Spatially Resolved Magnetic Resonance: Methods, Materials, Medicine, Biology, Rheology, Geology, Ecology, Hardware

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Spatially Resolved Magnetic Resonance Edited by P. Blumler, B. Blumich R. Botto, E. Fukushima

@3WILEY-VCH

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Spatially Resolved Magnetic Resonance Methods, Materials, Medicine, Biology, Rheology, Geology, Ecology, Hardware

Edited by P. Blumler, B. Blumich, R. Botto, E. Fukushima

8WILEY-VCH Weinheim . New York Chichester Brisbane .Singapore .Toronto 1

Editors: Dr. Peter Bliimler Prof. Dr. Bernhard Bliimich Lehrstuhl fur Makromolekulare Chemie und Magnetic Resonance Center, MARC, RWTH Aachen Worringer Weg 1 D-52074 Aachen, Germany

Prof. Dr. Robert E. Botto Chemistry Division Argonne National Laboratory 9700 South Cass Avenue Argonne, Illinois 60439-4828 USA

Dr. Eiichi Fukushima 2425 Ridgecrest Dr. SE Albuquerque New Mexico 87108 USA

This book was carefully produced. Nevertheless, authors, editors and publisher do not warrant the information contained therein to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.

Cover picture: Velocity NMR image of shear bands in a cone-plate rheometer. For details see chapter 49. Reproduced with permission of M. M. Britton and P. T. Callaghan.

Library of Congress Card No. applied for A catalogue record for this book is available from the British Library Die Deutsche Bibliothek - CIP-Einheitsaufnahme Spatially resolved magnetic resonance : methods, materials, medicine, biology, rheology, geology, ecology, hardware / ed. by Peter Bliimler ... Weinheim ; New York ; Chichester ; Brisbane ; Singapore ; Toronto : Wiley-VCH, 1998 ISBN 3-527-29637-9

0 WILEY-VCH Verlag GmbH, D-69469 Weinheim (Federal Republic of Germany), 1998

Printed on acid-free and low chlorine paper All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form - by photoprinting, microfilm, or any other means - nor transmitted or translated into machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law. Printing: betz-druck GmbH, D-64291 Darmstadt Bookbinding: GroBbuchbinderei J. Schaffer, D-67269 Griinstadt Printed in the Federal Republic of Germany

Foreword Just as the ,,Heidelberg Conference" has moved about, even as far as the American Southwest, it has broadened its scope to include essentially all non-clinical magnetic resonance imaging. The immense variety of techniques and applications in human diagnostic NMR imaging is driven by medical needs, but limited by considerations of safety, time, and economics. In the broader worlds of science and technology, the seemingly-unlimited ways spin magnetization can be manipulated, and the forms of matter that can be studied, are much more various, and the experiments involve a broader range of the knowledge and skills of physicists, chemists, and materials scientists. The addition of spatial resolution to the tools available for such studies allows them to be applied to many heterogeneous objects, and to processes, such as transport, that involve spatial dimensions on the supramolecular scale. Still, however, much of the ingenuity of practitioners in the field is devoted to overcoming difficulties and artifacts that limit its usefulness. NMR, with or without imaging, is a powerful but fragile technique, and all too often promising approaches to beautiful experiments are blocked by ugly details. One way to read this volume is to look for the implicit terrain maps of practicality. What is being attempted, and why not something else? Why is a particular set of techniques, a particular piece of equipment, being used? Because it is available, or because nothing else will do? In clinical studies, the questions to be asked and the priorities are often better defined, but in other areas NMR spectroscopy and imaging often seem to be answers looking for questions. As practitioners learn more about the wider world, and outsiders become more familiar with the possibilities, limitations and peculiarities of magnetic resonance methods, the field is maturing. This volume documents a long stride toward such maturation and integration, along with the ever increasing power and subtlety of techniques and analyses, and should inspire developers and users in all areas, from medicine to geology.

Urbana, January 1998

Paul C . Lauterbur

Preface In the year 1991 the First Conference on Magnetic Resonance Microscopy has taken place in Heidelberg, Germany. Based on the contributions to this meeting the book Magnetic Resonance Microscopy: Methods and Applications in Materials Science, Agriculture and Biomedicine, VCH Weinheim, 1992, had been edited by Bernhard Bliimich and Winfried Kuhn and provided an up-to-date reference on the subject of non-medical imaging. At the time the methods in magnetic resonance imaging evolved largely from the area of clinical diagnostics, but were adapted more and more to other applications, and extensive studies on test phantoms demonstrated potential use in various fields of science and engineering. Six years later, the Fourth International Conference on Magnetic Resonance Microscopy was held in Albuquerque, New Mexico, and it was felt, that an update of the Microscopy Book was needed. During this time, the field has advanced significantly, and several new techniques were introduced as well as interesting new applications covering such diverse areas as polymer and elastomer characterization, analysis of construction materials and material flow, various topics in biomedicine, and plants studies. The focus on microscopy features was broadened to include magnetic resonance of macroscopic systems. Applications in the area of oil-well analysis, and non-destructive quality and process control are made possible by the development of dedicated instrumentation which can readily be moved to the site of interest. The editors are indebted to the authors for timely submission of their contributions and to the referees, who helped to improve a number of manuscripts. We are indebted to Tanja Rente for transforming the manuscripts into book format and to VCH for their cooperation and help with the final editing and production process.

September 1998

Peter Bliimler, Bernhard Blurnich, Robert E. Botto. and Eiichi Fukushima

Contents Foreword P. C. Lauterbltr ...................................................................................................

V

Preface P. Bliimler, B. Bliinziclz,R. E. Botto, and E, Fukushinia ....................................

VI

Methods 1.

Spatial Resolution in Spectroscopic Imaging

M. von Kienlin and R. Pohrnann ................................................................... 2.

3

CYCLOCROP Mapping of 13C Labelled Compounds: Perspectives in Polymer Science and Plant Physiology

M. Heidenreich, A. Spyros, W. Kockenberger, N . Chandrakunzar, R. Bowtell, R. Kimniich ............................................................................... 2 1 3. Contrast Enhancement Based on Intermolecular Zero Quantum Coherences for Magnetic Resonance Imaging and Microscopy R. R. Rizi, S. Ahn, J. Hopkins, J. S. Leigh, and W. S. Warren ................... 53 4.

Frequency Dependence of EPR Sensitivity G. R. Eaton, S. S. Eaton, and G. A. Rinnrd ................................................

65

5. SPRITE Imaging of Short Relaxation Time Nuclei B. J. Balconi ................................................................................................

75

6. Refocusing a Spin-Echo in the Presence of a Strong Readout Gradient Field Using an Underdriven Gradient Pulse G. PlaninSic and M . Syrnms........................................................................

87

7.

The Analysis and Development of Pulse Sequences for Self-Diffusion Weighted Stray-Field Imaging A. J. Bohris, D. A. Faux, D. G. Gillies, and P. J. McDonald .....................

95

VIII

Conterztc

8. Imaging Diffusion with Non-Uniform B, Gradients K. Woelk,B. L. J. Zwank, J. Bargon, R. J. Klingler R. E. Gerald 11, and J. W.Rathke .............................................................

103

9. In Situ Imaging of Charge Carriers in an Electrochemical Cell

R. E. Gerald 11, R. J. Klingler, J. W.Ratlike, G. Sandi, and K. Woelk..... 1 1 1

10. Efficient Simulation of Spin Echo, Gradient Echo, Fast, and Ultrafast NMR Imaging Sequences by Isochroinat Summation P. Shkarin and R. G. S. Spencer ...............................................................

121

11. A Novel Algorithm for Tumor Characterization by Analysis of Transversal Relaxation Rate Distributions in MRI

R. Martin and M. Martin-Landrove .........................................................

133

Materials 12. Materials Imaging with Examples from Solid Rocket Propellants W.E. Maas, L.H. Merwin, and D.G. Cory ..............................................

141

13. 129XeMRM Characterization of Pore Structures in Silica Aerogels

D.M. Gregovy, R. E. Gerald II, D. J. CEifSord, and R. E. Botto...............163 14. NMR Imaging of Mechanically Treated Polymers

B. Traub, S. Hafner, D. Maring, and H. W. Spiess...................................

179

15. Soft-Matter Relaxation by the NMR-MOUSE A. Guthausen, G. Zimmer, R. Eymael, U. Schmitz, P. Bliirnler, and B. Bliimich ......................................................................

195

16. Application of NMR-Imaging to Industrial Polymers M. Knorgen, U. Heuert, H. Schneider ......................................................

21 1

17. Electron Spin Resonance Imaging (ESPRI) of Transport Processes in Polymeric Systems S. Schlick, P. Eagle, K. Kruczala, and J. Pilar .......................................

.22 1

Contents

IX

18. Stray-Field Imaging and Magnetic Resonance Microimaging Studies of High Impact Polystyrene, an Elastomer-Toughened Material J. A. Chudek, G. Hunter, F. Mohd Soin, P. J. McDonald, and B. Newling .........................................................................................

235

19. Mixed Solvent Ingress into PMMA Measured by Stray-Field Magnetic Resonance Imaging D. M. Lane, P. J. McDonald, and J , L. Keddie ........................................

241

20. Stray-Field Imaging and Magnetic Resonance Microimaging Studies of the Anisotropic Absorption of Solvents by Extruded Polypropylene

R. J. Abbott, J. A. Chudek, G. Hunter, R. L. MacKay, P. J. McDonald, and L. Squires ................................................................

253

21. NMR Microimaging: A Useful Tool to Study the Dissolution of Solids N. Black, T. Vienneau, and Y. Pan ...........................................................

259

22. Observation of the Water Distribution During Drying of Textiles

J. Leisen, L. Hou, H. W.Beckham, and W. W. Carr .................................

265

23. A Broad-Line Magnetic Resonance Imaging Study of Water Transport in Cementitious Building Materials A. J. Bohris, U. Goerke, P. J. McDonald, MMulheron, B. Newling, and B. Le Page ......................................................................

273

24. Stray-Field Imaging and Magnetic Resonance Microimaging Studies of Water Intrusion/Stress Mobilisation in Dense Polymer Systems Used in Construction S. N. Scrimgeour, G. Hunter, W. J , Harvey, C. H. Lloyd, D. M. Lane, and P. J. McDonald ..............................................................

281

25. Stray-Field Magnetic Resonance Imaging of Hardening Materials T. G. Nunes, P. R. Bodart, and E. W.Randall ..........................................

287

26. Applications of Stray-Field Imaging to Dental Materials Science S. N. Scrimgeour, C. H. Lloyd, G. Hunter, D. M. Lane, and P. J. McDonald ..............................................................

293

x

Contents

27. Particle Compaction as Observed by MRI R. A. Waggoner, M. Nakagwa, S. J. Glass, M. Reece, and E. Fukushima .....................................................................................

299

Medicine and Biology 28. 2H Double Quantum Filtered NMR Histology and Diffusion Measurements in Isolated Nerves and Blood Vessels

H. Shinar, Y. S h a ~U. Eliav, Y. Seo, and G. Navon ................................

307

29. Translational Diffusion of Water in Lung Tissue B. Geil, D. C. Ailion, C. Laicher, and A. G. Cutillo .................................

323

30. Studies of Perfused Brain Slices with MR Microscopy

J. D. Bui, D. L. Buckley, M, I. Phillips, and S. J. Blackband ...................337 31. Application of NMR Micro-Imaging to the Study of Water Transport in Eye Lenses B. A. Moffut, R. J. W. Truscott, M. H. J. Sweeney, and J , M. Pope .......... 345

32. Relaxation Anisotropy as a Possible Marker for Macromolecular Orientations in Articular Cartilage Y. Xia ........................................................................................................

351

33. Morphometric Analysis of Cartilage Grown in a Hollow Fiber Bioreactor Using NMR Microscopy K. Potter, K. W.Fishbein, W.E. Horton, and R. G. S. Spencer ...............363 34. EPR Imaging of the Rat Heart J. L. Zweier and P. Kuppusumy................................................................

373

35. Application of High Resolution Cardiac Magnetic Resonance Imaging to Monitor a Rodent Model of Cardiac Dysfunction S. Chandru, K. G. Gurbanov, R. Strittmatter, E. H. Ohlstein, G. Z, Feuerstein, and S. K. Sarkar ...........................................................

389

36, Fast MR Imaging of Esophageal Motility Y. Seki, S. Naruse, Y. Seo, M. Murakami, T. Ozaki, M. Kitagawa, H. Zshiguro, Y.Nakue, and T. Hayakawa .................................................

395

Corntents

XI

37. Spatial NMR Studies of Tumor Spheroids K. R, Minard, R. A. Wind, W,E. Maas, K. Millis, and D. G. Cory ..........403 38. 19F Chemical Shift Imaging of F-nuc Formed from 5-FU in Mouse Tumor by Fast Spin Echo

Y. Doi and Y. Kunazawa ...........................................................................

413

39. I7O and 31P Magnetic Resonance Imaging and Spectroscopy: In Vivo Investigations of Cell Bioenergetics G. D. Mateescu, M. Cabrera, and D. Fercu .............................................

421

40. Volume Localized 'H MRS of Renal Osmolytes G. J. Cowin, I. A. Leditschke, S. Crozier, and 2.H. Endre ......................

431

41. MRM in the Modeling of the Ossicular Chain

E. W.Abel, J. A. Chudek, G. Hunter, R. M. Lord, R. L. MacKay, and R. P. Mills ..................................................................

439

42. NMR Imaging of Rigid Biological Tissues

Y. Seo, H. Takarniya, H. Ishikawa, T. Nakashima, Y. S h a e and G. Navon .............................................................................

445

43. Magnetic Resonance Microimaging of Teeth S. N. Scrimgeour, C. H. Lloyd, G. Hunter, J. A. Chudek, and R. L. MacKay ...............................................................

459

44. MRM, an Alternative Approach to the Study of HostParasitoid Relationships in Insects

1.A. Chudek, G. Hunter, R. L. MacKay, S. Moritz, A. N. E. Birch, I. E. Geoghegan, R. J , McNicol, and M. E. N. Majerus ...........................

467

45. Plant Growth Studies Using Low Field NMR L. van der Weerd, T. Ruttink, D. van Dusschoten, F. J. Vergeldt, P. A. de Jager, and H. Van As ..........................................

473

46. Fast Spatially Resolved Displacement Imaging in (Bio)Systems T. W.J. Scheenen, D. van Dusschoten, P. A. de Jager, and H. Van As ...481

XI1

Contents

Diffusion and Flow 47. Generalized Treatment of Modulated Gradient Spin Echo Attenuation for Restricted Diffusion in Spherical Pores S. L. Codd and P. T. Callaghan ................................................................

489

48. NMR-Imaging Techniques for Quantitative Characterization of Periodic Motions: 'Incoherent Averaging' and 'Spectral Side Band Analysis' U. Goerke and R. Kivnmich.......................................................................

499

49. Shear-Banding in a Cone-and-Plate Rheometer M. M. Britton and P. T. Callaghan ...........................................................

507

50. Applications of NMR Flow Imaging in Material Science S. Laukemper-Ostendor- K. Rombach, and P. Blumler ...........................

517

5 1. A Non-Invasive Investigation of Concentration Polarization in Crossflow Microfiltration of Colloidal Silica D. Airey, V. Chen, J. Wu, and J. M. Pope ................................................

531

52. Evaluation of Mixing Profiles of Power Law Fluids in Scraped Surface Heat Exchanger Geometry Using MRI W. Wang, J. H . Walton, M , J. McCarthy, and K. L. McCarthy ................539 53. The Self Diffusion of 1,3 Propylene Glycol in Track Etched Membrane Pores E. Vasina, V. Skirda, V. Volkov,A. Nechaev, and B. Mchedlishvili .........547

Geology and Ecology 54. Review: NMR Detection and Characterization of Hydrocarbons in Subsurface Earth Formations

R. L. Kleinberg, and C. Flaum .................................................................

555

55. Why Would an Oil Company Use MRI? B. A. Baldwin and R. L. King ....................................................................

575

Contents

XI11

56. Pore Structure and Connectkty of Porous Rock by High Resolution NMR Microscopy

D. A. Doughty and L. Tornutsa .................................................................

603

57. Relaxation-Diffusion Processes and Local Magnetic Field Distributions in Natural Porous Media

D. Pe'rez, A. Benavides, S. Gonzdez, D. Barrantes, and M. Martin-Lundrove ..........................................................................

617

58. MR Microscopy of Savannah River Tank Waste Simulants

K. R. Minard, R. A. Wind, and L. 0. Dworjanyn ......................................

627

Hardware 59. A Compact, Superconducting Magnet for Magnetic Resonance Microscopy S. Crozier and D. M. Doddrell .................................................................

639

60. MRI Gradient Coil Optimization

F. D. Doty ................................................................................................. 647 61. Novel, Asymmetric Gradient Coil Sets for Magnetic Resonance Microscopy S. Crozier, W. U. Roffmann, and D. M. Doddrell .....................................

675

62. Novel Gradient Coils for Magnetic Resonance Microscopy E. R. Andrew, M. Kempka, S. Sagnowski, and E. Szczesniak ................... 683

63. The NMR Endoscope R. Haken, P. Bliimler, and B. Bliimich .....................................................

695

64. Development of a Flexible Pulse Programmer for MRI Using a Commercial Digital Signal Processor Board K. Kose and T. Haishi ...............................................................................

703

XIV

Contents

Tutorial 65. Introduction to Magnetic Resonance Y.Xia ........................................................................................................

713

Author Index. ..................................................................................................

.74 1

Subject Index ...................................................................................................

745

Methods

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1. Spatial Resolution in Spectroscopic Imaging Markus von Kienlin and Roy Pohmunn Physikalisches Institut (Biophysik) Universitat Wurzburg, D-97074 Wurzburg, Germany

Abstract This contribution reviews various aspects of the spatial resolution obtained in spectroscopic imaging experiments. After showing the fundamental difficulty to define “spatial resolution”, it is shown that the precision in the determination of the location of a point source is only limited by the signal-to-noise ratio, and is much better than the nominal resolution. Then the resolving power is analyzed using the Rayleigh criterion, and the importance of a sufficient digital resolution is illustrated. Finally, the importance of the “spatial response function” is emphasized.

1.1 Introduction: Localized Spectroscopy Most conventional methods to examine physiologic parameters or metabolic processes directly in living tissue require to extract a sample, which then is analyzed with biochemical means. These biopsies in animals or humans can not only be painful, but often carry some risk. Localized NMR spectroscopy provides non-invasive biopsy: it can analyze the chemical composition of well defined regions within the body, without the need to extract a specimen. Localized NMR spectroscopy therefore has not only found many applications in fundamental research, where it contributes to a better understanding of metabolism, but is also gaining importance in clinical diagnostics. To these ends, a high quality and reliability of localization is prerequisite, and huge research efforts have been made to improve the sensitivity, the spatial resolution, the stability and the patient comfort of these techniques.

4

M. von Kienlin and R. Pohmann

First attempts to acquire NMR spectra within a larger object employed surface coils [1,2] or shaped the homogeneous region of the main, static magnetic field (“topical magnetic resonance TMR’ 13-51). P. Bendel et al. were the first to acquire spectroscopic information in the presence of a magnetic field gradient [6]. The first to employ pulsed magnetic field gradients and selective excitation pulses to select a voxel within the sample were W. Aue et al. [7]. Their work started the development of a large number of techniques which allow to measure the spectrum of more or less rectangular volumes; the best known of these are DRESS 181, ISIS [9], STEAM [lo-121 and PRESS 1131. These single voxel techniques today tend to be replaced by “spectroscopic imaging”, also called “chemical shift imaging CSI [14,15].” CSI has become available to a large number of users through the advent of actively shielded gradient systems and more sophisticated instruments. It offers the advantage to measure spectra not only in a single volume element, but simultaneously in a whole grid of many volumes across the sample, thus allowing to compare local variations within the studied object. In this contribution, we analyze the spatial resolution obtained in spectroscopic imaging. The knowledge of the spatial resolution is important for further technical developments, but it is also crucial for the correct interpretation of spectroscopic images. After a more precise definition of the topic, the basic principle of Fourier imaging will be briefly introduced. The concept of the spatial response function will be described, followed by an in depth analysis of the spatial resolution. Finally, the impact of numerical data representation will be clarified.

1.2 What is “Spatial Resolution”? The goal of localized NMR spectroscopy in vivo is to acquire spectra from well circumscribed anatomical areas. To achieve high specificity, a good discrimination from neighboring regions is essential, the contamination by signals from other regions must be as low as possible. It is furthermore advantageous to have as small a sensitive volume as possible, which fits well into the target region, and to avoid as much as possible tissue heterogeneity. The major hurdle is the poor sensitivity of NMR spectroscopy, which usually imposes the lower limit for the size of the sensitive volume.

1. Spatial Resolution in Spectrosropic Imnging

5

While this qualitative description of the goal of spntial resolution is straightforward, it is much more difficult to define a quantitative measure for the spatial resolution. The notion “spatial resolution” can be interpreted in many different ways. A possible meaning can be the precision, by which the location of a signal source within the sample can be determined. Another and completely different definition is to measure the minimal distance between two signal sources within the sample, which still allows to distinguish them. Both definitions allow to calculate some specific number for the spatial resolution of some measurement method. Such a number does allow to compare various methods its significance is nevertheless questionable. In biomedical applications, there are no point sources of NMR signal, but one has to deal with extended and heterogeneous regions with irregular shape. The knowledge of the “spatial response fimction SRF’ is essential for a correct interpretation of the results, and to estimate the degree of possible signal contamination from adjacent regions. The SRF indicates the weight of the contribution of every point in space to a localized spectrum. The shape of the SRF essentially depends on the number of image points, the sampling scheme, and eventual filtering and other parameters of the acquisition and the sample. It is therefore not sufficient to indicate only the nominal resolution of the experiment: one should also show the SRF! Other circumstances which can further deteriorate the quality of localization - like motion artifacts or diffusion - will not be considered in the following.

Fig. 1.1: The spatial resolution is mainly limited by the low sensitivity. If a spectrum with sufficient SNR can be acquired from the large sphere in only 10 min, it takes almost 11 hours (!) to obtain a spectrum with the same SNR from the smaller sphere with half the diameter!

6

M. von Kienlin and R. Pohmann

The issue of spatial resolution is mainly due to the low sensitivity of NMR spectroscopy. As demonstrated in Fig. (1. l), the low sensitivity is the main obstacle to increase the spatial resolution. The detected NMR signal is directly proportional to the sample magnetization within the sensitive volume. If the spin distribution is homogeneous, the signal decreases with the third power of the linear dimension of the volume. The signalto-noise ratio (SNR) is proportional to the square root of the total duration of an experiment, the duration required to achieve some given SNR therefore depends to the sixth power of the linear dimension of the sensitive volume. At the current state of coil and receiver technology, where the SNR already is mainly dominated by the properties of the sample, substantial further improvements in sensitivity cannot be expected. Sensitivity thus sets a lower limit to the size of volumes selected in localized spectroscopy. If their size can hardly be reduced, it is nevertheless possible to improve their sharpness. The following sections show which parameters influence the shape of the SRF, and how that shape can be improved in spectroscopic imaging.

1.3 Fourier Methods for Spectroscopic Imaging The most common way to acquire spectroscopic images is based on a Fourier method proposed by A. Kumar et al. [14]. As early as 1979, A. Maudsley applied phase encoding and Fourier reconstruction to map an inhomogeneous magnetic field by measuring the spatial dependence of the resonance frequency [16]. Successful experiments both on phantoms [15,17] and in vivo [18,19] have shown the numerous advantages of spectroscopic imaging, which now is being used in an increasing number of clinical studies. A more detailed survey can be found for instance in [20]. The simplest possible pulse sequence for spectroscopic imaging is plotted in Fig. 1.2. The excitation pulse is followed by a short gradient pulse of length T~ in one, two or all three directions, which encodes the spatial information as phase modulation of the transverse magnetization. Then, all gradient fields are switched off and the signal of the freely precessing spins is detected. This experiment is repeated for some number of repetitions, applying regularly incremented gradient strengths. The spectroscopic image is then obtained by applying Fourier-transformations in all spatial and the spectral dimensions. This simple sequence can be modified by generating spin-echoes or stimulated echoes, or by using slice-selective excitation or refocusing pulses, but these variations do not affect

I . Spatial Resolution in Spectroscopic Imaging

7

the basic principle of spectroscopic imaging. In the following mathematical description only one spatial dimension is treated, the generalization to two or three dimensions is straightforward.

a

RF I I I

Fig. 1.2: A pulse sequence of spectroscopic imaging. After excitation, gradients are switched on for a short time to modulate the phase of the magnetization. The signal is then acquired in the homogeneous field.

The volume covered by the spectroscopic image is usually called "field-of-view''

(FOV). The nominal resolution AT-,,,, is the size of the image elements (voxels). For an image with N points it is given by:

Ar,,,

= FOV/N

(1.1)

For the mathematical description, it is advantageous to define a variable k which describes the gradient strength integrated over time [21]:

with zG the duration of the gradient pulse. The variable k can be interpreted as the spatial

8

M. von Kienliri and R. Pohmann

frequency: the higher the value of k, the faster the spatial variation of the phase of the transverse magnetization after the gradient pulse. The required increment Ak between two successive gradient steps is determined directly by the F O E 1

Ak =-FOV The gradient steps are usually applied in increasing order, beginning at -NAk/2 and ending at (Nl2-1)Ak. It is, however, advantageous to use gradient values that are distributed symmetrically about zero, from - (N - 1)Ak12 to (N - 1)Ak12 [22-241. Using such a phase encoding scheme yields a purely real pointspread function (cf. section 1.4). The strength of the n* gradient pulse then is:

For high N , large values of the spatial frequency k are reached, and a small nominal resolution Ar is obtained. If p(r) is the signal emanating from location r, the signal that is detected after the nth phase encoding gradient can be written as the integral over the entire object, modulated by a phase which depends on the position and the gradient strength:

Performing a discrete Fourier transformation on the N acquired signals, one obtains for the signal from the point n' Ar (as long as the sampling theorem has been respected and the signal has not been truncated):

Except for the phase factor, the image represents the actual distribution of the magnetization in the sample. The phase factor can be compensated by either taking the magnitude of the image, or by applying an appropriate phase correction. Spectroscopic imaging has the considerable advantage that in only one experiment, the spectra from all N voxels are obtained simultaneously. Furthermore, the localization is not affected by chemical shift artifacts.

1. Spatial Resolution in Spectroscopic Imaging

9

A disadvantage of conventional spectroscopic imaging is the long minimal duration of an experiment: in contrast to techniques like STEAM or PRESS, which can acquire the spectrum of a voxel in a single transient, spectroscopic imaging requires at least N repetitions. Several methods for fast spectroscopic imaging have been proposed, which sample the signal in the presence of gradients and reduce the minimal duration drastically [25-301. However, they require high experimental complexity, and do not offer any gain in sensitivity.

1.4 The Spatial Response Function In contrast to conventional IH-imaging or to multi-dimensional spectroscopy techniques, the number N of voxels (i.e. phase encode steps) in spectroscopic imaging is usually very small. This is due to restrictions on the duration and to the low sensitivity of the experiment. The high spatial frequencies of the sample are then inevitably truncated, and the assumptions behind eqn. (1.6) are no longer valid.

A spectroscopic image thus does not reflect the actual distribution of the spins, but its convolution with a function that is caused by the lack of the high spatial frequencies, the pointspread function PSF [31-351. The signal from some location in the sample is found not in only one pixel of the spectroscopic image, but spread out across all pixels. The PSF describes the amplitude of the propagation of the signal from the point ro in the sample to the image pixel with coordinate rn=n Ar:

This equation can be read in two ways: for a fixed yo, the PSF indicates how the signal from spins at this position is distributed over all pixels of the image. The PSF is a discrete function consisting of N points. A complementary way of interpreting eqn. (1.7) is usually more relevant for localized spectroscopy: for a fixed yn, its dependence on yo yields the spatial response function SRF. This continuous function describes the contribution of every point of the sample to the spectrum in one image pixel.

10

M. von Kienlin and R. Pohmann

In Fig. 1.3, the shape of the SRF for the case of N = 8 phase encoding steps obtained with an unfiltered Fourier transformation is shown. Several important properties of Fourier imaging become visible: Not only does the magnetization from inside the volume of interest (VOI), nominally placed in the region n' Ar, contribute to the signal of its image pixel, but a more or less strong contamination by signals from outside this pixel is possible. The spatial response function even extends beyond the actual FOV. This has to be taken into account for samples that are larger than the FOV, and this can cause contamination of voxels close to the edge of the image by signals emanating from the opposite side of the image.

1.o

c 0.5

0 .-

I\

I\

I

\

c

0

c

3

a, rn

5Q

0.0

(I)

F (d .c

(d

% -0.5

4-

FOV

-1 .o

spatial coordinate r

Fig. 1.3: The spatial response function (SRF) of a spectroscopic image with N = 8 phase encode steps for an unfiltered Fourier transformation. The largest contribution to the signal emanates from the region marked 'VOI'. The SRF, however, extends beyond the VOI and even beyond the entire FOV. Signals from outside the FOV thus are aliased into the FOV. Mainly signals from sharply edged regions with high signal amplitudes can propagate over the entire image.

The contamination due to the SRF is particularly high if regions with a high signal amplitude and sharp edges are present. This situation is given for instance in spectroscopic IH-imaging of the brain, where a thin layer of fat outside the skull often contaminates all the spectra in the brain. The quality of the spectra then does not allow reliable

1. Spatial Resolution in Spectroscopic Imaging

11

conclusions about the spatial distribution of the examined substances as long as no additional measures are applied to correct or to avoid these effects. Only with an accurate knowledge of the SRF, the reliability of an experiment can be assessed.

1.5 Position of a Point Source In section 1.2, one possible definition for “spatial resolution” was given as the precision in the determination of the location of a single signal source. In the following section, it will be demonstrated that in a Fourier imaging experiment the exact location of a point

source can be determined with very high precision. The accuracy of this measurement is only limited by the signal-to-noise ratio, and it is in all practical circumstances much better than the nominal resolution. These statements will be further clarified and quantified. In a one-dimensional situation (see Fig. 1.4), a single point source is located at position xo. One conducts N phase-encoded experiments, in each of which the strength of the phase-encoding gradient is incremented by Akx. According to eqn. (lS), the detected signals s, can be written as: sn

=

A e-inAkk,xo

,

N n =-- N --+ 2’ 2

N 1, ...,-2

In this equation, A is the amplitude of all the signals, and i = f

1

i . The phase qn of the

measured signals is given by:

From the exponent in eqn. (1.Q one can also recognize the following relation for the phase of the signal:

qn = n Akx xo

(1.10)

This is the expression of a straight line through the origin, with the slope rn = Ak, xo (cf. Fig. 1.4). If one determines m from the measured values qn,the location of the signal

12

M. von Kienlin and R. Pohmann

source can be calculated as:

xo =-

m

(1.11)

Akx The values of the employed phase-encoding gradients are known, the precision of the calculated position xo hence depends mainly from on accuracy of the phase measurement. In principle, it is even possible to determine the position with only two independent experiments. In Fourier imaging, the detected signals are generally reconstructed with a Fourier transformation. A spatial Fourier transformation can be looked at as a correlation of the . Through variation of x the fremeasured signal with the reference function e-i quency of the reference function is changed, and the correlation yields the image of the spatial distribution of the spin magnetization. In our particular case of a single point source, this corresponds to determining the spatial frequency A k x o in the measured signal. Under these circumstances, (continuous) Fourier transformation and the determination of the slope (eqn. 1.10) are equivalent.

Fig. 1.4: The position of a single point source can be measured with an accuracy that is only limited by the signal-to-noise ratio. a) Let the location of the point source in a one-dimensional setup be x,,. b) The phase of the NMR signal is measured in N = 8 phase-encoded experiments. The location of the point source can be determined from the slope of the obtained phase ramp.

How precisely can one determine the position of a point source, if each of the measured signals is deteriorated by thermal noise? Let the signal-to-noise ratio SNR of each measurement be

A SNR = 0 s

(1.12)

1. Spatial Resolution in Spectroscopic Imaging

13

with os being the standard deviation of the thermal noise, and A the signal amplitude in each measurement. The noise in the real and imaginary parts of the signal is independent.

How does this noise propagate when computing the phase of the signals? In conventional error analysis, the standard deviation ototof a variable y i = f (x,,x2,...,xt) is given by the standard deviations oi as:

(1.13)

In eqn. (1.9), both the numerator and the denominator contain an uncertainty due to the (uncorrelated) noise. Partial derivatives according to eqn. (1.13) yield for the standard deviation of the phase ocp:

-

0,

(1.14)

>.Im2{sn}

JRe2 {sn

The slope m of the regression line through all phase values is calculated as [36]:

n=l

\n=~

,)

The standard deviation omof this slope becomes, using eqn. (1.14):

(1.15)

14

M. von Kienlin and R. Pohmann

(1.16)

The position of the point source is calculated from eqn. (1.11). The standard deviation (T,

in this calculation, which is the uncertainty of the position, is related to the standard deviation of the slope as:

(1.17)

-

1 SNR

FOVfi N f i

Incorporating the expression for the nominal resolution Ax = FOV/N , one finally obtains the following, simple expression for the relative error of the position:

(1.18)

The error in the determination of the position of a point source is inversely proportional to the signal-to-noise ratio of the individual measurements, and to the square root of the number of phase-encoding steps. With an SNR of 25 and N = 8 phase-encoding steps, one obtains (3, /Ax = 0.049 : the precision is more than twenty times higher than the nominal resolution! On the other hand, a low SNR can be the factor limiting the resolution.

1. Spatial Resolution in Spectroscopic Imaging

15

1.6 The Rayleigh Criterion One of the possible definitions for spatial resolution which were mentioned in section 1.2 was the minimal distance between two objects required for them to be distinguishable in the image. This can be analyzed with the Rayleigh criterion which is well known from optics. According to the Rayleigh criterion, two objects can be distinguished if the maximal intensity of one occurs at the first diffraction minimum of the other. A different description of the same criterion runs that the intensity between the two image maxima has to drop to 8 1% of the maximum value for the two maxima to be distinguishable. This criterion is also applicable to Fourier NMR imaging. Figure 1.5 elucidates the Rayleigh criterion for two neighboring point sources. The thin lines represent for each of the two sources the intensity (the square of the SRF‘) as a function of space, the thick line is the sum of the two. The two sources must be at a distance which is just equal to the size of a voxel (which is the nominal resolution according to eqn. 1.1) for the intensity to drop to 81% of its maximum value. In this position, the maximum of one source occurs exactly at the first minimum of the other. At first glance, this result doesn’t appear to be surprising: the spatial resolution according to the Rayleigh criterion is equal to the nominal resolution. However, closer inspection reveals that the two objects nevertheless would be indistinguishable on a conventionally processed image: two neighboring image pixels would have the same gray value, and there is no way to tell whether the image originates from a single larger or two smaller objects. In order to distinguish the two objects, at least one image pixel with lower image amplitude needs to appear between the two. This is a first indication that the

digital resolution of the image needs also to be considered; this will be treated further in section 1.7. Lord Rayleigh himself was very critical towards his own rule to quantify the resolving power. He wrote [37]: “This rule is convenient on account of its simplicity and it is sufficiently accurate in view of the necessary uncertainty as to what exactly is meant by resolution.” The Rayleigh criterion is not an absolute, quantitative measure for the limit of resolution, but only indicates its order of magnitude. Indeed, there are even other criteria which are used in optics, for instance the less stringent Stokes-criterion. The difficulty to give an exact measure of resolving power is mainly due to the fact that the examined objects are not point sources, but have some finite dimensions and irregular shapes. In every single case, one would have to examine how accurately any claim about the exact position of

16

M . lion Kienlin and R. Pohmann

some border or the size of some object can be - the Rayleigh criterion can only give an indication. The best accurate statement that can be given is that the visualized image arises from a convolution of the real distribution with the pointspread function of the imaging method. 1.2

1.o

,

I

p . 0 4

0.8

x .-+

2a,

0.6

c

S .-

0.4

0.2

0.0 0

1

2

3

4

5

6

7

8

spatial coordinate r

Fig. 1.5: Rayleigh criterion in Fourier NMR imaging. The intensity between two image drops to 81% if the distance between two objects is just equal to the nominal resolution. According to the Rayleigh criterion, this is the minimal distance for the objects to be distinguishable.

1.7 Digital Resolution and Fourier Interpolation Up to here, only the influence of the acquisition parameters of a Fourier imaging method on the spatial resolution has been considered. The processing and the visualization methods also affect the ultimately obtained resolving power. In contrast to most optical instruments, NMR instruments usually use digitized signals and numerical processing prior to some graphical visualization. As long as there is no violation of the sampling condition (also called “Shannon theorem”), there is essentially no loss of information due to

I . Spatial Resolution in Spectroscopic Imaging

17

the digitization. Indeed, it is possible to show that -provided some requirements are fulfilled, which is the case in most practical situations - one can at any time switch to and fro between a discrete and a continuous representation of a signal: both representations are equivalent. The connection between a bandlimited, digitized signal and its analog counterpart is given by the Fourier interpolation [38]. The eye of a human observer only performs a linear interpolation between discrete points. Information contained in a signal which is only represented by its values at some discrete sample points can therefore remain invisible until Fourier interpolation has been conducted. On most instruments, it is easier not to apply some Fourier interpolation algorithm directly, but to expand the measured data with zeroes prior to Fourier transformation. Mathematically, this “Zerofilling” procedure is strictly equivalent to Fourier interpolation. In NMR spectroscopy, the importance of zero filling has been known for a long time. J. Lindon et al. for instance demonstrate an example where some line splitting became only visible after eightfold zero filling [39].

Fig. 1.6: Zero filling in NMR imaging. a) high-resolution NMR image of a phantom containing various structures. b) NMR image of the same phantom acquired with identical FOV, but with only 8 x 8 phase encoding steps. c) Image reconstructed from the same raw data as in (b), after zero filling to 256 x 256 points. The structures in the phantom can be distinguished much better yet all the information was already present in panel b).

The same holds true in NMR imaging. Figure 1.5 showed a situation where two sources with a distance of one voxel size have been imaged. On an image processed without zero filling, the two points appear in adjacent pixels. Both pixels have the same gray value, and one cannot decide whether these represent one larger or two smaller objects. Applying zero filling, the dip between the two maxima appears, and the two

18

M. von Kienlin and R. Pohmann

objects become discernible. The effect of zero filling in a two-dimensional image is further illustrated in Fig. l .6. Even if the positive effect of zero filling appears clearly, it is important to note that zero filling does not add any information to the signal: it only makes all the information contained in the signal visible to the observer. Now that the positive effect of zero filling is manifest, it may not be overestimated: zero filling only improves the digital resolution in discrete data, but by no means the spatial response function or the resolution according to the Rayleigh criterion! This important issue may become clearer knowing that zero filling mathematically is strictly equivalent to %oxel shifting [33,35,40-42]”. Voxel shifting means to shift the grid of data points in space, until a voxel fully covers the desired region in the object. This is used to reduce partial volume effects. Zero filling is a way to move the voxel in smaller steps across the object, resulting in a finer gridding - the size of the voxel remains unaffected.

1.8 Conclusion In Fourier spectroscopic imaging, one usually indicates the nominal resolution (i.e., the field-of-view divided by the number of phase encoding steps) as the resolving power. The goal of this contribution was to show the difficulty of defining what “spatial resolution” really means. When looking for the position of some small object, the resolution is mainly limited by the signal-to-noise ratio, and can be much better than the nominal resolution (cf. eqn. 1.18). When the separation of two objects is required, the Rayleigh criterion is a convenient indicator, which can be computed from the spatial response function. To fully exploit the information contained in the acquired data, Fourier interpolation (or zero filling) is essential to increase the digital resolution. When dealing with extended objects, an exact definition of resolution is not possible. The acquired image represents a convolution of the object with the pointspread function of the imaging method. This implies that signals can propagate across the whole image and lead to substantial contamination. A good shape of the pointspread function therefore is crucial for a high quality of the results, and this is particularly true in the low resolution images typically acquired in spectroscopic imaging. The Rayleigh criterion only considers the shape of the central section of the pointspread function, but disregards

1. Spuriul Resolution in Spectroscopic Imuging

19

any undulations on its baseline. These undulations can be significantly reduced by some spatial filtering applied during processing - at the cost of reduced resolution. No penalty in resolution or sensitivity has to be paid when using acquisition weighted spectroscopic imaging [33,40,42-47]. These techniques can significantly reduce the signal contamination between adjacent voxels, and should be employed in any spectroscopic imaging experiment. Finally, the spatial resolution can be somewhat increased by including a priori knowledge in the data reconstruction. Examples are the limited support assumption [48], extrapolation of k-space in the Papoulis-Gerchberg algorithm [49,50] or the incorporation about geometric information of compartments in the object [51]. A full discussion of these modern techniques is beyond the scope of this article.

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J. Ackerman, T. Grove, G. Wong et al., Nature 283 (1980) 167.

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R. E. Gordon, P. E. Hanley, D. Shaw, et al., Nature 287 (1980) 736.

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R. E. Gordon, P. E. Hanley, D. Shaw, Prog. NMR Spectrosc. 15 (1982) 1.

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P. Bendel, C.-M. Lai, P. C. Lauterbur, J. Mugn. Reson. 38 (1980) 343.

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W. P. Aue, S. Miiller, T. A. Cross, J. Seelig, J. Magn. Reson. 56 (1984) 350.

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P. A. Bottomley, T. B. Foster, R. D. Darrow, J. Mugn. Reson. 59 (2) (1984) 338.

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R. J. Ordidge, A. Connelly, J. A. B. Lohman, J. Magn. Reson. 66 (1986) 283.

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G. C. McKinnon, 5th Annual Meeting of the SMRM (1986) 168.

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J. Frahm, K. D. Merboldt, W. Hanicke, J. Mugn. Reson. 7 2 (1987) 502.

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R. Kimmich, D. Hoepfel, J. Mugn. Reson. 7 2 (1987) 379.

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M. Dtcorps and D. Bourgeois, NMRBasic Principles and Progress 27, (1992) 119

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A. Bax, A. F. Mehlkopf, J. Smidt, J. Magn. Reson. 35 (1979) 373.

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2. CYCLCROP Mapping of 13 C Labelled Compounds: Perspectives in Polymer Science and Plant Physiology M . Heidenreichl, A. Spyros’, W.Kockenberge?, N. Chandrakumarl *, R. Bowtel12,and R. Kimmichl Sektion Kernresonanzspektroskopie, Albert Einstein Allee 11, Universitat Ulm, 89069 Ulm, Germany * On leave from the Central Leather Research Institute, Madras, India Magnetic Resonance Centre, Department of Physics, University of Nottingham, Nottingham NG7 2RD, United Kingdom

Abstract The 13C nucleus has scarcely been considered as a nucleus for magnetic resonance imaging. The reasons are the low natural abundance and the low gyromagnetic ratio so that the sensitivity appears to be not particularly promising. However, 13C NMR imaging and spectroscopy can be of particular interest in experiments where high chemical shift selectivity is required to identify a certain molecule of interest. The wide range of chemical shifts of the 13C nucleus makes such unambiguous identification possible even under demanding conditions which are encountered for example in heterogeneous mixtures or in vivo experiments. Furthermore, the low natural abundance of the 13C nucleus allows its use as a tracer which, once incorporated into the samples, permits to follow its redistribution or conversion into newly formed products in a time resolved manner. In close analogy to conventional radioactive tracers, this labelling strategy opens a whole class of in vivo experiments to be performed, but with the additional advantages of product identification and the non-invasive spatial mapping without any radioactive emission. Indirect detection of the 13C nucleus via proton signals combines an optimal NMR sensitivity with the potential of 13C NMR. Here we are referring to the cyclic J crosspolarization technique (CYCLCROP) which is based on two consecutive J cross-polari-

22

M. Heidenreich, A. Spyros, W. Kockenberger, N. Chandrukumnr, R. Bowtell, R. Kimmich

zation steps with an intermediate module for the saturation of all non-selected proton signals. To our experience, CYCLCROP turned out to be particularly reliable, robust and convenient. Indirectly detected 13C NMR imaging on this basis is demonstrated in heterogeneous polymer mixtures and with the observation of the synthesis and movement of labelled sucrose in plants.

2.1 Introduction Up to now I3C has scarcely been judged as a nucleus suitable for magnetic resonance imaging. The reasons are the low natural abundance and the low gyromagnetic ratio so that the sensitivity appears to be rather unfavorable. However, the latter problem can be overcome by recording proton signals edited in such a way that only hydrogen nuclei coupled to 13C are detected whereas signals due to all other protons are suppressed. That is, using double-resonance radio frequency (rf) pulse sequences designed appropriately, 13C nuclei in hydrocarbon groups can be detected in principle with about the same sensitivity as an equal number of protons. In particular, if the spatial distribution of I3C enriched compounds is to be mapped, one can expect reasonable acquisition times permitting a good temporal resolution. Labelling of compounds by isotopic enrichment makes only sense if background signals due to natural abundance are minor. That is, the low natural abundance of I3C may be considered as an advantage rather than a drawback.

Proton detected I3C imaging schemes might be regarded as an alternative to spectroscopic proton imaging of hydrocarbon distributions, i.e. a more conventional but easy to apply method (for a comparison see ref. [I]). However, the main motivation for hydrocarbon monitoring employing 13C nuclei is the rather unique potential of chemically inert labelling. Furthermore chemically selective signal generation can easily be achieved as a consequence of the about ten times wider chemical shift range of 13C relative to protons. Mapping of concentrations of pre-selected compounds of interest thus becomes possible. The spatial distribution of products of chemical reactions taking place in the course of the experiments can also be selectively imaged. For biological systems this means that metabolisms can be studied in a particularly informative way. In the literature different principles of proton-detected 13C imaging have been suggested [2-51. These include SEDOR (Spin Echo Double Resonance, a two-transient

2. CYCLCROPMapping of”C Labelled Compounds

23

subtraction method [4]), HYCAT (Hydrogen CArbon Tomography, a single-transient multiple-quantum filtering technique [3]), and CYCLCROP (CYCLic J CROss-Polari-

Zation, a scheme based on rotating-frame coherence transfer back and forth between the two nuclear species [ 5 ] ) . With the SEDOR method, similarly large signals are subtracted from each other leading to small differences which are unavoidably prone to severe experimental errors. HYCATand other pulse schemes implying free-evolution intervals in the spectral editing part of the sequence tend to be subjected to motional artifacts. We have therefore focused on cyclic cross-polarization techniques from which to our experience the CYCLCROP method turned out to be particularly reliable, robust, and convenient. The insensitivity to motions within the sample and the radio frequency power deposition has been tested and discussed in ref. [6]. In the following we first describe the basic principle of rotating-frame cross-polarization (CP) [7,8]. The transfer efficiency and the susceptibility to Hartmannmahn m i s match of diverse CP schemes are discussed. In section 2.3 we describe the CYCLCROP imaging pulse sequence employed in the 13C’mappingstudies referred to later on. The influence of relaxation is discussed in view of how quantitative 13C concentrations can be mapped. Section 2.4 contains an application to polymer science. The selective mapping of different polymer species in mixtures is demonstrated. As a second field of useful applications transport and metabolism of 13C enriched (i.e. labelled) hexoses were studied in plants. This not only demonstrates the temporally resolved migration of the labelled compounds into the plants, but also their chemical conversion by metabolism. Finally the future prospects of the technique also with respect to biomedical applications are outlined.

2.2 Principles of Rotating Frame Cross-Polarization 2.2.1

The Oscillatory JCP Process

Originally cross-polarization in the rotating fi-ame was invented primarily as a method for NMR sensitivity enhancement of rare spins with low gyromagnetic ratio y in the solid state. This is accomplished by tapping the much higher polarization of abundant high y

24

M. Heidenreich, A. Spyros, W. Kockenberger, N. Chandrakumar, R. Bowtell, R. Kimmich

spins, especially protons. In their pioneering 1962 work [q Hartmann and Hahn also indicated the application of the technique to solution state J cross-polarization (JCP) where one is dealing with spin systems comprising only a few spins. The essential idea of CP is the realization that polarization could be transferred by matching the resonance frequencies of the two spin species in the rotating frame, under rf irradiation - even though their Larmor frequencies in the laboratory frame differ widely. Thus HurtmundHuhn match with respect to the rf fields B,,,, B I S is specified by the condition on-resonance:

where the indices Z and S refer to the two coupled spin species. One may arrange to satisfy the above with respect to rf field amplitudes, although not with respect to the Zeeman field Bo:

Under Hartmanflahn match, dipolar couplings in the solid state

-

or J couplings in

solution state - then effect the desired transfer of magnetization - or more generally, of coherence. Assuming rf irradiation for each spin to be along the x axis of the (doubly) rotating frame, the effective JCP Hamiltonian in the rf interaction frame (otherwise known generally as the toggling frame, or specifically in the context of CP as the synchronized doubly rotating frame) takes the following form when Hartmanflahn match is satisfied

181: -

H = $(ZySy + ZzSz)

The great merit of cross-polarization for practical applications is its ability to effect inphase magnetization transfer, as may be seen with reference to a two-spin-112 AX system:

1,

Ht

> l2z , (1 + COS(RJt))+ 3s. (1 - cos(nJt)) (2.4)

+ (zYsz - z,~,)sin(n~t)

2. CYCLCROPMapping of 13C Labelled Compounds

25

For this prototype spin system, magnetization residing initially on the spin I (X) is thus completely transformed into magnetization residing on spin S(A) after a cross-polarization time t = J-' , in an experiment that commences with the establishment of transverse I magnetization in phase with the subsequent I spin rf irradiation. In-phase transfer occurs because the coupling between the two heteronuclear species, which is weak by definition - owing to truncation of non-secular terms in the doubly rotating frame has been transformed under the influence of matched rf fields into a strong coupling which has axial symmetry in spin operator space.

2.2.2

Damped Coherence Transfer

In practice, quantitative transfer at the theoretical mixing time occurs - even in a twospin-1/2 AX system - only when spectral linewidths are much smaller than the coupling constant in question, J. To assess the effect of relaxation processes occurring during cross-polarization, we may define a coherence transfer function f(t), employing a coherence damping term with an effective rotating-frame relaxation time constant Tp,effto damp the oscillatory term corresponding to transverse S(A) magnetization in eqn. (2.4): f(t) =

(

t ( ~ - c o s ( . n ~ r ) ) e x p--

TP:B

)

With a Tp,eEsuch that the 'linewidth' Av = (.nTp,eff)-lranges from one-tenth to the full coupling, for example, we find from eqn. (2.5) the ranges for the optimum cross-polarization times and maximum transfers, respectively, as being 94% to 50% and 74% to 10% of the values predicted by eqn. (2.4). Note, however, that coherence damping active during the cross-polarization process could be slower than T2.

26

M. Heidenreich. A. Spyros, W. Kockenberger. N . Chandrakumar, R. Bowtell, R. Kimmich

0.2 -

0.0.

*

1

0.2

.

*

.

*

I

0-4&

*

1

.

[ J ] 0.6

a

*

1

*

*

a

0.8

1.o

Fig. 2.1: Transfer efficiency and optimum contact times topt for the single J cross-polarization as a function of the 'linewidth Av = ( ~ T , , , ~ f f ) - l .

2.2.3

HartmandHahn Mismatch

The price paid for in-phase transfer and a possibly longer effective relaxation time is, however, continuous rf irradiation and high sensitivity to Hurtnznnn/Huhn mismatch, transfer efficiency reducing to 50% for a mismatch k that amounts to half the coupling. Indeed, with the mismatch parameter defined on-resonance as: k=,, A

A=v

1I

-v1s

(2.6a)

we find for the modified average Hamiltonian : -

H = f ( ( Z y S y+ZzSz)+k(Zx -Sx))

This leads to modified coherence transfer in a two-spin-1/2 AX system [9,10]:

(2.6b)

2.CYCLCROPMapping of 13C Lubelled Compounds -

Ix+ Ht

L

Z

27

x

2(1+4k2)

+ 2(1+4k2) L S x { l

-

cos[ (1 + 4k2)'7CJtl

+ (1+4k2) (z ,S, + I , Sz)

{

1- cos[ (1 + 4 k 2 ) i m ] }

+1 .J1+4k2 (ZyS, - Z z S y ) {sin[ (1 + 4 k 2 ) ' ~ J t ] ] The maximum in-phase transfer clearly corresponds now to the maximum value of the coefficient of the S, term in eqn. (2.71, i. e., (1+4k2)-I. The mismatch characteristics of JCP makes it a delicate sequence for solution state applications. However, this limitation has been overcome by a number of strategies, including refocused JCP [10,11], conversion to heteronuclear zero quantum coherence [ 121 or the use of phase alternated pulse sequences to effect coherence transfer under JCP [ 13,141. Continuous, phase modulated irradiation is the principal strategy employed currently to effect broadband JCP. Several schemes of this kind are in use, including those based on MOZST [6], WALTZ [15] and DIPSI; MGS-type sequences [161 belong in this same general category. The performance of these sequences on-resonance may be judged straightaway on the basis of the zeroth order average Hamiltonian that they give rise to. Numerical simulation would appear preferable to map the off-resonance behavior.

28

2.2.4

M. Heidenreich, A. Spyros, W. Kockenberger, N. Chandrakurnar, R. Bowtell, R. Krnmich

Mismatch Optimized IS Transfer (MOIST)

It may be readily shown, for instance, that the average oflset Hamiltonian for MOIST (which is a back-to-back phase alternated pulse sequence of the form 8x(x,,,)- 8,(~,)) takes the form:

H

=

6Zz

-

-

= -J[Ze

z sine

+

~,(cos0-1)]

Qx

.

Q-x

.

Fig. 2.2: Element of the back-to-back phase alternated MOIST pulse sequence.

Here, 6 is the resonance offset, 8 refers to the individual pulse flip angle in the back-toback phase alternated pulse sequence, while 7, is the individual pulse duration, the sequence cycle time being 27,; H refers to the Hamiltonian in the toggling frame [17]. The average Hamiltonian for bilinear z coupling, on the other hand, takes the form:

H

=

JZzSz

(2.9) -&(l-C0S28)

(zysz+ z z s y ) ]

This expression reduces to the desired form of eqn. (2.3) for 8 = nn (n = 1,2,...).

29

2. CYCLCROPMupping of 13C Labelled Compounds

2.2.5

Pulsed Rotating Frame Transfer Sequence with Windows (PRAWN)

It turns out, however, that for the application in view, i.e., selective, on-resonance transfer of magnetization within a specific coupled proton-carbon spin system (of type AX, AX, or AX,, where X indicates protons), a simple possibility exists to achieve JCP highly efficiently, and with a useful degree of tolerance to Hartmann-Hahn mismatch. We have shown recently [ 181 that highly windowed cyclic pulse sequences with constant pulse phase, say x,flip angle 8 and pulse interval T,, issued on both spin channels, fit the bill very well indeed. They may be represented as (8, - T&.

Fig.2.3: Windowed cyclic pulse sequence on which the PRAWN method is based.

Cyclicity (or unimodularity) implies simply that n8 = 27c. Typically just one cycle of the sequence is required to cover the JCP mixing period. These sequences, which we term PRAWN (Pulsed Rotating frame trAnsfer sequence with WiNdows), have proved extremely desirable because of their robustness, very low rf power deposition and consequent acceptability both from the point of view of the sample and the probehead electronics. Furthermore, they are very undemanding on the hardware in the sense that no rf phase or amplitude modulation is employed throughout the mixing sequence. The average offset Hamiltonian of PRAWN takes the following form, which is independent of the sequence parameters: n

n

n

+%I,

++

C (sin me - sin(m - i)e) m=l n

I

c

m=l

(cos me-cos(m - l)8) = 0

(2.10)

30

M. Heidenreich, A. Spyros, W. Kockenberger, N. Chandrakurnar, R. Bowtell, R. Kimmich

For the case 0 = 2n, the average offset Hamiltonian takes the form:

For bilinear weak coupling, the average Hamiltonian now takes the parameter independent form:

+z(zzsy + I Y S ,j

1

~(cos(2Pn~)-cos(2(~-1)0)) [m=l

For the two cases corresponding to 0 = n: and 0 = 27c, however, we find:

The tolerance of PRAWN to Hartmann-Hahn mismatch may be understood in terms of the fact that any number of PRAWN sequences would be possible in principle, subject only to cyclicity; in particular, the low flip angle solutions cluster closely together. Equivalently, it may be said that PRAWN effectively scales up or transforms the mismatch tolerance of continuous wave (CW) JCP by the inverse of the duty cycle factor. PRAWN sequences have the further interesting property of being tunable for broadband or for narrowband applications. For example, by simply inserting a single n: pulse in the middle of the cycle on both spin channels (i. e., (0, - T,),/~ - (n:)$ - (0, - QnI2), and depending on its phase, either the bandwidth may be substantially reduced ((I = x) - or alternatively the mismatch tolerance substantially increased ((I= t y ) ; further, this strat-

2. CYCLCROP Mapping of 13C Labelled Compounds

31

egy offers the capability of selective transfer under a remote coupling while refocusing couplings to directly bonded spins. On the other hand, the bandwidth may be substantially increased by inserting a 7c pulse in the middle of every (0 - TJ segment. Other such refocusing options are clearly available to generate a range of behaviour.

2.2.6

Coherence Transfer Spectra

The actual behaviour of various mixing sequences for JCP may be readily determined experimentally by means of coherence ti*aizsfer spectra, which correspond to the Fourier transformation of the coherence transfer functionf(t), of eqn. 2.5. These may be simply obtained by acquiring a series of JCP free-induction decays, as a function of the JCP mixing time, which may be systematically incremented from experiment to experiment. A double Fourier transformation, once with respect to the normal acquisition time t2 and a second time with respect to the variable mixing time tl then generates the desired coherence transfer spectrum along the F , dimension, for each transition in F2. The PRAWN family of sequences also permits a quick 1D acquisition of the CT spectrum by sampling during the windows of the sequence, at the expense of information relating to the relevant individual transitions.

2.2.7

Adiabatic J Cross-Polarization

A quite different strategy may, on the other hand, be adopted to effect J cross-polarization, as well. This is the approach of adiabatic J cross-polarization [19,201. Here, the rf irradiation amplitude on spin Z(X) is decreased while that on spin S(A) is increased adiabatically, following initial establishment of transverse Z spin magnetization in phase with the subsequent Z spin rf irradiation. In a two-spin-112 system, for example, the avoided crossing between the levels T 1 ) and 1 T ) results in the desired polarization

I

I

transfer. The transfer is no longer oscillatory and can be accomplished in a J-independent manner if adiabaticity is satisfied with respect to the smallest coupling. Typically, simple linear ramps may be used to effect the adiabatic passage in rf amplitudes, the ramp time T being of the order of lo2 ms. The rate of passage must satisfy the condition of adiabaticity :

32

M. Heidenreich, A. Spyros, W. Kockenberger, N. Chandrakumar, R. Bowtell, R. Kimmich

(2.14) Here, wll is the rf field amplitude on spin I, while

is the effective rf amplitude inclu-

sive of the effect of resonance offset Amop

0

T

Fig. 2.4: Radio frequency pulses for adiabatic J cross-polarization (AJCP).

The bandwidth over which adiabatic J cross-polarization works is in turn governed by the rf field mismatch at the start and at the end of the ramp-time, respectively, for the S and the I spins:

Considering typical contact times and power deposition levels, however, it appears that

AJCP is sub-optimal for applications that require selective J cross-polarization.

33

2.CYCLCROPMapping of 13C Labelled Compounds

2.3 Pulse Sequences for Cyclic J CrossPolarization Imaging 2.3.1

The Cyclic J Cross-PolarizationImaging Scheme

The CYCLCROP pulse sequence for indirect mapping of 13C concentrations consists of two sections, the spectral-editing part and the imaging part (Fig. 2.5) [5,8]. The purpose of spectral editing procedure is to select a certain resonance while all other signals are suppressed. The selectivity achieved in this way permits one to specifically address the chemical compounds of interest. The resulting selective proton coherences are then used for conventional proton magnetic resonance imaging rendering information on the spatial distribution of the pre-selected compound. The imaging method can be any of the well known standard NMR imaging pulse schemes [ S ] .

sL

'

1

Fig. 2.5: Basic CYCLCROP pulse scheme for proton-detected chemical-shift selective 13C spin density mapping.

34

M. Heidenreich, A. Spyros, W. Kockenberger, N. Chandt-akumnr,R. Bowtell, R. Kimmich

The spectral-editing principle may be illustrated by considering a small J coupled spin system such as a CHN group within a certain compound. In a first step, the 13C magnetization is enhanced by cross-polarization from the proton to the 13C side. The resulting 13C rotating-frame coherences are then stored in the form of z-magnetization. That is, it is not effected by the subsequent comb of gradient - and proton rf pulses serving to saturate the levels and to spoil any coherences of all protons (see section 2.3.3). The second cross-polarization pathway leads inversely from the 13C to the proton side. The 13C magnetization stored before is now transferred back to proton rotatingframe coherences. The only signal detectable at the end of the editing cycle thus arises from protons coupled to 13Cin the selected CHN group.

2.3.2

Transfer Efficiency and Selectivity of CYCLCROP

If the case of off-resonance irradiation is included, the Hartmandahn condition [7,8] reads generally:

where Beff,[ and Beg,S represent the magnetic flux densities effective for protons and 13C nuclei in the doubly rotating frame, respectively. Violation of the Hartmanmahn condition either by B,-field mismatch andlor by off-resonant irradiation leads to a reduced transfer efficiency. The relative roles played by B1-field mismatch and off- resonant irradiation depend on the pulse scheme employed. They need not to be equivalent. The MOIST [13,14] and PRAWN [18] variants of J cross-polarization, which were used in the applications to be described in the following are B, compensated but nevertheless remain frequency selective. That is, these methods are easy to use even under in vivo conditions without sacrificing the high spectral selectivity of the 13C nucleus. As mentioned before, the efficiency of proton to carbon polarization transfer depends on the spin system size. For AX (IS) systems, the proton polarization is completely transferred to the carbon side whereas for A2X (Z2S) and A3X (Z3S) systems only 50 and 35% of the proton magnetization is exploited, respectively. That is, the resulting 13C polarization is essentially the same irrespective of the number of coupled protons. In the absence of relaxation effects, the finally acquired proton CYCLCROP signal intensity Sois expected to reflect the spin density ps of the S nucleus according to [21]

2. CYCLCROPMapping of 13C Labelled Compounds

system, respectively.

35

(2.17)

For quantitative concentration mapping it may be important to take reZaxation effects into account. The signal intensity may then be estimated with the aid of the modified formula

WI

where Tp,effis the relaxation time of the total spin system effective during the crosspolarization period topt, as defined in eqn. 2.5. The quantities TI,^ and T2,1 are the longitudinal and transverse proton relaxation times, respectively. The longitudinal relaxation time of the 13C spins is represented by . The time required for proton saturation and coherence spoiling is denoted by T,,. Finally, TR is the recycle delay of the pulse sequence implying the echo time TE. In most cases, the 13C carbon longitudinal relaxation times are much longer than the interval needed to saturate the proton spin levels and to spoil proton coherences. Therefore the last factor in eqn. (2.18) almost always approaches unity. The first exponential factor in eqn. (2.18) plays a role only whenever the effective relaxation times in the doubly rotating frame are in the order of typical contact times tOpt5 .I(see ' Fig. 2.1). On the other hand, longitudinal and transverse proton relaxation losses can be kept minor if the parameters TR and TE are chosen long and short enough, respectively. Keeping these factors in mind, it should be possible to evaluate 13C spin density maps quantitatively with reasonable accuracy from CYCLCROP imaging experiments.

36

2.3.3

M. Heidenreich, A. Spyros, W.Kockenberger, N. Chandrakumar, R. Bowtell, R. Kimmich

Saturation Schemes

In special cases such as with applications to polymers (vide infia) proton coherences in the interval between forward and backward cross-polarization can be spoiled by a short “blank“ delay of a few milliseconds in which the coherences die away owing to the short proton T; values in such materials [22]. Otherwise proton saturation and coherence spoiling is achieved by “suppression by mismatched echo and repetitive gradient episodes“ [23]. That is, a train of hard rf pulses with subsequent field gradient pulses is applied. The hard rf pulses may be replaced by adiabatic halfpassages in combination with field gradient pulses (see the pulse scheme shown in Fig. 2.5) [24]. This turned out to be particularly favourable in the plant experiments to be described below. The major difficulties in this context were: (i) the ratio of T2 and Tl is no longer small, (ii) the proton resonances to be saturated are dispersed over a wide range of proton frequencies, and (iii) the sample extends beyond the homogeneous volume of the rf coil. The adiabatic half passages permitted us to obtain good results despite of extreme B1-field inhomogeneities. Typically four adiabatic half passages were applied with their frequencies shifted towards the most intense resonance: in our case the water signal. Moreover a simple twostep phase cycle was employed in order to remove all possible residual proton signals having leaked through the spectral-editing process.

2.4 Selective Mapping of Polymer Species in Mixtures Special polymers and most polymeric products used in everyday applications are heterogeneous materials, either blends of different polymers, or mixtures of polymer and additives such as fillers, cross-linking agents, antioxidants, etc. CYCLCROP imaging has the ability to probe the spatial distribution of one component out of an heterogeneous polymeric material, and is therefore ideal for the study of inhomogeneities, phase separation, or ageing in such systems. Elastomers represent a class of commercially important polymers which can be studied using conventional ‘high resolution’ imaging techniques due to their reduced static linewidth resulting from a combination of increased segmental

2. CYCLCROPMapping of I3C Labelled Compounds

37

mobility and reduced crystallinity. For this reason they represent an excellent candidate for the demonstration of advantages of CYCLCROP in selective mapping of polymers in heterogeneous mixtures.

2.4.1

Heterogeneous 13C Labelled Polymer Systems

cis-Polyisopreneand Polybutadiene CYCLCROP imaging was first tested in a polymer sample consisting of a mixture of cispolyisoprene, PI, and polybutadiene, PB. PI was 54% 13C-enrichedat the methylene C-4

position and was synthesized in the laboratory (Fig. 2.6). The sample was constructed by mixing 43 mg of PI with 31 mg PB in a perspex holder, heating for -3 h at 60 "C in an oven and cooling for a period of several weeks at room temperature. This procedure resulted in the preparation of an heterogeneous polymer mixture containing 58% w/w PI. Smaller quantities of pure PI and PB were placed at the higher left and right corner, respectively, of the perspex sample holder to serve as external reference. Fig. 2.7a presents the conventional 'H image of this PIPB sample. A rather homogeneous distribution of proton intensity throughout the sample is observed. Both PI and PB external references can be seen.

5CH3

\ L

'C =3CH

JX

Fig. 2.6: Polyisoprene, PI, 54% 13C enriched at the methylene C-4 position (*)

The CYCLCROP image of the PIPB mixture using the MOIST cross-polarization variant, with the lH and I3C channel frequencies centered on the 13CH, moiety of PI is presented in Fig. 2.7b. The PI reference can still be seen in the upper left comer of the image, whle the PB reference at the upper right produces no intensity at all. Thus it can be concluded that the CYCLCROP image of the polymer mixture represents the spatial

38

M. Heidenreich, A. Spyros, W. Kockenbergei; N. Chandrukumur, R. Bowtell, R. Kimmich

distribution of PI in this sample. With the help of the PI and PB references, difference images can be produced by subtracting the scaled CYCLCROP image (cf. eqn. 2.17) of Fig. 2.7b from the conventional proton image of Fig. 2.7a, scaling being empirically adjusted to give minimum intensity at the PI reference. The resulting semi-quantitative difference IH image is displayed in Fig. 2 . 7 ~and represents the spatial distribution of PB in the polymer mixture, as can be easily verified by the appearance of the PB reference in the upper right. It is important to note that in the 1D proton spectrum of the PIPB sample the H-4 methylene resonance of PI are covered by an unresolved broad peak of the PI H-1, H-5 and the methylene protons of PB. After editing with CYCLCROP the proton spectrum consists of a single resonance resulting from the H-4 methylene protons of PI, with all other proton resonances successfully suppressed. Thus, the lack of resolution in the nonedited 'H spectrum of a polymer mixture does not present any obstacle for performing the cyclic CP transfer, and it is demonstrated that CYCLCROP allows the 13C-edited imaging even of completely unresolved proton peaks. For reasons of comparison a 13C direct detected image of the PVPB sample was also acquired. Although its appearance was similar to that of the CYCLCROP image of Fig. 2.7b, the S/N of the 13C image was 2.8 times smaller than that of the CYCLCROP image, under identical experimental imaging conditions. Thus the time needed to acquire a CYCLCROP image is 1/8 of that needed for a directly detected 13C image of the same S/N, resulting in significant savings in experimental time for the acquisition of I3C-edited images of elastomeric materials.

cis-Polyisoprene and Polyhydroxyoctanoate Figure 2.8 shows the CYCLCROP images of another polymer mixture, a homogeneous blend of PI and polyhydroxyoctanoute, PHO, recorded to compare the efficiency of the two different CP variants, MOIST and PRAWN. Although both PRAWN and MOIST are very efficient in selectively editing the PI signals and suppressing the PHO reference visible on the top right of the conventional lH image, the S/N ratio of the image acquired with PRAWN is about 65% of the MOIST variant. A 50% rf duty cycle was used for PRAWN in the imaging of the PI/PHO blend. CYCLCROP experiments performed on polymer solutions showed that both methods are equally efficient in effecting CP [22], in accordance with a recent application of this technique to the imaging of sugar metabolism in plants [21]. Thus, it appears that the reduced S/N of the PRAWN image in bulk PWHO is a result of the relaxation properties and the heterogeneity of elastomers in the bulk phase compared to solution.

2. CYCLCROPMapping of "C Labelled Compounds

39

Fig. 2.7: 1H NMR images of a PVPB sample, no slice selection, sample thickness -1 mm: (a) conventional 1H NMR image showing the PI and PB references and the PVPB mixture. Parameter values: FOV 2 x 2 cm*; Read gradient 81 mT/m; Phase gradient 43 mT/m; TR = 0.5 s; TE = 2.4 ms; pixel matrix 256 x 64 zero-filled to 256 x 256. @) CYCLCROP image of the same sample with MOIST tuned to the frequencies of the methylene C-4 group of PI, and displaying the spatial distribution of PI in the polymer mixture. The PB reference is no longer visible. Same parameter values as in (a), but l k transients; experiment time 7.5h. (c) Difference image (a)-(b) normalized empirically to minimum overall intensity at the PI reference (top left). Qualitative information regarding the distribution of PB in the polymer mixture is obtained from this difference image.

40

M. Heidenreich, A. Spyros, W. Kockenberger, N. Chandrakumar, R. Bowtell, R. Kimmich

Fig. 2.8: 1H NMR images of a PLPHO blend, no slice selection, sample thickness -1mm: (a) conventional 1H NMR image showing the PHO reference (top right) and the PWHO blend. Parameter values: FOV 2 x 2 cmz; Read gradient 81 mT/m; Phase gradient 43 mT/m; TR= 0.5 s; TE = 2.4 ms; pixel matrix 256 x 64 zero-filled to 256 x 256. (b)-(c) CYCLCROP image of the same sample tuned to the frequencies of the methylene C-4 group of PI, using PRAWN (b), and MOIST (c) and displaying the spatial distribution of PI in the polymer blend. The PHO reference is no longer visible. Same parameter values as in (a), experiment time 7.5h.

2. CYCLCROPMapping of I3CLnbelled Compounds

41

Bulk magnetic susceptibility and spin diffusion are factors that become important in the solid state [25]. Since with PRAWN rf irradiation is not ‘on’ continuously it is possible that semi-rigid or interphase regions close to crystallites, where spin diffusion is more effective, are less likely to be efficiently cross-polarized. This means that the reduced intensity and the somewhat different contrast obtained in the PRAWN image of the PVPHO blend in Fig. 2.8 could be related to the absence of contribution to the signal intensity from regions of lower mobility. Thus it is demonstrated that an additional relaxation contrast might be created with CYCLCROP depending on the method (MOIST or PRAWN) used to achieve the cyclic polarization transfer.

2.4.2

Natural Abundance 13C Samples

Finally, Fig. 2.9 depicts the IH and CYCLCROP images of a sample consisting of a piece of natural abundance PI placed next to a piece of a common laboratory hose. Although both are visible in the ‘H image, only the PI piece can be seen in the CYCLCROP image, while any signal from the rubber hose has been edited out. The above images demonstrate the applicability of CYCLCROP for the acquisition of I3Cedited images of natural abundance elastomeric materials of moderate size.

Fig. 2.9: 1H NMR images of the PUrubber hose sample: (a) conventional 1H NMR image showing both polymer pieces. Parameter values: FOV 4 x 4 cm2; Read gradient 41 mT/m; Phase gradient 44 mT/m; TR = 0.5 s; TE = 2.4 ms; pixel matrix 256 x 128 zero-filled to 256 x 256. (b) CYCLCROP image of the same sample with MOIST tuned to the frequencies of the methine C-3 group of PI, where the proton signal from the rubber hose has been eliminated. Parameter values: FOV 4 x 4 cm2; Read gradient 41 mT/m; Phase gradient 11 mT/m; TR = 0.6 s; TE= 2.4 ms; pixel matrix 256 x 32 zero-filled to 256 x 256; 128 transients; experiment time 43 min.

42

M. Heidenreich, A. Spyros, W. Kockenberger, N. Chandrakumar, R. Bowtell, R. Kimmich

2.5 Spatially and Temporally Resolved Study of Transport and Metabolism in Plants 2.5.1

Motivation

In plants not all leaves are equally able to produce energy rich compounds by CO, fixation and photosynthesis. Developing leaves, fruits, shoots and roots rely on the import of energy rich compounds from more mature leaves (sources). Plants possess a specialised tissue, the phloem, in which photoassimilates such as sucrose are conducted from the source to the site of their consumption (sinks). In this tissue a system of communicating small tubular cells (sieve tubes) expands through the whole plant. The investigation of the mechanism and the control of the transport process has long been of great interest to plant physiologists since the partitioning of photoassimilates between different plant organs has a strong effect on growth patterns of the whole plant and particularly on the development of agricultural products such as tubers and fruit [26].

Conventional Techniques Several techniques can be used to monitor long distance transport in plants. A common tool is the application of 14C labelled compounds [27,28]. After supplying either 14C0, or other labelled compounds such as sucrose to the source leaves, the accumulation of radioactivity is measured in other parts of the plant by harvesting and sectioning of the plant, followed by determination of radioactivity in the plant tissue. Since for each point in a time course study of radioactivity accumulation a new plant must be harvested, the data obtained in this manner are strongly affected by natural physiological variations between different plants. Ideally a non-destructive technique is required to make time course studies with a single plant possible. Such a technique is labelling of photoassimilates with 11C02 [29-311. The movement of the incorporated llC tracer within the intact plant can be observed with external monitors since the decay of the isotope l l C results in the emission of p and y rays. Unfortunately it is difficult to identify the compound in which the 'C tracer has been incorporated because the isotope has a short half-life time

(zlI2 = 20.4 min) and a rapid extraction and separation technique is therefore required. Recently the versatility of lH NMR microimaging techniques in plant physiology has been successfully demonstrated in the in vivo study of metabolite distribution in small plants [32-371. Using this non-invasive technique, metabolic maps with high spatial

2. CYCLCROPMapping

0f13cLabelled

Compounds

43

resolution can be obtained. However, labelling of metabolites is essential for the observation of either movement or metabolic conversion of these metabolites within plants by NMR microimaging. Labelling can be achieved with the stable isotope 13C in experiments similar those employing the radioactive carbon isotopes.

2.5.2

13CLabelling

The use of the isotope 13C is a well known tool in organic chemistry. The NMR spectrum of natural abundance 13C forms a characteristic fingerprint of a compound and the appearance, increase and disappearance of resonance lines in the I3C NMR spectrum indicate the chemical conversion of one compound into another during chemical synthesis. This ability to observe the conversion of chemical compounds by NMR has made the use of the isotope 13C particularly attractive for studies of metabolic pathways in medical research [38], as well as in plant physiology [3943]. The natural abundance of 13Cnuclei is low (1.1%) and additionally in most situations the metabolites under investigation are only weakly concentrated in the living system. Hence, applications of direct detected 13CNMR to intact systems with natural abundance 13C have been limited. However, the low natural abundance of 13C means that it can be used as an excellent tracer in labelling studies. Therefore compounds with positions highly enriched in 13C are commonly used to increase the sensitivity of the NMR experiment and to study selected metabolic pathways. Any NMR signal detected from a sample can also be spatially encoded by the superposition of magnetic field gradients on to the main field. Therefore, images of the distribution of the compound carrying the 13C tracer can be obtained. However, imaging of 13C labelled compounds is limited by the intrinsically low NMR sensitivity in the direct detection of 13C nuclei. Hence, the observation of the movement of 13C labelled compounds in intact living systems has not been possible using direct detected 13C NMR imaging. Indirect detection techniques for 13C nuclei such as cyclic J cross-polarization (CYCLCROP) result in a significant enhancement of the NMR signal and so make the spatially resolved acquisition of the NMR signal in a reasonably short experimental time possible. Using the combination of NMR imaging with cyclic J cross-polarization we have studied the movement of 13C labelled metabolites in an intact plant for the first time in a dynamical experiment. In these experiments castor bean seedlings were used as a model system.

44

2.5.3

M. Heidenreich, A. Spyros, W. Kockenberger, N. Chandrakumnr, R. Bowtell, R. Kimmich

Castor Bean Seedlings - a Model System

Castor bean (Ricinus cornrnunis L.) plants have been used extensively in the investigation of phloem transport. This is a consequence of the relatively inefficient wound sealing system in the castor bean plant; a feature which is shared with only a very small number of other plant species. In most plants this system would normally block phloem transport following an incision, via callose production in the sieve tubes. In the castor bean plant exudate can however be collected after incision of the plant stem. This technique has been used to demonstrate photoassimilate transport, by monitoring the increase of radioactivity in the exudate after exposure of source leaves to l4CO, [44]. Detailed studies of phloem transport have been carried out with seedlings of the castor bean plant [45-501.

\

nutrient depot

Fig. 2.10: Experimental setup for 13C observations of movements of sucrose in castor bean seedlings. Plants were grown on top of glass tubes which could be inserted into the probehead. During the experiment, the root system was aerated from below by a gentle stream of air bubbles. The cotyledons were incubated in a small nutrient depot containing the labelled hexoses. The shaded region within the hypocotyl indicates the position of the NMR rf coil.

2. CYCLCROPMapping of I3C Labelled Compounds

45

Castor bean seedlings have a hook shaped hypocotyl with two cotyledons at the apical end and the root system at the basal end (Fig. 2.10). The cotyledons are embedded in

the endosperm, a tissue rich in oil and fat [51], which supplies the seedling with nutrients during the first days after germination. Instead of taking up the nutrients from the endospem, the cotyledons can absorb nutrients from an aqueous solution, if the endospem is removed and the cotyledons are incubated in a weak buffer (the incubation medium). Since the seedlings take up carbohydrates and amino acids directly from the incubation medium 13Clabelled compounds can be easily introduced into the plant in this manner. We used 50 mM 13C1 glucose and 50 mM 13C1fructose in our first experiments. These hexoses are readily taken up by the cotyledons [50] and fructose is particularly rapidly converted to the disaccharide sucrose [50,52]. Sucrose is the major transport form for carbohydrates and it is exported from the cotyledons into the hypocotyl and the roots of the seedling by active loading into the phloem. Concentrations of up 300 mM sucrose have been reported in the phloem exudate of castor bean seedlings [47,49]. After de novo synthesis of sucrose from the supplied 13C labelled hexoses within the cotyledons, the sucrose molecule is either labelled on the C, position of the fructose moiety, the C, position of the glucose moiety or on both positions.

2.5.4

Experimental Setup of the Castor Bean Experiment

A probehead for a BRUKER 400 MHz wide bore magnet which can host an intact castor bean seedling and which provides a small vessel for the incubation of the cotyledons during the NMR experiment has been designed. A double resonance saddle coil was used for simultaneous irradiation of both the lH and 13C nuclei. Castor bean seedlings were grown hydroponically on top of glass tubes (14 mm o.d, 200 mm length) containing a weak solution of CaC12 (0.5 mM) for six days in the dark [53]. The NMR experiment was carried out on a region of the hypocotyl about 10 mm below the hook.

46

2.5.5

M. Heidenreich, A. Spyros, W. Kockenberger, N. Chandrakumar, R. Bowtell, R. Kimmich

Spectroscopic Experiment

We used the CYCLCROP sequence (Fig. 2.5) to enhance the signal in a spectroscopic experiment. Immediately after the end of the second transfer, the signal in the proton channel was recorded (1024 points). Signal averaging over 256 scans was performed. Total acquisition time was 3 min. The irradiation frequencies for polarization transfer between the protons coupled to the 13C1 of the glucose moiety (termed GI) were 5.33 ppm and 93.1 ppm. For the transfer between the protons coupled to the 13C1of the fructose moiety (termed F1) 3.56 ppm and 62.3 ppm were used. We repeated the spectroscopic experiment for both labelled positions in the sucrose molecule every 30 min thus observing the increase of the signal intensity of the F1 and the GI frequencies due to the accumulation of labelled sucrose in the sensitive area of the rf coil (8 mm) (Fig. 2.1 la)

,

-

,

-

,

.

i

I

.

0 mrn (center of the coil) -4 rnm (bottom)

L

0

I

100

200

300

400

Time of incubation [min]

Fig. 2.11: Increasing 13C labelled sucrose concentration measured from (a) the F1 and GI resonances of sucrose and (b) from three different 2 mm thick slices of the hypocotyl, using the G1 resonance.

Slice Selection By applying a slice selective refocusing rf pulse after the CYCLCROP sequence, the signal of the G1 and the F1 resonances was acquired alternately for three different slice positions along the axis of the hypocotyl. Figure 2.11b shows the increase of the G1 signal intensity in the three separate slices. The different slopes in the increase are caused by variation in unloading of the labelled sucrose from the phloem. Such time dependent

2. CYCLCROP Mapping of 13C Labelled Compounds

47

curves can be analysed using an input/output model to obtain transport velocities of the labelled sucrose within the phloem.

2.5.6

Imaging Experiment

CYCLCROP spectral editing was combined with a spin echo imaging sequence. We found the PRAWN version of cross-polarization with an rf duty cycle of only 8% to give highest efficiency and lowest power deposition in our experiment. The total acquisition time for one image was reduced by almost a factor of 2 through the use of acquisition weighted k-space sampling [54-561. The number of averages taken for each phase encoding step is calculated according to the Hanning filter, resulting in the highest number of averages at zero phase encoding gradient strength and a decreasing number of averages with increasing phase encoding gradient. The total acquisition time for an image with an in-plane resolution of 500 km x 62.5 pm and a slice thickness given by the sensitive region of the coil (8 mm) was 90 minutes. This was fast enough to allow observation of the movement of 13C labelled sucrose in the hypocotyl through repetition of the experiment. Figure 2.12 shows a series of 11 images obtained for the F, resonance of sucrose. The total measured signal intensity corresponding to each image is shown on the right hand side. Starting from a baseline level due to the signal from naturally abundant 13C nuclei present before the incubation of the cotyledons with labelled hexoses, the intensity increases in time throughout the experiment. An enrichment by a factor of 14 was achieved at the end of the 16 h experiment. The first image was also acquired with naturally abundant 13C. In the second image, no contrast is visible although the total intensity of the observed resonance has already increased, indicating the arrival of labelled sucrose in the observed slice. The signal is clearly visible in the third image, showing the arrival of the labelled sucrose within the phloem. The intensity of the signal within the phloem increases during the experiment, corresponding to either an increase in the sucrose 13C enrichment factor or a process of sucrose storage within the phloem parenchyma. In the course of the study the signal spreads out into the periphery of the vascular bundles particularly in the cortex parenchyma. This indicates that either the flux of sucrose is directed after unloading from the phloem into this tissue or that sucrose delivered from the phloem is rapidly metabolised within the pith parenchyma.

48

M. Heideareich, A. Spyros, W.Kockenberger, N. Chandrakumar, R. Bowtell, R. Kimmich

u ! ! 1

T1 proton image

Fig. 2.12: Indirect detected 13C CYCLCROP images of the distribution of labelled sucrose from the hypocotyl of 6 days old castor bean seedlings. The first image is recorded before incubation with labelled hexoses (50 mM fructose and 50 mM glucose). The acquisition time for each image was 1.5 h, in plane resolution is 500 pm x 62 ,urn, the slice thickness is given by the sensitive volume of the rf coil to 8 mm. On the bottom right side, the total F1 edited spectra of sucrose (13C decoupled).

2. CYCLCROPMapping of 13C Labelled Compounds

49

2.6 Discussion and Outlook The purpose of CYCLCROP indirect I3C imaging is to map 13C concentrations in softmatter objects quantitatively, with molecule specificity, insensitivity to motions, and with spatial and temporal resolution. This is in contrast to ordinary magnetic resonance imaging of morphologies where contrasts are usually weighted representations of local spin-lattice and transverse relaxation times, diffusivities and spin densities. In order to comply with these requirements, the pulse sequence must be designed in such a way that relaxation losses are prevented as far as possible while the detection sensitivity is optimized. We have shown that cyclic cross-polarization (or rotating-frame polarization transfer) in the sense of the HartmannMahn experiment as a spectral editing element optimally serves the goal of an operational 13Cmapping scheme. From a more practical point of view, a further requirement is the ease of experimental handling in particular in the frame of in vivo experiments where time consuming adjustments are not possible. As concerns cross-polarization this condition means that the pulse sequence should be insensitive to HartmandHahn mismatch. In this respect we have successfully tested the MOIST and, as a new pulsed version of cross-polarization, the PRAWN modifications. In this context, the radio frequency power deposition connected with the pulse sequence may also be a limiting factor. It was shown that both methods, the latter somewhat better than the former, are uncritical in this respect. The theoretical sensitivity enhancement of proton mediated detection of 13C nuclei is a factor of roughly ( ~ ~ =: 644 relative ~ to) the~direct acquisition of 13C signals without nuclear Overhauser effect enhancement. It should be noted here that the number of protons coupled to a 13C nucleus virtually does not matter as our considerations proved. A further sensitivity gain is due to the fact that the signals are acquired in the proton channel, that is, that the repetition rate is limited by proton spin-lattice relaxation rather than that of 13Cwhich may be slower by a factor of ten or so. This is a crucial point: Since the purpose of CYCLCROP mapping is to render the spatial distribution of 13C concentration quantitatively as accurate as possible, the pulse sequence should be applied to the totally relaxed sample only. Ernst angle optimization of the repetition rate is therefore not feasible in this context. The application of CYCLCROP 13C mapping on polymer mixtures, i. e., heterogeneously distributed polymers of a different chemical nature, showed that a clear distinction is possible on a total acquisition time scale which is adequate for materials. The short relaxation times intrinsic to polymers permit one to simplify the spectral editing

50

M. Heidenreich, A. Spyros, W.Kockenberger, N . Chandrakumar, R. Bowtell, R. Kimmich

part of the pulse sequence because "saturation" of the protons in this case simply means to wait a period T2 in the order of 1 ms. It was shown that the chemical selectivity of the procedure is unambiguous. We have demonstrated that movement and metabolism of 13C labelled compounds in castor bean seedlings could be observed by CYCLCROP indirect 13C imaging. The tremendous progress in plant molecular biology within the last few years now allows the transformation of a whole range of transporter and key enzymes genes in plants. The non-invasive approach of measuring the movement and the metabolic conversion of labelled I3C metabolites in intact plants, described here, may provide a versatile and valuable supplementary technique in plant molecular biology. By using cyclic J crosspolarization techniques it should be possible to measure metabolic flux rates and transport velocities of labelled metabolites. These important parameters will facilitate the evaluation of the success of transformation of a target and how the physiology of the plant is affected. Since NMR imaging experiments are non-destructive, different techniques can be used with one plant. Thus, it is possible to carry out an experiment for the measurement of water flow in the phloem [53],followed by an experiment for the determination of the flux of 13C labelled photoassimilates in the phloem. Such experiments are important for the investigation of the mechanism and regulation of phloem transport. Indirect 13C imaging applications for biomedical purposes may be more demanding because the total acquisition time may conflict with what one can expect of a patient. However it has already been demonstrated that 13C resonances in humans can be probed even under natural abundance conditions. For example, in ref. [57] glycogen in the human liver was detected in vivo with a 2 T whole-body tomograph. The acquisition time may be reduced combining CYCLCROP spectral editing with echo planar imaging. Furthermore, the metabolic pathways of 13C enriched nutrients or drugs may be sensitively traced also for diagnostic purposes. The feasibility of biomedical applications of CYCLCROP indirect I3C imaging under in vivo conditions is also corroborated by the striking insensitivity to motions [6].

2. CYCLCROPMupping of 13C Labelled Compounds

51

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3.

Contrast Enhancement Based on Intermolecular Zero Quantum Coherences for Magnetic Resonance Imaging and Microscopy

Rahim R. Rizi2, Sangdoo Ahnl, Jeff Hopkins2, John S. Leigh2, and Warren S. Warren1 lDepartment of Chemistry, Princeton University, Princeton, NJ 08544-1009, USA 2Department of Radiology, University of Pennsylvania, Philadelphia, PA 19104,USA

Abstract A new method for Magnetic Resonance Imaging (MRI) is reported based on the detection of relatively strong signal from intermolecular zero-quantum coherences (iZQCs) using a simple pulse sequence. Such a signal would not be observable in the conventional framework of magnetic resonance; it originates in long range dipolar couplings (10 pm - 10 mm) which are traditionally ignored. Unlike conventional MRI, where image contrast is based on variations in spin density and relaxation times (often with injected contrast agents), contrast with iZQC images comes from variations in the susceptibility over a distance dictated by gradient strength.

3.1 Introduction We have demonstrated a new type of MRI based on detection of intermolecular zeroquantum coherences (iZQCs) [11. These coherences correspond to detecting the signal produced by simultaneously flipping two water spins in opposite directions on molecules separated by 10 p m - 1Omm. Such a signal is completely unobservable in the conventional picture of solution magnetic resonance, where couplings between independent molecules in solution are ignored. Over the last few years, however, strong signals from such "impossible" intermolecular cross-peaks and extra resonances have been detected

54

R. R. Rizi, S.Ahn, J. Hopkins, .I S. .Leigh, and W. S.Warren

[2-71. As we Qscuss below, the iZQC linewidth (hence the image contrast) is determined by local susceptibility gradients, which are not measured by any other technique. P

a

x TEI2

RF

G, (slice)

n

r----,

;

W

Fig. 3.1 : Intermolecular zero-quantum coherence (iZQC) imaging pulse sequence. A standard spin echo echo-planar imaging pulse sequence was modified to include a slice selective preparation pulse and filter gradient before the normal excitation and refocusing pulses. The filter (correlation) gradient is applied immediately after the a pulse (flip angle 90" in our experiments). A second slice selective RF pulse of variable flip angle (0) is applied after a delay 4. A typical delay time between a and p pulses was 50 ms. Similarly a typical delay of 100 ms was used between the p pulse and the K refocusing pulse.

The sequence we use to detect an iZQC image is shown in Fig. 3.1. If the first pulse were omitted, this would be a conventional echo-planar imaging (EPI) sequence and would generate contrast only because of differences in T2 relaxation during the delays after the second pulse. Instead, however, the pulse labeled a (a d 2 pulse) converts the equilibrium magnetization I , into I , . The gradient after the interval 7, which we will call the correlation gradient, modulates this transverse magnetization. None of the later gradient pulses ever match this correlation gradient, so a conventional treatment would predict no signal except from spins that relax back towards equilibrium during z. This treatment turns out to be incorrect-iZQC signal is detectable because of the direct dipoledipole interaction between nuclei in solution. This direct dipole-dipole interaction is proportional to (3cos2 O-l)/r3 , where Y is the internuclear separation and 0 is the angle the internuclear vector makes with the applied magnetic field. Diffusion makes the angle 8 vary rapidly for pairs of nearby spins, so the coupling is generally assumed to be

3. Contrast Enhancement Based on Intermolecular Zet-o Quantum Coherences (iZQC)

55

averaged away [S]. However, this assumption is only valid for spins closer than the distance molecules diffuse on an NMR time scale [5] (typically 10 pm). If the magnetization is not spatially uniform (as happens if the spins precess in a gradient, as in virtually all imaging sequences), the interaction between distant spins can be quite important, and detection of intermolecular resonances is possible.

3.2 Theory Several different theoretical models have been used to quantitatively understand these effects One approach treats the couplings classically [4,5,9-111 using Bloch equations modified to include the “dipolar demagnetizing field“, which had been introduced almost two decades earlier to explain multiple echoes in concentrated solutions [12,13]. It is also possible to use a fully quantum treatment [2,4] (retaining the dipolar couplings, and discarding the high temperature approximation to the density matrix) or a classical/quantum hybrid [14]. Both treatments can make fully quantitative predictions of the signals for simple sequences [4,14,15] but the quantum approach leads to an easier understanding of this experiment. The equilibrium density matrix for N spin-1/2 nuclei is pe4 = 2--Nn(1-3Z,i);

3 =2tanh(qoo/kT)

(3.1)

Z

where ZZi is the operator for z-magnetization spin i, coo is the resonance frequency, and kT is the thermal energy. The a pulse (90° in all of our experiments) rotates the equilibrium z magnetization into transverse magnetization p = 2 - N n ( 1 - 3 ~ , i ~ i n a - 3 1 ,cosa) ~

(3.2)

i

The S2 and higher even order terms give double- and zero-quantum coherences between every pair of spins in the entire sample:

During the delay T the last two terms in eqn. (3.3) (the iZQC terms) evolve at the differ-

56

R. R. Rizi, S. Ahn, J. Hopkins, J. S. Leigh, and W. S. Warren

ence between resonance offsets of the two spins i andj. They will not evolve at all when the gradient is off for two water molecules in regions with the same susceptibility (Am, - A m j = 0 ) . However, during the correlation gradient (strength G,, duration t,, and direction s) they may evolve at different frequencies if the two spins are separated. Assuming uniform magnetization (no density or resonance frequency variations) for the moment, at the end of the delay z the iZQC component of the 2-N-1

32 sin . 2

g2 term will then be [ 1,4]:

[ ( Z + ~ I+- ~ I - ~ Z + ~ ) C O ~ {-(~Aw~~~ ) T + y c , ( S- S~j ) t c } ]

(3.4)

i>j

The p RF pulse transfers these ZQ coherences into two-spin single quantum (IQ) terms such as IxiZzj.Finally, the magnetization can be rendered observable by a number of small intermolecular dipolar couplings, which remove the I , term, leaving one-spin 1QC terms for detection. Still assuming uniform magnetization, the exact signal is [l]

M + =iMosin2 a c o s p J 1 As = {3(s .Z ) - 1}/2

(3.5)

where the dipolar demagnetization time z d = 240 ms for pure water at room temperature in a 4 Tesla magnet). Note that this signal can be quite substantial (the maximum value of the Bessel function J , is 0.58). In the conventional picture, which ignores dipolar couplings, the signal vanishes completely because the correlation gradient wipes out the magnetization. We previously showed [3J that the intermolecular double-quantum coherence (iDQC) signal without inhomogeneous broadening comes primarily from spiiis separated by a distance d = n/(yG,t,) - half a cycle of the magnetization helix generated by the correlation gradient - thus we observed crosspeaks between coaxial tubes when the helix pitch was long. Reference [7] extended this approach to extract more structural detail. With inhomogeneous broadening, an additional contrast mechanism becomes available because iZQC evolution during the delay z (100 ms in our experiments) is only affected by the resonance frequency difference between spins i and j . In these phantom experiments, this frequency difference arises from two sources-residual imperfections in the shimming and susceptibility variations near the edges. Both effects increase as the

3. Contrast Enhancemenr Based on Intermolecular Zero Quantum Coherences (iZQC)

57

separation between spins increases. This also will generate an inhomogeneous linewidth 1/Ti on each pixel, but there is a fundamental difference. The measured value of 1/Tl reflects the linewidth averaged over an entire voxel (typically 1 x 1 x 5 mm in the images below), but the iZQC evolution is only affected by frequency differences dictated by the correlation gradient (typically G, = 1 G/cm and t, = 4 ms, giving d = 300 pm, which is much smaller than the slice thickness). We thus expect the iZQC image to partially refocus inhomogeneous broadening, giving T2,zgcontrast in general whch is somewhat different from T2 or T; contrast.

3.3 Experimental Results Images were acquired using a twelve-strut birdcage headcoil in a GE SIGNA 4T whole body scanner equipped with experimental, high speed, 2.3 G/cm shielded gradients. The a pulse phase (which does not affect the iZQC signal) and the receiver phase are inverted on alternate cycles. Single quantum coherence generated by the a pulse is completely dephased by the correlation gradient and is undetectable; however, the sequence could be modified to cancel the a pulse phase inversion. A 10 cm spherical head phantom filled with polydimethyl siloxane (TI = 0.78 s, T2 = 0.21 s) was used to demonstrate contrast generated near interfaces. The phantom is nearly homogeneous except for an air bubble at the top and two screws on either side, which were intentionally placed in the imaging plane. A sixteen average image of a 64 x 64 one shot spin echo (TE = 100 ms, TR = 4 s) EPI image of the Si oil head phantom with a total scan time of less than one minute is shown in Fig 3.2A. The image was expanded to 128 x 128 pixels by bilinear interpolation. The image is mostly homogeneous except for the bright ring near an air bubble at the top, an intensity variation on the upper right edge caused by the screw capping a filling hole, a slight brightening and distortion on the lower right edge presumably from RF inhomogeneity, and what might be a slight intensity variation on the middle left edge caused by the screws. Figure 3.2B-D also shows images acquired using the iZQC filtered pulse sequence with a 1 G/cm correlation gradient applied for 4 ms (d = 300 pm) and T = 50 ms. These images were signal averaged 128 times. These images exhibit broad internal banding structure from residual shimming imperfections; they also exhibit sharp structures due to

58

R. R. Rizi, S.Ahn, J. Hopkins, J. S. Leigh, and W. S.Warren

Fig. 3.2: Comparison of standard EPI images (parts A and E) with Z Q C images (B,C,D,F) for a silicone oil phantom with an air bubble (top) and a head phantom (bottom). The iZQC images were taken with two different methods for suppression of residual transverse magnetization: coadding p = 45" and p = -135" spectra (part B) and subtracting x-correlation gradient spectra from z-correlation gradient (parts C,D,F). Shifting the phantom down (parts C verses D) shows that features around the air bubble are susceptibility differences, whereas the broad bands are residual static inhomogeneity .

susceptibility variations (primarily near the air-liquid interface where the susceptibility changes rapidly). To demonstrate that the broad banding is dependent on shimming, the phantom was lowered in the head coil to bring it closer to the lower struts; the broad bands do not move, but the sharp bands move to remain near the air-liquid interface. It is important to point out that no contrast agent is required for this sort of contrast enhancement, although it certainly would be possible to develop and investigate ZQ-sensitive contrast agents (paramagnetic ions shft the resonance frequency as well as increase the linewidth). A resolution test phantom filled with water ( T I = 1.16 s, T2 = 0.18 s) was used to examine the sensitivity of the new contrast technique to small structures (Fig.

3.2E-F), and verifies that in this case, with a susceptibility-matched housing, we produce a normal looking image. Figure 3.3 shows 128 x 128 pixel phantom iZQC images, taken as a function of correlation gradient strength (z = 10 ms, TE = 100 ms, gradient length t, = 4 ms). This changes the characteristic separation d = .n/yGt, of the pair of spins in the observed iZQC coherences. For very close spins the resonance frequency difference is small; for more distant spins the resonance frequency variation due to residual static inhomogeneity and susceptibility variations causes enhanced contrast.

3. Contrast Enhancement Based on Intermolecular Zero Quantum Coherences (iZQCj

2G/cm

0.5 G/cm

1G/cm

59

0.25 G/cm

Fig. 3.3: Phantom iZQC images, taken as a function of correlation gradient strength from 2 G/cm to 0.25 G/cm. This changes the characteristic separation d = x/yGt, of the pair of spins in the observed iZQC coherences.

Numerous control experiments confirm that the image actually arises from iZQCs, rather than some unaccounted source of transverse magnetization. If the second pulse flip angle is changed from +45" to -135" the desired signal is unaffected, but transverse magnetization excited from residual z magnetization before the second pulse (generated by RF pulse imperfections or T1 relaxation during 2) is inverted (Fig. 3.2B). Another approach is to alternate between z ( A , = 1) and x ( A , = -1/2 ) correlation gradients, which inverts the desired signal and leaves transverse magnetization unaffected, and take the difference between the two spectra (Fig. 3.2C). In this case we can estimate the total magnetization in regions where nearby spins are at nearly the same frequency:

3TE

= - iM0 sin2 a si n(2~)__ 8ed

In our experiments both approaches work, but the latter approach is better because the slice profile is unaltered. No signal was observed when the correlation gradient axes were switched to alternate between the x and y directions instead of the x and z directions, or if the p pulse was omitted. Equation (3.6) shows that the iZQC signal grows during the echo delay, whereas new transverse magnetization would decay with T2 relaxation during this time. Figure 3.4 shows a graph of signal intensity from a series of

60

R. R. Rizi, S. Ahn, J. Hopkins, J . S. Leigh, and W. S. Warren

images obtained for echo times ranging from 120 ms to 320 ms, and shows an the increase in signal intensity up to an echo time of 220 ins followed by decreasing signal. A theoretical calculation predicts that maximum signal is achieved for an echo time of 200 ms, which is in good agreement with our experimental results. The iZQC-based signal will be maximized when the second pulse has a tip angle of p = 45"; ordinary transverse magnetization generated by the second pulse would continue to increase up to 90" and then decrease. Figure 3.5 shows a graph of signal intensity as a function of with a correlation gradient of 2 G/cm, and a single data point collected with a 1 G/cm correlation gradient demonstrating a smaller average signal (as expected since the iZQC signal now comes from more separated spins). Also shown is a (scaled) calibration curve obtained by turning off the a pulse and matching the p pulse phase to that of the receiver in order to observe transverse magnetization as a function of flip angle.

3.4 Future Directions How can this technique be generalized? Resonance frequency variations due to the bulk magnetic susceptibility can be significant for structured materials [16,17]. Well characterized examples include lung tissue [I81 (at the interface between air with = 0.4 ppm and normal tissue with = -9 ppm; 1 ppm is 170 Hz in a 4 T magnet), arterial blood

x

x

x

vessels (with different degrees of blood oxygenation on either side, changing by about 0.3 ppm) and sites of tissue necrosis (fully deoxygenated hemoglobin, changing by about 1 ppm). In conventional MRI this variation shows up as an inhomogeneous broadening but iZQC detection would provide a much more sensitive, and distance-selected,

x

method for measuring these variations. Figure 3.4 shows that the signal is approximately 5% of the conventional epi signal in our 4T experiments. It would also be trivial to extend these results to multiple echoes or other imaging sequences to further enhance the detected signal, and this might be advantageous in applications where chemical shift variations (e.g. water verses fat) are significant complications. However, we should note that the signal-to-noise ratio (SNR) in conventional MRI scales with concentration (C), gyromagnetic ratio (y) and magnetic field (B) as SNR

0~

yl1I4 C B7I4 (conventional MRI)

3. Contrast Enhancement Based on Intermolecular Zero Quantum Coherences (iZQCj

n

0'06

s 0.05

.-c0

I

1 1 v 0

m

0.04

61

0

.

0

0

0 S

0 0.01

' J

0

E .c

v

0

I-

0

100

0

200

Simulation Experiment

300

I

400

500

Echo time

Fig. 3.4: Dots: experimental signal intensity as a function of the echo time for the resolution phantom. Solid line: simulation of iZQC intensity based on experimentally measured values of 7'1 and T2.

(The fractional powers come from the assumption that, for constant probe Q, the noise scales as the 1/4 power of the frequency). Equation (3.5) shows that, for TE
This suggests that iZQC contrast enhancement is most appropriate for water imaging in relatively large fields, or with nonequilibrium magnetization (e.g. spin polarized Xe). Note that the correlation distance does not enter into these equations-the iZQC signal will have the same sensitivity for pairs of spins separated by 1 pm as for pairs of spins separated by 1 mm, if diffusion can be neglected during the intervals zZqand TE. In practice, it takes tens of 1-1s for a significant signal to grow in, hence this type of imaging in water would be appropriate for distance scales >10 pm (the approximate distance water molecules diffuse in 10 ms), although for more viscous materials the distance could be made shorter.

62

R. R. Rizi, S. Ahn, J. Hopkins, J. S. Leigh, and W. S. Warren

30 25

-I

-4

sin 0 iZQC (1G/cm) 0

20

40

60

80

100

Second pulse flip angle (degrees) Fig. 3.5: Experimental signal intensity as a function of the flip angle of the p pulse, for iZQC images and conventional epi images (the conventional image is obtained by setting the first pulse flip angle to zero). Equation (3.6) shows that the iZQC signal should be proportional to sin p cos p (= sin (2p)) for TE < ‘rd; the signal in a conventional image should be proportional to sin p. Note that the average iZQC signal decreases as the gradient pulse strength is decreased, reflecting the onset of resonance frequency differences (but enhanced contrast).

3.5 Conclusion In summary, we have shown on phantom samples that it is possible to produce spatially resolved images with good signal-to-noise ratios and contrast coming from a mechanism that is different from T2 or T; . Applications to a variety of structured materials should be possible, including extensions to in vivo imaging [191.

Acknowledgements This work was supported by the NIH under grants GM35253 (Princeton), RR02305, and HL07614 (Penn). W2 wishes to thank Drs. John Videen, Michael Middleton, and Eric Wong (UCSD) for useful discussions.

3. Contrast Enhancement Eased on Intermolecular Zero Quantum Coherences (iZQC)

63

References 1.

S. Vathyam, S. Lee, and W. S. Warren, Science 272 (1996) 92.

2.

W. S. Warren, W. Richter, A. H. Andreotti, and S. Farmer, Science 262 (1993) 2005.

3.

W. Richter, S. Lee, W. S. Warren, and Q. He, Science 267 (1995) 654.

4.

S. Lee, W. Richter, S. Vathyam, and W. S. Warren, J. Chem. Phys. 105 (1996) 874.

5.

W. S. Warren, S. Lee, W. Richter, and S. Vathyam, Chem. Phys. Lett. 247 (1995) 207; Q. He, W. Richter, S. Vathyam, and W. S. Warren, J. Chem. Phys. 98 (1993) 6779.

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P. Broekaert, A. Vlassenbroek, J. Jeener, G. Lippens, and J-M. Wieruszeski, J. Mug. Reson. A 120,

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P. Robyr and R. Bowtell, J. Mag. Res. A 121 (1996) 206; R. Bowtell and P. Robyr, Phys. Rev. Lett. 76

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N. Bloembergen, E. M. Purcell, and R. V. Pound, Phys. Rev. 73 (1948) 679.

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M. Levitt, Concepts in Magnetic Resonance 8 (1996) 77.

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M. Augustine and K. Zilm, J. Mag. Reson. A 123 (1996) 145.

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G. J. Bowden, T. Heseltine, and M. J. Prandolini, Chem. Phys. Lett. 233 (1995) 639.

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G. Deville, M. Bernier, and J. M. Delrieux, Pkys. Rev. E 19 (1979) 5666; D. Einzel, G. Eska,

(1996) 97.

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589; A. S. Bedford, R. Bowtell, and R. M. Bowley, J. Mug. Res. 93 (1991) 516. 13.

X. Zhou, C. S. Potter, and P. C. Lauturbur, Proc. SOC.Magnetic Resonance in Medicine (1991) 345.

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J. Jeener, A. Vlassenbroek, and P. Broekaert, J. Ckem. Phys. 103 (1995) 1309.

15.

W. S. Warren and S. Ahn, J. Chem. Phys. 108 (1998) 1313.

16.

C. S. Springer, NMR in Physiology and Medicine, R. J. Gillies (ed.), Academic Press, Orlando,

17.

Z. M. Bhujwalla, D. C. Shungu, Q. He, J.P. Wehrle, and J. D. Glickson, NMR in Physiology and

1994, p. 75-99.

Medicine, R. J. Gillies, (ed.), Academic Press, Orlando, 1994, p. 311-328 and references therein. 18.

C. H. Durney, J. Bertolina, D. C. Ailion, R. Christmas, A. G. Cutillo, A. H. Morris, and S. Hashemi, J. Magn. Reson. 85 (1989) 554.

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W. S. Warren, S. Ahn, M. Mescher, M. Garwood, K. Ugurbil, W. Richter, R. R. Rizi, J. Hopkins, J. S. Leigh, Science, in press.

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4. Frequency Dependence of EPR Sensitivity G. R. Euton, S. S. Euton, and G. A. Rinard Departments of Chemistry and Biochemistry and Engineering, University of Denver, Denver, CO, 80208, USA

Abstract Contrary to some prior derivations, it is shown that the sensitivity of EPR measurements is the same as for NMR, and that in general comparisons of EPR sensitivity as a function of frequency u) have been pessimistic by one factor of u). The frequency dependence of EPR signal intensity depends on what parameters are held constant. At constant microwave magnetic field ( B , ) signal intensity varies as u)0714 if the sample and resonator size are constant, as u)0-1’4 if sample and resonator size both scale as o0-l, or as if the sample size is constant and resonator size is scaled as oOp1. SIN as a function of frequency depends on the dominant source of noise. Predictions are made for the case in which thermal noise due to resistance of the resonator materials dominates and for the case in which losses in the sample dominate.

4.1 Introduction To obtain adequate depth penetration into large aqueous samples, including animals, EPR imaging is performed at the lowest feasible frequency - typically between 250 MHz and 2 GHz. The feasibility of imaging physiologically significant signals at these frequencies is dependent upon obtaining adequate signal-to-noise (SIN). A frequently-posed question is “what, in principle, should one expect to be able to achieve with an ideal spectrometer”? This paper presents a basis for making such predictions, and concludes that the potential for imaging at low frequency is more optimistic than has been suggested by others.

66

G. R. Euton, S. S. Euton, and G. A. Rinard

The issue of EPR signal intensity as a function of frequency has been confused for many years because of an unfortunate error in Poole's book [ 11. Experimental tests of the frequency dependence of SIN have typically compared performance on extensively engineered X-band systems with results obtained on low-frequency EPR systems that have been built with minimal budget andlor for specialized purposes and are unlikely to approach ultimate sensitivity. The predictions and experimental results in the literature have provided a rather pessimistic picture. We have re-derived the expressions for EPR signal intensity as a function of frequency. NMR and EPR traditions, reflecting the historic differences in frequency range of interest and the associated technologies, express frequency dependence of sensitivity differently. An attempt at translation between these traditions is presented. Derivations of some of the equations stated in this paper are presented in a general discussion of signal and noise [2], which should be referred to for more detail.

4.2 Frequency Dependence of EPR Signal Intensity A general expression for EPR signal intensity is eqn. (4.1) [2], where AE is the signal

voltage at the end of the transmission line connected to the resonator, q is the resonator filling factor, QL is the loaded quality factor, Q, of the resonator, Z, is the characteristic impedance of the transmission line, and P is the microwave power to the resonator produced by the external microwave source. The magnetic susceptibility of the sample, f',

is the imaginary component of the effective RF susceptibility. For a Lorentzian line with linewidth Am at resonance frequency coo, substitution for the susceptibility in (4.1) yields (4.2), where S = 1/2, N is the number of spins per unit

(4.2)

volume and Tsampleis the temperature of the sample.

4. Frequency Dependence of EPR Sensitivity

67

Prediction of the frequency dependerzce of EPR signal intensity involves examination of the frequency dependence of each term in eqn. (4.1). Equation. (4.2) explicitly shows the frequency dependence of the magnetic susceptibility. We now seek the frequency dependence of the filling factor, r\, and of Q. Since an experiment may be done at constant incident power or constant B , , we also derive the frequency dependence of these terms. We then consider three cases: case 1 - the size of the sample and resonator are constant, case 2 - the size of the sample and resonator are scaled with mop,, and case 3 the size of the sample is constant and the size of the resonator is scaled as oopl.

4.2.1

Frequency Dependence of Q for LGR

The loaded Q, QL, for a loop gap resonator (LGR), is given by QL = ooLl2R. The inductance, L, is related to the length z and the cross-sectional area of the loop, A = mi 2/4, by eqn. (4.3). A L=po2

(4.3)

The resistance, including skm effect, (skin depth 6 = [opo 0 / 2 ] - ~ of / ~the ) resonator loop is

(4.4)

Substitution of (4.3) and (4.4) into the definition of Q, gives the frequency dependence of

Q, (4.5): (4.5)

where o is the conductivity of the surface of the resonator and po is the permeability in a vacuum. Since o is assumed to be independent of frequency, the frequency dependence of Q is determined by o0li2d (d is the diameter of the resonator), which is if the resonator size is kept constant, and is oop1’2 if the LGR size is scaled proportional to o0-1.

68

G. R. Eaton, S. S. Eaton, and G. A. Rinard

4.2.2

Frequency Dependence of Filling Factor

Thefilling factor, q, must be determined for each sample and resonator combination, and requires a detailed analysis of the electromagnetic fields in the resonator. However, we often can make an educated guess for q. We will assume as a first approximation that the filling factor for LGRs as a function of frequency will scale as if the microwave magnetic field were uniform and confined to the loop. For resonators with a constant loop size and sample size, this approximation overestimates 11 at higher frequency because the gap spacing must increase with frequency for a constant loop size, and as the gap increases, the magnetic field will no longer be completely confined to the loop.

4.2.3

Signal Intensity at Constant Incident Power

Substitution of eqn. (4.5) into eqn. (4.2) gives

( A q= K , q d o y f i

(4.6)

where terms that do not depend on frequency are combined in K , = ~0 ,/-/8Aw, and

xo = Ng2p2S(S+ 1)/3kTs.Equation. (4.6) indicates that the frequency dependence of

the ESR signal is a function of filling factor

4.2.4

and diameter d as well as w0312.

Frequency Dependence of Microwave Field B1

The frequency dependence of B , is given by eqn. (4.7) [2]:

where: K , = k , f 2 p & ~ / n and ~ k , is a constant of proportionality between B , , the rms magnitude of the circularly polarized component of the microwave magnetic field that is perpendicular to the external magnetic field and in phase with the Larmor precession and

4. Frequency Dependence of EPR Sensitivity

69

B1,, the total magnetic field in the resonator. Typically, one would seek to maintain the same B , at the sample, unless the spin relaxation time changed with frequency.

4.2.5

Application to Three Specific Cases

In case 1 we assume constant sample size and constant loop size. For example, one could have a LGR of a given loop size, with the frequency varied by changing the gap dimension. In this case, the variation with frequency is that given in eqns. (4.5-4.7) with filling factor and resonator dimensions held constant. In case 2 (“unlimited sample”) we assume that sample and loop sizes scale as m0-l. The length z and diameter d of the resonator scale with frequency. With this assumption eqn. (4.6) and (4.7) give eqn. (4.8) and (4.9).

In case 3 (“limited sample”) we assume that the sample size is constant and the dimension of the loop scales as m0-l. Since the sample volume is constant and the resonator volume varies as the frequency dependence of the filling factor is,

7 =k4mi

(4.10)

Substituting eqn. (4.10) into eqn. (4.6) gives,

]AE/ =K , k 3 k 4 ~ 0 i / ~ f i

(4.11)

The expression for B , in this case is the same as for case 2. The results obtained for these three cases are summarized in Tab--: 4.1. Alt..ough results were derived for the case of an LGR, they are also applicable to other resonators, including cavities, provided the assumptions for each case are matched. For the unlimited sample case, the dependence on wo1/2 agrees with the predictions of Abragam and Bleaney [3], Wilmshurst [4], and Fraenkel [5]. For the limited sample case the depen-

70

G. R. Eaton, S.S.Eaton, and G. A. Rinard

dence on w07/2 agrees with the results of many others, including Feher [6], Abragam and Bleaney [31, and Fraenkel [5]. The dependence of signal at constant power [3,5] (unlimited sample, case 2) on of signal intensity for constant sample (case 3) at constant power [3,5-71 on and of constant sample [7] (case 3) at constant B , on w011/4 agrees with predictions in the references cited, among others. In the frequently cited discussion of Nminin [ 11, an additional factor of wO-l was included based upon a set of assumptions concerning the frequency dependence of the relationship between incident microwave power in the waveguide outside a cavity and B , in the cavity. The relationships in Table 4.1 do not bear out this assumption. The range of exponents in Table 4.1 indicates that one needs to exercise great care in selecting the appropriate relationships to predict frequency dependence of signal intensity for a particular situation. One also needs to consider practical realities. Scaling a resonator design over a wide frequency range may not be possible because of machining tolerances, or because gaps become too small to prevent arcing during high-power pulses. In addition, resonator dimensions may become so much smaller at higher frequencies that it is not possible to maintain a constant sample size. Thus the practical need for different resonators at different frequencies may prevent one from taking advantage of theoretically predicted advantages. Table 4.1. Predicted Frequency Dependence of EPR Signal Intensity

Case 1 const. Sample size

Case 2 sample size oc wO-l

Case 3 const. sample size

const. LGR size

LGR size = wO-l

LGR size = wO-l

L

1

(4.3)

wO-l

(4.3)

wO-1

(4.3)

R

w01/2

(4.4)

w01/2

(4.4)

w01/2

(4.4)

Q

oo1/2

(4.5)

00-%

w0-%

(4.5)

r\

1

EPR signal, AE,at constant P

w03/2

(4.6)

wo1/2

0-?4

(4.7)

P to maintain constant B ,

wo1/2

(4.7)

EPR signal, AE,at constant B ,

007/4(4.6,4.7)

/fi

B1

(4.5,4.7)

(4.10)

(4.8)

wo3 w07/2

w03/4

(4.9)

030314

(4.9)

w0-3/2

(4.9)

w0-312

(4.9)

1

w0-1/4

(4.8,4.9)

(4.11)

(4.9,4.11)

aThe equation numbers that are the bases for the various statements are given in parentheses. The table lists overall frequency dependence and does not include proportionality constants.

4. Frequency Dependence of EPR Sensitivity

71

4.3 Comparison with Frequency Dependence of NMR Since the fundamental spin resonance is the same, the frequency dependencies predicted in Table 4.1 should agree with the predictions for NMR when the same assumptions are made. In NMR the signal typically is represented as a current induced in a coil by precession of the spins [S-151. The typical NMR case would be case 1, i.e., a constant sample size and constant loop size, for which the inductance L is constant. The NMR expression derived for the same assumptions as the table entries gives an 002 dependence, where one factor of coo comes from (as in eqn. 4.1 and 4.2) and the second factor of wo comes from Lenz’s law. To compare this frequency dependence with that described for EPR signals note that since QL = wd;/2R, eqn. (4.2) can be written as

x“

Thus, both approaches predict an O$ dependence at constant power if the frequency dependence of R is ignored. Frequency dependence of sensitivity (signal-to-noise, SIN) depends on the frequency dependence of both signal and noise. The NMR literature discusses “sample noise” and “coil noise,” while the EPR literature, largely based on microwave engineering descriptions of cavity resonators, describes these features in terms of changes in Q of the resonator. For example, losses or dissipation of power must be due to resistance, and whether one describes the losses separately, or as part of what contributes to a change in Q, the effect must be the same. If one increases gain to compensate for the decrease in signal due to the lower Q, there is an increase in the noise relative to the signal. T h s is the origin of the concept of sample noise. This effect increases as w2 [13-161. Based on early work by Lauterbur, Hoult, Andrew and others [9,13-151 it is now generally agreed that the SIN in MRI and spectroscopy in living systems follows a o~~~ to w1 frequency dependence. Since EPR approaches the same frequencies for imaging and in vivo EPR, the analysis is relevant. The NMR signal voltage is proportional to w2, where w is the operating frequency. Noise voltage due to resistance in the radiofrequency coil probe circuit is proportional to o ~ whle / ~ , noise due to losses in the patient’s body is proportional to a.At low frequencies where losses are small, the SIN varies as At higher frequencies, where the coil losses are less important, the SIN depends linearly on w.

72

G. R. Euton, S. S. Euton, and G. A. Rinard

Analogies with MIU informed the effort to strive for lower frequency for EPR imaging (see, for example, Halpern and Bowman [17]). Thus, the EPR signal at constant Q should be proportional to w2 while the thermal noise should be proportional to all2, resulting in an overall SIN proportional to w3l2. If inductive losses in tissue dominate, the effective resistance is proportional to 02,and SIN is predicted to scale linearly with W. Measurements at low frequency have confirmed the linear dependence of SIN on frequency in EPR [ 181 and NMR [ 16,191.

4.4 Design of EPR in vivo Imaging Experiments The real situation for animal samples will be somewhere between the extremes of and 0712. One might scale the resonator size with frequency (case 2) from X-band to Lband, in order to be able to study a mouse. But then there would be no further benefit in making the resonator large relative to the mouse, so then one would switch to keeping both the sample and resonator size constant (case 1) as the frequency is lowered by another factor of 5 to 200 MHz. For this one would pay a signal amplitude price of about 17. However, this loss would be ameliorated somewhat by the greater penetration depth of the RF at the lower frequency. If the signal came from the center of the mouse, one might not lose much signal by lowering frequency, since the skin depth is proportional to and is significant for an animal the size of a mouse at frequencies above about 200 MHz. Together with the noise due to losses in the sample discussed above, the net result is that in practical applications sensitivity (SIN) appears to increase approximately linearly with frequency for animal imaging in the RF range [ 16,18,19]. As measurements proceed to larger animals, it will be necessary to scale the resonator size to fit them, and the best results will be obtained if the wavelength is large compared with the size of the animal. If the organ of interest increases in size proportionately with the overall size of the animal, the situation is more like case 2, and SIN should not be much worse at lower frequency. Interaction of the dielectric and conductivity properties of the sample with the microwaves also decreases SIN. Aqueous and conducting samples have frequencydependent skin depths [ 17,201. The dielectric properties can produce phase changes that can null signals from certain locations in samples [ZO]. The much larger penetration

4. Frequencj Dependence of EPR Sensitivity

73

depth at low frequencies can result in many more spins in a large sample being visible at low frequency than at high frequency. This effect can reverse the general trend toward greater sensitivity at higher frequency. Heterogeneous samples appear to have greater penetration depth than homogeneous samples of the same type of material. The physical interactions that result in the losses mentioned here also result in reduction of the resonator Q, and the detected ESR signal is proportional to resonator Q. All of the above discussion is relevant to signal intensities in both CW and pulsed EPR, if the relaxation times are long enough, as they usually are in NMR. However, if electron spin relaxation times are short enough to be comparable to instrument deadtimes, then new sensitivity considerations apply. If Q is constant, and the electron spin relaxation time is constant and equal to the dead-time at one frequency, then the sensitivity for pulsed EPR decreases as e-nz, where n is the proportional relative frequency. To avoid this strong dependence on frequency, it is necessary to reduce the dead-time proportional to the reduction in frequency. This could be done with a combination of a crossed-loop resonator [21,22], active Q-spoiling [23], and passive or active pulse cancellation [24,25]. Pulsed EPR imaging of a radical injected into a mouse has been achieved [26]. The reduction in Q due to a given lossy sample decreases with frequency, even for the same filling factor. This effect also tends to favor lower frequency ESR for lossy samples. All of these effects together could even reverse the expected trends of SIN with frequency, such that it is conceivable that the ultimate molar (spins per volume) sensitivity for biological samples and other lossy samples could increase as the frequency decreases. This remains to be demonstrated, but there is good basis for exploration in this direction.

Acknowledgments We appreciate discussions with Richard W. Quine (University of Denver) and with Professors Howard J. Halpern (University of Chicago), Jack H. Freed (Cornell University), R. Linn Belford (University of Illinois) and others.

74

G. R. Eaton, S. S. Eaton, and G. A. Rinard

References I. 2.

C. P. Poole, Jr., Electron Spin Resonance, Wiley, New York, 1967, chapter 14.

G. A. Rinard, S. S. Eaton, G. R. Eaton, C. P. Poole, Jr. and H. A. Farach, in Handbook of Electron Spin

Resonance, Vol. 2, C. P. Poole, Jr. and H. A. Farach, eds, Springer-Verlag.in press. 3.

A. Abragam and B. Bleaney, Electron Paramagnetic Resonance of Transition Ions. Oxford University Press, Oxford, 1970.

4.

5.

T. M. Wilmshurst, Electron Spin Resonance Spectrometers, Plenum Press, New York, 1968.

G. K. Fraenkel, Paramagnetic Resonance Absorption, Chapter XLII in Technique of Organic Chemistry, Vol. I

-

Part IV, Physical Methods of Organic Chemistry, Third Edition, A. Weissberger, ed.,

lnterscience Publishers, New York, 1960.

6.

G. Feher, Bell System Technical Journal 36 (1957) 449.

7.

Varian spectrometer manual 87-125-052, page 3-8.

8.

A. Makovski, Mugn. Reson. Med. 36 (1996) 494.

9.

E. R. Andrew, Magnetic Resonance and Related Phenomena, Elsevier, 1989 (241hAmpere Congress, Poznan, 1988), page 45-51.

10.

A. Abragam, The Principles of Nuclear Magnetism. Oxford University Press, Oxford, 1961.

11.

D. I. Hoult, Encyclopedia of NMR.D. M. Grant and R. K. Harris, eds., 7 (1996) 4256.

12.

D. I. Hoult and R. E. Richards, J. Magn. Reson. 24 (1976) 71.

13.

D. I. Hoult and P. C. Lauterbur, J. Mugn. Reson. 34 (1979) 425.

14.

C.-N. Chen and D. I. Hoult, Biomedical Magnetic Resonance Technology,Adam Hilger, Bristoi, 1989.

15.

M. T. Vlaardingerbroek and J. A. den Boer, Magnetic Resonance Imaging, Springer, 1996.

16.

D. L. Hoult, C.-N. Chen, and V. J. Sank, Magn. Reson. Med. 3 (1986) 730.

17.

H. J. Halpem and M. K. Bowman, in EPR fmaging and in vivo EPR, G. R. Eaton, S. S. Eaton, and K. Ohno, eds., CRC Press, Boca Raton, FL, 1989, Ch. 6.

18.

L. G. Stoodley, J. Elect. Control 14 (1963) 531.

19.

W. A. Edelstein, G. H. Glover, C. J. Hardy, and R. W. Redington, Magn. Reson. Med. 3 (1986) 604.

20.

M. Sueki, G. A. Rinard, S. S. Eaton, and G. R. Eaton, J. Magn. Reson. A 118 (1996) 173.

21.

G. A. Rinard, R. W. Quine, B. T. Ghim, S. S. Eaton, and G. R. Eaton, J. Magn. Reson. A 122 (1996) 50.

22.

G. A. Rinard, R. W. Quine, B. T. Ghim, S. S. Eaton, and G. R. Eaton, J. Magn. Reson. A 122 ( 1 996) 58.

23.

S. Pfetminger, W. Froncisz, J. Forrer, J. Luglio, and J. S. Hyde, Rev.Sci. Instrum. 66 (1995) 4857.

24.

J. L. Davis and W. B. Mims, Rev. Sci. Instrum. 52 (1981) 131.

25.

P. A. Narayana, R. J. Massoth, and L. Kevan, Rev. Sci. Instrum. 53 (1982) 624.

26.

R. Murugesan, J. A. Cook, N. Devasahayam, M. Afeworki, S. Subramanian, R. Tschudin, J. A. Larsen,

J. B. Mitchell, A. Russo, M. C. Krishna, Mugn. Reson. Med. 38 (1997) 409.

5. SPRITE Imaging of Short Relaxation Time Nuclei Bruce J. Balcom MRI Center, Department of Physics, University of New Brunswick, P.O. Box 4400, Fredericton, New Brunswick, Canada, E3B 5A3

Abstract A generic pulse sequence based on the Single Point Imaging method is introduced. The pulse sequence, Single Point Ramped Imaging with T I Enhancement (SPRITE) is a pure phase encode technique with broadband RF excitation pulses and a stepped or ramped primary phase encode gradient. The technique, which is a version of the constant time imaging method, permits visualization of nuclei with T2*relaxation times of well under 100 ps. Applications of the method to imaging porous media, gas phase nuclei and bone materials are described.

5.1 Introduction Magnetic Resonance Imaging (MRI) has proven to be a superior method of visualizing internal structure in a large range of non-medical systems [ 11. It is nevertheless true that the majority of these applications correspond to materials or systems with relatively long lived MR signals, and that the imaging methods employed are traditional spin echo or gradient echo methods popular in clinical MRI. There exist a large number of interesting and important systems where the MR signal lifetimes are short, < 1 ms, and therefore not readily visualized with these methods. We are interested in the development of MRI methods which are able to image systems with short relaxation times due to surface relaxation in water bearing porous mate-

rials, quadrupolar relaxation of quadrupolar nuclei in asymmetric environments, polymer and other ‘solid’ materials with short T2 due to dipolar broadening, and gas phase

16

6.J. Balcom

nuclei with short relaxation times due to spin rotation relaxation [2]. In all but the third area listed above not only are transverse relaxation times typically under 1 ms but the spin lattice relaxation times are also usually on the order of milliseconds. In porous concrete materials, the area in which we have the greatest experience, the T2*relaxation time of evaporable water is typically under 200 ps with TI relaxation times of several ms.

5.1.1

Review of Short T i Methods

Many groups have proposed short

T.* imaging methods. Three dimensional projection

reconstruction (PR) has been espoused by several groups [3-5). Unfortunately the PR techniques inherently corrupt the origin of k space, due to the RF pobe ring down andlor gradient switching. These methods require data correction and regridding prior to Fourier reconstruction. The PR technique is not an imaging method wherein contrast is easily manipulated and since it is based on frequency encoding it has an inherent resolution limitation. Multiple pulse line narrowing methods have been successful for small scale samples which have short transverse relaxation times due to the dipolar interaction [6]. These methods however require RF pulses with well defined flip angles and phases and therefore are not likely to be amenable to use with larger samples. These multiple pulse methods are useful for MRI of dipolar broadened solids but not any of the other three classes of problems outlined above. The STRAFZ technique has recently grown in popularity [7]. It is well suited to the visualization of ultra short relaxation time nuclei and has superior spatial resolution. However the technique is slow and not readily implemented in two or three dimensions because of the necessity of physical motion of the sample in the static Bo gradient. The range of flip angles experienced by off resonance nuclei also complicates the interpretation or imposition of contrast in the image. The oscillating gradient technique [8,9] shows promise for the rapid visualization of short relaxation time nuclei however it requires a specialized gradient set and k space is not rectilinearly sampled, requiring, once more, regridding prior to Fourier reconstruction. The technique is also not useful for nuclei with transverse relaxation times less than the period of the oscillating gradient.

5. SPRITE Imaging of Short Relaxation Time Nuclei

5.1.2

77

Single Point (Constant Time) Methods

We seek an MRI method which employs conventional ideas of raster k space sampling and Fourier reconstruction, that maintains flexibility of contrast through changes in timing parameters, and does not require specialized hardware. The method must, by definition, be able to encode very short lived signals, ideally signals which are of the order of the RF probe dead time (tens of ps). In a concrete sample the transverse relaxation time, 200 ps, is of the order of a gradient rise time. Therefore one must excite the sample in the presence of a magnetic field gradient rather than pulsing the field gradient after excitation as is the usual practice. Furthermore, excitation will require broadband RF pulses of duration much less than T,*. Single Point Imaging (SPZ), satisfies these conditions and was suggested as a solids imaging method by Cory in 1994 [lo]. Despite its promise, SPI, Fig. 5.1, has been sparsely utilized [ 11,121.The technique is also known as Constant Time Imaging.

Fig. 5.1: One dimensional SPI sequence. Note the broadband RF pulse applied in the presence of the phase encode gradient. k Space is sampled, point by point, by amplitude cycling the phase encode gradient with repetitive RF excitation pulses. The encoding time is tp, the repetition time is TR.

SPI relies on broadband RF pulses of limited duration with the pulse bandwidth greater than the maximum spectral width (Gmaxx sample size) of the object under study [lo]. Position is encoded in reciprocal space, S(k), where k = 1 4 2 ~yG ) t, by amplitude cycling of the applied phase gradients G. A single point on the FID is sampled in quadrature a fixed encoding time tp after the RF pulse. Unlike frequency encoded images, SPI images are free from distortions due to B, inhomogeneity, susceptibility variations, and

78

B. J. Balcom

chemical shift [lo]. In addition, as a pure phase encode technique SPI avoids the line width restrictions on resolution common to time based sampling, frequency encode, methods [lo].

5.2 SPRITE The signal intensity, S , from any point in an SPI image is related to local proton density, p, by eqn. (5.1) where the pulse flip angle is 8 [ 131

The term in square brackets represents steady state longitudinal magnetization established through a succession of excitation pulses where we assume transverse magnetization is completely dephased between pulses. This term suggests the possibility of introducing TI contrast into the image by employing large flip angle pulses with repetition times on the order of T I .The short TI of many systems of interest further suggests that rapid pulsing should permit rapid k space traversal. The finite time required to safely and repetitively switch magnetic field gradients can be the limiting condition on a minimum TR [13]. Intense, rapidly switched gradient pulses in this sequence can lead to excessive, even dangerous gradient vibration. In response to these limitations we have developed the SPRITE sequence which greatly reduces imaging times, minimizes gradient vibration and also enables the introduction of quantitative TI contrast, or T I suppression, into a variety of images 1131. In the SPRITE sequence we ramp the primary phase encode gradient in discrete steps and apply an RF pulse, collecting a single data point, at each gradient step, Fig. 5.2. A major advantage of SPRITE is that we retain, for short T2*samples, the traditional flexibility of contrast manipulation through relaxation time weighting. The SPRITE experiment, due to minimal overall dBJdt, is silent.

5. SPRITE Imaging 01 Short Relanation Timr Nit( lei

79

RF

Fig. 5.2: Two dimensional SPRITE sequence. The primary phase encode gradient is stcpped betwecn discrete values as a function of the secondary phase encode gradients (one shown). The encoding time is tp, the repetition time is TR. A single point is acquired at cach gradient value. SPRITE phantom tests showed that we are readily able to observe

T7*signals under

100 ps in duration with T , contrast over at least four orders of magnitude [13]. Large flip angle pulses permit suppression of long TI signal components, from lH containing plastics in the RF probe or sample holder. The SPRITE cxperiment does not permit slice selection with KF pulses, therefore unless the samplc symmetry permits one or two dimensional imaging, it is inherently a three dimensional method.

5.3 SPRITE Implementation The principal SPRITE acquisition time limitations are gradient amplifier or gradient coil overheating. Actively cooled gradient coils, with modern gradient amplifiers will however support 100%gradient duty cyclcs in which case thc SPRITE acquisition time limitation will become experimental sensitivity. A 1 ms TR, h43 SPRITE acquisition, with no signal averaging, will require under 5 minutes to acquire. Lacking slice selection, it is not possible to average signal over an arbitrarily thick slice. This may however be desirable for low sensitivity SPRITE experiments. We have shown that physical slice selection with an RF shield works surprisingly well I 13,141.

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B. J. Balcom

The primary and secondary phase encode gradients in the SPRITE sequence inherently spoil transverse magnetization everywhere except at the origin of k space. In some instances, with long T, signal components, we have observed spin echo contribution to the k space origin signal which produces an elevated baseline artifact in the image. These artifacts are easily removed by the imposition of a pseudo random low amplitude spoiling gradient following the observed point at low amplitudes of the primary phase encode gradient [15]. This removes spin echo artifacts and reintroduces a small amount of periodic gradient noise to the experiment. This noise is a useful audio queue to the progress of the SPRITE acquisition. Quadrature RF probes are highly advantageous to increase the experimental sensitivity in order to avoid signal averaging. It is possible to sample multiple time points following each RF pulse in a SPRITE experiment and reconstruct one image from each set of detected points. Although these images differ in field of view, they may be interpolated onto a common field of view and added to effectively signal average without any increase in acquisition time! [16] As a pure phase encode technique SPRITE is immune to distortions in B, introduced by nearby sensors and ancillary equipment within the RF probe. We have undertaken a large number of temperature controlled SPRITE experiments, including MRI calorimetry with thermocouples implanted in and on samples under study [16,17]. The thermocouples, and other sensors, do not introduce image artifacts. In order to predict and understand contrast in SPRITE images it is useful to quantitatively measure, spatially resolved, T I , T2, and

T2*relaxation times. Relaxation time

mapping also provides a better understanding of the sample properties. We have recently developed, tested and validated a battery of methods to make these measurements [ 181.

5.3.1

Concrete Materials

The behavior of water in concrete presents a unusual dichotomy. Water is essential to formation of the material through the hydration process. However, once substantially formed the uncombined (free) water usually acts as the prime agent for distress or deterioration of the material. In commercial and industrial settings, concrete is moist cured (kept water saturated) for several days and then allowed to dry out naturally with the drying process continuing at a decreasing rate for months or years. The free water content prior to drying is usually at least 5%. The actual moisture content as a function of

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81

space and time depends on the size of the concrete member and the drying conditions. Our inability to predict moisture levels at the local level, and to understand the role this moisture plays in the various deterioration mechanisms, is one of the main reasons we have major problems with decay of our civil engineering infrastructure in Canada and the world.

Fig. 5.3: Proton density weighted three dimensional SPRITE image of a non porous aggregate embedded in a small concrete sample (diameter 3.3 cm). The 64 x 64 x 128 image had an encoding time 130 ps and the repetition time 1.5 ms. The image, 8 averages, required 8 hours principally due to a conservative delay introduced following each primary phase encode ramp to prevent gradient amplifier overheating.

We have employed SPI and SPRITE imaging techniques to study one dimensional drying of real concrete samples [19,20]. Due to sample size restrictions the STRAFI technique is unable to study concrete specimens which contain aggregates. These aggregates however are vital to the function of concrete, and cement paste samples alone are known to have different behavior (in many ways) from real concrete specimens. We are

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employing high resolution three dimensional SPRITE imaging to examine cement paste structure in close proximity to aggregates, in model samples, because the aggregate/paste interface is known to be a source of weakness and failure in many concretes [21]. We are also able to use our single point relaxation time mapping techniques and SPRITE calorimetry to study cement paste structure in the interfacial zone. Figure 5.3 is a high resolution three dimensional SPRITE image, rendered, and cut to reveal a single aggregate embedded in a concrete specimen.

5.3.2

Gas Phase Imaging

The high diffusion coefficient, low density and short relaxation times (spin rotation) of most gas phase nuclei largely prevent MRI of the gas phase. Non-equilibrium hyperpolarized gases 3He and 129Xe(which have unusually long T,) have attracted attention recently due to their potential for lung imaging [22]. Other investigators have proposed the use of hyperpolarized gases to probe the void space of porous materials. However the non-equilibrium hyperpolarized magnetization will regress to equilibrium governed by the time constant T,. If, in a porous medium, T , is short, due to for example surface interactions, the hyperpolarization will be rapidly depleted and a thermal equilibrium reestablished. We feel a more useful and aesthetically pleasing approach is to exploit the short relaxation times of most gas phase nuclei with gas phase SPRITE. Sulfur hexafluoride, SF, is an ideal tracer, it is inert and has a bulk T, of approximately 1 ms with a T2*of 900 ps. We anticipate negligible background 19F signal in most porous solids and plastic materials in sample holders and RF probes. One must avoid the use of Teflon materials. Figure 5.4 shows a three dimensional 643 I9F gas phase SPRITE image of a balloon containing one atmosphere of SF, which has penetrated a small sample of coral. The coral, a porous limestone material, is an ideal gas phase MRI phantom because it contains structure with a variety of size scales [23]. The largest scale structure is associated with the wedge shaped slices of high and low density limestone which originate from the center of the coral. The coral/gas phantom was sealed for several hours, under one atmosphere of SF,, prior to image acquisition. Note the region of high uniform signal from bulk gas surrounding the coral. Within the coral high signal regions (wedges) which originate from the sample center are clearly visible. These structures correspond to the low density, high porosity regions in the coral.

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Fig. 5.4: Three dimensional SPRITE image of an SF6 containing balloon, diameter approximately 4 cm, with a porous limestone phantom (coral) inside. The low density, high porosity channels in the coral readily take up SF6 and are clearly visualized in this rendered, cut, image. The encoding time was 320 ps and the repetition time 1.5 ms. The image was acquired overnight.

5.3.3

Solid Bone Imaging

Knowledge of bone mineral density is of crucial importance in the diagnosis of osteoporosis, predicting the risk of fracture and monitoring healing. Despite prolonged attention by several well known clinical MRI research groups [24-261, a flexible MRI method suited to the detection and quantification of signal directly from the solid bone material has not been developed. We feel that a low flip angle SPRITE experiment, which does not significantly deplete z magnetization, may provide a fast flexible and quantitative method of assessing bone mineral density. A three dimensional lH 643 SPRITE image of a bovine femur is shown in Fig. 5.5. As shown, the low flip angle SPRITE experiment permits observation of signal from all components of the femur including marrow, cartilage, flesh and compact bone [27].

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B. J. Balcom

Fig. 5.5: Three dimensional SPRITE 128 x 128 x 64 image of a bovine femur. Note the compact bone surrounding the bone marrow in the interior. With these imaging parameters, the bone signal is 25% of the marrow signal. The field of view was 14 x 14 x 28 cm3. The encoding time was 150 ps and the repetition time 1.5 ms. The image, 4 averages, required 5 hours. Once more the long acquisition time ensured the gradient amplifiers did not overheat.

31P low flip angle SPRITE experiments reveal signal only from bone mineral in the compact bone. The marrowlsolution concentration of 31P is much less than the solid phase 31Pconcentration. We are exploring methods of suppressing the unwanted long T I , T2 signal from marrow and flesh to isolate the true solid signal from trabecular and compact bone.

5. SPRITE Imaging of Short Relaxation Time Nuclei

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5.4 Conclusion The SPRITE technique appears to be a robust flexible method of imaging a wide range of systems with short T2*signals. For example, we feel that the SPRITE technique will be a viable method of imaging free radical species, with attendant short relaxation times, in the fringe field of a superconducting magnet. SPRITE employs traditional ideas of k space sampling and permits the introduction of both T2*and T, contrast. Derivatives of the technique permit T1, T2 and T2*mapping. The technique requires good hardware but no unusual or custom built equipment.. The technique is still rapidly evolving. Our current work is aimed at increasing the sensitivity and speed of the method. We are also exploring alternative k space trajectories to minimize the acquisition time and manipulate the image contrast.

Acknowledgments The development of the SPRITE technique has been a collaborative effort of the many members of the MRI Center at the University of New Brunswick. Special thanks are due Robin Armstrong, without whom the MRI Center would not exist. We have been greatly assisted by colleagues from other departments and institutions who have presented a litany of interesting short T;” problems. These include Jon Shah, Joseph White, Frank Rack, Theodore Bremner, Alan Logan, Eric Gozna and Patrick Grattan-Bellew. The work has been supported by NSERC through equipment and operating grants and an NSERCNRC Research Partnership award with a consortium of concrete/building materials companies. The New Brunswick Medical Research Fund has supported the work on SPRITE bone imaging.

References 1.

B. Bliimich, W. Kuhn, eds. Magnetic Resonance Microscopy, VCH, Weinheim, 1992.

2.

J. A. Courtney, R. L. Armstrong, Can. L Phys. 50 (1972) 1252.

3.

G. H. Glover, J. M. Pauly, K. M. Bradshaw, Magn. Reson. Med. 8 (1988) 231.

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F. E. Boada, J. S. Gillen, G. X. Shen, S. Y. Chang, Magn. Reson. Med. 37 (1997) 706.

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D. Kuethe, A. Caprihan, E. Fukushima, R. A. Waggoner, Abstracts of the 5th ISMRM, (1997) 1066.

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D. G. Cory, Ann. Rep. NMR Spectrosc. 24 (1992) 87.

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7.

P. J. McDonald, Prog. NMR Spectrosc. 30 (1997) 69.

8.

M. J. Mallett, S. L. Codd, M. R. Hake, T. A. Green, J. H. Strange, J. Magn. Reson. A 119 (1996) 105.

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J. M. Star-Lack, M. S. Roos, S. T. Wong, V. D. Schepkin, T. F. Budinger, J. Magn. Reson. 124 (1997)

420. 10.

S. Gravina. D. G. Cory, J. Magn. Reson. B 104 (1994) 53.

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A. Nauerth, B. Gewiese,Abstracts of the 12th SMRM (1993) 1215.

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D. E. Axelson, A. Kantzas, T. Eads, Can. J. Appl. Spec. 40 (1995) 16.

13.

B. J. Balcom, R. P. MacGregor, S. D. Beyea, D. P. Green, R. L. Armstrong, T. W. Bremner,

J. Magn. Reson. A 123 (1996) 131. 14.

F. R. Rack, B.J. Balcom, R. P. MacGregor, R. L. Armstrong, J. Paleolimnology 19 (1998) 255.

15.

C. B. Kennedy, B. J. Balcom, I. V. Mastikhin, submitted.

16.

P. J. Prado, B. J. Balcom, S. D. Beyea, R. L. Armstrong, T. W. Bremner, Solid State NMR 10 (1997) 1.

17.

P. J. Prado, B. J. Balcom, S. D. Beyea, T. W. Bremner, R. L. Armstrong, P. E. Grattan-Bellew, Cem. Concr. Res. 28 (1998) 261.

18.

S. D. Beyea, B. J. Balcom, P. J. Prado, A. R. Cross, C. B. Kennedy, R. L. Armstrong, T. W. Bremner, submitted.

19. 20.

M. Bogdan, B. J. Balcom, R. L. Armstrong, J. Magn. Reson. A 116 (1995) 266.

S. D. Beyea, B. J. Balcom, T. W. Bremner, P. J. Prado, D. P. Green, R. L. Armstrong, P. E. GrattanBellew, Cein. Concr. Res. 28 (1998) 453.

21. 22.

S. D. Beyea, B. J. Balcom, P. J. Prado, manuscript in preparation.

M. S. Albert, G. D. Cates, B. Driehuys, W. Happer, €3. Saam, C. S. Springer, A. Wishnia, Nature

370 (1994) 199. 23.

P. J. Prado, B. J. Balcom, I. V. Mastikhin, A. C. Cross, R. L. Armstrong, A. Logan, submitted.

24.

K. Selby, S. Majumdar, D. C. Newitt, H. K. Genant, J. M a p . Reson. Inzag. 6 (1996)549.

25.

H. Chung, F. W. Wehrli, J. L. Williams, S. D. Kugelmass, Proc. Natl. Acad. Sci. 90 (1993) 10250.

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C. Ramanathan, Y . Wu, B. Pfleiderer, M. J. Lizak, L. Ganido, J. L. Ackerman, J. Magn. Reson. A

121 (1996) 127. 27.

C. B. Kennedy, J. Dysart, B. J. Balcom, manuscript in preparation.

6. Refocussing a Spin-Echo in the Presence of a Strong Readout Gradient Field Using an Underdriven Gradient Pulse G. PlaninSic Physics Department, University of Ljubljana, Slovenia M. Symrns Department of Clinical Neurology, Institute of Neurology, London, UK

Abstract A decrease in the amplitude of a spin-echo in the presence of a strong readout gradient field is explained for the pulse sequence where defocusing and refocusing gradients are applied with equal amplitudes. It is shown that the spin-echo can be completely refocused by applying different gradient rise time values.

6.1 Introduction A basic assumption commonly used to simplify calculations in MRI is that the crossterms caused by application of a "gradient field" are negligible. This is not the case when the gradient field is strong, when these concomitant or Maxwell terms can cause image distortions [11. Such distortions have been discussed in low-field MRI, phase-contrast flow sequences [2], and even in exotic variants such as electron spin resonance and Overhauser imaging [ 3 ] .It has been observed that echo-planar imaging (EPI) can also be subject to distortions caused by concomitant gradients [4]. Previously, we showed how a pi-pulse-refocused EPI variant, which is similar to the snap-shot fast spin-echo (SS-FSE) sequences now becoming available on commercial machines, could be made relatively insensitive to the effect of concomitant gradients [5].

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G.PlaninSic and M . Symms

Here we extend this analysis and develop a novel method of refocusing a spin-echo in the presence of concomitant gradients: the "underdriven"pulse.

6.2 Theory The envelope of the spin-echo is calculated in two steps: first the time dependence of the phase angle at a particular point in the selected plane is calculated using the adiabatic approximation. In the second step, the spin-echo envelope for a square sample is calculated by integrating the magnetic moment projections. For simplicity spin relaxation effects have been neglected. Consider a main magnetic field Bo = (O,O,Bo)and a time dependent real gradient field of the form

where H(t) is a dimensionless function describing the gradient time dependence and Go is the gradient amplitude. Therefore the total magnetic field vector Btot = Bo

+ B,

changes both in magnitude and direction. It has been shown [6] that if the rate of change in the direction of B,,,(t) is much smaller than the Larmor frequency (adiabatic approximation) the spins precess in the plane perpendicular to B,,,(t) direction all the time. The angle subtended by B,,(t) and the z axis is given by

8 = arctan((-H(t) Go y)l(Bo+H(t) Go z ) )

(6.2)

The angular velocity deldt at switch-on of the trapezoidal gradient waveform (rise time T)

for the corner points of a square sample with sides 2a is given by T). deldt = (Go ~)l(Bo

(6.3)

For typical parameters occurring in a commercial whole-body EPI scanner (Go = 22 mT/m, T = 0.184 ms, a = 0.25 m, Bo = 1.5 T) we have deldt = 20 Hz which clearly fulfils the adiabatic approximation. The phase angle of spins at a particular point in the sample can be calculated by treating the B,, magnitude only but bearing in mind that the plane of precession is perpendicular to the direction of BtOt.The phase angle in this case

6. Refocussing a Spin-Echo in a Strong Gradient Using an Underdriven Gradient Pulse

89

is defined as the angle in the time varying plane which is always perpendicular to BtOt.

For spins at coordinates (y,z) the phase angle accumulated during time tl in the time dependent total magnetic field is given by

Let us now calculate the total phase accumulated by spins at point (y,z) during the pulse sequence shown in Fig.6.1. where we may choose a different second gradient rise time. n

z

z’

z

t

I 90’

180’

Fig. 6.1: SE pulse sequence with underdriven second gradient pulse.

For now we still allow the arbitrary gradient switch-odoff shape function H ( t ) requiring only that all the ramps are described with the same shape function which can be mirrored

for switch-off or stretched to give a different z. Using eqn.(6.4) the total phase angle can be described in the form

where q = Bd(Goa),to measures the time of constant gradient field Go between ramps, z and z’ are the first and second gradient rise time values, indexes C and SW indicate constant and switching gradient and M(y,z), N(y,z) are functions of y and z only, defined

90

G.PlaninSic and M. Symms

by the sample geometry. Note that time t is measured from the end of second gradient switch-on. The following conclusions can be drawn from eqn. (6.5): 1) In practice normally all gradient switches are performed with the same rise time T. In this case the term T M b , z ) represents an additional position-dependent phase

shift at point b,z) in the sample. This phase shift does not allow all the spins to refocus at the same time and so causes the decrease in SE amplitude. The decrease can be reduced by shortening the rise time value, providing the adiabatic approximation remains valid and gradient performance permits. 2) If the second gradient is switched with rise time ‘c’ = 27 then the term with M(y,7) vanishes for all y and z. Complete spin refocusing occurs at t = to. This holds for an arbitrary gradient switch shape function as long as the switch-on and switchoff shapes are mirror images of each other. Using the expressions above the SE envelope for trapezoidal gradient waveforms with fixed rise time T and a sample with square cross section (2a x 212) centered in the plane @,z) can be calculated. Since Bo > Goa in all practical cases, the expression under the integral in eqn. (6.4) can be written using the following approximation

where coordinates are measured in units a (y’ = yla, 2’ = ?/a). Using this approximation the integrals in eqn. (6.5) can be calculated, taking the linear shape function for trapezoidal waveforms. The resultant total phase angle can be expressed in the following form

W y ’ , ~ ’ ,=t C ) ~+ ~ Dz’ ~ +EY’~ where

c = 2 d tL (2T - ’C’ + to - t ) D = X I (q tL) (22 - 2’ + 2(to - t>) E = XI(3q2 tL) (2T - ‘C’

+ 3(to - t))

(6.7)

6. Refocussing a Spin-Echo in a Strong Gradient Using an Underdriven Gradient Pulse

91

and tL = 2n/yB0is the Larmor period. The signal is given by the integration of the spin projections in the direction of the detection coil axis all over the sample slice: 1

1

-1

-1

Combining the eqns. (6.7), (6.8) and (6.9) the following result can be obtained S(t) = So (sin(D)/D) (Fcos(p)/p)

(6.10)

where Fcos is the Fresnel cosine, p 2 = 2IElh and So is the signal amplitude obtained for complete refocusing. This result can be interpreted in the following way: the Fourier transform of the square sample, which is known to be a sinc function, is modulated by the factor that comes from the concomitant gradient components. The value of modulation is less or equal to unity and is shown as a function of p in Fig. 6.2.

Y 1 0.8 0.6

0.4 0.2

0

1

2

3

4

‘P

Fig. 6.2: Fcos(p)/p as a function of p .

It can be shown that the SE peek occurs approximately at time t = to + T - ~ ’ / 2From . the eqn. (6.10) the decrease in SE amplitude for pulse sequence with constant gradient rise time T can be calculated. The results of calculation of the SE amplitude as a function of ratio q for several rise times T and T = T’ are shown in Fig. 6.3. The results were obtained with Mathematica 3.0 .

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G.PlaninSic and M. Symms

Fig. 6.3: Normalised SE amplitude as a function of logarithm of q = Bd(Goa)for different rise time values T and T’ = T. Rise time values are measured in Larmor periods tL. The SE amplitudes has been obtained using Mathematics 3.0. The oscilations at high gradient values (low q) are due to partial refocussation.

6.3 Discussion As the range of applications of MRI continues to develop, images will be acquired in more extreme regimes where commonplace assumptions can fail. In order to preserve maximal signal-to-noise and information content, experiments will have to increase in complexity to meet these ever more stringent demands. Concomitant gradients are an example of the challenges that can be posed in numerous different MFU regimes, and while post-processing correction algorithms are often useful, the underdrive pulse as part of a spin-echo refocused imaging sequence offers a theoretically perfect solution. SS-FSE, for instance, is potentially a very attractive imaging acquisition module, with a speed and flexibility approaching that of EPI, but without the latter‘s sensitivity to off-resonance effects that cause undesirable image distortions in many applications. In the clinical realm, a SS-FSE sequence that is immune to concomitant gradient distortions would be particularly suitable at low-field where the Specific Absorption Rate (SAR) is low: open-magnet configurations for claustrophobic patients or interventional scanners, and Overhauser-enhanced imaging systems that cannot switch their main field [7], are two possible areas of exploitation. The underdrive pulse may also find application in

6. Refocussing a Spin-Echo in a Strong Gradient Using an Underdriven Gradient Pulse

93

particular EPI acquisitions that are refocused under a spin-echo (SE-EPI), where the suggestion of Weisskoff et. al. of a "pre-warping" pulse [4] might be implemented. Other areas that might warrant investigation are the use of very large uni-polar gradients for diffusion-weighting, especially in the microscopic regime. There are only two small drawbacks of the underdrive pulse. The first is the need to produce a gradient lobe with half the slew-rate of the rest of the imaging sequence. In some modern clinical systems where all the gradient slew-rates are limited in an attempt to prevent neural stimulation, some additional pulse-sequence programming complexity will ensue. The second drawback is a slight increase in the minimum possible echo time. In spite of these obstacles, the underdrive pulse offers the ability to completely refocus concomitant gradients in a spin-echo sequence.

References 1.

D. G. Noms, J. M. S. Hutchison, Mugn. Reson. Zmug. 8 (1990) 33-37.

2.

J.-H. Gao, A. W. Anderson, J. C. Gore, Phys. Med. Biol. 37 (1992) 1705-1715.

3.

D. G. Gillies, L. H. Sutcliffe, M. R. Symms, J. Chem. SOC.Furuduy Trans. 90 (1994) 2671-2675.

4.

R. M. Weisskoff, M. S. Cohen, R. R. Rzedzian, Magn. Reson. Med. 29 (1993) 796-803.

5.

M. R. Symms, G. Planinsic, 4th Meeting ISMRM,New York, 1996, Abstract #1391.

6.

J. StepiSnik, M. Kos, G. PlaninSic, V. Erzen, J. Mugn. Reson. A 107 (1994) 167-172.

7.

T. Claasen-Vujcic, J. Slotboom, A. F. Mehlkopf, 3rd Meeting ZSMRM,Nice, 1995, Abstract #314.

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7. The Analysis and Development of Pulse Sequences for Self-Diffusion Weighted Stray Field Imaging A. J. Bohris, D. A. Faux, D. G. Gillies, and P. J. McDonald

School of Physical Sciences, University of Surrey, Guildford, Surrey, GU2 5XH, UK

Abstract A Fourier method of solving the Bloch equations for nuclear magnetisation precession in

a strong magnetic field gradient has been developed for the purpose of simulating the increasing number of pulse sequences now used in stray field experiments. The simulation explicitly includes the action of the gradient during rf-pulses and the effects of spin relaxation and diffusion. The method is used here to analyse a multiple echo diffusion sequence which is designed to offer spatially resolved one-shot (multiple wave vector, 4 = yG6/27c; near constant diffusion time, A) measurement of self-diffusion in the stray field. A rapid one-shot method is required because stray field imaging is inherently slow since the measurement must be repeated at each spatial location.

7.1 Introduction Stray field magnetic resonance imaging [l] is increasingly used to image broad line

systems such as cementitious materials and polymers. Stray field self-difision techniques [2] are used to measure small diffusion coefficients in systems such as polymer melts. Both the imaging and diffusion applications exploit the extremely strong and stable magnetic field gradients found around high field superconducting magnets. However, this gradient cannot be switched off. Consequently, in multiple pulse sequences a large number of coherence pathways are excited and complex phase cycling is required to eliminate signals from unwanted pathways. Moreover, the effects of spin relaxation cannot be eliminated by comparative measurements with and without

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A. J. Bohris, D. A. Faux, D. G. Gillies, and P. J. McDonald

gradients, unless a second magnet operating with a centre frequency equivalent to the stray field frequency of the first is available. Careful pulse sequence analysis is therefore required before any new sequences can be used with confidence. The Fourier method of solving the Bloch equation presented here has been developed with the purpose of simulating the increasing number of pulse sequences, which are now used in stray field experiments. The simulation explicitly includes the action of the gradient during the pulses and the effects of spin relaxation and diffusion. The simulation has been applied in particular to show that the sequence (2~~-a,),z1-90,-z1-(echo-2zl),-(z2-(2n + l)zl)-90,-z,-(echo-221), (Fig. 7. I), where a is a low flip angle pulse, affords an excellent means for achieving a spatially resolved one-shot diffusion sequence. The sequence is an adaptation of standard stimulated echo [3] and DANTE [4] type sequences.

I..... I

,

t

n a,- pulses

9OY n direct echoes

90

n stimulated echoes

Fig. 7.1: The one-shot diffusion pulse sequence.

Following Kimmich and Fischer [5], the diffusion coefficient is evaluated from the ratios of the amplitudes of the direct and stimulated echo intensities so that the measurement is independent of T2 relaxation. Moreover, T , relaxation enters only as a constant factor which need not be known. For the proposed sequence the functional dependence of the ratio of the i-th stimulatvd and direct echo on the diffusion coefficient is given by

where 6iand Ai are defined as 6i= (2i+ l)zl and Ai = z2 + 6,.

7. The Analysis and Development of Pulse Sequencesfor Self-DiffusionWeightedSTRAFI

97

7.2 Fourier Solution of the Bloch Equation The starting point is the Bloch equation including the diffusion term [6]

where all the parameters have their usual meanings. The magnetic field is of the form B = B, + B(z)where B, is the constant field (along z ) and B(z)is a function of z. In the absence of rf pulses B(z) is equal to G z where G is the field gradient. The calculation initially proceeds as Torrey. The complex transverse magnetisation is defined as rn =

M;, + M y and the analysis leads to a differential equation involving rn which can be solved by writing

This is the same substitution made by Torrey except that Q is now a function of both z and t, rather than t alone. Allowing (I to be a function of z is the critical advance which enables the time evolution of the magnetisation to be evaluated when the initial magnetisation is z-dependent. It can be shown by substitution and solving that

(7.4) A(z,t ) = c c : exp(k ik, z ) expk D yGt2k, - Dk;t)

(7.5)

n

where kn = n d l are a set of Fourier wave numbers and 1 is a suitably large length. Starting at t = 0, the complex constants cn* are written as

* 1 c, = $7,

1 k s,)+-i(., 2

T 4,)

(7.6)

98

A. J. Bohris, D. A. Faux, D. G. Gillies, andP. . I McDonald .

Expanding the complex exponential involving kn z into cosine and sine terms, it may be shown that

so that M,(z,O) and M&O) are represented as a Fourier series, with p,, q,, appropriate Fourier coefficients. For the z-magnetisation

Y,

and s, the

where g, and the hn are the Fourier coefficients required to reproduce the z-magnetisation at t = 0. In the presence of a pulse field the total applied field is a vector of magnitude B,. pointing along the 2’-axis at an angle p to the z-axis where Bzq=

and

p = arctan[z)

(-7~125 p 5 ~ / 2 ) (7.10)

IzI In the (x’,y’, z’) frame of reference the applied field has a magnitude given by eqn. 7.10 and points along the 2’-axis. The same procedure as already described can be adopted to solve for the magnetisation during the application of a pulse by first rotating the (x,y , z ) frame to the (x’,y’, z’) frame, solving for M as described, before rotating back to the (x,y , z ) frame. To simulate the evolving magnetisation during a pulse sequence the time evolution has to be calculated sequentially for each time period with either a pulse field switched on or off.

99

7. The Analysis and Development of Pulse Sequences f o r Self-DiJusion Weighted STRAFI

7.3 Experiment and Results 7.3.1

The Simulation

Figure 7.2a shows the direct and stimulated echoes for the sequence shown in Fig. 7.1 obtained from the simulation using the following parameters: T2 = T1 = 00, z1 = 15 ps,

z2= 275 ps, D

cm2 smland G = 50 T m-*. The low flip angle pulses had a

= 2.5 .

duration of 3 ps with a nominal flip angle a = 4.5" and 8 low flip angle pulses were applied. The 90" pulses had a length of 10 ps. Keeping the phase of the a pulses constant at (+x>the phases of the two 90" pulses were cycled in the following manner +y+y, +y-y, -y+y and -y-y. In Fig. 7.2b the ratios of stimulated to direct echo intensities are plotted against 8Z(Ai - &J. The diffusion coefficient obtained from these data yields D = cm2 s-l which is in excellent agreement with the input value for D.

2.51 .

10 r

I

I

I

I

1

I

bl

direct echo stimulated echo

I

I

I

I

0 ._

I

-2

d

0

100 200 Time [ps]

Io - ~

300

Fig. 7.2: a) The simulated echo trains for the direct echo (dash-dot line) and the stimulated echo (solid line). b) The ratios of the stimulateddirectechoes plotted against 6?(Ai - 6J.

7.3.2

The Experiments

All experiments were performed on a Chemagnetics Infinity spectrometer and a Magnex 400 MHz, 89 mm bore, superconducting magnet. The magnetic field strength is B , = 5.5 T at the sample position and the magnetic field gradient strength is G = 58 Tm-I. Water and glycerol were used as standard samples. For the spatially resolved measurements a phantom was used consisting of two small glass vials filled with water

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A. L Bohris, D. A. Faux, D. G. Gillies, and P. .I McDonald .

and hexadecane which were placed one above the other in an 8 mm (0.d.) glass tube with a separation between the liquids of about 1.2 mm. The temperature was 20" f 1 "C. Figure 7.3a shows the echo profile of an experiment with glycerol. The pulse duration for both low flip angle and 90" pulses was 5 ps. The flip angle a was nominally 4.5". The pulse separations were zl= 40 ps and z2 = 5 ms. 16 a pulses were applied. In Fig. 7.3b the ratio of the echo amplitudes is plotted against 6:(Ai - 6,) The diffusion coefficient extracted from these data is D = 1.58 . cm2 s-l which is in reasonable agreement with literature values and reference measurements at this temperature.

0 .-

iii

U

0

800

1600 Points

2400

3200

Fig. 7.3: a) The experimental echo train obtained from glycerol. Acquisition parameters are as specified in the text. b) The ratio of the stimulated to direct echoes plotted against Si2(Ai - SJ.

In the imaging experiment all pulse durations were again 5 ps which corresponds to an excitation slice thickness of = 70 pm. The low flip angle a was nominally 4.5". The other parameters were: zl= 10 p;22 = 400 p;12 a-pulses; slice separation 0.3 mm and number of slices = 21. Figure 7.4a shows a spatial density map obtained from the intensities of the first direct echo across the vial interface region. The spatial distribution of diffusion coefficients is seen in Fig. 7.4b. The mean values of the self-diffusion coefficients measured in the experiment are for hexadecane D = 6.2 f 0.7 . cm2 s-l. These cm2 s-l and for water D = 2.3 f 0.2 . values are in good agreement with reference measurements using the modified stimulated echo sequence discussed in ref. [ 5 ] . The total imaging time was 18 hours, acquiring 1024 averages per slice and using a TI recycle time of 3 seconds.

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7. The Analysis and Development of Pulse Sequencesfor SelfDifision Weighted STRAFI

-B

1o4

1.o

.-

[I)

c

2

%

0.8

u

hexadecane

Y

.,x 0.6 S u)

a,

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oooooo

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t

r 0 .U

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0 .[I) zl c .0

0.2

i

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-

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0

1

2

3

4

5

6

7

1o-6

-

Position [mm]

1

0

1

2

3

4

5

6

7

Position [mm]

Fig 7.4: a) Spin density map of the sample interface region of the hexadecane-water phantom over a sample region of 6 mm. b) Spatial distribution of the diffusion coefficients in the same region. The gap arises from the glass of the vial walls.

7.4 Conclusions A Fourier method for solving the Bloch equations including a diffusion term has been presented. This technique has been used to simulate the effects of pulse sequences applied in the presence of strong and time-independent magnetic field gradients. A novel one-shot diffusion sequence has been proposed for use in stray field imaging. The envelope of the experimental echo decays indicates imperfections to which the ratios are insensitive. Most important is that the decrease of the ratio is independent of T2 relaxation, since the corresponding terms in the direct and stimulated echo decay cancel out. The proposed pulse sequence has been implemented in a one-dimensional imaging routine to obtain spatially resolved diffusion data. Acquiring multiple wave vector q = y6GI2n data may prove useful for use in the analysis of restricted diffusion.

Acknowledgements We thank the EPSRC (GWK12397) for support of the STRAFI facility at Surrey University. AJB acknowledges an EPSRC RoPA studentship (GWK64525) and the University of Surrey for financial support. Furthermore, AJB thanks the NMR Discussion Group and the IoP C.R. Barber Trust Fund for travel grants.

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References 1.

A. A. Samoilenko, D. Yu. Artemov and A. L. Sibel’dina, JETP Lett. 47 (1988) 348.

2.

R. Kimmich. W. Unrath, G. Schnur and E. Rommel, J. Magn. Reson. 91 (1991) 136.

3.

J. E. Tanner, J . Chern. Phys. 52 (1970) 2523.

4.

G. A. Moms and R. Freeman, J . Magn. Reson. 29 (1978) 433.

5.

R. Kimmich and E. Fischer, J. Magn. Reson. A 106 (1994) 229.

6.

H. C. Torrey, Phys. Rev. 104 (1956) 563.

8. Imaging Diffusion with Non-Uniform B1 Gradients Klaus Woelk,Bernd L. J. Zwank, and Joachim Bargon Institut fiir Physikalische und Theoretische Chemie, Universitat Bonn, Wegelerstr. 12, D-53 115 Bonn, Germany Robert J. Klingler, Rex E. Gerald 11,and Jerome W.Rathke Chemical Technology Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA

Abstract Rotating-frame imaging with the mathematically well-defined, non-uniform magnetic field gradient of toroid cavity detectors represents a new technique for evaluating diffusion in solids, fluids, or mixed-phase systems. While conventional NMR methods for measuring diffusion utilize constant (i.e., uniform) magnetic field gradients and, therefore, constant k-space wave numbers across the sample volume, the hyperbolic B , fields of toroid cavity detectors exhibit large ranges of wave numbers radially distributed around the central conductor. As a consequence, signal amplitudes decay, depending on the radial distance from the center axis of the torus. Applying a numerical finite-difference procedure to solve partial differential transport equations makes it possible not only to determine diffusion in toroid detectors to a high precision, but also to include and accurately reproduce transport phenomena at or through singularities, such as phase transitions, membranes, or impermeable boundaries.

8.1 Introduction The difusion measurements introduced here are based on the rotating-frame imaging (RFI) technique, i.e., on B,-gradient imaging, first introduced by Hoult [l]. In RFI, spatial resolution is obtained from NMR spectra taken at incrementally increased pulse

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K. Woelk,B. L. J. Zwank, J. Bargon, R. J. Klingler, R. E. Gerald II, J . W.Rathke

widths. After a two-dimensional Fourier transformation, nutation frequencies of NMRactive nuclei are derived versus chemical shift. Since nutation frequencies are proportional to the B , field at the location of a nucleus, a transformation into spatial information is easily accomplished if the B , field distribution is known. More recent RFI applications utilize the time-saving, chemical-shift selective method called rapid-imaging pulse train (RIPT) [2-41, where a one-dimensional, real-data Fourier transformation reveals an image of nuclei precessing at the transmitter frequency. A quantitative image of spin density versus distance is revealed [5] when signalintensities are corrected by considering the sample volume and the principle of reciprocity [6].

8.1.1

Magnetization-Grating Rotating-Frame Imaging

To measure diffusion coefficients of fluids, Kimmich et al. [7] introduced magnetization-

grating rotating-frume imaging (MAGROFI), which uses constant B , gradients of surface coils to create homogeneous z-magnetization gratings across a sample. The gratings are generated by single hard pulses (preparation pulse PI in Fig. 8.1) applied with the same constant gradient that is used later for recording the image (P2 in Fig. 8.1). During an evolution time T between the preparation pulse and the imaging procedure, the initial grating decays because of TI relaxation and diffusion. If the evolution time is shorter than five times T,, undesired transverse magnetization remains from the preparation pulse. This unwanted part of the magnetization is usually removed by putting the pulse sequence through a transmitter phase cycling of the preparation pulse versus the imaging pulses. The remaining z-grating is sampled by RFI and analyzed to determine the diffusion coefficient.

z

IIIII

P2

AQ

I I I I I

t Fig. 8.1: Pulse sequence of an NMR experiment using the MAGROFI technique. In a B 1 gradient, the preparation pulse P1 generates a z-magnetization grating that, after an evolution period z, is imaged with the RFI procedure, i.e., with incrementally increased pulse widths P2 followed by the acquisition time AQ.

8. Imaging Diffusion with Nan-Uniform B, Gradients

105

Unfortunately, a single experiment using surface-coil MAGROFI delivers only one data point for a linear regression of amplitudes versus evolution time [7] or, alternatively, versus k-space wave number. Accordingly, many experiments at different evolution times or different preparation pulse widths must be performed using the MAGROFI technique to determine a single diffusion coefficient.

8.1.2

Imaging Diffusion in Toroid Cavity Detectors

The MAGROFI technique can also be applied to the non-uniform gradients of coaxial

toroid cavity detectors (Fig. 8.2) [8]. However, as a consequence of the hyperbolic B , field of toroids (B1 = A h , where A is a proportionality constant, i.e., the torus factor, and r is the radial distance from the long axis of the torus), the wave number of the grating changes continuously with the radius. Diffusion causes a fast decay of the grating, where the wave number is high, and a slow decay, where the wave number it low (Fig. 8.3). In contrast, the form of the grating, either symmetric or asymmetric, does not affect T , relaxation that uniformly returns z-magnetization to Boltzmann equilibrium. Because of the large range of wave numbers exhibited in toroid detectors, a single RFI experiment is sufficient to determine diffusion coefficients from three-parameter computer fits of propagation equations [8], refining longitudinal relaxation time ( T I ) , diffusion coefficient (D), and signal amplitude (I). In addition, because B , gradients in toroid cavity detectors are very “clean” (i.e., mathematically well-defined) and very strong, diffusion coefficients are determined to a high precision.

8.2 Partial Differential Transport Equations Fick’s first and second laws of difision are basic partial difSerentia1 equations with which one can analyze isotropic transport of matter because of Brownian motion. For z-magnetization gratings generated by MAGROFI experiments, Fick’s equations can be solved analytically if the gradient is strictly constant, the sample expands evenly perpendicular to the gradient, and no singularities exist along the gradient. Furthermore, the diffusion coefficient must be independent of concentration and space. Therefore, analysis

106

K. Woelk,B. L. J. Zwank, J. Bargon, R. J. Klingler, R. E. Gerald II, J. W.Rathke

of experimental data with analytical solutions is limited to homogeneous samples remote from the walls of the sample container. Phenomena that occur at singularities, such as phase transitions, membranes, or impermeable boundaries (e.g., dz@sive edge enhancement [9], Fig. 8.3), must be analyzed by numerical approaches.

Fig. 8.2: Schematic drawing of a toroid cavity detector used for diffusion measurements with the MAGROFI technique. The detector consists of a central conductor and a cylindrical hollow body. The sensitive volume is confined to the inside of the torus. Inside the detector, a z-magnetization grating generated by a single hard pulse PI is shown.

The decay of magnetization by diffusion represents an open-ended propagation problem that starts with an initial condition, i.e., the initial grating generated by the preparation pulse. In addition, impermeable boundaries (the walls of the sample container) or other known singularities confine the spatial range of analysis.

107

8. Imaging Diffusion with Nun-Unzfui-mB, Gradients

t

7

8

9

10

RADIAL POSITION, mm

0.8

1.0

1.2

1.4

1.6

1.8

Fig. 8.3: Results of an experiment in a toroid cavity detector using the MAGROFI technique. The wave number of the asymmetric magnetization grating is large near the central conductor and drops off with increasing radial distance. Experimental data (open circles) from a chloroform solution are compared to the analysis based on analytical propagation equations (solid line). Diffusive edge enhancement is visible at the central conductor (lower detailed plot) .

8.2.1

Finite-Difference Approach

If the time progress of a function with complex boundary conditions cannot be reproduced by analytical equations, finite-diference calculations are commonly used to numerically solve propagation problems [101. In a finite-difference procedure, data points of an initial condition are repeatedly advanced by finite time steps until the experimental data set is matched to a maximum likelihood. Thereafter, the transport parameter or function is evaluated from the number and width of time steps.

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K. Woelk,B. L. J. Zwank, J. Bargon, R. J. Klingler, R. E. Gerald II, J. W. Rathke

Applying Finite-Differences to Magnetization Gratings To use finite differences in time and space for the analysis of magnetization gratings received from the MAGROFI technique, the locations of the experimental data points are used to calculate the grating’s decay during the evolution time z by finite time steps, starting from the initial grating. For each location, the change of magnetization density is estimated by solving the parabolic partial differential equation &/at = d(D3c)/(&)2, where c is the magnetization density, and x is the spatial dimension along the B , gradient. Concentration-dependence of the difSusion coefficient, the shape of the sample volume, or boundary conditions and singularities can all be included in the parabolic differential equation. For example, data points remote from singularities need the magnetization densities of the two neighboring data locations as boundary conditions. For points adjacent to singularities, however, a boundary condition such as the impermeability of the sample container applies. The maximum time step (At) that can be used without the numerical solution diverging from the true solution is given by the Einstein-Smoluchowski relation [ 111, which determines the mean square distance a particle travels by random walk [i.e., (Ax)2 = ~ D A TThe ] . distance Ax must not be larger than the smallest interval between two

data points. Otherwise particles would travel further than from one data-point location to the next. As a consequence, data points farther apart than the neighboring data must be included as boundary conditions, and higher-order partial differential equations must be solved. The relation that limits the time step of finite-difference procedures is generally known as Courant’s condition [12].

Fit to Experimental Data Figure 8.4 shows the finite-difference simulation that has been fitted to experimental data by a least-squares optimization, in which TI, D, and Z are refined. Clearly, the diffusive edge enhancement is accurately reproduced. In contrast, the analytical propagation equation can only be used to analyze data remote from singularities (Fig. 8.3). In addition, the finite-difference solution shows that in toroid detectors, grating extrema tend to shift to smaller radii. This effect has been observed before [8], when grating extrema decayed to less than 10% of their initial values, but is not accounted for by analytical propagation equations.

8. Imaging Diffusion with Non-Uniform BI Gradients

109

> t v)

z

W

+ z

o

0.7

09

1.1

13

15

1.7

19

RADIAL POSITION, mm

Fig. 8.4. Finite-difference analysis of diffusive edge enhancement at the central conductor (hatched area) of a toroid cavity. The numerical simulation (solid line) matches the experimental data (open circles) even at the impermeable boundary. A diffusion coefficient of D = 2.16 . 10-9 m2 s-1 was found for the chloroform sample.

8.3 Summary The MAGROFI technique is a robust and versatile method to evaluate diffusion. If applied along with the non-uniform, mathematically well-defined, and strong B , gradient of toroid cavity detectors, it is an excellent tool to measure diffusion precisely in a single RFI experiment. Since the analytical propagation equations are limited to uniform, i.e., constant gradients and areas remote from singularities, a finite-difference numerical procedure is required to determine the effects of diffusion correctly. Furthermore, this numerical approach makes it possible to analyze diffusion in mixed-phase systems and through membranes or other singularities. As an example, diffusive edge enhancement observed adjacent to impermeable boundaries has been reproduced accurately by this numerical approach.

Acknowledgments This work was supported by the U.S. Department of Energy, Division of Chemical Sciences, Office of Basic Energy Sciences, under Contract W-3 1-109-Eng-38 and by the German Research Foundation (DFG) under program WO 61312-1. We thank Prof. Dr. G. Woelk, Technical University of Aachen, Germany, for many helpful discussions.

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K. Woelk,B. L. J. Zwank, J. Bargon, R. J. Klingler, R. E. Gerald II, J. W.Rathke

References 1.

D. I. Hoult, J. Magn. Reson. 33 (1979) 183.

2.

K. R. Metz and J. P. Boehmer, Magn. Reson. Imaging 6 (Suppl. 1) (1988) 53.

3.

J. L. Bowers, P. M. Macdonald, and K. R. Metz, J. Magn. Reson. Ser. B 106 (1994) 72.

4.

D. Canet, Progr. NMR Spectr. 30 (1997) 101.

5.

K. Woelk, J. W. Rathke, and R. J. Klingler, J. Mugn. Reson. A 109 (1994) 137.

6.

D. I. Hoult and R. E. Richards, J. Magn. Reson. 24 (1976) 71.

7.

R. Kimmich, B. Simon, and H. Kostler, J. Magn. Reson. A 112 (1995) 7.

8.

K. Woelk, R. E. Gerald 11, R. J. Klingler, and J. W. Rathke, J. Magn. Reson. A 121 (1996) 74.

9.

B. Piitz, D. Barsky, and K. Schulten, Chem. Phys. Lett. 183 (1991) 391.

10.

J. Crank, “The Mathematics ofDiffusion,” 2nd Ed, p. 141, Oxford University Press, Oxford, 1975.

11.

P. W. Atkins, “Physical Chemistry,” 3rd Ed., p. 681, Oxford University Press, Oxford, 1986.

12.

R. Courant, K. Friedrichs, and H. Lewy, Mathematische Annalen 100 (1928) 32.

9. In Situ Imaging of Charge Carriers in an Electrochemical Cell Rex E. Gerald II, Robert J. Klingler, Jerome W.Rathke, and Giselle Sand$ Chemical Technology and k h e m i s t q Divisions, Argonne National Laboratory,

9700 South Cass Avenue, Argonne, Illinois 60439, USA Klaus Woelk Institut fur Physikalische und Theoretische Chemie Universitat Bonn, Wegelerstr. 12, D-53 115 Bonn, Germany

Abstract A toroid cavity nuclear magnetic resonance (NMR) detector capable of quantitatively recording radial concentration profiles, diffusion constants, displacements of charge carriers, and radial profiles of spin-lattice relaxation time constants was employed to investigate the charge/discharge cycle of a solid-state electrochemical cell. One-dimensional radial concentration profiles (1D-images) of ions solvated in a polyethylene oxide matrix were recorded by 19F and 7Li NMR for several cells. A sequence of I9F NMR images, recorded at different stages of cell polarization, revealed the evolution of a region of the polymer depleted of charge carriers. From these images, it is possible to extract the transference number for the Li+ ion. Spatially localized diffusion coefficients and spin-lattice relaxation time constants can be measured simultaneously for the ions in the polymer electrolyte by a spin-labeling method that employs the radial B1-field gradient of the toroid cavity. A spatial resolution of 7 pm neas the working electrode was achieved with a gradient strength of 800 G/cm. With this apparatus, it is also possible to investigate novel intercalation anode materials for lithium ion storage. These materials are coated onto the working electrode in a thin film. The penetration depth of lithium cations in these films can be imaged at different times in the charge/discharge cycle of the battery.

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9.1 Introduction The demand for solid state energy storage devices that are transportable has encouraged research on solid polymer electrolytes. At room temperature, however, polymer electrolytes are currently incapable of achieving the conductivity requirements for batteries with high current output [l]. The ideal electrolyte would have the physical and mechanical properties of solids, the high conductivity characteristic of fluids, and the ability to transfer the electroactive ion exclusively [2]. Traditional NMR methods have been used to study ionic mobility in bulk polymer electrolytes [3]. The application of NMR imaging methods, however, can provide details of the temporal and spatial transport of charge carriers in typical polymer electrolyte systems. In particular, by combining an electrochemical cell with a toroid cavity NMR detector probe [4], it is possible to measure the macroscopic transport properties, local dynamics, and chemistry of ions as functions of distance from the electrodes.

9.2 Materials and Experimental Apparatus The chemicals used in this work were obtained from Aldrich Chemical Co. and were used without further purification. The polyethyleize oxide and lithium trifZnte were dissolved in hot tetrahydrofuran, which was subsequently removed by heating under vacuum. A white solid nionolith remained after complete removal of the solvent. The white solid was heated for several minutes at 174 "C in a closed container until the solid melted into a moderately viscous, clear liquid that could be handled easily. The plasticized polymer electrolyte was prepared by mixing the hot liquid polyethylene oxide polymer electrolyte with tetraglyme, propylene carbonate, and additional lithium triflate salt. The mole ratio of the electrolyte used in this work was 1.000 LiCF3S03: 0.043 CH3(0CH2CH2)9,0CH3:0.840 CH3(OCH2CH2),0CH3: 1.682 propylene carbonate. A quantity of 1.255 g of the polymer electrolyte mixture was placed in the electrochemical cell that forms part of the toroid cavity NMR detector. The cylindrical cell was formed by a glass tube with an inside diameter of 10.4 mm and a length 19.6 mm. Circular rubber septa of diameter 11 mn and thickness 3 mni (Varian Instruments, Palo Alto, California) were used to seal the tube at both ends. A 0.80 mm diameter gold wire

9. In Siru Imriging ($Charge Carriers in c i n Electrochemical Cell

113

counterelectrode was formed into a 5 turn helix and placed against the inner wall of the glass tube. One end protruded through the top septum. A 0.62 mm diameter copper wire (22 gauge QT, Phoenix Wire, Inc. South Hero. Vermont) passed through the center axis of the cell, piercing both septa. A potential was applied across the cell, with the negative and positive terminals of a potentiostat (Model EG&G 273A) connected to the central working electrode and the outer counterelectrode, respectively. The working electrode of the electrochemical cell assembly also functioned as the central conductor of the toroid cavity NMK probe. Fluorine- 19 NMR rotating-frame images were recorded at room temperature by using a Varian “N1TYINOVA-300WBspectrometer at the following settings: spectrometer frequency, 282.224 MHz; spectral width, 6 kHz; 1024 data points; 4 s recycle delay; four transients per spectrum; 128 spectra were recorded with a pulse width increment of 4 ps (spectral width, 125 kHz). The two-dimensional data sets were processed with 50 Hz and 2000 Hz line broadening in the F2 and F1 dimensions, respectively. Onedimensional T , spatial images, which record the spin-lattice relaxation as a function of radial position, required that a composite 180” pulse be executed prior to the acquisition of the normal rotating frame image [5].

9.3 Results and Discussion The current vs. time profile of an electrochemical cell subjected to an applied potential is determined by the cell geometry, the equivalents of charge carried by the charge carriers, and the mobility of the charge carriers. Electrochemical cell polarization is the deleterious result of the transport of nonelectroactive ions of opposite charge. In a polarized cell, the charge carriers near one of the electrodes (the working electrode) are depleted to zero, thereby effectively forming an open circuit. In such a case, the cell ceases to function until the charge carriers near the working electrode are replenished by diffusion or other means of mass transport. The conduction of charge through solid polymer electrolytes in an electrochemical cell can proceed very slowly, requiring an extended period of time to obtain sufficient cell polarization (i.e., decrease in total number of ions near the electrode) for observation by NMR. Therefore, we formulated a plasticized polymer electrolyte (as described

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R. E. Gerald II, R. J. Klilzgler, J. W.Rathke, G. Sand;, and K. Woelk

Fig. 9.1: 19F NMR images of the tnflate (CF$03-) anion in an amorphous polyethylene oxide based electrolyte monitoring the formation of the depletion zone during the charge half-cycle. (a) Initial profile; (b) After 50 mC; (c) After 3.5 h charging; (d) Following several days charging. The radial profile images are presented in reciprocal space so that the region of interest (near the working electrode) is expanded. The total number of spins decreases in the concentric annular shells closest to the working electrode, therefore, in this region the signal-to-noise ratio diminishes.

9. In Situ Imaging of Charge Carriers in an Electrochemical Cell

115

7.0

6.0

5.0 >I

+ .cn 4.0

a, +

S

6 3.0 S

.-m

cn

2.0

0 7

1.0

0.0 03

0.4

05

06

07

08

09

Radial Position (mm) Fig. 9.2: Radial profiles of the images in Fig. 9.1. The gray rectangle on the left side of the figure represents the working electrode, which has a 0.31 mm radius. The signal intensity of each radial profile was scaled using a scale factor that was determined by averaging the measured 19F signal intensity values in the region of the electrochemical cell between 0.60 and 1.73 mm. Across this region of the electrochemical cell all of the intensity profiles were nearly constant before and after charging the cell. The plot insets indicate a nonlinear decrease in charging current with increasing time for the time period between image profiles a and b. We recorded the current and total accumulated charge passed through electrochemical cells of identical geometry to the cell used here to estimate the size of the depletion region at various stages of cell charging. For long charging times the current decreased linearly with the square root of charging time, and typical charging currents were 10 - 40 FA. All the radial profiles shown here were recorded during cell charging, that is, while current was flowing through the charging circuit. No deleterious effects from the charging current on the external magnetic field homogeneity were observed under these conditions.

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R. E. Gerald 11,R. J. Klingler, J. W. Rathke, G. Sandi, and K. Woelk

above) that exhibits substantially larger charge conduction at room temperature. However, at room temperature, the plasticized polymer electrolyte slowly transforms from a viscous liquid to a heterogeneous gel or to a homogeneous waxy solid, depending on the composition. We used this electrolyte to investigate various aspects of cell polarization, including the physical dimensions and profile of the depletion zone, as depicted in Figs. 9.1 and 9.2, and the molecular dynamics of the anions through measurements of spatially resolved spin-lattice relaxation time constant (Figs. 9.3 and 9.4). The conductivity of this electrolyte is sufficient to make electrochemical processes observable by NMR methods that utilize the high sensitivity near the central electrode of a toroid cavity probe. In fact, while the total number of 19F spins in the detector is substantial, 13.59 mmol, the decrease in the number of 19F spins next to the working electrode following 50 mC of charge is only 1.55 ymol. This decrease (about 1 part in 9000) can be seen in the difference between the vertical regions of curve a and curve b in Fig. 9.2. Of course, this miniscule change in the total number of 19F spins can be observed because it is spatially confined to a very small volume (an annular shell of radius 310 ym, thickness 10 - 20 ym, and height 12.9 mm), where the change in the 19F spins is nearly 100%. Figure 9.4 shows the spin-lattice relaxation time constants (including their respective standard errors) plotted as a function of the radial distance from the working electrode. The curve suggests that the triflate anions are not entirely depleted in the volume around the working electrode. These data were recorded for the cell in the state of polarization depicted by image d of Fig. 9.1. The spatial resolution near the electrode surface is 7 pm; therefore, the TI value for the region next to the working electrode is obtained from the residual 19F signal from a shell volume of radius 310 ym, thickness 7 pn, and height 12.9 mm. Very little is known about the effects on the polymer structure and the ion mobility by

concentration gradients in the electrolyte. It is generally believed that the cations tend to crosslink the polymer chains, thereby influencing the segmental motion of the polymer [1,6]. Furthermore, the segmental motion is commonly believed to be the most important factor controlling the ionic conductivity in polymer electrolytes. Importantly, there are fluctuating effects in the region adjacent to the electrodes due to the dynamic nature of the concentration gradients of ions in the polymer matrix. With the toroid cavity/electrochemicalcell NMR imager described here, it is possible for the first time to probe for structure and mobility differences in the polymer and ions across the concen-

9. In Situ Imaging of Charge Carriers in an Electrochemical Cell

117

Fig. 9.3: T l ( r ) images of the triflate anion across the concentration gradient of charge carriers in the plasticized polymer electrolyte.

1I8

R. E. Gerald II, R. J. Klingler, J. W.Rathke, G. Sandi, and K. Woelk

1 .o 0.8

I--

0.4

0.2 03

OB

05

Oh

0

n

oa

Radial Position (mm)

Fig. 9.4: Spin-lattice relaxation time constant measurements of the 19F nuclei in the triflate anions dissolved in the plasticized polyethylene oxide electrolyte as a function of the distance from the working electrode in the polarized electrochemical cell. (a) The solid and dashed curves are the radial profiles shown as curves a and d in Fig. 9.2, respectively. (b) The function T I(r) (including standard confidence intervals) measured for the dashed curve in (a).

tration gradients in the electrolyte. This is done by measuring the N M R spin relaxation time constants (TI, TIP,and T . )as a function of distance from the electrodes. Thus, the N M R imaging method described here is capable of addressing some of the most important questions with regard to the dynamics of the polymer-electrolyte performance. Does the ratio of amorphous-to-crystalline polymer phases change in the immediate vicinity of the electrodes as the concentration gradients in the electrolyte evolve? Is the segmental motion of the polymer uniform throughout the cell? How quickly do the ionic crosslinks reform as the concentration of the ions in the polymer matrix increases? On what timescale do the ions in the amorphous and crystalline polymer-electrolyte phases undergo exchange? In addition, since the toroid cavity/electrochemical cell N M R imager records chemical shifts and coupling constants, we are able to explore various chemical transformations that occur during cell operation. What ancillary oxidatiodreduction reactions take place at the electrodes? What side reactions do lithium ions undergo when they intercalate into the pores of carbon based materials, which serve as novel electrodes? How is the irreversible capacity of an electrochemical cell related to the chemistry of lithium ion intercalation and deposition, and electrolyte degradation? These are just a few of the questions that are significant to modern battery research and development. In

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119

this paper we have demonstrated the feasibility of several in situ NMR imaging methods that will allow us to investigate these questions.

Acknowledgments We are indebted to Dr. Christopher Johnson of the Chemical Technology Division at k g o n n e National Laboratory for providing materials and helpful advice. This work was performed under the auspices of the Office of Basic Energy Sciences, Division of Chemical Sciences, U.S. Department of Energy, under contract no. W-3 1-109-ENG-38.

References 1.

Ratner, M. A,, Shnver, D. F. Chem. Rev. 88 (1988) 109.

2.

Mellander, B.-E., Albinsson, I. Solid State Ionics: New Developments, Ed. Chowdari, B. V. R., 1997, 97.

3.

Ward, I. M., Boden, N., Crnickshank, J., Leng, S. A. Electrochimica Actu, 40 (1995) 2071.

4.

Woelk, K., Rathke, J. W., Klingler, R. J. J. Magrz. Reson. A 109 (1994) 137.

5.

Woelk, K., Rathke, J. W. J. Magn. Reson. A 115 (1995) 106.

6.

Bruce, P. G., Vincent, C. A,, J. Chem. Soc. Faruday Trans. 89 (1993) 3187.

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10. Efficient Simulation of Spin Echo, Gradient Echo, Fast, and Ultrafast NMR Imaging Sequences by Isochromat Summation Pave1 Shkarin and Richard G. S. Spencer National Institutes of Health, National Institute on Aging, 4940 Eastern Avenue, Baltimore, MD 21224, USA

Abstract One of the earliest computational methods used to simulate imaging sequences is based upon following the time evolution of spin isochromats as they evolve in response to rf pulses and periods of free precession. While accurate, application of this method has been limited by the enormous number of isochromats required to achieve accurate results, resulting in excessively long computation times. We have re-examined this approach and developed an efficient, flexible, and accurate isochromat summation algorithm which permits the simulation of the full time-domain signal resulting from arbitrary two-dimensional Fourier imaging sequences. The number of isochromats required to achieve a specified degree of precision as compared with the exact image is calculated, talung into account transverse relaxation and the potential for artifactual refocusing due to finite isochromat spacing. No assumptions are made regarding transverse dephasing, so that complicated sequences of direct and stimulated echoes are fully modeled. This permits modern single-shot methods such as Burst to be simulated readily.

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10.1 Limitations of the Imaging Equation and Advantages of Time-Domain Simulation The imaging equation may be written: (10.1)

where by Sect) we indicate the exact signal, Mo (x) is the local transverse magnetization prior to acquisition, and

l r G(t') dt'

k ( t )= t'E

(10.2)

(0,t)

In writing this, an assumption which is implicitly made is that Mo(x)is not a function of k(t),the order in which k-space in traversed. There are a number of circumstances in which this assumption is false. Examples include 1) the early readouts of spin warp imaging when TR = T2, 2) Burst imaging, when large flip angles are used, leading to echo amplitude distortions, 3) any inultipulse sequence when unwanted stimulated or Hahn echoes occur, or when parts of FID's intrude into the acquisition window, and 4) when a significant amount of transverse relaxation occurs during the imaging sequence.

10.2 Basics of the Time-Domain Simulation: Effect of Hard Pulses and Free Precession For the nthhard pulse, of flip angle 0 and phase x, we have

(10.3)

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123

For free precession over the time At = t2 - t,, two cases must be distinguished. In the spectroscopic case, there is an initial distribution of isochromat frequencies given by f(v). Then M,(t2) =

bx(tl) cos(2nvAt)

-

M , ( t l ) sin(2nvAt)]exp(-At/T2)

M y ( t 2 ) = [M,(tl) sin(2mAt) + M y ( t l ) cos(2.nvAt)]exp(-At/T2)

(10.4)

With these, explicit calculation of echo timings and amplitudes for a sequence of strong pulses of arbitrary number, timing, flip angle, and phase can be performed in one dimension [ 11. In the imaging case, with (piecewise) constant gradients, we take f(v) = 8(v-vo) and obtain M,(t2)

= [M,(t,)

cos(2n yG.xiAt) - M , ( t , ) sin(2nyG.xiAt)]exp(-AtlT2) (10.5)

M , ( t 2 ) = [M,(t,) sin(2nyG.xiAt) + M y ( t l ) cos(2nyG.xiAt)]exp(-At/T2)

These expressions give us the magnetization vector for each isochromat, and the summation over isochromats gives the net signal: (10.6)

10.3 Required Number of Isochromats 10.3.1 One Dimension We first consider the one-dimensional case, with magnetization distributed uniformly over the field of view. The values of the parameter k which are reached can be calculated from the preceding definition of k. The maximum excursion in k-space can then be We also define by derived; we denote this by AK = kmaX- kmin, where kfin < k < k,. S,(k) the approximate signal, obtained by replacing the integral in the imaging equation by a sum over J isochromats - that is, the Fourier integral is replaced by a truncated

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Fourier series. The number of terms in the Fourier series, that is, the number of isochromats in the simulation, can be selected to achieve a desired degree of accuracy. The required value of J also depends on AK,as expected. We define the overall error in the image as the maximum value of FT(S,(k) - S,(k)). We have selected, as a reasonable criterion for required accuracy, a value of approximately 1% for this error. It can be shown explicitly [2] that an overall error < 1.5% will result if J23AK

(10.7)

For FOV = 1, then AK = N , number of pixels in the image reconstruction. Then the criterion becomes: J23N

(10.8)

If number of pixels in the source matrix, M , is M > 3N, this becomes J 2 A4 to ensure at least one isochromat per pixel in the source matrix.

10.3.2 Two Dimensions In two-dimensions, the phase dimension is treated as above, since k-space is traversed only once in that dimension. However, k-space can be scanned multiple times in the read direction. Therefore, in a single-shot experiment of total duration T in which full transverse relaxation never occurs, the maximum range of kread, u r e a d = kread,max- kread.min, must be calculated using the expression

(10.9)

where t takes values over the time interval (0, T). This is also required for multiple-shot experiments, such as spin warp, when TR is on the order of T2, so that full transverse relaxation cannot be assumed to occur. The read condition is therefore: aread

(10.10)

Two further comments are in order. When full transverse relaxation occurs between

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125

acquisitions, one can use the same calculation as for the phase dimension. Also, the required number of isochromats may be greatly reduced by considering transverse relaxation. Artifactual refocusing cannot occur at a time greater than approximately 5T2 following a pulse, so that AKread may be replaced by the maximum variation of k for all time intervals of duration 5T2 in the sequence. In general, this is considerably smaller than AKr,,d. These considerations can decrease computation time by an order of magnitude or more, rendering the simulation very efficient while maintaining accuracy.

10.4 Computation Outline The source object consists of regions with assigned density (p), TI and T2.Typical CPU times for calculations performed on a Silicon Graphics Challenge XL with 6 processors (one gigabyte of RAM, 450 MFLOPS) are: 1) 64 x 64 spin warp, full relaxation between acquisitions: < 1 minute; 2) 64 x 64 spin warp with incomplete relaxation: < 20 minutes; 3) 32-echo Burst: < 3 minutes. Figure 10.1 shows the object used in spin-warp, Burst, and PREVIEW simulations. The matrix size is 256 x 256. The pixels within each region, A, B, C, and D, are respectively characterized by a given isochromat density and set of relaxation times. These are specified for each example. The eye has zero density. Note that the matrix size chosen

Fig. 10.1: Object used in simulations of the spin-warp, Burst, and QUEST imaging sequences.

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P. Shkurin and R. G. S. Spencer

provides a fine-grain source image. The actual image matrix size, generally 64 x 64 in the following, is determined by the specifics of the pulse sequence. For example, in spinwarp imaging, it is determined by the number of phase encode steps and the data size of each digitized echo. The minimum number of isochromats used in the simulation is equal to the source image matrix dimension, that is, 256 x 256 = 65,536.

Fig. 10.2: Spin-warp simulation. A) Stripe artifact resulting from pulse imperfections. B) Removal of the stripe artifact by homospoil pulses.

10.5 Spin-Warp Imaging The standard spin-warp pulse sequence was simulated as a basic demonstration of the method. Figure 10.2 shows the stripe artifact due to imperfect pulses. TR = 100 s, TE = 15 ms. Object parameters: spin density = unity. ( T I ,T2) values: Region A: (5000 ms, 1000 ms); Region B: (2000 ms, 1000 ms); Region C: (3000 ms, 1000 ms); Region D:

(4000 ms, 1000 ms). A) 90" - 180" pulses misset by 30% to become 63" - 126". Artifact results from occurrence of an FID after the imperfect 180" pulse. B) Removal of the stripe artifact by placement of balanced homospoil gradients about the 180" refocusing pulse. Figure 10.3 shows the zipper artifact due to TR = T,. All object parameters as in the previous figure. A) TR = 5000 ms, leading to T , weighted image. B) TR = 1000 ms, with artifact due to stimulated echoes formed at end of each phase-encode. C) TR = 1000 ms, with removal of zipper artifact by placement of homospoil gradient after signal

10. Efficient Simulation of NMR Imaging Sequences by Isochroinat Summation

127

Fig. 10.3: Spin-warp simulation. A) T I weighted image, with TR >> T2. B) Zipper artifact resulting from TR on the order of T2. C) Removal of zipper artifact by homospoil pulses.

Fig. 10.4: Spin-warp simulation. A) Aliasing artifact in the phase-encode dimension. B) Aliasing artifact in the read dimension.

acquisition. Figure 10.4 shows aliasing artifacts. ( T I ,T2) values for the regions are: Region A: (5000 ms, 1000 ms); Region B: (2000 ms, 250 ms); Region C: (3000 ms, 300 ms); Region D: (4000 ms, 500 ms). TE = 500 ms. Ideal YGread = l/(dwell.FOV) =10 kHz/cm. Since the duration of Gphase is one-half the duration of Gread,the maximum of yGphasein the ideal case is also 10 kHz/cm. A) YGphase= 20 kHz/cm. B) YGphase= 20 kHz/cm, yGread= 20 kHz/cm.

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P. Shkarin and R. G. S.Spencer

10.6 FLASH Imaging FLASH imaging utilizes a gradient-eL,,o rather than a spin-echo for refocusing [3 This forms the basis for a number of rapid imaging sequences. Figure 10.5 shows the FLASH sequence used for simulation and indicates the position of optional homospoil gradients. The phantom characteristics are defined as indicated, with column TI values and row T, values as labeled. The expected TI weighting is seen across rows, with increased image intensity for shorter TI values. For TR >> T2,both spoiled (not shown) FLASH and nonspoiled FLASH produce accurate images. For TR = T . , the effect of residual transverse

%

i

.ri

I

U

0

I

a

m 0 v, 0

TR

TI ,ms

5000

3000

1000

8-

-~

.+ 0

a

m

TR = 800 ms

TR = 200 ms

Fig. 10.5: FLASH pulse sequence and simulation. For TR on the order of T2, residual transverse magnetization leads to zipper and shadowing artifacts. These artifacts are removed by homospoil pulses.

10. Efficient Simulation of NMR Imaging Sequences by Isochromat Summation

129

magnetization in non-spoiled FLASH leads to a zipper artifact across the entire image, as well as image shadows. These are greatly reduced or eliminated by application of the homospoil gradients in the position indicated in the pulse sequence. Other simulations (not shown) demonstrate that susceptibility artifacts, greatly attenuated in spin-echo imaging sequences, are maintained with the FLASH sequence.

10.7 Burst Imaging Burst is an ultrafast spin echo sequence which produces density-weighted images. A large number of equidistant rf pulses (32 in the present simulations) are followed by a refocusing pulse of 180". Refocused echoes are then sampled under constant read and phase gradients. One important feature of the sequence is that it makes only very modest

demands on gradient performance [4]. Figure 10.6 shows the Burst sequence used in the simulation, incorporating symmetric k-space sampling and requiring zero filling prior to reconstruction. Figure 10.7 shows that increasing pulse angle, a, results in increasing image distortion. Object parameters: TI = 5000 ms and T2 = 2000 ms throughout. Density in each region: Region A: 5; Region B: 2; Region C : 3; Region D: 1. Figure 10.8 shows the increasing influence of transverse relaxation during the Burst sequence as the object T2 decreases. Object parameters: T2 as shown in the figure; all others the same as in Fig. 10.7. density: Region

f

hase

1 Fig. 10.6:Burst pulse sequence.

@ad

130

P. Shkurin and R. G. S. Spencer

A: 5 ; Region €3: 2; Region C: 3; Region D: 1. A) For T2 = 400 ms, echo distortions increase more rapidly as a function of a than in Fig. 10.7, where T2 = 2000 ms. The images themselves are similar. B) For T . = 200 ms, further nonidealities in the echoes are seen, and subtle increases in image distortion are evident. C) For T2 = 100 ms, severe distortions of echoes and images are present even at small excitation pulse angles.

Fig. 10.7: Burst simulation. Increasing the pulse angle a results in increasing image distortion.

10.8 PREVIEW Imaging PREVIEW is an imaging sequence which is similar to Burst, except that it makes use of all echoes generated by relatively few rf pulses spaced at specific intervals [5]. For example, four pulses with interpulse intervals related as 1:3:9 generate 27 equidistant echoes. As in the case of Burst, these pulses are followed by a refocusing pulse of 180". Figure 10.9 shows image distortions resulting from an imperfect refocusing pulse of

120", resulting in unwanted additional echoes. Figure 10.10 shows the effect of using different excitation pulse sets, with an ideal refocusing pulse, on noisy images. The standard PREVIEW sequence pulse angles are derived such that performance is optimized. However, in the presence of significant noise the original set of PREVIEW pulses, {45", -60", 120°, -90') is no longer optimal. In both panels of Fig. 10.10 pseudorandomnoise of 5% maximum magnetization amplitude has been added to the signal, resulting in significant image degradation. Some performance is recovered by use of a new set of rf pulses optimized to give high average echo amplitude (right hand panel), as compared with the original set of PREVIEW pulses (left hand panel).

10. Efficient Simulation of NMR Imaging Sequences by Isochrornat Summation

131

Fig. 10.8: Burst simulation. Artifacts resulting from transverse relaxation. The distortions are seen to be more pronounced with larger pulse angle a.

10.9 Conclusions We have presented representative results for simulations of the standard spin-warp experiment, for FLASH, and for Burst and PREVIEW, modern ultrafast single-shot experiments. As demonstrated, our algorithm permits the simulation of a number of real effects which depend on specifics of the pulse and gradient sequences implemented. As nearly any pulse sequence can be simulated, the algorithm is exceedingly flexible. In addition, the characteristics of a large number of artifacts, including several which arise specifically from stimulated echoes, may be investigated. We have found this simulation to be of great utility in understanding new imaging sequences and correcting imaging artifacts. Further details of some of this work can be found in [ 11 and [2].

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Fig. 10.9: PREVIEW simulation. Distortion resulting from refocusing pulse imperfection.

Fig. 10.10: PREVIEW simulation. Demonstration of improved image quality with non standard excitation pulses in the presence of noise.

References 1.

P. Shkarin, R. G. S. Spencer, ConceptsMugn. Reson. 8 (1996) 253-268.

2.

P. Shkann, R. G. S. Spencer, Intern. J. Imag. Systemsand Technol. 8 (1997) 419-426.

3.

A. Haase, J. Frahm, D. Matthaei, W. Hanicke, K. D. Merboldt, J. Mugn. Reson. 67 (1986) 258-266.

4.

J. Hennig , M. Hodapp, MAGMAl(1993) 39-48.

5.

C. J. R. Counsell, Mugn. Reson. Imug. 11 (1993) 603-616.

11. A Novel Algorithm for Tumor Characterization by Analysis of Transversal Relaxation Rate Distributions in MRI R. Martin and M. Martin-Landrove Departamento de Fisica and Centro de Resonancia Magnktica, Facultad de Ciencias, Universidad Central de Venezuela, A.P. 47586, Caracas 1041-A, Venezuela

Abstract A novel algorithm to determine transversal relaxation rate distributions is presented to

characterize tumors and neoplasic tissue. The methodology is applied to a variety of tumors with different degrees of malignancy as well as to healthy tissue. The results show that when there is malignancy it frequently happens in a definite relaxation rate window outside of which only liquid or benign neoplasic tissue are present. The methodology developed in this work can be easily implemented in any type of scanner at any magnetic field and can be extended to study other pathologies.

11.1 Introduction In complex and heterogeneous systems, as for instance living tissues, the proton transversal magnetization decay is not governed by a single relaxation rate but by a superposition of different relaxation rates, each one corresponding to different dynamical environments. In general, this situation is represented by a continuous distribution function and the measured decay corresponds to its Laplace transform. In the present work a novel algorithm is developed and used to invert the Laplace transform in order to obtain the relaxation rate distribution function from the experimental decay. The methodology is applied to a variety of tumors, with different degrees of malignancy as well as to healthy tissue.

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R. Martin and M. Martin-Landrove

11.2 Materials and Methods The measurements were realized in a Siemens Magnetom operating at 1 Tesla. More than 40 patients were studied including diagnosis of lymphoma, lung cancer, human papiloma, etc.. The standard Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence was used, and images for different echoes were registered and then for the same region of interest in each image, the pixel intensity was averaged in order to obtain the decay curve of the average intensity for that specific region. Only even numbered echoes were considered in order to control 180" pulse adjustment. The number of regions selected for each tumor depended on the size and heterogeneity as observed on the nmr image. In the case of patients with positive diagnostic of cancer, samples on the tumor periphery and in different tissues were taken in order to control for possible metastasis. The decays so obtained were processed by the proposed algorithm and correlated to results obtained by biopsies. The total number of samples processed was 60. Finally, the intersection of the spectra is obtained in order to determine characteristic zones assigned to the presence of malignancy in the tumor.

Inverse Laplace Transform Algorithm There are a wide variety of different approaches [ 1,2] to solve numerically the Inverse Laplace Transform Problem and some of them are of standard use in very many laboratories around the world. Such is the case of DISCRETE and CONTIN programs [I], which are applicable in many situations. Most of this attempts make use of assumptions about the mathematical properties of the function to be obtained by the inversion procedure and rely on this properties in the general development of the algorithm, while others introduce regularization parameters or a fixed number of components in the relaxation spectrum. None of those problems are present in the algorithm described in this work The signal is known in a finite number of points on the real axis, and can be represented as a first kind Fredholm integral equation of the form:

(11.1)

where M ( t ) corresponds to the transversal magnetization and h is the relaxation rate. Equation (1 1.1) represents a very general way to express the transversal relaxation decay

11. Algorithmfor Tumor Characterization by Analysis of Trunsversal Relaxation Rate Distributions

135

depending on the particular relaxation rate distribution P(h)[3,4]. This distribution can be represented by a histogram or collection of bars of variable width, which is given by N

p(A>=

pk

(I)

(11.2)

k=l

where N is the number of components and Pk (1)is the k-th elemental component given by

This representation can be used for the description of discrete and continuous distributions as well. The problem to be solved can be stated as an optimization procedure where a set of distribution components, which provides the best fit for the M ( t ) function, has to be found. For that purpose Simulated Annealing and Metropolis algorithms [5-81 are used. The configuration to be tested in each Metropolis algorithm cycle is given by a finite , number of elementary components which are sampled in the relaxation rate position 1 and width 6?Lk for the k-th element. At the same time, the total number of components N for the configuration is also changed, which is a new feature in an optimization procedure of this kind. This sampling in the total number of components is performed by considering two options with the same probability within the Metropolis algorithm cycle: a) The total number of components N is unchanged and in this case one component is taken with equal probability from the current configuration set to change its numerical value of the relaxation rate position and width. b) A new component is created and added to the existing configuration. The new component is located either within the existing set or it is the maximum of a new configuration set. In the latter case, its position is determined with a non-uniform probability distribution vanishing at large relaxation rates. The simplest choice corresponds to an exponential distribution, but other distributions can be considered as well and it is an open problem. The cost function was chosen on results of robust statistics to noise filtering and it is known in the literature as Least Absolute Deviation (LAD) optimization [9]. For n p points it is given by

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R. Martin and M.Martin-Landrove

and it can be seen as an average relative error. In the presence of information loss the absolute value provides a better noise filtering than the usual quadratic value since the median is much less sensitive than the mean to the presence of fluctuations of any size. The quantity Mexp( t ) corresponds to the measured signal and Mop( t ) is the optimized signal given by

Mop( t ) =

2J'dhe-"

Pk (A)

(11.5)

k o

In this work a fast simulated annealing approach is used (Cauchy machine) [ 101 and then it means that the temperature parameter is proportional to the inverse of the Monte Car10 iteration number. In order to avoid the problem of the appearance of metastable states [5-81 which are intrinsic to the Metropolis algorithm, up to 20 parallel simulations with different initial conditions were performed. The final histogram is taken by averaging the total set of particular histograms corresponding each one to different initial conditions. This procedure is performed in order to avoid the increase in condition number for the matrix used in the least square procedure when the number of components is also increased.

11.3 Results and Discussion The results show that when there is malignancy it occurs in a very defined relaxation rate window and outside of it only liquid or benign neoplasic tissue are present. This situation can be easily depicted in Fig. 11.1 in which results for 60 samples, including also healthy tissue are presented. Some of the results in the Figure are represented with some uncertainty which corresponds to a positive diagnostic of malignancy but for a sample taken on the tumor periphery or in a different tissue where there is a finite probability of a benign situation. Only those samples taken on tumors with positive diagnostic of malignancy were used to

137

11.Algorithm for Tumor Characterization by Analysis of Transversal Reluxation Rate Distributions

produce the intersected spectrum. Other parameters of the relaxation rate distribution are also under study to correlate them with clinical data. It is worthwhile to mention that CPMG sequences are very sensitive to exchange and diffusional processes and the sort of algorithm implemented in this work could be particularly useful for their study. The methodology developed in this work can be implemented easily in any type of scanner working at any magnetic field and can be extended to study other pathologies.

104

h

I

,

,

103

0

Q

E

v

102

* E

10’

0

10

20

30

40

Sample

50

60

70

10’ 0.008

0.010

0.012

h (msec-’)

Fig.ll.1: On the left, transversal relaxation time obtained for different samples including malignant tumors, benign tumors and healthy tissue. Circles represent malignancy, triangles possible malignancy and squares benign tissue. On the right the intersected relaxation rate spectra.

Acknowledgments We would like to thank the cooperation of the Instituto de Resonancia MagnCtica for the use of the NMR scanners and also the financial support given by CONICIT to present this work.

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R. Martin and M. Martin-Landrove

References S. W. Provencher, Comput. Phys. Comm. 27 (1982) 213 and Comput. Phys. Comm. 27 (1982) 229. J. P. Butler, J. A. Reeds, and S. V. Dawson, SIAMJ. Numer. Anal. 18 (1981) 381. M. Martin-Landrove, R. Martin, and A. Benavides, Bull. Magn. Reson. 17 (1995) 73.

I. Bonalde, M. Martin-Landrove, A. Benavides, R. M a t h , and J. Espidel, J. A[?$. Phys. 78 (1995) 6033.

5.

G. Bhanot, Rep. Prog. Phys. 51 (1988) 429.

6.

S. Kirkpatrick, C. D. Gelat, and M. P. Vecchi, Science 220 (1983) 671.

I.

S. Kirkpatrick, J. Stat. Phys. 34 (1984) 975.

8.

E. Bonomi and J. L. Lutton, SIAM Rev. 26 (1984) 551.

9.

A. Scales and A. Gersztenkorn, Inverse Problems 4 (1988) 1071.

10.

H. Szu and R. Hartley, Phys. Lett. A 122 (1987) 157.

Materials

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12. Materials Imaging with Examples from Solid Rocket Propellants W. E. M u a d , L.H. Merwin2, aizd D.G. Cory3 1Bruker Analytical Systems, Inc., 19 Fortune Drive, Billerica, MA 01821, USA 2Chemistry and Materials Branch, Weapons Division, Naval Air Warfare Center, China Lake, CA 93555, USA 3Department of Nuclear Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Abstract: Methods for NMR imaging of solids have been developed over the past decade in parallel to those for medical imaging and microscopy. The major challenges in the solid state are (I) the large NMR linewidths, and (2) developing a sufficient contrast to noise ratio. Unlike biomedical applications where the vast majority of studies are of water, the systems studied in materials applications vary widely, as do the NMR properties and suitable methods. Here the range of methods is briefly reviewed followed by a detailed case study of solid rocket motor propellants. This particular system was chosen since the methods used are straightforward and relatively accessible, and since useful information about the processing of these materials can be derived from the images.

12.1 Introduction to Materials Imaging A wide variety of imaging methods specific to proton rich solid materials have been developed which reflect the great variations in the NMR linewidth. These methods are carefully tailored to the NMR characteristics of the sample and often include the need for specialized hardware such as very strong or very fast switching gradients. The particulars of these methods have been described in reviews [l-31 and will not be repeated here. Instead, the range of solutions will be briefly described and, in the second portion of this

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W . E. Muus, L.H. Merwin, and D. G. Cory

paper, a case study of NMR imaging of a complex elastomeric system will be described. The choice of system was dictated first by the available methods as elastomers can be successfully studied using extensions of liquid state schemes that are widely available. Stray field, constant time and coherent averaging approaches to imaging are less available and are mainly still restricted to the laboratories of experts. This system is also of interest since useful information is directly available from the images. Much of the work in solid state imaging of rigid proton rich samples has been directed towards methods development and few applications have been explored where the image provided information that was not available elsewhere. For the filled elastomeric systems, the length scales of interest for processing problems are well matched to those available in the image.

12.1.1 Encoding of Spatial Information via Spin Evolution in a Magnetic Field Gradient The measurement of spatial information in NMR at length scales greater than that resolvable by dipolar couplings depends up011 the creation of a magnetization grating with a period commensurate with the spatial scale [4]. Such a grating is most directly developed through the differential rate of spin precession in a magnetic field gradient [5],

o(r) =YBo + Y

(12.1)

which spatially and periodically modulates the phase of the spin magnetization. The normal NMR symbols are used throughout, y is the gyromagnetic ratio, B the magnetic field, r the location of a test spin and p(r) the spin density. The latter is assumed to be spatially complex and the object of the imaging experiment. The magnetization then becomes,

M , p(r)

gradient evolution

> M , p(r)exp(- i k . r )

(12.2)

12. Materials Imaging with Examples from Solid Rocket Propellants

143

The wave-vector of the grating, k, describes the pitch of the grating, and in the simplest case is proportional to the area of the gradient waveform,

k = y J V B z( t ) dt

(12.3)

The NMR signal is the spin magnetization integrated across the sample,

s ( k ) =y j p ( r ) e x p ( - i k . r ) d r

(12.4)

so that what is directly measured in the presence of a magnetic field gradient is a Fourier component of the spin density. Clearly if a sufficient set of Fourier components are measured, then the signal may be simply recovered by an inverse Fourier transform. The image field of view and the reso-

lution are governed by the normal Nyquist sampling conditions. In solid state studies an important additional consideration is the decay of the transverse magnetization. There is thus a competition between the decay rate (1/T2) and the rate of creating a grating, so that in a time independent magnetic field gradient where k increases according to,

-dk_ dt

-

YVB,

(12.5)

the time dependent signal includes attenuation due to spin-spin relaxation, (12.6)

The Fourier relation is clearer when the signal is described in terms of a wave number, and the rate of change of the wave number, as,

(12.7)

It is clear from the convolution kernel of the Fourier mapping that the image resolution is limited by,

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W. E. Muas, L.H. Merwin, and D. G. Cory

(12.8)

The spin-spin relaxation time varies greatly from sample to sample and the methods available to obtain high-resolution images vary with this.

12.1.2 Length Scales of Spatial Information Available in Solid State NMR The ranges of spatial measurements available by NMR are shown schematically in Fig.

12.1.

1 cm

lmm

Imaging

100 pm

Molecular diffusion based scattering

10 pm

LtEL

100 nm

10 nm

Dipolar coupling based scattering

1 nm Dipolar coupling

1A

Fig. 12.1: Spatial scale of NMR measurements.

In general the range of length scales is divided into three regions: an absolute length scale area in which the signal (image) is directly related to a specific location in the sample; a relative area, at intermediate length scales where the distances between features are obtained, but the information is that averaged over the sample; and a spectroscopic length scale where the information is obtained directly from a resolved dipole-dipole interaction between spins. The first two of these provide a spatial mapping based on an applied magnetic field gradient and so the spatial scale is linear.

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The lower limit of resolution for NMR imaging is determined by the sensitivity (or lack there of) of NMR and is approximately 10 pm, though this is somewhat dependent on the sample characteristics and the methods used. In general the resolution is limited by the smallest volume that contains a minimum number of detectable spins. Scattering methods avoid this sensitivity limit by measuring an average property of the local geometry to which the entire sample contributes [5]. The resolution limit is determined solely by the strength of the gradient. The information from scattering methods is the conditional probability of spin translational displacements, over a time interval:

s(q) = jp(r) P(rlr’,t) exp(-ig.(r-r’))drdr’

(12.9)

where r and r‘ are the location of the spin, P denotes the probability and q is the wave vector. Where the displacements are introduced by molecular motions, diffusion coefficients and the geometry of barriers to free diffusion can be measured. Recent developments in gradient hardware have significantly extended the spatial range of these experiments to permit the direct observation of the extent of magnetization transport in rigid, strongly coupled spin systems via the dipole-dipole interaction [6,7]. In addition to the resolution limit for materials imaging, there is a related limit on the field of view and size of the sample. Most imaging methods depend upon strong gradient and/or RF fields, and these tend to dictate that the sample be relatively small to physically fit within a confining coil structure. The short spin-spin relaxation times also limit the number of Fourier components that can be measured and, thus, the field of view. Typically, the number of voxels across any axis of an image is limited to being equal to, or less than 256. So for a 1 cm diameter sample (that is easily contained within a high field magnet and gradient set), the highest resolution is 40 pm, even though the minimum number of detectable spins may be contained within a much smaller volume.

12.1.3 Approaches to NMR Imaging of Solids The various approaches to NMR imaging of materials are outlined in table 12.1, based primarily on the experimental setup required. The comments point to the types of materials that can be successfully imaged with these methods and provide a rough idea of the sensitivity and resolution. What is not described is the level of expertise necessary to

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successfully employ these methods. With the exception of the liquid state and constant time methods, all require specialized hardware that is presently found only in a limited number of laboratories. Of these, only the hardware for stray field imaging is commercially available. Table. 12.1: Classes of materials imaging methods

Type

Useslcomments

liquid state methods

Restricted to samples with sharp lines, such as elastomers. Resolution and sensitivity depends on the line-width. Relatively easy to include contrast.

constant time methods

No restriction on the sample. The resolution can be high, but the sensitivity depends on the line-width (typically low).

stray field

No restriction on the sample. The resolution is tied to the experimental setup. The sensitivity depends on the TIP and is typically low.

force detection

Samples must have a long Tip. The resolution depends on the mechanical setup and can be very high. These methods are still being developed [8].

coherent averaging

Resolution and sensitivity can be high and depend on the residual line-width.

- magic angle spinning

Works best for samples with small dipolar couplings or large susceptibility variations.

- multiple-pulse

No restrictions of the sample, but works best with very rigid materials. Care must be taken to avoid distortions

Liquid state and constant time methods [9,10] are widely available via micro-imaging accessories to NMR spectrometers and permit high quality images to be obtained for select materials. In neither of these is the NMR linewidth modified by coherent averaging, and so this presents a fundamental limit to the available sensitivity. In the liquid state approach the gradient is used to frequency encode spatial information in the presence of the full linewidth and so the resolution is that given by eqn. (12.8). This method is most appropriate for materials with relatively sharp NMR lines. With a magnetic field gradient of 100 Gkm, typical of commercial micro-imaging probes, a resolution of 10 pm can be obtained for samples with T2’s longer than about 0.5 ms (corresponding to

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147

linewidths of less than 650 Hz). Examples of suitable samples include elastomers and solvent swollen plastics. Constant time methods rely on the high field truncation of spin Hamiltonians to their secular components, to decouple the gradient and dipolar contributions to the NMR linewidth at a fixed time. Gradient encoding may still be achieved, while leaving the dipolar evolution fixed, by incrementing the strength of the magnetic field gradient systematically between observations. The method then becomes a single point acquisition, which is very inefficient in sampling terms, although when sampled with a matched filter it may be very sensitive. Since the decoupling of the dipolar contributions to the linewidth arise not from a refocusing of the interaction, but rather from observing at a fixed point, the spin-spin relaxation time still leads to significant signal attenuation. However, this only influences the image sensitivity. The image resolution is limited solely by Nyquist sampling conditions. Stray field imaging (STRAFI) [ 111 approximates a continuous wave detected wideline experiment in a static magnetic field gradient. It typically utilizes the region near the end of the superconducting magnet windings where there is a very large magnetic field gradent. The field strength at this point is approximately 0.4 the field strength of the homogeneous region of the magnetic field. The maximum gradient varies with the central field strength of the magnet, and is found to be 40 T/m for a 4.7 T magnet and 80 T/m for a 9.4 T magnet. This gradient is homogeneous over a disk approximately 30 mm in diameter for a wide-bore magnet. Since the gradients are large, RF pulses at accessible power levels will only excite a small portion of a macroscopic sample placed in the field. The principle of STRAFI then is that a pulse selectively excites a plane transverse to the gradient with the selected thickness on the order of 100 pm. The sample is translated and another slice is observed, etc. Since each slice is observed separately, there is no need for a relaxation delay and the entire sample may be rapidly scanned. One version of this device can scan up to 512 slices with a separation of 60 pm in 1 second. A two-dimensional image is acquired by the back projection reconstruction technique. Each scan of the sample through the selective plane yields a projection of the spin density directly (no Fourier Transformation is required). The sample is then reoriented transverse to the gradient direction and scanned again. This is repeated until sufficient projections are accumulated to calculate the back-projection image. The process can be repeated in a third orthogonal direction to acquire a full three-dimensional image.

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The STRAFI method is conceptually straightforward, but the probe is extremely complex, having to reorient the sample about two orthogonal axes and translate the sample along a third axis and perform all of this in a well controlled and reproducible manner while in a high magnetic field. Coherent averaging schemes [4,12] aim to artificially reduce the NMR linewidth by suppressing the time averaged spin evolution from all internal Hamiltonians while simultaneously restoring the evolution from the magnetic field gradient. This is most often accomplished as a combination of multiple-pulse and pulsed gradient methods, although magic angle spinning approaches [ 131 have also been demonstrated. The hardware for these methods is demanding, and the methods are prone to artifacts unless great care is exercised since the gradient and internal Hamiltonians interact in a profoundly non-linear fashion [ 14). Table 12.2: Common contrast mechanisms in solid state NMR imaging

Relaxation Times T1

Spectral density of molecular motions at the Larmor frequency

T2

Range of local fields Spectral density of molecular motions at the Larmor frequency in the rotating frame (typically tens of kilohertz)

Tl x

Spectral density of molecular motions at a pulsed effective field frequency (typically low audio frequencies)

Chemical Shifts Isotropic chemical shifts

Chemical species, morphology

Anisotropic chemical shifts

Orientation, dynamics

Susceptibility

Morphology, chemical heterogeneity

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12.1.4 Contrast in Solid State Imaging Table 12.2 lists the range of commonly available relaxation and contrast methods in solid state imaging. Most studies develop contrast based either on spin density or T, differences since these show up immediately without the need to modify the imaging sequence. Other relaxation times are best introduced by preceding the imaging measurement by a sequence to create the desired contrast [ 151.

12.2 Case Study: NMR Imaging of Rocket Motor Propellants 12.2.1 Introduction Elastomers are most widely used as binder in composite materials and NMR imaging has been shown to be a useful tool to obtain physical and chemical information from the elastomer distribution [2,16,17]. Solid rocket motor propellants are an example where a binder material is highly filled with particulate oxidizer [21]. Characteristics such as the burn rate and mechanical properties depend on the distribution, size and concentration of the filler material as well as the properties of the polymer matrix. This problem is a good example of where NMR imaging can make a unique contribution to understanding materials processing [ 18-20].

12.2.2 Experimental Section The NMR imaging experiments were performed at magnetic field strengths of 3 T and 14.1 T. The 3 T imaging system has a magnet with a horizontal room temperature bore of 15 cm. This system is based on a Bruker AMX console, operating at a proton frequency of 125 MHz. RF probes that accommodate samples of 18 mm, 8 mm and 6 mm were employed in a gradient set capable of generating 300 Gkm.

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W. E. Maas, L.H. Merwin, and D. G. Cory

In addition we have obtained images with higher resolution on a 14.1 T system, with a vertical bore magnet which has a room temperature bore of 54 mm. This system is based on a Bruker AMX console, operating at a 600 MHz proton frequency. The NMR imaging experiments are obtained with a special RF probe for microscopy studies [22], capable of image resolutions as fine as 2 pm. The RF probe employs a 1 mm sample coil tightly wound around the sample, resulting in a high filling factor which leads to an increased S/N and further offsets the losses in sensitivity from going to a higher image resolution. The gradient set is capable of generating 1000 G/cm in two directions and

300 G/cm along the coil axis. The propellant simulants studied here consist of a hydroxy terminated polybutadiene (HTPB) matrix, with a solids loading of 82% by weight. The binder material (HTPB, 5% by weight) is cured with isopherone diisocyanate and plasticized with dioctyl phtalate (12% by weight). The propellants are inert materials in which ammonium sulfate replaces the oxidizer ammonium perchlorate. The solids loading consists either entirely of ammonium sulfate or a mixture of ammonium sulfate and aluminum powder. The ammonium sulfate crystals have a bimodal distribution, consisting of crystals with an average size of 200 pm, and crystals with an average size of 20 pm, while the aluminum particles are approximately S pm in size.

12.2.3 Imaging of Propellants at 3 T For a number of propellant compositions, a 3D image was obtained to show the most important spatial heterogeneities. The images display the proton density of the binder material, i.e. that of the HTPB and the plasticizer. A single transverse relaxation time, T2 of 8 ms is observed for these protons. The protons present in the ammonium sulfate filler have a much shorter T2and are not observed. The images were acquired with spin echo methods and display an excellent contrast as well as a good signal to noise ratio. Spin echo methods are well suited for propellant imaging, since the image contrast is derived from the heterogeneity of the sample rather than from differences in transverse relaxation times. In addition, the spin echo sequences have a higher sensitivity. The 3D methods employed are efficient in the sense of experiment time and do not impose a restriction on the thickness of the image planes.

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151

Some representative planes from the 3D images of two propellant samples are shown in Figs. 12.2 and 12.3. Three dimensional images were obtained in about 12 hours with 16 phase encoding steps in the z-direction and 128 x 128 points per plane. The in-plane resolution is 35 ym x 35 pm and the thickness of the planes is about 120 pm. The echo time was 1 ms.

Fig. 12.2: Four planes from a 3D image of a HTPB based propellant with a solids loading of 82%. The image resolution is 35 pm x 35 pm, the plane thickness is 120 pm. The top left plane is from the edge of the sample, which appears to consist of unfilled HTPB.

Figure 12.2 shows four planes from a 3D image of an HTPB based propellant with a solids loading of 82% ammonium sulfate. The images reveal a clear granularity, due to a heterogeneous distribution of the filler material. Two prominent features are observed, a coarse structure characterized by ‘holes’ due to lack of proton material, and a finer structure. The coarse ‘holes’ are attributed to particles or agglomerates of filler material

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and are up to several hundred micrometers in size. The finer structure is likely caused by smaller particles and this has been studied in more detail at 14.1 T (see below). In these samples a single proton T2 is observed (8 ms) and since the images are obtained with an echo time of 1 ms, the intensity fluctuations in these regions can not be attributed to small differences in transverse relaxation times. The appearance of both small and large heterogeneities is consistent with the bimodal distribution of the filler particles. The top left plane differs from the others in that it appears to consist of predominantly unfilled HTPB. This plane corresponds to the top of the sample and the lack of filler particles is a result of gravitational displacement, which occurred before the sample was fully cured. This phenomenon extends over approximately four planes from which a thickness of the boundary layer of about 600 pm is determined. Some of the larger voids are partially surrounded by a higher intensity rim. These rims are not caused by susceptibility artifacts, since they are observed both in the read and phase encoding directions. They indicate an increased proton density adjacent to the filler particles. Some of these features are revealed more clearly in the 600 MHz images, shown below. Note the excellent signal to noise of the images despite the 82% solids loading. Figure 12.3 displays planes from a 3D image obtained from a similar propellant sample, but with the addition of 6.5% (by weight) aluminum powder (5 pm particles). The images reveal a similar granularity caused by the larger filler particles. The aluminum particles are not individually resolved. The bright edge of the images is again caused by unfilled binder material on the top

of the sample, however, the sample was prepared in a different orientation than the previous sample. In addition to this bright edge, the lower two images display a high intensity region at the upper side of the sample. Such a phenomena may be caused either by a volume of unfilled or uncured HTPB, a concentration of plasticizer agent or it may be due to a susceptibility artifact caused by a magnetic impurity in the sample. The latter possibility was examined by rotating the sample in the magnet and acquiring a new image. In the case of a susceptibility artifact the phenomena will change, while in the case of unfilleduncured HTPB or plasticizer migration the spots will remain at the same place. From our experiments we have concluded that these phenomena can not be attributed to a susceptibility artifact and are due to regions with a higher proton intensity. This higher intensity is most likely caused by a higher local proton density, since the echo time of 1 ms is short compared to the transverse relaxation time of this sample.

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Compared to the sample without aluminum, some differences in the material packing are observed. In general we see a tighter packing, however with seemingly more gaps or holes, corresponding with regions from which HTPB is excluded. The size of these exclusions is approximately equal to those observed in the previous sample. It appears that the aluminum powder is finely and homogeneously distributed in the polymer matrix, whereas the holes are caused by regions of unmixed ammonium sulfate. Also note the ridge through the right two images in Fig. 12.3, perhaps caused by either a trace of HTPB or a small crack in the sample.

Fig. 12.3: Four planes from a 3D image of a HTPB based propellant with a solids loading of 82%. The image resolution is 35 pm x 35 pn; the plane thickness is 120 Fm. The bright edge is due to unfilled HTPB. The propellant is similar to that of Fig. 12.2, but for the addition of 6.5% aluminum powder.

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12.2.4 Imaging of an Aged Propellant Sample Besides the results on relatively freshly prepared samples described above, we have also examined an older piece of a related simulant. This explosive simulant consists of aluminum and ammonium sulfate filled HTPB and has a solids loading of about 80%. The images (Fig. 12.4) of this compound display a much less clearly defined granularity, resulting in a generally fuzzier image. In addition bright spots were detected in some of the planes, extending over several planes.

Fig. 12.4: Four subsequent planes from a 3D image of an aged, HTPB based propellant material. The image resolution is 35 x 35 x 120 pm3. The images display high intensity spots that are believed to be caused by plasticizer migration.

We have attempted to determine whether the bright spots, observed in the images of this aged sample, are caused by a susceptibility mismatch between an inclusion and the bulk material. However, images acquired after interchanging the phase and frequency

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encoding gradients display the bright spots in the same location, indicating that these spots are not due to susceptibility artifacts. Possible explanations are that these regions contain either unfilled binder material, or that they are pockets of plasticizer material, due to incomplete mixing or plasticizer migration. In an attempt to visualize these regions better we have resorted to three dimensional rendering, displayed in Fig. 12.5. The high intensity regions have a spherical appearance with a diameter of 200-400 pm. The spherical appearance might suggest a concentration of plasticizer component, since unfilled HTPB does not tend to form globular regions. It is possible that upon aging, voids develop in the sample, to which plasticizer migrates.

Fig. 12.5: Three dimensional image rendering of the propellant sample shown in Fig. 12.4, with the threshold adjusted in order to display only the bright regions shown in the two dimensional image planes.

12.2.5 Distinguishing Between Different Levels of Solids Loading An important issue in the characterization of propellant materials concerns the distribution of the filler material. In the previous section we already showed the occurrence of regions of unfilled binder material at the edges of the propellant samples. In this section we explore the possibility of using NMR imaging to distinguish between more subtle differences in solids loading.

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For this study a sample was prepared, composed of three cylindrical sections with solids loading of 78, 80 and 82%, respectively. A three dimensional image was obtained and is displayed in Fig. 12.6.

0

2

80

4

60

6 40

8 20

10 12

0

1

3

4

5

7

8

height (mm)

Fig. 12.6: Three dimensional image of a sample consisting of propellant material with three levels of solids loading. The figure on the right is a projection of the intensities of a 5 mm x 12 mm section of the image shown on the left.

The image in Fig. 12.6 clearly reveals the three different sections of the sample. The right plot displays a projection of the intensities of the image onto the vertical axis. The projection is obtained from a 5 mm wide extract of that image, so that the edges of the sample are not taken into account, and the intensities are normalized with respect to the highest data point. This projection clearly reveals the differences in proton density and therefore the differences in solids loading. The highest proton density and, therefore, the lowest solids loading in the center section of the sample. Whereas the proton densities in the top two sections of the sample, displayed in both the image and the projection, are distributed evenly over space, the proton density in the lower section, which is the part of the sample with the highest solids loading, decreases towards the bottom of the sample. We have examined this phenomena by testing the possibility that this decrease was due to RF inhomogeneity. However, by moving the sample to the center of the coil (at a location previously occupied by the middle section in Fig. 12.6) t h s decrease in proton density is still observed. We must, therefore, con-

157

12. Materials Imaging with Examples from Solid Rocket Propellants

clude that this phenomena is real, and that in this part of the sample a gradient in filler material exists. In an attempt to quantify the differences in proton densities and solids loadmg, regions of equal volume were extracted from the image of Fig. 12.6. We have examined the distribution in proton densities in each of these regions by displaying the data as histograms (Fig. 12.7).

B

I I ~

I

$50

$00

?SO

lo(

Fig. 12.7: Histogram extracted from equal volumes of the three sections of the image of Fig. 12.6. A, B and C correspond to the top, center and bottom sections, respectively.

The left two histograms display a more or less Gaussian distribution of the proton density around a mean value, whereas the right histogram, obtained from the lower section of the sample, deviates from this due to the gradient in filler material. If one extracts a smaller region with a more homogeneous proton density from the lower section of the image, then the histogram displays a similar distribution as those from the upper two sections. The mean values found from the histograms of the different sections of the sample are 700, 765 and 620 ('homogeneous' region) for the upper, middle and lower sections, respectively. In addition we have determined the average proton density in each of the regions. The values found relate as 691 : 749 : 526 (615), with the value in brackets obtained from the 'homogeneous' part of the lower section of the sample. It is clear from these results that we can accurately distinguish between different levels of solids loading and that even gradual differences, such as a gradient in the amount of filler material, can be detected. In order to relate these results to the amount of filler material in each section of the sample, additional information is needed such as the densities of the filler and binder material.

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12.2.6 Imaging of Propellants at 14.1T The 3T NMR images of the propellant materials were acquired at a planar resolution of 35 pm x 35 pm and they display the large and small voids, caused by the ammonium sulfate filler particles, which are present in a bimodal distribution. In addition, it seems that the images reveal a small scale, roughly periodic fluctuation of the proton density. In order to examine these findings in more detail, the samples were reexamined at a resolution of 8.5 pm x 8.5 pm x 45 pm and at a magnetic field strength of 14.1 T. A difficulty in increasing the image resolution is that this naturally decreases the volume of the voxel and hence the number of spins per voxel. All else being equal, this would lead to a decrease in the signal-to-noise ratio of the image. This loss is partially overcome by performing the imaging experiments at a higher magnetic field strength since the sensitivity of the NMR experiment scales with the field strength to the power 7/4. In this case, the approximately 40 fold decrease in voxel volume has been compensated by a nearly 5 fold increase in field strength and a higher efficiency detection circuit. Figures 12.8 and 12.9 show some planes from three dimensional images of the propellant samples corresponding to the samples shown previously in Figs. 12.2 and 12.3. The samples are contained in 1 mm 0.d. glass tubes and the experimental parameters are given in the figure captions. Not all of the images appear round, due to the presence of large filler particles at the edges of the sample.

Fig. 12.8: Planes from a 600 MHz 3D image of a HTPB based propellant sample. The in-plane resolution is 9 p m x 9 p m and the thickness per plane is 45 pm. The rectangles in the upper right image indicate the expanded areas discussed below. The 3D image was acquired with 128 x 128 x 16 data points, an echo time of I ms, repetition time 1 s, phase encoding time 0.5 ms, and the total experiment time was 10 hours. A gradient strength of 2.5 T/m and a receiver bandwidth of 125 kHz were used.

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Fig. 12.9: Four subsequent planes from a 3D image of similar HTPB based propellant, which in addition to ammonium sulfate contains aluminum filler particles. The images were obtained at 14.1 T. The in-plane resolution is 8.3 km x 8.3 pm and the plane thickness is 45 pm. The experimental conditions are similar to those listed in the caption to the previous figure.

The images clearly display the large filler particles in addition to individual ammonium sulfate crystals as small as 20 pm. Apart from these obvious features, the images are characterized by a very heterogeneous density distribution in between the filler particles with intensities ranging from near zero to approximately three times the nominal intensity, revealed in the images as bright spots. This heterogeneity may be caused by differences in the chemical composition of the binder material (resulting in different transverse relaxation times), by traces of unfilled binder material or by an uneven distribution of the small filler particles in combination with an averaging of the proton intensities over the thickness of the imaged planes. Images obtained from a sample of unfilled HTPB, however, display a very homogeneous density distribution and the short echo time used to obtain the propellant images eliminates the possibility of (strong) T2 weighting. A preliminary conclusion is that the heterogeneities observed in the propellant images are most likely due to the distribution of small filler particles. An interesting phenomena observed in the 125 MHz proton images is the appearance of a higher intensity rim around the larger filler particles. The origin of this phenomena is revealed in the high resolution images at 14.1 T and detailed by expanding regions of the images of Fig. 12.8. The images, shown in Fig. 12.10 and obtained by expanding and smoothing the original data, display the immediate surroundings of two filler particles found in the lower left corner of the original image. The expansions reveal a thin polymer film of about 10 - 30 pm surrounding the filler particles. The film closely follows the contour of the filler particle and is most likely caused by adhesion to the ammonium sulfate crystal.

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Fig. 12.10: Two expanded from the center image of Fig. 12.8, displaying the presence of a thin polymer film, surrounding the filler particles.

12.2.7 Conclusions By exploring in some detail the application of NMR imaging to rocket motor propellants we have attempted to document that the field is sufficiently mature to successfully tackle problems with length scales on the order of 5 to 100 pm. Many significant challenges remain, particularly being able to explore larger length scales for these studies and shorter length scales for process engineering.

Acknowledgements The authors thank Dr. T. Stephens and Dr. A. Wallner for the preparation of the propellant samples. This work was funded in part by the Department of Defense (SBIR N68936-96-C-0178), the National Science Foundation (DMR-9357603), the Whitaker Foundation and the National Institute of Health (ROI-GM52026, RR-00995).

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D.G. Cory, Annu. Rep. NMR Spectrosc. 24 (1992) 87. P. Bliimler and B. Bliimich, NMR-Basic Principles and Progress 30 (P. Diehl, E. Fluck and R. Kosfeld, Eds.), 1993.

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B. Bliimich and W. Kuhn, eds., Magnetic Resonance Microscopy, VCH, Weinheim, 1992.

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P.T. Callaghan, Principles of Nuclear Magnetic Resonance Microscopy, Oxford University Press, Oxford, 1991.

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E. Fischer, R. Kimmich and N. Fatkullin, J. Chem. Phys. 106 (1997) 9883.

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S. Gravina, and D.G. Cory, J. Magn. Reson. B 104 (1994) 53.

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A.A. Samoilenko, D.Yu Artemov, and L.A. Sibel'dina, JETP Lett. 47 (1988) 417.

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G.C. Chingas, J.B. Miller,andA.N. Garroway,J. Magn. Reson. 60(1984) 337.

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W. Kuhn, P. Barth, P. Denner and R. Muller, Solid State NMR, 6, (1996), 295

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L.H. Menvin, R.A. Nissan, T.S. Stephens and AS. Wallner, J. Appl. PolymSci, 62, (1996), 341

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129

Xe MRM Characterization of Pore Structures in Silica Aerogels

D. A4. Gregory, R. E. Gerald II, D. J. Clifford, and R. E. Botto

Chemistry Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439-4828, USA

Abstract In this work, we show that magnetic resonance microscopy (MRM) provides important new insights into the pore structure of silica aerogels. The use of xenon as a gaseous probe, in combination with spatially-resolved NMR techniques is demonstxated to be a powerful approach for characterizing these materials. In particular, this new approach offers unique information and insights into the nanoscopic pore structure and microscopic morphology of aerogels and the dynamical behavior of occluded adsorbates. MRM provides spatially-resolved information on the nature of the pore structure found in these materials. Dynamic NMR magnetization transfer experiments and pulsed-field gradient (PFG) measurements have been used to characterize exchange processes and diffusive motion of xenon in samples at equilibrium. Pseudo first-order rate constants for magnetization transfer among the bulk and occluded xenon phases indicate xenonexchange rate constants on the order of 1 s-l, for specimens having volumes of 0.03 cm3. PFG diffusion measurements show evidence of anisotropic diffusion for xenon occluded within aerogels, with nominal self-diffusivity coefficients on the order of D = 10 -3 cm%

13.1 Introduction Aerogels represent a new class of open-pore materials with pore dimensions in the nanometer range, typically between 2 and 50 nm, and are thus classified as mesoporous materials. In particular, silica aerogels have many remarkable properties, including extremely low densities (0.003 - 0.35 g/cm2), high thermal resistance, low refractive

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index and sound velocity, and high surface area. These unique properties allow for their use in many new applications such as insulated windows for solar applications, catalysts, gas separation media and Cherenkov counters [ 1-51, Silica aerogels have been synthesized using conventional sol-gel processing techniques from an ‘alcogel’ precursor followed by supercritical solvent extraction, a process which leaves the original structure of the gel virtually intact [6,7]. Understanding the phenomena that control pore structure is paramount to developing approaches for producing more uniform and precisely tailored microstructured materials. The inherent limitations of the various techniques used in the determination of pore structure of aerogels has left several important aspects of their structure unresolved. It is apparent that BET gas adsorption measurements do not account for the entire pore volume of aerogels [8]. Does the missing pore volume result from limitations of BET methods to account for the entire pore structure, or rather does it reflect on the complete ”openness” of the aerogel pore network? In this paper, we show that the combination of 129XeN M R spectroscopy and chemical-shift selective magnetic resonance microscopy (MRM) methods can resolve some of the important issues regarding the structure of silica aerogels. The use of xenon as a probe for aerogels is suitable for characterizing the pore structure and the steady-state spatial distributions of probe atoms in different physico-chemical environments. Dynamic N M R and diffusion experiments characterize the mobility and diffusive motion of xenon atoms in samples at equilibrium. Spatially-resolved N M R methods offer unique insights into the nanoscopic pore structure and microscopic morphology of aerogels, and the dynamical behavior of occluded atomic and molecular adsorbates.

13.2 Experimental Section 13.2.1 Sample Preparation A heavy-wall borosilicate glass sample tube was loaded with specimens of aerogel. The bottom of the tube was immersed in liquid nitrogen while the sample was under vacuum. Xenon gas was allowed to enter the tube to create 30 atmospheres pressure at room temperature. The tube was then flame sealed. Prior to seal-off under liquid nitrogen, a small

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amount of relaxation agent (0, gas) was added to the sample tube to enhance the spinlattice relaxation rate of 129Xenuclei. Three aerogel specimens were placed in this sample tube. The aerogel specimens measured approximately 3 mm x 3 mm x 3 mm in size. A second sample was prepared containing a single aerogel specimen, to which 20 atmospheres of methane gas was added.

13.2.2 NMR Parameters NMR spectroscopy and chemical-shift imaging experiments were performed at a field of 9.4 T (lH frequency of 400.6 MHz) on a Tecmag Libra system, which was interfaced to a Bruker Instruments three-axis, shielded imaging probe and BR-40 gradient amplifiers. At this field, xenon nuclei resonate at a frequency of 110.8 MHz. Ampules with a nominal length of 40 mm were placed in a home-built solenoid coil having a diameter of 9 mm and a length of 20 mm. The coil geometry (orthogonal to the main field) was designed to optimize both the filling factor and the fraction of the total signal due to occluded xenon. Care was taken to insure that all of the aerogel specimens were located inside the coil. A 90O-pulse width of 10 ps was employed in all experiments. Spin-spin relaxation time (Tz)measurements were performed using the standard Hahn spin-echo method [9]. Spin-lattice relaxation times ( T I )were measured using the inversion-recovery method [lo]. The diffusion coefficients were measured using the APGSTE sequence of Lecus et al. [ 111. Gradient strengths ranged from 0 - 20 G/cm in 1.54 G/cm increments. The other APGSTE parameters were 6 = 0.6 ms, A = 50 ms, t = 0.8 ms, tl = t2 = 0.1 ms. The diffusion coefficients were found by fitting the integrated peak intensities to: (13.1) where y is the magnetogyric ratio of the observed nucleus, D is the local apparent diffusion coefficient, gais the local applied gradient strength, P is a function of the acquisition sequence timing parameters, and A , is the equilibrium magnetization generated in the absence of diffusion-encoding gradients.

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13.2.3 Chemical Shift Imaging and Exchange Chemical-shift selective imaging was accomplished using the SECSI method of Gerald, et al. [12]. The selection sequence is 90°X- T~~ - 90°, - ~ ~ ~ 90" 1 1- Image. The resonance(s) from the spin(s) to be imaged is placed at (or near) resonance. Because the TI times of the three resonances in the sample were similar, it was possible to suppress two resonances simultaneously; this was accomplished by implementing the SECSI sequence in the appropriate fashion, as described below. The ~ ~ times ~ used 1 1in the experiments ranged from 0.7 - 0.9 s, and the recycle delay was 5 s. Images of either occluded or free xenon gas were obtained by setting the value of T~~ = 150 ms in the experiment. Selected images of the individual resonances of occluded xenon, at 52 ppm and 47 ppm, were obtained with values of T~~ = 910 and 1030 ms, respectively. After chemical-shift selection was achieved using the SECSI filter, conventional 2D spin-echo imaging [ 131 was carried out using 64 phase encoding steps; each step required 200 - 600 transients in order to obtain an adequatre S/N ratio. The time to echo zE = 2.8 ms . The in-plane pixel resolution is 420 pin x 420 pm. Slice selection was accomplished using a sinc 90" pulse in place of the third hard 90" pulse in the SECSI sequence. Slices were taken perpendicular to the main axis of the superconducting magnet. Magnetization transfer experiments were performed using a simple pulse sequence comprised of three sequential 90" pulses, analogous to the SECSJ sequence described above. Following the second 90" pulse, magnetization vectors of spin ensembles with differing frequencies become aligned antiparallel along the direction of the z-axis. The variable delay period following the second 90" pulse allows transfer of spin magnetization; a third 90"-readout pulse was used to record the signal

13.3 Results and Discussion The 129Xespectrum of a high-pressure sample containing 30 atmospheres of xenon gas is shown in Fig. 13.1. The chemical shift reference, 6 = 0 ppm, is for pure xenon gas extrapolated to zero concentration. The resonance at 17 ppm corresponds to free xenon gas while the two smaller resonances at 46 and 52 ppm result from occluded gas as described below. The 129Xespin-lattice relaxation times ( T I )ranged from 1.2 - 1.6 s for

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the three resonances. The similarity of the Tls suggest that enhancement in the relaxation rates due to 0, gas was reasonably uniform throughout the sample; the Tls were also measured to determine the T~~~~values to be used in the SECSI experiments. On the other hand, the spin-spin relaxation times (T,) of the resonances were very different. The T2 of the signal for free xenon gas was found to be considerably longer than T2s for occluded xenon: 40 ms for free xenon gas versus 10.9 and 4.9 ms for the occluded xenon resonances at 46 and 52 ppm, respectively.

3 I

I

PPm

160

L I

140

I

50

b

I

Fig. 13.1: Xenon spectrum of the high pressure sample; 64 scans were averaged. The reference is to xenon gas extrapolated to zero pressure.

2.3.1

NMR Imaging

129Xechemical-shift MRM provides the first conclusive evidence of a direct correlation between a,, and the location of xenon within a microporous material. Figure 13.2 shows 129Xe imaging results for the high-pressure xenodaerogel sample. Slices of SECSI images of occluded and bulk-phase xenon gas are shown in Figs. 13.2A and 13.2B, respectively. Chemical-shift selected spectra are shown directly below each of their respective images. A photograph of the three aerogel specimens sealed inside the highpressure ampule is shown in Fig. 13.2C for comparison.

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Comparing the photograph with the NMR image of occluded xenon clearly reveals a general overall correspondence between internal structural features and the specimen morphologies. It is apparent from viewing the images that the adsorption properties of xenon are very different in the three specimens. For instance, the middle image appears to be smaller and is considerably less intense than the image directly to its right, even though the two physical specimens are comparable in size. In the aerogel specimen on the right, the signal appears to be most intense toward the center. The image on the left is intermediate in intensity and is also smaller than the specimen size would suggest. Figure 13.2D represents the composite image from both experiments, in which Figs. 13.2A and 13.2B have been added together. The addition has been performed in a manner as to allow a direct comparison between signal intensity resulting from free and occluded gas. The most striking result is the observation that there are entire regions devoid of xenon signal, in paticular, in the specimens at the left and center. In these regions little or no xenon gas has been adsorbed. These regions tend to be along the edges of the aerogel specimens. Moreover, it is apparent that the concentration of xenon adsorbed in the right sample is significantly greater than its concentration in the free gas. It was possible to select the different occluded xenon resonances in the imaging experiment. This is demonstrated in Fig. 13.3; where 13.3A shows that xenon at 6 = 52 is contained in the middle sample while 13.3B shows that xenon with 6 = 47 is consistent with xenon in the other two aerogel specimens. This unique, spatially-resolved information has important implications about the pore structure of aerogel networks, and clearly illustrates that the two xenon chemical shifts are associated with entirely different pore structures. The images presented in Figs. 13.2 and 13.3 illustrate the ability of the xenon MRM method to study heterogeneity associated with the pore structure of aerogels. For instance, the xenon signal in the aerogels is clearly heterogeneous as shown in Fig. 13.2C. The signal intensity of the free xenon is relatively uniform throughout the 1-mm slice. This is not true of adsorbed xenon gas that has been occluded in the specimens. Loss of signal near the edges of the left specimen might be attributable to exchange between occluded and free xenon. However, notice that loss of signal intensity is not symmetric, as would be expected if a uniform halo were to be seen around the aerogel specimens. In fact, this would be expected if signal loss were due entirely to gas exchange. Also, loss of signal is much more extreme for the two specimens on the left and at the center of Fig. 13.2D. Thus, it is more likely that adsorption of xenon varies significantly within different regions of aerogels, indicating a heterogeneity in their pore structures.

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A

loL wm

wm

C

40

D

Fig. 13.2: Slices (thickness of 1 mm) of chemical-shift selective images; in-plane resolution is 420 pm. Lighter pixels indicate more signal intensity. (A) Image of the xenon adsorbed inside the aerogel samples. Below the image is a spectrum acquired with the identical chemical shift selection sequence as was used to record the image. Signal from the larger peak at 17 ppm has been suppressed. The spectrometer frequency was set to the resonance at 46 ppm. (B) Image of the xenon gas outside the aerogel samples. Signal from the resonances at 46 and 52 ppm has been suppressed as shown in the spectra below the image. The spectrometer frequency was set to the resonance at 17 ppm. (C) Photograph of the high pressure sample showing the three aerogel samples. Opaque and translucent regions appear brighter in the photograph. Transparent regions appear dimmer. (D) Image showing the direct addition of the data shown in (A) and (B). Signal intensity can be compared directly pixel by pixel. Black regions show were there is apparently no detectable signal (the signal intensity is below the noise threshold).

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A

Fig. 13.3: Slices of chemical-shift selective images: (A) Signal from the resonance at 52 ppm has been selected while the other resonances have been suppressed; (B) Signal from the resonance at 46 ppm has been selected.

More importantly, MRM data appears to be useful for understanding differences in the physical properties of aerogels. In particular, we have been able to correlate the NMR parameters to optical features of the specimens. Three distinct regions in the specimens can be clearly distinguished on the basis of differences in the xenon NMR parameters, and imaging facilitates their visualization. Recall that the middle specimen appears translucent, while the other two specimens are largely transparent, and that the specimen on the left has translucent regions at two of its edges (see Fig. 13.2C). Adsorbed xenon gas in the middle, more translucent specimen is found to resonate at a higher frequency than xenon adsorbed in the other two specimens, and is readily distinguished in the image depicted in Fig. 13.3A. The regions highlighted in Fig. 13.3B constitute a second type of pore structure associated with optical transparency. The third pore regime is defined by regions where no NMR signal is found, see the center and left specimens in Fig. 13.2D. These regions are apparently inaccessible to xenon and are consistent with a collapsed pore network, which may have resulted from physical damage to the specimens. The lower signal intensity of xenon in the middle specimen can be partly accounted for by T2 weighting effects (see beginning of section 13.3). To quantify this effect, we calculated the integrated signal intensity for 25 pixels near the center of the three aerogel

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images in Fig. 13.2A. The T2 relaxation time of xenon inside the translucent specimen is less than half that of the transparent samples. However, this difference does not completely account for the entire reduction of signal intensity that is observed; therefore, we can conclude that less xenon is adsorbed in the middle specimen. The results obtained thus far indicate that the pore structures in translucent and transparent specimens are fundamentally different. The shorter T2 relaxation time of xenon in the translucent specimen (middle) is consistent with its having a more disordered pore network. Greater disorder would tend to induce nanoscopic magnetic field gradients at the interfacial regions of the walls that would enhance the relaxation rate due to bulk magnetic susceptibility anisotropy. The observation of a chemical shift to lower field is consistent with the average pore size being smaller for the translucent specimen. Furthermore, the loss of signal intensity in the translucent regions at the edges of the left specimen suggests that several of the pores have been closed off to xenon gas. We surmise that the specimen at the left of Fig. 13.3 had been physically damaged and may have been, at one time, more similar to the transparent specimen located at the right. On the other hand, the translucent specimen in the center has a characteristically different pore network to those of the other specimens, and its pore structure is likely to be a direct consequence of different processing conditions.

13.3.2 Xenon Atom Exchange The selective chemical-shift imaging experiments afford us with the opportunity to investigate exchange of xenon atoms between the free gas and occluded aerogel phases. Germane to this is the issue that NMR images obtained through the application of the SECSI pulse sequence requires a finite period of time to select one of the 129Xe spin reservoirs. During the time scale of the SECSI experiment, the negatively (bulk-xenon phase) and positively (occluded phase) generated spin magnetizations admix via translational diffusion of xenon atoms between phases. Regions near the surface of the specimen tend to experience the greatest degree of mixing; consequently, positive spin magnetization in those regions should be diminished via exchange. In order to quantify the rate of the exchange, magnetization transfer experiments were carried out at room temperature on the high pressure sample, see Fig. 13.4 below. A 29% decrease in the signal intensity of occluded xenon was observed during the T1-null evolution period in the SECSI experiment. This decrease in signal intensity can be accounted for by assuming a simple, single-atom transfer mechanism between xenon reservoirs.

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D.M. Gregory, R. E. Gerald 11, D. J. Clifford, and R. E. Botto

Xenon G a s

I

0

Occluded G a s

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.5

4.5

5.5

t i n e (s) Fig. 13.4: 129Xe NMR magnetization transfer experiments as a function of delay time. The top trace represents the time evolution of the resonance (6 = 0 ppm) corresponding to free xenon gas; the lower traces are the time evolutions of occluded xenon resonances at 46 and 52 ppm.

From NMR magnetization transfer experiments on specimens with nominal volumes of 0.03 cm3, we estimate that about 29% of the xenon atoms in aerogels were exchanged on the time scale necessary to perform the chemical-shift imaging experiment. Further study of xenon exchange phenomena under non-equilibrium conditions may illuminate the velocity and composition distribution profiles in flow of xenon near the surface of aerogels, and thus can in the future be used to better define mixing efficiencies responsible for gaseous diffusion processes in these systems.

13.3.3 Estimation of Pore Size and Porosity Several authors have attempted to correlate xenon chemical shifts with pore size and shape [14-181. Fraissard and coworkers studied several microporous zeolites [16]. They were able to find a simple relationship between the mean free path of a xenon atom

13. 129XeMRM Characterization of Pore Structures in Silica Aerogels

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inside a pore and the 129Xechemical shift extrapolated to zero pressure. In a later paper by the same group [19], it was shown that Fraissard’s empirical relationship did not apply in the case of mesoporous aerosils. Unexpectedly, the xenon shift was found to decrease slightly with increasing xenon pressure. Our xenon NMR results on silica aerogels are strikingly similar to those found previously for aerosils. A plot of the chemical shift of xenon in aerogels over a range of pressures from 100 to 1500 torr reveals a slight decrease in the 129Xeshifts of ca. 10 ppm. BET isotherm measurements on our samples indicate that they exhibit a narrow pore-size distribution, with an average pore diameter of ca. 20 nm. Extrapolating the 129Xeshifts to zero xenon density grossly underestimates the pore size of aerogels, by a factor of about 20. Perhaps the conventional approach of correlating 129Xechemical shifts to pore size is generally not valid for mesoporous systems. Apparent limitations in the use of Fraissard’s empirical relationship have prompted us to consider an alternate approach for investigating pore size and porosities of aerogels. Recently, Zeng and coworkes [20] derived a mathematical relationship for the restricted motion of gases confined within a solid matrix, in order to assess the thermal conductivity properties of gases in confined geometries. In addition to collisions between gas atoms, their approach accounted for collisions of the gas with the solid matrix. They applied the basic principles of the kinetic theory of gases to determine the mean free path, i.e. the average distance traveled between successive collisions of gas atoms. Equation (13.2) below describes the mean free path of gas molecules in free space:

(13.2)

The fundamental transport relation had to be modified to include the total scattering cross-section (SCS) relevant for gas confined within a restricted pore network. The total SCS is comprised of both the SCSs of the solid particles and gas atoms per unit volume. For a spherical particle, this relationship can be expressed as: (13.3)

where ng is the number density of gas atoms, dg is the diameter of a gas atom (in our case xenon), Ss is the specific surface area per unit mass of the network, pporis the density

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D. M. Gregory, R. E. Gerald II, D. .I Clifford, . and R. E. Botto

and II is the porosity. Equation (13.3) predicts that the first term in the denominator is dominant at sufficiently high gas densities, > 3 bar, and that the mean free path is determined primarily by collisions between gas atoms. At gas densities well below 1 bar, the latter term dominates, and the mean free path of gas is determined exclusively by collisions with the pore walls, reaching an asymptotic limit that defines the pore dimension. Based on the approximate expression for diffusivity of a gas in a confined space derived from Fick’s law, ie. D = C 1, II, and a derivation of the mean free path in free space, where Do = C lmo, one can derive an expression for the porosity in terms of the diffusion coefficients as follows:

(13.4)

At sufficiently high xenon gas pressures, 1, = lm0 (eqns. 13.2 and 13.3) and the porosity simply becomes the ratio of the diffusion coefficients, ie. II = D/D,. Using the value of the porosity determined in this manner, one is then able to estimate an extrapolated value of the mean free path, where Da is the limiting value of the diffusion coefficient, to zero xenon pressure. Hence, the pore size of the aerogel is obtained using the following relationship: 1, =-3 Da

cn

(13.5)

PFG diffusion measurements were carried out at several pressures of xenon gas. The x-gradient is aligned along the direction of the long axis of the sample tube, and the zgradient is aligned along the direction of the superconducting magnetic field axis. The data are summarized in Table 13.1. Diffusion coefficients measured by the APGSTE method are the same in all three directions for free gas, within an experimental error of 0.1 cm2/s. On the other hand, diffusion coefficients measured along the three spatial axes for the resonance of transparent regions display anisotropic behavior, which suggests that the pore network structure is fractal in nature, and thus does not assume a simple spherical geometry.

*

13. 129XeMRM Characterization of Pore Structures in Silica Aerogeis

175

Table 13.1: Xenon Self Diffusion Coefficients (cm2/s) at Various Pressures -

Xenon Pressure (bar)

D , Bulk Phase

D , Occluded Phase

1.3

49

14

3.0

27

11

5.1

18

8.0

30

G, 1.7, Gy 1.7, G, 1.6

G, 1.1, Gy 1.4, G, 1.2

Using eqn. (13.4), a value of 0.71 is estimated for the porosity of the aerogel from the diffusion coefficients, D and Do, obtained at 30 bar. Estimates of mean free paths for xenon in free space and in aerogels at various pressures are calculated from the data in Table 13.1, according to eqns. (13.2) and (13.5) for PFG data, and to eqn. (13.3) for BET data. The results are plotted in Fig. 13.5 below. L o g a r i t h c plots of the data show the anticipated trends [20]; a linear log-log relationship is observed for the pressure dependence of lmo, and the departure from linearity to a limiting value is seen for 1, at low xenon pressures. Extrapolation of the PFG data (eqn. 13.5) to low xenon pressures yields a limiting value for the mean free path, and hence, an estimate of about 33 nm for the pore size. PFG data yield substantially larger values for the porosity and mean free path than do BET adsorption measurements, which afford values of approximately 0.46 and 6 nm, respectively. The generally larger values obtained from NMR diffusion measurements are concordant with previous experimental observations that the total pore volume of aerogels shrinks considerably, as a direct consequence of liquid nitrogen condensation in the pores during BET measurements [21]. At present, limited sensitivity of 129XeNMR has precluded PFG measurements to be carried out at lower pressures. Future work will involve performing these experiments using enriched or hyperpolarized xenon gas, in an attempt to extend the present studies to the low pressure regime.

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D. M. Gregory, R. E. Gerald II, D. J. Cl@ord, and R. E. Botto

- e - BET Aerogel

- - - - - - - --c

0.1

-

1

10

100

Pressure (bar)

Fig. 13.5: Variation in Mean Free Path for Free and Occluded Xenon with Xenon Pressure.

Acknowledgement The authors would like to thank David Noever for providing us with aerogel samples and Marshall Space Flight Center for partial support. This work was performed under the auspices of the Office of Basic Energy Sciences, Division of Chemical Sciences, U.S. Department of Energy, under contract number W-3 1-109-ENG-38.

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A. J. Hunt, K. D. Lofftus, ”Process Considerations in Monolithic Aerogels,” Better Ceramics Through Chemistry IIZ, D. E. Clark, and D. R. Ulrich (Eds.), Materials Res. SOC.121, Pittsburgh, 1988, p. 679-684.

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K. D. Lofftus, K. V. S. Shastri, and A. J. Hunt, Proc. Adv. Mater. Sot. SME (1990) 229.

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E. Anglaret, A. Hasmy, E. Courtens, J. Pelous, R. Vacher, J. Non-Ctryst. Sol. 186 (1995) 13 1.

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A. J. Lucas, S. J. Gibhs, W. G. Jones, M. Peyron, J. A. Derbyshire, and L. D. Hall, J. Magn. Reson. A 104 (1993) 273.

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R. E. Gerald 11, A. 0. Krasavin, R. E. Botto, J. Magn. Reson A 123 (1996) 1.

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P. T. Callaghan, Principles of Nuclear Magnetic Resonance Microscopy, Clarendon Press, Oxford 1991.

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J. A. Ripmeester, J. Magn. Reson. 56 (1982) 247.

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J. Demarquay and J. Fraissard, Chem. Phys. Lett. 136 (1987) 314.

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J. Am. Chem. Soc. 110 (1988) 4465.

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W. C. Comer, E. L. Weist, J. Fraissard, T. Ito, Q . Chen, and M. A. Spinguel-Huet, Int. Con! Fundam. Adsorpt., A. B. Mersmann and S. E. Scholl (Eds.), AIChE, New York, N. Y . , 1991,977.

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S. Q. Zeng, A. Hunt, and R. Greif, J. Non-Cryst. Sol. 186 (1995) 264.

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14. NMR Imaging of Mechanically Treated Polymers B. Traub, S.Hafner, D. Maring, H. W.Spiess MPI fur Polymerforschung, Postfach 3 148, D-5502 1 Mainz, Germany

Abstract The use of NMR imaging techniques for probing local chain orientation and dynamics in mechanically deformed polymers is shown. A conventional chemical-shift imaging sequence is used for the detection of lamellar orientation in a soft solid (PS-PI diblock copolymer) that has been subject to a shearing procedure. For the investigation of more rigid polymers such as polycarbonate, a 2D-FT magic-echo imaging sequence is presented, that has been supplemented by a relaxation-filter sequence for mobility contrast. The sequence is applied to polycarbonate samples which have been stretched under different experimental conditions. Characteristic regions of chain immobilization are distinguished that reflect the corresponding mechanical treatment.

14.1 Introduction Although the potential of NMR imaging in materials science was recognized relatively early, its application was for a long time hampered by the difficulties related to the broad NMR lines found in materials [ 1-31. As a direct consequence of this line-broadening, a severe degradation in the spatial resolution is found when applying conventional imaging techniques. For rigid solids, these techniques which usually rely on Hahn spin echoes or gradient echoes even fail completely. In this case, solid-state imaging techniques have to be applied where the broad lines are dealt with either by taking advantage of the extremely strong gradient found in the fringe field of super-conducting magnets [4-51 or by using line-narrowing techniques [6-151. In particular multiple-pulse line-narrowing techniques [7-151 and constant-time phase-encoding techniques have been successfully

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B. Truub, S. Hufner, D. Muring, H.W. Spiess

applied in the latter case [15-201. The most promising variants of these two techniques are those based on the magic-echo sequence as the basic building block [211. Another point delaying the application of N M R imaging to materials is the relatively modest resolution which is limited to about (10 ~ m for) signal-to-noise ~ reasons. Such a spatial resolution is often not sufficient for resolving morphological structures in materials and certainly cannot be compared with the resolution achievable by other microscopic techniques such as light or electron microscopy. On the other hand there is a considerable number of applications in materials science for which such a high resolution is not required whereas the non-invasiveness and the spectroscopic selectivity provided by

N M R imaging are invaluable advantages. For instance, the ingress of liquids in a solid can be conveniently investigated by N M R imaging since it allows to acquire selectively the image of the liquid [22,231. Also processes such as the polymerization [24,25] or the swelling of polymers [26] can be monitored in situ using relaxation times as contrast parameters. Apart from monitoring processes, also the investigation of the spatial distribution of microscopic material properties by N M R imaging is of interest. The material properties to be investigated are probed by a filter sequence for parameter contrast or acquired in an additional spectroscopic dimension. The homogeneity of the crosslink density [26,27], the orientation of polymer chains [28,29] and oxidative aging [30] of materials have been investigated. In some cases even images of the corresponding material parameters could be derived from the N M R parameter images [27,29,30].

In samples with a homogeneous distribution of a given material property, an inhomogeneity can be created by imposing external influences [ 13,15,29,31]. The resulting spatially inhomogeneous distribution of the investigated material property then represents not only the external manipulation but also the answer of the system, thus providing valuable information on the investigated material properties. Because of the manifold of possibilities to treat samples, a wealth of applications of NMR imaging for material testing can be envisioned. In this contribution we confine to the investigation of mechanically deformed polymer samples, both, soft and rigid solids, and apply the two strategies of chemical-shift imaging and parameter-selective imaging.

14. NMR Imaging of Mechanically Treated Polymers

181

14.2 Chemical-Shift Imaging in Sheared Polymers: Orientation Distribution 14.2.1 Sample Preparation Lamellar diblock-copolymer systems are known to form polydomain structures [32]. When subjected to shear flow above the glass-transition temperature of both blocks and below the order-disorder transition temperature (ToDT), these systems can be turned to a single-domain structure where all the lamellae are oriented in the same direction [33]. Using large oscillatory shear flow, one can produce two different macroscopic orientations depending on the shear frequency, the shear amplitude and the temperature [34]. Both orientations are perpendicular to each other as is known from Small-Angle X-ray Scattering (SAXS) measurements. In the so-called intermediate frequency regime and with a plate-plate shear geometry where the strain amplitude varies linearly with the radius, it is possible to generate both orientations within a sample: one with low shear amplitude near the middle and the other with higher amplitude near the rim of the disk. The sharpness of the cross-over between the two orientations depends on the applied frequency and the temperature.

14.2.2 Experimental and Results For the investigation of the lamellar orientation in dynamically sheared polystyrenepolyisoprene (PS-PI) diblock copolymers, a conventional spin-echo imaging technique is applied. Figure 14.1 shows the chemical-shijit imaging scheme used in this investigation. It consists of a 2D spin-echo technique with spatial encoding by two phase-encoding gradients. No gradient is applied during the acquisition so that the full chemical-shift information is available in the direct dimension. The experiments have been performed on a Bruker DSX-300 spectrometer using a conventional Bruker micro-imaging system with microprocessor-controlled gradient driver and a standard wide-bore micro-imaging probe. A solenoid coil with 5 mm inner diameter was used with a 90O-pulse length of 5 p.The maximum gradient strength was 480 mT/m. The gradient was stepped by 75 steps in the first and 150 steps in the second dimension leading to a field of view of 15 mm and 7.5 mm, respectively. The spatial

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resolution thus was (100 pm)2. Four scans were added with a repetition time of 1.7 s resulting in a total experiment time of 21 hours. Before the imaging experiment, spin echoes were acquired for an oriented PS-PI diblock copolymer with lamellar orientation perpendicular and parallel to the magnetic field. For comparison, also the echo of an untreated sample with isotropic orientation of the lamellae was acquired. The acquisition parameters were chosen such that only the more mobile polyisoprene component contributes to the signal. From the decay of the echoes, IH-NMR spectra are evaluated (Fig. 14.2b). They are found to be shifted with respect to each other due to susceptibility effects which depend on the lamellar orientation. Although this shift is relatively small compared to the linewidth, it can be used as a contrast parameter in the imaging experiment.

90,

\

180"

I

Fig. 14.1: Pulse sequence used for chemical-shift imaging of PS-PI diblock copolymers. The sequence consists of a conventional spin-echo sequence with two phase-encoding gradients. For the spectroscopic information, the echo decay is acquired. No slice selection was necessary since the samples consist of thin polymer stripes.

For the imaging experiment, the pulse sequence shown in Fig. 14.1 is applied to PSPI diblock copolymer samples which have been dynamically sheared as described above and thus show regions of different orientations. Strips are cut along the diameter of the disk-shaped samples which have been used during the shearing process (see Fig. 14.2a). Figure 1 4 . 2 ~shows the chemical-shift image of such a strip which has been prepared such that the transition between the two orientations takes place within a relatively small

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region (so-called "sharp transition"). An additional PS-PI strip in which the lamellae are fully oriented parallel to the magnetic field has been placed on top of the investigated sample as a reference. Figure 14.2d shows a sample which has been sheared under somewhat different conditions so that now the transition region is larger compared with those of the previous sample ("smooth transition"). This is clearly reflected in the corresponding chemical-shift image (Fig. 14.2d). N M R imaging thus can serve as an alternative or a supplement to Small-Angle X-ray Scattering (SAXS) for the study of blockcopolymer samples that have been prepared under various shearing conditions. In comparison to SAXS investigations, where the sample has to be scanned point by point by a beam of about 1 mm diameter, N M R imaging provides a better spatial resolution.

parallel

V

b 4 perpendicular 20

I

q

in 3 3

10

0

-10 -20

I-4

m

3 3

Fig. 14.2: a) Sketch of the sample. The orientation of the lamellae in the different regions are indicated b) Proton spectra acquired in a test sample with isotropic orientation of the lamellae (gray line) and in a sample with the orientation of the lamellae perpendicular (solid line) or parallel (dashed line) to the magnetic field. There is a small chemical-shift difference visible in the three spectra which can be used as an image contrast. c) Chemical-shift image of a sample which has been sheared such that the transition between both orientations takes place within a small region (sharp transition). As a reference, a strip with parallel orientation is shown on top of the investigated sample. d) Chemical-shift image of a sample that has been treated such that the transition as described in Fig. 1 4 . 2 ~ takes place over a larger region (smooth transition). The intensity scale in both images corresponds to a chemical-shift range of 1.6 ppm.

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14.3 Parameter-SelectiveMagic-Echo Imaging in Drawn Polymers For more rigid solids such as those investigated in the following, conventional imaging techniques fail and solid-state NMR imaging techniques have to be applied. As already stated above, the problems related with the broad lines of rigid solids can be solved using extremely strong gradients or by applying line-narrowing techniques. We confine to the latter case and concentrate in particular on techniques based on the magic echo. Two variants are distinguished [21]: the first is a multiple-pulse imaging technique [9-151 with the magic sandwich sequence [35-371 as the basic cycle, while the second is a constant-time phase-encoding technique [ 15-20]. Both have been extensively treated theoretically [17,211 using density-operator formalism in the tilted rotating frame. Here we refrain from such an extensive treatment and analyze the technique in a more intuitive way using basic average Hamiltonian theory [38] in zero-order approximation.

14.3.1 Principle of the Magic-Echo Technique Figure 14.3 shows the basic magic-echo sequence. The 90°, excitation pulse is followed by a free-evolution period of duration T, in which the coherences dephase in the presence of the dipolar Hamiltonian HD and the Hamiltonian H, which is linear in the spin operators. It represents the chemical-shift Hamiltonian and the magnetic-field inhomogeneity, for instance the applied gradient. The free-evolution period is followed by the so-called magic-sandwich sequence. As will be outlined in more detail below, the dipolar Hamiltonian is transformed by the magic-sandwich sequence to H', = -1/2 HD while H, = 0. The dipolar dephasing of the coherences during the free-evolution period T is therefore refocused during the first half of the magic sandwich. The coherences then dephase again in the second half but now with the dipolar Hamiltonian -H,/2. In the free-evolution period following the magic sandwich, the coherences thus rephase again under influence of the normal dipolar Hamiltonian H,. For the full cycle, the average dipolar Hamiltonian thus vanishes and at total time 67 the magic echo appears. The magic echo can be spatially encoded by applying gradients during the two freeevolution periods. The gradients are preferentially applied in form of gradient pulses or, if fast switching is not possible, left on during the whole sequence. In the latter case one

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has to assure that B , is sufficiently strong to dominate the influence of the field gradient

for the dimensions of the sample. Then the Hamiltonian corresponding to the gradient is averaged to zero dusing the magic-sandwich. Because of the two evolution periods, howeves, the magic echo is spatially encoded by 27 y G z , where y is the magnetogysic ratio, G the applied gradient strength and x the spatial coordinate.

90;

90;

X

90;

90;

90;

-x

90%

90;

Fig. 14.3: Magic-echo sequence with the Hamiltonian states for the description in terms of zeroorder average Hamiltonian theory. The toggling-frame states of the dipolar Hamiltonian and the spin operators are indicated. In the blow-up, the x-burst pulse is divided into a series of 90°x pulses in order to allow a convenient description in terms of toggling-frame states. More details on the analysis are found in the text.

For a deeper understanding of the properties of the magic sandwich sequence, we now analyze it in more detail in terms of basic zero-order average Hamiltonian theory (see [35] for a brief introduction). The corresponding spin-operator states (toggling-frame states) that determine the relevant Hamiltonians for the different time intervals are given in Fig. 14.3. The sequence starts with the operator I, and the usual dipolar Hamiltonian

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(14.1)

112

where DG = po Ii 147crij3 is the dipolar coupling constant, ei,is the angle relating the internuclear interaction vector rij to the magnetic field direction, 11, I, are spin operators and the subscript zz indicates that the spin-operators components I,,, I,, (a = x,y,z) in the dipolar Hamiltonian eqn. (14.1) are aligned in z direction of the spin space. The chemical-shift or off-resonance Hamiltonian is given by H, = o I, where o is the frequency offset to the transmitter frequency. The excitation 90°, pulse (dashed) creates transverse magnetization and thus is not considered for the determination of the average Hamiltonian. The magnetization evolves for a time T under the dipolar Hamiltonian H,, and the Hamiltonian H,. After the time T, the 90°, sandwich pulse is applied and transforms I, to I,. The continuous burst x-pulse of the magic sandwich now is treated by dividing it into a series of 90°, pulses. As indicated in the blow-up below the magic-echo sequence (see Fig. 14.3), these virtual 90°, pulses with finite pulse widths (gray lines) are approximated by 6-pulses placed in the middle of the original pulse. This is a reasonably good approximation, if the excitation of double-quantum coherences during the pulses is avoided. Rules for canceling such undesired terms are described for instance in Ref. [36]. As can be easily checked, these rules are fulfilled in our case so that in a sufficiently good approximation the x-burst pulse can be approximated by a series of 9O0,-6-pulses spaced from each other by the width of the original pulse. These 6 pulses now flip the toggling-frame states as indicated in the blow-up of Fig. 14.3. The chemical-shift Hamiltonian for a given time interval is proportional to the spin-operator state that governs this interval. For determining the average chemical-shift Hamiltonian of the burst pulse, we simply have to add the corresponding toggling-frame states, i.e. I, - I, - I, + I, = 0. Thus, during the sandwich pulse, the chemical-shift Hamiltonian is averaged out. For the dipolar Hamiltonian which is bilinear in the spin operators, we obtain 2 H, + 2 H, were x and y indicate the corresponding toggling-frame states I, and I, that enter the dipolar Hamiltonian (compare eqn. (14.1)). We now use the so-called magic-zero condition H,, + H, + H,, = 0, which can be easily verified by writing the three states of the dipolar Hamiltonian eqn. (14.1) with the corresponding spin states I,, I, and I,. Thus, we obtain: T (2H, + 2Hyy)= T (-2Hzz)=4~(-H,d2). Consequently, the evolution during the burst pulse takes place under an average dipolar Hamiltonian which is scaled by a factor -112. The sandwich -y-pulse then flips back the

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operator I, in I, and the evolution in the last z interval takes place under the conventional dipolar Hamiltonian H, = Hzz. For the full magic-echo sequence, the dipolar Hamiltonian thus vanishes, while the encoding by a gradient which is applied during the two free-evolution intervals is preserved.

14.3.2 2D-FT Magic-Echo Imaging Scheme Compared with conventional multiple-pulse sequences, the magic-echo sequence has two main advantages with respect to imaging. First, since the sequence in principle allows the complete refocusing of the dipolar interaction, the z intervals for the encoding of the spatial information can be chosen to be relatively long compared with the corresponding intervals of a conventional multiple-pulse sequence. Second, in conventional imaging sequences it is assumed that the evolution of the coherences under the chemical-shift can be neglected for the time between two pulses of a pulse cycle. In this way an effective axis is defined around which the average chemical-shift evolution is assumed to take place for a cycle. However, when applying strong gradients during selected intervals of the sequence, the evolution of the coherences between two pulses cannot be neglected anymore and this approximation breaks down. In the case of a magic-echo sequence this problem does not arise, since the coherences are evolving freely for all times around the corresponding axis of preference, that is, the B, direction during the free-evolution periods and the €3, direction during the magic sandwich. It is therefore not necessary to neglect the chemical-shift evolution for any of the time intervals z. Thus, in the case of magic-echo based sequences, from this point of view no limitations apply to the strength of the gradient or the length of the encoding intervals. As already stated, there have been two approaches to magic-echo imaging of solids based on frequency- and phase-encoding. Both now are combined to the 2D Fourier imaging sequence shown in Fig. 14.4 and supplemented by a filter sequence for relaxation contrast. After this filter sequence, which will be discussed later, transverse magnetization is present which dephases under the influence of the dipolar interaction. Applying the magic-sandwich sequence this dephasing is refocused. In the multiple-magic-echo train during the time t2 this refocusing takes place several times resulting in a final magic-echo at the end of the t2 interval. In principle, the intensity of this echo corresponds to the full initial magnetization, however, due to incomplete refocusing (finite

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B , -strength, misadjustments,...) and relaxation effects, a certain decay occurs during t2. Applying a phase-encoding gradient during the free-evolution intervals of the sequence, a spatial encoding in the indirect dimension takes place [16-171. It is essential for the application of such phase-encoding techniques for the imaging of solids, that the spatial encoding is achieved by incrementing the gradient strength and not the time T. Then the decay due to incomplete refocusing is not sampled which results in an efficient effective line-narrowing. Since the Hamiltonian that corresponds to the gradient is the only influence which is varied in successive acquisition steps of the experiment, it represent the only encoding of the magic-echo amplitude. Following the phase-encoding, the signal is acquired during the time t3 under the influence of a read gradient which is applied in the free-evolution periods of a multiplemagic-echo train [9-151. Now, however, the decay of the magnetization by incomplete refocusing and relaxation is acquired. For the direct dimension therefore a satisfactory multiple-pulse adjustment is required. In order to exclude contributions from the chemical-shift interactions, the phase of the last sandwich pulse is changed from -y to y which leads to a refocusing of the chemical-shift contribution within one magic-echo cycle. To avoid the elimination of the gradient encoding (which has the same form as the encoding by the chemical shift), the gradient is alternated during two successive free-evolution intervals [ 121. A similar procedure for the refocusing of the chemical shift in the indirect dimension would be also possible and advantageous but could not be applied for technical reasons. However, such a refocusing is not essential for the indirect dimension since the evolution under the chemical-shift is not sampled and therefore does not contribute to the linebroadening. Only the signal intensity of the resulting image might be slightly affected. In order to increase the achievable spectral range, the signal is acquired during each of the free-evolution intervals of the time tg. For eliminating undesired signal intensities in the center of the image ("zero point artefact") the signal was acquired with alternating receiver phases moving the zero-point artifact to the borders of the spectral range [ 121. The 2D Fourier magic-echo sequence as described above can be optionally supplemented by a relaxation-filter sequence, whch is incremented to obtain a data set from which the coi-responding relaxation time can be calculated. Examples for such filters are sequences for the measurement of T1, T2, TIP, Tld and, as shown in Fig. 14.4, for the relaxation time Tze. This relaxation time characterizes the decay under the action of a multiple solid-echo pulse train [41] and was found to be particularly suitable for studying the dynamics of polymers.

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The full sequence of Fig. 14.4 now is performed as follows. For the determination of the relaxation time TZe,the time tl is incremented by incrementing the number of cycles of the multiple solid-echo train. The phase-encoding then is performed in the t2 interval by successively incrementing the strength of the phase-encoding gradient. Finally, the signal is detected in the direct dimension under the action of the multiple magic-echo pulse train and a frequency-encoding gradient. The whole experiment including the relaxation filter thus essentially is a three-dimensional experiment with two spatial dimensions.

Fig. 14.4: 2D-FT magic-echo imaging pulse-sequence used in the experiments. It consists of a multiple magic-echo phase-encoding part (time t2) followed by data acquisition under a frequency-encoding gradient and a multiple magic-echo imaging sequence for line-narrowing. The sequence is supplemented by a relaxation filter for parameter contrast. In the experiments, a multiple solid-echo sequence has been used providing the relaxation time Tze which was found to be particularly suitable for probing mobility in solid polymers.

14.3.3 Experimental The sequence has been implemented on a Bruker DSX-300 NMR spectrometer. Because of the need for fast gradient switching, a home-build gradient system has been used. The lab-designed gradient coils for the x,y,z, gradients have a diameter of 25 mm and a low inductance. They are placed directly on a modified Bruker probe which allows a pulse length of 2.5 ps for a 7 mm solenoid coil. For generating the gradient, home-made equipment is used. It consists of two power supplies with a maximum current of 60 A and a lab-designed power switch. With the low-inductance gradient system described above this allows a switching time of less than 1 ps so that the gradients can be

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conveniently switched within the free-evolution periods of the magic-echo pulse train. The usual multiple-pulse adjustment procedure is applied for proper setting of the pulse length and phases [42]. This is necessary in particular for the frequency-encoding variant, whereas it is less important for the phase-encoding part. However, since such an adjustment is less demanding on a modern spectrometer than it was some years ago, it is also recommended when only using the phase-encoding variant. The sequence corresponding to Fig. 14.4 is applied now to polycarbonate samples that have been drawn under different experimental conditions. Polycarbonate samples were chosen since they are transparent and thus allow the application of polarization microscopy for comparison. For the imaging experiments the experimental parameters have been set as follows. The field of view in the images is 12,s mm x 6,4 mm and 128 x 64 pixels have been acquired in the read and the phase-encoding dimension, respectively. This corresponds to an isotropic pixel resolution of 100 pm. The number of echoes during the phase-encoding period was set to be 175 whereas 128 echoes have been generated during the frequency-encoding interval. The cycle time of the magicecho train was 62 = 60 ys for both, the phase-encoding and the frequency-encoding intervals. A maximum phase-encoding gradient of 2 10 mT/m and a frequency-encoding gradient of 46 mT/m have been used.

As a first example, a sample was prepared in which crossed shearbands have been created. For this, two small cuts have been made on either side of the polycarbonate strip. Then the sample was cold-drawn up to an elongation of h = 1.1 with a velocity of 0,5 m d s . A small piece of sample was cut from the interesting part of the polycarbonate strip as indicated in the schematic of Fig. 14.5.

No indication for the appearance of shearbands is found in the spin density image (not shown). The generation of a shearband obviously is not related to significant changes in the density of the sample. As already observed in previous work [15], the shearband however is revealed using the full sequence with the T2e filter probing the chain dynamics. Fig. 14.5a shows a T2,-image of the sample in which the crossed shearbands are easily recognized as a region of lower mobility (note, that the rate 1/T2,is displayed).

As a second example demonstrating the use of NMR imaging for the investigation of stretched samples, the polycarbonate strip was drawn up to an elongation of h = 2,7. The drawing was terminated just before the sample broke into two pieces. Figure 14.5b shows the corresponding image of the T2,-relaxation rate which reveals the immobilization of the chains in the regions around the break.

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W

1

I

E E f W

Fig. 14.5: a) TZ,-magic-echo image of a piece of polycarbonate (see schematic) in which a crossed shearband has been created. The parameter T2, clearly reveals the shearband as a region of lower molecular mobility. b) T2,-magic-echo image of a sample that has been stretched nearly to the point where it breaks into two pieces. The regions of higher intensity correspond to the parts with low chain mobility (the rate l/Tze is displayed in both cases).

14.4 Discussion and Conclusions Solid-state NMR imaging techniques now increasingly reach the state where they become useful for the investigation of polymers. In a first example it was demonstrated, that proton chemical-shift imaging is possible for less rigid materials and provides useful information also when the line-broadening is relatively large compared to the investigated chemical-shift difference. It was shown, that the isotropic chemical shift could serve as a probe for the orientation of polymer chains in a spatially inhomogeneous sample.

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For more rigid polymers, magic-echo techniques can be applied and provide satisfactory resolution in a comparatively convenient way. In particular the phase-encoding variant in its simplest form can be applied on any spectrometer with imaging equipment since it does not require any specific hardware. But also when the frequency-encoding variant is used like in the presented experiments, the magic-echo sequence is much more forgiving with respect to misadjustments and allows longer free-evolution periods for the spatial encoding than conventional multiple-pulse sequences. When comparing NMR imaging techniques with other microscopy techniques, one has to accept that the achievable resolution is less even under optimum conditions. However, there are many applications for which the achievable resolution of NMR imaging is sufficient and the possibility to incorporate the full spectroscopic information is an invaluable advantage. Rather than optimizing the resolution to the ultimately possible limit, we thus concentrated on introducing NMR spectroscopic information to provide information that is not accessible by other techniques. In this way, microscopic properties as derived from NMR spectroscopy techniques or relaxation contrast can be correlated with the macroscopic structures that are accessible by NMR imaging. As a particular interesting example we have investigated samples which have been drawn under various conditions and could locate the regions of chain immobilization. Further investigations along these lines are straightforward and are expected to supplement the results obtained by other methods.

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15. Soft-Matter Relaxation by the NMRMOUSE A. Guthausen, G. Zimmer, R. Eymael, U. Schmitz, P. Bliimler, and B. Bliimich Magnetic Resonance Center l R l C , RWTH Aachen, D-52074 Aachen, Germany

Abstract The NMR-MOUSE (Mobile Universal Surface Explorer) is a device, which has been constructed for relaxation and diffusion measurements in surface-near volume elements of arbitrarily shaped samples. Both the static polarization field B, as well as the rf field B , are inhomogeneous. The B, gradient is an approximately linear function of space with a value of about 10 T/m near the surface. Different pulse sequences known from conventional NMR are investigated and modified for use with the MOUSE. Selected applications of the MOUSE in different areas of materials science are reviewed.

15.1 Introduction The NMR-MOUSE is designed for measurements of relaxation times in surface-near volume elements of arbitrarily large objects [l]. The experimental setup is shown in Fig. 15.1. Given the current design the penetration into the material amounts to about 0 4 111111, depending on the B, and B , fields. The rf field is delivered by the stray field of a multi-layered, solenoidal surface coil. The spatial dependence of B , is therefore determined by the particular geometry of the coil. B, is provided by two permanent magnets with anti-parallel magnetization. The resulting B, field is approximately parallel to the surface of the probe, and its magnitude strongly depends on the gap between the two magnets as well as on the distance from the surface. The B, field strength exhibits a close to quadratic dependence on space in the lateral dimension perpendicular to the magnet gap resulting in an approximately linear B, gradient. Together with the equation of motion for the nuclear magnetization (Bloch equations or von Neumann equation) the

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inhomogeneities of the B, and B , fields define the sensitive volume in which the NMR conditions are satisfied. Typical field strengths amount to about 0.41 T, and the gradient of B, is 10.4 T/m near the surface of the MOUSE. Given the strong field gradient, even a short pulse selects magnetization from a narrow space region, in which B , i s approximately constant, so that a close to sinusoidal dependence of the NMR signal on the nominal pulse flip angle is observed, and phase cycling schemes can be used in extended pulse sequences. Typical pulse lengths are 2 ps for a nominal n/2 pulse. Similar approaches of NMR in inhomogeneous magnetic fields are used for mapping of geological formations in oil wells [2], and a related device for single-sided NMR has been reported for measurements of moisture content in building materials [3J. Similar experimental conditions prevail in STRAFI experiments [4,5]. In this contribution, different pulse sequences, which are suitable for the NMR-MOUSE, and selected applications in materials science are presented.

Fig. 15.1: Experimental setup of the NMR-MOUSE. The Bo field is produced by two permanent magnets, and B l by a solenoidal surface coil. The gap width determines the resonance frequency and influences the sensitive volume.

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15.2 Investigation of Pulse Sequences Pulse sequences well known from conventional NMR in homogeneous magnetic fields can be adapted for measurements with the NMR-MOUSE. Because of the inhomogeneities of B , and B , , some pulse sequences are more suitable than others. The continuous presence of the B , gradient implies that all pulse sequences applicable to the NMRMOUSE must involve at least partial refocusing of linear spin interactions. For rapid measurements of transverse relaxation the multi Hahn-echo (CPMG) and the multi solidecho (OW4) sequences are of interest. For fast determination of longitudinal and transverse relaxation steady-state pulse sequences, which allow weighted TI and T, measurements, are in demand. In the case of elastomers the question of an accurate and sensitive measurement of residual dipolar couplings arises and can be addressed by different pulse sequences. The relatively large gradients can also be used for self diffusion measurements and allow an intrinsic suppression of the more diffusive components in suspensions.

15.2.1 Multi-Echo Decays: Influence of Inhomogeneous Fields and Spin-Lock Effect For dipolar coupled spin systems the decay time of the echo envelope in multi-echo experiments depends on the flip angle of the refocusing pulses. For nI2 the OW4 sequence with complete refocusing of bilinear and partial refocusing of linear interactions is obtained, and for 71: the CPMG sequence with complete refocusing of linear interactions results. In addition to this flip-angle dependence the effect of the field inhomogeneities is observable. The initial decay of transverse magnetization of styrene-cobutadiene rubber (SBR) as function of the flip angle of the refocusing pulses is shown in Fig. 15.2. Instead of a monotonic decay, an initial increase of echo amplitude is observed especially for small flip angles. It is interesting to note that a similar behavior is found in

STRAFI experiments despite the fact that there a nearly constant magnetic field gradient is involved, whereas the gradient of the MOUSE is an approximately linear function of space.

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Fig. 15.2: Echo amplitude of transverse magnetization decay as obtained by a multi-echo sequence. The flip angle of the refocusing pulses is varied. The influence of Bo and B , inhomogeneity is clearly visible in the initial increase of the measured magnetization. For comparison, echo amplitudes calculated for OW4 under STRAFI conditions are shown (solid line) [5].

Fig. 15.3: Transverse relaxation times as function of echo time 22. Note the spin-lock effect in the data obtained by a CPMG sequence, which is avoided by applying a XY 16 sequence.

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199

Another characteristic effect is a spin lock of the transverse magnetization in multipulse sequences, which leads to longer effective relaxation times at short echo times. The effect is related to multi-pulse line narrowing in solid-state NMR and can be described by the model of an effective field. The observed effective transverse magnetization decay-time constant is a mixture of TlP and T,. The spin lock effect can be circumvented by application of an extended phase cycle as for example in the XY 16 sequence, which works satisfactorily for reasonable long pulse distances [6] (Fig. 15.3).

15.2.2 Steady-State Free Precession The signal-to-noise ratio ( S / N of the NMR-MOUSE is limited by the low value of the B , field strength and the size of the sensitive volume. Two different approaches for SIN improvement are distinguished: 1) Improvement of hardware for higher field strengths and larger sensitive volumes. 2) Optimization of pulse sequences following the concept of the Ernst angle. An example of the latter is a modification for use in inhomogeneous fields of the steady-state free-precession (ssfp) concept, known from conventional NMR [7,81. For use in magnetic field gradients the classical ssfp sequence can be extended by refocusing pulses for echo formation within the original inter-pulse windows. This idea

can be extended to multiple refocusing in order to obtain echo trains for measurements of longitudinal and transverse relaxation times. For example, Fig. 15.4 depicts the pulse sequence (top) and the echo trains of SBR for measurement of TI-weighted Tz relaxation via an s s f p CPMG sequence (bottom). The Tl weight is determined by the saturation delay zl, and m determines the number of echoes with echo time 27,. The rapid detection of Tl and Tz [9] by the extended ssfp techniques is illustrated in Fig. 15.5 with the pulse sequence (top) and the experimental data horn SBR (bottom). The magnetization build-up with time constant T1 is obtained by variation of T~ in the saturation loop with echo count n, and subsequently the magnetization is measured by a multi-echo sequence as in Fig. 15.5, where m counts the number of echoes with echo time 2 ~ ~ .

200

A. Guthausen, G. Zimmer, R. Eymael, U. Schmitz,P. Bliimler, and B. Bliimich

m

m

n

1400 1200 T

?

cd

u

1000

800

200

n

*---** 2mz, Zmz, 2mz, 2mt, 2mz, 2mz, ~0.5

n=l

n=1.5

n=2

n=2.5

n=3

Fig. 15.4: Measurement of TI-weighted Tz relaxation via an ssfp CPMG sequence. Top: Pulse sequence. Bottom: Typical sequence of echoes for SBR. The time constants deduced from the individual echo-envelope decays are given.

15.2.3 Monitoring Cross-Link Density by Dipolar Couplings A very important contrast parameter for the characterization of cross-link densities in elastomers is the residual dipolar coupling among protons, which remains from fast but anisotropic motion of inter cross-link chains, NMR parameters which are sensitive to the

I S . So@-Matter Relaxation by the NMR-MOUSE

20 1

time scale of these fluctuations are (Fig. 15.6a) 1) T2,measured by the Hahn, CPMG, and XY16 echo sequences, 2) Tze, which is measured in solid-echo and multi solid-echo (OW4) sequences, and also 3) TIP, the relaxation time in the rotating frame, which is measured under spin-lock conditions in an effective B , field. Another possibility to monitor dipolar interactions is to use the stimulated-echo sequence [lo], where the primary and the stimulated echo are influenced differently by the dipolar couplings (Fig. 15.6b). The ratio of both echo amplitudes is a sensitive measure of the residual dipolar coupling and can be applied to detect differences in cross-link density with the NMR-MOUSE.

- -

c

i

n

I

I

m

H 72

500 400 T 3

300

.-0

i3

+

.-G

zoo I00 0

0

500

1000

points

Fig. 15.5: Rapid measurement of T2-weighted TI and T2. Top: Pulse sequence. Bottom: Experimental results for SBR. Points 0 - 1250 show the increase of magnetization with time constant Ti, followed by a T2 decay (points 1250 - 3000).

202

A. Guthausen, G. Zimmer, R. Eymael,

U.Schmirz, P. Bliimler, orid B. Bliimich

>-

c =2

TI

Fig. 15.6: a) CPMG and b) modified stimulated echo sequences for the measurement of dipolar couplings. The OW4 sequence is obtained from a) by replacing the 20, refocusing pulse with a 0,. pulse. By the multi-echo sequence, the complete echo decay is measured, whereas the modified stimulated-echo sequence gives access only to one value of the ratio of the primary and the stimulated echo.

15.2.4

Molecular Self Diffusion and its Consequences

The gradients of the MOUSE can be used for investigations of molecular self diffusion. From the early days of NMR different pulse sequences are known to be suitable for this purpose: Hahn echo sequences, the stimulated echo, as well as multi-echo sequences have been used in order to measure molecular self-diffusion coefficients in static magnetic field gradients (see for example [ I I]). Figure 15.7 shows two examples: Water and glycerine exhibit diffusion coefficients which are different by three orders of magnitude: m2/s and 2.15.10-'*m2/s, respectively. Both The literature values at 298 K are 2.299. have been measured with an accuracy of better than 2% by the NMR-MOUSE applying a

IS. Sop-Matrer R e l a t i o n by the NMR-MOUSE

203

Hahn echo sequence. Stimulated echo sequences as well as multi-echo sequences lead to similar results. The knowledge of the gradient is required, which was calibrated for a given sample geometry by diffusion measurements on water [12] and verified by field calculations [ 131. 4504501 7 400-

a,

300-

.A

P

.-

2 250: ': 2200cd E 150: 0 100-

-3a,

'

50-

Glycerine Glycerine

I .

I . .

: '

: Water oo

0 1 .

~

1

~ I

0,O 2,5

~

~ .

o I

5,O

~ ~

o n" I

7,5

o

-

o0 o 0 I

-

.

"

0 I

-

:

t

9

&

r

10,O 12,5 15,O 17,5 2

Fig. 15.7: Hahn-echo decays of glycerine and water (CuS04). The transverse magnetization decays are dominated by the influence of molecular self diffusion.

0,O 0,5 1,0 1,5 2,O 2,5 3,O 3 3 4,O 4 3 5,O t

[msl

Fig. 15.8: The decay curves of polybutadiene latices, normalized to the amplitude of the first echo, show different decay times for small (circles), intermediate (squares) and high (triangles) crosslink densities. The water signal is sufficiently suppressed by self diffusion and a long longitudinal relaxation time T I .The difference in offset is due to normalization.

204

A. Gurhuusen, G. Zimnrer, R. Evmnel,

(1. ScAriiitz,

P. Bliirnler, m d B. Bliimich

The sensitivity of the MOUSE to molecular self diffusion can favorably be exploited for signal suppression of liquids in relaxation measurements of suspensions. An example is shown in Fig. 15.8 with experimental data for the signal decay of polybutadiene latices in water. The water signal is efficently suppressed by T , and by a fast (< I ms) transverse magnetization decay due to self diffusion. The decay of the polybutadiene signal is much slower which provides good discrimination of water and polymer. Consequently the differences in cross-link density of the latex particles can be monitored by the T2 decay.

15.3 Applications of the MOUSE The measurement of self-diffusion coefficients and of cross-link densities in latices has been demonstrated in Figs. 15.7 and 15.8, respectively. Further selected applications of the MOUSE are summarized below.

15.3.1 Cross-Link Density of Elastomers Variation of the cross-link density in elastomers can be achieved by different cross-linker contents and by different curing times. Two examples are given, which demonstrate, that cross-link density can be monitored by measuring NMR parameters sensitive to the residual dipolar coupling. One experiment exploits echo decays, the other the ratio of primary to stimulated echo.

Cross-Link Density Variation via Cross-Linker Content Figure 15.9 depicts transverse relaxation times for two SBR samples differing in crosslink density from variation of the cross-linker content (dicuniyl peroxide, DICUP, phr: parts per hundreds rubber). At high DICUP content molecular mobility is expected to be low with an associated low value of the transverse relaxation time. whereas the mechanical stiffness is high. This reasoning is confirmed by the experimental results, measured with a CPMG sequence.

15. Soft-Mutler Relwcatiori by the NMR-MOUSE

10o rn

9-

-8 u

H*

87: 6I

5-

‘i 2

f id4

205

MOUSE 0.75 phr MOUSE 15phr DMX 0.75phr DMX 15phr

P

x d2

71

pulse length Fig. 15.9: The relaxation parameter Tz is a measure for cross-link density and has been determined with the MOUSE and with a Bruker DMX 300 for two elastomers with different DICUP contents. The difference in cross-link densities as well as the agreement of the results obtained by the MOUSE with those obtained by conventional NMR equipment are evident.

In addition to the measurements by the MOUSE, relaxation times obtained by a commercial system at 7 T are shown. It should be noted that the experimental conditions for the commercial system and the NMR-MOUSE are quite different concerning the strength and homogeneity of the magnetic fields and that therefore the measured results come to remarkably good agreement. In particular, a dependence of the relaxation rates on the field strength is well known. Also the dependence of transverse relaxation time on the flip angle is obvious and is due to the refocusing properties concerning dipolar interactions.

Cross-Link Density Variation via Curing Time in Industrial Samples Knowledge of the dependence of cross-link density on curing time is essential for optimization in vulcanization processes. The value of the cross-link density can be mapped by T2 relaxation rates for different curing times. But also the residual dipolar coupling can be probed for instance by the ratio of primary to stimulated echo. This is illustrated in Fig. 15.10 for four natural rubber (NR) samples with different curing times. i. e. crosslink densities and consequently different time-dependent dipolar couplings.

206

A. Guthausen, G. Zimmer, R. Evmael.

U.Sclunitz, P. Bliimler, rind B. Blumich

.

0,55

curing time

:

0,50n 0,45-

=t

A

0,40-

.z

0,35-

0

U

c,

E.

3

A

m

0

0

A

5.0 min 7.5 min 10.0 min

I

A

0~30-

A

7

0,25: crf

.

Omin

A

v

v

v

I A

v

v A

0,20 I

'

I

'

I

'

I

-

I

.

I

Fig. 15.10: The amplitude ratios (stim. echo/primary echo) for four NR elastomers with different curing times. An increase of contrast can be achieved by the variation of the second pulse of the modified stimulated echo sequence described in section 15.2.3.

A pronounced dependence of amplitude ratio on flip angle of the first refocusing

pulse is observed in the inhomogeneous magnetic fields of the MOUSE which can be associated with the transformation properties of dipolar interactions in a coupled network of spins. It should be noted that this method is most sensitive with respect to contrast for discrimination of these different soft materials.

15.3.2 Aging of Polymers Aging of polymer products often starts at the surface. Therefore, the MOUSE is a device particularly suitable for investigations of aging processes. For example polyvinylidendifluorine (PVDF) samples have been heated in oil at different temperatures. The aging process was monitored by a CPMG measurement of the transverse relaxation parameter

T2. In Fig. 15.11 a systematic dependence of the NMR parameter on the aging temperature is evident. With the increase of the aging temperature an increase of the molecular mobility is observed via an increase of T2. Possible mechanisms for this behavior are chain scissions as well as a plasticizer effect of the oil diffusing into the polymer.

15. Soft-Matter Relo.ratioti by the NMR-MOUSE

‘“1

207

rn

35

rn

rn

-

increasing Temperature Fig. 15.1 1: T2 as function of the aging temperature for PVDF samples heated in oil. The aging effect can be monitored by an increase of the relaxation parameter T2. Two independently prepared samples (two squares at the same temperature) have been measured to show the reliability of the method.

15.3.3 Application on Biological Samples: 1D and 2D Images Both, biological tissues and technical elastomers are soft matter. Thus from an NMR point of view similar methods apply for their investigation. The relaxation times of different biological tissues can readily be distinguished, and T I - , T2- and spin-density weighted images can be obtained simply by displacement of the relative position of the sensitive volume with respect to the sample coordinates. For demonstration purposes only, a cross section through a pork leg obtained from a butcher has been imaged in the scanner plane (Fig. 15.12). The sequence used was a steady-state sequence as described in 15.2.2 (Fig 15.5). In a single experiment spin-density weighted, T1-weighted and T2- parameter images can be produced. Tissues like bone, marrow, and muscle can clearly be distinguished. Depending on the chosen parameter, different contrast is obtained. The spatial resolution is given by the geometry of the rf coil, because no additional B, gradient system has been used. The digital resolution amounts to 0.5 x 0.5 cm’, and the field of view is 5 x 3 cm*.

208

A. Gutknusen, G. Zimmer, R. Eymnel,

meat

U.Schrnitz, P. Bliirnler, uiid B. Bliimich

bone marrow

bone marrow

meat

Fig. 15.12: T2 parameter image (left) and T I weighted image of a cross section through a pork leg. Muscle, bone, and marrow can be discriminated, and images with differing contrast can be obtained.

r( subcutis)

T,(subcutis) A

T,(epidermis) r(epidemis) i

-

0,4

1

0,6

.

1

0,s

-

1

1,0

-

1

.

1,2

1

1,4

-

1

1,6

-

1

1

1,8

depth [mm] _________(

epidermis

subcutis

Fig. 15.13: Relaxation times in pork skin as function of frequency, which corresponds to depth. The values of epidermis and subcutis differ, and the tissues can consequently be distinguished. The amplitude ratios were determined from a biexponential fit, where the signal is described by s(f) = A exp(-t/T,(epidermis)) + B exp(-t/T,(subcutis)).

IS. So)-Matter Relaxation by the NMR-MOUSE

209

The Bo-field of the MOUSE exhibits a pronounced field variation along the axis perpendicular to the scanner surface. This fact can be exploited for depth resolution. Because of the high field gradient strength (10 - 15 T/m), good depth resolution can be achieved which allows discrimination of different components of the skin. Investigations have been carried out on pork skin (Fig. 15.13). T, and also T2 relaxation differ for the epidermis and the subcutis as the fat content varies strongly. In the case of T2, the amplitude ratio of a biexponential fit reflects the relative signal contributions from epidermis and subcutis. At the highest frequency (17.5 MHz), the relaxation times correspond to the values for the epidermis, and with decreasing frequency, the amount of signal from the subcutis increases.

Acknowledgments The project is financially supported by the Deutsche Forschungsgemeinschaft (DFG grants BL-23 1/17-1 and Zi-550/1-1). Industrial cooperations are gratefully acknowledged.

References 1.

G. Eidmann, R. Savelsberg, P. Bliimler, and B. Bliimich, J. Magn. Res. A 122 (1996) 104.

2.

R. L. Kleinberg, ,,NMR well Logging" in: Encyclopedia of NMR, eds: D. M. Grant, R. K. Harris, Vol. 8, 1996, p. 4960.

3.

G. A. Matzkanin, in: Nondestructive Characterization of Materials, eds: P. Holler, V. Hauck, C. 0. Rund, R. E. Green, Springer Berlin, 1989.

4.

A. A. Samoilenko. D. Yu. Artemov, and L. A. Sibeldina, Russ. J. fhys. Chern. (Engl. Transl.) 61, 1623; JETf 47 (1988) 348.

T. B. Benson and P. J. McDonald, J. Magn. Res. A 112 (1995) 17, ibid, A 109 (1995) 314. T. Gullion, D. B. Baker, and M. S. Conradi, J. Magn. Res. 89 (1990) 479. R. Bradford, C. Clay, and E. Strick, f h y s . Rev. 84 (1951) 157; H. Y. Cam, fhys. Rev. 112 (1958) 1693. R. R. Emst, G. Bodenhausen. and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon Press, Oxford, 1994. 9.

A. Sezginer, R. L. Kleinberg, M. Fukuhara. and L. L. Latour J . Magn. Res. 92 (1991) 504.

10.

R. Kimmich, E. Fischer, P. T. Callaghan, and M. Fatkullin, J. M a p . Res. A 117 (1995) 53.

11.

P. T. Callaghan, Principles of Nuclear Magnetic Resonance Microscopy, Clarendon Press, Oxford, 1993.

12.

R. Eymael, Diploma Thesis, RWTH Aachen, 1997.

13.

G. Eidmann, PhD Thesis, RWTH Aachen, 1997.

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16. Application of NMR-Imaging to Industrial Polymers M.Knorgeti, U.Heuert, utid H . Schneider Fachbereich Physik, Martin-Luther-Universitat Halle-Wittenberg, D-06108 Halle, Germany

Abstract A complex aging regime occurs in the course of thermal aging of elastomers. Depending

on the type and the content of the rubber and filler materials, the temperature, the chemical environment (normally air) and the time, a different aging process can be observed also by NMR [ 1 4 ] . The methods used are the common spin-echo ‘H-NMR including variable echo times and parameter selective NMR-imaging (marerial properties imaging; lH). The decay of the echo-magnetization is discussed on the basis of a single chain model with a distribution of dipolar interactions. This model is based on the influence of a very fast but anisotropic local motion as well as faster and slower motions which are able to diminish the residual dipolar interaction. Silica and carbon black filled E-SBR (Free radical polymerization with the monomer dispersed in water by the use of an emulsifier.), widely used for tyres, and S-SBR (Polymerization with the monomer dissolved in a solvent as a diluent.) are the systems under investigation showing some characteristical features of the aging course observable by NMR.

16.1 Introduction The thermal aging course of (un-)filled samples exhibits a typical NMR-relaxation behavior, beginning with a strong decrease of T2 followed by a weak increase through aging times of 10 to about 50 hours and aging temperatures of about 90 “C - 130 “C (Fig. 16.1) [3]. In rubber technology this is a well-known fact, called “reversion”, characterizing the point of maximum effectiveness of the crosslinking agents. The reason is the

212

M. KnBrgen, U.Heurrr. and H. Schneider

interplay of network formation and destruction processes whereby the latter (e.g. i n N R ) or the former (e.g. in SBR) gains precedence for longer curing times. However, at longer aging times and/or higher aging temperatures (more than 130 “C) the solidlike behavior becomes more obvious, showing up by a faster decrease of the FID. In opposite to the first (“soft aging”), the latter is sometimes called “hard aging”. and it is determined by a radical formation of crosslinks between the polymer chains and a simultaneous deconiposition of the polymeric backbone itself. This process should be strongly influenced by the diffusion of any radical molecules like oxygen or ozone. Indeed, the formation of’ reversion fronts by aging in air could be observed [2,3]. (In opposite no aging fronts are detectable when doing the aging process in N, [3]). Both processes (soft and hard aging) can be observed in terms of a simple exponential decay of the Htrhn spin echo with the time constant T,; its decrease or increase shows the more solidlike or liquidlike behavior respectively.

Om5L---- 0 0.0

20

40

60 80 100 120 140

t(aging) / h Fig. 16.1: (left) The aging course of carbon black filled ( S O phr) natural rubber i n nitrogen showed by the relaxation time T2 of the Hahn echo decay. The aging temperature was 100 “C for ..soft aging“. Notice the minima (1) caused by reversion and the maxima (2) caused by radical polymerization of the polymer backbones. The error bars are determined as a maximum deviation of a mean value calculated for all in all four measurements and fit-procedures.

Another important point of interest is the influence of filler materids on the aging process. The replacement of carbon black by so-called “white filler” materials is a principal focus of research of tire materials in the rubber industry. The aim of this work is to demonstrate the influence of silica on aging compared to carbon black.

16. Application qfNMR-Imaging to Industrial Polymers

213

16.2 Magnetization Decay and Material Parameters The residual part of the dipolar interaction can be discussed using the scaling concept [ 5 ] : The basic idea is based on the existence of very fast (5 10T9s),small (inside a monomeric unit) but anisotropic (due to the fixed chain geometry of larger chain parts) motion. This motion scales down the dipolar interaction A = p0y A 44x13) between the nuclear dipols. At least it causes a relaxation time T2 as one (besides other) parameter of the magnetization decay. We simplify our model by considering only pairwise dipolar coupling like such in CH2-groups, often occurring in nrbber materials. The residual interaction, nonaveraged by the anisotropy motion, is less then 1% of the starting value. Of course, for longer times (but short in relation to T I )it will decay to zero, too. However, the mechanism of this isn’t quite clear: On the one hand it can be thought that it is caused by a distribution of the time integrals [6-81 of the residual interactions over the s). This would require a large scaled isotropic motion typical NMR-scale ( I h , = which is difficult to explain in strong crosslinked systems. Similar results one can obtain using a distribution of the end-to-end vectors of the crosslinkedpolyrner segments [ 5 ] . In this case no long correlation time zs (-1 ms) is used; the polymer system is viewed as a rigid lattice for larger scales. In spite of these different starting points the results concerning the length of intercrosslink chains are very similar. Indeed, it could be shown that there is a relation of only &%% between the number of statistic independent polymer segments (Kuhn segments) N of the latter in relation to the former model [9]. A distribution of the contour length of the intercrosslinked chains isn’t under consideration until now. But recent calculations have shown that there is no further influence until mediumsized distribution widths (Really, there can be more than one fifth of the mean value of a Gaussian like distribution without remarkable influence on the second moments.). However, it is better to take this in mind as a source of bad fits for inhomogeneous crosslinked rubber.

Model Description We choose a single chain model of pairwise dipolar interaction (see above) with a Gaussian distribution over the NMR-time scale. In other words, we assume the existence of a large-scale motion described by a correlation time zs (- 1 ms for the exp. conditions see below) additionally to an fast, but anisotropic motion zf (< s). This leads us to the following fit-function of the Hahn echo decay [6,7].

214

M. Knorgen, U.Heuert, cind H. Schneider

M ( t ) = exp[-t/T2 - q M2r1 T~~ f(fl'cs)l

(16.1)

is the with the Debye function f(t/.ss) = exp(-t/'cs) + ( t / ~ $- 1 and /T3 = zf MZr1(MZr1 second moment of the rigid lattice as can be measured at temperatures well below the glassy point [6]). Taking into account the different parts (intercrosslink chains, dangling ends, sol part) within the rubber sketched in Fig. 16.2, and a bad signal to noise ratio mainly in the case of NMR microscopy, where the fitting is done for each spatially resolved pixel (voxel) -, one needs to do some simplifications, like setting the sol part to zero and expanding exp(-r/Ts) to (1 - t/zs + r2/(22s2)).Thus, we get M(t) = A exp[-t/T, - q MZr1t2/2)+ B exp(-t/T2) with

(1 6.2)

A = part of intercrosslink chains, B = part of dangling chain ends, T2 = relaxation time (= 1/(qM2)),

q = anisotropy parameter ( =

residual/ M 2rigid lattice)

The mean value of the length of intercrosslink chains follows from (16.3)

with c, being the number of backbone bonds in a Kuhn segment, M , being the molecular mass of a repetition unit and b as the number of backbone bonds in one monomeric unit [6,7].

Fig. 16.2: Network model: (a) intercrosslinked chain, (b) dangling chain end, (c) free chain (sol part), (x) chemical crosslink, (y) physical loop (entanglement).

215

16. Application of NMR-Iniaging t o Industrial Polymers

16.3 Experiment and Samples We investigated the aging course depending on the kind of filler, filler content and polymerization of the basic polymer (E- or S-SBR; see introduction). The samples are provided by the Continental AG (Hannover). The thermal aging was done at a temperature of 150 "C in normal atmosphere and for a duration up to 1070 min. Besides the overall changing of the parameters related to the elastomeric network, we focus our attention on the occurrence of local inhomogeneities, mainly the growth of surface layers. The experiments were performed on a self-made NMR-microscope attached to a

VAFUAN unity 400 spectrometer. The actively shielded gradient coils of the probe were able to produce a gradient up to 50 G k m , which enables together with a line width of Table 16.1: Sample program. N

E-SBR S-SBR cb.N 121 silicaVN3 HAR-Oil

s109

sll0

slll

s112

s113

s114

s115

s116

s118

90 -

-

90

-

90

-

-

-

-

90

-

S-SBR

50

90 80

-

-

90 -

E-SBR

90 50

90 -

-

-

-

-

-

-

44

44

70

70

-

-

5

5

35

35

5

5

35

35

1

1

80

s119

Fig. 16.3: The pulse sequences used for integral (nonlocal) (left) and locally resolved (right) Hahn echo measurements. The z-parameter is arrayed to get the relaxation decay. The 2D-backprojection sequence (right) with a T2-filter placed before the Hahn echo enables a relatively simple and robust experiment; no problems with the phase correction (magnitude calculation) and adjustment (pre-emphasis and gradients of equal length causes more stability). Only the very beginning of the relaxation is modified in comparison to the integral measurement.

216

M. Knorgen, U.Heuen, and H. Schneider

about 2 MIz a resolution of about (100 ~ m voxel ) ~size. The pulse sequences for the bulk and spatially resolved measurements are shown in Fig. 16.3. The sample was cut in small pieces of about 4 mm x 2.5 mm and a thickness of 0.5 mm. All images were taken without slice selection. A filtered 2D-backprojektion was used for imaging. By appropriate preparation we made sure that the sample contains an aging front. The measurements were carried out at 60 "C.

16.4 Results The influence of kind and content of the filler and the rubber type on the overall aging of the bulk is shown by integral measurements. In a second step the occurrence of inhomogenities or aging fronts will be investigated.

16.4.1 Integral Characterization The weak decays of the T2-parameter of the E- and S-SBR (Fig. 16.4) in relation to the unfilled samples could be a hint to the protective quality of the filler material. Despite this fact, the anisotropy parameter 4M2 (Figs. 16.5 and 16.6; left) rises faster for the filled systems and also does the ratio of dangling ends for some highfilled material (Figs.

+

6

--0-

5

2

.c

4

3

2 1

.

s109 50ppm c.b. slll 8Opprn c.b. sl13 50DDm silica sl15 80ppm silica

tN

< . 'r----

--------

'I

I error bar 200 400 600 SO0 aging time in min

* - -

-.

Z--------

---,

O ' , ' , . ,

0 0

2 -

. _ A

1000 1200

0

200 400 600 800 1000 1200 aging time In min

Fig. 16.4: The decay of the fit parameter T2 during the aging process. Comparison of E- and SSBR. The error bars in Figs. 16.4. to 16.6. are determined as maximum deviation of a mean value of all in all three measurements and fit-procedures for each point.

217

16. Application of NMR-lnmging lo Industrial Polvmers

-s118 ---s109 2.5 -

E-SBR

Slll

I error bar

0.2 0.0 J

I

'

0

-s113 * s115

0.0

I

200

600 800 aging tlme In mln

400

7

1000 1200

0

200

400 600 800 loo0 1200 aging time in min

Fig. 16.5: The aging course of the yM2- (left)and dangling end ratio-(right)parameter of E-SBR.

1

S-SBR

3.01

%

-E E

2.0 -

S-SBR A

08 -

2.5 -

/

I error bar

, '

, '

"

1

1.5-

'

0.5 0.01

I

0

'

I

200

'

I

'

0.04

I

400 600 800 aging time in min

O2

1000 1200

I errorbar I

0

,

I

200

s116 ' ,

I

400

,

I

600

.

I

800

.

I

,

I

1000 1200

aging time in min

Fig. 16.6: The aging course of the 4M2-(left) and dangling end ratio-(right)parameter of S-SBR.

16.5 and 16.6; right). However, there is a difference in the effectiveness of the aging time: Whereas the dangling ends change more in the first aging interval (with exception of high filled c.b. SBR), an opposite trend is observed for the anisotropy parameter. One explanation could be, that the chain cracking process starts immediately, whereas the radicalic crosslinking has an onset at longer aging times, depending on the diffusion of radicals from the surface. The final result would be a highly crosslinked material but having a higher content of dangling ends. The same was already observed in natural rubber [3]. The most clearest difference between the E- and the S-SBR aging is observed in the qM2-diagrams (Figs. 16.5 and 16.6; left): The S-SBR shows a much less increase of the anisotropy parameter, which is also a hint of the (less) effectiveness of radicalic crosslinking. There is no clear difference between the silica and carbon black filled samples during the aging process by the integral characterization.

218

M. Kniirgen. U.Heuert, and H.Schneider

16.4.2 NMR-Imaging Results The presentation shows the course of aging in dependence on aging time (0, 300 min, 1070 min from left to right in each image). The influence of the filler material on the formation of aging fronts is imaged in Fig. 16.7 for the case of S-SBR: It is shown. that the filler loading prevents the occurrence of an aging front of higher q M , (brighter areas). The front shows the opposite trend of the overall aging of an increasing q M , : ;I hint of additional crosslinking by radicals. The front stands out also by a higher part of dangling ends (Fig. 16.8), due to additional chain splitting there. It is also shown that the carbon black is more effective in preventing aging fronts i n relation with silica; even 50 phr c.b. content will prevent this (Fig. 16.8, middle). No front can be detected in the T2- image also; here not shown. In the case of E-SBR (Fig. 16.9) only a weak aging front can be detected even in the unfilled rubber. The qM2-parameter images show higher levels (darker areas) for the filled samples. N o influence of the aging time of all parameters is established for the high filled c.b. sample ( s l l l ) . However, it is - like expected for filled rubber - on a much higher level of anisotropy in relation to the unfilled sample (Fig. 16.9, right). In opposite to this, silica don’t prevent overall aging (Fig. 16.9, middle); the anisotropy parameter will rise considerably, even for higher contents of it. However, only a weak aging front occurs - i n opposite to the unfilled samples.

Fig. 16.7: The formation of aging fronts in S-SBR pieces (= 2.5 nun x 4 mm) of unfilled (sl19: left) and silica filled 44 phr (sl14; middle) and 70 phr (sl16; right) material shown by the qM2 parameter picture. The left side of each picture shows the unaged sample followed by the 300 min and 1070 min aged ones. The color scale is in (ms)-?.Aging fronts can be clearly observed in the unfilled (right) and in the strongest aged of the weak filled material (nuddle).

16. Applicarion of NMR-lnrizging to Industrial Polymers

219

Fig. 16.8: The formation of aging fronts in S-SBR pieces of unfilled (sl19; left) and carbon black filled 50 phr (sl10; middle) and 80 phr (sl12; right) material shown by the BI(A + B ) - parameter picture. An aging front occurs only in the unfilled sample. (The dark areas of the right images of the filled samples (middle and right pictures) are artefacts caused by a nonconvergent fit and an successive smoothing-procedure.).

Fig. 16.9: E-SBR pieces of unfilled (sl18; left), 70 phr silica filled (sl15;middle) and 80 phr c.b. filled (sl 1 1; right) material shown by a q M 2 -parameter picture. The scale is in ms-2.

16.5 Conclusions It was demonstrated that the investigation of rubber materials by NMR relaxation and NMR-imaging can provide some additional information of the aging process. The model parameters T2, 4M2 and B lead to qualitative and also quantitative statements of the rubber network. First of all, this concerns the interplay of the several aging processes (reversion, chain cracking, crosslinking by radicals) in the front and in the entire sample volume. Second, the influence of different rubber materials and filler substances on the aging process was shown.

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M . Knorgen, U.Heuer!,and H. Schneider

The advantage of the NMR-imaging is the ability to distinguish between processes of overall aging and such only concerning an aging front. For instance it was shown, that the strong parameter changes of unfilled rubber mainly arises in an aging front. In opposite to this, the aging process of high filled material takes places in the entire sample volume. As a result the assumptions of the aging process given in an earlier work 131 will be confirmed: The aging starts by a cracking of crosslinks (reversion) and/or polymer chains. At longer aging times an additional crosslinking caused by radicals occurs: mainly in an aging front in the case of unfilled rubber. The result is a material of short intercrosslink chains showing a high anisotropy, but also a high content of dangling ends.

Acknowledgment The authors would like to thank Dr. G. Heinrich, Continental AG, for providing the samples and for helpful discussions.

References 1.

B. Blumich, W. Kuhn, eds., Magnetic Resonance Microscopy, VCH, Weinheim, 1992.

2.

Blunder, B. Bliimich, Macromolecules 24 (1991) 2183.

3.

M. Knorgen, U. Heuert, H. Schneider, P. Barth, W. Kuhn, Polym. Bullerin 38 (1997) 101.

4.

P. Barth, S. Hafner, W. Kuhn, Macromolecules 27 (1994) 5713.

5.

P. Sotta, C. Fulber, D. E. Demco, B. Bliimich, H. W. Spiess, Macromolecules 29 (1996) 6222

6.

G. Simon, H. Schneider, Macromol. Chem., Macromol. Symp. 52 (1991) 233.

7.

U. Heuert, M. Knorgen, H. Menge, G. Scheler, H. Schneider, Polym. Bull. 21 (1996) 489.

8.

P. T. Callaghan, E. T. Samulslu, Macromolecules 30 (1997), 113.

9.

unpublished results.

17. Electron Spin Resonance Imaging (ESRI) of Transport Processes in Polymeric Systems S. Schlick', P. Ecigle2, K. Kruczalal*, and J. Pilar1s3 Departments of Chemistry' and Mechanical Engineering*, University of Detroit Mercy, Detroit, Michigan 48219, USA Institute of Macromolecular Chemistry3, Academy of Sciences of the Czech Republic, 16206 Prague 6, Czech Republic *On leave from the Department of Chemistry, Jagiellonian University, Cracow, Poland

Abstract 2D (spectral-spatial) electron spin resonance imaging (ESRI) is applied in our lab for the determination of the spatial distribution and dynamics of paramagnetic species in ioncontaining polymers, polymer solutions, cross-linked polymers swollen by solvents, and self-assembled polymeric surfactants. Projections taken in a range of magnetic field gradients are used to reconstruct a two-dimensional (2D) image that consists of the ESR spectrum along the chosen spatial coordinate. The method provides the concentration profile and the ESR line shape of the diffusant in each slice of the sample perpendicular to the direction of the gradient; the determination of the translational and rotational diffusion rates in one experiment is therefore possible. The determination of the translational diffusion coefficient, D, of nitroxide spin probes, spin-labelled polymers, and paramagnetic MoV in the polymeric systems mentioned above will be presented.

17.1 Introduction Electron spin resonance imaging (ESRI) can supply information on the spatial distribution of paramagnetic molecules in a sample, and has been used successfully for measurements of translational diffusion. Diffusion coefficients of paramagnetic dif-

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S.Schlick, P. Eagle, K. Kruczala. a d J. Pilar

fusants can be deduced from an analysis of the time dependence of the concentration profiles along a selected axis of the sample [ I ] . The determination of diffusion coefficients for spin probes in liquid crystals and model membranes, and the effects of polymer and tracer polydispersity, have been described in a series of papers by Freed and coworkers [2,3]. In our laboratory, ESRI in two dimensions (spectral-spatial) is used for measuring transport rates and dynamics in ion-containing polymers, cross-linked polymer gels, and self-assembled polymeric surfactants [4-91. Imaging is based on neutral and ionic spin probes, spin-labelled polymers, and paramagnetic cations such as Mo". In some experiments deuteriated spin probes were used as tracers, in order to improve the spatial and spectral resolution. The goal of these experiments is to assess the effects of polymer concentration (in the solutions), network content (in the gels), temperature, and solvent on the transport properties of the tracers, and to compare with results obtained by other methods. Based on the results presented below, it appears that the development of 2D ESRI is important for the evaluation of transport properties of materials suitable in medical and industrial applications.

17.2 ESR Imaging Spectrometer and Data Acquisition The ESR imaging system in Detroit is based on a Bruker 200D ESR spectrometer, equipped with two Lewis Coils (George Associates, Berkeley, USA, type 503D), and two regulated DC power supplies (Kikusui Electronic Corp., Japan, model PAE 35-30). The two sets of coils, each consisting of a figure-eight coil, are fixed on the poles of the spectrometer magnet, and supply a maximum linear field gradient of = 320 G/cm in the direction parallel to the external magnetic field ( z axis), or = 250 G/cm in the vertical direction (along the long axis, x , of the microwave cavity), with a maximum control voltage of 20 V applied to each power supply. The magnetic field gradient was measured by recording ESR spectra of a sample consisting of two specks of 2,2-diphenyl- 1-picry]hydrazyl (DPPH) fixed at a distance of 1.0 cm along the direction of the gradient, on the surface of a quartz tube (10 mm o.d.), in a range of gradients generated with control voltages 0 - 20 V; no departure from linearity was detected for gradients along the x or z

17. Elecfron Spin Resonance Imaging of Trnnsport Processes in Polynteric S y s t e m

223

axes. The coils were positioned so that the zero point of the gradient field coincided with the center of the microwave cavity. The imaging spectrometer was interfaced to a 386 AST PC equipped with software developed in our lab and designed to control the magnitude of the field gradient by set input voltages to the DC power supplies, and to collect the data. The data were processed and simulated with a NEC READY 486 PC, using the software MATLAB. The progress of diffusion was followed from spatial-spectral images measured as a function of time. Each image was reconstructed from a complete set of projections taken as a function of the magnetic field gradient [lo], using a convoluted back-projection algorithm [4]. The number of points for each projection (4096) was kept constant. The can be calculated from the maximum experimentally accessible projection angle amax maximum gradient G,,, according to tan amax = (L/m G,,, where L is the sample length, and AH is the spectral width in the absence of gradient (a = 0). The maximum sweep width Sw,,, = h AHIcos~,,. For AH = 54.5 G (which was broad enough for motionally narrowed ESR spectra of the nitroxide spin probes used as diffusants), a sample length of 1.0 cm and a maximum field gradient of 200 G/cm along the vertical axis, amax = 74.8" and SW,,, = 293.2 G . A complete set of data for one image consisted of 65 projections, taken for gradients corresponding to equally spaced increments of a in the range -90" to +90"; of these projections, typically 55 were experimentally accessible projections and 10 were projections at missing angles (for a in the intervals 74.8" to 90", and -74.8" to -90"). The projections at the missing angles were assumed to be same as those at the maximum experimentally accessible angle amax. Each projection required 1 - 3 scans to reach an acceptable signal-to-noise ratio, and each scan was obtained with scan time 10 s, microwave power 2 mW, modulation 1 G, and a time constant of 10 - 50 ms. The spectrometer gain was 2.103 - 5 1 O 3 in most cases, and l.105 for measurements involving the slow diffusion of spin-labelled polymers. The acquisition of the projections necessary for each image at a given time t required 20 - 30 min. These conditions imply that the method may be used for the study of relatively slow diffusion processes, when the change of the concentration profile during acquisition time can be considered negligible. The first-derivative ESR spectra taken in the presence of gradients were numerically integrated and multiplied by the square of the sweep width in order to obtain a constant integrated intensity, as required by the image reconstruction algorithm; the 4096 points for each spectrum were compressed by averaging to 256 points. The reconstruction algorithm produced a three-dimensional spatial-spectral-intensity image of the diffusant dis-

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tribution in the sample consisting, after averaging, of 64 x 64 points. The concentration of the diffusant at each point of the spatial axis of a sample at a given time was obtained by integrating the ESR spectra at this point along the spectral (magnetic field) axis, thus creating the corresponding experimental concentration profile. The experimental profiles were splined using a cubic spline with 16 control points.

17.3 Determination of the Diffusion Coefficients Diffusion coefficients were deduced by comparing the experimental splined concentration profiles with calculated profiles obtained on the basis of Fick's laws of diffusion [ 111. The diffusant is initially confined in the region 0 < x < h, and the spin probes diffuse into a finite system of length 1. The boundary conditions at t = 0 are: C = C, for x I h, and C = 0 for x > h; C is the tracer concentration. An additional condition is 6C/6x = 0 at x = 1 (no flow of the diffusion substance through the closed part of the tube). The solution for this sample configuration is given in eqn. 17.1, h+2nl-x

+ erf

h - 2nl+ x

(17.1)

2JDt

where

For each time-dependent concentration profile 2 1 equally spaced points were calculated using eqn. 17.1, with five terms (n = -2,...,2) in the summation needed for convergence. The 21 calculated points were then multiplied by the final experimental concentration profile of the sample, measured when a homogeneous distribution of the diffusant in the sample was reached. In this way the sensitivity of the ESR cavity along the (vertical) diffusion direction was taken in consideration for each specific position of the tracer in the cavity. The three parameters D,h and Co can be varied for each experimental profile, until the best fit is reached. In practice, the thickness of the initial layer of the diffusant, h, was determined by simulating the profiles taken in the earliest stage of diffu-

17. Electron Spin Resonance Imaging of Transport Processes in Polymeric Systems

225

sion and the h value was then kept constant during the simulation of all profiles for a given sample. The initial concentration was varied in a narrow range in some cases, due to the uncertainty in splining noisy experimental concentration profiles.

17.4 Results and Discussion 17.4.1 Diffusion in HEMA-DEGMA Hydrogels The monomers HEMA and DEGMA, Chart 17.1, were polymerized using the initiator 4,4'-azobis-4-cyanopentanoicacid and cross-linked by glycol dimethacrylate in an aqueous medium at 333 K for 24 h [ 6 ] .

Chart 17.1: Monomers (for hydrogels) and tracers

Pb

c y = cocycyocycyw

DEGMA

HEMA

P

a i2 b PDTEMPONE

TMATEMPOI

SLPEO

The amount of water corresponded to the equilibrium content in the gels. Three gel systems were prepared, containing 100, 80, and 50 mol % DEGMA, with equilibrium water contents of 75, 67, and 55 wt % water, respectively. The notation is DE100, DE80, and DE50. Capillaries (1 - 2 mm i.d., = 8 mm long) soaked at one end by the paramagnetic diffusant were used for imaging at 300 K. The spin probes used as diffusants are shown in Chart 17.1.

226 DEB0 TMA"0I

S. Schlick P. Eagle. K. Kruczala arid J. Pilur

TMATEMPOI

Fig.17.1: Perspective plots of the initial (A) and final (B) images for the diffusion of TMATEMPOI in DE80 at 300 K. The viewing angles 0 and @ in the L (spatial), I (intensity) and H (magnetic field) axes are given in square brackets. The length range is 15.6 mm and the magnetic field range is 77 G.

Typical perspective representations of the spatial-spectral images, for the initial and final stages of diffusion of TMATEMPOI in DE80, are shown in Fig. 17.1. The experimental splined profiles for the diffusion of TMATEMPOI in DE80 (Fig. 17.2A) are in excellent agreement with the simulated profiles (Fig. 17.2B). The D values thus calculated for all gels are given in Table 17.1. The dependence of the solvent diffusion coefficients on the concentration of polymers in solution or gels has been often found to follow the free volume theory [ 121. At polymer concentrations lower than = 50% by weight, a particularly simple expression has been suggested, eqn. 17.2, log (DDo)= Aw,/( 1 - ~ 2 )

(17.2)

where Do is the diffusion coefficient in the absence of polymer, A is a system-dependent constant, and w 2 is the weight fraction of the polymer [ 131. Plots of the data in log D vs. w2/(I - w 2 ) axes fit well the expected linear dependence (the correlation factors are 0.996, 0.999 and 0.988 for TMATEMPOI, PDTEMPONE and SLPEO, respectively). The D values decrease significantly in gels with lower water contents, and the effect is more pronounced for SLPEO.

227

17. Electron Spin Resonance lniagirig of' Trcinsport Processes in Polymeric Sjstemr

0.2

0.0

0 1

0 s

O L

0.6

DifTusion Distance (cm)

Diffusion Distance (cm)

Fig. 17.2: Complete set of experimental splined (A) and calculated (B) concentration profiles for the diffusion of TMATEMPOI in DE80 at 300 K. Consecutive experimental images were measured at t=4940 s, 12140 s, 22940 s, 33740 s, 40940 s, 77300 s and 112220 s.

Table 17.1:Diffusion coefficients (in units of 10-7 cm2 s-1) at 300 K of diffusants in HEMNDEGMA hydrogels (M is the molecular mass of the diffusant).

Sample (water content, wt YO)

TMATEMPOI (M = 211)

PDTEMPONE (M = 170)

SLPEO (M =1832)

DElOO (75)

24f4

24+4

3.4 0.5

DE80 (67)

17+3

13f2

1.8k0.3

DE50 (55)

6f 1

3+1

-- 0.1

+

17.4.2 Diffusion in Polystyrene Systems The translational diffusion of PDTEMPONE (Chart 17.1) was measured in polystyrene (PS) solutions and in cross-linked polystyrene (cPS) networks as a function of polymer concentration, degree of cross-linking by divinylbenzene (DVB), temperature, and solvent [ 5 ] . The study was initiated in order to assess the effect of the swelling solvent on the diffusion rates, to compare the transport properties of the exogenous tracer to those of the solvent, and to compare diffusion rates in polymer solutions and in swollen networks with the same polymer content.

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S.Schlick, P. Eagle, K. Kriiczaln, and J . Pilar

Fig. 17.3: Dependence of the translational diffusion coefficients for PDTEMPONE on the polymer content in PS/toluene solutions ( 0 )and in cPS swollen by toluene (W) at 300 K. Data for the selfdiffusion of toluene in PS/toluene determined by PFGSE NMR [14] at 298 K (A), and for the "dimer" Mz of styrene in PShenzene (0) [ 151 are given for comparison. Full and dashed lines are linear fits to the experimental data.

Plots of log D for PDTEMPONE determined at 300 K vs. w2/(1 - w2)in toluene solutions of PS and in cPS networks swollen by toluene are presented in Fig. 17.3 and fit the linear dependence well. The data were compared with two sets of literature data, which are also shown in Fig. 17.3: Data for the self-diffusion of toluene in the presence of PS at 298 K determined by pulsed field-gradient spin echo (PFGSE) NMR [14], and for the diffusion of M2, a "dimer" of styrene, 1,3-diphenyl-1-butanol (M= 226) in PShenzene at the same temperature [ 151. The diffusion coefficients observed for PDTEMPONE and M2 are very close; the slightly lower diffusion coefficient for M2 is probably due to both the higher molecular weight of M2 and to the higher viscosity of benzene compared to toluene. In contrast, the diffusion of toluene in the PS/toluene binary system is considerably higher than for PDTEMPONE in the ternary system, at comparable polymer content.

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229

The intercept of the data for PDTEMPONE in PS solutions is = 1.3.10-5cm2 s-l, and that for the cPS systems is = 1.6.10-5cm2 s-'; the average, = 1.4.10-5cm2 s-l, represents the diffusion of the spin probe in toluene at 300 K. By comparison, the intercept of the data for self-diffusion of toluene in PS/toluene is 2.5.10-5 cm2 s-', and for M2 in PShenzene is 0.9. cm2 s-'. The observed effect of cross-linking on D values is in agreement with qualitative observations of solvent penetration into cPS: Both swelling experiments for a series of cross-linked PS by different solvents [ 161 and NMR imaging studies of dioxane penetration in cPS as a function of the degree of cross-linking [ 171 have indicated that the transport of solvents in cPS becomes slower with increasing degree of cross-linking. In contrast to these conclusions, some studies have suggested similar diffusion rates in polymer solutions and in swollen networks with the same polymer content: A PFGSE NMR study of the diffusion coefficients of toluene in cross-linked PS beads (DVB in the range of 5.7 - 40%) swollen by toluene has detected no measurable differences compared to PS solutions in toluene containing a similar polymer content [18]. We are unable to explain the discrepancy at this time. We note, however, the significant difference between the swelling ratios (and consequently polymer content) of networks cross-linked in the presence of 5% DVB: 2.1 for the beads and 4.03 for the cPS gels used in our study. The different swelling ratios suggest significant morphological differences between the two types of samples, probably as a result of the different ways of preparation, suspension vs. block copolymerization. More experimental data on the diffusion rates of tracers, preferably by various techniques, on carefully characterized samples are needed. We believe that in general the diffusion coefficients of tracers depend not only on the network content, but also on the degree of cross-linking, molecular mass of diffusant, flexibility of polymer chains, morphology and homogeneity of the medium, and probe-polymer and solvent-polymer interactions. The temperature dependence of diffusion coefficients is often discussed in terms of an Arrhenius energy of activation. Plots of the diffusion coefficients for PDTEMPONE as tracer in PS/toluene follow an Arrhenius behavior very well. The activation energies for tracer diffusion, determined from the slopes of the corresponding plots, are in the range 52 f 6 kJ/mol for PS solutions containing 30 - 50 wt % polymer in toluene, with the higher value for the higher PS content. The faster diffusion of PDTEMPONE at 300 K detected in PS/DMF solutions containing 30 and 40 wt % polymer, compared to the PS solutions in toluene, could be due to the lower viscosity of DMF; differences in the conformations and flexibility of the

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S. Schlick, P. Eagle. K. Krucmltr, atid J. Pilar

polymer chains in the two solvents are also expected to play important roles in the transport properties of diffusants.

17.4.3 ESRI Based on MoV Molybdenum catalysts, in the form of oxides MOO:, or various molybdates. are used extensively in redox processes and acid-base catalysis [ 191. The ability of molybdenum to participate in redox and ligand exchange reactions in species containing many ligand types is crucial to the catalytic properties of this center. The presence of paramagnetic Mo" cations in these catalytic systems is an important advantage, because it allows the study by ESR of the various steps of sample preparation and catalysis. ESR spectra of Mo", a 5d' cation, consist of strong signals from 92M0, "Mo, 96M0, 98M0 and looMo ( I = 0, total natural abundance 74.32%), from which the g-tensor components can be deduced. Additional structural information can be obtained from an analysis of the hyperfine interaction of 95M0 and 97Mo (I = 512, similar magnetic moments, natural abundances 15.78% and 9.69%, respectively). The X-band ESR spectrum of MoCl, in dimethylformamide (DMF) at 300 K, which is the basis for the ESRI experiments reported here, is shown in Fig. 17.4 (inset) and consists of the isotropic signal from the nonmagnetic Mo nuclei with giso= 1.946, and an isotropic sextet from the magnetic nuclei with Aiso = 5 1.6 G. The imaging window indicated in the inset consists of the central signal; in solution the signal is about 10 G peakto-peak, and is broadened by the unresolved weaker signals corresponding to the inl = 112 and mI= -1/2 nuclear transitions. The imaging window shown in the inset is =80 G in the absence of magnetic field gradients. Imaging is based therefore on a signal that consists of one main signal. ESRI experiments were performed to deduce the diffusion coefficient of MoV (as MoCI,) in solutions of polyacrylic acid (PAA) [7]. Typical initial and final contour plots are shown in Fig. 17.4, for diffusion in a 5 wt % PAA solution in DMF. The simplicity of the image is evident in the initial and final perspective 2D plots shown in Fig. 17.5A, for diffusion in the 15 wt % PAA solution in DMF. Views in the spatial ( L ) and spectral (H) coordinates for the initial and final stages of diffusion are shown in Figs. 17.5B and 17.5C, respectively. We note the increased resolution of the hyperfine lines in the final image in the spectral dimension, due to the lower concentration of the diffusant. The signal at the lower magnetic field (vertical arrows) is more resolved, due to second order shifts of the hyperfine sextet to lower magnetic field.

23 1

17. Elecrron Spin Rcsoriance Imaging of Transport Processe.y in Polymeric Sxstems

I

I

Fig. 17.4: Two-dimensional contour plots of the initial (A) and final (B) spatial-spectral images for the diffusion of MoCl5 at 300 K in a solution of PAA in DMF ( 5 wt %). The inset shows the ESR spectrum of M&15 in DMF at 300 K, and the imaging window.

The results suggest that increasing the concentration of PAA leads to lower diffusion coefficients. Plot of the data in log D vs. w2/(1-w2) axes are consistent with the linear dependence predicted by eqn. 17.2. Extrapolation to w2 = 0 gives Do = 9.0.10-6 cm2s-l. ESRI based on MoV was also applied to the measurement of the diffusion coefficients of MoV (as MoCl,) in perfluorinated ionomers (“Nafion”) swollen by ethanol [8]. The diffusion coefficients in Nafiodethanol are 5.0.10-7 cm2 s-’, 7.1.10-7 cm2 s-l, 10.4.10-7 cm2 s-l and 13.3.10-7 cm2 s-l at 280 K, 300 K, 315 K, and 330 K, respectively, all k 15%. The activation energy for diffusion is 15.4 kJ mol-I. Because of the sensitivity of the ESR signal from MoV to oxygen and water, the use of 2D spatial-spectral imaging was very important: this method enabled the tracking of the ESR intensity as a function of time as MoCl, advanced through the diffusing medium. We expect that the method illustrated above for MoV become important for measuring transport properties, and temporal and spatial characteristics of reactions in catalytic systems. The spatial resolution can be significantly improved by using molybdenum enriched in 98M0, which is the most affordable of the nonmagnetic Mo isotopes and is available from Oak Ridge National Laboratories as MOO, (97.27% enrichment).

232

S. Schlick, P. Eagle, K . Kruczala, and J . Pilar

L

c -

H

L

H

L Fig.17.5: (A), perspective plots of initial (top) and final (bottom) spatial-spectral images for the diffusion of MoCIs at 300 K in a solution of PAA in DMF (15 wt %). (B), initial and (C), final spatial and spectral images for the diffusion of MoCIS at 300 K in a solution of PAA in DMF (5 wt %). Vertical arrows show the low-field satellite line from the magnetic nuclei in the imaging window.

17.4.4 Diffusion in a Self-Assembled Polymeric Surfactant The aggregation of the triblock copolymer poly(ethy1ene oxide)-b-poly(propy1ene oxide)-b-poly(ethy1ene oxide) EO13P030E0,, (Chart 17.2, commercial name Pluronic L64) in aqueous solutions, and the hydration of the PEO blocks, were deduced from ESR spectra of the nitroxide spin probe PDTEMPONE at 293 - 330K [9]. The phase diagram of L64 consists of micellar, cubic, hexagonal, lamellar, and reverse micellar regions. The isotropic 14N hyperfine splitting of the nitroxide, aN,is a key parameter that reflects the local polarity, and its variation with temperature and polymer concentration is an indicator of aggregation. The translational diffusion coefficients of the spin probe were measured by ESRI in the L64 solutions containing 10 to 100 wt % polymer; the D values are presented in Fig. 17.6.

17. Electron Spin Resonance Imaging of Transport Processes in Pol.ymeric S.ystems

233

Chart 17.2: PEO-PPO-PEO triblock copolymers. HO[-CH,CH,O-],[

-CH(CH3)CH,O-],[ -CH?CH20-],H

l.OE-06

-+a

1

"E

l.OE-06 0

9

I

0

l.0E-07

1

I

I

I

I I I

I I I

1.OE-08

0

20

40

\

I

60

80

100

L64 wt Yo

Fig.17.6: Diffusion coefficients (in cm* s-1) as a function of L64 content in aqueous solutions (.). Also presented are the diffusion coefficients of L64 chains measured by PFGSE Nh4R (0)[20].

The D values of the spin probe decrease with increase in the polymer content, but the decrease is more prominent for L64 contents in the range 10 to 30 wt %. At 90 wt % polymer, D is similar to that of the polymer chains (determined by Nh4R [20]). We suggested that water provides an important pathway for the translational diffusion of the probe. These conclusions are supported by the ESR results for PDTEMPONE, which show that the probe is located at the interface between the EO fragments and water. Moreover, preliminary results indicate that the concentration dependence of the D values is different for different probes, and depends on the probe locations. For cationic probes we found that the D values are higher compared to PDTEMPONE, and constant in the concentration range that was measured, 50 - 90 wt % L64 [211.

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S. SchlicX, P. Eagle, K. Kruczala. and J . Pilnr

Acknowledgements This ESRI research was supported by the National Science Foundation (NSF, Polymers Program), American Association of University Women (AAUW), the US-Czech Science and Technology Program, and Ford Motor Company.

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11.

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S. Pickup, F. D. Blum, Macromolecules 22 (1989) 3961.

15.

M. C. Piton, R. G. Gilbert, B. E. Chapman, P. W. Kuchel, Macromolecules 26 (1993) 4472.

16.

D. Kim, J. M. Caruthers, N. A. Peppas, Macromolecules 26 (1995) 1841.

17.

M. Ilg, B. Pfleiderer, K. Albert,W. Rapp, E. Bayer, Macromolecules 27 (1994) 2778.

18.

S. Pickup, F. D. Blum, W. T. Ford, M. Periyasami, J. Am. Chem. SOC.108 ( I 986) 3987.

19.

J. Haber, Molybdenum: An Ourtine ofirs Chemistry and Uses, E.R. Braithwaite. J. Haber (eds.). Elsevier, Amsterdam, 1994, Chapter 10.

20.

K. Zhang, B. Lindman, L. Coppola, Langmuir 11 (1995) 538.

21.

Unpublished results from this laboratory.

18. Stray Field Imaging and Magnetic Resonance Microimaging Studies of High Impact Polystyrene, an Elastomer-Toughened Material J. A. Chudek, G. Hunter, and F. Mohd Som Department of Chemistry, University of Dundee, Dundee DD14HN, Scotland, UK

P. .I. McDonald, and B. Newling Department of Physics, University of Surrey, Guildford GU2 5XH, England, UK

Abstract Plastic deformations induced by compression in the thermoplastic composite material High Impact Polystyrene (HIPS) cause significant changes in the transverse relaxation times of the 'H's of the polybutadiene (PB) elastomer phase but not in those of the polystyrene (PS) matrix. Stray Field Imaging (STRAFI) has been used to image both types of polymer and, from the effect on T2 of changes in the PB chain mobility, the degree of stress induced within the rubbery disperse phase of HIPS has been monitored.

18.1 Introduction - High Impact Polystyrene HIPS is an example of a thermoplastic composite with a rubbery disperse phase which reduces both the tensile and compressive yield stress of the brittle polystyrene matrix to give much improved impact properties to the material [ 11. Bulk styrene monomer is usually polymerised in the presence of about 8 wt % of dissolved PB. The process is homogeneous up to about 6%of the monomer conversion, and thereafter heterogeneous with a rubber-rich continuous phase; the disperse phase is practically pure PS. A phase inversion occurs at about 15 - 20% conversion, after which the matrix remains as the continuous phase. A graft copolymer accumulates at the interfaces, stabilising the heterogeneous

236

J . A. Chudek. G. Hunrer,

F. Mottd Som. P. J. McDutmld, and

B. N w l i n g

mixture and favouring the phase inversion [2]. Electron microscopy shows that the micron-sized rubber particles have a ‘salami’ structure, with numerous PS subinclusions embedded in a continuous PB phase [3]. The volume fraction of the rubber particles (including all material enclosed within the outer layer of PB in each particle; ahout 3% for HIPS containing 8 wt % polybutadiene [3]) and their internal microstructures affects the bulk properties of the composite [4,5]. The mechanisms of yielding in HIPS are distinctly different in compression from those operating in tension [6]. Under tensile loading, the dominant plastic deformation mechanism is crazing, visible as a diffuse zone of ‘stress whitened’ material in which a large number of small crazes are present [7]. Crazes cannot, however. develop under compression and the PS yields by forming shear bands with the rubber particles co-operating in the deformation of the yielded polymer [6]. An early report by Komoroski and Sarkar on diblends of PB and styrene-butadiene rubbers describes changes in magnetic resonance image intensity caused by changes in polymer chain mobility. which is a determinate in T2 [8]. We now describe changes in the magnetic resonance images of HIPS subjected to compressive stress; STRAFI monitored both PS and PB phases, MRM monitored only the rubber disperse phase.

18.2 Experimental and Results The HIPS samples were cut from a sheet of Athpol 90TM(Athlone Extrusions Ltd., Republic of Ireland) of 3 mm nominal thickness. For an initial series of experiments, at ambient temperature 11 samples of uncompressed size ca. 10 x 10 m m were separately compressed in a simple hydraulic press over the range from ca. 10 to 100 kN in 10 kN increments from sample to sample in the series, for a period of one minute before releasing the pressure. Up to 30 kN, some elastic as well as plastic deformation occurred; above 30 kN there was only plastic deformation and no recovery in thickness even after several months. The individual samples were bound together with cotton thread to form a single stack for simultaneous imaging (Fig. 18.1). For a second experimental series, with more precisely controlled compression provided by an Instron 4469 Mechanical Testing Machine, 19 circular samples of initial diameter ca. 10 mm were each reduced at a displacement rate of

mm s-’ from a

18. STRAFI and MRM of High Impact Pol.vstyrene, un Elustomer-Toughened Material

237

P

Increasing pressure

Fig. 18.1: Drawing of the stack of compressed HIPS samples prepared for first MRM series

Fig. 18.2: Image intensity of a slice (broken line) through the stack. (Numbers: compression x 10 kN)

common initial thickness of 3.06 mm to that targeted, incremented in steps of 0.1 mm from sample to sample. The Instron screw movement was stopped and after about 10 seconds under compression, the applied force was unloaded. Mostly elastic deformation occurred up to a compression of 2 kN and the samples had recovered almost to their original thickness after about 24 hours. Above 2 kN, plastic deformation occurred in addition to elastic deformation, and the reduction in sample thickness was permanent and Fist order with respect to the force originally applied (Fig. 18.3). For the MRM studies, the samples were assembled into three stacks held closely together by Cling Film TM. MRM was performed using a Bruker NMR AM300WB spectrometer (89 mm bore 7.05 T magnet) fitted with a Bruker microimaging accessory 110%

100%4&

90%

80% -~ 70% 60%

Elastic Region

-~

~-

** .aa. a**.

-

Plastic Region Exp.

CUNe -@

7

Fig 18.3: Percentage of original sample thickness (ordinate) 3 days after unloading compression (abscissae)

238

J. A. Chudek. G. Hunter. F. Mohd Som, P. J. McDonald, and B. Newling

(25 mm diameter cavity resonator rf coil). Slice selective soft pulses required for 2D imaging made the elapsed time to echo too long for the rapid signal decay caused by short T2 values. Standard Bruker 3D spin-echo imaging sequences (requiring only hard pulses) were therefore used to acquire the imaging data, subsequently processed using a Bruker Aspect X32 work-station. The images (Figs. 18.2 and 18.4) were accumulated with TE = 2.28 ms and a voxel size of 391 x 391 x 391 pm. The field gradients used were, G, = 0.094; G, = 0.036; G, = 0.036 T m-*.Image acquisition time - 96 hours.

Fig. 18.4: Image intensity of a slice through the second stack imaged, showing the effects of plastic deformation on the rubber disperse phase. Numbers are authors’ references for HIPS samples

The plot of image intensity (at TE = 2.28 ms) of a slice through the stack illustrated i n Fig. 18.1 clearly showed a decrease with increasing compression (Fig. 18.2), in line with our earlier findings [9]. The sharpest decrease occurred on increasing the compression load from 10 to 20 kN. Image intensity thereafter remained approximately constant, although the samples remained intact and plastic deformation continued as shown by the continuing decrease in their thickness. In a second series of experiments, designed to explore in detail the regime during which had occurred the very rapid decreases in image intensity, the ultimate compression load, incremented over the 19 samples, was kept to below 5.7 kN, corresponding to a maximum permanent reduction of 0.9 mm in the thickness of the compressed samples (Fig. 18.4). Where necessary the compressed samples were recut to 10 mm diameter to fit within the STRAFI rf. coil. STRAFI data were obtained at ambient temperature (298 K) using a Chemagnetics CMX-400 Infinity console attached to a Magnex superconducting magnet of nominal field 9.4 T and a home built STRAFI probehead. In the 58 T m-* fringe field gradient accessed, B, was 5.57 T and the samples were stepped through the gradient in 250 pm slices to give one-dimensional profiles [lo]. A solid echo pulse sequence { (d2), -z-[(d2), -z -acquire], } (z = 20 ps; n = 128) was used. The data for each sample were fitted to eqn. (18.1), where s

18. STRAFI und MRM of High Inrpnct Polwyene, LIII Elusionier-Toughened Material

239

and 1 refer to long and short transverse relaxation times (T2 with some contribution from TIP)respectively. Curve fitting was by the Easyplot@commercial software package [ 111 (T2,s, (PS) was constant at - 60 ps; T2,1,(PB) decreased from 8 to - 5 ms as sample thickness decreased).

0

1

2

3

4

5

6

7

Dlstance (mm)

+T2*(x10 p e e ) Tz~(msec)

Fig. 18.5: STRAFI profiles constructed from T2,s and T2,, for a stack consisting of an uncompressed sample (left) and one compressed at 90 kN (right)

Figure 18.5 shows two STRAFI profiles constructed from TzSsand T2,1of a stack of an unstressed sample and one compressed at 90 kN. The boundary between the two samples is clearly delineated in the profile given by T2,, but not in that given by Figure 18.6 shows a plot logeT2,1(STRAFI) vs. sample thickness after recovery from elastic deformation for a series of samples compressed from 2.0 to 5.7 kN. The decrease in T2,] was first order with respect to the decrease in sample thickness. The initial MFW results had shown that there is no further reduction in T2,]at compressions greater than 20 kN.

18.3 Conclusion Unidirectional compression of HIPS changes the shape of its rubber particles from spheroidal to ellipsoidal, causing elongation of the PB chains and significantly affecting the chain motions. Beyond the ultimate chain extensions there is no further decrease in T2 1, although plastic deformation of the material continues and must be accommodated, either by cavitation within the rubber particles or failure of the PB - PS bond.

240

J . A. Chudek G. Hunter. F. Molid Som P. J. McDonald, and B. Newlirig

2.05 2.00

;1.95

h

4 1 .go 1.85 Y

-

bm 0

1.80 1.75 1.70

4

3 .oo

I.

2.80

2.60

2.40

2.20

2 .oo

Thickness (mm)

Fig. 18.6: Plot logeT2,,vs. sample thickness for plastically deformed HIPS samples

Acknowledgement We thank the EPSRC for financial support.

References 1.

J. L. Amos, Polym. Eng. Sci. 14 (1984) 1.

2.

F. M. Peng, J. App. Polym. Sci. 40 (1990) 1289.

3.

C. B. Bucknall, F. F. P.CBte, and I. K. Partridge, J. Mafer. Sci. 21 (1986) 301.

4.

D. M. Shiozaki and A. Klauzner, J. Muter. Sci. 26 (1991) 5865.

5.

C. B. Bucknall, P. Davies, and I. K. Partridge, J. M a w . Sci. 21 (1986) 307.

6.

C. B. Bucknall, P. Davies, and I. K. Partridge, J. Muter, Sci. 22 (1987) 1341.

7.

L. Castellani, and C. Maestrini, Polymer 31 (1990) 2278.

8.

S. N. Sarkar and R. A. Komoroski, Macromolecules, 25 (1989) 600.

9.

G. Hunter and J. A.Chudek, J. Muter. Sci. Letr.,ll (1992).

10.

P. J. McDonald, Prog. NMR. Specr., 30 (1 997) 69.

1 1.

EasyPlot", Spiral Software, USA.

19. Mixed Solvent Ingress into PMMA Measured by Stray Field Magnetic Resonance Imaging D. M.Lane, P. J. McDonuld, J. L. Keddie

School of Physical Sciences, University of Surrey, Guildford, Surrey, GU2 5XH, UK

Abstract Solvent ingress into polymeric materials is of widespread industrial importance in the context of polymer durability. Evidence suggests that the synergetic effects of two or more mixed solvents acting together and of residual solvent left over in the polymer from manufacture can be particularly important. Stray-field magnetic resonance imaging has been used here to study these effects for methanol ingress into poly (methyl methacrylate) (PMMA) pre-swollen with acetone. The ingress of methanol into PMMA exhibits Case I1 diffusion dynamics. It is shown that the incorporation of small fractions of acetone during manufacture of glassy PMMA dramatically enhances the subsequent uptake rate of methanol and a transition from Case I1 to Fickian dynamics is observed. The transition is reversed by lowering the temperature of the sample. The results are analysed using the Thomas and Windle model of solvent diffusion in polymers.

19.1 Introduction It has been known for many years that solvents ingressing glassy polymers display a rich variety of behaviour ranging from Fickian to Case I1 diffusion. Fickian diffusion is characterised by smooth concentration profiles varying with the square root of time. Case I1 diffusion is observed when the mechanical relaxation of the polymer at the solvent front, and hence the ability of the polymer to incorporate the solvent, is slow in comparison with the diffusion of solvent to the front through the already swollen material. It is char-

242

D.M . h n e . P. J . McDonuld. and J. L. Keddie

acterised by a sharp solvent front advancing linearly with time into the polymer. Behind the front, the solvent concentration is uniform. In the early 1990's, however, a few niagnetic resonance imaging experiments were beginning to show that the solvent dynamics were not always correspondingly uniform [I] and in 1993, an early stray-field imaging experiment looking at acetone and PVC showed evidence that the polymer chain dynamics were also non-uniform [2]. Methanol ingress into PMMA is often studied as a model system. It has been shown to follow Case I1 diffusion dynamics at temperatures below the glass transition temperature of PMMA and gradients in NMR mobility parameters related to the solvent have been seen [ 1,3]. Experiments that visualise the ingress of methanol and acetone vapour mixtures into PMMA have also been reported [4]. In this case gradients in both the polymer and solvent dynamics were observed. In the current study, experiments to visualise the ingress of liquid methanol and acetone mixtures with one component deuterated have been performed to determine if one component ingresses faster than the other. Moreover, experiments which focus on the ingress of methanol into PMMA pre-swollen with acetone are reported. These experiments are performed in order to understand further how polymer deterioration depends on residual solvents left over from manufacture. They reveal a transition from Case I1 to Fichan diffusion and permit careful testing of the Thomas and Windle model of solvent diffusion in polymers in the important anomalous diffusion regime. Stray-jield magnetic resonance imaging is used throughout this work. With strayfield imaging the rigid and swollen polymer and the solvent are separately visualised with a resolution of the order of 2 0 p m and a first echo time as short as 20ys. The different components are distinguished on the basis of their differing spin-spin relaxation times.

19.2 Experimental PMMA samples in sheet form typically 500- 550ym thick were prepared from uncrosslinked powder (Aldrich Chemical Co.) with a molecular weight of 996,000. The powder was either pressed into sheet form at a temperature of 165 "C, as previously described [4] or dissolved in acetone. In the latter case, the acetone was allowed to

19. Minrd Solvent hrgress inro PMMA Measured bv Srray Field MRI

243

evaporate, often over a period of weeks to produce pre-swollen samples containing between 0 and 8 weight % acetone. As long as the drying process was sufficiently slow, the procedure produced homogeneous samples. After the desired weight fraction was achieved, the samples were sealed for a further period of days to ensure the full spatial equilibration of the acetone in the PMMA. Differential scanning calorimetiy (DSC) and dynamical inechanical thermal analysis (DMTA) were used to measure the glass transition temperature ( T g )of the pre-swollen polymer with varying acetone fraction. This temperature marks the onset of the transition from the glassy to the rubbery phase of the polymer. The transition is associated with increased mobility of polymer chains. A second transition due to increased mobility of side groups can also be detected with the DMTA at the lower fl transition temperature, Tp. Stray-field imaging was used to profile through the pre-swollen and pressed PMMA samples during exposure to solvents, using the frequency swept surface coil method previously described [ 5 ] . This technique profiles a small central volume of the exposed PMMA sheet. The advantages of this method are threefold: compared to other stray-field methods sample levelling and hence spatial resolution are improved; errors due to the ingress of solvent around the sides of the sample are eliminated and acquisition speeds are increased. However, the use of this technique sacrifices the profile signal-to-noise ratio. At each spatial location across the sample, quadrature echo trains were acquired, typically using a pulse length of 20 ps, which corresponds to approximately 24 ym spatial resolution in the 58 T/m stray field gradient and a pulse gap of 25 ps. All profile intensities were normalised to a standard rubber sample.

19.3 Results Figure 19.1 shows the solvent front position as a function of time in samples of PMMA exposed to an 80 : 20 methanol : acetone liquid mixture at 18 "C, first with the acetone deuterated and then with methanol deuterated. In both cases, the front advance is linear in accordance with Case I1 dynamics. The rate of ingress of the two components is seen to be the same within the spatial resolution of this technique.

244

D.M. Lone. P. J . M c D o ~ ~ Iand L ~ ,J . L. Keddie

150.0

7

n n V."

0.0

2.0

4.0 6.0 8.0 10.0 Time (hours)

Fig. 19.1: Solvent front position as a function of time for a 80 : 20 methanol-acetone liquid rnixture into PMMA showing the acetone (circles) ingress (1 1 pm/hr) and methanol (squares) ingress (13 pm/hr). In each case, the alternate component was deuterated. The solid lines are least squares fits to the data.

1.o

0.5 0.0 0 .'i 1.0

a

IL' 0.5

-;0.0 (g 1.0 CI

0.5 0.0 0

250 Distance (pm)

500

Fig. 19.2: Methanol ingress profiles into PMMA containing a) 0% b) 3.3% and c) 8% acetone shown at 60, 80 and 17 minute intervals respectively, all starting at t = 0. The dotted lines are profiles calculated according to the Thomas and Windle model for solvent diffusion in glassy polymers as described in the text.

19. Mixed Solvent Ingress into PMMA Measured by Slray Field MRI

500-0 h

E

r--l

b

S

2a, 0

(d -

250.0

s

i i E

e U

125.0

0.0

'

I

'

1

'

-

-

375.0 I-

1

245

i: Time (hours)

0.0 0.5 1.0 1.5 2.0 Sqrt. Time ( h o ~ r s ~ ' ~ )

Fig. 19.3: The front displacement as a function of time for methanol ingress into a) pure PMMA and b) PMMA containing 8 weight % acetone. The solid lines are least squares fits to the data.

Figures 19.2a, b and c show exemplar methanol ingress profiles into thin PMMA sheets containing 0, 3.3 and 8 weight % acetone recorded at 25 "C and at intervals of typically 4 - 15 minutes. It is immediately clear that the methanol ingresses much more rapidly into the pre-swollen samples. More interestingly, it is found that the solvent front advances linearly with time into the pure PMMA sample, as shown in Fig. 19.3a, but with the square root of time into the most pre-swollen sample, Fig. 19.3b. This is a clear indication of a transition from Case I1 to Fickian diffusion with pre-swelling. The temperature dependence of the diffusion of methanol into pure PMMA and PMMA swollen by 8 weight % acetone has been explored in the range -20 to + 65 "C. Figure 19.4 shows exemplar profiles for methanol ingress into pure PMMA recorded at 65 "C and at 8 minute intervals. From the data it is clear that the diffusion remains Case I1 throughout the temperature range studied although the front velocity increases dramatically from 27 pm/h at 25 "C to 755 pm/h at 65 "C. For acetone pre-swollen PMMA, it is possible to return to Case I1 diffusion by lowering the temperature. Figure 19.5 shows profiles recorded at -4 "C for a sample preswollen with 8 weight % acetone. The front displacement as a function of time varies as (Fig. 19.5 inset) placing this sample in the anomalous regime. By -20 "C the mecha

246

D. M.Dine, P. J . McDonald, and J . L. Kerldie

1.o

0.8 0 .c

2

I

0.6

LL

s

c

> -

0.4 0.2 0.0

0.0

200.0

400.0

Distance (pm) Fig. 19.4: Methanol ingress profiles into pressed PMMA at 65 "C shown at 8 minute intervals. starting at r = 0. The dotted lines are theoretical profiles calculated using the Thomas and Winrlle model for solvent diffusion in glassy polymers as described in the text.

1.o 8 K

0 .c 0

E I.L

c

0.5

c

9

0

cn

0.0

0.0

200.0 Distance (pm)

400.0

Fig. 19.5: Methanol ingress profiles into PMMA pre-swollen with 8 weight % acetone at -4 "C recorded at 78 minute intervals, starting at t = 0. The front displacement (inset) varies as W4 (solid line) indicative of anomalous dynamics. The dotted lines are theoretical profiles calculated using the Thomas and Windle model for solvent diffusion in glassy polymers as described in the text.

247

19. Mired Solvent Ingress into PMMA Measured bv Stray Field MRI

nism is fully Case 11, t l . Results from both DSC and DMTA studies are shown in Table 19.1. Both techniques, show a decrease in Tg with increasing acetone fraction in the preswollen PMMA. The temperature of the lower beta transition, Tp' also decreases with increasing acetone fraction. Table 19.1. DSC and DMTA Data % Acetone

Tg (DSC)

Tg (DMTA)

Tp (DMTA)

0 2.0 4.3 5.5 6.5 8.5

109.9 89.4 75.9 73.9 72.1 70.6

104.1 92.4

35.4 29.9

-

-

85.0 79.5 75.3

23.6 21.5 21.4

19.4 Discussion Observing the ingress of methanol into PMMA pre-swollen with acetone allows the experimenter to move smoothly between Case I1 and Fickian diffusion regimes in much the same way as, for example, can be achieved by varying temperature 131. This provides a means of testing the applicability of analytic models in this key regime where the diffusion is controlled by the mechanical properties of the system. Importantly the change is achieved at constant temperature (so as to remove one variable from the analysis) with the minimum disruption to the polymer sample. The model tested here is that derived by Thomas and Windle [6]. This model has so far achieved widespread but not universal acceptance, although it has not been rigorously tested in the anomalous regime. The model involves the coupling of di'sion and viscoelastic relaxation in the polymer and solvent system described by the following coupled differential equations;

3 at ="(ax

D(@)&?)

( 19.1a)

(19.lb)

24%

D. M. Lnrie. P. J. McDonald, and J. L. Kerldie

where $ is the fractional solvent concentration in the polymer relative to the equilibrium value (so that 0 I $ I 1); it is a function of space ( x ) and time (I). D(@)is the solvent mutual diffusion coefficient in the polymer, q($) is the polymer viscosity and T is temperature. The Thomas and Windle parameter, B, is a constant of the system, here taken as 9 . lo5 N m-2 K-l [6]. Thomas and Windle assume that the mutual diffusion coefficient and viscosity vary exponentially with concentration, according to D($) = Doexp(Q/Qo) and q(@) = qoexp(-m$) respectively. Equation (19. la) represents concentration driven Fickian diffusion processes. Equation ( 19.1b) represents changes in solvent concentration due to temperature and viscoelastic response in the polymer. The coupling of these two terms determines whether the solvent diffusion dynamics are dominated by mechanical relaxation of the polymer resulting in Case I1 dynamics or solvent concentration gradients resulting in Fickian diffusion dynamics. The coupled differential equations (19.1) can be numerically integrated to yield concentration profiles $(x,z) which can be compared to experiment. However the equations are notoriously unstable and require great care in solution by finite difference methods. Thomas and Windle proposed a relatively simple numerical algorithm [6]. Wu and Peppas [7] later devised a more rigorous algorithm although they adopted asymmetric finite differences. We have implemented both the Thomas and Windle and the Wu and Peppas methods and also the latter scheme using symmetric finite differences. We have calculated profiles for a wide variety of diffusion, viscosity and temperature parameters with typical boundary conditions $ = 0, x > 0, t = 0 and $ = 1, x = 0, t 2 0. In different ways, we have found all these algorithms lacking in analysing our data. Thomas and Windle solutions yield profiles which scale with the space step in the Case I1 limit, while Wu and Peppas solutions differ dependent on the direction of ingress due to the asymmetric finite differences. The symmetric version is unstable. The theoretical curves in Figs. 19.2, 19.4 and 19.5 are all based on the Thomas and Windle algorithm. They have been calculated with the same space-step size (24 pm) for internal self-consistency and have been convoluted with a Gaussian resolution broadening function. It is suggested that the absolute values of D(@)in particular are necessarily subject to some error, but that they nonetheless show the correct functional dependence on temperature, viscosity and acetone fraction. The curves here have been calculated using a viscosity exponent m = 15, as suggested by Thomas and Windle, and a diffusivity exponent l/@o= 4.2, based on our own earlier measurements of Dself [4]. In general, the front velocity is well fitted by the model although the profile shape is less well reproduced particularly in the anomalous regime. The variation of viscosity with

19. Mixed Solvent Ingress into PMMA Measured by Stray Field MRI

249

temperature corresponding to equilibrium methanol swelling of the polymer, q( l), is shown in Fig. 19.6 for both pure and 8% acetone pre-swollen polymer. The temperature dependence of viscosity of polymer melts and solutions is often well described by the Williams-Landel-Feny (WLF) equation [8], (19.2)

where TR is a reference temperature and c1 and c2 are constants. For a variety of polymers c1 = 17 and c2 = 50 "C [8], using Tg as the reference temperature. On this basis, using qTg (1) and Tg as fitting parameters, we have calculated that Tg of the methanolswollen PMMA at equilibrium concentration is -57 "C and the methanol swollen, acetone pre-swollen polymer is -130 "C. The corresponding viscosities are of the order

lo1* and lOI9N m-3 s respectively. We note that the calculated Tg values are independent of the scaling errors in the Thomas and Windle fitting procedure. The solid lines in Fig. 19.6 are fits to the WLF equation. This type of WLF analysis has been applied elsewhere [9] to extract values of Tg for PMMA swollen with up to 50 vol. % diethyl phthalate. In that case, there was good agreement between values of Tg determined from WLF analysis and values determined

7.5

7*0F

6-ot

5.5 -20

,

,

, ,\ \ ,

0

20 40 60 Temperature ("C)

1 80

Fig. 19.6: The variation in viscosity with temperature for equilibrium methanol swelling of pure PMMA (circles) and PMMA pre-swollen with 8 weight % acetone (squares). The solid lines are fits to the data using the WLF equation as described in the text.

250

D.M. Lane, P. J. McDonald, and J. L. K e d i e

from conventional measurements. We can calculate the expected Tg for PMMA at equilibrium swelling using the Kelley-Bueche equation [9]; (19.3)

where Tgp and Tgsare the glass transition temperature of the pure polymer and solvent and $eq is the equilibrium solvent fraction in the polymer. K is a constant dependent on thermal expansivities of the two materials. Using Tgp,Tgsand K equal to 109 "C, - 163 "C and 3.8 respectively and qq = 0.3 taken from earlier stray-field experiments [4], we obtain Tg= - 60 "C for the glass transition temperature, which is in good agreement with the value of -57 "C obtained via the WLF analysis of the stray field profile fit data. Another approach to the analysis of the viscosity data followed by Lasky et a]. [ 101 is to view viscosity as a thermally activated process, applicable when out of the WLF region, i.e. T > Tg + 100 "C. On this basis we calculate activation energies of 83 lillrnol and 41 kl/mol for the same pure PMMA and pre-swollen data. respectively. However, we suggest that it is more reasonable to view, rather than the viscosity, the diffusivity as a thermally activated process. Figure 19.7 shows the dependence of D(4) on temperature for the 8% pre-swollen PMMA and pure PMMA in the temperature range -20 to 25 "C and 25 to 65 "C respectively. The methanol diffusion coefficient in both the pure PMMA and pre-swollen PMMA shows an Arrhenius dependence on temperature with a thermal activation energy of approximately 55 kJ mot', comparable to that derived by Ercken et al. [3], 57 kJ mol-I, for the diffusion of methanol into pure PMMA in the Fickian diffusion limit. Interestingly, it is noted that the activation energy of the coefficient does not seem to vary with pre-swelling the polymer. We suggest that the activation energy for diffusion of the solvent molecules is approximately the same for methanol and acetone. Viscosity on the other hand is dependent on the mobility of the polymer molecules which in turn varies with the solvent type. Finally, Lasky et a]. have observed that the Thomas and Windle model predicts that the Case I1 front velocity, v, should scale according to: (1 9.4)

Using parameters derived from the fits to the stray-field imaging data, it is possible to verify this relationship. Figure 19.8 shows that this linear behaviour holds well in the temperature ranges examined here for Case I1 diffusion of methanol into pure PMMA.

19. Mixed Solvent Ingress into PMMA Measured b.v Stray Field MRI

t 2.8

25 1

i 3.0

3.2

3.4

3.6

3.8

1 OOO/T( K-') Fig. 19.7: The variation in solvent mutual diffusion coefficient with temperature at equilibrium methanol swelling in pure PMMA (circles) and and PMMA pre-swollen with 8 weight % acetone (squares). The solid line is a least squares fit to the data.

3.0e-07

1

~

1

'

1

'

2.0e-07 -

0

200 400 600 Velocity (pm/hr)

800

Fig. 19.8: The relationship between Case I1 front velocity and the square root of (Diffusion x TemperatureNiscosity) as described in the text. The solid line is a least squares fit to the data.

252

D. M. Lone, P. J. McDonald, and J. L. Keddie

Acknowledgements The authors wish to thank the Engineering and Physical Sciences Research Council (EPSRC) for project funding (Grant No.GWK12397). DML acknowledges EPSRC and Chemagnetics for studentship support. In addition, we thank Dr. Ian Hopkinson, Cavendish Laboratory, Cambridge and Dr. Adam Chaplin, DERA, Farnborough for assistance with DSC and DMTA studies.

References 1.

L. A. Weisenberger,J. L. Koenig, Macromolecules 23 (1990) 2445.

2.

K. L. Perry, P. J. McDonald, E. W. Randall, K. Zick, Polymer35 (1994) 2744.

3.

M. Ercken, P. Adriaensens, G. Reggers, R. Carleer, D. Vanderzande, J. Gelan, Macromolecules 29 (1996) 5671 and 28 (1995) 8541.

4.

D. M. Lane, P.J. McDonald, Polymer 38 (1997) 2329.

5.

P. M. Glover, P. J. McDonald, B. Newling, J. Magn. Reson. 126 (1997) 207.

6.

N. L. Thomas, A. H. Windle, Polymer 23 (1982) 529.

7.

J. C. Wu,N. A. Peppas, J. Appl. Polym Sci. 49 (1993) 1845.

8.

J. D. Ferry, Viscoelastic Properties of Polymers, Wiley and Sons 3" edn.. 1980.

9.

F. N. Kelley, F. Bueche, J. Polym. Sci. 50 (1961) 549.

10.

R. C. Lasky, E. J. Kramer, C. -Y Hui, Polymer 29 (1988) 1131.

20. Stray Field Imaging and Magnetic Resonance Microimaging Studies of the Anisotropic Absorption of Solvents by Extruded Polypropylene R. J. Abbott’, J. A. Chudek’, G. Hunter1,R. L. MacKay‘, P.J. McDonald2, L. Squires3 Department of Chemistry, University of Dundee, Dundee DD14HN, UK Department of Physics, University of Surrey, Guildford GU2 5XH, UK 3 Non-wovens Division, Don and Low plc., Glamis Road, Forfar, Angus DD8 IEY, UK 1

Abstract MRM and STRAFI studies show that the absorption of organic solvents, such as carbon tetrachloride, toluene, and cyclohexane, into extruded isotactic polypropylene samples is strongly anisotropic and occurs much more rapidly via cut surfaces than through intact moulded surfaces. This phenomenon is attributed to the formation during the extrusion process of a highly oriented skin layer, resistant to penetration by normally good solvents. At ambient temperature the absorption follows Case I1 kinetics, and is at least an order of magnitude faster through cuts than through undamaged surfaces.

20.1 Introduction Isotactic polypropylene is a widely-used semi-crystalline thermoplastic made from the monomer using a stereospecific catalyst with the result that all of the methyl group branches are arranged on the same side of the polymer backbone. Most of its uses involve some form of moulding or extrusion. For example, for non-woven fabrics, fibres are produced by the extrusion of molten polymer through a die and then rapidly cooled in air while under tension. The effects of this extrusion on the material are qualitatively similar to those which occur during injection moulding where the pressure and resultant

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flow into the mould produce a high degree of molecular alignment. Very rapid freezing occurs where the melt is in contact with the cooled mould, causing the polymer to retain a high degree of molecular orientation along the direction of flow. The core of the sample undergoes a much slower cooling, allowing time for randomisation of the polymer chains, and the degree of orientation is therefore much less. Between the extremes of the well-oriented skin layer (about 15 pm thick [l]) and the randomly oriented core there exists a sub-surface transition zone with a high shear orientation which is often the site of mechanical failure. This zone itself consists of a number of sub-layers with decreasing polymer chain orientation as the core is approached [1,2]. STRAFI is able to image unswollen polypropylene with its very short (ps) transverse relaxation time. However, even above its glass transition temperature. isotactic polypropylene does not normally give a sufficiently narrow 'H NMR spectral line to allow imaging by conventional MRI techniques. Liquid imbibition causes varying degrees of swelling [3] and increased chain mobility results in a sufficiently long T2 (2 500 ps) to allow conventional MRM. MRM [4] and STRAFI [5] have already been shown to be valuable techniques in studying the sorption of liquids by polymers.

20.2 Experimental The samples were long cylinders (ca. 10 mm diameter) of isotactic polypropylene (Shell grade KY 6100) which were the sprue associated with injection moulded blanks. As the mould was injected via the sprue, the very rapidly cooled samples were anticipated to have a high degree of molecular orientation. Samples were soaked by full immersion in the solvent at ambient temperature (- 298 K) but removed for imaging. MRM studies were carried out using a Bruker AM300WB NMR spectrometer (89 mm bore, 7.05 T magnet) fitted with a Bruker Microimaging Accessory. Bruker 3D gradient-echo imaging sequences were used to acquire the imaging data which were processed using a Bruker Aspect X-32 workstation. The images (Figs. 20.1 and 20.2) were accumulated with an echo time of 1.97 ms and a repetition delay of 1 s. Standard data sets were reconstructed into a 64 x 64 x 64 image from which volumes of interest were selected and interpolated up to a final image matrix size of 128 x 128 x 128 voxels. STRAFI data were obtained at 298 K using a Chemagnetics CMX-400 console attached to a Magnex superconducting

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255

magnet of nominal field 9.4 T and a home-built STRAFI probehead. In the 58 T m-l fringe field gradient accessed, B, was 5.57 T and the samples were stepped through the gradient in consecutive 250 pm slices to give one-dimensional profiles [5]. A ( ( X / ~ ) ~ - T [(~2)y-~-acquire],,](T = 20 ps; n = 128) solid echo sequence was used to acquire signal from both swollen and unswollen sample; a pulse gap T = 75 ps allowed the decay of

virtually all of the signal from unswollen polypropylene while retaining most of that from the swollen regions.

20.3 Results and Discussion A preliminary account has already described the MRM imaging of the anisotropic uptake of liquid carbon tetrachloride into isotactic polypropylene (Fig. 20.1) [6]. Over a six day period there was no apparent uptake of solvent via the cylinder sides and solvent fronts advanced through the sample only from its cut ends. The distance penetrated was proportional to time (Case I1 diffusion) and the rate of advance at ambient ms-l. As an example, Fig. 20.2 shows a 3D maximum temperature (298 K) was 4.2. intensity projection image of the swollen polymer regions of a polypropylene sample in whch the solvent had penetrated only from the cut ends and from a localised cut (mid point along the cylinder) through the skin layer. The solvent appeared to diffuse radially away from the cut. A bright band beneath the cylinder surface joined the region at the top

R ,x

I200

600 400 200

0 . 0

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30

40

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60

P i x e l Position

Fig. 20.1: MRM profile along the lengths of two polypropylene samples soaked in CCl4 for 3 days (pixel positions 9-3 1) and 6 days (pixel positions 35-58).

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end of the cylinder to the swollen polymer associated with the cut. The joining band thickness was much less than the anticipated total thickness for a transition zone ( 2 250 pm) [2]. Preferential solvent uptake through the cut ends of the samples also occurred with toluene and cyclohexane (Case II kinetics; D,toluene, 9.2. cyclohexane, 5.1. ms-' ). After an initial period (toluene, - 17 hours; cyclohexane, -60 hours), solvent also penetrated from the cylinder sides, although at much slower rates than from the cut ends. The minimum echo time available (1.97 ms) did not permit MRM for other than highly swollen material.

Fig. 20.2: Three-dimensional maximum intensity projection MRM image of an extruded polypropylene cylinder with a localised cut prior to immersion in carbon tetrachloride.

STRAFI one-dimensional profiles along the length of the cylinder, measured at intervals of six hours, were obtained for the solvent-soaked samples. From the whole range of T2 values it was possible to observe in detail the effects of the ingress of the solvents on the polypropylene. For example, Fig. 20.3 shows a profile of longer T2 values through a sample soaked in cyclohexane for periods of 60, 84, and 108 hours. Case I1 diffusion rates of end penetration (longitudinal absorption) were obtained at ambient temperature ms-i ). There was a time lag in each case be(toluene, 8.3. cyclohexane, 4.8. fore the observation of a solvent front (toluene, 3.3; cyclo-hexane, 1.8 hours) and this was attributed to the time required for a small Fickian precursor to penetrate and cause swelling of the polymer 171.

20. STRAFI and MRM Studies of Anisotropic Absorption of Solvents by Extruded Polypropylene

251

'I I-

0

500

lo00

1500

+ , 2000

2500

3000

3500

4000

Depth Into Rod (pn)

Fig. 20.3: T2 profile through one end of a sample soaked in cyclohexane for 60,84,and 108 hours.

The rate of transverse absorption was determined by assuming that in the 1D profiles obtained with pulse gap T = 75 ps: (i) the height of signal at the centre of the profile was proportional to the depth of penetration from the sides; (ii) the rate of solvent ingress in the fully immersed sample was the same all around its circumference. For a polypropylene cylinder of cross-sectional radius r, let rx and ry be the radii of the interior region of the cylinder still unswollen at times tx. and ty after immersion in the solvent. If i, and iy are the measured image intensities of the one-dimensional longitudinal profile at the mid-point of the sample at times tx and ty,then: (20.1)

Relative image intensities determined at a minimum of three time intervals are therefore required to calculate the kinetics of the transverse absorption. For toluene, the rate of transverse diffusion was found to be consistent with Case I1 diffusion ( D - 3.1 . m s l ; only about one fortieth of the longitudinal rate along the sample). There was a delay of 17.0 hours before the skin layer was penetrated by this solvent, consistent with the MRM results. An accurate transverse diffusion rate for cyclohexane has yet to be determined.

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R. J. Abbort. J . A. Chrrdek. G. Hunter, R. L. MacKay. P. J. McDonald, and L. Squires

20.4 Conclusion The observation of a skin layer resistant to the penetration of normally good solvents into extruded polypropylene and the significant difference in the rates of longitudinal and transverse solvent absorption were unexpected. The findings are of commercial significance in the context of polypropylene non-woven fabrics used to make inexpensive disposable protective clothing intended for the petrochemical industry.

Acknowledgements We thank the EPSRC and Don & Low (Holdings) plc. for financial support.

References 1.

L. C. Sawyer, D. T. Gxubb, Polymer Microscopy, Chapman & Hall, London, 1987.

2.

D. Jarvis, A. Scheibelhoffer, A. Hittner, E. Baer, J. Appl. Polym. Sci.60 (1996) 209.

3.

N. M. Sammes, S. Vohara, A. M. Cartner, J. Muter. Sci. 35 (1994) 6255.

4.

See, e.g., W. M. Ritchey, L. Maylish-Kogovsek, A. Wallner, Appl. Spect. Rev. 29 (1994) 233

5.

P. J. McDonald, Prog. NMR Spect. 30 (1997) 69.

6.

R.J. Abbott, J. A. Chudek, G. Hunter, L. Squires, J. Muter. Sci. Lett. 15 (1996) 1108.

7.

N. L. Thomas,A. H. Windle, Polvmer 23 (1982) 529.

21. NMR Microimaging: A Useful Tool to Study the Dissolution of Solids Nicole Black, Todd Vienneau', and Yong Pan

The Procter & Gamble Company, Miami Valley Laboratories, P. 0. Box 538707, Cincinnati, OH 45253, USA Procter & Gamble Pharmaceuticals, 8700 Mason-Montgomery Road, Mason, OH 45040, USA

Abstract We have used NMR microimaging to study the dissolution of a newly formulated pain reliever. A series of NMR images of the pain reliever tablets in regular and deuterated dissolution medium clearly showed that water penetration was not the rate-controlling step in release of the drug. Instead, the diffusion of the solubilized actives into the dissolution medium was the key to control drug release. The diffusion was significantly reduced by the interaction between the actives in the newly formulated drug. NMR imaging and standard dissolution tests showed that a bilayer formulation improved drug release.

21.1 Introduction Dissolution is an important issue and a complicated process for many consumer products. Factors that affect dissolution include the compounds intrinsic solubility, particle size, inter- and intra-particle porosity, and molecular interactions among the ingredients. A complete dissolution normally includes the following steps: 1) water penetration to the solid dry core, 2) disintegration of the solid into small fragments or particles, 3) solubilization of the disintegrated particles, and 4) diffusion of the solubilized molecules into the homogeneous dissolution medium. The dissolution rate of a solid is often controlled by one or more of these steps. The identification of the rate-controlling step is the key to controlling the release of actives.

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The conventional dissolution tests measure only the rate of drug release. No information on the dissolution mechanism is provided. The conventional analytical methods for measuring water penetration require physical manipulation of samples, which may introduce considerable errors in the measurement. NMR imaging can map the spatial distribution of mobile spins (protons) in a sample. The intensity in an image voxel reflects intrinsic NMR properties, namely, spin density, spin-lattice relaxation, and spin-spin relaxation [ 11. NMR imaging is non-invasive and, therefore, is ideal to monitor a dynamic process. Using NMR imaging, Litchfield and his coworkers measured 3D moisture transfer in corn during drying [2]; McCarthy, et al., studied the stability of oil/water systems [3]; and Fyfe and his group investigated the freezing-thawing phenomena of meat [4]. We have recently used NMR imaging to study the dissolution of a new pain reliever product. The NMR imaging method provides a unique way to identify the rate-controlling step in a complicated dissolution process. The new pain reliever contains a sleep-aid in addition to an analgesic as active ingredients. As shown in Fig. 21.1, the analgesic release rate for the sleep-aidanalgesic tablets was much slower than that for the analgesic-only tablets in a standard dissolution test. The goal of the study was to understand the dissolution mechanism and identify the ratecontrolling step in the drug release process.

100

c

20 0 15

30

45

60

Time (min) Fig. 21.1: Analgesic release profiles shown as the percentage of analgesic released versus the dissolution time in a standard dissolution test.

21. NMR Microimaging: A Useful Tool to Study the Dissolution of Solids

26 1

21.2 Experimental NMR imaging experiments were performed using a Bruker MSL-300 spectrometer. The tablet was a 15 mm long and 6 mm in diameter oval shape caplet vertically glued to a plastic plug in a 15-mm tube filled with a regular or a deuterated dissolution medium at a pH of 7.4. Magnevist was added to the dissolution media as a relaxation agent. The images of a 400-pm thick transverse plane at the center of the tablet were acquired every two minutes for four hours at 37 "C using a spin-echo imaging pulse sequence [1]. The in-plane resolution is 98 x 98 pm2. An imaging analysis program, Optimas, was used to measure the area of the dry core in the tablet as it decreased upon water penetration. The contrast between dry core and dissolution medium intensities was used to select each region of interest by thresholding the image at different intensity levels. An Optimas macro was written to facilitate these measurements. With this program, selection parameters were determined initially on representative images, and the program ran automatically throughout the entire data set. Results were exported to a Microsoft Excel spreadsheet.

21.3 Results Figure 21.2 shows the images of the analgesic-only and sleep-aid/analgesic tablets after 30 minutes of dissolution in a regular dissolution medium. Within 30 minutes, water completely penetrated into the inner core of the sleep-aid/analgesictablet while there was still a significant amount of dry core left in the analgesic-only tablet. The asymmetry in the picture may be due to the misalignment of the tablet to the test tube. The dry-core areas over time were measured and plotted in Fig. 21.3. The results clearly show the water penetration rate of the sleep-aid/analgesictablets was much faster than that of the analgesic-only tablets. The high intensity in the inner area of the sleepaidhalgesic tablet indicates the drug active was solubilized, but could not be released to the dissolution medium.

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Analgesic Only

Sleep-aid/Analgesic

Fig. 2 1.2:. The cross-sections of the analgesic-only and sleep-aid/analgesic tablets after 30 minutes of dissolution in the regular dissolution medium.

-C- Analgesic Only

+SleepAid/ Analgesic

-. A

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Time (min) Fig. 21.3: The dry-core area of the analgesic-only and sleep-aid/analgesic tablets as a function of dissolution time.

21. NMR Mict-oimnging: A Useful Tool to Study ihe Dissolution of Solids

263

Using the regular dissolution medium, the signals in the images arise from both water and solubilized drug actives. Using the deuterated dissolution medium, the signals in the images come only from the solubilized actives. Therefore, it is a better way to visualize the drug solubilization and release. The images of the two tablets in the deuterated dissolution medium (Fig. 21.4) confirmed that the water penetration rate of the sleepaid/analgesic tablets was much faster than that of the analgesic-only tablets. The drug actives in the sleep-aid/analgesic tablet were quickly solubilized; however, the release to the medium was very slow. Note the receiver gain was set differently while acquiring these images.

Analgesic Only

Sleep-aid/Analgesic

Fig. 21.4: The cross-sections of the analgesic-only and sleep-aid/analgesic tablets after 30 minutes of dissolution in the deuterated dissolution medium.

21.4 Discussion The NMR imaging results suggest that water penetration is not the rate-controlling step in the dissolution of the sleep-aid/analgesic tablets. The drug release rate is controlled by the diffusion of drug actives into the dissolution medium. A gel-like material appeared in the image of the sleep-aid/analgesic tablet, which is likely due to the formation of an ion pair complex between the two actives. The complex was isolated as a precipitate in a mixture of solution with both actives and identified by GC, IR, and solution NMR.

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To reduce the interaction between the two active ingredients, a bilayer tablet was made by pressing the two ingredients into two separate layers. Figure 21.5 is the image of the bilayer tablet after one minute of dissolution. The image shows that the sleep-aid half of the tablet dissolves and disperses rather quickly and the analgesic half dissolves subsequently. The interactions between the two layers are reduced. The standard dissolution tests also confirmed that the release of analgesic was improved (Fig. 21.1). NMR imaging is an ideal tool to study water penetration and active release in general. In our studies of several other systems, we have identified dissolutioncontrolling processes as water penetration, gel formation, individual particle solubilization, or disintegration, depending upon the nature and composition of the systems. Although dissolution conditions in NMR imaging experiments are often different from those in the standard dissolution tests (agitation, saturation, etc.), the mechanistic information provided by NMR imaging is very useful to direct the efforts to improve the dissolution profile.

Fig. 21.5: The cross-sections of a sleep-aid/anaIgesicbilayer tablet after one minute of dissolution in the regular dissolution medium.

References 1.

P. T. Callaghan, Principles of Nuclear Magnetic Resonance Microscopy, Oxford University Press, New York, 1991.

2.

H. P. Song, J. B. Litchfield, Cereal Chem. 33 (1990) 1286.

3.

M. Winkler, M. J. McCarthy, J. B. Gemman, J. Food Sci. 56 (1991) 811.

4

C. A. Fyfe, S. A. Isbell, N. E. Burlinson, Magn. Reson. Chem. 32 (1994) 276.

22. Observation of the Water Distribution During Drying of Textiles J. Leisen, L. Hou, H . W.Beckham, and W. W. Carr Georgia Institute of Technology, School of Textile & Fiber Engineering, Atlanta, GA 30332-0295, USA

Abstract The distribution of moisture within wet carpet samples was followed by spin-echo magnetic resonance imaging sequences during the simulation of an industrial drying process. Due to an increase in capillary forces (i.e., smaller capillaries) water tends to concentrate in the tufts close to the backing of cut-pile nylon carpet samples. Significantly different drying rates were found for the pile region close to the surface of the carpet as compared to the region close to the baclung. Whether the air stream is incident on the surface or back of the carpet influences the local drying rates.

22.1 Introduction Most textile production processes include a drying step for fibrous substrates that are wet as a result of the application of dyes and finishing chemicals via aqueous solutions. This study focuses on industrially produced carpets, where drying is achieved by air flow through large carpet sheets. About 30% of the thermal energy needed for the manufacturing process is used for the drying step [1,2]. A thorough understanding of the drying mechanism will allow process optimization, leading to time and energy conservation. In order to achieve this understanding it is important to know the spatial distribution of water within samples [3] and observe how this distribution changes as a function of different drying conditions (i.e., air-flow rate and direction, temperature, etc.) ~41.

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While optical imaging methods are well-suited for analysis of surfaces and transparent substrates, magnetic resonance imaging (MRI) is the only technique that can provide reliable information concerning water distributions within opaque textile constructions. In this study the water distribution in carpet samples is monitored by MRI while an industrial drying process is simulated in an NMR microscope.

22.2 Experimental Section The samples used in this study were cut-pile greige carpet constructed of nylon carpet yarns tufted through a polypropylene primary backing. These carpet yarns are bundles of nylon monofilaments that are referred to as tufts once incorporated into carpet structures. The tufts above the primary backing are known collectively as the pile region. Standard spin-echo sequences [5] were used to record two-dimensional (2D) images and onedimensional (1D) profiles. Experimental parameters are provided in the respective figure captions. A commercial magnetic resonance microscope (Bruker DSX-400, operating at a 'H frequency of 400 MHz) was used, which was equipped with an NMR-microscopy probe holding a 25-mm diameter coil. A piece of carpet was cut to fit this diameter, tufts were removed from the edges and the exposed primary backing was sealed with tape. By pinching these sealed edges between two glass tubes, the samples were held in the center of the coil. Special care was taken to seal the probe so that the air supply normally employed for variable temperature experiments was directed entirely through the carpet samples. The flow rate was monitored by an external flow meter (Omega Engineering, Inc.) and set to 3 l/min. This value corresponds to air flow rates comparable to those used in the carpet indusby. For the studies described below, pre-dried air at room temperature (295 K) was used. Samples were wet by storing them for at least 24 hours in distilled water. Water concentrations were adjusted to typical values of 60% (based on the sample dry weight) by applying mechanical pressure on a sample placed between two absorbent papers. The initial moisture concentration in each sample was determined by weighing the dry and the wetted carpet sample. This accurately determined moisture concentration was used to reference the measured spectral density of NMR experiments to actual moisture concen-

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trations. Since the evaporation of water in the drying process initially causes a drop in temperature, changes in spectral density due to temperature-dependent relaxation effects must be taken into account. This was best achieved empirically by calibrating changes in spectral density with controlled temperature changes for a carpet sample sealed in a glass container (to eliminate spectral density changes due to water loss). The temperature changes during the drying experiment were measured in a separate experiment using thermocouples; the spectral density changes attributed to temperature changes could then be corrected by utilizing the previously established calibration curve. This approach was quite accurate for drying times longer than 80 seconds, since the temperature dropped to a constant value (about 280 K) during this time interval and persisted until the sample was fully dried.

22.3 Results and Discussion 22.3.1 Water Distribution within Carpets In order to achieve a better understanding of the drying process the distribution of water within wet carpets was measured before and during drying. Figure 22.1 demonstrates the information that can be extracted from MR images taken of a wet carpet sample with a moisture concentration of about 70%. Figure 22.lb displays a transverse slice through the wet carpet near the backing; this region is marked in the optical micrograph shown in Fig. 22.la. For standard conditions used in a spinecho sequence, the MR image clearly shows the water distribution within the carpet tufts, since only mobile water molecules and not the rather rigid polymers of the carpet itself are contributing to the detectable signal. It is obvious that within the region of the backing, water is almost exclusively present within the carpet yarns and not within the polypropylene backing (cf. Fig. 22.lb). Otherwise, the water would be uniformly distributed across the sample. The variation of water concentrations along the carpet yarns is visualized in Fig. 22.lc, displaying a sagittal slice through the carpet sample. It is clearly visible that water tends to concentrate in those parts of the tufts located close to the backing of the carpet sample (backing region). The individual nylon filaments bundled into a carpet yarn are more densely packed within this region, which leads to smaller

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a>

b)

Fig. 22.1: Images of a piece of carpet containing about 70% water (dry basis): a) Optical micrograph (dry sample). b) Transverse spin-echo MR image (TE = 12 ms, TR = 2 s, slice thickness = 0.6 mm). c) Sagittal spin-echo MR image (TE = 12 ms, TR = 0.5 s, slice thickness = 10 mm). d) Projection of c) experimentally determined using the spin-echo sequence (TE = 6 ms, TR = 2 s, no slice selection).

capillaries and consequently increased capillary forces holding the water in place. If the carpet sample is turned upside down the high moisture concentration within the backing region persists, indicting that gravitational effects do not significantly influence the moisture distribution. The variation of water distribution from the carpet surface to the backing can be visualized best through a projection of the sagittal image of Fig. 2 2 . 3 ~on an axis parallel to the average tuft orientation. However, especially for monitoring of drying processes occurring on time scales of minutes, it is advantageous to measure these

1D moisture profiles directly by the use of a spin-echo sequence, as opposed to calculating them from 2D NMR images.

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22.3.2 Observation of Moisture Profiles During Drying Moisture profiles as a function of drying time are shown in Fig. 22.2 for the case of air blown on the surface of the carpet. In a second experiment the effects of a reverse air flow was investigated (moisture profiles not shown here). For this through-flow arrangement, air is incident upon the back of the carpet.

Fig. 22.2: Moisture profiles measured while air was blown through the carpet sample. Each slice represents 1 average recorded directly by using the spin-echo sequence (TE = 6 ms, TR = 20 s).

In order to obtain insight into the drying mechanism, two integral regions were considered: the tufts in the region close to the backing, referred to as the backing region; and the tufts in the region above the backing, referred to as the pile region (cf. Fig. 22.ld). Figure 22.3 displays the reduction of water concentration for these regions during the drying process. Comparison of drying data for the pile and backing regions reveals for air flow on both surface and back, a significantly faster moisture loss for the backing region, which initially contains the higher moisture concentration. For the air flow on the surface, a low moisture concentration is reached for the pile region after 8 minutes, while at this time a moisture concentration greater than 40% is still present in the bachng. However, when air is blown on the back, both pile and backing regions reach low moisture concentrations at the same time.

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air flow on surface

0

5

air flow on back

10 t i m e l m i n

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Fig. 22.3: Moisture concentrations in the pile and backing regions during the drying process (0). The solid lines are the apparent moisture concentrations obtained when no correction for temperature-induced relaxation effects is made.

The drying curves of Fig. 22.3 have different shapes for the pile and backing regions. An approximately linear drying cuwe is apparent for the pile region. On the other hand, the drying curve for the backing clearly deviates from linearity. A detailed characterization of drying curves can be obtained by looking at drying rates. The drying rate is simply the slope of the drying curve at a certain time. Hence, the numerical derivative of the drying curves yields a plot displaying the change of drying rates during the drying process (cf. Fig. 22.4). Following an initial equilibration period, the drying rates of the pile region exhibit a general decrease for both drying directions. After about 5 min, this drying-rate decrease becomes more pronounced for air blown on the carpet surface. For the backing region the drying rates show a behavior opposite to that of the pile region. The drying rate, which is generally higher for the backing than for the pile, increases during the drying process, and only decreases rather abruptly when low moisture concentrations are reached. So far a full explanation of these observations has not been made. These carpet samples are 'soft' porous materials for which analysis is complicated by the ability of the underlying pore structure to change during wetting or drying processes. Drying-induced changes in the pore structure within the backing region could be responsible for the observed increase in drying rates with drying time.

22. Observation of the Water Distribution During Drying of Textiles

0

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15 time I min

Fig. 22.4: Drying rates obtained from the data of Fig. 22.3.

22.4 Conclusions The current data provide insight into the industrial drying process of carpet. It is evident that the drying rates and perhaps the drying mechanisms vary significantly for different regions within the sample. The results obtained so far are of immediate technical relevance. An industrial drying process requires that all areas of the sample reach moisture concentrations below 5 - 7% in order to prevent the local formation of mildew. Hence, the drying of the backing area is important since it is the area with the highest moisture concentration and the most difficult to dry. For a drying process employing forced convection only, the air flow should be incident on the back of the carpet. In this case, faster drying rates are found for the backing region and both pile and backing regions reach low moisture concentrations at about the same time. However, the data also suggest an improved process can be designed that effectively reduces the time required for drying: combine forced convection directed on the carpet surface (which dries the pile region most efficiently) with a second device such as an infrared source directed on the back (which locally dries the region most concentrated with water). With remote fiber optics delivering IR radiation into the MRI probehead, monitoring such a process may be possible using MR imaging techniques.

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Acknowledgments The research described here was funded by the National Science Foundation (DMR9502246) and the National Textile Center. Access to NMR instrumentation through the Georgia Tech NMR Center has been made possible by an NSF DMR instrumentation grant (DMR-9503936).

References 1.

W. W. Carr, W. C. Tincher, Textile Research Journal 53 (1983) 219.

2.

R. D. O'Dell, W. W. Carr, Textile Research Journal 66 (1996) 366.

3.

N. D. Francis, W. J. Wepfer, Textile Research Journal 63 (1993) 1.

4.

D. W. Lyons, C. T. Vollers, Textile Research Journal 41 (1971) 661.

5.

P. Callaghan, Principles of Nuclear Magnetic Resonance Microscopy, Clarendon, Oxford, 1991

23. A Broad Line Magnetic Resonance Imaging Study of Water Transport in Cementitious Building Materials A. J. Bohrisl, U. Goerkel, P. J. McDonald], M. Mulheron2, B. NewlingI, B. Le Page2 Schools of Physical Sciences1 and Chemical, Civil and Environmental Engineering2, University of Surrey, Guildford, Surrey, GU2 5XH, UK

Abstract Stray field imaging (STRAFI) measurements of water content and water transport in Portland cement pastes as a function of water-to-cement ratio (w/c) and hydrophobic treatment have been undertaken. The concentration dependence of the hydraulic diffusion coefficient is calculated for samples prepared with a 0.5 wlc ratio and, therefore, an open pore structure. Water uptake is shown to differ in air-dried samples and those dried more completely by methanol exchange. In the case of 0.3 w/c ratio samples, little water transport is observed and a closed pore structure is inferred. A silane-based hydrophobic treatment is shown to be effective in halting water transport into cured pastes.

23.1 Introduction The pore structure of cementitious building materials depends critically upon the presence of water and water transport during cure. That pore structure is, in turn, fundamental in determining the water transport properties, and therefore durability, of the cured material. Traditional techniques for the study of water transport in cement pastes are generally invasive or destructive or lacking in spatial resolution. Proton magnetic resonance imaging, (MRI), on the other hand, is both non-invasive and spatially resolved and, in addition, is exquisitely sensitive to water dynamics [1,2]. However, cements are NMR, because the resonance line difficult to image using conventional, liquid state

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widths are broadened by self-diffusion in large magnetic susceptibility-induced field gradients across pore surfaces and by rapid 'H exchange between mobile and strongly adsorbed sites. Other water is chemically bound. Broad line NMR techniques are therefore required. Stray field imaging (STRAFI) [3-51 is a particularly powerful broad line technique for its high spatial resolution (pm) and ability to visualise all cement paste water, rather than just the freely mobile water in the largest pores and cracks which is accessible to conventional MRI. We present the results of a STRAFI study of the water uptake properties of 21 day cured cement samples dried either in air, at room temperature and pressure, or by a cycle of methanol exchange and oven drying up to 50 "C. Samples of 0.3 and 0.5 w/c ratio were chosen, to represent capillary pore structures conventionally assumed to be completely closed (isolated pores) and open (connected) respectively. Where appropriate, hydraulic diffusivities have been determined. In addition, the effect of a silane-based protective treatment was assessed. These latter results extend a wider STRAFI, gradient echo MRI and relaxometry NMR study reported elsewhere [6].

23.2 Materials and Methods Portland cement powder (Cement Manufacturers Federation standard grade) was mixed with water (w/c 0.3 or 0.5) before being transferred to a home-built PMMA mould. A vibration table was used to remove trapped air from the cast samples, which were then sealed for curing. The cured cement paste pellets were subsequently fixed into a cylindrical glass tube using epoxy resin to render the glasskement interface water impermeable. The samples were then either left to dry at room temperature and pressure or forcibly dried by a repeated cycle of methanol exchange and oven drying at gradually increasing temperatures to a maximum of 50 "C. The latter procedure was adopted to minimise damage to the pore structure. Sample weights were monitored throughout. Water was added above the pellet and its ingress studied by STRAFI. STRAFI was carried out at 235 MHz in a magnetic field gradient of 5800 G/cm. The conventional STRAFI method is to increment the sample position relative to the RF coil and acquire an echo train at each position, thereby accumulating a profile of the sample lH content. The process is time consuming and any profile of dynamic IH concentration,

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like an advancing water front, is distorted by that finite acquisition time. A more accurate impression of water front shape can be gained by observing successive echo trains at one fixed position, while waiting for the front to pass, as no time is required to move the sample and the acquisition is considerably accelerated [7]. Both methods have been used in this study, and the results combined in the data analysis. In either case, quadrature echo trains are collected. The pulse interval, z, was 25 p, which is sufficiently short to collect signal from the chemically combined, gel and capillary waters. It is noted that the signal from the chemically combined water reflects a degree of line narrowing, while that from mobile water is strongly diffusion attenuated in the large field gradient.

23.3 Results and Discussion The recorded quadrature echo trains can be well represented by two component exponential relaxation decays, corresponding in the proportion of their amplitudes to primarily capillary water and to the total of gel and chemically combined waters respectively and in broad agreement with accepted values [8]. Figure 23.1 shows a STRAFI profile of an air dried (RTP), 0.5 w/c ratio sample recorded 1 hour after the top was exposed to water. The water reservoir lies to the left. A sharp water front (solid curve) has ingressed 2.7 mm into the sample. The calculated intensities of the capillary water (lower dashed curve; long T2 component) and of the gel and combined water (upper dashed curve; short T, component) indicate that the advancing water front is capillary water, which has mostly been removed by air drying. Water transport in cementitious materials can be modelled as an effective Fickian

diffusion process in which the concentration dependent hydraulic diffusion coefficient is defined as the product of the hydraulic conductivity, K and the derivative of the capillary potential, y~ with respect to water concentration, c [9]. Hence (23.1)

where x and t are position and time variables respectively. For the boundary conditions of these experiments, the hydraulic diffusion coefficient can be calculated from profile and time of flight data by applying the Boltzmann transform, q = ~ / ( 2 t ~ which ' ~ ) , results in a single master curve c(q) [lo].

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A. J. Bohris, U . Goerke, P. J. McDonald, M. Mulheron, B. Newling, and B. Le Page

/ 0

long component (capillary)

5 Position (mm)

0

10

Fig. 23.1: STRAFI profile of water content after one hour of exposure. The water reservoir lies to the left. The amplitudes of two components (broken lines) of a biexponential fit and their sum (solid line) are shown.

I

I

0.003

I

I

0.006

0.009

q (cm/@) Fig. 23.2: Master diffusion curves and fits for several STRAFI experiments.

Figure 23.2 shows the master diffusion profiles for water ingress into both air dried (circles) and methanol exchanged (squares) 0.5 w/c samples collated from the results of several profiling and time of flight experiments. The invading water fractions are in reasonable agreement with those expected for capillary water, in the air dried case, and capillary and gel waters, in the methanol exchanged case. It is also apparent that water ingresses much more rapidly into the

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methanol exchange dried sample than the air dried sample. While it is possible that this is due to the additional drying damaging the delicate gel structure of the cement, we believe that the result is significant and reflects the different uptake characteristics of cement to capillary and to combined capillary and gel water. Two of the master curves have been fitted to three line trapezoidal functions, which, although physically unrealistic, preserve the essential features of the data. Based on the fits, the relationship between hydraulic diffusion coefficient, D(c), and volume fraction of water, c, may be calculated in a limited range. These curves are shown in Fig. 23.3. In the case of the 0.3 w/c ratio samples, the water uptake into an air dried sample was minimal, reflecting the closed capillary pore structure. For a methanol exchange dried sample extremely rapid uptake was observed. However, in this case, the drying procedure had clearly damaged the pore structure and resulted in observable cracking of the sample.

J

0.40

0.45

0.50

0.55

0.60

C

Fig. 23.3: Calculated hydraulic diffusion coefficient from the fits of Fig. 23.2. The lower trace is for the ingress of capillary water only and the upper trace for combined capillary and gel water ingress.

Finally, Fig. 23.4 shows profiles collected at 0 and 12 hours after the exposure of a treated 0.5 w/c sample to water. The cured paste was dried at up to 50 "C (without methanol exchange) and immersed in an alkylaloxysilane agent for 12 hours. The treatment was allowed to cure for 48 hours before exposure to water. The two T, components are shown as broken lines and their sum as solid lines. The treatment is shown to be effective by the lack of any water ingress over the 12 hours of data shown.

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1.o 0.8 C

0 ._

5 0.6 2

Lc

a

5

0.4

3 0.2

I

i

0.0

..I d+k~TA-y---y..+.=.-7-Lp

0.0

2.0

4.0 6.0 8.0 10.0 12.0 Position (mm)

Fig. 23.4: STRAFI profiles through the surface region of dry treated cement and of the same sample after 12 hours of water exposure. The amplitudes of each of the two T, components are shown for each profile (broken lines) with their sum (solid lines). The profiles are identical except for the presence of the water reservoir to the left, showing that the treatment has been successful.

23.4 Conclusions STRAFI has been demonstrated as a technique to provide a quantitative, spatially resolved measure of all waters in a cured cement paste. Differences between the uptake of capillary water and of combined capillary and gel water have been observed and quantified. The efficacy of a hydrophobic cement treatment has been demonstrated.

Acknowledgements The authors thank the UK Engineering and Physical Sciences Research Council for a Research Grant (GWK94881). AJB also thanks the council for a studentship.

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References 1.

R. Gummerson, C. Hall, W. Hoff, R Hawkes, G. Holland, W. Moore, Nature 281 (1979) 56.

2.

G. Papavassiliou, F. Milia, M. Fardis, R. R u m , E. Laganas, J. Am. Ceram. SOC.76 (1993) 2109.

3.

A. Samoilenko, D. Artemov, L. Sibeldina, JETP Lett. 47 (1988) 417.

4.

P. McDonald, Prog. NMR Spectroscopy 30 (1997) 69.

5.

S. Black, D. Lane, P. McDonald, M. Mulheron, G. Hunter, M. Jones, 1.Mat. Sci. Letts. 14 (1995) 1175.

6.

A. Bohris, U. Goerke, P. McDonald, M. Mulheron, B. Newling, B. LePage, ,,A broad line MRI and

NMR study of water and water transport in Portland cement pastes", accepted for publication in Magn.

Reson. h a g . 7.

M. Halse, private communication.

8.

A. Neville, Properties of concrete, Longman, Harlow, 1995.

9.

C. Hall, Magazine of concrete research 41 (1989) 51.

10.

J. Crank, The mathematics of diffusion, Oxford University Press, 1975.

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24. Stray Field Imaging and Magnetic Resonance Microimaging Studies of Water IntrusiodStress Mobilisation in Dense Polymer Systems Used in Construction S. N. Scrimgeour, G. Hunter, W.J. Harvey1, and C. H. Lloyd2

Departments of Chemistry, Civil Engineering1 and Dentistry2, University of Dundee, Dundee DD1 4HN, UK D. M. Lane, and P. J. McDonald

Department of Physics, University of Surrey, Guildford GU2 5XH, UK

Abstract Epoxy adhesives absorb water from the environment, adversely affecting their mechanical and physical properties. The consequences of this water sorption are not readily accounted for since the mechanisms for such movement into the bulk of such polymers are largely unknown. Magnetic Resonance Microimaging (MRM) and Stray Field Imaging (STRAFI) show that the sorption of water by the adhesives studied is a two stage process.

24.1 Introduction High density and high modulus thermoset adhesives and stress transfer materials based on polyester and epoxide resins are used in the construction industry. Some epoxy adhesives absorb water from the environment adversely affecting their mechanical and physical properties [l]. Water may also be preferentially sorbed at interfaces [2]. Since the materials have high moduli, substantial swelling pressures can be expected and the resulting stresses have been implicated in the degradation of adhesive joints [ 3 ] . All

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S.N. Scrimgeour, G. Hunter, W. J. Harvey, C. H. Lloyd, D. M. Lane, and P. J. McDonald

applications involve bonding in situations which may well be strain intolerant and if the component undergoes significant dimensional change and the containment does not allow strain relaxation then high stresses can be mobilised. Such stresses if localised could result in distortion and perhaps fracture of the containment. In bonded structures made from glass reinforced plastic (GRP) composites moisture penetration may take place through the resin or at the interface between resin and glass, particularly at the cut ends of the pultruded sections. Moisture sorption may also be affected by the conditions under which the adhesive is mixed and applied and this in turn may affect the mechanical properties of the materials. The consequences of water sorption, however, are not presently accounted for since the mechanisms for its movement into the bulk of structural polymers are largely unknown. Previous sorption studies have been based on material weight changes and Fickian behaviour has been assumed. As the transport of ‘fluid’ molecules is coupled to the mechanical response of the polymer (which depends on the molecular chain mobility), which itself is strongly influenced by the presence of those fluid molecules, a wide range of behaviour is likely to occur. MRM [4] and STRAFI [ 5 ] have already been shown to be valuable techniques in studying the sorption of liquids by polymers.

24.2 Experimental IH MRM studies were performed using a Bruker AM300WB NMR spectrometer (89

mm bore, 7.05 T magnet) fitted with a Bruker microimaging accessory. Because of the low concentration of sorbed water in the samples it was necessary to null the signal from the soaking water using an inversion recovery imaging sequence. While MRM was the principal method used to study the actual distribution of sorbed water in intact polymer samples, the presence or otherwise of tightly confined water with very short T2’s was investigated by STRAFI imaging. STRAFI data were obtained at ambient temperature (298 K) using a Chemagnetics CMX-400 Infinity console attached to a Magnex superconducting magnet of nominal field 9.4 T and a home built STRAFI probehead. In the 58 T fringe field gradient accessed, B , was 5.57 T. Solid state IH and 13C MAS NMR spectra were obtained with a Chemagnetics CMX-300 solids NMR spectrometer (89 mm bore 7.05 T magnet). Bulk and Young’s moduli and Poisson’s ratio were determined using the NOL method [6].

24. STRAFI and Microimaging Studies of Water in Polymer Systems Used in Construction

283

The adhesives studied included three manufactured by Ciba - 2015,201 1, and 2005 along with FD808 (Formulated Resins), Sikadur 31 (Sika) and Epofix (Struers). Specimens, except for 2015, were cut from rods 120 mm long and 6.25 mm diameter. Most commercial adhesives include filler, usually about 75 wt %, to improve their rheological and mechanical properties. We found that the nature of the filler is crucial to the mechanism and kinetics of water sorption into the adhesive and some filler-free 'model' epoxy systems were therefore prepared from bis-phenol A diglycidyl ether (BPA) ( M 5 700) and either triethylenetetramine (TET), Model I , or diethylene-triamine (DET), Model 2. Three sets of cylindrical samples were immersed in deionised water at 4 "C, 23 "C, and 37 "C for periods of up to 21 months. The sorption of water into 'sandwiches' of pultruded GRP bonded with 2015 adhesive was studied using samples cut from a specimen joint originally manufactured to test its mechanical properties. These, and dry stored controls, were used to determine moduli and Poisson's ratio.

\

Fig. 24.1: 1H MAS spectra (vrOt,4 M z ) of dry samples of adhesive 2015 (below) and Model 2 resin (BPAIDET) (above)

284

S. N. Scrimgeour, G. Hunter, W . J. Harvey, C. H. Lloyd, D. M. Lane, and P . J. McDonald

24.3 NMR Studies lH and 13C MAS NMR spectroscopy revealed an unexpected degree of polymer chain mobility, given the cross-linked nature of the polymer, in adhesives 2015 and 2011. Well-resolved spectra for those adhesives (see e.g. Fig. 24.1 (above)) were obtained with no hint of a significant broadline background, indicating that nearly all of the sample displayed significant chain mobility. This was not the case for their ‘model’ epoxy (i.e. un-filled) systems (Fig. 24.1 (below)) indicating that the presence of filler can have major effects on polymer chain mobility. In contrast, Sikadur 3 1 and FD808 gave spectra consistent with rigid, essentially immobile polymers. STRAFI imaging of 2015 and 201 1 was unable to detect any component with short, microsecond range T2 values, confirming the polymer chain mobility of those adhesives. The resinhardeners showed components with only ps T2’s. MRM showed that water sorption by adhesives 2015 and 2011 is a two stage process, while adhesive 2005 showed only the first stage of water sorption and that only after soaking for 15 months. Liquid imaging did not detect any water imbibition by Sikadur 31 or FD808. For 2015 and 2011 there was an initial rapid increase in image intensity without a clear solvent front (Fig. 24.2). Soaking in MRM-invisible D 2 0 instead of H20 did not lead to an increase in image intensity, strongly suggesting that such an increase was unlikely to have been caused by changes in polymer chain mobility on water sorption. More detailed studies showed that this initial increase in image intensity was actually anisotropic (Fig, 24.3) with water sorption occurring not through intact or set surfaces but apparently via the cut ends of the samples.

Fig. 24.2: MRM of adhesive 2015; dry (below) and soaked (above).

Fig. 24.3: Electronically sectioned 3D micro-image of adhesive 201 1 soaked for 5 months.

24. STRAFI and Microimaging Studies of Water in Polymer Systems Used in Construction

285

Numerous attempts were made to locate a solvent front and obtain the kinetics of the anisotropic sorption, but the image merely became brighter with increasing time. The second stage of sorption occurred through all of the surfaces and did show a solvent front, the shape of which was independent of temperature up to the maximum observed of 37 “C and was strongly indicative of a more conventional Fickian diffusion (Fig. 24.4), consistent with significant polymer chain mobility. However, diffusion was slow and the total amount of uptake was typically only 1 - 2% after 21 months. Even that period of observation was still too short to fully confirm that the distance travelled by the water front was proportional to (Fickian diffusion; D m2 s-l). One-dimensional STRAFI differentiated water sorption for all the adhesives,

-

although the sorbed water in Sikadur31 and FD808 was tightly bound, with submillisecond T2’s. The role of the filler was crucial in the sorption of water, with uptake strongly coupled to the local dynamics of the adhesive polymer chains, as there was none by the parent resinhardeners without filler. In totally immersed GRPladhesive ‘sandwiches’ the water entered the adhesive first and from there into the GRP, even though the surface area of GRP was much greater, and there was no sorption via cut edges nor at the glass fibreladhesive interface. GRPladhesive sandwiches subjected to 50 freezelthaw cycles showed an increased adhesive T2, coinciding with a significant drop in shear bond strength of the samples. Mechanical failure in dry composite structures occurred in the GRP, but at the GRPladhesive interface after soaking in water.

Fig. 24.4: The shape of the image profile for the second stage of sorption for adhesive 2015 after 21 months’ soaking.

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S. N . Scrimgeour, G. Hunter, W. J. Harvey, C. H. Lloyd, D. M. Lane, and P. J . McDonald

24.4 Conclusions Fillers significantly affected the polymer chain dynamics of the adhesives; when absent the parent polymers did not imbibe significant amounts of water. All the adhesives examined imbibed water to some extent, with a two stage sorption process. Changes in Poisson’s ratio were not observed even after 15 months soaking. There were changes in Young’s and bulk moduli; none indicated a catastrophic loss of property, although mechanical failure in the composite structures occurred at the GRP/adhesive interface. Water penetration into bonded GRP structures was via the adhesive.

Acknowledgement We thank the EPSRC for financial support.

References 1.

R. C. L. T a , Z. Szklarska-Smialowska,J. Muter. Sci. 28 (1993) 6199.

2.

Second International Conference on Interfacial Phenomena in Composite Materials Leuven, Belgium, 17

- 19 September (1991). 3.

J. Comyn (ed.), Polymer Permeability, Elsevier, London, 1985, 177.

4.

See, e.g., W. M. Ritchey, L. Maylish-Kogovsek,A. Wallner, Appl. Spect. Rev. 29 (1994) 233

5.

P. J. McDonald, Prog. NMR Spect. 30 (1997) 69.

6.

R. W. Warfield, J. E. Cuevas, R. Barnet, Rheologica Acta 9 (1970) 439.

25. Stray-Field Magnetic Resonance Imaging of Hardening Materials Teresa G. Nunes ICTPOLDST, Departamento de Engenharia de Materiais, Av. Rovisco Pais 1, 1096 Lisboa Codex, Portugal Philippe R. Bodart Department of Chemistry, Durham University, South Road, Durham DH1 3LE, UK Edward W.Randall Chemistry Department, Queen Mary and Westfield College, Mile End Road, London E14NS, UK

Abstract The hardening processes of medical polymers and cement pastes were investigated insitu, using the stray-field imaging technique (STRAFI MRI), with a magnetic field gradient of 37.5 T/m, and a IH frequency of 123.4 MHz. Analysis of one-dimensional projections (magnetisation profiles) yielded information about the spatial dependence of the free-radical polymerisation kinetics for the polymers, and of the hydration rates for the cements.

25.1 Introduction MRI allows the visualisation of molecular dynamics and chemical environment, in nondestructive and physically and chemically non-invasive experiments. However, broad NMR lines, obtained for example from rigid solids or from liquids confined into pores, demand the use of large magnetic field gradients, not usually employed in conventional MRI spectrometers.

288

T. G. Nunes, P. R. Bodart, and E. W. Randall

The stray-field imaging (STRAFIMRI) technique utilises the large static field gradients, present outside the central field region of a superconducting magnet [I]. The image acquisition is performed with the application of a pulse-sequence, usually a PowlesMansfield sequence, of very short RF pulses. Consequently, very short echo times can be achieved. This fact and the use of the large gradient enable, for example, the study of materials with strong magnetic susceptibility inhomogeneities, like Portland cement hydrating paste [2,3], or of images of quadrupolar nuclei of half-integer spin (41. We report here new STRAFI MRI findings on spatially dependent hardening reactions, either occurring in a period of the order of minutes (like a radical polymerisation of a self-cure polymer blend) or of over 120 h (the early hydration period of a Portland cement paste). In the last case, additional information on the spatial distribution of mobile water molecules was gained via the acquisition of relaxation weighted magnetisation profiles.

25.2 Experimental The starting paste for the preparation of the polymer blend consisted of two components: poly(ethylmethacryZate), as a powder, containing 3 wt % initiator (Lucidol CH50, a 5050 master batch of benzoyl peroxide and dicyclohexylphthalate) and n-butylmethacrylnte, a liquid monomer, containing an activator (2.5 vol % N,N dimethyl-p-toluidine) and 20 ppm of hydroquinone (Bonar Polymers Ltd.). The paste was prepared, following the instructions of the manufacturers, in a cylindrical glass vial (height 1.1 cm and diameter 1.3 cm), subsequently placed in the STRAFI probe. The Portland cement (Type I ) pastes were prepared with the following waterkement (w/c) ratios (by weight): 0.24,0.36 and 0.48. A cylindrical glass vial (with dimensions as before) was filled with the Portland cement paste immediately after the preparation. A Bruker MSL 300 P NMR spectrometer was used to acquire IH stray-field profiles, recorded at 123.4 MHz with a magnetic field gradient of 3750 G/cm. A PowlesMansfield pulse sequence [90°,-z-(900y-z-echo-z)n] was used for the acquisition of profiles along the axis of the cylindrical glass vial, parallel to the gradient direction. Typical values for data acquisition were: RF pulse duration - 10 ys, echo time - 30 ys and repetition time - 1 s. The profiles were obtained every 2 or 14 min (the duration of 8 or 50 scans) respectively from the polymer or from the cement pastes, and each slice is the integral of 64 echo signals. The linear resolution was better than 100 pm,

25. Str-uy-FieldMagnetic Resonance fmugiag of Hardening Materials

289

25.3 A Free-Radical Polymerisation of N-Butylmethacrylate In a chemical reactor, the polymerisation reaction occurs under controlled pressure and temperature. A similar control is not achievable in medical applications that require insitu polymerisation, like orthopaedic practice. Consequently, the reaction may proceed with spatial dependent rates. The hardening process following a free-radical potymerisation of n-butylmethacrylute (BMA), in a 2: 1 blend of polyethylmethacrylate (PEMA) and BMA used for hip bone prosthesis, was investigated. Figure 25.1 shows the normalised intensities obtained from the indicated slices versus time, immediately before the reaction was complete. The curves are the result of fitting the experimental magnetisation data (M), obtained over the first 15 minutes, with the function: M/Mo = 1(A/Mo)e(t'T).M , is the initial magnetisation of the reacting molecules and A is a constant (also a magnetisation in arbitrary units: 0.17). The time-constants (7) deduced are: surface slice 4.16 f 0.04 min, middle slice 3.62 k 0.02 min and bottom slice 3.46 f 0.03 min.

l,o -

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-

.

:

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..@: -.*. :..::: -. -..

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..

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0,6

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-

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Fig. 25.1: The normalised intensities versus time obtained from the indicated slices of a paste used in the preparation of a polymer blend of PEMA and PBMA. The dotted lines are the fits to the function 1 - (A/Mo)e(t/T),that no longer correctly represents the experimental data after the reaction is complete.

290

T. G. Nunes, P. R. Bodart, and E. W.Randall

Therefore, the reaction rate increases along the axis of the cylindrical reactor (see section 25.2), from the surface to the bottom of the vial, by 0.05 f 0.01 min-I. It is worth noting that the degree of polymerisation increases in the opposite direction and, accordingly, also increases the residual unsaturation in the final product, which is of considerable concern especially in terms of deleterious effects on the mechanical properties of the polymer blend.

25.4 The Hardening of Portland Cement Paste A spatial dependence of the hydration kinetics of Portland cement pastes was observed by STRAFI MRI from pastes with initial water to cement ratio (R) in the range 0.24 0.48 [3]. The decays of the magnetisation with time were fitted to mono-exponential functions, and the highest spatial variation of rate constants was observed from the paste with R equal to 0.36; as an illustration, Fig. 25.2 shows the decay of the signal intensity with time obtained from different slices. Each point represents the sum of the 64 acquired spin-echoes, corresponding to the magnetisation of the totality of the detectable protons. The experimental data were fitted to mono-exponential functions (solid lines) with the following time-constants: slice at 5 mm 17.6 k 0.3 h, slice at 2.5 mm 14.8 f 0.2 h and slice at 0 mm (slice at the bottom of the sample) 10.9 f 0.4 h. A relaxation-weighted study of similar cement pastes is now reported, in order to present the spatial distribution of the more mobile water molecules. Figure 25.3 shows the variation of the sum of the 4 last echoes (of a total of 64) with time, acquired from two slices of the cement paste prepared with w/c ratio of 0.36, from which the highest spatial variation of hydration rates is, again, observed. Mono-exponential and double-exponential functions were used to fit the experimental data; the corresponding time-constants, expressed in hours, are shown in Table 25.1. Under an oversimplified approach, it may be pointed out that the first 30 hours of the hydration reaction follow a mono-exponential decay but, after that period of time, the magnetisation decays primarily with a time-constant aii order of magnitude higher; this result is in agreement with water molecules in two different environments and may be correlated with water in open gel pores and in capillary pores [S].

25. Stray-Field Magnetic Resonance Imaging of Hardening Materials

400000

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.%

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Fig. 25.2: The normalised intensities versus time obtained from the indicated slices of the cement paste with the w/c ratio of 0.36, expressed in mm with reference to the bottom of the sample: W 5 mm and +K 2.5 mmand A 0 mm.

Table 25.1: Time-constants in hours of mono- and double-exponential fits to the data.

Slice

1

at 5 mm

at 0 mm I

0.24

WaterICement (wlw) I 0.36

6.9 k 0.4 4.6 f 0.2 (88%) 54 f 20 (12%)

15.0 k 0.9 12.1k 0.25 (95%) 116 f 42 (5%)

23.5 f 0.4

11.2 f 0.7 8.2 f 0.2 (93%) 122 k 47 (7%)

25.3 f 0.4

5.6 f 0.4 4.5 f 0.5 (81%) 90 f 38 (19%)

I

I

0.48

-

I

Between parentheses are shown the weight fractions obtained from the double-exponential procedure.

Comparing the time-constants obtained from mono-exponential fits to the data shown in Figs. 25.2 and 25.3, we may conclude that a similar behaviour is observed for the slices at 0 mm but not for the slices at 5 mm. Numerical calculations were recently reported on the T2 contribution for the spin-echoes built by a train of 9OoX-(9O0,), RF pulses, assuming that the pulses were infinitely sharp [6]; using these results, a T2 contribution of ca. was found for the intensity of the 64* echo, whereas the intensity of the first echo was found to be exclusively dependent on T,. Accordingly, TIP and TI (a few

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orders of magnitude longer than T2 for water confined into cement pores) mainly govern the decay of the last echoes, fact that allows the acquisition of long echo-trains from cement pastes.

4

I

I

I

0

20

40

I

60

80

Time I h

Fig. 25.3: The normalised intensities obtained from the indicated slices (expressed in mm with reference to the bottom of the sample) versus time, acquired in relaxation weighted mode (4 last echoes): W 5 and A 0. The solid lines represent the fits to double-exponential functions decaying with time-constants indicated in the Table.

25.5 Conclusions Spatially resolved information on hardening reactions may be obtained using STRAFI MRI. Constraints, like very short relaxation times and/or chemical reaction times of the order of minutes, do not impose limitations to the use of this technique.

References 1.

A. A. Samoilenko, D. Yu Artemov, L. A. Sibeldina, JETP Lett. 47 (1988) 417.

2.

T. Nunes, P. Bodart, E. W. Randall, A. A. Samoilenko, G Feio, J. Phys.D: Appl. Phys. 29 (1996) 805.

3.

T. Nunes, P. Bodart, E. W. Randall, Proceedings of the Second International Conference on NMR Spectroscopy of Cement Based Materials, P. Colombet, H. Zanni (eds.), Springer Verlag, 1997.

4.

P. Bodart, T. Nunes, E. W. Randall, Solid State NMR, in press.

5.

W. D. Halperin, J.-Y. Jehng, and Y:Q.

6.

A. Bain and E. W. Randall, J. Magn. Reson. A 123 (1996) 49.

Sung, Magn. Reson. Imag. 12 (1994) 169.

26. Application of Stray-Field Imaging to Dental Materials Science S. N. Scrimgeour, C. H. Lloyd, G. Hunter

Dental School and Department of Chemistry, University of Dundee, Dundee DD14HN, UK

D.M. Lane, P. J. McDonald Department of Physics, University of Surrey, Guildford GU2 5XH, UK

Abstract STRAFI has been applied to three diverse aspects of the science of dental restorative materials: visible light curing, absorption of liquid, and fluoride release. In this preliminary study valuable information has been obtained, already indicating the actual and potential value of STRAFI for such studies.

26.1 Visible Light Activated Polymerisation Polymerisation of the monomer in dental composite filling material is brought about by the application of visible light. The rate of free radical production (hence setting) is dependent upon light intensity. Absorption causes the intensity to fall with depth which leads to a “depth of cure” limitation for clinical use. Product composition and light source factors affect this in a complex interaction which has defeated modelling and requires practical determination. A number of non-imaging techniques have been used previously, but each has its limitations [ 11.

Experimenta1 A commercial product with 6 tooth shades, Occlusin@(ICI Dental) was selected. Pastes were packed in PTFE tubes and the curing light (Luxor, ICI Dental) applied to one end for either 20 s or 60 s. Specimens were stepped through the 58 T m-l fringe field gradient, using a quadrature echo sequence with a pulse gap of 20 ps to acquire the lH signal

294

S. N . Scrimgeour, C. H. Lloyd, G. Hunter, D. M. Lane, and P. J. McDonald

in consecutive 100 pm slices and give a one-dimensional profile [2]. The signal intensity was different for the polymerised composite and the remaining uncured composite paste at the opposite end of the cylinder. For both exposures a further 4 cylinders of each shade were made. Uncured paste was scraped away with a scalpel and the remaining polymerised material measured with a micrometer. This may be a more primitive technology, yet it is sufficiently reliable to be adopted in the IS0 standard and is included for comparison.

Results The cure front exists over a finite distance (Fig. 26.1), therefore a point on the curve must be defined for the “depth of cure”. For other techniques the distances to 50% or

90% of the measurement on cured material (from the value on uncured material) have been selected. Distances to these values are presented in Fig. 26.2, together with average values obtained from scraping specimens. 0.6 0.5

0.4

0.3

0.2 0.1 0 0.1

1

2

3

4

5

6

6.9

Fig. 26.1: T2 weighted profiles for Occlusins shade G. Magnetisation (arbitrary units, vertical axis) as a function of distance (mm, horizontal axis) from the end to which the curing light was applied.

Discussion STRAFZproduces smooth cure profiles with a 100 pm resolution, which is adequate for depth of cure studies. With the exception of “liquid” magnetic resonance microimaging (MRM) other techniques do not match this, particularly over the cure front. However,

MRM cannot image the polymer in this dental composite [ 11. Therefore STRAFI should

295

26. Application of Stray-Field Imaging to Dental Materials Science

be the preferred NMR technique for studies which require high spatial resolution of short T, materials. (e.g. polymer or partly converted material). 20s Cure Time

60s Cure Time

I 90%

[I

0 XL

LY

LG

S

G

DY

50% Scrape XL* LY*

LG

S

G

DY

Fig. 26.2: The depth of cure (vertical axis, mm). The composite shade is given by the letters code. The criterion used to obtain the depth of cure is given in the centre key. *Note: A 60 s exposure to shades XL and LY produced 100% transition throughout. Thus values limited by cylinder length.

The results show that product shade causes the depth of cure to change. All three criteria produce the same ordering. For both exposures darker shades decrease the depth of cure. Knowledge of a depth of cure using an agreed, if arbitrary criterion is useful in clinical dentistry for product comparison, but a knowledge of the polymer dynamics will shed new light on the kinetics of the process.

26.2 Absorption of Liquid Mixtures in Cured Materials Restorative dental materials are in continuous contact with a varying solvent mixture from food substances and saliva. Though the material may absorb some liquid this should not lead to its softening as this will result in excessive wear. The softening potential of the liquid has been related to the combination of liquid and polymer compositions [3]. It follows that diffusion of liquid mixtures must be measured. Theoretical models are not yet available and the use of pure liquids to assess performance cannot be relied upon.

296

S. N. Scrimgeour, C. H. Lloyd, G. Hunter, D. M. Lane, and P. J. McDonald

Experimental To simplify this initial experiment an unfilled mixed resin used in some dental composites (50% UDMA / 50% TEGDMA) was selected. 300 to 500 ym thick films were light cured. One surface of the polymer was exposed to water: ethanol mixtures while the ingress was followed by a STRAFI surface coil and acquisition technique [4]. Profiles were obtained for solvent within consecutive 24 pm slices across the sensitive volume.

Results Solvent profiles were recorded at 30 minute intervals over a 10 hour period. A set of such profiles is shown in Fig. 26.3. Front displacement I time relationships were derived from such data and plotted as in Fig. 26.4 to produce information on the diffusion mechanism and rate. A simple power relationship was used to fit curves to the data. The diffusion is approximately Fickian ( n = 0.5) with the diffusion rate increasing progressively with ethanol content in the mixture.

Discussion STRAFI can produce diffusion profiles with excellent resolution which show that diffusion into this resin is Fickian in nature. This contrasts with a suggestion that diffusion into composite is Case I1 at ambient temperature [5]. That the diffusion rate increases progressively with ethanol content and does not show a mid-composition maximum was not expected from solubility parameter predictions [3,5]. At present it would be unwise to speculate on the reason for this difference.

26.3 Fluoride Releasing Materials Relatively low concentrations of fluoride significantly reduce the incidence of dental caries. Glass polyalkenoate cement sets by a reaction between polyacrylic acid and a glass powder which also releases fluoride from the glass into the adjacent tooth. However, its other properties are limited which has resulted in the development of materials which, as part of their chemistry, include this reaction to release fluoride. These include visible Light cured glass polyalkenoate cement and compomer (modified composite). Clinical benefit depends on continued release of the fluoride at the interface with the tooth and as a consequence fluoride studies are important to dentistry.

26. Application of Stray-Field Imaging to Dental Materials Science

297

Signal from solvent well

0

48

96

144

192 240

288

336

Fig 26.3: Diffusion profiles for the 35% ethanol: 65% water mixture at 22 "C. The magnetisation (arbitrary units) as a function of distance (pm) into the resin.

1

2

3

4

5

6

7

8

9

Fig 26.4: The diffusion front displacement (vertical axis x, pm) with time (horizontal axis t, hours) for 45%, 35%, 25% ethanol in water. n = 0.43, 0.46, and 0.41 respectively for a fit x = c tn.

Experimental Products listed in Table 26.1 were packed into glass tubes and fully cured. Profiles were recorded following procedures given in section 26.1, in this instance for 500 pm slices. Table 26.1: Products used.

Name

Type

Manufacturer

F- release

Fuji IX Vitremer Dyract

Glass Polyalkenoate VLC Glass Polyalkeoate Compomer

Yes Yes Yes

ZlOO

Composite

GC Corp. Tokyo 3M Healthcare St Paul Dentsply GmbH Konstanz 3M Healthcare St Paul

No

Results The decay of magnetisation was recorded using a train of 16 echoes at each spatial location (Fig. 26.5). For the pulse gap selected (20 ps) a single exponent produced the best curve fit for lH, whereas two exponents produced this for 19F.Figure 26.6 is an example of the intensity profiles along the cylinder length. Though the coil is at the position for the I9F resonance frequency there was some lH pickup followed by an overlap then the 19F signal which gives rise to a three step profile. Both the production of the profile and values for the exponent parameters (Table 26.2) are significant.

298

40

S. N . Scrimgeour, C. H. Lloyd, G. Hunter, D. M. Lane, and P. J. McDonald

120 200 280 360 440 520 600

Fig. 26.5: Decay of magnetisation (vertical axis, arb. units) with time (horizontal axis, ks) for 1H

Fig. 26.6: 19F profile along the length of the Fuji IX cylinder. Horizontal axis - distance

and 19F.

(m).

Table 26.2 Values from fitting the curves with one (1H) or two (19F) exponent(s).

Product

'H T2 ps

Short 19FT2 ps

Long I9F T2 ps

F: H intensity %

Fuji IX Vitremer Dyract ZlOO

183 114 63 76

56 50 54 no signal

824 740 85 1 no signal

22.9 27.0 20.2

Discussion For resin matrix materials residual unreacted groups are the most probable source of molecular motion associated with IH T2's of the order of 100 ps. The matrix of glass polyalkenoate has more flexible polyacid chains linked by ions and a relatively longer 'H T2 is to be expected. It follows that visible light cured glass polyalkenoate which has elements of both reactions should have a IH T2 of intermediate value. When set, most of the fluoride remains within the glass structure, is rigidly bound and its I9F T2 values are probably dominated by components arising from the glass. Differences 19FT2 in may be due to a requirement for the glass in each product to be compatible with its acid. It is possible that matrix fluoride, leached from the glass, may moderate the T2value.

References 1.

C. H. Lloyd, S. N. Scrimgeour, J. A. Chudek, et al., Dent. Muter. 10 (1994) 128.

2.

D. M. Lane, P. J. McDonald, Polymer 38 (1997) 2329.

3

J. E. McKinney, W. Wu, J. Dent. Res. 64 (1985) 1326.

4

P. M. Glover, P. J. McDonald, B. Newling, J. Mag. Rex. 126 (1997) 207.

5

W. Wu, J. E. McKinney, J. Dent. Res. 61 (1982) 1180.

27. Particle Compaction as Observed by MRI R. A. Waggoner The lnstitute of Physical and Chemical Research (RIKEN), Saitama, Japan

M. Nakagawa Colorado School of Mines, Golden, CO, USA S. J. Glass and M. Reece Sandia National Laboratories, Albuquerque, NM 87 185, USA E. Fukushima New Mexico Resonance, 2425 Ridgecrest Dr., SE Albuquerque, NM 87108, USA

Abstract The behavior of particles undergoing compaction is of interest in a variety of areas such as ceramic engineering, civil engineering, and food processing. Observing the effects of compaction on individual particles and particle properties can provide unique insights into the compaction process. MRI offers the ability to observe a system at successive stages of compaction and, in particular, it can resolve individual particles in model systems. When individual particles are located, orientation of contacts can also be determined. Here we present MRI data of a model system undergoing compaction.

27.1 Introduction Compaction of particles is of interest in many areas, but here we will focus on compaction of ceramic powders and present MRI data of compaction of a model system. Ceramic components are often formed by compressing a ceramic powder in a die and then sintering. A non-uniform packing density of the green powder will result in differential densification during sintering, as shown in Fig. 27.1. The resulting ceramic com-

300

R. A. Waggoner, M . Nakugawu, S.J. Glass, M. Reece, unrl E. Fukiiskitnn

ponent will have less than optimum mechanical properties and it may require an additional processing step of machining to be usable [ 11. To better understand and control the compaction to produce more uniform packing densities, particle compaction is studied by a variety of techniques such as mercury porisometry, ultrasound, x-ray radiography, and microscopy. When individual particles can be resolved, contacts between particles can be determined as well as the distribution of these contacts in space. Three-dimensional MRI allows the full characterization of the organizational structure of a pack, orfi7Dt-k

[ 2 ] ,to be determined if individual particles can be resolved [3]. Here we present MRI data for compaction of a model system simulating compaction in a dye. Green Ceramic

Sintered Ceramic

Fig. 27.1: Effect of sintering on green ceramic with non-uniform void space density.

27.2 Experimental The compaction of 3 mm diameter oil filled pharmaceutical pills has been observed by three-dimensional MRI. The pills were placed in the compaction device shown in Fig. 27.2. The entire device was place inside an 1.89 T, 31 cm horizontal bore Oxford magnet interfaced to a Nalorac Quest 4400 imaging spectrometer. Images of the sample at four stages of compaction were acquired. Each stage was achieved by adjusting the pressure screw shown if Fig. 27.2. Each image is 64 x 64 x 64 pixels with each voxel being 1 mm3.

27. Panicle Compaction ( I S Observed by MRI

PVC Pipe 4

301

Z Particles

Pressure Screw

Phenolic Plunger

Fig. 27.2: Schematic of compaction device used in MRI.

To determine the number of particles and the locations of the particles in each image the pixel containing the center of each particle was identified. In this study, the particles are small enough relative to the size of a voxel so that only one pixel for each particle is completely within the particle. Therefore, the pixels containing the particle centers were obtained by sweeping a 3 x 3 x 3 cube through the image and setting every pixel within the cube that was less than the maximum intensity to zero. There is only one non-zero pixel left for each particle and that pixel should contain the particle center. When this is done for the entire image, the number of non-zero pixels is then counted to determine the number of particles. Contacts between particles were determined by determining the distances between particle centers and any distance that is below a threshold value is considered a contact. The lowest threshold value that would give at least two contacts for each particle was the value that was used. This threshold was chosen since a particle only having one contact is a highly unstable and therefore highly unlikely state. Once a contact is determined the contact angles can be determined from a vector connecting the two centers.

27.3 Results The images of the particles undergoing compaction are shown in Fig. 27.3. Image A is for the uncompressed sample with just enough pressure being applied by the plunger to keep the particles in place. It was determined that there were initially 640 particles from this image. The decrease in the number of particles in subsequent images is probably due

302

R. A. Waggoner, M . Nakagawa, S. J . Glass. M. Reece. arid E. Fitkicshirna

to the loss of particles due to rupture, although, it is also possible that for a highly c o n pressed system the assumption used to determine the centers may become questionable.

Plane through the middle of particles undergoing compaction

A

B

C

Number of particles as determined by MRI

640

639

638

628

Packing Density

0.64

0.71

0.77

0.86

D

3D rendering of particles undergoing compaction

Fig. 27.3: Images of a sample of 3mm pharmaceutical pills at successive stages of compaction.

y... e\.

X

..1

Y

.......

.***

Fig. 27.4: Definition of the contact angles, where the vector is the contact vector and the axis system is the compaction device axis system.

The contact angles are defined by, the contact vector, the vector connecting the centers of the two particles involved in the contact, and the axis system of the compaction device. The principle axis of the compaction device is the z-axis, as shown in Fig. 27.2. Figure 27.4 gives graphic definition of the contact angles. 8 is the angle that the projec-

27. Particle Cortipczction as ObrenJedby MRI

303

tion of the contact vector in the x-y plane makes with the x-axis. @ is the angle that the Contact vector makes with the x-y plane. Figure 27.5 shows the histograms of the contact angles for the system of particles in the least (A) and most compressed (D) states. The distributions of the angles in the x-y plane, 0, do not show any obviously significant changes upon compression. The distributions of the angles relative to the x-y plane, $, show that upon compression the contacts

are shifting more toward the preferred contact angles of 0", -+ 15", & 45". 90

90

D

A 90

e

180

90

0

270

I80

0

270

Fig. 27.5: Histogram of contact angles, @ and 8 (see Fig. 27.4), at stages A and D (see Fig 27.3) of compaction. With compaction, the distribution of I$, the out of plane contacts, is shifted toward the preferred angles of contacts.

304

R. A. Waggoner, M. Nahgawa. S.J . Glass, M. Reece. and E. Fukushinia

27.4 Conclusions We have demonstrated that at least for a model system MRI is capable of providing insight into the behavior of particles, numbers of particles and contact angles, rather than just systems properties as a whole such as density or mechanical properties. With further refinement of the analysis methods this technique should be able to provide very unique and valuable insights into the compaction process. It is true that actual ceramic systems would be impossible to image directly, as was done with this model system, with MRI techniques currently available. However, the use of this method to provide experimental verification of theoretical concepts and computer algorithms based on those theories should prove to be quite valuable.

Acknowledgment This work was supported in part by Sandia National Laboratories and the National Science Foundation.

References 1.

K. G. Ewsuk. "Consolidation of Bulk Ceramics", Characterization of Ceramics. R. E. Loehman, (ed.). Butterworth-Heinemann. Greenwich, CT, 1993, pp. 77-101.

2.

R. Bewer. Fabric arid Mineral Analysis of Soils, John Wiley and Sons, Inc., 1964

3.

R. A. Waggoner, M. Nakagawa, and E. Fukushima, Non-invasive measurement of Fabric of Particle

Packing by NMR in Introduction to Mechanics Publishers, Rotterdam, Netherlands, 1998.

of

Granular Flow, M. Oda, (ed.), A. A.Balkema

Medicine and Biology

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28. 2H Double Quantum Filtered NMR Histology and Diffusion Measurements in Isolated Nerves and Blood Vessels Hadassah Shinarl, Yehuda Shag2, Uzi Eliav', Yoshiteru Sea? and Gil Navonl lSchoo1 of Chemistry and 2School of Physics, Tel Aviv University, Ramat Aviv ,Tel Aviv 69978, Israel 3Department of Physiology, Kyoto Perfectural University of Medicine, Kamigyo-ku, Kyoto 602, Japan

Abstract 2H double quantum filtered (DQF) NMR enables the resolution of water signals from different ordered anatomical environments. In the present work the method is demonstrated on sciatic nerve and bovine arteries. For sciatic nerve the large bulk water signal is eliminated and at least 4 different water populations inside the nerve can be distinguished by 2H DQF NMR. This is achieved without the addition of shift reagents. The exchange of the water molecules between the different compartments is slow, relative to the difference in their splitting. Thus the assignment of the water signals to the different compartments and the measurements of their dynamic properties is facilitated. Three of the compartments were assigned to the endoneurium, epineuriuni and the axon. The signal of the endoneuriurn is further split below 5 "C. Diffusion measurements by DQF NMR enabled us to measure the water diffusion coefficients of the three compartments. Applying the gradients during the DQ evolution time, doubles their effective strength. The water diffusion in the three compartments was found to be anisotropic and in the axon, the diffusion is heavily restricted in the perpendicular direction, yielding an effective diameter of the axon of 7.5 pm. In the case of blood vessels, the water signal from the different layers of the vessel's wall is resolved. Histological and strain images can be obtained by the spectroscopic 2H DQF MRI. In this technique two contrast mechanisms are utilized: (a) the creation time

308

H.Shintir, Y.Sliarf; U. Elinv. Y. Seo, arid G. Nrivoti

of the second rank tensors and (b) the spectroscopic dimension. In this way images of distinct layers of the blood vessel wall are obtained. Moreover, the spectroscopic dimension provides quantitative information about the degree of strain. By a proper calibration, an image representing the strain map of the blood vessel wall was obtained.

28.1 Introduction Double quantum filtered (DQF) NMR spectroscopy is a sensitive technique which can reveal otherwise undetectable anisotropic motion of quadrupolar nuclei in biological systems. Recently, the detection of anisotropic motion of sodium ions in bovine nasal and articular cartilage [1,2], red blood cells [3,4] as well as well as in human brain and muscle [ 5 ] has been reported. Similarly, anisotropic motion of water molecules has been detected by 2H DQF measurements of a variety of biological tissues such as cartilage, tendon, skin, brain and blood vessels [2,6-81. The 2H DQF NMR lineshapes and linewidths vary considerably among the various organs with different degrees of local and macroscopic order. Measurements performed on the isolated cartilage constituents [1,7] as well as measurements of proteoglycan depleted articular cartilage 191 have revealed that the anisotropic motion of both sodium ions and water molecules in these systems stems from their interaction with the oriented collagen fibers. Parallel studies of NMR and light microscopy [lo] have attributed the NMR detected motional anisotropy of water molecules in blood vessels to their interaction with collagen fibers and excluded the role of elastin, present in these tissues, as a source of orientational ordering. The method presented here allows to differentiate between different regions in the tissue on the basis of the different 2H quadrupolar splitting of the water molecules. It allows to selectively image the different layers of the vessel wall and obtain an “histological image”. The separation of the water signals from the different anatomical compartments in sciatic nerve enables the measurement of the water diffusion coefficients from each compartment, independently.

28. ' H DQF and Diffusiori Imaging onlsolnted Nerves and Blood Vessels

309

28.2 Materials and Methods Wistar Hamamatsu rats (250-350 g) and rabbits (about 2 kg) were anesthetized with sodium pentobarbital (50 mgkg body weight, i.p.). Sciatic nerves were isolated and the outer coat of adipose and connective tissue was carefully removed. Each nerve was placed in 100 yl capillary tube and positioned with its long axis parallel to the magnetic field. Tendon fibers were separated from rat tail tendon. Samples of aorta and coronary arteries were removed from freshly slaughtered healthy cows. For the imaging experiments, a coronary artery was mounted on a 3.3 mm diameter Teflon rod, by tying the ends of the artery to the ends of the rod. The stretching was accomplished by shortening the connecting strings. All samples were equilibrated in 150 mM NaCl immersed in D,O prior to the NMR measurements. NMR measurements were carried out on ARXSOO, AMX360 WB and AMX300 WB Bruker NMR Spectrometers. The latter was equipped with 200 Glcm gradient unit and an imaging probe tuned to the deuterium frequency of 46.05 MHz. 2H DQF spectra were measured using the conventional pulse sequence:

90" - 712 - 180" - 712 - 90" - tDQ - 90" - Acq

(28.1)

where z is the creation time of the second rank tensors and tDQ is the evolution time of the DQ coherences. TDQ,the DQ relaxation time, was measured by introducing a R pulse in the middle of the DQ evolution time (eqn. 28.2): 90" - d 2 - 180" - 712 - 90" - t ~ ~- /180" 2 - f ~ d -290" - Acq

(28.2)

In the DQF MRI experiment (Fig. 28.1, eqn. 28.3) the phase encoding gradients were applied during the first half of the DQ evolution time. In the DQF diffusion measurements two gradient pulses were introduced during the DQ evolution time, before and after the 180" refocusing pulse (eqn. 28.4):

90" - 712- 180" - 712 - 90" - t3 - - t4 - 180" - ts - g - ts - 90" - A c ~(28.4) where: t3 + t4 = ts + t6 .

3 10

H. Shitiar, Y. Shad U. Eliov. Y. Seo, nnd G.Navon

creation

...................................

evolution

detection

, 2

................................... ................................................ ........................................................................ .......... ........................... ................................................... ..................... ..........

p=- 1 p=-2

Fig. 28.1: DQF MRI pulse sequence (eqn. 28.3) and coherence transfer pathway.

28.3 Results 28.3.1 'H Double Quantum Filtered NMR Study of Water Compartmentation and Diffusion in Rat Sciatic Nerve Peripheral nerves comprise bundles of nerve fibers held together and surrounded by a collagen network - the endoneurium [ 1 11. The nerve fibers consist of axons surrounded by a phospholipid bilayer and wrapped by many layers the myelin sheath. Hundreds of myelinated axons are enclosed in the flat squamous cell layer - the yerineurium [ 121. The perineurium whose structure is similar to that of the endothelium of blood vessels, serves as the blood nerve barrier and is permeable to water and ions. Several perineurial bundles are wrapped together and separated from the rest of the tissue by an outer layer

of collagen fibers and fibrocytes - the epineurium. A graphical representation of the structure and dimension of a rodent sciatic nerve is given in Fig. 28.2.

28. ' H DQF and Diffusion Inuiging onlsolated N e n m and Blood Vessels

311

Fig. 28.2: Sciatic nerve.

We have recently shown that the 2H DQF NMR spectrum of isolated rat sciatic nerve, equilibrated in deuterated saline, is composed of three quadrupolar-split water signals [ 131. On the basis of the time course of their shift by Co-EDTA*- and CoCI2, the signals with quadrupolar splitting of about 120, 470 and 9 Hz were assigned to water in the epineurium, endoneurium and the intra-axonal compartment, respectively. The signal of the bulk water, which experiences isotropic motion, was eliminated by the DQF pulse sequence. The fact that three different quadrupolar-split pairs are observed, indicates that on the time scale of the NMR experiment, the water exchange between the different compartments of the nerve is slow. Similar results are obtained for rabbit sciatic nerve. Three quadrupolar-split paus with splittings of about 230, 450 and 1300 Hz respectively, are evident in the SQ spectrum (Fig. 28.3). Since the nerve is immersed in D,O solution, the central transition is mostly due to the free D,O molecules. The DQF spectra are composed of a superposition of the four pairs of satellite transitions evolving at different rates (Fig. 28.4). It is evident from the spectra that the large central water signal has been eliminated by the DQ filter and a new, very narrow signal which evolves at longer creation times, is revealed. We are therefore detecting ordered water in four different compartments. The three signals with the splittings of 230, 450 and 5 Hz are very similar to those observed in rat sciatic

3 12

H. Shinar.

Y. Shad U. Eliav, Y. Seo, and G. Navon

nerve and thus may be assigned to water in the epineurium, endoneurium and the axon respectively. The broad signal with splitting of 1300 Hz which is evident at very short '5 values, was not reported before for the sciatic nerve. However, further ?H DQF measurements of rat sciatic nerve at very short creation times, showed a weak broad signal with similar splitting of approximately 1300 Hz for this nerve as well. The origin of the broad component is currently under investigation. 0.4ms

1 " " " ' " 1 " " " " ' I " '

1800

8

HZ

Fig. 28.3:ZH S Q spectra of rabbit sciatic nerve.

0.8msA

-500 0

BZ

500

0

Hz

Fig. 28.4: *H DQF spectra of rabbit sciatic nerve. Creation times are given on the figure.

We have also measured the temperature dependence of the 2H SQ and DQF spectra of rat sciatic nerve. At room temperature two quadrupolar split pairs with splittings of 526 and 72 Hz are observed at T = 400 ps. When the temperature is lowered, the quadrupolar splitting for the outer pairs decreases and at 2 "C three pairs of quadrupolar split signals with splittings of 619, 351 and 71 Hz are observed (Fig. 28.5). In an experiment with another rat sciatic nerve, the signal with the 440 Hz splitting did not shift when the nerve was equilibrated in Co-EDTA2-. When this nerve was cooled to 2 "C, two pairs of unshifted signals with splitting of 570 and 190 Hz are observed. This is in accordance with our previous finlngs [I31 which have assigned the unshifted signal to the water inside the perineurial sheath which is impermeable to Co-EDTA'.. Probably, at room temperature there is fast exchange between water molecules at two distinct sites interacting with different networks of collagen fibers. Indeed, different collagen networks are

28. ' H DQF and Difitsion Imaging onlsolated Nerves aid Blood Vessels

313

observed by electron microscopy in the endoneurium [ 1 I]. At lower temperatures the exchange becomes slow relative to the difference between the splittings of the two sites, giving rise to two distinct signal pairs. A graphical representation of the observed splitting of the outer satellite pair, as a function of temperature is given in Fig. 28.6. 3dk

2°C

rn 600 -

-500

0

Hz

500

0

Hz

Fig. 28.5: 2H SQ and DQF spectra of rat sciatic nerve.

350 280

290

300

31 0

T,K Fig. 28.6: The splitting of the water of the etldoneuriuni as a function of temperature.

Recently , it has been clearly demonstrated that the apparent water diffusion coefficients in the central and peripheral nervous systems is orientation dependent [ 14-1 81. In MRI of an intact brain tissue, the signal in each pixel is a superposition of water in many different compartments. In isolated nerves it has been shown that the magnetization decay curve, measured by PGSE sequence, is resolved into two or more exponentials [ 19,201, each representing a unique water population. By resolving the magnetization decay curve, Seo et al. [21] have found three anisotropic water diffusion coefficients in rat sciatic nerve. The major part of the signal which remained after the addition of MnC12, showed both anisotropic and restricted diffusion and was assigned to the intra-axonal water. Since the maximum intensity of the 2H DQF signal of water in the three compartments of rat sciatic nerve is obtained at different z values, the relaxation times and the diffusion coefficients in each of the three compartments can be measured independently [13,22] without the addition of shift reagents. In the present work 2H diffusion measurements for water in the epineurium, endoneurium and the axon were performed by the DQF-PGSE sequence (eqn. 28.4). The apparent diffusion coefficients for each diffusion

3 14

H. Stiinar, Y. Slirirf: U. Elinv. Y. Seo, and G. Navori

time were calculated from the attenuation of the echo. The three different water DQF signals exhibit anisotropic diffusion. For the intra-axonal compartment, the apparent diffusion coefficient perpendicular to the nerve axis is dependent on the diffusion time (Fig. 28.7). A model for restricted diffusion in cylinders, based on the dependence of the trace of the diffusion tensor on the diffusion time was used to interpret the results [23]. From the restricted diffusion of the intra-axonal water the inner diameter of the axon was estimated as 7.5 pm. The calculated effective diameter of the assumed cylindrical diffusion barrier (7.5 p m ) is in good agreement with the mean inner diameter of the axons 6 f 1 pm [24]. In the endoneuriuin and epineurium, anisotropic diffusion of water may be caused by the thick collagen fibers and the myelinated axons. These structures reduce the effective diffusion distance of the water perpendicular to the axis of the fibers.

Diffusion time( msec) Fig. 28.7: The dependence of the water epineurium, endoneurium and axon diffusion coefficients on the diffusion time and orientation. Empty symbols - measured parallel to Bo, full symbols measured perpendicular to Bo. 0 axon, # endoneurium, epirteuriunt.

28.3.2 2H Double-Quantum-Filtered MRI of Strain Exerted on the Blood Vessel Wall The blood vessel wall is composed of three layers: the outer layer, the tunicn ndventitia, the intermediate layer, the tunica media and the inner layer - the tunicn intima. In large arteries, the adventitiu and the media constitute most of the tissue. At normal blood pressure, the length of the vessel is as much as 40% longer and its circumference is about

28. 2H DQF mid Difiuioti Imaging onlsolated Nerves and Blood Vessels

315

30% greater than in the unstressed condition. Recently, we have found that 2H DQF NMR spectral lineshapes of water molecules inside the walls of large blood vessels vary between the different tissue layers [8]. Measurements of bovine carotid and coronary arteries have indicated that the 2H DQF NMR spectrum of the inner layer, the tunica media, is insensitive to strain and is characterized by a relatively narrow signal and long relaxation times. On the other hand the spectral lineshape of the outer layer, the tunica adventitia, is much broader and is highly sensitive to strain (Fig. 28.8) [8]. Thus, an imaging method based on *H DQF Nh4R can give us a map of both tissue composition and strain distribution within the blood vessel walls [25].

-1.0

0

-1.0

1.0

0

-1.0

kHz Fig. 28.8: 21 QF spectra of the outer layer of bovine coronary artery as a function o .he elongation (z = 0.3ms). The spectra were obtained by subtracting the contributions of the isolated inner layers from that of the intact tissue.

The DQF MRI sequence was tested on a phantom composed of rat tail tendon fibers (Fig. 28.9a) immersed in D,O. The rat tail tendon consists of collagen fibers and exhibits a well resolved quadrupolar splitting of the deuterium NMR spectrum as expected from a macroscopically oriented system [26,27]. This feature allows a convenient assessment of the effectiveness of the double quantum filtration in suppressing the signal of bulk water.

316

H. Shinar, Y. Shad U. Eliav, Y. Seo, and G. Navott

F

1.0

mm

l x

kHz

Fig. 28.9: *H double quantum filtered spectroscopic imaging (at z = 0.3 ms) of rat tail tendon fibers. (a) scheme of the phantom. (b) 2H gradient echo 2D image of the XZ plane. (c) 2H DQF 2D image of the same plane. This low resolution image (16 x 16) is constructed by projecting the spectroscopic dimension onto the XZ plane. Note that the brighter regions in the gradient echo image 0)correspond to the regions containing free D20 in the spaces between the fibers and in the capillary containing pure D20. Whereas only intrafibrillar water are apparent in the DQF image (c). In (d) DQF 1D spectroscopic image of two rat tail tendon fibers immersed in D20 i n a single capillary (denoted as X-F, i.e. one spatial dimension X, and one spectroscopic dimension F); Magnitude calculation is used for imaging however the spectroscopic dimension is preserved as can be seen from the characteristic anti-phased DQF spectral lineshape associated with the right fiber. The relatively high effective spatial resolution of about 40 pm, is achieved by the high field gradient strength (200 G/cm). (Taken from ref. 25).

Indeed, the strong signal of isotropically rotating water molecules which predoniinates the conventional gradient echo image (Fig. 28.9b) is completely filtered out in the DQF image (Fig. 28.9~).The preservation of the spectroscopic dimension is presented in the DQF 1D spectroscopic image of two rat tail tendon fibers immersed in D,O (Fig. 28.9d).

28. ' H DQF and Diffusion Imaging onlsolated Nerves arid Blood Vessels

317

2H DQF 1D spectroscopic (X-F) images of longitudinal strip cut of bovine aorta and coronary arteries were acquired for various creation times, z (Fig. 28.10). The relative signal intensities of water in the tunica media and tunica adventitin depend on the acquisition parameters, i.e. the creation time z and the frequency segment. For a relatively short creation time the signal intensity of the center frequency segment originates from all tissue layers and is roughly proportional to the total amount of anisotropic water [25], whereas signals with frequencies shifted by more than 100 Hz from the center frequency display water in the outer layer whose residual quadrupolar interaction is larger. For long creation times the signal of water in the outer layer has decayed and the center frequency segment represents only the narrow signal of water in the inner layers (practically the tunica media). out

in

(a) Gradient Echo Z

1

10.0 mm

-1.0

F

0 kHz -1 .o

-1.o

F

0

kHz

-1.o

2.0mm

X

Fig. 28.10: The selection of tissue layers is demonstrated for a longitudinal strip cut of bovine aorta. top: a 2D GE image is given to trace sample profile; middle: 1D DQF spectroscopic image acquired for a relatively short z value (0.3 ms), water from all tissue layers contribute to the center of the DQF spectrum whereas only water in the outer layer are present for off-center frequencies; bottom: for a long z value (2.0 ms) the inner layer (tunica media) signal reaches its maximum intensity while the signal from the outer layer has already decayed. (Taken from ref. 25).

318

H. Shinnr, Y. Shurj: I/. Eliav. Y. Seo, arid G.Nnvon

A 2D gradient echo image of D 2 0 hydrated bovine coronary artery mounted on a

3.3 mm diameter stabilizing Teflon stick is shown in Fig. 28.1 la. ' H DQF 2D was measured at two creation times. The DQF 2D images of the artery (Fig. 28. l l b-d) are constructed for selected frequency segments of 200 Hz each. For a relatively short z (0.3 ms), water in both layers, tunica media and tunica ~ i ~ f v e n t i t icontribute a, to the center of the NMR spectrum (v = 0 f 100 Hz, Fig. 28.1 lb) whereas only water i n the outer layer are present for v = 300 f 100 Hz (Fig. 28.1 Id). For a long z value (3.0 ms) the signal from the inner layer is at its maximum while the signal from the outer layer has already mostly decayed (Fig. 28.1 Ic). The inner and outer layers are 0.9 mm and I .O mm thick respectively. The smaller inner diameter (3.3 mm) obtained in the gradient echo image is due to free water accumulated between the tissue and the stabilizing stick (3.3 mm in diameter). Thus comparison between the gradient echo image (Fig. 28.1 la)

(a) Gradient Echo

(c) DQF - Inner layer (2=2.0rns, Av=O Hz)

(b) DQF(z=0.3 rns, Av=O Hz)

(d) DQF- Outer layer (z=0.3 ms, Av=300 Hz)

Fig. 28.1 1: *H DQF 2D images of a cross section of D20 hydrated bovine coronary artery (taken from ref. 25).

28. -'HDQF nnd Diffusion lrnagirig onlsokitecl Nerves arid Blood Vessels

319

and the DQF images (Fig. 28.11b-d) demonstrates both the ability of the method to filter out free, isotropically rotating water ,and the separation of the different tissue layers (either the tunica media or the tunica adventitiu or both).

*H DQF spectroscopic imaging may provide a measure of the distribution of the

*

strain throughout the sample. We have previously shown that the H residual quadrupolar splitting of the water in the advenririu is sensitive to the strain exerted on the wall in the longitudinal direction (Fig. 28.12) [8]. In order to assess the strain, the average residual quadrupolar interaction for each elongation was calculated from the DQF spectra measured at short creation times, according to a method recently described [ 10,251. DQF MRI spectroscopic imaging was performed on a sample of fully relaxed and 55% elongated coronary artery and the average residual quadrupolar interaction was calculated for each pixel The images obtained are given in Fig. 28.13. The gray scale corresponds to ranging from 0 to 800 Hz. The dark colors in both images demonstrate the relatively narrow DQF spectrum of the tunica media which is insensitive to strain. The bright colors that dominate the outer layer in the left image correspond to d v q > values of 350-

450Hz for the unstressed vessel, while in the right image, the brighter colors reflect larger values of residual quadrupolar interaction ( 4 v q > ranges between 550 and 800 Hz) associated with regions with higher strain. When as a function of the

elongation is properly calibrated, the images obtained can be presented as strain maps.

8o01 7001 6001

300 0% I

I

20%

40%

60%

Elongation Fig. 28.12: The average quadrupolar splitting, ,as a function of elongation. The calculation was performed on a set of spectra obtained by subtracting the contributions of the isolated inner layers from that of the intact tissue.

320

H . Shinar. Y. S h a d U.Eliav, Y. Seo. and G. Nnvon

No elongation

55% elongation aoo 700 600

500 400 300 200 100

0

Fig. 28.13: Two calculated 2H quadrupolar splitting 2D images of a bovine coronary artery, unstressed (left) and 55% elongated (right). The average quadrupolar splitting was calculated using 256 spectral points for each of the (64x64) pixels of the 2H DQF spectroscopic images. The left image was acquired using TR = 1 s, r = 0.3 ms. In order to optimize the signal to noise ratio for both tissue layers, the right image was calculated combining two sets of data. For the outer layer data were acquired using TR = 0.1 s and z = 0.3 ms. For the inner layer data were acquired using TR = 0.1 s, r = 2.0 ms. The field of view of both images was 0.75 cm (taken from ref. 25).

References I.

U. Eliav, H. Shinar, and G. Navon, J. Magn. Reson. 98 (1992) 223.

2.

H. Shinar, U. Eliav, T. Knubovetz, Y. Sharf. and G. Navon, Quart. Magn. Reson. B i d . Med. 2 (1995) 7.

3.

H. Shinar, T. Knubovetz, U. Eliav, and G. Navon, Biopys. J. 64 (1993) 1273.

4.

T. Knubovetz, H. Shinar, U. Eliav, and G. Navon, J. Magn. Reson. B. 110 (1996) 16.

5.

R. Reddy, L. Bolinger, M. Shinnar, E. A. Noyszewski, and J. S. Leigh, Magn. Reson. Med. 33

(1995) 134. 6.

Y.Assaf, G. Navon, and Y. Cohen, Magn. Reson. Med. 37 (1997) 197.

7.

Y.Sharf, U. Eliav, H. Shinar, and G. Navon, J. Magn. Reson. B. 107 (1995) 60.

8.

Y.Sharf, S. Akselrod, and G. Navon, Magn. Reson. Med. 37 (1997) 69.

9.

H.Shinar, U. Eliav, R. Schneiderman,. A. Maroudas, and G. Navon, ISMRM 3rd Annual Meeting, Nice, Abstract p.432 (1995).

10.

Y. Sharf, T. Knubovets, D. Dayan, A. Hirshberg, S. Akselrod, and G. Navon, Biophjs. J. 73 (1997) 1198.

11.

T.Ushiki and C. Ide, Arch. Hisrol. Jap. 49 (1986) 553.

28. 'H DQF and DiJfitsion Imnging oiilsolafed Neives and Blood Vessels 12.

K.lshii and N.Takeuchi, Acia Otoluryngol 113 (1993) 632.

13.

H. Shinar, Y. Seo, and G. Navon. J. Mngn. Reson. 129 (1997) 98.

14.

32 1

M.E. Moseley, Y. Cohen, J. Kucharczyk, J. Mintorovitch, H. S. Agri, M. F. Wendland, J. Tsuruda, and D. Norman, Radiology 176 (1990) 439.

15.

H. Sakuma. Y. Nomura, K. Takeda, T. Tagami, T. Nakagawa, Y. Tamagawa, Y. Ishii, and T. Tsukamoto, Rndiol. 180 (1991) 229.

16.

F. A. Howe, A. G. Filler, B. A. Bell, and J. R. Griffiths, Magn. Reson. Med. 28 (1992) 328.

17.

D. LeBihan, R. Turner, and P. Douek, NeuroReporr 4 (1993) 887.

18.

C. Pierpaoh, P. Jezzard, P. Basser, A. Barnett, and G.Di Chiro, Radiol. 201 (1996) 637.

19.

C. Beaulieu and P. S . Allen, Magn. Reson. Med. 31 (1994) 394.

20.

R. M. Henkelman, G. J. Stanisz, J. K. Kim, and M. J. Bronskill, Magn.Reson. Med. 32 (1994) 592.

21.

Y. Seo. Y. Morita, Y. Kusaka, M.C. Steward, and M. Murakami, Jpn. J. fhysiol. 46 (1996) 163.

22.

Y. Seo, H. Shinar, and G . Navon , ISMRM 4th Annual Meeting, p. 258 (1996).

23.

P. van Gelderen, D. DesPres. P. C. M. van Zijl, and C. T. W. Moonen, J. M a p . Reson. B 103 (1994) 255.

24.

R. A. Bergman and A. K. Afifi, Nervous Tissue In: Atlas of Microscopic Anatomy, Saunders, Phila-

delphia, pp. 107-150 (1974). 25.

Y. Sharf, Y. Seo, S. U.Eliav, S. Akselrod, and G. Navon, Proc. Nntl. Acad. Sci. USA, 95 (1998) 4108.

26.

C. Berendsen, J. Chem. fhys. 36 (1962) 3297.

27.

L. Tsoref, H. Shinar, and G. Navon, M a p . Reson. Med. 39 (1998) 11.

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29. Translational Diffusion of Water in Lung Tissue B. Geil', D.C. Ailion2, G. Laiche$. and A. G. Cutillo3 1 Fachbereich

Physik, Universitat Dortmund, D-4422 1 Dortmund, Germany 2 Department of Physics, University of Utah. Salt Lake City, Utah 841 12, USA 3 Department of Medicine, University of Utah, Salt Lake City, Utah 841 12, USA

Abstract Dynamic processes involving the motion of atoms and molecules play an essential role in many biological systems. In the present work an investigation of the diffusion of water in lung tissue using field gradient NMR methods is described. We used two different experimental approaches in which errors due to internal magnetic field gradients associated with aidwater interfaces were minimized. The water diffusion coefficients obtained with these methods are significantly smaller than bulk water diffusion coefficients and exhibit a time dependence that indicates spatially restricted diffusion andor heterogeneous diffusion (i.e., a distribution of diffusion coefficients). In order to analyze these time dependent apparent diffusion coefficients, we used a simple model of completely restricted diffusion. With this model we were able to obtain from our experimental data a value for the mean size of the restricted regions and a rough estimate of the distribution of these sizes.

29.1 Introduction Lung tissue exhibits many physical properties (especially those relevant for NMR and MRI studies) which are closely related to its microscopic structure. A large volume fraction of the lung consists of small air filled compartments (the alveoli) with typical dimensions of 70 pm, surrounded by flat epithelial cells of approximately 3 pm thickness. The water (approximately 78 percent by weight) can be divided into intracellular and extra-

324

B. Geil, D.C.Ailion, G. Laicher. and A. G. Curillo

cellular water wetting the surface of the alveoli. The present work focuses on the dynamical properties of these different water species. Many NMR properties of lung tissue are well understood in terms of the underlying heterogeneous structure: (a) proton spin-lattice relaxation can be explained by waterbiopolymer cross-relaxation theory [ 11; (b) the spectral NMR lineshape is characterized by a distribution of local internal magnetic fields arising from discontinuities of the magnetic susceptibility at the air/water interfaces [2]. Due to the large surface-to-volume ratio in lung tissue these heterogeneous internal fields dominate most of the NMR properties. The decay of the Hahn echo of water protons is much faster than the pure T2 decay (e.g. obtained by a Carr-Purcell-Meiboom-Gill pulse sequence). This additional dephasing of the magnetization of the Hahn echo is due to translational diffusion of the water molecules in the internal magnetic field gradients arising from the susceptibility difference between air and water. When measuring the diffusion coefficient directly, known external field gradients are superimposed on the (unknown) internal gradient distribution. Careful analysis or special experimental techniques are required to separate these two contributions to the echo decay. (c.f. Sections 29.2 and 29.3.1).

29.2 Experimental Techniques NMR field gradient diffusion measurement techniques are based on the principle that a displacement of spins in a spatially heterogeneous magnetic field leads to an irreversible loss of magnetization in phase inverting spin echo experiments. Usually the decay of a Hahn echo (d2-z-1r-z-echo) or a stimulated echo (n/2-z-n/2-r-d2-~-echo) pulse sequence in combination with pulsed or static field gradients is recorded as a function of T, f, or the applied field gradient g. In the case of free diffusion (Gaussian propagation) of the particles in a constant field gradient, the decay of the echo is known to be

M ( z , g ) = M, exp - - y ~

[;I

g z D exp 3

--

1

(29.1)

325

29. Translational Diffusion of Water in Lung Tissue

for the Hahn echo and M(z,f,g)

=

[

Moexp-y-g

;) 3 [ 3 [ r ; 7

* z ?( r + - - Z

D

exp--

exp--

(29.2)

for the stimulated echo. Here y is the gyromagnetic ratio and D the diffusion coefficient. For simplicity we have assumed both the spin-lattice and the spin-spin relaxation to be (mono)exponential. 90"

goo

90"

Fig. 29.1: The 3 pulse sequence for the stimulated echo.

In many cases the stimulated echo experiment is much more suitable for measuring translational molecular motions because it exhibits a well defined separation between the spin dephasing (and rephasing) times z and the diffusion time t (in contrast to the Hahn echo experiment). Furthermore, during the time period r, the longest time in the experiment, the magnetization is stored in the longitudinal direction where it is unaffected by the spin-spin relaxation. Therefore the longest possible diffusion time t is limited only by the spin-lattice relaxation time T,,which is typically much longer than the spin-spin relaxation time T2. In cases where the internal gradients go are comparable in magnitude with the applied external gradients g, the expression for the diffusion decay in the stimulated echo, eqn. (29.2), has to be replaced by [3]

M(z,t,g) 0~ exp[ - y 2 D [ z 2 ( f +$)go'

+z2(r

+$I2[" -

3

-

z (t + z)g.go])] (29.3)

326

B. Geil, D.C. Ailioti, G. Laicher, and A. G. Cutillo

A plot of log M (T,t , g ) versus g2 would result in a straight line of slope proportional to D only in the absence of the g .go term (i.e. if the internal gradients can be neglected). Note, that this expression is derived assuming a constant internal field gradient. However, in lung tissue the internal gradients are distributed in size as well as in direction. The generalization of eqn. (29.3) that correctly includes the actual distribution

of field gradients in lung would be exceedingly difficult, if not impossible to derive. We use two different complementary experimental techniques to overcome these problems with the internal field gradients. The first method, a pulsed field gradient (PFG) method, uses a sophisticated pulse sequence (the so-called 13-interval sequence [4]) to cancel the effects of the internal field gradients on the phase evolution of the spins. The second method uses static external field gradients (SFG) which are large enough to make any contributions due to the internal gradients negligible.

29.2.1 The 13-Interval PFG Pulse Sequence This pulse sequence [4] is a modification of the simple stimulated echo pulse sequence such that two additional 7c-pulses and equal bipolar gradient pulses are inserted during the spin dephasing and rephasing times T,as shown in Fig. 29.2. If diffusion can be neglected during the times of the gradient pulses, the simultaneous inversion of the signs of phase and gradient completely cancels out the dephasing due to the g - g o term of eqn. (29.3). The diffusional component of the decay of the 13-interval echo is then found to be

M(T,6,t,g)

0~

[ (A

exp - y D -T go + 6

(

;)

4t+32--6

g2)]

(29.4)

where the first term in the exponent is independent of the applied gradient g. In all experiments performed with constant values of T this term can be absorbed into the preexponential factor. Our measurements have been performed in a wide-bore imaging magnet that allows the investigation of intact excised rat lungs. The amplitude of the gradient pulses was varied up to 0.25 T/m. The gradient pulses had a width 6 = 6.5 ms and were symmetrically embedded in the RF-pulse spacings of T = 20 ms. Using the same values of T and 6 in all measurements reduces the T2 relaxation to a constant attenuation pre-factor.

29. Tmnslational Diffusioii of Wutcr in Lung Tissiie

90" 180" 90"

327

90" 180"

Fig. 29.2: The 13-interval pulse sequence for a stimulated echo in pulsed field gradient experiments.

29.2.2 Ultra High Static Field Gradient NMR The second approach to overcome the difficulties arising from the internal field gradients is to use SFG techniques with very large external field gradients. We used a specially designed magnet with two superconducting coils in an anti-Helmholtz arrangement [5,6]. Depending on the position of the sample in the magnetic field, gradients up to 200 Tlm are accessible. In such field gradients it is no longer necessary to compensate the internal gradients. Thus we can use the simple 3-pulse stimulated echo sequence varying T over a range from 10 ps up to several ms. These extremely short values of 'I: allow diffusion measurements in systems characterized by short T2 values (down to T2 =. 200 p).Such large field gradients allow the measurements of very small diffusion coefficients (down to D =. 10-15 m2s-'). However, when z is varied during an experiment, there may be an additional loss of magnetization due to the T2 relaxation superimposed on the diffusional decay. This effect must then be included in the data analysis. The SFG equipment used in this work allows a sample size of 4 x 4 x 20 mm3. Accordingly, small strips from the outer alveoli region of rat lung were investigated. Furthermore, in our SFG experiments the resonance condition was fulfilled for only a thin sample slice of width of the order a few hundred microns. Compared with PFG methods the reduced number of excited spins leads to a significantly lower signal-tonoise ratio, which has to be compensated by a higher number of accumulations.

328

B. Geil. D.C. Ailion, G. Laicher, und A. G. Cutillo

29.3 Experimental Results Figure 29.3 shows two typical examples of the spin echo decay in lung tissue. Figure 29.3a is a stimulated echo decay from an SFG experiment ( g = 30 T/m, r = 10 ms, T =

5 "C)and Fig. 29.3b is a similar decay obtained with the 13-interval pulse sequence ( t = 50 ms, T = 25 "C).In plotting the logarithm of the echo amplitude versus either T? or g2. one would expect to obtain straight lines with slopes proportional to the diffusion coefficient for free (Gaussian propagating) diffusion of a single species. Thus, the strong curvature in these plots suggests either restricted diffusion or heterogeneous diffusion consisting of several components which differ in their diffusion coefficients.

'

lou L

66 .

2 2

10-1 5

,

.. . f

*\ \'

Fig. 29.3: Raw data of echo decays in the SFG experiment (a) and in the 13-interval PFG experiment (b). See text for details on the parameter settings.

As a first step in the data evaluation we parametrize these echo decay curves in terms

of an apparent initial diffusion coefficent Diand a final diffusion coefficient D,, corresponding to large values of T or g. It is important to distinguish these apparent initial and final diffusion coefficients from the short time and long time diffusion coefficients which will be introduced in Section 29.3.3. Both, D iand D, themselves depend on the diffusion time t . In this article we concentrate on the information obtained by the initial diffusion coefficient.

29. Translarionul Diffrision of Water in Lung Tissue

329

29.3.1 Internal Gradients In this subsection we present experimental data that allows an estimate to be made of the approximate size of the internal gradients go. In the absence of external field gradients eqn.(29.3) reduces to e q ~ ( 2 9 . 2 with ) g replaced by go. Figure 29.4 shows the decay of the 3-pulse stimulated echo sequence as a function of the dephasing time z for several diffusion times t . In this experiment an intact excised rat lung was placed in the widebore imaging magnet in the absence of external field gradients. The observed decays are due to both T2 relaxation as well as diffusional decay in the internal gradients. T2 relaxation alone, which depends only on z, can not explain the t dependence of the echo damping.

3

0.0

I

0.002

.

I

0.004

.

I

0.006

.

I

0.008

TIs

.

I

0.01

.

I

0.012

..I 0.014

Fig. 29.4: Raw data of stimulated echo decays in the absence of external field gradients for several values of the diffusion time t.

A fit of these data to eqn.(29.2) can, in principle, determine go2 provided D and T2

are known. A lower limit for T2 can be obtained if we completely neglect diffusion in the decay of the t = 5 ms data. The dashed line in Fig. 29.4 shows that this lower limit for T2 is approximately 35 ms. If, additionally, we know the dependence of Di on the diffusion time (see Section 29.3.3), we can use the initial decay of the t = 100 ms and t = 600 ms data to estimate a lower limit for the effective internal gradients. The square root of the

330

B. Geil, D.C. Ailion. G. Lnicher. and A. G. Cutillo

fitting parameter go2is then found to be of the order 0.1 T/m, a value comparable with the gradient amplitudes used in our PFG experiments but small enough to be neglected i n the SFG experiments.

29.3.2 Temperature Dependence of Di The temperature range accessible for investigations of biological tissue is generally very narrow, limited by the freezing of the water at lower temperatures and by the denaturation of the proteins at temperatures slightly above the physiological temperature. Nevertheless, it is often desirable to work at lower temperatures (avoiding the fast decomposition of the tissue), in which case it is important to know the temperature dependence of the physical quantities and to scale the results to the physiologically relevant temperature. In Fig. 29.5 we show the temperature dependence of Di at a diffusion time t = 300 ins compared with the temperature dependence of bulk water diffusion [7]. It is obvious from these plots that diffusion in lung tissue is significantly slower than bulk water diffusion but exhibits the same temperature dependence. The reduction factor depends on the diffusion time t (see results shown in the following subsection) but is independent of temperature. Therefore, the quantity Di(T )/D,,u,k(T ) can be used (to a very good approximation) to scale and compare measurements of lung tissue obtained at different temperatures.

2

lo-'

m

5

mE

lungtissue 2

2 1 '

0

'

' 5

'

' 10

'

' 15

'

'

.

20

' 25

'

' 30

'

' 35

'

1 1

40

T/"C Fig. 29.5: The temperature dependence of the initial diffusion coefficient of lung tissue compared with the temperature dependence of bulk water diffusion [7]. In these measurements the diffusion time was 300 ms.

29. Trunslurior7ulDiffusion of Wuter in Lung Tissue

33 1

29.3.3 Diffusion-Time Dependence of Di In systems where the diffusion is spatially restricted, we expect that the diffusion coefficient itself will be a function of diffusion time. At very short times, when (most of) the molecules do not touch the restricting walls, the mean squared molecular displacement, , should be that of the bulk liquid, and will be proportional to the diffusion time, thus leading to a constant diffusion coefficient D = /6t. In the long time limit, all molecules will have experienced several reflections at the walls and the mean square displacement will have become independent of the diffusion time. In this limit, therefore, the diffusion coefficient is expected to decrease with increasing diffusion time, D 0~ t - l . A plot of log D versus log t should exhibit a transition from an initial slope equal to zero to a slope of -1 at long diffusion times. The crossover between both slopes occurs at diffusion times which correspond to diffusion lengths comparable with the size of the restricted regions. In lung tissue the structure of the restricted regions is irregular and is characterized by a distribution of sizes and orientations. For this reason it seems difficult to apply solutions of the diffusion equation available in the literature for specific geometries of the restrictions. Instead we use a model introduced by Wang and Uhlenbeck [8] which qualitatively shows the time dependence decribed above and leads to a very simple analytic expression for D(t). In this model the diffusing particles are subjected to a (harmonic) attracting force pulling them back to their spatial orgin. If P is the proportionality factor between this force and the distance to the origin (in units of the friction constant), the time dependence of the diffusion constant is obtained as (29.5)

If we compare the long time limit for this expression (lim (t+m) Dapp= D /Pt) with that obtained by the solution of the diffusion equation for particles confined to spherical restrictions of radius R, we find that P = 5D/R2, a relation which we will use to estimate the length scales relevant for the diffusion in lung tissue. Figure 29.6(a) shows the time dependence of the apparent diffusion coefficient obtained by the model of Wang and Uhlenbeck for two different values of P and, accordingly, of R. Figure 29.6b shows experimental results obtained with the SFGmethod (g = 43 T/m) at two different temperatures and normalized to the corresponding

332

B. G d , D.C. Ailion, G. Lnicher, and A. G. Cutillo

diffusion coeffient of bulk water. In the long time region these data clearly exhibit the t '-behavior (dashed line in Fig. 29.6b), an indication that at these diffusion times the molecular motion is completely restricted. However, in contrast to the short time behavior of the model, the experimental data do not reach a constant plateau value (the water bulk diffusion coefficient) in the limit of short diffusion times. The simplest explanation of the remaining slope at short diffusion times is the assumption of a distribution in the sizes of the restricted regions. As a very first step we can estimate an average size of the restrictions using the diffusion time at the crossover between the two regimes in Fig. 29.6b and calculate the corresponding diffusion length, assuming the diffusion coefficient to be that of bulk water. Using the value o f t = 62 ms (the intersection of the two dashed lines in Fig. 29.6b) we find a value (<$>)-l" of 19 pm. The complete crossover regime is located between values of 10 pm and 25 pm. A more detailed analysis of the same experimental data, i.e., the application of eqn.(29.5) with a distribution of restriction sizes (and hence of p-values), is shown in Fig. 2 9 . 6 ~ The . slope of the diffusion coefficient at short diffusion times can be modeled assuming the distribution of the radii shown in Fig. 29.6d. In this distribution more than 45% of the restrictions have R-values that are smaller than 0.3 pm, but the distribution has to extend up to values of 18 pm. The mean value of R for this distribution is found to be 3.7 pm. A different way to interpret the time dependent apparent diffusion coefficients in restricted geometries has been suggested by Mitra et al. [9]. In this model, the number of molecules which have already touched the impermeable walls is calculated as a function of the diffusion time. The volume containing molecules that can reach the refecting walls in a given time t increases with t and depends characteristically on the surface-to-volume ratio of the porous medium. An expansion of the apparent diffusion coefficient with respect to this surface-to-volume ratio leads to the following expression in the short time limit: (29.6)

Here Do is the corresponding bulk diffusion coefficient (Do = Dapp(0) ) and S N is the surface-to-volume ratio of the restricting geometry. With the knowledge of Do one should obtain the surface-to-volume ratio from the initial slope of a plot of log Dapp versus t-'I2. In Fig. 29.7 the same experimental data as shown in Fig. 29.6 are plotted

333

-79. Translational Diffusion o j Water in Lung Tissue

versus rl'*Using the initial slope, indicated as a solid line, we can estimate the surfaceto-volume ratio to be 1 pm-'. If, for simplicity, we now assume that the water is diffusing in a close dense packing of spheres, this surface-to-volume ratio corresponds to a radius of approximately 8.5 pm. This result again is in good agreement with the results shown above and with the known length scales of spatial structures in rat lung tissue.

loo 3

a"

i

a 10"

2

lo-;

t/ms

t/ms 0.5

loo

0.4 3

2

P=

10-1

0.3

W

a 0.2

d

0.1 Ll

loo

.

. . .....

. . . .....

I

I

lo1

t / ms

lo2

.

.

. .LJ lo3

0.0

0

5

10

15

20

R/Pm

Fig. 29.6: The time dependence of restricted diffusion. (a) The apparent diffusion coefficient obtained by the model of Wang and Uhlenbeck explained in the text for p = 5 104 ( R = 0.3 pm) and p = 5 102 ( R = 3 pm). (b) Experimental data (SFG, g =43 T/m) at two different temperatures scaled to the bulk water diffusion coefficient. The dashed lines indicate a slope of - 1 in the long time regime and a non-zero slope in the short time range. (c) The same data as shown in (b). The solid line is a fit to the model with a distribution of the sizes of restrictions. This distribution is shown in Fig. (d).

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B. Geil. D. C. Ailion, G. Laicher. and A. G. Cutillo

Fig. 29.7: The same experimental data as shown in Fig. 29.6, now plotted as a function of The solid line shows the initial slope used to evaluate the surface-to-volume ratio.

(-”’

29.4 Conclusions Diffusion measurements in lung tissue are complicated by the presence of internal magnetic field gradients. After these “artifacts” are eliminated, either by using appropriate pulse sequences (13-interval PFG sequence) or huge external field gradients, the observed echo decays indicate an anomalous diffusional decay due to either restricted or heterogeneous diffusion. These echo decay curves are parametrized in terms of two (additive) processes associated with the two diffusion coefficients Di and D, A detailed analysis of the dependence of the initial diffusion coefficient on the diffusion time allows some conclusions to be made about the fundamental mechanism of the water diffusion.

For large diffusion times we find that the initial diffusion coefficent decays proportional to t - ’ , a clear indication of completely restricted diffusion. At shorter diffusion times this t-dependence becomes weaker and the measured diffusion coefficient seems to approach that of the bulk water at diffusion times in the order of 100 ps, which is slightly smaller than the shortest times in our NMR experiments. The crossover between both time regimes can be related to the sizes of the confining structures, leading to values in the range of 10 - 20 pm. Fitting the crossover regime with a very simple model of restricted diffusion that assumes a distribution in the size of the restrictions, we can

29. Translnriorinl Diflusion of Water in Lung Tissue

335

roughly estimate the shape of this distribution. We need a large contribution of very small restrictions (below 0.5 pm) but also contributions up to sizes of approximately 18

P. A different analysis of the same data gives access to the surface-to-volume ratio of the confined geometry. Models for the structure of the lung tissue can be used to relate these surface-to-volume ratios to the sizes of these structures. The values we found are in good agreement with the values obtained by analysis of the transition regime in the diffusion time dependence. In our current work we analyze the shape of the echo decays in more detail including the final diffusion coefficient D, and the transition between Di and D, Investigations currently in progress indicate that models based purely on restricted diffusion are not sufficient to explain all observed phenomen. It seems that some additional contributions due to heterogeneous diffusion should be included.

Acknowledgments This work was partially supported by the National Lung, Heart and Blood Institute, Grant HL-31216. The authors want to thank Dr. F. Wehner and Dr. T. Wanatabe for preparing rat lung samples. The authors are particularly grateful to Prof. Dr. F. Fujara for allowing them to use his anti-Helmholtz magnet and spectrometer and for his encouragement in this project. Also, the authors are grateful to the Alexander von Humbold Stiftung for a Senior Research Award (D.C.A.) and for a Feodor Lynen Fellowship (B.G.).

References 1.

A. Hackmann, D. C. Ailion, K. Ganesan, K. C. Goodrich, S. Chen, G . Laicher and A. C. Cutillo, J. Magn. Reson. 110 (1996) 136.

2.

T. A. Case, C. H. Dumey, D.C. Ailion, A. G . Cutillo and A. H. Moms, J. Mugn. Reson. 73 (1987) 304.

3.

J. E.Tanner, J. C k m . Phys. 52 (1970) 2523.

4.

R. M. Cotts, M. J. R. Hoch, T. Sun and J. T. Markert, J. Mugn.Reson. 83 (1989) 252.

5.

G. Fleischer, F. Fujara, NMR Basic Principles and Progress 3 (1994) 159.

6.

I. Chang, F. Fujara, B. Geil, G. Hinze, H. Sillescu, A. Tolle, J. Non-Cryst. Solids 172-174 (1994) 674.

7.

J. H. Simpson and H. Y. Cam, Phys. Rev. 111 (1958) 1201.

8.

M. C. Wang and G.E. Uhlenbeck, Rev. Mod. Phys. 17 (1945) 323.

9.

P. P. Mitra and P. N. Sen, Phys. Rev. B 45 (1992) 143.

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30. Studies of Perfused Brain Slices with MR Microscopy J. D. Bui, D. L. Buckley, M.I. Phillips, and S. J. Blackband

Center for Structural Biology, Departments of Neuroscience, Physiology, the UF Brain Institute, University of Florida and the National High Magnetic Field Laboratory, Gainesville, Florida 326 10, USA

Abstract This chapter reviews recent MR microitnaging studies on a perfused hippocampal brain slice model. We report signal changes after osmotic perturbation, and describe quantitative measurements of water diffusion in the slices, showing that they exhibit biexponential diffusion behavior. Further, after ouabain induced cell swelling, the diffusion coefficients of the compartments remain constant but the fractional compartmental sizes change. We believe that the perfused brain slice model represents a novel way to study in vivo MR signal changes at the cellular level and may also be applied to study cellular responses to a variety of neuropathologies.

30.1 Introduction MRI adds greatly to the diagnosis of soft tissue diseases. However, diagnostic MRI is still largely dependent upon the physician’s clinical impressions based on qualitative MR signal changes [ 11. We believe that a better understanding of the physiological basis for clinically observed MR signals will provide the information necessary to link signal changes to specific disease processes. A quantitative understanding of MR signals requires understanding of the cellular basis for these signals. MR microscopy on isolated perfused cells showed significant differences in the MR characteristics of cell nucleus and cytoplasm. Osmotic perturbation studies on isolated cells suggest that water redistribution contributes significantly to MR signal intensity changes [ 2 ] . We hypothesize that potential changes in the ratios of extracellular, cytoplasmic and nuclear volumes follow-

338

J. D. Bui. D. L. Bucklev. M. 1. Phillips. and S. J . Blackband

ing cell injury in various clinical pathologies [3,4] may explain MR signal changes seen in clinical imaging. Since isolated cells lack a physiologic extracellular compartment, we have recently implemented studies on perfused brain slices. In addition, the brain slice model may provide an avenue to examine physiological mechanisms to compensate for cellular insults.

30.2 Experimental Procedures 30.2.1 Sample Preparation and MR Microscopy Male Sprague-Dawley rats (150-200 g) were anaesthetized with Metofane. Following decapitation, the brain was rapidly excised and placed into ice-cold artificial cerebrospinal fluid (aCSF in mM: 120 NaCl, 3 KCl, 10 Glucose, 26 NaHC03, 2 CaCl,, 1.5 KH,PO,, 1.4 MgSO,), gassed with 95% 0,/5% CO,, pH 7.4. The hippocampus was removed and sliced into 500 pm thick coronal sections with a McIlwain tissue chopper. A perfusion chamber was constructed from Delrin and consisted of a hollow cylindrical support arrangement consisting of three parts with a central ring holding the brain slice between gauze sections. The gauze sections were made of nylon monofilament with a 0.25 mm mesh opening. Input and output perfusion tubes were connected to a peristaltic pump. Two output tubes were used in the chamber to ensure that the magnet was not flooded. This construct was then placed in a 10 mm MR tube. All experiments were carried out using a commercial Doty microimaging probe (Doty Scientific Inc.; Columbia, SC) interfaced to a Varian 600 MHz narrow bore instrument and Unity console (Varian Associates; Palo Alto, CA). Images were acquired at room temperature (18-19OC) using a standard spin echo imaging sequence with diffusion gradient lobes placed on either side of the refocusing pulse.

30.2.2 Baseline Studies To determine slice stability, hippocampal slices were monitored over an 8 hour period. Slices were placed in the perfusion chamber that was filled with isotonic aCSF. Images were acquired every 35 minutes (TR = 3 s, TE = 22 ms, b = 1000 s/rnm' , 2 averages,

30. Studies of Perfused Brain Slices With MR microscopy

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resolution: 80 x 80 x 300 pm,). Signal intensity as a function of time was recorded. In separate experiments, 3 sets of images were acquired followed by a 5 minute perfusion of aCSF and this cycle repeated every 1.5 hours.

30.2.3 Osmotic Perturbations Slices were initially perfused with isotonic aCSF. The perfusate was then exchanged with a 20% hypotonic solution followed by a 20% hypertonic solution. An image was acquired (TR = 2 s, TE = 22 ms, 0 = 1000 s/mm' , 2 averages) under each condition. The slices were perfused for 15 minutes between scans to allow for complete perfusion medium exchange and tissue stabilization. Perfusate flow was suspended during data acquisition to limit flow artifacts. Images were collected at a resolution of 80 x 80 x 300 pm in approximately 8 minutes each.

30.2.4 Blockade of Na+/K' ATPase by Ouabain Slices were perfused with isotonic aCSF. Prior to image acquisition, perfusion was suspended. A series of 8 images, each with an increasing diffusion weighting, was collected in 35 minutes. Subsequently the slice was perfused for 15 minutes with 1 mM ouabain and the imaging sequence was repeated. Images were collected at a resolution of 120 x 230 pm with a 300 pm imaging slice. Each image was acquired in 4.3 minutes and ADCs were estimated from a series of 8 images acquired with a range of gradient amplitudes (A - 6/3 = 12.3 ms, b = 76 - 4256 s/mm2).

30.3 Results MR microimages have been collected at spatial resolutions ranging from 15 x 15 pm to 120 x 230 pm in plane. Figure 30.la shows a high-resolution image acquired in 14 hours while Fig. 30. lb is a rapidly acquired image (4.3 minutes) used with live perfused brain slices.

340

J . D. Bui, D. L. Buckley, M . 1. Phillips, and S. J . Blackbarid

Fig. 30.1: a) High resolution (15 pm in plane) image of a rat hippocampus; b) Image acquired in an experiment on live perfused brain slices.

30.3.1 Baseline Studies Thirteen hippocampal slices from 13 different rats were imaged over an 8 hour period each. The data show that signal intensity significantly increased as a function of time when the slices were bathed in aCSF without perfusion

(ti

= 7). Perfusion with aCSF for

5 minutes every 1.5 hours, resulted in stable signal intensity over the experimental time. (n = 6). Figure 30.2 summaries these results. 1600

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(J , n = 6) and non perfused ( 0 ,n = 7) slices. Perfusion maintains hippocampal slice viability.

30. Studies of Perfused Brain Slices With MR microscopy

34 1

30.3.2 Osmotic Perturbations In experiments on 7 slices, isotonic aCSF was exchanged for hypotonic and then hypertonic solutions [ 5 ] . Hypotonic perturbation resulted in a 16 (+ 11) % increase in signal intensity relative to isotonic aCSF. A 26 (k 10) % signal decrease was seen after hypertonic perturbation @ < 0.0005, repeated measures ANOVA).

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30.3.3 Blockade of Na'/K' ATPase by Ouabairz Nine slices from 5 rats were successfully examined in both aCSF and 1 mM ouabain [6]. The mean signal intensity of the entire slice in each image series was fitted to a two compartment model and estimates of the apparent diffusion coefficient (ADC) and fractional volume of each compartment were obtained. Data from the slices exhibited biexponential diffusion behavior in all cases, fitting the model well (9= 0.99). The ADC

mm2/s, and 0.09 (i-0.03). mm2/s respectively. After treatment with 1 mM ouabain, there was no significant change in the ADC of either compartment but the relative fractions of the compartments changed significantly. The fraction of the fast diffusing compartment decreased from 0.53 (k 0.06) to 0.44 (+ 0.05) after treatment (p < 0.0005, paired t-test). Typical changes are shown in Fig. 30.3. in the fast and slow diffusing compartments were 1.02 (k 0.16).

342

J . D. Bui. D. L. Buckley, M. 1. Phillips, a n d S.J . Blackband

30.4 Discussion The experiments summarized herein represent novel MR microimaging studies on a recently developed perfused brain slice model. The resolutions achieved depend primarily on the acquisition time. Acquisition times of 12-14 hours yielded spatial resolutions of 15 - 20 pm, which would be useful for morphological studies. However, since our goal was to perform functional studies on live perfused hippocampal slices, lower spatial and faster temporal resolutions were chosen. The baseline studies indicate that without perfusion, the signal intensity in diffusion weighted images increased over several hours. This is consistent with the notion that cellular edema occurs as the slice undergoes cytopathological changes due to nutrient deprivation. We established that a short perfusion of 5 minutes every 1.5 hours was sufficient to maintain slice viability for 8 hours. The brain slice model has been used extensively and viability has been well characterized [7] using various parameters including morphology, electrophysiology, metabolite levels, phosphorylation, and protein synthesis. We have demonstrated that physiologically relevant perturbations cause significant MR signal changes. Hypotonic perturbation resulted in a signal increase, consistent with an increase in the water content of the intracellular compartment as would be expected after exposure to a hypotonic solution. Quantitation of T I , T2 and ADC coupled with cellular volume measurements using independent techniques are important to definitively test the hypothesis of tissue compartmentation changes. Our first quantitative MR studies involve measurement of water difision. The data indicate that water diffusion in the rat hippocampal slice is biexponential. We believe that the fast and slow diffusing fractions correspond to the extracellular and intracellular space respectively though confirmation is required. The estimated relative fractions of the compartments do not match those reported with other techniques, which may be due to differences in the T2 of the compartments; a more detailed treatment is found in the work of Buckley et. al. [6]. Since the results indicate that the ADCs of the two compartments do not change after Na+/K+ ATPase blockade but that the fraction of the slow diffusing compartment increases (i.e. the intracellular space), they are consistent with the notion of cell swelling as the primary mechanism for average ADC decreases seen during the acute phase of ischemic injury in clinical MRI [8]. Neuronal edema is a manifestation of a wide range of neuropathologies [3,4] and the sensitivity of MR to cellular water fluxes in brain slices make it ideal to study the pathogenesis of these diseases. For example, in preliminary studies [9] on an excitotoxic

30. Studies of Petjiused Brain Slices With MR microscopy

343

model of ischemic stroke, we have shown that NMDA treated brain slices exhibited significant increases in the slowly diffusing fraction, which is consistent with edematous changes. Prior treatment with MK-801, an NMDA antagonist, abolished this response, which suggest that measured changes in compartmentation were specific to NMDA receptor activation. In summary, the experiments described in this chapter represent recent work, implementing MR microimaging studies on the perfused brain slice model. The data show that MR can detect responses following physiologically relevant challenges and demonstrate the potential of the brain slice model for elucidating the cellular basis for MR contrast changes which may lead to development of realistic models of tissue compartmenation. These developments will allow a more quantitative approach to MR and may result in an increased diagnostic and prognostic value of clinical MRI.

Acknowledgements We thank the support of the University of Florida Brain Institute, the Center for Structural Biology, University of Florida and the National High Magnetic Field Laboratory, Tallahassee, Florida, and NIH grant #lROlNS36992. JDB was supported by an American Heart Association Fellowship Award.

References 1.

P.A. Bottomley, C. J. Hardy, R. E. Argersinger, and G. Allen-Moore, Med.Phys. 14 (1987) 1.

2.

E. W. Hsu, N. R. Aiken, and S. J. Blackband, Atti J. Physiol.Cel1 Physiology 40 (1996) C1895.

3.

L. Schilling and M. Wahl, Kidney In!. Suppl. 59 (1997) S69.

4.

F. Joo, Neuropathol. Appl. Neurobiol. 13 (1987) 161.

5.

S. J. Blackband, J. D. Bui, D. L. Buckley, T. E l l e s , H. D. Plant, B. A. Inglis, and M. I. Phillips,

Magn. Reson. Med. 38 (1997) 1012. 6.

D. L. Buckley, J. D. Bui. M. I. Phillips, T. Zelles, B. A. Inglis. H. D. Plant, and S. J. Blackband, Magn. Reson. Med. (1998) in press.

7.

P. G. Aitken, G. R. Breese, F. F. Dudek, F. Edwards, M. T. Espanol, P. M. Larkman, P. Lipton, G. C. Newrnan, T. S. J. Nowak, and K. L. Panizzon, J . Neurosci. Methods 59 (1995) 139.

8.

M. E. Moseley, K.Butts, M. A. Yenari, M.Marks, and A. de Crespigny, NMR Biomed. 8 (1995) 387.

9.

J. D. Bui, D. L. Buckley, M. I. Phillips, and S. J. Blackband, Inr. Soc. Magn. Reson. Med. 6rh Annual Meeting, Sydney, Australia (1998) Abstract.

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31. Application of NMR Micro-imaging to the Study of Water Transport in Eye Lenses B. A. Moffat', R. J. W. Truscott2, M. H. J. Sweeney2, and J. M . Pope' 1 Centre for Medical

and Health Physics, Queensland University of Technology,

GPO Box 2434, Brisbane, Australia, 4001 Australian Cataract Research Foundation, Department of Chemistry, University of Wollongong, NSW, Australia, 2522

Abstract Magnetic resonance microscopy (MRM) has been used to study the kinetics of water transport in human eye lenses. Lenses were incubated at 34.5 "C in artificial aqueous humour (AAH) containing nutrients and metabolites similar to those present in v i v a MR images were acquired over approximately a twenty hour period following replacement of

H 2 0 based AAH with deuterium oxide (D20) based AAH. NMR signal intensity from the lenses decreased with time corresponding to a decrease in concentration of H 2 0 within the lenses. A statistically significant correlation (p < 0.001) was found between the rate of NMR signal loss from the lens nuclei and increased age of the lenses. The results show that as lenses age there is a reduction in the rate at which water (and presumably also water soluble low molecular weight metabolites) can enter the cells of the lens nucleus via the epithelium and cortex. A decrease in the rate of transport of water, nutrients and anti-oxidant species would be expected to lead to increased damage to lenses with age, and ultimately a potential cause of presbyopia and senile cataract.

31.1 Introduction The human eye lens is a unique tissue in that it increases in size continuously throughout life. Lens cells are not shed, but new cells are laid over already existing cells. Thus, the cells in the centre of a lens contain protein molecules (crystallins) that are as old as the

346

B A Moffut. R J W Triiscott, M H J Sweeney. and J M Pope

individual. As the lens grows it becomes stiffer and less accommodating [ l ] . The accommodating power of the lens reduces from 14 dioptre at age 8 years to -1 - 9, dioptre at 50 years. This is known as presbyopia. Almost all lenses undergo presbyopia with age and in addition, it has been estimated that 15.8 million people world wide suffer blindness due to cataract [ 2 ] .In spite of extensive research on changes in the human eye lens that occur with age [ 11, the causes of presbyopia and senile cataract remain unclear. The majority of lens cells, particularly those in the nucleus of the lens, have no organelles and hence the cells are metabolically inactive ‘‘containers’‘ of water and crystallins. They have no capacity for replacing damaged proteins. However, it is vital for the structures of these crystallins to be maintained, as far as possible, in the same form as they were originally synthesised. Minor alterations of their structures over time may change the protein-protein interactions and eventually render the crystallins insoluble [3]. It is believed that these processes may be at least partly responsible for the onset of presbyopia [4] and senile cataract respectively. Since, cells in the centre of the lens have no means of protecting themselves from metabolic insults that can cause changes to the crystallin structures, transport of water containing nutrients and antioxidant species from the cortex and epithelial cells to the nucleus may be vital for maintaining the structures of the crystallins.

Fig. 31.1: Schematic diagram of the human eye. A presbyopic lens has insufficient power to coinpletely focus light from near objects onto the retina (dashed lines).

While conventional pulsed field gradient (PFG) methods [ 5 ] facilitate study of “short range” difSusion (over distances comparable to cell dimensions) they do not allow for the study of “long-range” wafer transport (over distances comparable to lens dimensions) on

31. Application of N M R Micro-inuigirrg to rlie Smdy of Water Transport in Eye Lenses

347

a time scale of minutes or hours. This work seeks to contribute information to the understanding of the causes of presbyopia and cataract by developing and applying MRM methods to study the kinetics of long-range water transport from the metabolically active outer regions of the lens (cortex and epithelial cells) to the centre of the lens (nucleus).

31.2 Experimental Methods Human lenses were obtained from the Queensland Eye Bank and stored at 34.5 "C in artificial aqueous humour (AAH) containing nutrients and metabolites similar to those present in vivo. The lenses were placed in a 10 mm NMR tube and the H 2 0 based AAH was replaced with deuterium oxide (D20) based A A H (Fig. 31.2), the ratio of D,O mass to lens H 2 0 mass (10:1) being kept constant to allow for variations of lens size. Immediately following this, a series of conventional T , weighted spin-echo 'H MR images (Figs. 31.3a and 31.4a) was acquired over approximately a twenty hour period, (referred to hereafter as a D 2 0 time course), using a 4.7 T Bruker MSL200 micro-imaging system operating at 200 MHz. D20 based Artificial Aqueous Humour

NMR Tuhe

-

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Fig. 31.2: Lens sample arrangement for D20 time course experiments.

Signal intensities from regions of interest in the cortex and nucleus were plotted against time (Figs. 31.3b and 31.4b) and fitted to a decaying exponential curve using a Levenberg-Marquardt method of non-linear regression. The decay constants from these curves were then correlated against age.

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31.3 Results The NMR signal intensity from the lenses decreased with time during the D,O time courses (Figs. 31.3b and 31.4b) corresponding to a decrease in concentration of H,O (and HDO) within the lenses. From the difference in contrast between the brighter nuclear region and the darker cortical region in the images of the older lenses (Fig. 3 1.4) it appears that the diffusion of water into and out of the lens nucleus is significantly restricted. This was not observed in younger lenses (age less than 65 years) where there appeared to be no clear distinction between the cortex and nucleus in the MR images (Fig. 31.3a). The rate of NMR signal loss from lens nuclei (Fig. 31.5a) was found to decrease with increasing age of the lenses (p value of the gradient is less than 0.001), confirming the observation of an age dependent restriction to diffusion of water in to the nuclei of human lenses. Conversely, there was no correlation (p value of 0.96) between the rate of signal loss in the cortex region with age (Fig. 3 1Sb).

349

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31.4 Conclusions These results demonstrate how the use of magnetic resonance micro-imaging in conjunction with a contrast agent (D20) can be applied to study the diffusion of water in the human lens. While the diffusion of specific metabolites into the lens can be performed using radio-labeled materials [6], MRM enables more data to be acquired during the diffusion process using a considerably less invasive method. The results of the D,O time courses suggest that as lenses age there is a reduction in the rate at which water (and presumably also water soluble low molecular weight metabolites) can enter the cells of the lens nucleus via the epithelium and cortex. Since this is the mechanism by which nuclear cells obtain nutrients and anti-oxidants to protect the crystallins from degradation, the decrease in transport rates could lead to increased damage to lenses with age, and ultimately be a potential cause of presbyopia and senile cataract.

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References: 1.

B. K. Pierscionek, Clinical and Experimental Optometr?. 76(3) (1993) 83.

2.

B. Thylefors, R. Pararajasegaram, and K. Y. Dadzie, Bulletin of the World Health Orgnnisarion 73(1), (1995) 115.

3.

R. J. W. Truscott and R. C. Augensteyn, Exp. Eye. Res. 25 (1977) 139.

4.

B. K. Pierscionek, Clinical and Exp. Eve. Res. 60 (1995) 325.

5.

E. 0. Stejskal and J. E. Tanner, J. Clzetn. Pliys. 42(1) (1965) 292.

6.

M. H. J . Sweeney and R. J. W. Truscott, Exp. Eye R e x , submitted.

32. Relaxation Anisotropy as a Possible Marker for Macromolecular Orientations in Articular Cartilage Yang Xia Physics Department, Oakland University, Rochester, MI 48309, USA

Abstract Study of cartilage by MRI is motivated by the role of cartilage in various stages of osteoarthritis, one of the most common diseases in adults. In this study, imaging experiments at 14pm pixel resolution were conducted by obtaining 2D T I and T2 relaxation maps of canine articular cartilage placed at a series of orientations with respect to the external magnetic field (-35",3", 25", 40", 57" and 85"). The selected orientations form a series of discrete sampling points for the geometrical factor (3cos28 - 1) that dominates the non-zero dipolar Hamiltonian. In the T I mapping experiments, the proton intensity images of cartilage were influenced strongly by the cartilage orientation in the magnetic field. However, no orientational dependence of TI was observed in the quantitative T I maps of cartilage. The T , profiles are essentially identical, and fairly uniform as a function of the cartilage tissue depth. In the T2 mapping experiments, a distinct orientational dependence of T2 was observed in cartilage. The T2 characteristic of cartilage exhibits three unique regions: the f i s t region occupies about 10% of the cartilage thickness and exhibits a tissue-depthdependent T2 anisotropy; the second region occupies about 13% of the cartilage thickness and exhibits an isotropic and depth-independent T2; and the third region occupies about 77% of the cartilage thickness and exhibits a distinct T2 anisotropy. These three unique regions in pMR images correspond approximately to the three histological zones in cartilage tissue. These findings are consistent with the understanding that collagen fibrils are oriented randomly in the transitional zone and are perpendicular to the articular surface in the radial zone. The correlation between the T2 anisotropy and the curve of (3cos28 - 1) suggests that water molecules that are closely associated with proteoglycans are 'confined' within the collagen network in articular cartilage. The T, anisotropy pro-

352

Y. Xin

vides an indirect but sensitive indicator for the orientational structures of collagen fibrils and proteoglycan macromolecules in cartilage.

32.1 Introduction Articular cartilage is the soft connective tissue covering the load bearing surfaces at the ends of bones. Cartilage has a unique molecular and spatial structure which provides a smooth surface for joint motion and may also cushion the joint against impact. MRI studies of cartilage and its degradation are motivated by the role of cartilage in the development of osteoarthritis (OA), a common disease affecting 15% of US population (38 million people) [l]. Most previous MRI studies of cartilage have used clinical MRI scanners to examine the appearance of cartilage tissue in order to correlate the image features with the clinical indicators of cartilage health status. Relatively few studies have quantitatively characterized cartilage tissue using several NMR contrast parameters such as self-diffusion, relaxation times, and magnetization transfer [2-61. With a spatial resolution up to tens of microns, NMR microscopy (pMFU) is exceptionally well-suited for the study of spatially heterogeneous biological materials such as cartilage. The ability to produce images of soft tissues with good contrast as well as images of molecular-level activities such as relaxation and diffusion distinguishes pMRI from other microscopic imaging methods such as X-ray tomography or ultrasound.

32.1.1 Articular Cartilage With regards to its molecular structure, articular cartilage consists primarily of water (- 75%), collagen (- 15%) and proteoglycans (- 10%) [7-91. The collagen in cartilage is organized as triple-helical fibrils in an intricate three-dimensional meshwork. The proteoglycans (PG) have a bottle-brush like structure, with a central protein core and many glycosaninoglycan (GAG) side-chains. The sulfated GAG chains carry a high concentration of negatively charged groups, and thereby preferentially attract positive ions (and water molecules) to ensure electroneutrality. This strong water-binding ability of proteoglycans produces a strong osmotic pressure which must be balanced by the restraining force in the collagen fibril network.

32. Relaxation Anisotropy as a Marker for Macromolecular Orientations in Articular Cartilage

353

Histologically, the heterogeneous and non-linear cartilage tissue can be conceptually divided into three distinct structural zones: the superficial zone, the transitional zone, and the radial zone. The cartilage tissue is interfaced to the underlying subchondral bone via a thin and wavy calcified layer. The proteoglycans are compressed and entrapped to fill the extra-collagen space [ 101. Regarding the fiber architecture in articular cartilage, it is generally understood in the literature that most of the collagen fibrils are oriented perpendicularly to the articular surface in the radial zone, randomly in the transitional zone and parallel with the articular surface in the superficial zone (Fig. 32.1). (In this text, the word 'zone' refers to a histological zone in the tissue; whereas the word 'region' refers to a characteristic feature observed in MR images of cartilage.)

surface

I.

I

Superficial Zone

Transitional Zone

I

Radial Zone

4

Calcified Zone

Cancellous Bone

Fig. 32.1: Illustration of a section through articular cartilage demonstrates the various layers of collagen fibers [Adapted from A. Balkissoon, TopicsMagn. Reson. Imaging 8 (1) (1996) 571.

32.1.2 NIRI Characteristics of Cartilage In clinical MRI studies of cartilage, it has been known that normal articular cartilage appears laminated when placed at certain orientations with respect to the external magnetic field [ll-141. Bi-laminar or tri-laminar appearances of cartilage tissue were observed in clinical MR images. The number, apparent thickness, and the relative intensity of the cartilage laminae varied in different studies. Figure 32.2 shows several images of a cartilage sample at different orientations. The orientational dependence of the cartilage image intensity is obvious.

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L

L

Y

L

Fig. 32.2: Illustration of the laminated appearance of articular cartilage in MRI (37.1 pm pixel resolution, 0.5 mm slice thickness).

It is known that the relaxation processes becomes complicated in biological tissues because the tissues are complex molecular systems with complex NMR properties. In addition to the nuclear dipolar interaction described by the dipolar spin Hamiltonian (HD),exchange between different molecular environments and cross relaxation between protein macromolecules and water become important aspects of the relaxation mechanism in biological materials. At present the relation of relaxation of tissues to theory or to any other measurable properties of the tissues are still imperfectly understood [ 1.51. This report concerns the orientational dependence of T , and T2 relaxation in articular cartilage. It has been shown that there is an orientational dependence of T2 relaxation of dried and wet tendon [16,17] or collagen [lS] in the magnetic field. In particular, it has been shown [16] that T2 of bovine tendons has two components, and that the long T2 component varies approximately as the curve of (3cos28 - l), the geometrical factor that dominates the non-zero dipolar Hamiltonian HD. A useful feature of this geometrical factor is its zero-crossing point at 8 = 54.7". This factor goes to zero when the position vector from one spin to the other in the two concerned spins is at an angle 8 = 54.7" with respect to the external magnetic field. Therefore, even when HD is non-zero, the contribution of H , to spin relaxation can be minimized if 8 = 54.7" (the magic angle condition in NMR). In this report, two-dimensional T , and T2 maps were acquired for cartilage placed at a series of orientations with respected to the external magnetic field (Bo).

32. Relaxatioii Anisotropy a s a Markerfor Mucrotnolecular Orientations in Articular Curtiluge

355

32.2 Materials and Methods For imaging experiments, articular cartilage attached to the underlying bone was harvested from the central load-bearing location at the humeral head of the shoulder joints of eight-month-old beagles. The plugs were bathed in physiological saline and sealed in precision glass tubes with an internal diameter of 2.34 nun. For bulk TI and T2 measurements, cartilage tissue pieces were excised from the underlying bone with a surgical scalpel from the same joints where the plugs were harvested, and were put into a 4 mm NMR tube. The TI and T2 imaging pulse sequences were based on the concept of the magnetization-prepared sequence [ 191. The advantage of the magnetization prepared sequences is the clean separation of the contrast segment and the imaging segment so that the effects of the intrinsic diffusion-weighting as well as the T2-weighting during the imaging segment do not influence the outcome of the subsequent calculations [20]. Figure 32.3 shows the imaging sequences where an inversion recovery sequence was executed prior to the imaging segment in the T, experiment, and a spin-echo sequence was executed prior to the imaging segment in the T2 experiment. (c) Imaging segment

(a) TIcontrast segment

:

GY (b) TIcontrast segment

a

Fig. 32.3: T I and T2 imaging pulse sequences. The sequences consisted of two completely separated segments. All timings in the imaging segment were kept constant throughout the experiment.

The pMRI experiments were performed on a Bruker AMX 300 NMR spectrometer equipped with a 7 Tesld89 nun vertical-bore superconducting magnet and micro-imaging accessory. The angle 0 is defined as the angle between the normal to the articular

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surface of cartilage and the direction of the magnetic field (Bo).The in-plane resolution was 14 pm and the slice thickness was 1 mm. Other experimental parameters can be found elsewhere [21,22]. Calculations of T , and T2 were carried out by employing a single-exponential least-squares fit. No manual scaling or adjustment was made when plotting several cross-sectional profiles, which came from independent pMRI experiments, into one graph.

32.3 A Phantom T2 Result As a comparison for the orientational dependence in cartilage, an artificial plug was made to mimic the experimental conditions of a cartilage-bone plug in the magnetic field [21,22]. The artificial plug was constructed by gluing a 0.8 mm thick agarose gel block to a small piece of teflon block, bathed in the same saline solution, and sealed in a samesized glass tube. T2 bulk and imaging experiments were carried out using the identical experimental parameters as in the cartilage-bone plug experiments at 0" and 55". No orientational dependence was observed in the T, and proton intensity images of the artificial plug (Fig. 32.4). The bulk T2 of the agarose gel was 33.2 ms, comparing well with the T2 value of 28 f 3 ms averaged from the slice profiles in the imaging experiments. We have, therefore, established a set of highly reliable experimental protocols and conditions for both microscopic imaging and spectroscopy.

50

40 30

20 10 0

100

200

300

400

500

600

700

800

Depth (pm) Fig. 32.4: Cross sectional profiles of T2 of the artificial plug at about 0" and 55" respectively.

32. Relaration Anisotropy as a Marker,for Macronrolecular Orietilatiotis in Articular Cartiloge

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32.4 Cartilage T2 Result T2 imaging experiments were carried out using identical imaging parameters at angles of -35", 3", 25", 40°, 57" and 85". At each of the six angles, four two-dimensional T2 weighted images were acquired. Two sets of such T, weighted images are shown in Fig. 32.5. Note that the proton intensity images were sensitive to the orientation of the tissue with respect to the magnetic field.

TEc = 0

TEc = 16ms

TEc = 30ms

TEc = 60ms

3"

57"

lBo

Fig. 32.5: The T2-weighted proton images (the imaging echo time TEi = 8.862 ms).

At each orientation, a 2D T2 image was calculated. Figure 32.6 shows the cross sectional profiles of cartilage T2, taken from the same spatial position in the images. It is clear that T2 is a strong function of the tissue orientation with respect to the direction of the external magnetic field. This T2 anisotropy translates into the orientational dependence and laminated appearance of the MR image intensity of the cartilage tissue. Five unique features can be observed from Fig. 32.6: (1) Immediately beneath the articular surface (from 0 pm to 60 pm, region l), T, is a strong function of the tissue's orientation and a function of the tissue depth. (2) At about 80pm to 120pm deep as measured from the articular surface (region 2), T2 is insensitive to the tissue's orientation with respect to the magnetic field. (3) There is a dramatic orientational dependence of T2 for the cartilage tissue at about 140 pm to 500 pm (region 3). (4) The T2 profiles for the tissue at about 300 pm to 500 pm depth (sub-region 3b) are nearly parallel to each other

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Histological zone

Schematic Orientation of Collagens

T,(ms) 0

20

40

60

80

0

superficial transitional

100

200

300

radial

400

500

600

700

Fig. 32.6: Cross sectional profiles of T2 for the cartilage images. The open circles, solid triangles. open squares, crosses, solid circles and pluses are the T2 profiles at -35", 3", 25", 40°, 57" and 85" respectively. The profiles have three featured regions, labeled as I , 2, 3 (see text for discussion). A simplified model of collagen fibril architecture, based on previous electron and optical microscopic results, is also shown.

for all angles. (5) Variations in the T2 profile are most pronounced at 3", and are least affected at 40"and 57". The tissue was not histologically examined due to the equipment limitation. However, the lack of histology is not a major defect of this study because the orientation of cartilaginous fibers is well known in literature. Moreover, the boundaries between each region in pMRI experiment coincide with those demarking the histological zones described in the cartilage literature [13,23]. To further verify these features in the T2 images of cartilage and to correlate the T2 features with the histological zones in cartilage, we calculated, at several specific tissue depth ranges, the percentage variation of the T2 with respect to the T2 of the least varied

359

32. Relaxation Atiisorropy ns a Marker for Macromoleculnr Orienlalions iti Articular Cartilage

profile (40") at the same tissue depth. Figure 32.7a shows the results for two tissue depth ranges: from 55 to 110 pm in region 2, and from 400 to 500 ym in region 3b. Figure 32.7b shows the results at and just beneath the articular surface (from 0 to 54.7 pm in region 1).

80 60

a

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m

p

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80

-20

3

1.

- 0 -1

-40 -20

0

20

40

60

80

-20

5-

Fig. 32.7: Percentage change of T2 in cartilage at the three featured regions in p M R images, plotted as a function of the orientational angle 8. The solid lines in both a) and b) are the curve of (3cos28 - I)*. In a), the solid circles are the 400-500 pm depth, and the crosses are the 55-1 10 pm depth. In b), the solid circles, open circles, open triangles, crosses and squares are the 0, 13.7, 27.4,41.O, 54.7 pn depth respectively.

The spatial and directional variations in T2 within canine articular cartilage suggest that T2 anisotropy is a reliable marker of oriented ultrastructure. It s e e m very likely that molecular level structure due to local directionality in the collagen fibril network is somehow implicated in this relationship. Let us now consider more specific observations by region. In region 3b, T2 varied up to 80% with orientation with respect to the magnetic field (the solid circles and the dash line). Furthermore, this variation qualitatively followed the which is proportional to the dipolar second moment. Note that the curve of (3cos28 pMRI experiment presented in this text does not intend to verify whether the signal is motionally narrowed or not. The comparison in Fig. 32.7 simply shows the qualitative similarities between the (3cos20 - 1)2 factor and the variations of T2 at various regions and tissue depths. Previous hlstological studies have shown that most of the fibrils in this region would be aligned perpendicular to the articular surface and parallel to each other. The strongly anisotropic relaxation response lends credence to the idea that T2 anisotropy is linked to fibril orientation.

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Y. Xia

In region 2, T2exhibited little dependence on angle (the crosses and the dotted line). This also lends support to the idea that T2 anisotropy is linked to fibril orientation, since previous histological studies have shown that the collagen network does not exhibit a strong preferred orientation in this zone. One would therefore expect to obtain an isotropic average T2. In region 1, T2 was very sensitive to the tissue depth, with the percentage difference (relative to 40" reference) varying about 1% per micron of depth: from about 5S% at the articular surface to about 35% at the 27.4 ym and to about 5% at the 54.7 ym. It is interesting to note that the pattern of T2 variation with angle in the superficial zone is qualitatively similar to that in the radial zone. This observation is a hint that T2 anisotropy may not be a direct measure of fibril orientation, and more experimental work will be required to clarify this issue. Thus, T2 profiles through the thickness of articular cartilage are characterized by three distinct MRI regions: Starting from the surface, the first region exhibits a depthdependent T, anisotropy; the second region exhibits a depth-independent and isotropic T2;and the third region exhibits a strong and almost-depth-independent T2 anisotropy. The above results were obtained using the cartilage tissue from the central loadbearing area of the canine shoulder joints. In a separate experiment, we studied cartilage from the peripheral area of the same canine shoulder joints. The results have showed that the peripheral tissue has distinctly different T2 characteristics compared to the T2 of the cartilage from the central load-bearing area [24]. It can therefore be concluded that there is a heterogeneity of the T2 anisotropy, which depends upon the areas from where the tissue is harvested (and hence the difference in biomechanical loading conditions). We are currently studying the tissues from several different areas in a joint (central heavy load-bearing, light load-bearing, peripheral) to investigate the heterogeneity of T2 anisotropy and to compare the pMRI results with the histology.

32.5 Cartilage TI Result At each of the 3" and 57" position, a T , image was constructed by acquiring a series of four 2D T,-weighted images. As in the T2 case, the proton intensity images were influenced significantly by the orientation of the sample. Unlike the T2 case, however, the quantitative T , images calculated from these two sets of data do not show orientational

32. Relmarion Anisotropy as a Marker for Mocromolecular Orientations in Articular Cartilage

361

dependence. Figure 32.8 shows the cross-sectional profiles of T I from two TI images (3" and 57" positions) at the same tissue location. Two TI profiles are essentially identical, and fairly uniform as a function of the cartilage tissue depth.

0

100

200

300

400

500

600

700

Distance from articular surface (urn)

Fig. 32.8: Cross sectional profiles of T I of the cartilage-bone plug at about 0" and 55" respectively.

The quantitative T , values and the shape of the T , profiles agreed well with one of our previous pMRI results where mature canine cartilage was studied [ 5 ] . This microscopic imaging result is also consistent with the spectroscopic result by Henkelman et al [3] where no orientational dependence of T , was observed in cartilage. The bulk TI value (1.4 f 0.1 s) and the mean T I values of the cartilage tissue over the cartilage tissue depth (3": 1.63 f 0.13 s; 57": 1.69f 0.10 s) are mutually consistent with each other.

32.6 Discussion and Summary This pMRI study shows that a distinct T2 anisotropy exists in canine cartilage, while T , is found to be isotropic. The results in this study are significant in three respects: (a) The

spatial resolution of the T , and T2 images is the highest that has ever been reported in MRI studies of articular cartilage. We demonstrated that pMRI can be used for the quantitative study of heterogeneous biological tissue at microscopic resolution. (b) Our pMRI results show that a distinct T2 anisotropy exists in canine cartilage, while the T I is found to be isotropic in the tissue. The quantitative imaging results register the individual components of the T I and T2 profiles to the full depth of the cartilage tissue. (c) We have found three unique regions in the p M R images. These three regions, especially the mid-

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dle and the deep regions, correspond approximately to the three histological zones in cartilage. T2 anisotropy could therefore be used as a sensitive and non-invasive marlier for molecular level orientations in articular cartilage.

Acknowledgment This work is supported in part by a Research Excellence Fund in Biotechnology from Oakland University.

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D. Burstein, et al., J. Orthopaedic Research 11 (1993) 465 -478.

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Y.Xia, et al., Orthopaedic Transactions 18 (1994) 403-404. Y.Xia, et al., Magn. Reson. Med. 31 (1994) 273-282.

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A. Maroudas, Biorheology 12 (1975) 233-248.

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K. B. Lehner, et al., Radiology 170 (1989) 495499.

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C. W. Hayes, et al., Radiology 176 (1990) 479-483.

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J. M.Modl, et al., Radiology 181 (1991) 853-855.

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C. W. Hayes, J. A. Parellada, Topics in Magn Reson Imaging 8 (1996) 51-56.

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G . D. Fullerton, I. L. Cameron, in Biomedical magnetic resonance imaging - Principles. Methhodologj, atld Applications F. W. Wehrli, D. Shaw, I. B. Kneeland, MS. (VCH Publisher, New York. 1988) pp.

16.

G. D. Fullerton, et al., Radiology 155 (1985) 433-435.

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S. J. Erickson. et al., Radiology 181 (1991) 389-392.

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A. Haase, et al., J. Magn. Reson. A 105 (1993) 230-233.

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Y. Xia, Concepts in Magnetic Resonance 8 (1996) 205-225.

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Y. Xia, et al., 4th Meeting Intern. SOC. Magn. Reson. Med. (ISMRM), New York (1996) 7, #204.

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Y.Xia, et al., Journal ofMagn Reson fmaging 7 (1997) 887-894.

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24.

Y. Xia, 6th Meeting Intern. SOC.Med. Reson. Med. (ISMRM), Sydney (1998). #40.

115-155.

33. Morphometric Analysis of Cartilage Grown in a Hollow Fiber Bioreactor Using NMR Microscopy K. Potter, K . W. Fishbein, W. E. Hortonl, and R.G.S. Spencer

Nh4R Unit and 'Cartilage Biology Unit, National Institute on Aging, National Institutes of Health, Baltimore, MD 21224, USA

Abstract NMR microscopy was used to monitor the formation of cartilage, from isolated chondrocytes, in a NMR-compatible hollow fiber bioreactor (HFBR). By comparing NMR images with histologic sections, the effect of tissue morphology on the NMR properties of the tissue was investigated. During development, changes in tissue morphology were accompanied by changes in the NMR properties of the tissue, consistent with increased macromolecular content. Furthermore, regional variations in cell size observed in histologic sections resulted in regional variations in the NMR properties of the tissue. The different morphologies present in growth plate cartilage (GPC) were also distinguished by NMR imaging. Finally, the production of human cartilage in a HFBR, with and without growth factor treatment, was assessed with NMR imaging.

33.1 Introduction Previous NMR studies of explunt cartilage have focused on how changes in the extracellular matrix (ECM) composition affect N M R measurable parameters such as water proton relaxation times [ 1,2], the water diffusion coefficient [2,3], and magnetization transfer rates [4,5]. Nevertheless, the effect of tissue cellularity and ECM composition on the NMR properties of cartilage is poorly understood. The HFBR permits the study of these relations, as well as investigation of effect of exogenous factors on cell proliferation and matrix production in siru.

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K. Potter, K. W. Fishhein. W.E. Hortoti, mid R.G.S. Spcticcr

33.2 Experimental Details about the construction, sterilization and inoculation of the HFBR systrni hiive been presented elsewhere [6]. Briefly HFBR consisted of a high purity glass tubing ji.d. 4 mm, height 60 mm) containing six porous polypropylene hollow fibers (id. 330 p m .

0.2 pm pores). Bioreactors were inoculated, through a rubber septum on the side-port, with 2 . lo7 chondrocytes isolated from either distal sterna of Day 16 chick embryos (61 or from the cartilage of patients undergoing knee replacement surgery. Human cells were allowed to proliferate in vitro and redifferentiated to the chondrocyte phenotype by inoculating to high cell densities in the HFBRs. After inoculation the bioreactors were perfused using a pin compression pump (Cellco, Germantown, MD) and maintained in a 5% CO, I 95% air incubator. Bioreactors containing avian cells were analyzed with proton NMR microscopy under incubator-like conditions (5% CO, 195% air, 37 "C), at weekly intervals for four weeks. Bioreactors containing human cells were imaged 5 weeks post-inoculation. For GPC studies, coronal NMR images of an embryonic chick femur, dissected free of muscle tissue and immersed in media, were acquired at 37 "C. All NMR experiments were conducted on a Bruker AMX spectrometer operating at 9.4 T (400.1 MHz for IH). The following quantitative NMR images were calculated for HFBR tissue and GPC: water proton longitudinal ( T I ) ,and transverse relaxation times (T2), the magnetization transfer ( M T ) value, and the wuler diffusion coeficient ( D ) . Maps of T , were calculated from 10 images acquired with a saturation recovery sequence with repeat times ranging from 0.2 - 10 s. Maps of T, were calculated from 16 images acquired with a multiecho sequence. MT maps were calculated from: MT = [ 1 - MsO/MO], where Mso/Mo gives the ratio of image intensities acquired with and without the application of an 12 pT pulse 6000 Hz off-resonance. Maps of the water diffusion coefficient were calculated from a series of images acquired with the pulsed-gradient spin-echo (PGSE) technique with a 5 ms gradient encoding time (6), a 10 ms diffusion time (A), and gradient values from 0 - 100 mT/m. Diffusion measurements are presented as percentages of the free water diffusion coefficient (Dw). After NMR imaging, HFBR tissue and GPC were fixed in formalin, sectioned, and stained with alcian blue, a metachromatic dye than binds to chondroitin sulphate of aggrecan [7]. Histologic sections clearly show changes in tissue morphology based on changes in cell size, cell number, and matrix metachromasia.

33. Analysi.~of Cartilage G r o w in a Hollow Fiber Bioreactor Using NMR Microscopy

365

Fig. 33.1: Histologic sections of bioreactor generated tissue, stained with Alcian blue, at (a) 1 and (b) 4 weeks post-inoculation. Sections were derived from two different bioreactors at their respective time points. Quantitative proton MT maps of cartilage produced (c) 1 and (d) 4 weeks postinoculation. The resolution of the NMR images was 60 pm x 60 p m x 2 mm and the image slice was taken perpendicular to the fiber axis, showing the fibers in cross-section.

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K.Potter. K. W. FishDein, W. E. Horton, and R.G.S. Spencer

33.3 Results and Discussion 33.3.1

Cartilage Formation from Chick Chondrocytes

Stable three-dimensional cartilage was formed in accordance with a defined sequence of events. Initially, a tissue composed of cells with some interstitial matrix, lacking significant metachromasia, was produced (Fig. 33. la). This was followed by the formation of a defined territorial matrix around each cell, cellular proliferation, and the deposition of highly metachromatic matrix. At this stage cells were aligned in columns radiating out from the fibers. Finally, the average cell size increased, reducing the volume fraction of ECM and the intensity of stain (Fig. 33.lb). A gradient of cell maturation was observed in tissue produced after 4 weeks of growth. Immature cartilage, composed of small cells, was nearest the fibers and mature cartilage, composed of larger cells, was furthest from the fibers. This sequence of events is analogous to that observed for chondrocytes grown in suspension culture. M T images of neocurtiluge formed at 1 and 4 weeks post-inoculation, in Figs. 33. lc and 33. Id, show the spatial and temporal evolution of tissue volume and tissue M T values. After one week of growth, the tissue occupied about 10% of the extracapillary volume, and the M T value was comparable to that for a dilute collagen gel [ 5 ] . At week 4 the HFBR volume was filled with cartilage, and the M T value of the tissue was coniparable to that of mature articular cartilage [ 5 ] . The M T values of tissue decreased with increasing distance from the fibers. This was consistent with a decrease in ECM content due to an increase in cell size. At the periphery of the HFBR, where there is non-staining fibrous matrix, the M T values were the highest. Graphs of (a) MT, (b) T , , (c) T2, and (d) D values for developing neocartilage, measured at weekly intervals over a four week period, are presented in Fig. 33.2. Culture medium within the fibers and within incompletely filled HFBRs was excluded from the analysis. The steady increase in the M T value of the tissue with development (Fig. 33.2a), was consistent with an increase in the collagen content since the contribution of glycosaminoglycans to M T is relatively weak [ 5 ] . With increasing cell number. from weeks 1 to 3 , the M T value increased. The increase in M T from week 3 to 4 was likely due to an increase in the collagen content of the ECM since tissue cellularity remained fairly constant during this period. Accordingly, tissue M T values might be used to stage the cartilage formation process.

33. Analysis of Curtiluge G r o w l in u Hollow Fiber Bioreuctor Using NMR Microscopy

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L

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Fig. 33.2: Graphs of the average (a) MT, (b) T I ,( c ) T2, and (d) D values for neocartilage tissue at 1, 2, 3, and 4 weeks post-inoculation. The error bars give the standard deviation of each rneasurement for a single bioreactor.

In the first three weeks of growth, both T I and T., decreased monotonically with increasing cell numbers and matrix deposition (Fig. 33.2b and c). However, between weeks 3 and 4 the decrease in T , was more dramatic than the decrease in T2. This result suggests that T2, although sensitive to the overall macromolecular content of the tissue, was insensitive to the relative amounts of collagen and proteoglycan in the matrix. In contrast, the increased proportion of collagen in the ECM at week 4 produced a marked reduction in T I .Spatially, the smaller amounts of collagen correlated with increasing cell size which was visualized directly by larger values of T I .Thus, T I might be used to map the collagen distribution in neocartilage. During weeks 1 to 3, the water diffusion coefficient was steady at 75% (Fig. 33.2d). Between weeks 3 and 4, the marked reduction in the ECM volume due to cell enlargement resulted in a notable reduction in the water diffusion coefficient. This result is con-

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K. Potter. K . W.Fishbein, W.E. Horton, and R.G.S. Spencer

sistent with other studies [8]. At week 4, mature cartilage had a higher diffusion coefficient than immature cartilage. Thus, diffusion measurements might provide a measure of cartilage maturity. This hypothesis was further explored i n the GPC system.

33.3.2 Growth Plate Cartilage Chick growrh plate cartilage (GPC) was used to verify correlations between tissue NMR properties and morphology. GPC was selected for this study because the size of the resident chondrocytes increases with distance from the articular surface and the spatial variation in ECM composition has been well documented [9]. The histologic section through the distal growth plate of an embryonic chick femur, in Fig. 33.3a, can be divided into four distinct regions (see Fig. 33.3b): the epiphyeal cartilage (EC) zone composed of small round chondrocytes embedded in a matrix of aggrecan and type I1 collagen matrix, the proliferaring zone (PZ) composed of flattened chondrocytes embedded in an intensely metachromatic matrix with a less permanent collagen scaffold, the mature zone (MZ) composed of rounded chondrocytes with defined territorial and inter-temtorial matrix consisting of aggrecan and type I1 collagen, and the hypertrophic zone (HZ) composed of enlarged cells with a well defined territorial matrix composed mostly of aggrecan and fype X collagen. The ECM content as well as tissue collagen content decreases with distance from the articular surface due to increasing cell numbers and size. It was therefore hypothesized that quantitative NMR imaging is able to discriminate between the four different tissue morphologies represented in Fig. 33.3b. Quantitative NMR images of (c) T,, (d) T2, (e) M T, and (f) D for growth plate cartilage are shown in Fig. 33.3. These four distinct regions have characteristic NMR properties which are summarized in Table 33.1 below. The reduction in T , was consistent with an increase in collagen content, as observed for HFBR cartilage. However, the highest T2 value did not occur in the hypertrophic zone, because of the partial calcification of this zone. Instead T2 was highest in the proliferating zone, which had the least interstitial matrix. We conclude that both T , and T2 can be related to the macromolecular content of the tissue. The MT value was largest in zones with the highest cell numbers (PZ and MZ), as also observed for HFBR tissue. This implies that water diffusion coefficient was lowest in the proliferating zone and highest in zones with large cells (HZ), consistent with what was found for HFBR tissue. Overall, of the four defined zones, the NMR parameters for EC and MZ were the most similar. These are also the two zones with the greatest histologic and biochemical similarity.

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Fig. 33.3: Histologic sections of chick femur at (a) 5x and (b) 2 0 ~ The . zones indicated in the histologic section represent: epiphyseal cartilage (EC), proliferating zone (PZ), mature zone ( M Z ) , and hypertrophic zone (HZ). Proton NMR maps of (c) T I ,(d) T2, (e) MT, and (0 D for distal end of femur from a 20 day chick embryo, immersed in media and maintained at 37 "C. The in-plane resolution was 100 microns, the slice thickness was 2 mm, and the FOV was 25 mm.

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K. Potter, K. W. Fishbein. W.E. Horion, oiid R.G.S. Spenrer

Table 33.1: NMR parameters of different zones in growth plate cartilage.

3.0 (0.1)

74 (2)

0.78 (0.05)b

PZ MZ

3.1 (O.l)a

77 (2)

0.81 (0.05)c

53 (6)

3.1 (0.l)a

72 (3)

0.81 (0.02)C

66 (6)

HZ

3.3 (0.1)

63 (9)

0.78 (0.02)b

70 (8)

EC

62 (6)

Values marked with the same symbol were not statistically different.

33.3.3 Cartilage Formation from Human Cells Optimization of cartilage formation by human chondrocytes, isolated from osteoarthritic cartilage, may be an important step in the development of a treatment for this disease. Using our NMR-compatible HFBR system, we can study the effect of different growth factors on chondrocyte proliferation and matrix deposition under a defined set of growth conditions. Preliminary NMR studies show that HFBRs inoculated with human secondary chondroprogenitor cells produced more tissue when treated with a cocktail of IGF-I and TGF-0, as compared with a control HFBR (Fig. 33.4). The MT values for the cartilage formed were comparable to that produced by chick sternal chondrocytes after two weeks of growth.

Fig. 33.4: Quantitative proton MT images of (a) control and (b) growth factor treated bioreactors inoculated with human secondary chondroprogenitor cells. Images were acquired 5 weeks postinoculation with a nominal in-plane resolution of 60 p and slice thickness of 2 nim.

33. Anal~xisof Cnrtiluge Grown in n Hollow Fiber Bioreactor Using NMR Microscopy

37 1

33.4 Conclusions Cartilage NMR properties are dependent on the volume fraction and composition of the ECM. During development, the nature and composition of the ECM changes, making it possible to use NMR imaging to characterize the sequence of maturational events that occur during cartilage formation. The different tissue morphologies present in growth plate cartilage also demonstrated unique NMR properties, analogous to the HFBR tissue. Future studies will focus on using the NMR-compatible bioreactor to study the complex regulatory mechanisms that control the growth and development of cartilage.

Acknowledgments The authors would like to thank Dr. Bill Landis for supplying the histologic section of the chick femur stained with safranin 0.

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E. Petersen, K. Potter, J. Butler, K. W. Fishbein, W. E. Horton, R. G. S . Spencer,E. W. McFarland,

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34. EPR Imaging of the Rat Heart J. L. Zweier and P. Kuppusamy

Molecular and Cellular Biophysics Laboratories, Department of Medicine, Division of Cardiology and the EPR Center, Johns Hopkins University, Baltimore, Maryland, USA

Abstract It has been hypothesized that free radical metabolism, oxygenation, and nitric oxide generation in biological organs such as the heart may vary over the spatially defined tissue structure. We have developed instrumentation optimized for 3D spatial and 3D or 4D spectral-spatial imaging of free radicals at 1.2 GHz. Using this instrumentation high quality 3D spectral-spatial imaging of nitroxide metabolism was performed, as well as, spatially localized measurements of oxygen concentrations, based on the oxygen dependent linewidth broadening observed. With 3D spatial imaging using single-line labels resolutions down to 100 to 200pm were obtained. It is demonstrated that the EPR imaging is a powerful tool which can provide unique information regarding the spatial localization of free radicals, oxygen, and nitric oxide in biological organs and tissues.

34.1 Introduction After a decade of development and application, the fields of electron paramagnetic resonance (EPR) spectroscopy and imaging (EPRI) have progressed to the point of enabling useful physiological and biochemical information to be obtained from living tissues [ 151. The development of low frequency EPR instrumentation at L-band, 1 - 2 GHz, or lower frequencies, and lumped circuit resonators has made it possible to perform EPR measurements on these lossy samples [6-121. Previous in vivo or ex vivo EPR spectroscopy studies focused on global measurements of free radical metabolism or generation as well as measurements of tissue oxygenation [9,10,12,13]. Studies that require measurements of the spatial distribution of free radicals within the sample, however, can be performed utilizing magnetic field gradients [14-201 in a manner similar to that of NMR

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imaging. EPR imaging, however, is faced with a number of technical problems, which make this technique more difficult to achieve in practice than those of NMR. The linewidths associated with EPR signals are 3 orders of magnitude larger compared to that of N M R signals and hence EPR imaging requires 100 - 1000 times more powerful gradients. The paramagnetic centers to be studied are present in sub-millimolar concentrations compared to more than 100 molar concentrations of water protons utilized in N M R imaging. In addition, the EPR absorption function of most stable paramagnetic labels contains multiple lines due to hyperfine splitting which occurs secondary to nuclearelectron interactions. In spite of these difficulties, instrumental and software techniques have been developed to improve image quality and enable important information to be obtained in studies of a variety of biological samples. Over the last decade we have focused on developing instrumentation optimized for measurements of free radicals in isolated beating hearts and over the last several years we have extended our efforts to develop hardware and software to enable spatial and spectral-spatial imaging of free radicals in the heart [14,19-341. The present chapter provides a summary of the development and application of the imaging techniques with examples including imaging of stable free radical labels, oxygen concentrations, and nitric oxide generation in the normal or ischemic heart.

34.2 Why Image Free Radicals in the Heart? One of the major research efforts in cardiovascular medicine has been to salvage myocardium at risk of death in heart attack patients. While modem clinical treatment is aimed at establishing early coronary reperfusion, it is known that reperfusion itself can result in further myocardial damage. Free radical generation has been proposed as the central mechanism responsible for this reperfusion damage. Until recently, there was only indirect evidence for free radical generation in the heart based on beneficial effects of free radical scavengers in animal models. There was a great need for direct techniques of measuring free radical generation in experimental models of this disease [35,36]. The isolated perfused heart model is an important and versatile model that is commonly used to study normal cardiac physiology and the basic mechanisms of cardiac disease [37]. When the heart is deprived of flow, a process called ischetnicr, it becomes hypoxic and on reflow oxygen supply is restored. There is extensive evidence that free

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radical generation and metabolism is greatly altered by this process and there has been a great need to be able to measure and map alterations in myocardial radical generation, and metabolism as well as tissue oxygenation in this setting. However, there was no prior technique, which could provide this information. More recently it has been demonstrated that alterations in nitric oxide (NO) generation also occur and there has been much interest in being able to measure and image this process. Thus, EPR spectroscopy and imaging studies of the isolated heart offered the unique potential to provide important insights regarding the basic mechanisms of heart damage during and following heart attack.

34.3 Instrumentation 34.3.1 Hardware Instrumentation and computer software were developed enabling high resolution multidimensional imaging of free radicals in isolated organs and tissues. A particular challenge in building this instrumentation was to be able to fit the resonator and 3 sets of powerful gradient coils into the relatively small magnet gaps available in standard resistive magnets. Three sets of water-cooled gradient coils were built for the n,y and z gradients, and powered by six power supplies. The resonator and gradient coils were fitted into the gap of a 38 cm pole face iron-core electromagnet whose pole caps and ring shims were machined to yield a 104mm gap with field homogeneity of greater than 10 mG over a 25 mm diameter sphere. The gradients and power supplies were designed to achieve gradient fields of up to 150 Gkm.

34.3.2 Software Computer software was developed for IBM compatible PCs for acquiring spatial or spectral-spatial EPR projections via GPIB (IEEE-488) bus control of a Bruker signal channel and field controller. Image reconstruction was performed by filtered-backprojection methods [38,391. Algorithms were developed to remove hyperfine-based image artifacts further enhancing the image resolution [31,321. In extensive validation

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studies on phantoms, hearts and other tissues it was observed that high quality, spatially accurate images of the distributions of free radicals could be obtained with submillimeter resolution.

34.3.3 Resonators EPR imaging of biological samples has many technical challenges for instrumentation development in general, and for the sample resonator design in particular, beyond those of simple spectroscopy. The most important is the need for a resonator design of minimum thickness, which makes it possible to achieve higher magnetic field gradients for a given coil's driving power. Thinner resonators also enable multidimensional gradient coils to be placed in the gap.

Fig. 34.1: Assembled ceramic sample resonator. A, microwave rotary joint; B, rotating coaxial with a coupling loop; C , reduction gear; D, coupling control shaft; E, ceramic resonator inserts; F, modulation coils; G, aluminum frame; and H, sample tube with holder.

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Loop-gap resonators (LGR) provide straightforward design and high filling factors 161. However, due to the open structure of the inductive loop element, LGRs require a shield. The need for the shield leads to problems in achieving an optimum magnitude of modulation field and a minimum 20 per cent increase of overall resonator thickness. Reentrant resonators (RER) do not require a shield; however, since they were constructed from milled and silver plated plastic they had low rigidity and consequently microphonics, and poor thermal stability [8,40]. Ceramics, being a rigid material with high structural strength and stable mechanical and thermal parameters, are thus a good choice for resonator construction. Several RER sample resonators were designed and fabricated using ceramics [21]. Figure 34.1 gives a general view of a ceramic resonator. To further decrease the overall thickness, modulation coils were wound as a thin coil, epoxy impregnated and mounted onto the side walls of the resonator with adhesive. We observed that for a fixed concentration of free radical sample the ceramic L-band RERs yield sensitivity similar to that which can be obtained at X-band using standard microwave cavities, assuming that optimal filling of the resonators is performed with suitable cylindrical tubes (Fig. 34.1). The L-band resonator can accommodate much larger volumes of lossy aqueous samples and can thus compensate for the inherently lower sensitivity of L-band measurements. In addition we have shown that this design can be modified with a peizoelectric actuator to serve as an electronically tunable resonator with frequency locked to that of a low noise fixed frequency source [22]. This latter approach eliminates any frequency drift and is useful in that it maintains the isofrequency condition for a given imaging experiment.

34.4 Three-Dimensional Spectral-SpatialEPR Imaging We have applied the imaging instrumentation to obtain images of free radicals and oxygen concentrations in isolated rat hearts [14,26]. Isolated rat hearts were perfused at 37 O C in a constant pressure mode with Krebs bicarbonate-buffered perfusate solution. Hearts were infused with 1 mM TEMPO (2,2,5,5-tetramethylpiperidine-N-oxyl)for 10min to reach steady state and EPR acquisitions of 64 projections were performed every 12 min. The 3D spectral-spatial images were reconstructed using filtered back-

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projection algorithm. These images corresponded well with cross-sectional short axis sections through the rat heart as would have been expected from the orientation of the heart in the center of the resonator (Fig. 34.2). In another heart after loading and acquisition of control images, the heart beat was arrested using cardioplegic perfusate containing 110 mM NaCI, 24.6 mM NaHC03, 16 mM KCl, 16 mM MgCI,, 1.2 mM CaCI2, 16.7 mM glucose, and then the heart was subjected to global ischemia at 24 OC. A series of images, at 12 min intervals, were obtained during global ischemia. During ischemia the label was observed to clear more rapidly from the outer myocardial walls, epicardium, than from the inner walls, endocardium.

Fig. 34.2: Cross-sectional transverse 2D spatial EPR image of the rat heart obtained from a 3-D spectral-spatial data. A) A spectral slice (mid slice, slice width 0.125 G). B) Intensity map.

The spatially deconvoluted spectral functions of the images were used to discern oxygen induced linewidth changes at selected regions of the heart. Examination of the spectral data from the images of the cardiopleged heart showed a gradual decrease in the linewidth at each spatial location (Fig. 34.3). Over a 60 min duration of ischemia, the linewidth decreased by 0.45 G and approached the linewidth observed in the absence of oxygen. This would correspond to a drop in myocardial oxygen concentration from 625 pM to near 0 pM.

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TIME (MINI Fig. 34.3: Graph of the alterations in EPR linewidth (closed circles) observed within the heart images (Fig. 34.3) as a function of the duration of ischemia. The semilogrithmic plot of the width as a function of time is shown in the inset.

34.5 Four-DimensionalSpectral-Spatial EPR Imaging To enable full 3D spatial mapping of the spectral information, 4D spectral-spatial EPR imaging techniques were developed using three-dimensional gradient sets [ 19,231. We have demonstrated that high quality and high resolution 4D spectral-spatial images of biological organs and tissues of sizes up to 25 mm diameter can be obtained. A variety of free radical labels including nitroxides, and dispersions of solid state probes have been

evaluated as potential probes for EPR oximetry and metabolic studies. The feasibility of studying small linewidth differences of less than 0.1 G in samples of up to 25 mm in size was demonstrated. To evaluate the ability of EPR imaging to resolve more detailed anatomical structure within the heart, we infused a stable colloidal aqueous suspension of the glucose char oximetry label and imaged the isolated, globally ischemic rat heart. The glucose char material is highly oxygen sensitive with a linewidth of 0.19 G in the absence of oxygen and more than 100 G in air [41]. Thus, in air-equilibrated suspension or in the normally

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perfused oxygenated heart, no EPR image data can be obtained. However, under the severe hypoxic conditions that occur during ischemia this label can be used for EPR imaging. The 4D image of the rat heart the spectral shape at each spatial point. The image data showed a uniform linewidth of 0.52 k 0.05 G throughout the heart (Fig. 34.4) suggesting that the concentration of oxygen was relatively uniform as would be expected with prolonged global ischemia. Thus, 4D spectral-spatial EPR imaging can provide useful and reliable information regarding the distribution of free radicals and paramagnetic labels along with their associated EPR spectral data. While this technique is applicable to biological samples or tissues and allows detailed mapping of spectral information over the three-dimensional spatial structure of the object, there are a number of concerns and limitations that need to

Fig. 34.4: 4D spectral-spatial images of rat heart. Spectral-spatial plots along three mutually orthogonal lines (A, longitudinal; B and C, transverse) across the heart are shown. The spectra showed a uniform linewidth of 0.52 f 0.05G .

34. EPR Imaging of the Rat Heart

38 1

be considered regarding its application to living tissues. These limitations include the need for EPR labels of adequate sensitivity and stability. The requirement of considerably longer data acquisition times for 4D spectral-spatial imaging compared to 2D or 3D imaging can limit the study of the physiology and pathophysiology of living organs and in vivo animals. Further improvements in sensitivity and speed of data collection of this instrumentation should enable further extension and application of this powerful technique.

34.6 Three-DimensionalSpatial Imaging Three-dimensional (3D) spatial imaging is necessary to obtain a complete unambiguous image of an asymmetric object. However, in the past, most of the EPR imaging experiments were performed only in two-dimensions (2D), in some cases making use of the axial symmetry of the object avoiding the need for a third gradient and the extra time required for data acquisition. A 2D image superimposes all the slices along the third dimension onto the plane of projection. This naturally integrates the information along the third axis and provides only a 2D projection of the image. We have developed and optimized 3D spatial imaging instrumentation for biological samples [20]. We used a variety of phantoms and free radical labels to validate the accuracy and quality of the images. An example of the 3D image from a rat heart obtained with glucose char label is shown in Fig. 34.5. After 15 min of normal perfusion glucose char label was infused and the heart subjected to no-flow global ischemia. EPR spectra were continuously measured to monitor the sharpening of the signal due to the decrease in oxygen concentration. The heart was then imaged by collecting 1024 projections. In the compiled 3D images shown in Fig. 34.5, the external shape of the epicardium, large vessels including the aorta and pulmonary arteries were clearly seen and corresponded with the visually observed external surface of the rat heart. The internal endocardia1 surface of the left ventricle was also clearly seen in Fig. 34.5. Within the image the ascending aorta, aortic root, the left main coronary artery and the bifurcation of the left anterior descending coronary and the circumflex coronary arteries could be seen. The left anterior descending coronary artery could be observed down to a diameter of 0.2 mm.

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0

256

Fig 34.5: 3D images of ischemic rat heart infused with glucose char suspension. A, Full view of the heart; B, a longitudinal cutout showing the internal structure of the heart; Legends: C, cannula; Ao, aortic root; PA, pulmonary artery; LM, left main coronary artery; LAD, left anterior descending artery; LV, left ventricular cavity.

34.7 Gated EPR Imaging of the Beating Heart Of the constraints that limit or compromise application of EPR imaging, the problems associated with organ movement, such as the contractile motion of the heart, or respiratory motion with breathing have considerably limited applications to living systems where motion occurs during the process of data acquisition. Thus in vivo EPR spectroscopy and imaging studies to-date have provided only time-averaged information. This results in a loss of information regarding the temporal and spatial changes. While random motional artifacts are difficult to control, periodic motions such as heart beat can be controlled by pacing at a fixed frequency and synchronizing the data acquisition system to that frequency, a process known as gated-acquisition [42]. Recently we have developed instrumentation capable of performing gated imaging measurements on perfused beating rat hearts [27].

34. EPR Imaging ofrhe Rat Heart

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Fig. 34.6: The principle of gated data acquisition. A sinusoidal wave is shown as the source signal for illustration. Data are collected at n field steps. At each step, the receipt of the pulse (odd pulse, 0)triggers the acquisition of g number of data points (shown for g = 8) over the cycle, data transferred, field incremented at e (even pulse, e), and acquisition continued at the receipt of the next pulse (0).Every other cycle between the end of acquisition (at e) and the beginning of the next acquisition (at 0)is used for field advance and stability.

The principle of gated acquisition is schematically shown in Fig. 34.6. The heart is paced continuously using a stimulator. The stimulator also outputs synchronized 'ITL pulses that drive the data acquisition system. The gated data acquisitions are performed for each field step. When the field is set, the data acquisition will be triggered at the receipt of the next pulse and an array of g number of data points will be collected over the cardiac cycle using a high speed analog-to-digital converter. At the end of the cycle the field is incremented to the next step. The acquisition of the next cycle begins at the following pulse and the process is repeated for a full sweep consisting of n discrete field steps. The resulting data array is then rearranged to give g number of spectra of n discrete samplings. The present instrumentation is capable of performing gated acquisitions of up to 256 images per cycle, with rates of up to 16 Hz. Thus a temporal resolution of 4096 Hz is possible at this maximum rate. We used 6 Hz (z = 167 ms) pacing for per-

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fused rat hearts and collected 16 points per cardiac cycle for 64 field steps. The typical data acquisition time was 20 - 25 s per spectrum. Female Sprague-Dawley rat hearts were perfused by the method of Langendorff with a modified Krebs bicarbonate perfusate. The aluminum support tube of the aortic cannula served as one of the pacing electrodes, while a copper wire connected to the ventricular wall functioned as the other electrode. The heart was paced at 360 bpm (6 Hz) with an electrical stimulator using a pulse of 5 volts and 7 ms duration. EPR imaging measurements were performed on these hearts, while maintaining continuous pacing and perfusion.

n.................... ............. .....................................................................................n 167 msec

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Fig. 34.7: 3D spatial images of the beating heart. A mid vertical slice (top) and a transverse slice (bottom) through the LV cavity are shown for 8 out of the 16 three-dimensional images of the perfused heart as a function of cardiac cycle. The pacing frequency was 6 Hz. The data acquisition parameters were: number of gates 16; number of field points, 64; projections, 144; gradient, 20 Gkm; time constant, 1.2 ms, acquisition time 64 min.

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After 15 min of equilibration, the heart was transferred to the resonator and the perfusate solution was switched to that containing 1 mM PDT (4-oxo-2,2,5,5,tetramethylpiperidine-d16-N-oxylor perdeuterated-Tempone). Gated projections were acquired using a field gradient of 20 Gkm. A total of 144 projections were acquired, decomposed into 16 data sets, and images reconstructed. Vertical and transverse slices of 8 out of 16 images of the heart are shown as a function of cardiac cycle in Fig. 34.7. The contraction- relaxation cycle is clearly seen in these images. The systolic and end-diastolic pressures during the cycle were 120 mmHg and 8 mmHg, respectively. The aorta is identified at the top-left corner of the vertical slices in Fig. 34.7. The aortic cannula was not visible in these images due to the aluminum tubing that was used in the cannula. The LV cavity is clearly seen as the central void and the two bright spots appear to correspond to the proximal coronary arteries. During systole the LV cavity clearly narrows with vertical elongation. The LV wall also is seen to markedly thicken.

34.8 Imaging of Nitric Oxide in the Heart Recently, we have shown that rat hearts subjected to global ischemia generate NO via an enzyme- independent pathway involving direct reduction of nitrite under the acidic and reducing conditions that occur during myocardial ischemia [43,44]. In view of the important implications of this enzyme independent mechanism of NO generation on the pathogenesis and treatment of tissue injury, we performed real time isotope tracer measurements of the mechanism of NO generation in the heart. When rat hearts were loaded with the NO trap, Fe(MGD)2 (bis(N-methyl-D-glucaminedithiocarbamate) iron(II)) and 15N-nitrite,while no signal was seen at the onset of ischemia, a prominent doublet signal characteristic of the Fe(MGD),-15N0 complex appeared. We mapped the spatial distributions of this NO generation in the ischemic myocardium using L-band EPR [29]. Rat hearts were loaded with I5N-nitrite and subjected to global noflow ischemia, during which time a series of 3D spatial EPR images of the distribution of NO were obtained using the NO trap Fe(MGD)2. The images (Fig. 34.8) clearly showed that NO is formed throughout the myocardium enabling visualization of the external shape of the epicardium, right ventricular (RV) myocardium and internal endocardial surface of the LV and LV chamber. Kinetic experiments show that maximum NO generation and trapping

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occurs at the midmyocardium and spreads out to endocardium and epicardium of the left ventricle. The magnitude of generation in the RV myocardium is 4 - 5 fold lower than in the LV. Thus, real time kinetics and 3D mapping of NO generation can be performed in whole biological organs using EPR imaging.

Fig. 34.8: 3D EPR images of Fe(MGD)2-N0 in the rat heart. The heart was loaded with 2 mM Fe(MGD)? and 10 mM nitrite and subjected to noflow global ischemia at room temperature. The images were acquired at the end of 60 min ischemia.

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34.9 Conclusions We have summarized the instrumentation, and techniques which we have developed and applied for EPR imaging of the isolated heart. These techniques of spatial and spectral spatial imaging have progressed to the point of enabling unique information to be obtained with spatial mapping of free radical metabolism, oxygenation, and nitric oxide generation. We are currently applying these methods to address a series of important questions regarding the pathophysiology of heart disease.

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G. R. Eaton, S. S. Eaton, K. Ohno, eds., EPR Imaging and In Vivo EPR, CRC, Boca Raton, FL, 1991.

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35. Application of High Resolution Cardiac Magnetic Resonance Imaging to Monitor a Rodent Model of Cardiac Dysfunction Sudeep Chundra', Konstuiitin G. Gurbanov2,Robert Strittmatter], Eliot H. Ohlstein2, Giora Z. Feuerstein2 and Susuntu K. Sarkar'

lDepartment of Physical and Structural Chemistry and 2CardiovascularPharmacology, SmithKline Beecham Pharmaceuticals, 709 Swedeland Road, King of Prussia, PA- 19406, USA

Abstract We demonstrate here the feasibility of using high resolution MRI for routine assessment of cardiac dysfunction in a rat model of congestive heart failure induced by aorta-caval fistula (ACF). The hemodynamic parameters like ejection fraction, left ventricular enddiastolic and end-systolic volumes, and stroke volume have been derived from MR measurements. It is shown that animals with ACF displayed a significant increase in both end-systolic and end-diastolic volumes and decrease in ejection fraction, compared to the sham-operated animals.

35.1 Introduction Animal models of congestive heart failure are important for routine evaluation of test agents in pre-clinical pharmaceutical research and development. Congestive heart failure (CHF) is a complex pathological and clinical syndrome in which changes in heart function and structure play an important role in development and progression of the disease. Experimental characterization of CHF involves the assessment of ventricular wall thickness, left ventricular end-systolic and end-diastolic volumes (LVESV and LVEDV, respectively), stroke volume (SV), ejection fraction (EF) and cardiac output [ 1-31. Traditional methods like thermodilution, flowmetry or echocardiography are either invasive

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and non-volumetric or lack high resolution for accurate and precise measurements [ 1-31. Recent data showing the use of MRI in experimental cardiac research. indicate the feasibility of using high resolution serial MRI to monitor structural changes in hearts of rats, rabbits and mice [4-71. The objective of this study was to demonstrate the feasibility of using high resolution MRI for routine assessment of cardiac dysfunction in rats. As a representative example, changes in heart function in rats with aorta-caval fistula (ACF) is presented.

35.2 Methods MR imaging was performed on a 4.7 T/40 cm BRUKER imaging spectrometer (Billerica, MA) with a 15 cm self-shielded gradient coil insert. A 9 strut half-birdcage radio frequency (RF) resonator [9,10] was built and used for both transmission and reception of the RF signal. In order to characterize the RF profile of the coil, images were acquired from a 0.1 M NaCl sample. Male Wistar rats (Charles River-Kingston) weighing 280-350 g were maintained on normal rat diet (n = 12 - 13) and provided water ad libitum. An aorto-caval fistula was surgically created between the abdominal aorta and the inferior vena cava [8] of rats ( n = 7) under ketamine and xylazine (10 mgkg and 50 mgkg, i.p., respectively). On week 11, both groups of rats were imaged to compare hemodynamic parameters such as EF, LVEDV, LVESV and SV. The sham operated animals served as controls. For imaging, these animals were lightly anesthetized with a mixture of 1.5% isoflurane and 1 Vmin of 0,.Each animal was secured on the bench and hooked up with EKG leads. The RF coil was placed on the thoracic cavity and secured on the animal. A simple cardiac-gated spin echo sequence (TRITE = 5500/13 ms; 256 x 128; slice thickness = 1 mm; number of averages = 2; number of slices = 22; FOV = 4 x 4 cm?) was used with the trigger delay for data acquisition set to 12 ms from the R-wave of QRS complex for diastole and 65-80 ms for systole (depending on heart rate). Respiratory gating was not used for the MRI scans since motion artifacts from respiration did not significantly degrade any pilot images acquired with this protocol. All experiments were performed in accordance with the guidelines of the SmithKline Beecham Pharmaceuticals animal care committee, and the American Association of Laboratory Animal Care (AALAC).

35. High Resolution Cardiac MRI to Monitor a Rodent Model of Cardiac D.vsfunction

39 1

The sum of lumen areas from nine contiguous slices provided an estimate for LV volume. End-diastolic and end-systolic images were used to calculate the SV and EF according to the formulae SV = LVV(diasto1e) - LVV(systole), and

(35.1)

EF (%) = 100 x SV / LVV(diasto1e)

(35.2)

All calculated volumes were expressed in microliters. Unpaired Student's f-test was used for comparison between groups at each time point. A p < 0.05 (i.e. 95% confidence level) was considered statistically significant. Data are presented as mean standard error of mean (SEM).

+

35.3 Results Figure 35.1 shows the intensity variation across the imaging plane of the water phantom. The in-plane intensity profile can always be adjusted further by changing the RF transmission power levels, to generate more uniform signal profiles from anatomical structures of interest within the imaging plane. The anatomical location of the rat heart, being immediately close to the anterior side of the thoracic cavity, permits the use of this coil for generating high resolution contiguous images with some signal variation in-plane and almost no variation out-of plane (along the slice dimension). Figure 35.2 shows the simple cardiac-gated pulse sequence used in this study. Figures 35.3a and 35.3b show typical MR images obtained at systole and diastole from the mid-ventricular region of a rat heart. Similar images were used to derive quantitative information from the animals of the study. Quantitative parameters were obtained using manual tracing. The inter and intra-observer error for measuring the quantitative parameters was < 2%. Placement of ACF produced progressive changes in cardiac dimensions which were characterized by increase in LV volume at week 11. Table 35.1 summarizes the data on hemodynamic parameters in rats with ACF and control rats on week 11. Compared with the sham-operated group, animals with ACF displayed a significant increase in both endsystolic and end-diastolic volumes (+151.6% and +66.4%,respectively ) and decrease in ejection fraction (-17.6% ). There was no significant change in the heart rate of either group of animals.

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S.Chandra, K . G. Gurbanov, R. Strittmatter. E. H. Ohlsrein, G. Z. Feuersrein, and S.K . Sarkar

Fig. 35.1: Intensity variation in the imaging plane of a water phantom (shown by the vertical line) with a 0.1 M NaCI. All acquisition parameters were identical to that used for rat heart imaging in this study.

65-70

I” Qr end systole

St end diastole

ECG RF signal .c

slice

phase

U

read Fig. 35.2: The cardiac-gated spin echo pulse sequence used for imaging.

__

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Fig. 35.3: Representative MR images obtained from mid-ventricular region of a rat heart at systole (a) and diastole (b). Similar images were used to derive quantitative information in the study.

Table 35.1: Hemodynamic parameters in two groups of rats (sham and CHF) on week 11 post surgery. a) indicates p < 0.001 and b) p < 0.05 with respect to the sham operated animals at this time point.

CHF

SHAM

LVEDV (ml)

597 f 3 1.9 a)

359 f 7.9

LVESV (ml)

310 f 18.8 a)

123.4 f 4.7

SV (ml)

286.8 k 14.8 b,

235.7 f 6.7

EF (%)

48.1 f 0.9 b,

65.7 f 1.1

Parameter measured

35.4 Discussion The non-uniformity in RF intensity, if any, across the imaging plane did not affect anatomical quantitation since relative intensities were not used for any calculations. The RF coil further provided adequate signal-to-noise ratio to optimize in-plane resolution (150 x 150 pm2). The feasibility of using this simple set-up for routine MR imaging

provides the option of exploring serial changes in these animals by repeating these mea-

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surements along the time course of the disease development. Such an approach based on non-invasive, volumetric and high-precision measurements, will be useful in evaluating the effectiveness of pharmacological interventions during development and progression of CHF. The data presented here shows that under high end-systolic and end-diastolic volumes, an increase in stroke volume is obtained in this model with no observed changes in heart rate, leading to an increase in cardiac output. This observation is consistent with what has been observed before in this model [ 1,8] The increase in SV is accompanied by a large increase in end-diastolic volume which in turn reduces the EF. These data confirm that chronic volume overload in rats with ACF produces cardiac dysfunction. In summary, we have implemented a high resolution MRI method for analysis of cardiac structure and function in rats with ACF. This provides a frame-work for investigating the efficacy of pharmacological interventions in this model using high resolution MRI.

References 1.

X-P. Yang, H. N. Sabbah, Y-H. Liu, V. G. Sharov, E. J. Mascha, I. Alwan, 0. A. Carretero, Am. J . Physiol. 265 (1993) H1946-H1952.

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Y-H. Liu, X-P. Yang, 0. N u s , H. N. Sabbah, E. Peterson, 0. A. Carretero. Am. J . Physiol. 272 (1997) H722-H727.

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Y-H. Liu, X-P. Yang, V. G. Sharov, 0. Nass, H. N. Sabbah, E. Peterson, 0. A. Carretero, J. Clin. Invest. 99 (1997) 1926-1935.

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K. Umemura, W. Zierhut, M. Rudin, D. Novosel, E. Robertson, B. Pedersen, R. P. Hof, J. Cardiovasc. Phurmacol. 19 (1992) 375-381.

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W. Zierhut, M. Rudin, E. Robertson, H-G. Zerwes, D. Novosel, J-P. Evenou, R. Stirnimann, R. P. Hof, J .

Cardiovasc. Pharinacol. 21 (1993) 937-946.

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W. G. Rehwald, S. B. Reeder, E. R. McVeigh, R. M. Judd, Magn.Reson. Med. 37 (1 997) 124- 130.

7.

S. E. Slawson, B. B. Roman, A. P. Koretsky, Proc. ISMRM, 5th Annual Meeting, Vancouver, 1997, p. 890.

8.

J. Winaver, A. Hoffman, J. C. Burnett, Jr, A. Haramati, Am J. Physiol. 254 (1988) R776-R784.

9.

J. F. Dunn, A. Azzawi, J. H o o p , Y. Cremillieux, Proc. of the 4th Annual Meeting of ISMRM, New York, 1996, p. 328.

10.

D. Ballon, M. C. Graham, M. L. Devitt, J. A. Koutcher, Proc. of the 8th Annual Meeting of SMRM, Amsterdam, 1989, p. 950.

36. Fast MR Imaging of Esophageal Motility Yasunaga Seki, Satoru Naruse’, Yoshiteru Seo2, Masataka Murakumi, Tsuyoshi Ozaki3, Motoji Kitagawu, Hiroshi Ishiguro, Yasuyuki Nukae, Tetsuo Huyakawa’ 1

Internal Medicine 11, Nagoya University School of Medicine, 65 Tsurumai-cho, Showa-ku, Nagoya 466, Japan

* Physiology I, Kyoto Prefectural University of Medicine, Kawaramachi-Hirokoji, Kamigyo-ku, Kyoto 602, Japan National Institute for Physiological Sciences, Myodaiji, Okazaki 444, Japan

Abstract Advances in fast MR imaging techniques enable us to visualize the dynamic movements of organs in living animals and humans. Esophageal contraction following the act of swallowing is one of the fastest movement in the gastrointestinal tract. In the present study we have tried to record the swallowing of a balloon by esophageal peristalsis of conscious rabbits. ‘H imaging of the esophagus was performed with a 4.7 T magnetic resonance spectrometer for animal studies (Biospec ABX 47/40, Bruker, Germany) with a bird-cage RF-coil (inner diameter of 20 cm). Japanese white rabbits (3.0 - 3.7 kg) were fixed firmly on an animal support in the prone position without anesthesia, and a pair of earplugs was applied to exclude noise from gradient coils. Median sagittal images were taken by a fast gradient-echo imaging (Snapshot) at 3 image&. Typical values used were as follows: field-of-view 22.5 cm, data matrix 96 x 96, spectral width 72 kHz, relaxation delay 3.4 ms, echo-time 1.9 ms, slice-thickness 6 111111, number of accumulation 1. A silastic tube (outer diameter 1.9 mm) with a balloon at the tip was inserted nasally into the upper esophagus and was placed just distal to the upper esophageal sphincter. The balloon was then inflated to 1 cm diameter by infusion of 0.6 ml of 0.3% (w/v) ferric ammonium citrate. The esophagus was clearly visualized from the pharynx to the esophago-cardia junction in the median sagittal image of rabbits. One to 10 s after inflation the balloon moved from the upper esophagus to the lower esophagus. The balloon often staged just proximal

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to the lower esophageal sphincter for two to five seconds and then moved into the stomach by the next peristaltic movement started from the upper esophagus. The calculated maximal velocity of the balloon was 8.3 c d s . Fast MR imaging allows us to observe clearly a rapid movement of a bolus along the entire length of esophagus during swallowing.

36.1 Introduction The esophagus is a hollow muscular organ whose primary function is to direct and propel food or fluid boluses from the pharynx into the stomach. Esophageal filling occurs during the pharyngeal swallow. Esophageal emptying is achieved through a sequenced peristaltic contraction progressing aborally in concert with appropriately timed relaxation of the lower esophageal sphincter. Fluoroscopy and scintigraphy are the two current techniques commonly applied to image the transit of a swallowed bolus and to determine the effectiveness of esophageal clearance. However, ethical considerations limit the repeated exposure of subjects to ionizing radiation. Magnetic resonance imaging (MR imaging) has been used as a noninvasive diagnostic tool in clinical medicine. Acquisition rates of conventional MR imaging, such as spinecho imaging and gradient-echo imaging, were too slow to allow visualization of rapid esophageal motility. Newer MR imaging scanning techniques, such as echo-planar and fast gradient-echo imaging, allow more rapid acquisition of images. These techniques have been applied to various areas in medicine. The purpose of this study is to visualize the passage of a bolus along the entire esophagus by MR imaging and to measure its speed in relation to the esophageal structure.

36.2 Method All the protocols were approved by the Ethical Committee of Nagoya University and the Animal Use Committee of the National Institute for Physiological Sciences and followed the guidelines of animal care and experiments of Nagoya University School of Medicine and the National Institute for Physiological Sciences.

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Studies were performed on five Japanese white rabbits of either sex, weighing 3.0 3.7 kg. The rabbit was firmly fixed on an animal support in the prone position without general anesthesia, and a pair of earplugs was applied to exclude noise from gradient coils. Intranasal anesthesia by lidocaine jelly were performed and a silastic tube (outer diameter 1.9 mm) with a balloon at the tip (cpcon Co. Ltd.) was inserted nasally into the upper esophagus and placed just distal to the upper esophageal sphincter. An initial scan was performed to determine the position of the esophagus within the thorax. The balloon was then inflated to 1 cm diameter by infusion of 0.6 ml of 0.3% (w/v) ferric ammonium citrate, and MR imaging scans were performed to determine the rapid movement of the balloon within the esophagus. MR imaging technique ‘H imaging of the esophagus was carried out using a 4.7 T magnetic resonance spectrometer for animal studies (Biospec ABX 47/40, Bruker, Germany) with a bird-cage RF-coil (inner diameter of 20 cm). Median sagittal images were taken by fast gradient-echo imaging (Snapshot) at 3 imageds. Typical values used were as follows: field-of-view 225 mm, data matrix 962, spectral width 72 kHz, relaxation delay 3.4 ms, echo-time 1.9 ms, s l i c e - h h e s s 6 mm, number of accumulations 1. A Gaussian RF pulse (1 ms duration, flip angle 7S0, band width 3 kHz) was used for excitation. The total MR imaging scans were 64 frames in this study. Data presentation and analysis The real time-domain image data were stored on a computer hard disk. Each image occupied 125 Kbytes of computer storage, thus for a 64 frame study, a total of 12 Mbytes was required. After the experiment, magnetic resonance images were reconstructed by two-dimensional Fourier transformation and displayed as a 2562 data matrix. Images could then be viewed by the ‘movie’ subroutine. Image data were also transferred to a Macintosh PC via Ethernet, and analyzed by the NIH image software. The velocity of the balloon was calculated by dividing the distance between two consecutive images of the balloon by the interval time (329 ms).

36.3 Result The esophagus was clearly visualized from the pharynx to the esophago-cardiajunction in a median sagittal image of a rabbit. Motion artifacts caused by cardiac contractions in a conventional gradient echo image (Fig. 36.la) were not seen in the snapshot image (Fig. 36.Ib).

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One to 10 seconds after inflation, the balloon started to move from the upper esophagus to the lower esophagus. The balloon often stopped just proximal to the loweresophageal sphincter for 1 to 5 s and then moved into the stomach on the next peristaltic movement started from the pharynx (Fig. 36.2). The calculated velocity of the balloon was 25 - 83 mm/s (Fig. 36.3).

Fig. 36.1: a) A median sagittal image of a rabbit by a conventional gradient echo method. Fieldof-view 225 mm, data matrix 1282, spectral width 72 kHz, relaxation delay 11 ms, echo-time 3.2 rns, slice-thickness 6 mm, number of accumulations 1. A sinc RF pulse (2 ms, flip angle 15'. band width 2.5 kHz) was used for excitations. The image was obtained with an acquisition time of 1400 ms. Note motion artifact (a) caused by cardiac contraction. b) A median sagittal image of a rabbit by snapshot imaging. A two dimensional image was obtain with an acquisition time of 329 ms for 962 pixel matrices. Respiratory and cardiac motion artifacts were not significant.

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Fig. 36.2: Sagittal images of a balloon moving along the esophagus every 329 ms. The balloon stopped just proximal to the lower esophageal sphincter for about 1 s (# 6 - 8) and then moved into the stomach on the next peristaltic movement started from the pharynx.

36.4 Discussion The rabbit esophagus is a muscular tube, about 17 cm in length, connecting the pharynx and the stomach. It is positioned between the trachea and heart ventrally and vertebrae dorsally. Thus, one median sagittal image of the rabbit, with 225 x 225 x 6 mm was sufficient to visualize the entire esophagus in this study (Fig. 36.1).

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0

5

10 15 20 Distsnoc from the epiglottis[cm]

Fig. 36.3: The velocity of a balloon at each point of the esophagus calculated from the images in Fig. 36.2.

Conventional clinical MR imaging uses relatively long echo-times and relaxation delays which may take several minutes to complete one image. Therefore, it is only suitable for the study of static organs. Imaging of organs that are characterized by periodic motion, such as respiration or the beating heart, can be obtained by synchronized data acquisition of the MR imaging scanner with, for example, the QRS signal of the ECG. The heart and respiratory rates of resting rabbits are reported to be 123 - 304 /min and 38 - 60 /min [ 11, respectively. In a conventional gradient echo image, with an acquisition time of 1400 ms,motion artifacts which may obscure the image due to cardiac contractions were present (Fig. 36. la). When acquisition intervals were shortened to 329 ms by a snapshot method, motion artifacts which may obscure the image above or below the heart were no longer seen (Fig. 36.1b). Thus, in the present study, we need not synchronize the MR imaging scanner with ECG or respiration. Cineradiography provides the best time resolution in visualizing the passage of the ingested bolus (30 frames/s) [ 2 ] , which is about 10 times faster than the present MR imaging. At present a rapid oropharyngeal movement can only be visualized by cineradiography. However, it requires contrast media to visualize the esophagus and no information on esophageal motility is available.

36. Fasi M R imuging of Esophageul Motiliy

40 1

Esophageal manometry using a slender bundle composed of several small-caliber catheters, each with a side hole several cm distance apart and perfused with water using a low compliance system, is another commonly employed method for the analysis of esophageal motility. Esophageal contraction can be detected as an elevation of the intra luminal pressure. Though this is a reliable method for diagnosis of motor disorders of the esophagus, it does not provide information about the passage of the ingested bolus. Thus, for the analysis of the passage of the bolus, these two methods have to be combined

WI. The present study clearly visualized the anatomical structure of the esophagus and its surrounding tissues as well as the movement of a balloon along the esophagus. As shown in Fig. 36.2, the position of the balloon when it stopped was easily identified in relation to the anatomical structure. Furthermore, its speed of movement can be calculated at each point of the esophagus (Fig. 36.3). In conclusion, we have shown that fast MR imaging can be used to record and quantify a rapid movement of a bolus along the entire length of esophagus during swallowing. This method will provide a new approach for the qualitative and quantitative assessment of the esophageal function.

Acknowledgment This work was supported by a grant from the Ministry of Education, Science, and Culture, Japan and was carried out as a Joint Research Project for magnetic resonance imaging and spectroscopy in the Natl. Inst. for Physiol. Sci. The authors thank Dr. V. Wray (Gesellschaft fuer Biotechnologische Forschung, Braunschweig, Germany) for editing the manuscript, and H. Okawara and M. Takagi (Natl. Inst. for Physiol. Sci.) for technical assistance.

References 1.

C. E. Adams, F. C. Aitken, A. N. Worden, The UFAW Handbook on the Care and Management of

Laboratory Animals, (1967) 396. 2.

M. Shimada, Nihonihoukuishi 53 (1993) 1040.

3.

E. G. Hewson, D. J. Ott, C. B. Dalton. Y . M. Chen, W. C. Wu, J. E. Richter, Gastroenterol. 98 (1990) 626.

4.

D. J. Ott, Y. M. Chen, E. G. Hewson, J. E. Richter, C. B. Dalton, D. W. Gelfand, W. C . Wu, Radiol. 173 (1989) 419.

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37. Spatial NMR Studies of Tumor Spheroids K. R. Minard', R. A. Wind', W. E. Maas2, K. Millis? and D. G. Cory4 1

Environmental and Molecular Science Laboratory, Battelle, Pacific Northwest National Laboratory, Richland, WA 99352, USA Bruker Analytical Systems, Inc., 19 Fortune Drive, Billerica, MA 01821, USA Cambridge Isotope Laboratories, 50 Frontage Road, Andover, MA 01810, USA Department of Nuclear Engineering, Massachusetts Institute of Technology, Cambridge, MA 02 139, USA

Abstract Spatial NMR measurements can take many forms, from direct measurements of spatial properties via imaging through indirect determination of average load probabilities via diffusion through susceptibility variations. Here, a variety of spatial NMR studies of multicellular lung tumor spheroids are presented. In the current context, the spheroids primarily served as a well structured model system of spatially heterogeneous, biological tissue. The avascular growth of spheroids in vitro results in a central necrotic region due to a local deficiency of oxygen and nutrients. Spatial heterogeneity is easily seen in highresolution NMR images of water acquired with either T2 or diffusion weighting. However, compared with proton spectra acquired from a homogeneous liquid, spectra acquired from spheroids exhibit rather poor resolution due to local variations in the bulk magnetic susceptibility arising from their heterogeneous microstructure. Even so, we demonstrate that pronounced regional differences can still be observed using small-volume localized spectroscopy. We also show that high resolution, magic angle spinning (MAS) may be used to remove the susceptibility broadening, thereby permitting the observation of additional spectral features. Furthermore, since the necrotic center of the spheroid is more fluid than the surrounding shell of viable cells, diffusion-weighted MAS spectroscopy may be useful as a simple means of differentiating between spectral contributions that arise from different fluid compartments. In contrast with a static

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K . R. Miturd, R. A. Wind, W. E. Moos. K . Millis. and D.G. Cory

measurement, quantification of molecular diffusion is unaffected by the existence of large, susceptibility-induced field variations provided magnetic field gradients are applied along the spinner axis.

37.1 Introduction One of the strengths of NMR is the tremendous flexibility in defining experiments. Typically this freedom has been used to control effective Hamiltonians to establish either a clean coherence pathway selection, or to make a small interaction observable by suppressing an overwhelming one. A very similar approach may be employed to selectively measure spatial properties of complex heterogeneous samples. This is particularly promising in the case of biological tissue where samples are spatially well structured, and their function is tied to structure and compartmentalization. Here we explore a variety of means of extracting spatial information via NMR both directly, in terms of an image, and indirectly via the susceptibility interaction and molecular diffusion. Tumor spheroids are used as a model system. Multicellular tumor spheroids are used as in vitro models to study avascular tumor growth, the effects of therapy, and to monitor the kinetics of tumor invasion [ 1,2]. It is found that when spheroids grow, the lack of oxygen and nutrients in the spheroid center causes cell death and necrosis in the center. Several regions can be distinguished in a spheroid: a necrotic center, surrounded by an outside viable rim, which is further divided as an outside layer containing proliferating cells, and one or more inner layers containing non-proliferating cells in different stages of starvation. NMR microscopy has been used successfully to visualize the viable rim and the necrotic center in a non-invasive way, investigate regional differences in the distribution of intra- and intercellular water and monitor the kinetics of tumor invasion [2-51. Volume localized spectroscopy is a logical extension of imaging since it makes it possible to study metabolic changes in deceased tissues and the effects of therapy. These are observed as intensity variations in several cellular compounds such as choline and mobile lipids which have been linked to tumorgenisis, increased proliferation of cells, cell apoptosis, and necrosis [6-81. In this work we have explored spheroids grown from a V79 lung tumor. The spheroids were cultured from Chinese hamster V79 lung tumor cells, and spheroid growth was initiated by plating cells from confluent cultures in bacteriological plates.

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After 48 hours, the spheroids were transferred to a 500-ml spinner flask and stirred at 50 rpm. After 5 days, spheroids typically had diameters between 500 and 900 pm. The 1H microscopy and volume localized spectroscopy were measured on a Varian 500 MHz UNITY Plus spectrometer equipped with an imaging accessory, and a micro-imaging probe built at MIT and described in the literature [9]. Prior to measurement, spheroids were removed from their spinner flask, immobilized in 1.0% low melting point agarose gel made with the minimal essential media supplemented with 10% fetal bovine serum and antibiotics, and placed in 1.2 mm (i.d.) glass sample tubes. To preserve the spheroids as much as possible, the sample temperature was maintained at about 12 "C. At this temperature, no noticeable changes in the images or spectra were observed during the first 12 hours. Images were acquired using a 2D spin echo sequence, and localized spectroscopy was performed using STEAM to select the regions of interest. The magic angle sample spinning and diffusion measurements were performed at MIT in a gradient, high resolution MAS probe on a Bruker DRX-500 spectrometer. The samples were flown from Richland to Cambridge stored at about 4 "C and run immediately.

37.2 Microscopy Figure 37.1 shows 'H images of a spheroid with a diameter of about 760 pm, with various echo times. At even a relatively small echo time of 4 ms the diffusion weighting is sufficiently large to distinguish the spheroid from its surroundings (water in the agarose gel diffuses practically as free water). Increasing the diffusion weighting with an echo time of 11 ms makes it possible to observe the necrotic center of the spheroid, and two regions within the outer ring become visible when the echo time is further increased to 50 ms. These are probably associated with proliferating and non-proliferating tumor cells [ 11. It was established that the contrast between these outer regions is mainly due to T, differences and not differences in diffusion. This is a further indication that the cells on both layers are intact.

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Fig. 37.1: 2D proton images of a 5-day-old, V79 tumor spheroid with a diameter of - 760 pm, Images were obtained with different TE values - 4 ms (A), 1 I ms (B), and 50 ins (C). In all cases, FOV= 1.3 x 1.3 mm2; slice thickness = 200 p;in-plane resolution 10 x 10 km2; TR = I s; for A and B 2 transients were added, while C was obtained with 16 averages.

37.3 Spectroscopy 37.3.1 Static Spectra Figure 37.2A shows the 'H image of a second spheroid with a similar size as that in Fig. 37.1 and displaying similar features. Also shown in this figure are the 'H (water suppressed) spectra of the whole spheroid and of its necrotic center. Several resonance lines can be distinguished, which are due to a variety of low-molecular weight, mobile compounds. The line at 3.8 ppm arises from the protons in alkyl groups bound to oxygen or nitrogen and present in a variety of amino acids and other metabolites. The resonance at 3.2 ppm originates from the methyl groups of trimethylamine bearing metabolites present in e.g. phospholipid precursors and degradation products (usually called the choline line). The line at 2.9 ppm arises mainly from the methyl groups in the energy metabolites creatine and phosphocreatine. The resonances at 2.3 and 2.1 ppm are due to methylene groups in glutamate, glutamine, and in mobile lipids; and the resonances at 1.3 and 0.9 ppm originate mainly from the methylene chains respectively methyl endgroups in triglycerides and other mobile lipids [ 10,l I]. As seen in Fig. 37.2, the necrotic center is composed mainly of mobile lipids and the other metabolites are predominantly concentrated in the viable rim.

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-

Fig. 37.2: T2-weighted image of a V79 tumor spheroid with a diameter of 720 pm (A), and proton MRS spectra of the whole spheroid (B) and of its necrotic center (C). Image: FOV = 1.3 x 1.3 mm’; slice thickness = 300 pm; in-plane resolution = 10 x 10 pm*; TR = 3 s; T E = 23 ms; NEX = 2. Spectra: TR = 4 s; NEX = 256 (B); NEX = 1024 (C); ROI = 720 x 730 x 700 p 3 (B); ROI = 260 x 260 X 260 pm3 (C). For the spectra a Lorentzian broadening of 20 Hz was applied.

An additional series of spectra is obtained from another spheroid and displayed in Fig.

37.3. Data were obtained both immediately and one day after the spheroid was placed in a sample tube. A comparison between Fig. 37.3B and C shows that the intensity of the resonance at 1.3 ppm has decreased considerably. This may explain why the spectrum of the necrotic center shows no lipid lines unlike that shown in Fig. 37.2 (acquired within 12 hrs of sample preparation). The reason for the decrease in the (mobile) lipid intensity with time is still under investigation.

37.3.2 High Resolution, MAS Spectra Recently a number of NMR studies have been reported in which magic angle sample spinning (MAS) was applied to increase the resolution of spectra from non-solid materials, including examples of tissue [ 12-14]. While such samples generally have sufficient mobility to average part of the anisotropic interactions, the spectral resolution for the static samples are still much lower than that which is achieved for liquid samples, primarily due to the excess broadening from local variations in the bulk magnetic susceptibility. As described by Garroway [ 151 and shown in the above studies, MAS is efficient at averaging these local field variations and leads to NMR spectra that display resolution approaching that of liquid samples.

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ll

L

Fig. 37.3: Proton image (A) and MRS spectra of the whole spheroid after 2 hours (B) and one day (C) in the sample tube, and of three selected regions 1, 2, and 3 (D, and E, and F, respectively) within the spheroid. The regions are indicated in the image shown in Fig. 37.3A. Spectra shown in D - F were all acquired after the spheroid was in the tube for one day. Note the decrease of the lipid resonance at 1.3 ppm after the spheroid has been in the sample tube for one day.

Preliminary experiments have shown that both the structural integrity and the viability of the spheroids can survive spinning. Although more work is needed to investigate this issue in more detail, this result indicates that MAS is a promising approach to enhance resolution in a non-invasive way, even in relatively large cellular agglomerates such as multicellular spheroids. Figure 37.4 shows the 'H spectrum of a number of spheroids contained within a MAS rotor and spun at 2.5 kHz. Notice the much higher resolution of this spectrum compared to those in Figs. 37.2 and 37.3. Some of the sharpest resonances are presumed to arise from metabolites in the agarose media, which are so mobile that they even display resolved scalar couplings. These are not observed in the volume-localized spectra shown in Figs. 37.2 and 37.3, since the localization excluded the major part of the spheroid surroundings.

37. Spatial NMR Studies of Tumor Spheroids

5.5

5

0

d

5

4

0

1.5

3

0

: . 5

2

0

1.5

1 . 0

409

p p m

Fig. 37.4: 500 MHz Magic Angle Spinning proton spectrum of spheroids, obtained at a spinning speed of 2.5 kHz.

37.4 Pulsed Gradient, MAS Diffusion Measurements In removing selectively the excess linebroadening arising form susceptibility variations in the sample the spatial selectivity of the original measurement has been lost, and it is correspondingly difficult to relate the spectral features back to the structure of the sample. While conceptually it is possible to combine MAS and volume localized spectroscopy the experiment is challenging and has not been implemented. An alternative approach is to use local variations in molecular mobility as a marker for compartmentalization. These differences are easily revealed via the pulsed gradient diffusion sequence, as was already evident in the images of Fig. 37.1. Figure 37.5 shows a series of diffusion weighted MAS spectra. Compared to Fig. 37.4, first the small metabolites and water are attenuated so that many of these resonances that arise from the growth media and agarose disappear. The resonances in the lower spectra with higher diffusion attenuation arise from the spheroids. We expect that the necrotic core is more fluid than the viable surrounding cells and so the intermediate changes seen with increased diffusive weighting include large contributions from this core, but challenges of sample handling from Richland to Cambridge have so far prevented a complete analysis.

410

K. R. Minard, R. A. Wind, W. E. Maas, K. Millis, and D. G. Cory

It follows from Figs. 37.2 - 37.5 that regardless of the amount of diffusion weighting the spectra obtained with MAS show superior spectral resolutions compared with the spectra measured in the static samples, illustrating the potentials of the MAS technique.

I " " I " " I " " I " " 1 " " 1 ' " ' 1 " ' ' ~ " " ~ " " ~ ' ' " ~ " ~ ' '

5.5

/

'

"

'

I

'

"

'

l

'

5.5

I

"

"

l

"

"

5.5

4.5

5.0

'

'

'

I

"

I

'

"

'

"

5.0

"

l

'

'

'

4.5

5.0

'

'

'

I

4.5

3.5

4.01

'

I

"

"

l

'

"

'

~

'

4.0

'

'

'

"

I

'

"

3.5

2.5

3.0

2.5

'

1

3.5

4.0

3.0

'

"

"

~

3.0

'

"

'

~

2.5

2.0

'

"

'

~

"

1.5

"

1

'

'

2.0

'

'

'

'

~

2.0

"

'

1.0

pprn

1.5

1.0

pprn

1.5

1.0

ppm

"

"

'

'

~

"

Fig. 37.5:500 MHz MAS proton spectra of spheroids, obtained at a spinner speed of 2.5 kHz. The spectra are obtained with diffusion weighting using a stimulated echo sequence. The diffusion weighting increases from top to bottom.

37. Spatial NMR Studies of Tumor Spheroids

41 1

37.5 Conclusions We have shown in preliminary studies that a variety of absolute and local measurements of spatially resolved NMR can reveal details of structure and function of spheroids. In ongoing work, the variation of metabolism across the shell of viable cells will be interesting.

Acknowledgments The Pacific Northwest National Laboratory is a multiprogram laboratory operated by Battelle Memorial Institute for the U.S. Department of Energy under contract DE-ACO676RLO 1830. The work at MIT is supported by DOE, the Whitaker Foundation and NIH (RR-00995).

References 1.

W. Mueller-Klieser. J. of Cancer Res. and Clin. Oncol. 113 (1987) 101.

2.

R. M. Sutherland. Science 240 (1988) 177.

3.

L. 0. Sillerud, J. P. Freyer, M. Neeman, and M. A. Mattingly, Mugn. Res. in Med. 16 (1990) 380.

4.

M. Neeman, K. A. Jarrett, L. 0. Sillerud, and J. P. Freyer, Cancer Research 51 (1991) 4072.

5.

M. Brandl, J.-C. Tom, K. Kotitschke, R. Goldbrunner, S. Kerkau, and A. Haase, Magn. Res. Med. 34 (1995) 596.

6.

P.F. Daly and J. S . Cohen, Cancer Research 49 (1989) 770.

7.

B. D. Ross, MMR in Biomedicine 5 (1992) 215.

8.

W. Negendank, NMR in Biomedicine 5 (1992) 303.

9.

S. M. Choi, X. Tang and D. G. Cory, The Internarional Journal of Imaging System and Technology 8 (1997) 263.

10.

A. C. Kuesel, G. R.Sutherland, W. Halliday, and 1. C . P.Smith, NMR in Biomed. 7 (1994) 149.

11.

W. Willker, J. Engelmann, A. Brand, and D. Leibfritz, J. of Magn. Reson. Analysis 2 (1996) 21.

12.

W. E. Maas, F. H. Lauken, and D. G. Cory, J. Am. Chem. SOC.118 (1996) 13085.

13.

K. K. Millis, W. E. Maas, D. G. Cory, and S . Singer, Mag. Res. in Med. 38 (1997) 399.

14.

L. L. Cheng, C. Lean, A. Bogdanova, S. Wright, J. Ackerman, and R. G. Gonzalez, Mag. Res. in Med. 36 (1996) 653.

15.

A. N. Garroway, J . Magn. Reson. 49 (1980) 168.

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38. 19FChemical Shift Imaging of F-nuc Formed from 5-FU in Mouse Tumor by Fast Spin Echo Yoshihiro Doi and Yoko Kanazawa Faculty of Pharmaceutical Sciences, Kyushu University, Fukuoka 812-8582, Japan

Abstract I9F NMR image was obtained from the effective metabolites of anti-tumor drug 5-FU for the first time. In order to obtain metabolic images from drugs of very low concentration in tissue, high magnetic field 9.4 T was used. Fast Spin Echo (FSE) with alternate chemical shift selection was successful for the present system. Sufficient image quality was obtained by FSE under a proper scan trajectory. However, multi line imaging by FSE will be of limited use for the signal of short T2. We also showed a new method for the simultaneous evaluation of T2 with FSE imaging.

38.1 Introduction In vivo monitoring of drug dynamics by NMR is a promising method for the new drug exploitation and for clinical dose control. MRS has been used extensively on the established anticancer drug 5-FU and its prodrug in vitro [ 11 or in vivo [2]. Metabolite mapping by NMR imaging will be further advantageous for the same purpose. I9F imaging of

5-FU and its catabolite F-P-alanine (FBAL) in rat has been reported by Brix et al. where the individual image from these 2 compounds have been acquired subsequently by gradient recalled echo with a chemical shift selective pulse [3]. We have shown a simultaneous imaging of 5-FU and FBAL+F-ureido-propionic acid (FUPA) in mice by using interleaved chemical shift selected spin echo [4].However, these methods give only a part of drug information, catabolism. For the evaluation of 5-Fu and its prodrugs, it is important to monitor F-nuc, the effective metabolites of 5-FU consisting of nucleoside

414

Y. Doi and Y. Kanazuwu

and nucleotide forms of 5-FU giving a I9F signal in the close vicinity of 5-FU. To the best of our knowledge, the image of F-nuc has not been obtained supposedly because of its short T2 and of lower concentration. Here, we report the first 19F image of F-nuc in mouse tumor. From the requirement for imaging with the NMR signal of weak intensity, which is intrinsic to pharmaceuticals in vivo, high magnetic field of 9.4 T was used. Among many methods for rapid data acquisition, fast spin echo (FSE) was used here because gradient recalled echo is not favorable for a distribution map from a small object at high field. More sophisticated sequences were not chosen because of rather short T2 which often applies to drugs in wiwo. Fast spin echo with chemical shift selective rf pulses was compared with a standard method of spin echo (SE). The method of simultaneous measurement of T2 and image by fast spin echo is also proposed.

Fig. 38.1: 19F in vivo Spectrum of a 5-Fu administrated mouse with a 12 mm surface coil at lower abdomen. 9.4 T (376 MHz), C3H mouse with MH134 as ascitic tumor, 1 mmol/kg 5-FU p.0. [4].

38.2 Methods Female C3H mice were transplanted with MH134 cells as subcutaneous tumor 1 - 2 weeks prior to the NMR experiments. After 3 - 4 hours fasting, 1 or 2 mmol/kg of 5-FU was administrated orally as the solution in a CMC suspension. NMR imaging was performed under halothane anesthesia on the Varian Unity-INOVA with a 9.4 T vertical magnet and 19F/'H tunable 40 mm rf coil tuned to 376 MHz for 19F. Rectal temperature was monitored by a fluorescent probe during NMR measurements. After 'H scout image and 19Fspectrum, 19F chemical shift selected images were obtained by either spin echo

38. I9F Chemical Shift Iniaging of F-nuc Formed from 5-FU in Mouse Tumor by Fast Spin Echo

415

or fast spin echo with FOV of 8 x 4 cm2 without slice selection and 64 x 16 data points, TR = 1.0 s and TE or echo spacing (esp) of 3 or 6 ms. Simultaneous acquisition of 3 or more signals were achieved by the alternate data sampling using both chemical shift selective d 2 and K pulses (TEor esp = 6 ms) [5] as in Fig. 38.2. In order to obtain an image of F-nuc efficiently, non selective pulse was used for refocussing to make TE or esp (3 ms) shorter, abandoning the information of the other signals. Tissues were excised immediately for the metabolite quantification by I9F NMR [6].

38.3 Results In vivo T2 obtained by CPMG method using volume coil were in the wide range of 15 30 ms for F-nuc, 20 - lo00 ms for 5-FU, 15 - 30 ms for FUPA and 30 - 100 ms for FBAL whereas Tl’s order of 1 s for F-nuc, 2 s for FU, 2.5 s for FUPA and FBAL. The 2D imaging of F-nuc, as well as FU and FUPA+FBAL, was successful by spin echo and also by fast spin echo especially with a short T, or esp of 3 ms (Figs. 38.3 and 38.4). The spatial information of F-nuc distribution by FSE was comparable to that of SE of common TE and esp (Figs. 38.3b and c, Figs. 38.4b and c): Considerable reduction in the accumulation time was attained by the use of FSE without loosing image quality. The metabolite mapping under lower dose (1 mmol FUkg) was also successful by FSE as seen in Figs. 38.5 and 38.6. The image of F-nuc with esp = 3 ms had a better quality compared with esp = 6 ms as anticipated from the in vivo T, value of 15 - 30 ms (Figs. 38.5b and c or d, Figs. 38.6b and c). Single shot FSE could also be applied to the system (Fig. 38.6). In vivo T, was determined from the k-space intensities obtained by the 2-shot FSE as shown in Fig. 38.7, while the real space images were obtained by the addition off+ 1 and f - 1 runs. The intensity ratio of lStand 9h phase encoded data combined with the other order as (38.1) gives T,. The T2’s obtained by FSE were consistent with CPMG data. (38.1)

The effect of high rf pulse density due to repeated K pulses of FSE in the present conditions (esp = 3 ms, or 6 ms with multiline observation) as evaluated by the measurement of rectal temperature during data acquisition was below the detection limit.

416

Y. Doi and Y. Kutmmwu

k-space data

Single Line Selection Te. esp = 3 ms

I I

I

Spectrum

k-space data

'O

k-space data

Fig. 38.2: Chemical shift selected SE and FSE with sequential orders used in this work.

9F ,.......

mm 15

0

FU

FUPA+FBAL

'H

.,.,,Ci"

a

-30 m

-15

F-nuc

F-nuc

Tumor Liver

42 minSE, 63 min)

.................. 15

0

-30 m

-15

b

. 4 J L C 15

0

-15

(.'*I....................................

-30 m

p,

-k 15

-15

x 1R

F-nuc FU FUPA + FBAL

C

.................. p m :.

0

Conc. in Excised Tissudw rnoVkg

,.,.11'

225 min(FSE, 80 min)

i

Stomach

.b1+

124 rnin(SE, 51 min)

FBAL

Rmwyn7

jlll.l*,,,

Intestine 130 520 4.7 h after 2 mmoVkg p.0. Mouse I.D.DH86

-30 m

Fig. 38.3: 19F in vivo spectra, chemical shift selected images (coronal) by SE and FSE of 5-FU and metabolites and 1H image of MH134 bearing female mouse administrated with 2 mmol/kg of 5-FU.19F spectra were taken in between 19F images to show the rough idea of metabolic rate. The starting time of 19F image after the drug administration and the duration of sampling were shown in min. a) Multiline selected SE, TE= 6. b) Single line selected SE, TE = 3. c j Single line selected 2-shot FSE, esp = 3 ms. (2-shot FSE:f+ 1 andf- 1 FSE data were combined for real space image.) Final concentrations of the metabolites in the tissues determined after the imaging were tabulated.

417

38. "F Clicmicul Shift lniuging of F-tiiic Formedfroni 5-FU in Mouse Tumor by Fasr Spit1 Echo W\

!

-. /,I

15

0

'H

'9F

FUPA

F-nuc

-",-

-15

-30

FU

FUPA+FBAL

a

~m

Tumor Liver

35 min(FSE, 40 mln)

F-nuc

\

J u i Stomach 15

0

-15

-30 wm

15

0

.15

-30 Ipn

Conc. in Excised Tissudw moVkg F-nuc FU FUPA+FBAL Tumort,, 550 200 N.D. Tumorbotom 350 200 200 Liver 400 N.D. 2500 4.0 h after 2 mmoVkg p.0. Muse I.D. DH87

C 157 min(FSE, 66 min)

F-nuc

Fig. 38.4: 19F in vivo spectra, chemical shift selected images (coronal) by SE and FSE of 5-FU and metabolites and IH image of MH134 bearing female mouse administrated with 2 mmovkg of 5-FU. a) Multiline selected FSE, TE= 6. b) Single line SE, TE= 3. c) Single line 2-shot FSE, esp = 3 ms. The image quality of c was better than that of b showing the success of FSE.

7 k'"'"

F-nuc

r n y - s ' ~ 15

0

15

WJ

0

15

30

-

FUPA+FBAL

4""

Tumor Liver

3640 mlnmln)

m15

FU

a

-30 m

F-,,jJzesw,

'H

9F

nJW+.+

1

8

b

Stomach

I _111.**/jcrJle.p=3,30 87 mlnmln)

15

0

-16

-30 wm

C

Conc. in Excised Tissue ILL moVkq Fnuc 5FU FUPA + FBAL TU,,

350

40 250 30

N.D.

TULiver

100

1000

25

N.D.

5.5 h afler 1 mmoVkg p.0. Mouse I.D. DHS5

Fig. 38.5: 19F in vivo spectra, chemical shift selected images (coronal) by 2-shot FSE of 5-FU and metabolites and 1H image of MH134 bearing female mouse administrated with 1 mmovkg of 5FU.a) Multi line selected, esp = 6. b) Single line selected, esp = 3. c,d) Multi line selected, esp = 6 ms. Starting time, esp and acquisition periods were shown next to each image.

418

Y. Doi and Y. Kanaznwa

F-nUC

{:> 0

15

-15

-30

FU

FUPA+FBAL

a

ppn

Tumor

Liver Stomach

C ."_." ............. 0

15

-15

-30

!&use 1.0. DY97

ppn

Fig. 38.6: 19F in vivo spectra, chemical shift selected single shot (centric) FSE images (coronal) of 5-FU and metabolites and 1H image of MH134 bearing female mouse administrated with 1 mmovkg of 5-FU.a) Multiline selected, esp = 6. b) single line selected, esp = 3. c) Single line selected, esp = 6 ms.

t

1~

Image

f-1

f+l

F-nuc

FU

FUPA+FBAL

Fig. 38.7: The T2 determination from the k-space data of FSE with the sequential order off- I and f+ 1. a) Definition of 2 sequential orders for erl = 16. b) Intensity projection of k-space data. c) kspace data. d) Images in the real space. T2: (F-nuc) = 25 - 35, (5-FW) = 20 - 40, (FUPA+FBAL) = 30 - 50 ms.

38. 19F Chemical Shifr Inmging of F-nuc Formed front 5-FlJ in Mouse Tumor by Fasr Spin Echo

419

38.4 Discussion The 19F image of F-nuc was obtained by using a short echo time of 3 ms both by SE and FSE. By the use of FSE in 2-shots, images of metabolites were obtained almost 8 times efficiently than by SE. As anticipated, long esp in FSE or TE in SE affected image quality (cf. esp = 3 vs. 6 ms) for the short T2 signal. Therefore, it was preferable to use single line selected image with esp = 3 ms rather than multiple line selected images with esp = 6 ms for the metabolites with T2 shorter than ca. 4 esp. In general, nevertheless, SNR gained by the multi line acquisition seemed to overcompensate the effect of T2 decay during the echo train length resulting in the better visibility of drug metabolites at low concentration. Thus, we could reduce the dose to 1 mmol/kg. We showed a new method of in vivo T2 determination from FSE image data, utilizing k-space data, without taking extra observation time for the purpose. In the case of 5-FU, where T2, not T,, was not a constant through the sites and time, which may be due to the effect of drug environments, this method should be of use. In the present experiment, rf heating during the repeated TC pulses of FSE was below the detection limit. FSE was shown to be an appropriate sequence for the imaging of weak signals of drugs in small animals at high field. Considering the serious side effect of 5-FU known to be caused by the excess formation and retention of F-nuc from 5-FU or its prodrugs [7], the chemical shift imaging information on F-nuc will be useful as the guide to clinical dose control for individual patient.

Acknowledgements This work was partly supported by the Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture, Japan.

References 1.

W. E. Hull, R. E. Port, R. Harmann et al., Cancer Res. 48 (1988) 1680.

2.

A. N. Stevens, P. G. Moms, R. A.Iles, et al., Br. J. Cancer. 50 (1984) 113.

3.

G. Brix, M.E. Bellemann et al., Magn. Reson. Med.34 (1995) 302.

4.

Y. Doi, Y. Kanazawaet al., Proc. 5th ISMRM, Vancouver, Canada 3 (1997) 1083.

5.

M. Narazaki and Y. Kanazawa, 25th JMRM Meeting, Omiya, Japan (1997) 41.

6.

Y.Kanazawa, H. Yamane, S. Shinohara et al., J.Neurochem. 66 (1996) 21 13.

7.

For example, C. Desgranges et al., Cancer Res. 48 (1986) 1094.

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39. "0 and 31PMagnetic Resonance Imaging and Spectroscopy: In Vivo Investigations of Cell Bioenergetics Gheorghe D. Muteescu. Marc0 Cabrera, and Dart Fercu

Department of Chemistry, Case Western Reserve University, Cleveland, Ohio 44106-7078, USA

Abstract This paper describes 170/ 31P magnetic resonance spectroscopy (MRS) and I7O imaging (MRI) as a noninvasive bioanalytical method for in vivo determination of oxihtive phosphorylation (OXPHOS) and evaluates its potential application in studies of OXPHOS uncouplers or inhibitors such as physical factors (temperature, pressure, etc.), anesthetics, drugs, and DNA mutations (degenerative diseases). Preliminary results suggest that chloroform poisoning affects the complex V of the mitochondria1 respiratory chain. Similar effects are observed in organisms subjected to excessive temperature.

39.1 Introduction In mitochondria (Fig. 39.1) the reaction of oxygen with substrate hydrogen provides the free energy required for physiological function of tissues and organs [ 141. This energy is stored in adenosine triphosphate (ATP) via phosphorylation of adenosine diphosphate (ADP). The water formed in these coupled reactions,

(4Hf + 0, + 4e- -3 2H,O)-(ADP

+ ATP)

is generally known as water of oxidation, or simply metabolic water. We call it nascent mitochondrial wafer in order to emphasize its time and place of formation. Normally, the rate of oxygen utilization is proportional to the energy consumption (ATP hydrolysis) in

422

G. D.Maieescu. M. Cabrera, and D.Fercu

the tissue and it is thus an important indicator of the physiological and pathophysiological state of the organism. Any factor or process diminishing the mitochondria1 energy output below a critical threshold will lead to temporary or irreversible impairment of the function of tissues, organs, or of the entire organism. Indeed, extensive iri vitro experiments with isolated mitochondria have shown that various chemical agents can be uncoicplers or inhibitors of the OXPHOS reactions. For example, protonophores such as carbonyl cyanide p-trifluoromethoxyphenylhydrazone (FCCP) and oleic acid iiizcoiiple OXPHOS by increasing the inner membrane conductance. In addition, oleic acid has a inhibitory action on both the ATPase and the electron-transfer enzymes. However, the overall enhancement of electron transfer is not entirely accounted for. The presence of specific binding interactions to the energy transducing enzymes is therefore invoked. On the other hand, chloroform can fully inhibit ATP synthesis while causing only a slight increase of membrane conductivity. Its action cannot be explained by the classical chemiosmotic hypothesis [4]. Prolonged exposure to respiratory decouplers and inhibitors (dinitrophenol, cyanide, sodium azide) results in hearing and vision impairment, ataxia, myoclonus, seizures, etc. [ 5 ] .

NADH

1 1 \

1

112''O2+

2e

-

17 H2 0

Outer Mitochondrlal Membrane

Fig. 39.1: Schematic representation for OXPHOS. The oval and mushroom features within the inner mitochondrial membrane represent subgroups of the five respiratory complexes: I - IV are oxidative (electron transfer) complexes (I-NADH dehydrogenase, 11-succinate-CoQ reductase, IIIcoenzyme Q-cytochrome reductase, IV-cytochrome oxidase) and V contains the ATP synthase (one ATP per electron-pair). Up to 12 protons may contribute to the prorori motive force. Even though much progress has been done so far, the complexity of OXPHOS still remains incompletely known.

39. 170and 3'P MRI and Spectroscopy: In Vivo Investigations of Cell Bioenergetics

423

During the past few years increasing evidence has been accumulated regarding the connection between nuclear (n) and mitochondrial (mt) DNA mutations and aging and degenerative diseases (e.g., Alzheimer and Parkinson diseases, ischemic heart, late-onset diabetes, mitochondrial myopathy) via mitochondrial dysfunction [5]. A known cause of mutation is the formation of oxygen radicals. These damage the mtDNA sixteen times more than nDNA. In rats, aging has been associated with accumulation of oxidative damage of mtDNA [5]. Both nDNA and mtDNA encode proteins which are constituents of the electron transfer and ATPase complexes. For example, in humans seven of the 25 - 30 polypeptides of the respiratory complex I are encoded by the mtDNA and of the 12 - 14 polypeptides of complex V, two are encoded by the mtDNA. Mutations in the corresponding DNAs will result in altered polypeptides which will no longer perform the normal electron transfer or ATP synthesis. If complex I is affected, the rate of formation of mitochondrial water will drop. If complex V is affected, the ATP synthesis will diminish while the metabolic water generation may take one of the three possible courses: unchanged, enhanced or inhibited. No analytical method is known for simultaneous, in vivo determination of nascent mitochondrial water and ATPase activity. The methods currently available for the measurement of oxygen consumption, Kety-Schmidt [6] and positron emission tomography, PET [7] are invasive and do not address uncoupling. In vivo and in vitro determination o f oxygen consumption via 170-MRS [8] has been reported in recent years in small vertebrates [9-111. However, we chose to conduct preliminary 170/31P-MRSinvestigations on very small invertebrates (Tenebrio molitor larvae) in order to be able to perform in uncomplicated manner a large number of experiments at a much lower cost. We present here preliminary results of simultaneous measurements of nascent mitochondrial H2I70 and phosphate metabolites in Tenebrio molitor larvae (meal worm) and a discussion of their significance with regard to mitochondrial function.

39.2 Experimental Methods Tenebrio molitor larvae were obtained from a pet shop. For a given series of experiments very similar specimens were selected. Molecular 1702was prepared by electrolysis of H,O enriched to 37 - 45 atom % I7O (ISOTEC Inc., Miamisburg, Ohio). Enriched air

424

G. D.Mateescu, M. Cabrera, and D.Fercu

with or without chloroform vapors was circulated by a Buchler (Monostaltic@)pump in a respirator fitted in an open-ended 10 mm NMR tube. Interleave 170/31PMRS was performed on a Varian Gemini-200 spectrometer with a double tuned (27/80MHz) Doty probe. For I7O, 6000 scans were taken with 20 ms acquisition time (AT) and no pulse delay (D). For P-31, 5 12 scans were taken with AT = 0.5 s and D = 0.5 s. Microimaging was performed on a Bruker MSL - 400 system (5 mm tube in a probe with built-in x,y,zgradients). A 128 x 128 FLASH image (2.5 mm xz-coronal slice; z-phase encoding in 64 increments; TE = 1.5 ms; TR = 7 ms; NS = 12;NR = 256; FOV = 15 cm; a = 90") taken at the end of the experiment described in Fig. 39.3 is shown in Fig. 39.2. With T , = T2 c 4 ms this is a (170) spin density image which, in spite of the low resolution (yH/yo = 7.37) clearly reveals the unequal distribution of the labeled water within the body of the larva. It appears that the largest amount of H2I7O is found at the site of the largest mass of nervous tissue, which is known to have the highest rate of oxygen consumption.

Fig. 39.2: 1 7 0 image of a 2.8 x 20 mm larva.

The rate of oxygen consumption, MRO, (pmoVmin.g) is given by: pH20

MRO, =-

2w

(39.1)

where W is the weight of the larvae and PHZO is the rate of production of metabolic water

39. I7O and j l P MRI and Specrroscopy: In Vivo Investigations of Cell Bioenergetics

425 (39.2)

The fraction y of nascent mitochondrial water is given by

P =

SlPO - 1 k-1

(39.3)

where So is the integrated intensity of the natural abundance signal, S, is the signal at time t after starting the 1 7 0 2 respiration and k, the isotopic enrichment. MHz0 is the molar body water of the larvae determined by spiking with natural abundance water: (39.4)

where Ws is the weight of the spiking (added) water, So is the natural abundance signal and S, is the intensity of the signal after addition of spiking water.

39.3 Results and Discussion These experiments are based on the outstanding tracer properties of 170. Indeed, compared with natural abundance (0.037%), even modest enrichments lead to reductions of measurement times by two or three orders of magnitude. The natural abundance 170signal constitutes an excellent reference for quantitative measurements. This is illustrated in Fig. 39.3. Typical 31P spectra are shown in Fig. 39.4. The time-course of formation of mitochondria1 water in larvae breathing 170-enriched air in the presence and the absence of chloroform is shown in Fig. 39.5. The simultaneous evolution of inorganic phosphate, phosphoarginine and P-ATP is shown in Fig. 39.6 and 39.7. It is seen that chloroform enhances the oxygen consumption, but at the same time it is inhibiting the formation of ATP. According to previous observations [4,5] such a pattern indicates inhibition at the level of the respiratory complex V. This wasteful oxidation reveals the loss of respiratory control which ensures the efficient coupling between ATP synthesis and oxygen consumption ( P I 0 ratio). Similar effects are observed when the temperature of the body is increased considerably above 35 "C.This is shown in Fig. 39.8.

426

G. D.Mnteescu. M. Cabrern. and D.Fercu

After breathing

Control Naturai Abundance 0.037%(-20 mM)

. . , .

m Fig. 39.3: Oxygen-17 spectra of Tenebrio molitor after breathing 1702-enriched air mixed with chloroform vapors.

10

,

.

0

.

I

,

-20 ppm

-10

Fig. 39.4: P-31 spectra during the same experiment as in Fig. 39.3. SP = sugar Phosphates; Pi = inorganic phosphates; PA = phosphoarginine.

1.molitor (017 + CHC13)

T. molitor (017 only)

F & a

i

Natural Abundance (0.037%)

20 0

300

600

900

1200

1500

Tim. min

Fig. 39.5: Formation of metabolic water in the absence (a) and in the presence (b) of CHC13.

50-

'0

3W

'

6&

'

&

'

IdOO. 1500

Time, min

Fig. 39.6: Evolution of Pi during the same experiment as in Fig. 39.5.

427

39. 170and 31P MRI and Spectroscopy: In Vivo Inves~igntionsof Cell Bioenergetics

300

-.-

250

ln c

-

-.

5 200 -

I

.

I

.

I

T

I

3 0 0 - .

I

I

I

.

I

- T. molitor (017+ CHC13) . Phosphoarginine z200 -

T. m i i t o r (017+ CHCI3) beta-ATP

250

-

4

C

s 150 E 7 100 -

4 a

150 -

Y

Zl00-

B

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c 0

50

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0

I

'

I

.

'

.

'

.

'

'

-

0

'

'

.

I

.

"

'

.

Fig. 39.7: Time course of P-ATP and PA during the same experiment as in Figs. 39.5 and 39.6.

~~

0

TIME (min)

270

Fig. 39.8: Effect of temperature on oxygen consumption and phosphate metabolites. The time of death, marked by an asterisk, is indicated by the cessation of mitochondria1 function. The arrows are pointing to the phosphoarginine peak (see text).

428

C. D. Mareescu, M . Cabrera, and D. Fercu

As expected, the phosphorylation potential remained constant well above 30 "C, but rapidly deteriorated beyond 45 "C, together with the PAIP, ratio. Piformation continued at a significant rate after death. Interestingly, the larvae remained alive for more than 80 min after the temperature was increased to 45 "C. This experiment was conducted in order to evaluate the Q , , which is the ratio between the oxygen consumption at a temperature T + 10 "C and that measured at T. This factor is of particular interest for the elucidation of the protective mechanism of hypothermia in traumatic or ischemic brain damage [12,13]. It should be noted that the MRO, values we found in Terzebrio molitor are smaller than those reported in the literature (cf. [14]). Thus, at 20 "C we measured rates of 0.033 kO.007 pmoYg min as compared with 0.064 kO.016 pmol/g min at 30 "C. The average Q , , factor (n = 6) was approximately 2. The average body water in larvae was found to be 36 f 5%.

39.4 Conclusions Preliminary data from interleave 170/31P-MRS and 1 7 0 MRI measurements demonstrate the usefulness of the method as a complementary tool for monitoring in vivo mitochondrial metabolism. While its novelty consists in the employment of the excellent tracer qualities of 1 7 0 and its unique involvement in the detection of nascent mitochondria1 water, its success will be based in great part on the considerable amount of existing OXPHOS knowledge acquired by other in vivo and in vitro methods, including 3 IP-NMR. The most important applications will probably be the monitoring of

OXPHOS in order to better understand and treat degenerative diseases, as well as the functional mapping of the brain. The method should work much better in humans (3000 voxels could be measured in the cerebrum of an adult), but the high cost of the isotope prevents such use.

39. I7O and 31P MRI and Spectroscop.v: In Vivo Invesiigations ofcell Bioenergeiics

429

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G. E. Palade, JAMA 198 (1966) 143-153.

2.

A. L. Lehninger, Principles ofBiochemistq, Worth Publishers, New York, 1982.

3.

B. Chance et al., J. Biol. Chem. 260 (1985) 3947-3954, and references cited therein.

4.

D. Pietrobon et al., Biochernisty 26 (1987) 7339-7347.

5.

D. C. Wallace, Science 56 (1992) 628432.

6.

S. S. Kety and C. F. Schmidt, J. Clin. Invest. 27 (1948) 476-483.

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Ter-Pogossian et al., J. Clin. Invest. 49 (1970) 381-391.

8.

G. D. Mateescu, G. M. Yvars, and T. Dular, Proc. Soc. Magn. Reson. Med. 6 (1987) 929.

9.

G. D. Mateescu, Spectr. Inil. 3 (1991) 14-18.

10.

G. D. Mateescu, J. LaManna, D. Lust, L. Mars, and J. Tseng, Proc. SOC.Magn. Reson. Med. 10 (1991) 1031.

11.

J. Pekar, L. Ligeti, Z. Ruttner, R. Lyon, T. Sinnwell, P. van Gelderen, D. Fiat, C. T. Moonen, A. McLaughlin, Magn. Reson. Med. 21 (1991) 313-319.

12.

E. M. Nemoto, R. Klernentavicius, J. Melick and H. Yonas, J. Neurosurg. Anesih., in press.

13.

H. Minamisawa, C. Nordstrorn, M. Smith,and B. Siesjo, J. Cereb. Blood Flow Metab. 10 (1990) 365.

14.

L. Gyulai, Z. Roih, J. Leigh, Jr., and B. Chance, J. Biol. Chem. 260 (1985) 3947-3954.

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40. Volume Localised 'H MRS of Renal Osmolytes Gary J. Cowin, I. Anne Leditschke. Stuart Crozier1,and Zoltan H. Endre Department of Medicine and 'Centre for Magnetic Resonance, University of Queensland, Brisbane, 4072, Australia

Abstract The structural and biochemical heterogeneity of the kidney complicates the investigation of renal metabolism. Regional metabolic studies have required the use of excised regional kidney samples, freshly isolated medullary cells and of cultured renal cell lines. We have recently used volume-localized proton nuclear magnetic resonance spectroscopy as an assay of regional biochemistry in the isolated perfused rat kidney (IPRK) [ l l . This model eliminated artefacts caused by respiratory and cardiac motion experienced in vivo. Immersion of the kidney under its venous effluent reduced the susceptibility artefacts evoked by tissue-air interfaces. This study investigates the time-dependent response of renal osmolytes in the cortex and medulla of the IPRK.

40.1 Introduction A technique for non-invasive assessment of regional biochemistry in the kidney would help us understand normal physiological responses as well as disease-induced adaptation in this complex organ. The biochemistry of the renal cortical and medullary regions differs significantly as a consequence of the unique heterogeneity provided by the combination of regional and axial variation in cell types and function along the nephron. The application of 'H MRS to the intact kidney has occurred only recently, because of difficulties in localising the kidney in vivo in the presence of substantial respiratory motion. 'H MRS of the human kidney in vivo has been performed using the STEAM sequence and large voxels containing both medulla and cortex in volumes of 27 cm3 [2] without

432

G. J. Cowin, 1. A. Leditschke, S. Crozier, and 2.H. Endre

respiratory gating or 43 cm3 [3] and 15.6 cm3 with respiratory gating [4). In v i m TR FLASH 'H MR microscopy has been used to provide good regional flow-dependent differentiation of renal anatomy in the isolated perfused kidney [ 5 ] . Similar results have been obtained using the RARE and IR-RARE sequences [ 11. Renal medullary cells are subject to high and variable osmolality as a consequence of the high medullary interstitial osmolality generated by the countercurrent multiplier mechanism. Renal cells balance the osmolatity of the cytoplasm against the extracellular osmolality by concentrating organic osmolytes [6], which protect the cells from high ionic concentrations in the interstitial space. These osmolytes include the methy lamines, glycerophosphorylcholine and betaine, the polyols, inositol and sorbitol and amino acids such as taurine [7]. Image-guided volume localized 'H magnetic resonance microspectroscopy was used to investigate the regional response of renal osmolytes to diuresis in the IPRK.

40.2 Methods The right kidney (average weight 0.7 g) from male Sprague-Dawley rats (weighing 150 180 g) were perfused at 37°C with Krebs-Henseleit buffer (KHB) containing bovine serum albumin (6.7 g/100 ml), glucose and 20 amino acids and gassed with 95% 0,/5% CO, as previously described [ 11. The perfused kidney was placed in a modified 20 mm NMR tube as shown (Fig. 40.1). Perfusate and urine samples were collected at 10 to 15 min periods. Kidney function was estimated from the ratio of *4C-inulinin urine flow, glomerular filtration rate and fractional excretion of urine to plasma (UP), sodium (FEN,). Imaging and localized spectroscopy were performed on a Bruker AMX300 console interfaced to a 7 T 15 cm vertical bore magnet with gradients and RF probes custom designed at the Centre for Magnetic Resonance, University of Queensland. Scout images for voxel localization were acquired using the RARE pulse sequence [8]. Regional 'H microspectroscopy was performed using the VOSY pulse sequence [9]. This allowed a voxel (approximately 24 p1 in volume) to be located exclusively within the cortex and medulla of each kidney. A microspectrum from renal cortex and medulla was acquired alternately at intervals of 12 min during each experiment. Typical VOSY parameters

40. Volume Localised ' H MRS of Renal Ostttolytes

433

were: voxel dimensions 2 x 4 x 3 mm (24 pl), TR = 2 s, TE = 12 ms. TM and TE crusher gradients of 8 G/cm were used for flow and unwanted echo suppression. Water suppression was carried out using a 3 directional SUBMERGE pulse sequence [ 101. Typically, 320 transients were collected with a recycle time of 2 s. 8 Hz line broadening was applied. The first spectrum in each series of control cortical and medullary spectra was adjusted to a start time of 60 min to emphasize time-dependent changes. PERFUSATE LINES in out I

venous effluent kidney

out

t

1

kidney holder birdcage resonator transmitter coil

decoupled surface receiver coil

ureteric line

Fig. 40.1:Modified 20 m m NMR tube for the IPRK. Modified from Cowin et al. [ 11.

40.3 Results Comparison of representative spectra from the cortex, medulla and perfusate are shown in Fig. 40.2. Similar spectra were obtained from 8 kidneys. The distinguishing features of spectra from these two regions were found primarily within the 3 to 4 ppm frequency range, where the renal osmolytes resonate. Peaks in medullary spectra were assigned as follows: N-methyl protons of betaine and GPC, 3.2 ppm; inositol, 3.55 ppm; inositol and GPC, 3.65 ppm; betaine, 3.9 ppm and inositol,

434

G. J. Cowin, I. A. Leditschke. S. Crozier, and 2. H. Endre

betalne GPC

I

betaine tnositiol

glutamate glutamine

medulla

cortex

Fig. 40.2: Regional IH spectra of the LPRK. Representative spectra acquired from voxels located in the medulla, cortex or perfusate are shown. Spectral peak assignment has been previously described [ 11. Modified from Cowin et al. [ 11.

U/P inulin (dashed Line)

Fractional excretion of sodium (FEN.) (solid Line) I . . . I . . . I . . . I . . . I . . . I . . .

20

...

10

0

1

0.4

15

5

o.5

-

,I-,-, -,-,&

0.3

0.2 0.1

1 I . . . I . . . I . . . [ . ‘ . I . . . I . . . I . . .

0

Fig. 40.3: Renal water and sodium transport. Values at each 10 min interval represent the mean i SD of five experiments.

40. Volume Locnlised

435

'HMRS of Renal Osmofyres

4.1 ppm (Fig. 40.2). In contrast, only the betaine-GPC peak at 3.2 ppm was clearly resolved in the cortex (Fig. 40.2). The perfusate peaks at 3.0, 3.55 and 3.75 ppm appeared to correlate with peaks of similar chemical shifts in the cortex and present to a lesser extent in the medullary spectra (Fig. 40.2). Renal function was well maintained during the 160 min of perfusion, as indicated by the ability of the kidney to reabsorb water and sodium, as indicated by U/P inulin and FENa,respectively (Fig. 40.3). The intensity of the betaine-GPC peak decreased in both the cortex and medulla during the perfusion. The medullary betaine-GPC decreased at a greater rate and displayed less scatter than the cortical data.

1.1 X

- - 0 --medulla +cortex 0.4

4 40

, ,

.

, , 60

,

,

, , , , , , , , , , , , , , , 80 100 120 140 160 180

Time (min) Fig. 40.4: Time dependent change of betaine-GPC peak intensity. The combined data from five experiments are plotted. Linear regression of the data gave the following equations; medulla, y = 1.180 - 0.003~ ( R = 0.84, n = 20, p < 0.01, dotted line); cortex, y = 1.077 - 0.002~( R = 0.52, n = 19, p < 0.05, solid line), where y represents betaine-GPC intensity and x represents perfusion time.

436

G. J . Cowin, 1. A. Leditschke, S. Crozier, andZ. H . Endre

40.4 Discussion This study is the first investigation of a time-dependent relationship between regional osmolyte levels and kidney function in the intact kidney. This was made possible by the combination of microimaging and volume-localized spectroscopy. The isolated perfused rat kidney proved to be an excellent model for the application these techniques, since both respiratory movement and magnetic susceptibility artefacts created by tissue-air interfaces were eliminated. The cortical and medullary spectra from the intact kidney could be distinguished by the dominance of the osmolytes betaine, GPC and inositol in the medulla. Previous 'H NMR studies of cortical and medullary extracts combinated with GC-MS and chemical analysis identified the major renal osmolytes as the trimethylamine compounds, betaine and GPC, and the polyols, inositol and sorbitol [ 11,121. The predominance of the osmolytes in the medulla reflects the uptake of osmolytes by the cells to protect against the high and variable osmolarity of the medulla. The decrease in intensity of the betaine-GPC peak during perfusion is consistent with the IPRK perfused without erythrocytes being a hypoosmotic model [13]. This suggestion is a consequence of the washout of the corticomedullary osmotic gradient by the high perfusate flow required to maintain adequate oxygen delivery to the medulla in the absence of erythrocytes and also a consequence of the low viscosity of erythrocyte-free perfusate [13]. Osmolytes exiting from the cells would also be washed out of the kidney by the perfusate flow, further decreasing in the intensity of the betaine-GPC peak. The characteristics, mechanism and control of the rapid release of osmolytes following a hypoosmotic insult are not completely understood. However, specific channel activation has been implicated in the release the osmolytes [ 141. The parameters of renal function which reflect water and Na reabsorption function, U/P and FENa,respectively, were well maintained throughout perfusion in control kidneys (Fig. 40.3) despite washout of the osmolytes. This is consistent with preservation of the active transport mechanisms in the proximal tubule, which must be the primary site of electrolyte and water reabsorption in the IPRK perfused without erythrocytes. Loss of the high medullary osmolality would limit passive absorption of fluid within the medulla. Furthermore, the m-TAL is very sensitive to hypoxic injury in the erythrocyte-free IPRK [ 15,161 whereas, good proximal tubular viability is retained in this model [ 16,171. In conclusion, this study investigated the time-dependent correlation between regional biochemistry and kidney function in the intact kidney. RARE microimaging and

40. Volume Localised

'HMRS of Renal Osmolytes

437

VOSY microspectroscopy were ideally suited to these IPRK experiments. Medullary spectra were dominated by the osmolytes betaine, GPC and inositol, which were present to a lesser extent in the cortex. The time-dependent decrease in the intensity of the betaine-GPC peak is consistent with washout of osmolality in the erythrocyte-free IPRK, primarily as a consequence of hypoosmotic shock. In contrast, functional parameters measured in this study were maintained during perfusion, indicating function of the IPRK primarily reflects proximal tubule transport with limited contribution from hyperosmotically driven medullary transport.

Acknowledgments We thank the Australian National Health and Medical Research Council for supporting this project.

References 1.

G. J. Cowin et al., MAGMA 5 (1997) 151.

2.

N. J Shah et al., Mag. Reson. Med. 20 (1991) 292.

3.

M. J. Avison et al., Proc Narl. Acad. Sci. USA 88 (1991) 6053.

4.

R. M. Dixon and J. Frahm, Mag. Reson. Med. 31 (1994) 482.

5.

K.-P.Fichtner et al., JMRI. (in press).

6.

M. 8. Burg, Kidney Inr. 49 (1996) 1684.

7.

A. Garcia-Perez and M. B. Burg, Physiological Reviews 71 (1991) 1081.

8.

J. Hennig, A. Nauerth and H. Friedburg, Mag. Reson. Med. 3 (1986) 823.

9.

R. Kimmich and D. Hoepfel, J. Magn. Reson. 72 (1987) 379.

10.

D. M. Doddrell et al., J. Magn. Reson. 70 (1986) 176-180,.

11.

S. Bagnasco et al., J. B i d . Chem. 261 (1986) 5872.

12.

R. S. Gullans et al., Am. J. Physiol. 255 (1988) F626.

13.

W. G. Guder, FX Beck, and M. Schmolke, Klinische Wochenschrift 68 (1990) 1091.

14.

P. C. B. Sizeland et al., Kidney Int. 43 (1993) 448.

15.

D. Alcom et al., Kidney Inf. 19 (1981) 638.

16.

P. J. Ratcliffe et al., Clin. Science 74 (1988) 437.

17.

T. Maack, Am. J. Phvsiol. 238 (1980) F71.

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41. MRM in the Modelling of the Ossicular Chain E. W. Abel', J. A. Chudek2. G. Hunte?, R. M. Lord', and R. L. MacKay2 Departments of 'Biomedical Engineering and *Chemistry,University of Dundee, Dundee, Scotland DD 1 4HN, UK

R. P. Mills Department of Otolaryngology, Ninewells Hospital, Dundee, Scotland DD 1 9SY, UK

Abstract Chronic suppurative otitis media is an important cause of conductive hearing loss. This disease can be treated surgically using procedures first performed three decades ago and, while they have been improved over the intervening period, still involve the creation of a link between the ear drum and the stapes head based loosely on the structure of the columella ears found in birds and reptiles rather than on the mammalian three-ossicle ear. In a project to develop a more successful treatment for this complaint, finite element analysis is being used to conduct vibrational studies on different configurations of physiological ossicular chain reconstruction, for experimental evaluation. However such analysis requires an accurate representation of the geometry of both the ossicular chain and the surrounding tissues to which it is attached. Conventional methods of measurement have proved inadequate. In contrast MRM has been successfully used in this work.

41.1 Introduction The human ossicular chain consists of three bones which connect the tympanic membrane with the cochlea. They comprise a lever mechanism which forms part of the the impedance transformer mechanism of the middle ear. Reconstruction of the ossicular chain was first carried out during the 1950s [ 11. The techniques that have developed from this early work involve the creation of a link

440

E. W.Abel, J . A. Chudek. G. Hunter, R. M. Lord, R. L. MacKay, and R. P. Mills

between the drum or malleus handle and the stapes head or foot plate and must all be considered unphysiological because they do not reproduce the human three ossicle pattern (Fig. 41.1). The designs of these reconstructions are based on the structure of the columella ears found in birds and reptiles. Despite their simpler design. these ears perform almost as well as mammalian three ossicle ears [2]. There are, however, some important differences between the detailed morphology of the typical avian ear and that of human middle ears reconstructed using conventional techniques.

Malleus

\ ; /-

Modified Incus

Fig. 41.1: Representation of healthy ossicular chain (left) and the result of an ossiculoplasty operation (right).

Conventional ossiculoplasty operations produce good hearing results in some cases but the results do not compare favourably with those obtained following operations for otosclerosis operations, in which a relatively physiological reconstruction is performed and excellent hearing results are obtained [3]. These considerations have lead us to explore the possibilities of developing more physiological ossiculoplasty operations. As part of this process we are developing a computer model of the middle ear, with the first phase being the creation of an accurate three dimensional model of middle ear structures. Conventionally, small bones are measured by embedding them in a wax or other matrix, slicing or grinding a layer of known thickness off one end, photographing the exposed surface, measuring the bone section, and transposing each element into a computer to reconstruct a three-dimensional image. We consider that Magnetic resonance microimaging (MRM) is a non-destructive, but more accurate and more practical technique for obtaining the digitised data necessary for the three-dimensional image reconstruction. Its high resolution allows fine detail to be identified and a large number of slices to be created in the image. It has the additional advantage of being able to image not only the bones of the ossicular chain but also the tissues that attach them to the skull.

41. MRM in the Modelling of the Ossicular Chain

44 1

This gives important information about the geometry of these structures and their orientation with respect to the ossicular chain. This cannot be done using conventional methods.

41.2 Experimental 41.2.1 MRM A piece of human skull (ca. 25 mm long by 25 mm dia.) including the middle ear was excised and placed in a 25 mm outer diameter N M R tube. The bone was submerged in silicone oil, ensuring that any trapped air was expelled from the ear canal. The oil was imaged using a Bruker AM300WB NMR spectrometer fitted with a Bruker microimaging accessory. Data were accumulated using a standard 'H Bruker 3D spin-echo pulse sequence. The gradients were set to give a field of view of 25 mm on a side, which gave a pixel resolution of 200 pm x 200 pm x 200 pm. The data were worked up on a Bruker X32 work station. After transformation, uninterpolated image slices were used to give data for the finite element model. In order to locate the ossicular chain within the bone fragment, interpolation and surface reconstruction techniques were used to section the specimen electronically (Fig. 41.2), locate the ossicular chain and determine the exact coordinates of the various bones within it.

Fig. 41.2: Surface rendering of data showing ossicular chain in electronically sliced middle ear.

442

E. W. Abel, J . A. Chudek, G. Hunter, R. M. Lord, R. L. MacKay. and R. P. Mills

41.2.2 Finite Element Analysis A finite element model of the middle ear is being constructed to simulate prosthetic incus designs used in the experimental work. Parameters such as shape, mass and stiffness can be adjusted to give the best approximation to a predefined spectral response at the stapes. The geometry of the ossicles is being reconstructed from the data provided by MRM. A software technique, used previously for automated 3D reconstruction of bone shapes from 2D CT scans [4], is being used to extract the image from the NMR voxel data set for use in the finite element software program ANSYS. By tracing contours in the voxel image slices, keypoints can be identified to allow the construction of the finite element model. This enables not only the complicated geometrical structure of the middle ear to be modelled, but also the sound transmission characteristics of existing and new prosthesis designs to be studied.

41.2.3 Contour Tracing In order to use the MRM scans in the finite element package, ANSYS, the bone geometry was extracted from the images by contour tracing (Fig. 41.3). The contour tracing algorithm links neighbouring elements if the intensity magnitude differences are within predefined thresholds [ 5 ] . At a particular pixel location, P , the eight neighbouring pixels are assigned numbers indicating the direction with reference to P (Fig. 41.4). The contour is traced in a clockwise fashion, by testing the eight neighbouring pixels to decide the next location.

Intensity Slice

Fig. 41.3: Contour extraction.

Contours

41. MRM in the Modelling of the Ossiculnr Chain

443

X

1_ Y

Fig. 41.4: Pixel assignment.

41.2.4 Image Reconstruction The contours of many slices were used to build a reconstructed image of the ossicular chain and this corresponded well with a surface rendered magnetic resonance microimage of the ossicular chain (Fig. 41.5).

10

Fig. 41.5: Partial contour reconstruction of the ossicles vs. a surface rendered MRM image.

444

E. W. Abel, J. A. Chudek, G. Hunter, R. M.Lord, R. L. MacKav, and R. P. Mills

Acknowledgement We thank the Scottish Hospital Endowments Research Trust for their support of this project.

References 1.

A. Hall and C. Rytzner, Acta Otolaryngol. 47 (1957) 3 18.

2.

B. M.Johnstone and P. M. Sellick, Quart. Rev. Biophys. 5 (1972) 1.

3.

R.P.Mills, Clin. Otolaryngol. 21 (1996) 499.

4.

T. P. Sng, B. Sc. (Hons.) Project Thesis, University of Dundee, 1996.

5.

D.Kirk, Graphic Gems Ill, AP Professional. 1992.

42. NMR Imaging of Rigid Biological Tissues Yoshiteru SeoI, Hisatake Takamiyaz, Hiroki Ishikawa3, Toshiaki Nakashimaj, Yehuda Shad4,and Gil Navon4

Department of Physiology, ,Department of Orthopedic Surgery and 3 Department of Medicine 111, Kyoto Prefectural University of Medicine, Kamigyo-ku, Kyoto 602, Japan School of Chemistry, Tel Aviv University, Ramat Aviv, Tel Aviv, 69978 Israel

Abstract We have tried anatomical imaging of rigid biological tissues, such as bone, cartilage, teeth, tendon and calculus. 'H transverse relaxation times of teeth and cortical bone are ca. 100 ps. Gradient-echo (GE) and spin-echo (SE) imaging sequences can not depict teeth and cortical bone even using the shortest echo-time (ca. 1 ms). Constant-timeimaging (CTI) is a 3D-phase-encoding sequential point imaging method so that a single data point in k-space is taken with a minimum echo-time (ca. 100 ps). We can get images from teeth and cortical bone without any artifacts from chemical-shift and susceptibility differences in sample. 'H transverse relaxation times of tendon, cartilage and calculus are in the range of few milliseconds. Gradient-echo and spin-echo imaging sequence are valuable for these samples with relatively short T, relaxation times. We can get 3D-GE images of gall bladder stoneswith a resolution of 63 pm3. The other direction of effort is getting N M R information from ordered biological tissues. Tendon consists of well ordered collagen fibers, and the ordered structure is essential for its physical strength. The *H double-quantum-filter (DQF) NMR spectra of the tendon raised a big residual quadrupolar splitting (va ca. 2.5 Wz), and the muscle raised a small splitting (ca. 50 Hz). The 2H double-quantum-filter spectroscopic imaging (DQF-SI) of the Achilles tendon and soleus muscle depicted that a denaturated part of tendon represented smaller vQ which represented loss of order structure of collagen fibers. These imaging techniques now open a new field to study the rigid biological tissues.

446

Y. Seo. H. Takarniya, H. Ishikawa, T. Nakashima, Y.Sharf; arid G. Navon

42.1 Introduction Rigid biological tissues such as bone, teeth, tendon, cartilage and calculus usually appear almost "black" in nuclear magnetic resonance (NMR) images obtained with conventional pulse sequences. Compared with soft biological tissues such as muscle, these solid tissues have relatively short transverse relaxation times typically lying in a range from 10 ps to 10 ms (Fig. 42.1). Due to the short transverse relaxation time of solid tissues, the NMR signal fades away during the spatial encoding process in conventional NMR imaging. Their anatomical structures are therefore invisible and their presence can only be detected by their contrast with the bright background from surrounding soft tissues such as adipose tissue and skeletal muscle. There have been several attempts to obtain structural information and images using NMR information from solid or rigid materials with short transverse relaxation times (cf. review by Cory [I]). We summarize here the results of our attempts to image bone, cartilage, teeth, tendon and calculus using pulse sequences for gradient-echo imaging, spin-echo imaging, constant-time imaging and *H double-quantum-filtered spectroscopic imaging.

-

T2

Tissues

low

Calculus (short) Teeth (short)

MRl seq.

b

--my

Teeth OWN Cortical bone Trabecular bone

- lms

Hyaline cartilage Tendon (short) Calculus (tong)

-

10ms

Tendon (long) Fibroelastic cartilage

CTI DQF-SI t&

GE SE

Fig. 42.1: Typical values for the IH transverse relaxation times (T2) of rigid biological tissues at 7.05 T. Values were obtained by either spin-echo pulse sequences or by line-shape analysis of the spectra.

42. NMR Imaging of Rigid Biological Tissues

447

42.2 Instrumentation All experiments were performed at 7.05 T using an NMR spectrometer (AMX-300 wb, Bruker) with a gradient control unit including preemphasis control and Bo compensation (BGU II), 3 audio-frequency amplifiers with a blanking unit (B-AFPA 40), and a microimaging probe (micro5.0) with 12 mm diameter RF-coils tuned for either 'H or 2H Larmor frequencies (300.17 or 46.06 MHz). The spectrometer was controlled by an X32/3 computer running a ParaVisiodUXNMR software (Version 9405 10.B.6.1). The gradient coil was cooled with water at 20 -C, and the temperature of the sample was kept at 24 "C. Typical imaging-related performance parameters were as follows: rise time 60 ps, eddy current settling time 150 ps, maximum gradient strength 195 G/cm, and image resolution ca. 50 pm3 in soft tissue samples [ 2 ] .

Fig. 42.2: IH constant-time imaging of a human tooth. a) A series of transverse section images of the tooth. b) The 17" slice of the image in which the layers of enamel and dentine appear with the same intensity. c) 3D reconstruction with a cut for visualizing the dental tubule. Parameters used were as follows: field of view 8 x 8 x 12 mm, data matrix 64 x 64 x 32, voxel resolution 125 x 125 x 375 pm, spectral width 125 W z , relaxation delay 100 ms, phase encoding time 0.1 ms, phase encoding gradient 92.5 x 92.5 x 30.3 G/cm, number of accumulations 4, and total data acquisition time 14 hr 35 min. A rectangular pulse (duration 2.1 ps, flip angle 8') was used for excitation.

448

Y. Seo, H. Takamiya, H. Ishiknwa. T. Nakasliimn, Y. Sharj and G. Navon

42.3 Bone and Teeth Observed by CTI The 'H transverse relaxation times (T2) of cortical bone and teeth are ca. 100 ps, and are among the shortest T2 values observed in biological tissues. To imagine such structures we have used Constant-time-imaging(CTI) which is a 3D-phase-encoding sequentialpoint imaging method allowing data points in k-space to be obtained at very short echotime (ca. 100 ps) [l]. Figure 42.2 shows 3D CTI of human anterior tooth with a phaseencoding time of 100 ps. Despite the short T2 relaxation time (60 IS), the 3D structures

of the enamel and dentine appear clearly with a voxel resolution of 125 x 125 x 375 Frn. Before imaging, the tooth was kept for a week at a room temperature. Thus the pulp of the tooth dried completely and the dental tubule is shown as an empty cavity.

a) 1H GE MRI

b) 1H CTI

Fig. 42.3: a) IH gradient-echo imaging of a rabbit toe. Parameters used were as follows: field of view 15 m*,data matrix 2562, slice thickness 0.2 mm, spectral width 125 kHz, relaxation delay 300 ms, echo-time 3.5 ms, number of accumulations 16, and total data acquisition time 20 min 30 s. A sinc shape pulse (duration 2 ms, 3 cycles, band width 2.5 kHz, flip angle 30") was used for excitation. b) 1H constant-time imaging of a rabbit toe. Parameters used were as follows: field of view 20 x 20 x 6 mm, data matrix 128 x 128 x 32, voxel resolution 156 x 156 x 188 pm, spectral width 125 kHz, relaxation delay 75 ms, phase encoding time 0.1 ms, maximum phase encoding gradient 74.6 x 74.6 x 60.7 G/cm, number of accumulations 2, and total data acquisition time 21 hr 50 min. A rectangular pulse (duration 1.3 ps, flip angle 5") was used for excitation.

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CTI images of bone were next compared with conventional gradient-echo (GE) and

spin-echo (SE) images. The 3D CTI method clearly visualized the structures of the cortical as well as the trabecular bone within the femoral head, and also the cortical bone of a bovine vertebral body, of the toe of a rabbit and of the diaphysis of a rabbit femur. In contrast, the GE and SE images contained no significant signal from the trabecular bone or the cortical bone, even using the shortest echo-time (ca. 1.5 ms), and only showed signal from the adipose tissue in the bone marrow. Morphological observation of bone by GE imaging is also hindered by magnetic susceptibility as well as chemical shift artifacts. A typical GE image of the toe joint of a rabbit is shown in Fig. 42.3a. Using a relatively long echo-time (3.5 ms), bone, cartilage and tendon appear almost 'black', and only skeletal muscle, adipose tissue and bone marrow appear 'bright'. Figure 42.3b shows a corresponding slice obtained by 3D CTI. The image of soft tissues is almost protondensity image, but only cortical bone appears at a lower signal intensity than the sur

Fig. 42.4: a) *H gradient-echo imaging of a cholesterol-based mixed gallstone. Parameters used were as follows: field of view 8 mm2, data matrix 1282, slice thickness 0.5 mm, number of slices 8, spectral width 125 kHz, relaxation delay 300 ms, echo-time 1.6 ms, number of accumulations 512, and total data acquisition time 5 hr 27 min. A rectangular pulse (duration 250 ps, band width 4.5 kHz, flip angle 60") was used for excitation. b) 1H gradient-echo imaging of a pigment gallstone. Parameters used were as follows: field of view 10 mm2, data matrix 2562, slice thickness 0.5 mm, number of slices 16, spectral width 125 kHz, relaxation delay 400 ms, echotime 2.6 ms, number of accumulations 512, and total data acquisition time 14 hr 34 min. A rectangular pulse (duration 250 p,band width 4.5 kHz, flip angle 45") was used for excitation.

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rounding soft tissues which is due to its shorter T2 relaxation time. Tendons appear almost the same as skeletal muscle and adipose tissue, since their T2 relaxation time (ca. 0.5 ms) is much longer than the phase-encoding time (0.1 ms). In summary, using CTI we can get images from teeth and cortical bone without any artifacts from chemical shift and susceptibility differences in the sample, and the voxel resolution is reasonably good at around 150 pm3. CTI does not require any special instrumentation but does require more time for data acquisition.

42.4 Calculi Observed by GE Imaging 'H transverse relaxation times of calculus and hyaline cartilage are around one millisecond. Gradient-echo imaging and spin-echo imaging sequences are valuable for times such as those with relatively short T2 relaxation times. Cholesterol gallstones and pigment gallstones are typical calculi found in lithiasis. MR cholangiography is generally performed using heavily T2-weighted gradient-echo or fast spin-echo sequences, and is considered to be the most sensitive technique for finding stones compared with X-ray cholangiography, ultrasonography and X-ray computed tomography [3]. The stones are detected as signal-void foci in clinical MR images. There have been few attempts to image stones in vitro, and these have not revealed any fine inner structure at all [MI. Two 'H T2 relaxation times were detected in cholesterol-based mixed stones and pigment stones from human subjects. The shorter, dominant one (ca. 10 ps) can not be imaged even by using CTI, but the longer, minor one (ca. 1 ms) is detectable by GE imaging with short echo-times. Cholesterol-based mixed stones are firm,yellow-gray and cuboidal in shape. Figure 42.4a shows four consecutive GE slices of a cholesterol-based mixed stone. The core of the stone consists cholesterol. The central cavity appears black and cholesterol crystals produce radiating clefts. The outer layers contain some calcium bilirubinate, and the layer structure corresponds to the different composition of the precipitate from bile with time. Pigment stones are brown, small and irregularly shaped. Figure 42.4b shows four consecutive GE slices of a pigment stone which consists of calcium salts of unconjugated

42. NMR Imaging of Rigid Biological Tissues

45 1

bilirubin. The internal structure has a lobulated "mulben-y" pattern: small calcium-bilirubin cores (1 - 2 mm in diameter) are connected by a soft matrix of bilirubinkalciumbilirubinate. Cores have very short T2 values (ca. 10 ps) so them appear almost black. The intermediate matrix has a longer T2 and appears brighter. The fine network of the matrix shows that a single core consists of a number of smaller particles. A 3-dimensional reconstruction from the 3D GE images of the pigment stone are shown in Fig. 42.5. The intrinsic spatial resolution of the image is 62.5 pm3. The fine structure of the intermediate matrix is well depicted and looks like a nebula in the sky. This is the first NMR imaging study of the fine internal structure of calculi. The quality of the NMR image is much better than that of a X-ray radiograph, and is similar to that of images obtained by light microscopy of thin slices of the stones. The advantage of NMR imaging is its capability for analyzing 3-dimensional structure.

Fig. 42.5: A IH 3-dimensional gradient-echo image of a pigment gallstone. Parameters used were as follows: field of view 8 mm3, data matrix 1283, voxel resolution 62.5 pm3, spectral width 50 kHz, relaxation delay 300 ms, echo-time 3.2 ms, number of accumulations 8, and total data acquisition time 10 hr 55 min. A rectangular pulse (duration 250 p,flip angle 45") was used for excitation. After 3-D FT, a 3-D reconstruction routine was applied with a given threshold and set to display clusters bigger that 32 voxels.

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Y. Seo, H . Takumiya, H. Ishikuwa, T. Nakashima, Y. Sharf; and G. Navon

42.5 Tendon Observed by 2H DQF-SI Our other direction of effort is in obtaining NMR information from ordered biological tissues. In general, ordinary MR images provide little information about the physiological and pathological changes in tendons. Minor information relates to anatomical changes such as rupture and hypertrophy, and only an increase in the 'H T I relaxation time is considered to be a sign of inflammation [7]. Tendons consist of well-ordered collagen fibrils averaging 1750 A and 600 8, in diameter, and the ordered structure is essential for its physical strength. The 'H nucleus has often been used as a molecular probe for detecting ordered structures. Figure 42.6 shows the energy levels of a spin = 1 nucleus such as 2H. In molecules with fast isotropic motion, the quadrupolar interaction of the 2H nucleus is averaged out and the 2H NMR spectrum consists of a single resonance. Such an isotropic spectrum is obtained for example from pure deuterium water. When the 2H nucleus is restricted by a macroscopically anisotropic environment, the quadrupolar interaction is not averaged and the splittings of the energy levels are no longer equivalent. In this case, the anisotropic 2H NMR spectrum consists of two peaks with a separation of vQ, where vQ is the partially averaged, residual quadrupolar interaction.

n

I

,

t

'~-\

I A

A

iol

Fig. 42.6: Energy diagram of a spin I = 1 nucleus in the isotropic fast motion condition and in the anisotropic slow motion condition. Single-quantum spectra of deuterium water and of Achilles tendon are shown as typical isotropic and anisotropic 2H NMR spectra respectively.

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c)

Fig. 42.7: a) 2H single-quantum spectrum of the musculotendinous junction of the Achilles tendon and gastrocnemius muscle of a rabbit. The longitudinal axis was set parallel to the static field. b) *H double-quantum filter (DQF) NMR spectrum measured with a double-quantum creation time of 0.2 ms, which corresponds to the resonance from water in the tendon. c) *H DQF NMR spectrum measured with a double-quantum creation time of 6 ms, which corresponds to the resonance from water in skeletal muscle. Parameters used were as follows: spectral width 10 kHz, data size 4096, 90"pulse 22 ps, 180" pulse 44 ps, double-quantum evolution time 5 ps, number of averages 256.

A typical anisotropic 2H NMR spectrum is obtained from deuterionated rabbit Achilles tendon, in which there is a residual quadrupolar splitting of vQ = 2.4 kHz. The observed quadrupolar splitting is ca. 1% of that of solid hydrates [8], since processes of fast chemical exchange, diffusion and heterogeneous orientation of water molecules average the intrinsic vQ of the water molecules. But the value of 2.4 kHz is significantly bigger than that other biological tissues such as cartilage and nerve [9,10] which suggests that water molecules align well to the longitudinal axis of the collagen fibers of the tendon [Ill. The 'H single-quantum spectrum of the musculotendinous junction of the Achilles

tendon and gastrocnemius muscle consists of a large (2.5 Wz) splitting originating from

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Y. S e a H . Takumiyu. H . Ishikaun, T. Nnkushinla. Y. Shad and G. Navon

water molecules in the tendon and an isotropic resonance which presumably originates from water molecules in the skeletal muscle (Fig. 42.7a). 'H double-quantum-filter (DQF) NMR (90"-~/2-1 80"-~/2-90"-t~~/2-180°-tdq/290"-(acq)) selectively detects 2H nuclei in the anisotropic environment and eliminates resonances from nuclei in the isotropic motional condition [12]. Molecules with large residual quadrupolar splittings are detected at shorter double-quantum creation times (z ca. 100 ps) and molecules with small residual quadrupolar splittings are detected at longer creation times (ca. 10 ms). Figure 42.7b shows a 'H DQF NMR spectrum of the musculotendinous junction at a creation time of 0.2 ms. As expected from the DQF NMR spectra of I = 1 nuclei, the two quadrupolar-split resonances corresponding to the water in the tendon have opposite phases. The central, mostly isotropic signal in the single quantum spectrum is almost completely eliminated in the DQF spectrum at a creation time of 0.2 ms. DQF NMR is also sensitive to molecules with very small residual quadrupolar splittings. Thus, at a relatively long creation time of 6 ms, we can detect weakly ordered water molecules which presumably are situated in the skeletal muscle (Fig. 42.7~).These results demonstrate that we can detect water molecules in the Achilles tendon and in the skeletal muscle separately by using two different creation times. We have recently extended the application of 2H DQF NMR to spectroscopic imaging (double-quantumfilter spectroscopic imaging; DQF-SI): (90°-d2-1 8O0-z/2-90"-t 1A-t2-1 80°-tdq/2-900-(acq)) [ 13,141. We simply added a phase-encoding gradient (A) during the double-quantum evolution time (fdq), where fdq/2 = tl + A + t 2 is kept constant. The anatomical structure of the musculotendinous junction of the Achilles tendon and gastrocnemius muscle are shown by *H GE imaging in Fig. 42.8a. The phaseencoding gradient was applied along the longitudinal axis of the sample so that the upper part and lower part of the ID-DQF-SI images correspond to the gastrocnemius muscle and Achilles tendon respectively (Fig. 42.8b). The tendon water 'H had a large residual quadrupolar splitting (vQ = ca. 2.5 kHz) which observed at a short DQ creation time (300 ps), and the muscle showed a small splitting (ca. 50 Hz) at a longer DQ creation time (6 ms) (Fig. 42.8b). We also have some preliminary results from DQF-SI of denatured tendon in which the structure of the collagen fibers is less ordered. The DQF-SI reveals the anatomical distribution of the denatured part of the tendon which becomes apparent at intermediate creation times corresponding to its smaller quadrupolar splitting.

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b) 2H I D DQF Spectroscopic Imaging IC = 0.2ms z=6ms

NMR frequency (Hz) Fig. 42.8: a) 1H gradient-echo image of the musculotendinous junction of the Achilles tendon and gastrocnemius muscle of a rabbit. The longitudinal axis was set parallel to the static field, and the center of junction was positioned in the center of the field-of-view. Parameters used were as follows: field of view 20 mm2, data matrix 2562, slice thickness 0.5 mm, number of slices 16, spectral width 125 kHz, relaxation delay 100 ms, echo-time 5.9 ms, number of accumulations 16, and total data acquisition time 6 min 50 s. A sinc shape pulse (duration 2 ms, band width 2.5 kHz, flip angle 30") was used for excitation. b) One-dimensional 2H double-quantum filter spectroscopic imaging (1D *H DQF SI) with a double-quantum creation times of 0.2 ms and 6 ms, which corresponds to the resonance from water in the tendon, and the resonance from water in skeletal muscle, respectively. The horizontal and vertical axes represent the frequency and spatial axes, respectively. The gray scale indicates the intensity of the power spectrum. Parameters used were as follows: field of view 20 kHz x 20 mm, data matrix 1024 x 128, voxel resolution 19.5 Hz x 156 pm, relaxation delay 1 s, phase encoding time (A) 3.3 ms, phase encoding gradient +. 7.64 Gkm, 90" pulse 15 ps, 180" pulse 30 ps, double-quantum evolution time (tdq) 6.91 ms, number of accumulations 64,and total data acquisition time 2 hr 17 min.

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42.6 Conclusion In this chapter, we have reviewed the possibilities for NMR imaging of bone, cartilage, teeth, tendon and calculus by using pulse sequences for a gradient-echo imaging, constant-time imaging and 2H double-quantum-filtered spectroscopic imaging (Fig. 42.1). There is no question that spin-echo and gradient-echo imaging are still the most useful techniques for imaging biological tissues with T2 relaxation times longer than 1 ms. The typical spatial resolution of these methods is less than 100 pm3 which is not much worse than that obtained in the soft tissues (50 pm3). Constant-time imaging, however, is useful for tissues with shorter T2 relaxation time (100 ps). CTI requires very long acquisition times so its spatial resolution is limited by the time available for data acquisition. However, a new sequence named SPRITE (single point ramped imaging with T1 enhancement [ 151) is much more time efficient so it may be possible to get an image with a data matrix of 323 and field-of-view of 15 mm3 within a reasonable acquisition time. Double-quantum-filter NMR spectroscopic imaging, on the other hand, allows us to add a new imaging parameter. With this techniques we can relate the microscopic environment of water to particular anatomical structures. These imaging techniques clearly provide many new opportunities for the study of rigid biological tissues.

Acknowledgments This work was partly supported by the Collaborative Research Project of the Laboratory of Magnetic Resonance Imaging & Spectroscopy, National Institute for Physiological Sciences, grants from the Ministry of Science and Culture of Japan and a grant from the Israel Science Foundation. The authors are grateful for the contributions of Dr. M. Murakami (Natl. Inst. for Physiol. Sci.) for Physiology, Dr. Y. Kusaka and Dr. 0. Uemura (Kyoto Pref. Univ. of Med.) for Orthopaedic Surgery, Dr. S . Naruse and Dr. Y. Seki (Nagoya Univ.) for Gastroenterology, Dr. H. Shinar, Dr. U. Eliav and Ms. L. Tsoref (Tel Aviv Univ.) for double-quantum NMR, Dr. D. Gross, Dr. V. Lehmann, Dr. K. Zick (Bruker) for constant-time imaging, and Dr. M. C. Steward (Univ. of Manchester) for editing English. We also thank Mr. H. Okawara and M. Takagi (Natl. Inst. for Physiol. Sci.) for technical assistance with the NMR hardware, and Ms. R. Panigel (Tel Aviv Univ.) for technical support. We finally thank Ms. J. Seo for providing her anterior tooth.

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References D. G. Cory. A m Rep of NMR Speclr. 24 (1992) 88. I. Koizuka, Y. Seo, M. Murakami, R. Seo, and I. Kato, NMR in Bionied. 10 (1997) 31. F. L. Chan, J. K. F. Chan, and L. L. Y . Leong, Hepuro-Gusiroefrferol.44 (1997) 358. K. L. Moon, H. Hricak, A. R. Margulis, R. Bernhoft, R. A. Filly, and L. E. Crooks, Rudiol. 148 (1983) 753.

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F. Moriyasu, N. Ban, 0. Nishida. T. Nakamura, Y . Soh, T. Kawasaki. T. Tamada. M. Sakai, T. Miyake, and H. Uchino, Afner. J . Gasrroenterol. 82 (1987) 139.

6.

R. L. Baron, W. P. Shurnan, S. P. Lee, C. A. Rohrmann Jr., R. N. Golden, T. L. Richards, M. L. Richardson, and J. A. Nelson, Amer. J . Rudiol. 153 (1989) 497.

7.

T. M. Haygood, Clin. Orthopaed. Relat. Res. 336 (1997) 3 18.

8.

S. Ketudat, R. V. Pound, J. Chem. Phys. 26 (1957) 708

9.

Y. Sharf, U . Eliav, H. Shinar, and G. Navon, J. Magn. Reson. B 107 (1995) 60.

10.

H. Shinar, Y. Seo, G. Navon, J. Magn. Reson. 129 (1997) 98.

11.

L. Tsoref, H. Shinar, G. Navon, Magn. Reson. Med. 39 (1998) 11.

12.

H. Shinar, U. Eliav, T. Knubovets, Y. Sharf, and G. Navon, Quurr. Magn. Reson. Biol. Med. 2(1995)73.

13.

M. KLinkenberg, P. Bliirnler, and B. Bliirnich, J. Magn. Reson. A 119 (1996) 197.

14.

Y. Sharf, Y. Seo, U. Eliav, S. Akselrodand, and G. Navon, Proc. Nail. Acad. Sci., USA, (in press)

15.

B. J. Balcom, R. P. MacGregor, S. D. Beyea, D. P. Green, R. L. Armstrong, and T. W. Bremner, J . Magn. Reson. A 123 (1996) 131; see also chapter 5.

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43. Magnetic Resonance Microimaging of Teeth S. N . Scrirngeourl, C. H. Lloyd’, G. Hunte?, J. A. Chudek’, and R. L. MacKay2

‘Dental School and *Chemistry Dept., University of Dundee, Dundee DD1 4HN, UK

Abstract A human third molar has been examined using magnetic resonance microimaging (MRM) with a spin-echo pulse sequence to create a full surface reconstruction and transverse voxel thick image slices. The latter correlate well with optical microscopy. Narrow low intensity features visible on the MR image slices are absent from the surface reconstruction. A carious lesion in the enamel on the occlusal surface is revealed by MRM and the image clearly shows the extent of demineralisation.

43.1 Introduction Although the mineralised structures in human teeth do not give a ‘H NMR spectrum with sufficient resolution to produce a conventional “liquid” image, the soft tissue and fluid in the pulp do. Encapsulating the tooth in an appropriate elastorneric material enables the image of the external mineralised tissue surface to be recorded by conventional “liquid” MRM through knowledge of the position of the tootWelastomer interface. Thus it is possible to create an image showing the spatial relationship between soft tissues and fluid occupying the pulp cavity and the tooth surface [ 11. This is important information since human teeth have a natural variability and normal calcification processes can in time alter the morphology of the cavity. Dental caries is still an extremely common disease. The presence of localised high concentrations of acid producing bacteria on the tooth surface leads to a reduction in pH at that site as organic acids are produced through the breakdown of dietary sugars by bacteria. Enamel is porous at the microscopic level and this acid can penetrate into the

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tissue. The very earliest stage in the carious process is characterised by a subsurface demineralisation (the “white-spot lesion”). Often the surface of the enamel remains intact when Ca2+ and PO,’. ions released by subsurface demineralisation reprecipitate at the surface. The carious lesion may arrest or progress until ultimately it spreads into the softer dentine and a cavity forms as support for the enamel is lost. Early arrested caries may discolour with the passage of time as oral fluids enter and stain the lesion. It is possible to image carious lesions by conventional “liquid” MRM. Research is continuing to evaluate the application of MRM to this important aspect of dentistn,.

43.2 Materials and Imaging A 37 years old female was referred to Dundee Dental Hospital for the treatment of chronic periodontitis. Extraction of a non-functional erupted third molar was part of this treatment. The tooth was removed with the minimum trauma and placed in 4% formalin buffered saline, in which it remained until imaging a few days later. Visual examination

revealed that the tooth was fully formed with a “closed” apical foramina and an atypical morphology, having the roots fused along their entire length. Dark discolouration of the enamel existed around a very small occlusal cavity. When a steel probe was applied to this discoloured enamel it felt no different to other enamel. To minimise magnetic susceptibility effects at the aidtooth interface the tooth was encapsulated in a silicone based adhesive putty (Blue-tak@,Bostik Ltd., Leicester). The image was acquired using a Bruker AM300WB (7.1T) spectrometer fitted with a Bruker microimaging attachment and utilising a 25 mm cavity resonator. A standard Bruker spin-echo pulse sequence was used to collect the 256 x 128 x 128 dataset and this was transformed to a 128’ voxel image. A medium resolution image with an approximately 100 pm voxel was considered acceptable at this stage of the study, but even so the data collection time was about 12 hours. After the MRM experiment had been completed the tooth was cut by conventional histological methods into 290 f 60 pm serial slices, approximately at right angles to the tooth axis. The width of the cut made by the diamond wheel was 180 pm. Therefore, a histological slice spans 470 pm of the tooth, equivalent to four spin echo slices.

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46 1

Fig. 43.1: A spin-echo image full surface reconstruction of a human upper third molar. a) Viewed from the side. A darker grey carious lesion can be seen on the occlusal surface to the left between the cusps b) viewed in an axial direction to show the occlusal surface. The carious lesion is seen as a darker central area. c) virtual sectioning reveals the depth of the carious lesion and the pulp cavity. (The “ Y shape in the centre. d) after the “fully mineralised tissue” has been removed.

43.3 Results The transverse slices from the transformed data show the encapsulating material, the pulp cavity and the carious lesion (the latter two being of higher relative intensity). From these images grey ranges corresponding to the three were selected and the data points used to create a pseudo-3D rendered image of the tooth. Electronic removal of the outer surface of the encapsulating material leaves the inner surface to represent the surface of the tooth, (Fig. 43.la and b). This surface also shows a darker central area which corre

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Fig. 43.2: Spin-echo images 112 pm thick slices approximately at right angles to the tooth axis. [NB Images were recorded with artificial colour applied according to grey level (red most intense, blue least intense). For this figure reproduction in monotone has converted the most intense (red) areas to dark grey (see spectra). These intense (reddark grey) regions are outlined by light grey zones. (This applies to Figs. 43.3 and 43.4. also).] The encapsulating elastomer is seen surrounding the non-imaging dentine. a) at 2.40 mm from the apex of the root. The narrow low intensity root canals can be seen. b) at 4.77 mm; the root canals are more apparent. c) at 5.83 mm; these canals widen further. d) at 7.33 mm; the root canals begin to merge. e) at 8.79 mm; the canals merge to form the pulp chamber which contains soft tissues and fluid producing a high intensity image. The higher intensity material outside the tooth is probably periodontal ligament which had not been removed. f) at 9.38 mm; the image cuts through the centre of the pulp chamber. g) at 9.70 mm; the upper limit of the pulp chamber. h) at 10.86 mm; the pulp horns appear. i) at 1 1.42 mm; above the pulp.

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Fig. 43.3: A comparison of spin-echo image slices (a and c) and their corresponding optical microscopic images (b and d, respectively). Figures a,b are at a distance of 5.83 mm from the apex and c,d are at 9.13 mm. Correlation is very good.

sponds to the visible discolouration seen on the occlusal surface of the tooth. Virtual bisection of the tooth reveals the depth to which the lesion extends (Fig.43.1~).Further subtraction of the intensities which produce the surfaces of the elastomer (and hence tooth surface) leaves an image of the pulp cavity and the carious lesion (Fig. 43. Id). The absence of root canals is at variance with the large well-defined pulp chamber and would require an exceptional and unusual pathogenesis. A series of one voxel thick (1 12 pm) slices from the 3D spin-echo dataset were examined to determine whether the apparent absence of canals is an artefact of the full surface reconstruction procedure. It is clear from Fig. 43.2a-j that root canals do exist and are continuous between the apex and the pulp chamber, although they are narrow and have a low intensity. At places the diameter approaches the voxel size. Enhancing the image contrast outside the normal default settings to reveal lower intensity features did not change significantly the apparent diameter of the root canals. The spin echo image correlates well with the corresponding light microscopy image (Fig. 43.3a-d). Given the age of the tooth the production of secondary dentine can account for this narrowing of the root canals. The intensity

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of material within the root canals combined with the possibility that these narrow canals are shared between adjacent voxels has resulted in an intensity below the threshold selected to generate a clearly defined surface reconstruction. Whereas the full surface reconstruction may give an image in which sub-threshold components of features are not displayed, all the relevant information is contained in the spin echo slices. Resolving this problem was essential to progress to a study of less well defined structures, such as the carious lesion. As can be seen in Fig 43.1, the occlusal surface is fissured naturally. The enamel sur-

face layer follows the convolution. This complicates the interpretation of planar section images which cut through this region. Nevertheless it is apparent that demineralisation increases over a finite distance in the surface of the lesion on a line from the unaffected enamel towards the centre of the lesion. Also, that the lesion advances more rapidly in some places than others (Fig. 43.4a to f).

Fig. 43.4: Spin-echo image slices through the carious lesion. The greatest demineralisation is seen at the centre of the lesion. The occlusal surface contains fissures and cusps consequently islands and ridges appear once this region has been entered (c). Slices are presented for a) 12.54 mm from the apex (the extremity of the lesion) b) 13.55 mm c) 14.22 mm d) 14.56 mm e) 14.90 mm and f) 15.25 mm.

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43.4 Conclusions The images of teeth which are produced by MRM are suitable for research on dental anatomy (and in particular the pulp cavity) and dental caries. Caution must be exercised when full surface reconstructions are used since features such as narrowed mineralised root canals may have intensities less than the threshold selected for reconstruction. Adequate information is contained in spin-echo slices for investigating healthy structures and those which result from the carious process.

Reference 1.

C. H. Lloyd, S. N. Scrimgeour, J. A. Chudek, G. Hunter, R. L. MacKay, Quintessence In?. 28 (1997) 349

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44. MRM, an Alternative Approach to the Study of HosVParasitoid Relationships in Insects J , A. Chudek, G. Hunter, R. L. MacKay, and S. Moritz

Department of Chemistry, University of Dundee, Dundee, DD1 4HN, UK A. N. E. Birch, I. E. Geoghegan, arid R. J. McNicol Scottish Crop Research Institute, Invergowrie, Dundee, DD2 5DA, UK

M.E. N. Majerus Department of Genetics, University of Cambridge, Cambridge, CB2 3EH, UK

Abstract MRM provides a hitherto unavailable insight into the interactions between host and parasitoid in the insect kingdom. Conventional dissection techniques can only give circumstantial evidence as to the behaviour of parasitoids within host insects. MRM is allowing this behaviour to be examined in living insects, confirming much data on these relationships which was previously conjectural.

44.1 Introduction At a time of increasing concern over the use of chemical insecticides in the control of pests, alternative methods must be found to control insect populations. One approach is to use natural enemies (e.g. predators) to control pest insect population. This cannot be done randomly, the interaction between each species must be studied with care. Equally so, as in the study described here, it is often necessary to protect one species beneficial to mankind from the ravages of another.

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J . A. Cliudek, G.Hunter, R. L. MacKuj, S. Moriri, A. N . E. Birch, 1. E. Geogliegati, e t t i l .

Another problem is to monitor the interaction between native and introduced species of insect. This has received considerable recent attention as a result of the introduction of

Harmonia axyridis into America. The threat to native species from those introduced as part of classical biological control programmes has renewed the need for proper understanding of the role played by native aphidophagous species in integrated pest management. Magnetic Resonance Microscopy provides a unique method of studying host/parasitoid interactions in the insect kingdom.

The Problem Under Investigation By eating aphids which damage crops and plants, ladybirds annually save millions of pounds sterling for the agricultural and horticultural industries of the United Kingdom. Each seven spot ladybird (Coccinella 7-punctata) (Coleoptera: Coccinellidae), the commonest species in the British Isles, consumes of the order of 5.5. lo3 aphids during its life-time. However, infection by a small parasitic wasp, Dinocantpus coccinellae (Hymenoptera: Braconidae), has adverse effects on the ladybird reproductive capabilities and population densities and poses an increasing threat to the viability of some coccinella populations. Some populations in Scotland have been found to be 50% infected [ I ] . It has therefore become urgently necessary to introduce policies which reduce the impact of this wasp. A necessary precursor has been to develop a method whereby the wasp larva can be identified inside the ladybird and its larval stages non-invasively monitored.

Fig. 44.1: a) The 7 spot ladybird (Coccinella 7-punctata) (Coleoptera: Coccinellidae) in its natural habitat. The small dark objects are the remains of aphids consumed by the ladybird. and b) A female ladybird being infected by the parasitic wasp, Dinocninpus cocririellae (Hymenoptera: Braconidae).

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469

44.2 Experimental Sample Preparation and Imaging The specimen ladybird was placed without restraint in the bottom of a 10 mm 0.d. NMR tube filled with CO, gas from a generator and sealed with a standard cap. This kept the insect comatose for up to eighteen hours without apparently causing it physical damage. Imaging data were collected on a Bruker AM300NB spectrometer fitted with a Bruker microimaging accessory using a 10 nun cavity resonator rf coil. A standard Bruker 3D spin-echo sequence was used. The data were transformed and worked up into slices, maximum intensity projections, and surface rendered reconstructions using a Bruker X32 workstation. The real pixel resolution was 78 pm on a side (although the data shown here have been interpolated up to a pseudo-resolution of 25 pm), sufficient to allow observation of larvae as early as the first instar. It was found that maximum contrast was obtained using a TE of 5 ms and a TR of 520 ms.

44.3 Results MRM clearly revealed the presence of the larva of the parasitic wasp Dinocampus coccinellae inside the body of its host Coccinella 7-punctata. Figures. 44.2 and 44.3 respectively show maximum intensity projections and surface rendered reconstructions of Coccinella 7-punctata before and 16 days after infection. Also seen (as an increase in the bulk of the host) was the effect of teratocyte cell generation initiated by the presence of the parasite. When fully formed the prepupal parasitoid emerged and constructed a cocoon beneath its host, using the latter’s body for protection (Fig. 44.4). No trace of the parasitoid remained in the host.

470

J . A. Chudek. G. Hunter, R. L. MacKuy, S. Moritz, A. N . E. Birch, 1. E. Geoghegan, er al.

Fig. 44.2: Maximum intensity projection of: a) an uninfected ladybird and b) an infected ladybird containing a stage 2 larva clearly seen in the tail of the insect (left hand end). Note especially the change in bulk brought about by the production of teratocytes (trophic cells) within the ladybird.

Fig. 44.3: Surface rendered reconstruction of: a) an uninfected ladybird and, b) an infected ladybird containing a stage 2 larva (the head of the parasitoid larva can be seen). Again the change in bulk of the host brought about by the production of teratocytes (trophic cells) can be seen clearly.

Fig. 44.4: a) Maximum intensity projection and, b) surface rendered projection of the ladybird with the pupa of the wasp lying underneath it. The image attributed to the larva inside the host ladybird has now gone.

44. MRM, an Alternntive Approach to the Study of Host/Parasiloid Relationships in Insects

47 1

44.4 Conclusions Potential of MRM for the Study of Host Parasitoid Interactions in Insects By making use of the non-invasive nature of NMR to determine the parasitoid infection status of field collected insects the entomologist can redesign many basic tests both to make them more meaningful and more economically viable. For example in the present investigation it enables: 1 . Inspection of the parasitoid infection status of field collected coccinellids prior to formal choice tests of parasitoid host preferences in respect of host species, size, sex, age, infection status, nutritional and reproductive condition, or no-choice tests to assess the level of relative versus absolute host quality. 2. Effects on the copulatory behaviour of infected hosts, and of uninfected hosts, towards infected hosts to be examined, e.g. willingness to mate, rejection behaviour rates and mating duration by determining parasitoid development. 3. The in vivo quantitative assessment of the lipid content of both the parasitoid and its host, thus allowing the nutritive condition of hosts to be monitored throughout the development of the parasitoid larva. These studies would not be possible by normal conventional dissection studies followed by light microscopy because of the large number of individual specimens required to follow such a developmental sequence.

References 1.

M. E. N. Majerus, Brif. J. En!. Nut. Hist. 10 (1997) 15.

2.

I. Hodek, A. Honek, Ecology ofthe Coccinellidae, Kluwer Academic Publishers, 1996.

3.

I. A. Chudek, A. M. E. Crook, S. F. Hubbard, G . Hunter, Magn. Res. h a g . 14 (1996) 679.

4.

I. E Geoghegan, W. P. Thomas, M. E. N Majerus, Entomologist 116 (1997) 179.

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45. Plant Growth Studies Using Low Field NMR L. van der Weerd, T. Ruttink, D. vun Dusschoten, F. J. Vergeldt, P. A. de Juger, and H. Vari As Laboratory of Molecular Physics, Wageningen Agricultural University, Dreyenlaan 3,6703 HA Wageningen, The Netherlands

Abstract The effect of osmotic stress on plant water status and apical plant growth has been studied in six week old maize plants in well defined and controlled climate conditions using quantitative low field NMR imaging. Simultaneous with the NMR measurements several other techniques including water uptake measurements and photosynthetic activity measurements were used. Quantitative single parameter images of spin density and T2 were used to follow the water status and to discriminate between the different tissue types. Growth appeared to be strongly inhibited by mild stress, whereas water uptake and photosynthetic activity are far less effected by the stress conditions. T2 is strongly dependent on cell size in the growing tissue, but does not change during mild osmotic stress.

45.1 Introduction One of the least understood aspects of plant physiology is the integration and coordination of processes at the organ and whole plant level. This deficiency is scarcely surprising; technological developments that would make it possible to routinely and accurately measure performance of the whole plant have received little attention. By being able to study fluxes and plant water balance it will be possible to explicitly or implicitly examine many aspects of plant function and plant responses to environmental changes, such as changes in water status, redistribution of water between vital organs and changes in stem or leaf growth rates. In this chapter we will focus on one process in particular, namely the response of plant growth to drought stress.

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L. v m der Weerd, T. Ruttink. D. van Dusschoten, F. J . Vergeldt, P. A. de Joger, and H . Vnn A.r

Plant growth is known to be one of the most sensitive processes to water deficits in

the plant [I], which makes this process an excellent parameter to study drought tolerance mechanisms in plants and differences between species. The Plant water status is strongly affected by the water potential applied to the roots, which influences the water uptake, and by the leaf water potential, which has a strong effect on the evaporation rates. Plant growth is the third factor to complete the water balance [ 1,2]. Plant growth during water deficits has been a major research area for decades and many groups reported on growth of the entire plant [3] and of specific organs such as roots [4,5] and leaves [6,7]. Growth of the shoot apex however was only a subject of minor interest, because of the required invasive methods which impeded the measurement of fast dynamic growth changes [8]. NMR imaging proves to be a strong tool for the research of internal plant development. The use of this technique provides the possibility to perform non-invasive stress studies in which the response of the various organs to stress as well as the time dependency of the response can be monitored.

45.2 Information from Low Field NMR For reliable plant studies it is necessary to obtain quantitative single parameter images representing e.g. the spin density Ao(r) and the relaxation time T2(r), which are not affected by the other parameters. Quantitative and reliable Ao(r) and T2(r)images can be obtained by use of multi-echo imaging at low magneticfields [9]. By extrapolation of the multi-echo amplitude images to TE = 0 real spin-density images are obtained, which represent tissue density times water content per pixel [ 101. The amplitude is a powerful parameter to monitor tissue dehydration and rehydration, especially in combination with information on tissue shrinkage and swelling, which is available from the tissue area in images. Plant tissue typically is composed of cells, kept in shape by rigid cell walls, with a large amount of intercellular air spaces. These air spaces cause susceptibility boundaries which create strong local field gradients, thus attenuating the water signal. To minimise susceptibility artefacts and to cover the shortest possible relaxation times one has to use as short as possible echo times in imaging plants [9-111. The effect of the echo time and the magnetic field strength on the obtained spin density and T2 images for water in mush-

45. P l a n t Growth Studies Using Low Field NMR

475

room has been reported by Donker et al. [9,10]. Due to the actual low signal-to-noise ratio it is hardly possible to observe non-monoexponential signal decay behaviour per pixel in an image. In tissue with vacuolated cells the vacuole contains the largest amount of water and mainly vacuolar water is reflected in the T2 images. Thus, the observed T2 is mainly influenced by the physiological characteristics of the vacuole, of which the vacuole size and the loss of magnetisation at the vacuole membrane, characterised by the sink strength parameter H (ms-I), are the most important. For a spherical vacuole the relationship between the vacuole radius and the observed T2 is given by eqn. (45.1), (45.1) where Tz,obsis the measured T2, T2,bulkis the intrinsic T2 of water in the vacuole and r is the vacuole radius [13]. One has to be aware that the actual observed T2 values in an image strongly depend on the imaging details [9,12].

45.3 Experimental Setup The low field system used for the measurements has several major advantages. First, the use of low magnetic fields reduces susceptibility artefacts and permits the measurement of valid parameters, which are not governed by the effect of susceptibility on relaxation. Second, it allows the use of other electrical equipment such as climate control, weight balances and fluorometers simultaneously, which is extremely difficult at high magnetic field strengths. By using this combination it is not only feasible to follow apical growth, but also to correlate the NMR images to the stress behaviour of roots, leaves and the different tissues surrounding the apex. The vertical open access of the electromagnet assures good accessibility for plants and physiological relevant measuring circumstances for both small and large plants. Plants of a length up to 2 meters have been studied in this setup (Fig. 45.1), consisting of a 20.35 MHz S.M.I.S. imager in combination with a 0.47tT Bruker electromagnet and a Doty probe with a 45 mm inner diameter cylindrical sample access. Photosynthetic activity is measured on the second top leaf in a fixed position using a modulated fluorometer. The effective quantum yield of photosystem I1 can be calculated according to Schreiber et al. [14]. The plant roots are placed in a glass container. Root

476

L. van der Weerd T. Rurtink, D. van Dusschoten. F. J. Vergeldt, P . A. de Jager, and H .

Viin As

medium is pumped into the container from below, while the excess of medium is removed at the top, assuring a constant volume of water in the container. The weight of the root medium vessel is measured using a balance. Osmotic stress is applied by replacing the normal root medium by a Polyethylene Glycol 6000 (PEG) solution. halogen light

climate chamber fluorometer

Pump magnet

root medium vessel balance

Fig. 45.1: Experimental setup combining a low field N M R imager, climate control, water uptake measurement and photosynthetic activity measurement (using a PAM fluorometer).

45.4 Growth Studies The system described has been used to monitor growth changes in a six weeks old maize plant during PEG stress. Part of the images are shown in Fig. 45.2. In these longitudinal images it can clearly be seen that in the images 1 - 3 and 6 - 10 the shoot apex moves upwards in time within the plant stem. After 54 hours the slice position is changed to the region just above the apex. Osmotic stress is applied from t = 54 to t = 105 hours. During the stress period hardly any apical growth is observed.

15.Plant Growth Studies Using Low Field NMR

477

Fig. 45.2: Longitudinal 1/T2 images of a six week old maize plant during PEG stress. At f = 55 h the plant stem was repositioned.

The results of the chlorophyll fluorescence measurements, the water uptake and the growth rate measurements are shown in Fig. 45.3. These results were obtained after one or two days of adaptation of the plant in the experimental setup. After this adaptation period the water uptake rate and fluorescence activity attain constant values. Apical growth is completely inhibited during the first hours after placing the plant in the probe. This indicates that plant behaviour is strongly affected by inserting it in the experimental setup, so that an adaptation period of at least one day is needed before physiologically relevant measurements can be performed. After adaptation comparison with data acquired on plants outside the experimental setup (not shown) yields no effect of the measurements on water uptake and photosynthetic activity. Apical growth can not be measured non-invasively outside the NMR system, but the stabilisation of the growth rate after adaptation in the NMR system and the accordance of the found rates with the rates for internodial growth measured by monitoring the displacement of external visible internodes indicate that the plants are not severely influenced by the experiments. After applying osmotic stress the uptake rate during the light period on average decreased to 75% of the normal value. Elongation growth is presented in this figure for all internodes which could be clearly discriminated by T2 in the images. After applying osmotic stress the growth rates were immediately reduced completely. During the night some growth was observed. When stress is prolonged a minor recovery can be seen, but

478

L. van der Weerd. T. Ruttink, D. van Dusschoten, F. J . Vergeldt, P. A. de Jager, and H . Van As

0

24

48

72

96

120

144

time (hours) Fig. 45.3:Water uptake, absolute growth rate of a number of nodes and photosynthetic activity of a six week old maize plant during -0.25 MPa PEG stress. Dark periods are presented as dark regions in the figure. The stress period is indicated by the dotted area.

45. Plant Growfh Studies Using Low Field NMR

479

growth remains strongly affected by PEG stress. During recovery however, growth rate increases up to 50% compared to the rates before stress was applied. Chlorophyll fluorescence remained fairly constant during the entire experiment, indicating that the applied osmotic potential causes no serious damage of the photosynthetic apparatus by dehydration, although some dehydration of the leaves surrounding the apical zone was observed (Fig. 45.2). In the experiment shown the discontinuity in the photosynthetic activity data after 80 hours was caused by a displacement of the measured leaf. The spin-spin relaxation time T2 shows a good correlation with the elongation of the apical cells. Far more than in the amplitude images, the nodes and internodes can be distinguished in the T2 images. The most important cause of the differences observed is the size of the vacuole. The relationship described by eqn. (45. l), adapted for cylindrical vacuoles, appeared to be observed by the growing apical cells. The next step in these plant studies is to combine the presented studies with PFG Turbo Spin Echo measurements to monitor water flow and diffusion during osmotic stress [ 151.

References 1.

T. C. Hsiao,An. Rev. Plant Phys. 24 (1973) 519.

2.

I. N. Saab, R. E. Sharp, J. Pritchurd Plant Phys. 99 (1992) 26.

3.

G. S. Premachandra, H. Saneoka, M. Kanaya, S. Ogata, J. Plunf Phys. 135 (1989) 257.

4.

J. M. Ribaut, P. E. Pilet, Phys. Plantaruni 81 (1991) 156.

5.

P. M. Neumann, in F. Baluska, ed., Structure and Function of Roofs, Kluwer Academic Publishers, Dordrecht, 1995.

6.

E. Van Volkenburgh, J. S. Boyer, Plant Plzys. 77 (1985) 190.

7.

S. J. Palmer, W. J. Davies, J. Exp. Bof. 47 (1996) 339.

8.

Y. Hasjimoto, P. J. Kramer, H. Nonami, B. S. Strain, eds., Measurement Techniques in Plant Science, Academic Press Inc., San Diego, 1990.

9.

H. C. W. Donker, H. Van As, H. T. Edzes, A. H. W. Jans, Magn. Reson. Imiging 14 (1996) 1205.

10.

H. C. W. Donker, H. Van As, H. J. Snijder, H. T. Edzes, Magn. Reson. Imaging 15 (1997) 113.

11.

P. T. Callaghan, Principles of Nuclear Magnetic Resonance Microscopy, Clarendon Press, Oxford, 1991.

12.

H. T. Edzes, D. van Dusschoten, H. Van As, Magn. Reson. Imaging 16 (1998) 185.

13.

J. E. A. Reinders, A Nuclear Magnetic Resonance Srudy of Plant-wafer Relationships, PhD Thesis Wageningen Agricultural University, 1987.

14.

U. Schreiber, U. Schliwa, W. Bilger, Photosynfh. Res. 10 (1986) 51.

15.

T.W. J. Scheenen, D. van Dusschoten, P. A. de Jager, H. V'an As, see chapter 46.

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46. Fast Spatially Resolved Displacement Imaging in (Bio) Systems T. W. J. Sclieenen, D. van Dusschoten, P. A. de Jager, and H. Van As

Laboratory of Molecular Physics, Wageningen Agricultural University, Dreyenlaan 3, 6703 HA Wageningen, The Netherlands

Abstract A Pulsed Field Gradient Turbo Spin Echo sequence is presented which is able to resolve flow and diffusion information in two spatial dimensions accurately and quantitatively. A three-dimensional image set (128 x 128 x 32 matrix, resolution 3000 x 120 x 120 pm), which is used for the calculation of the so-called Displacement Propagator for each pixel, is acquired in 30 minutes. Measurements on a fully grown, intact tomato plant demonstrate the power of this technique for future plant studies.

46.1 Introduction Flow andlor difision in heterogeneous (bio)systems can be measured with Pulsed Field Gradient Nuclear Magnetic Resonance (PFG NMR) experiments. In a PFG experiment the attenuation of the signal amplitude is caused by random displacement of spins during

the observation time A between two PFG’s of duration 6. If the displacement of the spins is caused by a net flow in the gradient direction then a phase shiji @ is observed, proportional to the product y6G and R, the displacement in the direction of G of the spins during the observation time. Without prior knowledge of the flow-profile, flow within the pixel is difficult to quantify. The solution to this problem is to measure the complex signal S as a function of G . A Fourier Transform (FT) of S(G) results in the average propagator P(RIA). This function gives the probability that a spin at any initial position is displaced by R during the time A. This type of measurement is called displacenient or q-space imaging and can

482

T. \I/. J . Srliecwen, D.van Dirsschoreri, P . A. de Jager. arul H. Van As

be performed spatially unresolved [l], by resolving a line through the sample [2] or resolving two dimensions [ 3 ] ,although this experiment can take several hours. Here a method is presented which is able to record a full 2D spatially resolved (1space image in a short acquisition time (30 min). The method has been used to measure three objects: a simple phantom to test the accuracy of the method, an artificial kidney as a more complicated model for plant stems and an intact tomato plant.

46.2 The PFG Turbo Spin Echo Sequence Flow measurements have been performed using Echo Planar Imaging (EPI) [4]. Multiple spin echoes together with PFG's have been used to study diffusion [ 5 ] . The Pulsed Field Gradient Turbo Spin Echo (PFG TSE) pulse sequence is a unique combination of using PFG's to investigate flow andor diffusion and the Turbo Spin Echo technique, which uses a train of echoes to phase-encode the NMR-signal. The advantage of using multiple spin echoes instead of gradient echoes (as in an EPI experiment ) is the sensitivity of EPI for in situ field inhomogenities. EPI requires a long T l and therefore the gradient set used must be of extremely high quality. Spin echoes overcome the local field inhomogenity problems by reversing the phase of the NMR-signal. The fact that the echoes are phase-sensitively detected creates the possibility to observe the phase of the echoes as a function of the PFG's and not just follow the signal amplitude attenuation, so flow and diffusion information is obtained simultaneously. In the PFG TSE sequence (Fig. 46.1) the magnetisation after a slice-selective 90" pulse is displacement encoded by two PFG's with duration 6 and observation time A. The height of the PFG's is varied from minus to plus GPFmax.The displacement encoded complex NMR-signal is recorded in the train of spin-echoes. The number of echoes used for phase-encoding the NMR-signal (the turbo-factor) is variable and depends on the T2 of the sample. Typically 32 phase-unwrapped echoes were acquired giving 16 phaseencode steps since even and odd echoes need to be acquired separately. In all measurements 32 steps were used to sample q-space which was zero filled once prior to FT. Because both complex images contain identical information after phase correction, FT and mirroring the odd and even echo images can be combined to increase the signal to noise ratio.

483

46. Fast Spafial1.yResolved Displacement Imaging in (Bio)Systems

I

(1 8O0k

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Fig. 46.1: The new PFG TSE pulse sequence. Between the two PFG's and in the echo train 180" pulses are used to overcome signal loss by field inhomogenities. Signals due to imperfections in 180" pulses were crushed by gradient crushers.

46.3 Phantom Studies Measurements on a simple phantom which will be reported elsewhere [6] showed the accuracy of the flow and diffusion measurements: deviations between measured flow velocities and theoretical velocities forced upon the system by a pump are smaller than 3%. The artificial kidney consists of a glass tube (i.d. 10 mm) with stationary water surrounding 1000 capillaries with flowing water (id. 200 mm and semi-permeable walls, 16 nun thick, Fig. 46.2a). If a pixel contains exactly one capillary (Fig. 46.2b, curve 111) then its propagator contains a distribution of dsplacements from 0 to approx. 40 pm (velocities up to 2.9 m d s ) . Pixels with only stationary water show Gaussian propagators centred at zero displacement (Fig. 46.2b, curve I) and pixels with both stationary and flowing water show a combination of the two previous propagators (Fig. 46.2b, curve 11).

484

T. W . J . Scheenen. D. van Dusschoren, P . A. de Jager, and H . Van As

3.oc

'

'

I

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Fig. 46.2: a) The two images in the middle of q-space of the artificial kidney before FT (upper, at G = 0) and after FT (lower, at zero displacement). b) Propagators of three neighbouring pixels: one pixel with only stationary water (I), one pixel with flowing water only (ILI) and one pixel in between (11). Parameters: A = 13.86 ms, field of view = 20 mm, slice = 3 mm, acquisition time = 57 min, rep. time = 1500 ms, pump speed = 2.0 ml/min, rf coil diameter = 30 mm.

46.4 Plant Studies The t o m t o plant studied had been growing for ten weeks, was about 60 cm tall and was put in the instrumental setup (light intensity around 150 Lux, relative humidity 65%, temperature 26 "C)two days before measuring. The measurements on the stem of the growing intact tomato plant showed three areas with xylem-transport. These areas have a lower water content then the surrounding tissues and show a higher T2 variance (Fig. 46.3). In the flowing regions flow velocities up to 4 m d s were found in the propagators.

46. Fast S p d a l l y Resolved Displacetnetir Imaging in (Bio)Systems

485

Fig. 46.3: Single parameter cross-sectional images of the stem of an intact 10 weeks old tomato plant. The amplitude and T2 images have been obtained by use of a multi-echo imaging sequence [ 7 ] . The flow-area image is constructed by summating displacement images 38 to 52 out of 64 (from 17 to 56 mm displacement in time A). Parameters for amplitude and T2 image: 48 echoes, echo time = 5.2 ms, rep. time = 1.5 s, pixel size = 100 x 100 x 3000 Vm, rfcoil diameter = 12 mm. Extra parameters for q-space data set: A = 12.16 ms, rep. time = 800 ms, acquisition time = 30 min.

46.5 Discussion The successful implementation of the new PFG TSE pulse sequence allows the reliable measurement of phase and amplitude effects on the complex echo signal due to diffusion and flow. This enables afust, accurate ‘model free’ measurement of flow velocities and diffusion constants in all kinds of (bio)systems. At a magnetic field strength of 0.5 T it is possible to record a full 2D spatially resolved image set (128 x 128 matrix) combined with q-space information within 30 minutes. By using a lower number of PFG-steps (16 steps instead of 32) the total acquisition time can become even less (15 min). This time resolution is much higher than the several hours (4.5 hours) that has been reported for displacement imaging of flow in model systems [8] and Castor bean seedlings [9,10]. The artificial kidney, as a simple model for a plant stem, shows that flowing and stationary water within one pixel can easily be discriminated and quantified. The results in the intact tomato plant demonstrate that this technique enables one to follow changes in the water balance on a physiological relevant time resolution and a microscopic spatial resolution (3000 x 120 x 120 l m ) which makes this technique an outstanding tool for studies on plants. Fast, quantitative flow and diffusion measurements on full grown, intact plants with satisfying accuracy are now within reach.

486

T. W. J . Scheenen. D. van Diuschoteri, P. A. de Juger. and H. Van As

Acknowledgements This research is financially supported by the Netherlands Technology Foundation

(STW), and is coordinated by the Life Sciences Foundation (SLW), and the EU large scale activity WNMRC.

References 1.

T. J. Schaafsrna, H. Van As. W. D. Palstra, J. E. M. Snaar, P. A. de Jager, Mugn. Reson. /mug. 10 (1992) 827-836.

2.

D. van Dusschoten, J. van Noort, H. Van As, G e o d e m a 80 (1997)405-416.

3.

P. T. Callaghan, Principles of nuclear magnetic resonance microscopy, Clarendon Press, Oxford, 1991.

4.

D. N. Firmin, R. H. Klipstein, G. L. Hounsfield, M. P. Paley, D. B. Longmore, Mugn. Res. Med. 12 (1989) 316-327.

5.

C. F. Beaulieu, X. Zhou, G. P. Cofer, G. A. Johnson, Mugn. Res. Med. 30 (1993) 201-206.

6.

T. W. J. Scheenen, D. van Dusschoten, P. A. de Jager, H. Van As, in preparation.

7.

H. C. W. Donker, H. Van As, H. T. Edzes, A. H. W. Jans, Mugn. Res. h a g . 14 (1996) 1205.

8.

Y. Xia, P. T. Callaghan, Mugn. Res. Med 23 (1992) 138-153.

9.

P. T. Callaghan, W. Kockenberger, J. M. Pope, J. Magn. Reson. 104 (1994) 183-188.

10.

W. Kockenberger, J. M. Pope, Y. Xia, K. R. Jeffrey, E. Komor, P. T. Callaghan, Planta 201 (1997) 5363.

Diffusion and Flow

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47. Generalized Treatment of Modulated Gradient Spin Echo Attenuation for Restricted Diffusion in Spherical Pores S. L. Codd and P. T. Callaghan Department of Physics, Massey University, Palmerston North, New Zealand

Abstract A simple matrix formalism presented in reference [ l ] and based on the impulse-propa-

gator approach of Caprihan et al. [2] allows for the calculation of the echo attenuation, E(q), in spin echo diffusion experiments, for practically all gradient waveforms and for the case of restricted diffusion in enclosing pores, with or without wall relaxation. The gradient waveform is broken into discrete time intervals and E(q) is expressed as a product of an appropriate combination of three matrix operators corresponding to the spin phase evolution and Brownian diffusion in each time interval. Previously this method was adopted [ I ] to evaluate the finite width gradient pulse PGSE and CPMG pulse trains for the case of restricted diffusion between parallel reflecting plates. Here the method has now been applied to the more useful case of restricted diffusion in spherical geometries, and the finite width gradient pulse PGSE experiment has been evaluated and compared with published simulations.

47.1 Introduction The Pulsed Gradient Spin Echo (PGSE) experiment [3] allows us to study the spectrum of translational motion of the spins via a Fourier relationship between the echo attenuation, E(q) and the average propagator, P, = ( 2 , A ) .

490

S.L. Codd arid P. T. Callaghan

(47.1) where C ( Z , A ) = jp(z,O) P,(zlz

+Z,A)dz

and q = (2n)-’yg6 corresponds to the area

under the gradient pulse In the case of particles moving in a porous medium, where the motion is restricted due to collisions with the bounding walls, the echo attenuation will contain the Fourier spectrum of the pore space explicitly [4]. This idea has been extended to the analysis of PGSE experiments in porous media in which the pores are interconnected [ 5 ] . In this case the Fourier spectrum of the pore appears as a form factor in the diffraction pattern associated with Bragg interference between the pore sites. Provided that the pore structure is relatively monodispersed quite accurate structural information can be ascertained using the PGSE method. The range of dimensions accessible to the method is largely determined by the self-diffusion coefficient of the “probe molecule”, or, in the case of flow-driven dispersion [6], by the local fluid velocity. To date pore dimensions in the range 1 pm to 100 pm have been measured. In order to analyze E(q) using the expression above, it must be a valid approximation to represent the gradient waveform as two narrow pulses and this is the limiting feature of the PGSE experiment. The narrow pulse approximation will only hold when the duration, 6, of the gradient pulses is much smaller than the gradient separation, A, and the distance diffused by the particles in time 6 is less than the characteristic dimensions of the porous medium. In the case of restricted diffusion in a porous medium 6 << a2/D is required, where a is the pore radius and D is the self diffusion coefficient. Fundamental experimental limits on the maximum gradient pulse amplitudes restricts the distance scales it is possible to probe and these distance scales are constrained even further by the condition that the rms displacements over time 6 must be less than this distance scale. As smaller pore morphologies are probed, larger gradient pulses are required. With limits on the maximum gradient strengths available, it can be seen that a situation will eventually arise whereby the narrow pulse approximation is not valid and where it is necessary to have a theoretical model appropriate for the analysis of the finite pulse PGSE experiment. Recently several authors have addressed the problem of analysis of the finite gradient pulse PGSE experiment. One approach has been the use computer simulations to examine restricted diffusion in the key geometries [7-91. However a significant and successful analytical treatment has been demonstrated by Caprihan et al. [2]. This approach is based

37. Generalized Trenttnent of Modulated PGSE Atrenuntionfor Restricted Diffusion

49 1

on the idea that the finite gradient pulse can be represented by a series of infinitessimal impulses, thus retaining the propagator representation of eqn. (47.1). A mathematical simplification of this method has been the use of a matrix formalism resulting in closed form expressions appropriate to any gradient waveform [ 11. As a result of these developments it is now possible to use the finite gradient pulse PGSE experiment to non-invasively probe length scales which were previously inaccessible due to the narrow pulse restriction.

47.2 Theory In the treatment of Caprihan, Wang and Fukushima [2] restricted diffusion under general gradient waveforms is handled by breaking the gradient pulse into successive intervals bounded by gradient impulses and writing a diffusion propagator for each interval. All the spin phase evolution is considered to occur at the gradient impulses and the conditions of the narrow pulse PGSE experiment hold for each interval. However their expressions involve a multiple sum over a large number of independent terms. Recently Callaghan [ 11 derived a simpler, and quite general, closed form expression. The generalized gradient waveform is treated as a sequence of discrete time intervals during which the spatial diffusion of the spins takes place. These intervals are separated by impulses of gradient where all the spin phase evolution occurs and the conditions of the narrow pulse PGSE experiment hold for each interval. The key feature in "the matrix formalism" analysis is the use of the eigenfunction expansion for the propagator, (47.2)

these eigenmodes are well known for the case of planes, cylinders and spheres. For any given geometry, three matrix operators are all that is required. A matrix product of these matrices is formed easily and the expression demonstrates clearly the time sequence of spin phase evolution. E(q) = S(q) R A(q)"' R A(q)m3R.......RA(q)"("-')RA(q)In"R S(q)'

(47.3)

(47.4) (47.5) (47.6)

47.3 Spherical Pore Solutions To apply the matrix formalism to the case of restricted diffusion in spherical pores it is necessary to obtain solutions for the three matrix operators S(q), A ( q ) and R (eqns. (47.4) to (47.6)) using the appropriate eigenfunctions. For the spherical boundary case the eigenfunction solutions, that can be found in reference [ 101, are

where bnn,are the normalisation coefficients,

(47.8)

and arm, are the roots of the transcendental (47.9)

Incorporation of relaxation at the walls corresponds to a non-zero value for M.

47. Generalized Treatment of Modulated PGSE Attenuation for Reslricted Diftiuion

493

Substituting these eigenfunctions into eqns. (47.4) to (47.6) gives

S, (4)=

d P,,,m 1j , (a,,,,,

1

)r2J'P, (cos 0) exp(iqrcos 0) d(cos

a

R,

(

e) dr

(47.10)

-1

= exp - a;,,,

(47.11)

) : 7

(47.12) 1

x pn (cos 8)pk (cos e) exp(iqr cos e) d(cos e) dr -1

Evaluation of these integrals is the primary new result of this work and yields

(47.13)

R,,

[ ::)

= exp

-a;nr -

n ( n + k + ~ + 2 p1+ 2 m + 2 s + 3

(47.14)

494

S. L. Codd and P. T. Callaghan

Where n+k+l c=, I n - k l < I S n + k a n d n + k + I is odd 2

The truncation to finite matrices is only possible if the diagonal elements of R have reduced sufficiently at the point of truncation. The eigenfunction associated with each matrix indice p or v is determined by arranging that the root annincreases with increasing p, thus ensuring that the most significant elements are included in the matrix product. The correspondence between n, n’and p is shown in Table 47.1 for p = 1 to 5 . k and k ’ are the indices corresponding to the value of v. I

Table 47.1 : Correspondence between n, n ‘and p.

VIP 1

2 3 4 5

n/k 0 1

2 0 3

n’/k’ 0 0

0 1

0

anrl / (Xkk, I

0.00 2.08 3.34 4.49 4.5 1

47.4 Results Results obtained using the above analytic expressions were verified by comparing them with Monte Car10 computer simulations published by Linse and Soderman [9]. These simulations analyse E ( q ) by keeping the Gradient amplitude, G, constant and varying the duration, 6, of the gradient pulse, see Fig. 47.1. The matrix operator product required to represent their experiment is E(qTo-pA) = s(q) [R(T)A(4)lM R(T)N-M[R(T)A(4)IM R(T)s(q)

(47.16)

where qTOT is increased from 0 to nla by setting q to d ( M m a x a)and incrementing the integer M from 0 to M,,,,,. The ratio Mmax/N = Gmax/A. The results for A = 0.2a2/Dand yg = 40D/u3 and 200D/a3 are shown in Fig. 47.2 as solid lines and discrete points taken from the computer simulations are overlaid as solids points. The narrow pulse limit of

47. Generalized Treattnent of Modulated PGSE Attenictrtionfor Restricted Drfision

495

A = 0.2a2/D and yg = 00 is evaluated using the above matrix product with M = 0 and a = qTOT.The S(q) and A(q) matrices were calculated in a C-programme and the matrix product was evaluated in ‘MATLAB’. This entire calculation takes only a few minutes on a PowerMac.

N-M

N-M

I’

2N+ 1

Fig. 47.1: E(q) is analysed by keeping G constant and varying the duration, 6, of the gradient pulse.

Note that these comparisons involve no fitted parameters. The calculations are absolute. The excellent agreement between the simulated and analytical data confirms the validity of the solutions to the matrix operators for spherical pores and provides further evidence of the ability of the matrix formalism to analyse the finite pulse PGSE experiment.

47.5 Discussion The extension of the impulse propagator methodology to the case of spherical pores is significant. Many natural porous media are based on a spherical pore structure. This geometry is also of particular significance in the study of emulsions and colloidal structures. From a mathematical standpoint the spherical pore treatment is more challenging than that of the rectangular geometry demonstrated in reference [ 13. However, once the S, A and R matrices are expressed in analytical form, the evaluation of E(q) for any gradient waveform whatsoever is no less straightforward. Of course the further extension to cylindrical pores is trivial and we will present these expansions in a later publication [ 1 I].

496

S. L. Codd and P. T. Cnllaghan

100

Yg

' 40D/a3 200~1~3 10-1

o m

10-3

10-4

Fig. 47.2: The results for A = 0.2a2lD with yg = 40D/a3 and 2OOD/a3 are shown as solid lines and discrete points taken from the computer simulations are overlaid as solids points. The narrow pulse limit of A = 0.2a2/D and yg = m is also shown.

Another issue of practical concern is the treatment of restricted diffusion in interconnected porous media. Provided the pore space can be represented in an eigenmode expansion, then the extension is, in principal, straightforward. However, such a representation is only possible in regular geometries [12] and not, for example, in glassy, disordered structure. One possible approach in this latter case is to use a real space (rather than an eigenspace) representation of the propagator and proceed with the matrix evaluation somewhat in the manner of a numerical simulation. Finally we note that the methods presented here are not only applicable to the PGSE q-encoding experiment but can also be used for handling the case of NMR microimaging via k-space encoding. It is well known that restricted diffusion in NMR microimaging can lead to significant edge enhancement and distortion effects. The analytical treatment

of this problem is extremely simple using the matrix formalism, and has been published elsewhere [ 131. The resulting comparisons of theory and experiment provide further evidence of the general utility of this method.

47. Geiieru1i:ed Treatment of Modulated PGSE Attenuation fiir Restricted Diffusion

497

References 1.

P. T. Callaghan, J. Mngn. Reson. 129 (1997) 74-84.

2.

A Caprihan, L. Z. Wang and E. Fukushima, J. Mag". Reson. A 118 (1996)94-102.

3.

E. 0. Stejskal and J. E. Tanner. J. Chemical Phys. 42 (1965) 288-292.

4.

D. G. Cory and A. N. Garroway, J. Magn. Reson. Med. 14 (1990) 435-444.

5.

P. T. Callaghan, A. Coy, T. P. J. Halpin, D. Macgowan. K. J. Packer, and F. 0. Zelaya, J . Chem. Phys. 97 (1992) 651-662.

6.

J. D. Seymour and P. T. Callaghan, J. Mngn. Reson. A 122 (1996) 90-93.

7.

M.H. Blees, J. Mugn. Reson. A 109 (1994) 203-209.

8.

A. Coy and P. T. Callaghan, J. Chem. Phys. 101 (1994) 4599.

9.

P. Linse and 0. Sodennan. J. Mugn. Reson. A 116 (1995) 77-86.

10.

P. T. Callaghan, J. Mugn. Reson. A 113 (1995) 53-58.

11.

S. L. Codd and P. T. Callaghan, to be published.

12.

D. J. Bergman and K. J . Dunn, Phys. Rev. E 51(4) (1995) 3401-3416.

13.

P. T. Callaghan and S. L. Codd, Magn. Reson. tmaging (1997) in press.

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48. NMR-Imaging Techniques for Quantitative Characterization of Periodic Motions: ‘Incoherent Averaging’ and ‘Spectral Side Band Analysis’ U, Goerke and R. Kimmich Sektion Kernresonanzspektroskopie, Universitiit Ulm, D-89069 Ulm, Germany

Abstract Motion-sensitive magnetic resonance imaging techniques - the method of incoherent averaging and the spectral side band analysis - have been developed to quantitatively characterize time-dependent motions with a pulsation period shorter than the total imaging time. Unlike standard methods, these techniques do not require the correlation between the periodicity of the motion and the acquisition governed by the repetition time of the transients. Using incoherent averaging of either temporal or spatial fluctuations of the motion the spatial distribution or the temporal characteristics, respectively, is probed. The spectral side band analysis, instead, relies on the - in conventional imaging undesirable - phase-modulation owing to periodic motions. Both methods were applied on pulsating motions which have been discovered in incubated bird eggs [1,2].

48.1 Introduction Motion-sensitive Fourier magnetic resonance imaging is relatively time-consuming because a series of transients have to be acquired for the phase-encoding of spatial and velocity dimensions. The detection of motions is based on the sensitivity of the signal phase to movements of spins in the presence of static magnetic field gradients. Thus, motion which fluctuates on a time scale less than the total imaging time causes a phase-

500

I/. Goerke orid R. Kirnmich

modulation of the signal which deteriorates phase encoded structure information. Conventional techniques therefore aim at minimising temporal velocity fluctuation during the experiment by using fast imaging or synchronising the acquisition with the periodicity of motions to avoid motional artifncts. In contrast, the methods which are presented in this paper do not require adjusting the experimental timing to the pulsation rate of the motion. Experiments were performed on incubated bird eggs in which localised pulsation have been observed starting on about the fourth incubation day [ 1,2].

48.2 Incoherent Averaging Techniques The incoherent averaging technique is based on averaging of the motions which are uncorrelated in respect to the temporal andor spatial resolution of the experiment.

48.2.1

Spatially Resolved Distribution of Motions

A gradient echo imaging sequences is supplemented with a bipolar magnetic field to probe motion with spatial resolution. To eliminate the time-dependent phase-modulation due to temporally fluctuating motions, the signal is averaged by accumulation of as many transients as required to cover all the states in the cycle of the periodic motion in a statistically representative way [3-51. Amplitude-weighted images are shown in Fig. 48.1 for two different directions of the motion-sensitive bipolar field gradient pulse pair (see white double arrows). The region above the egg yolk shows strong signal attenuation (darker grey shades) resulting from (temporally) uncorrelated motions at the presumed position of the embryo. The attenuation appears to depend on the probed velocity component revealing a strongly anisotropic motion with a preferential direction perpendicular to the yolk sac membrane.

501

48. NMR-Imaging Techniquesfor Quantitative Clinracterization of Periodic Motions

2

Y=xP

x=xR

x=xp

'max

0

Fig. 48.1 : Amplitude-weighted images of (temporally) uncorrelated motions in a quail egg at a incubation period of about 140 h. The intensity is normalised relative to the signal without motion weighting. Pixels with signal below the noise level are set black as it is the case in the egg yolk (black region in the middle of the egg) due to comparatively short T2. Light grey shades represents no signal attenuation, darker shades strong signal attenuation due to uncorrelated motions. The white double arrows indicate the probed velocity component. The white bar represents 2 mm.

48.2.2 Temporally Resolved Pulsations To gain temporal resolution the spatial phase-encoding is omitted acquiring one dimensional images (profiles) resolved in the direction of the read gradient xR. A strong gradient pulse pair is applied for amplitude-weighting of (spatially) incoherenf motion which is averaged in the spatial dimension xp previously being phase-encoded. A series of single transients are acquired (Fig. 48.2 a and b) to study the temporally fluctuating characteristics of the pulsations with a temporal resolution determined by the repetition time between the transients. As shown in Fig. 48.2 a and b the intensity-modulationof profiles is much stronger in the later stage of incubation. At each time point the integral intensity of the pixels between the white dashed lines is calculated. Fourier-analysis (Fig. 48.2 c and d) of these temporally modulated intensity curves reveals a pulsation frequency of 0.4 Hz on the sixth incubation day which was not detected at the earlier incubation stage.

502

U. Goerke and R. Kimmich

119 h

167 h

a)

b)

-20

-E 20

Y

Y

E E

E

x" 10 0

a10

X

0

10 20 30 time [s]

0

0

-1 0 1 frequency [Hz]

10 20 30 time [s]

-1 0 1 frequency [Hz]

Fig. 48.2: A series of single transient profiles strongly weighted for spatially uncorrelated motions by a bipolar magnet field gradient pulse pair are acquired for two different incubation times a) and c). The integral intensity of the pixel between the two white dashed lines in each column is calculated to obtain a intensity curve as a function of time. Fourier analysis b) and d)) of the timedependent modulation of these intensity curves reveals a pulsation frequency of 0.4 Hz at the later incubation stage (see arrows).

48.3 Spectral Side Band Analysis In contrast to the previous methods, the spectral side band analysis combines both spatial resolution by phase-encoding of one of the spatial dimensions and probing the timecourse of temporally fluctuating motions by phase-modulation. A 'pseudo spectral dimension' is acquired in addition to the two spatial (frequency-encoded xR, phaseencoded +) dimension. The periodic motion is now probed as a phase-modulation of the signal in both the phase-encoded (spatial) and the pseudo spectral dimension. That is, the

48. NMR-Imaging Techniques for Quantitative Characterization of Periodic Motions

503

phase shifts by motions in this pseudo spectral dimension are interpreted as if they would arise from coherences evolving with a stationary frequency distribution like that ordinary spectroscopy is dealing with. In the experiment presented in this paper (Fig. 48.3), the pseudo spectral dimension coincides with the chemical shift coordinate which is phaseencoded by incrementing the echo time fn. After the 3D-Fourier transformation, spectral information of the chemical shift and of the periodic motions can be easily distinguished by identification of the dominant water peak. To calculate the 3D-Fourier transform, a sinusoidal time-dependence of the motion with a velocity amplitude yo is assumed. In the chosen frequency range, the velocity can be approximated to be constant during the echo acquisition, but varies from transient to transient. Then, blurring occurs, i.e., signal intensity spreads into neighbouring voxels in the phase-encoded dimension(s), when the motion causes a phase twist equal or larger than a phase-encoding step or, in analogy, when the apparent frequency shift due to motion in the presence of the read gradient is larger than the spectral resolution in the frequency-encoded dimension. Moreover, even if the velocity amplitude is smaller than the minimal velocity which creates blurring the phase-modulation owing to the temporal Q + nQ') in changes of the motions causes the appearance of side bands p ( x R , xp + dP, the Fourier transformed data set represented by the modified spin density p'(xR, xp, Q):

These side bands are shifted in both phase-encoded dimensions xp and !2 by n

~

and ' ~

nu in respect to the original spin density p ( x R , xp. Q). Therefore, they do not overlap as in usual Fourier imaging in which the (pseudo) spectral dimension Q would be omitted. Thus, spatial as well as motional information can be extracted from the data set. The relation between the pulsation frequency and experimental cycling, determined by the ~ op NE TRXmx and repetition time T R , is represented by the constants x ' = = on TRQmax (X,,,, Qmax: 1/2 field of view of the spatial and of the pseudo spectral dimension, respectively; NE: number of chemical shift phase-encoding steps). The apparent pulsation frequencies op and on take into account eventual aliasing of the pulsation frequency in respect to the two phase-encoded dimensions. The intensity of the side bands is determined by Bessel functions Jn of order n. The function a(kR, kp, tn) = IG(t)t dr describes the influence of the gradients which in the presented experiment solely comprises the imaging gradients of the chemical shift spin echo sequence.

504

U . Goerke and R. Kimmich

The experimental results are shown in Fig. 48.3. At the later incubation stage, side bands are clearly visible in the spectra. As in the pseudo spectral dimension the sampling rate of the periodic motion is l/TR it is assumed that aliasing does not occur in this dimension. In this case, a pulsation frequency can be calculated from the separation of the side bands to be 0.3 Hz. The motions reveal themselves to be located at the presumed position of the embryo (see black ellipse). The localisation appears to be more difficult in the xp-dimension then in the xR-direction due to the shifts of side bands in respect to the phase-encoded coordinate. 128 h

155 h

a)

d) 8

8

$

2

OT 3 -8

-8-

-2

-2 0

-8

8

x, [mml

0

-8

x, [mml

8

9

8

X

0

O?

3

-8-2

-1

0

v [kHz]

1

2 -2 -1

0

v [kHz)

1

2

Fig. 48.3: 3D data sets of a quail egg at two different incubation stages (128 h and 155 h) acquired by chemical shift spin echo pulse sequence. a) and d) show the maximal intensity of the water peak in each pixel. The white lines mark rows and columns of which spectra are displayed in b), c), e), and 9. The black ellipse in d) indicates the presumed location of the embryo. Side bands due to pulsating motions are clearly visible at the later stage of incubation.

38. NMR-Imaging Techniqitesfor Quantitative Cturocterizarion of Periodic Motions

505

48.4 Conclusions Two fundamentally different methods - the technique of incoherent averaging and the spectral side band analysis - have been developed to characterise periodic motion without correlating experimental cycling to temporal changes of spin movements. These techniques were applied on pulsation which were discovered in incubated bird eggs. Consistently, motions above the yolk sac were observed to start on about the fourth day of incubation. These motions are preferently directed perpendicular to the yolk sac membrane. Quantitative analysis revealed a pulsation frequency of approximately 0.4 Hz on about the sixth incubation day. As temporal averaging has shown to be more time consuming than acquiring a third dimension the spectral side band analysis appeared to be the faster method in rendering qualitative information about spatial distribution and temporal characteristics of pulsating motion. However, quantitative data obtained by the spectral side band analysis are limited by the resolution determined by the sampling rate of the motion in the phase encoded dimensions. Nevertheless, the incoherent averaging technique and spectral side band analysis both have been theoretically and experimentally proved to be suitable methods for the quantitative characterisation of periodic motions with a pulsation period less than the total imaging time.

References 1.

U. Goerke, R. Kimmich, and J. Weis, J. Magn. Res. B 111 (1996) 236.

2.

U. Goerke, R. Kimmich, and J. Weis, Magn. Reson. I m g . 14 (9) (1996) 1079.

3.

D. D. Stark and J. T. Fermcci, Jr., Diagn. Imaging 11 (1985) 118.

4.

D. Stark,P. L. Hahn, R. E. Hendrick, and J. T. Fermcci, Jr., Radiologs 164 (1987) 183.

5.

T. Q. Li, J. D. Seymour, R. L. Powell, K. L. McCarthy, L. Oedberg, and M. J. McCarthy, Magn. Reson. Imag. 12 (1994) 923.

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49. Shear-Banding in a Cone-and-Plate Rheometer M. M. Britton and P. T. Callaghan Department of Physics, Massey University, Palmerston North, New Zealand

Abstract Using NMR microscopy we have measured velocity distributions for a wormlike micelle solution, cetylpyridinium chloride/sodium salicylate (100 mM/60 mM) in a 4” cone-andplate. This fluid is shown to shearband under conditions of uniform stress above a critical shear rate. The fluid separates into a region of high shear in the middle of the gap, with a region of low shear on either side.

49.1 Introduction In recent years the behaviour of fluids that exhibit a stress minimum in their stress vs rate-of-strain curve (the flow curve) has been the subject of much theoretical conjecture [ 1-41 and several rheological and rheo-optical studies [5-71. One consequence of such a minimum is flow instability, leading to the “spurt effect” in pipe flows. Such an effect was first seen experimentally by Bagley [8] and Vinogradov [9] in separate studies on flow discontinuities in high-molecular weight polymer melts. An explanation for what was observed is found in the theory of McLeish and Ball (21, which is based on the tube model of Doi and Edwards [lo]. Figure 49.1 shows the flow curve for a fluid exhibiting the spurt effect. Below a critical shear rate the fluid behaves in a Newtonian manner, but past this point a double valued-ness in shear stress with respect to shear rate is possible. The first inflexion in the flow curve is dependent on the tube disengagement time, zd, and the second on the Rouse time, zR.In turn both zd and zR are dependent on the molecular weight cubed and squared respectively of the polymer. Any polydispersity in the system will result in an effective blurring of the two inflexion points and thus the

508

M.M. Britton and P. T.Callaglum

doubled valued-ness of the system. Hence with the polydispersed nature of most polymers this phenomenon has proved difficult to probe further. An alternative system with which to study this phenomenon is that of wormlike micelle solutions. I n semidilute concentrations they form entangled networks, which behave in a similar manner to high-molecular weight polymer solutions. In these systems the long range electrostatic repulsions between surfactant headgroups are screened, thus favouring the formation of wormlike micelles over spherical micelles. The behavior of these solutions has been an area of increasing interest.

shear

stress ( 0 )

. . YI

YC

y2

shear rate (y) Fig. 49.1: Flow curve for a fluid exhibiting non-monotonic stress behaviour.

The microphysical model of Cates [4,11,12] shows how the tube disengagement time of wormlike micelles affects the stress relaxation of the system, as in the theory of Doi and Edwards for entangled polymer systems. However, unlike polymer systems, wormlike micelles have an additional stress relaxation time, 2bre&, associated with the rapid and repeated breaking and formation of micelles. So when Tbre& << T~ the result is a single stress relaxation process, at low frequencies, with a unique characteristic relaxation time dependent on Tbre& and 2d. From this the effects of polydispersity are believed to be minimised and so the non-monotonic behaviour shown in the flow curve above (Fig. 49.1) is predicted. Experimentally these systems are shown [13] to reach a stress plateau past a critical shear rate. It is such behavior that is indicative of shear banding, i.e. where the fluid separates into regions of different shear rate. Here one of the major

49. Shear-Banding in a Cone-and-PlateRheometer

509

limitations with standard rheology is highlighted. Rheological measurements are integrated over the entire sample, so to see how the fluid is behaving at a local (or even molecular) level, a more sophisticated means of observing the fluid is required. NMR spectroscopy and velocity imaging has proven to be an invaluable tool in the studying complex fluids under shear [ 14-18]. Recently NMR microscopy has been successfully applied to studying of wormlike micelle solutions in the pipe and Couette cell geometry [15,19,20], and to the cone-and-plate geometry [21]. In cone-and-plate rheometry the equations of motion require that the shear stress must be close to uniform throughout the gap. However while it is intuitive, and hence generally assumed, that the shear rate is uniform in the gap (both the cone surface velocity and width of the gap increase linearly with radius) there are no physical laws which require that this must be the case. Hence if shear-banding occurs in the cone-andplate geometry then the applicability of this device in the study of complex fluids is brought into question, unless independent evidence is available concerning the shear rate prevailing within the gap. We shall demonstrate here that NMR microscopy is ideally suited to providing such evidence.

49.2 Experimental A 4.5% (w/v) wormlike micelle solution was made up from cetylpyridinium chloride, 100 mM (Aldrich) and sodium salicylate, 60 mM (Aldrich) using distilled water. This particular system has been shown, by Rehage and Hoffmann [ 5 ] , to exhibit single exponential (Maxwell fluid) properties in the linear response regime. The solution was left to equilibrate over a few days, until all the bubbles had disappeared The micelle solution studied undergoes a phase transition at 19 "C, so all NMR experiments were performed at 25 "C. NMR experiments were carried out on a Bruker AMX300 spectrometer equipped with a specialised microimaging system. The cone and plate apparatus was manufactured out of the machinable glass, MACOR (Coming, New York) and fitted inside a 25 mm rf resonator. The width of both cone and plate was 24 mm, with the cone having a 4" angle. A stepper motor with step-down gearbox was used to control the velocity of the cone.

510

M. M. Britton atd

P. T. Calhghan

The velocity imaging technique used is based on the pulsed gradient spin echo method, a detailed description of which can be found elsewhere 1221. Typical experimental parameters include a field of view of 25 mm with a slice thickness of 2 nun, 8 (Iencoding slices with 6 and A of 1 - 2 ms and 15 - 25 ms respectively and a maximum gradient amplitude of 18 Gkm. A x6 vertical expansion of the gap in the cone-and-plate is achieved by increasing the strength of the phase gradient, giving a pixel size of 195 mm by 65 mm. A repetition time of 2s was used with 4 signal-averaging acquisitions per k-space point. It should be noted that the signal arises predominantly from the protons in the solvent. A schematic of the apparatus setup is shown in Fig. 49.2 with a proton density image of the micelle solution.

Fig. 49.2: a) Schematic diagram of the cone-and-plate rheometer used in the NMR microimaging apparatus. b) Spin density image of wormlike micelle solution in 4" cone gap.

49.3 Results Velocity images and shear rate maps, both below (1.5 s-') and above (12 s-') the critical shear rate, are presented in Figs. 49.3a4 and 49.3e-h respectively. The velocity images are presented using three different formats: graduated greyscale, contour plot and stack

49. Shear-Banding in a Cone-and-Plate Rheorneter

511

plot. The shear rate map is produced by calculating the vertical derivative of the velocity image and is presented as a greyscale image. Below the critical shear rate the fluid shows no deviations from linearity, as expected. There is a gradual increase in velocity with increasing vertical distance from the plate to the cone. This is seen more graphically in the contour and stack plots. Associated with such a gradual uniform increase in velocity is a uniform shear rate, as seen in Fig. 49.3d. Indeed a uniform shear rate is the expectation for all flow in a cone-and-plate geometry. Above the critical shear rate there is a marked deviation from normal Newtonian flow. The velocity image no longer shows a gradual uniform increase in velocity. Instead the fluid separated into regions of different shear rate. Three regions are present, with a low shearhigh shearAow shear structure. There are a number of very important consequences of the shear banding observations presented here. First, they provide significant insight regarding the behavior of wormlike micelles under shear. In particular, we have shown [21] that the shear band develops in a characteristic manner when the average shear rate is enhanced by increasing the cone rotation speed. That is, the maximum shear rate remains constant while the width of the band increases so as to accommodate the larger average shear. Such behavior is absolutely characteristic of a first order phase transition in which the proportions of the co-existing phases change as the intensive "thermodynamic" parameters are altered. Furthermore the edges of the band exhibit a finite transition region, characteristic of an interfacial energy, a phenomenon suggest by Spenley, Yuan and Cates [3]. These findings have important consequences in the study of micellar phase behavior and in the subtle interplay between dynamics and molecular organization under non-equilibrium conditions. Second, the experiments presented here raise important general questions concerning the nature of fluid behavior under shear in the case of materials exhibiting flow-instability in their stress vs rate-of-strain relations. For example, if the stress is close to uniform across the gap, then the stress-optical law [ 101 suggests that the optical birefringence (in other words, the molecular order parameter) should be equally uniform, a point which is hard to reconcile with the extreme heterogeneity of the fluid. Furthermore, the fact that the fluid separates into three distinct regions (given phase coexistence, why not two or indeed, any number at all?) with the high shear rate region at gap centre (in polar coordinates) is extremely interesting. What is it about the mid-gap which can "pin" this particular phase, given that the stress, to the extent that it varies at all, exhibits a monotonic transition from plate to cone?

512

M. M.Britron a i d P . T. Callaghan

Fig. 49.3: Velocity images and shear rate maps for the wormlike surfactant cetylpyridinium chloride/sodium salicylate (100mM/60mM) below (1.5 s-l), (a-d), and above (12 s-I),.(e-h), the critical shear rate. Velocity distributions (a-c and e-g) presented in greyscale map, contour plot and stacked profile plot formats with the shear maps (d and h) in greyscale.

49. Shear-Banding in a Cone-and-Plate Rlieometer

513

Finally our experiments point to the dangers inherent in the usual assumptions concerning cone-and-plate rheometry. We have shown [ 18,231 that such shear rate heterogeneity is not confined to "pathological" model fluids such as the wormlike micellar system whose behaviour is exhibited here. Such effects, albeit with differing geometric distributions, have been found by us in systems as diverse as polyacrylamidelwater solutions and commercial tomato sauce, systems whose rheology might be commonly studied within the polymer and food industries. The tomato sauce example is shown in Fig. 49.4. While the shear-banding exhibited is more delicate than that apparent in the micellar solution, it is manifestly obvious that some degree of heterogeneity prevails and that a measured flow curve, based on the uniform rate-of-strain assumption will be in error. A particularly intriguing aspect of the Fig. 49.4 example is that the banding structure is reversed in comparison with the micellar solution. Instead of the high shear rate region being confined to gap centre it is found near the shearing surfaces and bounds a central region of low shear.

cone

-

plate

1

0

1

Fig. 49.4: a) Greyscale image of the shear rate map for tomato sauce in a 7" cone-and-plate at a shear rate of 19.7s.'. b) Shear rate profile taken through gap.

5 14

M. M. Britton and P. T. Callaghan

49.4 Conclusions It is clear that NMR microscopy can provide important new insights regarding complex fluid rheology. Indeed it is hard to envisage any other method which would be capable of non-invasively measuring local shear rates under flow over such a wide class of fluids (including the optically opaque) and with such precision and spatial resolution. We believe that this method will become an important new tool in the study of the fundamental physics of non-equilibrium phase transitions. For example, we envisage the extension of the shear band visualization to include the imaging of NMR spectroscopic properties such as dipolar and quadrupolar interactions which can provide insight regarding molecular order, and relaxation times and diffusion coefficients which can provide insight regarding molecular dynamics and mesoscale organization. Furthermore, we would argue that without such independent flow visualization, much of the classical rheometry based on cone-and-plate of Couette cell shearing geometries can be at risk of misinterpretation. NMR microscopy can provide the essential adjunct to the standard stress vs rate-of-strain measurements. Of all the potential applications by which NMR Microscopy is capable of making a uniquely powerful contribution to science and technology, the field of "Rheo-NMR" may prove to be among the most important.

References 1.

P. Espanol, X. F. Yuan and R. C. Ball, J. Non-Newtonian FluidMech. 65 (1996) 93-109.

2.

T. C. B. McLeish and R. C. Ball, J. Polym. Sci. Polym. Phys. Ed. 24 (1986) 1735-1745.

3.

N. A. Spenley, X. F. Yuan and M. E. Cates, J . Phys. II France 6 (1996) 551-571.

4.

N. A. Spenley, M. E. Cates and T. C. B. McLeish, Phys. Rev. Lert. 71 (1993) 939-942.

5.

R. Rehage and H. Hoffmann, Mol. Phys. 74 (1991) 933-973.

6.

J.-F. Berret and D. C. Roux, J. Rheol. 39 (1995) 725-741.

7.

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E. B. Bagley, I. M. Cabot and D. C. West, J. App. Phys. 29 (1958) 109-110.

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G . V. Vinogradov, et al., J . Polym. Sci. 10 (1972) 1061-1084.

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M. Doi and S. F. Edwards, The Theory of Polymer Llynamics, Oxford University Press,Oxford, 1987.

11.

M. E. Cates, Macromolecules (1987) 2289-2296.

12.

M. E. Cates and S. J. Candau, J. Phys. Condens. Mutter 2 (1990) 6869-6892

49. Shear-Banding in a Cone-and-flare Rheomerer 13.

P. T. Callaghan, M. E. Caies, C. J. Rofe and J. B. A. F. Smeulders, J. Ph.vs. I1 France 6 (1996) 375-393.

14.

B. Manz and P. T. Callaghan, Macromolecules 30 (1997) 875-3309-3316

15.

C. J. Rofe, R . K. Lambert, and P. T. Callaghan, J. Rheol. 38 (1994) 875-887.

16.

Y. Xia and P. T. Callaghan, Macromolecules 24 (1991) 47774786.

17.

A. I. Nakalani, M. D. Poliks, and E. T. Samulski, Mocrotnolecules 23 (1990) 2686-2692.

18.

M. M. Britton and P. T. Callaghan, J. Rheol. 41 (1997) 1365-86.

19.

R. W. Mair and P. T. Callaghan, J . Rlieol. 41 (1997) 901-924.

20.

R. W. Mair and P. T. Callaghan, Europhys. Lett. 36 (1996) 719-724.

21.

M. M. Britton and P. T. Callaghan, Phys. Rev. Lett. 78 (1997) 4930-4933.

22.

P. T. Callaghan, Principles of Nuclear Magnetic Resonance Microscopy, Oxford University Press, Oxford, 1991.

23.

M. M. Britton and P. T. Callaghan, Magn. Reson. Chern. 35 (1997) 537-546.

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50. Applications of NMR Flow Imaging in Materials Science K. Rombnch, S. Laukemper-Ostendor$ and P . Bliimler Magnetic Resonance Center @ M ,RWTH Aachen, D-52074 Aachen, Germany

Abstract Although the spatial resolution of NMR imaging is inferior to many other imaging techniques, the possibility to combine spatial features with various forms of contrast makes the method superior and unique. Besides NMR parameters like spin density, relaxation and spectroscopic information, self-diffusion, convection and flow can be used to generate contrast due to mass transport. Furthermore, all these contrast schemes can be combined to investigate phenomena separated by molecular and macroscopic interactions. The pure detection of spatial features can thus be functionalized with regard to various chemical and physical properties of the sample. In this paper the spatially resolved detection of velocities is described and applied to a set of applications of technical relevance. The principles of velocity compensation and velocity encoding are explained and demonstrated by a robust sequence. The applications focus on single and multi component flow in mixers and extruders as well as hemodialyzers and surface waves. The spatial variation of all three velocity components was measured in mixers of complicated geometry and rotating single-screw extruders. The measurements were performed on water and watedoil suspensions, where chemical shift selection allows the differentiation of the velocities for each chemical component. The efficiency of hemodialyzers highly depends on the velocity distribution in the container. Two extreme designs are compared. Finally surface waves on water were investigated. Here the imaging sequence was synchronized to the excitation of waves. This allows the investigation of time resolved surface patterns as well as the velocities in the waves. The correlation between a given excitation and the detected response frequency and phase allows detailed insight into the system.

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K. Roinbacli, S. hukemper-Osiendorf: and P. Bliimler

50.1 Introduction Recently Callaghan et al. [l] have shown that sheared liquids with structure dependent viscosities can phase separate in shear bands. These bands correspond to different spatial viscosities and thus exhibiting different local velocities. This observation has important consequences to many processing devices, which were optimized by computational fluid dynamics (CFD) while neglecting the possibility of such shear dependent phases. Polymer melts and solutions are known to have structure dependent viscosities and are usually processed in devices which were optimized by CFD or empirical methods. Thus, the investigation of the spatial distribution of velocities in the often complicated geometries of mixers, extruders and filters is of great interest. NMR imaging has proven to be an excellent method to determine velocities qualitatively and quantitatively by various techniques [2,3]. To this end ‘time-of-flight’, ‘tugging’ and phase-encoding techniques are being used. But ‘time-of-flight’ and ‘tagging’ methods are disadvantageous because the velocity components detected are not independent of the spatial components, and the extraction of velocities requires the use of models. Therefore, to study the flow in mixers, extruders, dialysis modules and surface waves phase detection of velocities with velocity compensated spatial detection was used.

50.2 Basic Principles The effect of coherent motion of spin ensembles on the NMR signal has been known almost since the discovery of NMR [4]. It gained considerable importance with the development of NMR angiography around the years 1980. While in clinical applications a qualitative detection of velocities is often sufficient, a quantitative measurement is necessary for analysis of technical processes. Phase methods are perfectly suited for this purpose. The idea of phase encoding of velocities is analogous in principle to phase encoding of spatial components. If a spin is moving during a time interval dt over a distance r(t)it will gain a phase change q(t)in the presence of a gradient G ,

(50.1)

50. Applications of N M R Flow Iniaging in Marerials Science

519

In standard imaging experiments such phase changes due to motion of spin ensembles give rise to characteristic artifacts. In order to avoid such distortions, velocity induced phase changes have to be canceled for all spatial dimensions. On the other hand the accumulation of phase can directly be utilized for a quantitative detection of the velocity components along G preferably in an additional dimension. Therefore, it is useful to expand the time dependence of the space vector into a Taylor series, dr dt

1 d'r 2 dt2

r(t) = r + - t + - - - r -

= r + vt + -at 2

2

9

+... (50.2)

+...

Thus, with Eq.(50.1) and neglecting higher terms the phase evolution can be separated into a stationary and velocity part,

(50.3)

The imaging sequence (e.g. the modified spin-warp sequence in Fig. 50.1) has to be designed in such a way, that only the second (velocity dependent) term is zero during the detection of the spatial encoded dimensions (velocity compensation), while only the first

90"

180"

echo

G Fig. 50.1: 3D velocity compensated and velocity encoding pulse sequence. To minimize imaging artifacts all gradients applied for spatial encoding are velocity compensated. The use of a bipolar velocity encoding gradient (marked by *) generates a phase shift from motion of spins which is directly proportional to the component of velocity in the corresponding gradient direction. By stepping the flow encoding gradient through a range of negative and positive values velocity components can be measured.

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K. Rombach, S. Luukemper-Ostendotfi

and P. Bliirnler

(position dependent) term cancels for velocity encoding. A detailed description of the principles of velocity encoding and velocity compensation can be found elsewhere

[2,3,5,61. A typical result of such a sequence on a flow phantom is demonstrated in Fig. 50.2, where the experimental data are compared with an analytical solution for laminar flow of Newtonian fluids. The agreement is excellent.

0

0

Fig. 50.2: How of water through two tubes in opposite directions. a) Calculation of the expected velocity distribution for laminar flow of a Newtonian liquid by application of the HagenPoiseuille law. b) Experimental results using the sequence in Fig. 50.1. Right: Surface plot. Left: Grayscale image. Spatial axes in mm and velocity axis in c d s . For better presentation the threedimensional data set was reduced by one dimension using a special algorithm [ 6 ] .

50.Applications of NMR Flow Imaging in Morerials Science

52 1

50.3 Examples of Applications Phase encoding of velocity requires stationary flow conditions during the duration of the experiment, which is in the order of about 0.5 - 3 hours depending on the dimensionality and the resolution. In many interesting processes such stationary or periodic situations are quite common. In the following sections this is demonstrated by flow in mixers, extruders, hemodialyzers, and by surface waves.

50.3.1 Flow in a Static Mixer [7] Even for laminar flow of Newtonian liquids the spatial variation of velocities can become extremely complicated in complex geometries. Such a situation is demonstrated by the velocity distribution of water flowing through a stationary mixer (KENICSTM type) which is typically used for mixing two-component resins (Fig. 50.3a). The geometry of the stationary double helix screw is already too complicated for simulation of flow patterns by established CFD-programs. Figures 50.3b and c illustrate the complicated velocity distribution v,(n,y) at the positions marked in Fig. 50.3a. Transverse flow velocities were obtained by changing the direction of the flow encoding gradient in Fig. 50.1 to G, and Gy. Here positive and negative velocity components were detected and are displayed in Fig. 50.3d and e. The images clearly visualize opposite flow directions above and below the screw center. From the x- and y-velocity components a velocity vector field was calculated with reduced spatial resolution as shown in Fig. 50.3f, where the direction of the arrows indicates the direction of transverse flow while their length determines the speed. Combination of the pulse sequence in Fig. 50.1 with chemical shift selective excitation also allows the investigation of multi-phase or multi-component flow. This is demonstrated by an example of flow through the mixer in Fig. 50.3a which was fed with oil and water at separate inlets. Figure 50.4 shows the results in terms of separate water and oil velocity images at position 1 in Fig. 50.3a. It can be seen that the water passes the mixer in narrow inner channels with high velocities while the oil covers the walls and flows with lower velocities.

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K. Rombach, S. Laukemper-Ostendorf; and P. Bliimler

a)

v

11 c m l s

+ 10 c m l s

t

0 cmls

0 cmls

t

8 cmls

t

a cm/s

- 8 cmls

Fig. 50.3:a) Schematic drawing of a KENICSTMmixer with the slices selected for the experiment and with the spatial coordinate frame. The arrows indicate the flow through the mixer. b) Flow of water in z direction through a static mixer at position 1. c) Same as b) but acquired at position 2. d) Transverse flow in x direction at position 1. e) Transverse flow in y direction at position 1. f) Two-dimensional velocity vector field calculated from d) and e) with reduced spatial resolution. The boundaries of the screw and the mixer wall are overlaid to clarify orientation. The images in d) and e) are reduced 3D data sets obtained by an algorithm described in [6].

50. Applications of NMR Flow Imaging in Materials Science

13 cmls

8.8 cmls

0 cmls

0 cm/s

523

Fig. 50.4: Chemical shift selective images of velocity v,(x,y) at position 1 for the mixer in Fig. 50.3a fed with water and silicone oil. a) Water velocity image. b) Silicone oil velocity image. Both liquids were fed into the mixer with the same volume flow rate. It should be noted that the gray coding corresponds to different velocity values in a) and b) as marked at the right of each image. The images were produced with an algorithm described in [6].

50.3.2 Flow in a Single Screw Extruder How of materials through mixers provide nice examples to demonstrate the possibilities of velocity imaging. Other devices of great interest in polymer processing are extruders [8-111. In particular, the optimization of extruders is of key interest. Therefore, a single screw extruder was build from non metallic materials for imaging of transport during operation. The imaging sequence was synchronized with the rotation period of the screw. Figure 50.5 shows images of flow in the x and y directions as well as a resultant vector plot. Although water was used for this demonstration, non-Newtonian liquids and multicomponent systems can be studied as well.

50.3.3 Flow in Hemodialyzers One of the most important medical applications of hollow-fiber membranes is hemodialysis [ 121. Factors that strongly influence the efficiency of hemodialyzers include design and flow geometry within the dialyzer. However, not much about flow profiles and flow-velocity distributions in such modules is known. This is mainly caused by the fact that the non-invasive observation of flow within the hollow-fiber membranes (the blood compartment) and the dialysate compartment is not trivial. Using the pulse

524

K. Rombacli, S. Lmkemper-Ostetidoi$ aid P. Blunder

+

6.6 c m l s

- 7.5 c m l s

- 7.5 c m l s

7

Fig. 50.5: NMR images of the transverse velocity components in a single screw extruder pumping water at a rotation of 1.6 Hz.The slice thickness corresponds to that of a single screw thread. a) Velocity image v,(x,y). b) Velocity image v,(x,y). c) Resultant vector plot with reduced spatial resolution. The boundaries of the screw and housing are overlaid to clarify orientation.

525

50. Applications of NMR Flow Imaging in Marerials Science

sequence of Fig. 50.1 it is possible to determine flow-velocity distributions in both the dialysate compartment and the hollow-fibers, simultaneously [ 13-1 61. Experiments were carried out on two model hemodialyzers filled with about 170 hollow-fiber membranes with 200 pm inner diameter and 8 pm wall thickness. The second dialyzer was additionally filled with textile fiber yarns to achieve a higher packing density. Figure 50.6 shows the corresponding velocity images exhibiting significant differences concerning the dialysate flow [17]. In the first model hemodialyzer the dialysate builds up a ‘shunt flow’ caused by the low packing density of the membranes. This effect does not arise in the case of the second model hemodialyzer which can directly be seen in the corresponding image.

-0

-0

Fig. 50.6: Velocity images of two model hemodialyzers. a) Model dialyzer containing about 170 hollow-fiber membranes. b) Model hemodialyzer with fibers of different chemical composition and additional textile fiber yarns. Both images were taken from the middle sections of the dialyzers. The velocity images were produced by an algorithm described in [6].

50.3.4

Flow in Surface Waves

Surface waves are interesting in many respects. They are a simple example of elastography and have technical importance for mass and heat transport in hydrodynamics as well as in falling films which are used, for instance, in cooling towers. To generate surface waves a special probe was designed, which uses a little coil on top of a paddle made from a polymer film light enough to float on the water surface of a half-filled, horizontal tube (cf. Fig. 50.7a). If an AC (f= 1 - 10 Hz) current is fed into the coil it starts to swing

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K . Rombnch, S. hukemper-Os~endot$ and P. Bliimler

like a loudspeaker membrane in the magnetic field of the horizontal bore NMR magnet. This vibration stimulates surface waves which are phase locked to the AC. Therefore, traveling water ,bills" and ,,valleys" appear stationary if their observation is synchronized to the AC and can be followed by variation of a mixing time prior to imaging (cf. Fig. 50.7b).

50-70m m

imaging X

region spectrometer

Fig. 50.7: Generation of surface waves. a) Experimental setup designed for a horizontal bore magnet. A 50 loop coil was glued on a plastic foil to form the paddle (8 x 20 mm) and mounted at the end of the tube. b) NMR imaging sequence triggered by the AC stimulation.

Simple projections along the tube axis (z direction) for different mixing times thus display the modulation of the water surface. This is shown in Fig. 50.8 where the periodicity of the waves can clearly be recognized. However, the simple ,,sine"-like modulation is overlaid by more complex features which are probably due to overtones induced by the paddle and by wall reflections. To measure spatial velocity distributions in such waves the sequence of Fig. 50.1 was triggered to the phase of the exciting AC at a mixing time indicated by the arrow in Fig. 50.8. The result is shown as a vector plot in Fig. 50.9. It can clearly be seen that the main movement of water is upwards to form the hill. However, in the encircled region a rolling motion can be recognized which is expected in wave motions.

50. Applications of NMR Flow Imaging in Materials Science

527

31 20-

I

Fig. 50.8: 1D images along the z axis for different mixing times. The AC-stimulation frequency was set to 1.5 Hz.The increase in intensity for long mixing times is a T I artifact due to an insufficiently short recovery delay.

Fig. 50.9: NMR velocity image of a surface wave displayed as a vector plot. The data were acquired with a mixing time indicated there by the arrow in Fig. 50.8.

Finally the fact that excitation and response frequency and phase of the system are known can be utilized to construct state diagrams [18]. To this end the excitation frequency (AC current) is directly correlated with the response (surface modulation). In case of a linear system, the result is a straight line (Fig. 50.10a). In the actual case of

5 28

K. Rombach, S. kukemper-Osteidoi$ and P . Bliirnler

water waves reflected by a hard wall (cf. Fig. 50.lob), moderate deviations from linearity can be recognized, defining the state space of the system.

4

Simple model

Waves with reflection r

% C 0

J ? ze!:

0-

Fig. 50.10: Correlation of excitation and response frequencies and phases of surface waves in the form of state diagrams. a) Simple linear model. b) Measured profiles of surface waves reflected from a hard wall for different mixing times. Left: Surface modulation for various mixing times (cf. Fig. 50.8). Right: State diagram. It shows the trajectories from the right correlated with the AC frequency and corrected phases for the spatial positions along z.

50. Applications of NMR Flow Imaging in Materials Science

529

50.4 Conclusions NMR imaging of velocities appears to be the only technique that allows the detection of spatially resolved velocity distributions in arbitrary directions through optically opaque objects. In particular the independence of space and velocity coordinates has to be realized by a phase-encoded velocity sequence, which allows a ,,model-free" determination of local velocities. Possible applications were demonstrated by imaging spatial velocity distributions in static mixers with complicated screw geometries, single screw extruders, hemodialyzers and surface waves. Work in progress employs the same setup but focusses on non Newtonian liquids for comparison of experimental data with CFD-simulations.

References 1.

R. W. Mair and P. T. Callaghan, Europhys. Left. 36 (1996) 716; M. M. Britton and P. T. Callaghan, Phys. Rev. Left. 78 (1997) 4930; see also previous chapter.

2.

A. Caprihan and E. Fukushima, Phys. Reports 198 (1990) 195.

3.

J. M. Pope and S. Yao, Concepts Magn. Reson. 5 (1993) 281.

4.

H. Y. Cam, ,,Free Precession Techniques in NMR" Ph. D. Thesis, Cambridge MA, 1952.

5.

P. T. Callaghan, Principles of NMR Microscopy, Clarendon Press, Oxford 1991.

6.

S. Laukernper-Ostendorf. K. Rombach, P. Bliimler. and B. Bliimich, Bruker Application Note, 1997.

7.

K. Rombach and P. Bliirnler, J. Polym. Colloid Sci., submitted.

8.

C. Rauwendaal, Polymer Extrusion, Hanser Publ., Munich 1990.

9.

J. Gotz and H. Buggisch, J. Non-Newtonian Fluid Mech. 49 (1993) 25 1.

10.

K. L. McCarthy, R. J. Kauten, and C. K. Agemura, Treruls Food Sci. Technol. 3 (1992) 215.

11.

M. J. McCarthy and K. L. McCarthy, Sci. FoodAgric. 65 (1994) 257.

12.

E. Staude, Metnbranen und Membranprozesse, Grundhgen und Anwendungen, VCH Publ., Weinheim 1992.

13.

C. A. Heath, G. Belfort, B. E. Hammer, S. D. Mirer. and J. M. Pimbley, AIChEJ. 36 (1990) 547.

14.

B. E. Hammer, C. A. Health, S. C. Mirer, and G. Belfort, Biorechnology 8 (1990) 327.

15.

S. Yao, M. Castello, A. G. Fane, and J. M. Pope, J. Membrane Sci. 99 (1995) 207.

16.

J. Zhang, D. L. Parker, and J. K. Leypoldt, ASAIO J. 41 (1995) M678.

17.

S. Laukemper-Ostendorf, H. D. Lemke, P. Bliimler, and B. Bliimich, J. Membrane Sci. 138 (1998) 287.

18.

W. L. Ditto and L. M. Pecora, Sci. American 269 (1993) 78.

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51. A Non-Invasive Investigation of Concentration Polarization in Crossflow Microfiltration of Colloidal Silica D. Airey', V. Chen2, J. Wu2,and J. M . Pope' Centre for Medical and Health Physics, Queensland University of Technology, GPO Box 2434, QLD 400 1, Australia UNESCO Centre for Membrane Science and Technology, University of New South Wales, Sydney NSW 2052, Australia

Abstract Spin-echo NMR micro-imaging has been used to study, non-invasively, the development of concentration polarisation layers in a crossflow microfiltration system. The feedstock used was 5% wt/wt colloidal silica (average particle diameter 12 nm) filtered through a tubular polypropylene membrane (pore size 0.2 - 0.4 pn). The concentration polarization layers were observed to be highly asymmetric, in some cases being more than 3 mm thick at the thickest part and less than 70 pm thick at the thinnest. This asymmetry is caused by the flow of the layer under gravity, although colloidal silica of this particle size normally exists as a suspension and resists settling. This asymmetry means that the performance of the filter is strongly affected by the orientation of the module. T , weighted images were used to study the distribution and time evolution of the layer while T2 weighted images revealed some of the structure of the layer.

51.1 Introduction Microfiltration is a process for separating particles of size 0.01 to 10 pm from solution or suspension. Separation is achieved by maintaining a pressure difference across a microporous membrane which is chosen to be impervious to the particles concerned. The

532

D.Airey. V. Chen. J .

Wu, and J .

M.Pope

process is important in a wide range of industrial and environmental applications, including brewing, paint manufacture and dairy and mineral processing. In crossflow filtration the flow of feedstock is arranged to be tangential to the surface of the mem-

brane, thus limiting the accumulation of retained particles at the membrane surface. The dynamics of the process are not well understood, however, with traditional models under-predicting filtration rates by up to two orders of magnitude. The concentration polctrization (CP) layer is the accumulation of retained particles at the membrane wall which occurs as they are transported to, but not through, the membrane (Fig. 5 1.1). This polarization layer can greatly increase hydraulic resistance and reduce the flux of solvent through the membrane [ 11. After filtration begins, there is usu-

ally a rapid drop in the permeate flux rate from its initial value as the CP layer builds up (see Fig. 51.7). By arranging the filter in a crossflow configuration, where the feedstock flows tangentially across the surface of the membrane, the growth of the CP layer may be controlled and improved flux rates result. Under steady state conditions, typical CP layers can range up to a few hundred microns in thickness. Crossflow Concentration

Fig. 51.1: Diagram of the concentration polarization (CP) layer which builds up at the membrane wall while a transmembrane pressure difference is maintained. Because it is the result of a delicate balance of convective and diffusive forces, the CP layer often dissipates rapidly after the transmembrane pressure difference (TMPD) is removed. A non-invasive method is therefore needed to study the formation and development of the CP layer while the filter is operating [2-51. Better knowledge of the properties of the CP layer would allow for improved design and more efficient operation of filters. Of particular interest are the spatial distribution, density and mobility of the layers and how they respond to parameters such as feedstock crossflow rate, transmembrane pressure difference, feedstock concentration, and pH.

51. Investigation of Concenrralion Polarizarion in Crossflow Microfillration of Colloidal Silica

533

51.2 Filtration Apparatus A filter module (Fig. 5 1.2) was constructed consisting of a tubular polypropylene membrane manufactured by Akzo (pore size: 0.2 - 0.4 pm, wall thickness 1.65 mm, inner diameter 5.2 mm) sealed inside a glass envelope (inner diameter 10.0 mm, wall thickness 1.0 mm, length 500 mm) with epoxy resin.

Imaging

j Plane

Inlet (Feedstock)

Outlet (Retentate)

I

/

Membrane

I

j

/

Envelope

I

I

I

Permeate

Fig. 51.2: The filtration module showing the plane of imaging. It was possible to adjust the position of the module within the magnet to image anywhere between the feedstock inlet and a point approximately 250 mm from the inlet.

Feedstock was fed to the inner lumen of the membrane and permeate removed from the outer annulus between the membrane and the glass envelope. The filter module was incorporated into a complete filtration rig (Fig. 51.3). Pressure at the feedstock inlet and outlet and the permeate outlet was continuously monitored using purpose-built pressure transducers. The crossflow and permeate flow rates were also measured using a rotary flow meter and a mass balance respectively. Two computer-controlled peristaltic pumps allowed independent control of crossflow rate and Th4PD. Active feedback was used to hold the system parameters constant during imaging. The retentate was fed back into the feedstock reservoir. To maintain the feedstock at a constant concentration, permeate was also periodically returned to the reservoir. A solution of colloidal silica was used as a feedstock. Colloidal silica (DuPont, LUDOX 40% with an average particle diameter of 12 nm) normally exists as a suspension. A sample left undisturbed for several weeks showed no settling. For the experiments described here, the stock solution was diluted to 5% wtfwt by the addition of distilled water.

534

D.Aitey, V. Clien, J . Wid, and J . M. Pope Filter Module

Reservoir

t d

Fig. 5 1.3: The filtering rig incorporating the filter module.

51.3 Results Images were obtained using a horizontal-bore Bruker MSL 200 micro-imaging system with a home-made RF saddle coil insert which allowed for the flow of feedstock through the NMR probe. Conventional spin echo sequences were used. The relative concentration of silica was reflected in the images via its effect on the relaxation times T , and T2 of the surrounding water (see Fig. 51.4b). For time evolution studies, 128 x 128, 12 mm FOV and 2mm slice thickness images were used. A repetition time (TR) of approximately 0.5 seconds provided good T, contrast Such images took approximately two minutes to acquire. Once a transmembrane pressure was applied, the system typically took 40 minutes to reach a steady state. Images with longer acquisition times (up to two hours) could be obtained once this steady state had been established. These included higher resolution images (512 x 512 with a 10 mm FOV) and T2 weighted images which required a TR of up to 8 seconds.

51. Investigation of Concentration Polarization in Crossflow Microfiltrationof Colloidal Silica

535

51.3.1 The Structure of the CP Layer In a T , weighted image (Fig. 51.4a) of the filter module, the CP layer is visible as a bright region around the inside of the membrane. The extraordinary asymmetry of the layer is immediately evident. It is more than 1.5 mm thick at the thickest part (and can be up to 3.5 mm in some situations) and less that 70 pm at the thinnest. This asymmetry is caused by the flow of the layer under gravity. The CP layer is only present while a pressure difference is maintained across the membrane. If the flow of permeate is cut off or the pressure difference removed, the silica particles re-suspend. The polypropylene membrane itself is visible as a ring which is slightly darker than the surrounding water because of a lower proton density. A bright inflow artifact is also visible in the center of the image. In a T2 weighted image (Fig. 51.5a), the membrane is again visible as a dark ring, however, the inflow artifact has disappeared. In this image, areas of high silica concentration (short T2) appear dark rather than bright. This contrast mechanism reveals a gradual rather than a sharp transition in concentration between that in the bulk feedstock and

O

3.-2

0

Transverse Relaxation LongitudinalRelaxation

10

20

30

40

Concentration (% vol/vol)

Fig. 51.4: a) A typical 512 x 256 image of the filter module at steady-state with a TR of 0.5 s. The image, taken 75 mm from the inlet, is strongly TI weighted. b) shows the dependence of relaxation rate (the inverse of the relaxation times T , and T2) on the local concentration of silica. Regions of high concentration relax more rapidly and appear brighter in the image. Calculation of the volume concentration assumed a specific gravity of 2.2 for dry colloidal silica.

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D.Airey, V. Chen, J. Wu.and J. M.Pope

that at the wall (Fig. 51.5b). A calculation of silica concentration based on the ratio of signal intensity in the CP layer to that in the permeate suggests that the layer reaches a maximum concentration of 40% vol/vol. This is an overestimate as part of the reduction in image intensity is due to a reduction in proton density.

250 ----200

-rn 150 C

.F100 u)

50

0

250

200

150

100

50

0

Position

b) Fig. 5 1.5: Typical 5 12 x 256 images of the filter module at steady-state.The image was taken 130 mm from the feedstock inlet obtained with TR = 8 s, TE = 23.65 ms and shows the structure of the thick part of the polarization layer revealed by Tz contrast. A signal intensity profile is shown in b) with points of correspondence between the two figures labeled A-G.

51.3.2 Time Evolution of the CP Layer The growth of the CP layer with time may be followed in the series of images in Fig. 5 1.6. From an initially clear module, the layer of increased concentration rapidly builds until it fills nearly one third the available lumen cross section. The change in the shape of the bright inflow artefact reflects changes in the pattern of the feedstock flow which is now restricted to the upper portion of the lumen. The asymmetry in the layer is evident from the commencement of the growth process. Growth in the CP layer is correlated with a decline in the permeate flux as the increase in concentration at the wall produces a hydrodynamic resistance in series with the membrane. This can be clearly seen in Fig. 5 1.7a. The gravity-induced asymmetry of the CP layer suggests that the orientation of the module will affect its performance. Fig.

537

51. Invesfigationof Concenrrntion Polarization in Crossflow Microfillration of Colloidal Silica

5 1.7b shows a comparison between flux rates for horizontal and vertical orientations. When the module is vertical, it is reasonable to assume that the CP layer will be distributed symmetrically around the circumference of the membrane. At steady state, the flux rate for the horizontal case is approximately twice that of the vertical. In the vertical case, there appears to be no significant flux difference, whether the feedstock flow is up or down.

Fig. 51.6: The growth of the polarization layer at times 2, 8, 26 and 80 minutes following application of the Th4PD. Note the change in the shape of the inflow artifact reflecting the changing shape of the flow profile as the more viscous CP layer forms.

-

5

0

E E

UP

i4

o

Y 0

E3

4

m

h*****

c

ilP

Honlontal

0 .

2

n

0

5'

.-E

I'

X

0

I

0

o

20

40

80

80

Time (mln)

100

im

140

0015

0010

0

a

40

80

80

1w

120

110

Time (mln)

Fig. 5 1.7 a): A time course showing the growth of the polarization layer, measured at its thickest part, 135 mm from the feedstock inlet. Also shown is the corresponding decline in the permeate flux following the application of the TMPD. b): The permeate flux as a function of time in the case where the module is held in the horizontal direction and when it is held vertically.

538

D. Airey. V. Chen, J. Wu.and J. M. Pope

51.4 Conclusions Useful quantitative information concerning the development and distribution of concentration polarization layers in a colloidal silica system has been obtained. Significant structure is observed in the thick part of the CP layer, reflecting the balance of convective and diffusive forces which cause the layer. A significant asymmetry in the layer is observed due to the flow of the layer under gravity. This asymmetry correlates well with the changes in filter performance at different orientations and has profound implications for the design of industrial filtration installations.

References 1.

R.H. Davis, Membrane Handbook, W. S . Ho, K. K. Sirker (eds.),Van Nostrand Reinhold, New York, 1992, pp. 480-505.

2.

J. M. Pope,S. Yao. J. Wu, A. G . Fane, Proc. International Membrane Science and Technology Conference (IMSTEC), UNSW, November 12-l4th, 1996.

3.

J. M. Pope., S.Yao, A. G. Fane, J. Membrane Sci. 118(2) (1996) 247-257.

4.

S. Yao, M. Costello, A. G. Fane, J. M. Pope,J. Membrane Sci. W(3) (1995) 207-216.

5.

S. Yao, A. G. Fane, J. M. Pope, Magn. Reson. h a g . 15(2) (1997) 235-242.

52. Evaluation of Mixing Profiles of Power Law Fluids in Scraped Surface Heat Exchanger Geometry Using MRI W. Wang, J. H. Walton', M. J. McCarthy, and K. L. McCarthy Department of Biological and Agricultural Engineering, 'NMR Facility, University of California, Davis, CA 95616, USA

Abstract The application of scraped surface heat exchangers in the food industry is varied; applications include continuous cooking of starch jellies, production of shortening, cooling of aerated marshmallow, and pasteurization of tomato paste. Mixing induced by the scraped surface heat exchanger promotes heat transfer and thus uniform cooking. In this study we imaged the mixing of a fluid stream injected through the wall of a scraped surface heat exchanger geometry. The apparatus consisted of coaxial cylinders in which a straight flight rotates with the inner cylinder and spans the annulus between the surfaces. Fluid doped with MnCl, to provide T2 contrast was introduced upstream of the Nh4R coil while fluid was flowing in the axial direction through the rotating scraped surface heat exchanger. T2-weighted images were used as a noninvasive method to evaluate mixing profiles in the angular directions downstream from the injection point. The degree of mixing obtained at a fixed distance from the injection point increased with rotation speed and decreased with axial flow rate.

52.1 Introduction Mixing is an important operation which promotes heat transfer, mass transfer, and chemi-

cal reaction. The scraped surjiuce heat exchanger (SSHE)is used mainly for heating and cooling highly viscous fluids. It consists of a jacketed cylinder fitted with a rotating inner

540

W. Wang. J . H . Walton, M. J . McCanhv. atid K . L. McC(irtliy

cylinder, or a shaft, on which scraping blades are mounted. A product is pumped through the cylinder while heating or cooling media is circulated in the jacket. The blades, spring-loaded or free-floating, are attached to the shaft and are forced against cylinder wall as the shaft rotates. The product is consistently scraped off the cylinder wall by the blades, which allows continuously changing portions of the product to be exposed to the thermal treatment. The scraped product mixes with the rest of the product and moves axially through the SSHE. There are two types of flow for the product: flow in the rotation (angular) direction and in the axial direction. The two flows form a helical path for the product through the SSHE. Clearly, the flow patterns control the radial mixing of the scraped product in the annular space and distribution of new product to the heat transfer cylinder wall. Also, the flow patterns affect the axial mixing and thus residence time distribution of the product. However, axial mixing should be minimized because it increases the residence time distribution of the product in the SSHE and decreases the average temperature difference which is the driving potential for heat transfer. Therefore, understanding mixing in SSHE is essential for understanding the heat transfer mechanism of the SSHE and the thermal-time effect on the product during processing in order to model and optimize the process [ 1,2]. The approach of using magnetic resonance imaging (MRI) in SSHE provides both qualitative and quantitative ways to assess mixing quality. In the past, study of mixing by statistical analysis involved tedious sampling and measuring process [3,4]. MRI utilizes the different magnetic resonance properties of two materials, specifically the spin-spin and spin-lattice relaxation times (TI and T . ) ,to relate the signal intensity on the images to the degree of mixing of the two materials. This type of work was fist reported by Smith ef al. [ 5 ] to study the effect of the number of rotations on the mixing of two viscous fluids in Couette geometry. Developed upon the same principle, the study of mixing under the continuous steady-state mixing process of two components was conducted in this research in the scraped surface heat exchanger geometry. A 1% aqueous carboxylmethyl cellulose (CMC) solution was used to study the effect of rotation speed and axial flow on the mixing in the scraped surface heat exchanger geometry.

52. Evaluation ojMixing Profiles of Power LAW Fluids in Heat Exchanger Geometry Using MRI

54 1

52.2 Material and Methods The SSHE geometry consisted of two concentric cylinders with a flight, or blade, attached to the inner cylinder. The flight rotates with the inner cylinder and sweeps fluid in the annular direction (Fig. 52.1). Fluid is also forced through in the axial direction due to a pressure gradient. The proton intensity of fluid at the plane designated P-P (Fig. 52.1) is imaged during steady flow.

Magnet

/

Protective Casing

/

\

Blade

Inner Cklinder

\

-

Outer cylinder

r'

LP

I

Exit

Fig. 52.1: Schematic of the experimental scraped surface heat exchanger geometry.

The test fluid, a 1% sodium carboxymethyl cellulose solution (CMC), was characterized as a power law fluid with a flow behavior index 0.72 and consistency index of 3.10 Pa sn. The pure CMC solution was considered the primary fluid (A). The secondary fluid (B) consisted of the primary fluid doped with manganese chloride. Manganese chloride was added into the second stream to shorten T2 and provide contrast. Fluid B was injected continuously into the SSHE, 14.5 cm upstream of the imaged region, using constant ovemding air pressure. Images were taken at different rotation speeds and volumetric flow rates. The secondary fluid appeared dark on the image due to doping. The variation of signal intensity on the image indicated the degree of mixing between A and B.

542

W. Wang, J . H. Wallon, M. J. McCartky, and K. L. McCarthv

52.3 NMR Techniques 52.3.1 Imaging Pulse Sequence The MRI signal intensity is a function of the relaxation times T, and T2, the repetetioti time (TR) and the echo time (TE). The expression is: I = K [l - exp(-TR/T1)]exp(-TEIT,)

(52.1)

where K is a constant which depends on the sample's proton density, as well as its chemical and physical environment [ 6 ] .Under the experiment conditions, TR was much longer than T, of the major component; eqn. 52.1 can then be simplified to:

I = K exp(-TEIT2)

(52.2)

In other words, the images were spin-echo T2-weighted images. Short echo time was desirable because the signal intensity is inversely proportional to the echo time. Figure 52.2 shows the timing diagram of the imaging pulse sequence used on the Tecmag Spectrometer (Tecmag, Inc., Houston TX)for the experiment. The pulse sequence started when it was triggered by a gating device. The gating device consisted of an optical sensor which detected a mark on the rotating shaft The sensor output was a TT'L pulse which

External Triggerring

180'

90"

Phase

Gx

-Encoding -

Fig. 52.2: The timing diagram of the imaging pulse sequence example of a figure.

52. Evaluation of Mixing Profiles of Power Law Fluids in Hear Exchanger Geomeny Using MRI

543

triggered the spectrometer.This way, the blade was always at the same step (128 steps total). The time between the middle of the 90" and 180" pulses was one half of the echo time. The frequency-encoding step had 256 sampling points.position as the sequence started. A 1.56 crn slice perpendicular to the z-direction was selected by a selective 90" RF pulse. A 180"refocus RF pulse followed a phase-encoding

52.3.2

Image Analysis

Imaging files for the blank (no minor stream) and mixing images were imported to Matlab (the Mathworks, Inc., Natick, MA) to be processed. The signal intensity of the blank images without any doping had a distribution of values instead of a single value, due to the RF coil inhomogeneity. The blank images were first thresholded to filter out all the background noise. Only the signal from the fluid remained. In order to achieve more accurate results for the mixing images, the signal intensity values from the blank images were inverted and then multiplied to the mixing images point by point to correct for the RF coil inhomogeneity.The resulting matrix was used for final analysis.

52.4 Results and Discussion The following series of images (Fig. 52.3) represents the change in the signal intensity due to the incorporation of the minor component. At the higher axial flow rate of 94 d m i n and slower rotation speed of 7.5 rpm, the stream lines introduced by the minor component can be easily distinguished. At a slower axial flow rate of 45 d m i n and faster rotation speed of 15 rpm, instead of seeing stream lines, the minor component was more evenly distributed near the inner and the outer cylinder, and near the blade. A histogram gives a general description of the signal intensity change with the rotation speed and axial flow rate. As shown in Fig. 52.4, the signal intensity distribution of the image at higher axial flow rate and lower rotation speed exhibited a normal distribution pattern. But at the rotation speed of 15 rpm and 45 ml/min axial flow rate, the mixing was improved. The number of pixels at the high intensity region decreased and the number of pixels at the low intensity increased significantly, which changes the signal

544

W. Wung, J. H.Wulton. M. J. McCarthy. and K.L McCurthy

intensity distribution to bimodal. Since the relationship between minor component concentration and signal intensity was exponential, the increase in the frequency of lower signal intensity values signifies the incorporation of minor component into major component, and therefore, improved mixing.

Fig. 52.3: The series of images to display the signal intensity of a pure component, two components at high axial flow rate and low rotation speed and two components at low axial velocity and high rotation speed.

0.035 0.03 U

0.025

~

A

oA

0

0.02 A A

t

0.015

A A 4

0.01

0.005

0 0

0.2

0.4

0.6

0.8

1

Relative Signal Intensity Fig. 52.4:The histogram of signal intensity of the mixing images. The x-axis, the signal intensity, was normalized by the blank image and the y-axis, the frequency, was normalized by total number of nonzero pixels in the images.

52. Evaluation of Mixing Profiles of Power Law Fluids in Heat Exchanger Geometry Using MRI

545

52.5 Conclusions The magnetic resonance imaging technique explored a new way to study mixing in a complex rotating geometry. In the scraped surface heat exchanger, mixing was more favorable at lower axial flow rate and faster rotation speed. Under those conditions, there were more pixels at the low intensity region and the signal intensity distribution was bimodal. In contrast, the faster axial flow rate and slower rotation speed gave a normal distribution. In both cases, mixing was more complete in high shear regions, near the inner and the outer cylinder and the blade.

References 1.

M.Harrd, J. Food Process Engineering 9 (1986) 1.

2.

H. Abichandani, S.C. Sarma, and D.R. Heldman, J. Food Processing Engineering 9 (1987) 143.

3.

S . Middleman, Fundmnentals of Polymer Processing, McGraw-Hill, 1977.

4.

Z . Tadmor and C.G. Gogos, Principles ofPolyrner Processing, John Wiley & Sons, 1979.

5.

E.G. Smith, R. Kohli, P.A. Martin, N. Roberts, and R.H.T. Edwards, Frontiers In Industrial Process Tomography, Proceedings of Engineering Foundation Conference, Engineering Foundation, 1995.

6.

P.T. Callaghan, Principles of Nuclear Magnetic Resonance Microscopy, Oxford, 1993.

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53. The Self-Diffusion of 1,3-Propylene Glycol in Track Etched Membrane Pores E. Vasina, V. Skirda Department of Molecular Physics, Kazan State University, Kremlevskaya str. 18, Kazan 420008, Russia V. Volkov, A. Nechuev, B. Mchedlishvili Shubnikov Institute of Crystallography, Russian Academy of Sciences, Leninskii pr. 59, Moscow 117333, Russia

Abstract The results of the 1,3-propylene glycol self-diffusion investigations in truck etched membrane with Pulsed Field Gradient (PFG) NMR spectroscopy are presented. The restricted diffusion of 1,3-propylene glycol in membrane pores was registered and the sizes of restrictions were estimated. The difSusion exchange between the diffusate in pores and the bulk diffusate was observed.

53.1 Introduction The Pulsed Field Gradient NMR techniques are widely used for the diffusion investigations of liquids confined in porous media having both random and controlled structure. PFG NMR techniques give us the opportunity to study the diffusion in different spatial scales by varying the diffusion time (the time of observation) that is very important for porous media investigations. By that kind of investigations one can derive the information about structural organization of porous media (from the point of view of an injected liquid) and their permeability for the liquid molecules. In this report some of the results of investigations of the 1,3-propylene glycol translational diffusion in polyethyleneterephthalate track membranes [ 11 with PFG NMR are presented.

548

E. Vusina. V. Stirah. V. Volkov. A. Nechaev, iznd B. Mchedlishvili

53.2 Experimental The diffusion experiments were carried out on the pulsed NMR spectrometer (Kazan) operating at 64 MHz frequency for protons using the stimulated echo pulse sequence (Fig. 53.1). The maximum pulse gradient intensity was about g, = 200 T/m. The temperature of sample was about +30 "C. The errors in the measurements did not exceed 5 10%.

90'

90"

90

go

Fig. 53.1: Stimulated echo pulse sequence with magnetic field gradient pulses. z and 71 are the time intervals between the first and the second 90" pulses, respectively; 6 the duration of the gradient pulses; A the gradient pulse separation; g the pulse gradient; go the constant gradient.

For a system characterized by only one self-diffusion coefficient D, (system with one diffusion phase from the point of view of NMR) the diffusion attenuation for the stimulated echo pulse sequence (if 6 g << Tg,) is written in the following form

where A ( 2 2 , ~ ~ ,=0 A(0) ) exp( -2dT2 - .cl/T1)for the case of the exponential relaxation, A(0) is the stimulated echo amplitude at g = 0, T2 the transverse relaxation time, T I the longitudinal relaxation time, y the nuclear gyromagnetic ratio, td = (A - 6/3) the diffusion time. In the case of the diffusion in porous media the diffusion attenuation may have a complex non-exponential shape. In some cases, if the shape of the diffusion attenuation

53. The Self-Drffi4sion of 1,3-Propylene Glvcol in Track Etched Membrane Pores

549

is not caused the non-Gaussian ,,propagator,,, the expression for the echo attenuation is presented by the superposition of the exponentials (here the summation is over i) (53.2)

(53.3)

where p i are the relativ populations of resonant nuclei that are characterized by T2i,T I , DSi.Generally in the study of such systems one uses the average self-diffusion coefficient ( D ) that is determined from the tangent to the initial curve (g + 0) of the diffusion attenuation [2,3]

(53.4)

( D )=

CPI Dsi I

53.3 Materials and Sample Preparation The track membranes are made by the irradiation of a thin polymer film with high energy ions. The irradiated film is etched and in this way the tracks after passing ion beams are removed. The diameter of pores depends on the type of ions and their energy. The diameter of obtained pores is varied from some nanometers to some micrometers [ 11. The thickness of the used polyethyleneterephthalatemembrane film is about 10 pm, the pore diameter is about 0.2 - 0.25 pm (from electron microscopy data). The angular distribution of the channel orientation towards the normal drown to the film surface is in the range from 0" to 30". It gives the opportunity of channels to cross among themselves inside the membrane film.

550

E. Vasina, V. Skirda, V. Volkov. A. Nechaev, and B. Mchedlishvili

The pack of the membrane film sheets was saturated with 1,3-propylene glycol. The sample tube was put in the sensor of the NMR spectrometer so that the gradient vector g was directed parallel to the film surfaces in the pack (i.e. perpendicular to the pore channels).

53.4 Results and Discussion The registration of the echo attenuations lg[A(g*)/A(O)] from 1,3-propylene glycol protons was made under various diffusion times and the constant 6 value, that allows to easily identify the presence of thefully restricted difision when D, td-': under these conditions the slope of the "fully restricted" components of the echo attenuation does not depend on the diffusion time. The fully restricted diffusion regime was observed for the component of echo attenuations with the least self-diffusion coefficient (see Fig. 53.2). In this regime the = 6 D, td can be used for the estimation of the linear restriction Einstein relation (9) sizes [2]. The calculated restriction sizes were estimated to be about 0.26 pm, which is in good accordance with the pore diameter sizes obtained from the electron microscopy investigations. The population p a of the echo attenuation component characterized by the self-diffusion coefficient D, decreases while the diffusion time td increases. At the same time the average self-diffusion coefficients (D)were constant. From above two facts we have concluded that the molecular diffusion exchange of the diffusate in pore and the bulk propylene glycol (between the membrane films) taken place [2]. According to the procedure proposed in [3], the experimental lifetime distribution function F(td) in pores was obtained: from the experimental dependence of the population pa on the diffusion time td by use of the eqn. (53.5) 0~

(53.5)

where the integrating is between 0 and td. The experimental function F(t) was compared with the calculated lifetime distribution function F'(t) obtained as the solution of the First Passage Problem [4]eqn. (53.6)

53. The Self-Diffusion of 1.3-Propylene Glycol in Track Etched Membrane Pores

55 1

where A is the length of the pore channels, D the self-diffusion coefficient of bulk 1,3propylene glycol. Both these lifetime distribution functions were similar and the reduced rate of decay of F'(t) we have explained by that the onedimensional First Passage Problem doesn't consider the cross pore size (the pore diameter).

1

b b

1E-4 0

1000

2000

3000

4000

5000

6000

g2 [T2/m2] Fig. 53.2: Echo attenuations Ig[A($)/A(O)] from 1,3-propylene glycol protons in the system of track membrane films recorded under various diffusion times td and the 6 = const. condition.

552

E. Vasina. V. Skirda, V. Volkov, A. Nechaev, a d B. Mchcdlishvili

53.5 Conclusions We have investigated the self-diffusion of 1,3-propylene glycol in pores of the track etched membranes with Pulsed Field Gradient NMR technique. The echo attenuations of the diffusate have a complex shape which depends on the diffusion time. We have observed the fully restricted diffusion and the estimated sizes of the restrictions for the diffusate were in good accordance with the sizes of the pore diameters obtained by the electron microscopy. The molecular diffusion exchange of the diffusate in pores and the bulk diffusate was observed. The experimental lifetime disribution function of 1,_?-propylene glycol in pores was obtained and that may be describe by function derived as the solution of the First Passage Problem.

References 1.

B. V. Mchedlishvili, V. V. Beriozkin et al., J Mernb. Sci. 79 (1993) 285.

2.

R. R. Valiullin, V. D. Skirda et al., Phys. Rev. E 55 (1997) 2664.

3.

A. I. Maklakov, V. D. Skirda. N. F. Fatkullin, Encyclopedia of Fluid Mechanics, Chap22 (1990) 705.

4.

D. A. Darling, A. J. Siegert, Ann. Math. Statist. 24 (4) (1953) 624.

Geology and Ecology

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54. Review: NMR Detection and Characterization of Hydrocarbons in Subsurface Earth Formations R. L. Kleinberg and C. Flaunt Schlumberger-Doll Research, Ridgefield, Connecticut 06877, USA

Abstract Petroleum reservoirs are usually sedimentary earth formations composed of porous rock. Pore sizes may range over orders of magnitude within a single rock, and, in general, water, oil, and natural gas can coexist within each pore. In order to efficiently exploit a reservoir, it is necessary to know the location, quantities, and physical properties of the pore fluids. Well bore nuclear magnetic resonance measurements are now helping to provide this information. In favorable cases, water and crude oil proton magnetizations relax at distinct rates. However, many conditions can limit the NMR observability of hydrocarbon in reservoirs: 1) there is substantial decay of magnetization within the dead time of the receiver, 2) water and oil signals decay at overlapping rates, making them difficult to distinguish, or 3) longitudinal relaxation time is sufficiently long that hydrocarbon spins cannot be fully polarized in the cycle time of the measurement. A number of methods have been developed to overcome these problems. Some are purely NMR methods, others employ combinations of physical measurements.

54.1 Introduction Oil and gas are found up to 10 km underground in beds of sedimentary or other porous rock. Only a part of a typical sedimentary rock is solid mineral matter. The pore space, which accounts for up to about 35% of the volume, can be filled by combinations of oil, water, or natural gas. In order to find and characterize deposits of oil and gas, geologists and petroleum engineers need continuous measurements of physical properties of earth

556

R. L. Kleiriberg and C. Flaum

formations over depth intervals of hundreds or thousands of meters. Since these measurements are performed at drilling rigs, the cost of which can be as high as $100,000 per day, speed and efficiency are of the utmost importance. Rock samples can be brought to the surface, but this process is time consuming and does not provide information in a depth-continuous or timely manner. Thus instruments have been designed and built that can be lowered into a well bore to measure physical properties of earth fortnations in situ. The process of making these measurements is called "well logging" [ 1,2]. A large variety of electromagnetic, acoustic, and nuclear borehole instruments are now used for various purposes. Each technique has drawbacks and limitations, and no one logging device is adequate to give a complete description of an earth formation. Nuclear magnetic resonance measurements are used to quantify a number of reservoir characteristics of interest to petroleum engineers [3]. These include the volume fraction pore space (porosity), the hydraulic permeability, and the fraction of formation fluid that is prevented from flowing by capillary forces or physisorption on clay minerals. It is also used to identify hydrocarbon-bearing zones, and to quantify hydrocarbon properties. Most oil and gas reservoirs are identified by borehole resistivity measurements. At great depth, water is usually very saline, and therefore a good conductor of electricity, whereas hydrocarbons are insulating. Thus high electrical resistivity, in a zone with substantial porosity, can be a good indicator of oil or gas. However, this technique is not infallible. Rocks are generally water-wet, or at least mixed-wet, and have continuous paths for the conduction of electric current. A hydrocarbon formation can have a low electrical resistivity when there is a large amount of electrically conductive clay in the pore space, or when saline water is trapped by capillary forces in the pores of very fine hydrophilic silts. Conversely, there will be a false indication of hydrocarbon when the ground water is unexpectedly fresh. In such cases, NMR can resolve the ambiguity. Characterization of the hydrocarbon is of considerable interest, even when resistivity measurements provide an accurate indication of its presence. Tar, bitumen and coal have electrical signatures identical to that of light oil, but are of little or no economic interest in many parts of the world. More generally, the rate of production determines the design of pipelines and surface facilities, and thus oil viscosity is an important input into the planning of a petroleum production project. Although various production tests are used to obtain viscosity information, only nuclear magnetic resonance measurements provide a spatially resolved indication of in situ oil viscosity.

54. NMR Detection and Characterization of Hydrocarbons in Subsurface Earth F o m t i o n s

557

54.2 Limitations of Borehole NMR Instruments NMR measurements of intact earth formations are perforce made outside of the apparatus [MI.Therefore the static magnetic field is highly inhomogeneous over the sample volume. In fact, the inhomogeneous linewidth due to “magnet inhomogeneity”, yAB,, is approximately equal to the rate of spin tipping by the RF field, yBl. This precludes chemical shiji spectroscopy by the usual liquid techniques. The static magnetic field is in the range 15 - 50 mT, the coupling of the sample to the RF antenna is poor, and borehole temperatures can be as high as 175 “C. These factors combine to depresses the signal and increase the noise. In practice, these factors limit NMR measurements to the amplitude and transverse decay of the proton signal, measured using the Carr-Purcell-Meiboom-Gillsequence with phase cycling. The necessity of characterizing hundreds of meters of earth formation in a reasonable time requires the apparatus to be moved at velocities on the order of 10 c d s . To obtain a vertical resolution of less than a meter, only a few seconds of measurement time is permitted. Low viscosity fluids at high temperature can have longitudinal relaxation times ( T I )of up to 10 s. Thus the usual laboratory practice of waiting five times T I between CPMG acquisitions is precluded. To obtain the required quantitative amplitudes, a polarization correction must be applied. Receiver dead time is also a significant limitation. At the low frequencies employed, 0.6 - 2 MHz, the dead time is several hundred microseconds. The practical limit of observability is several times longer, due to poor signal to noise ratio. Fluids relaxing faster than this are NMR-invisible.

54.3 Properties of Oil and Water in Porous Rock Hydrocarbon reservoirs are usually composed of porous rock formations, in which oil and water coexist in the pore space. Most NMR measurements of oil- and watersaturated rocks are consistent with a picture in which water lines pore surfaces while oil forms drops at the centers of pores. The proton densities of crude oil and water are equal, to within a few percent, so the NMR signal is a volumetrically weighted sum of water and oil responses. However, the complexity of the fluids and the environment in which they reside make the magnetization decays complicated.

558

R. L. Kleinberg und C. Flnum

54.3.1 Relaxation Mechanisms Magnetization decay is controlled by a number of processes operating in parallel. For fluids in rocks, the mechanisms are relaxation at surfaces, dephasing by diffusion through magnetic field gradients, and bulk relaxation.

Surface Relaxation Pore sizes vary widely, but are often in the range of 0.1 - 10 pm, and NMR relaxation times are typically in the range 0.01 - 1 s. Thus molecular diffusion ensures that any fluid molecule having access to a grain surface has ample opportunity to interact with that surface several times during the NMR measurement. Moreover, electron spins are relatively abundant in sedimentary rocks; sandstones are usually about 1% iron by weight, and oxide surfaces appear to have abundant unpaired electrons trapped at defects [7]. Thus fluid protons are efficiently relaxed by grain surfaces via hyperfine interactions [8,9]. The NMR decay rate is a function of grain composition and the surface to volume ratio of the pore, (S/V)pore.The longitudinal and transverse decay rates have the same form:

-=Pi(;) 1 TlS

(54.la) pore

-=1I%(;)

T2s

(54.1b) Pore

The surface relaxivities p1 and p2 are functions of the combination of fluid and solid, and incorporate the details of the proton-electron interactions.

Diffusion in Gradient The second mechanism is that of molecular difision in magneticfield gradients. This process is well understood when the gradient is uniform throughout the sample and when diffusion is unrestricted [lo]. Neither condition holds in porous rocks. One source of magnetic field gradient is the magnetic susceptibility contrast between grain material and pore fluid. The resulting internal field gradient, and hence the importance of this relaxation mechanism, grows with increasing B,. The inhomogeneous Bo of the borehole NMR

54. NMR Detection and Charncterizarion of Hydrocarbotts in Subsuflace Earth Formations

559

instruments also contributes significantly to the magnetic field gradient. The CarrPurcell-Meiboom-Gill (CPMG) method mitigates the effect of diffusion in a magnetic field gradient. Keeping both the CPMG echo spacing, TE, and the applied magnetic field, B,, to a minimum reduces the contribution of diffusion to T2 relaxation. The manner in which diffusion effects become important as TE and B, increase is, in porous media, rather complex [ 111.

Bulk Relaxation Bulk relaxation is important when the two mechanisms already discussed are suppressed, e.g. at low field and small echo spacing, and when the fluid is in large pores, or does not have contact with grain surfaces. Bulk processes are most important when the pore fluid is viscous or when it has a high concentration of paramagnetic ions.

Summary The relaxation processes act in parallel, so the rates add: (54.2a)

is the surface contribution, (1/T2)Dis the diffusion in field gradient contriwhere (1/T2)s bution, and (1/T2)~ is the bulk contribution. The corresponding equation for TIis (54.2b)

There is no diffusion contribution to T1 because the diffusion process is strictly a dephasing mechanism.

560

R. L. Kleinberg and C. Fhum

54.3.2 Distributions of Relaxation Times All of the NMR mechanisms discussed above give rise to multiexponential magnetization decays.

Surface Relaxation Rocks have a very wide distribution of pore sizes, even within a small sample of uniform appearance. Consequently, water saturated rocks are characterized by a correspondingly broad distribution of NMR relaxation times [ 121. The transverse magnetization decay of water protons in rock can be represented by (54.3) where -=P2(;)i 1

(54.4)

T2i

and where mi is proportional to the fluid volume associated with (SlV),and therefore relaxing with decay time TZi.This model has been validated by numerous laboratory experiments on rocks and synthetic porous media [ 131. Figure 54.1 shows an example of a relaxation time distribution mi for a visually homogeneous 10 cm3 sandstone sample. Note that the relaxation times vary over several orders of magnitude.

Diffusion in Gradient The transverse relaxation rate due to diffusion in a static field gradient is proportional to the square of the gradient. Thus any distribution of magnetic field gradients leads to a distribution of transverse relaxation rates. The internal gradients in porous media are widely distributed, due to the irregularity of pore sizes and shapes. The borehole NMR instruments are also characterized by substantial B, gradients. Whereas one of these has a uniform gradient of 0.17 T/m [5], others have distributions of gradients [4,6].

54. NMR Detection and Characterizaiion of Hydrocarbons in Subsurface Earth Formations

56 1

Pore Diameter (km)

10-2

10-1

100

101

lo2

I Berea 100 Sandstone

'"i

Fig. 54.1: Transverse relaxation time distribution for a typical rock saturated with water. The ordinates are values of miestimated from a CPMG decay using eqn. (54.3). The broad distribution of relaxation times (lower axis) reflect a broad distribution of pore sizes (upper axis). Upper and lower axes are related by eqn. (54.4) where S/V = 4/D, appropriate to a cylindrical pore model.

Bulk Relaxation The magnetization decays of water and aqueous electrolytes are exponential. However, the decays of crude oils are notably nonexponential, and may be analyzed in terms of distributions of exponential relaxation times [ 141. These transverse relaxation time distributions may span several orders of magnitude in T2, and can be described by eqn. (54.3).

54.3.3 Fluid Relaxation Data Crude Oils In water-wet rock, hydrocarbons do not have access to grain surfaces, and usually the water-oil interface is not an efficient surface for relaxation [13]. Therefore the surface relaxation mechanism is not operative. This is true even if a water film of only a few molecular layers covers the solid surface [9]. Therefore the relaxation times of oils are independent of grain composition and pore size. They do depend on temperature, which is measured in the well bore. Thus if the type of hydrocarbon is known, its in situ NMR

562

R. L. Kleinberg and C. Flaum

relaxation times can be accurately predicted. Conversely, if the relaxation time is measured, fluid properties can be determined. As stated above, crude oils have broad distributions of relaxation times. However, it has been found that oils with low viscosity relax more slowly than those with higher viscosity. A single relaxation time parameter which captures the viscosity dependence is the logarithmic mean T2:

(54.5)

In one investigation [ 141, the relaxation times of 66 oil samples were measured at room temperature. Over the range 1 cp to 300 cp, T2LM(in seconds) is related to viscosity q (in centipoise) by T2LM =-

1.2

(54.6a)

q0.9 and T I = T2. Between 300 cp and lo5 cp laboratory data is described by T2LM =

0.13

(54.6b)

Bloembergen, Purcell and Pound [15] theory predicts that relaxation times depend on viscosity (q) and temperature ( T ) as T I = T2 - T/q in the motionally narrowed (short correlation time) regime. As viscosity, and hence correlation time, increase, T2 is expected to become independent of viscosity. Thus although the crude oil results do not conform fully with simple theory, there are many common elements. Note that almost all the temperature dependence of the relaxation times is carried in the viscosity. The crude oils measured in the laboratory were free of dissolved gas. In contrast, many native state crude oils have significant amounts of dissolved methane, with attendant viscosity reduction. It is believed, but has not been proved, that dissolved methane only affects crude oil relaxation times through the viscosity. Near and above the vaporliquid critical point, this assumption is expected to break down. Laboratory measurements are made in homogeneous magnetic fields. As explained above, magnetic field gradients are associated with borehole NMR measurements, so

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diffusion will reduce T,. For low viscosity crude oils, the difSusion coefficient is proportional to T/q. At room temperature it is [16]

D=

1.340-9m2 / s

?1

(54.7)

where the viscosity is measured in centipoise. Diffusion in magnetic field gradients only affects T2, not T , . Figure 54.2 shows the relaxation times derived from the above equations. Unrestricted diffusion in a gradient of 0.2 T/m, and a CPMG echo spacing of T, = 0.32 ms have been assumed in the calculation of T2.

NMR Relaxation of Crude Oils

1oo h

v)

Y

b

10-2

7

I-

1o

-~ 10-1

1o1 1o3 Viscosity (cP)

Fig. 54.2: Longitudinal and transverse relaxation times of crude oil, plotted against viscosity (centipoise).

Water The primary relaxation mechanism for water in water-wet rock is Juid-sutfizce interaction. Relaxation time increases with pore size until the bulk relaxation time is attained, see eqns. (54.1) and (54.2). The strength of the surface relaxation parameters p1 and p2 have been determined for the two most common kinds of sedimentary rocks, sandstones and carbonates [ 171. There is considerable variability in the values, depending on grain

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R. L. Kleinberg and C. Flaunt

-

-

composition, but in general, for sandstones, p1 2.5 p d s and p2 5 p d s , while for carbonates p 0.8 pm/s and p2 1.7 p d s . Surface relaxation is independent of temperature [9], while bulk relaxation is not. Although laboratory measurements of water relaxation times above 100 "C are lacking, it has been estimated that TI is more than 20 s at 150 "C (in the absence of dissolved oxygen or other relaxation agents) [18]. Diffusion in a magnetic field gradient reduces T, considerably, however.

-

-

54.3.4 Mixtures of Oil and Water in Rock NMR magnetization decays of mixed fluids in rock can be very complicated, since each fluid relaxes with a distribution of relaxation times. In general, the relaxation time distributions overlap. The signal component decaying with a relaxation time T2can be written

Terms for water, oil, and gas have been included for completeness. The rni(T2)are proportional to the volumes having relaxation time T,. HI (hydrogen index) is the proton density for each fluid, normalized to the proton density of water at 20 "C and 0.1 MPa pressure [18]. The last factor on each line is the correction needed to account for insufficient polarization time. W is the wait time from the end of one CPMG sequence (when all components of the magnetization are zero) to the start of the next. Use of eqn. (54.8) is complicated by the fact that the relationship between TI and T2 is different for each of the fluids 1181.

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54.4 Formation Fluid Alteration During Drilling In an undisturbed reservoir, formation fluids sometimes partially support the overburden pressure of the earth. When a fluid-bearing formation is penetrated by drilling, formation fluids will flow into the borehole if it is at a lower pressure. The uncontrolled escape of combustible hydrocarbons to the surface (“blowout”) is extremely dangerous, so oil wells are drilled under pressure. During drilling, fluid (“mud”) is circulated through the well to carry rock chips to the surface. The mud is weighted with heavy minerals such as barite (barium sulfate, 4.5 g/cm3) to ensure that borehole pressure is higher than formation pressure. Consequently, fluid may be forced into the formation from the borehole (“invasion”). Usually particles are prevented from entering the formation by the filtering action of the porous rock. Indeed, the filtration process is self-limiting because solids, purposely mixed in the drilling fluid, form a filter cake (“mud cake”) at the surface of the borehole. Nonetheless liquid (“mud filtrate”) can penetrate quite deeply as much as several meters into the formation. The filtrate can be either water with various soluble ions, or oil, depending on the type of mud used by the driller. Since most borehole instrumentation is only sensitive to the rock body near the borehole, the fluids actually measured are a mixture of native formation fluids and mud filtrate. This considerably complicates the interpretation of measurements, but also can be used to advantage, as subsequent examples will show.

54.5 Oil Detection and Characterization Techniques The immense variability of earth formations and crude oil properties implies that a multiplicity of techniques must be used to detect and characterize hydrocarbons in siru. The four examples presented here indicate the range of techniques that have been developed, but do not by any means encompass all of them.

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R. L.Kleinberg ntul C. Flauni

54.5.1 Example: Viscosity Determination Borehole nuclear magnetic resonance measurements provide uniquely useful information even when other techniques are perfectly adequate to locate productive oil zones. Figure 54.3 shows data from an oil reservoir [19]. The vertical axis is depth; a 30 meter interval is shown. The first column is the output of a 'y-ray sensing instrument. The uniformly low reading throughout the depth interval shows that the formation is relatively free of clay minerals. The second column is the output of several electrical resistivity devices having various radii of investigation, ranging to about one meter. The rightmost curve is the output of the deepest-investigating device. The horizontal scale is logarithmic, ranging from 0.2 to 2000 ohm-meters. In the lower half of the plot (deeper into the earth) resistivity is low, indicating rock saturated with salt water. Resistivity is higher in the upper section, which is evidence of oil or gas. Resistivity increases with radial distance into the formation (multiple curves), consistent with saline mud filtrate from the borehole partially displacing native formation oil. The third column is the output of several porosity-measuring instruments, including NMR, on a scale of -15% to 45%. increasing from right to left. The curves are not in perfect agreement, but all show a very porous formation that is uniform over the depth interval shown. The fourth column is the NMR T2 distribution. There is a small graph at each depth. The horizontal axis is T, on a logarithmic scale, ranging from 3 ms to 3000 ms. Plotted vertically in each small graph is the amplitude, mi, associated with a given relaxation time, T2i, see eqn. (54.3). In the lower water zone, the T2 distribution is unimodal, reflecting the pore size distribution of the rock body. Low amplitude features at short T2 are due to processing artifacts of the rather noisy magnetization decays. In the upper oil zone, the T2 distribution is bimodal. Longer time components originate from native water mixed with the mud filtrate. Shorter time components are due to native oil remaining in the NMR volume of investigation, two to three centimeters inside the formation. Resistivity measurements clearly indicate the presence of oil in this formation. However, NMR provides information on the characteristics of the oil. The short relaxation time of the oil, about 13 ms, corresponds to a viscosity of about 100 cp. Since the viscosity of the oil determines its flow rate and ultimate economic value, this is critical information in evaluating the prospect.

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30 mt.

Fig. 54.3:Viscosity determination by well logging. (Courtesy of J. White, Schlurnberger).

54.5.2 Example: Very Viscous Hydrocarbon Crude oils are found over the entire range of viscosities, from a few tenths of a centipoise to the glassy state. Generally speaking, oils with low viscosity are the most economically valuable. Only NMR measurements are able to determine, in situ, viscosity of hydrocarbon. An example is shown in Fig. 54.4 [20]. A depth interval of about 30 meters is shown. The first column is an analysis of the natural radioactivity of the formation, which indicates organic content. The second column shows resistivity, plotted on a logarithm scale from 0.2 to 2000 ohm-meters. The resistivity varies between 10 and 1000 ohm-meters,

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indicating the presence of hydrocarbon. In the third column the dotted curve is formation porosity determined by neutron scattering methods, plotted on a scale from 0 to 30%, increasing from right to left. These three data streams have, in the past, been the conventional measurement suite in common oilfield use. Based on this information, the formation shows every indication of being an excellent oil reservoir. NMR amplitude measurements are shown in the third column (gray shading), indicating almost no porosity. The formation indeed has high porosity and is rich in hydrocarbon, but the hydrocarbon is invisible to NMR. The NMR signal decayed within the dead time of the measurement, effectively 3 ms in this case, denoting a viscosity greater than 3000 cp. Subsequent measurements on rock samples confirmed that the formation was filled with bitumen, and that therefore the formation should be bypassed.

54.5.3 Example: Overlapping Oil and Water Signals In the examples discussed so far, water and oil signals could be distinguished on the basis of strongly contrasting relaxation times. However, if the bulk relaxation time of oil happens to coincide with the relaxation time of water, which depends on grain composition and surface to volume ratio, then the NMR methods described so far are inadequate to distinguish them. In such cases, filtration of borehole fluid into the formation can be exploited to advantage. If the borehole fluid is doped with paramagnetic ions, the relaxation time of water can be reduced without affecting the relaxation of the hydrocarbon. The usual procedure is to first drill the well using an aqueous drilling mud with little or no paramagnetic ion content. The water from the borehole mixes with formation water, with no effect on the NMR signal from the water. The oil is pushed away from the borehole, but usually enough oil remains in the NMR volume of investigation to make a substantial, though not necessarily separable, contribution to the overall signal. After the preliminary NMR measurement, paramagnetic ion is added to the drilling mud. The borehole is then slightly enlarged to clear the surface of the borehole of particulate solids, thereby restarting the infiltration of borehole fluid into the formation. When the NMR measurement is made a second time, the relaxation time of water is reduced while oil, inaccessible to solvated ions, is unaffected. The efficacy of this method is demonstrated in Fig. 54.5 [21]. The left panel shows the initial NMR measurement after the well was drilled with a water-based drilling fluid

54. NMR Detection and Characierization of Hydrocarbons in Subsur$ace Eanh Formarions

569

Fig. 54.4: Anomalously low Nh4R signal indicates very viscous hydrocarbon. (Courtesy of C. Cao Minh, Schlumberger).

free of magnetic ions. Essentially all the signal appears at long relaxation time. When the well is doped with paramagnetic ion and redrilled, the filtration of fresh borehole fluid reduces the water relaxation time, clearly separating it from the slowly relaxing oil signal, as shown in the right panel. The oil first appears about one-quarter of the way up the depth interval shown in the figure.

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R. L. Kleinberg and C. Flnurn

N M R T, distributions for a 50 meter depth interval (vertical axis). Each panel shows distributions from 3 ms to 3000 ms on a logarithmic scale (horizoneal scale). The amplitude of the distribution at each depth and value of T, is coded by the color: darker colors correspond to hgher amplitude. Left panel: Rrst NMR measurement. Throughout the int?nral, T, distribution is centered around 500 ms. Right panel: Result after well ms sdriUed with manganese chloride in the drilling fluid. Manganese ion has entered the formation, reducing the relaxation time of water to about 30 ms,while leaving the oil signal unaffected.

Fig. 54.5: Use of paramagnetic ions in the drilling fluid to alter the relaxation time of formation water. (Courtesy of D. Logan, Schlumberger).

54.5.4 Example: Utilizing 7'1 Contrast Wells are increasingly being drilled with oil-based drilling fluids. When oil from the borehole invades the formation it displaces native water to a radius of a few tens of centimeters. Resistivity instruments with a large radius of investigation can usually distinguish true hydrocarbon zones from water zones flushed with borehole oil. Sometimes, however, clay or saline water trapped in small pores give an anomalously low resistivity in hydrocarbon zones. Oils used in drilling muds are typically alkanes in the hexadecane range, having downhole viscosities of a few centipoise. The most valuable native oils are mixtures of smaller molecules, and are often rich in gas; thus their viscosity may be less than 1 cp. There is little contrast in T2 between such fluids for three reasons. First, the transverse

54. NMR Detection and Characterization of Hydrocarbons in Subsurface Earth Formations

57 1

relaxation time levels out at low viscosity due to diffusion in the magnetic field gradients of rock and apparatus, as shown in Fig. 54.2. Second, T2 contrast is reduced by the effect of instrument motion past the formation, which frequently limits apparent T,- to about 1 s. Third, fluids cannot be resolved even if their transverse relaxation times differ by a factor of two or three; the T,- distributions are broad because the fluids are mixtures, and because of the limitations of processing noisy data [ 121. Drilling oil and native light oil have a stronger contrast in T , than in T2. Unfortunately, T , is not directly measured by borehole measurements, because the measurement is far too time consuming. Nonetheless, the very haste that dictates suboptimal wait times between CPMG acquisitions (see section 54.2) makes the measurements sensitive to T , through the lack of complete polarization. To compensate for insufficient wait time, long T, components are increased by a polarization correction mi,uncorr

1

mi = 1- expi- W I T ]

(54.9)

where mi,uncorris an uncorrected component of the T2 distribution, and W is the time from the end of a CPMG echo train to the start of the next, i.e. the polarization time. In one case, a well drilled with oil-based mud penetrated a formation containing low viscosity oil, see Fig. 54.6 [22]. NMR measurements were made with a wait time W = 0.45 seconds, which was far to short to fully polarize these fluids. The T2 distribution of the partially polarized signal is shown in the second column: throughout the 40 meter section the T2 distribution shows primarily long relaxation time components characteristic of water in large pores, oil-based mud filtrate, or light oil. Gamma-ray scattering measurements, shown in dashed red in the first column, measured formation porosity. The nuclear porosity was much higher than porosity found from uncorrected NMR amplitude, but a constant value TI = 2.5 s was used in eqn. (54.9) to match the NMR amplitude (solid black) to nuclear porosity in the bottom half of the interval shown. The match is imperfect, but generally satisfactory considering the various assumptions that underlay the interpretation of the measurements. The two curves separate at the arrow. Above that depth, the polarization correction using T , = 2.5 s is inadequate to correct the NMR porosity measurement. This indicates T , has suddenly increased; it is estimated to be 6 s, consistent with oil from the borehole mixed with native light oil.

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R.

L. Kleinberg

nnd C. Flaum

porosity

T2 Distribution

Fig. 54.6: Use of T I contrast to distinguish native oil from oil invaded from the borehole.

54.6 Conclusion Nuclear magnetic resonance has long been used to identify and characterize hydrocarbons in the laboratory, but the subsurface environment presents unique challenges. Instrumental limitations preclude standard spectroscopic techniques. Relaxation time analysis is hampered by the highly variable nature of subsurface hydrocarbons and the interfering effects of water in porous media. Some of the hydrocarbons to be characterized are NMR-invisible. Invasion of extraneous fluid from the borehole is a further complication. Nonetheless, a number of methods have been developed which circumvent - or exploit - these difficulties. This paper has presented a sampling of methods now in use which contribute to the discovery and efficient exploitation of petroleum reservoirs.

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Acknowledgments The authors wish to acknowledge their colleagues at Schlumberger, particularly J. White, C. Cao Minh, and D. Logan. S.A. Farooqui assisted in production of this paper.

References 1.

J. R. Hearst, P. H. Nelson, Well Loggingf o r Physical Properties, McGraw-Hill, New York, 1985.

2.

D. V. Ellis, Well Logging for Earfh Scientists, Elsevier. New York, 1987.

3.

R. L. Kleinberg, "Well Logging", in Encyclopedia of Nuclear Magnetic Resonance, vol. 8 pg. 4960, Wiley, Chichester, 1996.

4.

R. K. Cooper, J. A. Jackson, J. Magn. Reson. 41 (1980) 400;L. J. Burnett, J. A. Jackson, J. Magn. Reson. 41 (1980)406; J. A. Jackson, L. J. Burnett, J. F. Harmon, J. Magn. Reson. 41 (1980) 411.

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2. Taicher, G. Coates, Y. Gitartz, L. Berman, Magn. Reson. Imaging 12 (1994) 285.

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R. L. Kleinberg, A. Sezginer, D. D. Griffin. M. Fukuhara, J. Magn. Reson. 97 (1992) 466.

7.

I. Foley, S. A. Farooqui, R. L. Kleinberg, J. Magn. Reson. A 123 (1996)95.

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J. Komnga, D. 0. Seevers, H. C. Torrey, Phys. Rev. 127 (1962) 1143.

9.

R. L. Kleinberg, W. E. Kenyon, P. P. Mica, J. Magn. Reson. A 108 (1994) 206.

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H. Y.Cam E. M. Purcell, Phys. Rev. 94 (1954) 630.

11.

G. C. Borgia, R. J. S. Brown, P. Fantazzini, Phys. Rev. E 51 (1995) 2104.

12.

D. P. Gallegos, D. M. Smith, J. Colloid Interface Sci. 122 (1988) 143.

13.

C. Straley, C. E. Momss, W. E. Kenyon, J. J. Howard, in Transactions of the SPWLA 32nd Annual Logging Symposium, 1991; Log Analyst Jan.-Feb. 1995, pg. 40.

14.

C. E. Momss, R. Freedman, C. Straley, M. Johnston, H. J. Vinegar, P. N. Tutunjian, in Transactions of the SPWLA 35th Annual Logging Symposium, 1994; Log Analyst, March-April 1997, pg 44.

15.

N. Bloernbergen, E. M. Purcell, R. V. Pound, Phys. Rev. 73 (1948) 679.

16.

H. Vinegar, personal communication

17.

R. L. Kleinberg, Magn. Reson. Imaging 14 (1996) 761.

18.

R. L. Kleinberg, H. J. Vinegar, Log Analyst, Nov.-Dec. 1996, pg. 20.

19.

J. White, Society of Petroleum Engineers Paper 3855 1 (1997)

20.

A. A. Latif, D. Sungur, R. Nurmi, C. Cao Minh, Society of Petroleum Engineers Paper 37771 (1997)

21.

W. D. Logan, J. P. Horkowitz, R. Laronga, D. Crornwell, Society of Petroleum Engineers Paper 38740 (1997)

22.

C. Flaum, R.L. Kleinberg, Schlumberger internal report (1997)

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55. Why Would an Oil Company Use MRI? Bernard A. Baldwin and Ruby L. King

Phillips Petroleum Co., 103GB Bartlesville, OK 74004, USA

Abstract Although Magnetic Resonance Imaging was developed to examine soft tissue and organs of humans, it has proven to be a useful tool in several non-medical industries. In our oil company MRI has been used to measure: porosity and fluid distributions in porous reservoir rocks, residual fluids (both concentration and distribution) and fluid flow path and rates. We have identified: core samples which are suitable to represent the reservoir in laboratory testing, the shape of a front as fluids flow through porous rocks, the amount of oil left in the rock after water or gas floods, the parameters which retain oil in porous reservoir rocks, the location of microbial growth inside porous rocks, diffusion of fluids through pore networks and the spontaneous uptake rate of water to displace oil from reservoir rocks.

55.1 Introduction It is well know, that Magnetic Resonance Imaging (MRI) was developed to produce noninvasive pictures of soft tissue and organs in humans [ 141. However, the technique has also proven useful for several non-medical industries [5-81. In our oil company, interest in MRI is driven by the desire to measure: A) porosity and fluid distributions in porous reservoir rocks, B) residual fluids (both concentration and distribution) and C ) fluid flow direction and rates. Figure 55.1 portrays the size scales associated with an oil reservoir which ranges from kilometers to nanometers. The kilometer scale defines the volume of the reservoir, while the centimeter to nanometer scales determine the flow paths and amount of hydrocarbon which ultimately can be recovered from the reservoir’s porous

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B. A. Baldwin and R. L. King

rock. MRI is a 'natural' tool for reservoir characterization on the smaller, mesoscopic and microscopic scale, since 1) imaging measures centimeter to millimeter features,

2) relaxation rate measures the interaction between the fluids and the rock surface, and 3) the fluids of interest, oil and water, both contain hydrogen. In addition, sodium is a component of reservoir brines and fluorine is a useful tracer for either the water or the oil phase.

Fig. 55.1: Scales of heterogeneity in a reservoir.

Before oil companies had the capability to measure porosity distribution inside cores without destroying them, we used to 1) assume that the sample was homogeneous, 2) estimate the heterogeneity from a visual inspection of the outside appearance, or 3) run the test and at the end cut the core to look inside for heterogeneities. The first assumption generally means that oil production modeling based on the effluent production is compromised, because without imaging there is no way of knowing through which parts of the porous rock the fluid passed. The second method which estimates heterogeneity from visual appearance, millimeters to centimeters, generally describes the wrong scale, since the pore network associated with fluid flow is on a scale of hundreds of micrometers or

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577

less. The third method is destructive and prevents the sample from being used for multiple testing or for direct comparison between different production processes. The advantages of MRI are the ability to image with a 100 ym resolution with relaxation times reflecting pore sizes and local interactions of water and oil with the rock surface, micrometers to nanometers. Thus, MRI information is relevant to fluid movement inside reservoir rocks. We use the time-dependent information to determine pore size distribution when the core is saturated with a single fluid and to distinguish oil and water when the core is saturated with two fluids. By holding the measurement time and excitation power constant, we determine the amount, or saturation, of the fluids in the core. Often we use a fluid which is not imaged, such as heavy water or a frozen hydrocarbon, so that we can quantitatively image the second fluid, thus independently imaging oil and water. A second method of resolving oil and water involves adding MR-active tracers, such as 22Na or 19F, which resonate at frequencies far removed from the hydrogen in oil or water. More detailed information about the MRI processes is readily available [7,9]. The major interference for MRI, when imaging fluids in reservoir rocks, is the presence of ferromagnetic and paramagnetic minerals. If evenly distributed, these minerals produce very short T2 ( c 1 ms), and if concentrated in a small volume produce chemical shift artifacts. The magnetically shorted T2 makes it a challenge to obtain good signal-tonoise ratios and often causes a loss of the most rapidly decaying components. However, even with these limitations good images and quantitative results have been obtained and oil production problems have been solved which could not have been addressed any other way. We have two goals for MRI: A) determine new, previously unmeasurable information about the distribution and movement of oil and water inside porous rocks and B) develop faster, cheaper and/or better methods of determining mformation which is currently obtained for reservoir characterization. Figure 55.2 shows how MRI information fits into the decision-making process of our oil company. Pore size distribution and fluid movement generally are used to determine the mechanisms of fluid movement and the bypass of hydrocarbons. Images of porosity distribution are often used to determine the suitability of a specific core plug to be subjected to further testing. The concentration of fluids as a function of time becomes input data for computer programs which simulate reservoir properties. These programs forecast oil and water production over the projected life of the reservoir. When the production projection is combined with the costs of setting up production and hydrocarbon transportation facilities, a financial

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forecast is prepared. In addition to the engineering data, these forecasts consider location (in particular offshore vs onshore), taxes and the political stability of the location. With all this information, management decides which projects to fund.

MRI CONTRIBUTIONS TO COMPANY DECISIONS

* * *

Management Decisions Financial Forecasts Hydrocarbon Production Forecasts Mathematical Reservoir Simulaters

*

Mechanism Analysis MRI analysis of pore disstribution in porous media

MRI monitoring of fluid movement in reservoir core

*

Core Analysis MRI determination of core suitability for reservoir property tests

Fig. 55.2: Schematic showing how MRI is used in an oil company.

55.2 Experimental The MRI images were obtained with a Varian 85/310 CSI, which has a 31 cm bore, 2 T superconducting magnet and operates at 85.55 MHz for hydrogen protons. Either a 9 cm or a 12.7 cm I.D. saddle coil was used as the combination transmittedreceiver coil. The coil was matched to sample size. Signals from hydrogen protons were obtained using the Hahn spin-echo sequence. The echo time and recovery time were adjusted to maximize signal intensity; typically echo times ranged from 7 to 3 ms and recovery times from 4 to 0.5 s. The field of view was adjusted to fit the sample but typically was in the 5 to 16 cm range, giving a pixel resolution of 0.2 to 0.7 mm. Images were obtained in all three orientations because heterogeneities are often more apparent in one orientation than the others. The images consisted of 255 levels of gray in a 256 x 256 display. The intensity and contrast of the individual pictures were adjusted to produce a presentable visual display; however, for quantitative determinations absolute intensities were used. Image

55. Why would an Oil Company Use MRI?

579

intensities were transferred to a spreadsheet, where quantitative saturations were calculated. For several flow processes, images were collected as a function of time and animated to enhance visualization of the flow patterns. T , maps were obtained by sequentially collecting a series of images, 9 to 15, at different inversion recovery times then fitting these images pixel by pixel to a single exponential. The resulting image displayed the T I relaxation times, and separately, the timeback-projected mo map, as two-dimensional distributions. For a single fluid these maps showed relative pore size and porosity distributions, respectively. When two fluids were present, it was possible to separate the fluid which interacted strongly with the rock surface from the fluid which interacted weakly with the surface, by the former’s shorter relaxation time. The samples typically used for reservoir characterization are 1 to 3 inch long and 1 or 1.5 inch diameter cylindrical plugs, drilled from whole core. Because of the saddle coil design, the plug’s long cylindrical axis was normally aligned with the z-axis of the magnet; thus coronal and sagittal images appear as rectangles, while a transverse image appears as a circle. The fluids imaged included pure water, brine (water containing a variety of salts that are typically found in oil field reservoir water), pure hydrocarbons, refined oils and crude oils. The fluids used were selected to give optimal results for the particular study. Brines and live crude oils (crude oils containing reservoir gases) are the most representative of the reservoir, but are also the most difficult to handle. For most studies, the reservoir conditions can be simulated with simpler fluids. Samples were typically prepared by placing the cleaned and dried core in a vacuum chamber and pumping out the air. When the core reached a reasonable vacuum, degassed test liquid was transferred into the chamber and the pressure returned to atmospheric. This procedure was necessary to saturate the small pore spaces with fluids. Subsequent changes in fluid were then made by centrifuging or pumping a second fluid into the core.

55.3 Results and Discussion The most straight forward use of MRI for an oil company is to characterize porous rocks. Since MRI measures fluids rather than the rock, it characterizes the rock by determining the spatial distribution of fluid and the quantity of fluid present. Figure 55.3 shows a

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sagittal slice along the cylindrical axis of a carbonate rock plug. This particular sample had an average porosity, i.e. non-rock volume filled with fluid, of 20.6%. However, MRI showed that porosity in this sample ranged from 8% near the top of the image to about 45% near the bottom of the image. The low porosity region, near the top of the image, determines the permeability, the ability of the core to transmit a fluid or electricity. The high porosity region, near the bottom of the image, was the major source of fluid, containing about 5.5 times the amount of the fluid in the low porosity region. This high porosity region dominated both the rate of fluid production and the quantity of fluid produced. Thus, each end of this plug had a different effect on the mean experimental properties. Without the MRI information, the reservoir engineer would use the average porosity and permeability and incorrectly interpret flow and production properties. Because the nonuniform porosity distribution would compromise interpretation of fluid flow, this particular plug was not used for further testing. Figure 55.4 shows a carbonate rock in which snail shells have dissolved, leaving open voids, or molds, which filled with fluid. From this dramatic image the size and orientation of these molds can be easily determined without destroying the core. Although this type of rock can hold large quantities of oil, there are often only small channels between the molds. The low permeability of these paths prevents the production of hydrocarbon at an economical rate.

Fig 55.3: Sagittal slice through a carbonate rock with dual porosity.

55. Why would an Oil Company Use MRI?

58 1

Fig. 55.4: Carbonate rock containing molds from dissolved snail shells, left coronal, right trans-

verse.

Figure 55.5 shows a chalk core which has undergone bioturbation. After the algae, the source of the chalk minerals, died and settled to the ocean floor, various creatures and worms burrowed through the ooze, where their tracks produced local changes in porosity. The bright lines show regions of greater porosity, more fluid filled open spaces in the rock, while the darker regions represent more closely packed microscopic chalk particles, which produced a lower porosity. The changes in porosity are not as dramatic as the images imply, the black and white levels and intensity range were adjusted to produce an easy-to-view image. For quantitative work we used only the absolute values of the MRI signal for each pixel. In this case, the absolute porosity only varied a few percent, from about 38% to 35%, and flow through this sample was not significantly affected by the readily apparent geometric differences. Figure 55.6 shows bedding planes in a sandstone deposited in a river delta. These deposits were formed by periodic strong storms which washed sediment down a river channel and deposited it in the delta, where the river flowed into a lake or sea. Following burial under more sediment and cementing of the individual grains together by a precipitating mineral, the rock was formed. The individual bedding planes, one dark streak

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to the next, represent separate events. For example, the river currents following a 100year storm will be strong enough to wash larger sand grains into the delta, which then dropped rapidly to the bottom when the water velocity slowed down upon expansion of the channel. The larger grains are observed as the bright areas, produced by the larger pore space between the sand grains. After the initial rush, smaller particles settle at rates inversely proportional to size, producing smaller pore spaces. Finally, in the quiescent period between storms, clays and very fine particles settle to the delta floor. The latter are observed as the darker streaks. The reduced MRI signal in the darker-appearing layers can be due to smaller pore size, or iron-containing minerals and clay which reduce the relaxation time. In many cases the reduced MRI signal is a combination of both.

Fig. 55.5: Bioturbation in a chalk core.

Figure 55.7 shows a rock which formed as the result of an undersea avalanche. Chalk previously deposited on a steep slope broke loose, possibly triggered by an earthquake or violent storm, and slid to a lower part of the ocean bed. During this process the chalk was fluidized, it flowed and was redeposited in processes very similar to a snow avalanche. Thus the matrix of this core is extremely uniform and apparently was buried at least tens of centimeters below the surface. The latter is evident by the lack of bioturbation. However, in the process of flow and redeposition several small rock fragments were incorporated into this sample. They are observed, in Fig. 55.7, as dark round areas. Chemical shifts observed below the largest dark area indicated that this small rock contains significant amounts of iron. It was recommended that this plug not be used in flow experiments because the unknown cross-sectional area would compromise the interpretation of the results.

55. Why wouldan Oil Company Use MRI?

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Fig. 55.6: Bedding planes - sandstone formed in a river delta.

Transverse

Coronal

Fig. 55.7:Small rock fragments incorporated in a chalk core.

Figure 55.8 shows encapsulated fractures in a chalk core. This particular core had a slightly higher than expected permeability, 8 mD as opposed to 1 - 3 mD. If the permeability had been 100 mD or greater, it would have been obvious that a fracture was the primarily flow path for fluids. No evidence of a continuous fracture was observed in this

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core. The bright lines in the MRI image are fluid filled fractures which were only a few mm long and totally enclosed in the interior of the core. A fracture is 100% porosity, i t . no rock, and since the distance between open fracture surfaces is wider than in the matrix

pores, the fluid in the fracture has a longer relaxation time than the same fluid in the matrix. Both properties, volume and relaxation time, appeared to contribute to the increased intensity. In this case the fractures and higher permeability justified the elimination of this core’s data from a cross plot of matrix permeability and porosity.

Fig. 55.8: Chalk core containing encapsulated fractures.

Figure 55.9 shows a core that was initially saturated with D20 brine containing radioactive sodium (22Na) and then flooded with oil. In this case oil was imaged while the water phase was not. The flood shown in Fig. 55.9 consisted of an oil front pumped in from the left, forcing the brine out to the right. Of major concern to oil production was the appearance of the interface between oil and water. If fingering, small streaks of fluid which penetrate the matrix ahead of the bulk, is the dominant fluid propagation mechanism, much of the initial fluid will be bypassed resulting in an excessively high residual saturation. Flushing a water saturated rock with oil was of interest to us as a method of preparing a sample filled with oil at the residual water saturation. Normally an oil company is not interested in forcing water out of a porous rock by injecting oil. The MRI images show the flood front was fairly uniform; however, streaks of oil were observed to move more rapidly along the interface between the core and epoxy coating than through the matrix. It was later determined that the epoxy did not cure properly and left several very thin spaces along the outside of the core. The variability of this bonding is apparent in the transverse images, where the bright areas indicate poor adhesion. Figure 55.10

55. Why would an Oil Coiiipany Use MRI?

585

shows a comparison of MRI images with 1D radio tracer imaging. The 1D distribution of radioactive water, including the streaks, is shown as the squares in Fig. 55.10. The MRI data are plotted in two ways, with and without the oil in the streaks. When the oil in the streak was included the brine distributions measured with the MRI and with the radio tracer method overlapped. Excluding the oil located in the streak produced a sharper flood front, left curve in Fig. 55.10. In this case the MRI 2D data provided additional information which the 1D image could not. When imaging the same volume, the two techniques agreed very well.

a) Coronal images near the center of the core showing the oil front.

b) Sagittal images near the center of the core showing the oil front.

Behind the oil front

At the oil front

Ahead of oil front

c) Transverse images at several locations along the core. Fig. 55.9: Magnetic Resonance Images for three orientations and several locations along an oil flooded core. Intensity is proportional to oil saturation.

586

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0.800

z

v

5

0.700 0.600

*=

0.500

E3

0.400

c,

u MRI with streaks

0

a

0.300 0.200 0.100 0.000 0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

Position along core (cm) Fig. 55.10: Comparison of profiles for MRI and Nuclear Tracer Imaging at 0.3 1 PV of oil injected into brine saturated sandstone core.

Figure 55.11 shows hydrocarbon concentration in a chalk core as a function of gas desaturation. This is equivalent to driving hydrocarbon out of a reservoir by gas injection. The objective of this experiment was to determine if the fluid would cross the gouge fracture which runs from lower left to upper center. A gouge fracture is believed to be produced when one rock mass slides across another and crushes the rock at the interface. If the fracture was a barrier to fluid flow, the upper left portion of the core should remain at the initial fluid concentration, while the fluid concentration in the matrix to the lower right of the fracture would decrease. This would appear as an intensity drop in the lower right and a constant uniform intensity in the upper left. Figure 55.1 1 shows six stages of desaturation. Two features are noted: signal intensity was the same on both sides of the fracture during all steps of the test and fluid was retained in the fracture. This means that this fracture was not a barrier to fluid flow. The slower reduction in intensity and therefore fluid concentration in the fracture indicates that more energy, pressure difference in this case, was required to expel fluids from the fractured volume than from the matrix on either side. This suggests that the pore size in the fractured portion of the rock is smaller than in the surrounding matrix.

55. Why would an Oil Company Use MRI?

82.2%Decane

63.9% Decane

42.3% Decane

35.6%Decane

30.6% Decane

24.4% Decane

5 87

Fig. 55.11: Decane concentration as a function of gas desaturation in a fractured chalk core.

More detailed images for the initial and final steps of the desaturation described above are shown in Fig. 55.12. The intensity of the image for the desaturated core has been increased to show detail. In the original image, left, the gouge fracture is barely visible as a slightly darker region running from lower left to upper center, which means that when fully saturated, the fracture contained only slightly less fluid than the matrix.

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However, after desaturation, the right image, the fracture stands out because it contained more fluid than the surrounding matrix. The amount of fluid in the fracture decreased from its fully saturated value, but the rate of fluid removal was lower than in the surrounding matrix. It is apparent in this image that the fracture is not uniform: it appears to consist of multiple paths. It is speculated that these are regions of reduced pore size are caused by reorganization of the individual chalk grains to achieve stress reduction. These paths may represent individual stress vectors, analogous to the tortuous path lightning takes as it follows the most conductive path during its discharge. The exact interpretation of these features will require additional work.

Fig. 55.12: Images of decane before and after gas desaturationin a fractured chalk core.

Figure 55.13 shows T , maps for a core containing three porosity types. Two types were identified above, the chalk matrix and the gouge fracture, the third is a stylolite appearing as the dark wiggly line running from center left to upper center. The visible portion of stylolites consists of clay, bitumen and insoluble organics left behind as a layer of chalk dissolves. Stylolites are often considered permeability barriers, but this has seldom been tested. Desaturation of this core was performed to determine the extent, if any, of restriction to flow produced by the stylolite or the two gouge fractures. Again, these particular features had minimal affect on flow through this core. The T , maps in Fig. 55.13 were obtained to determine the relative fluid properties in the stylolite and

55. Why would an Oil Company Use MRI?

589

gouge fractures when the core was completely saturated and after desaturation. The constant matrix intensity in the T , map, Fig. 55.13A indicates that the saturated matrix is very uniform, the slightly lower intensity for the two gouge fractures, lower right and lower left, denote a shorter relaxation time indicating slightly smaller pore size. The stylolite should contain little to no fluid, but the thickness of this layer is smaller than the

MRI resolution, so no unequivocal conclusions can be drawn. However, it is possible that the pore size adjacent to the stylolite may have been reduced by stress during chalk dissolution or were partially filled by redeposition of the dissolved material, both of which would reduce pore size and relaxation time. The reduction of TI in the gouge fractures is consistent with the reduction in porosity of a typical gouge fracture observed in scanning electron micrographs, 2 to 5 porosity units (volume percent of rock). After desaturation, Fig. 55.13B, the uniform matrix intensity indicates an efficient desaturation. The gouge fractures have a slightly longer relaxation time than the matrix; which suggests that the residual fluid in the fracture is contained in larger volumes than the residual fluid in the matrix. This observation is consistent with desaturation being dictated by the smallest pore throat, or cross-sectional area, of a specific continuous fluid flow path, i.e. the matrix more readily desaturates to smaller pore sizes than the fracture. Knowing the amount of residual fluid which will be left in the reservoir is extremely important for determining economic value.

A

B

Fig. 55.13: T I map of chalk core containing gouge fractures. A) Fluid saturated, B) desaturated.

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B. A. Baldwin and R. L. King

A

B

Fig. 55.14: r q , map of chalk core containing gouge fractures. A) Fluid saturated, B) desaturated.

The mo maps in Fig. 55.14 confirm the previous study, Figs. 55.11 and 55.12, by showing higher residual saturation in the gouge fractures and uniform desaturation of the matrix with no detectable restrictions due to the gouge fractures. These images also show that this stylolite had no effect on flow. In Fig. 55.14B the lack of porosity in the stylolite is also apparent. The force needed to drive a fluid out of a pore network is determined by capillary pressure. Capillary pressure is controlled by 1) the interaction between the fluid and the pore walls and 2) pore geometry, primarily the smallest cross-sectional area in a single continuous fluid-flow path. Capillary pressure is one of the most important properties used in predicting how much oil can be obtained from a reservoir. However, capillary pressure measurements either take a long time, or require computer modeling to simulate an unknown fluid concentration distribution, or require the use of non-representative fluids, for example, mercury. Since MRI can determine the fluid concentration distribution inside an intact core, it is possible to obtain a capillary pressure curve by centrifuging the core to simulate a greatly enhanced gravitational field and measuring the resulting local fluid concentration distribution. The local pressure is calculated from the density difference of the fluids, the speed of the centrifuge and the location in the sample along the centrifugal axis while centrifuging. Figure 55.15 shows the image of water

55. Why would an Oil Company Use MRI?

59 1

distribution in a sandstone core after centrifuging and three capillary pressure curves produced by starting at different initial fluid distributions. The core is located in the center of the image with structural support and a reference material to the right side. The curves are the saturation distributions after centrifuging at three different initial conditions. The first curve, primary drainage, was produced by forcing oil into a 100% water saturated core. This mimics the displacement of water, which was deposited with the porous rock, as oil migrated from its source into the reservoir. The force exerted by the oil determines how much water was displaced and the quantity of oil trapped in the reservoir. The second curve, primary imbibition, was obtained by first driving the core to it’s residual

-2

1 Water Saturation (%)

5-

5-

c u) Y

n

Y

B

:I : : ( \ : : , 50

100

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B. A. Baldwin arid R. L. King

807

-20

f

L

50

sw MRI image of chalk plug after centrifuging to primary drainage.

sw Water concentration distribution at primary imbibition.

Water concentration distribution at primary drainage.

sw Water concentration distribution at secondary drainage.

Fig. 55.16: Capillary pressure measurements for chalk core collected under three different set of conditions to produce scanning curve data.

water saturation then centrifuging under a mixture of oil and water. This curve mimics production from the reservoir as a function of water pressure, either from the height of the water head in the reservoir or from water injection pressure. The third curve, secondary drainage, was obtained by first forcing the core to its residual oil saturation, then centrifuging under a mixture of oil and water. This curve mimics the movement of displaced oil through a previously water contacted portion of the reservoir. It is useful for

55. Why would an Oil Company Use MRI?

593

evaluating the reservoir pore network and the efficiencies of potential tertiary recovery processes. A similar set of curves for a chalk core is shown in Fig. 55.16. The capillary pressure curves for Berea sandstone and chalk from all three treatments are compared in Fig. 55.17. The Berea sandstone has a lower threshold pressure, i.e. the pressure at which oil initially begins to enter the core, compared to the chalk. The small separation between the imbibition and secondary drainage curves for the sandstone indicate a relatively wide range of pore sizes; a greater range of pore sizes increases this separation while a narrower range decreases it. The chalk has a very narrow range of pore sizes and the two curves nearly overlap. The advantages of the MRI technique for determining capillary pressure are 1) it simultaneously measures both positive and negative portions of the capillary pressure curve and 2) it determines the imbibition and secondary drainage more accurately than any other technique. 80

o

Primary Drainage

A

Secondary Drainage

+ irnblbltlon

0

I : : : : ;

n

t

-2 I

-20

m

r Saturation (%)

Smoothed capillary pressure curves for Berea

Water Saturation (%)

Capillary pressure curves for chalk

Fig. 55.17: Capillary pressure scanning curves for Berea sandstone and chalk.

The images in Fig. 55.18 show a direct application of MRI to a field problem. The sample is a sidewall core, a 1-inch diameter core plug, drilled with a rotary drill into the side of an open well from a potentially oil-producing formation. This sample originated about 12,000 feet below the surface. The reservoir engineer's question was ,,how far did drilling-mud solids penetrate into the reservoir?,,. Drilling muds are used to form a mud cake on the surface of the well bore and minimize the penetration of drilling fluids into

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B. A. Bn/dwin and R.L. King

the porous formation around the well bore. The Hahn spin-echo image showed the mud penetration; however, the T , and mO maps, Fig. 55.18, provided additional information. The brighter region in the center of the T , map in Fig. 55.18 indicated the presence of oil. In this core, oil did not interact as strongly with the rock surface as water and therefore had a longer relaxation time. This image shows water, in the darker zone around the edge of the core, that was spontaneously imbibed by the pore network, displacing the oil. If the engineer had recorded the time between the drilling of this core and the time it was retrieved at the surface, removed from water, an imbibition rate could have been estimated. The uniform appearance of the mo map in Fig. 55.18, indicates that this core had a uniform porosity distribution. The streaks across the core indicated where this core was fractured during the drilling, but was subsequently healed, so that the core, as received, was intact. The darker areas near the top of each image, the well-bore side, show that drilling mud solids penetrated about 5 mm into the reservoir. This latter information will help the reservoir engineer design his reservoir stimulation process, i.e. determine how far the perforations need to penetrate the rock around the wellbore to obtain full flow of producing fluids. Since this core fractured and healed it was not used in further testing. Bacteria exist in all oil reservoirs. Their uncontrolled growth can plug off oil production or produce unacceptable levels of H,S. However, their controlled growth can be used to reduce permeability in 'thief zones, thin high-permeability streaks which divert injected water away from oil-containing, lower-permeability rock. Figure 55.19 shows MFU images taken after the growth of bacterial colonies and their byproducts. The ,,rocks,, used in this study were high-permeability ceramic cores which were determined

Tl map Fig. 55.18: MRI T I and q maps of a chalk sidewall core.

mo map

55. Why would an Oil Company Use MRI?

595

Inlet T1 map

Outlet T1 map

Outlet standard spin-echo image Fig. 55.19: Bacteria growth in a porous ceramic core.

to have a very uniform porosity distribution. Bacteria and their food were injected and allowed to grow while the pressure differential across the core was monitored. If the bacteria or their byproducts restricted flow, the pressure drop will increase. After sufficient growth had occurred and a significant pressure drop increase was observed, the core was imaged again. The lower intensity, shorter relaxation time for the inlet and outlet T , maps in Fig. 55.19 show the location of bacteria. Hahn spin-echo images, at the same location, did not show the location of the bacteria because the bacterial colonies and the surrounding brine had approximately the same hydrogen density. Bacteria locations were obvious in the TI maps because the water's relaxation time was significantly

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reduced in the bacteria cells compared to that in the matrix. The lower intensity, shorter relaxation time at the left side of the inlet T , map, Fig. 55.19, shows face plugging over about the first two pixels, approximately 1 mm. This accumulation of bacteria or their by-products accounts for the immediate pressure drop measured across the first 5 cm of the core. Near the outlet end, Fig. 55.19, bacterial colonies appear to have formed in larger masses. These colonies are many times larger than the individual pores. Their general appearance is similar to that observed for bacterial growth in Petrie dishes, suggesting that growth occurred at the perimeter of the colony. These colonies also affect the readily available cross-sectional area for flow through the core resulting in an additional pressure drop.

A

B

C

D

E

F

Fig. 55.20: Diffusion of normal water into a heavy-water-saturated core from a simulated fracture at the right end of the core. Diffusion time increases from A to F.

55. Why would an Oil Company Use MRI?

597

Sometimes images are collected as a function of time. These are then used to calculate the rates of the specific process andor determine the mechanism of oil production under specific conditions. These are, in effect, experimental analogs to mathematical modeling and can be used to validate the mathematical model. The first example, Fig. 55.20, was designed to mimic the exchange between water flowing through a fracture and water in the reservoir. The core, to the left of the fracture, was initially saturated with D,O and not imaged (D,O was used as the base fluid because it is easier to image small increases of intensity in a dark image than to determine small decreases of intensity in a bright image).

5.000 10.000 15.000 20.000 25.000 3o.ooO 35.000 4O.ooO Distance (mm)

Fig. 55.21: Comparison between measured saturation distributions (squares) during self-diffusion and values calculated from no-flow boundary diffusion theory (circles).

These images show the exchange over a 200 hour period. The fit between the measured saturation distribution at four different times and the saturation distribution calculated from a standard diffusional model with a no flow boundary is shown in Fig. 55.21. The fit is reasonably good, which suggests that diffusion coefficients calculated from this data set are valid. The next three sets of images, Figs. 55.22 - 55.24, show the spontaneous imbibition of water into a strongly water-wet chalk with the displacement of hydrocarbon. The first set of conditions, Fig. 55.22, consisted of a 100%hydrocarbon-saturated core completely surrounded by heavy water; the core was supported by four contact points. Only the hydrocarbon was imaged, the heavy water appears black. The displaced hydrocarbon

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first collected as bubbles on the side of the core, then floated to the surface to form a film on the water. Two observations to note: imbibition always started at the bottom of the core and the imbibition front was very sharp. Since this core had a uniform porosity distribution, the start of imbibition at the bottom, independent of core orientation, was probably due to the slightly higher pressure at the bottom of the core produced by the small additional height of the water column. The sharp fronts reflect the mechanism of water movement: in a 100% hydrocarbon saturated core, water movement required the displacement of hydrocarbon; there were no channels for water to advance into the core ahead of the water-oil contact.

A

B

C

D

E

F

Fig. 55.22: Spontaneous imbibition of water by a chalk core initially saturated with 100% hydrocarbon / 0% water. Imbibition time increases from A to F.

55. Why would an Oil Company Use MRI?

A

B

C

D

E

F

599

Fig. 55.23:Sponateous imbibition of water by a chalk core initially saturated with 85% hydrocarbon / 15% water. Imbibition time increases from A to F.

Figure 55.23 shows a similar experiment with the core treated to initially contain 15% water. Since the core was strongly water-wet, most of the surface will be contacted by water, which displaced the oil to the middle of the pores. Most notable in the sequence was the initiation of imbibition: water imbibed at all faces. The front formed by the imbibing water was less sharp than in the 100%saturated case and imbibition did not stop when the apparent fronts moved through the core. Significant, but uniformly distrib-

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uted, reductions of hydrocarbon concentration were observed after the fronts passed. This suggests that the mechanism of water imbibition was different from that i n the 100%hydrocarbon saturated case. At 15% water concentration, water films would cover most of the chalk surface. With the initial presence of these films water can now imbibe by a thickening of the water films, which forces the oil out by the volumetric increase of water. After the front passed through the core, the oil and water permeability were balanced and additional imbibition occurred at a spatially uniform, but decreasing, concentration distribution.

A

B

C

D

E

F

Fig. 55.24: Spontaneous imbibition of water in a chalk core initially saturated with 67% hydrocarbon / 33% water. Imbibition time increases form A to F.

60 1

55. WIIJwould an Oil Company Use MRI?

Figure 55.24 shows the imbibition experiment with an initial water saturation of 33%. The images are similar to Fig. 55.23, except that the front moved more rapidly through the core and was not observable after about 20 minutes. These results are consistent with the explanation above, except that now the water surface films were initially thicker and therefore water movement was more rapid.

55.4 Conclusions From these examples the following conclusions can be drawn: a) MRI is a powerful tool for solving problems encountered in oil production. b) Fluid concentration distributions can be monitored both at a specific static condition or during dynamic processes c) Core selection and subsequent reservoir characterization can be improved by eliminating cores which contained non-representative heterogeneities

Acknowledgment The authors wish to thank the following co-workers for supplying samples and engaging in stimulating discussions about the pertinence of MRI: J. H. Hedges, J. J. Howard, J. H. Jack, C. D. Javine, G . E. Jenneman, J. A. Johnson, T. L. Nichols, D. W. Rhett, D. L. Snyder, E. A. Spinler, D. P. Tobola, R. H. WebbandD. R. Zornes.

References 1.

P. C. Lauterbur, Nature 242 (1973) 190-91.

2.

R. Darnadian, U.S. Patent 3,789,832 (March 17, 1972).

3.

P. Mansfield and P. G. Moms, NMR Imaging in Biomedicine, Academic Press, New York, 1982.

4.

G. D. Fullerton and I. L. Cameron, Bio Techniques 3 (1985) 458-65.

5.

W.P. Rothwell and H. J. Vinegar, Applied Optics 24 (1985).

6.

B. A. Baldwin and W . S. Yamanashi, SPEpreprint # 14884 (1986); SPE Reservoir Engineering 4 (1989) 207-12.

7.

,,Proceedings of the Second International Meeting on Recent Advances in MR Applications Media,,, Mag. Reson. h a g . 12 (1994) 161-375.

to

Porous

8.

M. Sardashti, B. A. Baldwin, and D. J. ODonnel, J. Polymer Sci. B: Polymer Physics 33 (1995) 571-76.

9.

C. L. Durnoulin, Spectroscopy 2 , 3 2 4 2 .

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56. Pore Structure and Connectivity of Porous Rock by High Resolution NMR Microscopy D.A. Doughty and L. Tomiitsa BDM Petroleum Technologies, PO Box 2543, Bartlesville, OK 74005, USA

Abstract The application of high field magnetic resonance imaging (MRI) microscopy to the study of pore geometry in porous rock must overcome the short T2 relaxation times and broad natural RF line widths which characterize fluids in this environment. An imaging protocol based on 3D projection reconstruction using strong imaging gradients has overcome many of these constraints resulting in image resolutions of 11.5 pm per voxel on small core plugs. Magnetic field gradient strengths used in the imaging process for these small core plugs were about 90 Gkm. MRI experiments were performed on brine saturated core plugs from several sandstones including Bentheim and Fontainebleau. A novel method was developed using this high resolution data to independently determine the porosity from histograms of image voxel intensity which estimates the contribution from fractionally filled voxels. Results in excellent agreement with traditional porosity determinations were obtained for the natural sandstone samples. Using software developed in our laboratory 3D pore size calculations on binarized MRI data using a process of successive erosioddilations showed significant differences in the pore connectivity in the different samples. The results reveal that the pore throats in the Fontainebleau sandstone are significantly smaller than the 11.5 pm resolution in the image data while the more porous Bentheim sandstone has larger average pore throats two or more times larger than the image resolution. Comparison with measurements from petrographic image analysis (PIA), mercury injection porosimetry, and low field NMR for these rock types show excellent agreement with the MRI microscopy data.

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56.1 Introduction Several techniques have been used to obtain direct information about the 3-dimensional pore structure within porous rock at pore scale: ( I ) magnetic resonance imaging microscopy, (2) computed tomography using thin beam X-ray sources, and (3) laser scanning confocal microscopy. Magnetic resonance imaging (MRI) responds to the proton content (the most sensitive and common nuclei detectable by MR) of fluids saturating the pores and fractures within the rock and therefore directly images the accessible pore space within the rock matrix. Computed tomography (CT) images rock matrix density contrast by mapping X-ray attenuation across the sample volume [ 1,2]. The pore spaces in porous rock, whether fluid-filled or empty, show up as regions of low attenuation. Laser scanning confocal microscopy can precisely image thin optical planes within thicker porous rock samples with high resolution but relies on the general transparency of the sample and therefore has limited depth of penetration into the rock matrix for ordinary rock specimens [3]. This paper focuses on the use of MRI microscopy to obtain high resolution 3D images of the pore structure of porous rock and from this data to develop more realistic models of actual pore systems for network model fluid flow simulators. The application of high field MRI microscopy to the study of pore structure and connectivity in porous rock must overcome the short T2 relaxation times and broad natural RF line widths which characterize fluids in this environment. These effects are caused by the magnetic susceptibility contrast between the fluid and rock grains and the presence of paramagnetic ions such as iron or manganese on the rock grain surfaces [4]. An imaging protocol based on 3D projection reconstruction using strong imaging gradients has overcome many of these constraints resulting in image resolutions of 23 pdvoxel on small core plugs [5,6].Data from these higher resolution images were used to develop a methodology for obtaining the porosity of the core plug without relying on a porosity value obtained by other techniques. These higher resolution image data were then used to investigate the pore size and connectivity of several porous rock types. Recent imaging experiments on clean sandstone samples have doubled the attainable resolution to 11.5 pdvoxel. The results from these very high resolution MRI images were compared to measurements on rock porosity using petrographic image analysis (PIA) of thin sections, mercury injection porosimetry, and low field NMR T2 relaxation measurements.

56. Pore Structure and Co?nectivity of Porous Rock b y High Resolution NMR Microscopy

605

56.2 Experimental Magnetic resonance imaging experiments were performed using very small core plugs of several sandstones including Bentheim and Fontainebleau. All the core plugs were approximately 3.8 nun in diameter and 3.8 - 4.2 nun long and encased in a core holder fashioned from Teflon end caps and Teflon shrink tubing and saturated with brine (0.5% NaCl with 0.025 % MnCI2) under vacuum. A projection reconstruction imaging protocol was used incorporating a stimulated echo pulse sequence with two hard 90" RF pulses (P90 was 3.0 - 4.0 ps using approximately 200 watts of RF power.) The time-to-echo was 1.76 ms and the sequence repetition time was 250 ms, accumulating 8 echoes at each gradient orientation for increased signal/noise. For the current imaging experiments 128 K projections (512(8) x 256($)), each containing 512 data points over a receiver bandwidth of 200 kHz, were acquired. The full echo was acquired and a magnitude FFT performed to obtain the projection with 512 points. Gradient strengths of 90 G/cm were used and the gradient was turned on several milliseconds before the first RF pulse and left on until echo data acquisition was completed. The total acquisition time for each experiment was 96 hours. A two-stage reconstruction algorithm was used to obtain the 3D data set with 5123 voxels, giving resolutions of 11.5 pdvoxel in the final reconstructed images. The NMR instrument used for imaging operates at 270 MHz for protons and was adapted for MRI microscopy using imaging probes and gradient coils constructed in-house. Standard MRI protocols for preparing and saturating the core plugs, obtaining the image data and processing the raw data files to obtain the final images were followed as described previously [6,7]. Petrographic imaging analysis (PIA) measurements of porel areas from images obtained from standard petrographic thin sections of the two rock types were performed using an image analysis system together with a petrographic fluorescent light microscope. Erosionfdilations were used to open narrow connections between neighboring areas in the 2D images. The digitized images consisted of 5 12 x 400 pixels with the pixel size 1.63 pdpixel. The porel areas measured on 24 images from the thin sections were sorted in increasing size. For mercury injection porosimetry measurements, which are available commercially, mercury is intruded into the pore space of small samples of the clean, dry sandstones while precise measurements of intruded volume and corresponding injection pressure are made. The data obtained are presented as differential mercury capillary pressure curves calibrated in terms of effective pore throat diameters.

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A MARAN-2 low field NMR instrument with a 500gauss permanent magnet (2.1 MHz proton frequency) was used in measuring T2 relaxation times on 1.5 in diameter core plugs. The Can-Purcell-Meiboom-Gill (CPMG) pulse sequence was used for the T2 measurements where a single 90" RF pulse is followed by a string of N (delay-180" RF pulse-delay) components where the delay is fixed for a given experiment. At the end of each of the N components an echo of the initial RF signal is formed and the amplitude of this echo signal is measured as a function of the total time from the initial 90" RF pulse. The amplitude of the echo signal decays as a function of the T2 relaxation time for the sample. Typically the delay was set from 80 to 400 ps with N = 2048 for an experiment. The entire sequence was repeated 256 times to accumulate signal at each echo for improved signal-to-noise.

56.3 Results and Discussion Table 56.1 summarizes the results of rock property measurements for the Fontainebleau and Bentheim rock used in this study. The porosify values obtained by the various methods are very consistent for both sandstones. The permeability values show considerably more variability, particularly for the Fontainebleau sandstone. Only the gas permeability value was obtained using a direct method. The PIA method uses the Kozeny-Carman equation to calculate the Permeability value while the low field NMR result was obtained using

k = 4.6 T 22 m Cp4

(56.1)

as the permeability estimator where T2m is the logarithmic mean T2 value that bisects the area under the T2 distribution curve [8]. Figure 56.1 shows 3D surface-rendered views cropped from the center of the 3D data sets for each sample presented as gray scale pictures with 256 levels of voxel intensity. The voxel intensity threshold used to render the pore surface was 32 for the Fontainebleau image and 37 for the Bentheim image to select the known porosities of 8.0% and 23.0% for each sample. The size of the cubical region shown for each view is 0.55 mm on edge (48 voxels) with the order of the pictures in the figure as A) Fontainebleau and

56. Pore Structure and Connectivity of Porous Rock by High Resolution NMR Microscopy

607

Table 56.1. Rock property measurements. Property

Method

Porosity, %

Permeability, mD

Fontainebleau

Bentheim

Gravimetric PIA ’ Low field NMR

8.7 9.4

23.0 23.1

8.7

Gas (N2) PIA Low field NMR

106

23.5 2487

52

87 1

4

2360

B) Bentheim. Voxels below the respective intensity levels were made transparent to eliminate noise and the rock grains and reveal only the brine-filled porosity. Voxels of intermediate intensity or brightness represent voxels only fractionally filled with fluid

because they overlap the rock grain surface. The relationship between fractional filling of voxels and their intensity appears to be linear so techniques can be used to enhance the resolution of MR images by interpreting the relative brightness of voxels as fractionally filled porosity. Calibration of this fractional filling of voxels and its effects on voxel intensity was described previously [6]. Figure 56.1 shows that there is significant variation in pore size and fluid filled porosity between the two samples. Measured values of the porosity obtained from larger samples of the materials were 8.7% and 23.3%. The Fontainebleau sample has larger pores which are isolated by narrow pore throats while the Bentheim sample has extensive larger pore throats in a well connected pore system.

Fig. 56.1: 3D brine filled porosity imaged at 11.5 pm and rendered at voxel intensities matching rock porosity. A) Fontainebleau-32 (8.0%). B) Bentheim-37 (23.0%). A cubical volume 0.55 mm on edge is shown in each case.

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Porosity calculation using pore-scale MRI data is strongly influenced by the intensity levels of voxels in the 3D images, and an independent determination of porosity from MRI data has been ambiguous. Voxels from the centers of large pores or fluid-filled voids in the sample generally have a high average intensity with some variability coming from noise and image reconstruction processes. Voxels near the edges of large pores or voids or in regions of small pores have intermediate or lower intensities. The reduced intensity comes from pores smaller than the voxels and totally enclosed, or it arises from the voxel being fractionally filled at the edges of a larger pore as discussed above. Previously, a threshold intensity was selected for a given MFU data set to eliminate the noise contribution and give a porosity for the sample (expressed as a fraction of voxels at or above the threshold divided by the volume of the sample in voxels) that agrees with the known porosity determined by other independent methods. If histograms of the voxel intensities in MRI image data sets are plotted vs. histogram bin number using a semilog format, as shown in Fig. 56.2 for the data set for a Bentheim core plug, a linear region is evident. 107

106

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Fig. 56.2: Semilog plot of histograms of voxel intensities versus bin number for the high resolution MR image data for brine saturated Bentheim sandstone. Shown are 128 bin and 64 bin histogram data together with the linear fit to the central part of the data for each histogram.

56. Pore Structure and Connectivity of Porous Rock b.v High Resolution NMR Microscopy

609

Two sets of data are shown in the figure: one using a histogram with 128 bins and the other using 64 bins. At low bin numbers, the histogram deviates above the linear trend as noise in the image data at low voxel intensities starts to accumulate. At high bin numbers, the histogram falls below the linear trend because the voxel intensity has a finite upper limit. A novel approach to resolving the ambiguity in choosing a threshold is that the linear trend in this histogram represents the true distribution of voxel intensities, including the contributions from fractionally filled voxels, with the noise eliminated. Voxel intensity measurements on the 3D image data of a fluid-filled wedge-shaped void have shown a linear relationship between voxel intensity and fractional filling of the voxel as mentioned previously [6]. The weighted sum of the voxel counts under the linear fit to the histogram, X(Niwi), where the weight factor accounts for the fractional filling of the voxels and the width of the bins, would then represent the actual volume of the fluid-filled porosity in the sample. The porosity is calculated by dividing this volume by the volume of the sample, independent of any threshold selection. Shown in Fig. 56.2 are the two linear fits to the histogram data. The voxel count, Ni, and the weight factor, wi,at bin number i are given by Ni = No exp(-ai)

(56.2) (56.3)

where No and a are the fitted parameters to the linear region in the histogram, b , is the bin width, and V,,, is the average voxel intensity for a fully filled voxel. V,,, is determined from the histogram where the data start to fall below the linear fit (168 for the Bentheim data). Using the fitted data from the two curves in the figure, the weighted sum is 589,688 for the 128 bin data and 588,827 for the 64 bin data. The volume of the sample was 2,545,300 voxels from the image data, giving a porosity of 0.231 or 23.1%.This compares very well with porosity values obtained for this rock type using volumetric porosity measurements (23.3 - 23.8%).Applying this technique to the histogram data for the Fontainebleau sample resulted in a porosity value of 8.0%which compares favorably with the results using other types of measurements (8.7 - 9.4%). Figures 56.3 and 56.4 directly compare the MRI results for the two sandstones to actual photographs of the petrographic thin sections. In these thin sections the porosity was filled by a dye-tinted low viscosity epoxy which filled and set within the pores. The epoxy-filled pores in the figures show up as the light blue regions (darker in printed

610

D. A. Doughty ond L. Totnirrsa

paper). For comparison a comparable sized 2D region from each of the MRl data sets was selected and is displayed using a colortable with a narrow range of voxel intensity (28 - 36 for the Fontainebleau and 33 - 42 for the Bentheim) to give essentially a binarized image of the porosity at the appropriate threshold corresponding to the measured porosity. The brine-filled pores show as white with the rock matrix as red (dark). While the thin sections obviously come from a different specimen of the respective rocks than the sample used for MRI, the figures show the great similarity in quality between the two types of images and show that MRI can faithfully reproduce most of the features of the pore space at the resolution obtained for this work. Software developed in-house to do a true 3D pore size analysis was applied to the MRI image data for the two sandstones [6]. This software can do a true 3D tracking of porosity within the imaged volume of the sample as the active plane moves through the image data set. As connections are located between previously isolated pore volumes in successive planes the total voxel count is assigned to the lower indexed volume and the higher indexed volume is zeroed and freed for later accumulation. A companion routine in the software can perform successive 3D erosions and dilations of the pore volumes contained in the image data. Erosions peel away the outer layer of voxels from the 3D pore volumes while dilations replace the outer layer. If two pore volumes are connected by a narrow throat, erosion will break the connection and dilation will restore the pore volume but not reestablish the connection, resulting in an increase in the number of pores and a reduction in average pore size. For a well-connected pore system most of the porosity can end up in one apparent pore extending throughout the image volume. Figure 56.5 shows 2D slices from the MRI data for the Fontainebleau sample converted to a binarized image at the voxel intensity threshold of 32. In the figure the four pictures (A), B), C), and D)) show the binarized porosity (black) following 0, 1, 2, and 3 stages of erosiorddilation (EID).The Fontainebleau sample has large isolated pores with most connections between pores below the resolution threshold and thus not visible. The small pores or cross-sectioned pore throats disappear in successive pictures following increasing EID stages until only the large isolated pores remain. Similar results for the Bentheim sample are illustrated in Fig. 56.6 where the binarization was done at a threshold of 37. The Bentheim sample has larger pores with more obvious visible connections to other pores even in the 2D views. Some of these connections survive the first stage of EID shown in B) in the figure. Results of the application of the pore size software to the binarized data sets are shown in Fig. 56.7 where the largest pore found expressed as a fractional size of the total porosity is plotted versus the number of E/D stages applied in

56. Pore Structure and Connectivity of Porous Rock b y High Resoluiion NMR Microscopy

61 1

binarizing the MRI data set [6,9]. For no E/D the Bentheim sample had such well-developed pore connectivity that the largest pore found had 94% of the total porosity. In contrast to this the Fontainebleau results show a much reduced level of connectivity at this high resolution with the largest pore containing less than 3% of the total porosity.

A

I I

E

3.

0 0 0 d

Fig. 56.3: 2D view of pore space in Fontainebleau sandstone. A) MRI image obtained from the 3D data set at 1 1.5 pm. B) Thin section photomicrograph.

A

B

E

2

0 0 0

rl

Fig. 56.4: 2D view of pore space in Bentheim sandstone. A) MRI image obtained from the 3D data set at 1 1.5 mm. B) Thin section photomicrograph.

612

D. A. Doughpi and L. Tomutsa

D

.* .*

4

3

C

a

B

A

4

.

) .* .‘ 1 -. 2950 pm

Fig. 56.5: 2D slices of Fontainebleadbrine MRI image data binarized at a voxel intensity threshold of 32 (8.0%) following 0, 1,2, or 3 (A), B), C), or D)) successive stages of E D .

3

a

V

B

C

a

A

D

OS6Z

2950 pm Fig. 56.6 2D slices of Bentheimbrine MRI image data binarized at a voxeI intensity of 37 (23.0%)following 0, 1,2, or 3 (A), B), C), or D)) successive stages of E/D.

After one stage of E/D the Bentheim sample sample still exhibits a high degree of connectivity implying that the average pore throats approximate two or more voxel dimensions of 11.5 pm for this sample. After two stages of ZZZI much of the pore connectivity has been broken for this sample and the results start to approach the isolation between pores shown in the results for the Fontainebleau sample. Pore1 areas from the PIA measurements, sorted in increasing size and plotted versus pore number, are shown in Fig. 56.8 for the two samples (Fontainebleau and Bentheim). The figure indicates the differences between the two samples, both regarding the porel sizes (the plot height) and the total porosity (the area under the plot). Large porel sizes, observed for the Bentheim sample, indicates both well connected or large pores, while

613

56. Pore Structure and Connectiviry of Porous Rock by High Resolution NMR Microscopv

smaller pore1 sizes, observed for Fontainebleau, indicate smaller disconnected pores, in good agreement with the MRI 3D images. Performing the E/D proce dure described previously can separate the individual pores for a detailed study of size and connectivity. Porosity and permeability calculations (using Kozeny-Carman equation) for the two samples compare favorably with gas permeability values as shown in Table 56.1. 1 .O

I

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-m0.6

-

0.4

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0.2

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-

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Fig. 56.7: Largest pore size expressed as a fraction of the total porosity plotted versus number of successive stages of E/D for the two sandstones.

Measurements of pore throat diameters from the mercury intrusion measurements are shown in Fig. 56.9 for the two samples. The incremental injected volume of mercury, expressed as the percent of pore volume injected, is plotted versus the apparent pore throat diameter. The figure shows the larger diameter pore throats for Bentheim (with a peak at 26 pm and a relatively narrow range) and smaller, more dispersed pore throat diameters for Fontainebleau (peak about 12 pm with a substantial amount less than 10 pm). This is in good agreement with the 3D MRI data analysis which indicates a large fraction of pore throat diameters in the 20 - 40 pm range for Bentheim and smaller than 10 - 20 pm for Fontainebleau. For liquids in porous rock the relaxation rate is strongly enhanced by contact between the fluid molecules and the pore surface where most of the relaxation occurs [4]. The properties of the rock grain surface in the pores, the ratio of pore surface area to pore volume, and the degree of contact between a given fluid and the pore surface thus control

614

D. A. Doughty nnd L. Tomursa

the relaxation in porous rock. By using a sum of several exponential terms the relaxation data for any fluid saturated porous rock can be closely fitted. By extending this process further a distribution of exponentials using many terms can be fitted to the relaxation data [lo]. Software for this fitting of a distribution of exponentials to the relaxation data was obtained with the MARAN low-field NMR instrument. Figure 56.10 shows the results of the distributed exponential fit to the T2 data for the two samples using 127 terms for each fit. Because of the strong connection between pore size and the relaxation process this resulting distribution of relaxation terms is believed to closely represent the actual distribution of pore sizes within the rock sample. Comparisons of such distributions of relaxation time with mercury porosimetry data for porous rock have shown a strong correlation between pore throat size distributions and T2 distributions of exponentials [S]. The present work confirms these findings. 200000

150000

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Fig. 56.8: Sorted pore1 areas from PIA measurements on the thin sections are plotted versus pore number for the two sandstones.

56. Pore Struciirre and Connectivity of Porous Rock by High Resolution MMR Microscopy

PORE THROAT DIAMETER, pm

Fig. 56.9: Incremental injected volume of mercury as a function of pore throat diameter.

Fig. 56.10: Distributed exponential fits of the T . relaxation data for the two sandstones.

615

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D. A. Doughty and L. Tornutsa

56.4

Conclusions

1. Using small core plugs and high imaging gradient strengths, 3D MRI images of the fluid-filled porosity in porous rock were obtained with the highest resolutions to date (1 1.5 pdvoxel). 2. Pore size measurements on binarized MRI image data using successive stages of erosion/dilations has revealed information about the connectivity of the rock pore system and estimated the sizes of typical pore throats. Fontainebleau sandstone has isolated pores with most narrow pore throats below the limit of resolution of 11.5 pm. The Bentheim sandstone has pore throats two or more times the image resolution. 3. Porosity, pore sizes, and connectivity measured from MRI imaging data agree closely with results from PIA, mercury intrusion, and low field NMR.

Acknowledgments The authors thank the Department of Energy and BDM Petroleum Technologies for supporting this work and Sam W. Swan for his enthusiastic help with the graphics.

References 1.

Coles, M. E., Hazlett, R. D., Muegge, E. L., Jones, K. W., Andrews, B., Dowd, B., Siddons, P., Peskn. A., Spanne, P. and Soll, W. E., SPE 36517, Proceedings of the Annual Technical Conference and Exhibit of The Society of Petroleum Engineers, October 6 9 , 1996, Denver, Colorado.

2.

Jasti, J. K., Jesion, G. and Feldkamp, L., SPE Formation Evaluation, September, 1993, 189-193.

3.

Fredrich, J. T., Menendez, B. and Wong, T. F., Science 268 (1995) 276279.

4.

Kleinberg, R. L., Kenyon, W. E. and Mitra, P. P.,J. Magn. Reson. A, 108, (1994) 206214.

5.

Doughty, D. A. and Tomutsa, L., Int. J. Rock Mech. & Min. Sci. 3 4 5 - 4 (1997) Paper No. 069.

6.

Doughty, D. A. and Tomutsa, L., Magn. Reson. Imag. 14:7-8 (1996) 869-873.

7.

Doughty, D. A., Tomutsa, L. and Madden, M. P., ACS National Spring Meeting Symposium on Applications of Magnetic Resonance Imaging in Enhanced Oil Recovery, March 28-April 2, 1993, Denver, Colorado.

8.

Straley, C., Rossini, D., Vinegar, H., Tutunjian, P., and Morriss, C., SCA-9404, International Symposium of the Society of Core Analysts, September 12-14, 1994, Stavanger, Norway.

9.

Ehrlich, R., Crabtree, S. J., Kennedy, S. K. and Cannon, R. L., J. ofSedbrierit. Petrol. 54 (1984) 13651376.

10.

Howard, J. J. and Kenyon, W. E.. Marine and Petroleum Geology 9 (1992) 139-145.

57. Relaxation-Diffusion Processes and Local Magnetic Field Distributions in Natural Porous Media D. Pe'rez', A. Benavides2, S. Gonza'lez', D. Barranted and M. Martin-Landrove' Departamento de Fisica and Centro de Resonancia Magnttica, Facultad de Ciencias, Universidad Central de Venezuela, A.P. 47586, Caracas 1041-A, Venezuela

* Instituto de Ciencias de la Tierra, Facultad de Ciencias, Universidad Central de Venezuela, Caracas, Venezuela

Abstract Carr-Purcell-Meiboom-Gill experiments were made upon sedimentary rock samples at different FW pulsation rates. A dispersion of the transversal relaxation rate was observed. The experiments revealed that due to the diffusional processes there is a diminution of the second moment with the delay time between RF pulses and the echo time. In order to understand the nuclear magnetic relaxation process for a fluid in the restricted geometry of the pore space, numerical simulations were performed. The magnetic field fluctuations were calculated assuming an appropriate propagator for the molecules in the fluid and the geometry of the pore space. From the time series obtained, it is possible to calculate the spectral densities for the relaxation processes and the local magnetic field distribution function. The simulations were qualitatively in accordance to experimental results.

57.1 Introduction In heterogeneous systems, it is well known that the transversal relaxation rate is dependent on the time spacing between RF pulses in a CPMG experiment [ 1,2], due to the quenching of different relaxation channels. Particularly in sedimentary rocks there has been some evidence of strong relaxation rate dispersion [3,4] possibly associated to

618

D. Pe'rez, A. Benavides, S. Gonzdlez, D. Bnrranres, atid M. Martin-Lmdrove

restricted diffusion through the porous material. In the present work we developed a simple experimental methodology to determine the evolution of the mean local magnetic field by the careful measurement of the spin-echo signal for different time spacing and echo time. From the theoretical point of view, the relaxation process in a porous material is not a well understood problem due to the disordered geometrical and physicochemical properties of the pore space. It is commonly assumed that the relaxation in a porous material is multiexponential or stretched exponential, with the inclusion of some phenomenological parameters, i.e., mean relaxation rates or stretched exponents. This description is rather simple and avoids the possibility to establish a relationship between the measured relaxation and the microscopic properties of the porous material neither to properly account for the observed variations in the second moment or local magnetic field distributions. Some theoretical approaches has been done [5-71 and numerical simulations [81 to derive the dependence of the relaxation rate on the geometrical properties of the pore space and its disordered nature, but generally on the assumption that the physicochemical properties are homogeneous over the entire pore system. In the present work, we have performed numerical simulations to evaluate the relaxation rate distributions for different model pore spaces and compare them to predictions obtained by analytical models and experimental results.

57.2 Materials and Methods The experiments were performed for different echo times and time spacing between RF pulses in a CPMG experiment so a two dimensional array of data could be obtained for each sample. The time intervals were varied depending on the transversal relaxation time of the sample. The measurements were done at 90 MHz using a CXP100 BRUKER spectrometer, upgraded with a MacSpect TECMAG interface, on a wide variety of sedimentary rocks including Berea sandstone and local rock samples. Each measured echo was carefully fitted on the top by a fourth degree polynomial. To obtain the second moment, the following expression was used [9,10]:

57. Relaxation-Difision Processes and Magnetic Field Distributions in Porous Media

619

(57.1)

where E(t) represents the echo signal and to, the time of its maximum. It is also assumed that the echo is symmetrical around to, so only even terms are considered in the fitting polynomial.

" \

T

t Fig. 57.1: Variation of the second moment as a function of the RF pulse time interval. Right, measurements for three samples of the same oil reservoir, El Furrial, Venezuela. Left, the average of the second moment for the same samples on the right.

In Fig. 57.1 the experimental second moment for three local samples is shown. It is interesting to notice that the samples exhibit a common trend in the evolution of the second moment even though they were not taken from the same rock nucleus. This result suggest that this type of measurements could be used to characterize geological properties of the samples. The dependence on the echo time can be very well illustrated in Fig. 57.2. It is also possible to obtain a bidimensional array of experimental data showing the dependence with the RF time spacing and the echo time, a result that is shown in Fig. 57.3. In general the experiments reveal that due to the diffusional process, there is a diminution of the spectral second moment as the RF time spacing or the echo time are increased.

620

D.PPrez, A. Bennvides, S. Gonzalez, D. Bnrrnntes, nnd M. Murtin-Landrove

n

8

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4 0.04

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Fig. 57.2: Variation of the local magnetic field as a function of the echo time for one of the samples shown in the previous figure. Clearly the dependence is of the power law type.

To understand the effect of diffusion on the second moment the following qualitative model can be used. In a porous material there is a distribution of magnetic local fields depending on the pore and throat size distribution, the physical and chemical properties of the inner pore and throat surface, the surface roughness and so on. For RF times smaller than the time required for a water molecule to get out of a pore, the local magnetic field averages to a value whch is typical of that pore, so the distribution of averaged local magnetic fields should be related to the distribution of pore sizes. It is generally expected that the average local magnetic field distribution is peaked at high values of the local magnetic field since there are a majority of small pores and throats in the rock. As the RF time spacing is increased, water molecules can reach other pores, which in most of the cases will have a different geometry and with a high probability a lower value of the local magnetic field. This situation brings, as a consequence. a blurring of the magnetic field distribution and the reduction of the average magnetic field. The exact way by which the local magnetic field distribution is changed or blurred, depends on the geometry and physicochemical properties of the pore surface, so it will be necessary to use simulations to obtain further information about these processes. Some of the models that can be used to simulate the relaxation processes and local magnetic field distributions are discussed in some detail in the next section.

57. Relaxation-Difision Processes and Magnetic Field Distributions in Porous Media

62 1

Fig. 57.3: Variation of the second moment as a bidimensional plot in the RF time spacing and echo time.

A similar explanation could be used for the variation observed with the echo time. In this case, a larger time scale is observed and possibly the attenuation of the average second moment depends on some intermediate geometrical scale present in the pore system. As the echo time is increased, some loss of correlation in the local magnetic field appears due to the movement of the water molecules outside a grain to another with different geometrical and physicochemical properties. This correlation loss introduces variations in the average second moment which corresponds to the observed results. Some simulations performed predict most of the results presented in this work by very simple models for the pore system. In particular, a simple system given by the coexistence of two different pore geometries and physicochemical properties is enough to characterize the observed results. A more general treatment can also be done and this introduces the possibility to understand, by rather simple models, the transport properties of fluids in porous materials.

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D. Pirez, A. Benavides, S.Gonzcilez, D. Barrantes, and M. Martin-Landrove

57.3 Models Two different types of simulations were tried in this work. The first one assumes that Bloch equations are valid, combined with Fick's law to account for diffusional effects. The pore space is divided into two zones, one called the bulk space with homogenous relaxation time r b and diffusion constant Db, while the other is called the surface, with parameters T, and D,

104

103

10-2

lo-'

I/R (prn-') Fig. 57.4: Dependence of the normalized relaxation rate for different DdDs ratios. It is assumed that Tb = 1, TdTs= 100 and Db = 2000.

N random walkers are initially created within the pore space and moved at each step

according to the diffusion propagator which corresponds to the specific zone on which the random walker is positioned at that time, so the length of the step is variable and adaptive to the particular shape of the pore surface. The magnetization change is determined at each time step by the solution of Bloch equations corresponding to the position of the random walker. After N random walkers. The magnetization decay is averaged and the relaxation rate is determined. Figure 57.4 shows the results for spherical pores at different pore sizes and different diffusion ratios, which are in correspondence with analytical models [5-81.

57. Relaxation-Diffusion Processes and Magnetic Field Distributions in Porous Media

623

The second method used for the simulations evaluates the spectral density associated to the magnetic field fluctuations inside the porous material. For each random walker, time series for each of the components of the local magnetic field are calculated, and from them their respective spectral densities. Relaxation rates are determined according to [ 111:

(57.2)

(57.3) where:

with:

and the assumption of a very simple Hamiltonian:

(57.6)

After N random walkers, a histogram composed from the individual contributions is obtained, representing the distribution function of relaxation rates. From the local magnetic field time series, it is possible to calculate the mean quadratic deviation of the magnetic field for each random walker. In the same way as relaxation rate distributions, local magnetic field distributions are also calculated. To calculate the local magnetic field time series similar assumptions to the first simulation are made but with some variants depending of the particular pore model used, for example, in the case of spherical pores, it is assumed that the two regions, i.e., bulk and surface, exhibit different magnetic fields distributions, correlation times and diffusion constants. The total simulation time, i.e., the time required for a single random walker to perform its walk, can be changed in this type of simulation in order to take into account dynamical effects due to the timing in the experiments, i.e., in the Cam-Purcell-Meiboom-Gill (CPMG) pulse sequence, the trans-

624

D. Pirez, A. Benuvides. S. Gonzblez, D. Barruntes, and M. Murtin-Landrove

verse relaxation is strongly dependent on the RF pulses time spacing due to molecular exchange or diffusional processes present in the system [4]. Figure 57.5 represents the evolution of relaxation rate distributions as the time interval for the simulation is changed. 10 2

T 10’

?

Q

W h

B\

100

Fig. 57.5: Longitudinal relaxation rate distribution function for spherical pores calculated at different total simulation times. The time interval used in each simulation was from left to right, l@lO,

10-11, 10-12, 10-13 s, respectively.

The distribution of local magnetic field can be also calculated. For a system with coexistence of pores with two different sizes distributed in grains, and under the assumption of a confinement time characteristic for each pore size and homogeneity in the dynamical parameters within the grain, i.e., local magnetic field fluctuations and diffusion constant, the evolution of the local magnetic field distribution with the total simulation time can be traced very easily. In Fig. 57.6, two distribution functions are shown as an example. From the figure it can be easily seen that the average of the local magnetic field for short times is larger than the one for a long time. Qualitatively there is an agreement

57. Relaration-Diffusion Processes a i d Magnetic Field Distributions in Porous Media

625

between the observed variation of average second moment of the absorption line and the simulations. By choosing appropriately the parameters of the model, keeping it as much as simple as possible, a quantitative accordance with the experiment can in principle be made.

.s

c)

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long time

-I 2000 -I 4000

0

-:

/

0.003 0.004 0.005 0.006 0.007 0.008 0.009

Local Magnetic Field Fig. 57.6: Local magnetic field distributions for different total simulation times. The evolution of the average value calculated with these distributions coincides with the observed experimental results in CPMG and echo experiments.

57.4 Conclusions The different types of simulations tried in this work only represent one small portion of what can be tested to fully understand relaxation processes in porous media. More sophisticated models assuming fractal or multifractal geometry should be tested to fully account for what is observed in experiments. In particular, models including disordered pore sizes and disordered physicochemical properties on the pore surface show a better agreement with the observed variation of relaxation rate distributions and local magnetic field distributions.

626

D.Pe'rer, A. Benavides, S. GonzAlez, D. Barrantes, and M. Martin-Landrove

The two types of simulations presented in this work give in principle two valid approaches to calculate the relaxation rate in porous media, but the direct calculation of relaxation rates by spectral densities seems to be a more general treatment of the problem and indeed, more powerful. In particular, relaxation rate distributions and local magnetic field distributions can be obtained and very simple models for the pore system can be included to account for the experimental results and a simple picture of what otherwise is a very complex system can be proposed.

Acknowledgments We would like to thank the financial support given by INTEVEP, S.A., CONICIT grant S 1-2259, Volkswagen Foundation and the Consejo de Desarrollo Cientifico y Humanistic0 (CDCH) of the Universidad Central de Venezuela for the realization of this work.

References 1.

J. R. Zimmerman, W. E. Brittin, J. Phys. Chem. 61 (1957) 1328.

2.

B. P. Hills, S. F. Takacs, P. S. Belton, Mol. Phys. 67 (1989) 903 and Mol. Phys. 67 (1989)919.

3.

R. L. Kleinberg et al., SPE 26470 (1993) 553.

4.

M. Martin-Landrove, R. Martin, A. Benavides, Bull. Magn. Reson. 17 (1995) 73.

5.

K. R. Browstein, C. E. Tan; Phys. Rev. A 19 (1979) 2446.

6.

M. H. Cohen, K. S. Mendelson, J. Appl. Phys. 53 (1982) 1127.

7.

P. P. Mitra, P. Le Doussal, Phys. Rev. B 44 (1991) 12035.

8.

M. Leibig, J. Phys. A: Math. Gen. 26 (1993) 3349.

9.

I. V. Aleksandrov, The Theory of Nuclear Magnetic Resonance, Academic Press, New York. 1966.

10.

M. Martin-Landrove, J. A. Moreno, Chem. Phys. Lett. 108 (1984)76.

11.

C. P. Slichter, Principles of Magnetic Resonance, Springer-Verlag, New York, 1990.

58. MR Microscopy of Savannah River Tank Waste Simulants Kevin R. Minard', Robert A. Wind', and Lee 0.Dworjanyn2

'Pacific Northwest National Laboratory, P.O. Box 999, Richland, WA 99352, USA 2Westinghouse Savannah River Co, Aiken, SC 29808, USA

Abstract At the Savannah River Site, an In-Tank Precipitation (ITP) process, designed to remove soluble radioactive cesium-137, employs tetraphenylborate (TBP) as a precipitation reagent. During initial tests, it was found that this process unexpectedly generated large concentrations of benzene. As a result, all ITP operations were shut down and a systematic effort has since been undertaken to gain a better understanding of the factors controlling benzene generation, retention, and release in ITP slurries. In this paper results are presented of a MR microscopy study to characterize the microscopic environment of benzene in a simulated ITF' slurry, consisting of water, 4 wt % potassium tetraphenylborate (KTPB), 5 molfl Na salts, and 5 vol % benzene. Work was performed at 11.7 Tesla using a Varian UNITYplus micro-imaging spectrometer. Three-dimensional images of the benzene distribution in 1.5 mm3 samples were acquired with spatial resolutions as h g h as 10 x 10 x 10 pm3. It was found that liquid benzene was retained in pure droplets with diameters between 50 and 150 pm. It was also observed that when shaken, the KTPB penetrates the droplets and relatively large KTPBbenzene agglomerates are formed in which the KTF'B and benzene become more and more tightly associated with increasing agitation. These results were confirmed by bulk restricted diffusion measurements.

628

K . R. Minnrd, R. A. Wind. and L. 0. Dworjanvn

58.1 Introduction The production of fissionable materials for the nuclear weapons program led to the generation of significant amounts of highly radioactive nuclear waste that has been ternporarily stored at a number of sites in large volume storage tanks. For example, there are 177 tanks at the Hanford Site and 51 tanks at the Savannah River Site (SRS), with a combined waste volume in excess of 100 million gallons. This waste needs to be processed so that it can be permanently stored in a repository where it will have minimal impact on human health and the environment. At Savannah River, radioactive cesium137, with a half-life of approximately 30 years, constitutes a large portion of the total radioactive material currently stored in the waste tanks at that site. To remove the cesium from the alkaline solutions contained within, an In-Tank Precipitation (ITP)process was designed at SRS that made use of sodium tetraphenylborate (NaTPB) as a precipitation reagent. Once added to the liquid waste, NaTPB would, in principle, react with cesiumbearing salts to form the precipitate cesium tetraphenylborate (CsTPB), which could then be separated, concentrated via filtration, washed, and ultimately sent to vitrification for final storage in a stable glass form. Then the decontaminated residual salt solution could be disposed on-site in the form of saltstone. Unfortunately, this process is complicated by the presence of potassium-bearing salts which react equally well with NaTPB to form the precipitate potassium tetruphenylborute (KTPB), present as a slurry at the top of the treated tank waste. This is of particular importance since these salts are found in concentrations 100 times higher than the cesium salts, and as a result, a hundred fold more NaTPB was required than would have been needed if no potassium salts were present. In fact, another 30 - 40% excess of NaTPB was added on top of this to ensure effective precipitation of the cesium. A large problem arose during initial ITP operations, March 1996, when it was found that dangerously high levels of liquid benzene, a known carcinogen, were unexpectedly generated, orders of magnitude above the mass transfer rate expected from the 300 mg/l equilibrium benzene solubility in the salt solution. Surprisingly, much of the generated benzene was retained in the slurry. In fact, it was found that the slurry, mainly consisting of water and 4 wt % KTPB, can retain added liquid benzene with concentrations as high as 50 g/l. Subsequently, uncontrolled releases of flammable benzene vapor occurred, which have forced a complete shut-down of all ITP operations. Since then systematic efforts have been undertaken in order to gain an understanding of the benzene generation, retention, and release in ITP slurries, so that the clean-up activities can be improved and resumed safely.

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It is worth noting that, although it may ultimately be possible to reduce the amount of benzene generated by the ITP process, it is unlikely that the formation of benzene can be avoided completely. Furthermore, since benzene retention and release are both likely to depend strongly on the state of benzene in ITP slurries, information regarding this state is needed to develop appropriate methodologies for controlling these important processes. Initial efforts to characterize the benzene retention in ITP slurries have exploited nonradioactive simulants, mainly consisting of water, sodium salts, KTPB, and benzene. When briefly shaken, these simulants repeatedly form a milky white dispersion even after they are allowed to settle. However, when shaken continuously for an extended period of time, a startling, irreversible transformation takes place in which the KTPB and benzene become more and more tightly associated until finally forming a single agglomerate suspended in KTPB-free salt solution. These findings dramatically illustrate the potential variability of the benzene environment in ITP slurries and highlight the need for a versatile experimental method capable of investigating a broad spectrum of morphological changes. In the current study, results are presented of a MR microscopy investigation for characterizing the microscopic environment of benzene in simulated ITP slurries. Based on both spatially resolved MR imaging data and unresolved restricted diffusion measurements, the approach was found to be well suited to determine the three-dimensional benzene distribution, the average size of benzene-containing compartments, and the local benzene concentration in observed microstructures. Taken together, these measures provide an improved understanding of both the state of benzene in simulated ITP slurries and the changes induced by agitation.

58.2 Experimental 58.2.1 Sample Preparation The experiments were performed on a simulated non-radioactive tank waste slurry. The slurry composition was based on various tests performed to characterize the tank waste leaving out intermediate decomposition products or soluble metals. The slurry consists of water, approximately 5 molA of various dissolved Na salts, rendering the pH to 13 14,4 wt % insoluble KTPB, and 50 g/l benzene, injected into the slurry. The benzene was

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K. R.Minard. R. A. Wind, andL. 0.Dworjanvit

dispersed by gently shaking the sample by hand. This sample will be referred to as the non-agitated slurry. In order to investigate the effects of more pronounced shaking, two types of agitation were applied: (i): A horizontal half-filled vial was shaken slowly back and-forth for about 1/2 hour; (ii): The slurry was put in a blender for a few minutes. These procedures are referred to as gentle and strong agitation, respectively.

58.2.2 MR Microscopy Proton MR microscopy experiments were performed in a 89 mm i.d. vertical bore magnet operating at 1 1.7 Tesla, using a Varian UNITYplus imaging/spectroscopy console, and a microimaging probe manufactured by D. G. Cory and coworkers at the Massachusetts Institute of Technology (MIT) as part of a collaborative project between PNNL and MIT to develop MR microscopy in fields up to 21 T. The probe is capable of generating gradients up to 10 T/m. The measurements were performed at room temperature on samples contained in sealed glass tubes with an i.d. of 1.3 mm, mounted in a NMR coil of both an i.d. and a length of 1.7 nun. Three-dimensional ( 3 0 ) images were acquired using a spin-echo imaging sequence that employed standard phase and frequency encoding methods for sampling k-space. With isotropic resolutions between 10 and 25 pm, the point spread function was dominated by T2-losses rather than diffusion-losses, and therefore data was collected using a T2-optimal acquisition bandwidth. Water suppression was achieved by using an inversion-recovery preparation period that employed a hard n-pulse. With gross differences in TI-relaxation rates between water and benzene (Tl(CbH6) 7.0 s and T,(H,O) 1.0 s), the water signal was easily nulled by an appropriate choice of the inversion time. Additional water suppression was achieved by using a benzene-selective refocusing pulse for forming the spin-echo. Together with the hard inversion pulse and appropriately placed crusher gradients, water was typically suppressed more than 200 fold during benzene-only 3D data acquisitions. Moreover, by using a hard inversion pulse, even water near air bubbles was adequately suppressed despite large frequency offsets from susceptibility effects. It was found that if only frequency selective methods for water suppression were used, such water tended to contaminate benzene-only images. In addition to 3D images, two-dimensional multislice (20) benzene-only and wateronly images were acquired. For the benzene-only images a sequence was used that employed the water suppression scheme similar to that already described above. For the

-

-

58. M R Microscopv of Savannah River Tank Waste Simulants

63 1

water-only imaging adequate benzene suppression was obtained by omitting the inversion sequence, and by simply using a short recycle delay time of 1 s. In order to detect and quantify possible benzene-containing voids below the spatial resolution of acquired images, pulsed-field gradient diffusion measurements were performed. These were conducted using a hybrid of the original 13-interval Cotts sequence that was previously described in detail by others [3]. Briefly, this sequence employed a stimulated echo, which allowed molecular motion to be probed over time scales larger than 5 seconds since the benzene T , was sufficiently long. To eliminate the effects of background gradients, the sequence employed additional refocusing rf pulses and gradient pulses of alternating sign. In addition, an eddy-current stabilization period prior to each data acquisition ensured that eddy currents induced in the 4.2 molar saline solution would be in a steady state during actual data acquisition. As a result, eddy-currents merely distorted the final shape of the applied gradient waveform and experimental results were easily corrected via calibration with appropriate standards. In the strongly agitated sample the effects of eddy currents could be ignored completely since little water was actually present in the sample region. This was confirmed using identical samples that had been washed repeatedly with distilled water to remove conducting sodium ions. In the other samples the effects of eddy-currents on the measured water diffusion could be used as an internal calibration for correcting the benzene-diffusion data. For all three samples a series of echo-attenuation measurements were carried out in which the mixing time was arrayed, keeping all other parameters constant. From these measurements the apparent diffusion coefficient was determined, and plots were generated of this coefficient as a function of the diffusion time.

58.3 Results and Discussion Figure 58.1 shows water-only, benzene-only, and composite 2D images of a slice through the non-agitated tank waste simulant. The composite image was obtained by simply superimposing the water-only and benzene-only images. It follows that in this sample the benzene is present in isolated droplets. It can also be seen from the composite image that the droplets are surrounded by 10 - 20 pm thick dark layers, presumably consisting of the solid KTPB.

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K. R. Minard, R. A. Wind. and L. 0. Dworjanyn

Fig. 58.1: 2D images of the water distribution a), the benzene distribution b), and the composite image c) of a region in the non-agitated sample. Slice thickness = 150 pm, FOV = 1.3 x 1.3 m 2 , planar resolution = 10 x 10 l m 2 , TE = 3.3 rns, TR = 1.0 s a) and 20 s b).

Figure 58.2 shows the three-dimensional distribution of the benzene in the three samples. Figure 58.2a shows the result for the non-agitated waste simulant, confirming the presence of benzene droplets with diameters of 50 - 200 pm. Comparison of the benzene signal-to-noise ratio inside of the droplets with that of identical images of a bulk benzene standard indicated that the droplets consist of pure benzene. Figures 58.2b and 5 8 . 2 ~ display the three-dimensional benzene distribution in the gently and strongly shaken samples. It follows that the agitation has a profound impact on the way the benzene is dispersed: after gentle agitation part of the benzene is distributed in much smaller droplets, which become a compact agglomerate after intense agitation. It was also found that agitation decreases the benzene concentration in the benzene-containing voxels from 100% in the non-agitated sample to 40 - 70% in the gently agitated sample to 20 - 50% in the strongly agitated sample. As no water was detected in these voxels, this means that after agitation the individual droplets become filled with KTPB particles, forming stable agglomerates with the benzene. This means that in the agitated samples benzene-containing microstructures occur with sizes well below the spatial resolution of the images. These results are confirmed by the restricted diffusion measurements. In Fig. 58.3 the apparent diffusion coefficients, normalized by the diffusion coefficient of free benzene, D/Do, and plotted as a function of the diffusion time (A), are shown for the three samples. In the non-agitated sample, the diffusion coefficient gradually decreases with time, indicative of restricted motion. As a complete analysis of the results is difficult to perform in this heterogeneous sample, a simpler approach was used, in which only the short-time and the long-time behavior of the diffusion coefficient was considered. From

58. MR Microscopv of Snvatituih River Toilk WnsfeSimulants

633

the initial slope of the curve D/D, versus A, the average diameter (d) of the droplets governing this time-dependent behavior can be calculated [3,4]. Assuming spherical droplets, the result is: d = 65 pm. At long diffusion times, the apparent diffusion coefficient (D)approaches the limit: D = d' (20A)-' (ref. [2] p. 374). ). For the non-agitated sample D was measured for long diffusion times as well, and became given by 0.070, for a diffusion time of 6 s, corresponding to d = 140 pm. Hence, in the non-agitated sample, the droplet sizes following from the restricted diffusion are similar to the ones observed in the images.

Fig. 58.2: a) Three-dimensional images of the benzene distribution in the non-agitated, b) the gently agitated, and c) the strongly agitated tank waste simulant. FOV = 1.3 x 1.3 x 1.3 mm3, spatial resolution = 10 x 10 x 10 pm3 a), 20 x 20 x 20 pm3 b), and 25 x 25 x 25 pm3 c). TE = 9.1 ms. TR = 5 s, NA = 2,64 x 64 phase-encoding steps. The bars represent a distance of 200 pm.

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K. R. Minard, R. A. Wind, und L. 0. Dworjanyn

It follows from Fig. 58.3 that the benzene mobility is significantly reduced in the agitated samples. We first consider the strongly agitated sample. It is found that even for the shortest diffusion times the apparent diffusion coefficient is reduced to a value 0.4D0, and that this value hardly changes with increasing diffusion times (we found this result to be true even for diffusion times as long as 5 s). Two scenarios are possible to explain these results [ 5 ] : (i): The benzene is present in small voids with diameters of a few pm (causing the initial fast, undetected, decrease in D), which are interconnected, thereby allowing the benzene to diffuse over distances much larger than the void size (this explains the long-time behavior); (ii): The diffusion coefficient is reduced because the benzene is diffusing in thin layers bound to KTPB surfaces, but the total surface area of the layers is large, allowing the benzene molecules to move over large distances. Which of these explanations is correct is still under investigation. However, in either case the restricted mobility of benzene must result from an intimate mixture of the benzene with the KTPB, which is again in accordance with the imaging results. Finally, it follows from Fig. 58.3 that the diffusion curve for the gently agitated sample is an intermediate case between those of the non-agitated and strongly agitated samples, probably indicating that both larger droplets of more or less pure benzene and benzeneKTPB agglomerates are present simultaneously.

1.0 l 4 . u

0.6

1'

H

Diffusion Time A (msec) Fig. 58.3: Normalized apparent diffusion coefficients measured as a function of diffusion time (A) in bulk benzene and in the non-agitated (H), gently agitated and strongly agitated (1) tank waste simulant. The diffusion coefficient of free benzene, Do,was measured to be: Do = 2.2.10-9m2s-1, in accordance with the literature (ref. [2] p. 165).

(m,

(a),

58. MR Microscopv of Snvanmh River Tank Waste Simulants

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58.4 Summary and Conclusions The MR microscopic imaging and diffusion experiments reported in this paper were of considerable help in understanding the benzene retention in simulated tank waste slurries. Based on the outcomes of this investigation and several other studies, performed by other research groups, the following picture has been developed regarding the generation and retention of the benzene in the In-Tank Precipitation process [ 11: When NaTPB is added to the tank waste, about 4 wt % KTPB is formed as a precipitant, which is lighter than water and floats to the surface of the waste to form a slurry. Benzene is generated by the decomposition of the excess NaTPB, added to assure that all the Cs will be precipitated. This process is catalyzed by the presence of metal traces in the waste. The benzene floats to the slurry, and is dispersed with minimal agitation into droplets with sizes of 50 -150 pm, coated by the hydrophobic KTPB. The coated droplets are stabilized and retained in the slurry. The dense coating prevents benzene droplets from agglomerating, and slurry shear stress prevents the coated droplets from floating to the top. When the tank waste is stirred during the processing, the benzene is dispersed into small droplets, and become partially filled with KTPB. With continued agitation large three-dimensional KTPB-benzene agglomerates are formed in which the benzene is allowed to diffuse over large distances. Under the liquid waste surface the benzene is stable, and the benzene can evaporate only when the surface is disturbed, forcing the agglomerates above the surface. More studies are needed before it will be decided which actions need to be undertaken to improve the In-Tank Precipitation process. One of these studies will be an investigation of simulated (non-radioactive) tank waste in a column, in which the benzene is generated in situ by the catalytic decomposition of NaTPB. MR microscopy on a small (30 mm diameter) column may assist in determining the benzene distribution and propagation in these ,,bulk" opaque slurries. However, initial proton NMR experiments revealed that the large sample conductivity due to the high salt concentration created rf penetration problems in these relatively large samples, and that the presence of dissolved metals in these simulants broadened the water line to about 6 ppm. This makes the water suppression considerably more difficult than in the samples examined in the present study. Therefore, more research is needed to determine the feasibility of the in situ MR microscopy approach.

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References 1.

L. 0. Dworjanyn. .,Benzene Retention in TPB Slurry", Status Report, WSRC-RP-977217. March 26, 1997.

2.

P. T. Callaghan. Principles of Nuclear Magnetic Resonance Microscopy, Clarendon Press, Oxford, 1993.

3.

E. J. Fordham, S. J . Gibbs, and L. D. Hall, Mngn, Reson. bnaging 12 (1994) 279.

4.

P. P. Mitra. P. N. Sen, and L. M. Schwartz. fhys. Rev. B 47 (1993) 8565.

5.

P. T. Callaghan, K. W. Kolley, and R. S. Humphrey, J. of Coll. and Interf: Sci. 93 (1983) 521.

Hardware

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59. A Compact, Superconducting Magnet for Magnetic Resonance Microscopy Stuart Crozier and David M.Doddrell

Centre for Magnetic Resonance, The University of Queensland, St. Lucia, Qld 4072, Australia

Abstract Magnetic Resonance Microscopy (MRM) [ 1-31 depends on the use of high field, superconducting magnet systems for its operation. The magnets that are conventionally used are those that were initially designed for chemical structural analysis work. A novel, compact magnet designed specifically for MRM is presented herein that, while preserving high field, high homogeneity conditions, has a length less than one-third that of conventional systems. This enables much better access to samples, an important consideration in many MRM experiments. As the homogeneity of a magnet is strongly dependent on its length, novel geometries and optimization techniques are required to meet the requirements of MRM in a compacf system. An important outcome of the stochastic optimization performed in this work, is that the use of a thin superconducting solenoid surrounded by counter-wound disk windings provides a mechanism for drastic length reductions over conventional magnet designs. The design algorithm may be used to design magnets of a variety of geometries.

59.1 Introduction All commercial MRM systems use magnets designed for molecular structure determinations, and these magnets are typically very long relative to their bore size, offering little access to the sample under study. Ths limited access is a distinct disadvantage in many MRM applications. Long magnet systems also require significant siting space, particularly in ceiling height.

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S. Crozier and D. M. Doddrell

In this article, we describe a novel geometry for a superconducting magnet suitable for high field MRM. As the homogeneity of a magnet system is strongly dependent on its length, the design of a compact system is not trivial. We also discuss a generalized optimization procedure for the design of such systems based on stochastic descent. The result of the optimization is a high homogeneity magnet of length less than one-third of conventional systems operating at 7 T. All conventional MRM magnets have main coils that are all wound in the same direction. When the optimization techniques presented here was applied to the problem of MRM magnet design with a significantly constrained length, the algorithm consistently designated an internal solenoid with windings opposing to the windings to all other coils, this somewhat surprising designation provides a mechanism for compact magnet design of high purity. The methodology presented here may be applied to many magneto-static design problems.

59.2 Magnet Design NMR magnets for high field applications have been based on multiple solenoidal coils connected with two or more “correction” coils in the fashion described some time ago by Garrett [4,5]. These layouts have formed the basis of even the most modem coil structures [6,7]. The requirements of this design are that it is “homogeneous” over a diametersensitive-volume (&), that the conductors are operating with suitable factors of safety in terms of their critical current carrying capacity and the field within which they reside [8101. Furthermore, the magnet may be shielded to reduce stray fields and siting costs. We detail the coil structure here, not the cryogenic structures. In MR we are usually concerned with the Laplacian of the longitudinal component of the field, which may be expanded in spherical harmonics over a sphere in the usual way [8]. In the case of systems possessing total cylindrical symmetry, as in the structures discussed here, only zonal spherical harmonics (no tesseral components) need to be considered in the design process 181. In order for the magnet to be deemed homogeneous over it is dsv, the sum of all zonal harmonics should be less than a prescribed amount of the zero order harmonic; the Bz field, usually termed the B, field in NMR. The harmonic terms of interest are further restricted to even order zonal terms as the current density distribution in these magnets is even and axi-symmetric [8].

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A bare magnet homogeneity requirement of 20 ppm or less over the dsv is common for MRI systems. It is also important that the spatial distribution of the field inhomogeneity in the field be characterized by low order terms after construction, so that they may be removed by passive or active (superconducting) shimming. The theoretical design process, therefore, must place special emphasis on reducing the higher order terms. The problem then, is to generate a coil structure to satisfy the harmonic purity requirements while restricting the total length of the magnet. We [ 11-13] and others [ 141 have shown that the Simulated Annealing method (SA) [ 151 is effective for compact MRI gradient design and so now apply this method to magnet design. By imposing length constraints, the SA routine effectively attempts to find the ‘best’ solution possible within these limits. Here ‘best’ refers to the minimization of an error function which, in this case, contains terms representing the homogeneity of the dsv and its quality of shielding. The homogeneity term consisted of a weighted summation of even order zonal harmonics and the shielding term consisted of field summations at the desired 5 gauss contour points. It is possible to include other terms in the function as the designer requires. A disadvantage of the SA procedure is that it takes many iterations to achieve its “frozen” state [15] and it is therefore important that the time for each iteration be as short as possible. Fortunately, the method for direct field harmonic calculation presented by Garrett [4] is rapid, calculating harmonics up to 18” order from a 14-coil magnet in under 100 ms on a SUNSPARCstation 10. A calculation of the field in the dsv by elliptic integral calculations [ 161 for all turns in a typical magnet takes more than two minutes on the same computer. To calculate the stray field outside the magnet for shielding quality, the field in the superconductors and for checking the peak-to-peak and rms field variations over the dsv, we have developed a rapid field calculation routine based on the coil cross-section (that is, the computation time is independent of the number of turns) [17]. This routine was designed to be numerically efficient and easily implemented for the calculation of fields from what is essentially a circular bar of current density. The total time per iteration to evaluate an error function consisting of 18” order harmonics and shielding fields for each magnet configuration was less than 300 ms for all designs presented here, thus permitting the thousands of iterations necessary for stochastic optimization to be performed in reasonable times. The parameters for perturbation in the design process for each iteration were; the axial and radial dimensions of each coil, the number of turns per coil and the radial and axial position of each coil. In order to introduce sufficient degrees of freedom in these constrained problems, we begin with relatively large numbers of coils (twelve) and allow

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the SA process to redistribute them. Adaptive step sizing was implemented and initial step sizes and temperatures selected by testing each coil for parametric sensitivity prior to the SA run. Each magnet design took 4 - 6 hours to compete and consisted of 2 SA runs, the first having coarse steps and was limited to one hour, after which overlapping coils were coalesced and the algorithm restarted.

59.3 Results Consider the exemplary design of a 7 T 89 mm (industry standard “wide-bore”), shielded magnet system. Figure 59.1 shows the schematic of the resultant compact design in cross-section. The inner and outermost coils are counter wound to the others. The counter winding of the innermost coil appears to be essential to the length reduction process, as the algorithm repeated made this selection in a variety of different constrained length magnet configurations. Figure 59.2 shows a perspective view of the optimized structure. The total length of the coil structure is approximately 20 cm, which is less than half the length of currently available 7 T/89 magnet systems. The performance of the magnet is detailed in Table 59.1 and indicates the high homogeneity of the magnet for its length. The harmonics of the field were calculated to 18” order and the peak-to-peak and rms field deviations were calculated over 800 points on the surface of the dsv in 20 planes, the distribution of these planes being chosen to be the zeros of the 20* order Legendre polynomial so that Gaussian integration may be readily implemented [S], and to ensure that Nyquist sampling requirements were met for lS* order harmonic analyses. We have verified the accuracy of our field and harmonic calculations by comparison with commercial electromagnetics software (Vector Fields, Oxford), the results were within 0.01% of each other. Note that the homogeneity figures are bare homogeneity values, that is, that no additional superconducting or room temperature coils were added to further improve the field purity. We note that with the addition of such shims, the magnet described in Table 59.1 and Figs. 59.1 and 59.2 would be appropriate for chemical applications as well as MRM. An important consideration in superconducting magnets is to ensure that the conductors are operating within acceptable limits of current density and submersed field strengths [8-lo]. The maximum field in any conductor was calculated to be 11.2 T. In

59. A Compact, Superconducting Magnet for Magnetic Resonance Microscopy

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these windings, a Nb3Sn conductor, with a turns density of 0.64 mm-2, and a superconductor to matrix filling ratio of 0.44, the operating current density to critical current density ratio is approximately 0.6 - quite a reasonable operating safety margin [S].

400

-400

Fig. 59.1: The cross-section of the compact magnet pattern.

Fig. 59.2: A perspective view of the coil pattern of Fig. 59.1. The central solenoid and the outermost rings are counter-woundto the coils in the middle.

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Table 59.1 : Compact magnet homogeneity. Transport current for 7.05 T (Amps)

260

Length of conductor (km)

30.6

Homogeneity (35 mm dsv) (ppm) Peak-to-peak

< 0.3

Shielding (5g)

1.7mx2.1 m

Field harmonics (ppm) 22

-1.le-2

24

7.5e-3

26

-7.8e-2

28

-1.3e-2

210

3.9e-4

212

l.le-4

214

-2.9e-7

216

-7.3e-8

218

1.3e-9

59.4 Conclusion In summary, we have shown that stochastic optimization produces novel, compact MRM magnet designs having excellent homogeneity. A new class of superconducting magnets for MRMNMR has been described, where an inner thin solenoid counter-wound to the other coils provides a mechanism of extreme length reduction while maintaining the stringent homogeneity requirements of the MR system. We have restricted ourselves to cylindrical magnets in this work, but the method could be easily applied to magnets of other configurations.

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Acknowledgments We thank the Australian Research Council for support and Simon Teed for drafting the perspective figure.

References 1.

2.

P. T. Callaghan, Principles of NMR Microscop.y, Oxford University Press. Oxford. 1991.

X. Zhou and G. A. Johnson, The Biomedical Engineering Handbook (editor-in-chiefJ. D. Bronzino), C Press, 1995.

3.

Z. H. Cho, J. P. Jones, and M. Singh, Foundations of Medical Imaging, John Wiley and Sons, Inc., New York, 1993.

4.

M. W. Garrett, J. Appl. Phys. 22 (1951) 1091.

5.

M. W. Garrett, J. Appl. Phys. 38 (1967) 2563.

6.

T. Kamikado et al., lEEE Trans. Magn. 30 (1994) 2214.

7.

S.-T. Wang et al., IEEE Trans. Magn. 30 (1994) 2340.

8.

H. Brechna, Superconducting Magnet Systems, Springer, Berlin,1973.

9.

J. E. C. Williams, Superconductivity and its Applications, Pion Ltd., London, 1970.

10.

C. P. Poole, H. A. Farach, and R. J. Creswick, Superconductivity, Academic Press, New York, 1995.

11.

S. Crozier and D. M. Doddrell, J. Magn. Reson. 103 (1993) 354.

12.

S. Crozier, L. K. Forbes, and D. M. Doddrell, J. Magn. Reson. 107 (1994) 126.

13.

S. Crozier, S. Dodd, and D. M. Doddrell, IEEE Trans. Magn. 30 (1994) 1242.

14.

M. L. Buszko et al., J. Mugn. Reson. 112 (1996) 207.

15.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vechhi, Science 220 (1983) 67 1.

16.

D. Craik, Magnetism. Principles and Applications, Wiley, New York, 1995.

17.

L. K. Forbes, S. Crozier, and D. M. Doddrell, IEEE Trans. Magn. 33 (1997) 4400.

18.

A. Corona, M. Marchesi, C. Martini, and S. Ridella, ACM Trans. Math. Soft. 13 (1987) 262.

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60. MRI Gradient Coil Optimization F. David DOQ Doty Scientific, Inc. 700 Clemson Road, Columbia, SC 29229, USA

Abstract A more complete set of largely dimensionless optimization parameters is introduced to better address the requirements of microscopy gradients. New parameters include DC efficiency, acoustic efficiency, nearest gradient null point, switching efficiency, continuous gradient rating, nerve stimulation, and volume current density ratios. The standard parameters of gradient uniformity, shielding effectiveness, recovery time, impedance matching, gradient gain, inductance, and rf shielding are also discussed. A novel design for transverse gradient coils utilizing crescent-shaped coils in combination with golay coils is shown to have substantial advantages in reduced acoustic response, increased continuous gradients, and reduced image fold back. Very high amplifier output impedance in constant current mode is also shown to be critical in certain applications.

60.1 Introduction More than a decade after high-performance shielded gradients were introduced [ 1,2], there is still considerable confusion about the importance of various technical issues and performance parameters in gradient coil design. Some will insist that linearity is the main issue, others inductance or resistance, others gradient gain, and still others shielding. In truth, none of these in itself is very meaningful, though all are important when put into proper relationship to other parameters. In practice, one of the most important characteristics is reliability, which is most closely related to minimum conductor cross-section, encapsulation quality, and coil-form stiffness in smaller systems, though in larger systems it may be more dependent on cooling. An increasingly important parameter appears to be continuous gradient strength. However, the main point of this paper is that gradient optimization is a multi-dimensional problem. The two-orders-of-magnitude increase in com-

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putational power per unit cost during the past decade has decreased the value of analytical optimization of a few parameters, and the method of error minimization is also now inconsequential. The focus must be on system requirements, design tradeoffs, cost, and construction of the objective function in the optimization routine, as all gradient designs have been done numerically for at least the last six years. Moreover, this paper will address only transverse gradients in detail, as axial gradients have been well covered in the literature. In addition to the gradient coil, we will look briefly at critical amplifier issues. From a design perspective, the MRI gradient coil is best evaluated in terms of the following (mostly dimensionless) parameters: switching efficiency, differential (or local) linearity, relative residual eddy current gradient, settling time, DC efficiency, cooling effectiveness, and acoustic efficiency. The gradient amplifier is best evaluated in terms of VA (peak power) per dollar, power bandwidth, settling time to 0.2%. low frequency noise ( 1 - 1000 Hz), DC drift, constant-current (CC) output impedance, total harmonic distortion at 1 W z , and power efficiency at 30% of peak current and voltage. Optimizing the gradient inductance or resistance for a given amplifier is not particularly critical.

-

60.2 Definitions, Specifications,and Coil Optimization 60.2.1 Switching Efficiency Because the inductive time constant is UR,it is often asserted that one of the frst objectives in gradient coil design is to minimize inductance, but it is trivial to reduce inductance by more than an order of magnitude below values commonly used in the industry. Rather, it is straight-forward to show that, neglecting resistance, the proper figure of merit for switching the maximum gradient over a given sample diameter d, and length h, in the minimum amount of time with a given amplifier power (VA product) is the ratio of gradient magnetic energy in the sample to total gradient energy [3]. Dropping a constant coefficient, we designate this as the dimensionless gradient switching eflciency, qs, in SI units:

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649

(60.1)

where O! is the gradient gain (T/Am) or coefficient (also called "efficiency" by some authors), JL is the permeability of free space, and L (H> is the total inductance. In large, high-power gradient systems, qs is one of the most important parameters because the amplifiers and their operations cost are both greater than the cost of the gradient coils. For actively shielded gradients, qs depends strongly on the ratio of the separation distance between the shield and gradient coils to the gradient coil diameter. It is also dependent, but to a lesser extent, on the maximum allowable coil length, which often is constrained for rf lead length or sample-access reasons. This switching efficiency ranges from 12% to 35% for most state-of-the-art shielded gradients for larger samples, where sample diameter is about 70% to 85% of the gradient coil diameter, but qs is less than 3% in some of the older MRI designs and in many gradients designed for high-resolution NMR of small samples. For microscopy gradients, the IR voltage drop in the windings at peak gradient strength is often comparable to the peak amplifier voltage, so eqn. (60.1) has limited utility, and DC efficiency (discussed shortly) is usually more important. There is yet another reason for the limited value of eqn. (60.1) in microscopy. With small rf coils where sample losses are negligible, sensitivity suffers if the external rf shield diameter is less than 2.5 times the rf coil diameter, and resolution is usually limited by sensitivity here. Thus, one must use a relatively large gradient coil for best resolution and accept its amplifier requirements. Switching efficiency of the gradient coil is then best characterized simply by the ratio a2/L,except in the case of very small coils, as noted later under the discussion of amplifiers.

-

60.2.2 Impedance Options The coil designer has considerable control over L, a, and R [4]. For given dimensions, the gradient gain is proportional to the number of turns n, and the inductance is proportional to n2. The resistance is also approximately proportional to n2 and inversely proportional to the copper mass. By varying the thickness of the layers, the cross-section of the conductors, the number of layers, and parallel or series interconnections of the four

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F. D. Dory

quadrants, the designer has a wide range of control over these three parameters, whether using etched foil or wire, without serious effect on important figures of merit. This allows optimal use of various amplifiers. For a given switching efficiency and size, the rise time is determined by the gradient amplifier power (VA product) and impedance matching. The two halves of the gradient coils, which have precisely equal resistance and inductance, may be wired independently so that they may be connected either in series or in parallel. The coil parameters in Table 60.1, for example, are listed for the low-impedance (parallel) option. Switching to the series configuration may improve the impedance match and increase the peak gradient, but rise time to a given gradient is increased - gradient gain is doubled, resistance and inductance are multiplied by four, and r\, is unchanged. In some coils, this is userswitchable, and in some coils it is dynamically switchable to allow faster rise time with amplifiers of lower continuous power rating [ 5 ] . Matching the DC resistance of an optimized coil to the design load resistance of the amplifier for maximum output achieves maximum continuous gradient (assuming it does not exceed the coil's rating), but this is seldom the preferred choice. Rise time is improved by reducing the coil's impedance relative to the power-match optimum, but the extent of the mismatch must be limited by its effect on peak gradient. Another complication is that optimum power-match impedance for most amplifiers at pulse lengths under 1 ms is less than that for very long pulses. Thus, impedance matching in gradient coils is not a well defined concept, but simply reflects the emphasis on rise time vs. peak gradient strength. See section 60.3 for more comments on amplifiers.

60.2.3 Gradient Uniformity (Differential Linearity) A key question is how much non-linearity is to be allowed in the sample volume, as a 10% increase in d, and h, in eqn. (60.1) increases r\, by over 60% for a given gradient coil. It is not uncommon to define linearity as the relative error in actualfield (generated by the gradient coils) at the surface of the sample region compared to the targetfield that would be measured if the gradient had been constant (Turner [6]), regardless of the linearity along the path to the target field. The standard formulation of the Turner definition essentially weighs errors inversely in proportion to their distance from the center of the sample [7]. With this definition (which was generally used in early works), it is easy to achieve linearity under 2% even though the gradient in many places throughout the sam-

60. MRI Gradient Coil Optimization

65 1

ple may be less than half the mean value and the field may not even be monotonic. Figure 60.1 shows a typical curve for a transverse gradient field B , near the axial ends of the sample region and explains the common "telescoping" or compressing effect in this region. (The opposite curvature was typical near the equatorial plane in early designs.) Note that the field error at point x is zero, but the gradient error is large except near x2=x1.

Bz

t

Fig. 60.1: Typical transverse gradient field near the end of the sample region.

A more useful specification is gradient non-uniformity (also called differential lin-

earity) - i.e., relative root-mean-square (rms) local deviation o of the gradient from its mean value throughout the sample volume [4,7,8]. This is still not unambiguous, as it

depends on the number of elements examined within the imaging region. (Using fewer elements averages localized errors. We typically look at over 1500 elements per octant of the sample region.) The linearity also depends on whether one is specifying a spherical or a cylindrical sample region - which gives 50% more imaging volume. While some authors have used maximum errors, most have used rms sums and a few have used weighted rms methods in which the error is weighted by a function that somewhat reflects the significance of the location in typical images. The above variations allow numerous definitions of gradient accuracy, and most have probably been used at one time or another. Most authors prior to ca. 1994 (and several as recently as 1996) appear to be using definitions similar to number 8 or 9 below when not otherwise specified. In order from most stringent to least stringent, the more common gradient accuracy definitions are:

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F. D. Dory

1.

Maximum local gradient error throughout sphere or ellipsoid

2.

RMS local gradient error throughout a cylinder

3.

RMS local gradient error throughout sphere or ellipsoid

4.

Weighted RMS local gradient error throughout cylinder

5.

Weighted RMS local gradient error throughout sphere or ellipsoid

6.

Maximum field error on surface of cylinder

7.

RMS field error on surface of cylinder

8.

Maximum field error on surface of sphere

9.

RMS field error on surface of sphere or ellipsoid

Note that the last four only address position error at the boundaries of the image. Another minor variation on the ellipsoid is to use a slightly chamfered cylinder. We generally ignore a small (10% of radius) chamfer on the edges of the cylinder, as it is not likely that this region will have sample of interest, or be able to be shimmed, or have usable B , homogeneity. Local gradient coils with rms relative deviations 0 above 40% have been used by the major MRI manufacturers and have not posed serious problems in distortion correction [9-111. However, for microscopy, it may be better to specify the size of the 4% and 10% cylindrical regions, as the gradient amplifiers are relatively inexpensive and sophisticated distortion correction software is not available from all microscopy vendors. In practice, distortion from B, susceptibility effects is usually more significant than distortion from gradient non-linearity in microscopy, irrespective of gradient coil design, as the sample is usually less than half the gradient coil diameter. General methods have recently been demonstrated that appear to be quite robust in dealing with a variety of sources of distortion, including gradient non-uniformity, susceptibility, temporal distortions in gradient waveform, and B , inhomogeneity [10,11]. As image postprocessing becomes more widely available in microscopy, we expect future trends to be in the direction of greater gradient non-uniformity so that higher continuous ratings and efficiencies (both switching and DC) and lower nerve stimulation can be achieved - a point we will return to later.

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60.2.4 Gradient Null Point In many microscopy applications, especially where the sample is quite long compared to its diameter (mice, rats, plants, etc.) and in human head MRI with local gradient coils, the location of the nearest gradient null point (field inflection poinr, zo) is more important than linearity, as signal from this region begins folding back and there is nothing that can be done to improve a multi-valued function by post-processing. Most conventional inductance-minimization optimizations put this point (which is located on the z axis) at an axial distance from the center just 20% to 30% beyond the edge of the nominally linear region. In our recent microscopy optimizations, the gradient null point is pushed axially outward an additional 30% to 40% for all gradients (see Table 60.1). This makes it much easier to insure that rf sensitivity from a body coil is low enough in this region to avoid fold-buck problems with long samples. While this also helps linearity near the center at the axial ends, it comes at a price - primarily in reduced qs and increased Bo eddies. It also requires an increase in overall coil length, which may compromise multinuclear rf tuning, but it is usually justified for the above applications.

60.2.5 Eddy Currents and Recovery Time The external fields from unshielded gradient coils may induce enormous currents, similar in pattern to the gradient windings but of opposite sign, in the external construction materials. The time constants for the major eddies from unshielded gradients in moderately large magnets are typically characterized by a relatively fast component (several milliseconds) from the stainless cryostat, a moderate component (tens of milliseconds) from the first copper radiation shield (78 K), and a slow component (hundreds of milliseconds) from the cold (- 20 K)radiation shield. In small magnets, the time constants are proportionally smaller. The typical magnitudes of the induced gradient fields are about 60%, 20% and 4% for coilhore diameter ratios of 0.9, 0.7 and 0.5 respectively. The time dependence imparted by the eddies may be largely compensated either in hardware or in software by multi-exponential eddy current compensation (ECC),which is achieved by simply applying the proper combination of high-pass filters to the gradient waveform [12], but this does not address cryogen boiling from Z2R heating of the shields and acoustic modes in the shields. Moreover, power dissipation in the amplifier output devices is increased dramatically, and resistance changes from eddy heating of the shields make the compensation strongly dependent on the pulse sequence

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and history. More effective post-processing methods based on wavelet transforms, which eliminate eddy current effects under many conditions [ 131, have recently been demonstrated, but still one is left with the effects of strong acoustic modes and heating in the radiation shields. The best solution is to start with external active shielding coils [1,14,15]. A shielding factor (SF)can be defined as GdGE, where G, is the gradient produced by a long square current pulse at the rated peak current and GE is the mean residual firstorder gradient in the sample region shortly after the current pulse vanishes. It is probably more customary to characterize shielding effectiveness by the relative residual linear gradient or GE/GP. SF depends sharply on the distance to the cryostat cold shield; in microscopy, we typically assume a cryostat cold shield radius 40% greater than the gradient shield radius. When the ratio of magnet bore diameter to gradient coil diameter is greater than 2, shielding is often not required, even for fast waveforms with relatively large residual gradients if the compensation is sufficiently accurate and complete - for example, with asymmetric torque-balanced unshielded gradient coil designs [4,16]. (It should be noted that the above referenced asymmetric designs assume a uniform B,. More accurate designs that take into account the non-uniformity of the external B, have also been proposed, but they have a large dipolar far-field component and hence generate larger eddy currents.)

-

e

Fig. 60.2:The Schenck transverse "finger-print"gradient coil.

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The classic, etched 'fingerprint' design of John Schenck et a1 [2], as illustrated in Fig. 60.2, achieves high qs and linearity, and it can easily be shielded, as shown by Pete Roemer et al. [14]. The first-order cryostat eddies from minor shielding errors have time constants about an order of magnitude less than B, eddies and thus may be easily compensated or sometimes ignored. However, the high current-concentration ratio of the inductance-minimized design limits power handling and exacerbates acoustic problems, as will be seen later. Another minor problem with low-inductance coils of this type is that the high-frequency current distribution in the wide portions of the foils is quite different from the low-frequency distribution [ 171. That is, eddy currents are generated within the gradient and shield conductors on the driven axis and on the orthogonal axes, although these time constants are quite short. While the dominant eddy from an unshielded gradient is always the respective linear component, the largest residual eddy in 3-axis shielded gradients is usually the B, eddy from manufacturing tolerances in the z-gradient [ 181. Low-amplitude, slow B, eddies (tens or hundreds of milliseconds) are induced in the magnet shields primarily from minute variations in coil diameters along the axis or from axial registration errors between the gradient and shield coils. Fast components (under 100 ps) may arise from axially asymmetric distributions of metallic structures in probes, cryostat shields, or shim sets. Whatever the source, they can easily be compensated by a time-dependent correction (a derivative of the gradient signal) applied to a B, shim coil. The correction is normally quite small (usually 0.1 to 1 ppm, depending strongly on the shieldgradient coil diameter ratio and manufacturing processes). It is often easier to add a separate, light-weight B, coil to the gradient coil assembly than to apply the correction to the existing room-temperature Z , shim coil driver. Another approach is to add a time-dependent correction to the receiver reference frequency or to the FID phase [ 191, When ECC (high-pass filters or "pre-emphasis")is not available (as on some older NMR spectroscopy systems), the gradient in a perfectly shielded gradient coil driven by a constant-voltage amplifier will decay exponentially with a time constant given by UR, where RE is the resistance of the gradient coil. This time constant is often tens or hundreds of microseconds for small coils and milliseconds for large coils. When the coil is driven by a constant-current (CC) supply, the appropriate resistance is the small-signal amplifier output impedance, which is infinite for the ideal CC amplifier. However, the output impedance in real, high-power CC amplifiers varies from -100 R to perhaps 10 kR below -100 Hz and decreases inversely with frequency above 500 Hz, which limits actual U R time constants under CC to typically 1 to 100 ps. More comments about amplifiers will be made later.

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F. D.Doty

Interaction between the rf and the gradient coils makes rf tuning unpredictable unless a full, symmetric rfshield is included between the gradient coils and the rf. Some prior rf shields have introduced image artifacts because of acoustic resonances, some have caused eddy current problems for fast gradient techniques, and many have severely degraded rf coil performance [20,21]. A surprisingly large number of patents have been issued for various slit patterns that minimize gradient interactions while providing rf shielding (generally with high loss and over a narrow band), but their utility is primarily limited to large gradient systems where gradient power loss otherwise can be several kilowatts. For microscopy, where rf tuning flexibility and unloaded rf sensitivity are paramount, the best approach is a full cylindrical copper shield about three skin depths thick at the imaging frequency (20 microns at 100 MHz, for example) just inside a somewhat thicker shield of low-conductivity alloy at the largest possible diameter. Even then, sensitivity is improved about 20% (for a 12 mm rf coil at 400 MHz, for example) when the rf shield-to-coil diameter ratio in increased from 1.5 to 1.8. The time constants and power dissipation of the eddy currents induced in the rf shield depend as much on the distance between the gradient coil and rf shield as on the shield conductance. There has been some confusion in the literature about the time constants and significance of these eddy currents in echo planar imaging (EPZ). The appropriate U R comes from the leakage inductance between the coil and the rf shield and the loop resistance in the rf shield. Minimizing the separation distance minimizes the rf shield time constant (by reducing leakage L) but increases power loss during switching. For small coils with closely spaced continuous rf shields as described above, this time constant can easily be under 1 ps, and the gradient attenuation (a simple resistive loss) will be quite acceptable up to at least 10 kHz. The increased gradient power loss at high frequencies is distributed between the rf shield and the stainless steel bore tube of the cryostat, as the presence of the rf shield spoils the gradient shielding at higher frequencies. The time constants of eddies in the stainless steel tube are also very short. More significant (but still minor) internal eddy currents arise from the interactions between the three orthogonal gradient coils when heavy windings are used, as the skin depth in copper at 6 lcHz is only 1 mm, and there are indications that some future imaging modalities (e.g., transverse acoustic strain elastography) may benefit from gradient frequencies at least this high. Some improvement is obtained by restricting the z windings from the narrow window regions of the transverse gradient coils, as their transverse DC fields are highest there. This restriction is somewhat detrimental to z-gradient linearity,

657

60. MRI Gmtiient Coil Optimiztitioii

but appears to be justified for EPI, as ghosts generated from eddy currents above first order are not well addressed by standard ECC and calibration scan methods, although more sophisticated methods appear to work better [22].

60.2.6 DC Efficiency and Continuous Gradient Rating Surprisingly, almost all prior optimizations are completely silent on what is coming to be recognized as the most important problem in microscopy gradient optimization - the continuous gradient rating. The few prior works that recognize the importance of resistive losses in the coil usually calculate this parameter after, and essentially independent of, the coil optimization [4,17]. Yet, if resistive losses can be kept low enough, forced air cooling is often adequate, which simplifies experimental setup and improves reliability. Also, high-velocity water cooling may cause image artifacts of microphonic origin. Low frequency (LF) or DC efSiciency qLmay be shown to be given by the following expression [ 31:

"=

200a2 d i hs poRE

(60.2)

where RE is the coil resistance in ohms and the constant coefficient has units of m/s. This expression stands apart from the rest of our efficiencies in that it is dimensionless only by virtue of the constant's units, and it implies that cooling problems become more severe with smaller gradient systems. Since a is proportional to n and RE is approximately proportional to n2 for a given coil geometry and copper mass, qL, like qs, is essentially independent of the number of turns. LF efficiency increases with conductor mass, but it is particularly sensitive to conductor thickness in regions of high surface current density. For reliability, cooling effectiveness at local hot spots near the ends, where surface current density is higher by factors of two to four in conventional optimizations [2,4,6,7,1416,23,24], is even more significant than total LF efficiency. Because of the importance of reliability we typically limit current concentration ratios (volume density ratios) to about a factor of 1.4. Multi-layer wire windings in critical areas combined with crescent coils [3] have permitted high-gain designs with higher LF efficiency and much lower current concentration than is possible with etched or laser-cut foil patterns, particularly in small coils

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F. D. Dory

with extended imaging lengths. This is only partly because the use of enameled wire and the elimination of composite substrates allow a higher ratio of copper to insulator in critical areas. Among other factors, the total thickness of the windings in our gradient coil for a 3-axis microscopy set is about 15% of the radius in regions of maximum current density, which appears to be 2 to 7 times thicker than most other designs. Even with this much copper, internal eddy currents may be kept small by proper attention to symmetries and transparency in critical areas. For example, we typically measure inductance at 15 lcHz before the rf shield is added to be only 2% less than that at 4 kHz. As with switching efficiency, the above LF efficiency is less meaningful in microscopy applications where the sample is quite small compared to the gradient coil; the simple ratio, a2/R,, is more useful. This "DC"ratio, the current concentration ratio, and the cooling effectiveness determine the maximum continuous gradient. Unfortunately, the cooling effectiveness is not easily reduced to a simple expression of well-defined variables and it is often highly dependent on localized coolant flow rate - whether air or water. Thus, it is essential that a maximum continuous gradient (meaning many months, DC) be determined by the manufacturer for a specified coolant flow rate for the specific model. Some manufacturers have confused continuous gradient ratings by calling a rating for one second a continuous rating, even though many microscopy applications require hours of run time and t h e m 1 time constants in microscopy coils are typically 3 to 30 minutes. Since thermal time constants are usually at least three orders of magnitude greater than the gradient pulse length, maximum duty cycle (at least down to 0.3%) is simply (ims/ip)2, where i, is the pulse current and ,,i is the hue continuous rating, assuming the coils and leads are very well secured. Continuous ratings are normally given for a single, driven axis and must be lowered about 10% to 30% when two or three axes are driven hard simultaneously.

-

60.2.7 Water Cooling Using an alumina-ceramic gradient-coil former (rather than a plastic composite) increases stiffness by nearly two orders of magnitude, which gives exceptional dimensional stability for improved gradient accuracy and greatly reduces low-frequency noise and vibration, as discussed later in more detail. However, its greatest advantage may lie in the simplification it permits in cooling [3]. Its very high thermal conductivity helps

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659

equilibrate hot spots and allows efficient cooling via a thin water jacket on the inside of the gradient coil. This approach has proven effective in several small microscopy gradients sets (up to 1000 Gkm) and PFG coils up to 2000 Gkm. Using an internal water cooling jacket has the additional advantage of keeping the internal rf shield at a relatively low temperature (below room temperature), thereby reducing its contribution to Johnson noise in the rf coil. The efficient flow geometry of an internal water jacket permits operation at reduced pressures and minimizes turbulence for reduced microphonics, but excellent results have also been acheved with water directly flooding epoxy-coated conductors. The most significant limitation to heat removal in multilayer windings is the polymeric insulation between layers, which must withstand a high-voltage (often >300 V) isolation test, but this limitation becomes even more severe with composite substrates between etched coils. Water cooling of microscopy coils typically increases the continuous gradient rating by a factor of two to three, which is comparable to the improvement that is possible by simply optimizing for high DC efficiency. Water cooling of large gradient coils has often been implemented by running water through copper cooling coils bonded over the hot spots on the gradient coils. Here, the cooling coils, in addition to requiring low thermal resistance to the windings, must satisfy a rather stringent serpentine path requirement: To avoid coupling to the gradient transients, they must be magnetically orthogonal to the X, Y, and Z gradient coils. Moreover, since they are located in the near-field region, a detailed time-dependent electro-magnetic FEA model is required to achieve sufficiently low internal eddy currents. This is the only time orthogonality becomes a real issue in gradient design. With expensive apparatus, it is standard procedure to use an isolated cooling loop of distilled or deionized water and a commercial heat exchanger connected to the external water supply. Standard pumps, over-temp, coolant flow, and coolant-level sensors are required along with a simple control system.

60.2.8 Force Cancellation and Acoustic Efficiency All symmetric gradient designs have zero net torque and zero net force in a uniform external field, and this is essential unless substantial effort is put into magnet and gradient structure reinforcement and safeguards. However, there are always large local forces and torques within the coil system that cause localized deflections, vibration, and acoustic noise [25].Moreover, most failures we see are fatigue-related (inadequately secured

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F. D. D o ~ y

conductors that are too thin in the radial direction) and only indirectly heat related - the low-frequency vibrations increase sharply above the glass-transition temperature of the coil encapsulant or coil-form matrix. While it is desirable to eliminate acoustic noise in whole-body MRI for reasons of patient and operator comfort and safety [26], another reason is that some of the image artifacts attributed to eddy currents in actively shielded gradient coils are more likely acoustic in origin. We have compared the recovery time of a conventional (minimum inductance) microscopy gradient coil with SF (shielding factor) greater than 200 but with high acoustic efficiency to a crescent-type coil (at comparable Bods) with SF c 70 but having ultra low acoustic efficiency. The former had recovery time (to field homogeneity of 0.2 ppm) greater than 20 ms. The latter had recovery time less than 20 ps, which is three orders of magnitude improvement! Moreover, EPI ghosts are often completely undetectable with crescent coils, even without employing advanced artifact reduction techniques. Four ways of addressing the acoustic noise problems are currently being pursued by various groups: (1) ear plugs and enhanced acoustic absorption in gradient construction 126,271, (2) active acoustic cancellation headphones, (3) increased coil-form sfifiess [28], and (4) force-cancellarion to minimize electro-mechanical acoustic eflciency [3,29,30]. The last of these approaches is the most beneficial in improving image quality, as the reduction in the efficiency of generating acoustic energy will reduce the efficiency of the acoustic energy coupling back into the magnetic field and altering it. This acoustic efficiency is a complex function of frequency, but some low-frequency and high-frequency approximations can be expressed in simple form. The electro-mechanical efficiency - which we desire to minimize - is defined as the ratio of peak mechanical energy (potential plus kinetic) of the coils to electromagnetic gradient energy in the sample region. The acoustic problem may be divided into three regimes: low frequency, near fundamental resonances, and high frequency. The fundamental transverse bending mode of a uniform, medium-walled cylinder, heavily loaded at both ends (the typical case), is the mode most strongly excited in the standard, torque-balanced transverse gradient coil. Its angular frequency q, is approximately mb

5rf c

h2

(60.3)

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66 1

where rf is the mean cylinder radius, h is the cylinder length, c = (Y/p)”* (the velocity of transverse acoustic waves), Y is Young’smodulus of elasticity, and p is the mass density. This assumes that the multi-layer coil-forndcoil structure is solidly laminated and may be characterized by an effective Y and an effective p. For a typical microscopy fiberglass gradient-coil form, 80-mm in diameter, covered with copper windings, %/2n is in the range of 300 to 1500 Hz. The bending stiffness k, (N/m) of a cylinder with wall thickness w (where w << rf) is approximately

(60.4) The mechanical energy U , in the LF regime (well below %) is approximately

UM

=

Fb2 -

(60.5)

2kb

where Fb is the Lorentz bending force near the center. By using ceramic coil forms (very large Y) or by placing stiffening struts in the space between the gradient-coil form and the shielding-coil form (effectively increasing w and Up), k, and +,CI are increased and U , may be reduced to a negligible level throughout the LF regime. Similar results are readily obtained for the axial gradient built from distributed Maxwell pairs. Partially filling the space between the gradient-coil form and the shielding-coil form with rigid composite struts has the additional beneficial effect of reducing LF acoustic efficiency by providing a rigid mechanical coupling (of length much less than an acoustic U4) between oppositely directed forces, thereby achieving partial force cancellation [ 2 8 ] . For Roemer and related coils with typical shieldgradient ratios, the force cancellation is about 30% and this approach now appears to be common practice. Even with ceramic coil forms and rigid struts between the gradient- and shieldingcoil forms, it is not possible to make % large enough to ensure that mechanical resonances will not be excited by the high-frequency components in fast-switching pulses. Hence, it is also necessary to look at the resonant and high-frequency acoustic regimes. It may be shown that for shielded Golay coils [31] of the type shown in Fig. 60.3 in external magnetic field B,, the acoustic efficiency in the high-frequency regime qmhis approximately (in SI units),

662

F. D.Do@

(60.6)

where rg is the coil radius, rg is the gradient pulse length, inC is the effective mass of the coils, and rs is the shield coil radius. Note that the efficiency in eqn. (60.6) is independent of coil-form stiffness but is inversely proportional to coil I I Z U S S . This efficiency normally increases with rg because tg increases faster than inc/rg.

Fig. 60.3: Heavy, wire-wound Golay coils.

The above acoustic efficiency may range from less than 1% to more than 1000% meaning the acoustic energy may be more than 10 times the useful gradient magnetic energy. (With a little reflection, this should not come as a surprise, as the gradient field energy within the sample can easily be less than 5% of its total magnetic energy, and highly efficient loudspeakers are driven by voice coils in fields of about 1 T.) As the pulse repetition frequency approaches a,,. eqn. (60.6) under-estimates acoustic efficiency by a factor comparable to the mechanical Q , which may exceed 10. The increased acoustic motion from the high-cun-ent-density regions in inductance-minimized etched, lasercut, or even wire designs can lead to rapid failure at high fields. Note that it is the volume

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(not surface) current density and other tightly coupled mass that are important here. Recall that volume current density is also the more important (but often ignored) factor in continuous gradient rating. There are two methods of reducing HF coil motion: (1) Increasing the effective coil mass, especially where volume current density is high; and (2) Increasing the efficiency of force cancellation, which may increase the constant in the denominator of eqn. (60.6) from 2 to 20. Force cancellation requires coil geometries not constrained to simple cylindrical surfaces [29,32,33]. Also, these coil geometries shift the acoustic response to the low-frequency regime, where the electro-mechanical efficiency is several orders of magnitude lower and is inversely proportional to stiffness and other geometric factors. Increasing coil-form stiffness, on the other hand, will increase coil motion of the dominant HF modes. This seemingly counter-intuitive result has been well understood for many decades in the loudspeaker and sonar industries [34]. Although manufacturing of the above referenced force-cancelled approaches for 3-axis systems may appear impractical, we have developed related geometries, crescent coils, with similarly low acoustic efficiencies that are readily manufacturable [3]. Moreover, the crescent coils may be readily combined with golay coils to permit much higher DC efficiency while still retaining 90% force cancellation in the critical, central region. This approach to force cancellation, which we will return to in more detail in a later section, typically gives a 25 to 35 dB reduction in vibration and noise with dramatic reductions in EPI ghosts while permitting higher continuous gradient ratings - largely by eliminating hot spots. The conventional approach, on the other hand, to MRI noise reduction (adding absorptive materials) seldom reduces broadband acoustic noise by more than I 1 dB [26] and may complicate access, thermal, background, and tuning problems.

60.2.9 Nerve Stimulation For research groups planning to use fast gradient techniques on relatively large, live animals, nerve stimulation is likely to become an issue, as it is presently the critical, limiting factor in whole-body MRI [35]. Force-cancelled designs have been shown to have lower nerve stimulation than traditional designs [32] because of lower transverse fields and lower peak field regions (which is the critical regulatory criterion).

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If EPI or related techniques are eventually to be used in whole-body MRI at high fields, it will be necessary to develop the techniques with gradients of high non-uniformity and improved distortion correction software [10,11], as this is the only way to further reduce maximum field within the subject for a given mean gradient in the region of interest. Even in microscopy, it may be desirable to trade some gradient uniformity for reduced nerve stimulation and enhanced switching performance. We find, for example, that a degradation in gradient uniformity from 10% to 12%, gives a 5% to 10% decrease in rise time and nerve stimulation is decreased by about 10%. We have quantified peripheral nerve stimulation by indicating BMIBG, where BM is the largest change in field magnitude, averaged over any area equal to 10% of the sample cross-section, generated by the gradient coils anywhere within an arbitrarily long cylinder of diameter equal to the maximum sample diameter, and BG is the maximum i component of the gradient field within the sample region for an ideal gradient field having perfect uniformity.

60.3 Gradient Amplifiers The matching of the gradient coils to the gradient amplijier with peak current capability i p and peak output voltage Vp is characterized by the following parameters: peak gradient G , = a i , (when i p R E c Vp) and rise time 2, from 5% to 95% of G,. For an amplifier with zero rise time, 2,

z

L ip L GP Vp - ip R E 12 a(Vp- ip RE 1 2 ) ’

(60.7)

when ipREc Vd2, which is often not satisfied in microscopy. In fact, ipRE is often not much less than V,, in which case Gp = a Vp/R,. The rise time of the amplifier (typically 4 to 6 p)must be added to the above for total rise time, and more accurate values may be readily obtained by solving the appropriate differential equations when the above approximations are not adequate. The rise time increases linearly with G, for small values thereof, but 2, increases exponentially as the limit is reached. As previously mentioned, settling time to withm 0.2% of the final value is usually greater than rise time in microscopy. With well designed gradients, this is primarily

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determined by amplifier bandwidth and ECC flexibility unless pre-emphasis is not used, in which case it is determined by output impedunce in CC mode. Clearly, fast switching requires high voltage, and high gradients require high current. In microscopy coils, the high values of gradient gain

( a ) make DC drift and noise critical specifications, and

balanced input (or optical isolation) is absolutely essential. The use of crossed-diodes (even Schottkey type) in the output for noise squelch is generally not an acceptable alternative

-

especially for multiple-quantum techniques, which depend on a linear response

to very low levels. Extra high output impedance is beneficial for fast settling of inductive loads without pre-emphasis, but it is even more essential for minimizing the coil heating effects on gradient magnitude, as a 30 "C increase in coil temperature reduces coil current by 10% with a constant-voltage amplifier. In some diffusion experiments, the integrated gradient in bipolar pulses must be matched within 10 ppm, which is quite difficult with amplifier output impedances less than 1000 times the coil resistance. The HighlandTh' amplifiers excel in this regard, although their low VA product (- lo00 W) imposes serious limitations on gradient strength and rise time with all but the smallest gradient coils - i.e., settling time may be less than rise time. One reason for the common perception that minimizing inductance is a primary objective is that linear power amplifiers become much more expensive (per watt) for V, above 300 V. However, they also become more expensive for i, above 250 A, and 1000 V dual-level amplifiers are becoming available. Switch-mode amplifiers become more cost-effective for VA above 20 kW (especially above 300 V) and have been used very successfully in conventional whole-body MRI, but their low bandwidth (-5 kHz) severely limits their utility in microscopy, EPI, and elustogruphy using MRI with transverse acoustic waves [36]. An alternative approach that appears to combine the best of both approaches is a linear amplifier powered by a "piggy-back'' power supply (a lowvoltage supply riding on a high-voltage supply) that is able to efficiently provide high voltage at low current and low voltage at high current with virtually no switching noise and minimal charge-up delay [37]. Transmission line inductance (typically 1 pWm) in the cables between the amplifiers and the coils becomes significant for coil inductance below 100 to 200 pH. The use of cumbersome low-impedance cables (0.2 pWm) is necessary with very-low-inductance coils. Hence, optimum coil inductance is typically 50 to 200 pH except for whole body

EPI, where somewhat lower values may be needed until higher-voltage supplies become more readily available.

666

F. D. Doty

For EPI with tuned gradients, qsQE is a useful electrical efficiency figure of merit, where the gradient coil electrical quality factor QE (typically 2 to 4 for large microscopy coils at 2 kHz) is measured at the read frequency. In this case, transmission line losses and rise time considerations essentially vanish. One simply matches the amplifier design load impedance to wLQE. The amplifier cost may be cut by nearly an order of magnitude, even though QE is rather low. However, tuned gradients are unsuitable for other fast gradient methods, such as spiral scan, and are not even well suited for EPI, as trapezoidal waveforms are better than sinusoidal.

60.4 The Crescent Coil Design At least three groups (Mansfield, Roemer, and Doty) were independently working on actively shielded gradient coils by 1985; and in early 1991, we began exploring approaches to solve motion-related artifacts in high-field microscopy coils and to increase duty cycle. The crescent coil design which evolved along with the dimensionless analysis has proven to be extremely effective in controlling the vibrational problems otherwise encountered in high-field high-performance microscopy. The crescent gradient coil design is described in more detail elsewhere [3], but a brief description is provided here. A high-conductivity ceramic coil form is used to improve rigidity and cooling effectiveness for 3-axis MRI gradient coil configurations on a single

Fig. 60.4: Crescent coils - zero net torque when aligned with Bo.

60. MRI Gradient Coil Optitnizarion

667

cylindrical coil form aligned with Bo. Normally, eight crescent-shaped, axially aligned solenoid-like coils, as shown in Fig. 60.4, are attached around the perimeter, bisecting the equatorial plane. The four crescent coils aligned on an X or Y axis contain windings for the X or Y gradients respectively. The four crescent coils between them contain windings for both axes with proper phasing of the X and Y coils.

Fig. 60.5: Partially assembled crescent gradient unit.

The design is similar to the "ConcentricReturn Path" concept by Brey, Andrew, and co-workers, the force-cancelled arc-loops of Mansfield and co-workers, and the reducednerve-stimulation design by Frese et al. However, the first key improvement (which makes this design manufacturable) is that fewer 3D coils are required, and they may be independently wound, encapsulated, and tested prior to mounting on the main cylindrical form. The second key achievement is that qs and qLmay be improved by nearly an order of magnitude (compared to the alternative force-cancelled approaches) by (a) using inclined crescent windings that reduce the surface current density on the outside relative to that on the inside, (b) by combining the crescent coils in an optimized way with heavy Golay coils, and (c) by permitting higher surface coverage by the windings. The third improvement is that heat removal in regions of high power density is much more effective; and the fourth advantage is that by properly controlling the current densities on the crescent coils, the severe over-shielding near the center that characterizes other force-

668

F. 0. D o ~ y

canceled designs is eliminated. It is usually also beneficial to add minor transverse shielding Golay coils at each end, but power density there is very low so vibration is easily controlled and resistive losses are negligible. Figure 60.5 shows a mostly complete 50-72 gradient assembly (some shielding coils, one crescent coil, and some z-windings at one end are omitted for better clarity). Some have suggested that using wire is inherently inferior to using etched (or lasercut, or water-jet machined) foil patterns. One argument for machined foils is more control over surface current density, which helps a little with linearity and switching efficiency in most cases. Unfortunately, it also creates high-current-density regions which limit the maximum gradient rating and are the source of most of the acoustic noise. The combination of wire-wound crescent coils with wire-wound golay coils allows adequate control over current densities for comparable linearity and switching efficiency with the advantages of greater robustness, higher continuous and pulse ratings, much less vibration, reduced internal eddy currents with heavy windings, less image fold-back, and less nerve stimulation. It often appears initially that machined foil patterns permit easier manufacturing. Indeed, considerable effort has been required to develop effective manufacturing processes for precision crescent coils and heavy-gage golay coils. However, except for low power applications, we doubt that alternative approaches are significantly less costly. Finally, it has been suggested that etched coils are more precise, but it appears the crescent/golay coil approach achieves lower Bo eddies, which is probably the best indicator of manufacturing precision. Perhaps one reason this design has not been explored by other research groups is that it lacks the simple symmetries that are required for analytical solution. For that reason have never even attempted an analytical solution, although we have developed approximate parametric models. However, the fields, resistance, inductance, forces, torques, and gradients can easily be calculated by numerical methods from elementary laws (BiotSavart equation, Ohm’s law, and various basic relationships) for any set of conductors with known currents, from which the various dimensionless optimization efficiencies are easily calculated. Hence, our approach was to develop robust, flexible, easy-to-use software with simplex optimization capabilities and let the simple-minded computer go to work on it. We have not incorporated coil susceptibility calculations into the optimization, as we have not found this difficult to address separately from the rest of the optimization space. However, the software has also been found to have advantages in solving certain rf and susceptibility problems [38].

60. MRI Gradient Coil Optimization

669

Using predominantly dirnensiqnless parameters (a carefully weighted sum of qs, qL, and qmh)with less weight on a few dimensioned variables (L, RE, q,, mc) in the simplex optimization function makes it much easier to consistently arrive at a globally optimum solution that addresses all of the issues in MRI gradient coil design for different systems. Of course, trade-offs are a part of any optimization. For example, moving the nearest gradient null point zo further out and improving linearity come primarily at the expense of reduced switching efficiency. Increasing the continuous gradient rating comes from reducing current concentration ratios and increasing copper mass - which requires some loss in switching efficiency or linearity and increased manufacturing costs. It is difficult to fully incorporate all of the manufacturing constraints into the software, so an experienced engineer has to periodically apply additional constraints in guiding it to an optimal, manufacturable solution. However, one of the strengths of our computational approach is that discretization of current distributions after the optimization is not required, as wire dimensions and even end allowances are incorporated into the optimization from the very beginning. The design typically ends up as follows: (a) the crescent coil length is comparable to the length of the high-homogeneity (4%) sample region; (b) the volume current density in the Golays is about 40% higher than in the axial crescent coils; and (c) the volume current density in the Golays is comparable to that in the diagonal crescent coils, as these coils require windings for both transverse axes. Also, the Golay coils typically (a) have axial length comparable to the length of the crescent coils, (b) have maximum subtended angles of about 176", and (c) have window lengths about 4 times the wire diameter. The calculated performance parameters consistently agree within several percent with measured values, as shown in Table 60.1. For the standard supercon geometry, the data listed are for the two transverse axes, and the performance of the z-axis is considerably better. (Note that the second row is in the more familiar Gaussian units as preferred by most users.) The design of the z-gradient will not be discussed in detail because it is rather simple in comparison to the transverse gradients for a cylindrical coil aligned with Bo and because it has been extensively discussed in the literature [39,40]. Briefly, low-density foil windings are laid down before the crescent coils are mounted in the central region, and additional, high-density z-gradient windings are placed over the x and y Golay windings at each end. Performance of the z-gradient based on these modified Maxwell pairs always exceeds that of the transverse gradients, and for that reason the main z windings are placed outside the Golays. However, this results in more cumulative radial 0,SF,

670

F. D. Doty

positioning errors for the z-gradient and hence larger B, eddies, which may be addressed by a B, correction coil or data processing [13,18]. An alternative under consideration is to lay the entire z winding down first, as this should allow the B, eddy from the z-gradient to be reduced to about that of the transverse gradients, although performance of the transverse gradients will be reduced by about 10%. (This will also reduce acoustic problems in the z-shield windings, which are presently the primary acoustic source in our coils.) The B, eddy from a 10 ms x-gradient pulse of 10 G/cm in Doty model 50 - 72 W in an 89 mm magnet, for example, is usually less than 0.1 ppm with a time constant of about 15 ms. Space also does not permit detailed discussion of numerous, critical, manufacturing details that can end up killing an otherwise excellent design. Chief among these are (1) wire routing to minimize lead stray fields, as they can be too complex to shield effectively, (2) copper surface preparation for adequate adhesion to the encapsulant, (3) wire forming and bend relaxation allowances, (4) precision bench testing during production to permit detection and correction of errors, (5) formulation of an encapsulant having high thermal conductivity, arc resistance, and bond strength, and (6) fluid-tight designs that permit access to and repair of some of the more failure-prone components, such as power and fluid connectors and bridging conductors.

60.5 Quadrupolar Gradients for use in Transverse 230 Before concluding, a few brief remarks will be made about the other class of high-performance microscopy gradients - gradients for use in a transverse B, [41,42]. Even though electromagnets are not used at high fields and transverse access is inconvenient in a supercon, the quadrupolar windings commonly used in atomic beam confinement are sometimes chosen for PFG applications. They permit much higher efficiencies and linearity on two axes (Y and Z , where X is aligned with the coil-form cylinder axis) with respect to B , than can be obtained by the standard Maxwellian z-gradient - which outperforms conventional transverse gradients by a factor of 1.5 to 2. These coils owe their improved performance to their ability to produce a pure quadrupolar field throughout almost all of their enclosed volume, while other gradient coils produce substantial higher-order components.

67 1

60.MRI Gradient Coil Optimizution

Table 60.1. Doty 3-axes high-field gradient sets (low-impedance option).

Parameter'

Units'

Model Model Model

Model

Model

Model

20-42T 24-40 50-728 50-72W 66-98T I

2500

Pulse gradient Pulse dutvcvcle "..

1500

I I

2

%

12

Cooling method

water

I

Alumina ceramic coil form I

yes

Ring down time4

15 18

Gradient null point, h,-, 4% inhomo cvlin. Dia.. d ,

1

mm

16

10% inhomo cylin. Dia., d

18

10% inhomo cylin., lgh5

25

I

mm

18.0

Cu RF shield dia, dR

mm

20.0

Outside dia, do

mm

42.0

Coil half-length, ho

mm

28

Max L

I.LH

Clear I.D., d,

70 ~~

Max RE

a

0.8

Grad. Gain, a

mT/Am

125 1800 20

(single axis)

LF Efficiency, q

45

** * * 260

90

1

-

Shielding error7 at 1.5 d Total mass

0.8 kg

(Notes to Table 60.1 see page 672)

0.2

1

8

2

20

water

2

1I

9

2-k water

yes 15

14 15

I

25

37

32

32

46

1

64

38

50

22.0

47.0

47.0

66.0

84.6

50.0

72.6

119.5

85

1

21

1

35

42

65

1

130

110

I

32

75

I

75

~~

0.6

7.5

2000

1

250

180 35

4.1

65

Nerve stimulation: B

85-120W I

I

70

70

1.5

0.6

0.2

1.5

672

F. D. Dory

Notes to Table 60.1: 1. Performance is indicated with a Techron model 7780 amplifier: 180 Ap; 140 Vp; 100 dB SIN: DC-30 kHz power bandwidth. Data for models with T suffix (Transverse Bo) are given for the two strong axes. For the other (standard supercon) models, data are given for the two transverse axes, and performance of the z gradient is considerably better. 2. Continuous rating (100% duty cycle) is indicated for a single axis. For the magic-angle gradient ( X + Y + Z),the resultant gradient (1.7 Gc) is rated at 50% duty cycle. 3. Rise time, with leads, 5% to 95%, for at least two axes. 4. Ring down, approx. time from 5% to 0.2% with optimized ECC and rf shield. 5. RMS gradient inhornogeneity, excluding 10% chamfer on edges of sample cylinder. 6. Noise, approx. A-weighted; 128 x 128 EPI scan, 30 G/cm read, at 7 T. 7. Shielding error is the relative 1st-order residual gradients from eddies in a cryostat radiation shield 1.4 times the outside diameter of the gradient set.

Table 60.1 includes several of these coils denoted with the suffix T, for Transverse geometry. The data listed for these coils are for the two high-performance axes. The third axis is obtained from a conventional transverse coil design, and its performance is less by at least a factor of 2.

60.6 Conclusion The switching efficiency is one of the more important figures of merit for high-performance MRI in large samples at high fields because gradient amplifier cost is proportional to ipVp High DC efficiency, low current concentration ratios, and high cooling effectiveness are more important in microscopy because of their relationship to maximum continuous and pulsed gradient ratings. The location of the nearest gradient null point is often more important than linearity, as standard methods of specifying the latter have not been agreed upon and distortion correction methods are becoming more successful. Effective RF shielding must be included in the gradient design, and its RF loss is often critical in microscopy but rarely adequately addressed. Achieving low acoustic efficiency and high shielding factor are also extremely important because of their relationship to recovery time, image artifacts, and reliability. Noise, drift, and output impedance in constant-current mode are critical amplifier specifications for microscopy. Perhaps other manufacturers will follow by providing more detailed and well-defined gradient coil specifications to better enable researchers to plan experiments.

60. MRI Grudienr Coil Optimization

References 1.

P. Mansfield and B. Chapman, J. Mugn. Reson. 66 (1986) 573-576.

2.

J. Schenck, M. Hussain. and W. Edelstein, U.S. fat.4,646.024 (1987) GE.

3.

F. D. Doty and J. Wilcher, U.S. fat.5,554,929 (1996) Doty Scientific.

4.

D. C. Alsop, T. J. Connick, Magn. Reson. Med. 35 (1996) 875-886.

5.

W. H. Muller, U.S. Par. 5,406,205 (1995) Bruker.

6.

R.Turner,J. fhys. D:Aypl. fhvs. 19(1986) 151.

7.

Y.P. Du and D. L. Parker, Mugn. Reson. Itnug. 14(2) (1996) 201-207.

8.

S . Crozier and D. M. Doddrell, J. Mugn. Reson. A 103(3) (1993) 354357.

9.

P.Roemer, U.S. fut.4,926,125(1990)GE.

10.

P. S. Morgan, R. W. Bowtell, and B. S. Worthington, Proc. 5th ISMRM, Vancouver, 1997.

11.

N. Gai and L. Axel, Mugn. Reson. Med. 37 (1997) 275-284.

12.

J. J. Van Vaals and A. H. Bergman, J. Mugn. Reson. 90 (1990) 52-70.

13.

D. Barache, J-P. Antoine, J-M. Dereppe, J. Mugn. Reson. 128 (1997) 30-41.

14.

P. B. Roemerand J. S. Hickey, U.S. fat.4,737,716 (1988) GE.

15.

P. Mansfield, B. L. W. Chapman, R. Turner, and R. M. Bowley, U.S. Pat. 4,978,920 (1990) N.R.D.C., London.

16.

A. M. Abduljalil, A. H. Aletras, and P-M. L. Robitaille, Mugn. Reson. Med. 31(4) (1994) 450-3.

17.

M. A. Morich, J. L. Patrick and G. D. DeMeester. US.Pat. 5,424,643 (1995) Picker.

18.

Q. Liu, D. G. Hughes, P. S. Allen, J. Mugn. Reson. B 108 (1995) 205-212.

19.

R. J. Ordidge and I. D. Cresshull, J. Mugn. Reson. 69 (1986) 151-155.

20.

P. B. Roemer and W. A. Edelstein, U.S.f a t . 4,871,969 (1989) GE.

21.

R. Rzedzian and C. Martin, US.Par. 5,243,286 (1993) Advanced NMR, Mass.

22.

M. H. Buonocore and L. Gao, Mugn. Reson. Med. 37 (1997) 591-599.

23.

G. Pausch, U.S. Put. 5,309,107 (1994) Siemens.

24.

M. A. Morich, L. Petropoulos, D. A. Lampman, U.S. f a t . 5,485,087 (1996) Picker.

25.

R. Hunvitz, S. R. Lane, R. A. Bell, M. N. Brant-Zawadzki, Radiology 173 (1989) 545-548.

26.

S. A. Counter, A. Olofsson, H. F. Grahn, E. Borg, J. Mugn. Reson. I m g . 7 (1997) 606-61 1 .

27.

G. Miyajima and Y. Igarashi, U.S. fur. 5,256,969 (1993).

28.

D. Lehme el al, U.S. f u r . 5,235,283 (1993) Siemens.

29.

B. Chapman and P. Mansfield, J. Magn. Reson. B 107 (1995) 151-157.

30.

R. Bowtell and P. Mansfield, Mugn. Reson. Med. 34 (1995) 494-97.

31.

M. J. E. Golay and N. J. Rumson, U. S. fur. 3,569,823 (1971).

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F. D.Doh/

32.

G. Frese and E. Stetter, U.S. for. 5,198,769. (1993) Siemens, Munich.

33.

W. W. Brey. T. H. Mareci, and J. Dougherty, J . Mngn. Reson. B 112 (1996) 124-130.

34.

L. E. Kinder, A. R. Frey, Fundamenrals qfAcowtics, 2nd ed., Wiley, NY (1962)

35.

P. R. Harvey and P. Mansfield, M a p . Reson. Med. 32 (1994) 23641.

36.

R. Muthupillai, P. Rossman, D. Lomas, J. Greenleaf, S. Riederer, R. L. Ehrnan, Mngn. Reson. M e d 36 (1996) 266-274.

37.

W. F. Wirth and T. G. McFarland, U S . f a r . 5,451,878 (1995) GE.

38.

F. D. Doty, G. Entzminger, and A. Yang, Concepts in NMR 10 (1998) 133-156.

39.

B. H. Suits and D. E. Wilken, J . fhys. E. 22 (1989) 565-573.

40.

E. C. Wong, A. Jesmanowicz, and J. S . Hyde, Magn. Reson. Med. 21 (1991) 3 9 4 8 .

41.

R. A. Beth, US.f a r . 3,466,499 (1969).

42.

R. Bowtell and P. Mansfield, Meas. Sci. Technol. 1 (1990) 43 1439.

61. Novel, Asymmetric Gradient Coil Sets for Magnetic Resonance Microscopy Stuart Crozier, Wolfgang U. RofSmnim,and David M.Doddrell

Centre for Magnetic Resonance, The University of Queensland Brisbane, Qld. 4072 Australia

Abstract In the vertical bore magnets typically used for Magnetic Resonance Microscopy, space is at a premium. Usually, gradient sets in these systems have a large length-to-diameter ratio. For rat and mouse neural imaging, however, it is often preferable to use as large an animal as possible, and though the brain is the organ for imaging, it is the thorax that delimits the space. We have, therefore, developed an asymmetric gradient set that does not restrict the thorax of the subject. Asymmetric transverse gradient designs have been presented for MRI neural imaging applications [ 1-31 and are quite well understood, their major design challenge being to balance the residual forces and torques inherent in their structure. The more novel aspect of this work is the design of asymmetric G, gradients. In conventional head gradients symmetric G , coils are used. We present designs for G, coils where the linear region is very close to one end of the coil, importantly the effect of unbalanced B, components must be considered in such designs. The coil sets designed here are suitable for use in wide-bore (89 mm) magnet systems.

61.l Introduction We [4,5] and others [6] have shown that the Simulated Annealing method (SA) [7] is effective for compact MRI gradient design and so now apply this method to force and torque compensated asymmetric designs. With imposed dimensional constraints, the SA

676

S. Crozier, W.U. R o f i a n n . nnd D. M . Doddrell

routine effectively attempts to find the 'best' solution possible within these limits. Here 'best' refers to the minimization of an error function which, in this case, contains terms representing the linearity of the gradient under design, its quality of shielding and the residual forces and torques in the structure. It is possible to include other terms in the function such as efficiency and inductance as the designer requires. In both longitudinal and transverse coil designs, therefore, the optimization proceeds as a real space minimization problem. For each system re-arrangement a new coil configuration is generated. To evaluate each transverse configuration the coil is segmented, with each "loop" being segmented into at least 51 pieces. The transverse gradient was evaluated by Biot-Savart summations over a central quadrant of 17.5 mm by 17.5 mm at 60 points, the shielding characteristics were evaluated by summing the field along the z axis at 40 points for the extent of the magnet used at a radial distance of 45 mm, corresponding to the first eddy current source. For longitudinal gradient calculations, the Biot-Savart summations used for linearity measurements are replaced by a summation of zonal harmonics up to 12h order and referenced to the first zonal harmonic, which can be calculated directly from the coil pattern without field calculations and are therefore very rapidly deduced. The relative significance of each term may by adjusted by varying the weighting factors. By selecting a starting point for the coil configuration an initial error is calculated, a small random move in wire positions is then performed and the error re-evaluated. The stochastic algorithm decides which re-arrangements are to be accepted [4-71. We note that all components of B must be considered in the force and torque calculations as the coil extents outside the homogeneous region of the magnet and significant divergence of the field at the coil may be evident. A divergent field in this case is one in which B, and By are significant relative to B,. Importantly, torque compensation must take account of the characteristics of the particular magnet to be used. Using a similar argument, it is obviously preferable to use restricted length coils such that each end of the coil set experiences as similar static fields as possible. In a shielded set, the outer windings effect both a high degree of torque compensation and shielding and retain modest lengths for the gradient set. If the shielding and torque terms are equally weighted in the error function, the SA routine provides a compromise between the minimum of each of these two characteristics. In this case, additional windings were generated by the algorithm on the primary of the coil set to complete the forcehorque balancing.

61. Novel, As.vtnrnelric Gradient Coil Sets for Magnetic Resonance Microscopy

677

61.2 Transverse Coil Designs Design calculations were performed for shielded, asymmetric, transverse coils with torque and force compensation. A number of different magnet systems were used for the calculations to test the different compensatory requirements. The design process attempted to balance shielding quality, force and torque compensation with extreme positioning of the beginning of the linear region, that is, a high degree of asymmetry. Figure 61.1 shows the wire pattern for the compensated primary of a shielded transverse set where the force and torque compensation was optimized for a short, shielded magnet system [8]. The forces and torques experienced by Gy set before compensation were approximately 285 N and 42 Nm and those after compensation were 1.6 N and 0.9 Nm. Shielded magnet systems tended to generate more force and torque in gradient sets than unshielded systems; this is presumably due to the cancellation fields between the primary and the secondary coils creating a more rapidly diverging field at the ends of the coil structure. Figure 61.2 shows the 5% contours of the gradient field generated by Gy. Note that the coil end is arbitrarily set to be 0 mm and that it is approximately 120 mm long; the linear region begins approximately 15 mm from the end of the coil, indicating strong asymmetry with the coil structure. The gradients generates approximately 21 G/cm at

compensated primary 150

100 A

E E

Y

50

.-2 0

0

-50

0

20

40

60

80

100

z (mm) Fig. 61.1: Compensated primary pattern for G, in a short, shielded magnet. The vertical axis is circumferential in mm.

678

S. Crozier,

W.U. Rofiann, and D.M. Doddrell

50 amps and have a switching time of approximately 105 ps. Our preferred construction method for the transverse coils is laser-cutting of streamline sheets. The advantages of this method is that for a predetermined radial space they provide a low inductancehesistance implementation.

Gy 5% contours 21 G/cm 0 50A -60

-40

N

-20

20

0

-20

Y (mm) Fig. 61.2: A contour plot at 5% levels of the transverse gradient linearity in the zy plane.

61. Novel, Asymmetric Gradient Coil Sets for Magnetic Resonance Microscopy

679

61.3 Longitudinal Coil Designs Axi-symmetric designs for use in headheck gradient coils can present a difficulty in providing a linear regions close to the ends of the coil set. We therefore chose to investigate the design of non mi-symmetric sets with consequent non zero B, shifts. These B, shifts are able to be compensated by RF modulation techniques now available on most modem spectrometers [9,10]. This correction takes the form of phase/frequency modulation of rf transmitter and/or receiver as an offset to automated eddy current correction.

-mgnbe -0

-.- 90 ........210

-im

Fig. 61.3: The experimental field plots from the prototype coil. The field is in arbitrary units. Note the asymmetry of the linear region with the coil structure.

It was found that it was actually possible to position the beginning of the linear region exactly at one end of the gradient coil, the consequence of this extremity was a large B, shift. These calculations were confirmed by commercial analysis software (Vector Fields, UK). The dependency of extremity on B, shift was non-linear, although

680

S.Crozier. W.U.RofjCnarm. arid D.M. Doddrell

the obvious trend was a reduction of shift as the epoch of the linear re,'Oion was positioned more centrally within the coil structure, as expected. The design algorithm was therefore modified so that, for a specified degree of extremity, the B, shift was minimized along with the other terms in the error function. The shielded G, coil set generated 2% G/cm at 50 amps with a switching time of approximately 125 ys. The residual forces were < 3 N z thrust and 0.1 Nm net torque. The final B , shift was 84 Hz, which is very easily corrected [9,10]. Figure 61.3 shows the 5 % linearity contours of the Gz gradient where the linear region begins at approximately 12 mm from the end of the coil. A prototype of this coil was built and the experimental field plot shown in Fig. 61.4 and indicates both the linearity and asymmetry of the generated field.

Fig. 61.4: A schematic of the coil pattern, showing its asymmetry

61.4 Conclusion We have shown that force and torque compensated asymmetric gradient sets may be designed for use in Magnetic Resonance microscopy and as such are tailored to the magnet of their intended use. A novel type of non axi-symmetric longitudinal gradient coil was presented, such that the linear region may be positioned close to one end of the coil set. This longitudinal coil was designed to be used in conjunction with B, modulation units.

61. Novel. Asyninietric Gradient Coil Sersjor Magnetic Resonance Microscopy

68 1

Acknowledgments We thank the staff of the workshop at the Centre for Magnetic Resonance for constructing the prototype coils.

References 1.

A. M. Abduljalil, A. H. Aletras, and P-M. L. Robitaille, Magn. Reson. Med. 31 (1994) 450.

2.

L. S. Petropoulos and M. A. Morich, IEEE. Trans. Mugn. 31 (1995) 3536.

3.

D. C. Alsop and T. J. Connick, Magn. Reson. Med. 35 (1996) 875.

4.

S. Crozier and D. M. Doddrell, J. Magn. Reson. 103 (1993) 354.

5.

S. Crozier and D. M. Doddrell, J. Magn. Reson. 107 (1994) 126.

6.

M. L. Buszko et al., J. Magn. Reson. 112 (1996) 207.

7.

S. Kirkpatrick. C. D. Gelatt, and M. P. Vecchi, Science 220 (1983) 673.

8.

S. Crozier and D. M. Doddrell, J. Magn. Reson. 127 (1997) 233. See also chapter 59 in this book.

9.

S. Crozier, C. D. Eccles, F. A. Beckey, J. Field, and D. M. Doddrell, J. Magn. Reson 97 (1992) 661.

10.

S. Crozier, F. A. Beckey. C. D. Eccles, J. Field, and D. M. Doddrell, J. Magn. Reson. 103 (1994) 115.

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62. Novel Gradient Coils for Magnetic Resonance Microscopy E. R. Andrew, M . Kempka, S. Sagnowski, and E. Szczesniak Departments of Physics and Radiology, University of Florida, Gainesville, Florida 3261 1, USA

Abstract This paper describes three magnetic field gradient coils of considerable simplicity, two for transverse gradients and one for longitudinal gradients. The coaxial arc gradient coil has a simple unit construction of symmetric form. It features a large volume of uniform transverse field gradient, high efficiency and low inductance for rapid switching. A prototype coil was first constructed and a smaller coil set was then constructed for NMR microscopy, with excellent results. The system may be used for all sizes from microimaging to whole-body MRI. The second transverse gradient coil uses full circle current paths rather than current arcs. It has an even simpler form of construction and has closely similar properties to the coaxial arc transverse gradient coil. A prototype coil set was first made and two smaller coil sets have been made for NMR microscopy. The longitudinal gradient coil is based on an analysis of the multipole expansion of the external field of a gradient coil system. It is first shown that a Maxwell pair has no hexadecapole moment. The field outside such a pair therefore falls as r4from the quadrupole moment and as r-8 from the 64-pole moment. Using a nested pair of Maxwell pairs the quadrupole term is canceled leaving only the rapid attenuation of the r8term, thus providing a simple screened longitudinal gradient coil.

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E. R. Andrew, M. Ketnpka, S. Sagnowski, arid E. Szczesniak

62.1 Introduction The generation of magnetic field gradients lies at the heart of all MRI systems since they provide the essential spatial encoding. The design of an ideal gradient system continues to present a challenge especially as switching times get shorter and extended linearity is demanded. In this paper, we discuss three approaches which we have found to have virtues, two transverse and one longitudinal. We begin by listing some desirable features of a gradient system: simple, compact and easy to construct low inductance, assuring fast switching and settling times high power efficiency extended field gradient linearity some shielding symmetric, absence of torque

62.2 Coaxial Arc Coil Our first transverse gradient design is based on a unit construction we developed several years ago [1,2]. Each unit consists of current carrying arcs with current returning in a larger coplanar arc as illustrated in Figs. 62.2 and 62.3. We call this the coaxial arc unit. The transverse gradient coil is made up from a number of identical units mounted coaxially, connected in series and driven by the same current. The placing of the units along the axis is important. This was computed from first principles to achieve the optimum internal gradient linearity. We used a gradient descent technique [ 11 and also a simulated annealing method [3], the two methods yielding essentially similar results. The optimum length of the coil was found to be equal to the inner diameter. Eight units was found to be ideal in removing the departures of gradient uniformity due to the discreteness of the units. More than eight units did not greatly improve the uniformity and had the undesirable effect of significantly increasing the inductance.

62. Novel Gradient Coils for Magnetic Resonance Microscopy

1

685

lr

0.5.

0

- 00. 5. 1

-0.15

-1t.

-1 -1

-0.5

0

0.5

1

Fig. 62.1: 5% contours of field gradient in the xz plane at y = 0, a) for the circle current path transverse coil, b) for the coaxial arc coil.

Fig. 62.2: Prototype 8 unit coaxial arc coil with one unit detached.

If the eight units were equally spaced, their locations would be F 1/7, f 3/7, f 5/7, f 1 in units of the inner arc radius, which in decimals is -C 0.143, f 0.429, f 0.714, +- 1. The optimum placing was found to be 2 0.143, 2 0.427, f 0.775, k 1. It will be seen that essentially we have adjusted the placing of the penultimate unit. The calculated 5% contours [ I ] in the xz plane at y = 0 are shown in Fig. 62. lb. A gradient uniform within 5%

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E. R. Andrew, M. Ketnpka, S.Sagnowski, and E. Szczesniak

is provided over 75% of the coil length and 70% of its diameter. The solution is not unique; an alternative is f 0.135, k 0.410, +. 0.717, f 1. Here we have essentially adjusted inner units. This alternative arrangement gives a rather better extent of uniformity in the xy plane at the expense of a somewhat reduced axial extension [ 11. A 13 cm inner diameter model was constructed (Fig. 62.2) in order to check the computer simulations. The coil formers were made of plexiglass and were wound with 32 gauge wire. X gradients are wound on one side of the plate and Y gradients, identical but rotated through 90°, on the reverse side. The field was explored inside the assembled coil with a small search coil. The results agreed well, within 2%, with the computed expectations [ 11.

Fig. 62.3: An 8 unit coaxial arc coil for NMR microimaging. One unit has been detached. The coin is a US quarter which is 23 mm in diameter.

With the eight units connected in series, the inductance of the coil was found to be 81 pH, resistance 11.8 0 and the time constant U R was 6.9 ps. However since the 8 units are identical and are fed with the same current, they may alternatively be driven in parallel. When connected in parallel, the total inductance was reduced to 1.65 pH. If the resistance is loaded up to say 2 0, we can thus have a microsecond time constant. We next made a smaller gradient set for microimaging (Fig. 62.3) in a 7 T, 300 MHz 50mm bore NMR system [2]. The transverse gradient coil again consisted of 8 units with internal diameter 22 mm. The coil former was made from the peffluorinated

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polymer Kel-F. 30-gauge wire was used for the X and Y gradients. The inductance was 4.7 yH for series connection, resistance 1.5 SZ, time constant WR 3 ys. When fed with a current of 20 A, the x,y,z gradients were 7, 7, 20 G/cm respectively. This coil set has been used for microimaging pieces of human spinal cord in vitro [2]. Figure 62.4 shows a 1 mm thick central slice showing excellent detail of nerve bundles and membranes in an estimated in-plane resolution of about 30 ym on a 256 x 256 matrix display. A set of 21 contiguous 1 mm thick slices of a piece of human spinal cord were recorded extending k 10 mm from the center of the coil. High quality images were recorded within a f 7 mm central region. The outermost slices showed distortion due to non-linearity of the gradient beyond the central region.

Fig. 62.4: MR image of the central slice of a piece of spinal cord in vitro, using the gradient coil system shown in Fig. 62.3.

62.3 Circle Current Path Coil Our second transverse coil arrangement is illustrated in Fig. 62.5. Arcs C and D provide the gradient as before and the outer arcs E and F are the return paths. If the current in C returns through E, and the current through D returns through F, we have two crescent-

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moon shaped components. On the other hand since the current is the same in both halves, but opposite in sense, the current through C could just as well return through F and the current in D could return through E. In that situation the arrangement simply reduces to two full circles with the current in the inner left hand arc returning in the outer right hand arc and vice versa. This makes an extremely simple geometry and construction. Because the two circles are not concentric, we have called it the NON-CON gradient coil 141. Alternatively it may be called the circle current path coil since it uses full circles rather than current arcs as in other designs.

B

A Fig. 62.5: Schematic arrangement of the circle path coil.

A transverse gradient coil assembled from nine units with 14 cm diameter circles is shown in Fig. 62.6. The optimum placing of the units was computed from fist principles in the manner described earlier for the coaxial arc coil. The computed 5% gradient contours are shown in Fig. 62.la where they may be compared with those for the coaxial arc coil in Fig. 62.lb. A search coil investigation showed experimental agreement with the computer calculations within 2%. The volume of 5% linearity is slightly larger for the non-con gradient coil, but its efficiency is slightly less.

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Fig. 62.6: Prototype 9 unit circle path coil with 14 cm diameter circles.

Fig. 62.7: A 9 unit gradient set using circle path transverse coils for N M R microimaging. The coin is a US quarter 23 m m in diameter.

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We next made a small nine unit set for microimaging, shown in Fig. 62.7. Again the Y coils are mounted on the opposite side of the Kel-F plates from the X coils but rotated through 90". The set illustrated was constructed for use in our 300 MHz 50 mm bore NMR microscope. Another set for a 300 MHz 89 mm bore NMR spectrometer has also been constructed.

62.4 High Order Multipole Coil Our third contribution is concerned with a new longitudinal gradient coil which exploits high multipole behavior and has some useful and interesting properties in yielding a well-shielded coil of great simplicity. Consider a simple system of two identical coaxial coils of radius a with equal currents circulating in opposite directions, the Maxwell pair arrangement. With origin at the center we calculate from the Biot-Savart law that the axial field B, is

B , = L p o N I a 2 { [a2 + ( z - d )2 2

]-t - [ a 2 +

(Z

+d)2]t}

(62.1)

in SI units. The separation of the coils is 2d, N is the number of terms on each coil and I is the current. Expanding around the center we can readily show that the gradient is most linear when (62.2)

2d = &a

This is the well-known Maxwell condition and gives the frequently used Maxwell pair. Let us now focus attention on how the field behaves outside this coil system. The field of a current distribution may be viewed as the superposition of magnetic multipoles at the origin: dipole, quadrupole, octupole, and so on. The antisymmetry of the Maxwell pair means that there will be no 2k poles with k odd, just quadrupole (k = 2), hexadecapole (k =4), 64 pole (k = 6 ) and so on. A dipole field falls off with distance r from the source as r3,a quadrupole field as r4,a 2k pole field falls off as dk 2). For z > a, it is convenient to expand B, in (1) in inverse powers of z: +

62. Novel Gradienr Coilsfor Magiietic Resonance Microscopy

69 1

(62.3)

The first two terms in the expansion are readily found to be those for k = 2 and k = 4, with coefficients C2 = 3p0 NIa2d

5 C4 = -poNIa’d(4d2 2

-3a2)

(62.4a) (62.4b)

The first term C, z - is~ evidently the quadrupole term ( k = 2). The second term C, z - is~ the hexadecapole term. But we see from eqns. (62.4b) and (62.2) that for the Maxwell condition C4 is zero. Now as Purcell [ 5 ] has shown in a related discussion of Helmholtz coils, the field of any axially symmetrical multipole cannot be zero along the whole symmetry axis unless it is zero off the axis everywhere also. Consequently the entire hexadecapole field, not just B, on the axis, will vanish if 2d = &a. We therefore conclude that every Maxwell pair has zero hexadecapole moment. The authors hesitate to suggest that they have discovered something new in classical physics, but they have not seen this result mentioned before. So the external field of a Maxwell pair falls as r4, and the next higher order term falls as r-*. So the external stray field is dominated by this quadrupolar r4term. Suppose however that we could somehow suppress the quadrupolar term. Then because the hexadecapole term is absent for a Maxwell pair, the stray field would fall off extremely rapidly as r-* and higher inverse powers. This is rather easy to do. We can surround the Maxwell pair with another larger Maxwell pair with opposed currents arranged so that their quadrupole moments given by eqn. (62.4a) cancel. For example, if the outer pair has twice the radius, we need NI to be 8 times smaller to achieve exact cancellation. We constructed such a nested Maxwell pair system with inner diameter 12.8 cm and outer 19.2 cm (a ratio of 2:3), and arranged the number of turns to cancel the quadrupolar moments when the two coils are fed in series. We explored the field by search coil along various directions. A typical result is shown in Fig. 62.8. The field does indeed fall off much more rapidly when both coils are energized compared with the inner Maxwell pair alone. The lower graph in Fig. 62.8 is particularly instructive on a log-log plot. The

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experimental points fall well on the straight line of slope -4 for the inner Maxwell pair alone. and on a straight line of slope -8 for the nested Maxwell pairs both energized. It is clear that nested Maxwell pairs provide a very simple well-shielded longitudinal magnetic field gradient, which in some circumstances may prove to be useful.

ii!iL I

0.08

unshielded

G~ 0 . 0 4 m

0.03 0.02

shielded

0.01 0

Logarithmic Plot

1.1

1.2

1.3 log r

1.4

1.5

(-1

Fig. 62.8: The decay of magnetic field outside a nested pair of Maxwell coils demonstrating the much more rapid decay wHen the outer shielding coil is energized compared with the unshielded inner coil alone. When the inner coils only are energized the experimental points fall on a straight line of slope -4 on the log-log plot. When both coils are energized the experimental points lie close to the straight line of slope -8 on the logarithmic plot.

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References I.

E. R. Andrew and E. Szczesniak, Mag. Res. Itnag. 13 (1995) 607-613.

2.

E. R. Andrew, B. A. Inglis, M. Kempka, T. Mareci, and E. Szczesniak, MAGMA 4 (1996) 85-91.

3.

M. L Buszko. M. F. Kempka, E. Szczesniak, D. C. Wang, and E. R. Andrew, J . Mngn. Reson. B 112 (1996) 207-213.

4.

E. R. Andrew and M. Kempka, 28" Congress AMPERE, Canterbury, 1996. 197-198.

5.

E. M. Purcell, Atn. J. Phys. 57 (1989) 18-22.

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63. The NMR Endoscope R. Haken, P. Bliimler, and B. Bliimich

Magnetic Resonance Center fiEIWAM, RWTH Aachen, D-52074 Aachen, Germany

Abstract The NMR endoscope consists of a micro coil which is attached to MRI suitable instruments like endoscopes or catheters. The micro coil is connected to a circuit which can be used in three different modes. The first mode generates a local distortion field for tracking the instrument on the MFU screen. The second is a spectroscopic mode where different nuclei of interest can be probed from the tip of the endoscope. The third mode uses the stray field of the micro coil in order to produce radial images by variation of the excitation field strength. A prototype of the NMR endoscope was build and sucessfully tested in all three modes.

63.1 Introduction Magnetic resonance imaging (MRI) is an established method in clinical diagnosis. Improved contrast which can be functionalized as well as reduced health risks has made MRI to the most adaptive and flexible imaging technique in radiology. Furthermore, surgeons apply MRI for guidance during complex interventions, while another branch is specializing on minimal-invasive, endoscopic surgery. For NMR-guided surgery so called “open” magnets have been developed with improved access to the patient. The ongoing surgery is monitored by continuously acquired MRI scans. Especially for minimal-invasive abdominal surgery specific MRI-instruments and tracking devices were introduced recently [ 1-81. We propose a new surgical device, which combines different features in a single circuit. It is designed for minimal-invasive operations and consists of a small NMR-probe which is inserted into the body via a catheter. The NMR endoscope can be used in three different modes, which enable the surgeon to locate the instrument (tracking mode),

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characterize tissue and body liquids around the micro-coil (spectroscopy mode) and acquire radial images of the surrounding vessel (imaging mode). A first prototype of the NMR endoscope has been realized and tested. Explorations of clinical applications are in progress.

63.2 Features The endoscope consists of a flexible shaft with a micro coil attached to the tip. The main part of the circuit encompassing adjustable capacitors and switches is integrated in the handle (cf. Fig. 63.1). The coil is part of an rf-resonant circuit which is operated in three modes described in more detail below. micro coil

adjustment and switch unit

adjustment u n i t w i t h switch a n d t r i m m capacitors

Fig. 63.1: Physical appearance (left) and wiring diagram (right) of the endoscope. Diameter and length of the flexible shaft depends on the investigated organ or nuclei respectively. While the diameter can be varied in the range of 1 to 10 or more millimeter to get an optimal fit to the examined lumen, the length of the shaft is determined by AJ2 of the Larmor frequency of the stimulated nuclei (about 1.5 m for proton in a 1.5 T magnet).

63.2.1 Tracking Mode Minimal-invasive techniques are a low-priced and gentle alternative to classical operations and preventive medical checkups which in addition significantly reduce the recovery period of the patients. Miniaturized instruments and endoscopes are routinely employed to either gain information from local areas or to manipulate tissues. When

63. The NMR Endoscope

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surgery is combined with MRI guidance special instruments are required. In the MR image these instruments do not contribute any signal, and they can be only spotted by the displaced tissue or unspecified susceptibility artifacts. However, in most applications these instruments need to be located with great precession during the intervention. It would be preferable, if this tracking option could be toggled between “visible” and “invisible” on the MRI-screen at liberty of the surgeon. To solve this problem the probe can be switched to ,,tracking mode” to function similar to a pointer on the MRI screen. To visualize the pointer on the screen a weak AC current of low frequency is fed to a micro coil. The actual size of the point can be controlled by the amplitude of the AC current. It causes a magnetic field at the very tip of the probe resulting in a local distortion of the image (cf. Fig. 63.2). After accurate positioning the current is switched off and images without disturbances can be acquired.

Fig. 63.2: Demonstration of the tracking mode with a solenoidal micro coil submerged in a water filled tube of 17 mm diameter. The micro coil has an outer diameter of about 1.8 mm and is suspended from the background. The image plane is perpendicular to Bo and the image was generated by a FLASH sequence with a slice thickness of 1 mm. Left: Sketch of the coil position. Middle: Image with without coil current (tracking mode off). The coil can only be spotted by the lack of water in the slice. Right: A weak AC current is fed to the coil and disturbs the local magnetic field. The increased signal loss clearly marks the position of the coil. The 1H images were acquired on a Bruker 300 MHz spectrometer with micro imaging accessory.

63.2.2 Spectroscopy Mode The same micro coil used for tracking of the instrument can be connected to an rf-resonant circuit and operated like an internal surface coil. In this way spectroscopic experiments can be performed of various nuclei (e.g. 13C, 23Na, 31P). If the investigated

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nucleus is different from ‘H, which is assumed to be the nucleus used for MRI, the spectroscopic experiments can be intercalated with the MRI experiment by an additional spectrometer which operates in sync with the MRI experiment. The resulting spectroscopic data from the inserted NMR micro probe can provide additional information about chemical and physical properties of tissues, body liquids and implants. The sampled region can be chosen to be only from the stray field of the coil, whose inner volume can be added by simply removing a plug. This setup enables the surgeon to monitor additional medical parameters like for example pH-values or concentrations of metabolites. Compared to standard MRI equipment micro coils exhibit also an increased sensitivity, which may allow in-vivo spectroscopy to be performed “on-line”. Figure 63.3 depicts a measurement of an ‘Hspectrum of ethanol acquired in a 90 MHz permanent magnet which was chosen to be close to the typical IH frequency range of commercial whole body tomographs. The ethanol was located in the lumen of the micro coil which was accessible after removing a plug. Unfortunately this magnet had no shim supplies, which limited the spectral resolution dramatically. r

-1wOO 10

9

8

7

6

5

4

3

2

I

0

-1

-2

Fig. 63.3: Test measurement of a 1H-spectrum of ethanol (chemical shifts at 1.11, 3.55 and 5.16 ppm) acquired by a single scan (left). The right picture shows the same spectrum after apodization with a sine-function for resolution enhancement. The data were measured on a 90 MHz permanent magnet without shimming supplies.

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63.2.3 Radial Imaging Standard endoscopes are equipped with high resolution cameras which only display the surface of the surrounding tissue. On the other hand, clinical MR images acquired online usually have only a spatial resolution in the order of millimeters. The NMRendoscope described above has an additional feature which can be used to obtain limited spatial information. This feature is the rf gradient of the micro coil, which can be used to phase-encode the spatial dimension by varying the amplitude of the gradient or in other words by increasing the B , field strength. This type of imaging is known as “rotatingframe” imaging [9]. Because solenoids have rf gradients with radial symmetry, the resulting “image” displays features averaged over the circumference. The excitating field Bl(r) decays non-linearly which makes a correction of the image intensity necessary. Another consequence of this non-linear field is a non-constant gradient requiring an additional correction of the space coordinate. For first measurements a phantom with radial geometry (mimicking the structure of vessels, ureters etc.) has been constructed. The phantom has two radial grooves at a distance of 1.1 and 2.2 mm from the coil surface. First imaging experiments were performed on *H,O filled in these grooves (Fig. 63.4). Deuterium (46 MHz) was used to reach the ‘H-frequency range of commercial MRI tomographs while working on a 300 MHz spectrometer. The grooves can be clearly distinguished. Due to the larger gradient for smaller radii the resolution is decreasing with increasing radius. For the correction of space-scale distortions by the gradient variation, the B , component B,, parallel to the coil [lo] is estimated by assuming its value to be constant over the length of the coil.

is representing a correction factor according to the number of turns, I the coil current, p0 the permeability in vacuum and R the radius of the micro coil. The numerically determined solution of eqn. (63.1) has been used on rescaling the space scales in Fig. 63.4 using KT = 1. K

700

R. Haken, P. Bliimler, nttd B. Bliinliclr

a)

b)

flexible endoscope shaft

tcflon

:t

groove I

7

two grooves, filled with *H*O 2

groove 2

9

I

41

01 I

3

r lmml

:t

groove 2

5

1

2

3

Fig. 63.4: Demonstration of radial imaging with rf-gradients: a) Geometry of the phantom with two radial grooves at distances of 1.1 and 2.2 mm from the surface of the coil. b) Radial image of the phantom with only the inner groove filled with 2H20. c) Same as b) with only the outer groove and d) both grooves filled. The stronger gradient at shorter distances from the coil results in a higher resolution which can be recognized by the higher density of points after rescaling of the space dimension. The NMR measurements were performed at the deuterium frequency of 46 MHz to match the IH frequency range of clinical MRI equipment.

63.3 Sensitivity and Signal-to-Noise Ratio A general advantage of micro coils [ 11-13] is their high sensitivity due to an high filling

factor when compared with standard surface and whole-body coils. The signal-to-noise ratio (SIN) can be estimated according to SIN= K q M, (po Q 00 V c 1 4F k Tc AF')'I2

(63.2)

63. The NMR Endoscope

701

where K is a numerical factor (-1) dependent on the receiver coil geometry, q the tilling factor, Mo the nuclear magnetization, Q the quality factor of the coil, coo the Larmor frequency, V, the volume of the coil, F the noise figure of the preamplifier, k the Boltzmann constant, Tc the probe temperature and A F the bandwidth of the receiver [14]. Assuming that technical parameters like noise figures, bandwidths etc. are essentially the same for endoscopic as well as whole-body experiments, the SIN depends decisively on the quality factor Q and the coil volume (q,Vc). SIN - ( 1 1 VC)”* .

(63.3)

Comparing a micro coil (Vc c 10 mm3) with a whole-body coil (Vc > lo7 mm3) and assuming that the micro coil has at least the same quality factor, the improvement of the S/N is in the range of lo3 - l o 4 .

63.4 Conclusion The NMR endoscope is a new diagnostic instrument which enables a surgeon to obtain a maximum level of information volume elements surrounding his instrument during an MFU guided intervention. For this purpose a small coil is added to the instrument and connected with a circuit which allows three different operational modes. The first mode is for reliable positioning of the instrument by improved tracking. In the spectroscopy mode clinical parameters can be measured which help to characterize tissues, liquids and implants. Finally, radial images of the direct vicinity of the probe can be acquired by utilizing the rf-gradient of the same micro-coil. This can support tissue differentiation at the spot of action during surgery.

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References 1.

P. Erhart, M. E. Ladd. J. F. Debatin et al.. Proceediugs of the ISMRM 4IhScieritific Meeting, 1996, p. 1740.

2.

C. L. Dumoulin, R.D. Darrow R.J. Herfkens et al., Proceedings of the ISMRM 4" Scientific Meering,

1997. p. 1927. 3.

M. E. Ladd, P. Erhart, J. F. Debatin, et al., Mugn. Reson. Med. 36 (1996) 646.

4.

M. Burl, G. A. Coutts, and I. R. Young, Magn. Reson. Med. 36 (1996) 491.

5.

E. Atalar et al., Magn. Reson. Med. 36 (1996) 596.

6.

G.G. Zimmermann et al., Radiology 204 (1997) 769.

7.

C. Dumoulin, S. Soucza. and D. Darrow, Magn. Reson. Med. 29 (1993) 41 1.

8.

P. Bomen and B. Aldefeld, Proceedings of the ISMRM 4" Scientific Meeting, 1997, p. 1925.

9.

D. I. Hoult, J. Mugn. Reson. 33 (1979) 183.

LO. I. Wolff, Grundlagen und Anwendungen der Manvellschen Theorie I t , WissentschaftsverlagMannheimlleipzig, 731 (1992) 91. 11.

M. R. Bendall and D.T. Pegg, J. Mugn. Reson. 68 (1986) 252.

12.

E. W. McFarland and A. Mortara, J. Mugn. Reson. 10 (1992) 279.

13.

T. L. Peck, u" International Conference on Magnetic Resonance Microscopy, Wiirzburg, 1995.

14.

D. I. Hoult and R. E. Richards, J. Mugn. Reson. 24 (1976) 71.

64. Development of a Flexible Pulse Programmer for MRI Using a Commercial Digital Signal Processor Board Katsumi Kose, and Tomoyuki Haishi

Institute of Applied Physics, University of Tsukuba, Tsukuba, 305, Japan

Abstract A flexible pulse programmer for advanced NMR imaging experiments has been developed using a commercial DSP (digital signal processor) board. The DSP is the 32-bit word floating-point chip TMS320C3 1 of Texas Instruments running at a 40 MHz clock frequency with an instruction cycle of 50 ns. The DSP program to generate the pulse sequence has been developed using the interrupt function of the internal timer with a 100 ns clock cycle. As a result, a time resolution of 100 ns and minimum pulse interval of 3.7 ps are achieved without any additional hardware devices.

64.1 Introduction Recent sophisticated fast NMR imaging sequences require a high performance pulse programmer as well as a high speed gradient and RF system. However, to develop such a pulse programmer is difficult because many parameters including three channel gradient amplitudes must be controlled at high time resolution. One approach to the MRI pulse programmer is to use a hardware logic circuit consisting of a clock counter, an address counter, a digital comparator, and a word memory of about 128 bits, that includes timing data bits (around 32 bits), event words (gradient waveforms and RF control bits), and some system control words. The logic circuit for such a pulse programmer, however, becomes very complicated and the wiring increases

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explosively. The use of some computer system for the NMR pulse programmer is a well known solution. But personal computers or other usual board computers cannot be used to generate exact time sequences because these computers have system interruptions by the system timers and refresh cycles for dynamic memory devices. Most of digital signal processor (DSP)board systems are, however, made to give exact time sequences which can be used for NMR pulse sequences. We have thus developed a flexible pulse programmer for MRI using a commercial DSP board.

64.2 Hardware System The DSP board we used is the DSP6031 of mtt Instruments Corp. Tokyo, Japan, which has a 32-bit floating point DSP chip (TMS320C31, Texas Instruments Inc.) running at 40 MHz clock frequency with 50 ns instruction cycle. In addition, this board has four 12bit ADC, four 12-bit DAC, and an 8-bit digital I/O port. All of them are assembled on a full size PC-AT BUS extension card. This DSP board can be connected to other extension boards (full size PC-AT cards) using a 32-bit I/O bus. We used one extension card for 32-bit digital outputs. These two PC-AT BUS full-size cards connected with the DSP I/O bus were installed in an IBM compatible PC running under MS-DOS or Windows95. The DSP has an internal 32-bit timer synchronized with the main clock frequency of the DSP [I]. Because of the timer can generate interrupt signals to the DSP operation at a minimum clock cycle of loons, the DSP can generate pulses with 100ns time resolution.

64.3 Program for the Pulse Programmer Figure 64.1 shows an overview of the program developed for the pulse programmer. This program consists of three major components. The first component is the time table of the pulse sequence (Fig. 64.2) written using a text editor. The first column shows the times written in 100 ns units at which the events (RF pulse, gradient, ...) take place. Because the internal timer of the DSP has a 32-bit word length, the maximum time in this table can be extended to 99.9999999 seconds.

64. Development of a Flexible Pulse Programmer for MRI Using a Commercial DSP Board

705

The second column describes the kind of the event such as Gx, G,, Gz, RF phase, RF shape, RF trigger, AD trigger, and so on. The third column shows the gradient amplitude, RF phase, channel of the RF pulse shape, and so on. Because this file is a simple time table and does not include "commands" or "macros", DSP programs are required for 2 D or 3D image acquisition loops. gradient waveforms RF control lines text editor

cross and assembler

time table conversion & DSP program download

table

r l

pulse generation according to the time table

on DSP

DSP BOARD

HOST PC

Fig. 64.1: Overview of the pulser program. All of the program components are developed on the host PC and the programs and timing data are downloaded to the DSP memory area via the dual port memory on the DSP board.

Time ( in 100 ns)

Event

Amplitude (Hex)

00.000.010.0 00.000.030.0

GZ RF

8600

00.000.110.0 00.000.120.0 00.000.130.0 00.000.160.0

GZ GX GY GZ

7A00 4000

00.OOO. 170.0

GY GX AD GX

8000

00.000.180.0

00.000.200.0 00.000.300.0

8000

cooo 8000

cooo 8000 8000

Fig. 64.2: Time table for the pulse sequence made with a text editor. The time can be written up to 99.9999999 s in the 100 ns unit.

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The second component is the DSP program to generate pulse sequences. The key operation in the program is the timer interrupt operation (Fig. 64.3): At first, the delay time is loaded to the timer register, then the interruption from the timer takes place after the delay time, and the event is output according to the events in the time table. The DSP program was developed using a C cross compiler and a cross assembler for the DSP chip running on the host PC under MS-DOS version 6.2. By using these cross software tools, the DSP binary program code was made as a disk file in the host system.

0000 0001 0002 0003 0004 0005 0006

LDI SUB1 LDI RPTB

"AR1,RO l,RO RO ,RC LOOP

LDI STI

*ARl++,RO RO,@8028H

0007 0008

STI

R7,@8020H

0009 0010 0011 0012 0013 0014 0015 0016 0017 0018 0019 0020 0021 0022

STI

R6,@8020H

LDI LDI STI LDI LDI STI LDI LDI STI LDI LDI LOOP

*AR1++,AR2 *ARl++,RO RO, *AR2 *ARl++,AR2 *ARl++,RO RO,*AR2 *AR1++,AR2 *ARl++,RO RO,*AR2 *ARl++,AR2 *ARl++,RO STI RO,*AR2

IDLE

;

number of the events

; ;

load to the repeat counter repeat to LOOP

; ; ; ; ; ; ;

time interval data store to the timer counter register COUNT DOWN START wait for interrupt from the timer HOLD the TIMER-0

;

load event load event output the load event load event output the load event load event output the load event load event output the

address data 1 event 1 address data 2 event 2 address data 3 event 3 address data 4 event 4

1

2 3

4

Fig. 64.3: Key program code in the pulser program. AR1 is the address register pointing at the timing data table. LOOP is the events output loop: The delay time stored in 100 ns unit is loaded to the timer counter register (0006) and the count down starts (0007). The DSP waits for the interruption by zero from the timer (0008: IDLE). Then four 32-bit event words are output to the output address assigned in the timing table. The loop overhead is 3.3 ps.

64. Development of a Flexible Pulse Programmerjor MRI Using a Commercial DSP Board

707

The third component is the program to convert the time table to DSP data and to download the DSP program code and timing data to the DSP memory. Because the basic operation in the pulse generator program is the timer interrupt operation as described above, the time table has to be converted to a sequence of delay times in 100 ns unit. In addition, overhead times have to be subtracted from the delay times to make the time intervals exact because many instruction cycles were used for the output of the events as shown in Fig. 64.3.

64.4 Results and Discussion Figure 64.4 shows gradient waveforms of a FLASH sequence (repetition time: 0.4 ms) generated with the pulse programmer. This pulse sequence was generated using the time table shown in Fig. 64.2. The minimum time interval between two successive events was 3.7 ps. This was because of 3.3 ps the overhead time in the pulse output loop, and some overhead time (400 ns) existed between the count down start and the idling loop waiting for the interruption. The achieved 100 ns time resolution was confirmed using a digital oscilloscope (HP54602B, Hewlett Packard). We have assigned 8 bits for the data-acquisition control, 8 bits for the transmitter RF phase, 6 bits for the selection of the tailored RF pulse stored in a ROM, and 2 bits for the RF pulse trigger. These bit widths are compatible with our analog RF system. Because the digital output width of the pulse programmer can be extended by the unit of 32 bits, the programmer can be connected to any advanced RF system. Because the word length of the DSP is 32 bits, the pulse programmer cannot change different kinds of outputs (RF and gradients) at the same time. However, the amplitudes of the three gradients can be changed at the same time because the event output loop includes four output commands as shown in Fig. 64.3, and the DA converters for gradients have a common output trigger signal. The specification of the pulse programmer are summarized in Fig. 64.5. The time resolution required for the NMR pulse programmer is closely related to the bandwidth of the NMR signal. If an RF pulse or gradient pulse must be applied exactly at a specified time to the spin system, the time resolution should be roughly 100 times that of the frequency of the fastest spins. Because the bandwidth of the NMR signal is around f 100 lcHz in the advanced fast imaging sequences, the time resolution for the pulse programmer must be around 10 MHz or 100 ns. Thus, the time resolution of the pulse programmer developed here, is enough for most advanced fast imaging sequences.

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Fig. 64.4: Gradient waveforms in a FLASH sequence (TR = 0.4 ms). The switching speed of the waveforms is determined by the DA converters' conversion time (10 ps). The horizontal axis is 100 ps/div.

word length programmabletime resolution maximum programmable time minimum pulse (event) interval gradient channel gradient amplitude resolution gradient switching time digital output ports number of loop counters

32 bits (*) 100 ns 99.9999999 s 3.7 ps 3 (+I) 12 bits 10 ps 8 + 32n bits (n: 1, 2, 3....) no restriction

Fig. 64.5: Specifications of the pulse programmer developed using a DSP board. The word length is 32 bits but three gradient amplitudes can be changed at the same time.

64.Development of a Flexible Pulse Programmer for MRI Using a Commercial DSP Board

709

Because the DSP board has a dual port memory which can be accessed from the host PC and the DSP, the data table for the pulse generation program can be changed from the PC even when the pulse generator is running. Thus by combining this pulse programmer with some real-time image reconstruction system [2]. we can construct a real-time and interactive MRI system. In conclusion, we have succeeded in constructing a flexible pulse programmer that can be used for advanced NMR imaging experiments by using a commercial DSP board without any additional hardware devices.

References 1.

TMS320C31 users manual, Texas Instruments, 1996.

2.

K.Kose, T. Haishi, A. Caprihan, E. Fukushima, J. Magn. Reson. 124 (1997) 35-41.

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Tutorial

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65 Introduction to Magnetic Resonance Y. Xia Physics Department, Oakland University, Rochester, MI 48309, USA

Abstract The phenomenon of Nuclear Magnetic Resonance (NMR) was discovered in 1946 by two independent groups [1,2]. In essence, NMR relies on the interaction between an external magnetic field and an atomic nucleus. Because the properties of a single nucleus that can be observed as a result of a measurement belong to a discrete set of possibilities (quantum states), a deep understanding of NMR [3-101 lies in the realm of quantum mechanics. However, in reality, we deal with a large number of nuclei acting largely independently, so that at the macroscopic level the collection of particles appears continuous. Therefore, a semiclassical (non-quantum mechanical) model exists for most N M R applications where the Hamiltonian for the nuclear interaction is always of a simple magnetic (vector) form. In this review, we will start with some quantum mechanical concepts, but treat the behavior of the nuclear system using a semiclassical vector approach wherever appropriate. In general, an NMR experiment consists of three essential 'stages'. First, the sample is placed in an external magnetic field and allowed to reach the equilibrium state governed by the Zeeman interaction and Boltzmann distribution (the preparation stage). Next, a perturbation (rf field) is applied to the sample in order to force the spins in the sample into a non-equilibrium state (the excitation stage). Finally, the response of the sample's spin system to this perturbation, which provides a means to observe specific features of the spin Hamiltonian, is recorded with a detector (the detection stage). The first three sections in this review discuss theoretically these three essential stages. We then turn our attention to the basic instrumental aspects that facilitate the measurement of these NMR concepts in practice. The last two sections discuss several weak nuclear interactions, other than the dominant Zeeman interaction, in NMR and some basic aspects of NMR spectroscopy.

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65.1 Establishment of Magnetization This section discusses the preparation stage of an NMR experiment: the establishment of magnetization. We will first discuss the situation where a signal nucleus is placed in a magnetic field. We will then examine the macroscopic magnetization in any practical sample, where a semiclassical approach is appropriate.

65.1.1

Nuclear Magnetism

A single nucleus in an external magnetic field oriented along the z axis (B = B&) experi-

ences the Zeeman interaction with the magnetic field, for which a quantum mechanical description is given by the Hamiltonian operator

H = -yBoA I ,

(65.1)

where the constant y is termed the magnetogyric ratio' (the ratio of magnetic dipole moment @) to the angular momentum ( A I> of a specific nucleus), A is Planck's constant divided by 27c, and I, is the z component of the dimensionless nuclear spin angular momentum operator 1. I* has eigenvalues of I(I + 1) where I is either an integer or halfinteger and is termed the spin quantum number (or simply, the spin). (Note that if I = 0 (for example, '*C), then the nucleus has no angular momentum and consequently cannot be observed in NMR.) From the energy eigenvalue equation, one obtains the energy eigenvalues

E(m) = -myA Bo

(65.2)

where rn is called the azimuthal quantum number which can take values of integer or half-integer between I and -I in steps of unity. Therefore, the energy difference between any two adjacent eigenstates of a spin system, known as the Zeeman splitting, is

In many books and articles, y is also termed as gyromagnetic ratio. Strictly speaking, this terminology is literally incorrect. Because y is the ratio of magnetic dipole moment to the angular momentum, the name 'gyromagnetic ratio' would imply that it is the inverse of this ratio [Private communication, Dr. D. Traficante, University of Rhode Island].

65. Introducrion to Magnetic Resononce

715 (65.3)

AE=yhBo

As indicated in eqn. (65.2), a spin system with I = 1/2 has only two eigenstates (Fig. 65.1), corresponding to m = 1/2 (a or spin up) and m = -1/2 (p or spin down), given by (65.4)

Energy levels

-I

B=O

T

\

m

State

E(m)

TL

Population

-1/2

p

+hwo

spin-down

PP

1/2

a

- T1 h o 0

spin-up

L

AE=hoo

B=Bo

1

?. Pa

M

t

Fig. 65.1: A spin-half system.

The time evolution of a spin system is described by the time-dependent Schrijdinger equation. If the Hamiltonian, H, is time-independent, the evolution of the spin system can be derived from the Schrodinger equation. The derivation contains an evolution operator U(t), which corresponds to a rotation of the spin state, v(r),about the z axis with an angular frequency o = -yB

(65.5)

This frequency is known as the Larmor precession frequency (0 = 27@. The negative sign indicates a clockwise precession for positive y. For nuclear spins in ordinary laboratory magnetic fields, this frequency has a magnitude in the radio frequency (rf) region of the electromagnetic spectrum.

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65.1.2 Macroscopic Magnetization Any practical sample, no matter how small, contains an enormous number of nuclei. It is the macroscopic ensemble average of the observable quantities in which we are interested. For such an ensemble average, it is convenient to employ the density matrix

operator p. The usefulness of p lies in the fact that the expectation value of any operator A may be written as the trace of (or diagonal sum over) the matrix product (Ap). In the current context, the observable quantity is just the (macroscopic) magnetization M , given by

M

= ( N y h I ) = Nyh

[ mi+mj+mk]

(65.6)

where 1refers to the ensemble average, N is the number of spins per unit volume, i, j and k are the unit vectors along x-, y- and z-axis, respectively. In the absence of an external magnetic field, the ensemble average of the magnetization vector should be zero due to the random directions of the magnetic dipoles of the nuclei in the sample. Equation (65.6) is important because it can be shown [3,8] that any state of the density matrix for an ensemble of non-interacting spin-half particles may be described using the macroscopic magnetization defined in this manner, thus permitting a semiclassical description of the nuclear spin system. In the following, we shall be dealing with spinhalf Hydrogen nuclei (protons) attached to molecules in the liquid state for which internuclear dipolar terms in H can be ignored. Furthermore, we shall not be concerned with the delicate scalar coupling between spins. (We will introduce, very briefly, the dipolar and scalar interactions later in this review.) Consequently, the semiclassical description will be appropriate to describe the spin dynamics in the liquid state. Now let us consider the situation when a sample is in an external field and in thermal equilibrium. Each nucleus has a certain probability of being in a specific spin state. We denote these probabilities by Pa in the spin-up state or Pp in the spin-down state. (And we have Pa + Pp = 1.) For any sample of practical size, Pa and Pp become the relative populations of the corresponding energy levels. These probabilities obey the Boltzmann distribution, i.e.,

(65.7)

65. Introduction

10 Magnetic

Resonance

717

where E( 4 112) are defined in eqn. (65.4), k , is the Boltzmann constant, and T is the absolute temperature of the spin system. The transverse component of M is obviously zero due to the even distribution of the azimuthal phase angles of the processing nuclei in the transverse plane. The z component of the magnetization M arises from the difference in populations between the upper and lower energy states. At room temperature and for typical values of Bo, we can replace the exponential in eqn. (65.7) by its first order term in the expansion with very little error (the so-called 'high temperature approximation'). Thus, the population difference between the m = -1/2 and the in = +1/2 states can be written as, (65.8)

Given that N is the number of spins per unit volume and p the magnetic dipole (p = y h 0, the magnitude of the net magnetization in the equilibrium state, Mo, is [9]

(65.9)

65.2 Excitation of a Spin System The magnetization in the equilibrium state (established in the last section), however, tells us nothing new. It is the response of the spin system following a perturbation that forces the spins into a non-equilibrium state that interests us. Therefore, the time evolution of magnetization has now to be considered. In the semiclassical description, the time evolution of the macroscopic magnetization in the presence of a magnetic field can conveniently be described by employing Newton's second law. Equating the torque to the rate of change of the angular momentum, we have dM dt

-= y(M x B )

(65.10)

When B = Bo k, the above equation has a solution which corresponds to a processional

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motion about k at the rate %. This 00 derived from Newton's law is identical to that given by the quantum mechanical approach in eqn. (65.5). The usual perturbation to the spin system is achieved by the application of a small linearly polarized rf field Bl(t) oscillating in the transverse plane. This field is actually a superposition of two counter-rotating fields in the transverse plane (Fig. 65.2b)

Bl(t) = i2Blcoswt = [ iBlcos(wt) -jB,sin(wt)] + [ iB,cos(wt) +jB,sin(ot)l (65.1 1) It is convenient to introduce a frame of reference (2, y', z') that rotates about B, at o (Fig. 65.2a). In this rotating frame, one component of B , ( t ) is stationary while the other component rotates at 2w in the opposite direction (Fig. 65.2~).Since M is rotating at the Larmor frequency q, about z axis in the laboratory frame, it will rotate at a slower frequency (00 - 0) in this rotating frame.

....... at

2B lCOSOt

no effect

Fig. 65.2: a) A frame of reference (x'y'z') is rotating about z at O. The components of the B , field are in b) the laboratory frame (nyz) and c) the rotating frame (on resonance, o = ~ 0 ) .

When o is equal to q, (i.e., on resonance), M will appear to be stationary in this rotating frame. Because - o = 0, the apparent longitudinal field B, vanishes and B , ( t ) will provide the only non-zero field along the transverse x'-axis. M will therefore respond to the effect of B l ( t ) .One of the two components in B l ( t ) will have a 'dramatic' influence on the nuclei despite its small magnitude compared with B, while the other component which rotates at 2% in the opposite direction will have negligible effect (provided B , <<

B,) . Combining eqn. (65.10) and the first term of eqn. (65.11) yields the equation for motion of the magnetization. In the rotating frame and given the initial condition, M ( t = 0 ) = M, k,the solution to this equation is

65. Introduction to Magnetic Resonance

719

MI, = 0

(65.12a)

My,= Mo sin(o,t)

(65.12b)

Mil = Mo cos(olt)

(65.12~)

where o1equals yB,. The direction of the rf field in the rotating kame defines the x' axis. Equation (65.12) states that when a small perturbation field B , is applied at the Larmor frequency, the magnetization M will process about this perturbation field B , at a frequency o1in the rotating frame of reference (Fig. 65.3). Since switching B , off at a later time can control the amount of rotation for M , we can therefore rotate M at will.

Fig. 65.3: Macroscopic magnetization vector in a) the laboratory frame and b) the rotating frame.

Since the duration of the rf field is often on the order of micro-seconds, the B, field is often referred to as the B , pulse. For a square pulse, the amount of rotation, Cp, is given by

Cp = r q p

(65.13)

where B , is the amplitude of the rf field and tP is the time duration during which B , is applied. If the magnitude of the B , pulse field is not constant (as in selective excitation in imaging), an integral over the duration of the pulse is required in eqn. (65.13). A pulse field with the amplitude and duration appropriate to tip M by Cp degrees is denoted as a Cp pulse. For example, when the direction of B , is defined as x', a B , that is capable of rotating M by 90" to the transverse plane can be written as a 90"Ix3pulse. By appropriately phase shifting the rf field other axes in the rotating frame may be defined.

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Y. Xia

65.3 Detection of Magnetization 65.3.1 Relaxation Processes Following the disturbance from equilibrium, the magnetization M suffers relaxation processes that are caused by various time-dependent nuclear interactions of the spin system. (Relaxation processes account for the eventual return of M to thermal equilibrium.) Two distinct relaxation times (TI and T2)are used to describe the longitudinal and transverse relaxations of the oscillatory motion following the excitation, which are given by (65.14a)

(65.14b)

where T , is known as the spin-lattice (or longitudinal) relaxation time, T2 is called the spin-spin (or transverse) relaxation time, and MI is the transverse component of magnetization. There are many complicated and molecular-motion-related mechanisms that contribute to the relaxation processes, the most important one being the dipolar interaction [ 111. TI is the time required for the spin system to return to thermal equilibrium with its surroundings after the excitation ends. Because each nucleus has a magnetic moment, it generates a small local magnetic field at its neighbor's space. This local field is fluctuating constantly because the molecule is tumbling randomly. This random molecular fluctuation has a time scale ( T ~the , correlation time) on the order of tens of pico-seconds for simple liquids. In other words, the frequency spectrum that describes this random or near random fluctuating motion can be as wide as hundreds of GHz (- I/Q. Consequently, the fluctuating local magnetic fields of the nuclei making up the lattice (surroundings) must have appropriate (resonant) frequency components to stimulate the transitions between energy levels. The T I process therefore involves an energy exchange between the spin system and its surrounding thermal reservoir. T2 corresponds to the decay of phase coherence between the individual spins. In contrast to the T , process where the local magnetic fields need to fluctuate at or near the resonant frequency, the T2 process can also occur under the influence of a static or

65. Introduction to Magnetic Resononce

72 1

slowly fluctuating magnetic field. After the end of the excitation, the local magnetic fields associated with the magnetic properties of neighboring nuclei will cause the processing nuclei to acquire a range of slightly different processional frequencies, thus dephasing the coherent magnetization vector. It should be noted that T2 processes arise from both the fluctuations of local magnetic fields and the influence of static magnetic fields while T I processes arise only from the influence of fluctuating magnetic fields, and so T , 2 T2 for any spin system. In practice, the magnetization normally decays faster than the rate due to relaxation alone. Other contributions include, for example, non-uniformity of B, across the sample. It is known that the decay of the signal in the time domain leads to spectral broadening in the frequency domain. Broadening due to relaxation processes is named homogeneous and is inherently irreversible; broadening due to non-uniformity of B, is named inhomogeneous and can be removed using an appropriate rf pulse sequence. When the inhomogeneous broadening is included, we use T; to replace T2 in eqn. (65.14b), and we have T2> Ti.

65.3.2 Bloch Equation If it is assumed that the change in the magnetization following an excitation is independently caused by external magnetic fields and relaxation processes, then the equation of motion for M can be written by combining eqns. (65.10) and (65.14) as

This is the well-known Bloch equation [12]. The fist term is due to the processional motion and the second term is due to the relaxation. While a precise evaluation of the spin system requires quantum mechanical treatment, the Bloch equation does provide a phenomenological description for liquids and 'liquid-like' systems where the Hamiltonian is always of a simple magnetic (vector) form.

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65.3.3 Motion of the Magnetization Following the Perturbation Immediately following a 901' , pulse, the magnetization is given by

and

MJO) = M,(O) = 0

(65.16a)

M,(O) = M,

(65.16b)

Subsequently, assuming a uniform field B,, the evolution of the magnetization can be obtained by solving the Bloch equation, as

and

MJr) = M, exp(-t/T2) sin(q,r)

(65.17a)

My(t) = Mo exp(-r/T2)cos(oot)

(65.17b)

M,(t) = M, [ I - e x p ( - t / ~ ~ ) ]

(65.17~)

NMR detection is achieved by means of a transverse receiver coil. A resonant rf pulse induces non-zero transverse components whose precession in the transverse plane will induce a weak but detectable oscillating electromotive force (emf) signal. The motion described by eqn. (65.17) is illustrated in Fig. 65.4 and is termed the Free Induction Decay (FID). Because the NMR signal is complex in the mathematical sense, My(r) is called the real (or in-phase) part of the NMR signal and M,(r) is called the imaginary (or quadrature-phase)part of the NMR signal. The final step in signal detection is to unravel the frequency components in the FID as a spectrum, i.e., to obtain the NMR signal intensity as a function of frequency o.This is done efficiently by employing a Fourier transformation [13,14]. Since every timevarying signal has an equivalent frequency spectrum, the Fourier transform produces a mathematical equivalence between the time and frequency spectrum. For high resolution spectra, the Fourier transformation of the FID signal is a Lorentzian in the frequency if we consider inhomogedomain (Fig. 65.5) with a line-width of (nT2)-l, or (nT.)-* neous broadening. (A Lorentzian line shape is characteristic of damped oscillatory motions such as those in liquids whereas a Gaussian line shape is common in crystalline solids. [7])

65.Introduaion to Magnetic Resonance

Mx(t)

723

t

Fig. 65.4: The motion of the magnetization after the application of a 90"1, rf pulse.

Fig. 65.5: The real part a) and the imaginary part b) of the Fourier transform of the FID.The peak shift, AJ in the frequency domain corresponds to the oscillation in the time domain.

65.4 Basic NMR Instrumentation This section discusses a few basic aspects of NMR instrumentation and experimental considerations that are common in all NMR experiments. Two common pulse sequences, the spin-echo and the inversion recovery, will also be discussed. More details on instrumentation and experimental techniques can be found in a number of books [5,15-171.

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Y. Xia

65.4.1 Three Essential Stages in Experiments We first take a look at practical instrumental aspects that facilitate and accomplish the NMR concepts that we have discussed theoretically in the last three sections. The first stage requires an external magnetic field to establish the magnetization. This magnetic field is always named B, field, and is always taken to be along the z axis, i.e., B, = B&. However, the direction of the z axis can be either vertical (for vertical-bore superconducting magnets), or horizontal (for electromagnets or horizontal-bore superconducting magnets). The second stage requires the application of transverse fields to the sample via a transmit coil that is wound around the sample. All excitation and detection processes are under the control of a pulse sequence, a series of commands linked up in a certain order of time. The simplest sequence consists of a 90" hard rf pulse to tip the equilibrium magnetization to the transverse plane (in Fig. 65.4). The third stage requires the ability to detect the NMR signal induced by the precessing M in the transverse plane. The heart of the N M R detector is a sensitive rf receiver coil, which is used to pick up the induced emf signal which is often on the order of several micro-volts or less. Although the functions of transmission and reception are very different in nature, one can actually use a single rf coil for both functions.

65.4.2 A Block Diagram of an NMR Spectrometer A block diagram for a basic NMR spectrometer is given in Fig. 65.6. It has the following six major components: (a) A superconducting magnet is commonly used in modern Nh4R systems to establish the polarization because its magnetic field is very stable and can be made very high (an advantage for high resolution spectroscopy). (b) A computer is used to provide the human-machine interface, to control the process controller in the spectrometer, and to process and analyze the data. (c) A process controller consists of a pulse programmer that converts a pulse sequence into the command codes in a machine language, and a crystal oscillator (the so-called master clock) that synchronizes various local oscillators and experimental timings because well-defined timings and frequencies (and hence phases) are critical in NMR experiments.

65.Introduction to Magnetic Resonance

725

(d) An amplifier channel (transmitter channel) is used to phase-adjust, frequency-adjust and amplify the small-amplitudeoscillations into a high-voltage rf pulsed B l ( t ) field. (e) A second amplifier channel (receiver channel) is used to amplify the micro-volt level FID into a final amplitude of several volts to drive the Analog-to-digital converter (ADC). Because we are interested only in a small frequency range, on the order of kHz, the receiver uses the phase-sensitive heterodyne detection method to subtract the base frequency, leaving only the audio frequency components or offsets of the FID. (f) An important part of an NMR spectrometer is the probe. The purpose of the probe is to house the sample, the rf coil and its tuning circuits, and other necessary hardware. It is effectively a metal box that is situated between the magnet pole faces for electric-magnet, or a metal tube that fits inside the bore of a superconducting magnet. In a high-resolution probe, an additional rf coil with its tuning circuit is often included in the probe for decoupling purposes. In imaging probes, a set of gradient coils is fitted into the probe. If the probe is used in electromagnets, it also holds the external lock system used to provide long term stability for the main field. The designing of the probe and its construction is an art. One needs to fit everything, often seemingly more than space permits, into the box or tube and to optimize the performance of the probe (the rf system, the gradient system, and other functional accessories such as a life supporting system in an in vivo experiment). Receiver

- 5v

Transmitter

Fig. 65.6: A schematic representation for an NMR system.

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65.4.3 The Signal-to-Noise Ratio An NMR signal is proportional to the population difference of the nuclei at thermal equilibrium, which is governed by eqn. (65.8). For protons at 20 "C and B, = 0.5 G (the Earth's magnetic field), 1 Tesla = od2n = 42.86 MHz), and 7 Tesla = 300 MHz), 3.5and 24. respectively. These the population differences equal 1.75tiny population differences at room temperature are caused by the small value of yA B , (Zeeman splitting) compared to kBT (Boltzmann energy) in eqn. (65.8). Small values of nuclear magnetization will limit the detection sensitivity and lead to the resolution limitation in NMR. The emf induced by the transverse magnetization in the receiver coil is on the order of several microvolts. This rather weak signal is superposed on experimental noise arising from a number of sources. It is the available signal-to-noise ratio (S/N) which is important in any NMR experiment. In practice, the SIN of a spectrum can be estimated as

vo

uo

SIN

2.5

Signalp Noise,

___

(65.18)

where Signalp is the peak signal and Noisepp is the peak-to-peak noise. This equation is more commonly used in practice than an equation using the root-mean-square (rms) noise level in the spectrum. In noise theory, the rms noise has its significance but the peak-to-peak noise doesn't. In practice, however, the latter is straightforward to measure from the spectrum but the former isn't. Hence eqn. (65.18) includes a conversion factor, 2.5, since the probability of the peak-to-peak noise equaling or exceeding 2.5 times the rms noise is only 1%. eqn. (65.18) is very useful in practice but it doesn't tell us anything as to how to improve the SIN. In this regard, we have to refer to theoretical equations to provide some insights on'this issue. The fundamental NMR signal is given by eqn. (65.9). Sources of noise may be numerous. In a well-designed instrument, the overall experimental noise is determined by the dielectric and inductive losses in a biological sample, the fundamental thermal noise in the rf receiver coil, and the noise in the preamplifier (the first amplifier in the receiver channel). The starting point for the SIN calculation considers the fundamental signal due to the magnetization and the thermal noises in the instrument [18], which gives the proton SIN expressed in terms of the peak signal over the rms noise as

65. Introduction

to Magnetic

Resonance

727

where B , , accounts for the effective field over the sample volume produced by unit current flowing in the receiver coil, N , is the number of spins per unit volume, Vs is the sample volume, T, is the sample temperature, T, is the coil temperature, p is the perimeter of the coil, L is the length of the coil conductor, F is the noise figure of the pre-amplifier, Af is the bandwidth of the receiver's band-pass filter, and p, is the resistivity of the coil conductor (which is of course a function of temperature). Equation (65.19a) provides the upper limit to the SIN. A major simplification in the derivation of eqn. (65.19a) is the absence of the dielectric and magnetic losses in biological samples that contain conductive tissues [17,19]. For a given sample in a welldesigned system, the use of a scaling law [20] for SIN in NMR gives the following equation that provides some intuitive insights:

where r is the linear scale dimension of the sample and receiver coil, and a, b and c are empirical constants depending upon practical situations. The three terms in the total noise come from the sample, the receiver coil and the preamplifier. Now let's see how to maximize SIN.

Nucleus The most sensitive nucleus is the proton, because it has the largest magnetogyric ratio y (= 2.67520. lo8 rad T-I s-]) and almost 100% isotopic abundance. The relative sensitivities for other nuclei can be found in most textbooks [9,21].

Resonant Frequency or Field Strength Because 00 is proportional to the strength of the magnet, a higher field will give a better sensitivity. It is therefore advantageous to use a high field magnet in the experiments. This statement is generally true for solution NMR. For imaging involving biological samples (as opposed to chemicals dissolved in solutions), however, experimental

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Y. Xia

artifacts and distortions due to magnetic susceptibility inhomogeneities also increase with the field strength [22,23]. For solid-state NMR, a low field magnet may also be advantageous when we consider the spinning sideband problem and the transmitter power requirement.

Thermal Noises All three noise terms are temperature dependent. The lower the temperature, the less the noise. In practice, one is not always free to change the sample temperature due to the biology or chemistry of the system under investigation. Using the scaling laws [20] in eqn. (65.19b),it has been shown that the noise voltage from the sample dominates the total experimental noise in clinical situations where samples are large and the magnetic fields are low. For sample sizes in the range of 1 cm or less in a field of 7 T, the noise voltage from the receiver coil becomes dominant. In NMR microscopy, therefore, cooling the rf coil and probe circuit can significantly improve the SIN [20,24], because the NMR sensitivity is inversely proportional to the square root of the receiver coil temperature, a term reflecting the Johnson noise contributions. Because the noise figure in the preamplifier dominates the instrumental noise in the receiver channel, any investment in a 'quieter' preamplifier such as cooling or better electronics may offer additional SIN improvement in NMR microscopy.

Fig. 65.7: Schematic diagram of two classical receiver coils a) solenoid coil and b) saddle coil.

65. Introduction to Mqnetic Resormnce

729

Geometry of the RF Coil Due to the B1, term in eqn. (65.19a), it is clear that the choice of receiver coil's geometry is important in the optimization of the SIN. Two classical coil configurations are the solenoid coil and the saddle coil, given in Fig. 65.7. Both the saddle coil in vertical-bore superconducting magnets and the solenoid coil in electromagnets provide an easy access to the center of the probe, while the employment of a solenoid coil in superconducting magnets requires a side-entry for the sample. In terms of sensitivity, however, a solenoid coil is about three times better than that of a saddle coil [ 18,25I!

Optical Pumping Recently [26], a completely new approach to improve SIN has been implemented in NMR experiments. This approach uses hyperpolarized noble gases 3He and 129Xe,the only two noble gas isotopes with spin-half nuclei. By collisional spin exchange with laser-optically-pumped rubidium (Rb) vapor [27,28], one can increase the population difference in noble gases from a net polarization of only a few in lo6 to 10 - 30%!This astonishing increase in polarization more than overcomes the spin density difference between the gas and liquid states, consequently permitting high resolution NMR experiments of gaseous spaces such as the lungs [26,29]. These two noble gases are harmless to inhale and can stay hyperpolarized for long times (several minutes to hours). To image air spaces such as a lung or other cavity, 3He is more sensitive because it has a larger magnetogyric ratio. However, 3He has very poor solubility in water and lipids. 129Xeis lipophilic and has a solubility in blood an order of magnitude greater than that of helium. 129Xe also shows very large chemical shift differences (ca. 200ppm) between the gas and tissue-dissolved environments [30], consequently permitting differential studies of gas and tissue-dissolved phases. Another interesting feature is that the SIN in 3He and 129XeNMR does not depend upon the resonant frequency o (assuming the thermal noise in the sample dominates in experiments). This is because the hyperpolarized gases are no longer polarized by the magnet. Consequently, low-field NMR systems can be just as sensitive as high-field systems in hyperpolarized gas NMR. Optical pumped 3He and 129XeNMR have the potentials for a range of entirely new applications with temporal and spatial resolutions comparable to proton NMR.

730

Y. Xia

65.4.4

Spin-Echo Sequence

There are numerous pulse sequences for spin manipulation. The spin-echo (or Hahn echo) [31] is important because it has the effect of removing all the dephasing due to inhomogeneous broadening. For example, immediately following a 90" pulse, all spin magnetization precess coherently in the transverse plane. If the steady magnetic field B& is not perfectly uniform but varies slightly across the sample space, the Larmor frequency at different parts of the sample will vary, each frequency corresponding to a small region (an 'isochromatic group') where the variation of Bo is negligible. Viewed from the rotating frame at the resonance frequency a+,, some isochrornatic groups will therefore process faster than q, while others will be slower than q,.Consequently the bulk magnetization vector will soon be dephased at a rate faster than that due to the transverse relaxation alone.

rf

0

t

M

Fig. 65.8: The 9O0I,-t-1

t

80°1,~ spin-echo pulse sequence.

If at a time 7 after the application of the 90" pulse a 180" pulse is applied, the direction of the dephasing magnetization will be reversed but the positions of the nuclei associated with local fields will remain the same. Then at time 27 an echo signal will appear as the refocused transverse magnetization vector with a signal amplitude (c.f. eqn.

65. Introductioti to Magneric Resonance

73 1

(65.17b)) in the rotating frame given by MY(2z)= Moexp( -2z/T2 )

(65.20)

Thus any reduction in the amplitude of M y will only be due to T2 and the loss due to the field inhomogeneity is recovered. It is worth noting that a requirement for the spin-echo sequence is that the spins have not moved from one isochromatic group site to another during the time 2 ~ In. other words, there is no translational motion of molecules. There are two basic forms of the spin-echo sequence, namely 9Oo1,~-f-18O"1,~ and 90"1,m-r180"1,.. Figure 65.8 shows the evolution of the magnetization for the 90°1,~-~-180"1,~ sequence.

65.4.5 Inversion-Recovery Sequence For measuring T , relaxation as well as selectively suppressing unwanted spin signals (T1-contrasting), an inversion recovery (IR) sequence can be used. The unique feature of this pulse sequence is the zero-crossing over from the negative M, to the positive M, at 0.693T1. Figure 65.9 shows this sequence and the evolution of the magnetization. The first 180"1, pulse inverts the magnetization vector. The spin-lattice relaxation time govems the spin motion after the 180" pulse. After a time delay T, we can inspect M by tipping M to the transverse plane using a 90" pulse. A TI experiment can be carried out by repeating the IR pulse sequence with a variable delay time T. By fitting the data points (obtained at each peak signal) to the equation M(t) = Mo[ 1 - 2exp(-dT1)]

(65.21)

a T I value of the sample can be obtained. The second use of the IR sequence is the selective suppression of unwanted signal. Now let's suppose that we have a sample that contains two components with two different TI s, say T , , = 3 s and TI,, = 1 s. By using the IR sequence with z = 2.1 s (= 0.693T1, ), the FID will contain a contribution from the component b only. This is because at z = 2.1 s when the spins are flipped to the transverse plane for detection, the component a is at the zero-crossing point hence it contributes nothing to the transverse signal. A choice of z = 0.69 s will suppress the component b in a similar manner. The requirement for this T , contrast using IR is that

732

Y. Xia

the wanted and the unwanted components have different relaxation times. The bigger the difference, the better the suppression effect. The price to pay for using IR for selective suppression is the loss of signal in the wanted component because the signal acquisition starts at T instead of 0.

1 807 x'

90"1,~ t

Fig. 65.9: The inversion recovery pulse sequence and the motion of M.

65.5 Other Nuclear Interactions The nuclear interaction we have discussed so far is called the (nuclear) Zeeman interaction (H,), the interaction between the longitudinal magnetic field B, and the nuclear ensemble (eqn. (65.1)). We have shown that the energy difference is given by AE = yAB, between different energy levels. In general, the spin Hamiltonian in NMR may contain several other nuclear interactions and can be written [3,4,7] as

H = H,

+ HD+ H,, + H, + HQ

(65.22)

A detailed discussion of the rest of the nuclear interactions in NMR is beyond the scope

of this review. This section is intended to introduce the terminology and provide some insight to the topic.

65. Introduction to Magnetic Resonotice

733

65.5.1 Dipolar Interaction (HD) The dipolar interaction is the direct through-space mutual interaction between spins ( R coupling) [9,21]. For a pair of protons with a separation of 1.5 A,the strength of the dipolar interaction given by the dipolar coupling constant is around 100 kHz. When the molecules move rapidly (tumbling), the average over orientations will cause this Hamiltonian to vanish, i.e., there is no dipolar interaction for isotropically tumbling molecules in all but the most viscous liquids. This is good news since the much weaker interactions such as the scalar coupling can then be observed. For samples containing less mobile molecules such as certain biological tissues as well as solids, however, H D is no longer averaged to zero, and will make a significant contribution to the relaxation processes. In articular cartilage for example, because the collagen network in the tissue is spatially anisotropic, protons in water molecules will have different rotational rates for different molecular axes in space. This will result in T2 anisotropy [32,33] in the tissue. The dominant terms in H D are the zero component of the rank-2 spin operator tensor, which contains a geometric factor of (3cos20 - 1). This is an important factor in solid state NMR. This factor goes to zero when 0 = 54.7" (the magic angle). Therefore, even when H D is non-zero, the contribution of H D can be minimized by setting 0 = 54.7".

65.5.2 Chemical Shift Interaction (H,) The chemical shift interaction comes from the electron orbital shielding which perturbs the Zeeman interaction [21]. The phenomenon of the chemical shift arises because the magnetic field experienced by a nucleus in an atom or molecule differs slightly from the applied field B,. This is because in the presence of B,, electrons in an atom are induced to circulate around the nucleus about the direction of Bo with an angular velocity that is in the opposite sense to the proton spin precession. Since the circulation involves a motion of charge, there will be an associated induced magnetic moment p i which produces a small induced field Bi.The direction of the induced field produced by the circulating electrons opposes the primary field B,. (We have assumed diamagnetism, i.e., negative magnetic susceptibility.) This effect is essentially analogous to the situations of Lenz's law. Hence we have, instead of the straightforward eqn. (65.5) previously,

(65.23)

734

Y. Xia

where (3 is a dimensionless number, called the shielding constant and often expressed in parts per million (1 ppm = 1. Note that Q is a molecular parameter which does not depend on the magnetic field. The chemical shift effect is characteristic of the local chemical environment of the molecule, making NMR a valuable tool in structural chemistry. Because the absolute value of a magnetic field is difficult to measure accurately and the difference of B, and B,(1 - 0)is very small, the chemical shift is, in practice, measured by comparing the resonance frequency of an unknown sample with that of a reference. The usual reference for 'H and 13C is tetramethylsilane, Si(CH&, which is commonly referred to as TMS. TMS gives a very narrow line which occurs at the low frequency end of most of the other proton resonances. Therefore, we have the "6-scale" in proton solution NMR: (65.24)

where we note that Aef = (yB0)/2rc. 6 is a molecular parameter that depends only on the sample conditions (solvent, concentration, temperature, ...) and not on the spectrometer's resonant frequency. If 6 is positive, then msample> mref, and the sample peak is resonant at a higher frequency than the reference. In the spectrum, the sample peak will be plotted at the left of the reference peak (due to an early convention). Since Q is the shielding constant, a higher resonant frequency indicates a reduced shielding. Since the disposition of electrons in a molecule is related to the orientation of chemical bonds and therefore is anisotropic, the shielding depends on the orientation of the molecule with respect to the applied magnetic field. This is called chemical shift anisotropy. Consequently, the shielding effect should be, in general, expressed by a tensorial Hamiltonian with two terms, the secular term and the anisotropic term. For liquids, rapid molecular tumbling causes an effect known as "isotropic averaging", and consequently the anisotropic term disappears while the secular term remains. The shielding constant Q in solution NMR equals one-third of the trace of Hcs. This isotropic averaging results in the narrow Lorentzian lineshapes observed in solution spectra. However, for solids and liquid crystals where the environment is more stationary and ordered, both terms are nonzero. Chemical shift anisotropy broadens lineshapes in solid-state NMR.

65. Introduction to Magnetic Resonance

735

65.5.3 Scalar Interaction (H,) The scalar interaction is an indirect interaction between nuclei mediated by the electrons in molecular orbitals. The nuclear spin causes a slight electron polarization which, because of electron delocalization, is transmitted to neighboring nuclei. Because the interaction requires a molecular orbital, its acts only through the medium of covalent bonds, i.e., the same molecule. Hence it is an intramolecular interaction. This is in contrast to the direct dipolar-dipolar interaction which acts through space. Therefore, the scalar interaction is also called the spin-spin interaction, or indirect interaction, or simply J coupling. Because the Hamiltonian involves a scalar product of vectors, J coupling is rotationally invariant. H, and H,, are responsible for fine line-splitting patterns seen in NMR spectra of liquids [9,21] and have been used extensively for conformation analysis.

65.5.4 Quadrupole Interaction (HQ) The quadrupole interaction, for spin I > 1/2, is the interaction between the nuclear quadrupole moment and the surrounding electric field gradient (dE/dr = d2V/d?; or V E = - V 2V, Poisson's Equation). When spin I > 1/2, a simple vector description is no longer possible and quantum mechanical analysis has to be used. This is because the spin states will no longer have two basic states (spin-up and spin-down). For spin = 1, the Hamiltonian will contain quadrupole terms which are quadratic in the spin operations. The quadrupole interaction is useful for determining the electrostatic potential in solids and molecules. We can study electron distributions, intermolecular and intramolecular binding, molecular motions, phase transitions, and other properties of solids and molecules [34].

65.5.5

Comparison of Nuclear Interactions

NMR only concerns situations in which the nuclear Zeeman Hamiltonian predominates in eqn. (65.22).For commonly used magnets, the size of the Zeeman interaction is on the order of tens or hundreds of MHz. A unique feature of NMR is that many weak nuclear interactions can be observed as a consequence of the remarkable coherence times exhibited by spin ensembles. This is especially true in liquids where the dipolar interaction is

736

Y.Xia

averaged to zero. The following two tables list the orientational properties and typical magnitudes (ranges) of nuclear interactions for three selected spin-half nuclei at B, = 2 T

[9,21]. The higher the atomic number of the nucleus, the wider the range of possible chemical shift interactions, because of the large number of electrons surrounding the nucleus. We note also that the larger y (as in proton) is, the larger the dipolar interaction will be. Figure 65.10 shows a diagrammatic NMR spectrum derived from the energy level diagram. The nuclear interactions involved are illustrated in the figure. Table 65.1: Magnitudes of nuclear interactions.

Y

Zeeman

Dipolar

Chemical Shift

Scalar

(lo7 rad T-1s-1)

(MHz)

(MZ)

Wz)

(Hz)

1H

26.7520

85.2

90

2

20

13c

6.7283

21.4

20

10

100

31P

10.841

34.5

35

57

150

Nucleus

Table 65.2: Orientational properties of nuclear interactions. Sample Solution Solid

Zeeman

Dipolar

Chemical Shift

scalar

zero

isotropic

isotropic

anisotropic

often too small to be seen

3COS20-

1

65.6 1D Spectroscopy and Imaging This last section discusses a few basic aspects of 1D NMR proton spectroscopy in liquids [21,35]. We have three parameters in solution spectroscopy that can specify the characteristics and environment of the specific nucleus in the sample: the peak shift, the peak intensity, and the peak splitting. The peak shift is a measure of the chemical shift. The peak intensity can be used to provide a relative nuclear count. It is also a straightforward matter to obtain absolute concentrations for a given chemical in solution if standard concentrations can be prepared. The peak splitting provides a means to determine the spinspin coupling in the nuclear system.

65. Introduction to Magnetic Resonance

Nuclear Interactions Nucleus

Energy level diagram

Zeeman

bare nucleus in B

B=O

T

Zeeman + Chem. shift

Zeeman + Chem. shift

Zeeman + Chem. shift + Scalar

a nucleus in an atom

two nuclei (independent)

coupled nuclei in a molecule

737

LJ

:i$ A

X

f

Fig. 65.10: A diagrammatic NMR spectrum of a two spin system, derived from the energy level diagram (not to scale).JAx is the scalar coupling constant between nuclei A and X. The actual line pattern is determined by the chemical shift and scalar interactions.

The following 1D spectrum was obtained from a sample of water in a glass tube (Fig. 65.11). We notice that the line width increased as the homogeneity of the B, deteriorated. Equation (65.5) states that the Larmor frequency of nuclear spins is a measure of the external magnetic field experienced (Am = y bB). Hence any variation in the external field leads to a change of the Larmor frequency. In high resolution NMR spectroscopy, specific efforts are made to improve the uniformity of the field over the sample space so that each chemically identical nucleus in the sample resonates at the same frequency. On the other hand, if the non-uniformity of B is such that we know the spatial profile of the field non-uniformity, can we tell, from the distribution of Larmor frequencies, which resonance frequency comes from which part of the sample space? The answer is yes! If we can make every spatial location in a defined 3-D space have a unique set of values for the magnetic field vector, each resonance frequency should tell us where the signal comes from. In other words, the nuclear spins are spatially encoded! That is the physical principle for NMR imaging [ 16,23,36-40].

738

Y. Xia

1

I

300

200

1

100

1

0

I

I

I

-100 -200 -300

1

I

I

I

300

200

100

0

I

I

I

-100 -200 -300

Hz

Fig. 65.1 1 : Illustrations for 1D spectroscopy and imaging. a) A spectrum of water in a 4 mm glass tube. The line-width is about 8 Hz. The identical sample and parameters were used for b) to d) expect the x-shim values of the superconducting magnet was increased by b) IOOOunits, c) 2500 units, and d) 4500 units. The vertical gain of the plot was increased by 2, 4, and 8 for b), c), and d) respectively.

Acknowledgment This work is supported in part by a Research Excellence Fund in Biotechnology from Oakland University.

References 1.

F. Bloch, et al., Phys. Rev. 69 (1946) 127.

2.

E. M. Purcell, et al., Phys. Rev. 69 (1946) 37-38.

3.

A. Abragam, The Principles of Nuclear Magnetism, Clarendon, Oxford, 1960.

4.

C. P. Slichter, Principles of Magnetic Resonance. 3rd ed., Springer-Verlag. Berlin, 1992.

5.

E. Fukushima, S. €3. W. Roeder, Experimental Pulse NMR: A Nuts and Bolts Approach, AddisonWesley, Reading, Massachusetts, 1981.

6.

R. R. Emst, et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford, 1987.

7.

C. P. J. Poole, H. A. Farach, Theory of Magnetic Resonance. 2nd ed., John Wiley & Sons, New York, 1987.

8.

M. Goldman, Quantum Description of High-Resolution NMR in Liquids, Clarendon Press, Oxford, 1988.

9.

J. W. Hennel, J. Klinowski, Fundamentals of Nuclear Magnetic Resonance, Longman Scientific & Technical, Essex, 1993.

10.

D. Canet, Nuclear Magnetic Resonance - Concepts and Methods, John Wiley & Sons, Chichester, 1996.

65. Introduction to Magnetic Resonance

11.

N. Bloembergen, et al., Phys Rev 73 (1948) 679-71 2.

12.

F. Bloch, Phys. Rev. 70 (1946)460-474.

739

13.

R. Bracewell, The Fourier Transform and its Applications, McGraw-Hill. New York, 1965.

14.

E. 0. Brigham, The Fast Fourier Transform, Prentice-Hall, New Jersey, 1974.

15.

D. Shaw, Fourier Transform NMR Specrroscop.v, Elsevier, Amsterdam, 1976.

16.

P. G. Moms, NMR Imaging in Bio1og.v and Medicine, Oxford University Press, Oxford, 1986.

17.

C.-N. Chen, D. Hoult, Biomedical Magnetic Resonance Technology,Adam Hilger, Bristol and New York, 1989.

18.

D. I. Hoult, R. E. Richards, J. Magn. Reson. 24 (1976) 71-85.

19.

D. I. Hoult, P. C. Lauterbur, J Magn Reson 34 (1979) 425433.

20.

R. D. Black, et al., Science 259 (1993) 793-795.

21.

R. K. Hams, Nuclear Magnetic Resonance Spectroscopy - A Physicochemical View,Longman Scientific & Technical, Essex, 1983.

22.

P. T. Callaghan, J. Magn. Reson. 87 (1990) 304318.

23.

Y. Xia, Concepts in Magnetic Resonance 8 (1996) 205-225.

24.

E. W. McFarland, A. Mortara, Magn. Reson. Imaging 10 (1992) 279-288.

25.

D.I. Hoult, Progress in NMR Spectroscopy 12 (1978)41-77.

26.

M.S. Albert, et al., Nature 370 (1994) 199-201.

27.

W. Happer, et a]., Phys Review A 29 (1984) 3092-31 10.

28.

B. Driehuys, et al., Appl Phys Lett 69 (1996) 1668-1670.

29.

H. Middleton, et al., Magn Reson Med 33 (1995) 271.

30.

M. E. Wagshul, et al., Magn Reson Med 36 (1996) 183-191.

31.

E.L. Hahn, Phys. Rev. 80 (1950)580-594.

32.

Y. Xia, et al., Journal of Magn Reson Imaging 7(5)(1997) 887-894.

33.

Y. Xia, Chapter 32 in tius book.

34.

P. Jezzard, et al.,Progress in NMR Spectroscopy 23 (1991) 1-41.

35.

H. Friebolin, Basic One- and Two-dimensionalNMR Spectroscopy. 2nd ed., VCH, New York, 1993.

36.

P. C. Lauterbur, Nature 242 (1973) 190-191.

37.

P.Mansfield, P. K. Grannell, J. Phys. C: Solid State Phys. 6 (1973) L422.

38.

P. Mansfield, P. G. Moms, NMR Imaging in Biomedicine, Academic Press, New York, 1982.

39.

P. T. Callaghan, Principles of Nuclear Magnetic Resonance Microscopy, Oxford University Press, Oxford, 1991.

40.

B. Bliimich, W. Kuhn, eds., Magnetic Resonance Microscopy, Methods and Application in Materials Science, Agriculture and Biomedicine, VCH, Weinheim, 1992.

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Author Index Chapter numbers are indicated.

Abbott, R. J. 20 Abe1,E. W. 41 Ahn, S . 3 Ailion, D. C. 29 Airey, D. 51 Andrew, E. R. 62 Balcom, B. J. 5 Baldwin, B. A. 55 Bargon, J. 8 Barrantes, D. 57 Beckham, H. W. 22 Benavides, A. 57 Birch, A. N. E. 44 Black,N. 21 Blackband, S . J. 30

15, 63 15, 50, 63 Bodart, P. R. 25 Bohris, A. J. 7, 23 Botto, R. E. 13 Bowtell, R. 2 Britton, M. M. 49 Buckley, D. L. 30 Bui, J. D. 30 Cabrera, M. 39 Callaghan, P. T. 47, 49 c a r r , w . w . 22 Chandra, S . 35 Chandrakumar, N. 2 Blumich, B. Bliimler, P.

Chen, V. 51 Chudek, J. A. 18,20,41,43,44 Clifford, D. J. 13 Codd, S. L. 47 Cory, D. G. 12,37 Cowin, G. J. 40 Crozier, S . 40, 59,61 Cutillo, A. G. 29 de Jager, P. A. 45,46 Doddrell, D. M. 59, 61 Doi, Y. 38 Doty, F. D. 60 Doughty, D. A. 56 Dwojanyn, L. 0. 58 Eagle, P. 17 Eaton, G. R. 4 Eaton, S . S . 4 Eliav, U. 28 Endre, Z. H. 40 Eymael, R. 15 Faux,D. A. 7 Fercu, D. 39 Feuerstein, G. Z. 35 Fishbein, K: W. 33 Flaum,C. 54 Fukushima, E. 27 Geil, B. 29 Geoghegan, I. E. 44 Gerald 11, R. E. 8, 9, 13

742

Author Indei

Gillies. D. G. 7 Glass, S. J. 27 Goerke, U. 23,48 Gonzilez, S. 57

Laukemper-Ostendorf, S. 50 LePage,B. 23 Leditschke, I. A. 40 Leigh, J. S. 3 Leisen, J. 22

Gregory, D. M. 13 Gurbanov, K. G. 35 Guthausen, A. 15 Hafner, S. 14 Haishi, T. 64 Haken,R. 63 Harvey, W. J. 24 Hayakawa, T. 36 Heidenreich, M. 2 Heuert, U. 16 Hopkins, J. 3 Horton, W. E. 33 Hou, L. 22 Hunter, G . 18, 20, 24, 26,41,43,44

Lloyd, C. H. 24,26,43 Lord, R. M. 41 Maas, W. E. 12, 37 MacKay, R. L. 20,41,43,44 Majerus, M. E. N. 44 Maring,D. 14 Martin,R. 11 Martin-Landrove, M. 11,57 Mateescu, G. D. 39 McCarthy, K. L. 52 McCarthy, M. J. 52 McDonald, P. J. 7, 18, 19, 20, 23,24,26 Mchedlishvili, B. 53

Ishiguro, Y. 36 Ishikawa, H. 42

McNicol, R. J. 44 Merwin, L.H. 12

Kanazawa,Y. 38 Keddie, J. L. 19

Millis, K. 37 Mills, R. P. 41 Minard, K. R. 37,58 Moffat, B A 31 Mohd Som, F. 18 Moritz, S . 44 Mulheron, M. 23 Murakami, Y. 36 Nakae, Y. 36 Nakagawa, M. 27 Nakashima, T. 42 Naruse, S. 36 Navon, G. 28,42 Nechaev, A. 53 Newling, B. 18, 23

Kempka,M. 62 Kimmich, R. 2, 48 King,R.L. 55 Kitagawa, Y . 36 Kleinberg, R. L. 54 Klingler, R. J . 8, 9 Knorgen, M. 16 Kockenberger, W. 2 Kose, K. 64 Kruczala, K. 17 Kuppusamy, P. 34 Laicher,G. 29 Lane, D. M. 19,24,26

Aiahnr Index

Nunes, T. G. 25 Ohlstein, E. H. 35 Ozaki, Y. 36 Pan,Y. 21 PCrez, D. 57 Phillips, M. I. 30 Pilar, J. 17 PlaninSic, G. 6 Pohmann,R. 1 Pope, J M 31.51 Potter, K. 33 Randall, E. W. 25 Rathke, J. W. 8 , 9 Reece,M. 27 Rinard,G. A. 4 Rizi, R. R. 3 Roffmann, W. U. 61 Rombach, K. 50 Ruttink, T. 45 Sagnowski, S. 62 Sandi, G. 9 Sarkar, S. K. 35 Scheenen, T. W. J. 46 Schlick, S. 17 Schmitz, U. 15 Schneider, H. 16 Scrimgeour, S. N. 24,26,43 Seki, Y. 36 Seo, Y. 28,36,42 Sharf, Y. 28,42 Shinar,H. 28 Shkarin,P. 10

Skirda, V. 53 Spencer, R. G . S. 10,33 Spiess, H.W. 14 Spyros, A. 2 Squires, L. 20 Strittmatter, R. 35 Sweeney, M. H. J. 31 Symms.M. 6 Szczesniak, E. 62 Takamiya, H. 42 Tomutsa, L. 56 Traub,B. 14 Truscott, R J W 31 Van As, H. 45,46 van der Weerd, L. 45 van Dusschoten, D. 45,46 Vasina, E. 53 Vergeldt, F. J. 45 Vienneau, T. 21 Volkov, V. 53 von Kienlin, M. 1 Waggoner, R. A. 27 Walton, J. H. 52 Wang,W. 52 Warren,W.S. 3 Wind, R. A. 37,58 Woelk, K. 8, 9 Wu, J. 51 Xia, Y. 32, 65 Zimmer, G . 15 Zwank,B.L. J. 8 Zweier, J. L. 34

743

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Subject Index A a priori information 18 acoustic - absorption 659 - efficiency 659 -noise 659 acquisition weighted k-space sampling 47 active shielding 653 actual field 650 adhesives 281 adiabatic half passage 36 adiabatic J cross polarization 3 1 aerogels 163 - optical properties 167 - pore structure 163, 167 - porosity 172 - silica 163 aggrecan 368 aggregates 80 aging 421 - of polymers 206 -thermal 213 agitation, gentle and strong 629 alumina-ceramic 658 alveoli 323 amplifier 664 amplitude 474 - measurements 567 - spin-echo 87 analgesic 259 anisotropic absorption 255 anisotropic T, of cartilage 360 aorta-caval fistula 389

APGSTE pulse sequence 165,172 articular cartilage 352 artifacts; motional 499 asymmetric gradients 677 average Hamiltonian (theory) 28, 184

B Boeddy 653 B , pulse field 717 backprojection (BP), see projection reconstruction benzene - generation 628 - retention 628 -images 630 BET gas adsorption 163,172 betaine 433 biexponential diffusion 342 bilayer tablets 263 biological samples, NMR-MOUSE 207 bioreactor, hollow fiber 363 bird eggs 499 bitumen 555 Bloch equation 95,721 blood vessel walls 307 Boltzmann distribution 716 bone 83,448 - bovine femur 83 - hip prosthesis 289 - mineral density 83 brain slice model 337 Brownian motion 103 bulk relaxation 558 burst 129

746

Subject Index

C calcification 368 calculus 450 capillary forces 267 carbon black 21 1 carbonates 564 cardiac dysfunction 393 carious lesion 459 carpets 265

Cam-Purcell-Meiboom-Gill (CPMG), see pulse sequences cartilage - anisotropic T2 360 -articular 352 - epiphyseal 368 - explant 363 - formation process 366 -growth plate 368 - histology 352 -hyaline 450 - isotropic TI 357 -laminae 357 - molecular orientations 361 -neo- 366 - relaxation processes 353 case I1 diffusion 241,255 castor bean seedlings 44 cavity, toroid 112 cell - bioenergetics 421 -edema 342 cement 273 - glass polyalkenoate 296 cesium-137, removal 628 characterization, (oil) reservoir 575 chemical shift 181 - anisotropy 733

- imaging 165, 167,413,414 - interaction 733 - spectroscopy 557 - xenon 166, 172 cholesterol gallstone 450 chondrocytes 364 -human 370 circle current path coil 687 cis-polyisoprene 37 coal 555 coaxial arc unit 684 Coccinella 7 punctata 467 coherence transfer spectra 3 1 coil(s) - crescent 666 - -form stiffness 659 -Golay 659 -mass 659 -noise 71 - circle current path 687 - longitudinal gradient 690 - surface- 103,295 collagen 352 - content 366 -fiber 452 - fibril orientation 360 -type11 368 -typeX 368 compact bone 83 compact magnets 639 compaction 299 comparison of nuclear interactions - magnitudes 735 - orientational properties 735 compomer 296 composite images 630 composite, dental 293 composites, elastomer-toughened 235

Subject Index

compression effects 236 concentration - gradients 113 - polarization 53 1 -profiles 222 - -dependent diffusion coefficient 103 concentric return path 666 concomitant gradient components 87 concrete 80 cone-and-plate 507 congestive heart failure 389 constant time imaging 77,448 constant-current (CC) 653 construction industry 281 contact angles 300 contamination 9 continous gradient 657 contrast 149 - enhancement 53 copolymer - PEO-PPO-PEO triblwk 232 - diblock 181 coral 82 correlation gradient 55 correlation time 561,720 cortex 433 coupled reactions 42 1 Courant condition 103 crescent coils 666 cross polarization - efficiency 34 - selectivity 34 - adiabatic J 31 -cyclic J 22 cross relaxation 353 cross section, scattering 172 crossflow 531 cross-link density 200, 204, 2 13

747

cross-linked -polymer 213 - polystyrene 227 cure, depth 293 current concentration ratios 657 CYCLCROP 33 cyclic J cross polarization 22 cylindrical 650

D D,O, *H20 see deuterium oxide damaged surfaces 255 DC efficiency 657 deformation, elastic, plastic 236 degenerative diseases 428 density matrix 55 - operator 7 16 dental -caries 459 - composite 293 dentistry 459 depletion zone 1 13 depth of cure 293 detector, toroid cavity 103 deuterated dissolution medium 261 deuterium oxide 347 diblock copolymers 18 1 dielectric properties 72 differential linearity 659 differential scanning calorimetry (DSC) 242 diffusion 95, 103, 171,202,247,259, 275,307,323,342,345,481,575,617 - biexponential 342 - case I1 24 1,255 -exchange 547 - Fickian 241,281,295 - fully restricted 60

748

Subject Index

- heterogeneous

328 - in magnetic field gradients 558 - measurements 630 - of liquid mixtures 295 - restricted 328,489 - translational 171 - weighting 405,409 diffusion coefficient(s) 103, 165, 172, 221,224,561 - apparent 328 - concentration-dependence 103 -initial 328 - long time limit 328 - short time limit 328 -water 364 diffusive edge enhancement 103 digital resolution 16 dimensionless 666 Dinocampus coccinellae 467 dipolar - broadening 75 - demagnetization field 55 - interaction 213, 353,733 dipolar couplings - elastomers 200 - couplings in solution 55 - couplings, monitoring 200 disintegration 259 displacement imaging 48 1 dissolution 259 distortion 650 distribution of pore sizes 560 distribution of relaxation times 560 DNA 421 doping 541 double quantum filtered NMR 307,452 drift 664 drug dynamics 4 13

dry core 261 drying -curve 269 - mechanism 265 -process 265 -rates 269 &-scalein proton solution NMR 733 DSP 703 dynamical mechanical thermal analysis 242

E earth formations 555 echo decays measured by the NMR-MOUSE 197 echo planar imaging (EPI) 57,653 - n-pulse-refocussed 87 echo time 474,542 eddies 653 eddy current compensation 653 edge enhancement, diffusive 103 efficiency - acoustic 659 -DC 657 - switching 648 eggs 499 Einstein-Smoluchowskirelation 103 ejection fraction 390 elastic deformation 236 elastography 664 elastomer 41, 149, 195,213 - cross-link density 200,204 - dipolar couplings 200 - -toughened composites 235 electrical resistivity 555 electrochemical cell 1 12 electrolytes, polymer 1 12 electron orbital shielding 733

Subject Index

electron paramagnetic resonance - gated imaging 387 - imaging 22 1,373 -in vivo 72 -pulse 72 - signal intensity 66 - spectroscopy 373 enamel 459 end diastolic volume 390 endoscope (NMR) 695 end-systolic volume 390 energy - conservation 265 - eigenvalue 7 14 - level 714 epiphyseal cartilage 368 epoxide resin 28 1 EPR / ESR, see electron paramugnetic resonance esophageal motility 395 2D ESRI 221 exchange 171 explant cartilage 363 extruder 523 extrusion 253 eyelens 345

F 19F 413 fabric 299 fast MR imaging 395 F-P-alanine (FBAL) 413,415 fibrous substrates 265 Fjck’s laws 103, 172, 224 Fickian diffusion, see difision FID 721 field inflection point 653 filler material 2 11

filling factor 66 filtration 531 finite element analysis 439 finite-difference approach 103 FLASH 128,707 flow (imaging) 48 1 , 517 - multi phase 521 -of fluid 575 -profile 481 -rate 543 fluid-surface interaction 56 1 fluoride 296 F-nuc 413 fold-back 653 force-cancellation 659 Fourier - interpolation 16 -method 87 - transformation 721 freeenergy 421 free radical 85, 373 free volume theory 225 free-radical polymerisation of n-butylmethacrylate 289 frequency -dependence 66 - encoding 184 -spatial 6 fructose 44 5-Fu 413 full surface reconstruction 459 fully restricted diffusion 550 functional mapping of the brain 428

G gamma-ray scattering 570 gas (phase) 82,555 gated EPR imaging 387

749

750

Subject Index

Gaussian 721 - propagation 324 generation of benzene 628 gentle and strong agitation 629 ghosts 653 glass polyalkenoate cement 296 glassy polymers 24 1 glucose 44 -char 385 glycosaminoglycan 352 Golay coils 659 GPC 433 gradient(s) 222,558 - asymmetric 677 -coils 375 - concomitant components 87 - correlation 55 - distribution 324 - -echo imaging 450 -gain 648 -internal 329 - longitudinal coil 690 - NON-CON coil 687 - null point 653 - oscillating 76 - pulsed field, see pulsedfield gradients - pulses, bipolar 326 -residual 653 -sets 675 -spoiling 79 -tuned 664 - underdriven pulse 87 - vibration 78 grating, z-magnetization 103 growth factors 370 growth plate cartilage 368 GRP composites 28 1

H Hahn spin echo 21 1,323 Hamiltonian, average 28, 184 Hartmanflahn -match 23 -mismatch 26 heart - congestive failure 389 -ischemic 374 -perfused 374 heat exchanger, scraped surface 539 helium 726 hemodialyzer 523 hexoses 44 high impact polystyrene 235 high multipole (behavior) 690 hip bone prosthesis 289 hippocampus 338 histogram 543 hollow fiber - bioreactor 363 - hemodialyzer 523 homogeneous broadening 720 human chondrocytes 370 hyaline cartilage 450 HYCAT 22 hydration kinetics, spatial dependence 290 hydrocarbon 555 hydrogels 225 hydrogen index 564 hyperpolarized gas NMR 82,726 hypertrophic zone 368 hypoosmotic 436

Subject Index

I IBM compatible PC 704 image reconstruction 222,375 image - pseudo-3D rendered 461 - real-time reconstruction system 707 - water-only, benzene-only, composite 630 imaginary signal 72 1 imaging (MU, MRM) 53,133, 163,236,254,337,355,364, 385,405,439,467,499,539,575,604, 736 - I3C proton detected 22 -19F 413,419 -2D 630 -3D 630 -4D 381 - chemical shift 413 - constant time 77,448 - displacement 48 1 - double-quantum filter 307,452 -EPR 373 - fast 395 - functional mapping of the brain 428 - gated EPR 387 - gradient-echo 450 - magnetization-gratingrotatingframe 103 - material properties 141, 2 1 1 -methods 145 - nitric oxide 385 - q-space 481 -radial 699 - rapid pulse train 103 - real-time and interactive 707 - rotating frame 103, 112,699 - single point 77

75 I

-solid state 141, 184 - spectroscopic 6,43 1 - spin-echo 450 - stray field (STRAFI) 76,95, 236,241, 254,274,287,293 -2-1 112 - velocity 509, 5 17 -window 230 impact resistance 235 impedance 664 - matching 649 in vivo EPR 72 incoherent motion 501 inductance 649 inhibitors 421 inhomogeneous - broadening 55,720 - fields (relaxation) 195 inositiol 433 in-tank precipitation process 628 interactions in NMR 732 intermolecular - multiple-quantum coherences 55 - zero-quantum coherences 53 internal gradient distribution 329 13-intervalpulse sequence 326 inverse Laplace transform 133 inversion-recovery sequence 73 1 ion mobility 113 IRsource 271 ischemic heart 374 isochromat 122 isolated perfused rat kidney 43 1 isotactic polypropylene 253 isotropic TI of cartilage 357

752

Subject Index

J Johnson noise 658

K kidney 43 1,483 kinetic theory of gases 172 k-space, acquisition weighted sampling 47

L lamellar 181 Larmor precession frequency 714 larval development 467 L-band 379 least-squares optimization 103 Legendre, second polynomium 353 lifetime distribution function 550 limited support 18 linearity 650 lithium triflate 112 local - deviation 650 -field 617 localized NMR spectroscopy 3,406 longitudinal gradient coil 690 loop gap resonator 66,377 Lorentzian 721 low magnetic field NMR 473,605 lung tissue 323

M macroscopic magnetization 716 magic angle 733 - spinning (MAS) 409 - condition 353 magic-echo 184 magnet 724 - compact 639

-shielded 642 - superconducting 639 magnetic resonance micro-imaging, see imaging magnetic resonance microscopy, see itnaging magnetic susceptibility anisotropy 167 magnetization 7 13 -grating 103 - grating rotating-frame imaging 103 - multiexponential decay 558 - prepared sequence 355 -transfer 171,364 magnetogyric ratio 7 14 maize 476 malignancy 133 manganese chloride 54 1 material properties imaging 141,211 materials - mesoporous 163 -porous 75 - restorative dental 295 mature zone 368 Maxwell -pairs 666 -terms 87 mean free path 172 medulla 433 membrane 523,531 - track etched 547 mercury injection porosimetry 605 mesoporous materials 163 metabolic mapping 4 13 metabolism in plants 42 methanol and acetone mixtures 241 micelles, wormlike 507 microfiltration 53 1 mitochondrial dysfunction 421

Subject Index

mixer (KENICS) 521 mixing 539 mixtures - diffusion 295 - methanol and acetone 241 mobility. ion 1 13 model, brain slice 337 MOIST 28 moisture - concentration 269 - distribution 267 -loss 269 -profiles 269 molecular level orientations in cartilage 361 molecular self diffusion, see dzffusion molybdenum, paramagnetic cations 230 monitoring of dipolar couplings 200 motion - artifacts 499 - incoherent 501 -periodic 502 motions, polymer chain 236 mouse tumor 413 MR cholangiography 450 MRI microscopy (MRM), see imaging MR02, metabolic rate 423 MS-DOS 704 multi phase flow 521 multiexponential magnetization decay 558 multiple-pulse 184 - line narrowing 76 multiple time points 79 multiple-quantum coherences, intermolecular 55 multipole (behavior high) 690 mutations 421

753

N nascent mitochondrial water 421 n-butylmethacrylate 288 neocartilage 366 nerve stimulation 663 nerve, sciatic 307 neutron scattering 567 NIHimage 396 nitric oxide 385 nitroxide spin probe 225 NMDA excitotoxicity 342 NMR, see nuclear magnetic resonance noise - acoustic 659 -coil 71 - experimental 726 -Johnson 658 - preamplifier 726 -rfcoil 726 - sample 7 1,726 non axi-symmetric systems 679 NON-CON gradient coil 687 nuclear magnetic resonance (NMR) 7 13 - emf signal 721 - endoscope 695 - experiment 724 - imaging, see imaging - instrumentation 723 - line shape 721 - line width 721 - microscopy, see imaging --MOUSE 195 - -MOUSE, echo decays 197 - -MOUSE-images on biological samples 207 - quantum mechanical approach 713 - semiclassical approach 7 13 -signal 726

754

Subject Index

- spectrometer - a block diagram 724 - spectroscopy 43 1,736 - spectroscopy, localized 3 nuclear magnetism 7 14 number of turns 649 nylon 266

parameter-selective 184 parasitoid 467 partial differential equations 103 partial refocussation 87 Peak - intensity in NMR spectroscopy 736 - shift in NMR spectroscopy 736

0

- splitting in NMR spectroscopy 736

I7O 421 oil 555,575 open-ended propagation problem 103 optical properties, aerogels 167 optical pumping 726 optimas 261 optimization, least-squares 103 organic - osmolytes 43 1 - solvents 255 oscillating gradient 76 osmolytes, organic 43 1 osmotic - perturbation 34 1 -stress 475 ossicular chain 439 osteoarthritis 352 osteoporosis 83 ouabain 341 oxidative phosphorylation 421 OXPHOS 421 oxygen concentration 38 1 oxygen-17 421

PEO-PPO-PEO triblock copolymer 232 perfused heart 374 periodic motion 503 PFG, see pulsed8eld gradients PGSENMR 489 pharmacological intervention 393 phase 481 -cycling 103 - encoding 181 -shift 481 phosph01~s-31 421 phosphorylation potential 425 photosynthetic activity 475 x-pulse-refocussed EPI 87 PIA 605 pigment gallstone 450 plant(s) 473,48 1 -growth 473 - metabolism 42 -transport 42 - water status 473 plastic deformation 236 point source 11 pointspread function 9 Poisson’s ratio 282 polarization correction 570 polarization, membranes 531 poly(ethylmethacry1ate) 288 polyacrylic acid 230 polybutadiene 37

P 31P 421 pain reliever 259 Papoulis-Gerchbergalgorithm 18 paramagnetic ions 568 paramagnetic molybdenum cations 230

Subjeci Index

polyester 28 1 polyethylene oxide 112 polyhydroxyoctanoate 37 polymer(s) 36 -aging 206 - chain motions 236 - crosslinked 2 13 - electrolytes 112 -glassy 241 - networks, swollen 227 - viscosity 247 polymeric surfactant 232 polymerisation of n-butylmethacrylate 289 polypropylene 266 - isotactic 253 polystyrene 227 - high impact 235 population difference 716 P d S >

- connectivity

606 -size 606 - sizes, distribution 560 - structure, aerogels 163, 167 porosimetry, mercury injection 605 porosity 606 - aerogels 172 porous medidmaterials 75,489,547, 575,617 Portland cement (Type I) pastes 288 potassium tetraphenylborate 628 power - deposition 29 -law fluid 541 PRAWN 29 pre-emphasis 653 presbyopia 345 PREVIEW 130

755

probe 724 projection 222 projection reconstruction 76,215,605 proliferating zone 368 propagation - equation 103 - problem, open-ended 103 propagator 48 1 propellants 149 properties - dielectric 72 - optical aerogels 167 proteoglycans 352 proton 726 - detected 13C imaging 22 - NMR microscopy, see imaging protonophores 42 1 pseudo-3D rendered image 461 pulp 459 pulse -EPR 72 - programmer 703 - underdrive 87 pulse sequence 542,724 -APGSTE 165,172 -CPMG 323 - 13-interval 326 - inversion-recovery 73 1 - magnetization-prepared 355 - multiple-pulse 184 - multiple-quantum 53 - quadrature echo sequence 293 -SECSI 166 - snapshot 396 -SPI 77 -spin echo 266 - spin-echo 730 -SPRITE 78

756

Subject Index

- steady state CPMG

199 - steady state free precession 199 - stimulated echo 548 -STRAFT 95 -XY16 197 - zero-quantum 53 pulsed field gradients (PFG) 165, 172, 324,481,547,630 pure phase encode 77

Q Q of resonator 7 1 Qlofactor 425 q-space imaging 481 quadrature echo sequence 293 quadrupolar - relaxation 75 - splitting 452 - interaction 735

R radial imaging 699 radio frequency (rf) 7 14 -coil 726 - pulse sequences, see pulse sequences - shield 79,653 rapid-imaging pulse train 103 rate controlling 259 Rayleigh criterion 15 reactions, coupled 421 real signal 721 real-time image reconstruction system 707 receiver 724 - dead time 557 reconstruction, full surface 459 re-entrant resonators 377 reflecting walls 33 1

relaxation (times) 275, 539,713 164 -bulk 558 - distribution 560 - effects 34,266 - in inhomogeneous fields 195 - processes 720 - - in cartilage 353 - quadrupolar 75 -rate 617 - rate distribution 133 - rate, transversal 133 - spin rotation 75 - spin-lattice ( T I ) 103, 166,731 - spin-spin (T2) 166, 167, 296, 413,474,730 --by CPMG 415 --byFSE 413 - - from k-space data 4 15 - steady state T , and T2 199 -surface 75 - T i 720 - agent

- T 2 , q 55 - TZe 184 - time mapping 79 release 259 removal of cesium- 137 628 repetition time (TR) 542 reservoir characterization 575 reservoir rock 575 residual gradients 653 resistance, impact 235 resistivity, electrical 555 resolution - limitation in NMR 726 -digital 16 - spatial 4 resolving power 15

Subject Index

resonant condition 7 17 resonator 375 - loop gap 66,377 - Q 71 - re-entrant 377 respiratory control 425 restorative dental materials 295 restricted diffusion, see diffusion restrictions, distribution of sizes 33 1 retention of benzene 628 rheometer, cone-and-plate 507 rigid solids 184 risetime 664 rock 555 - (oil) reservoir 575 rootcanal 461 rotating frame 7 17 - images 103,112,699 rotation speed 543 rubber, see elastomers

S sample noise 71 sandstones 561 saturation 36 SBR 211 scalar interaction 735 scattering - cross section 172 - gamma-ray 570 -neutron 567 sciatic nerve 307 scraped surface heat exchanger 539 second moment 6 17 SECSI pulse sequence 166 SEDOR 22 self diffusion, see diffmion

semiclassical description of the nuclear spin system 716 senile cataract 345 sensitivity 4,65,648 - enhancement of rare spins 23 settling time 664 SFG 324 shear-banding 507 shield, rf 653 shielded magnets 642 shielding - factor (SF) 653 -active 653 signal intensity 542 -EPR 66 signal-to noise ratio 60, 700 -how to maximize 726 - practical calculation 726 - scaling law 726 - theoretical calculation 726 silicone oil phantom 57 silica 211 - aerogels 163 simulated annealing 133,640,675 simulated tank waste slurries 629 simulation 123, 617 single point imaging 77 singularity 103 skeletal muscle 452 skindepth 72 sleep-aid 259 snapshot 396 sodium carboxymethyl cellulose solution 541 sodium tetraphenylborate 628 solid state imaging 141 solids loading 155 solubilization 259

757

758

Subject Index

solution, dipolar couplings 53 solvents, organic 255 sorption studies 281 spatial - dependence of the hydration lunetics 290 -frequency 6 - resolution 4 - response function 9 spectra, coherence transfer 3 1 spectral -density 266 -editing 33 - -spatial 379 spectrometer from Tecmag 542 spectroscopic imaging 6,452 spectroscopy - chemical shift 557 -EPR 373 - localized 406 spherical 650 -pores 492 spheroids 403 SPI 77 spin - echo sequence 87,266,450,460,730 - -half nucleus 714 - Hamiltonian in NMR 732 - -lattice relaxation ( T I ) ,see relaxation - -lock effect 197 - -operator 184 - perturbation 7 17 - probe, nitroxide 225 - rotation relaxation 75 - -spin relaxation (T2),see relaxation -warp 126 spoiling gradient 79 SPRITE 78

spurt effect 507 static field gradients 327 steady state -CPMG 199 - free precession 199 stimulated echo 200, 204, 324, 548 stray field imaging (STRAFI) 76,95, 236,241,254,274,287,293 - self-diffusion 95 stroke volume 390 sucrose 44 superconducting magnet systems 639 surface 558 - coil 103,295 - relaxation 75 -waves 525 surface-to-volumeratio 323, 331 surfactant, polymeric 232 surgery 695 susceptibility 474,650 - difference 323 - variations 55,57,60 switching efficiency 648 swollen networks 227

T 9.4T 413 T I ,see also relaxation - contrasting 73 1 - spatial images 112 T2,see also relaxation 413 - agarose gel 356 - anisotropy 361 -byCPMG 415 -byFSE 413 - from k-space data 415 T i -relaxation 720 T2,-relaxation 184

Subject Index

tar 555 target field 650 Tecmag spectrometer 542 teeth 448,459 temperature calibration 266 tendon 452 Tenebrio molitor 421 textile production processes 265 thermal -aging 213 -noises 726 -time constants 657 - treatment 539 thermocouples 266 Thomas and Windle 247 three essential stages in NMR 7 13 tissue 404 - cellularity 366 - compartmentation 342 - oxygenation 373 toggling frame 23 tomato 484 -ketchup 510 toroid cavity (detector) 103, 112 track etched membrane 547 tracking 696 translational diffusion, see diffusion transmitter 724 transport -in plants 42 -water 345 transversal relaxation rate, see T2 relaxation transverse magnetization 720 tumor 133 tuned gradients 664 turbo-factor 482 type I1 collagen 368

type X collagen 368

U uncouplers 421 underdriven gradient pulse 87

V vacuole 474 velocity imaging 509,5 17 vessel, blood 307 viscosity 561 -polymer 247 visible light cured glass polyalkenoate 293 voxel - localization 432 -shifting 16

W water 555 -cooling 658 - diffusion coefficient 330,364 - distribution 267 - extracellular 323 - intracellular 323 -images 630 - penetration 259 -phantom 60 -transport 345 -uptake 476 waves, surface 525 well logging 555 Windows95 704 wormlike micelles 507

759

760

Subject I n d a

X

Z

X-band 379 xenon 726 - chemical shifts 166, 172 XY 16 sequence 197

Zeeman -interaction 714 -splitting 714 zero filling 16 zero-quantum coherences, intermolecular 53 z-magnetization grating 103

Y yarns 266 Young's moduli

282,659

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