a New York Academy of Sciences symposium, Prof Clark described how “to make electrochemical sensors more intelligent” by adding “enzyme transducers as membrane enclosed sandwiches.” The concept was illustrated by an experiment in which glucose oxidase was entrapped at a Clark oxygen electrode using dialysis membrane. The decrease in measured oxygen concentration was proportional to glucose concentration. The sensor invented by Clark was the basis of numerous later variations on the basic enzyme electrode design and many other oxidase enzymes were immobilized by various workers in subsequent publications. In nature, glucose oxidase as well as other oxidase enzymes act by oxidizing their substrates, accepting electrons in the process and thereby changing to an inactivated reduced state. The purified enzymes are normally returned to their active oxidized state by transferring these electrons to molecular oxygen, resulting in the consumption of oxygen and the production of hydrogen peroxide (Fig. 2.4).

FIGURE 2.4: First generation glucose biosensor schematic [4]

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It is worthy of note at this point that, in addition to monitoring oxygen consumption, the glucose concentration can also be measured by following the oxidation of hydrogen peroxide amperometrically at a potential of +0.7V, versus a silver-silver chloride electrode, using a platinum working electrode.

2.5.2 Yellow Springs Instrument In 1975, the construction of biosensors based on the Clark approach became a commercial reality with the successful re-launch of the Yellow Springs Instrument [4]. These instruments were based on the amperometric detection of hydrogen peroxide and they have remained on the market ever since, becoming a standard for clinical diagnostic work in hospitals and chemistry laboratories worldwide. Over the years, this type of biosensor constuction has not changed significantly. The basic format is based on the immobilization of glucose oxidase between two membrane layers. The outer polycarbonate membrane retains the enzyme, allowing glucose to pass, but prevents many larger molecules from entering, reducing the interference. The glucose enters the enzyme layer, where it is oxidized and hydrogen peroxide is produced. The peroxide passes through the cellulose acetate membrane to a platinum electrode, where it is measured amperometrically. The second membrane acts as a further size exclusion barrier preventing many other potentially interfering (electroactive) compounds from reaching the electrode surface. What has been concluded from the construction of these devices over the years is that they are robust, but not straightforward to miniaturize. They are also relatively expensive to fabricate and the high detection voltage required makes the system prone to interference in the absence of the membrane structures utilized.

2.5.3 Mediated biosensors Around 1980, our group based at Cranfield and Oxford Universities was working on biofuel cells. We realized that the electron transfer compounds used for this and related projects showed promise for use in biosensor applications [19, 20]. These mediator compounds were able to shuttle electrons between the redox center of the enzyme and the electrode. The most commercially important early example of these mediators turned out to be ferrocene and its derivatives, since they have a wide range of redox potentials, are easily derivatized, exhibit reversible electrochemistry at low potentials and are relatively stable in the presence of oxygen. These mediators were the crucial components in the construction of inexpensive enzyme electrodes and formed the basis for the screen-printed enzyme electrodes launched by Medisense in 1987, in conjunction with a pen-sized meter, for home blood glucose monitoring. The use of mediators was one of the most important breakthroughs, which led glucose biosensors forward and allowed them to largely supercede reflectance devices for home testing of blood glucose. An advantage of blood glucose measurement is that it is acceptable to use a biosensor design that is suitable only for a single measurement. This is convenient from the point of view of using a mediated biosensor,

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since one of the major drawbacks of most mediators is that they are relatively soluble, leading to short operational lifetimes and irreproducible results in continuous use. However, for on-shot use they have proved robust and accurate [21].

2.6 Current Commercial Home Blood Glucose Monitoring Biosensors can be found addressing many applications [22]. They have been applied to a wide variety of analytical problems included in: medicine and healthcare, environmental protection and biotechnology [23]. The largest market opportunity is represented by the biomedical area and this is one of the major reasons that biosensor research and development has been largely concentrated in this specific area. A single analyte dominates this market and this is glucose. Blood glucose sensors account for 85% of the current world market for biosensors and are the most widely studied and commercialized of all biosensors [4].

2.6.1 General principles But what exactly is a biosensor and which are the key components for its functionality? “A biosensor is an analytical tool or system consisting of an immobilized biological material which converts information about the properties of the analyte into a quantifiable signal via a suitable transducer” [24]. In principle, several types of transducer can be incorporated into a biosensor for the measurement of glucose, but electrochemical methods have dominated and this is because of the sensitivity, reproducibility and inexpensive manufacture that they offer. The most often employed electrochemical method is amperometry, which relies on the application of a potential between two electrodes and the measurement of the resultant current flow. This is easily achieved in a three electrode cell, composed of a reference electrode, typically a Ag/AgCl electrode, a working electrode, which is usually made of a noble metal or carbon and a counter or auxiliary electrode. In many configurations, the counter electrode and reference electrode are combined to simplify the construction to a two-electrode device. Another key component in the manufacture of a glucose biosensor is the enzyme. The most commonly used enzymes in the design of glucose biosensors contain redox groups that change redox state during the biochemical reaction. Enzymes of this type are glucose oxidase and quinoprotein glucose dehydrogenase, which have found wide application in commercial devices. Finally, the performance of glucose biosensors is strongly linked to the mediator employed [25]. Some of the most significant examples are ferrocene and its derivatives, as already mentioned, osmium and TMPD (Table 2.1).

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TABLE 2.1: Examples of mediators Device Name Precision Elite Sure Step AccuCheck FreeStyle

Mediator Ferrocene Ferricyanide Ferricyanide Ferricyanide Osmium

2.6.2 Commercial aspects Commercial blood glucose meters are produced by many companies worldwide (Table 2.2), but the biosensor industry is currently dominated by four multinational companies, Roche Diagnostics, LifeScan, Abbott and Bayer [26].

TABLE 2.2: Market leading glucose biosensor companies in 2003 [26] Company Name Roche Diagnostics LifeScan Abbott Bayer Diagnostics Becton Dickinson Hypoguard

Annual Sales (Millions) $ 1,494 $1,288 $977 $460 $23 $19

2.6.2.1 Roche Diagnostics Roche Diagnostics is one of the major healthcare companies worldwide and now offers a range of biosensor products to researchers, physicians, patients, hospitals and laboratories. In May of 1997, Roche re-entered the biosensor market (after an early unsuccessful foray into the area in 1977) with the purchase of all shares of the diagnostics and pharmaceuticals businesses of the Boehringer Mannheim Group, which had a successful optical colorimetric and electrochemical biosensor program. The purchase price was around 11 billion US dollars. Roche Diagnostics reports that it now conducts research mainly into electrochemical biosensors that permit near-painless, continuous measurement of blood glucose level. It acquired from Boehringer Mannheim the very successful Accu-Chek family of products for bloodglucose monitoring. The blood glucose systems for patient self-testing comprise blood glucose monitors (Table 2.3), test strips and lancing devices as well as diabetes data management for professional use. It is worth noting that Roche has one

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TABLE 2.3: Blood glucose meters by Roche Diagnostics Device

Time

Specifications

Accu-Chek Aviva System

Sample Volume 0.6 µ L

5 sec

Accu-Chek Active System

1 µL

5 sec

Review of past results right on the net Audible test reminders Large memory capacity with averaging Underdosing detection Integrated test strips Integrated Safety Acoustic test reminder Hypoglycemia threshold warning Large memory capacity with averaging Maximum safety Review of past results right on the meter Acoustic test reminder Visual hypoglycemia warning Combines all information pertaining to blood sugar, insulin doses, carbohydrates, ketones, HbA1c, exercise, and event markers Large memory capacity with averaging

Accu-Chek Compact Plus 1.5 µ L System Accu-Chek Go System 1.5 µ L

5 sec

Accu-Chek Compact Sys- 1.5 µ L tem

8 sec

Accu-Chek Advantage/ 4 µ L Accu-Chek Sensor System

40 sec

Accu-Chek Complete Sys- 4 µ L tem

40 sec

5 sec

of the few meters with an integrated lancing device. In addition, the Accu-Chek Compact Plus has an integrated 17 test drum, which eliminates the need for strip handling [26, 27]. However, the Compact still uses the last generation colorimetric strip technology while the Aviva, Active, Go and Advantage use the more modern electrochemical biosensor approach. 2.6.2.2 LifeScan LifeScan is part of the Johnson & Johnson family. The company entered the electrochemical biosensor market late in 2001, by the acquisition of the diabetes care business of Inverness Medical [26, 28]. Prior to this, the company had a very successful colorimetric strip product based on reflectance photometry. LifeScan now presents an array of products for blood glucose testing on the market under the

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umbrella of One Touch products, like blood glucose meters (Table 2.4), test strips, lancets and lancing devices and diabetes management software [29]. The low volume, high performance devices are based on electrochemistry, while the Basic and SureStep still use color reflectance technology.

TABLE 2.4: Blood glucose meters by LifeScan Device

OneTouch Ultra 2 OneTouch UltraSmart

Sample Time Volume 1 µL 5 sec 5 sec 1 µL

OneTouch UltraMini OneTouch Ultra OneTouch Basic OneTouch SureStep

1 µL 1 µL 10 µ L 10 µ L

5 sec 5 sec 45 sec 15 sec

Specifications

Multiple test sites Multiple test sites Test results are entered automatically into 9 charts and graphs Small size Multiple test sites Test memory with date and time Test memory with date and time Automatic 14-day, 30-day test averages

2.6.2.3 Abbott Abbott is a global, broad-based health care company supplying a range of products for the diagnosis and treatment of diseases. In 1996, it acquired MediSense for $ 867 million, which was the first company to commercialize electrochemical home blood glucose biosensor technology. Following the purchase of two further biosensor companies, Therasense for $ 1.2 billion and i-STAT for $ 392 million in early 2004, Abbott has cemented itself in the top three largest biosensor companies worldwide [30]. The company offers a range of instruments for blood glucose testing, including blood glucose meters (Table 2.5), strips and lancets [31]. 2.6.2.4 Bayer HealthCare Bayer HealthCare is a health care company of international repute. The Diabetes Care Division is one of the world’s market leaders in the field of blood glucose monitoring systems and it markets, under the umbrella brand of Ascenia, blood glucose meters (Table 2.6), test strips and other accessories and services for blood glucose monitoring. Bayer acquired its biosensor technology via a Japanese alliance with Kyoto Daiichi. It is worthy of note that at the beginning of 2003 the Diagnostics Division of Bayer HealthCare LLC and Matsushita Electric Industrial Co. Ltd. expanded their relationship with the signing of a joint venture agreement and estab-

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TABLE 2.5: Blood glucose meters by Abbott Device

Time

Specifications

FreeStyle Flash

Sample Volume 0.3 µ L

5 sec

FreeStyle Mini

0.3µ L

7 sec

Precision Xtra

0.6 µ L

5 sec

Optium Xceed with Optium 0.6 µ L Xceed Plus test strips

5 sec

Optium Xceed w/o Optium 1.5 µ L Xceed Plus test strips

10 sec

25 µ L

20 sec

Alternative site testing Presents 4 programmable alarms to remind patients when to test Alternative site testing Presents 4 programmable alarms to remind patients when to test Large memory capacity Automatic 14-day test averages Auto Calibration Simple blood calibration Large memory capacity Automatic 7-day, 14-day, 30-day test averages Blood ketone testing Alternative site testing Large memory capacity Automatic 7-day, 14-day, 30-day test averages Blood ketone testing Alternative site testing Alternative site testing Blood ketone testing Alternative site testing Large memory capacity

MediSense Optium MediSense Soft-Sense

20 sec

lished “Viterion TeleHealthcare LLC,” a Bayer-Panasonic company, to market products and services for the rapidly growing telehealth market [26, 32].

2.7 Integrated Devices Pelikan Technologies in Palo Alto, California has developed the first, fully integrated, blood sampling and glucose measurement device. It is called Pelikan Sun

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TABLE 2.6: Blood glucose meters by Bayer Device

Time

Specifications

Ascenia Contour

Sample Volume 0.6µ L

15 sec

Ascenia Elite

2 µL

30 sec

Ascenia Elite XL

2 µL

30 sec

Ascenia Breeze

2.5-3.5 µL

30 sec

Alternative site testing Large memory capacity No coding required 20 tests saving information with dates and times “Sip-in Sampling” Alternative site testing 120 tests saving information with dates and times “Sip-in Sampling” Alternative site testing Large memory capacity “Autodisc” Alternative site testing No coding required

FIGURE 2.5: Pelikan Sun [4]

(Fig. 2.5) and based on the company’s “one-step, one-button” approach, this lancing device is the first fully-automated, electronically-controlled, self-contained system that allows a patient to execute the entire lancing process at the touch of a button in a virtually painless operation [33]. Unlike existing mechanical lancing devices, the

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Pelikan Sun detects the location of the skin and penetrates to the exact depth without hitting sensitive nerves in the finger. It contains a disc of 50 lancets, which is replaced after 50 uses so the person does not have to handle the lancets. The Pelikan Sun is ideal for children, frequent testers and people who do not like the pain of lancing.

2.8 Alternative Glucose Monitors The home blood glucose biosensor market is dominated by four large diagnostic companies selling “finger-prick” tests which use a tiny sample of capillary blood. These companies are continually challenged by new start-ups, which are often the engines of change, and the most successful, such as MediSense and TheraSense, usually end up being acquired by a larger company. The majority of the business of these companies in this market is based on single-use mediated amperometric biosensor technology. Alternative strategies include minimally invasive testing meters and continuous glucose monitoring.

2.8.1 Minimally invasive testing The GlucoWatch G2 Biographer [34, 35] is a wrist worn device for detecting trends and tracking patterns in glucose levels in adults with diabetes, for use at home and in health care facilities. The device obtains automatic measurements of glucose concentrations every 20 minutes for up to 12 hours at a time. It is minimally invasive, since the skin is not punctured to obtain a sample. The measurements obtained by GlucoWatch are not a substitute for finger-prick blood glucose readings, since there is a 20 minute lag between the GlucoWatch monitor and the actual blood glucose value, but they can be used for the detection and assessment of episodes of hypoglycemia and hyperglycemia, facilitating both acute and long-term therapy adjustments. The device uses reverse iontophoresis to collect glucose samples through intact skin. The glucose molecules are collected in a gel collection disk, which contains the glucose oxidase. As glucose enters the disk it reacts with glucose oxidase in the gel in order to form hydrogen peroxide. A biosensor detects the hydrogen peroxide and generates an electronic signal and by the calibration value previously entered by the patient, the signal is converted into a glucose measurement, which is displayed on the biographer and stored in the memory of the device. The Glucowatch is produced by Cygnus (Redwood City, CA, USA) and was recently acquired by Animas, which was, in turn, acquired by Johnson and Johnson. The company does not appear to be actively promoting the device at present following some debate about its performance, but is still “supporting” the device in the market.

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2.8.2 Continuous Glucose Monitoring System [36, 37] Much attention has been given to the development of subcutaneously implantable needle-type electrodes, which were first described by Schichiri et al. [38]. Usually the sensor is configured as a fine needle or flexible wire, with the active sensing element at or near the tip, and implanted in the subcutaneous tissue. Such sensors are regarded as “minimally invasive” and their subcutaneous implantation avoids the problems of septicemia, fouling with blood clot, and embolism, which are potentially associated with intravascular placement [39–44]. Such devices are designed to operate for a few days and be replaced by the patient. 2.8.2.1 Continuous glucose monitoring system – Electrochemical detection of glucose oxidase The typical construction of these devices includes the glucose oxidase immobilized at a platinum anode, an inner membrane, such as cellulose acetate, acting like an interfering substance filter and an outer membrane, such as polyurethane, controlling the diffusion of glucose and improving the biocompatibility. The hydrogen peroxide produced by glucose oxidase is detected electrochemically [39]. Success in this direction has reached the level of short-term human implantation in the hands of Minimed Medtronic[40] (Northridge, CA, USA) and Dexcom (San Diego, USA). Such devices could enable a swift and appropriate corrective action through a closed-loop insulin delivery system, for example an artificial pancreas. Algorithms correcting for the transient difference (time lag) between blood and tissue glucose concentrations have been developed. Medtronic is best known for its implantable devices. It traces its history back 20 years in diabetes and supports a research program for the development of a continuous glucose sensor as well as an implantable insulin pump. The CGMS (Fig.2.6) is a sensor about the size of an AA battery that transmits radio signals to a pager-sized receiver. The device provides up to 288 glucose measurements every 24 hours, which means 72 times more data than patients testing their blood sugars four times a day would obtain. Some patients can obviously benefit from this rich source of information, while for others it may be considered simply data overload. The CGMS System Gold sensor can measure glucose values up to 72 hours while patients go about their

FIGURE 2.6: CGMS System Gold sensor [4]

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normal activities. The CGMS System Gold sensor is typically inserted into subcutaneous tissue in the abdominal area and worn for one to three days. A Holter-style monitor stores continuous glucose data measured by the sensor at five-minute intervals. This data can be downloaded into a computer and reports can be easily printed for retrospective analysis. The system uses a needle to insert a very narrow gauge enzyme electrode beneath the skin, where it encounters interstitial fluid. It is designed to be inserted into the subcutaneous tissue, usually in the abdominal area, utilizing a soft cannula-type device. This diagnostic device is worn by the patient for three days and gathers and stores continuous glucose readings that can then be downloaded to a personal computer for analysis. The hypoglycemia alarm alerts the patient when the glucose level drops below the limit established by the administering physician [41]. Another very similar approach of continuous glucose monitoring has recently been established by Dexcom and it is called DexCom STS Continuous Glucose Monitoring System [44]. It is a patient insertable short-term sensor that wirelessly transmits blood glucose readings to the DexCom STS Receiver. The sensor, a small insertable or implantable device, continuously measures glucose levels in subcutaneous tissue just under the skin and transmits the glucose levels at specified intervals to a small external receiver. With the push of a button, the receiver displays the patient’s current blood glucose value, as well as one-hour, three-hour and nine-hour trends. The receiver also sounds an alert when an inappropriately high or low glucose excursion is detected. 2.8.2.2 Continuous glucose monitoring system – Optical detection of glucose oxidase In 2004, at the University of California, a research group developed a novel optical glucose sensor that could be used to provide continuous monitoring of glucose levels in diabetics and hospitalized patients. The optical glucose sensor consists of a fluorescent chemical complex immobilized in a thin-film hydrogel. The hydrogel, a biocompatible polymer similar to that used to make soft contact lenses, is permeable to glucose. The sensing system has two components: a fluorescent dye and a quencher that is responsive to glucose. In the absence of glucose, the quencher binds to the dye and prevents fluorescence, while the interaction of glucose with the quencher leads to dissociation of the complex and an increase in fluorescence. The researchers have also applied the hydrogel to the end of an optical fiber, enabling the signal from the glucose sensor to be transmitted through the optical fiber. The technology has been applied in a marketable product, called GluCath. GluCath is a catheter device, for monitoring blood glucose levels in hospitalized patients. It is inserted into a blood vessel and gives a continuous reading and can sound an alarm if the glucose level goes too high or too low. Glucose modulates the fluorescent signal by binding reversibly to a boronic acid component attached to the quencher molecule. The fluorescence is stimulated by light from an LED and can be easily measured because it occurs at a distinct wavelength from the LED light [43]. In 1997, Animas started developing a long-term (5 years), implantable, optical sensor designed to provide continuous and accurate monitoring of blood glucose

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levels. This sensor will be equipped with alarms to give warnings of impending hypoglycemia and hyperglycemia. Ultimately this sensor will be tied into an insulin infusion pump to provide closed-loop control of blood glucose levels. The Animas sensor measures the near-infrared absorption of blood. The sensor will be implanted across a vein with readings transmitted via radio waves (RF telemetry) to a small Display Unit worn on the wrist. Hence, there will be no percutaneous (through the skin) wires. The Display Unit will be about the size of a wristwatch and the implanted sensor about the size of a pager. The Animas sensor is based on Spectroscopy. In theory, by probing a substance with light and by accurately measuring the resultant spectrum, one can identify and determine the concentration of each chemical constituent. In practice it is often difficult to determine the concentrations of the constituents, particularly if the constituent is in low concentration or if its spectra (or signature) overlaps the spectra of other constituents. Spectroscopic determination of glucose in blood has proved difficult because glucose is in relatively low concentration and its spectra overlaps that of other blood constituents, such as proteins, urea, uric acid, hemoglobin and, most notably, water. Many attempts to measure glucose through the skin or mucous membranes have failed, due to loss of light energy in the intervening tissues and the problem of extracting the blood spectra from that of intervening tissues. The Animas sensor sidetracks these limitations because the sensor is implanted and, therefore, has direct access to blood. A further advantage is that the system offers the potential to overcome many of the limitations of other chemical sensors and biosensors associated with biocompatibility and the encapsulation tissue which forms around implanted sensor devices. At the selected wavelengths used, this tissue is transparent. At present, the device has been demonstrated over a course of at least two weeks on an in vivo basis in dogs. The company is in the progress of designing a miniaturized sensor, which is currently undergoing preliminary human trials [45].

2.9 Challenges and Hurdles Facing Glucose Biosensors Over the past forty years there has been intense activity and tremendous progress in the development of electrochemical glucose biosensors. Major advances have been made to enhance functionality of glucose measuring devices. Despite the impressive advances in glucose biosensors, there are still many challenges related to the achievement of tight, stable and reliable glycemic monitoring. Desirable features of a biosensor system are accuracy, reliability, ultra sensitivity, fast response and low cost per test. It is very important that the biosensor system is user-friendly and understood by the patient, thus reducing incorrect results due to human error. This is one of the reasons that the major companies dealing with glucose monitoring are driving towards the creation of integrated devices. In US patent 6,497,845 [45] issued on behalf of Roche, in December of 2002, an

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invention is described including a storage container for holding analytical devices (an integrated device). This invention became a commercial product after a couple of years with the launch of Accu-Chek Compact Plus [46]. This device is a blood glucose monitoring system based on reflectometric technology. The system consists of a meter and dry reagent test strips designed for capillary blood glucose testing by people with diabetes or by health care professionals. Compact Plus uses drums with 17 test strips, and the meter is automatically calibrated by inserting a new drum. An electronic check is performed automatically and a test strip is pushed forward when the meter is turned on with a button. The system requires a blood volume of 1.5 µ L and provides a result within 5 seconds. The test principle of Compact Plus relies on the reaction of glucose oxidase with pyrroloquinolone quinone (PQQ). An indicator changes from yellow to blue by means of a mediator and a redox-process. The blue color is read reflectometrically. The meter has the capacity to store 300 results in memory. Accu-Chek Softclix Plus lancet pen is fastened to the Compact Plus meter. The lancet pen can be used either when fastened to the meter or it can be taken off the meter. A method and apparatus for handling multiple sensors in a glucose monitoring instrument system is described in US patent 5,510,266 [47] issued in April of 1996, in favor of Bayer. The invention is generally related to a glucose monitoring system and, more particularly, to an improved device for handling multiple sensors that are used in analyzing blood glucose. This invention became a reality in 2003, with the launch of Ascenia Dex [48], which was the first blood glucose monitor to store multiple strips inside the meter. This device was very easy to use and its integration reduced incorrect results due to the human error. The integration of the test strips in the device was a major innovation, resulting in significant profit to the companies. This is one of the reasons that these patents became a subject of litigation between Roche and Bayer, since there is an apparent similarity between the drum and the disk that Accu-Chek Compact and Ascensia Dex have. Another challenge that glucose biosensors manufacturers had to face is the many manual operating steps in conventional lancet systems (lancet and lancing device), which is obviously disadvantageous to the user. In most of the systems that are available at present, the lancets for use in lancing devices are provided in a loose form and for each lancing process, the user manually removes a lancet from a pack and has to insert it into the lancet holder of the lancing device and fix it there. Numerous attempts to eliminate the above disadvantage have been described. In US patent 6,616,616 [49], issued in September 2003, Roche describes an invention concerning a lancet system comprising a plurality of essentially needle-shaped lancets, a drive unit which has a drive element in order to move the lancet from the resting position into the lancing position, a storage area to store the lancets, a withdrawal area to guide at least the tip of the lancet out of the system during the lancing process and a transport unit which can transport lancets from the storage area into the withdrawal area. The above invention became a reality in 2004, with the launch of the MultiClix [50]. MultiClix is now one of the most popular lancing devices. It is the only one with a six-lancet drum, combining safety and convenience, since no handling of lancets is necessary. It also provides 11 penetration depth settings, letting the patient

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adjust the penetration according to his skin type, reducing by this way the pain by avoiding contact with deeper nerves. If one follows this evolution, then the next logical product is multiple sensors combined with multiple lancets as announced by Pelikan Technologies Inc. This presents many technical challenges including achieving sufficiently high density of sensing sites. While electrochemical technology has continued to dominate this field, one paper by the Pelikan team has explored optical solutions [51]. This paper describes a new type of fluorescence-optical glucose biosensor. The membrane consisted of an emulsion that incorporated the enzyme glucose oxidase to catalytically consume sample glucose and to co-consume oxygen. The emulsion additionally contained an oxygen-quenchable fluorescent indicator that determined the concentration and, hence, consumption of oxygen within the sensor by exhibiting a change in fluorescence related to the sample glucose concentration. The particular advantage was seen as a high density array sensor for glucose that could be fabricated within the stringent cost restraints associated with this market.

2.10 Future Perspectives & Conclusions Diabetes is one of the leading causes of death and disability in the world. 171million people in the world are suffering from this disease and several studies have demonstrated the likely increase of this figure to 366 million by 2030. Thus quick diagnosis and early prevention are critical for the control of the disease. Forty years have passed since Clark and Lyons proposed the concept of glucose enzyme electrodes. Since then, excellent economic prospects and fascinating potential for basic research have led to many sensor designs and detection principles for the biosensing of glucose. The first-generation of biosensor devices relied on the use of an oxygen co-substrate, and the production and detection of hydrogen peroxide. Extensive efforts during the 1980s were devoted to minimizing the error associated with electroactive interferences in glucose electrodes. Particularly useful has been the use of artificial mediators at the second generation of glucose biosensors. Nowadays commercial blood glucose meters are produced by many companies worldwide, but the major players are Roche Diagnostics, LifeScan, Abbott and Bayer who mostly employ mediated amperometric biosensor technology. Some other alternative strategies include minimally invasive testing meters and continuous glucose monitoring. As this field enters the fifth decade of intense research, the market size and the huge demand is creating the need for the development of new approaches, like painless, in vitro devices, non-invasive monitoring and miniaturized long term implants with advanced biocompatible membranes. Opportunities for new technology abound and novel optical approaches continue to be published. The rigorous demands of commercialization have so far selected in favor of electrochemical devices, but the trend towards high

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density arrays and multi-analytes may yet tip the balance in favor of optical techniques such as fluorescence. These and similar developments are expected to greatly improve the control and management of diabetes to the overall benefit of the World’s population.

References [1] B. Tuch, M. Dunlop, and J. Proietto, Diabetes Research, A Guide for Postgraduates, Australia : Harwood Academic, 2000 [2] Peter J. Watkins, ABC of Diabetes, (Fifth Edition), London : BMJ Books, 2003 [3] International Diabetes Federation, Diabetes Atlas (Second Edition), 2004 [4] A.P.F. Turner, J.D. Newman, L.J. Tigwell, and P.J. Warner, (2006) Biosensors: A global view. The Ninth World Congress on Biosensors, 10-12 May 2006, Toronto, Canada. O31. [5] R. Walkers and J. Rodgers, Diabetes: A Practical Guide to Managing your Health [6] American Diabetes Association, A Field Guide to Type 1 Diabetes, (Second Edition) [7] American Diabetes Association, Gestational Diabetes - What to Expect, Fifth Edition [8] S. Wild, G. Roglic, A. Green, R. Sicree, and H. King, “Global Prevalence of Diabetes. Estimates for 2000 and projections for 2030.” Diabetes Care, vol. 27, 2003, pp 1047–1053 [9] H. King and RE Aubert, “WH Herman, Global burden of diabetes, 19952025: prevalence, numerical estimates and projections,” Diabetes Care, vol. 21, 1998, pp 1414–31 [10] International Diabetes Federation, The Diabetes Atlas (Second edition), International Diabetes Federation: Brussels, 2003 [11] H.E. Turner and J.A.H Wass, Oxford Handbook of Endocrinology and Diabetes, Oxford : Oxford University Press, 2002 [12] H.D. Park et al. “Design of a portable urine glucose monitoring system for health care,” Comput Biol Med, vol. 35, 2005, pp 275–86 [13] E. Renald, “Monitoring glycemic control: the importance of self-monitoring of blood glucose,” Amer. J. Med., vol. 118, 2005, pp 2–19 [14] R. Johnson, and J. Baker, “Accuracy of devices used for self-monitoring of blood glucose,” Ann Clin Biochem, vol. 35, 1998, pp 68–74

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[15] E. Boland et al., “Limitations of conventional methods of self-monitoring of blood glucose,” Diabetes Care, vol. 24, 2001, pp 1858–1862 [16] http://diabetes.webmd.com/ (13/12/06) [17] G. Margaret et al, “Clinical application of “Dextrostix” in estimating blood glucose levels,” Diabetologia, vol. 1, 1996, pp 245–247 [18] L.S. Stephenson and M.C. Latham, “Rapid and portable methods of lactose tolerance test administration,” The American Journal of Clinical Nutrition, vol. 28, 1975, pp 888–893 [19] G. Ramsay and A. P. F. Turner, “Development of an electrochemical method for the rapid determination of microbial concentration and evidence for the reaction mechanism,” Analytica Chimica Acta, vol. 215, 1988, pp 61–69 [20] A.P.F. Turner, G. Ramsay and I.J. Higgins, “Applications of electron transfer between biological systems and electrodes,” Biochem. Soc. Trans., vol. 11, 1983, pp 445–448 [21] A.P.F. Turner, I. Karube, and G.S.Wilson, Biosensors: Fundamentals and Applications, Oxford : Oxford University Press, 1987 [22] Fuji-Keizai, Biosensors Market, R&D, Applications and Commercial Implication, New York, 2004 [23] C.R. Yonzon et al. ”Towards advanced chemical and biological nanosensorsAn overview,” Talanta, vol. 67, 2005, pp 438–448 [24] A.P.F. Turner and Y.M. Yendokimov, Biosensors: A Russian Perspective. Advances in Biosensors, vol. 3, 1995, London : JAI Press, 1995. [25] A. Chaubey and B.D. Malhotra, “Mediated biosensors,” Biosensors & Bioelectronics, vol. 17, 2002, pp 441–456 [26] J.D. Newman, L.J. Tigwell, A.P.F. Turner, and P.J. Warner, Biosensors - A Clearer View, 2004 [27] http://www.roche-diagnostics.com (13/12/06) [28] http://www.invernessmedical.com (13/12/06) [29] www.lifescan.com (13/12/06) [30] G. Parkinson and B. Pejcic, Using Biosensors to Detect Emerging Infectious Diseases, Australia, 2005 [31] http://www.abbott.com (13/12/06) [32] http://www.bayerhealthcare.com (13/12/06) [33] A.P.F. Turner and S. Piletsky, Biosensors and Biomimetic Sensors for the Detection of Drugs, Toxins and Biological Agents. In: Defense Against Bioterror (Eds. D. Morrison, F. Milanovich, D. Ivnitski and T.R. Austin), NATO STS Series, Springer, The Netherlands. pp 261–272, 2005

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[34] The Diabetes Research in Children Network (DirecNet) Study Group, “Accuracy of the GlucoWatch G2 Biographer and the continuous glucose monitoring system during hypoglycemia,” Diabetes Care, vol. 27, 2004, pp 722–726 [35] T.C. Dunn, R.C. Eastman, and J.A. Tamada, “Rates of glucose change measured by blood glucose meter and the lucoWatch Biographer during day, night, and around mealtimes,” Diabetes Care, vol. 27, 2004 , pp 2161–2165 [36] D.C. Klonoff, “Continuous glucose monitoring: Roadmap for 21st century diabetes therapy,” Diabetes Care, vol. 28, 2005, pp 1231–1239 [37] B. Guerci, M. Floriot, P.B¨ohme, D. Durain, M. Benichou, S. Jellimann, and P. Drouin, “Clinical performance of CGMS in type 1 diabetic patients treated by continuous subcutaneous insulin infusion using insulin analogs,” Diabetes Care, vol. 26, 2003, pp 582–589 [38] M. Schichiri et al., “Needle-type glucose sensor for wearable artificial endocrine pancreas,” Futura, 1985, pp. 197–209 [39] J. Pickup, L. McCartney, O. Rolinski, and D. Birch, “In vivo glucose sensing for diabetes management: progress towards non-invasive monitoring,” BMJ, vol. 319, 1999, pp 1289 [40] http://www.minimed.com/products/cgms/index.html [41] S.K. Garg, S. Schwartz, and S.V. Edelman, “Improved glucose excursions using an implantable real-time continuous glucose sensor in adults With type 1 diabetes”, Diabetes Care, vol. 27, 2004, pp 734–738 [42] http://www.diabetesnet.com/diabetes technology/dexcom.php [43] http://currents.ucsc.edu/03-04/03-15/glucose.html [44] http://www.animascorp.com/products/pr glucosesensor.shtml [45] Sacherer, Storage container for analytical devices, US patent no 6,497,845 [46] http://www.Accu-Chek.co.uk (14/12/06) [47] Bonner et al., Method and apparatus of handling multiple sensors in a glucose monitoring instrument system, US patent 5,510,266 [48] www.bayercarediabetes.com (14/12/05) [49] Fritz, et al., Lancet system, US patent 6,616,616 [50] http://www.abbottdiabetescare.co.uk (15/12/06) [51] Bernhard H. Weigl, Ron L. Bardell, Thomas H. Schulte, David C. Cullen, and James N. Demas, “Coordinated efforts of mathematical modeling and experimental testing efficiently advance a design project through the prototype stage,” In Vitro Device Technology, June 2004

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3 Monte Carlo Simulation of Light Propagation in Human Tissues and Noninvasive Glucose Sensing Alexander V. Bykov, Mikhail Yu. Kirillin Physics Department and International Laser Center, M.V. Lomonosov Moscow State University, Moscow, Russia, and Department of Technology, University of Oulu, Oulu, Finland Alexander V. Priezzhev Physics Department and International Laser Center, M.V. Lomonosov Moscow State University, Moscow, Russia 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of Glucose on Optical Parameters of Particulate Media . . . . . . . . . . . . . . Principles of the Monte Carlo Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Modeling of Glucose Sensing with OCT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Modeling of Glucose Sensing with Spatial Resolved Reflectometry . . . . . . . . Modeling of Glucose Sensing with Time Domain Technique . . . . . . . . . . . . . . . Modeling of Glucose Sensing with Frequency Domain Technique . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66 67 68 72 76 82 86 90 91

In this chapter, we shall briefly describe the Monte Carlo algorithm adapted for biomedical optics applications and discuss several implementations of this algorithm for modeling of glucose sensing with OCT, spatial resolved reflectometry, time domain, and frequency domain techniques. Key words: Monte Carlo simulation, optical parameters, biotissues, glucose sensing, time domain technique, frequency domain techique, optical coherent tomography.

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3.1 Introduction Monte Carlo-based simulations of photon transport in living tissues have become the “gold standard” technique in biomedical optics. Indeed, Monte Carlo enables to numerically solve the nonlinear radiative transfer equation that can not be solved analytically but for simplest particular cases which do not describe real biological objects. With Monte Carlo, light transport in biological objects of high complexity can be studied in a wide range of optical parameters and experimental geometries, including different modes of object illumination and signal detection. It allows accounting for optical phenomena that can take place when light interacts with biotissues: absorption, scattering, fluorescence, reflection and refraction at interfaces. As in all other types of modeling, the adequacy of results obtained with Monte Carlo simulation heavily depends upon the choice of basic parameters that govern light propagation in the tissue. In the frames of the discrete particle model of biotissues and representation of the light flux as a train of single photons or photon packets, which are typically used to implement the Monte Carlo algorithm in the biomedical optics field, the process of light propagation in tissue is simulated by a chain of successive random events of scattering, absorption, reflection and, in some cases, emission of fluorescence photons forming random photon trajectories inside the tissue. Some of the photons that do not get absorbed in the tissue may reach a photodetector (photodiode, CCD camera, etc.) after leaving the tissue and contribute to the signal. The basic parameters that are used in Monte Carlo simulation of photon trajectories and, consequently, the output signal of the detector are: absorption and scattering coefficients of the medium, scattering particle phase function, and the particle scattering anisotropy factor defined as a mean cosine of the scattering angle. These parameters determine all the important characteristics of light propagation in the particulate media: mean free path and transport pathlength of the photon, reduced scattering coefficient of the medium. The geometric structure of the modeled object or medium and the boundary conditions are also accounted for. When the Monte Carlo algorithm is implemented, the random values of the photon free path and two scattering angles are calculated at each scattering event using random number generators thus yielding a three-dimensional trajectory for each photon. The number of photon trajectories that need to be calculated mainly depends upon the statistical precision that has to be achieved in the given numerical experiment which in its turn depends on the number of photons that reach the detector and contribute to the signal and insure the needed signal-to-noise ratio. These numbers heavily depend on the optical properties of the tissue under study at the wavelength that is used. Typically from 105 to 1010 input photons are used to insure the statistical validity of the simulated signal. Monte Carlo simulation is used to solve both the direct and inverse optical problems. In the first case the output signal formed by the detected photons is the final goal of the simulation. In the second case this signal is further used to calculate

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the optical parameters of the tissue by comparing it with experimentally measured signal and/or theoretical predictions. Usually this is performed as an iterative procedure. Actually the basic parameters that were mentioned above (absorption and scattering coefficients of the medium, and the particle scattering anisotropy factor) can not be measured experimentally. They are usually calculated from the physically measurable values: diffuse backscattering of light from the tissue and diffuse and collimated transmission of light through the tissue. These values can be determined numerically with the help of Monte Carlo simulation of photon trajectories. The anisotropy factor can also be calculated from the particle scattering phase function, which can be either defined from general theoretical considerations or calculated for certain types of scattering particles (e.g., basing on the precise Mie theory in the case of spherical particles [1], on approximations of the Mie theory or more complicated numerical solutions of the Maxwell equations in the case of nonspherical shapes [2]). Another option is to measure the particle scattering phase function experimentally with a goniophotometer. This option has become feasible with the development of optical trapping technique.

3.2 Effect of Glucose on Optical Parameters of Particulate Media The origin of light scattering in biotissues is in the refractive index mismatch between their neighbouring components (cells, nuclei, intercellular and extracellular liquids, etc.). The amount of scattering is determined by the sizes, shapes and concentrations of the components and by the level of the refractive index mismatch. Being dissolved in water, blood plasma or interstitial fluid, glucose changes their refractive indexes, the value of this change being proportional to the concentration of the glucose in solution. The refractive index mismatch between intra- and extracellular liquids affects the cell’s phase function and scattering cross-section. The effect of glucose dissolved in a solution on the refractive index of the latter was studied quantitatively by Tuchin et al. [3]. It was shown that the glucose-induced change in the refractive index is δ n = 2.73 × 10−5 mM−1 . Larin et al. report on the value δ n = 2.55 × 10−5 mM−1 [4]. The effect of glucose concentration on the optical parameters µs , µa , g, and n of the media was discussed in Refs. [5, 6]. The effect of glucose on the suspension of polystyrene particles was considered in Ref. [5]. It was shown that for this solution the changes in the scattering coefficient, µs , are of the order of −0.02% mM−1 glucose concentration. The anisotropy factor, g, also changes with the increase in the glucose concentration by +0.0007% mM−1 . It was shown [6] that an increase in the glucose concentration in the physiological range (3–30 mM) may also decrease the scattering coefficient by 0.22% mM−1 due to cell volume change. The authors considered the rabbit ventricular myocytes as an example of the scattering media,

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however they generalize the results to other solutions. The mentioned values for the effect of glucose on optical properties were further used by other authors, e.g., in papers [7–9].

3.3 Principles of the Monte Carlo Technique 3.3.1 Basics of the Monte Carlo method The basic idea of the Monte Carlo method is obtaining the required solution via numerous repetition of random tests and further statistical analysis of the obtained results. When applied to solving the problem of light propagation in a scattering medium, the Monte Carlo method is based on numerous calculations of random motion trajectories based on the preset medium characteristics. The Monte Carlo method can be used for the study of the propagation of photons [10, 11], electrons [12], protons [13] and other moving particles and quasi-particles. It is widely applied for comparison of experimental or theoretical data with results of computer simulation and further interpretation of the obtained results [14–17]. The application of the Monte Carlo method is based on using the macroscopic properties of a medium that are supposed to be uniform in a certain area. The simulation does not account for the radiation energy redistribution within a single scatterer. Known algorithms allow one to consider light propagation in complex multilayer media with various optical properties [10], different geometries [18], finite size of the incident beam [19, 20] and light polarization [21–23]. Theoretical solution of the problem of light propagation in scattering media implies a solution of the radiative transfer equation (RTE) which can be written as follows [24]:

∂ L(r, s) µs = −µt L(r, s) + ∂s 4π

Z

4π

L(r, s′ )p(r, s, s′ )dΩ′ ,

(3.1)

where L(r, s) is radiance at point r to the direction s; p(r, s, s′ ) is the scattering phase function characterizing also spatial distribution of scatterers; dΩ′ is the unit solid angle to the direction s′ . Eq. (3.1) is valid for the case of absence of light sources inside the medium. The Monte Carlo method is a convenient tool for simulating the light propagation in biotissues [25–28] because the direct analytical and numerical solution of RTE is strictly limited by the complexity of boundary conditions. The main limitation of the Monte Carlo method is the requirement for significant calculation powers, but it becomes less important due to modern development of computers.

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3.3.2 Monte Carlo algorithm Simulation of the photon transport in single- and multilayer media with various geometries can be performed implementing the Monte Carlo algorithm. Each layer is basically described by the following optical parameters: scattering coefficient µs , absorption coefficient µa , anisotropy factor g or scattering phase function p(s, s′ ), where s, s′ are directions of photon propagation before and after scattering, refractive index n, thickness and boundary shape. The refractive index of the medium surrounding the object is also taken into account. The photon propagation in the object is described in Cartesian coordinates. The current position of the photon is determined by the coordinates (x, y, z) and its current movement direction is determined by the orienting cosines: γx = ex · r, γy = ey · r, γz = ez · r, where r is a unit vector of the photon velocity, ex , ey , ez are unit vectors of the coordinate axes. Reflection and refraction of the photon on the boundary between the media with different refractive indices are calculated according to the Fresnel law for non-polarised radiation: Ri,t (ξ ) =

Ri,t (ξ ) =



nt − ni nt + ni

2

,

  1 sin2 (αi − αt ) tan2 (αi − αt ) + , 2 sin2 (αi + αt ) tan2 (αi + αt ) Ri,t (ξ ) = 1,

αi = 0;

0 < αi ≤ sin−1 (ni /nt );

αi > sin−1 (ni /nt ),

where αi and αt are the incident and refraction angles of the photon, ni and nt are the corresponding refractive indices of the media. The refraction angle αt is calculated in accordance with Snell’s law ni sin αt = . sin αi nt The calculation algorithm used in the simulations is schematically represented in Fig. 3.1. Let us consider an iteration of this algorithm in more details. The impinging point of a photon and its initial direction are determined by a random generator in accordance to the preset parameters of the incident beam describing the spatial and angular power distributions. The technique of generation of random numbers with a given probability distribution is described in details in [29]. Further, basing on the optical parameters of the upper layer (the only one in the case of l-layer medium) the photon free path length is calculated using the following probability density function: P(l) =

1 −l/hli e , hli

where the average free path length is defined as hli =

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The random free path is determined according to the following formula: l = − ln(1 − ξ )hli, where ξ is a random number uniformly distributed in the interval [0,1] and generated by a random number generator program. Further, a new photon propagation direction is calculated according to the scattering phase function: p(s, s′ ) = p(θ )p(ϕ ). The scatterers are usually supposed to be spherically symmetrical and, consequently, the polar angle ϕ is supposed to be uniformly distributed in the interval [0, 2π ], while the azimuthal angle θ is calculated in accordance with the phase function for a single scatterer implementing the algorithm described in [29]. The direc-

FIGURE 3.1: Monte Carlo algorithm used in the simulations.

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tional cosines of the velocity vector at each scattering event are modified as follows:

γ x = √sin θ 2 (γ x γ z cos ϕ – γ y sin ϕ ) + γ x cos θ , 1−γz

γ y = √sin θ 2 (γ y γ z cos ϕ + γ x sin ϕ ) + γ y cos θ , 1−γz

γ z = - sin θ cos ϕ

p 1 − γz2+ γ z cos θ .

If the incident angle is close to normal (i.e., |γz | > 0.99999 ) the modification of the directional cosines is calculated according to the following formulae:

γ x = cos ϕ sin θ , γ y = sin ϕ sin θ , γ z = sign γ z cos θ . After the calculation of the free path length and the directional cosines, the new coordinates are calculated as follows: x = x0 + l γ x , y = y0 + l γ y , z = z0 + l γ z , where x0 , y0 , z0 are the initial photon coordinates. After this calculation, the processing of one scattering act is finished and all these steps are repeated to process the next scattering act. Accounting for the absorption of radiation is performed in the following way. In order to increase the statistics of the calculation it is supposed that each photon is rather a photon packet characterized by initial weight [11, 20], the latter being decreased at each scattering event by the value of P = P0 µsµ+aµa , where P0 is the current photon weight. Alternative way of absorption account is a modification of the photon weight in accordance with the Lambert-Beer law at each scattering event: P = P0 exp(-µ al), where l is a pathlength between two consequent scattering events. However the latter variant averages the absorption over space making it separated from the exact scattering events. In the simulations the former variant of absorption account is usually used.

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Calculation of the new coordinates and propagation direction is repeated until the photon reaches a boundary of the layer or becomes absorbed. In the case when the photon reaches a boundary the probability of its reflection or refraction is determined by the Fresnel’s coefficients. If the photon is reflected from the boundary the calculation of the propagation parameters is repeated; otherwise these calculations are performed based on the optical properties (µ s , µ a , g or p(s, s′ ), n) of the other layer into which the photon penetrated. In the case when the photon leaves the considered medium or becomes absorbed, the final parameters of the photon (final position, direction, weight, etc.) are processed and stored and the tracing of a new random photon trajectory begins. The processing of the output photon data consists in saving the information about the photon trajectory for collecting the necessary statistics and further generalization of the data. For each simulated measurement technique the specific output data set is important. The photons collected are selected according to the preset detection conditions (detector size and position, numerical aperture).

3.4 Modeling of Glucose Sensing with OCT 3.4.1 Principles of OCT Optical coherence tomography (OCT) is a modern method of noninvasive imaging of the inner structure tissues, tissue phantoms and other strongly scattering media based on the principles of low-coherent interferometry [30, 31]. The basis of any OCT setup is a Michelson interferometer with a low-coherent light source (superluminiscent light emitting diode (SLD) or femtosecond laser) placed in one of its arms (Fig. 3.2). The studied object is situated in the sample arm, a scanning mirror moving with constant speed is placed in the reference arm, a photodetector detecting the interference signal originated from optical mixing of the light coming from the sample and the reference arm is placed in the fourth (detector) arm. The in-depth scanning (in z-axis direction) is performed by uniform movement of the scanning mirror in the reference arm of the interferometer (so-called A-scan). The amplitude of the signal detected by the photodetector is proportional to local value of the scattering coefficient at the corresponding probing depth while the signal frequency is determined by the velocity of the mirror. Presence of the local areas with optical properties different from the average ones in the object under study leads to an alteration in the detected signal amplitude. Hence, from the dependence of the signal amplitude on the scanning time during a scan one can obtain the in-depth distribution of scattering and absorption coefficients inside the object. In transversal direction the scanning is performed by consecutive shifting of the probing beam axis at a definite step, for example, using an electromechanical system.

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FIGURE 3.2: Schematics of the OCT setup (BS is the beam splitter).

3.4.2 Simulation of the OCT A-scan When simulating the OCT signal, the photon tracing inside the object under study is performed by Monte Carlo technique. The simulation technique was developed in papers [27, 28, 32–37]. For the calculation of the OCT signal only the photons fitting the given detection conditions (detector position, size and numerical aperture) are selected. For the calculation of the OCT signal the process of interference signal formation resulting from the interaction of waves reflected from the reference mirror and backscattered from the object should be simulated. The beam splitter reflection coefficient is supposed to be 0.5 and the numbers of photons injected into the reference and sample arm of the OCT setup are supposed to be equal. When simulating the photon propagation in the object its optical pathlength is calculated. After completing the simulations for a large number of photons the distribution of the detected photons over their optical pathlengths is obtained as the output data. This distribution can be considered as an envelope of the OCT signal with very narrow (δ -function) coherence function, because it characterizes the in-depth distribution of object optical properties [34, 38]. The OCT signal itself can be calculated in accordance with the formula for the interference part [8]: √ Iint = 21 Ir Is cos( 2λπ ∆l), where Ir and Is are the amplitudes of waves scattered from reference and sample arms correspondingly; ∆l is their optical pathlength mismatch. Consequently, accounting for the low coherence of the probing radiation, the interference signal can be calculated as follows: p I(t) = ∑ Nr Ns (t, ∆li ) cos( 2λπ ∆li )C(∆li , lcoh ), i

where Nr (t, ∆li ) and Ns (t, ∆li ) are the numbers of photons detected from the reference and the object arm, respectively, C(∆li , lcoh ) is the coherence function, and lcoh

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is the coherence length of the probing radiation. This time-dependence can be recalculated into depth-dependence given the scanning mirror velocity is known. In our simulations the coherence function is supposed to be Gaussian, and the OCT signal is calculated according to the following formula:   p I(t) = ∑ Nr Ns (t, ∆li )cos ( 2λπ ∆li ) exp − (∆li /lcoh )2 . i

In Ref. [34] the Monte Carlo simulation of OCT signal was performed without accounting for the coherence function. In this study the OCT signal was obtained as a square root of the distribution of the detected photons over their optical pathlengths. Accounting for the photons phase shifts when propagating in a medium in the presence of moving scatterers allows one to simulate the optical coherence Doppler tomography (OCDT) signal [28]. However, due to the fact that the photon packets are considered in the simulations it is necessary to account for the independent interference of each detected photon packet with the reference radiation and the simulated OCT signal should be calculated as a superposition of these partial interference fringe patterns. The number of injected photons needed for the simulation of one A-scan is usually chosen in regard to the required calculation time and statistical accuracy. Accounting for the speckle formation is an important problem for the simulation of OCT signals. The main sources of speckles in OCT are fluctuations of the position of the studied object and multiple scattering in the medium causing random phase shifts. The first type of the speckles is not taken into account in the simulation because it is assumed that the object is fixed and this type of speckles can be neglected. Moreover, modern OCT devices utilizing the fiber optics allow one to fix the optical fiber directly to the studied object avoiding this kind of speckles. It is worth mentioning that the speckle effect is present in the simulated OCT signal because the latter is calculated as a sum of partial interference fringe patterns. The summation of the fringe patterns with random phase shifts results in a speckle structure of the signal. In the experiment this speckle structure is caused by a random position of the scatterers inside the scattering medium. To suppress the speckle effect, the spatial or temporal averaging of the OCT signal is usually implemented. In Monte Carlo simulation of the OCT signal, the calculation of the output signal as a sum of envelopes of the partial interference signals is used instead of spatial averaging. The formula for the interference signal calculation in this case will be the following: I(t) = ∑ i

  p Nr Ns (t, ∆li ) exp − (∆li /lcoh )2 .

Another problem that may appear when simulating the propagation of a broadband radiation is the dependence of the medium optical properties on the wavelength leading to dispersion effects. However, the optical properties of biotissues and their phantoms in the NIR range exhibit weak wavelength dependence and these effects can be neglected in simulations related to these tissues.

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Alternative approaches to Monte Carlo simulations of OCT signals were proposed in papers [39, 40], in which the simulations were based on the extended HuygensFresnel principle allowing one to account accurately wave effects. In paper [41] a fixed-particle Monte Carlo method was considered allowing one more accurate calculation of speckle patterns.

3.4.3 Comparison of simulated and experimental results The comparison of the experimental and simulated OCT signals from intralipid solution with various concentrations of glucose was performed in paper [8]. The solution under study was positioned in a plain 1-mm thick cuvette. Intralipid solution is the medium widely used for mimicking the scattering properties of dermis and epidermis. The basic idea of the Monte Carlo simulations of the glucose effect on the signals obtained in various optical diagnostics techniques including OCT is the changing of the optical parameters of the media in which the light is propagated according to the relations mentioned in section 2. The slope of the OCT signal was chosen as criterion for glucose sensing because the changes in glucose level affect the scattering properties of the medium affecting the slope of the signal. Increasing the concentration of glucose reduces the refractive index mismatch between scattering particles and the solution media and hence decreases also the scattering coefficient. As a consequence, the signal attenuation decreases and more optical power can be detected from larger depths, which results in a change of the OCT signal slope in accordance with the Lambert-Beer’s law: I(z) = I0 e−(µt z) , where µt = µa + µs and z is the depth co-ordinate in the media. The comparison of experimental and Monte Carlo results for 5% Intralipid solution are presented in Fig.3.3 with solid and empty circles, respectively. The results for 2% Intralipid solution have larger deviations from the fitting line compared to the case of 5% solution because the total amount of the backscattered photons, contributing to the level of the signal, decreases with the decrease in concentration, and, hence, we need more accurate intensity detection in the experiment and larger statistics in the simulations. The results for 5% Intralipid solution exhibit a 4.4% signal slope change in the experiment and about 7% change in the simulations, when the amount of glucose is varied from 0 mg/dl to 1000 mg/dl. The results for 2% Intralipid solution (see Fig. 3.4) exhibit about 13% signal slope change in the simulations, when the amount of glucose changes from 0 to 1000 mg/dl. The difference in experimental and simulated glucose-induced changes may be caused by the assumption that the glucose effect on µs equals to −0.22% mM−1 , as stated for blood samples in refs [4–6]. However, for Intralipid solutions this effect may be different and needs additional studies. In conclusion, it is worth saying that both the simulation and experimental results show the sensitivity of the OCT signals to glucose concentration. Although quanti-

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FIGURE 3.3: Glucose-induced changes in the OCT signal slope for 5% IntralipidTM , obtained from the experiment and the simulation; error bars indicate ±1 standard deviation [8].

FIGURE 3.4: Glucose-induced changes in the OCT signal slope for 2% IntralipidTM , obtained from the simulation.

tatively they differ due to details not accounted in the model, qualitatively they look alike which proves that Monte Carlo simulations can be effectively used for qualitative estimation of the OCT technique in glucose sensing.

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3.5 Modeling of Glucose Sensing with Spatial Resolved Reflectometry One of the methods that can potentially be implemented for noninvasive measurements of blood glucose level is spatial resolved reflectometry (SRR) [9, 42]. The essence of this technique is in measuring the dependence of the diffuse backscattered light intensity on the source-detector separation. Such measurements are usually performed with the help of an array of detectors or a stepwise moving detector. The SRR technique was also demonstrated to be effective for blood oxygenation detection [43].

3.5.1 Multilayer biotissue phantom and its optical properties for Monte Carlo simulation In this section we shall consider the numerical study of SRR potentialities for glucose level detection implementing Monte Carlo technique in the case of a threelayer biotissue phantom and discuss the choice of the measurement parameters. The schematic layout of the simulated experiment is shown in Fig. 3.5.

FIGURE 3.5: Schematic layout of the simulated experiment.

In our calculations, the embedding depth L1 of the blood layer varied from 100 to 300 µ m which corresponds to the range of depths of the upper plexus in human skin. The thickness of the blood layer L2 was fixed and equal to 200 µ m. The thickness of the lower skin layer was chosen so that the total thickness of the sample resulted in 10 mm allowing to consider the lower skin layer as semi-infinite according the values of its optical properties. The optical parameters of the skin-mimicking layers were averaged from the values reported in papers [18, 44–46], while for the bloodmimicking layer the values were chosen basing on the data reported in [14, 47]. The values used for simulations are shown in Table 3.1. The wavelength was chosen as 820 nm which belongs to the so-called diagnostic transparency window (600–

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1300 nm) and is widely used in the noninvasive diagnostics of tissues. In the table the transport length in both media ltr = 1/(µa + µs′ ) characterizing the chaotization of the photon movement direction is also shown.

TABLE 3.1: Optical parameters of the layers used in the simulation (λ = 820 nm).

Blood Skin / intralipid

µ s, mm−1 57.3 10

µ a, mm−1 0.82 0.002

g

n

0.977 1.4 0.9/0.7 1.4

ltr , mm 0.468 0.98/0.33

For the simulations, two values of the anisotropy factor characterizing skin (0.9) and water solution of Intralipid (0.7) were used. Because this parameter plays a significant role in the process of light propagation in a scattering medium, the analysis of its effect on the obtained results is of importance. The variation of the glucose level is considered in the range from 0 to 500 mg/dl, the extreme low and high values corresponding to strictly pathological cases for a human organism. In simulation, it was supposed that the change in glucose concentration does not affect the optical properties of the superficial skin layer because in human organism the glucose level changes at first in blood and then in tissues neighboring to blood vessels, while in superficial layer the changes are late and non-significant. The number of launched photons in the simulation was chosen as 109 . To increase the calculation statistics in the case of axial-symmetrical medium the dependence of the backscattered intensity on source-detector separation is calculated not along a definite direction, but in all directions which allows obtaining the result accounting for more photon trajectories.

3.5.2 SRR-signal The signals obtained for the medium mimicking the skin with g = 0.9 for embedding depth of the blood layer of 200 µ m and glucose concentration of 0 mg/dl and 500 mg/dl are shown in Fig. 3.6(a). Figure 3.6(b) shows the same signals scaled for the region where the relative signal difference is maximal. The presented results are normalized by the detector area and the probing beam power with an assumption that the numerical aperture of the detector NA=0.24 which corresponds to the detection angle of 28◦. Thus, the magnitude I in Fig. 3.6 has the dimension of mm−2 . Fresnel reflection from the detector surface is about 1% of the signal level; therefore it was not taken into account in the simulation. Fresnel refraction can be also reduced by administering an index-matching liquid onto the surface of the object (optical clearing [48]). The scattered light power P registered on

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FIGURE 3.6: a) SRR-signals for the 3-layered medium at the embedding depth of blood layer L1 = 200 µ m for glucose concentration of 0 mg/dl (solid line) and 500 mg/dl (dashed line); b) the same signals for the region of maximal relative difference (shown in Fig. 3.6a with a rectangle).

the detector surface can be calculated from data in Fig. 3.6 according to the formula: P = P0 (1 − R)ISd , where P0 is the power of the probing radiation, Sd is the detector area, R is Fresnel reflection from the surface of medium. It is obvious that the calculation according to this formula is correct only in the case when the linear size of the detector is less than the distance over which the change of the SRR-signals is significant. An important measurement parameter is the intensity of the probing radiation. In the case of glucose detection the limitations for this intensity are quite strict, because even an increase in the light-induced heating temperature of the probed medium by 1◦ C can cause changes in the optical properties of the object leading to an error in the determination of the glucose level [7]. According to Ref. [44], the maximal admissible intensity of the probing radiation for the considered problem is around 1 W/mm2 . The spatial resolution in the SRR-signal calculation corresponding to the linear size of the detector (or optical fiber diameter) is 20 µ m. In this case the detector area is about 400 µ m2 . At the source-detector separations ranging from 0 to 8 mm, for the maximal admissible intensity of the probing radiation the detected power varies from 10−4 to 10−8 W and the corresponding intensity varies from 10−1 to 10−5 W/mm2 . At the wavelength used, the radiation power of such orders can be detected with modern photo detectors with high accuracy. To raise the power of the detected signal we can increase the detector area, as the selected value of 20 µ m is basically a parameter of simulation rather than the real fiber diameter.

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3.5.3 Relative sensitivity of SRR For optimizing the position of the detector relative to the source, an estimation of relative sensitivity S of the SRR-signal to the glucose concentration in dependence on the source-detector separation r can be performed according to the following expression [9]: I0 (r) − I500(r) , S(r) = I0 (r)

where I0 and I500 are SRR, signals corresponding to the glucose concentration of 0 and 500 mg/dl. The results obtained for three considered embedding depths of the blood layer are shown in Fig. 3.7. From this figure one can see that for g = 0.9 (Fig. 3.7a) the relative sensitivity S has a local maximum at the source-detector separations below 0.5 mm. The minimum at r above 2 mm is due to the fact that the difference I0 − I500 changes its sign; however the magnitude S is defined as nonnegative. Consequently, at the condition I0 − I500 = 0 it has a minimum.

FIGURE 3.7: Relative sensitivity of the SRR-signal to the change of glucose level from 0 to 500 mg/dl in the blood layer and the deeper skin layer for the embedding depths of the blood layer of 0.1, 0.2 and 0.3 mm; the anisotropy factor g = 0.9 (a) and 0.7 (b) [9].

One can see that as the source-detector separation increases the relative sensitivity S reaches again the value corresponding to the local maximum around r = 7 mm. At this distance from the source, the power of the detected signal decreases by three orders of magnitude in comparison to its value at r = 0.4 mm, which makes reason to perform the measurements at r = 0.4 mm. Moreover, as it will be shown further, the photons forming the backscattering signal at r = 7 mm reach the depths comparable with r in the considered medium. However, the human skin thickness is only 2– 3 mm although in this model we have considered a thicker phantom.

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For the case g = 0.7 (Fig. 3.7b) the relative sensitivity S also has a local maximum around 0.5 mm. However, as one can see from this figure, in this case the dependence of the maximum position and maximum value on the blood layer embedding depths is stronger. Moreover, S for small r values is lower than in the case of g = 0.9, which is related to an increase in randomization of the photons’ directions before they reach the layers where the optical parameters are sensitive to glucose (blood layer and below). Although for the case g = 0.9 the photon transport length significantly exceeds the embedding depths of the blood layer, for g = 0.7 it is only 0.3 mm (see Table 3.1), which is comparable with the blood layer embedding depths. Thus, at the maximal value of the considered blood layer embedding depths, the regime when the photon direction is already chaotic before entrancing the glucose sensitive layers takes place. In this case, higher sensitivity to glucose is observed at larger r values, where the backscattering is quite diffuse.

3.5.4 Scattering maps For a more detailed analysis of the photon trajectories forming the SRR-signal, the scattering maps describing the density of photon scattering events in the medium under study can be considered [9]. The scattering maps shown in Fig. 3.8 were obtained for the embedding depth of the blood layer L1 = 200 µ m and for three different values of r: 0.4, 0.8, and 1.2 mm. The scattering maps show the trajectories distribution which has higher density and lower width in the points of emission and detection and lower density and higher broadening width between these points. The density of the trajectories is proportional to the local brightness which is higher in the region corresponding to the blood layer because the maps show the density of scattering events of the photons forming the signal and the scattering coefficient of blood is approximately five times higher than that of skin. For the case g = 0.9 the trajectory distributions are less broadened than for the case g = 0.7, which is caused by higher randomization of the photon directions in the latter case. With an increase in the source-detector separation the overlap of the picture parts with the highest brightness in the regions of the source and the detector is reduced.

3.5.5 Dependence of SRR-signal on glucose concentration Finally, let us analyze the dependence of the SRR-signal on glucose concentration in blood and deep skin layers for the embedding depth of blood layer L1 = 100 µ m at 2 combinations of parameters: (a) skin anisotropy factor g = 0.9 at r = 0.4 mm; (b) skin anisotropy factor g = 0.7 at r = 0.3 mm. As it was shown before, these combinations are close to optimal. The simulation results obtained in Ref. [9] are shown in Fig. 3.9a and 3.9b, respectively. It is seen that in the range of glucose concentrations from 0 to 500 mg/dl there exists a clear correlation between the detected SRR-signal and the glucose concentration in the medium. In the case of a fiber with the cross section area of 400 µ m2

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FIGURE 3.8: Scattering maps of photons forming the SRR-signal from a 3layered skin model for the embedding depth of the blood layer L1 = 200 µ m and the skin anisotropy factor g = 0.9 (a) and 0.7 (b). Distances along X and Z axis are measured in mm [9].

and the maximal input intensity of 1 W/mm2 , which were mentioned above, the detected power would change from 1.28 to 1.7 µ W at the change of the glucose concentration from 0 to 500 mg/dl. Such measurement would demand quite high accuracy of the detection. However, as noted before, the mentioned value of detecting fiber cross section area is a parameter of simulation rather than the real characteristic of the measuring system. It is obvious that with an increase in the detector area the detected power will increase too, which reduces the requirements to the sensitivity of the photodetector. For instance, for the ThorLabs detector APD210 the sensitivity is 105 V/W in the considered wavelength range, which is sufficient for the reliable measurements with the detector fiber cross section area about 0.01 mm2 . In this case the detected power would vary from 32.1 to 34.7 µ W, which would lead to a change in the detected voltage from 3.21 to 3.47 V. Hence, the sensitivity to glucose changes would be around 0.52 mV/(mg/dl).

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FIGURE 3.9: Dependence of signal intensity at a) g = 0.9 and r = 0.4 mm, b) g = 0.7 and r = 0.3 mm on glucose concentration in blood and deep skin layers at the embedding depth of blood layer L1 = 100 µ m [9].

3.6 Modeling of Glucose Sensing with Time Domain Technique The effect of glucose concentration on propagation of ultrashort laser pulses in a model light-scattering suspension was studied in Ref. [49]. It was shown that it is possible to estimate the glucose level in the physiological range of concentrations (100–500 mg/dl) by measuring the peak intensity and total energy of the detected pulses in backscattering geometry. In this section we shall discuss the applicability and advantages of the time domain (time-of-flight) technique in the problem of noninvasive glucose sensing taking into consideration a three-layer model of the skin. Figure 3.10 schematically represents the arrangement of the simulated experiment. The geometry and the optical properties of the skin phantom as well as the parameters of the detecting fibers are similar to those described in the previous section.

FIGURE 3.10: Schematic layout of the simulated experiment.

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The only difference is the type of a light source and the arrangement of the probe. The latter consists of 5 adjacent optical fibers placed in line on the top of a phantom as shown in Fig. 3.10. In this case, we consider the incoming (probing) signal as a δ -pulse in time domain.

3.6.1 Output time-of-flight signal The output pulses for all five fibers calculated at L1 = 100 µ m and two glucose concentrations are presented in Fig. 3.11. From this figure one can see that for all considered fibers the time profiles of the scattered pulses corresponding to different glucose concentrations slightly differ. This fact allows one to consider the time-offlight (TOF) technique as potentially applicable for glucose sensing. The essential difference between g = 0.9 and g = 0.7 cases is that in the former case the scattered pulse has one peak while in the latter case it has two peaks. This effect is caused by the fact that the amount of light backscattered from a definite layer is characterized by the value of (1 − g). In this connection, the mismatch between these values for the skin and blood layers is larger in the case g = 0.7 causing larger difference in the amounts of backscattered light and, hence, in the amplitude of the detected pulse. For g = 0.9 this difference can be seen only for the first fiber. Once the difference in pulse shapes for different glucose concentrations is discovered one should find the proper quantitative characteristics for recovering the glucose level value from the measured pulse shape.

FIGURE 3.11: TOF signals for two different glucose concentrations: 0 (solid line) and 500 (dashed line) mg/dl for L1 = 100 µ m, anisotropy factor g = 0.7 (a) and 0.9 (b).

TOF measurements allow to use more parameters (e.g., total pulse energy, peak intensity, peak position) for signal characterization as compared to spatial resolved

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measurements and thus seem to be more informative for glucose sensing, however, more expensive. It is also possible to increase the sensitivity implementing the time gating (see below).

3.6.2 Relative sensitivity of the TOF signals to glucose concentration Let us consider the peak value of the measured pulse, the time-integral value (total energy of the pulse) and the partial time-integrals in the intervals from zero to some prefixed time (i.e., the integration time). Dependencies of the peak value and the total energy of the pulse on glucose concentration for the first fiber are presented in Fig. 3.12. One can see that both chosen values exhibit fairly linear dependence on the glucose concentration. However, we should mention that the numerical simulations are performed for an ideal case and when applying the TOF method experimentally one should take into account the measurement error, effect of possible noises and limited dynamic range of the measuring system.

FIGURE 3.12: TOF signals for two different glucose concentrations: 0 (solid line) and 500 (dashed line) mg/dl for L1 = 100 µ m, anisotropy factor g = 0.7 (a) and 0.9 (b).

Now let us consider the partial pulse energies calculated under the condition that the photons are collected only within the definite time intervals. In our simulation we chose these intervals to be 5, 10, 20, 30, 40, 50 and 130 ps long. The relative sensitivities of the partial pulse energies to glucose concentration for all five fibers for L1 = 100 µ m and g = 0.9 are presented in Fig. 3.13. From this figure one can see that the maximal sensitivity is characteristic to the second and the third detectors placed at distances corresponding to the distances of maximal sensitivity obtained with the SRR technique. The dependence of the sensitivity on the integration time differs for different fibers. However for the second and the third fibers the sensitivity decreases with an increase in the integration time.

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FIGURE 3.13: Relative sensitivities of the partial pulse energies to glucose concentration change from 0 to 500 mg/dl for L1 = 100 µ m and g = 0.9 for different fibers (the numbers are shown above the curves) versus the integration time interval. From this fact one can conclude that given the detecting system allows such integration, the shorter integration time intervals (around 5 or 10 ps long) are preferable.

3.7 Modeling of Glucose Sensing with Frequency Domain Technique In this section we will consider the applicability and advantages of the frequency domain technique in the problem of noninvasive glucose sensing. It has close connection with the time-resolved (time domain) measurements considered in the previous section. The hardware or software Fourier-analysis of the scattered pulses allows to simultaneously obtain the amplitude and phase responses of the medium for the continuous set of harmonics.

3.7.1 Principles of frequency domain technique This method is based on the registration of dynamic response of intensity of scattered light to the modulation of the incident laser beam intensity within a wide frequency modulation band (0.1 - 10 GHz). The measuring parameters in the case of frequency domain measurements are the modulation depth of scattered intensity m and the phase shift between modulation phases of incident and detected radiation ∆φ as shown schematically in Fig. 3.14. In comparison with the time-of-flight method, the frequency domain method is simpler for implementation, easier for the interpretation of the results and has greater noise immunity. In the frequency domain, the signal formation can be interpreted in terms of socalled photon density waves. These waves resemble the heat-waves arising due to

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FIGURE 3.14: Schematic representation of the reflectance (a) and transmittance (b) modes of the frequency domain measurement technique. the absorption by a medium of the modulated laser radiation. Each photon makes a random walk inside the scattering medium; however all together they form a photon density wave, spreading from the source, with a frequency equal to the modulation frequency of the source. The photon density waves have all the properties typical of the waves of other types, e.g., refraction, interference, diffraction, and dispersion [50]. In highly scattering media with small absorbance far from the borders, light sources and detectors, the light propagation can be considered as a diffusion process described by the time-resolved diffusion equation for the photon density function Φ(~r,t). For a point light source located in the point r = 0 with the harmonic modulation of the intensity I(t) = I0 (1 + mI exp(iω t)) the solution of the diffusion equation for the homogeneous infinite medium can be presented in the following form [51]: Φ(r,t) = ΦDC (r) + ΦAC (r) exp(iω t + iφ (r)), where ΦDC (r), ΦAC (r) and φ (r) are the constant (direct current) component, amplitude and phase of the photon density wave, respectively, measured at a distance r between the source and detector; ω = 2πν , where ν is the frequency of modulation. The modulation depth of the detected signal is defined by the relation: mΦ (r, ω ) =

ΦAC (r, ω ) . ΦDC (r)

The variable component of the obtained solution represents an outgoing spherical wave with the centre in the point r = 0, which oscillates at the modulation frequency ω and has a phase shift relative to the phase value at the point r = 0. The measurements of vΦ (r, ω ), and φ (r, ω ) values allow to determine the reduced scattering

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coefficient µs′ = µs (1 − g), absorption coefficient µa and the distribution of these parameters inside the medium under study. Measurements of the reduced scattering and absorption coefficients using the frequency domain technique with the accuracy high enough for glucose sensing have been reported in [52].

3.7.2 Simulation of frequency domain signals Monte Carlo simulation of scattering signals in frequency domain is based on the fact that the values of the phase shift and modulation depth of detected radiation can be obtained for the continuous modulation frequency band just with the help of Fourier-transform of the medium transfer function h(t) (the medium response to a δ -pulse) [53]:   ˜ ω ) ∼ m1 exp(iφ ), F˜ {h(t)} = H( m0 where m1 and m0 is the modulation depth of the detector and source, respectively, φ is the phase shift. Figure 3.15a shows the calculated responses of semi-infinite homogeneous scattering media with scattering coefficients µs = 1 and 5 mm−1 to a δ -pulse for the case of back reflectance measurements. Absorption coefficient was assumed to be 0, the anisotropy factor g = 0.7, the detector radius was 0.5 mm and the distance between source and detector was 6 mm.

FIGURE 3.15: Responses of the scattering media with different values of scattering coefficient to a δ -pulse (a); frequency dependences of phase shift between source and detector (b) and modulation depth (c) for the same values of the scattering coefficient obtained with help of Fourier-transform.

Figures 3.15b and 3.15c show the frequency dependencies of the phase shift between source and detector and the modulation depth calculated for the same values of the scattering coefficient obtained with help of Fourier-transform. One can see that a decrease in the scattering coefficient of a homogeneous semi-infinite medium leads to a decrease in the phase shift and an increase in the modulation depth of the

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detected signal at the certain value of modulation frequency.

3.7.3 Analysis of glucose sensing potentialities of the frequency domain technique Let us consider a semi-infinite layer of a medium with optical properties similar to those of Inralipid solution of 2% concentration [54] and a 1 mm-thick layer with optical properties close to those of blood [14, 47] embedded at a depth of 1 mm. Parameters of the detector and source-detector separation are the same as mentioned above. Fig. 3.16 shows the calculated phase response of the medium with blood glucose concentrations of 0 and 500 mg/dl.

FIGURE 3.16: Frequency-resolved dependences of the phase shifts between the source and detector for the blood layer with glucose concentration of 500 mg/dl (dashed line) and without glucose (solid line) embedded into the scattering medium (2% Intralipid solution).

From this figure one can conclude that even the maximal possible physiological change of blood glucose concentration causes but changes in the phase shift. This fact demands that special measures should be taken to raise the sensitivity of the measuring device. Figure 3.17 shows that with an increase in the modulation frequency the difference between the phase shifts presented in Fig. 3.16 gradually increases. In general this result is clear since with an increase in the modulation frequency the sensitivity of the frequency domain method to changes of the scattering coefficient should increase. However, the nonmonotonous character of this dependence needs additional interpretation. It has been experimentally tested that the uncertainty of phase measurements for the majority of devices is about 0.1 deg and does not depend on the modulation frequency. According to this estimate, the detection of the maximal glucose changes is possible at the modulation frequencies higher than ∼400 MHz. However in real practice it is necessary to detect smaller changes in glucose concentration resulting

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FIGURE 3.17: Frequency-resolved dependence of difference of phase shifts for blood layer with glucose concentration of 500 mg/dl and without glucose embedded into the scattering medium (2% intralipid solution) (boxes) and its approximation (solid line). in the phase shift differences lower than in the above considered case. Thus we can conclude that such measurements should be performed with higher modulation frequencies (in the gigahertz range).

3.8 Conclusion The Monte Carlo method of stochastic numerical simulation of light propagation in strongly scattering media is a powerful technique that can be efficiently implemented for solving various biomedical problems. In particular, it can be used to predict the effect of glucose on the output signal in glucose sensing experiments implementing different measurement techniques. In this chapter, we have shown that the signals of optical coherence tomograph, as well as reflectometers performing measurements in spatial resolved, time resolved, and frequency domain modes can be simulated with the Monte Carlo method. The simulation results that we described demonstrate the sensitivity of the signals obtained in application of the considered techniques to glucose concentration changes in the physiological range. However, even in the case of rather simple biotissue models which do not account for local structural nonhomogeneities and dynamic instabilities typical for live objects, e.g., human skin, this sensitivity, as of today, is not so high that would satisfy practical implementations for in vivo measurements in human patients. Evidently, more sophisticated models of human skin and experimental measurement techniques should be designed to get further progress in this field. Monte Carlo simulations can be used on all stages of their development to evaluate the attained sensitivity to glucose.

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References [1] H.C. Van de Hulst, Light Scattering by Small Particles, New York: Wiley, 1957. [2] I.M. Mischenko, J.W. Hovenier, and L.D. Travis, Light scattering by nonspherical particles, San Diego: Academic Press, 2000. [3] V.V. Tuchin et al. “Light propagation in tissues with controlled optical properties,” J. Biomed. Opt., vol. 2, 1997, pp. 401–417. [4] K. Larin, M. Motamedi, T. Ashitkov, and R.O. Esenaliev, “Specificity of noninvasive blood glucose sensing using optical coherence tomography technique: a pilot study,” Phys. Med. Biol., vol. 48, 2003, pp. 1371–1390. [5] J. Qu and B. C. Wilson, “Monte Carlo modeling studies of the effect of physiological factors and other analytes on the determination of glucose concentration in vivo by near infrared optical absorption and scattering measurements,” J. Biomed. Opt., vol. 2(3), 1997, pp. 319–325. [6] K.V. Larin, M. Motamedi, T.V. Ashitkov, and R.O. Esenaliev, “Specificity of noninvasive blood glucose sensing using optical coherence tomography technique: a pilot study,” Phys. Med. Biol., vol. 48, 2003, pp. 1371–1390. [7] M. Tarumi, M. Shimada, T. Murakami, M. Tamura, M. Shimada, H. Arimoto, and Y. Yamada, “Simulation study of in vitro glucose measurement by NIR spectroscopy and a method of error reduction,” Phys. Med. Biol., vol. 48, 2003, pp. 2373–2390. [8] M.Yu. Kirillin, A.V. Priezzhev, M. Kinnunen, E. Alarousu, Z. Zhao, J. Hast, and R. Myllyl¨a, “Glucose sensing in aqueous IntralipidTM suspension with an optical coherence tomography system: experiment and Monte Carlo simulation,” Optical Diagnostics and Sensing IV, A. Priezzhev, G. Cot´e, Eds., Proc. SPIE, vol. 5325, 2004, pp. 164–173. [9] A.V. Bykov, M.Yu. Kirillin, A.V. Priezzhev, and R. Myllyl¨a, “Simulations of a spatially resolved reflectometry signal from a highly scattering three-layer medium applied to the problem of glucose sensing in human skin,” Quant. Electron., vol. 36(12), 2006, pp. 1125–1130. [10] L. Wang, S.L. Jacques, and L. Zheng, “MCML – Monte Carlo modeling of light transport in multi-layered tissues,” Comp. Meth. Progr. Biomed., vol. 47, 1995, pp. 131–146. [11] S.A. Prahl, M. Keijzer, S.L. Jacques, and A.J. Welch, “A Monte Carlo model of light propagation in tissue,” Dosimetry of Laser Radiation in Medicine and Biology / SPIE Institute Series, vol. IS 5, 1989, pp. 102–111.

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[12] B. Faddegon, E. Schreiber, and X. Ding, “Monte Carlo simulation of large electron fields,” Phys. Med. Biol., vol. 50, 2005, pp. 741–753. [13] A. Tourovsky, A.J. Lomax, U. Schneider, and E. Pedroni, “Monte Carlo dose calculations for spot scanned proton therapy,” Phys. Med. Biol., vol. 50, 2005, pp. 971–981. [14] A. Roggan, M. Friebel, K. Dorschel, A. Hahn, and G. Muller, “Optical properties of circulating human blood in the wavelength range 400–2500 nm,” J. Biomed. Opt., vol. 4, 1999, pp. 36–46. [15] R.R. Anderson and J.A. Parrish, “The optics of human skin,” J. Invest. Dermatol., vol. 77, 1981, pp. 13–19. [16] Y. Du, X.H. Hu, M. Cariveau, X. Ma, G.W. Kalmus, and J.Q. Lu, “Optical properties of porcine skin dermis between 900 nm and 1500 nm,” Phys. Med. Biol., vol. 46, 2001, pp. 167–181. [17] A.N. Yaroslavsky, P.C. Schulze, I.V. Yaroslavsky, R. Schober, F. Ulrich, and H.-J. Schwarzmaier, “Optical properties of selected native and coagulated human brain tissues in vitro in the visible and near infrared spectral range,” Phys. Med. Biol., vol. 47, 2002, pp. 2059–2073. [18] I.V. Meglinsky and S.J. Matcher “Modelling the sampling volume for skin blood oxygenation measurements,” Med. Biol. Eng. Comput., vol. 39, 2001, pp. 44–50. [19] L.-H. Wang, S. L. Jacques, and L.-Q. Zheng, “CONV - Convolution for responses to a finite diameter photon beam incident on multi-layered tissues,” Comp. Meth. Prog. Biomed., vol. 54, 1997, pp. 141–150. [20] M. Keijzer, S. Jacques, S. Prahl, and A. Welch, “Light distribution in artery tissue: Monte Carlo simulation for finite-diameter laser beams,” Las. Surg. Med., vol. 9, 1989, pp. 148–154. [21] D.A. Zimnyakov, Yu.P. Sinichkin, P.V. Zakharov, and D.N. Agafonov, “Residual polarization of non-coherently backscattered linearly polarized light: the influence of the anisotropy parameter of the scattering medium,” Waves Random Media, vol. 11, 2001, pp. 395–412. [22] M. Xu, “Electric field Monte Carlo simulation of polarized light propagation in turbid media,” Opt. Express, vol. 12(26), 2004, pp. 6530–6539. [23] J.C. Ramella-Roman, S.A. Prahl, and S.L. Jacques, “Three Monte Carlo programs of polarized light transport into scattering media: part I,” Opt. Express, vol. 13 (12), 2005, pp. 4420–4438. [24] A. Ishimaru, Wave Propagation and Scattering in Random Media, Academic press, New York, vol. 1, 1978.

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[25] V.V. Tuchin, S.R. Utz, and I.V. Yaroslavsky, “Skin optics: modeling of light transport and measuring of optical parameters,” in: Medical Optical Tomography: Functional Imaging and Monitoring, Proc. SPIE , vol. IS 11, 1993, pp. 234–258. [26] C.-L. Tsai, Y.-F. Yang, C.-C. Han, J.-H. Hsieh, and M. Chang, “Measurement and simulation of light distribution in biological tissues,” Appl. Opt., vol. 40(31), 2001, pp. 5770–5777. [27] M.Yu. Kirillin, A.V. Priezzhev, J. Hast, and R. Myllyl¨a, “Monte Carlo simulation of low-coherent light transport in highly scattering media: application to OCT diagnostics of blood and skin,” Proc. SPIE, vol. 5474, 2003, pp. 192–199. [28] A.V. Bykov, M.Yu. Kirillin, and A.V. Priezzhev, ”Monte-Carlo simulation of OCT and OCDT signals from model biological tissues,” in: Proc. OSAV, 2005, pp. 233–240. [29] L. Wang and S. Jacques, Monte Carlo Modeling of Light Transport in MultiLayered Tissues in Standard C, University of Texas, M.D. Anderson Cancer Center, 1992. [30] J.M. Schmitt “Optical coherence tomography (OCT): a review,” IEEE J. Select. Top. Quant. Electron., vol. 5(4), 1999, pp. 1205–1215. [31] D.A. Zimnyakov and V.V. Tuchin, “Optical tomography of tissues,” Quant. Electron., vol. 32 (10), 2002, pp. 849–867. [32] G. Yao and L.V. Wang, “Monte Carlo simulation of an optical coherence tomography signal in homogeneous turbid media,” Phys. Med. Biol., vol. 44, 1999, pp. 2307–2319. [33] T. Lindimo, D. Smithies, Z. Chen, J. Nelson, and T. Milner, “ Accuracy and noise in optical Doppler tomography studied by Monte Carlo simulation,” Phys. Med. Biol., vol. 43, 1998, pp. 3045–3064. [34] R.K. Wang, “Signal degradation by multiple scattering in optical coherence tomography of dense tissue: a Monte Carlo study towards optical clearing of biotissues,” Phys. Med. Biol., vol. 47, 2002, pp. 2281–2299. [35] M.Yu. Kirillin, A.V. Priezzhev, V.V. Tuchin, R.K. Wang, and R. Myllyl¨a, “Effect of red blood cell aggregation and sedimentation on optical coherence tomography signals from blood samples,” J. Phys. D: Appl. Phys., vol. 38 , 2005, pp. 2582–2589. [36] M.Yu. Kirillin, R. Myllyl¨a, and A.V. Priezzhev, “Optical coherence tomography of paper: Monte Carlo simulation for multilayer model,” in: Saratov Fall Meeting 2006: Coherent Optics of Ordered and Random Media VII, D.A. Zimnyakov, N.G. Khlebtsov, Eds., Proc. SPIE, vol. 6536, 2007, 65360P. [37] R. Myllyl¨a, M. Kirillin, J. Hast, and A.V. Priezzhev, “Monte Carlo simulation of an optical coherence tomography signal,” in: Optical Materials and Applications, A. Rosental, Ed., Proc. SPIE, vol. 5946, 2005, pp. 59461P1–14.

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[38] Y. He and R.K. Wang, “Dynamic optical clearing effect of tissue impregnated with hyperosmotic agents and studied with optical coherence tomography,” J. Biomed. Opt., vol. 9(1), 2004, pp. 200–206. [39] L. Thrane, H.T. Yura, and P.E. Andersen, “Analysis of optical coherence tomography systems based on the extended Huygens–Fresnel principle,” J. Opt. Soc. Am. A, vol. 17, 2000, pp. 484–490. [40] A. Tycho, T.M. Jørgensen, H.T. Yura, and P.E. Andersen, “Derivation of a Monte Carlo method for modeling heterodyne detection in optical coherence tomography systems,” Appl. Opt. vol. 41, 2002, pp. 6676–6691. [41] G. Xiong, P. Xue, J. Wu, Q. Miao, R. Wang, and L. Ji, “Particle-fixed Monte Carlo model for optical coherence tomography,” Opt. Express, vol. 13(6), 2005, pp. 2182–2195. [42] J.T. Bruulsema, J.E. Hayward, T.J. Farrell, M.S. Patterson, L. Heinemann, M. Berger, T. Koschinsky, J. Sandahl-Christiansen, H. Orskov, M. Essenpreis, G. Schmelzeisen-Redeker, and D. B¨ocker, “Correlation between blood glucose concentration in diabetics and noninvasively measured tissue optical scattering coefficient,” Opt. Lett., vol. 22, 1997, pp. 190–192. [43] M.Yu. Kirillin, A.V. Priezzhev, and R. Myllyl¨a, “Comparative analysis of sensitivity of different light scattering techniques to blood oxygenation on the basis of multilayer tissue model,” Proc. SPIE, vol. 6163, 2006, 6163-25. [44] V.V. Tuchin, Tissue Optics. Light Scattering Methods and Instrumentation for Medical Diagnosis, PM 166, SPIE Press, Bellingham, 2007. [45] A. Knuttel and M. Boehlau-Godau, “Spatially confined and temporally resolved refractive index and scattering evaluation in human skin performed with optical coherence tomography,” J. Biomed. Opt., vol. 5, 2000, pp. 83–92. [46] T.L. Troy and S.N. Thennadil, “Optical properties of human skin in the near infrared wavelength range of 1000 to 2200 nm,” J. Biomed. Opt., vol. 6, 2001, pp. 167–176. [47] A.N. Yaroslavsky, A.V. Priezzhev, J. Rodrigues, I.V. Yaroslavsky, and H. Battarbee. “Optics of Blood,” Chapter 2 in: Handbook of Optical Biomedical Diagnostics, V.V. Tuchin, Ed., SPIE Press, 2002. [48] V.V. Tuchin, Optical Clearing of Tissues and Blood, SPIE Press, Bellingham, 2006. [49] A.P. Popov, A.V. Priezzhev, and R. Myllyl¨a,“Effect of glucose concentration in a model light-scattering suspension on propagation of ultrashort laser pulses,” Quant. Electron., vol. 35(11), 2005, pp. 1075–1078. [50] J.M. Schmitt, A. Knuttel, and J.R. Knutson, “Interference of diffusive light waves,” J. Opt. Soc. Am. A, vol. 9(10), 1992, pp. 1832–1843.

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[51] B.D. Guenther (ed.), Encyclopedia of Modern Optics, Elsevier Academic Press, 2004. [52] M. Gerken and G.W. Faris, “High-accuracy optical-property measurements using a frequency domain technique,” Proc. SPIE, vol. 3597, 1999, pp. 593–600. [53] S.R. Arridge, M. Cope, and D.T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol., vol. 37, 1992, pp. 1531–1560. [54] S.T. Flock, S.L. Jacques, B.C. Wilson, W.M. Star, and M.J.C. van Gemert, “Optical properties of intralipid: a phantom medium for light propagation studies,” Las. Surg. Med., vol. 12, 1992, pp. 510–519.

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4 Statistical Analysis for Glucose Prediction in Blood Samples by Infrared Spectroscopy Gilwon Yoon Seoul National University of Technology, Nowon-gu Kongneung-dong, Seoul, Korea

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Selection of Optimal Wavelength Region Based on the First Loading Vector Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Minimization of Hemoglobin Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Independent Component Analysis without Calibration Process . . . . . . . . . . . . . 4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

98 100 105 108 111 113

Methods to improve the accuracy in glucose prediction based on infrared spectroscopy were investigated. 1) An optimal wavelength region for spectral measurement in determining glucose concentration could be obtained by a partial least squares regression loading vector analysis method. Experiments were performed and this loading vector analysis method was verified. 2) Another issue is minimization of the spectral interference by other components. Hemoglobin is the major component in blood and blood spectrum is dominated by hemoglobin. We found the distribution of hemoglobin concentrations in the samples affects the accuracy of glucose prediction. Hemoglobin concentrations in the calibration samples should be evenly distributed in the entire physiological range. 3) An approach using independent component analysis was applied to eliminate the calibration process. The method was successfully verified by using the mixtures which contained different concentrations of glucose and sucrose. Their concentrations and pure spectra were successfully extracted only from measured sample spectra. It has a potential of predicting glucose without calibration process. Key words: glucose, statistical analysis, infrared spectroscopy, diabetes, partial least squares regression (PLSR), independent component analysis (ICA).

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4.1 Introduction Measurement of blood glucose has attracted a great attention since diabetes is an epidemic disease that inflicts many people all over the world. Spectroscopic measurement of blood glucose has a few distinct advantages. First, it does not require chemical reagent which is normally used by a strip in the blood-extracted device. Cost of using reagent constitutes a substantial portion of operating expenses. Another advantage is its multi-component analysis capability. Concentrations of several components can be estimated at the same time [1]. Above all, much interest in spectroscopic measurement is its potential use for noninvasive or minimally invasive determination of blood glucose [2–5]. In this chapter, principles of spectroscopic prediction of glucose are explained and statistical techniques for improving the prediction accuracy are discussed using whole blood samples.

FIGURE 4.1: Spectroscopic detection block diagram.

Figure 4.1 shows a spectroscopic measurement scheme. A target component is in the medium with interfering substances. For our case, the target component is glucose and the medium is blood. Blood contains many substances whose spectra interfere with glucose spectrum. Red blood cell is the most dominant interfering substance since its blood volume is 38–52% for men and 37–47% for women. There are other interfering substances such as proteins, etc. Another important substance is water itself. Water in the visible band is transparent. However, water becomes highly absorbing in the near infrared band and becomes the most dominant absorber in the mid infrared band where the fundamental glucose absorption lies. Measurement setup consists of a broad band light source, frequency dispersion unit and detector, as is illustrated in Fig. 4.1. Glucose has its fundamental absorption in the mid infrared (MIR) including around 9.6 µ m. Other absorption bands include the combination spectral band between 2.0 and 2.5 µ m and the first overtone band between 1.52 and 1.85 µ m approximately. Some investigators use a wavelength

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region of 700 to 1300 nm that contains higher orders of overtone regions. However, higher orders of the overtone bands exhibit extremely weak glucose absorption, less than 0.1% compared to the fundamental absorption band. In the fundamental band, on the other hand, water, which is the medium in blood, has very high absorption and light path length is less than a few score of micrometers. For glucose measurement based on absorption spectroscopy, the fundamental and combination bands are of practical use. Measurement setup also plays an important role. For instance, glucose prediction depends on measurement sites and experimental configurations such as reflectance and transmittance setup [6]. Discussions on measurement configuration are out of scope for this chapter, however. It is also worthy to mention the importance of electronics that renders a high signal-to-noise. Normally the system resolution should be up to an absorbance of 10−5. Once spectra are measured, the spectra are converted to a target absorption using statistical analysis. This statistical analysis is sometimes called chemometrics. Chemometrics is defined as the chemical discipline that uses mathematical and statistical methods to design or select optimal measurement procedures and experiments, and to provide maximum chemical information by analyzing chemical data [7]. The word “multivariate calibration” is also used [8]. Transformation of measurements (spectra) into informative results (glucose concentration) is required and calibration is the process of this transformation. Partial least squares regression (PLSR) is one of the most widely-used calibration methods. The steps involved with statistical analysis are as follows. First, the spectra of samples or subjects are measured. At the same time, the actual glucose values are measured from a well established known method or device. Calibration process generates a statistical model that converts the measured spectra into a particular glucose concentration. Principal component analysis (PCA) and PLSR are among the calibration methods. Once a calibration model is obtained, the calibration model converts a spectrum of a sample or subject, whose glucose level is not known, into a glucose value and this process is called prediction. In this chapter, we are going to investigate some subjects that are closely related with prediction accuracy. For example, a proper selection of wavelength region can improve prediction accuracy. Another subject is minimization of the spectral influence by interfering substances in blood. The existence of the interfering substances influences calibration and prediction modeling. The influence of hemoglobin in glucose prediction is studied. In addition, a statistical method called independent component analysis is introduced in order to eliminate a calibration process. Calibration requires time and cost. The glucose clinical test especially involves human subjects and it is not an easy task to recruit human subjects whose blood glucose concentrations vary in the entire physiological range.

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4.2 Selection of Optimal Wavelength Region Based on the First Loading Vector Analysis In spectroscopic analysis, one has to choose a wavelength region over which spectrum is measured. The wavelength region should include absorption wavelength(s) of a target component as well as reference wavelength(s). The reference band often includes wavelength(s) at which the target component has negligible absorption. The wavelength region should be wide enough so that the influences of interfering substances can be effectively minimized during statistical analysis. Therefore, the dependency of prediction accuracy on a wavelength region is examined in this section. In order to select an optimal wavelength region, we used the first loading vector (FLV) in PLSR analysis. The FLV in PLSR corresponds to the first-order approximation of a pure-component spectrum of a component and is a meaningful parameter in the selection of the wavelength region [9]. Two wavelength regions are of interest: the fundamental glucose absorption band in the MIR and the near infrared (NIR) region of containing the combination and first overtone bands. For our experiment, we studied two regions of 6.6–10.6 µ m (or 1515–917 cm−1 ) and 1100–2500 nm. From now on, we will use the notations of wave number, cm−1 , in the MIR and nanometer, nm, in the NIR since these are more frequently used units.

4.2.1 Optimal wavelength region in the mid infrared For the experiment 78 whole blood samples were prepared [10]. These samples had a glucose distribution between 17–458 mg/dl and a hemoglobin distribution between 6.9–17.0 g/dl. A sealed cell of 50 µ m path length, which was made from ZnSe, was used. The cell volume was 20 µ L. The absorption spectra were measured by a Nicolet Avatar 360 Fourier-transform IR spectrophotometer. Actual glucose values of the samples were obtained from a Beckman chemistry analyzer based on the hexokinase method. Hemoglobin values were measured based on the hemoglobincyanide method with a Sysmex SE8000 automated hematology analyzer. Statistical analysis was carried out by a Pirouette program (Infometrix). Figure 4.2 shows the measured spectra at 1515–917 cm−1 (or 6.6–10.6 µ m). A whole blood spectrum is very similar to that of hemoglobin solution. The graphs in the figure are not necessarily in the order of hemoglobin concentrations. Each spectrum has a slightly different base line due to experimental conditions. Glucose contributes a negligible effect in shaping the spectrum. Glucose absorption is so small compared to absorption produced by other components even at the fundamental glucose absorption band. Our observation was that even a sharp difference in glucose concentration, for example, between 0 mg/dl and 500 mg/dl, often does not produce more absorption difference than that produced by repetitive measurements of the same sample to our naked eyes. A complete statistical analysis should be performed in order to estimate even hemoglobin concentration. FLVs for glucose and hemoglobin were computed from PLSR analyses and are

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FIGURE 4.2: 78 whole blood spectra in the region of 1515∼917 cm−1 .

displayed in Fig. 4.3. Peaks of FLV were assigned, and we found that the absorption peaks of hemoglobin and glucose matched to those reported by Zeller et al. [11]. Glucose peaks in FLV were 1398, 1306, 1157, 1105, 1082, 1038 and 993 cm−1 . Some of these peaks were similar to those of hemoglobin FLV peaks such as 1400, 1304 and 1105 cm−1 . We arranged seven spectral regions on a subjective judgment considering these FLV peaks. Table 4.1 shows these seven spectral regions. Table 4.1 also gives the results at each region with Standard Error of Calibration (SEC) [mg/dl], correlation coefficient of calibration (rCal ) and coefficient of variation in cross validation (VCCVal ) [%]. The entire spectral region of 1515–917 cm−1 did not give the best results. To the contrary, the inclusion of unnecessary wavelength region produced poor results. The spectral regions including the dominant hemoglobin FLV peaks such as 1400 cm−1 and 1304 cm−1 generated the worst SEC and VCCVal . 1471–1381 cm−1 had a SEC of 124.2 mg/dl and a VCCVal of 57.4%. 1335–1267 cm−1 had 124.3 mg/dl and 57.5%. These values were by far bigger than those computed at other spectral regions. The best results were obtained by 1119–1022 cm−1 , where SEC was 10.8 mg/dl and VCCVal was 5.9%. 1119–1022 cm−1 has three major peaks of glucose FLV at 1105, 1082 and 1038 cm−1 . Even though they are similar to those of glucose FLV peaks, the values of hemoglobin FLV peaks at 1105 and 1090 cm−1 were small and in turn their contribution in regression must have been minimal. Our optimal region did not include a glucose FLV peak of 993 cm−1 . Peak at 993 cm−1 is an apparent glucose FLV peak; however, the absolute value is small and comparable to the absolute value of hemoglobin FLV.

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FIGURE 4.3: First loading vectors of glucose and hemoglobin obtained from the PLSR analysis using all 78 samples.

TABLE 4.1: The standard errors of glucose calibration with respect to different mid-infrared spectral regions. All 78 spectra were used. Spectral region [cm−1] SEC [mg/dl] rcal VCCVal [%]

1515 -917

1471 -1381

1335 -1267

1119 -1022

1097 -1026

1097 -1062

1062 -997

10.0 124.2 124.3 10.8 17.4 19.1 24.9 0.9974 0.2733 0.2703 0.9967 0.9913 0.9895 0.9820 9.2 57.4 57.5 5.9 8.4 9.5 11.8

SEC [mg/dl]: Standard Error of Calibration, rcal : correlation coefficient of calibration, VCCVal [%]: coefficient of variation in cross validation, SECV/mean×100 where SECV [mg/dl] is Standard Error of Cross Validation.

4.2.2 Optimal wavelength region in the near infrared The MIR light propagates only into a few scores of micrometer and may be applied for extracted blood sample. On the other hand, the NIR light has deeper penetration into biological medium up to a few millimeters. The NIR has a potential to be applied for noninvasive or minimally invasive blood analysis even though glucose absorption is not as high as in the MIR region. In the same manner described in subsection 4.2.1, we performed blood glucose analysis. 98 blood samples were newly made for our NIR experiment [12]. Whole blood was put into a 0.5 mm detachable cell. A NIRSystems 6500 spectrophotometer was

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FIGURE 4.4: a) Whole blood spectra of 98 samples and saline spectrum, b) Whole blood spectra are correlated with hemoglobin and glucose concentrations at each wavelength and the computed correlations coefficients are shown.

used to obtain NIR spectra. Spectra were measured between 1100 and 2400 nm. Figure 4.4 displays all the measured spectra. The glucose reference values were measured from a Beckman chemistry analyzer based on the glucose hexokinase method. Using another portion of the same blood, hemoglobin concentration was measured by the Sysmex SE8000 hematology analyzer. Measured glucose and hemoglobin values for 98 samples were distributed between 45 and 432 mg/dl, and 7.5 and 16.6 g/dl, respectively. In this NIR region, whole blood spectrum somewhat looks like saline (i.e., water) spectrum as in Fig. 4.4(a). Figure 4.4(b) shows correlation between whole blood spectra and hemoglobin. The correlation coefficients between blood spectra and hemoglobin concentration are very high (∼0.8). This indicates that blood spectra were highly dependent on hemoglobin concentration at each wavelength. The correlation coefficients became smaller around 1440 and 1940 nm which are water absorp-

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tion peaks. On the other hand, the correlation coefficients between blood spectra and glucose were only between 0.05 and 0.1. Glucose concentrations had little effects on blood spectrum profiles. PLSR analysis was performed. In order to select an optimal band, all 98 sample spectra were examined. Before calibration, the spectra were mean-centered. Loading vectors were studied as done in the case of the MIR analysis. In arranging different wavelength regions, a band from 1500 to 1800 nm (including the first overtone band) and a band from 2.0 to 2.4 (covering the combination band) were considered. Also the entire region of 1100 and 2400 nm was assigned as one of the wavelength regions. There is a strong water absorption peak at 1940 nm. The elimination of 1900 nm band produced more combinations in choosing wavelength regions. Hemoglobin absorption increased towards 1100 nm. Use or no use of the short wavelength region including 1100 nm was another consideration. As a result, a total of nine wavelength regions were selected and summarized in Table 4.2.

TABLE 4.2: Predictions of glucose concentrations at various near-infrared spectral regions. Spectra of all 98 samples were used. The best SECV and VCCVal were obtained when 1390–1888 and 2044–2392 nm were used. Spectral Region [nm]

1100 -2498

SEC [mg/dl] rCal VCCVal [%]

21.5

11001888 20442392 23.5

0.9860 0.9822 24.1 12.9

13901888 20442392 21.6

15161816 20622352 30.2

1100 -1888

1390 -1888

2044 -2392

31.7

32.2

33.1

0.9847 12.3

0.9696 16.0

0.9677 0.9663 0.9630 19.8 18.6 19.2

SEC [mg/dl]: Standard Error of Calibration, rCal : correlation coefficient of calibration, VCCVal [%]: coefficient of variation in cross validation, SECV/mean×100 where SECV [mg/dl] is Standard Error of Cross Validation.

The best results were achieved when the regions of 1380–1888 and 2044–2392 nm were used. The smallest VCCVal (12.3%) was calculated at this band. When the entire range between 1100 and 2498 nm was used, the worst prediction error (24.1%) was obtained. Whole blood spectra and the saline spectrum had different slopes between 1100 and 1380 nm. Absorption of saline decreases as the wavelength becomes shorter. This is a typical feature of water spectrum. On the other hand, blood absorption increases toward 1100 nm and this reflects hemoglobin absorption. Absorbance around 1940 nm is extremely high due to water absorption peak. Therefore, it is speculated that the optimal region excluded the bands of water absorption peak and shorter wavelength region towards 1100 nm. In finding the optimal region, only mean centering was performed. Once we found

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the optimal region, we examined whether further improvements could be made by applying different data preprocessing technique. Table 4.3 summarizes the effects of applying different data preprocessing techniques. Applying scattering correction methods of mean scatter correction (MSC) and standard normal variate (SNV) did not improve the prediction accuracy. In case of the second derivative method that has been widely used for baseline correction, the results were the worst. It is speculated that whole blood spectra are dominated by hemoglobin feature. Hemoglobin profiles appear to be more enhanced than glucose features during differentiation. A wide wavelength region, which was not optimized in PLSR analysis, may improve glucose prediction when different preprocessing techniques are applied to raw spectra. However, once the wavelength region was optimized based on the FLV analysis, it seems that mean centering was sufficient and that other data preprocessing techniques produced no further improvement.

TABLE 4.3: The effects of spectral data preprocessing in terms of SEC: all 98 samples were calibration-modeled using different preprocessed spectra at the wavelengths of 1390–1888 and 2044–2392 nm. Preprocessing method Mean centering MSC mean centering SNV mean centering 2nd derivative (15∗) mean centering

SEC

rCal

VCCVal [%]

21.6 23.8 22.0 26.8

0.9847 0.9810 0.9810 0.9768

12.3 12.5 12.6 19.5

MSC : mean scatter correction, SNV : standard normal variate ∗ 15 points smoothing was made before differentiation in order to reduce noises.

4.3 Minimization of Hemoglobin Interference Two substances, water and hemoglobin, determine blood spectrum to a substantial degree. Water, which is the major substance, plays a role as a dominant absorber in the infrared wavelength. Red blood cells are over almost 40% of blood volume and hemoglobin is the major substance of red blood cell. In a way, we may say that a whole blood spectrum in the infrared has a baseline of water spectrum and an individual feature determined by hemoglobin level. Hemoglobin level varies according to an individual. It is necessary to study the influence of hemoglobin level during

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statistical analysis.

4.3.1 Hemoglobin influence in the mid infrared region 78 samples had a glucose distribution between 17–458 mg/dl and a hemoglobin distribution between 6.9–17.0 g/dl [10]. Samples were made such that hemoglobin and glucose concentrations were evenly distributed in the entire concentration range. For the investigation of hemoglobin influence, the best band of 1119–1022 cm−1 was used for analysis in this section. To study the effect of hemoglobin on the prediction of glucose concentration, 78 samples were divided into several subsets such that each set has a different hemoglobin distribution. Using these subsets, we performed calibration and prediction analysis. Hbtotal was defined as a set containing the entire 78 samples. Hbcal represented 52 samples that were used as calibration set. Hbpre was named for the set of 26 samples that was used in prediction. Each of the above three sets (Hbtotal , Hbcal , Hbpre ) was arranged to have full ranges of hemoglobin and glucose concentrations. Next, 78 samples were also divided into three groups depending on hemoglobin level (Hbhigh, Hbmid , Hblow ). The number of samples grouped in Hbhigh , Hbmid and Hblow were 23, 31 and 24 respectively. Glucose concentrations were evenly distributed in the entire range for each set of Hbhigh , Hbmid and Hblow . Another important consideration was to ensure no correlation between hemoglobin and glucose levels. The coefficients of correlation between hemoglobin and glucose were between 0.12 and 0.33 for all the subsets. The correlations between glucose and hemoglobin concentrations among the subsets were insignificant with a significance level of 5%. Calibration and prediction analysis in the region of 1119–1022 cm−1 was performed using Hbcal , Hbhigh , Hbmid and Hblow . Using these four calibration models, glucose values in the four different sets were predicted. Table 4.4 summarized the results. For example, glucose concentrations in Hbhigh were predicted with a SEP of 19.8 mg/dl when the calibration model obtained from Hblow was applied. The same calibration model produced a SEP of 20.9 mg/dl when Hbmid was predicted. Our results showed that the errors were increased when calibration and prediction models have different hemoglobin levels. For example, SEP was the largest (22.5 mg/dl) when calibration modeling was done with Hbhigh and this same calibration model predicted glucose concentrations for Hblow . Remember that our analysis in subsection 4.2.1 used Hbcal as a calibration set and Hbpre as a prediction set. Both Hbcal and Hbpre had an entire range of glucose and hemoglobin concentrations and the excellent results were achieved.

4.3.2 Hemoglobin influence in the near infrared region In the same manner, we investigated hemoglobin influence using 98 blood samples prepared for the NIR experiment [12]. 98 samples were divided into several groups. First, the entire samples were divided into two groups that are the calibration set (Hbcal , 63 samples) and the prediction set (Hbpre , 35 samples). Both groups were

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TABLE 4.4: Prediction results using the four calibration models based on 1119–1022 cm−1 band. Calibration set

Hbcal Hbhigh Hbmid Hblow

Prediction Mean set value of glucose [mg/dl] Hbpre 226 Hbmid 195 Hblow 220 Hbhigh 251 Hblow 220 Hbhigh 251 Hbmid 195

SEP (rpre )

VCpre (%)

13.3 (0.9951) 23.2 (0.9853) 49.6 (0.9832) 13.9 (0.9940) 21.4(0.9903) 19.8 (0.9924) 20.9 (0.9897)

5.9 11.9 22.5 5.5 9.7 7.9 10.7

SEP (mg/dl): Standard Error of Prediction, rpre : correlation coefficient of prediction, VCpre (%): coefficient of variation in prediction, SEP/mean×100.

arranged such that hemoglobin and glucose concentrations were evenly distributed. Next, the entire 98 samples were grouped into three depending on hemoglobin level (Hbhigh : 16.6÷13 g/dl, Hbmid : 12.8÷10.9 g/dl, Hblow : 10.7÷7.5 g/dl). The number of samples grouped in Hbhigh , Hbmid and Hblow were 36, 31 and 31 respectively. Each of three groups had its glucose concentrations evenly distributed in the entire range. It is important that hemoglobin and glucose concentrations in each group are not correlated. All five groups were checked for the correlation between hemoglobin and glucose concentrations. Correlations were negligible as the values ranged between -0.13 and 0.11. Calibration was done using the four calibration groups (Hbcal , Hbhigh , Hbmid and Hblow ). Wavelength bands of 1390–1888 nm and 2044–2392 nm with mean centering were used for the PLSR analysis in this section. Table 4.5 shows SEP and rpre . Since glucose values were different among the prediction sets, prediction accuracy was analyzed in terms of the coefficient of variation in prediction (VCpre ). VCpre is defined as (SEP/mean value of glucose)×100 [%]. The same observation as in MIR analysis was made. The errors were higher when calibration and prediction models have different hemoglobin levels. For instance, glucose SEP was the largest (74.2 mg/dl) when calibration modeling was done with Hblow and prediction modeling was performed Hbhigh. Therefore, it is very important to make sure that calibration and prediction sets use samples with all the range of hemoglobin concentration.

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TABLE 4.5: Prediction of glucose concentrations based on the four calibration models. PLSR was performed using the band of 1390 to 1888 and 2044 to 2392 nm with mean centering.

Calibration Prediction set set Hbcal Hbhigh Hbmid Hblow a SEP

Hbpre Hbmid Hblow Hbhigh Hblow Hbhigh Hbmid

Mean value of glucose [mg/dl] 228 213 221 207 221 207 213

SEP a (rpre b )

VCpre c [%]

25.5 (0.9764) 23.1 (0.9817) 48.7 (0.9279) 39.3 (0.9465) 46.9 (0.9328) 74.2 (0.8672) 33.8 (0.9603)

11.2 10.8 22.0 19.0 21.2 35.8 15.9

[mg/dl]: Standard Error of Prediction for glucose.

b r : correlation coefficient of prediction. pre c VC pre [%] : coefficient of variation in prediction

of glucose, SEP/mean×100.

4.4 Independent Component Analysis without Calibration Process . Independent component analysis (ICA) is a statistical approach that was recently developed to separate unobserved, independent source variables from observed variables that are the combination (or mixtures) of these source variables without a priori information on the sources and the process of the mixture. Since it was developed in the 1990s, ICA has proven to be successful in the various fields of biomedical signal processing [13–16]. The ICA-based method is therefore particularly useful in identifying the unknown components in a mixture as well as in estimating their concentrations [17]. Especially for noninvasive glucose monitoring, calibration process itself requires an extensive effort in terms of arranging human subjects with different blood glucose concentrations. The ICA method, in principle, does not require calibration process as long as a pure-component spectrum of a target substance is known. In this section, we presented a method that can identify the pure absorption spectrum of a component from the MIR spectrum of a sample that contains multiple components. The only input of ICA is the spectra of mixtures. This method does not require additional information on the mixture. Pure-component spectra of the constituents dissolved in the mixture are separated by the ICA combined with principal component analysis (PCA). The detail had been reported [18]. This method was tested with a two-component system consisting of an aqueous solution of glucose

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FIGURE 4.5: 25 measured mid-IR spectra for the mixtures of glucose and sucrose.

and sucrose that exhibit distinct but closely overlapping spectra. We prepared a total of 25 mixtures of glucose and sucrose dissolved in de-ionized water from 200 mM stock solution. We used an orthogonal concentration design, in which the concentrations of different components are statistically independent. Single-beam mid-IR spectra of 25 samples were measured with a Nicolet AVATAR 360TM FT-IR spectrophotometer. ATR configuration was used for measurement. Pure spectra of dissolved glucose and sucrose were obtained from the stock solution spectra. Figure 4.5 shows the measured spectra. All 25 spectra were analyzed. No spectra were discarded as outliers. First, we performed Digital Fourier Filtering to eliminate the detector drift and related noise from the spectral data. Next, as in the simulation study, spectra were imported into Pirouette 3.0TM for PCA. Only two scores were used for the subsequent ICA. Figure 4.6 shows the extracted pure-component spectra from 25 measured spectra shown in Fig. 4.5 based on the ICA analysis combined with PCA. The extracted glucose and sucrose spectra (‘ICA’ in Fig. 4.6) agree well to the actual pure spectra of aqueous glucose and sucrose (‘Pure’ in Fig. 4.6). Furthermore, a strong correlation between independent components and reference concentrations is shown and the results are given in Fig. 4.7. Although measured sample spectra have baselines as shown in Fig. 4.5, our method can strip baselines and resolve overlapping spectral bands. PLSR has been extensively used in the field of biomedical spectroscopy. ICA, on

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FIGURE 4.6: Extracted pure-component spectra from measured IR spectra of 25 samples. ‘Pure’ and ‘ICA’ represent pure-component absorption spectrum and the ICA-method extracted absorption spectrum, respectively.

the other hand, which has been used in the field of engineering (for example, audio signal processing), is new to biomedical spectroscopy. The main difference is that ICA does not require a reference value. PLSR and other methods require a calibration data set and having a proper calibration set is critical to accurate predictions. The calibration set should comprise the entire set of possible compounds and encompass the results of experiments done under different external conditions. Consequently, the method requires extensive time and expense, especially when used in the clinical setting. PLSR does not assume statistical independency even in cases where statistical independence among the components in the mixture exists. PLSR analysis, in fact, does not rely on the mathematical relation between spectra and concentrations. PLSR, instead, finds the best fit for given spectral data and reference values. For this reason, it is so important for a calibration set to represent the population over the entire range of blood components and conditions that will be encountered experimentally. In terms of prediction accuracy, it is difficult to say which technique is superior, PSLR or ICA. However, it is expected theoretically, that ICA becomes more accurate than PLSR when components in the mixture become more statistically independent since ICA utilizes further information on statistical independence.

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FIGURE 4.7: Scatter plot for the reference concentrations and ICs from measured MIR spectra.

4.5 Conclusion We determined the concentration of blood glucose based on infrared spectroscopy. Two separate experiments were performed, one for the MIR wavelength and the other for the NIR wavelength. For the MIR experiment, we studied a region of 1515– 917 cm−1 (or 6.6–10.6 µ m). We found that the prediction accuracy depending on a wavelength region under statistical analysis. The entire spectral region did not necessarily produce the best results. An optimal band selection based on FLV analysis proved to be 1119–1022 cm−1 for our case. The influence of hemoglobin levels in the samples was examined by using different calibration and prediction sets. The accuracy of glucose prediction depended on hemoglobin distribution in the calibration model. The sample set should represent the entire range of hemoglobin concentration. Experiment was done using 78 blood samples whose glucose concentrations were between 17 and 458 mg/dl. We obtained a SECV of 12.9 mg/dl (5.9% in terms of the coefficient of variation in cross validation) in glucose prediction. For the NIR experiment, the spectra of 98 samples were measured from 1100 to 2400 nm. A concentration distribution of glucose was between 45 and 432 mg/dl. The same analysis protocols were applied both for the selection of an optimal wavelength region and for study of hemoglobin influence. Very similar observations were obtained in the NIR analysis case, too. The best results were achieved when the regions of 1380–1888 and 2044–2392 nm were used. The accuracy of glucose pre-

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diction was a SECV of 25.5 mg/dl (11.2% in terms of the coefficient of variation in cross validation). Prediction of blood glucose using the MIR wavelength region gave much better results (12.9 mg/dl and 5.9%). This seems to be obvious since the MIR contains the fundamental absorption of glucose. However, path length in the MIR wavelength is only a few score of micrometers and this should be considered for applications. A preliminary investigation of using ICA for glucose prediction was done in the MIR region. This method was able to identify pure, or individual, absorption spectra of constituent components from the mixture spectra without a priori knowledge of the mixture. Experiment was performed for a two-component system that consists of aqueous solution of both glucose and sucrose. Their spectra are heavily overlapped. ICA combined with principal component analysis was able to identify a spectrum for each component, the correct number of components and the concentrations of the components in the mixture. This method does not need calibration process and is advantageous in noninvasive glucose monitoring since expensive and time-consuming clinical tests for data calibration are not required. However, whole blood contains a lot more substances than our experimental setup of a simple two-component system. Further studies are necessary.

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References [1] Y.-J. Kim and G. Yoon, “Multicomponent assay for human serum using midinfrared transmission spectroscopy based on component-optimized spectral region selected by a first loading vector analysis in partial least-squares regression,” Appl. Spectr., vol. 56, 2002, pp. 625–632. [2] I. Amato, “Race quickens for non-stick blood monitoring technology,” Science, vol. 258, 1992, pp. 892–893. [3] H.M. Heise, “Non-invasive monitoring of metabolites using near infrared spectroscopy: state of the art,” Horm. Metab. Res., vol. 28, 1996, pp. 527–534. [4] O.S. Khalil, “Spectroscopic and clinical aspects of noninvasive glucose measurements,” Clin. Chem., vol. 45, 1999, pp. 165–177. [5] R. McNichols and G.L. Cot´e, “Optical glucose sensing in biological fluids: an overview, ” J. Biomed. Opt., vol. 5, 2000, pp. 5–16. [6] K.J. Jeon, I. D. Hwang, S. Hahn, and G. Yoon, “Comparison between transmittance and reflectance measurements in glucose determination using near infrared spectroscopy,” J. Biomed. Opt., vol. 11, 2006, 0140221. [7] M. Otto, Chemometrics, WILEY-VCH, Berlin, 1999. [8] H. Martens, T. Nes, Multivariate Calibration, John Wiley & Sons, Chichester, 1989. [9] D.M. Haaland and E.V. Thomas, “Partial least-squares methods for spectral analyses. 1. Relation to other quantitative calibration methods and the extraction of qualitative information,” Anal. Chem. vol. 60, 1988, pp. 1193–1202. [10] Y.-J. Kim, S. Hahn, and G. Yoon, “Determination of glucose in whole blood samples by mid-infrared spectroscopy, ” Appl. Opt., vol. 42, 2003, pp. 745– 749. [11] H. Zeller, P. Novak, and R. Landgraf, “Blood glucose measurement by infrared technology,” Int. J. of Artificial Organs, vol. 12, 1989, pp. 129–135. [12] Y.-J. Kim and G. Yoon, “Prediction of glucose in whole blood by near-infrared spectroscopy: Influence of wavelength region, preprocessing, and hemoglobin concentration,” J. Biomed. Opt., vol. 11, 2006, 041128. [13] A. Hyvarinen, J. Karhunen, and E. Oja, Independent Component Analysis, John Wiley & Sons, 2001. [14] H. Farid and E. H. Adelson, “Separating reflections from images by use of independent component analysis,” J. Opt. Soc. Am. A, vol. 16, 1999, pp. 2136– 2145.

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[15] N. Tsumura, H. Haneishi, and Y. Miyake, “Independent-component analysis of skin color image,” J. Opt. Soc. Am. A, vol. 16, 1999, pp. 2169–2176. [16] L. De Lathauwer, B. De Moor, and J. Vanderwalle, “An introduction to independent component analysis,” J. Chemom., vol. 14, 2000, pp. 123–149. [17] J. Chen and X. Z. Wang, “A new approach to near-infrared spectral data analysis using independent component analysis,” J. Chem. Inf. Comput. Sci., vol. 41, 2001, pp. 992–1001. [18] S. Hahn and G. Yoon, “Identification of pure component spectra by independent component analysis in glucose prediction based on mid-infrared spectroscopy,” Appl. Opt., vol. 45, 2006, pp. 8374–8380.

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5 Near-Infrared Reflection Spectroscopy for Noninvasive Monitoring of Glucose — Established and Novel Strategies for Multivariate Calibration H.Michael Heise ISAS - Institute for Analytical Sciences at the Technical University of Dortmund, Germany Peter Lampen ISAS - Institute for Analytical Sciences at the Technical University of Dortmund, Germany Ralf Marbach VTT Optical Instruments Centre, Oulu, Finland 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Design and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results Obtained by Conventional Calibration and Discussion . . . . . . . . . . . . . Advantages of the “Science-Based” Calibration Method . . . . . . . . . . . . . . . . . . . Theory and Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Specificity of Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Illustration of the Science-Based Calibration Method . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

116 118 124 132 133 136 141 151 152 153

This chapter elucidates the opportunities and pitfalls of multivariate calibrations used for noninvasive blood glucose measurements by near-infrared diffuse reflection spectroscopy. Lip mucosa spectra of a type 1 diabetic patient were obtained with oral glucose tolerance testing and random blood glucose levels including parallel capillary blood glucose measurements. Partial least-squares calibration was based on spectral data between 9000 and 5400 cm−1 without and with additional spectral variable selection. Compared to full spectrum calibration, the latter procedure generally led to improved performance and robustness of the models with underlying physico-

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chemical causality through tissue glucose induced absorption changes. Different validation methods were applied to test for possible model overfitting. In addition, a new method of multivariate calibration is introduced, for which the name “science based calibration” was coined by a community of early users from the pharmaceutical industry. Both the procedure and the advantages of the method will be discussed. The in vitro clinical chemistry application example illustrates the usefulness of the novel multivariate calibration technique for estimating key performance parameters of multivariate spectrometric assays in biomedical and pharmaceutical science. Key words: noninvasive blood glucose assay, in vivo near-infrared spectroscopy, diffuse reflection technique, multivariate statistical calibration, science based calibration.

5.1 Introduction Noninvasive blood glucose assays have been promised for many years and nearinfrared (NIR) spectroscopy of the skin seemed to be a good candidate for achieving such a goal. The first part of this chapter describes possible pitfalls and desirable best practices when performing “statistical” calibrations based on skin spectra and simultaneously recorded blood glucose reference concentration data, e.g., using partial least squares (PLS) or principal component regression (PCR). The second part will introduce novel strategies for multivariate calibration, for which the name “science based calibration” was coined and advantages will be elucidated in detail. More information on the mathematics of statistical calibrations is provided in that part. Measurements of blood glucose and its regulation are necessary for patients with disorders of their carbohydrate metabolism, particularly caused by diabetes mellitus. The results from intensive studies within the Diabetes Control and Complications Trial [1] or the UK Prospective Diabetes Study [2] recommended treatment programs for either type 1 or type 2 diabetic patients, which require frequent testing of blood glucose to achieve regulated glucose levels close to euglycemia. Selfmonitoring of the blood glucose concentration is part of the daily routine for such patients, for which an invasive methodology is still required [3]. Noninvasive spectroscopic methods have been proposed, which are based on specific optical characteristics of glucose, for example, wavelength dependent absorptivities and refractive indices preferably in the near-infrared (NIR) [4]. The early successful implementation of NIR spectroscopic glucose assays using serum or blood plasma samples, e.g., [5, 6], raised hope that a noninvasive assay based on transcutaneous spectrometric measurements may be realized for the diabetic patient community. Furthermore, many activities can still be noted for improving statistical calibrations models with regard to selectivity and robustness [7 - 9]. An important issue has always been the determination of the most useful spectral range within the wide near-infrared spectral region

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[4]. Scattering and absorption effects in the glucose assay for whole blood using the combination, first-overtone and short-wavelength region were recently studied [10]. The outcome was that combination and overtone regions can be favored in contrast to results achieved using data from the short-wavelength region. After our first paper on transcutaneous diffuse reflection near-infrared spectroscopy of the lip [11] used for calibration modeling with regard to a noninvasive blood glucose assay, several other groups published their results. However, some of these must be questioned because the calibration models used were very likely not based on glucose absorption but rather on accidental correlations. The literature on multivariate analyses in general is full of improperly validated calibration models, and, unfortunately, the area of noninvasive blood glucose assays can not be excluded from this statement, e.g., [12, 13]. Several times, pitfalls in multivariate statistical calibrations have been described and guidelines for acceptable strategies have been suggested [14, 15]. There have been different skin tissue areas favored, for example, forearm skin or tongue, but our group has focused on criteria such as the blood volume inside the skin tissue probed by diffuse reflectance spectroscopy [16]. Our strategy allowed us to probe the highly vascularized dermis section of the lip, utilizing a broad spectral range between 9000 and 5400 cm−1 , which is advantageous for achieving the required selectivity with respect to the tissue glucose monosaccharide. This extended range is reasonable, because the diffuse reflectance measurement technique provides, in contrast to a transmission measurement with a constant tissue layer, a larger pathlength for spectral regions of lower absorptivities at shorter wavelengths. In other words, the attenuation of the probing radiation is increased at the shorter wavelengths, allowing us to exploit the spectral information in this region. Other successful applications of near-infrared spectroscopy must be mentioned, i.e., the work by Olesberg and coworkers using a rat animal model and transmission measurements through a skin fold [17] and recent publications from the group around K. Maruo in Japan using a fiber-optic probe for diffuse reflection measurements in human subjects [18, 19]. The aim of this chapter is to elucidate the pitfalls of statistical calibrations used for transcutaneous blood glucose measurements by near-infrared diffuse reflection spectroscopy. PLS calibration with and without additional wavelength selection was considered. The selection procedure, when compared to full spectrum “statistical” calibration, generally led to improved performance and robustness of the calibration models with underlying physico-chemical causality through tissue glucose induced absorption changes in the lip spectra. For validation, different methods such as crossvalidation, leave-out one and ten samples, as well as using day-to-day testing were applied to test for possible overfitting with too many spectral data points. Problems of overfitting and how to avoid those have been recently addressed again by Faber and Raik´o [20]. Statisticians have pointed out that leave-one-out cross-validation is a poor candidate for estimating the prediction error of multivariate calibration models, since it often causes overfitting and gives an overly optimistic estimate of the true prediction error; see also literature in Ref. [21]. Important issues in statistical calibrations, as used for noninvasive blood glucose

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calibration, are the selection of wavelengths containing significant information with respect to the compound to be analyzed and the validation of the calibration model. It can be shown experimentally that the parsimony principle for achieving robust calibration models becomes relevant [22]. Considerable effort has been directed towards developing and evaluating different methods to find useful spectral variables or to eliminate noisy ones; see, for example, [23-25]. The measurements presented here were carried out within an older feasibility study, and a detailed description of previous results can be found in earlier publications [11, 26], but the data are still well suited to deriving further insights into the calibration strategy and problems involved. Compared to our earlier PLS calibration studies, more rigorous testing strategies than cross-validation have been applied, using validation of daily sub-sets. Besides evaluating the effect from a different number of wavelengths, which can drastically change the degree of overdeterminedness of the calibration linear equation system, the size of the calibration population was also reduced by considering a correspondingly larger number of sample standards for independent validation. Differences in the blood glucose time profiles are essential for validation of models aimed at continuous glucose monitoring. With calibration data from quasi-continuous recordings, as obtained by glucose tolerance testing, leave-one-day-out testing based on different blood glucose concentration profiles could verify useful calibration models, although with a loss of prediction ability due to off-set effects compared to results from leaveone-out cross-validation. Under the scheme of quasi-continuous calibration measurements, additional regression calculations were carried out here. First, actual (“real”) lip spectra were calibrated against arbitrary glucose concentration time profiles. Second, “real” glucose time profiles were calibrated against spectral noise, which was obtained from the SpectralonTM reference spectra. Both cases resulted in poor prediction results when challenged by day-to-day testing. This is even more obvious when using parsimonious models employing fewer spectral variables. A drastic deterioration in the prediction ability indicates lack of physico-chemical causality.

5.2 Experimental Design and Methods 5.2.1 Patients and calibration design The experiments reported were in accord with the ethical standards for human experimentation and with the informed consent of the subject. Two sets of spectra of lip mucosa of a type 1 diabetic patient were obtained, first, with oral glucose tolerance testing over two days and, second, with random blood glucose levels over two weeks. Parallel measurements on the capillary blood glucose concentration were carried out using the hexokinase/G6P-DH method. Further details on the two-day trial are presented as follows. The oral-glucose tolerance test (OGTT) of the first day was started at 11:15 a.m. at a low blood glucose

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concentration, and after 20 min Dextro O.G.T. (Boehringer Mannheim, Germany), providing a glucose dose of 50 g after enzymatic cleavage, was ingested raising the blood glucose level within 90 minutes. Additional carbohydrates were consumed, so that blood glucose reached a maximum. Insulin was administered, resulting in the glucose concentration dropping to low values within a further 90 min. The second day test began at 9:15 a.m. with a slightly increased blood glucose concentration above normal fasting level. After a lapse of 90 min, the equivalent glucose dose of 50 g was ingested as potion. The differences in the temporal blood glucose profiles of both days are pointed out. Total time duration for the OGTT-experiments was 15 hours gathering a total of 133 lip spectra. The reference concentrations within the two-day experiment were uniformly distributed between 1.7 mmol/L (30 mg/dL) and 33.3 mmol/L (600 mg/dL) (population average cav = 16.7 mmol/L (301 mg/dL), and standard deviation SD = 9.3 mmol/L (168 mg/dL)). The second series with testing at randomized glucose levels was carried out over a period of two weeks. Three different sessions were measured each day with target glucose levels randomly assigned as low, medium, or high. Each measurement session lasted about 40 minutes and consisted of three blood samplings with three repeat lip spectra recorded in between two subsequent blood tests, with additional spectra taken before and after the blood collection procedure giving eight spectra in total with repositioning of the diffuse reflectance device onto the lip mucosa. The glucose concentrations, as determined by the reference method in duplicate, were used for interpolation to yield the actual glucose values at the time a spectrum was recorded. The range of all concentration values obtained for this calibration experiment with 219 lip spectra was the same as for the two-day data set (cav = 14.9 mmol/L (269 mg/dL), standard deviation SD = 9.0 mmol/L (162 mg/dL)).

5.2.2 Reference measurements and calibration method Reference blood glucose concentration values were obtained by standard enzymatic methodology (test combination Glucoquant Glucose from Boehringer Mannheim, Germany) with the use of hexokinase/G6P-DH available on an ACP 5040 analyzer from Eppendorf (Hamburg, Germany). The capillary blood samples were taken with 20 µ L capillary pipettes from Brand (Wertheim, Germany) after finger pricking. As the timing of the reference blood sampling did not coincide with those of the spectrum recording, and the time gap between each reference measurement was about 15 min, spline approximations between reference concentrations were calculated by fitting a cubic spline function. Multivariate calibration using logarithmized single beam spectra (absorbance equivalent) of the inner lip was carried out using a PLS software package programmed by ourselves in MATLAB (The Mathworks, South Natick, MA, USA). Apart from full spectrum interval regression, also a special wavelength selection procedure was chosen, which renders improved and more robust statistical models. The selection was done stepwise using pairs of selected individual wavelengths, as suggested by the decreasing weights of the minima and maxima of the optimum PLS regression vector, calculated from all data points within a broad spectral interval provided by a priori

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knowledge of glucose and water absorption bands [24]. With ill-conditioned linear equation systems, the validation of calibration models, i.e., the testing of their prediction performance, is of most importance. For such calibrations the standard error of calibration (SEC) is not an appropriate statistic [27], although with well-conditioned, largely overdetermined linear equation systems, the differences shrink between SEC results and corresponding results obtained from testing with calibration-independent samples. The calibration data are usually split into calibration and validation sub-sets, which is a reasonable strategy when (a) a large number of standards is available or (b) the composition complexity of the calibration samples is low and the spectral quality is high, i.e., high signal-to-noise ratio, fine baseline stability, adequate photometric accuracy and absence of signal non-linearities. With a limited number of standards under more adverse conditions, cross-validation with “leave-one-out” strategy is used. For this, one standard is removed from the calibration set, a regression is calculated and the concentration is predicted using the calibration model for that single standard. These steps are repeated until all standards are considered. The root mean-squared error of prediction (RMSEP = Σ(cref,i − cpred,i )2 /M 1/2 with M samples), which is also called standard error of prediction (SEP), is a suitable statistic for optimum calibration model selection with stepwise increased number of PLS factors. It is also called ‘standard error of cross-validation’ (SECV) by several authors. Furthermore, groups of several standards — in this study we used packets of 10 or data from whole days — can be tested for independent prediction. These cases also reduce the size of the calibration population, thereby further challenging the calibration robustness.

5.2.3 Experiments and spectroscopic data Using spectrometry within the so-called therapeutic window with wavelengths between 600 nm and 1300 nm (equivalent to 16,600 cm−1 and 7700 cm−1 ), transmission measurements are feasible, for example, of a finger tip. For longer wavelengths, such NIR-measurements give extremely low transmission values, but experiments using diffuse reflection (DR) of skin can be realized. In Fig. 5.1 experimentally derived optical constants from the upper skin layers are shown, i.e., absorption and scattering coefficients; the inset in panel B shows also the anisotropy factor g, which describes the mainly forward scattering characteristics of NIR photons. The optical constants were compiled from three publications [28-30]. As the NIR-spectrometric assay mainly relies on the absorption effects of glucose inside the aqueous intravascular and interstitial compartments in the skin tissue, glucose absorptivities from aqueous solution are presented in Fig. 5.2. Some data are taken from Ref. [31]. Other measurements were carried out within our laboratory. Interestingly, the spectral features of glassy sugars, as obtained from syrup samples after careful water evaporation, show the same wavelength dependencies as the aqueous phase spectra. However, the otherwise opaque spectral intervals with strong water absorption can now be derived, despite some still existing uncompensated water absorptions in the regions of the water band maxima. Shown are the spectra of glucose and fructose, which are both relevant for the noninvasive measurement. Best discrimi-

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FIGURE 5.1: Optical constants of dermis and epidermis in the visible and NIR spectral range including standard deviation confidence bands (µa absorption coefficient, µs′ reduced scattering coefficient with µs′ = (1 − g)µs , which is a property incorporating the scattering coefficient µs and the anisotropy g; all data were from Refs. [28-30]; for the skin data, measurements were from integral tissue consisting of stratum corneum, epidermis and dermis [28]; note the significant differences in the scattering coefficients for the VIS/NIR (besides the wavelength scale also wavenumbers have been provided on top).

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FIGURE 5.2: Absorptivities of glucose and fructose obtained from the measurement of an aqueous solution and of glassy monosaccharides from syrup after water evaporation (scaled to the aqueous phase absorptivities); part interval data are taken from Amerov and coworkers [31] (dashed curves).

nation between both monosaccharides can be obtained by using spectral data from the combination band region. Shorter wavelength absorptivities will result in severe cross-sensitivity between both sugars. Further insight into possible complications from components administered (hydroxyl ethyl starch (HES) solutions have been used as blood plasma expander after severe blood losses) or through alcoholization with similar spectral features as glucose is provided by Fig. 5.3. The design of the reflection-accessory is based on an on-axis ellipsoidal mirror collecting the diffusely reflected radiation from the lip tissue in a much more efficient manner than is possible using commercially available accessories [32]. Emphasis had been placed on the measurement of skin tissue with a minimum of inconvenience for patients while achieving highest possible signal/noise ratios and spectral reproducibility for the tissue studied. As temperature is a critical parameter when measuring biosamples due to the sensitive temperature dependency of the water spectrum, means for thermostating the contact material of the accessory at 37 ˚ C were provided. Prior to the spectral lip measurements, the patient was asked to rinse his mouth with mineral water. The lip spectra were recorded by placing the inner lip against the immersion lens of the reflection-accessory. Measurement time was about 1 minute to accumulate 1200 single sided interferograms equivalent to a spectral resolution of 32 cm−1 after Fourier transformation. For calculating reflectance spectra (R = Is /I0 with Is and I0 the single beam spectra of the sample and the reflectance standard, respectively) it was necessary to record reference spectra by means of stan-

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FIGURE 5.3: (A) Absorbance NIR spectra of monosaccharides (glucose, fructose and galactose) in aqueous solution (83 mmol/L (1.5 %), 0.5 mm optical pathlength, with water absorbance compensation); (B) Absorbance spectra of an aqueous hydroxyethyl starch solution (10 %), of glucose (278 mmol/L or 5 %) and of ethanol (325 mmol/L or 1.5 %) with water absorbance compensation (10 mm optical pathlength); for clarity, spectra have been offset (reproduced from Ref. [14] with permission of Wiley-VCH).

dards of different reflectivity made from Spectralon (Labsphere, North Sutton, NH, U.S.A.). For details, see also Fig. 5.4A for single beam spectra of lip tissue and gray Spectralon, and panel B for an exemplary lip spectrum and the noise level in absorbance equivalent units. An offset was applied to the lip spectrum to compensate for the fact that the gray standard had only 10% reflectance; the enlarged noise spectrum was obtained from two consecutive lip measurements. The noise level in √ the logarithmized single beam spectra is by a factor of 2 smaller than the noise in the absorbance spectra.

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FIGURE 5.4: (A) Diffuse reflection NIR spectra of inner lip mucosa and of a gray Spectralon reflectance standard of about 10% reflectivity (single beam spectra as measured by a Fourier Transform spectrometer showing the spectral radiation intensities); (B) Absorbance equivalent spectrum calculated from the spectra above (an offset was applied to correct for the effect of referencing against a gray Spectralon standard); in addition, an enlarged noise spectrum from two consecutive lip measurements is shown (in absorbance units).

5.3 Results Obtained by Conventional Calibration and Discussion The quantification of glucose in complex multi-component systems requires a unique absorption pattern and a significant contribution to the spectrum from this component above the existing spectral noise level. In Figs. 5.2 and 5.3 absorbance spectra of glucose in aqueous solution are shown. These spectra were obtained with

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scaled water absorbance subtraction. There is an incomplete compensation due to the disturbance of the water hydrogen bonding network by the sugar molecules which is shown by the dips in the spectra. The smaller absorptivities at the shorter wavelengths are shown enlarged in Fig. 5.3B, and were obtained with 10 mm optical pathlength. Another deficit of the short-wave NIR is that the absorption bands become more featureless compared to the regions around 6000 cm−1 or even above 4000 cm−1 , where a discrimination of different monosaccharides is possible due to spectral differences (see Fig. 5.3A). For comparison, the spectra of some other compounds with importance to noninvasive glucose measurements are also presented in Fig. 5.3B. To analyze data from radiation with sufficient skin penetration, our calibrations were limited to the wavenumber range of 9000–5400 cm−1 , which still affords significant glucose absorption signatures. The mean optical pathlength for radiation within mucosa tissue, as given for our diffuse reflection accessory, is wavenumber dependent. By comparison with absorbance spectra of liquid water, as measured in cells of different optical pathlengths [33], an estimate of transmission equivalent sample thicknesses can be obtained. Results from Monte-Carlo simulations of radiation transport [32], as well as from experimental evidence on optical pathlengths within tissue, were previously presented [33]. In Table 5.1 results from different calibration models are displayed, where we constrain ourselves to two different scenarios: One is the use of 115 spectral data points resulting from the 32 cm−1 resolution spectrum (one outlier sample was removed due to its high leverage value), whereas a second set of calculations was performed with a reduced number of wavelengths from the spectral interval given above (two further outliers removed due to large studentized residues). The number of wavelengths optimally required for calibration is still a subject of intense debate. In fact, once the analyst uses as many variables as there are independent spectral constituents with overlapping spectral features, the addition of further wavelengths should serve to reduce the effects from noise. On the other hand, as more wavelengths are used, the probability of encountering additional spectral interferences increases with the result of degrading the accuracy of the concentration prediction. Another problem often faced is the existence of spectral collinearity, which is defined as approximate linear dependencies among the spectral variables, rendering ill-conditioned linear equation systems, so that biased estimators, e.g., based on PLS, are needed. Table 5.1 provides statistics for sensing the influence of the calibration population size and the number of standards used for independent validation. The wavelengths derived from our variable selection scheme based on extreme values of the full spectral range PLS regression vector provide an optimized set of reduced variables. These wavelengths were kept fixed for all further calculations, when utilizing different validation strategies within the respective two-day and 2-week experiments. The validity of the spectral wavelength selection procedure was also tested for NIR-transmission spectra of blood plasma samples from a hospital population [34]. This in vitro data set will also be used for demonstration of the novel calibration algorithm below. A discussion of the PLS-regression vector shape obtained for such in vitro samples with that obtained for noninvasive blood glucose monitoring was

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TABLE 5.1: Standard errors of noninvasive blood glucose concentration prediction (SEP) for different PLS calibration models using NIR-spectra of a single patient’s inner lip from the two-day tests (SDP standard deviation of the reference values within the prediction set) Spectrum/reference value

Packet size for crossvalidation lip series / glucose 1 lip series / glucose 10 lip series / glucose 1st day lip series / glucose 2nd day lip series / spectrum 1

1st 1st 1st 1st 1st no. 1st lip series / spectrum no. 1st lip series / spectrum no. 1st lip series / spectrum no. Spectralon10% / glucose Spectralon10% / glucose Spectralon10% / glucose Spectralon10% / glucose

SEP [mg/dL]a, 115 data points 45.6 (20) 51.2 (20) 88.5 (20) 185.5 (20) 7.1 (21)

SEP [mg/dL]a, 24 data points 36.6 (17) 40.4 (17) 82.8 (17) 56.9 (17) 9.6 (18)

SDP [mg/dL]

10

8.2 (21)

12.7 (18)

38.2

1st day

187.0 (21)

189.1 (18)

16.6

2nd day

35.3 (21)

83.0 (18)

21.8

1 10 1st day 2nd day

75.0 (13) 115.2 (16) 694.0 (13) 171.3 (13)

97.9 (13) 146.6 (14) 926.3 (13) 527.7 (13)

167.9 167.9 123.5 179.6

167.9 167.9 123.5 179.6 38.2

a

The numbers in parentheses refer to the number of PLS-factors used for the optimum calibration model; for regressions with spectrum numbers, the given figures are dimensionless. To convert the concentration values given to mmol/L, divide these by 18. The spectral range used for PLS-regression with equally spaced data points was between 9000 and 5400 cm−1 ; for the reduced sets the wavelengths of the data points were selected from the same interval. For day-to-day testing, the calibration models were calculated from the data of one day, applied for validation to those of the other day and crosswise.

recently given [35]. For the in vivo studies, it can be stated that the reliability of calibration models improves with a reduced number of spectral wavelengths under these measurement conditions (see also Table 5.1). In Figure 5.5 the results from two different validation procedures are shown. For part A, cross-validation with leave-one-out was chosen, where the optimum SEP of 2.0 mmol/L (36.6 mg/dL, see also Table 5.1 first line) is equivalent to a mean absolute error of 1.7 mmol/L (30.0 mg/dL), which gives smaller values than the corresponding SEP values). For part B, a validation of models calculated from the data of one day is shown, whereby those of the other day were used for independent prediction

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FIGURE 5.5: Comparison of time dependent capillary blood glucose concentration values (solid curves) and prediction results based on PLS-calibration (circles and asterisks) using diffuse reflectance lip spectra in experiments with a type 1 diabetic subject: (A) Results with 24 spectral data points and leave-one-out cross-validation (the time gap between the two daily profiles is deliberately reduced for better presentation); (B) Predictions within one day are from calibration models using the same 24 spectral data points as above, but calculated separately from the data of the other day with crosswise repeated procedure; reproduced from Ref. [14] with permission of Wiley-VCH.

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and again crosswise (SEP-values are provided in Table 5.1, lines 3 and 4). We see, for example, that an offset of -1.8 mmol/L (33.0 mg/dL) could be applied to the prediction data of the second day which would improve the SEP down to 2.6 mmol/L (46.4 mg/dL) instead of 3.2 mmol/L (56.9 mg/dL). We argue that this can be traced back in part to a difference of glucose concentrations within the intravascular and the interstitial tissue compartments, which is affected by dynamic exchange processes. It can be made plausible that the integral tissue glucose concentration at the beginning of the second day OGTT was slightly larger than that found for capillary blood. An opposite offset and a slope is evident for the results of the first day (see part of the temporal glucose profile with increasing concentrations). In this case, the calibration model used for prediction is mainly based on data from an experimental phase with an increasing blood glucose concentration (see second-day data). The slope of the temporal glucose profile in the beginning of the first day is even steeper than that of the corresponding second day phase, which results in a greater gap between the intravascular glucose level and mean tissue concentration. This leads to an underestimate of the blood glucose concentration when using the calibration model derived from data of the second OGTT. The opposite effect can be explained when the predictions for the descending wing of the first day profile are inspected where the blood glucose profile is running ahead to that of the delayed tissue level (see also the similar results from our previous modeling of tissue glucose [26], using capillary blood glucose concentration values and a profile delay through glucose diffusion between the intravascular space and residual aqueous tissue compartments). Since integral tissue glucose is probed spectroscopically and reference values rely on blood analysis, transport processes between the vascular and interstitial space certainly need to be considered, resulting in a temporal shift between the respective glucose concentration profiles of blood and tissue, see also Ref. [36]. Offset effects in concentration prediction were also obtained by Arnold and coworkers [6] when they used their in vitro serum NIR calibration model on a set of serum spectra recorded several months later, which is explainable by a sample or instrument response change over time. It must be noted that the offset was obtained for an experiment where random sampling was incorporated, thereby diminishing the possibility of chance correlations. An explanation could be slight localized changes in baseline, leading to such offsets for concentration prediction: We recall that the estimate for the sample to be analyzed is calculated from the scalar product of a mean-centered spectrum and the regression vector with positive and negative coefficients oscillating around zero. Similar effects can also be expected for the noninvasive measurements. An important question arose, whether the data from the two weeks testing could be used to predict the blood glucose concentration profiles of the OGTT experiments carried out five months earlier, using the corresponding lip spectra (see Figure 5.6; SEP = 136.7 mg/dL (SD = 123.5 mg/dL) for 32 variables and first day spectral data; SEP = 78.8 mg/dL (SD = 179.6 mg/dL) for second day spectral data). However, we had changed the spectroscopic conditions, because a larger FTIR-spectrometer aperture size for illuminating the skin tissue had been used in the two week trial compared to the two-day experiments, so we used series-mean centered spectra for model building and prediction. The scatter for the predicted concentration values

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FIGURE 5.6: Predictions of blood glucose concentrations using NIR-lip spectra from the two-day OGTT experiment and a calibration model calculated from data obtained during a two-week period after 5 months with 32 selected spectral data points (due to changes in the spectral measurement, population mean-centered data were employed for calibration and prediction).

is unacceptably large, but the overall shape of the blood glucose profiles can be reproduced apart from an offset for the data of the first day. Two further scenarios are presented, illustrating the problems with statistical calibrations: for one set of calculations we changed the blood glucose profile deliberately by assigning to each consecutively recorded spectrum its number in the sample population rather than the “real” reference glucose value. Results are provided for cross-validation leaving either one sample or data of a whole day out (see Fig. 5.7). A second worryingly impressive set used the blood glucose concentration profile in combination with the Spectralon reference spectra (see Fig. 5.8) which can give some insight into spectrometer drifting over the measurement campaign. With fictitious concentration profiles provided we see a deterioration of the prediction performance when the number of spectral data points is reduced by about a factor of four. The opposite result was obtained for our measured calibration data, i.e., lip spectra with corresponding blood glucose values. In this context it is again interesting to compare the structure of the regression vectors from noninvasive studies with that from blood plasma calibrations; their similarity was presented elsewhere [35]. With our study data from previous measurement campaigns with a diabetic test person, the problems of method validation have been illustrated. As shown above, calibration and validation design are essential for judging the general applicabil-

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FIGURE 5.7: Comparison of mischievously constructed data points (sample numbers are displayed by the solid curves) and their prediction results based on PLScalibration (circles and asterisks) using diffuse reflection lip spectra in experiments with a type 1 diabetic subject: (A) Results with 115 spectral data points and leaveone-out cross-validation; (B) Predictions within one day are from calibration models using the same data points as above, but calculated separately from data of the other day; reproduced from Ref. [14] with permission of Wiley-VCH.

ity of the calibration models presented. Therefore, many of the published papers on noninvasive blood glucose assays should be revisited by applying stricter rules for validation. Such rules, for example, were not taken into account in a recent paper from Gabriely et al. [13], giving the impression that mean absolute prediction errors for blood glucose concentration between 0.14 mmol/L and 0.24 mmol/L (2.6 mg/dL and 4.4 mg/dL) were possible. We commented on these results already in a recent letter [37]. These values were calculated for estimates obtained within the calibration, selecting segments with changes in blood glucose concentration of

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FIGURE 5.8: Comparison of time dependent capillary blood glucose concentration values (solid curves) and prediction results based on PLS-calibration (circles and asterisks) using diffuse reflectance reference spectra from gray Spectralon (free of glucose information) in experiments with a type 1 diabetic subject: (A) Results with 115 spectral data points and leave-one-out cross-validation (see also Fig. 5.5); (B) Predictions within one day are from calibration models using the same 115 spectral data points as above, but calculated separately from the data of the other day; reproduced from Ref. [14] with permission of Wiley-VCH.

0.56 mmol/L (10 mg/dL). For one of their experiments as shown in their Fig. 5.2, we calculated a mean concentration of cav = 4.2 mmol/L (76 mg/dL) and a standard deviation of SD = 0.94 mmol/L (17 mg/dL) for the blood glucose concentrations. It is well known that the standard error of the calibration (SEC), based on ill-conditioned linear equation systems with many variables, can be much lower than the leaveone-out cross-validated SEP values (for our first series with lip spectra and blood glucose concentration profiles, the SEC value for the calibration models calculated from 115 spectral data points was 1.74 mmol/L (31.4 mg/dL) (SEP = 2.53 mmol/L

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(45.6 mg/dL)), whereas for models based on 24 wavelengths the discrepancy is much smaller (SEC = 1.93 mmol/L (34.8 mg/dL), SEP = 2.03 mmol/L (36.6 mg/dL)). The number of test measurements depends on the calibration strategy: our recommendation is to have overdetermined linear equation systems for calibration, especially, when this is ill-conditioned. Thus, the number of calibration samples must exceed the number of spectral variables, underlying the spectral range selected for regression analysis. Another important aspect is the selectivity of the spectral range for glucose prediction, which needs investigation, but with heavy cross-talk of glucose absorptivities to other components’ spectral features, the implementation of standards from a large calibration population allows more accurate, less noisy estimates of the regression vector and/or factor spectra. As shown here, there are cases where a spectroscopic discrimination between two components will fail: an example are the monosaccharides glucose and fructose in aqueous solution. Spectroscopic expertise is needed to judge the spectral calibration data with respect to the rather minor contributions of the analyte. Other factors, mainly from water and its temperature dependency, will usually dominate the spectra. Therefore, we carried out a principal component analysis of our spectral calibration data [35, 36], which supported the need of a relatively large number of factors for calibration modeling. Shortage of data is always a poor basis for testing the applicability of calibration models. On the other hand, we discuss a validation strategy with a minimum of expenditure to prove the feasibility of a concept statistically. With in vivo spectroscopy, however, the variability by physiological factors, repositioning problems, etc., need to be investigated before calibration robustness can generally be proven (avoiding systematic errors). Validation testing of such sensitive in vivo calibration models requires much effort with clinical support to confirm the applicability under everyday life conditions of the patient, possibly with needs for recalibration. Further problems, e.g., from glycated proteins, blood volume changes, etc., were discussed recently [36]. With integral tissue monitoring, the different tissue compartments, i.e., the intravascular, the interstitial and the intracellular glucose space, need to be taken into account for calibration fine tuning and validation. While the temporal relationship of blood glucose profiles from the first two compartments has been investigated intensively using various invasive probes, the intracellular space has so far been paid no attention. These topics may give an impression of the complexity we have to face in noninvasive blood glucose monitoring.

5.4 Advantages of the “Science-Based” Calibration Method This Section now will introduce a relatively new method of multivariate calibration, for which the name “science-based calibration” (SBC) was coined by a community of early users from the pharmaceutical industry. Both the procedure and the advantages of the method will be discussed. The SBC method has been described

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in detail elsewhere [38-40]. The approach eliminates most of the problems currently associated with the task of multivariate calibration. This is achieved by combining the best features of the two prior approaches, viz. so-called “classical” or “physical” calibration (spectral fitting) and so-called “inverse” or “statistical” calibration (e.g., PLS or PCR). By estimating the spectral signal in the physical way and the spectral noise in the statistical way, the prediction accuracy of the inverse model can be combined with the low cost and ease of interpretability of the classical model. The cost of calibration is significantly reduced compared to today’s standard practice of PLS or PCR. The need to intentionally introduce sample variation for the purpose of generating “calibration standards” is eliminated. The hitherto rather elusive property of specificity of response can now be proven from spectroscopic first-principles, i.e., without the need for a reference method. All of these advantages stem from the fact that the calibration becomes science-based and fully transparent to the user. Today’s standard approach for calibrating noninvasive blood glucose data is the so-called statistical modelling approach, with most users preferring the PLS algorithm. Disadvantages of “statistical modelling” include (a) the cost and difficulty of obtaining calibration standards with widely varying glucose concentrations; (b) the inability to guarantee or prove specificity of response; and (c) the high cost and risk associated with R&D efforts trying to develop new optical measurement methods/instruments. The last disadvantage comes into being because the hardware specifications required for a new instrumental approach can not be derived in advance. Instead, a series of expensive, “statistical” calibration experiments has to be performed at the end of the development process. SBC eliminates all of these disadvantages. The result is science-based and optimal in the mean-square prediction error sense. In other words, measurement accuracy is as good as or better than the results from costly statistical calibration. The organization of this Section is as follows. First, we shortly introduce the theory behind the SBC method. Second, we describe how SBC notation can be used to define, in exact mathematical terms, the concept of “specificity” also known as “selectivity” in the multivariate case; and why this definition is relevant to all multivariate calibrations (SBC or other). Third, we present an example where the SBC method is applied to an in vitro glucose measurement, viz., NIR spectra of blood plasma samples. And finally, we comment on how the SBC method could in the future also be applied to the noninvasive case of blood sugar monitoring.

5.5 Theory and Background For explanatory purposes, it is helpful to assign exemplary physical units to the quantities involved. In the following, we assume that near-infrared (NIR) absorbance spectra are used to determine the glucose concentration; and that the spectra are measured in “absorbance units” [AU] and the glucose concentration is measured in

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units of [mg/dL]. Imagine that all spectroscopic details of the measurement situation were known. Then, we could write the measured spectrum as xT (t) = y(t) · gT + c1 (t) · kT1 + c2 (t) · kT2 + . . . + iTbaseline (t) + . . . + iTnoise (t),

(5.1)

where vector xT (t) is the measured spectrum (in absorbance units [AU], in our example). The spectrum and its various components are a function of time, t. Scalar y(t) is the true (and sought-after) concentration of glucose at time t (in units of [mg/dL] in our example); gT is the so-called glucose “response spectrum” [AU/(mg/dL)]; the c1 (t), c2 (t), etc. and kT1 , kT2 , etc. are the concentrations and response spectra of all the interfering components (water, proteins, triglycerides, etc.); and the iTbaseline (t), . . . , iTnoise (t) are all the spectral effects generated by the instrument and its sampling interface, including the hardware noise floor, baseline offsets, baseline slopes (scatter changes), wavelength axis shifts, and whatever else may be occurring. The transpose sign, T , in the equation above merely means that the spectra are written as row vectors, not column vectors. For example, gT is a row vector whereas g is a column vector. To fully understand the SBC method, three insights are necessary; i.e., three distinct “break-aways” from the traditional framework of thinking are required. The first is as follows: For the purpose of calibration, it is not necessary to describe the “other” effects (other than glucose) in detail. Rather, the correct approach is to summarize all the “other” effects into one term, and write xT (t) = y(t) · gT + xTn (t)

(5.2)

where xTn (t) is everything in the measured spectrum that is not from the glucose component, including instrumental effects and interfering spectra. The first term, y(t)·gT (and associated terms), will be referred to below as “spectral signal”; whereas the second term, xTn (and associated terms), will be referred to as “spectral noise.” The key to the applicability of the SBC method is knowledge of the shape of the response spectrum of the analyte of interest, gT . In the case of a noninvasive glucose measurement, this requires knowledge not only about the absorption coefficient spectrum of glucose but also about the wavelength-dependent “effective pathlength” probed in the skin using a given diffuse-reflection geometry. Once the application-specific shape of gT is determined, however, it turns out that the rest of the SBC procedure is simple. All we need to do is to describe the spectral signal and noise by their first- and second-order statistics [38]. The spectral signal is described by a mean, y¯ · gT , and a root-mean-square (RMS), σy · gT . For example, in the case of a type-I diabetic patient the standard deviation σy of the true blood glucose concentration y(t) can typically be as large as about 90 mg/dL. The spectral noise is described by a mean x¯ Tn and a covariance matrix Σ. The latter describes the (multidimensional) variation in the spectra that occurs independently of the glucose, i.e., the variation from the interferents and the various instrumental effects. In the case of the noninvasive glucose measurement, the spectral noise Σ could relatively cheaply be determined by measuring spectra from, say, one thousand healthy people

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(with near-constant glucose concentration). Writing these spectra into one matrix X, the covariance matrix Σ can be determined as Σ∼ =

˜ TX ˜ X 1000 − 1

[AU2 ],

(5.3)

where the “∼” tilde indicates that the matrix is mean-centered. Note: if the spectra ˜ has a dimension of 1000 rows x contain, say, 64 wavelengths, then the matrix X 64 columns, and the matrix Σ has a dimension of 64 x 64. In this way, “patientto-patient” noise would be included in the noise estimate, which may be a fairly good estimate for the worst-case, long-term variation in blood chemistry within a single patient. If a “patient-specific” estimate were desired, then spectra from a single person could be collected over a period of time and used to estimate the noise covariance. Similar statements also hold for instrument-to-instrument “noise.” In the author’s experience, estimation of Σ is usually a combination of experiment and theory, i.e., a combination of measuring representative “noise” spectra and describing some components of the noise “manually” from technical expertise and application knowledge. The important point of this discussion is this: Determination of Σ is virtually always relatively cheap, because reference values of the glucose concentration are not necessary. Also, should there be some variation of glucose concentration present in the spectra measured for estimating Σ, then the method still works, see details below. Using the notation introduced above, the optimum regression vector (also known as “b-vector”) for glucose measurement can be shown to be bopt(1) =

Σ−1 g , Σ−1 g

(5.4)

gT

where Σ−1 is the inverse of Σ. Equation (5.4) provides the minimum mean-square “prediction” error under the condition of unity prediction slope (indicated in the subscript), which is necessary for measurement purposes [40]. When bopt(1) is used to “predict” the concentration of a newly measured spectrum xTpred , y pred = y¯ + (x pred − x¯ )T · bopt(1)

[mg/dL],

(5.5)

where y¯ and x¯ T are the mean glucose concentration and mean spectrum of the “noise” spectra that were used for estimating Σ, then the RMS prediction error, also known as standard deviation of y pred − y, can be shown to be: SEPopt =

s

1 gT · Σ−1 · g

[mg/dL].

(5.6)

No other b-vector can measure with a smaller SEP. In other words, Eq. (5.6) is the multivariate limit of detection or, as called here, limit of sensitivity when measuring that signal g in that noise Σ. It can be shown [38] that the familiar SEP result of a PLS or PCR calibration tries to converge with increasing number of calibration standards

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against the value of Eq. (5.6). However, this only happens under the following, rare circumstances. First, the laboratory reference method must be highly accurate. Second, the prediction slope must be one. And third, unspecific correlations (see below) must be zero. Note: neither the optimal b-vector, Eq. (5.4), nor the limit of detection, Eq. (5.6), is dependent on the laboratory reference values. Rather, they only depend on the spectroscopic “building blocks.”

5.6 Specificity of Response There is currently no peer-reviewed publication available that correctly addresses the issue of specificity of response in the multivariate case; see also the discussion in Ref. [41]. The “net analyte signal” concept is useful and comes close to the correct definition in those relatively well-behaved measurement situations where enough of the analyte response spectrum is “left” after the orthogonalization to clearly “stick out” over the instrument noise floor. In other words, in those situations where the repeatability error, i.e., the short-term RMS scatter error from the hardware noise floor, alone is almost identical to the total scatter error described by Eq. (5.6). In many NIR and other challenging applications, however, the net-analyte concept is not sufficient and is inconsistent with practical experiences [42]. The exact definition of specificity of response was recently presented at conferences [43], and a publication to be peer-reviewed is in preparation [44]. We summarize shortly here by saying that two further “mental leaps” away from traditional thinking are necessary in order to be able to arrive at the correct definition. First, the analyst must realize that all multivariate calibrations can be written in the form of Eq. (5.4), not just SBC. In other words, regardless of the form of model (“inverse” or “classical”), number of wavelengths, number of factors or nature of pre-processing steps or any other algorithmic details; in the end there is always an estimate used as signal (gc ) and another estimate used as noise (Σc ), and the resulting b-vector can T − − be written in the form of Eq. (5.4), bc = Σ− c gc gc Σc gc , where the notation Σc indicates that the inversion can be rank-deficient. In this context, the SBC method is “special” merely in the sense that both estimates, signal and noise, are put directly under user-control, whereas in the other methods at least one of the estimates is implicitly made “by the algorithm.” Second, the analyst must realize that the measured spectra are dependent on two independent variables, wavelength and time; and that the “other” variable is instrumental for the definition of specificity. A different type of the second variable, e.g., patient number, can be more appropriate in some applications. Time, however, can be used as a placeholder for all of those, and in the case of noninvasive glucose sensing is also practically appropriate. Thus, we will use time as the “other” independent variable in our discussion here. Different parts of the spectral noise exist at different (electrical) frequencies [Hz].

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The noise floor created by the photodetector and associated electronics is typically “white” over a relatively wide frequency range (kHz). Its random amplitude value therefore changes very quickly, typically within milliseconds or quicker. On the other hand, for example, temperature fluctuations within instrument enclosures often have cycle times from hours to days (0.3 mHz . . . 12 µ Hz). And long-term effects, e.g., seasonal effects, can drift into one direction even for months (1 month ∼ = 0.4 µ Hz). These facts are well known, and analysts therefore routinely distinguish between, for example, short-term “repeatability” and long-term “stability.” What is not sufficiently appreciated so far, however, is the fact that the correlation between particular noise components and the glucose concentration can also exist (as a correlation spectrum) at different frequencies [Hz]. In practice, when these correlations exist at very low frequencies (days to years, i.e., much longer than humans are typically prepared to wait for the result of a measurement) then the correlation will affect the outcome of the measurement in a “systematic” way. To reflect the practical reality in these cases, the measured spectrum has to be written as xT (t) = y(t) · gT + S · r · y(t) · uT + xTn (t),

(5.7)

where, as above, y(t) is the true (and sought-after) glucose concentration; g is the glucose response spectrum; and xn (t) is the spectral noise. The latter is, by definition, 100% uncorrelated in time with the glucose concentration y(t). The “new” term, S · r · y(t) · uT , describes the “unspecific correlation” (UC) present in the spectrum. The defining feature of a UC effect is that its amplitude, S · r · y(t) · uT , is 100% correlated in time with the glucose concentration y(t). These definitions are independent of the spectral shapes, i.e., whether or not any spectral overlap with the glucose response spectrum g exists. Graphically speaking, an unspecific correlation (UC) is a spectral effect that time-wise behaves like the analyte, but spectrally is something else. For example, in the case of noninvasive glucose sensing, water displacement is a UC effect, because the water concentration is virtually guaranteed to go down whenever the glucose concentration goes up and vice versa. Note: not all multivariate measurements are affected by UC effects, but in the case of NIR applications, many are affected. The spectral shape of the UC effect is described by its response spectrum u, and  the amplitude is described by factor, S · r, which contains a scaling factor, S = σuc σgluc , and a correlation coefficient r, both relating the concentration of the glucose and the concentration of the UC; see the discussion around Eq. (21) in Ref. [40]. When several components are unspecifically correlated, e.g., water displacement and a systematic change of scatter, then the total UC effect can still be described as a one-dimensional spectral effect, S · r · y(t) · uT : with the resulting response u and “effective” concentration both being functions of a weighted sum of the individual contributions [43, 44]. Now, in order to arrive at the general definition of “specificity,” we also need to allow the analyst to make an error ∆g, when estimating the true glucose response g. Thus, we assume that the analyst has estimated the glucose response as gc = g + ∆g

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Further, assume the analyst defines his estimate of the spectral noise as Σc , which also may be different from the true covariance, Σ = Cov [xn ]. Having made both estimates, the scientist computes the solution, Eq. (5.4), as bc =

Σ− c gc . T gc Σ− c gc

(5.9)

When a newly measured spectrum of the general form, Eq. (5.7), is ”predicted” using the regression vector of the general form, Eq. (5.9) (which is “general” because the b-vector solutions of all methods can be written in this form, see above) the result is:
y(t) ˆ = xT (t) · bc = y(t) · gT + S · r · y(t) · uT + xTn (t) · bc n o − = y(t) · (gc − ∆g + S · r · u)T + xTn (t) · gTΣcΣ−gcg c

= y(t) ·

n 1+

(S·r·u−∆g)T Σ− c gc gTc Σ− c gc

o

+

c

c

(5.10)

xTn (t) Σ− c gc . gTc Σ− c gc

Equation (5.10) summarizes most of the important facts about multivariate measurement. A first important conclusion is that UC affects the prediction slope whereas spectral noise xTn (t) affects the prediction scatter. This gives rise to the two familiar limits of detection, specificity and sensitivity, respectively, just like in the univariate case. For completeness, we say a few words about the limit of sensitivity first, which here refers to the minimum possible amount of scatter in the concentration estimate. The definition is straightforward when the mean-square criterion is used for measuring the amplitude of the scatter, which can be shown to be [43, 44],

E

"

xTn (t) Σ− c gc gTc Σ− c gc

2 #

=

− gTc Σ− 1 c · Σ · Σc gc ≥ T −1
2 − T g Σ gc c gc Σc gc

[(mg/dL)2 ].

(5.11)

The sensitivity is maximized, i.e., the mean-square prediction scatter error, Eq. (5.11), is minimized whenever the calibration noise is “matched,” i.e., whenever the −1 analyst chooses Σ− c = Σ . The RMS scatter error then achieves its absolute lowest possible value, which was already given in Eq. (5.6) above. On the other hand, when the analyst includes either “too much” or “too little” noise into his estimate Σc , then the scatter increases. Regarding the definition of specificity also known as “selectivity,” Eq. (5.10) reveals the following: If a calibration is significantly affected by UC then the prediction slope deviates from the ideal value of one. A calibration can be said to be “specific,” i.e., free of UC, if and only if, (S · r · u − ∆g) T Σ− c gc ∼ (5.12) = 0. gTc Σ− g c c The magnitude of the UC effect, Eq. (5.12), depends on the user’s selections of both gc and Σc . This is the mathematical reflection of the fact that proof of specificity ∆slope =

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is a two-step process. First, the analyst must prove that he measures the correct signal, i.e., that gc ∼ = g or ∆g ∼ = 0. In this step no mathematics is involved, only spectroscopy. Second, the user must prove that his “correct” estimate gc can be T − ∼ measured with the correct slope, (S · r · uT Σ− c gc ) (gc Σc gc ) = 0. This second step involves the definition of Σc , see the discussion below. Only if a scientist knows that his estimate of the response spectrum is reliable (∆g ∼ = 0 ) and if the slope turns out to be close to unity is proof of specificity achieved, i.e., is it proven that UC does not significantly affect the measurement. Proof of the first step, ∆g ∼ = 0, alone is not sufficient because the measurement can still be “hit” by a potentially existing UC, S · r · uT . Likewise, the current practice of omitting the first step of the proof of specificity in “statistical” calibrations (e.g., PLS, PCR) and testing only the second step (in an empirical way on so-called “independent” test spectra) leads to a situation where only “spurious” correlations can be spotted, but the presence of unspecific correlations can not be detected [43, 44]. The current standards of checking for specificity, e.g., ASTM 1655 or ICH Q2B, should therefore be amended. Note, unspecific correlations are different from “spurious” correlations. The latter ones do not exist in SBC. Rather, they only exist in statistical calibrations like PLS or PCR, where they are often a major problem because their convergence towards zero with increasing number of calibration standards is quite slow. Unspecific correlations, on the other hand, do not disappear with increased number of calibration standards because they are a “real” part of the spectral data. Assume a situation where an analyst knows he has passed the first step (∆g ∼ = 0), yet still the prediction slope turns out to deviate from the ideal value of one. This is proof that UC does exist. Since gc is fixed, the only means available to the analyst to improve the situation is to change the definition of Σc . In the past, the only practical way to achieve this was to select a “better” wavelength range for the calibration (which is mathematically equivalent to re-defining Σc [44]). Today, a more direct and less wasteful way is available. The user can simply add (in software) a large and targeted amount of “extra” (u · uT )-noise to his estimate of Σc , see [40] and the example below. In this way, specificity can be achieved in a completely sciencebased way [43, 44]. The price paid for introducing this “extra” mis-match, Σc 6= Σ, is a de-matching of the calibration and thus an increase in the prediction scatter error, see Eq. (5.11). The good news is that with SBC the analyst has for the first time a tool available by which this trade-off between specificity and sensitivity can be performed in a user-controlled, transparent, and scientifically optimal way. The key to this capability is user-control over both inputs of the calibration, signal (gc ) and noise (Σc ). Note, the procedure of adding “extra” noises to Σc is a user-controlled “stabilization” process, which, in practice, is not only used to address the issue of specificity of response, but also the issues of (a) long-term stability of calibration and (b) ease of calibration transfer from instrument-to-instrument [43, 44]. In the discussion following Eq. (5.3) above we mentioned that if the noise, Σ, is estimated by using measured spectra, X, that are affected by a (known or unknown) amount of glucose variation, then the SBC method “still works.” This statement is true in very many practical cases, but the NIR measurement of glucose is chal-

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lenging enough to warrant an exact mathematical discussion of the requirements for this statement to hold. If the glucose concentration of the measured “noise” spectra fluctuates, then the result of the estimate, Eq. (5.3), will be ˜ TX ˜ X T ∼ (5.13) = Σ + σu2 (g + S · r · u) · (g + S · r · u) , 1000 − 1 where the second summand describes the variation caused by the glucose concentration not staying constant. In practice, in addition to the “de-matching” caused by σu2 , the analyst may also choose to intentionally add other “extra” noises, Σextra , in order to improve the specificity and/or long-term stability of the calibration. In general, the total estimate used in the calibration is thus Σc = Σ + σu2 (g + S · r · u) · (g + S · r · u) T + Σextra ,

(5.14)

where the first and last summand describe that part of the estimate that is intentionally made by the user, Σintent = Σ + Σextra ; and the second summand describes the “un-intentional” part. For further discussion, the following dimensionless quantity is defined

F = σu2

    

(S · r · u − ∆g) T Σ− intent (S · r · u − ∆g) −

h i2  T −  (S · r · u − ∆g) Σintent gc  gTc Σ− intent gc

 

.

(5.15) Because of the Cauchy inequality, F ≥ 0 holds. It can be shown that as long as F is small, the effect of the un-intentional part on the measurement results is negligible [unpublished]. For example, when F < 0.01, the prediction slope will change by less than 1% relative to the value that would be achieved at σu2 = 0; and the rms prediction scatter error will increase by less than a few percent typically (dependent on the particular application; further details to be published [44]). Now, in practice, in order to achieve specificity of response, a user will try to control the “intentional” . part of the noise estimate, Σintent , anyway in such a way that T − ∼ (S · r · u − ∆g) T Σ− g intent c gc Σintent gc = 0, see Eq. (5.12) above. Therefore, usual practice will “automatically” tend to result in F ∼ = 0, justifying the initial statement that the SBC method “still works” if σu2 > 0. Note, however, that while the b-vector estimate and prediction results are hardly affected as long as F ∼ = 0, the value of Eq. (5.11), which can be used to estimate the prediction performance, will be affected by σu2 > 0. Determination of an “unaffected” estimate Σintent is therefore often preferred in practice. Next, an example SBC calibration will be performed on a data set of in vitro NIR spectra, which were measured from blood plasma samples. This example is meant to illustrate the potential of the SBC method for the noninvasive glucose application. It is hoped that these opportunities will be fully utilized in the future. The most important step towards this goal will be the exact estimation of the in vivo glucose response spectrum for a given sampling optics. This may include detailed radiation

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transport simulations using information on the layered structure of skin, their optical constants (see also Fig. 5.1), and any gradients or inhomogeneities in tissue glucose concentrations. First steps into this direction have already been made [18].

5.7 Illustration of the Science-Based Calibration Method The spectral data used here have been mentioned already above and described in detail in Ref. [5, 45]. A total of 126 blood plasma samples from mostly diabetic patients were measured in transmission using a 1-mm Infrasil cuvette mounted in the sample compartment of an FTIR instrument (Bruker IFS-66). A spectroscopic reference was measured from water immediately before each plasma spectrum. Samples were thermostated at 27 ± 0.02oC and measured over a time period of four days. The FTIR instrument was equipped with a 50-W tungsten-halogen bulb, CaF2 beamsplitter, and an InSb photodiode. The speed of the mirror was 1.90 cm/s. Measurement time per single-beam spectrum was approximately 1.5 minutes (1500 scans). Nominal spectral resolution was 32 cm−1 . After apodization, the interferograms were “zero-filled” and Fourier-transformed, resulting in a digital point spacing of 15.43 cm−1 . Two of the plasma samples were highly lipaemic, i.e., they contained very high triglyceride/cholesterol concentrations resulting in significant baseline distortion due to emulsion scattering. These two samples had been eliminated as outliers in the earlier PLS results [45] and were also eliminated here, even though tests showed that they could have been included in the SBC calibration without any noticeable effect. Examples of the absorbance spectra are shown in Figure 5.9A. The water bands are “over-compensated” because pure water was used as the spectroscopic reference. To reiterate, for the SBC procedure the analyst must perform the following steps. First, he must determine the response spectrum of glucose, gc , in units of [AU / (mg/dL)], using his spectroscopic expertise and application knowledge. Second, he must estimate the spectral noise Σc , “against which” the glucose response must be measured in his application. This step can involve the collection of a representative population of “noise” spectra (similar to the approach used by PLS and PCR, but without the need for reference values) and can also involve the intentional addition of “extra” noise(s) for the purpose of improving the specificity and/or long-term stability of the measurement (always at the price of decreased sensitivity, i.e., increased scatter error, see discussion above). The third step is to compute the b-vector; see also Eq. (5.9). And the final step is to predict new spectra, see Eq. (5.5), where y¯ and x¯ T are the mean glucose concentration and mean spectrum “around which” the covariance Σc was estimated. The first step is critical and quite challenging in this application, because the glucose absorbance signal is so small. The response spectrum was derived from an aqueous glucose absorbance spectrum and absorptivities have been shown in Fig.

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FIGURE 5.9: (A) Twenty absorbance spectra randomly selected from the population of 124 plasma samples and mean single-beam spectrum (dashed, in arbitrary units and auto-scaled); (B) Glucose response spectrum used for SBC (gc , solid) and the one implicitly used in PLS or PCR calibration (gPLS/PCR, dashed). The two calibration wavelength ranges are indicated by bars.

5.2 above. This spectrum was scaled to units of AU/(mm · (mg/dL)). The estimate shows some residual artefacts in the vicinity of the water bands, cp. Fig. 5.9B. However, these regions were not used in the calibration. For comparison to the previously published PLS results [5, 45], the same wavenumber range is used here for the SBC calibration, viz., 6788 to 5461 cm−1 and 4736 to 4212 cm−1 . As in [45], every other data point is selected, resulting in a total of 60 spectral data points. The rationale for selecting only every other point in the previous PLS calibration was to reduce the number of variables, by matching the point spacing to the spectral resolution. In SBC, however, this restriction is not necessary because spurious correlations do not exist. In other words, in SBC there is no penalty

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for including “too many” variables. In fact, tests confirmed that the accuracy of the SBC results improved slightly when including every data point, as expected from Eq. (5.6). To preserve the direct comparison to the previously published results, however, below we only show results achieved when using every other point. For completeness, we show in Fig. 5.9B not only the response spectrum determined from spectroscopic expertise, gc , but also the response spectrum that is implicitly derived “by the algorithm” in any PLS or PCR  calibration on this data set, ˜ T y˜ R y˜ TR y˜ R , where y˜ R are the (meangPLS/PCR . The latter is defined as gPLS/PCR = X centered) glucose reference values [40, 44]. The response spectrum derived from statistical correlation, gPLS/PCR , shows an unspecific correlation to scatter change in the plasma samples (higher glucose leads to more scatter, i.e., steeper baseline slope). However, in spite of being clearly visible in the figure, this effect is small. The correlation coefficient between the glucose reference values and the slope of the spectral baselines in the 12,000 to 9,000 cm−1 region is only 0.249. It is only because of the minute amplitude of the true glucose response that the scatter effect appears to be so large in Fig. 5.9B. Another UC effect also seen to affect gPLS/PCR is water displacement, and this effect is much more significant in practice, see the discussion below. The spectral noise Σc was estimated as the sum of the following parts. First, the hardware noise floor, which populates the diagonal of Σc , was estimated as follows. From experiments, it was known that the random noise on the 100% baseline computed from two consecutive water spectra was approximately 3 µ AU RMS in the region around 6300 cm−1 . This value is very close to that between plasma and water. The noise floor over the full spectral range was approximated by weighting this value by the inverse of the single-beam intensity of the (average) plasma. In other R notation, the random noise floor, “RndNoise,” was comwords, using MATLAB puted as: tmp = (3e-6) * MeanSingleBeam at 6300 ./ MeanSingleBeam; RndNoise = diag( tmp.ˆ 2 ); % [AUˆ 2], 60x60 matrix Next, an offset noise component, “OffNoise,” was computed as follows, OffNoise = (25e-3)ˆ 2 * ones(60,1)*ones(1,60); Offset noise describes a spectrally perfectly flat baseline with an amplitude that fluctuates randomly up and down by 25 mAU RMS. Inspection of the example spectra in Fig. 5.9A shows that the spectra actually do not contain that much offset variation. OffNoise is defined and added here mainly as an example to show how a particular instrumental effect can be simulated and added as “extra” noise in order to achieve long-term robustness of calibration against such possible future effects. In the case of OffNoise, it was confirmed that the price paid in terms of loss of sensitivity, i.e., increase in prediction scatter error, is minute. No other instrumental effects were added. In particular, wavelength axis “shift noise,” which is otherwise often added in order to achieve long-term stability, was not added here because FTIR instruments produce a very stable wavelength scale. Next, we need to estimate the actual PlasmaNoise, i.e., the spectral variation between different plasmas. This variation is mostly caused by the varying concentrations in the interfering components (proteins, cholesterol, etc.). Since the

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124 plasma samples came from different patients, the data set can be used to estimate the patient-to-patient variation. A first approach could be to simply com ˜ TX ˜ (124 − 1), where X ˜ is the 124×60 matrix containing the meanpute ΣPlasma ∼ =X centered plasma spectra in the wavelength range selected for calibration. However, this estimate would contain the full amount of glucose variation of approximately 91 mg/dL RMS, which was intentionally large in this data set when it was collected for PLS calibration in the first place (from mostly diabetic patients). In order to show that the SBC method eliminates not only the need for glucose reference values, but also the need for collecting spectra with a high amount of glucose variation, we proceed here as follows. The 124 samples were sorted according to their glucose reference concentration into a histogram as shown in Fig. 5.10. The covariances of the spectra were then computed individually within-each-bin, and the results from the bins were averaged (with the averaging being weighted by the numR ber of samples in the bin, see the MATLAB code below). In this way, the resulting estimate of PlasmaNoise is identical to that which would have been estimated if (only) a population of spectra with constant glucose concentration had been available. In other words, even though the glucose references are known in this case and are utilized in this way, the knowledge of the reference values is used only to “undo” the knowledge of the reference values, so to speak. This procedure is chosen to demonstrate the advantages of SBC calibration in the most convincing way possible, given this existing in vitro data set. A number of 30 bins was used in the histogram computation. This number was chosen rather arbitrarily in order to (a) decrease the width of each bin to below the accuracy of the glucose reference method (approx. 9.2 mg/dL RMS [45]) and (b) still keep more than one sample in most bins so that a within-bin variance could be computed. The few bins containing only a single sample were eliminated from the computation so that a total of 120 samples (“N used”) were still available for the computation of PlasmaNoise. Note, the histogram shown in Fig. 5.10 was plotted using 29 bins in order to make the tick marks on the x-axis visible. The resulting very slight change in the histogram shape causes a fifth single-sample bin to appear in Fig. 5.10. The code used is shown below. NoBin=30; N bin=hist(GlucRef, NoBin); % returns No of samples in each bin [tmp,sort ind] = sort(GlucRef); % returns sorting index X sort=X(sort ind,:); % sorted spectra PlasmaNoise=zeros(60,60); % initialization, 60x60 matrix of zeros N used=0; for b=1:NoBin % loop over the bins if N bin(b)>1 PlasmaNoise = PlasmaNoise + N bin(b) * mc(X sort(N used+1:N used+N bin(b),:))’ * mc(X sort(N used+1:N used+N bin(b),:))/(N bin(b)-1); % weighted average of the within-bin variances N used = N used + N bin(b);

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end end PlasmaNoise = PlasmaNoise / N used; The function mc(..) returns the mean-centered spectra. Because of the low number of samples in each bin, it is important to use the un-biased estimate of the variance, i.e., division by n − 1, and not by n. The total noise was then estimated as the sum of the three components described above, i.e., Σc ∼ = RndNoise + OffNoise + PlasmaNoise. The b-vector was computed according to Eq. (5.9) using full-rank matrix inversion; and the 124 spectra were then “predicted” according to Eq. (5.5). The results are shown in Fig. 5.11A. It is important to note that the prediction results shown in Fig. 5.11A are “independent” (using the lingo of the older statistical calibration approach) even though the samples for concentration prediction were used in the calibration as part of the noise estimate Σc . In PLS/PCR practice, the word “independent” referred to the avoidance of “overfitting” also known as “spurious correlation,” an effect which made the results from calibration routinely look better than those from prediction. In the SBC approach, however, spurious calibrations do not exist because both inputs of the calibration, signal and noise, are under user-control. The only way to apply the word “independent” in the context of SBC is to discuss whether these two estimates, i.e., signal and noise, are scientifically sound for future use or not. In the case at hand, the signal gc came from a completely different experiment, i.e., was “independent” by anybody’s standards and will certainly hold in the future. The noise estimate Σc did make use of the spectra intended for concentration prediction, however, only for the noise estimate, and not for the signal estimate. Since the PlasmaNoise computed from the 124 given samples is not unique in any way to these samples, but is

FIGURE 5.10: Histogram of glucose reference values of the 124 samples.

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FIGURE 5.11: (A) Prediction results of SBC calibration using the glucose response spectrum gc , as shown in Fig. 5.9B, as signal and Σc ∼ = RndNoise + OffNoise + PlasmaNoise as noise. The ideal prediction line (dashed) is shown for comparison. MSE = 38.8 mg/dL RMS; scatter = 10.1 mg/dL RMS; slope = 0.586; R2 = 0.965; (B) “Prediction” results of SBC calibration after including water displacement noise, Σc ∼ = RndNoise + OffNoise + PlasmaNoise + WaterDispNoise. MSE = 17.7 mg/dL RMS; scatter = 13.1 mg/dL RMS; slope = 0.867; R2 = 0.973. representative of the PlasmaNoise in any other population of samples, the SBC results can be considered “independent” also in terms of the noise estimate. In fact, the patient-to-patient variation included in the definition of PlasmaNoise here is probably a worst-case estimate of the variation occurring within a single patient over time, and in this sense the estimate may even be considered by some as too conservative. The only noise contribution that is not yet included in the calibration here (and therefore could make future “predictions” look worse than those shown in Fig. 5.11A) is long-term drift effects in the absorbance spectra originating inside the instrument,

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because the 124 spectra were measured over a relatively short time period (few days). These long-term effects (if existing) are cancelled out, however, by the separate water reference measured immediately before each plasma sample. The plasma absorbance spectrum should therefore be free from any such effects also in the long term, especially in the case of FTIR instruments, which are considered very reliable in this respect. The results shown in Fig. 5.11A can therefore be considered realistic estimates also in the long-term sense. Note that PlasmaNoise already contains a contribution from the hardware noise floor, and thus it appears that RndNoise is counted twice in the total estimate, Σc . This is indeed the case, and the estimate Σc is conservative also in this sense. However, the effect of this particular form of “de-matching” is small in practice. The reason for this procedure is that there are not enough samples available in this data set to estimate the hardware noise floor reliably using just PlasmaNoise, see the discussion in [38], and therefore a separate effort (RndNoise) must be made. Otherwise, an eigenvalue decomposition of Σc could show that some of the higher eigenvalues are estimated below the true hardware noise floor, which must be avoided. The important point about Fig. 5.11A is that the prediction slope is significantly different from the ideal value of one. Since the SBC measurement “measures the right thing” (viz., the gc shown in Fig. 5.9B), the first step of the proof of specificity is passed. The fact that the second step of the proof is not passed means that the measurement is “hit” by an unspecific correlation (UC). In order to remove the effect of the UC on the prediction results, “extra” noise component(s) describing the UC effect must therefore be added to Σc [43, 44]. The most likely cause of UC in this application is water displacement. When the glucose concentration in the plasma increases, the water concentration in the plasma goes down and vice versa. Because of the large absorption coefficient of water, this effect (in units of [AU]) is relatively large. Water displacement noise (“WaterDispNoise”) was estimated by loading the water absorption coefficients published by Bertie [46]; scaling the data from units of [AU / (cm ×(mol/L))] to units of [AU / (mm ×100%)]; and then multiplying the resulting “water displacement response” by a rather arbitrarily chosen amplitude of 50 µ m RMS. The following code was used. load(’Bertie.txt’); % John Bertie data % nue Bertie 15557x1 [cm-1] (from 15,000 to 0 cm-1) % Wat Bertie 15557x1 [AU10 per cm per (mol/L)] Wat Bertie = 0.1*(1000/18.0153)*Wat Bertie; % [AU/ mm 100%] Wat = interp1(nue Bertie, Wat Bertie, nue, ’linear’)’; % interpolation to the wavenumbers selected in calibration WaterDispNoise = (0.050)ˆ 2 * Wat*Wat’; % [AUˆ 2] % 50 microns worth of RMS displacement The water displacement noise was then added to the noise estimate used above, Σc ∼ = RndNoise + OffNoise + PlasmaNoise + WaterDispNoise, and the b-vector was re-computed. The improved “prediction” results are shown in Fig. 5.11B.

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The slope of the prediction results in Fig. 5.11B is considerably improved compared to the previous result. This improvement in specificity was achieved at the expense of a relatively mild decrease in sensitivity (increase in scatter), see the figure captions. In other words, adding water displacement noise as an “extra” noise into Σc was a worthwhile and scientifically sound step. The amplitude of 50 µ m RMS was chosen to be relatively large compared to the actual displacement effect occurring in the cuvette. Choosing this number controls the trade-off between specificity and sensitivity. The more water displacement noise is added, the better the specificity (versus this water effect) becomes, but the sensitivity (prediction scatter) becomes worse. When an infinite amount is added, the effect assumes a quasi “netanalyte-signal status,” i.e., its effect on the slope is completely removed [44]. Adding 50 µ m RMS of displacement noise is a “near-infinite” amount in this case. This was confirmed by increasing the amplitude to 50 mm RMS, which left the prediction results virtually unchanged (the MSE value, e.g., changed only in the third digit after the comma). This means that the remaining slope deficiency seen in Fig. 5.11B can not be further reduced by adding more WaterDispNoise, but, rather, that different UC effects must be considered. Because of the remaining slope deficiency of about 13%, the results achieved in Fig. 5.11B are still not 100% specific. The main reason for this is probably the fact that the type of water present in blood plasma is different from the “free” water for which Bertie [46] published his spectral data (see, e.g., [47]). The WaterDispNoise simulated here is therefore likely not 100% identical to the actual water effect (displacement and/or other) happening in the plasmas. Another factor that may contribute to the residual 13% is a possible scaling error in the estimate of the glucose response gc . However, the scaling of the response spectrum presented here is very likely accurate to better than 5%, which means that the bulk of the remaining slope deviation of 13% is still due to a “true” UC effect. Since the glucose concentration in diabetic patients undergoes relatively large and rapid changes, the concentrations of the other blood substrates can not correlate with the glucose concentration. It is therefore likely that the remaining UC effect of 13% is connected to a residual water effect. It is interesting to note that the scatter error from just the hardware noise floor alone, i.e., the repeatability, is only 5.8 mg/dL RMS. This is slightly under half of the total RMS scatter error seen in Fig. 5.11B. In other words, the bulk of the scatter error is due to other random effects, which are unlikely to vary on short time scales. For example, the concentrations of the other, interfering blood substrates vary only slowly over time within a single patient and, thus, could not be averaged out during the time of a single measurement. Further improvements in specificity would require a deeper spectroscopic analysis than was presented here. In particular, the exact effects of glucose concentration changes on the spectrum of water need to be studied. However, the main conclusion is already clear from Fig. 5.11B: It is relatively straightforward to measure the glucose concentration in blood plasma in the NIR wavelength range. To the authors’ knowledge, this is the first SBC result published on glucose and thus the first result that is guaranteed to be specific to glucose. Both the first step

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(“measure the right thing”) and the second step (“measure the right thing right,” i.e., prediction slope near unity) of the proof of specificity are fulfilled. Previously published PLS results (like those of other statistical calibration methods) failed to prove the first step, which invalidated any attempt to conclude about specificity by interpreting their prediction slope [43, 44]. Note, the fact that the response spectrum, gPLS/PCR, shown in Fig. 5.9B looks different from the “correct” response spectrum gc does not necessarily mean that the PLS calibration was significantly affected by unspecific response. The underlying mathematical reason for this is given in Eq. (20) of Ref. [40]. The visual standards by which humans tend to judge the quality of a spectrum are different from the standard that counts for calibration. The spectral subspaces where mistakes in the estimate of g are most likely to occur tend to be exactly those subspaces that are affected by the most spectral noise. Fortunately, this means that these errors have a tendency to not “count” in calibration because the multivariate calibration will tend to “avoid” exactly those subspaces. This is good news for a posteriori evaluations of existing PLS and PCR calibrations. In the particular case at hand, however, it is virtually certain that prior PLS calibrations did (wrongly) use water displacement as a signal to a significant degree and, therefore, were at least partially unspecific. The SBC result shown in Fig. 5.11B can be compared to the PLS result previously achieved on the same data set, which was SEP =18.8 mg/dL (leave-one-out) [45]. Numerically speaking, the SBC result is about 20% better. A simple numerical comparison does not, however, give the complete picture. The PLS predictions very likely used water-displacement as a signal and thus enjoyed an (unfair) advantage in terms of “signal” size. Still, the numerical result of PLS was worse, which was likely due to the fact that spurious correlations in the signal estimate, gPLS/PCR , were “hit” by the hardware noise floor. The SBC result, on the other hand, did not enjoy the unfair signal-advantage (because it only measured the correct signal, gc ); however, it apparently more than made up for this “disadvantage” by better describing the spectral detail features of gc . In other words, in this example SBC outperformed PLS on both accounts: specificity and sensitivity (and, very likely, also on long-term stability, known as robustness). The results presented for the in vitro example are encouraging also for the noninvasive case. The accurate definition of the glucose response vector, gc , is challenging in the noninvasive case because a wavelength-dependent determination of “effective” pathlength has to be performed. This will likely require, as mentioned above, detailed Monte-Carlo studies of the photon propagation in the skin, including details of the layered structure in the skin, as well as design details of the given sampling optics. However, the potential benefits are large. Using SBC, as soon as the analyte response spectrum is defined, the spectroscopy is no longer a “secondary” method that needs calibration against a “primary” reference method. Rather, SBC spectrometry is a “primary” measurement method that is firmly based on physics and chemistry. A number of important advantages become available from this change, including the following: • First, the need for lab-reference values is virtually eliminated from calibra-

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• Second, it is likely that the “noise” spectra necessary for estimating the “skin noise” can be collected from healthy volunteers, instead of from diabetic patients. The fact that these “healthy proband spectra” will contain only a minimal amount of glucose variation is actually an advantage in the SBC approach. • Third, specificity of response can be proven to regulatory agencies and concerned end-users. • Fourth, robustness of calibration can be increased in a simple and efficient way by adding targeted “extra” noises into the estimate, Σc , thereby incurring only minimal expense in terms of loss of sensitivity. From practical experience we can say that this fine-tuned way of “blanking out” spectral subspaces is often much less costly in terms of sensitivity than the old-fashioned, crude way of eliminating whole wavelength ranges. • Fifth, when developing a new type of instrument, the spectrometer hardware specifications can be directly and in advance derived from the desired output accuracy via Eq. (5.6). This, in turn, often enables significant reduction in R&D time and expense required for the development of new instruments. • Sixth, the calibration process itself becomes transparent and “easily communicated.” Method validation, which requires application-specific evaluations and actions and is an important issue for manufacturers of biomedical devices, and which has not been straightforward in the case of NIR methods so far (e.g., Ref. [48]), should therefore also become easier.

5.7.1 Outlook for the novel calibration method The recently introduced method of science-based calibration (“SBC”) is described. The SBC solution can be directly computed from the user-estimates of the spectral signal g and spectral noise Σ. Delivering these two estimates using scientific means is the main task for the user. The actual numerical task of SBC calibration, i.e., computation of the b-vector, is trivial by comparison. The method mechanizes the whole calibration process, so to speak, by removing choices and by forcing the user to substantiate each of his inputs with scientific backup information. The method provides significant benefits when compared to the current practice of PLS or PCR, both in economic and in scientific terms. In particular, specificity of response can be proven. The method is applicable whenever the response spectrum of the analyte of interest (in this case, glucose) can be determined from spectroscopic expertise and application knowledge. Taking a bird’s eye view, it turns out that all calibration methods, no matter how differently they may look on the surface, are based on estimates of spectral signal and spectral noise and all can be written in the form of Eq.(5.9). In other words, there

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is always an estimate used as signal and second estimate used as noise. In SBC, both estimates are “explicit,” i.e., visible to and individually and directly controlled by the user. In classical calibration (spectral fitting), the estimate of the signal is explicit but the estimate of the noise is “implicit,” i.e., visible only after cumbersome mathematical transformation and not controlled by the user. In statistical calibration (PLS, PCR), both estimates are implicit. By deriving the mathematical formulas for the implicit estimates, it can be shown [40] that (a) classical calibration makes a good estimate of g but a bad estimate of Σ; (b) statistical calibration, vice versa, makes a bad estimate of g and a good (but overly expensive) estimate of Σ; and (c) SBC can be interpreted as a “picking of the cherries” between the two. The SBC analysis of the in vitro example data shows that glucose in blood plasma can be measured in the NIR with sufficient selectivity and precision, using a 1-mm cuvette and an FTIR-spectrometer. Future applications of the SBC method to noninvasive glucose measurements will likely reveal that a different type of instrument is more advantageous, because FTIR instruments are affected by a relatively high hardware noise floor (in the NIR region). In order to successfully tackle the noninvasive measurement, three aspects need to be taken into account. First, a further suppression of the hardware noise floor; second, an accurate estimation of the glucose response spectrum, g, in the noninvasive case; and third, a scientific evaluation of the mechanisms causing lack of (time-) correlation between the glucose concentration in the blood and the measured one in the skin.

5.8 Conclusions The validation of “statistical” calibration models (e.g., PLS, PCR) for a transcutaneous, noninvasive blood glucose assay using near infrared spectra of body tissue is an extremely critical issue. Within our study several procedures were presented to test the prediction performance of different calibration models. The exclusive basis was independent data of different packet size, not used in the calibration stage. We discussed a minimization of the potential for false validations. In particular, an indicator was the change in prediction performance within validation under the scheme of reducing the number of wavelengths and/or enlarging the validation package size. We could show that day-to-day testing under the condition of different blood glucose profiles was successful to recognize effects from spurious correlations, e.g., spectrometer drifting, skin surface changes, etc., when calibration data from quasicontinuous measurements were taken into account. A different scenario to avoid chance correlations is random testing, where the effort for the collection of a sufficient number of calibration samples is much larger and more time consuming than under the quasi-continuous sampling scheme. On the other hand, it is also our aim to have continuous monitoring for the patient, which is close to the calibration and validation scenario from whole day measurements.

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One conclusion is that there is so far no unique tool for prediction testing. A clear separation of the analyte signal from other competing factors is hopefully possible using the SBC calibration strategy as outlined in the second part. To fight chance correlations, the SBC strategy is an excellent tool which is expected to become an indispensable methodology in the not too distant future. Costly clinical tests with diabetic volunteers extending into the hypo- and hyperglycemic ranges to prove the general applicability of the noninvasive methodology could be reduced. With non-diabetic subjects only a limited variance in the reference concentration data is available, but this is actually of advantage for proceeding in the alternative route of multivariate calibration models. Protocols for validation strategies should be set up and generally agreed on, allowing also a better comparison of proposed assays within the literature, which would be most profitable for the diabetic community.

Acknowledgments The authors are indebted to Prof. Dr. med. Th. Koschinsky from the Deutsches Diabetes-Zentrum in D¨usseldorf for providing the analytical reference data. Financial support by Deutsche Forschungsgemeinschaft, Ministerium f¨ur Innovation, Wissenschaft, Forschung und Technologie des Landes NRW and Bundesministerium f¨ur Bildung und Forschung is gratefully acknowledged.

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References [1] The Diabetes Control and Complications Trial Research Group, “The effect of intensive treatment of diabetes on the development of diabetes on the development and progression of long-term complications in insulin-dependent diabetes mellitus,” N. Engl. J. Med., vol. 329, 1993, pp. 977–986. [2] UK Prospective Diabetes Study Group, “Intensive blood-glucose control with sulphonylureas or insulin compared with conventional treatment and risk of complications in patients with type 2 diabetes (UKPDS 33),” Lancet, vol. 352, 1998, pp. 837–853. [3] V.R. Kondepati and H.M. Heise, “Recent progress in analytical instrumentation for glycemic control in diabetic and critically ill patients,” Anal. Bioanal. Chem., vol. 388, 2007, pp. 545–563. [4] O.S. Khalil, “Non-invasive glucose measurement technologies: an update from 1999 to the dawn of the new millennium,” Diabetes Technology & Therapeutics, vol. 6, 2004, pp. 660–697. [5] H.M. Heise, R. Marbach, A. Bittner, and Th. Koschinsky, “Clinical chemistry and near infrared spectroscopy: multicomponent assay for human plasma and its evaluation for the determination of blood substrates,” J. Near Infrared Spectrosc., vol. 6, 1998, pp. 361–374. [6] K.H. Hazen, M.A. Arnold, and G.A. Small, “Measurement of glucose and other analytes in undiluted human serum with near-infrared transmission spectroscopy,” Anal. Chim. Acta, vol. 371, 1998, pp. 255–267. [7] M. Ren and M.A. Arnold, “Comparison of multivariate calibration models for glucose, urea, and lactate from near-infrared and Raman spectra,” Anal. Bioanal. Chem., vol. 387, 2007, pp. 879–888. [8] Bo-Yan Li, S. Kasemsumran, Y. Hu, Yi-Z. Liang, and Y. Ozaki, “Comparison of performance of partial least squares regression, secured principal component regression, and modified secured principal regression for determination of human serum albumin, γ -globulin, and glucose in buffer solutions and in vivo blood glucose quantification by near-infrared spectroscopy,” Anal. Bioanal. Chem., vol. 387, 2007, 603–611. [9] K.E. Kramer and G.W. Small, “Blank augmentation protocol for improving the robustness of multivariate calibrations,” Appl. Spectrosc., vol. 61, 2007, pp. 497–506. [10] A.K. Amerov, J. Chen, G.W. Small, and M.A. Arnold, “Scattering and absorption effects in the determination of glucose in whole blood by near-infrared spectroscopy,” Anal. Chem., vol. 77, 2005, pp. 4567–4594.

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[11] R. Marbach, Th. Koschinsky, F.A. Gries, and H.M. Heise, “Noninvasive blood glucose assay by near-infrared diffuse reflectance spectroscopy of the human inner lip,” Appl. Spectrosc., vol. 47, 1993, pp. 875–881. [12] M.R. Robinson, R.P. Eaton, D.M. Haaland, et al., “Noninvasive glucose monitoring in diabetic patients: a preliminary evaluation,” Clin. Chem., vol. 38, 1992, pp. 1618–1622. [13] I. Gabriely, J. Kaplan, R. Wozniak, et al., “Transcutaneous glucose measurement using near-infrared spectroscopy during hypoglycemia,” Diabetes Care, vol. 22, 1999, pp. 2026–2032. [14] H.M. Heise, “Applications of Near-Infrared Spectroscopy in Medical Sciences,” in: Near-Infrared Spectroscopy – Principles, Instruments, Applications, H.W. Siesler, Y. Ozaki, S. Kawata, H.M. Heise (eds.), Wiley-VCH, Weinheim, 2002, pp. 289–333. [15] M.A. Arnold and G.W. Small, “Noninvasive glucose sensing,” Anal. Chem., vol. 77, 2005, pp. 5429–5439. [16] H.M. Heise, A. Bittner, and R. Marbach, “Near-infrared reflectance spectroscopy for non-invasive monitoring of metabolites,” Clin. Chem. Lab. Med., vol. 38, 2000, pp. 137–145. [17] J.T. Olesberg, L. Liu, V. Van Zee, and M.A. Arnold, “In vivo near-infrared spectroscopy of rat skin tissue with varying blood glucose levels,” Anal. Chem., vol. 78, 2006, pp. 215–223. [18] K. Maruo, T. Oota, M. Tsurugi, et al., “New methodology to obtain a calibration model for noninvasive near-infrared blood glucose monitoring,” Appl. Spectrosc., vol. 60, 2006, pp. 441–449. [19] K. Maruo, T. Oota, M. Tsurugi, et al., “Noninvasive near-infrared blood glucose monitoring using a calibration model built by a numerical simulation method: trial application to patients in an intensive care unit,” Appl. Spectrosc., vol. 60, 2006, pp. 1423–1431. [20] N.M. Faber and R. Rajk´o, “How to avoid over-fitting in multivariate calibration – The conventional validation approach and an alternative,” Anal. Chim. Acta, vol. 595, 2007, pp. 98–106. [21] Q.-S. Xu, Y.-Z. Liang, and Y.-P. Du, “Monte Carlo cross-validation for selecting a model and estimating the prediction error in multivariate calibration,” J. Chemom., vol. 18, 2004, pp.112–120. [22] M.B. Seasholtz and B. Kowalski, “The parsimony principle applied to multivariate calibration,” Anal. Chim. Acta, vol. 277, 1993, pp. 165–77. [23] C.H. Spiegelman, M.J. McShane, M.J. Goetz, et al., “Theoretical justification of wavelength selection in PLS calibration: development of a new algorithm,” Anal. Chem., vol. 70, 1998, pp. 35–44.

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[24] H.M. Heise and A. Bittner, “Rapid and reliable spectral variable selection for statistical calibrations based on PLS-regression vector choices,” Fresenius’ J. Anal. Chem., vol. 359, 1997, pp. 93–99. [25] D. Chen, W. Cai, and X. Shao, “Removing uncertain variables based on ensemble partial least squares,” Anal. Chim. Acta, vol. 598, 2007, pp. 19–26. [26] H.M. Heise, R. Marbach, Th. Koschinsky, and F.A. Gries, “Noninvasive blood glucose sensors based on near-infrared spectroscopy,” Artificial Organs, vol. 18, 1994, pp. 439–447. [27] R. Marbach and H.M. Heise, “On the efficiency of algorithms for multivariate linear calibration used in analytical spectroscopy,” Trends Anal. Chem., vol. 11, 1992, pp. 270–275. [28] T.L. Troy and S.N. Thennadiel, “Optical properties of human skin in the near infrared wavelength range of 1000 to 2200 nm,” J. Biomed. Opt., vol. 6, 2001, pp.167–176. [29] E. Salomatina, B. Jiang, J. Novak, and A.N. Yaroslavsky, “Optical properties of normal and cancerous human skin in the visible and near-infrared spectral range,” J. Biomed. Optics, vol. 11, 2006, 064026. [30] A. Roggan, J. Beuthan, S. Schr¨under, and G. M¨uller, “Diagnostik und Therapie mit dem Laser,” Physikalische Bl¨atter, vol. 55, 1999, pp. 25–30. [31] A.K. Amerov, J. Chen, and M.A. Arnold, “Molar absorptivities of glucose and other biological molecules in aqueous solutions over the first overtone and combination regions of the near-infrared spectrum,” Appl. Spectrosc., vol. 58, 2004, pp. 1195–1204. [32] R. Marbach and H.M. Heise, “Optical diffuse reflectance accessory for measurements of skin tissue by near-infrared spectroscopy,” Applied Optics, vol. 34, 1995, pp. 610–621. [33] H.M. Heise, “Near-infrared spectrometry for in vivo glucose sensing,” in: Biosensors in the Body, D.M. Fraser (ed.), John Wiley & Sons, Chichester, 1997, pp. 79–116. [34] H.M. Heise and A. Bittner, “Multivariate calibration for near-infrared spectroscopic assays of blood substrates in human plasma based on variable selection using PLS-regression vector choices,” Fresenius’ J. Anal. Chem., vol. 362, 1998, pp. 141–147. [35] H.M. Heise, R. Marbach, A. Bittner, and Th. Koschinsky, “Clinical Chemistry and Near-Infrared Spectroscopy: technology for non-invasive glucose monitoring,” J. Near Infrared Spectrosc., vol. 6, 1998, pp. 349–359. [36] H.M. Heise, “In vivo assay of glucose,” in: Encyclopedia of Analytical Chemistry - Instrumentation and Applications, R.A. Meyers (ed.), Wiley, Chichester, 2000, Vol. I, pp. 56–83.

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[37] H.M. Heise and P. Lampen, “Transcutaneous glucose measurements using near-infrared spectroscopy: validation of statistical calibration models,” Diabetes Care, vol. 23, 2000, pp. 1208–1209. [38] R. Marbach, “On Wiener Filtering and the Physics Behind Statistical Modeling,” J. Biomed. Optics, vol. 7, 2002, pp. 130–147. [39] R. Marbach, “Methods to significantly reduce the calibration cost of multichannel measurement instruments,” US Pat. No. 6,629, 041, 30 Sep. 2003. [40] R. Marbach, “A New Method for Multivariate Calibration,” J. Near Infrared Spectrosc., vol. 13, 2005, pp. 241–254. [41] A.C. Olivieri, N.M. Faaber, J. Ferre, et al., “Uncertainty estimation and figures of merit for multivariate calibration (IUPAC Technical Report),” Pure Appl. Chem., vol. 78, 2006, pp. 633–661. [42] C.D. Brown, “Discordance between net analyte signal theory and practical multivariate calibration,” Anal. Chem., vol. 76, 2004, pp. 4364–4373. [43] R. Marbach, “Exact definition of “specificity of response” in the multivariate case and consequences for today’s practice of multivariate calibration,” Presentation 31-Jan-2007 at IFPAC-2007, Baltimore, MD; and “Recent scientific understanding leads to exact definition of “specificity of response” in the multivariate case. Severe consequences for today’s practice of multivariate calibration,” Presentation 18-June 2007 at NIR-2007 Conference, Umea, Sweden. [44] R. Marbach, “Figures of merit for multivariate measurement systems: selectivity and sensitivity,” in preparation. [45] R. Marbach, “IR-spectroscopic Methods for the Measurement of Blood Glucose (in German),” PhD thesis, University of Dortmund, Germany, 1993; see also R. Marbach, Fortschr.-Ber. VDI, Reihe 8, vol. 346 VDI-Publishers, D¨usseldorf, 1993. [46] Data available at http://www.ualberta.ca/∼jbertie/JBDownload.htm, and originally described in: J.E. Bertie, Z. Lan, Appl. Spectrosc., vol. 50, 1996, pp. 1047–1057. [47] R. Tsenkova, “AquaPhotomics: Water Absorbance Pattern as a Biological Marker,” NIR News, vol. 17 (6), 2006, p. 13. [48] G.E. Ritchie, R.W. Roller, E.W. Ciurczak, et al., “Validation of a near-infrared transmission spectroscopic procedure - Part B: Application to alternate content uniformity and release assay methods for pharmaceutical solid dosage form,” J. Pharm. Biomed. Anal., vol. 29, 2002, pp. 159–171.

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6 Characterizing the Influence of Acute Hyperglycaemia on Cerebral Hemodynamics by Optical Imaging Qingming Luo, Zhen Wang, Weihua Luo and Pengcheng Li Britton Chance Center for Biomedical Photonics, Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, PR China

6.1 6.2 6.3 6.4

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optical Imaging Techniques of Functional Brain . . . . . . . . . . . . . . . . . . . . . . . . . . Influence of Acute Hyperglycaemia on CBF and SD in Rat Cortex . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

157 159 164 168 169 174

Disturbances in glycaemia can significantly alter brain functions. Several brainmapping techniques have been developed to characterize complex functional topography of the brain. This chapter introduces basic principles and instrumentations of two optical imaging techniques used for investigating cerebral hemodynamics: intrinsic optical signal imaging and laser speckle imaging. Especially, these two imaging techniques are used to study influences of acute hyperglycaemia on cerebral blood flow and spreading depression in rat cerebral cortex. Key words: acute hyperglycaemia, cerebral blood flow (CBF), laser speckle imaging, intrinsic optical signal imaging.

6.1 Introduction Glucose is the usual fuel of brain tissue; the brain does not store glycogen and perform gluconeogenesis, and it relies on a continuous supply of glucose from blood. Disturbances in glycaemia can alter significantly brain functions. Electrophysiological data [1, 2] suggest that changes in systemic glucose can influence neuronal excitability. There is evidence indicating that certain brain responses are altered when

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blood glucose levels are changed from a short-term to a maintained different state [3]. Most clinical studies indicate that the cognitive impairment in patients with type 1 diabetes mellitus is related to recurrent hypoglycemia closely [4]. Hyperglycemia induces a pro-oxidative and proinflammatory state that can cause direct neuronal toxicity. Hyperglycemia-mediated increase in matrix metalloproteinase-9 can cause neuronal damage by an increase in cerebral edema. Moreover, hyperglycemia may be responsible for a procoagulant state that can further compromise blood supply to penumbral areas in acute ischemic stroke [5]. Transient or permanent focal cerebral ischemia, clinically called stroke, may result from a transient or permanent reduction in cerebral blood flow (CBF) that is restricted to the territory of a major brain artery [6]. Hyperglycemia is common and involves up to 50% of the acute stroke patients. Several clinical studies have revealed that hyperglycemia is associated with a poor outcome in terms of mortality and neurological recovery. The results obtained from experimental studies have shown that hyperglycemia exacerbates the ischemic lesions and is associated with an increase of the edema and size of the infarct [7]. Both human and animal studies have showed that hyperglycemia is particularly detrimental in ischemia/reperfusion. Decreased reperfusion blood flow has been observed after middle cerebral artery occlusion in acutely hyperglycemic animals, suggesting the vasculature as an important site of hyperglycemic reperfusion injury [8]. Cortical spreading depression (SD) is a non-physiological global depolarization of neurons and astrocytes that can be induced typically with electrical stimulation, needling of the cerebral cortex, or superfusion of isotonic or more concentrated potassium chloride solution. The phenomenon propagates across the cerebral cortex at a rate of 2–5 mm per minute. SD is characterized by marked but transient increases in CBF and probable changes in metabolic rate [9] and intrinsic optical signal (IOS) [10–13]. SD is believed to be involved in some neurological diseases such as migraine and ischemia [12–14]. A few reports have described alterations in brain ability to produce and propagate SD after glycaemic change during the SD-recording session: Recently, SD velocities of propagation in adult hyperglycaemic rats were significantly lower than in the controls. In contrast, hypoglycaemic rats presented SD velocities significantly higher than the controls [15]. However, the frequency, amplitude, and duration of direct current potentials were unaltered in hyperglycemic SD animals [16]. Early, the effect of hyperglycemia on the initiation and propagation of spreading depression-like peri-infarct ischemic depolarization induced by focal cerebral ischemia in rats also was investigated, which demonstrated that hyperglycemia delays the terminal depolarization in the ischemic core and supports a faster repolarization in severely mal-perfused penumbral tissue after SD, which reflects the increased availability of energy substrates in the state of hyperglycemia [17]. Several optical brain mapping techniques have been developed to characterize the as yet undefined and complex functional topography of the brain. Among all the techniques, intrinsic optical signal imaging (IOSI) and laser speckle imaging (LSI) stand out because they offer a superior combination of spatial sampling, spatial resolution, and temporal resolution; on the other hand, they have no need to use exoge-

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Characterizing the influence of acute hyperglycaemia on cerebral hemodynamics 159 nous contrast agents. Great developments also have been obtained in both techniques and applications of brain optical imaging, and they have become powerful tools for in vivo studying functional architecture and pathophysiology in cerebral cortex with high spatial and temporal resolution by monitoring hemodynamics [18–28]. Thus, the two imaging techniques are promising methods to research hyperglycaemia influence on brain functions.

6.2 Optical Imaging Techniques of Functional Brain Recording neuronal activity via hemodynamics relies on the fact that neuronal activation causes local vasculature to respond, a notion which had been postulated already by Roy and Sherrington in their pioneering study 06x29. The notion is a basis for hemodynamics-based functional brain imaging techniques such as functional magnetic resonance imaging (fMRI), positron emission tomography (PET), IOSI, LSI, and near infrared optical tomography [30–32]. These brain mapping techniques have ever-since experienced growing popularity within the neuroscience community. Indeed, as opposed to electroencephalogram, magnetoencephalography, and singleand multi-unit electrical recordings, those techniques allow mapping the activity of large neuronal populations at comparatively high spatial resolution and completely noninvasive character. Although PET and fMRI have the capability to collect three-dimensional spatial information at multiple time points in one subject, the spatial resolution of these techniques is on the order of millimeters. Optical imaging methods - either alone or in combination with other recording techniques- have proven a fruitful approach to explore both physiological and pathological aspects of hemodynamic responses in cortex[18–20, 25–27, 33-35]. One of the main advantages of optical imaging consists in its high spatio-temporal resolution (in the order of few microns and milliseconds).

6.2.1 Laser speckle imaging 6.2.1.1 Laser speckle phenomenon In the early 1960s the inventors and first users of the laser had a surprise: when laser light fell on a diffusing (nonspecular) surface, they saw a high-contrast grainy pattern, i.e., speckle [36]. The fact that speckle patterns only came into prominence with the invention of the laser suggests that the cause of the phenomenon might be the high degree of coherence of the laser [37]. Further investigation shows that this is, indeed, the case. Laser speckle was an interference pattern produced by the light reflected or scattered from different parts of the illuminated rough (i.e., nonspecular) surface. When the area illuminated by laser light was imaged onto a cooled charge coupled device camera (CCD), there produced a granular or speckle pattern [37, 38]. If the scattered particles were moving, a time-varying speckle pattern was gener-

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ated at each pixel in the image. The intensity variations of this pattern contained information of the scattered particles [37]. 6.2.1.2 Laser speckle contrast analysis Since the spatial and temporal intensity variation of time-varying speckle pattern contains information on the scattered particles, statistics of speckle patterns has been developed to quantify the speed of scatters. Briers et al. have done some pioneering works in this field [37, 39, 40]. Through analyzing the spatial blurring of the speckle image obtained by CCD, the two-dimensional velocity distribution with a high spatial and temporal resolution has been shown [21–23, 28, 38, 41–46]. This blurring is represented as a local speckle contrast, which is defined as the ratio of the standard deviation to the mean intensity: C=

σs , hIi

(6.1)

where C, σ , and hIi stand for speckle contrast, the standard deviation of light intensity, and the mean value of light intensity, respectively. The speckle contrast lies between the values of 0 and 1. The higher the velocity, the smaller the contrast is; the lower the velocity, the larger the contrast is. A speckle contrast of 1 demonstrates no blurring of speckle, namely, no motion, whereas a speckle contrast of 0 indicates rapidly moving scatterers. The link between the speckle contrast and the correlation time can be manifested by the following equation [38]: C=

σs = hIi

     1/2  1 τc 2 −2T T exp , +2 −1 2 T τc τc

(6.2)

where τ c = 1/(α k0 v) is inversely proportional to the velocity, v is the mean velocity, k0 is the light wavenumber, and α is a factor that depends on the Lorentzian width and scattering properties of the tissue. The value of τ c can be computed from the corresponding value of C, and therefore get the relative velocity. The above method is also called laser speckle spatial contrast analysis (LASSCA). Dunn et al. have implemented LSI for CBF [38, 41, 47]. Cheng et al. have extended this technique to study regional blood flow in the rat mesentery [21, 22]. Further, our lab has provided a modified LSI method with laser speckle temporal contrast analysis (LASTCA) [28]. The speckle temporal contrast image was constructed by calculating the speckle temporal contrast of each image pixel in the time sequence. The value of speckle temporal contrast Ct (x, y) at pixel (x, y) is calculated as [25]:

σx,y = Ct (x, y) = hIx,y i

q (n) ∑Nn=1 (Ix,y − hIx,y i)2 /(N − 1) . hIx,y i

(6.3)

Some advantages of LASTCA have been shown, including imaging obscured subsurface inhomogeneity [48] and even imaging CBF through the intact rat skull [25].

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FIGURE 6.1: LASSCA compared to LASTCA. (A) The raw speckle image of a nylon ring on the dura of a rat; (B) The raw speckle image after nylon ring ligated with the dura; (C) The speckle contrast image calculated with the conventional method of LASCA; D: The speckle contrast image calculated with the method of LASTCA.

Compared to the LASSCA, the LASTCA could provide higher spatial resolution [28] and suppress the influence of the speckle contrast from the stationary structure [25], such as the skull, nylon ring, and the ligation knots (see Fig. 6.1). 6.2.1.3 Instrumentation of laser speckle imaging Here the LSI system used widely in our lab will be introduced. The technical details of LSI have been described elsewhere [38, 49]. Briefly, a 17 mW He-Ne laser (λ =632.8 nm, Melles Griot, U.S.A) was coupled into a fiber bundle with 8mm diameter, which was adjusted to evenly illuminate the interested cortex. A 12-bit cooled charge coupled device camera (CCD, Pixelfly, 480×640 pixel array, PCO Computer Optics, Germany) attached to a stereomicroscope (SZX12, Olympus, Japan) was employed for raw speckle image acquisition. The raw images are acquired at 40 frames per second, which is controlled by the computer, and the exposure time of CCD is 20 ms. The LSI system offers a high spatial resolution (25 ms), temporal resolution (13 µ m), and the discrimination of 9% change of velocity (Fig. 6.2). 6.2.1.4 Measuring CBF through LSI It has been known that changes in CBF are closely related in space and time to neural activity. Monitoring the spatio-temporal characteristics of cerebral blood flow is crucial for studying the normal and pathophysiologic conditions of brain metabolism. In the previous study of CBF changes, laser-Doppler flowmetry (LDF) was used extensively and provided high-temporal resolution measurements of relative blood flow changes at a single point on the cortex, yet no spatial information is obtained. Although scanning laser Doppler systems provide some spatial resolution, their tem-

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FIGURE 6.2: Schematic illustration of setup for laser speckle imaging of cerebral blood flow. A He-Ne laser (λ =632.8 nm, 17 mW) beam is expanded to illuminate a 7 × 9 mm area of cortex, which is imaged onto the CCD camera. The computer acquires raw speckle images and computes relative CBF maps.

poral resolution is insufficient for imaging the response to most functional stimuli because of the need for scanning [50–54]. Laser speckle contrast analysis (LASCA) (also called laser speckle contrast imaging or laser speckle flowmetry, LSF) has recently been demonstrated as a promising approach to investigate CBF responses in the brain under normal functional [49, 55, 56] and pathophysiologic conditions [38, 57–59]. Since it does not require laser scanning, laser speckle contrast imaging with less exposure time (typically 10–50 ms) is useful for noninvasive assessment of twodimensional cerebral blood flow with high transverse spatial (µ m) and temporal (ms) resolution [49]. LSI [38], as a means of measuring two-dimensional CBF changes, has recently attracted extensive attention due to its high spatial and temporal resolution, and has already been successfully applied to revealing the CBF changes in the cortex induced by cortical SD [60], cerebral ischemia [27, 49], and sensory stimulation [56].

6.2.2 Intrinsic optical signal imaging 6.2.2.1 Principles on intrinsic optical signal imaging In principle, the technique of IOSI is simple, the brain of an animal is exposed and illuminated with light of an appropriate wavelength (typically between 600 and 730 nm). Generally, the technique recorded the reflected light intensity from the cortex with a few exceptions of transmission [61, 62]. Importantly, the changes in optical properties of brain tissue are associated with brain activity. At least three characteristic physiological parameters affect the degree to which incident light is reflected by the active cortex [63]. These are: (a) changes in the blood volume;

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Characterizing the influence of acute hyperglycaemia on cerebral hemodynamics 163 (b) chromophore redox, including the oxy/deoxy-hemoglobin ratio (oxymetry); intracellular cytochrome oxidase and electron carriers; and (c) light scattering. For brain functional imaging, the dominant tissue absorber for visible wavelengths is hemoglobin with its oxygenated and deoxygenated components [64]. At some isobestic points of hemoglobin (approximately 550 nm, 570 nm), deoxygenated hemoglobin and oxygenated hemoglobin have the same absorbance and therefore changes in total hemoglobin concentration or cerebral blood volume (CBV) are emphasized [24, 65, 66]. In the low 600-nm range, oxyhemoglobin absorbance is negligible compared with that of deoxyhemoglobin absorbance. By imaging at 600– 630 nm, one emphasizes changes in deoxyhemoglobin concentration or hemoglobin oximetry [65, 66]. Light scattering occurs over the entire visible spectrum and near infrared. At 700–850 nm wavelengths, the light scattering component dominates the intrinsic signal, while hemoglobin absorption is low [65, 66]. Usually, cellular swelling would reduce light scattering [67]. Thus, IOSI can be used to map different physiological processes depending on the specific wavelength chosen for illumination. 6.2.2.2 Instrumentation of intrinsic optical signal imaging The typical system of IOSI shares almost the same system with LSI (see Fig. 6.1). The main difference in the equipment between IOSI and LSI lies in the nature of the light source. Even illumination is best achieved by using at least two fiber-optic light guides directed at the region of interest with an oblique angle about 30 ˚ [18]. Commonly, the halogen lamp and mercury xenon arc lamp [41] are used as the light source. Band-pass interference filters are used to determine the wavelength of the illuminating light. An alternative use of light source is the illumination by a ring of light-emitting diodes (LEDs) of specific wavelengths [68]. 6.2.2.3 Monitoring IOS changes during SD by IOSI SD is characterized by transitory, spreading neuronal depolarization, temporary disruption of ion homeostasis, and changes in IOS [10–13]. SD is believed to be involved in some neurological diseases such as migraine and ischemia [12–14]. IOSI is a neuroimaging technique that allows monitoring a large region of the cortex with both high temporal and spatial resolution [66, 69], which is particularly suitable for the investigation of SD wave propagation [70–73]. IOSI at 550 nm wavelength is commonly used, as the intensity of the reflected signal is primarily related with regional changes in cerebral blood volume (CBV). The reflectance change induced by SD at 550 nm is of large amplitude thus allowing for sufficient detection of SD waves [71, 72]. Indeed, it was relatively easy to observe the SD by IOSI; the reliable detection of small signal changes during SD was crucial, especially for the early and small reflectance changes. Much work has been done by IOSI to delineate the spatiotemporal evolution of SD [18–20, 74].

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6.3 Influence of Acute Hyperglycaemia on CBF and SD in Rat Cortex 6.3.1 Long-term monitoring the influence of glucose upon CBF in rat cortex Previous studies have found that CBF is reduced during acute hyperglycemia in rats and the mechanism of this change is still not well known [75–79]. However, these measurements of blood flow were based on the diffusible blood flow indicator (iodoantipyrine), which provides a single measurement of flow integrated over a 30 s period [75, 76, 78] or using continuous laser-Doppler flowmetry at a spot of the cortex over a period of 20 min. Due to these sampling restrictions of the previous techniques, long-term and in vivo full field observation of CBF during acute hyperglycemia is lacking to promote the understanding of the mechanisms underlying these CBF changes. Laser speckle imaging based on laser speckle contrast analysis (LASCA) was first introduced by Briers et al. [80] and applied to monitor the evolution of CBF in normal [81–83] and pathological conditions, such as cortical spreading depression [81, 84] and ischemia [46, 81, 85, 86], due to its simplicity and high spatiotemporal resolution. Here, LSI was utilized to reexamine the effect of acute hyperglycemia on regional CBF and its full field distribution over a rat cortical area during a long period lasting up to 3 hours. Acute hyperglycemia was induced in α -chloralose (50 mg/kg) with urethane (600 mg/kg) anesthetized rats (n = 10) by intraperitoneal injection of 2 ml 50% D-glucose, as well as the rats (n = 10) in the control group were similarly treated with 2 ml saline. Skull bone overlying parietal and temporal cortex was removed with a high speed dental drill (Fine Science Tools, USA) under constant saline cooling to form a 7.0 mm × 9.0 mm cranial window (imaging window). The window was bathed with normal saline/artificial cerebrospinal fluid at 37 ± 0.5 ◦ C. The technical details of LSI used in this experimental system have been described in a part of this chapter. LSI was started 10 min before the administration of agents (50% D-glucose or saline), and repeated at a series of time points with an interval of 15 min after the administration of agents. At each time point of images acquiring, 5 to 10 trials (each including 30 frames, 40 fps) were accomplished at intervals of 1 min for further averaging. As shown in Figs. 6.3 and 6.4, immediately after the injection of glucose, the CBF has an initial decreasing tendency lasting about 45 min; this result is in accordance with the measurements acquired in the previous studies using the conventional techniques [75–79]. Unexpectedly, the change in CBF has a distinctly increasing phase that occurred from 60 min to 180 min after the administration of glucose and peaked at time of 105 min after injection with a magnitude of 1 to 2 times the baseline value. In the control group (saline injection), the random fluctuations (between a decrease of 30% and an increase of 60% the control value) in CBF were observed in several regions selected in the imaged cortex (Figs. 6.5 and 6.6).

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Characterizing the influence of acute hyperglycaemia on cerebral hemodynamics 165

FIGURE 6.3: Spatial distribution maps of rat CBF were measured by LSI at different time points covering from before the injection of glucose (0 min), to 180 min after this administration of glucose in a representative subject. The time points presented at the top of each image are the time elapsed after the onset of glucose administration. A, anterior; M, medial. Bar, 1 mm.

FIGURE 6.4: (A) Three regions of interest (ROIs) were selected in the parenchyma over the CBF maps acquired during acute hyperglycemia in rat cortex. (B) The time courses of CBF changes relative to the control value (the CBF value measured before the injection of glucose) in the three representative ROIs.

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FIGURE 6.5: Spatial distribution maps of CBF were measured by LSI at different time points covering from before the injection of saline (0 min), to 180 min after this administration of saline in a representative subject. The time points presented at the top of each image are the time elapsed after the onset of the administration. A, anterior; M, medial. Bar, 1 mm.

FIGURE 6.6: (A) Three regions of interest (ROIs) were selected in the parenchyma over the CBF maps acquired during acute hyperglycemia in rat cortex. (B) The time courses of CBF changes relative to the control value (the CBF value measured before the injection of glucose) in the three representative ROIs.

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Characterizing the influence of acute hyperglycaemia on cerebral hemodynamics 167 Based on the long-term and high resolution full-field monitoring of CBF over a broad region in the rat cortex, the initial decrease in CBF that lasts for 45 min followed by an extensive increase in CBF over the imaged cortex during acute hyperglycemia was first shown in this work. These data will incur further studies to understand the mechanism underlying the significant blood flow increase.

6.3.2 Optical imaging of hemodynamic response during cortical spreading depression in the normal or acute hyperglycemic rat cortex The brain is critically dependent on a continuous supply of blood to function. As the blood flow is disrupted, brain function in the territory of blood supplying ceases within seconds and irreversible damage to its cellular constituents ensues within minutes [87, 88]. This cerebral ischemia, clinically called stroke, may result in severe or lethal neurological deficits. Clinical studies suggested that hyperglycemia is a risk factor for stroke and that it increases brain injury during stroke or cardiac arrest [76, 89]. There is also considerable evidence that hyperglycemia can exacerbate brain injury after cerebral ischemia, particularly in models of global and focal ischemia with reperfusion [89]. Spreading depression (SD) (Le˜ao [90]) is characterized by transitory, spreading neuronal depolarization, temporary disruption of ion homeostasis, and changes in hemodynamic response that propagates like a wave on the cortical surface at a speed of 2–5 mm/min [10–13]. SD is believed to be involved in some neurological diseases such as migraine and ischemia [12–14]. SD is one of the complex series of pathophysiological events following focal cerebral ischemia. The intermittent SD waves which spread from the vicinity of the infarcted area could cause a stepwise expansion of the infarct core, while therapeutic suppression of CSD could minimize infarct size [90–92]. However, pre-conditioning of the normal cortex with CSD enhances the tolerance to focal ischemia [93]. Therefore, SD is also a critical role or risk factor for stroke. Hyperglycemia [75–79] and SD can both induce extensive hemodynamic changes, such as the long-lasting decrease in CBF [93]. The hemodynamic changes that resulted from hyperglycemia or SD are potential factors to worsen the outcome of stroke. However, the relationship or interaction between the hyperglycemia and SD is not well known. Here, we combined IOSI and LSI to compare the hemodynamic response of SD during acute hyperglycemia with that in normal condition. The rats were divided into two groups, glucose group (n = 10) was treated with intraperitoneal injection of 2 ml 50% D-glucose, as well as the rats (n = 10) in the control group were similarly treated with 2 ml saline. Two cranial windows were formed in the ipsilateral frontal bone, parietal and temporal bone (Fig. 6.7). The former one is inserted with a pair of stimulating electrodes for the induction of SD; the other one is bathed with artificial cerebrospinal fluid at 37 ± 0.5 ◦ C and inserted with recording electrode for combined optical imaging and electrical recording. IOSI at wavelength of 550 ± 10 nm was performed to trace the cerebral blood volume (CBV) response during SD at the following time points: 10 min before the intraperitoneal injection of glucose or saline, 30 min, 60 min, 90 min, 120 min, 150 min, and 180 min after the

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FIGURE 6.7: White light images of an induction window (circle shown) inserted with stimulating electrode and an imaging window (rectangle indicated) inserted with recording electrode.

administration. Prior to each trial of IOSI experiment, LSI was applied to monitor the CBF distribution in the imaged cortex. SD was induced 3 min after the start of optical image acquisition by intra-cortical electrical stimulation (5 mA, 1 s duration). The propagation and time course of SD waves over a long time range from before the injection of glucose to 180 min after the administration were shown in Figs. 6.8 and 6.9. After acute administration of glucose solution, the SD-associated DC signal has no significant change, while the average duration of the SD-associated optical signal increases extensively (Fig. 6.7). The CBF after each induction of SD has a stepwise reduction. At time of 180 min after acute administration of glucose, the CBF level reduced to about 35% the control value that was acquired before the injection of glucose (Figs. 6.10 and 6.11A). Similarly to the tendency of CBF changes, beside for a little rebound during 60–120 min after the glucose administration, the propagating velocity of SD reduced after the administration of glucose (Fig. 6.11B). The hemodynamic characteristics of CSD and the CBF following the SD induction were also observed by IOSI and LSI techniques in the rats treated with intraperitoneal injection of saline (Figs. 6.12–6.14). At an interval of 30 min between two inductions of SD, the decrease of CBF induced by SD could be inversed in some cases in the normal cortex. The CBF has an increase comparing to the control level (0 min) except for two time points (120 and 150 min after the glucose injection). Similarly, in these series of successive SD waves, the propagating velocity has an increasing tendency. From these data, we found that acute hyperglycemia could aggravate the severity of decrease in CBF that resulted from SD and slow the propagating velocity of SD waves.

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Characterizing the influence of acute hyperglycaemia on cerebral hemodynamics 169

FIGURE 6.8: The spatiotemporal evolution of SD waves at different time points in glucose group was revealed by subtracting consecutive images. Each row denotes a single SD wave induced at each time point denoted left to the image row panel. The interval between consecutive images is 10 s. Grayscales represent the change in reflectance signal intensity. The scale bar is 2 mm, as given in the bottom of the last image. M, medial; P, posterior.

6.4 Conclusion In this chapter we have introduced two optical imaging techniques and shown their application to study the influence of acute hyperglycaemia on CBF and SD in rat cerebral cortex. Based on the long-term and high resolution full-field monitoring of CBF over a broad region in the rat cortex, the initial decrease in CBF that lasts for 45min followed by an extensive increase in CBF over the imaged cortex during acute hyperglycemia was first shown in this work. Furthermore, we also found that acute hyperglycemia could aggravate the severity of decrease in CBF that resulted from SD and slowed the propagating velocity of SD waves.

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FIGURE 6.9: Relative changes in optical reflectance and DC potentials were simultaneously recorded to characterize spreading depression waves at a series of time points denoted at the top of each panel. Changes of DC transients and optical reflectance are both shown using the same time axis.

Acknowledgment This work was supported by the grants from the National Natural Science Foundation of China (Grant No. 60478016, 30500115, 60410131) and Major Program of Science and Technology Research of Ministry of Education (Grant No.10420).

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Characterizing the influence of acute hyperglycaemia on cerebral hemodynamics 171

FIGURE 6.10: Spatial distribution maps of CBF were measured by LSI at different time points in a representative subject treated with the injection of glucose. The time points presented at the top of each image are the time elapsed after the onset of the administration. A, anterior; M, medial. Bar, 1 mm. Three regions of interest (ROIs) were selected from cortical parenchyma in the last image for further calculation of relative changes in CBF.

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FIGURE 6.11: (A) The time course of relative changes in CBF in ROI 1-3 selected in Fig. 6.10. (B) Changes in SD velocity of propagation at different time points during acute hyperglycemia.

FIGURE 6.12: The spatiotemporal evolution of SD waves at different time points in saline group was revealed by subtracting consecutive images. Each row denotes a single SD wave induced at each time point denoted left to the image row panel. The interval between consecutive images is 10 s. Grayscales represent the change in reflectance signal intensity. The scale bar is 2 mm, as given in the bottom of the last image. M, medial; P, posterior.

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Characterizing the influence of acute hyperglycaemia on cerebral hemodynamics 173

FIGURE 6.13: Spatial distribution maps of CBF were measured by LSI at different time points in a representative subject treated with the injection of saline. The time points presented at the top of each image are the time elapsed after the onset of the administration. A, anterior; M, medial. Bar, 1 mm. Three regions of interest (ROIs) were selected from cortical parenchyma in the last image for further calculation of relative changes in CBF.

FIGURE 6.14: (A) The time course of relative changes in CBF in ROI 1-3 selected in Fig. 6.13. (B) Changes in CSD velocity of propagation at different time points in saline group.

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[55] M.A. Webster, K.J. Webb, A.M. Weiner, et al., “Temporal response of a random medium from speckle intensity frequency correlations,” J. Opt. Soc. Am. A: Opt. Image Sci. Vis., vol. 20, 2003, pp. 2057–2070. [56] T. Durduran, M.G. Burnett, G. Yu, et al., “Spatiotemporal quantification of cerebral blood flow during functional activation in rat somatosensory cortex using laser-speckle flowmetry,” J. Cereb. Blood Flow Metab., vol. 24, 2004, pp. 518–525. [57] H. Bolay, U. Reuter, A. K. Dunn, et al., “Intrinsic brain activity triggers trigeminal meningeal afferents in a migraine model,” Nat. Med., vol. 8, 2002, pp. 136–142. [58] A. Kharlamov, B.R. Brown, K.A. Easley, et al., “Heterogeneous response of cerebral blood flow to hypotension demonstrated by laser speckle imaging flowmetry in rats,” Neurosci. Lett., vol. 368, 2004, pp. 151–156. [59] B. Choi, N.M. Kang, and J.S. Nelson, “Laser speckle imaging for monitoring blood flow dynamics in the in vivo Rodent Dorsal skin fold model,” Microvasc. Res., vol. 68, 2004, pp. 143–146. [60] C. Ayata, H.K. Shin, S. Salomone, et al., “Pronounced hypoperfusion during spreading depression in mouse cortex,” J. Cereb. Blood Flow Metab., vol. 24, 2004, pp. 1172–1182. [61] M. Tomita, I. Schiszler, Y. Tomita, et al., “Initial oligemia with capillary flow stop followed by hyperemia during K+-induced cortical spreading depression in rats,” J. Cereb. Blood Flow Metab., vol. 25, 2005, pp. 742–747. [62] Y. Tomita, M. Tomita, I. Schiszler, et al., “Repetitive concentric wave-ring spread of oligemia/hyperemia in the sensorimotor cortex accompanying K(+)induced spreading depression in rats and cats,” Neurosci. Lett., vol. 322, 2002, pp. 157–160. [63] A. Zepeda, C. Arias, and F. Sengpiel, “Optical imaging of intrinsic signals: recent developments in the methodology and its applications,” J. Neurosci. Methods, vol. 136, 2004, pp. 1–21. [64] M. Kohl, U. Lindauer, G. Royl, et al., “Physical model for the spectroscopic analysis of cortical intrinsic optical signals,” Phys. Med. Biol., vol. 45, 2000, pp. 3749–3764. [65] A.M. Ba, M. Guiou, N. Pouratian, et al., “Multiwavelength optical intrinsic signal imaging of cortical spreading depression,” J. Neurophysiol., vol. 88, 2002, pp. 2726–2735. [66] R.D. Frostig, E.E. Lieke, D.Y. Ts’o, et al., “Cortical functional architecture and local coupling between neuronal activity and the microcirculation re-

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Characterizing the influence of acute hyperglycaemia on cerebral hemodynamics 179 vealed by in vivo high-resolution optical imaging of intrinsic signals,” Proc. Natl. Acad. Sci. U.S.A, vol. 87, 1990, pp. 6082–6086. [67] A. Villringer and B. Chance, “Non-invasive optical spectroscopy and imaging of human brain function,” Trends Neurosci., vol. 20, 1997, pp. 435–442. [68] J.E. Mayhew, S. Askew, Y. Zheng, et al., “Cerebral vasomotion: A 0.1-Hz oscillation in reflected light imaging of neural activity,” Neuroimage, vol. 4, 1996, pp. 183–193. [69] D. Malonek and A. Grinvald, “Interactions between electrical activity and cortical microcirculation revealed by imaging spectroscopy: implications for functional brain mapping,” Science, vol. 272, 1996, pp. 551–554. [70] R.S. Yoon, P.W. Tsang, F.A. Lenz, et al., “Characterization of cortical spreading depression by imaging of intrinsic optical signals,” Neuroreport, vol. 7, 1996, pp. 2671–2674. [71] S. Chen, P. Li, W. Luo, et al., “Time-varying spreading depression waves in rat cortex revealed by optical intrinsic signal imaging,” Neurosci. Lett., vol. 396, 2006, pp. 132–136. [72] A.M. Ba, M. Guiou, N. Pouratian, et al., “Multiwavelength optical intrinsic signal imaging of cortical spreading depression,” J. Neurophysiol., vol. 88, 2002, pp. 2726–2735. [73] A.M. O’Farrell, D.E. Rex, A. Muthialu, et al., “Characterization of optical intrinsic signals and blood volume during cortical spreading depression,” Neuroreport, vol. 11, 2000, pp. 2121–2125. [74] S. Chen, P. Li, W. Luo, et al., “Using running subtraction to detect the wavefront of cortical spreading depression,” Conf. Proc. IEEE Eng. Med. Biol. Soc., vol. 2, 2005, pp. 1446–1448. [75] R.B. Duckrow, D.C. Beard, and R.W. Brennan, “Regional cerebral blood flow decreases during hyperglycemia,” Ann. Neurol., vol. 17, 1985, pp. 267–272. [76] R.B. Duckrow, D.C. Beard, and R.W. Brennan, “Regional cerebral blood flow decreases during chronic and acute hyperglycemia,” Stroke, vol. 18, 1987, pp. 52–58. [77] R.B. Duckrow and R.M. Bryan, Jr., “Regional cerebral glucose utilization during hyperglycemia,” J. Neurochem., vol. 48, 1987, pp. 989–993. [78] G.E. Kikano, J.C. LaManna, and S.I. Harik, “Brain perfusion in acute and chronic hyperglycemia in rats,” Stroke, vol. 20, 1989, pp. 1027–1031. [79] R.B. Duckrow, “Decreased cerebral blood flow during acute hyperglycemia,” Brain Res., vol. 703, 1995, pp. 145–150. [80] J.D. Briers and S. Webster, “Laser speckle contrast analysis (LASCA): a nonscanning, full-field technique for monitoring capillary blood flow,” J. Biomed. Opt., vol. 1, 1996, pp. 174–179.

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[81] C. Ayata, A.K. Dunn, O.Y. Gursoy, et al., “Laser speckle flowmetry for the study of cerebrovascular physiology in normal and ischemic mouse cortex,” J. Cereb. Blood Flow Metab., vol. 24, 2004, pp. 744–755. [82] A.K. Dunn, H. Bolay, M.A. Moskowitz, et al., “Dynamic imaging of cerebral blood flow using laser speckle,” J. Cereb. Blood Flow Metab., vol. 21, 2001, pp. 195–201. [83] T. Durduran, M.G. Burnett, G. Yu, et al., “Spatiotemporal quantification of cerebral blood flow during functional activation in rat somatosensory cortex using laser-speckle flowmetry,” J. Cereb. Blood Flow Metab., vol. 24, 2004, pp. 518–525. [84] C. Ayata, H.K. Shin, S. Salomone, et al., “Pronounced hypoperfusion during spreading depression in mouse cortex,” J. Cereb. Blood Flow Metab., vol. 24, 2004, pp. 1172–1182. [85] A.J. Strong, E.L. Bezzina, P.B. Anderson, et al., “Evaluation of laser speckle flowmetry for imaging cortical perfusion in experimental stroke studies: quantitation of perfusion and detection of peri-infarct depolarisations,” J. Cereb. Blood Flow Metab., vol. 26, 2006, pp. 645–653. ¨ [86] D.N. Atochin, J.C. Murciano, Y. G¨ursoy-Ozdemir, et al., “Mouse model of microembolic stroke and reperfusion,” Stroke, vol. 35, 2004, pp. 2177–2182. [87] K.A. Hossmann, “Viability thresholds and the penumbra of focal ischemia,” Ann. Neurol., vol. 36, 1994, pp. 557–565. [88] C. Warlow, C. Sudlow, M. Dennis, et al., “Stroke,” Lancet, vol. 362, 2003, pp. 1211–1224. [89] L. Gisselsson, M.-L. Smith, and B.K. Siesjo, “Hyperglycemia and focal brain ischemia,” J. Cereb. Blood Flow Metab., vol. 19, 1999, pp. 288–297. [90] A.A.P. Le˜ao, “Spreading depression of activity in the cerebral cortex,” J. Neurophysiol., vol. 7, 1944, pp. 359–390. [91] H. Martins-Ferreira, M. Nedergaard, and C. Nicholson, “Perspectives on spreading depression,” Brain Res. Brain Res. Rev., vol. 32, 2000, pp. 215– 234. [92] G.G. Somjen, “Mechanisms of spreading depression and hypoxic spreading depression-like depolarization,” Physiol. Rev., vol. 81, 2001, pp. 1065–1096. [93] T. Otori, J.H. Greenberg, and F.A. Welsh, “Cortical spreading depression causes a long-lasting decrease in cerebral blood flow and induces tolerance to permanent focal ischemia in rat brain,” J. Cereb. Blood Flow Metab., vol. 23, 2003, pp. 43–50.

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7 Near-Infrared Thermo-Optical Response of the Localized Reflectance of Diabetic and Non-Diabetic Human Skin Omar S. Khalil Pharos Biomedical Research, Chicago, IL, USA

7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Temperature Dependence of µa and µs′ of Individual’s Skin . . . . . . . . . . . . . . . . Temperature Modulation of µa and µs′ of Skin Over Prolonged Interaction Between the Optical Probe and Skin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dependence of Thermo-Optical Response of Localized Reflectance of Human Skin on Diabetic State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Test for Diabetic State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Biological Noise and Glucose Determinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

181 184 185 190 192 193 194 197 198 199

This chapter reviews use of temperature modulated localized reflectance studies to elucidate the role of the skin as an optical window for the noninvasive determination of glucose. What is the role of probe-skin interaction on the optical signal, what is the effect of temperature on the measured absorption and scattering coefficients of human skin? Does the effect of temperature vary with the diabetic state of a person? Contact between a measurement probe and skin leads to temperature changes, change in skin hydration by blocking water vapor permeation and mechanical pressure, which causes partial occlusion. Key words: light scattering, diffuse localized reflectance, temperature modulation, thermo-optical response, diabetic and non-diabetic skin

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7.1 Introduction Several of the noninvasive methods for the determination of blood glucose (BG) are optical measurements performed through the skin. Skin is generally considered to act as a passive window for the optical measurements of glucose. This assumption must be questioned. Is the skin an active component affected by the diabetic state and the interaction between the probe and the skin? How does diabetes affect the structural and circulatory properties of skin? How does this, in turn, affect the noninvasive method to determine glucose? To seek answers to these questions, our group at Abbott Laboratories studied the Near Infrared (NIR) thermo-optical response of the localized reflectance of diabetic and non-diabetic human skin [1–9]. Our goal was to understand some of the factors affecting the noninvasive (NI) determination of BG concentration, which is the concentration determined by home glucose monitors, and is widely used for monitoring treatment of diabetic patients. We previously reviewed some aspects of the NI determination of glucose and whether the values determined would be BG or glucose in the interstitial fluid [2, 4]. A noninvasively-determined glucose value may be the average concentration over several tissue compartments. The signal from each compartment may be associated with a different source of noise [4]. Human skin has a layered structure that has several uneven layers, namely, stratum corneum, epidermis, dermis, and adipose tissue [10]. Interposed between them are the interconnected upper plexus and lower plexus of the cutaneous vascular system. The interstitial fluid (ISF) surrounds the collagen fibrous structures and cells. The refractive index mismatch between the ISF and cutaneous fibrous material controls skin scattering properties. Sweat glands are connected to the surface of the skin through sweat ducts. The cutaneous vascular system plays an important role in stabilizing body temperature. It acts as a radiator to control body temperature by changing blood flow to the upper plexus. When the body generates excess heat more blood flows to the upper plexus to dispose of extra heat. When the environment temperature drops, blood flow to the upper plexus is restricted to preserve body temperature. Thus the skin is an active thermal element that regulates the interaction between the body and its environment. This thermal role of the skin is not considered in the majority of published or patented methods on the NI determinations of glucose. Diabetes is associated with a set of microvascular complications such as neuropathy, retinopathy, and nephropathy. It also affects cutaneous tissue. Laser Doppler flowmetry (LDF) studies on human skin showed decrease in cutaneous blood flow in diabetics. There was a difference in blood flow response to cooling or warming, which suggested that diabetes impaired microvascular circulation [11–14]. Vascular walls in cutaneous microvasculature of diabetics were abnormally thick [15], size and number of the veil cells increased [16], and the vessels were reported to respond abnormally to heat, injury, and to histamine [17–19]. Autonomic sympathetic dysfunction was detected in diabetic patients [20].

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Other studies such as capillary microscopy, LDF perfusion, and occlusion effects showed differences in cutaneous blood flow between diabetics and non-diabetics [12, 13, 21–27]. While skin capillary density was similar for the diabetic and non-diabetic populations [21], nail-fold capillary pressure was elevated in diabetics as compared to non-diabetics [22]. Maximal hyperemia in diabetic subjects was reduced compared to non-diabetics [23]. Other reported microvascular effects of diabetes were impaired peripheral vasomotion [24], difference in response to contralateral cooling [25], difference in skin microvascular regulatory response [26], and different flow motion in patients with peripheral diabetic neuropathy [27]. Thus, circulatory thermal responses differ between diabetics and non-diabetics. Structural effects associated with diabetes such as thickened skin, accelerated collagen aging, elastic fiber fraying, increased cross-linkage, and change in dermal collagen structure in diabetic patients were reported, and can affect the scattering of diabetic skin [4]. Difference in dermal collagen structure and in its X - ray diffraction patterns were reported and attributed to glycation and cross-linking of cutaneous collagen fibers resulting from frequent hyperglycemic episodes in diabetics [28–30]. Thus, diabetes leads to cutaneous circulatory effects as well as to dermal structural differences for those inflected with it. In addition to the capillary vascular differences between diabetic and non-diabetic, structural differences between the red blood cells (RBCs) of diabetics and nondiabetics were also reported. Diabetes caused aggregation of capillary RBCs [31]. Studies of nail fold capillary blood showed that RBCs do aggregate the capillary vessels of diabetics. The average aggregate size for newly diagnosed diabetics was less than that observed for long duration diabetics. There was no aggregation for the case of non-diabetics [32]. Light scattering of aggregated RBCs differed from that of the non-aggregated cells [33]. It is expected that this weak aggregation, and hence light scattering by capillary RBCs in tissue, will vary with temperature and can contribute to the response or optical signal to temperature changes. Another difference in RBC characteristics that can affect their scattering properties is the difference in refractive index of RBCs between diabetic patients and healthy individuals. The mean refractive index of diabetics RBCs was higher than the mean refractive index of RBCs of non-diabetic individuals [34]. We studied localized reflectance of human skin in the red and near infrared (NIR) region of the spectrum (550–980 nm) [1–9]. In this wavelength range there is no glucose absorption (combination or overtone) bands with any appreciable strength [2]. Water has an overtone band at 980 nm. The absorbing chromophores in these studies were the hemoglobin in the flowing RBCs, in the cutaneous microvascular structure, and the stationary pigment molecules in the epidermis. The source-detector distances in the localized reflectance measurements were selected to confine the observation depth in cutaneous tissue to approximately 2 mm. The scattering centers are the components of the dermis and epidermis and blood cells.

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FIGURE 7.1: Schematic of the dual-probe temperature-controlled localizedreflectance system, reprinted with permission from J. Biomed. Opt., [1].

7.2 Experimental Setup We used several versions of the probe design. Two of the latest designs will be described here. We first used a tungsten lamp/optical shutter system [1]. A dualhead design was subsequently built, which incorporated frequency-modulated light emitting diodes and a quadrant photodiode detector [5]. Fig. 7.1 shows a schematic diagram of dual-probe breadboard (see photo in Fig. 7.2). The dual-probe detection head was spring-loaded in a mount. The mount was in a cradle that was part of an arm-rest, The volunteer placed his/her arm in the cradle, pulled the detection head back, and when prompted by the operator released it to come in contact with the forearm skin. All measurements were performed on the dorsal side of the forearm. The dual probe design allowed simultaneously performing measurements on two adjacent sites on the human arm. The temperature of each probe was controlled and changed at an independent rate from the other one. Thus, one probe was heated and the other was cooled, or one probe was heated or cooled, while the other was kept at a constant temperature. This allowed flexibility in performing different combinations of temperature control programs. The LEDs, detectors, LED driver electronics, and signal extraction electronics were in special mounts in an aluminum briefcase next to the armrest. Fiber optic bundles delivered light from the LEDs to the probe and delivered localized-reflected light from the probes to the detectors. The temperature of each probe was controlled by a thermoelectric element and its associated power supply. In a later design, four light emitting diodes, a photodiode detector, and a reference

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FIGURE 7.2: A photo of the dual head probe.

photodiode were integrated in the detection probe. Light was delivered from the photodiodes to the skin by one common fiber and four fibers at four distances from the illumination fiber delivered light to the detection photodiode. All LEDs were modulated at defined frequencies. The signal at the photodiodes was demodulated and analyzed to obtain light intensity at each source-detector fibers distance. A photo of the integrated photodiode is shown in Fig. 7.3. The electrical leads were connected to the LEDs, signal photodiode, reference photodiode, the thermoelectric element, and temperature-control thermistor. All optical components were within the metallic body of the probe. Fig. 7.4 shows the integrated system, which included the arm-rest (to the left) with the two probes mounted in it. The computer chassis housed the computer-processing unit, thermoelectric control boards and power supply boards for the LEDs, and photodiodes. The values of µa and µs′ of human skin were derived from the localized reflectance signals, established calibration plots using tissue-simulating phantoms of known optical properties, and Monte Carlo simulation of light propagation in tissue using the geometry of the probe [1].

7.3 Temperature Dependence of µa and µs′ of Individual’s Skin Laufer et al. [35] and Bruulsema et al. [36] studied temperature dependence of µa and µs′ of human skin. Laufer studied excised sections of human cadaver skin using

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FIGURE 7.3: Integrated temperature controlled localized reflectance probe.

FIGURE 7.4: The integrated probe instrument. The armrest is on the left-hand side of the photo.

reflectance and transmittance measurements on both sides (epidermis and adipose tissue side of the excised sections). Bruulsema et al. studied the localized reflectance of intact human skin at much longer wavelengths 900 to 1300 nm, where scattering was much lower [36]. Our group studied the NIR localized reflectance of intact human skin in the spectral range between 550 nm and 980 nm. We studied the effect of temperature on the absorption coefficient, µa , the scattering coefficient, µs′ , and other derived transport parameters as skin temperature at the measurement site(s) was changed or modulated. The change in skin localized-reflectance because of temperature change was dubbed the tissue thermo-optical response (THOR). We attempted to use this response to understand factors affecting optical measurements through skin and their

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FIGURE 7.5: Relation between µs ′ (vertical axis) and probe temperature (horizontal axis) for several light-skin subjects at 590 nm. Probe temperature was raised step-wise in the range from 25◦ C to 41◦ C, and then returned back in the same manner. The lines are the linear least square fitting of the experimental data, with their slopes labeled beside individual’s line. The letters A through F refer to the different subjects. Tissue temperature deviates from the probe temperature at the upper and lower limits. Reprinted with permission from J. Biomed. Opt., [1].

relations to diabetes. In one of our earlier studies of localized reflectance of the skin of five light-skin subjects reflectance was measured at 590 nm with the dorsal side of the forearm in constant contact with the temperature-controlled probe. Temperature was switched back and forth among three values between 25 and 41◦C [1]. Regression lines for µs′ vs. probe temperature at 590 nm are shown in Fig. 7.5. The linear least-squares-fitted slope (∂ µs′ /∂ T ) for individual subjects was 0.053 ± 0.0094 cm−1 / ◦ C. The intercept and the slope of the regression lines of µs′ vs. probe temperature plots varied from subject to subject. There were also differences in intercept for different measurements on the same subject which were attributed as probably due to differences in repositioning the probe on skin. The behavior of µa determined at 590 nm differed from that of µs′ at the same wavelength, using the same temperature controlling steps as shown in Fig. 7.6. The data points in Fig. 7.6 look randomly distributed, similar to what was reported for ex-vivo human skin experiment by Laufer et al. [35]. However, connecting the data points in the sequence the temperature was changed and using arrows to indicate the direction of time sequences reveals a trend shown in Fig. 7.6. Measurements are designated A through F in both Figs 7.5 and 7.6. Data used for plots A and C were

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FIGURE 7.6: Plot of the absorption coefficient (vertical axis), at 590 nm, as a function of temperature (horizontal axis) for the same subjects in Figure 7.5. Data points for subjects B, C, and D were connected to show the time sequence of temperature effect on µa . Arrows indicate the direction of time sequences. Reprinted with permission from J. Biomed. Opt., [1].

from measurements performed on the same subject. Tracking the changes for subject A, for example, shows that µa increased as temperature increased from 34◦ C to 41◦ C; there was no change in µa as temperature was subsequently lowered to 25◦ C. The value of µa increased again as temperature was raised from 25◦ C to 41◦C. It did not change as temperature was subsequently lowered to 25◦C, and showed a slight increase as temperature was raised again. The general trend is a much less reversible increase in µa that zigzags upwards as the number of temperature cycles increased. The trend shown in this figure was absent in Laufers’s data on excised cadaver skin [35]. The difference in µa behavior as a function of temperature between intact human skin (in vivo measurement) and the excised skin (in vitro measurement) can be attributed to the absence of cutaneous blood flow in Laufer’s study, which plays an important role in skin thermal response. The reversible response of µs′ to temperature change suggested a physical phenomenon that was attributed to the effect of temperature on the refractive index of the interstitial fluid. Modeling of different refractive index values of ISF and cutaneous scattering centers, as a function of temperature, supported this interpretation [1]. The effect of temperature on µa is quite different from its effect on µs′ in several aspects:

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• There was a short-term irreversibility of µa values upon heating to and above 38 ◦ C. • Consecutively determined µa values zigzagged upwards. • There is a cumulative effect of multiple cycles of heating and cooling. The value of µa depended on the skin thermal history and an upward drift of µa , which could be explained by changes in blood perfusion as temperature increased. LDF measurements indicated enormous variation in the red blood cells flux from comparable sites in the same individual and even for the same site at different times [37, 38]. Correlation between LDF patterns and morphology of the underlying vasculature identified 1-mm2 areas of vascular “territories” surrounded in part by relatively avascular areas [39–41]. The “vascular territories” under each probe position may differ from subject to subject. Several in vitro (glucose in lipid suspensions) and in vivo human studies showed that there is a relationship between the concentration of glucose and µs′ of the tissue or turbid medium [42–44]. As glucose concentration increased, µs′ decreased. The dependence of the tissue scattering coefficient on temperature complicates the relationship between tissue µs′ and glucose concentration. As µa and µs ′ change with temperature, i.e., increasing on raising temperature and decreasing upon lowering temperature, light penetration depth in cutaneous tissue will follow suit. The penetration depth is defined as δ = 1/[3µa (µa + µs ′ )]1/2 . The values of µa , µs ′ , and the light penetration depth δ were calculated between 22 and 38◦ C from the data. The results are shown in Table 7.1. Also listed is p, the probability of data overlap between the penetration depth δ values at 22◦ C and 38◦ C.

TABLE 7.1: Mean values µa , µs′ , and ∆δ of intact human skin at 22◦ C and 38◦ .

Optical parameter

µa (cm−1 ) at 22◦ C µs′ (cm−1) at 22◦ C µa (cm−1 ) at 38◦ C µs′ (cm−1) at 38◦ C ∆δ (µ m) = [δ (22◦ C) − δ (38◦ C)] p[δ (22◦C) = δ (38◦ C) ]

Wavelength 590 nm 2.372± (0.282) 9.191± (0.931) 2.869± (0.289) 9.613± (0.894) 139.86± (32.58) 0.0040

750 nm 0.966± (0.110) 7.34± (0.901) 1.157± (0.106) 7.649± (0.971) 232.4± (98.62) 0.0122

950 nm 0.981± (0.073) 6.067± (0.847) 1.135± (0.123) 6.234± (0.928) 194.3± (58.92) 0.0422

Reprinted with permission from J. Biomed. Opt., [1], with modifications

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Light penetrated deeper into the cutaneous tissue by changing temperature and this change in depth was modulated in the same manner temperature was modulated. This fact introduces the possibility of the localized reflected light was sampling different cutaneous layers at different temperatures. Light penetration depth also increases at longer wavelengths. The interplay of using temperature change at different wavelengths may allow mapping optical properties of tissue layers.

7.4 Temperature Modulation of µa and µs′ of Skin Over Prolonged Interaction Between the Optical Probe and Skin Our group investigated the effect of long-term interaction between the probe and the skin on µa and µs ′ . Localized reflectance of the skin of three volunteers was continuously measured for 90 minutes while the probe temperature was stepped between 22◦ C and 38◦ C for 15 temperature cycles [1]. Experiments where probe-skin contact occurs over a long period are relevant to continuous monitoring of optical properties of tissue for tracking of glucose change during a meal tolerance test or glucose clamp studies [42–44]. Increase in glucose concentration decreased tissue µs′ , but glucose-independent decrease in µs′ was also reported [43]. The purpose of the work reviewed in this section was to understand the nature of long-term signal drift upon prolonged contact between skin and a measurement probe. We continuously collected reflectance data over 90 minutes of probe-skin contact and determined µa and µs′ as temperature was repetitively stepped between 22◦C and 38◦ C for 15 temperature modulation cycles [1]. Each temperature modulation cycle comprised the following steps: skin was equilibrated for 2 minutes at a probe temperature of 22◦C, temperature was raised to 38◦ C over the course of 1-minute, and maintained for 2 minutes, then lowered to 22◦ C over a 1-minute period. At each temperature limit (during the 2-minute window), four optical data packets were collected and values of µa and µs′ were calculated. Three light-skin volunteers were tested after 12 hours fasting and their glucose levels were tested before and after the experiment and were close to 90 mg/dL [5], i.e., no change in glucose concentration during the experiment. The temperature-controlled probe detected photons re-emitted from different depths in the tissue down to ∼ =2 mm. Thermal modeling suggested that temperature of the optically sampled tissue volume was controlled at a probe temperature between 20◦ C and 44◦C [1]. For a given subject, µs ′ was linearly dependent on temperature. µa was not as linear but was distinguishably larger at 38◦ C than at 22◦ C. Light penetration depth in tissue, δ , is higher at the low temperature; δ increased upon cooling and was modulated over a large number of temperature cycles spanning up to 90 minutes total time. Changes in µa of cutaneous vascular blood was the major contribution to changes. δ is in the 500–980 nm wavelength range [1].

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FIGURE 7.7: Effect of temperature modulation on µa , µs′ of subject 1; a) modulation of µs′ at the 590 nm (top), 800 nm (center), and 950 nm (bottom); b) modulation of µa at 590 nm; and c) modulation of µa at 800 nm (triangles) and at 950 nm (bullets). Reprinted with permission from J. Biomed. Opt., [1]. The following three effects of probe-skin interaction were recognized: • There was a short-term reversible within-temperature-modulation of µa and µs′ as discussed in the previous section. • Superimposed on the reversible response there was a long-term drift in µa and µs′ . • There was a change in [∆µa /µa ]T and [∆µs′ /µs′ ]T upon prolonged probe-skin interaction that varied for each individual and wavelength. We interpreted the short-term reversible change in µa to blood perfusion and the long-term upward drift in µa to increased blood perfusion to the dermis. Temperature

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dependence of µa resulted from physiological response of the vascular bed and surrounding areas [1]. The short-term change in µs ′ is due to the effect of temperature on nISF (i.e., a physical phenomenon). We attributed the smaller long-term decrease in µs′ to structural factors in the skin, such as hydration of the protein fibers, which may cause a slow and consistent change in dimensions of the scattering centers at constant volume fraction [1]. Further, the refractive index values vary in different cutaneous layers [45, 46].

7.5 Dependence of Thermo-Optical Response of Localized Reflectance of Human Skin on Diabetic State One question to ask; do the reported vascular and structure differences between diabetic and non-diabetic skin manifest themselves in the localized reflectance measurements, and more specifically in temperature modulated localized reflectance measurements? We used the dual probe optical detection system in Fig. 7.3 to measure the localized reflectance measurements of human skin at two adjacent sites on the human body under different temperature perturbations. In this section we review the effect of temperature perturbations on the localized reflectance of the skin of diabetic and non-diabetic subjects, and how the temperature effect on the localized reflectance signals was used as a classifier for diabetic disease state [6, 9]. The presented data show the possibility for such a classification for the limited population studied. In this study the values of the localized reflectance signals were used in the regression equations without deriving the values of the absorption and the scattering coefficients [6]. Yeh et al. [6] derived a function f from optical signals at two areas of the skin, where the temperature is controlled at each area by independent temperature programs: f (RA1T 1 , RA1T 2 , RA2T 3 , RA2T 4 ) = ln(RA1T 1 /RA1T2 ) − ln(RA2T 3 /RA2T 4 ).

(7.1)

RA1T 1 is a localized reflectance within skin area 1 at time t1 , corresponding to a temperature T1 . RA1T 2 is the localized reflectance within area 1 at temperature T2 ; RA2T 2 is a localized reflectance within skin area 2 at time t1 ; and RA2T 2 is the same localized reflectance within area 2 at t2 . The function(s) f (RA1T 1 , RA1T 2 , RA2T 3 , RA2T 4 ) were determined at 4-source-detector distances and at four wavelengths. The known diabetics or non-diabetic state of each of a set of subjects, together with the optical data, were used to generate a discriminant function D. A subject was classified as diabetic if D > 0, and nondiabetic if D < 0. D is a quadratic expression comprising a multiple function of the type f (RA1T 1 , RA1T 2 , RA2T 3 , RA2T 4 ), in the form [48]: D = ∑i

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∑ j ai j (δi fi )(δ j f j ) + ∑i ai δi fi + ao,

(7.2)

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where

δi = 1 or 0;

∑i δi = K;

δ j = 1 or 0;

∑ j δ j = K.

(7.3)

ai j , ai , and a0 are constants determined from the calibration set, and i or j are indices to specific combinations of wavelength λ and source-detector distance (s-d). The number K limited the total number of λ /s-d combinations used in D, and δi and δ j were determined from the training set through a leave-one-out cross validation procedure [6]. The true diabetic state of a subject was represented by Si where Si = +1 for a diabetic subject, and Si = −1 for a non-diabetic subject. D was calculated for each subject i as Di . The coefficients of the quadratic function D of the calibration set were used to calculate the value of Di for the prediction set. If Di was positive, the subject was classified as diabetic. If Di was negative, the subject was classified as non-diabetic. A subject is categorized as concordant if Di and Si had the same sign and as discordant if they had different signs [6].

7.6 Test for Diabetic State Yeh et al. [6] used the above-mentioned approach to investigate the possibility of determining the difference between diabetic and non-diabetic volunteers and the possibility of differentiating between the two populations. Subjects were non-diabetics and Type 2 diabetics with diabetes duration 2–15 years. The subject’s disease state was determined by previous diagnoses as diabetic or non-diabetic. The training set consisted of 4 diabetic and 4 non-diabetic subjects, each tested 6 times (total of 48 data points). The independent test set, or prediction set, consisted of 6 diabetic and 6 non-diabetic subjects, each tested twice (total of 24 data points) [6]. Three programmed-temperature perturbations were used and are described in details in Ref. 6. Measurements for the training set were performed at the time slots during the day. They were selected to cover several blood glucose concentrations and to insure that different physiological and circadian rhythm conditions were included in the training set [6]. Table 7.2 shows a summary of the results. The temperature programs were temperature-change steps at each of the two probes. Differentiation between diabetics and non-diabetics was not sensitive to the contact time between the skin and the probe at contact times > 120 s. The quality of the separation was not appreciably enhanced by increasing the probe-skin contact times. Further, the classification was achievable at any of the three programmed temperature perturbations. The results presented in Table 7.2 show the ability to differentiate between the two groups, based on the thermo-optical response of human skin, in this limited population experiment [6].

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TABLE 7.2: Prediction of the diabetic status at 120 seconds after probe-skin contact. Temperature Program 1 2 3

Optical Test Result Diabetic Non-diabetic Diabetic Non-diabetic Diabetic Non-diabetic

True Diabetic State Diabetic 11 1 11 0 10 2

Non-diabetic 3 9 1 9 0 12

Reprinted with permission from J. Biomed. Opt., [6].

7.7 Biological Noise and Glucose Determinations There is limited information on the noise sources in an NI glucose measurement. Body interface noise includes probe-repositioning error with respect to skin, change in skin properties due to environmental temperature and humidity. Biological noise includes circadian changes in cutaneous circulation, and sweating due to long contact between skin and the measuring probe. The role of biological and structural effects of skin as noise sources has not been adequately explored. Trans-cutaneous NI glucose optical methods considered human skin as a passive translucent optical window to perform optical measurement. Skin properties change with diabetes [48– 51], on gender [52], and on application of external stimuli [53]. Interaction between a measuring probe and skin involves heat transfer from the probe to the skin and vice versa. NIR optical properties of human skin vary with temperature [1], and skin thermo-optical response to test the diabetic state and track changes in glucose concentration [6, 7]. Lowery et al. used temperature modulated localized reflectance measurements to study the effect of body interface noise and biological noise on the potential correlation between BG and optical signal. Temperature-induced change in localized reflectance was used to calculate the change in skin optical density as a function of temperature, ∆ODT , which incorporated temperature effects on both µa and µs′ . The purpose of this work was to answer two questions. First, can ∆ODT be used to segregate glucose-related signals from the biological and body-interface noise? Second question: does skin play a role of mere optical window for NI determination of BG or it is an active component contributing to the measurement noise because of the effect of diabetes and glucose on its properties? A human experiment was performed on 20 diabetic volunteers, who stayed three days in a hospital, and were fed standard meals and had their diabetes medications and other medications as prescribed by their physicians. NI measurements and refer-

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ence glucose BG measurement were performed during the day and correlated in the subsequent algorithm. The study was conducted at a local hospital, using a protocol approved by the hospital institutional review board. The reference BG values per day were determined using a home glucose meter. The details of the temperature program are in Ref. 5. Data sets with signal changes associated with motion artifacts were rejected using an exponential moving point average on the data stream method developed by Lowery et al. [54]. Signals were collected at each λ , r, and probe temperature T , as the localized reflectance R(λi , r j , T ). T1 and T2 are the probe temperatures at the start and end of temperature ramping. Since the change in temperature induces a small change in R, using the expansion ln(1 + x) = x + x2 /2! + x3/3! + . . . ≈ x, when x ≪ 1, leads to the following equation: ln[R(λi , r j , T2 )/R(λi , r j , T1 )] = ln(1 ± ∆RT ) = ∆RT

(7.4)

∆RT was expressed in optical density terms as ∆ODT , cooling-induced change, ∆ODTC , and heating-induced change, ∆ODT H , leading to   R(λi , r j , T2 ) 2.303 log10 (7.5) cooling = 2.303∆RTC = −∆ODTC (λi , r j ) R(λi , r j , T1 ) 2.303 log10



 R(λi , r j , T2 ) heating = 2.303∆RTH = −∆ODT H (λi , r j ) R(λi , r j , T1 )

(7.6)

The correlation between BG and either or both of ∆ODTC , and ∆ODT H was tested using the 4-term linear regression equations (7.5) and (7.6). [BG] = a0 + ∑ an ∆RTC (λi , r j )n = c0 + ∑ cn ∆ODTC

(7.7)

[BG] = b0 + ∑ bn ∆RT H (λi , r j )n = d0 + ∑ dn ∆ODT H

(7.8)

n

n

n

n

∆ODTC (λi , r j ) and ∆ODT H (λi , r j ) were determined from (R20◦C /R30◦C ) and (R40◦C /R30◦C ), and were fitted to BG values. The set of coefficients c0 , d0 , cn , and dn for each possible combination of ∆ODTC and ∆ODT H to provide least squares fit to BG were calculated. We used 16 λi /r j or 32 λi /r j variables combinations in the regression analysis, using the output of both probes. We selected the regression model having lowest standard error of predicting BG in day 3. Lowery et al. designed a statistical test to rank the likelihood of a true correlation of ∆ODT , at several wavelengths and source-detector distances, with BG rather than with random noise [5]. The model correlation coefficient R2 in day 3 was calculated and ranked its magnitude against R2 values calculated using randomized BG values and the experimentally determined ∆ODT data in day 3. The calculation was performed separately for each volunteer and the results were used to assess the contribution of random noise to the correlation between ∆ODT and BG.

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Lowery et al. established a noise threshold above which we considered a BG prediction is valid by generating 499 random sequences of reference BG values in day 3 for each volunteer and correlating these sets with ∆ODT values [5]. These random permutations were assumed to mimic the sum of body interface and physiological noise. The regression model was applied to predict BG values for each random permutation and to identify a new optimum set of ∆ODT , which was used to recalculate the R2 value for day 3. This process yielded 499 new R2 values for each patient to compare with R2 using the correct sequence of BG in day 3. For a volunteer to exhibit a valid correlation between BG and ∆ODT the R2 value for true glucose correlation must rank higher in 70% of the 499 R2 values generated using randomized BG data. A ranking < 70% threshold indicated that biological and body-interface noise dominated ∆ODT data and produced a correlation with BG equivalent to random chance correlation [5]. Lowery et al. [5] tested the dependence of ability to correlate ∆ODTC and BG above the noise threshold with the age of the volunteer, mean body mass index, glycated hemoglobin (%HbA1c), gender, and duration of diabetes as summarized in Table 7.3. There was considerable overlap among patient data, except for the presence of two distinct groups, one with diabetes duration < 20 years (mean =11.1 ± 4.2) and another with diabetes duration > 20 years (mean = 24.3 ± 7.3). Six of the eight volunteers with R2 greater than the noise threshold (75%) had diabetes duration greater than 20 years. Five of these six patients (62%) were females. One female patient had diabetes duration < 20 years, but R2 for her data set was lower than that of the noise threshold. Cooling-induced change in localized reflectance from 30◦ C to 20 ◦ C, at a temperature ramping rate of −3.3◦C/min, allowed establishing regression equations for predicting BG from the noninvasive measurement with R2 ranking above the noise threshold for diabetic patients that were mostly females and had less than 20 years of diabetes duration. Diabetes was reported to cause changes in the properties of human skin. These include skin thickness at the extremities and collagen structure [48–51]. Skin thickness varied with gender [52]. Diabetes affects response of the cutaneous vascular system to temperature and pressure changes [53], and affects skin structural properties [30]. This, in turn, affects its optical parameters and heat transmission between the probe and the skin, and hence the effect of the transmitted heat on cutaneous structural and vascular properties. Females have thinner cutaneous layers and thicker subcutaneous fat layers than males [52]. Variation in skin thickness by gender and diabetes duration may have caused this subpopulation result reported by Lowery et al. [5]. Extending these arguments (in Refs. 48-53, and 25-30) suggests that females with short diabetes duration have thinner cutaneous layers than males with longer diabetes duration, which may have led to a better correlation between ∆ODTC and BG in their case.

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TABLE 7.3:

Relation between glucose signal correlation and demographic and medical data for the diabetic volunteers. Duration of diabetes < 20 years > 20 years Number of volunteers (total 8 7 15) Mean age (years) 43.3 ±13.8 55 ± 8.2 Duration of diabetes (years) 11.1 ± 4.2 24.3 ± 7.3 Body mass index 30.4 ± 7.3 28.5 ± 2.9 %HbA1c 7.2 ± 1.1 6.8 ± 0.9 Number of females 6 0 Number of males 2 7 Number (%) with R2 ranking 6 (75%) 2 (29%) above noise Number (%) with R2 ranking 2 (25%) 5 (71%) below noise Parameters

Reprinted with permission from J. Biomed. Opt., [5].

7.8 Conclusions Study of the effect of temperature on the localized reflectance of human skin revealed: • Linear reversible response of µs′ as a function of temperature and less reversible response of µa . • There is a drift in µa and µs′ values upon prolonged contact between probe and skin, more so for µa . This is independent of change in glucose concentration. • Thermo-optical response of human skin varied between diabetics and nondiabetics and it was possible to segregate the two groups in a limited population. • The body interface nose and biological noise dominated the signal in patients with long duration of diabetes. Correlation between the signals and blood glucose concentration was better in a subpopulation that was mainly females, and mainly has less than 20 years of diabetes duration. • Due to the structural and vascular effect of diabetes, the skin is an active component in the optical measurement and is not a passive optical window. Thermal response of the optical signal can be due to: • Change in blood perfusion, leading to a change in the absorption coefficient,

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• Change in the refractive index of tissue interstitial fluid, • Change in the capillary RBC aggregation, • Change in hydration of the stratum corneum and epidermis as a result of the effect probe-skin interaction on change in water permeation through the layers. Elucidating the noise sources in the noninvasive optical measurements is necessary to achieve a successful measurement of blood or interstitial glucose concentrations.

Acknowledgments The work reviewed in this chapter was performed while at Abbott Diagnostics Division, Abbott Laboratories, Abbott Park, Il, USA. I would like to thank my former colleagues at Abbott Labs: Shu-jen Yeh, Charles Hanna, Stan Kantor, Eric Shain, Ron Hohs, Mike Lowery, Xiaomao Wu, Brenda Calfin, and Tzyy-Wen Jeng.

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References [1] O. S. Khalil, S-j Yeh, M. G. Lowery, et al., “Temperature modulation of the visible and near infrared absorption and scattering coefficients of intact human skin,” J. Biomed. Opt., vol. 8, 2003, pp. 191–205. [2] O. S. Khalil, “Non-invasive monitoring of diabetes; Specificity, compartmentalization and calibration issues,” in Advances in Fluorescence, C. Geddes Editor, Kulwar Publications, vol. 11, 2006, pp. 157–188. [3] S-j Yeh, S. Kantor, C. F. Hanna, et al., “Calculated calibration models for glucose in cutaneous tissue from temperature modulation of localized reflectance measurements,” Proc. SPIE, vol. 5771, 2005, pp. 166–173. [4] O. S. Khalil, “Non-invasive glucose measurement technologies: An update from 1999 to the dawn of the new millennium,” Diabetes Technol. Ther., vol. 6, 2004, pp. 660–697. [5] M. G. Lowery, B. Calfin, S-j Yeh, et al., “Noise contribution to the correlation between skin temperature-induced localized reflectance skin and blood glucose of diabetic patients,” J. Biomed. Opt., vol. 11, 2006, 054029-1–0540298. [6] S-j Yeh, O. S. Khalil, C. F. Hanna, et al., “Near infrared thermo-optical response of the localized reflectance of intact diabetic and non-diabetic human skin,” J. Biomed. Opt., vol. 8, 2003, pp. 534–544. [7] S-j Yeh, C. F. Hanna, and O. S. Khalil, “Tracking blood glucose changes in cutaneous tissue by temperature-modulated localized reflectance measurements,” Clin. Chem., vol. 94, 2003, pp. 924–934. [8] O. S. Khalil, S-j Yeh, and X. Wu, “Response of near IR localized reflectance signals of intact diabetic human skin to thermal stimuli,” Proc. SPIE, vol. 5086, 2003, pp. 142–148. [9] S-j Yeh, C. F. Hanna, S. Kantor, et al., “Differences in thermal optical response between intact diabetic and nondiabetic human skin,” Proc. SPIE, vol. 4958, 2003, pp. 213–224. [10] V. Tuchin, Tissue Optics, Light Scattering Methods and Instruments for Medical Diagnostics, SPIE Press, Billington, WA, 2000, chapter 1. [11] N. Wiernsperger, “Defects in microvascular haemodynamics during prediabetes: contributor or epiphonomenon?” Diabetologia, vol. 43, 2000, pp. 1439–1449. [12] J. E. Tooke, “Microvascular Function in Human Diabetes: A Physiological Perspective,” Diabetes, vol. 44, 1995, pp. 721–726.

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[13] M. Rendell, T. Bergman, G. O’Donnell, et al., “Microvascular blood flow, volume, and velocity, measured by laser Doppler techniques in IDDM,” Diabetes, vol. 38, 1989, pp. 819–824. [14] M. Rendell and O. Bamisedun, “Diabetic cutaneous microangiopathy,” Am. J. Med., vol. 93, 1992, pp. 611–618. [15] I. M. Braverman and A. Keh-Yen, “Ultrastructural abnormalities of the microvasculature and elastic fibers in the skin of juvenile diabetics,” J. Invest. Dermatol., vol. 82, 1984, pp. 270–274. [16] I. M. Braverman, J. Selby, and A. Keh-Yen, “A study of the veil cells around normal, diabetic and aged cutaneous micro vessels,” J. Invest. Dermatol., vol. 86, 1984, pp. 57–62. [17] G. Rayman, S. A. Williams, P. D. Spenser, et al., “Impaired microvascular hyperemic response to minor skin trauma in type 1 diabetes,” Br. Med. J., vol. 292, 1986, pp. 1295–1298. [18] F. Khan, T. A. Elhadd, S. A. Green, et al., “Impaired skin microvascular function in children, adolescent, and young adults with type 1 diabetes,” Diabetes Care, vol. 23, 2000, pp. 215–220. [19] J. E. Tooke, J. Ostergren, P-E. Lins, et al., “Skin microvascular blood flow control in long duration diabetics with and without complications,” Diabetes Research, vol. 5, 1987, pp. 189–192. [20] S. Bornmyr, J. Castenfors, H. Svensson, et al., “Detection of autonomic sympathetic dysfunction in diabetic patients,” Diabetes Care, vol. 22, 1999, pp. 593–597. [21] A. J. Jaap, A. C. Shore, A. J. Stockman, et al., “Skin capillary density in subjects with impaired glucose tolerance and patients with type 2 diabetes,” Diabetic Medicine, vol. 13, 1996, pp. 160–164. [22] D. D. Sandeman, A. C. Shore, and J. E. Tooke, “Relation of skin capillary pressure in patients with insulin-dependent diabetes mellitus to complications and metabolic control,” New Eng. J. Med., vol. 327, 1996, pp. 760–764. [23] A. J. Jaap, M. S. Hammersley, A. C. Shore, et al., “Reduced microvascular hyperemia in subjects at risk of developing Type 2 (non-insulin-dependent) diabetes Mellitus,” Diabetologia, vol.37, 1996, pp. 214–216. [24] K. B. Stansberry, S. A. Shapiro, M. A. Hill, et al., “Impaired peripheral vasomotion in diabetes,” Diabetes Care, vol. 19, 1996, pp. 715–721. [25] E. Haak, T. Haak, Y. Grozinger, et al., “The impact of contralateral cooling of skin capillary blood cell velocity in patients with diabetes mellitus,” J. Vasc. Res., vol. 35, 1998, pp. 245–249.

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[26] J. E. Tooke, P. E. Lins, J. Ostergren, et al., “Skin microvascular autoregulatory response in Type 1 diabetics: the influence of duration and control,” Int. J. Microcirc: Clin. Exp., vol. 4, 1985, pp. 249–256. [27] S. J. Benbow, D. W. Pryce, K. Noblett, et al., “Flow motion in peripheral diabetic neuropathy,” Clin. Sci., vol. 88, 1995, 191–196. [28] R. G. Sibbald , S. J. Landolt, and D. Toth, ”Skin and diabetes,” Endocrinol. Metab. Clin. North Am., vol. 25, 1996, pp. 463–472. [29] V. M. Monnier, O. K. D. Bautista, D. R. Sell, et al., “Skin collagen glycation, glycoxidation, and crosslinking are lower in subjects with long-term intensive versus conventional therapy of type 1 diabetes: Relevance of glycated collagen products versus HbA1c as markers for diabetic complications,” Diabetes, vol. 48, 1999, 870–880. [30] V. J. James, L. Belbridge, S. V. McLennan, et al., “Use of X - ray diffraction in study of human diabetic and aging collagen,” Diabetes, vol. 40, 1991, pp. 391–394. [31] N. N. Firsov, A. V. Priezzhev, O. M. Ryaboshapka, et al., “Aggregation and disaggregation of erythrocytes in whole blood: study by back scattering technique,” J. Biomed. Optics, vol.4, 1999, pp. 76–84. [32] Y. I. Gurfinkel, K. V. Ovsyannikov, A. S. Ametov, et al., “Early diagnosis of diabetes mellitus using noninvasive imaging by computer capillaroscopy,” Technical Digest, Optical Society of America Biomedical Topical Meetings, Miami Beach, Florida, USA, April 7-10, 2002, Su-D4-1, pp. 62–64. [33] L. D. Shvartsman and I. Fine, “RBC Aggregation effects on light scattering from blood,” Proc. SPIE, vol. 2162, 2000, pp. 120–129. [34] G. Mazarevica, T. Freivalds, and A. Jurka, “Properties of erythrocyte light refraction in diabetic patients,” J. Biomed. Opt., vol. 7, 2002, pp. 244–247. [35] J. Laufer, R. Simpson, M. Kohl, et al., “Effect of temperature on the optical properties of ex vivo human dermis and subdermis,” Phys. Med. Biol., vol. 43, 1998, pp. 2479–2489. [36] T. Bruulsema, J. E. Hayward, T. J. Farrell, et al., “Optical properties of phantoms and tissue measured in vivo from 0.9-1.3 µ m using spatially resolved diffuse reflectance,” Proc. SPIE, Vol. 2979, 1997, pp. 325–334. [37] I. M. Braverman, ”The cutaneous microcirculation: ultrastructure and microanatomical organization,” Microcirculation, vol. 4, 1997, pp. 329–340. [38] A.A. K. Hassan and J. E. Tooke, “Effect of change in local skin temperature on postoral vasoconstriction in man,” Clin. Sci., vol. 74, 1988, pp. 201–206. [39] T. Tenland, E. G. Salerud, E. G. Nilsson, et al., “Spatial and temporal variations in human skin blood flow,” Int. J. Microcirc. Cli. Exp., vol. 2, 1983, pp. 81–90.

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[40] I. M. Braverman, A. Keh, and D. Goldminz, “Correlation of laser Doppler wave patterns with underlying microvascular anatomy,” J. Invest. Dermatol., vol. 95, 1990, pp. 283–286. [41] I. M. Braverman, “Anatomy and physiology of cutaneous microcirculation,” in Bioengineering of the Skin: Cutaneous Blood Flow and Erythema, E. Berardesca, P. Elsner, H. I. Maibach, eds., CRC Press, Boca Raton, Florida, 1995, pp. 3–22. [42] J. Maier, S. Walker, S. Fantini, et al., “Non-invasive glucose determination by measuring variations of the reduced scattering coefficient of tissues in the near-infrared,” Opt. Lett., vol.19, 1994, pp. 2062–2064. [43] J. T. Bruulsema, J. E. Hayward, T. Farrell, et al., “Correlation between blood glucose concentration in diabetics and noninvasively measured tissue optical scattering coefficient,” Opt. Lett., vol. 22, 1997, pp. 190–192. [44] L. Heinemann, G. Schmelzeisen-Redeker on behalf of the Non-invasive task force, “Non-invasive continuous glucose monitoring in Type I diabetic patients with optical glucose sensors,” Diabetologia, vol. 4, 1998, pp. 848–854. [45] A. Kn¨uttel and M. Boehlau-Godau, “Spatially confined and temporally resolved refractive index scattering evaluation of human skin performed with optical coherence tomography,” J. Biomed. Optics, vol. 5, 2000, pp. 83–92. [46] A. Kn¨uttel, M. Bohlau-Godau, M. Rist, et al., “In-vivo evaluation of layered scattering coefficients and refractive indices with OCT,” Proc. SPIE, vol. 3597, 1999, pp. 324–334. [47] C. Arhtur, and R. M. Huntly, “Quantitative determination of skin thickness in diabetes mellitus. Relationship to disease parameters,” J. Med., vol. 21, 1990, pp. 257–264. [48] R.O. Duda, P. E. Hart, and G. E. Stork, Pattern Classification, WileyInterscience, 2000, pp. 215–225. [49] A. Collier, A. W. Patrick, D. Bell, et al., “Relationship of skin thickness to duration of diabetes, glycemic control, and diabetes complications in male IDDM patients,” Diabetes Care, vol. 12, 1989, pp. 309–312. [50] R. A. Malik, J. Metcalfe J., A. K. Sharma, et al., “Skin epidermal thickness and vascular density in type 1 Diabetes,” Diabetes Med., vol. 9, 1992, pp. 263–267. [51] T. Forst, P. Kaan, A. Pfutzner, et al., “Association between “diabetic thick skin syndrome” and neurological disorders in diabetes mellitus,” Acta Diabetol., vol. 31, 1994, pp. 73–77. [52] S. Shuster, M. M. Black, and E. McVitie, “The influence of age and sex on skin thickness, skin collagen and density,” Br. J. Dermatol., vol. 93, 1975, pp. 639–643.

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[53] G. Rayman, S. A. Williams, P. D. Spenser, et al., “Impaired microvascular hyperemic response to minor skin trauma in type 1 diabetes,” Br. Med. J., vol. 292, 1986, pp. 1295–1298. [54] M. G. Lowery, E. B. Shain, and O. S. Khalil, Inventors, “Method for detecting artifacts in data,” United States Patent, US 7,254,425 B2 (2007).

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8 In Vivo Nondestructive Measurement of Blood Glucose by Near-Infrared Diffuse-Reflectance Spectroscopy Yukihiro Ozaki, Hideyuki Shinzawa Department of Chemistry, School of Science and Technology, Kwansei-Gakuin University, Japan Katsuhiko Maruo Advanced Technologies Development Laboratory, Matsushita Electric Works Ltd., Japan Yi Ping Du Research and Analysis Center, East China University of Science and Technology, China Sumaporn Kasemsumran Nondestructive Quality Evaluation Unit, Kasetsart Agricultural and Agro-Industrial Product Improvement Institute (KAPI), Kasetsart University, Thailand Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Importance of NIR In Vivo Monitoring of Blood Glucose . . . . . . . . . . . . . . . . . . The NIR System for Noninvasive Blood Glucose Assay . . . . . . . . . . . . . . . . . . . NIR Spectra of Human Skin and Built of Calibration Models . . . . . . . . . . . . . . New Chemometrics Algorithms for Wavelength Interval Selection and Sample Selection and Their Applications to In Vivo Near-Infrared Spectroscopic Determination of Blood Glucose . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.6 Multi-Objective Genetic Algorithm-Based Sample Selection for Partial Least Squares Model Building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.7 Region Orthogonal Signal Correction (ROSC) and Its Application to In Vivo NIR Spectra of Human Skin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8.1 8.2 8.3 8.4 8.5

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This chapter reviews in vivo noninvasive monitoring of blood glucose by near-infrared (NIR) diffuse-reflectance (DR) spectroscopy. The NIR spectra of human forearm were measured in vivo by use of an NIR system equipped with a pair of illuminating

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and detecting optical fibers newly developed by our group. The optical geometry of the fibers enables the NIR measurements selectively from dermis tissue and reduces the interference noise arising from the stratum corneum. Oral glucose intake experiments were performed with six subjects (including single type I diabetes) whose NIR skin spectra were measured at the forearm. Partial least square regression (PLSR) analysis was carried out for the NIR data and calibration models were built for each subject individually. We also developed new chemometrics algorithms and data pretreatment methods that are useful for the blood glucose assay. In the former part of this review, first the importance of in vivo noninvasive monitoring of blood glucose by NIR measurement is described, and then the NIR system we developed for the in vivo measurement is outlined. Following these the results of NIR spectral measurements and calibration models for blood glucose assay are explained. In the latter part of this review, new chemometrics algorithms for wavelength and sample selections and those for removing interference components are introduced and their applications to the in vivo NIR spectra of human skin are described. Keywords: Near-infrared (NIR) spectroscopy, noninvasive glucose monitoring, chemometrics, human skin, blood glucose, multivariate analysis.

8.1 Introduction Serious diabetic patients, especially type I patients, need to measure their blood glucose contents at least 4 times a day by themselves for a present therapy (Intensive Insulin Therapy). The self-monitoring blood glucose (SMBG) instruments currently used are all invasive types that need a blood drop withdrawn from a fingertip or other measurement site of the body by a needle puncture. NIR spectroscopy has been known to have a potential in realizing noninvasive blood glucose monitoring, and there have been many trials for in vivo blood glucose assay using NIR spectroscopy over the years [1–30]. NIR spectroscopy has the following advantages for in vivo blood glucose determination. Firstly, NIR spectroscopy is a nondestructive and noninvasive analytical technique. Secondly, no pretreatments are requested for the NIR measurements. Thirdly, reagents and preprocessing samples are needless. Moreover, it requires minimal technical expertise. NIR noninvasive blood glucose assay has been investigated extensively for many years [1–30]. Robinson et al. [13] used a shorter wavelength NIR region, i.e., the region between 800 and 1300 nm for finger spectra measurements. They reported that the cross-validated average absolute error of 1.1 mmol/l (19.8 mg/dl) was obtained from their calibration model. Muller et al. [4] also used a shorter wavelength region of 800–1350 nm for finger DR spectra measurements. They obtained the cross-validated root mean standard error of prediction (RMSEP) from 1.02 mmol/l (18.4 mg/dl) to 1.88 mmol/l (33.8 mg/dl). Heise et al. [15] and Marbach et al.

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[16, 17] carried out intensively the in vivo determination of glucose on a single diabetic using glucose tolerance test and that on a population of 133 different subjects. They measured the DR of NIR light at the oral mucosa. The RMSEP for the prediction of glucose they obtained was 36.4 mg/dl. Irrespective of these intensive studies, there is still no reliable NIR noninvasive blood glucose monitor at present, and in addition, none of the previous innovations gained approval by the Food and Drug Administration (FDA) of United States.

8.2 Importance of NIR In Vivo Monitoring of Blood Glucose Noninvasive NIR blood glucose monitoring is very much a challenging project because it deals with very weak signals of glucose directly from human skin, and the physiological conditions of skin tissue such as body temperature vary easily with time. One critical difficulty associated with in vivo blood glucose assay is an extremely low signal-to-noise ratio (S/N) of a glucose peak in an NIR spectrum of human skin tissue. In an in vitro study using NIR transmittance spectroscopy, if one measures the difference of 10 mg/dl glucose using a 1 mm cell, one will obtain the absorbance change of less than 10 µ AU (absorbance unit) [2]. This means that background noise easily hides the glucose signal when an NIR spectrum is measured in vivo. Therefore, the quality of spectra is critical for reliable assay of blood glucose. From this standpoint of view, the measurement methods of some former studies cannot avoid tissue noise, because finger or skin tissue they used contains bone, nail, fat, stratum corneum etc., in which the glucose content may not correspond to the blood glucose content. To avoid the influence of stratum corneum, Heise et al. [18] measured NIR spectra of oral mucosa for the blood glucose measurement. To overcome the difficulties mentioned above we developed a new NIR system that can detect very weak glucose signal in human tissue and realize a noninvasive blood glucose measurement [5–7]. The region of 1300 to 1900 nm was chosen for the NIR measurements. A maximum light path length of the 1300–1900 nm region is expected to be a few millimeters due to strong absorption of water contained in human tissue. For this limitation, the skin tissue, which has a simple anatomical structure with only a few millimeters in depth, may be the most suitable for blood glucose monitoring among the various human tissues. Figure 8.1 shows the human skin. It consists of three layers, i.e., the epidermis, dermis and subcutaneous tissue [5]. The epidermis contains the stratum corneum, and capillary vessels are not developed sufficiently in it. The subcutaneous tissue is composed mainly of fatty tissues. These facts mean that these two layers of skin tissue may have lower correlation to a change in blood glucose content. There are well-developed capillary vessels in the dermis, and blood glucose is easily transferred to the dermis tissue due to its high permeability. Thus, the glucose content in the dermis is assumed to correlate with the blood glucose content in the same way

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as that in the interstitial fluid. If NIR spectra could be obtained selectively from the dermis, the interference noise originating from the epidermis or subcutaneous tissue would be largely removed.

8.3 The NIR System for Noninvasive Blood Glucose Assay We developed a new NIR spectrophotometer system with a set of two optical fibers to obtain the dermis spectra selectively [5–7]. As shown in Fig. 8.1 [5], one set of optical fibers is attached to the skin surface vertically; the skin surface is illuminated by the measuring light through the inlet optical fiber, and the scattered light is collected by the detecting optical fiber. When one would choose an adequate fiber distance, one could control the penetration depth of measuring light. The light path property of this condition was confirmed by computer simulation based on Monte Carlo method by Iino et al. [33]. We also calculated the light path and the light path length by simulating the light propagation in skin tissue. For this simulation a Monte Carlo method, which is adequate for strongly scattering media, just like human skin tissue, was chosen. The details of the simulation were reported in [5].

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FIGURE 8.2: (a) Schematic diagram of the instrument developed in the present study. (b) Schematic diagram of the cross section of the probe.

8.3.1 Outline of the NIR instrument Figure 8.2 depicts the NIR system that we developed [5–7]. It consists of a tungsten halogen lamp (150 W), an optical fiber bundle, switching device for selecting a light path, a flat field type grating, a 256 InGaAs photodiode array sensor extended to a cut-off 2100 nm (Hamamatsu Photonics K.K., Japan), a 16 bit A/D converter and a signal processor. The optical fiber probe contains optical fibers with a cladding diameter of 0.2 mm and a core diameter of 0.175 mm (numerical aperture: NA=0.2, Fujikura Ltd., Japan). The actual optical fiber probe used for the system consists of one central detecting fiber and twelve illuminating fibers arranged in a circle (Fig. 8.2 (b)). The distance between the detecting optical fiber and each of the surrounding fibers is 0.65 mm. The diameter of this optical fiber probe is 9 mm. The optical fiber bundle is divided into two parts at the light source end (Fig. 8.2(a)), one part transmitting light to the reference site, and the other to the measurement site. The sensing end A-a is attached to the skin tissue and the sensing end B-a is connected to the standard reflectance target (Labshere, Inc.,USA). Both ends have the same structures shown in Fig. 8.2(b). The mechanical shutters select the measuring signals, both of which are transmitted to the grating (Horiba Jobin Yvon,

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France). For data acquisition, software named “LabVIEW” (National Instruments, USA) was used. The spectral sampling interval was about 3 nm which corresponded to the width of each element of array photodiode. The stability of this instrument described by root-mean-square noise was under 100µ AU (Absorbance Unit).

8.3.2 Spectral measurements For the measurements of NIR spectra of skin, a subject sat on a chair silently, and then the optical fiber probe was placed vertically on the inside of the forearm [5, 6]. During the measurements the contact pressure of the sensing end A to the skin was maintained at 46 kPa. The sensing end A was attached to the site for about one minute while measuring the signals and was released from the site until the next measurement. The subjects were six male volunteers; five males were healthy and one male suffered from type I diabetes [5, 6]. Six subjects were subjected to oral glucose intake experiment. The detailed experimental design for in vivo measurements was reported elsewhere [5, 6]. About 50 paired data sets, i.e., the reference blood glucose contents and the NIR spectra, were obtained for each experiment. The oral glucose intake experiments were performed five or six times for each subject to develop calibration models for predicting blood glucose content. Thus, a total of about 250 paired data sets was used for calibrating the data. Partial least squares regression (PLSR) was used for building the calibration models. In the paired data sets the reference data were taken one minute before each spectral measurement, so that the spectral data had one minute delay in the analysis. It should be noted that the calibration models developed from oral glucose intake types of experiments often have chance temporal correlation. It is considered that the utilization of plural experiment data sets for the quantitative modeling is most useful to avoid the chance temporal correlation at present [2, 25]. The validation of the calibration models was done by prediction of the blood glucose contents for another oral glucose intake experiment of the same subject.

8.4 NIR Spectra of Human Skin and Built of Calibration Models 8.4.1 NIR spectra of human skin Figure 8.3 shows 50 NIR spectra of the forearm skin of one subject measured during one oral glucose intake experiment [6]. These spectra have a strong band at 1450 nm assigned mainly to the combination of the antisymmetric and symmetric OH stretching modes of water. Weak features arising from blood glucose, proteins, lipids and so on in the skin overlap with the strong water band. This sharp absorbance peak at 1450 nm suggests that our system using the novel fiber probe can reduce interference from absorption by the stratum corneum.

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8.4.2 Calibration models PLS calibration models for blood glucose determination were obtained from the NIR spectra of six subjects individually [6]. The spectra data used in these multivariate analysis were not subjected to any pre-treatment method. The regression coefficients of individual optimum calibration models are shown with a black line in Fig. 8.4 (a)-(f) [6]. In this PLSR analysis the optimum number of principal components for the calibration models is 8 or 9. It is noted that Fig. 8.4 (c) and (e) show the typical feature of the regression coefficient of the in vitro study; both regression coefficients have two positive and negative peaks below 1530 nm, a broad positive peak around 1580 nm and some narrow positive and negative peaks above 1660 nm. The other four regression coefficients in Figure 8.4 have spikes in the above features at the optimum number of principal components but show the tendency of the three characteristic features obviously.

8.4.3 Blood glucose assay The validation for the calibration models was performed by the prediction of the blood glucose contents for other data sets of the same subjects [6]. The blood glucose contents were predicted using the individual calibration model for other oral glucose intake experiments. The time sequence relations between the reference blood glucose contents and the predicted blood glucose contents are presented in Fig. 8.5 (a)-(f) [6]. The prediction bias was compensated in these graphs, and the bias occurred in each prediction is indicated on each graph also. Unfortunately, the absolute

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contents of blood glucose were not able to be predicted in this study; only changes in the relative blood glucose contents were predicted.

8.4.4 The regression coefficient characteristics An in vitro study using bovine serum by Maruo et al. [34, 35] showed the important role of the glucose absorption peak at 1580 nm for a glucose assay. The characteristics of the peak observed in the in vitro study are in accord with that of the present in vivo study. This result means that the small absorbance change of glucose can be detected by the newly developed NIR instrument for blood glucose measurement. The similar result was also obtained by Heise et al. [18]. They studied the oral mucosa and human plasma using a straightforward spectral variable selection based on choice from optimum PLSR vector within the same wavelength range as Maruo et al. [6]. There is a difference between these two studies, i.e., the results by Maruo et al. [6] were obtained from full spectra and those by Heise et al. [18] were obtained from selected variables. The regression coefficients from PLSR analysis by Heise et al. [18] have similar features to the regression coefficients by Maruo et al. [6], i.e., a positive peak at about 1580 nm.

8.4.5 The prediction of blood glucose content We obtained the correlation coefficient R = 0.934 and standard error of prediction (SEP)equal to 23.7 mg/dl for the six subjects using individual calibration models. Comparing with other studies using the similar wavelength region [18], our SEP result shows the good performance for blood glucose monitoring. Figure 8.6 presents the result for Clarke error grid analysis obtained using the same data sets as those in Fig. 8.5. The data plots included are, for the A zone: 71.3%, B zone: 21.3%, C zone: 0%, D zone: 7.4%, and E zone: 0%. Almost all prediction plots exist in zones A and B. However, it is noted that there are some plots in zone D. The plots in zones A and B are clinically acceptable while those in zones C, D and E are potentially dangerous, and, therefore, they may have the clinically significant errors. In this study, the plots in D zone have an overestimated value below 70 mg/dl of blood glucose contents. To improve these prediction errors below 100 mg/dl, not only the reduction of measurement noise but also the preparation of analytical data sets with adequate blood glucose contents are important.

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8.5 New Chemometrics Algorithms for Wavelength Interval Selection and Sample Selection and Their Applications to In Vivo Near-Infrared Spectroscopic Determination of Blood Glucose Chemometrics is an essential tool for analyzing in vivo NIR spectra of human skin that show overlapping absorption bands. In the construction of a calibration model, PLS regression is the most popular multivariate method. In general, PLS is a powerful method, but when it is applied to NIR spectra of very complex samples consisting of a number of components, it does not always yield good results. This is because such NIR spectra usually contain interference signals, such as those due to water and other components. The crucial point for building the best calibration models for the determination of blood glucose is to select the informative NIR regions where one obtains an optimized calibration model for glucose. We developed several new chemometrics algorithms for wavelength interval se-

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FIGURE 8.7: Scheme for explanation of (a) MWPLSR and (b) CSMWPLS. (Reproduced from Ref. 3 with permission. Copyright (2004) Elsevier).

lection and sample selection in multicomponent spectral analysis [8–11]. These are very useful for in vivo NIR determination of blood glucose. In this section recently proposed new wavelength selection methods, Moving Window Partial Least Squares Regression (MWPLSR) [Fig. 8.7(a)] [8], Changeable Size Moving Window Partial Least Squares (CSMWPLS) [Fig. 8.7(b)] [9], and Searching Combination Moving Window Partial Least Squares (SCMWPLS) (Figure 8.8) [9], are outlined. PLS is a full-spectral calibration method and has a built-in capacity to deal with the overdetermined problem of full-spectrum calibration [36, 37]. However, the selection of a wavelength or wavenumber region is still very important. There is increasing evidence indicating that wavelength selection can significantly refine the performance of these full-spectrum calibration techniques. In fact, various methods of wavelength or wavenumber selection have recently been proposed and used [4, 8]. We demonstrated that the prediction error of indirect (or inverse) calibration may be inflated by including nonideal spectral regions, and a common feature of the nonideal spectral regions is the increased complexity in (LV) models when these regions are used

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FIGURE 8.8: Scheme for explanation of SCMWPLS (Reproduced from Ref. 9 with permission. Copyright (2004) Elsevier).

for calibration modeling [8]. We, thus, proposed a new method of spectral interval selection called MWPLSR [8].

8.5.1 Moving window partial least squares regression (MWPLSR) The goal of MWPLSR is to search for informative spectral regions for the multicomponent spectral analysis. The informative regions contain useful information for

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PLS model building, and thus are helpful to improve the performance of the model. In MWPLSR, a series of PLS models are built for every window that moves over the whole spectral region, and then informative regions, in terms of the least complexity of PLS models reaching a desired error level, are located [8]. A PLS model is described as follows: ˆ = Xb + e, Y

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ˆ (m × 1 vector) is the prediction of a given concentration Y (m × 1 vector), where Y X (m × n matrix) is the matrix consisting of m samples and n spectral channels, b (n × 1 vector) is the regression coefficient vector, and e (m × 1 vector) is the residual vector containing errors and undescribed elements. In MWPLSR, a spectral window starting at the ith spectral channel and ending at the (I + h − 1)-th spectral channel is constructed, where h is the window size. There are (n − h + 1) windows over the whole spectra, each window corresponding to a subset of the original spectral X. One may build PLS models with varying LV numbers from 1 to a fixed value k, and then calculate the sums of squared residuals (SSRs) for each subset. After calculations for all the subsets, SSR is plotted as a function of the position of the window. This plot shows a number of residue lines, each line associated with the SSR for a certain LV number in the corresponding window position (see, for example, Fig. 8.10). A figure containing such residue lines provides two kinds of information; the information about informative regions and that about the estimation of LV numbers. A representative informative region should show low values of the SSR and often shows the shape of an upside down peak, corresponding to a band in the same region. Thus, one can easily select the beginning and end points of the region. However, such a selected region possibly does not supply the best predictive results, i.e., this region is not optimum, and possibly there still exists a special sub-region in this region, which may supply the optimum results. Therefore, it is necessary to search for the optimum sub-region for an informative region obtained by MWPLSR in order to further improve the prediction of the PLS model. In practice, more than one informative region is often found by MWPLSR in vibrational spectra because of the existence of many spectral bands. In such cases, the combination of regions seems to be needed to collect more useful information from the spectra to construct the PLS models. To search for an optimized sub-region for each selected informative region and the optimized combination of informative regions we proposed CSMWPLS and SCMWPLS methods [9]. In CSMWPLS, the window size is changed and the window is moved over a selected informative region with each window size (Fig. 8.7(b)). SCMWPLS aims at looking for an optimized combination of informative regions by performing CSMWPLS for every informative region step by step (Fig. 8.8). In this way, MWPLSR is used first to identify informative regions from spectra of a system like human skin, and then an optimized sub-region is searched for each selected informative region by CSMWPLS or directly is searched for the optimized combination of regions by SCMWPLS.

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8.5.2 Changeable size moving window partial least squares (CSMWPLS) and searching combination moving window partial least squares (SCMWPLS) The basic idea of CSMWPLS is to change the moving window size w from 1 to p for a given information region with p special points [9]. A moving window is moved from the first spectral point to the (p − w + 1)-th point over the informative region and to collect all possible sub-windows for every window size (Fig. 8.7(b)). When w = 1, moving the window from the first to the end point will collect all possible sub-windows with the window size of one. Similarly, for other cases of w, all sub-windows with the size of w may be obtained. Therefore, CSMWPLS considers all possible spectral intervals (sub-window or sub-regions) in the range of the informative region. For every window, a PLS model with a selected LV number is constructed, and RMSEC is calculated. The sub-region with the smallest value of RMSEC is considered as the optimized spectral interval. SCMWPLS searches for the optimal combination of information region based on CSMWPLS [9]. As described above, every informative region obtained by MWPLSR contains an optimized sub-region. Although these sub-regions are optimum in their corresponding regions, their direct combination possibly cannot show an optimum performance. Thus, it is necessary to develop a method to search for the optimized combination of informative regions [9]. Exhaustive search, which considers all possible combinations of spectral points in all informative regions, can guarantee to find out the global optimum. However, the calculation by exhaustive search will take much more time; even it cannot be finished by a general microcomputer. For example, in a system with three informative regions A, B and C, where the numbers of spectral intervals are a, b and c, respectively, the number of possible combinations equals to a(a + 1)/2 × b(b + 1)/2 × c(c + 1)/2. If a = 40, b = 50, c = 60, exhaustive search method will deal with 40(40 + 1)/2 × 50(50 + 1)/2 × 60(60 + 1)/2 = 1.9133 × 109 combinations. SCMWPLS is a local optimized algorithm to search for the optimized combination of informative regions [9]. In the first step of SCMWPLS, CSMWPLS is applied to the first region (region a in Fig. 8.8) that shows the minimum residue level to search for the optimized sub-region with the smallest value of RMSEC in a reasonable LV number selected by cross validation. This optimized sub-region is viewed as the base-region. The second step is to perform CSMWPLS for the second informative region (region b in Figure 8.8), in which one uses the combinations of the baseregion and one of the possible spectral intervals selected from the second informative region, to build PLS models and calculate their RMSEC values. After that, a new base-region will be selected, which shows the smallest value of RMSEC. The next step is to look for another new base-region with the similar procedure for the next informative region, until the last informative region. The base-region after finishing calculation for all informative regions is considered as the optimized combination. This algorithm, not like exhaustive search, only needs to search for a few parts of all possible combinations of the informative regions, whose number is a(a + 1)/2 + b(b + 1)/2 + c(c + 1)/2 for the system with three informative regions A, B and C,

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where the numbers of spectral intervals are a, b and c, respectively. When a = 40, b = 50, c = 60, SCMWPLS will deal with only 40(40 + 1)/2 + 50(50 + 1)/2 + 60(60 + 1)/2 = 3925 combinations. When one uses SCMWPLS, one must consider the order of informative regions to search for. Usually, the value of RMSEC for an expected LVs number of a PLS model including an informative region reflects the importance of the region. Therefore, the region with the smallest RMSEC, i.e., the most informative region, should be the first in the order, and then the region with the second smallest RMSEC, and so on. Even so, if possible, all the possible orders are suggested to try, e.g., for the three informative regions A, B and C, it is best to attempt all the orders, A-B-C, A-C-B, B-A-C, B-C-A, C-A-B and C-B-A.

8.5.3 Application of MWPLSR and SCMWPLS to noninvasive blood glucose assay with NIR spectroscopy We applied MWPLSR and SCMWPLS to the blood glucose assay by in vivo NIR spectra of human skin [12]. Figure 8.9 shows normalized NIR spectra of glucose powder (solid line) and human skin measured noninvasively (dash line) [12]. The latter spectrum was calculated by averaging 48 skin spectra collected during an oral glucose tolerance test. As already described in subsection 8.4.1, the features due to blood glucose are interfered significantly with those due to water and other components in the skin. Wavelength selection methods are very useful to deal with such problems of the interferences. Therefore, MWPLSR and SCMWPLS were applied to the in vivo NIR spectra of skin for the blood glucose assay. The original spectra were subjected to MSC before MWPLSR, SCMWPLS and multivariate analysis were applied. All the 48 skin spectra were employed to build PLS calibration models. The model performance was validated by use of the four segments cross-validation method (12 spectra per each segment) and RMSEV was calculated. Figure 8.10 displays 15 residue lines for blood glucose obtained by applying MWPLSR to the NIR spectra of skin [12]. Three informative regions, the 1228–1323, 1574–1736, and 1739–1800 nm regions, can easily be found. The informative regions of 1574–1736 and 1739–1800 nm contain bands due to the first overtones of OH and CH stretching modes of glucose, respectively. The region of 1228–1323 nm has only weak absorption feature due to glucose but it has weak interference from water. SCMWPLS was applied to these three informative regions for optimizing the combination of informative regions. It was found that the optimized combination obtained by SCMWPLS contains only one informative region, i.e., the 1574– 1736 nm region. Table 8.1 compares statistical results of blood glucose models built by use of the whole region, the individual informative regions, their direct combinations, and the optimized informative region[12]. The PLS calibration model developed by using the whole region of 1212–1889 nm yields the large RMSEV of 20.1977 mg/dl with a high PLS factor of 7 and the correlation coefficient of 0.8936. The informative region of 1574–1736 nm gives the best validation results among the three informative

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FIGURE 8.9: A normalized NIR spectra in the 1212–1889 nm region of glucose powder (solid line) and a normalized averaged of 48 human skin spectra (dashed line) measured during an oral glucose tolerance test (Reproduced from [12] with permission. Copyright (2005) Elsevier).

FIGURE 8.10: Residue lines obtained by MWPLSR for the NIR spectra of skin (Reproduced from [12] with permission. Copyright (2005) Elsevier).

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TABLE 8.1: Prediction results for PLS calibration models for blood glucose determination developed by use of the whole spectral region and the regions selected by MWPLSR and SCMWPLS [12].

.

Method

Spectral region (nm)

PLS factor

Whole region MWPLSR MWPLSR MWPLSR MWPLSR

1212-1889

7

Correlation RMSEV coeffi(mg/dl) cient 0.8936 20.1977

1228-1323 1574-1736 1739-1800 1228-1323, 1574-1736, 1739-1800 1228-1323, 1574-1736 1574-1736, 1739-1800 1616-1733

6 4 4 6

0.8519 0.9091 0.8302 0.8840

24.2398 18.3642 24.8947 20.9073

6 5 4

0.8984 0.9060 0.9205

19.4118 18.7775 17.1924

MWPLSR MWPLSR SCMWPLS

regions with the correlation coefficient of 0.9091 and the RMSEV of 18.3642 mg/dl with the PLS factor 4. The direct combinations of informative regions cannot supply better validation results than the individual informative region of 1574–1736 nm. It can be seen from Table 8.1 that the PLS calibration model based on SCMWPLS using the best optimized informative region of 1616–1733 nm yields the best validation results with the highest correlation coefficient of 0.9205 and the lowest RMSEV of 17.1924 mg/dl with the PLS factor 4 [12]. The significant improvement of the validation results shows that this optimized region selected by SCMWPLS contains larger information about blood glucose and less interference than others [12]. Figures 8.11 (a), (b) and (c) show EGA plots for the three PLS models developed by using the whole region, the region of 1574–1736 nm suggested by MWPLSR, and the optimized region of 1616–1733 nm yielded by SCMWPLS [12]. All the EGA plots show that the mainstream of the prediction values is located within zone A that is defined as the clinical correction. These EGA plots confirm that the prediction results for the noninvasive blood glucose measurements by NIR spectroscopy are clinically acceptable. However, the EGA plots for those three models are significantly different from each other in terms of the numbers and positions of points in each zone. It was found that 85.5%, 80.2%, and 83.3% of the predicted blood glucose concentrations fall in zone A for the models obtained with SCMWPLS, MWPLSR, and the whole region, respectively. 7.2%, 9.4%, and 8.3% of the predicted values are found in zone B, and their 7.3%, 10.4%, and 8.4% are seen in zone D for these three models. The EGA results clearly reveal that the PLS model obtained by using the optimized region selected by SCMWPLS provides not only the best performance in statistical point, but also presents the best clinical accuracy among the three models

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(a)

(b)

(c)

FIGURE 8.11: EGA plots between the actual and predicted blood glucose concentrations for (a) the PLS model based on the whole region, (b) the PLS model obtained by using the informative region of 1574–1736 nm suggested by MWPLSR, and (c) the PLS model developed by use of the optimized informative region of 1616–1733 nm obtained by SCMWPLS (Reproduced from Ref. 12 with permission. Copyright (2005) Elsevier). © 2009 by Taylor & Francis Group, LLC

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[12].

8.6 Multi-Objective Genetic Algorithm-Based Sample Selection for Partial Least Squares Model Building In the previous section, we described MWPLSR and SCMWPLSR as variable selection methods for more accurate and robust PLS calibration. Another type of method that improves the performance of a PLS model is sample selection methods. These ensure the representativity and balance of training set. In a less controlled experiment, there may exist some samples with systematic errors including outliers. They can unbalance the data set and just lead to undesirable statistical distribution of samples. Such samples are usually identified by means of X-residuals, Maharanobis distance and robust statistics [3, 8]. However, it is still difficult to optimize the combination of such samples. These methods just indicate some statistic criteria for the samples including systematic errors. Thus, a heuristic searching method is needed to solve this problem. Shinzawa et al. [19] proposed multi-objective genetic algorithm (GA) for optimizing the combination of samples to be removed in a PLS modeling. Compared with other optimization methods, for example, calculus-based and enumerative method, the unique feature of multi-objective GA is that it does not request restrictive assumptions about search space, such as continuity, existence of derivative and unimodality. Basically, it is possible for multi-objective GA to optimize several objective variables simultaneously. In the applications of some heuristic-based optimization methods to PLS model buildings, a problem is that they often search the solutions too accurately only in a mathematical meaning. Generally, these solutions yield poor results in practical applications. Multi-objective GA searches the solution by optimizing several objective functions simultaneously, which reduces undesirable effects of over-fitting to the training set. In a PLS model building, multi-objective GA is carried out as follows. The original data are divided into three data subsets, i.e., training, validation and test sets. The least median squares (LMedS) of the prediction errors of training and validation sets are used as objective functions to be minimized in the multi-objective GA. The optimized combinations of samples with systematic errors are yielded as Pareto-optimal solutions by multi-objective GA. Finally, the PLS models developed with these solutions are evaluated with the test set.

8.6.1 Multi-objective genetic algorithm As for the basic principle of GA, one can find detailed description in [38]. Some problems contain multiple objects, which should be considered their optimization si-

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multaneously other than separately. Such multi-objective problems sometimes have no single optimal solution in the result of GA [38]. They generates a set of solutions with different trade-offs among the objectives. These sets of solutions are found using the Pareto dominance concept. The basic idea is that a given solution x1 dominates another solution x2 if and only if: 1. Solution x1 is not worse than solution x2 in any of objectives; 2. Solution x1 is strictly better than solution x2 in at least one of the objectives. Pareto-based ranking proposed by Fonseca and Fleming is introduced to evaluate each solution [39]. In Pareto-based ranking, if a solution x is dominated by nx solutions, it is ranked as follows rx = 1 + nx,

(8.2)

where rx is the rank of x. Then, the selection of individual is achieved according to its rank. In the multi-objective GA, all the individuals ranked 1 by Pareto-based ranking are unaltered to the next generation by elitism. The other individuals are selected by roulette selection with their ranks. Hence, crossover and mutation are achieved according to their ranks.

8.6.2 Sample selection by multi-objective GA in PLS In multi-objective GA the training set is used to develop the PLS model, the validation set is used to restrict the effects of the multi-objective GA, namely to reduce the undesirable effect of over-fitting to the training set in the multi-objective GA run, and the test set to evaluate the model improved by the multi-objective GA. The LMedS, which is defined below, is used as the objective function to be minimized in the multi-objective GA [39]. The LMedS method estimates the parameters by solving the nonlinear minimization problem as follows: LMedS = min med(yi − yˆi )2 ,

(8.3)

yˆi = xi b + ei,

(8.4)

where yˆi is the predicted value to actual yi by the regression model

xi , b, and ei are the variables corresponding to yi sample, regression coefficient, and error for the regression, respectively. Herein, the LMedS based calibration models are built instead of the least sum of squared (LS) method. Such a statistical model is robust to false matches as well as outliers [19]. However, the solution of the LMedS can only be given by an exhaustive search, such as the Monte Carlo technique. This algorithm is able to lead a good approximation to the solution although it may not be an exact one [19]. This algorithm can be described as follows: Step 1. Select the arbitrary number of samples from whole data. Step 2. Calculate parameter b with the selected samples by the LS method. Step 3. Calculate the LMedS with b. This procedure is repeated until the smallest LMedS is obtained. It is chosen as the solution of the LMedS. It is noted that this algorithm aims at searching the optimal

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combination of the samples that include no systematic error. Multi-objective GA is substituted for this algorithm. It searches the optimal combinations that minimize the LMedS of the training set (LMedStrain ) and LMedS of the validation set (LMedSvali ) simultaneously. This method can balance the robustness of both training set and validation set, not to overfit to only one set. It is also important to analyze the systematic errors to obtain the qualitative information underlying the original data in the PLS modeling. Shinzawa et al. [19] defined an index shown below to identify mathematical difference between the loading vectors of the original data and that of a specific Pareto-optimal solution obtained by sample selection with the multi-objective GA qk = (p0k − pk ) ⊗ (p0k − pk )

(8.5)

where vector p0k means the loading vector of the k-th LV from the original data without the sample selection and pk indicates the loading vector of the k-th LV from a specific Pareto-optimal solution. This index qk represents squared difference between the loading vectors resulting in positive values. This index signifies the information along variable dimensions; namely, it reveals the wavelength related to the systematic errors.

8.6.3 Applications of multi-objective GA to NIR spectra of human skin The proposed method was applied to NIR spectra of human skin shown in Fig. 8.3. As a result of the sample selection by multi-objective GA, six Pareto-optimal solutions were obtained and shown in Fig. 8.12 [19]. It can be clearly seen in Fig. 8.12 that each solution dominates the original solution without the sample selection. Each solution has a more robust estimator than the original one. Table 8.2 summarizes the LMedStrain , LMedSvali , Rtrain , Rvali , Rtest , RMSEC, RMSEV, and RMSEP of the Pareto-optimal solutions and the original solution. All the solutions provide significant improvement LMedStrain : LMedS of training set, LMedSvali : LMedS of validation set, Rtrain : Correlation coefficient of training set, Rvali : Correlation coefficient of validation set, Rtest : Correlation coefficient of test set, RMSEC: root mean square errors of calibration of training set, RMSEV: root mean square errors of valibration of validation set, RMSEP: root mean square errors of prediction of test set for all of the Rtrain , Rvali , Rtest , RMSEC, RMSEV, and RMSEP values. It is noted that Solution D shows the best results in the Rtest and RMSEP. Herein, Solution D was used for the calculation of the index. Solution D removed two samples from the training set and two samples from validation set as a result of the sample selection by multi-objective GA. The PLS models developed by use of solution D and original solution without sample selection were compared with the proposed index. Loading vectors of the original solution and Solution D were substituted into Eq. (8.4) as p0k and pk , respectively. The loading vectors, p0k and pk , are shown in Fig. 8.13 A and B. It is still difficult to identify the differences between p0k and pk by the simple comparison. Fig. 8.14 shows the index qk of p0k and pk . A peak can be seen at 6900 cm−1 in q1 . It

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LMedSvali

Original

C

D

E

LMedStrain

FIGURE 8.12: Pareto-optimal solutions obtained by multi-objective GA and the original solution (Reproduced from [19] with permission. Copyright (2004) Elsevier).

TABLE 8.2: Statistical results for PLS models of Data set 2 developed with the sample selection and without the sample selection. LMed- LMed- Rtrain Strain Svali

.

Original Solution C Solution D Solution E

Rvali

Rtest

RMSEC RMSEV RMSEP (mg/dl) (mg/dl) (mg/dl)

71.52 30.04

190.64 0.9574 0.887 0.8809 14.01 22.60 0.9705 0.9703 0.9231 11.96

16.69 7.15

24.24 20.86

38.40

22.15

0.9708 0.9170 0.9219 11.64

13.70

20.88

49.76

18.30

0.9668 0.8748 0.9216 12.75

17.14

20.75

is due to the combination of the symmetric and antisymmetric OH stretching modes of water. It indicates the interference from water because of the strong absorption in this region. This result shows that water with the strong absorption can be a systematic error in this PLS modeling. In the 8250–7200 cm−1 region, the index apparently shows high values. The main reason for this tendency may be the effects of the baseline drift in this region. The variation of the sampling site causes the baseline drift, and its effect can be seen not as a form of a peak but the tendency shown in the region of 8250–7200 cm−1 . In q2 a peak can be observed at 7180 cm−1 . The peak may be attributed to combination of CH stretching and bending modes, arising largely from

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FIGURE 8.13: Loading vectors of (A) the original solution and (B) Solution D. (Reproduced from Ref. 19 with permission. Copyright (2004) Elsevier).

other components in the blood or some human tissue, such as epidermis, dermis, and fat. The presence of these interferences reduces the performance of the PLS model. A peak is clearly seen around 5800 cm−1 in q3 . This peak seems to be due to the first overtone of CH stretching modes. A slope also can be seen around 8250–7500 cm−1 in q3 and q4 . The possible reason for this tendency is the effects of tissue scattering. These results reveal that the components in blood, water, some human tissue, epider-

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q1

q2

q3

Wavenumber / cm-1 q4

FIGURE 8.14: Index q by the original solution and Solution D (Reproduced from ref. 19 with permission. Copyright (2004) Elsevier). q5

mis, dermis and fat, and several physical effects such as tissue scattering can be the factors of the systematic errors. This study has demonstrated that the sample selection by multi-objective GA is very effective for PLS model building with NIR spectroscopic data.

8.7 Region Orthogonal Signal Correction (ROSC) and Its Application to In Vivo NIR Spectra of Human Skin It is clearly seen from Fig. 8.9 that glucose has absorption bands in the 1530– 1830 nm region, while water shows high absorption signal in the wide range of 1370–1890 nm, especially in the region around 1440 nm. The large amount of water in blood coupled with the strong NIR absorption characteristics of water makes water become the primary interference component for glucose measurements in blood [11]. Clearly, for such spectra, the removal of the strong absorbance of water will enhance relatively the signal-to-noise ratio of glucose signals and will improve the performance of a PLS calibration model for the determination of blood glucose. Du et al. [11] proposed a novel chemometric method named region orthogonal signal correction (ROSC) for the pretreatment of NIR spectra to remove interference signals mainly of water from the spectra in the skin spectral determination of glu-

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cose contents. ROSC is a new type of OSC, which was originally introduced by Wold [40]. The purpose of OSC is to remove strong structured variation (OSC components) from spectra that is not correlated to concentration, i.e., is orthogonal to concentration. Since the introduction of OSC, a number of different OSC algorithms have been developed to improve the Wold’s OSC procedure [3, 11]. ROSC, being different from OSC, uses a special region of spectra to estimate the variations in interference components and remove these components for other regions, while OSC only uses one fixed region of spectra to calculate OSC components and remove them in the same region. In this region, not only the interference components, but also the interested components are contained. A clear advantage of ROSC is that the orthogonal components estimated by ROSC are more interpretable than OSC components obtained by OSC, because one can select a spectral region to remove signals of a special component such as water. In this review, the detailed theories and the application results of OSC and ROSC are not described. They were reported in [11]. Results of the applications of ROSC demonstrated that ROSC-pretreated spectra including the whole spectral region 1221– 1889 nm or an informative region of 1600–1730 nm selected by MWPLSR provide very good performance of the PLS results. Especially, the latter region yields a model with RMSECV of 15.8911 mg/dL for four PLS components, which is significantly better than a model with RMSECV of 17.1708 mg/dL developed by using the same region without pretreatment.

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References [1] H.M. Heise, “Applications of near infrared spectroscopy in medical sciences” in Near-Infrared Spectroscopy-Principles, Instruments, Applications, H. W. Siesler, Y. Ozaki, S. Kawata, Eds, WILEY-VCH, Weinheim, Germany, 2002, p. 289. [2] H.M. Heise, “Near-infrared spectrometry for in vivo glucose sensing,” in Biosensors in the Body Continuous in Vivo Monitoring, John Wiley & Sons, Chichester, UK, 1997, pp. 79–116. [3] Y.P. Du, S. Kasemsumran, J. Jiang, and Y. Ozaki, “In vivo and in vitro nearinfrared spectroscopic determination of blood glucose and other biomedical components with chemometrics,” in Handbook of Near-Infrared Analysis, 2007, pp. 1–26. [4] H.M. Heise, “Clinical applications of near- and mid-infrared spectroscopy,” in Infrared and Raman Spectroscopy of Biological Materials, Marcel Dekker, New York, 2000, pp. 259–322. [5] K. Maruo, M. Tsurugi, J. Chin, T. Ota, H. Arimoto, Y. Yamada, M. Tamura, M. Ishii, and Y. Ozaki, “Noninvasive blood glucose assay using a newly developed nesr-infrared system” IEEE J. Select. Top. Quant. Electr., vol. 9, 2003, pp. 322–330. [6] K. Maruo, M. Tsurugi, M. Tamura, and Y. Ozaki, “In vivo noninvasive measurement of blood glucose by near-infrared diffuse-reflectance spectroscopy,” Appl. Spectrosc., vol. 57, 2003, pp. 1236–1244. [7] K. Maruo, T. Oota, M. Tsurugi, T. Nakagawa, H. Arimoto, M. Tamura, Y. Ozaki, and Y. Yamada, “New methodology to obtain a calibration model for noninvasive near-infrared blood glucose monitoring,” Appl. Spectrosc., vol. 60, 2006, pp. 441–449. [8] J.H. Jiang, R.J. Berry, H.W. Siesler, and Y. Ozaki, “Wavelength interval selection in multicomponent spectral analysis by moving window partial leastsquares regression with applications to mid-infrared and near-infrared spectroscopic data,” Anal. Chem., vol. 74, 2002, pp. 3555–3565. [9] Y.P. Du, Y.Z. Liang, J.H. Jiang, R.J. Berry, and Y. Ozaki, “Spectral regions selection to improve prediction ability of PLS models by changeable size moving window partial least squares and searching combination moving window partial least squares,” Anal. Chim. Acta, vol. 501, 2004, pp. 183–191. [10] S. Kasemsumran, Y.P. Du, B.Y. Li, K. Maruo, and Y. Ozaki, “Moving window cross validation: a new cross validation method for the selection of a rational number of components in a partial least squares calibration model,” Analyst, vol. 131, 2006, pp. 529–537.

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[11] Y.P. Du, Y.Z. Liang, S. Kasemsumran, K. Maruo, and Y. Ozaki, “Removal of interference signals due to water from in vivo near-infrared (NIR) spectra of blood glucose by region orthogonal signal correction (ROSC),” Anal. Sci., vol. 20, 2004, pp. 1339–1345. [12] S. Kasemsumran, Y.P. Du, K. Maruo, and Y. Ozaki, “Improvement of partial least squares models for in vitro and in vivo glucose quantifications by using near-infrared spectroscopy and searching combination moving window partial least squares,” Chemometr. Intellig. Lab. Syst., vol. 82, 2006, pp. 97–103. [13] M.R. Robinson, R.P. Eaton, D.M. Haaland, G.W. Koepp, E.V. Thomas, B.R. Stallard, and P.L. Robinson, “Noninvasive glucose monitoring in diabetic patients: A preliminary evaluation,” Clin. Chem., vol. 38, 1992, pp. 1618–1622. [14] K. Maruo, M. Tsurugi, T. Ishii, and M. Tamura, “Noninvasive blood glucose monitoring by near-infrared spectroscopy,” Proc. Asian Symp. Biomed. Optics Photomed., 2002, pp. 212–213. [15] A. Bittner, S. Thomassen, and H. M. Heise, “In-vivo measurements of skin tissue by near-infrared diffuse reflectance spectroscopy,” Mikrochim. Acta [Suppl.], vol. 14, 1997, pp. 429–432. [16] R. Marbach, T.H. Koschinsky, F.A. Gries, and H.M. Heise, “Noninvasive blood glucose assay by near-infrared diffuse reflectance spectroscopy of the human inner lip,” Appl. Spectrosc., vol. 47, 1993, pp. 875–881. [17] R. Marbach and H.M. Heise, “Optical diffuse reflectance accessory for measurements of skin tissue by near-infrared spectroscopy,” Appl. Opt., vol. 34, 1995, pp. 610–621. [18] H.M. Heise, R. Marbach, and A. Bittner, “Clinical chemistry and near infrared spectroscopy: multicomponent assay for human plasma and its evaluation for the determination of blood substrates,” J. Near Infrared Spectrosc., vol. 6, 1998, pp. 361–374. [19] H. Shinzawa, B. Li, T. Nakagawa, K. Maruo, and Y. Ozaki, “Multi-objective genetic algorithm-based sample selection for partial least squares model building with applications to near-infrared spectroscopic data,” Appl. Spec., vol. 60, 2006, pp. 631–640. [20] M. A. Arnold, J. J. Burmeister, and G. W. Small, “Phantom glucose calibration models from simulated noninvasive human near-infrared,” Anal. Chem., vol. 70, 1998, pp. 1773–1781. [21] J.W. Hall and A. Pollard, “Near-infrared spectrophotometry: a new dimension in clinical chemistry,” Clin. Chem., vol. 38, 1992, pp. 1623–1631. [22] U.A. Muller, B. Mertes, C. Fischbacher, K.U. Jageman, and K. Danzer, “Noninvasive blood glucose monitoring by means of near infrared spectroscopy: Methods for improving the reliability of the calibration models,” Int. J. Artific. Org., vol. 20, 1997, pp. 285–290.

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[23] K.H. Hazen, M.A. Arnold and G.W. Small, “Measurement of glucose in water with first-overtone near-infrared spectra,” Appl. Spec., vol. 52, 1998, pp. 1597–1605. [24] H.M. Heise, A. Bittner, and R. Marbach, “Clinical chemistry and near infrared spectroscopy: Technology for noninvasive glucose monitoring,” J. Near Infrared Spec., vol. 6, 1998, pp. 349–359. [25] D.M. Haaland , M.R. Robinson, G.W. Koepp, E.V. Thomas, and R.P. Eaton, “Reagentless near-infrared determination of glucose using multivariate calibration,” Appl. Spectrosc., vol. 46, 1992, pp. 1575–1578. [26] K. H. Norris and J. T. Kuenstner, “Rapid measurement of analytes in whole blood with NIR transmittance,” in Leaping Ahead with Near Infrared Spectroscopy, G.D. Batten, P.C. Flinn, L.A. Welsh, and A.B. Blakeney, Eds., Royal Austral. Chem. Inst., Melbourne, 1994, pp. 431–436. [27] G. C. Cot`e, “Innovative non- or minimally-invasive technologies for monitoring health and nutritional status in mothers and young children,” J. Nutr., vol. 131, 2001, pp. 1596S–1604S. [28] K.H. Hazen, M.A. Arnold, and G.W. Small, “Measurement of glucose in water with first-overtone near-infrared spectra,” Appl. Spectrosc., vol. 52, 1998, pp. 1597–1605. [29] O.S. Khalil, “Spectroscopic and clinical aspects of noninvasive glucose measurements,” Clin. Chem., vol. 45, 1999, pp. 165–177. [30] M.S. Borchert, M.C. Storrie-Lombardi, and J.L. Lambert, “A noninvasive glucose monitor: Preliminary results in rabbits,” Diabet. Technol. Ther., vol. 1, 1999, pp. 145–151. [31] K. Maruo, J. Chin, and M. Tamura, “Noninvasive blood glucose monitoring by novel optical fiber probe,” Proc. SPIE, vol. 4624, 2002, pp. 20–27. [32] J. Qu and B. C. Wilson, “Monte Carlo modeling studies of the effect of physiological factors and other analytes on the determination of glucose concentration in vivo by near infrared optical absorption and scattering measurements,” J. Biomed. Opt., vol. 2, 1997, pp. 319–325. [33] K. Iino, K. Maruo, H. Arimoto, K. Hyodo, T. Nakatani, and Y. Yamada, “Monte Carlo simulation of near infrared reflectance spectroscopy in the wavelength range from 1000 nm to 1900 nm,” Opt. Rev., vol. 10, 2003, pp. 600–606 [34] K. Maruo and M. Oka, “Method of determining a glucose concentration in a target by using near-infrared spectroscopy,” U.S. Patent 5 957 841, Sept. 28, 1999. [35] K. Maruo, K. Shimizu, and M. Oka, “Device for non-invasive determination of a glucose concentration in the blood of a subject,” U.S. Patent 6 016 435, Jan. 18, 2000.

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[36] B.G.M. Vandegiste, D.L. Massart, L.M.C. Buydens, S. de Jong, P.L. Lewi, and J. Smeyers-Verbeke, Handbook of Chemometrics and Qualimetrics : Part B, Elsevier, Amsterdam, 1998. [37] H. Martens and T. Næs, Multivariate Calibration, John Wiley & Sons, Chichester, 1989. [38] K. Deb, Multi-Objective Optimization using Evolutionary Algorithms, John Wiley & Sons, Chichester, 2001. [39] C.M. Fonseca and P.J. Fleming, “An overview of evolutionary algorithms in multiobjective optimization,” Evolutionary Computation, vol. 3, 1995, p. 1– 16. [40] S. Wold, H. Antti, F. Lindgren, and J. Ohman, “Orthogonal signal correction of near-infrared spectra,” Chemom. Intell. Lab. Syst., vol. 44, 1998, pp. 175– 185.

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9 Glucose Correlation with Light Scattering Patterns Ilya Fine Elfi-Tech Ltd., Science Park, Rehovot, Israel

9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Principles of Occlusion Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spectro-Kinetic Features of Aggregation Assisted Signal . . . . . . . . . . . . . . . . . . Refractive Index of RBC as a Function of Blood Glucose . . . . . . . . . . . . . . . . . . Parametric Slope as a Function of BG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PS Glucose Dependence for Single RBCs and Small Aggregates . . . . . . . . . . . PSS in the Framework of WKB Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

238 244 247 252 256 262 267 273 275 276

This chapter examines light scattering related approach, commonly entitled ”occlusion spectroscopy.” The key element of occlusion spectroscopy is the fact that light scattering changes, originated solely by the blood, drive the optical response of the media. Light scattering fluctuations are associated with the red blood cells aggregation process. The red blood cells aggregation is triggered by artificial blood flow cessation. Kinetic behavior of optical signal changes is ruled by the diffraction pattern of light that is scattered on the aggregates. Thanks to the multiple-scattering effect, which is caused by the surrounding media, the scattering effect of red blood cells is amplified. Thus, the scattering driven kinetic is combined with the multiplescattering effects. It results in clearly observable and unique optical patterns. Consequently, very subtle changes in scattering pattern of red blood cells can be observed and analyzed. We will show that based on this principle, increased sensitivity to the changes in glucose concentration of blood plasma is gained. Key words: light scattering, RBC aggregation, Mie scattering, WKB scattering, blood glucose, refractive index of RBC, multiple-scattering, diabetes.

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9.1 Introduction 9.1.1 Clinical need for blood glucose measurement In recent decades, many new and exciting developments in the theory and methods of noninvasive and semi-invasive glucose measurements within interstitial fluid (ISF) have emerged. However, many concerns about applicability of ISF monitoring have been raised in the clinical community. Indeed, the concentration of glucose in the blood plasma (Blood Glucose or BG) and red blood cells (RBC) remains the gold standard for self-monitoring of persons with diabetes mellitus [1]. Thus, the ISF glucose measurements has to be represented in terms of BG readings. The calibration procedure, transforming ISF glucose readings to BG results, can be performed by means of conventional capillary BG measurements. The basic assumption underlying ISF glucose calibration methodology is that there is a long term stable equilibrium between ISF glucose and blood glucose. However, the equilibrium point between ISF and BG levels is affected by many uncontrollable factors such as humidity or skin temperature. The relationship between changes in BG and ISF glucose, with respect to both time and concentration, is not well understood, especially during dynamic changes. In fact, a delay of up to 30 minutes between changes in the glucose level of the ISF and the glucose level of the blood is not a rare occurrence. This lag-time is dependent not only upon physiological parameters, but on instrumental factors, such as the glucose sensor technology in use. In addition, stable calibration of ISF measuring devices has proven to be problematic because of glucose-like chemicals in the blood, which interfere with the reading. The concentration of such chemicals can vary from time to time and can not be easily accounted for by means of the intermittent calibration procedure. As a result of so many unresolved issues related to the calibration of ISF readings, regulatory authorities and medical communities have become reluctant to accept ISF measurement as a full substitute of BG readings for self-monitoring of diabetes. Therefore, a noninvasive BG measurement is called to fulfill an unmet medical need where noninvasive ISF glucose measuring has been found not sufficient.

9.1.2 Current art of noninvasive blood measurements Many of the existing optical techniques are designed to measure blood related parameters. In order to distinguish between blood regions and non-blood regions on a kinetic basis, most of them work by processing the time-dependent representation of the optical transmission or reflection signal within the RNIR (Red Near InfraRed) spectral range. The most popular example of such an approach is the technique of pulse oximetry, which is an accepted standard in clinical practice for the determination of blood oxygenation [2, 3]. According to this technique, the measured optical signal, which passes through a reasonably transparent peripheral site of the body (for instance: finger, ear lobe, or toe), is modulated by the waveform of a heartbeat. Each

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cardiac cycle appears as a peak. By utilizing any signal-processing scheme designated for this purpose along with the appropriate algorithm, the pulsatile component of the obtained optical signal can be extracted [2]. The derived pulsatile component of such a signal is ascribed to the periodic inflow of arterial blood within the peripheral vascular bed. The most accepted mechanism to explain the origin of heartbeat waveform signal is the following: with each heart beat there is an increase of arterial blood volume across the measuring site. The increase of blood volume results in increased light absorption. This volumetric assumption is widely used in the theory of pulse oximetry. This being said, there are yet other co-existing mechanisms, which may be responsible for the pusaltile optical response and have been suggested elsewhere [4]. One of the most remarkable characteristics of the pulse-oximetry technique is the ability to eliminate the variable absorption of light by tissue, skin, bones, pigments, etc. and thereby revealing only blood-related signals for further analysis. It is no less noteworthy that, although the shape of the photoplethysmograph waveform differs from subject to subject, and varies with the location and manner in which the pulse oximeter is attached, there is no need to recalibrate the device for each subject or measurement location. Another very important characteristic of pulse-oximetry is its ability to measure arterial blood. This is due to the fact that the pressure waveform and the corresponding optical waveform are preserved in arteries and arterioles [2]. Hence, the primary goal of pulse-oximetry is the determination of oxygen blood saturation (S) in arterial blood. Usually, the arterial oxygen saturation is received from the analysis of the magnitudes of the optical modulation at two basic wavelengths (e.g., 670 nm and 960 nm). Oxygenated hemoglobin absorbs more infrared light and reduced hemoglobin absorbs more red light (Fig. 9.1). Based on the principle of Beer’s law, the HbO2 saturation is determined by using the results of the pulsatile transmission signal being measured at two chosen wavelengths. Because of lack of a comprehensive description of the light propagation in blood and tissue in terms of universal constants, the commercial pulse oximeters rely on empirical calibration coefficients rather than theoretically derived constants. The outstanding success of the pulse oximetry, which is based on an apparent volumetric approach, has given rise to many other volumetric techniques. In these techniques, the artificial changing of the blood volume has been utilized. For example, in the case of a venous occlusion [6] in limbs, venous blood variations are achieved by inflating a pneumatic cuff around the thigh of the subject. Physiological blood volume changes (the so-called respiratory pumps) that facilitate venous return are another way to track blood related volumetric changes without using an external pressurizing technique. Some of the above blood monitoring related techniques could be readily tailored for blood analyte measurements, provided that a specific analyte has a noticeable spectral signature in the RNIR. With respect to glucose measurement, RNIR region is located very far from the band of glucose absorption, which makes the signature of glucose absorption almost negligible in comparison to very strong absorption of

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Absorption cross section ( µm )

Handbook of Optical Sensing of Glucose

1.6 1.4 1.2 1.0 0.8

Hb

0.6 0.4

HbO2

0.2 0.0 550

600

650

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900

950

1000

Wavelength (nm)

FIGURE 9.1: Absorption cross-section of Oxy-Hemoglobin and Reduced Hemoglobin at R-NIR region (based on [5]).

Hb derivatives. For all that, if one still wants to attempt to trace the very small light absorption signature of glucose at RNIR, a substantial signal to noise ratio would be required to begin with. However, even an artificially induced volumetric signal does not exceed 10–15% of the baseline level (or so-called DC signal). The natural pulsatile signal component (AC) contributes only a few percent to the overall optical signal. This AC/DC ratio limitation, combined with the very weak light absorption signature of glucose, makes it practically impossible to accomplish the task of blood glucose measurements in blood by means of absorption related technique. A new concept, which is based on non-volumetric blood related optical signal, has been recently described [7–9]. The proposed concept is based on light scattering phenomena rather than a volumetric one. The major difference between the light scattering related approach and the volumetric one is that scattering pattern is sensitive to glucose presence in blood at RNIR spectral region. Light scattering phenomena produces multifarious information, which is embodied in spectro-kinetic characteristics of the measured signal. The major source of this information is grounded on the phenomena of erythrocyte aggregation.

9.1.3 Red blood cells aggregation phenomena The observable fact of reversible RBC aggregation was first described by John Hunter [12]. Since then RBC aggregation has been studied for decades. It has been observed that erythrocytes in normal human blood tend to form face-to-face morphology similar to a stack of coins (Fig. 9.2) and this one-dimensional “stack” or

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aggregate is called a rouleaux [10, 11]. This occurs with plasma protein bridging the membranes of adjacent erythrocytes, specifically in the presence of fibrinogen and globulin.

FIGURE 9.2: Typical structure of RBC aggregates in vitro.

The aggregation properties of the RBCs are dependent on their shape and concentration. Under certain conditions RBCs begin to clump together in large groups, such as occurs with sludge. Alternatively, aggregates can also appear as spherical globules. RBC aggregation was long considered to be principally of pathophysiologic importance since aggregation is elevated in many disease states. It has been suggested that under low flow or circulatory shock conditions, RBC aggregates would significantly impede the flow of blood in vivo. Yet, red cell aggregation is also normally present in humans and in many other “athletic” species while it is absent in sedentary animals [40]. Robin Fahraeus pointed out that RBC aggregation might be advantageous to the blood flow, based on the observations made in capillary tubes using horse, human and bovine blood [14]. This raised the possibility that normal levels of aggregation may serve a homeostatic function and play an important role in rheology of the blood [13, 37]. At present, there are two co-existing models to explain the RBC aggregation mechanism [15–17, 27]; the bridging model assumes that the aggregation occurs when long-chain macromolecules such as fibrinogen may be absorbed onto the surface of more than one cell, leading to a bridging effect between cells. These bridging forces exceed disaggregation forces due to electrostatic repulsion, membrane strain and mechanical shearing. Alternatively, the so-called depletion model postulates that a reduced concentration of macromolecules in the vicinity of red cells causes fluid to move away, thereby generating an osmotic gradient and a movement of adjacent cells together. According to both the bridging and depletion theories, the total adher-

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ent force between two cells is maximal when the cells are oriented en face; thus it is not uncommon to observe cells arranged in rouleaux formation.

9.1.4 Shear forces and blood viscosity RBC aggregation status together with the blood hematocrit and plasma viscosities is defined as the major parameter, which can be used to determine blood viscosity. It is commonly agreed that RBC aggregation plays an important role in blood flow, particularly in the microvascular system [18–21]. In the context of flowing blood, the increase in shear rate results in the break up of large aggregates into smaller ones or into individual red blood cells. The size of RBC aggregates is inversely proportional to the magnitude of shear forces. For shear rates greater then 100 sec−1 , all RBC aggregates are broken up to single erythrocytes. The shear stresses in normal circulation are too high to allow appearance of erythrocyte aggregate in arterioles and capillaries [22]. Thus, aggregates are observed in the axial regions of large vessels and under low flow conditions in smaller vessels. The equilibrium point between the shear forces and aggregating forces relates to blood viscosity status, both on a systemic and local level. As shear rate gradually increases, the higher shear forces acting on the red cells allow smaller aggregates to form, decreasing effective viscosity. The effect of aggregation on the reduction of apparent viscosity is due to the increase in effective particle size and axial accumulation of erythrocytes facilitating the trapping of the plasma and formation of a cell-free plasma sleeve around the wall. RBC aggregation plays an important role in the regulation of oxygen delivery to the tissue [22]. When RBCs are stacked or grouped together, it is very difficult for RBCs to receive or to release fresh oxygen. Effective O2 uptake and release in circulating RBCs depends on the ratio of surface area to cell volume. In enhanced cell aggregation, O2 diffusion from the inside to the outside of aggregates is reduced because of extension of the diffusion distance in the aggregates [23, 24]. Therefore, in large rouleaux, oxygen binding to hemoglobin is impeded. This is exactly what happens in arterial blood where the loss of oxygen due to the circulation has to be minimized. When the arterial blood reaches a peripheral capillary network, the aggregates are exposed to an impact of very strong shear forces resulting in disaggregation. Some of the smallest capillaries are so tiny that only a single RBC can pass through. Consequently, surface to volume ratio drastically increased and the process of oxygen exchange is effectively accomplished. It needs to be pointed out that when incorporated in an aggregate, RBCs tend to change their shape. Increased adhesion strength enlarges the contact area between the cells, flattens the cells, and consequently promotes a discoid shape.

9.1.5 Clinical relevance of RBC aggregation Many hemo-rheological abnormalities and various disorders have been found to be related to RBC aggregation, especially in diabetes, venous thrombosis, arteriosclerosis and other cardiovascular disorders [25, 26]. It was shown that alterations in

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RBC aggregation are associated with conditions such as atherosclerotic heart disease. Other changes have been observed in patients undergoing surgical procedures such as cardio-bypass surgery or in women going through normal full-term pregnancy. Obesity, independently of the other cardiovascular risk factors, is associated with significant changes in RBC rheology. Infections, inflammatory diseases, and some types of cancer are found strongly correlated with increased aggregability of RBCs. Another clinically important fact is that enhanced tendency for erythrocytes to aggregate can warn clinicians of the danger of the formation of an ischemic brain infarct.

9.1.6 Measurement of RBC aggregation In current clinical practice, all available techniques allowing the characterization of RBC aggregation require the withdrawal of blood and analysis in a laboratory setting. The formation of aggregates can be visualized when blood is placed on a glass slide under a microscope. The other important indirect method of studying RBC aggregation is the sedimentation rate test [12, 31]. This method utilizes the fact that the fall velocity of RBCs in plasma depends on rouleaux formation. However, this process is also subject to many other factors that determine the velocity of sedimentation, such as plasma viscosity, hematocrit and RBCs flexibility. Optical method for studying RBC aggregation is based on the fact that reflection or transmission of light in the blood depends on the degree of rouleaux formation [29]. This method (initially called sylectrometry [28]) permits the observation of fast dynamic process of RBC aggregation. In principle, the method consists of a mechanical means for breaking aggregate complexes (e.g., through the use of a stirring device) followed immediately by the measurement of light reflection [30] (or light transmission). An example of the commercial realization of sylectrometry is the Myrenne aggregometer. This device consists of a transparent cone-plate viscometer with photometer, measuring the extent of aggregation immediately after their dispersion by high shear stress. Another example of a backscattering based device signal is the Sefam erythro-aggregometer [48]. This device measures backscattered light upon abrupt cessation of blood flow at different shear rates. As an alternative approach for in vitro monitoring the optical changes, associated with whole blood sedimentation and aggregation, the OCT technique, has been recently introduced by Tuchin et al. [67]. A direct approach to monitoring RBC aggregation kinetics is through the visualization of aggregation processes [33, 34]. Aggregation can be visualized in appropriate flow chambers and recorded through a microscope connected to a video camera, which subsequently transfers the image to the CPU where it is analyzed with image processing software in order to provide the final parameters of aggregation kinetics. In vitro measurement of aggregation does not permit one to estimate the real in vivo status of aggregates in the circulating blood. The true nature of aggregation in blood vessels is determined by a complicated interplay of rouleaux shape and length, shear stresses, hematocrit, plasma fibrinogen concentrations, blood vessel properties and many other parameters. Recently, the dynamic light scattering based approach

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aiming at in vitro and in vivo studies of aggregation kinetics has been shown as a functional method to trace in vivo aggregation status [35].

9.2 Principles of Occlusion Spectroscopy 9.2.1 Aggregation assisted optical signal in vivo A new approach, known as Occlusion Spectroscopy [7, 36] was established as an noninvasive method to evoke blood specific variations of spectral characteristics. The Occlusion Spectroscopy technique is based on the observation that the cessation of blood flow triggers a change in time of the optical characteristics of blood in vivo (Fig. 9.3). According to this approach, a brief application of over-systolic occlusion causes a stoppage of blood flow and eliminates the influence of shear forces. Because a state of temporary blood flow cessation at the measurement site is created, the average size of aggregates, which are the main scattering centers, begin to grow. Consequently, the mean free path, the light scattering pattern and the mean absorption coefficients start to evolve with a growing in average size of the scattering particles.

Transmission signal in vivo Wavelength 810nm

1.20

T ransmission ( A.U.)

1.16

Over-sy stolic occlusion Post-occlusion signal

Pulse

1.12

1.08

1.04

1.00

6

8

10

12

14

T ime, sec

FIGURE 9.3: Typical post-occlusion transmission signal measured at fingertip location [36].

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Thus, the process of RBC aggregation induces changes in the basic optical characteristics of blood and these changes are transformed into a measured optical response. During the stage of blood flow cessation, optical responses, both in transmission signal (Fig. 9.3) and in reflection (Fig. 9.4), start to change dramatically and can vary in some cases by as much as 35% as compared to the pulsatile signal which fluctuates only about 2–5%. In many cases, creating perturbations of the occluded media with the secondary pressure wave during the blood flow cessation facilitates occlusion spectroscopy. This mode of signal modulation, or Modulated Occlusion Mode (MOM), enables the generation of optical changes induced by blood volume perturbation (Fig. 9.5).

Reflection signal in-vivo Wavelength 650nm 1.02 1.00

Reflection (A.U.)

0.9 8 0.9 6 0.9 4 0.9 2 0.9 0 0.88 0.86 0.84 0.82 0

2

4

6

8

Time (in sec)

FIGURE 9.4: Typical post-occlusion reflection signal measured at finger base location.

9.2.2 The occlusion spectroscopy system A typical Occlusion Spectroscopy device consists of the following sub-units: the pressurizing assembly, the data acquisition system, the control unit and the hand-held sensor probe [9, 36]. As a light source, a multi-LED or laser diode matrix can be used. LED’s light source is preferable in terms of cost and availability. The main disadvantage of an LED-based optical system is that a more complex interpretation of spectral measurement results is required. In the case of LEDs, the detected transmission signal represents the convolution of transmitted or reflected signals over a wide (about 20 nm width) spectral band illuminated by a specific LED. The reverse process of

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Occlusion location: Finger base Measurement location: Finger tip

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T ime (in sec)

FIGURE 9.5: Typical post-occlusion signal measured at fingertip. Over systolic pressure of 200 mm Hg is applied at finger base. Pressure modulation (0–30 mm Hg) is applied on the fingertip.

de-convolution can not always be carried out easily. It may result in the loss of important spectral information. The task of the pressurizing assembly is to squeeze the cuff in a controlled predefined manner and apply the over-systolic occlusion to the base of the patient’s finger. The over-systolic pressure being applied on the cuff affects the sudden cessation of blood flow. The probe configuration is generally adopted for transmission measurement on the fingertip, as in pulse oximetry (Fig. 9.6). In the above case, the patient’s finger is enclosed between the opposite sides of the clip. Another site for transmission measurement is a finger root, which is sometimes preferable in terms of accessing better blood flow and blood perfusion conditions. In this case, the cuff is built in a ring-like form and is mounted on the finger root of the patient’s finger. The cuff location is always upstream or in close vicinity to the point of the optical unit. The measurement procedure is two staged. The initial stage begins by applying moderate, under systolic pressure on the testing site (fingertip) in order to deplete the tissue from venous blood to a standard volume. The second stage involves applying an over-systolic pressure. Keeping the occluded volume of blood and tissue unchanged is essential to guarantee the stable evolvement of a post-occlusion optical signal.

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FIGURE 9.6: Typical view of occlusion spectroscopy system [8].

9.3 Spectro-Kinetic Features of Aggregation Assisted Signal 9.3.1 The parametric slope Blood flow cessation gives rise to a time dependent optical signal. According to occlusions spectroscopy measurement paradigm, this signal is measured simultaneously at a number of wavelengths within the RNIR spectral region. The major goal of this methodology is to determine the optical properties of blood, related to its biochemical content, which are not time dependent (in scale of seconds) by using a time-dependent signal. In order to link the time dependent signal with the sought after blood parameter, there is a need to eliminate time dependent characteristics. This can be achieved by using a method of parameterization where one of the signals at a pre-determined wavelength is chosen as a reference. The definition of the parametric slope (PS) for the two signals I(λ ) and I(λref ) being measured at two wavelengths, λ , λref (reference) is given by [7, 38]

∂ ln(I(λ ,t)/∂ t . (9.1) ∂ ln(I(λref ,t)/∂ t The mathematical meaning of PS is similar to the parameter called γ , widely used in pulse-oximetry. γ for the pulsatile signal is defined as PS =

γ=

δ (I(λ ,t))/I(λ ,t) , δ (I(λref ,t))/I(λref ,t)

(9.2)

where δ (I(λ ,t)) is the fluctuation of pulsatile component of the measured optical signal. It should be understood the value δ (I(λ ,t)) in expression (9.2) is calculated

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by using an appropriate signal processing procedure, which is required to reduce all unrelated alterations of the signal. It is obvious that PS for small signal fluctuation is practically equivalent to γ . The very extraordinary property of γ , which was established in pulse-oximetry practice, is that the γ value is practically unaffected by varying factors of the human body, such as local blood volume, blood hematocrit, measurement geometry, tissue hematocrit, thickness of the skin and pigmentation. It implies that the value of γ possesses a striking feature of the invariant, which depends upon absorption and scattering properties of the measured blood only. This unique feature of γ renders it extremely valuable and of high practical and theoretical importance. Hence, it has been suggested that the PS of the post-occlusion signal, adopting the analogy of γ , inherits its very important future, namely resistance to non-blood related interferences. Thus, the results of spectro-kinetic measurements being expressed in terms of PS have been identified as practically functional for the description of a post-occlusion signal.

9.3.2 Structure of parametric slope in vivo The typical spectral structure of PS, being obtained at the initial stage of the postocclusion signal, looks very similar to the spectral structure of γ , as has been derived from the pulsatile component (Fig. 9.7). As shown in Fig. 9.7, the value of PS and γ are very close in the vicinity of the minimal absorption point of HbO2 , near 660 nm. Both curves closely resemble the form of the absorption spectrum of HbO2 . This remarkable fact is a sign of the dominant role, which the oxy-hemoglobin absorption spectrum plays on the nature of occlusion-originated PS. Bearing in mind the fact that about 97% of arterial blood consists of HbO2, it is reasonable to assume that post-occlusion signal is driven by the changes occurring in arterial blood. This assumption was tested by performing a comparison between PS from the occlusion measurement and γ obtained from the pulsatile signal for different levels of hemoglobin saturations [38]. It was shown that PS, which is calculated at 1 second after blood flow was stopped, and γ , which was obtained from the previous pulsatile signals, are strongly correlated with each other (Fig. 9.8). In addition, when juxtaposed against pulse oximeter readings, both PS and γ reveal similar dependence on oxygen saturation in the range of 90–99% of oxygen saturations (Fig. 9.9). Beyond practical usefulness of non-pulse or occlusion oximetry, the very fact that arterial blood drives post-occlusion signals reveals an important connection to the rheological source of the aggregation related signal. At peripheral sites of the body, where the post-occlusion signal is measured, the arterial blood is delivered mainly by arterioles, which are the smallest part of the arterial tree. The diameter of an arteriole ranges from capillary size to around 20 µ m, depending largely on specific location of the vessels. This is an important point to define since aggregates are broken up to single cell within such a small channel. This leads to a very important conclusion that immediately after blood flow ces-

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Glucose correlation with light scattering patterns Pulsatile and Post-occlusion signals (at 1 second) in vivo 1.5

PS (for occlusion), γ for pulse

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FIGURE 9.7: Comparison between γ of pulse and PS, which has been measured at the first second after application of occlusion [36].

sation, the process of RBC aggregation in arterioles is initiated from the very beginning, specifically from the stage of separate single RBCs. The key implication of this fact is that initial conditions of the process are well defined by the nature of arterial blood rheology. The reproducibility of initial conditions guarantees a reproducibility of PSs at initial stages, not considering the unsteadiness of the aggregation kinetics. This is the reason why the value of PS at the initial stage of occlusion can be considered as the unequivocal function of scattering and absorption properties of dense suspension of single erythrocytes. Such a close similarity between the γ and PS disappears when the aggregation process progresses and particles grow according to the aggregation rate. Due to the course of aggregation, the optical properties of the distribution of RBCs and aggregates progressively diverge from their initial ones. Consequently, the value of PS, at each instant of time, deviates from the initial value. For a given spectral range, the rate of PS is a predefined function of the wavelength kinetic processes of RBC aggregation. In Fig. 9.10 the changes of PS were measured during the first 8 seconds interval, following the starting occlusion point, over the range of 600–940 nm, with a reference signal measured at 870 nm. Delta PS is defined as the difference between the PS at t = 8 sec and PS at the very initial stage of blood flow cessation. It was observed that the rate of PS change follows a monotonic function of wavelengths.

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PS (670 nm vs. 870 nm)

0.68

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0.55

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γ (670nm, 870nm)

FIGURE 9.8: Comparison between γ (of pulse) and PS (at 1 sec. of occlusion). γ - for pulse PS - for occusion

Parametric Slope, γ

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0.50

0.45 93

94

95

96

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99

Hb Oxygen Saturation (SpO2) in %

FIGURE 9.9: PS and Gamma for 670 nm and 870 nm vs. SpO2 measured by oximeter.

9.3.3 In vitro measurement of POS signal The main features of aggregation related optical signals can be observed in vitro by creating conditions where RBC aggregation mechanisms are triggered artificially and the corresponding optical signal is measured. There are a variety of in vitro

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Transmission Reference 876nm 0.3

Delta (Parametric Slope)

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FIGURE 9.10: Dynamic of the changes in the PS after 8 seconds passed from the occlusion start [37].

configurations, which enable one to regulate the process of RBC aggregation. For example, a non-aggregating erythrocyte suspended in Ringer’s solution, being mixed with 1% Dextran, starts to manifest, in terms of RBC aggregation, the rheological properties of the whole blood [38]. In [8] such a methodology was utilized for in vitro measurement of optical signal due to the RBC aggregation. The volumetric effect was excluded by using a cuvette with a rigid wall. The RBC suspension with Dextran was pumped into a reservoir where two pipes were connected to a specially designed rigid glass cuvette of 1 mm thickness. The blood flow through the cuvette was carried on by applying a peristaltic pump. Within the peristaltic pump, the tube walls have been squeezed together to form a seal as the roller moves along the tube. Immediately after the peristaltic pump was operated, the pulse-like variations of transmission signals were observed. Prior to blood flow cessation, the shear forces associated with blood flow resulted in disassembling of rouleaux complexes in blood. The frequency of disassembling and reassembling events was controlled by beats of the peristaltic pump, which evokes shear forces fluctuations. These scattering associated fluctuations resemble the typical heart-pulse optical pattern in vivo. Such a remarkable similarity within well-known volumetric puslatile in vivo signals gave rise to the speculation that the actual reason behind the pulsatile form in vivo signal, which is well recognizable as the plethysmographic one, might be caused by a scattering driven and aggregation-related effect [39].

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During the next stage, the operation of the peristaltic pump was stopped and the blood flow cessation stage was established. With the cessation of the blood flow, shear forces disappear and free aggregation processes begin. The non-impeding RBC aggregation process evolved within the cuvette and transmission measurement at all stages of experimentation were performed (Fig. 9.11)

Wavelength 880nm

In vitro cuvette RBC 1.00

+ dextran

F ree flow

Transmission (A.U.)

0.9 5 0.9 0

Blood flow cessesion

0.85 0.80 0.75 0.70 0

5

10

15

20

Time (in sec)

FIGURE 9.11: Transmission signal before and after blood flow cessation. RBC suspension. Hematocrit 40% with 1% of Dextran. Glass cuvette (0.3 mm thickness).

This type of experiment revealed that rapid changes in the measured light transmission signal can occur instantaneously after blood flow cessation events come about. The characteristic rise time and relative changes of the signal reasonably resemble in vivo behavior. The mutually supporting in vitro and in vivo experimental facts contributed to comprehension of the underlying nature of the post occlusion signal. It revealed that the main source of this time dependent optical signal originates from aggregation processes of erythrocytes which in turn are the major source of light scattering changes associated with non-flowing blood. Therefore, the time dependent transformations of the pattern of the scattering are the major driver behind the optical signal changes. The size, form, orientation, volume, refractive index of RBC and refractive index of the plasma are the key parameters needed to determine the scattering properties of RBCs. Either changes of relative refractive index of the scatterer or its size and shape will bring about a deviation in the pattern of light scattering [39].

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9.4 Refractive Index of RBC as a Function of Blood Glucose 9.4.1 Mismatch of refractive index The most commonly used approach is based on the concept that the erythrocyte is considered to be a homogeneous particle with dielectric constant ε . The complex refractive index of the particle is given by: n(λ ) = nr + i ni , where nr and ni are bounded by the Kramers-Kronig relations connecting real and imaginary parts of the complex refractive index. At the near infrared region of spectrum, distantly located from the Soret absorption bands, the real and the imaginary parts are essentially independent. As opposed to other blood cells, the red blood cells are composed mainly of hemoglobin with a refractive index 1.615. Other components are water with a refractive index 1.333 and a relatively small fraction of membrane components. Since hemoglobin is a major protein component of RBC, its concentration is the essential factor determining the refractive index of the RBC. The mismatch of the refractive index of the erythrocyte and surrounding plasma is the major factor of light scattering by single erythrocytes and by RBC aggregates [69]. It has to be pointed out that the measured values of the erythrocyte refractive index are dispersed around some average estimation, dependent on methods and conditions of the experimental measurements [41–46, 60, 61]. Some of the methods to estimate the sought refractive index value are based on MCHC (mean cell hemoglobin concentration) calculation while others rely on direct experimental measurements of the refractive index. The lack of a consensus between all the methods can be partially explained by the fact that the internal structure of Hb is not necessarily identical to the highly concentrated hemoglobin solution. Another potential source of disparity within the results is that Hb refractive index is affected by different variable factors like the level of pH, hemoglobin oxygen saturation or the concentration of the HbA1 C (glycosylated hemoglobin) [43]. One of the most accepted methods of estimation of RBCs refractive index is to use the mean cell hemoglobin concentration. The nRBC at red–near infrared spectral region is given by nRBC = n0 + β · MCHC (g/dl), (9.3) where n0 =1.335 is the refractive index of cell fluid and β =0.001942 dl/g. The values of MCHC for the normal RBCs are in the range of 32–36 g/dl. According to this estimation, the refractive index of RBC is in the range of 1.397–1.404. The above calculation is based on the assumption that dense solutions of hemoglobin behave identically to a hemoglobin solution inside the RBCs. Actually, the nontrivial nature of the interaction of hemoglobin molecules with cell membranes and the surrounding water may violate this assumption. In fact, direct refractive index measurements of RBCs yield slightly different values as compared to results presented by MCHC based estimation. In connection to the highly precise measurement of the refractive index assisted by the OCT technique, the refractive index of an RBC

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was found to be close to 1.42 (Tuchin et al. ) [44]. As we have already pointed out, one of the factors that may affect the refractive index of the erythrocyte is the percentage of HbA1 C. Normally, only a small fraction (3%–5%) of Hb molecules is glycated, and most of the hemoglobin can be considered to be non-glycated. However, for diabetic patients in whom the HbA1 C significantly exceeds the normal range, this effect needs to be accounted for. Another clinically related factor that affects refractive indices of RBCs is the disparity of pH values [43]. This case may be associated with respiratory or metabolic acidosis, where the blood has too much acid resulting in a decrease in blood pH. The pH affects the charge of the Hb molecule and therefore, according to the classic theory of refraction, the refractive index increases with the increase in charge. The second critical parameter defining the mismatch of refractive index is the refractive index of plasma. The spectral dependence of the refractive index of blood plasma is given by [61] n p = 1.3254 +

8.4052 × 103 3.9572 × 108 2.3617 × 1013 − − λ2 λ4 λ6

,

(9.4)

where λ is the wavelength in nm. In the range of RNIR, n p can be fairly approximated as a constant. The refractive index of plasma is dependent on the concentration of plasma proteins such as serum albumin or fibrinogen, which is predominant in the plasma of blood. Excessive amounts of proteins can result in the deviation from the average refractive index given by Eq. (9.4). The relative refraction index is given by nr = nRBC /n p and the functional dependence of nr on glucose predetermines how the measured optical response of the aggregation is affected by the glucose concentration.

9.4.2 Mismatch of refractive index as a function of glucose Glucose molecules easily penetrate through the membrane of RBCs. Thus, the glucose concentration in plasma water is nearly the same as in RBC non-hemoglobin space over a wide range of blood glucose concentrations. Only at the point when plasma glucose concentrations become extremely high is when this balance is disturbed due to the saturation of erythrocyte glucose transporters. On the other hand, the only free room available for glucose penetration in to erythrocytes is the space, which is not preoccupied by hemoglobin. Therefore, on a concentration basis, the glucose content in plasma is higher than the glucose concentration within RBCs. Eventually, these factors quantify the rate and amplitude of variations in refractive index mismatch as related to the penetration of glucose into the red blood cells. The effect of glucose on the refractive index of plasma is estimated by the following (Zhernovaya et al. [47]): nPG = n p + 0.1515 × 10−5 ·Cgl (mg/dl).

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The explicit estimation of the refractive index of the RBC surrounded with plasma with glucose (Cgl ) can be estimated as the weighted average of the refractive index of the pure Hb fraction (with refractive index 1.65) and the refractive index of glucose solution [44, 49]

nRBC = nHb · FR + (1 − FR)(nw + 0.1515 × 10−5Cgl ) ,

(9.6)

where FR is a volume fraction of Hb in RBC. If we take FR= 0.32, then the calculated nRBC approached 1.41–1.42 which resembles results obtained by using OCTbased measurement (Tuchin et al. [44]). The dependence of mismatch of refractive index in the physiological range on BG change is shown in Fig. 9.12.

Mismatch of refractive index

∆n

( nRBC - nplasma )

0.076700

0.076695

0.076690

0.076685

0.076680

0.076675 0

100

200

300

400

500

Glucose (mg/dl)

FIGURE 9.12: Mismatch of refractive index of RBC and plasma as a function of glucose.

As it is seen in Fig. 9.12, the effect of glucose on the mismatch of the refractive index is about 0.3%. The main question is whether such small changes of refractive index can be precisely measured in vivo and a secondary issue to address is how such changes can be expressed in terms of a Parametric Slope, which is a preferable way to represent the measured results in vivo.

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9.5 Parametric Slope as a Function of BG 9.5.1 Time dependent optical parameters As has been pointed out, one of the most prominent characteristics of the Parametric Slope is its very weak dependence upon non-blood related parameters at the measured site. This implies that non-desirable parameters such as tissue pigmentation or the amount of blood at the measurement location are cancelled out when the PS is used. On the other hand, PS is strongly dependent upon the optical properties of arterial blood at the measured site. A general expression for the PS, therefore, has to be formulated in terms of scattering and absorption parameters of the blood. The absorption and scattering coefficients of RBC can be expressed in terms of scattering and absorption cross section, as has been shown by Ishimaru [55]:

µBs =

σs (t)PH ; V (t)

µBa =

σa (t)H V (t)

;

(9.7)

where σs (t) is the scattering cross section, V (t) is the mean volume of the scatterer and P is the packing factor of scatterers initially introduced by Twersky [50] and then experimentally modified. For the suspension of single RBCs, this factor is commonly taken as P = (1−H)(1.4−H) where H is the hematocrit (expressed in relative units). It should be taken into consideration that there are no available data providing a similarly expression related to the aggregates, which may behave differently than P, as determined for single RBCs. In the framework of the aggregation model, the factor σ (t)/V (t) is responsible for the evolution of the scattering term. It is clear that the real part of the relative refractive index is incorporated into this factor. An additional parameter that is subject to changes during the blood flow cessation process is µBa . It is possible to assume that the time dependency may originate via the hemoglobin oxygen saturation signal. Actually, the absorption cross section of RBCs depends on hemoglobin saturation (S) according to   σa = (σaHbO2 − σaHb )S + σaHb W + (1 − W)σH2 O ,

(9.8)

where S is the oxygen saturation of the blood and W is the percentage of Hb and HbO2 within RBCs. Following blood flow cessation, the balance between oxygen consumption by tissue and oxygen delivery by blood is disturbed. This may result in oxygen saturation to start to decrease progressively. The rate of oxygen saturation change is far from linear in behavior. The oxygen consumption in limb areas is relatively slow since metabolic activity by peripheral tissue and skin is very low in comparison to the central organs oxygen consumption. Thus, the time constants of oxygen de-saturation are significantly slower as compared to the rate of RBC aggregation processes, which are measured in seconds. For example, the changes in the absolute hemoglobin saturation of a forearm muscle during arterio-venous occlusion, as has been shown by

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Suzuki et al. [68] begin to decrease only 60 seconds after the application of the occlusion. In a particular case related to the arterial blood, the process of oxygen uptake from hemoglobin molecules runs slower as compared to the identical process in venous blood. This is due to the relatively flat character of the oxyhemoglobin dissociation curve for the arterial blood. According to the hemoglobin dissociation curve, even exceptionally significant decreases of oxygen, dissolved in the plasma, result in only minute changes of hemoglobin blood saturation. Therefore, in spite of the fact that in principle the S is a time-dependent parameter, it comes into force only for very late stages of the post-occlusion process. Another potential source of possible variations of µa can be related to the redistribution of hemoglobin during aggregation events. The absorption coefficient µBa is a product of two factors: the density ρ of the absorbers and their absorption cross section σa . Each one of these parameters is dependent on the aggregation status. In order to leave the product constant, these parameter changes must cancel each other. During the aggregation, the volume of the particle V increases while the hematocrit is kept unchanged. By following Eq. (9.7) µBa = (σa /V )H. Formally σa /V can be calculated explicitly [55] by using the WKB solution for sphere with radius a:

µBa =



4nr (nr + 1)2 + n2i

  3 2 2 exp(−Y ) + 2 [exp(−Y ) − 1] 1+ Y Y 4a

,

(9.9)

where Y = 4 k ni a, k = 2 π /λ and n is the index of refraction for RBCs relative to plasma, such that n = nr + i ni . If we take, for example, ni = 0.248 for λ =685 nm and nr = 1.036, then for very wide range of a, the changes of µa as a result of aggregation can be easily calculated (see Fig. 9.14). This result show that the absorption cross section of the aggregate is practically additive and maintains µa as a constant. However, there are some additional considerations that need to be taken into account with respect to the absorption change during aggregation, for example, the shadowing effect by which for most orientations of the aggregate the elementary (disc) absorbers shadow those situated behind them on the path of the incoming radiation. For erythrocytes, shadowing is important for large aggregates. Shadowing effects create an asymmetrical situation with respect to the absorbing particles in terms of the wave front of the incident light. This effect can violate the underlying assumption for Eq. (9.9). Another simple occurrence that may break down the additivity of the absorption cross section is the re-scattering of light at the interfaces of the aggregate. This effect is expected to be most apparent in relation to small aggregates of erythrocytes at oblique incidences. In terms of modeling, it means that an aggregate can not be considered as a homogenous particle but rather as a particle with variable refractive indices inside of it. The experimental results show the absorption coefficient of the media with aggregating RBCs is not a constant [54]. Yet, a lack of explicit formal description prevents one from incorporating this effect in the modeling of the optical signal.

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FIGURE 9.13: Change of the absorption during aggregation, assuming the WKB approximation.

9.5.2 General expression for the PS Mathematical descriptions of light propagation in optically turbid media have been developed and extensively applied to tomographic imaging of tissues or in the monitoring of physiological status of different local tissues. For the light propagation in tissue, the classical diffusion approximation of transport in scattering media has been widely utilized [51, 53, 62]. As a large number of scattering events occur when light propagates through a blood layer, the problem has been defined as a problem of multiple scattering by highly anisotropic particles [50]. The wave multiple scattering model takes into consideration the interference effect, which results in non-trivial dependence of the scattering cross-section on the RBC concentration. Another type of approach is connected to the idea of treating the transport of photons as a random walk, characterized by a distribution of path lengths [64]. The final approach enables one to combine the transport approach with some elements of wave multiple scattering model [52]. The fusion of models is achieved if the packaging effect is accounted for within the calculation of mean free path between the scattering events. The explicit expression based on the random-walk model for the transmission in a finite slab x was given by Gandjabakche et al. [64] " # p exp(−2 µBa l) cosh( 24µBa l − 1 p , (9.10) T= p 24µBal sinh( 6µBa l(x/l) where l =

√

2 µBs (1−g) .

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It has to be pointed out that in pulse oximetry and occlusion spectroscopy, the commonly used light source is LED. For this case Eq. 9.10 should be replaced with

T=

Zλ2

λ1

" # p cosh( 24µBa(λ )l(λ ) − 1 exp(−2µBa (λ )l(λ )) p dλ , G(λ ) p 24µBa(λ )l(λ ) sinh( 6µBa (λ )l(λ )(x/l(λ ))

(9.11)

where G(λ ) is the normalized distribution of LED’s intensity between λ1 and λ2 . In the case where the source of time dependent signal is volumetric, the PS appears as the volumetric parametric slope (PSV). The variation of slab thickness x(t) is responsible for the transmission changes. Assuming the light source to be monochromatic, the PSV is readily calculated from Eq. (9.10). PSV =

∂ ln(I(λ ,t)/∂ x . ∂ ln(I(λref ,t)/∂ x

  √ 2.45x µBa (λ )l(λ ) tanh l(λ ) µBa (λ )l(λ )   PSV = p √ 2.45x µBa (λref )l(λref ) µBa (λref )l(λref ) tanh l(λ ) p

.

(9.12)

ref

Analysis of Eq. (9.12) shows that PSV is a very weak function of x and is defined entirely by the scattering and absorption coefficients of the RBCs and aggregates for chosen wavelengths. As opposed to the volumetric case, in evaluating the Parametric Slope for scattering induced changes (PSS), the changes in transmission are ascribed to the variation of µBs (t) . In order to expand the PSS, an explicit model describing µBs (t) behavior as a function of time is required. Expression (9.10) is only an example of one out of many descriptions being generated by the experimental and theoretical studies devoted to modeling of the phenomena of light propagating through the turbid media, which is composed of the tissue or the blood. Each of the models discloses an additional aspect of this complicated process. However, when it comes to the reality of implementing such methods in the real world, the light diffusion model appeals handiest to users, or as a proper approximation to start with. For the diffusion approximation, an optical response of scattering and absorption media is governed by the diffusion coefficient of blood Db (t), which is time dependent for the scattering driven process, Dt (diffusion coefficient of the tissue), blood thickness xb (t) (which is time dependent for the volumetric process) and the local blood/tissue hematocrit ξ . The value of ξ may play a significant role in PS only if the mean free path of the light is greater than the mean path of the light via one single blood vessel (which is averaged over all directions). The most generalized assumption is that all blood-related parameters are time dependent, whereas the tissue-related components are taken as a constant.

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I(t) = I(Db (t), xb (t))I(Dt , ξ , dt ).

(9.13) ′

The diffusion coefficient Db is given in terms of µa and µs (absorption and reduced scattering coefficient, correspondingly): Db =

1 3(µa (t) + µs′ (t))

.

(9.14)

The absorption and scattering coefficients can be determined through the properties of RBC and aggregates by using different approximation approaches [55]. In the case of the diffusion approximation, the “inverse diffusion length” is defined by the well-known formula:

µd (t) =

p 3(µa (t)(µa (t) + µs (t)(1 − g(t))) .

(9.15)

A more generalized approach is to represent the inverse diffusion length by the following:

µd∗ (t) =

q α µa2 (t) + β µa µs [1 − g(t)]) .

(9.16)

′ = The absorption and reduced scattering coefficients for the blood are µBa and µBs µBs (1 − g), where g is the factor of scattering anisotropy and α and β are defined as adjustable parameters. According to the most simplistic approach, the transmission signal behaves as an exponential function of blood thickness xb . The use of this exponential approximation for an in vivo measurement is justified by the experimentally established fact that the parametric slope used in pulse oximetry, which is defined as the ratio of the logarithmic changes of signals being measured at two different wavelengths, is independent of the amount of blood. Neither blood-related transport models nor tissue scattering models provide a rigorous and comprehensive description for such heterogeneous media as tissue containing network of the blood vessels. One may speculate that this sort of problem calls for a new model approach such as homogenization analysis or stochastic differential equations, which have been developed by Papanicolaou [63] and others for addressing alternative problems in physics. In a widely used semi-empiric approach, tissue and blood are considered as entirely separate substances. Simply stated, this means the following:

ln I(t) = lnUt − µd (t)xb (t),

(9.17)

where Ut is the energy loss due to all non-blood factors and xb is the effective thickness of the blood. In the case of the volumetric model (applicable for the pulsatile signal) time dependent signal driven by xb (t), then by using Eqs. (9.16) and (9.17), PSV can be given by:

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PSV =

1/2  ∂ ln I(λ )/∂ (xb ) α µa (λ ) + β µa(λ )µs (λ )(1 − g) = ∂ ln I(λref )/∂ (xb ) α µa (λref ) + β µa(λref )µs (λref )(1 − g)

, (9.18)

where λ and λref (reference wavelength) are the two wavelengths chosen for the parametric slope. In another extreme case, the only change in the illuminated media is associated with the growth of aggregates. In this instance, the scattering coefficient change is almost entirely responsible for signal changes (if the time dependent absorption related effect is disregarded). Given the function relating to particle size with time is c(t), where c is the average size of the aggregate, then from Eqs. (9.16) and (9.17) one can obtain the expression for a scattering driven parametric slope (PSS): PSS =

∂ ln(I(λ ,t)/∂ µd (λ , c(t)) = R1 R2 R3 ∂ ln(I(λref ,t)/∂ µd (λref , c(t))

.

(9.19)

s

α µa2 (λref ) + β µa(λref )µs′ (λref ,t) ∂ µs′ (λt ,t)/∂ c ; R3 = . 2 ′ α µa (λ ) + β µa(λ )µs (λ ,t) ∂ µs′ (λref ,t)/∂ c (9.20) The term R1 is responsible for the prominent dependence of PSS on the hemoglobin absorption spectra. This term is responsible for the sensitivity of PSS to oxygen saturation of hemoglobin. The term R2 is mainly dependent upon the scattering coefficient of the relevant particles. The reduced scattering coefficient µs′ is a dominant factor in this term. The third term, R3 , plays an important role for large aggregates whereas for small aggregates this term approaches unity. As indicated above, the absorption coefficient change which is associated with RBC aggregation process is a plausible and experimentally supported phenomenon. For this particular case, the changes µa (t) will drive the variation of signal. The absorption-driven parametric slope (PSA) will be defined by: µa (λ ) R1 = ; R2 = µa (λref )

PSA =

∂ ln(I(λ ,t)/∂ µa (λ ) ∂ µa (λ )/∂ t ∂ ln(I(λref ,t)/∂ µa (λref ) ∂ µa (λref )/∂ t

(9.21)

or, more explicitly s

α µa2 (λref ) + β µa2(λref )µs (λref ) ∂ µ (λ )/∂ c . α µa2 (λ ) + β µa2(λ )µs (λ ) ∂ µa (λref )/∂ c (9.22) In the most general case, where all kinds of changes in scattering, absorption and blood volume take place, the measured PS will given by the sum of all contributions: 2α µa (λ ) + β µs (λ1 ) PSA = 2α µa (λref ) + β µs (λref )

PS = PSS + PSA + PSV.

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9.6 PS Glucose Dependence for Single RBCs and Small Aggregates 9.6.1 RBC scattering pattern In order to calculate the effect of glucose on the PS, the scattering pattern has to be estimated by an appropriate model. The critical features of the scattering, which are required for this calculation, are the scattering cross section and the scattering phase function. An individual RBC has a scattering phase function that strongly peaks in the forward direction (anisotropic scattering function of g is close to 1). The factor of anisotropy plays an extremely important role within the turbid media and in diffusion theory it is accounted for by the factor (1 − g). Different approximations characterized by an effective scattering phase function have been suggested elsewhere [54, 56, 57]. Twersky [50] adopted the use of the Reyleigh and Born approximation for calculating angular distribution for spheroid RBCs scattering description. Among the most popular are the Henyey-Greenstain phase function, the Fraunhofer diffraction method and the Genenbauer phase functions. The list of scattering computational methods includes the T-matrix method, the discrete dipole approximation, the multiple dipole method, the finite difference time domain technique and some other techniques. In [56] Henyey-Greenstein, Gegenbauer, and Mie, phase function suitability has been tested for the description of whole blood. In this and other publications [58, 59] it has been shown that the best correspondence is achieved by using the Mie scattering computation formula, which is a complete analytical solution of Maxwell’s equation for spherical particles. Naturally, the use of the Mie solution for non-spherical particles requires one to assume that the particle has the form of a sphere. The Mie apparent scatterer’s size for single RBC is obtained by an averaging of a beconcave shape with a mean diameter 7.6 µ m and a mean thickness of about 1.5 µ m over all possible orientations. In the case of rouleux, which includes n-RBCs, the thickness is determined to be n × 1.55 µ m. It is a reasonable approach to approximate the aggregate of RBCs by a sphere of equivalent volume. The process of the growth of the ensemble of randomly oriented rouleuxes, therefore, can be represented by the model of inflating sphere.

9.6.2 PS for Mie scattering approximation The Mie scattering function provides one with a complete solution of both the scattering cross section value and the phase scattering function. The process of RBC aggregation is represented by an inflation of the sphere-like scatterers wherein the number of scatterers goes down so the total hematocrit is kept unchanged. Eqs. (9.10), (9.19) and (9.20) now can be used with the Mie scattering model for PSS calculation. Figure 9.14 represents the spectrum of PSS, calculated on the

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263

bases of the Mie scattering model for the initial stage of aggregation and by using the photon migration model represented by Eq. (9.10). It is seen that even a small change of the size of the particle (from 3 to 4.5 µ m) is responsible for evolution of PSS. This result is in accordance with the in vivo finding showing that PS in vivo evolves with time. Alternatively, the Mie solution can be incorporated to the simplified diffusion model, by using Eq. (9.19). By using the particular case α = β = 3 the Mie scattering function was utilized to calculate PSS and PSV spectrum for the beginning of aggregate growth. In Fig. 9.15 three graphs are plotted together, where PSS and PSV have been calculated for small aggregates being represented by a 3 µ m diameter sphere. The PS was obtained in vivo post occlusion measurement by LED’s. The same reference signal measured at wavelength 880 nm was chosen for all cases.

FIGURE 9.14: The PSS calculation based on the Mie scattering solution; reference wavelength is 940 nm.

Exceptional correspondence was found between the calculated PSS and measured PSS in vivo, indicating a good foundation of the underlying assumptions. A notable fact is that in spite of essentially the different nature of signals, the volumetric PS spectra and the scattering driven PS spectrum appear remarkably similar. This aspect can be explained by a dominant role of absorption term R1 in Eqs. (9.19), (9.20). This also helps to understand the similarity between the calibration curves obtained for PSS related oximtery (non-pulse oximetry) and the calibration curve of the pulsatile signal, providing the volumetric nature of the pulsatile signal.

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Handbook of Optical Sensing of Glucose Reference λ = 880nm 1.8

PSV (volumetric PS) 3 micron Mie, PSS in vivo

PS (Parametric Slope)

1.6 1.4 1.2 1.0 0.8 0.6 0.4 550

600

650

700

750

800

850

900

950

1000

Wavlength (nm)

FIGURE 9.15: Comparison between PSV and PSS based on the Mie scattering solution and PSS, measured in vivo.

Another important result which is revealed by using Mie scattering solution for the aggregation modeling is the dependency of PSS on the blood hematocrit (Fig. 9.16) which is one of the key parameters affecting scattering and absorption properties of the blood. The graph of PSS for hematocrit 0.1 minus PSS for the hematocrit 0.5 resembles a form of the spectrum of HbO2 . This result is a direct outcome of Eqs. (9.19), (9.20) where the absorption term is multiplied by the scattering term. Another factor that is revealed in Fig. 9.16 is that sensitivity of PSS to the hematocrit increases with the increase of the aggregate length. PSV-based sensitivity to hematocrit is the weakest. Consequently, natural volumetric pulsation, which is commonly associated with a pulse, has a limited potential to serve for hematocrit measurements as opposed to the aggregation based signal.

9.6.3 PSV as a function of glucose In order to evaluate the effect of glucose on the PS, owing to volumetric changes for small aggregates, and by using the Mie scattering model, the refractive index mismatch as a function of glucose has to be included via Eqs. (9.5) and (9.6). The results of the Mie scattering based calculation, where Eqs. (9.5) and (9.6) are incorporated into the calculation path, are shown in Fig. 9.17. The graph depicts the difference between PSVs for two glucose concentrations, 500 mg/dl and 0 mg/dl as a function of wavelengths. Very similar to the hematocrit related dependencies, the sensitivity of PSV to glucose basically mimics the spectral behavior of PSV as

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265

Glucose correlation with light scattering patterns 0.35

PSV a=4.5 mµ a=6 mµ a=7 mµ

Reference 720 nm

PS (Hct=0.1)-PS (Hct=0.5)

0.30 0.25 0.20 0.15 0.10 0.05 0.00 -0.05 550

600

650

700

750

800

850

900

950

1000

Wavelength (in nm)

FIGURE 9.16: Difference between the PS for the hematocrit of 0.1 and the PS for the hematocrit of 0.5 for PSV, and PSS for 5, 6 and 7 mµ particles.

a function of wavelength. However, in terms of absolute changes of PSV resulting from glucose changes, the calculated sensitivity to blood glucose appears to be very weak.

Volumetric PS (PSV)

Mie scattering H ematocrit =0.4

Reference wavelenght =720nm 0.007

PS (500mg/dl)-PS(0)

0.006 0.005 0.004 0.003 0.002 0.001 0.000 -0.001 550

600

650

700

750

800

850

9 00

9 50

1000

Wavelenght (nm)

FIGURE 9.17: The sensitivity of PS to glucose for the volumetric changes (PSV).

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9.6.4 PSS as function of blood plasma glucose for small aggregates Similarly to the previous PSV calculation and based on general expressions for the transmission and the Mie scattering function, PSS for different stages of aggregation can be calculated for different concentrations of glucose. Figure 9.18 shows the calculated difference between the PSS for 500 mg/dl glucose concentration and PSS for the blood without glucose. The calculation was performed for different wavelengths, ranging from 600 nm to 940 nm where a reference signal was chosen at wavelength 940 nm. As shown in Fig. 9.18, the value PSS is a function of glucose concentration, wavelength and the size of aggregates. Sensitivity to glucose behaves differently for different wavelengths. It is clear that PSS for the wavelengths, in vicinity of the reference point, produces almost zero sensitivity to glucose. The choice of the reference point is revealed as very important criteria for the optimization of the PSS sensitivity to glucose.

Reference 9 4 0nm 0.003

604 nm 610nm 620nm

Mie Scattering

H ematocrit 0.4

0.002

PS(500mg/dl) - PS(0 mg/dl)

680nm 0.001

720nm 0.000

760nm -0.001

880nm

-0.002

9 80nm

-0.003 -0.004 -0.005 -0.006 2

4

6

8

10

12

14

Diameter of sphere (in microns)

FIGURE 9.18: The sensitivity of PSS to glucose as a function of the aggregate where the reference point is chosen at 940 nm.

In Figs. 9.18 and 9.19 the graphs of sensitivity to glucose for different reference wavelengths are shown. For the reference wavelength of 720 nm, maximum sensitivity to glucose was found. For all cases, a general tendency was revealed such that the sensitivity to glucose increases for larger aggregation stages. However, an attempt to broaden the scope of the Mie scattering model in order to include more prolonged stages of aggregation is not fairly justified and another

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Glucose correlation with light scattering patterns

approximation which will account for the spheroid-like form of the growing particle must be chosen.

Ref = 720nm

Mie scattering

H ematocrit =0,4

0.002

PS (500 mg/dl) - PS (0)

0.000 -0.002 -0.004

604 nm 610nm 64 0nm 700nm 84 0nm 860nm 880nm 9 60nm

-0.006 -0.008 -0.010 -0.012 -0.014 -0.016 2

4

6

8

10

12

14

Diameter of the sphere (in microns)

FIGURE 9.19: The sensitivity of PSS to glucose as a function of the aggregate where the reference point is chosen at 720 nm.

9.7 PSS in the Framework of WKB Model 9.7.1 WKB approximation WKB approximation, which is the approximation of the anomalous diffraction, is applicable to any scatterer of arbitrary shape and size. Therefore, WKB based solutions allow one to obtain a microscopic scattering coefficient of radiation for substantially large aggregates. In accordance with this approximation, radiation propagates inside the particle in the same direction that the incident radiation does (lowrefractive particles), and the radiation wave number inside the particle is equal to the wave number of the radiation in the particle material. The effect of scattering in such a case is connected with the radiation phase change when the radiation propagates inside the particle or more specifically in the hemoglobin of the erythrocyte. The WKB approximation is valid when:

(n2rel − 1)kD ≫ 1

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where D is the characteristic size of the particle and nrel is the relative refractive index. Where (nrel − 1)kD is smaller than 1, the Mie solution or Rayleigh and Born approximations should be used. The size of developed aggregates is much larger than λ , and their relative index of refraction is close to unity. It is clear that the larger the aggregate, the more valid is the inequality above. Therefore, the usage of the WKB approach for a single act of scattering is mostly justified when dealing with very large aggregates. The next assumption that applies toward this kind of aggregation modeling is based on rheological considerations. It posits that in narrow vessels, the dominant geometry of RBC aggregates is quasi-one-dimensional (i.e., erythrocytes aggregate side to side). Based on this model, the erythrocyte aggregates can be approximated (Shvartsman et al. ) [39], as a linear rouleux. It means that the shape of an average center of scattering may be successfully approximated by a growing spheroid (Fig. 9.20). The small axis of one RBC is 2c (c = 1.34 µ m), and the large axis is 2a (a = 4 µ m). Its large axis c grows with time, while two equal axes a remain equal to the large axis of a single erythrocyte. In this case, the reduced scattering coefficient decreases with time and the transparency of blood grows. It has to be understood that a more realistic approach has to take into consideration that the statistics of an ensemble of randomly oriented spheroids has to be corrected by a statistics of the distribution of the average sizes of rouleaux in different blood vessels.

FIGURE 9.20: The schematic illustration of the approximation of aggregate by spheroid [39].

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9.7.2 Expression for the K-function The critical function that governs the scattering process is the so-called function K (Fig. 9.21), given by K(ρ ) = 1 − sin(2ρ )/ρ + (sin ρ /ρ )2 ,

(9.25)

where ρ is the dimensionless ratio of re-normalized single scatterer characteristic size and determined by

ρ = 2π cΞ(nRBC − n p)/λ .

(9.26)

1.8 1.6 1.4 1.2

K (ρ)

1.0 0.8 0.6 0.4 0.2 0.0 0

2

4

6

8

10

ρ

FIGURE 9.21: K as a function of ρ .

The dimensionless parameter Ξ is equal to Ξ = (1/2ε ) log[(1 + ε )/(1 − ε )]

(9.27)

where

ε = (1 − (c/a)2)1/2

for c < a.

(9.28)

Within the WKB approximation function, K(ρ ) reflects the interference nature of each single act of scattering. When the size of aggregate grows substantially (c > a), Ξ has to be continued in a complex plane and one gets:

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Ξ = (1/z) arctan z ,

(9.29)

z = ((c/a)2 − 1)1/2.

(9.30)

where

The aggregates have all possible orientations in space. Averaging over all angles yields the transport coefficient in the form

µtr = µs (1 − g) = π (a2 + c2 Ξ)/V0H(1 − H)(1 − g)K(ρ ),

(9.31)

I(t) = F[µtr (c(t))].

(9.32)

where V0 = 4π a2 c/3 is the spheroid volume and g is related to the averaged angle of scattering. Estimations based on Eq. (9.31) give µtr values around 5–13 mm−1 already for a single erythrocyte. On the other hand, µa ∼0.1–0.8 mm−1 , so µtr > µa . The non-monotonic character of function K(ρ ) leads to a complicated behavior of µtr and the transmission signal reflects this non-monotonic characteristic;

9.7.3 Critical wavelength According to the diffusion model, the light transmission through the slab of RBC aggregates can be calculated by using Eq. (9.19). Fig. 9.22 shows the behavior of the transmission for different wavelengths being calculated by using Eqs. (9.31) and (9.20). As shown in this figure, light transmission at certain wavelengths, such as 760 nm and 940 nm, behaves monotonically with the growth of the aggregate, whereas other signals (such as transmission at 660 nm) reveal non-monotonic characteristics. The physical reason for this is clear. For λ =670 nm, the growth of the aggregate leads to such values of ρ that the growing branch of K(ρ ) corresponding to ρ > ρmin = 3.8 is activated. At the range of around 730–740 nm the light transmission reaches a point where its value does not change as a function of aggregate size. In terms of time, this means that according to the WKB model, regardless the rate of aggregation kinetics governing the process, there is a wavelength for which at a certain instance of time, the transmission ultimately reaches saturation. This specific wavelength is called the critical wavelength. The major and very important feature of the critical wavelength is that it does not depend on the geometry of measurement, amount of blood, scattering and absorption properties of skin or surrounding tissue, or kinetics of the aggregation process. It is a direct function of the miss-match of the refractive index between RBCs and plasma. If the assumption of linear growth is violated, the thickness of rouleaux is also and, thus, affects the critical point value. In Fig. 9.23 the most typical results for in vivo measurements of transmission evolution for the case of the long over-systolic occlusion are presented.

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Glucose correlation with light scattering patterns WKB model

Hematocrit =0.4

Critical wavelength=720nm

1.01

Tr ansmission (A. U. )

1.00 0.99

660mn 700mn 720mn 760mn 940mn

0.98 0.97 0.96 0.95 0.94 0.93 2

3

4

5

6

7

8

9

10

11

Length of the aggregate (c) in µm

FIGURE 9.22: Change of transmission by using WKB approximation for the spheroid.

As it is seen for the signal measured at 940 nm, the transmission increases monotonically at all times. For the signal measured at λ =670 nm, the growth of the transmission becomes non-monotonic (i.e., it is followed by a decline). Another signal within close proximity to 930 nm manifests the characteristics of a critical wavelength and is kept unchanged where the signals at all other wavelengths continue changing. In terms of a real time measurement, the critical point is achieved in 10 seconds after application of the occlusion. In Fig. 9.24 the behavior of the transmission signal in close proximity to the critical points is shown. It is seen that in this particular case the wavelength 727 nm is the closest to the critical wavelength. The critical wavelength obeys the condition dT (t, λ )/dt = 0 for all t > tcritical , where t is a certain instant of time after occlusion. Practically, the actual value of the large axis c of the aggregate is a result of averaging of a certain distribution of different sizes of aggregates. This distribution is strongly dependent on particular aggregation kinetics, varying from case to case. However, for a very long over-systolic occlusion, the asymptotic behavior of T (t, λ ) for high c/a ratios is expected to be stable. The asymptotic behavior can be clarified by performing the expansion Eq. (9.31) over small a/c [39]. dT /dc = (dT /d µtr )(d µtr /dc).

(9.33)

Therefore, for large values c/a one gets: ρ = ρas − (2a/π c). Thus, keeping the terms of second order in a/c for the case c/a → ∞

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660nm 730nm 765nm 780mn 9 4 0nm

I n vivo measurement F inger tip

T ransmission ( A. U)

1.0

0.9

0.8

0.7

0

10

20

30

4 0

50

60

70

80

T ime (in sec)

FIGURE 9.23: Growth of the transmission signal in vivo after application of occlusion.

µtr = µtras −

2π a(nRBC − n p) a 3π H (1 − H)(1 − g)K ′(ρas ) 8a λ c

"  2 #   π a(n − n ) 2 3π H a 2 p RBC + . (1 − H)(1 − g) K(ρas ) + K ′′(ρas ) 16a λ c

(9.34)

The first two terms in Eq. (9.34) are responsible for asymptotic behavior of transmission for large one-dimensional aggregate sizes. This behavior (growth or decline) depends on the sign of K ′ (ρas ). For λ = 940 nm, K ′ (ρas ) < 0, and µtr asymptotically declines, the transmission grows. For λ = 670 nm, K ′ (ρas ) > 0, and, in the contrary case, µtr asymptotically grows, while transmission declines. The transition from the first kind of behavior (i.e., monotonic) to the non-monotonic one happens on wavelengths λcr satisfying the equation ρas = ρmin,max , where the symbol ρmin,max corresponds to the extreme points of function K(ρ ). At these wavelengths, the first order term in Eq. (9.34) disappears and the resulting dependence becomes very “flat” and all the time dependencies ultimately saturate. For the standard set of RBC parameters, (i.e., a ∼ 4 µ m, ∆n ∼ 0.07 ÷ 0.074), one can expect λcr corresponding to the minimum of K(ρ ) to be around 725–767 nm. As it has been shown experimentally, this is very close to what has been observed. While approaching the asymptotic limit the λcr can be found. λcr is directly proportional to the mismatch of refractive index; however, for this end a very precise spectrophotometer measurement has to be performed.

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712nm 727nm 735nm 750nm 760nm

C ritical wavelenght 1.000

T ransmission (A. U.)

0.9 9 5

0.9 9 0

0.9 85

0.9 80

0.9 75

0.9 70 0

10

20

30

4 0

50

60

70

80

T ime (in sec)

FIGURE 9.24: Transmission changes in close proximity to the critical wavelength point.

9.7.4 Effect of glucose on the light transmission for very long aggregates As shown [1–4], detailed behavior of transparency as a function of time contains the information on the volume fraction of scatterers (hematocrit), the mismatch of refraction indexes (glucose), and the average absorption of whole blood (oxygen saturation). Across the whole range of possible physiological changes of glucose (0 mg/dl< G <500 mg/dl), the corresponding changes of ∆n are minor. In spite of this fact the effect of glucose on transmission behavior is quite observable (Fig. 9.25). While expressed in terms of PS, the resulting dependency of PSS upon blood glucose manifests notable sensitivity (Fig. 9.26).

9.8 Conclusions Scattering is the key factor, which governs the optical responses due to RBC aggregation. It depends critically both on an RBC aggregate shape and size and on the mismatch of refractive index of the aggregate and its surrounding media. The size of the aggregate depends on RBC aggregation kinetics, which varies strongly from subject to subject. For these reasons, the use of the parametric slope helps to escape

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0.0035

T (500 mg/dl)-T(0) (normilized)

0.0030 0.0025 0.0020 0.0015 0.0010 0.0005 0.0000 -0.0005 -0.0010 -0.0015 -0.0020 -0.0025 -0.0030 2

3

4

5

6

7

8

9

10

11

Length of the aggregate (in µm)

FIGURE 9.25: Sensitivity to glucose for long aggregates in the framework of WKB model. the influences of individual kinetics and volumetric features. Hemoglobin values may be successfully extracted from occlusion curves in two physically different cases: based on pure absorption signatures and based on aggregation assisted scattering changes. The very existence of the second option proves that the relevant physical mechanism involved is through the evolution of RBC aggregates and is reflected in optical response. There are still many obstacles in the modeling of aggregation assistance signals in the blood: • There is no satisfactory description of light propagation and interaction within the blood, whereas the blood is randomly distributed in small vessels and is surrounded by the absorption and scattering tissue. The so-called homogenization approach might be fruitful. • The changes of the absorption coefficient as a result of aggregation may have a critical impact while dealing with delicate glucose probing. There is no such formal description as of yet. • The effects of orientation of RBCs as well as effect of distribution of aggregates by their size have yet to be incorporated. • The angular pattern of scattering for big aggregates has yet to be incorporated. • The lack of a uniform distribution of RBCs across all vessels has yet to be accounted for.

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Glucose correlation with light scattering patterns 650nm 720nm 760nm 800nm 840nm 880 nm 980mn

WKB , spheroid

Reference =940nm

PS S (500 m/dl)-PSS (0)

0.25

0.20

0.15

0.10

0.05

0.00

-0.05 6

8

10

12

14

16

Length of aggregate c ( in µm)

FIGURE 9.26: Sensitivity of PSS to glucose for large aggregates.

Acknowledgments Author would like to thank Dr. Michael Baewitch and Diana Gedzelman for technical assistance.

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References [1] P.J. Stout, N. Peled, B.J. Erickson, M.E. Hilgers, J.R. Racchini, and T.B. Hoegh, “Comparison of glucose levels in dermal interstitial fluid and finger capillary blood,” Diabetes Technology & Therapeutics, vol. 3, 2001, pp. 81– 90. [2] Y. Mendelson, “Pulse oximetry: theory and applications for noninvasive monitoring,” Clin. Chem., vol. 38, 1992, pp.1601–1607. [3] J.W. Severinghaus, P.B. Astrup, and J.F. Murray, “Blood gas analysis and critical care medicine,” Am. J. Respir. Crit. Care Med., vol. 4, 1998, S114– S122. [4] L.D. Shvartsman and I. Fine, “RBC Aggregation effects on light scattering from blood,” Proc. SPIE, vol. 4162, 2000, pp. 120–129. [5] O.W. Assendelft, Spectrophotometry of Hemoglobin Derivates, Royal Vangorcum Ltd., Assen, 1970. [6] M.A. Franceschini, D.A. Boas, A. Zourabian, et al., “Near-infrared spiroximetry: noninvasive measurement of venous saturation in piglets and human subjects,” J. Appl. Phys., vol. 92, 2002, pp. 372–384. [7] I. Fine, “Non-invasive method and system of optical measurements for determining the concentration of a substance in blood,” US Patent 6400972, 2002. [8] I. Fine, B. Fikhte, and L.D. Shvartsman, “Occlusion spectroscopy as a new paradigm for non-invasive blood measurements,” Proc. SPIE, vol. 4263, 2000, pp. 122–130. [9] A. Finarov, Y. Kleinman, and I. Fine, “Optical device for non-invasive measurement of blood related signals utilizing a finger holder,” US Patent 6,213,952B1, 2001. [10] S. Chien, “Biophysical behavior of red cells in suspensions,” in The Red Blood Cell, D.M. Surgenor (ed.), vol. 2, Academic, New York, 1975. [11] H.J. Meiselman, “Red blood cell role in RBC aggregation: 1963–1993 and beyond,” Clin. Hemorheol., vol. 13, 1993, pp. 575–592. [12] J. Madrenas, P. Potter, and E. Cairns, “Giving credit where credit is due: John Hunter and the discovery of erythrocyte sedimentation rate,” The Lancet, vol. 366, 2005, pp. 2140–2141. [13] J.J. Bishop, A.S. Popel, M. Intaglietta, and P.C. Johnson, “Rheological effects of red blood cell aggregation in the venous network: A review of recent studies,” Biorheology, vol. 38, 2001, pp.263–274.

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[14] H.L. Goldsmith, G.R. Cokelet, and P. Gaehtgens, “Robin Fahraeus: evolution of his concepts in cardiovascular physiology,” Am. J. Physiol. Heart Circ. Physiol., vol. 257, 1989, H1005–H1015. [15] S. Chien and K.M. Jan, “Red cell aggregation by macromolecules: roles of surface adsorption and electrostatic repulsion,” J. Supramol. Struct., vol. 1, 1973, pp. 385–409. [16] K.M. Jan and S. Chien, “Role of surface electric charge in red blood cell interactions,” J. Gen. Physiol., vol. 61, 1973, pp. 638–654. [17] B. Neu and H.J. Meiselman, “Depletion-mediated red blood cell aggregation in polymer solutions,” Biophys. J., vol. 83, 2002, pp. 2482–2490. [18] H. Schmid-Sch¨onbein, P. Gaehtgens, and H. Hirsch, “On the shear rate dependence of red cell aggregation in vitro,” J. Clin. Invest., vol. 47, 1968, pp. 1447–1454. [19] W. Reinke, P.C. Johnson, and P.Gaehtgens, “Blood viscosity in small tubes: effect of shear rate, aggregation, and sedimentation,” Am. J. Physiol., vol. 253, 1987, H540–H547. [20] M. Cabel, H.J. Meiselman, A.S. Popel, and P.C. Johnson, “Contribution of red blood cell aggregation to venous vascular resistance in skeletal muscle,” Am. J. Physiol., vol. 272, 1997, H1020–H1032. [21] K. Boriczko, W. Dzwinel, and D. Yuen, “Modeling fibrin aggregation in blood flow with discrete–particles,” Comp. Meth. Progr. Biomed., vol. 75, 2004, pp. 181–194. [22] ML. Ellsworth, C.G. Ellis, A.S. Popel, and R.N. Pittman, “Role of microvessels in oxygen supply to tissue,” New Physiol. Sci., vol. 9, 1994, pp.119–123. [23] Cicha, Y. Suzuki, N. Tateishi, and N. Maeda, “Changes of RBC aggregation in oxygenation-deoxygenation: pH dependency and cell morphology,” Am. J. Physiol. Heart Circ. Physiol., vol. 284, 2003, H2335–H2342. [24] L. Dintenfass, “Red cell aggregation in cardiovascular diseases and crucial role of inversion phenomenon,” Angiology, vol. 36, 1985, pp. 315–326. [25] L. Dintenfass, “The clinical impact of the newer research in blood rheology: an overview,” Angiology, vol. 32, 1981, pp. 217–229. [26] N. Bolokadze, I. Lobjanidze, N. Momtselidze, R. Shakarishvili, and G. Mchedlishvili, “Comparison of erythrocyte aggregability changes during ischemic and hemorrhagic stroke,” Clin. Hemorheol. Microcirc., vol. 35, 2006, pp. 265–267. [27] M. Rampling and J.A. Sirs, “The interactions of fibrinogen and dextrans with erythrocytes,” J. Physiol., vol. 223, 1972, pp. 199–212.

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[28] N.J. Jansonius and W.G. Zijlstra, “Various factors influencing rouleaux formations of erythrocytes, studies with the aid of syllectometry,” Proc. K. Ned. Akad. Wet. C., vol. 68, 1965, pp. 121–127. [29] A.V. Priezzhev, O.M. Ryaboshapka, N.N. Firsov, and I.V. Sirko, “Aggregation and disaggregation of erythrocytes in whole blood: study by backscattering technique,” J. Biomed. Opt., vol. 4, 1999, pp.76–84. [30] M. Tomita and N. Tanahashi, “RBC aggregometer head as a warning monitor of flow disturbance in extracorporeal systems,” Int. J. Artif. Organs, vol. 10, 1987, pp. 295–300. [31] T.L. Fabry, “Mechanism of erythrocyte aggregation and sedimentation,” Blood, vol. 70, 1987, pp. 1572–1576. [32] E.M. McKay, “The distribution of glucose in human blood,” J. Biol. Chem., vol. 97, 1932, pp. 685–689. [33] G. Barshtein, D. Wagnblum, and S. Edgar, “Kinetics of linear rouleaux formation studied by visual monitoring of red cell dynamic organization,” Biophys. J., vol. 78, 2000, pp. 2470–2474. [34] T. Shiga, K. Imaizumi, N. Harada, and M. Sekiya, “Kinetics of rouleaux formation using TV image analyzer. I. Human erythrocytes,” Am. J. Physiol. Heart Circ. Physiol., vol. 245, 1983, H252–H258. [35] I. Fine and A. Kaminsky, “In vivo dynamic light scattering measurements of red blood cells aggregation,” Proc. SPIE, vol. 6436, 2007, pp. OC–1–10 [36] I. Fine, “The origin of artificial kinetic spectroscopy and its applications,” In Proc. of the Workshop on Biosignal Processing and Classification (BPC) of ICINCO, 2005, Barcelona. [37] H. B¨aumler, B. Neu, E. Donath, and H. Kiesewetter, “Basic phenomena of red blood cell rouleaux formation,” Biorheology, vol. 36, 1999, pp. 439–442. [38] I. Fine, B. Fikhte, and L.D. Shvartsman, “RBC aggregation assisted light transmission through blood and occlusion oximetry,” Proc. SPIE, vol. 4162, 2000, pp. 130–139. [39] L.D. Shvartsman and I. Fine, “Optical transmission of blood: Effect of erythrocyte aggregation,” IEEE Trans. Biom. Eng., vol. 50, 2003, pp. 1020–1026. [40] A.S. Propel, P.C. Johnson, M.V. Kameneva, and M.A. Wild, “Capacity for red blood cell aggregation is higher in athletic mammalian species than in sedentary species,” J. Appl. Phys., vol. 77, 1994, pp. 1790–1794. [41] B. Rappaz, A. Barbul, F. Charri´ere, et al., “Erythrocytes volume and refractive index measurement with a digital holographic microscope,” Proc. SPIE, vol. 6445, 2007, pp. 64409–1–5.

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[42] M. Friebel and M. Meinke, “Model function to calculate the refractive index of native hemoglobin in the wavelength range of 250–1100 nm dependent on concentration,” Appl. Opt., vol. 45, 2006, pp. 2838–2842. [43] G. Mazarevica, T. Freivalds, and A. Jurka, “Influence of hydrogen ion concentration on refractive index value in red blood cells of diabetic patients,” Proc. SPIE, vol. 4622, 2002, pp. 291–296. [44] V.V. Tuchin, R.K. Wang, E.I. Galanzha, J.B. Elder, and D.M. Zhestkov, “Monitoring of glycated hemoglobin by OCT measurement of refractive index,” Proc. SPIE, vol. 5316, 2004, pp. 66–77. [45] K. Zierler, “Whole body glucose metabolism,” Am. J. Physiol. Endocrinol. Metab., vol. 276, 1999, E409–E426. [46] M. Friebel and M. Meinke, “Determination of the complex refractive index of highly concentrated hemoglobin solutions using transmittance and reflectance measurements,” J. Biomed. Opt., vol. 10, 2005, pp. 064019–1–5. [47] O.S. Zhernovaya, A.N. Bashkatov, E.A. Genina, et al., “Investigation of glucose-hemoglobin interaction by optical coherence tomography,” Proc. SPIE, vol. 6535, 2006, pp. 65351C–1–7. [48] A. Chabanel and M. Samama, “Evaluation of a method to assess red blood cell aggregation,” Biorheology, vol. 26, 1989, pp. 785–797. [49] A.N. Yaroslavsky, A.V. Priezzhev, J. Rodriguez, I.V. Yaroslavsky, and H. Battarbee, “Optics of blood,” in Handbook of Optical Biomedical Diagnostics, V.V. Tuchin (ed.), SPIE Press, Bellingham, WA, 2002. [50] V. Twersky, “Absorption and multiple scattering by biological suspensions,” J. Opt. Soc. Am., vol. 60, 1970, pp. 1084–1093. [51] G.D. Pedersen, N.J. McCormick, and L.O. Reynolds, “Transport calculations for light scattering in blood,” Biophys. J., vol. 16, 1976, pp. 199–207. [52] I. Fine and A. Weinreb, “Multiple-scattering effects in transmission oximetry,” Med. Biol. Eng. Comp., vol. 31, 1993, pp. 516–522. [53] J. Schmitt, “Simple photon diffusion analysis of the effects of multiple scattering on pulse oximetry,” IEEE Trans. Biomed. Eng., vol. 38, 1991, pp. 1194– 1203. [54] M. Friebel, A. Roggan, G. M¨uller, and M. Meinke, “Determination of optical properties of human blood in the spectral range 250 to 1100 nm using Monte Carlo simulations with hematocrit-dependent effective scattering phase functions,” J. Biomed. Optics, vol. 11, 2006, pp. 034021–1–10. [55] A. Ishimaru (Ed.), Wave Propagation and Scattering in Random Media, vol. 1, Academic Press, New York, 1978.

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[56] A.N. Yaroslavsky, I.V. Yaroslavsky, T. Goldbach, and H.J. Schwarzmaier, “Influence of scattering phase function approximation on the optical properties of blood determined from the integrating sphere measurements,” J. Biomed. Opt., vol. 4, 1999, pp. 47–53. [57] M. Hammer, D. Schweitzer, B. Michel, E. Thamm, and A. Kolb, “Single scattering by red blood cells,” Appl. Opt., vol. 37, 1998, pp. 7410–7418. [58] J.M. Steinke and A.P. Shepherd, “Comparison of Mie theory and the light scattering of red blood cells,” Appl. Opt., vol. 27, 1988, pp. 4027–4033. [59] M. Hammer, A.N. Yaroslavsky, and D. Schwitzer, “A scattering phase function for blood with physiological haematocrit,” Phys. Med. Biol., vol. 46, 2001, pp.65–69. [60] D.M. Zhestkov and V.V. Tuchin, “Optical immersion of erythrocytes in blood: a theoretical modeling,” Proc. SPIE, vol. 5068, 2003, pp. 387–392. [61] V.V. Tuchin, D.M. Zhestkov, A.N. Bashkatov, and E. Genina, “Theoretical study of immersion optical clearing of blood in vessels at local hemolysis,” Opt. Exp., vol. 12, 2004, pp. 2966–2971. [62] E.E. Gorodnichev and D.B. Rogozkin, “Small-angle multiple scattering of light in a random medium,” J. Exp. Theor. Phys., vol. 80, 1995, pp. 112–126. [63] G.C. Papanicolaou, “Diffusion in random media,” in Surveys in Applied Mathematics, vol. 1, J.B. Keller, D.W. McLaughlin, and G.C. Papanicolaou (Ed.), Plenum Press, New York, 1995. [64] A.H. Gandjabakche, G.H. Weiss, R.F. Bonner, and R. Nossal, “Photon pathlength distribution for transmission through optically turbid slabs,” Phys. Rev. E., vol. 48, 1993, pp. 810–818. [65] V. Lodwig and L. Heinemann, “ Continuous glucose monitoring with glucose sensors: calibration and assessment criteria,” Diabet. Techn. Therap., vol. 5, 2003, pp.572–586 [66] D. C. Klonoff, “Microdialysis of interstitial fluid for continuous glucose measurement,” Diabetes Technology & Therapeutics, vol. 5, 2003, pp.539–543. [67] V. V. Tuchin, R. K. Wang, and X. Xu, “Whole blood and RBC sedimentation and aggregation study using OCT,” Proc. SPIE, vol. 4263, 2001, pp. 144–149. [68] S. Suzuki, S. Takasali, T. Ozaki, and Y. Kobayashi, “A tissue oxygenation monitor using NIR spatially resolved spectroscopy,” Proc. SPIE, vol. 3597, 1999, pp. 582–592. [69] V. S. Tsinopoulos, E. J. Sellountos, and D. Polyzos, “Light scattering by aggregated red blood cells,” Appl. Opt., vol. 41, 2002, pp.1408–1417.

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10 Challenges and Countermeasures in NIR Noninvasive Blood Glucose Monitoring Kexin Xu College of Precision Instrument and Opto-Electronics Engineering, Tianjin University, Tianjin 300072, P.R. China Ruikang K. Wang Department of Biomedical Engineering, Oregon Health & Science University 3303 SW Bond Avenue, Portland, OR 97239 10.1 The Principles and Issues on the Measurement of Blood Glucose Using Near-Infrared Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Factors of Influencing the Measuring Precision of Glucose Monitor . . . . . . . . 10.3 Noninvasive Glucose Measurement and Human-Spectrometer Interface Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4 Challenges and Solutions in In Vivo Noninvasive Blood Glucose Monitoring References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

282 287 297 307 316

Over the past decades, noninvasive blood glucose monitoring has become an increasing important topic in the realm of biomedical engineering. Particularly, the introduction of optical approaches has brought exciting advances to this field. However, there is still no clinically feasible method for continuously monitoring of the in vivo human blood glucose concentration at the physiological level. This is probably because the instrumental response to the glucose specific signal is feeble compared to those of other compounds in the complex physiological system. An effective solution to this problem will represent a major advance in this field. This chapter analyzes the challenges faced by continuous in vivo blood glucose monitoring by use of near-infrared spectroscopy on both the aspects of methodological and instrumental implement. Some critical and imperative issues are identified and the promising and viable countermeasures are suggested at the end of this chapter. Key words: NIR spectroscopy, noninvasive measurement, blood glucose concentration, diffuse reflectance, floating-reference method.

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10.1 The Principles and Issues on the Measurement of Blood Glucose Using Near-Infrared Spectroscopy 10.1.1 The principle of blood glucose measurement using near infrared spectroscopy Electromagnetic waves in the wavelength range between 780 and 2500 nm (equivalent to wavenumbers from 12820 to 4000 cm−1 ) are known as the near-infrared (NIR) wavelength region, and between 2500 and 25000 nm (equivalent to wavenumbers from 4000 to 400 cm−1 ) as mid-infrared (MIR) wavelengths. The fundamental vibrational frequencies of most organic and inorganic compound molecules occur in the MIR range, whereas the absorption in NIR ranges is based on overtone and combination bands primarily in MIR region. The wavenumbers in the near-infrared range are above 4000 cm−1 ; thus, the absorption of first overtone will occur only when the fundamental molecular vibration frequencies are above 2000 cm−1 . The functional groups, for which the fundamental vibrations are above 2000 cm−1 , are usually the hydrogen functional groups such as C–H, O–H and N–H. Therefore, the near infrared spectroscopy is based on the overtone and combination bands primarily of O–H, C–H and N–H groups whose fundamental molecular vibrations lie in the MIR region. The concentration of blood glucose refers to the concentration of glucose in blood. The molecular formula of glucose is C6 H12 O6 and several hydroxyl and methyl groups are contained in this structure. They are main hydrogen functional groups whose absorption occurs in the near infrared region. According to the characteristics of molecular structure, the absorption spectra of glucose and water in the near infrared region are shown in Fig. 10.1. The second overtone absorption of glucose molecule is in the spectral region between 1100 and 1300 nm and the first overtone absorption of glucose molecule is in the region of 1500 to 1800 nm. This information provides the theoretical basis for the measurement of blood glucose using near infrared spectroscopy. NIR region is ideal for the noninvasive measurement of human body compositions because biological tissue is relatively transparent to the light in this window, so called the therapeutic wavelength window. With the development of computer technology and chemometrics, the sensitivity, accuracy and reliability of the NIR spectroscopy for quantitative analysis has seen marked improvement. Noninvasive glucose monitoring by use of NIR spectroscopy is mainly based on absorption of electromagnetic radiation. According to the Beer-Lambert law, the relationship between the intensity of incident optical radiation I0 , the transmitted intensity I and the pathlength L of light passing in the analyte is expressed as " # n

I(λ ) = I0 exp

∑ εi (λ )ci L

,

(10.1)

i=1

where εi (λ ) and ci are the molar absorptivities and concentrations for each of the n components in the sample, respectively.

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FIGURE 10.1:

The absorption curves of glucose and water.

The transmitted light intensity changes with the concentration of compounds in the matter, thereby, the compound’s concentration can be obtained by the measurement of light transmission through the medium. However, there are a number of substances other than glucose alone in the human body; for example, proteins, water, etc. that also have absorptive characteristics in the NIR region that overlap with the glucose spectrum. Therefore, the measurement of the transmitted light intensity is generally made over multiple wavelengths. On the other hand, the Beer-Lambert law only describes the ideal transmission scenario. In fact, light particles (photons) do not travel along a straight path for the noninvasive glucose measurement. Both the absorption caused by absorbers and the scattering caused by scatters attenuate the incoming light intensity. Furthermore, the variation of optical pathlength in the turbid medium due to the light scattering would complicate the problem further which will be discussed later in this chapter.

10.1.2 Noninvasive glucose measurement by diffuse reflectance spectroscopy According to the detection modes of transmitted light, the methods generally include the modes of transmittance and diffuse reflectance measurements. When light propagates in tissue, light interacts with particles. Some of the photons are attenuated due to absorption and others due to scattering. Forward scattering photons exit from the other side of tissue and these photons are known as transmitting photons, whereas backscattering photons exit from the same side as the incident light and these photons are known as diffuse reflectance photons. Most studies on noninvasive glucose measurement by transmittance spectroscopy use the wavelength region between 700 and 900 nm, the therapeutic optical window. In this region, water presents a relative weak absorption, which makes it possible to detect absorption signal from deep tis-

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Skin È Ë Ìå ×é Ö¯

Compositions(Glucose,water,...)

Average Pathlength

FIGURE 10.2: Schematic showing noninvasive blood glucose concentration measurement by diffuse reflectance spectroscopy.

sue. Many research groups have targeted to the sites where they are relatively thin, such as fingers, ear lobe, etc., for the study of transmittance measurement. However, the weakness of transmittance measurement is that the absorption of glucose is relative weak in these regions. For the overtone and combination regions dominated by glucose absorption, the absorption by water is also significant, and further due to the added scattering effect, it is difficult for light to pass through, even for the thin body sites. Consequently, diffuse reflectance spectroscopy is usually applied for monitoring of glucose contents at relatively convenient tissue sites, for example arms and palms [1–5]. Generally speaking, the measurement with NIR diffuse reflectance spectroscopy can be described by the diagram shown in Fig. 10.2. A NIR beam irradiates onto a human body site and then exits at some distance away from the incident point through propagation distance L. Light is absorbed and scattered by components present in the target, including glucose, when light propagates through tissue. Since diffuse reflectance light contains the absorption information of glucose, the corresponding glucose concentration can be obtained by measuring the diffuse reflectance spectra and then with the help of the appropriate mathematical models to predict the glucose concentration. As mentioned previously, the diffuse reflectance spectral signals detected include the contributions not only from glucose but also from many other substances. Therefore, it is difficult to obtain directly the glucose concentration at single wavelength. The chemometric technique is usually employed to establish a mathematical model between spectral data and glucose concentration in order to predict glucose concentration (Fig. 10.3). Firstly, a series of training set samples with gradient distributed variations of glucose concentrations are designed and the corresponding NIR spectra are collected. Secondly, the calibration model by regression analysis for the spectral matrix and glucose concentration using multivariate analysis technique is established to obtain the regression coefficient of the calibration model. Finally, for the predicted sample with unknown glucose concentration, its NIR spectrum is measured to solve

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Challenges and countermeasures in NIR noninvasive blood glucose monitoring 285 Spectra Matrix of the Calibration Set

Concentration Matrix of the Calibration Set

Multivariate Regression Spectra Matrix of the Prediction Set

Calibration Model

Glucose Concentration

FIGURE 10.3: Multivariate calibration modeling to predict blood glucose concentration.

the spectrum matrix by calibration model to obtain the glucose concentration value through the regression coefficient of the calibration model. Human skin tissue exhibits layered structures, which can be described as three distinct layers starting from the surface: epidermis, dermis and subcutaneous tissue. The smallest blood vessels lie within the dermal papillary layer. Compared to the diffuse reflectance light from the epidermis, the signals from the dermis contain abundant glucose information. Likewise, the detected signals of the diffuse reflectance from the dermis are stronger than the signals from subcutaneous tissue. For noninvasive glucose measurement by diffuse reflectance spectroscopy, the actual diffuse reflectance spectra of the dermis contain glucose information from blood and tissue. Due to the isotonicity of glucose molecule, the exchange of glucose molecules in blood and dermal tissue is made by the osmotic pressure through the vessel wall; therefore, the changes between glucose concentration in tissue and that in vessel wall have good correlation [6]. This follows that the diffuse reflectance spectra from dermis could reflect effectively the body glucose information. Moreover, the maximal light penetration depth increases with the radial distance under the same measurement conditions. Therefore, it is vital to appropriately select the radial distance at which diffuse reflectance spectra represent the information of dermal tissue. Our group has used the NIR wavelength region from 1100 to 1700 nm and the dermal tissue of the palm as measurement sites for noninvasive blood glucose measurement [5]. The main reason for the selection of the palm as the measurement site is that the palm region does not contain hair and hair follicles and it is therefore convenient for the spectroscopic measurement. An image orientation system has been developed based on the specification of palm print, in order to eliminate the effect of the variations of measurement sites on spectra. Meanwhile, it is convenient to design the human-spectrometer interface that is acceptable by measurement subjects. In order to detect the diffuse reflectance signal efficiently, an optical probe with a shape of a coaxial ring has been designed. The radius of incident fiber bundle is 1.5 mm. The inner and external diameters of the ring for the receiving fiber

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bundle are 1.8 mm and 3.3 mm, respectively. Based on the computational results of the Monte Carlo method, the average photon penetration depth of diffuse reflectance photons at 1600 nm is 0.69 mm [7] when the optical probe is used for the measurement of diffuse reflectance spectrum of the palm. The average thickness of the epidermis of the adult palm is ∼0.5 mm [8]. Therefore, the photons can penetrate the epidermis of the palm and the requirements for the diffuse reflectance spectroscopic measurement of glucose within dermis layer of tissue can be satisfied. The diffuse reflectance energy from the dermal layer received by the probe is 54% of the total diffuse reflectance energy [7].

10.1.3 The main questions of noninvasive glucose measurement by NIR spectroscopy Although the principle of the noninvasive glucose measurement techniques based on NIR is clear, the subject is the live body, the physiological conditions of which are continuously variable, and spectral signals related to the glucose concentrations are very weak. These make it necessary to extract weak information of glucose concentration from the background with complex changes. Therefore, the clinical feasibility of the noninvasive glucose measurement so far has been proved neither in measurement methodology nor clinical examining accuracy. In summary, several critical obstacles have prevented the success of measuring glucose noninvasively. 1) The requirement of high performance instrumentation. In the measurement of the human body glucose, the normal proportion of glucose concentration in blood and tissue is only 0.1% of water content. The variations of spectral signals due to the changes of glucose concentrations are very weak. Moreover, NIR spectra in in vivo measurement are affected by various factors such as instrumentation, ambient conditions, physiological fluctuation of the subject, etc. Consequently, the required signal to noise ratio (SNR) of instrumentation must be high enough in order to assure the quality information of the spectra. 2) How to establish an effective calibration model. To establish the correlation calibration model of variations of spectra and glucose using multivariate regression, many systematic and chance temporal variation factors exist. The systematic variations make the model complex, and the chance temporal variations easily lead to pseudo-correlation. As a result of these issues, we must consider how to build a model and evaluate its effectiveness. 3) Variations in human-spectrometer interface conditions. Because the subject is the live body, variations of human body and spectrometer interface conditions in measurement, such as the temperature of measurement sites, sweat conditions, contact pressures, slight shakes and position displacement of the measuring sites, etc., have effects on the spectroscopic measurements. Therefore, in order to eliminate the extra variations of spectra, we must combine the specific measurement scheme with the fusions of mechanics, optics, medicine and other aspects to design a reliable and friendly human-spectrometer interface. 4) The determination of measuring optical path. Light in human body tissue is both scattered and absorbed by substances, resulting

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Challenges and countermeasures in NIR noninvasive blood glucose monitoring 287 in light propagation which does not follow a straight path. The photons received at a fixed spatial distance are generally the combination of photons passing through different optical pathlengths and the propagation routes change with the concentration of substances measured. In order to obtain the glucose information of the selected position, therefore, it is necessary to consider how to make the light reach the measured tissue position. Meanwhile, it is also necessary to consider how to implement proper pathlengths in order to obtain a proper SNR. 5) The time dependent variations in background. Factors, such as metabolism, physiological period, fluctuations in emotion and in ambient conditions, will directly or indirectly lead to the variations of constituent in human body tissue and affect the precision of glucose measurement. Because these time dependent variations in background are complex and related to many factors, it is difficult to implement qualitative prediction or real-time monitoring. Consequently, how to obtain a relative reference measurement will be a feasible approach. Our group is now focusing onto how to find a floating reference point to realize a relative measurement. Our group has been devoted to the study of noninvasive glucose monitoring techniques for many years. We have made innovative progress in some aspects, such as the relations among SNR of the instrumentation, optical pathlength and measurement precision, the optimization of data models, considerations of human measurement conditions, the design of the human-spectrometer interface, etc. Preliminary clinical model prototype has been designed and reduced into clinical trials, from which good clinical experiment results have been made. Due to the interference of time dependent variations in human physiological background, however, the present human measurement model can be applied only on the oral glucose tolerance test (OGTT) for single subjects at one time but not on the predictions for multiple days. These are the critical obstacles preventing the clinical application of NIR noninvasive glucose measurement techniques. Nevertheless, a solution, so called floating-reference method, has been proposed in our recent research. The solution is to first determine the radial reference position at which the diffuse reflected light is not sensitive to the variation of glucose concentration, and then use this reference as the inter-reference signal among the measured signals to eliminate the influence of the physiological background variation on the final prediction. A detailed description of this approach will be given in section 4.

10.2 Factors of Influencing the Measuring Precision of Glucose Monitor Near-infrared (NIR) spectroscopy for noninvasive glucose measurement is an indirect measuring technique. This means that multivariate calibration models have to be used to build the relationship between instrumental response and component

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concentrations, which include two key factors: 1) relative high SNR and long-time stability of spectrometer are necessary in order to measure the absorption or diffusion spectroscopy accurately and reliably; 2) an accurate and robust calibration model is a prerequisite. Obviously, the measuring precision using NIR spectroscopy is significantly related to instrumental precision, chemometrics and analyte.

10.2.1 The relationship between measuring precision and instrumental precision According to Eq. (10.1), the variation ∆I induced by the changes of glucose concentration is given by " # n dI dc i ∆cg = I · l · ∑ εi · ∆cg , ∆I = dcg dcg

(10.2)

i=1

where l is the optical pathlength, ci is the concentration of different absorbent, εi (function of wavelength) is the absorbance coefficient corresponding to absorbent, n are the numbers of total components in solution and ∆I is the variation of light intensity induced by glucose concentration changes. dci /dcg is the correlation of concentration changes of different components and glucose. If the signal-to-noise ratio of repeated spectral measurement is defined as SNR, then the noise from instrument is given by σN = I/SNR. We can believe that glucose concentration data will not be extracted under the condition that variation of light intensity ∆I induced by glucose concentration changes is equivalent to instrumental noise σN , i.e., ∆I = σN . This condition is called the limit detection condition. The detection limit of glucose concentration ∆clim g in the pathlength l is given by lim ∆cg =

1 n

(∑ i=1

dci εi dc ) · l · SNR g

.

(10.3)

Thus, it is believed that the variations of glucose concentration just induce the changes of water concentration, that is, we only consider replacement action between glucose and water. According to the research by Weast [9], at the temperature of 20◦ C, ∆cw = c0w · (−0.0111%) · ∆cg = −0.6149∆cg, then the formula (10.3) can be simplified as lim ∆cg =

1 . (εg − 0.6149εw) · l · SNR

(10.4)

It can be seen that the detection limit of glucose concentration is in inverse proportion to instrumental signal-to-noise ratio under the fixed wavelength and pathlength. According to Eq. (10.4), at the pathlength l, the curves of variation relation between the limit detection precision of glucose concentration and spectral repeatability SNR are shown in Fig. 10.4. Under the same wavelength and pathlength, the higher the instrumental SNR, the lower the limit detection error of glucose concentration is.

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FIGURE 10.4: The variation correlation between detection limit of glucose concentration and instrumental SNR at single wavelength (1 mm pathlength). However, after the instrumental SNR reaches a certain level, more stringent conditions are required in the improvement of instrumental SNR to reduce the detection limit of glucose concentration. Meanwhile, the pursuit of too high instrumental SNR in hardware will increase the overall cost of the instrumentation; therefore, it is desirable that improvements are made in the modeling methods.

10.2.2 An effective calibration method to improve the measuring precision of glucose concentration Absorption spectra of different compounds in the NIR spectral range are usually significantly overlapped. It is difficult to achieve ideal measuring precision at one single wavelength. Spectral measurements have to be constructed at multiple wavelengths and chemometrics methods are needed to build multivariate calibrations. As a consequence, measuring precision of glucose concentration by NIR spectroscopy is restricted not only by the instrumental precision but also by the calibration methods. The quantitative relations between the root mean square standard error of prediction (RMSEP), the regression coefficient of calibration models and SNR of instrumental repeatability can be described as [10, 11] s  1 2 2 (10.5) ) ·B , ( RMSEP = SNR h i 1 2 1 2 , ( 1 )2 , ( 1 )2 , · · · , B2 denotes the where ( SNR ) represents the vector ( SNR ) SNR2 SNR3 1   vector b21 , b22 , b23 , · · · , the dot denotes the inner product, SNRi is SNR of instrumental repeatability at the i-th wavelength, bi is the regression coefficient corresponding to the i-th wavelength.

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Regression coefficient B is related to calibration method and parameters such as wavelengths and the selection of principal component numbers. For a certain object, under the condition that the instrumental precision and calibration method are known, the prediction precision of concentration can be calculated according to Eq. (10.5). Meanwhile, the hardware requirements to achieve the expected measuring precision, i.e., the repeatability SNR of spectrometer, can be determined by Eq. (10.5) and the simulated calculation under the condition that the instrumental precision and calibration method are known. The simulated experiment is conducted using glucose aqueous solution. The respective curves of relation between the measuring precision RMSEP of glucose concentration and instrumental precision using the univariate calibration method and multivariate PLS calibration method are shown in Fig. 10.5. It is obvious that the measuring precision limit is higher using the multivariate PLS calibration method than univariate calibration methods under the same instrumental precision. In a similar way, the instrumental SNR obtained by simulated calculation with different calibration methods that achieves prediction accuracy of 5 mg/dl is shown in Fig. 10.6. In the experiment of glucose aqueous solution with 1 mm optical pathlength, the instrumental SNR should be higher than 19000:1 using univariate calibration methods at the wavenumber 4620 cm−1 to achieve prediction accuracy of 5 mg/dl; the instrumental SNR should be higher than 9000:1 using multivariate PCR calibration methods in the spectral range 4400–4800 cm−1 ; the instrumental SNR should be higher than 8000:1 using multivariate PLS calibration methods in the spectral range 4400– 4800 cm−1 ; the instrumental SNR should be higher than 5000:1 using PLS calibration methods after the wavelength selection in the spectral range 4400–4800 cm−1 by Genetic Algorithm [12, 13]. The results above show that the improvement of prediction precision will be limited by the increase of instrumental precision after it has got to a certain degree. However, if effective calibration methods are applied, the prediction precision of glucose measurement can be enhanced greatly when the instrumental precision is constant. Correspondingly, the requirements for instrumental precision to achieve the anticipated prediction accuracy of glucose measurement can be decreased. Consequently, it is important to select effective calibration methods in order to improve the measuring precision of glucose measurement by NIR spectroscopy.

10.2.3 The influence of sample complexity on measuring precision When multiple wavelengths are used, the prediction precision RMSEP of glucose concentration is inversely proportional to the synthesized sensitivity at multiple wavelengths [14] RMSEP = σr /SENg ,

(10.6)

where σr is the noise of spectral measurement. Selectivity is another key parameter for the multivariate model. It reflects the overlapping degree of the spectra of special components in the total spectral signals

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FIGURE 10.5: The curves of relation between the measuring precision of glucose concentration and instrumental repeatability SNR using different calibration methods.

FIGURE 10.6: Instrumental repeatability SNR to achieve prediction accuracy of 5 mg/dl using different calibration methods.

and plays a significantly restrictive role to multivariate sensitivity and detection limit, thus, important to the model performance. The relationship between the sensitivity SENg of multivariate calibration models and selectivity ξg is

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FIGURE 10.7: Prediction errors expressed as RMSEP for different experiments.



rg , SENg = ξg cg

(10.7)

where rg is the orthogonal net signal of glucose with the information from other components [15]. The overlapping of spectral absorbance peak between different components could be serious when the number of sample components is increased. Therefore, based on Eq.(10.7), the selectivity of the measured component decreases, leading to deterioration in sensitivity, and correspondingly, the prediction precision of glucose concentration will be decreased. Under the condition that the instrumental repeatability SNR is 10000:1 and the path length is 1 mm, two-component sample experiment (glucose and de-ionized water), three-component sample experiment (glucose, de-ionized water and albumin), four-component sample experiment (glucose, de-ionized water, albumin and bovine hemoglobin ) and blood plasma solution experiment (glucose, de-ionized water and plasma) are constructed respectively. PLS calibration method is applied and full cross validation is used to evaluate the prediction precision of the model. The results of the experiment are shown in Fig. 10.7. The prediction precision of glucose concentration decreases with the increase of sample complexity. The influence of component complexity on required instrumental precision is analyzed further. The relation curves of measuring precision RMSEP of glucose concentration and instrumental precision SNR in the two-component and four-component experiments are shown in Fig. 10.8. The required instrumental SNR to achieve prediction accuracy of 5 mg/dl is 8000:1 in the two-component experiment and 13700:1 in the four-component experiment using multivariate PLS calibration methods. It can be concluded that requirements for instrumental precision to achieve the same expected measuring precision are increased greatly with the sample becoming complicated. In practical application, the chances of increasing the measuring precision

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FIGURE 10.8: The relation between measuring precision of glucose concentration and instrumental precision under the different sample complexities.

by the hardware improvements are very limited after the instrumental precision has been achieved to a certain degree. Therefore, it is necessary to improve the validity of the calibration method and other measuring conditions (such as the selection of the optimal pathlength and constant measuring temperature), in order to effectively increase the measuring precision of glucose concentration.

10.2.4 The optimal pathlength method to improve the measuring precision of glucose concentration The error of glucose concentration measurement by NIR spectroscopy is in inverse proportion to sensitivity of the model and in direct proportion to instrumental noise. Therefore, error can be decreased from the following aspects: to improve the instrumental SNR and the sensitivity of the model. At single wavelength, the sensitivity of glucose measurement can be given by sg , # " n n − ∑ εi ci l rg dI dc i = I0 · e i=1 , (10.8) = sg = · l · ∑ εi cg dcg i=1 dcg

where rg denotes the glucose net signal, dI is the variations of light intensity induced by the changes of glucose concentration, dci /dcg denotes the concentration variations of the component i induced by the changes of glucose concentration in the sample. When the variations of glucose concentration only cause the replacement of glucose and water, n

sg = I0 · e

− ∑ εi ci l i=1

· l · (εg − 0.6149εw) .

(10.9)

The sensitivity of spectral measurement is related to path length, incident light intensity, the analyte component concentration and absorbance coefficient. Under the condition that other measuring factors, including the sample, wavelength for cali-

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bration and spectrometer characteristics, are constant, measuring sensitivity is determined by path length. The path length corresponding to the maximum sensitivity of glucose concentration measurement is defined as the optimal path length. ds Make dlg = 0, then the optimal path length at single wavelength can be derived, # " n n − ∑ εi ci l rg dI dc i = = I0 · e i=1 , (10.10) · l · ∑ εi sg = cg dcg i=1 dcg

where rg denotes the glucose net signal, dI is the variations of light intensity induced by the changes of glucose concentration, dci /dcg denotes the concentration variations of the component i induced by the changes of glucose concentration in the sample. When the variations of glucose concentration only cause the replacement of glucose and water, # " n

sg = I0 · exp − ∑ εi ci l · l · (εg − 0.6149εw) .

(10.11)

i=1

The sensitivity of spectral measurement is related to pathlength, incident light intensity, the analyte component concentration and absorbance coefficient. Under the condition that other measuring factors, including the sample, wavelength for calibration and spectrometer characteristics, are constant, measuring sensitivity is determined by pathlength. The pathlength corresponding to the maximum sensitivity of glucose concentration measurement is defined as the optimal pathlength. ds Make dlg = 0, then the optimal pathlength at single wavelength can be derived, loptimum =

1 n

.

(10.12)

∑ εi ci i=1

According to Eq. (10.10), the optimal pathlength of glucose aqueous solution in the NIR overtone region can be calculated and the results are shown in Fig. 10.9. The optimal pathlengths in different NIR wavelength regions are different and vary greatly, so the selection of the optimal pathlengths for multivariate analysis is difficult. If a single pathlength is used, it is difficult to obtain ideal prediction precision. Focusing on the issue, our group has proposed a combined optimal-pathlengths (COP) method [16], that is, under the conditions that sample, wavelength for calibration model and regression method are fixed, different optimal pathlengths are selected for different wavelength regions according to Eq. (10.10) and spectra are measured with their optimal pathlengths in each wavelength. Then the spectra data with the optimal pathlengths in each wavelength are combined for calibration in order to improve the model sensitivity and decrease the prediction error of glucose concentration. Simulated experiments are prepared to validate the effect of the COP method. These experiments include a two-component (glucose aqueous solution), three-component (glucose, de-ionized water and albumin) and four-component (glucose, deionized water, albumin and haemoglobin) mixture system. The wavebands cho-

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FIGURE 10.9: The optimal pathlength of glucose aqueous solution in the NIR overtone region.

sen for calibration include 4624–4720 cm−1 , 5296–5344 cm−1 , 6032–6240 cm−1 , 7504–7600 cm−1 and 8672–8832 cm−1 . The corresponding optimal pathlengths are approximately 0.4 mm, 0.3 mm, 1.5 mm, 5.0 mm and 15 mm. For all samples, under the condition that the concentration and absorbance coefficients of each component are known, pathlengths are changed and the corresponding transmitted light intensities are calculated. Random Gaussian noise with a mean of zero and a standard deviation of 0.001 is added to noise-free transmitted spectra. The spectra data for each pathlength are calibrated. Moreover, the spectra with the COP method are also processed in the same way. For each model, the leave-one-out full cross validation [17] is applied. The root mean square error of cross validation (RMSECV) is used to evaluate the results of the models. The prediction error of the models with different pathlengths is shown in Fig. 10.10. It is obvious that the COP method can significantly improve the measuring precision of glucose concentration.

10.2.5 Precision analysis of the glucose concentration measurement by diffuse reflectance spectroscopy from dermis layer Diffuse reflectance spectroscopy from dermis layer is applied to measure the glucose concentration. In order to extract the glucose information from dermal layer efficiently, an optical probe with a shape of coaxial ring is designed. Based on the structure parameters of the probe, structural parameters of layer tissue and optical parameters of each layer [18], Monte Carlo simulations [19] are applied to calculate light transmission in skin tissue. Shown in Fig. 10.11 is the obtained average pathlengths of photons in dermal layer. Comparing Fig. 10.9 with Fig. 10.11, the average pathlengths of photons in dermal layer are very similar to the ones in glucose aqueous solution. Near the water absorption region 1400–1500 nm, the average pathlength of photons in dermal layer

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FIGURE 10.10: Simulation of the relationship between model error and the different pathlengths from: (a) two-component, (b) three-component and (c) fourcomponent models.

is about 0.5 mm, while optimal pathlength of glucose aqueous solution is 0.4 mm. Near the specific absorption region of glucose 1600 nm, the optimal pathlength of the glucose aqueous solution and the average pathlength of photons in dermal layer are all about 1.5 mm. Only in the short wavelength 1200–1400 nm regions, the average pathlength of photons in the dermal layer, only about 4 mm, is smaller than the one in glucose aqueous solution. Without the influence of glucose concentration variations on other components, the simulated calculation is conducted to obtain the transmitted light intensity with the average pathlength at each wavelength according to glucose and water concentrations, molar absorbance coefficient and the average pathlengths of photons in dermal layer. Random Gaussian noise with a mean of zero and a standard deviation of 0.001 is added to the simulated spectra. PLS model between glucose concentration and simulated spectra is built and the leave-one-out full cross validation is applied to evaluate the prediction error of the model. In the short-wavelength region between 1200–1300 nm, the absorbance of glucose is weak, but the average pathlengths of photons are relatively long. The RMSECV obtained in this region is 12.6 mg/dl. In the long-wavelength region between 1500– 1700 nm, the absorbance of glucose is strong, but the average pathlengths of photons are relatively short. The RMSECV obtained in this region is 6.38 mg/dl. The PLS model using the whole spectral region between 1200–1700 nm is built and the RMSECV obtained is 4.21 mg/dl.

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FIGURE 10.11: The obtained average pathlengths of photons in dermal layer.

Therefore, if the influence of other components in tissue and temperature variations on glucose measurement is not considered, it would be possible to extract the glucose concentration in the dermal layer efficiently by use of the overtone region of glucose by use of the optical probe described.

10.3 Noninvasive Glucose Measurement and Human-Spectrometer Interface Technique Compared to the measurement in vitro, the noninvasive glucose measurement in vivo is easily influenced by variations in measurement conditions such as measurement position and contact pressure. Therefore, it is an important precondition to design a proper human-spectrometer interface between subject and instrumentation to minimize the possible errors. In this section, the influences of measurement positions and contact pressure on measurement will be analyzed, the design of the human-spectrometer interface will be discussed and the results of clinical experiments by applying the system on the noninvasive glucose monitoring will be given.

10.3.1 The influence of measurement site and position When NIR spectroscopy is used for noninvasive glucose measurement, the microstructures of skin and subcutaneous tissue between the different persons or different sites of the same person will lead to great variations in the propagation pathlength of the NIR light. Therefore, even under the condition of the same glucose concentration, variability will still present in the spectra. The diffuse reflectance spectra

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Palm Position 1 Palm Position 2 Palm Position 3 Palm Position 4

Intensity

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(a)

0.8

(b)

0.6 0.4 0.2 1100

1200

1300

1400

1500

1600

1700

1800

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FIGURE 10.12: The diffuse reflectance spectra (a) at different measurement sites (b) at the same measurement site with the slight differences of the probing position.

collected from the same person with the same probe at different measurement sites under the constant glucose concentration are shown in Fig. 10.12(a). Even at the same site of the same person, the slight change of the probing position leads to clear spectral variations. However, shown in Fig. 10.12(b) are the measurements collected from the same person with the same probe at the same sampling site under the constant glucose concentration, but with the measurement positions within less than 5 mm radius. It can be seen that the obvious differences present in the diffuse reflectance spectra either at different measurement sites or different measurement position of the same site. Moreover, the differences in spectra are much greater than the ones introduced by the glucose concentration variations. In order to decrease the spectral variations induced by the measurement position, the probing position should be restricted, that is, the same probing site should be used either in the establishment of glucose calibration or in the application of instruments with established model. Moreover, spectra should be measured at the same measurement position as accurately as it can be possible. Although the mathematical model using the method is only applicable for the measurement position, the method could effectively reduce the difficulties of the extraction of weak signal, and it is also acceptable for the different individuals. The reason is that the energy of NIR light is so weak that no site effect to the human tissue can be made, even if the same measurement position is used every time. Therefore, a reproducible orientation method is devised to ensure measurement position repeatable so that the interference caused by the differences of measurement positions can be reduced as much as possible [20, 21]. Here, the palm is selected as the measurement site in the study. The reason is that the palm print, as an important characteristic of the human body, is unique and lifetime invariant. The palm print has become an important basis for authentic identification. Correspondingly, a palm print reproducible system has been developed as shown in Fig. 10.13(a). For each subject, the palm print image is first collected as a reference palm print image. Before

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(a)

(b)

FIGURE 10.13: (a) The diagram of image orientation system based on palm print identification; (b) The stability validation of spectra based on the measuring condition reproducible system (MCRS).

each spectral measurement, the scale of the image captured by the system is kept constant (that is, the distance between CCD lens and palm surface, focal length of lens and enlargement factor are fixed), and the current matching palm print image is collected. The image processing includes the following steps. Firstly, the two images are corrected by rotation in spatial domain. Secondly, relative matching is sought by using the phase correlation technique. Finally, after the pixel translation change is obtained, the parabolic surface fit technique is applied to achieve sub-pixel precision, achieving the precise orientation of the image. The orientation error of the system can be made less than 0.2 mm in X and Y axis. Based on the MCRS shown in Fig. 10.13(a), the repeatability of spectra is evaluated under the following three conditions: (1) the palm is placed on the probe and remains static; (2) the palm is lifted after every spectral measurement and re-positioned with the MCRS for precise orientation; (3) the palm is lifted after every spectral measurement and re-positioned without the MCRS for orientation. The coefficients of variation (CVs) of the spectra under the three repeated measurements are computed and the results are shown in Fig. 10.13(b). It can be concluded that spectral stability by using the MCRS can be achieved with the same order of magnitude when the subject keeps static, which is much better than when the palm is placed randomly.

10.3.2 The influence of contact pressure In diffuse reflectance spectral measurement of human tissue, it is common to use contact measurement in order to reduce the effect of specular reflection. However, the skin tissue deforms due to the pressure induced by the optical probe, leading to the changes of the microstructures of tissue and constituent distribution. This would in turn have the influence on the tissue optical properties, causing a change in the

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Palm

Computer

Pressure sensor Optical fiber probe

NIR measurement system

Drive device

z

FIGURE 10.14: Schematic of the compression apparatus.

measured diffuse reflectance spectra and spectral stabilities. Chan [22] and Shangguan et al. [23] investigated the effects of contact pressure on tissue optical properties under in vitro experimental conditions. They concluded that absorption, effective scattering coefficients and transmittance energy increased while diffuse reflectance energy decreased with the pressure. In this Section, the characteristics of changes of contact pressure will be investigated based on the human diffuse reflectance spectral measurement experiments. A solution to decrease the influence of contact pressure on the stability of in vivo spectral measurement will be discussed. 10.3.2.1 Experiment on the influence of contact pressure The experimental apparatus used to investigate the influence of pressure is shown in Fig. 10.14 [24]. The optical probe is driven to move along the Z axis by a computer control system (the step interval is 0.25 mm), which results in the changes of contact pressure between probe and palm. The diffuse reflectance spectra under different contact pressure are shown in Fig. 10.15. With the increase of contact pressure between the probe and the skin (corresponding to an increase of SZS axis, Z = 0 means that the probe and the skin are just in contact), the diffuse reflectance spectral energy decreases, and the variation trends are similar at each wavelength. Move the optical probe to make it contact with skin until the Z axis of the probe is 0.5 mm. Keep the relative position between the probe and skin constant, then measure the diffuse reflectance spectra of the palm continuously. The measurement time for each spectrum is 6 s. The variation of diffuse reflectance with contact time for a period of 60 s is shown in Fig. 10.16. Under the same contact pressure, the energy of diffuse reflectance light fluctuates significantly over time during the first period. However, after a certain time, the fluctuations become smaller and the trends of variations tend to flatten.

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FIGURE 10.15: The diffuse reflectance spectra at different contact states plotted against the wavelengths. z represents Z-position of the probe, and the negative value of z means that the probe doesn’t contact with the skin.

(a)

(b)

FIGURE 10.16: The diffuse reflectance spectra of palm at different contact time under the same contact state (a) 1100 to 1380 nm and (b) 1380 to 1700 nm.

10.3.2.2 The optimal contact state The following relation can be obtained after the experimental process of pressure influence is analyzed: the change of the probe position at Z axis → the change of contact pressure between the probe and skin → the change of optical parameters of skin tissue → the change of transcutaneous diffuse reflectance light energy. In the practical measurement, a slight flutter of the palm will cause the variation of contact pressure, which is the same as the influence of the change of probe position at the Z axis. Therefore, the spectral changes caused by the palm shaking up and

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FIGURE 10.17: The relative variations of diffuse reflectance spectra caused by the changes of relative position of probe and palm at different contact states: (a) probe moves down 0.25 mm (pressure decrease) and (b) probe moves up 0.25 mm (pressure increase).

down by 0.25 mm can be simulated by calculating the relative variations δe d and δe′ d corresponding to the diffuse reflectance energy of the previous contact state (pressure decrease) and the next contact state (pressure increase) relative to that of current contact state respectively, which can be used as the basis of improving the stability for in vivo spectral measurement. The results of simulation are shown in Fig. 10.17. The spectral differences caused by the change of probe position decrease relatively with the increase of the contact pressure. In the measurement of diffuse reflectance spectra of human tissue, it is appropriate, in theory, to bring the optical probe into firm contact with the skin to reduce the absolute differences of spectral energy caused by the palm shaking and to increase the SNR. But, on the other hand, with increasing contact pressure between the probe and skin, the energy of diffuse reflectance spectra of skin and SNR of measurement will decrease. Besides, excessive extrusion on skin tissue is likely to cause discomfort, which would alter the blood circulation and state of other tissue constituents, and even cause blood or other liquid constituents in tissue to be displaced outside of the spectral measurement region. All these will influence the precision of the blood glucose measurement. Therefore, it is necessary to consider comprehensively the above factors to determine an optimal contact state at the measurement position. According to the experimental results, it can be concluded that the relative error of diffuse reflectance energy caused by the palm flutter up and down by 0.25 mm is small when the depth of skin pressed is greater than 0.5 mm. Press at the depth of 0.5 mm would not cause discomfort to people, but the depth of over 1 mm would. Therefore, the optimal contact state of diffuse reflectance spectral measurement is that the depth of the probe is 0.5 mm. As shown in Fig. 10.18, the stability of human body spectral measurement can be improved greatly when diffuse reflectance spectra are collected at the optimal contact state.

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FIGURE 10.18: contact states.

The CVs of diffuse reflectance spectral measurement at different

10.3.2.3 The optimal measurement time For each measurement time after the probe has contacted with the skin, we define the relative variations of the diffuse reflectance energy at current measurement time relative to that of the next measurement time (after 6–10 s) as the time variation factor δe t . The time variation factor δe t at different measurement time is computed and shown in Fig. 10.19. In the first 30 s after probe contacts palm, the diffuse reflectance spectra fluctuate significantly with time. The relative variability of the spectra is greater than 0.15% at wavelengths ranging from 1100 to 1380 nm and greater than 0.6% at wavelengths ranging from 1380 to 1700 nm. However, after 30 s, the fluctuations become smaller. The relative variability of spectra is less than 0.07% at wavelengths ranging from 1100 to 1380 nm and less than 0.2% at wavelengths ranging from 1380 to 1700 nm. Thus, the stability of the spectra increases with the increase of contact time. Thus, for measurement of diffuse reflectance in vivo, it is not proper to collect the spectra at the initial phase when the palm contacts with the probe; some waiting time is necessary for stability. However, a long measurement time would cause unnecessary discomfort to people psychologically and physiologically. Furthermore, this does not meet the requirement for rapid measurement. In order to make a trade-off between comfort, measurement time and spectra stability, it is suggested that the optimal measuring time is at the 30th second after the probe contacts the measuring site. The effectiveness of the optimal measuring time is evaluated as follows. Eight diffuse reflectance spectra are continuously acquired from the beginning of contact, as well as from the 30th second since contact. For each measurement, the CV is calculated. The results are plotted in Fig. 10.20, where the repeatability of the diffuse

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FIGURE 10.19: The time variation factors of palm diffuse reflectance spectra at different contact time under the same contact state.

FIGURE 10.20: The CV values of diffuse reflectance spectra at different contact time under the same contact state.

reflectance spectra is markedly improved when the measurement is performed at the optimal measuring time.

10.3.3 The measuring conditions reproducible system (MCRS) and human glucose sensing experiments Based on the results above, an intelligent human-spectrometer interface system is designed and a noninvasive glucose sensing system with near-infrared spectroscopy

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Computer control system

palm

palm Reflectance standard

LEDs for lighting image capture card

CCD Camera

pressure sensor

COMx A/D converter

NIR spectrometer system AOTF driver

fiber probe

z 3D servo device

y x

measurement signal detector reference signal detector

Light source

AOTF

FIGURE 10.21: Schematic diagram of noninvasive glucose sensing system with near-infrared spectroscopy.

is developed [24]. As shown in Fig. 10.21, this system incorporates the following three parts: (1) NIRS spectrometer subsystem; (2) human-spectrometer interface subsystem; (3) data processing and computer control subsystem. In the design of the human-spectrometer interface, the influences of the variations of measuring conditions, such as measuring position, contact pressure, etc., are carefully considered. A 3-D servo is installed under the measuring table. An optical probe is fixed on the 3-D servo and may move in 3-D space. The optical probe contacts the palm through a circular computer controlled aperture and the diffuse reflectance spectra of palm are measured. An image orientation system is introduced to achieve the reproduction of sampling positions. Below is a brief description of the system. Before each measurement, a LED light source under the circular aperture is turned on and the current palm print image is captured by CCD camera at the fixed position under the circular aperture. Then the offset in the position of the current palm and the template image is calculated. Based on the calculating results, the system automatically adjusts the movement of the 3-D servo in X and Y axis to achieve the repeatable positioning for data sampling. A pressure analysis subsystem is used to reduce the influence of contact pressure on the spectral measurement. When the optical probe contacts with the palm, the pressure sensor installed on the optical probe acquires the current pressure signal. Before the first spectral measurement for each subject, the influence of pressure is first analyzed to determine the optimal contact point and measuring time. At this point, the corresponding coordinate in Z axis of the probe is recorded and saved. In the subsequent spectral measurements, the fiber probe in Z axis direction is adjusted

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to this optimal contact point and the spectrum is collected at the optimal measuring time. Based on the system presented above, OGTT experiments for fifty subjects have been conducted. With the aid of clinicians, the experiments were performed strictly in accordance with OGTT operation regulations [25]. The reference values of blood glucose concentration were measured using the minimally invasive blood glucose monitor GLUCOCARD (Kyoto Co., Japan). For each OGTT experiment, 35–45 points of blood glucose concentrations were measured corresponding to each reference point of glucose concentrations. Based on the results presented above, the measuring sites were kept constant by using the image orientation system and the spectra were measured at the optimal measuring time under the optimal measuring state.

TABLE 10.1: The statistic results of the OGTT tests for 50 subjects Information of subjects Class

Total numbers of subjects 20

Healthy volunteers Type II di- 30 abetic patients All sub- 50 jects

Results of PLS model (Ave±Std) Average age (year)

CC for RMSEC CC for RMSEP calibra(mmol/l) valida(mmol/l) tion tion

25.6

0.9732 ±0.0105 0.9900 ±0.0065

0.3487 ±0.0643 0.4216 ±0.0847

0.9828 ±0.0126

0.3973 0.9618 ±0.0822 ±0.0174

59.2

45.8

0.9496 ±0.01923 0.9688 ±0.0124

0.6700 ±0.1128 0.6816 ±0.0743 0.6773 ±0.0886

Ave: the average of the statistical items; Std: the standard error of the statistical items; CC: correlation coefficient.

The experimental data were processed. For each OGTT experiment, a PLS regression model is built based on the reference values of glucose concentration and the corresponding absorbance data and validated by full leave-one-out cross-validation. Table 10.1 describes the statistical results of the experiment. The RMSEP is 0.6773 mmol/l for single OGTT experiment.

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10.4 Challenges and Solutions in In Vivo Noninvasive Blood Glucose Monitoring In the study of NIR noninvasive blood glucose monitoring, the covered range of calibration models is crucial to the prediction precision and practicability of the models. However, for the in vivo measurement, the variations, which are induced by the changes of circumstance influencing the physiological state of human body during different periods and instrumentation, affect the spectral characteristics of NIR diffuse reflectance spectra, and the signal variations induced are usually much greater than that induced by changes of glucose concentration. When the variations in background dominate the space covered by calibration models, the precision for glucose concentration prediction will be low. Besides, in particular, variations from the human body are very complex phenomena and difficult to estimate and control, which is also a crucial issue of current noninvasive blood glucose monitoring technique. In the in vitro experiments of measuring glucose concentration by NIR spectroscopy, a standard material with characters similar to the measuring object is generally used as the background sample. The spectrum of the background sample is used as a reference to eliminate the noises induced by all the variations of the background and improve the measurement precision of glucose concentration. However, the background deduction method has not been applied in in vivo measurement due to the difficulty to find a standard material with optical characteristics similar to the human body. For instance, we have used a reflectance standard board with a reflection index of similar magnitude to that of human skin as the background to eliminate the influence of instrumental drifts. However, because the variations from the human body can not be reflected on the spectrum of the reflectance standard board, the method can not effectively eliminate the interference induced by the background variations, which brings great challenges to noninvasive glucose monitoring for clinical applications. Recently a floating-reference method has been proposed to mitigate this problem [26, 27]. The basic principle of the method is to determine the radial position at which diffuse reflectance light is not sensitive to the variations of glucose concentration as a reference position. Then the signal at this position is considered as an internal reference to eliminate the noise induced by the variations of the background from human body and improve the specificity of extraction of glucose concentration signal.

10.4.1 The influence of the time dependent variations from physiological background on the glucose measurement An OGTT experiment is conducted on a type II diabetic patient (male, fifty years of age). During the experiments, the variation of glucose concentration is shown in Fig. 10.22. The zero point of the abscissa in the figure corresponds to the time of oral glucose intake. Total 56 effective samples are measured. Among them, there are

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FIGURE 10.22: The variations of glucose concentration in the OGTT experiment; the zero time of the abscissa corresponds to the time of oral glucose.

(a)

(b)

FIGURE 10.23: The mutual prediction results of odd and even sample set models in the same OGTT experiment: (a) the prediction result using the odd sample set model to predict even sample set; (b) the prediction result using the even sample set model to predict odd sample set.

30 samples whose glucose concentrations are in the ascending stage and 26 samples in the descending stage. The 56 samples are divided into odd and even sets according to the measuring sequence. The two sets are respectively used to establish the models to predict each other. The predicted results are shown in Fig. 10.23. The RMSEP values are 0.6159 mmol/l and 0.6194 mmol/l, respectively. The relative prediction error of each sample is mostly within 5%. In the same way, the 56 effective samples are divided into two sets according to the ascending and descending stages of glucose concentration with the measuring time. The two sets are respectively used to establish the models to predict each other. The prediction results are shown in Fig. 10.24. The RMSEP values are

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FIGURE 10.24: The mutual prediction results of ascending and descending stages sample set models in the same OGTT experiment: (a) the prediction result using the ascending stage sample set model to predict descending stage sample set; (b) the prediction result using the descending stage sample set model to predict ascending stage sample set.

6.9451 mmol/l and 5.5096 mmol/l, respectively. The maximal relative error of each sample is greater than 100%. In the experiments above, the self-correlation of each calibration model is good and the self-precision for full cross validation is high. However, for mutual prediction, the results are obviously different. For the mutual prediction of odd and even sample sets, good prediction precision is achieved due to the fact that the sample sets for calibration effectively cover the variant range and tendency of glucose concentration in prediction set. However, for the mutual prediction of ascending and descending stages of sample sets, though the calibration model covers the variant range of the samples for prediction, the characteristics of human body physiological change are different in the two stages of glucose concentration, leading to an inability of the calibration model to cover the variant characters of sample sets for prediction that fails successful extraction of glucose concentration information. Consequently, the interference from the variations of the human body physiological background has become an obstacle that restricts the precision of in vivo noninvasive glucose measurement. Only when an effective solution is found out to correlate with the samples measured in different days and strengthen the robustness and versatility of calibration models can noninvasive glucose measurement technique be applied in clinic.

10.4.2 The floating-reference method solution The noninvasive glucose measurement technique by NIR diffuse reflectance spectroscopy is a method measuring the transcutaneous diffuse reflectance spectra with

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FIGURE 10.25: Measuring principle of the floating-reference method.

different glucose concentrations, applying the model processing technique to build the relation between glucose concentration and spectra, and then predicting the corresponding glucose concentration. The variation of glucose concentration will affect the diffuse reflectance spectra through the changes of tissue optical parameters, for example absorption and scattering. The influence of glucose concentration through optical parameters on the spatially radial distribution of diffuse reflectance light is depicted in Fig. 10.25. At some radial distance, the effects of absorption and scattering are identical in magnitude and inverse in direction. The combined effect leads to that the diffuse reflectance light at this radial position is not sensitive to the variation of glucose concentration. The position is defined as a reference position and then the variations of diffuse reflectance light intensity at the position can be considered as noise induced by the changes in human body physiological background and other interferences. Using the signal at the reference position as the internal reference for human body measurement can improve the specification for extraction of glucose information. In the same way, the position where the combined effects of absorption and scattering are maximal can be used as the effective measuring position to obtain the maximal sensitivity of glucose measurement. The floating-reference method based on the reference position will be one of the best solutions to eliminate the influence of human body physiological background. For the glucose measurement, the diffuse reflectance measured from human body can be divided into the signals related to the glucose concentration IS and that related to the noise from human body physiological background and other factors IN ,

I r, cg , N = IS r, cg + IN (r, N) ,

(10.13)

where r is the radial distance of light source and detector, cg is the blood glucose concentration, N is the physiological noise from human body. When differential measurement is used, the variations of diffuse reflectance light intensity with the changes of blood glucose concentration are obtained as

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∆I r, ∆cg , ∆N = ∆IS r, ∆cg + ∆IN (r, ∆N) ,

(10.14)


∆IS rr , ∆cg = 0.

(10.15)


∆I rr , ∆cg , ∆N = ∆IN (rr , ∆N) .

(10.16)



∆I rm , ∆cg , ∆N = ∆IS rm , ∆cg + ∆IN (rm , ∆N) .

(10.17)

∆IN (rm , ∆N) = η · ∆IN (rr , ∆N) ,

(10.18)




where ∆IS r, ∆cg is effective glucose concentration signal. However, the interference noise ∆IN (r, ∆N) due to the physiological changes of human body is dominant that changes with time, which makes it difficult to extract directly the blood glucose
signal from ∆I r,∆cg , ∆N . Here the principle of the floating-reference method is introduced. Firstly, a reference position rr is found, where the diffuse reflectance light intensity is not sensitive to the variation of glucose concentration, that is,

Then the variations of light intensity at the reference position are induced completely by noises,

Correspondingly, the variations of diffuse reflectance light intensity at the effective measuring position rm are obtained,

The inter-relation between the noise variation ∆IN (rr , ∆N) at the reference position rr and the noise variation ∆IN (rm , ∆N) at the measuring position rm is constant, and the linear relation is made under the assumption,

where η is a proportional factor. The value of η can be obtained by repeated measurements under the condition of the relative constant glucose concentration. Then the effective glucose signal can be expressed by Eqs. (10.17), (10.18) and (10.19),


∆IS rm , ∆cg = ∆I rm ,∆cg , ∆N − η · ∆I rr ,∆cg , ∆N .

(10.19)

Clearly, the glucose information obtained by the differential treatment on the diffuse reflectance signal at the reference position contains
higher specificity than
that obtained by Eq. (10.17). In Eq. (10.19), ∆I rm ,∆cg , ∆N and ∆I rr ,∆cg , ∆N can be obtained by practical measurement. The key factor and precondition of the floating-reference method are the existence of the reference position where diffuse reflectance light is not sensitive to the variations of glucose concentration. Radial distribution of the diffuse reflected light is calculated in the human skin tissue model at different blood glucose concentrations by Monte Carlo simulation. The simulation is conducted using the tissue optical parameters of three layered model of skin at the wavelength 1600 nm [18]. Total number of photons used in the simulation is 108 . The simulation results are shown in Fig. 10.26. The variation curves of diffuse reflected light intensity induced by the changes of glucose concentration intersect each other at the radial separation of

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FIGURE 10.26: Variation trend of diffuse reflection with glucose concentration plotted against the source-detector separations (Simulation). Incident Fiber

Collecting Fiber

Moving direction of collecting fiber

Sample

FIGURE 10.27: The radial light distribution measurement system.

2 mm with the light intensity variation of zero, which means that the reference point where the light intensity is not sensitive to glucose concentration change is at the radial distance of 2 mm.

10.4.3 The preliminary experimental validation of the floating-reference method The preliminary experimental validation of the floating-reference method is conducted in this section. The experimental sample is the intralipid solution. A radial diffuse reflectance light measurement system is used to measure the diffused light at different source-detector separations as show in Fig. 10.27 [27]. A laser diode (1750A-C06, AGERE Company, USA), working at wavelength of 1550 nm and power of 20 mW, is used to provide the near-infrared light. The incident fiber is fixed, while the collecting fiber moves along the radial direction from 0 to 6 mm, at

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TABLE 10.2: The design of different glucose concentration samples ∆cg cg of intralipid background Measurement time Curve (mg/dl) (mg/dl) 4000 0 First day 4000-0-1 4000 0 Second day 4000-0-2 8000 0 First day 8000-0-1 8000 0 Second day 8000-0-2 4000 4000 First day 8000–4000-1 4000 4000 Second day 8000–4000-2

an 0.2 mm interval. The 10%-intralipid solution is used as the mother liquid. Glucose is added to the mother liquid and glucose solutions with concentration of 0, 4000 mg/dl and 8000 mg/dl are obtained. The experiment is performed repeatedly within two days and a random measurement is used. In order to effectively simulate the measuring conditions of human body background noise, samples with different glucose concentrations are selected to perform matching operations and combinations of different glucose concentration and different sample background states are obtained. The matching samples and the corresponding representations are shown in Table 10.2. The reference point for the glucose measurement in the intralipid solutions is analyzed. The variance of diffuse reflectance light is calculated between the pure intralipid sample and the intralipid solution with glucose concentration 4000 mg/dl. Fig. 10.28 shows that the radial distribution of reflected light changes with the variation of glucose concentration, and the reference point of 10% intralipid solution locates at the source-detector separation of 2.7 mm. The experimental data of the samples shown in Table 10.2 are processed. First, according to Eq. (10.14), the differential diffuse reflectance light at different radial distances is considered as the signal containing glucose concentration information and differences of glucose concentration under different background noise are calculated without using the floating-reference method. The calculated curves are shown in Fig. 10.29(a). Next, under the same conditions, the diffuse reflectance light at the radial reference distance 2.7 mm is used as the internal reference and the glucose concentration information at different source-detector distances is extracted according to Eq. (10.19) (the proportion factor η at each radial distance is set 1). The differences of glucose concentration under different background noise are shown in Fig. 10.29(b). From Fig. 10.29(a), the difference information of glucose concentration can only be distinguished for the same background condition, but not for the different backgrounds. Therefore, if background changes in different measurements, then the measuring results can not reflect the true information of glucose concentration, which is an unavoidably real problem for in vivo noninvasive glucose measurement. In Fig. 10.29(b), after the data are processed by the floating-reference method,

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FIGURE 10.28: Variation trend of diffuse reflection with glucose concentration in 10%-intralipid solution plotted against the source-detector separations.

FIGURE 10.29: Different glucose information under different backgrounds plotted against the source-detector separations: (a) Data processing without floatingreference method, (b) Data processing with floating-reference methods.

the influence induced by the change of measuring circumstance and the concentration variation of intralipid background is diminished effectively. Each curve can be well recognized according to glucose concentration and has no relation to measuring time and the characteristics of background samples. Thus, the application of floating-reference method on the noninvasive glucose measurement may solve the key difficulty of inconstant human physiological properties.

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10.4.4 Summary The preliminary study on the floating-reference method indicates the effect of the technique on improving the specificity of glucose signal extraction. However, the technique has only been applied on in vitro experiments. In future work, the application conditions of the floating-reference method in human body need to be investigated and further improvement of the algorithm for extracting glucose specificity deserves attention. The reference position depends on human tissue optical parameters and thus it is different from person to person. For different subjects, the spatial resolution method to determine the reference position and the optimal measuring position with the maximal sensitivity is necessary. This can be done with proper determination of the radial distance between the optimal measuring point and light source. Further, the fine tuning of radial distance in a certain range to adapt the subject population with some differences in skin characteristics is also needed. The floating-reference method could be one of the solutions with the promising prospects for solving the interference caused by the variations of human physiological background. The perfection of the technique may provide a new method for improving the noninvasive glucose measurement precision and promoting the clinical application of NIR noninvasive glucose measurement.

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References [1] J. S. Maier, S. A. Walker, S. Fantini, et al., “Possible correlation between blood glucose concentration and the reduced scattering coefficient of tissues in the near infrared,” Opt. Lett., vol. 19, 1994, pp. 2062–2064. [2] M. Kohl, M. Essenpreis, D. Bocker, et al., “Glucose induced changes in scattering and light transport in tissue-simulating phantoms,” Proc SPIE 2389, 1995, pp. 780–788. [3] K. Maruo, M. Tsurugi, M. Tamura, et al., “In vivo noninvasive measurement of blood glucose by near-infrared diffuse-reflectance spectroscopy,” Appl. Spectrosc., vol. 57, 2003, pp. 1236–1244. [4] J. Chung, K. Fan, T. Wong, et al., “Method for predicting the blood glucose level of a person,” USP 20060253008, 2006. [5] K. Xu, Q. Qiu, J. Jiang, et al., “Non-invasive glucose sensing with near-infrared spectroscopy enhanced by optical measurement conditions reproduction technique,” Opt. Lasers Eng., vol. 13, 2005, pp. 1096–1106. [6] S. N. Thennadil, J. L. Rennert, B. J. Wenzel, et al., “Comparison of glucose concentration in interstitial fluid, and capillary and venous blood during rapid changes in blood glucose levels,” Diab. Technol. Ther., vol. 3, 2001, pp. 357– 365. [7] W. Chen, Study on Theories and Experiments of Signal Acquisition for NonInvasive Blood Glucose Sensing with Near-Infrared Spectroscopy, Ph.D. dissertation, Tianjin University, China, 2005. [8] D. Wang, H. Fu, and Y. Wang, Colour Atlas of Human Skin Tissue, Chap. 2, Shandong Science & Technology Press, China, 1999. [9] R. C. Weast and M. J. Astle (eds.), CRC Handbook of Chemistry and Physics, 63th Edition, CRC Press, 1982. [10] A. J. Berger and M. S. Feld, “Analytical method of estimating chemometric prediction error,” Appl. Spectrosc., vol. 51, 1997, pp. 725–731. [11] Q. Li, Study on Several Key Techniques of Near-Infrared Spectroscopy Analysis, Ph.D. dissertation, Tianjin University, China, 2002. [12] A. S. Bangalore, R. E. Shaffer, and G. W. Small, “Genetic algorithm-based method for selecting wavelengths and model size for use with partial leastsquares regression: application to near-infrared spectroscopy,” Anal. Chem., vol. 68, 1996, pp. 4200–4212. [13] H. Wang, Q. Li, Z. Liu, et al., “Application of genetic algorithms in fundamental study of non-invasive measurement of human blood glucose concentration

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Challenges and countermeasures in NIR noninvasive blood glucose monitoring 317 with near infrared spectroscopy,” Chin. J. Anal. Chem., vol. 30, 2002, pp. 779– 783. [14] J. H. Kalivas and P. M. Lang, “Response to comments on interrelationships between sensitivity and selectivity measures for spectroscopic analysis,” Chemom. Int. Lab. Syst., vol. 38, 1997, pp. 95–100. [15] A. Lorber, K. Faber, and B. R. Kowalski, “Net analyte signal calculation in multivariate calibration,” Anal. Chem., vol. 69, 1997, pp. 1620–1626. [16] R. Liu, K. Xu, Y. Lu, et al., “Combined optimal-pathlengths method for nearInfrared spectroscopy analysis,” Phys. Med. Biol., vol. 49, 2004, pp. 1217– 1225. [17] B. Droge, “Asymptotic optimality of full cross-validation for selecting linear regression models,” Statist. Prob. Lett., vol. 44, 1999, pp. 351–357. [18] K. Maruo, M. Tsurugi, J. Chin, et al., “Noninvasive blood glucose assay using a newly developed near-infrared system,” IEEE J. Sel. Topics Quan. Elect., vol. 9, 2003, pp. 322–330. [19] L. Wang, S. L. Jacques, and L Zheng, “MCML-Monte carlo modeling of light transport in multi-layered tissue,” Comput. Meth. Prog. Biol., vol. 47, 1995, pp. 131–146. [20] J. Jiang, X. Hu, K. Xu, et al., “Repetitive positioning technology based on correlation matching of palmprint image,” J. Tianjin Univ., vol. 36, 2003, pp. 300–303. [21] J. Jiang, X. Hu, K. Xu, et al., “Phase correlation-based matching method with sub-pixel accuracy for translated and rotated images,” ICSP’02 Proceedings, 2002, pp. 752–755. [22] E. K. Chan, B. Sorg, D. Protsenko, et al., “Effects of compression on soft tissue optical properties,” IEEE J. Sel. Topics Quan. Elect., vol. 2, 1996, pp. 943–950. [23] H. Shangguan, S. A. Prahl, S. L. Jacques, et al., “Pressure effects on soft tissues monitored by changes in tissue optical properties,” Proc SPIE 3254, 1998, pp. 366–371. [24] W. Chen, R. Liu, K. Xu, et al., “Influence of contact state on NIR diffuse reflectance spectroscopy in vivo,” J. Phys. D: Appl. Phys, vol.38, 2005, pp. 2691–2695. [25] http://www.diabetesselfmanagement.com/article.cfm?aid=403&sid=6 [26] Y. Luo, L. An, and K. Xu, “Discussion on floating-reference method for noninvasive measurement of blood glucose with near-infrared spectroscopy,” Proc SPIE 6094, 2006, 60940K. [27] W. Chen, Z. Ma, L. An, et al., “Applying the floating-reference method to improve the precision of noninvasive blood glucose measurement,” Proc SPIE 6445, 2007, 64450M.

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11 Fluorescence-Based Glucose Biosensors Gerard L. Cot`e, M. McShane Department of Biomedical Engineering, Texas A&M University, TX, USA M.V. Pishko Department of Chemical Engineering, Texas A&M University, TX, USA 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Historical Review of Fluorescence-Based Glucose Assays . . . . . . . . . . . . . . . . . Issues Involved with In Vivo Glucose Monitoring Using Fluorescent Sensors Fluorescence-Based Glucose-Binding Protein Assays . . . . . . . . . . . . . . . . . . . . . Fluorescence Resonance Energy Transfer Systems for Glucose Monitoring . Enzyme-Based Glucose Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Boronic Acid Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary and Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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This chapter describes the general requirements for using fluorescence for in vivo glucose monitoring. A survey of reported work in the areas of glucose receptors, assays for glucose using these receptors, and various fluorescence phenomena is discussed. In addition, the materials and methods for interfacing measurement instrumentation with receptors for construction of biosensors are described. Key words: fluorescence spectroscopy, biosensors, glucose.

11.1 Introduction Fluorescent effects have been observed for thousands of years but it was not until recently that its potential for many products including biomedical applications had been realized. Chinese books were written about fluorescence and phosphorescence as far back as 1500 B.C. and luminous materials were known in the times of the Greeks and Romans. Throughout the 1600’s to 1800’s phosphorescent substances were discovered but it was in 1852 that most people would claim the true science of

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fluorescence was brought to light by Sir George Stokes [4]. He named and explained the phenomenon of fluorescence, which dictates that the wavelength of fluorescence emission must be greater than that of the exciting radiation. Luminescence is indeed a phenomenon in which an excited molecule absorbs energy and subsequently releases energy in the form of a lower energy photon. Photo-induced luminescence takes two primary forms: fast (sub-microsecond) emission processes that accompany transitions from singlet excited states to ground states are characterized as fluorescence, and slower emissions (microseconds to hours) accompanying the transition from triplet excited states to the ground state are categorized as phosphorescence. In both cases, the emitted light is shifted in wavelength relative to the excitation light, which enables highly sensitive measurements due to the zero background contributed by a properly filtered excitation source. The average between excitation and emission—the lifetime τ of a luminophore—is also characteristic of the luminescent groups involved as well as the local environment. The use of fluorescence in medicine soared in the 1950’s with the development of the spectrophotofluorometer (SPF) by Dr. Robert Bowman at NIH [5]. The origins of the SPF came from the antimalarial research of the 1940’s. During World War II, the United States government issued a call for scientists and doctors to find a treatment for malaria since Japan had taken over most of the world’s supply of quinine, the best known treatment drug at the time. Fluorescence was used for in vivo tracking of drugs used to combat malaria, as these therapeutic molecules possessed aromatic moieties [5]. To date, for molecular detection, fluorescence-based techniques have proven to be highly sensitive, even affording single-molecule detection, due in part to low background signals [6]. Molecular fluorescence is characteristic of certain chemical groups, including benzene rings and double and triple bonds. Additionally, both energetics and kinetics of the process are dependent upon the environment of the fluorophores at the time of excitation. Thus, the time- and spectral-domain features of fluorescence carry information regarding the environment of these groups, making them extremely attractive candidates as optical transducers of chemical information. As a result, a large body of work has been dedicated to exploiting various fluorescence phenomena to “read out” interactions between glucose and molecular recognition elements. In terms of this chapter, a brief history of fluorescence sensing for glucose will be covered first, followed by a description of the major issues involved with glucose monitoring and a more thorough discussion of many of the primary approaches toward fluorescent glucose detection being explored today.

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11.2 Historical Review of Fluorescence-Based Glucose Assays The use of fluorescence for glucose monitoring in vivo effectively began in the late 1970’s and early 1980’s when Schultz used a naturally-occurring glucose-binding protein, Concanavalin A (Con A), in a competitive binding assay with a high molecular weight dextran and an indwelling fiber optic approach [7–9]. This approach was enhanced in the early 1990’s by this group through the use of a resonance energy transfer (RET) technique [10]. At this same time fluorescence lifetime approaches were also being explored using this same assay with a variety of fluorescent dyes [11]. In addition to Con A, other glucose binding protein (GBP) approaches were also beginning to be explored in the late 1990s [12, 13]. The early 1990’s also sparked an interest in a new approach using a synthetic receptor known as boronic acid [14]. In addition to these two approaches throughout the late 1980’s and all through the 1990’s, an enzyme approach using glucose oxidase (GOx) was developed to measure intrinsic flavin fluorescence of GOx, along with RET systems, and measuring fluorescence of the by-products of the reaction including pH, oxygen, and hydrogen peroxide [15–25]. In the late 1990’s, research toward a reagentless glucose sensor, using the deactivated apo-GOx enzyme [26], was started, which used the enzyme as a receptor rather than a catalyst. This work showed that apo-GOx retained its high specificity and in many ways paved the way for advances in the development of a new biosensor genre throughout the 2000’s [17, 28, 29]. To date, the primary approaches being explored involve the use of glucose-binding lectins [30–37], apoenzymes [26, 28, 29, 38], and synthetic boronic acid receptors [39–46]. A good review of many of the fluorescent-based glucose sensing approaches can be found in recent topics in a fluorescence spectroscopy textbook on glucose sensing edited by Geddes and Lakowicz [47]. Before discussing each of these approaches individually it is instructive to give a general overview of the issues involved with in vivo glucose monitoring using any of the fluorescent sensing techniques.

11.3 Issues Involved with In Vivo Glucose Monitoring Using Fluorescent Sensors In this chapter the focus will be on describing the primary exogenous reagents used to assay glucose by producing a change in fluorescence properties proportional to glucose concentration. These reagents must be packaged and placed in contact with a biological fluid including, for example, blood, interstitial fluid, sweat, lachrymal fluid, saliva, aqueous humor, or tear fluid. For in vivo measurement these packages may take the form of a contact lens, a material placed under the skin, or an indwelling fiber optic through the skin. The materials used must be sufficiently biocompatible to avoid severe acute or sustained long-term host response to the foreign object. While

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contact lenses or other superficially located devices have less stringent requirements, an object inserted into tissue will elicit at least an acute inflammatory response due to local tissue trauma during the procedure and possibly a stronger and more prolonged reaction due to recognition of the foreign material. The host response is primarily determined by the surface properties of the implant [48]. Therefore, if the implant has suitable surface properties (smooth, anionic or neutral, hydrophilic, mechanically matched to environment, etc.) and so long as the contents are not released or degraded over time, a stable relationship will typically be formed between the implant surface and the host. Hence, the composition and purity of the materials used in sensor fabrication can be a key factor in determining biocompatibility. For short-term applications, the host response to the foreign material should reach steady-state rapidly and resist fouling during the duration of use. Also, if indwelling, such as a fiber optic, the risk for infection needs to be minimized and typically a 72 hour maximum implantation time is before replacement of the catheter is required. For long-term implantations, the steady-state immune response must be limited to minimal fibrous tissue formation. The extent of fibrotic response, seen as the thickness and density of the collagen matrix deposited at the implant interface, may affect transport and optical properties of the sensor; dense collagen may inhibit glucose diffusion to the sensing assay, resulting in response delays in or even altered sensitivity (if sensor relies on glucose flux). Moreover, fibrous encapsulation of the implants interfere with light propagation to and from the implant (most likely in the form of increased scattering), resulting in decreased light escaping skin, corresponding in a decreased signal-to-noise ratio of the measurement. The second key requirement for fluorescence-based sensing systems is a strong, fully reversible and sufficiently rapid response over the range of interest. For clinically viable systems, the measured signal must be strong enough to be detected with low-cost instrumentation, sensitive over the clinical range of interest, resistant to errors arising from noise or system perturbations, and must accurately reflect current glucose levels. Neglecting the influence of the optical instrumentation employed, this essentially requires a combination of properties: adequate amounts of fluorophore with high quantum yield, proper selection of wavelengths to maximize light delivery and detection to the implants, and a glucose-sensitive assay that produces a large percentage change from baseline measurements over the range of interest. Ideally, a linear response that produces a 2-10 times change in the measurand (e.g., intensity ratio, wavelength, or lifetime) over the 0–600 mg/dL range within a few seconds of change in glucose concentration could be achieved. However, even nonlinear profiles and response times on the order of a few minutes, sufficiently short to accurately reflect details of blood glucose excursions, would be sufficient if glucose could be measured with error < 10% [49]. The third desired property of fluorescent glucose sensors is a stable assay response over the lifetime of the sensor. Temporal changes in sensitivity and signal levels due to denaturation, relaxation, or poisoning of molecular recognition elements or due to photo-induced oxidation can be compensated, to a degree, by calibration. However, any “minimally invasive” measurement approach loses appeal if frequent readjustments using blood samples are required to obtain accurate glucose values. Thus, it

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is desirable to use maximally photostable elements and an environment that stabilizes proteins or imprinted polymers against irreversible conformational changes or irreversible binding to non-glucose interferents. In this case, synthetic systems such as boronic acid [41, 50] or rigid molecularly imprinted polymers may be advantageous over protein receptors [51–53] though they often exhibit drift in sensitivity with fluctuations in ionic strength and pH, as well as suffer from lack of specificity [54, 55]. Specificity is a key aspect of all sensing systems, and this is a prime reason for great attention given to enzymatic transduction schemes for electrochemical and other sensor types. However, it can be generally stated that specificity need only be defined in terms of what will be encountered in extremes of normal operation. For example, specificity to glucose is desired in a glucose sensor, but if a sensor is to be implemented for monitoring interstitial fluid (ISF), the response to glucose need only be such that the glucose sensitivity is minimally affected by the presence of potential interferents at their maximum expected physiological levels in the ISF. Thus, while sensors that demonstrate high specificity for glucose over other sugars like mannose or dextrose or potentially interfering species are attractive, sensors exhibiting low specificity should not be excluded from consideration in systems on that basis alone. This fact has encouraged continual development and modification of polymeric and boronic acid receptors. Another attribute desired in implants is minimal or zero consumption of analytes and minimal or zero byproduct formation. Enzymatic systems, while attractive because of specificity and potential for high sensitivity, generally consume glucose and co-substrates, decreasing the local levels, while producing other species that may have deleterious effects on the sensors or the surrounding tissue. For example, when glucose oxidase is used in enzymatic-based glucose detection systems, molecular oxygen is consumed and gluconic acid and hydrogen peroxide are produced [56]. These co-substrates and byproducts can affect sensor performance through several means, including: 1) changing enzymatic activity due to pH-induced conformational alterations; 2) changing fluorescence signals from slightly pH-sensitive fluorophores; 3) irreversible degradation of enzyme structure due to peptide bond cleavage from peroxide; and possibly other mechanisms. Furthermore, damage to surrounding tissue caused by removal of key nutrients (oxygen, glucose) or production of toxic materials (acid, peroxide, reactive oxygen species, etc) must also be avoided. Thus, careful consideration must be given to reactants and byproducts and appropriate design features used to reduce or eliminate their influence on the sensor and host, considerations which are often non-trivial. Thus, fluorescent glucose assays based on non-consuming glucose-binding reactions (e.g., Concanavalin A [8, 9], boronic acid [40, 41, 57–59], glucose/galactose binding protein, and apo-enzymes [28] are advantageous in this regard. Fiber optic probes enable deployment of fluorescence glucose assays in a manner similar to electrodes (hence, the term “optodes”) should the assay chemistry be appropriately immobilized on the tip or other optically-accessible section of the fiber. This approach may enable use of low-cost disposable indwelling probes; however, fluorescent measurements from implanted assay reagents located in the skin

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or subcutaneous space may also be performed by transmitting excitation light and collection of emission light right through superficial tissue. In such cases, the fluorescent glucose assay must have optical properties that enable interrogation with reasonable signal-to-noise ratio (SNR). The achievement of a reasonable SNR essentially requires the implanted materials to have excitation and emission in spectral regions that can be probed with low-cost instrumentation, while still allowing sufficient propagation of excitation light to elicit strong signals and collection of emitted photons at the skin surface. Given the reasonably well-understood optical properties of skin [60, 61] the ideal range for optical communication with implants just under the skin is in the long wavelength visible and near-infrared region, for example 600–1000 nm, due both to decreased scattering and the minimal absorption by tissue chromophores and water. However, it has been shown that even shorter wavelengths can be feasibly used with an appropriately-designed system, even for steady-state measurements [62, 63]; improvement in SNR can be expected when modulated light or phase lifetime methods are employed. Overall, fluorescence-based techniques have proved to be highly sensitive, affording even single-molecule detection [6]. Additionally, since fluorescence-sensing techniques rely on specific reporter molecules with unique optical properties to transduce concentration information, readings are highly specific, unlike many other spectroscopic techniques that rely on the intrinsic absorbing or scattering properties of glucose. Also, a variety of techniques that target different fluorescence phenomena can be used to measure analyte concentrations, providing researchers a means to develop an array of sensing schemes for a particular analyte of interest. Furthermore, given that fluorescence techniques are optically based, implantable devices could be developed to allow minimally-invasive monitoring of analytes. Thus, it is evident why an increasing amount of work has been focused on developing various methods to quantify glucose levels using fluorescence techniques [64]. However, translation of these quantitative analytical methods into useful devices for long-term in vivo sensing remains a significant challenge. Overcoming the intrinsic limitations of photostability and loss of recognition capability represents one challenging aspect of this problem, while materials and methods for packaging to create indwelling sensors or systems add another level of complexity. Options for meeting these needs are being aggressively explored individually and in combination by many groups worldwide, giving hope for practical devices to be available in the near future.

11.4 Fluorescence-Based Glucose-Binding Protein Assays In general, assays for glucose employing fluorescence transduction have been developed using a number of different molecular recognition strategies, from naturallyoccurring glucose-binding proteins to genetically engineered mutants and even synthetic materials, and encompassing a broad region of the spectrum, from the ultra-

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FIGURE 11.1: Single fluorophore hollow fiber sensor using a glucose binding protein assay originally developed by Schultz in 1982. (Reprinted with permission from Ibey, 2006 [141].)

violet (UV) to the near-infrared (NIR). Optical transduction has been accomplished using intrinsic fluorescence, dual-label systems that transduce binding or conformational changes as alterations in energy transfer or solvent effects, or complex enzymatic systems that monitor consumption of co-reactants or formation of reaction products with specific indicators. The glucose-dependent changes have been monitored using both intensity and fluorescence lifetime measurements.

11.4.1 Concanavalin A-based approaches As described above, the original work of Schultz, started with a fiber optic probe as depicted in Fig. 11.1 [8]. The sensing element consisted of a short length of hollow dialysis fiber remotely connected to a fluorimetry instrument via a single optical fiber. This sensing chemistry consisted of a carbohydrate receptor, Concanavalin A (Con A), immobilized on its inner surface and a high molecular weight fluorescein labelled dextran, a hydrophilic polysaccharide chain made up of α -D-1,6-glucose molecules and a large portion of D-glucopyransoyl residues, as a competing ligand. Glucose in the external medium diffuses through the dialysis fiber into the sensing element and competes with dextran for binding to Con A. At equilibrium, the level of free fluorescein in the hollow fiber lumen is measured via the optical fiber and is correlated to the concentration of glucose. Preliminary results showed a response that is linear from 50 to 400 mg% glucose. The details of the specific assay used in this approach are described below.

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The assay depicted in Fig. 11.1 begins with the glucose binding protein, Concanavalin A (Con A). Con A is a globulin isolated from jack bean meal, possessing a pH-dependent tetrameric (pH> 7) or dimeric (pH< 7) structure and a deep pocket that binds saccharides. The sugar-binding behavior requires the presence of metal ions Mn2+ and Ca2+ . Con A was initially observed to form precipitates with glycogen and yeast mannan, due to the multiple saccharide-binding regions of the molecule [65]. This ability to bind sugars is not highly selective, and it has been noted that Con A will react with a large class of polysaccharides and sugars with varying association constants depending on the structural properties of the ligands. While the affinity for D-glucose is below that of many other sugars (when compared in inhibition of α -D-mannopyranoside), (kd =1.7 mM=31 mg/dL), compared to kd =0.71 mM for D-fructose and maltose, respectively [66, 67], the potential for Con A as a receptor for β -D-glucose in biosensors has been explored due to the expected low levels of competing molecules such as fructose in vivo. However, as a result of its sugar-binding capacity, Con A has an affinity for cell-surface receptors, such as those on lymphocytes [68, 69], and, therefore, has biological activity. For lymphocytes, Con A attachment is mitogenic; binding to the cell surface also restricts mobility of other immunoglobulin receptors in the cell membrane [70] and inhibits phagocytosis by leukocytes [71]. As a result, Con A has potential toxicity issues [72]; however, recent research has suggested that the dose of protein, even if completely released from implants, would not pose a significant health risk [31]. Specifically, results from direct administration of Con A to rats indicated that, even at 10 times the amount of Con A present in the implant, no significant toxicological or systemic response was observed. In reality, however, the risk of even a small exposure is very low, as the protein is typically covalently bound to the implant matrix. As mentioned above, this original glucose sensor was based upon the affinity reaction between Con A and a high molecular weight dextran (70 kD). Using a hollow fiber membrane, Con A was immobilized by adsorbing the protein onto the hollow fiber with glutaraldehyde so that it would irreversibly bind to the luminal side. The sensor was constructed by filling the hollow fiber membrane with fluorescein isothiocyanate (FITC) dextran solution and sealed at one end using a sealant. A raw optical fiber was inserted into the open end and sealed creating an optical path for light to travel from the fiber into the assay solution containing fluorescent molecules and back through the fiber to a detector. The optical fiber was designed to have a low numerical aperture resulting in a light path traveling through the center of the solution and not illuminating the edges of the hollow fiber. The sensor was placed into a buffer solution for testing and showed minimal fluorescence emission from FITC-dextran due to binding to the immobilized Con A and removal from the excitation path. Upon placement of the fiber sensor into a glucoseenriched buffer, a rise in fluorescent emission was seen due to displacement of the FITC dextran by glucose. This increase in fluorescent emission was directly proportional to the amount of glucose which had diffused into the hollow fiber. This glucose concentration was shown to equilibrate with the surrounding media’s concentration within 5–10 minutes. The assay was theoretically determined to respond within seconds whereas the diffusion time for glucose into the membrane was calculated to be

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FIGURE 11.2: Diagram of the FRET based hollow fiber sensor devised by Meadows et al. [54]. (Reprinted with permission from Ibey, 2006 [141].)

on the order of minutes proving to be the limiting factor of the sensor’s response. The largest overall response to glucose seen in this sensor was approximately 60% over a range of 0–10 mM of glucose. This sensor modality proved the feasibility of the Con A/dextran system as a sensing element for biological concentrations of analytes such as glucose. In addition to the time lag, the limitation of this sensor was the lack of an internal reference, making the sensor unusable in long term studies due to drift which required recalibration using known standards [8]. Due to this lack of internal reference and in hope of avoiding the immobilization procedure of the previous modality, which proved to be complicated and hard to repeat, a new assay was created by Meadows and Schultz that used a fiber optic resonance energy transfer (RET) based approach (Fig. 11.2) sometimes known as fluorescence resonance energy transfer (FRET) [10]. The FRET technique is discussed thoroughly in section 11.4; briefly, by labeling Con A with tetramethylrhodamine isothiocyanate (TRITC) dye and placing it into a hollow fiber with FITC labeled dextran, a quenching of the FITC dye was realized. This quenching was due to a development of a FRET reaction between the FITC and TRITC dye resulting in a loss of emission of the FITC dye due to the energy transfer. The TRITC dye was reported to show very little increase in intensity and was therefore used as an internal reference. The sensing system was modified to include two excitation sources which were swapped on and off alternately to preferentially excite the FITC and TRITC dye separately. The TRITC dye acted as an internal reference recording any loss of protein due to denaturation and mechanical disturbance in the excitation and detection pathways. Results indicated a linear correlation with

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glucose levels up to 200 mg/dL and 60% change in ratiometric intensity over the range of 0–900 mg/dL. A significant problem of irreversible aggregation of the Con A was noted within a few hours, complicating the development of this type of sensor without modification of the Con A to improve stability. A novel scheme was then devised to eliminate the need for Con A immobilization on the microdialysis fiber wall while avoiding Con A aggregation [73]. In this work, Sephadex beads comprising pendent glucose moieties and two highly absorbing dyes were used. Safranin O and Pararosanilin were selected as dyes to block the excitaR tion of Alexa Flour 488, the fluorophore used to label Con A (AF488-Con A). When in the absence of glucose, excitation light passing through the beads is preferentially absorbed by the Safranin O and Pararosanilin, resulting in poor emission from AF488-Con A. Upon glucose diffusion into the fiber, glucose-binding releases AF488-Con A from the beads, causing an increase in emission intensity that is well correlated with glucose levels. Additional efforts have extended the operating wavelength of this assay into the NIR (to potentially make a system more suitable for transdermal applications) by using alternative fluorophores [74]. However, studies performed to evaluate long-term use of both systems indicated leakage of the components from the membrane over time, resulting in poor long-term performance and ultimately proving that additional advances were necessary for future success. In general, fiber probes are a reasonable first step for packaging a glucose sensor because the sensor can be placed at the tip and all of the optical coupling is through the fiber as opposed to through tissue. The fiber can be inserted into samples, including tissue, and removed as needed and all optical instrumentation may be designed to match the fiber. Fiber optics can also be easily deployed through catheters. However, the biomedical considerations of infection pathways presented by transcutaneous lines make this approach less attractive than fully-implanted/disconnected systems for situations requiring constant measurements. Thus, many investigators throughout the 1990’s proposed methods to make the sensor implantable beneath the skin. These innovations came in both the form of novel materials for implanting the assay and sensing methods such as fluorescent lifetime measurements to overcome problems with the intensity based approaches. In terms of fluorescence lifetime measurements, the Lakowicz group was among the first to prove that these measurements could potentially alleviate problems observed with intensity-based RET measurements [75]. Given that fluorescence lifetime – the average time at which the fluorophore remains in the excited state before returning to the ground state – is independent of fluorophore concentration and light scattering and absorption properties of the sample, this particular measurement is potentially promising for in vivo monitoring [76]. In this work, the assay is based on the decreased decay time of a donor fluorophore linked to Con A upon binding of acceptor-labeled α -D-mannoside. Upon introduction of glucose into the system, the displacement of the labeled sugars results in a decrease in energy transfer and an increase in the donor decay time. Results indicated that this assay scheme could be used with various donor-acceptor pairs, demonstrating the robustness and generality of this approach. Additional studies were performed on similar systems based on long lifetime fluorophores such as ruthenium complexes, reducing the need for high

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FIGURE 11.3: A scanning electron microscope image of a PEG hydrogel [43].

frequency light-modulation for phase-domain lifetime measurements [77, 78]. With regard to novel materials, Russell et al. showed that a Con A FRET system could be encapsulated within polyethylene glycol spheres and retain functionality [37]. In this work, TRITC-Con A and FITC-dextran were entrapped within polyethylene glycol (PEG) millispheres, where the addition of glucose resulted in FITC-dextran displacement and alterations in FRET efficiency. Poly(ethylene glycol) hydrogels have been shown to be very biocompatible and are currently used for drug delivery devices and for coating orthopedic implants to inhibit thrombosis [79–87]. PEG has also been shown to work very well for in situ glucose biosensors acting as a barrier between the body fluids and electrode [88]. One embodiment of a fluorescent glucose sensor is the collection of PEG hydrogel spheres which contain the functional glucose assay [37]. Poly(ethylene) glycol diacrylate, when polymerized using a high intensity UV light, forms a hydrogel which will swell when placed into a buffered solution. This swelling increases the mesh size within the hydrogel allowing for diffusion of small molecules such as glucose while inhibiting the loss of large molecules such as Con A and dextran (Fig. 11.3) [37, 62]. To construct the PEG spheres, the Con A/dextran assay was mixed with α -acryloyl, ω -N-hydroxysuccinimidyl ester of PEG-propionic acid, a compound which acts to bind the Con A to the polymer backbone to inhibit leaching. Following the chemical binding, the material is polymerized via cross-linking using a long wavelength UV source ensnaring the dextran molecules and protein within the hydrogel. The ideal sensor would be placed just underneath the epidermal layer of the skin allowing free exchange of analytes within the interstitial fluid [37, 62]. In the original work by Russell et al. 1999 it was shown that the traditional FRET assay originally devised by Schultz could be encapsulated into a PEG microsphere and still retain functionality [37]. The assay was made with TRITC labeled Con A and 2000 kDa MW FITC labeled dextran. Preliminary results showed a 35% change across the 0–1000 mg/dL range of glucose concentration and a 20% change across 0–2000 mg/dL range for mannosylated FITC dextran. It was also discovered that the optimum mass ratio be-

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FIGURE 11.4: A schematic representation of the Con A-glycodendrimer assay system which shows single binding between the assay components and complete dissociation upon introduction of glucose eliciting a large optical response. (Reprinted with permission from Ibey, 2006 [141].)

tween FITC dextran and TRITC Con A was 100:1 resulting in a 60% difference in fluorescence due to a 800 mg/dL insult [43]. The response time of the sphere from 0–200 mg/dL glucose was shown to be long at about 15 minutes comparable to the hollow fiber membrane technology. In addition to the material for encapsulation, there was work done using ConA with the goal of increasing the dynamic range of the competitive binding assay [35, 89]. In this case, a modification of previous assays using dextran was recently reported, in which a fourth-generation polyamidoamine (PAMAM) glycodendrimer was employed as the competing ligand. The globular dendrimer had its surface amine groups modified to contain both glucose-like binding sites and Alex Fluor 594 (AF594) dye. The spherical shape of the molecule insures that only a single bond can be formed with each Con A tetramer, thus eliminating the potential for incomplete dissociation (Fig. 11.4). A solution-phase response of ∼100% was observed for 0–360 mg/dL concentrations, with response time of five minutes (Fig. 11.5) [35, 89]. Most recently, an in vivo investigation of a NIR Con A RET system was reported and the host response characterized [30]. In this work, Cy-7-labeled Con A and R AlexaFluor 647-labeled dextran system were entrapped with a hollow microdialysis fiber immobilized on the tip of an optical fiber. The device was characterized in vitro, the result of which indicated a response range of 2–25 mM. More importantly, the device was implanted in vivo and the response characteristics monitored throughout the course of 16 days. Results were promising, as the implant read-out retained a high degree of correlation with blood glucose fluctuations (as measured by blooddraw methods). The authors noted that an increase in response time was observed

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FIGURE 11.5: The glucose response of the ConA–glycodendrimer assay. This figure shows the resultant fluorescent emission of the AF647 dye as a function of glucose concentration. (Reprinted with permission from Ibey, 2006 [141].)

at the end of the experimental period, citing fibrous encapsulation of the sensor as the cause. Additionally, the authors tested the cytotoxicity of Con A through direct administration to the animal. Results indicated that even at 10 times the amount of Con A present in the implant, that no significant toxicological or systemic response was observed [31].

11.4.2 Engineered glucose-binding proteins As the field of protein engineering advances rapidly, several researchers have adapted a glucose-binding protein (GBP) commonly found in the periplasmic space of Escherichia coli (E. coli ) [90] for use in glucose sensor applications. These ellipsoidal proteins possess a single substrate-binding site in a cleft located between two globular domains. Electron density maps have confirmed selective binding with β -D-glucose, with 13 strong hydrogen bonds linking polar side groups from both protein domains to the hydroxyls and ring oxygen of the sugar. Upon binding, the sugar becomes completely buried within the cleft, resulting from a “Pac-man”-style hinge-bending motion that effectively surrounds the small ligand [91]. It has been shown that this process of trapping glucose and galactose induces a sufficient conformational change to allow optical transduction via incorporation of environmentallysensitive dyes [92–94] or dual-labeling the proteins with energy transfer pairs [95] as

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described in Fig. 11.6 in the FRET section below. The glucose-initiated conformational shift of the bacterial GBP was exploited for transduction of glucose concentration by inclusion of cysteine residues via site-directed mutagenesis, and subsequent attachment of environmentally-sensitive fluorophores into the glucose binding site [96]. Two fluorophores were used, both them showing an approximate change in fluorescence intensity of 80% at saturating levels of glucose. In follow-up work, a similar protein engineering approach was employed to strategically place cysteine for labelling with ANS, an environmentally-sensitive probe [92]. Results showed that ANS-GBP displayed a two-fold decrease in intensity when exposed to saturating levels of glucose, with a dissociation constant of ∼ 1 µ M. The same report also showed that immobilization of ANS-GBP along with a long-lifetime ruthenium complex onto the surface of a cuvette could be successfully used in low frequency phase-modulation lifetime measurements to predict bulk glucose levels within the cuvette. These receptors are technologically advantageous because of the ability to produce them in large quantities using bacterial bioreactors as well as the potential to directly modify the structure via protein engineering. However, the primary disadvantage of current forms of GBP is the high affinity for glucose. As mentioned, the dissociation constant is on the order of 1 µ M [92], which implies near-saturated receptors at physiological concentrations of glucose and, as a consequence, very low sensitivity to variations at these levels. Such receptors are attractive for monitoring approaches involving analysis of dilute fluid (e.g., extracted interstitial fluid, lachrymal fluid), but are not truly appropriate for true in vivo analysis. Although the majority of GBPbased sensors reported to date show very low sensitivity over physiological glucose levels, future development in protein engineering techniques is likely to facilitate further advances in recognition molecules with tunable affinity constants.

11.5 Fluorescence Resonance Energy Transfer Systems for Glucose Monitoring Fluorescence Resonance Energy Transfer (FRET) refers to the non-radiative energy transfer of excited state energy from an excited state fluorophore (the donor, D) to another fluorophore (the acceptor, A). FRET occurs between donor and acceptor molecules when certain conditions are present, specifically: (1) the fluorophores are in close proximity, (2) the emission spectrum of donor overlaps with the excitation spectrum of the acceptor (Fig. 11.6), and (3) the respective emission and excitation dipoles are sufficiently aligned [76]. FRET can be regarded as the interaction of transition dipoles of donor and acceptor groups, thus the name fluorescence resonance energy transfer (FRET) [97, 98]. A simplified theory of FRET is sufficient to describe affinity sensors used in fluorescence transduction of glucose concentrations. A key quantity that describes the

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(b) (a)

(b) (a)

FIGURE 11.6: Fluorescence excitation and emission spectra of (a) donor and (b) acceptor molecules. (Reprinted with permission from Chinneyelka, 2005 [128].)

potential FRET interaction between a donor-acceptor pair is the F¨orster distance, R0 , the distance at which half the donor molecules are quenched by the acceptor molecules.pR0 is proportional to several parameters of the fluorophores, according to R0 = K 6 κ 2 n−4 φD J[λ ], where K is a constant. The variable κ 2 refers to the relative spatial orientation of the dipoles of D and A, taking on values from 0 to 4 for completely orthogonal dipoles and collinear and parallel transitional dipoles κ 2 = 4, respectively. For random orientation (as is usually assumed, especially for solutionphase measurements), κ 2 value is set as 2/3. The remaining terms n, φD , and J[λ ] correspond to the solvent refractive index, quantum yield of D in the absence of A, and the overlap integral, which measures the degree of overlap between the emission spectrum of D and the absorption spectrum of A, respectively. A key point from this discussion is that there must be significant spectral overlap for the dipoles to interact and for the proper excitation of A by D. The energy transfer efficiency is directly proportional to the spectral overlap, and this also directly effects the F¨orster distance of a particular D-A pair. Figure 11.4 shows the D and A excitation and emission spectra in an ideal energy transfer system, wherein D and A have very distinct excitation spectra (so that A can only be excited by energy transfer, and not by direct photon absorption at the wavelengths used to excite D); the D emission and A excitation spectra overlap strongly; and the D and A emission maxima are well separated, so that the quenching of D fluorescence and the enhancement of A fluorescence can be individually measured [99, 100]. In practice, R0 values vary significantly for different D-A FRET pairs, ranging ˚ This distance must be comparable to the size of the proteins or other from 40–80 A. biomacromolecules being used for efficient energy transfer from D to A. The energy transfer (E) is given as the fraction of photons absorbed by D that are transferred to A and, therefore, is given as the ratio of transfer rate to the total decay rate of the donor, E = kT /(τD−1 + kT ) or E = R06 /(R06 + r 6 ). It should be clear from these

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Transfer Efficiency (E )

100

75

50

r = R0

25

0 0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

Distance between donor and acceptor molecules (r /R 0)

FIGURE 11.7: Distance-dependent efficiency of energy transfer between donor and acceptor molecules, where r is the intermolecular distance and R0 is the F¨orster distance for the pair of molecules. (Reprinted with permission from Chinneyelka, 2005 [128].)

equations that when D and A are separated by F¨orster distance R0 , the FRET is 50% efficient. However, another noticeable property is that the FRET efficiency is highly dependent on the distance between D and A molecules, as is shown graphically in Fig. 11.7. These mathematical and graphical representations serve to highlight the main advantages of using FRET as a transduction mechanism; it is highly sensitive to the distance between two molecules, and the ratiometric nature allows variations in instrumental parameters, interrogated volume, and measurement configuration to be internally compensated [101]. Most of the work toward realization of fluorescence affinity-based glucose sensors has focused on the development of competitive binding-based assays, which rely on changes in fluorescence emission properties modulated by fluorescence resonance energy transfer (FRET) to optically transduce glucose levels [26,89,102–104]. Changes in FRET result from the competitive binding of a fluorescent ligand and analyte to receptor sites on lectins, glucose-binding proteins, or deactivated glucosespecific enzymes, such that the ligand is displaced from the receptor when in the presence of the analyte, causing changes in energy transfer efficiency between the donor-acceptor pair, ultimately resulting in measurable shifts in emission spectra [73, 74]. There are essentially two types of sensors constructed using energy transfer for transduction. The first type (Fig. 11.8(A)) is the method we discussed used by Meadows and Schultz to overcome the problems with the single-fluorophore fiber optic approach and requires the interaction between receptors and ligands that compete with the target analyte for the receptor binding site (Con A and dextran); in this case, the receptors and ligands are labeled with acceptor and donor dye pairs, respectively, or vice versa, and energy transfer occurs when the ligand is bound to the receptor. The second type of FRET system, Eq. (11.8(B)), involves donors and

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FITC-dextran

Addition

(Donor-ligand)

of glucose

TRITC-Con A

(b)

(a)

(Acceptor - Receptor)

Glucose (Analyte)

(c)

(d)

(A)

(B) FIGURE 11.8: (A) Illustration of the combination of FRET and with competitive binding (a) FITC-dextran/TRITC-Con A complexes, and corresponding spectrum (c) exhibiting significant energy transfer; (b) displacement of dextran from Con A in the presence of glucose, and associated spectrum (d), possessing a strong donor peak relative to acceptor peak in the presence of glucose. (Reprinted with permission from Chinneyelka, 2005 [128].) (B) Design of a single-molecule glucose assay (glucose indicator protein, GIP) based on FRET. The GBP adopts an ”open” form in the presence of glucose (•), moving the two fluorescent protein domains away from the center of the GBP, resulting in a decrease in FRET [3]. (Reprinted in part with c permission from Ye and Schultz [3], 2003 American Chemical Society.) acceptors attached at appropriate sites on the same receptor molecule (for instance a glucose binding protein described previously), and the distance between them is modulated by conformational changes that occur upon glucose binding.

11.5.1 Single-molecule RET systems using dual-labeled engineered proteins A single-molecule RET-based sensor was created using a GBP mutant by fusing two fluorescent reporter proteins (green fluorescent protein as the donor and yellow

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fluorescent protein as the acceptor) to the C and N terminus of the receptor, respectively [105]. This represents an efficient approach to assay reagent fabrication, since the fluorogenic groups are built directly into the probe at the stage of recombinant protein production, implying that large-scale production is possible and only immobilization of a single molecule type is necessary. During a glucose-binding event, the spatial separation between the fluorescent proteins is altered, causing a change in RET efficiency. The reporters were encapsulated within microdialysis fibers, and experimental observations showed that the emission intensity at 527 nm was reduced upon exposure to solutions containing glucose. The response was shown to be reversible; however, a maximum intensity change was observed at 0.36 mg/dL, well below the physiological range. This again highlights the limitation of current bacterial glucose-binding proteins as noted previously, extremely high glucose affinity.

11.6 Enzyme-Based Glucose Sensors In analogy to the enzyme-modified Clark electrode developed for glucose sensing [106], enzymatic fluorescent sensors—“optodes”—have been demonstrated through a combination of selective enzymes and optical indicators [21, 107, 108]. In general, the active elements catalyze an oxidation-reduction reaction, and the consumption of a substrate or the resulting formation of a product is monitored using fluorescence [108]. Three well-known enzymes for reacting with glucose are glucose oxidases (GOx) [56], glucose dehydrogenases (GDH) [109, 110], and hexokinases (HEX) [110–112]. Each of these has been used, in different forms, to demonstrate potential for glucose sensing using intrinsic and extrinsic fluorescence changes. One of the most widely researched enzymatic sensing schemes relies on GOxcatalyzed oxidation of glucose in the following reaction [56]: GOx

glucose + O2 + H2 O −→ gluconic acid + H2 O2 . Using this reaction, several opportunities are presented to indirectly monitor glucose levels, including fluorescence-based measurement of pH change due to gluconic acid formation [17, 18, 21, 113], hydrogen peroxide produced [15, 24, 25], or oxygen consumed [16, 19, 22, 107, 114–119]. Enzymatic-based sensors are inherently very selective due to the stereospecific catalytic binding sites and are also fully reversible, making them ideal for use in biosensor applications. With the main difference being that optical indicators are non-consuming, contrasted with surface reduction of oxygen typically used in Clark-type electrodes, the extensive literature on electrochemical biosensors can still be applied to optical devices in many cases, making available a broad spectrum of lessons and design ideas [108]. However, there are several drawbacks to using enzymatic schemes: (1) enzymes tend to spontaneously deactivate (denature) over time, potentially resulting in drifts of sensitivity and/or range; (2) the consumptive nature of the enzyme could potentially result in local de-

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pletion of glucose levels, leading to ambiguous readings, as well as possible tissue damage due to excessive consumption of glucose and oxygen; and (3) to obtain accurate indirect measurements of glucose, the reaction must remain glucose-limited, requiring careful control of reaction-diffusion kinetics. This latter point is a critical design aspect, and has been explored in detail from a theoretical point of view [120–122]; however, the key features can be understood intuitively by considering the relative concentrations of glucose and oxygen expected in vivo. Since both reactants must be present for the reaction to proceed, and because the stoichiometry involves reaction of one mole of molecular oxygen per mole of glucose, it is obvious that the relative concentrations of the two substrates will determine which one is limiting. In blood and interstitial fluid, glucose levels are typically around 72–108 mg/dL (4–6 mM), whereas dissolved oxygen concentrations average in the 100–250 µ m range. As a result, assuming near-equal diffusion rates, oxygen will be depleted rapidly and the range over which response is proportional to glucose will be limited to low concentrations. At higher concentrations, there will be no significant dependence of product formation rate or local oxygen levels on glucose. The result of this behavior is the need to limit glucose diffusion rate relative to oxygen, so that proportional changes can occur over a wider concentration range. This point has been established in regards to electrochemical sensors, and has been considered again more recently in the context of downscaling optical sensors to function at micro- and nanometer scales [137].

11.6.1 Apo-glucose oxidase The intrinsic flavin fluorescence, which is environmentally-sensitive, of GOx was shown to be an indicator of glucose-binding events [123]. This work, which proved that sufficient conformational changes occur in the process of binding glucose, laid the foundation for the use of GOx as a receptor rather than a catalyst. The early findings showed changes in the intrinsic fluorescence over the low end of the physiologically-relevant range (27–36 mg/dL). By labeling the enzyme with a fluorescein derivative, a glucose responsive RET system, which exploited the distance-dependent energy transfer between the intrinsic flavin group and the attached fluorescein, responded with changes that correlated with glucose levels [124]. Yeast hexokinase was also shown to exhibit a 30% decrease in intrinsic tryptophan fluorescence during exposure to 216 mg/dL of glucose [125]. With HEX labeled with an ANS derivative, a decrease in sensitivity was observed, contrary to results with GOx and GDH [126]. Furthermore, HEX-based transduction schemes are particularly vulnerable to excessive quenching when exposed to serum, indicating that a separation from the biological environment is necessary for in vivo applications [64]. In each of these cases, though, the fluorescence change varied with time after exposure to glucose, due to the enzymatic activity of the protein that continued to consume glucose. In an effort to overcome the limitations of the catalytically-active system, and to improve poor understanding of the underlying mechanism of the previous systems, additional studies were performed on deactivated enzyme using apo-GOx [26]. In this work, apo-GOx was labeled with the environmentally-sensitive fluorophore 8-

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FIGURE 11.9: Equilibrium and conformation of different forms of the boronic acid group with and without sugar [2]. (Reprinted with permission from DiCesare c and Lakowicz [2], 2001 American Chemical Society.) anilino-1-naphthalene sulphonic acid (ANS). It was found that the binding of glucose to apo-GOx results in a conformational change such that the steady state intensity of ANS decreased 25% and the mean lifetime of ANS decreased about 40% over the range of 180–360 mg/dL glucose. This work showed that apo-GOx retained its high specificity and, similarly, the apo form of glucose dehydrogenase has been shown to retain glucose binding specificity. These results suggested the utility of deactivated enzymes as analyte recognition elements in optical sensors [127] and in many ways paved the way for advances in the development of a new reagentless biosensor genre [102, 128–130].

11.7 Boronic Acid Derivatives In addition to the protein-based glucose receptors, synthetic receptors such as Boronic acid (BA) compounds have been explored for glucose monitoring. Boronic acids are weak Lewis acids consisting of one boron (electron-deficient) atom and two hydroxyl group and form a reversible complex with cis 1,2- or 1,3- diols, such as the common biological carbohydrates glucose, galactose, and fructose (Fig. 11.9). Since the complex is reversible, the integration of boronic acid derivatives as recognition elements in glucose sensors is being aggressively explored. Many fluorescencebased readout systems are predicated upon the signaling of the diol binding event through modulation of fluorescence properties of a boronic acid compound, which are typically comprised of a binding moiety and a complementary fluorogenic group responding to photoinduced electron transfer, pH change, or another local interaction [14, 131]. Many fluorescent transduction systems are predicated upon the signaling of the

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diol binding event through modulation of fluorescence properties of the boronic acid compound, which are typically comprised of a binding moiety and a fluorescent signaling moiety [131]. The first report on this concept presented anthrylboronic acidbased fluorescent saccharide sensors, successfully showing saccharide binding could signal a change in fluorescence properties [14]. The high apparent pKa (∼8.8) of the compound resulted in an emission intensity decrease with increasing saccharide concentration through a process termed “chelation-enhanced quenching”. While this initial work was indeed an important “proof-of-concept,” anthrylboronic acid was found to be more sensitive to fructose binding events than glucose. The concept was then advanced through the integration of an amino group positioned between the boronic acid and anthracene. The amino group effectively increased the compound’s saccharide binding affinity by lowering the pKa and enhanced photoelectron transfer, resulting in increased emission intensities with elevating saccharide levels (the opposite of which was seen with anthrylboronic acid) [132]. However, preferential binding of fructose over glucose (approximately 50-fold specificity for fructose at physiological pH) was also observed in this case. In an attempt to further increase binding affinity and enhance glucose selectivity, bisboronic acid compounds were developed, and it was demonstrated that glucose selectivity may be enhanced by appropriately orienting the boronic acid compounds relative to the diol pairs on glucose [133]. Further work showed that linker chain length (and type) between the boronic acid moieties greatly affects glucose selectivity, paving the way for the development of additional compounds with engineered affinity properties [134]. Based on these findings, a derivative with a glucose selectivity 43-fold greater than that of fructose was then developed, increasing the likelihood that boronic acid based sensors could indeed be designed for applications in glucose sensing [135]. The effect of fluorophore choice on the selectivity, stability, and sensitivity of the BA-based sensors, and the use of multiple pendant fluorophores to extend the emission wavelengths of the sensors through fluorescent resonance energy transfer (FRET) was also explored [136]. This system utilized a phenanthrene donor and pyrene acceptor, such that, when excited with 299 nm light (the excitation maxima of phenanthrene), the entire system would emit at 417 nm (the emission maxima of pyrene). To compensate for source fluctuations and variations in probe concentration, ratiometric functionality was introduced by using 3-nitronaphthalic anhydride and 3-aminophenylboronic acid with various linker moieties to form a monoboronic acid sensor possessing bimodal emission spectra with peaks at 430 and 550 nm upon excitation with 377 nm light [137]. These results seemed to contradict earlier findings that demonstrated poor glucose selectivity with monoboronic acid derivatives. The authors suggest that competing factors may be simultaneously operating, such as conformational restriction between the phenylhydroxy-boronate:saccharide complex and its influence on the excited state, which could result in enhanced glucose selectivity [41]. A more recent approach to designing direct fluorescent indicators for glucose involves two-component boronic acid sensors, where the fluorophore — usually anionic in nature – is quenched by a physically separate boronic acid substituted vio-

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FIGURE 11.10: Two-component saccharide-sensing system using boronic acid c receptor [1]. (Reprinted with permission from Gamsey, et al. [1], 2006 American Chemical Society.)

logen receptor. As the saccharide binds with the receptor, the quenching efficiency of the viologen is reduced, resulting in an increased emission intensity of the fluorophore (Fig. 11.10). This facile approach readily allows the interchange of fluorophores without any modification of the receptor, a considerable advantage since transformations can cause unwanted changes in the photophysical dye properties. This work demonstrated that sensitivity and selectivity as well as optical properties of the boronic acid derivatives can be modulated by interchanging different viologens and fluorophores [138, 139]. For these indicators immobilized in poly(HEMA) hydrogels attached to an optical fiber measurement system, the sensitivity was 0.1%/(mg/dL) over the range of 0–360 mg/dL, the response was fully reversible, and the response time was on the order of 5–10 minutes. The response was also very stable for up to 36 hours under constant glucose challenges. These findings are extremely encouraging, and support optimism that BA-based sensors can be developed for in vivo monitoring applications. Overall, however, boronic acid receptors have a principal disadvantage with respect to their potential for medical glucose monitoring: a lack of specificity. Typical values for comparing binding of fructose and glucose with phenylboronic acids indicate approximately 50-fold specificity for fructose at physiological pH [132]. Bisboronic acid configurations have been demonstrated to enhance glucose selectivity by appropriate orientation of the boronic acid compounds relative to the diol pairs on glucose as well as adjustment of length and type of chain used to link the boronic acid moieties greatly affects glucose selectivity, paving the way for the development of additional compounds with engineered affinity properties [133, 134]. As a result, a BA derivative has been prepared with a glucose affinity 43-fold greater than that of fructose [D-glucose (kd = 0.34 mM=6.1 mg/dL) > D-allose (kd = 1.6 mM) > D-fructose (3.2 mM) > D-galactose (6.3 mM)]; this should be sufficient for any in vivo monitoring purpose [140].

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11.8 Summary and Concluding Remarks As described in this chapter, a wide array of different techniques for fluorescencebased transduction of glucose concentration have been explored. The major foci of these efforts have relied upon glucose binding proteins, including Con A and engineered GBP’s and enzymes including GOx and apo-GOx, as well as synthetic receptors such as boronic acid. While no fluorescence-based sensing devices have yet been made available commercially, it appears that a number of the techniques have been sufficiently developed to expect that clinically-viable devices are just over the horizon, and more activity in trials will be observed in the next few years. While the progress in fluorescence-based glucose sensing is significant, and many in vitro experimental validations have shown impressive results, whether these can be translated to survive in vivo for a sufficient time, and made with a reliable process in a format that is amenable for self-testing, remains to be seen. Other key obstacles remaining include stability of receptors and fluorophores, challenges that will possibly be met partially by results of the intense efforts of molecular biology, polymer science, and nanotechnology. Advances in nanomaterials such as quantum dots will likely enable improvements in optical stability and choice of excitation/emission wavelengths for various transduction methods. Stabilization of natural and artificial enzymes and rendering immunogenic protein receptors “stealthy” may also aid the pursuit.

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References [1] S. Gamsey, J.T. Suri, R.A. Wessling, and B. Singaram, “Continuous glucose detection using boronic acid-substituted viologens in fluorescent hydrogels: Linker effects and extension to fiber optics,” Langmuir, vol. 22, 2006, pp. 9067–9074. [2] N. DiCesare, and J.R. Lakowicz, “Spectral properties of fluorophores combining the boronic acid group with electron donor or withdrawing groups. Implication in the development of fluorescence probes for saccharides,” J. Phys. Chem. A, vol.105, 2001, pp. 6834–6840. [3] K.M. Ye and J.S. Schultz, “Genetic engineering of an allosterically based glucose indicator protein for continuous glucose monitoring by fluorescence resonance energy transfer,” Anal. Chem., vol. 75, 2003, pp. 3451–3459. [4] F. James, “The conservation of energy, theories of absorption and resonating molecules, 1851-1854: G.G. Stokes, A.J. Angstr¨om, and W. Thomson,” Notes Records Roy. Soc. London, vol. 38, 1983, pp. 79–107. [5] Office of NIH History, The AMINCO-Bowman Spectrophotofluorimeter: Stetten Museum, NIH DHHS web site: http://history.nih.gov/exhibits/bowman/HSfluor.htm [6] S. Weiss, “Fluorescence spectroscopy of single biomolecules,” Science, vol. 283, 1999, pp. 1676–1683. [7] S. Mansouri and J.S. Schultz, “A miniature optical glucose sensor based on affinity binding,” Bio-Technol., vol. 2, 1984, pp. 885–890. [8] J.S. Schultz, S. Mansouri, and I.J. Goldstein, “Affinity sensor: a new technique for developing implantable sensors for glucose and other metabolites,” Diab. Care, vol. 5, 1982, pp. 245–253. [9] J.S. Schultz and G. Sims, “Affinity sensors for individual metabolites,” Biotechnol. Bioeng. Symp., vol. 9, 1979, pp. 65–71. [10] D.L. Meadows and J.S. Schultz, “Design, manufacture and characterization of an optical-fiber glucose affinity sensor-based on an homogeneous fluorescence energy-transfer assay system,” Anal. Chim. Acta, vol. 280, 1993, pp. 21–30. [11] J. Lakowicz and B. Maliwal, “Optical sensing of glucose using phasemodulation fluorimetry,” Anal. Chim. Acta, vol. 271, 1993, pp. 155–164. [12] J. S. Marvin and H. W. Hellinga, “Engineering biosensors by introducing fluorescent allosteric signal transducers: construction of a novel glucose sensor,” J. Am. Chem. Soc., vol. 120, 1998, p. 7.

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[26] S. D’Auria, P. Herman, M. Rossi, and J.R. Lakowicz, “The fluorescence emission of the apo-glucose oxidase from Aspergillus niger as probe to estimate glucose concentrations,” Biochem. Biophys. Res. Commun., vol. 263, 1999, pp. 550–553. [27] S. Chinnayelka and M. J. McShane, “Glucose-sensitive nanoassemblies comprising affinity-binding complexes trapped in fuzzy microshells,” J. Fluoresc., vol. 14, 2004, pp. 585–595. [28] S.Chinnayelka and M.J. McShane, “Resonance energy transfer nanobiosensors based on affinity binding between apo-enzyme and its substrate,” Biomacromol., vol. 5, 2004, pp. 1657–1661. [29] S. Chinnayelka and M.J. McShane, “Microcapsule biosensors using competitive binding resonance energy transfer assays based on apoenzymes,” Anal. Chem., vol. 77, 2005, pp. 5501–5511. [30] R. Ballerstadt, C. Evans, A. Gowda, and R. McNichols, “In vivo performance evaluation of a transdermal near- infrared fluorescence resonance energy transfer affinity sensor for continuous glucose monitoring,” Diab. Technol. Ther., vol. 8, 2006, pp. 296–311. [31] R. Ballerstadt, C. Evans, R. McNichols, and A. Gowda, “Concanavalin A for in vivo glucose sensing: A biotoxicity review,” Biosens. Bioelectr., vol. 22, 2006, pp. 275–284. [32] R. Ballerstadt, A. Gowda, and R. McNichols, “Fluorescence resonance energy transfer-based near-infrared fluorescence sensor for glucose monitoring,” Diab. Technol. Ther., vol. 6, 2004, pp. 191–200. [33] R. Ballerstadt, A. Polak, A. Beuhler, and J. Frye, “In vitro long-term performance study of a near-infrared fluorescence affinity sensor for glucose monitoring,” Biosens. Bioelectron., vol.19, 2004, pp. 905–914. [34] R. Ballerstadt and J.S. Schultz, “A fluorescence affinity hollow fiber sensor for continuous transdermal glucose monitoring,” Anal. Chem., vol. 72, 2000, pp. 4185–4192. [35] B. L. Ibey, G. L. Cot´e, V. Yadavalli, V. A. Gant, K. Newmyer, and M. V. Pishko, “Analysis of longer wavelength alexafluor dyes for use in a minimally invasive glucose sensor,” Proc. of the 25th Annual Int. Conf. of the IEEE EMBS, V4, Cancun, Mexico, September 17–21, 2003, pp. 3446–3449. [36] B.L. Ibey, M.A. Meledeo, V.A. Gant, V. Yadavalli, M.V. Pishko, and G.L. Cot`e, “In vivo monitoring of blood glucose using poly(ethylene glycol) microspheres,” Proc. SPIE, vol. 4965, 2003, pp. 1–6. [37] R.J. Russell, M.V. Pishko, C.C. Gefrides, M.J. McShane, and G.L. Cot`e, “A fluorescence-based glucose biosensor using concanavalin A and dextran encapsulated in a poly(ethylene glycol) hydrogel,” Anal. Chem., vol. 71, 1999, pp. 3126–3132.

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[38] S. Chinnayelka and M.J. McShane, “RET nanobiosensors using affinity of an apo-enzyme toward its substrate,” Proc. 26th Annual Int. Conf of the IEEE EMBS, San Francisco, CA, 2004, pp. 3126–3132. [39] R. Badugu, J.R. Lakowicz, and C.D. Geddes, “A wavelength-ratiometric pH sensitive probe based on the boronic acid moiety and suppressed sugar response,” Dyes and Pigments, vol. 61, 2004, pp. 227–234. [40] R. Badugu, J.R. Lakowicz, and C.D. Geddes, “A wavelength-ratiometric fluoride-sensitive probe based on the quinolinium nucleus and boronic acid moiety,” Sens. Actuat., B: Chem., vol. 104, 2005, p. 103. [41] H. Cao, D.I. Diaz, N. DiCesare, J.R. Lakowicz, and M.D. Heagy, “Monoboronic acid sensor that displays anomalous fluorescence sensitivity to glucose,” Org. Lett., vol. 4, 2002, pp. 1503–1505. [42] D.B. Cordes, S. Gamsey, Z. Sharrett, A. Miller, P. Thoniyot, R.A. Wessling, and B. Singaram, “The interaction of boronic acid-substituted viologens with pyranine: The effects of quencher charge on fluorescence quenching and glucose response,” Langmuir, vol. 21, 2005, pp. 6540–6547. [43] D.B. Cordes, S. Gamsey, and B. Singaram, “Fluorescent quantum dots with boronic acid substituted viologens to sense glucose in aqueous solution,” Angew. Chem. - Int. Ed., vol. 45, 2006, pp. 3829–3832. [44] H. Fang, G. Kaur, and B. Wang, “Progress in boronic acid-based fluorescent glucose sensors,” J. Fluoresc., vol. 14, 2004, pp. 481–489. [45] G. Kaur, N. Lin, H. Fang, B. Wang, Eds. Boronic Acid-Based Fluorescence Sensors for Glucose Monitroing, vol. 11, Springer, NY, 2006. [46] T.D. James, K.R.A.S. Sandanayake, R. Iguchi, and S. Shinkai, “Novel saccharide-photoinduced electron transfer sensors based on the interaction of boronic acid and amine,” J. Am. Chem. Soc., vol. 117, 1995, pp. 8982–8987. [47] C.D. Geddes and J.R. Lakowicz, Eds. Glucose Sensing, vol 11, Springer, NY, 2006. [48] J.M. Anderson, in Biomaterials Science: An Introduction to Materials in Medicine, B.D. Ratner, A.S. Hoffman, F.J. Schoen, and J.E. Lemons, Eds., Elsevier Academic Press, London, 1996. [49] V. ThomeDuret, G. Reach, M.N. Gangnerau, F. Lemonnier, J.C. Klein, Y. N. Zhang, Y.B. Hu, and G.S. Wilson, “Use of a subcutaneous glucose sensor to detect decreases in glucose concentration prior to observation in blood,” Anal. Chem., vol. 68, 1996, pp. 3822–3826. [50] N. DiCesare, D.P. Adhikari, J.J. Heynekamp, M.D. Heagy, and J.R. Lakowicz, “Spectroscopic and Photophysical Characterization of Fluorescent Chemosensors for Monosaccharides Based on N-Phenylboronic Acid Derivatives of 1,8-Naphthalimide,” J. Fluoresc., vol. 12, 2002, p.147.

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[105] K. Ye and J.S. Schultz, “Genetic engineering of an allosterically based glucose indicator protein for continuous glucose monitoring by fluorescence resonance energy transfer,” Anal. Chem., vol. 75, 2003, pp. 3451–3459. [106] L.C. Clark and C. Lyons, “Electrode systems for continuous monitoring in cardiovascular surgery,” Annals NY Acad. Sci., vol. 102, 1962, p. 29. [107] M.C. Moreno-Bondi, O.S. Wolfbeis, M.J. Leiner, and B.P. Schaffar, “Oxygen optrode for use in a fiber-optic glucose biosensor,” Anal. Chem., vol. 62, 1990, pp. 2377–2380. [108] O.S. Wolfbeis, “Fiber optic biosensing based on molecular recognition,” Sens. Actuat., B: Chem., vol. B5, 1991, p. 1. [109] T.E. Curey, A. Goodey, A. Tsao, J. Lavigne, Y. Sohn, J.T. McDevitt, E.V. Anslyn, D. Neikirk, and J.B. Shear, “Characterization of multicomponent monosaccharide solutions using an enzyme-based sensor array,” Anal. Biochem., vol. 293, 2001, pp.178–184. [110] J.C. Pickup, F. Hussain, N.D. Evans, O.J. Rolinski, and D.J. Birch, “Fluorescence-based glucose sensors,” Biosens. Bioelectron., vol. 20, 2005, pp. 2555–2565. [111] F. Hussain, D.J. Birch, and J.C. Pickup, “Glucose sensing based on the intrinsic fluorescence of sol-gel immobilized yeast hexokinase,” Anal. Biochem., vol. 339, 2005, pp. 137–143. [112] J.C. Pickup, F. Hussain, N.D. Evans, and N. Sachedina, “In vivo glucose monitoring: the clinical reality and the promise,” Biosens. Bioelectron., vol. 20, 2005, pp. 1897–1902. [113] K.S. Bronk and D.R. Walt, “Fabrication of patterned sensor arrays with aryl azides on a polymer-coated imaging optical fiber bundle,” Anal. Chem., vol. 66, 1994, pp. 3519–3520. [114] J.Q. Brown and M.J. McShane, “Modeling of spherical fluorescent glucose microsensor systems: design of enzymatic smart tattoos,” Biosens. Bioelectron., vol. 21, 2006, pp. 1760–1769. [115] D.W. Lubbers and N. Opitz, “Optical fluorescence sensors for continuous measurement of chemical concentrations in biological systems,” Sens. Actuat., vol. 4, 1983, pp. 641–654. [116] D.B. Papkovsky, “Luminescent porphyrins as probes for optical (bio)sensors,” Sens. Actuat., B: Chem., vol. B11, 1993, p. 293. [117] Z. Rosenzweig and R. Kopelman, “Analytical properties of miniaturized oxygen and glucose fiber optic sensors,” Sens. Actuat., B: Chem., vol. B36, 1996, p. 475.

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[118] H. Xu, J. W. Aylott, and R. Kopelman, “Fluorescent nano-PEBBLE sensors designed for intracellular glucose imaging,” Analyst, vol. 127, 2002, pp. 1471–1477. [119] H. Zhu, R. Srivastava, J.Q. Brown, and M.J. McShane, “Combined physical and chemical immobilization of glucose oxidase in alginate microspheres improves stability of encapsulation and activity,” Bioconjug. Chem., vol. 16, 2005, pp. 1451–1458. [120] J.Q. Brown, “Modeling, design, and validation of fluorescent spherical enzymatic glucose microsensors using nanoengineered polyelectrolyte coatings,” in Biomedical Engineering, Louisiana Tech University, Ruston, LA, 2005. [121] J.Q. Brown and M.J. McShane, “Modeling of spherical fluorescent glucose microsensor systems: Design of enzymatic smart tattoos,” Biosensors and Bioelectronics, vol. 21, 2006, pp. 1760-1769. [122] J.Q. Brown, R. Srivastava, and M.J. McShane, “Encapsulation of glucose oxidase and an oxygen-quenched fluorophore in polyelectrolyte-coated calcium alginate microspheres as optical glucose sensor systems,” Biosens. Bioelectron., vol. 21, 2005, pp. 212–216. [123] W. Trettnak and O.S. Wolfbeis, “Fully reversible fibre-optic glucose biosensor based on the intrinsic fluorescence of glucose oxidase,” Anal. Chim. Acta, vol. 221, 1989, pp. 195–203. [124] J.F. Sierra, J. Galban, S. De Marcos, and J.R. Castillo, “Direct determination of glucose in serum by fluorimetry using a labeled enzyme,” Anal. Chim. Acta, vol. 414, 2000, pp. 33–41. [125] H. Maity, N.C. Maiti, and G.K. Jarori, “Time-resolved fluorescence of tryptophans in yeast hexokinase-PI: effect of subunit dimerization and ligand binding,” J. Photochem. Photobiology. B: Biol., vol. 55, 2000, pp. 20–26. [126] H. Maity and S.R. Kasturi, “Interaction of bis(1-anilino-8naphthalenesulfonate) with yeast hexokinase: a steady-state fluorescence study,” J. Photochem. Photobiol. B, vol. 47, 1998, pp. 190–196. [127] S. D’Auria, N.Di Cesare, Z. Gryczynski, I. Gryczynski, M. Rossi, and J.R. Lakowicz, “A thermophilic apoglucose dehydrogenase as nonconsuming glucose sensor,” Biochemical. Biophys. Res. Communs., vol. 274, 2000, pp. 727– 731. [128] S. Chinnayelka, Microcapsule biosensors based on competitive binding and fluorescence resonance energy transfer assays, Ph.D. Dissertation, Louisiana Tech University, Ruston, LA, 2005. [129] S. Chinnayelka and M.J. McShane, “Glucose-sensitive nanoassemblies comprising affinity-binding complexes trapped in fuzzy microshells,” J. Fluoresc., vol. 14, 2004, p. 585.

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[130] S. Chinnayelka and M.J. McShane, “Resonance energy transfer nanobiosensors based on affinity binding between apo-enzyme and its substrate,” Biomacromol., vol. 5, 2004, p. 1657. [131] H. Fang, G. Kaur, and B. Wang, “Progress in boronic acid-based fluorescent glucose sensors,” J. Fluoresc., vol. 14, 2004, p. 481. [132] T.D. James, K.R.A.S. Samankumara, and S. Shinkai, “Novel photoinduced electron-transfer sensor for saccharides based on the interaction of boronic acid and amine,” Chem. Communs., vol. 4, 1994, pp. 477–478. [133] T.D. James, K.R.A.S. Samankumara, R. Iguchi, and S. Shinkai, “Novel saccharide-photoinduced electron transfer sensors based on the interaction of boronic acid and amine,” J. Am. Chem. Soc., vol. 117, 1995, p. 8982. [134] B. Appleton and T.D. Gibson, “Detection of total sugar concentration using photoinduced electron transfer materials: Development of operationally stable, reusable optical sensors,” Sens. Actuat., B: Chem., vol. 65, 2000, pp. 302–304. [135] K. Gurpreet, N. Lin, H. Fang, and B. Wang, “Boronic acid-based fluorescence sensors for glucose monitroing,” in Topics in Fluorescence Spectroscopy, C.D. Geddes and J.R. Lakowicz, Eds., Springer, New York, 2006. [136] M.D. Phillips and T.D. James, “Boronic acid based modular fluorescent sensors for glucose,” J. Fluoresc., vol. 14, 2004, pp. 549–559. [137] M.D. Heagy, “N-phenylboronic acid derivatives of arenecarboximides as saccharide probes with virtual spacer design,” in Topics in Fluorescence Spectroscopy, C.D. Geddes and J.R. Lakowicz, Eds., Springer, New York, 2006, pp. 1–17. [138] D.B. Cordes, A. Miller, S. Gamsey, Z. Sharrett, P. Thoniyot, R. Wessling, and B. Singaram, “Optical glucose detection across the visible spectrum using anionic fluorescent dyes and a viologen quencher in a two-component saccharide sensing system,” Org. Biomolec. Chem., vol. 3, 2005, p. 1708. [139] D.B. Cordes, J.T. Suri, F.E. Cappuccio, J.N. Camara, S. Gamsey, Z. Sharrett, P. Thoniyot, R.A. Wessling, and B. Singaram, “Two-component optical sugar sensing using boronic acid-substituted viologens with anionic fluorescent dyes,” in Topics in Fluorescence Spectroscopy, C.D. Geddes and J.R. Lakowicz, Eds., Springer, New York, 2006, 47–84. [140] V.V. Karnati, X. Gao, S. Gao, W. Yang, W. Ni, S. Sankar, and B. Wang, “A glucose-selective fluorescence sensor based on boronic acid-diol recognition,” Bioorg. Med. Chem. Lett., vol. 12, 2002, pp. 3373–3377. [141] B.L. Ibey, Enhancement of a fluorescent sensor for monitoring glucose concentration in diabetic patients, Ph.D. Dissertation, Texas A&M University, College Station, TX, December 2006.

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12 Quantitative Biological Raman Spectroscopy Wei-Chuan Shih, Kate L. Bechtel and Michael S. Feld George R. Harrison Spectroscopy Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139

12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Quantitative Considerations for Raman Spectroscopy . . . . . . . . . . . . . . . . . . . . . . Biological Considerations for Raman Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Data Pre-Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . In Vitro and In Vivo Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Toward Prospective Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Raman spectroscopy is a powerful technique for identifying the molecular composition of materials. It can also be used to quantify the substances present. Recently, quantitative Raman spectroscopy has been used in biological tissue for disease diagnosis and, in blood, to measure concentrations of analytes such as glucose noninvasively. A characteristic feature of biological tissue is its high turbidity, due to the interplay of scattering and absorption. In addition, the complexity of biological tissue results in significant spectral overlap. These factors make the quantification of analyte concentrations difficult. Measurement accuracy can be improved if these difficulties can be overcome. This chapter discusses the application of quantitative Raman spectroscopy to biological tissue. Section 12.1 provides an introduction to Raman spectroscopy. Section 12.2 reviews existing work relevant to quantitative analysis in biological media. Quantitative and biological aspects of Raman spectroscopy are discussed in sections 12.3 and 12.4. Section 12.5 discusses instrumentation, using the instrument developed in our laboratory as an example. Data preprocessing is discussed in section 12.6. In section 12.7 we review our glucose studies in blood serum, whole blood and human subjects. Section 12.8 introduces two new techniques, constrained regularization (CR) and intrinsic Raman spectroscopy (IRS), which are shown to significantly improve measurement accuracy. Additional consid-

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erations are discussed in the context of future directions. Section 12.9 concludes the chapter. Key words: Raman spectroscopy, glucose sensing, turbidity, scattering, absorption, biological tissue, intrinsic Raman spectroscopy (IRS).

12.1 Introduction 12.1.1 Introduction to Raman spectroscopy Light scattering is a well-known form of the light-matter interaction process. Scattering redirects light incident on an atom or molecule. Most of the scattered light has the same frequency as the incident light, and therefore there is no energy exchange. This process is called elastic scattering and, for scatterers small compared to the wavelength, it gives rise to Rayleigh scattering. A tiny amount of the scattered light, however, is shifted in frequency due to transfer of energy, most commonly vibrational energy, to or from the molecule. The excitation light can set the molecule into vibration at the molecular vibrational frequency, νV . This process, called Raman scattering, is an inelastic scattering process, as energy is exchanged between the molecule and the incident light. From a quantum-mechanical point of view, an incident photon of frequency νL , wavelength (c0 /νL ), and energy hνL , with c0 the speed of light and h Planck’s constant, is instantaneously taken up by the molecule, forming a “virtual state” that is usually lower in energy than the electronic transitions of the molecule. A new photon is created and scattered from this virtual state. If the new photon is down-shifted in frequency, the process is called Stokes-Raman scattering [1]. The resulting photon will have a reduced energy h(νL − νV ). Similarly, a molecule can begin in an excited vibrational state and proceed, via the virtual state, to the ground state. This generates an up-shifted “anti-Stokes” Raman scattered photon, with an increased energy h(νL + νV ). The processes of Rayleigh, Stokes Raman, anti-Stokes Raman with unshifted, down-shifted, and up-shifted frequencies of the scattered light, respectively, are illustrated in Fig. 12.1. Raman scattering, discovered by Raman and Krishnan in 1928 [2], provides a way to measure molecular composition through inelastic scattering. The frequency shift of the scattered light is a direct measure of the vibrational frequency (i.e., energy) of the molecule. Each molecule has its own distinct vibrational frequency or frequencies. The frequency spectrum of the Raman-scattered light thus provides a unique fingerprint of the molecule. The Raman spectrum of material with multiple constituents can thus be used to determine its molecular composition. A Raman spectrum consists of scattered intensity plotted vs. energy, or frequency, as shown in Fig. 12.2 for glucose in water. Each peak corresponds to a given Raman shift from the incident light energy hνL . The energy difference between the

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FIGURE 12.1: Energy diagram for Rayleigh, Stokes Raman, and anti-Stokes Raman scattering.

initial and final vibrational states, hνV , the Raman shift νV , is usually measured in wavenumbers (cm−1 ), and is calculated as νV /c. Raman shifts from a given molecule are always the same, regardless of the excitation frequency (or wavelength). This provides flexibility in selecting a suitable laser excitation wavelength for a specific application. Infrared (IR) absorption, which probes vibrational structure in the energy range 400–4000 cm−1 (25–2.5 µ m wavelength range), is also indicative of molecular vibrations. However, these wavelengths are not readily transmitted by most materials. Raman spectroscopy and IR absorption both probe the vibrational structure of molecules, and in many cases the same vibrations are observed. IR absorption is sensitive to vibrational frequencies that change the permanent dipole of the molecule. Raman scattering measures vibrational frequencies that result in a change of polarizability. Near-infrared (NIR) absorption spectroscopy probes the energy range from 4000 to 10000 cm−1 (2.5–1 µ m wavelength range), where overtone and combination bands of molecular vibrations occur. Such transitions are quantum mechanically “forbidden,” and are significantly weaker, and with broader features, than those observed in IR absorption. However, in contrast to IR absorption, shorter wavelength NIR light is conveniently transmitted by common optical materials, conferring a substantial advantage over IR absorption in instrumentation. As mentioned earlier, Raman shifts are independent of excitation wavelength, and thus there is flexibility in choosing the wavelength range.

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FIGURE 12.2: A Raman spectrum consists of scattered intensity plotted vs. energy. This figure shows an aqueous glucose solution as an example.

12.2 Review This section briefly reviews the literature relevant to quantitative biological Raman spectroscopy. Raman spectroscopy of biological tissue was initially demonstrated using NIR Fourier transform Raman spectroscopy [3, 4]. In contrast to the visible wavelength range, water absorption and background due to laser-induced autofluorescence are both smaller in the NIR, thus enabling deeper penetration depth and observation of order-of-magnitude weaker Raman peaks. In its early development stages, Raman spectroscopy was primarily employed as a qualitative tool for chemical identification, with limited ability for quantification. Through the introduction and improvement of lasers, CCDs, and other optical components, quantitative analysis became possible. In the following, we review three categories of work: semi-quantitative, univariate, and multivariate analyses. Such distinctions are made based on the types of analysis carried out. For instance, the hallmark of semi-quantitative work is normalization to the overall peak intensity. Although absolute intensity information is lost in the normalization step, quantitative analysis can be applied afterwards. Univariate analysis uses one or a few characteristic peaks through measurement of peak heights or integration of the area under the peaks. In contrast to univariate analysis, multivariate techniques are often called “full spectral range” methods. This type of analysis is usually carried out when spectral overlap exists, and therefore the characteristic peaks of interest are not obvious or are

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“contaminated” by adjacent features not belonging to the substance of interest. As the analysis becomes more sophisticated and more multivariate in nature, the issue of model robustness must be considered. We discuss various aspects of this topic in the subsection 12.3.1.

12.2.1 Semi-quantitative implementation Raman spectroscopy has been employed in disease diagnosis using morphological models, with the rationale that characteristic morphological features are representative disease biomarkers. This approach is based on the unique correspondence between a particular morphological structure and the underlying chemical substance. These models are constructed via ordinary least squares (OLS) analysis, which assumes that the (important) spectral components are all precisely known, and that the observed experimental spectrum can be represented as a linear superposition of these spectral components, weighted by their concentrations [5]. Haka et al. [6] developed a morphological model for breast cancer diagnosis using confocal Raman microscopy. They analyzed the Raman spectral features of normal, benign, and malignant tissue samples in terms of the relative amount of collagen, fat, keratin, etc. Van de Poll et al. [7] and Buschman et al. [8] studied atherosclerosis using a similar approach. Spectra of individual morphological structures were obtained using confocal Raman microscopy, and then applied to fit tissue spectra collected with an optical fiber probe. In these studies, spectra of both the model components and those taken in tissue were normalized to their respective highest peaks, and absolute intensity information was not retained. However, the chemical composition could be quantified in terms of the relative proportions of the model components and then correlated with disease. For example, the relative quantity of collagen to fat was found to be a relevant breast cancer biomarker.

12.2.2 Univariate implementation For some applications, characteristic and distinct Raman peaks of the chemical (molecule) of interest can be observed with little difficulty. Peak height measurement or integration of the area under the peak can be used as a quantitative indicator of the substance. Caspers et al. [9] developed confocal Raman microscopy to perform noninvasive determination of the water profile in human skin in vivo. Peterson et al. [10] reported the acquisition of whole blood Raman spectra in vivo using tissue modulation. Glucose concentrations were subsequently extracted from the area under particular spectral peaks of the whole blood spectra. A calibration model derived from one individual was then used to generate meaningful predictions on independent data.

12.2.3 Multivariate implementation In the Raman spectra of more complicated chemical systems, the various underlying components (called “interferents”) generally exhibit substantial spectral overlap.

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Therefore, no distinct Raman peak is available for peak height or area measurement, and the full spectrum must be used. This is called multivariate analysis. The goal of multivariate analysis is to obtain a spectrum of numbers, b( j), with j the wavelength index. When b( j) is projected onto an experimental spectrum s( j), one obtains accurate prediction of the analyte’s concentration, c [5]. Such spectra are often described as column vectors, with each dimension corresponding to a given sampling point on the wavelength axis. In these terms, c is obtained as the scalar product of b with the experimental spectrum, b: c = sT b

(12.1)

where lowercase boldface type denotes a column vector, and the superscript T denotes the transpose. Note that Eq. (12.1) assumes linearity, i.e., the observed spectrum can be represented as a linear superposition of underlying spectral components. Multivariate analysis proceeds in two steps. In calibration, one correlates known concentrations with spectra to obtain b. The resulting b, sometimes called the regression vector, is then used to predict the concentration of an unknown sample. Multivariate calibration is further discussed in detail in subsection 12.3.1, below. Noninvasive measurement of blood analyte concentrations is a widely pursued topic, and most studies employ multivariate techniques to extract analyte-specific concentration information. However, from a data analysis standpoint multivariate calibration presents more challenges than univariate methods, because of system complexity and the resulting spectral overlap. Owing to its potential impact on diabetes, glucose has been often used as a model analyte. In vitro measurements of glucose have been performed in filtered blood serum [11, 12], blood serum [13], and whole blood [14]. Rohleder et al. [12] discovered that measurements from serum are greatly improved by ultrafiltration to remove macromolecules that cause intense Raman background and subsequently impair measurement accuracy. Results from whole blood were found to have greater error than those from filtered or unfiltered serum, but were still within the clinically acceptable range. Lambert et al. [15] measured human aqueous humor, simulating measurements in the eye, a convenient target for optical techniques. Our group studied glucose noninvasively in human subjects using Raman spectroscopy coupled with multivariate analysis; Enejder et al. [16] accurately measured glucose concentrations in 17 nondiabetic volunteers following an oral glucose tolerance protocol. Results based on analysis of spectra from individual and multiple volunteers indicated that the calibration model was based on glucose rather than spurious correlations.

12.3 Quantitative Considerations for Raman Spectroscopy Traditionally, Raman spectroscopy has been utilized as an analytical tool for chemical identification and fingerprinting, where analysis has been based on observation

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of characteristic Raman peaks. As mentioned in the previous section, many more challenges are encountered when Raman spectroscopy is used as a quantitative analytical tool. We discuss the challenges below.

12.3.1 Considerations for multivariate calibration models As discussed previously, although Raman spectroscopy provides good molecular specificity, spectral overlap is inevitable with the presence of multiple constituents. Since the glucose Raman signal is only ∼0.3% of the total skin Raman signal [17, 18], and the spectrum is complicated by shot noise and varying fluorescence background, multivariate calibration is necessary. There are two types of multivariate techniques, explicit and implicit. In explicit techniques such as OLS [5], the b vector is calculated from the full set of known spectral components. In implicit techniques, such as partial least squares (PLS) [19, 20] analysis, the b vector is derived from a calibration data set composed of samples with known concentrations of the analyte of interest. Since multivariate calibration models are often built on an underdetermined data set, careful assessment of model validity is required. Here we present some considerations for evaluating a calibration model. The reader is referred to the references for more detailed information about multivariate calibration.

12.3.2 Fundamental and practical limits In spectroscopy, the amplitude of the Raman spectrum of the analyte of interest depends on the number of analyte molecules sampled by the incoming light. The effective path length (in transmission mode) and sampling volume (in reflection mode) of the light are important parameters in estimating detection limits in turbid media. Modeling techniques such as diffusion theory [21] and Monte Carlo simulation [22] can be employed to calculate the fluence distribution inside the sample and the angular and radial profiles of the transmitted or reflected flux. Simulations with synthetic data or experiments employing tissue-simulating physical models (called “phantoms”) can be of great value in determining how close the theoretical limit can be realized in practice. In these studies, experimental conditions (e.g., signalto-noise ratio (SNR), instrumental drifts) and tissue phantom composition (e.g., interferents, concentrations) can be precisely controlled and well characterized in advance. Demonstrating that the chosen technique and instrument can measure physiological levels of the analyte of interest in phantoms is necessary but not sufficient to validate in vivo results. In vivo calibration models can only be validated by prospective studies.

12.3.3 Chance or spurious correlation Multivariate calibration algorithms are powerful, yet can be misleading if used without caution. Owing to the nature of the underdetermined data set, minute correlations present in the data set can be misinterpreted by the algorithm as actual

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analyte-specific variations. For example, Arnold et al. [23] measured the NIR absorption spectra of tissue phantoms devoid of glucose, and used temporal glucose concentration profiles published by different research groups to demonstrate that the calibration model could produce an apparent correlation with glucose even though none was present. It is important to note that calibration results such as these satisfied multiple criteria for judging the validity of a calibration model. Overfitting is another cause for spurious correlations. In multivariate calibration, a large number of sample spectra can be reduced to fewer factors. In practice, only a subset of factors is significant in modeling the underlying analyte variations, while others are more likely to be dominated by noise and measurement errors. Although an apparently lower calibration error may be obtained by including more factors in the calibration model, the reduction in error may be fortuitous and the resulting model may have less predictive capability. The lesson here is that chance or spurious correlations may be inadvertently incorporated in the calibration model even when rigorous validation procedures have been followed. Additionally, if these chance or spurious correlations exist in prospective data, even good prediction results can be based on non-analyte-specific effects. Incorporating prior or additional information into the calibration model has been shown to provide more immunity to chance correlations [24–27].

12.3.4 Spectral evidence of the analyte of interest The difficulty in visualizing analyte-specific information in biological spectra makes it challenging to verify the origin of the spectral information used by the calibration model and confirm that positive results are actually based on the analyte of interest. However, some of this information can be obtained by examining the b vector. The b vectors obtained from spectroscopic data contain spectral information about all the components of the model. Under ideal, noise-free conditions, b can be explicitly derived from the model component spectra (via OLS), or implicitly obtained from the calibration data set. This ideal b vector is also termed the net analyte signal [28, 29]. As mentioned above, b is identical (within a scale factor) to the pure component spectrum of the analyte of interest if no other interferents are present. In other words, b should “look” progressively more like the glucose spectrum as model complexity decreases. For example, when spectral overlap is low, as in Raman spectroscopy, spectral features of glucose can be identified in the experimentally derived b vector as supporting evidence that the model is based on glucose rather than spurious correlations [13, 14, 16]. Although a complete model is virtually never available for in vivo experiments, a good approximation to the actual b vector is often obtainable from an OLS estimate. Therefore, it is always useful to compute a theoretically “correct” b vector and compare it to the experimentally derived b. If the two significantly differ, the discrepancy should be investigated.

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12.3.5 Minimum detection limit If all component spectra in a mixture sample are known, the minimum detection error, ∆c, can be calculated via a simple formula derived by Scepanovic et al. [30] of our laboratory: ∆c =

σ OLFk , ksk k

(12.2)

1 . corr(bOLS , sk )

(12.3)

where the subscript k designates the constituent analyte to be measured. The first factor on the right hand side, σ , is the standard deviation of the noise in the measured spectrum. The second factor, ksk k, is the signal strength of the analyte, represented as the norm of its Raman spectrum. The last factor, OLFk , is termed the “overlap factor,” and can take on values between 1 and infinity. OLFk indicates the amount of overlap between the Raman spectrum of the analyte and those of the interferents. Mathematically, OLFk is the inverse of the correlation coefficient between the analyte spectrum and the OLS regression vector (bOLS ): OLFk =

bOLS is the portion of the analyte spectrum sk that is orthogonal to all interferents. When there are no interferents, bOLS is identical to the analyte spectrum and thus OLFk = 1. When interferents are present, corr(bOLS , sk ) is always smaller than one and therefore OLFk is always larger than 1. To estimate the overlap factor for glucose measurements in skin, we built a 10-constituent model, approximating the Raman spectrum of human skin. Starting with only glucose, the Raman spectra of other constituents, including collagen type I, keratin, triolein, actin, collagen type III, cholesterol, phosphatidylcholine, hemoglobin, and water, were progressively added, increasing model complexity. The correlation between bOLS and the glucose spectrum was reduced from 1 to 0.73, as shown in Fig. 12.3, indicating that the detection limit indeed becomes worse for more complex chemical systems. Equation (12.2) provides a practical way to estimate the minimum detection limit, ∆c, based on easily obtainable experimental parameters. Lower fluorescence background introduces less shot noise and therefore increases the Raman SNR. High molecular specificity in the Raman spectra leads to less spectral overlap and thus reduces the OLF for a specific analyte. A practical estimate of the minimum detectable glucose concentration in blood for our instrument (section 12.5) is ∆c ∼ 2 mg/dL.

12.4 Biological Considerations for Raman Spectroscopy 12.4.1 Using near infrared radiation Raman shifts are independent of excitation wavelength and thus offer flexibility in choice of wavelength range. NIR excitation provides three advantageous features for

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FIGURE 12.3: Correlation between the OLS regression vector (bOLS ) and the glucose spectrum versus model complexity.

studying biological tissue: low-energy optical radiation, deep penetration depth, and reduced background fluorescence. Excitation wavelengths in the NIR region prevent hazardous ionization of tissue constituents. The lack of prominent absorbers in the NIR region enables sampling over sufficient depth, of the order of ∼ 1 mm. The reduced shot noise associated with the low fluorescence background induced by NIR excitation provides an order of magnitude improvement in sensitivity in extracting Raman signals. As a result, our Raman studies of biological tissue employ 830 nm as the excitation wavelength. As shown in Fig. 12.4, this provides Raman spectra over 830-1000 nm, a wavelength range in the “diagnostic window” (deep penetration), in which silicon-based charge coupled device (CCD) detectors have very high quantum efficiency. Figure 12.4 illustrates the absorption spectra of major endogenous tissue absorbers, water, skin melanin, hemoglobin, and fat. Also shown is the scattering spectrum of 10% Intralipid, a lipid emulsion often used to simulate tissue scattering. The diagnostic window is indicated by the rectangle.

12.4.2 Background signal in biological Raman spectra Raman spectra of biological samples are often accompanied by strong background. The source of the background is often attributed to fluorescence, particularly when UV/visible laser excitation is employed. Proteins and lipids present in biological tissue can contribute to the fluorescence background [11]. The autofluorescence of skin from endogenous fluorophores with UV/visible light excitation is well known and, in fact, it has been applied to the diagnosis of disease states such as psoriasis [31]

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FIGURE 12.4: Absorption spectra of water, skin melanin, hemoglobin, and fat. Also shown is the scattering spectrum of 10% Intralipid, a lipid emulsion often used to simulate tissue scattering. Data are obtained from http:// omlc.ogi.edu/spectra/index.html.

and diabetes. In these cases, collagen fluorescence changes owing to glycation, the process in which a single sugar such as glucose binds to a protein or lipid molecule without the controlling action of an enzyme [32]. Furthermore, our laboratory utilizes the autofluorescence of epithelial tissue components to diagnose dysplasia [33]. The shot noise accompanying this fluorescence background limits the detection capability. Time-dependent background variations influence subsequent multivariate analysis. In a human skin study using UV/visible light excitation, Zeng et al. [34] described the temporal background intensity decay as fluorescence photobleaching. They fit the intensity decay to a double-exponential function, with the time constants ascribed to photobleaching rates of different fluorophores in the stratum corneum and dermis. On the other hand, Jongen and Sterenborg [35] found that even for a single fluorophore, the turbidity of tissue causes fluorescence decay to deviate from single-exponential behavior. Hence, double-exponential behavior need not be ascribed to two fluorophores. The reasoning for this argument is that the fluorescence signal from a multi-layered turbid medium is the sum of the contributions from each layer. Fluorescence from a deeper lying layer appears weaker and will photobleach at a slower rate because of diminished laser power. Thus, the relative contribution of fluorescence from deeper layers will appear as smaller signals that decay slower, whereas the superficial layers will exhibit stronger signals that decay faster. This

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illustrates the strong influence that the optical properties of the sample can have on the observed behavior of light. While implicit multivariate calibration techniques can remove the detrimental effects of the background to some extent, their efficacy is impaired. Thus, it is desirable to either reduce the background during data collection or subtract it via modeling, without introducing artifacts. Most background subtraction methods in the literature are based on polynomial fitting. Since the background has little structure, a slowlyvarying low-order polynomial can characterize it [4, 36–38]. Refs. [36–38] find that a fifth-order polynomial is the most effective fit to the background.

12.4.3 Heterogeneities in human skin Uniform analyte distribution is often a good assumption for liquid samples such as serum or whole blood with continuous stirring. However, for biological tissue, human skin in particular, heterogeneity is a major feature. Detailed morphological structure and molecular constituents associated with skin heterogeneity have been studied using confocal Raman spectroscopy [39]. Skin has two principal layers: epidermis and dermis. The epidermis is the outmost layer, and itself consists of multiple layers including the stratum corneum as the major component, stratum lucidum, and stratum granulosum. The major chemical constituent of human epidermis is keratin, comprising approximately 65% of the stratum corneum. The dermis is also a layered structure composed mainly of collagen and elastin. Blood capillaries are present in the dermis, and thus this region is targeted for optical analysis for glucose detection. However, it has been suggested that the majority of the glucose molecules sampled by optical techniques arise from the interstitial fluid (ISF), which is primarily found at the epidermis-dermis interface [40]. The role of skin heterogeneity in noninvasive measurement of blood analyte concentrations is an important factor that has not yet been fully studied.

12.5 Instrumentation As discussed previously, background fluorescence from biological tissue impedes observation of Raman signals with UV/visible excitation wavelengths. To overcome this limitation, the use of NIR excitation was introduced, initially using Fouriertransform spectrometers [3]. With the advent of high quantum efficiency CCD detectors and holographic diffractive optical elements, our group and others have led the way in switching to CCD-based dispersive spectrometers [4, 10, 11, 13-15]. The advantages of dispersive NIR Raman spectroscopy are that compact solid-state diode lasers can be used for excitation, the imaging spectrograph can be f -number matched with optical fibers for greater throughput, and cooled CCD detectors offer shot-noiselimited detection. As a tutorial for the selection of building blocks for a Raman in-

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strument with high collection efficiency, we present a summary of the key design considerations.

12.5.1 Excitation light source Laser excitation at one of two wavelengths, 785 and 830 nm, is most common. The tradeoff is that excitation at lower wavelengths has a higher efficiency of generating Raman scattering but also generates more intense background fluorescence. The current trend is towards the use of external cavity laser diodes because they are compact and of relatively low cost. Other researchers use argon-ion laser pumped titanium-sapphire lasers. The titanium-sapphire laser provides higher power output with broader wavelength tunability, but it is bulkier and much more expensive than diode lasers. Narrow-band excitation must be used to prevent broadening of the Raman bands. Further, the wings of the laser emission (amplified spontaneous emission) can extend beyond the cutoff wavelength of the notch filter used to suppress the elastically scattered light, and can obscure low wavenumber Raman bands. This problem is most severe with high power diode lasers, and a holographic bandpass or interference laser line filter with attenuation greater than 6OD is usually required. Lastly, for quantitative measurements a photodiode is often needed to monitor the laser intensity to correct for power variations.

12.5.2 Light delivery, collection, and transport The filtered laser light can be delivered to the sample either via free-space transmission or through an optical fiber. In free-space embodiments, beam shaping is usually performed to correct for astigmatism and other laser light artifacts. The incident light at the sample can be either focused or collimated, depending on collection considerations. For biological tissue, the total power per unit area delivered to the tissue must be limited for safety, and thus spot size on the tissue is an oft-reported parameter. Raman probes constructed from fused silica optical fibers have gained much attention recently. Typically, low-OH content fibers are utilized to reduce the fiber fluorescence. The probe design also includes filters at the distal end to suppress the fused silica Raman signal from the excitation fiber and prevent the elastically scattered light entering the collection fibers [41]. Commercial probes are now available, and they offer ruggedness and easy access to samples with geometrical or other constraints. As Raman scattering is a weak process, high collection efficiency is required. Specialized optics such as Cassegrain microscope objectives and non-imaging paraboloidal mirrors have been employed to increase both the collection spot diameter and the effective numerical aperture of the optical system [40]. The majority of light that exits the air-sample interface is elastically scattered at the laser wavelength. This light must be properly attenuated or it will saturate the CCD detector. Holographic or interference notch filters are extensively employed for this purpose, and can at-

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tenuate the elastically scattered light to greater than 6OD, while passing the Raman light with greater than 90% efficiency. However, notch filters are very sensitive to the incident angle of the light, and thus provide less attenuation for off-axis light. In some instances the diameter of the notch filter is one of the determining factors of the throughput of an instrument. Specular reflection, light that is elastically scattered without penetrating the tissue, is also undesirable. Strategies such as oblique incidence [42], 90-degree collection geometry [11], and bringing in excitation light via a hole in the collection mirror have all been employed to reduce its effect [27]. After filtering out most of the elastically scattered light, the Raman scattered light must be transported to the spectrograph with minimum loss. To match the shape of the entrance slit of a spectrograph, the circular shape of the collected light can be relayed by an optical fiber bundle with the receiving end arranged in a round shape and the exiting end arranged in a line [14].

12.5.3 Spectrograph and detector In dispersive spectrographs for Raman spectroscopy, transmission holographic gratings are often used because of their compactness and high dispersion. Holographic gratings can be custom-blazed for specific excitation wavelengths and provide acceptable efficiency. In addition, liquid nitrogen cooled and, more recently, thermoelectric cooled CCD detectors offer high sensitivity and shot-noise-limited detection in the near infrared wavelength range up to ∼1 µ m. These detectors can be controlled using programs such as Labview to facilitate experimental studies. To increase light throughput in Raman systems, the CCD chip size can be increased vertically to match the spectrograph slit height. However, large format CCD detectors show pronounced slit image curvature that must be corrected for in preprocessing (described in subsection 12.6.1). As an example of these design considerations, Fig. 12.5 shows a schematic of the high-throughput Raman instrument currently used in our laboratory. We opted for free space delivery of the excitation light through a small hole in an off-axis half-paraboloidal mirror. Backscattered Raman light is collimated by the mirror and passed through a 2.5-inch-diameter holographic notch filter to reduce elastically scattered light. The Raman light is focused onto a shape-transforming fiber bundle, with the exit end serving as the entrance slit of an f/1.4 spectrometer. The pre-filtering stage of the spectrometer was removed to reduce fluorescence and losses from multiple optical elements. The back-thinned, deep depletion, liquid nitrogen-cooled CCD, 1300×1340 pixels, is height-matched to the fiber bundle slit. This instrument was specifically designed for high sensitivity measurements in turbid media.

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FIGURE 12.5: Schematic of a free space Raman instrument for noninvasive glucose measurements used at the MIT Spectroscopy Laboratory. The white light source is for diffuse reflectance measurements and is not always present.

12.6 Data Pre-Processing After data collection, various pre-processing steps are undertaken to improve data quality. The pre-processing steps chosen can lead to different calibration results. Therefore, it is important to carefully consider the exact procedures used. The major pre-processing steps are described in the following.

12.6.1 Image curvature correction Increasing the usable detector area is an effective way to improve light throughput in Raman spectroscopy employing a multi-channel dispersive spectrograph. However, owing to out-of-plane diffraction, the entrance slit image appears curved [43]. Direct vertical binning of detector pixels without correcting the curvature results in degraded spectral resolution. Various hardware approaches, such as employing curved slits [42, 43] or convex spherical gratings, have been implemented. In the curved slit approach, fiber bundles

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are employed as shape transformers to increase Raman light collection efficiency. At the entrance end the fibers are arranged in a round shape to accommodate the focal spot, and at the exit end in a curved line, with curvature opposite to that introduced by the remaining optical system.This exit arrangement serves as the entrance slit of the spectrograph and provides immediate first order correction of the curved image, as described below. However, for quantitative Raman spectroscopy, with substantial change of the image curvature across the wavelength range of interest (∼ 150 nm) and narrow spectral features, this first order correction is not always satisfactory. As an alternative to the hardware approach, software can be employed to correct the curved image, with potentially better accuracy and flexibility for system modification. In past research, we developed a software method using a highly Ramanactive reference material to provide a sharp image on the CCD [44]. Using the curvature of the slit image at the center wavelength as a guide, we determine by how many pixels in the horizontal direction each off-center CCD row needs to be shifted in order to generate a linear vertical image. This pixel shift method, as well as the curved-fiber-bundle hardware approach, ignores the fact that the slit image curvature is wavelength dependent. The resulting spectral quality of the pixel shift method is thus equivalent to the curved-fiber-bundle hardware approach [43]. This issue becomes more important when large CCD chips and high-NA spectrographs are employed for increasing the throughput of the Raman scattered light. Recently, a software approach using multiple polystyrene absorption bands was developed for infrared spectroscopy [16]. In this section we present a similar method that we developed concurrently, which calibrates on multiple Raman peaks to generate a curvature map. This curvature mapping method shows significant improvement over first-order correction schemes. The curvature mapping method requires an initial calibration step. In this step, a full-frame image is taken with a reference material that has prominent peaks across the spectral range of interest, for example, acetaminophen (Tylenol) powder. We chose nine prominent peaks across the wavelength range of interest, indicated by the arrows in Fig. 12.6. The calibration algorithm generates a map of the amount of shift for each CCD pixel and a scale factor to maintain signal conservation in each CCD row. Once the map and the scale factor are generated, usually when the system is first set up, the correction algorithm can be applied to future measurements. Figure 12.7 shows that significant improvement is obtained from the pixel shift method to the curvature mapping method, especially toward either side of the CCD (compare Figs. 7(c) and 7(e)). The overall linewidth reduction in 14 prominent peaks is 7% (FWHM). Such improvement is significant, considering that the equivalent slit width is ∼360 µ m. If a narrower slit is employed for better spectral resolution, the overall linewidth reduction is even more significant. Note that the images were taken with 5-pixel CCD hardware vertical binning to reduce the amount of data, since the curvature is barely noticeable within such a short range. The error introduced by the hardware binning is much less than 1 pixel, and thus negligible.

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FIGURE 12.6: Raman spectrum of acetaminophen powder, used as the reference material in the calibration step. Nine prominent peaks used as separation boundaries are indicated by arrows.

FIGURE 12.7: CCD image of acetaminophen powder. Images were created with 5-pixel hardware binning. (a) Raw image; (b) after applying pixel shift method; (c) zoom-in of the box in (b); (d) after applying curvature mapping method; (e) zoom-in of the box in (d).

12.6.2 Spectral range selection Multivariate calibration methods attempt to find spectral components based on variance. The presence of a spectral region with large non-analyte-specific variations may bias the algorithm and cause smaller analyte-specific variance to be overlooked. Therefore, the ‘fingerprint’ region from approximately 300-1700 cm−1 is

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often chosen for analysis.

12.6.3 Cosmic ray removal Cosmic rays traverse the CCD array at random times with arbitrary intensities, resulting in spikes at individual pixels. When the array is summed and processed, sharp spectral features of arbitrary intensities may appear in the Raman spectra. These artifacts are typically removed before multivariate calibration. One approach is based on the assumption that the spectrum does not change its intensity from frame to frame other than due to noise and cosmic rays. Therefore, by comparing multiple neighboring frames, a statistical algorithm can be used to identify cosmic rays. Another solution compares adjacent pixels in the same spectrum and detects abrupt jumps in intensity from pixel to pixel. Once a cosmic ray contaminated pixel is identified, its value can be replaced by the average of neighboring pixels.

12.6.4 Background subtraction As mentioned in section 12.4, the background signal in Raman spectra is a limiting factor in determining the detection limit. Background subtraction techniques only approximate the shape of the background, and thus place a limit on extracting information. The contrasting approach is to not subtract that background, and instead rely on multivariate calibration algorithms to process both the Raman signals and the background. However, for qualitative analysis, background-subtracted spectra provide better interpretation of the underlying constituents.

12.6.5 Random noise rejection and suppression Photon shot-noise-limited performance can be achieved using a liquid nitrogen cooled CCD camera. When a detector is shot noise limited, the noise can be estimated as the square root of the number of photoelectrons collected in the integration time window. The most effective way to increase the SNR under shot-noise-limited conditions is to increase the integration time of the CCD or the throughput of the instrument. However, extending the integration beyond a certain time scale offers less additional benefit, as other errors begin to dominate performance [40]. Once the data are collected, signal processing is the only way to further enhance the SNR. Pixel binning along the wavelength axis is one method of increasing the SNR, and results indicate that there is an optimal number of binned pixels for optimizing SNR [40]. However, the drawback to this method is degradation in spectral resolution. More commonly employed are Savitzky-Golay smoothing algorithms, which also improve the SNR while better retaining spectral resolution.

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12.6.6 White light correction and wavelength calibration When spectra collected from different instruments or on different days are to be compared, white light correction and wavelength calibration are required. White light correction is performed by dividing the Raman spectra by the spectrum from a calibrated light source, for example a calibrated tungsten-halogen lamp measured under identical conditions. The combined spectral response of the optical components, the diffraction grating, and the CCD camera can be effectively removed, thus revealing more of the underlying Raman spectral features. Wavelength calibration is performed to transform the pixel-based axis into a wavelength-based (or wavenumber-based) axis, enabling comparison of Raman features across instruments and time.

12.6.7 Wavelength selection Although in most experiments Raman spectra are acquired over a continuous wavelength range, analyte-specific information can be distributed non-uniformly across this range. In addition, the overlap factor can change if different wavelengths are chosen for multivariate calibration. Further, because the background is usually non-uniform in wavelength, the shot noise is usually not constant across the entire spectral range. These factors, considered in combination, suggest that there may be advantages when particular wavelength channels (e.g., CCD pixels) are excluded from the spectra. The theoretical basis of wavelength selection and algorithms to perform such selection have been studied [45]. In our laboratory, wavelength selection has not been implemented, but we will consider it in future studies.

12.7 In Vitro and In Vivo Studies In this section, we review the application of quantitative Raman spectroscopy to measure blood analytes, e.g., in particular the glucose studies performed in our laboratory. In vitro studies have been performed using unprocessed human blood serum and human whole blood. In vivo studies have been performed with human volunteers under glucose tolerance test protocols.

12.7.1 Model validation protocol and summary statistics In our studies, leave-one-out cross validation has been employed as a way to use small data sets efficiently. Validation of the calibration model is crucial before prospective application. Two types of validation schemes can be employed, internal and external. Internal validation, or cross validation, is used when the number of calibration samples is limited. In cross validation, a small subset of calibration data is withheld in the model building step, from which the b vector is obtained. The

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model is then applied to the withheld data. A different subset of calibration data is next withheld and the model rebuilt, and again applied to the withheld data. This process is repeated until all the combinations have been studied. In determining the optimal model via cross validation, the root mean square error of cross validation (RMSECV) is calculated. RMSECV is defined as the square root of the sum of the squares of the differences between extracted and reference concentrations. The RMSECV is calculated for a particular choice of the number of model parameters, e.g., the number of factors in PLS. An iterative algorithm is often employed to vary the number of parameters and recalculate the RMSECV. The statistically significant minimum RMSECV and the corresponding number of model parameters are then chosen for determining the optimal calibration model. Various strategies can be employed for grouping spectra for calibration and validation. For example, a single sample can be withheld in a “leave-one-out” scheme, and the calibration and validation process repeated as many times as the number of samples in the calibration data set. In general, “leave-n-out” cross validation can be implemented with n random samples chosen from a pool of calibration data. When the calibration data set is sufficiently large, external validation, i.e., predictive testing, can be employed. As opposed to internal validation, external validation tests the calibration model and optimizes the number of model parameters on data that never influences the model, and therefore provides a more objective measure than internal validation. The b vector obtained by the validation procedure can be employed prospectively to predict concentrations of the analyte of interest in independent data. Similar to the calculation of RMSECV, root mean square error of prediction (RMSEP) for an independent data set is defined as the square root of the sum of the squares of the differences between predicted and reference concentrations. For feasibility studies, RMSECV is a good indicator of performance as long as the number of calibration samples is statistically sufficient. RMSEP, on the other hand, provides the objective metric by which a technology ultimately must be evaluated.

12.7.2 Blood serum Our laboratory began investigating noninvasive blood analysis using Raman spectroscopy in the mid 1990’s [46–48]. The first biological sample study was conducted on serum and whole blood samples from 69 patients over a seven-week period [13]. No sample processing or selection criteria were employed, with the exception of locating a few samples with extreme glucose concentrations to represent the range of diabetes patients’ glucose levels. An 830 nm diode laser was employed for excitation and a microscope objective for light collection. The laser power at the sample was ∼ 250 mW, and the integration time for each spectrum was equivalent to 300 seconds. The glucose measurement results in serum were quite encouraging, with PLS calibration providing an RMSECV of 1.5 mM. However, the glucose measurement results in whole blood result were not satisfactory because of reduced signals from the highly turbid samples. Glucose spectral features were identified in both the PLS weighting vector and the b vector, supporting that the calibration model was based

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on glucose.

12.7.3 Whole blood The main difficulty in measuring analyte concentrations in whole blood as compared to serum was attributed to the much higher absorption and scattering of whole blood because of the presence of hemoglobin and red blood cells, respectively. The combined effect resulted in a factor of four decrease in collected Raman signal size. A subsequent whole blood study in our laboratory by Enejder et al. [14] confirmed this hypothesis. A four-fold increase in Raman signal collection size was achieved by employing a paraboloidal mirror and a shape-transforming fiber bundle for better collection efficiency, as depicted in Fig. 12.5. Accurate measurement of multiple analytes was then demonstrated in 31 whole blood samples with laser intensity and integration time similar to the previous serum study [13]. PLS leave-one-out cross validation was performed, and an RMSECV of 1.2 mM was obtained. The ratio of the number of PLS factors to that of the samples (∼1:3) raised the concern of overfitting. However, glucose spectral features were identified in the regression vector, providing confidence that the model was based on glucose.

12.7.4 Human study Enejder et al. [16] conducted a transcutaneous study on 17 non-diabetic volunteers using a version of the instrument depicted in Fig. 12.5 without the white light source. The objective of this study was to provide an initial evaluation of the ability of Raman spectroscopy to measure glucose noninvasively, with the focus on determining its capability in a range of subjects. Spectra were collected from the forearms of human volunteers in conjunction with an oral glucose tolerance test protocol, involving overnight fasting followed by the intake of a high-glucose containing fluid, after which the glucose levels are elevated to more than twice that found under fasting conditions. Periodic reference glucose concentrations were obtained from finger-stick blood samples and subsequently analyzed by a Hemocue portable glucose meter. The glucose concentrations for all volunteers ranged from 3.8 to 12.4 mM (∼68– 223 mg/dL). Raman spectra over the spectral range 1545–355 cm−1 were selected for data analysis. An average of 27 (461/17) spectra were obtained for each individual. Each spectrum was obtained with excitation power ∼300 mW in a 1 mm spot diameter on the forearm, and integration time equivalent to 3 minutes. Spectra from each volunteer were analyzed using PLS with leave-one-out cross validation, with 8 factors retained for development of the regression vector. PLS with leave-one-out cross validation was first performed on each individual, a mean absolute error (MAE) of 7.8% (RMSECV ∼ 0.7 mM) and an R2 of 0.83 were obtained. When the data from 9 volunteers were combined, the MAE was 12.8% with R2 ∼ 0.7, while combining all 17 volunteers gave MAE ∼ 16.9% (RMSECV ∼ 1.5 mM). In individual calibrations, the adequacy of the ratio of the number of PLS factors and that of the samples was a concern. However, in the combined data set, the grouping schemes involving 9 (244 spectra) and 17 (461 spectra) volunteers utilized 17 and

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21 factors, respectively, which is acceptable [16]. Another encouraging piece of evidence was that multiple glucose spectral features were identified in the regression vectors, indicating that the calibration was at least partially based on glucose. Since this was a feasibility study, the protocol did not include measurements on the volunteers over a number of days, and thus independent data was not obtained. Further, oral glucose tolerance test protocols are susceptible to correlation with the fluorescence background decay, which may enhance the apparent prediction results. Therefore, more studies, preferably involving glucose clamping performed on different days, are required.

12.8 Toward Prospective Application The results from the in vitro and in vivo studies reviewed above are encouraging. They demonstrate the feasibility of building glucose-specific in vivo multivariate calibration models based on Raman spectroscopy. To bring this technique to fruition, prospective application of a calibration algorithm on independent data with clinically acceptable prediction results needs to be demonstrated. This requires advances in extracting glucose information without spurious correlations, and correcting for variations in subject tissue morphology and color. We have developed two new tools to address these issues. The first is a novel multivariate calibration technique with higher analyte specificity than present techniques, and is more robust against interferent co-variations and chance correlations. This technique, constrained regularization, is described in subsection 12.8.1. In addition, we have developed a new correction method to compensate for turbidity-induced sampling volume variations across sites and individuals. This method, intrinsic Raman spectroscopy, is discussed in subsection 12.8.2. Other considerations for successful in vivo studies, such as reference concentration accuracy and optimal collection site determination, will be discussed in the context of future directions.

12.8.1 Analyte-specific information extraction using hybrid calibration methods Multivariate calibration methods are in general not analyte-specific. Calibration models are built based on correlations in the data, which may be due to the analyte or to systematic or spurious effects. One way to effectively boost the model specificity is by incorporating additional analyte-specific information, such as its pure spectrum. Hybrid methods merge additional spectral information with calibration data in an implicit calibration scheme. In the following, we present two of these methods developed in our laboratory.

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12.8.2 Hybrid linear analysis (HLA) Hybrid linear analysis was developed by Berger et al. [24]. In this method, analyte spectral contributions are first removed from the sample spectra by subtracting the pure spectrum according to reference concentration measurements. The resulting spectra are then analyzed by principal component analysis (PCA), and the significant principal components extracted. These principal components are then used as basis spectra to orthogonalize the pure analyte spectrum. This orthogonalization results in a b vector that is essentially the portion of the pure analyte spectrum that is orthogonal to all interferent spectra, akin to the net analyte signal. HLA was implemented experimentally in vitro with a 3-analyte model composed of glucose, creatinine, and lactate. Significant improvement over PLS was obtained owing to incorporating the pure glucose spectrum in the model development. However, because HLA relies on subtracting the analyte spectrum from the calibration data, it is very sensitive to the accuracy of the spectral shape and intensity. For turbid samples with multiple analytes in which absorption and scattering can alter the analyte spectral features, we find that the performance of HLA is impaired. Motivated by advancing transcutaneous measurement of blood analytes in vivo, constrained regularization was developed as a more robust method against inaccuracies in the pure analyte spectra.

12.8.3 Constrained regularization (CR) To understand constrained regularization, multivariate calibration can be viewed as an inverse problem. Given the inverse mixture model for a single analyte: c = ST b

(12.4)

where capital boldface type denotes a matrix. The goal is to invert Eq. (12.4) and obtain a solution for b. Factor-based methods such as principal component regression (PCR) and PLS summarize the calibration data, [S, c], using a few principal components or loading vectors. In contrast, CR seeks a balance between model approximation error and noise propagation error by minimizing the cost function, Φ [49]:

2 Φ(Λ, b0 ) = ST b − c + Λ kb − b0k2

(12.5)

with kek the Euclidean norm (i.e., magnitude) of e, and b0 a spectral constraint that introduces prior information about b. The first term on the right-hand side of Eq. (12.5) is the model approximation error, and the second term is the norm of the difference between the solution and the constraint, which controls the smoothness of the solution and its deviation from the constraint. If b0 is zero, the solution is the common regularized solution. For Λ = 0 the least squares solution is then obtained. In the other limit, in which Λ goes to infinity, the solution is simply b = b0 . A reasonable choice for b0 is the spectrum of the analyte of interest, because that is the solution for b in the absence of noise and interferents. Another choice is the

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net analyte signal [28] calculated using all of the known pure analyte spectra. Such flexibility in the selection of b0 is possible because of the manner in which the constraint is incorporated into the calibration algorithm. For CR, the spectral constraint is included in a nonlinear fashion through minimizing Φ, and is thus termed a “soft” constraint. On the other hand, there is little flexibility for methods such as HLA, in which the spectral constraint is algebraically subtracted from each sample spectrum before performing PCA. We term this type of constraint a “hard” constraint. Numerical simulations and in vitro experiments indicate that CR gives lower RMSEP than methods without prior information, such as PLS, and that it is less affected by analyte co-variations. We further demonstrated that CR is more robust than HLA when there are inaccuracies in the applied constraint, as often occurs in complex or turbid samples such as biological tissue [27]. The simulation and experimental results for RMSEP are summarized in Table 12.1, where all values were normalized to the PLS values. Glucose and creatinine were used as the analytes of interest with urea the major interferent. India ink and intralipid were used to provide turbidity with absorption and scattering levels similar to those of biological tissue.

TABLE 12.1: Comparison of RMSEP values for PLS, HLA, and CR. Glucose (G) and creatinine (C) are the analytes of interest. All RMSEP values are normalized to those of PLS. Note that all values of turbidity span the physiologically relevant range.

Simulation Clear samples Turbid samples

PLS G&C

HLA G

C

CR G

C

1 1 1

0.64 0.73 1.15

0.53 0.95 1.12

0.8 0.73 0.8

0.59 0.89 0.88

An important lesson learned from this study is that there is a trade-off between maximizing prior information utilization, and robustness concerning the accuracy of this information. Multivariate calibration methods range from explicit methods with maximum use of prior information (e.g., OLS, least robust when the calibration model is inaccurate), hybrid methods with an inflexible constraint (e.g., HLA), hybrid methods with a flexible constraint (e.g., CR), and implicit methods with no prior information (e.g., PLS, most robust, but prone to be misled by spurious correlations). We believe that CR achieves the optimal balance between these ideals in practical situations.

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FIGURE 12.8: Turbidity-induced sampling volume variations simulated by the Monte Carlo method. Steady-state fluence rate owing to excitation for three turbidity-induced sampling volumes: (left) large; (middle) medium; (right) small sampling volume.

12.8.4 Sampling volume correction using intrinsic Raman spectroscopy Sample variability is a critical issue in prospective application of a calibration model. For optical technologies, variations in tissue optical properties, particularly absorption (µa ) and scattering (µs ) coefficients, can distort the measured spectra. Figure 12.8 shows the results from Monte Carlo simulations, demonstrating that the effective sampling volume strongly depends on the optical properties of the medium. Note that the three values of turbidity shown are within the physiologically relevant range. If these turbidity-induced sampling volume variations are not corrected for, large errors will be introduced into the subsequent multivariate analysis. This section provides an overview of techniques to correct turbidity-induced spectral and intensity distortions in fluorescence and Raman spectroscopy. Photon migration theory is employed to model diffuse reflectance, fluorescence, and Raman scattering arising from turbid biological samples. Monte Carlo simulations are employed as an effective and statistically accurate tool to numerically model light propagation in turbid media. Using the photon migration model and Monte Carlo simulations, preliminary results of the use of intrinsic Raman spectroscopy to correct the effects of turbidity are presented. Details of these results will be published separately [50].

12.8.5 Corrections based on photon migration theory Radiative transfer theory [21] provides an intensity based picture of light propagation in turbid media. However, the analytical solution to this integro-differential equation can be found only for very special conditions and approximations. The most extensively studied approximation is diffusion theory, which is used to model photons that undergo multiple scattering events [21]. Another very useful approximation, developed in our laboratory, is photon migration theory [51, 52]. This method employs probabilistic concepts to describe the scattering of light, and sets up a framework for an analytical expression relating the measured fluorescence to the intrinsic fluorescence, defined as the fluorescence as measured from a optically-thin slice of tissue free of the effects of scattering and absorption. This expression has been employed to recover turbidity-free fluorescence spectra from various types of tissue.

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FIGURE 12.9: Ramobs µs′ versus Rd for samples of two different sizes (left) and for two different elastic scattering anisotropies (right). Note that all values of turbidity span the physiologically relevant range.

The correction facilitates interpretation of underlying fluorophores and consequently improves the accuracy of disease diagnosis [33, 53]. The same general principle should hold true for Raman spectroscopy, as well. Unlike fluorescence spectroscopy, spectral lineshape distortions caused by prominent absorbers is less of an issue in the NIR wavelength range. However, for quantitative analysis, the turbidity-induced sampling volume variations become significant. Monte Carlo simulations and experimental results show that the intrinsic Raman signal for arbitrary samples and collection geometries can be described by: Ramint = µs′

Ramobs f (Rd )

(12.6)

with µs′ = µs (1 − g) and g the tissue anisotropy, and f (Rd ) the calibration factor with Rd the diffuse reflectance measured at the Raman wavelength. Fit parameters for f (Rd ) in Eq. (12.6) can be experimentally calibrated, and employed to obtain the intrinsic Raman signal in prospective spectra [54].

12.8.6 Intrinsic Raman spectroscopy (IRS) Figure 12.9 (left) plots the product Ramobs µs′ versus Rd for two sample sizes, using the results from Monte Carlo simulations. A fit to this curve approximates the product of the intrinsic Raman signal and f (Rd ), and can be used to correct for sampling volume variations. We find that the curvature of f (Rd ) depends on the size of the sample. We also find that the curvature depends on g, as shown in Fig. 12.9 (right). Note that the higher spread for the samples of smaller size and larger anisotropy results from less returned photons, and thus a lower SNR. IRS can be implemented either with numerical simulations or tissue phantoms. In either case, the implementation is done in two steps: calibration and application. In

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the calibration step, a set of samples with a wide range of turbidity values (within the physiological range) is studied, with a Raman scatterer of the same concentration inserted in each sample as a probe. Fig. 12.9 (left) can then be generated with fit parameters to obtain the functional form of f (Rd ). This function can then be used in the application step, in which the concentrations of the analytes are varied, to extract the intrinsic Raman signal from the measured Raman signal. Note that to apply IRS one needs to know µs′ for the samples. Extraction of optical properties has been studied by many researchers [55–58]. The majority of methods are based on diffusion theory or its variants. Our laboratory extracts optical properties from biological tissue routinely in other wavelength ranges, and a similar method can be employed for this purpose [56]. Intrinsic Raman spectroscopy is a novel technique. We look forward to incorporating it in our future in vivo studies. In addition, since CR and IRS both address the issues associated with non-analyte-specific correlations, yet from entirely different aspects, they can be applied in tandem. It will be interesting to study the resulting synergistic effects.

12.8.7 Other considerations and future directions CR and IRS are two exciting topics for continued study. As mentioned earlier, there are several other areas also worthy of study. These are briefly discussed below. 12.8.7.1 Data quality Reference concentrations greatly affect the performance of the calibration algorithm. In spectroscopic techniques such as Raman spectroscopy, a large portion of the collected glucose signal likely originates from the glucose molecules in the interstitial fluid (ISF). In addition, it is well known that the ISF glucose concentration in humans lags the plasma glucose concentration by 5 to 30 minutes [59]. As a result, use of plasma glucose as the reference concentration may introduce errors. Methods for extracting interstitial fluid for glucose reference measurements are being developed and should be incorporated in future studies [60, 61]. As discussed in subsection 12.4.2, the background and issues associated with it impose a limit on the SNR, and can influence multivariate calibration. Although the present background subtraction techniques address this issue, there is room for improvement. Thus, methods to reduce the background signal at its origin should be explored. One approach to separate fluorescence from Raman scattering is to study the spectrum at two closely-spaced excitation wavelengths and take the difference between them. It will be interesting to see if this technique can provide insight into the origin of the background signal and its variation. 12.8.7.2 Tissue morphology and skin heterogeneity Sampling depth and sample positioning are critical for optimal collection of glucosespecific Raman scattered light. These may play a role in calibration transfer. In experiments, the effective sampling depth can be estimated from study of extracted

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optical properties, and therefore the correct distance between the sample and the collection optics can be determined for each measurement site. A study of morphological and layered structures at the sampling site with confocal microscopy and a properly designed human-instrument interface could shed light on the sampling depth and positioning. By knowing the exact sampling volume and its coverage of various skin morphological structures, it may be possible to estimate how much of the glucose-containing region (dermis in the two-layer model) is sampled.

12.9 Conclusion Quantitative biological Raman spectroscopy is a powerful technique for non-invasive tissue analysis and analyte concentration measurements. From its early development with in vitro studies, in vivo studies have been realized with the aid of more advanced instrumentation and calibration algorithms. The in vivo studies performed to date have demonstrated the feasibility of obtaining glucose-specific multivariate calibration models. The next step in advancing the technology is to conduct prospective studies. Some of the issues to be addressed are enhancing analyte specificity, correcting for diversity across individuals, and issues relating to improved reference concentrations, and study of the role of tissue morphology and skin heterogeneity. This chapter has reviewed recent developments in the first two categories by introducing constrained regularization and intrinsic Raman spectroscopy. With the aid of additional analyte spectral information, CR effectively improves analyte specificity. IRS, on the other hand, greatly reduces turbidity-induced sampling volume variations, one of the most challenging factors in multivariate calibration. These techniques will play a crucial role in prospective studies involving multiple sites/subjects/ days. We are currently planning a multi-subject and multiple-day in vivo study, first on dogs and then on human subjects. We believe that these new developments will enable us to demonstrate that quantitative Raman spectroscopy can accurately measure blood analyte concentrations prospectively.

Acknowledgments Our own work was performed at the MIT Laser Biomedical Research Center and supported by NIH NCRR, Grant No. P41-RR0594, and a grant from Bayer Health Care, LLC.

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tion of tissue optical-properties in vivo,” Med. Phys., vol. 19, 1992, pp. 879– 888. [56] G. Zonios, L.T. Perelman, V.M. Backman, R. Manoharan, M. Fitzmaurice, J. Van Dam, and M.S. Feld, “Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo,” Appl. Opt., vol.38, 1999, pp. 6628–6637. [57] R.M.P. Doornbos, R. Lang, M.C. Aalders, F.W. Cross, and H.J.C.M. Sterenborg, “The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy,” Phys. Med. Biol., vol. 44, 1999, pp. 967–981. [58] M.G. Nichols, E.L. Hull, and T.H. Foster, “Design and testing of a whitelight, steady-state diffuse reflectance spectrometer for determination of optical properties of highly scattering systems,” Appl. Opt., vol. 36, 1997, pp. 93–104. [59] M.S. Boyne, D.M. Silver, J. Kaplan, and C.D. Saudek, “Timing of changes in interstitial and venous blood glucose measured with a continuous subcutaneous glucose sensor,” Diabetes, vol. 52, 2003, pp. 2790–2794. [60] D.G. Maggs, R. Jacob, F. Rife, R. Lange, P. Leone, M.J. During, W.V. Tamborlane, and R.S. Sherwin, “Interstitial Fluid Concentrations of Glycerol, Glucose, and Amino-Acids in Human Quadricep Muscle and Adipose-Tissue Evidence for Significant Lipolysis in Skeletal-Muscle,” J. Clin. Invest., vol. 96, 1995, pp. 370–377. [61] J.P. Bantle and W. Thomas, “Glucose measurement in patients with diabetes mellitus with dermal interstitial fluid,” J. Lab. Clin. Med., vol. 130, 1997, pp. 436–441.

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13 Tear Fluid Photonic Crystal Contact Lens Noninvasive Glucose Sensors Sanford A. Asher and Justin T. Baca Department of Chemistry, University of Pittsburgh, Pittsburgh, PA 15260, USA

13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8

Importance of Glucose Monitoring in Diabetes Management . . . . . . . . . . . . . . Eye Tear Film . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glucose in Tear Fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Previously Reported Tear Fluid Glucose Concentrations . . . . . . . . . . . . . . . . . . Recent Tear Fluid Glucose Determinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . In Situ Tear Glucose Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Photonic Crystal Glucose Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Financial Disclosures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

388 389 390 392 396 400 401 409 410 410 411

We are developing a photonic crystal contact lens sensor for the noninvasive determination of glucose in tear fluid. Success requires a photonic crystal sensor with the sensitivity to glucose required to differentiate normal levels from hyperglycemic and hypoglycemic levels. In addition, the tear glucose levels need to track those of blood. In this chapter we review our progress in developing a photonic crystal glucose sensor for incorporation into a contact lens. We also review all previous tear fluid glucose studies, which, while suggesting that tear glucose concentrations tracks that of blood, significantly disagree as to the tear glucose concentrations in both normal and diabetic subjects. These studies also disagree as to the relationship between blood and tear fluid glucose concentrations. We also present new measurements of tear glucose concentrations by using a method designed to avoid tear stimulation. We conclude that the various previous tear collection methods biased the measured tear glucose concentrations. We also review recent studies which attempt to monitor tear glucose concentrations in situ by using contact lens-based sensing devices. On the basis of these results, we are optimistic about the future of in vivo tear glucose sensing. Key words: glucose, glucose sensing, photonic crystals, photonic crystal sensors,

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tear fluid glucose, tear collection, tear production, tear stimulation, conjunctiva, glucose transport, in situ tear analysis, contact lens sensors.

13.1 Importance of Glucose Monitoring in Diabetes Management 20.8 million people in the United States and 180 million people in the world are estimated to have diabetes mellitus [1]. The prevalence of this disease is expected to double by 2030 [2]. The cost for treating diabetes related illnesses is estimated to be 10% of all healthcare expenditures in the United States [3]. The Diabetes Control and Complications Trial clearly demonstrated that tight glycemic control is critical to preventing complications such as retinopathy, nephropathy, and neuropathy [4]. Current standards of care require self-monitoring of glucose several times daily, with an increase in frequency for patients receiving insulin [5]. Self-monitoring of blood glucose utilizes finger-stick blood sampling.

FIGURE 13.1: Photonic crystal glucose sensing material for determining tear fluid glucose concentrations. The sensing material is embedded within a contact lens or ocular insert. The color diffracted changes with the tear fluid glucose concentration. A mirrored compact-like device illuminates the sensor with white light. The sensor color is determined by viewing the reflected (diffracted) light and compared to a color wheel calibrated in blood glucose concentration.

While many noninvasive approaches to blood glucose monitoring have been investigated, none have, as yet, replaced fingerstick direct measurements of glucose in

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blood [6]. Recently developed 3-day implantable, continuous glucose sensors show some promise for improving glycemic control [7, 8]. However, the existing approved devices must be calibrated at least twice daily with a direct blood measurement, and must be replaced after 3-7 days. Noninvasive glucose monitoring approaches currently being investigated include IR [9, 10] and Raman spectroscopy [11, 12], birefringence measurements [13], photoacoustic phenomena [14], optical coherence tomography [15], fluorescence [16, 17], surface-plasmon resonance in nanoparticles [18], and electrical impedance measurements [19]. The GlucoWatch (Cygnus, Redwood City, CA) which is a quasi-noninvasive electrochemical measurement device which extracts interstitial fluid through the skin has been approved by the FDA for supplementary blood glucose monitoring. However, it requires frequent calibration against fingerstick blood glucose measurements. We have been working towards developing a photonic crystal contact lens for the noninvasive monitoring of glucose in tear fluid [20-22,24] (Fig. 13.1). Tear glucose in diabetic patients has been studied for over 80 years [23] and recently at least three independent groups have developed glucose sensors that can be incorporated into contact lenses [24–27]. Obviously, for this approach to be successful it is essential that the blood and tear glucose concentrations correlate. Unfortunately, there is presently significant disagreement as to the actual concentrations of tear glucose in normal and diabetic subjects, as well as to how, or whether, tear glucose concentrations correlate with blood glucose concentrations. There is surprisingly little known about the origin of glucose in tear fluid, as discussed below. In this chapter we will present an abbreviated overview of the present understanding of the correlation of tear and blood glucose concentrations and then discuss our photonic crystal tear fluid glucose sensor approach. We also review the other competing approaches for noninvasive tear glucose contact lens sensing. We refer the interested reader to our more extensive review published elsewhere [28].

13.2 Eye Tear Film The tear film on the surface of the eye is composed of several layers. Most superficially there is a lipid layer that is less than 100 nm thick which serves several functions including preventing evaporation of the underlying aqueous layer and providing a smooth optical surface over the cornea [29]. This layer is composed of sterol esters, wax esters, and many other minor lipid components [30]. These are secreted from the Meibomian glands located on the margins of the eyelids, just posterior to the eyelashes. Dysfunction of these glands can lead to increased evaporation of tears from the eye, causing an increased tear osmolarity and clinical dry eye [31]. The lipid layer is compromised when contact lenses are worn; this layer may be completely absent over rigid contact lenses [30]. Just below the lipid layer is a predominantly aqueous layer. Measurements of

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the thickness of this layer over the cornea varies from 2.7 µ m to 46 µ m, with the most recently reported value of 3.3 µ m [32]. In the presence of contact lenses, the aqueous tear film can be measured both in front of the contact lens (pre lens), and between the lens and the cornea (post lens). Both the pre lens and post lens tear films are approximately 3 µ m thick [32]. In both the presence and absence of contact lenses, the tear film is considerably thicker near the margins of the eyelids, where a meniscus forms. The total volume of the aqueous tear film is about 7 µ L [33], and its production and elimination are discussed below. Below the aqueous layer of the tear film is a mucin layer, consisting of glycoproteins which lubricate the eye surfaces. At least 20 different mucins are present. They provide a hydrophilic surface, over which the aqueous fraction rapidly flows [34, 35]. This layer is approximately 30 µ m thick [29] and its components are produced by both the cornea and conjunctiva [36]. The mucin layer moves freely over the glycocalyx, which is comprised of membrane-associated mucins bound to the cornea and conjunctiva. The rate of tear production can vary 100-fold between basal tear production and active tearing [37]. The average rate of tear fluid production ranges between 0.5 and 2.2 µ L/min (with an average of 1.2 µ L/min) at baseline [33]. While estimates of the rate of baseline tear fluid production have not varied significantly since the 1966 report of Mishima et al. [33], the relative contributions of different sources to the aqueous tear fraction continue to be debated. Aqueous tear fluid was thought to be almost entirely produced by the main lacrimal gland with minor contributions from the accessory lacrimal glands and goblet cells in the conjuctiva [38]. Recent studies, however, have shown that the rate of tear fluid flow across the conjunctiva can be as high as 1–2 µ L/min and may account for a large proportion of basal tear production [39]. While estimates of the contribution of conjunctival secretion to basal tear fluid production vary widely, recent models of tear production suggest that 25% of tear fluid is produced by the conjunctiva in the absence of reflex tearing [40]. While the aqueous fraction in stimulated tears derives primarily from the lacrimal glands, unstimulated tears may have significant contributions from conjunctival sources.

13.3 Glucose in Tear Fluid 13.3.1 Tear fluid glucose transport The source of glucose in tears remains unclear. The studies that used mechanically irritating methods to obtain tear fluid find the highest glucose concentrations and find correlations between blood and tear glucose concentrations [38, 41-43]. Mechanical irritation abrades the conjunctiva and probably causes leakage of glucose from epithelial cells or the interstitial space directly into the tear fluid [38, 44]. Studies that attempt to avoid abrasion of the cornea and stimulation of tearing

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measure the lowest glucose concentrations [44–46]. Many studies of chemically stimulated tears also find decreased concentrations of glucose, suggesting that very little, if any, glucose comes from the lacrimal glands [42, 44, 47]. There is only limited evidence for glucose transporters in the tear glands, the conjunctiva, and the cornea. The constitutive glucose transporter, GLUT-1, is present in the apical corneal epithelium [48], but absent in the lacrimal glands and conjunctiva [49]. Expression of GLUT-1 in the corneal epithelium is increased after corneal abrasion, and appears to have a role in corneal wound healing [50]. A sodium/glucose cotransporter, SGLT-1, is present on the apical side of the bulbar and palpebral conjunctiva [51, 52]. This transporter operates in both directions, allowing both secretion and absorption of glucose, depending on sodium and glucose concentrations [53]. While this transporter removes glucose from the tear fluid under physiological conditions [54], it can add glucose to the tear fluid during the hypoosmotic stress that occurs when rinsing the eye with water or swimming [40, 53–55]. Recent models of electrolyte and metabolite transport in the tear fluid suggest that a paracellular transport mechanism is required to fully explain observed electrolyte concentrations [40]. Studies of polyethylene glycol oligomer permeability in the cornea and conjunctiva of rabbits suggest that there are paracellular pores with diameters of ∼4 nm and ∼2 nm in the conjuctiva and cornea respectively [56]. While glucose should be able to pass through these pores and into the tear fluid, its transit has not been directly measured. While the distribution and regulation of glucose transporters affecting the tear glucose concentration are not yet fully characterized, glucose transport across the conjunctiva appears to be the major determinant of tear glucose concentrations in the absence of reflex tearing.

13.3.2 Tear glucose in diabetic subjects If tear glucose analysis is to be used to monitor diabetes, we must consider the effects of diabetes on aqueous tear production and glucose transport in tear fluid. While the relative importance of different molecular mechanisms in diabetes pathogenesis is debated, the increased intravascular concentration of glucose that results from diabetes ultimately leads to microvascular and nerve damage [57, 58]. Damage to either the vasculature supplying blood to the eye or the nerves of the lacrimal reflex arc might be expected to alter tear production. Dry eye is more common in diabetic patients, and correlates with poor glycemic control [59]. Basal tear secretion rates are indistinguishable between normal and diabetic subjects [60, 61]. Reflex tearing, as measured by a Schirmer test, is decreased significantly in diabetic subjects [60, 61], probably due to a decreased sensitivity of the conjunctiva resulting from neuropathy [62]. During episodes of hyperglycemia, increased osmolarity in the extracellular fluid may also impede aqueous tear flux across the conjunctiva or into the lacrimal gland [59]. Increased tear glucose concentrations in diabetic subjects have been repeatedly demonstrated [23, 41–43, 45, 63–66] However, many of these studies used filter paper to collect the tear sample, and the observed high glucose levels may be due to intercellular fluid leaking through the abraded conjunctiva [44]. A recent study of tear

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glucose concentration in 50 non-diabetic subjects and 33 diabetic subjects specifically tried to avoid chemical or mechanical stimulation by collecting tear samples with a glass microcapillary [45]. This study observed overlapping ranges of tear glucose concentration in fasting normal and diabetic subjects, but found a statistically significant increase in average tear fluid concentrations in the diabetic subjects (89 µ M for normal and 150 µ M for diabetic subjects). While tear glucose concentrations are clearly increased in diabetic subjects, the precise mechanism remains unclear. Studies using sampling methods that cause mechanical stimulation of the conjunctiva are likely to be simply measuring analytes in direct equilibrium with intercellular fluid. Studies of non-stimulated tears may measure increased glucose due to paracellular glucose transport in the conjunctiva. It is also possible that these studies did not avoid eye irritation during the required five minute sampling periods [44, 45].

13.4 Previously Reported Tear Fluid Glucose Concentrations Reported values for tear glucose in normal individuals range from 0 to 3.6 mM (65 mg/dL) [55], while concentrations as high as 84 mg/dL (4.7 mM) were reported for diabetic persons [23]. The reported tear glucose concentrations are generally lower for analytical techniques which require smaller tear volumes. Recently, median glucose concentrations of 89 µ M were measured in 5 µ L tear samples [45], while we recently measured 28 µ M concentrations in 1 µ L collected tear samples [46], all from fasting, non-diabetic individuals. Fig. 13.2 shows the variation in the measured tear glucose tear fluid concentrations for all published studies. Older studies generally measured glucose in larger volumes of chemically or mechanically stimulated tears, while more recent studies specifically tried to avoid conjunctival irritation and tear stimulation (Fig. 13.2). Although the dependence of the tear glucose concentration on the collection method was previously noted [44], there has been little discussion of this sampling bias. As discussed below, we developed a new mass spectral method to determine glucose in 1 µ L volumes of tear fluid collected in such a way as to minimally perturb the eye of the subject. We also examined how the tear fluid glucose concentrations track those of blood [28, 46, 67].

13.4.1 Previous measurements of tears in extracted tear fluid The first quantitative report of glucose in tear fluid in 1930 found tear glucose concentrations of 3.6 mmol/L (65 mg/dL) [68]. The tear volume studied was 0.2 mL, requiring that tearing was induced in order to collect such large volumes. Reported values of tear glucose concentrations have steadily decreased as the analytic methods required less sample volume. At the opposite extreme, LeBlanc et al. recently

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FIGURE 13.2: Summary of average tear glucose concentrations found in nondiabetic subjects from 1930 to present. Studies are grouped by the type of stimulation used to induce tearing (chemical, mechanical, and noninvasive). These are arranged in chronological order from left to right within each section. The details of each study are discussed in the tables and text below. Note that studies employing mechanical stimulation measure the highest tear glucose concentrations.

reported an average tear glucose concentration of 7.25 ± 5.47 µ mol/L in five patients in an intensive care unit [69]. Glucose was measured using HPLC with pulsed amperometric detection. The sample volumes studied were variable and were not individually reported, but were presumably less than 1 µ L [70, 71]. The fact that the reported values of tear glucose concentrations varied by more than 1000-fold between all of these studies demonstrates the need for careful consideration and control of experimental parameters such as collection method, analysis method, and selection of the clinical population.

13.4.2 Mechanical tear fluid stimulation Van Haeringen and Glasius compared glucose concentrations in the chemically and mechanically stimulated tears of normal and diabetic subjects [44]. They first stimulated tearing with 2-chloracetophenon and collected 20 µ l tear samples with a capillary tube. They then collected a second tear sample using filter paper strips. Higher tear glucose concentrations for all subjects were measured using filter paper collection. The increase was between 0.1 and 1.5 mM for subjects with blood glucose below 10 mM (180 mg/dL) and as high as ∼9 mM for extremely hyper-

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glycemic subjects with blood glucose concentrations of ∼20 mM (360 mg/dL). A 1969 dissertation by Lax, which is cited by Van Haeringen and Glasius, found glucose concentrations of 0.206 ± 0.027 mM (mean ± SD) using capillary collection and 1.141 ± 0.159 mM using filter paper collection in non-diabetic subjects [44, 72]. Daum and Hill used capillaries to collect 5 µ L tear samples at different times from non-diabetic subjects after mechanical stimulation of the conjunctiva with a cotton applicator [73]. They measured an increase in tear glucose concentration from ∼0.28 mM (∼5 mg/dL) before stimulation to a maximum of ∼2.5 mM (∼45 mg/dL) 10 min after stimulation. Tear glucose concentrations remained elevated for 30 min, but returned to baseline after 60 min. This indicates that unrecognized conjunctival stimulation early in a time course study of tear glucose could affect many subsequent measurements. A similar increase in tear glucose concentration after corneal or conjunctival irritation occurs in rabbits [74, 75]. Daum and Hill also observed an increase in tear glucose after hypoosmotic stress induced by immersion of the eye in distilled water for 60 sec. Studies of mechanically stimulated tears generally find a correlation between the tear and blood glucose. This is not surprising as the glucose measured in these studies likely comes directly from the interstitial space in the conjunctiva. Rabbit studies suggest that short term contact lens use increases tear glucose concentrations in a manner similar to mechanical stimulation [37, 75]. However, it should be noted that our recent study found no statistically significant evidence of increased tear glucose concentrations in fasting subjects wearing contact lenses [46].

13.4.3 Chemical and non-contact tear fluid stimulation Early analytical techniques used to study tear glucose concentration required analyte volumes that would take hours to collect at basal rates of tear secretion. Hence, many studies used a chemical lachrymator to induce tearing and quickly collected samples. In 1984 Daum and Hill collected 5 µ L tear samples every 20 sec for 2 min after non-diabetic subjects were exposed to raw onion vapors for 30 sec [73]. Tear glucose concentrations decreased monotonically from 0.3 mM (6 mg/dL) before tearing, to 0.1 mM (2 mg/dL) at 2 min after exposure. Comparison between studies that chemically stimulated tears is difficult, as different lachrymators were used, some of which caused corneal and conjunctival edema and epithelial erosion or ulceration [76]. Hence, long term exposure to lachrymators may cause a significant increase in glucose concentration as the physical barriers of the ocular surface are compromised. Use of lachrymators is also likely to cause subjects to rub their eyes, which we have anecdotally found to increase tear glucose concentrations [46]. Overall, the average tear glucose concentrations measured in studies of chemically stimulated tears fall within the range of tear glucose concentrations measured in non-stimulated tears. Some studies of chemically stimulated tears do not find a correlation between tear and blood glucose for all subjects [47]. However, these studies were often able to broadly classify subjects as diabetic or non-diabetic through tear glucose measurements, especially when postprandial samples were considered

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[42, 64].

13.4.4 Non-stimulated tear fluid With the development of more sensitive analytical methods there were attempts to determine glucose concentrations in non-stimulated, or basal tears. These nonstimulated tear samples are generally collected with a capillary by gently touching it to the tear film meniscus. One of the first large studies of non-stimulated tears measured an average tear glucose concentration of 0.42 ± 0.356 mM in 875 tear samples from 12 non-diabetic subjects [55]. This average tear glucose concentration was somewhat higher than more recent measurements of chemically stimulated tears. While studies using lachrymators could be measuring artificially low tear glucose concentrations, it is also possible that some mechanical stimulation was involved in the collection of basal tears in this study. The method used in that study required sample volumes of 5 µ L, which would require sample collection times over at least 5 min. Even if mechanical stimulation were avoided during sampling, increased evaporation due to the prolonged suppression of blinking could alter the glucose concentration. One of the largest and most recent studies of tear glucose by Lane et al. [45] monitored tear glucose concentration in 73 non-diabetic subjects and 48 diabetic subjects before and after an oral glucose bolus. These groups were further divided into fasting and non-fasting groups. The 5 µ L tear samples collected at each time point were analyzed with liquid chromatography-pulsed amperometric detection. Average tear glucose concentrations found for non-diabetic subjects was 0.16 ± 0.03 mM while average tear glucose concentrations for diabetic subjects was 0.35 ± 0.04 mM (mean ± standard error). Individual glucose determinations, however, varied from below the limit of detection to over 9.1 mM. They were able to show a modest correlation between average tear and blood glucose concentrations at the five time points in the study. Unfortunately, only results averaged over the subject population were given. Thus, there is no direct indication of how well tear and blood glucose concentrations correlate within individual subjects. The collection of 5 µ L tear samples may have precluded the study of truly non-stimulated tears for the reasons noted previously. A few recent studies analyzed µ L or sub µ L tear volumes [46, 67, 69, 70, 77]. The previously mentioned study of critically ill patients attempted to assess the feasibility of monitoring tear glucose instead of blood glucose in an intensive care unit [69]. The investigators obtained 44 simultaneous blood and tear samples from 5 sedated subjects receiving insulin, two of whom had a history of diabetes. This study measured the lowest average tear glucose concentration (7.25 ± 5.47 µ mol/L) of any study where glucose was detected in tears. Despite a wide range of blood glucose concentrations, the study did not detect a clinically useful correlation. However, these data obtained from critically ill patients are likely of little use in predicting whether tear fluid can be used to monitor glucose in more healthy people. However, it is clear that tear glucose monitoring with this method in the ICU is not a feasible replacement for blood glucose monitoring.

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13.5 Recent Tear Fluid Glucose Determinations We recently found a median (range) tear glucose concentration of 28 (7–161) µ M or 0.50 (0.13–2.90) mg/dL in 25 fasting subjects [46]. The mean ±(standard deviation) tear glucose concentration was 37 ± 37 µ M. We found a highly skewed distribution of tear glucose values; tear glucose concentrations were <42 µ mol/L in 80% of subjects. We found no statistically significant difference between contact lens wearers and non-wearers. Linear regression showed a modest correlation between tear and blood glucose concentrations (R = 0.5). We compared tear glucose concentrations within subjects over 30 min and did not see any significant trend with time, suggesting that in our study conjunctival irritation was minimized or eliminated. We believe our study to be the most reliable measurements of baseline tear glucose to date because we collected only 1 µ L tear samples, studied non-diabetic fasting subjects, and found negative evidence for the occurrence of conjunctival stimulation. As described in detail above, there is very little reliable information on whether glucose concentrations in unstimulated tears track blood glucose concentrations. While previous studies showed correlations between averaged tear and blood glucose concentrations, there is little direct information about the existence of such a correlation within individual subjects.

FIGURE 13.3: Tear and blood glucose concentrations in a non-diabetic, male subject. Blood glucose concentration doubles by ∼ 70 minutes after glucose ingestion.

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We recently used our mass spectrometry method to investigate the relationship between blood and tear glucose concentrations in subjects during a glucose tolerance test (oral administration of 75 grams of glucose) [67]. Fig. 13.3 shows how blood and tear glucose concentrations track over time for a non-diabetic subject. The rise of tear glucose concentrations appear to track that of blood glucose in this subject with a time lag of ∼20 min. The left eye tear glucose concentration remains elevated even after the blood glucose concentration decreases. While this may be the true physiological response for this subject, it could also be explained by an unrecognized irritation of the left conjunctiva during the latter half of the experiment (140–160 min). An essential point is that, while the blood glucose concentration increases ∼2-fold, the left and right eye tear glucose concentrations both increase ∼7-fold. This demonstrates a complex relationship between tear and blood glucose concentrations for this subject. Fig. 13.4 shows a similar plot of blood and tear glucose concentrations during a glucose tolerance test for a diabetic subject. Blood and tear glucose glucose concentrations are clearly higher for the diabetic subject at all times, even at the beginning of the study, when subjects are fasting. Prior to glucose ingestion, the blood glucose concentration in this subject was about twice that for the non-diabetic subject of Fig. 13.3. However, the basal tear glucose concentration of the diabetic subject is ∼10fold higher than for the non-diabetic subject! This clearly continues to demonstrate a complex relationship between tear and blood glucose concentrations.

FIGURE 13.4: Tear and blood glucose concentrations in a diabetic, female subject. Blood glucose concentration peaks at ∼ 80 minutes after glucose ingestion with a ∼ 60% increase. The extraordinary ∼5 fold increase in tear glucose concentration after glucose in-

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gestion in the left eye differs completely from the change in the right eye, where (excepting for the single point at ∼95 minutes) a ∼60% increase in tear glucose concentration occurs which is roughly proportional to the increase in blood glucose concentration. Except for that point the lag time is similar to that for the non-diabetic subject. It is possible that the dramatic increase in the left eye tear glucose concentrations results from unrecognized conjunctival irritation, causing interstitial glucose to leak into the tear fluid. A replicate of the glucose tolerance test shown in Fig. 13.3, with the same nondiabetic subject, demonstrates the challenges of determining a correlation between tear and blood glucose concentrations (Fig. 13.5). Identical sampling and tear glucose determination procedures were followed, and the same glucose load was given. Prior to glucose ingestion the blood glucose concentrations were similar for both measurements (∼105 mg/dL). Basal tear glucose concentrations at the earliest times were also similar (∼20 µ mol/L). In contrast to the first study, we see an abrupt extraordinary increase in the tear glucose concentration before glucose intake. The right eye tear glucose concentration increases by ∼100 fold, while the left eye tear glucose concentration increases by ∼50 fold, suggesting non-physiologic transport of glucose into the tear fluid. The timing and magnitude of this spike in tear glucose concentration suggests that the increase may be due to a perturbation during sampling. While we attempted to exclude this possibility, the increased glucose concentration in both eyes might suggest that the subject may have rubbed their eyes after slight conjunctival irritation. The tear glucose concentrations appear to return to baseline after about 60 min. This timescale agrees with that of Daum and Hill measured for tear glucose to return to baseline after the conjunctiva was stimulated by a cotton applicator [73]. When the results of the replicate study are plotted on the same scale as Fig. 13.3, we see that the tear glucose concentrations at latter times (after 60 min) appear to track changes in the blood glucose concentration. However, the relative tear glucose elevation (∼5-fold) in the left eye is much less than observed in the previous study of Fig. 13.3, whereas the relative increase in tear glucose concentration in the right eye is comparable. To summarize, considering the large number of studies we have carried out we conclude that tear glucose concentrations generally correlate with an increase in hyperglycemic blood glucose concentrations. Repeat measurements of tear glucose concentrations in the presence of a constant blood glucose concentrations appear to show a constant ratio between the tear and blood glucose concentrations. After glucose ingestion, the blood and tear glucose concentrations generally increase together, with an apparent 20–30 min delay between increases in blood glucose and in tear glucose concentrations. In our other studies of tear glucose concentrations in subjects undergoing glucose tolerance test, we see only a few instances of the 50–100-fold spikes in tear glucose concentration seen in Fig. 13.5. In general, these abrupt changes do not seem to correlate between the different eyes of the same subject. Our preliminary results suggest that tear glucose may differ between the left and right eye of a single subject. While we previously showed a general correlation be-

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FIGURE 13.5: Tear and blood glucose concentrations in a replicate of the study shown in Fig. 13.2. a) The tear glucose concentration scale must be expanded to show the large and abrupt increase in tear glucose before glucose intake. Blood glucose concentration peaks at ∼ 40 min after glucose ingestion with a ∼ 80% increase. b) Plotting the tear glucose on the same scale as in Fig. 13.2 highlights that the tear glucose concentration appears to track the blood glucose concentration except for the early spike in tear glucose concentrations.

tween the tear glucose in the right and left eyes of fasting subjects [46], we occasionally observe significant differences in glucose concentration between eyes. While we do not yet have enough data to specify the precise relationship between tear and blood glucose concentrations over time and the variation of this correlation between subjects, we believe that our tear collection method, which specifically attempts to avoid mechanical stimulation of the conjunctiva, could definitively answer some of the outstanding questions regarding the utility of tear glucose sensing for monitoring

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or detecting diabetes, if enough subjects were studied to deconvolve the deviations due to sampling perturbations of the eye. It is important to note that tear fluid glucose concentration studies represent among the most challenging bioanalytical chemistry sample collection challenges: it is essential to note that reflex tearing can also be elicited for psychological reasons. Nevertheless, the large body of tear fluid studies, including our recent studies, clearly indicate that blood and tear glucose concentrations are correlated for probably most individuals.

13.6 In Situ Tear Glucose Measurements There are limited reports of in situ tear glucose determinations using contact lensbased devices. March et al. developed and reported the first clinical trial of a contact lens tear glucose sensor [26]. This sensor uses fluorescence to report on the tear glucose concentration using a competitive binding mechanism. They showed that as the glucose concentration increases in the modified contact lens, quenching groups were displaced resulting in an increase in the fluorescence intensity. Unfortunately, in this study, the absolute fluorescent signal was not calibrated which prevented determination of absolute glucose concentrations. Rather, the fluorescence intensity changes demonstrated relative changes in the tear glucose concentrations. This group also developed a hand held fluorometer to monitor the fluorescent signal. March et al. reported a glucose tolerance test for five diabetic subjects wearing these in situ sensors. The fluorescent signal appears to track blood glucose concentrations. However, the response had to be individually scaled for each subject in order for the fluorescence signal to fit the blood glucose concentration profile. This study clearly shows, however, that changes in tear and blood glucose concentration correlate. Domschke et al. developed a holographic, glucose-sensitive contact lens and tested it in a single subject [27]. The wavelength of light diffracted from the contact lens changed as the holographic spacing changed in response to glucose binding in a manner similar to our photonic crystal sensors discussed below. A red-shift in the diffracted wavelength resulted from an increase in glucose concentration. This sensor motif eliminates the challenge of measuring absolute fluorescence intensities. This sensor also detected relative changes in tear glucose concentrations. Domschke et al. did not show a calibration curve for the diffracted wavelength dependence on glucose concentration, but only reported changes in the peak diffraction wavelength as a function of time. The peak diffraction wavelength monitoring tear glucose concentrations appeared to track the increasing blood glucose concentrations with little or no delay. These important in situ results clearly demonstrate correlations between blood and tear glucose concentrations. What is not clear is whether these anecdotal studies are reproducible within individuals over different days and weeks. Also it is still un-

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known whether the blood and tear glucose correlations are identical between normal people or between diabetic subjects. The results to date suggest that the worst case scenario is that a reliable and useful correlations between blood and tear glucose occur for only a subset of the population and that the correlations between tear fluid and blood glucose differ between individuals. Thus, the use of a contact lens glucose sensor in the future may require fitting by a physician who would determine the correlation and sensor sensitivity required for the glucose sensing contact lens. The value of using a glucose sensing contact lens to achieve a noninvasive method to easily and continuously monitor the glucose concentrations would revolutionize life for people with diabetes mellitus. We believe that there is clearly enough evidence of a correlation between tear and blood glucose to justify continued efforts to develop contact lens glucose sensors such as the contact lens photonic crystal glucose sensor described below.

13.7 Photonic Crystal Glucose Sensors Our program [20–22, 24] to develop a tear fluid glucose sensing device envisions a photonic crystal sensing disc encased within either a contact lens or an ocular insert, as shown in Fig. 13.1. The ocular insert would be used by subjects who do not tolerate contact lenses well. The ocular insert, which consists of the photonic crystal sensor sandwiched between thin dialysis membranes, would be placed beneath the lower eyelid.

FIGURE 13.6: Prototype of IPCCA photonic crystal glucose sensor in commercial contact lens on glass eye.

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Diabetic subjects would use a mirror to examine the color of the photonic crystal sensor in the contact lens or the ocular insert. For the ocular insert, the lower eyelid would be lowered to view the photonic crystal color. The color reflected (diffracted), which will vary with the tear fluid glucose concentration, would be viewed with a mirror and compared to that of a color wheel whose colors are calibrated in terms of the blood glucose concentrations. For those people who find it difficult to do color matching we will instrument this measurement by using a simple spectrometer which utilizes a color camera.

CCA Self-Assembly H+

XH

HX

Solvent

-X

H+

HX

H+

-X

XH

H+

Dialysis / Ion Exchange Resin - - -- -- -- -

+ + + + + ++ + + + + + + +

Self-Assembly

-

+

+ +

-- - -- - + +

X-

X-

+ --+ -+ - --+- - - - +- - --- +- - -- - - - -+ - - ++ +- - -- - - + +- - -- - +-- -- - + + - - -- - -- + - -- -+ - -+-- - - + - --- - +- + - - -- -- + - - -- - - -- -- - - + -- - -+ -- -+ - -+- + -- -- - -++ -- -- + + + +-+- - -- - + - -- - ++- - -- - - - -+- -- - - ++- -- -+ - - -- + - +- --- - --+ - - -- -- -- - - -- + + +- - -- - - - ++- - - -- - -- + -- +- - - + - -+ +

FIGURE 13.7: A dispersion of monodisperse colloidal particles with strong acid groups on their surfaces self-assemble into fcc or bcc crystalline colloidal arrays in low ionic strength solution. Ions can be removed from colloidal dispersions by techniques such as dialysis, for example.

Fig 13.6 shows our first prototype of the photonic crystal sensor embedded within a commercial contact lens placed on a glass eye. The contact lens contours to the eye allowing the embedded photonic crystal sensor to contact the tear fluid. The sensor changes diffraction wavelength in response to changing glucose concentrations. We fabricate the glucose sensing photonic crystals by using crystalline colloidal self-assembly [78] to form the photonic crystal template (Fig. 13.7). In this approach highly charged monodisperse spherical polystyrene colloidal particles are synthesized, for example, by using emulsion polymerization [79]. These particles are then cleaned by dialysis and ion exchange and then dispersed in pure water. The synthesized spherical particles are also functionalized with thousands of strong acid groups which ionize in water to result in a high surface charge (Fig. 13.7). Be-

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FIGURE 13.8: The potential energy of repulsion between two charged colloidal particles separated by distance r, U(r) is given by the DLVO potential which depends upon the number of charges, Z, the electron charge, e, the dielectric constant, ε , the radius, a, the Boltzmann constant, kB , the temperature, T , and the particle concentration, n p . κ is the inverse of the Debye length which depends on the concentration of ionic impurities, ni . U(r) can be much larger than kB T resulting in the self-assembly of the colloidal particles into a robust fcc CCA.

cause these highly charged spheres repel each other over macroscopic distances (Fig. 13.8), the system finds a well defined minimum energy state where the particles selfassemble into an fcc lattice [80]. Diffraction from the CCA photonic crystals is extraordinarily efficient. For example, Fig. 13.9 shows transmission measurements through an fcc colloidal crystal [81] made from ∼120 nm diameter polystyrene spheres in water which is oriented with the normal to the fcc (111) planes parallel to the incident light propagation direction. The diffraction of ∼500 nm light gives rise to a symmetric bandshape as shown in the Fig. 13.9 extinction spectra whose ordinate is scaled as -log of the transmission. We fabricated more robust photonic crystal materials (Fig. 13.10) by polymerizing acrylamide hydrogels around the CCA lattice of colloidal particles [82]. These polymerized CCA (PCCA) possess the responsive properties of hydrogels. These PCCA can also be chemically functionalized to make them responsive to changes in their chemical environment. This enables the fabrication of novel chemical sensing photonic crystals [83]. The resulting volume changes in response to changes in chemical

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FIGURE 13.9: Extinction spectra of CCA of ∼120 nm polystyrene particles. The ∼500 nm diffraction band shows a top-hat profile since all incident light within a 5 nm bandwidth is diffracted. The diffraction blue-shifts as the crystal is tilted to 80o off normal, as expected from Bragg’s law.

environment alter the diffraction wavelength which results in an optical readout of the presence and concentration of analytes. A crosslinked hydrogel is a responsive soft material whose volume is controlled by three competing phenomena [83] (Fig. 13.11), the free energy of mixing of the hydrogel polymer with the medium, electrostatic interactions of charges bound to the hydrogel, and the restoring forces due to the hydrogel crosslinks. The free energy of mixing of the hydrogel with the medium involves the entropic propensity of the hydrogel to fill all space (analogous to the entropy increase associated with the expansion of an ideal gas), and an enthalpic term which accounts for dissolution of the hydrogel polymer into the medium. The electrostatic free energy gives rise to osmotic pressures associated with electrostatic interactions between bound charges and the changes in the water chemical potential associated with the immobilization of counterions within the hydrogel system. Each charge immobilizes at least one counterion, to give rise to a hydrogel Donnan potential in low ionic strength solution, which causes water to flow into or out of the hydrogel. Finally, the crosslinks act to determine the lengths of the hydrogel chains whose configurational entropy constrains the hydrogel volume to prevent hydrogel volume expansion. We functionalized [83] the PCCA with molecular recognition agents to create intelligent PCCA (IPCCA) which can be used for chemical sensing applications. These molecular recognition agents are designed to actuate hydrogel volume changes as they interact with their target analytes. These volume changes alter the embedded CCA lattice constant, which results in diffraction wavelength shifts which report on the analyte concentrations.

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PCCA Fabrication

+ - - +---+ - - + - - --- - +- - - -+ - - --- - + +- - --- - +- - - + +- - --- - -- +-- -- - + + + - - -- - -- + - -+- - - + - --- - +- + - -+-- -- - - -- - - - - - + - -- - - -- + -- -+ - -+- + -- -- - -+ + -- -- + - -+ - + +-+ - -- - + - - --- - -- -++ -- - -+- -- - - ++- --- -+ - - -- + -+- --- - --+ -- -- - -- -- -- - + -+ - - + +- - - --+ - - --- -- + -+- - - + - -+ - -+ +-

+ - - +---+ - - + - - --- - +- - - -+ - - --- - + +- --- - +- - - + +- - --- - - +- -+ -- -- - - - - -+ + - --- Acrylamide - +- - + - - + - - +- + - --+- - Bisacrylamide - - -- - -- - - - + - -- - - -- + - --- + - + + + - -- - + -+- - -- - -- Photopolymerize +- -+ + -- - - - - -+ -- - + + - -- - - +- - - +- - -+- +- -- -+ - - -- + - - -- -- -+ - - --+ -- -- -- - -- +- - -- - -+ - - + +- - - --+ - - + -- -+- - - + - -+ + +-

FIGURE 13.10: Synthesis of polymerized colloidal array (PCCA) by adding polymerizable monomers of acrylamide and bisacrylamide and a UV initiator to a CCA. UV polymerization forms a hydrogel network around the CCA (∼90 % water). The CCA crystal structure is maintained during polymerization and also upon hydrogel volume changes.

The selectivity of these IPCCA sensing materials are determined by the selectivities of their molecular recognition agents. Our first glucose sensor was highly selective for glucose since we used the enzyme glucose oxidase (GOD) [83]. GOD converts glucose to gluconic acid. During this reaction a flavin is reduced on the enzyme. This anionic flavin acts as an anion immobilized onto the hydrogel, which gives rise to a Donnan potential which swells the PCCA in proportion to the glucose concentration. This GOD PCCA operates as a steady-state glucose sensor since oxygen in solution reoxidizes the flavin. When oxygen is excluded, concentrations of glucose as low as 10−12 M are easily determined [83]. We recently developed another glucose IPCCA sensor that also utilizes a Donnan potential by attaching boronic acid recognition groups to the PCCA [20–22, 24]. Boronic acid derivatives are known to bind to the cis diols of carbohydrates such as glucose. The binding of glucose to neutral boronic acid derivatives shifts the boronic acid equilibrium towards the anionic boronate form. This charged boronate attached to the hydrogel results in a Donnnan potential which results in an osmotic pressure which swells the IPCCA. As shown in Fig. 13.12, this IPCCA is an excellent glucose sensor for low ionic strength aqueous solutions [22]. We also developed a glucose sensor for high ionic strength bodily fluids such as in our target tear fluid [20–22, 24]. This sensor motif utilizes changes in the hydrogel

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Hydrogels are Responsive Enabling Materials FREE ENERGY CONTRIBUTIONS TO GEL VOLUME

D Gtot = D Gmix + D Gion + D Gelas

+ D Gmix

+

D Gion D G mix D Gelas D Gelas

FIGURE 13.11: Dependence of hydrogel volume on the free energy of mixing, the free energy of ionic interactions, and the free energy associated with the elastic constraints of the hydrogel crosslinks. The hydrogel volume in equilibrium with bulk water is determined by the balance of osmotic pressures induced by these phenomena.

crosslinking induced by glucose binding. This sensor, which also utilizes boronic acids, additionally incorporates polyethylene glycols in order to bind Na+ to screen the charge repulsion between the two boronate anions which bind to the two cis diols of glucose. Glucose is one of the few natural sugars that has two appropriately oriented cis diols that can form cross links as shown in Fig. 13.13. The formation of these crosslinks shrinks the hydrogel as shown in Fig. 13.14 and blue shift the diffraction for glucose concentrations between 0 and 10 mM (which spans the physiological ranges of glucose in tear fluids and blood). Higher glucose concentrations break the crosslinks because the higher concentrations of glucose allow glucose molecules to singly bind to each boronic acid groups. The visually evident IPCCA diffraction color shifting is clearly seen in the photographs of the IPCCA seen in Fig. 13.14. Although the diffraction wavelength is angularly dependent as evident from Bragg’s law, the possible variation about normal incidence is negligibly small, when viewed by reflection in the compact mirror assembly shown in Fig. 13.1 above. The sensitivity of the glucose sensors is presently within a factor of four of that needed to function as a hyperglycemic sensor in tear fluid. We also now understand the equilibrium sensing mechanism in sufficient detail such that we can fully model this sensor response using our fundamental understanding of the hydrogel volume phase transitions.

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FIGURE 13.12: Response to glucose of boronic acid IPCCA. The IPCCA in pure water redshifts as the glucose concentration increases until ∼ 3 mM glucose concentration where the response saturates.

O

O OH

OH

O

-B HO O

+ Na

O O

O

O

O O

O

O

GLU

+

O

Na

O O

-

B

OH

FIGURE 13.13: Model of crosslinks formed by a glucose molecule across two boronic acid groups within the IPCCA. The polyethylene glycol serves to localize two Na+ cations next to the boronates to reduce the electrostatic repulsion between them.

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FIGURE 13.14: Glucose concentration dependence of diffraction of the AFBAAA-PEG PCCA sensor in 2 mM gly-gly buffer at pH 7.4, 150 mM NaCl. Top: diffraction color changes from red to blue upon glucose concentration increases. A) The dependence of diffraction wavelength on glucose concentration. The diffraction peaks are labelled with their glucose concentration (mM). B) Dependence of diffraction peak maxima on glucose concentration.

We find similar responses of these IPCCA glucose sensors to glucose in synthetic tear fluid solutions as compared to that in buffered saline (2 mM gly-gly, pH=7.4, 150 mM NaCl). The fact that we do not observe any interference from the additional species present in the tear fluid indicates the viability of our sensing approach for determining glucose in tear fluid. The acrylamide IPCCA glucose sensors originally responded rather slowly to changes in glucose concentrations (∼30 min). We worked to modify the hydrogel composition to increase the response rate such that it could sense changes in glucose concentrations at rates comparable to the expected rates of change of glucose

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600

590

580

570

560 0

20

40

60

80

FIGURE 13.15: Response kinetics of hexylacrylate IPCCA glucose sensors upon exposure to multiple additions of a freshly prepared 0.2 mM D-glucose solution in 5 mM gly-gly buffer, 150 mM NaCl, pH=7.4 at 37o C. A repeatable rapid blue shift of diffraction is observed which saturates within ∼5 min. concentrations in blood. After examining diffusion constants of molecules in the IPCCA hydrogel we hypothesized that the response speed limit was determined by the friction experienced by the water and hydrogel polymer that limit the water and hydrogel polymer terminal flow velocity in response to the osmotic pressure. We recently incorporated hydrophobic monomers into the hydrogel to decrease the extent of hydrogen bonding of water to the hydrogel polymer. This successfully increased the response rate, making it adequate for physiological sensing [21] (Fig. 13.15). We are still working to increase the sensor glucose sensitivity to make it useful for the visual determination of the normal ∼30 µ M tear fluid glucose concentrations. The remaining challenges are to demonstrate that these sensors successfully determine glucose in situ and that variations in the basal tear glucose concentration are not large enough to confound correlations between tear fluid and blood glucose concentrations. We are presently investigating these issues.

13.8 Summary It is clear that the glucose concentrations in tear fluid track that of blood for a significant number of individuals. This indicates that a glucose sensor within a contact lens has the potential to revolutionize glycemic determination and glycemic control

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in subjects with diabetes mellitus. We have developed a new photonic crystal glucose sensor that we are incorporating into a contact lens. While there is significant risk in this endeavor, it also has the possibility to dramatically aid human health.

Acknowledgments This research was supported by the National Institutes of Health Fellowship 1 F31 EB004181-01A1 to Justin T. Baca, and Grant 2 R01 EB004132 to Sanford A. Asher.

Financial Disclosures Sanford A. Asher is the scientific founder of Glucose Sensing Technologies LLC, a company developing PCCA sensors for glucose sensing.

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[54] O.A. Candia, “Electrolyte and fluid transport across corneal, conjunctival and lens epithelia,” Exp. Eye Res., vol. 78, 2004, pp. 527–535. [55] K.M. Daum and R.M. Hill, “Human tear glucose,” Invest. Ophthalmol. Vis. Sci., vol. 22, 1982, pp. 509–514. [56] K.M. Hamalainen, K. Kananen, S. Auriola, K. Kontturi, and A. Urtti, “Characterization of paracellular and aqueous penetration routes in cornea, conjunctiva, and sclera,” Invest Ophthalmol. Vis. Sci., vol. 38, 1997, pp. 627–634. [57] The Writing Team for the Diabetes Control and Complications Trial/Epidemiology of Diabetes Interventions and Complications Research Group. “Effect of intensive therapy on the microvascular complications of type 1 diabetes mellitus,” J. Am. Med. Assoc., vol. 287, 2002, pp. 2563–2569. [58] G.L. King and M. Brownlee, “The cellular and molecular mechanisms of diabetic complications,” Endocrinol. Metab. Clin. North Am., vol. 5, 1996, pp. 255–270. [59] I. Kaiserman, N. Kaiserman, S. Nakar, and S. Vinker, “Dry eye in diabetic patients,” Am. J. Ophthalmol., vol. 139, 2005, pp. 498–503. [60] M. Goebbels, “Tear secretion and tear film function in insulin dependent diabetics,” Br. J. Ophthalmol., vol. 84, 2000, pp. 19–21. [61] T.R. Stolwijk, J.A. van Best, H.H.P.J. Lemkes, R.J.W. de Keizerl, and J.A. Oosterhuis, “Determination of basal tear turnover in insulin-dependent diabetes mellitus patients by fluorophotometry,” Int. Ophthalmol., vol. 15, 1991, pp. 337–382. [62] M. Dogru, C. Katakami, and M. Inoue, “Tear function and ocular surface changes in noninsulin-dependent diabetes mellitus,” Ophthalmol., vol. 108, 2001, pp. 586–592. [63] M.S. Gaur, G.K. Sharma, S.G. Kabra, P.K. Sharma, and L.K. Nepalia, “Tear glucose in uncontrolled and chemical diabetics,” Indian J. Ophthalmol., vol. 30, 1982, pp. 367–369. [64] P.R. Chatterjee, S. De, H. Datta, S. Chatterjee, M.C. Biswas, K. Sarkar, and L.K. Mandal, “Estimation of tear glucose level and its role as a prompt indicator of blood sugar level,” J. Indian Med. Assoc., vol. 101, 2003, pp. 481–483. [65] R.K. Mediratia and J.N. Rohatgi, “Glucose-estimation in tear fluid–its diagnostic significance–a preliminary study,” Indian J. Ophthalmol., vol. 31, 1983, pp. 635–638. [66] B.M. Desa, M.T. Desai, and B.C. Lavingia, “Tear and blood glucose levels in diabetes mellitus,” J. Assoc. Physicians India., vol. 35, 1987, pp. 576–577. [67] C.R. Taormina, J.T. Baca, S.A. Asher, J.J. Grabowski, and D.N. Finegold, “Analysis of tear glucose concentration with electrospray ionization mass spectrometry,” J. Am. Soc. Mass Spectrom., vol. 18, 2007, pp. 332–336.

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[68] F. Ridley, “The intraocular pressure and drainage of the aqueous humor,” Exp. Path., vol. 11, 1930, pp. 217–240. [69] J.M. LeBlanc, C.E. Haas, G. Vicente, and L.A. Colon, “Evaluation of lacrimal fluid as an alternative for monitoring glucose in critically ill patients,” Intensive Care Med., vol. 31, 2005, pp. 1442–1445. [70] Z. Jin, R. Chen, and L.A. Colon, “Determination of glucose in submicroliter samples by CE-LIF using precolumn or on-column enzymatic reactions,” Anal. Chem., vol. 69, 1997, pp. 1326–1331. [71] Y.C. Lee, “Carbohydrate analyses with high-performance anion-exchange chromatography,” J. Chromatogr. A., vol. 720, 1996, pp. 137–149. [72] F. Lax, “Uber die Spiegel einiger Metaboliten in der Tranenflussigkeit,” Inaugural- Dissertation, Marburg, 1969. [73] K.M. Daum and R.M. Hill, “Human tears: glucose instabilities,” Acta. Ophthalmol., vol. 62, 1984, pp. 530–536. [74] M. Reim, F. Lax, H. Lichte, and R. Turss, “Steady state levels of glucose in the different layers of the cornea, aqueous humor, blood and tears in vivo,” Ophthalmologica, vol. 154, 1967, pp. 39–50. [75] H. Kilp and B. Heisig, “Glucose and lactate concentration in tears of rabbits following mechanical stress and wearing of contact lenses,” Albrecht V Graefes Arch. Klin. Exp. Ophthal., vol. 193, 1975, pp. 259–267. [76] E.J. Olajos and H. Salem, “Riot C,” J. Appl. Toxicol., vol. 21, 2001, pp. 355– 391. [77] S.A. Perezand and L.A. Colon, “Determination of carbohydrates as their dansylhydrazine derivatives by capillary electrophoresis with laser-induced fluorescence detection,” Electrophoresis, vol. 17, 1996, pp. 352–358. [78] R.J. Carlson and S.A. Asher, “Characterization of optical diffraction and crystal structure in monodisperse polystyrene colloids,” Appl. Spectrosc., vol. 38, 1984, pp. 297–304; P.L. Flaugh, S.E. O’Donnell, and S.A. Asher, “Development of a new optical wavelength rejection filter: demonstration of its utility in Raman spectroscopy,” Appl. Spectrosc., vol. 38, 1984, pp. 847–850; S.A. Asher, U.S. Patent # 4,627,689, #4,632,517 (1986); S.A. Asher, P.L. Flaugh, and G. Washinger, “Crystalline colloidal Bragg diffraction devices: the basis for a new generation of Raman instrumentation,” Spectroscopy, vol. 1, 1986, pp. 26–31. [79] C. Reese, C. Guerro, J. Weissman, K. Lee, and S.A. Asher, “Synthesis of highly charged, monodisperse polystyrene colloidal particles for the fabrication of photonic crystals,” J. Colloid and Interface Sci.., vol. 232, 2000, pp. 76–80; C. Reese and S.A. Asher, “Emulsifier-free emulsion polymerization produces highly charged, monodisperse particles for near infrared photonic crystals,” J. Colloid Interface Sci., vol. 248, 2002, pp. 41–46.

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[80] J.C. Zahorchak, R. Kesavamoorthy, and R.D. Coalson, “Melting of colloidal crystals: a Monte Carlo study,” J. Chem. Phys., vol. 96, 1992, pp. 6873–6879. [81] P.L. Flaugh, S.E. O’Donnell, and S.A. Asher, “Development of a new optical wavelength rejection filter: demonstration of its utility in Raman spectroscopy,” Appl. Spectr., vol. 38, 1984, pp. 847–850. [82] S.A. Asher, J. Holtz, L. Liu, and Z. Wu, “Self assembly motif for creating submicron periodic materials. Polymerized crystalline colloidal arrays,” J. Am. Chem. Soc., vol. 116, 1994, pp. 4997–4998; S.A. Asher and S. Jagannathan, U.S. Patent # 5,281,370 (1994); G. Haacke, H. P. Panzer, L.G. Magliocco, and S.A. Asher, U.S. Patents # 5,266,238 (1993), #5,368,781 (1994). [83] J.H. Holtz and S.A. Asher, “Polymerized colloidal crystal hydrogel films as intelligent chemical sensing materials,” Nature, vol. 389, 1997, pp. 829–832; J.H. Holtz, J.S.W. Holtz, C.H. Munro, and S.A. Asher, “Intelligent polymerized crystalline colloidal arrays: novel chemical sensor materials,” Anal. Chem., vol. 70, 1998, pp. 780–791.

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14 Pulsed Photoacoustic Techniques and Glucose Determination in Human Blood and Tissue Risto Myllyl¨a, Zuomin Zhao and Matti Kinnunen Department of Electrical and Information Engineering, University of Oulu, 90014 Oulu, Finland

14.1 14.2 14.3 14.4 14.5

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theoretical Aspects of PA Techniques Used in Glucose Measurements . . . . . Optical Sources and Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PA Glucose Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Problems and Future Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

419 422 430 437 445 448

This chapter first offers an introduction to the photoacoustic (PA) effect, PA techniques and chemical trace measurements, followed by a discussion on theoretical aspects of applying pulsed PA techniques to the study of fluids and tissues, with a focus on glucose measurements. Next, commonly used optical sources and detection techniques are presented, complemented by a description and discussion on in vitro studies of glucose determination in water, tissue phantoms, tissues and blood. This section is complemented by a concise review of in vivo studies on animals and human subjects. Finally, major problems of PA glucose determination are summarized and future perspectives are sketched. Key words: photoacoustic (PA), spectroscopy, time-resolved stress detection, glucose, blood tissue, pulsed lasers, acoustic detectors.

14.1 Introduction The photoacoustic effect – generation of acoustic waves by modulated optical radiation in optically absorbing media – was discovered as early as 1880 [1]. Since the mid-1970s, this effect has been applied widely to the study of gases and condensed matter, thanks to the appearance of lasers, highly sensitive microphones and

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piezoelectric transducers. For instance, the use of photoacoustic spectroscopy to obtain optical absorption spectra of fluids or to analyze trace amounts has undergone a tremendous growth and attracted considerable interest, particularly in the analytical community [2–5]. Today, photoacoustic techniques, together with other relevant techniques [6–11], are becoming increasingly important tools for such applications as measuring properties of matter, sensing and analyzing trace contents and imaging the internal structure of objects in the relatively disparate fields of material physics, analytical chemistry, biology, biomedicine and engineering. Mechanisms for generating the photoacoustic effect include thermal elastic expansion, boiling, photochemical processing, breakdown, electrostriction and radiative pressure [8]. In material characterization and medical diagnosis, the most popular mechanism is thermal elastic expansion for two main reasons: it does not break or change the properties of the sample under study, and it has a linear or a definite relationship with many of the physical parameters of diverse materials. As a process, thermal elastic photoacoustic generation can be described in the following manner: when a modulated light source irradiates an absorbing medium, specific absorption of optical energy in the illuminated region produces heat, due to non-radiative relaxation. This heat causes the region to expand. If the modulated frequency is rapid enough, the thermal expansion will be exceedingly fast. In this case, inertial effects within the medium cause the illuminated region to extend and compress, thereby generating an acoustic wave, which then propagates outside. Early photoacoustic spectroscopy utilized a gas-phase microphone to sense the heating and cooling of a gas layer in thermal contact with a condensed matter sample irradiated by a chopped light beam. However, the gas-phase microphone technique relies on thermal diffusion into gas and can be viewed as a photothermal, rather than a photoacoustic technique, since the acoustic signal generated in the sample plays only a minor role. This technique has a low sensitivity in comparison with a later technique, based on using a pulsed laser beam to irradiate a condensed sample and a piezoelectric transducer in direct contact with the sample to receive the acoustic signal produced in it. Since the 1990s, photoacoustic techniques have found frequent use in biomedical study; the core of these techniques is to use ultrasonic detection to display or reconstruct the distribution of optical absorption in biological tissues. Relevant techniques here include time-resolved stress detection (TRSD), applied to measuring tissue optical properties [12], blood oxygenation level [13] and blood glucose concentration [14–16]; photoacoustic depth imaging, applied to monitoring subcutaneous blood vessels (skin structure) [17–19] and chemical penetration in the skin [20]; and photoacoustic tomography, applied to imaging breast tumours in humans [21–23] and cancerous growths in small animals [24]. As bio-tissues are optically highly scattering, optical signals from internal tissues are strongly scattered and information is easily lost. However, this disadvantage can be avoided by photoacoustic techniques, because acoustic signals are much less scattered and attenuated in tissue. Thus, by offering the high intrinsic contrast of optical techniques and the high spatial resolution of ultrasonic ones, photoacoustic techniques can be exploited to advantage in tissue diagnostics and imaging technology. As said above, one application of photoacoustic techniques is human glucose mea-

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surement. In the human body, food is converted into sugar, which provides energy to all tissues and organs through blood circulation system. In terms of its chemical composition, human blood sugar consists of D-glucose that exists mainly in the water base of blood plasma [25]. In blood, the physiological glucose concentration is in the region of 18–450 mg/dl. Arterial and capillary blood taken from the fingertip have an identical glucose content, while the glucose level of venous blood is lower than the corresponding arterial level (1–17 mg/dl in healthy subjects and up to 30 mg/dl in diabetic patients). Glucose also exists in other bio-fluids such as intracellular fluids and interstitial fluids in tissues, humour, saliva, sweat and urine. In the steady state condition, the glucose level in intracellular and interstitial fluid is approximately identical to the concentration of glucose in blood. It is also known that the glucose level in humour correlates strongly with the glucose content of blood, while the glucose level in saliva, sweat and urine does not. Being very weak, the absorption spectrum of glucose is always embedded in the spectra of water and other tissue components in the visible and near-infrared regions [26, 27]. The absorption spectrum shows a marked increase in the infrared wavelength range from 8.5 µ m to 10 µ m [28], but at these wavelengths strong absorption by the skin surface makes the use of laser light unsuitable for noninvasive measurements. On the other hand, being osmotic and hydrophilic, glucose influences tissue scattering, as glucose molecules change the refractive index mismatch between scattering particles and the bio-fluid surrounding them. Theory and experiment demonstrate that the reduced scattering coefficient of bio-tissues correlates closely with glucose concentration [29–31]. An early report on the application of the photoacoustic technique to glucose determination centred on using pulsed photoacoustic spectroscopy for the study of glucose in aqueous solutions and blood components [32]. The achieved sensitivity in detecting physiological glucose concentrations in human whole blood was comparable to that of commercial enzyme-based diagnostic systems presently used in clinical chemistry environments at hospitals [28]. The research group built a portable apparatus for noninvasive blood glucose monitoring, comprising one or more laser diodes emitting at the 904 nm wavelength. Measuring glucose concentrations in blood, they reported a correlation coefficient of 0.967 between PA signal responses and hospital tests on a venous blood sample [33]. Moreover, Spanner and Niessner used a modulating array of laser diodes to investigate haemoglobin and glucose in the human body [34]. Unfortunately, glucose absorption in the visible and near-infrared “tissue window” is so weak that it is usually embedded into or interfered with by the tissue and its physiological chemical components. This problem greatly hinders the appearance of commercial products based on the technique. On the other hand, the osmotic and hydrophilic properties of glucose change the scattering properties of bio-tissues in step with increase in glucose concentration. Based on this principle, time-resolved photoacoustic technique has been applied to tissue glucose monitoring. These in vivo experiments, conducted on a rabbit’s sclera, demonstrated that, by measuring a laser-induced acoustic profile at wavelength of 355 nm, an increase of 1 mmol/l (mM) in glucose concentration resulted in a 3% decrease in optical attenuation [15, 35], representing the highest sensitivity achieved by noninvasive PA techniques. However, it has also been reported that physiological

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shifts excluding the glucose level may produce a drift of up to 15% in the scattering coefficient of the epidermis in just 20 minutes [?]. Furthermore, an in vivo PA test showed that signals recorded in the human index finger fluctuated by about 10% in a 20 minute time interval. This fluctuation was attributed to physiological shifts and contacting pressure draft between the finger and the piezoelectric detector [37, 40]. What these findings imply is that the PA, or any other noninvasive, glucose detection method based on measuring scattering or attenuation coefficient changes in human tissue, is not a viable option—at least before these problems are solved or circumvented.

14.2 Theoretical Aspects of PA Techniques Used in Glucose Measurements Photoacoustic generation can be classified as either direct or indirect, depending on the location where the acoustic waves are generated [8]. In the direct scheme, acoustic waves are generated within the studied sample and are thus closely connected with its optical, thermal and acoustic properties. Usually, the produced acoustic waves are detected by piezoelectric transducers. In the indirect PA method, acoustic waves are produced in a coupling medium adjacent to the sample, usually by means of heat leakage and transmission from the sample. As the coupling medium is typically a fluid, it generally requires an enclosed PA cell and uses microphones for detection. Consequently, the method is unsuitable for in vivo and noninvasive measurements. In accordance with the modulating characteristics of the light source, PA generation can also be classified as continuous-wave (CW) or pulsed. In CW mode, the duty cycle of the modulated beam may produce spurious effects such as heating of the sample and convection currents, thereby lowering its PA efficiency and sensitivity. These disadvantages can be avoided in the pulsed mode, where the optical energy is deposited in a relatively short time (usually in the region of a few nanoseconds to a microsecond), allowing the thermal diffusion effect to be largely ignored. Combined with the time-gating technique, the PA signal produced in the target region is capable of discriminating against other spurious PA signals produced by window absorption or light scattering. As a result, detection sensitivity is greatly improved. Moreover, in the pulsed mode, the wavelength of the generated acoustic wave is usually around one millimetre or shorter, which is much smaller than the ordinary sample scale. Hence, the sample’s boundary condition is usually unimportant for PA generation. In the following presentation, attention is focused on direct PA generation in the pulsed mode, which is a popular method in PA glucose determination and in biomedical imaging and diagnostics at large. The theory of PA generation by thermal elastic expansion is based on the Equation of Volume Thermal Expansion and the Equation of Motion:

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∇~u = −

p +βθ, ρ v2

423

(14.1)

∂ 2~u = −∇p, (14.2) ∂ t2 where θ is the temperature rise due to optical radiation, p is the acoustic pressure generated by the thermo-elastic wave, ~u is the acoustic displacement vector and β , ρ and v are the cubic thermal expansion coefficient, density and acoustic velocity of the illuminated medium, respectively. Neglecting thermal diffusion (which is usually the case when the laser pulse duration is much shorter than the thermal diffusion time in the medium) and viscous effects and combining both equations, we get the NonHomogeneous Wave Equation:   β ∂H 1 ∂2 ∇2 − 2 2 p = − , (14.3) v ∂t Cp ∂ t where C p is the specific heat of the illuminated region, H is a function of the heat energy deposited in the region, causing a temperature rise θ . Because H correlates closely with the parameters of the light source and the properties of the medium, providing a general analytic solution for any laser pulse shape and medium property is impossible, excepting some special cases shown in Fig. 14.1. ρ

FIGURE 14.1: Three special cases of acoustic wave generation in a PA source, which can be cylindrical (left), plane (middle) or spherical (right) in shape, depending on the relationship between the laser beam radius a and the light penetration −1 . depth µeff

14.2.1 Cylindrical PA source in a weakly absorbing liquid If an illuminated medium is optically weakly absorbing such that the pulse laser beam penetrates a (infinitely) long distance into it, forming a cylindrical PA source, Eq. (14.3) becomes:

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Handbook of Optical Sensing of Glucose   1 ∂2 αβ ∂ I 2 ∇ − 2 2 p=− , v ∂t Cp ∂ t

(14.4)

where α is the optical absorption coefficient of medium and I is the intensity of the laser pulse depositing the heat. Assuming that, in terms of time and cross area, I has a Gaussian form [38, 39], Eq. (14.4) has the following analytic solution: √
k αβ v p= (14.5) Ω t ′ /τe . C p √r τe3/2

The right-hand side of Eq. (14.5) reveals that the first term is based on the medium’s properties. Thus, k is an amplitude factor including the pulse laser energy, r is the detecting distance and Ω is a function that merely describes q the PA ′ ′ pulse shape. Further, t is the retarded time, t = (t − r/v)/τe ; where τe = τ p2 + τa2 , i.e., the square root of the square sum of the light pulse duration and the acoustic transit time. The first two terms in the right-hand side of Eq. (14.5) determine the acoustic pressure amplitude. By applying Eq. (14.5), we may deduce how the PA pressure changes with varying glucose concentrations (or other traces) in liquids (or bio-fluids). If glucose causes an √ absorption change ∆α and a combination change in the physical parameter ∆ (β v/C p ), the relative amplitude change in PA pressure can be expressed as   √ √ ∆ (β v/C p ) ∆ (β v/C p ) ∆P ∆α √ √ + . (14.6) = 1+ P α β v/C p β v/C p

In actuality, Eq. (14.6) holds true for laser pulses whose duration is much longer than the acoustic transit time. For a short pulse duration τ p ≫ τa , it becomes:
!
∆ β v2 /C p ∆ β v2 /C p ∆P ∆α 1+ + , (14.7) = P α β v2 /C p β v2 /C p 3/2

3/2

because τe ≈ τa = (Rb /ν )3/2 ; where Rb is the radius of the laser beam. These equations are very important in that they disclose the advantages of pulsed PA spectroscopy. The first term on the right side indicates that the effects of optical absorption changes are actually magnified. This is the reason why pulsed PA spectroscopy has a higher sensitivity than optical absorption spectroscopy. Moreover, the second term contributed from the change of physical parameters will further increase detection sensitivity. As a result, trace concentration detection by PA spectroscopy is possible in wavelength regions where optical absorption spectroscopy simply does not work (∆α ≈ 0). Pulsed PA spectroscopy has a very high sensitivity for detecting chemical traces in liquids. According to research, the technique is capable of detecting a minimum absorption coefficient of 10−7 cm−1 [7]; this corresponds to detect minimum concentrations of up to 0.012 parts per billion (β carotene in chloroform) or of the order of ng/ml for some porphyrins and drug solutions [2, 5]. Such results encourage the

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application of PA spectroscopy to human glucose determination. Experimental findings, based on the effect of glucose on the expansion coefficient, specific of heat and acoustic velocity of water solutions, have shown that, when glucose concentration increases to the maximum physiological level, the second term in Eqs. (14.6) and (14.7) is about 0.01 [40]. Therefore, the magnification factor of optical absorption in the first term of these equations is about 1.01. In the visible and near-infrared regions the absorption spectrum of glucose is very weak and always embedded in the spectrum of water. Consequently, when the glucose concentration increases to the maximum physiological level, the relative change in the PA signal amplitude is about 1%, which is much higher than that resulting from optical absorption spectroscopy.

14.2.2 Plane PA source in strongly absorbing and scattering tissues In contrast to the previous section, when a pulsed laser beam penetrates a short distance into a medium such that the penetrating depth is much smaller than the beam’s diameter, a plane PA source is formed, produced either by strong absorption or simultaneous absorption and strong scattering within the medium. Consider first a strongly absorbing medium irradiated by a laser pulse with a short duration (delta function) and light intensity I. In this case, the laser energy is absorbed in the medium in accordance with Beer’s law, and the heat deposited in it can be described by the curve and equation shown in Fig. 14.2.

FIGURE 14.2: Plane PA model of an acoustic wave generated in a purely absorbing medium.

In this case Eq. (14.3) has an analytic solution [41]: p (τ ) =

 E0 αβ v2  Θ (−τ ) eα vτ + Rc Θ (τ ) e−α vτ , 2CP

(14.8)

E0 αβ v2 (14.9) T Θ (τt ) e−α vt τt , 2CP where Rc = (ρt vt − ρ v)/(ρt vt + ρ v), T = (2ρt vt )/(ρt vt + ρ v), τ = t − z/v and τt = t + z/vt . pt (τt ) =

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E0 is the energy fluence (i.e., energy per unit area in the laser beam), Θ(τ ) is the Heaviside unit function and ρ and v are the density and acoustic velocity of the absorbing medium, respectively. The subscript t labels the parameters in a transparent medium. In Eq. (14.8) the first term represents a forward-going wave under the absorbing medium, while the second term is a reflection wave at the incident interface. When a short pulsed laser is fired (t < z/v), τ < 0 forces the second term in Eq. (14.8) to zero. As a result, only a forward-going wave can be detected at any point in the absorbing medium. After the time t > z/v has passed, τ > 0 reduces the first term to zero, but the second term begins to operate. This means that the forward-going wave has passed the point, and the wave shape is now dominated by the reflected wave. Equation (14.9) describes an acoustic wave that is transmitted back to the transparent medium from the pressure in PA source in the absorbing medium. All the waveforms are exponential, just like the form of the heat function or the optical absorption distribution. In a strongly absorbing liquid the specific acoustic waveform is determined by its reflection coefficient Rc . Practical applications involve three common cases. In the case of a rigid boundary, light incidents a liquid sample from a glass plane (such as a cuvette window), and the resulting Rc is roughly equal to 1. In the case of a free boundary, the liquid is irradiated directly (although there may be a layer of air on the liquid surface), with the result that Rc is near equal to −1. In the non-boundary case, the laser beam first passes through a non-absorbing liquid before arriving at the absorbing medium. If these two liquids have similar acoustic properties, Rc is nearly equal to zero. On the basis of Eq. (14.8), when a short laser pulse is fired into an absorption medium, the PA source produced in it can be expressed as: p (z) =

E0 αβ v2 −α z e . 2C p

(14.10)

It can be seen that the acoustic pressure shape is described by an exponential slope (−α z) similar to the spatial distribution of the heat function in the medium (shown in Fig. 14.2). When τ = t − z/v , the spatial distribution of heat deposited by a short light pulse can be mapped directly onto the photoacoustic wave time profile. This is the theoretical background of the time-resolved PA technique. Equation (14.10) enables us to measure the medium’s absorption coefficient either by exponential fitting of the wave shape or by measuring the wave’s amplitude. Of the two methods, the former is more convenient to use, because it only requires knowledge of the acoustic velocity in the medium. A more complicated situation arises for weakly absorbing and strongly scattering media (whose reduced scattering coefficient µs′ is much larger than the absorption coefficient µa ). In such media, which include bio-tissues like the human skin, a wide laser beam is required to form a plane PA source. However, due to backscattering, the produced subsurface energy fluence is higher than the incident laser fluence. A typical depth profile for laser radiation intensity can be simulated by the Monte Carlo

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FIGURE 14.3: Depth profile of light intensity in a semi-infinite, randomly inhomogeneous medium (circles – experimental data, solid line – analytical calculation in the diffusion approximation, dashed line – Monte Carlo calculation). (From Ref. [42] with permission.) method, as demonstrated in Fig. 14.3. It shows that the intensity has a local minimum at the incident surface z = 0 and a maximum at the subsurface at the depth zmax . Obviously, in turbid media, light distribution along the z-axis and the corresponding pressure distribution do not satisfy Beer’s law, but have a complicated profile with a maximum at the subsurface layer. The pressure distribution was deduced by [43]   ∗ ∗ 1 (z > 2l ∗ ), (14.11) p(z) = ΓE0 µeff eµeff l − e−µeffl (2∆+1) exp(−µeff z) 2 p where l ∗ = 1/µs′ , µeff = 3µa (µa + µs′ ), Γ = β v2 /C p and ∆ is a constant which depends on the ratio of the refractive indices of the transparent and turbid media. When 0 ≤ z ≤ 2l ∗ , there is no analytical solution for pressure [43]. Eq. (14.11) shows that it is possible to measure the exponential decrease of PA pressure to determine the extinction coefficient µeff of the studied medium. Equations (14.10) and (14.11) are very useful for determining glucose concentration in fluids and bio-tissues. Variations in glucose concentration change the medium absorption coefficient or effective attenuation coefficient. These optical parameters can be easily extracted by exponential fitting of the photoacoustic wave shape, i.e., reconstructing the optical absorption distribution curve [14–16] without measuring the absolute pressure amplitude. This serves to avoid some unnecessary calibrations, including temperature and irradiative intensity. It is well known that glucose induces a much larger change in the reduced scattering coefficient µs′ than in the absorption

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coefficient µa of tissues in the visible and near-infrared region. As a result, the glucose detection sensitivity of methods based on measuring the effective attenuation coefficient µeff exceeds the sensitivity of methods based on optical absorbing spectroscopy in this region. A technique based on the method described in this section is referred to as a timeresolved stress detection or time-resolved photoacoustic technique. Its application range contains biomedical diagnostics and imaging as well as optical parameter determination in turbid tissues. In many cases, a change in a medium optical parameter correlates closely with a change in its composition. Therefore, measuring optical parameter changes is an effective way of monitoring variations in composition. In biomedical monitoring, for instance, haemoglobin, blood oxygenation or melanosome content are closely related with certain human illnesses and have an obvious effect on the absorption coefficient of normal tissue. To separate absorption and scattering from effective attenuation, we can measure absolute pressure amplitude [12, 43] or total diffuse reflectance [12]. However, the former method is not practical, because the physical parameters (β , v and C p ) of many turbid media are usually unknown. The latter method, on the other hand, is inconvenient in that it requires using the so-called adding-doubling method to determine the relationship between total diffuse reflectance and µs′ /µa , otherwise the error could be too large. To circumvent these disadvantages, it is better to measure the depth zmax of the maximum optical intensity under the subsurface of a turbid medium using a photoacoustic reconstruction profile. A theoretical analysis shows that the quantity zmax µeff is a function of the ratio µa /µeff . Photoacoustic measurements and Monte Carlo simulations demonstrate this relationship [44]:    µa zmax µeff = 0.267 1 − exp −13.42 . µeff

(14.12)

Thus, knowing zmax and µeff allows both the absorption coefficient µa and the reduced scattering coefficient µs′ to be calculated directly. It needs to be noted, however, that Eq. (14.12) is applicable when µa /µeff < 0.35, provided that the anisotropic factor g > 0.8. Fortunately, most of bio-tissues (including the human skin) satisfy these requirements. The error between photoacoustic measurements and Monte Carlo simulations is in the range of 5–7%.

14.2.3 Spherical PA source A spherical PA source is generated when the optically absorbing region in a medium is spherical in shape. This includes two cases: the first is when the diameter of the radiative laser spot matches to some degree the optical penetration depth in the medium, and the second is when the laser pulse radiates an absorbed sphere in a transparent medium such that the absorbed energy within that sphere can be assumed to be homogeneously distributed. PA generation in a spherical PA source has been explored for the cases of a long [45] and a short light pulse (corresponding to a heat function represented by a three-dimensional heat pole) [46]. In addition, a single

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effective time scale τe , similar to the case of a cylindrical source, has been suggested [47, 48]. For a Gaussian laser beam, the pressure can be expressed by: (     ) t − r/v t − r/v 2 Ea β exp − , (14.13) p(r,t) = 3 2π C p τe2 r τe τe where Ea is the absorbed energy in the spherical PA source. The pressure waveform consists of a positive and a negative peak with the same amplitude. If the duration of the laser pulse is short, the initial pressure formed in an absorbed sphere located in a transparent medium has the form:  2 ! r αβ v2 , (14.14) exp − p (r) = k Cp Ra where Ra is the radius of the absorbed sphere and k is a constant that includes the energy fluence of the laser beam. On the other hand, if the pulse duration is longer than the acoustic transit time within the sphere, the pressure wave propagating from the sphere becomes:     ! k′ αβ t − r/v t − r/v 2 pl (r,t) = exp − , (14.15) r Cp τp τp where τ p is a measure of the laser pulse duration and k′ is a constant that includes the energy fluence of the laser beam. Due to weak absorption and a low physiological level of glucose, the radius of the absorbing sphere can be assumed to remain unchanged when its glucose concentration rises. It is evident that by changing the glucose level of the absorbed sphere, the relative pressure change deduced from Eqs. (14.14) and (14.15) becomes similar in form to that of Eqs. (14.6) and (14.7). When the effective attenuation of the illuminated medium is so large that the laser beam’s optical penetration depth matches its spot size, the produced PA source is semi-spherical in shape. If the duration of the laser pulse is short, the relative change in PA pressure caused by a change in the medium’s composition can be deduced from Eq. (14.13): ∆p ∆Ea = p Ea

!

∆ β v2 /C p ∆ β v2 /C p ∆Ra ∆Ra 1+ + −3 −3 . β v2 /C p Ra β v2 /C p Ra

(14.16)

The right side of Eq. (14.16) consists of three terms. The first one represents a change in absorbed energy multiplied by a factor (in brackets), the second one a change in the uniting physical parameter (the so-called Gr¨uneisen parameter Γ) and the third a change in the PA source volume. Maximum sensitivity is achieved when ∆Ea and ∆(β v2 /C p ) are positive, while ∆Ra is negative. In blood glucose measurements, this is entirely possible. It has been established that when glucose is added to a whole blood sample, red blood cells shrink for about 10 minutes, thereby increasing the effective attenuation coefficient [49]. As a result, the value of ∆Ra is

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negative. At the same time, glucose improves the mismatch between the refractive indices of the cuvette window, plasma and red blood cells [29, 50] and increases Γ [40], producing positive ∆Ea and ∆(β v2 /C p ) values. Therefore, Eq. (14.16) can explain why the detection sensitivity of PA glucose measurements is probably higher in blood than in water solutions and tissue phantoms, such as polystyrene and Intralipid microsphere suspensions, as described in section 14.4.

14.3 Optical Sources and Detectors 14.3.1 Optical sources Basically, a range of pulse lasers can be used in biomedical diagnostics and imaging, as well as in glucose determination. The most commonly used sources are Qswitched pulsed Nd:YAG lasers and lasers pumped by them, as well as semiconductor diode lasers working in the pulse mode. It is also possible that other lasers, such as Ti3+ sapphire lasers and fiber lasers emitting at different wavelengths, will eventually be used in glucose determination. In Q-switched pulsed Nd:YAG lasers, Nd3+ ions are embedded in a solid yttrium aluminum garnet matrix (Y3 Al5 O12 ). Laser action is induced by level transitions of the Nd3+ ions. Usually, a flashlamp or diode lasers are used for pumping the lasers in high power pulsed operation at transition wavelength of 1.06 µ m. If the peak power of the pulse is sufficiently high, a suitable crystal can be used to generate the second and third harmonic at 532 nm and 355 nm, respectively. The laser output energy is usually on the order of mJ and can reach the order of sub-Joule, with a pulse duration of a few nanoseconds. In spectroscopic studies, the tunability of the laser wavelength plays a significant role. Q-switched Nd:YAG lasers emitting at 1064 nm can pump a graded index multi-mode optical fibre to produce tuneable near-infrared radiation with a pulse duration varying between 190 ns and 600 ns, depending on the output wavelength [32]. Wavelength selection is achieved with a scanning grating monochromator, and the output energy is on the order of microjoule. This type of tuneable near-infrared optical source has been used in the PA detection of glucose and oil in aqueous systems [32, 51]. In another experiment, a tuneable laser system pumped by the third harmonic of a Nd:YAG laser with an output wavelength range from 400 nm to 2300 nm was employed to study glucose in a solution also containing other blood analytes, such as sodium chloride, cholesterol and bovine serum albumin (BSA) [52]. This laser system was also used to measure the optical absorption coefficient of a glucose solution by the time-resolved PA technique [16]. Optical parametric oscillators are based on the non-linear optical process in which the energy of a pump photon is split into two photons, known as signal and idler, while preserving total energy and photon momentum [53]. Crystals such as beta barium borate (BBO) are often used as non-linear media. The pump requirements for

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BBO are typically met by a XeCl excimer or a Nd:YAG laser. This type of system provides a tuning range extending from the near-ultraviolet to beyond 3 µ m in the near-infrared with an output pulse energy of several tens of millijoules across the tuning range. The linewidth of the radiation is usually ∼10 nm. An OPO system, pumped by a Q-switched Nd:YAG laser emitting at the foundational wavelength of 1064 nm, can output a tuneable wavelength range from 1500–3500 nm. A measurement system of this type, based on PA infrared spectroscopy, was used to study soft tissues in Ref. [54]. A Ti3+ sapphire laser utilizes electronic-vibrational transitions between different 3+ Ti energy levels. Ti3+ ions are impurities formed within a sapphire crystal. Systems based on Ti3+ sapphire lasers have a broad laser transition linewidth, resulting in a wide tuning range. They can be operated either in CW or pulsed mode, with an emission range from 660 nm to 1180 nm. Moreover, they can output 100 mJ in a 10 ns pulse and produce an extremely short (20 fs) pulse. In recent years Ti3+ sapphire lasers have been used in high-resolution PA spectroscopy to investigate the vibration-rotation structure of C-H and C-C bonds [55]. In addition, they have also been applied to photoacoustic tomography and imaging in tissues [56, 57]. Fiber lasers comprise an optical fibre doped typically with a rare earth element (such as erbium, ytterbium or neodymium) and pumped by a variety of sources. These lasers can usually be tuned across tens of nanometres. It is worth noting that fiber lasers have greatly progressed in the past few years and are now capable of outputting nanosecond pulses with energy up to several mJ [58]. As a result, some products are already commercially available. In the near future, fibre lasers will probably extend their application range to NIR PA sensing and imaging of biotissues. Semiconductor diode lasers operating in the pulsed mode and producing a high output power are becoming increasingly attractive to manufacturers of portable PA instruments. This is because diode lasers are light in weight, small in volume, high in efficiency, low in price and compact in size. Currently, most diode lasers emit in the visible and near-infrared wavelengths, which are very suitable for biomedical diagnostics and imaging. When operated in pulse mode, their pulse duration can range from a few nanoseconds to microseconds, with a pulse repetition frequency of up to several tens kHz. Pulsed diode lasers have been used in portable PA instruments for monitoring oil contamination in water [59], in PA experiment analysis of particles in aqueous matrices and glucose determination in blood and tissue [?, 61], and in PA imaging of blood vessels [62]. However, diode lasers have a relatively low output energy (on the order of µ J) and poor directionality (their beam angle may spread up to ∼ 25 ˚ ), limiting their usability for biomedical diagnostics and imaging. These disadvantages can be partly overcome by combining the outputs of several high power laser diodes and applying an excellent lens system. For example, a combination of 12 laser diodes would provide an SNR equivalent of a 10 mJ Q-switched Nd:YAG laser pulse [63]. This type of diode laser system is suitable for the PA visualization of superficial vascular anatomy in the brain or skin of small animals [64]. It is also notable that the output wavelength of diode lasers can be tuned easily by changing the temperature or using an adjustable external cavity. Moreover, combining a few

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diode lasers radiating at different centre wavelengths into one instrument will further improve the system’s wavelength range—and thereby its suitability for use in portable PA spectrometers [64].

14.3.2 PA detectors A pulsed PA wave is a wideband acoustic wave with a typical frequency range from the sub-MHz to around 100 MHz. Various types of acoustic detector are applicable to PA detection [8], the choice of detector for a particular application being largely based on factors such as detection style, sensitivity, response time, bandwidth, impedance matching, noise, size and ruggedness. Most common detectors in the PA study of condensed matter, including bio-tissues, are piezoelectric transducers, which offer high sensitivity and a good acoustic impedance match with the studied media. Also optical detectors are widely used, as they form all optical devices and support non-contact measurements [65, 66]. 14.3.2.1 Piezoelectric detection The piezoelectric effect is based on the fact that electric charges are produced on the surface of a material when it is deformed by pressure. Common piezoelectric materials fall into three categories: single crystals (quartz, lithium niobate), polycrystalline ceramics (lead zirconate titanate, Brium titanate, lead metaniobate) and polymer materials (copolymer, PVDF, Teflon and Mylar). The most widely used materials in piezoelectric PA transducers are lithium niobate (LiNbO3 ), lead zirconate titanate (PZT-5A) and polyvinylidene fluoride (PVDF), whose salient properties and parameters are listed in Table 14.1. Recent years have seen the development of a piezo-composite material, consisting of a piezo-ceramic and a polymer. It will broaden the choice of transducers available and improve signal detection for improved performance. Piezoelectric elements are generally disk-shaped, since that form readily accepts acoustic waves produced by point-like, planar or cylindrical acoustic sources. They come in two vibration modes: thickness and radial. In liquid or soft tissue measurements, acoustic waves are longitudinal, so only vibrations in the thickness mode are considered. Element thickness must be carefully selected, especially when applying ceramic or crystal element to detecting PA amplitudes. The elements’ resonance frequency must be identical to that of the received signal to ensure the efficient production of electrical signals. On the other hand, a tubular shape is more efficient for the high sensitivity detection of cylindrical acoustic waves produced by a thin laser beam [67]. In this case, the sample under study fills the tube and the laser beam passes through the tube centre axis, producing a cylindrical acoustic source in it. All the emitted PA signals are received in equi-phase along the entire cylindrical surface of the tube, resulting in maximum sensitivity. However, piezoelectric tubes are unsuitable for noninvasive biomedical detection, owing to the geometric limitations, high scattering and in-homogeneity of the human body. Instead, disk shaped transducers operating in the backward mode are used to detect PA signals, as shown in

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TABLE 14.1: Properties of commonly used piezoelectric materials LiNbO3 (z-cut)

PZT-5A

PVDF

Unit

Piezoelectric constant

d33 = 6 g33 = 0.023

d33 = 374 g33 = 0.025

d33 = 39–44 g33 = 0.32

10−12 C/N Vm/N

Mechanical Q factor

100

75

5–10

Density

4.64

7.7

1.78

g/cm3

Sound velocity

7316

4500

2260

m/s

Acoustic impedance

33

35

4

106 kg/(m2s)

Work temperature

< 1100

< 300

< 80

◦C

Advantages

wideband, rugged

high sensitivity, inexpensive

wideband, inexpensive

Disadvantages

expensive

narrowband, non-rugged ringing

Fig. 14.4(a)–(d). Also the forward detection mode is useful in some cases, such as breast cancer detection [68]. The response sensitivity of piezoelectric transducers is strongly dependent on element thickness. In ceramic elements, responses gradually become saturated with increasing thickness [59]. A typical response value is 30 µ V/Pa for a disk-shaped PZT-5A transducer with a diameter and thickness of 4 mm [7]. Because the frequency response curve of ceramic transducers is not flat, they must be calibrated at the used PA frequencies. Further, their acoustic impedance, being 35×106 kg/(m2s) for the PZT-5A, is much higher than that of many soft tissues. Even though the acoustic impedance mismatch causes part of the incident acoustic energy to be reflected, ceramic transducers offer a higher acoustic response than polymer transducers or single-crystal transducers. Hence, if the prime requirement is high response, as in PA spectroscopy to determine the concentration of glucose or other analytes, a ceramic transducer is a better choice. However, their responses are often dominated by their own frequency characteristics, which usually differ from those produced by the received acoustic signal. Hence, the shape of the electrical response produced by a ceramic transducer cannot faithfully reproduce the shape created by PA generation. This is a drawback for applications based on time-resolved PA detection, especially

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piezotransducer

piezotransducer

optic fiber

optic fibers electrical output

electrical output metal case

metal case

preamplifier

preamplifier piezotransducer

piezotransducer

acoustic waves

acoustic waves tissue

tissue blood vessels

exciting beam

blood vessels

exciting beams

(b)

(a) electrical output

electrical output metal case

preamplifier

metal case preamplifier piezo-transducer transparent prism

exciting beam

lenses exciting beam

acoustic waves

transparent prism acoustic waves

tissue

tissue (c)

optic fiber

piezotransducer

(d)

FIGURE 14.4: Four schemes of PA detection in backward mode: (a), (b), (c) and (d), based on the design idea in [10, 35, 69, 70].

in medical imaging. By contrast, polymer film transducers are capable of satisfying this requirement, due to their fast response, wideband characteristics and flatter sensitivity–frequency curve. Thus, a specific PVDF film has a fast rise-time (< 5 ns) and a wide bandwidth (> 100 MHz). Moreover, the acoustic impedance of PVDF is about 4.1×106 kg/m2 s, closely matching that of soft tissues and water (∼ 1.5× 106 kg/m2s). The mechanical Q factor of PVDF is sufficiently low to prevent ringing at the relevant frequencies, which is most important for raising the longitudinal resolution of the PA depth profile. Although film thickness is a significant consideration, film diameter is also important in time-resolved measurements. In reality, the active part of a piezoelectric film integrates the pressure experienced over its entire active area to produce a voltage output. To assure a broad angular response and to preclude diffraction effects from the frequency filtering of the transducer’s response, the diameter of the active area of a PVDF film is ideally restricted to the order of a quarter wavelength at the highest frequency of interest. If the active diameter is larger than that, the alignment of the transducer relative to the acoustic wave under measurement is of importance. In addition, there is a trade-off between the size of the active area and sensitivity. An

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obvious advantage of polymers is their flexibility and thinness (a few micrometers), as they allow the transducer’s receiving surface to be shaped at will. On the other hand, their robustness and long-term stability is not good enough for applications requiring accurate absolute calibration. Lithium niobate transducers can circumvent these deficiencies, since lithium niobate is a single-crystal piezoelectric material, which is characteristically very hard and has a high Curie temperature. If it is cut as thin as 20 µ m, a resonance frequency can be achieved in excess of one hundred MHz. Moreover, the longitudinal velocity of acoustic waves in a z-cut lithium niobate crystal is very high, up to 7316 m/s, enabling a fast response and a wide bandwidth. For instance, a transducer with a crystal thickness of 30 µ m and size of 2 mm × 2 mm offers sensitivity on the order of 1 µ V/Pa and a response time of ∼4 ns [46]. Owing to their high sensitivity and wide bandwidth, lithium niobate transducers are suitable for PA imaging and tissue optical parameter measurements based on time-resolved stress detection [12]. However, these transducers are more expensive and their sensitivity seems lower than that of PVDF devices. 14.3.2.2 Optical detection The optical detection of ultrasonic waves offers some advantages over piezoelectric detection. First, it allows remote, wireless and non-contact monitoring. Second, it maintains operational capability in magneto-electrically noisy and hazardous environments. Third, it can be positioned in places where even an opaque piezoelectric transducer may either obstruct or be affected by an irradiating light beam. Fourth, it is not difficult to assemble imaging arrays with sufficiently small element sizes and interelement spacings, while still retaining adequate sensitivity. However, compared with piezoelectric transducers, optical detectors usually tend to be less sensitive or require more complicated methods to rebuild the PA profile generated in a medium. To the best of the authors’ knowledge, no literature exists on PA glucose determination based on optical detectors. Nonetheless, optical methods have gradually appeared in PA biomedical diagnostics and imaging [71–75] and may in the future become a potential alternative for glucose detection. Relevant techniques for the optical detection of ultrasound can be classified into interferometric and non-interferometric formations. In interferometric measurements, an optical interferometer is used to detect distortions or displacements caused by physical parameters (such as pressure, temperature and so on) on the surface of an object. A beam whose optical path length is affected by PA pressure is compared to an unperturbed reference beam. The effects of pressure changes can then be observed in the interference pattern. Non-interferometric measurements usually rely on detecting the deflection of a probe beam when it transmits through or reflects from a medium, whose refractive index varies as a function of pressure changes caused by PA waves [76, 77]. Since the interferometric formation is more popular in biomedical applications, some examples will be described below. Dual-beam interferometric detection has been applied to study laser-induced PA waves from buried absorbing objects by Jacques et al. [78]. They simulated the

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detection of subcutaneous, optically absorbing objects in the human skin, such as haemorrhages or vascularized tumours, which generate PA waves. When two beams are reflected onto a surface, pressure waves arriving at the surface first reach one beam site before arriving at the second one. This produces a differential surface movement and a difference in the pathlength of the beams, which can be detected by an interferometer. The detectable surface movement was in the range of 0.1–63 nm with good linearity, and the dynamic range of the linear measurement was 20 mbar– 200 bar at 20 mV/bar. Sub-mm resolution was achieved in imaging an absorbing object at the depth of 11 mm within an aqueous phantom medium. Further, the sensitivity and noise level of the interferometer were equal to or even exceeded those of lithium-niobate piezoelectric transducers. A modified Mach-Zehnder interferometer, built to measure surface displacements resulting from the generation of PA waves in the target [79, 80], succeeded in measuring effective attenuation depths ranging from 0.1 to 2 mm with the high precision of < 4%. An application of this interferometric detection in optoacoustic tomography showed an angstrom-level displacement resolution and nanosecond temporal resolution in detecting subsurface blood vessels within tissue phantoms and the human forearm in vivo [75].

CW interrogating laser beam

ns excitation laser pulse

substrate dielectric coatings PA waves

polymer sensing film

tissue

absorbers FIGURE 14.5: Schematic of a photoacoustic sensor based on Fabry-Perot interferometry.

Yet another alternative method for PA imaging is self-referential or single-beam interferometric detection [81, 82], where the sensing mechanism is based on detecting acoustically-induced variations in the optical thickness of a Fabry-Perot polymer film. As presented in Fig. 14.5 for backward-mode PA sensing and imaging, nanosecond excitation laser pulses are transmitted through the sensing film into the target, generating PA contributions from each absorbing point in the diffusely irradi-

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ated volume. When illuminated by a CW interrogating laser source (aligned coaxially with the pulsed excitation beam), the film acts as a F-P interferometer, whose mirrors are formed by the deposition of wavelength-selective dielectric coatings on both surfaces of the polymer sensing film. They are designed to be reflective at the wavelength of the CW interrogating laser, but transparent at the wavelength of the excitation laser pulse. The PA signal modulates the optical thickness of the polymer film, thereby affecting the reflected light. A representation of the incident acoustic field across the sensing film can be obtained by leading the reflected light beams onto an optical detector or an array, such as a CCD or a photodiode array. It has been demonstrated that the achieved detection sensitivity (< 10 kPa, without signal averaging) and bandwidth (30 MHz) are comparable to wideband piezoelectric PVDF ultrasonic transducers, with the prospect of achieving substantially smaller element sizes (< 35 µ m) [83]. This type of Fabry-Perot ultrasonic sensor proved very useful in the three-dimensional anatomic and functional imaging of superficial vasculature in small animals when applied to the characterization of cancer and brain injury models [84]. Another application of the Fabry-Perot sensing interferometer involved an all fiber optic ultrasonic transducer used for ultrasonic tissue biopsy [85]. In addition to exhibiting a sensitivity comparable to that of piezoelectric devices, the prototype had an almost flat bandwidth extending up to 20 MHz.

14.4 PA Glucose Determination Noninvasive glucose monitoring commonly relies on the pulsed mode of PA generation, in which the incoming laser pulse enters the sample and generates pressure waves via thermo-elastic expansion. Glucose monitoring with the PA technique is based on detecting changes in the peak-to-peak value and the profile of the pressure waves. Since the sample thermal, optical and acoustic properties have an effect on pulse generation (see Eqs. (14.4) and (14.5)), the PA amplitude is proportional to Γ, α (or µa in the case of weakly absorbing samples with strong scattering) and H0 , whereas the rising edge is proportional to α (or µeff ), τ and v (see Eqs. (14.10) and (14.11)). Within the 300-900 nm wavelength range, the optical absorption of a solution with a glucose concentration of up to 200 mM is still comparable to that of pure water, within an accuracy range of 0.01 mm−1 [86]. Glucose absorption in the NIR and MIR wavelength ranges is shown in Fig. 14.6, where CG is the relative absorption change between a 10% glucose solution and water. As can be seen, glucose has relatively large absorption in the NIR range at wavelengths of around 1050 nm, 1600–1750 nm and 2100–2200 nm; whereas in the MIR region, glucose has higher absorbance peaks at wavelengths between 8.5–10 µ m. Nevertheless, in the MIR region, background absorption caused by water is too strong to permit light penetration into skin.

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(a)

(b)

FIGURE 14.6: Glucose absorption in the wavelength range from NIR to MIR. Figure (a) from Ref. [27], copyright Elsevier (1998), with permission. Figure (b) from Ref. [28] with permission.

14.4.1 In vitro glucose studies 14.4.1.1 Water solutions Figure 14.6 (b) shows that there are strong glucose absorption peaks in the MIR spectral range. MacKenzie et al. [28] studied the effect of glucose solutions on the PA response at 9.676 µ m using concentrations of 150 mg/dl–76.6 g/dl and found that the response was linear in the range of 0–599.4 mg/dl with a response sensitivity of about 1.08 %/mM. Moreover, the response became saturated towards the upper end of the concentration range (76.6 g/dl). Fig. 14.6 (a) shows that there is a glucose absorption peak around the wavelength of 1700 nm. At this wavelength, MacKenzie et al. studied aqueous glucose solutions with a concentration range of 1.7 mM–33 mM and obtained a linear relationship between glucose concentration and the percentage change of PA response. This allowed them to deduce that the achieved response sensitivity was about 0.19 %/mM [52]. Another glucose absorption peak occurred in the NIR range near the 2150 nm wavelength, as shown in Fig. 14.6 (a). A study by the time-resolved PA method investigated a glucose solution at this wavelength [16] and deduced a slope of 0.5 %/55 mM for the absorption increase with glucose concentration. This result, however, is rather qualitative, because the laser beam was slightly focused due to the low output energy of the MOPO laser system at this wavelength. Although the result did not establish the response sensitivity of glucose to PA amplitude, it serves to indicate that, at this wavelength, sensitivity is less than that at 1700 nm (0.19 %/mM), as shown in Fig. 14.6. Figure 14.6 (a) also reveals that there is a small glucose absorption peak near 1050 nm. This wavelength was accessed in an experiment using the fundamental frequency of a Nd:YAG laser output (1064 nm wavelength) [26]. Glucose solutions with a concentration range of 0–1000 mM were flowed through a plastic tube simulating a blood vessel and embedded in a gelatin-based tissue phantom. The results

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revealed that PA signals increased linearly with glucose concentration and gave a response sensitivity of 0.07 %/mM. However, another report [33] gives a response sensitivity of 0.53 %/mM at this wavelength. This value is much larger than that obtained at 1700 nm (0.19 %/mM), which does not seem reasonable. Early attempts at PA glucose determination used NIR pulsed laser diodes as exciting source, with a view to creating a noninvasive instrument that is portable (small volume) and can be used in homecare (low price). Also pulsed laser diodes with a wavelength of 905 nm have been used as exciting sources, because they have maximal output energy in comparison with other diodes at different wavelength [33, 40]. The response sensitivity of PA signals to glucose concentration has been found to be about 2%/% (≈ 0.04 %/mM) [40]. At 905 nm, glucose absorbs light at a slightly smaller amount than water; therefore, an increase in the PA signal is caused by changes in thermal and physical parameters, not by changes in the optical absorption of glucose, as predicted by Eq. (14.7). For an experimental demonstration, the response sensitivity of the thermal expansion coefficient, specific of heat and acoustic speed in glucose solutions, was measured separately. As the obtained values were about 1.2%/%, −0.6%/%, and 0.28%/%, respectively [40], the corresponding response sensitivity of the Gr¨uneisen parameter to glucose concentration is about 2.1%/%, which is nearly equal to the PA response sensitivity value (2%/%) at 905 nm. This confirms the finding that, in the wavelength range from 300 nm to 905 nm, glucose absorption has a negligible effect on PA signals obtained from water. In addition to glucose, blood and tissues contain a number of other analytes, whose contribution to the PA response of glucose should be investigated so that potential interference effects could be compensated for. MacKenzie et al. investigated the PA response of sodium chloride (NaCl), cholesterol and BSA as well as glucose solutions in the spectral region of 800–1200 nm [52]. The results showed that despite differences in spectroscopic shape, the PA response of glucose is apparently larger than that of the other three, particularly around the glucose absorption peak at 1050 nm. Moreover, the presence of constant amounts of NaCl, cholesterol and BSA increased the base level of the PA signal, while not affecting the sensitivity of the glucose response, as seen in Fig. 14.7. Hence, if the concentration of analytes other than glucose changes, spectroscopic methods will be necessary to measure glucose and to correct the changes induced by other analytes. 14.4.1.2 Tissue phantoms Different phantoms offer a way of studying how glucose affects the PA response. In a scattering suspension, the effect of glucose can be measured not only by changes in absorption, but also through changes in scattering. Increasing glucose concentration raises the refractive index of the bulk medium, decreases the refractive index mismatch and reduces scattering. The registered PA response is influenced by the changed photons spatial distribution and energy density in the studied sample. IntralipidTM is an intravenous nutrient consisting of an emulsion of phospholipid micelles and water. It is a homogeneous turbid medium, which is chemically rela-

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FIGURE 14.7: Response to glucose solutions in the presence of other blood analytes. Black diamonds: glucose; boxes: glucose + NaCl (3 g/L); black triangles: glucose +cholesterol (1.8 g/L); black squares: glucose + BSA (63 g/L) (from Ref. [52] with permission).

tively inert [87]. As its scattering properties (e.g., reduced scattering coefficient µs′ ) resemble those of human skin [88], it can be used as a tissue simulating phantom. Developing a phantom with similar light transport characteristics to skin requires finding the right combination of µa and µs′ [89]. The acoustic impedance of Intralipid suspensions is almost the same as for water, at least when using low Intralipid concentrations. Also the optical transmission and reflectance spectra of Intralipid show good comparability with those of skin [90]. Average changes in the peak-to-peak values of PA signals measured with a Nd:YAG laser at 1064 nm are in the range of 0.05–0.08 %/mM for 1% and 0.06 %/mM for 2% Intralipid, respectively [91, 92]. What is the reason behind the different effect of glucose in 1% and 2% Intralipid remains somewhat unclear. Polystyrene microspheres with potassium chromate K2 CrO4 have been used as a model medium to simulate the optical properties of sclera at the 355 nm wavelength. Polystyrene microspheres act as scattering particles, whereas K2 CrO4 is used to adjust the absorption of the sample medium to equal that of real tissue. A 3.5% polystyrene suspension (particle diameter of 760 nm) was used in connection with time-resolved stress detection of PA signals to determine light absorption distribution in illuminated samples. It was found that, in a polystyrene phantom, an increase in glucose concentration reduced µeff by 0.045 %/mM glucose [14, 86]. Within the wavelength range of 300–900 nm, glucose was found to have a negligible effect on

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absorption and a more pronounced effect on scattering [86]. The so-called scattering photoacoustic method [93], which can simultaneously detect both the reduced scattering coefficient and PA signal amplitude in highly scattering, weakly-absorbing samples, has been used to study the effect of glucose on four suspension bases: non-fat milk, light milk (1.5% fat), Intralipid (1%) and microsphere polystyrene (0.5%) [94]. A group of samples was made from each suspension base with a glucose concentration of 0, 1%, 1.96% and 4.76% and tested successively. The reduced scattering coefficient was deduced for all these samples at 1064 nm, with an estimated relative error no larger than 3%. In this error range, glucose-induced changes in the measured value of µs′ proved insignificant for nonfat milk and polystyrene (0.5%) suspensions. However, in light milk and Intralipid (1%) suspensions, glucose apparently decreased the value such that adding 4.76% of glucose reduced µs′ by about 10% (≈ 0.04 %/mM). The results are reasonable, for the refractive index of a 4.76% glucose solution (n ≈ 1.34) better matches that of lipid particles (n ≈ 1.45) than polystyrene microspheres (n ≈ 1.57). A simultaneous measurement of the effect of glucose on the amplitude of PA signals produced in these suspensions demonstrated that the PA amplitudes generated in light milk and Intralipid (1%) suspensions were nearly equal, although milk scatters more strongly than Intralipid (1%). This means that, when monitoring a highly scattering suspension, the amplitude of PA signals is not sensitive to scattering. The relative change in signal amplitude was 14% in an Intralipid (1%) sample and larger than 10% in other suspensions, when the glucose concentration increased to 4.76%, resulting in a concentration sensitivity of 2.1–2.9%/% (≈0.04–0.05 %/mM). It may be concluded that, in the NIR range, the observed increase in PA amplitude in the suspension samples was mainly caused by the Gr¨uneisen parameter and less by scattering changes induced by glucose. 14.4.1.3 Tissue Since tissue samples contain different particles and structures resembling those of living tissues, they offer a better means of studying the effects of glucose than different phantoms. PA studies with the time-resolved detection method have been used to directly measure glucose-induced changes in the µeff of the rabbit sclera. In diameter, collagen fibrils found in sclera closely matched the used wavelength (355 nm), and because the mean distance between the fibrils was about 300 nm, the fibrous tissue was highly scattering (µs = 800 cm−1 ). A decrease of 0.3–0.5 %/mM in µeff was found as a function of glucose concentration. The application of mechanical pressure by the PA transducer as well as changes in temperature may induce substantial errors in the measured µeff . In vitro experiments showed that variation in µeff may be as high as 30%, which highlights the importance of stabilizing the measurement setup. Although scattering changes can be measured at different wavelengths, the effect of glucose on scattering was more pronounced in the UV than the IR spectral range [86]. Being one of the main components of blood that contains free glucose, plasma is a highly fascinating object for a study on PA responses. One such study demonstrated

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different responses at two different wavelengths (1700 and 1180 nm) [32]. These wavelengths corresponded to the first and second C–H stretching overtones of the glucose molecule at 1180 and 1700 nm, respectively. The used glucose concentrations varied from the physiological range (18–450 mg/dl) up to 1.8 g/dl. A linear increase in the PA response was found at both wavelengths as a function of glucose concentration, with the glucose-induced change in human plasma being larger at 1700 nm (0.13 %/mM) than at 1180 nm. The PA signal level was higher in plasma than in water, but lower than in blood. However, the accuracy in these measurements was not sufficiently high for clinical measurements. Christison et al. [28] used the glucose fingerprint range of 8.5–10 µ m to examine whole blood samples at 9.603 µ m and 9.676 µ m. Their results revealed that glucose increased the PA signal quite strongly at 9.676 µ m. At 9.603 µ m, however, the PA signal was practically immune to glucose. A sensitivity of 23.76 %/mM at 9.676 µ m is very high, in comparison with results achieved in other samples. Although this wavelength region (8.5–10 µ m) offers promising results in vitro, it must be noted that tissues and water are strongly absorbing in this range, which prevents light penetration into skin and introduces severe problems for in vivo measurements. To overcome the limitations imposed by low light penetration depth in the MIR spectral range, NIR light has been applied to detecting glucose-induced changes in circulating human blood. A study based on using laser diodes excited at 905 nm showed that increasing glucose concentration increased the peak-to-peak value and produced a response sensitivity of 0.3 %/mM [61]. Similar experiments have also been conducted on pig whole blood using a Nd:YAG laser at the wavelengths of 1064 nm and 532 nm. Chief among the results was that the peak-to-peak value of PA signals was larger at 532 nm than at 1064 nm (Fig. 14.8), the explanation being the different µa values of blood at these wavelengths. Glucose-induced changes in the peak-to-peak value were about 0.4%/mM and 0.2%/mM at 1064 nm and 532 nm, respectively [91]. The origin of these glucose-induced changes in the PA signal is not entirely clear.

(a)

(b)

FIGURE 14.8: Glucose-induced change in PA signals obtained from pig whole blood at 1064 nm (a) and 532 nm (b) (from Ref. [91] with permission).

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Bednov et al. [49] studied sheep blood samples with glucose concentrations of 20 mM – 100 mM at 1064 and 532 nm. Using time-resolved detection of PA pulse profiles to determine changes in µeff , they established that the effect of glucose on µeff is 0.10 %/mM at 1064 nm and 0.14 %/mM at 532 nm. Figure 14.9 (a) shows the dependence of µeff on glucose concentration at 532 nm. In addition, Bednov et al. explored the time dependence of µeff (Fig. 14.9 (b)). Initially, increased glucose concentration raised the value of µeff , but after a 10-minute time period, optical attenuation decreased. This can be explained by morphological changes in red blood cells and by adaptation to hyperglycemic conditions. What the results show is that glucose-induced changes have a larger effect on scattering than on the relative refractive index. Moreover, morphological changes in blood were found to be fully reversible for glucose concentrations below 100 mM [49]. Finally, response sensitivity seems to be lower in the measurements of µeff than in PA amplitude measurements.

(a)

(b)

FIGURE 14.9: Optical attenuation measured as a function of glucose concentration (a) and time-dependence of µeff (b) (from Ref. [49] with permission).

Common to different phantom and tissue measurements in vitro is the application of high glucose concentrations. These measurements typically start from the physiological range and extend high over its upper end. This highlights the small effect of glucose and the need to improve measurement sensitivity, increase repeatability and decrease standard deviation of measurements.

14.4.2 In vivo noninvasive glucose determination The earliest publication on PA glucose experiments in vivo was by MacKenzie et al. [3]. They used a Nd:YAG laser to illuminate a finger and an orthogonal detector position to monitor PA responses. A standard glucose tolerance test was performed on four normal subjects, three type II diabetics and two type I diabetics. Preliminary results for normal and diabetic persons are shown in Fig. 14.10. Type I diabetics (the

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lower figure) were first given a 30 g glucose load, followed by insulin doses at 35 and 150 minutes. After individual calibration, the results showed that the correlation between PA glucose concentration and clinical concentration was good: the correlation coefficient between PA glucose experiments and laboratory glucose values was 0.967. In the clinical measurement of blood glucose concentration, the coefficient of variation was ±5%, while varying between ±1 and ±12% for the PA response, depending on instrument gain settings [95]. These results showed that, in clinical measurements, about 91% of the data points describing the percentage change in the PA response lie within ±20% of the clinical glucose concentration range, corresponding to zone A in Clarke error grid analysis [52]. The response sensitivity deduced from Fig. 14.10 (a) is about 2.15 %/mM, which is much larger than the corresponding values for water solutions and tissue samples. It probably means that the effect of glucose on the PA signal is much larger in the human body than in tissue samples, which is a promising result for noninvasive glucose determination. Meanwhile, a specific PA sensor head, coupled via an optical fiber bundle to an array of 8 laser diodes emitting at various wavelengths in the NIR region, was developed for noninvasive blood glucose determination [34]. By applying a special modulation scheme, tiny changes, caused by variations in blood glucose concentration, could be measured in the absorption coefficient of whole blood. The achieved resolution was 70 mg/dl (≈ 3.9 mM). An oral glucose tolerance test, administered to several persons, indicated that the results of the PA measurement were identical to those obtained by a clinical enzymatic glucose analyzer. Another in vivo measurement was carried out on the rabbit sclera by the timeresolved PA method to deduce the optical attenuation coefficient at the 355 nm wavelength [15]. PA profiles were measured in the sclera both before and after the administration of intravenous glucose, and the glucose concentration in rabbit blood was simultaneously determined with a commercial device for the chemical analysis of blood. It was found that when the glucose concentration increased by 1 mM, the attenuation coefficient decreased by 3%, which was the maximum measurable response sensitivity detected by the time-resolved PA method until now. Similar in vivo experiments are also described in an US patent [35]. A new concept for in vivo glucose detection in the MIR spectral range was put forward a couple of years ago, based on using two QCL lasers emitting at 1080 and 1066 cm−1 (wavelengths of 9.26 µ m and 9.38 µ m, respectively) to produce PA signals in the forearm skin [96]. One of the wavelengths correlates closely with glucose absorption, while the other does not. As the light penetration depth in the wavelength region is about 50 µ m, light is capable of reaching the stratum spinosum layer, located just below the 20-µ m thick stratum corneum. Determining glucose concentration in the extracellular fluid of the stratum spinosum permits deducing the glucose concentration of blood, because the two factors correlate closely with each other. Fig. 14.11 presents the results of an oral glucose tolerance test taking account of the 10-minute time delay between PA signals recorded in the forearm and blood glucose concentration. However, these experiments are preliminary and data from a large amount of people are not available. Aiming to design a portable noninvasive glucose monitor for home diagnostics,

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A

B

FIGURE 14.10: PA responses for normal persons (a) and type I diabetics (b) durc [1995] IEEE, with permising a standard glucose tolerance test (from Ref. [33], sion).

Glucon Inc. is in the process of developing a new sensor [97]. Their wrist clock type sensor uses several optical wavelengths to improve glucose specificity and to remove the effect of other blood substances. Analyzing the results of experiments made on 10 healthy and 7 Type I diabetic persons showed that the glucose level range of the diabetics varied between 100–449 mg/dl with a mean absolute deviation of 25.0 mg/dl. Moreover, the correlation coefficient was 0.93, and all data points were located well within zones A and B in the Clark error grid. The glucose level of the healthy group ranged from 68–180 mg/dl, with a mean absolute deviation of 14.9 mg/dl and a correlation coefficient of 0.72. As the work is still in the research stage, no product is currently available.

14.5 Problems and Future Perspectives PA glucose determination has been investigated for more than fifteen years. An early choice was NIR-pulsed PA spectroscopy, because it offered high sensitivity

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FIGURE 14.11: Relationship between mean PA signal values and corresponding blood glucose value during an oral glucose tolerance test (from Ref. [96], Copyright Elsevier (2005), with permission).

for trace detection and deep penetration of near-infrared light in tissues. However, glucose is so weakly absorbing in the visible and near-infrared regions that it is usually embedded in the spectra produced by other chemical traces in human blood and tissue components, which greatly impedes the applicability of the technique for the purpose. Although in vitro studies have demonstrated that the sensitivity of the PA response to glucose is unimpaired by the presence of other analytes, they also highlight the need to enhance the glucose response sensitivity to eliminate responses produced by other analytes. At some wavelengths in the MIR region, glucose exhibits a more pronounced PA response, but the shallow penetration depth of light at these wavelengths prohibits it from reaching subcutaneous blood vessels. In the opinion of the present authors, MIR pulsed PA spectroscopy is well worth investigating, particularly in view of the development of new, more suitable light sources. Besides weak optical absorption, glucose has the characteristic that it increases the refractive index of the solution/body fluid it is dissolved in. This decreases the refractive index difference between extracellular fluid and cellular components, thereby changing the tissue’s reduced scattering coefficient. Detecting this change or a corresponding change in the total attenuation coefficient can therefore be used to determine the tissue’s glucose level. Taking advantage of this effect, the time-resolved PA technique was applied to measure optical scattering in sclera tissue in the ultraviolet region (355 nm wavelength). The results demonstrated that the technique gave unprecedented detection sensitivity in noninvasive measurement until now. On the other hand, the experiment also showed that measurement accuracy is strongly influenced by such factors as transducer pressure and position, temperature fluctuations

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as well as physiological variations, because they have a direct effect on tissue optical scattering. To reduce these effects, non-contact detection techniques (e.g., optical interferometry) must be developed or an optimum body position must be determined to precisely control temperature at the measuring position. Also the measured subcutaneous layer must be selected with care, to minimize the fluctuations of endogenous metabolites. Before these problems are solved, the application of the time-resolved PA technique to noninvasive human glucose measurements will continue to suffer from low repeatability. To conclude, it is going to take a while before portable devices for the noninvasive determination of glucose levels will be available on the market or in use at home. Besides continuously refining current detection techniques and data analysis methods, researchers need to explore possibly existing new effects of glucose on tissues and PA generation. This is of utmost importance for the development of more advanced detection techniques with higher sensitivity and specificity. Another possible path toward improved sensitivity is to explore the possibility of applying nano-particle techniques to glucose detection, similar to nano-particle PA imaging to improve tumour detection. Meanwhile, new materials, laser devices, detection techniques and data processing will further raise the method’s sensitivity and repeatability. Due to the complicated composition and fluctuating physiological factors of the human body, absolute noninvasive determination of glucose may in the future require combining the PA technique with other optical techniques or physical measurements.

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[71] G. Paltauf, H. Schmidt-Kloiber, and H. Guss, “Optical detection of laserinduced stress waves for measurement of the light distribution in living tissue,” Proc. SPIE, vol. 2923, 1996, pp. 127–135. [72] S.A. Carp and V. Venugopalan, “3-D interferometric optoacoustic imaging,” Proc. SPIE, vol. 5697, 2005, pp. 307–312. [73] P.C. Beard, A. Hurrell, and T.N. Mills, “An optical detection system for biomedical photo-acoustic imaging,” Proc. SPIE, vol. 3916, 2000, pp. 100– 109. [74] S.A. Telenkov, D.P. Dave, and T.E. Milner, “Low-coherence interferometric detection of photothermal and photoacoustic effects in tissue,” Proc. SPIE, vol. 4960, 2003, pp.142–146. [75] B.P. Payne, V. Venugopalan, B.B. Mikic, and N.S. Nishioka, “Optoacoustic tomography using time-resolved interferometric detection of surface displacement,” J. Biomed. Opt., vol. 8, 2003, pp. 273–280. [76] B. Sullivan and A.C. Tam, “Profile of laser-produced acoustic pulse in a liquid,” J. Acoust. Soc. Am., vol. 75, 1984, pp. 437–441. [77] G. Paltauf and H. Schmidt-Kloiber, “Measurement of laser-induced acoustic waves with a calibrated optical transducer,” J. Appl. Phys., vol. 82, 1997, pp. 1525–1531. [78] S.L. Jacques, P.E. Andersen, S.G. Hanson, and L.R. Lindvold, “Non-contact detection of laser-induced acoustic waves from buried absorbing objects using a dual-beam common-path interferometer,” Proc. SPIE, vol. 3254, 1998, pp. 307–318. [79] B.P. Payne, V. Venugopalan, B.B. Mikic, and N.S. Nishioka, “Optoacoustic determination of optical attenuation depth using interferometric detection,” J. Biomed. Opt., vol. 8, 2003, pp. 264–272. [80] S. A. Carp, A. Guerra, S.Q. Duque, et al., “Optoacoustic imaging using interferometric measurement of surface displacement,” Appl. Phys. Lett., vol. 85, 2006, pp. 5772–5774. [81] P.C. Beard, F. Perennes, and T.N. Mills, “Transduction mechanisms of the Fabry Perot polymer film sensing concept for wide band ultrasonic detection,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 46, 1999, pp. 1575–1582. [82] P.C. Bead, A. Hurrell, and T.N. Mills, “The characterisation of a polymer film optical fiber hydrophone for the measurement of ultrasound fields for use in the range 1–20 MHz: a comparison with PVDF needle and membrane hydrophone,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 47, 2000, pp. 256–264. [83] P.C. Bead, A. Hurrell, and T.N. Mills, “An optical detection system for biomedical photo-acoustic imaging,” Proc. SPIE, vol. 3916, 2000, pp. 100–109.

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[84] E.Z. Zhang, J. Laufer, and P. Beard, “Three dimensional photoacoustic imaging of vascular anatomy in small animals using an optical detection system,” Proc. SPIE, vol. 6437, 2007, 64370S. [85] A. Acquafresca, E. Biagi, L. Masotti, and D. Menichelli, “Toward virtual biopsy through an all fiber optic ultrasonic miniaturized transducer: A proposal,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 50, 2003, pp. 1325–1335. [86] A.A. Bednov, and A.A. Oraevsky, “Comparison of glucose effect in model media and biological tissue measured using time-resolved optoacoustic method,” Asian J. Phys., vol. 15, 2006, pp. 55–66. [87] S.T. Flock, S.L. Jacques, B.C. Wilson, W.M. Star, and M.J.C. van Gemert, “Optical properties of Intralipid: a phantom medium for light propagation studies,” Laser. Surg. Med., vol. 12, 1992, pp. 510–519. [88] H.J. van Staveren, C.J.M. Moes, J. van Marle, S.A. Prahl, and M.J.C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400– 1100 nm,” Appl. Opt., vol. 30, 1991, pp. 4507–4514. [89] T.L. Troy, and S.N. Thennadil, “Optical properties of human skin in the near infrared wavelength range of 1000 to 2200 nm,” J. Biomed. Opt., vol. 6, 2001, pp. 167–176. [90] K.J. Jeon, I.D. Hwang, S. Hahn, and G. Yoon, “Comparison between transmittance and reflectance measurements in glucose determination using near infrared spectroscopy,” J. Biomed. Opt., vol. 11, 2006, pp. 014022–1–7. [91] M. Kinnunen, and R. Myllyl¨a, “Effect of glucose on photoacoustic signals at the wavelengths of 1064 and 532 nm in pig blood and Intralipid,” J. Phys. D: Appl. Phys., vol. 38, 2005, pp. 2654–2661. [92] M. Kinnunen, Z. Zhao, and R. Myllyl¨a, “Glucose-induced changes in the optical properties of Intralipid,” Opt. Spectr., vol. 101, 2006, pp. 54–59. [93] Z. Zhao and R. Myllyl¨a, “Measuring the optical parameters of weakly absorbing, highly turbid suspensions by a new technique: photoacoustic detection of scattering light,” Appl. Opt., vol. 44, 2005, pp. 7845–7852. [94] Z. Zhao and R. Myllyl¨a, “Scattering photoacoustic study of weakly-absorbing substances in aqueous suspensions,” J. de Phys. IV, vol. 137, 2006, pp. 385– 390. [95] H.S. Ashton, H.A. MacKenzie, P. Rae, Y.C. Shen, S. Spiers, et al., “Blood glucose measurements by photoacoustics,” CP463 Photoacoustic and Photothermal Phenomena: 10th International Conference, 1999, pp. 570–572. [96] H. von Lilienfeld-Toal, M. Weidenmuller, A. Xhelaj, and W. Mantele, “A novel approach to non-invasive glucose measurement by mid-infrared spectroscopy:

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The combination of quantum cascade lasers (QCL) and photoacoustic detection,” Vibr. Spectr., vol. 38, 2005, pp. 209–215. [97] www.glucon.com

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15 A Noninvasive Glucose Sensor Based on Polarimetric Measurements Through the Aqueous Humor of the Eye Gerard L. Cot`e and Brent D. Cameron Texas A&M University, Department of Biomedical Engineering, USA

15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.2 Theory of Polarized Light for Detecting Chemical Compounds . . . . . . . . . . . . 15.3 The Anterior Chamber of the Eye as a Site for Polarimetric Glucose Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.4 Polarimetric Glucose Monitoring Using a Single Wavelength . . . . . . . . . . . . . . 15.5 Measurement of Optical Rotatory Dispersion of Aqueous Humor Analytes . 15.6 Corneal Birefringence Simulation and Experimental Measurement . . . . . . . . . 15.7 Dual Wavelength (Multi-Spectral) Polarimetric Glucose Monitoring . . . . . 15.8 Concluding Remarks Regarding the Use of Polarization for Glucose Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

458 458 462 469 470 475 480 481 483

This chapter begins with coverage of the basics of optical polarimetry and optical rotatory dispersion as a technique for monitoring chiral molecules, in particular glucose. The chapter describes why the aqueous humor of the eye is the sensing site of choice for polarimetric measurements due to the optical window into the body and lack of light scatter and hence depolarization. A description of an optical system that can be used to make the very small millidegree measurement along with preliminary data is presented. Data describing the main issues affecting the measurement approach in the eye are covered including time lag between the blood and aqueous humor, corneal birefringence, and motion artifact. Lastly, a multi-wavelength system is described and preliminary data presented that shows how these issues may be overcome in a final in vivo device. Key words: polarimetry, biosensors, glucose, chiral molecules, eye.

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15.1 Introduction The first documented use of polarized light for stereochemistry, or rather the study of sterioisomers such as sugar and other chemicals, was to determine sugar concentration, where it was used for monitoring industrial sugar production processes [1– 3]. In particular, in the 1800’s, two French physicists, by the names of Dominique Franc¸ois Arago and Jean Baptiste Biot, were the first to investigate the branch of science, known as stereochemistry. However, it has only been a little more than two decades that the use of polarized light has been applied to the physiological measurement of glucose. This initiative began in the early 1980’s, when March and Rabinovich [4, 5] proposed the application of this technique in the aqueous humor of the eye for the development of a noninvasive blood glucose sensor. Their idea was to use this approach to noninvasively obtain aqueous humor glucose readings as an alternative to the invasively acquired blood glucose readings. Their findings and that of prior work by Pohjola [6] indicated that such a successful quantification of glucose concentration would highly correlate with those of actual blood. During the same period, Gough [7] reported that the confounding contributions of other optically active constituents in the aqueous humor may be a barrier for this technique to be viable. In the following decade, motion artifact coupled to corneal birefringence [8, 9], low signal-to-noise ratio [10], and the potential time lag between blood and aqueous humor concentrations during rapid glucose changes [4, 5, 11, 12] were identified as problems yet to be overcome for this technique to be viable. Throughout the 1990’s, considerable research was conducted toward improving the stability and sensitivity of the polarimetric approach using various techniques while addressing the issue of signal strength and establishing the feasibility of predicting physiological glucose concentrations in vitro, even in the presence of optical confounders [12–14, 16]. To date, many of the prior issues have been addressed; however, overcoming the problematic effects of corneal birefringence due to motion artifact is still a main issue being investigated with potential solutions being reported [17, 18].

15.2 Theory of Polarized Light for Detecting Chemical Compounds To understand the foundations of polarimetry, it is helpful to first understand the nature of plane-polarized light. In general, a beam of light is composed of electromagnetic waves oscillating perpendicular to the direction of light propagation. Normally, light exists in an unpolarized state that has electromagnetic oscillations which occur in an infinite number of planes. As depicted in Fig. 15.1, a device known as a linear polarizer can be used to transmit light that exists in a single plane, known as plane-polarized light, while an analyzer (typically another polarizer with its transmission axis rotated ninety degrees) can be used to eliminate or block out

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FIGURE 15.1: An example of plane-polarized light.

light transmitted through the initial polarizer. In this case, no light will pass through the analyzer, unless there is something between these two polarizers, such as a sample tube filled with a chiral molecule such as glucose, that causes the plane of polarization to rotate. In this case, the component of the electric field projected onto the transmission axis of the analyzer will pass. Therefore, since light intensity is proportional to the square of the electric field, the intensity of light transmitted through the analyzer is related to the amount of rotation in polarized light due to the sample. With regards to the sample, in 1815 Biot observed that certain natural organic compounds in solution could rotate the polarization plane of a light beam as it propagated through the medium. He designated these substances as “optically active”; however, it took more than 30 years to recognize the underlying cause behind this rotational effect. These molecules later were termed chiral molecules, which is defined as any organic molecule that does not contain a structural plane of symmetry. Depending on the molecular conformation of an optically active compound, the plane of polarization may either be levorotatory (molecules possessing the ability to rotate light to the left or counter-clockwise) or dextrorotatory (molecules that rotate light to the right or clockwise). For glucose, only the dextrorotatory component (D-glucose) is biologically active. This form (D-glucose) is often referred to as dextrose (dextrose monohydrate). Glucose (C6 H12 O6 ) contains six carbon atoms and an aldehyde group and is therefore referred to as an aldohexose. An asymmetric center at C-1 (called the anomeric carbon atom) is created when glucose cyclizes and two ring structures, called anomers, are formed — α -glucose and β -glucose. These anomers differ structurally with respect to the relative positioning of their hydroxyl group linked to C-1 and the group at C-6, which is termed the reference carbon. The rotation in the plane of polarization is an intrinsic property of optically active

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molecules. Therefore, it follows that the amount of rotation would be proportional to the number of molecules encountered by a polarized light beam as it passes through a sample of an optically active compound. This observance leads to the conclusion that the amount of rotation is dependent upon the sample concentration and path length. The polarimetric approach is thus based on the fact that chiral molecules, such as glucose, due to their asymmetric nature rotate the azimuthal angle of the plane of polarization of a propagating linear polarized beam by an amount, α , that is proportional to their concentration, C, and path length, L. The equation that describes this effect is given as: [α ]Tλ ,pH =

α , LC

(15.1)

where [α ]Tλ ,pH is a particular molecule’s unique specific rotation which is dependent on the wavelength, λ , of light, the pH, and the temperature, T , of the aqueous sample. This specific rotation is typically given in degrees/(dm g/ml), while α , the observed rotation, is given in degrees ( ˚ ), the path length, L , is given in dm, and the sample concentration, C, is in grams of mass per ml of solution. The specific rotation of a compound is often specified at a temperature of 25 ˚ C for the yellow sodium D-line at the wavelength of 589.3 nm. A negative (−) value of specific rotation means the chemical compound is levorotatory and a positive (+) value means it is dextrorotatory. Since the biologically active form of glucose is dextrorotatory, its specific rotation will always be positive. However, since in its solid crystal state it is composed of two anomers (α -glucose and β -glucose), it has two specific rotations of 112.0 ˚ /(dm g/ml) for α -glucose and 18.7 ˚ /(dm g/ml) for β -glucose. However, when dissolved in an aqueous solution, the α and β forms of glucose interconvert over a timescale of hours to a final stable ratio of α :β equal to 36:64, in a process called mutarotation. This effect certainly needs to be considered when working with glucose in vitro, in a test cell; however, in the body this mutarotation or equilibrium condition has already occurred giving an overall specific rotation for glucose of 52.7 ˚ /(dm g/ml). Thus, if the specific rotation of a compound is known, as it is for glucose in the human body, and the amount of rotation can be measured for a given path length, equation 15.1 can be solved for the sample concentration. This relation forms the foundation and basis of polarimetry for analyte quantification. For given chiral substances found in the body, the specific rotation varies only slightly with pH and temperature around the physiologic range. The wavelength dependence of specific rotation, however, does vary dramatically, especially around the absorption wavelength of the compound. This variation is known as the Optical Rotatory Dispersion (ORD) characteristic of the constituent molecule. The ORD values for glucose throughout the visible spectrum are summarized in Table 15.1 [1]. Every optically active molecule possesses its own unique ORD curve based on its molecular makeup (i.e., bonds and structure), and provides the basis for multispectral polarimetry. The relationship between wavelength and specific rotation is described mathematically by Drude’s equation:

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TABLE 15.1: Specific rotations of glucose at various wavelengths of light Wavelength (nm) Specific rotation ˚ /(dm g/ml)

656 41.9

[α ]Tλ ,pH =

589 52.8

k1 2 λ − λ12

+

535 65.4

k2 2 λ − λ22

+

508 73.6

k3 2 λ − λ32

479 83.9

+ ...,

447 96.6

(15.2)

where λ is the wavelength of interest, k1 , k2 , and k3 are the rotational constants corresponding to the wavelengths (λ1 , λ2 , λ3 ,. . . ) of maximal absorption in the optically active region [19]. For wavelengths away from or between the absorption bands, Eq. 15.2 can be simplified to an approximation of Drude’s equation given as [20]: [α ]Tλ ,pH =

k0 . λ 2 − λ02

(15.3)

In the case where λ = λ0 , Eq. (15.3) approaches infinity and a transition in rotation occurs. This phenomenon is known as the Cotton effect [21]. The importance of this equation is that once the constants k0 and λ0 are computed by determining the specific rotation at two different wavelengths, one can then determine the specific rotation for any wavelength, λ , within the range. If a solution contains only a single optically active component, the use of a single-wavelength polarimeter is sufficient to predict the unknown concentration. However, if solutions contain more than one optically active constituent that does not remain constant between samples, the use of a single wavelength is insufficient to determine the unknown concentrations. This is because each optically active compound contributes additional amounts of rotation that vary between samples. In a situation where more than one chiral component is present in a sample, determining the specific rotation at different wavelengths enables the isolation of the contributions of a particular analyte of interest. This is accomplished by applying the superposition theorem to build a multispectral regression model [22]. Knowing the ORD characteristics for each constituent chiral component enables the optimal selection of wavelengths to produce the best possible prediction model, for the analyte(s) of interest. This is the case for glucose prediction in the aqueous humor, where other optically active analytes are present that may confound glucose measurements. It should be noted, however, that glucose is the only significant optically active component that changes in concentration especially in the case of individuals afflicted with diabetes mellitus. It is also conceivable that multiple wavelengths could be used to compensate for motion induced changes in the corneal birefringence.

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15.3 The Anterior Chamber of the Eye as a Site for Polarimetric Glucose Monitoring 15.3.1 Why use the eye? To use polarimetry for in vivo glucose detection, a suitable sensing site must be chosen that will allow passage of the light beam, cause a polarimetric change unique to glucose, and minimize the depolarization of the light due to optical scattering. Several tissues in the body, including the skin, are extremely scattering in nature and will significantly depolarize the light making it difficult to measure the small rotations due to physiological glucose levels (i.e., low signal to noise ratio). In addition, individual scattering events in themselves can also affect the overall state of polarization, thus masking the glucose signal [23]. In addition, the blood and interstitial fluid contains a large amount of proteins and other chiral molecules that would cause the plane of polarization to rotate independent of glucose. The varying path length(s) of the light within the tissue resulting from structural scattering would also be problematic in terms of both changes in the polarized light due to scatter as well as the apparent change in the polarization due to the change in the number of confounding chiral molecules in the light path. Due to these reasons, polarimetric detection through the skin or any highly scattering tissue is a very difficult task. However, the anterior chamber of the eye is unique in that the cornea and aqueous humor provide low scattering windows into the body. Although the eye is virtually void of scatter and provides a glucose concentration correlated to that of blood, it also has its own drawbacks as a sensing site. For instance, the eye is meant to focus light onto the retina; thus coupling light across the anterior chamber of the eye requires shining the light at a glancing angle or using a coupling device such as a scleral lens [4, 5]. Secondly, the cornea of the eye due to collagen and other structures is a birefringent material similar to a calcite crystal that can cause linear polarized light to become circular or elliptical [24]. There are also chiral analytes other than glucose present in the aqueous humor; however, for the most part they are either present in significantly lower concentrations or have specific rotations considerably lower than that of glucose [7]. In addition, the eye can also physically move during polarimetric measurements, which may lead to variations in sample path length and birefringence. These variations in the detected signal may contribute significant errors, hindering the in vivo polarimetric measurement of glucose. There is also the potential for a minor time lag between blood and aqueous humor glucose concentrations. Lastly, there is always a concern about safety when coupling a laser into the eye. These are some of the challenges that must be overcome if a laser-based polarimetric glucose monitoring system is to be realized.

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15.3.2 The anatomy and physiology of the eye toward glucose monitoring The basic anatomy of the mammalian eye is illustrated in Fig. 15.2. The structure can be divided into three main layers or tunics; namely, the outer, fibrous tunic, the middle, vascular tunic, and the inner, nervous tunic. The fibrous tunic is the outer layer consisting of the sclera and cornea. The nervous tunic contains the retina which includes the photosensitive rods and cones for visualization. The vascular tunic contains the choroid, ciliary body, and iris. As depicted in Fig. 15.2, the eye can also be divided into two main sections separated by the lens, namely the anterior and posterior segments. For the purposes of this chapter, we will concentrate our attention on the anterior segment and the outer and middle layers since these are directly relevant in terms of glucose concentration monitoring and coupling polarized light into the eye.

Anterior Chamber

Posterior Chamber

Iris

Choroid Ciliary Body Retina

Lens

Vitreous Humor

Optic Nerve Cornea Aqueous Humor Sclera

FIGURE 15.2: Anatomy of the eye (reprinted from the National Eye Institute, National Institutes of Health web site figure NEA04).

The anterior chamber contains the compartment in front of the lens in humans which is approximately 250 µ L in volume and contains a clear fluid known as aque-

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ous humor [25]. The ciliary body is part of the choroid and the epithelium on the inner surface of the ciliary body is responsible for the formation of the aqueous humor [26]. The aqueous humor is considered to be secreted from the ciliary body into the posterior chamber of the eye. From there the fluid flows to the anterior chamber and via the canal of schlemm to the venous system. The iris’s posterior surface lies next to the lens; however, the aqueous humor can flow between the two objects. The aqueous humor flows at a rate of approximately 3 µ L/min in humans [25]. The fluid bathes the cornea and lens and serves to provide nutrients and dispose of wastes in a similar fashion as the blood does for other tissues. The transfer of substances from the plasma into the aqueous occurs at different speeds depending on the penetration of the particular molecule through the blood-aqueous barrier. For instance, it is known that the blood-aqueous barrier is hardly penetrated at all by the very large protein molecules, in part since these would cause scatter and inhibit a clear visual response of the eye, thereby leaving the concentration of proteins in the aqueous humor at about 1/200 of the plasma protein level. It is also known that the most important nondissociated diffusible substance in the intra-ocular fluids is sugar, or more specifically glucose. However, there is a time lag between the blood and aqueous humor glucose levels as described in the results section below. In addition to the transient time delay, at steady state the diffusion or secretion of glucose into the aqueous was originally thought to be equal to that of blood plasma levels [27, 28]; however, it was later proven that the steady state glucose level is lower in aqueous than in plasma. It was not until 1966, when Pohjola [6] specifically studied the aqueous glucose content versus blood plasma glucose concentration in humans and accounted for age variations that a consistent ratio, that accounted for previous discrepancies, was determined. His results depicted in Table 15.2 showed the steadystate ratio of aqueous glucose to plasma glucose declined with age from 0.76 ± 7.3 percent (s.d.) for patients aged twenty to 0.63 ± 7.3 percent (s.d.) for patients of age eighty. Since the blood glucose content of plasma does not change with advancing age, the change is due to a decrease in the glucose content of the aqueous humor with age. It should be noted, however, that although age-induced change is obvious in the material as a whole, the values obtained in Pohjola’s work [6] show that there are elderly people who do not have a low steady-state ratio of aqueous glucose. In terms of the aqueous humor composition, it is almost identical to plasma with the exception of a few constituents. There are both optically active (chiral) components that affect polarized light and nonchiral components that do not affect the polarized light; however, for the purposes of this chapter we focus only on the typical concentrations and specific rotations of the optically active components which are given in Table 15.3. In terms of their ability to confound the polarimetry signature for glucose detection, the majority of these components are not of concern because of their low concentrations or low specific rotations compared to glucose. That being said, the major components that contribute to the specific rotation and concentration in the aqueous humor are glucose, albumin, and ascorbic acid. Therefore, when we discuss the use of multiple wavelengths later in the chapter these constituents will be the focus of the discussion.

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TABLE 15.2: Effect of age on the steady-state ratio (r) of glucose in human aqueous humor to that in human blood (from Pohjola [6]) Age (years)

r ± 7.3% (s.d.)

20 30 40 50 60 70 80

0.76 0.74 0.71 0.69 0.67 0.65 0.63

15.3.3 Corneal curvature and birefringence In order to probe the constituents within the aqueous humor of the eye, the light must first pass through the cornea. The cornea is a continuous extension of the sclera composed of transparent tissue which allows light to enter the eyeball. The cornea, although transparent to visible light, is problematic if it is desired to propagate light directly through the anterior chamber of the eye. This is mainly due to its curvature and its interfaces between the air and aqueous humor. This curvature and refractive index mismatch between the air and aqueous humor lead to the corneal interface providing the majority of the focusing power in the eye [29]. Although this makeup is a seemingly good property for vision, it provides a challenging problem if it is desired to couple light in and back out of the aqueous humor of the eye for glucose monitoring. To illustrate this problem, paraxial ray analysis [30, 31] is used to model the propagation of a light beam through the eye. Table 15.4 summarizes some of the physical parameters of the eye that are used in the analysis [30, 32–34]. All heights are with respect to the base of the hemisphere defined by the radius of curvature of the anterior corneal surface. Using an input beam height of 3.2 mm (corresponding to a point near the base of the cornea) and a slope of zero, the system of paraxial matrices to trace the input beam through the cornea is given in Eq. (15.4) [11, 30].

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TABLE 15.3: Optically active constituents of human aqueous humor Constituent Ascorbic acid Lactic acid Citric acid Glucose Alanine Arginine Cysteine Glutamine Histidine Isoleucine Leucine Lysine Methionine Phenylalanine Proline Serine Threonine Tyrosine Valine Total protein (mg/dl) Albumin (mg/dl)

Aqueous (mmol/L) 1.100 4.500 0.120 2.7-3.9 0.307 0.105 0.015 0.010 0.069 0.066 0.139 0.167 0.059 0.095 0.047 0.825 0.132 0.094 0.286 12.4-23.4 5.5-6.5

Plasma (mmol/L) 0.04-0.06 0.5-1.9 0.12 5.6-6.4 0.326 0.071 0.134 0.058 0.078 0.053 0.104 0.254 0.024 0.048 0.231 0.660 0.114 0.053 0.216 7000 3400

Ratio 18.33-27.50 2.37-9.0 1.00 0.48-0.70 0.94 1.48 0.11 0.17 0.88 1.25 1.34 0.66 2.46 1.98 0.20 1.25 1.16 1.77 1.32 0.002-0.003 0.002

Specific rotation 24.00 -2.26 —52.70 2.70 12.50 9.80 6.50 -39.01 11.29 -10.80 14.60 -8.11 -35.14 -85.00 -6.83 28.40 —6.42 —-59 - -109

S3 S5 Output ! S4 !  pac   S6  pc    S7  1 0 1 0 1 naq 1 0 1 nc ho = nair −nc nc nc −naq nc nc −naq naq mo 01 01 ra nair nair r p nc nc r p naq naq ×

S2  pc  S1  Input    1 0 1 nc hi nair −nc nair mi 01 ra n c nc

=



1 0 −0.049 1.376

×



1 0.509 01

=



 2.130 . −0.229





1 0.509 01



1 0 0.004 0.971

1 0 −0.036 0.727



3.2 0

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1 9.371 01



1 0 0.004 1.030





(15.4)

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TABLE 15.4: Optical and physical properties of the eye Index of refraction

Path length (mm)

Cornea nc =1.376 Aqueous humor naq =1.336 Water nw =1.33 Air na =1.00

Corneal thickness at base pc = 0.70 Anterior chamber pac = 12.52 —

Corneal radius of curvature (mm) Anterior surface ra =7.7 Posterior surface r p =6.8 —

—

—

From this, it is predicted that for a collimated beam entering at the base of the cornea, the beam would theoretically exit at a height of 2.13 mm with a slope of −0.23. Given this trajectory the beam would not exit the eye as shown in Fig. 15.3 and would either be blocked by the iris or possibly the sclera of the eye. It can be shown that by using an input path with a glancing angle at the input to the cornea that a light beam can potentially be transmitted through the anterior chamber (dotted line in Fig. 15.3), although this configuration is extremely cumbersome. However, through the use of an eye-coupling device such as a contact lens, it can be shown that an input light beam can be propagated in an almost straight path through the anterior chamber of the eye. Alternatively, as discussed in another chapter (Brewster angle reflection), the light may potentially be reflected from the iris or lens such that the net rotation is a function of glucose concentration. However, it should be noted that if the light were directed straight in from the top and reflected from the lens like a mirror that the net rotation would always be zero since you would cancel out the rotation in the forward and reverse directions. In addition to the challenges involved in coupling light through the anterior chamber of the eye, the cornea is also problematic for glucose monitoring in that it is birefringent. In general, if the velocity of any wave-train of light is the same in all directions through a substance, it is said to be isotropic. Many crystalline and most organic substances are, however, anisotropic or, rather, the velocity of a light wave in them is not the same in all directions, and the substance has more than one refractive index. These substances are thus doubly refracting; that is, they exhibit birefringence, and the light passing through them is split, in general, into an ordinary and an extra-ordinary ray, which are plane polarized in mutually perpendicular directions. The two wave-fronts travel at different speeds, i.e., a “slow” and a “fast” axis, and these emerge with one retarded behind the other, producing a phase difference between them [30]. The cornea of the eye is one such anisotropic substance due to its underlying structure. The cornea consists of five main layers with the stroma

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FIGURE 15.3: Light coupling through the eye (reprinted from the National Eye Institute, National Institutes of Health web site, figure NEA04).

accounting for most of the thickness and birefringence [24]. The stroma is composed of approximately 200 sheets of lamellae that are further composed of collagen fibers aligned parallel to each other. Each successive sheet of lamella is oriented differently with the previous layer. Each of these layers contains their own inherent birefringence and the stack shows an overall birefringence [24]. When examined using polarized light the corneal lamellae were found to be doubly refracting with the optic (slow) axis along their length [35]. As was shown by Stanworth and Naylor [36], the position of the cornea at which measurements are made as well as the direction of the incident and emergent light are of considerable importance when measuring corneal birefringence. It was shown [36] that the retardation of one axis with respect to the other, with the light normal to the surface of the cornea, is very small across the entire corneal surface. The birefringence of the cornea, expressed as the absolute value of the difference between the ordinary and extraordinary refractive indices, was found to vary from zero in the center to about 0.00012 at the edge of the optical zone and, allowing for the increased thickness, to about 0.00028 at the extreme periphery of the cornea. For a nonmoving cornea, this birefringence would produce elliptical light which can be managed since the glucose would cause a rotation of the main axis of the ellipse. However, variations in corneal birefringence due to eye motion artifact are a major noise source for this approach and consequently a

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primary focus for future systems as described in sections 15.6 and 15.7. However, we will first describe the type of single wavelength system required to enable the sensitivity and accuracy to measure the milli-degree rotations observed for the physiologic concentration of glucose through a 1 cm path length indicative of the anterior chamber of the eye.

15.4 Polarimetric Glucose Monitoring Using a Single Wavelength As depicted in Fig. 15.4 and described previously by this group [11, 37], we designed and implemented a very sensitive single wavelength polarization modulated closed-loop polarimetric system. The system uses a single laser that is passed through a linear polarizer. The polarization vector is modulated by roughly ±1 degree using a function generator coupled to an electro-optic device known as a Faraday rotator. The function generator is modulated at a single frequency (Fig. 15.5 (a), top) producing a crossed polarized optically modulated signal (Fig. 15.5 (a), bottom). This optically modulated signal is then passed through either a test cell filled with glucose or the anterior chamber of the eye containing aqueous humor, which causes the signal to be modulated asymmetrically (Fig. 15.5 (b)) as seen by the detector after passing through the analyzer (polarizer crossed at 90 degrees to the input polarizer). This signal is then passed to a lock-in amplifier that measures the phase sensitive amplitude of the single frequency component which is proportional to the rotation due to glucose. This amplitude information is sent to a computerbased controller and fed back to a second Faraday rotator to null the system (i.e., negate the optical rotation of the sample). The voltage required to null the system is the measured parameter of interest and is proportional to the glucose concentration. Mathematically, the operation of the system has been previously derived by this group [11] using Jones theory. The detected signal is represented by Eq. (15.5), where θm is the depth of the Faraday modulation, ωm is the modulation frequency, and φ represents the rotation due to the optically active sample subtracted by any feedback rotation due to the compensation Faraday rotator. From Eq. (15.5) it is evident that, without an optically active sample and with the DC term removed, the detected signal only consists of the double modulation frequency (2ωm ) term, represented by the bottom signal in Fig. 15.5 (a). However, when an optically active sample is present, such as glucose, the detected signal then becomes an asymmetric sinusoid, represented in Fig. 15.5 (b), which contains both the fundamental (ωm ) and the 2ωm modulation frequency terms.   θ2 θ2 I ∝ E 2 = φ 2 + m + 2φ θm sin (ωmt) − m cos (2ωmt) . 2 2

(15.5)

As derived in Eq. (15.5), the signal from this single wavelength polarimeter is based on three terms: a DC term, a fundamental frequency term, and a double fre-

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quency term. It is the second amplitude parameter in the fundamental frequency term (ωm ) that contains the glucose information, φ .

ED FR

FC

D

Red Laser 635nm

Digital Lockin Amplifier DLIA

P

A Line Driver

Amplifier

eye

Function Generator

P = polarizer FR = Faraday Rotator ED = eyecoupling device FC = Faraday Compensator A = analyzer D = detector

D/A

Desktop computer

FIGURE 15.4: Block diagram of the designed and implemented digital closedloop controlled polarimeter, where the sample holder is used for in vitro samples and the eye coupling device is used for in vivo studies (reprinted with permission from Baba, 2002).

The feedback voltage applied to the Faraday rotator from the lock-in amplifier which locks into this fundamental frequency term is used to quantify the glucose. This system was developed and calibrated followed by independent validation. The sample calibrations for four individual runs of glucose doped water are presented in Table 15.5 [15]. As depicted in Table 15.5, all results show a standard error corresponding to better than 10% accuracy which exceeds the standard 15% accuracy provided by most commercial finger stick glucose meters. Thus, the results demonstrate the system robustness and establish a system sensitivity capable of accurately resolving physiological concentrations of glucose. One sample plot for the validation results (i.e., using a previously formed calibration model and an independent set of data for prediction) is shown in Fig. 15.6.

15.5 Measurement of Optical Rotatory Dispersion of Aqueous Humor Analytes As described with Eqs. (15.2) and (15.3), specific rotation for a given optically active molecule varies as a function of wavelength. This phenomenon is known as optical rotatory dispersion (ORD). When more than one optically active component is present in solution, a single wavelength can not be used to distinguish the amount

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(a)

(b)

FIGURE 15.5: (a) The top sinusoid is the Faraday modulation signal (1.09 kHz, ωm ) used as the reference for the lock-in amplifier and the bottom sinusoid is the double modulation frequency (2.18kHz, 2ωm ) signal detected for a perfectly nulled system. (b) This curve is the detected signal, that contains both ωm and 2ωm when an optically active sample, like glucose, is present (reprinted with permission from Cameron, 2000).

FIGURE 15.6: Predicted versus actual glucose concentrations for the hyperglycemic glucose doped water experiments, where the line represents the error free estimation (y = x) (reprinted with permission from Cameron, 2000).

of rotation that each analyte contributes to the overall rotation since this would be equivalent to trying to solve one equation for more than one unknown. Thus, if it is desired to distinguish the optical rotation solely due to glucose in the presence of the other optically active component, additional information from multiple wavelengths is required. Since every chiral molecule has its own ORD curve, the use of multiple wavelengths can potentially be used to reduce the prediction error associated with single wavelength polarimetric measurements. It is therefore desirable to know

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TABLE 15.5: Summary statistics for four individual data sets collected for water doped glucose samples Medium

Run

Correlation coefficient (r)

Glucose and water

1 2 3 4

0.99888 0.99909 0.99956 0.99975

Standard error of prediction in calibration [mg/dl] 9.24 8.30 5.77 4.34

Standard error of prediction in validation [mg/dl] 7.26 8.64 9.69 9.76

exactly how the wavelength dependencies for a given optically active molecule behaves, such that the optimum and minimal number of wavelengths can be chosen in order to minimize prediction error. For example, suppose it is desired to measure glucose rotation in the presence of albumin; ideally, it would be preferable to choose at least one wavelength that is more sensitive to glucose rotation and less sensitive to albumin. For the application of in vivo glucose sensing, the eye is better suited for the glucose measurement because the blood-aqueous humor barrier within the eye is a very selective membrane that acts as a filter [25, 38, 39]. Specifically, it will not let particulate matter, such as large chiral globular proteins, pass into the aqueous humor of the eye. In addition, the barrier is also very selectively permeable to certain molecules, such as glucose, that can easily traverse the membrane. In terms of optically active molecules, the aqueous humor of the eye contains several. However, the majority of these optically active components are either present in very minute concentrations (such as amino acids) and/or have negligible specific rotations (i.e., lactic acid) [7, 22]. The three main optically active components present in the aqueous humor of the eye are glucose, ascorbic acid, and albumin [7]. The specific rotation for other chiral molecules found in the aqueous humor of the eye has been measured; however, this information is usually limited to the sodium D-line at 589.3 nm. The ability to measure the complete ORD does provide the opportunity to optimize polarimetric glucose calibration in the eye through the use of a multi-spectral approach. To measure the optical rotatory dispersion (ORD) characteristics of the major optically active components in the aqueous humor of the eye, namely, glucose, albumin, and ascorbic acid, a device similar to that depicted in Fig. 15.7 can be employed. A light source such as a Xenon arc or tungsten halogen lamp can be used as an input multi-wavelength light source. The purpose of the first polarizer is to linearly polarize the input light which then propagates through a 5 cm rectangular sample cell (Starna Cells Inc., Atascadero, CA). This cell contains the optically active sample under investigation. The beam is then transmitted through the analyzer, which is merely another polarizer oriented perpendicular to the initial polarizer. The purpose of the analyzer is to convert the rotation in the polarization plane, due to the optically

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A noninvasive glucose sensor f Monochromator and PMT Detector

Unpolarized Light

Optically Active Sample

Polarizer

Analyzer

FIGURE 15.7: Generalized block diagram of the experimental ORD measurement system (reprinted with permission from Cameron 2000). active sample, into a proportional intensity. An optical fiber is used to collect the light coming from the analyzer and route it into a monochromator/photo-multiplier tube (PMT) configuration. The monochromator is employed after the fiber to separate the individual intensities present at each wavelength, which are proportional to the individual optical rotations in polarization. A light detector, such as a PMT, then measures the individual light intensities as the monochromator sweeps across the wavelength range of interest. Mueller matrix theory provides a convenient method to model this system [31]. The system of matrices that represent the operation of the system depicted in Fig. 15.7 is given by:  SO  S1    =  S2  S3 Detected signal 



1  1 1 2 0 0

10 10 00 00

 0 0  0 0

Analyzer

   1 −1 0 0 10 0 0  0 cos(2θ ) sin(2θ ) 0  1  −1 1 0 0       0 − sin(2θ ) cos(2θ ) 0  2  0 0 0 0  01 1 1 0 0 00 Optically Active Polarizer Sample 



 IO 0    0  0 Input signal

 1 − cos2θ  1 − cos2θ  , = I4O  0  0 

(15.6) for which S0 is the detected light intensity that is proportional to optical rotation, θ , of the sample. The values for S1 , S2 , S3 are the remaining output Stokes parameters [31] and I0 is the input light intensity which is a function of wavelength. The main component of interest in Eq. (15.6) is that of S0 which is given by: I0 (1 − cos2θ ). 4 Equation (15.7) can then be solved for optical rotation, θ , which yields:   1 4S0 θ = arccos − +1 . 2 I0 S0 =

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To demonstrate the measurement of ORD, the chemicals D-glucose, L-ascorbic acid, and rabbit albumin (Sigma Chemical, St. Louis, MO) are used. For sample preparation, stock solutions of each chemical were prepared at concentrations of 10,000 mg/dl, 15,000 mg/dl, and 10,000 mg/dl, respectively. The relation in Eq. 15.8 was applied to compute the ORD characteristics for each chemical between the wavelengths of 475 to 800 nm in 1 nm increments. A water reference was used to measure the relative input spectrum, I0 , and the system was calibrated for optical rotation using the glucose ORD curve. Once the optical rotation, θ , was measured for the sample under investigation, the specific rotation, [α ], was computed using the relation in Eq. (15.1) where the α = θ (i.e., α is the observed rotation in Eq. (15.1) which is equivalent to θ in Eq. (15.8)) Shown in Fig. 15.8 (a) are the ORD curves for D-glucose, L-ascorbic acid, and rabbit albumin measured with the experimental apparatus and methods described above. As can be seen, compared to ascorbic acid and albumin, the specific rotation of glucose is the most significant of the three. As expected, the specific rotation of glucose is positive due to its dextrorotatory nature and that of albumin is negative due to its levorotatory nature. As for L-ascorbic acid, one would expect that its specific rotation would be negative since in dry form it is levorotatory; however, it is transformed into a dextrorotatory configuration when dissolved in water. As seen in Fig. 15.8 (a), for the visible region of light, the specific rotation of each analyte approaches zero as wavelength increases. Shown in Fig. 15.8 (b) are the actual observed rotations in polarized light for each analyte. This is computed using Eq. (15.1) and using the previously measured specific rotations and assuming a path length of 1 cm (average path length of a human eye) and normal physiological concentrations. The normal physiological concentrations within the aqueous humor are 100 mg/dl for glucose, 20 mg/dl for ascorbic acid, and 6 mg/dl for albumin [25, 38, 39]. As can be seen, when the overall contribution to observed rotation is considered, the majority of rotation is due to glucose, specifically 94 to 97% depending on the wavelength of light. Therefore, the combined error contribution due to ascorbic acid and albumin would be at most 6%. Even though the rotations due to these substances are much less than that of glucose, a multi-wavelength system was used by this group to show that glucose prediction error can be minimized even further through the use of multiple wavelengths [11]. In fact, when glucose and albumin were combined, the error in glucose prediction was reduced by a factor of two by merely using a two wavelength polarimetric approach [11]. In addition to error reduction in multi-component chiral samples, multi-spectral polarimetric approaches may also be used to help minimize the effects of corneal birefringence in the presence of motion artifact as described in sections 15.6 and 15.7.

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(a)

(b)

FIGURE 15.8: ORD measurements. (a) measured ORD Curves for glucose, ascorbic acid, and albumin, (b) actual observed rotation within the aqueous humor for normal physiological concentrations (reprinted with permission from Cameron 2000).

15.6 Corneal Birefringence Simulation and Experimental Measurement In the description of the following experiments, the cornea of the eye is modelled as a linear retarder, meaning that for a linear input polarization state, the cornea’s linear birefringence causes change in the state of polarization (SOP) from a linear to an elliptical state. This is due to an introduced phase retardance, δ , as defined in Eq. (15.9) [13], where ηo and ηe are the refractive indices encountered by the ordinary and extraordinary components, respectively. This then creates a change in the detected signal as the ellipticity of the ensuing elliptically polarized beam varies directly with any change in birefringence (ηo − ηe ),

δ=

2π t (ηo − ηe ) . λ

(15.9)

If the cornea were a stable, fixed, birefringent element such as a waveplate, its effects could be theoretically eliminated. However, there is valid concern that corneal birefringence may become problematic when there is motion artifact because the effect of nonstationary birefringence may mask the glucose signature. To assess and quantify this problem, the single wavelength experimental system described in Fig. 15.4 was used on an anesthetized rabbit. The main difference is that instead of a cuvette an inverted test tube designed with plane parallel windows and filled with saline for index matching was placed over the rabbit eye. The test tube apparatus that surrounds the anesthetized rabbit eye allows for better light coupling and direct propagation through the anterior chamber without experiencing any light bending ef-

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fects as described in subsection 15.3.3. This is because the apparatus eliminates any refractive index mismatch which would normally be present at the corneal interface. This eye coupling system is thoroughly described by our group in the dissertation of Cameron [11]. In the polarimetric based rabbit experiments, to identify and characterize the motion artifact, the double frequency, 2ωm , component of the detected polarimetric signal is continuously monitored during the course of a rabbit experiment (the third component in Eq. (15.5)). As can be seen in this derivation, the double frequency component is not a function of glucose rotation, which is the reasoning behind not using it as part of the controller input. Any motion artifact, however, which will result in a variation in birefringence during the course of measurement, will be directly superimposed on this term. Therefore, the overall amplitude of this term is especially suited for directly monitoring motion artifact. Through the use of a digital lock-in amplifier, the amplitude of the double frequency term (second harmonic) can be continuously monitored during the course of the rabbit experiment. A partial time series of the amplitude of the second harmonic term is presented below [Fig. 15.9 (a)]. In ideal circumstances (i.e., no motion artifact), the overall amplitude of the second harmonic term should be constant (i.e., a straight line with zero slope). Therefore, for the ideal case, the plot should merely consist of a horizontal line since the lock-in amplifier outputs a DC value proportional to the amplitude of the signal of interest. However, as can be seen [Fig. 15.9 (a)], the overall amplitude of the second harmonic term varies considerably as a function of time. The motion artifact is specifically the cause of these variations. Therefore, we wanted to determine the specific frequencies present in the oscillations of the discrete time series in order to isolate the main sources of the motion artifact. To achieve this task, spectral analysis utilizing the fast Fourier transform was performed on the full discrete time series to determine the relative energy present as a function of frequency. The second graph [Fig. 15.9 (b)] is the corresponding energy spectral analysis plot. Ideally, in an anesthetized rabbit model in which the rabbit is lying on its side, possible motion sources include breathing and the cardiac cycle. In a human patient, presumably monitoring upright, these artifacts should be less than in the rabbit model. These artifacts occur at approximately 60-100 breaths/min and 200-300 beats per minute, respectively. In terms of cycles per second (Hz), these correspond to 1 to 1.7 Hz (breathing) and 3.3 to 5 Hz (cardiac). As can be seen in the spectral analysis plot [Fig. 15.9 (b)], a peak occurs at roughly 1.6 Hz, corresponding to breathing. Other high frequency peaks also occur past 3.4 Hz, which are due to the cardiac cycle. In addition, the peak near 0 Hz is due to the average value of the second harmonic signal that manifests itself as a DC component. In addition to cardiac and respiratory noise, eye motion occurs at both high frequency involuntary fixation (50 to 80 movements per second) including saccadic motion and low frequency voluntary fixation that occurs when a person moves their eyes to find the object on which they wish to fixate. In an anesthetized rabbit the voluntary motion artifact is insignificant and when the system is ready for human trials, a fixation point can be used to minimize this type of motion.

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Time (seconds)

(a)

(b)

FIGURE 15.9: (a) In vivo time series plot of the double-frequency term (should be flat when there is no motion artifact); (b) frequency analysis showing the respiratory peak at 1.6 Hz and the cardiac peak at 3.4 Hz (reprinted with permission from Cameron 2000).

In order to compensate for motion induced corneal birefringence artifact one must have a better understanding of how these birefringence changes affect the detected measurement signal. This can be accomplished through both simulation and experimentation. Figure 15.10 is a MATLAB-generated simulation of the effects of linear birefringence. The birefringence values used for the simulation are within the range based on the measured refractive index variations available in literature for the fast and slow axes of rabbit cornea [13]. As indicated in the literature, birefringence (ηo − ηe ) varies in the eye within the range of zero at the apex or top of the cornea to 5.5 × 10−4 at the base of the cornea, where it attaches to the sclera. Therefore, a net change in the retardance, δ , can be calculated using Eq. (15.9) for a given corneal thickness, t, and wavelength, λ . Figure 15.10 substantiates the changes of a horizontal linear SOP into an elliptical SOP whose ellipticity changes with variations in the sample birefringence when the input SOP is neither aligned with the slow or fast axis of birefringence. For this simulation a fast axis of birefringence of 160 degrees was used, comparable to that found experimentally, and the value of the retardance was varied by varying the refractive indices around the center of the eye (1.0 × 10−4 to 3.0 × 10−4) for a given corneal path length of 0.407 mm and wavelength of 633 nm. This variation showed a slight shift in the minimum as seen in Fig. 15.10 (a) and spreading of the ellipse as depicted in Fig. 15.10 (b). This would be comparable to slight changes in the retardance with position of the beam on the cornea as is likely the case for the three eyes used in the experiment. The experimental setup for assessing corneal birefringence in excised rabbit eyes is shown in Fig. 15.11. The light source is a 3.5 mW 635 nm red diode laser (Meredith Instruments, Glendale, AZ). An optical chopper wheel (Oriel Corporation, Stratford, CT) at a frequency of 1.1 kHz modulates the light beam from the laser. The modulated light beam is then separated into two orthogonal propagating beams by

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Relative normalized intensity

Angle of analyzer (degrees)

(a)

Theoretical normalized intensity (cos of analyzer angle squared)

(b)

FIGURE 15.10: These MATLAB derived simulations illustrate the effects of changing birefringence, (ηo − ηe ), on the detected intensities. (The index difference varied from 1 × 10−4 (triangles), to 2 × 10−4 (diamonds), to 3 × 10−4 (circles).) The plots were derived by rotating the analyzer with respect to the polarizer to determine the effect of a birefringent sample placed in between them. (a) For a birefringent crystal the detected intensities vary sinusoidally as the polarizer/analyzer plane is rotated through 180 ˚ . The birefringence has the effect of introducing a phase shift in the detected intensities. (b) This plot was produced by plotting the detected intensity at a given angle versus the normalized theoretical detection intensity for a polarizer and rotating analyzer combination without a sample (i.e., the cosine squared of the input angle). Without birefringence you would have a straight line. With a changing birefringence you can see the conversion of the linear polarization into elliptical polarization states of varying ellipticity and azimuthal angle of the major axis (reprinted with permission from Baba, 2002).

a nonpolarizing beam-splitter (Melles Griot, Boulder, CO). The beam propagating perpendicular with respect to the original input beam passes through a polarizer (Edmund Scientific, Barrington, NJ) before being detected by a biased photo-diode detector (Thorlabs Inc., Newton, NJ), for use as a reference measurement. The beam propagating forward with respect to the original input beam is apertured before being passed through a Glan-Thompson 100,000:1 polarizer (Newport Corporation, Fountain Valley, CA) that converts it into a linear horizontally polarized beam. This beam is then converted into a right circular polarized beam by a QWP, with a fast axis at +45 ˚ with respect to the vertical axis. The circular-polarized beam is apertured to 0.5 mm diameter before probing the eye sample contained in a nonbirefringent, saline filled, eye sample cell holder that was made in house. The eye holder used suction to fixate the eye in place and was mounted on a stage that could be adjusted both vertically and horizontally for placement of the eye in the beam path. The ensuing beam is passed through another Glan-Thompson polarizer, whose polarization axis is manually incrementally rotated through 210 degrees, to produce a corresponding

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measurement intensity. The light intensity is detected by another pin photo-diode detector (Thorlabs Inc., Newton, NJ). The two photo-diode detectors convert the measured intensities to proportional voltages, that are extracted by lock-in amplifiers SR830 and SR850 (Stanford Research Systems, Sunnyvale, CA) using the 1.1 kHz optical chopper frequency reference. The output voltage from the lock-in amplifiers is then acquired for processing by a Pentium II PC via NI-DAQ board operated by a c 5.1 (National Instruments, Austin, TX) program [37]. LabVIEW

Lock-in Amplifier

Lock-in Amplifier

QWP

reference detector

NI-DAQ Board

Desktop computer

Polarizer

R-circular

Eye sample holder

Polarizer

Red Laser 635nm

A BS P BS - beam splitter A - aperture QWP - 1/4 wave plate

Polarizer

A

QWP

Suction

rotated axis

sample detector

ED

FIGURE 15.11: Experimental setup to assess corneal birefringence across various points in an excised rabbit eye (reprinted with permission from Baba, 2002).

As shown in Fig. 15.12, the birefringence curves for three separate rabbit eyes have been obtained using the experimental setup depicted in Fig. 15.11. The light beam was centered at roughly the midpoint between the apex of the cornea and the base of the cornea (where it meets the sclera). As can be depicted in Fig. 15.12 (a) the minimum point varies slightly between eyes. This is likely due to a slight change in the retardance between eyes as a result of a slightly different index of refraction change. In addition, this change in birefringence is shown in Fig. 15.12 (b) by the change in ellipticity. This is confirmed by the simulation depicted in Fig. 15.10 in which the retardance has been varied. The change in corneal retardance is likely caused by the well-documented change in corneal retardance with position from the apex of the cornea. This confirms that slight changes in position with motion artifact can greatly affect the polarization signal. These recent findings are encouraging and suggest that the birefringent portions of the corneal surface, in a rabbit model, may have a relatively universal fast axis located at approximately 160 ˚ from the vertical axis, defined as a line that runs from the apex of the cornea and through the pupil. Though more rabbit eyes need to be investigated with the light source at various locations across the cornea, this preliminary finding coupled with the understanding of how birefringence affects the detected signal allows for the theoretical elimination

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FIGURE 15.12: (a) Normalized plot of corneal birefringence from three different rabbit eyes showing a minimum and hence fast axis of birefringence at roughly 160 degrees. (b) Plot of cosine of the angle of the analyzer squared (from 0-180 degrees) versus the normalized values in which the minimum for each plot was set to zero. This shows the characteristic elliptical birefringence (reprinted with permission from Baba, 2002).

of the effects of changing birefringence on the measurement of the azimuthal rotation of the linear polarization vector due to glucose.

15.7 Dual Wavelength (Multi-Spectral) Polarimetric Glucose Monitoring In an effort to illustrate the proof of concept of how multi-spectral polarimetry may be able to minimize the effects of varying birefringence observed with corneal motion, a dual wavelength closed-loop system is evaluated with a birefringent test cell containing varying concentrations of glucose. This system, described in a recent publication [18], was very similar to the single wavelength system described in Fig. 15.4 with the exception that a second laser, Faraday rotator, and beam combiner were incorporated. The test cell possessed a birefringence slightly higher than that reported in prior corneal measurements. The system was evaluated using various concentrations of glucose contained in a birefringent test cell which was subject to motion artifact. The results in Fig. 15.13 (a) and (b) show that for a static, nonmoving sample, glucose can be predicted to within 10 mg/dl for the entire physiologic range

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(a)

(b)

FIGURE 15.13: Actual versus predicted glucose concentration for glucose-doped water for sample experiments without motion, where (a) includes two separate experiments run at 635 nm using a single closed-loop system and (b) is two separate experiments run at 523 nm using a single closed-loop system (reprinted with permission from Wan, 2005).

(0-600 mg/dl) for either laser wavelength (523 nm or 635 nm). As expected, in the presence of moving birefringence, each individual wavelength produced standard errors on the order of a few thousand mg/dL as shown in Fig. 15.14 (a). However, when the data from the two wavelengths were combined [Fig. 15.14 (b)], this error was less than 20 mg/dL. It should be noted that the controller for the system was not optimized and so was slow; thus the test cell was moved slower than what would be expected in the eye. However, this data does show that multiple wavelengths can be used to drastically reduce the error in the presence of a moving birefringent sample and thus may have the potential to be used to noninvasively monitor glucose levels in vivo in the presence of moving corneal birefringence.

15.8 Concluding Remarks Regarding the Use of Polarization for Glucose Monitoring In this chapter, an introduction to the use of polarized light in the aqueous humor of the eye has been described as a potential means for noninvasively quantifying physiologic glucose levels. Furthermore, the reasoning behind choosing the eye as the preferred sensing site for polarimetric glucose measurements was described. The ability to develop a single wavelength polarimetry system sensitive enough to measure the milli-degree rotations depicted for physiologic glucose concentrations across a 1 cm path length was demonstrated. The results for the in vitro multi-spectral studies were presented, indicating that polarimetry does indeed have enough specificity

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8000

6000

Predicted Concentration [mg/dl]

Predicted Concentration [mg/dl]

580 4000

2000

0

-2000

-4000

*: Corr.Coef.= 0.067; SEP = 2895 mg/dl o: Corr.Coef.= 0.046; SEP = 4236 mg/dl -6000

0

100

200

300

400

Actual Concentration [mg/dl]

(a)

500

600

480

380

280

180

80

-20 0

100

200

300

400

500

600

Actual Concentration [mg/dl]

(b)

FIGURE 15.14: (a) Response of a single wavelength for predicting glucose concentration when there is motion artifact from a varying birefringence (* — 635 nm wavelength, o — 523 nm wavelength). Note that using either single wavelength system did not allow for any reasonable predictive capability with motion artifact. However, shown in (b) are the mean predicted concentrations with error bars for three repetitions using the dual wavelength (635 nm and 523 nm) closed-loop system in the presence of motion artifact. Note that by using two wavelengths that the system is now capable of predicting glucose in the presence of motion (reprinted with permission from Wan, 2005). to measure glucose concentration in the eye, which in part is due to the ability of the eye to filter out several of the optically active components that are found in the blood. The effect of time varying corneal birefringence on polarimetric glucose measurements has been characterized in vivo and the system modelled and characterized for the eye in vitro. Using a dual-wavelength closed-loop system, the compensation for birefringence changes due to motion artifact was accomplished. It was successfully shown that the glucose concentration could be measured in vitro when motion artifact is present. The future research in this technology will need to focus on development and testing of a robust multispectral polarimetric system for in vivo studies in animals and humans.

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References [1] C.A. Browne and F.W. Zerban, Physical and Chemical Methods of Sugar Analysis, 3rd edition, John Wiley & Sons, New York, 1941. [2] B.E.R. Newlands, Sugar, Spon & Chamberlain, New York, 1909. [3] G.L. Spencer, A Handbook for Cane-Sugar Manufacturers, 6th edition, John Wiley & Sons, New York, 1917. [4] W.F. March, B. Rabinovitch, and R.L. Adams, “Noninvasive glucose monitoring of the aqueous humor of the eye: part II. Animal studies and the scleral lens,” Diab. Care vol. 5, 1982, pp. 259–263. [5] B. Rabinovitch, W.F. March, and R.L. Adams, “Noninvasive glucose monioring of the aqueous humor of the eye: part I. Measurement of very small optical rotations,” Diab. Care, vol. 5, 1982, pp. 254–258. [6] S. Pohjola, “The glucose content of the aqueous humour in man,” Acta Ophth., vol. 88, 1966, pp. 11–80. [7] D.A. Gough, “The composition and optical rotatory dispersion of bovine aqueous humor,” Diab. Care, vol. 5, 1982, pp. 266–270. [8] G.L. Cot`e, M.D. Fox, and R.B. Northrop, “Noninvasive optical polarimetric glucose sensing using a true phase technique,” IEEE Trans. Biomed. Eng., vol. 39(7), 1992, pp. 752–756. [9] G.L. Cot`e, “Noninvasive optical glucose sensing-an overview,” J. Clin. Eng., vol. 22, 1997, pp. 253–259. [10] D.C. Klonoff, “Noninvasive blood glucose monitoring,” Diab. Care, vol. 20, 1997, pp. 433–437. [11] B.D. Cameron, The Application of Polarized Light to Biomedical Diagnostics and Monitoring, College Station, Texas, 2000. [12] C. Chou, C.Y. Han, W.C. Kuo, Y.C. Huang, C.M. Feng, and J.C. Shyu, “Noninvasive glucose monitoring in vivo with an optical heterodyne polarimeter,” Appl. Opt., vol. 37, 1998, pp. 3553–3557. [13] S. Bockle, L. Rovati, and R.R. Ansari, “Polarimetric glucose sensing using the Brewster-reflection off-eye lens: theoretical analysis,” Proc. SPIE, vol. 4624, 2002, pp. 160–164. [14] B.D. Cameron, H.W. Gorde, B. Satheesan, and G.L. Cot`e, “The use of polarized light through the eye for noninvasive glucose monitoring,” Diab. Technol. Ther., vol. 1, 1999, pp. 135–143.

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[15] B.D. Cameron and G.L. Cot`e, “Noninvasive glucose sensing utilizing a digital closed-loop polarimetric approach,” IEEE Trans. Biomed. Eng., vol. 44, 1997, pp. 1221–1227. [16] M.J. Goetz, Jr., Microdegree Polarimetry for Glucose Detection, Storrs, CT, 1992. [17] B.D. Cameron and H. Anumula, “Development of a real-time corneal birefringence compensated glucose sensing polarimeter,” Diab. Technol. Ther., vol. 8, 2006, pp. 156–164. [18] Q. Wan, J.B. Dixon, and G.L. Cot`e, ”Dual wavelength polarimetry for monitoring glucose in the eye,” J. Biomed. Opt., vol. 10, (024029) 2005, pp. 1–8. [19] B.D. Cameron, Polarimetric Glucose Sensing Utilizing a Digital Closed-Loop Control System, College Station, Texas, 1996. [20] F. Ciardelli and P. Salvadori, Fundamental Aspects and Recent Developments in Optical Rotatory Dispersion and Circular Dichroism, Heyden & Son Ltd., London, 1973. [21] B. Jirgensons, Optical Rotatory Dispersion of Proteins and Other Macromolecules, Springer-Verlag, New York, 1969. [22] T. King, In Vitro Development of a Noninvasive Polarimetric Glucose Sensor for Diabetic Home Monitoring, College Station, Texas, 1993. [23] H.C. van de Hulst, Light Scattering by Small Particles, Dover, New York, 1981. [24] J.W. Jaronski, H.T. Kasprzak, and E.B. Jakowska-Kuchta, “Numerical and experimental study of the corneal anisotropy,” Proc. SPIE, vol. 2628, 1996, pp. 263–268. [25] M. Civan, The Eye’s Aqueous Humor — From Secretion to Glaucoma, Academic Press, San Diego, CA, 1998. [26] W.H. Hollinshed and C. Rosse, Textbook of Anatomy, Harper & Row, Philadelphia, 1985. [27] F. Ask, “Uber den Zuckergehalt des Kammerwassers,” Biochem., vol. 59, 1913, pp. 1–62. [28] W.S. Duke-Elder, Textbook of Ophthalmology, Mosby Co., St. Louis, 1956. [29] A.C. Guyton, Human Physiology and Mechanisms of Disease, 5th Ed., W.B. Saunders, Philadelphia, 1992. [30] G.L. Cot`e, Development of a Robust Optical Glucose Sensor, Storrs, Connecticut, 1990. [31] E. Hecht, Optics, Addison-Wesley, Reading, MA, 1987. [32] A. Cowan, Refraction of the Eye, Lee & Febiger, Philadelphia, 1938.

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[33] A. Gullstrand, “Uver astigmatismus, koma und aberration,” Ann. Phys., vol. 18, 1905, p. 941. [34] A. Stanworth and E.J. Naylor, “Polarized light studies of the cornea I. The isolated cornea,” Exp. Biol., vol. 29, 1953, pp. 160–163. [35] W. His, Beitrage zur Normalen und Pathologischen Histologie der Hornhaut, Inaug.-Dissert., Basel, 1856. [36] A. Stanworth and E.J. Naylor, “The polarized light studies of the isolated cornea,” Brit. J. Ophth., vol. 34, 1950, pp. 201–211. [37] J.S. Baba, B.D. Cameron, S. Theru, and G.L. Cot`e, “The effect of temperature, pH, and corneal birefringence on polarimetric glucose monitoring in the eye,” J. Biomed. Opt., vol. 7, 2002, pp. 321–328. [38] H. Davson, The Physiology of the Eye, Academic Press, New York, 1972. [39] S.I. Rapoport, Blood-Brain Barrier in Physiology and Medicine, Raven Press, New York, 1976.

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16 Noninvasive Measurements of Glucose in the Human Body Using Polarimetry and Brewster-Reflection Off of the Eye Lens Luigi Rovati Department of Information Engineering, University of Modena and Reggio Emilia, Modena, 41100 Italy Rafat R. Ansari NASA Glenn Research Center, Cleveland, OH 44135, USA 16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.2 Basic Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.3 Anatomy and Properties of the Human Eye of Interest for Polarimetric Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.4 Optical Access to the Aqueous: Tangential Path and Brewster Scheme Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.5 Glucose Sensor Based on the Brewster Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.6 Performance of the Glucose Sensor Based on the Brewster Scheme . . . . . . . . 16.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

488 489 490 493 498 501 523 524

The objective of this chapter is to introduce a new optical concept for measuring glucose concentration in the aqueous humor. This concept involves reflecting the incident circularly polarized light off of the ocular lens at Brewster angle and by detecting and analyzing the linearly polarized light as it traverses through the eye’s anterior chamber. This light acts as a glucose measuring “tool” by giving information on the optical activity of the glucose molecules present in the aqueous. Potentially this technique can be very useful in the management of diabetes. Key words: eye glucose sensing, polarimetric measurements, Brewster reflection, diabetes care.

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16.1 Introduction Diabetes is a serious systemic disease affecting millions of people worldwide. There are no known medical cures for diabetes. It can only be managed by proper use of medication, insulin, and diet & exercise. If glucose levels in the human body are not regulated at normal concentration range (80-110 mg/dl), it can affect almost every system of the human body resulting in complications such as renal failure, retinopathy, cataract, hypertension, heart failure, limb amputations, and others. Achieving tight control of blood-glucose concentration is easier said than done because of the poor patient compliance. The current gold standard for blood-glucose monitoring requires frequent poking of distal finger tips and other soft body tissues for collecting small quantity of blood for analysis. In the future, noninvasive and non-painful methods may significantly increase the compliance rate and reduce diabetes complications. The eye’s anterior chamber potentially offers an ideal site for optical measurements of glucose levels in humans [1, 2]. Glucose concentration in the aqueous humor of the eye is similar to that of concentrations found in the blood elsewhere in the human body [1]. The polarization of light is as old as the creation of light itself. The measurement of the state of polarization of light is achieved by polarimetry. This technique is commonly used in the measurements of optical activity of chiral molecules, e.g., glucose and, therefore, in the determination of refractive indexes of materials in exvivo applications. The advantage of this approach, with respect to other optical methods, is the relatively low effects of the unwanted variables of influence to the measurement signal. Interferences occur due to other optically active substances present in the aqueous. The influence of such confounders has been estimated to be less than 10% [1, 3–5]. This estimation is based upon the assumption that the concentrations of the confounders fluctuate minimally and slowly in the aqueous humor compared to those of glucose. Furthermore, due to the specificity of the wavelength dependence of optical rotatory power, the influences of potential confounders can be eliminated by the application of a multi-spectral measurement system [6, 7]. The influence of pH and temperature is shown to be negligible [4, 5, 8]. A general disadvantage of polarimetry is the very weak nature of the effect of optical activity of glucose, which requires extremely sensitive schemes to be able to measure rotation angles in the sub-millidegree range. Another known drawback is the birefringence of the cornea since birefringence greatly affects the polarization state of the polarized light. It is possible to circumvent these problems and mitigate uncontrolled eye movements with a new approach mentioned earlier [9] and described below.

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16.2 Basic Theory The source of optical activity in glucose is its chiral molecular structure. Such a structure shows circular birefringence upon interaction with light. This means that l-circularly polarized light propagates with different phase velocity through an optically active medium than r-circularly polarized light. An arbitrarily polarized light beam can always be described by superposition of l- and r-circular components. As a consequence, the polarization state of a light beam propagating through a glucose solution is modified, when its polarization differs from a pure circular polarization state. The wave-number of each circular polarization component is determined by the refractive indices nl and nr for l- and r-circular components. Thus, the optical rotatory power or specific rotation of a generic optically active substance is defined as: [α ]Tλ ,pH =

π (nl (λ ) − nr (λ )) , λ

(16.1)

where λ represents the wavelength of the incident radiation. The optical rotation is right-handed (clockwise) if nl > nr and left-handed (counter-clockwise) if nr > nl . The optical rotatory power allows the calculation of the net rotation of the polarization plane of a linear polarized beam propagating into an optically active solution:

ϑ = [α ]λT ,pH l c,

(16.2)

where l is the path length of the light beam inside the sample and c is the concentration of the optically active substance. This equation is known as the Biot law [8]. Besides glucose, several other optically active substances are present in the aqueous. Each one of these molecules can be characterized by its specific optical rotatory power dispersion since this parameter describes the basic property to rotate the orientation of light polarization by different amounts at different wavelengths. Formally, this is described by the dependence of optical rotatory power on wavelength λ ; its general form is given by the law of Drude [10]: [α ]Tλ ,pH ∼ = [α ]λ = ∑ i

Ci . λ 2 − λi2

(16.3)

The parameters Ci are constants and λi are the absorption wavelengths in the visible and near ultraviolet spectral range. In the present application, we consider the effects of the temperature and pH negligible, as discussed by other researchers [4, 5, 8]. Table 16.1 reports the optical rotatory power of glucose for different visible wavelengths [8, 11].

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TABLE 16.1: Optical rotatory dispersion of glucose as reported by Browne [8] and in Ref. [11]

Wavelength (nm) 447 479 508 535 589 656

Optical Rotatory Power (deg·ml /dm·g) Browne [8] 96.62 83.88 73.61 65.35 52.76 41.89

Int. Crit. Tab. [11] 95.79 83.05 73.03 64.90 52.52 41.47

16.3 Anatomy and Properties of the Human Eye of Interest for Polarimetric Measurements 16.3.1 Polarization effects in the eye’s anterior chamber Since polarimetric techniques exploit the changes in polarization to detect glucose content in the aqueous, the knowledge of the polarization effects into the ocular tissues is crucial. In this section we consider only the tissues involved in the optical path of interest, i.e., cornea, aqueous, and crystalline lens. The human cornea is known to show linear birefringence [12, 13], which may highly affect the polarization state of transmitted polarized light. This birefringence results from the internal structure of the stroma. The corneal stroma consisting of bundled collagen fibrils is a layered structure known as lamellae which runs roughly parallel to the corneal surface. The stroma contains about 100 such layers. The corneal lamellae fibers have been found to show a preferred direction, in general, nasally downwards. This preferred directional order is the cause of corneal birefringence that can be estimated as the difference between the principal refractive indices ∆n = 0.0028 [13–15]. Several substances, e.g., glucose, protein, lactic acid, ascorbic acid and amino acid, present in the aqueous are optically active. However, glucose remains the dominant substance followed by protein or albumin, and ascorbic acid [1, 3–6]. The difference between the principal refractive indices in human crystalline lens ∆n is in the order of 10−6 [16, 17]. Thus the amount of birefringence in the ocular lens is about two orders of magnitude lower compared with the cornea and therefore can be neglected.

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16.3.2 The Navarro eye model The study of light propagation into the anterior chamber requires a precise model to describe the entering light beam’s optical path and state of polarization. The Navarro eye model considers the human ocular media to be linear, isotropic and homogeneous characterized by their average refractive indices. The refracting surfaces of the human eye are described by centered quadric surfaces (conicoids), which are then fitted to anatomical data [18, 19]. All surfaces show rotational symmetry along the optical axis, so that the optical system of the model eye shows rotational symmetry as well. Thus, a simplified two-dimensional cross-section of the Navarro eye that contains the optical axis can be applied. The anterior chamber includes the surfaces of anterior-posterior cornea, the aqueous humor and portion of the lens anterior. The corresponding curves of the eye profile can be given by: p R − R2 − (1 + Q) · x2 , (16.4) z(x) = 1+Q where the corresponding parameters of the model are given in Table 16.2. As shown in Fig. 16.1, the anterior cornea is described by an ellipse, the posterior cornea by a circle and the anterior lens by a hyperbola.

TABLE 16.2: Navarro eye model parameters. R and Q are the surface parameters, d is the axial thickness and n is the refractive index Ocular Surface Anterior cornea Posterior cornea Anterior lens Posterior lens

R (mm) 7.72 6.50 10.20 -6.00

Q

Ocular Medium

d (mm)

n

-0.26 0.00 -3.13 -1.00

Cornea Aqueous humor Lens Vitreous

0.55 3.05 4.00 16.32

1.3760 1.3374 1.4200 1.3360

Corneal diameters in adult human eyes typically range from about 10.5 to 12.5 mm [20]. The finite spot size of a measurement light beam and potential boundary effects near the cornea-sclera transition restricts the usable corneal aperture to an estimated average value of 10 mm. This value of the usable clear aperture of the cornea is defined by the bold line in Fig. 16.1 The dispersion of the eye media is expressed by the Herzberger formula [21] and reported in reference [22]:   a1 (λ )  a2 (λ )     (16.5) n(λ ) =   a3 (λ )  · n1 n2 n3 n4 , a4 (λ )

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FIGURE 16.1: Navarro eye model profile. The bold lines represent the interfaces used in our study. The size of the useful cornea aperture is estimated to be about 10 mm.

where · represents the array scalar product. The coefficients ai (λ ) are given by a1 (λ ) = a11 + a12λ 2 + λ 2a−13λ 2 + 0

a2 (λ ) = a21 + a22

λ2 +

a3 (λ ) = a31 + a32λ 2 + a4 (λ ) = a41 + a42λ 2 +

a23 λ 2 −λ02 a33 λ 2 −λ02 a43 λ 2 −λ02

+ + +

a14

2

,

2

,

2

,

(λ 2 −λ02 ) a24

(λ 2 −λ02 ) a34

(16.6)

(λ 2 −λ02 ) a44 2, (λ 2 −λ02 )

where the constant λ02 is 0.028 µ m2 and the wavelength λ has to be inserted in units of µ m. The matrix ai j and the array ni are defined respectively as 

a11  a21   a31 a41

a12 a22 a32 a42

a13 a23 a33 a43

   0.6615 −0.4035 0.2804 0.03 39 a14   a24   =  −4.2015 2.7350 1.5054 0.1159  , a34   6.2983 −4.6941 1.5751 0.1029  −1.7583 2.3625 0.3501 −0.0208 a44

      Cornea :  1.3975 1.3807 1.3740 1.3668 , n1 n2 n3 n4 = Aqueous : 1.3593 1.3422 1.3354 1.3278 ,  Lens : 1.3565 1.3407 1.3341 1.3273 .

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(16.7)

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16.4 Optical Access to the Aqueous: Tangential Path and Brewster Scheme Approaches The tangential path approach for polarimetric glucose detection in the human eye is simple and attractive [1, 4, 7, 23–30]. However, computer simulations show that this nice approach has limitations and therefore may not be practical eventually for human use due to the anatomical and refractive properties of the cornea. Thus we investigated a new scheme applying Brewster reflection off of the ocular lens. Both schemes to optically access the eye are investigated theoretically. The investigations are performed applying the anatomical Navarro eye model [22, 31] presented in the previous section. For the theoretical investigations a simulation program built on R MATLAB was developed. Starting at the specified initial geometrical condition (position and direction of the light beam), the geometrical properties of the light propagation are calculated applying the Snell’s law of refraction and reflection. This helps in determining the intersecting light beam with the eye surfaces and the respective refraction and reflection angles.

16.4.1 Tangential path approach In this approach linearly polarized light enters the cornea and passes tangentially through the aqueous, as shown in Fig. 16.2. As this light travels through the aqueous its linear state of polarization starts to rotate due to the optical activity of the glucose molecules. A measurement of this rotation at the end of the output provides a direct determination of the glucose concentration according to Eq. (16.2). The incident light beam must enter the anterior cornea at a minimum distance xe from the optical axis to achieve this tangential path. Applying the simulation, this value amounts to xe = 5.45 mm. However, as discussed in subsection 16.3.2, corneal diameters in adult human eyes typically range from about 10.5 to 12.5 mm. The finite spot size of the light beam and potential boundary effects at the cornea-sclera transition will further restrict the usable corneal aperture to an estimated average value of 10 mm. In Fig. 16.2 the first possible entrance condition is indicated by the dashed beam path, which does not exit through the aperture of the cornea. To overcome this difficulty a contact lens could be applied to the eye for index-matching purposes. Indeed, index-matching was used in previously reported work during in vivo experiments in rabbits [4, 28].

16.4.2 Brewster scheme A new non-contact approach to access the aqueous of the eye is presented in Fig. 16.3. Part of the polarized probe beam is reflected off the ocular lens at the Brewster’s angle φB that, according to the data reported in subsection 16.3.2, can be calculated to be 46.72 ˚ for wavelength λ = 589.3 nm. The reflected light at this angle is purely linearly polarized with polarization orientation perpendicular to the

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FIGURE 16.2: Tangential optical access to the human eye (bold line). The grey obstacles delimit the useful cornea aperture whereas the dashed line denotes the first possible tangential beam path.

plane of refraction. On its way out of the eye the polarization state of this beam is rotated by the glucose molecules in the aqueous and thus carries the concentration information. To achieve this optical path the probe beam must enter the cornea at xe = 3.12 mm from the ocular axis with an entrance angle with respect to the ocular axis of φe = 55.4 deg. In contrast to the tangential path approach, these values are not difficult to achieve in a human eye. Besides the more convenient optical access, the Brewster scheme is less sensitive to the effect of the corneal birefringence. In fact, the effective measurement light is that of the reflected beam; thus the birefringence of the cornea ideally affects measurement results only by the transition of the outgoing light through the cornea. In contrast, in the tangential path approach, measurement results are affected by both transitions of the light beam through the cornea. The polarization orientation of the incident beam is of great importance in the Brewster scheme. The use of circular polarization offers an advantage over the linear polarization as light propagates inside the optically active sample prior to the Brewster reflection. The circularly polarized incoming light is not affected by the optically active sample as the linearly polarized light does. Consider the reflection at the aqueous-lens interface. The Fresnel equations show that the electromagnetic wave reflected at the interface between media of different

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FIGURE 16.3: Optical access to the human eye: the new scheme applying Brewster reflection off of the lens. refractive indexes goes through a phase shift. This phase shift is a function of the reflection angle and the functionality differs for the p and s-component of the electric field vector [32]. For reflection angles smaller than φB = 46.72 ˚ the s-component of the electric field vector (s-mode) performs a phase shift of π , while the p-component (p-mode) shows no phase shift. This means that the polarization state is mirrored at the horizontal axis of the polarization plane, i.e., polarization flip occurs. For reflection angles higher than φB both components of the electric field vector show equal phase shifts of π ; thus, there is no polarization flip. Also the transmitted light at the air-cornea and cornea-aqueous interfaces goes through the rotation of the polarization state. This rotation occurs due to different transmission coefficients for the p- and s-components of the electric field vector. This effect is more evident for the air-cornea interface. Figure 16.4 (a) shows the transmission coefficients Tp and Ts for this interface as functions of the incident angle. Additionally, the ratio of the coefficients tsp = Ts /Tp is shown. In Fig. 16.4 (b) the reflection coefficients R p and Rs for the aqueouslens interface are shown as functions of the incident (reflection) angle. The ratio rsp = Rs /R p is also shown. Thus, when circularly polarized light crosses the cornea it shows elliptical polarization. Considering the aqueous-lens interface, the case rsp = 0 occurs at the Brewster’s angle φB , where only part of the s-component of the incident electric field

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FIGURE 16.4: (a) Transmission coefficients for air-cornea interface. Tp (shortdashed line) and Ts (long-dashed line) are the transmission coefficients of the p- and s-component of the electric field vector, respectively. The ratio of the coefficients tsp (solid line) is also reported. (b) Reflection coefficients for aqueous-lens interface. R p (long-dashed line) and Rs (short-dashed line) are the reflection coefficients of the pand s-component of the electric field vector. The ratio of the coefficients rsp (solid line) is reported.

FIGURE 16.5: Polarization modification for linearly polarized entrance light (smode) when refracted at the cornea and subsequently reflected at the lens. (1) polarization state of entrance light, (2) after the cornea has been crossed (no change), (3) after rotation due to glucose in the aqueous, (4) reflection at the ocular lens without (solid) and with (dotted) polarization flip, (5) rotation at lens reflection due to influences of the reflection coefficients for non-flipped (solid) and flipped (dotted) polarization state.

vector is reflected. For the remaining incident angles the polarization state is rotated. In Fig. 16.5 the findings for the case of linearly polarized entrance light in the s-mode are summarized schematically for deviations from the ideal optical path. Due to the s-mode of the entrance light (1) refraction at the cornea does not change the polarization state (2). The glucose present in the aqueous leads to clockwise rotation of polarization (3). The reflection at the ocular lens is separated into two steps. First, the influence of the phase shift of the p- and s-mode is indicated (4). The solid line represents the case where no polarization flip occurs. The dotted line represents polarization flip. In step (5) the modifications due to the reflection coefficients are in-

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FIGURE 16.6: Polarization modification for circularly polarized entrance light when refracted at the cornea and subsequently reflected at the lens. (1) polarization state of entrance light, (2) after the cornea has been crossed, (3) after rotation due to glucose in the aqueous, (4) reflection at the ocular lens without (solid) and with (dotted) polarization flip, (5) rotation and deformation at lens reflection due to influences of the reflection coefficients for non-flipped (solid) and flipped (dotted) polarization state.

dicated for the non-flipped (solid) and the flipped (dotted) polarization states. Thus, for deviations from the ideal optical path and linearly polarized entrance light in the s-mode, the refractive properties of light propagation lead to positive measurement errors when no polarization flip occurs (φlens > φB ) and to negative errors in the case of polarization flip φlens < φB . For linear entrance polarizations, differing from smode, these properties are only valid as long as the optical rotation due to glucose leads to a positive azimuth of polarization prior to lens reflection. If the polarization state prior to lens reflection has a negative azimuth, the error will be negative for non-flipping reflection and positive for flipping reflection. Figure 16.6 summarizes the findings for circularly polarized entrance light for deviations from the ideal optical path. The cornea modifies the circularly polarized entrance light (1) and leads to elliptically polarized light with azimuthal orientation at 0◦ (2). This polarization state is rotated clockwise by the glucose in the aqueous (3). Again, at lens reflection these effects are modified and separated due to the phase shift (4) and the influence of the reflection coefficients (5). The case of non-flipped polarization is indicated by the solid line whereas the case of polarization flip is represented by the dotted line. In contrast to the case of linearly polarized entrance light in the s-mode, deviation from the ideal optical path for circularly polarized entrance light leads to negative concentration errors when no polarization flip occurs and to positive errors in the case of polarization flip. This is due to the refraction at the cornea as indicated in (2).

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FIGURE 16.7: Glucose sensor based on the Brewster scheme. The detection system applies a multiwavelength light source, a high quality polarizer and a detection unit that resolves spectrally the detected signal and profits from optical rotatory dispersion of glucose. A fixation target helps the patient to reduce eye movements.

16.5 Glucose Sensor Based on the Brewster Scheme 16.5.1 Working principle As discussed in the previous section, the Brewster scheme offers an efficient access to the anterior chamber of the eye for polarimetric measurements. This scheme can be combined with the analysis of optical rotatory power dispersion to design a glucose sensor for the aqueous. The measurement system shown in Fig. 16.7 uses a multiwavelength light source. The relative rotation of light polarization due to glucose present in the aqueous can be performed by spectrally resolved signal detection of the angle detection unit. The light beam from the multiwavelength light source is passed through a high quality polarizer that fixes the polarization characteristics of the entrance beam. This beam is aligned onto the anterior cornea in such a way that it performs Brewster reflection at the vertex of the anterior lens surface. The resulting reflected light is then purely linearly polarized perpendicular to the plane of refraction. This light performs rotation of polarization orientation when passing through the aqueous. The amount of polarization rotation is a function of glucose concentration in the aqueous, the optical path length of the reflected beam inside the aqueous and the radiation wave-

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length. The angle detection unit separates the wavelengths and detects the signals at each chromatic channel. At the control unit, the resulting relative polarization rotations are determined from the acquired signals. The functionality of the relative polarization rotation with wavelength is specific for each optically active substance. Thus contributions from optically active confounders other than glucose present in the aqueous can be filtered out [6, 7]. Consider the simplest case when no confounders are present, applying only two different wavelengths λ1 and λ2 . The corresponding values of optical rotatory power coefficients of glucose [α ]λ 1 and [α ]λ 2 can be determined interpolating the data reported in Table 16.1. Applying the Biot law, the glucose concentration can be calculated as c=

∆ϑ , ([α ]λ 1 − [α ]λ 2 ) lah

(16.8)

where lah denotes the optical path length of the reflected beam inside the aqueous that can be theoretically determined to be lah = 3.63 mm and ∆ϑ is the relative rotation of polarization of the two beams at wavelengths λ1 and λ2 . Assuming λ1 = 543 nm (green emission) and λ2 = 633 nm (red emission) the values of the optical rotatory power can be determined to be [α ]543 = 63.02 degrees/(dm g/ml) and [α ]633 =45.10 degrees/(dm g/ml), respectively. Thus, the calibration constant of the measuring system is: CK =

1 c = 153728 (mg/dl)/degrees. = ∆ϑ ([α ]λ 1 − [α ]λ 2 ) lah

(16.9)

The glucose concentration in the body of a normal healthy person is typically around c = 100 mg/dl. Thus, the expected relative rotation of polarization ∆ϑ measured in a healthy subject’s aqueous will be 650 microdegrees. It’s worth noting that this value is highly dependent on the selection of the beam’s wavelength. As an example, if we employ the typical emission of the new UV LEDs with λ1 =255 nm the corresponding relative rotation of light polarization at c = 100 mg/dl will be 10.4 millidegrees.

16.5.2 Angle detection unit The angle detection unit should assure sufficient sensitivity to detect relative rotation of polarization in the microdegree range. In our study, this component is based on a true-phase detection system. We consider two approaches: (i) true-phase detection based on a rotating linear polarizer, and (ii) true-phase detection based on a rotating phase-retarder [33]. In both cases a rotating optical element is precisely moved by a motor, thus limiting the minimum measuring time achievable. First approach is based on a rotating linear polarizer, as shown in Fig. 16.8. A linearly polarized, monochromatic, incident light beam with plane of polarization oriented vertically in the drawing plane passes through a continuously rotating ideal linear polarizer. As the polarizer continues to rotate, only the part of the incident

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FIGURE 16.8: True-phase detection scheme applying a rotating linear polarizer (RLP). Without (1) and with (2) the optically active sample (OAS). The right-hand side shows the theoretical optical power signals at the photodetector (PD) without (solid) and with (dashed) the OAS in the beam path.

power, which corresponds to the projection of light polarization orientation onto the polarizer axis, is transmitted. Thus, the transmitted power changes sinusoidally with azimuth angle θ . If the polarization orientation and the polarizer axis are perpendicular (θ =90 ˚ ), theoretically no power is transmitted and the detected signal equals zero. Due to the symmetry of the linear polarizer this functionality repeats twice for one revolution. Thus, the detected power signal shows double of the rotation frequency of the linear polarizer. The optical power signal as a function of azimuth angle θ is shown in the right-hand side of Fig. 16.8. Positioning a sample containing an optically active solute into the incident beam path, the light entering the linear polarizer shows rotated orientation of polarization, with respect to the case without the sample. To measure the glucose concentration, two different beams at different wavelengths (chromatic channels) perform equal optical paths; thus as the effect of optical rotatory dispersion the resulting detection signals show a phase difference related to the glucose concentration. Second detection scheme is based on a rotating phase retarder, as shown in Fig. 16.9. In contrast to the rotation linear polarizer approach, this scheme exploits a rotating λ /4 plate followed by a fixed linear polarizer. Like the previous case, the phase shift is a measure for the rotation angle of light polarization due to optical activity. In a previous study [33], it has been shown that the rotating wave retarder polarizer exhibits better performance especially in the measurement of circular polarization parameters. However, this approach is more critical in the alignment and requires complex calibration procedures.

16.5.3 Experimental set-up Figure 16.10 shows the experimental setup designed to prove the concept of the Brewster scheme detection. The in vitro model used to describe the eye is shown in the dashed circle whereas the dashed box specifies the angle detection unit. Two He-Ne laser light sources (λx = 543 nm, 1 mW and λy = 633 nm, 2 mW) were aligned by the dichroic mirror DM1, which reflected the green laser light and transmitted the red. The two light beams were passed through the linear polarizer LP and subse-

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FIGURE 16.9: True-phase detection scheme applying a rotating phase-retarder (λ /4 plate) followed by a fixed linear polarizer (FLP). Without (1) and with (2) the optically active sample (OAS). The right-hand side shows the theoretical optical power signals at the photodetector (PD) without (solid) and with (dashed) the OAS in the beam path.

quently reflected at the plane side of the plano-convex lens PLC at the Brewster’s angle φB =55.54 ˚ at 633 nm. The linearly polarized reflected light was then passed through the cuvette C (optical path l = 10 mm) containing the glucose sample. Here, linearly polarized incident light was used instead of the preferred circularly polarized one since this aspect is not crucial in the in vitro experiments. After passage through the cuvette the two beams, carrying the glucose concentration information, were detected by the angle detection unit. This consists of a rotating optical element (linear polarizer or rotating phase retarder), a second dichroic mirror (DM2) of same type as DM1 and two photo detectors (PD543 and PD633). Additional spectral interference filters (F543 and F633) were placed in front of the photo detectors to avoid interferences between the two chromatic signals due to the non-ideality of the dichroic mirror DM2. Furthermore, the linear polarizer FP was placed just after the rotating element in the case of rotating phase retarder. The output signals from the photo detectors were digitized, using a digital data acquisition board plugged into a PC.

16.6 Performance of the Glucose Sensor Based on the Brewster Scheme The performance of the glucose sensor has been evaluated theoretically and experimentally. Numerical simulations have been devoted to the estimation of measurement errors whose origin is from the optical properties of the eye media, inter- and intraindividual variation of anatomical features of the eye globe, misalignments of the measurement beam and eye movements. To theoretically investigate such influences for the Brewster scheme, a simulation program was developed according to the eye model presented in section 16.3.2. First, the geometrical properties of light propagation are calculated. Here, influences of dispersion of the eye media, misalignment,

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FIGURE 16.10: Experimental setup designed to prove the concept of the Brewster scheme detection. Dichroic mirrors (DM1 and DM2), linear polarizer (LP), plano-convex lens (PCL), sample cuvette (C), diaphragm (D), rotating linear polarizer (RLP) or rotating phase-retarder (RPR), additional fixed polarizer used in the case of RPR (FP), spectral filters (F 543 nm and F 633 nm), photodiodes (PD 543 nm and PD 633 nm). The components that represent the eye are indicated by the dashed circle.

eye movements, as well as variations of the cornea and lens shape are considered. Then the geometrical properties were used to determine the electromagnetic and polarization properties of light propagation. Scattering and diffusive effects were neglected and the light was assumed to be completely polarized. Both the detection schemes, i.e., rotating linear polarizer and rotating phase retarder, have been implemented according to the experimental setup described in the previous section. The measurements were performed over a wide range of glucose concentrations simulating human physiological values.

16.6.1 Theoretical analysis 16.6.1.1 Error due to optical path length variations As shown in Eq. (16.2), the optical path length of the reflected beam inside the aqueous lah has to be known for the determination of glucose concentration. Theoretically the optical path length can be assumed to be lahB = 3.63 mm, leading exactly to Brewster reflection at the lens for λ =589.3 nm. If the optical path deviates from the ideal one, path length lah will deviate as well. This, in turn, will lead to a systematic

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FIGURE 16.11: Percent relative error due to variations of the optical path length for different entrance angles of the light beam. The dashed vertical line indicates the ideal entrance condition. error in concentration determination when the constant value lahB is assumed in Biot equation. For each condition of the entrance angle, the corresponding value of the path length lah has been calculated and the relative error has been calculated according to the Biot equation. The results are reported in Fig. 16.11. The dashed vertical line indicates the ideal entrance condition, where φB = 55.4 ˚ and error equals zero. It can be seen that the errors are still moderate for relatively high deviations of ±10 ˚ from the ideal condition. For high deviations from ideal entrance condition the error rises approximately by 0.7% per degree deviation of entrance angle. This indicates that the optical path length lah may be eliminated from Biot equation by calibration of the instrument. 16.6.1.2 Error due to reflection off the ocular lens Errors due to reflection off of the ocular lens may occur for deviations of light propagation from the ideal optical path, i.e., when the reflection angle differs from the Brewster’s angle. For concentration calculation, the actual value of the path length in the aqueous lahB was applied. Thus, the error due to deviation from the ideal optical path was composed of the error due to refraction of the incoming beam at the cornea and subsequent reflection at the lens. The simulation results are reported in Figs. 16.12 (a) and (b), where Fig. 16.12 (a) shows the case of linearly polarized

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entrance light (s-mode) and Fig 16.12 (b) the case of circular entrance light. In Fig. 16.12 (c) the reflection angle at the lens φlens is presented for the different entrance conditions. Figure 16.12 (d) reports the ellipticity of the polarization state after the beam has crossed the cornea for the case of circular entrance light. The dashed vertical lines indicate the case of ideal optical path. Starting at the ideal entrance condition in Fig. 16.12 (a) the error of concentration determination is positive for entrance angles higher than that at ideal condition and negative for lower values. This is due to non-flipped polarization in the first case and polarization flip in the last case. Fig. 16.12 (c) shows that the deviation of the reflection angle at the lens from the ideal angle, i.e., Brewster’s angle, increases with increasing deviation of the entrance condition from the ideal entrance condition. Further, from Fig. 16.4 (b) can be noticed that rsp rises in both directions with increasing deviation from φB . Therefore, rsp rises with increasing deviation from ideal entrance condition. The polarization orientation prior to lens reflection is slightly rotated clockwise, due to optical activity of glucose. The higher values of rsp , the lower rotation of this polarization state towards the ideal s-direction. Thus, the absolute value of the error increases with increasing deviation from the ideal entrance condition, which explains the positive slope of the curve. The sign properties for the circular case in Fig. 16.12 (b) are opposite to the linear case. We first address the case of entrance angles that are higher than at ideal condition. In this case, there is no polarization flip and the resulting error is negative. As for the linear entrance polarization, the rise of the ratio rsp results in an increase of the absolute value of the error, with increasing deviation from ideal entrance condition. Additionally, the deformation of the circular entrance polarization due to refraction at the cornea increases and results in a lower absolute value of ellipticity as is reported in Fig. 16.12 (d). Both effects combined explain the increasing absolute value of the negative slope for entrance angles higher than that at ideal condition. For lower and decreasing values of the entrance angle the positive error increases first, reaches a local maximum, decreases, reaches a local minimum, then increases rapidly. The error is always positive due to polarization flip at reflection. The initial rise of the error is due to the rising value of rsp . However, the absolute value of the slope of the error decreases. The reason being that the absolute value of ellipticity of polarization [Fig. 16.12 (d)] increases, which, according to Fig. 16.4 (b), increases rotation towards s-orientation. As the influence of the ellipticity increases, the curve reaches its local maximum, then the error begins to decrease. The local minimum of the error has been found at entrance angle φin = 23.35 ˚ . Here, the entrance beam impinges perpendicularly upon the anterior cornea and the light prior to lens reflection is approximately circularly polarized ( e ≈ 1). Deviation from circular polarization appears only due to the (weak) refraction at the cornea-aqueous interface. For even lower values of the entrance angle the deformation of circular polarization begins to increase. This, together with the increasing value of rsp , leads to the increase of the error. Comparing the results of the two entrance polarizations it can be noticed that the net error due to refraction at the cornea and subsequent reflection at the lens is much smaller for the case of circular entrance polarization.

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FIGURE 16.12: Percent relative errors due to reflection off of the ocular lens for different entrance angles: linearly polarized entrance light (s-mode) (a), circularly polarized entrance light (b), angle of reflection off of the ocular lens (c), ellipticity of polarization of incoming beam after transition of the cornea for circular entrance light (d). The dashed lines indicate the ideal entrance condition.

16.6.1.3 Error due to refraction at the cornea When the reflected light beam crosses the cornea to leave the eye, the refractive properties of the cornea interfaces will lead to an error in glucose concentration determination. This error even occurs at ideal optical path. Its origin is the rotation of polarization state due to different transmission coefficients of the p- and s-components of the electric field vector. The glucose concentration in the aqueous, which is crossed by the incoming light prior to lens reflection, was set to zero for this light, while the concentration for the light after reflection was kept at 100 mg/dl. This modification is achieved when the polarization state directly after reflection at the ocular lens was oriented in the ideal s-direction for all entrance conditions. Thus, the lens reflection error has been eliminated, but the typical parameters of the ellipse

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of polarization were maintained. For glucose concentration calculation the actual value of the path length in the aqueous lah has been applied. Both interfaces of the cornea show similar effects and lead to errors with same sign. However, the dominating interface is the cornea-air interface due to its high difference in refractive index. Figure 16.13 (a) reports the results for linear entrance polarization (s-mode) and Fig. 16.13 (b) for circular entrance polarization. The incident angle at the cornea-air interface as a function of the entrance angle at the eye is shown in Fig. 16.13 (c). In the case of circular entrance polarization the ellipticity of the reflected beam inside the cornea is reported in Fig. 16.13 (d). The case of ideal optical path is indicated by the dashed vertical lines. Note that the relative error is different from zero for ideal optical path. From Fig. 16.13 (c) it can be noticed that the absolute value of the incident angle at the cornea-air interface increases constantly with increasing entrance angle. According to Fig. 16.4, the transmission coefficient tsp of this interface decreases constantly for increasing values of the entrance angle at the eye. Further, the polarization orientation of the outgoing beam, after having crossed the aqueous, is slightly rotated clockwise from the s-direction, due to optical activity of glucose. Thus, the decreasing value of tsp leads to increasing rotation towards the p-direction and to an increasing positive error with increasing entrance angle at the eye. This explains the results for linear entrance polarization as reported in Fig. 16.13 (a). For circular entrance polarization, the error is positive as well, following the same reasons as in the linear case. However, the ellipticity of polarization influences the results. For higher values of the entrance angle at the eye both the decreasing value of tsp and the increasing absolute value of ellipticity inside the cornea lead to a rise of negative polarization rotation. Thus, this contributes to the positive error in the concentration determination. For smaller and decreasing values of the entrance angle, with respect to ideal condition, the increasing value of tsp and the increasing absolute value of ellipticity have opposite effects. Comparing Figs. 16.13 (a) and (b) it can be noticed that the corneal refraction error is similar for linear and circular entrance polarization covering a wide range around the ideal entrance condition. 16.6.1.4 Error due to dispersion of the eye media Multiwavelength approach leads to slightly different optical paths for the different wavelengths. Thus, for the ideal entrance condition, which was defined for λ = 589.3 nm, each chromatic channel provides a different net error in glucose concentration determination. This error will include the above discussed path length error, lens reflection error and cornea refraction error. The results of the simulation to investigate the net errors due to dispersion are reported in Figs. 16.14 and 16.15. Figures 16.14 (a) and (b) report the error for the cases of linear and circular entrance polarization. This net error is a superposition of the corresponding lens reflection error and cornea refraction error. In Fig. 16.15 (a) reports the path length of the reflected beam inside the aqueous whereas Fig. 16.15 (b) shows the incident or

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FIGURE 16.13: Percent relative errors due to refraction at the cornea for different entrance angles: linearly polarized entrance light (s-mode) (a), circularly polarized entrance light (b), incident angle at the cornea-air interface (c), ellipticity of polarization of the outgoing beam inside the cornea for circular entrance light (d). The dashed vertical lines indicate the ideal entrance condition.

reflection angle at the lens and the Brewster’s angle as functions of the wavelength. Figure 16.15 explains the sign properties of the lens reflection errors due to polarization flip, according to the discussion reported in the previous sections. The dashed vertical lines indicate the case of λ =589.3 nm. For linearly polarized entrance light the curve shape of the net error is determined by the lens reflection error, which shows a much higher value than the cornea refraction error and the path length error. The lens reflection error is more than one order of magnitude higher than the corresponding error for the case of circular entrance polarization. The cornea refraction error mainly leads to an offset of the net error to positive values. For circularly polarized entrance light, the net error is dominated by the cornea refraction error, due to the relatively small, opposite and quantitatively similar con-

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FIGURE 16.14: Percent relative errors at ideal entrance condition due to dispersion of the eye media. Linearly polarized entrance light (s-mode) (a), and circularly polarized entrance light (b). The dashed vertical lines indicate the case of λ =589.3 nm.

FIGURE 16.15: Beam path properties as a function of the beam wavelength at ideal entrance condition. Path length of the reflected beam inside the aqueous (a), and reflection angle at the lens (solid) and Brewster’s angle (dashed) as functions of wavelength (b). The dashed vertical lines indicate the case of λ =589.3 nm.

tributions of the lens reflection error and the path length error. Therefore, the net error shows opposite slope compared with the error for linear entrance polarization. Figure 16.15 (a) demonstrates that the optical path length inside the aqueous only differs little in the range of a few microns due to dispersion of the eye media.

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16.6.1.5 Overall uncertainty In this section the overall uncertainty of glucose concentration determination for the Brewster scheme is investigated. Measurement uncertainty depends on different variables of influence related to the measurement procedure and real eye variability. These variables of influence include wavelength of the measurement light, entrance parameters, shape parameters of the lens, shape parameters of the cornea, and eye movements. The knowledge of the relationships between the measurement result, i.e., glucose concentration, and these parameters allows the determination the overall measurement uncertainty using the ‘law of propagation of uncertainty,’ following quantification of uncertainties in individual influence factors [34]. In this subsection the relationships between glucose concentration and the variables of influence are determined. The simulations have been performed considering the multiwavelength approach. A reference light beam at λ = 589.3 nm was applied to each setting of the eye model. As discussed in previous sections, the glucose concentration was determined by comparing the azimuth calculation of the output light at the measurement wavelength to that of the result at the reference wavelength. Thus, for each setting of the parameters of the eye model, the calculation was performed twice, once for the reference wavelength at λ = 589.3 nm and once for the measurement wavelength. For the concentration calculations the constant optical path length at ideal entrance condition lah = 3.63 mm was assumed. Therefore, the calculations have been performed according to Eq. (16.2). In consequence, the overall uncertainty of concentration determination is composed of path length error, lens reflection error, and cornea refraction error. Simulations have been performed for linearly polarized entrance light and circularly polarized entrance light. 16.6.1.5.1 Influence of wavelength variations. The error at ideal entrance condition is investigated for varying wavelength (450-910 nm) of the measurement light and for varying glucose concentration (10-200 mg/dl). The results are reported in Figs. 16.16 and 16.17. Figure 16.16 reports the results for linearly polarized entrance light in the s-mode (a) and circularly polarized entrance light (b). The results are similar to the discussion of dispersion in paragraph 16.6.1.4. As a matter of fact, the only difference of this simulation was the application of the multiwavelength approach. Comparing the case of linear polarization with the corresponding results of previous section, it can be noticed that the cornea refraction error seems to cancel for the multiwavelength approach. In contrast, it does not do that in the case of circular polarization. Note the constancy of the relative error with glucose concentration. Figure 16.17 reports the case of linearly polarized entrance light, which differs from the s-mode by +0.01 ˚ (a) and -0.01 ˚ (b). This demonstrates the high sensitivity for linearly polarized entrance light to the orientation of entrance polarization. Adjustment to the s-direction has to be performed within ∆θ pi = 10 millidegrees. The elevated errors for deviations from smode are due to lens reflection errors. In contrast to the case of linear entrance polarization in the exact s-mode, the error curve is found to be highly dependent on

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FIGURE 16.16: Percent relative errors at the ideal entrance condition as a function of the measuring wavelength and glucose concentration. Linearly polarized entrance light (s-mode) (a), and circularly polarized entrance light (b).

FIGURE 16.17: Percent relative errors when the ideal entrance condition is applied for non-s-mode linear entrance polarization: θ pi =-89.99 ˚ (a) and θ pi =+89.99 ˚ (b).

glucose concentration. Highest relative errors occur for low concentrations. Note, however, that the relative error of about 70% for glucose concentration of c= 10 mg/dl corresponds to an absolute error of 7 mg/dl and is still acceptable for practical applications.

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FIGURE 16.18: Beam path variations from the ideal entrance condition at λ = 589.3 nm. Ideal entrance condition xe = 3.12 mm, φe =55.4 ˚ and lah = 3.63 mm (a). Extreme paths for linear entrance polarization, xe = 4.22 mm, φe =52.4 ˚ (solid) and xe = 2.42 mm, φe =58.4 ˚ (dashed) (b). Extreme paths for circular entrance polarization, xe = 4.72 mm, φe =29.4 ˚ (solid) and xe = 2.32 mm, φe =59.4 ˚ (c). 16.6.1.5.2 Influence of entrance condition variations. Variations of the entrance condition were performed under the limitations put forth by the 10 mm usable aperture of the cornea. Limitations due to the iris were not considered and may put even more stringent limitations on entrance condition. The ranges of entrance angles and entrance positions for each of the two investigated entrance polarizations have been chosen to focus on the range of relative errors that are of practical interest. Therefore, the ranges of the entrance parameters xin and φin differ for the distinct entrance polarizations. The beam paths for the extreme situations of the investigated ranges of entrance parameters are reported in Fig. 16.18 for λ = 589.3 nm. Figure 16.18(a) denotes the ideal entrance condition xin = 3.12 mm, φin =55.4 ˚ . Figures 16.18 (b) and (c) represent the extreme entrance conditions for linear and circular entrance polarization, respectively. Simulations have been performed for the two wavelengths λ = 488 nm (emission wavelength of argon laser) and λ = 830 nm (emission wavelength of laser diode). Results are reported for the case of c = 100 mg/dl in Fig. 16.19. In Figs. 16.19 (a) and (c) the case of linearly polarized entrance light in the s-mode is presented for wavelength λ = 488 nm and λ = 830 nm, respectively. The corresponding results for circular entrance polarization are reported in Figs. 16.19 (b) and (d). For both entrance polarizations, the demands on the entrance parameters to stay within acceptable error limits are modest. The limitations for the entrance angle are much more stringent in the case of linear entrance polarization. This is due to

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FIGURE 16.19: Percent relative errors due to variations from the ideal entrance condition (vertical lines) at c = 100 mg/dl. Linearly polarized entrance light (smode) at λ = 488 nm (a). Circularly polarized entrance light at λ = 488 nm (b). Linearly polarized entrance light (s-mode) at λ = 830 nm (c). Circularly polarized entrance light at λ = 830 nm (d).

the higher lens reflection error for linearly polarized entrance light, as discussed in previous section. The comparison between Figs. 16.19 (a) and (b) with Figs. 16.19 (c) and (d) shows the influence of wavelength on the relative error. The dependence of the results on the actual glucose concentration was found to be negligible for the physiological range. 16.6.1.5.3 Influence of anterior lens shape variations. The influence of variations of anterior lens asphericity is investigated in this section. The basis for the amount of variability of this parameter has been reported in Ref. [19]. In this study 60 pairs of human cadaver lenses from 33 males and 27 females, ages 1 to 87 years, were examined. The asphericity of the anterior lens surfaces has been reported in terms of the conic constant. This conic constant was found to have values between

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zero and 5.5 with mean value at 2.46. The value zero denotes a sphere, thus corresponds to the asphericity parameter Q = 0 whereas higher values denote hyperbolas. The mean value 2.46 corresponds to Q = −3.1316, as has been reported in Table 16.2. According to [35], the radius of curvature of the anterior lens was not changed after removal. Errors due to variations of anterior lens shape occur only for optical paths that differ from the ideal one. Therefore, the simulations have been performed varying the entrance parameters as in the previous section. The value of the asphericity parameter Q of the anterior lens has been changed, by applying the values of the upper and lower limit Q = 0 and Q = −21.25 to the eye model, respectively. The results for wavelength λ = 488 nm and c = 100 mg/dl are reported in Fig. 16.20. Figures 16.20 (a) and (b) report the results of Q = 0 for linear (s-mode) and circular entrance polarization, respectively. Figures 16.20 (c) and (d) show the cases of Q = −21.25. The vertical lines indicate the ideal entrance condition. The comparison between Figs. 16.20 (a) and (b) and Fig. 16.19 (a) and (b) shows that the variation of the asphericity parameter of the anterior lens influences the error curves minimally. In the case of Q = 0 the influence is negligible as this value is close to the default value Q = −3.1316. Some small changes occur in the case of Q = −21.25. Here, the anterior lens is notably more even, influencing the lens reflection error. This explains the higher changes for linear entrance polarization, which is more sensitive to this type of error. Around the ideal condition the changes to the relative error curve are minimal for both entrance polarizations as the beam impinges the lens close to the vertex, where changes of asphericity have minimal influence.

16.6.1.5.4 Influence of anterior cornea shape variations. In contrast to the lens, variation in the anterior cornea shape parameters leads to deviations from ideal optical path even at ideal entrance condition. Published data from in vivo measurements for both asphericity parameter and radius of curvature are available [18]. These data are based on 176 eyes from 49 males and 39 females at ages evenly distributed from 16 to 80 years. Inter-individual variations of asphericity parameter occurred in the range from Q = −0.76 to Q = +0.47. 80% of intra-individual variations at perpendicular meridians of the eye have been reported to amount to |∆Q| ≤ 0.5. The mean value of asphericity parameter of Q = −0.26 denotes the default value of the eye model. The same holds true for the reported mean value of the radius of curvature of R = 7.72 mm. For this parameter inter-individual variations were found to cover the range from R = 7.06 mm to R = 8.64 mm and 78% of intraindividual variations at perpendicular eye meridians have been reported to amount to |∆R| ≤ 0.3 mm. Simulations were performed at ideal entrance condition, varying both corneal shape parameters simultaneously. The absolute limits of inter-individual variations have been applied for the investigated ranges of the shape parameters. Considered wavelengths were λ = 488 nm and λ = 830 nm. Results are reported for the case of c = 100 mg/dl in Fig. 16.21. Figures 16.21 (a) and (b) report the case of λ = 488 nm

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FIGURE 16.20: Percent relative errors due to variations of the anterior lens asphericity at λ = 488 nm and c = 100 mg/dl. Linearly polarized entrance light (smode) and Q = 0 (a). Circularly polarized entrance light and Q = 0 (b). Linearly polarized entrance light (s-mode) and Q = −21.25 (c). Circularly polarized entrance light and Q = −21.25 (d). for linear (s-mode) and circular entrance polarization, respectively. In Figs. 16.21 (c) and (d) the cases for λ = 830 nm are reported. Figure 16.21 shows as the influence of wavelength on the error curves is relatively low. The reported errors for linearly polarized entrance light are notably higher than those for circular entrance polarization. This is due to the changed refraction of the entrance beam at the anterior cornea. This leads to a deviation from ideal beam propagation prior to reflection at the lens, which results in a lens reflection error. Linear polarization, however, is more sensible to lens reflection variations as discussed in the previous section. 16.6.1.5.5 Influence of involuntary eye movements. Small movements of the eye globe occur even at fixation [32]. These involuntary eye movements can be

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FIGURE 16.21: Percent relative errors due to variations of the anterior corneal shape parameters at c = 100 mg/dl. Linearly polarized entrance light (s-mode) at λ = 488 nm (a). Circularly polarized entrance light at λ = 488 nm (b). Linearly polarized entrance light (s-mode) at λ = 830 nm (c). Circularly polarized entrance light at λ = 830 nm (d).

classified into three types: drift, tremor, and small involuntary saccades. Drift is an irregular and relatively slow movement of the axes of the eyes with typical velocity of 6 minutes of angle per second. During drift the image of the point of fixation remains always inside the fovea. Drift is always accompanied by tremor, which is an oscillatory movement of the axes of the eyes at high frequency (typically 7090 Hz), but has a very small amplitude (20-40 seconds of angle). Small involuntary saccades are fast movements of the axes of the eyes with typical duration between 0.01 and 0.02 seconds. They usually arise when the duration of fixation exceeds 0.3–0.5 seconds or when, as a result of drifts, the image of the point of fixation becomes too far removed from the center of the fovea. Thus, the small involuntary saccades have a correcting function. Typical amplitudes are reported to be smaller

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FIGURE 16.22: Percent relative errors due to eye rotation angle at different beam wavelength for c = 100 mg/dl. Linearly polarized entrance light (s-mode) (a). Circularly polarized entrance light (b).

than 25 minutes of angle, but most happen to show amplitudes smaller than about 16 minutes of angle. Due to the correcting character of small involuntary saccades this corresponds to ±0.133 ˚ . The small involuntary saccades denote the movement with highest amplitudes at fixation. The simulation has been orientated at their amount of eye axis deviation. Accordingly, simulation has been performed for deviations of the optical axis of the eye in the range of ±0.133 ˚ from the ideal orientation. Figure 16.22 reports the results for the case of the default anterior lens asphericity Q = −3.1316 and for glucose concentration c = 100 mg/dl. Figures 16.22 (a) and (b) denote the case of linearly polarized entrance light and circularly polarized entrance light, respectively. In both cases the error is relatively small. It can be seen that the dynamic range of the relative error for linear entrance polarization is much higher than that for the circular case. This is due to the higher sensibility of the linear entrance polarization to lens reflection errors.

16.6.2 In vitro experiments 16.6.2.1 Rotating linear polarizer In vitro experiments were performed using the optical setup reported in subsection 16.5.3. As expected, the detected signals from the photodetectors exhibit a sine wave trend as the continuously linear polarizer rotates. The glucose concentration in the sample leads to different rotations of polarization for the two wavelengths.

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As described in Eq. (16.8), this relative polarization changes linearly with glucose concentration. The detection unit transforms the polarization shift between the two beams into a relative phase between their corresponding sinusoidal signals. Since the frequency of the sine waves is double in respect to the linear polarizer rotation frequency, relative signal phase and relative azimuth of polarization are correlated by a factor of two. The detection signals were acquired for one revolution of the rotating linear polarizer. Rotation frequency amounted to about 0.66 Hz. Thus, a single measurement took 1.5 seconds. Acquisition synchronization, with respect to the angular orientation of the RLP, was achieved by using an encoder. The total number of acquired data points was limited to 65535. The glucose samples were prepared by dissolving pure alpha-D-glucose in 50 ml distilled water. Uncertainties of sample preparation have been estimated to be σ g = 0.3 mg for the glucose weight and σ w = 0.5 ml for the water volume. The solutions were only used after at least 9 hours to ensure chemical equilibrium between alphaand beta-D-glucose. Measurements were performed using eight different glucose concentrations between 0 and 500 mg/dl. At each concentration the measurements were repeated 50 times for statistical analysis. Figure 16.23 shows an example of the acquired raw signals for glucose concentration c = 0 mg/dl. From the acquired measurement signals a noise-level of about 0.03% was estimated. The peak power values of the light beams at the photo detectors were adjusted to generate approximately equal electrical signal amplitudes at identical amplification configuration of the detectors minimizing interference effects. This adjustment was possible due to the combination of the linear polarizer (PL) and the characteristics of the red He-Ne lasers delivering partially linearly polarized output light. Thus, the power of the red laser light could be appropriately adjusted to that of the green laser by simply rotating the laser axially. The resulting peak power values amounted to 13 µ W at λ =543 nm and 7.5 µ W for the λ =633 nm. The raw data were analyzed without any further signal processing applying the Stokes-Method discussed in our previous paper [37]. The results are reported in Fig. 16.24. The relative rotations of light polarization with the glucose concentrations show a correlation coefficient of R2 =0.986. The slope of the linear regression amounts to 0.0166 ± 0.0020 millidegrees dl/mg. The theoretical value for l = 10 mm optical path length in the sample amounts to 0.0179 millidegrees dl/mg. This is in agreement with the experimental findings. The theoretical slope was obtained by applying the values of the optical rotatory power at respective wavelengths to Eq. (16.8). The vertical error bars in Fig. 16.24 show the standard deviations σ calculated from the 50 repetitions of each measurement. These values fluctuate between 0.86 and 2.08 millidegrees with a mean value of 1.38 millidegrees corresponding to a glucose concentration of 76 mg/dl. The higher value of standard deviation may have various origins. The power of the lasers was found to fluctuate within a range of approximately 10%. For the time interval of 1.5 seconds of one measurement, standard deviations of output power of both lasers were determined to be smaller than 0.01% and may not disturb mea-

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FIGURE 16.23: Typical raw signals as detected by the RLP-scheme for concentration c = 0 g/dl. Signal at λ = 543 nm (solid) and signal at λ = 633 nm (dashed).

surement accuracy. However, the fluctuations at higher time scale may change the characteristics of the detection electronics and influence the detected relative signal phase. This should also be regarded in relation to the mentioned influence of the amplification configuration of the photodiodes. Another additional source of measurement uncertainty may result from inhomogeneities, scattering centers, and dust on the surface of the rotating optical element, which may lead to deformation of the optical power signal. Finite accuracy in alignment of the rotating optical element may result in slightly varying incident angles of the light beam and varying beam paths after transmission. As transmission and reflection properties of light propagation through the optical components depend on light polarization and propagation direction, this may deform the optical power signals and result in measurement errors. The experimentally achieved alignment accuracy of the RLP amounted to about 0.3 ˚ of incident angle, with respect to the normal to the surface of the RLP. The measurement signals were digitized directly after detection. At this stage no signal conditioning or data processing of the raw data has been performed. The application of low noise and signal phase keeping detection electronics is expected to improve system accuracy in future experiments. The mechanical components of the rotation unit may also require further improvements as well. These combined features have the potential of providing the necessary resolution of approximately 0.3 millidegrees relative azimuth detection for applications in the human eye. 16.6.2.2 Rotating λ /4 plate Acquisition of the detection signals and preparation of the glucose samples were performed in the same manner as described in the previous section for the rotating linear polarizer scheme. Figure 16.25 shows an example of the acquired raw signals

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FIGURE 16.24: Experimental results obtained by the RLP-scheme. Relative polarization angle as a function of the glucose concentration. The data shows good linearity (R2 = 0.986). The calculated standard deviations from the statistics of 50 measurement repetitions provided a mean value of σ =1.38 millidegrees.

for glucose concentration c = 0 mg/dl. The optical power emitted by the lasers was adjusted to generate approximately equal electrical signal amplitudes at identical amplification configuration of the detectors to minimize interference effects, resulting in 7.4 µ W for the 543 nm signal and 4.7 µ W for the 633 nm signal. After calibration, this scheme provides the advantage of possible access to the complete polarization state of the measurement light. As in the case of rotating linear polarizer, the raw data were analyzed without any further signal processing, applying the Stokes-Method [37]. The experimental results of relative polarization rotation detection are reported in Fig. 16.26. The relative rotations of light polarization with the glucose concentrations show a correlation coefficient of R2 =0.987. The slope of the linear regression amounts to 0.0187 ± 0.0021 millidegrees dl/mg. The theoretical value for l = 10 mm optical path length in the sample amounts to 0.0179 millidegrees dl/mg. Thus, the experimental findings are in good agreement with the theoretical expectations. The vertical error bars in Fig. 16.26 show the standard deviations calculated from the 50 repetitions of each measurement. These values fluctuate between 1.18 and 2.07 millidegrees with a mean value of 1.68 millidegrees corresponding to a glucose concentration of 93 mg/dl for the wavelengths used. Thus, the performance of this scheme is similar to the scheme presented in the previous section. Also in this case, the detection signals of the relative rotation angle measurement for pure water sample also showed a non-zero relative phase.

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FIGURE 16.25: Typical raw signals as detected by the RPR-scheme for a rotating λ /4 wave plate and for concentration c = 0 mg/dl. Signal at λ = 543 nm (solid) and signal at λ = 633 nm (dashed).

The results of calibration were used to determine two additional properties of light polarization that may be of interest for polarimetric applications. These are the degree of polarization and the ellipticity of polarization of the measurement light. From the calibration results the complete Stokes vectors were determined for all investigated samples and for both measurement beams. The results as functions of the investigated glucose concentrations are reported in Figs. 16.27 and 16.28, respectively. Figure 16.27 demonstrates the high degree of polarization of both measurement beams over the full range of glucose concentrations. The standard deviations from the 50 measurement repetitions are indicated by the vertical error bars.

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FIGURE 16.26: Experimental results obtained by the RPR-scheme. Relative polarization angle as a function of the glucose concentration. The data show good linearity (R2 = 0.987). The calculated standard deviations from the statistics of 50 measurement repetitions provided a mean value of 1.68 millidegrees.

FIGURE 16.27: Polarization degree of the detected beam as a function of the glucose concentration. Measurement beam at 543 nm (bullets). Measurement beam at 633 nm (blacksquares). The vertical error bars denote the standard deviations calculated from the 50 repetitions of each measurement whereas the bold lines represent the mean polarization degrees of the two beams.

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FIGURE 16.28: Polarization ellipticity of the detected beam as a function of the glucose concentration. Measurement beam at 543 nm (bullets). Measurement beam at 633 nm (blacksquares). The vertical error bars denote the standard deviations calculated from the 50 repetitions of each measurement whereas the bold lines represent the mean polarization ellipticity of the two beams.

FIGURE 16.29: Prototype table-top set-up for human measurements.

The beam at λ =633 nm performs slightly better with a higher degree of polarization than the beam at 543 nm. This is because the Brewster reflection was optimized for 633 nm. The measurements describe approximately constant functions (bold line).

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Figure 16.28 reports the results for ellipticity of polarization e. The standard deviations from the 50 measurement repetitions are indicated by the vertical error bars. Also this property of the polarization state shows an approximately constant behaviour (bold line) for different glucose concentrations for both measurement beams. As expected, ellipticity is weak for both measurement beams. The 633 nm signal performs slightly better with respect to ellipticity of polarization due to optimization of the Brewster reflection at this wavelength.

16.7 Conclusion A new optical scheme to access the eye’s anterior chamber for colorimetric glucose sensing is described. The theoretical analysis presented in this chapter indicates this scheme to be more convenient than the approaches previously proposed for non-contact measurements since it does not require any external index matching techniques or devices. Although it is an important stepping stone in achieving the goal of a noninvasive glucose sensor, the practicality of this new scheme to a real eye in clinical settings is yet to be demonstrated. Currently, this work is underway. A prototype table-top set-up is shown in Fig. 16.29 for human measurements.

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References [1] W.F. March, B. Rabinovich, and R.L. Adams, “Noninvasive glucose monitoring of the aqueous humor of the eye: Part II. Animal studies and the scleral lens,” Diab. Care, vol. 5, 1982, pp. 259–265. [2] B.D. Cameron, J.S. Baba, and G.L. Cot`e, “Measurement of the glucose transport time delay between the blood and aqueous humor of the eye for the eventual development of a noninvasive glucose sensor,” Diab. Techn. Ther., vol. 3, 2001, pp. 201–208. [3] D.A. Gough, “The composition and optical rotatory dispersion of bovine aqueous humor,” Diab. Care, vol. 5, 1982, pp. 266–270. [4] J.S. Baba, B.D. Cameron, S. Theru, and G.L. Cot`e, “Effect of temperature, pH, and corneal birefringence on polarimetric glucose monitoring in the eye,” J. Biomed. Opt., vol. 7, 2002, pp. 321–328. [5] J.S. Baba, A.M. Meledeo, B.D. Cameron, and G.L. Cot`e, “Investigation of pH and temperature on optical rotatory dispersion for noninvasive glucose monitoring,” Proc. SPIE, vol. 4263, 2001, pp. 25–33. [6] T.W. King and G.L. Cot`e, “Multispectral polarimetric glucose detection using a single Pockels cell,” Opt. Eng., vol. 33, 1994, pp. 2746–2752. [7] B.D. Cameron, H.W. Gorde, and G.L. Cot`e, “Development of an optical polarimeter system for in vivo glucose monitoring,” Proc. SPIE, vol. 3599, 1999, pp. 43–49. [8] C.A. Browne and F.W. Zerban, “Physical and chemical methods of sugar analysis,” Chapman & Hill, New York, London, Third Edition, Chap. 8, 1948, pp. 263–273. [9] R.R. Ansari, S. Boeckle, and L. Rovati, “New optical scheme for a polarimetric-based glucose sensor,” J. Biomed. Opt., vol. 9, 2004, pp. 103– 115. [10] L.D. Barron, Molecular Light Scattering and Optical Activity, Cambridge University Press, Cambridge, 1982. [11] National Research Council, International Critical Tables of Numerical Data, Physics, Chemistry and Technology, McGraw-Hill, New York, 1927. [12] L.J. Bour and N.J. Lopes Cardozo, “On the birefringence of the living human eye,” Vis. Res., vol. 21, 1981, pp. 1413–1421. [13] J.M. Bueno and F. Vargas-Mart`ın, “Measurements of the corneal birefringence with a liquid-crystal imaging polariscope,” Appl. Opt., vol. 41, 2002, pp. 116– 124.

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[14] G.J. van Blokland and S.C. Verhelst, “Corneal polarization in the living human eye explained with a biaxial model,” J. Opt. Soc. Am. A, vol. 4, 1987, pp. 82– 90. [15] R.W. Knighton and X. Huang, “Linear birefringence of the central human cornea,” Inves. Ophthal. Vis. Sci., vol. 43, 2002, pp. 82–86. [16] R.A. Weale, “On the birefringence of the human crystalline lens,” J. Physiol., vol. 284, 1978, pp. 112–113. [17] F.A. Bettelheim, “Induced optical anisotropy fluctuation,” J. Colloid Interface Sci., vol. 63, 1978, pp. 251–258. [18] P.M. Kiely, G. Smith and L.G. Carney, “The mean shape of the human cornea,” Opt. Acta, vol. 29, 1982, pp. 1027–1040. [19] M.J. Howcroft and J.A. Parker, “Aspheric curvatures for the human lens,” Vis. Res., vol. 17, 1977, pp. 1217–1223. [20] M. Hosny, J.L. Ali`o, P. Claramonte, W.H. Attia, and J.J. P`erez-Santonja, “Relationship between anterior chamber depth, refractive state, corneal diameter, and axial length,” J. Refract. Surg., vol. 16, 2000, pp. 336–340. [21] M. Bass, Handbook of Optics, McGraw-Hill, New York, 1995. [22] R. Navarro, J. Santamar´ya, and J. Besc`os, “Accommodation-dependent model of the human eye with aspherics,” J. Opt. Soc. Am. A, vol. 2, 1985, pp. 1273– 1281. [23] G.L. Cot´e, M.D. Fox, and R.B. Northrop, “Noninvasive optical polarimetric glucose sensing using a true phase measurement technique,” IEEE Trans. Biomed. Eng., vol. 39, 1992, pp. 752–756. [24] T.W. King and G.L. Cot´e,“Multispectral polarimetric glucose detection using a single Pockels cell,” Opt. Eng., vol. 33, 1994, pp. 2746–2752. [25] B.D. Cameron and G.L. Cot´e, “Noninvasive glucose sensing utilizing a digital closed-loop polarimetric approach,” IEEE Trans. Biomed. Eng., vol. 44, 1997, pp. 1221–1227. [26] C. Chou, C.Y. Han, W.C. Kuo, Y.C. Huang, C.M. Feng, and J.C. Shyu, “Noninvasive glucose monitoring in vivo with an optical heterodyne polarimeter,” Appl. Opt., vol. 37, 1998, pp. 3553–3557. [27] R.J. McNichols, B.D. Cameron, and G.L. Cot´e, “Development of a noninvasive polarimetric glucose sensor,” IEEE-LEOS Newsletter, vol. 12, 1998, pp. 30–31. [28] B.D. Cameron, H.W. Gorde, B. Satheesan, and G.L. Cot´e, “The use of polarized laser light through the eye for noninvasive glucose monitoring,” Diab. Techn. Ther., vol. 1, 1999, pp. 135–143.

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[29] C. Pu, Z. Zhu, and Y.H. Lo, “A surface-micromachined optical selfhomodyne polarimetric sensor for noninvasive glucose monitoring,” IEEE Photon. Techn. Lett., vol. 12, 2000, pp. 190–192. [30] R.J. McNichols and G.L. Cot´e, “Optical glucose sensing in biological fluids: an overview,” J. Biomed. Opt., vol. 5, 2000, pp. 5–16. [31] I. Escudero-Sanz and R. Navarro, “Off-axis aberrations of a wide-angle schematic eye model,” J. Opt. Soc. Am. A, vol. 16, 1999, pp. 1–11. [32] E. Hecht, Optics, Addison-Wesley, Reading, MA, 1974. [33] S. Pelizzari, L. Rovati, and C. De Angelis, “Rotating polarizer and rotating retarder plate polarimeters: comparison of performances,” Proc. SPIE, 4285, 2001, pp. 235–243. [34] ISO, Guide to the Expression of Uncertainty in Measurement, International Standards Organization, Geneva, 1993. [35] R. Navarro, J. Santamar´ıa, and J. Besc´os, “Accommodation-dependent model of the human eye with aspherics,” J. Opt. Soc. Am. A, vol. 2, 1985, pp. 1273– 1281. [36] A.L. Yarbus, Eye Movements and Vision, Plenum Press, New York, Chap. 3, 1967, pp. 103–127. [37] S. Boeckle, L. Rovati, and R.R. Ansari, “Polarimetric glucose sensing using the Brewster-reflection off the eye lens: theoretical analysis,” Proc. SPIE, 4624, 2002, pp. 160–164.

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17 Toward Noninvasive Glucose Sensing Using Polarization Analysis of Multiply Scattered Light Michael F. G. Wood, Nirmalya Ghosh, Xinxin Guo and I. Alex Vitkin Division of Biophysics and Bioimaging, Ontario Cancer Institute and Department of Medical Biophysics, University of Toronto Toronto, Ontario, Canada

17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.2 Polarimetry in Turbid Media: Experimental Platform for Sensitive Polarization Measurements in the Presence of Large Depolarized Noise . . 17.3 Polarimetry in Turbid Media: Accurate Forward Modeling Using the Monte Carlo Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.4 Tackling the Inverse Problem: Polar Decomposition of the Lumped Mueller Matrix to Extract Individual Polarization Contributions . . . . . . . . . . . . . . . . . . . 17.5 Monte Carlo Modeling Results for Measurement Geometry, Optical Pathlength, Detection Depth, and Sampling Volume Quantification . . . . . . . . 17.6 Combining Intensity and Polarization Information via Spectroscopic Turbid Polarimetry with Chemometric Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.7 Concluding Remarks on the Prospect of Glucose Detection in Optically Thick Scattering Tissues with Polarized Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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This chapter introduces the concept of polarized light measurements in biological tissues. Polarimetry has a long and successful history in various forms of clear media. However, as tissue is a complex random medium that causes multiple scattering of light and thus extensive depolarization, a polarimetric approach for tissue characterization may at first seem surprising. Nevertheless, we and others have shown that multiple scattering does not fully depolarize the light, and reliable measurements and analysis of surviving polarized light fractions can be made in some situations. As polarized light interacts with optically-active molecules such as glucose in characteristic ways, the possibility arises of measuring a glucose polarization signal in light multiply scattered by tissue. We therefore describe the variety of experimental and theoretical tools, illustrated with selected results, aimed at evaluating the prospect of

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noninvasive glucose detection via turbid polarimetry. Key words: polarized light, multiple scattering, optical activity, birefringence, chirality, Stokes vectors, Mueller matrices, turbid media.

17.1 Introduction Noninvasive glucose monitoring in diabetic patients remains one of the most important unsolved problems in modern medicine. The problem is indeed getting more acute, as the incidence of type II diabetes continues to grow at an alarming rate. Tight regulation of glucose levels is needed to avoid long-term health complications; thus the crucial need exists to measure these levels in order to regulate insulin and caloric intakes, exercise regiments, and so forth. Unfortunately, the most reliable current method necessitates the drawing of blood, usually by a finger prick. Because of the inconvenience, many diabetics do not comply with the required minimum of 5 times a day determination regimen, and instead rely on their symptoms and experience to guide caloric intake and insulin administration. Because of the tremendous clinical importance of this problem and its huge commercial potential, a significant research effort has been undertaken, and is ongoing, in finding a noninvasive replacement for the finger-prick way for measuring blood glucose levels. Research and commercial activities have been intense, and have included fully noninvasive, as well as minimally invasive approaches (e.g., glucose-drawing patch, glucose-sensitive fluorescent tattoos, implantable sensors). A subset of actively investigated techniques involves optical methods, as described in detail in the different chapters of the present volume. A common difficulty with the various proposed noninvasive techniques is the indirect, and often weak, relationship between the change in the measured signal and the corresponding change in the absolute glucose levels. This results in a lack of sensitivity (small signal changes) and, perhaps more importantly, a lack of specificity, in that many other glucose-unrelated factors can cause similar small signal changes. This is referred to as the calibration problem, and various approaches to its solution have been reviewed [1]. Optical polarimetry is particularly promising in this respect [2, 3], in that its measurable polarization parameters (e.g., optical rotation) can be directly related to the absolute glucose levels. Specifically, glucose is an optically active (chiral) molecule that rotates the plane of linearly polarized light by an amount proportional to its concentration and the optical pathlength. This proportionality is described in Eq. (17.1), and has been verified numerous times in clear media; in fact, one of the earliest application of polarimetry relied on this relationship to determine sugar concentration in industrial production processes [4]:

α = R(λ , T ) ·C · hLi.

(17.1)

In Eq. (17.1) α is the measured optical rotation, R is the (known) rotatory power

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of the molecular species (e.g., glucose) at a particular light wavelength λ and temperature T , C is the concentration (of glucose) to be determined, and hLi is the optical pathlength. This simple linear relationship is exploited for the glucose monitoring problem in the only transparent tissue in the body, specifically the eye. Chapter 15 of this monograph describes the exciting research in developing a glucose sensor by polarimetric measurements through the aqueous humor of the eye that can be related to blood glucose levels, and outlines the remaining outstanding challenges of this promising approach. With the exception of transparent ocular tissues, however, the human body is highly absorbing and scattering in the UV-IR range, and the validity of Eq. (17.1) is questionable. Specifically, (i) light is highly depolarized upon tissue multiple scattering, so even initial detection of a polarization-preserved signal from which to attempt glucose concentration extraction is a formidable challenge, (ii) the optical pathlength hLi in turbid media is a difficult quantity to define, quantify, and measure, and really represents a statistical distribution metric of a variety of photon paths that depend in a complex way on tissue optical properties and measurement geometry, (iii) other optically active chiral species are present in tissue, thus contributing to the observed optical rotation and hiding/confounding the specific glucose contribution, (iv) several optical polarization effects occur in tissue simultaneously (e.g., optical rotation, birefringence, absorption, depolarization), contributing to the resultant polarization signals in a complex interrelated way and hindering their unique interpretation. Despite these difficulties, we and others have recently shown that even in the presence of severe depolarization, measurable polarization signals can be reliably obtained from highly scattering media such as biological tissue. We have demonstrated surviving linear and circular polarization fractions of light scattered from optically thick turbid media, and measured the resulting optical rotations of the linearly polarized light [5 - 10]. A comprehensive polarization-sensitive Monte Carlo model has complemented our experimental studies by helping with signal interpretation and analysis, validation of novel approaches, quantification of variables of interest, and guidance in experimental design optimization. Further, we have developed various experimental and analytical methods to maximize polarization sensitivity, quantify pathlength distributions of polarized and depolarized light in multiple scattering media, model the effect of several simultaneous optical effects that can mask the glucose polarization signature, and examine the utility of spectroscopic methods to account for the polarization effects of glucose-unrelated confounding species. In this chapter, we summarize this (and related) research on turbid polarimetry, and discuss the implication of this approach for the human glucose detection problem. This chapter is organized as follows. In section 17.2, we describe the highsensitivity polarization modulation / synchronous detection experimental system capable of measuring small polarization signals in the presence of large depolarized background of multiply scattered light. Both Stokes vectors and Mueller matrix approaches are discussed. This is followed by the description of the corresponding theoretical model in section 17.3, based on the forward Monte Carlo (MC) modeling, with the flexibility to incorporate all the simultaneous optical effects; selected validation studies of both the MC model and the experimental methodology are presented.

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Having established the ability to accurately measure and model turbid polarimetry signals, we now turn to the complicated inverse problem of separating out the constituent contributions from simultaneous optical effects; thus, section 17.4 reviews the polar decomposition studies aimed at quantifying individual contributions from ‘lumped’ Mueller matrix experimental results. Section 17.5 deals with the quantification of the polarized pathlength / sampling volume effects in turbid media, and examines the effects of experimental geometry. In section 17.6, we discuss the initial results of spectral chemometric studies, aimed at combining turbid polarimetry data with diffuse reflectance data, in order to increase the glucose-related information content and to (spectrally) filter out the confounding effects of other tissue constituents. The chapter concludes with a discussion of the applicability of the turbid polarimetry approach to the noninvasive glucose detection problem.

17.2 Polarimetry in Turbid Media: Experimental Platform for Sensitive Polarization Measurements in the Presence of Large Depolarized Noise In order to perform accurate glucose concentration measurements in scattering media such as biological tissues, a highly sensitive polarimetry system is required. Multiple scattering leads to depolarization of light, creating a large depolarized source of noise that hinders the detection of the small remaining information-carrying polarization signal. One possible method to detect these small polarization signals is the use of polarization modulation with synchronous lock-in amplifier detection. Many sensitive detection schemes are possible with this approach [5 - 12]. Some perform polarization modulation on the light that interrogates the tissue sample; others modulate the light that has interacted with the sample, placing the polarization modulator between the sample and the detector. The resultant signal, when analyzed in the context of Mueller matrix/Stokes vector formalism (see below), can yield samplespecific polarization properties that can then be linked to the quantities of interest (as, for example, linking glucose concentration to the measured optical rotation, provided that some form of Eq. (17.1) applies in turbid media). By way of illustration, we describe below a particular experimental embodiment of the polarization modulation/synchronous detection. This arrangement carries the advantage of being assumption-independent, in that no functional form of the sample polarization effects is assumed [5]. This turns out to be quite important in complex media such as tissues, since there are typically several polarization-altering effects occurring simultaneously. Thus, a unique and unambiguous tissue polarization description is difficult, so an approach that does not requite assumptions on how tissue alters polarized light, but rather determines it directly, is preferred. The described methodology can yield both Stokes vector of the light exiting the sample and calculate its Mueller matrix. A Stokes vector S is comprised of four ele-

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ments completely describing the polarization of a light beam, S = (I Q U V )T . The first element I represents the overall intensity of the beam, the second element Q represents the amount linearly polarized light in the horizontal and vertical planes, the third element U represents the amount of linearly polarized light in the ±45◦ planes, and the final element V represents the amount of circularly polarized light. The interactions of polarized light with any optical element, including the tissue sample being examined, are applied to the polarization of a light beam through multiplication of the incident Stokes vector with a 4 × 4 Mueller matrix M. Given an input Stokes vector Si impinging on a polarization affecting element, the output Stokes vector So is given as So = MSi . Both the measured Stokes vector and calculated Mueller matrix can be used to quantify the polarizing properties of the sample, including optical rotation produced by optically active (chiral) molecules such as glucose. A schematic of our current turbid polarimetry system is shown in Fig. 17.1 [5]. Unpolarized light is used to seed the system; the experimental results reported here are for a 632.8 nm HeNe laser excitation. Spectroscopic excitation (possibly whitelight source with a monochromator) may be preferable in the future, as suggested by the chemometric analysis of spectral polarimetry data (section 17.6). The light first passes through a mechanical chopper operating at a frequency fc ∼ 500 Hz; this is used in conjunction with lock-in amplifier detection to accurately establish the overall signal intensity levels, as described below. The input optics (a linear polarizer with/without the quarter wave-plate) allow for complete control of the input light polarization that interrogates the sample. The light that has interacted with the sample is detected at a chosen direction as the detection optics can be rotated around the sample. The detection optics begin with a removable quarter wave plate oriented at −45◦ to the horizontal plane: when present, Stokes parameters Q and U (linear polarization descriptors) are measured, and the Stokes parameter V (circular polarization descriptor) when removed. Sample-scattered light then passes through a photoelastic modulator (PEM), which is a linearly birefringent resonant device operating at f p = 50 kHz. Its fast axis at 0◦ and its retardation is modulated according to the sinusoidal function δPEM (t) = δ0 sin(ω t), where ω p = 2π f p and δ0 is the userspecified amplitude of PEM maximum retardation. The light finally passes through a linear analyzer orientated at 45◦ , converting the PEM-imparted polarization modulation to an intensity modulation suitable for photodetection. The detected signal is sent to a lock-in amplifier, with its reference input toggled between the chopper and PEM frequencies for synchronous detection of their respective signals. The data analysis proceeds as follows. The Stokes vector that carries the samplespecific information is given as (detection quarter wave-plate in place):   10 If  Qf  1  0 0  =   Uf  2  1 0 00 Vf 

  10 10 0 0 1 0 1 0  0 0 0 0   1 0   0 0 cos δ sin δ   0 0 0 − sin δ cos δ 00 0

and when the detection quarter wave-plate is removed as

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  0 00 I Q 0 0 1   0 1 0 U  −1 0 0 V

(17.2)

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FIGURE 17.1: Schematic of the turbid polarimeter. C, mechanical chopper; P1 , P2 , polarizers; WP1 , WP2 , removable quarter wave plates; A, aperture; L1 , L2 lenses; PEM, photoelastic modulator; D, photodetector; fc , f p modulation frequencies of mechanical chopper and PEM, respectively. The detection optics can be rotated by an angle θ around the sample (adapted from reference [5]).

  10 Ifr  Qfr  1  0 0     Ufr  = 2  1 0 00 Vf r 

   10 0 0 10 I 0 1 0  Q  0 0 0   . 1 0   0 0 cosδ sinδ   U  0 0 −sinδ cosδ 00 V

(17.3)

The detected intensity signals are thus (q = Q/I, u = U/I, and v = V /I) I (17.4) I f (t) = [1 − q sin δ + u cos δ ]; 2 I I f r = [1 − v sin δ + u cos δ ], (17.5) 2 where δ = δ (t) = δ0 sin ω t is the time-varying PEM retardation of user-specified δ0 magnitude. A time-varying circular function in the argument of another circular function, as is present in Equations (17.3) and (17.4), can be Fourier expanded in terms of Bessel functions [13] to yield signals at different harmonics of the fundamental modulation frequency. It can be advantageous in terms of SNR to choose the peak retardance of the PEM such that the zeroth order-Bessel function J0 is zero [10]; with this selection of δ0 = 2.405 radians (resulting in J0 (δ0 ) = 0), Fourier-Bessel expansion of Eq. (17.4) and (17.5) gives 1 I f (t) = [1 − 2J1(δ0 )q sin ω t + 2J2(δ0 )u cos 2ω t + . . .]; 2

(17.6)

1 I f r = [1 − 2J1(δ0 )v sin ω t + 2J2(δ0 )u cos 2ω t + . . .]. 2

(17.7)

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The normalized Stokes parameters of the light scattered by the sample (u, q, v) can thus be obtained from synchronously-detected lock-in amplifier signals at the first harmonic of the signal at the chopper frequency V1 f c (the ‘zeroth’ harmonic, or the dc signal level), and at the first and second harmonics of the signal at the PEM frequency V1 f p and V2 f p respectively. The experimentally measurable waveform in terms of the detected voltage signal is √ √ (17.8) V (t) = V1 f c + 2V1 f p sin ω t + 2V2 f p cos 2ω t, which takes into account the rms nature of lock-in detection [5]. Applying Eq. (17.8) to the set-up with detection waveplate in the analyzer arm (Eq. (17.6)) gives

√

I V1 f c = k; 2

(17.9)

2V1 f p = −IkJ1 (δ0 )q; √ 2V2 f p = IkJ2 (δ0 )u,

(17.10) (17.11)

where k is an instrumental constant, the same for all equations. The normalized linear polarization Stokes parameters q and u are then found from q= √

V1 f p

;

(17.12)

V2 f p u= √ . 2J2 (δo )V1 f c

(17.13)

2J1 (δ0 )V1 f c

Comparing Eqs. (17.8) and (17.7) when the detection quarter wave plate is removed yields I (17.14) V1 f c = k; 2 √ (17.15) 2V1 f = −IkJ1 (δ0 )v, and the circular polarization Stokes parameter v is then found from V1 f p v= √ . 2J1 (δo )V1 f c

(17.16)

The negative signs in Eqs. (17.10) and (17.15) are dropped in the final equations as positive voltages are measured; instead, the sign of the Stokes parameters is determined from the lock-in amplifier phase of the detected signals. The measured Stokes parameters thus obtained allow for complete characterization of the polarization of the light exiting the sample. The orientation of the plane of linear polarization γ can be calculated as   −1 u γ = tan . (17.17) q

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Based on the known input plane of the incident linear polarization γi , the optical rotation produced by the sample can be calculated as

α = γ − γi .

(17.18)

The optical rotation can be related to the concentration of optically active constituents, for example through the simple relationship α = R · C · hLi of Eq. (17.1); however, in the case of scattering media such as tissue, the ambiguity of the average optical pathlength hLi may necessitate more complex analysis (section 17.5). Measured glucose-induced optical rotation in scattering phantoms (1.4 µ m diameter polystyrene microspheres in water, resulting scattering coefficient of µs = 28 cm−1 as calculated from Mie theory) with added glucose concentrations down to physiological levels (5 to 10 mM) are shown in Fig. 17.2. These measurements were performed in the forward direction (θ = 0◦ in Fig. 17.1) through 1 cm of scattering material (1cm ×1cm × 4cm quartz cuvette containing the turbid chiral suspensions). A moderate scattering level was selected (∼1/3 of biological tissue in the visiblenear IR range [14]), as depolarization in the forward direction through thick samples (1 cm in this case) is quite severe, limiting the accuracy with which small optical rotation values due to small glucose levels can be accurately measured. While the degree of surviving polarization, and thus the accuracy of optical rotation determination, can be greater at other detection directions θ , the contribution of scattering-induced optical rotation can also be greater, masking the small chirality-induced optical rotation due to glucose (see section 17.5). The ways to decouple these glucose-induced and scattering-induced polarization effects, and various trade-offs associated with optimum detection geometry, are discussed elsewhere in this chapter. Nevertheless, the results in Fig.17.2 demonstrate the potential for measuring very small optical rotations (milli-degree levels) in turbid media using the sensitive polarization modulation / synchronous lock-in detection experimental platform. Measurements of glucose induced optical rotation (1.2 M glucose concentration) as a function of the scattering coefficient are shown in Fig. 17.3. As in Fig.17.2, these measurements were performed in the forward direction through a similar quartz cuvette. The optical rotation increases with increasing scattering due to the increase in average optical pathlength (hLi in Eq. (17.1)) produced with additional scattering events. However, the optical rotation begins to plateau and eventually decrease as the medium becomes highly scattering (µs > 40 cm−1 ). This is due to the eventual depolarization caused by multiple scattering. The light that has lost its polarization no longer contributes to the net optical rotation and as a result there is a reduction in optical rotation. The implication to glucose monitoring is that measurement sites and geometries must be chosen such that a reasonably large portion of the light remains polarized to contribute to the net optical rotation. In addition, as discussed later (section 17.5), the measurement geometry also plays a large role in the scatteringinduced optical rotation which must also be taken into account. Although the Stokes vector description can yield sample-specific information as above, the measured and derived results also depend on the state of the input light (as evident from the basic mathematical set-up of the problem, Ssample = Msample ·

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FIGURE 17.2: Logarithmic plot of optical rotation as a function of glucose concentration in scattering media (1.4 µ m diameter polystyrene microspheres in water, µs ∼28 cm−1 ) down to physiological glucose levels. Measurements were performed in the forward direction (θ = 0◦ ) through 1 cm of turbid media in a quartz cuvette (adapted from [6]). Sinput ). Arguably a more ‘intrinsic’ descriptor of sample properties, independent of the input polarization state and representing the true sample polarization transfer function, is its Mueller matrix M. Fortunately, the described PEM-based experimental platform can also perform sensitive Mueller polarimetry, by measuring the output Stokes vectors for four incident polarization states: input linearly polarized light at 0◦ , 45◦ , and 90◦ , and input circularly polarized light. The four input states are denoted with the subscripts H (horizontal), P (45◦), V (vertical), and R (right circularly polarized, although left incidence can be used as well, resulting only in a sign change). The elements of the resulting 4 measured Stokes vectors can be combined to yield the sample Mueller matrix as 1

2 (IH

+ IV )

 1  (QH + QV ) 2 M(i, j) =  1  (UH + UV ) 2  1 2 (VH

+ VV )

1 2 (IH

− IV )

IP − M(1, 1) IR − M(1, 1)



  − QV ) QP − M(2, 1) QR − M(2, 1)    (17.19)  1  2 (UH − UV ) UP − M(3, 1) UR − M(3, 1)  

1 2 (QH

1 2 (VH

− VV ) VP − M(4, 1) VR − M(4, 1)

where the indices i, j = 1, 2, 3, 4 denote rows and columns respectively. As will be described later, the measured Mueller matrix can also be used to quantify the optical rotation produced by a sample, which can be related to the concentration of optically active molecules such as glucose.

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FIGURE 17.3: Measured optical rotation with 1.2 M glucose as a function of scattering coefficient (1.4 µ m diameter microspheres) in the forward direction (θ = 0◦ ) through 1 cm of turbid media contained in a quartz cuvette (adapted from [15]). In summary, the described experimental approach based on polarization modulation and synchronous detection is suitable for sensitive polarimetric detection in turbid media. Several fundamental studies of turbid chiral polarimetry have been published [5–10, 15]. Continuing experimental improvements to maximize detection sensitivity to small glucose levels, such as the use of balanced detection, geometrical optimization, and spectroscopic extension, are ongoing. We now turn to the equally challenging problems of accurately modeling the polarization signals in turbid media, both in the forward (section 17.3) and inverse senses (section 17.4).

17.3 Polarimetry in Turbid Media: Accurate Forward Modeling Using the Monte Carlo Approach To aid in the investigation of polarimetry-based glucose monitoring in biological tissue, accurate forward modeling is enormously useful for gaining physical insight, designing and optimizing experiments, and analyzing / interpreting the measured data. The glucose polarimetry modeling is particularly formidable, as there are several complex polarization effects occurring in tissue simultaneously, and the potential for losing the small glucose-induced polarization signal, or misinterpreting it, is high. The use of electromagnetic theory with Maxwell’s equations is the most rigorous and best-suited method for polarimetry analysis, at least in clear media with well-defined optical interfaces; however, due to the ensuing complexity, the

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Maxwell’s equations approach for polarized light propagation in turbid media is impractical in most circumstances [16]. Instead, light propagation through multiply scattering media is often modelled through transport theory; however, transport theory and its simplified variant, the diffusion equation, are both intensity-based techniques, and hence typically neglect polarization [17, 18]. A more general and robust approach is the Monte Carlo (MC) technique, with its advantage of applicability to arbitrary geometries and arbitrary optical properties. The first Monte Carlo models were also developed for intensity calculations only and neglected polarization, the most commonly used being the share-ware code of Wang et al. [19]. More recently, a number of implementations have incorporated polarization into their Monte Carlo models by keeping track of the Stokes vectors of propagating photon packets [15, 20–25]. In polarization-sensitive Monte Carlo modelling, it is assumed that scattering events occur independently of each other and have no coherence effects. The position, propagation direction, and polarization of each photon are initialized and modified as the photon propagates through the sample. The photon’s polarization, with respect to a set of arbitrary orthonormal axes defining its reference frame, is represented as a Stokes vector S and polarization effects are applied using medium Mueller matrices M. The photon propagates in the sample between scattering events a distance sampled from the probability distribution exp(−µt d), where the extinction coefficient µt is the sum of the absorption µa and scattering µs coefficients and d is the distance travelled by the photon between scattering events. Upon encountering a scattering event, a scattering plane and angle are statistically sampled based on the polarization state of the photon and the Mueller matrix of the scatterer. The photon’s reference frame is first expressed in the scattering plane and then transformed to the laboratory (experimentally observable) frame through multiplication by a Mueller matrix calculated through Mie scattering theory [26]. Upon encountering an interface (either an internal one, representing tissue domains of different optical properties, or an external one, representing external tissue boundary), the probability of either reflection or transmission is calculated using Fresnel coefficients [15]. As no interference effects are considered, the final Stokes vector for light exiting the sample in a particular direction is computed as the sum of all the appropriate directional photon sub-populations. Various quantities of interest such as detected intensities, polarization (Stokes vectors) properties, average pathlengths, and so forth can be quantified once sufficient number of photon (packets) have been followed and tracked to generate statistically acceptable results (typically 107 –109 photons) [15]. We and others have performed a number of Monte Carlo simulation studies to gain insight into the behavior of polarized light in tissues and tissue-like media [15, 20–25, 27]. However, most current Monte Carlo models for polarized light propagation do not fully simulate all of the polarization-influencing effects of tissue. This is because modeling simultaneous polarization effects is difficult, especially in the presence of multiple scattering. Yet in biological tissue, effects such as optical activity due to chiral molecules (e.g., glucose and proteins) and linear birefringence due to anisotropic tissue structures (e.g., collagen, elastin, and muscle fibers) must be incorporated into

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the model in the presence of scattering. This is particularly important in glucose polarimetry, as many tissues at accessible anatomical sites (finger, lip, ear lobe) exhibit anisotropic structures manifesting itself as linear birefringence (also known as linear retardance). Fortunately, there exists a method to simulate simultaneous polarization effect in clear media through the so-called N-matrix formalism, and applying this approach in tissue-like media between scattering events can yield an accurate Monte Carlo tissue polarimetry model [27]. Briefly, the Mueller matrices for linear birefringence and optical activity are known and can correctly model these effects individually; the problem arises in applying the combined effect when both are exhibited simultaneously, especially in the presence of scattering by the sample. Matrix multiplication is in general not commutative; thus different orders in which these effects are applied will have different effects on the polarization. Ordered multiplication in fact does not make physical sense, as these occur simultaneously and not one after the other as sequential multiplication implies. This necessitates the combination of the effects into a single matrix describing them simultaneously. The N-matrix algorithm was first developed by Jones [28]; however, a more thorough derivation is provided in Kliger et al. [29]. The issue of noncommutative matrices is overcome by representing the matrix of the sample as an exponential function of a sum of matrices, where each matrix in the sum corresponds to a single optical polarization effect. This overcomes the ordering issue, as matrix addition (summation) is always commutative, and applies to differential matrices representing the optical property over an infinitely small optical pathlength. Derived from their parent matrices, these are known as N-matrices. The differential N-matrices corresponding to each optical property exhibited by the sample can then be summed to express the combined effect. The formalism is expressed in terms of 2 × 2 Jones matrices applicable to clear nondepolarizing media, rather than the more commonly used 4 × 4 Mueller matrices previously discussed. However, a Jones matrix can be converted to a Mueller matrix, provided there are no depolarization effects, as described in Schellman and Jensen [30]. This is indeed applicable to our Monte Carlo model, as depolarization is caused by the (multiple) scattering events, and no depolarization effects occur between the scattering events. Results from validation experiments are shown in Fig. 17.4, where measurements from phantoms with controllable scattering, linear birefringence, and optical activity were used to test the developed model [27]. The plot shows the change in the normalized Stokes parameter q = Q/I with increasing birefringence, measured in phantoms and calculated from the MC model in the forward direction of a 1 × 1 × 1 cm3 sample with input circularly polarized light. Good agreement between the developed Monte Carlo model and controlled experimental results is seen. As the input light is transferred from circular to linear polarization due to the increasing sample birefringence (the sample in effect acting like a turbid wave-plate), optical rotation due to optical activity of dissolved sugar (the use of sucrose instead of glucose was dictated by experimental considerations of sample preparation) is seen as an increase in parameter q. No such effect is seen in the absence of chirality. While these validation experiments were carried out with much higher levels of optical activity than those present physiologically, the model can be used to simulate physiologically relevant

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FIGURE 17.4: Experimental measurements (squares) and Monte Carlo calculations (lines) of the change in the normalized Stokes parameter q with and without optical activity (dotted lines and circles) in the forward (θ = 0◦ ) detection geometry with input circularly polarized light and a fixed scattering coefficient of µs = 60 cm−1 . Birefringence was varied from δ = 0 to 1.4364 rad (∆n = 0 to 1.628 × 10−5) and the magnitude of optical activity was χ = 1.965◦ cm−1 , corresponding to a 1 M sucrose concentration. Refractive index matching effects have been ignored in the MC simulations (adapted from reference [27]).

levels as discussed in the spectral chemometrics section (section 17.6). Lower levels of optical activity can be handled with noise reduction methods such as smoothing or interpolating, to deal with statistical noise due to discrete nature of the Monte Carlo model. Figure 17.5 plots the Monte Carlo calculated normalized Stokes parameters with fixed optical activity and increasing birefringence similar to Fig. 17.4, except that several levels of glucose are now simulated (0 M, 1 M, and 10 M). As we are interested in the optical activity-induced effects of glucose only, the glucose-induced refractive index matching effects [7] have been ignored in these MC simulations. Similar to the previous results, the sample was a 1 × 1 × 1 cm3 cube and the input light was circularly polarized. The large magnitude birefringence effects on the parameters u and v are quite evident due to the transfer from the input linear to circularly polarized light; however, the optical activity induced effects are small and only evident for the parameter q. The simulated levels of birefringence (0 to 1.5 rad) are actually somewhat lower than those present in most tissue [27]; however, the levels of glucose are several orders of magnitude higher than that present in biological tissue. The glucose effects on the resulting Stokes parameters for this geometry and sample properties are not large. To conclude the forward-modeling section, we have described and validated a comprehensive polarization-sensitive Monte Carlo model capable of simulating complex tissue polarimetry effects, including simultaneous optical activity and birefrin-

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FIGURE 17.5: Monte Carlo calculations with optical activity χ = 0◦ cm−1 (dashed lines), χ = 0.8194◦ cm−1 (solid lines), and χ = 8.194◦ cm−1 (dotted lines) corresponding to 0 M, 1 M, and 10 M glucose concentrations respectively. The normalized Stokes parameters are plotted in the forward detection geometry with input circularly polarized light and a fixed scattering coefficient of 60 cm−1 for all glucose concentrations. Birefringence is varied from δ = 0 to 1.4364 rad (∆n = 0 to 1.628 × 10−5 ). Only a small chirality-induced change in q is apparent. Glucose-induced refractive index matching effects have been ignored in the MC simulations (adapted from reference [27]).

gence in the presence of scattering. The refinement and use of this model is ongoing, specifically as applied to the glucose detection problem, viz. detection geometry optimization, pathlength / sampling volume quantification, and evaluation of spectral polarimetry. Some of these studies are described subsequently.

17.4 Tackling the Inverse Problem: Polar Decomposition of the Lumped Mueller Matrix to Extract Individual Polarization Contributions Having established the ability to accurately measure and model turbid polarimetry signals in the forward sense, we now turn to the complicated inverse problem of separating out the constituent contributions from simultaneous optical effects. That is, given a particular Mueller matrix obtained from an unknown complex system such

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as biological tissue with some glucose level, can it be analysed to extract constituent polarization contributions? This is a formidable task because when many optical polarization effects are simultaneously occurring in the sample (as is the case for biological tissue that often exhibit depolarization, linear birefringence, and optical activity), the resulting elements of the net Mueller matrix reflect several ‘lumped’ effects, thus hindering their unique interpretation. Mueller matrix decomposition methodology that enables the extraction of the individual intrinsic polarimetry characteristics may be used to address this problem [31]. Preliminary results on the use of this approach for extraction of the component of optical rotation arising purely due to circular birefringence (caused by glucose and other optically active molecules) by decoupling the other confounding effects in a complex turbid medium are encouraging, as summarized in this section. Polar decomposition of an arbitrary Mueller matrix M into the product of three elementary matrices representing a depolarizer (M∆ ), a retarder (MR ), and a diattenuator (MD ) can be accomplished via [31] M = M∆ · MR · MD .

(17.20)

The validity of this decomposition procedure was first demonstrated in optically clear media by Lu and Chipman [31]. As mentioned before in the context of forward modelling with the N-matrix approach, matrix multiplication is generally not commutative; thus the order of these elementary matrices is important. It has been shown previously that the order selected in Eq. (17.20) always produces a physically realizable Mueller matrix; it is thus favorable to use this order of decomposition when nothing is known a priori about an experimental Mueller matrix [32]. The three basis Mueller matrices thus determined can then be further analyzed to yield a wealth of independent constituent polarization parameters. Specifically, diattenuation (D, differential attenuation of orthogonal polarizations for both linear and circular polarization states), depolarization coefficient (∆, linear and circular), linear retardance (δ , difference in phase between two orthogonal linear polarization, and its orientation angle Θ), and circular retardance or optical rotation (ψ , difference in phase between right and left circularly polarized light) can be determined from the decomposed basis matrices [31,33]. Proceeding as outlined above, the magnitude of diattenuation (D) can be determined as D = {1/MD (1, 1)} × [{MD(1, 2)}2 + {MD (1, 3)}2 + {MD (1, 4)}2 ]1/2 .

(17.21)

Here M(i, j) are the elements of the 4 × 4 Mueller matrix M. The coefficients MD (1, 2) and MD (1, 3) represents linear diattenuation for horizontal (vertical) and +45◦ (-45◦) linear polarization respectively, and the coefficient MD (1, 4) represents circular diattenuation. Turning to depolarization, the diagonal elements of the decomposed matrix M∆ can be used to calculate the depolarization coefficients [M∆ (2, 2), M∆ (3, 3) are depolarization coefficients for incident horizontal (or vertical) and 45◦ (or −45◦) linearly polarized light, and M∆ (4, 4) is the depolarization coefficient for incident circularly

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polarized light]. The net depolarization coefficient ∆ is defined as ∆ = 1 − |Tr M∆ − 1|/3.

(17.22)

Note that this definition of depolarization coefficient is different from the conventional Stokes parameter-based definition of degree of polarization (Q2 + U 2 + V 2 )1/2 /I. The latter represents the value of degree of polarization resulting from several lumped polarization effects, and also depend on the incident Stokes vector. In contrast, the depolarization coefficient (∆) defined by Eq. (17.22) represents the pure depolarizing transfer function of the medium. Finally, the following analysis can be performed on the retardance matrix MR . This matrix can be further expressed as a combination of a matrix for a linear retarder (having a magnitude of linear retardance δ , its retardance axis at angle Θ with respect to the horizontal) and a circular retarder (optical rotation with magnitude of ψ ) [33]. Using the known functional form of the linear retardance and optical rotation matrices, the values for optical rotation (ψ ) and linear retardance (δ ) can be determined from the elements of the matrix MR as [33]

ψ = tan−1 {[MR (3, 2) − MR(2, 3)]/[MR (2, 2) + MR(3, 3)]};

(17.23)

δ = cos−1 {[(MR (2, 2) + MR (3, 3)2 + (MR (3, 2) − MR(2, 3)2 ]1/2 − 1}.

(17.24)

Note that there are important differences between the optical rotation ψ defined through Eq. (17.23) and the rotation of the Stokes linear polarization vector α defined through Eqs. (17.17) and (17.18) of section 17.2. The parameter α represents the net change in the orientation angle of the linear polarization vector. In addition to rotation due to circular birefringence, this may also have contributions from several other confounding factors like the scattering induced rotation and the rotation of the polarization ellipse resulting from linear birefringence and its orientation. In contrast, the parameter ψ represents the component of optical rotation that is purely due to the circular birefringence property of the medium (introduced by the presence of chiral substances such as glucose). The validity of the matrix decomposition approach summarized in Eqs. (17.20)– (17.24) in complex turbid media was tested with both experimental (section 17.2) and MC-simulated (section 17.3) Mueller matrices, whose constituent properties are known and user-controlled a priori. In the experimental studies, a PEM-based polarimeter [5, 27] (section 17.2) was used to record Mueller matrices in the forward detection geometry (sample thickness 1 cm, detection area of 1 mm2 and an acceptance angle ∼ 18◦ around the forward directed ballistic beam were used) from polyacrylamide phantoms having strain-induced linear birefringence, sucrose-induced optical activity, and polystyrene microspheres-induced scattering. The Mueller matrix was calculated from the standard relationships between its sixteen elements and the measured output Stokes parameters [I Q U V ]T for each of the four input polarization states (Eq. (17.19)) [34, 35].

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FIGURE 17.6: The experimentally recorded Mueller matrix and the decomposed matrices for a birefringent (extension = 4 mm), chiral (concentration of sucrose = 1 M), turbid (µs = 30 cm−1 , g = 0.95) phantom. The Mueller matrix was measured in the forward direction through the 1 cm thickness.

Figure 17.6 shows the experimentally attained Mueller matrix and the corresponding decomposed depolarization (M∆ ), retardance (MR ), and diattenuation (MD ) matrices. These results are from a solid polyacrylomide phantom that mimics the complexity of biological tissues, in that it simultaneously exhibits birefringence (extension 4 mm for strain applied along the vertical direction), chirality (concentration of 1 M of sucrose corresponding to magnitude of optical activity per unit length of χ = 1.965◦ cm−1 was used here instead of glucose for practical reasons of phantom construction), and turbidity (1.4 µ m diameter polystyrene microspheres in water, resulting in a scattering coefficient of µs = 30 cm−1 and anisotropy parameter g = 0.95). The measurement was performed in the forward direction (θ = 0◦ ) through a 1 cm×1 cm×4 cm phantom. Note the complicated nature of the lumped Mueller matrix and the relatively unequivocal nature of the three basis matrices derived from the decomposition process. Eqs. (17.21)–(17.24) were then applied to the decomposed basis matrices to retrieve the individual polarization parameters (diattenuation D, linear retardance δ , optical rotation ψ , and depolarization coefficient ∆). The determined values for these are listed in Table 17.1. The comparison of the derived and the input control values for the polarization parameters reveals several interesting trends. The expected value for diattenuation D is zero, whereas the decomposition method yields a small but nonzero value of D = 0.034. Scattering induced diattenuation that arises primarily from singly (or weakly) scattered photons [33] is not expected to contribute to the nonzero value for D because multiply scattered photons are the dominant contributor to the detected photons in the forward detection geometry. Presence of small amount of dichroic absorption (at the wavelength of excitation λ = 632.8 nm) due to anisotropic alignment of the polymer molecules in the polyacrylamide phantom may possibly contribute to this slight nonzero value for the parameter D.

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TABLE 17.1: Comparison of the polarization parameters derived [via Eqs. (17.21)–(17.24)] from the basis matrices of Fig. 17.6. Parameters D δ ψ ∆

Estimated value (from M∆ , MR , MD ) 0.032 1.384 rad 2.04◦ 0.790

Expected value 0 1.345 rad 2.07◦ 0.806

The agreement in the linear retardance value of this turbid phantom (δ = 1.384 rad) and that for a clear (µs = 0 cm−1 , extension = 4 mm) phantom (δ =1.345 rad) is quite reasonable. The Mueller-matrix derived value of optical rotation ψ = 2.04◦ of the turbid phantom was, however, slightly larger than the corresponding value measured from a clear phantom having the same concentration of sucrose (ψ0 = 1.77◦). This small increase in the ψ value in the presence of turbidity is likely due to an increase in optical pathlength engendered by multiple scattering. Indeed, the value for ψ , calculated using the optical rotation value for the clear phantom (ψ0 = 1.77◦) and the value for average photon pathlength (hLi = 1.17 cm, determined from Monte Carlo simulations, see section 17.5) [ψ = ψ0 × hLi = 2.07◦]) was reasonably close to the Mueller matrix derived value (ψ = 2.04◦). To account for the contraction of the phantom due to longitudinal stretching, the thickness of the scattering medium was taken to be 0.967 cm (reduction in thickness at 4 mm extension using the Poisson ratio ∼ 0.33 of polyacrylamide [36]) instead of 1 cm for the calculation of average photon pathlength. The overall slight lower experimental optical rotation values of the phantoms as compared to that expected for concentration of sucrose of 1 M (the experimental value of ψ0 = 1.77◦ for the clear phantom as compared to ψ0 = χ × L = 1.90◦, expected for path length of L = 0.967 cm and χ = 1.965◦ cm−1 ) possibly arises due to an uncertainty in the concentration of sucrose during the process of phantom fabrication. Finally, the calculated decomposition value of total depolarization of ∆ = 0.79 seems reasonable, although this is harder to compare with theory (there is no direct link between the scattering coefficient and resultant depolarization). The value shown in the theoretical comparison column of the table was determined from the Monte Carlo simulation as described in the previous section. The resultant agreement in the depolarization values is excellent. It is worth noting that decomposition results for an analogous purely depolarizing phantom (same turbidity, no birefringence nor chirality, results not shown) were within 2% of the above ∆ values. This self-consistency implies that decomposition process successfully decouples the depolarization effects due to multiple scattering from optical rotation and retardation effects, thus yielding accurate and quantifiable estimates of the δ and ψ parameters in the presence of turbidity. In order to gain additional quantitative understanding of the dependence of the

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estimated value for optical rotation ψ on the propagation path of multiply scattered photons, Mueller matrices were generated using Monte Carlo simulations for transmitted light (1 cm thick sample as before), collected at different spatial positions at the distal face of the scattering medium. Decomposition analysis was then performed on these Monte Carlo generated Mueller matrices. Figure 17.7 displays the variation of the parameter ψ of transmitted light as a function of distance from ballistic beam position at the distal face of a birefringent (linear retardance of δ = 1.35 radian for optical pathlength of 1 cm) turbid medium (µs = 30 cm−1 , g = 0.95). The axis of linear birefringence was kept along the vertical direction (Θ = 90◦ ) in the simulations and the different spatial positions were perpendicular to the direction of the axis of linear birefringence. The results are shown for two different values of optical activity (χ = 0.0820 and 0.1640◦ cm−1 , corresponding to 100 mM and 200 mM concentration of glucose, respectively). As one would expect, the Mueller-matrix derived values for ψ increase with increasing average photon pathlength and the values are also reasonably close to those calculated using the linear relationship (ψ = χ × average photon pathlength). Note that the average path length has contributions from both the polarization preserving and the depolarized photons. The fact that the propagation path of the polarization preserving photons (which would show experimentally detectable optical rotation) is shorter than the average photon path length of light exiting the scattering medium [37] should account for the slightly lower value for the Mueller-matrix derived ψ (particularly at larger off-axis distances). The results of the experimental studies on phantoms having varying optical properties and the corresponding results of Monte Carlo generated Mueller matrices demonstrate that decomposition of Mueller matrix can be used for simultaneous determination of the intrinsic values for optical rotation (ψ ) and linear retardance (δ ) of a birefringent, chiral, turbid medium. For conceptual and practical reasons, the extension of this methodology to backward detection geometry is warranted. This work is currently ongoing in our laboratory. To summarize, we have described a theoretical approach for solving the inverse problem in turbid polarimetry. The Mueller matrix decomposition methodology allows the extraction of the individual intrinsic polarimetry characteristics from the lumped Mueller matrix description of a complex turbid medium. Experimental and theoretical studies in complex tissue-like media for extracting the intrinsic value for optical rotation (which is related to the concentration of chiral molecules such as glucose) yielded very promising results. This bodes well for the potential application of this methodology for quantification of the small optical rotations due to blood glucose in diabetic patients, but this remains to be rigorously investigated. Further refinements of the highly sensitive Mueller matrix measurement set-up capable of detecting small changes in the matrix elements corresponding to the physiological glucose levels and selection/optimization of the measurement geometry will be required. It is also pertinent to note that determination of the concentration of glucose using the measured optical rotation from a multiply scattering medium like tissue would require additional quantitative information on the pathlength distributions of polarization preserving and depolarized photon populations. Further, the

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FIGURE 17.7: Variation of optical rotation parameter ψ of transmitted light as a function of distance from ballistic beam position at the distal face of a 1-cm-thick birefringent (δ = 1.35 radian for optical pathlength of 1 cm) turbid (µs = 30 cm−1 , g = 0.95) medium. The results are shown for two different values of optical activity (χ = 0.0820 and 0.1640◦cm−1 , corresponding to glucose concentrations of 100 and 200 mM, respectively). The open symbols are the ψ values estimated from the decomposition of Monte Carlo generated Mueller matrices; the solid symbols were calculated via ψ = χ × average photon pathlength. The inset shows the MC calculated average photon pathlength as a function of the off-axis distance (see section 17.5).

use of single-wavelength measurements is unlikely to yield unequivocal results in real tissues, and the use of multi-spectral / spectroscopic turbid polarimetry will be essential. The following two sections attempt to address some of these challenges.

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17.5 Monte Carlo Modeling Results for Measurement Geometry, Optical Pathlength, Detection Depth, and Sampling Volume Quantification One of the many advantages of a comprehensive forward model of polarized lightbiological tissue interaction (section 17.3) is the ability to explore in silico the wide parameter space potentially available for polarimetric tissue measurements, in an effort to determine optimum geometry for glucose sensing. Another is the ability to quantify and interpret the measured parameters by examining the sampling volume probed by light, and determining the average light pathlength in interrogated tissues. In this section, we present representative results from Monte Carlo studies and selected experimental measurements that address these issues [37–39]. Unlike the previous square/rectangular sample geometries examined to date, a cylindrical tissue model is used here. This geometry is of special relevance because the curved surfaces of human anatomy such as finger or lip are of interest in optical glucose sensing. Further, sites like the finger offer the potential geometric advantage of multiple-direction detection capability (0◦ to 360◦ , compared with 0◦ and 180◦ detections for slab-like structures and 180◦-only detection for semi-infinite set-ups), and may also be more practical and convenient in a clinical setting. Fortunately, the inherent flexibility of the Monte Carlo modeling platform makes the simulations of any arbitrary sample geometry equally accessible. Utilizing the cylindrical model, the effects of detection direction on the polarimetric signal, and specifically its influence on glucose-induced optical rotation, have been investigated. Monte Carlo predictions were validated/confirmed with selected experimental measurements. For the results reported below, turbid chiral samples in the absence of birefringence were examined. The modeling geometry shown in Fig. 17.8 mimics the experimental conditions [5, 38]. A 632.8 nm horizontally polarized beam of 1 mm diameter is incident at the point O on the center of a vertically orientated cylindrical sample of 0.8 cm in diameter and 4 cm in height. The scattered photons at point P (z, θ ), within acceptance angle φ ∼ 48◦ , are collected and focused onto a detector of ∼ 0.7 mm2 sensing area. The detection angle varies from 0◦ to 180◦ . The vertical position of the surface detection element z ranges from −4.0 cm to +4.0 cm, with the signs indicating the relative position with respect to the horizontal incident plane. The samples are highly turbid media (water suspension of microspheres of different diameter) containing D-glucose, with birefringence values set to zero. The glucose concentration ranges from 0 mM to 900 mM and the scattering coefficient µs is varied from 93 cm−1 to 100 cm−1 , depending on glucose levels. The scattering coefficient range is chosen to approximate typical turbidity of biological tissue. In the simulations, the cylindrical sample is characterized by a set of surface elements that are rectangular on the sides and triangular on the bottom and top (48 on each of the three surfaces). Additional modeling details can be found in the original articles [37 -39]. The results indicate the dramatic effects of the detection geometry. In moder-

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FIGURE 17.8: Cylindrical geometry used in the experiments and the Monte Carlo simulations. Linearly polarized light incidents at the point O on a vertically oriented cylindrical sample. The scattered light is collected by a small detector element at the point P (z, θ ) on the surface of the cylinder with an acceptance angle φ . z is the distance of the detector off the horizontal incident plane (z = 0) and θ is the detection direction (adapted from reference [37]).

ately scattering samples (µs ∼ 20 − 60 cm−1 ), the degree of polarization preservation decreases as one moves from forward to backward hemisphere (increasing θ ), although a slight increase is seen as one approaches the exact backscattering direction (θ = 180◦). However, for tissue-like scattering (µs ∼ 100 cm−1 ), polarization preservation can become higher when measured at higher detection angles (backwards hemisphere). For all cases, the highest polarization preservation was observed in the incident plane (z = 0). Further, the angular dependence of optical rotation α is significant as well. Figure 17.9 shows measurement and simulation results for an achiral (glucose-free) highly scattering sample, where the observable α values are caused by the scattering process only (and can thus be considered as ‘noise’ in the context of the glucose detection problem). The effects of moving the detector off the incident plane is negligible in the forward direction, and very significant at other detection angles [Fig.17.9(a)]. Fig. 17.9(b) presents the entire modeled α response surface in the θ , z parameter space, indicating the complicated behavior and the necessity of cautious interpretation of the measured α values — optical rotation in the presence of multiple scattering is not only caused by the chirality of the glucose molecules as is the case in clear-media glucometry. Note that although the scattering-induced optical rotation can be as large as 40◦ , it is not observable anywhere in the incident plane (z = 0), or in the exact forward and backwards directions (θ = 0◦ and 180◦ ) due to symmetry [Fig.17.9(b)]. These geometries may thus be

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FIGURE 17.9: Optical rotation of light scattered from highly turbid (µs = 100 cm−1 ) achiral birefringence-free sample. (a) Simulations and measurements at θ = 0◦ and 135◦ as z changes from −4 cm to 4 cm. The symbols are experimental data and the lines are Monte Carlo results. At θ = 135◦ the optical rotation is seen to oscillate symmetrically about the incident plane with a large amplitude of ∼ 40◦ . This scattering-induced optical rotation is not observable at θ = 0◦ for all examined z-values. (b) θ –z response surface of optical rotation from the MC simulation with θ changing from 0◦ to 180◦, and z changing from −4 cm to 4 cm. In the absence of glucose, the scattering-induced optical rotation is minimal (∼ 0) at θ = 0◦ or θ = 180◦ , and everywhere in the incident plane (z = 0) (adapted from reference [38]).

preferable for measuring pure glucose-induced optical rotation in the highly scattering environment, subject to many other considerations (e.g., ease of measurement, degree of polarization preservation). Figure 17.10 shows the experimental optical rotation results from tissue-like turbid medium in the presence of glucose (see [38] for corresponding Monte Carlo predictions). The trends in the forward direction in the incident plane (Fig. 17.10(a)) are similar to those previously observed (Fig. 17.2), although the sample size/shape/scattering parameters are somewhat different. As one explores the backward hemisphere (θ = 135◦ in 17.10(b)), other effects come into play. The effects of added glucose are rather modest, even in the incident plane (z = 0), where the interference from the scattering induced signals was shown to be minimal. Conversely, measuring off the incident plane ( z ∼ 3 mm) at this detection angle yields considerable variation in detected α values as the glucose concentration is varied. Given the large magnitude of observed changes, this is probably not caused by the chiral nature of glucose, but is likely due to the glucose refractive index matching effect [7]. That is, the glucose-caused changes in the scattering coefficient manifest themselves as large changes in scattering-induced optical rotation, as measured in this off-incidentplane backwards-hemisphere detection geometry. This effect may or may not prove useful as a measurable metric for glucose detection in real tissues, but clearly it must be taken into consideration in system design and data interpretation. Further

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FIGURE 17.10: Optical rotation due to changes in glucose concentration in highly turbid chiral phantoms (µs = 100 cm−1 in the absence of glucose, glucose concentration from 0 M to 0.9 M), measured at different detection geometries. (a) θ = 0◦ , z = 0 mm. A significant increase over the baseline level is observed, likely due to chiral nature of glucose. (b) θ = 135◦ , z = 0 mm, and z = 3 mm. Optical rotation varies greatly with glucose concentration at z = 3 mm, caused by the glucose-induced refractive index matching effect; corresponding changes are not easily detectable at z = 0 mm. The symbols are experimental data and the lines are guides for the eye (adapted from reference [38]). Confirmatory Monte Carlo results are available in reference [38].

studies also suggest the advantage of backward detection geometries due to better polarization preservation at high levels of (tissue-like) turbidity [38]. Clearly then, the sensitivity of turbid polarimetric glucose measurement is strongly dependent on detection geometry, and further studies are ongoing to shed additional light on this complicated issue. Monte Carlo modeling can also offer some insights on a variety of important ‘hidden’ variables inherent in turbid polarimetry. Specifically, the pathlength, the detection depth, and the sampling volume of tissue-interrogating photons are all crucial for accurate glucose quantification, in that they are needed to analyze/quantify/interpret the obtained polarimetry results. However, these quantities are difficult or impossible to obtain directly from experiments. The complicated zig-zag nature of photon paths in multiply scattering media necessitates the use of statistical models such as the Monte Carlo approach. Here we show representative results for pathlength distribution studies of linearly polarized photons incident onto cylindrical turbid samples (µs ∼ 100 cm−1 ) [37]. In the simulations, the collected photons are binned based on the number of scattering events N they experienced within the sample, and their pathlength, polarization states, and intensity are extracted from each bin and compared with the total (N-unresolved) averaged ones. The pathlengths of photons spread out due to multiple scattering as shown in Fig. 17.11(a). Note the relatively confined pathlength distributions of polarization-maintaining photons, with their well-defined upper limit; in contrast, the total photon fields (polarized + depolarized) exhibit a

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FIGURE 17.11: MC-derived pathlength distribution of photons within the incident plane (z = 0) at backwards detection angles (θ > 90◦ ). (a) typical pathlength distributions of the polarization-maintaining photon subpopulations (hollow symbols) and the whole photon population detected at θ = 135◦ and 158◦ . The average pathlength decreases with detection angle and the intensity increases with detection angle (also seen at other values of θ , see reference [37]). (b) Angular dependence of average pathlengths for both photon populations. The average pathlengths of polarization-maintaining photons hLip are shorter than the corresponding hLitot of the total photon field, as quantified in the figure inset (adapted from reference [37]).

much broader pathlength distribution without a definite upper limit. It is possible to calculate the corresponding average pathlengths for the polarized (hLip ) and total (hLitot ) photon fields, by summing the weighted contribution from N = 1 to N → ∞ (in practice, the upper limit of N was ∼ 70 for hLip , as the surviving polarization fraction was too low for higher N). The summary results for this sample turbidity are shown in Fig. 17.11(b). The average pathlength of polarized photons hLip is seen to be 2–3 times smaller than the average pathlength of all collected photons, the latter being dominated by the longer traveling photon histories. The strong angular dependence of both pathlength averages is also evident. Additional simulation results show that the change in (lowering of) the scattering coefficient µs , as such can be engendered by the glucose index matching effect, shortens the average photon pathlengths [37]. We have also estimated the penetration depths and sampling volumes of the polarized and depolarized light in cylindrical turbid samples, using these MC-derived pathlength distributions [39]. In this approach, the zig-zag photon path is approximated by two straight-line segments, the length sum of which is equal to the pathlength of the photon. The joined points of all the possible combination of two segments in the incident plane form an ellipse-shaped detection depth distribution and an ellipsoid-shaped sampling volume distribution. Not surprisingly, it is found that the smaller average pathlength of polarization-preserving photon subpopulation

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FIGURE 17.12: Optical sampling volume (the volume formed by the surface of the partial ellipsoid and the sample wall) and detection depth distribution (top view of sampling volume) at θ = 135◦. Photons enter the cylindrical sample at O and exit at P (in the scattering plane, z = 0). (a) total photon population (hLitot = 1.44 cm). (b) polarized photon subpopulation (hLip = 0.44 cm). As seen, the polarized photons have smaller sampling volume and shallower detection depth than the total photon population, which is dominated by longer-travel depolarized photons (adapted from reference [39]).

results in shallower penetration depths and smaller sampling volumes than that of all collected photons in the backward hemisphere. To quantify these trends, Fig. 17.12 shows a particular example of the two sampling volumes at a detection angle θ = 135◦. As evident from the MC results for pathlength distributions, the detection depth and sampling volume are also strongly dependent on the detection geometry. The implication for glucose detection is that the control of spatial interrogation extent of light in tissues can be achieved (and quantified) by changing the detection angle. Small angle detection provides deeper penetrations and larger sampling volumes, whereas large angle detection (approaching the back-scattering direction at θ = 180◦) offers near surface and localized information from within the turbid media. Any changes in glucose concentration which affects the photon pathlengths will also influence the penetration depths and sampling volumes. In concert with the polarization preservation and scattering- vs glucose-induced optical rotations results, such modelling is beginning to be applied for design considerations in a turbid polarimetry glucose detection system.

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17.6 Combining Intensity and Polarization Information via Spectroscopic Turbid Polarimetry with Chemometric Analysis Nearly all of the developing optical glucose monitoring techniques measure a signal caused not only by glucose but also by many other biological constituents. As a result, the techniques suffer in glucose specificity. The sensitivity is often lacking as well, as the signal due to glucose is generally much smaller than that due to other constituents. One method to minimize these limitations is to increase the glucose signal content via a spectral approach that collects data over a range of wavelengths. Another possibility is to utilize a dual modality optical methodology that combines the complementary strengths of the two selected techniques. Specifically, combining near-infrared (NIR) spectroscopy (see chapters 5, 6, 8 and 10 of this monograph), arguably the most promising glucose-sensing optical method to date, with spectral polarization information lends itself well to such a hybrid approach, as simultaneous measurements can be made with a single polarization-sensitive optical system. In addition to potential experimental convenience and practicality, there is a scientific motivation for this spectroscopic combination. This combination exploits three optical effects of glucose: its NIR absorption spectrum as manifest in the NIR spectroscopy, its optical rotatory dispersion (ORD, also known as optical activity) as manifested in the polarimetry data, and its refractive index matching effect which can influence the results of both techniques. The last is the change in the refractive index of the media with changes in constituent glucose concentrations; this influences the scattering coefficient of the tissue [7]. For the initial simulation study described below, only the first two effects were explored (NIR absorption and ORD); unlike the index matching effect, these two are potentially specific to glucose. The effects of glucose-induced refractive index matching will be examined subsequently. To test the combination of NIR and ORD spectroscopy for glucose concentration determination, a model of blood plasma containing glucose and plasma proteins was used to generate intensity and polarization spectra in both clear and scattering media. The effects of absorption due to water, plasma proteins, and glucose in the visible and NIR were modeled using experimental data from a number of reports [40–43]. As data for individual plasma protein absorption dispersion could not be found, the total plasma protein (albumin, globulin, and fibrinogen) absorption was used. Figure 17.13 (a) shows the resulting absorption coefficients µa (λ ) per concentration of analyte and optical pathlength, given as a function of wavelength for water, total protein, and glucose. Additional details related to water displacements effects and other subtleties for accurate determination of these spectra can be found in [44]. The similarity of the glucose absorption spectrum with that for the plasma proteins should be noted, as this leads to difficultly in separating their absorption effects and corresponding concentrations. The high level of absorption due to water as the wavelength increases beyond 1400 nm also leads to difficulty as this will greatly reduce the intensity of the light exiting the sample. The effects of optical activity due to proteins and glucose in the visible and NIR

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FIGURE 17.13: (a) Absorption spectra of blood plasma proteins and glucose in the visible and NIR. (b) Optical rotatory dispersion of blood plasma proteins and glucose as given by Drude’s equation (Eq. (17.25)) in the visible and NIR. The parameters for the Drude’s equation are: for glucose A = 1.72 × 107 and λc = 150 nm, for albumin A = −1.75 × 107 and λc = 264 nm, for globulin A = −1.48 × 107 and λc = 211 nm, and for fibrinogen A = −1.37 × 107 and λc = 260 nm (adapted from reference [46]). were modeled using Drude’s equation, [α ]λ =

A , λ 2 − λc2

(17.25)

deg. where [α ]λ is the specific rotation of the molecule in units of g/ml−dm at the wavelength λ , A is constant specific to the molecule, and λc is the center wavelength [22]. The resulting ORD spectra are displayed in Fig. 17.13 (b), with the parameter of the Drude’s equation for the plasma proteins [44] and glucose [1] shown in the figure caption. The induced rotations due to proteins and glucose have opposite signs, the proteins rotate to the left (negative sign) while glucose rotates to the right (positive sign). From the plot of the Drude’s parameters it is evident that the spectral dependence for glucose and proteins, while having opposite senses of rotation, is very similar. This leads to difficultly in separating the rotation due to glucose from that due to proteins. For clear media, the values for µa (λ ) and α (λ ) can be used to calculate the Mueller matrix for the sample and the resulting Stokes vector for light after propagating through the sample. For scattering media, the Monte Carlo model (section 17.3) was used to generate spectral values for the output Stokes vectors with the µa (λ ) and α (λ ) spectral inputs of Fig. 17.13. The turbidity of the medium was set to be µs = 60 cm−1 (somewhat lower than tissue in order to reduce computational time), the sample was a 1 × 1 × 1 cm3 cube, and forward-detection geometry (θ = 0◦ ) was simulated. The birefringence value was set to zero for this initial study; its effects will be investigated later. As generating the full spectrum through Monte

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Carlo simulations is computationally intensive, a lookup table method was found to be useful. Here, the input values of µa and α are varied in regular intervals to create a table from which the spectra of the output Stokes parameters can be generated. The lookup table also allows for noise reduction, as the data can be smoothed to reduce statistical noise due to the discrete nature of the model. This is particularly important, as the simulated physiological glucose levels are small (3–17 mM), as are the resulting glucose dependent effects. As with nearly all of the developing optical techniques, this methodology must now isolate the glucose-specific contribution from signals (Stokes vectors over many wavelengths in this case) influenced by many other confounding factors (plasma proteins and water in this case). For the lumped Mueller matrix formulation at a single wavelength, the polar decomposition method was developed (section 17.4). Here we explore the use of spectroscopic analysis of Stokes vectors via a chemometric approach. The field of chemometrics provides a number of well-developed techniques for analyzing measurements of complex chemical systems, to yield constituent concentrations or other properties of interest [45]. Most of these techniques regress one block of data, such as a set of NIR absorption spectra, to a single sample property of the sample, such as glucose concentrations, to build a predictive model. In our case, we wish to regress two blocks of spectroscopic data (NIR intensity signals — element I of the Stokes vector, and ORD polarization signals—elements Q and U (and potentially V ) of the Stokes vector) to improve the predictive abilities of the chemometric model. This requires the use of multi-block chemometrics to combine two or more of the data sets into a single predictive model. For this study, multiblock partial least squares (MB-PLS) was employed as the regression technique. The MB-PLS is based on the widely used PLS regression method. In PLS, a regression relationship is found between a descriptor block or matrix of data (in our case, a set of intensity or polarization spectra) and a response block or matrix (in our case, a set of corresponding glucose concentrations). This is achieved by decomposing both the descriptor and response blocks into so called latent variables that describe the maximum variance in the data. The regression is calculated based on how the variances in each block explain each other, in other words finding the covariance between the blocks. In situations where there is more than one descriptor block, as in this case where we have intensity and polarization measurements, a method of combining the information in both descriptor blocks must be used in order to predict the response block. In this method the blocks are used to create a single super descriptor block as shown in Fig. 17.14, which is then regressed to the response block using PLS. The creation of this super-block involves finding the common information contained in each of the descriptor blocks, referred to as the “consensus” in the literature. In other words, the variations in the signals that are common in both descriptor blocks are identified as the consensus between the two blocks. As each block contains measurements done on the same samples, looking at the common information contained in each block can provide better predictive ability for analytes that affect both measurement techniques (as those in our plasma model do). For example, glucose (as well as plasma proteins) influences both the intensity and polarization signals caus-

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FIGURE 17.14: Schematic summarizing how multiblock partial least squares (MB-PLS) chemometric algorithm combines and regresses the generated spectroscopic intensity [I(λ )] and polarization [Q(λ ), U(λ )] data; V (λ ) was not used for regression calculations as glucose chirality does not affect circular polarization (adapted from reference [46]).

ing a common variation in both signals, and are identified in the calculation of the consensus. Two steps are required in the development of a chemometric model: calibration and testing. In calibration, often referred to as training, a set of data (both descriptor and response blocks) is used to create the PLS model. In our case, a set of intensity and polarization spectra (descriptor blocks) as well as glucose concentrations corresponding to each spectrum (response blocks) were used to calculate the regression parameters using MB-PLS. Once the model is built in this calibration step, it must be tested with new data to ensure the validity of the model and assess its predictive ability. A new set of intensity and polarization spectra along with corresponding glucose concentrations were generated for the purposes of testing both regression techniques. The size of both the calibration and testing data sets were 400 spectra with corresponding glucose concentrations. The predictive ability of the methods can then be determined by calculating the root mean square error of prediction using the testing data set, with increasing noise added to both the training and testing spectra. Results from predictions in both clear and scattering media are shown in Fig. 17.15. The added noise level in the Stokes vectors was taken to be small, typical to that attainable with high precision polarimetry system. Here I(λ ) was regressed individually and then combined with Q(λ ), U(λ ) and regressed using MB-PLS. The

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parameter V (λ ) was not included in regression as circularly polarized light is not affected by the chirality of glucose. Significant improvement in error can be seen when the intensity and polarization information are combined in both clear and scattering media. For clear media a reduction in error of approximately 25% was achieved and in scattering media a reduction in error of approximately 15% was achieved. The improvement was somewhat diminished with the addition of scattering to the model as this effectively reduces the magnitude of the polarization signals due to depolarization.

(A) (a)

(b)

FIGURE 17.15: Percent error as a function of simulated noise in (a) clear media and (b) scattering media for I(λ ) regressed with PLS as well as I(λ ), Q(λ ), and U(λ ) combined and regressed using MB-PLS. The standard deviation of added noise differs as the spectra in (a) were calculated directly while those in (b) were generated with the Monte Carlo model (adapted from reference [46]).

A significant improvement (approximately 15%) in predictive ability is still achieved with the combination of intensity and polarization information from simulated multiple scattering media. Future work will further investigate the influence of scattering, in an effort to determine up to what level of scattering an improvement is still realized. As this rather large reduction in improvement has already been observed from clear to a scattering coefficient of 60 cm−1 , it would seem unlikely that predictions with more realistic tissue scattering values (∼ 100 cm−1 ) will exhibit significant improvement. However, this is yet to be determined, as smoothing or other preprocessing steps can be used to reduce the signal noise. The present results demonstrate the potential for the methodology in clear or moderately scattering biological media, such as blood plasma or extra-cellular fluid [46].

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17.7 Concluding Remarks on the Prospect of Glucose Detection in Optically Thick Scattering Tissues with Polarized Light In this chapter, the use of polarized light for tissue assessment has been discussed in the context of noninvasive glucose detection. Despite the inherent difficulty of polarimetric approach for examinations of complex turbid media such as tissue, reliable measurements and analyses can be performed. A variety of experimental and theoretical tools have been developed to maximize measurement sensitivity, interpret the measurement results, isolate specific polarization contributions, quantify ‘hidden’ important variable such as photon pathlength and sampling volume, and evaluate the validity of the spectroscopic tissue polarimetry. Specifically, a comprehensive turbid polarimetry platform has been described, comprising of a highly sensitive experimental system, an accurate forward model that can handle all the complex simultaneous polarization effects manifested by biological tissues, and an inverse signal analysis strategy that can be applied to complex tissue polarimetry data to isolate specific quantities of interest (such as small optical rotation that can be linked to glucose concentration). Illustrative examples from tissue-simulating phantoms of increasing biological complexity have been presented, with consistent and encouraging results. The application of this methodology for glucose detection and quantification in real tissues remains to be investigated, and is currently being initiated in our laboratory. Certainly, the low physiological glucose levels, the high (and variable) levels of tissue scattering, the varying levels of tissue optical absorption, the presence of other opticallyactive molecules, and the confounding effects of various biological variables (pH, temperature, etc.) will pose significant challenges to any noninvasive glucose monitoring approach, including the one described in this chapter. Nevertheless, the turbid polarimetry progress to date bodes well for future in vivo developments. Finally, it may come to pass that the solution for noninvasive glucose monitoring lies in utilizing two or more of the methods described in this monograph, judiciously combining their complementary strengths to overcome the formidable biological complexity inherent in this important clinical problem.

Acknowledgments Our turbid polarimetry research is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). The authors would also like to thank Dr. Daniel Cˆot´e for his contributions in some of the studies discussed in this chapter.

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References [1] R. J. McNichols and G. L. Cot´e, “Optical glucose monitoring in biological fluids: an overview,” J. Biomed. Opt., vol. 5, 2002, pp. 5–16. [2] V.V. Tuchin, L. Wang, and D.L. Zimnyakov, Optical Polarization in Biomedical Applications, Springer-Verlag, Heidelberg, 2006. [3] V.V. Tuchin, Optical Clearing of Tissues and Blood, vol. PM 154, SPIE Press, Bellingham, WA, 2006. [4] C.A. Browne and F.W. Zerban, Physical and Chemical Methods of Sugar Analysis, Wiley, New York, 1941. [5] X. Guo, M.F.G. Wood, and I.A. Vitkin, “Angular measurement of light scattered by turbid chiral media using linear Stokes polarimetry,” J. Biomed. Opt., vol. 11, 2006, 041105. [6] D. Cˆot´e and I.A. Vitkin, “Balanced detection for low-noise precision polarimetric measurements of optically active, multiply scattering tissue phantoms,” J. Biomed. Opt., vol. 9, 2004, pp. 213–220. [7] K.C. Hadley and I.A. Vitkin, “Optical rotation and linear and circular depolarization rates in diffusely scattered light from chiral, racemic, and achiral turbid media,” J. Biomed. Opt., vol. 7, 2002, pp. 291–299. [8] I.A. Vitkin, R.D. Laszlo, and C.L. Whyman, “Effects of molecular asymmetry of optically active molecules on the polarization properties of multiply scattered light,” Opt. Exp., vol. 10, 2002, pp. 222–229. [9] R.C.N. Studinski and I.A. Vitkin, “Methodology for examining polarized light interactions with tissues and tissue-like media in the exact backscattering direction,” J. Biomed. Opt., vol. 5, 2000, pp. 330–337. [10] I.A. Vitkin and E. Hoskinson, “Polarization studies in multiply scattering media,” Opt. Eng., vol. 39, 2000, pp. 353–362. [11] J. Badoz, M. Billardon, J.C. Canit, and M.F. Russel, “Sensitive device to measure the state and degree of polarization of a light beam using a birefringence modulator,” J. Opt., vol. 8, 1977, pp. 373–384. [12] M.P. Silverman, N. Ritchie. G.M. Cushman, and B. Fisher, “Experimental configurations using optical phase modulation to measure chiral asymmetries in light specularly reflected from a naturally gyroptopic medium,” J. Opt. Soc. Am. A., vol. 5, 1988, pp. 1852–1863. [13] M. Abramowitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Institute of Standards and Technology, Washington, D.C., 1964.

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[14] W.F. Cheong, S.A. Prahl, and A.J. Welch, “A review of the optical properties of biological tissues,” IEEE Journal of Quantum Electronics, vol. 26, 1990, pp. 2166–2185. [15] D. Cˆot´e and I.A. Vitkin, “Robust concentration determination of optically active molecules in turbid media with validated three-dimensional polarization sensitive Monte Carlo calculations,” Opt. Exp., vol. 13, 2005, pp. 148–163. [16] A.J. Welch and M.J.C. van Gemert, Optical-Thermal Response of Laser Irradiated Tissue, Plenum Press, New York, 1995. [17] A. J. Welch, G. Yoon, and M. J. van Gemert, “Practical models for light distribution laser-irradiated tissue,” Lasers Surg. Med., vol. 6, 1987, pp. 488–493. [18] M.S. Patterson, B.C. Wilson, and D.R. Wyman, “The propagation of optical radiation in tissue I. Models of radiation transport and their applications,” Lasers Med. Sci., vol. 6, 1990, 155–166. [19] L. Wang, S.L. Jacques, and L. Zheng, “MCML – Monte Carlo modeling of light transport in multi-layered tissues,” Computer Methods and Programs in Biomedicine, vol. 47, 1995, pp. 131–146. [20] F. Jaillon and H. Saint-Jalmes, “Description and time reduction of a Monte Carlo code to simulate propagation of polarized light through scattering media,” Appl. Opt., vol. 42, 2003, pp. 3290–3296. [21] B. Kaplan, G. Ledanois, and B. Drevillon, “Mueller matrix of dense polystyrene latex sphere suspensions: measurements and Monte Carlo simulations,” Appl. Opt., vol. 40, 2001, pp. 2769–2777. [22] M. Moscoso, J.B. Keller, and G. Papanicolaou, “Depolarization and blurring of optical images by biological tissues,” J. Opt. Soc. Am. A., vol.18, 2001, pp. 949–960. [23] J.R. Mourant, T.M. Johnson, and F.P. Freyer, “Characterization of mammalian cells and cell phantoms by polarized backscattering fiber-optic measurements,” Appl. Opt., vol. 40, 2001, pp. 5114–5123. [24] S. Bartel and A.H. Hielscher, “Monte Carlo simulations of the diffuse backscattering Mueller matrix for highly scattering media,” Appl. Opt., vol. 39, 2000, pp. 1580–1588. [25] W. Wang and L.V. Wang, “Propagation of polarized light in birefringent media: A Monte Carlo study,” J. Biomed. Opt., vol. 7, 2002, pp. 350–358 [26] H.C. van de Hulst, Light Scattering by Small Particles, Dover, New York, 1981. [27] M.F.G. Wood, X. Guo, and I.A. Vitkin, “Polarized light propagation in multiply scattering media exhibiting both linear birefringence and optical activity: Monte Carlo model and experimental methodology,” J. Biomed. Opt., vol. 12, 2007, 014029.

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[28] R. Clark Jones, “New calculus for the treatment of optical systems. VII. Properties of the N-matrices,” J. Opt. Soc. Am., vol. 38, 1948, pp. 671–685. [29] D.S. Kliger, J.W. Lewis, and C.E. Randall, Polarized Light in Optics and Spectroscopy, Academic Press–Harcourt Brace Jovanovich, New York, 1990. [30] J. Schellman and H.P. Jenson, “Optical spectroscopy of oriented molecules,” Chem. Rev., vol. 87, 1987, pp. 1359–1300. [31] S. Yau Lu and R.A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A, vol. 13, 1996, pp. 1106 – 1113. [32] J. Morio and F. Goudail, “Influence of the order of diattenuator, retarder, and polarizer in polar decomposition of Mueller matrices,” Opt. Lett., vol. 29, 2004, pp. 2234–2236. [33] S. Manhas, M.K. Swami, P. Buddhiwant, N. Ghosh, P.K. Gupta, and K. Singh, “Mueller matrix approach for determination of optical rotation in chiral turbid media in backscattering geometry,” Opt. Exp., vol. 14, 2006, pp. 190 – 202. [34] R.A. Chipman, “Polarimetry,” Chap. 22 in Handbook of Optics, 2nd ed., M. Bass, Ed., Vol. 2, pp. 22.1–22.37, McGraw-Hill, New York, 1994. [35] C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach, Wiley, New York, 1998. [36] I.S. Sokolnikoff, Mathematical Theory of Elasticity, Krieger, Malabar, 1983. [37] X. Guo, M.F.G. Wood, and I.A. Vitkin, “Monte Carlo study of pathlength distribution of polarized light in turbid media,” Opt. Exp., vol. 5, 2007, pp. 1348–1360. [38] X. Guo, M.F.G. Wood, and I.A. Vitkin, “Stokes polarimetry in multiply scattering chiral media: effects of experimental geometry,” Appl. Opt., vol. 46, 2007, pp. 4491–4500. [39] X. Guo, M.F.G. Wood, and I.A. Vitkin, “Detection depth and sampling volume of polarized light in turbid media,” Opt. Commun., 2007, SK-4383R1 (in press). [40] K. Murayama, K. Yamada, R. Tsenkova, Y. Wang, and Y. Ozaki, “Nearinfrared spectra serum albumin and γ -globulin and determination of their concentrations in phosphate buffer solution by partial least squares regression,” Vibr. Spectros., vol. 18, 1998, pp. 33–40. [41] G. Yoon, A.K. Amerov, K.J. Jeon, and Y. Kim, “Determination of glucose concentration in a scattering medium on selected wavelengths by use of an overtone absorption band,” Appl. Opt., vol. 41, 2002, pp. 1469–1475. [42] S. Kasemsumran, Y. Du, K. Murayama, M. Huehne, and Y. Ozaki, “Simultaneous determination of human serum albumin, γ -globulin, and glucose in a

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Handbook of Optical Sensing of Glucose phosphate buffer solution by near-infrared spectroscopy with moving window partial least-squares regression,” Analyst, vol. 128, 2003, pp. 1471–1477.

[43] Y. Kim and G. Yoon, “Prediction of glucose in whole blood near-infrared spectroscopy: influence of wavelength region, preprocessing, and hemoglobin concentration,” J. Biomed. Opt., vol. 11, 2006, 041128. [44] B. Jirgensons, Optical Rotatory Dispersion of Proteins and Other Macromolecules, Springer-Verlag, New York, 1969. [45] M. Otto, Chemometrics: Statistics and Computer Application in Analytical Chemistry, 2nd ed., Wiley, New York, 2007. [46] M.F.G. Wood, D. Cˆot´e, and I.A. Vitkin, “Combined optical intensity and polarization methodology for analyte concentration determination in simulated optically clear and turbid biological media,” J. Biomed. Opt. (in press).

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18 Noninvasive Monitoring of Glucose Concentration with Optical Coherence Tomography Rinat O. Esenaliev Laboratory for Optical Sensing and Monitoring, Center for Biomedical Engineeering, Department of Neuroscience and Cell Biology, and Department of Anesthesiology, The University of Texas Medical Branch, Galveston, TX 77555-0456, USA Donald S. Prough Department of Anesthesiology, The University of Texas Medical Branch, Galveston, TX 77555-0591, USA 18.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.2 Noninvasive Optical Techniques for Glucose Monitoring . . . . . . . . . . . . . . . . . . 18.3 Optical Coherence Tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.4 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.5 Studies in Tissue Phantoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.6 Animal Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.7 Specificity Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.8 Clinical Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.9 Mechanisms of Glucose-Induced Changes in Optical Properties of Tissue . . 18.10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

564 566 567 569 570 571 572 574 576 578 578 579

Monitoring and control of blood glucose concentration substantially minimize complications, mortality, and morbidity associated with diabetes. We have developed a high-resolution optical technique, Optical Coherence Tomography (OCT), for noninvasive, continuous, accurate monitoring of blood glucose concentration. OCT is based on detection of backscattered low-coherent light and utilizes scattering contrast in tissues. It has a resolution of 1–15 µ m and a probing depth of about 1 mm. In this chapter we review major achievements in the development of this technique for noninvasive glucose monitoring from the concept phase to successful clinical studies. Our initial phantom, animal, and clinical tests on glucose monitoring with this technique demonstrated that the OCT signal slope is linearly dependent on glucose

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concentration. Initial in vivo studies in animals and volunteers revealed good correlation of the OCT signal slope with blood glucose concentration. Then we modified the hardware, software, and signal acquisition and processing algorithms and performed another set of animal and clinical studies. The modified system allows for robust measurement of OCT signal slope with high accuracy and resolution from specific tissue layers. The results obtained with the modified system demonstrated substantially higher correlation of the OCT signal slope with blood glucose concentration and minimal (a few minutes) lag time between them. Moreover, our in vivo studies with the modified system revealed reproducibility, accuracy, and specificity approaching that of standard invasive techniques. The obtained results demonstrate that the proposed technique may be used for noninvasive, continuous, accurate monitoring of blood glucose concentration. Key words: Optical Coherence Tomography (OCT), light scattering, glucose, monitoring.

18.1 Introduction Blood glucose monitoring accompanied by tight glucose control significantly decreases complications and mortality in diabetic patients [1, 2]. While the importance of glucose monitoring in diabetics has been well recognized for decades, recent studies demonstrated the importance of glucose monitoring in a large population of nondiabetic patients: critically ill patients [3–7]. In both nondiabetic and diabetic patients, hyperglycemia and insulin resistance commonly complicate critical illness [3–7]. Even moderate hyperglycemia, at levels that conventionally have not been treated acutely with insulin because of the risk of inducing hypoglycemia, contributes to morbidity and mortality [6–10]. Stressinduced hyperglycemia is associated with poorer outcome in both nondiabetic and diabetic patients after stroke [9, 10] and acute myocardial infarction [11–13]. Until recently, hyperglycemia was recognized as a common laboratory abnormality in critically ill patients but was not regarded as an important factor contributing to (rather than associated with) poor outcome. In general, hyperglycemia has been considered to be a secondary response to stress and infection and not an independent risk factor for poor outcome; recently, however, evidence has increased that hyperglycemia is in fact a risk factor for poor outcome [14, 15]. In nondiabetic patients with protracted critical illnesses, high serum levels of insulin-like growth factor-binding protein 1, which reflect an impaired response of hepatocytes to insulin, increase the risk of death [15, 16]. Despite considerable interest in the influence of tight glycemic control in outpatients on the incidence and severity of the chronic microvascular and macrovascular complications of diabetes [17–20], most clinicians until recently have loosely con-

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trolled blood glucose in critically ill patients. The reasoning behind loose control in critically ill patients included several considerations: 1) assumed low likelihood that a short interval of poor glycemic control would significantly influence the progression of chronic complications; 2) difficulty of anticipating insulin requirements in patients with unstable levels of stress; and 3) risk of inducing hypoglycemia with excessive insulin therapy. Subsequently, several investigators have performed clinical trials of tight glucose control in both diabetic and nondiabetic patients with a variety of critical illnesses. In diabetic patients with acute myocardial infarction, maintenance of blood glucose concentration [Glub ] < 215 mg/dL (11.9 mmol/L) improved mortality at one year and 3.5 years [11-13]. In a recent landmark study, Van den Berghe et al. randomized 1548 critically ill patients (87% of whom were nondiabetic) to receive conventional management or intensive insulin therapy to tightly control [Glub ] between 80 and 110 mg/dL, as a result, intensive insulin therapy reduced mortality from 8.0% to 4.6% [14]. Other secondary analyses of the study also are important. The greatest reduction in mortality involved deaths due to multipleorgan failure with a proven septic focus. Intensive insulin therapy also reduced overall in-hospital mortality by 34%, bloodstream infections by 46%, and critical-illness polyneuropathy by 44%. The need for dialysis or hemofiltration to manage acute renal failure, a particularly morbid and highly lethal complication of critical illness, was reduced by 41%. Reduction of the median number of red-cell transfusions by 50% may have reflected improved erythropoiesis or reduced hemolysis, since this benefit was associated with a lower incidence of hyperbilirubinemia. Intensive insulin therapy also may reduce the risk of cholestasis, since adequate provision of glucose and insulin to hepatocytes is crucial for normal choleresis [21, 22]. Patients receiving intensive therapy were less likely to require prolonged mechanical ventilation and intensive care. Tight glycemic control may reduce the deleterious effects of hyperglycemia on macrophage or neutrophil function [23-27] or support insulin-induced trophic effects on mucosal and skin barriers. Much of the benefit of intensive insulin therapy was attributable to its effect on mortality among patients who remained in the ICU for more than five days (20.2% vs. 10.6% with intensive insulin therapy). However, tight glycemic control also was associated with complications. Intensive insulin therapy carried a 5.0% risk of inducing severe hypoglycemia (blood glucose < 40 mg/dL) [14]. The authors stated that these episodes of hypoglycemia did not induce additional morbidity, but it is unlikely that experience outside the rigorously controlled environment of a single-institution clinical trial would be so favorable. Ideally, insulin therapy should be adjusted during continuous infusion so that blood glucose is not permitted to decrease below 60 mg/dL; that degree of precision is difficult to avoid with intermittent glucose sampling and requires frequent, ideally continuous monitoring. In the discussion in their pivotal paper, Van den Berghe et al. [14] noted that glycemic control compares highly favorably to other interventions that have been proposed to improve survival of critically ill patients. One of the few to improve survival is treatment of sepsis with the highly expensive intervention, activated protein C, which only reduced mortality by 20% at 28 days [23]. In contrast, tight glycemic

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control is applicable to a much larger proportion of critically ill patients and reduced mortality by more than 40% [14]. Intensive insulin therapy also reduced the utilization of expensive intensive care resources and the risk of complications, including episodes of septicemia and the associated need for prolonged antibiotic therapy. This evidence strongly indicates that intensive insulin therapy to maintain blood glucose between 80 and 110 mg/dL reduces morbidity and mortality among critically ill patients [14] but that evidence also indicates an important risk of inducing hypoglycemia. Therefore, in critically ill patients, continuous, noninvasive glucose monitoring would facilitate tight control of [Glub ], avoiding both hyperglycemia and hypoglycemia and reducing morbidity and mortality. We acknowledge that continuous subcutaneous monitoring techniques have been developed [28–34]. Although these systems have been extensively tested for chronic control of insulin-dependent diabetic patients, they require further refinement for accurate, reliable glucose control in critically ill patients (both nondiabetic and diabetic). Moreover, responses produced by critical illness (such as wound and stress responses) reduce the accuracy and reproducibility of subcutaneous glucose measurements. Nevertheless, subcutaneous monitoring does establish a benchmark for accuracy of continuous [Glub ] monitoring devices.

18.2 Noninvasive Optical Techniques for Glucose Monitoring Several scientific groups have been developing noninvasive techniques for blood glucose monitoring using various approaches (reviewed in this book and in several recent publications [35–38]) including polarimetry [39], Raman spectroscopy [40, 41], near infrared (NIR) absorption and scattering spectroscopy [42–46], and photoacoustics [47–48]. Despite significant efforts, these techniques have limitations associated with low sensitivity, accuracy, and insufficient specificity of glucose concentration measurement within the relevant physiological range (4–30 mM or 72–540 mg/dL). Invasive devices for home use have a reported accuracy of 20%, e.g., a true [Glub ] of 5 mM (90 mg/dL) would measure between 4 and 6 mM (72– 108 mg/dL). A noninvasive glucose sensor should have a comparable accuracy. Glucose-induced changes in tissue scattering are greater than changes in tissue absorption in the NIR spectral range. The scattering coefficient of tissue is dependent on the refractive index (n), which is a function of the mismatch between the extracellular fluid (ECF) and the cellular components. In the NIR spectral range the index of refraction of ECF is 1.35–1.36, whereas the index of refraction of the cellular components and protein aggregates is in the range of 1.35–1.41 [49, 50]. If the refractive index of the scatterers (cell membranes and intracellular organelles) remains the same and is higher than the refractive index of the ECF, the increase of glucose concentration in the ECF reduces the refractive index mismatch, ∆n = nscatterers − nECF , and, hence, the tissue scattering coefficient is also reduced. Therefore, an increase

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of [Glub ] will raise the refractive index of the ECF and that in turn will decrease the scattering coefficient of the tissue as a whole. Glucose-induced changes are substantially greater than those induced by variation of concentration of other osmolytes in physiologically relevant ranges because the influence of other analytes on the refractive index is much less [51, 52]. The decrease in tissue scattering induced by glucose (and other agents) can be used for tissue clearing which may enhance the diagnostic and therapeutic capabilities of optical techniques [53–55]. The glucose-induced effect of decrease in the scattering coefficient was demonstrated by Kohl et al. in tissue-simulating phantoms [42], Tuchin et al. in vitro [49], and Maier et al. and Bruulsema et al. in vivo in human subjects [45, 56]. Results of these studies showed the potential of optical methods to monitor [Glub ] by detecting small changes in tissue scattering. Although these techniques are promising, detection of diffusively scattered photons results in low sensitivity and accuracy of [Glub ] measurements due to integration of the signal over the entire optical path in many tissue layers. A clinically useful blood glucose monitor must be more sensitive and accurate than the systems applied in previous studies.

18.3 Optical Coherence Tomography OCT is a new optical diagnostic technique that provides depth-resolved images of tissues with resolution of about 10 µ m or less at depths of up to 1 mm. Fujimoto and co-workers [57] at the Massachusetts Institute of Technology introduced this technique in 1991 to perform tomographic imaging of the human eye. Since then OCT has been rapidly developed by several research groups for many diagnostic applications. OCT has been applied for imaging of human skin [58, 59], animal cerebral cortex [60] and gastrointestinal and respiratory tracts [61], the human gastro-intestinal tract, larynx, esophagus, cervix, and bladder [62], cardiac function in Xenopus Laevis [63], atherosclerotic plaque morphology in human coronary arteries [64], and human nervous, reproductive, and vascular systems [65]. Izatt et al. and Chen et al. [66, 67] have also shown that OCT can be used to measure velocity profiles in blood vessels in vivo using Doppler velocimetry. Colston et al. [68, 69] and Warren et al. [70] have applied OCT to in vitro and in vivo imaging of hard dental tissues. Recently we proposed to use the OCT technique for monitoring of [Glub ] by measuring and analyzing light coherently backscattered from specific tissue layers [71, 72] and performed phantom, animal, and clinical tests of the OCT-based glucose sensor [71–87]. The basic principle of the OCT technique is to detect backscattered photons from a tissue of interest within a coherence length of the source using a two-beam interferometer (Fig. 18.1). Low-coherence light from a superluminescent diode is aimed at objects to be imaged using a beam splitter. Light scattered from

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FIGURE 18.1: Optical Coherence Tomography (OCT) system used in the glucose monitoring studies. the tissue is combined with light returned from the reference arm, and a photodiode detects the resulting interferometric signal. Intereferometric signals can be formed only when the optical path length in the sample arm matches the reference arm length within the coherence length of the source (10–15 µ m). By gathering interference data at points across the surface, cross-sectional 2D images can be formed in real time with resolution of about 10 µ m at depths of up to one millimeter or deeper, depending on the tissue optical properties. By averaging of the 2D OCT images into a single 1D distribution of light in depth, one can measure the optical properties of the object by analyzing the profile of light attenuation. Attenuation of light intensity, I (ballistic photons), in a medium with scattering and absorption is described by the Beer-Lambert law: I = I0 e−µt z , where µt = µs + µa is the attenuation coefficient of ballistic photons, µs and µa are the scattering and absorption coefficients, respectively, and I0 is the incident light intensity. Since absorption in tissues is substantially less than scattering (µa << µs ) in the NIR spectral range, the exponential attenuation of light in tissue is dependent mainly on the scattering coefficient: I = I0 e−µs z . Since the tissue scattering coefficient (µs ) changes with glucose concentration, the exponential profile of light attenuation in tissue is dependent on glucose concentra-

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tion. Therefore, one can monitor glucose concentration by measuring the exponential slope of light attenuation in tissue with the OCT technique. The high resolution of OCT may provide accurate and sensitive measurements of scattering from a specific tissue layer. Moreover, due to coherent light detection, photons that are scattered from other tissue layers as well as diffusively scattered photons have minimal contribution to the OCT signal recorded from the tissue layer of interest. These features of the OCT technique may provide accurate, sensitive, noninvasive, and continuous monitoring of [Glub ]. Variation of [Glub ] may change tissue structure due to osmotic effects. Since OCT provides information on tissue structure, the glucose-induced changes in tissue structure can be detected by the OCT. Therefore, sensitivity of OCT to glucose-induced changes in refractive index (scattering coefficient) and tissue structure can be used for noninvasive glucose monitoring.

18.4 Experimental Setup The experimental setup used in our studies is depicted in Fig. 18.1. The experiments were performed with a portable OCT system with an output power of 300 µ W, wavelength of 1300 nm, and coherent length of 14 µ m. The system uses an interferometer, in which light in one arm is directed into the objects to be imaged using a single mode optical fiber and focused with a lens. Light scattered from the sample and light reflected from the reference arm forms an interferogram, which is detected by a photodiode. Signal from the photodiode is amplified by a logarithmic amplifier and recorded on a laptop computer (PC) for processing. Specially designed optical probes were used to scan the incident beam over the sample surface in a lateral direction. In-depth (Z-axial) scanning by the interferometer and the lateral scanning by the probe allowed for reconstruction of twodimensional images (300 by 400 pixels). The lateral scanning length was approximately 1–5 mm. Each lateral scan was accomplished every 20–30 seconds (each scan in Z direction was averaged 5–7 times). The position of the NIR beam was visualized using an aiming 640-nm continuous wave (CW) diode beam, which travels together with the NIR beam. The operation of the OCT system was automated and controlled by the laptop PC. In our initial studies [71–76, 79, 80] the two-dimensional images were averaged in the lateral (X-axial) direction into a single curve to obtain an OCT signal that represents one-dimensional (1D) distribution of light in depth. The OCT signals were plotted in logarithmic scale and the slopes of the signals were calculated by the linear Least Squares Method at different depths. Four to six images were obtained for each experimental data point. In the recent studies we used lateral scanning in two directions (X and Y ) [77, 78, 81-87]. The 2D lateral scanning allowed for better averaging of speckle noise that improved accuracy of glucose monitoring. The 2D

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lateral averaging minimized motion artifacts as well.

18.5 Studies in Tissue Phantoms Aqueous suspensions of polystyrene microspheres (diameter 760 nm; Bangs Laboratories, Inc., Fishers, IN) were chosen to simulate tissue scattering in phantom studies because of stable optical properties and simplicity of theoretical calculations of their scattering coefficient. Polystyrene spheres have strong scattering and negligible absorbance in the NIR spectral range and have been widely used to simulate tissue scattering. Six phantoms with the same concentrations of polystyrene microspheres and different concentrations of D-glucose (Sigma Chemical Co, St. Louis, MO) (0, 50, 100, 150, 200, and 250 mM) were used in these experiments. The concentration of the spheres was chosen to provide a scattering coefficient similar to that of skin in the NIR spectral range (µs ∼ = 100 cm−1 ). The high, nonphysiologic concentrations of D-glucose were chosen because of the much greater mismatch between the refractive indices of polystyrene (npol = 1.57) and water (nwater = 1.33). As a consequence, glucose-induced changes in the OCT signal slope were small in comparison to tissue. The suspensions were placed in a quartz cuvette (thickness = 5 mm) and the incident beam from the OCT system was directed perpendicular to the cuvette wall. Five OCT images were recorded for each glucose concentration and processed as described above. The experiments were performed with three sets of the suspensions that were independently prepared. Standard deviations were calculated for each data point. The Mie theory of scattering [88] was used to calculate the scattering coefficient as a function of glucose concentration in the phantoms. An algorithm given by Bohren and Huffman [89] was applied to polystyrene microspheres (diameter = 760 nm) in water. The wavelength dependences of refractive indices of water, nwater , and polystyrene, npol , used in our calculations are: nwater (λ ) = 1.3199 +

npol (λ ) = 1.5626 +

6.878 × 103 1.132 × 109 1.11 × 1014 − + , λ2 λ4 λ6

1.169 × 104 1.125 × 109 1.72 × 1014 − + , λ2 λ4 λ6

where λ is in nanometers [90]. The glucose-induced change in refractive index is 2.73 × 10−5 per 1 mM [49]. We found good correlation between the decrease of the OCT slope and the theoretically calculated scattering coefficient as glucose concentration increased [71]. The small and linear decrease of the slope (3.2% per 100 mM of glucose) was in good agreement with the theoretical calculations performed using the Mie theory of scattering. These results obtained in the phantoms studies demonstrated the capabil-

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ity of the OCT technique to detect glucose-induced changes in scattering with high accuracy and sensitivity.

18.6 Animal Studies Hairless Yucatan micropigs or farm pigs were used in animal studies. The hairless Yucatan micropig is recognized as the best model of human skin [91, 92]. All procedures with the animals were performed in accordance with an animal protocol approved by the Institutional Animal Use and Care Committee of the University of Texas Medical Branch (UTMB). Animals were pre-anesthetized with a telazol/xylazine/ketamine mixture given intramuscularly. The pigs were placed in a specially designed holder in order to minimize motion of the animals during experiments. In some studies, the pigs were heavily sedated using diazepam to minimize influence of the anesthesia on the usual metabolism rate, while in the rest of the studies the animals were anesthetized using isoflurane. Glucose was infused through the left femoral vein and blood samples were taken from the right femoral vein. Blood samples were analyzed using the HemoCue (Ryan Diagnostic, Inc., Naperville, IL), a laboratory blood glucose analyzer or a portable clinical analyzer (PCA) (i-STAT, Abbott Laboratories, Abbott Park, IL). The OCT probe was positioned directly on the tissue surface with special holders in order to minimize motion artifacts. OCT images were taken from the dorsal or abdominal area of the skin. Euthanasia was performed by using i.v. injection of saturated potassium chloride solution. After euthanasia, samples of tissue under optical probe were taken, sectioned, stained with hematoxylin and eosin (H&E), and analyzed under a microscope. The thickness of tissue slices was 5 µ m. In these animal studies we performed glucose clamping experiments which allowed slow, controlled intravenous administrations of glucose at desired rates to simulate normal physiological changes in [Glub ]. Therefore, it minimized the contributions of possible tissue physiological responses, such as change of cell volume, ECF fractional volume, and blood microvessel diameter that are attributable to the abrupt increases of glucose concentrations that can be induced by bolus injections. Good correlations between changes in actual [Glub ] and the slopes were observed. The maximum correlation between OCT signal slope and [Glub ] was delayed, i.e., there was a lag time between changes in [Glub ] and corresponding changes in the OCT signal slope. The lag time is assumed to relate to physiological and physical aspects of equilibration and metabolism between interstitial and intravascular systems in skin. In our experiments, if skin temperature was not actively maintained, the lag time between an increase of [Glub ] and a decrease of the OCT signal slope averaged 20 minutes (range: 0 to 40 minutes). In contrast, during subsequent physiological decreases of [Glub ], no lag time was observed. This result was in agreement with data in the literature.

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Changes in the OCT signal slopes obtained in in vivo experiments were greater than those measured in the phantom studies. The slopes changed approximately 1.7–1.8% per 10 mg/dL in these experiments [71]. This is due to smaller refractive index mismatch in the probed tissue compared with the polystyrene sphere suspension as well as due to morphological changes in skin induced by osmotic effects of glucose. The changes in the OCT signal slope correlated with variation of [Glub ]. Slow, digitally controlled infusion of glucose increased [Glub ] at a physiological rate. Therefore, possible tissue responses to abrupt increases of osmolyte concentration (cell volume decrease, increase of ECF fraction volume, blood microvessel diameter change, etc.) were minimized in these experiments.

18.7 Specificity Studies Changes in other variables such as skin temperature, pressure exerted by the OCT probe, concentration of blood analytes, heart rate, blood pressure, administration of anesthetic drugs in the animal studies may produce changes in the OCT signal slope. Several experiments were performed to characterize the influence of skin temperature on the OCT signal slope. Experiments performed in skin tissue in vivo showed a dependence of the OCT signal slope on the skin temperature [80]. Skin temperature was monitored using a thermocouple placed on the skin surface near the OCT probing beam. Most likely the mechanism of the temperature-induced changes in tissue optical properties is changing perfusion in tissue and changing tissue structure. However, normal temperature fluctuations of the skin (±1◦ C) did not change the OCT signal slope in a control experiment without heating [80]. Optical properties of tissue depend on temperature and pressure applied to tissue (including skin tissue) [93–97]. Moreover, blood perfusion and glucose equilibration between interstitial and microvascular systems in skin (including the lag time) are dependent on temperature. To minimize these effects and the lag time (as well as motion artifacts), we developed a holder for the OCT probe that provided minimal and constant pressure to the skin and maintained stable temperature by using a heating element and a thermocouple. This reduced the lag time observed in unwarmed skin from 20 min to a clinically acceptable average interval of 2.5 min. When the holder was used, OCT signal slope closely followed changes in [Glub ] with no lag time and the long-term drift [87]. Heart rate and average blood pressure were recorded in most animal experiments. No significant effect of the blood pressure and heart rate as well as surgical and anesthetic procedures on the OCT signal slope was observed in these experiments [80]. Comparison between H&E-stained sections was performed to identify specific layers on the OCT images (Fig. 18.2 a and b) that were used to produce OCT signals. Although the OCT signal slope correlated well with [Glub ] in all pigs, the best corre-

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FIGURE 18.2: (a) OCT image of pig skin (bar = 500 µ m); (b) corresponding histological section of pig skin.

lations between the OCT signal slope and [Glub ] occurred at specific depths of tissue rather than the full thickness of pig skin. A strong correlation (|R| > 0.8) between [Glub ] and OCT signal slope was found near the boundary between the dermis and hypodermis at a depth of 500–650 µ m. The OCT signal slope also correlated with blood [Glub ] in other skin layers, especially near the papillary and reticular junction in the dermis at a depth of 130–230 µ m. In general, only glucose concentration and sodium concentration ([Na+ ]) correlated with the OCT signal slope [84]. The maximum correlation of the OCT signal slope with blood [Na+ ] was also observed in separate layers. However, the relative changes in OCT signal slopes induced by variation of [Glub ] were much greater than changes due to [Na+ ] variation. Averaged glucose-induced changes in OCT signal slope were five-fold greater than the changes in OCT signal slope associated with [Na+ ] variation in the physiological range [84]. Other analytes, i.e., serum chloride concentration ([Cl− ]), serum potassium concentration ([K+ ]), serum bicarbonate concentration ([HCO− 3 ]), hematocrit (Hct), partial pressure of carbon dioxide (pCO2 ), blood pH and blood urea concentration, correlated poorly [84]. However, in one-half of the experiments, during infusion of sodium chloride, the OCT signal slope correlated with [Cl− ] (|R| = 0.7 ÷ 0.8). The correlation coefficients of the OCT signal slope with other analytes were calculated at the depths where the maximal correlation of OCT signal slope with glucose was observed. The dependence of the OCT signal slope on [Glub ] measured in our experiments is substantially greater than glucose-induced changes in tissue optical properties mea-

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sured by using other optical techniques. This is due to the capability of the OCT technique to probe specific layers in tissues without unwanted background signal from other layers. The data obtained in the specificity studies indicate that: (1) the OCT signal slope correlates with changes in [Glub ]; (2) the sensitivity of the OCT signal slope was fivefold greater for [Glub ] than for [Na+ ] in the physiological range of these osmolytes; (3) [K+ ], [HCO− 3 ], PCO2 , pH, and urea did not influence the OCT signal slope; and (4) control of pressure and temperature decreased the long-term drift of the OCT signal slope and reduced lag time to 2.5 minutes.

18.8 Clinical Studies Healthy subjects aged from 22 to 82 years were studied in the clinical experiments. The subjects were in good health, took no medication, and were selected from different ethnic groups. The study protocol was approved by the Institutional Review Board of the UTMB. A signed informed consent was obtained from all subjects. A standard oral glucose tolerance test (OGTT) using 75 grams of glucose was performed in all volunteers starting at 8:00 a.m. (time t = 0) after an overnight fast. The duration of each experiment was approximately 190–200 minutes (10–20 minutes for recording of a baseline and 180 minutes after consuming the glucose solution). OCT images were taken from the left forearm. During the measurements the volunteers were asked to remain still to minimize motion artifacts, and food and drinks were not permitted. Whole-blood samples were serially drawn at 5 or 15 min intervals during the experiment from the right forearm using an intravenous catheter. Plasma glucose concentrations were measured with a clinical glucose analyzer (Vitros 950, Ortho-Clinical Diagnostics, Inc.). The results of our clinical studies performed in healthy volunteers demonstrated good correlation between changes in slopes of noninvasively measured OCT signals and actual [Glub ]. On average, the slope changed 1.9% per 10 mg/dL change of the [Glub ] in these studies. The obtained results were in good agreement with those obtained in the animal studies. Although our studies in animals and human subjects demonstrated good correlation between the OCT signal slope and [Glub ], the scattering of data points was significant in the in vivo experiments. This reduces the accuracy and sensitivity of glucose concentration monitoring with the OCT technique. The major sources of inaccuracy of glucose monitoring in animals and humans with the OCT technique are tissue inhomogeneity and speckles [78]. The speckle noise reduces the accuracy of measurement of tissue optical properties with the OCT technique [78, 86, 98, 99]. To improve the accuracy of measurement, we need to use speckle averaging. The results of our studies with homogeneous scattering media with very low speckle noise (water suspension of polystyrene spheres) demonstrated high stability of OCT image and signal that provided measurements of changes in

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FIGURE 18.3: OCT image obtained from human skin using 2D lateral scanning (left) and corresponding OCT signal (right) obtained from the image.

the scattering coefficient with accuracy of about 1% [71]. Such high stability of the signal and accuracy of scattering measurements in tissues in vivo would provide accuracy of glucose concentration monitoring < 1 mM. To reduce speckle noise in tissue, we modified our system to provide scanning over a rectangular or a square area of skin [78, 84–87]. An external voltage generator was used to obtain scanning in the Y axis in addition to the lateral scanning in the X axis that was provided by the internal voltage generator in the OCT system. Figure 18.3 (left) shows a typical image obtained from human skin using the 2D lateral scanning. Although the details of the tissue structure were less with 2D lateral scanning than in the images obtained with 1D lateral scanning (Fig. 18.2b), the corresponding OCT signal (Fig. 18.3, right) had less noise associated with speckles. In tissue, noise in OCT signals is produced not only by speckles but also by nonuniform distribution of scatterers resulting from tissue inhomogeneity. Linear scanning over the tissue surface reduces the noise associated with speckles and tissue inhomogeneity. However, square scanning dramatically reduces noise in OCT signals recorded from tissue compared with the linear scanning because: 1) it allows for averaging of greater number of speckles; 2) it allows for integration over greater number of inhomogeneities in tissue; and 3) the OCT signal is less prone to motion artifacts (this is because the unwanted minor displacements of the OCT probe (and, therefore, beam) do not lead to measurements from different skin areas). The results of these studies demonstrated that 2D scanning of the incident OCT beam provides better signal stability and reduces noise associated with speckles and tissue inhomogeneity [85, 87]. In our recent clinical tests we also evaluated the temperature and pressure control systems. Figure 18.4a shows the OCT signal slope measured from a forearm of a volunteer during an oral glucose tolerance test with minimal skin pressure and with

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and without temperature control. We used three conditions of temperature control: temperature control turned off (initial temperature 32.7◦C, final temperature 33.8◦C); temperature control turned on and temperature stabilized at 39.0◦±0.3◦C; and temperature control turned on, but temperature not in the target range. It is evident in Figure 18.4a that, at stable temperature within the target range, the OCT signal slope closely follows [Glub ]. Fourier filtering of the OCT signal slope yielded a high correlation of the OCT signal slope with [Glub ] (Fig. 18.4b). We used the data at baseline and during increasing [Glub ] (Fig. 18.4c) to calibrate the OCT system and the data obtained during decreasing [Glub ] to validate the accuracy of [GluOCT ] calculated by using Bland-Altman analysis [100]. Figure 18.4d shows the difference between [Glub ] and [GluOCT ] including the standard deviation. The bias and standard deviation (±2 SD) are 5.9 mg/dL (0.33 mM) and 12.8 mg/dL (0.71 mM), respectively. This results in an accuracy of 1.42 mM.

18.9 Mechanisms of Glucose-Induced Changes in Optical Properties of Tissue Glucose-induced changes in the optical properties of tissue have been attributed to several mechanisms that alone or in combination could contribute to changes in the OCT signal. These mechanisms are described in detail in our recent publication [85]. Briefly, increasing [Glub ] in vivo induces two parallel matter transport effects: water moves out of interstitial fluid (ISF) into blood vessels (osmotic effect) and glucose diffuses out of blood vessels into the interstitial space (glucose diffusion). The osmotic effect causes general dehydration of tissue and results in three possible processes: a) tissue shrinkage (observed in vivo in [85]) and therefore morphological alteration of skin layers that can locally change scattering tissue properties; b) increase of the packing density of tissue collagen fibers (ordering of scatterers) that may also influence tissue clearance [55, 101]; and c) decrease of the volume fraction of the interstitial fluid in comparison to the volume fraction of scattering centers (e.g., collagen fibers). The effect of glucose diffusion into the interstitial space increases the refractive index of ISF, thus matching the refractive index of collagen fibers and ISF and reducing scattering. Concurrently, higher glucose concentrations in ISF osmotically dehydrate collagen fibers, which will increase the refractive index of the collagen fibers and correspondingly increase local scattering. In parallel with matter transport effects, increasing [Glub ] may change light scattering attenuation in skin and therefore change the OCT signal slope due to glycation of biomolecules. However, glycation is a long process that typically takes weeks; thus the influence of acute glucose changes on glycation should be negligible and should not influence the OCT signal slope. Because blood vessels represent approximately 5% of skin volume [102], the influence of aggregation of blood constituents

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FIGURE 18.4: a). OCT signal slope and [Glub ] measured during oral glucose tolerance test (OGTT) in a healthy volunteer; b). Fourier filtering of the OCT signal slope measured during oral glucose tolerance test (OGTT) in a healthy volunteer; c). Relative changes in the OCT signal slope (dots) during the increase of [Glub ]. The linear regression (line) was used for [GluOCT ] calculation; d). Difference between [GluOCT ] and [Glub ] during decrease of [Glub ]. The bias and standard deviation (±2 SD) are 5.9 mg/dL (0.33 mM) and 12.8 mg/dL (0.71 mM), respectively. on the OCT signal slope also should be negligible. However, one cannot rule out those mechanisms. Although the refractive index matching/mismatching mechanisms are likely playing a role in the observed alterations of OCT signal slope, we suggest that they were mostly caused by morphological changes in tissue [85].

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Conclusions

The results of our studies demonstrated that: 1. In phantom studies the OCT technique can detect changes in scattering coefficient with an accuracy approaching 1%; 2. In animals, changes in the OCT signal slope in skin correlate well with changes in [Glub ]; 3. In humans, changes in the OCT signal slope in skin correlate well with changes in [Glub ]; 4. Glucose-induced changes in the OCT signal slope are substantially greater than those induced by other blood analytes, including the major osmolytes Na+ , Cl − , K+ , and urea; 5. Control of OCT probe pressure and skin temperature and optimized (2-D) scanning improve the accuracy, sensitivity, and specificity of noninvasive monitoring of [Glub ] with the OCT technique.

Acknowledgments The authors would like to thank Drs. Kuranov R.V., Sapozhnikova V.V., Larin K.V., Motamedi M., Cicenaite I., Deyo D.J., Kholodnykh A.I., Petrova I.Y., Ashitkov T.V., Eledrisi M.S., Larina I.V., Gelikonov V., and Bell B. for their contribution in these studies and the Texas Higher Education Coordinating Board Advanced Technology Program (grant #004952-0133-1999) and the National Institutes of Health (National Institute of Diabetes and Digestive and Kidney Diseases, grant #R21DK58380 and the National Institute for Biomedical Imaging and Bioengineering, grant #R01 EB001467) for support of these studies.

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[81] A.I. Kholodnykh, I.Y. Petrova, M. Motamedi, et al., “Accurate measurement of tissue total attenuation coefficient of thin tissue with optical coherence tomography” IEEE Journal on Selected Topics in Quantum Electronics (Special Issue on Lasers in Medicine and Biology), vol. 9, 2003, pp. 210–221. [82] V.V. Sapozhnikova, R.V. Kuranov, D.S. Prough, et al., “In vivo study of blood glucose concentration prediction with optical coherence tomography,” Biomedical Optics 2006 Technical Digest, Optical Society of America, Washington, DC, 2006. [83] R.V. Kuranov, V.V. Sapozhnikova, D.S. Prough, et al., “Depth-dependent correlation of optical coherence tomography signal with blood glucose concentration,” Biomedical Optics 2006 Technical Digest, Optical Society of America, Washington, DC, 2006. [84] V.V. Sapozhnikova, R.V. Kuranov, D.S. Prough, et al., “Influence of osmolytes on in vivo glucose monitoring using optical coherence tomography,” Exp. Biol. Med., vol. 231, 2006, pp. 1323–1332. [85] R.V. Kuranov, V.V. Sapozhnikova, D.S. Prough, et al., “In vivo study of glucose-induced changes in skin properties assessed with optical coherence tomography,” Phys. Med. Biol., vol. 51, 2006, pp. 3885–3900. [86] R.V. Kuranov, V.V. Sapozhnikova, D.S. Prough, et al., “Correlation between OCT images and histology of pig skin,” Appl. Opt., vol. 46, 2007, pp. 1782– 1786. [87] R.V. Kuranov, V.V. Sapozhnikova, D.S. Prough, et al., “Prediction capability of optical coherence tomography for blood glucose concentration monitoring,” J. Diab. Sci. Tech., vol.1, 2007, pp. 164–171. [88] H.C. Van de Hulst, Light Scattering by Small Particles, Dover Publications, Inc., New York, NY, 1981. [89] C.F. Bohren, and D. R. Huffman, Absorption and Scattering of Light by Small Particles, Wiley, New York, NY, 1983. [90] R.C. Weast (Ed.), CRC Handbook of Chemistry and Physics, 70th ed., CRC Press, Cleveland OH, 1989. [91] M. Fujii, S. Yamanouchi, N. Hori, et al., “Evaluation of yucatan micropig skin for use as an in-vitro model for skin permeation study,” Biol. Pharm. Bull., vol. 20, 1997, pp. 249–254. [92] T. Kurihara-Berhstrom, M. Woodworth, S. Feisullin, et al., “Characterization of the yucatan miniature pig skin and small intestine for pharmaceutical applications,” Lab. Anim. Sci., vol. 36, 1986, pp. 396–399. [93] A.J. Welch and M.J.C. Van Gemert, Optical-Thermal Response of LaserIrradiated Tissue, Plenum Press, New York, NY, 1995.

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[94] T. Vo-Dinh (Ed.), Biomedical Photonics Handbook. CRC Press, Boca Raton, FL, 2003. [95] O.S. Khalil, S.-J. Yeh, M.G. Lowery, et al., “Temperature modulation of optical properties of human skin,” J. Biomed. Opt., vol. 8, 2003, pp. 191–205. [96] S.-J. Yeh, O.S. Khalil, C.F. Hanna, et al., “Near infrared thermo-optical response of the localized reflectance of intact diabetic and non-diabetic human skin,” J. Biomed. Opt., vol. 8, 2003, pp. 534–544. [97] S.-J. Yeh, C.F. Hanna, O.S. Khalil, et al., “Tracking blood glucose changes in cutaneous tissue by temperature-modulated localized reflectance measurements,” Clin. Chem., vol. 49, 2003, pp. 924–934. [98] J.M. Schmitt, A. Kn¨uttel, and R.F. Bonner, “Measurement of optical properties of biological tissues by low-coherence reflectometry,” Appl. Opt., vol. 32, 1993, pp. 6032–6042. [99] J.M. Schmitt, S.H. Xiang, and K.M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt., vol. 4, 1999, pp. 95–105. [100] J.M. Bland and D.J. Altman, “Statistical methods for assessing agreement between two methods of clinical measurement,” Lancet, vol. 8, 1986, pp. 307– 310. [101] R.K. Wang, X. Xu, V.V. Tuchin, et al., “Concurrent enhancement of imaging depth and contrast for optical coherence tomography for hyperosmotic agents,” J. Opt. Soc. Am. B, vol. 18, 2001, pp. 948–953. [102] T. Kochinsky, L. Heinemann, “Sensors for glucose monitoring: technical and clinical aspects,” Diabetes Met. Res. Rev., vol. 17, 2001, pp. 113–123.

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19 Measurement of Glucose Diffusion Coefficients in Human Tissues Alexey N. Bashkatov, Elina A. Genina Institute of Optics and Biophotonics, Saratov State University, Saratov, 410012, Russia Valery V. Tuchin Institute of Optics and Biophotonics, Saratov State University, Saratov, 410012, Russia, Institute of Precise Mechanics and Control of RAS, Saratov 410028, Russia 19.1 19.2 19.3 19.4 19.5 19.6

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spectroscopic Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Photoacoustic Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Use of Radioactive Labels for Detecting Matter Flux . . . . . . . . . . . . . . . . . . . . . . Light Scattering Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

588 589 596 598 600 612 613 614

In this chapter we have reviewed the main experimental methods, which are widely used for in vitro and in vivo measurements of glucose diffusion and permeability coefficients in human tissues. These methods are based on the spectroscopic and photoacoustic techniques, on the usage of radioactive labels for detecting matter flux, or on the measurements of temporal changes of the scattering properties of a tissue caused by refractive index matching including interferometric technique and optical coherence tomography. The methods provide reliable basis for measurement of glucose diffusion characteristics in tissues. The obtained results can be used in diagnostics and therapy of different diseases related to glucose impact. Key words: glucose, optical clearing, diffusion coefficient, penetration, diabetes.

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19.1 Introduction Recent technological advancements in the photonics industry have led to a resurgence of interest in optical imaging technologies and real progress toward the development of noninvasive clinical functional imaging systems. Application of the optical methods for physiological-condition monitoring and cancer diagnostics, as well as for treatment, is a growing field due to simplicity, low cost, and low risk of these methods. In clinical dermatology, oncology, gastroenterology, and gynecology optical methods are widely used for vessels imaging, detection, localization, and treatment of subcutaneous malignant growths and photodynamic therapy. Frequently, the optical methods use dyes and drugs for cell sensitizing and enhancement of the local immune status of a tissue; therefore the development of noninvasive measurement techniques for monitoring of exogenous and endogenous (metabolic) agents in human tissues and determination of their diffusivity and permeability coefficients are very important for diagnosis and therapy of various human diseases. Glucose is one of the most important carbohydrate nutrient sources and is fundamental to almost all biological processes. A significant role for physiological glucose monitoring is in the diagnosis and management of diabetes. Goal of diabetes management is maintenance of blood glucose levels via insulin injection, modified diet, exercise, or a combination of these. For successive diabetes therapy, regular measurement of blood glucose levels (up to five times per day) is required [1, 2]. Since current glucose sensing methods require invasive puncture of the skin to obtain a blood sample for analysis, efforts to develop noninvasive glucose detection techniques and implantable glucose sensors using optical methods have been important [3] (see also chapters 2–18). A number of invasive and noninvasive techniques have been investigated for glucose monitoring, including use of implanted sensors, reverse iontophoresis, direct transmission through blood vessels, measurement of glucose in interstitial fluid in the dermis, light transmission through or light reflection from blood containing body parts (including the ear-lobe, the lip, the finger, and the forearm), and optical examination of the aqueous humor of the eye [1, 3–7]; however, unfortunately, the problem of glucose monitoring in final form is not solved yet. Another important problem of application of optical methods in medicine deals with the transport of laser (light) beam through fibrous tissues such as skin dermis, eye sclera, dura mater, etc. [8, 9]. Due to high scattering of visible and NIR radiation at propagation within these tissues, there are essential limitations on spatial resolution and light penetration depth for optical diagnostic and therapeutic methods to be successfully applied. Control of the tissue optical properties is a very appropriate way for solution of the problem. The temporary selective clearing of the upper tissue layers is the key technique for structural and functional imaging, particularly for detecting local static or dynamic inhomogeneities hidden within a highly scattering medium [10]. Aqueous glucose solutions are widely used for the control of tissue scattering properties [8–21]. Increase of glucose content in tissue reduces re-

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fractive index mismatch and, correspondingly, decreases the scattering coefficient. On the other hand, measurement of the scattering coefficient allows one to monitor the change of glucose concentration in the tissue and blood, which is very important for monitoring of diabetic patients. However, in spite of numerous investigations related to delivery of drug and cosmetic substances into human tissues and to control of the tissue optical properties the problem of estimating diffusion coefficient of the drugs and various chemicals, including glucose, in tissues has not been studied in detail. The knowledge of the diffusion coefficients is very important for development of mathematical models describing interaction between tissues and drugs, and, in particular, for evaluation of the drug and metabolic agent delivery through tissue. Many biophysical techniques for study of penetration of various chemicals through living tissue and for estimation of the diffusion coefficients have been developed over the last fifty years. The methods are based on the fluorescence measurements [22–25] (including fluorescence correlation spectroscopy [25]), on the spectroscopic [26–33], Raman [34] and photoacoustic techniques [35,36], on the usage of radioactive labels for detecting matter flux [37–49], on the technique of nuclear magnetic resonance [50, 51], or on the measurements of temporal changes of the scattering properties of a tissue caused by dynamic refractive index matching [8–10, 12–21, 52–54] including interferometric technique [52–54] and optical coherence tomography (OCT) [20, 21]. However, fluorescence techniques cannot be used for direct measurement of glucose diffusion coefficients, although these techniques are very appropriate to measure protein diffusivity in tissues, and since the proteins are widely used for glucose detection then the techniques are important for development of new and increased accuracy of existing methods of glucose detection and monitoring. The spectroscopic, Raman, and photoacoustic methods have great potential for measuring glucose diffusion coefficients in tissues because the methods provide excellent sensitivity to glucose detection and monitoring, and the methods based on usage of radioactive labels for detecting matter flux and on the measurements of temporal changes of the scattering properties of the tissue are widely used for measurements of glucose diffusion and permeability coefficients now. The purpose of this chapter is to review methods for measurement of glucose diffusion and permeability coefficients in human tissues in vitro and in vivo.

19.2 Spectroscopic Methods The ability to measure noninvasively concentration of various chemicals in tissues could provide a variety of benefits for pharmacological research and, ultimately, clinical applications. In the previous section we described the technique of fluorescence measurements, which can be used for measurement of chemicals concentration and diffusion coefficient in biological tissues. However, many of exogenous

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and metabolic agents (in particular glucose) are not fluorescent, and therefore cannot be directly measured by the fluorescence techniques. Therefore, for the direct detection of these substances and estimation of their diffusivity the optical absorption measurements can be performed [5, 26–33]. The method is based on the time-dependent measurement of the tissue optical absorbance in the spectral range, which corresponds to absorption bands of the substance under study. The transport of low-molecular chemicals within tissue can be described in the framework of free diffusion model [12–23, 27–49]. It is assumed that the following approximations are valid for the transport process: 1) only concentration diffusion takes place; i.e., the flux of the chemical into tissue at a certain point within the tissue sample is proportional to the chemical concentration at this point; 2) the diffusion coefficient is constant over the entire sample volume; 3) penetration of a chemical into a tissue sample does not change the drug concentration in the external volume; 4) in the course of diffusion the chemical does not interact with tissue components. Geometrically, the tissue sample can be presented as an infinite plane-parallel slab with a finite thickness. In this case, the one-dimensional diffusion problem has been solved. The one-dimensional diffusion equation of a drug transport has the form

∂ C (x,t) ∂ 2C (x,t) , =D ∂t ∂ x2

(19.1)

where C (x,t) is the chemical concentration, D is the diffusion coefficient, t is the time, and x is the spatial coordinate. The key approach in characterization of transfer of a chemical agent is that a set of boundary conditions defines the concentration profiles. Depending on the analytical solution used, tissue type, and the experimental setup, three kinds of initial and boundary conditions are most commonly used for studies of agent transport in tissues. All, however, are based on concentration C (x,t) as determined by Fick’s second law [Eq. (19.1)]. The initial condition corresponds to the absence of an agent inside the tissue before the measurements, i.e., C (x, 0) = 0,

(19.2)

for all inner points of the tissue sample. In the case when a tissue is presented as a slab, the three kinds of boundary conditions are the following: 1) A tissue slab free of agent is immersed in solution with the agent concentration of C0 C (0,t) = C0 and C (l,t) = C0 ,

(19.3)

where l is a tissue sample thickness. The solution of Eq. (19.1) with the initial [Eq. (19.2)] and the boundary [Eq. (19.3)] conditions has the form [12, 15, 16, 18, 55]:

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!!   4 (2i + 1)2 Dπ 2t (2i + 1) π x C (x,t) = C0 1 − ∑ exp − . sin l l2 i=0 π (2i + 1) (19.4) The integral of Eq. (19.4) over x gives another physical quantity, average concentration (total solute entering the tissue) as: ∞

C (t) = C0

!  .  8 ∞ 1 2 2 2 , exp − (2i + 1) t π D l 1− 2 ∑ π i=0 (2i + 1)2

(19.5)

where C (t) is the volume-averaged concentration of an agent within tissue sample. 2) A tissue slab free of agent, one side of the slab contacts a solution with the agent concentration of C0 and the other side is isolated from agent penetration

∂ C (l,t) = 0. (19.6) ∂x The solution of Eq. (19.1) with the initial [Eq. (19.2)] and the boundary [Eq. (19.6)] conditions has the form [27]: !!   ∞ (2i + 1) π x 4 (2i + 1)2 Dπ 2t . sin C (x,t) = C0 1 − ∑ exp − 2l 4l 2 i=0 π (2i + 1) (19.7) The volume-averaged concentration in this case can be expressed as: C (0,t) = C0 and

C (t) = C0

  ! 2 8 ∞ 1 2 π 1− 2 ∑ exp − (2i + 1) t D l 2 . π i=0 (2i + 1)2 4

(19.8)

3) A tissue slab free of agent, where one side contacts a solution with the agent concentration of C0 , and the other side is kept at zero concentration C (0,t) = C0 and C (l,t) = 0.

(19.9)

The solution of Eq. (19.1) with the initial [Eq. (19.2)] and the boundary [Eq. (19.9)] conditions has the form [28–30,56]:   2 2 !  i Dπ t x ∞ 2 iπ x exp − 2 . (19.10) C (x,t) = C0 1 − − ∑ sin l i=1 π i l l The average concentration can be expressed as: C0 C (t) = 2

!  .  8 ∞ 1 2 2 2 . exp − (2i + 1) t π D l 1− 2 ∑ π i=0 (2i + 1)2

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(19.11)

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When penetrating agent is administered to tissue topically and the tissue is a semiinfinite medium, i.e., x ∈ [0; ∞), the boundary conditions have the from: C (0,t) = C0 and C (∞,t) = 0.

(19.12)

Solution of Eq. (19.1) with the initial [Eq. (19.2)] and the boundary [Eq. (19.12)] conditions, in this case, has the form [57]:    x , C (x,t) = C0 1 − erf √ 2 Dt where erf(z) =

√2 π

Rz 0


exp −a2 da is the error function.

(19.13)

Several methods and instrumentations based on absorbance measurements have been developed for estimation of agent diffusion coefficients. The methods using the attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy [28–32], spatially-resolved reflectance spectroscopy [27, 33], and Raman spectroscopy [34] are available (see also chapters 5–8, 10, 12). ATR-FTIR spectroscopy was used for measuring tissue absorption bands in the mid-infrared (mid-IR) spectral region and for study of diffusion of topically applied chemicals in the tissue. The mid-IR lies in the spectral range between 2.5 µ m (4000 cm−1 ) and 10 µ m (1000 cm−1 ). Bands in this spectral range correspond mainly to frequencies of fundamental molecular vibrations, which are characteristic of the specific chemical bonds. In contrast to the NIR spectral range contains combination and overtone bands that are broad and weak, bands in the mid-IR are sharp and have a higher absorption coefficient [4]. The ATR phenomenon occurs when radiation propagating through a medium with refractive index n1 crosses an interface with another medium with lower refractive index n2 . If the incident beam crosses the interface at an angle, which is greater than the critical angle, defined as θc = arcsin (n2 /n1 ), the beam will penetrate slightly into the medium with lower refractive index as it is being totally reflected. If the medium with lower refractive index has absorption bands in the frequency range of the incident radiation, each penetration will result in an energy loss due to absorption. Energy losses due to scattering may also occur. These combined energy losses are amplified by successive reflections within the internal reflection element (IRE). The ability of ATR spectroscopy to detect absorbance and scattering depends upon a number of factors, including the intensity, wavelength, and entry angle of the incident radiation, the absorption coefficient of the absorber, the degree of contact between the two media, the number of internal reflections, and the ratio of n2 to n1 [58]. According to ATR theory [59], the sensitivity of the technique is especially dependent upon energy coupling between the two media and the depth of beam penetration into the medium with the lower refractive index. Coupling can be increased by choosing IRE with refractive index close to, but greater than, the sample, while the depth of penetration can be increased by choosing an incident angle close to, but greater than, the critical angle.

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For recording of the ATR-FTIR spectra Fourier transform infrared spectrometer equipped by ATR with ZnSe (refractive index is 2.42) or Ge (refractive index is 4.0) a crystal of rectangular shape can be used. Typically, the ATR-FTIR spectrum is obtained by the Fourier transform of 64 or 128 interferograms, where Happ-Genzel apodization is used [60]. Spectral analysis can be performed by band fitting based on a nonlinear least-squares searchusing Gaussian band intensity shapes of the form   2 Ii (ν ) = Ai exp − (ν − ωi ) Wi , where I represents the infrared absorbance, ν is a current value of wave number, and ω , W , and A are frequency, width, and amplitude of the ith band, respectively. When the spatially-resolved reflectance spectroscopy has been used for determination of agent diffusion coefficient in tissue, the approach suggested by Mourant et al. [33] can be applied. The method is based on the use of modified Lambert-Beer law and, in this case, tissue absorbance can be determined as A = µa σ ρ + G,

(19.14)

where µa is the absorption coefficient, ρ is the source-detector distance, σ is the differential factor of photon pathlength, taking into account the lengthening of photon trajectories due to multiple scattering, and G is the constant, defined by geometry of the experiment. To simplify calculations, ρσ can be replaced by parameter L, that is defined by both absorption and scattering tissue properties and source-detector distance. The source-detector distance is a parameter, which is defining sensitivity of parameter L to absorption or to scattering of the tissue. The large separation of the source and detector (from millimeters to centimeters) results in large distances of photon travel and therefore a strong sensitivity to absorption. On the other hand, because of strong absorption by hemoglobin bands and detector limitations, largedistance measurements are limited to a spectral range of about 600–950 nm, reducing the number of chemicals that can be monitored. Additionally, the spatial resolution is low due to the large tissue volume that is probed. For small source-detector distance (about a few hundreds microns), which is commensurable with photon free pathlength, parameter L is defined by tissue scattering properties only [33, 61, 62]. The penetration of an agent into a tissue increases the tissue absorbance in the spectral range corresponding to absorption bands of the agent substance. Thus, the tissue absorbance measured in different time intervals can be determined as A (t, λ ) = A (t = 0, λ ) + ∆µa (t, λ ) L,

(19.15)

where t is the time interval, λ is the wavelength, ∆µa (t, λ ) = ε (λ )C (t) is the absorption coefficient of an agent within the tissue, ε (λ ) is the agent molar absorption coefficient, C(t) is the agent concentration in the tissue, which can be described by one of a series of Eqs. (19.5), (19.8), (19.11) in dependence on drug delivery method and geometry of measurements, and A (t = 0, λ ) is the tissue absorbance, measured at initial moment. Thus, the equation

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∆A (t, λ ) = A (t, λ ) − A (t = 0, λ ) = ∆µa (t, λ ) L = ε (λ )C (t) L

(19.16)

can be used for calculation of the drug diffusion coefficient. This set of equations represents the direct problem, i.e., describes the temporal evaluation of the absorbance of a tissue sample dependent on agent concentration within the tissue. Based on measurement of the evolution of the tissue absorbance, the reconstruction of the drug diffusion coefficient in a tissue can be carried out. The inverse problem solution can be obtained by minimization of the target function Nt

F(D) = ∑ (A (D,ti ) − A∗ (ti ))2 ,

(19.17)

i=1

where A (D,t) and A∗ (t) are the calculated and experimental values of the timedependent absorbance, respectively, and Nt is the number of time points obtained at registration of the temporal dynamics of the absorbance. To minimize the target function, the Levenberg-Marquardt nonlinear least-squares-fitting algorithm described in detail by Press et al. [63] can be used. Iteration procedure repeats until experimental and calculated data are matched. Infrared and near-infrared absorption spectroscopy techniques became the basis for nondestructive chemometric analysis and therefore hold great potential for the development of noninvasive blood and tissue glucose measurement techniques. The optical absorption methods are based on the concentration-dependent absorption of specific wavelengths of light by glucose or other compounds of interest. In theory, a beam of radiation may be directed through a blood-containing portion of the body and the exiting light is analyzed to determine the content of glucose. The mid-IR spectral bands of glucose and other carbohydrates have been assigned and are dominated by C–C, C–H, O–H, O–C–H, C–O–H, and C–C–H stretching and bending vibrations [4, 64, 65]. The 800–1200 cm−1 fingerprint region of the infrared spectrum of glucose has bands at 836, 911, 1011, 1047, 1076, and 1250 cm−1 , which have been assigned to C–H bending vibrations [4,64,66]. A 1026 cm−1 band corresponds to C–O–H bend vibration [4,66] and 1033 cm−1 band can be associated with the ν (C–O–H) vibration [66] or with the ν (C–O–C) vibration [67]. Despite the specificity offered by infrared absorption spectroscopy, its application to quantitative blood glucose measurement is limited. A strong background absorption by water and other components of blood and tissues severely limits the pathlength that may be used for transmission spectroscopy to roughly 100 µ m or less. Further, the magnitude of the absorption peaks and the dynamic range required to record them make quantitation based on these sharp peaks difficult. Nonetheless, attempts have been made to quantify blood glucose using infrared absorption spectroscopy in vitro and in vivo [4, 6, 60, 68–71]. In contrast to the mid-IR the incident radiation in the NIR spectral range passes relatively easily through water and body tissues allowing moderate pathlengths to be used for measurements. Thus, a large amount of effort has been devoted to the

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development of NIR spectroscopy (NIRs) techniques for noninvasive measurement of blood glucose [6] (see also chapters 5–8, 10). In the NIR spectral range absorption bands of glucose have been connected with C–H, O–H, and N–H vibrations [3, 6, 64, 66]. The strongest bands are the broad O–H stretch at 3550 cm−1 (2817 nm) and the C–H stretch vibrations 2961 and 2947 cm−1 (3377 and 3393 nm). Possible combination bands are a second O–H overtone band at 939 nm (3ν OH), and a second harmonic C–H overtone band at 1126 nm (3ν CH). A first O–H overtone band can be assigned at 1408 nm (2ν OH). The 1536 nm band can be assigned as an O–H and C–H combination band (ν OH + ν CH). The 1688 nm band is assigned as a C–H overtone band (2ν CH). Other bands at wavelength longer than 2000 nm are possibly combinations of a C–H stretch and a CCH, OCH deformation at 2261 and 2326 nm (ν CH + ν CCH, OCH) [3, 72]. Though all methods of optical glucose sensing require use of a prediction model relating to optical measurements of glucose concentration, the broad overlapping peaks and a complicated nature of multi-component NIR spectra make single or dual wavelength models inadequate. NIR absorption bands may be significantly influenced by factors such as temperature, pH, and the degree of hydrogen bonding present; the unknown influence of background spectra further complicates the problem. For this reason, quantitative NIR spectroscopy has long relied on the development of very high-order multivariate prediction models and empirical calibration techniques. For this reason, high-order multivariate models, which incorporate analysis of entire spectra, must be used to extract NIR glucose information [6] (see also chapter 5). For glucose detection in NIR spectral range, it can be useful to break the NIR region into the region from 700 to 1300 nm and the region from 2.0 to 2.5 µ m. In the NIR region from 700 to 1300 nm optical detectors and sources are readily available and relatively easy to use, transmission through tissue is rather good, and transmissive fiber optics can be used to facilitate a probe design. However, glucose absorption bands are particularly weak in this region, and it may be difficult to acquire signals with substantial signal to noise ratio to allow robust measurement. Further in the NIR spectrum, a relative dip in the water absorbance spectrum opens a unique window in the 2.0 to 2.5 µ m wavelength region. This window, saddled between two large water absorbance peaks, allows pathlengths or penetration depths of the order of millimeters and contains specific glucose peaks at 2.11, 2.27, and 2.33 µ m [72]. Thus, this region may be very applicable for quantifiable glucose measurement using NIR spectroscopy. In addition to NIRs, Raman spectroscopy can provide potentially rapid, precise, and accurate analysis of glucose concentration and biochemical composition (see chapter 12). Raman spectroscopy provides information about the inelastic scattering, which occurs when vibrational or rotational energy is exchanged with incident probe radiation. As with IR spectroscopic techniques, Raman spectra can be utilized to identify molecules such as glucose, because these spectra are characteristic of variations in the molecular polarizability and dipole moments. However, in contrast to infrared and NIRs, Raman spectroscopy has a spectral signature that is less influenced by water [4]. In addition, Raman spectral bands are considerably narrower

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(typically 10–20 cm−1 in width [73]) than those produced in NIR spectral experiments. Raman also has the ability to permit the simultaneous estimation of multiple analytes, requires minimum sample preparation, and would allow for direct sample analysis [6]. Like infrared absorption spectra, Raman spectra exhibit highly specific bands, which are dependent on concentration. As a rule, for tissue Raman analysis the spectral region between 400 and 2000 cm−1 , commonly referred to as the “fingerprint region,” was employed. Many different molecular vibrations lead to Raman scattering in this part of the spectrum. In many cases bands can be assigned to specific molecular vibrations and or molecular species, much aiding the interpretation of the spectra in terms of biochemical composition of the tissue. In this spectral range Raman spectrum of glucose contains bands with maxima at 420, 515, 830, 880, 1040, 1100, 1367, and 1460 cm−1 [6].

19.3 Photoacoustic Technique Photoacoustic spectroscopy (PAS) can be used to acquire absorption spectra noninvasively from samples, including biological ones. The photoacoustic signal is obtained by probing the sample with a monochromatic radiation, which is modulated or pulsed. Absorption of probe radiation by the sample results in localized shortduration heating. Thermal expansion then gives rise to a pressure wave, which can be detected with a suitable transducer. An absorption spectrum for the sample can be obtained by recording the amplitude of generated pressure waves as a function of probe beam wavelength. The pulsed PA signal is related to the properties of turbid medium by the equation [4, 74]: 
PA = k β υ n C p E0 µe f f ,

(19.18)

where PA is the signal amplitude, k is the proportionality constant, E0 is the incident pulse energy, β is the coefficient of volumetric thermal expansion, υ is the speed of sound in the medium, C p is the specific heat capacity, n is a constant p between one and two, depending on the particular experimental conditions, µe f f = 3µa ( µa + µs′ ), µ a is the medium absorption coefficient, µs′ = µs (1 − g) is the medium reduced or transport scattering coefficient, and µ s and g are the medium scattering coefficient and anisotropy factor, respectively. To generate PA signals efficiently, two conditions, referred to as thermal and stress confinements, must be met [75]. The time scale for heat dissipation of absorbed electromagnetic (EM) energy by thermal conduction can be approximated by  τth ∼ L2p 4DT , where L p is a characteristic linear dimension of the tissue volume being heated (i.e., the penetration depth of the EM wave or the size of the absorbing structure). Actually, heat diffusion depends on the geometry of the heated volume, and the estimation of τ th may vary. Upon the absorption of a pulse with a temporal duration of τ p , the thermal diffusion length during the pulse period can be estimated

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p by δT = 2 DT τ p , where DT is the thermal diffusivity of the sample. The pulse width τ p should be shorter than τ th to generate PA waves efficiently, a condition that is commonly referred to as thermal confinement where heat diffusion is negligible during the excitation pulse. Similarly,  the time for the stress to transit the heated region can be estimated by τst = L p c, c is the speed of sound. The pulse width τ p should be shorter than τ st , a condition that is commonly referred to as stress confinement. In the photoacoustic spectroscopy technique, the choice of a wavelength in a region of greater absorbance presents a great advantage to give a large magnitude of acoustic signal up to the limit of photoacoustic saturation. However, the optical penetration depth is reduced when the optical absorption increases, so the tissue thickness probed is more superficial. The compromise on the choice of the wavelength is thus obtained by a good signal to noise ratio and with a penetration as large as possible. Because high signal-to-noise measurements require reasonable penetration of the sample by the probe radiation, the NIR spectral region has been attractive for the measurements. The advantage of PAS is that the signal recorded is a direct result of absorption only, and scattering does not play a significant role in the acquired signal. The basic equipment required to realize investigations based on the usage of photoacoustic spectroscopy includes a picosecond or nanosecond laser system, and a wide-band acoustic transducer, which can detect both high and low ultrasonic frequencies of acoustic pressure at once [76]. In photoacoustic systems for glucose detection pulsed laser sources with wavelength 355 nm [77], 780, 830, 1300, 1440, 1550 and 1680 nm [3], 1.064 µ m [78], and 9.7 µ m [74, 79] have been used. The outgoing ultrasound from the initial source reaches the tissue surface and then can be picked up by an ultrasound transducer. Since it serves only as an acoustic receiver, and the emission efficiency is of no importance, the detector for PA measurement can be specially designed to provide required sensitivity. The most often used ultrasound detectors are piezoelectric based; they have low thermal noise and high sensitivity and can provide a wide band from 20 kHz to 100 MHz [75, 76]. Although the previous works [74, 79] in the mid-infrared region demonstrated the potential of photoacoustics as a method of measuring glucose concentration, this wavelength region is not regarded as viable for human tissue studies because of the high water absorption that reduces penetration depths to microns. This penetration may not be sufficient to investigate blood constituents within human tissue, although interaction with interstitial fluid yields measurements, which correlate with blood glucose concentrations but with a time shift [74]. The spectral region that shows the most promise for absorption by the analytes within blood is within the “tissue window,” around the 1–2 µ m [3, 80]. Although measurements within this region are advantageous for tissue studies, due to reasonable penetration of the sample by the probe radiation, they coincide with a region of lower glucose absorption. Despite the fact, both in vitro and in vivo studies have been carried out in this spectral range to assess the feasibility of photoacoustic technique for noninvasive glucose detection [74, 79], and the investigation demonstrated applicability of PAS to measurement of glucose concentration (see also chapter 14). Greatest percentage of change in the photoacoustic response was observed in region

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of the C–H second overtone at 1126 nm, with a further peak in the region of the second O–H overtone at 939 nm [74]. In addition, the generated pulsed PA time profile can be analyzed to detect the effect of glucose on tissue scattering, which is reduced by increasing glucose concentration [3, 4, 6, 8–21]. For study of glucose diffusion in human tissues the simple approach, which has been presented in Refs. [35] and [36], can be applied. In accordance with the approach the laser-induced heat/emission from the tissue served to increase the temperature, i.e., pressure, which can be detected by a transducer. Integrating the transducer response over time the pressure signal P(t), which is directly related to the amount of heat emitted by the tissue, can be obtained. The pulse is characterized through its maximum, both the amplitude (Pmax) and time delay (tmax ) of appearance with respect to the beginning of the pulse. The signal evolutions can be characterized by fitting the curves Pmax versus t by an expression derived from a model of diffusion in a semi-infinite medium. The applied model has been shown to be in good agreement with diffusion pattern [81]. The mathematical expression used is [36]:  q 
 Pmax (t) = P∞ + Pc exp t τD erfc t τD , (19.19)

q   √ t τD is where Pc , P∞ , and τ D are fitting parameters, and erfc( t /τD ) = 1 − erf the complementary error function [see, Eq. (19.13)]. This model yields a characteristic time of diffusion τ D , as well as a total diffusion amplitude Pc + P∞. While τ D represents the time necessary for half of the glucose to penetrate into the depth of the tissue, the sum Pc + P∞ represents the global initial amount of the agent contributing to the signal. Pmax denotes the main heat emission; tmax represents the time needed for the main heat emission in the tissue to diffuse towards its surface and to be detected. These two parameters, Pmax and tmax , serve to provide a macroscopic characterization of the diffusion process.

19.4 Use of Radioactive Labels for Detecting Matter Flux Many investigations based on the usage of radioactive labels for detecting matter flux have been performed in last decades for studies of penetration of various chemicals through living tissue and for estimation of diffusion coefficient of the chemicals in the tissues [37–49]. This method has both some advantages and some disadvantages. The main advantage of this method is connected with the possibility of measurement of very small amount (concentration) of penetration agents and the main disadvantage is connected with a necessity of use of radioactive isotopes that can be dangerous, especially in case of in vivo measurements. Typically, in vitro permeability experiments are performed using a side-by-side two-chamber diffusion cell and scintillation counter [37–42, 44–49]. In the twochamber diffusion cell, the tissue sample is placed between the two chambers and

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the radiolabeled penetration agent diffuses from a donor chamber through the tissue into an acceptor chamber, as a rule filled by PBS solution for preventing tissue drying. In case of in vivo measurements the radiolabeled agents can be intravenously injected and thereafter urine [44] or interstitial fluid [43] was collected to determine its radioactivity. Analysis of agent diffusion through a membrane (that can be skin, mucous, sclera or other tissues) in this case can be performed on the basis of the first Fick’s diffusion law. The law states that the steady state flux (J) of penetration agents per unit pathlength is proportional to the concentration gradient (∆C) and the diffusion coefficient (D, cm2 /s) [37, 55, 82]:  J = −D∆C l = P∆C.

(19.20)

  P = J (Cd − Ca ) = KD l,

(19.21)

Here ∆C = Cd − Ca , Cd is the concentration of radiolabeled agent in the donor chamber and Ca is the concentration of the agent in the acceptor chamber (g/cm3 ), l is the membrane thickness (cm), and P is the permeability coefficient (cm/s). The negative sign indicates that the flux is in the direction of the lower concentration. On the other hand, the permeability coefficient can be defined as [37, 55, 82]:



where K = k12 k21 is the partition coefficient; k12 is the binding constant and k21 is the dissolution constant; J is the steady state flux of the radiolabeled agent measured in g·cm−2·s−1 . The partition coefficient can be estimated from [41]:  (radioactivityin tissue) (weightof tissue)  K= . (19.22) (radioactivityin solution) (weightof solution) In turn, the permeability coefficient deals with structural properties of the tissue (membrane) through the relation [38,42]:

ε D0 , (19.23) τl where ε , τ , and l are the porosity, tortuosity of the diffusional pathway, and thickness of the membrane, respectively, D0 is the diffusion coefficient of the penetration agents in the tissue (membrane) interstitial fluid, and the diffusion coefficient D0  can be calculated using the Stokes-Einstein equation: D0 = kT (6πη rs ), where k is Boltzmann’s constant, T denotes the absolute temperature, η is the solvent viscosity, and rs is hydrodynamic (Stokes) radius of the diffusing molecules. In vitro the permeability coefficient can be calculated from the following equation [42, 45]: P=

P=

V · dC , S ·C0 · dt

(19.24)

where dC/dt is the change in concentration per volume sample per unit time, and V is the volume of the acceptor chamber. Therefore, the quantity V · dC dt is the © 2009 by Taylor & Francis Group, LLC

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steady-state flux per unit time. S is the surface area of the membrane, and C0
is the initial concentration of the diffusing agent. Note that the parameter dC dt can be measured as the slope of linear region of the amount of permeant in the acceptor chamber versus time plot. Using the technique, Horibe et al. [49] have found that permeability coefficient of mannitol through pigmented rabbit conjunctiva in the mucosal-to-serosal direction is (27.70 ± 4.33) × 10−8 cm/s and in the serosal-to-mucosal direction is (25.50 ± 4.40) ×10−8 cm/s. Grass and Sweetana [45] measured the permeability coefficients of Lglucose, D-glucose, and mannitol through rabbit jejunum as (3.03 ± 0.33) × 10−6 cm/s, (14.99 ± 2.02) × 10−6 cm/s, and (3.59 ± 0.22) × 10−6 cm/s, respectively. Myung et al. [40] measure glucose diffusion flux across human, bovine, and porcine corneas and determine the diffusion coefficient in each type of cornea as (3.0 ± 0.2)× 10−6 cm2 /s, (1.6 ± 0.1) × 10−6 cm2 /s, and (1.8 ± 0.6) × 10−6 cm2 /s, respectively. Ghanem et al. [46] have shown that permeability coefficient of full-thickness mouse skin for mannitol is 3 × 10−8 cm/s. Similar result has been obtained by Ackermann and Flynn [47] for glucose, urea, and glycerol with hairless mouse skin. Wang et al. [43] measure the permeability coefficient of D-glucose through rat jejunum and ileum as 7.54 × 10−5 cm/s and 2.45 × 10−5 cm/s, respectively. Larhed et al. [39] measure diffusion coefficient of mannitol in phosphate buffer and native pig intestinal mucus as 9.8 × 10−6 cm2 /s and 8.6 × 10−6 cm2 /s, respectively. Peck et al. [42] presented that diffusion coefficients of mannitol and sucrose in human epidermal membrane are (9.03 ± 0.3) × 10−6 cm2 /s and (6.98 ± 0.2) × 10−6 cm2 /s, respectively. It should be noted that mannitol has the same molecular weight as glucose and similar structure, and, thus, transport (diffusing) characteristics of the substance in tissues can be similar as for glucose. Khalil et al. [48] have found that diffusion coefficient of glucose in skin dermis is (2.64 ± 0.42) × 10−6 cm2 /s, and the glucose diffusion coefficient in viable epidermis is (0.075 ± 0.050) × 10−6 cm2 /s.

19.5 Light Scattering Measurements 19.5.1 Spectrophotometry It is well known that the major source of scattering in tissues and cell structures is the refractive index mismatch between mitochondria and cytoplasm, extracellular media, and tissue structural components such as collagen and elastin fibers [83, 84]. The scattering properties of tissues (such as skin dermis, sclera, dura mater, etc.) are significantly changed due to action of osmotically active immersion liquids, in particular by glucose solutions [8–19]. Measurement of the scattering coefficient allows one to monitor the change of glucose concentration in the tissue and thus for measurement of glucose diffusion coefficient. The optical method for estimating the diffusion coefficient in a tissue has been suggested by Tuchin et al. [12]. This method is based on the measurement of temporal changes of the scattering properties

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FIGURE 19.1: Schematic representation of osmotically active immersion liquid diffusion into the tissue sample and the geometry of light irradiation. of a tissue caused by dynamics of refractive index matching. It can be used both for in vitro and in vivo measurements. Experimentally, the simplest method for estimation of diffusion coefficients of osmotically active liquids in tissues is based on the time-dependent measurement of collimated transmittance of tissue samples placed in immersion liquid [8–10, 12–16, 18]. Schematic representation of the osmotically active immersion liquid diffusion into the tissue sample and the geometry of light irradiation are presented in Fig. 19.1. Since transport of immersion liquid (glucose solution) within the tissue can be described in the framework of the free diffusion model (see section 19.3), then Eqs. (19.4), (19.5), (19.7), (19.8), (19.10), and (19.11) can be used to describe the spatial and temporal evolution of glucose concentration within a tissue. The time dependence of collimated optical transmittance of a tissue sample impregnated by an immersion solution is defined by Bouguer-Lambert law: Tc (t) = (1 − Rs)2 exp (− (µa + µs (t)) l (t)) ,

(19.25)

where Rs is the specular reflectance and µa is the tissue absorption coefficient. Since glucose does not have strong absorption bands in the visible and near-infrared spectral regions, then the changes of collimated transmittance of a tissue sample can be described only by the behavior of the tissue scattering. µs (t) is the tissue timedependent scattering coefficient and l(t) is the time-dependent thickness of the tissue sample. The time dependence of the tissue thickness occurs due to osmotic activity of immersion agents, because it is well known that action of hypo-osmotic liquids on the tissue causes tissue cells swelling, and application of hyper-osmotic solutions causes shrinkage process [11]. Thus, the application of osmotically active liquids can be accompanied by tissue swelling or shrinkage, which should be taken into account. Since aqueous glucose solutions have pH different from pH of the interstitial fluid of the native tissue, placing tissues sample into the solutions produces the swelling (shrinkage) process in dependence on pH of the solutions. The temporal dependence of the tissue sample volume can be described assuming that increasing tissue vol-

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ume is the result of additional absorption of the osmotically active liquids [85] and decreasing tissue volume is the result of water loss from the tissue sample. The temporal dependence of the swelling H(t) and shrinkage HD (t) indices of the tissue sample can be calculated from weight measurements as [16]: H (t) =

M (t) − M (t = 0) Mosm (t) Vosm (t) × ρosm = = , M (t = 0) M (t = 0) M (t = 0)

(19.26)

HD (t) =

MH2 O (t) VH O (t) × ρH2 O M (t = 0) − M (t) = = 2 , M (t = 0) M (t = 0) M (t = 0)

(19.27)

where M(t) is mass of the tissue sample in the different moments in the swelling (shrinkage) process, Mosm (t), Vosm (t), and ρosm (t) are mass, volume, and density of osmotically active liquid (glucose solution) absorbed by the tissue sample, respectively. Let V (t) represent the volume of swelling (shrinkage) tissue, then  V (t) = V (t = 0) ± Vosm (t) = V (t = 0) ± H (t) M (t = 0) ρosm .

(19.28)

Here sign “plus” corresponds to swelling process and sign “minus” to shrinkage process. The temporal dependence of swelling (shrinkage) index can be approximated by the following phenomenological expression [16]: 

H (t) = A 1 − exp −t τs .

(19.29)



V (t) = V (t = 0) ± A 1 − exp −t τs .

(19.30)



l (t) = l (t = 0) ± A∗ 1 − exp −t τs ,

(19.31)

Therefore, the temporal dependence of tissue volume during osmotically active liquid action [Eq. (19.28)] can be presented as

In this case A and τs are some phenomenological constants describing a swelling (shrinkage) process caused by glucose action. Volumetric changes of a tissue sample are mostly due to changes of its thickness l(t), which can be expressed as

A∗



where = A S, and S is the tissue sample area. The constants A and τs can be obtained both from direct measurements of thickness or volume of tissue samples and from time-dependent weight measurements [16]. For example, for dura mater samples immersed in the mannitol solution, we have estimated parameter A as 0.21 and the parameter characterizing the swelling rate, i.e., τs as 484 s. For dura mater samples immersed in glucose solution with concentration 0.2 g/ml, we have estimated the parameter A as 0.2 and τs as 528 s [16]. By changing volume of a tissue the swelling (shrinkage) produces the change of the volume fraction of the tissue scatterers, and thus the change of the scatterer packing factor and the numerical concentration (density or volume fraction), i.e., number of the scattering particles per unit area (for long cylindrical particles, density

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fraction) or number of the scattering particles per unit volume (for spherical particles, volume fraction). Taking into account Eq. (19.30), the temporal dependence of the volume fraction of the tissue scatterers is described as

φ (t) =

φ (t = 0) × V (t = 0) Vs = , V (t) V (t = 0) ± A (1 − exp(−t /τ ))

(19.32)

where Vs is the volume of the tissue sample scatterers. The optical model of fibrous tissue can be presented as a slab with a thickness l containing scatterers (collagen fibrils) – thin dielectric cylinders with an average diameter of about 100 nm, which is considerably smaller than their lengths. These cylinders are located in planes, which are parallel to the sample surfaces, but within each plane their orientations are random. In addition to the small, so-called Rayleigh scatterers, the fibrils are arranged in individual bundles in a parallel fashion; moreover, within each bundle, the groups of fibers are separated from each other by large empty lacunae distributed randomly in space [86]. Collagen bundles show a wide range of widths (1 to 50 µ m) and thicknesses (0.5 to 6 µ m) [87, 88]. These ribbonlike structures are multiple cross-linked; their length can be a few millimeters. They cross each other in all directions but remain parallel to the tissue surface. For noninteracting particles the time-dependent scattering coefficient µs (t) of a tissue is defined by the following equation

µs (t) = N σs (t) ,

(19.33)

where N is the number of the scattering particles (fibrils) per unit area and σs (t) is the time-dependent cross-section of scattering. The number of the scattering particles per unit area can be estimated as N = φ /(π a2 ) [89], where φ is the volume fraction of the tissue scatterers and a is their radii. For typical fibrous tissues, such as sclera, dura mater, and skin dermis, φ is usually equal to 0.2-0.3 [86]. To take into account interparticle correlation effects which are important for tissues with densely packed scattering particles the scattering cross-section has to be corrected by the packing factor of the scattering particles, (1 − φ ) p+1 /(1 − φ (p − 1)) p−1 [84], where p is a packing dimension that describes the rate at which the empty space between scatterers diminishes as the total number density increases. For spherical particles the packing dimension is equal to 3, and the packing of sheetlike and rod-shaped particles is characterized by packing dimensions that approach 1 and 2, respectively. Thus, Eq. (19.33) has to be rewritten as

µs (t) =

φ (1 − φ )3 σ . (t) s π a2 1+φ

(19.34)

In accordance with Mie theory [83], if incident light is nonpolarized, scattering properties of cylindrical particles (the collagen fibrils and fibers) can be described by following set of relations:

σs = 2aQs = 2a

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QsI + QsII , 2

(19.35)

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where a is a radius of the cylinder and Qs is an efficiency factor of the scattering. # "  ∞  2 QsI = |b0I |2 + 2 ∑ |bnI |2 + |anI |2 , x n=1 QsII

# "  ∞  2 2 2 2 = , |a0II | + 2 ∑ |anII | + |bnII | x n=1

anI =

anII = −

An = iξ



CnVn − Bn Dn Wn Bn + iDnCn , bnI = 2 WnVn + iDn WnVn + iD2n AnVn − iCn Dn CnWn + An Dn , bnII = −i WnVn + iD2n WnVn + iD2n

ξ Jn′ (η ) Jn (ξ ) − η Jn (η ) Jn′ (ξ )



,

(1) Dn = n cos ζ η Jn (η ) Hn (ξ )



 ξ2 −1 η2

  2  2 ′  ξ ′ Bn = ξ m ξ Jn (η ) Jn (ξ ) − η Jn (η ) Jn (ξ ) , Cn = n cos ζ η Jn (η ) Jn (ξ ) −1 η2 h i (1) (1)′ Vn = ξ m2 ξ Jn′ (η ) Hn (ξ ) − η Jn (η ) Hn (ξ ) , h i (1)′ (1) Wn = iξ η Jn (η ) Hn (ξ ) − ξ Jn′ (η ) Hn (ξ )

ξ = x sin (ζ ) ,

q η = x m2 − cos2 (ζ ).

Here ζ is the angle between direction of incident field and the axis of cylinder. If wave vector of the incident field is directed perpendicularly to the axis of cylinder (ζ = 90◦ ), the coefficients anI and bnII turn to zero, i.e.,
bnI ζ = 900 = bn =
anII ζ = 900 = an =

Jn (mx) Jn′ (x) − mJn′ (mx) Jn (x)

,

mJn (mx) Jn′ (x) − Jn′ (mx) Jn (x)

.

(1)′

Jn (mx) Hn

(1)′

mJn (mx) Hn

(1)

(x) − mJn′ (mx) Hn (x) (1)

(x) − Jn′ (mx) Hn (x) (1)

Here Jn (ρ ) is the Bessel function of the 1-st  kind of n-order, Hn (ρ ) is the Bessel function of the 3-rd kind of n-order, m = ns nI is the ratio of the refractive indices of © 2009 by Taylor & Francis Group, LLC

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 the particle (ns ) and surrounding medium (nI ), and x = 2π anI λ is the size parameter, where λ represent wavelength in the surrounding medium. Asymmetry factor of light scattering g (average cosine of scattering angle) for the case of the infinite cylinder illuminated by nonpolarized light is defined by following relation [83]:

g = hcos θ i =

Rπ 0

T11 T11norm

Rπ 0

T11 =

|T1 |2 + |T2 |2 , 2

T11norm =

cos (θ ) sin (θ ) d θ ,

(19.36)

T11

T11norm sin (θ ) d θ

|b0I + 2bnI cos θ |2 + |a0II + 2anII cos θ |2 , 2

∞

∞

T1 = b0I + 2 ∑ bnI cos (nθ ), T2 = a0II + 2 ∑ anII cos (nθ ), n=1

n=1

where T1 , T2 are the components of the amplitude forward scattering matrix; T11 is the component of the scattering matrix. For spherical particles (the nucleus and mitochondria in cells of epithelial tissue, e.g., skin epidermis or mucous tissue) the scattering cross-section and anisotropy factor can be described as [83]:  2  ∞   λ 2 2 σs = , (19.37) (2n + 1) |a | + |b | n n ∑ 2π n2I n=1 "

# ∞ n (n + 2)  ∗ 2n + 1 Re an an+1 + bn b∗n+1 + ∑ Re {an b∗n } , ∑ n=1 n + 1 n=1 n (n + 1) (19.38) where an and bn are the Mie coefficients, and a∗n and b∗n are their complex conjugates.

λ2 g= 2 π nI σs

∞

an =

mψn (mx) ψn′ (x) − ψn (x) ψn′ (mx) , mψn (mx) ξn′ (x) − ξn (x) ψn′ (mx)

bn =

ψn (mx) ψn′ (x) − mψn (x) ψn′ (mx) . ψn (mx) ξn′ (x) − mξn (x) ψn′ (mx) (1)

Here, ψn (ρ ) = ρ Jn (ρ ) and ξn (ρ ) = ρ Hn (ρ ) are the Riccati-Bessel functions, (1) Jn (ρ ) is the Bessel function of the first kind of the n-order, and Hn (ρ ) is the Bessel function of the 3-rd kind of the n-order. The time dependence of the refractive index of the interstitial fluid can be derived using the law of Gladstone and Dale, which states that the resulting value represents an average of the refractive indices of the components related to their volume fractions [90]. Such dependence is defined as

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nI (t) = (1 − C (t)) nbase + C (t) nosm ,

(19.39)

where nbase is the refractive index of the tissue interstitial fluid at the initial moment, and nosm is the refractive index of the glucose solutions. Numerous values of refractive indices of interstitial fluid and other tissue components are presented in Refs. [10] and [86]. Wavelength dependence of aqueous glucose solution can be estimated as nosm (λ ) = nw (λ ) + 0.1515C,

(19.40)

where nw (λ ) is the wavelength dependence of water, and C is the glucose concentration, g/ml [91]. The wavelength dependence of water has been presented by Kohl et al. [92] as

nw (λ ) = 1.3199 +

6.878 × 103 1.132 × 109 1.11 × 1014 − + . λ2 λ4 λ6

(19.41)

As a first approximation, we can assume that during the interaction between the tissue and the immersion liquid (glucose solution) the size and refractive index of the scatterers does not change. This assumption is confirmed by the results presented by Huang and Meek [85]. In this case, all changes in the tissue scattering are connected with the changes of the refractive index of the interstitial fluid described by Eq. (19.39). The increase of the refractive index of the interstitial fluid decreases the relative refractive index of the scattering particles and, consequently, decreases the scattering coefficient. This set of equations describing glucose concentration dependence on time represents the direct problem. The reconstruction of the diffusion coefficient of the glucose in tissue can be carried out on the basis of measurement of the temporal evolution of the collimated transmittance. The solution of the inverse problem can Nt

be obtained by minimization of the target function: F(D) = ∑ (Tc (D,ti ) − Tc∗ (ti ))2 , i=1

where Tc (D,t) and Tc∗ (t) are the calculated and experimental values of the timedependent collimated transmittance, respectively, and Nt is the number of time points obtained at registration of the temporal dynamics of the collimated transmittance. The mannitol and glucose diffusion coefficients in the human sclera [18], dura mater [16], and rat skin [14] were estimated using the temporal dependence of the collimated transmittance and the method presented in this section. The diffusion coefficients are presented in Table 19.1. It is well known that diffusion coefficient increases with the increase of temperature of the solution. The temperature depen1) [93]. Here D (T ) is diffusion dence was accounted for as D (T2 ) = D (T1 ) TT21 ηη (T (T2 ) coefficient at temperature T and η (T ) is viscosity of the solution. The values of the diffusion coefficients, corrected to the physiological temperature of 37◦ C, are also presented in Table 19.1. The differences between the diffusion coefficients of these substances in water and in tissue are connected with the structure and composition of

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the tissue interstitial matter, since the scleral, dura mater, and skin interstitial fluid contains the proteins, proteoglycans, and glycoproteins.

TABLE 19.1: The experimentally measured diffusion coefficients of glucose and mannitol in living tissues [14,16,18] Tissue Human sclera Human sclera Human sclera Human dura mater Human dura mater Rat skin

Diffusing solution 20%-aqueous glucose solution 30%-aqueous glucose solution 40%-aqueous glucose solution 20%-aqueous glucose solution

Diffusion coefficient at Diffusion coefficient 20 ˚ C, cm2 /s at 37 ˚ C, cm2 /s −6 (0.57 ± 0.09) × 10 [18] (0.91 ± 0.09) × 10−6 (1.47 ± 0.36) × 10−6[18]

(2.34 ± 0.36) × 10−6

(1.52 ± 0.05) × 10−6[18]

(2.42 ± 0.05) × 10−6

(1.63 ± 0.29) × 10−6[16]

(2.59 ± 0.29) × 10−6

20%-aqueous (1.31 ± 0.41) × 10−6 [16] mannitol solution

(2.08 ± 0.41) × 10−6

40%-aqueous glucose solution

(1.101 ± 0.16) × 10−6 [14] (1.75 ± 0/1) × 10−6

These measurements have been performed using a commercially available multichannel spectrometer LESA-6med (BioSpec, Russia) in transmittance mode. The scheme of the experimental setup is shown in Fig. 19.2. As a light source a 250 W xenon arc lamp with filtering of the radiation in the spectral range from 400 to 800 nm was used. During the in vitro light transmittance measurements, the glass cuvette with the tissue sample was placed between two optical fibers with a core diameter of 400 µ m and a numerical aperture of 0.2. One fiber transmitted the excitation radiation to the sample, and another fiber collected the transmitted radiation. The 0.5-mm diaphragm placed 100 mm apart from the tip of the receiving fiber was used to provide collimated transmittance measurements. Neutral filter was used to attenuate the incident radiation. The measurements have been performed every 30 seconds during 15–20 min for different human sclera and dura mater tissue samples. The experiments with the rat skin samples have been performed every 1 min at the beginning and every 5 min afterwards during about 190 min. Experimental error does not exceed 5% in the spectral range from 500 to 800 nm and 10% in the spectral range from 400 to 500 nm. All experiments have been performed at room temperature about 20◦ C. Figure 19.3 illustrates the dynamics of collimated transmittance of skin sample measured at different wavelength concurrently with administration of 40% glucose

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FIGURE 19.2: Experimental setup for measurements of collimated transmittance and reflectance spectra from tissue: 1 – optical irradiating fiber; 2 – neutral filters; 3 – cuvette; 4 – tissue sample; 5 – osmotically active immersion agent (the glucose and mannitol solutions); 6 – the 0.5 mm diaphragm; 7 – optical receiving fiber; 8 – aluminum holder. solution [14]. It is easily seen that the untreated skin is a poorly transparent media for visible light. Glucose administration makes this tissue highly transparent; the 50-fold increase of the collimated transmittance is seen, and, as following from Fig. 19.3, the characteristic time response of skin optical clearing is about 1 hour. Using algorithm presented above, glucose diffusion coefficient in rat skin has been estimated as (1.101 ± 0.16) × 10−6 cm2 /s. For in vivo measurements [17,19] the experimental setup has been used in reflectance mode (see Fig. 19.2). The in vivo reflectance measurements were performed using an originally designed fiber optical probe with a system of optical fibers (designed by Yu.P. Sinichkin). The fibers were enclosed in a cone-shaped aluminum holder to provide a fixed distance between the fibers and tissue surface. Light from a stabilized light source (xenon arc lamp) was delivered to the tissue by means of the fiber fixed normally to the surface of tissue. The receiving fiber was displaced at an angle of 20 degrees to the sending fiber in such a way for the irradiated area to have a 5-mm diameter, and the area of light collection had a 10-mm diameter. Figure 19.4 presents the in vivo reflectance spectra of rabbit eye sclera measured at different time intervals after administration of 40%-glucose solution [13]. For calculation of tissue reflectance the Monte Carlo (MC) algorithm developed by Wang et al. [94] can be used. The stochastic numerical MC method is widely used to model optical radiation propagation in complex randomly inhomogeneous highly scattering and absorbing media such as biological tissues. Basic MC modeling of an individual photon packet’s trajectory consists of the sequence of the elementary simulations [94]: photon pathlength generation, scattering and absorption events, reflection or/and refraction on the medium boundaries. The initial and final states

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FIGURE 19.3: The time-dependent collimated transmittance of the rat skin samples (1 h after autopsy, hair were removed using tweezers) measured at different wavelength in a course of administration of 40%-aqueous solution in a bath [14]. of the photons are entirely determined by the source and detector geometry, i.e., the incident light is assumed to be distributed on the area with diameter 5 mm, the photons’ packets are launched normally to the tissue surface, and collected from the area with diameter 10 mm. At the site of scattering a new photon packet direction is determined according to the Henyey–Greenstein scattering phase function: fHG (θ ) =

1 − g2 1 , 4π (1 + g2 − 2g cos θ )3/2

where θ is the polar scattering angle. The distribution over the azimuthal scattering angle was assumed as uniform. MC technique requires values of absorption and scattering coefficients, anisotropy factor, thickness and refractive index of tissues, and the required data and optical parameters can be calculated on the basis of Mie theory, previously measured or obtained from literature. The calculation of glucose diffusion coefficient in tissue was carried out on the basis of measurement of the temporal evolution of the tissue optical reflectance. The solution of the inverse problem can be obtained by minimization of the target funcNt

tion: F(D) = ∑ (R (D,ti ) − R∗ (ti ))2 , where R (D,t) and R∗ (t) are the calculated and i=1

experimental values of the time-dependent reflectance, respectively, and Nt is the number of time points obtained at registration of the temporal dynamics of the reflectance. Using the approach the glucose diffusion coefficients in rabbit sclera in vivo has been measured as (5.4 ± 0.1) × 10−7 cm2 /s [19]. Another approach for calculation of tissue reflectance connected with use of diffusion approximation of radiation transfer theory. According to the diffusion theory, the spatial dependence of the diffuse reflectance, R (ρ ), of continuous light remitted

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FIGURE 19.4: The in vivo time-dependent reflectance spectra of the rabbit eye sclera measured concurrently with administration of 40%-glucose solution: 1 — 1 min, 2 — 4 min, 3 — 21 min, 4 — 25 min, 5 — 30 min after drop of glucose solution onto the rabbit eye surface [13]. from a semi-infinite scattering medium at a separation of ρ from the source is [95]

R (ρ ) =

I0 4π µt′



µeff +

1 r1



    e−µeffr1 1 e−µeff r2 4 A + 1 + , (19.42) µ + eff 3 r2 r12 r22

q q 

 ′
2 2 4 + ρ 2, µt′ = µa + µs′ , I0 is the where r1 = 1 µt′ + ρ 2 , r2 = 3 A + 1 µt initial light source intensity, and A is an internal specular reflection parameter, depending only on the relative refractive index of the tissue and surrounding medium. For matching of this formula with geometry of the experiments the function R (ρ ) has been integrated over all area from which reflected radiance was collected. Using the approach the glucose diffusion coefficients in human skin in vivo has been measured as (2.56 ± 0.13) × 10−6 cm2 /s [17].

19.5.2 OCT and interferometry Optical coherence tomography is a new imaging technique, which provides images of tissues with resolution of about 10 µ m or less at a depth of up to 1 mm depending on optical properties of tissue [96, 97]. It allows determination of refractive index and scattering coefficient values in layered structures in skin and other tissues. Since its introduction in 1991 several research groups actively developed the OCT technique for many diagnostic applications. In its most basic configuration, OCT system consists of a Michelson interferometer excited by a low temporal coherence

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laser source, in-depth scanning system in the “reference” arm, an object under study in the “sample” arm, and registering photodiode at the output. Usually, the sample arm has additional scanning system that allows formation of cross-sectional twoand three-dimensional images of tissues. The interferometric signals in OCT system can be formed only when the optical path length in the sample arm matches that in the reference arm within the coherence length of the source. Therefore, the coherence length of the source and the group refractive index of tissues will determine the in-depth resolution of the OCT system [97]. Attenuation of light intensity for ballistic photons, I, in a medium with scattering and absorption is described by the Bouguer-Lambert law: I = I0 exp (−2µt z), where I0 is the incident light intensity, µt = µa + µs is the attenuation coefficient for ballistic photons, µs and µa are the scattering and absorption coefficients, respectively, and z is the tissue probing depth. Since absorption in tissues is substantially less than scattering ( µa ≪ µs ) in the NIR spectral range, the exponential attenuation of ballistic photons in tissue depends mainly on the scattering coefficient: I = I0 exp (−2µs z) [10]. Since the scattering coefficient of tissue depends on the bulk index of refraction mismatch, an increase in refractive index and the interstitial fluid and corresponding decrease in scattering can be detected as a change in the slope of fall-off of the depthresolved OCT amplitude [10, 97–99]. The permeability coefficient of drug and solutions in tissues can be measured by OCT system and calculated using two methods, OCT signal slope (OCTSS) and OCT amplitude (OCTA) measurements [20] (see also chapter 20). With the OCTSS method, the average permeability coefficient of a specific region in the tissue can be calculated by analyzing the slope changes in the OCT signal caused by analyte diffusion. For this two-dimensional OCT images have to be averaged in the lateral (xaxial) direction into a single curve to obtain an OCT signal that represented the onedimensional distribution of intensity in-depth. A region in the tissue, where the signal is linear and has minimal alterations, has to be selected, and its thickness (zregion ) has to be measured. Diffusion of the agents in the chosen region has to be monitored, and ¯ time of diffusion has to be recorded (tregion ). The average permeability coefficient (P) can be calculated by dividing the measuredthickness of the selected region by the  zregion [20]. time it took for the agent to diffuse through P¯ = tregion The OCTA method can be usedto calculate the permeability coefficient at specific depths in the tissues as P (z) = zi tzi , where zi is the depth at which measurements were performed (calculated from the front surface) and tzi is the time of agent diffusion to the depth. The tzi has to be calculated from the time agent was added to the tissue until agent-induced change in the OCT amplitude was commenced [20]. Using the methods, permeability coefficient of mannitol through rabbit cornea has been measured as (8.99 ± 1.43) × 10−6 cm/s [20]. The permeability coefficients of mannitol and 20% glucose solution through rabbit sclera are measured as (6.18 ± 1.08) × 10−6 and (8.64 ± 1.12) × 10−6 cm/s, respectively [20]. The permeability coefficient of 20% glucose solution through pig’s aorta tissue was found as (1.43 ± 0.24) × 10−5 cm/s [21]. The interferometric methods [52–54] are also based on measurements of refractive

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index variation. Holographic interferometry, electronic speckle pattern interferometry (ESPI), and digital holography have been successfully used to measure diffusion coefficients in liquids for binary systems and in membranes [54]. When applied to membranes, compared with traditional methods, ESPI offers the advantages of easily discriminating between a semi-permeable and a permeable membrane and the full control of experimental conditions gained by using a nonagitated cell [53]. For composite systems in which diffusion is one-dimensional, an interference pattern characterized by parallel fringes is obtained when an image taken during the diffusion process is subtracted from a reference image, usually obtained at time zero. In this case it is possible to obtain a concentration profile by using the position of the fringes. The diffusion coefficient can be calculated by fitting the concentration profile to a diffusion model like Fick’s law. Alternatively, an interference pattern characterized by two turning points is obtained by subtracting two images when fringes parallel to the direction of diffusion have been introduced during the diffusion coefficient [52]. When one concentration profile is subtracted from another, a typical concentration curve presenting a maximum and a minimum is obtained. The turning points of the interference pattern occur at a position where the maximum and the minimum of the concentration curve are located. The diffusion coefficient can be calculated by measuring the distance between the turning points. This second method offers the advantage of the faster calculation process, especially in the case when the diffusion problem can be solved analytically [54]. Using the method, Marucci et al. [54] measured the glucose diffusion coefficient in a model cellulose membrane and the diffusion coefficient is equal to (1.6 ± 0.15) × 10−7 cm2 /s.

19.6 Conclusion In this chapter we have reviewed the main experimental methods that are widely used for in vitro and in vivo measurements of glucose diffusion and permeability coefficients in human tissues. Importance of these investigations deals with glucose monitoring in the diagnosis and management of diabetes. Moreover, knowledge of the transport characteristics is very important for development of mathematical models describing interaction between tissues and drugs, and, in particular, for evaluation of the drug and metabolic agent delivery through the tissue. These methods are based on the spectroscopic and photoacoustic techniques, on the usage of radioactive labels for detecting matter flux, or on the measurements of temporal changes of the scattering properties of a tissue caused by dynamic refractive index matching including interferometric technique and optical coherence tomography. As discussed in section 19.2, the absorbance spectroscopy and photoacoustics (section 19.3) can be used for measurement of glucose diffusion coefficients in the NIR and mid-infrared spectral ranges; the technique based on refractive index

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matching (section 19.5) is of great importance for measurement of the glucose diffusion and permeability coefficients in the visible. Usage of radioactive labels for detecting matter flux (section 19.4) provides a powerful instrument for independent (reference) measurement of transport characteristics of glucose in tissues, because all spectral measurements depend on intrinsic tissue properties. Indeed, in this chapter we reviewed only the main methods of measurement of diffusion characteristics of various chemicals in tissues but these methods provide reliable basis for measurement of glucose diffusion characteristics in the tissues, and the obtained results can be used in diagnostics and therapy of different diseases related to glucose impact.

Acknowledgments This work has been supported in part by grants PG05-006-2 and REC-006 of U.S. Civilian Research and Development Foundation for the Independent States of the Former Soviet Union (CRDF) and the Russian Ministry of Science and Education, and grant of RFBR No. 06-02-16740-a. The authors thank Dr. S.V. Eremina (Department of English and Intercultural Communication of Saratov State University) for the help in manuscript translation to English.

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[78] K.M. Quan, G.B. Christison, H.A. MacKinzie, et al., “Glucose determination by a pulsed photoacoustic technique: an experimental study using a gelatinbased tissue phantom,” Phys. Med. Biol., vol. 38, 1993, pp. 1911-1922. [79] G.B. Christison and H.A. MacKenzie, “Laser photoacoustic determination of physiological glucose concentrations in human whole blood,” Med. Biol. Eng. Comp., vol. 31, 1993, pp. 284-290. [80] J.-L. Boulnois, “Photophysical processes in recent medical laser developments: a review,” Lasers Med. Sci., vol. 1, 1986, pp. 47-66. [81] R.E. Imhof, C.J. Whitters, and D.J.S. Birch, “Time-domain opto-thermal spectro-radiometry,” In Photoacoustic and Photothermal Phenomena II, J.C. Murphy, J.W. Maclachlan-Spicer, L. Aamodt et al. (eds.), Springer, Berlin, Heidelberg, 1990. [82] H. Schaefer and T.E. Redelmeier, Skin Barier: Principles of Percutaneous Absorption, Karger, Basel et al., 1996. [83] C.F. Bohren and D.R. Huffman, Absorption and Scattering of Light by Small Particles, Wiley, New York, 1983. [84] J.M. Schmitt and G. Kumar, “Optical scattering properties of soft tissue: a discrete particle model,” Appl. Opt., vol. 37, 1998, pp. 2788-2797. [85] Y. Huang and K.M. Meek, “Swelling studies on the cornea and sclera: the effects of pH and ionic strength,” Biophys. J., vol. 77, 1999, pp. 1655-1665. [86] V.V. Tuchin, Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis, vol. PM 166, SPIE Press, Bellingham, WA, 2007. [87] I.S. Saidi, S.L. Jacques, and F.K. Tittel, “Mie and Rayleigh modeling of visible-light scattering in neonatal skin,” Appl. Opt., vol. 34, 1995, pp. 74107418. [88] Y. Komai and T. Ushiki, “The three-dimensional organization of collagen fibrils in the human cornea and sclera,” Invest. Ophthal. Vis. Sci., vol. 32, 1991, pp. 2244-2258. [89] J.L. Cox, R.A. Farrell, R.W. Hart, et al., “The transparency of the mammalian cornea,” J. Physiol., vol. 210, 1970, pp. 601-616. [90] D.W. Leonard and K.M. Meek, “Refractive indices of the collagen fibrils and extrafibrillar material of the corneal stroma,” Biophys. J., vol. 72, 1997, pp. 1382-1387. [91] J.S. Maier, S.A. Walker, S. Fantini, et al., “Possible correlation between blood glucose concentration and the reduced scattering coefficient of tissues in the near infrared,” Opt. Lett., vol. 19, 1994, pp. 2062-2064. [92] M. Kohl, M. Esseupreis, and M. Cope, “The influence of glucose concentration upon the transport of light in tissue-simulating phantoms,” Phys. Med. Biol., vol. 40, 1995, pp. 1267-1287.

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[93] I.S. Grigoriev and E.Z. Meylikhov (eds.), Physical Values: Handbook, Moscow: Energoatomizdat, 1991. [94] L. Wang, S.L. Jacques, and L. Zheng, “MCML – Monte Carlo modeling of light transport in multi-layered tissues,” Comp. Meth. Progr. Biomed., vol. 47, 1995, pp. 131-146. [95] T.J. Farrell, M.S. Patterson, and B.C. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys., vol. 19, 1992, pp. 879-88. [96] J.G. Fujimoto and M.E. Brezinski, “Optical coherence tomography imaging,” in Biomedical Photonics Handbook, ed. T. Vo-Dinh, Chap. 13, CRC Press, Boca Raton, FL, 2003. [97] K.V. Larin, M. Motamedi, T.V. Ashitkov, et al., “Specificity of noninvasive blood glucose sensing using optical coherence tomography technique: a pilot study,” Phys. Med. Biol., vol. 48, 2003, pp. 1371-1390. [98] R.O. Esenaliev, K.V. Larin, I.V. Larina, et al., “Noninvasive monitoring of glucose concentration with optical coherence tomography,” Opt. Lett., vol. 26, 2001, pp. 992-994. [99] K.V. Larin, T. Akkin, R.O. Esenaliev, et al., “Phase-sensitive optical lowcoherence reflectometry for the detection of analyte concentrations,” Appl. Opt., vol. 43, 2004, pp. 3408-3414.

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20 Monitoring of Glucose Diffusion in Epithelial Tissues with Optical Coherence Tomography Kirill V. Larin Biomedical Engineering Program, University of Houston, Houston, TX 77204, USA; Institute of Optics and Biophotonics, Saratov State University, Saratov, 410012, Russia Valery V. Tuchin Institute of Optics and Biophotonics, Saratov State University, Saratov, 410012, Russia; Institute of Precise Mechanics and Control of RAS, Saratov 410028, Russia 20.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.2 Basic Theories of Glucose-Induced Changes of Tissue Optical Properties . . 20.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Functional imaging, monitoring, and quantification of glucose diffusion in epithelial and underlying stromal tissues in vivo as well as controlling of tissue’s optical properties are extremely important for many biomedical applications including development of noninvasive or minimally-invasive glucose sensors as well as for therapy and diagnostics of various diseases, such as cancer, diabetic retinopathy, and glaucoma. In order to obtain clinically acceptable accuracy and sensitivity of a noninvasive glucose biosensor, physiology and kinetics of glucose diffusion in tissues should be assessed in vivo. Difference in glucose diffusion rates in healthy and diseased tissues could potentially be used for development of novel early diagnostic methods. Furthermore, the selective translucence of the upper tissue layers is a key technique for structural and functional imaging, particular for detecting of local static or dynamic inhomogeneities hidden by a highly scattering medium. In this Chapter we describe recent progress made on developing of a noninvasive molecular diffusion biosensor based on Optical Coherence Tomography (OCT) technique. The diffusion of glucose and other macromolecules was monitored and quantified in several epithelial tissues both in vitro and in vivo. Due to capability of the OCT technique for depth-resolved imaging of tissues with high in-depth resolution, the molecular diffusion could be quantified not only as a function of time but also as a function of depth.

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Key words: glucose, permeability, noninvasive, depth-resolved, optical coherence tomography.

20.1 Introduction Development of noninvasive methods for functional imaging, monitoring, and quantification of glucose transport in epithelial tissues in vivo as well as controlling of tissue optical properties are extremely important for many biomedical applications including therapy, diagnostics, management, and advanced imaging of various devastating diseases, such as cancer, arteriosclerosis, diabetes, and glaucoma. Successful management of these diseases requires long-term treatment with drugs. In contrast to the traditional oral route, the use of topical and trans-dermal drug delivery by-passes first pass metabolism of the liver, the acidic environment of the gastrointestinal tract, and problems of pulsed absorption in the stomach. Topical drug delivery (TDD) through skin and ocular tissues is currently recognized as a preferred route for drug administration. Trans-dermal drug delivery is a promising route for drug administration because it is readily available, enables control of input, and can avoid many problems associated with the oral or intravenous routes (such as drastic pH changes, the presence of enzymes, variable transit times, and rapidly fluctuating drug plasma concentrations). However, one of the greatest disadvantages of this method is that a limited number of drugs could be administered this way due to skin’s protective functions. To improve permeability of skin, several penetration enhancers and specific procedures (e.g., heating and electrophoresis) can be applied [1–6]. Traditionally, in vitro methods have been used to assess skin absorption for different drugs [7]. Systematic in vivo study of trans-dermal drug delivery is required because physical, physiological, and optical properties of living tissues might be quite different from in post mortem tissues [8]. Significant recent advances have optimized delivery of drugs to target tissues within the eye for pharmacologic treatment and diagnostics of many ocular diseases [9]. Four main approaches are currently used to deliver drugs to different segments of the eye: systemic, intraocular, topical, and transscleral (Fig. 20.1). The success of systemic administration is governed by drugs’ convective transport through blood vessels, diffusion across blood-vessel walls, and through tissues of the eye. For effective treatment, large systemic doses are required to overcome these rate-limiting barriers [10]. However, frequent administrations of drugs in large doses often cause severe systemic side effects. Furthermore, large macromolecular drugs (larger than 40 kDa and globular molecules larger than 70 kDa) are unable to diffuse through the internal limiting membrane of the retina [11, 12]. Therefore, the systemic drug delivery route is not practical in some cases and is rarely used for treatment of ocular

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diseases. Intravitreal injections and intravitreal sustained-release implants provide the most direct approach for delivering therapeutic concentrations of drugs to eye tissues [13–16]. However, these approaches are essentially surgical procedures and require repeated injections. These invasive procedures frequently cause pain and have potential side effects of infection, retinal detachment, hemorrhage, endophthalmitis, and cataract [17, 18]. Topical drug delivery (TDD) through cornea and sclera of the eye is currently recognized as a preferred route for drug administration for treatment of many ocular diseases [19]. However, TDD is limited by the low permeability of the multilayered cornea and sclera, rapid clearance by tear drainage, and absorption into the conjunctiva. Recent advances in development of different TDD methods demonstrate improved ocular drug delivery by increasing drug contact time (e.g., by application of ointments, gels, liposome formulations, and various sustained and controlled-release substrates). The development of newer topical delivery systems using polymeric gels, colloidal systems, and cyclodextrins will provide exciting new therapeutics [20]. Therefore, more and more evidence suggests that corneal and transscleral TDD could be effective noninvasive methods for treatment of the eye disease and preferred ways of drug administration [19–25]. For example, human sclera has a high degree of hydration, a few protein binding sites, and its permeability does not decline with age [22, 23, 26, 27]. Cornea and sclera are permeable to a wide range of solutes with different molecular sizes [18, 21, 24, 25, 28–38]. All of these suggest that cornea and sclera are the ideal sites for the periocular drug delivery.

FIGURE 20.1: Ocular drug delivery routes.

Controlling of tissue optical properties is another important application of drug (or clearing agent) delivery into epithelial tissues [8, 39]. The turbidity of biological tissues can be effectively controlled by using optical immersion methods based on the concept of matching refractive indices of scatterers and ground material. This technique proved useful in contrasting images of a living tissue and getting more precise structural, functional, and spectroscopic information from tissue depths otherwise

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inaccessible with different optical techniques [8, 39–48]. Recently, a novel Optical Coherence Tomography (OCT)-based method for noninvasive assessment of glucose in animal and human tissues has been developed [49– 60] (see also chapter 18). This method is based on interferometric measurement and analysis of in-depth amplitude distribution of low-coherent light backscattered from specific layers of tissues. The preliminary studies in animals and human subjects demonstrated that this OCT-based method is capable of sensitive and rapid assessment of changes in glucose concentration measured in interstitial fluid (ISF) of skin. However, insufficient accuracy, variability in measured lag time between changes of glucose concentrations in blood and ISF, fundamental difficulties with development of proper calibration algorithm, and problems with repeatability might limit its application in homes and clinics. Several fundamental questions still exist such as “why there is variability in measured lag time between changes of glucose concentrations in blood and tissues?” and “where we have to measure in order to reduce the lag time and produce maximal signal-to-noise ratio?” In order to answer these questions, in vivo glucose diffusion coefficient in epithelial tissues must be known. Early diagnostics is required for successful treatment and therapy of various epithelial disorders [61–66]. Currently, many diseases are diagnosed by simple visual examinations. However, in addition to being subjective, this method could sometimes be a relatively inefficient predictor of epithelial diseases and, in some cases, it is not possible to diagnose a disease by visual examination without biopsy [67, 68]. Therefore, availability of a simple noninvasive objective method allowing early identification of different abnormalities with high degree of specificity and accuracy could enhance diagnosis of various human epithelial conditions and provide another option for physicians for diagnosis and/or monitoring therapy/disease progression. Since many diseases alter structural organization of tissues (e.g., by rearranging/modifying collagen organization and, thus, directly affecting transport properties for molecules in these tissues) changes in diffusion or permeability of different chemical compounds and organic solutions, including biologically inert glucose molecules, may help development of a novel objective method for diagnosis of different tissue diseases and abnormalities [69, 70]. Additionally, noninvasive, real time imaging and sensing of molecular diffusion can potentially monitor the in vivo distribution and pharmacokinetic properties of a drug delivery system. Optical-based techniques have great intrinsic potential to achieve the goal of noninvasive imaging, assessment, and treatment of different epithelial disorders. In the past few decades, different optical modalities have been extensively developed and applied in many areas of clinical practice ranging from cosmetic surgery to noninvasive histology [71], including spectrofluorometers and Ussing apparatus [18, 29, 35, 36, 72, 73], fluorescence microscopy [21, 74-78], Fourier-transform infrared spectroscopy (FTIR) [79-85], and Raman spectroscopy [81, 86-90]. However, each of these techniques have limitations for accurate and sensitive assessment of molecular transport due to low probing depth (microscopic, FTIR, and Raman techniques are limited to the first - that is the epidermis layer) and low in-depth resolution and requirement of dyes to enhance signal-to-noise ratio (spectroscopy, confocal and fluorescent microscopy). Structural imaging with OCT technique has a great potential

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for noninvasive assessment of normal and diseased tissues [91-106]. However, careful comparison of histometric data obtained by structural OCT and routine histology demonstrated unsatisfactory numerical agreement between the two methods [107]. Development of novel methods of analysis of OCT images [108] or combination with other (e.g., fluorescent) imaging techniques [105, 106, 109] might offer improvements in tissues imaging and classification. Recently, a few groups reported application of Magnetic Resonance Imaging (MRI) for the study of drug surrogate transport in ocular tissues in vivo [34, 110]. Results suggest that MRI might be a powerful tool for imaging and quantification of molecular distribution inside the eye. However, several drawbacks of this technology (such as the limited availability of actual molecules possessing paramagnetic properties, long time required for image acquisition and processing, and low resolution) limit its application for molecular and glucose diffusion studies in tissues. Permeability of sclera, cornea, and other ocular tissues for different molecular weight compounds was summarized by Prausnitz based solely on in vitro studies [38]. Currently, there is no technique capable of noninvasive imaging, monitoring, and quantification of diffusion of macromolecules through epithelial tissues in vivo, in real-time, and with high resolution. In this chapter we demonstrate results on our recent efforts for development of instrumentation, based on OCT, capable of realtime, sensitive, accurate, and noninvasive assessment of topical molecular diffusion in epithelial tissues that is of great scientific, clinical, and pharmacological importance.

20.2 Basic Theories of Glucose-Induced Changes of Tissue Optical Properties An important ability of a chemical compound (agent) to change the tissue scattering properties is based on a number of biophysical processes [39, 47, 49, 50, 52, 111-113]. The concept of two fluxes — agent into tissue and bulk tissue water out, which may be relatively independent or interacting fluxes — defines the dynamic properties of tissue optical properties [113]. For example, diffusion of optical clearing agent (OCA) inside tissue to interstitial space leads to increase of refractive index of the interstitial fluid (ISF), thus to refractive index matching of collagen fiber (and other tissue components — scatters) and ISF. A hyperosmotic OCA may induce an intensive water flow from tissue, thus may cause its strong dehydration and corresponding alteration of tissue morphological and optical properties by: • refractive index matching/mismatching (generally for whole tissue matching and locally mismatching may take place), • increase of tissue collagen fibers packing density (ordering of scatterers), • and decrease of tissue thickness.

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Tissue collagen reorganization also may take place [112]. The scattering coefficient of tissues depends on the refractive index, n, mismatch between the ISF and the tissue components (fibers, cell components). In a simple model of scattering dielectric spheres, the reduced scattering coefficient, µs′ = µs (1 − g), where g is the tissue anisotropy factor, can be approximated as [114]

µs′

2

= 3.28π r ρs



2π r λ

0.37 

ns nmedium

2.09 −1 ,

(20.1)

where r is the sphere radius, ρs the volume density of the spheres, λ the wavelength of the incident light, and ns and nmedium the refractive indices of the scattering centers and the surrounding medium, respectively. If the refractive index of the scattering centers remains constant and is higher than the refractive index of the medium, the increase of the drug concentration in the medium reduces the refractive index mismatch, ∆n = ns − nmedium , and, hence, the scattering coefficient is also reduced:

µs′

2

= 3.28π r ρs



2π r λ

0.37 

2.09 ns , −1 nmedium + δ nagent

(20.2)

where δ nagent is the agent (glucose)-induced increase of nmedium . Therefore, increase of tissue glucose concentration will raise the refractive index of the ISF that will decrease the scattering coefficient of the tissue as a whole. Note that these equations are derived from Mie theory of light scattering on dielectric spheres and, strictly speaking, do not fully describe complexity of light-tissues interaction. However, they are frequently used as the first approximation and utilized here to demonstrate the effect. More rigorous approximation of light-tissue interaction requires Monte Carlo calculations (described in, e.g., [115–119]). Alternatively, the change in local concentrations of scattering particles such as cell components or collagen fibers could change scattering as well. Tissues mean refractive index can be calculated by the law of Gladstone and Dale as a weighted average of refractive indices of interstitial fluid (nISF ) and collagen fibers or cell components (nc ): n¯ = φc nc + (1 − φc)nISF ,

(20.3)

where φc is the volume fraction of collagen fibers and/or cell components in tissues. Therefore, changes in the volume fraction of tissue components φc (e.g., by shrinkage or swelling of the tissues) will change the overall refractive index of the tissues. A micro-optical model developed by Schmitt and Kumar [120] can be used to describe optical clearing effects caused by tissue dehydration (tissue shrinkage), because it treats the tissue as a collection of differently sized scattering particles with distribution function modified to account for correlated scattering among densely packed particles. Assuming that the waves scattered by the individual particles in a thin slice of the tissue volume add randomly, then the scattering coefficient and scattering anisotropy factor of the volume can be approximated as the following expressions [120]:

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Np

∑ µs (2ai )gi (2ai )

Np

η (2ai ) σs (2ai ), vi i=1

µs = ∑

g=

i=1 Np

(20.4)

∑ µs (2ai ) i=1

where N p is the number of particle diameters; η (2ai ) is the volume fraction of particles of diameter 2ai ; σs (2ai ) is the optical cross section of an individual particle with diameter 2ai and volume νi . At the limit of an infinitely broad distribution of particle sizes,

η (2a) ≈ (2a)3−D f

,

(20.5)

where D f is the (volumetric) fractal dimension; for 3 < D f < 4, this power-law relationship describes the dependence of the volume fractions of the subunits of an ideal mass fractal on their diameter 2a. To account for the interparticle correlation effects which are important for systems with volume fractions of scatters higher than 1-10% (dependent on particle size), the following correction should be done [120]:

η (2a) →

[1 − η (2a)] p+1 η (2a), [1 + η (2a)(p − 1)] p−1

(20.6)

where p is the packing dimension that describes the rate at which the empty space between scatters diminishes as the total density increases. For spherical particles p = 3, for rod-shaped and sheet-like particles p → 2 and 1, respectively. Since the elements of tissue have all of these different shapes and may exhibit cylindrical and spherical symmetry simultaneously, the packing dimension may lie anywhere between 1 and 5. Since the OCT technique measures the in-depth light distribution with high resolution, changes in the in-depth distribution of the tissue scattering coefficient and/or refractive index are reflected in changes in the OCT signal [49–52, 121–124]. Thus, because the diffusion of macromolecules in tissues introduces local changes in their optical properties (scattering coefficient and refractive index), one can monitor and quantify the diffusion process by depth-resolved analyses of the changes in the OCT signal recorded from a sample.

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20.3 Experimental Results 20.3.1 Materials and methods Encouraging results have been obtained on monitoring and quantifying diffusion of glucose and other molecules in various epithelial tissues (such as cornea and sclera of the eye, skin, and coronary artery) with OCT [121–128]. The experiments were performed by using a time-domain OCT system. The optical source used in this system is a low-coherent broadband, near-infrared (NIR) light source with wavelength of 1310±15 nm and output power of 3 mW (Superlum Inc, Russia). Light scattered from a sample and light reflected from reference arm mirror formed an interferogram, which was detected by a photodiode. In-depth scanning was produced electronically by piezo-electric modulation of the fiber length. Two-dimensional images were obtained by scanning the incident beam over the sample surface in the lateral direction and in-depth (Z-axial) scanning by the interferometer. The acquired images were 450 by 450 pixels (Fig. 20.2 a, c). The in-depth scanning was up to 2.2 mm, while the lateral scanning was 2.4 mm. The full image acquisition rate was approximately 3 sec per image. The 2D images were averaged in the lateral direction (over ≈ 1 mm, that was sufficient for speckle-noise suppression) into a single curve to obtain OCT signal that represents 1D distribution of light in depth in logarithmic scale (Fig. 20.2b, d). Ex vivo and in vitro experiments were performed with rabbit and monkey eyes and porcine skin and coronary artery. Pilot in vivo experiments were performed on monkey’s skin. The experiments were performed within 24 hours after tissue nucleation. Tissues were kept cooled in a solution of appropriate physiological saline during transportation and storage. Right before ex vivo and in vitro experiments, the tissues were placed in a specially designed dish containing a physiological saline of normal room temperature. All experiments were performed at 22◦ C. Continuous monitoring of tissue optical properties upon application of different molecules was performed for up to 2–2.5 hours. After experiments, the tissues were placed in ∼200 mL physiological solution and stored at +4◦ C for 12–24 hours. The eye tissues were used in no more than two experiments while arteries and skin were used only once. Three experimental protocols were utilized during ex vivo and in vitro experiments (Fig. 20.3): Isolated tissues. The tissues were carefully isolated by cutting in a dissecting dish (the tissues were always kept in physiological solution of room temperature during isolation procedures). For eyes, the anterior ciliary body was separated from the sclera and cornea by running forceps between these tissues. Isolated sclera and cornea samples and skin were placed on a specially designed holder for the experiments. Laser beam was directed perpendicular to the tissues’ epithelium surface. The tissues were kept partially hydrated by placing endothelial surface in physiological solution. A single application of a droplet of an agent to the tissues’ surface at the site of laser beam was performed at 4–10 min after the onset of the experiment.

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FIGURE 20.2: Typical OCT images and corresponding 1D signals recorded from rabbit cornea ((a) and (b)) and human skin ((c) and (d)). Whole eyeball experiments (partially submersed). Diffusion of glucose and other molecules in sclera and cornea was studied in whole eyeballs partially submersed in physiological solution. Laser beam was directed perpendicular to the tissues’ epithelium surface. To avoid dehydration during experiments, the tissues were kept partially hydrated by placing whole eyeball in physiological solution except a small (∼ 1 cm2 ) area where diffusion studies were performed. A single application of a droplet of an agent to the tissues surface at this site was performed at 4–10 min after the onset of the experiment. Whole eyeball experiments (fully submersed). Diffusion of different molecules in sclera and cornea was studied in whole eyeballs fully submersed in physiological solution of known volume. Laser beam was directed perpendicular to the tissues’ epithelium surface. The agents were dissolved in the physiological solution and the final concentrations were calculated (e.g., 20 mL of 40% glucose added to 20 mL

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of glucose-free physiological solution resulted in 20% glucose final concentration). All indicated concentrations in this chapter are the final concentrations applied to the epithelial surface of the tissues. The concentration of the agents in the solution was assumed to remain constant during described experiments. The permeability coefficients of molecules in tissues were calculated by using two different methods: OCT signal slope (OCTSS) and amplitude (OCTA) methods (Fig. 20.4). The OCTSS method was used to calculate the average permeability coefficient P¯ of tissue stroma. The P¯ was computed by dividing the thickness of the region used to calculate the OCTSS (typically,around 155–255 µ m) by the time of agents’ diffusion inside this region P¯ = zregion tregion . Since diffusion of molecules reflected in changes of the OCTSS and the signals were relatively constant before application of an agent and after saturation, tregion was calculated as the time when the saturation stage was reached minus the time when the OCTSS started to change. The OCTA method of measurements was used to calculate the permeability coefficient  at the specific depths in the tissues as P(z) = zi tzi , where zi - the depth at which measurements were performed (calculated from the front surface) and tzi - the time of agent diffusion to this depth. The tzi was calculated from the time agent was added to the tissue until agent-induced change in the OCT amplitude was commenced. Note that unlike in OCTSS method, the zi was calculated from epithelial surface of tissues to the specific depth in tissues’ stroma in OCTA.

FIGURE 20.3: Three experimental protocols during in vitro experiments with animal tissues (a) isolated tissues; (b) partially submersed whole eyeballs; and (c) fully submersed whole eyeballs.

20.3.2 Quantification of molecular diffusion in ocular tissues (cornea and sclera) in vitro Figure 20.5 shows an example of typical results obtained from isolated rabbit sclera during water diffusion experiments. The OCT signal slope was calculated

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FIGURE 20.4: Schematic diagram showing basic principles of two methods used to calculate molecular permeability coefficients: OCT Signal Slope (calculating the average permeability coefficient in tissues’ stroma and computed by dividing the thickness to the time — denoted by rectangle) and OCT Amplitude (calculating permeability coefficient at different depths, thickness from epithelial layer to particular depth, time is computed from instant agent was added until agent-induced change in the OCT amplitude was commenced — denoted by bars and arrows).

from 279 µ m region at scleral depth of approximately 105 µ m from the surface. A single application of a water droplet to the scleral surface was performed at fifth minute after the onset of the experiment. The propagation of water inside the sclera changed the local scattering coefficient and it was detected by OCT. The increase in local in-depth water concentration resulted in the decrease of the OCT signal slope during the hydration process and vice versa during passive scleral dehydration (due to exposure of the sclera surface to air). The calculated water permeability rate, w P¯isolated , was approximately 6.6×10−5 cm/s in this experiment. Typical results obtained during water and dexamethasone diffusion experiments in rabbit isolated cornea are shown in Fig. 20.6 and Fig. 20.7, respectively. The OCT signal slopes were calculated from 314 µ m region at corneal depth of approximately 100 µ m from the epithelial surface. A single droplet of agents was applied at fifth minute after the onset of the experiment to the corneal surface. The calculated water and dexamethasone permeability rates were approximately 9.5×10−5 and 5.2×10−5 cm/s, respectively. OCT signal slope as a function of time recorded from cornea (partially submersed whole eyeballs experiments) during water diffusion experiment is shown on Fig. 20.8. The OCT signal slopes were calculated from 280 µ m region at corneal depth of approximately 100 µ m from the epithelial surface. The permeability coefficient in this experiment was 1.86×10−5 cm/s. OCT signal slope as a function of time

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FIGURE 20.5: OCTSS as a function of time recorded from isolated sclera during water diffusion experiment. The arrow in this and all similar graphs indicates time of added agents.

FIGURE 20.6: OCTSS as a function of time recorded from isolated cornea during water diffusion experiment.

recorded from sclera in fully submersed whole eyeballs experiments during glucose and mannitol diffusion experiment are shown in Figs. 20.9 and 20.10, respectively. The calculated glucose and mannitol permeability coefficients were approximately 1.0×10−5 and 6.84×10−6 cm/s, respectively. Fifty five experiments were performed with different sclera and 52 with different rabbit cornea. Molecular permeability rates for all experiments with ocular tissues are described in [123]. These results correlate with coefficients published in earlier studies. For example, the permeability coefficient of ciprofloxacin in rabbit sclera

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FIGURE 20.7: OCTSS as a function of time recorded from isolated cornea during dexamethasone diffusion experiment.

FIGURE 20.8: OCTSS as a function of time recorded from cornea (partially submersed whole eyeballs experiments) during water diffusion experiment.

was measured to be 1.88±0.62×10−5 cm/sec [129]. Results for glucose diffusion are in a good correlation with results for human sclera [130]. Comparing results from cornea and sclera, one can note that the permeability coefficients for the same molecules in the cornea and sclera are different. This discrepancy is likely due to the structural and physiological differences. Hydration is also considered a key factor in the study of permeability coefficients of agents through biological tissues. With hydration the fibrils move further apart creating extra space between them [131]. Swelling could come from the glycosaminoglycan (GAGs) or from anion bindings occurring in the tissue [132, 133]. The sclera has 10 times less GAGs than the cornea and the scleral stroma has a greater degree of fibrillar interweave than corneal stroma [134]. Thus, even though the cornea swells to many times its original weight in aqueous solution, the hydration of sclera increases only

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FIGURE 20.9: OCTSS as a function of time recorded from sclera (fully submersed whole eyeballs experiments) during glucose diffusion experiment.

FIGURE 20.10: OCTSS as a function of time recorded from sclera (fully submersed whole eyeballs experiments) during mannitol diffusion experiment.

20–25% [132]. It has been demonstrated that permeability coefficient is proportional to the tissues’ hydration state. As the hydration in a tissue increases, the permeability coefficient increases as well [135].

20.3.3 Quantification of glucose diffusion in skin in vitro Figure 20.11 shows a typical result from glucose diffusion studies in pig skin in vitro. The calculated permeability coefficient was approximately 8.95×10−6 cm/s in this experiment. Average glucose permeability in pig skin in vitro was 7.69±0.56× 10−6 cm/s calculated from 5 independent experiments.

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FIGURE 20.11: OCTSS as a function of time recorded from pig skin (in vitro) during glucose diffusion experiment.

20.3.4 Quantification of glucose diffusion in skin in vivo Figure 20.12 shows results obtained for glucose (20%) diffusion experiments in rhesus monkey (Macaca mulatta) skin in vivo. Even though typical skin layers of monkeys are thinner than that of humans (e.g., thickness of epidermal skin layer is around 10–30 µ m in monkeys and 50–100 µ m in human), the anatomy and physiology are similar. All animal procedures were performed per protocol approved by University of Houston animal care committee. The animals were anesthetized according to the protocol. The animals were positioned and stabilized in a specially designed holder to restrict movements. OCT signals were obtained from monkeys’ skin at dorsal area. The area of OCT measurements was gently shaved and OCT probe was attached by using special holder and taped (double-side tape) to the skin. An application of 20% glucose solution (∼1 mm3 ) to the skin was performed at 10– 15 min after onset of the experiment at the site of OCT imaging. In-depth changes of glucose concentration in skin were reflected in changes of OCT signal slope (Fig. 20.12). Calculated average glucose permeability from 5 independent experiments in skin in vivo was 2.32±0.2×10−6 cm/s.

20.3.5 Quantification of glucose diffusion in healthy and diseased aortas in vitro Interesting results have been obtained on quantification of glucose diffusion in healthy and arteriosclerotic pig aortas in vitro. Aortic tissues harvested from hypercholesterolemic pigs were surgically removed and experiments were conducted within 2 hours. The aortas were cut sagittally to create a sheet which was then cut to approximately 1 cm2 square samples with and without arteriosclerosis. Figures 20.13a,b show the 2D OCT images of a normal pig aortic tissue and an aortic tissue with early atherosclerosis, respectively. Typical results obtained from the H&E histological examination of aortas on the same area of OCT imaging are

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FIGURE 20.12: OCTSS as a function of time recorded from monkey skin (in vivo) during glucose diffusion experiment.

FIGURE 20.13: (a) and (c) OCT and histology images of a normal pig aorta, respectively; (b) and (d) are the OCT and histology images from an atherosclerotic lesion

shown in Fig. 20.13c-d. Vertical view of normal tissues (Fig. 20.13c) shows the layers look compact and with a normal distribution (note that the endothelium is in one single cell layer, as it should be). In comparison, Fig. 20.13d, which represents the thinnest sample from diseased sections, can be seen with significant neointimal thickening.

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Figure 20.14a represents a typical OCTSS graph for a normal pig aorta during glucose diffusion experiment. The region monitored was about 70 µ m in thickness and 157 µ m away from the epithelial layer. The OCTSS decreased due to the reduction of scattering within the tissue caused by the local increase of glucose concentration. Glucose solution reached the monitored region approximately 20 minutes after administration and took another 20 minutes for it to completely diffuse through. At that point, a reverse process in the OCTSS was shown. This change in the slope could be due to diffusion via concentration gradient differences on either side of the tissue; the net fluid (mainly water) movement from areas of high concentration to those of lower concentration would occur until equilibrium is reached. The permeability coefficient of glucose-20% from 4 different experiments was found to be (6.80±0.18)×10−6 cm/sec. Figure 20.14b displays an atherosclerotic pig aorta tissue OCTSS graph during a glucose diffusion experiment. The same procedure was implemented as the normal tissues experiments. The specimen was imaged for about 7 minutes before glucose was added to the saline bath. The region selected in the diseased tissue was about 140 µ m thick and 70 µ m from the epithelial layer. Diffusion of glucose in the monitored region started about 7 minutes from the onset of diffusion. The same reverse process occurred 12 minutes later. The permeability coefficient of glucose-20% in atherosclerotic aorta tissues was (2.69±0.42)×10−5 cm/sec (n = 7).

FIGURE 20.14: Typical OCTSS graph as a function of time recorded from a normal (a) and diseased (b) places of a pig aorta sample.

The results from this study indicate that atherosclerotic tissue had a higher permeability coefficient compared to that of healthy arterial regions (Fig. 20.15). These findings support the hypothesis that this OCT-based functional imaging method could measure glucose permeability coefficient as well as to distinguish among normal and abnormal regions of the tissues. The increased rate at which glucose diffused into the atherosclerotic tissue could

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FIGURE 20.15: Glucose permeability coefficients measured in normal and diseased aorta samples.

be explained anatomically. Low-Density Lipoproteins (LDL) usually diffuse through the different layers of the aortic tissue to reenter circulation but at times can become trapped inside the intima. Inside the intima, the LDL’s undergo oxidation and become modified. Macrophages migrate between the endothelial linings of the intima and start taking up the modified LDLs where they become engorged. This can lead to foam cell formation and eventually lead to an accumulation of plaque that protrudes into the lumen of the aorta. As the atherosclerotic plaque increases in size over time, the elastic tissues that form the aortic layers expand in order to compensate for the blockage and maintain adequate blood flow throughout the body. The expansion of the aorta could cause the numerous cells, fibers, and tissues of the aorta to readjust their organization. From that organizational change, glucose could find the tissue easier to diffuse through. This expansion could explain the observed increase in the permeability coefficient of glucose with atherosclerotic tissue. The structural OCT images from our experiments did not allow effective differentiation of normal from diseased tissues (see Fig. 20.13). However, the functional images provided by the OCT enabled effective distinguishing of normal and abnormal tissue regions (Fig. 20.15). This information could significantly increase the specificity and accuracy of tissue classification and further OCT’s use in clinical imaging. It is possible that functional imaging using OCT could potentially differentiate even further the different components contained in advanced atherosclerotic lesions such as necrotic core and collagen.

20.3.6 Comparative studies for assessment of molecular diffusion with OCT and histology Recently, comparative studies for monitoring of dye diffusion with OCT and standard histological examination have been performed. Experiments with OCT were performed as described above but tetramethylrhodamine dextran (TMR-D) dye was used. Typical result obtained during TMR-D diffusion experiment in coronary artery is shown in Fig. 20.16a. A single drop of 0.5% TMR-D dye (MW 10 kDa) was applied to the endothelial surface of healthy porcine aorta at the eighth minute after on-

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set of the experiment. Diffusion of dye inside aorta dynamically changed absorption coefficient and was commenced by increase of OCTSS. The calculated permeability OCT rate, P¯TMR−D , was 3.16×10−6 cm/s in this experiment. Four experiments were performed with coronary aorta from different pigs yielding average permeability rate of 3.04± 0.3×10−6 cm/s. Standard histological examination of time-dependent diffusion of TMR-D dye was performed in porcine aorta. An artery was cut in 6 or 7 previously defined segments (∼ 1 cm2 ). After adding a droplet of the dye (same concentration as above), each piece was left standing for its given time: 30 minutes, 60 minutes, and so on up to 180 minutes (as in previous experiments with OCT, the epithelial sides were submersed in saline to prevent dehydration of tissues). After the given time, the tissue R was placed in the center of a Shandon Cryotome SME Cryocassette and left to completely freeze in about 15 to 20 seconds. After completely frozen, the cryocasR sette was placed in a cryogenic slicing machine, Shandon Cryotome FSE, and each specimen was in-depth sliced down to about 14 microns in width. Standard fluorescent microscope was used to capture in-depth dye distribution (Fig. 20.16 b-h). The permeability of TMR-D dye was calculated by dividing penetration depth (from fluorescent images) on the time the dye allowed to diffuse. The average permeability coFluo efficient of TMR-D dye in porcine aorta, P¯TMR−D , was found to be 2.07×10−6 cm/s Fluo in these experiments. The P¯TMR−D value is close to that obtained by OCT technique OCT ¯ (PTMR−D ).

FIGURE 20.16: a) OCT signal slope as a function of time recorded from pig aorta during TMR-D dye diffusion experiment. b)-h) permeability of TMR-D dye captured by a fluorescent microscope. All images were obtained from the same porcine aorta and were all imaged with the same amount of TMR-D dye. The meter bar in the lower right hand corner of the images equal to 0.14 mm.

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20.3.7 Assessment of optical clearing of ocular tissues with OCT As we mentioned above, OCT has many advantages over other popular imaging systems such as X-ray, MRI, and Ultrasound in terms of safety, cost, contrast, and resolution. However, lack of penetration depth into tissue is the main drawback of OCT. The turbidity of most biological tissues could prevent the ability of OCT to be fully engaged in various diagnostic and therapeutic procedures. In these experiments, we studied diffusion of glucose in tissues for its dual exploitation: depth-resolved quantification of its permeability as well as creating a “clearer” medium which could assist in achieving higher depth penetration and, thus, enhancing diagnostic possibilities of light-based techniques. The permeability coefficient of glucose was calculated in two different regions in the rabbit sclera: the upper 80–100 µ m which constitutes a layer that includes the episclera and the following 100 µ m region (which is thought to be in the stroma or the second layer). From five independent experiments, the permeability coefficient of glucose was found to be (6.01 ± 0.37) × 10−6 cm/sec in the upper region and (2.84 ± 0.68) × 10−5 cm/sec in the lower one. Additionally, the clearing effect of glucose on the sclera was computed using the OCT amplitude signal at different depths in the tissue during the diffusion process. The amplitude at a certain location inside the tissue was monitored during the diffusion process and the change in the light signal was observed (Fig. 20.17 represents an OCT signal graph acquired at about 80 µ m away from the epithelial layer of the rabbit sclera); thus, the percent of optical clearing was calculated. The percentage of the clearing was estimated using the formula: %clearing = 100 × (I1 − I2 )/I1 , where I1 and I2 are the OCT signal amplitude values for the selected location before glucose started diffusing and after it had penetrated through, respectively (see Fig. 20.17). Figure 20.18 summarizes the percent clearing of a rabbit sclera with glucose 40% measured at different depths in the two selected regions. Roughly, the first 100 µ m cleared around 10% while the deeper 100 µ m region cleared about 17–22% in these experiments. The presented results and experiments suggest capability of OCT technique for quantifying the permeability coefficient of glucose and its clearing effect in different layers of rabbit sclera. Additionally, our study suggests that more clearing is occurring in the inner region than in the upper one. The disparity in the collagen fibril sizes among the various layers in the sclera could have been the main reason for the dissimilarity in the clearing effect among different regions in the tissue. The structures of the different layers could have also been another source of differentiation in the optical clearing. The refractive index mismatch between the mitochondria, cytoplasm, cell membrane, extracellular media, and its components such as collagen and elastin fibers could be the major source of scattering. Penetration of glucose in the episclera could have been mainly through the intracellular spaces; thus less glucose enters the cells and matches its organelles inside to the surrounding environment. The results for clearing in the rabbit stroma correlated well with previous studies.

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FIGURE 20.17: Typical OCT signal graph as a function of time recorded from about 80 µ m away from the epithelial layer of rabbit sclera during glucose 40% diffusion experiment where I1 and I2 value are about 0.98 at 0.87, respectively.

FIGURE 20.18:

Optical clearing at different depth in a rabbit sclera.

20.3.8 Depth-resolved assessment of glucose diffusion in tissues OCT technique has some unique properties that distinguish it from other optical imaging modalities. Among those are high resolution and ability for noninvasive depth-resolved imaging. These properties allowed investigating glucose diffusion not only as a function of time but also as a function of depth. Using OCT system, we quantified diffusion of different analytes at various depths away from the surface

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of tissues. Figures 20.19 and 20.20 show typical permeability coefficients of glucose measured at different depths in a sclera with OCTA method. These figures show that the glucose diffusion rate inside epithelial multilayered tissues is non-linear and is increased (with saturation) with tissue depth. This non-linearity is due to glucose diffusion through at least two layers: epithelium (slow diffusion) and stroma (faster diffusion). Different inclusions of these two processes at different time intervals affect the calculated permeability coefficients and we believe is the major source for such non-linearity. The layered structure of the tissues, the difference in the diameter sizes of the collagen fibers in each layer, and the diverse organizational patterns of the collagen bundles at different depths are likely to contribute to the observed trend. For instance, the sclera has three distinct layers including episclera, the stroma, and lamina fusca. The outer layer, the episclera, primarily consists of collagen bundles that intersect at different angles along the surface of the sclera. That inconsistency of the organization of the collagen bundles imposes a resistance force that reduces the speed of penetration of the drugs into the tissue, thus resulting in lower permeability coefficient of the agent. In the stroma and the lamina fusca, the collagens are more organized and oriented in two patterns: meridianally or circularly. This attributes to increased permeability in the stroma. Additionally, the collagen bundles differ in size throughout the different layers of the sclera: the collagen bundles in the external region of the sclera are narrower and thinner than those in the inner region. The different diameters of the collagen fibers in different tissue depths might also influence the diffusion in tissues.

FIGURE 20.19: OCT signal as a function of time recorded at different depths during glucose diffusion experiment in the sclera. Arrows indicate glucose front reaching different depths.

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FIGURE 20.20: Glucose permeability coefficients measured at different depths in the sclera. The average standard deviation for the permeability coefficients was ±0.29 × 10−6 cm/sec.

Acknowledgments The authors would like to acknowledge contribution of number of graduate and undergraduate students to the presented results, including Mohamad Ghosn, Steven Ivers, Natasha Befrui, Esteban Carbajal, and Narendran Sudheendran (University of Houston). The study was supported in part by grants from W. Coulter Foundation and Office of Naval Research (KVL) and Federal Agency of Education of Russian Federation and CRDF BRHE (VVT).

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pression of contact hypersensitivity response,” Pol. J. Pathol., vol. 56, 2005, pp. 155-160. [68] A.J. Sober, “Diagnosis and management of skin cancer,” Cancer, vol. 51, 1983, pp. 2448-2452. [69] L. Mastropasqua, M. Nubile, M. Lanzini, P. Carpineto, L. Toto, and M. Ciancaglini, “Corneal and conjunctival manifestations in Fabry disease: In vivo confocal microscopy study,” Am. J. Ophthalmol., vol. 141, 2006, pp. 709-718. [70] K. Koga, Y. Ishitobi, S. Kawashima, M. Taniguchi, and M. Murakami, “Membrane permeability and antipyrine absorption in a rat model of ischemic colitis,” Int. J. Pharm., vol. 286, 2004, pp. 41-52. [71] J. Serup, B. E. Jemec, and G.L. Grove, Handbook of Non-invasive Methods and the Skin, 2nd ed., Boca Raton, London, 2006. [72] C.W. Lin, Y. Wang, P. Challa, D.L. Epstein, and F. Yuan, “Transscleral diffusion of ethacrynic acid and sodium fluorescein,” Mol. Vis., vol. 13, pp. 243251. [73] J.A. Gilbert, A.E. Simpson, D.E. Rudnick, D.H. Geroski, T.M. Aaberg, and H.F. Edelhauser, “Transscleral permeability and intraocular concentrations of cisplatin from a collagen matrix,” J. Control Release, vol. 89, 2003, pp. 409417. [74] T.W. Kim, J.D. Lindsey, M. Aihara, T.L. Anthony, and R.N. Weinreb, “Intraocular distribution of 70-kDa dextran after subconjunctival injection in mice,” Invest. Ophthalmol. Vis. Sci., vol. 43, 2002, pp. 1809-1816. [75] J.D. Lindsey and R.N. Weinreb, “Identification of the mouse uveoscleral outflow pathway using fluorescent dextran,” Invest. Ophthalmol. Vis. Sci., vol. 43, 2002, pp. 2201-2205. [76] S. Langer, O. Goertz, L. Steinstraesser, C. Kuhnen, H. U. Steinau, and H. H. Homann, “New model for in vivo investigation after microvascular breakdown in burns: use of intravital fluorescent microscopy,” Burns, vol. 31, 2005, pp. 168-174. [77] S. Langer, D. Nolte, M. Koeller, H.U. Steinau, A. Khandoga, and H.H. Homann, “In vivo visualization of platelet/endothelium cell interaction in muscle flaps,” Ann. Plast. Surg., vol. 53, 2004, pp. 137-140. [78] S. Langer, F. Born, A. Breidenbach, A. Schneider, E. Uhl, and K. Messmer, “Effect of C-peptide on wound healing and microcirculation in diabetic mice,” Eur. J. Med. Res., vol. 7, 2002, pp. 502-508. [79] D. Bello, T.J. Smith, S.R. Woskie, R.P. Streicher, M.F. Boeniger, C.A. Redlich, and Y.C. Liu, “An FTIR investigation of isocyanate skin absorption using in vitro guinea pig skin,” J. Environ. Monit., vol. 8, 2006, pp. 523-529.

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[80] J.J. Escobar-Chavez, D. Quintanar-Guerrero, and A. Ganem-Quintanar, “In vivo skin permeation of sodium naproxen formulated in pluronic F-127 gels: Effect of Azone (R) and Transcutol (R),” Drug Dev. Ind. Pharm., vol. 31, 2005, pp. 447-454. [81] S. Wartewig and R.H.H. Neubert, “Pharmaceutical applications of Mid-IR and Raman spectroscopy,” Adv. Drug Deliv. Rev., vol. 57, 2005, pp. 11441170. [82] C. Laugel, N. Yagoubi, and A. Baillet, “ATR-FTIR spectroscopy: a chemometric approach for studying the lipid organization of the stratum corneum,” Chem. Phys. Lipids, vol. 135, 2005, pp. 55-68. [83] Q. B. Li, Z. Xu, Y. Z. Xu, Y.F. Zhang, N.W. Zhang, L.X. Wang, X.J. Sun, L. Zhang, F. Wang, L. M. Yang, Y. Zhao, Y. Ren, Z. Liu, S. F. Weng, W. J. Zhou, and J.G. Wu, “Application of Fourier transform infrared spectroscopy to non-invasive detection of breast tumor in vivo and in situ,” Chem. J. Chinese Univer.-Chinese, vol. 25, 2004, pp. 2010-2012. [84] I. Notingher and R.E. Imhof, “Mid-infrared in vivo depth-profiling of topical chemicals on skin,” Skin Res. Technol., vol. 10, 2004, pp. 113-121. [85] C. Curdy, A. Naik, Y.N. Kalia, I. Alberti, and R.H. Guy, “Non-invasive assessment of the effect of formulation excipients on stratum corneum barrier function in vivo,” Int. J. Pharm., vol. 271, 2004, pp. 251-256. [86] J.T. Motz, M. Fitzmaurice, A. Miller, S.J. Gandhi, A.S. Haka, L.H. Galindo, R.R. Dasari, J.R. Kramer, and M.S. Feld, “In vivo Raman spectral pathology of human atherosclerosis and vulnerable plaque,” J. Biomed. Opt., vol. 11, 2006, 021003-1-9. [87] J.T. Motz, S.J. Gandhi, O.R. Scepanovic, A.S. Haka, J.R. Kramer, R.R. Dasari, and M.S. Feld, “Real-time Raman system for in vivo disease diagnosis,” J. Biomed. Opt., vol. 10, 2005, 031113-1-7. [88] B.R. Hammond and B.R. Wooten, “Resonance Raman spectroscopic measurement of carotenoids in the skin and retina,” J. Biomed. Opt., vol. 10, 2005, 054002-1-12. [89] Z.W. Huang, H. Lui, D.I. McLean, M. Korbelik, and H.S. Zeng, “Raman spectroscopy in combination with background near-infrared autofluorescence enhances the in vivo assessment of malignant tissues,” Photochem. Photobiol., vol. 81, 2005, pp. 1219-1226. [90] M.E. Darvin, I. Gersonde, M. Meinke, W. Sterry, and J. Lademann, “Noninvasive in vivo determination of the carotenoids beta-carotene and lycopene concentrations in the human skin using the Raman spectroscopic method,” J. Phys. D: Appl. Phys., vol. 38, 2005, pp. 2696-2700.

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[91] D.L. Farkas and D. Becker, “Applications of spectral imaging: detection and analysis of human melanoma and its precursors,” Pigment. Cell Res., vol. 14, 2001, pp. 2-8. [92] N.D. Gladkova, G.A. Petrova, N.K. Nikulin, S.G. Radenska-Lopovok, L.B. Snopova, Y.P. Chumakov, V.A. Nasonova, V.M. Gelikonov, G.V. Gelikonov, R.V. Kuranov, A.M. Sergeev, and F.I. Feldchtein, “In vivo optical coherence tomography imaging of human skin: norm and pathology,” Skin. Res. Technol., vol. 6, 2000, pp. 6-16. [93] J. Welzel, M. Bruhns, and H.H. Wolff, “Optical coherence tomography in contact dermatitis and psoriasis,” Arch. Dermatol. Res., vol. 295, 2003, pp. 50-55. [94] T. Gambichler, G. Moussa, M. Sand, D. Sand, P. Altmeyer, and K. Hoffmann, “Applications of optical coherence tomography in dermatology,” J. Dermatol. Sci., vol. 40, 2005, pp. 85-94. [95] T. Yamashita, K. Negishi, T. Hariya, N. Kunizawa, K. Ikuta, M. Yanai, and S. Wakamatsu, “Intense pulsed light therapy for superficial pigmented lesions evaluated by reflectance-mode confocal microscopy and optical coherence tomography,” J. Invest. Dermatol., vol. 10, 2006, pp. 2281-2286. [96] Y. Yasuno, T. Endo, S. Makita, G. Aoki, M. Itoh, and T. Yatagai, “Threedimensional line-field Fourier domain optical coherence tomography for in vivo dermatological investigation,” J. Biomed. Opt., vol. 11, 2006, 014014-17. [97] F.G. Bechara, T. Gambichler, M. Stucker, A. Orlikov, S. Rotterdam, P. Altmeyer, and K. Hoffmann, “Histomorphologic correlation with routine histology and optical coherence tomography,” Skin Res. Technol., vol. 10, 2004, pp. 169-173. [98] M.E. Brezinski, G.J. Tearney, B.E. Bouma, J.A. Izatt, M.R. Hee, E.A. Swanson, J.F. Southern, and J.G. Fujimoto, “Optical coherence tomography for optical biopsy - Properties and demonstration of vascular pathology,” Circulation, vol. 93, 1996, pp. 1206-1213. [99] M.E. Brezinski, G.J. Tearney, S.A. Boppart, E.A. Swanson, J.F. Southern, and J.G. Fujimoto, “Optical biopsy with optical coherence tomography: Feasibility for surgical diagnostics,” J. Surg. Res., vol. 71, 1997, pp. 32-40. [100] M.E. Brezinski, G.J. Tearney, B. Bouma, S.A. Boppart, C. Pitris, J.F. Southern, and J.G. Fujimoto, “Optical biopsy with optical coherence tomography,” Ann. NY Acad. Sci., vol. 838, 1998, p. 68-74. [101] W. Drexler, ‘Methodological advancements. Ultrahigh-resolution optical coherence tomography,” Ophthalmol., vol. 101, 2004, p. 804-812.

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[102] J.G. Fujimoto, M.E. Brezinski, G.J. Tearney, S.A. Boppart, B. Bouma, M.R. Hee, J. F. Southern, and E.A. Swanson, “Optical biopsy and imaging using optical coherence tomography,” Nat. Med., vol. 1, 1995, pp. 970-972. [103] U. Seitz and N. Soehendra, “Endoscopy: Current state and future trends in tumor diagnosis,” Anticancer Res., vol. 23, 2003, pp. 827-829. [104] M. Volker, K. Shinoda, H. Sachs, H. Gmeiner, T. Schwarz, K. Kohler, W. Inhoffen, K.U. Bartz-Schmidt, E. Zrenner, and F. Gekeler, “In vivo assessment of subretinally implanted microphotodiode arrays in cats by optical coherence tomography and fluorescein angiography,” Graefes Arch. Clin. Exp. Ophthalmol., vol. 242, 2004, pp. 792-799. [105] E.M. Kanter, R.M. Walker, S.L. Marion, M. Brewer, P.B. Hoyer, and J.K. Barton, “Dual modality imaging of a novel rat model of ovarian carcinogenesis,” J. Biomed. Opt., vol. 11, 2006, 041123-1-10. [106] L.P. Hariri, A.R. Tumlinson, D.G. Besselsen, U. Utzinger, E.W. Gerner, and J.K. Barton, “Endoscopic optical coherence tomography and laser-induced fluorescence spectroscopy in a murine colon cancer model,” Laser. Surg. Med., vol. 38, 2006, pp. 305-513. [107] T. Gambichler, S. Boms, M. Stucker, A. Kreuter, M. Sand, G. Moussa, P. Altmeyer, and K. Hoffmann, “Comparison of histometric data obtained by optical coherence tomography and routine histology,” J. Biomed. Opt., vol. 10, 2005, 44008-1-6. [108] K.W. Gossage, C.M. Smith, E.M. Kanter, L.P. Hariri, A.L. Stone, J.J. Rodriguez, S.K. Williams, and J.K. Barton, “Texture analysis of speckle in optical coherence tomography images of tissue phantoms,” Phys. Med. Biol., vol. 51, 2006, pp. 1563-1575. [109] A.R. Tumlinson, L.P. Hariri, U. Utzinger, and J.K. Barton, “Miniature endoscope for simultaneous optical coherence tomography and laser-induced fluorescence measurement,” Appl. Opt., vol. 43, 2004, pp. 113-121. [110] S.K. Li, E.-K. Jeong, and M.S. Hastings, “Magnetic resonance imaging study of current and ion delivery into the eye during transscleral and transcorneal iontophoresis,” Invest. Ophthalmol. Vis. Sci., vol. 45, 2004, pp. 1224-1231. [111] V.V. Tuchin, “Improvements of laser biomedical spectroscopy and imaging at tissue and blood optical clearing,” Proc. SPIE, vol. 6633, 2007, 66330B-7. [112] A.T. Yeh and J. Hirshburg, “Molecular interactions of exogenous chemical agents with collagen-implications for tissue optical clearing,” J. Biomed. Opt., vol. 11, 2006, 14003-1-6. [113] V.V. Tuchin, “Optical clearing of tissues and blood using the immersion method,” J. Phys. D: Appl. Phys., vol. 38, 2005, pp. 2497-2518.

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[114] R. Graaff, J.G. Aarnoudse, J.R. Zijp, P.M.A. Sloot, F.F.M. Demul, J. Greve, and M.H. Koelink, “Reduced light-scattering properties for mixtures of spherical-particles - a simple approximation derived from Mie calculations,” Appl. Opt., vol. 31, 1992, pp. 1370-1376. [115] D.Y. Churmakov, I.V. Meglinski, and D.A. Greenhalgh, “Influence of refractive index matching on the photon diffuse reflectance,” Phys. Med. Biol., vol. 47, 2002, pp. 4271-4285. [116] D.Y. Churmakov, I.V. Meglinski, and D.A. Greenhalgh, “Amending of fluorescence sensor signal localization in human skin by matching of the refractive index,” J. Biomed. Opt., vol. 9, 2004, pp. 339-346. [117] I.V. Meglinski and S.J. Matcher, “Quantitative assessment of skin layers absorption and skin reflectance spectra simulation in the visible and nearinfrared spectral regions,” Physiol. Meas., vol. 23, 2002, pp. 741-753. [118] I.V. Meglinski and S.J. Matcher, “Computer simulation of the skin reflectance spectra,” Comput. Methods Programs Biomed., vol. 70, 2003, pp. 179-186. [119] S.V. Patwardhan, A.P. Dhawan, and P.A. Relue, “Monte Carlo simulation of light-tissue interaction: three-dimensional simulation for trans-illuminationbased imaging of skin lesions,” IEEE Trans. Biomed. Eng., vol. 52, 2005, pp.1227-1236. [120] J.M. Schmitt and G. Kumar, “Optical scattering properties of soft tissue: a discrete particle model,” Appl. Opt., vol. 37, 1998, pp. 2788-2797. [121] M.G. Ghosn, V.V. Tuchin, and K.V. Larin, “Depth-resolved monitoring of glucose diffusion in tissues by using optical coherence tomography,” Opt. Lett., vol. 31, 2006, pp. 2314-2316. [122] K.V. Larin and M.G. Ghosn, “Influence of experimental conditions on drug diffusion in cornea,” Quant. Electron., vol. 36, 2006, pp. 1083-1088. [123] M.G. Ghosn, V.V. Tuchin, and K.V. Larin, “Non-destructive quantification of analytes diffusion in cornea and sclera by using optical coherence tomography,” Invest. Ophthalmol. Vis. Sci., vol. 48, 2007, pp. 2726-2733. [124] K.V. Larin, M.G. Ghosn, S.N. Ivers, A. Tellez, and J.F. Granada, “Quantification of glucose diffusion in arterial tissues by using optical coherence tomography,” Laser Phys. Lett., vol. 4, 2007, pp. 312-317. [125] M.G. Ghosn, Y. Cheng, and K.V. Larin, “Monitoring of drug diffusion in ocular tissues,” Proc. SPIE, vol. 6163, 2006, 616303-01- 05. [126] M.G. Ghosn, A. Glasser, and K.V. Larin, “In vivo assessment of molecular diffusion in monkey’s skin: pilot data,” Laser. Surg. Med. (submitted). [127] S. Oh, K.V. Larin and T.E. Milner, “Quantitative determination of glucose concentration by swept-source spectral interferometry and spectral phase analysis,” Proc. SPIE, vol. 6430, 2007, 64301-01-05.

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[128] K.V. Larin and M.G. Ghosn, “Depth-resolved monitoring of analytes diffusion in ocular tissues,” Proc. SPIE, vol. 6429, 2007, 642918-01-04. [129] T.L. Ke, G. Cagle, B. Schlech, O.J. Lorenzetti, and J. Mattern, “Ocular bioavailability of ciprofloxacin in sustained release formulations,” J. Ocul. Pharmacol. Ther., vol. 17, 2001, pp. 555-563. [130] A.N. Bashkatov, E.A. Genina, Y.P. Sinichkin, V.I. Kochubei, N.A. Lakodina, and V.V. Tuchin, “Estimation of the glucose diffusion coefficient in human eye sclera,” Biophysics, vol. 48, 2003, pp. 292-296. [131] R.A. Farrell and R.L. McCally, “Corneal transparency,” in Principles and Practice of Ophthalmology, Saunders, Philadelphia, PA, 2000. [132] G.F. Elliott, J.M. Goodfellow, and A.E. Woolgar, “Swelling studies of bovine corneal stroma without bounding membranes,” J. Physiol., vol. 298, 1980, pp. 453-470. [133] S. Hodson, D. Kaila, S. Hammond, G. Rebello, and Y. al-Omari, “Transient chloride binding as a contributory factor to corneal stromal swelling in the ox,” J. Physiol., vol. 450, 1992, pp. 89-103. [134] D.M. Maurice, “The cornea and the sclera” in The Eye., vol. 1, Academic Press, New York and London, 1969. [135] O.A. Boubriak, J.P. Urban, S. Akhtar, K.M. Meek, and A.J. Bron, “The effect of hydration and matrix composition on solute diffusion in rabbit sclera,” Exp. Eye. Res., vol. 71, 2000, pp. 503-514.

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21 Glucose-Induced Optical Clearing Effects in Tissues and Blood Elina A. Genina, Alexey N. Bashkatov Institute of Optics and Biophotonics, Saratov State University, Saratov, 410012, Russia Valery V. Tuchin Institute of Optics and Biophotonics, Saratov State University, Saratov, 410012, Russia, Institute of Precise Mechanics and Control of RAS, Saratov 410028, Russia 21.1 21.2 21.3 21.4 21.5

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Structure and Optical Properties of Fibrous Tissues and Blood . . . . . . . . . . . . . Glucose-Induced Optical Clearing Effects in Tissues . . . . . . . . . . . . . . . . . . . . . . Glucose-Induced Optical Clearing Effects in Blood and Cellular Structures Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

658 659 666 679 683 683 684

This chapter describes tissue and blood optical clearing effects induced by action of glucose solutions. The main mechanisms of glucose-induced optical clearing are discussed. Tissue permeation for glucose, glucose delivery, tissue dehydration and swelling caused by glucose solutions are considered. Optical models of tissues and blood are presented. Optical clearing properties of fibrous (eye sclera, skin dermis and dura mater) and cell-structured tissues (liver) are analyzed using spectrophotometry, time- and frequency-domain, fluorescence and polarization measurements; confocal microscopy; two-photon excitation imaging; and OCT. In vitro, ex vivo, and in vivo studies of a variety of human and animal tissues, as well as cells and blood, are presented. Key words: glucose, optical clearing, permeation, spectroscopy, fibrous tissues, cells, blood.

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21.1 Introduction Over the last decade, noninvasive or minimally invasive spectroscopy and imaging techniques have obtained wide spread occurrence in biomedical diagnostics, for example, optical coherence tomography (OCT) [1–4], visible and near-infrared elasticscattering spectroscopy [4–7], fluorescent [1, 5, 8] and polarization spectroscopy [4, 9, 10] and others. The use of optical methods in the development of noninvasive clinical functional cerebral imaging systems for physiological-condition monitoring [11–13], intracranial hematoma and cancer diagnostics [14–16] can be alternative of conventional X-ray computed tomography, magnetic resonance imaging and ultrasound imaging [17–20] due to their simplicity, safety and low cost. Spectroscopic techniques are capable of deep-imaging of tissues that could provide information of blood oxygenation [21, 22] and detect cutaneous and breast tumours [10, 22], whereas confocal microscopy [23, 24], OCT [1–4] and multi-photon excitation imaging [24, 25] have been used to show cellular and sub-cellular details of superficial living tissues. Spectroscopic and OCT techniques are applicable for blood glucose monitoring with diabetic patients [4, 26–28] (see also chapters 3–10 and 18). Besides diagnostic applications, optical methods are widely used in therapy, for example, for photodynamic [29, 30] and laser interstitial thermotherapy [31], and for laser surgery of different diseases [32, 33]. In particular, in ophthalmology laser technology is used for transscleral photocoagulation of ciliary body [34, 35]. However, in spite of numerous benefits in the use of optical methods in medicine there are some serious disadvantages. One of the problems deals with the transport of the light beam through the turbid tissues, such as skin, eye sclera, cerebral membrane (dura mater), to the target region of the investigation or damage. Due to low absorption and comparatively high scattering of visible and NIR radiation at propagation within tissues, there are essential limitations on spatial resolution and light penetration depth for optical diagnostic and therapeutic methods to be successfully applied. In addition complex character of light interaction with the superficial tissue layers caused by tissue scattering properties modifies spectral and angular characteristics of light propagating within a tissue which may be a reason for false diagnostics or light dosimetry at therapeutic action [4, 36]. The evident solution of the problem is the reduction of light scattering by a tissue, which gives improvement of image quality and precision of spectroscopic information, decreasing of irradiating light beam distortion and its sharp focusing. Various physical and chemical actions, such as compression, stretching, dehydration, coagulation, UV irradiation, exposure to low temperature and impregnation by biocompatible chemical solutions, gels and oils, are widely described in literature as tools for controlling of tissue optical properties [4, 11]. All these phenomena can be understood if tissue is considered as a scattering medium that shows all optical effects that are characteristic to turbid physical systems. In general, the scattering properties of a tissue can be effectively controlled by providing matching refractive indices of the scatterers and the ground material (i.e., optical immersion) and/or by the change

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packing parameter, and/or scatterer sizing [4]. Aqueous glucose solutions are widely used for the control of tissue scattering properties [37–65]. Increase of glucose content in tissue interstitial space reduces refractive index mismatch and, correspondingly, decreases the scattering coefficient. At the same time, the increase of scatterer’s volume fraction caused by dehydration of tissues may partly compensate the immersion effect. This chapter describes tissue and blood optical clearing effects induced by action of glucose solutions. In vitro, ex vivo and in vivo studies of a variety of human and animal tissues, such as fibrous (eye sclera, skin dermis and dura mater) and cellular tissues (liver), as well as cells and blood, are presented.

21.2 Structure and Optical Properties of Fibrous Tissues and Blood 21.2.1 Structure, physical and optical properties of fibrous tissues Fibrous tissues, such as sclera, dermis and cerebral membrane (dura mater), show similar structure and, consequently, similar optical properties. These tissues consist mainly of conjunctive collagen fibers packed in lamellar bundles [4, 40, 66–68] that are immersed in an amorphous ground (interstitial) substance, a colorless liquid containing proteins, proteoglycans, glycoproteins and hyaluronic acid [69]. Fibrils are arranged in individual bundles in a parallel fashion; moreover, within each bundle, the groups of fibers are separated from each other by large empty lacunae distributed randomly in space. Collagen bundles show a wide range of widths (1 to 50 µ m) and thicknesses (0.5 to 6 µ m) [40, 66, 67]. These ribbon-like structures are multiple cross-linked; their length can be a few millimeters. They cross each other in all directions but remain parallel to the tissue surface. The glycosaminoglycans play a key role in regulating the assembly of collagen fibrils and tissue permeability to water and other molecules [70, 71]. It should be noted that these molecules are excellent space filters. Due to glycosaminoglycan chains, these molecules concentrate negative charges. They are highly hydrophilic, and their presence can provide a selective barrier to the diffusion of inorganic ions and charged molecules [69]. In spite of similarity of the fibrous tissues, some differences in their structure are caused by their different functions in an organism. This requires to overview briefly main features of the structure of these tissues. The sclera is the turbid nontransparent medium that covers about 80% of the eyeball and serves as a protective membrane. Together with the cornea, it allows the eye to withstand both internal and external forces to maintain its shape. The thickness of the sclera is various. It is thicker at the posterior pole (0.9 to 1.8 mm); it is thinnest at the equator (0.3–0.9 mm) and at the limbus is in the range of 0.5 to 0.8 mm [4, 40, 72]. Hydration of the human sclera can be estimated as 68%. About 75% of its dry

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weight is due to collagen, 10% is due to other proteins and 1% to mucopolysaccharides [72]. The sclera contains three layers: the episclera, the stroma and the lamina fusca [4]. At the in vivo investigations, it is necessary to take into account the presence of the conjunctiva and Tenon’s capsule (∼ 200 µ m in thick), which both cover the scleral tissue from the external side. They impede the immersion liquid penetration into the sclera and, consequently, decrease the degree of eye tissue clearing. The thickness of the scleral collagen fibers also shows regional (limbal, equatorial and posterior pole region) and aging differences. In the equatorial region of the eye collagen fibrils exhibit a wide range of diameters, from 25 to 230 nm. The fibers in the scleral stroma have a diameter ranging from 30 to 300 nm [72]. The average diameter of the collagen fibrils increases gradually from about 65 nm in the innermost part to about 125 nm in the outermost part of the sclera [40, 72]; the mean distance between fibril centers is about 285 nm [73]. The episclera has a similar structure with more randomly distributed and less compact bundles than in the stroma. The lamina fusca contains a larger amount of pigments, mainly melanin, which are generally located between the bundles. The sclera itself does not contain blood vessels but has a number of channels that allow arteries, veins and nerves to enter or leave the eye [72]. Human dura mater is a protective membrane which surrounds brain. As an object for light propagation, this is a turbid, nontransparent medium. Typically, with the age the dura mater thickness changes from 0.3 to 0.8 mm [68, 74]. The average diameter of the dura mater collagen fibrils is about 100 nm [60]. Dura mater contains five layers: the external integumentary layer, the external elastin network, the collagen layer, the internal elastin network and the internal endothelium integumentary layer [68]. The collagen layer is the main layer of human dura mater. Thus, its optical properties are defined mainly by the optical properties of the collagen layer. It should be noted that those abrupt boundaries between upper, middle and lower layers are absent. The main difference between the structure of sclera and dura mater is the presence of the branched net of blood vessels in dura mater [68].

21.2.2 Structure, physical and optical properties of skin Skin presents a complex heterogeneous medium where blood and pigment content are spatially distributed variably in depth [75–78]. Skin consists of three main visible layers from surface: epidermis (50–200 µ m thick, the blood-free layer), dermis (1–4 mm thick, vascularized layer) and subcutaneous fat (from 1 to 6 mm thick depending on the body site). The randomly inhomogeneous distribution of blood and various chromophores and pigments in skin produces variations of average optical properties of skin layers. Nonetheless, it is possible to define the regions in the skin, where the gradient of skin cell structure, chromophores or blood amount change with a depth equals roughly zero [78]. This allows subdividing these layers into sublayers regarding the physiological nature, physical and optical properties of their cells and pigments’ content. The epidermis can be subdivided into the two sublayers: nonliv-

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ing and living epidermis. Nonliving epidermis or stratum corneum (about 10–20 µ m thick) consists of only dead squamous cells, which are highly keratinized with a high lipid and protein content, and has a relatively low water content [76, 78, 79]. Living epidermis (50–200 µ m thick) contains most of the skin pigmentation, mainly melanin, which is produced in the melanocytes [80]. Physical and optical properties of the dermal layers are mainly defined by the fibrous structure of the tissue. Dermis is a vascularized layer and the main absorbers in the visible spectral range are the blood hemoglobin, carotene and bilirubin. Following the distribution of blood vessels [77] skin dermis can be subdivided into the four layers: the papillary dermis (∼ 150 µ m thick), the upper blood net plexus (∼ 100 µ m thick), the reticular dermis (1–4 mm thick) and the deep blood net plexus (∼ 100 µ m thick). In fibrous tissues light scatters by both single fibrils and scattering centers, which are formed by the interlacement of the collagen fibrils and bundles. The average scattering properties of the skin are defined by the scattering properties of the reticular dermis because of relatively big thickness of the layer (up to 4 mm [79]) and comparable scattering coefficients of the epidermis and the reticular dermis. Large melanin particles such as melanosomes (> 300 nm in diameter) exhibit mainly forward scattering. Whereas melanin dust whose particles are small (< 30 nm in diameter) has the isotropy in the scattering profile, and optical properties of the melanin particles (30–300 nm in diameter) may be predicted by the Mie theory. Absorption of hemoglobin and water in skin dermis and lipids in skin epidermis define absorption properties of whole skin. It should be noted that absorption of hemoglobin is defined by the hemoglobin oxygen saturation, since absorption coefficients of hemoglobin are different for oxy and deoxy forms. For an adult the arterial oxygen saturation is generally above 95% [81]. Typical venous oxygen saturation is 60–70% [82]. Thus, absorption properties of skin in the visible spectral range depend on absorption of both oxy- and deoxyhemoglobin. In the IR spectral range absorption properties of skin dermis depend on absorption of water. To design the optical model of fibrous tissue, in addition to form, size and density of the scatterers (collagen fibrils) and the tissue thickness, we are able to have information on the refractive indices of the tissue components. In the visible and near infrared spectral ranges, the refractive index of collagen fibrils and interstitial fluid (ISF) of human tissues has a weak dispersion and, thus, in a first approximation, can be used as a constant. The experimental mean values of refractive indices of tissues, blood and their compounds, measured in vitro and in vivo, have been presented [4, 65, 83].

21.2.3 Optical model of fibrous tissue The optical model of fibrous tissue can be presented as a slab with a thickness l containing scatterers (collagen fibrils) – thin dielectric cylinders with an average diameter of 100 nm, which is considerably smaller than their lengths. Taking into account the similar structure of the dura mater, eye sclera and skin dermis, we can assume that the refractive index of the collagen fibrils (nc ) and ISF (nI ) has the

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similar wavelength dependence in the visible spectral range for all fibrous tissues [60]. nc (λ ) = 1.439 +

15880.4 1.48 × 109 4.39 × 1013 − + λ2 λ4 λ6

(21.1)

nI (λ ) = 1.351 +

2134.2 5.79 × 108 8.15 × 1013 + − , λ2 λ4 λ6

(21.2)

and

where λ is the wavelength, nm. These cylinders are located in planes that are in parallel to the sample surfaces, but within each plane their orientations are random. These simplifications reduce considerably the difficulties in the description of the light scattering by fibrous tissue. For a thin dielectric cylinder in the Rayleigh-Gans approximation of the Mie scattering theory the scattering cross-section σs (t) for unpolarized incident light is given by [84, 85]
2 2 π 2 ax3 2 1+ m −1 σs = 2 2 8 (m + 1)

!

,

(21.3)

where m = nc /nI is the relative refractive index of the scattering particle, i.e., ratio of the refractive indices of the scatterers and the ground materials (i.e., ISF), and x is the dimensionless relative scatterers size which is determined as x = 2π anI /λ , where λ is the wavelength and a is the cylinder radius. Considerable refractive indices mismatching between collagen fibers and a ground substance causes the system to become turbid, i.e., causes multiple scattering and poor transmittance of propagating light. The refractive index of the background is a controlled parameter and may transit the system from multiple to low-step and even single-scattering mode. For nc = nI , the medium becomes totally homogeneous and optically transparent if absorption is negligible. The temporal dependence of the refractive index of the ISF caused by the clearing agent permeation into a tissue can be derived using the law of Gladstone and Dale, which states that for a multi-component system the resulting value of the refractive index represents an average of the refractive indices of the components related to their volume fractions [86, 87]. Such dependence is defined as nI (t) = [1 − C (t)] nbase + C (t) nosm ,

(21.4)

where nbase is the refractive index of the tissue ISF at the initial moment and nosm is the refractive index of an agent solution. In practice any of the available optical clearing agents (OCAs) can be taken to provide light scattering reduction [65]; however in this chapter the advantages of the glucose solution will be considered. Wavelength dependence of aqueous glucose solution can be estimated as [63] nosm (λ ) = nw (λ ) + 0.1515C,

© 2009 by Taylor & Francis Group, LLC

(21.5)

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663

where nw (λ ) is the wavelength dependence of the refractive index of water [88], and C is the glucose concentration, g/ml. As a first approximation we assume that during the interaction of the immersion liquid with a tissue, the size of the scatterers does not change. This assumption is confirmed by the results presented by Huang and Meek [89] for scleral and corneal tissue at action of polyethylene glycol solutions at pH values near 4. In the case of unchangeable scatterer size, all changes in the tissue scattering are connected with the changes of the refractive index of the ISF described by Eq. (21.1). The increase of the refractive index of the ISF provides the decrease of the relative refractive index of the scattering particles and, consequently, the decrease of the scattering coefficient. For noninteracting particles the scattering coefficient of a tissue is defined by the following equation

µs (t) = N σs (t) ,

(21.6)

where N is the number of the scattering particles (fibrils) per unit area and σs (t) is the time-dependent cross-section of scattering [Eq. (21.3)]. The number of the scattering particles per unit area can be estimated as N = φ /(π a)2 [84], where φ is the volume fraction of the tissue scatterers. For fibrous tissues φ is usually equal to 0.3 [36, 40, 90]. To take into account interparticle correlation effects, which are important for tissues with densely packed particles, the scattering cross-section has to be corrected by the packing factor of the scattering particles, (1 − φ )3 / (1 + φ ) [36]. Thus, Eq. (21.6) has to be rewritten as

µs (t) =

φ (1 − φ )3 σ . (t) s π a2 1+φ

(21.7)

Tissue swelling (or shrinkage) caused by action of an OCA leads to change of tissue sample volume that produces the corresponding change of the volume fraction of the scatterers and their packing factor, as well as the numerical concentration, i.e., the number of the scattering particles per unit area.

21.2.4 Structure, physical and optical properties of blood From an optical point of view, whole blood is a highly concentrated turbid medium consisting of plasma (55–60 vol%) and blood particles (40–45 vol%) [91, 92], 99% of which are erythrocytes and 1% are leukocytes and platelets [92]. In normal physiological conditions human erythrocytes (red blood cells – RBCs) are anucleate cells in the form of biconcave disks with a diameter ranging between 5.7 and 9.3 µ m and mean size of about 7.5 µ m [92], and maximal thickness varying between 1.7 and 2.4 µ m [93]. Average volume of a RBC is about 90 µ m3 [91, 94, 95] and, according to different data, varies between 70 and 100 µ m3 [93], from 50 to 200 µ m3 [94] or from 30 to 150 µ m3 [95]. In the presence of different pathologies, as well as under changes of osmolarity or pH of the blood plasma, the normal (discocytes) can change shape without changing in volume [92, 93]. The RBCs consist

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of a thin membrane (with a thickness from 7 nm [94] to 25 nm [93]) and cytoplasm, which, in general, is an aqueous hemoglobin solution [95, 96]. Hematocrit is the volume fraction of cells within the whole blood volume and ranges from 36.8% to 49.2% under physiological conditions [91]. The hemoglobin concentration in completely hemolyzed blood lies between 134 and 173 g/L [91], while the hemoglobin concentration in erythrocytes varies from 300 to 360 g/L, with mean concentration being equal to 340 g/L [95]. The content of salts in the erythrocyte cytoplasm is about 7 g/L, and concentration of other organic components (lipids, sugars, enzymes and proteins) is approximately equal to 2 g/L [96]. A change in osmolarity induces a variation of the RBC volume due to water exchange and therefore has an impact on the hemoglobin concentration within the RBC [91]. Flow induced shear stress can influence RBC sedimentation, their reversible agglomeration, axial migration or deformation, and orientation. The flow parameters depend on the blood viscosity and they are influenced by the fact that blood is not a Newton fluid [91, 96]. Under normal physiological conditions, the RBCs may aggregate into rouleaux. The rouleaux may further interact with other rouleaux to form rouleaux networks (or clumps in pathological cases) [91, 93, 96].

21.2.5 Optical model of blood The optics of whole blood at physiological conditions is determined mainly by the optical properties of RBCs and plasma, whereas the contribution to scattering from the remaining blood particles can be neglected. Analysis of light propagation and scattering in such medium can be performed on the basis of description of absorption and scattering characteristics of individual blood particles by taking into account concentration effects and polydispersity of the particles. In radiative transfer theory the absorption coefficient µa , scattering coefficient µs and anisotropy factor g of an elementary volume of investigated medium are determined by the size of RBCs, as well as real (n) and imaginary (χ ) parts of the complex refractive index (n + iχ ) of the scattering particles (RBCs) and their environment (blood plasma). The scattering properties of blood are also dependent on RBC volume, shape and orientation, which are defined in part by blood plasma osmolarity [91], aggregation and disaggregation capability and hematocrit [97]. In the blood optical model, scattering particles can be represented as absorbing and scattering homogeneous spherical particles with volume of each particle being equal to the volume of a real RBC [98, 99]. Contribution to the scattering from the RBC membrane can be neglected due to small thickness of the membrane [95]. Polydispersity of RBCs can be taken into account based on the data presented in Ref. [94]. According to the data obtained in Ref. [95], the concentration of hemoglobin can be related to the RBC volume as:

CHb = 0.72313 − 0.00451V,

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(21.8)

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where CHb is the concentration of hemoglobin, g/ml, and V is the erythrocyte volume, µ m3 . Both the real and the imaginary parts of the refractive index of erythrocytes are directly proportional to the hemoglobin concentration in erythrocytes [91, 92], i.e.: ne = n0 + α CHb ,

(21.9)

χe = β CHb ,

(21.10)

where n0 = 1.34 is the refractive index of the erythrocyte cytoplasm [95] and α and β are spectrally dependent coefficients. For the wavelength of 589 nm, α = 0.1942 ml/g [91], while, for the wavelength 640 nm, α = 0.284 ml/g and β = 0.0001477 ml/g [92]. Since the content of salts, sugars and other organic components in the erythrocyte cytoplasm is insignificant, the spectral dependence of the erythrocyte cytoplasm correlates with the spectral dependence of the refractive index of water, i.e., n0 (λ ) = nw (λ ) + 0.007. Spectral dependence of the refractive index of water is determined in Ref. [88]. The spectral dependences of the coefficients α and β can be calculated on the basis of the data presented in Ref. [92] and using a value of the hemoglobin concentration in RBC equal to 322 g/l, which can be obtained from Eq. (21.9) with the coefficient α = 0.1942 ml/g. The blood plasma contains up to 91% water, 6.5–8% (about 70 g/l) proteins (hemoglobin, albumin and globulin) and about 2% low-molecular-weight compounds [61]. The spectral dependence of the real part of the refractive index of the blood plasma (n p ) in the spectral range 400–1000 nm is determined by the expression [64, 100] 8.4052 × 103 3.9572 × 108 2.3617 × 1013 − − , (21.11) λ2 λ4 λ6 where λ is the wavelength (nm). Since the blood plasma does not have pronounced absorption bands in this spectral range, the imaginary part of the refractive index of the plasma can be neglected in calculations. In terms of the Mie theory, the scattering (σs ) and the anisotropy factor of a homogeneous sphere are expressed by Eqs. (19.37) and (19.38) of Ref. [85]. According to [36], the scattering and absorption coefficients and the anisotropy factor of whole blood considered as a system of closely packed polydisperse particles are given by n p = 1.3254 +

M

µs = (1 − H) ∑ Ni σsi ,

(21.12)

i=1

M

µa = ∑ Ni σai ,

(21.13)

i=1

M

g = ∑ µ si g i i=1

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,

M

∑ µ si .

i=1

(21.14)

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Here H is the hematocrit value; Mis the number of volume fractions of erythrocytes; Ni = Ci /Vei is the number of particles per unit volume of the medium; Ci is the volume fraction occupied by particles of the ith diameter; Vei = 4π a3i /3 is the erythrocyte volume. In Eq. (21.12) the necessity of introduction of the factor (1 − H) [94, 101, 102], which is called the packing factor of scatterers, is determined by interference effects of radiation scattered by the neighboring particles.

21.3 Glucose-Induced Optical Clearing Effects in Tissues 21.3.1 Mechanisms of optical immersion clearing Numerous publications discuss advantages of methods of tissue optical clearing using OCAs and investigation of the mechanisms of clearing [45, 47, 49, 54, 57, 60, 65, 103–106]. There are a few main mechanisms of light scattering reduction induced by an OCA [57, 65, 103–106]: 1) dehydration of tissue constituents, 2) partial replacement of the ISF by the immersion substance and 3) structural modification or dissociation of collagen. Both the first and the second processes mostly cause matching of the refractive indices of the tissue scatterers (cell compartments, collagen and elastin fibers) and the cytoplasm and/or ISF. Tissue dehydration and structural modification lead to tissue shrinkage, i.e., to the near-order spatial correlation of scatterers and, as a result, the increased constructive interference of the elementary scattered fields in the forward direction and destructive interference in perpendicular direction of the incident light, that may significantly increase tissue transmittance even at some refractive index mismatch [65]. For some tissues and for nonoptimized pH of clearing agents, tissue swelling may take place that may be considered as a competitive process in providing of tissue optical clearing [65, 89]. It was shown that dehydration induced by osmotic stimuli such as OCA appears to be a primary mechanism of optical clearing in collagenous and cellular tissues, whereas dehydration induces intrinsic matching effect [65, 103]. The space between fibrils and cell organelles is filled up by water and suspended salts and proteins. Water escaping from tissue having cellular or fibrillar structure is a more rapid process than OCA entering into tissue interstitial space due to the fact that OCA typically has greater viscosity (lower diffusion coefficient) than water. As water is removed from the intrafibrillar or intracellular space, soluble components of ISF or cytoplasm become more concentrated and a refractive index increases. The resulting intrinsic refractive index matching between fibrils or organelles and their surrounding media, as well as density of packing and particle ordering, may significantly contribute to optical clearing [56, 65, 103]. Replacement of water in the interstitial space by the immersion substance leads to the additional matching of the refractive indices between tissue scatterers and ground matter [4, 56].

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21.3.2 Optical clearing of fibrous tissues 21.3.2.1 In vitro spectral measurements For in vitro studies of tissue optical glucose-induced clearing fiber optical gratingarray spectrometer LESA-5, 6med (Biospec, Russia) or similar are suitable thanks to their fast spectra collection during glucose solution action [11, 41, 42, 44–52, 56–58, 60]. Typically, the spectral range of interest is from 400 to 1000 nm. For providing of measurements in transmittance mode the glass cuvette with the tissue sample was placed between two optical fibers. One fiber transmitted the excitation radiation to the sample, and another fiber collected the transmitted radiation. The 0.5-mm diaphragm placed 100 mm apart from the tip of the receiving fiber was used to provide collimated transmittance measurements [41, 44, 45, 49, 51, 60]. The tissue samples were fixed inside cuvette filled up with the glucose solution. In the reflectance mode the spectrometer fiber probe consists of seven optical fibers: one fiber delivers light to the object, and six fibers collect the reflected radiation [44, 46, 47, 51, 52, 57]. The same configuration was used also in in vivo investigations. The total transmittance and diffuse reflectance were measured in the wavelength range 200-2200 nm using spectrophotometer with an internal integrating sphere Cary 2415 (Varian, Australia) [40, 43] or PC1000 (Ocean Optics Inc., USA) [59]. The spectrometers were calibrated using a white slab of BaSO4 with a smooth surface. To reconstruct the absorption and reduced scattering coefficients of a tissue from the measurements, the inverse adding-doubling (IAD) [107] or inverse Monte Carlo (IMC) were applied [108]. Figures 21.1 and 21.2 illustrate dynamics of glucose-induced change of the transmittance spectra of two types of fibrous tissues: sclera and dura mater. In the figures symbols correspond to experimental data [42, 60], the error bars show the standard deviation values and the solid lines correspond to the data calculated using the optical model of fibrous tissue. It is easily seen that the untreated tissue is poorly transparent for the visible light. Administration of 40%- as well as 20%-glucose solutions makes fibrous tissue highly transparent. The approximated time of maximal tissue clearing is about 8 min. Figures show that the clearing process has at least two stages. At the beginning of the process the increase of the transmittance is seen; that is followed by saturation and even the decrease of the transmittance. Two major processes could take place. One of them is diffusion of glucose inside tissue and another is tissue dehydration caused by osmotic properties of glucose. In general, both processes lead to matching of refractive indices of the scatterers and the ISF that causes the decrease of tissue scattering and, therefore, the increase of the collimated transmittance. Dehydration also leads to the additional increase of optical transmission due to decrease of tissue thickness (shrinkage) and corresponding scatterer ordering (packing in order) process due to increase of particle volume fraction. However, the increase of scatterer volume fraction may also cause some competitive increase of scattering coefficient due to random packing process (growth of particle density) that partly compensates the immersion effect. The saturation of optical clearing kinetic curves (see Figs. 21.1 and 21.2) can be explained as the saturation of glucose and water diffusion processes.

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FIGURE 21.1: The time-dependent collimated transmittance of the human sclera sample measured in vitro at different wavelengths concurrently with administration of 40%-glucose solution. The symbols correspond to the experimental data. The solid lines correspond to the data calculated using the optical model of fibrous tissue [42].

FIGURE 21.2: The time-dependent collimated transmittance of the human dura mater sample measured at different wavelengths concurrently with administration of 20%-glucose solution. The symbols correspond to the experimental data. The error bars show the standard deviation values. The solid lines correspond to the data calculated using the optical model of fibrous tissue [60].

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Some darkening at the late time period may be caused by a few reasons, such as the above mentioned particle density growth and interaction of modified ISF (containing glucose and less water) with hydrated collagenous fibrils [65]. 21.3.2.2

In vivo spectral measurements

It is known that at in vivo application of the designed optical immersion technology additional factors such as metabolic reaction of living tissue on clearing agent application, the specificity of tissue functioning and its physiological temperature can significantly change kinetic characteristics and the magnitude of the clearing effect. Temporal dependence of the sclera reflectance at two wavelengths in the course of the optical clearing of rabbit eye in vivo is presented in Fig. 21.3 [46]. As it was shown in in vitro studies [40, 41, 43], visible and NIR reflectance of scleral samples monotonically decreases under the action of the 40%-glucose solution, unlike in vivo measurements. The oscillatory character of kinetic curves is caused by the alternation of processes of clearing, which appears after the application of glucose solution to the eye surface (glucose solution drop), and recovery of the optical properties of sclera after diffusion of glucose from the detection region to surrounding tissues and diffusion of water from surrounding tissues to the detection region. Each oscillation corresponds to time of a new glucose drop applied topically. The time during which the maximum transparency of sclera was achieved in vivo considerably exceeds the clearing time of sclera in vitro. While this time was 8–10 min upon the action of the 40%-glucose solution on sclera samples in vitro [40, 41, 43], the clearing processes during in vivo experiments proceeded for no less than 20 min. There are at least two reasons for that. In in vitro studies typically both sides of the samples are impregnated by a solution; in in vivo case glucose solution could be applied only from one side of a tissue at topical application. Another reason is that the upper cellular epithelial layer of the sclera may have some impact (hindering) on glucose diffusivity. The kinetic curves measured for two wavelengths, one of which (568 nm) is within and another (610 nm) is outside the absorption band of blood (Fig. 21.3), are considerably different. The reflectance within blood absorption band decreased much faster (for 10–12 min) that is explained by the response of the eye (inflammation) to intense illumination during measurements as well as by the osmotic action of glucose. Such induced inflammation increases the local concentration of hemoglobin due to blood inflow through vessels. A further small increase in R in this wavelength range can be explained by a decrease in the absorption of light in sclera due to the stasis of capillaries and microvessels caused by the hyperosmotic action of glucose inside sclera [52]. This effect will be discussed below. Since sclera is the tissue with low blood content, blood absorption practically does not become apparent in the spectra at in vitro measurements [40, 41, 43]. Therefore the reflectance demonstrates uniform falling due to the immersion clearing at all wavelengths. The appearance of the blood spectral bands at in vivo measurements is mainly connected with the existence of choroid under scleral layer, which is usually deleted at in vitro experiments, and functioning capillary net inside the sclera.

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FIGURE 21.3: Temporal dependence of the sclera reflectance at two wavelengths during the optical clearing. Symbols and solid curves correspond to experimental data and result of their approximation, respectively [46].

The change of regime of photon scattering from multiple to low-step leads to the increase of photon’s free path length. Thus, more photons pass the scleral layer almost without the scattering and are absorbed in choroid layer. This corresponds to more significant decreasing of the reflectance in the blood absorption bands in comparison with the range 600–750 nm. Besides, the action of osmotic agent causes the irritation of eyeball that causes more blood coming to the area under study and, thus, additionally reduces the reflectance of tissue in the range of blood absorption bands. By numerical simulation of scleral optical clearing process under the action of the 40%-glucose solution, the time dependences of the fraction of absorbed photons in each layer of the eye cover (sclera, retinal pigmented epithelium and choroid) has been evaluated [46]. The fraction of photons absorbed in sclera decreases with time, on average, by 10%, in accordance with sclera clearing. The fraction of photons absorbed in retinal pigmented epithelium layer increases, on average, by 30%. The fraction of photons absorbed in the choroid increases by 40%. This means that, despite sclera clearing, the main part of light transmitted through sclera is absorbed in pigmented and vascular layers. As a result, the intensity of light incident on the internal tissues of the eye increases insignificantly. This should be taken into account in the dosimetry of laser radiation in transscleral surgery of the inner eye ball tissues because a considerable increase in the absorption of light in retinal pigmented epithelium and choroid layers at sclera clearing can cause their overheating and damage.

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FIGURE 21.4: The time-dependent polarization degree (I|| − I⊥)/(I|| + I⊥ ) of collimated transmittance measured at different wavelengths for the rabbit eye sclera sample at administration of 40%-glucose [41].

On the other hand, scleral optical clearing may provide more precise and effective coagulation of retinal pigmented epithelium and choroid layers [65]. 21.3.2.3 Polarization measurements The kinetics of the polarization properties of the tissue sample at immersion can be easily observed using an optical scheme with a white light source and a tissue sample placed between two parallel or crossed polarizers [41]. At a reduction of scattering, the degree of linearly polarized light propagating in fibrous tissue improves [11, 41, 109]. This is clearly seen from the experimental graphs in Fig. 21.4. As far as the tissue is immersed, the number of scattering events decreases and the residual polarization degree of transmitted linearly polarized light increases. As a result, the kinetics of the average transmittance and polarization degree of the tissue are similar. It follows from Fig. 21.4 that glucose-induced optical clearing leads to increasing in the depolarization length [109]. Due to less scattering of the longer wavelengths, the initial polarization degree is higher for these wavelengths. Tissue clearing has the similar impact on scattering and correspondingly on the improvement of polarization properties on these long wavelengths and especially on the shorter ones.

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21.3.3 Optical clearing of skin 21.3.3.1 Confocal microscopy Skin has a principle limitation that makes the optical clearing method less efficient and more complicated to be applied and described. The origin of this limitation is the dense upper cellular layer stratum corneum (SC), which has a protective function preventing penetration of any chemicals including immersion agents inside the skin. The specific structure of skin defines the methods of its effective optical clearing. The heterogeneous nature of skin provides some possible pathways for solute transport: appendageal, transcellular (through corneocytes) and intercellular (through the lipid phase — lipid bridges) [110]. Lipophilic solutes are permeants believed to be transported via the lipoidal pathway of SC and polar permeants are transported via the pore pathway of SC [111]. It is well known that the diffusion of aqueous solutions of substances (such as glucose) through SC barrier is hindered. The main limitation of the confocal microscopy in skin studies is skin high scattering that distorts the quality of cell images. The increase in the transparency of the upper skin layers can improve the penetration depth, image contrast, and spatial resolution of confocal microscopy [53, 54]. At administration of an OCA to the skin superficial layers they are greatly cleared during the first minute of the process. It is connected mainly with a high porosity of the SC dead cell structure, where airfilled small spaces exist. In depth of SC, where very dense structure is formed by corneocytes that are attached to each other by lipid bridges, diffusion of any agent, including glucose and water, is dramatically reduced. Living epidermis cell layers are a few orders more permeative; however its thickness is 5–10 times bigger than of SC, thus the overall diffusion rate through SC and living epidermis may be comparable [58]. Skin dermis is characterized by a faster diffusion that is characteristic to any fibrous tissue. In the upper blood net plexus region permeability of dermis may be modified (typically fastened) due to blood and lymph vascular net structure [112]. In the deep skin layers OCA diffusion is more homogeneous. The diffusivity of glucose and water is a few orders higher than in living epidermis, and only a half of the order less than diffusion in water [65]. However, because of considerable thickness of dermis in comparison with SC and living epidermis the overall permeation could be comparable with permeation of SC and living epidermis. Using Monte Carlo simulation of the point spread function it was shown recently that confocal microscopic probing of skin at optical clearing is potentially useful for deep reticular dermis monitoring and improving the image contrast and spatial resolution of the upper cell layers [54]. The results of the simulation predict that, to 20th min of glucose diffusion after its intradermal injection, a signal from layers located twice as deeply in the skin can be detected [53]. 21.3.3.2

Two-photon microscopy

The application of glucose may prove to be particularly relevant for enhancing two-photon microscopy [113], since it has been shown that the effect of scattering is to drastically reduce penetration depth to less than that of the equivalent single pho-

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ton fluorescence while largely leaving resolution unchanged [114, 115]. This happens mostly due to excitation beam defocusing (distortion) in the scattering media. On the other hand, this technique is useful in understanding molecular mechanism of tissue optical clearing upon immersion and dehydration [56]. For two-photon scanning fluorescence microscopy system, a mode-locked laser provides the excitation light. The fluorescence is collected by the objective and retraces the same optical path as the laser excitation. In Ref. [55] Ti:Sapphire laser (Coherent MIRA900) as a source of the excitation light, which comprises 100-fs width pulses at an 80-MHz repetition rate, tuneable in wavelength between 700 and 1000 nm, was used. The wavelength range of the detection has an upper limit of 670 nm, and a lower limit of 370 nm. Samples were taken from normal human skin excised during plastic surgery procedures. Images were taken at depths of 20, 40, 60 and 80 µ m from the sectioned surface of the skin tissue. Aqueous solution of glucose (5 M) was investigated. The tissue was immersed in 0.5 ml of the glucose solution and one image stack was acquired every 30 seconds for 6–7 minutes. After the OCA was removed the sample was immersed in 0.1 ml of phosphate buffered saline (PBS), in order to observe the reversibility of the clearing process. The upper limit of tissue shrinkage was estimated as 2% in the course of 6–7 min of OCA application [55]. The average contrast in each image and relative contrast (RC) were defined as [55] Contrast =

Nlines

∑

i, j=1

RC = 100

 Ii, j − Ii, j ,

Contrast[OCA] − Contrast[PBS] Contrast[PBS]

(21.15)

(21.16)

 where Ii, j is the mean intensity of the nearest eight pixels and Nlines = N − 2, with N = 500; Contrast[OCA] and Contrast[PBS] are calculated using Eq. (21.15), for OCA and PBS immersion, respectively. Contrast, as defined by Eq. (21.15), is linearly dependent on the fluorescence intensity and varies according to structures in the image. Hence, its usefulness is primarily to enable comparison between images of the same sample at the same depth maintaining the same field of view. Normalization to the total intensity would be required in order to compare different images. The relative contrast RC also serves for the purpose of comparison. In Ref. [55] it was shown that glucose is effective in improving the image contrast and penetration depth (by up to a factor of two) in two-photon microscopy of ex vivo human dermis. Such improvements were obtained within a few minutes of application. For 5M glucose solution RC = 10.9% at 20 µ m depth, ∼ 134% at 40 µ m depth, ∼ 471% at 60 µ m depth and ∼ 406% at 80 µ m depth. These data are worst in comparison with both pure glycerol and propylene glycol, but glucose diffuses three times faster than glycerol and five times faster than propylene glycol. There was found some specificity in action of glucose in comparison with other OCAs. Effects of glucose have not been shown to be reversible. Results presented in Ref. [55] have not demonstrated for glucose a slowing in rate of contrast increase

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following addition of PBS rather than a decrease as it was seen for glycerol. Such behavior may be associated with a lesser inclusion of the dehydration mechanism in optical clearing for glucose, and a greater amount of this OCA diffused into a tissue in comparison with glycerol [4]. 21.3.3.3

OCT imaging

The typical optical coherence tomography (OCT) fiber optical system employs a broadband light source (a superluminescent diode) to deliver light at a central wavelength of 820 to 1300 nm with a bandwidth of 25-50 nm. Such OCT provides 10– 20 µ m of axial and transverse resolution in free space with a signal to noise ratio up to 100 dB [116, 117]. For OCT measurements, the intensity of reflected light as a function of the depth z and transverse scanning of the sample is obtained as the magnitude of the digitized interference fringes. The result is the determination of optical backscattering or reflectance, R(z, x), versus the axial ranging distance, or depth, z, and the transverse axis x. The reflectance depends on the optical properties of the tissue or blood, i.e., the absorption (µa ) and scattering coefficients (µs ). The relationship between R(z) and attenuation coefficient, µt = µa + µs , is, however, very complicated due to the high and anisotropic scattering of tissue and blood, but for optical depths less than four, the reflected power will be approximately proportional to −2µt z on an exponential scale according to the single scattering model [56, 118], and µt can be obtained from reflectance measurements at two different depths z1 and z2 :

µt =

  R (z1 ) 1 , ln 2 (∆z) R (z2 )

(21.17)

where ∆z = |z1 − z2 |. A few dozen of repeated scan signals from the sample are usually averaged to estimate the total attenuation coefficient µt of the sample. The optical clearing (enhancement of transmittance) ∆T by agents is calculated according to [61] ∆T =

Ra − R × 100%, R

(21.18)

where Ra is the reflectance from the back surface of the sample with an agent and R that with a control sample. The OCT images captured from a skin site of a volunteer at a hyperdermal injection of 40%-glucose allowed one to estimate the total attenuation coefficient [see Eq. (21.17)] [62]. The attenuation initially goes down and then over time goes up. Such a behavior correlates well with the spectral measurements shown in Fig. 21.6 and also illustrates the index matching mechanism induced by the glucose injection. The light beam attenuation in tissue, I/I0 ∼ exp(−µt ), for intact skin (0 min) was found from OCT measurements as I/I0 ∼ = 0.14, and, for immersed skin at 13 min, I/I0 ∼ = 0.30; i.e., the intensity of the transmitted light increased by 2.1 times. That value also correlates well with the spectral measurements.

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FIGURE 21.5: The time-dependent collimated transmittance of the rat skin sample measured in vitro at different wavelengths concurrently with administration of 40%-glucose solution [48].

It should be noted that the high sensitivity of the OCT signal to immersion of living tissue by glucose allows one to monitor its concentration in the skin at a physiological level [25–27]. 21.3.3.4

In vitro spectral measurements

Figure 21.5 shows the time-dependent collimated transmittance of the rat skin samples measured in vitro at different wavelengths concurrently with administration of 40%-glucose solution through dermis, which has fibrous structure [48]. Experimental studies of glucose-induced optical clearing of skin in vitro presented in Refs. [44, 47, 48, 51] have demonstrated similarity in kinetics of the process in skin and fibrous tissues as sclera and dura mater. However, comparing time of the clearing of skin with data obtained at the clearing of another fibrous tissue, it can be concluded that permeability of the agent into the skin is less than that into the sclera [40, 41, 43] or into the dura mater [44, 59, 60]. From Fig. 21.5 it is seen that the glucose solution can effectively control the optical properties of whole skin. At the initial moment the skin is nontransparent for optical radiation. Application of the OCA makes the skin to be more transparent: during 60 min the collimated transmittance increases by more than 30 times at the wavelength 700 nm. 21.3.3.5

In vivo spectral and fluorescence measurements

When in vivo measurements of skin reflectance are carried out, one needs to exclude influence of SC corneum barrier on the clearing process. To increase efficiency

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FIGURE 21.6: The time-dependent reflectance of the human skin measured in vivo at different wavelengths concurrently with administration of the 40%-glucose solution. The symbols correspond to the experimental data [57].

of OCA permeation through SC, epidermal stripping, electrophoresis or flashlampinduced micro-damages can be used [58, 119]. For topical application of glucose-gel compositions these methods lead to the enhancement of the kinetics of in vivo optical clearing of human skin. For example, application of glucose-gel to skin with removed upper layers of SC gave a rapid 10% drop of reflected light intensity [119]. The administration of glucose solution by intradermal injection is a more effective method. In vivo investigations of skin clearing were done with hamsters [47], white rats [44, 48, 51, 57] and male volunteers [49, 51, 57]. As OCAs 40%-glucose solution [44, 48, 51, 57] and highly concentrated glucose (7 M) [47] were used. Kinetics of reflectance spectra, measured concurrently with intradermal injection of 40%-glucose solution, has shown more than 2-times decreasing of the signal [44, 51]. Figure 21.6 presents kinetics of the human skin reflectance measured at different wavelengths. In the figure it is well seen that immediately after glucose injection the skin reflectance significantly decreases. During the first 20 min the reflectance increases but during the following time interval from 20 to 60 min the skin reflectance decreases again. In the time interval from 60 to 140 min the skin reflectance increases slowly, with oscillating behavior. The reflectance of the skin decreased by about 3.5 times at 700 nm, and then the tissue went slowly back to its normal state. The significant decreasing of reflectance observed at initial moment is connected with changing geometry of the experiment after glucose injection. The injected solution forms a vesicle filled with the glucose solution in skin, and the vesicle is observed on the skin surface as a swell. Presence of the swell reduces the distance between the collecting fiber and skin surface, decreases area of detection of the backreflected radiation and hence decreases the reflectance. Injection of the 40%-glucose

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FIGURE 21.7: The changes of skin reaction on injection of 40%-glucose solution. The symbols correspond to the experimental data: bullets — the diameter of virtual transparent window, mm; squares — the diameter of swelling area around the window, mm; triangles — the height of the swell, mm [57].

solution creates the virtual transparent window in skin, which is observed during about 30 min. This window allows one to clearly identify visually blood microvessels in the skin by the naked eye [50, 52]. The swelling white ring appears around the window after the glucose injection. The images of skin were recorded by a digital video camera; diameters of the swelling area and the transparent window were measured [50]. The results are presented in Fig. 21.7. Assuming that the shape of the vesicle can be presented as an ellipsoid of rotation and taking into account the temporal evolution of the diameter of the swelling area, the height of the swell can be calculated. In 1 min after injection the height is 3.5 mm. During first 5 min after injection the height of the swell decreases to 2.4 mm. In the next 10 min (from 5 to 15 min) the height of the swell does not change. In 30 min after injection the swell on the skin surface disappears. Schematically the optical clearing at glucose injection can be represented as the following. The clearing agent forms a vesicle filled up with the aqueous solution of glucose in skin dermis. Since skin dermis is elastic porous medium and the glucose solution is incompressible liquid then tissue surrounding the vesicle becomes compressed. Its porosity decreases [120] and ISF is extruded from pores of the dermis. In the initial moment from 0 to 5 min after injection the size of the vesicle decreases significantly under the influence of mechanical pressure of deformed tissue. In the time interval from 5 to 15 min the skin pressure compensates by elastic properties of the glucose solution, and, as a result, the skin reflectance (and size of swell on the

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skin surface) does not change [57]. During the time interval from 20 to about 60 min glucose solution diffuses from the vesicle to the surrounding tissue and the corresponding tissue clearing takes place. The glucose-injected region becomes more transparent. Skin scattering decreases and, as consequence of the fact, the reflectance of the skin decreases by about 3.8 times in an hour. Then the reflectance increases gradually, that shows the beginning of glucose diffusion from the observed area and corresponding reduction of tissue immersion. On the basis of the experiments, one can conclude that partial matching of refractive indices of the collagen fibres of dermis and the interstitial medium under action of 40%-glucose solution prevails. It should be noted that the skin was transparent during a few hours. The second phase of tissue interaction with glucose is connected with taking down of the matching effect. It is determined by diffusion of glucose along the skin surface between two cellular layers with a few orders less permeability — epidermal and subdermal fat cells. For the used aperture of the detector system, optical clearing was registered during a few hours [57]. Intradermal injection of glucose influences also the functioning properties of skin, in particular the state of blood microcirculation in dermis. Glucose penetrates vessel walls, interacts with blood cells and leads to local dehydration of tissue and cells [4, 47, 91]. It causes a short-term slowing down and local stasis in different microvessels (arterioles, venules, capillaries), and dilation of microvessels in the area of its application [52]. The effect of glucose has some specific features [52] in comparison with other agents. The degree of dilation of vessels for glucose is larger than that for glycerol. The mean diameter increased by 30% at 30 s after glucose topical application to rat mesentry, and it continued to rise constantly throughout. At the fourth minute it rose by 2.5 fold on average. On the other hand, stasis was maintained in the majority of vessels, but blood flow appeared again in a few of the microvessels from the third to the fifth minute. The velocity of reflow was markedly slower than in controls; throughout the observation the intravascular hemolysis was not seen. There were only aggregates of cells. Individual cells with a clear form in blood aggregates in the lumens of microvessels were found. Vessel walls were registered exactly and, as a whole, after glucose application microvessels were visualized better than in controls (before glucose action) (see Fig. 21.8). The changes in blood flow were also local, but they were observed in a larger area (approximately 1 × 1 cm2 ) in comparison with the glycerol action [52]. It is important to know how the function of blood microvessels changes with decreasing of glucose concentration, i.e., with the loss of its hyperosmolarity. A 30%glucose solution caused stasis and dilation only in a part of the microvessels. In a few vessels a slowly oscillating blood motion without hemostasis was observed. A 20%-glucose solution also immediately slowed down the blood flow in all microvessels, but stasis is not observed. After 0.5–1.5 s of glucose application the flow rate reduced by half, and it continued to decrease till 20–25th second. From 35 to 40th second the rate in microvessels began to rise. Sometimes reversed shunts can be observed. After 3–4 min of glucose application blood flow in all vessels was not significantly different from the initial one [52].

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FIGURE 21.8: The effect of 40%-glucose solution on blood microvessels of rat mesentery: (a)—intact state before glucose application (control); (b)—at the 30th second of glucose action; (c)—at the 5th minute of glucose action [52].

Fluorescence measurements were performed for hamster dorsal skin with glucose applied to the subdermal side of the skin and rhodamine fluorescent film placed against the same skin side. Fluorescence was induced by a dye laser pulse at 542 nm delivered to the skin epidermal side by a fiber bundle and was detected by a collection fiber bundle from the epidermal surface at wavelengths longer than 565 nm. On average, up to 100% increase in fluorescence intensity was seen for 20-min glucose application [47].

21.4 Glucose-Induced Optical Clearing Effects in Blood and Cellular Structures 21.4.1 Optical clearing of blood The main scatterers in blood are RBCs. The major part of this cell is the hemoglobin solution: 90% of the weight of dry RBC is hemoglobin [121]. So the refractive index mismatch between hemoglobin solution in RBC cytoplasm and blood plasma provides strong blood scattering. Intravenous injection of glucose aqueous solutions is widely used in clinical practice [122]; thus optical clearing effects could be ex-

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FIGURE 21.9: Absorption spectra of blood at glucose injection calculated in the context of the optical model of blood. The glucose concentration is Cgl = 0, 0.5, and 1 g/ml [64]. pected. Upon introduction of glucose into blood, the refractive index of the blood plasma increases and becomes comparable with that of RBCs. As a consequence, the scattering coefficient decreases, while the blood anisotropy factor increases [65]. The spectral dependence of the refractive index of an aqueous glucose solution is defined by the Eq. (21.5). By analogy with this expression, the refractive index of a glucose solution in the blood plasma can be defined as nim p (λ ) = n p (λ ) + 0.1515Cgl,

(21.19)

where n p (λ ) is the refractive index of the blood plasma defined by Eq. (21.11). A change in the osmolarity of the plasma leads to changes in the size and the complex refractive index of RBCs due to their osmotic dehydration [91] and, consequently, to changes in their scattering and absorption properties. Normally, the osmolarity of blood amounts to 280–300 mosm/l [91]. The introduction of glucose into the blood plasma leads to a linear increase in the osmolarity, which reaches the value 6000 mosm/l at a glucose concentration in the blood plasma of about 1 g/ml. At introduction of glucose into the blood plasma, the hematocrit of the blood decreases. The osmotic dehydration leads to an increase in the concentration of hemoglobin in blood and, as a consequence, to an increase in both the real and the imaginary parts of the refractive index of RBCs. The changes in the real and imaginary parts of the refractive index were estimated using Eqs. (21.9) and (21.10) and account for the change in the hemoglobin concentration defined by Eq. (21.8). The absorption and reduced scattering coefficients and anisotropy factor of whole

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FIGURE 21.10: Calculated spectra of the transport scattering coefficient of blood at glucose injection. Cgl = 0, 0.1, 0.3, 0.4, 0.5, and 0.65 g/ml [64].

FIGURE 21.11: Calculated spectral dependence of the scattering anisotropy factor of blood at glucose injection. Cgl = 0, 0.2, 0.4, 0.6, and 1.0 g/ml [64].

blood at glucose injection (see Figs. 21.9–21.11) were calculated on the basis of optical model of blood [see Eqs. (21.12)–(21.14)]. Maximal optical clearing is observed at a glucose concentration of 0.65 g/ml [64].

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21.4.2 Time-domain and frequency-domain measurements The kinetic response of optical properties of blood, cell suspensions and tissue treated by glucose was measured using a time-domain and frequency-domain techniques [37–39, 63]. The waves in the near infrared (816, 830 and 850 nm) were used. Time-resolved spectroscopy is effective for measuring the optical properties of highly scattering medium; the frequency-domain can give a transient response of mean path length change [122, 123]. Intensity and phase of photon density waves are measured at several source-detector separations.

21.4.3 Experimental results For the noninvasive in vivo measurement the response of a nondiabetic male subject to a glucose load of 1.75 g/kg body weight, as in a standard glucose tolerance test, was used by continuously monitoring the product nµs′ measured on muscle tissue of the subject’s thigh [63]. The values of blood glucose concentrations lay in physiological range 80–150 mg/dL. The correlation between the blood glucose as measured with the home blood glucose monitor with the measured product nµs′ was indicated. An increase of glucose concentration in the physiological range decreases the total amount of tissue scattering [68]. A number of studies deals with the control of scattering properties of cellular tissues such as liver [37–39] and cell cultures and phantoms [37, 68, 88] using aqueous glucose solutions. It was demonstrated that light scattering of the rat liver results mainly from both the whole hepatocyte volume and the intracellular organelles, including mitochondria [37–39, 123]. Those studies suggested that mitochondria are the major source for light scattering in tissue by showing that about 85% of the reduced scattering of the liver originates from mitochondria. In living tissue light scattering depends not only from the extracellular refractive index (nex ) but also from the intracellular refractive index (nin ) and cell size upon exposure to osmotic pressure. If additions of OCAs are involved, one may encounter multiple effects due to changes in cell size and in cellular refractive indexes [37–39]. The addition of glucose solution into tissue can cause both a decrease in cell volume and an increase in refractive index of the extracellular fluid. These two changes contradict each other in the overall scattering behavior of the tissue. The effect of an increase of extracellular refractive index is larger, giving an overall decrease in µs′ . However, if the intracellular refractive index also increases when the added glucose permeates to the cells, the change of cell size becomes the major factor since the effects of intra- and extracellular refractive indexes cancel one another. Specifically, in the liver glucose perfusion measurements represented by Ref. [39], the mean path length of the perfused liver increased rapidly and then returned to its original value within 2 to 3 min. This increase in path length indicates that: (1) glucose may enter the cells and result in increases of both nin and nex so that the effect of changes in refractive indexes is relatively small, and (2) a decrease in cell size and cell volume fraction must occur in the beginning of the perfusion, leading to an increase in path length and µs′ , but soon the shrunken cells regain some of their original volumes [39].

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Thus, addition of glucose solution to cellular suspension and tissue affects the size of cells and the refractive indices of extra- and intracellular fluid, and thus affects the overall tissue scattering properties.

21.5 Conclusion This chapter shows that glucose administration in tissues and blood allows one to control effectively its optical properties. Such control leads to the essential reduction of scattering and therefore causes much higher transmittance (optical clearing) and the appearance of a large amount of least-scattered and ballistic photons, allowing for successful applications of different imaging techniques for medicine. The kinetics of tissue optical clearing, defined, in general, by both the kinetics of dehydration and refractive index matching, is characterized by different time intervals in dependence on tissue and used agents. The swelling or shrinkage of the tissue and cells under action of clearing agents may play an important role in the tissue clearing process. Along with common features in character of tissue clearing under action of immersion agent, glucose has a number of peculiarities in its influence on tissues and blood. The immersion technique has a great potential for noninvasive medical diagnostics using reflectance spectroscopy, frequency-domain measurements, OCT, confocal microscopy and other methods where scattering is a serious limitation. Optical clearing can increase effectiveness of a number of therapeutic and surgical methods using laser action on a target area hindered in depth of a tissue.

Acknowledgment This work has been supported in part by grants PG05-006-2 and REC-006 of U.S. Civilian Research and Development Foundation for the Independent States of the Former Soviet Union (CRDF) and the Russian Ministry of Science and Education, and grant of RFBR No. 06-02-16740-a.

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[41] V.V. Tuchin, A.N. Bashkatov, E.A. Genina, and Yu.P. Sinichkin, “Scleral tissue clearing effects,” Proc SPIE 4611, 2002, pp. 54-58. [42] A.N. Bashkatov, V.V. Tuchin, E.A. Genina, et al., “The human sclera dynamic spectra: in-vitro and in-vivo measurements,” Proc SPIE 3591, 1999, pp. 311319. [43] A.N. Bashkatov, E.A. Genina, V.I. Kochubey, et al., “Osmotical liquid diffusion within sclera,” Proc SPIE 3908, 2000, pp. 266-276. [44] A.N. Bashkatov, E.A. Genina, and V.V. Tuchin, “Optical immersion as a tool for tissue scattering properties control,” in Perspectives in Engineering Optics, K. Singh and V.K. Rastogi (eds.), Anita Publications, New Delhi, India, 2002, pp. 313-334. [45] A.N. Bashkatov, E.A. Genina, Yu.P. Sinichkin, et al., “Estimation of the glucose diffusion coefficient in human eye sclera,” Biophys., vol. 48, 2003, pp. 292-296. [46] E.A. Genina, A.N. Bashkatov, Yu.P. Sinichkin, et al., “Optical clearing of the eye sclera in vivo caused by glucose,” Quant. Electr., vol. 36, 2006, pp. 1119-1124. [47] G. Vargas, K.F. Chan, S.L. Thomsen, et al., “Use of osmotically active agents to alter optical properties of tissue: effects on the detected fluorescence signal measured through skin,” Lasers Surg. Med., vol. 29, 2001, pp. 213-220. [48] A.N. Bashkatov, E.A. Genina, I.V. Korovina, et al., “In vivo and in vitro study of control of rat skin optical properties by action of 40%-glucose solution,” Proc SPIE 4241, 2001, pp. 223-230. [49] V.V. Tuchin, A.N. Bashkatov, E.A. Genina, et al., “In vivo investigation of the immersion-liquid-induced human skin clearing dynamics,” Techn. Phys. Lett., vol. 27, 2001, pp. 489-490. [50] E.I. Galanzha, V.V. Tuchin, Q. Luo, et al., “The action of osmotically active drugs on optical properties of skin and state of microcirculation in experiments,” Asian J. Phys., vol. 10, 2001, pp. 503-511. [51] E.A. Genina, A.N. Bashkatov, I.V. Korovina, et al., “Control of skin optical properties: in vivo and in vitro study,” Asian J. Phys., vol. 10, 2001, pp. 493501. [52] E.I. Galanzha, V.V. Tuchin, A.V. Solovieva, et al., “Skin backreflectance and microvascular system functioning at the action of osmotic agents,” J. Phys. D: Appl. Phys., vol. 36, 2003, pp. 1739-1746. [53] I.V. Meglinskii, A.N. Bashkatov, E.A. Genina, et al., “Study of the possibility of increasing the probing depth by the method of reflection confocal microscopy upon immersion clearing of near-surface human skin layers,” Quant. Electr., vol. 32, 2002, pp. 875-882.

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