Plaque Imaging: Pixel to Molecular Level (Studies in Health Technology and Informatics, Vol. 113) (Studies in Health Technology and Informatics)

PLAQUE IMAGING: PIXEL TO MOLECULAR LEVEL Studies in Health Technology and Informatics This book series was started in ...

Author: J.S. Suri; C. Yuan; D.L. Wilson; S. Laxminarayan

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PLAQUE IMAGING: PIXEL TO MOLECULAR LEVEL

Studies in Health Technology and Informatics This book series was started in 1990 to promote research conducted under the auspices of the EC programmes Advanced Informatics in Medicine (AIM) and Biomedical and Health Research (BHR), bioengineering branch. A driving aspect of international health informatics is that telecommunication technology, rehabilitative technology, intelligent home technology and many other components are moving together and form one integrated world of information and communication media. The complete series has been accepted in Medline. In the future, the SHTI series will be available online. Series Editors: Dr. J.P. Christensen, Prof. G. de Moor, Prof. A. Hasman, Prof. L. Hunter, Dr. I. Iakovidis, Dr. Z. Kolitsi, Dr. Olivier Le Dour, Dr. Andreas Lymberis, Dr. Peter Niederer, Prof. A. Pedotti, Prof. O. Rienhoff, Prof. F.H. Roger France, Dr. N. Rossing, Prof. N. Saranummi, Dr. E.R. Siegel and Dr. Petra Wilson

Volume 113 Recently published in this series Vol. 112. T. Solomonides, R. McClatchey, V. Breton, Y. Legré, S. Nørager (Eds.), From Grid to Healthgrid Vol. 111. J.D. Westwood, R.S. Haluck, H.M. Hoffman, G.T. Mogel, R. Phillips, R.A. Robb, K.G. Vosburgh (Eds.), Medicine Meets Virtual Reality 13 Vol. 110. F.H. Roger France, E. De Clercq, G. De Moor and J. van der Lei (Eds.), Health Continuum and Data Exchange in Belgium and in the Netherlands – Proceedings of Medical Informatics Congress (MIC 2004) & 5th Belgian e-Health Conference Vol. 109. E.J.S. Hovenga and J. Mantas (Eds.), Global Health Informatics Education Vol. 108. A. Lymberis and D. de Rossi (Eds.), Wearable eHealth Systems for Personalised Health Management – State of the Art and Future Challenges Vol. 107. M. Fieschi, E. Coiera and Y.-C.J. Li (Eds.), MEDINFO 2004 – Proceedings of the 11th World Congress on Medical Informatics Vol. 106. G. Demiris (Ed.), e-Health: Current Status and Future Trends Vol. 105. M. Duplaga, K. Zieliński and D. Ingram (Eds.), Transformation of Healthcare with Information Technologies Vol. 104. R. Latifi (Ed.), Establishing Telemedicine in Developing Countries: From Inception to Implementation Vol. 103. L. Bos, S. Laxminarayan and A. Marsh (Eds.), Medical and Care Compunetics 1 Vol. 102. D.M. Pisanelli (Ed.), Ontologies in Medicine Vol. 101. K. Kaiser, S. Miksch and S.W. Tu (Eds.), Computer-based Support for Clinical Guidelines and Protocols – Proceedings of the Symposium on Computerized Guidelines and Protocols (CGP 2004) ISSN 0926-9630

Plaque Imaging: Pixel to Molecular Level

Edited by

Jasjit S. Suri Fischer Imaging Corporation

Chun Yuan University of Washington, Seattle, USA

David L. Wilson Case Western Reserve University, Cleveland, USA

and

Swamy Laxminarayan Idaho State University, Pocatello, USA

Amsterdam • Berlin • Oxford • Tokyo • Washington, DC

© 2005 The authors. All rights reserved All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without prior written permission from the publisher. ISBN 1-58603-516-9 Library of Congress Control Number: 2005925943 Publisher IOS Press Nieuwe Hemweg 6B 1013 BG Amsterdam Netherlands fax: +31 20 620 3419 e-mail: [email protected] Distributor in the UK and Ireland IOS Press/Lavis Marketing 73 Lime Walk Headington Oxford OX3 7AD England fax: +44 1865 750079

Distributor in the USA and Canada IOS Press, Inc. 4502 Rachael Manor Drive Fairfax, VA 22032 USA fax: +1 703 323 3668 e-mail: [email protected]

LEGAL NOTICE The publisher is not responsible for the use which might be made of the following information. PRINTED IN THE NETHERLANDS

Dedication

Jasjit Suri would like to dedicate this handbook to Swamy Laxminarayan, who has dedicated his life for the growth of Biomedical Engineering.

Chun Yuan would like to dedicate this handbook to his family and students.

David Wilson would like to dedicate this handbook to his family and students.

Swamy Laxminarayan would like to dedicate this book in memory of his beloved parents who were a constant source of inspiration in his life and to his in-laws Corie and Derk Zwakman for their genuine sense of family attachments and friendship.

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Plaque Imaging: Pixel to Molecular Level J.S. Suri et al. (Eds.) IOS Press, 2005 © 2005 The authors. All rights reserved.

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Preface

Chapter 1 presents the review of the plaque imaging techniques. It introduces the segmentation techniques for plaque classiﬁcation and quantiﬁcation. Chapter 2 we present an overview of the work on medical image retrieval and present a general framework of medical image retrieval based on plaque appearance. We stress on two basic features of medical image retrieval based on plaque appearance: plaque medical images contain complex information requiring not only local and global descriptors but also context determined by image features and their spatial relations. Additionally, given that most objects in medical images usually have high intra- and inter-patient shape variance, retrieval based on plaque should be invariant to a family of transformations predetermined by the application domain. To illustrate the medical image retrieval based on plaque appearance, we consider a speciﬁc image modality: intravascular ultrasound images and present extensive results on the retrieval performance. The increasing amount of medical images produced and stored daily in hospitals needs a database management system to organizes them in a meaningful way, without the necessity of time-consuming textual annotations for each image. One of the basic ways to organize medical images in taxonomies consists of clustering them depending of plaque appearance (for example, intravascular ultrasound images). Although lately, there has been a lot of research in the ﬁeld of Content-Based Image Retrieval systems, mostly these systems are designed for dealing a wide range of images but not medical images. Medical image retrieval by content is still an emerging ﬁeld, and few works are presented in spite of the obvious applications and the complexity of the images demanding research studies. Chapter 3 reviews current MRI techniques to differentiate stable versus high risk atherosclerosis and discusses the development of non-invasive MR imaging techniques to characterize atherosclerotic plaques. Tissue speciﬁc MR signal features will be described according to histo-pathological evaluation standards and comprehensive imaging protocol for the identiﬁcation of different lesion types will be introduced. Chapter 4 presents the material composition and morphology of the atherosclerotic plaque as these components are considered to be more important determinants of acute coronary ischemic syndromes than the degree of stenosis. When a vulnerable plaque ruptures it causes an acute thrombotic reaction. Rupture prone plaques contain a large lipid pool covered by a thin ﬁbrous cap. The stress in these caps increases with decreasing thickness. Additionally, the cap may be weakened by macrophage inﬁltration. IntraVascular UltraSound (IVUS) elastography might be an ideal technique to assess the presence of lipid pools and to identify high stress regions. Elastography is a technique that assesses the local elasticity (strain and modulus) of tissue. It is based on the principle that the deformation of tissue by a mechanical excitation is a function of its material properties. The deformation of the tissue is determined using ultrasound. For intravascu-

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lar purposes, the intraluminal pressure is used as the excitation force. The radial strain in the tissue is obtained by cross-correlation techniques on the radio frequency signals. The strain is color-coded and plotted as a complimentary image to the IVUS echogram. IVUS elastography, and IVUS palpography (which uses the same principle but is faster and more robust), have been extensively validated using simulations and by performing experiments in vitro and in vivo with diseased arteries from animals and humans. Strain was shown to be signiﬁcantly different in various plaque types (absent, fatty, ﬁbrous or calciﬁed). A high strain region with adjacent low strain at the lumen vessel-wall boundary has 88% sensitivity and 89% speciﬁcity for detecting vulnerable plaques. High strain regions at the lumen plaque-surface have 92% sensitivity and 92% speciﬁcity for identifying macrophages. Furthermore, the incidence of vulnerable-plaque-speciﬁc strain patterns in humans has been related to clinical presentation (stable angina, unstable angina or acute myocardial infarction) and the level of C-reactive protein. In conclusion, the results obtained with IVUS (strain and modulus) elastography/palpography, show the potential of the technique to become a unique tool for clinicians to assess the vulnerability and material composition of plaques. Chapter 4 presents the analysis of the soft tissue based on computer vision techniques. Numerical simulations, which are based on reliable biomechanical models of blood vessels, can help to get a better understanding of cardiovascular diseases such as atherosclerosis, and can be used to develop optimal medical treatment strategies. Blood vessels consist of three different soft tissue layers that all have different mechanical properties. The adventitia (tunica externa) is the outer most layer and its mechanical properties are essentially determined by the three-dimensional, structural arrangement of collagen ﬁbre bundles embedded in the tissue. Global information such as the orientation statistics of the ﬁbre bundles as well as detailed information as the crimp of the single ﬁbres within the bundles is of particular interest in biomechanical modeling. In order to obtain a sufﬁciently large amount of data for biomechanical modeling, a fully automatic method for the structural analysis of the soft tissue is required. In this contribution we present methods based on computer vision to fulﬁll this task. We start by discussing proper tissue preparation and imaging techniques that have to be used to obtain data, which reliably represents the real three-dimensional tissue structure. The next step is concerned with algorithms that robustly segment the collagen ﬁbre bundles and cope with various kinds of artifacts. Due to the wide variety of different appearances of collagen ﬁbres in images the segmentation is non trivial. Novel segmentation techniques for robust segmentation of individual ﬁbril bundles and methods for estimation of their parameters, such as location, shape, ﬁbril density, mean ﬁbril orientation, crimp of ﬁbrils, etc. is discussed. The proposed algorithms are based on novel perceptual grouping methods operating on the extracted orientation data of ﬁbrils. Finally, we demonstrate the results obtained by our fully automatic method on real data. In addition, for a more quantitative assessment, we introduce a generative structural model that enables the synthesis of three-dimensional ﬁbre bundles with well-deﬁned characteristics. Chapter 6 we present recent developments in the modeling of coronary artery biomechanics. We ﬁrst introduce the pathology and localization of lesions in the circulatory system. Recent ﬂuid and structural modeling of CAD is presented and discussed. At the end of the chapter, we present recent effort in coupling these two modeling domains using ﬂuid-structure interaction (FSI).

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Chapter 7 presents the Cardiac CT for the assessment of cardiovascular pathology with an emphasis on the detection of coronary atherosclerosis. Cardiac CT is a robust technology for the non-invasive assessment for a spectrum of cardiovascular disease processes. This imaging modality can provide assessment of atherosclerotic plaque burden and coronary artery disease risk through coronary calcium scoring. Advances in spatial and temporal resolution, electrocardiographic triggering methodology, and image reconstruction software have helped in the evaluation of coronary artery anatomy and vessel patency, providing the ability to noninvasively diagnose or rule out signiﬁcant epicardial coronary artery disease. This technique also allows the 3-dimensional simultaneous imaging of additional cardiac structures including coronary veins, pulmonary veins, atria, ventricles, aorta and thoracic arterial and venous structures, with deﬁnition of their spatial relationships for the comprehensive assessment of a variety of cardiovascular disease processes. Chapter 8 details technical and practical issues regarding coronary atherosclerotic plaque imaging by CT, which then help deﬁne its technical capabilities and engineering limitations for clinical usage. The focus will be on coronary calcium imaging, but the principles are the same for atherosclerosis deﬁnition in any major artery. Chapter 9 demonstrates the feasibility of a non-invasive, in vivo determination of the IBS of arterial wall tissues, such as atherosclerotic plaques, despite the phase aberration of the intervening tissues. Studies done on carotid arteries suggest that the morphology and composition of atherosclerotic plaque are predictive of stroke risk. The goal of this investigation has been to demonstrate that the true acoustic integrated backscatter (IBS) from plaque regions can be measured non-invasively, based on which plaque composition may be inferred and thus become a tool to estimate the likelihood of a lesion or plaque being stable or vulnerable, i.e. having a risk of causing a stroke. To obtain the true IBS non-invasively, the scattering and aberrating effect of the intervening tissue layers must be overcome. This is achieved by using the IBS from arterial blood as a reference backscatter, speciﬁcally the backscatter from a blood volume along the same scan line as and adjacent to the region of interest. We have shown that the variance of the IBS estimate of the blood backscatter signal can be quantiﬁed and reduced to a speciﬁed tolerable level. Stroke is the third leading cause of death in the western world and the major cause of disability in adults. The objective of this work was to develop a computer aided system that will facilitate the automated characterization of carotid plaques for the identiﬁcation of individuals with asymptomatic carotid stenosis at risk of stroke. Ultrasound scans of carotid plaques were performed using duplex scanning and color ﬂow imaging. From the segmented plaque images texture feature sets and shape parameters were extracted. The plaques were classiﬁed into two types: (i) symptomatic because of ipsilateral hemispheric symptoms, or (ii) asymptomatic because they were not connected with ipsilateral hemispheric events. For the plaque classiﬁcation a modular system composed of neural self-organizing feature map (SOM) classiﬁers or statistical K-nearest nearest classiﬁers, was used. For each feature set, a classiﬁer was trained and their classiﬁcation results were combined using majority voting and weighted averaging. In Chapter 10 two independent studies were conducted. In the ﬁrst study with 230 plaques, ten different texture feature sets were extracted and used for classiﬁcation. The ten classiﬁcation results were further combined in order to improve the diagnostic yield. In the second study with 330 plaques, morphological features were extracted and their

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classiﬁcation results were compared with the results obtained by the most successful texture feature sets of the ﬁrst study. Both studies yielded comparable results verifying each other’s correctness. The highest diagnostic yield was 73.1% and was achieved by combing the ten SOM classiﬁers using weighted averaging. In conclusion, the results in this work show that it is possible to identify a group of patients at risk of stroke using neural network technology and texture features extracted from high resolution ultrasound images of carotid plaques. This group of patients may beneﬁt from a carotid endarterectomy whereas other patients may be spared from an unnecessary operation. Chapter 11 addresses the problem of reliable feature extraction and classiﬁcation process. Derivatives of Gaussian ﬁlter’s bank, co-occurrence matrices measures, cumulative moments and local binary patterns are the feature extraction processes selected for comparison. The classiﬁcation process used is the highly discriminative, adaptative boosting (AdaBoost). As a result, the recognition rate of each different pair of plaques involved in IVUS plaque characterization is assessed in an objective IVUS tissue database. It is known that is there is a high correlation between plaque rupture or endothelial erosion with subsequent thrombosis formation and acute coronary syndromes. The highrisk plaque is extremely related to the composition and morphology of the plaque itself. Therefore, plaque characterization in IVUS images is of great importance to the medical community since they provide a feasible way for identiﬁcation of high-risk plaques. The identiﬁcation of the different kind of plaques in medical imaging requires basically of two steps: First, a reliable feature extraction process, that characterizes the different plaques to be distinguished. And second, a classiﬁcation process that labels each incoming new plaque in one of the desired classes. Chapter 12 presents advanced mathematical techniques to extract spectral information from the RF data to determine the plaque composition. IVUS is a minimally invasive imaging modality that provides cross-section images of arteries in real-time, allowing visualization of atherosclerosis plaques in vivo. In standard IUVS gray scale images, calciﬁed region of plaque and dense ﬁbrous components generally reﬂect ultrasound ultrasound energy well and thus appear bright and homogeneous IVUS images. Conversely regions of low echo reﬂectance in IVUS images are usually is labeled as soft or mixed plaque. However this visual interpretation has been demonstrated to be very inconsistent in accurately determining plaque composition and does not allow real time assessment of qualitative plaque constituents. Spectral analysis of the backscattered RF ultrasound signals allows detailed assessment of plaque composition. Advanced mathematical techniques can be employed to extract spectral information from these RF data to determine composition. The spectral content or signature of RF data reﬂected from tissue depends on density, compressibility, concentration and size, etc. A combination of spectral parameters were used to develop the statistical classiﬁcation scheme of analysis of in-vivo IVUS data in real-time. The clinical data acquisition system in ECG gated and the analysis software developed by our group reconstructs IVUS images from from acquired RF data. A combination of spectral parameters and active contour models is used for 3-D of plaque segmentation followed by color-coded tissue maps for each image cross-section and longitudinal views of the entire vessel. The “ﬂy-through” mode allows one to visualize the complete length of the artery internally with the histology components at the lumen surface. In addition, the vessel and plaque matrices such as areas and

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volumes of individual plaque components (collagen, ﬁbro-lipid, calcium, lipid-core) are also available. Angiography or intravascular ultrasound (IVUS). Angiography provides information about the vessel lumen and its geometry. IVUS offers more detailed information that also includes the vascular wall. Chapter 13 describes these two imaging modalities and their geometrically correct fusion yielding a 3-D and/or 4-D representation of the coronary geometry and morphology. The image-derived information is used for assessment of coronary function and plaque severity, blood ﬂow related indices are determined using computational ﬂuid dynamics. Detailed description of the methodology is followed by validation and clinical studies. Chapter 14 reviews the state of the art in contrast-enhanced MRI of atherosclerosis. It begins with a section describing observed late-phase enhancement characteristics and their association with tissue types. The bulk of the chapter will discuss the challenges and quantitative advantages of dynamic contrast-enhanced imaging of plaque. Then a brief overview will be presented of tissue-speciﬁc agents such as USPIOs that target speciﬁc plaque features. These topics are illustrated with a variety of case studies. In all cases, subjects provided informed consent and the studies were approved by the institutional review boards. The chapter will close with a discussion of the comparative merits of each of these techniques. Chapter 15 presents the research to test the hypotheses that (1) vessel wall volume measurements from dark blood MR images with multiple contrast-weightings (T1W, T2W and PDW) are highly reproducible, and that (2) the intra-observer and interobserver variability of carotid wall volume measurements will be less than those obtained with maximum wall area (MaxWA) measurements. Methods: Sixteen patients (aged 72 ± 7 years) with carotid stenosis documented by duplex ultrasound were recruited for the study. Dark blood T1W, PDW and T2W MR images were used to measure carotid wall volume and MaxWA by two independent observers for inter-observer and intra-observer variability assessment. Results: The intra-observer absolute difference of carotid wall volume for T1W, T2W and PDW images were 67.3 ± 47.5 mm3 (2.3 ± 1.8%), 63.2 ± 52.2 mm3 (2.0 ± 1.3%), and 69.8 ± 45.2 mm3 (2.4 ± 1.7%) respectively. The inter-observer absolute difference of carotid wall volume for T1W, T2W and PDW images were 103.5 ± 141.8 mm3 (3.0 ± 3.1%), 95.9 ± 102.1 mm3 (3.1 ± 2.6%), and 132.1 ± 87.8 mm3 (4.3 ± 2.7%) respectively. The intra-observer absolute difference of carotid MaxWA for T1W, T2W and PDW images were 6.9 ± 5.0 mm2 (4.2 ± 2.9%), 5.1 ± 4.2 mm2 (3.1 ± 2.3 %) and 7.5 ± 4.7 mm2 (4.2 ± 2.7 %) respectively. The interobserver absolute difference of carotid MaxWA for T1W, T2W and PDW images were 9.5 ± 4.2 mm2 (5.8 ± 2.3%), 6.4 ± 6.1 mm2 (3.8 ± 3.1 %) and 10.8 ± 7.3 mm2 (6.1 ± 3.7 %) respectively. Both intra- and inter-observer variability in carotid volume measurement tend to be smaller than that in carotid MaxWA measurement with intraclass correlation coefﬁcients ranged 0.932 to 0.987 for volume measurement and 0.822 to 0.946 for MaxWA measurement. Chapter 16 presents a three-dimensional image registration algorithm for magnetic resonance (MR) images of carotid vessels. We used a mutual information registration algorithm to compensate movements between image acquisitions. Proton density (PD), T1, and T2 images were acquired from patients and volunteers and then matched for image analysis. Visualization methods such as contour overlap showed that vessels well aligned after registration. Distance measurements from the landmarks indicated that the

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registration method worked well with an error of 1.09 ± 0.42 mm. Potential applications include atherosclerotic plaque characterization and plaque burden quantiﬁcation vectorbased segmentation using dark blood MR images having multiple contrast weightings (PD, T1, and T2). Another application is measurement of disease progression and regression with drug trials. Chapter 17 will present techniques for characterizing blood ﬂow patterns in large arteries from magnetic resonance angiography (MRA) and velocity-encoded phasecontrast magnetic resonance imaging. Considerable evidence has emerged that disturbed blood ﬂow patterns are a major factor in the onset of atherosclerotic disease and may play a role in disease progression. This technique, known as vascular computational ﬂuid dynamics (CFD), has been applied extensively to the bifurcation region of the carotid artery, a common site of plaque formation. Common hemodynamic features in this region will be presented based on imaging of a series of normal subjects. Hemodynamic features in the vicinity of the carotid bifurcation will also be presented for a series of subjects with advanced atherosclerotic disease. Chapter 18 will discuss some of the modeling tools developed to study drug delivery by drug eluting stents. In order to successfully prevent restenosis, drug eluting stents must deliver a therapeutic drug dose evenly through the treatment region for a deﬁned duration. Favorable results have come from animal trials in porcine models, unfortunately information about the dose distribution over time is difﬁcult to obtain from investigations of this nature. Moreover, porcine models of drug-eluting stents concentrate on measuring the degree of restenosis rather than drug concentrations in the tissue of interest. Clinical studies have shown impressive results with sirolimus-eluting stents even in complex disease vessels, however failure of the target vessel still occur in up to 10% in the ﬁrst year.

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The Editors Dr. Jasjit S. Suri received his BS in Computer Engineering in distinction from Maulana Azad College of Technology, Bhopal, India, his MS in Computer Sciences from University of Illinois, Chicago, and Ph.D. in Electrical Engineering from University of Washington, Seattle. He has been working in the ﬁeld of Computer Engineering/Imaging Sciences for over 20 years. He has published more than 125 technical papers in body imaging. He is a lifetime member of research engineering societies: Tau-Beta-Pi, Eta-Kappa-Nu, Sigma-Xi and a member of NY Academy of Sciences, Engineering in Medicine and Biology Society (EMBS), SPIE, ACM and is also a Senior Member of IEEE. He is in the editorial board/reviewer of several international journals such as: Real Time Imaging, Pattern Analysis and Applications, Engineering in Medicine and Biology, Radiology, Journal of Computer Assisted Tomography, IEEE Transactions of Information Technology in Biomedicine and IASTED Board. He has chaired image processing tracks at several international conferences and has given more than 40 international presentations/seminars. Dr. Suri has written six books in the area of body imaging (such as Cardiology, Neurology, Pathology, Mammography, Angiography, Atherosclerosis Imaging) covering Medical Image Segmentation, image and volume registration, and physics of medical imaging modalities like: MRI, CT, Xray, PET and Ultrasound. He also holds several United States Patents. Dr. Suri has been listed in Who’s Who 8 times, is a recipient of President’s Gold medal in 1980 and has received more than 50 scholarly and extra-curricular awards during his career. He is also a Fellow of American Institute of Medical and Biological Engineering (AIMBE) and ABI. Dr. Suri’s major interests are: Computer Vision, Graphics and Image Processing (CVGIP), Object Oriented Programming, Image Guided Surgery and Teleimaging. Dr. Suri had worked for Philips Medical Systems and Siemens Medical Research Divisions. He is also a Visiting Professor with Department of Computer Science, University of Exeter, Exeter, England, University of Barcelona, Spain. Currently, Dr. Suri is Senior Director, Research and Development, Fischer Imaging Corporation.

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Professor Chun Yuan is a researcher in the ﬁeld of magnetic resonance imaging of cardiovascular systems. He has pioneered multiple highresolution MRI techniques for imaging vulnerable atherosclerotic plaques, directed numerous studies examining carotid atherosclerosis with MRI, and has published extensively on the development of imaging sequences and processing techniques and new conceptual quantitative tools for biomedical use. He is a founding member of the Society for Cardiovascular Magnetic Resonance and sits on the Advisory Boards of the Vulnerable Plaque Organization, Pﬁzer Atherosclerosis, and the Center for Transnational Media Studies. He is presently Professor of Radiology in the School of Medicine at the University of Washington, Adjunct Professor of Electrical Engineering and Bioengineering in the College of Engineering at the University of Washington, the Founder and Executive Director of the Vascular Imaging Laboratory at the University of Washington Medical Center, Visiting Professor at the Post Graduate Medical College of the Chinese Military Service, and has been a Visiting Professor at the University of Lyon and Baylor Medical College. He earned his Ph.D. in Medical Biophysics and Computing at the University of Utah – Salt Lake City. Currently Dr. Yuan designing new technological imaging processes to quantify the morphological and compositional aspects of atherosclerosis. He is also working on making the Vascular Imaging Lab a model interdisciplinary hub that brings together scholars from a broad range of disciplines – from Engineering to Anthropology, from Medicine to Philosophy – to study both the medical and social dimensions of cardiovascular disease. Professor David Wilson is a Professor of Biomedical Engineering and Radiology, Case Western Reserve University. He has research interests in image analysis, quantitative image quality, and molecular imaging, and he has a signiﬁcant track record of federal research funding in these areas. He has over 60 refereed journal publications and has served as a reviewer for several leading journals. Professor Wilson has six patents and two pending patents in medical imaging. Professor Wilson has been active in the development of international conferences; he was Track Chair at the 2002 EMBS/BMES conference, and he was Technical Program Co-Chair for the 2004 IEEE International Symposium on Biomedical Imaging. Professor Wilson teaches courses in biomedical imaging, and biomedical image processing and analysis. He has advised many graduate and undergraduate students, all of whom are quite exceptional, and has been primary research advisor for over 16 graduate students since starting his academic career. Prior to joining CWRU, he worked in X-ray imaging at Siemens

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Medical Systems at sites in New Jersey and Germany. He obtained his PhD from Rice University. Professor Wilson has actively developed biomedical imaging at CWRU. He has led a faculty recruitment effort, and he has served as PI or has been an active leader on multiple research and equipment developmental awards to CWRU, including an NIH planning grant award for an In Vivo Cellular and Molecular Imaging Center and an Ohio Wright Center of Innovation award. He can be reached at [email protected]. Professor Swamy Laxminarayan currently serves as the Chief of Biomedical Information Engineering at the Idaho State University. Previous to this, he held several senior positions both in industry and academia. These have included serving as the Chief Information Ofﬁcer at the National Louis University, Director of the Pharmaceutical and Health Care Information Services at NextGen Internet (the premier Internet organization that spun off from the NSF sponsored John von Neuman National Supercomputer Center in Princeton), Program Director of Biomedical Engineering and Research Computing and Program Director of Computational Biology at the University of Medicine and Dentistry in New Jersey, Vice-Chair of Advanced Medical Imaging Center, Director of Clinical Computing at the Monteﬁore Hospital and Medical Center and the Albert Einstein College of Medicine in New York, Director of the VocalTec High Tech Corporate University in New Jersey, and the Director of the Bay Networks Authorized Center in Princeton. He has also served as an Adjunct Professor of Biomedical Engineering at the New Jersey Institute of Technology, a Clinical Associate Professor of Health Informatics, Visiting Professor at the University of Brno in Czech Republic and an Honorary Professor of Health Sciences at Tsinghua University in China. As an educator, researcher and technologist, Prof. Laxminarayan has been involved in biomedical engineering and information technology applications in medicine and health care for over 25 years and has published over 250 scientiﬁc and technical articles in international journals, books and conferences. His expertise are in the areas of biomedical information technology, high performance computing, digital signals and image processing, bioinformatics and physiological systems analysis. He is the co-author of the book on State-of-the-Art PDE and Level Sets Algorithmic Approaches to Static and Motion Imagery Segmentation published by Kluwer Publications and the book on Angiography Imaging: State-of-the-Art Acquisition, Image Processing and Applications Using Magnetic Resonance, Computer Tomography, Ultrasound and X-ray, Emerging Mobile E-Health Systems, published by the CRC Press and two volumes of the Handbook of Biomedical Imaging to be published by the Kluwer publications. He has also authored as the editor/co-editor of 20 international conferences and has served as a keynote speaker in international conferences in 43 countries. He is the Founding Editor-in-Chief and Editor Emeritus of the IEEE Transactions on Information Technology in Biomedicine. He served as an elected member of the administrative and executive committees in the IEEE Engineering in Medicine and Biol-

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ogy Society and as the Society’s Vice President for 2 years. His other IEEE roles include his appointments as Program Chair and General Conference Chair of about 20 EMBS and other IEEE Conferences, an elected member of the IEEE Publications and Products Board, member of the IEEE Strategic Planning and Transnational Committees, Member of the IEEE Distinguished Lecture Series, Delegate to the IEEE USA Committee on Communications and Information Policy (CCIP), U.S. Delegate to the European Society for Engineering in Medicine, U.S. Delegate to the General Assembly of the IFMBE, IEEE Delegate to the Public Policy Commission and the Council of Societies of the AIMBE, Fellow of the AIMBE, Senior Member of IEEE, Life Member, Romanian Society of Clinical Engineering and Computing, Life Member, Biomedical Engineering Society of India, U.S. Delegate to IFAC and IMEKO Councils in TC13. He was recently elected to the Administrative Board of the International Federation for Medical and Biological Engineering, a worldwide organization comprising 48 national members, overseeing global biomedical engineering activities. He was also elected to serve as the Publications Co-Chairman of the Federation. His contributions to the discipline have earned him numerous national and international awards. He is a Fellow of the American Institute of Medical and Biological Engineering, a recipient of the IEEE 3rd Millennium Medal and a recipient of the Purkynje award from the Czech Academy of Medical Societies, a recipient of the Career Achievement Award, numerous outstanding accomplishment awards and twice recipient of the IEEE EMBS distinguished service award. He can be reached at [email protected].

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Acknowledgements

This book is the result of collective endeavours from several noted engineering and computer scientists, mathematicans, medical doctors, physicists, and radiologists. The editors are indebted to all of their efforts and outstanding scientiﬁc contributions. The editors are particularly grateful to Drs. Petia Reveda, Chun Yuan, David Wilson, Chris L. de Korte, Horst Bischof, Richard Mongrain, John A. Rumberger, Peder C. Pedersen, Costas Pattichi, Anuja Nair, Milan Sonka, Andreas Wahle, William S. Kerwin, Shaoxiong Zhang, and Peter Yim and their team members for working with us so closely in meeting all of the deadlines of the book. We would like to express our appreciation to IOS Press, The Netherlands for helping create this invitational book in plaque imaging. We are particularly thankful to Einar Fredriksson, Director, publications division of IOS press, Anne Marie de Rover, book production coordinator, and Carry Koolbergen editorial administration, rights and permissions, The Netherlands for their excellent coordination of the book at every stage. Dr. Suri would like to thank Fischer Imaging Corporation for their encouragements during his experiments and research. Special thanks are due to Harris Ravine, Roman Janer, and Janine Broda. Thanks go to Philips Medical Systems for their data sets during their experiments. Thanks also go to: Dr. Larry Kasuboski and Dr. Elaine Keeler from Philips Medical Systems, Inc., for their support and motivations. Thanks are also due to my past Ph.D. committee research professors, particularly Professors Linda Shapiro, Robert M. Haralick, Dean Lytle and Arun Somani, for their encouragements. We extend our appreciations to Drs. Ajit Singh, Siemens Medical Systems, George Thoma, Chief Imaging Science Division from National Institutes of Health, Dr. Sameer Singh, University of Exeter, UK for his motivations. Special thanks go to the Book Series Editor, Professor Evangelia Micheli-Tzanakou for advising us on all aspects of the book. We thank the IEEE Press, Academic Press, Springer Verlag Publishers, and several medical and engineering journals for permitting us to use some of the images previously published in these journals. Finally, Jasjit Suri would like to thank his wife Malvika Suri for all the love and support she has showed over the years and to our baby Harman whose presence is always a constant source of pride and joy. I also express my gratitude to my father, a mathematician, who inspired me throughout my life and career, and to my late mother, who most unfortunately passed away a few days before my Ph.D. graduation, and who so much wanted to see me write this book. Special thanks to Pom Chadha and his family, who taught me life is not just books. He is one of my best friends. I would like to also thank my in-laws who have a special place for me in their hearts and have shown lots of love and care for me. David Wilson would like to acknowledge the support of the Department of Biomedical Engineering, Case Western Reserve University in this endeavor. Special thanks are

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due to the many colleagues and students who make research in biomedical engineering an exciting, wondrous endeavor. Swamy Laxminarayan would like to express his loving acknowledgements to his wife Marijke and to his kids, Malini and Vinod for always giving the strength of mind amidst all life frustrations. The book kindles fondest memories of my late parents who made many personal sacriﬁces that helped shape our careers and the support of my family members who were always there for me when I needed them most. I have shared many ideas and thoughts on the book with numerous of my friends and colleagues in the discipline. I acknowledge their friendship, feedbacks and discussions with particular thanks to Prof. David Kristol of the New Jersey Institute of Technology, Peter Brett of Ashton University, Ewart Carson of the City University, London, Laura Roa of the University of Sevilla in Spain, and Jean Louis Coatrieux of the University of Rennes in France, for their constant support over the past two decades. Chun Yuan would like to acknowledge the support of my colleagues at the Vascular Imaging Lab and the University of Washington – none of this would be possible without their dedication, hard-work, and patience. I thank the National Heart and Lung Institute, Pﬁzer, and Astra Zeneca for the critical ﬁnancial support they have provided. And ﬁnally, I would also like to express my gratitude to my friends and family for their emotional sustenance.

xix

The Contributors Jasjit S. Suri, Ph.D. Case Western Reserve University Cleveland, OH, USA

Stavros Kakkos, Ph.D. Imperial College University of London London, UK

Chun Yuan, Ph.D. University of Washington Seattle, WA, USA

Maura Grifﬁn, Ph.D. Imperial College University of London London, UK

David L. Wilson, Ph.D. Case Western Reserve University Cleveland, OH, USA

Andrew Nicolaides, Ph.D. Imperial College University of London London, UK

Swamy Laxminarayan, DSc. Idaho State University Pocatello, ID, USA

Jaume Amores, Ph.D. Centre de Visió per Computador Barcelona, Spain

Thomas S. Hatsukami, M.D. University of Washington Seattle, WA, USA Jianming Cai, Ph.D. University of Washington Seattle, WA, USA Efthyvoulos Kryiacou, Ph.D. University of Cyprus Nicosia, Cyprus

Petia Radeva, Ph.D. Centre de Visió per Computador Barcelona, Spain Radj A. Baldewsing, M.Sc Thoraxcenter, Erasmus MC Rotterdam, The Netherlands Johannes A. Schaar, M.D. Thoraxcenter, Erasmus MC Rotterdam, The Netherlands

Marios S. Pattichis, Ph.D. University of New Mexico Albuquerque NM, USA

Chris L. de Korte, Ph.D. Laboratory of Clinical Physics Institution, UMC St. Radboud Nijmegen, The Netherlands

Christodoulos I. Christodoulou, Ph.D. University of Cyprus Nicosia, Cyprus

Frits Mastik Thoraxcenter, Erasmus MC Rotterdam, The Netherlands

Constantinos S. Pattischis, Ph.D. University of Cyprus Nicosia, Cyprus

Patrick W. Serruys, Ph.D. Thoraxcenter, Erasmus MC Rotterdam, The Netherlands

xx

Antonius F. W. van der Steen, Ph.D. Thoraxcenter, Erasmus MC Rotterdam, The Netherlands

Dongxiang Xu, Ph.D. University of Washington Seattle, WA, USA

Jerold S. Shinbane, M.D. UCLA CA, USA

William S. Kerwin, Ph.D. University of Washington Seattle, WA, USA

Matthew J. Budoff, M.D. UCLA CA, USA

Shaoxing Zhang, Ph.D./M.D. CWRU OH, USA

John A. Rumberger, M.D. The Ohio State University Columbus, OH, USA

Olivier Salvado, M.S. CWRU OH, USA

Peder C. Pedersen, Ph.D. Worcester Polytechnic Institute Worcester, MA, USA

Yiping Chen, Ph.D. CWRU OH, USA

Ruben Lara-Montalvo, Ph.D. Worcester Polytechnic Institute Worcester, MA, USA

Claudio Hillenbrand, Ph.D. CWRU OH, USA

Jacob Chakareski, Ph.D. Worcester Polytechnic Institute Worcester, MA, USA

Frank K. Wacker, Ph.D. CWRU OH, USA

Anuja Nair, Ph.D. Cleveland Clinic Foundation Cleveland, OH, USA

Jeffrey L. Durek, Ph.D. CWRU OH, USA

John D. Klingensmith, Ph.D. Cleveland Clinic Foundation Cleveland, OH, USA

Jonathan S. Lewin, M.D. CWRU OH, USA

D. Geoffrey Vince, Ph.D. Cleveland Clinic Foundation Cleveland, OH, USA

Baowei Fei, Ph.D. CWRU OH, USA

Andreas Wahle, Ph.D. University of Iowa Iowa City, IA, USA

Horst Bischof, Ph.D. Graz University of Technology Austria

Milan Sonka, Ph.D. University of Iowa Iowa City, IA, USA

Pierre Elbischger, MSc Graz University of Technology Austria

xxi

Gerald Holzapfel, Ph.D. Graz University of Technology Austria

J. Kevin J. DeMarco, M.D. UMDNJ New Brunswick, NJ, USA

Peter Regitnig, M.D. Graz Medical University Austria

Juan R. Cebral, Ph.D. UMDNJ New Brunswick, NJ, USA

Rosaire Mongrain, Ph.D. McGill University Montreal, Quebec, Canada Richard Leask, Ph.D. McGill University Montreal, Quebec, Canada Ramses Galaz, MEng McGill University Montreal, Quebec, Canada Adrian Ranga, BEng. McGill University Montreal, Quebec, Canada Jean Brunette, Ph.D. Université de Montréal Montreal, Quebec, Canada Anil Joshi, MSc. University of Toronto Toronto, Ontario, Canada Jean-Claude Tardif, M.D. Université de Montréal Montreal, Quebec, Canada

Marcelo A. Castro, Ph.D. George Mason University Farifax, VA, USA Isam Faik, MEng McGill University Quebec, Canada Neil Bulman-Fleming, MEng McGill University Quebec, Canada Trongtin Nguyen, MEng McGill University Quebec, Canada Chunming Li, Ph.D. University of Connecticut Storrs, CT, USA Jim Macione, Ph.D. University of Connecticut Storrs, CT, USA

Olivier F. Bertrand, M.D., Ph.D. Laval University Quebec City, Quebec Canada

Zhi Yang, Ph.D. University of Connecticut Storrs, CT, USA

Peter Yim, Ph.D. UMDNJ New Brunswick, NJ, USA

Martin D. Fox, Ph.D., M.D. University of Connecticut Storrs, CT, USA

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xxiii

Contents Preface

vii

The Editors

xiii

Acknowledgements

xvii

The Contributors

xix

Plaque Imaging Using Ultrasound, Magnetic Resonance and Computer Tomography: A Review Jasjit S. Suri, Constantinos S. Pattichis, Chunming Li, Jim Macione, Zhi Yang, Martin D. Fox, Dee Wu and Swamy Laxminarayan Medical Image Retrieval Based on Plaque Appearance and Image Registration Jaume Amores and Petia Radeva MRI Plaque Tissue Characterization and Assessment of Plaque Stability Chun Yuan, Thomas S. Hatsukami and Jianming Cai Intravascular Ultrasound Elastography: A Clinician’s Tool for Assessing Vulnerability and Material Composition of Plaques Radj A. Baldewsing, Johannes A. Schaar, Chris L. de Korte, Frits Mastik, Patrick W. Serruys and Antonius F.W. van der Steen Computer Vision Analysis of Collagen Fiber Bundles in the Adventitia of Human Blood Vessels Pierre J. Elbischger, Horst Bischof, Gerhard A. Holzapfel and Peter Regitnig

1

26

55

75

97

Image Based Biomechanics of Coronary Plaque Rosaire Mongrain, Richard L. Leask, Ramses Galaz, Adrian Ranga, Jean Brunette, Anil Joshi, Jean-Claude Tardif and Olivier F. Bertrand

130

Computed Tomographic Cardiovascular Imaging Jerold S. Shinbane and Matthew J. Budoff

148

Tomographic Plaque Imaging with CT John Rumberger

182

Absolute Measurement of Integrated Backscatter from Arterial Wall Structures Peder Pedersen, Ruben Lara-Montalvo and Jacob Chakareski

208

xxiv

Ultrasound Imaging in the Analysis of Carotid Plaque Morphology for the Assessment of Stroke Efthyvoulos Kyriacou, Marios S. Pattichis, Christodoulos I. Christodoulou, Constantinos S. Pattichis, Stavros Kakkos, Maura Griffin and Andrew Nicolaides

241

On the Assessment of Texture Feature Descriptors in Intravascular Ultrasound Images: A Boosting Approach to a Feasible Plaque Classification Oriol Pujol and Petia Radeva

276

Real-Time Plaque Characterization and Visualization with Spectral Analysis of Intravascular Ultrasound Data Anuja Nair, Jon D. Klingensmith and D. Geoffrey Vince

300

Coronary Plaque Analysis by Multimodality Fusion Andreas Wahle and Milan Sonka

321

Imaging of Plaque Cellular Activity with Contrast Enhanced MRI William Kerwin

360

Inter- and Intra-Observer Variability Assessment of in Vivo Carotid Plaque Burden Quantification Using Multi-Contrast Dark Blood MR Images Shaoxiong Zhang, Jasjit S. Suri, Olivier Salvado, Yiping Chen, Frank K. Wacker, David L. Wilson, Jeffrey L. Duerk and Jonathan S. Lewin Three-Dimensional Volume Registration of Carotid MR Images Baowei Fei, Jasjit S. Suri and David L. Wilson Characterization of Shear Stress on the Wall of the Carotid Artery Using Magnetic Resonance Imaging and Computational Fluid Dynamics Peter Yim, Kevin DeMarco, Marcelo A. Castro and Juan Cebral

384

394

412

Numerical Modeling of Coronary Drug Eluting Stents Rosaire Mongrain, Richard Leask, Jean Brunette, Iam Faik, Neil Bulman-Feleming and T. Nguyen

443

Author Index

461

Plaque Imaging: Pixel to Molecular Level J.S. Suri et al. (Eds.) IOS Press, 2005 © 2005 The authors. All rights reserved.

1

Plaque Imaging Using Ultrasound, Magnetic Resonance and Computer Tomography: A Review Jasjit S. SURI a , Constantinos S. PATTICHIS b , Chunming LI c , Jim MACIONE c , Zhi YANG c , Martin D. FOX c , Dee WU d and Swamy LAXMINARAYAN e a Fischer Imaging Corporation, Denver, CO, USA b Department of Computer Science, University of Cyprus, Cyprus c University of Connecticut, Storrs, USA d Department of Radiological Sciences, University of Oklahoma Health Sciences Center, OK, USA e Idaho State University, Pocatello, ID, USA Abstract. Different classiﬁcations have been proposed in the literature for the characterization of atherosclerotic plaque morphology, resulting in considerable confusion. For example plaques containing medium of high level uniform echoes were classiﬁed as homogeneous by others and correspond closely to dense and calciﬁed plaques, other types. This survey is to understand different types of plaque when imaged using ultrasound and MR. Keywords. Carotid artery, magnetic resonance angiography, phase-contrast magnetic resonance imaging, computational ﬂuid dynamics, shear stress

1. Ultrasound Vascular Imaging Ultrasound is widely used in vascular imaging because of its ability to visualise body tissue and vessels in a non invasive and harmless way and to visualise in real time the arterial lumen and wall, something that is not possible with any other imaging technique. B-mode ultrasound imaging can be used in order to visualise arteries repeatedly from the same subject in order to monitor the development of atherosclerosis. Monitoring of the arterial characteristics like the vessel lumen diameter, the intima media thickness (IMT) (see Fig. 1) of the near and far wall and the morphology of atherosclerotic plaque (see Fig. 2) are important in order to assess the severity of atherosclerosis and evaluate its progression [1]. The arterial wall changes that can be easily detected with ultrasound are the end result of all risk factors (exogenous, endogenous and genetic) known and unknown and are better predictors of risk than any combination of conventional risk factors. Extracranial atherosclerotic disease, known also as atherosclerotic disease of the carotid bifurcation has two main clinical manifestations a) asymptomatic bruits and b) cerebrovascular

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a) No ﬁltering

b) After despeckling

Figure 1. B-mode ultrasound imaging of the carotid artery illustrating the IMT measurement before and after despeckle ﬁltering. a) No ﬁltering: IMTaver = 0.837mm, IMTmax = 1.024mm, IMTmin = 0.663mm, IMTmedian = 0.783mm. b) After despeckling: IMTaver = 0.845mm, IMTmax = 1.030mm, IMTmin = 0.667mm, IMTmedian = 0.788mm.

a) Snakes segmentation

b) Expert’s segmentation

Figure 2. Ultrasound imaging segmentation of atherosclerotic carotid plaque at the far wall.

syndromes such as amaurosis fugax, transient ischaemic attacks (TIA) or stroke which are often the result of plaque erosion or rupture with subsequent thrombosis producing occlusion or embolisation [2,3]. Carotid plaque is deﬁned as a localized thickening involving the intima and media in the bulb, internal carotid, external carotid or common femoral arteries (Fig. 2). Recent studies involving angiography, high resolution ultrasound, thrombolytic therapy, plaque pathology, coagulation studies and more recently molecular biology have implicated atherosclerotic plaque rapture as a key mechanism responsible for the development of cerebrovascular events [4–6]. Atherosclerotic plaque rapture is strongly related to the morphology of the plaque [7]. The development and continuing technical improvement of non invasive high resolution vascular ultrasound enables the study of the presence, rate of progression or regression of plaques and most importantly their consistency. The ultrasonic characteristics of unstable (vulnerable) plaques have been determined [8,9] and populations or individuals at increased risk for cardiovascular events can now be identiﬁed [10]. In addition, high resolution ultrasound enables the identiﬁcation of the different ultrasonic characteristics of unstable carotid plaques associated with amaurosis fugax, TIAs, stroke and different patterns of CT-brain infraction [8,9]. This information has provided new insight into the pathophysiology of the different clinical manifestations of extracranial atherosclerotic cerebrovascular disease using noninvasive methods.

J.S. Suri et al. / Plaque Imaging: A Review

3

2. Image Analysis Visual assessment of vascular images and/or video on the monitor of the ultrasound machine is widely used in clinical practice. In recent years, digital image analysis techniques facilitate the possibility of extracting additional useful information in quantitative form, enabling the early diagnosis, disease monitoring, and better treatment. In this section, a brief overview of image processing and analysis techniques like despeckle ﬁltering, normalization, segmentation, feature extraction and selection, and classiﬁcation are presented. 2.1. Pre-Processing: Normalization In order to extract comparable results when processing images obtained by different operators and equipment and vascular imaging laboratories a standardization method was proposed using blood and adventitia as reference points [11]. The images are standardized manually by adjusting the image so that the median gray level value of the blood is 0–5, and the median gray level value of the adventitia (artery wall) is 180–190 [11]. The image is then linearly adjusted between the two reference points, blood and adventitia. This simple procedure facilitates standardized quantitative analysis for vascular imaging feature extraction and classiﬁcation. 2.2. Preprocessing: Despeckle Filtering Ultrasound images show a granular appearance known as speckle, which is a form of locally correlated multiplicative noise reducing image contrast and detailed resolution, corrupting medical ultrasound imaging making visual observation difﬁcult, and the signal difﬁcult to detect [12]. Different speckle techniques have been introduced in the literature that are based on local statistics [13], linear scaling of the gray level values [14], the most homogeneous neighbourhood around each pixel [15], geometric ﬁltering [16], homomorphic ﬁltering [17], anisotropic and speckle anisotropic diffusion [18], coherence enhancing diffusion [19] and wavelet ﬁltering [20]. In two recent comparative studies of despeckle ﬁltering techniques evaluated in a large number of asymptomatic and symptomatic ultrasound images of the carotid artery [21,22], it was shown that the local statistics ﬁlter is more suitable for the analysis of plaque morphology and texture analysis, whereas the homogeneous mask area ﬁlter is more suitable for measuring the intima-media thickness (see Fig. 1) as well as for identifying the degree of stenosis, and the outline of the plaque contour. 2.3. Intima Media Thickness and Plaque Segmentation in Ultrasound Imaging Segmentation in vascular imaging is one of the most difﬁcult tasks in image processing. It targets to subdivide an image into its constituent regions or objects. For example, in the automated segmentation of an ultrasound image of the carotid artery, interest lies in identifying the intima media and subsequently measure its thickness, and furthermore, determine the presence or absence of a plaque, and if there is a plaque determine its contour.

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For lumen delineation in transversal ultrasound imaging, the Hough transform was investigated [23] as well as to ﬁnd an initial approximation of the lumen area in the left ventricle [24]. Dynamic programming [25] and cost function optimisation [26] were applied for determining the optimal vessel wall. In intrvascular ultrasound imaging of the carotid artery for detecting the vessel wall the following methods were developed: texture based [27], morphology operators [28], optimal graph searching [29], and dynamic contour-modeling [30]. Furthermore, snakes or deformable models to detect the IMT in 2D [31] and 3D [32] ultrasound images of the carotid artery were developed. These methods are based on the active contour model ﬁrst introduced by Kass [33] where an active contour is expressed as an energy minimization process, based on internal energy derived from the physical characteristics of the snake based on two components, the continuity energy, and the curvature energy. In general, the snake-based methods require that the initial contour must be drawn by an experienced ultrasonographer. A new method using image normalization as described above, despeckle ﬁltering, automatic initial contour estimation, and snakes for the measurement of IMT was proposed [34] The method requires minimum user interaction and was evaluated on 100 longitudinal ultrasound images with measurements carried out by two experts. The results can be summarized as follows: i) there is no signiﬁcant difference for the measurement of IMT between the manual and the snakes segmentation measurements, and ii) better segmentation results (smaller inter-observer variability, and smaller coefﬁcient of variation) were obtained for the normalized despeckled images. The manual measurements were smaller than the automated and this ﬁnding was also reported in other studies [25,27,30,32]. The no signiﬁcant difference between the manual and the automated method, shows that the IMT, an important predictor for myocardial infraction and stroke can be reliably computed automatically. To the best of our knowledge there is no technique published enabling the ultrasound automated segmentation of atherosclerotic carotid plaque. A new method was proposed by our group based on snakes for the segmentation of atherosclerotic carotid plaque [35] that is illustrated in Fig. 2. In this method, the initial estimate of the contour of the plaque is automatically estimated by cross correlating the B-mode image with the blood ﬂow image. This initial contour is then deformed on the B-mode image using snakes to ﬁnd the ﬁnal contour as shown in Fig. 2a (that could be visually compared to the expert’s segmentation shown in Fig. 2b). The method was compared with the expert’s segmentation results on 35 images where the true positive fraction, TPF, true negative fraction, TNF, false negative fraction, FNF and false positive fraction, FPF, were 86.4%, 84.0%, 8.5%, and 7% respectively. Furthermore, the similarity kappa index, KI, and the overlap index between the expert’s segmentation results and the snakes segmentation results were 85% and 74% respectively, which are considered very satisfactory. These results are comparable to the manual delineation procedure without requiring manual correction in most of the cases. The limitations of this approach i.e. using the blood ﬂow image to locate the blood borders are the following: i) the blood sometimes hides areas of the tissue (verbarations), and ii) the colour does not always ﬁll up the places where blood has a low speed.

J.S. Suri et al. / Plaque Imaging: A Review

5

Asymptomatic SGLDM(mean) Features

SF Features

Angular second moment Contrast

.00064

Mean

44.0

485.18

29.9

Correlation Variance Homogeneity Entropy

0.78 1078.5 0.21 7.86

Standard Deviation Median Skewness Kurtosis

38.5 1.0 1.8

Symptomatic SGLDM(mean) Features Angular second moment Contrast Correlation Variance Homogeneity Entropy

SF Features 0.0027

Mean

25.8

528.56

Standard Deviation Median Skewness Kurtosis

19.2

0.57 595.9 0.32 6.87

21.9 1.40 2.4

Figure 3. SF and SGLDM(mean) texture features for an asymptomatic and a symptomatic ROI images. In each case, top and bottom images represent near wall and far wall ROI plaques respectively (see also [43]).

2.4. Ultrasound Plaque Feature Extraction and Classiﬁcation Following the segmentation, texture and morphological features are extracted from the segmented plaque images in order to be used for the characterization of the carotid plaques. These features are usually computed on a region of interest (ROI), for example the region prescribed by the plaque contour that is automatically or manually drawn as shown in Fig. 2. ROI images for an asymptomatic and a symptomatic case are shown in Fig. 3. Some of the most common texture feature algorithms that have been used for ultrasound texture analysis are brieﬂy described. Simple statistical descriptors, SD, are computed that include the ROI mean, median, standard deviation, skewness, and kurtosis values (see Fig. 3, and 4a). The spatial gray level dependence matrices, SGLDM, texture features as proposed by Haralick et al. [36] are the most frequently used texture features. These features are the following: angular second moment, contrast, correlation, inverse difference moment, sum average, variance (sum and difference), and entropy (sum and difference). For a chosen distance d that is usually one pixel and for angles θ = 0◦ , 45◦ , 90◦ and 135◦ four values for each of the above texture measures are computed. The mean (see Fig. 3) and range of these four values are usually computed for each feature, and they are used as two different feature sets. The Gray Level Difference Statistics, GLDS, algorithm [37] uses ﬁrst order statistics of local property values based on absolute differences between pairs of gray lev-

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J.S. Suri et al. / Plaque Imaging: A Review

Figure 4. Boxplots of two texture features for class 1) symptomatic and class 2) asymptomatic plaques (see also [43]): a) SF Mean, and b) NGTDM Coarseness. The notched box shows the median, lower and upper quartiles and conﬁdence interval around the median for each feature. The dotted line connects the nearest observations within 1.5 of the inter-quartile range (IQR) of the lower and upper quartiles. Crosses (+) indicate possible outliers with values beyond the ends of the 1.5 × IQR.

els or of average gray levels in order to extract the following texture measures: contrast, angular second moment (see Fig. 4b), entropy, and mean. Amadasun and King [38] proposed the Neighborhood Gray Tone Difference Matrix, NGTDM, in order to extract textural features, which correspond to visual properties of texture. The following features are extracted: coarseness, contrast, busyness, complexity, and strength. The statistical feature matrix SFM [39], measures the statistical properties of pixel pairs at several distances within an image, which are used for statistical analysis. Based on the SFM the following texture features are computed: coarseness, contrast, periodicity, and roughness. For the Laws TEM feature extraction [40,41] vectors of length l = 7, L = (1, 6, 15, 20, 15, 6, 1), E = (−1−4, −5, 0, 5, 4, 1) and S = (−1−2, 1, 4, 1−2−1) are used, where L performs local averaging, E acts as edge detector and S acts as spot detector. If the column vectors of length l are multiplied by row vectors of the same length, we compute the Laws lxl masks. In order to extract texture features from an image, these masks are convoluted with the image and the statistics (e.g. energy) of the resulting image are used to describe texture. Fractal Dimension Texture Analysis, FDTA, is based on the work of Mandelbrot [42] who developed the fractional Brownian motion model in order to describe the roughness of natural surfaces. The Hurst coefﬁcients H (k) [41] are computed for different image resolutions, where a smooth texture-surface is described by a large value of the parameter H whereas the reverse applies for a rough texture-surface. The Fourier Power Spectrum, FPS, computes the radial and angular sum of the sample Fourier power spectrum where coarse texture has high values concentrated near the origin, and in ﬁne texture the values are more spread out. Furthermore plaque imaging morphological analysis was carried out as documented in [43] in this book. Statistical analysis of texture features was carried out for a large number of asymptomatic and symptomatic ultrasound images of carotid atherosclerotic plaques [43–45]. It was shown that asymptomatic plaques tend to be brighter, with less contrast, more homogeneous, smoother, with large areas with small gray tone variations, and more periodical, whereas, in symptomatic plaques texture tends to be darker, with higher contrast, more heterogeneous, more rough and less periodical. These ﬁndings are summarized in Table 1. Figure 4 shows boxplots of two texture features and the range of values for the asymptomatic and symptomatic groups. The gray scale mean or median indicates how

J.S. Suri et al. / Plaque Imaging: A Review

7

Table 1. Texture characteristics of asymptomatic vs symptomatic plaques. (From [44], © 2003 IEEE, with permission.) Asymptomatic Plaques

Symptomatic Plaques

Brighter

More dark

Less contrast More smooth More homogeneous More periodical More coarse, i.e. large areas with small gray tone variations

Higher contrast More rough More heterogeneous Less periodical Less coarse, i.e. less local uniformity in intensity

bright (high values) or dark (low values) the image is in average. The sum entropy computed with the SGLDM algorithm, is high when the image intensity in neighbouring pixels is more equal and small when the image intensity is more unequal. Angular Second Moment (ASM) of GLDS is small when the gray level probability density values are very close and large when some values are high and others low. Coarseness computed with the NGTDM algorithm, is high when large areas with small gray tone variations are present in the image and small when there is less local uniformity in density. As illustrated in Fig. 4, asymptomatic plaques tend to be brighter (higher mean or median gray level), have higher sum entropy (i.e. the image intensity in neighbouring pixels is more equal), have lower values for ASM and are more coarse, whereas symptomatic plaques tend to be darker (lower mean or median gray level), have lower sum entropy (i.e. the image intensity in neighbouring pixels is more unequal), have higher values for ASM and are less coarse. In an extensive study carried out by Polak et al. [46] where subjects were followed up for an average of 3.3 years, they found that darker (i.e. hypoechoic) carotid plaques are associated with increased risk of stroke. Also, Elatrozy et al. [47] reported that plaques with gray scale median less than 40 are more related to ipsilateral hemispheric symptoms. Wilhjelm et al. [48] in a study with patients scheduled for endarterectomy, carried out a quantitative comparison between subjective classiﬁcation of the ultrasound images, ﬁrst and second order statistical features of the ultrasound imaging plaque, and a histological analysis of the surgically removed plaque. They reported some correlation between the aforementioned three types of data where the feature with the highest discriminatory power was contrast. In automated quantitative methods for classifying vascular imaging patterns, both statistical pattern recognition and artiﬁcial neural networks (ANN) were used [43–45]. In statistical pattern recognition the k-nearest-neighbour (KNN) classiﬁer was used, whereas in ANN pattern recognition the unsupervised self-organizing map (SOM) was used [44,45], Probabilistic Neural Networks (PNN), and the Support Vector Machines (SVM) algorithms [43]. A brief description is given for the SOM study [44,45]. Nine different SOM models were developed one for each texture feature set as described above, with the output classiﬁed into two classes: asymptomatic because the subject was not connected with ipsilateral hemispheric events or symptomatic because the subject was connected with ipsilateral hemispheric symptoms. The percentage of correct classiﬁcations score of the above mentioned texture feature sets using the SOM classiﬁer

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on the evaluation dataset was computed. The highest diagnostic performance was obtained for the SGLDM range feature set where the percentage of correct classiﬁcations was 70%, followed by the NGTDM and TEM feature sets. Furthermore the outputs of the SOM classiﬁers were combined improving the percentage of correct classiﬁcations score to 73%. These results are comparable with the results derived with the KNN, PNN and SVM classiﬁers [43]. Furthermore, the performance of morphological features for carotid plaque classiﬁcation was also investigated [43,45]. The ﬁndings of these studies showed that the percentage of correct classiﬁcations score for certain morphology features was slightly lower than the best texture feature sets.

3. Future Trends 3.1. 3D Vascular Ultrasound Imaging In everyday clinical practise, the ultrasonographer manipulates the transducer and mentally transforms the two dimensional (2D) images into anatomical volume, or structure, or lesion, in order to make a diagnosis. Three dimensional imaging (3D) attempts to provide the ultrasonographer or physician with a more realistic reconstruction and visualization of the 3D structure under investigation. In addition, 3D imaging can provide quantitative measurements of volume, surface distance in vascular anatomy, especially in pathological cases. In vascular imaging, a 3D representation was investigated for the visualization of the carotid artery and the quantiﬁcation of the atherosclerotic plaque volume and morphology [1,32]. Although 3D vascular imaging is very promising in revealing vascular structure and pathology, more work is needed in the directions of fast and accurate free hand scanning, automated or semi-automated segmentation, real-time and user friendly visualization, and 3D texture analysis [1,32]. 3.2. Ultrasound Plaque Imaging and Genetics Atherosclerosis is a multifactorial disease that makes the process of prevention and disease management highly complex. In addition to the many factors that are useful in assessing an individual’s risk of developing a cardiovascular event, recently, new biochemical markers for cardiovascular disease have been identiﬁed such as homocysteine, Creactive protein and ﬁbrinogen. However, further work in this area is needed in order to understand and identify their exact role in disease. High resolution ultrasound imaging offers the potential of determining phenotypes more accurately than using conventional risk factors and clinical events. This is achieved because plaque echodensity can characterize the plaques that are unstable and likely to rupture [49]. The ability to identify this type of plaques and hence high risk individuals also offers the advantage of monitoring plaque stabilization drug therapies and the development of new therapeutic strategies, contributing towards the implementation of the most effective strategy to minimize cardiovascular death, and offering a better service to the citizen.

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4. Boundary Detection for Ultrasound Carotid Artery Images Using Covariance Matrix of Feature Vectors An edge can be deﬁned as a discontinuity in pixel intensity within an image. Edge detection is one of the most important tasks in image processing and computer vision. In ultrasound images, edges appear on the boundaries of organs, blood vessels, and other tissues. The edge information in ultrasound can be used for 3D reconstruction and also, quantiﬁcation of organ, lesion or tissue size. Although much research has been done on edge detection [1–8], not much has been done for ultrasound images due to the difﬁculty caused by speckle noise. Most of the conventional edge detectors, e.g., Canny, LoG, or Sobel operators are based on derivative operations. However, derivative operations are sensitive to noise which limits the utility of the derivative-based edge detectors. In this chapter, we present a new edge detection method, with application to the detection of the boundary of the carotid artery in ultrasound images. Our method avoids taking derivative of images, and therefore is more robust to noise. In our edge detection method, edge operations are not directly performed on the original image. For each pixel, we deﬁne a feature vector, which characterizes the pixel more adequately than the pixel value. Thus, we derive a feature vector ﬁeld from the original image. Then we can apply our edge detection technique [84] to the feature vector ﬁeld. In ultrasound images, the intensity of an individual pixel may not characterize it adequately. It is necessary to ﬁnd additional parameters, which can characterize a pixel more precisely or provide more reliable information about the pixel, to be used for edge detection. We call these parameters the features of a pixel, and the vector with them as components is called feature vector. If an appropriate feature vector is chosen, it can be expected that the edge detection result can be improved by applying edge detection operations on the feature vector space. It is well known that the speckle noise in ultrasound images is signal dependent. In ultrasound images, different homogenous regions take on different statistical characteristics. In particular, the pixel value on the two sides of an edge has not only different mean but also different standard deviation. The mean and standard deviation of a pixel is the sample mean and standard deviation of a pixel block centered at the pixel of interest. By using both mean and standard deviation as features, we have more information about the pixels, which makes the pixels on the two sides more distinguishable. 4.1. Statistical Edge Models for Vector Valued Images In this section, we consider edge detection on general vector valued images f(i, j ) for two edge models: step edge and ramp edge models. The results in this section is for vector valued images, and will be used for the feature vector ﬁeld derived from a gray level image in the next section. 4.2. Step Edge Model For a vector valued image f(i, j ), we consider each vector f(i, j ) as a random vector obeying a certain distribution. For an image I (i, j ) with a step edge, we assume that the random vectors f(i, j ) on the two sides of the edge have different means and the covariance matrices. More speciﬁcally, we assume that the random vectors f(i, j ) on the two sides of the edge have the means μ1 and μ2 and the covariance matrices 1 and 2 .

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The edge in the image f(i, j ) can be characterized by the covariance matrix of a random vector X deﬁned as follows. Let be a circular window centered at the pixel (i, j ). Then X is deﬁned as a vector randomly picked up from the set {f(m, n) : (m, n) ∈ }. If a step edge lies in , then it divides into two parts, 1 and 2 , with N1 and N2 pixels, respectively, as shown in Fig. 1. According to the above assumptions, the vector f(i, j ) is a random vector Xi with mean μi and covariance matrix i when the pixel (i, j ) is in i , for i = 1, 2, respectively. The two sides of the step edge are referred to as homogeneous regions, since the vectors f(i, j ) on each side of the edge follow the same distribution. It can be shown that the random vector X has the mean μX = p1 μ1 + p2 μ2 where p1 =

N1 N1 +N2 , p2

=

(1) N2 N1 +N2 ,

and the covariance matrix

X = E{(X − μ)(X − μ)T } = E{XX T } − μμT = p1 E{X1 X1T } + p2 E{X2 X2T } − (p1 μ1 + p2 μ2 )(p1 μ1 + p2 μ2 )T = p1 E{X1 X1T } − p1 μ1 μT1 + p2 E{X2 X2T } − p2 μ2 μT2 + p1 μ1 μT1 + p2 μ2 μT2 + (p1 μ1 + p2 μ2 )(p1 μ1 + p2 μ2 )T = p1 1 + p2 2 + p1 μ1 μT1 − p12 μ1 μT1 + p2 μ2 μT2 − p22 μ2 μT2 − p1 p2 (μ1 μT2 + μ2 μT1 ) = p1 1 + p2 2 + p1 p2 C(μ1 , μ2 )

(2)

Under the assumptions in Eq. (1) and Eq. (2), the covariance matrix of X is approximated by X ≈ p1 p2 (μ1 − μ2 )(μ1 − μ2 )T p1 p2 C(μ1 , μ2 )

(3)

And therefore, the largest eigenvalue of X , denoted by λmax (X ), can be approximated by λmax (X ) ≈ p1 p2 λmax (C(μ1 , μ2 )) = p1 p2 ||μ1 − μ2 ||2

(4)

Note that p1 + p2 = 1, so we get p1 p2 ||μ1 − μ2 ||2

1 ||μ1 − μ2 ||2 4

(5)

where the equality holds when p1 = p2 = 12 , in which case the center of is on the edge. This leads to an important property that the largest eigenvalue of the covariance matrix X reaches its local maximum when the center of moves across the edge. If 1 = 2 , then the above local maximum property of λmax () still holds without the assumptions in Eq. (1) and Eq. (2). In fact, in this case

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Figure 5. Step edge model.

= 1 + p1 p2 C(μ1 , μ2 )

(6)

It has been proved in [9] that 1 λmax () ≤ λmax 1 + C(μ1 , μ2 ) 4

(7)

where the equality holds when p1 = p2 = 12 . 4.2.1. Ramp Edge Model In ultrasound images, the edges usually do not appear as step edges. It is more appropriate to model them as ramp edges. Let be a circular window centered at the pixel (i, j ). Similarly as in the step edge case, a random vector X is deﬁned as a vector randomly picked up from the set {f(m, n) : (m, n) ∈ }. If there is a ramp step edge in , the window can be divided into three parts, the two homogeneous regions 1 and 2 as in the step edge case, and a ramp region 3 between them, with N1 , N2 , and N3 pixels, respectively. According to the above assumptions, the vector f(i, j ) is a random vector Xi with mean μi and covariance matrix i when the pixel (i, j ) is in i , for i = 1, 2, 3, respectively. Then it can be shown that the random vector X has the mean μ = p1 μ1 + p2 μ2 + p3 μ3

(8)

and the covariance matrix = p1 1 + p2 2 + p3 3 + +

p1 p2 (μ1 − μ2 )(μ1 − μ2 )T p1 + p2

p3 (μ3 − μ)(μ3 − μ)T p1 + p2

(9)

It has been shown [84] that the largest eigenvalue of the above covariance matrix achieves 3 its maximum when p1 = p2 = 1−p 2 , i.e., when the window is centered at the edge. 4.2.2. Local Covariance Matrix of a Vector Valued Image In the previous subsections, we have shown that the covariance matrix has a property that its largest eigenvalue achieves its maximum when the window is centered at the edge. This property directs us to our edge detection for vector valued images using the local covariance matrix , which will be deﬁned as follows. In practice, the covariance matrix is unknown, but it can be estimated by the local covariance matrix of the sample vectors f(ik , jk ) of the N pixels (ik , jk ), k = 1, . . . , N , in . The local covariance matrix of the feature image f(i, j ) in the window is deﬁned by

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ˆ =

N T 1 ˆ j ) f(ik , jk ) − μ(i, ˆ j) f(ik , jk ) − μ(i, N

(10)

k=1

ˆ j ) is the local mean of the feature vectors of pixels in , deﬁned by where μ(i, ˆ j) = μ(i,

N 1 f(ik , jk ) N

(11)

k=1

ˆ is an estimate of , λmax () can be estimated by Since the local covariance matrix ˆ It is interesting that, the sample covariance matrix ˆ also has the similar form λmax (). as the covariance matrix given in Eq. (4) ˆ 1 + p2 ˆ 2 + p1 p2 C(μˆ 1 , μˆ 2 ) ˆ i,j = p1

(12)

ˆ 2 are the local covariance matrices, and μˆ 1 and μˆ 2 the sample means of ˆ 1 and where the feature image f(i, j ) on 1 and 2 , respectively. For an ideal case that the feature ˆ1 = ˆ 2 = 0 and ˆ reduce vector f(i, j ) are constant f1 on each side of the edge, then to ˆ i,j = p1 p2 (μˆ 1 , μˆ 2 )

(13)

whose largest eigenvalue λ(i, j ) reaches its local maximum when p1 = p2 = 12 . 4.3. Edge Detection on the Feature Vector Field Since our edge operation is applied to the feature image, instead of the original ultrasound images, it is very important to choose an appropriate feature vector. In this work, we adopt the sample mean and standard deviation as the components of the feature vector. For each pixel (i, j ), we calculate the sample mean and standard deviation of the intensity of the neighboring d × d pixels. The sample mean and standard deviation are denoted by μ(i, ˆ j ) and σˆ (i, j ), respectively, and then deﬁne the feature vector f(i, j ) as μ(i, ˆ j) f(i, j ) = (14) σˆ (i, j ) Based on the analysis of the covariance matrix of feature vectors in Section II, our edge detection algorithm is presented and can be described by the the following three steps: 1. Calculate the feature vector for every pixel (i, j ). 2. For each pixel (i, j ), calculate the local covariance matrix of the feature vectors, ˆ i,j , and its maximum eigenvalue λ(i, j ). denoted by 3. Threshold on λ(i, j ) with a threshold T . 4. Find the local maxima of λ(i, j ) for the pixels with λ(i, j ) > T . In this chapter, the local covariance matrix of feature image is calculated on an 5 × 5 pixel block centered at the pixel of interest. We review two types of signal dependent noise models. The ﬁrst one is multiplicative noise model, for which the observed image can be written as I (i, j ) = s(i, j )η(i, j )

(15)

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13

(a)

(b)

(c)

(d)

Figure 6. An edge corrupted by signal dependent noise. (a) The original noisy edge. (b) The largest eigenvalues of the local covariance matrices, with 5 × 5 mask. (c) Magnitude of gradient, with σ = 2.0. (d) Magnitude of gradient, with σ = 3.0.

where η(i, j ) is the noise. For images with multiplicative noise, a standard method to process the image, such as edge detection and noise reduction, is to transform the multiplicative noise to additive noise by taking logarithm of the pixel value. Then the conventional edge detection techniques, most of which are designed for additive noise, can be applied to the transformed image. There is another type of signal dependent noise, which cannot be transformed to additive noise simply by taking logarithm or some other operations. For example, a noise model for ultrasound image was reported in [7] and [8], where the observed image I (i, j ) was modeled as (16) I (i, j ) = s(i, j ) + s(i, j )n(i, j ) where n(i, j ) is the identically independent distributed Gaussian noise. To see the above property of the local covariance matrix, we simulated a noisy edge image and calculated the largest eigenvalue of the local covariance matrix. Figure 6(a) shows a edge corrupted by the noise according to the noise model in Eq. (16). The largest eigenvalue of the local covariance matrix of feature vector, denoted by λ(i, j ), is shown

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(a)

(b)

(c)

(d)

Figure 7. Comparison of edge detections on an ultrasound carotid artery image. (a) The original ultrasound image of a carotid artery. (b) Edge map obtained by our edge detector. (c) Edge map obtained by Sobel edge detector. (d) Edge map obtained by Canny’s edge detector.

in Fig. 6(b). In this example, a 5 × 5 pixel block is used to compute the local covariance matrices. From Fig. 6(b), we can observe that the largest eigenvalue of the local covariance matrix is much larger at the true edge. For comparison, we plot the magnitude of the gradient of the smoothed image by convolution with Gaussian kernel with standard deviation σ . The magnitude of gradient is plotted in Fig. 6(c) and 6(d), for σ = 2.0 and σ = 3.0, respectively. From Figs 6(b), 6(c), and 6(d), we can see that λ(i, j ), shown in Fig. 6(b), is smoother and has a well deﬁned ridge compared to the magnitude of the smoothed image by convolution, shown in Fig. 6(c) and 6(d). This shows that the edge can be more easily detected by our method by thresholding and non-maxima suppression on λ(i, j ). 4.4. Application to Ultrasound Carotid Artery Images and Performance Evaluation Our algorithm has been applied to ultrasound images of carotid arteries, and compared with the traditional edge detectors, such as Sobel and Canny detectors. For example, Fig. 7(a) shows an ultrasound carotid artery image, and the edge map obtained by our method is shown in Fig. 7(b). For comparison, we also used Sobel and Canny’s edge detectors to get the edge maps of the same image, shown in Fig. 7(c) and 7(d), respectively. By visual comparison of the results, we observed that the edge map obtained by our edge detector had better edge localization, edge continuity, and fewer false edges than the one

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Figure 8. Performance evaluation of edge detection by Pratt’s ﬁgure of merit.

by Sobel and Canny’s detectors. For the image shown in Fig. 7(d), we used a Gaussian kernel with σ = 3.0 for the Canny’s edge detector. In order to quantitatively evaluate our edge detection algorithm, Pratt’s ﬁgure of merit (FOM), was used to compare our and Canny’s methods. The FOM is deﬁned as D 1 1 max{ND , NI } 1 + α(di )2

N

FOM =

(17)

i=1

where di is the distance between a declared edge pixel and the nearest true edge pixel, α is a calibration constant, and NI and ND are the ideal and the detected edge pixels respectively. In order to use FOM as a metric to compare the edge detection performances, we used simulated images so that we are able to know the location of the true edge and therefore compute the metric. The noise performance of the edge detectors was evaluated for images with different signal-to-noise ratios (SNR). We use the deﬁnition of the SNR of an edge image in [4] as below SNR = 20 log

k σ

(18)

where k is the edge contrast and σ is the standard deviation of the additive Gaussian noise. Figure 10 plots the FOM vs. SNR for our and Canny’s edge detection methods. For Canny’s edge detector, we used the Gaussian kernel with σ = 2.0. The evaluation by FOM shows that our method has better performance, especially for the case of low signal-to-noise ratio. 4.5. Conclusion and Future Work In this chapter, we present a new edge detection method using the covariance matrix of feature vector. The edge detection is performed on the feature image calculated from the original gray level image. Our edge detection algorithm has been implemented and applied to real and simulated images. Pratt’s ﬁgure of merit was used to quantitatively evaluate the performance or our and Canny’s edge detectors. The results show that our method is superior to the conventional edge detection methods, especially for the case of low signal-to-noise ratio. In our future work, we will try to ﬁnd more types of feature vectors for ultrasound images of different organs or tumors using different statistical parameters, according to the distributions of pixel intensity shown by different objects in the images.

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5. MR Angiography For ease of explanation, we classify MRA into four subtechniques: 1) Time-of-Flight imaging, 2) Phase Contrast Angiography, 3) Contrast Enhanced MRA, and 4) Black Blood Imaging. All four methods have their particular advantages and limitations. All four also beneﬁt from improved RF coil design [90] as described later in the book. Our goal in this section is to describe the advantages and challenges of each technique in the context of clinical evaluation of disease. Of particular note are black blood imaging techniques (Section 5.1.4) which are used to evaluate plaque formations. 5.1. Time-of-Flight (TOF) Imaging TOF Imaging is clinically easy to implement and can produce images without contrast agents. This bright blood technique relies on the inherent sensitivity to MR physics of moving spins because fresh ﬂowing spins into the slice/slab have no previous excitation history and thus will have relatively brighter signal. For stationary spins, previous RF excitation in the slice/slab will decrease their signal and result in more saturated signal (i.e. reduced signal). In a nutshell, at locations where there are a greater number of ﬂowing spins, a brighter resultant signal is observed by the TOF effect. MR parameters play an important role in TOF imaging. Short echo times(TE) and short repetition times(TR) are used to enhance the TOF effect. Additionally, the larger the ﬂip angle (FA), the more signal-to-noise ratio is gained (SNR) and overall suppression of stationary tissue is achieved. The user/technologist should be aware that TOF effect on slower moving spins is also more adversely affected with greater FA; therefore, increasing the FA to a certain degree will make contrast stronger with the sacriﬁce of less vascular detail. This is due to the fact that as FA is increased, the distance blood will travel prior to saturation is shortened. In these conditions, slower ﬂow will receive more saturation. The effects of improved background suppression and SNR increases must be balanced against sensitivity to a smaller ﬂow regime. In summary, slice/slab thickness, distance traveled, relaxation time, ﬂow velocity, and the duration of TE should be considered for TOF imaging. Saturation bands can also be used in speciﬁc protocols to selectively suppress arterial or venous ﬂow. A band can be placed superiorly or inferiorly to the direction of ﬂow. The purpose of this band is to selectively suppress either descending ﬂow (typically venous) with a superior saturation band, or ascending ﬂow (typically arterial) with an inferior saturation band. In Fig. 9, a MR venogram of a 20-year-old post-partum female who is to be screened for venous thrombosis is shown. When saturation pulses are applied (see Fig. 9) less arterial ﬂow is suppressed. This saturation band technique provides potentially better visualization on strictures or stenosis after projection. A limitation of 2D imaging with TOF is the potential creation of mis-registration artifacts. In general, such artifacts are produced when the time of encoding differs between the frequency and phase axes. Figure 10 demonstrates the MR science behind this artifact. In addition, complex ﬂow, turbulence, and the above mis-registration artifact threaten the geometric spatial integrity of vessels with the TOF technique. TOF also offers an advantage as a way to providing angiographic images without the use of a contrast agent, thus saving expense and decreasing inconvenience to the patient, thereby increasing throughput and efﬁciency of care. Similar to many hospitals,

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Figure 9. Left: Diagram demonstrating the MR physics diagram of production of bright signal in moving ﬂow using Time-of-Flight Imaging. Note that TR«T1, as the fresh unsaturated spins are bright (red) compared with stationary tissue (blue). Note the acquired slice is dotted around its border. Right 2 panels: Post-partum patient by TOF to evaluate for venous thrombosis. Arrow points to saturated arterial ﬂow when a saturation band is applied (far right).

Figure 10. Left: Blood vessels with ﬂow rate (v) will appear shifted in position. This shifted appearance is known as the mis-registration artifact. Right: Six Slab and Two Slab MOTSA, displaying different levels of slab boundary artifact.

our institution represents a joint partnership between a Physician/Academic group and a managed health care group. Efﬁcient/cost-effective delivery of health care is an essential part of our mission. It is often preferred to acquire these images in a 3D acquisition mode to achieve high-resolution. The advantage of the 3D technique (over a 2D technique) is the capability of high through-plane resolution that is achieved with the boost in SNR. A disadvantage of the 3D technique is the reduced sensitivity to slow ﬂow (due to the thicker slabs) and reduced background suppression. Another major problem of 3D imaging is the slab-boundary-artifact that results from a reduced sensitivity in the application of uniform RF excitation over a wide slab. Limitations in this excitation are due to the fact that there is only a ﬁnite time available for short TE pulse sequences. While there have been traditional and sophisticated ways to get around this artifact, the two most notable are the “multiple overlapping thin slab acquisitions” (MOTSA) technique initially popularized by Dennis Parker [88]. Recent developments in TOF slab imaging include “SLiding Interleaved KY” (SLINKY) by Kecheng Liu [87]. 5.2. Contrast Enhanced Magnetic Resonance Angiography (CE-MRA) Another way to perform bright blood imaging is to rely on timing the acquisition with the arrival of the contrast agent bolus during the enhancement period(CE-MRA). The advantages of the CE-MRA technique over TOF are overall shorter scan times, the ability to produce images from different phases of uptake (e.g. arterial and/or venous phase) as shown in Fig. 11, and higher CNR/SNR than conventional TOF. CE-MRA when applied correctly can provide a more accurate depiction of the geometry than conventional TOF.

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Figure 11. Left: Arterial and venous phase scans using CE-MRA showing to different looks acquired at different times post-contrast injection. Right: Desirable(left) and undesirable(right) timing for bolus chase CE-MRA of carotids.

Figure 12. Moving Table Implementation using CE-MRA for peripheral vascular examination. Produced with assistance of Medical Physics Section at OUHSC.

The major limitation of the CE-MRA techniques is achieving correct bolus timing. Variability of blood ﬂow rates, particularly in different aged individuals with different habitus, causes a challenge in achieving uniform exam conditions and therefore reproducible imaging. Some techniques to improve CE-MRA include the use of elliptic centric ordering, bolus timing (smart prep), and or ﬂuoroscopic timing bolus as described by Martin Prince [89]. Figure 11 illustrates a good timing bolus (left) as compared with a failed bolus timing (right). Achieving desirable timing, is very dependent on the operator gaining conﬁdence in evaluation of the delay in timing and bolus operation. Technical factors should be discussed with basic science faculty and physicians; however, most important is the seasoning of the technologist in regards to selecting proper timing and parameters. When a level of comfort with bolus timing is achieved by the operator, CE-MRA strategies are very useful in run-off studies where the Bolus is chased as the couch bed is moved from station to station. With correct timing one can piece these images together to make full body views for screening. Many vendors now provide the ability to paste together several CE-MRA images together to make the whole-body MRA scans as shown in Fig. 12. These illustrations were provided with assistance of clinical medical physics group at OU Medical Center. 5.3. Phase Contrast Angiography (PCA) PCA is another MRI technique that holds promise in the quantiﬁcation and evaluation of blood ﬂow. It has utility for a quick and easy localizer, carotid imaging, as well as for quantiﬁcation of stenotic ﬂow. Another application is for co-arctation of the aorta. An example is for coarctation in which PCA can provide additional information concerning the level of disease by evaluation of the ﬂow rate in the aorta. A pitfall for PCA is the complexity of setting the correct velocity encoding, which provides additional burden to the technologist who may not routinely use PCA. In ad-

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Figure 13. Velocity and TE play an essential role in the contrast of black blood spin echo images. If distance traveled of ﬂow is faster than TE/2 then can potentially only see the 180 degree pulse = Void signal. For all the beginning arrow is at time TA1, end of arrow is at TA2. Note only case A in the diagram, will receives an adequate 90–180 pair that produces normal signal, all other combinations (B,C,D) lead to signal loss in the moving spins(ﬂow). Also, demonstration of Moya-moya which bright blood imaging and dark blood imaging.

Figure 14. a) Black blood imaging surveys of heart in a coronal b) 4 chamber view of the heart and c) black blood localizer for the thoracic artery showing both the exterior and intimal layer of the vessel.

dition the lengthy time involved in acquiring these images can present a challenge to the use of PCA. The operator should consult with technical staff and receive specialized training (potentially by the MR faculty at our institution). 5.4. Black Blood MRA Black blood images make excellent localizers providing detail inside and outside the vessel. A downside to black blood imaging is its inherent long scan time. A challenge is for projections as minimum intensity projections (MinIP) must be maintained. MinIP techniques in the presence of air structures in lungs and surrounding tissue and surrounding air make it hard to generate fast turn-around with this type of post processing. Figure 13 illustrates black blood imaging in a patient with suspected Moya-moya disease. The increased prevalence in angiogenesis can be easily seen on bright blood images. However, the ﬂow voids are best visualized on black blood images in the areas of faster ﬂow in the insular/border zone region in this patient. Another clinical application for black blood imaging is for thoracic aneurysm (Fig. 13). The thoracic aneurysm on black blood images demonstrates both the interior and exterior wall (not possible to visualize on bright blood imaging). Additionally, misregistration makes using TOF imaging less satisfactory for visualizing the extent of the disease. Black blood imaging has received increasing attention in the last couple of years as popularized by Fayad and Edelman [85,86]. The method relies on the passage of blood ﬂow and the combination of spin echoes. A late TE will provide a greater sensitivity to slower ﬂows than a conventional TOF image. Too great an echo time will of course result in ﬂow loss. The main advantage of black blood is that it beneﬁts from more integrity in the signal voids and does not have the inherent ﬂow misregistration problems that the TOF imaging.

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Figure 15. Left: an A1 segment aneurysm shown on MIP CTA images. Right: Volume Reconstructed CTA images, illustrating shape and morphology of the pseudoaneurysm.

Figure 16. Post-processed CTA images, speciﬁc arterial supplies can be enhanced on projected MIP images.

6. Computed Tomography Angiography (CTA) An alternative to MRA (although a more invasive approach) is to use Computed Tomography Angiography. CTA provides signiﬁcantly higher resolution and more spatial integrity than MRA techniques. CTA can also achieve higher resolution in matter of seconds while MRA imaging (by TOF/CE-MRA) can require approximately 30–40 seconds. The drawbacks to CTA are in the large X-ray dose, the poorer visibility near bone (beam hardening), and the separation of arterial/venous phases that is achievable with MRI TOF imaging. Nevertheless, due to the 24 hr availability of CTA at many institutions as well as the relatively less invasive nature of the exam (compared to commonly used ﬂuoroscopic DSA techniques) and the ability to perform cross-sectional imaging with the possibility of retrospective reformat of the image. Recent technology enables multiple dimensional reconstruction using C-arms; however, at much radiation dose to the patient. It is the practical goal also to be able to visualize the general morphology of the tumor. Aneurysm present in fusiform or sacular manner, the size of the neck, and the size of aneurysm on a sacular tumor are also important for GDC coiling. Coiling a fusiform aneurysm would lead to obstruction of the entire vessel and inevitable complications. The location of the aneurysm is critical; for example it would be unwise potentially to coil an aneurysm located in a major branch of the MCA. However, these decisions should be discussed as part of the patient and surgeon consultation. With detailed work by the MP and physician visualization team, detailed CTA that can extract deﬁnition of vascular arterial phase are shown in Figs 15 and 16. Producing images that aid interpretation is key; at our institution the neurosurgeons receive these images and desire to grasp the 3D nature of the problem quickly. Such 3D visualization is better accepted by the surgeons then the conventional 2D images. CTA images are acquired with so many thousands of slices that to review these images would be exceedingly time consuming without 3D visual summary, though it is always essential to return to conventional 2D raw images for conﬁrmation. Vital to CTA is the ability to have an effective visualization workstation that will handle large numbers of high resolution images. While acquisition is a primary goal, it is important to capture as much of the arterial phase as possible for producing high quality

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work. Timing is the key in capturing the arterial phase. Retrospective reconstruction that produces large numbers of thin isotropic high resolution images for 3D rendering is needed. The workstation enables 3D MIPs and the ability to cut out venous ﬂow as well as bone. Sufﬁcient familiarity with cerebrovascular anatomy is absolutely a prerequisite. Anatomical ﬂuency and facility with the computer workstation are key components to the success of our team. Extraction of the correct vascular phase can take 25 minutes for a well trained person, but may take longer for the inexperienced. Often the complexity of the anatomy or the time consuming procedures make the evaluation of CTA more difﬁcult in a routine clinical practice, which has relegated the procedure to academic or bigger hospitals that have the appropriate stafﬁng. CTA plays a major role in the analysis of aneurysms. CT angiography also can be used to evaluate vessel integrity and its function. The utilization of CT methods (especially EBCT) which are particularly useful for plaque imaging are discussed in the subsequent chapters of this book.

Acknowledgements The ﬁrst authors would like to thank all the team members for their contributors to this review chapter. The IVUS contributions were made by Constantinos S. Pattichis, the boundary estimation techniques for IVUS were made by Chunming Li, Jim Macione, Zhi Yang and Martin Fox and MR and CT contributions were made by Dee Wu.

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Plaque Imaging: Pixel to Molecular Level J.S. Suri et al. (Eds.) IOS Press, 2005 © 2005 The authors. All rights reserved.

Medical Image Retrieval Based on Plaque Appearance and Image Registration Jaume AMORES and Petia RADEVA Centre de Visió per Computador, Ediﬁci O, Campus UAB, 08193 Bellaterra, Barcelona, Spain Abstract. The increasing amount of medical images produced and stored daily in hospitals needs a datrabase management system that organizes them in a meaningful way, without the necessity of time-consuming textual annotations for each image. One of the basic ways to organize medical images in taxonomies consists of clustering them depending of plaque appearance (for example, intravascular ultrasound images). Although lately, there has been a lot of research in the ﬁeld of Content-Based Image Retrieval systems, mostly these systems are designed for dealing a wide range of images but not medical images. Medical image retrieval by content is still an emerging ﬁeld, and few works are presented in spite of the obvious applications and the complexity of the images demanding research studies. In this chapter, we overview the work on medical image retrieval and present a general framework of medical image retrieval based on plaque appearance. We stress on two basic features of medical image retrieval based on plaque appearance: plaque medical images contain complex information requiring not only local and global descriptors but also context determined by image features and their spatial relations. Additionally, given that most objects in medical images usually have high intra- and inter-patient shape variance, retrieval based on plaque should be invariant to a family of transformations predetermined by the application domain. To illustrate the medical image retrieval based on plaque appearance, we consider a speciﬁc image modality: intravascular ultrasound images and present extensive results on the retrieval performance. Keywords. Retrieval, contextual information, registration, elastic mathching, medical imaging, IVUS

1. Introduction Images provide a powerful means to represent data, and many applications have as fundamental components the acquisition, processing and storing of huge amount of images. A typical example of such application is medical imaging. In hospitals working with medical images, large amounts of image data are received daily for processing, analysis and archiving. This arises the necessity of constructing database management systems able to organize, analyze and retrieve this type of data. The ﬁrst image retrieval systems were based on information retrieval methodologies applied to textual annotations. As it has been seen in the last decade, describing images by textual annotations is not satisfactory for three main reasons: i) there is too much information in an image, so that small sets

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of words cannot describe it well; ii) labelling an image by words is a subjective task, as different individuals can apply different labels (words) depending on what they consider more relevant in the current image; iii) a complete manual labelling in a large collection of images is a very tedious task. These reasons have led to the use of image content for processing and organizing the database, constituting the so-called content-based image retrieval systems. Such content-based image retrieval (CBIR) systems are necessary for a wide range of applications dealing with vast volumes of images. In the medical image ﬁeld, retrieval by content is necessary for performing guided diagnosis and therapy. Having medical images archived along with their descriptions, retrieval by content allows the physician to present a query image representing the current clinical case, and obtain the most similar stored images and their associated descriptions, so that the diagnosis of the image at hand is more easily taken by comparison. Indeed, whenever the type of the medical image is of great complexity it is common for the physician to base its diagnostics on manuals containing for each pathology its representative images. Other applications are the construction of electronic atlases with a high number of examples for each case, and educational uses. In this chapter, we overview the work on medical image retrieval, underline the peculiarities of medical image retrieval as opposed to image retrieval of general domains, and present a general framework of medical image retrieval based on plaque appearance. A fundamental aspect of any CBIR system is the use of an appropriate feature space. This feature space should be able to represent all aspects of the image relevant to its description. For doing so, not only global information, but also local and contextual information is necessary. Global information is necessary for describing the statistics of relevant features inside the image. Local information is fundamental for dealing with images in which important parts are localized in small regions such as the pathology bearing regions of medical images. In addition to local and global information, the feature space should also be able to describe the spatial relations of the different structures conforming the overall image. In retrieval of general scope, this contextual information is good for describing semantically complex scenes as the relation between the objects conforming them. In the medical image retrieval ﬁeld, the relative disposition of pathological structures respect to other structures play key roles in diagnosis. Finally, in complex domains such as retrieval of medical images the design of the feature space must be ﬂexible enough to incorporate descriptors speciﬁc to the concrete problem, as general descriptors perform poorly in describing them. 1.1. State of the Art in General Content-Based Image Retrieval and Medical Image Retrieval Most of the general CBIR systems up to day try to characterize the whole image by using only global information, i.e. a set of global signatures such as histograms of color, texture or shape [30,13]. Pentland et al. ([24]) use different global descriptors depending on the type of the image. Their global description is based on an orthogonal feature space representing the content, using eigenimages for objects such as faces, eigenmodes for retrieving shapes and the world-based features for textured images. In retrieval of general scope, some authors [28,7,31,9] have included recently local information able to differentiate between images in which an important part of the discriminant information

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is localized in small regions. Schmid et al. ([28]) extract characteristic points localized in discriminant parts, and compute a set of invariant local features around each characteristic point. Carson et al. [7] segment the images using expectation–maximization based on texture and color. They achieve weak segmentation: the image is segmented into blobs which may represent objects as a whole, parts of objects, or unions of different objects. This weak segmentation, although does not represent isolated objects, approaches the semantics by which users organize images, and permits better retrieval results when the user queries for discriminant objects in the image. Wang et al. [31] computes a weak segmentation based on k-means clustering of color and texture features. Their algorithm is faster than the used by Carson in [7], but achieves more inaccurate segmentations. They propose a similarity measure among images that compensates inaccurate segmentations by allowing multiple matchings from regions of the query to regions of the target image. Chen et al. [9] following the same idea compensates inaccurate segmentations by treating the segmented regions as fuzzy sets and using a uniﬁed fuzzy matching between regions. Contextual information or (relative) spatial layout have also been explored by some authors. A typical way to deal with spatial organization is generalizing the concept of string to a plane, conforming the so-called 2D string descriptor [8] and 2D C string [17]. In this descriptor, objects are represented by nodes and their spatial relationship by strings. 2D strings requiere very accurate segmentations of the objects in the image, what leads in practice to manual segmentations. Another descriptor for describing context is the correlogram. A correlogram is an histogram measuring the distribution of features such as color in the image as well as their spatial relationship (or their co-ocurrence). Huang et al. use these correlograms in retrieval of images by color, and Belongie et al. use another type of correlogram, called shape context, for taking into account the statistics of the distributions of points in shape matching and retrieval. These descriptors are good for taking into account the spatial distribution of the colors [15] or the spatial distribution of binary shapes [4], but do not permit to take into account context of different structures. We will show how generalizing them we can have this contextual information without needing manual segmentations. The extension of image retrieval to medical image applications is a challenging and emerging ﬁeld where few works have been published. Y. Liu et al. [19] characterizes retrieval as a classiﬁcation problem. This is correct when the images can be categorized as belonging to known classes (e.g. representing different diseases in medical diagnosis) and the user wants to retrieve images that belong to the same class as the example presented. Following this idea the authors begin with a big set of descriptors and ﬁnd the set of weights that achieves the lowest classiﬁcation error. They basically use global descriptors speciﬁcally chosen for CT brain images, exploding the symmetry in the brain as a basic property of normal (not diseased) brains. Local information is also extracted for asymmetrical regions. Other authors such as Korn et al. [16] explore the use of fast spatial access methods such as R-trees and fast nearest neighbor search. Their work is based on artiﬁcial sets of data that simulate tumor-like shapes. Focusing on the design of appropriate feature spaces, Kak and Brodley [29,11] take local and speciﬁc information for each of the pathology bearing regions (PBR) previously delineated by the user (the physician). Their work is speciﬁcally applied to highresolution computer tomographies (HRCT) of the lungs. For each image, low-level features are extracted locally at every region and globally for the whole image. They use an

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exhaustive set of descriptors that includes the usual features based on texture, gray-level and shape, but also includes very speciﬁc descriptors designed to describe the different lung diseases and their appearance in high-resolution computed tomographies (HRCT). Finally, they take only the most relevant information by sequential forward selection search, which reduces the dimension of the feature set. Very speciﬁc contextual information is also extracted by recording the relative position of the manually segmented region respect to manually extracted ﬁssures of the lung ([29]). The high cost of the manual delineation makes it impractical for regularly actualized large image collections. Liu and Sclaroff [18] perform segmentation of blood cell micrographs based on deformable shape models. The image is over-segmented and candidate regions are then merged into whole objects by using a deformable shape model and the regions color compatibility. Finally, they perform population-based retrieval of cells. For every image, an histogram of the shapes of the cells in the image is computed, and retrieval is achieved by shape histogram similarity. Paredes, Lehmann et al. [23] represent each image by several square windows which may overlap, and use them as a set of local appearances for the image. A condition for robust retrieval using local appearance is the preservation of shape. Regarding contextual information P. Liu et al. [14] use the centers of mass of manually segmented objects and their geometric relations to deal with the contextual information in retrieval of magnetic resonance images (MRI) of the chest. Petrakis et al. [25] use graphs, for retrieval of MRI images of the brain. Both 2D strings used by Chang et al. [8] and graphs used by Petrakis [25] permit a ﬂexible form of describing any type of image in terms of its structures (including their local attributes) and their spatial relations. The authors achieve in these works highly discriminative descriptors that can be indexed efﬁciently when the images have structures segmented manually, but not robust for automatic (non exact) segmentations. In addition to having an appropriate feature space, it is highly desirable to have invariance to a particular family of spatial transformations determined by the application domain. For achieving this we can employ either invariant feature spaces or similarity measures that are not affected by these spatial transformations. This invariance is very important in medical images, as there is a high degree of shape and appearance variability inter and intra subject. Despite this fact, there are few works in retrieval that deal with this type of invariance. In medical image retrieval, Lehmann et al. [10] use a distance measure invariant to small global transformations, and a distortion model that compensates more local deformations. This distortion model allows each pixel to be matched to any pixel of the destination image around a local neighborhood, without guaranteeing any regularity or topology preservation in the mapped object. Tagare et al. [27] compute the similarity between pairs of shapes by ﬁrst registering them. They forbid changes in topology by setting a set of constraints in the matchings, and solve the combinatorial problem by dynamic programming. Their method, however, is only valid for matchings between contours, and does not attempt to achieve any smoothness in the mapping. Y. Liu et al. [20] make retrieval of 3-D CT brain volumes by ﬁrst registering them, using a speciﬁc method based on the symmetric properties of the brain and an afﬁne transformation, non invariant to local elastic deformations. In this chapter we present a general framework of medical image retrieval based on plaque appearance, and consider a speciﬁc image modality: intravascular ultrasound images.

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Figure 1. IVUS image with different structures.

1.2. Medical Image Retrieval Based on Plaque Appearance, Application to IVUS An IntraVascular UltraSound (IVUS) image is obtained by inserting a catheter into the artery with a transducer on its tip. The transducer emits ultrasonic waves as it rotates, and these waves are propagated according to the physical properties of the media the catheter is in. Depending on the echogenic impedance of some structure, and its proximity to the tip, the wave will be reﬂected with some amplitude and some delay, which allows to form a cross-sectional image of the artery: the delay accounts for the distance of the structure from the tip, and the amplitude accounts for the intensity of the gray level used for representing the structure in the image. Figure 1 shows an IVUS image with two calcium plaque structures (regions of high level with a shadow behind), the catheter, and the usual adventitia tissue. The shadow behind the calcium plaques is due to the high impedance of the calcium, which does not allow the ultrasonic wave to pass through. We refer to [12] for an introduction on the topic. IVUS images of the coronaries are a novel and, at the same time, key tool in the correct diagnosis of coronary diseases such as atherosclerosis, which can provoke heart attacks. The great difﬁculty of these images makes it particularly interesting for the physician to perform analysis based on a history of similar cases, which motivates the construction of CBIR systems of IVUS. This CBIR should take into account the spatial relative distribution of structures such as atherosclerotic plaques, as studies have shown ([21]) that spatial characteristics such as the size of these atherosclerotic plaques, their eccentricity, and degree of embracement around the vessels; play important roles in the study of heart diseases. Furthermore, the intrinsic elastic properties of the arteries make these objects have an extraordinary high variation intra-subject and inter-subject, which demands invariance to elastic transformations in retrieval similarity between IVUS images. 1.3. Context Based Plaque Retrieval In contrast to the discussed approaches, the Context Based Plaque Retrieval method uses a feature space that integrates all types of information important in describing the content of the image: local, contextual and global information. This makes it appropriate to deal with medical images that hold complex information. For doing so we make a general-

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ization of the correlograms to deal with images presenting different types of structures. Correlograms are histograms that take into account not only the statistics of the features in the image, but also the relative spatial distribution of these features. Using this generalization of the correlograms to conform our feature space has various advantages: First, it incorporates all the types of information mentioned above. Second, it does not need accurate segmentation/classiﬁcation of the structures inside the image. This fact permits to make an automatic segmentation of the structures instead of making manual segmentation of the image, as opposite to the majority of descriptors used for dealing with this contextual information. Finally, the generalized correlograms permit easily to incorporate local information speciﬁc to the image application domain, which is mandatory in complex domains such as medical images [8,25,14]. For dealing with invariance to elastic transformations, an efﬁcient elastic matching method is proposed, aligning each pair of images before their comparison. This is achieved by using a sparse set of landmarks placed around salient regions of the image, and computing a fast transformation such as the thin-plate spline based on matching between these landmarks. The thin-plate spline produces elastic alignments modelling both global and local deformations, and restrains the object from undergoing unnatural deformations (e.g. changes in topology) by performing regularization. In the feature space component of the registration, we also make use of the proposed generalized correlograms. This allows us to match structures attending not only to their local properties (the type of the structure), but also to the global attributes (such as their size) and their context. Furthermore, these correlograms introduce spatial coherence and remove ambiguities in the computation of the correspondences, which makes the algorithm achieve good solutions with few iterations.

2. Feature Space As mentioned before, it is important that the feature space takes into account all types of information relevant to retrieve the image. Thus, we include local, global and contextual information, and we do so by using generalized correlograms. 2.1. Local Information By using local information we aim at describing the different types of structures inside the image. In the IVUS case, the discriminating structures are placed around the wall of the vessel [12]. A snake is placed at the center of the image after applying an anisotropic diffusion, and it is attracted to the wall. The set of landmarks is then obtained by sampling the snake (see Fig. 2). Associated to each landmark, a local feature vector is computed that describes the type of structure where the landmark lies. Here is where we include speciﬁc information about our domain, as these local feature vectors must be speciﬁcally chosen for characterizing the structures of our particular medical domain [11]. In our IVUS case, we take the gray level proﬁle along the normal to the wall at the landmark, in the direction from the landmark to the outward part of the vessel (Fig. 2). This descriptor is specially appropriate for characterizing IVUS structures, see [1] for further details. Finally, these local feature vectors are classiﬁed and labels are assigned to each landmark, giving more compact local information. In our case non-parametric discriminant analysis [5] is performed followed by K-NN classiﬁcation [1].

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Figure 2. Landmark and local feature vector extraction.

2.2. Global and Contextual Information We incorporate this local information into a generalization of correlograms that allows to provide this information along with contextual and global information about the image. Correlograms are histograms which not only measure statistics about the features of the image, but also take into account the spatial distribution of these features. For doing so a spatial quantization of the points inside the image must be done. Regarding this spatial quantization we provide two different deﬁnitions of the correlogram: a bidimensional deﬁnition and a periodic unidimensional correlogram. The bidimensional deﬁnition takes the same spatial quantization of the shape context descriptor of Belongie et al. [4]. The proposed generalized correlogram is then deﬁned by adding a dimension to the correlogram. This dimension takes into account the types of structures of the landmarks around the one being described. Let C be a set of n landmarks, and pi ∈ C the current one being described. Let lj be the label of the type of structure where the landmark pj lies. Let nc be the maximum number of classes. For pi the correlogram hi is deﬁned as: hi (r, θ, c) = #{pj ∈ C, pj = pi : (pj − pi ) ∈ Dr , (p j − pi ) ∈ Aθ , lj = c},

(1)

where Dr is the r-th interval of radius: r = 1 . . . nr , Aθ is the θ -th interval of angles: r θ = 1 . . . nθ , and c represents the class: c = 1, . . . , nc . The sets of intervals {Dr }nr=1 and nθ {Aθ }θ=1 constitute a spatial quantization of the possible angles and possible distances of the relative positions around the current landmark. Thus, the ﬁrst two dimensions of the generalized correlogram take into account the relative spatial position of the points (or landmarks), and the third dimension takes into account their type of structure. The correlogram can be interpreted then as an histogram measuring the density over relative positions of the different types of structures. The landmarks whose distance and angle relative to pi lie at Dr and Aθ constitute a cell in the plane (see Fig. 3(a)). The size of these cells is incremented exponentially as the positions move away from pi , so that more importance is given to local context. Figure 3(a) shows a bidimensional correlogram applied to a landmark of an IVUS image. The landmarks in this image have been classiﬁed into two classes: those belonging to calcium plaque (red points), and those belonging to adventitia (blue points). This correlogram has 12 intervals of angles (nθ = 12)

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(a)

33

(b) Figure 3. Bidimensional correlogram.

and 5 intervals of radius (nr = 5). Figure 3(b) shows a log-polar representation of the correlogram for each of the values of the third dimension: type of structure c = 1 and c = 2. In this plot, cells with a high density of points from a particular type of structure are represented by a high gray level. This correlogram has scale and orientation invariance by normalizing the distances pi − pj by the size of our object and orientating the correlogram along the tangent of the shape (see [4]). As said above, this bidimensional deﬁnition of the correlogram is a generalization of the one used by Belongie, by extending to take into account landmarks from different types of structures. At the same time, this spatial quantization deﬁned by Belongie can be regarded as a generalization of the one used by Huang et al. [15], as the latter takes only into account distances in the spatial organization. The main disadvantage of this bidimensional quantization is that the resulting correlograms are not robust against large shape changes of the object. This low robustness is accused before registering the images, however it can be avoided by using an appropriate feedback scheme (see below). Still, we make another deﬁnition of a correlogram by taking another type of spatial organization, robust to shape changes. This second deﬁnition represents a change of manifold from all the plane to the closed curve where the landmarks are placed, as in our case all the landmarks lie along the wall of the vessel. Now the landmarks pi are represented as the arc-length position inside the curve. Let : [0, 1) → R2 be the arc-length parameterized curve. The representation of the i-th characteristic point pi is now taken as its arc-length parameter ui inside this curve: (ui ) = pi , ui ∈ [0, 1). Let C = {ui }ni=1 be the set of arc-length parameters corresponding to the set of landmarks C. The correlogram for the i-th characteristic point is deﬁned as: hi (s, c) = #{uj ∈ C , uj = ui : (uj − ui ) ∈ Is , lj = c},

(2)

where Is is the interval of arc-length positions of the s-th cell, s = 1 . . . ns . By this deﬁnition, we are quantizing the possible values of arc-length differences between points of the curve. This difference must be computed with arithmetic modulus 1, in order to take into account the closed nature of the curve. Figure 4 shows a diagram of the spatial quantization of the 1D correlogram. As can be seen the cells form a partition of the closed curve where the landmarks lie. The picture shows cells of equal size for clarity

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Figure 4. Unidimensional correlogram.

purposes, although the size of the cells is incremented exponentially from pi to outwards, as occurred with the bidimensional correlogram. The advantage of this new spatial deﬁnition is that it is robust against changes of shape. The contextual information is now taken along the curve, without being affected by its changes in curvature. The main advantage of using correlograms is that they are robust against missclassiﬁcations, so that if some landmarks are missclassiﬁed the spatial distribution of the structures around pi is still represented. They also allow to include speciﬁc descriptors representing the types of structures in an easy way. We only have to choose a good descriptor for the structures of a particular medical domain, and classify the landmarks according to this descriptor. Then the labels are included in the correlograms as explained before. We also use generalized correlograms as a descriptor of the landmarks in the registration step. These contextual descriptors produce matching between structures attending not only to their type (local attributes) but also to their global attributes (such as their size) and their context. This solves ambiguities in the possible correspondences for each landmark. It also provides spatial information leading to regularity and coherence in the set of correspondences, accelerating the registration process. In this work we provide results when using bidimensional and unidimensional correlograms. Both of them are valid for registering the images, although as we will see unidimensional correlograms are more efﬁcient than bidimensional correlograms. The disadvantage of the former is that it is only valid when the landmarks form a closed curve. All along we have deﬁned the correlograms to measure the density over relative positions of the different types of structures around pi . We can also deﬁne an autocorrelogram, as called by Huang et al. [15] which takes into account only how the points from the same type of structure are organized around pi : hi (r, θ ) = #{pj ∈ C, pj = pi : (pj − pi ) ∈ Dr , (p j − pi ) ∈ Aθ , lj = li )} An analogous deﬁnition is done using an unidimensional deﬁnition as Eq. (2). Autocorrelograms are used just for registration purposes. Given two sets of landmarks from two structures of the same type, using auto-correlograms we produce matchings between points in the same relative position inside the structure, e.g. matching extremum points together, middle points together, and so on. This auto-correlogram is used in a reﬁnement step, once we have two structures of the same type and with the same context coarsely aligned. The aim is to make correspondences between homologous structures more exact and regular, discarding the information of the rest of structures.

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Figure 5. Scheme of the overall feature space design.

Finally, we can use fuzzy deﬁnitions of the correlograms deﬁned before. Until now each point pj lying in some cell adds 1 to the count of this cell, in the dimension lj = c. We can add to the count in the dimension c the probability P r[class(pj ) = c]. In this work, however, we do not use fuzzy deﬁnitions. In Fig. 5 we can see a scheme illustrating the whole feature space construction. Finally, regarding the similarity measure between correlograms, we use the χ 2 statistics to compare them: 1 (hi (k) − hj (k))2 2 hi (k) + hj (k) d

χ 2 (hi , hj ) =

k=1

where d is the dimension of the correlogram, if we treat it as a unidimensional vector (e.g. in the case of the deﬁnition of Eq. (1), we arrange the matrix of dimension nr × nθ × nc into a vector of one dimension d × 1, d = nr nθ nc ). This distance acts like the Euclidean metric normalized by the number of points falling in the k bin of both histograms hi and hj . It has been used among others by Huang et al. [15], and Belongie et al. [4].

3. Registration: Obtaining Invariance Against Elastic Transformations We obtain invariance against elastic deformations through registering the images before their comparison. The scheme followed in the registration is the so-called point-mapping (Fig. 6). First a set of landmarks is extracted from each image. The landmarks are described in some feature space, and a set of correspondences is computed which globally minimize the distance between landmarks in this feature space. Finally, a transformation is obtained based on these correspondences. The proposed registration method also includes a search strategy of the ﬁnal transformation. The feature space is the same as the explained in the previous section. 3.1. Computing Correspondences Once described the characteristic points in the feature space we compute the distance between any characteristic point in the image I1 and any characteristic point of the image I2 and based on this distance obtain our set of correspondences. We let for Section 3.3 the

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Figure 6. Scheme of the point-mapping paradigm.

expression of the exact distance. Let d(i, j ) be the distance between landmarks pi ∈ I1 and qj ∈ I2 . We want to obtain a correspondence function φ : {1, . . . , n} → {1, . . . , n} that minimizes ni=1 d(i, φ(i)). Such a function can be obtained by an assignment optimization algorithm such as the Hungarian’s method [22]. 3.2. Finding a Transformation Once we have our set of correspondences we want to ﬁnd a transformation function T : R2 → R2 , mapping the coordinates of I1 onto I2 . This function must map the characteristic points of I1 close to their correspondent positions of I2 , and produce a smooth mapping for the rest of points of I1 . Any registration algorithm is characterized by the family of transformations to which it provides invariance. Biological bodies have a great deal of variability, making necessary the use of elastic transformations. Elastic matching methods allow to model global changes or transformations and local (elastic) deformations. Furthermore, they lead to smooth (regular) transformations avoiding changes in topology of the object. For doing so, the transformation must incorporate a regularization component. In the present work we study the use of Thin-Plate Splines (TPS) as elastic matching method. TPS is an efﬁcient method when based on a small set of landmarks, as the computation of the transformation is done by a closed-solution formulae which involves inverting one matrix of n × n elements, n being the number of landmarks. A Thin-Plate Spline based transformation for an image can be expressed as Tλ (x, y) = (f x (x, y), f y (x, y)), where f x (x, y) and f y (x, y) are two independent surfaces obtained from the set of correspondences, and λ is the regularization parameter of the transformation. Let {xi , yi }ni=1 be the n landmarks of the origin, and {xi , yi }ni=1 the corresponding landmarks at the destination: f x (xi , yi ) = xi , i = 1, . . . , n and f y (xi , yi ) = yi , i = 1, . . . , n. We explain how to obtain one of the surfaces, let f (x, y) be such a surface. We call {ti }ni=1 the known data for the function we want to interpolate, so that we restrain f (xi , yi ) = ti , i = 1, . . . , n. Hence, if the surface f to estimate is f x , then {ti }ni=1 = {xi }ni=1 . If the surface f to estimate is f y , then {ti }ni=1 = {yi }ni=1 . Then f (x, y) can be expressed as:

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f (x, y) = d1 + d2 x + d3 y +

n

ci k (x, y) − (xi , yi )

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(3)

i=1

where k is the basis function or kernel: k(r) = r 2 log(r), k(0) = 0. The coefﬁcients d1 , d2 , d3 , c1 , . . . , cn are obtained solving a system of linear equations derived from applying the following restrictions: i) interpolation conditions (n equations): f (xi , yi ) = ti , i = 1, . . . , n; ii) in order for f (x, y) to have square integrable second derivatives we require: n

ci = 0,

i=1

n i=1

ci xi = 0,

n

ci yi = 0

i=1

which produces a total of n + 3 equations expressed by the following matrix notation: K P c t = (4) d 03×1 P T 03×3 where Kij = k((xi , yi ) − (xj , yj )), the ith row of P is (1, xi , yi ), c = (c1 , . . . , cn )T , d = (d1 , d2 , d3 )T , t = (t1 , . . . , tn )T and 03×1 denotes a 3 × 1 matrix of zero elements. Let L be the (n + 3) × (n + 3) matrix of the last equation, a the vector of coefﬁcients a = (c, d)T and v = (t, 03×1 )T . We need only to invert the matrix L for obtaining the coefﬁcients of Eq. (3), a = L−1 v, and as discussed in [26] this matrix is non singular. The steps described above obtain an interpolating surface f , for λ = 0. If we want to obtain a regularized (i.e. approximating) surface, we just have to substitute in Eq. (4) the matrix K by K + λIn×n , where In×n is the n × n identity matrix [2]. After applying TPS we can also obtain a measure of the bending energy this transformation has. Let ax be the vector of coefﬁcients a, deﬁned above, for component x of the transformation. Let K be the kernel matrix deﬁned also above, then the bending energy due to the component x of the transformation is: Ex = axT Kax

(5)

Let Ey be the energy employed in the y mapping f y , obtained in an analogous manner. We have as energy E of the whole transformation the sum of both components: E = Ex + Ey . Finally, the regularity of the TPS for different values of λ depends on the square of the scale of our objects. So if we have s as the size of our objects, we should compute λ = λnorm s 2 , and experimentally set values for λnorm on normalized objects. The λ parameter represents the tradeoff between approximation to the data (the computed correspondences) and smoothness. A high value of λ smoothes out irregularities in the correspondences, necessary in the ﬁrst steps of the algorithm. At the same time, a high λ leads to a more global (coarse) transformations, whereas a low λ makes the transformation more elastic. The transformation can then accommodate more local deformations, reﬁning the alignment. The regularity of the set of the correspondences depends on the stage of the algorithm. Initially they are quite irregular due to the complexity of the problem, and they become more and more regular through the feedback scheme we will explain below.

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Finally, the computed transformation also permits to produce a warping of image I1 , making it more similar to image I2 . This is necessary for taking into account the appearance similarity in the ﬁnal comparison (see Section 4). 3.3. Search Strategy Many registration algorithms [6] include some search strategy of the ﬁnal transformation. We include this component through a simple yet effective feedback scheme performed in an iterative manner. The complexity of the images leads to irregular nonreliable initial sets of correspondences. However, the correspondences do obtain the correct global information to align coarsely the images. Thus, we introduce feedback of coarse transformations to obtain ﬁner ones. The feedback is made by biasing the next set of correspondences towards the positions obtained by the last transformation. This is done by recomputing the distances between landmarks pi ∈ I1 and qj ∈ I2 as: dij = dijF + αTλ (pi ) − qj , where dijF is the distance between landmarks in the feature space, and α is the degree of inﬂuence of the last transformation in the next set of correspondences. This feedback achieves a simultaneous maximization of the regularity of correspondences and the similarity of corresponding points throughout the iterations. The regularity is enforced by the term αTλ (pi ) − qj , that represents the difference of the vector formed by the potential correspondence u = (qj − pj ) from a regular correspondence v = (Tλ (pi ) − pi ): v − u = Tλ (pi ) − qj . The similarity is enforced by the term dijF . It can also be seen as a form of cooperation, as deﬁned by Brown in [6]. In a cooperative scheme the correspondences computed for neighbor landmarks give information about the correspondence computed for the current landmark. Here the TPS mapping for the current point, Tλ (pi ), depends on the obtained correspondences in its neighborhood, and we restrict a potential matching point qi not to lie far away from this mapping. The α and λ parameters representing the inﬂuence of the last transformation and the degree of regularization are updated throughout the iterations following an annealing scheme. The α parameter represents the conﬁdence in the last transformation, whereas a low λ parameter represents conﬁdence on the last set of correspondences (i.e. correspondences without many irregularities). As both the correspondences and the transformation are improved throughout the iterations, we must increment α and decrement λ. Both are changed with an exponential ratio, see [1] for further details. Finally, we can consider part of the search strategy the hierarchical scheme followed in the computation of global to local transformations. Furthermore, a hierarchical scheme is followed in the use of global to local information, as we use bigger correlograms for computing the ﬁrst transformations (global alignments require more global information) and smaller correlograms for making more ﬁne alignments.

4. Similarity Measure in the Final Comparison Between Images The registration produces as output a function T which is regular and maps the characteristic points pi from I1 close to their corresponding ones in I2 . However, the mapped points are not exactly the characteristic points qi of I2 . For obtaining a regular ﬁnal set of correspondences φ from {pi }ni=1 to {qi }ni=1 , we simply take the Euclidean distances of

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mapped points and destination points: dij = T (pi ) − qj and compute the correspondences using the hungarian’s algorithm over this matrix of distances. Our similarity measure is based on the sum of three factors: the distance in the feature space described earlier, the amount of deformation necessary to align both objects, and a local appearance difference between the aligned image and the destination image. The amount of deformation is measured through the energy E of the Thin-Plate Spline computed over the regular correspondences obtained before. A high energy means that the amount of deformation is too high for considering natural this transformation. The distance in the feature space is in our case the distance of the correlograms. We can use either the 2-D correlograms or the 1-D correlograms. We have seen small difference between them in the results because the 2-D correlograms perform as well as the 1-D correlograms when the shapes are already aligned. As 2-D correlograms are more general, we used it. We recompute these correlograms orienting them now along the x axis of the image. This is done to reduce the little robustness that these correlograms have on the computation of the tangents, now that the alignment permits us to avoid the invariance to orientation. The size of the correlograms is the maximum size in the hierarchical approach, so that all the image is included in every correlogram. Let dijF be the χ 2 distance between correlograms of pi ∈ I1 and qj ∈ I2 . We compute the global distance between both images, d F (I1 , I2 ) as the symmetric sum over distances of best matching correlograms: d F (I1 , I2 ) =

1 1 arg min dijF + arg min dijF j i n m n

m

i=1

j =1

For computing the local appearance difference between both images, let IW be the image I1 warped according to the obtained transformation from the registration. We take local windows around the mapped points T (pi ) in IW and matching points qφ(i) in I2 . The local appearance difference is expressed as: d A (I1 , I2 ) =

w n w

2 G (x, y) IW (T (pi ) + (x, y)) − I2 (qφ(i) + (x, y))

i=1 x=−w y=−w

where G(r) is a gaussian-like function of the radius r, more sensitive to close positions. The warped image IW does not respect the original pattern of the textures, so it is better to remove them in the comparison. Therefore, we take as images I1 and I2 the anisotropic diffusion of the original images. Finally, the total distance between both images is computed as a combination of the distance components deﬁned above: d(I1 , I2 ) = α F d F (I1 , I2 ) + α A d A (I1 , I2 ) + α E E This distance is used by Belongie et al. in [4], for binary objects. We apply it generalized for objects with several structures. The weights α F , α A , α E are computed as the ones minimizing the classiﬁcation error on the IVUS database, following a leave-one-out procedure.

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Figure 7. Histogram of the efﬁciency of classiﬁcation.

5. Results In this section we evaluate the system in three aspects: i) the rate of success of the local classiﬁcation of tissues plaque/versus non-plaque, ii) the results of applying each of the components of the registration algorithm: the proposed feature space, the feedback scheme, and the overall registration results; and ﬁnally, iii) the overall retrieval results. All the experiments have been conducted on a database of 100 IVUS images, all of them presenting plaque structures. Studying the registration of images presenting plaques is of high interest for the following reasons: ﬁrst, there is a great difﬁculty in the differentiation between plaques and adventitia tissue, second, there is a high variability in the shapes of both the entire vessel and the plaque structures, and third it has been clinically seen that the relative spatial distribution of the plaques is important in diagnosis of heart diseases. This makes it interesting to study the use of the proposed contextual descriptors on these images in order to retrieve them. As explained in the introduction, retrieval of medical images is very interesting to perform computer-aided diagnosis. In particular, retrieval of IVUS images is useful to assist coronary diagnosis and intervention. 5.1. Local Classiﬁcation Results As explained in Section 2, when building the feature space, we ﬁrst obtain a set of local descriptors based on gray level proﬁles along the normal to the contour at this point, and then perform classiﬁcation of these feature vectors, assigning labels to each characteristic point. We have designed a classiﬁcation algorithm based on reducing the dimensionality by Non-Parametric Discriminant Analysis [5], and nearest neighbor classiﬁcation. The scope is to achieve moderately good classiﬁcation results. As the classiﬁcation efﬁciency is different depending on the particularities of each image, we evaluate the efﬁciency of classiﬁcation for all the landmarks in each image, and compute the mean efﬁciency and standard deviation of classiﬁcations across all the images. In Fig. 7 we show the histogram of the efﬁciency of classiﬁcation, the horizontal axis represents the efﬁciency of classiﬁcation and the vertical axis the ratio of images that whose landmarks are classiﬁed with this efﬁciency of classiﬁcation. The red line indicates the mean efﬁciency, which is 90.2%, and the green lines indicates the mean minus and plus the standard deviation. The standard deviation is of 7.8%. We must note that the scope of this work is neither to design a very accurate local speciﬁc feature, nor to employ a sophisticated classiﬁcation scheme over this local feature space. The results achieved in classiﬁcation are good enough to work with

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(c)

(d)

(e)

(f)

41

Figure 8. Some classiﬁcation examples. Red points indicate classiﬁcation as calcium plaque, and blue points as adventitia (the rest of the tissue). Correct calcium structures are indicated by green boxes surrounding the structure. (a–b) good results, (c–d) regular results, (e–f) bad results.

the proposed correlograms for performing registration and retrieval. In Fig. 8 we show some classiﬁcation examples. Red points represent landmarks automatically classiﬁed as belonging to plaque structure, whereas blue points represent landmarks belonging to non-plaque tissue. With cyan boxes we have indicated the correct regions where landmarks belong to plaque structure, in order to show the goodness of the automatical classiﬁcation. The majority of images has good classiﬁcation results, as in the case of Figs 8(a)–(b). The worst examples are shown in Figs 8(e)–(f). The main problem is that

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in some images compact regions are wrongly classiﬁed as belonging to plaque structure, and therefore, these regions are interpreted by the correlogram as structures (false structures). This is difﬁcult to avoid because there are some regions of adventitia resembling much to plaque. These are regions of high gray level and with a black region behind it, which is what characterizes mostly calcium plaque. Figures 8(e)–(f) show such regions. 5.2. Performance of the Correlograms In the registration algorithm, the use of correlograms has several advantages: ﬁrst, it allows to obtain more regular sets of correspondences, as it introduces spatial coherence information in the feature space. Second, it incorporates not only contextual information, but also global characteristics of the different types of structures. This produces matching of homologous structures having the same global characteristics such as size. We ﬁrst show how correlograms obtain regular correspondences. Figure 9 shows a couple to be registered. Both images have only one plaque structure, the homogeneous white structure. Figure 10 shows correspondences obtained by different descriptors for the couple of Fig. 9. The original landmarks are placed in a small region of adventitia in the left image of each pair. Figure 10(a) shows the correspondences when using local feature vectors. The set of correspondences does not hold spatial regularity as spatial information is not included in the descriptor. Figure 10(b) shows the correspondences when using local gray level windows of size 19 × 19. Taking local windows is not robust against shape changes, and gray-level windows are poor in IVUS. As can be seen, the set of correspondences is not regular. Figure 10(c) shows correspondences using 2D correlograms. The regularity is not complete, but is much higher than with the other descriptors. Finally, correspondences using 1D correlograms are shown in Fig. 10(d). The set has very few irregularities, and it is more regular than using 2D correlograms. Now we see the effect of using correlograms for taking into account global characteristics of the structures. Figures 11(a)–(b) show a new couple of IVUS images to be registered, (a) displays the image I1 to be aligned and (b) the destination image I2 . Figures 11(c)–(d) show the anisotropic diffusion of (a)–(b) respectively. In red we superpose the contour of the vessel from which the characteristic points are extracted in each image. The image I1 has two calcium plaques on both sides (indicated in the Fig. 11(a)), and the image I2 has three calcium plaques: two on both sides and one at the bottom (indicated in the Fig. 11(b)). Taking into account global characteristics the plaques on both sides should be matched in both images, leaving alone the small plaque at the bottom of the image I2 . We show how the global description is included with correlograms by comparing the result of a ﬁrst coarse transformation using contextual information (2D correlograms) and then using only local information (the local feature vectors). We show transformation results on the anisotropic diffusion of the images because it is visually more clear. Figure 12(a) shows the warped I1 when using correlograms. Figure 12(b) shows the image I2 with the edges of the warped I1 superposed in red. We can see how both calcium plaques of I1 are mapped close to the big plaques of I2 , as well as the adventitia tissue. Figures 12(c)–(d) show the warping result when using only local feature vectors. One of the calcium plaques (indicated in Fig. 12(e)) has not been mapped close to any of the plaques of I2 , as the mapped plaque (indicated by a green arrow in Fig. 12(d)) lies at an intermediate position between a big plaque and a small one (blue arrows). Using correlograms this matching is avoided as the size characteristic is included.

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Figure 9. First couple example to be registered. (a) I1 image to be aligned, (b) I2 destination image; (c)–(d) anisotropic diffusions of (a)–(b) respectively; (e)–(f) Classiﬁcation results for (a), (b): in red the landmarks classiﬁed as belonging to calcium plaque, in blue landmarks classiﬁed as belonging to adventitia tissue.

5.3. Evaluation of the Feedback Scheme The result of applying the feedback scheme is that the transformation becomes more and more approximate and at the same time the set of correspondences becomes more and more regular. This is illustrated ﬁrst qualitatively for the pair of images shown in Fig. 11,

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Figure 10. Correspondences using different descriptors (see text).

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Figure 11. Couple of images to register (a)–(b). Their anisotropic diffusions (c)–(d).

and then quantitatively by showing the evolution of the error through the iterations of the algorithm applied to 100 random registrations. Figure 13(a) shows the initial set of correspondences in the registration of the pair of images of Fig. 11, and Fig. 13(b) shows the ﬁnal set of correspondences. The initial set is very irregular, but holds information about the correct global matching. Figure 13(c) shows the transformation based on this set, where the plaques are placed with the correct orientation and position (see green arrows in right image of (c)). Figures 13(d) and 13(f) show respectively an intermediate and ﬁnal stage in the computed transformation. The intermediate transformation is coarse (rigid) but more approximated than the initial transformation, whereas the ﬁnal transformation is accurate and elastic. Now we see a quantitative evolution of the approximation error and degree of irregularity of computed correspondences throughout the iterations of the algorithm. We have made 100 random registrations, and computed the median of the approximation error and irregularity at the successive iterations of the algorithm. We measure the approximation error for an obtained transformation T as:

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(d)

Figure 12. Coarse alignment (ﬁrst step of the algorithm) using ﬁrst contextual information (a)–(b), and then only local information (c)–(d).

(a)

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(f) Figure 13. Evolution through the different stages of the algorithm.

Ea (I1 , I2 ) =

Eai (p, C)

nc 1 1 max 1 nc n i i=1

=

min

q∈C,class(q)=i

p∈C1 ,class(p)=i

T (p) − q ,

Eai (p, C2 ),

1 n2i

Eai (q, C1 )

q∈C2 ,class(q)=i

(6)

where I1 , I2 are the registered images, nc is the number of classes (types of structures) we deal with, n1i is the number of landmarks from I1 belonging to class i, and n2i is the same for image I2 , T is the obtained mapping, and Eai (p, C) measures the distance of the mapped point p to points of C from the same class.

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(a)

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Figure 14. Evolution through the iterations of the approximation error (a) and degree of irregularity (b) using 1D and 2D correlograms. The solid line with squares display the 1D correlogram case, and the dashed line the 2D correlogram case.

We measure the irregularity of each set of correspondences performing a TPS over this set and measuring its bending energy (see the Section 3.2). This measure is high whenever there are irregularities. Figure 14 shows a graphic of the median evolution of the approximation error (Fig. 14(a)) and irregularity (Fig. 14(b)) of the set of correspondences throughout the iterations of the algorithm. We compute this median over 100 randomly chosen pairs of images to be registered. Each pair consists of two images from the same category. In blue dashed line we have this evolution when using bidimensional correlograms, and in red solid line with squares when using unidimensional correlograms. Both using bidimensional and unidimensional correlograms, the approximation error and the irregularity are decreased throughout the iterations. This is due to the simultaneous maximization, in the proposed feedback scheme, of the approximation and regularity (see Section 3.3). Regarding the efﬁciency of using both types of correlograms, the unidimensional correlogram achieved better approximation errors and more regularity from the ﬁrst steps, whereas the bidimensional correlogram needed around eight iterations to achieve accurate results. With unidimensional correlograms we needed just two iterations in order to achieve almost the same error than with bidimensional correlograms. This is due to the robustness the unidimensional deﬁnition has against shape changes. However, both correlograms are valid for obtaining accurate correspondences with not many iterations. Finally, we see how a registration algorithm such as the one employed by Belongie et al. [4] without any cooperative feedback scheme can lead to poor results when dealing with the types of images we have. We take the same couple displayed in Fig. 11, and only use the landmarks from one type of structure (calcium plaque in this case) for registration. We do so because the descriptor of Belongie is not suitable for different types of structures. Figures 15(a)–(b) show the disposition of the mentioned landmarks in both images. We use Belongie’s registration algorithm with his shape-context descriptor rotated along the tangents of the points in order to achieve orientation invariance. Figure 15(c) shows the ﬁnal set of correspondences. The points structures are not mapped close to their destination, and the ﬁnal correspondences are quite irregular. Figure 15(d) shows the transformed image I1 according to these correspondences, and Fig. 15(e) shows in red the edges of this transformed image superposed onto the target image. The warping is very irregular as it is based on irregular correspondences. The

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Figure 15. (a)–(b) Points from the plaque structures of Fig. 11 (a)–(b). Final set of correspondences (c) and ﬁnal transformation: warped query (d), and edges of warped query superposed on the complementary (e) obtained with Belongies’s registration algorithm.

(a)

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Figure 16. Approximation error (a) and degree of irregularity (b) through the iterations using the shape context matching from [4].

irregularity is due to the high shape difference in both objects, which arises the necessity to enforce step by step some regularity in the correspondences. If this regularity is not enforced, the resulting transformation will map the points without preserving the spatial coherence. Thus, correlograms are good for modelling contextual and global information (as shown with the result in Fig. 13), but only if we strengthen the spatial coherence of the mapping by some feedback algorithm such as the explained in Section 3.3. Finally, Fig. 16 shows the evolution of the approximation error (Fig. 16(a)), and the evolution of the degree of irregularity of the correspondences (Fig. 16(b)). They use 6 iterations in the algorithm. Both the approximation error and irregularity do not decrease throughout the iterations, as the correspondences become more and more irregular.

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(a)

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Figure 17. Registration with mean approximation error.

5.4. Registration Results We see registration results now, using 1646 pairs of homologous images (i.e. from the same category) for computing the statistics. We obtain a mean approximation error of 4.6 pixels, a median error of 2.04 pixels and a standard deviation of 7.6 pixels. The mean distance between two neighbor characteristic points is of 3.1 pixels. Thus, the mapping is 1.5 times the distance between landmarks that are neighbors. Experimentally we have seen that errors below 6 pixels are fairly good. 75% of the alignments have an error below 4.23 pixels. In Fig. 17 we show the alignment with an error of 5 pixels, higher than the mean. Image (a) displays the couple, the left IVUS being the one to be aligned with the right IVUS. Red points are landmarks automatically classiﬁed as belonging to plaque structure, whereas blue points are classiﬁed as adventitia structure. In cyan we display polygons containing the correct manual classiﬁcation of plaque structure. Note the high difference in the shapes of the two contours. Images (b)–(c) show the correspondences for the plaque structure, and image (d) shows the global alignment of the two contours: in blue the contour of I2 and in red the mapped contour of I1 . Most of the error in alignment is due to the classiﬁcation error. Although this error is not high (90.1% of success), the problem is that the points classiﬁed incorrectly can spatially concentrate. This makes false structures appear, as shown in Fig. 18. Figure 18(a) shows the automatic classiﬁcation of landmarks for the couple of images (I1 on the left and I2 on the right), with cyan boxes indicating the correct classiﬁcation of plaque structure. The classiﬁcation of the landmarks from I1 is quite correct, but in I2 a false plaque structure is detected. Figure 18(b) shows the computed correspondences. As can be seen, the plaque structure from I1 is matched with the false plaque structure appeared at I2 . 5.5. Retrieval Results For assessing the retrieval efﬁciency, a database of 100 IVUS images has been used. Two examples of these categories are illustrated in Figs 19 and 20. Figure 19 shows a subset

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Figure 18. Registration with high alignment error due to the detection of false structures.

Figure 19. First example of a subset of images falling into the same category.

of IVUS from a ﬁrst category. We can see that in all of them the plaque structure has a high degree of embracement around the vessel. Figure 20 shows a subset of IVUS from another category. These IVUS present several plaque structures along the vessel. In this manner, the IVUS images in the database have been classiﬁed by a group of physicians into several categories. The categories are chosen attending to clinical properties (see [1]). We extract each image from the database, present it as query, and the system orders the rest of the images from the database in order of similarity to the query. From this ordered list, we take only the ﬁrst K images (i.e. the K most similar images to

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Figure 20. Second example of a subset of images falling into the same category.

our query). Two measures of retrieval efﬁciency are taken. The ﬁrst one is the estimated number of images we need to retrieve in order to include an image from the same category as the query. We obtained an average of 2.33 images necessary for including one of the same category. For K = 2 retrieved images the mean number of times in which an image from the same category is included is 89.7%. The second measure is the recall vs scope [15]: if query Q has N images from the same category, we compute for Q: E Q (K) =

#|I : rank(I ) ≤ K, category(I ) = category(Q)| N

and average over all the queries presented: E(K) =

1 Q E (K), NQ Q

where NQ is the number of query images presented to the database. We compare the efﬁciency of the Context Based Plaque Retrieval with the efﬁciency of the retrieval reported in Huang et al. [15]. They report results using two descriptors: Color Coherent Vectors (CCV) and auto-correlograms, both of them representing types of histograms that include spatial information. In Table 1 we present the E(K) measure for different values of K when using the proposed method versus the Color Coherent Vector-based method, and

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Table 1. Recall vs scope measure. K

CCV

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proposed method

10

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50

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0.75

0.73

Figure 21. Example of optimal retrieval result for K = 3.

the auto-correlogram. A Color Coherent Vector consists of two histograms, one of noncoherent color pixels of the image, and the other one of color-coherent pixels. A color coherent pixel set is a set of pixels that have a similar color and are spatially contiguous. Auto-correlograms are histograms measuring for some color and some distance the proportion of couples of pixels having this color and lying at this distance of each other. The results with CCV and auto-correlograms are obtained with the database reported in Huang et al. [15]. Huang uses a general database, as CCV and auto-correlograms are not intended to be used in medical domains such as the presented. We only make the comparison for illustration purposes of the goodness of these numbers. As the mean number of images from the same category is 16.56, we show the numbers obtained with CCV and auto-correlogram for experiment on query 4 (see [15]). The efﬁciency of the proposed approach can be considered to be between the efﬁciency of CCV and auto-correlograms. In Fig. 21 we see a result of three queries with high performance. In the three cases the ﬁrst K = 3 retrieved images are all of the same category. In Fig. 22 we see a result of three queries with low performance. Although in this example non of the retrieved images strictly belong to the same category as the query, the similarity of the retrieved images and the queries is quite high. For six of the nine retrieved images, the degree of embracement of the plaque in both the query and the retrieved image is the same. Most

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Figure 22. Example of worst retrieval result for K = 3.

times the failure of the retrieval system is due to the interpretation of false structures (in the local landmark classiﬁcation), as can be seen in Fig. 18. Although the correlograms presented are quite robust against non perfect classiﬁcations, they can not succeed if an entire spatially coherent region is missclassiﬁed.

6. Conclusions In this chapter, we presented a content-based image retrieval method that is able to deal with medical images of bodies with large shape and appearance variability. The proposed method uses a highly discriminant feature space that includes all types of information relevant to retrieve images: local, global and contextual information. This is achieved by generalizing the correlogram descriptor for dealing with different types of structures. The main advantage of the proposed generalization of correlograms is that they are robust against non-exact classiﬁcations/segmentations of the different structures inside the image. This allows automatic classiﬁcations of the structures. On the other hand, speciﬁc information can be easily introduced in this correlogram generalization. This makes the feature space designment suitable for different image domains. Speciﬁc information on the other hand is fundamental for dealing with complex domains such as medical image, as general features perform poorly in these domains. Finally, the comparison between images is made invariant to elastic transformations by means of registering the images before their comparison. The registration scheme is based on the point-mapping paradigm, the use of the same generalized correlograms, a thin-plate spline transforma-

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tion based on few landmarks around discriminant regions and a feedback scheme which strengthens the regularity of the ﬁnal transformation. Registration with TPS and few landmarks is very efﬁcient as compared to other registration methods such as the use of the Navier-Stokes PDE [3]. There are two main lines of work for improving the presented retrieval system. In the particular IVUS domain, there is still work to do in the characterization of the different types of structures. We have seen that the main cause of error in the system is the wrong classiﬁcation of entire regions in the image. In this sense, we could explore improved local descriptors. The inclusion of information along the longitudinal axis of the arteries is very important, as the physicians use this information for identifying the different types of structures. In general, considering the problem of medical image retrieval, we want to explore fast indexing techniques of the generalized correlograms by use of fast spatial access methods.

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Plaque Imaging: Pixel to Molecular Level J.S. Suri et al. (Eds.) IOS Press, 2005 © 2005 The authors. All rights reserved.

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MRI Plaque Tissue Characterization and Assessment of Plaque Stability Chun YUAN a , Thomas S. HATSUKAMI b and Jianming CAI a a University of Washington, Seattle, WA, USA b Department of Surgery and VA Puget Sound Health Care System, Seattle, WA, USA Abstract. This chapter reviews current MRI techniques to differentiate stable versus high risk atherosclerosis and discusses the development of non-invasive MR imaging techniques to characterize atherosclerotic plaques. Tissue speciﬁc MR signal features will be described according to histo-pathological evaluation standards and comprehensive imaging protocol for the identiﬁcation of different lesion types will be introduced. Keywords. Atherosclerosis, magnetic resonance, black blood, white blood, wall morphology, intraplaque hemorrhage, histology, quantitation

1. Introduction Stroke is a leading cause of death (4.4 million per year) and disability (5000 per million persons) worldwide. Due to the aging of the population, the rate of stroke is projected to increase and become an even greater healthcare concern. In the United States alone, the rate of stroke-related death is predicted to outpace population growth and may double over the next 30 years [1]. Better methods to detect atherosclerotic disease would considerably lower stroke-related mortality rates, improve the quality of life of stroke survivors, and reduce health care costs. Carotid atherosclerosis is a major contributor to the etiology of ischemic stroke. Autopsy studies have provided ample pathological evidence of athero-embolic material in the small arteries that supply infarcted tissue in the brain [2]. Several large randomized clinical trials have shown that the removal of high-grade carotid plaques (carotid endarterectomy) signiﬁcantly reduces incidence of recurring stroke compared to non-operatively treated individuals with similar degrees of carotid stenosis [3–6]. Secondary analysis of data from the North American Symptomatic Carotid Endarterectomy Trial (NASCET) has shown that the features of the carotid atherosclerotic lesion, such as plaque surface characteristics, are associated with a dramatically increased risk for stroke. For example, angiographic identiﬁcation of plaque ulceration increased the 2-year risk for ipsilateral stroke to 73% amongst those with 95% stenosis, compared to 21% of patients with non-ulcerated 95% carotid stenosis [7]. Although the randomized clinical carotid surgery trials have provided new insights into the role of carotid endarterectomy in the management of stroke patients, a better

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understanding of the mechanisms of carotid-related stroke is needed. A number of studies suggest that in addition to the plaque-lumen surface characteristics, the composition and morphology of the plaque itself are important determinants of risk of thromboembolic complications. Based on histopathological ﬁndings from excised surgical or autopsy specimens, the high-risk, vulnerable lesion has been typically described as containing a large necrotic core or intraplaque hemorrhage that is separated from the lumen by a thin ﬁbrous cap with inﬂammatory cellular inﬁltration [8–11].

2. Need for Atherosclerosis Imaging Currently, histopathological study of atherosclerotic plaque specimens obtained at autopsy is the primary method used to examine plaque characteristics. A shortcoming of this approach is that its assessment of such characteristics is limited to a single timepoint. Furthermore, research access to a wide spectrum of atherosclerotic lesions is limited. In order to better understand the fundamental mechanisms involved in the development and progression of high-risk plaque characteristics, serial in vivo assessment of the lesion is needed. To meet this need, the development of accurate, reproducible and preferably non-invasive imaging methods are required. High-resolution atherosclerosis imaging is also needed to develop novel pharmacological therapy. Recent developments in animal models of atherosclerosis are promising, but to date, they are unable to mimic the advanced lesions of human atherosclerosis. As a result, many pharmacological interventions that appeared promising in animal models were not effective when applied in human trials, resulting in signiﬁcant waste of health care resources. High-resolution atherosclerosis imaging is therefore needed to provide direct, serial, and in vivo assessment of how human atherosclerosis responds to therapeutic interventions. Given its superﬁcial location, relatively large size and immobility, and the presence of the full spectrum of American Heart Association (AHA) lesion types [12], the human carotid artery is better suited for serial imaging studies than other arterial sites. More importantly, the carotid artery is the only vascular bed where intact surgical specimens are readily available for histological veriﬁcation of ﬁndings from novel in vivo imaging techniques (Fig. 1). Magnetic resonance imaging has demonstrated great promise as an accurate, reproducible method for characterizing human carotid atherosclerosis in vivo. MRI has several inherent advantages compared to other imaging modalities: 1) it is non-invasive; 2) through advances in hardware and image acquisition protocols, sub-millimeter resolution is achievable; 3) it has superior capability to distinguish tissue types based on their chemical composition; and 4) advances in targeted MRI contrast agents show promise for superior identiﬁcation of speciﬁc molecular targets. In the sections that follow, the technical aspects of high-resolution MR imaging will be reviewed and validated.

3. Technical Aspects of Plaque Imaging Clinical carotid plaque imaging techniques that use a 1.5T clinical scanner set to the spatial resolution of 1 × 1 mm2 are unable to accurately detect the small volumes of

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Figure 1. The complexity of the carotid atherosclerotic plaque is well illustrated in this section taken from the common carotid portion of an excised endarterectomy specimen.

the major plaque components present in carotid lesions. Recent research shows that the evaluation of histologically processed endarterectomy specimens reveal the mean values for the volume of individual plaque components (lipid core, ﬁbrous intimal tissue, and calciﬁcation) that range from 0.3 mm3 and up [13]. While submillimeter voxel sizes can be achieved with whole body 1.5T scanners, it is necessary to use a phased-array surface coil to generate an acceptable signal-to-noise ratio (SNR) [14] for the high-resolution images required for carotid plaque characterization. Since high spatial resolution imaging sequences may also result in relatively long scan times (several seconds to a few minutes), hardware and software techniques that reduce the effects of motion and ﬂow artifacts are key to improving imaging quality. The following sections describe the hardware considerations and the imaging sequences that are valuable for producing high quality diagnostic multi-contrast MR images of the carotid arteries. 3.1. Hardware Considerations The carotid artery is a superﬁcial structure with lengths greater than their distance from the skin surface. Its conﬁguration makes possible the use of phased-array (PA) surface coils to simultaneously collect data from both its right and left sides. Accordingly, a dedicated PA coil assembly [15] with the dimensions of 6.4 × 10.8 cm was constructed to image carotid plaques. To make possible the imaging of both carotid arteries during the exam, the assemblage consisted of two separate sets of coils. Each coil is made of a soft ﬂexible material that can be comfortably ﬁtted and secured around the patient’s neck (Fig. 2). This coil assembly makes it possible to obtain data from a carotid longitudinal

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Figure 2. A picture of the carotid phased array coil. Notice the shape of the coil surface is designed to touch the human skin. The coil is ﬂexible for different size of the human neck.

coverage of up to 5 centimeters. Performance studies of these PA coils have shown a 37% improvement in the SNR when compared to commercially available 3-inch surface coils. This enhancement of the signal-to-noise ratio (SNR) enables the acquisition of diagnostic images of the common, internal and external carotid arteries with an average voxel size of 0.25 × 0.25 × 2.0 mm3 (0.25 mL). In addition to the carotid phased-array assembly, a custom designed headholder was constructed using vacuum formed PVC plastic. The headholder provides support for the occiput and neck, which not only improves patient comfort, but also makes possible repeatable scan positioning and reduces patient movement. 3.2. Black and Bright Blood Pulse Sequences T1 and T2 weighted images were the ﬁrst to be used to identify individual plaque components [16,17]. Recent research, however, has shown that the use of multiple contrast weightings can signiﬁcantly improve the precision and accuracy of MRI characterizations of plaque morphology [18–20]. To improve the quality of MRI depictions of plaque morphology, these studies recommend using a combination of spin echo (SE) based T1, T2 and proton density weighted images and gradient recalled echo (GRE) T2* images [21]. The SE techniques are primarily used for studying plaque morphology and tissue characterization — especially lipid, hemorrhage and ﬁbrous tissues. The GRE techniques (similar to those of the TOF) are used for studying lumen-plaque interface and plaque morphology. In other words, the pulse sequences designed for vascular imaging are either, depending on the signal of the blood ﬂow relative to the surrounding soft tis-

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sues, black blood or bright blood techniques. These two types of sequences offer speciﬁc advantages for carotid imaging. Black blood techniques are MR imaging techniques that suppress the signal obtained from blood ﬂow [22]. This technique is ideal for plaque imaging because the conspicuity of the vessel wall is increased when it is next to a hypointense lumen and the imaging echo (TE), and repetition (TR) times can be varied to optimize visualization of speciﬁc plaque components. The major disadvantages of black blood techniques include relatively long scan times, and the fact that these sequences are based on 2D data acquisitions requiring slice thickness between 2 and 5 mm. Common ﬂow suppression techniques employed with black blood imaging include the following: the use of pre-saturation radio frequency bands applied along the direction of the arterial blood ﬂow with a spin-echo sequence and a double inversion recovery (DIR) sequence [23]. When pre-saturation techniques are used — which are less effective than DIR with slowly ﬂowing blood — the complex ﬂow in the carotid bulb [24] often results in artifacts created by unsuppressed ﬂow. Artifacts may be misinterpreted as representing a signal from a diseased vessel wall, which leads to overestimations of the size of the atherosclerotic lesion (Fig. 3) [25]. On the other hand, DIR sequences tend to provide excellent ﬂow suppression as shown in T1 weighted images [26]. These images typically provide the most accurate quantitative measurements of disease burden and are thus used to identify necrotic cores in vivo [21]. Bright blood techniques refer to the gradient echo based imaging sequences that are typically used to acquire MR angiograms. These sequences, such as GRE and SPGR, enhance the signal of ﬂowing blood, and thus the lumen appears as hyperintense in relation to the adjacent vessel wall. Compared to SE sequences, bright blood techniques can produce images with shorter TE and TR times. The lack of a spin-echo in these sequences creates T2* sensitive tissue signals that appear to improve the visualization of the intimal calciﬁcations and the ﬁbrous cap, which is typically a dense structured layer of collagen [26,27]. Faster scanning also allows for the acquisition of high-resolution 3D data sets that will improve plaque characterization [28]. Based on the work of Hatsukami et al., we currently incorporate a 3D-TOF sequence to provide GRE weighted axial images to characterize carotid plaque. These images have been useful for evaluating the in vivo state of the ﬁbrous cap [26] and for detecting large intraplaque hemorrhages [21]. 3.3. Imaging Protocol of Multiple Contrast Weighting Based on extensive testing with normal volunteers and endarterectomy patients, a standardized, multicontrast imaging protocol was developed to assess the in vivo morphology of carotid plaques. This protocol uses black and bright blood techniques to acquire high spatial resolution axial images of the carotid arteries in each subject and provides an oblique view of the carotid artery, which lariﬁes the location of the carotid bifurcation process and the development of plaque distribution. It also uses the bifurcation area as an internal landmark to reproducibly prescribe slice locations for serial studies, and limits the total exam time to an average of 40 minutes. Currently, three axial imaging sequences (3D-TOF, T1W, PDW and T2W) are performed to generate four different contrast weightings at each slice location (Fig. 4). Applying a zero-ﬁlled Fourier Transform [29] to all imaging sequences, a voxel size of 0.25 × 0.25 × 2.0 mm3 was achieved for the black and bright blood sequences. Though the imaging protocol varies depending

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Figure 3. Comparison between the routine Spin Echo (SE) T1WI and Double IR T1WI. Notice the good luminal boundary delineation achieved from using the DIR technique. The long white arrow points to the bifurcation of left carotid artery. The * sign indicates the location of lumen. The ﬂow artifact is signiﬁcantly suppressed by DIR T1WI (short white arrow).

on patient body habitus, the typical set of parameters for the three axial sequences that were used are summarized in Table 1. Chemical selective fat saturation is also used to reduce, in all sequences, the subcutaneous tissue signal [30,31]. Cardiac Gating was found to reduce the ﬂow and motion artifacts and is incorporated in the long TE and TR sequences. 3.4. Histology as the Gold Standard Carotid endarterectomy of the atherosclerotic plaque creates a unique opportunity to verify by histological examination tissues visualized by in vivo MRI. Specimens are surgi-

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Figure 4. A set of images taken from a patient with severe carotid stenosis. The right hand ﬁgure is an oblique FSE view of the right carotid artery. PDWI and T2WI images are cross sectional images at the internal carotid artery. TOF image of the same location shows bright lumen (short white arrow). T1WI is a DIR FSE image of the same location. The lesion is eccentric (long white arrow) and caused a severe lumen stenosis.

Table 1. Image parameters. TOF

T1W∗

IW

T2W

TR (ms) TE (ms) Thickness (mm) Matrix Excitations ETL∗∗∗

23 3.8 2 256 × 256∗∗ 2

800 9 2 256 × 256∗∗ 2 8

Gated 20 2 256 × 256∗∗ 2 8

Gated 40 2 256 × 256∗∗ 2 8

Scan time (min) FOV (cm) Other Other

1.5-4 13 Fat suppression

6-7 13 Fat suppression

5-7 13 Fat suppression Spatial ﬂow

5-7 13 Fat suppression Spatial ﬂow

saturation

saturation

∗ T1W: Double inversion recovery with a TI of 650 ms was used. ∗∗ Zero-ﬁlled Fourier transform was used to create images of 512 × 512 matrix. ∗∗∗ ETL: echo traim length for FSE sequences.

cally excised using a technique that allows the specimen to remain intact. Fixation is accomplished with the standard 10% neutral buffered formalin. 10% formic acid is used to dissolve calciﬁcations that would interfere with sectioning. The specimen is processed, parafﬁn embedded and sectioned en-bloc. 10 μ sections are collected at every millimeter of the common carotid to the bulb and at 0.5 mm through the bulb and internal carotid.

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Figure 5. Carotid endarterectomy specimens are histologically processed en-block and serially sectioned producing 10 to 20 cross sections per centimeter. The varied composition of the carotid atherosclerotic plaque is well illustrated in this specimen.

The hematoxylin and eosin stain, special stains and selected antibodies are used to identify the morphological components of the plaque. Precision in matching the numerous histology sections to the MR images is crucial to the understanding of the capability and accuracy of MRI. Lumen size, shape, distance from the bifurcation and pieces of calciﬁcation are all used to attain the correct match. The histology sections are photographed and digitized. Plaque components are outlined and quantitative data is extracted that can be matched to similar data collected from outlined MR images. The status of the ﬁbrous cap, size of the necrotic core, amount and position of calciﬁcations and intraplaque hemorrhage all play an important role in the stability of the atherosclerotic plaque. These features are easily visualized with the light microscope making histology the gold standard used by MR imaging in the development of sequences and image analysis tools (Fig. 5). 4. MR Characterization of Human Carotid Plaque Morphology The vessel luminal diameter and area as measured by angiographic techniques is clinically used to describe plaque morphology. As MRI can visualize the luminal and the outer wall boundary as a series of plaque, size related parameters can offer a more comprehensive measure of plaque morphology in terms of plaque volume, thickness, and 3D distribution. MRI is therefore uniquely positioned to study in vivo the effects of compensatory enlargement of the artery.

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Figure 6. Cross-sectional image of carotid artery on in vivo (A) T1-weighted MRI. On Figure B, the area of low signal (short black arrow) represents a region of calciﬁcation, and the area of high signal (long black arrow) represents a region of recent hemorrhage. Outline of lumen (red) and the internal carotid artery outer wall boundary (green circle) are showed, and the areas can be measured. On Figure C, the Maximum Wall Thickness (long yellow line) and Minimum Wall Thickness (short yellow line) are showed.

4.1. Plaque Area/Volume Measurement Unlike lumen stenosis, plaque volume is considered a direct measure of the size and severity of atherosclerotic disease. Because MR is able to identify the adventitia boundary in transverse images of the vessel wall, MR imaging could provide a means to measure the total volume of the diseased vessel wall and to accurately determine the composition of plaque burden (Fig. 6) [32]. The high quality tissue contrast of the areas between the diseased portions of the vessel, lumen, and adventitia have made possible experiments that evaluate the quantitative capabilities of in vivo MR to evaluate the accuracy of such measurements and to corre-

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late vessel wall measurements to those used in conventional clinical settings (stenosis). One such study compared the images of cross-sectional areas of carotid plaques to those measured preoperatively with similar area measurements made of the excised endarterectomy specimens that were imaged ex vivo. A Bland-Altman analysis performed on the paired in vivo and ex vivo measurements of the same vessel segments demonstrated a strong correlation between the two values [32]. These results conﬁrmed the quantitative capabilities of MR for measuring total plaque volume and disease burden. 4.2. Accuracy of MRI Based Vessel Wall Morphology Measurement In a follow up study [33] by the same group, the accuracy and precision of the measurements of carotid plaque burden and lumen narrowing were determined. The study conﬁgurations was similar to the one used in [32]. In brief, a group of 37 patients who underwent CEA were scanned before surgery using a black blood MRI technique and an ex vivo MRI of the excised specimen was conducted immediately after surgery using the same technique. Three different plaque measurements were obtained and compared between paired in vivo and ex vivo MR images: maximum wall area (MWA), minimum lumen area (mLA), and wall volume (WV). MWA and WV are measures of plaque burden, while mLA is a measure of lumen narrowing. The in vivo and ex vivo measurements highly correlated to each other (the correlation coefﬁcients for in vivo/ex vivo WV, MWA, and mLA were 0.92, 0.91, 0.90 respectively). This study therefore shows that in vivo black blood MRI can be used to accurately estimate the morphology of the plaque. The minimum lumen area measurement (lumen narrowing) and the MWA or the WV were not highly correlated (the correlation coefﬁcients between mLA and MWA or WV < 0.3). This ﬁnding suggests that outer wall boundary is also actively involved in the atherosclerotic disease process and that MRI is a useful tool to study the relationship of these different aspects of morphological changes. 4.3. Reproducibility Since MRI is able to non-invasively identify both the luminal and outer wall boundaries, it can also be used to study the morphological changes of atherosclerosis. A ﬁrst step in such a direction is to test the inter-scan reproducibility of quantitative measures of plaque burden by MRI, which was assessed by two recent experiments [34,35]. By using the carotid bifurcation as an internal landmark, these studies showed that image slices of the same vessel segment can be reproducibly obtained at different exam times. One of these studies analyzed the precision of quantitative measurements for both the lumen and vessel wall areas of human carotid arteries [35]. Based on data obtained from independent MR scans conducted on 8 patients in the period of two weeks, the error of lumen area measurement was 6.2%, 9.2% and 9.7% for T1W, IW, and T2W images, respectively. The estimation of error is based on standard analyses of variance calculations of the mean and the standard deviation of the area measurements from pooled locations. Wall area measurement error was 10.8%, 10.9%, and 12% for the three contrast weightings. Errors in wall volume measurement ranged from 4–6% across different contrast methods. The vessel wall volume therefore can in fact be measured accurately. Among the factors that impact MRI area measurement, image quality is the most important.

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Table 2. Contrast of the main components of atherosclerotic plaque. MR Contrast Weighting T1W IW

Plaque Component

TOF

Recent Hemorrhage Lipid Rich Necrotic Core Intimal Calciﬁcations

++ +/− −−

++ ++ −−

Variable Variable −−

Variable Variable −−

+/− to −−

+/−

+

Variable

Fibrouis Tissue

T2W

∗ Tissue contrast is relative to the signals from sternocleidomastoid muscle.

4.4. Image Processing Techniques Needed for Plaque Morphology Evaluation Please refer to “MRI Based Quantitative Analysis System for Atherosclerotic Tissue Evaluation: CADCASDE”.

5. MR Characterization of Human Carotid Tissue Composition Histopathological studies indicate that the typical morphology of the vulnerable plaque consists of a large necrotic core that is separated from the lumen by an unstable ﬁbrous cap that can be thin, ulcerated, ﬁssured, or inﬁltrated by macrophages. The initial appeal of MR techniques for imaging atherosclerosis was its theoretical ability to image the lipids in the necrotic core. Early attempts to conﬁgure MRI to image atherosclerosis used T1W and chemical selective techniques to focus on the detection of lipid signals using T1W [36–39]. The predominant lipids of atherosclerotic lesions are cholesterol and cholesterol esters [40] rather than triclycerides. Since these lipids have short T2 components, initial attempts at plaque imaging produced limited success. It was the inclusion of either T1W and T2W sequences, or proton density weighted (T2W, T1W, or PDW) with ultra-short echo times (TE) that improved the speciﬁcity of MR imaging techniques and allowed for the differentiation of necrotic cores from ﬁbrous regions in ex vivo plaque specimens [16,41]. Follow up research added contrast weightings such as 3D-Time-of-Flight (TOF) [26] to magnetization transfer (MT) [42,43] and showed that diffusion sensitive [18,44,45] sequences facilitate atherosclerotic tissue characterization. These studies suggest that the major plaque components — lipid rich necrotic core, calcium deposits, ﬁbrous connective tissue, and intraplaque hemorrhage — can be identiﬁed by their signal characteristics in T1, T2, and proton density weighted images (Table 2) [17–19]. The six studies described below is informed by the research reviewed above and establish the accuracy of MRI in plaque tissue carotization. These studies used the same imaging protocol to produce four different contrast weightings — 3D-TOF, T1 weighted double-inversion recovery (DIR) SE sequence, and the SD and T2 weighted images from a shared-echo SE technique — at each imaged location of the carotid arteries of eighteen endarterectomy patients. All scans were conducted on a GE 1.5T Signa scanner using phased array coils. 5.1. In Vivo Accuracy of MR for Detecting Unstable Fibrous Caps Hatsukami et al. were the ﬁrst to use a 3D-TOF bright-blood imaging technique (multiple overlapping thin slab angiography or MOTSA [46]) to identify unstable ﬁbrous caps

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Figure 7. Example of plaque with ﬁbrous cap rupture on gross section, histology, and MRI. Figures A–C are three contiguous axial 3D TOF images of a diseased right CCA, D is a photo of the gross section at corresponding location, E is a low power photomicrography of a histology section with Masson’s trichrome stain (10×), and F is the same MR image as C. On the gross and histological sections, there is an area of cap rupture (arrow 1) across from a region where the ﬁbrous cap is thick (arrow 3). The cap rupture site corresponds to a region where the hypointense band is absent, and a hyperinternse region is seen adjacent to the lumen on MRI. The hyperintense regioin is a region in the plaque core on MRI that corresponds to regions or recent intraplaque hemorrhage on gross and histological cross sections (arrow 2). The ﬁbrous cap is made of a dense layer of collagen which appeared hypointense on the 3D TOF images.

in the atherosclerotic in vivo human carotid arteries [26]. The images were acquired using a spoiled gradient echo (SPGR) sequence that was set to a low ﬂip angle to better visualize both ﬂowing blood and soft tissue. The tissue contrast of these images were weighed more heavily on the T2* side than on the shorter TE side. After careful review of twenty-two preoperatively imaged endarterectomy patients, the authors found that the histological state of the ﬁbrous cap correlates well (Kappa value of 0.83) with the images of the hypointense juxtaluminal bands. Hypothesizing that the layered organization of the ﬁbrous cap was responsible for the relative signal loss in the MR images, they were able to prospectively characterize the in vivo state of the ﬁbrous cap as intact and thick, intact and thin, or ruptured (Fig. 7). These ﬁndings provided the basis of a research project that evaluated the ability of multi-contrast MR to characterize the in vivo state of the ﬁbrous cap [21]. In agreement with the work of Hatsukami et al., the results demonstrated a strong correlation between the MR image ﬁndings and the histological state of the ﬁbrous cap (Kappa value of 0.71). The authors were thus able to show that the availability of the three SE contrast weightings facilitated image interpretation in 17 of the 91 image locations The larger sample size made it possible to report test performance statistics (sensitivity of 81%, speciﬁcity of 90%) for noninvasive identiﬁcation of unstable ﬁbrous caps in vivo.

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5.2. In Vivo Accuracy of MR for Identifying Soft Necrotic Cores An important morphological characteristic of the vulnerable plaque is the presence of a large soft core that is comprised of a cellular lipid rich region or hemorrhage [47]. This study evaluated the in vivo accuracy of MR to detect the soft cores in human carotid plaques [21]. Based on the plaque tissue contrast features described in Table 2, lipid-rich, necrotic cores were identiﬁed by areas of hyper-intensive signal intensity in the T1W images that were of iso-intensity in the corresponding 3D-TOF images, and were of variable intensity on PDW and T2W. Recent intraplaque hemorrhages were similarly identiﬁed by their multi-contrast appearance (high signal on TOF, high on T1W, and of variable intensity on PDW and T2W). The results revealed that the MR ﬁndings agreed with either the histologic presence of a necrotic core or the recent intraplaque hemorrhage, with a sensitivity of 85%, speciﬁcity of 92%, and a calculated Kappa value of 0.69. The variation of signals from intraplaque hemorrhage of different ages was also observed but not yet documented. 5.3. Intraplaque Hemorrhage Aging and Its Corresponding MRI Signal Variations In clinical settings, knowledge of the age of intraplaque hemorrhage can give insight into the history and current condition of the biologically active plaque. Signal variations of brain hemorrhage is a well studied and reasonably understood problem [48]. This study used high-resolution MRI to establish reliable criteria for detecting hemorrhagic incidents in carotid atherosclerotic plaques and identify their evolutionary stage. Two readers — both unaware of histological data on the patients — reviewed the MR images and grouped hemorrhage into three categories (early, recent and old) using a modiﬁed cerebral hemorrhage criteria. Hemorrhage was histologically identiﬁed and staged in 145/189 (77%) of carotid artery plaque quadrants. MRI was able to detect intraplaque hemorrhage with high sensitivity (90%) but moderate speciﬁcity (74%). There was moderate to good agreement between MRI and histology classifying stages (Cohen’s κ = 0.7, 95% CI: 0.5–0.8 for reviewer 1 and 0.4, 95% CI: 0.2–0.6 for reviewer 2), and moderate agreement between the two MRI readers (κ = 0.4, 95% CI: 0.3–0.6). 5.4. MRI Based Atherosclerotic Lesion Type Deﬁnition Since in vivo MRI is able to identify the composition of the carotid atherosclerotic plaque, it follows that MRI may also be able to re-deﬁne lesion types. AHA deﬁnitions of lesion types aims to provide a uniﬁed method to stage lesions [49]. This study [50] used the AHA lesion type classiﬁcation system to determine the accuracy of in vivo high-resolution multi-contrast MR imaging of the human carotid atherosclerotic plaque. Using a 1.5T scanner, carotid endarterectomies were performed on 60 atherosclerotic patients (mean age 70, male 54). During the procedure, carotid plaques were removed intact and processed for histological examination. In order to decrease the dependency of MRI information on adjacent image locations, images were selected at 4mm distances. AHA lesion type classiﬁcation was slightly modiﬁed for MRI: Type I–II—near normal wall thickness, no calciﬁcation; Type III—slightly diffuse thickening or slightly eccentric thickening with no calciﬁcation; Type IV–V—plaque with a lipid or necrotic

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Figure 8. Example of type IV–V lesion in internal carotid artery (lipid-rich necrotic core was detected by histology). On multicontrast-weighted MR images, lipid-rich necrotic core (arrow) had iso signal intensity (SI) on both T1WI and TOF images, but iso-SI to slightly high SI on PDWI and T2WI images. Lumen is moderately stenosed. * indicates lumen. Original magniﬁcation ×10. (This Figure is originally published: Cai J.M., et al. Classiﬁcation of human carotid atherosclerotic lesions with in vivo multicontrast magnetic resonance imaging. Circulation. 2002; 106(11):1368–73).

core surrounded by ﬁbrous tissue with possible calciﬁcation; Type VI—complex plaque with possible surface defect, hemorrhage, or thrombus; Type VII—calciﬁed plaque; Type VIII—ﬁbrotic plaque with no or very small lipid core and possible small calciﬁcations. Both MR images and histological sections were independently reviewed and categorized and then compared. Sensitivity and speciﬁcity of different lesion types were calculated. Cohen’s Kappa (κ) and weighted Kappa value were computed to quantify the agreement between the MRI ﬁndings and histology. Overall, the classiﬁcation system obtained by MR imaging and the AHA classiﬁcations showed good agreement, with κ (95%CI) = 0.74 (0.67 to 0.82) and weighted κ = 0.79. Compared to the histological gold standard, the sensitivity and speciﬁcity of MR Imaging classiﬁcation were: type I–II, 67% and 100%; type III, 81%and 98%; type IV–V, 84% and 90%; type VI, 82% and 91%; type VII, 80% and 94%; type VIII, 56% and 100%. This study thus showed that in vivo high-resolution multi-contrast MRI is able to classify intermediate to advanced atherosclerotic lesions in the human carotid artery and to distinguish between advanced lesions from early and intermediate atherosclerotic plaque (Figs 8 and 9). 5.5. Overall Accuracy of MRI Quantitative Tissue Detection MRI plaque imaging techniques can be used for clinical plaque risk assessment and in clinical trials to evaluate the atherosclerotic lesion progression and regression. Currently, the endpoints used in clinical trials to study plaque progression and/or regression are based on wall thickness measurements. MRI could provide additional information in clinical trials regarding plaque composition. A baseline study to evaluate the ability of

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Figure 9. Example of type VI lesion just distal to carotid bifurcation (acute to subacute mixed hemorrhages were detected by histology). On multicontrast-weighted MR images, acute and subacute mixed hemorrhage had high SI on both TOF and T1WI images, iso-SI to slightly high SI on PDWI and T2WI images (arrow). * indicates lumen. Original magniﬁcation ×10. (This Figure is originally published: Cai JM, et al. Classiﬁcation of human carotid atherosclerotic lesions with in vivo multicontrast magnetic resonance imaging. Circulation. 2002; 106(11):1368–73).

MRI to not only identify the presence of carotid plaque constituents, but also to measure the quantity of composition material in vivo, compared to histology. In this study, twenty-two randomly selected patients with at least average image quality, scheduled for carotid endarterectomy were imaged with a 1.5T scanner after informed consent. Area measurements of lumen, wall area, lipid rich/necrotic core, hemorrhage, calcium, and loose matrix were compared between 144 in vivo MR images and matched histology sections. These measurements were performed using a customdesigned imaging analysis tool (QVAS). Sensitivity (S) and speciﬁcity (SP) is given for each tissue group at the 144 locations. The mean area of each component was calculated per artery and the Pearson correlation (R) coefﬁcient was used to correlate the MRI and histology measurements. The matched in vivo MR images and histology slices showed strong and highly signiﬁcant correlation for lumen area (R = 0.84), wall area (R = 0.80), size of the lipid rich/necrotic core (R = 0.76; S = 93%, SP = 62%), hemorrhage (R = 0.75; S = 90%, SP = 72%) and calciﬁcation (R = 0.78; S = 81%; SP = 89%). Agreement for loose matrix was moderate (R = 0.60; S = 62%; SP = 71%). In summary, MRI can be used to characterize and measure the components of the carotid atherosclerotic plaque. 5.6. Plaque Neovasculature and Inﬂammation Please refer to “Imaging of Plaque Cellular Activity with Contrast Enhanced MRI”.

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6. Plaque Features Visualized by MRI and Their Association with Patient’s Neurological Symptoms Histological studies have revealed some of the salient features of vulnerable plaques. These studies have pointed to the importance of the layer of collagen-rich ﬁbrous tissue that separates vessel lumen from the plaque bulk and the presence of necrotic, calciﬁc, and or hemorrhagic tissues near this layer. In a retrospective case-control study [51], the appearance of the ﬁbrous cap on MRI (intact thick, intact thin or ruptured) was shown to be highly associated with recent ischemic neurological symptoms. In this study, 53 consecutive patients (mean age 71, 49 male) scheduled for carotid endarterectomy were recruited after obtaining informed consent. 28 subjects had a recent history of TIA or stroke on the side appropriate to the index carotid lesion, and 25 were asymptomatic. Pre-operative carotid MRI was performed in a 1.5T GE Signa that generated T1-, PD-, T2-weighted, and 3D time-of-ﬂight images. Using previously reported MRI criteria, the ﬁbrous cap was categorized as intact-thick, intact-thin, or ruptured for each carotid plaque by blind review. There was a statistically signiﬁcant trend showing a higher percentage of symptomatic patients for ruptured caps (70%) compared to a thick cap (9%) (p = 0.001 Mann-Whitney test for cap status vs. symptoms). Compared to patients with thick ﬁbrous caps, patients with thin ﬁbrous caps were 10 times more likely to have had a recent TIA or stroke (95% CI = 1.0, 104), and those with ruptured ﬁbrous caps were 23 times more likely to have had recent ischemic neurological symptoms (95% CI = 3, 210). This study showed that MRI identiﬁcation of a ruptured ﬁbrous cap is highly associated with a recent history of TIA or stroke.

7. Practical Applications Advances in vascular biology have led to the introduction of new medical therapies that require clinical trials to evaluate their efﬁcacy. Noninvasive characterization of plaque morphology provides biologic endpoints for such therapeutic trials. The establishment of accurate biomarkers could signiﬁcantly reduce the sample sizes required to achieve statistical signiﬁcance, resulting in cost beneﬁts for future research on atherosclerotic disease. Indeed, these types of trials, which rely on an imaging based assessment of disease response, are ongoing [52]. MRI of atherosclerosis may provide useful information on how atherosclerosis responds to cholesterol lowering treatment and impacts the stability the lesions [53]. In the near future, these imaging techniques may be used to monitor disease progression in patients who are at risk of heart attack or stroke. Carotid MR can be used by vascular surgeons to improve surgical planning because the distribution and extent of disease involvement in both the CCA and ICA is better delineated by MR than by angiography. More importantly, these techniques are able to provide morphologic information that can accurately clarify the stability and conﬁgurations of a lesion regardless of the degree of stenosis. The morphology and composition of the plaque, as identiﬁed by MRI, may assist in selecting the optimal treatment – carotid endarterectomy versus angioplasty/stenting. For example, lesions with thin ﬁbrous caps, mural thrombus formation, or highly stenotic and irregular luminal surface morphology may be better treated with surgery than stenting.

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There are also some promising results that are based on other imaging modalities, such as ultrasonic carotid intima and media thickness measurements and their association to the incidences of myovardial infarction or stroke [54]. Future research on the association of carotid atherosclerosis morphology to myocardial infarction can result in new and important ﬁndings. With the development of new imaging and image processing techniques and the advent of new MR scanner hardware and software, current scan protocols will be converted into an efﬁcient and economically feasible screening tool. 8. Summary Over the past decade, there have been signiﬁcant advances in the ﬁeld of vascular biology. Plaque burden, morphology, and composition are now considered appropriate for noninvasive quantitation and clinicians no longer rely solely on the degree of luminal narrowing to assess the severity of atherosclerotic disease. As discussed earlier in this article, MR imaging holds much potential for developing into a modality that can be used to quantitatively characterize plaque morphology in vivo. Preliminary studies have demonstrated the ability of multi-contrast MR techniques to prospectively identify the major components of human carotid plaques and to characterize the morphologic features associated with the vulnerable lesion (unstable ﬁbrous caps, necrotic cores, intimal calciﬁcation, and intraplaque hemorrhages). Although the sample sizes of these studies are limited, continued patient recruitment and the growing number of similar or related studies performed at different institutions will hopefully establish the effectiveness of these techniques. The research results and associated technical developments described in this chapter open an exciting new era in vascular imaging and brings medical science one step closer to (1) noninvasive and prospective identiﬁcation of vulnerable plaque, which would allow for more timely clinical intervention; (2) being able to quantitatively monitor the changes in disease burden and biologic markers of instability, which would enhance our understanding of the pathogenesis of the disease and the efﬁcacy of new therapies. The high spatial resolution images presented in this article can be generated with 1.5T clinical scanners and phased-array surface coils. Currently, pulse sequences consisting of both black and bright blood techniques are recommended to characterize carotid plaque morphology in vivo. Ongoing ex vivo experiments, however, may demonstrate the utility of additional sequences like the 3D-FISP or magnetization transfer. Most importantly, the techniques described in this paper can readily be transferred, with minimal alterations, from major manufacturers to whole body scanners. Acknowledgements The authors would like to thank Andrew An Ho for his copyediting work on this manuscript. References [1] Elkins, J.S. and S.C. Johnston. Thirty-year projections for deaths from ischemic stroke in the United States. Stroke 2003; 34(9): 2109–12.

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[28] Coombs BD, Ursell PC, Reilly LM, Rarp JH, Saloner D. Carotid Bifurcation plaque structure: high resolution MRI with histologic correlation. Abs., ISMRM Sixth Annual Meeting, Sydney, 1998. [29] Du YP, Parker DL, Davis WL, Cao G. Reduction of partial-volume artifacts with zero-ﬁlled interpolation in three-dimensional MR angiography. J Magn Reson Imaging 1994; 4(5): 733–741. [30] Merickel MB, Carman CS, Brookeman JR, Mugler JP, Brown MF, Ayers CR. Identiﬁcation and 3-D quantiﬁcation of atherosclerosis using magnetic resonance imaging. Comput Biol Med 1988; 18(2): 89–102. [31] Yuan C, Petty C, O’Brien KD, Hatsukami TS, Eary JF, Brown BG. In vitro and in situ magnetic resonance imaging signal features of atherosclerotic plaque-associated lipids. Arterioscler Thromb Vasc Biol 1997; 17(8):1496–1503. [32] Yuan C, Beach KW, Smith LH Jr, Hatsukami TS. Measurement of atherosclerotic carotid plaque size in vivo using high resolution magnetic resonance imaging. Circulation 1998; 98(24):2666–2671. [33] Luo Y, Polissar N, Hatsukami TS, Yuan C. Accuracy and uniqueness of three in-vivo measurements of atherosclerotic carotid plaque morphology with black blood MRI. MRM, 50:75–82, 2003. [34] Yuan C, Schmiedl UP, Maravilla KR, et al. MR imaging of human carotid plaques: assessment of reproducibility and reader variability. Proceedings of the 82th RSNA 1996; 134. [35] Kang XJ, Polissar NL, Han C, Lin E, Yuan C. Analysis of the measurement precision of arterial lumen and wall areas using high resolution magnetic resonance imaging. MRM 2000; 44:968–972. [36] Mohiaddin RH and Longmore DB. MRI studies of atherosclerotic vascular disease: structural evaluation and physiological measurements. Br Med Bull 1989; 45(4):968–990. [37] Kaufman L, Crooks LE, Sheldon PE, Rowan W, Miller T. Evaluation of NMR imaging for detection and quantiﬁcation of obstructions in vessels. Invest Radiol 1982; 17(6):554–560. [38] Herfkens RJ, Higgins CB, Hricak, H, et al. Nuclear magnetic resonance imaging of atherosclerotic disease. Radiology 1983; 148(1):161–166. [39] Vinitski S, Consigny PM, Shapiro MJ, Janes N, Smullens SN, Rifkin MD. Magnetic resonance chemical shift imaging and spectroscopy of atherosclerotic plaque. Invest Radiol 1991; 26(8):703–714. [40] Small, DM and Shipley GG. Physical-chemical basis of lipid deposition in atherosclerosis. Science 1974; 185(147):222–229. [41] Gold GE, Pauly JM, Glover GH, Moretto JC, Macovski A, Herfkens RJ. Characterization of atherosclerosis with a 1.5-T imaging system. J Magn Reson Imaging 1993; 3(2):399–407. [42] Pachot-Clouard M, Vaufrey F, Darrasse L, Toussaint JF. Magnetization transfer characteristics in atherosclerotic plaque components assessed by adapted binomial preparation pulses MAGMA 1998; 7(1):9–15. [43] Kerwin W, Ferguson MS, Small R, Hatsukami TS, Yuan C. Magnetization transfer as a contrast enhancing mechanism in magnetic resonance images of human atherosclerotic plaques. Atherosclerosis 2000; 151(1):25. [44] Toussaint JF, Southern JF, Fuster V, Kantor HL. Water diffusion properties of human atherosclerosis and thrombosis measured by pulse ﬁeld gradient nuclear magnetic resonance. Arterioscler Thromb Vasc Biol 1997; 17(3):542–546. [45] Sharon EC, Robert RH, J. Ross M, et al. Quantitative assessment of carotid plaque composition using multicontrast MRI and registered histology. MRM 2003; 50(6): 1199–1208. [46] Parker, DL, Yuan C, Blatter DD. MR angiography by multiple thin slab 3D acquisition. Magn Reson Med 1991; 17(2):434–451. [47] Bassiouny HS, Sakaguchi Y, Mikucki SA, et al. Juxtalumenal location of plaque necrosis and neoformation in symptomatic carotid stenosis. J Vasc Surg 1997; 26(4):585–594. [48] Gomori JM, Grossman RI, Hackney DB, et al. Variable appearances of subacute intracranial hematomas on high-ﬁeld spin-echo MR. AJR Am J Roentgenol. 1988; 150; 171–178. [49] Stary HC, Chandler AB, Dinsmore RE, et al. A deﬁnition of advanced types of atherosclerotic lesions and a histological classiﬁcation of atherosclerosis. A report from the Committee on Vascular Lesions of the Council on Arteriosclerosis. [50] Cai J, Hatsukami T, Ferguson M, et al. Classiﬁcation of human carotid atherosclerotic lesions using in vivo multi-contrast MR imaging. Circulation 2002; 106: 1368–1373. [51] Yuan C, Zhang SX, Polissar NL, Echelard DE, Ortiz G, Davis, JW, Ellington E, Ferguson MS, Hatsukami TS. Identiﬁcation of ﬁbrous cap rupture with magnetic resonance imaging is highly associated with recent TIA or stroke. Circulation, 105:181–185; 2002. [52] Corti R, Badimon JJ, Worthley SG, Helft G, Fayad ZA, Fuster V. Statin therapy reduces burden in hu-

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Plaque Imaging: Pixel to Molecular Level J.S. Suri et al. (Eds.) IOS Press, 2005 © 2005 The authors. All rights reserved.

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Intravascular Ultrasound Elastography: A Clinician’s Tool for Assessing Vulnerability and Material Composition of Plaques Radj A. BALDEWSING a , Johannes A. SCHAAR a,b , Chris L. DE KORTE a,b,c , Frits MASTIK a , Patrick W. SERRUYS a and Antonius F.W. VAN DER STEEN a,b a Thoraxcenter, Erasmus MC, Rotterdam, The Netherlands b Interuniversity Cardiology Ins. of the Netherlands (ICIN), Utrecht, The Netherlands c Clinical Physics Laboratory, Univ. Children’s Hospital, Nijmegen, The Netherlands Abstract. The material composition and morphology of the atherosclerotic plaque components are considered to be more important determinants of acute coronary ischemic syndromes than the degree of stenosis. When a vulnerable plaque ruptures it causes an acute thrombotic reaction. Rupture prone plaques contain a large lipid pool covered by a thin ﬁbrous cap. The stress in these caps increases with decreasing thickness. Additionally, the cap may be weakened by macrophage inﬁltration. IntraVascular UltraSound (IVUS) elastography might be an ideal technique to assess the presence of lipid pools and to identify high stress regions. Elastography is a technique that assesses the local elasticity (strain and modulus) of tissue. It is based on the principle that the deformation of tissue by a mechanical excitation is a function of its material properties. The deformation of the tissue is determined using ultrasound. For intravascular purposes, the intraluminal pressure is used as the excitation force. The radial strain in the tissue is obtained by cross-correlation techniques on the radio frequency signals. The strain is color-coded and plotted as a complimentary image to the IVUS echogram. IVUS elastography, and IVUS palpography (which uses the same principle but is faster and more robust), have been extensively validated using simulations and by performing experiments in vitro and in vivo with diseased arteries from animals and humans. Strain was shown to be signiﬁcantly different in various plaque types (absent, fatty, ﬁbrous or calciﬁed). A high strain region with adjacent low strain at the lumen vessel-wall boundary has 88% sensitivity and 89% speciﬁcity for detecting vulnerable plaques. High strain regions at the lumen plaque-surface have 92% sensitivity and 92% speciﬁcity for identifying macrophages. Furthermore, the incidence of vulnerable-plaque-speciﬁc strain patterns in humans has been related to clinical presentation (stable angina, unstable angina or acute myocardial infarction) and the level of C-reactive protein. In conclusion, the results obtained with IVUS (strain and modulus) elastography/palpography, show the potential of the technique to become a unique tool for clinicians to assess the vulnerability and material composition of plaques. Keywords. Tissue characterisation, intravascular, ultrasound, elastography, vulnerable, plaque, stress, strain, modulus

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1. Introduction IntraVascular UltraSound (IVUS) is the only commercially available clinical technique providing real-time cross-sectional images of the coronary artery in patients [1]. IVUS provides information on the severity of the stenosis and the remaining free luminal area. Furthermore, calciﬁed and non-calciﬁed plaque components can be identiﬁed. Although many investigators studied the value of IVUS to identify the plaque composition, identiﬁcation of ﬁbrous and fatty plaque components remains limited [2,3]. IVUS RadioFrequency (RF)-based tissue identiﬁcation strategies appear to have better performance [3,4]. However, none of them is yet capable of providing sufﬁcient spatial and parametric resolution to identify a lipid pool covered by a thin ﬁbrous cap. Identiﬁcation of different plaque components is of crucial importance to detect the high-risk, vulnerable plaque since these are characterised by an eccentric plaque with a large lipid pool shielded from the lumen by a thin ﬁbrous cap [5,6]. Inﬂammation of the cap by macrophages further increases the vulnerability of these plaques [7]. The mechanical properties of ﬁbrous and fatty plaque components are different [8–10]. Furthermore, ﬁbrous caps with inﬂammation by macrophages are weaker than caps without inﬂammation [11]. The stress that is applied on an artery by the pulsating blood pressure must balance the circumferentially directed load integrated over the whole arterial wall. To maintain the connection between mechanically different tissue structures (like soft lipid pools and stiff ﬁbrous caps) during arterial deformation, relatively soft regions will therefore carry only a fraction of the total circumferential load and the surrounding stiffer material a greater portion [12,13]. This mechanism causes circumferential stress concentrations in and around the stiff cap, which will rupture if the cap is unable to withstand this stress. This increased circumferential stress will result in an increased radial deformation (strain) of the tissue due to the incompressibility of the material. Therefore, methods that are capable of measuring the radial strain provide information about plaques that may inﬂuence clinical decision-making. In 1991, Ophir et al. [14] proposed a method to measure the elasticity (strain and modulus) of biological tissues using ultrasound. The tissue was deformed by externally applying a stress on it. Different strain values were found in tissues with different material properties. Implementing this method for intravascular purposes has potential to identify the vulnerable plaque by (i) identiﬁcation of different plaque components and (ii) detection of high strain regions. This chapter discusses, the technique behind, the method for and the validation of IVUS elastography, which is differentiated into IVUS strain elastography/palpography when the strain is imaged and IVUS modulus elastography when the modulus is imaged.

2. Ultrasound Elastography 2.1. The Movement Begins In 1991, Ophir and colleagues [14,15] developed an imaging technique called elastography, which is based on (quasi-) static deformation of a linear elastic, isotropic material. The tissue under inspection is deformed by applying stress (i.e., force normalized by area) on a part of its boundary. The resulting distribution of strain (i.e., length of a small block of tissue after deformation, divided by its length before deformation) depends upon

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(i) the distribution of the tissue’s material properties (Young’s modulus and Poisson’s ratio) and (ii) the displacement or stress conditions on the remaining tissue boundaries. The Young’s modulus E (kPa) is a material property, which can be interpreted as the ratio between the stress S (kPa) (tensile or compressive) enforced upon a small block of tissue and its resulting strain (elongation or compression). The Poisson’s ratio is also a material property and it quantiﬁes a material’s local volumetric compressibility. The resulting strain is determined, directly or indirectly using displacement, with ultrasound using two pairs of ultrasound signals, one signal obtained before and the other after deformation [16]. The method was developed for detection and characterization of tumors in breast. Nowadays, this principle is applied on many other biological objects [17] including prostate, kidney, liver, myocardium and skin. Recently, some preliminary (simulation) results have been reported on the application of this principle to non-invasively assess elastic properties of superﬁcial peripheral arteries like carotid, brachial, radial and femoral [18–21]. Although Ophir et al. never explored the quasi-static approach for intravascular purposes this approach seems to be the most fruitful concept. In this application, beside knowledge of the material properties of the different plaque components, the strain in itself may be an excellent diagnostic parameter. Furthermore, in intravascular applications, the arterial deformation is naturally present and is caused by the pulsatile blood pressure. Eventually, user-controlled deformation is possible by using a compliant intravascular balloon [22]. 2.2. IVUS Strain Elastography/Palpography The principle of IVUS strain elastography is illustrated in Fig. 1. An ultrasound image of a vessel-phantom with a stiff vessel wall and a soft eccentric plaque is acquired at a low pressure. In this case, there is no difference in echogenicity between the vessel wall and the plaque resulting in a homogeneous IVUS echogram. A second acquisition at a higher intraluminal pressure (pressure differential is approximately 1 mm Hg) is obtained. The radial strain elastogram is plotted as a complimentary image to the IVUS echogram. The elastogram reveals the presence of an eccentric region with increased strain values thus identifying the soft eccentric plaque. The differences in strategies to perform IVUS strain elastography (i.e. assess the local deformation of the tissue) are due to (i) the way of detecting the strain and (ii) the type of source that deforms the vascular tissue. The principle of IVUS strain palpography is similar to the principle of IVUS strain elastography. There are two minor differences that make palpography faster and more robust and, therefore, more suited for real-time in vivo applications. Firstly, palpography restricts its region of interest to the innermost layer of the arterial wall (ﬁrst 500 micrometer), making it faster. Secondly, it uses a slightly larger amount of ultrasound signal making it more robust but at the expense of spatial resolution [23–25]. 2.3. Implementation of the Technique Typically in IVUS strain elastography/palpography, intraluminal pressure differences in the order of 1–5 mm Hg are used. The strain, induced by this pressure differential in vascular tissue is in the order of 2%. This means that a small block of tissue with an initial length of 100 micrometer will be deformed to 98 micrometer. To differentiate between strain levels, sub-micron estimation of the tissue displacement is required.

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Figure 1. Principle of intravascular ultrasound (IVUS) strain elastography measurement procedure. An intravascular ultrasound catheter is inserted into an object, in this case a vessel-mimicking phantom with a soft plaque (A). Next, at two different intraluminal pressures (B) an IVUS echogram is acquired (C and D). In each echogram, the grey circle indicates the catheter-tip of 1.1 mm diameter. Finally, the radial strain in the tissue is determined using cross-correlation processing on the acquired radio-frequency data. This information is plotted (strain elastogram) as an additional image to the IVUS echogram (E). In this example, the eccentric soft plaque of a vessel-mimicking phantom is clearly visible between 4 and 8 o’clock in the strain elastogram whereas this plaque cannot be identiﬁed from the IVUS echograms.

2.3.1. Envelope Based Two groups worked on intravascular elastography using the envelope of the ultrasound signal. Talhami et al. [26] introduced a technique to assess the strain that is based on the Fourier scaling property of the signals and uses the chirp Z-transform (i.e. a mathematical transformation of the ultrasound signal into another signal to make it suitable for some desired mathematical manipulations). The scaling property is a direct estimator of the strain in the tissue. The chirp-Z transform was determined from the envelope signal to overcome decorrelation of the Radio-Frequency (RF)-signal due to deformation of the tissue. The result was displayed as a color-coded ring superimposed on the IVUS echogram of the vessel. Initial results on vascular tissue in vitro and in vivo were described. Although the technique seems relatively easy to implement, it was not further developed and validated. Ryan and Foster [27] developed a technique to estimate displacement by using speckle tracking (i.e. following the movement of a signal pattern in series of images) in video signals. The strain can be determined from these displacement estimates. The technique was tested using vessel-mimicking phantoms. It was shown that in a phantom that was partly made of soft and partly made of stiff material the displacement in soft material was larger than the displacement in stiff material. An advantage of envelope-based methods is the fact that the correlation function is smoother than the RF-based correlation function. This prevents ‘peak hopping’, meaning that the correlation function is maximized around the wrong peak. This makes the method less noise sensitive. Furthermore, the video signal is commonly available from any commercial echo system. A disadvantage is the limited resolution and the low sensitivity of the method for low strain values. Since small tissue strains are expected for intravascular applications, and the arterial wall is relatively thin, it is expected that the use of the high

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frequency RF-signal will greatly improve the resolution. Based on work of Varghese and Ophir [28], a smaller variance of the strain estimate is expected using RF data instead of envelope data. 2.3.2. Radio Frequency Based Shapo et al. [29,30] developed a technique based on cross-correlation of A-lines. The group proposes a large deformation to maximize the signal-to-noise ratio of the displacement and strain estimation. Since the deformation that is needed is larger than the deformation that occurs in arteries in vivo, the artery is deformed using a non-compliant balloon that is inﬂated up to 8 atmospheres. Large displacement will decorrelate the ultrasound signals to such an extent that correlation detection is unreliable. For this reason, the cross-correlation is calculated in several intermediate steps of intraluminal pressure. For detection, they use a phase-sensitive speckle tracking technique. The technique was demonstrated in simulations and tissue mimicking phantoms. This group presented data on a compliant balloon containing an intravascular catheter [31,32]. The compliant balloon is inﬂated to 2 atmospheres to obtain strain values up to 40%. This method was tested in phantoms and in vitro. The phantom (with one half soft and one half stiff material) revealed strains from 20–40% in the soft part and strains lower than 20% in the stiff part. These results were corroborated by ﬁnite element analysis. In vitro, low strain values (7%) were found for ﬁbrous tissue in the human femoral artery and high strain values (35%) were found in thrombus in a rabbit aorta. De Korte et al. [33,34] incorporated ‘correlation-based’ elastography [14] for intravascular purposes. The vascular tissue is strained by different levels of the intraluminal pressure. The local displacement of the tissue is determined using cross-correlation analysis of the gated RF-signals (Fig. 2). A cross-correlation function between two signals will have its maximum if the signals are not shifted with respect to each other. If a shift between the signals is present, the peak of the cross-correlation function is found at the position representing the displacement of the tissue. For each angle, the displacement of the tissue at the lumen vesselwall boundary is determined. Next, the displacement of the tissue D micrometer from the vessel-wall boundary is determined. The strain of the tissue can be calculated by dividing the differential displacement (displacement of tissue at boundary – displacement of tissue in wall) by the distance between these two locations (D micrometer). The strain for each angle is color-coded and plotted as a ring (strain palpogram) on the IVUS echogram at the lumen vessel-wall boundary [23,24,35]. If the strain is determined for multiple regions per angle, a two-dimensional image of the strain can be constructed. This additional image to the IVUS echogram is called an IVUS strain elastogram. For palpography, the value for D is approximately 400 micrometers and for elastography approximately 200 micrometers. The method was validated using vessel phantoms with the morphology of an artery with an eccentric soft or stiff plaque [36]. The plaque could be clearly identiﬁed from the vessel-wall using the strain elastogram, independently of the echogenicity contrast between vessel-wall and plaque. The technique was validated in vitro and tested in atherosclerotic animal models and during interventions in patients (as discussed later). This cross-correlation based technique is especially suited for strain values smaller than 2.5% (for a signal segment in the order of 10 wavelenghts). These strain values are present during in vivo acquisitions when only a part of the heart cycle is used to strain the tissue [37]. The maximum strain that will be present between the systolic and diastolic pressure is much higher. In that case, another approach that takes

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Figure 2. Principle of time delay estimation using the peak of the cross-correlation coefﬁcient function. In the upper part, two segments (A and B) of the pre-deformation (solid line) and post-deformation (dotted, and preshifted for better visual comparison) radio-frequency (RF) signals are shown. Both segments start at a different position in the tissue. For each segment, the cross-correlation coefﬁcient function between the two signals is computed (C and D). The functions show a decreasing position of the peak with increasing echodepth. The difference in peak position represents the differential displacement.

into account the change in shape of the signals can be applied. This ‘local scaling factor estimation’ technique [38] has been recently described for intravascular purposes [39] and has proven to be more robust to large deformations. The signal after compression is processed as a delayed and scaled replica of the signal before deformation. An adaptive strain estimation method based on the computation of local scaling factors has been applied to compute strain elastograms of cryogel vessel-mimicking phantoms and of a freshly excised human carotid artery using a 30-MHz mechanical rotating single element ultrasound scanner (ClearView, CVIS, Boston Scientiﬁc Corp.) [40,41]. Recently, more

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Figure 3. IVUS strain elastography in vitro of a human femoral artery and corresponding histology. (A) IVUS echogram. (B) IVUS strain elastogram superimposed on the IVUS echogram. Histology: (C) Collagen, (D) Smooth muscle cells and (E) Macrophages. The elastogram reveals that the plaque contains a region of high strain between 1 and 4 o’clock. Histology shows that this region is heavily inﬁltrated by macrophages and lacks smooth muscle cells and collagen. Furthermore, the remaining plaque region between 4 and 1 o’clock shows low strain and, at this region, histology reveals that the plaque contains much smooth muscle cells and collagen but no macrophages.

groups have started to perform IVUS strain elastography using a rotating single element scanner [42–44].

3. IVUS Strain Elastography/Palpography: Results 3.1. In Vitro Validation on Human Arteries De Korte et al. [45] performed a validation study on excised human coronary (n = 4) and femoral (n = 9) arteries (Fig. 3) to investigate the capability of IVUS strain elastography to characterize different plaque components. Data were acquired at room temperature at intraluminal pressures of 80 and 100 mm Hg. Coronary arteries were measured using a solid state 20-MHz array catheter (EndoSonics, Rancho Cordova, CA, USA). Femoral arteries were investigated using a single element 30-MHz catheter (DuMed/ EndoSonics, Rijswijk, The Netherlands) that was connected to a modiﬁed motor unit (containing the pulser and receiver and a stepper-motor to rotate the catheter). The RF-data was stored and processed off-line. The visualized segments were stained on the presence of collagen, smooth muscle cells and macrophages. Matching of elastographic data and histology was performed using the IVUS echogram. The cross-sections were segmented in regions (n = 125) based on the strain value on the elastogram. The dominant plaque types in these regions (ﬁbrous, ﬁbro-fatty or fatty) were obtained from histology and correlated with the average strain and echo-intensity. Mean strain values of 0.27%, 0.45% and

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0.60% were found for ﬁbrous, ﬁbro/fatty and fatty plaque components. The strain for the three plaque types as determined by histology differed signiﬁcantly (p = 0.0002). This difference was independent on the type of artery (coronary or femoral) and was mainly evident between ﬁbrous and fatty tissue (p = 0.0004). The plaque types did not reveal echo-intensity differences in the IVUS echogram (p = 0.882). Conversion of the strain into an Incremental Stress-Strain Modulus (denoted as Eissm) was performed using the formula Eissm = (dP/2)/(meanstrain); where dP is the intraluminal pressure differential and ‘meanstrain’ is the mean of the strain around the circumference of the ﬁrst layer of vessel wall. Because the pressure differential and thus the stress are only known at the boundary between lumen and vessel-wall and due to non-linearity of this parameter this gives only a ﬁrst order approximation of the modulus. The resulting Eissm was 493 kPa, 296 kPa and 222 kPa for ﬁbrous, ﬁbro/fatty and fatty plaques. Although these values are higher than values measured by Lee et al. [10], the ratio between ﬁbrous and fatty material is similar. Since ﬁbrous and fatty tissue resulted in different strain values and high strain values often co-localised with increased concentrations of macrophages, these results reveal the potential of identiﬁcation of the vulnerable plaque. Recently, Schaar et al. [46] performed a study on human coronary arteries to quantify the predictive value of IVUS strain elastography to detect the vulnerable high-risk plaque. Postmortem coronary arteries (n = 24) were investigated with IVUS strain elastography using a 20-MHz phased array catheter (JOMED, Rancho Cordova, CA) connected to an echo apparatus (JOMED, Rancho Cordova, CA). Subsequently they were processed for histology. In histology, a vulnerable plaque was deﬁned as a plaque consisting of a thin cap (<250 micrometer) with moderate to heavy macrophage inﬁltration and at least 40% of atheroma. In a radial strain elastogram, a vulnerable plaque was deﬁned as a plaque with a high strain region at the surface with adjacent low strain regions (Fig. 4). In 24 diseased coronary arteries, they studied 54 cross-sections. In histology 26 vulnerable plaques and 28 non-vulnerable plaques were found. Receiver Operator Characteristic (ROC) analysis revealed a maximum predictive power for a strain value threshold of 1.26%. The area under the ROC-curve was 0.85. The sensitivity was 88% and the speciﬁcity 89% to detect vulnerable plaques. Linear regression showed high correlation between the strain in caps and the amount of macrophages (p < 0.006) and an inverse relation between the amount of smooth muscle cells and strain (p < 0.0001). Plaques, which were declared vulnerable in IVUS strain elastography, had a thinner cap than nonvulnerable plaques (p < 0.0001). They concluded that IVUS strain elastography has a high sensitivity and speciﬁcity to detect human vulnerable plaques in vitro and that strain in caps had a high correlation with vulnerable plaque features. 3.2. In Vivo Animal Studies IVUS strain elastography was also validated in vivo using an atherosclerotic Yucatan mini-pig to investigate the potential to identify different plaque components in vivo [47,48]. External iliac and femoral arteries were made atherosclerotic by endothelial Fogarty denudation and subsequent atherosclerotic diet for the duration of 7 months. Balloon dilation was performed in the femoral arteries and the diet was discontinued. Before termination, 6 weeks after balloon dilation and discontinuation of the diet, data were acquired in the external iliac and femoral artery in 6 Yucatan pigs. In total, 20 cross-sections were investigated with a 20-MHz phased array catheter (JOMED, Rancho

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Figure 4. IVUS strain elastography in vitro of a human coronary artery and corresponding histology. (A) IVUS echogram. (B) IVUS strain elastogram superimposed on the IVUS echogram. Histology: (C) Collagen, (D) Smooth muscle cells and (E) Macrophages. Histology shows that the plaque consists of a homogeneous soft lipid pool covered by a stiff ﬁbrous cap with much collagen and smooth muscle cells. Increased strain is found at both shoulders of the lipid pool. In the IVUS echogram, the grey circle deﬁnes the catheter-tip of 1.1 mm diameter and the black circle removes part of the catheter ringdown diameter 2 mm.

Cordova, CA). The tissue was strained by the pulsatile blood pressure. Two frames acquired at end diastole with a pressure differential of approximately 4 mmHg were taken to determine the elastograms. After the ultrasound experiments and before dissection, X-ray was used to identify the arterial segments that had been investigated by ultrasound. The specimens were frozen in liquid nitrogen. The cross-sections (7 micrometer) were stained for collagen (picro Sirius red and polarized light), fat (oil red O) and macrophages (alcalic phosphatase). Plaques were classiﬁed as absent, as early fatty lesion, early ﬁbrous lesion or as advanced ﬁbrous plaque. The mean strain in these plaques and normal cross-sections was determined. Strains were similar in the plaque free arterial wall and the early and advanced ﬁbrous plaques (Table 1). Univariate Analysis of Variance revealed signiﬁcantly higher strain values in cross-sections with early fatty lesions than in ﬁbrous plaques (p = 0.02). Although a higher strain value was found in plaques with macrophages than in plaques without macrophages, this difference was not signiﬁcant after correction for fatty components. The presence of a high strain spot had a high predictive value to identify the presence of macrophages (a sensitivity and speciﬁcity of 92%). In case there was no high strain spot present, no fatty plaque was found (Table 2). 3.3. In Vivo Patient Studies Preliminary acquisitions were performed using IVUS strain elastography in patients during percutaneous transluminal coronary angioplasty (PTCA) procedures [37,49]. Data were acquired in patients (n = 12) with an EndoSonics InVision echo apparatus equipped with an RF-output. For obtaining the RF-data, the machine was working in ChromaFlo mode resulting in images of 64 angles with unfocussed ultrasound data. The systemic

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Strain(%) Mean Range

Absent (n = 6) Early fatty lesions (n = 9)

0.21 0.46

0.13–0.33 0.28–0.80

Early ﬁbrous lesions (n = 3) Advance ﬁbrous plaque (n = 6)

0.24 0.22

0.21–0.27 0.17–0.28

Table 2. Relation between a high strain spot and fat or macrophages. High strain spot

Fat Present Absent

Macrophages Present Absent

Present

9

3

11

1

Absent

0

12

1

11

Figure 5. IVUS strain elastography of a human coronary artery in vivo. (A) IVUS echogram. (B) IVUS strain elastogram superimposed on the IVUS echogram. The echogram shows the presence of an eccentric plaque between 11 and 5 o’clock. The elastogram shows high strain values at the shoulders of this eccentric plaque.

pressure was used to strain the tissue. This strain was determined using cross-correlation analysis of sequential frames. A likelihood function was determined to obtain the frames with minimal motion of the catheter in the lumen, since motion of the catheter prevents reliable strain estimation. Minimal motion was observed near end-diastole. Reproducible strain estimates were obtained within one pressure cycle and over several pressure cycles. Validation of the results was limited to the information provided by the echogram. Strain in calciﬁed material (0.20%) was lower (p < 0.001) than in non-calciﬁed tissue (0.51%). Also, high-resolution elastograms were acquired using an EndoSonics InVision echo apparatus [50]. The beam-formed image mode (512 angles) ultrasound data (20-MHz center frequency) was acquired with a PC based acquisition system. Frames acquired at enddiastole with a pressure difference of approximately 5 mmHg were taken to determine the elastograms. Elastograms of soft, calciﬁed and stented plaques were determined. The elastogram of a soft plaque, as identiﬁed from the deformation during the pressure cycle, reveals strain values up to 2% with increased strain regions at the shoulders of the plaque (Fig. 5). Calciﬁed material, as identiﬁed from the echogram, shows strain values

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Figure 6. 3D IVUS strain palpography of a patient in vivo. (A) Angiogram of the right coronary artery. (B) 2D IVUS strain palpogram superimposed on the IVUS echogram, which was taken at the location indicated by purple arrow in A. The echogram shows an eccentric plaque and the high strain regions with adjacent low strains at the shoulders of this plaque suggest that it is vulnerable. (C) A map of multiple 2D IVUS strain palpograms stacked after each other. The green dotted line corresponds to the palpogram shown in B. This map provides an overview of the deformability of the inner layer of the arterial wall.

of 0–0.2%. The elastogram of stented plaques revealed very low strain values, except for two regions: these are between the stent struts and at the shoulders of the plaque. Recently, Schaar et al. [51] used 3D IVUS strain palpography in patients undergoing percutaneous intervention to assess the incidence of a speciﬁc strain pattern, which has shown in vitro to have a high sensitivity and speciﬁcity for detecting the thin-cap atheroma. Furthermore they explored the relation of such patterns to clinical presentation and to C-reactive protein levels. 3D strain palpograms were derived from continuous IVUS pullbacks through arteries (Fig. 6). Patients (n = 55) were classiﬁed by clinical presentation as stable angina, unstable angina, or acute Myocardial Infarction (MI). In every patient one coronary artery was scanned (culprit vessel in stable and unstable angina, non-culprit vessel in acute MI) and the number of plaques with a vulnerable plaque speciﬁc strain pattern were assessed. Stable angina patients had signiﬁcantly less deformable plaques per vessel (0.6 +/− 0.6) than unstable angina (p = 0.0019) patients (1.6 +/− 0.7) or acute MI (p < 0.0001) patients (2.0 +/− 0.7). Levels of C-reactive protein were positively correlated with the number of mechanically deformable plaques (R2 = 0.65, p < 0.0001). The main conclusion was that 3D IVUS palpography detects vulnerable plaque speciﬁc strain patterns in human coronary arteries that correlated both with clinical presentation and levels of C-reactive protein. Further studies should be performed to assess the potential role of the technique to identify patients at risk of future clinical events.

4. Ultrasound Modulus Elastography 4.1. Motivation The majority of acute coronary syndromes are caused by coronary thrombosis. Most of these thrombi are caused by rupture of Thin-Cap FibroAtheromas (TCFA) [52]. Their morphological features are a large lipid core, covered by a thin ﬁbrous cap. Considered as major determinants for the rupture of a TCFA are its material composition, geometry, and cap inﬂammation caused by inﬁltration of macrophages. As such, identiﬁcation of these determinants allows monitoring of atherosclerosis and selecting proper interven-

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tional procedures [53,54]. IVUS strain elastography has proven to be a clinically available tool that is able to detect the presence of such vulnerable high-risk plaques in vitro with high sensitivity and speciﬁcity [46]. In vivo animal experiments and in vitro human experiments demonstrated that discrimination between ﬁbrous and fatty plaques is possible [45,47]. In addition, the in vivo experiments showed that the presence of a high strain spot had high sensitivity and speciﬁcity to identify macrophages. However, a oneto-one relation between the local (radial) strain value in an IVUS strain elastogram and the local tissue component type (calciﬁed, ﬁbrous, fatty or inﬁltrated with macrophages) is not always possible. The underlying reason is that (radial) strain depends upon the material composition and geometry of the plaque components and the catheter position used during imaging [55–58]. Figure 4 exempliﬁes this. Histology shows a TCFA that consist of a soft homogeneous lipid pool covered by a stiff ﬁbrous cap. Because the lipid pool is soft and homogenous, one would expect high radial strain values throughout the same region in the IVUS strain elastogram. However, due to the stiffness of the cap and its circumferentially distributed geometry, stress concentrations occur at the shoulders of the lipid pool [13] resulting in local high strain, furthermore, the cap hinders deformation behind it resulting in low strain at the center of the lipid pool. IVUS modulus elastography is an experimental technique that computes a modulus elastogram from an IVUS strain elastogram. The Young’s modulus E (kPa) is a material parameter, which can be interpreted as the ratio between the stress S (kPa) (tensile or compressive) enforced upon a small block of tissue and its resulting strain (elongation or compression) [59]. Since there exists a large difference between moduli of plaque components [9,10,60–62] (especially between ﬁbrous and fatty components) this modulus elastogram gives a one-toone relation between the local modulus value and the local tissue component type. In this section, the technique behind, the methods for ultrasound modulus elastography and the preliminary results with IVUS modulus elastography are discussed. 4.2. Problem Statement Ultrasound modulus elastography solves a problem (i.e. compute a modulus from measured ultrasound) that can be classiﬁed as a parameter identiﬁcation problem or inverse problem, which are present in almost every existing ﬁeld of science and engineering [63]. In general, this problem can be formulated as follows: Given an adequate input-output description/model of a (real-life) system, compute some desired model parameters from a limited amount of data measured from the system. For example, the real-life system might be a 3D or 2D segment of an arterial wall. The measured data can be the radial strain assessed with IVUS strain elastography. The input-output model can be a computer model that calculates as output the radial strain distribution of the segment; consequently the computer model’s ‘input parameters’ are the geometry of the segment, the blood pressure at lumen boundary and the material properties of the wall, e.g., the Young’s modulus and Poisson’s ratio distribution (Poisson’s ratio is a material parameter that quantiﬁes a material’s local tissue volumetric compressibility). The desired model parameter can be the Young’s modulus distribution. For practical applications an inverse problem should satisfy the following criteria (i) existence and uniqueness; there exists only one set of the desired model parameters that results in/corresponds to the measurements. (ii) continuity; a slight change in the measurements (e.g. due to noise) corresponds to a slight change in the corresponding desired model parameters.

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4.3. Implementation of the Technique The general approach to perform ultrasound modulus elastography is to ﬁrstly use ultrasound displacement/strain elastography to measure one or more components of the displacement vector and/or strain tensor components of the deformed tissue (as explained earlier in this chapter). Next, a deformation model for computing the deformation, strain and/or stress of tissue is deﬁned. This model consists of a set of mathematical (partial differential) equations that describe the equilibrium of tissue, the relation between displacement and strain of tissue and ﬁnally the constitutive equation, which deﬁnes the relation between strain and stress of tissue [59]. Many research groups approximate the behaviour of biological tissue by a linear, isotropic, nearly incompressible (Poisson’s ratio > 0.49) elastic material. In those cases the constitutive relation contains only one material parameter, namely the Young’s modulus. Finally, the deformation model and the measured displacement/strain components are used to compute the modulus distribution by a ‘direct solution approach’ or by an ‘iterative solution approach’. • ‘Direct’: In the direct solution approach the measured displacement/strain data are plugged in the deformation equations, which are mathematically manipulated so that the moduli can be considered and expressed as the unknowns. Next, the moduli are computed using a discretization [64] or numerical integration of the manipulated deformation equations [65,66]. • ‘Iterative’: In the iterative approach, a Finite Element (computer) Model (FEM) is taken as the deformation model. The FEM ﬁlls the space of the tissue with a mesh that consists of small elements (e.g. triangles, bricks) and each element is given a constitutive relation, i.e. Young’s modulus. Next, an initial modulus value for each element deﬁned. Finally the modulus value of each individual mesh element or groups of mesh elements in the FEM are iteratively changed such that the computed FEM deformation output eventually closely matches the measured deformation (displacement/strain data). This matching is fully automatic performed by a minimization algorithm [67]. Much research has focussed on applying these two approaches on non-vascular tissue geometries like a two dimensional cross-section of a homogeneous rectangular medium with a circular or rectangular inclusion [64,66–72], or on a breast or brain part [73,74], or heart [75]. To date, only a few groups have investigated the inverse problem for vascular geometries. Most of them used an adjusted iterative reconstruction method [76–79] and [80], some others an adjusted direct reconstruction method [81,82]. All groups encountered difﬁculties in computing a modulus elastogram (related to uniqueness and continuity), which may be caused by noisy measurements, a limited number of measured displacement/strain components, type of boundary data [83], using an inadequate deformation model for the tissue, non-uniqueness of the inverse problem [84] and converging to non-optimal local minima by the minimization algorithm. 4.4. IVUS Modulus Elastography Recently, Baldewsing et al. [85] focused on solving the intravascular inverse problem for atherosclerotic vascular geometries using an iterative solution approach. Thereby, they used the arterial radial strain measured with IVUS strain elastography and an a priori

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Figure 7. Parametric ﬁnite element model for a vulnerable plaque. (A) Each circle is parameterized by its center (X,Y) and a radius R. The dynamic control points P, Q, R, S, T, and U are used to deﬁne the three plaque component regions. (B) Finite element mesh regions corresponding to geometry in A. Each ﬁnite element in a region has the same material property values as other elements in that region. Letters L and c denote respectively lipid and cap.

parametric-plaque-geometry computer model. Their motivation for using a priori information is threefold. Firstly, they want to compute a modulus image of an atherosclerotic plaque that is diagnostically useful and easy to interpret in clinical settings. Secondly, the computation should suffer at least as possible from convergence problems. Finally, they want to be able to investigate and quantify difﬁculties (uniqueness and continuity) and limitations for computing a modulus elastogram of plaques in a structured manner. There iterative solution approach is especially suited for ‘thin-cap ﬁbroatheromas’ (TCFA) [52,53]. Their approach is as follows: the deformation output calculated with a Parametric Finite Element Model (PFEM) representation of a TCFA, is matched to the plaque’s radial strain as measured with IVUS strain elastography. The PFEM uses only six morphology and three material composition parameters, but is still able to model a variety of these TCFA’s. The computed Young’s modulus image of the TCFA shows both the morphology and Young’s modulus value of three main plaque components, namely lipid, cap and media and should therefore be easy interpretable. In the next three subsections, the main parts of their iterative solution approach are discussed, namely the PFEM for a TCFA, the used deformation model and used minimization algorithm. • ‘PFEM Geometry for a Plaque’: An idealized ‘thin-cap ﬁbroatheroma’ [52] is used as a model for a plaque and is an extension of the PFEM model used by Loree et al. [12]. The PFEM geometry consists of a media area containing a lipid pool, which is covered by a ﬁbrous cap. The borders of the lipid, cap and media areas are deﬁned using circles (Fig. 7). Lipid is deﬁned by region QTQ, cap by region PQTSP, and media by the remaining area. Each circle is parameterised by its center with Cartesian coordinates (X,Y) and radius R. Resulting in a total of six morphology parameters. • ‘Material Deformation Model’: Baldewsing et al. [86] used coronary arteries (n = 5) to demonstrate that radial strain elastograms measured in vitro using IVUS strain elastography could be simulated with a ﬁnite element model. Their material

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deformation model treated the arterial tissue as a linear elastic, isotropic, planestrain, nearly incompressible material with a Poisson’s ratio of 0.4999 [55].The ﬁnite element model geometry and material properties were determined using the IVUS echogram and histology (collagen, smooth muscle cells and macrophages). The agreement between a simulated and measured elastogram was quantiﬁed by comparing features of high strain regions. Statistical test showed that there was no signiﬁcant difference between simulated and corresponding measured elastograms in location, surface area and mean strain value of a high strain region. The same material deformation model is used for the PFEM. Lipid, cap and media region are assumed to have a constant Young’s modulus value EL, EC, and EM, respectively. This results in a total of only three material composition parameters. The PFEM radial strain deformation is computed using the ﬁnite element package SEPRAN (Sepra Analysis, Technical University Delft, The Netherlands); the catheter center is taken as origin. This radial strain ﬁeld is called a PFEM strain elastogram. The whole process from deﬁning the PFEM morphology and material composition parameters up to the calculation of the PFEM strain elastogram is fully automatic. • ‘Minimization Algorithm’: The modulus elastogram of a plaque is determined by a minimization algorithm. This algorithm tries to ﬁnd values for the six morphology and three modulus parameters of the PFEM such that the corresponding PFEM strain elastogram ‘looks similar’ to the measured IVUS strain elastogram. Theire similarity is quantiﬁed as the Root-Mean-Squared (RMS) error between PFEM strain elastogram and measured IVUS strain elastogram. The sequentialquadratic-programming minimization algorithm fully automatic searches a local minimum of the RMS by iteratively updating the nine PFEM parameters. Each update gives a lower RMS error. The algorithm stops when the either the RMS itself or each of a few consecutive RMS values is below a threshold value. When the resulting ﬁnal PFEM strain elastogram has qualitatively enough strain pattern features in common with the measured IVUS strain elastogram, the corresponding modulus elastogram is considered to be a good approximation of the material composition of the investigated plaque.

5. IVUS Modulus Elastography: Preliminary Results Baldewsing et al. [87,88] have shown the feasibility of their approach by successfully applying their IVUS modulus elastography method on radial strain elastograms of vulnerable plaques that were (a) simulated, (b) measured in vitro and (c) measured in vivo in a patient. Two computer-simulated plaques, a plaque-mimicking phantom and two human coronary plaques (in vitro and in vivo) were used. Finite element models were used to simulate strain elastograms for two plaque geometries, both having a lipid pool covered by a cap; one geometry was deﬁned by circles, the other by tracing arterial histology. For their in vitro phantom and coronary artery, strain elastograms were processed from radiofrequency data obtained with a 20-MHz 64-element phased array IVUS catheter. For the patient’s case, multiple in vivo strain elastograms, obtained during the diastolic phase of a cardiac cycle were catheter motion was minimal, were averaged into one in vivo compounded strain elastogram to increase the signal-to-noise ratio. All their computed mod-

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Figure 8. Computing an IVUS modulus elastogram from an IVUS strain elastogram that was measured in vivo from a patient with a vulnerable plaque. (A) IVUS echogram. (B) In vivo measured compounded strain elastogram. (C) Computed Young’s modulus elastogram in kPa. (D) PFEM strain elastogram computed from C.

ulus elastograms approximated the geometry and material properties of the real plaque composition. Figure 8 shows computation of an IVUS modulus elastogram from the in vivo measured compounded IVUS strain elastogram of the patient. The echogram (Fig. 8A) reveals the presence of a large eccentric plaque between 10 and 5 o’clock, but cannot discriminate between the possible cap and lipid component of the plaque. The in vivo measured compounded IVUS strain elastogram (Fig. 8B) suggests the presence of a soft lipid pool covered by a stiff cap by means of a typical high radial strain region at the shoulders of the plaque and mechanical shadowing, which causes the low strain at the center of the plaque. The pressure differential was 1 mm Hg. The computed Young’s modulus elastogram (Fig. 8C) with (EL = 1, EC = 118, and EM = 111 kPa) is a likely candidate for the unknown material composition of the plaque, since the measured compounded IVUS strain elastogram (Fig. 8B) and the PFEM strain elastogram (Fig. 8D) show two co-localizing high strain regions and mechanical shadowing.

6. Discussion Identiﬁcation of plaque components and the proneness of a lesion to rupture is a major issue in interventional cardiology. Intravascular ultrasound (IVUS) echography is a real-time, clinical available technique capable of providing cross-sectional images and identifying calciﬁed plaque components. Since IVUS strain elastography only requires ultrasound data sets that are acquired at different levels of intraluminal pressure, it can

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be realised using conventional catheters. It has been shown by several research groups that IVUS strain elastograms of vessel-like phantoms and arteries in vitro and in vivo can be produced. Furthermore, the feasibility of IVUS strain elastography in vivo in animals and patients was demonstrated. Currently, there is no clinical available technique capable of identifying the rupture prone plaque. Identiﬁcation of these plaques is of paramount importance to investigate the underlying principle of plaque rupture, the effectiveness of pharmaceutical treatments and, on the long-term, preventing sudden cardiac deaths. IVUS strain elastography has proven to be able to identify the rupture prone plaque in vitro with high sensitivity and speciﬁcity and in vivo experiments demonstrate the power to identify ﬁbrous and fatty plaque components. Therefore, IVUS strain elastography is one of the ﬁrst techniques that can be applied in patients to assess the vulnerability of plaques. Since IVUS strain palpography is a faster and more robust technique, introduction of this technique in the catheterisation laboratory may be easier. Although IVUS strain palpography reveals no information on the composition of material deeper in the plaque, it may be a powerful technique to identify the weak spots in an artery. If a plaque will rupture, this rupture will start at the lumen vessel-wall boundary and this region is imaged with IVUS strain palpography. Recently 3D IVUS strain palpography was used in vivo to detect vulnerable-plaque-speciﬁc strain patterns in human coronary arteries and this study showed that the total number of these patterns correlated both with the clinical presentation and the level of C-reactive protein. Further studies should be performed to assess the potential role of this technique to identify patients at risk of future clinical events. Quantitative monitoring of atherosclerosis to study the effect of pharmaceutical therapies aimed at stabilizing plaques, e.g. by stiffening or reducing the lipids [89], requires a technique that provides quantitative information about the material properties of plaque components. IVUS modulus elastography seems most suited for this application, since it images the modulus of tissue, which is a material property and therefore its value is independent of the morphology and location of plaque constituents in the arterial wall, in contrast to strain. Since a large modulus contrast between soft and stiff plaque components exists, differentiation between them is straightforward. The feasibility of IVUS modulus elastography using an iterative solution approach and an a priori plaque geometry model was show using simulations and in vitro using a vessel phantom and a human coronary artery that both contained a TCFA. However, plaques can also have a complex, heterogeneous material composition consisting of mixture of plaque components, like lipids, ﬁbrotic tissue, calciﬁed nodules or tissues weakened by inﬂammation due to macrophage inﬁltration. Imaging of such complexes requires a different approach, which doesn’t enforce restrictions on the possible plaque constituents and their morphologies. A direct solution approach is an option. However, the following hybrid approach seems also fruitful: First an iterative approach with a priori plaque information is applied, like Baldewsing et al. [85] did, to obtain an global approximation of the modulus distribution. Next, this distribution is used as initilization in the iterative approach reported by Soulami et al. [79] that computes for each small individual ﬁnite element in the plaque a modulus. Although their approach does not require a priori information, the large number of moduli to be computed might compromise a successful convergence of the minimization algorithm. Finally, a hybrid construction between a direct and iterative approach should not be ruled out. To realize IVUS modulus elastography as a practical tool for clinical application, the following research still has to be performed (i) developing a solution approach for an arbitrary plaque that is robust

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(i.e. the inﬂuence of catheter position and measurement noise should not signiﬁcantly inﬂuence the outcome of the modulus elastogram), (ii) validation in vitro and/or in vivo and ﬁnally, (iii) investigating the need for and possibility of real-time application. All the results obtained up to now show the potential of IVUS (strain and modulus) elastography/palpography to become a unique tool for clinicians to detect vulnerable high-risk plaques, selecting proper interventional procedures and monitoring atherosclerosis.

7. Conclusion Intravascular ultrasound (IVUS) strain elastography has proven to be a technique capable of providing information about the vulnerability and material composition of plaques. In vivo studies in animals and patients demonstrate that IVUS strain palpography may develop into a clinical available tool to identify the rupture prone plaque. Future studies will reveal the potential of IVUS modulus elastography to quantitatively monitor atherosclerosis.

Acknowledgement The research discussed in this chapter has been funded by grants from the Dutch Technology Foundation (STW), the Netherlands Organization for Scientiﬁc Research (NWO), Deutsche Herzstiftung (DHS), Dutch Heart Foundation (NHS) and JOMED.

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Plaque Imaging: Pixel to Molecular Level J.S. Suri et al. (Eds.) IOS Press, 2005 © 2005 The authors. All rights reserved.

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Computer Vision Analysis of Collagen Fiber Bundles in the Adventitia of Human Blood Vessels Pierre J. ELBISCHGER a,1 , Horst BISCHOF a , Gerhard A. HOLZAPFEL b and Peter REGITNIG c a Inst.

for Computer Graphics and Vision, Graz University of Technology, Austria for Structural Analysis, Graz University of Technology, Austria c Inst. of Pathology, Graz Medical University, Austria

b Inst.

Abstract. Numerical simulations, which are based on reliable biomechanical models of blood vessels, can help to get a better understanding of cardiovascular diseases such as atherosclerosis, and can be used to develop optimal medical treatment strategies. The adventitia is the outer most layer of blood vessels and its mechanical properties are essentially determined by the three-dimensional, structural arrangement of collagen ﬁbre bundles embedded in the tissue. Global information such as the orientation statistics of the ﬁbre bundles as well as detailed information as the crimp of the single ﬁbres within the bundles is of particular interest in biomechanical modeling. In order to obtain a sufﬁciently large amount of data for biomechanical modeling, a fully automatic method for the structural analysis of the soft tissue is required. In this contribution we present methods based on computer vision to fulﬁll this task. We start by discussing proper tissue preparation and imaging techniques that have to be used to obtain data, which reliably represents the real three-dimensional tissue structure. The next step is concerned with algorithms that robustly segment the collagen ﬁbre bundles and cope with various kinds of artifacts. Novel segmentation techniques for robust segmentation of individual ﬁbril bundles and methods for estimation of their parameters, such as location, shape, mean ﬁbril orientation, crimp of ﬁbrils, etc., is discussed. The proposed algorithms are based on novel perceptual grouping methods operating on the extracted orientation data of ﬁbrils. Finally, we demonstrate the results obtained by our fully automatic method on real data. In addition, for a more quantitative assessment, we introduce a generative structural model that enables the synthesis of three-dimensional ﬁbre bundles with well-deﬁned characteristics. Keywords. Biomechanic modeling, structural analysis, soft tissue, collagen ﬁbers, microscopic images, computer vision

1 Corresponding Author: Pierre J. Elbischger, Inst. for Computer Graphics and Vision, Graz University of Technology, Inffeldgasse 16/II, 8010 Graz, Austria.

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1. Motivation and Background This book-chapter is concerned with an automatic method for structural analysis of collagen ﬁbrils in biological soft tissues. This section motivates research both from a biomechanical point of view and a computer vision perspective. 1.1. Why do we Need to Understand the Concentration and Structural Arrangement, and the Structure-Function Relationships of Native Tissues? Soft tissues are wide-ranging biological materials in which the cells are separated by extracellular material. They may be distinguished from hard (mineralized) tissues such as bones for their high ﬂexibility and their soft mechanical properties. Examples of soft tissues are tendons, ligaments, blood vessels such as arteries and veins, skins or articular cartilages among many others. Tendons are muscle-to-bone linkages that stabilize the bony skeleton (or produce motion), and ligaments are bone-to-bone linkages to restrict relative motion. Blood vessels are prominent organs composed of soft tissues which have to distend in response to pulse waves. The skin is the largest single organ (16% of the human adult weight). It supports internal organs and protects our body. Articular cartilages form the surface of body joints (which is a layer of connective tissue with a thickness of 1–5 mm), distribute loads across joints and minimize contact stresses, and friction (see [1] with more references therein). The mechanical behavior of soft biological tissues is strongly inﬂuenced by the concentration and structural arrangement of constituents such as collagen. The different behaviors of soft biological tissues commensurate with the different functions of individual tissues. A greater understanding of the foundations and interactions of structure and function of soft tissue, and, in particular, the associated mechanobiology is one of the research needs in the ﬁeld. Mechanobiology is aimed to understand how cells change their structure and function in response to changes in their mechanical environment. Mechanobiology is a perfect complement of biomechanics each focuses on similar issues, just from different philosophic perspectives (for example, induction versus deduction) [2]. It also studies the mechanical factors that may be important in triggering the onset of atherosclerosis or aneurysms. Springer-Verlag has launched a new Journal in 2002 called Biomechanics and Modeling in Mechanobiology [3], which shows the importance of the ﬁeld. A thorough understanding of the complex interrelation between mechanical factors and the associated biological responses may help to improve diagnostics which allow disease and injury to be treated earlier. It requires quantiﬁcation of the mechanical environment of the involved tissues, i.e. geometrical and constitutive models of all tissue components involved. A greater understanding of the structure-function relationships of native tissues is also a prerequisite for appropriate repair and replacement tissues. Tissue engineering requires a clear understanding of the structural arrangements and functions of the associated living tissues, because much of gene expression is via mechanotransduction mechanisms. The success of tissue engineering is clearly based on knowledge of the biomechanics of native tissue. As a matter of fact, 1998 the United States National Committee on Biomechanics formed a subcommittee, which seeks to address challenges in repairing or replacing tissues that serve a predominantly biomechanical function. One essential goal of the subcommittee in advancing ‘tissue engineering’ is to ‘identify the

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critical structural and mechanical requirements needed for each tissue engineered construct’. Hence, in particular, the quantitative knowledge of preferred orientations in biological soft tissues enhances the understanding of their general mechanical characteristics signiﬁcantly. It is important to note that realistic structural models rely strongly on this knowledge. Collagen ﬁbers are those components of many soft tissues that render the material properties anisotropic. In order to describe the anisotropic feature, appropriate geometrical data are required. They serve as an essential set of input data for numerical models. The focus of the proposed work will be on the concentration and structural arrangement of collagen in biological soft tissues, in particular, in arteries. 1.2. Background on the Structure of Soft Tissues – Collagen and Elastin Soft biological tissues of our body are complex ﬁber-reinforced composite structures. Their mechanical behavior is strongly inﬂuenced by constituents such as collagen and elastin, the hydrated matrix of proteoglycans, and the topographical site and respective function in the organism. Collagen. Collagen is a protein which is a major constituent of the extracellular matrix of soft tissue. It is the main load carrying element in a wide variety of soft tissues and is very important to human physiology (for example, the collagen content of (human) achilles tendon is about 20 times that of elastin). Collagen is a macromolecule with length of about 280 nm. Collagen molecules are linked to each other by covalent bonds building collagen ﬁbrils. Depending on the primary function and the requirement of strength of the tissue the diameter of collagen ﬁbrils varies (the order of magnitude is 1.5 nm [4]). The intramolecular crosslinks of collagen gives the soft tissues the strength which varies with age, pathology, etc. The function and integrity of organs are maintained by the tension in collagen ﬁbers. In the structure of tendons and ligaments, for example, collagen appears as parallel oriented ﬁbers [5], while many other tissues have an intricate disordered network of collagen ﬁbers embedded in a gelatinous matrix of proteoglycans. As far as arteries are concerned collagen ﬁbrils appear in the media (the middle layer of an artery). They are interconnected with muscle cells, and elastin within a complex three-dimensional network. The orientation of and close interconnection between the elastic and collagen ﬁbrils, elastic laminae, and smooth muscle cells together constitute a continuous ﬁbrous helix (Faserschraube) in the media [6,7]. The helix has a small pitch so that the ﬁbrils in the media are almost circumferentially oriented. This structured arrangement gives the media high strength, resilience and the ability to resist loads in both the longitudinal and circumferential directions. From the mechanical perspective, the media is the most signiﬁcant layer in a healthy artery. The adventitia is the outermost layer of the artery and consists also of collagen ﬁbrils, which appear in thick bundles forming a ﬁbrous tissue. In addition, ﬁbroblasts and ﬁbrocytes, and histological ground substance are present. The adventitia is surrounded continuously by loose connective tissue. The wavy collagen ﬁbrils are arranged in helical structures and serve to reinforce the wall. They contribute signiﬁcantly to the stability and strength of the arterial wall. The adventitia is much less stiff in the load-free conﬁguration and at low pressures than the media. However, at higher levels of pressure

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the collagen ﬁbers reach their straightened lengths and the adventitia changes to a stiff ‘jacket-like’ tube which prevents the artery from overstretch and rupture. For a more detailed account of the structure (distribution and orientation) of the interrelated arterial components, the morphological structure and the overall functioning of blood vessels, see, for example, [8–11], Section 2, [1] and [12]. Elastin. Elastin, like collagen, is a protein which is a major constituent of the extracellular matrix of soft tissue. It is present as thin strands in soft tissues such as skin, lung, ligamenta ﬂava of the spine and ligamentum nuchae (the elastin content of the latter is about ﬁve times that of collagen). The long ﬂexible elastin molecules build up a three-dimensional (rubberlike) network, which may be stretched to about 2.5 of the initial length of the unloaded conﬁguration. In contrast to collagen ﬁbers, this network does not exhibit a pronounced hierarchical organization. As for collagen, 33% of the total amino acids of elastin consists of glycine. However, the proline and hydroxyproline contents are much lower than in collagen molecules. 1.3. Realistic Mathematical and Computational Models of Soft Tissues Rely Strongly on Histological Information A thorough understanding of the structural arrangement provides a foundation for functional integration across interacting biological processes, provide information for the design of powerful, and realistic mathematical and associated numerical models. It is wellaccepted and indisputable in the scientiﬁc community, that computer models and computational methods, when based on histological information, are necessary to understand the functions of living tissues and to gain more insights in the underlying mechanobiology. Of course, powerful mathematical and computational models are still the greatest needs in the ﬁeld. Mathematical and computational models may predict observations across multiple length and time scales, and chemical, mechanical, and coupling responses of soft tissues. Computational methods are needed to model realistically many multidisciplinary processes encountered in biomechanics of soft tissues relevant to problems in medicine, surgery and bioengineering like diagnostic imaging, surgical planning and intervention, medical therapy, and biomedical engineering design for tissue engineering or medical devices. They are needed to solve the complex geometries and loading conditions, and the initial and boundary-value problems of clinical, industrial, and academic importance. Computational models may (i) predict the risk of rupture of aneurysms, (ii) identify the failure strength of an anterior cruciate ligament, (iii) improve diagnostics and therapeutical procedures that are based on mechanical treatments, (iv) study the mechanical factors that may be important in triggering the onset of aneurysms or atherosclerosis, the major cause of human mortality in the western world, (v) describe the pulse wave dynamics and the interaction between the heart and the circulatory system, (vi) investigate the changes in the arterial system due to age, disease, hypertension and atherosclerosis, which is of fundamental clinical relevance.

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1.4. The Focus of the Chapter Quantitative data about the structural arrangement of collagen are particularly rare for single layers of human arteries (i.e. intima, media and adventitia). In order to develop reliable biomechanical models, it is crucial to have a fast, reliable and inexpensive tool available for the identiﬁcation of the structural arrangement of collagen ﬁber bundles in the tissue. To relieve medical assistants from the tedious work of measuring structural data by hand, which is also prone to errors, it is reasonable to strive for an analysis of tissues by means of computer vision methods. The use of computer vision methods for the extraction of relevant structural data guarantees an objective (robust against human subjective impressions) way for data acquisition, and, furthermore, allows an exhaustive, automatic analysis of a tissue sample set, large enough to gain statistically meaningful results. The focus of this chapter is the identiﬁcation of the structural arrangement of collagen in biological soft tissues, in particular, in the outermost layer of human arteries, i.e. the adventitia (tunica externa). Our analysis is based on transmitted light microscopy (TLM) images of histological tissue samples. Once, the automatic structure analysis problem of adventitial tissue is solved, the algorithms can easily be adopted for similar problems, e.g. the structure analysis of the intima and media. Compared to other imaging techniques such as magnetic resonance imaging (MRI), computer thomography (CT) or microtomography (Micro-CT), where in particular the contrast of collagen ﬁbers almost vanishes, TLM images of stained soft tissues feature an extremely high contrast. This fact makes an automatic computer vision-based analysis procedure possible. Images from TLM do not contain already coded orientation information such as images obtained by polarized light microscopy (PLM), quantitative polarized light microscopy (QPLM) or small angle light scattering (SALS), however, they do represent the full structure information in a single image and additionally provide the possibility to segment artifacts. Our intention and goal is to extract and group orientation information of collagen ﬁbers by means of modern computer vision techniques and end up with a powerful approach that is capable of providing detailed structure information about the specimen. The major beneﬁts of our approach are: (i) with a resolution of 0.25 μm our setup is capable of resolving individual collagen ﬁbers. (ii) The TLM setup is inexpensive and easy to access for any scientist. (iii) The required histological preparation techniques are inexpensive and well established. (iv) The problem of structural information extraction is entirely solved in software and does not require any expensive equipment in the imaging setup. (v) The analysis is performed fully automatic, except the image capturing process. 1.5. Related Work While a great deal of research effort in the ﬁeld of medical computer vision has been devoted to the analysis of MRI, CT, Micro-CT and ultra sound images, there is little research performed on the automatic analysis of light microscopic histological images. Most studies that address the extraction of structural data related to histological microscopic images focus on blobs and cell shaped structures that represent blood cells or cell nucleus rather than ﬁbrous structures and their precise structural information (see, for example, [14–18]). Because of the importance of collagen ﬁbers, many researchers in the areas of medicine, biology and biomechanics have tried to reveal its structural information such as ori-

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entation, density, coherence, etc. using various techniques. Most of these studies do not use automatic algorithms for segmenting the structure in question. In the following we give a brief overview about the recent research in the ﬁeld of ﬁbrous structure analysis. High directional correlations between the long axes of cellular shapes and nuclei of, for example, a stained patch of a media may be studied under a microscope. The very ﬁrst contribution concerning the directional analysis of smooth muscle cells seems to be attributed to [19]. At a later date, [20] used a combination of microdissection and etching technique to show that dissected threads of muscle tissues are helically shaped with constant radius. The author concluded that the helical patterns are also present in muscular arteries and that the media is composed mainly of layered structures of helices. Quantitative studies regarding (helical) pitch angles were carried out by [21–23] and [24] for several organisms at different locations. These studies do not support the conclusion of a uniﬁed orientation of smooth muscle cells drawn by [20]. The non-uniformity of ﬁber orientations in specimens originating from different organisms and different locations was pointed out by [25]. Smooth muscle cells provide active contractile elements of arterial walls and have long and thin centrally located nuclei (see [22] and [26]), which can be stained with hematoxylin in order to reveal the cell (nuclei) orientations ( [25]). A number of techniques have been proposed for analyzing the orientation of nuclei: [25] used a digitizer to enter manually the coordinates of the nuclei of the human intracranial media into a computer. Thereby, the orientation is described by two angles (in the histological plane and in an orthogonal plane). In addition, [27] used a graphic tablet to digitize the coordinates of nuclei within the human brain artery. As a reference frame of coordinate axes they embedded a precisely trimmed block together with the vessel segment in parafﬁn wax. The most thorough study was undertaken by [28], in which shape, position, linear dimensions, volumes and orientation of nuclei within several vessel types of male Wistar rats are determined by means of computer-aided analyses. Sections with 0.5 μm thickness are produced by an ultramicrotome and then stained and cut again to produce ultra-thin sections with 60–80 (nm) thickness. Hence, the digitized contours of cells are assembled into a 3D model by appropriate software tools. Recent studies concentrate on SALS [29–32] and on PLM [32,33] using the birefringent optical property of collagen ﬁbers in order to obtain information about their structural arrangement [34]. PLM is generally recommended as the most appropriate method for detecting, describing and interpreting wave-like structures [35,36], whereas SALS makes it possible to detect the ﬁber orientation. SALS provides a maximal spatial resolution of about 50 μm and, therefore, prevents a detailed analysis of individual ﬁbers that requires a spatial resolution of at least 0.5 μm. Traditional crossed PLM provides essentially qualitative information (they detect birefringent materials) rather than quantitative measurements of the spatial distribution of the optical anisotropy of the specimen. So called QPLM [37] is capable to overcome this shortcoming of crossed PLM. Tower et al. [38] proposed a method to analyze the collagen ﬁber alignment during mechanical testing of soft tissues based on QPLM. With respect to our approach the technique proposed in [38] uses much thicker samples and, therefore, integrates the optical signal across the whole sample. The retardation does not distinguish between alignment among multiple ﬁber populations (for example, collagen and elastic ﬁbers) nor does it account for layers with distinct alignment ﬁelds. The power of the method is, that the structural analysis can be performed dynamically during mechanical testing of soft tissues. Mas-

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soumian et al. [39] describe a modiﬁcation to the optical system of a confocal microscope which analyzes the polarization state of the image light and came up with an enhanced method for QPLM. The system uses a novel form of rotating analyzer which, together with lock-in detection, permits images to be obtained where the image contrast corresponds to both specimen retardance and orientation. Compared to our approach which is based on histological samples, the special equipment required for a QPLM setup is much more complex and expensive. Most recently laser scanning microscopy (LSM) experiences an increasing interest for the analysis of collagen ﬁbers. In contrast to the above mentioned techniques, LSM is non-destructive and produces volume data directly. Axer et al. [40,41] performed a coarse analysis of the 3D architecture of the collagen ﬁbers in linea alba and rectus sheaths. The analysis was done manually. By using a commercial software, Young et al. [42] registered several LSM volume images to each other and performed a structural analysis of myocardial laminae and collagen network in rat hearts by visual inspection. The preliminary study [43] is aimed to investigate small angle X-ray scattering (SAXS) diffraction patterns of isolated arterial layers during tensile testing. The application of this analyzing technique to identify the structure of human soft tissues is new. It is a challenging approach for the analysis of very small periodic structures, however, it may not be appropriate for a precise macroscopic analysis. The diffraction pattern obtained in the preliminary study [43] is highly speciﬁc for collagen ﬁbrils. Highest intensities were observed for the adventitia, followed by the intima. Medial layers showed predominately diffuse scatter and only a weak ﬁrst order maximum. In particular, for the adventitia and the intima SAXS diffraction data in combination with tensile testing may provide valuable data for micro-and nano-structural constitutive modeling. Most of the above mentioned studies do not make extensively use of image processing techniques to automatically extract structural data. They either require massive manual interaction or use the output of an expensive analyzing setup directly (as, e.g., for QPLM). In the following we address approaches that make use of image processing algorithms. Smooth muscle cells provide active contractile elements of arterial walls and have long and thin centrally located nuclei (see [22] and [26]), which can be stained with hematoxylin in order to reveal the cell (nuclei) orientations ( [25]). A number of techniques have been proposed for manually (computer-aided) analyzing the orientation of nuclei [25,27,28]. In a recent paper [11] an automatic technique was postulated for obtaining information about preferred orientations in isolated arterial tissues, and, additionally, the concentration of nuclei. The authors assumed that the orientation of the muscle cells correlates with the orientation of the collagen ﬁbers, which enabled them to estimate the orientation statistics by analyzing the muscle cell nuclei. For the adventitia, however, the concentration of muscle cells is very small so that the intra-spatial voids between collagen ﬁber bundles may be used as indicators for preferred orientations of the tissues. An interesting 2D image analysis technique to characterize the collagen morphology of articular cartilage, which is the most similar to our approach, was proposed by Xia and Elder [44]. They digitized transmission electron microscopy (TEM) images and divided them into small square ROIs. A region was chosen to be large enough to include several ﬁbrils. The morphology of each small and localized region, was characterized by three quantities: the concentration of the ﬁbrils, the overall orientation of the ﬁbrils, and the anisotropy of the ﬁbrils. Nevertheless, they neither perform any grouping operation,

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which is essential in order to obtain reliable orientation information, nor any type of artifact segmentation to reject regions that hold no meaningful information. Furthermore, they require an expensive setup and need to digitize analog ﬁlm images before the image processing can take place. Wu et al. [45] demonstrate a vision algorithm designed to extract quantitative structural information about individual collagen ﬁbers (orientation, length and diameter) from LSM images of collagen gels. They trace individual ﬁbers in the volume data set. Althoug the LSM seems to be a challenging approach it has some drawbacks. It is expensive and, therefore, restricted to a small group of researchers. Using a stack of registered histological cross-section images, our approach can be extended to 3D too. Because LSM is based on back scattered light from single ﬁbers, the maximal analyzing depth for our samples is restricted to approximately 60 μm and the contrast of collagen as well as the spatial resolution decrease with increasing depth. Glazer [46] proposed an algorithm to segment single and well separative ﬁbrils in TLM images. However, the proposed algorithm is too weak to extract the complex, structural and hierarchical data of collagen ﬁbers from the microscopic images of soft tissues. It neither works on texture-like images nor does it perform any kind of ﬁbril bundle grouping. Beside collagen ﬁber analysis, Eberhardt and Clarke [47] used X-ray to nondestructively probe the internal structure of several ﬁbrous materials (glass ﬁbre reinforced composites and non-woven textile samples) in 3D. They are also the authors of a book about microscopy techniques in material science [48], in which they address an image processing based automatic analyzes of ﬁbrous structures. In their analyzes they use the proﬁle of single ﬁbers (cycles and ellipses), which are larger than 30 μm in diameter, to obtain structural information. Because the diameters of collagen ﬁbers (1 μm) are far smaller, these methods cannot be applied.

2. Imaging Techniques for Collagen A reliable structure analysis of collagen require a proper data set (images) that comprehensively represent the structural information of collagenous components within soft tissues. The properties and the quality of the raw data set strongly determine the accuracy of the entire analysis process. Hence, a careful choice of the used imaging technique is required. Important issues in the image acquisition process are: • Keep the number of artifacts as small as possible. • High contrast of the collagenous structures compared with artifacts and other tissue components (elastic ﬁbers, muscle tissue, etc.). • Choose an ‘optimal’ image resolution that provides adequate and detailed information (ﬁbrils) as well as global information (ﬁbrous bundles). • The data base should enable extraction of 3D data. • Keep the data volume as small as possible. • Establish an easy and reproducible setup for soft tissue analysis. In order to analyze collagen structures, different methods have been investigated and assessed. To avoid autolysis of the tissue, the time period between death and tissue ﬁxation (use, e.g., 4% formalin, 70% alcohol or bouin) is of particular importance and should be as close to the mortal time as possible.

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In the assessment of the different imaging techniques the following issues are particularly of interest. Destructiveness: Is the method non-destructive or destructive? If the tissue has to be sliced the method is destructive and a registration of successive slices will be necessary in order to reveal the 3D structure. The registration process may be difﬁcult as a result of the non-rigid tissue deformations during the preparation process, see [49]. On the other hand only one non-destructive imaging technique that achieves the necessary resolution is currently available, namely the laser scanning microscopy (LSM). Resolution in x and y-directions: A single collagen ﬁber has a thickness of about 1–2 μm, which requires the imaging technique to have a minimal resolution of 500 nm. Resolution in z-direction: Some imaging techniques require a mechanical slicing of the specimen into a stack of thin slices and others provide the possibility to scan an entire tissue volume at once. In both cases the slices that build up the volume have to be small enough to pursue the ﬁber bundles through the volume. Because entire ﬁber bundles and not single ﬁbers should be pursued through the image stack, the spatial resolution in z-direction may be lower than in x and y-directions. For TLM it has been shown, that ∼ 3 μm thick slices provide sufﬁcient information. The occlusion of the single ﬁbers at a slice thickness of ∼ 3 μm is moderate and allows the estimation of a single ﬁber and, therefore, the segmentation of a ﬁber bundle in 2D. Contrast of the structures in question: The way how the different structures within the tissue appear in the image, inﬂuence the reliability of the segmentation of collagen. If all structures have a good contrast it will be easier to obtain a correct segmentation. Fixation of the tissue: Typically the ﬁxation causes a shrinkage of the tissue and, therefore, alters the structure of the original tissue. In order to keep this inﬂuence small, the correct ﬁxation has to be chosen. Typical values of contractions for different ﬁxations are: formalin (5%–10%), alkohol (10%), bouin (<5%). We assessed various imaging techniques, such as TLM, PLM, ﬂuorescence micrcoscopy (FM), LSM and environmental scanning electron microscopy (ESEM), to their suitability to analyze collagen ﬁber bundles applying computer vision methods. The following section is mainly focused on TLM, which turned out to be the most suitable choice for our analysis purposes and gives due to space restrictions only a brief overview of the properties of the other methods. 2.1. Transmitted Light Microscopy (TLM) A typical research grade transmission light microscope consists of the following three important parts: the lighting system, the objective and a charge coupled devise (CCD) camera. All parts together determine the maximum resolution of the system. To avoid diffraction and, therefore, to obtain the necessary resolution, the wavelength of the used light source should be of the order of the smallest structures to be observed. A typical CCD camera mounted on a TLM for human operators has similar characteristics as a

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human eye. The wavelength-dependent sensitivity of the camera spans a range from 380 nm to 780 nm. The critical parameter of an objective is its numerical aperture denoted by NA, which is a measure for its capability to separate points in the image that are closely located to each other in the object. The numerical aperture (NA) is deﬁned as the sine of the half aperture angle β times the refractive index n of the medium between the objective and the object — refractive index for air (1), water (1.333), immersion oil (1.515), glass (1.4 to 1.55); thus NA = n sin β/2. The maximum possible magniﬁcation is in the range of 500 to 1000 times NA. Given the numerical apertures of the objective NAObj and the condenser NACon , and assuming a light source with wave length λ, then the maximum spatial resolution d can be estimated by means of the formula d = 1.22λ/(NAObj + NACon ). From this equation, one should be aware that the NA of the condenser is as important as the NA of the objective lens in determining resolution. Up to a NA of 0.95 the medium between the object and the ocular is allowed to be air. This is a consequence of the upper introduced formula 0.95 = 1 × sin(β/2) that results in a leaving angle of β/2 = 71.805◦ which is of the size of the critical angle of glass. For larger angles the light is reﬂected by the glass and, therefore, can not propagate through the objective. Objectives with a higher NA require another medium between the object and the objective, e.g., immersion oil. In this way NA up to 1.4 become possible and structures of size 0.2 μm can be resolved. More detailed information about TLM can be found in, for example, [50–52]. Tissue preparation. Before the soft tissue can be studied by a TLM, the tissue has to be properly prepared. The challenge in the preparation task is to prepare the tissue in a way so that the amount of artifacts become as small as possible. The main steps in the preparation process are: Fixation: In order to avoid autolysis the fresh tissue has to be ﬁxed with formalin, alcohol or bouin. Dissection: A small specimen is dissected from the tissue sample in question. Embedding: To make the underlying structure visible the histological samples have to be sliced very thin. To enable the slicing the tissues have to be embedded into polymethyl-methacrylat (MMA) or parafﬁn. Slicing: Next, with a microtome the embedded tissue samples are sliced with a thickness of 3 μm. Staining: To make the collagen ﬁber bundles visible the sliced tissue samples have to be stained with an Elastica van Gieson (EVG) or Hematoxylin-Eosin (HE) staining. In order to choose the best suited embedding and staining method for the collagen structure analyses, the different methods mentioned above have been investigated and compared to each other. Based on the results of the study we decided to use ﬁxation with Formalin that introduces only a moderate shrinking of 5%, Parafﬁn embedding that pronounces the structure of collagen ﬁbers well and EVG staining that reveals all tissue components and makes the detection of non-collagen regions more robust. Figure 2(a) shows a TLM image of a properly prepared tissue samples of the adventitia.

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(a)

(b)

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(c)

Figure 1. (a)–(c) show a stack of LSM images. The images show elastin (more thick strings) and collagen that appears in bundles.

2.2. Polarized Light Microscopy (PLM), Fluorescence Micrcoscopy (FM), Laser Scanning Microscopy (LSM) and Environmental Scanning Electron Microscopy (ESEM) In the following PLM, FM, LSM and ESEM are brieﬂy introduced and their properties are discussed. PLM. For the acquisition a standard TLM that is additionally equipped with a polarizer can be used. The achievable resolution is the same as for a TLM (∼ 0.25 μm). Collagen is the only birefringent tissue component in the adventitia and, therefore, becomes visible in the PLM alone. This makes the detection and segmentation of collagen more robust. Because of the rotation-dependent intensity of collagen it is possible to separate overlapping collagen ﬁber bundles with signiﬁcantly different orientations. Although the detection of collagen would reduce to a trivial task, the additional cost for a rotational specimen stage (motorized for automation purpose) and the costly pre-processing to combine the rotated sub-images to one image disqualiﬁes the PLM as an imaging technique for full structure analysis purpose. For a detailed information about PLM we refer to [39]. FM. The phenomenon of ﬂuorescence describes light emission that continues only during the absorption of the excitation light by a chromophore or other conjugated molecule, which is capable of emitting secondary ﬂuorescence [53,54]. Collagen has a strong autoﬂuorescence which makes it suitable for FM. Theoretically the observation of collagen within the tissue does not require any staining. Actually not only the collagen bundles, as was expected, but also some other tissue components such as hemoglobin of the erythrocytes located in vasa vasorum (tiny blood vessel that supply the arterial walls) and muscle tissue shows auto-ﬂuorescence. Because only intensity information was available, the segmentation of these structures become more challenging than in TLM images where color information is available. The method is also destructive and, therefore, has no real beneﬁts compared to other investigated methods. LSM. Similar to FM the LSM exploits ﬂuorescence characteristics of the observed specimen. Imaging is achieved by scanning the focused LASER spot over the sample. The back-scattered light from the sample is used to build an image pixel-wise. By changing the depth of the focal plane (up to 100 μm) and scanning subsequent slices of the sample a three-dimensional image is recorded. The LSM is the only non-destructive method that allows the direct 3D observation of collagen. Figure 1 shows a sequence of

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(a) TLM image of a parafﬁn embedded and EVG stained specimen.

(c) EVG stained specimen under a FM.

(b) In the PLM-image the collagen shows a high (but orientation dependent) contrast which enable an easy detection.

(d) ESEM image of collagen that have been cut with a scalpel.

Figure 2. Images of collagen ﬁber regions obtained by different imaging techniques. All tissue samples stem from different human aortas.

an LSM image stack. [55] gives an overview about the ﬁeld of biological confocal microscopy. The main beneﬁt of a LSM is the possibility to acquire a volume data set in a non-destructive way. This avoids embedding and slicing that has to be carefully done to avoid artifacts. Different tissue structures can be distinguished by excitation with a LASER that is tuned to different wave-lengths. Structures that show no autoﬂuorescence can be immunhistochemically stained to obtain immunﬂuorescence. LSM is expensive and typically provides intensity images only which makes artefact segmentation more challenging. ESEM. The observations with ESEM are restricted to the surface of tissue specimens. Although the tissue can be observed in a wet condition (naturally), embedding and slicing is prevented, which makes a 3D analysis impossible and, therefore, disqualify the method for our purpose. The high resolution of the ESEM allows to observe the surface structures in high detail. The structure of the collagen ﬁber bundles looks quite similar to the observed EVG-stained, Parafﬁn embedded and sliced tissue samples and, therefore, support the proposition, that the structure of the ﬁber bundles is not altered strongly

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Table 1. Overview of the different imaging techniques: y: yes, n: no, r: required, nr: not required, o: optional, 1–5: relative ordering (low-high). Property

TLM

PLM

FM

LSM

ESEM

destructive 3D imaging possible costs to obtain an image stack

y y 4

y y 5

y y 3

n y 1

n n –

ﬁxation staining embedding other structures are visible costs for artifact segmentation

r r r y 3

r o r n 1

r o r y1 2

r o r y1 2

o nr nr y –

observation of wet tissue color information

n y

n n

n n

n n

y n2

1 Depends on the staining. 2 When immunhistology is used, color may be possible.

by the preparation process, required for TLM. The many attempts and history that have led to the present development of ESEM have been reviewed and surveyed elsewhere [56–60]. 2.3. Conclusion Figure 2 shows images obtained by TLM, PLM, FM and ESEM. All imaging techniques require a stitching of images in x- and y-directions to obtain a single high resolution image and a large ﬁeld of view simultaneously. The TLM method combined with Parafﬁn embedded and EVG-stained tissue samples is the best choice among the destructive methods. TLM features the following advantages: (i) it is cheap (ii) different tissue structures yield a high contrast (iii) color information, that supports the artifact segmentation, is available (iv) artifacts can be well separated and (v) the entire structure is visible in a single image. Fixation is required for all proposed methods except ESEM. Table 1 gives an overview of the properties of the different imaging techniques.

3. Overview of the Image Analysis Concept The morphological structure, which is of particularl interest for the biomechanical modeling of the adventitia, appears in the microscopic images as red/magenta bundles of collagen ﬁbrils (see Figs 3 and 4). The ﬁbrils within the bundles roughly share a common ﬁber orientation. The aim of this study is to: • Discriminate between ﬁber and non-ﬁber areas, • extract regions with homogeneous ﬁber orientations, and • provide the size of the homogeneous regions, their mean ﬁber orientations and information about its location in the tissue, and to • characterize the relative stretching characteristics (RSC) of the ﬁber bundles, due to ﬁber crimp. Figure 5 depicts an overview of the proposed concept to reach these goals. The analysis of the collagen ﬁbers is based on TLM images of thin histological tissue samples.

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Figure 3. Microscopic image of an adventitia sample, stained with Elastica van Gieson. The arrow indicates a collagen ﬁber bundle. The ROIs in the image are used to show the mechanism of the proposed algorithm.

50

100 μm

Figure 4. The image shows several types of artifacts: A – back light, B – elastic ﬁbers, C – thick region (no reliable information), D – staining impurity. The arrow indicates a collagen ﬁber bundle.

A 3-CCD camera (Sony DXC-930P), that is built into the optical system of the transmission light microscope, is used to produce images of size 760 × 570 pixels. The optical magniﬁcation (objective ×40, adapter ×0.6) and the dimensions of the CCD chip (6.6 mm×8.8 mm) lead to a total resolution of 0.5 μm square per pixel. The large optical magniﬁcation results in a small ﬁeld of view. Image mosaicing has to be used to obtain large ﬁeld of view images. The mosaic up to six hundred subimages. Intensity inhomogeneities of the light microscope are corrected in the capturing process. The analysis process can be divided into four major tasks: (i) Detection and segmentation of artifacts.

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Figure 5. Overview of the concept.

(ii) Determination of ﬁber orientation. (iii) Segmentation of regions of homogeneously oriented ﬁbers. (iv) Determination of the relative stretching characteristics of the segmented ﬁber bundles. The tissue preparation process causes several artifacts, which have to be located and properly treated during the analyzing process. Unfortunately, the staining procedure used to make the collagen ﬁbers visible is not very stable and might result in a different coloring of the collagen ﬁbers. Figures 3 and 4 show tissue samples, which both have been stained by EVG, but on two successive days. A good algorithm has to be able to cope with the staining variabilities, i.e. neither the segmentation of collagen regions nor the extraction of orientational data are allowed to depend on the individual staining result. To

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cope with this variability we proposed a robust clustering in the RGB-space to segment ﬁbrous and non-ﬁbrous regions (see Section 4). Ridge and valley analyses are applied to the segmented ﬁbrous regions in order to detect the ﬁbers and their orientations (see Section 5.1). The detected ﬁber pixels form small ﬁber strips wherefrom the local ﬁber orientations can robustly be derived. Region growing based on an adjacency graph representation of the ﬁber strips is used to segment homogeneously oriented ﬁbrous regions (see Section 5.2). The analysis procedure ends up with homogeneously oriented ﬁber regions and provides data of their location, shape and mean ﬁber orientation. Due to the crimp of ﬁbers each bundle can be stretched by a certain amount. In Section 6 we show how the 2D orientation statistics of a ﬁber bundle can be exploited to estimate its RSC.

4. Detection and Segmentation of Artifact Artifacts that unavoidable arise in the tissue preparation have to be detected and excluded from analysis. Artifacts may be summarized as: • Tissue distortion caused by slicing – for example, only back light is visible. • Elastic ﬁbers that are also stained. • Sliced tissue which are too thick – no reliable information about the ﬁbrils can be extracted. • Staining impurities. • Pieces of other tissues are included – for example, muscle tissue. • Unstable coloring – different tissue sets are differently colored. Some typical artifacts that occur in histological images are shown in Fig. 4. The artifacts do not contain any information about the ﬁber structure and disturb the analysis of the real ﬁber properties. Generally, the entire process is driven by the motivation to robustly detect actual ﬁber regions. Non-ﬁber regions do not contain meaningful orientation information, and, therefore, if not rejected from further analysis it will adulterate the orientation statistics. On the other hand, classifying ﬁbers as non-ﬁbers is acceptable, because the global orientation statistics is not inﬂuenced. In order to allow an unsupervised ﬁber segmentation the algorithm requires the following properties from the images: • Fibers within a single image are colored equally. • Based on our experience we concluded that more than 50% of the image should be covered with ﬁbers. • Fibers emerge in bundles that feature a common ﬁber direction. These conditions require manual pre-selection of the images, which is typically performed in the required microscopic image capturing process anyway. Typical specimens contain many regions that satisfy these conditions. When these constraints are satisﬁed ﬁbers form a compact cluster of ellipsoidal shape in the RGB-space. In order to segment the ﬁber regions we use a robust clustering algorithm in the RGB-space to detect the ellipsoid. The clustering algorithm makes use of the so called Mahalanobis distance [73], [74, chapter A.5.1] to robustly detect the ﬁber cluster. The squared Mahalanobis distance r 2 (n) = (v(n) − mv )T C−1 v (v(n) − mv ) in a 3D space gives the same distance for all points located on an ellipsoid, where v(n) denotes the RGB

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(b)

Figure 6. Detected ﬁber regions (a), detected non-ﬁber regions (b) taken from Fig. 3. th feature vectors

Nof the n -pixel in the image. An ellipsoid can be speciﬁed by the mean mv = 1/N n=1 v(n) that deﬁnes the position in the feature space and the covariance

T matrix Cv = 1/(N − 1) N n=1 (v(n) − mv ) (v(n) − mv ) that deﬁnes its elongation and direction. In order to avoid inﬂuences from other regions an α-trimmed estimator [75] is used to iteratively reﬁne the estimate of mv and Cv that describe the ellipsoidal color cluster of ﬁbers, and stops if a stable clustering is found. In order to obtain a single gray level image for further analysis, a Hotelling transform [77, chapter 11] also known as principal component analysis (PCA) can be applied to the feature vectors associated with ﬁbers. The Hotelling transform is deﬁned as w(n) = E(v(n) − mv ), where the rows of the matrix E correspond to the eigenvectors of Cv . The eigenvectors are sorted in a manner so that the eigenvector with the highest eigenvalue is placed in the ﬁrst row and the eigenvector with the smallest eigenvalue is placed in the last row. The projection of the vectors v(n) − mv (n) onto the eigenvectors of Cv is denoted by w(n), whereby the projection to the eigenvector in the ﬁrst row – the ﬁrst principal component – features the highest variance. The ﬁrst principal component is then used to transform the entire RGB-image. With this approach the gray level image preserves the maximum information and is insensitive to the variations of staining. Typically the ﬁrst principal component accounts for more than 90% of the variance.

5. Orientation Analysis 5.1. Determination of Fiber Orientation The determination of the ﬁber orientation is based on a ridge and valley analysis [78]. The gray value proﬁle of a single ﬁber looks simple. If the ﬁbers appear as bright lines in the image, their proﬁles in the orthogonal direction show a dark-bright-dark transition that forms a ridge. If the ﬁbers appear dark or they are located near by each other and cause a small gap in between (like in our case), the proﬁle features a bright-dark-bright transition or a valley. Ridges (valleys) feature two signiﬁcant properties in their proﬁles. First, a high negative (positive) second derivative. Second, they should be a local maximum (minimum).

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The directional second derivative of a 2D image I in a direction, u say, can be calculated with the Hessian [79, Chapter 14.314] according to Ixx Ixy 2 . (1) (∇u I ) = Iyx Iyy The eigenvalues of (∇u2 I ) are equal to the minimum and maximum values of the second directional derivative. Their associated eigenvectors point in the corresponding directions. These two directions are orthogonal to each other. Compared with the algorithm described in [46], which is designed to work on images, where ﬁbers appear as continues curvy structures, in our case the ﬁbers do not appear as single continuous structures. Usually ﬁbers are grouped into bundles of ﬁbers, where one ﬁber may suddenly end/start, or will be occluded from other ﬁbers. This fact makes it difﬁcult to pursue a single ﬁber in a bundle. For the analysis of ﬁbers that appear as continuous curvy structures the algorithm described in [46] may be applied. However, for our case we have ﬁbers which are grouped into bundles, where one ﬁber may suddenly end/start, or will be hidden from other ﬁbers so that the algorithm in [46] would fail. The discontinuous ﬁber structure makes it difﬁcult to pursue a single ﬁber in a bundle. However, to gather overall statistical data of the tissue it is not necessary to know the exact shape of a single ﬁber within the tissue. It is sufﬁcient to know where bundles of nearly parallel ﬁbers are located, and what their mean ﬁber orientations are. Therefore, it is sufﬁcient to determine partial ﬁber segments and group similar segments. There are several beneﬁts that make the detection by ridge and valley analyses attractive: (i) The detected ﬁber pixels form small ﬁber strips in a natural way (no separate joining process is required). (ii) The detection of small ﬁber segments that connect a couple of pixels results in a more robust algorithm with respect to noisy data. (iii) The small ﬁber segments can be used in a further analysis to pursue the trace of a single ﬁber within a ﬁber bundle in order to gain information about its mean elongation. During the process two images are generated, one for ridges (positive eigenvalues), and the other one for valleys (negative eigenvalues). For each ridge and valley pixel the directional information (orthogonal direction to the eigenvector) is recorded. All possible directions in the 2D space are mapped into the angular space ranging from −π/2 to +π/2, whereby the value 0 corresponds to the vertical axis. To guarantee ﬁber strips with one pixel thickness a morphological thinning operation is performed [76, chapter 11]. Strips that consist of less than four pixels do not have an acceptable angular resolution and are removed. Based on the third region of interest (ROI) (Fig. 7(a)) according to Fig. 3, the resulting ridge and valley images are shown in Figs 7(b) and 7(c), respectively. To produce consistent ﬁber strips the ridges and valleys are cross-checked with each other. We can then exploit the fact, that neighboring valleys and ridges should feature a similar orientation. For each ridge (valley) pixel a cross-check operation with its nearest neighbor valley (ridge) pixel is performed. If their directional differences are lower than a predeﬁned threshold, the pixel is assumed to be a real ridge (valley) pixel, otherwise it is removed. Due to the fact that the intersection of detected ridge and valley pixels is zero, it is possible to combine the strips into one label image (see Fig. 7(d)), where each ﬁber is associated with a distinct label and the background (no detected ﬁber) is represented by the label 0.

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(a)

(b)

(c)

115

(d)

Figure 7. Fiber strip detection. 3rd ROI from Fig. 3 (a), thinned ridges (b), thinned valleys (c), and valid ridges and valleys (d).

In order to improve the robustness of the orientation estimate the directions of the ﬁber strips are derived from the end points of a strip. The end points that yield the largest Euclidian distance are chosen to represent the real ﬁber strip end points and determine its angle. Because the number of potential end points in a single ﬁber strip is very low (typically between two and four) the computational costs of the brute force calculation is acceptable. 5.2. Segmentation of Regions of Homogeneously Oriented Fibers Region-based segmentation [76, chapter 5] is used to segment regions of homogeneous ﬁber orientations. In order to enable the region growing it is necessary to establish neighborhood relations between the ﬁber strips. A distance map [80, chapter 7] that can be derived from the label image is used to create small patches around each ﬁber strip. Typically, neighboring ﬁbers are parallel to each other and have a similar mean orientation, i.e. they are homogeneously oriented. Therefore, it is possible to assign the orientation of a ﬁber strip to pixels in its close neighborhood. It has been experimentally veriﬁed that up to a distance of approximately 5μm (10 pixels) from the ﬁber strip the homogeneity assumption holds. This distance is used to create a small region of a homogeneous orientation around each ﬁber strip. The next task is the selection of proper seed patches for the region growing process. For each ﬁber patch the following data is calculated: • The Euclidian distance, i.e. dp , between the determined end points. • The orientation of the ﬁber strip αp . • Statistical parameters (mean and standard deviation) derived from the orientation data of the distinct ﬁber strip pixels. When calculating the statistics, the circular character of the angular distribution has to be taken into account [81,82]. It is not possible to use the standard summation formulas to estimate the mean and the variance of the distribution. For example, the angles −π/2 and +π/2 essentially describe the same orientation, namely that of a horizontal line. However, a straightforward summation and division by two would result in a middle angle of 0 which is equivalent to a vertical line! Also the distance between angles has to have a circular character, i.e. dcirc(α1 ,α2 ) = min(|α1 − α2 |, π − |α1 − α2 |). Histograms that divide the angular range into bins are built for each ﬁber strip. Before the statistical parameters can be derived from the histogram it is smoothed with a eight tap FIR low-pass ﬁlter [83, chapter 7]. The mean orientation of the

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ﬁber strip pixels is estimated by selecting the maximum value in the smoothed histogram. The standard deviation sp can be estimated by circular shifting the histogram so that the mean becomes zero and calculating the second moment of the distribution. The parameters dp and sp are used to generate a scalar value wp , i.e. a weight, for each patch that describes its suitability to be a seed patch. It is given by wp = pdp (n) [1 − psp (n) ], where the weight wp ∈ [0, 1] ranges between 0 and 1, and pdp (n) = dp(n) /max(dp ), psp (n) = sp(n) /max(sp ) are the normalized Euclidean distance values and values of standard deviations, respectively, and, as a result of the normalization, they also range between 0 and 1. Hence, long ﬁbers (pdp (n) 0) with a small angular standard deviation (psp (n) 1) will gain a large weight wp . Region growing that merges neighboring regions with similar characteristics is used to segment regions of a homogeneous ﬁber orientation. The circular character of the angle distribution has to be considered [81,84]. Among all non-grown patches the patch with the largest weight is used as the next seed patch in the region growing procedure. To reduce the computational costs of the growing process, a region adjacency graph is used [85, chapter 6]. A region adjacency graph features some essential beneﬁts compared with the pixel-oriented description: • Only a few thousand patches instead of hundreds of thousands pixels have to be considered. This speeds up the growing process by approximately 60% to 70% (the additional costs for the generation of the map are included!). • If one region is merged with another region, all regions that are adjacent to the new one are known immediately. The boundary does not have to be scanned pixelwise. • The pixel statistics of the new regions can be derived from the already calculated histograms by simply adding them. • The adjacency graph permits an easy way for a smart seed point handling by exploiting the structure of the adjacency matrix. • Subsequent processing steps can make use of the region adjacency graph. The adjacency matrix A that describes the graph consists of N columns and N rows, where N is the number of regions. If region number j is adjacent to region number i the corresponding elements (A)j i and (A)ij have to be set. This results in a symmetric matrix. Figure 8 shows the ﬁnally obtained grown regions. The angle values are depicted in false color representation. Figure 9 shows the major processing steps of the algorithm by means of the ﬁrst ROI (left column) and the second ROI (right column) taken from Fig. 3.

6. Relative Stretching Characteristics Beside the global structure information such as the location and principal orientation of a collagen ﬁber bundle in the soft tissue (see Sections 4 and 5.1), in biomechanic modeling the more detailed structure information such as the characterization of the bundles stretching characteristics is of particular interest. This section presents a method to obtain the relative stretching characteristics (RSC) of collagen (ﬁbrous) bundles based on

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Figure 8. Grown regions, based on Fig. 3, illustrated in a false color representation of the orientation information.

(a)

(b)

(c)

(d)

Figure 9. The major processing steps of the algorithm are shown by means of the ﬁrst ROI taken from Fig. 3: masked non-ﬁber region (a), and masked ﬁber region in the Hotteling transformed gray scale image (b). Both steps are based on the segmentation algorithm introduced in Section 4. Fiber patches (arbitrarily colored) with corresponding valid ﬁbers according to the ridge and valley analysis introduced in Section 5.1 (c). Grown region illustrated in a false color representation of the orientation information (d).

the analysis of microscopic tissue images. We show, how the orientation statistics of local orientations in a bundle can be directly related to the RSC. The von Mises distribution (VMD) – a circular probability distribution – is used to describe the 2D orientation statistics. The κ parameter of the VMD is used to obtain the mean stretching and the probability density function (PDF) of the bundles’ RSC is identiﬁed. Figure 10 shows a typical TLM image of adventitial collagen ﬁber bundles with a corresponding orientation histogram of a ROI. The collagen in the image appears as ﬁbrous bundles with a principal direction. The crimp of the ﬁbers within the bundle determine the stretching characteristics of the bundle. The bundles can be stretched until their ﬁbers reach their straightened lengths. Due to many occlusions and sectioning of the ﬁbers, as a result of the slicing procedure, the robust pursuing of single ﬁbers in the bundle is not a trivial task. Our goal is to directly estimate the RSC from the image gradients in a ﬁber bundle region, thereby avoiding the error-prone process of analyzing single ﬁbers. One of the most important ﬁber bundle parameters is the mean stretching of the bundle, thus =

Mean ﬁber arc-length . Length of the ﬁber bundle

(2)

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250 200 150 100 50 0 60

(a)

30

0

30

60

(b)

Figure 10. TLM image of adventitial collagen ﬁber bundles (a). Orientation histogram of the ROI, as depicted in (a), where on the x-axis α is plotted and the frequency on the y-axis (b).

6.1. Modeling the Fiber Bundles An application of accurate gradient ﬁlters [86] to the microscopic image results in large antiparallel gradients with the same orientation on opposing points of the ﬁber wall. The orientation of the measured gradient that has been rotated by π/2 rad can be interpreted as a tangent on the ﬁber or assuming a linear oriented ﬁber bundle, as the local slope of the ﬁber with respect to the principal bundle orientation. If the ﬁber is considered as a function, the slope corresponds to its ﬁrst derivative. Orientation histograms, calculated from the local orientation information of ﬁber bundles in TLM images, show approximately a VMD [82], according to p(α, μ, κ) = 1/(2π I0 (κ)) eκ cos(α−μ) , where 0 ≤ μ ≤ 2π, κ ≥ 0 are parameters, p is the PDF, I0 (κ) is the modiﬁed Bessel function of the ﬁrst kind [87, chapter 6], and α is the local ﬁber angle. The VMD is a circular probability densitiy function (CPDF) similar to the Gaussian distribution in the linear case, but accounts for the inherent discontinuity in circular data at 0 rad and 2π rad, respectively. Figure 10(b) shows the orientation histogram of a ROI taken from the TLM image shown in Fig. 10(a). It contains a huge part of collagen ﬁber bundles. A further observation that has been made is that ﬁber bundles are oriented along a principal orientation. Due to the fact that Gaussian processes remain Gaussian when processed by linear time invariant (LTI) system and a ﬁrst derivative ﬁlter belong to the class of LTI systems, the ﬁlter output, that was revealed as the local slope of the ﬁber, has also a Gaussian distribution. This is in agreement with the measured VMD of the orientation data within a bundle that under certain conditions [82] can be approximated by a normal distribution. Next, we will mathematically describe a bundle in order to derive a framework that allows us to estimate the stretching. Let t, x and y be the components of a coordinate system spanned by the orthogonal basis (t, x, y), whereby the vector t corresponds to the principal direction of the ﬁber bundle, and the vectors x and y span the plane of the bundle-cross-section. Then, η(t, x, y) = [ηx (t, x, y) ηy (t, x, y)]T denotes a 3D continuum (bundle volume) of the local 2D elongations – in the directions x and y – of the linear oriented bundle ﬁbers. The vector components of η can be approximated reasonably well as ﬁltered, zero-mean, 3D white Gaussian noise (WGN) processes (see also Fig. 13),

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45 40 6

35 30

4 y

25 20

2 15 0 6

10 4

5 2

0

0

t

x

(a) Figure 11. The images show a generated 3D ﬁber bundle. The ﬁbers located in the same x/t-plain are colored equally. Neighboring ﬁbers are correlated.

thus ηx (t, x, y) = N 3 (0, ση ) ∗ h, ηy (t, x, y) = N 3 (0, ση ) ∗ h, where ∗ denotes a 3D convolution, N 3 (0, ση ) is a 3D zero-mean WGN and h is a 3D LTI impulse response that determines the spectral content. The lack of a dominant vibration direction is modelled by a rotational symmetric Gaussian distribution, with the covariance matrix C = ση2 I, for the ﬁber elongation, with the non-zero components Cxx = ση2 and Cyy = ση2 . In other words, the measured Gaussian distribution of the ﬁber orientations can be assumed isotropic in all orthogonal directions to the main bundle orientation. This fact enables the estimation of the 3D RSC from 2D images. Figure 11 shows a 3D ﬁber bundle generated with the introduced generative model. 6.2. Stretching Characteristics The mean ﬁber arc-length E {a(l)} [88] of the 3D ﬁbers within a bundle of length l, where a denotes the random variable for the ﬁber arc-length, can be calculated as

l E {a(l)} = E η˙ x2 (t) + η˙ y2 (t) + 1dt 0

=E

η˙ x2 (t) + η˙ y2 (t) + 1

l

dt = l,

(3)

0

where (˙) denotes the ﬁrst derivative with respect to t, and =

E {a(l)} =E η˙ x2 (t) + η˙ y2 (t) + 1 = E {} l

(4)

denotes the mean stretching. Next we will derive the PDF p () of the random variable (RV) = η˙ x2 + η˙ y2 + 1 and show how the expectation value E {} can be calculated.√ First we introduce the RV r = η˙ x2 + η˙ y2 and rewrite = r + 1 = g(r), where g(r) is the function that relates both RVs. The components ηx and ηy are normal distributed random processes with distribution N (0, ση ), therefore their ﬁrst derivatives are also normal distributed with N (0, σd ) because of the linearity of the derivative operation,

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1.4

1.8

1.2

E{φ}

1.6

1 σ

1.4

0.8

d

0.6 0.4

1.2

0.2 1

0 0

0.2

0.4

σd

0.6

0.8

1

0

(a) σd [0 . . . 1]

100

200 κ

300

400

(b) σd (κ)

Figure 12. Mean stretching = E {} as a function of σd ∈ [0, 1], (a). Relation between σd and the parameter κ (b).

where σd denotes the standard deviation of η˙ x and η˙ y . The PDF of r, that is the sum of two squared identically and independently distributed RVs with the PDF N (0, σd ), is given by the chi-square distribution pr (r) χ 2 (2, σd ) [88]. The general relation of a PDF of a RV , which is the transformation of the RV r with PDF pr (r) by the invertible and differentiable function g(r) is given in [89]. Using this relation we may determine the PDF of to p () = /σd2 exp(−(2 − 1)/(2σd2 )). Because g(r) is a monotonically increasing function, the range of can directly be determined as : 1 ≤ ≤ +∞. The expectation value E {} or the mean stretching can now be calculated as +∞ 1 3 1 2 (5) (σd ) = p ()d = σd 2e σd , 2 , 2 2σd 1 where (a, x) denotes the upper incomplete gamma function with the gamma function argument a and the lower boundary x [88]. The integral in Eq. (5) has no closed solution but can be calculated using standard tables. Figure 12(a) shows the graph of the expectation value E {} as a function of σd . Using these results, we are able to calculate the stretching – actually the whole PDF – when σd is given. However, our goal is to use the parameter κ of the VMD, which can be measured directly from the image. Therefore, we are interested in the function σd (κ). The variance of the angle α to the principal axis of the bundle and the variance of the slope σd2 are related by, E α2 =

+∞

−∞

tan2 (ζ ) √

1 2πσd

2

e

− ζ2 σd

dζ ,

(6)

which represents an injective (one-to-one) relation. For σd < 1.5 (real ﬁbers have a maximal σd of approximately 0.5), the parameter κ of the VMD has also a one-to-one relation to the variance of α – as E{α 2 } increases monotonically, κ decreases monotonically. Hence, it is possible to establish a one-to-one relation σd (κ), see Fig. 12(b). Unfortu-

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nately, the function (6) has no closed-form solution. For practical calculations we have approximated (6) by a smoothing spline of order two that was ﬁtted into 300 numerically calculated data points. The proposed algorithm can be applied to the ﬁber bundle regions that have been segmented with the procedure described in Sections 5.1 in order to estimate their RSC and, in particular, to estimate their mean stretching that represents an important bundle parameter for biomechanical modeling.

7. Experimental Evaluation The tissue samples that have been used in our experimental evaluation come from human iliac arteries, which have the function to supply oxygenated blood to the feet. In order to obtain adventitial specimens the adventitia is ﬁrstly dissected from the two inner most tissue layers, i.e. the intima and media. Afterwards, small (1 cm × 1.5 cm) axial and circumferential (tissue) samples are cut out from the adventitia. To obtain specimens suitable for TLM, the tissue samples are embedded in parafﬁn and stained with EVG, which is standard in histology (see Section 2.1). The evaluation of our algorithms has proven to be difﬁcult. Because of the following reasons it became necessary to develop our own evaluation method: (i) No standardized method for the evaluation of ﬁber orientations in soft tissues such as blood vessels exists. (ii) We did not ﬁnd any standard data set to test our developed algorithms. (iii) Rare studies in this area were performed with different image acquisition techniques that require different preparation techniques and, therefore, prevent a direct comparison. Besides that, the detail-level (resolution) of other approaches typically is in another scale or the type of information is different and, therefore, meaningless. 7.1. Orientation Analysis For the purpose of comparison eight images were manually segmented and compared with data obtained from the proposed algorithm. The images were taken with the microscope setup described in Section 3 and manually pre-selected in order to meet the 50% ﬁber coverage condition, which we claimed in Section 4. In particular, between 27 and 164 polygonal regions of homogeneous ﬁber orientation were manually segmented per image, and mean ﬁber orientations indicated by straight lines. The manual segmentation contains no or only a negligible amount of artifacts and should be almost completely detected as ﬁber regions from the automatic analysis. Due to limited resources a tedious separate segmentation of small artifacts was not feasible. On average the algorithm required 30 seconds analyzing time for one image. The code is not optimized yet and further speedups are possible. Compared to manual segmentation that takes several hours per image, it is a signiﬁcant improvement. Furthermore, the automatic analysis generates more detailed information than a human is able to segment manually.

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Table 2. Area statistics of the grown and manually segmented regions of eight different images (rows of the table). GR: grown region, #GR: number of GR region, MS: manually segmented region, #MS: number of MS region, Intersec.: intersecting area of GR and MS regions, Overseg.: GR regions that are not intersecting with MS regions, Underseg.: MS regions that are not intersecting with GR regions. The percentages of the segmented regions are with respect to the entire image area (760 × 570).

#GR

#MS

GR

MS

Intersec.

Overseg.

Underseg.

1012 1024 1152 1227 1331 1252 1182 974

164 30 43 29 34 27 51 43

57.6% 54.2% 68.6% 66.0% 68.1% 67.8% 50.9% 38.8%

29.2% 17.4% 20.3% 8.7% 12.6% 7.1% 8.9% 5.8%

27.4% 16.2% 19.4% 8.0% 11.7% 6.8% 8.2% 4.5%

30.2% 38.1% 49.2% 57.9% 56.4% 61.0% 42.7% 34.3%

1.8% 1.2% 0.8% 0.6% 0.8% 0.3% 0.7% 1.4%

On average the algorithm segmented approximately 60% of an image into ﬁber areas. By visual inspection we saw no false segmentation. Because of the big effort necessary for a manual segmentation, on average only 14% of the image areas where manually segmented, i.e. only for those regions where it was easy to identify a ‘meaningful’ ﬁber orientation. Table 2 shows the area statistics of the grown and manually segmented regions of eight different images indicated by the rows of the table. The ﬁrst two columns indicate the numbers of segmented regions. The third and fourth columns indicate the percentages of the segmented regions with respect to the entire image area (760 × 570). Column ﬁve shows the percentage of intersecting areas between grown and manually segmented regions. It turns out that, on average, 92% of the manually segmented regions coincide with the grown regions, which is satisfying. This becomes apparent in the similar values of column four and ﬁve in Table 2. The intersecting regions were used for the comparison purposes. Columns six and seven result as the differences of columns three and ﬁve, and four and ﬁve, respectively. Typically, one manually segmented region is intersected with 4–10 automatically segmented regions. The angle differences of the intersections are used to determine a mean deviation of the angles for each manually segmented region. The angle differences are weighted with respect to their areas. Table 3 depicts the statistical parameters of the mean angles between manually and automatically segmented regions. Each row indicates the evaluation for one image, where N is the number of regions per image for which the evaluation is performed. We evaluated the mean angular deviation μ, its standard deviation σ , and the Median value of the differences. The mean angular differences and the corresponding standard deviation follow a Gaussian distribution over all manually segmented regions within an image. Table 3 shows the parameters of these distributions. The distribution of the angle differences over the entire image is about zero-mean, with a standard deviation of 10.75 degrees. The angular difference (standard deviation) within a single manually segmented region is about 14 degrees. The zero-mean distribution conﬁrms the reliability of the algorithm and the standard deviation indicates the higher angular resolution of the automatic analysis compared with the manual segmentation.

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Table 3. Statistical parameters of the mean angle distribution. The table depicts the relation between manual and automatic segmentations. For each manually segmented region a mean angular difference between itself and the intersecting grown regions is calculated. Each row indicates the evaluation for one image. N is the number of regions per image for which the evaluation is performed. We evaluated the mean angular deviation μ and its standard deviation σ as well as the Median value of the mean angular differences. N

μ

σ

Median

164

−2.0

11.0

−1.7

29 43 29 34 27 51

2.8 −1.2 6.8 −0.8 0.6 3.8

11.5 7.8 11.2 10.3 11.2 10.9

1.2 −0.5 6.4 −1.8 −1.1 3.3

39

−4.3

8.4

−4.8

The comparative study suggests the following beneﬁts of the automatic segmentation procedure over the manual procedure: • It is possible to segment a much larger part of the image. • Since individual ﬁber strips are assigned an angle we have a much ﬁner resolution of the angular distribution. • An automatic analysis needs only a fraction of the time with respect to a manual analysis. This comparison proves the reliability of the proposed algorithm, and shows, in addition, that the algorithm produces results that are comparable with a manual segmentation. 7.2. Relative Stretching Characteristics For an evaluation of the RSC it is hardly possible to manually extract meaningful stretching information from the microscopic images. Therefore, we have performed an exhaustive accuracy analysis of the proposed algorithm on artiﬁcial images of naturally rendered ﬁber bundles with well known characteristics and have compared the measurements with the expected RSC. Five images from 40 groups with different bundle characteristics over the entire valid range – bandwidth B : [0.02 0.25] normalized frequency and magnitude ση : [0.5 20] pixel – have been used for the analysis. Additionally, each group was rendered with ﬁbers of 1, 2 and 3 pixel in diameter, resulting in a total of 600 test images (see Fig. 13 for two examples). The RSC ranges between : [1 1.5], which corresponds to a σd : [0.1 1.2]. For stability we use gradients on Canny edges only. Figure 14 shows the distribution of the absolut error || and the relative error rel over the full RSC range, and Table 4 depicts the statistical parameters of the error distribution. The mae (mean absolut error) || for bundles that consist of ﬁbers with a typical diameter of two pixels is only a 0.4% while the mae of the relative error is 4.3%. Most of the larger relative errors occur for small values of < 5% that correspond to small absolute errors and are, therefore, negligible. For typical (expected) ﬁber bundles rel is below 3% over the entire range. The method was also tested on real images. The absolut error, using manually estimated ﬁbers as reference data, was typically below 2%.

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(a)

(b)

Figure 13. Artiﬁcial ﬁber bundle images with ﬁbers of a different variance (a) and frequency content (b).

8. Conclusion and Outlook In order to develop reliable biomechanical models of biological soft tissues it is crucial to have detailed insights in the structural arrangement of collagen ﬁbers. The quantitative knowledge of the actual ﬁber orientation statistics in soft tissues can be used to improve the biomechanical modeling. To obtain the speciﬁc (structural) parameters of homogeneously oriented collagen in soft tissues fully automatical, more precisely in the outermost layer of arteries, computer vision methods have successfully been applied to histological light microscopic images. The developed computational framework makes it possible to automatically analyze a large number of tissue samples for gaining signiﬁcant statistics about the ﬁber arrangement within the soft tissue. The method detects various artifacts in the microscopic images and excludes them from further analysis. Based on robustly determined orientational data, the ﬁbrous regions are segmented into regions of homogeneous ﬁber orientations. Parameters such as the area of a segmented region and the ﬁber orientation statistics are calculated for each region. It has been shown that the automatic analysis procedure features a couple of beneﬁts when compared with a manual segmentation process. It becomes possible to segment a much larger area with a higher angle resolution within a much smaller time period as it would be required by a human operator who performs manual segmentations. The main feature is the fact that the segmentation procedure guarantees an objective data analysis. Furthermore, a convenient method for the estimation of the relative stretching characteristics (RSC) of 3D ﬁbrous bundles based on TLM images was presented. The RSC estimation is based on orientation statistics in a ROI – ﬁber bundle – only, which makes it very fast and avoids the difﬁcult task of accurately estimating single ﬁbers. The estimated RSC are sufﬁciently accurate to be used in biomechanic models. In our future work the following issues will be of particular interest: • In our next step we want to analyze LSM images in addition to TLM images. Even though LSM features the possibility to easily obtain a registered 3D image stack, it typically provides intensity rather than color information. Therefore, we will study the artifact segmentation based on texture, that should work on TLM images and on LSM images respectively. • Furthermore, the grouping procedure in the segmentation may be enhanced by exploiting bundle characteristics such as the RSC (described by the model) in order to become more robust. For the ﬁber bundle segmentation also other approaches seem to be interesting. For example, it is possible to use the generative ﬁber bundle

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4

125

25 20

3

15

2 |ε|

ε

1

10 rel

5 0

0

5

1 2

10 15

0

10

20

ρ

30

40

0

50

10

20

30

40

50

ρ

(a)

(b)

Figure 14. Scatter plots of absolut errors || (a) and relative errors rel (b) of the estimated stretching for bundles over the entire RSC range with a ﬁber diameter of two pixels. All values are given in percent. Table 4. Error statistics for the relative error rel and absolut error || of the measured mean stretching . d: ﬁber diameter, std: standard deviation, mae: mean absolute error. error

d

mean

std

mae

median

rel || rel || rel ||

1 1 2 2 3 3

−3.921 0.097 1.503 0.126 6.595 1.233

10.211 3.488 5.825 0.715 16.720 6.692

6.375 0.570 4.345 0.403 9.064 1.470

−2.532 −0.201 0.351 0.017 0.907 0.046

model in a model based segmentation approach or to robustly estimate representative ﬁbers (single ﬁbers can not be extracted) directly into the gradient ﬁeld of the tissue image and group them in order to segment individual ﬁbers into bundles. • The ﬁber bundle model, shortly introduced in Section 6, can be used for the generation of artiﬁcial tissue images with well deﬁned characteristics. The bundle characteristics are determined by the model parameters. Vision algorithms for structure analysis can be applied to recover the bundle parameters from microscopic images as well as from artiﬁcial images. The recovered bundle parameters from microscopic images can be used to generate artiﬁcial images with same characteristics as the microscopic images, and the recovered parameters from artiﬁcial images can be compared to the known model parameters and, therefore, may serve as golden standard. • As a matter of course, to reveal the exact structure of collagen ﬁber bundles it is necessary to extend the analysis into the third dimension. One approach will be to use a stack of images of successive histological samples similar to the image stacks obtained by, e.g., CT, MRI or LSM. The individually segmented and registered histological tissue slices can be used to segment the collagen ﬁber bundles in the third dimension.

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Plaque Imaging: Pixel to Molecular Level J.S. Suri et al. (Eds.) IOS Press, 2005 © 2005 The authors. All rights reserved.

Image Based Biomechanics of Coronary Plaque Rosaire MONGRAIN a , Richard L. LEASK a , Ramses GALAZ a , Adrian RANGA a , Jean BRUNETTE b , Anil JOSHI c , Jean-Claude TARDIF b and Olivier F. BERTRAND d a McGill University, McGill, Canada b Montreal Heart Institute, Université de Montréal, Montreal, Quebec, Canada c University of Toronto, Toronto, Ontario, Canada d Laval University, Quebec City, Quebec, Canada Abstract. In this chapter we present recent developments in the modeling of coronary artery biomechanics. We ﬁrst introduce the pathology and localization of lesions in the circulatory system. Recent ﬂuid and structural modeling of CAD is presented and discussed. At the end of the chapter, we present recent effort in coupling these two modeling domains using ﬂuid-structure interaction (FSI).

1. Introduction The progression and treatment of coronary artery disease (CAD) is dependent on vessel biomechanics. Vascular cells respond to biomechanical forces by altering their structure and function. The focal nature of CAD is hypothesized to be due to endothelial cell dysfunction stimulated by abnormal hemodynamic forces1 . Treatment of coronary artery disease depends on reestablishing normal ﬂuid dynamics while stabilizing the solid mechanics of the vessel wall. Much recent advancement has been made in the study of coronary artery dynamics and plaque stability. 1.1. Coronary Artery Disease In humans, atherosclerosis starts at an early age in regions of complex hemodynamics2 . The ﬁrst stage of lesion formation is a ﬁbromuscular thickening of the intima (the tissue layer covered by the endothelial cells)3 , Fig. 1. Clinically, the early stages of atherosclerosis are often missed by traditional medical imaging diagnostics due to compensatory enlargement (remodeling) of the vessel preserving luminal geometry4 . With age, these lesions can accumulate lipids, calcify, erode, thrombose and rupture. The progression of atherosclerosis to plaque rupture is not required to create a clinical event. Intimal thickening itself may be sufﬁcient to constrict the ﬂow of blood. Moreover, erosion of the endothelial layer in areas of focal ﬁbromuscular IT (and little to no lipids) is a consistent feature in about 40% of sudden thrombotic cardiac deaths5 . Thrombosis associated with erosion and ruptured atherosclerotic plaques are principal causes of infarcts.

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Figure 1. A) A relatively healthy coronary artery with very little intimal thickening. B) An eccentric coronary plaque with a ﬁbrous cap.

Biomechanical forces can weaken and damage coronary plaques, allowing direct contact between the blood and the pro-aggregative content of the atheroma, resulting in an inﬂammatory process and thrombus formation6 . Whereas it was previously believed that the percentage of obstruction was the best predictor of clinical consequences, it has been demonstrated that the content of the plaque is more important determinant of plaque vulnerability. Vulnerable plaques are now understood, in general, to have less than 50% stenosis on angiography7 . High-risk plaques usually demonstrate a large lipid pool and a thin ﬁbrous cap. The rupturing of the plaque is ultimately a biomechanical process where the mechanical properties of the plaque are not sufﬁcient to withstand the different mechanical forces resulting from blood circulation. Plaque location within the coronary tree is not random. In the left coronary artery (LCA) lesion formation tends to localize to regions of bifurcation8,9 . The proximal portion of both the LCA and right coronary artery (RCA) are high probability sites of plaque formation10–12 . This pattern of disease has led to a “geometric risk factor” hypothesis implicating local hemodynamic factors in atherogenesis13,14 . The causal forces for this localization are still debated though it has been suggested that low wall shear stresses (WSS), present at the inner wall of bends and at the hips of branches and bifurcations, are atherogenic. Other studies have implicated low, or low and oscillating, WSS in atherogenesis in other arteries15–19 . 1.2. Biomechanics of Coronary Plaque Mechanical stresses applied on the arterial wall and blood are factors in CAD formation and stability. In recent years, numerical methods have played an increasingly important role in modeling and analyzing coronary artery dynamics. Numerical models have been used to investigate the role of hemodynamic forces in CAD, identify plaque conﬁgurations at a high risk of sudden rupture and to help design intravascular devices. These computational models have aided our understanding of the mechanisms involved in the development of atherosclerotic plaque. Many biomechanical measures have been shown to correlate with disease location, severity and proatherogenic biochemical pathways. From a mechanical and computational point of view, a main obstacle in developing realistic models of coronary artery pathologies has been the presence and interaction of two physical domains: the ﬂuid and the structural. Due to this difﬁculty, the vast majority of published computational studies have chosen to focus either on the structural mechanics of the atherosclerotic vessel wall, or on the ﬂuid mechanics within the lumen. New

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studies are now being conducted that take advantage of advancements in numerical computations to couple the solutions to both the ﬂuid and structural domains (ﬂuid-structure interaction or FSI).

2. Numerical Methods In this section, we present the constitutive models used to study the ﬂuid and solid mechanics of CAD and a method to study FSI. 2.1. Blood Flow Constitutive Model Blood is not a simple ﬂuid; it is a living tissue whose functions and properties are known to be inﬂuenced by chemical and mechanical factors. Therefore, modelling such a ﬂuid is a difﬁcult issue unless the model is restricted to speciﬁc ﬂow conditions where some simplifying assumptions can be made. Coronary artery blood ﬂow in the main branches can be adequately modeled as an incompressible, Newtonian ﬂuid in a rigid vessel. The continuity equation (1a) and the non-dimensional Navier-Stokes equation (1b) can be solved to describe the ﬂuid dynamics for pulsatile ﬂow. • u = 0 1 2 α 2 ∂ u + u • ∇ u = −∇p + ∇ u Re ∂t Re

(1a) (1b)

Equation (1a) governs a continuum of incompressible ﬂuid. In equation (1b), the time derivatives of the velocity vector is multiplied by a dimensionless coefﬁcient, where α is the Womersley number (α = R(ω/ν)1/2 with ω the heart beat frequency, R the diameter of the vessel and ν the kinematic viscosity), Re is the Reynolds number (which reﬂects the relative importance of convective forces to viscous forces), u is the velocity vector and p is the pressure (normalized with an appropriate reference pressure). 2.2. Vascular Wall Constitutive Model To properly model the biomechanics of coronary artery tissue including plaques requires an understanding of the material properties of the vessel wall20,21 . Histological studies have shown that the mechanical properties of atherosclerotic vascular tissues are very complex and depend on several factors such as topographical location, vascular wall composition, age, physiology and pathobiology22–26 . Owing to this complexity, most numerical studies of the arterial wall have assumed the vessel to be homogenous and elastic, however, newer studies are incorporating the heterogeneity of pathologic tissue. Biological soft tissue such as the vascular wall is known to exhibit high degrees of non-linearity in their mechanical response. Under normal physiological conditions, the radius of large arteries exhibit a maximum increase between 7 and 10% at a pressure of 100 mmHg. Experimental stress-strain results have been published (Fig. 2), and the challenge has been to incorporate this information into computational models. This behaviour is due to the presence of collagen ﬁbers, which at low strains are coiled up in a non-load bearing state, and at high strains uncoil and bear load in their

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Figure 2. The passive stress-strain relationship of human coronary arteries (modiﬁed from Canﬁeld 199527 ).

stretched conﬁguration. The various behaviours observed can be explained on the basis of the relative content of elastin ﬁbers (very elastic E ∼ 3 × 105 N/m2 ), collagen ﬁbers (not very elastic E ∼ 3 × 108 Pa) and muscle ﬁbers which stiffen in contraction (E ∼ 6 × 103 Pa – 3 × 106 Pa). It should be noted that most solid mechanical modeling assumes a passive response of the artery and no active contribution from the smooth muscle cells. In order to incorporate the experimental stress-strain curve into our ﬁnite element model, the framework of hyperelastic theory was adopted. For It has been suggested that normal cardiovascular tissue can be accurately modeled using hyperelastic theory27 . In non-linear continuum mechanics, the reference conﬁguration and the deformed conﬁguration of the continuum are distinguished. The reference conﬁguration is denoted by R0 and the actual deformed conﬁguration is denoted by R. The actual conﬁguration and the reference conﬁguration are related by a displacement vector u(X), where X is the position vector in the undeformed or reference conﬁguration. We deﬁne the deformation gradient F, the Green-Lagrange deformation tensor E and the right Cauchy-Green deformation tensor C by: Fij =

1 ∂xi 1 E = (F T F − I ) = (C − I ) ∂X 2 2

(2)

The deformation gradient F is related to the displacement vector u(X) by: Fij = ui,j + δij , where δij is the delta of Kronecker

(3)

The inﬁnitesimal volume element dv in the deformed conﬁguration and the corresponding volume element dV in the reference conﬁguration of a material undergoing a deformation are related by: dv = det(F )dV = (det(C))1/2 dV

(4)

For the soft tissue models, we use the concept of hyperelasticity, i.e. we deﬁne a strain energy function W depending on the three invariants I1 , I2 , I3 of the right Cauchy-Green deformation tensor C: W = W (I1 , I2 , I3 )

(5)

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Figure 3. Reference conﬁguration K 0 and deformed conﬁguration K.

The second Piola-Kirchhoff stress tensor S is obtained from the strain energy function by: S=

∂W ∂W =2 ∂E ∂C

(6)

If it is assumed that the tissue is an isotropic materials, the Mooney-Rivlin model (ﬁrst introduced to describe rubber-like materials) can be applied by using the following strain energy function. W = C10 (I1 − 3) + C01 (I2 − 3) +

1 (I3 − 1)2 d

(7)

This is the two-parameter form, where C10 and C01 are the two independent material constants characterizing the deformation of the material, d is the material incompressibility parameter, and I1 , I2 , I3 are the invariants of the Cauchy deformation tensor. The two-term Mooney Rivlin strain energy function has been shown not to be sufﬁciently accurate for large deformations27 while a 5-parameter model gave an excellent ﬁt to the experimental data. Thus, a 5-parameter Mooney-Rivlin model was used: W = C10 (I1 − 3) + C01 (I2 − 3) + C20 (I1 − 3)2 + C11 (I1 − 3)(I2 − 3) + C02 (I2 − 3)2 +

1 (I3 − 1)2 d

(8)

Biological tissues have a high water content, rendering them nearly incompressible. For incompressible materials, I3 = 0, eliminating the last term in the strain energy function. In order to avoid singularity problems in the numerical analysis, this condition was implicitly imposed by specifying a Poisson’s ratio of 0.49 instead of the fully incompressible 0.5. 2.3. Geometric Reconstruction of Coronary Arteries and Plaques It has been shown that proper representation of the coronary artery geometry is a primary factor in numerical modeling28 . Medical imaging has provided the data needed to create realistic 3D models of the coronary arteries. In this section we describe two techniques used to capture the geometry and composition of human coronary arteries.

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Figure 4. A) A Batson’s cast of a 61 year old female’s right coronary artery. B) An example of a surface reconstruction made from CT images of a Batson’s cast. An enlarged section near a branch shows the adaptive meshing used to resolve the complex ﬂow features of the branch region.

2.3.1. Right Coronary Artery Hearts collected at autopsy and transplantation have been used to study the biomechanics of human coronary arteries. Post-mortem tissue allow direct measurement of the histology, mechanical properties and vessel geometry to be made. In the ﬁrst stage, the hearts are carefully removed and the aorta dissected to provide access the coronary ostia. An anatomical casting compound (Batson’s #17, Polysciences USA) is injected through a catheter at a physiologic pressure (100 mm Hg). Once the cast has polymerized, the coronary artery and cast may be dissected and the tissue processed for histology or mechanical tissue testing. The cast is used to produce both experimental and numerical models. For numerical modeling, each cast is CT scanned and a ﬁnite element model of the artery constructed29 . The CT images of the artery are segmented using custom MATLAB (MathWorks, Natick, MA) routines to produce cross-sectional contours of the artery lumen perpendicular to the centroidal path of the artery. Some of the branches that were visible on the Batson’s cast were too small to segment from the image volume and thus were omitted in the model reconstruction. After smoothing of the contours, a computer aided design (CAD) software package (DDN, ICEM-CFD, Berkeley, CA) is employed to reconstruct the artery surface. To facilitate ﬂow modeling, straight inlet and outlet extensions are added to the model. Five inlet diameters in length and 15 outlet diameters in length were added to the models. In addition 15 branch diameter outlet extensions were added to each branch. The artery geometry was discretized into an unstructured ﬁnite element mesh, with quadratic tetrahedral elements, using the Tetra meshing module of ICEM-CFD (ICEM-CFD, Berkeley, CA). Figure 4 shows an example cast and numerical reconstruction of a right coronary artery (RCA) taken from a 61 year old female. 2.3.2. Plaque Reconstruction Clinical CT images are insufﬁcient to reconstruct the heterogenous nature of the vessel wall. For solid modeling and ﬂuid structure interaction, we have used 3D data from in vivo intravascular ultrasound (IVUS) clinical images to reconstruct the internal plaque structure. The IVUS data and modeled plaque is used to analyze the global wall stress distribution resulting from physiological pressure pulse.

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Figure 5. Typical IVUS slice as seen of the echographic console (left) and typical manual segmentation (right).

It has been hypothesized that plaque vulnerability can be determined simply by the structural arrangement of plaque constituents. During the progression of CAD, rearrangement of constituents may affect global structural integrity and make plaque rupture more probable. Plaques may contain different inclusions, such as lipid, ﬁbrosis, calcium, or any combination of these components. These inclusions have different mechanical properties and therefore different inhomogeneities can be observed throughout the wall. Often, these inclusions are not clearly delimited. Lipid pools have soft mechanical properties whereas calciﬁed inclusions are very stiff. Since lipids are unable to support large stresses, they transfer the load to structures in their vicinity, therefore creating stress concentration due to geometric irregularities. Shoulders of the plaque are common sites of rupture30–32 . The high stresses and mechanical fatigue are believed to promote plaques rupture at the shoulders. Pre-angioplasty and post-angioplasty IVUS acquisition (Clearview model, San Jose, CA) were used to identify the geometry and composition of plaques. A 30 MHz mechanical type, 3.2F in diameter catheter was used. The images were acquired with an automatic pullback of 0.5 mm/s and stored at a rate of 30 frames per second on a SVHS tape recorder (Panasonic MD830). The IVUS images were gated along with the electrocardiogram (ECG) in order to minimize artefacts due to cyclic dilation of the coronary arteries. Coronary arteries may expand as much as 10% between systole and diastole, due to blood pressure variations and myocardium contractions. Images were therefore gated ofﬂine and one image per end diastole, where diameter is maximum, were selected to identify the plaque composition and geometry. Figure 5 illustrates a typical image slice as seen on the echographic console. The IVUS data was manually segmented by marking the boundaries of the plaque and lipid core. Spline curves are ﬁt to the manually selected points. Reconstruction of a single plaque requires a total of about 300 to 500 frames. The delimited contours are the external elastic membrane, lumen and internal plaque architecture. The resulting segmentations are then edited within Matlab and subsequently sent to a CAD software (Pro-Engineer). The slices are aligned along the centroids to compile the 2D slices. The data is imported to a CAD program (Pro Engineer) where the data points are processed into a series of smoothed successive rings representing the 3D vessel wall and internal plaque structure, Fig. 7.

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Figure 6. Combination of angiography and IVUS for 3D reconstruction of the vessel trajectory and internal plaque architecture (left) and 3D reconstruction of the vessel trajectory and internal plaque architecture combining angiography and IVUS34 .

Figure 7. Surface rendering of the rings data set, internal lumen (left) and full vessel model (middle) and 3D CAD reconstruction of internal complex plaque structure (right).

3. Numerical Results 3.1. Flow in a Human Coronary Artery The ﬂow through anatomically realistic human coronary arteries has been previously described29,33 . Figure 8 shows the velocity proﬁles and secondary ﬂow within a reconstruction of a RCA of a 61 year old female. A well validated numerical solver was used to calculate the velocity ﬁeld. The wall shear stress was estimated from the velocity data. Pulsatile ﬂow simulations were conducted at a mean Reynolds number of 233 and a Womersley parameter of 1.8234 . The velocity ﬁeld is highly complex with signiﬁcant secondary ﬂow. The geometry of the RCA causes the bulk ﬂow to “slosh” along the length of the artery. This can be seen in the secondary contours shown in Fig. 8. The high momentum ﬂuid (red contours) orientation and shape vary signiﬁcantly as blood ﬂows through the RCA. 3.2. Flow Through a Stenosis A simpliﬁed model of a coronary stenosis has been used extensively to investigate hemodynamics35–40 . The geometry used in this study is a 3D model of a coronary artery with a 50% eccentric stenosis. The model was meshed using Gambit (Fluent Inc) with 22064 brick elements (Fig. 10).

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Figure 8. Velocity proﬁles in a human coronary artery. The secondary ﬂow at four locations along the artery show the movement of the high momentum ﬂuid core.

Figure 9. Wall shear stress pattern within a human RCA. The shear stress has been normalized by the inlet Poiseuille shear values.

The 3D time-dependent Navier-Stokes equations were solved for the above model using Fidap (Fluent Inc). The blood was modeled as a Newtonian incompressible ﬂuid and with a mean Reynolds number of 194. The vessel wall was assumed to be rigid. In Section 3.4 we present results that include vessel compliance and ﬂuid structure interaction. A fully developed coronary artery waveform was applied at the inlet (Fig. 11). The velocity results show that, for most of the blood ﬂow cycle, the post-stenotic ﬂow is characterized by a high-velocity jet and a region of ﬂow separation distal to the stenosis, Fig. 12. Around peak diastole the post-stenotic ﬂow develops large vortices, ﬂow separation and reattachment.

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Figure 10. 3D stenotic artery model meshed with brick elements.

Figure 11. Model coronary waveform used for the time dependent simulations.

Figure 12. Velocity ﬁeld for a plane cut at (a) peak systole and (b) diastole.

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Figure 13. Pressure change along the artery’s centreline.

Figure 14. Shear stress distribution along the artery’s centreline at the wall at (a) peak systole, (b) peak diastole and in the lumen at (c) peak systole and (d) peak diastole.

The pressure ﬁeld shows an increase in the pressure gradient across the stenosis obstruction at peak systole. Pressure loss through the stenosis is about 6%. During ﬂow reversal (at peak diastole) the pressure gradient across the obstruction is less signiﬁcant, Fig. 13. The shear stress results show a large increase in wall shear stress at the apex of the stenosis. The highest wall shear stress values remain at the stenosis apex throughout the ﬂow cycle. Within the blood, the ﬂuid shear calculated from the velocity data shows a region of high spatial gradients in shear between the high momentum jet and the recirculating ﬂow downstream of the stenosis. The temporal change in the shear stress within the ﬂuid changes noticeably over the cardiac cycle, exhibiting peaks in shear both at systole and diastole.

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Figure 15. Shear stress distribution for (a) linear elastic model and (b) non-linear hyperelastic model.

Figure 16. Wall stress distribution inside an anisotropic atherosclerotic plaque.

3.3. Solid Mechanics of a Stenosis Previous studies have emphasized the direct relation between high stress concentrations on lipid pool boundaries and an increased propensity of plaque to rupture at these locations41,42 . In the 50% area stenosis model we investigated the affect of modeling the wall as hyperelastic. Figures 15 shows a comparison between a linear and hyperelastic model for the same initial geometry. The stresses was computed using ANSYS with the hyperelastic model are two orders of magnitude less than the corresponding linear model. This phenomenon can be explained by the stress-stiffening characteristics of non-linear cardiovascular tissue material. It is also signiﬁcant to note that the localization of the maximal stresses occurs at the edge of the stenosis. Stress concentrations in this region may point to areas of potentially increased vulnerability. Attempts are now being made to include clinical data from IVUS reconstructions to better model the coronary wall. Figure 16 displays some initial computations performed

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Figure 17. Wall displacements at peak systole.

Figure 18. Stress distributions.

with the 3D reconstruction presented in Section 2.3.2. The vessel wall is assumed to be linear, elastic and each inclusion region within the stenosis is assumed to have isotropic tissue properties. A hyperelastic-Mooney-Rivlin model was used for the wall. 3.4. FSI Computations Recent advances in numerical methods, and in the integration of these into commercial software codes, have permitted a novel, integrative approach where the ﬂuid and structural domains are coupled and solved sequentially. Commercial programs such as Fidap allow for linear elastic solid mechanics to be coupled with the ﬂuid dynamics in simple geometries. In this manner, the ﬂow ﬁeld is initially solved, with varying stresses and pressures quantiﬁed at the boundary with the wall. In a second step, these become the input conditions at the boundary of the structural domain, eliminating the need for the constant pressure assumption. Thus, with this method, known as ﬂuid-structure interaction (FSI), the real complexity of the entire lumen and wall cardiovascular biomechanics can be captured. Only a limited number of studies have explored this approach. A transient ﬂuid-structure interaction (FSI) analysis was conducted using the ANSYS multi-physics software package on the 50% stenosis model. To couple the ﬂuid and solid dynamics an iterative solution is employed. The process involves the following steps: • Solve the ﬂuid domain velocity and pressure ﬁelds. • Calculate the traction vector at the ﬂuid structure interface. • Apply external loads and ﬂuid traction on the structural domain.

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• Integrate the equations of motion to solve for the elastic body displacement, velocity and acceleration vectors. • Calculate the displacement ﬁeld at the ﬂuid structure interface and update its location. • Apply displacement at the ﬂuid structure interface and solve for the updated ﬂuid domain mesh location. • Repeat until convergence is reached. • Go to next time step. For the numerical model 125,000 brick elements were used for the lumen and 100,000 tetrahedral elements for the arterial wall. In addition to the ﬂuid model presented in Section 2.1, FSI requires additional equations to couple the ﬂuid and solid domains: FIDAP employs the arbitrary Lagrangian-Eulerian (ALE) formulation to describe ﬂuid ﬂow for FSI problems. The (ALE) formulation can be written as ρ

∂ui + ρui,j (uj − uˆ j ) = σij,j + ρfi ∂t uj,j = 0

(9)

where i, j = 1, 2 for 2-D ﬂows or i, j = 1, 2, 3 for 3-D ﬂows; ui is velocity; ρ is density; σij is the stress tensor; fi is the body force per unit mass; ∂/∂t is the referential time derivative; uˆ is the mesh velocity. For a ﬂuid, the stress tensor, σ , can be written as: σij = −pδij + τij

(10)

where p is the pressure, τij is the deviatoric stress tensor, and δij is the Kronecker delta. For viscous, incompressible ﬂuids, the constitutive relation has the form: τij = 2μεij

(11)

where εij is the strain rate tensor deﬁned as: εij =

1 (ui,j + uj,i ) 2

(12)

The ﬂuid structure interface equilibrium equation: The boundary conditions can be expressed in the following forms: σij

nj = σi

(13)

where nj is the normal vector. The arterial wall constitutive equation: σij = Dij kl

εkl

(14)

where Dij kl is the material (Lagrangian) elasticity tensor, and εkl is the inﬁnitesimal strain tensor, the components of which are deﬁned by εkl =

1 (dk,l + dl,k ) 2

(15)

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where displacement is deﬁned as di = xi − xi0 , and xi0 is the stress-free position. The arterial wall was modeled as a nearly incompressible, isotropic, elastic material with a Young’s modulus of 2 MPa and a Poisson’s ratio of 0.45, similar to the linear FEA model. With a homogenous plaque conﬁguration, the largest displacements occur during the peak systolic phase. The overall deformation of the arterial wall is asymmetric with respect to the stenosis distal/proximal plane of symmetry. The maximum displacement is located downstream of the stenosis towards the stenotic wall where maximum pressure was also found. The largest displacements were an order of magnitude lower than the vessel wall thickness. Tissue stresses were larger in pre-stenotic regions and smaller in post-stenotic regions. Most of the stenosis body is subjected to compressive stresses whereas the nonstenotic side, facing the stenotic wall side, is subjected to tensile stresses.

4. Discussion and Conclusions The study of coronary biomechanics has wide reaching implications in the understanding of CAD and the design of treatment options. The hemodynamic environment created by the tortuous geometry of human coronary arteries is complex. Moreover, the geometry of each coronary artery is unique. This makes it very difﬁcult to resolve the causality of biomechanical forces in the development of CAD. New computational tools are emerging which will help to better understand these biomechanical forces. The ability to use medical imaging to recreate realistic coronary geometries has signiﬁcantly advanced the study of biomechanical stimuli. CFD simulations of human RCAs have shown very complex hemodynamics29 . Each RCA studied has shown unique shear patterns and little evidence of disease correlation with ﬁrst order shear measures. Much more work is needed to be able to resolve the role of shear stress in endothelial cell dysfunction leading to CAD. The rupture of the plaque is a frequent cause of myocardial infarction. Plaque rupture occurs because of stresses within the lumen and tissue. A 3D model was developed from segmentation of IVUS images. The 3D model was then imported into a ﬁnite element solver, in order to obtain the mechanical behavior of the coronary artery and its plaque, and to evaluate its vulnerability. In addition, an idealized coronary stenosis was evaluated for ﬂuid and structural stresses and a coupled ﬂuid-structure solution also investigated. In the idealized model, it was observed that the displacements and, more importantly, stresses are signiﬁcantly lower when the tissue is modeled as hyperelastic owing to stress-stiffening. Calciﬁc (hard) inclusions did not lead to signiﬁcant differences in displacements and stresses when incorporated into the model. Lipidic (soft) inclusions had a dramatic effect on displacements and stress distributions within the stenotic region, correlating with clinical observations where high lipidic content stenoses were found to exhibit increased vulnerability7,43 . The velocity and shear results are comparable in both analyses as differences remain within 5%. The presence of secondary ﬂow in both analyses highlight the need for the use of 3D analyses to capture radial velocities. Pressure results are different however as pressure loss through the stenosis increases by 25% between CFD and FSI results. This can be explained by the energy transfer between the ﬂuid and the vessel wall, which is only accounted for in FSI: blood, going through the stenosis, looses energy which goes into the deformation of the vessel wall.

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Based on these results, one can argue that for ﬂuid velocities and shear stresses, CFD analysis is sufﬁcient; however, FSI is necessary for accurate and more realistic pressure results. Pressure throughout the stenosis model changes signiﬁcantly: the pressure loss through the stenosis is about 7.5%, and varies by 15% within the whole ﬂuid domain. Furthermore, radial distribution of pressure at each section and particularly in the vicinity of the stenosis varies signiﬁcantly, and decreases towards the stenotic wall side. The assumption of constant pressure used in the FEA analysis is therefore not valid. Because of that same assumption used in the FEA analysis, the deformations were found to be symmetrical with respect to the distal/proximal stenosis plane of symmetry where radial displacements were higher at the non-stenotic side of the vessel compared to the stenotic side. This was expected, as a thinner side would certainly deform more than a thicker side if subjected to the same pressure. Displacements were found to be asymmetrical in the case of FSI analysis due to the pressure loss through the stenosis. At each cross-section, radial displacements were found to be more uniform than in the FEA analysis, and maximum radial displacements were found to be smaller; this is believed to be due to the unequal radial distribution of pressure. Similar observations can be drawn in the case of stresses where the longitudinal distribution was asymmetric with respect to the distal/proximal stenosis symmetry plane and stresses were found to be more uniform across the sections. Due to the nature of the simple pressure boundary conditions usually used in the ﬁnite element analyses, where a constant pressure is applied through the model, major differences in results can be found when comparing FEA to FSI which suggests that FSI is needed for accurate results in the structural analysis of stenoses. Further developments of these models will lead to increasingly accurate methods towards the understanding of the development of atherosclerosis, and will serve as diagnostic and predictive tools in the identiﬁcation of vulnerable plaque in a clinical setting. Ultimately, such a tool could be of a great utility for the understanding in general but also, in a clinical environment, to evaluate plaque vulnerability and therefore allowing a proper orientation of the patients toward a therapy adapted to their risk. This technique would allow for a better use and direction of the different clinical resources towards patients at risk. It could also allow the evaluation of the impact on plaque vulnerability of a pharmacological approach aimed at changing the physiologic nature of a plaque and therefore its mechanical properties.

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[30] Myers, J.G., Moore, J.A., Ojha, M., Johnston, K.W., Ethier, C.R., Factors inﬂuencing blood ﬂow patterns in the human right coronary artery. Ann Biomed Eng., vol. 29, pp. 109–120, 2001. [31] Gyongyosi, M., Yang, P., Hassan, A., Weidinger, F., Domanovits, H., Laggner, A., Glogar, D., Arterial remodelling of native human coronary arteries in patients with unstable angina pectoris: a prospective intravascular ultrasound study. Heart., vol. 82, pp., 68–74, 1999. [32] Richardson, P.D., Davies, M.J., Born, G.V., Inﬂuence of plaque conﬁguration and stress distribution on ﬁssuring of coronary atherosclerotic plaques. Lancet., vol. 2, pp. 941–944, 1989. [33] Fei, D.-Y., Thomas, J.D., Rittgers, S.E., The Effect of Angle and Flow Rate Upon the Hemodynamics in Distal Vascular Graft Anastomoses: A Numerical model Study. J Biomech Eng., vol. 116, pp. 331–336, 1994. [34] Sherknies, D., Meunier, J., Mongrain, R., and Tardif, J.-C., Assessment of an IVUS Transducer from Single-Plane Cineangiograms: a Phantom Study. Proceedings of the Annual International Conference IEEE Engineering in Medicine and Biology Society. vol. 1, pp. 690–693, 2003. [35] Kirpalani, A., Park, H., Butany, J., Johnston, K.W., Ojha, M., Velocity and wall shear stress patterns in the human right coronary artery. J Biomech Eng., vol. 121, pp. 370–375, 1999. [36] Matsuo, S., Tsuruta, M., Hayano, M., Imamura, Y., Eguchi, Y., Tokushima, T., Tsuji, S., Phasic coronary artery ﬂow velocity determined by doppler ﬂowmeter catheter in aortic stenosis and aortic regurgitation. Am J Cardiol., vol. 62, pp. 917–922, 1988. [37] Ahmed, S.A., Giddens, D.P., Pulsatile poststenotic ﬂow studies with laser Doppler anemometry. J Biomech., vol. 17, pp. 695–705, 1984. [38] Ahmed, S.A., Giddens, D.P., Velocity measurements in steady ﬂow through axisymmetric stenoses at moderate Reynolds numbers. J Biomech., vol. 16, pp. 505–516, 1983. [39] Ahmed, S.A., Giddens, D.P., Flow disturbance measurements through a constricted tube at moderate Reynolds numbers. J Biomech., vol. 16, pp. 955–963, 1983. [40] Tandon, P.N., Rana, U.V., A new model for blood ﬂow through an artery with axisymmetric stenosis. Int J Biomed Comput., vol. 38, pp. 257–267, 1995. [41] Yamaguchi, T., Hanai, S., Measured wall shear stress distribution pattern upstream and downstream of a unilateral stenosis by an electrochemical method. Biorheology., vol. 24, pp. 753–762, 1987. [42] Young, D.F., Tsai, F.Y., Flow Characteristics in models of arterial stenoses-1. Steady Flow. J Biomechanics., vol. 6, pp. 395–410, 1972. [43] Huang, H., Virmani, R., Younis, H., Burke, A.P., Kamm, R.D., Lee, R.T., The impact of calciﬁcation on the biomechanical stability of atherosclerotic plaques. Circulation., vol. 103, pp. 1051–1056, 2001. [44] Loree, H.M., Kamm, R.D., Stringfellow, R.G., Lee, R.T., Effects of ﬁbrous cap thickness on peak circumferential stress in model atherosclerotic vessels. Circ Res., vol. 71, pp. 850–858, 1992. [45] Schoenhagen, P., Stone, G.W., Nissen, S.E., Grines, C.L., Grifﬁn, J., Clemson, B.S., Vince, D.G., Ziada, K., Crowe, T., Apperson-Hanson, C., Kapadia, S.R., Tuzcu, E.M., Coronary plaque morphology and frequency of ulceration distant from culprit lesions in patients with unstable and stable presentation. Arterioscler Thromb Vasc Biol., vol. 23, pp. 1895–1900, 2003.

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Plaque Imaging: Pixel to Molecular Level J.S. Suri et al. (Eds.) IOS Press, 2005 © 2005 The authors. All rights reserved.

Computed Tomographic Cardiovascular Imaging Jerold S. SHINBANE and Matthew J. BUDOFF University of California, Los Angles, CA Abstract. The chapter presents the Cardiac CT for the assessment of cardiovascular pathology with an emphasis on the detection of coronary atherosclerosis. Cardiac CT is a robust technology for the non-invasive assessment for a spectrum of cardiovascular disease processes. This imaging modality can provide assessment of atherosclerotic plaque burden and coronary artery disease risk through coronary calcium scoring. Advances in spatial and temporal resolution, electrocardiographic triggering methodology, and image reconstruction software have helped in the evaluation of coronary artery anatomy and vessel patency, providing the ability to noninvasively diagnose or rule out signiﬁcant epicardial coronary artery disease. This technique also allows the 3-Dimensional simultaneous imaging of additional cardiac structures including coronary veins, pulmonary veins, atria, ventricles, aorta and thoracic arterial and venous structures, with deﬁnition of their spatial relationships for the comprehensive assessment of a variety of cardiovascular disease processes. Keywords. Angiography, computed tomography, cardiac CT, atherosclerosis, coronary artery calciﬁcation

1. Introduction Cardiac CT is a robust technology for the non-invasive assessment for a spectrum of cardiovascular disease processes. This imaging modality can provide assessment of atherosclerotic plaque burden and coronary artery disease risk through coronary calcium scoring. Advances in spatial and temporal resolution, electrocardiographic triggering methodology, and image reconstruction software have helped in the evaluation of coronary artery anatomy and vessel patency, providing the ability to noninvasively diagnose or rule out signiﬁcant epicardial coronary artery disease. This technique also allows the 3-Dimensional simultaneous imaging of additional cardiac structures including coronary veins, pulmonary veins, atria, ventricles, aorta and thoracic arterial and venous structures, with deﬁnition of their spatial relationships for the comprehensive assessment of a variety of cardiovascular disease processes. This chapter will detail the role of cardiac CT for the assessment of cardiovascular pathology with an emphasis on the detection of coronary atherosclerosis.

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2. Tomographic Imaging Modalities Tomographic imaging modalities including electron beam CT (EBCT), multidetector CT (MDCT), and magnetic resonance imaging (MRI) each have individual advantages and limitations in the evaluation of cardiovascular disease, depending on the particular clinical questions posed. EBCT is a fourth-generation CT imaging modality, which is able to rapidly obtain thin tomographic cardiac slices for the evaluation of coronary artery anatomy. The speed of image acquisition is possible due to the fact that the x-ray source is stationary. As opposed to rotating the x-ray tube around the patient as in conventional scanners, in EBCT the patient is positioned inside the x-ray tube, obviating the need for motion of any part of the scanner during image acquisition. The ability to rapidly acquire images decreases respiratory and cardiac motion artifacts, making the modality wellsuited for the evaluation of the coronary vasculature. The entire cardiac structure is imaged during a single approximate 30 second breath-hold. EBCT acquires high-resolution images of the heart with temporal resolution of 50–100 milliseconds (msec) and prospective gating to the cardiac cycle. This allows imaging during the diastolic phase, when cardiac motion is minimized.1 The newest generation of EBCT scanner is the e− Speed scanner, which allow for 50 msec image acquisition. The faster image acquisition associated with this device further decreases breath-hold time, radiation exposure and motion artifacts. Patients with a spectrum of heart rates and rhythms (including premature beats and atrial ﬁbrillation) can be scanned without the need to pharmacologically decrease heart rates to less than 60 beats/minute. With MDCT, the tube/mechanical detector head rotates around the patient. Simultaneous imaging from multiple detectors during tube/detector rotation provides greater spatial resolution than EBCT, but at the expense of temporal resolution which is limited by the speed of gantry rotation. Advances in technology have lead to scanners which can obtain images with a scan rotation of 375 msec; and with partial scanning, image acquisition between 200 and 300 msec. MDCT possesses greater versatility for peripheral vascular imaging. There is a narrower window of acceptable heart rates for scanning with MDCT compared to EBCT, with many patients requiring pharmacologic decreases in heart rate to less than 60 beats/minute. The strengths of magnetic resonance cardiovascular imaging include greater deﬁnition of tissue characteristics, perfusion, valvular function, lack of x-ray radiation, and lack of need for potentially nephrotoxic contrast media, compared to CT technologies. In comparison, the strengths of CT include superior imaging of coronary arteries, higher spatial and temporal resolution, ability to scan patients with metallic devices such as pacemakers and deﬁbrillators, and shorter study times.2

3. Coronary Artery Calcium Coronary artery calcium (CAC) is closely associated with coronary atheromatous plaque. Arterial calcium deposition occurs in association with atherosclerotic plaque evolution and is regulated by cellular calciﬁcation-regulating proteins.3−6 Calciﬁcation is a dynamic process which occurs in the development and progression of atherosclerosis.7,8 An association between coronary artery calcium as measured by EBCT and both

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Figure 1. CT study (axial image) demonstrating calciﬁcation of the left main and left anterior descending coronary arteries. The total coronary calcium score was 1223. LAD=left anterior descending coronary artery.

histopathologic9,10 and in-vivo intravascular ultrasound11−13 study ﬁndings has conﬁrmed the close correlation between extent of CAC and atherosclerotic plaque burden. EBCT can accurately and non-invasively quantitate CAC.14,15 The quantitative measure of coronary calcium in the coronary arteries by EBCT, known as the calcium score, is based on number, area and peak Hounsﬁeld number of CAC in the coronary arteries on serial axial cardiac slices (Fig. 1).16 Data regarding calcium score distributions in large numbers of asymptomatic persons have been published.17 These tables can be used to classify patients on the basis of the extent of their atherosclerotic disease compared with the expected norm. In men, there is a rapid increase in the prevalence and extent of coronary calciﬁcation after age 45, with this increase delayed for 10–15 years in women. In contradistinction to other noninvasive modalities which focus on diagnosis of obstructive coronary artery disease (CAD), EBCT coronary calcium represents an anatomic measure of plaque burden.13 Studies comparing pathologic and EBCT ﬁndings have shown that the severity of stenosis does not correlate strongly with the amount of calciﬁcation on a segment-by-segment basis,18−20 whereas total calcium score is more closely associated with the presence and severity of maximum angiographic stenosis.21−23 Detection of coronary calcium by EBCT has been demonstrated to be highly sensitive for the presence of signiﬁcant CAD. A report of 1764 persons undergoing angiography and EBCT similarly showed a very high sensitivity and negative predictive value in men and women (>99%).24 Therefore, a calcium score of 0, denoting no evidence of coronary calcium, can virtually exclude those patients with obstructive CAD, making this test an effective screen prior to invasive angiography. An important point in the interpretation of CAC scores relates to the detection of obstructive CAD. A negative test, no evidence of calciﬁed atherosclerotic plaque, can virtually exclude obstructive disease. A positive EBCT study, presence of CAC, is nearly 100% speciﬁc for atheromatous coronary plaque.25 However, since both obstructive and non-obstructive lesions have calciﬁcation present, CAC is not speciﬁc to obstructive disease.26 While increasing calcium scores are more predictive of obstructive CAD, there is not a 1:1 relationship between calciﬁcation and stenosis. The overall speciﬁcity of any

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CAC for obstructive CAD is approximately 66%.27 In a study of 1851 patients undergoing angiography and CAC measure,28 EBCT calcium scanning in conjunction with pretest probability of disease derived by a combination of age, gender and risk factors, could assist the clinician in predicting the severity and extent of angiographically signiﬁcant CAD in symptomatic patients. EBCT is comparable to nuclear exercise testing in the detection of obstructive CAD.26,29 As opposed to stress testing, the accuracy of EBCT is not limited by concurrent medications, ability to exercise, or baseline electrocardiogram abnormalities. Role of Coronary Calcium in Risk Stratiﬁcation Disease processes related to atherosclerosis are the primary cause of morbidity and mortality in industrialized nations.30 Identiﬁcation of individuals at high risk for cardiovascular events is important to primary prevention strategies, as lifestyle modiﬁcation and pharmacologic therapies can impact life expectancy in high-risk persons.31 The initial manifestation of CAD is a myocardial infarction (MI) or death in up to 50% of patients.32 Most cardiac events occur in the intermediate risk population, where aggressive riskfactor modiﬁcation is often not often recommended or applied. Unfortunately, traditional risk factor assessment helps predict only 60–65% of cardiac risk, therefore many individuals without established risk factors for atherosclerotic heart disease continue to experience cardiac events.33 An understanding of coronary plaque pathophysiology is necessary to recognize some of the limitations of traditional cardiovascular risk stratiﬁcation. Arterial segments with obstructive coronary plaque (stenosis in the artery of >50% severity) are often not the site of vessel occlusion in acute MI.34−37 Acute coronary occlusion most frequently occurs at the site of mild to moderate stenoses in association with the process of plaque rupture. Therefore, plaque burden, and not stenosis severity, is a more important marker of disease. Tests assessing for evidence of obstructive CAD, such as exercise testing or pharmacologic nuclear or echo cardiac imaging, will not identify a signiﬁcant number of asymptomatic patients with atherosclerotic plaque who are at risk for acute MI. Studies of patients dying from either acute MI or sudden cardiac death have demonstrated that the extent of coronary atherosclerosis, rather than the severity of stenosis, is the most important predictor.38 These studies emphasize the importance of measurement of atherosclerosis burden in the assessment of risk for future cardiovascular events, rather than relying solely on evidence of obstructive coronary artery disease. Coronary Artery Calcium in Symptomatic Individuals Studies have demonstrated that CAC has prognostic signiﬁcance in symptomatic individuals.39−43 Margolis et al.39 assessed the signiﬁcance of CAC found on ﬂuoroscopy in 800 patients undergoing coronary angiography. The patients with CAC had a 5-year survival rate of 58%, compared with a rate of 87% for the patients without CAC. A study of 192 patients observed for an average of 50 +/− 10 months, after undergoing an EBCT study while in the emergency department for chest discomfort, found that the presence of CAC (calcium score >0), and increasing absolute calcium score values were strongly related to the occurrence of hard events (p < 0.001) and all cardiovascular events (p < 0.001).43 The patients with absolute calcium scores in the top 2 quartiles

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had a relative risk of 13.1 (95% CI, 5.6 to 36; p < 0.001) for new cardiovascular events as compared with the patients in the bottom 2 quartiles. The annualized cardiovascular event rate was 0.6% for subjects with a coronary artery calcium score of 0 compared with an annual rate of 13.9% for patients with a coronary artery calcium score >400 (p < 0.001). Additional studies have shown not only that CAC provides prognostic information, but that the extent of CAC provides more prognostic information than angiography or risk factors in symptomatic patients. A multicenter study of 491 patients undergoing coronary angiography and EBCT scanning found that higher calcium scores were associated with an increased risk of coronary events over the next 30 months as compared to patients in the lowest quartile of score.41 In multivariate analysis, the only predictor of a hard cardiac event was log calcium score. In another study of symptomatic patients, EBCT detected CAC was a stronger independent predictor of disease and future events than a sum of all of the traditional risk factors combined.40 Keelan et al.42 followed 288 symptomatic persons who underwent angiography and EBT calcium scanning for a mean of 6.9 years, and found age and CAC score were the only independent predictors of future hard coronary events. Coronary Artery Calcium in Asymptomatic Individuals CAC is also a useful predictor of cardiovascular events in asymptomatic individuals. Unfortunately, at least half of all ﬁrst coronary events occur in asymptomatic individuals who are unaware that they have developed CAD. Often the initial clinical presentation is sudden death or acute myocardial infarction (MI).32 Several lipid-lowering trials have shown that signiﬁcant risk reduction can be attained with both secondary and primary prevention measures.31,44 However, these studies have required study of large patient populations to demonstrate beneﬁt, and documented that risk reduction is only on the order of 25–37%, suggesting that more effective screening modalities are needed to identify asymptomatic individuals at risk of cardiac events. Several prospective trials have demonstrated the prognostic ability of EBCT to identify asymptomatic patients at high risk of cardiac events. Arad et al.45 initially reported a 19 month follow-up of 1,173 patients. Asymptomatic individuals were scanned using EBCT as well as measures of traditional risk factors, and followed prospectively for cardiac events. This study demonstrated CAC to be the strongest predictor of future cardiac events, with patients in the highest score category over 20 times more likely to suffer a cardiac event (odds ratio 22.3, CI 5.1–97.4). This prospective study now has been carried out for a total of 3.6 years of follow-up, maintaining the strong power of this technology to predict future cardiac events.46 The subjects who had events had signiﬁcantly higher calcium scores than did the subjects with no events (764 +/− 935 vs 135 +/− 432, p < 0.0001). A calcium score ≥160 was associated with a high likelihood of having a soft event (odds ratio, 15.8) or a hard event (odds ratio, 20.2). The predictive ability of the absolute calcium score was excellent for all coronary events and for hard events alone. Detrano et al.47 published an analysis in an older population (1196 patients, 89% male, mean age 66 years). This study demonstrated that while CAC was a signiﬁcant predictor of future cardiac events, short term follow-up demonstrated it did not have great power over traditional risk factors to discriminate who will develop CAD events. This study utilized scanning protocols (6 mm thick slices) that have since proven to be not

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as sensitive as the standard protocol (3 mm slices), and a deﬁnition of a calciﬁc focus that was up to 16 times greater than other studies (>8 mm2 ).48 Long-term (median 7.0 years) follow-up has demonstrated that the CAC score adds predictive power beyond that of standard coronary risk factors Subsequent data in this same cohort49 have demonstrated that EBCT coronary calcium scores were incremental in predicting cardiac risk, consistent with prior studies. Greenland et al.52 published longer term follow up of the South Bay heart watch cohort. CAC was found to be predictive of risk in patients with a Framingham Risk Score of >10%, with a high CAC score able to predict risk beyond Framingham risk score alone. As compared to a CAC score of 0, a CAC score of >300 was highly predictive of cardiac events (HR 3.9, p<0.001). Wong et al.50 followed 926 asymptomatic patients (mean age 54 years) for an average of 3.3 years. Sixty percent of men and 40% of women had a positive scan at baseline. Calcium scores were signiﬁcantly higher in patients with events than in patients without events. The presence of CAC and increasing score quartiles were related to the occurrence of new MI (p<0.05), revascularization (p<0.001) and total cardiovascular events (p<0.001). The risk ratio for events in patients whose absolute calcium score was in the upper quartile (score >271) compared with individuals whose absolute calcium score was in the lowest quartile (score <15) was 12 (relative risk 8.8 and 0.72, respectively; p<0.001). Raggi et al.51 followed 632 asymptomatic individuals with risk factors for CAD for an average of 32 +/− 7 months and reported that 70% of events (MI or death) occurred in patients with a calcium score in the upper quartile for age and sex. A CAC score of zero was associated with a 0.11%/year event rate, compared to 4.8 %/year with a score >400. The event rate in patients with calcium scores in the highest quartile was 22 times the event rate in patients with calcium scores in the lowest quartile, and was 3 times greater than the relative risk of the upper quartile versus lower quartile of all NCEP risk factors combined, signiﬁcantly outperforming risk factors in cardiac event prediction. They additionally demonstrated the incremental beneﬁt of adding calcium scores to conventional risk factors. Multiple logistic regression analyses demonstrated that calcium score percentile was the only signiﬁcant predictor of events and provided incremental prognostic value when added to traditional risk factors for CAD. Larger trials have been reported, demonstrating approximately 10-fold increased risk with the presence of CAC. A prospective study of 5585 subjects aged 59 ±5 years, a calcium score ≥100 predicted all atherosclerotic cardiovascular disease events, all coronary events, and the sum of non-fatal myocardial infarction and coronary death events with relative risks of 9.5 to 10.7 at 4.3 years.53 The calcium score also predicted events independently of and more accurately than measured risk factors. The area under the receiver operating characteristic curve for event prediction with risk factors alone in this study was 0.71, increasing to 0.81 with EBCT testing (p<0.01). This prospective study strongly demonstrated the ability to utilize this test to rule out patients who do not require therapy. In this study, only 19% of patients had scores above the diagnostic threshold (calcium score ≥100), yet relying on this threshold had a negative predictive power of 99.2%. Thus, clinicians can focus on a smaller, yet higher risk population (10.7 fold increased risk in this group), for risk reduction therapy. Kondos et al.54 reported 37 month follow-up on 5,635 initially asymptomatic low to intermediate risk adults. In men, events (n = 192) were associated with the presence of CAC (RR = 10.5, P < 0.001), diabetes (RR = 1.98, P = 0.008), and smoking

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(RR = 1.4, P = 0.025) whereas in women events (n = 32) were linked to the presence of CAC (RR = 2.6, P = 0.037) and not risk factors. While follow-up was only obtained in 64% of patients, patients with scores >170 had a relative risk for developing of hard cardiac events of 7.24 (95% CI, 2.01–26.15), after multivariable analysis was performed with adjustment for age and other CAD risk factors. Coronary Artery Calcium: Guidelines and Applications The above mentioned studies demonstrate the ability of CAC to provide risk stratiﬁcation in asymptomatic and symptomatic populations with incremental prognostic information beyond traditional risk factors. Based upon results of these studies, modiﬁcation of the Framingham Global Risk Score by using a weighted factor based on the patient’s individual calcium score percentile has been suggested.55 In this modiﬁcation, the Framingham Risk Score assigned to a subject undergoing EBCT screening for asymptomatic CAD is increased if the calcium score is in a high percentile. Recommendations for use of CAC assessment have now been published.56 The National Cholesterol Education Program (NCEP) has made recommendations speciﬁcally for the use of EBCT to assist in risk stratiﬁcation in elderly and intermediate risk patients. The new NCEP guidelines57 support the conclusions of the Prevention Conference V and the ACC/AHA report that high coronary calcium scores signify and conﬁrm increased risk for future cardiac events, and state, “Therefore, measurement of coronary calcium is an option for advanced risk assessment in appropriately selected persons. In persons with multiple risk factors, high coronary calcium scores (e.g., >75th percentile for age and sex) denotes advanced coronary atherosclerosis and provides a rationale for intensiﬁed LDL-lowering therapy.” New guidelines for prevention of CAD in women recommend coronary calcium as a method of risk stratiﬁcation, with positive scores placing women at intermediate risk (10–20% 10-year risk), and high scores placing women at high risk for future cardiac events.58 European joint-society guidelines59 recommend employing aggressive risk-reduction therapy in asymptomatic patients if their absolute risk approximates that of patients with coronary heart disease. The absence of CAC in the asymptomatic patient identiﬁes a group of patients at very low risk of events over the next 3–5 years.60 Annual event rate of only 0.11% have been reported for patients with scores of zero.51 Both the American College of Cardiology/American Heart Association writing group and the Prevention V Conference agreed that the negative predictive value of EBCT is very high for short term events.61,62 Whether a calcium score of zero will allow therapy to be withheld remains to be prospectively tested. Current guidelines suggest that intermediate risk patients would beneﬁt most from further risk stratiﬁcation, as most cardiac events occur in this population.61 “Recent work suggests that electron-beam tomography (EBT) can also improve risk prediction in intermediate-risk patients. Thus, with a prior probability of a coronary event in the intermediate range (>6% in 10 years but <20% in 10 years), a calcium score would yield a posttest probability in virtually all such patients greater than 2% per year, that is, a level similar to that in secondary prevention, or a ‘coronary risk equivalent’.”61 Furthermore, Wong et al.63 demonstrated that persons with CAC have been reported to be more likely to undertake preventive health measures, including.lifestyle modiﬁcation and pharmacologic therapies.

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Risk stratiﬁcation using CAC may potentially reduce health care costs and better target patients who will derive beneﬁt. Drug therapy, although effective, is expensive. The average cost of statin therapy in the United States in the early 1990’s was approximately $720 (U.S.) per year,64 exclusive of physician visits or laboratory tests. The potential adverse effects of lipid lowering medications, such as liver function abnormalities and myositis, as well as cost stress the need to identify and target those persons who would truly beneﬁt from these medications. CAC screening with EBCT was demonstrated to be a cost-effective screening strategy in asymptomatic individuals between 45 and 65 years of age.65 The ability of CAC scoring to identify patients who require aggressive risk factor modiﬁcation coupled with effectiveness of cholesterol lowering medications, aspirin and other therapies should allow physicians to focus aggressive preventative treatment on those individuals with underlying atherosclerosis who are at highest risk of having cardiovascular events. There are some potential speciﬁc applications of CAC assessment that deserve mention. Based on the fact that a CAC score of zero is associated with a <1% chance of obstructive CAD, the use of EBCT prior to angiography has been recommended.66 In the symptomatic patient, evidence suggests that calcium scanning may be more costeffective at diagnosing CAD than traditional non-invasive testing, especially in women.65 Another potential application of cardiac CT relates to the triage of chest pain patients. EBCT has been shown to be an efﬁcient screening tool for patients admitted to the emergency department with chest pain to rule out myocardial infarction.43,67,68 These studies demonstrate sensitivities of 98–100% for identifying patients with acute MI, and very low subsequent event rates for persons with negative tests. The high sensitivity and negative predictive value may allow early discharge of those patients with non-diagnostic ECG and negative calcium scans. Exclusion of coronary calcium may therefore be used as an effective screen prior to invasive diagnostic procedures or hospital admission. Recent guidelines support the use of calcium scanning in symptomatic persons, stating that EBCT is “sufﬁciently accurate for predicting the presence of angiographic stenosis”.61 In patients with cardiomyopathy, CAC be useful in determining the etiology of cardiomyopathy. The clinical manifestations of patients with ischemic cardiomyopathy are often indistinguishable from those patients with non-ischemic dilated cardiomyopathy. Budoff et al.69 demonstrated in 120 patients with heart failure of unknown etiology that the presence of CAC was associated with a 99% sensitivity for ischemic cardiomyopathy. Electron Beam versus Multidetector CT for Assessment of Coronary Artery Calcium Temporal resolution, the speed of image acquisition, greatly differentiates EBCT from MDCT for CAC scanning.70,71 Preliminary studies demonstrated similar results between EBCT and MDCT, but consisted of elderly symptomatic men with very high plaque burdens.72,73 A comparison study in 70 asymptomatic patients undergoing both EBCT and MDCT concluded, “spiral CT has not yet proved to be a feasible alternative to EBCT for coronary artery calcium quantiﬁcation.”71 Becker et al.72 studied 100 patients comparing MDCT with EBCT and reported a modest correlation between the 2 modalities. In this study, the percentage variability was 32% between the two modalities for CAC score. Moreover, the level of individual precision was limited and the scores < 100 appeared to have the most deviation by MDCT as compared to EBCT. Horiguchi et al.74 demonstrated that MDCT with a retrospective ECG-gating algorithm showed a high cor-

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relation with CAC scores determined using EBCT in 20 normal volunteers. However, this retrospective approach led to a radiation dose which was 13 times higher than EBCT. The higher tube currents available with MDCT allow for images with better signalto-noise ratio and higher spatial resolution in comparison to EBCT, but at the expense of higher radiation exposure. Retrospective gating involves acquisition of many images which are not used subsequently as only those images that occurred with appropriate diastolic timing are used in image analysis. This retrospective approach markedly increases the radiation dose, image analysis time, inter- and intra-reader variability and inter-scan variability. A more practical approach is prospective gating, which is similar to the methods employed by EBCT. This methodology allows for image acquisition only at the speciﬁed time (diastole), and therefore reduces variability and radiation. For MDCT, the images are best when the resting heart rate is less than 60 beats per minute; at faster heart rates, motion artifacts may become more prominent. The radiation dose delivered by MDCT is anterior, and is therefore in closer proximity to radio-sensitive organs such as breast, thyroid and orbits. The radiation dose delivered by EBCT is posterior. Protocols are being developed that may reduce radiation doses with MDCT, by attempting to inactivate the beam when it passes behind the subject. Results from a recent study showed that ECG-controlled tube current modulation allows signiﬁcant dose reduction of 48% and 45% in males and females respectively, while performing retrospectively ECG-gated MDCT of the heart.75 New AHA Guidelines are being published discussing the advantages and disadvantages of each modality.76 These guidelines conclude: “The lower radiation doses, improved variability, and substantial validation data support the use of EBCT as the current reference (‘gold’) standard for measurement of CAC.” Reproducibility of Coronary Calcium Assessment The reproducibility of CAC measurement is essential to utilizing this modality for assessment of the efﬁcacy of therapeutic interventions. Reproducibility was initially a concern for repeated testing, but technologic improvements have reduced inter-scan variability to a median of 4–8%.77 With excellent inter- and intra-observer variability (1%), this test can measure plaque burden changes over time. Using new gating algorithms, EBCT inter-scan reproducibility has been shown to be approximately 11%, with inter-reader variability approximately 3% and intra-reader variability less than 1%.78 This has been signiﬁcantly more problematic with MDCT. The inter-scan variability is between 32% and 40%, leading to the conclusion that “helical CT is not sufﬁciently reproducible to allow serial quantiﬁcation of total calcium score over time”.79 Inter-reader variability with helical CT is also problematic, with a mean inter-reader variability was 4.5% for EBT compared to 41.5% for helical CT, and suggested double reading all studies to better assess coronary calcium.71 Helical CT CAC assessment is associated with higher radiation doses, lower reproducibility and lower temporal resolution than EBCT. The technique has higher spatial resolution than EBCT. Due to the limitations of helical CT, EBCT is currently the gold standard for cardiac CT calcium assessment. Two ongoing trials (MESA trial in the U.S. and the Heinz Nixdorf Recall Study in Germany) will examine the value of EBCT and MDCT derived CAC in the general population, and provide more answers in relation to the role of CAC in primary prevention of atherosclerosis.

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Figure 2. Electron beam angiography demonstrating the left and right coronary arteries, without evidence of obstructive coronary artery disease. LAD=left anterior descending coronary artery, LCx=left circumﬂex coronary artery, OM=obtuse marginal, RCA=right coronary artery.

4. Cardiovascular CT Angiography Coronary Artery Angiography The ability to visualize the coronary artery lumen has revolutionized CT imaging. Invasive coronary angiography, the reference standard for visualization of coronary artery stenoses, is an invasive procedure with a signiﬁcant cost and small but present procedure related morbidity and mortality. An alternative, less expensive, and non-invasive test for use as a diagnostic tool before possible intervention could have a major impact on health care practice and cost containment. Contrast-enhanced electron beam angiography (EBA) is an emerging technology with the potential for obtaining essentially noninvasive coronary arteriograms. Studies have reported contrast-enhanced, ECG-triggered, 3-Dimensional EBA for detecting and grading coronary stenosis.70,80−84 Coronary EBA was introduced nearly one decade ago,85 and since that time has improved due to technology and methodology advances. ECG-triggering is employed, so that each image is obtained at the same point in diastole. Iodinated contrast is administered through an antecubital or jugular vein with an injection rate of approximately 4 ml/sec and total volume of 120–160 ml. Images are obtained over a single breath-hold, usually over approximately 30 seconds. This entire protocol can be performed within 15–20 minutes. Image processing is rapid, with detailed analysis through the assessment of 2-Dimensional and 3-Dimensional views as well as maximum intensity projections in which serial overlapping thin slices are viewed in unison (Figs 2–7).86 Coronary EBA with 3-Dimensional techniques can image long segments of the major coronary arteries with high correlation to conventional coronary angiography (r = 0.83).87 In comparison to invasive angiography, this modality has been demonstrated to identify signiﬁcant coronary lumen narrowing (>50% stenosis) with the sensitivity of 74–92%, speciﬁcity of 79–100% and accuracy of 81.2–93.4%. Summary data from multiple studies demonstrates an overall sensitivity of 87% and speciﬁcity of 91% for the 583 patients reported in these studies. Coronary EBA had a success rate of 70–93% in the ability to correctly interpret all 3 coronary arteries per patient.84

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Figure 3. Electron beam angiography demonstrating the left anterior descending coronary artery and a large diagonal branch, without evidence of obstructive coronary artery disease. DA=diagnonal artery, LAD=left anterior descending coronary artery.

Figure 4. CT angiography demonstrating the left and right coronary arteries, without evidence of obstructive coronary artery disease. Calcium is seen at the junction of the left anterior descending and diagonal branch. DA=diagonal artery, LAD=left anterior descending coronary artery, LCx=left circumﬂex coronary artery, OM=obtuse marginal, RCA=right coronary artery.

Electron Beam Angiography after Revascularization EBA may play a role in the assessment and follow-up of patients who have undergone coronary interventions.88 The assessment of coronary artery bypass graft (CABG) patency with EBA was reported two decades ago.89 This is due to the fact that the larger caliber and minimal cardiac motion make these vessels less challenging to image than native coronary arteries (Figs 8–10). Flow studies, which determine the rate of contrast enhancement at a particular point in the anatomy, demonstrate graft patency with sensitivities of 93% to 96% and speciﬁcities of 86% to 100%.88,90−93 Both saphenous

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Figure 5. Electron beam angiography demonstrating a heavily-calciﬁed left anterior descending coronary artery with sequential sub-total followed by total occlusion. LAD=left anterior descending coronary artery, LCx=left circumﬂex coronary artery.

Figure 6. Maximal intensity projection demonstrating signiﬁcant disease at the origin of an obtuse marginal branch. LCx=left circumﬂex coronary artery, OM=obtuse marginal.

vein graft patency and stenosis can be determined from 3-Dimensional images in patients who have undergone revascularization. Studies have demonstrated a sensitivity of 92–100% and speciﬁcity of 91–100% for establishing patency of saphenous vein grafts as compared to coronary angiography.88,94,95 These studies demonstrated sensitivity and speciﬁcity for patency of left internal mammary of 80–100% and 82–100% respectively. Assessment of stenosis in the left internal mammary grafts is challenging due to vessel caliber. Interventional cardiology procedures such as percutaneous transluminal coronary angioplasty and stent placement have become important methods of treatment for signiﬁ-

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Figure 7. Electron beam angiography demonstrating the left coronary artery circulation proximally, with non-obstructive plaque. LAD=left anterior descending coronary artery, LCx=left circumﬂex coronary artery.

Figure 8. Non-invasive angiography demonstrating patent saphenous vein grafts to the left anterior descending coronary artery, ﬁrst and second obtuse marginals, and the posterior descending coronary artery. LAD=left anterior descending coronary artery, OM=obtuse marginal, PDA=posterior descending artery, SVG=saphenous vein graft.

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Figure 9. Non-invasive angiography demonstrating right coronary artery occlusion with a patent saphenous vein graft to the distal right coronary artery. RCA=right coronary artery, SVG=saphenous vein graft.

Figure 10. Electron beam angiography demonstrating patent left internal mammary artery graft to the left anterior descending coronary artery, patent saphenous vein graft to an obtuse marginal branch, and an occluded saphenous vein graft to the right coronary artery. LAD=left anterior descending coronary artery, LIMA= left internal mammary artery, OM=obtuse marginal, RCA=right coronary artery, SVG=saphenous vein graft.

cant stenoses of coronary arteries.96 Symptoms of chest pain after coronary interventions raise the possibility of restenosis, and visualization of the site of angioplasty to assess for restenosis is often required. EBA can visualize high-grade restenosis after coronary angioplasty. Achenbach et al.97 reported 50 cases that had performed coronary angioplasty without coronary stent placement. The sensitivity and speciﬁcity of EBA was 94% and 82%, respectively, to detect severe stenosis (≥70% stenosis). Arterial stents limit the ability to visualize the stented segment with EBA, MDCT and magnetic resonance an-

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Figure 11. Non-invasive angiography with plaque in the proximal left anterior descending coronary artery, with both calciﬁed and non-calciﬁed elements.

Figure 12. Electron beam angiography with non-calciﬁed plaque in left anterior descending coronary artery.

giography. EBA ﬂow studies though can evaluate contrast enhancement distal to the stent for patency.98−101 Pump et al.101 reported a sensitivity of 78% (18 of 23 stenoses detected) and speciﬁcity of 98% (189 of 193 stents correctly assessed to be free of stenosis) for the detection of signiﬁcant in-stent restenosis by EBA ﬂow measurements. Assessment of Non-Calciﬁed Plaque The role of CT coronary calcium and CT coronary angiography in the detection of atherosclerosis and obstructive CAD has been discussed. CT angiography’s ability to visualize and characterize “soft” non-calciﬁc coronary plaque is an emerging area of interest (Figs 7, 11, and 12). Autopsy and coronary intravascular ultrasound (IVUS) studies

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have shown that angiographically “normal” coronary artery segments may contain a signiﬁcant amount of atherosclerotic plaque38,102−104,2−5 IVUS allows for a direct, 360◦ visualization of the coronary atheroma within the vessel wall with identiﬁcation of both plaque distribution and composition.102,105 The utility of coronary IVUS over coronary angiography in detecting this plaques is somewhat limited though by a higher procedural complication rate.106 The potential role of identiﬁcation of early, non-obstructive coronary plaques with EBA requires further investigation. The non-calciﬁed “soft” plaque in coronary arteries is measured as the volume under 130 Hounsﬁeld units (HU) on non-enhanced images corresponding to ﬁlling defects on enhanced images. The non-calciﬁed plaque can be divided into low (< 0 HU) and high-density non-calciﬁed plaques (0–130 HU). A previous autopsy study employing EBCT and IVUS in assessment of atherosclerotic plaque challenged the accuracy of EBCT in quantitation of plaque volume and identifying non-calciﬁed atherosclerotic lesions.107 Another study demonstrated a linear relationship between coronary segments with calciﬁed and with non-calciﬁed plaques, but this ﬁnding was highly variable among individual patients.108 In one comparison study of MDCT with IVUS, investigators found a sensitivity of 82% to detect coronary artery segments containing atherosclerotic plaque in patients without signiﬁcant coronary artery stenoses.109 However, segments containing exclusively non-calciﬁed plaque were identiﬁed with a sensitivity of only 53%, and MDCT substantially underestimated plaque burden. Accuracy for plaque detection was lower for smaller plaques and plaques in distal versus proximal vessel segments. Additionally, in regard to non-contrast EBCT, calcium is thought to be more characteristic of stable coronary plaques with acute coronary syndromes resulting from non-calciﬁed lesions.109 The limitations of soft plaque detection potentially extend beyond the limited sensitivity to detect plaque burden. The reproducibility of the measure has not been reported. Additionally, there are no data assessing whether soft plaque adds prognostic information to traditional risk factors, angiographic disease severity and calciﬁed plaque quantitation. Finally, this procedure requires both contrast and radiation. These factors require further investigation in order to deﬁne the possible role and importance of CT coronary angiography as a non-invasive modality for soft plaque imaging. Multidetector CT Coronary Angiography The majority of coronary artery angiography studies reported with MDCT have used 4 slice scanners. Achenbach et al. reported 68% of vessels interpretable by angiography, with 32 of 58 high-grade stenoses were detected (sensitivity 58%).110 However, all four major coronary arteries could be evaluated in only 30% of patients. The authors note, “its clinical use may presently be limited due to degraded image quality in a substantial number of cases, mainly due to rapid coronary motion”. Giesler et al.,111 reported 115 of 400 (29%) coronary arteries uninterpretable, with only 39% of patients were all coronary arteries assessable by MDCT. Overall, 51 (49%) of 104 stenoses were revealed on MDCT. The ability to visualize coronary arteries and detect stenoses is limited with MDCT in patients with heart rates greater than 60 to 70 bpm. One study demonstrated overall sensitivity for stenosis detection decreased from 62% (heart rate <70 bpm) to 33% (heart rate >70 bpm),111 while in another sensitivity dropped from 82% (mean HR 55.8 bpm) to 32% (mean HR 81.7 bpm).112,113

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High radiation doses limit the clinical applicability of MDCT angiography. Radiation doses are two to ﬁve times higher than can be expected for conventional angiography, and 5–10 fold higher than doses obtained during EBA (1–1.7 mSv).114,115 One study reported EBA doses of 1.5–2.0 mSv, MDCT angiography 8.1–13 mSv, and coronary angiography 2.1–2.3 mSv,114 while another reported EBA doses of 1.1 mSv and MDCT doses of 9.3–11.3 mSv.115 There are some limitations which are inherent to both CT modalities in regard to coronary artery imaging. One major limitation is dense calciﬁcation of the coronary arteries, with investigators citing scores >500 or >1000 as problematic. Another limitation of all non-invasive angiography is the relative inability to visualize collaterals. The main determinant of false positive results for diagnosing ≥ 50% coronary luminal stenosis was small vessel size and the diameter of stenotic segments tends to be underestimated by CT angiography.81 The use of the 16–32 slice MDCT scanners allows for faster and thinner imaging than the 4-slice scanners. Two studies have been reported, each with improved accuracy as compared to prior reports with 4-slice scanners. These studies reported sensitivity of 73–95% and speciﬁcity of 86–93%.116,117 Both studies concluded the MDCT with beta-blocker pre-medication permits detection of CAD with improved accuracy. However, new studies demonstrate that radiation doses are still prohibitive with these newer multi-slice scanners.118 Reduced radiation doses and improved rotation times will make MDCT a more clinical useful modality. Additionally, newer generations of scanners with larger numbers of detectors may soon be available. Applications of CT Coronary Artery Angiography The most common clinical application of CT angiography is to evaluate patients with symptoms post-CABG surgery and coronary angioplasty evaluation, assessment of congenital heart disease and coronary anomalies,119 and measurement of wall motion, myocardial mass as well as right and left ejection fractions.120 Additional potential applications of non-invasive CT angiography include assessment after non-diagnostic stress tests in those persons with an intermediate likelihood of CAD, and for early detection of obstructive CAD in the high-risk person. CT angiography (EBA and MDCT) are rapidly evolving technologies for coronary artery assessment. These studies do not serve as an alternative to conventional coronary angiography in all cases. Given the high negative predictive values, use in patients with lower probabilities of obstructive disease will potentially allow physicians to exclude obstructive CAD in proximal and mid-vessels. Further study of this noninvasive coronary imaging technique may lead to broader clinical applications for the assessment of obstructive coronary artery disease. Ventricular Structure and Function Advances in image acquisition and data processing have allowed for characterization of ventricular structures and function with CT angiography, with reproducible quantitative measurement of left ventricular ejection fraction,121,122 ventricular volumes,123−125 ventricular mass,126,127 wall thickness,128 and regional wall motion129,130 in cardiomyopathic processes (Fig. 13). These data can be integrated with coronary artery assess-

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Figure 13. Profound four chamber enlargement in a patient with ischemic cardiomyopathy.

ment for a comprehensive assessment of the role that coronary artery disease plays in the cardiomyopathic process. Cine scanning allows for assessment of systolic and diastolic function. The spatial resolution and contrast enhancement adequately deﬁnes the endocardium of both the right and left ventricles, so that precise measurement of biventricular cardiac volume and ejection fraction is possible. Left ventricular mass can also be quantiﬁed. Quantitative measurement of regional wall motion and wall thickening can be performed, particularly useful for evaluating CAD patients. Application of this technique may prove useful for detecting changes in left ventricular function induced by myocardial ischemia, as well as accurately diagnosing ejection fraction post infarction.131 Bicycle exercise can be used with CT scanning to detect exercise-induced ischemia. A decrease in ejection fraction and development of a new wall motion abnormality have been shown to be accurate for detection of ischemia, with data indicating that exercise CT may be at least as sensitive and more speciﬁc than technetium 99m sestamibi stress testing.132 Noninvasive quantitation of myocardial blood ﬂow is also possible by evaluating ﬂow patterns of iodinated contrast on CT. Myocardial blood ﬂow is proportional to the peak iodine concentration in the myocardium after intravenous injection of contrast medium. The technique is accurate for myocardial ﬂows up to 2 ml/min/g. Technical factors may cause inaccuracies, therefore further research is required for the development of clinically useful methods for accurate quantiﬁcation of blood ﬂow measurements. Based on the principle that blood ﬂow is proportional to iodine concentration during contrast medium infusion, acute MI can be imaged by CT as a region of little or no iodine (low density). This technique has been used to detect MI, and quantitate the infarct size, as well as the patency of the infarct vessel, using both ﬂow and 3-Dimensional techniques. Complications of myocardial infarction, including ventricular septal defects, thrombi, aneurysms and pericardial effusions can all be visualized by CT. The ability to document abnormalities of ventricular structure and function coupled with the ability to assess coronary artery calcium and angiographic coronary artery disease makes EBCT a useful tool in the assessment of cardiomyopathic processes. Deﬁnition of etiology of cardiomyopathy, quantitate function, can facilitate decision-making

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as well as approaches to intervention in patients with dilated and ischemic cardiomyopathy. Recent large scale multicenter trials have generated criteria for treatment of speciﬁc cardiomyopathy substrates based on ejection fraction and etiology of cardiomyopathy for sudden death primary prevention as well as for the treatment of heart failure. In MADIT II, criteria for implantation of a deﬁbrillator for sudden death prevention are a substrate of ischemic cardiomyopathy with an ejection fraction of less than or equal to 30%.133 Since EBCT angiography can provide a quantitative volumetric assessment of ejection fraction, and can differentiate ischemic from non-ischemic dilated cardiomyopathy based on coronary calcium scores69 and direct visualization of coronary artery anatomy, this modality may prove useful in providing the information necessary to proceed with therapies.. As more large scale trials become available which deﬁne indications for therapy based on speciﬁc cardiomyopathic substrates, the ability to precisely deﬁne cardiac function of both the right and left ventricles by slice-by slice tomographic volumes may have greater importance. Hypertrophic cardiomyopathy can lead to heart failure symptoms and sudden cardiac death.134−136 Echocardiography is the main diagnostic modality for the diagnosis of hypertrophic cardiomyopathy and in addition to anatomy can assess resting and exercise gradients and associated valve function.137,138 The diagnosis can be made by CT angiography139−141 and magnetic resonance imaging,142−144 which can provide details of regional wall thickness, indexed ventricular mass, and ejection fraction. Assessment of right ventricular structure and function abnormalities has risen in importance due to the recognition of signiﬁcant disease processes involving the right ventricle.145 Visualization and assessment of right ventricular function is difﬁcult by echo and cardiac catheterization. EBCT angiography may potentially be an effective tool for assessment of right ventricular anatomy and function.146−148 Right ventricular pathology, such as right ventricular dysplasia can be difﬁcult to diagnose, and often the initial presentation is sudden death.149150 In terms of visualization of right ventricular abnormalities, echocardiography lacks sensitivity.151 MRI has been the modality of choice for anatomic evaluation of right ventricular dysplasia due to its superior ability to deﬁne tissue characteristics such as myocardial fat deposits, but the variation in fat content and location in patients without this process makes this criterion only of modest clinical utility.152 EBCT angiography has been assessed for ability to diagnose anatomic features associated with right ventricular dysplasia, such as epicardial and myocardial fat, low-attenuation trabeculations, and right ventricular free wall scalloping, but has not been assessed as a screening tool (Fig. 14).153−155 Aorta and Aortic Valve Pathology Aortic aneurysm is associated with risk for sudden death due to aortic dissection or rupture and can occur associated with connective tissue disorders or acquired cardiovascular disease.156 CT angiography can diagnose aneurysm, dissection, and wall abnormalities such as ulceration, calciﬁcation or thrombus throughout the full length of the aorta as well as involvement of branch vessels. CT can also indirectly help in the assessment of aortic valve disease. Critical aortic stenosis usually diagnosed by clinical exam coupled with echocardiography. Aortic valve calcium is a marker for signiﬁcant aortic valve stenosis, and patients with elevated calcium scores should be screened with echocardiography for aortic valve disease.157

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Figure 14. Right ventricular intramyocardial fat deposition associated with right ventricular dysplasia.

CT has also been used to further delineate tissue characteristics associated with aortic stenosis.158 Congenital Heat Disease Due to advances in surgical management, many patients with congenital heart disease are living into adulthood.159 The ability to assess the 3-Dimensionsional relationships between cardiac, arterial, and venous structures makes CT angiography useful in the diagnosis and follow-up of patients with congenital heart disease in its native and postoperative forms.160 CT angiography is well-suited to the evaluation of congenital abnormalities of the coronary arteries (Fig. 15). A rare but important abnormality relating speciﬁcally to coronary arteries is anomalous origin of the coronary arteries, with sudden death in young persons during exertion often being the initial presentation.161,162 Identiﬁcation can be difﬁcult by other modalities. Speciﬁc anatomies are associated with risk of sudden cardiac death including takeoff of the left coronary artery from the pulmonary trunk, left coronary artery from the right aortic sinus, and right coronary artery from left aortic sinus.163 Anomalous coronary arteries can be deﬁned non-invasively by EBCTA,164 as well as by magnetic resonance imaging165,166 and transesophageal echocardiography.167 A spectrum of cyanotic and acyanotic congenital anomalies can be visualized and characterized by CT angiography (Figs 16 and 17).168−171 Studies can assess patency of shunts, pulmonary hemodynamics associated with shunts, central pulmonary artery anatomy, anomalous vascular connections, pulmonary vein obstruction, partial anomalous pulmonary venous connections, and other associated thoracic abnormalities such as tracheobronchial abnormalities.172−179 CT angiography can provide detailed and comprehensive assessment of complex anatomy for surgical planning.180,181 Congenital abnormalities of the aorta such as coarctation can be easily identiﬁed and assessed with 3-Dimensional imaging (Fig. 18).182

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Figure 15. Anomalous coronary artery with left main coronary artery arising from the right coronary cusp. RCA=right coronary artery.

Figure 16. Secundum atrial septal defect with predominant left to right shunting. Right atrial enlargement and right ventricular hypertrophy are present. ASD=atrial septal defect, LA=left atrium, RA=right atrium, RV=right ventricle.

As many congenital abnormalities are associated with signiﬁcant conduction abnormalities or ventricular arrhythmias, many patients with congenital heart disease have pacemakers or implantable cardiac deﬁbrillators in place, contraindicating use of MRI for imaging. MRI may be more applicable to younger patients due to lack of radiation exposure, but longer study times require a greater need for anesthesia.183 Coronary Veins The same techniques that allow visualization of coronary arteries also visualize the coronary veins. The coronary venous anatomy has become increasingly important as many in-

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Figure 17. Subaortic restrictive ventricular septal defect to pulmonary outﬂow tract. The defect has a 5 mm origin and a tortuous course tapering in size as it enters the pulmonary outﬂow tract. ASD=atrial septal defect, LA=left atrium, RA=right atrium, RVOT=right ventricular outﬂow tract, VSD=ventricular outﬂow tract.

Figure 18. Coarctation of the aorta. Prominent vertebral artery vessels are noted.

terventional procedures use the coronary veins to obtain venous access to the left atrium and left ventricle. EBCT angiography is effective for visualization of the coronary sinus and its tributaries.184,185 CT angiography can provide detailed assessment of the coronary venous anatomy, with coronary sinus dimensions, branch vessel locations, diameters, angulations off of the coronary sinus/great cardiac vein, and associated myocardial segment location. Particular attention has been focus on coronary venous anatomy with the increasing application of resynchronization therapy.186−189 In resynchronization therapy, simultaneous biventricular pacing is performed in patients with dilated or ischemic cardiomyopathy, signiﬁcant heart failure, and prolonged interventricular conduction in order to

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“resynchronize” right and left ventricular activation and contraction. The left ventricular component of pacing is provided by a chronic pacing lead placed in a coronary sinus branch vessel, with placement often being challenging due to need to instrument small coronary vein branches for adequate pacing sites. Large multicenter randomized trials have demonstrated that resynchronization therapy decreased heart failure symptoms, improved quality of life, and improved ventricular function in selected heart failure populations.186−189 As potential left ventricular pacing sites are deﬁned by an individual patient’s coronary venous anatomy, detailed anatomic information could potentially play a role in the approach to resynchronization therapy. Many patients undergoing resynchronization therapy already have devices in place with upgrade to a biventricular system, precluding visualization of anatomy by MRI. Pulmonary Veins Characterization of pulmonary venous anatomy important to catheter-based therapies for atrial ﬁbrillation. Atrial ﬁbrillation has become a major area of research focus due to its increasing incidence in an aging population.190,191 In contrast to other atrial arrhythmias, pharmacologic and procedural therapies have proven challenging, as there appear to be a variety of different pathophysiologic mechanisms leading to the same endpoint rhythm including: pulmonary vein and other atrial foci,192−195 atrial scar,196,197 elevated atrial pressures and stretch,198 autonomic tone,199 and sinus node dysfunction.200 Due to the multiple and often coexisting triggers, treatment often consists of a multimodal approach with pharmacologic, pacing, and catheter-based and surgical ablation procedures. Procedural efforts have focused on ablation of pulmonary vein as well as other potential non-vein premature atrial contraction foci, isolation of pulmonary veins, and creation of preferential pathways of electrical conduction in the atria.201−206 CT angiography and MRI can provide detailed information on pulmonary vein location, variation, size, and complexity, difﬁcult to visualize by other techniques, is important for ablation of pulmonary vein triggers and electrical isolation of pulmonary veins.207,208 Endoscopic views of the left atrium can now be achieved through software advances to visualize the complexity of each pulmonary vein os. Additionally, follow-up of patients for such complications as pulmonary vein stenosis is extremely important.209−213 The incidence and time course of pulmonary vein stenosis requires further deﬁnition, through serial evaluation of pulmonary vein structure. As many patients with atrial ﬁbrillation pacemakers due to a history of sinus node dysfunction, the use of MRI for the evaluation of pulmonary vein anatomy may be limited in some patients. Summary CT coronary artery calcium assessment and CT coronary angiography using EBCT or MDCT are technologies which can provide risk stratiﬁcation for future cardiac events and deﬁnition of patient populations requiring aggressive risk factor modiﬁcation or interventional therapy for CAD. CT angiography is a robust technology which can identify a spectrum of cardiovascular disease processes and facilitation of invasive cardiac procedures. Further advances in technology and methodology will broaden the research applications for the understanding of cardiovascular pathophysiology and clinical applications for diagnosis and treatment of cardiovascular disease. These efforts will hopefully

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enhance our ability to non-invasively detect cardiovascular disease, so that appropriate therapies can be instituted.

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Plaque Imaging: Pixel to Molecular Level J.S. Suri et al. (Eds.) IOS Press, 2005 © 2005 The authors. All rights reserved.

Tomographic Plaque Imaging with CT John RUMBERGER HealthWISE Wellness Diagnostic Center Dublin, Ohio 43017 Abstract. X-ray computed tomography (CT) is widely available in the world and has the ability to provide high deﬁnition, thin section imaging of any body part. In particular, CT over the past decade has been shown in numerous publications to allow for quantitation of coronary calciﬁcation, a proven surrogate for coronary artery atheromatous plaque. Electron beam tomography (EBT) and multi-detector CT (MDCT) have been studied for these purposes; although the majority of the data has been derived from EBT studies. This chapter details the patho-biology of atherosclerotic disease, the basis of using EBT (and/or CT in general) to deﬁne atherosclerotic plaque including the technical and engineering pitfalls and promises, and details issues of clinical application. Keywords. Computer tomography, cardiac, atherosclerosis, coronary calcium, electron beam tomography, multi-detector computed tomography, resolution, calcium scoring, epidemiology

Introduction X-ray computed tomography (CT) can provide exquisite, rapid, high resolution imaging of the body and in particular the heart (and vascular system in general). Tomographic imaging by CT has had signiﬁcant advances in temporal and spatial resolution to facilitate non-invasive cardiac imaging. In particular both electron beam tomography (EBT) and multi-detector CT (MDCT) have shown applicability, under certain deﬁned circumstances, for coronary artery imaging and atherosclerotic plaque identiﬁcation. The current section details technical and practical issues regarding coronary atherosclerotic plaque imaging by CT, which then help deﬁne its technical capabilities and engineering limitations for clinical usage. The focus will be on coronary calcium imaging, but the principles are the same for atherosclerosis deﬁnition in any major artery.

Atherosclerosis Atherosclerotic plaque is the common feature of coronary and vascular disease. The process however proceeds at different rates and at different anatomic sites between individuals. Figure 1 demonstrates the spectrum of atherosclerotic plaque disease in the coronary arteries. This demonstrates also the path of time in many instances. So called “fatty streaks” can appear in the coronary artery wall (mural surface) in infancy and then

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Figure 1. Spectrum of atherosclerotic plaque development. Plaque begins as a “fatty streak” but develops over year to an advanced atherosclerotic lesion. See text for details.

may disappear by the time we are 3–5 years old. Atherosclerosis begins in earnest actually when most of us are teenagers. Studies using intravascular ultrasound in perspective heart donors for heart transplantation(1) have suggested as many as 25% of 16–19 year-olds have raised atheromatous plaque. Coronary calciﬁcation actually occurs relatively early in the atherosclerotic process. Figure 1 demonstrates the mural surfaces actually enlarging or “remodeling” as plaque develops. “Coronary remodeling” associated with the development and progression of atherosclerotic disease is a well-established phenomena whereby the luminal cross-sectional area and/or external vessel dimensions enlarge in compensation for increasing areas of mural plaque.(2) As plaque develops, largely due to an immune inﬂammatory response that is almost “self-sustaining” (i.e. the more cholesterol build-up, the more esteriﬁcation and inﬂux of inﬂammatory cells), the plaques can become unstable and may lead to plaque rupture, which can then lead to arterial blockage. The process can be summarized as follows: 1. Plaque builds up to a “critical mass” at one or many sites in the walls of the arteries. 2. A “trigger” due to continued inﬂammation surrounding the plaque causes sudden rupture of the plaque through the wall of the blood vessel. 3. This rupture exposes the inﬂammatory cells and cholesterol in the plaque to the blood ﬂowing through the artery. 4. For just the same reason that you don’t bleed to death when you cut yourself shaving, the body recognizes a “break” in the lining of the blood vessel and responds by attempting to close it off by having blood elements such as platelets and clotting factors come into play. 5. Often the small break in the blood vessel can be healed and the vessel continues its role of delivering blood to the part of the body supplied by that artery; however, all too often, the job of plugging the break results in plugging the entire vessel and then blood ﬂow stops to the region “downstream” from the clot. 6. If this blockage persists for as little as 20 minutes for the heart muscle in particular the section is then beyond help of being revived, the damage cannot be repaired, and a part of the body dies (becomes “infracted”).

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The process of inﬂammation, repair, rupture, and repair over and over again can lead to chronic blockage that produces enough restriction to blood ﬂow to produce “ischemia” of the involved organ. In the heart it is really the sheer number of potential “vulnerable” plaques that indicate the potential for a heart attack that actually are the culprits in most instances and not the number of “severe” blockages. General Pathology of Coronary Calcium Atherosclerosis is the only disease known to be associated with coronary calciﬁcation.(3−7) Recent studies have shown that calcium can be seen in all degrees of atherosclerotic involvement and is an active process.(8−12) Coronary calciﬁcation is common in patients with known coronary artery disease(13−17) , and is strongly related to age, increasing dramatically after age 50. McCarthy(13) studied 65 consecutive autopsy derived hearts (death not necessarily of cardiac causes) and found 63% to have some coronary artery calciﬁcation, nearly always associated with some degree of luminal coronary artery disease. Ninety-four percent of the coronary arteries studied from patients older than 60 years demonstrated some degree of calciﬁcation. In a series of 360 (living) patients undergoing cardiac catheterization and coronary ﬂuoroscopy, Bartel(18) found a 43% prevalence of calciﬁcation, and roughly 60% of patients studied over age 60 had some calciﬁcation noted by ﬂuoroscopic examination. In a separate study of individuals from the general population not known to have coronary disease, the prevalence of calciﬁcation by ﬂuoroscopy has been reported to be roughly 20%.(16) Since Faber(19) in 1912 noted that Mönckeberg’s calciﬁc medial sclerosis does not occur in the coronary arteries, atherosclerosis is the only vascular disease known to be associated with coronary calciﬁcation. Many reports relate the amount of coronary calciﬁcation to the severity of stenoses. For example, in the autopsy series mentioned above(13) , signiﬁcant stenosis and/or occlusion was virtually certain if calciﬁcation was present in segments longer than 1 centimeter. This relation has been borne out by other studies as well.(3,4,20) Hamby(21) found that 81% of patients with angiographic two or three-vessel disease had coronary artery calciﬁcation. Mintz et al.(22) studied 110 men and women undergoing coronary angioplasty for symptomatic coronary artery disease. The presence of target lesion calciﬁcation was identiﬁed in 75% of these individuals using intravascular ultrasound. Coronary artery calcium is an intimate component of some plaques. Clarkson(23) in a histopathology investigation has shown that plaques with microscopic evidence of mineralization were much larger and were associated with much larger coronary arteries than those sections without microscopic evidence of calciﬁcation. This was true in humans and in non-human primates. The compensatory enlargement of atherosclerotic coronary segments may explain why coronary angiography frequently underestimates the severity of coronary disease as compared with histopathologic studies. Studies attempting to correlate the site and amount of coronary calcium with percent luminal narrowing at the same anatomic site have shown a positive but non-linear relationship with large conﬁdence limits.(24) However, coronary plaque and its associated coronary calciﬁcation may have only a poor correlation with the extent of histopathologic stenosis,(22,24) which in turn is largely accounted for as a result of individual variations in coronary artery remodeling. In-situ coronary calcium, on the other hand, is associated with plaque size.(24) A study by Rumberger et al.(25) has emphasized that the total area of coronary artery calciﬁcation is correlated in a linear fashion with the total area of coronary artery plaque

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Figure 2. Left – an advanced atherosclerotic plaque demonstrating a very small residual lumen (blood ﬂow channel). The dark or black material is calcium hydroxy apatite. Right – An x-ray of the histologic section shown at right. The areas of “calciﬁcation”, corresponding to the calcium hydroxy apatite, are apparent.

Figure 3. Coronary artery calcium area as determined by direct x-ray (see Fig. 2) and planimetered atherosclerotic plaque area (see Fig. 2) along one coronary artery. Sampling was every 3 mm along the blood vessel. Note that the calcium precisely tracks the plaque, although the total calcium area underestimates the plaque area in a predictable fashion.

on a segmental, individual coronary artery, and whole coronary artery system basis. Figure 2 shows an advanced atherosclerotic plaque (left) and the corresponding “x-ray” image of that section. Furthermore, coronary artery calcium tracks plaque on a site-by-site basis (Fig. 3). However, the areas of coronary calciﬁcation are on the order of 1/5 that of the associated coronary plaque. Additionally, there are clear areas of plaque without associated coronary calcium as detected with x-ray. These data suggest that there may be a size of coronary plaque that is most commonly associated with coronary calcium but, in the smaller plaques, the calcium is either not present or is undetectable. The original autopsy study by Simons et al.(26) evaluating EBT consisted of 13 hearts included those from 5 women and 8 men. In this study, the 3 major epicardial arteries were dissected, each artery straightened, and scanned using EBT in contiguous 3 mm thick cross sections. After imaging, histologic sections were prepared at corresponding

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Figure 4. Measures of coronary artery calcium by EBT per autopsy heart and atherosclerotic plaque found at autopsy as a function of age. Total of 13 autopsy hearts in individuals between the ages of 17 and 80.

intervals and luminal area obstruction determined by planimetry. The total amount of plaque is also strongly dependent on age (Fig. 4). A total of 522 [182 in women and 340 in men] histologic specimens were examined and paired with corresponding EBT scans. Receiver-operating characteristic (ROC) analysis was used to deﬁne site speciﬁcity of calcium area for luminal area narrowing by atherosclerosis.(27) ROC curve areas for segmental EBT calcium and prediction of mild (maximum lumen stenosis <50% diameter narrowing), moderate (maximum stenosis at least 50% diameter narrowing), and severe (maximum stenosis at least 75% diameter narrowing) were, respectively, 0.712, 0.843, and 0.857 for women and 0.732 (p = NS), 0.793 (p = NS), and 0.841 (p = NS) for men. Curves relating false-positive rate sclerotic narrowing versus EBT quantiﬁed coronary calcium area were curvilinear. Examples of those data for women are shown on Fig. 5. Figure 5, left is the ROC curve for women based upon calcium area and the presence in the same histologic region of varying luminal stenoses. Figure 5, right represents the linear measure of the calcium area in a given histologic section and the false positive rate [deﬁned as {1-speciﬁcity}]. In both men and women, an EBT measured coronary calcium area of 1 mm2 in any histologic specimen gave a false positive rate of 0%. For both men and women a segmental calcium area of 2.0–2.5 mm2 by EBT showed no false positives for the presence of moderate coronary stenoses, while a segmental EBT calcium area of 3.0–3.5 mm2 was associated positively with the presence of severe luminal disease at the same anatomic site. However, coronary plaque disease is a diffuse process and although calcium may not be seen in one particular area, if the overall plaque burden is sufﬁcient, coronary artery calcium will be identiﬁed. Molecular Biology of Coronary Calcium Calcium phosphate, in the form of hydroxyapatite, and cholesterol accumulate in atherosclerotic lesions. Circulating proteins normally associated with bone remodeling play an important role in coronary calciﬁcation. Although the true role of calcium in the atherosclerotic process is unknown, new insights into the pathophysiology of coronary calciﬁcation have come within the past several years. Fitzpatrick et al.(28) used in-situ hybridization to identify mRNA of matrix proteins associated with mineraliza-

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Figure 5. ROC curves for coronary calcium and plaque severity (see text for details).

tion in coronary artery specimens. Speciﬁcally, they identiﬁed from autopsy coronary artery specimens a cell attachment protein (osteopontin), a protein associated with calcium (osteonectin) and a gamma carboxylated protein that regulates mineralization (osteocalcin). Similar studies have shown that osteopontin can be seen in tissue demonstrating atherosclerotic involvement and appears to be present only in sites of concomitant coronary atherosclerotic disease. Hirota et al.(12) demonstrated by Northern blotting that osteopontin mRNA expression is related to the severity of the atherosclerosis. Additionally, osteonectin expression of mRNA decreased with the development of atherosclerosis. Shanahan(9) and Ideda(11) have independently demonstrated the predominant cell types in these areas are macrophage-derived foam cells, although some smooth muscle cells were also identiﬁed. Finally, Bostrom et al.(8) identiﬁed bone morphogenetic protein-2a, a potent factor for osteoblastic differentiation, in calciﬁed human atherosclerotic plaque. Cells cultured from the vascular wall formed calciﬁed nodules similar to those found in bone cell cultures. The predominant cells in these nodules had immunocytochemical features characteristic of microvascular pericytes, which are capable of osteoblastic differentiation. These ﬁndings suggest that arterial calcium in atherosclerosis is a regulated process similar to bone formation rather than a passive precipitation of calcium phosphate crystals. In summary, numerous studies have conﬁrmed that arterial calcium development is intimately associated with vascular injury and atherosclerotic plaque evolution and is largely controlled by common cellular and sub-cellular mechanisms. Calcium can be seen in all degrees of atherosclerotic involvement and is an active process; thus, the long held notion of so-called “degenerative” calciﬁcation of the coronary arteries with aging is not correct. Although there is an increasing incidence of coronary calciﬁcation in patients as one grows older, this simply parallels the increased incidence of coronary atherosclerosis with advancing age. CT Methods This section will discuss methods related to coronary artery calcium identiﬁcation. Speciﬁc methods of contrast enhanced coronary lumen imaging using EBT and MDCT are discussed elsewhere.

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EBT Methods Electron Beam Tomography [EBT] is a mature FDA approved body-imaging device developed over 20 years ago and is the only CT device speciﬁcally designed from inception for cardiac imaging. Although the technique can quantify ventricular anatomy and global and regional function(29) as well as myocardial perfusion(30) , it is currently best known for deﬁning and measuring coronary artery calciﬁed plaque and for performing non-invasive coronary angiography. To date, and speciﬁcally over the past decade, there have nearly 1000 articles published regarding the validation of EBT for coronary artery plaque and lumen imaging. EBT [also referred to as “Ultrafast-CT”, GE/Imatron Inc., South San Francisco, CA] employs unique technology enabling ultrafast scan acquisition times currently of 33 msec, 50 msec, 100 msec, and multiples of 100 msec [up to 1.5 seconds] per slice. There have been 3 iterations for EBT since it was introduced clinically in the early 1980’s. The overall imaging methods have remained unchanged, but there have been improvements in data storage, data manipulation and management, data display, and spatial resolution. The original C-100 scanner was replaced in 1993 by the C-150, which was replaced by the C-300 in 2000. The current EBT scanner, the “e-speed” (GE/Imatron) was introduced in 2003. The “e-speed” is a multi-slice scanner and currently can perform a heart or body scan in one-half the total exam time required by the C-150 and C-300 scanners. The “e-speed”, in addition to the standard 50 msec and 100 msec scan modes common to all EBT scanners, is capable of imaging speeds as low as 33 msec, but as of this writing, no validation studies on the applicability of calcium scoring in this mode are available. Thus, the current discussion of EBT will focus on the established methods of the C-150 and C-300 imaging systems. EBT employs a stationary multi-source/split-detector combination coupled to a rotating electron beam and produces serial, contiguous, thin section tomographic scans in synchrony with the heart cycle. EBT is distinguished by its use of a scanning electron beam rather than a traditional x-ray tube and mechanical rotating device used in current “spiral” single and multiple detector scanners. The electron beam [cathode] is steered by an electromagnetic deﬂection system that sweeps the beam across the distant anode, a series of 4 ﬁxed tungsten “target” rings. A stationary, currently dual level, detector lies in apposition to the tungsten target rings. Thus, as opposed to physically moving the x-ray tube in a circle about the patient, as is done by the mechanical CT (spiral) scanners, only the electron beam is moved in EBT. Standardized methods for imaging, identiﬁcation and quantiﬁcation of coronary artery calcium using EBT have been established.(7) The scanner is operated in the high resolution, single slice mode with continuous, non-overlapping slices of 3 mm thickness and an acquisition time of 100 msec per tomogram. Patients are positioned supine and, after localization of the main pulmonary artery, a sufﬁcient number of tomographic slices are obtained to cover the complete heart through the left ventricular apex (usually 36 to 40 slices). Electrocardiographic triggering is done at end-diastole at a time determined from the continuous ECG tracing recorded during scanning. Current clinical protocols for EBT perform triggering during the cardiac cycle as varied depending on the patient’s resting heart rate. This is intended to minimize coronary motion artifacts since the ballistics of cardiac motion are highly dependent on resting heart rate. The presence of coronary calcium is sequentially evaluated in all levels. Coronary calcium is deﬁned as a hyperattenuating lesion above a threshold of 130 “Hounsﬁeld

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Units” with an area of 3 or more adjacent pixels [at least 1 mm2 .]. CT Hounsﬁeld Unit (HU) densities range from −1000 [air], through o [water], and up to +1000 [dense cortical bone]. The “calcium score” developed by Agatston(31) and predicated on a 3 mm slice thickness is a product of the area of calciﬁcation per coronary segment and a factor rated 1 through 4 dictated by the maximum calcium CT density within that segment. A calcium score is reported for a given coronary artery and segment and for the entire coronary system; however, most research studies have reported data related to the summed or total “score” for the entire epicardial coronary system. Quantiﬁcation of coronary artery calcium using EBT scanning has been proven as a valid surrogate for atherosclerotic plaque burden and as a measure of the severity of coronary disease in direct pathologic comparison studies(32) regardless of age or gender(27) , and in clinical studies using coronary angiography(33) and intravascular ultrasound(34) as reference standards. MDCT Methods The current generation of multi-detector computed tomography (MDCT) systems are capable of acquiring 4, 8, 16 or 32 (and potentially soon 64) levels of the heart simultaneously with ECG gating in either a prospective or retrospective mode. The MDCT differ from single slice helical or spiral CT systems principally by the design of the detector arrays and data acquisition systems that allow the detector arrays to be conﬁgured electronically to acquire multiple levels of various slice thickness simultaneously. Thus in the current 16 channel MDCT systems 16 slices can be acquired at nominally 1.25 mm slice widths for cardiac imaging. As of 2003, four channel MDCT systems are the most widely deployed with an estimated installed base in the U.S. of over 2,000 but more 16-channel systems are being installed currently. In MDCT systems, like the preceding generation of single slice helical scanners, the X-ray photons are generated within a specialized X-ray tube mounted on a rotating gantry. The patient is centered within the bore of the gantry such that the array of detectors is positioned to record incident photons after traversing the patient. Within the X-ray tube a tungsten ﬁlament allows the tube current to be increased (mA) which proportionately increases the number of X-ray photons for producing an image. This is a design difference with current generation EBT systems, which use a ﬁxed mA. The attenuation data (after passing from the source, through the body, and incident on the detector array) are recorded and transformed through a ﬁltered back-projection into the CT image. This ﬁnal step is common to both EBT and MDCT. Helical and MDCT systems have two principal modes of scanning which are dependent upon whether the patient on the CT couch is stationary (axial mode) or moved at a ﬁxed speed relative to the gantry rotation (helical mode). The axial mode utilizes prospective ECG triggered at predetermined offset from the ECG detected R wave analogous to EBT (but at a physically slower speed per image than EBT) and is the current mode for measuring coronary calcium at most centers using MDCT. This mode if preferred mainly due to issues of keeping the radiation dose similar to that of EBT (see later discussion on radiation dosimetry). Current MDCT systems allow 4, 8, 16 or 32 slices to be obtained within a single heartbeat. The temporal resolution of a helical or MDCT system is determined by the gantry speed, which determines the number of views per second possible. To reconstruct each slice 180 degrees plus the angle of the fan beam is required, typically a total of 220 degrees of rotation. For a 32-channel system with 0.4 sec rotation the temporal resolution

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is 0.244 seconds or 244 msec for a 50 cm display FOV (ﬁeld of view). By reducing the display FOV to the 20 cm to encompass the heart the number of views can be reduced to, theoretically further improving temporal resolution for a 32-channel scanner to approximately 200 msec. The majority of MDCT systems available in most hospitals in 2004 have gantry speeds of 0.5 to 0.75 seconds and temporal resolution of 320–500 msec per image when used for measuring coronary calcium, as compared to 100 msec or less for EBT. The rapid evolution of MDCT while potentially of great value for CAC quantitation makes current application of guidelines for MDCT uses more confusing. All comparisons between MDCT and EBT data show good group correlation values but with each improvement in MDCT speed and slice proﬁle the correlation with EBT is found to be better despite the strong claims of comparability declared by vendors of preceding generations. Another issue relates to the image “slice thickness” used for imaging, which varies between manufacturers. The issue of slice thickness and the effects on calcium scoring are discussed in a later section.

Variability and Calibration When comparing measurement devices calibration to an external standard is crucial for comparability between both EBT and MDCT over time. Signiﬁcant variability in the measurement of the 130 HU threshold has been documented within and between EBT scanners even when serviced and maintained at the same site.(35) Use of an external calibration phantom was shown to reduce scanner variation with EBT by 25%. Since there may be measurement errors both within the same and between different EBT systems [largely due to differences of FOV (ﬁeld of view) settings, thus affecting spatial resolution] comparison of MDCT systems to EBT by deﬁnition will included the measurement error of the EBT system plus the measurement error with MDCT. Furthermore, differences in scanner calibration, equipment age, hardware and software versions, KVp and reconstruction kernel will result in differences in CT scanners (EBT or MDCT) for measuring CT numbers at the threshold for measurable calciﬁed plaque. The papers by Goldin(36) and Carr(37) both document how agreement at various cut-points can be inﬂuenced based on whether a threshold of 90 HU or 130 HU was deﬁned as threshold for measurable calciﬁed plaque and document the need for calibration of the calcium score. Spatial Resolution Spatial resolution is important in all three dimensions when measuring coronary plaque. Even if limited to the proximal coronary arteries, the vessels course obliquely along the Z- (longitudinal) plane as well as within the X-Y (transverse) imaging plane. The inplane resolution of both EBT and MDCT systems is equivalent at the same display ﬁelds of view. For a display ﬁeld of view of 26 cm (preferred for EBT scanning) and 35 cm the respective pixel areas are 0.26 mm2 and 0.46 mm2 respectively. The Z dimension is determined by the slice collimation that with current protocol for coronary calcium is 3 mm for EBT but varies between manufacturers from 2.5 mm to 3.0 mm for MDCT. Since even the proximal coronary arteries are often less than 5 mm in diameter, this can easily

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result in an effect termed “partial volume averaging”. This can be explained as an object, in this case a small calciﬁed plaque, having dramatically different CT numbers related to whether it is centered within one slice or divided between two adjacent slices. Difﬁculties in measuring small plaques and distinguishing them from image noise is an established limitation of current methods and likely contributes to the observed variability with both EBT and MDCT when performing repeated scans in the same individual.(38,39) Improved spatial resolution in the Z-axis will reduce this source of measurement error and is possible with current MDCT systems(40,41) and with the latest generation of EBT.

Imaging Speed/Temporal Resolution Overall CT image quality is dependent upon multiple factors throughout the imaging sequence. These include image noise, blurring, spatial resolution and other factors related to both the imaging device and patient. In the case of measuring calciﬁed plaques of various sizes temporal resolution, spatial resolution, and image noise are important to varying degrees. Cardiac CT is dependent upon having a high temporal resolution to minimize coronary motion. By coupling rapid image acquisition with ECG gating (MDCT) or triggering (EBT), images can be acquired in speciﬁc phases of the cardiac cycle. Studies have indicated that temporal resolutions of 19 msec are needed to suppress all pulmonary and cardiac motion.(42) Cardiac MR motion studies of the coronary arteries indicates that the rest period of the coronary artery varies signiﬁcantly between individuals with a range of 66–333 msec for the left and 66–200 msec for the right coronary artery(43) and that for mapping coronary ﬂow temporal resolution of 23 msec may be required for segments of the right coronary artery.(44,45) Current generation cardiac CT systems that create images for measuring calciﬁed plaque at 100 msec (EBT) and 220–500 msec (MDCT) cannot totally eliminate coronary artery motion in all individuals (except possibly for the “e-speed” EBT scanner operating in the 33 msec mode). Motion artifacts are especially prominent in the mid-right coronary artery, where the ballistic movement of the vessel may be as much as 2–3 times it diameter with the twisting and torsion of the heart during a single cardiac cycle. Blurring of plaques secondary to coronary motion increases in systems with slower acquisition speeds. The resulting artifacts tend to increase apparent plaque area (“blooming”) and decrease plaque density, and thus alter calcium score measurements. It should be noted that utilizing more detectors (i.e. 2 vs. 4 vs. 8 vs. 16 vs 32 detector/channel systems) does not improve the temporal resolution of the images obtained. In a recent study of MDCT, a majority of non-invasive angiography cases could not be fully evaluated due to motion artifacts, especially when the heart rate was >65 beats per minute.(46) Thus, increasing numbers of detectors with MDCT will not decrease motion artifacts. The images from multidetector helical CT (MDCT) are best when the resting heart rate is <65 beats/minute; at faster heart rates, motion artifacts become more dominant. Generally, the higher x-ray ﬂux (mAs = tube current x scan time) available with MDCT devices leads to images with somewhat better signalto-noise ratio and higher spatial resolution when compared to EBT; this occurs at a cost of increased radiation depending upon the scanner and protocol used.

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Studies Comparing EBT and MDCT for Calcium Scoring Becker et al. studied 100 patients comparing MDCT with EBT and reported a high correlation between the 2 modalities.(47) In this study however, the percent variability between individuals was 32% for CAC scores. There were relatively few patients with scores <100, and the high correlation may have been driven by those individuals with high scores. Moreover, the level of individual precision was limited and the scores <100 appeared to have the most deviation by MDCT as compared to EBT. Although a high correlation indicates that these two measures have a linear relationship to one another, the spread about the line can still be signiﬁcant and can limit use in individuals. Knez et al. studied the diagnostic accuracy of MDCT compared to EBT in 99 symptomatic male patients (60 ± 10 years).(48) For quantiﬁcation of CAC, the volumetric calcium score was determined. The results indicated excellent correlation between the two modalities (r = 0.99). The mean variability between the MDCT and EBT derived scores was 17%. Importantly, the study population had 26 patients with score ranging from 0–100, and the mean variability between the test was 7 ± 8 (20%), which was not significantly different from very high scores. The above studies were performed in older male symptomatic adults with a mean age above 60 years and a high range of calcium score values.(47,48) The ﬁndings of extensive calciﬁcation and a good correlation over a large range of values, however does not fully address the need to measure CAC scores accurately and reproducibly in a given individual. In addition, these high correlations may not apply as well to a younger ‘asymptomatic’ population with generally much lower scores. The studies by Budoff(49) , Carr(37) and Goldin(36) , each comparing EBT and helical CT, indicated a range of poor to fair and fair to excellent agreement at a series of clinical cut-points as proposed by Rumberger(50) using the Agatston score. However, the study by Carr, et al.(37) indicated that agreement could be improved by calibration of the Agatston score to an external standard. It should be emphasized that the clinical value for CAC determination is to facilitate individual risk assessment and thus scoring for a given patient should be a accurate as possible. However, for epidemiologic studies and investigations of coronary calcium in broad population groups, measures by MDCT and EBT may provide similar insight into the atherosclerotic process.

Signal Versus Noise Early detection of calciﬁed plaque is dependent upon identifying the plaque from image noise. MDCT systems have reduced image noise compared to EBT systems. Image noise with EBT has been shown to have an association with body mass index(51) , which may result in falsely identifying noise as calciﬁed plaque or overestimation of true plaque burden. On the other hand, the image blurring by MDCT may result in false negative studies or underestimation of true plaque burden. Prospective gated imaging has resulted in partial scan times of 220–500 msec for MDCT; however, motion artifacts can be a signiﬁcant drawback for measurements within a given individual. On the other hand, retrospective ECG gating is an alternative method for data acquisition; this enables one to reconstruct the images at a desired slice position.

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In a beating heart phantom study, ECG-gated volume coverage with MDCT (2.5-mm collimation) and overlapping image reconstruction (1-mm increment) was found to signiﬁcantly improve the reliability of coronary arterial calcium quantiﬁcation, especially for small plaques (P < 0.05).(52) Mean inter-examination variability was reduced from 35 ± 6% (Agatston score, standard electron-beam CT) to 4 ± 2% (P < 0.05) (volumetric score). As a result of clear reductions in errors by doing volume versus area (Agatston) scoring, noted in the original study by Callister et al. on volume scoring(53) , all reported EBT scoring from clinical and research centers since 1998 has included both measures, as is also now being advocated with the newer MDCT systems. Recent studies have demonstrated that MDCT with a retrospective ECG-gating algorithm showed a high correlation with coronary calcium scores determined using EBT in 60 patients(54) , and a mean variability of 12% with Agatston and 7.5% with volumetric scoring(55) , respectively. Whether the number of missed plaques may be reduced with retrospective ECG gating, small incremental reconstruction and thinner slices needs to be investigated. However a limitation of retrospective gating is that the process is a very time-consuming manual analysis and often involves subjective selection of retrospectively gated CT sections. This process may also add signiﬁcantly to the inter-test variability of CAC scores for MDCT, because it is highly operator dependent.

Radiation Exposure One drawback of MDCT as compared to EBT is the higher radiation exposure to the patient.(36,52−56) Radiation exposure from prospectively gated studies is much less than from retrospectively gated studies. The x-ray photon ﬂux expressed by the product of xray tube current and exposure time (mAs) is generally higher with MDCT. For example, 400 mA with 0.5 sec exposure time yields 200 mAs in MDCT versus 614 mA (ﬁxed tube current) with 0.1 sec exposure time yields 61.4 mAs in EBT. The increase in radiation dose with MDCT compared to EBT has been estimated to range from 3–10 times higher, depending on the protocol employed and whether prospective or retrospective gating is employed.(54,57−61) The most modern MDCT devices used in the retrospective imaging mode probably expose the patient to about 30–40 mGy (3–4 rad), equivalent to a conventional angiographic study, and up to 10-fold higher than the doses delivered during EBT of 3–4 mGy (0.3–0.4 rad).(59,60) The radiation dose estimation has a wide margin of error and depends signiﬁcantly on the method of estimation. Furthermore, the distributions of radiation dose are different for MDCT and EBT. In EBT the maximum dose is delivered at the entrance surface to the patient’s anatomy lying closest to the target ring (usually the posterior elements) due to the conﬁguration of target rings, while in MDCT, the dose is uniform around the patient and decreases towards the center. This results in a decreased dose distribution in EBT to organs lying anteriorly such as breasts. Thus, with MDCT the effective dose in women is 25% higher than in males raising the mean dose from 30 mGy (3 rad) per study in men to 40 mGy (4 rad) per study in women.(59) In MDCT, using prospective gating, the radiation dose is lower than that of retrospective gated studies. However, results from a recent study showed that ECG-controlled tube current modulation allows signiﬁcant dose reduction of 48% and 45% in males and females respectively, while performing retrospectively ECG-gated MDCT of the heart.(56)

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Reproducibility of Calcium Scoring A promise of these technologies is to accurately measure atherosclerosis burden and to track changes over time in order to assess efﬁcacy of therapy.(62) This ability to assess progression is dependent upon the reproducibility of the technologies. EBT inter-scan reproducibility has been shown to be approximately 10%, with inter-reader variability approximately 3% and intra-reader variability <1%.(63,64) This has been signiﬁcantly more problematic with MDCT. The inter-scan variability in several studies is 32–40%.(65,66) A recent study demonstrated that inter-reader variability with MDCT is problematic, and suggested double reading all studies to better assess coronary calcium. In a paper by Goldin, mean inter-reader variability was 4.5% for electron-beam CT versus 41.5% for spiral CT.(36) However, large studies evaluating the reproducibility of MDCT are not yet available. The above studies support the idea that that the age- and gender-based calcium score percentiles using EBT cannot always be applied to the results obtained with MDCT scanners in patients with CAC score <100; furthermore these results may be altered by using slice thicknesses other than the 3 mm used for a foundation of the Agatston calcium scoring system. Moreover, it appears the calcium scores from various MDCT scanner manufacturers differ (confounded by different slice thicknesses) and their ability to monitor disease progression or regression remains to be fully established. In addition, CAC scores obtained using gated retrospective reconstruction algorithms from spiral CT scanners may not be directly comparable to those obtained by EBT; this discrepancy may result in differences in risk stratiﬁcation if one uses age and gender based percentile tables derived from EBT studies. Unfortunately, unlike the standards for EBT, no standards have been adopted to allow for comparable measurement of coronary artery using MDCT. The ‘ideal’ acquisition protocol is a subject of controversy for MDCT; ungated imaging should not be done, or the results interpreted only in a subjective and not objective manner. Recommendations for the standardization of coronary artery imaging by MDCT for prospective as well as retrospective ECG gating should be established in line with recommendations recently suggested by a group of German researchers and clinicians.(67) There are several areas regarding coronary artery calcium quantitation as it relates to use of EBT versus MDCT that require discussion. These involve temporal scan resolution and slice thickness during imaging. These issues also including intrinsic scan characteristics and revolves around other common parameters such as FOV [ﬁeld of view] and partial volume [or volume averaging] effects through the thickness of the tomogram. Table 1 shows technical information regarding the EBT and MDCT systems currently in clinical use. EBT has a “true” temporal resolution per image for coronary calcium quantitation of 100 msec [86 msec for “central time resolution”]. Data from an entire 360 rotation of the scanning gantry are not needed in order to produce CT tomograms. The requirement is only 180 degrees [assuming symmetry] and this is referred to as a “central time resolution” or central temporal resolution. Commonly MDCT scanner manufacturers refer to the temporal resolution of a 500 msec full rotation scanner as only 250 msec for this reason. By using a variety of partial scan reconstruction methods, that would require data from more than one full gantry rotation (and thus commensurate increases in radiation exposure), effective temporal resolutions as low as 125 msec [for this example] would theoretically be possible. However, this type of temporal resolution

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Table 1. Basic Description of CT systems. EBT

MDCT

Electron source (cathode)

Electron gun

Tungsten ﬁlament

Target (anode)

Tungsten rings in gantry

Tungsten Anode in X-ray tube

Gantry

Fixed – electron beam rapidly sweeps across tungsten rings

Rotates – tube and opposing detectors rotate within gantry

Detectors

Matrix array

Matrix array

Image reconstruction (180 degrees plus width of fan beam)

Partial Scan / Filtered back-projection Sharp kernel

Partial Scan / Filtered back-projection Standard kernel

CT number scale

Hounsﬁeld Unit (HU)

Hounsﬁeld Unit (HU)

mA

Fixed

User selectable

Exposure time for Coronary Calcium (temporal resolution)

100 msec (true prospective) at full FOV; 86 msec for “central time resolution”

230 msec (post processing) for 16-channel systems and longer for 8-,4-,2-, and channel systems (dependent upon gantry rotation speed and detector design)

mAs

Fixed mA X Exposure time

User selectable mA X Exposure time

Heart Rate Limitations1

<110 beats per minute

<65 beats per minute

Z Axis Resolution

1.5 mm

≤1.0 mm

applies only to a volume in the center of the image. In order for a complete scan to be created, data from 180 degrees plus the width of the scanning or “fan” beam must be included. Fan beam widths for MDCT are variable, but in general are on the order of 40–50 degrees. Thus data from 180+ 40 = 220 degrees is nominally required to produce a complete tomographic section of the body. This physical constraint is what then can be used to calculate the “true” temporal resolution for any given MDCT scanner. There are a variety of MDCT systems available that have been used or are advocated for use regarding coronary artery calcium measurements and their true temporal resolutions range from 220 msec (16-channel scanner) to 1000 msec (single-slice scanner). Motion artifacts during imaging in any given tomographic plane or through the volume of the tomogram [volume element or voxel] can alter the calcium measurements. At heart rates <65 beats per minute, the fastest of the MDCT systems result in limited motion artifacts while systems with temporal resolution approaching 1000 msec [which would be the entire cardiac cycle at a heart rate of 60 beats per minute] will still confound the quantitation of coronary calcium.

The Issue of Slice Thickness The Agatston calcium scoring was designed as an area measurement and is predicated on a 3.0 mm slice thickness. Although this is likely not the idea tomographic slice thickness for coronary artery imaging, it was chosen historically because the original EBT scanning system in use at the time for research had 3.0 mm as the thinnest slice available. Current EBT systems are now able to perform scanning at 1.5 mm and the latest MDCT systems can provide slice thicknesses that are ≤1 mm. However, current data are based upon the traditional Agatston scoring algorithm; although other methods such

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as “volume score” and “integrated area above background” may prove to be more reliable in serial studies. Manufacturers of MDCT have thus sought to duplicate Agatston scoring to rival the data from EBT. This has resulted in changing in the initial threshold CT density [Hounsﬁeld Unit – HU] for “calcium” from the traditional 130 HU(31) to 90 HU(37) to facilitate baseline similarities for calcium scores. Lowering the threshold can potentially reduce partial volume errors due to motion artifact [which would result in missing some coronary calcium] and increases the overall sensitivity of the scanner for very small areas of calciﬁcation. Some MDCT systems are capable of acquiring true 3.0 mm slices while others acquire images at 2.5 mm slice thickness. The Agatston score is a non-linear variable and information across the area of “calcium” within the tomogram is multiplied by 1, 2, 3, or 4 depending on the maximum HU within the area under interrogation. By “sampling” at 2.5 mm slice intervals rather than 3.0 mm slice intervals, the area is over-sampled. If all parameters are the same, such as FOV and spatial resolution, an a partial solution for estimating calcium scores done on a 2.5 mm scanner can be determined by adjusting the score by 2.5/3.0 = 0.8 in order to compare the result using a 3.0 mm scanner. Hoff and others using EBT and 3.0 mm slice thicknesses have published a very large population database.(68) These same data have been applied by various individuals using various MDCT systems, implying that the data would be similar under similar conditions. However, this is not entirely true and depends on which scanner was used for imaging. The MDCT scanner used in the paper by Carr et al.(37) used 3.0 mm slice thicknesses for the comparison. However, current scanners manufactured by vendors in Germany and Japan use a 2.5 mm slice thickness. Population data for studies done using an 8-channel MDCT, 2.5 slice thickness system(69) are shown in Table II and are compared with data using EBT as published by Hoff et al.(68) The authors of the former paper indicated that the data from the MDCT scanner were similar to those found using EBT, however, they failed to note the issue of slice thickness in the calculations. The data show calcium scores for men only, across all ages examined, and for selected percentiles. The “comparison” calcium scores, however, accounting for the differences in slice thicknesses are shown in Table II below the published data. These data indicate that there can be considerable differences in absolute calcium scores depending on the scanner used and underlines the need for using data that are speciﬁc for the CT scanner used and depend on the amount of calcium present. These results underscore the need to use data that are speciﬁc to the machine used for scanning. In the future, a more universal scoring system may be possible that would be machine independent, but at present data derived from MDCT should be compared with caution with those derived from EBT.

Angiographic Correlates of Coronary Calcium The direct pathologic studies noted above thus suggested that coronary artery calcium deﬁned by EBT had similar predictive values for similar extents of coronary disease, regardless of gender. The next step was then to assess the effect of patient sex on EBT studies done in patients undergoing direct coronary angiography. Rumberger(70) studied 50 women and 89 men who had EBT scans done 1 day after cardiac catheterization. The women were roughly a decade older than the men, but were matched for clinical indications for angiography and extent of luminal disease as

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Table 2. Sensitivity, speciﬁcity, predictive values, and standard errors for EBT detection of coronary calcium and angiographic disease severity.

EBT and Coronary Calcium Sensitivity Speciﬁcity

Any Arteriographic Disease Women 97 ± 3% 38 ± 12%

Men 94 ± 3% 35 ± 10%

Signiﬁcant Arteriographic Disease Women Men 100 ± 0% 98 ± 2% 66 ± 8% 57 ± 8%

Positive Predictive Value Negative Predictive Value

85 ± 6% 91 ± 9%

89 ± 4% 79 ± 9%

46 ± 8% 100 ± 0%

66 ± 6% 95 ±5 %

Any angiographic disease – presence of at least minimal luminal irregularities. Signiﬁcant angiographic disease – presence of any luminal stenosis representing ≥50% diameter narrowing.

conﬁrmed by angiography. Sixteen women (32%) had normal coronary arteriograms; 6 women (12%) had trivial stenoses (maximum <20%); 10 women (20%) had moderate stenoses (>20% but <50%); and, 18 women (36%) had signiﬁcant stenoses (>50%) [p=NS for all compared to men]. Sensitivity, speciﬁcity, and positive and negative predictive values for coronary calcium were nearly identical for men and women regardless of the degree of angiographic stenoses [see Table 2]. Overall negative predictive values were 91% in women for any angiographic disease and 100% in women for signiﬁcant angiographic disease. Receiver operating characteristic curve areas in women for prediction of any angiographic disease using EBT was 0.92 ± 0.02; in women for prediction of signiﬁcant angiographic disease using EBT the ROC curve area was 0.83 ± 0.06 [p = NS for both compared to men]. Based upon this study, it was concluded that in this middle-aged population, noninvasive deﬁnition of coronary calcium by EBT had similar predictive value for angiographic coronary artery stenoses in men and women.

Epidemiology of Coronary Artery Calcium by EBT A prospective study of >14,000 men and women found that coronary artery disease (CAD) risk increases with age, and that this increase is more dramatic in women. Most of the risk factors were more favorable in women, but the gender effect on risk factors diminishes with increasing age.(71) Another study found that the incidence of CAD is lower in premenopausal women compared with men. However, following menopause, the risk of mortality from CAD increases in women. The incidence of coronary artery calcium by EBT as a function of age has been shown to mimic that of the incidence of cardiovascular atherosclerotic disease in men and women. Figure 6 shows the incidence of coronary calciﬁcation by EBT in an unselected patient population of men and women between the ages of 20 and 80.(72) These data show the following: a) the incidence of coronary artery calcium increases from only a few percent in the second decade of life to nearly 100% by the 8th decade in men and women; b) the general incidence of coronary artery calcium in women is similar to that in men who are a decade younger; c) however, this separate in incidence with age is eliminated

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Figure 6. Epidemiology of coronary calcium – adapted from data presented in Reference 72.

Table 3. Percentile ranking of EBT coronary calcium scores as a function of age and sex. Age/Men Percentile Rank

35–39

40–44

45–49

50–54

55–59

60–64

65–69

25th

0

0

0

0

3

14

28

50th

0

0

3

16

41

118

151

75th

2

11

44

101

187

434

569

90th

21

64

176

320

502

804

1178

Age/Women Percentile Rank

35–39

40–44

45–49

50–54

55–59

60–64

65–69

25th

0

0

0

0

0

0

0

50th

0

0

0

0

0

4

24

75th

0

0

0

10

33

87

133

90th

4

9

23

66

140

310

362

Age = chronologic age in years. Adapted from data presented in Reference 68.

by approximately age 65–70, when the incidence of coronary calcium is similar to that of men of the same age. Coronary artery calcium score, as a measure of the extent of coronary disease also increases with age, but the magnitude of the estimated atherosclerotic plaque burden by EBT is quite different in men versus women. Table 3 shows calcium scores in a large group (9728) of unselected, consecutive male and female adults seen at one EBT scanning center.(73) Data are given as a function of age, gender, and percentile rank of EBT calcium scores. The median coronary calcium score is zero for women until their mid to late 50’s. In men of similar ages, already moderate EBT calcium scores are noted – again consistent with an overall low prevalence of advanced coronary atherosclerotic disease in men and especially women until the 5th decade of life.

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EBT Coronary Calcium and Risk of Future Cardiac Events Since EBT calcium scores do relate to conventional risk, but also provide an assessment that cannot be obtained by a blood test, that is the actual site and severity of atherosclerotic plaque disease, it is important to explore how EBT might be an “independent” predictor of risk. EBT coronary calcium scores have been shown to be predictive of cardiac and coronary vascular events in several studies. The data discussed so far are consistent with the “area” or “score” for coronary calciﬁcation quantiﬁed by EBCT being viewed as a surrogate for the overall atherosclerotic plaque burden. Although calciﬁcation may be a histologic feature of “stable” as well as “unstable” plaques, it is reasonable to assume that a greater overall plaque burden increases the likelihood of greater proportions of both plaque subtypes. Indeed, the extent of coronary atheromatous disease remains the most powerful predictor of subsequent or recurrent cardiac events.(74) The implications for prognostication using quantiﬁcation of coronary calcium by EBT should not be predicated solely on the site and severity of the calciﬁed plaque per se or even the likely severity of luminal narrowing, but by the fact that the extent of atherosclerotic disease and the presence of plaques of variable morphologic characteristics increase in direct proportion to the amount of detectable calciﬁed plaques. There have been several studies most recently published regarding cardiac prognosis and EBT calcium score. Arad and colleagues(75) initially reported a follow up study of 1173 initially asymptomatic patients (average age 53 ± 11 years) who had no known coronary disease for a mean of 19 months after a screening EBCT coronary calcium scan. The magnitude of the coronary calcium score at the time of the index EBCT scan was highly predictive of subsequently developing symptomatic cardiovascular disease during follow up. Odds ratios ranged from 20:1 for a calcium score of 100 to 35:1 for a calcium score of 160. This study has now been carried out for a total of 3.6 years of follow up. (76) Complete follow up was available in 99.6% of the original 1,177 patients. There were a total of 39 subjects with coronary events [only 1 event per patient was considered, even if some had multiple events] and included 3 coronary deaths, 15 nonfatal myocardial infarctions, and 21 coronary artery revascularization procedures. For the prediction of “hard” events only [nonfatal MI or coronary death], areas under the ROC curve was 0.86 and a coronary calcium score above 160 was associated with an odds ration of 22.2. The odds ratios for all cardiac events remained high (14.3 to 20.2) after adjustment for self-reported cardiovascular risk factors. However, the study by Arad did not speciﬁcally evaluate risk in women and, in fact, 71% of the participants were men. Wong et al.(77) have reported on a group of 926 initially asymptomatic men (n = 735) and women (n = 191) followed up for cardiovascular events a mean of 3.3 years after a baseline EBT scan. Although there were a total of 41 new cardiovascular events reported by the patients, only 28 could be veriﬁed by careful review of medical records and included 6 myocardial infarctions, 2 strokes, and 20 coronary revascularization procedures. Cox proportional-hazards regression showed coronary artery calcium by EBT to be associated with a greater risk for a cardiovascular event INDEPENDENT of age, gender, and other risk factors. Importantly, the RR (relative risk) for any cardiovascular event increased with the numerical value of the calcium score. Compared to scores of 1–15, those with scores exceeding 271 [highest quartile of “plaque burden”] were 8.8 times higher. The ﬁnding that these data were independent of gender at least is consis-

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tent with the data suggesting that, at a given EBT calcium score, women have similar disease extents as compared to men and thus should be expected to have similar numbers of events based upon estimates of total atherosclerotic plaque burden. The magnitude of the risk to an individual with moderate or greater coronary artery calcium, viewed as a surrogate to measures of total coronary atherosclerotic burden, is underscored when one considers relative risks of developing symptomatic coronary disease using conventional risk analysis. Exercise thallium scintigraphy was recently shown to predict coronary death and nonfatal MI with an odds ratio of 4.4 at six years in an already high-risk cohort.(78) Bostom(79) reported a 15-year follow up in 2191 middleaged initially asymptomatic men (20 to 54 years old at entry) as part of the Framingham database. The relative risk of developing symptomatic coronary artery disease in this group was 1.9:1 (95% CI, 1.2–2.9) for an elevated Lp(a), 1.8:1 (95% CI, 1.2–2.6) for total cholesterol >240 mg/dL, 1.8:1 (95% CI, 1.2–2.6) for an HDL < 35 mg/dL, 3.6:1 (CI, 2.2–5.5) for cigarette smoking, and 1.2:1 (CI, 0.8–1.8) for systolic hypertension. Thus, based upon these comparisons, EBCT calcium score alone appears to be more predictive of cardiac events than traditional risk factors individually, and as the only noninvasive method to localize and quantitate the extent of the total coronary atherosclerotic plaque burden, offers a measurable tool for improved risk stratiﬁcation and prognosis. Use of CAC in the Asymptomatic Patient The absence of CAC on EBT identiﬁes a group of patients at very low risk of events with a very high sensitivity and negative predictive value for obstructive disease (>99%).(80) A score of 0 (no coronary calcium) with EBT can virtually exclude those patients with obstructive coronary heart disease. Raggi et al.(73) demonstrated an annual event rate of only 0.11% for patients with scores of zero by EBT. Both the American College of Cardiology/American Heart Association writing group(81) and the Prevention V Conference agreed that the negative predictive value of EBT is very high for short term events.(82) This was reinforced by the St. Francis Heart Study, where a score of zero had a negative predictive value for cardiac events of 99.5%.(76) It remains to be determined if a zero score derived from MDCT devices has the same prognostic and diagnostic signiﬁcance in ruling out obstructive coronary heart disease. Only one study has looked at the predictive power of zero scores by MDCT and suggested a negative predictive value for obstructive coronary disease of approximately 60%. The most powerful and important data for CT scanning for coronary calcium relates to its ability to predict future coronary events in asymptomatic persons. Risk factors have been demonstrated to be suboptimal predictors of future events, failing to predict onethird of future deaths due to coronary heart disease. (83) At least half of all ﬁrst coronary events occur in asymptomatic individuals who are unaware that they have developed silent coronary heart disease. A sub-group of the Prevention V authorship supported the use of EBT for risk stratiﬁcation of intermediate risk patients. The new NCEP Adult Treatment Panel III guidelines(84) support the conclusions of the Prevention Conference V and the ACC/AHA report that high coronary calcium scores conﬁrm increased risk for future cardiac events, stating: “Therefore, measurement of coronary calcium is an option for advanced risk assessment in appropriately selected persons. In persons with multiple risk factors, high coronary calcium scores (e.g., >75th percentile for age and sex) denote advanced coronary atherosclerosis and provide a ra-

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Table 4. Table that was supposed to go in the AHA paper, look at it on overall use of calcium scoring in patients. Interpretation and recommendation for CT heart scanning and CAC scoring: 1.

A negative test (score = 0) makes the presence of atherosclerotic plaque, including unstable or vulnerable plaque, highly unlikely.

2.

A negative test (score = 0) makes the presence of signiﬁcant luminal obstructive disease highly unlikely (negative predictive power by EBCT on the order of 95–99%). A negative test is consistent with a low risk (<1% per year) of a cardiovascular event in the next 2–5 years. A positive test conﬁrms the presence of a coronary atherosclerotic plaque. The greater the amount of coronary calcium, the greater the atherosclerotic burden in men and women, irrespective of age. The total amount of coronary calcium correlates best with the total amount of atherosclerotic plaque, although the true “atherosclerotic burden” is underestimated. A high calcium score (an Agatston score >100 or any score above the 75th percentile for age and sex) is consistent with moderate to high risk of a cardiac event within the next 2–5 years. Coronary artery calcium measurement can improve risk prediction in conventional intermediate-risk patients and CAC scanning should be considered in individuals at intermediate risk for a coronary event (0.6%/yr to 2.0%/year) for clinical-decision making regarding reﬁnement of risk stratiﬁcation. High coronary calcium scores (an Agatston score >100 or any score above the 75th percentile for age and sex) denotes advanced coronary atherosclerosis and provides a rationale for intensiﬁed LDL-lowering therapy and assignment of coronary risk to a “coronary disease riskequivalency” status (i.e. secondary prevention goals such as a target LDL range <100 mg/dl).

3. 4. 5. 6. 7. 8.

9.

tionale for intensiﬁed LDL-lowering therapy. Moreover, measurement of coronary calcium is promising for older persons in whom the traditional risk factors lose some of their predictive power.” Thus, a high CAC score may make a clinician more likely to institute secondary prevention measures sooner (e.g. aspirin, aim for a lower blood pressure [<130/80 versus <140/90, an LDL-C less than < 100 mg/dl as opposed to < 130 or triglycerides <150 mg/dl versus <200 mg/dl). Table 4 suggests an overall application of CAC scoring with respect to deﬁning overall individual cardiac risk and suggested target goals for LDL (based upon current NCEP guidelines). Thus current recommendations are to use CAC to measure plaque burden in physician-referred, intermediate risk patients, irrespective of age, in whom the use of lifestyle and/or pharmacologic therapies can be more vigorously applied in a costeffective manner. Use of EBT or MDCT in very low risk cohorts has not demonstrated to have clinical utility, and focus on intermediate and high-risk cohorts is better substantiated. Generally, the data show that invasive procedures should be reserved for symptomatic patients with inducible ischemia since there is limited information showing beneﬁt in terms of prolongation or quality of life in asymptomatic patients.(85−87) To avoid inappropriate or unnecessary follow-up testing or invasive therapeutic procedures in patients who undergo EBT or MDCT, the clinician should determine a priori that the goal of such noninvasive testing is to reﬁne prognostic assessment and then employ, or not, well-proven preventive interventions based on test outcome. Heart Age and Calculation of Long Term Risk Using CAC The current NCEP ATP III guidelines(84) strongly encourage use of conventional risk factor analysis and calculation of annual risk in those without established coronary heart

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disease or known equivalents such as diabetes or pre-existing peripheral vascular disease. Although the goals of this exercise are to determine acceptably levels for LDL cholesterol targeting, they serve useful purposes in deﬁning an estimation of risk for all adults. The general ranges for risk, generally expresses as a risk per decade are as follows: <10% per decade – low risk; ≥10% but <20% per decade, intermediate or moderate risk; and, ≥20% per decade as high risk (or coronary disease risk equivalency). Calculation of risk incorporates data from the Framingham heart study that emphasized the values of combining risk factors into a single calculation.(88) Knowing the total cholesterol, the HDL cholesterol, blood pressure and information on history of hypertension, gender, smoking history, and chronological age this calculation is affected by summing “points” assigned to various ranges for these values. However, it is well known that after the age of 50, age becomes the dominant factor here in deﬁning risk. The incidence of symptomatic coronary heart disease increases with age and this is the major factor that has provided the evidence for chronological age as a dominant risk factor. The extent or severity of coronary disease increases with age, as has been noted earlier. However, there are numerous additional potential risks for a given individual that are not easily modeling. These include patterns of heredity, general lifestyle and habits, and environmental and social inﬂuences. As noted earlier, the coronary artery calcium score is a valid method to estimate coronary “plaque burden”. Furthermore, there are data showing how these scores compare between individuals as a function of age and gender. Grundy(89) was the ﬁrst to suggest that coronary calcium scores could be used to calculate “heart age” based upon chronological age and ranking of these scores in peer groups. For example, a man at age 50 who has a coronary artery calcium score at the median (50th percentile) for men at this age would have no adjustment in his heart age. However, were he to have a score that was either below the 25th percentile or above the 75th percentile, then his “heart age” would be adjusted downwards by 10 years or upwards by 10 years, respectively. Grundy then suggested that the point scoring system used in the Framingham calculation could be reassigned based upon coronary calcium scores deﬁned by EBT (Table 3). The EBT calcium score, as most experts suggest, should not be viewed in isolation for deﬁning coronary risk, but must be examined in the context of current and important risk factors. Although the calcium score is valuable, it gives no clue as to the reasons for these ﬁndings. This “clinical approach” or case management approach makes the most sense. By combining conventional risk factors analysis with “heart age”, an estimation of absolute cardiac risk can be deﬁned further risk stratifying the patient for implementation of appropriate risk factors modiﬁcation goals.

Conclusions EBT has undergone rigorous testing for reliability and validity and has proven to be useful in identifying individuals with, or at risk for, coronary heart disease. Although MDCT is a promising tool for coronary calcium scoring, more studies are needed comparing EBT and MDCT scans in the same patients, especially with calcium scores < 100. Further radiation dose reduction with MDCT is currently being evaluated. MDCT studies evaluating progression, reproducibility and outcomes studies are needed to fully evaluate its potential to measure and track atherosclerosis. Testing the beneﬁt of serial coro-

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nary calcium scores to non-invasively assess for progression or regression of coronary calcium is currently underway. EBT is a method that can be used to estimate the overall coronary atherosclerotic plaque burden. It can be used to diagnose its presence and determine its extent; furthermore, the information from the calcium score can be used to assess the likelihood of advanced obstructive disease and to provide prognostic information. Finally, it has the potential to determine the consequences of therapeutic interventions regarding progression, stabilization, or regression of coronary atherosclerotic disease.(62) The above has been a detailed discussion of the aspects of atherosclerotic plaque imaging using non-contrast CT. Quantitative measures of coronary (and vascular) calciﬁcation have been shown to directly related to plaque, albeit underestimating its total. Furthermore, these relationships have foundation in molecular biology. Finally, the data show that measures of coronary artery calcium area or score allow for prognostication in patients regarding future cardiovascular events. More research is needed to expand upon these principles and concepts, particularly as it related to non-calciﬁed plaque identiﬁcation using contrast enhanced CT. References [1] Tuzcu EM, Kapadia SR, Tutar E, et al. High Prevalence of Coronary Atherosclerosis in Asymptomatic Teenagers and Young Adults: Evidence from intravascular ultrasound. Circulation 2001; 103:2705–2710. [2] Glagov S, Elliot W, Zarins CK, Stankunavicius R, Kolettis GJ. Compensatory Enlargement of Human Atherosclerotic Coronary Arteries. NEJM 1987; 316:1371–1375. [3] Blankenhorn DH, Stern D: Calciﬁcation of the coronary arteries. Am J Roentgen 1959; 81:772–777. [4] Frink RJ, Achor RWP, Brown AL, Kincaid JW, Brandenburg RO. Signiﬁcance of calciﬁcation of the coronary arteries. Am J Cardiol 1970; 26:241–247. [5] McCarthy JH, Palmer FJ. Incidence and signiﬁcance of coronary artery calciﬁcation. Brit Heart J 1974; 36:499–506. [6] Rifkin RD, Parisi AF, Folland E: Coronary calciﬁcation in the diagnosis of coronary artery disease. Am J Cardiol 1979; 44:141–147. [7] Wexler L, Brundage B, Crouse J, Detrano R. Fuster V, Maddahi J, Rumberger JA, Stanford W, White R: Coronary Artery Calciﬁcation: Pathophysiology, Epidemiology, Image Methods and Clinical Implications – A Scientiﬁc Statement from the American Heart Association. Circulation 1996; 94:1175–1192. [8] Bostrom K, Watson KE, Horn S, Wortham HC, Herman IM, Demer LL: Bone Morphogenetic Protein Expression in Human Atherosclerotic Lesions. J Clin Invest 1993; 91:1800–1809. [9] Shanahan CM, Cary NR, Metcalfe JC, Weissberg PL. High expression of genes for calciﬁcationregulating proteins in human atherosclerotic plaque. J Clin Invest 1994; 93:2393–402. [10] Decisions for further testing (such as stress testing or cardiac catheterization) beyond assistance in risk stratiﬁcation in patients with a positive CAC score cannot be made based upon coronary calcium scores alone, as calcium score correlates poorly with stenosis severity in a given individual and should be based upon clinical history and other conventional clinical criteria. [11] Ideda T, Shirasawa T, Esaki Y, Yoshiki S, Hirokawa K. Osteopontin mRNA is Expressed by Smooth Muscle-derived Foam Cells in Human Atherosclerotic Lesions of the Aorta. J Clin Invest 1993; 92:2814–2820. [12] Hirota S, Imakita M, Kohri K, Ito A, Morii E, Adachi S, Kim HM, Kitamura Y, Yutani C, Nomura S. Expression of osteopontin messenger RNA by macrophages in atherosclerotic plaques. A possible association with calciﬁcation. Am J Pathol 1993; 143:1003–8. [13] McCarthy JH, Palmer FJ. Incidence and signiﬁcance of coronary artery calciﬁcation. Brit Heart J 1974; 36:499–506. [14] Tampas JP, Soule AB. Coronary artery calciﬁcation: Its incidence and signiﬁcance in patients over forty years of age. Abstract, Conference Proceedings September 1986; Annual Meeting of the American Roentgen Ray Society, 97(2):369–376. [15] Lieber A, Jorgens J. Cineﬂuorography of coronary artery calciﬁcation. Am J Radiol 1961; 86:1063.

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tomography. Am J Cardiol 2001; 88(suppl):46E–50E. [62] Mao SS, Bakhsheshi H, Lu B, Liu SCK, Oudiz RJ, Budoff MJ. Effect of ECG Triggering on Reproducibility of Coronary Artery Calcium Scoring. Radiology. 2001 Sep; 220(3):707–11. [63] Lu B, Mao SS, Zhuang N, Bakhsheshi H, Yamamoto H, Takasu J, Liu SCK, Budoff MJ. Coronary artery motion during the cardiac cycle and optimal ECG triggering for coronary artery imaging. Invest Radiol 2001; 36:250–256. [64] Shemesh J, Tenenbaum A, Kopecky KK, Apter S, Rozenman J, Itzchak Y, Motro M. Coronary calcium measurements by double helical computed tomography. Using the average instead of peak density algorithm improves reproducibility. Invest Radiol 1997 Sep; 32(9):503–6. [65] Qanadli SD, Mesurolle B, Aegerter P, Joseph T, Oliva VL, Guertin MC, Dubourg O, Fauchet M, GoeauBrissonniere OA, Lacombe P. Volumetric quantiﬁcation of coronary artery calciﬁcations using dual-slice spiral CT scanner: improved reproducibility of measurements with 180 degrees linear interpolation algorithm. J Comput Assist Tomogr 2001 Mar-Apr; 25(2):278–286. [66] Achenbach S, Daniel WG, Moshage W. Recommendations for standardization of EBT and MSCT scanning. Herz 2001 Jun; 26(4):273–7. [67] Hoff JA, Chomka EV, Krainik AJ, Daviglus M, Rich S, Kondos GT. Age and Gender Distributions of Coronary Artery Calcium Detected by Electron Beam Tomography in 35,246 Adults. Am J Cardiol 2001; 87:1335–1339. [68] Schmermund A, Erbel R, Silber S: Age and Gender Distribution of Coronary Artery Calcium Measured by Four-Slice Computed Tomography in 2,030 Persons with no Symptoms of Coronary Artery Disease. Am J Cardiol 2002; 90:169–173. [69] Rumberger JA, Sheedy PF, Breen JR, Schwartz RS: Coronary Calcium as Determined by Electron Beam Computed Tomography, and Coronary Disease on Arteriogram: Effect of Patient’s Sex on Diagnosis. Circulation 1995; 91:1363–1367. [70] Jousilahti P, Vartiainen E, Tuomilehto J, Puska P. Sex, Age, Cardiovascular Risk Factors, and Coronary Heart Disease: A Prospective Follow up study of 14,786 Middle Aged Men and Women in Finland. Circulation 1999; 99:1165–1172. [71] Janowitz WR, Agatston AS, Kaplan G, Viamonte M: Differences in Prevalence and Extent of Coronary Artery Calcium Detected by Ultrafast Computed Tomography in Asymptomatic Men and Women. Am J Cardiol 1993; 72:247–254. [72] Raggi P, Cooil B, Callister TQ. Use of electron beam tomography data to develop models for prediction of hard coronary events. Am Heart J 2001; 141:375–82. [73] Hasdai D, Bell MR, Grill DE, Berger PB, Garratt KN, Rihal CS, Hammes LN, Holmes DR: Outcome greater or equal to 10 years after successful percutaneous transluminal coronary angioplasty. Am J Cardiol 1997; 79(8):1005–11. [74] Arad Y, Spadaro LA, Goodman K, Liedo-Perez A, Sherman S, Lerner G, Guerci AD: Predictive Value of Electron Beam Computed Tomography of the Coronary Arteries: 19-Month Follow-up of 1173 Asymptomatic Subjects. Circulation 1996; 93:1951–1953. [75] Arad Y, Spadaro LA, Goodman K, Newstein D, Guerci AD. Prediction of Coronary Events with Electron Beam Computed Tomography. J Am Coll Cardiol 2000; 36:1253–60. [76] Wong ND, Hsu JC, Detrano RC, Diamond G, Eisenberg H, Gardin JM. Coronary Artery Calcium Evaluation by Electron Beam Computed Tomography and Its Relation to New Cardiovascular Events. Am J Cardiol 2000; 86:495–498. [77] Blumenthal RS, et al. Exercise thallium tomography predicts future clinically manifest coronary heart disease in a high risk asymptomatic population. Circulation 1996; 93:915–23. [78] Bostom AG, Cupples LA, Jenner JL, Ordovas JM, Seman LJ, Wilson PW, Schaefer EJ; Castelli WP: Elevated plasma lipoprotein (a) and coronary heart disease in men aged 55 years and younger. JAMA 1996; 276:544–8. [79] Haberl R, Becker A, Leber A, et al. Correlation of coronary calciﬁcation and angiographically documented stenoses in patients with suspected coronary artery disease: results of 1,764 patients. J Am Coll Cardiol 2001; 37:451–7. [80] O’Rourke RA, Brundage BH, Froelicher VF, et al.: American College of Cardiology/American Heart Association expert consensus document on electron beam computed tomography for the diagnosis and prognosis of coronary artery disease. Circulation 2000, 102:126–40. [81] Smith SC, Greenland P, Grundy SM. Prevention Conference V: beyond secondary prevention: identifying the high-risk patient for primary prevention. Executive summary. Circulation 2000; 101:111–6.

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[82] Grover SA, Coupal L, Hu XP. Identifying adults at increased risk of coronary disease: how well do the current cholesterol guidelines work? JAMA 1995; 274:801–806. [83] Third Report of the National Cholesterol Education Program (NCEP) Expert Panel on Detection, Evaluation and Treatment of High Blood Cholesterol in Adults (Adult Treatment Panel III). Circulation 2002; 105:3157–3373. [84] Gibbons RJ, Balady GJ, Bricker JT, et al. American College of Cardiology/American Heart Association Task Force on Practice Guidelines (Committee to Update the 1997 Exercise Testing Guidelines). ACC/AHA 2002 guideline update for exercise testing: summary article: a report of the American College of Cardiology/American Heart Association Task Force on Practice Guidelines (Committee to Update the 1997 Exercise Testing Guidelines). Circulation 2002 Oct 1; 106(14):1883–92. [85] Eagle KA, Guyton RA, Davidoff R, et al. ACC/AHA guidelines for coronary artery bypass graft surgery: executive summary and recommendations: a report of the American College of Cardiology/American Heart Association Task Force on Practice Guidelines (Committee to Revise the 1991 Guidelines for Coronary Artery Bypass Graft Surgery). Circulation. 1999; 100:1464–1480. [86] Forrester JS, Shah PK. Lipid lowering versus revascularization. An idea whose time (for testing) has come. Current Perspectives. Circulation 1997; 96:1360–2. [87] Wilson PWF, D’Agostino RB, Levy D, Belanger AM, Silbershatz H, Kannel WB. Prediction of coronary heart disease using risk factor categories. Circulation 1998; 97:1837–1847. [88] Grundy SM. Coronary plaque as a replacement for age as a risk factor in global risk assessment. Am J Cardiol 2001; 88 (supplement):8E–11E.

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Plaque Imaging: Pixel to Molecular Level J.S. Suri et al. (Eds.) IOS Press, 2005 © 2005 The authors. All rights reserved.

Absolute Measurement of Integrated Backscatter from Arterial Wall Structures Peder PEDERSEN, Ruben LARA-MONTALVO and Jacob CHAKARESKI Dept. of Electrical and Computer Engineering, Worcester Polytechnic Institute Worcester, MA 01609 Abstract. Studies done on carotid arteries suggest that the morphology and composition of atherosclerotic plaque are predictive of stroke risk. The goal of this investigation has been to demonstrate that the true acoustic integrated backscatter (IBS) from plaque regions can be measured non-invasively, based on which plaque composition may be inferred and thus become a tool to estimate the likelihood of a lesion or plaque being stable or vulnerable, i.e. having a risk of causing a stroke. To obtain the true IBS non-invasively, the scattering and aberrating effect of the intervening tissue layers must be overcome. This is achieved by using the IBS from arterial blood as a reference backscatter, speciﬁcally the backscatter from a blood volume along the same scan line as and adjacent to the region of interest. We have shown that the variance of the IBS estimate of the blood backscatter signal can be quantiﬁed and reduced to a speciﬁed tolerable level. Keywords. Intravascular ultrasound, atherosclerotic plaque, backscatter proﬁle, doppler ultrasound cardiac, phantoms, arterial vessel, signal processing

1. Introduction This chapter describes an ultrasound method for evaluating plaque composition noninvasively. This is a quantitative ultrasound technique, rather than an imaging method, and it attempts to measure the absolute integrated backscatter as a function of position along the carotid artery. The method has the potential for being developed into a screening tool that can be used for in vivo estimation of stroke risk of atherosclerotic plaque. Currently, no non-invasive ultrasound technique exists that both can consider the extent and the composition of the plaque. This section will ﬁrst review stroke risk and the risk factors associated with strokes that originate with plaque rupture, followed by a brief discussion of the rationale behind the ultrasound method. The last part of this section will review current techniques for atherosclerotic plaque characterization. 1.1. The Origins of Stroke – Evaluation of Stroke Risk Cerebral stroke is the third leading cause of death in North America and is the leading cause of long term disability in middle-age and older patients, afﬂicting roughly 500,000 Americans each year [1]. Nearly one third of these patients die as a direct result of the

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stroke, and most survivors are permanently disabled. The cost of lost productivity adds to the economical impact of stroke. Cerebral embolism and cerebral thrombosis are responsible for 70–80% of all strokes, with the remaining number produced by cerebral bleeding and hemorrhage. Strokes are caused by clots or particles that occlude one of the cerebral arteries; in the case of thrombosis these particles are an aggregation of blood constituents, while embolism refers to a sudden blocking of an artery by a clot or foreign material such as a plaque fragment. Studies indicate that a signiﬁcant fraction, maybe as high as 60%, of all strokes are directly due to rupture or ulceration of a carotid atherosclerotic plaque along with secondary thrombus formation [2]. The structure and composition of the carotid atherosclerotic plaque does not differ qualitatively from those of atherosclerotic plaques seen in other large and medium size arteries [3]. The understanding of the contributing factors to stroke risk has changed signiﬁcantly over the last decade. Up to 1990, the degree of carotid arterial stenosis was assumed to be the main indicator of stroke risk, and it was determined with ultrasound color Doppler ﬂow mapping or contrast arteriography. It is now understood that the plaque composition and plaque morphology provide the strongest indication of stroke risk, which has led to the notion of the vulnerable plaque [4]. Speciﬁcally, plaques with hemorrhage at the intima, with lipid pool under a thin layer of ﬁbrous cap or with embedded thrombi, are easily mechanically fatigued by the arterial pressure ﬂuctuations [5], making the risk of plaque rupture high. In contrast, calciﬁed and ﬁbrous plaques are considered mechanically more stable. Inﬂammation has also been identiﬁed as an important factor in creating vulnerable plaques [6]. 1.2. Rationale for the Integrated Backscatter-Based Plaque Classiﬁcation The rationale behind the IBS-based plaque classiﬁcation is based on two speciﬁc notions: (i) Different plaque compositions and structures carry very different stroke risk, and (ii) different plaque constituents, from calciﬁed to ﬁbrous to fatty, have dramatically different acoustic backscatter properties. Thus, plaque structure and composition may be inferred from the acoustic backscatter properties measured in an absolute sense, from which stroke risk can be assessed. The backscatter level is quantiﬁed in terms of the integrated backscatter (IBS), which is an energy measure of a speciﬁed segment of the received RF signal; as such, IBS is a more robust measure than the RF signal itself, i.e., less sensitive to random ﬂuctuation. To obtain the absolute IBS non-invasively from the vessel region of interest, the scattering and aberrating effect of the intervening tissue layers must be overcome. This is achieved by using the IBS from arterial blood as a reference backscatter, speciﬁcally the backscatter from an arterial blood volume along the same scan line as and adjacent to the plaque/arterial wall region of interest. This approach is based on the assumption that the backscattered signal from a range cell in the plaque and the backscattered signal from an adjacent range in blood are subjected to the same scattering and attenuation due to the overlying inhomogeneous tissue. The theoretical considerations and the experimental validation of this concept is described in this chapter. This work was carried out using a commercial ultrasound scanner, interfaced with a PC and modiﬁed to allow quantitative measurements. A vessel phantom (silicon rubber tube) with synthetic lesions is placed in a measurement tank

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and connected to a ﬂow system containing blood mimicking ﬂuid (BMF). Between the vessel and the transducer is either water (permitting the uncorrupted IBS proﬁle to be measured) or an inhomogeneous soft tissue phantom (yielding a corrupted IBS proﬁle). The results are in the form of IBS proﬁles (IBS versus beam position along the vessel). With the inhomogeneous tissue present, the non-normalized IBS proﬁle is corrupted by phase aberration and differs dramatically from the proﬁle obtained through water. As will be demonstrated, the normalized IBS proﬁle with the inhomogeneous tissue present resembles quite closely the IBS proﬁle measured through water. 1.3. Current Techniques for Atherosclerotic Plaque Characterization Since the early 1990s, there has been a concerted effort to develop reliable clinical methods for identifying the vulnerable plaque, both in the carotid arteries and the coronary arteries, for the purpose of identifying patients with elevated risk for stroke or heart attack. Along with that, therapeutic procedures have been introduced. A brief review of the efﬁcacy of surgical intervention is given below, in order to establish that effective treatment indeed is available. This is followed by a review of the diagnostic method in current use. 1.3.1. Surgical Intervention The surgical procedure to remove fatty deposits or blockage (atherosclerosis) in the carotid artery is termed carotid endarterectomy. The beneﬁt of this procedure was demonstrated in 1991 in the NASCET study (North American Symptomatic Carotid Endarterectomy Trial) [7]. In this study of patients with a least 70% carotid artery stenosis and symptoms of lack of oxygen in the brain, the individuals who received surgery had much lower stroke rate: the cumulative stroke rate after 2 years was around 30% for the patients in the medical group (treated with aspirin) and around 10% in the surgical group. A follow-up study from 1991 to 1997 [8] examined the risks and causes of the same type of stroke in the randomized groups and in those who had delayed endarterectomy or continued on medical therapy. The study showed that endarterectomy for patients with high degree of stenosis is successful in the long term. The risks and beneﬁts of placing a stent in the carotid artery (carotid stenting) have been heavily debated [23], and several clinical studies were completed in 2003 or are underway in 2004. Early studies indicate that the risk associated with carotid stenting is lower than the risk, associated with carotid endarterectomy. This is particularly true for stents with embolic protection [23]. 1.3.2. Current Diagnostic Methods The diagnostic approaches to plaque characterization that currently are receiving the greatest interest [9] are magnetic resonance imaging (MRI), optical coherence tomography (OCT), and intravascular ultrasound (IVUS). In addition, contrast angiography and duplex Doppler ultrasound are well-established methods for assessing the extent of the stenosis. The classical method for locating stenoses is contrast angiography, in which a radioopaque contrast material is injected into a blood vessel via a catheter. The technique is the gold standard in identifying the locations and severity of atherosclerotic plaque

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formation. Contrast angiography is at best a moderately good predictor of stroke risk, due to the correlation between degree of stenosis and stroke risk. In duplex scanning, Doppler ultrasound is combined with real-time ultrasound imaging of the carotid arteries [10]. The Doppler spectrum is analyzed at a number of locations at the stenosis and distal to the stenosis as a means of getting information about presence of disturbed ﬂow and the extent of the turbulence beyond the stenosis; a fairly quantitative evaluation of the degree of stenosis is in terms of the Spectral Broadening Index = SBI [10]. The ability of spectrum analysis to distinguish laminar from turbulent ﬂow was proposed by Green in 1974 [11], shown experimentally by Sigel et al. in 1970 [12] and applied in patients with carotid artery stenosis in 1976 by Felix [13]. Magnetic Resonance Imaging (MRI) is a widely used method in assessing atherosclerotic plaque [14]. MRI uses the transverse relaxation time (T2 )contrast to discriminate among the different constituents of the atherosclerotic plaque, such as ﬁbrous tissue and lipids [15,16]. Among the general advantages of MRI is the fact that it is non-ionizing, that images can be generated in close proximity to bone (since calcium does not generate a signal in spin echo images), and that MRI is able to create images indifferent planes. However, MRI is not practical to use for screening of at-risk population due to high cost, lengthy examination times, and limited availability. Furthermore, patients with pacemakers or orthopedic hardware (screws, plates, artiﬁcial joints) are not suitable for MRI. Optical Coherence Tomography (OCT) is an invasive technique for imaging the arterial wall and plaque, based on the intensity of reﬂected near-infrared light from arterial wall tissues [9]. It provides a very detailed image of the surface properties of the plaque as well as of structures immediately below the plaque surface [17]. The image resolution is on the order of 10 μm, or about 10 times better than Intravascular Ultrasound (IVUS). OCT was introduced by Brezinski et al. [18] for assessment of atherosclerotic plaque morphology. Notable disadvantages of OCT are the need to ﬂush the vessel lumen around the catheter with saline solution and its limited depth of penetration. Intravascular OCT is currently being evaluated clinically. Intravascular ultrasound (IVUS) performs imaging of the arterial wall using a transducer placed in the artery and is as such an invasive technique. The transducer is either a rotating single-element transducer or a ring-shaped array transducer, using frequencies in the range of 20 to 40 MHz. It can provide cross-sectional images of the artery wall and plaque with good axial resolution (around 100 μm), but much poorer lateral resolution [19]. As such, IVUS can provide a fairly detailed image with relatively inexpensive equipment and can provide detailed information about the contents of the plaque, to reveal the presence of thrombi and lipid pools. By moving the catheter along the vessel axis, a 3D image can be obtained. One limitation in the image analysis is the motion of the catheter-based transducer, introduced by the pulsatility of the blood ﬂow. Furthermore, due to the high transducer frequency, IVUS cannot measure areas behind calciﬁed regions. In [20], the ultrasound and MR techniques were compared by normalizing ultrasound measurements such as integrated attenuation, integrated backscatter compensated for the attenuation between the artery surface and the scattering volume and the Magnetic Resonance measurement, using the transverse relaxation time.

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2. Arterial Plaque Classiﬁcation Based on the Absolute Integrated Backscatter Proﬁle This section will discuss pertinent ultrasound properties of atherosclerotic plaque, which leads to the choice of absolute integrated backscatter for classiﬁcation of arterial plaque. This will be followed by a conceptual description of the non-invasive approach. Given the complexity of plaque structure and the broad range of manifestations of a vulnerable plaque, only quantitative ultrasound or ultrasound tissue characterization, rather than ultrasound imaging, will be able to provide sufﬁcient amount of information. Studies using ultrasound B-mode imaging have been unable to identify the vulnerable plaque [21], in part due to the qualitative nature of B-mode images and in part due to the phase aberration by of the intervening soft tissue. In contrast, ultrasound tissue characterization, such as a technique based on spectral analysis of the backscattered RF signal [22], can characterize plaques with moderate accuracy. 2.1. Ultrasound Properties of Atherosclerotic Plaque Based on pathologic studies, atherosclerotic plaque composition has been found to vary dramatically from individual to individual and to be associated with different clinical syndromes: Plaques can be ﬁbrous, heavily calciﬁed, loaded with lipid pools and/or cholesterol crystals, edematous, and/or hemorrhagic; their surface can be smooth, ﬁssured or ulcerated; an overlying thrombus can be present. Those characteristics are important because plaques may be grouped in 2 categories, which are associated with 2 different clinical syndromes: i) The stable plaque (smooth, ﬁbrous, calciﬁed plaque) is the most common plaque with a low stroke risk, and ii) the vulnerable (unstable) plaque (ulcerated, overlying thrombus, lipid pool, thin ﬁbrous cap) is a less common form, but with a high risk for stroke and transient ischemic attacks. Several published studies have elucidated the relationship between structure and surface nature of the plaque on one hand and ultrasound properties on the other hand. From in vitro measurements [24], the following observations have been made: • Frequency dependence of ultrasound backscatter — greater frequency dependence is observed in connective tissue than in fatty tissue • Integrated backscatter — signiﬁcant difference between normal, fatty, ﬁbrofatty, ﬁbrotic, and calciﬁed plaque was found • Angular dependence — strong angle dependence for calciﬁed and ﬁbrous plaques; weaker angle dependence for normal and ﬁbrofatty plaques; and minimal angle dependence for fatty plaques. An important paper [25] by Picano and Landini on the acoustic characterization of atherosclerotic plaque describes the backscatter level and the angle dependence at 10 MHz from normal arterial wall and from four different categories of atherosclerotic lesions (fatty, ﬁbrofatty, ﬁbrotic and calciﬁed). Fifteen specimens were evaluated in each category. The samples were fresh excised arterial samples, which were cut open, held ﬂat and scanned over ± 30◦ range with a 5 mm diameter 10 MHz focused transducer. A dramatic variation in backscatter coefﬁcient at normal incidence between the different categories was found, with as much as a factor 100 (20 dB) change in backscatter power from normal to calciﬁed.

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Speciﬁcally, the calciﬁed plaque have a high backscatter coefﬁcient at normal incidence and a strong angle dependence; ﬁbrous and ﬁbrofatty plaques have a moderate backscatter coefﬁcient at normal incidence and a moderate angle dependence; fatty plaque have a low backscatter coefﬁcient and practically no angle dependence, and ﬁnally normal arterial wall exhibit a low backscatter coefﬁcient and a moderate angle dependence. These results indicate the potential for categorizing plaques, based on measuring absolute backscatter level at normal incidence, with further categorization possible if the angle dependence is included. Note that only a moderate amount of angle variation, such as ± 10◦ to ± 15◦ , is needed to characterize the angle dependence. In [26], Picano, Landini et al. present a broad review the acoustic properties of arterial plaque, which are relevant for evaluation of plaque structure. These properties include attenuation, IBS level and frequency dependence of backscattering, and angle dependence of backscattering. Attenuation is low for normal and ﬁbrotic plaques, medium for ﬁbro-fatty plaques, and high for calciﬁed plaque. The paper argues that the composition of atherosclerotic plaque may be determined through quantitative ultrasound. 2.2. Concept Behind the Measurement of Absolute IBS The published results, discussed above, indicate that improved atherosclerotic plaque classiﬁcation can be achieved by determining the absolute ultrasound integrated backscatter (IBS) level, including angle dependence, from sequence of positions within the atherosclerotic lesion. However, a serious obstacle to the non-invasive measurement of the absolute IBS is the attenuation and phase aberrating effects of the soft tissue layers located between the transducer and the tissue region of interest – here is the carotid artery with atherosclerotic lesions. By normalizing the integrated backscatter from a given range cell in atherosclerotic lesion with the integrated backscatter from a range cell in the moving arterial blood, where both range cells are placed along the same scan line, most of these effects of the intervening tissues can be eliminated. Thus, the absolute IBS may be determined by using the absolute integrated backscatter level of blood as a reference backscatterer. The concept is illustrated in Fig. 1(a) where a focused transducer measures the IBS from two selected range cells: one range cell centered at the middle of the blood vessel and one range cell centered in the middle of the atherosclerotic lesion. The measured IBS from the range cell in blood provides a reference with which to compare the measured IBS level from the atherosclerotic plaque. If the true backscatter coefﬁcient for moving (arterial) blood has been determined previously, the IBS level of the selected plaque region can be determined in an absolute sense. As an extension of the method, the scattering from different angles may be determined, as illustrated in Fig. 1(b). A set of absolute backscatter values from a set of positions along the vessel, over the extent of the plaque, constitute a backscatter “signature.” This signature may also be augmented with IBS measurements under different angles. As will be described later, the acoustic backscatter properties of blood are rather complex, with dramatically different backscatter levels from venous blood to arterial blood. As the reference IBS will be determined solely in arterial blood and only during a short time interval at a given point in the cardiac cycle, these factors will not inﬂuence the validity of the results. Since the backscattered signal from blood is stochastic in nature, the IBS of arterial blood is an estimate of the true integrated backscatter and is

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Figure 1. Illustration of concept of normalizing the IBS of a tissue volume with the IBS of arterial blood.

obtained as a sample mean of a large number of measurements, after clutter removal. We have shown that the variance of the IBS estimate of the blood backscatter signal can be quantiﬁed and reduced to a speciﬁed tolerable level [43]. The concept of using moving (arterial) blood as a backscatter reference in order to determine the absolute value of integrated backscatter of an unknown tissue interface was proposed in 1988 by Nakayama [27] and has successfully been used for in vivo myocardial tissue characterization [28,29]. In [30], the absolute backscatter power was measured for the purpose of estimating the size of microemboli. Here, the power of the Doppler signal during embolus passage through the sample volume was compared to the power of the background Doppler signal when no embolus is present; the ratio of these two values was used for the size estimation. More recently, a related approach [31] for plaque classiﬁcation was published: the echogenecity of blood in the selected vessel was tagged to the color green, corresponding to the amplitude range of range of −54 dB to −58 dB, and the echogenecity of nearby tissues were divided into 9 ranges over a dynamic range from 0 dB to less than −56 dB, and a speciﬁc color assigned to each range, for the purpose of identifying regions containing fat-ﬁlled foam cells in atherosclerotic plaques.

3. Principles of Absolute Backscatter Measurements This section will present the underlying concepts for the technique of absolute backscatter measurements. First, a review of the acoustic backscatter properties of moving blood will be given, to describe how blood fulﬁlls the requirements for being the reference backscatter, followed by a derivation of how the absolute IBS can be obtained from an atherosclerotic lesion in vivo. Since the backscattered RF signal from blood is stochastic in nature, the IBS from a given RF signal from blood is likewise stochastic. 3.1. Use of Blood as a Reference Backscatterer It is well documented [32,33] that ultrasound backscatter from human blood is highly shear-rate dependent, due to the aggregation of red blood cells (RBCs). The effect can be dramatic, with slowly moving blood producing up to 40 dB higher backscattering

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than fast moving blood. More speciﬁcally, it has been found [30] that RBC aggregation is minimized for mean shear rate exceeding 50 s−1 . Shear rate is calculated as 8v/3a where v is the average velocity and a is the radius of the vessel. In a carotid artery with a 3 mm radius, a mean laminar velocity of only 6 cm/s will produce a shear rate of 50 s−1 . Fortunately, several seconds are required for signiﬁcant aggregation to take place, so no increase in backscatter level due to changes in aggregation should occur during the cardiac cycle even if the ﬂow is zero during a phase of the cardiac cycle. However, some variation in backscatter level from the central region of the vessel to the periphery of the vessel has been observed [32]. One further factor, not related to aggregation, may affect the backscattering from blood slightly: change in ﬂow characteristics from laminar to turbulent and variation in the degree of turbulence [34,35] will give a small variation in backscatter level. In a recent paper [36], cyclic variation in blood echogenecity was determined in vivo from the carotid artery, based on harmonic images with a fundamental frequency of 9 MHz. Blood echogenecity followed fairly closely the ﬂow variation during the cardiac cycle, such that blood echogenecity reached a maximum during systole and a minimum during diastole, with a variation from systole to diastole of 40–60% for all radial positions. This effect is attributed to enhanced red blood cell aggregation due to ﬂow acceleration. Given that the IBS of blood will be established at a given point during the cardiac cycle, speciﬁcally at the time of the highest ﬂow rate, this variation will have only a minimal effect on the accuracy. 3.2. Broadband Integrated Backscatter The broadband integrated backscatter (IBS) is a simple and robust measure of signal strength [37] and represents the normalized energy of the RF backscatter signal from a given sample volume. The rationale behind using IBS is that the integration operation removes much of the random ﬂuctuation in the RF signal while still preserving the spatial resolution. IBS has been used successfully for tissue characterization, such as for differentiating normal myocardium from ischemic myocardium, and for a number of NDE applications. The IBS has been deﬁned in somewhat differing ways in the literature. The deﬁnition for IBS, used here, is closely related to the form presented by O’Donnell et al. [37] and is given as the ﬁrst expression in (12): 2 2 +∞ +∞ −∞ Vsample (f ) df −∞ vsample (t) dt = . IBS = +∞ +∞ 2 2 −∞ |P (f )| df −∞ |p(t)| dt

(1)

The second form in (12) is obtained by the use of Parseval’s theorem and is more suitable for pulse-echo measurements. In (12), P (f ) is the Fourier transform of p(t), and p(t) is the impulse response of the ultrasound system in pulse-echo mode, obtained with a perfect reﬂector placed at the location of the sample volume. For determination of p(t), the medium between the transducer and the reﬂector is assumed homogeneous and with no attenuation. Next, vsample (t) is deﬁned as the windowed received signal which extracts the backscattered signal from the sample volume of interest from the plaque and Vsample (f ) is the corresponding Fourier transform.

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3.3. Formulation for Determining the Absolute IBS Let rref be the known reﬂection coefﬁcient between blood and a planar reﬂector with known acoustic properties, oriented normal to the transducer axis; rref is given as: rref =

zref − zblood zref + zblood

(2)

where zref is the acoustic impedance of the planar reﬂector. Note that (13) is a valid way to deﬁne rref even though blood is a stochastic medium. The acoustic impedance of blood has been published in the literature, and the reﬂected signal from the blood-reﬂector interface is far greater than the backscatter level of the blood. The received RF signal from a range cell placed at the interface between blood and the planar reﬂector will be called vref (t). Based on the deﬁnition of p(t) in Section 3.2, we have vref (t) = rref

p(t)

(3)

provided that the reﬂection measurement is performed through a homogeneous, nonattenuating medium, e.g. water. Applying (3) to (12) allows the expression for IBS to be restated as follows: +∞ vsample (t)2 dt 2 −∞ IBS = (rref ) +∞ . (4) 2 −∞ vref (t) dt Let the received, clutter-free backscattered RF signal from a range cell fully inside the blood volume be called vblood,ref (t) where it is likewise assumed that the measurement is performed through a homogeneous, non-attenuating medium, such as water. The signal vblood,ref (t) is therefore vsample (t) obtained for blood which, when applied to (14), yields IBSblood,ref . IBSblood, ref =

+∞ vblood, ref (t)2 dt 2 −∞ . (rref ) +∞ vref (t)2 dt −∞

(5)

Consider now an actual measurement through an inhomogeneous tissue, as shown in Fig. 1, where the RF signal from the range cell inside the blood volume is vblood (t) and the RF signal from a range cell placed at the plaque wall is vplq (t), producing the IBS values IBSblood and IBSplq , respectively, when calculated according to (14). The numerator in (14) yields the energy Eplq when vplq (t) is substituted for vsample (t). The absolute backscatter of the plaque wall, σ plq,abs , is then determined as: σplq, abs = IBSblood, ref

IBSplq Eplq = IBSblood, ref . ¯ IBSblood Eblood

(6)

As will be described in the next section, signal processing will be needed to estimate IBSblood from the RF signals from blood, and statistical analysis will be needed to determine the accuracy of the estimate.

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Figure 2. The N consecutive measurements yield N sets of digitized RF data which are arranged as columns in a data matrix. The signals within the highlighted (orange) region to the left represent the data matrix Y and the signals within the highlighted (green) region to the right represent the data matrix U.

3.4. Determination of Mean IBS from Moving Blood As the backscattered signal from blood is stochastic and nonstationary, the IBS based on actual measurements of the backscattered signal is itself a stochastic variable. Hence, utilizing blood as a reference ultrasound backscatter provides only an estimate of the true mean IBS value [43]. For pulsatile ﬂow, it is also necessary to consider the time interval over which the backscatter signal as a stochastic process can be considered stationary which deﬁnes the longest time interval that can be used for obtaining a backscatter estimate. A sequence of N ultrasound pulse-echo measurements is obtained from the artery of interest at a speciﬁed PRF; a backscattered RF signal of duration Tdur is then extracted from each echo, in such a way that the extracted RF signal contains both the front and back wall echoes of the artery. The extracted echoes are graphically illustrated in terms of the larger (orange) block on the left side of Fig. 2. If the echoes are sampled at a sampling rate fs then each extracted RF signal will contain K = Tdur · f s samples. The extracted and sampled signals are placed in a K × N data matrix Y, such that each column in the matrix contains an RF signal, as shown in (7). The elements y1,1 , y2,1 , . . . , yK,1 represent the RF signal associated with the ﬁrst pulse-echo measurement. ⎤ ⎡ y1,1 y1,2 .. y1,j .. y1,N ⎢ y2,1 y2,2 .. y2,j .. y2,N ⎥ ⎥. (7) Y= ⎢ ⎣ .. .. .. .. .. .. ⎦ yK,1 yK,2 .. yK,j .. yK,N Accurate estimation of the mean integrated backscatter from blood presents several challenges, apart from the stochastic nature of the backscatter signal from blood itself. The intervening inhomogeneous tissue and the arterial wall introduce clutter echoes of much larger amplitude than the scatterer echoes from the moving blood or blood mimicking ﬂuid. These clutter echoes dominate the RF signals and will greatly affect the value of IBSblood unless removed with a carefully designed clutter ﬁlter. Due to the pulsatile nature of the ﬂow, the clutter is not stationary. This is manifested in the spectra of the

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rows in Y where the spectral component due to clutter overlaps to some extent with the spectral component due to the moving scatterers. The measurement parameters are based on a 5 MHz linear array transducer insonifying a 6 mm silicone rubber tube, mimicking a vessel. The chosen PRF is 2.06 kHz, which will be rounded down to 2 kHz. A 13 μs range cell contains the RF signal for the whole vessel, including front wall and back wall. A sampling rate of 20 MHz will then yield a sampled signal consisting of K = 260 samples. Based on the clutter ﬁltered RF data, the part of the RF signal which contains the lumen echo is extracted, where a typical number of lumen samples is M = 81. After clutter ﬁltering (described in Section 6.3.2), only the backscattered signals corresponding to moving scatterers remain. From these signals, an algorithm determines the true lumen boundaries, which deﬁnes the size of the clutter ﬁltered data matrix, U. The matrix U contains the same number of RF signals, N , as Y, but the duration of each RF signal is reduced to M samples. This process is illustrated in Fig. 2. The sample values in U, ui,j , have been shown to be Gaussian distributed, with zero mean and variance σ 2 [38]. To ﬁnd an estimate of the true IBS, a new data matrix of instantaneous power values, P, is ﬁrst generated as shown in (8), such that pi,j = u2i,j . The entries in P are random variables with central Chi-Squared (χ 2 ) distribution with one degree of freedom. ⎤ ⎡ p1,1 p1,2 .. p1,j .. p1,N ⎢ p2,1 p2,2 .. p2,j .. p2,N ⎥ ⎥. (8) P=⎢ ⎣ .. .. .. .. .. .. ⎦ pM,1 pM,2 .. pM,j .. pM,N An estimate of the IBS, based on the j th echo, is denoted sj and is found as: sj = s

M

pi,j = s

i=1

M

u2i,j .

(9)

i=1

where s is the sampling interval for the RF signal. Carrying out the calculations in (9) for each column of P leads to an array, S, given in (10), of estimates of IBS values, containing the variable sj , j ∈ [1, N]. If the instantaneous power values pi,j were all independent, the random variable sj would have a central Chi-Squared (χ 2 ) distribution with M degrees of freedom [39]. In reality, the sample values of a given echo ui,j are not independent, and therefore neither are the corresponding instantaneous power values. S = [s1 s2 . . . , sj . . . sN ].

(10)

The sample mean of IBS from the moving blood, IBSblood , is calculated in (11), based on the array of N backscatter estimates in (10), S. IBSblood =

N 1 sj . N j =1

(11)

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4. Experimental System A commercial Hewlett Packard ultrasound scanner has been reconﬁgured to provide an experimental platform where ultrasound pulse-echo measurements can be performed on different artery-mimicking tubes, plaque phantoms and inhomogeneous tissue. The accuracy and reproducibility of experimental results are closely related to the design of the experimental set-up. This is particularly true for ultrasound backscatter measurements where the received RF signal is affected by diffraction, scattering, absorption and refraction, introduced by the intervening tissue layers. Given that echo amplitude can vary signiﬁcantly from scan line to scan line, due to tissue inhomogeneity, it is critical that the system operates in the linear range at all times and utilizes the dynamic range effectively. Therefore, a system with self-regulating gain and automatic localization of the arterial walls will minimize human error and improve quality. 4.1. Requirements to Experimental System In order to reliably measure the absolute Integrated Back-Scatter (IBS), the experimental system measurement must meet the following requirements: a. Rapid (albeit not real-time) transfer of digital RF signals to a PC for signal processing. b. Calibration of the ultrasound scanner system so that the precise change in gain associated with any change in gain and/or power setting is known. c. Scan parameters to be externally controllable. These include the initial scan line, the scan line spacing, the length of the excitation pulse, and the pulse repetition frequency (PRF). d. A ﬂow system must be included, with PC control of pump speed, and a measurement tank with vessel phantom and inhomogeneous tissue (real or phantom). e. Control signal processing routines needs to be developed for locating the front wall and the rear wall of the blood vessel and for automatically adjusting the gain settings for optimal dynamic range for each scan line. The experimental system, shown in the simpliﬁed block diagram in Fig. 3, is built around a commercial ultrasound scanner for medical imaging, the Hewlett Packard ImagePoint Multispecialty Ultrasound System. The scanner was modiﬁed to implement remote control of a number of scan parameters and to make the digital RF signal, after beam forming, available externally. The scanner acquires RF data from the artery mimicking tube (vessel phantom), through which blood mimicking ﬂuid ﬂows at a constant rate. The measurements at each scan line need to be repeated in the order of 100 times, in order to obtain a statistically reliable mean IBS value for the blood mimicking ﬂuid. The RF data is transferred to a Personal Computer (PC) for data analysis in MATLAB. The PC controls the most of the operations of the scanner, such as chosen scan line, number of repetitions of scan line, pulse repetition frequency (PRF), and the number of cycles in the excitation signal. The receive gain and transmit power are determined based on analysis of the actual received signal for a given scan line.

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Figure 3. Simpliﬁed diagram over the experimental system.

Figure 4. Diagram over data signals and control signals in experimental system.

4.2. The Acquisition and Signal Processing Hardware of the Experimental System The acquisition and signal processing hardware is described in Fig. 4. Not shown in this ﬁgure is the ultrasound transducer and the associated measurement tank and ﬂow system. The instruments are highlighted (yellow), the interface cards or boards in a lighter highlight (blue), the control lines are dashed and the data lines are solid. In this research, the measurements are carried out with the HP ImagePoint scanner in PW spectral Doppler mode, since it provides control on the number of cycles in the excitation signal to the transducer elements and allows us to specify a Doppler gate or “sample volume gate.” As seen, a large number of scan parameters can be controlled from the Pentium PC through a serial link, using a so called “backdoor” command.

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Figure 5. Photograph of actual hydraulic system used for experiments. The pump is seen on the bottom right (1), and clockwise: magnetic stirrer (2), open reservoir (3, with lid to avoid water evaporation), water tank with vessel-mimicking tube (4), and closed reservoir (5, to reduce pressure ﬂuctuations).

The array transducer for the ultrasound scanner is the 128 elements L7450 Linear Array Transducer. The scanner can generate 255 scan lines by activating groups of transducer elements. The computer is a 650 MHz AMD Athlon™ processor with 256 MB of RAM. Through the serial communication port, the computer controls remotely all the ultrasound scanner parameters needed to take the measurements, such as frequency, depth, gate position, gate width, scan line, beam angle, power, DC gain, etc. The pump, which determines the ﬂow rate of the blood mimicking ﬂuid, is also control by the Pentium PC, through a separate serial port. The PC receives the RF data from the ultrasound scanner via the logic analyzer using WPI’s local area network. 4.3. Design of the Flow System and Measurement Tank The closed-loop ﬂow system and measurement tank, as shown in the photograph in Fig. 5, consists of a pump (shown is a Micropump™ Pump, later replaced by a MASTERFLEX™ Roller pump), two reservoirs with magnetic stirrers, and a water ﬁlled measurement tank containing an artery mimicking tube (a 6 mm ID silicone rubber penrose tube) placed 60 mm from the acoustic window. The inﬂow reservoir is a closed reservoir that functions as a hydraulic low pass ﬁlter, in order to remove rapid pressure oscillations generated by the pump. If not removed, these vibrations will create high frequency clutter that cannot be removed by row ﬁltering. The outﬂow reservoir is an open reservoir.

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Figure 6. Detailed drawing of measurement tank (top view).

The measurement tank is depicted in Fig. 6. In order to quickly absorb the ultrasound energy, that tank has butyl rubber glued to the three sides and to the bottom; the butyl rubber on the back wall had vertical slots cut in order to further diffuse the ultrasound waves and minimize standing waves. Quick interchanges of vessels phantoms or actual vessel segment, as well as for repositioning the vessel relative to the transducer, is accommodated by means of sliding panels in each end. The measurements are carried out through a thin latex window at the side of the tank. The water inside the tank serves as coupling medium for the ultrasound measurements. The tank dimensions as well as the distance of the tube from the membrane are illustrated in Fig. 6. The 6 cm space between the coupling membrane and the artery mimicking vessel provides adequate space for insertion of inhomogeneous tissue phantom or actual soft tissue. In order to control the ﬂow remotely, the MASTERFLEX™ Computerized Drive 7550-10 was used. The pump is a computer-controlled, variable speed pump, capable of ﬂow rates between 0.8 ml/s and 50 ml/s. It was equipped with two drive heads, operated 180◦ out of phase, in order to provide a smoother ﬂow. Each drive head has three rolls that squeeze the tubing creating the ﬂow.

5. Blood Mimicking Fluid, Soft Tissue Phantoms and Artery Mimicking Materials The section will describe the preparation of the blood mimicking ﬂuid, and the design and pertinent features of the inhomogeneous soft tissue phantoms and artery mimicking materials. Proper design of these materials will allow parallels to be drawn between the observed results and the corresponding in vivo results. 5.1. Blood Mimicking Fluid The blood mimicking ﬂuid (BMF) was prepared in our laboratory, based on recently published papers [40,41]. This BMF has been certiﬁed to meet the requirements for

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evaluation of ultrasound Doppler systems. The BMF mixture is based on polyamide microspheres (Orgasol®Ultraﬁne polyamide powder, 2001 EX D NAT 1) as scatterers, which are mixed with glycerol, surfactant and boiled, distilled water. The microspheres have a mean diameter of 10 μm and a speciﬁed nominal density of 1.03 g/cm3 . A standard batch of BMF consists of 150 ml of glycerol, 15 ml of surfactant and 32 grams of polyamide spheres, added to 1500 ml of distilled water. The BMF mixture was prepared as follows: First the glycerol was added to 700 ml of distilled water and mixed with the surfactant, and then polyamide particles were added. The mixture was stirred for 45 minutes using magnetic stirrer until the mixture was visually homogeneous, after which the remaining amount of distilled water was added. In order to minimize the amount of dissolved air bubbles, the BMF was vacuum treated for 30 minutes before being used. Then the mixture was slowly added to the ﬂow system and circulated for 30 minutes before any measurements were taken. 5.2. Inhomogeneous Soft Tissue Phantoms The initial experiments for determining absolute IBS of vessel walls were performed using approx. 1” thick slices of fatty beef, warmed to room temperature. However, the acoustic attenuation of bovine muscle is very temperature dependent, and the deterioration of the meat began after only a few hours of being submerged in water. Thus, for both experimental and hygienic reasons, inhomogeneous soft tissue phantoms, imitating fatty muscle tissue, replaced actual slices of beef. The soft tissue phantoms were produced in collaboration with Computerized Imaging Reference Systems, Inc. (CIRS), Norfolk, VA. The phantoms that were used for the experiments described in this chapter were composed of urethane as a fat-mimicking material (c = 1420 m/s, density = 0.98 g/cm3 , atten. = 0.2 dB/cm/MHz) and Zerdine as a muscle mimicking material (c = 1540 m/s, density = 1.03 g/cm3 , atten. = 0.5 dB/cm/MHz). Speciﬁcally, irregular slivers of urethane, 8–12 mm long, 2–4 mm in thickness and 4–6 mm in width, were randomly mixed into Zerdine while it was still in liquid form. The inhomogeneous soft tissue material was contained in a circular plastic housing, such that the material formed a cylinder with a diameter of 50 mm and a thickness of 25 mm. This thickness dimension may exceed the average distance from the skin to the carotid artery while still being representative. Phantoms with 10% and 15% volume concentration of the fat-mimicking urethane were used for most of our measurements. Figure 7 shows two of the soft tissue mimicking phantoms, produced in connection with this research. The phantom in Fig. 7(a) consists of Zerdine with a 15% urethane slivers. The phantom in Fig. 7(b) is made up of Zerdine with 10% urethane slivers plus a coating of RTV for phase aberrating effect. 5.3. Arterial Vessel Phantoms The vessel phantoms were developed less with the intention of resembling actual plaques and more with the goals of having a well deﬁned IBS proﬁle. This allows for a more direct comparison of the measured IBS proﬁle with the physical design of the vessel phantom. The vessel tubing was made from silicone rubber, with an inner diameter of 6.3 mm. The reﬂectivity of the silicon rubber, immersed in water and with BMF ﬂowing

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Figure 7. (a) Zerdine phantom (muscle equiv.) with 15% volume concentration of urethane slivers (fat equiv.); (b) Zerdine phantom with 10% urethane volume concentration of slivers and RTV coating for additional phase aberration.

Figure 8. Silicone rubber vessel phantoms with one or three rings, made from silicone rubber tubing.

through it, is signiﬁcantly higher than what would be observed form an actual artery in vivo; still, silicone rubber was acoustically the most suitable of the candidate materials examined for use as an artery-mimicking tube. A plain tube was used to represent a vessel without any abnormalities, while vessels with one, two or three rings were used to represent vessels with an abnormal thickening. Two examples of such types of vessel phantoms are shown in Fig. 8, where the rings are cut from the silicone rubber tubing and simply opened and slipped over the intact tube. This design allowed simple manufacture and straight-forward adjustment, but it did not create a stenosis with the accompanying ﬂow disturbances. Other vessel phantoms were made with various coatings or layers on the outside of the tube. The coatings were produced with epoxies or rubber cement loading with chalk.

6. Signal Processing Steps for Extracting Absolute IBS of Arterial Wall 6.1. General Overview of the Signal Processing Challenge This section will describe the signal processing steps that are necessary in order to obtain the absolute IBS for a sequence of scan lines, forming a scan plane that contains the axis

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of the artery. The determination of the absolute IBS for the arterial wall, or plaque, is carried out for one scan line at a time, with a total of 64 scan lines used to produce the IBS proﬁle of the wall of the artery-mimicking vessel. Thus, every other of the available 125 scan lines that uses the full set of 64 active array elements is used. As the RF signal for each scan line has been subjected to its own unique attenuation and phase aberration, due to the intervening inhomogeneous soft tissue, a unique set of gain and transmit power values are established for each scan line. Furthermore, a set of RF data is acquired for each scan line, in order to extract the correct IBSblood with which to normalize the measured IBSwall . All the measurements are carried out at normal incidence. The range gate is 13 μs in duration, corresponding to a spatial range of 10 mm. It is positioned such that the acquired RF signals contain both wall and lumen echoes from the arterial vessel under consideration. The signal processing of the acquired signal must be carefully designed to achieve correct results, due to the following challenges: • Given the low number of bits representing the blood backscatter signal after clutter removal, the power and gain setting of the scanner must be carefully chosen to both ensure linearity and to fully utilize the dynamic range. The magnitude of the clutter signal in the lumen is inﬂuenced by the intervening tissue structures and the vessel wall structure and cannot be assumed knowna priori. • The lumen echoes consist of small-amplitude backscatter signals from blood mimicking ﬂuid (bmf) (or blood) and large amplitude clutter signals. The bmf (blood) backscatter signals are non-stationary, due to bmf scatterers (or red blood cells) moving into and out of the range cell, while the clutter signals are pseudostationary, in part due to turbulence-induced wall motion. Thus, a design of the clutter ﬁlter, based on the given experimental conditions, is critical for the adequate performance. • Due to the unknown appearance of clutter, the beginning and end of lumen are not readily identiﬁed. Therefore, only after clutter ﬁltering are the true locations of vessel walls and lumen revealed. • The backscattered signal from bmf (blood) is stochastic in nature and a sufﬁcient number of repeated measurements must be carried out so that the sample mean IBS is representative of the true mean IBS. • There is a possibility (at least in the experimental system) for air bubbles in the bmf, which can signiﬁcantly alter the IBS of the bmf. Hence an algorithm for detecting and removing echoes containing bubbles must be implemented. • The wall (or plaque) echoes are of far greater amplitude than the lumen echoes, and the optimal gain setting for the wall will therefore be different than the optimal gain setting for the lumen. To illustrate the corrupting inﬂuence of the overlying tissue layers, consider the test setup described in Fig. 9, along with the results in Fig. 10. Figure 9 describes a measurement set-up in the water-ﬁlled tank that was illustrated in Fig. 6, using the 5 MHz linear array transducer. RF signals are acquired from the target, which is an artery-mimicking tube in the form of a silicon rubber tube with a narrow ring of silicon rubber placed on it, and through which blood mimicking ﬂuid circulates. Figure 10 displays 32 scan lines in the form of 32 RF envelope signals, spanning a 17.3 mm segment of the artery-mimicking tube. The envelope signals are in the form of the analytic signal magnitude of the RF signals. In Fig. 10(a), only water exists between

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Figure 9. Measurement set-up in the water-ﬁlled tank, using a 5 MHz linear array transducer. The vessel phantom is a silicon rubber tube with a narrow ring of silicon rubber placed on it, through which blood mimicking ﬂuid is circulated. An inhomogeneous tissue phantom may be placed between the transducer and the vessel.

Figure 10. Display of 32 scan lines, representing a 17.3 mm segment of the artery-mimicking tube, illustrated in Fig. 9. Part (a) shows the 32 scan lines obtained with only water between the array transducer and the artery-mimicking tube, while part (b) shows the 32 scan lines obtained with a tissue mimicking phantom between the transducer and the artery-mimicking tube.

the artery-mimicking tube and the array transducer. Here, the presence of the ring can be clearly seen on the front wall, and the shadowing effect of the ring can also be observed on the back wall. Even for this situation, the lumen has a fairly high level of clutter, many times higher than the level of the backscatter signal from the blood mimicking ﬂuid. In Fig. 10(b), a tissue-mimicking phantom (described in the previous section) has been placed between the array transducer and the artery-mimicking tube. Now, the presence of the ring is no longer discernible, and both the front wall and the back wall have a somewhat random appearance due to the phase aberrating effects of the intervening inhomogeneous tissue layer. The clutter amplitude of the lumen, relative to the amplitude of the wall envelope signals, has also increased. The change in appearance from part (a) to part (b), that is, from water being present to typical inhomogeneous soft tissue being present, illustrates the challenge of in vivo quantitative ultrasound measurements.

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Figure 11. Block diagram of sequence of signal processing steps.

6.2. Overall Sequence of Signal Processing Steps The main signal processing steps, involved with determination of the absolute wall IBS for a single scan line, are laid out in the block diagram in Fig. 11. An initial set of RF signals is acquired, based on which the appropriate gain settings for acquiring wall echoes and lumen echoes are determined, as shown in the ﬁrst block. The criterion, as discussed earlier, is that the peak-to-peak value of the RF signal must not exceed 500 mV. Since clutter makes it difﬁcult to determine the exact lumen boundaries, N = 100 (typically) RF signals from the full width of the vessel are acquired with gain setting optimized for lumen measurements, as indicated in the second block in Fig. 11. The digitized echoes are entered as columns in the data matrix where high pass ﬁltering of the rows of the data matrix removes the clutter. An algorithm examines the ﬁltered RF signals for the presence of large amplitude echoes due to small air bubbles, and then removes such RF signals. The clutter-ﬁltered RF signals are used for two purposes: i) to establish the actual lumen boundaries which in turn deﬁnes the location of the front and back walls; ii) to calculate the IBSblood in the form of a sample mean. As seen in Fig. 11, the location of the front and back wall is established following bubble removal, and the IBSwall is determined based on a single measurement of the RF signal with a gain setting appropriate for the wall. The sequence of N clutter ﬁltered RF signals is then windowed based on the lumen boundaries now established, and this sequence is then processed to yield the IBS estimate of arterial blood, named IBSblood . Finally IBSwall is normalized with IBSblood and scaled by IBSblood,ref (as described in Section 3.3), to yield the absolute backscatter of the vessel wall or the atherosclerotic plaque. 6.3. Detailed Description of Key Signal Processing Steps This section will give a more detailed description of the implementation of the key signal processing steps. This section is provided for the readers who are interested in the algorithms and the speciﬁcations for the signal processing, but it can be skipped with-

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out any loss in continuity. Further details are given in a Masters Thesis by Ruben LaraMontalvo [42]. 6.3.1. Determination of Gain Setting for Vessel Wall and Vessel Lumen The measurements require two sets of TGC gain and power step values: The TGC gain and Power Step value appropriate for vessel wall measurements, and the TGC gain and Power Step value appropriate for lumen measurements. Determining the ﬁrst set of values is simple: TGC and Power Step are adjusted by the MATLAB program, using the look-up table, to ensure that the maximum amplitude is close to, but does not exceed 500 mVp−p . Acquiring the sequence of N lumen RF signals with the proper TGC and Power Step values is not straightforward since the true boundaries of the lumen can only be determined after clutter ﬁltering. Only at this point can it be seen whether the proper TGC and Power Step values were chosen to given an RF signal within the 500 mVp−p bound. The problem is handled in the following, somewhat ad hoc, fashion: An RF scan line is acquired with TGC and Power Step adjusted so that all vessel wall echoes are in the linear range. The envelope of the RF signal is determined and then smoothed by means of low pass ﬁltering with a zero-phase Butterworth low pass ﬁlter (LPF), using the ﬁltﬁlt operation in MATLAB, which performs one ﬁltering operation, time reverses the output signal, and then low pass ﬁlters the time reversed signal with the same Butterworth ﬁlter. The approximate lumen location is then estimated by applying appropriate threshold levels. The TGC gain and the Power Step are next adjusted by the MATLAB program so that highest amplitude of the lumen segment of the RF signal does not exceed 500 mVp−p . Finally, a sequence of N = 100 RF signals are acquired with this gain setting. The RF signals are of 13 μs length, hence they include the full vessel including the wall echoes, which are obviously clipped. The digitized RF signals are used to ﬁll a data matrix of the form, given in Y in Eq. (7). 6.3.2. Clutter Filtering The clutter ﬁltering for a single scan line is speciﬁcally developed for measurements with a 5 MHz linear array transducer on a 6 mm silicone rubber tube. The PRF is 2.06 kHz which for calculations will be rounded down to 2 kHz. A 13 μs range cell, corresponding to a 10 mm range gate, is sampled at a rate of 20 MHz, or 4 times the center frequency of the transducer. The sampled signal will therefore consist of M = 260 samples. Assume that N consecutive measurements of the backscattered RF signal from the vessel are made. The rows in Y in Eq. (7) correspond to samples acquired from a speciﬁc range from the transducer where the PRF represents the sampling frequency for the row signals. If the data matrix were a result of measurements on a stationary object, all the rows would have constant (or dc) values, assuming that all operations of the scanner are fully synchronized. Likewise, clutter from stationary structures will appear in Y as dc values in the rows. On the other hand, echoes from moving particles, such as the blood mimicking ﬂuid, will produce time-varying row signals whose spectra are determined by the ﬂow distribution in the lumen. An accurate estimation of the mean integrated backscatter from blood present several challenges. One is the stochastic nature of the backscatter signal from blood, which requires that a large number of repeated measurements be made, and the coefﬁcient of

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Figure 12. The envelopes of N = 100 repetitions of a given RF signal (scan line), which includes front and back walls of the vessel and the vessel lumen.

variance of the IBS sample mean understood. The other challenge lies with the fact that the non-stationary clutter echoes are of much larger amplitude than the scatter echoes from the moving blood or blood mimicking ﬂuid. These clutter echoes will dominate the RF signals and will greatly affect the value of IBSblood unless the backscattered RF signals are processed. Effective removal of the large amplitude clutter in the row signals depends critically on the ﬁlter type and on the choice of ﬁlter cut-off frequency. Before ﬁltering, the dc component of each row is subtracted, equivalent to removing stationary clutter. The ﬁlter is required to have a high stopband attenuation and a sharp cut-off frequency, despite the fact that the duration of the row signals is only 50 ms. For this task, a dual 14th order Butterworth IIR high pass ﬁlter was used, designed to create a zero phase delay ﬁlter, based on the ﬁltﬁlt operation in MATLAB. To minimize the effect of transients at the beginning and end of the row signals, an extrapolation to zero level is applied to each row signal using a 68 point long cosine squared function. This is followed by a 300 point zero padding both before and after the row signal. This ﬁlter has been shown to fulﬁll all the required speciﬁcations. The optimal cut-off frequency depends on the mean velocity of the blood mimicking ﬂuid, where 150 Hz is appropriate for mean ﬂow rates in the 0.5 to 1.5 m/s range. The effectiveness of the clutter ﬁltering is illustrated in Fig. 12 and Fig. 13. Specifically, Fig. 12 shows the envelopes of N = 100 consecutive acquisitions of a given scan line, with each acquisition consisting of 260 samples. Note that it is the RF data, not the envelope signals that are ﬁltered by the clutter ﬁlter. The signals in the data set appear almost stationary, and there is no evidence of the blood backscatter signal. As previously discussed, the TGC and Power Step have been adjusted so that the full dynamic range is available for the part of the RF signal associated with the lumen, resulting in the wall

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Figure 13. The envelope of N = 100 repetitions of a given RF signal (scan line), after clutter ﬁltering of the RF data whose envelope signals are shown in Fig. 12. The ﬁltered data clearly identiﬁes the lumen region. To illustrate the occasional need for bubble removal, a signal containing several bubbles is shown.

echoes being severely clipped. After acquisition, the echoes are scaled to TGC = 0 and Power Step = 4, which explains the displayed amplitude of only a few mV. Figure 13 shows the envelope of N = 100 repetitions of a given RF signal (scan line), after clutter ﬁltering. Now the lumen region can readily be identiﬁed in the ﬁltered data. In addition, the clutter ﬁltering has revealed the presence of several bubbles, whose removal will be discussed in the next sub-section. Note that bubbles only very infrequently are a problem, and that the appearance in Fig. 13 therefore is not representative in that regard. 6.3.3. Bubble Removal After clutter ﬁltering, the RF signals contains – apart from a small amount of higher frequency clutter – only backscatter data from the moving red blood cells (or particles in the blood mimicking ﬂuid). Occasionally, this backscatter signal contains spikes due to air bubbles dissolved in the blood-mimicking ﬂuid (bmf), as illustrated in Fig. 13. These echoes are of large amplitude and they can alter the scatterer signal energy considerably. In order to remove this air bubble echoes, a simple but effective two-step algorithm was implemented, as follows: • The average energy of the clutter free scatterers signal from all 100 RF signals in one data set was calculated. • All the RF signals with energy greater than twice the average energy calculated in the ﬁrst step were removed from the data matrix. Using this algorithm, the presence of a bubble will decrease the number of RF signals in the data matrix, but since each RF signal is separated in time by 0.5 ms (= 1/PRF;

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PRF = 2kHz), a given air bubble will at most appear in a couple of consecutive RF signals. For the vast majority of RF signals, no air bubbles are present. 6.3.4. Determination of Lumen Boundaries The automatic determination of the lumen boundaries takes place after clutter ﬁltering (and bubble removal, if needed). Several algorithms were developed and tested, and the following algorithm proved to be the most adaptive and suitable. It is based on energy consideration, and deﬁnes the lumen boundaries to be located at 5% and at 95% of the mean energy of the clutter ﬁltered backscattered signal. The individual lumen envelope signals, after clutter ﬁltering, are denoted ulum,i (t), i ∈ (1, N). The mean lumen envelope signal, < ulum (t) >, is determined as the mean of all 100 envelope signals; this is formulated in Eq. (12). < ulum (t) > =

1 N ulum, i (t). i=1 N

(12)

Next the total energy, Etot , of mean lumen envelope signal, and the energy as a function of range, or equivalent, travel time, E(t), are determined: ∞ (13) Etot = [< ulum (t) >]2 dt 0

t E(t) =

[< ulum (t) >]

2

dt.

(14)

0

Finally, the times corresponding to 0.05 Etot and 0.95 Etot are found, to deﬁne beginning and end of lumen region. A graph of E(t), with 0.05 Etot and 0.95 Etot speciﬁed, is shown in Fig. 14. 6.3.5. IBS of Arterial Blood With the bounds of the lumen identiﬁed based on the algorithm just described, the lumen backscattered data to ﬁll the data matrix has now been identiﬁed. The time separation between the beginning and end points of lumen, as shown in Fig. 14, is typically near 4 μs, corresponding to 80 samples and, equivalently, to a range dimension of 3 mm (using c = 1500 m/s). Given that the artery-mimicking tube is actual 6 mm in diameter, we see that only the central 3 mm is used for estimating the IBS of the moving blood or blood mimicking ﬂuid. The ﬂow near the walls is slower and therefore mostly removed by the wall ﬁlter. Even if the lumen backscatter data from closer to the wall could be retained, it would not contribute substantially to the accuracy of the IBSblood estimate, as consecutive RF signals from these parts of the lumen would be much more correlated than the RF signals from the central part of the lumen and therefore would contribute much less new information. The lumen backscatter data is processed, as described in Eqs. (8) to (11), Section 3.4, leading to the best estimate of IBSblood , from which the absolute backscatter of the plaque wall, σ plq,abs , is determined as given in Eq. (6).

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Figure 14. Graph of E(t) with beginning and end points of lumen identiﬁed.

7. Experimental Protocol and Results 7.1. Experimental Protocol The two previous sections have outlined the creation of the blood and tissue mimicking materials and the sequence of signal processing steps. This section will describe the experimental protocol and present and discuss some selected experimental results. The vessel phantom is mounted in the test tank, shown in Fig. 6, which is ﬁlled with distilled water. The pump speed is set to produce a mean ﬂow rate in the range from 0.25 m/s to 1.5 m/s. To evaluate the capability of the absolute backscatter measurements, the measurement protocol is ﬁrst carried out with water placed between the vessel phantom and the transducer, and then carried out with an inhomogeneous soft tissue phantom placed between the vessel phantom and the transducer. The results obtained with water will provide a reference IBS proﬁle against which the IBS proﬁle obtained with the inhomogeneous tissue phantom can be compared. A B-mode image of soft tissue phantom and vessel is ﬁrst produced. If necessary, the position of the transducer relative to the vessel phantom is adjusted, so that the set of 64 scan lines acquires the desired image area. These scan lines span 17.3 mm and are based on 64 active array elements (for additional details, see Section 4.2). The following description applies to each of the 64 scan lines, starting with the leftmost scan line. A single RF signal is acquired with a preset gain and power level. From the analytic signal envelope, an estimate of the lumen location is made, based on which the optimal TGC gain and Power Step setting for acquiring the lumen data are determined. For each scan line, 100 acquisitions of the whole vessel are carried out with a PRF = 2.06 kHz and a sampling rate of 20 MHz. The data is stored in the 260 × 100 data matrix, in which each digitized RF signal is stored as a column.

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The data matrix is processed to remove clutter and potential air bubbles and to calculate the mean envelope of the RF signal, based on which the bounds of the lumen is determined. An estimate of the lumen IBS is found based on the segment of the data matrix containing the lumen date. Last, the wall IBS is determined from the single RF signal. The ratio of the wall IBS to lumen IBS is the quantity of interest. An error source lies with the fact that the formulation in Section 3.3 assumes that all of energy reaching the front wall is propagated forward to the lumen. In fact, the reﬂectivity of the front wall reduces the energy that reaches the lumen, especially when a lesion is present on the front wall of the vessel. This in turn reduces the measures lumen IBS and thereby increases the front wall IBS/lumen IBS ratio above the correct value. A correction algorithm (not described in the signal processing section) is applied to correct for the effect of the front wall backscatter. When the wall IBS/lumen IBS ratio has been determined for a given scan line, the next scan line is chosen, with a typical lateral translation of the beam of 0.27 mm. A total 64 scan lines are typically used for characterizing a given vessel. As mentioned above, the measurements are ﬁrst carried out for just water between the transducer and the vessel, followed by a tissue mimicking phantom between the transducer and the vessel. 7.2. Experimental Results Experimental results have been carried out for several inhomogeneous soft tissue phantoms and several types of vessel phantoms, using mean ﬂow velocities in the vessel ranging from 0.25 m/s to 1.5 m/s. The best results were obtained with the highest ﬂow velocity because the variance on the sample mean of IBS in blood, IBSblood , is minimized at the highest ﬂow rate. The results given in this section were all obtained at a mean ﬂow rate of 1.0 m/s and a cut-off frequency of the clutter ﬁlter of 150 Hz, and were based on the inhomogeneous tissue phantom with a 15% volume concentration of urethane slivers, shown in Fig. 7(a). Only two sets of results are presented and analyzed. One set is based on a vessel phantom in the form of a uniform silicon rubber tube as the vessel phantom, representing a normal artery without lesions; these results are shown in Fig. 15. Another set of results is based on a vessel phantom in the form of a silicon rubber tube with one ring, illustrated in Fig. 8. This vessel phantom represents an artery with a well-deﬁned lesion. The results for this phantom are shown in Fig. 16. Note that the horizontal axis in both Fig. 15 and Fig. 16 spans 128 scan lines; however, only every other one of these are actually used in determining these IBS proﬁles. Figure 15(a) shows the IBS proﬁle of the front wall of the uniform vessel, measured through water. For a perfect tube under perfect alignment, the IBS proﬁle should have been a straight line proﬁle. The deviation reveals that even a ‘normal’ case exhibits noticeable deviations from the ideal case. However, when the IBS proﬁle of the front wall of the uniform vessel is measured through the inhomogeneous tissue phantom, as shown in Fig. 15(b), the random ﬂuctuation becomes much larger, and the whole level has decreased roughly 20 dB, due to the attenuation of the tissue phantom. In Fig. 15(c) is seen the IBS proﬁle from the blood mimicking ﬂuid, based on the sample mean for each scan line of the backscattered signal. Since there is only water between the transducer and the tube, this proﬁle is also fairly straight. It can be seen that

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Figure 15. IBS proﬁles for a uniform vessel phantom. The left column shows results for only water between the transducer and the artery-mimicking tube as a reference, and the right column shows results for a tissue phantom between the transducer and the artery-mimicking tube. (a) and (b): IBS proﬁle of front wall echo; (c) and (d): IBS proﬁle of lumen backscatter signal; (e) and (f): wall IBS proﬁle, normalized with lumen IBS proﬁle, with attenuation correction applied (dashed (blue) curve); the IBS proﬁles of front wall echo, as measured in (a) or (b), for comparison (solid (red) curve).

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Figure 16. IBS proﬁles for a vessel phantom with one ring. The left column shows results for only water between the transducer and the artery-mimicking tube as a reference, and the right column shows results for a tissue phantom between the transducer and the artery-mimicking tube. (a) and (b): IBS proﬁle of front wall echo; (c) and (d): IBS proﬁle of lumen backscatter signal; (e) and (f): wall IBS proﬁle, normalized with lumen IBS proﬁle, with attenuation correction applied (dashed (blue) curve); the IBS proﬁles of front wall echo, as measured in (a) or (b), for comparison (solid (red) curve).

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the IBS proﬁles in (a) and (c) are rather similar in appearance, with the lumen IBS proﬁle about 38dB below the level of the front wall IBS proﬁle. In (d) is seen the IBS proﬁle from the blood mimicking ﬂuid, measured through the inhomogeneous tissue phantom. Like with the IBS proﬁles in (a) and (b), the IBS proﬁles in (c) and (d) are also similar in appearance, with the shape following the attenuation proﬁle of the tissue phantom. The normalized results for the uniform vessel phantom are shown in (e) and (f). The solid (red) curve is the reference curve, in the form of the IBS proﬁle of the front wall without any correction applied, while the dashed (blue) curve is the normalized IBS proﬁle of the front wall, e.g. the IBS proﬁle of the front wall divided with the lumen IBS proﬁle, with the attenuation correction for the front wall applied. For comparison, the reference curve is appropriately scaled. Considering the graphs in (e), we should expect the two curves to be very similar, since the medium between the transducer and the vessel is non-attenuating, as indeed is the case. In (f), the graphs are very different, and the normalized IBS proﬁle of the front wall has indeed a reasonable similarity to the graph in (a), apart from a higher level of random ﬂuctuation and dip in the proﬁle above scan line 174, where there should have been a rise. The latter deviation may be attributed to the high attenuation level of the tissue phantom for these scan lines. Figure 16 is organized the same way as Fig. 15. Figure 16(a) shows the IBS proﬁle of the front wall of the vessel phantom with one ring, measured through water. The presence of the ring can clearly be seen, with large dips at each side of the ring, due to diffraction effects. In contrast, when the IBS proﬁle of the front wall of this vessel phantom is measured through the inhomogeneous tissue phantom, as shown in (b), the phase aberrating effects of the tissue phantom totally obscure the ring; in other words, the IBS proﬁle in (b) does not at all reveal the “lesion.” As with the results in Fig. 15, the signal level in (b) is in the order of 20 dB lower than the signal level in (a). Figure 16(c) shows the IBS proﬁle from the blood mimicking ﬂuid, based on the sample mean for each scan line of the backscattered signal. The presence of the ring is manifested in the form of a dip in the IBS proﬁle, but no other distortion is seen, since there is only water between the transducer and the tube. The lumen IBS proﬁle is in the order of 40 dB below the level of the front wall IBS proﬁle. Figure 16(d) shows the IBS proﬁle from the blood mimicking ﬂuid, measured through the inhomogeneous tissue phantom. This IBS proﬁle is shaped by the attenuation proﬁle of the tissue phantom in combination with the attenuation proﬁle of the front wall. The normalized results for the vessel phantom with one ring are shown in (e) and (f). As before, the solid (red) curve is the reference curve, in the form of the IBS proﬁle of the front wall without any correction applied, while the dashed (blue) curve is the normalized IBS proﬁle of the front wall, e.g. the IBS proﬁle of the front wall divided with the lumen IBS proﬁle, with the attenuation correction for the front wall applied. The graphs in (e) should be similar, given that the medium between the transducer and the vessel is non-attenuating. This is in fact the case, where it might be argued that the normalized curve is closer to the physical reality, since the large diffraction-related dips have been eliminated. In (f), the reference IBS proﬁle and the normalized IBS proﬁle are different indeed, where the normalized IBS proﬁle of the front wall now clearly reveals the presence of the “lesion” in the form of the single ring. In other aspects, the IBS proﬁle does deviate from the normalized proﬁle. The results in Figs 15 and 16 show a less than perfect restoration of the true IBS proﬁle; yet, signiﬁcant features have been made recognizable through the normalization

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process, and this effect has been observed in the majority of the experiments. The main cause is likely the difﬁculty in obtaining an accurate estimate of the lumen IBS after clutter removal. It should also be noted that the clutter level in this experimental system probably exceeds the clutter level observed in vivo, due to the larger acoustic impedance mismatches between soft tissue phantom and the distilled water and between the vessel phantom and the blood mimicking ﬂuid.

8. Conclusions This chapter has described a method for ultrasonic characterization of atherosclerotic plaque in vivo, with the carotid artery of particular interest, due to the relationship between stroke risk and the composition of plaques in the carotid artery. This relationship is based on the notion of the vulnerable plaque, i.e., a plaque that is likely to partially disintegrate into emboli or likely to be thrombi producing. Thus, the underlying motivation for this development is to develop a technique, which may be used as a screening tool for stroke risk. The method is based on the acoustic Integrated BackScatter (IBS), which has been demonstrated by other investigators to have the ability to differentiate between various plaque constituents. More speciﬁcally, an IBS proﬁle is obtained, consisting of the IBS of the arterial wall, including the atherosclerotic lesion, as a function of position along the artery. In order for the method to be clinically useful, the true IBS proﬁle must be acquired, which presents the challenge of overcoming the phase-aberrating, or distorting, inﬂuence of the soft tissue layers located between the transducer and the artery of interest. The corruption of the RF signal introduced by these intervening tissue layers is removed by normalizing the IBS proﬁle of the plaque structure with the IBS of arterial blood. The proﬁle is made up of a sequence of individual measurements, where each measurement of a plaque IBS value is normalized with a blood IBS value, obtained along the same scan line as the plaque IBS value. The rationale is that the backscattered signal from the plaque and the backscattered signal from the blood have experienced nearly identical phase-aberrating effects. To carry out this work, a commercial ultrasound scanner was modiﬁed to operate under complete control of a computer, that is, gain parameters, power level, scan line, PRF etc. was controlled by the PC, which also performed all of the data analysis. A carefully designed sequence of signal processing steps was developed, in order to determine absolute IBS proﬁle of a given plaque region. The most challenging of these were the clutter ﬁltering and the determination of the true lumen boundaries. Given that blood is a stochastic, not a deterministic, backscatter, statistical analysis is required to determine how many measurements of the backscatter signal from blood is required in order to achieve a reliable sample mean. To quantify the accuracy of the method, we chose to use phantom materials rather than actual biological specimens. Speciﬁcally, blood mimicking ﬂuid was used in place of blood, an inhomogeneous soft tissue phantom resembling fatty muscle was used in place of an actual muscle layer, and an artery mimicking tube, with or without a lesion, were used in place of a real artery. Results have been presented in the form of IBS proﬁles (IBS versus lateral beam position). Directly acquired IBS proﬁles, i.e. proﬁles not normalized with the IBS of the

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blood-mimicking ﬂuid, were measured for the vessel phantom with and without lesions, through water and through the intervening inhomogeneous medium. These results were then compared with the corresponding normalized IBS proﬁles. For a given vessel, the normalized and non-normalized IBS proﬁles measured through water are similar (apart from a scale factor). With the inhomogeneous tissue present, the non-normalized IBS proﬁle is corrupted by phase aberration and differs signiﬁcantly from the proﬁles obtained through water. The results show that it is possible to remove a large amount of the attenuation and phase aberration effects caused by the tissue phantoms, with the best performance obtained at the highest ﬂow velocities of the blood mimicking ﬂuid. Further improvements are needed before the method is ready for clinical evaluation. Two recent developments in medical ultrasound might likely help the performance of the atherosclerotic plaque classiﬁcation technique. One development is the use of tissue harmonic imaging, which has been shown to reduce clutter and increase resolution. Lower clutter in the lumen region will allow a higher gain and more signiﬁcant bits available after clutter ﬁltering, along with better deﬁnition of the lumen/wall boundaries. The other development is 3D imaging, speciﬁcally 3D imaging with registration, where the relative location of all scan planes are known. Having such 3D imaging available will permit quantitative volume rendering, thus clearly outlining the plaques boundaries and from that guiding where the contour of the IBS proﬁle through the plaque should be placed.

References [1] 2001 Heart and Statistical Update. American Heart Association, Dallas, Texas, pp. 14–16, 2001. [2] Bock, R.W., Gray-Weale, A.C., Mock, P.A., Robinson, D.A., Irwig, L., and Lusby, R.J., The natural history of asymptomatic carotid disease, Journal of Vascular Surgery, Vol. 17, pp. 160–171, 1993. [3] Moossy, J., Pathology of cerebral atherosclerosis, Stroke, Vol. 24, [suppl I], pp. I.22–I.23, 1993. [4] Ross, R., Atherosclerosis – an inﬂammatory disease, N. Eng. J. Med, Vol. 340, pp. 115–126, 1999. [5] Lee, R.T., Grodzinski, A.J., Frank, E.H., Kamm, R.D., and Schoen, F.J., Structure-dependent dynamic mechanical behavior in ﬁbrous caps from human atherosclerotic plaque, Circulation, Vol. 83, 1764–1770, 1991. [6] Bhatia, V., Bhatia, R., Dhindsa, S. and Virk, A., Vulnerable plaques, inﬂammation and newer imaging modalities, J. Postgrad Med, Vol. 49, pp. 361–368, 2003. [7] North American Symptomatic Carotid Endarterectomy Trial Collaborators, Beneﬁcial effects of carotid endarterectomy in asymptomatic patients with high-grade stenosis, New England J. of Medicine, Vol. 325, pp. 445–451, 1991. [8] Paciaroni, M., Eliasziw, M. et al., Long-term clinical and angiographic outcomes in symptomatic patients with 70% to 99% carotid artery stenosis, Stroke, Vol. 31, issue 9, pp. 2037–2042, 2000. [9] Naghavi, M. et al., New Developments in the Detection of Vulnerable Plaque, Current Atherosclerosis Reports 2001, Vol. 3, 125–135, 2001. [10] Diagnostic Vascular Ultrasound, edited by: Labs, K.H., Jaeger, K.A., Fitzgerald, D.E., Woodcock, J.P. and Neuerburg-Heusler, D., Edward Arnold, London, 1992. [11] Green, P.S., Spectral Broadening of acoustic reverberation in Doppler-shift ﬂuid ﬂowmeters, J. Acoust. Soc. Am., Vol. 36, pp. 1383–1390, 1964. [12] Sigel, B., Gibson, R.J., Amatneek, K.V., Felix, W.R.J. and Edelstein, A.L., A Doppler ultrasound method for distinguishing laminar from turbulent ﬂow. A preliminary report, J. Surg. Res., Vol. 10, pp. 221–224, 1970. [13] Felix, W.R.J., Sigel, B., Gibson, R.J., Williams, J. and Popky, G.L., Pulsed Doppler ultrasound detection of ﬂow disturbances in arteriosclerosis, J. Clin. Ultrasound, Vol. 4, pp. 275–282, 1976. [14] Bridal, S.L., Toussaint, J.F. et al., Multi-Parametric Imaging of Atherosclerotic Plaque by 50 MHz Ultrasound and 3 Tesla magnetic Resonance, 1997 IEEE Ultrasonics Symposium Proceedings, pp. 1071–1074, 1997.

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[15] Toussaint, J.F. et al., T2 contrast for NMR Characterization of Human Atherosclerosis, Arteriosc. Thromb Vasc Biol, Vol. 15, pp. 1533–1542, 1995. [16] Helft, G., Worthley, S.G. et al., Atherosclerotic aortic component quantization by non-invasive magnetic resonance imaging: An in vivo study in rabbits, J. Am. Coll. Cardiol., Vol. 37, pp. 1149–1154, 2001. [17] Fujimoto, J.G., Boppart, S.A., Tearney, G.J. et al., High resolution in vivo intra-arterial imaging with optical coherence tomography, Heart, Vol. 82, pp. 128–133, 1999. [18] Brezinski, M.E., Terney, G.J., Bouma, B.E. et al., Optical coherence tomography for optical biopsy. Properties and demonstration of vascular pathology, Circulation, Vol. 93, pp. 1206–1213, 1996. [19] Wilson, L. and Neale, M., Characterization of arterial plaque using intravascular ultrasound: In vitro and in vivo results, Int. J. Imaging Syst. Technol., Vol. 8, pp. 52–60, 1997. [20] Lori Bridal, S., Toussaint, J.F. et al., US Backscatter and Attenuation 30 to 50 MHz and MR T2 ant 3 Tesla for Differentiation of Atherosclerotic Artery Constituents In Vitro, IEEE Trans. UFFC, Vol. 45, pp. 1517–1525, 1998. [21] Montauban van Swijndregt, A.D., Elbers, H.R.J. et al., Ultrasonographic characterization of carotid plaques, Ultrasound in Med. & Biol., Vol. 24, pp. 489–493, 1998. [22] Lee, D.J., Sigel, B., Swami, V.K., Justin, J.R. et al., Determination of carotid plaque risk by ultrasound tissue characterization, Ultrasound in Med. & Biol., Vol. 24, pp. 1291–1299, 1998. [23] Carotid Stenting: Ready for Prime Time, Medtech Insight, Vol. 6, pp. 97 and 121–128, 2004. [24] Picano, E., Landini, L. et al., Different Degrees of Atherosclerosis detected by Backscattered Ultrasound: An in vitro Study on Fixed Human Arterial Walls, J. Clin Ultrasound, Vol. 11, pp. 375–379, 1983. [25] Picano, E., Landini, L. et al., Angle Dependence of Ultrasonic Backscatter in Arterial Tissues: A Study in vitro, Circulation, Vol. 72, pp. 572–576, 1985. [26] Picano, E., Landini, L. et al., Ultrasound tissue characterization techniques in evaluating plaque structure, Am. J. Card. Imaging, Vol. 8, pp. 123–128, 1994. [27] Nakayama, K. and Yagi, S., In vivo tissue characterization using blood ﬂow Doppler signal as a reference, Proc. of 52nd Mtg. of The Japanese Soc. of Ultrasonics in Medicine, Tokyo, June 22–24, pp. 399–400, 1988. [28] Shiba, A., Yamada, I. et al., A measurement method for absolute value of integrated backscatter, 1991 IEEE Ultrasonics Symp. Proc., Lake Buena Vista, Fl, Dec. 8–11, pp. 1089–1092, 1991. [29] Naito, J., Masuyama, T. et al., Validation of transthoracic myocardial ultrasonic tissue characterization: Comparison of Transthoracic and open-chest measurement of integrated backscatter, Ultrasound in Med. & Biol., Vol. 21, pp. 33–40, 1995. [30] Moehring, M.A. and Klepper, J.R., Pulse Doppler Ultrasound Detection, Characterization and Size Estimation of Emboli in Flowing Blood, IEEE Trans. Biom. Eng., Vol. 41, pp. 35–44, 1994. [31] Beach, K., Primozich, J.F., and Strandness, D.E., Pseudocolor B-mode arterial images to quantify echogenecity of atherosclerotic plaque, Ultrasound in Med. and Biol, Vol. 20, pp. 731–742, 1994. [32] Yuan, Y.W. and Shung, K.K., Ultrasound Backscatter from Flowing Whole Blood. I: Dependence on Shear Rate and Hematocrit, JASA, Vol. 84, pp. 52–58, 1988. [33] Shung, K.K., Ultrasound Characterization of Blood, in Tissue Characterization with Ultrasound, Vol. II, ed. J.F. Greenleaf, CRC Press, Boca Raton, FL, pp. 227–245, 1986. [34] Cloutier, G. and Shung, K.K., Cyclic Variation of the Power of Ultrasonic Doppler Signals Backscattered by Polystyrene Microspheres and Porcine Erythrocyte Suspensions, IEEE Trans. Biom. Eng., Vol. 40, pp. 953–962, 1993. [35] Bascom, P.A.J., Cobbold R.S.C. et al., On the Doppler Signal from a Steady Flow Asymmetrical Stenotic Model: Effects of Turbulence, Ultrasound in Med. & Biol., Vol. 19, pp. 197–210, 1993. [36] Paeng, D-G, Kim, BS, Choi, MJ, Chiao, R.Y. and Shung, K.K., In vivo observation of blood echogenecity variation during a cardiac cycle on human carotid arteries, 2003 IEEE Ultrasonics Symp. Proc., Honolulu, HI, Oct. 2003. [37] O’Donnell, M. et al., Broadband integrated backscatter: An approach to spatially localized tissue characterization in vivo, 1979 Ultrasonics Symposium Proceedings, Ed. B.R. McAvoy, pp. 175–178, IEEE, New York, 1979. [38] Mo, L.Y.L., and Cobbold, R.S.C., A uniﬁed approach to modeling the backscattered Doppler ultrasound from blood, IEEE Trans. BME, Vol. 39, pp. 450–461, 1992. [39] Schonhoff, T.A. and Giordano, A.A., Detection and Estimation Theory, Addison-Wesley, Reading, MA, 2001. [40] Ramnarine, K.V., Nassari, D.K, Hoskins, P.R., and Libbers, J., Validation of a new blood-mimicking ﬂuid

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Ultrasound Imaging in the Analysis of Carotid Plaque Morphology for the Assessment of Stroke Efthyvoulos KYRIACOU a,b,1 , Marios S. PATTICHIS a,c , Christodoulos I. CHRISTODOULOU a,b , Constantinos S. PATTICHIS a , Stavros KAKKOS d , Maura GRIFFIN d and Andrew NICOLAIDES a,b,d a Department of Computer Science, University of Cyprus, Nicosia, Cyprus b Cyprus Institute of Neurology and Genetics, Cyprus c Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque, USA d Department of Vascular Surgery, Faculty of Medicine, Imperial College, University of London, London, UK Abstract. The aim of this chapter is to summarise the recent advances in ultrasonic plaque characterisation and to evaluate the efﬁcacy of computer aided diagnosis based on neural and statistical classiﬁers using as input texture and morphological features. Several classiﬁers like the K-Nearest Neighbour (KNN) the Probabilistic Neural Network (PNN) and the Support Vecton Machine (SVM) are evaluated resulting to a diagnostic accuracy up to 71.2%. Keywords. Ultrasound plaque image, morphology analysis, texture analysis, assessment of stroke

Introduction High-resolution ultrasound has made possible the noninvasive visualisation of the carotid bifurcation and for that reason it has been extensively used in the study of arterial wall changes; these include measurement of the thickness of the intima media complex (IMT), estimation of the severity of stenosis due to atherosclerotic plaques and plaque characterization [1–3]. Applications of carotid bifurcation ultrasound include: i) identiﬁcation and grading of stenosis of extracranial carotid artery disease often responsible for ischemic strokes, transient ischemic attacks (TIAs) or amaurosis fugax (AF); ii) Followup after carotid endarterectomy; iii) evaluation of pulsatile neck mass; iv) investigation of asymptomatic neck bruits: severe internal carotid artery stenosis is a predictive factor for future stroke; v) cardiovascular risk assessment: the presence of carotid bifurcation atherosclerotic plaques is associated with increased cardiovascular mortality [4–7]; 1 Coresponding Author: Dr. Efthyvoulos Kyriacou, Department of Computer Science, University of Cyprus, 75 Kalipoleos Str, Nicolasia 1678, Cyprus, P.O. Box 20537; E-mail: [email protected].

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vi) clinical studies on the effect of lipid-lowering and other medications on carotid intima media thickness which includes plaque thickness (IMT) [8–12]. During the last decade, the introduction of computer aided methods and image standardisation has improved the objective assessment of carotid plaque echogenicity [13,14] and heterogeneity [13,15] and has largely replaced subjective (visual) assessment [1,16] that had been criticized for its relatively poor reproducibility [17]. In Section 1, a review of early studies using visual classiﬁcation for the assessment of atherosclerotic plaques using ultrasound is given. In this section, histology validation studies of ultrasonic tissue characterisation are discussed followed by the results of natural history studies. In Section 2, methodology on image acquisition, pre-processing and segmentation of plaque images are presented. Sections 3, 4 and 5 describe the texture analysis, morphology feature extraction algorithms and classiﬁcation algorithms as used by the authors. Section 6 describes the results and Section 7 is the conclusions and suggestions for future work.

1. Visual Classiﬁcation in the Assessment of Atherosclerotic Plaque in Ultrasound Imaging 1.1. Visual Classiﬁcation High-resolution ultrasound provides information not only on the degree of carotid artery stenosis but also on the characteristics of the arterial wall including the size and consistency of atherosclerotic plaques. Several studies have indicated that “complicated” carotid plaques are often associated with ipsilateral neurological symptoms and share common ultrasonic characteristics, being more echolucent (weak reﬂection of ultrasound and therefore containing echo-poor structures) and heterogeneous (having both echolucent and echogenic areas). In contrast, “uncomplicated” plaques which are often asymptomatic tend to be of uniform consistency (uniformly hypoechoid or uniformly hyperechoid) without evidence of ulceration [1,18–21]. Different classiﬁcations of plaque ultrasonic appearance have been proposed in the literature. Reilly classiﬁed [1] carotid plaques as homogenous and heterogeneous, deﬁning as homogeneous plaques those with “uniformly bright echoes” that are now known as uniformly hyperechoic (type 4) (see below). Johnson, classiﬁed plaques as dense and soft [22], Widder, as echolucent and echogenic based on the their overall level of echo patterns [23], while Gray-Weale described 4 types: type 1, predominantly echolucent lesions, type 2, echogenic lesions with substantial (>75%) components of echolucency, type 3, predominately echogenic with small area(s) of echolucency occupying less than a quarter of the plaque and type 4, uniformly dense echogenic lesions [16]. Geroulakos subsequently modiﬁed the Gray-Weale classiﬁcation by using a 50% area cut off point instead of 75% and by adding a ﬁfth type, which as a result of heavy calciﬁcation on its surface cannot be correctly classiﬁed [21]. In an effort to improve the reproducibility of visual (subjective) classiﬁcation, a consensus conference has suggested that echodensity should reﬂect the overall brightness of the plaque with the term hyperechoic referring to echogenic (white) and the term hypoechoic referring to echolucent (black) plaques [24]. The reference structure, to which plaque echodensity should be compared with, should be blood for hypoechoic, the ster-

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nomastoid muscle and for isoechoic and bone for hyperechoic plaques. More recently, a similar method has been used by Polak [25]. In the past a number of workers had confused echogenicity with homogeneity [1]. It is now realised that measurements of texture are different from measurements of echogenicity. The observation that two different atherosclerotic plaques may have the same overall echogenicity but frequently have variations of texture within different regions of the plaque has been made as early as 1983 [26]. The term homogeneous should therefore refer to plaques of uniform consistency irrespective of whether they are predominantly hypoechoic or hyperechoic. The term heterogeneous should be used for plaques of non-uniform consistency, i.e. having both hypoechoic and hyperechoic components (Gray-Weale [16] types 2 and 3). Although O’Donnnell had proposed this otherwise simple classiﬁcation in 1985 [18] and Aldoori in 1987 [27], there has been considerable degree of diversity in terminology used by others, as shown in Table 1. Because of this confusion, frequently plaques having intermediate echogenicity or being complex are inadequately described. For example, echolucent plaques have been considered as heterogeneous [20]. As a reﬂection of this confusion, a report from the committee on standards for non-invasive vascular testing of the Joint Council of the Society for Vascular Surgery and the North American Chapter of the International Society for Cardiovascular Surgery proposed that carotid plaques should be classiﬁed as homogeneous or heterogeneous [28]. Regarding the clinical signiﬁcance of carotid plaque heterogeneity, it seems that the heterogeneous plaques described in the three studies published in the 1980’s (Table 1), include hypoechoic plaques. Also heterogeneous plaques in all studies listed in Table 1 contain hypoechoic areas (large or small) and appear to be the plaques which are associated with symptoms or if found in asymptomatic individuals they are the plaques that subsequently tend to become symptomatic. 1.2. Correlation of Ultrasonic Characterisation of Unstable Plaques with Histology Reilly has shown for the ﬁrst time that carotid plaque characteristics on B-mode ultrasound performed before operation correlate with carotid plaque histology [1]. By evaluating visually the sonographic characteristics of carotid plaques, two patterns were identiﬁed: a homogeneous pattern containing uniform hyperechoic echoes corresponding to dense ﬁbrous tissue and a heterogeneous pattern containing a mixture of hyperechoic areas representing ﬁbrous tissue and anechoic areas that represent intraplaque hemorrhage or lipid. Thus, it was realised early that ultrasound could not distinguish between hemorrhage and lipid. Most heterogeneous lesions contained intraplaque hemorrhage and ulcerated lesions. It was thought at the time that the presence of a plaque hemorrhage reﬂected the potential for plaque rupture, which was associated with symptomatic plaques. However, it was subsequently realised that plaque hemorrhage was very common and was found in equal frequency in both symptomatic and asymptomatic plaques [31] and that ultrasound was highly sensitive in demonstrating plaque haemorrhage (27/29, 93%), as well as speciﬁc (84%) [18,32,34]. It was both sensitive and speciﬁc in demonstrating calciﬁcation in carotid endarterectomy specimens [35]. Aldoori reported that plaque hemorrhage was seen histologically in 21 patients, 19 (78%) of whom were diagnosed preoperatively as having echolucent heterogeneous

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E. Kyriacou et al. / Carotid Plaque Morphology Table 1. Ultrasound carotid plaque heterogeneity and clinical implications.

Author

Year

Ref.

Ultrasound carotid plaque heterogeneity

Clinical implications

O’Donnell Jr

1985

[18]

Visual classiﬁcation; distinguished ﬁne vs rough and random vs regular texture

Histology study

Aldoori

1987

[27]

Visual classiﬁcation

Plaque classiﬁcation

Leahy

1988

[19]

Plaques containing echolucent components. Homogeneous plaques had uniform consistency suggestive of sclerotic plaques

Heterogeneous plaques more frequently symptomatic and associated with ipsilateral infarction on CT scan

Sterpetti

1988

[43]

Mixed high-, medium-, and low-level echoes. Homogenous lesions had uniformly high-medium-level echoes

Heterogeneous plaques became symptomatic more frequently during follow-up

Langsfeld

1989

[20]

Predominantly echolucent plaques with a thin “egg shell” cap of echogenicity and echogenic plaques with substantial components of echolucency

Heteroneous plaques more frequently symptomatic. Heterogeneous plaques became symptomatic more frequently during follow-up

Widder

1990

[23]

Visual estimation, plaques being classiﬁed into four categories (homogeneous, slightly or markedly heterogeneous and non visible)

Histology study

Giannoni

1991

[29]

Not provided

Heterogeneous plaques progressed and became symptomatic

ECPSG

1995

[36]

Mixed composition

Heterogeneous plaques contained more calciﬁcation

Kagawa

1996

[30]

Plaques composed of a mixture of hyperechoic, isoechoic and hypoechoic plaques. Normal intima-media complex used to deﬁne isoechoicity

Heterogeneous lesions consisted of a mixture of atheroma and ﬁbrosis on histology and demonstrated calciﬁcation more frequently than the homogeneous ones

Kardoulas

1996

[35]

Mixed echo level pattern

Association of plaque heterogeneity with symptoms less consistent in comparison with echolucency

AbuRahma

1998

[31]

Plaques composed of a mixture of hyperechoic, isoechoic and hypoechoic plaques. Normal intima-media complex used to deﬁne isoechoicity

Heterogeneous plaques more frequently symptomatic

plaques on ultrasound imaging [27]. Gray-Weale [16] also validated his plaque classiﬁcation by demonstrating a statistically signiﬁcant relationship (p < 0.001) between ultrasound appearance of types 1 and 2 plaques (echolucent appearance) and the presence of either intraplaque hemorrhage or ulceration in the endarterectomy specimen. It is now apparent from those ultrasound-histology correlations that Reilly’s heterogeneous plaques correspond closely to Gray-Weale’s echolucent (type 1 & 2) plaques. The above ﬁndings were conﬁrmed by studies performed in the 1990s using the new generation of ultrasound scanners with their improved resolution. Van Damme [36]

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reported that ﬁbrous plaques (dense homogeneous hyperechoic lesions) were detected with a speciﬁcity of 87% and a sensitivity of 56%. Recent intraplaque hemorrhage was echographically apparent as a hypoechogenic area in 88% of cases, corresponding to a speciﬁcity of 79% and a sensitivity of 75%. Kardoulas [37], in another study, conﬁrmed Van Damme’s results on ﬁbrous plaques, with ﬁbrous tissue being signiﬁcantly greater (73%) in plaques with an echogenic character compared with those with an echolucent morphology (63%; p = 0.04). More recently the European carotid plaque study group that was a multi-centre study, conﬁrmed that plaque echogenicity on B-mode images was inversely related to haemorrhage and lipid, (p = 0.005) and directly related to collagen content and calciﬁcation (p < 0.0001) [38]. Plaque shape (mural vs nodular) on ultrasound has been shown to be associated with unstable histology features. Weinberger [39] demonstrated that mural plaques propagating along the carotid wall had a 72% frequency of recent organizing haemorrhage. Nodular plaques causing local narrowing of the vessel had only a 23% incidence of organising haemorrhage (p < 0.01). We now know that stable atherosclerotic plaques have on histological examination a thick ﬁbrous cap, a small lipid core, are rich in smooth muscle cells (SMC) which produce collagen and have a poor content of macrophages. In contrast, unstable plaques that are prone to rupture and development of symptoms have a thin ﬁbrous cap, a large lipid core, have few SMC and are rich in macrophages [40]. Macrophages are responsible for the production of enzymes, matrix metaloproteinases (stromelysins, gelatinases, collagenases) that play an important role in remodelling the plaque matrix and erosion of the ﬁbrous cap [41]. Recently, Lammie [42] reported a highly signiﬁcant association between a thin ﬁbrous cap and a large necrotic core (p < 0.002) in carotid endarterectomy specimens and a good agreement between ultrasound and pathological measurements of ﬁbrous cap thickness (thick vs thin ﬁbrous cap, kappa = 0.53). There is considerable debate on the question of whether thrombosis on the surface of the plaque, being an otherwise signiﬁcant feature of complicated plaques, can discriminate between symptomatic and asymptomatic plaques. Acute thrombosis on ultrasound appears as a completely echolucent defect adjacent to the lumen [43] and it is almost certain that by the time the operation is performed (usually several weeks after the event), the thrombus has undergone remodelling. Schulte-Altedorneburg reported that thrombosis at the plaque surface was often seen in “completely echolucent” plaques (p < 0.001) [44]. It is likely that the echolucent plaque component represents the thrombus or its combination with the lipid core. 1.3. Natural History Studies Reilly [1] suggested in 1983 that patients with asymptomatic carotid artery disease involving echolucent heterogeneous plaques might be at increased risk of future stroke. This was soon proved to be so by Johnson and his team [22] who conducted a prospective natural history study. They found that hypoechoic carotid plaques were associated with an increased risk of stroke during follow-up mainly in asymptomatic patients with carotid stenosis greater than 75%, in comparison with the hyperechoic or calciﬁed ones. In a subsequent study, Sterpetti [45] demonstrated that the severity of the stenosis (greater than 50%) and the presence of a heterogeneous plaque were both independent risk factors for the development of new neurological events (TIAs and stroke).

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Langsfeld conﬁrmed that patients with hypoechoic plaques (type 1 and type 2) had a twofold risk of stroke, 15% in comparison with 7% in those having hyperechoic plaques (type 3 and type 4) [20]. More recently, Polak et al. reported the association between stroke and internal carotid artery plaque echogenicity in a series of 4886 asymptomatic individuals aged 65 years or older, who were followed up prospectively for 48 months for the development of ischemic heart disease [25]. Two hunder and seventy patients (5.5% of the total population) had internal carotid stenosis greater than 50%. Plaques were subjectively characterised as hypoechoic, isoechoic or hyperechoic in relation to the surrounding soft tissues. In this prospective study hypoechoic plaques were associated with a signiﬁcantly higher incidence of ipsilateral, non-fatal stroke than isoechoic or hyperechoic plaques (relative risk 2.78). The authors suggested that computer assisted image analysis of plaques should be used in future studies. AbuRahma [33] in a similar study of patients with asymptomatic carotid stenosis reported that the incidence of ipsilateral strokes during follow-up was signiﬁcantly higher in patients having heterogeneous plaques than in those having homogeneous ones: 13.6% versus 3.1% (p = 0.0001; odds ratio: 5). Similarly, the incidence rate of all neurological events (stroke or TIA) was higher in patients with heterogeneous than in those with homogeneous plaques: 27.8% versus 6.6% (p = 0.001; odds ratio, 5.5). Heterogeneous plaques were deﬁned as those composed of a mixture of hypoechoic, isoechoic, and hyperechoic lesions, and homogeneous plaques those which consisted of only one of the three components. In the mid 1990s computers were used to obtain measurements of the grey scale of plaques. Although similar results were obtained by different teams [13,46,47], different cut off points had to be used by different centres. It became obvious that obtaining ultrasonic images is subjective. If ultrasonic scanning is performed in a relatively dark room the ultrasonographer reduces the gain; in a bright room the gain is increased. It was realised that if reproducible measurements of echodensity or texture were to be made some form of image normalisation was essential. Our team has introduced the method of image normalisation using blood and adventitia as two reference points with linear scaling so that blood would have a grey value of zero and adventitia a value of 190 [14]. As a result reproducible measurements of overall plaque echogenicity can be made with a high inter and intra-observer accuracy [48,49]. Finally, our group in Christodoulou et al. [50–53] has shown that it is possible to identify patients at risk of stroke based on texture features extracted from high-resolution ultrasound images of the carotid plaques. For this purpose, multiple texture feature sets and modular neural networks based on the self-organizing feature map (SOM) algorithm and the KNN classiﬁers, along with combining techniques were applied. The developed system was able to automatically classify carotid plaques into symptomatic or asymptomatic with a success rate of 73%.

2. Material, Image Acquisition, Preprocessing and Segmentation 2.1. Material Our group has been involved in several studies but for the sake of demonstating what can be achieved a crossectional study will be used. Two datasets of subjects were used:

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Table 2. Carotid plaque ultrasound images analyzed. Class

Dataset 1 No. of Subjects

Dataset 2 No. of Subjects

Class 1: Asymptomatic Class 2: Symptomatic Amaurosis Fugax TIA Stroke Total

199 137 33 60 44 336

137 137 33 60 44 274

i) dataset 1, a total of 336 carotid plaque ultrasound images (199 asymptomatic and 137 symptomatic) were analyzed, ii) dataset 2, a total of 274 carotid plaque ultrasound images (137 asymptomatic and 137 symptomatic) were analyzed (see Table 2). Dataset 2 is a subset of dataset 1 implemented for developing the PNN and SVM classiﬁer. Patients with cardioembolic symptoms or distant symptoms (> 6 months) were excluded from the study. Asymptomatic plaques were truly asymptomatic if they had never been associated with symptoms in the past. Carotid plaques were labeled as symptomatic after one of the following symptoms was identiﬁed: stroke, TIA, or amaurosis fugax. The aim of the computer aided diagnostic system was to identify: i) asymptomatic plaques or ii) symptomatic plaques associated with retinal or hemispheric symptoms (Stroke, TIA or AF), i.e. unstable plaques. 2.2. Image Acquisition The ultrasound images were collected in the Irvine Laboratory for Cardiovascular Investigation and Research, Saint Mary’s Hospital, UK, using an ATL (model HDI 3000 – Advanced Technology Laboratories, Seattle, USA) duplex scanner with a 5–10 MHz multifrequency probe. Longitudinal scans were performed using duplex scanning and colour ﬂow imaging [49]. Ultrasound was at right angles to the adventitia and the image was magniﬁed or the depth adjusted so that the plaque would ﬁll a substantial area of the linage giving approximately a resolution of 20 pixels/mm. B-mode scan settings were adjusted so that the maximum dynamic range was used with a linear post-processing curve. The position of the probe was adjusted so that the ultrasonic beam was vertical to the artery wall. The time gain compensation (TGC) curve was adjusted (gently sloping) to produce uniform intensity of echoes on the screen, but it was vertical in the lumen of the artery where attenuation in blood was minimal so that echogenicity of the far wall was the same as that of the near wall. The overall gain was set so that the appearance of the plaque was assessed to be optimal and slight noise appeared within the lumen. It was then decreased so that at least some areas in the lumen appeared to be free of noise (black). 2.3. Normalisation Initially linear scaling for image normalisation was achieved using the “curves” facility found in Adobe Photoshop. This method was taught by our team in several courses to most European Centres. It was quite satisfactory for measurements of overall plaque echodensity (Grey scale median), but could not provide any measurements of texture. A new programme is now used (Med-Oriom Publishing Co., c/o 18 Wigmore Street,

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a.

b. adventitia area (zoom in b image) Selected blood area sample

Final normalized image

Figure 1. Normalization of a carotid ultrasound image: two reference points are selected in order to normalize the image – a) blood area is selected b) adventitia area located over the plaque is selected.

London, W1H 9DE, UK) which makes image normalisation less cumbersome, provides the facilty for texture feature extraction (all features described below), for saving images and extracted texture features to ﬁles for subsequent statistical analysis. Before processing, the images were normalised by linear scaling so that the median gray level value of the blood was 0–5, and the median gray level value of the adventitia was 180–190. The scale of the gray level of the images on a PC ranged from 0 to 255. This standardization using blood and adventitia as reference points was necessary in order to extract comparable measurements in case of processing images obtained by different operators or different equipment [49]. Figure 1 shows the steps followed in order to normalise an ultrasound image, the adventitia and blood regions are used as reference points for standardization. Key points to maintaining a high reproducibility were to ensure that the ultrasound beam was at right angles to the adventitia, adventitia was visible adjacent to the plaque and that for image normalization a standard sample consisting of 2/4ths of the width of the brightest area of adventitia was obtained. The resolution of images was 20 pixels per mm. In order to maintain the uniformity of the set, images that were not 20 pixels per mm were transformed to this resolution using the bicubic method. Resolution was changed only in cases were we have similar resolution levels e.g from 18 pix/mm to 20 pix/mm or 23 pix/mm to 20 pix/mm. We have found that this was essential since the values of several texture features are resolution dependent (see Fig. 1 and Fig. 2). 2.4. Plaque Segmentation The plaque identiﬁcation and segmentation tasks are quite difﬁcult and were carried out manually by a physician or vascular ultrasonographer who are experienced in scanning. The main difﬁculties are due to the fact that the plaque edges cannot be distinguished from blood based on brightness level difference, or using only texture features, or other measures. Also calciﬁcation and acoustic shadows make the problem more complex. Thus, acoustic shadows were excluded. The identiﬁcation of the outline of hypoechoic plaques was facilitated using a color image indicating the blood ﬂow (see Fig. 2). Also, a temporary log image transformation facility was used in order to get a better deﬁnition of the edges of the plaque. This guaranteed that the plaque was correctly outlined.

E. Kyriacou et al. / Carotid Plaque Morphology

a.

249

b.

Gray scale image

Selection of plaque component on a logged image

Color blood flow image

Final crop of plaque component from the original image

c.

Figure 2. Selection of a plaque: a) The gray scale and the blood ﬂow colour image are loaded. b) User has selected a log transform on the gray scale image for better visualisation of the plaque. c) The ﬁnal selected plaque is saved in order to start feature extraction.

The procedure for carrying out the segmentation process, was established by a team of experts and was documented in the ACSRS project protocol [55]. The correctness of the work carried out by the single expert was monitored and veriﬁed by at least another expert. However, the extracted texture features depend on the whole of the plaque area and are not signiﬁcantly affected if a small portion of the plaque area is not included in the region of interest. 2.5. Plaque Segmentation The plaque identiﬁcation and segmentation tasks are quite difﬁcult and were carried out manually by a physician or vascular ultrasonographer who are experienced in scanning. The main difﬁculties are due to the fact that the plaque edges cannot be distinguished from blood based on brightness level difference, or using only texture features, or other measures. Also calciﬁcation and acoustic shadows make the problem more complex. Thus, acoustic shadows were excluded. The identiﬁcation of the outline of hypoechoic plaques was facilitated using a color image indicating the blood ﬂow (see Fig. 2). Also, a temporary log image transformation facility was used in order to get a better deﬁnition of the edges of the plaque. This guaranteed that the plaque was correctly outlined. The procedure for carrying out the segmentation process, was established by a team of experts and was documented in the ACSRS project protocol [55]. The correctness of

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E. Kyriacou et al. / Carotid Plaque Morphology

Figure 3. Shows some examples of segmented a) asymptomatic and b) symptomatic plaques. Under each plaque are the type of plaque and several other characteristics.

the work carried out by the single expert was monitored and veriﬁed by at least another expert. However, the extracted texture features depend on the whole of the plaque area and are not signiﬁcantly affected if a small portion of the plaque area is not included in the region of interest. Figure 2 illustrates an ultrasound image with the outline of the carotid plaque and the corresponding color blood ﬂow image. The next step includes feature extraction as described in the following section and Fig. 3 illustrates a number of examples of symptomatic and asymptomatic plaques as an expert physician segmented these. The examples were chosen at random. These examples demonstrate the difﬁculty to distinguish visually between asymptomatic and symptomatic plaques.

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251

3. Feature Extraction: Texture Analysis Texture features, shape parameters and morphological features were extracted from the manually segmented ultrasound plaque images in order to be used for the classiﬁcation of the carotid plaques. Texture contains important information, which is used by humans for the interpretation and the analysis of many types of images. It is especially useful for the analysis of natural scenes since they mostly consist of textured surfaces. Texture refers to the spatial interrelationships and arrangement of the basic elements of an image [56]. Visually, these spatial interrelationships and arrangements of the image pixels are seen as variations in the intensity patterns or gray tones. Therefore, texture features have to be derived from the gray tones of the image. Although it is easy for humans to recognize texture, it is quite a difﬁcult task to be deﬁned, and subsequently to be interpreted by digital computers. In this work, seven different texture features sets were extracted from the plaque segments using the following algorithms. Some of the extracted features capture complementary textural properties. However, features that were highly dependent or similar with features in other feature sets, were identiﬁed through statistical analysis and eliminated. The implementation details for the texture algorithms can be found in the referred papers. 3.1. Statistical Features (SF) The SF features are resolution independent [57]. The following SF features were computed: i) Mean value The mean of the gray level values I1 , . . . , IN of the pixels of the segmented plaque. N 1 I¯ = Ij . N

(1)

j =1

ii) Median value The median Imed of the distribution of the gray level values I1 , . . . , IN is the value of the middle item of the distribution. iii) Standard Deviation N 1 σ = (Ij − I¯)2 . N −1

(2)

j =1

iv) Skewness

! "3 N 1 Ij − I¯ Skew = . N σ

(3)

j =1

The skewness characterises the degree of asymmetry of a distribution around its mean.

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v) Kurtosis

⎧ ! "4 ⎫ N ⎨1 Ij − I¯ ⎬ Kurt = − 3. ⎩N ⎭ σ

(4)

j =1

Kurtosis measures the peakedness or ﬂatness of a distribution in relation to a normal distribution. 3.2. Spatial Gray Level Dependence Matrices (SGLDM) The spatial gray level dependence matrices as proposed by Haralick et al. (1973) [58] are based on the estimation of the second-order joint conditional probability density functions, f (i, j, d, θ ). The f (i, j, d, θ ) is the probability that two pixels (k, l) and (m, n) with distance d in direction speciﬁed by the angle θ , have intensities of gray level i and gray level j , (Wu et al., 1992). The estimated values for these probability density functions will be denoted by P (i, j, d, θ ). In a Nx × Ny image, let Lx = {1, 2, . . . , Nx } be the horizontal spatial domain, Ly = {1, 2, . . . , Ny } be the vertical spatial domain and I (x, y) be the image intensity at pixel (x, y). Formally, for angles quantized at 45◦ intervals the unnormalised probability density functions are deﬁned by P (i, j, d,0◦ ) = # ((k, l), (m, n)) ∈ (Ly × Lx ) ×(Ly × Lx ) : k − m = 0, |l − n| = d, I (k, l) = i, I (m, n) = j P (i, j, d,45◦ ) = # ((k, l), (m, n)) ∈ (Ly × Lx )

(5)

x(Ly × Lx ) : (k − m = d, |l − n| = d) or (k − m = −d, l − n = d), I (k, l) = i, I (m, n) = j P (i, j, d,90◦ ) = # ((k, l), (m, n)) ∈ (Ly × Lx ) ×(Ly × Lx ) : |k − m| = d, l − n = 0, I (k, l) = i, I (m, n) = j P (i, j, d,135◦ ) = # ((k, l), (m, n)) ∈ (Ly × Lx )

(6)

(7)

×(Ly × Lx ) : (k − m = d, l − n = d) or (k − m = −d, l − n = −d), I (k, l) = i, I (m, n) = j

(8)

where # denotes the number of elements in the set. Haralick et al. (1973) proposed the following texture measures which can be extracted from the spatial gray level dependence matrices: Notation: p(i, j ) (i, j )th entry in the normalised spatial gray level dependence matrix, = P (i, j )/R, where R is a normalising constant.

E. Kyriacou et al. / Carotid Plaque Morphology

px (i)

253

ith entry in the marginal probability matrix obtained by summing the

rows of p(i,j ), =

Ng

p(i, j )

(9)

j =1

Ng Number of distinct gray levels in the quantized image.

means

i

Ng ,

and

py (i) =

means

Ng

.

j =1

j

i=1 Ng

p(i, j )

(10)

i=1

px+y (k) =

Ng Ng i=1 i+j =k

px−y (k) =

p(i, j ), k = 2, 3, . . . 2Ng

(11)

j =1

Ng Ng i=1 |i−j |=k

p(i, j ), k = 0, 1, . . . Ng − 1.

(12)

j =1

Texture Measures i) Angular second moment f1 = {p(i, j )}2 . i

(13)

j

The angular second moment is a measure for homogeneity of the image. ii) Contrast )

Ng −1

f2 =

n

i=1

2

Ng Ng i=1 |i−j |=n

* p(i, j ) .

(14)

j =1

The contrast is a measure of the amount of local variations present in the image. iii) Correlation

j (i, j )p(i, j ) − μx μy

i

f3 =

σx σy

(15)

where μx , μy , and σ x , σ y , are the mean and standard deviation values of px and py . Correlation is a measure of gray tone linear dependencies. iv) Sum of squares: variance (i − μ)2 p(i, j ). f4 = i

j

(16)

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v) Inverse difference moment 1 f5 = p(i, j ). 1 + (i − j )2 i

(17)

j

vi) Sum average f6 =

2Ng

ipx+y (i).

(18)

(i − f6 )2 px+y (i).

(19)

px+y (i) log px+y (i) .

(20)

i=2

vii) Sum variance f7 =

2Ng i=2

viii) Sum entropy f8 =

2Ng i=2

ix) Entropy f9 =

i

p(i, j ) log(p(i, j )).

(21)

j

x) Difference variance f10 = variance of px−y .

(22)

xi) Difference entropy Ng −1

f11 =

px−y (i) log px−y (i) .

(23)

i=0

xii), xiii) Information measures of correlation H XY − H XY 1 max{H X, H Y } 1/2 f13 = 1 − exp − 2.0(HXY2 − HXY) H XY = − p(i, j ) log p(i, j ) f12 =

i

(25)

j

where HX and HY are entropies of px and py , and H XY 1 = − p(i, j ) log px (i)py (j ) i

H XY 2 = −

(24)

i

(26)

j

px (i)py (j ) log px (i)py (j ) .

(27)

j

For a chosen distance d (in this work d = 1 was used) we have four angular gray level dependence matrices, i.e. we obtain four values for each of the above 13 texture

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255

measures. The mean and the range of the four values of each of the 13 texture measures comprise a set of 26 texture features which can be used for classiﬁcation. Some of the 26 features are strongly correlated with each other, and a feature selection procedure may be applied in order to select a subset or linear combinations of them. In this work, the mean values and the range of values were computed for each feature for d = 1 and they were used as two different feature sets. 3.3. Gray Level Difference Statistics (GLDS) The Gray Level Difference Statistics algorithm [59] use ﬁrst order statistics of local property values based on absolute differences between pairs of gray levels or of average gray levels in order to extract texture measures. Let I (x,y) be the image intensity function and for any given displacement δ ≡ (x,y), let Iδ (x,y) = |I (x,y) − I (x + x, y + y)|. Let pδ be the probability density of Iδ (x,y). If there are m gray levels, this has the form of an m-dimensional vector whose ith component is the probability that Iδ (x,y) will have value i. The probability density pδ can be easily computed by counting the number of times each value of Iδ (x,y) occurs, where xand y are integers. In a coarse texture, if the δ is small, Iδ (x,y) will be small, i.e. the values of pδ should be concentrated near i = 0. Conversely in a ﬁne texture the values of pδ should be more spread out. Thus, a good way to analyse texture coarseness would be to compute, for various magnitudes of δ, some measure of the spread of values in pδ away from the origin. Four such measures are the following: i) Contrast CON =

i 2 pδ (i).

(28)

i

This is the second moment of pδ i.e. its moment of inertia about the origin. ii) Angular second moment ASM = pδ (i)2 .

(29)

i

ASM is small when the pδ (i) values are very close and large when some values are high and others low. iii) Entropy ENT = −

pδ (i) log(pδ (i)).

(30)

i

This is largest for equal pδ (i) values and small when they are very unequal. iv) Mean MEAN = (1/m)

ipδ (i).

(31)

i

This is small when the pδ (i) are concentrated near the origin and large when they are far from the origin. The above features were calculated for δ = (0, 1), (1, 1), (1, 0), (1, −1) and their mean values were taken.

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3.4. Neighbourhood Gray Tone Difference Matrix (NGTDM) Amadasun and King (1989) [56] proposed the Neighbourhood Gray Tone Difference Matrix in order to extract textural features which correspond to visual properties of texture. Let f (k, l) be the gray tone of a pixel at (k, l) having gray tone value i. Then we can ﬁnd the average gray-tone over a neighbourhood centered at, but excluding (k, l) " ! d d 1 ¯ l) = f (k + m, l + n) (32) A¯ i = A(k, W −1 m=−d n=−d

where (m, n) = (0, 0), d speciﬁes the neighbourhood size and W = (2d + 1)2 . The neighbourhood size d = 1 was used in this work. Then the ith entry in the NGTDM is s(i) = |i − A¯ i | for i ∈ Ni if Ni = 0, (33) = 0, otherwise where {Ni } is the set of all pixels having gray tone i. The following textural features are deﬁned as: i) Coarseness

⎡

fcos = ⎣ε +

Gh

⎤−1 pi s(i)⎦

(34)

i=0

where Gh is the highest gray-tone value present in the image and ε is a small number to prevent fcos to get inﬁnite. For an N × N image, pi is the probability of occurrence of Gray-tone value i, and is given by pi = Ni /n2 , where n = N − 2d

(35)

Amadasun and King (1989) deﬁne an image as coarse when the primitives composing the texture are large and texture tends to possess a high degree of local uniformity in intensity for fairly large areas. Large values of fcos represent areas where gray-tone differences are small. ii) Contrast fcon

⎤⎡ ⎤ Gh Gh Gh 1 1 =⎣ pi pj (i − j )2 ⎦ ⎣ 2 s(i)⎦ Ng (Ng − 1) n ⎡

i=0 j =0

(36)

i=0

where Ng is the total number of different gray levels present in the image. High contrast means that the intensity difference between neighbouring regions is large. iii) Busyness

⎡

fbus = ⎣

Gh i=0

⎤ ⎡ ⎤ Gh Gh pi s(i)⎦ / ⎣ ipi − j pj ⎦ , pi = 0, pj = 0. i=0 j =0

(37)

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A busy texture is one in which there are rapid changes of intensity from one pixel to its neighbour. iv) Complexity

fcom =

Gh Gh

(|i − j |)/(n2 (pi + pj )) pi s(i) + pj s(j ) ,

i=0 j =0

pi = 0, pj = 0.

(38)

A texture is considered complex when the information content is high i.e. when there are many primitives in the texture, and more so when the primitives have different average intensities. v) Strength fstr =

!G G h h

"! (pi +pj )(i − j )

2

i=0 j =0

ε+

Gh

" s(i) , pi = 0, pj = 0. (39)

i=0

A texture is generally referred to as strong when the primitives that comprise it are easily deﬁnable and clearly visible. 3.5. Statistical Feature Matrix (SFM) The statistical feature matrix [60] measures the statistical properties of pixel pairs at several distances within an image which are used for statistical analysis. Let I (x, y) be the intensity at point (x, y), and let δ = (x, y) represent the intersample spacing distance vector, where x and yare integers. The δ contrast, δ covariance and δ dissimilarity are deﬁned as CON(δ) ≡ E [I (x, y) − I (x + x, y + y)]2 (40) COV(δ) ≡ E [I (x, y) − η][I (x + x, y + y) − η] (41) DSS(δ) ≡ E [I (x, y) − I (x + x, y + y)] (42) where E{ } denotes the expectation operation and η is the average gray level of the image. A statistical feature matrix (SFM) Msf , is an (Lr + 1) × (2Lc + 1) matrix whose (i, j ) element is the dstatistical feature of the image, where d = (j − Lc , i) is an intersample spacing distance vector for i = 0, 1, . . . , Lr , j = 0, 1, . . . , Lc , and Lr , Lc are the constants which determine the maximum intersample spacing distance. In a similar way, the contrast matrix (Mcon ), covariance matrix (Mcov ) and dissimilarity matrix (Mdss ) can be deﬁned as the matrices whose (i, j ) elements are the d contrast, d covariance and d dissimilarity, respectively. Based on the SFM the following texture features can be computed: i) Coarseness FCRS = c/

(i,j )∈Nr

DSS(i, j )/n

(43)

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where c is a normalising factor, Nr is the set of displacement vectors deﬁned as Nr = {(i, j ) : |i|, |j | ≤ r} and n is the number of elements in the set. A pattern is coarser than another when they differ only in scale with the magniﬁed one to be the coarser and having a larger FCRS value. The deﬁnition of coarseness given here is different than the deﬁnition given by NGTDM in Eq. 7.31. ii) Contrast

⎡

FCON = ⎣

⎤1/2 CON(i, j )/4⎦

.

(44)

(i,j )∈Nr

Contrast measures the degree of sharpness of the edges in an image. iii) Periodicity FPER =

dss − Mdss (valley) M dss M

(45)

dss is the mean of all elements in Mdss and Mdss (valley) is the deepest where M valley in the matrix. Periodicity measures the appearance of periodically repeated patterns in the image. iv) Roughness (h)

(v)

FRGH = (Df + Df )/2

(46)

where Df is the fractal dimension (see Section 7) in horizontal and vertical directions. Df = 3 − H and E{|I |} = k(δ)H where H can be estimated from the dissimilarity matrix since the (i, j + Lc ) element of the matrix is E{|I |} with δ = (j, i). The larger the Df the rougher is the image. In this study an intersample spacing distance vector δ = (4, 4) was used. 3.6. Laws Texture Energy Measures (TEM) Laws texture energy measures [61,62] are derived from three simple vectors of length 3, L3 = (1, 2, 1), E3 = (−1, 0, 1) and S3 = (−1, 2, −1), which represent the one dimensional operations of center-weighted local averaging, symmetric ﬁrst differencing for edge detection, and second differencing for spot detection. If these vectors are convolved with themselves, we obtain new vectors of length 5, L5 = (1, 4, 6, 4, 1), E5 = (−1, −2, 0, 2, 1) and S5 = (−1, 0, 2, 0, −1). By further self-convolution we obtain new vectors of length 7, L7 = (1, 6, 15, 20, 15, 6, 1), E7 = (−1 − 4, −5, 0, 5, 4, 1), S7 = (−1 − 2, 1, 4, 1 − 2 − 1) where L7 again performs local averaging, E7 acts as edge detector and S7 acts as spot detector. If we multiply the column vectors of length l by row vectors of the same length, we obtain Laws l × l masks. In this work the following combinations were used to obtain 7 × 7 masks: LL = L7 t L7, LE = L7 t E7, LS = L7 t S7, EL = E7 t L7, EE = E7 t E7, ES = E7 t S7, SL = S7 t L7, SE = S7 t E7, SS = S7 t S7. In order to extract texture features from an image, these masks are convoluted with the image and statistics (e.g. energy) of the resulting image are used to describe texture. The following texture features were extracted:

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i) ii) iii) iv) v) vi)

259

LL – texture energy from LL kernel EE – texture energy from EE kernel SS – texture energy from SS kernel LE – average texture energy from LE and EL kernels ES – average texture energy from ES and SE kernels LS – average texture energy from LS and SL kernels

The averaging of matched pairs of energy measures gives rotational invariance. 3.7. Fractal Dimension Texture Analysis (FDTA) In 1828 the Scottish biologist Robert Brown (1773–1858) observed, while looking through his microscope at small particles ﬂoating in a liquid, that they made tiny, random, unpredictable movements [63]. He attributed this phenomenon to physical causes. The explanation for this Brownian motion was given later by Einstein based on the thermal motions of molecules. Mandelbrot [63] developed the fractional Brownian motion model in order to describe the roughness of nature surfaces. It considers naturally occurring surfaces as the end result of random walks. Such random walks are basic physical processes in our universe [62]. An important parameter to represent a fractal dimension is the fractal dimension Df estimated theoretically by the equation [62]. E(I 2 ) = c(r)(6−2Df )

(50)

where E( ) denotes the expectation operator, I is the intensity difference between two pixels, c is a constant and r is the distance between two pixels. A simpler method is to estimate the H parameter (Hurst coefﬁcient) from E(|I |) = k(r)H

(51)

where k = E(|I |)r=1 . By applying the log function we obtain log E(|I |) = log k + H log(r).

(52)

From the above equation the H parameter can be estimated and the fractal dimension Df can be computed from the relationship Df = 3 − H.

(53)

A smooth surface is described by a small value of the fractal dimension Df (large value of the parameter H ) where the reverse applies for a rough surface. Given an M × M image the intensity difference vector is deﬁned as IDV ≡ id(1), id(2), . . . id(s) (54) where s is the maximum possible scale, id(k) is the average of the absolute intensity difference of all pixel pairs with vertical or horizontal distance k. The value of the parameter H can be obtained by using least squares linear regression to estimate the slope of the curve of id(k) versus k in log–log scales. If the image is seen under different resolutions then the multiresolution fractal (MF) feature vector is deﬁned as

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MF ≡ H (m) , H (m−1) , . . . , H (m−n+1)

(55)

where M = 2m is the size of the original image, H (k) is the H parameter estimated from image I (k) , and n is the number of resolutions chosen. The multiresolution fractal (MF) feature vector describes also the lacunarity of the image. It can be used for the separation of textures with the same fractal dimension Df by considering all but the ﬁrst components of the MF vectors. In this work H was computed for four different resolutions. 4. Feature Extraction: Morphology 4.1. Motivation Morphological features are motivated from the need to study the basic structure of the plaque. We used a multi-level approach where the image intensity was thresholded at three different levels: lowimg = {(x, y) such that img (x, y) < 25} middleimg = {(x, y) such that 25 ≤ img (x, y) ≤ 50}

(56)

highimg = {(x, y) such that 50 < img (x, y)} to generate the binary images lowimg, middleimg, highimg. In Eq. (56), the binary images are represented by the pixel coordinates that assume the value 1. It is important to recognize that this speciﬁc multi-level decomposition can be thought of as a quantization of the original image at three different intensity intervals. The intensity intervals are chosen as follows. The ﬁrst binary image lowimg represents low intensity values that are considered to be difﬁcult to see against low intensity backgrounds. Structurally, these low intensity regions correspond to blood, thrombus, lipid or hemorrhage. Structurally, the binary image highimg describes the collagen and calciﬁed components of the plaque. The second binary image middleimg describes the image regions that fall between. To recognize the morphological features of the image components, we comment on the topology of the binary blob (white) components. The blob-components in the lowimg and the highimg are made up of solid (without holes) components. On the other hand, the blob-components of the middleimg are ﬁlled with holes that correspond to the lipid cores of the highimg. The morphological pattern spectra deﬁned in terms of the binary images aim at describing the different size components that are of diagnostic interest. For example, if the plaque image is captured as a single white component in the lowimg or the highimg, then the plaque structure is considered to be stable with little chance for rapture. Also, if the lipid core regions are made up of small scattered components, these are not considered to be dangerous. The most “dangerous” cases occur when the intermediate regions in the middleimg appear to be very thin. A somewhat less “dangerous” case occurs when these regions are relatively thick. In morphological image processing, we proceed to characterize the size distributions of both the blob-components which appear white, and the hole-components which appear

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261

black. For describing these components, we consider a ‘+’ structural element that does not exhibit any directional selectivity. The size distribution measures the presence of blob components of radius proportional to the positive index of the Pattern Spectrum. Similarly, the size distribution of the presence of holes is proportional to the negative index of the Pattern Spectrum. We will next provide a mathematical description of the Pattern Spectrum. 4.2. Morphological Features Mathematical Description We consider pattern spectra based on a ﬂat ‘+’ structural element B, made up of 5 pixels. The Pattern Spectrum is deﬁned in terms of the Discrete Size Transform (DST). We deﬁne the DST using [64–66]: f → . . . , d−k (f ; B), . . . d−1 (f ; B), d0 (f ; B), . . . , d1 (f ; B), . . . , (57) dk (f ; B), . . . where

)

dk (f ; B) =

f ◦ kB − f ◦ (k + 1)B, f • |k| B − f • (|k| − 1)B,

k≥0 k≤0

(58)

◦ denotes an open operation, and • denotes the close operation. The binary DST is a multi-resolution image decomposition scheme, which decomposes an image f into residual images f ◦ kB − f ◦ (k + 1) B, for k > 0, and f • |k| B − f • (|k| − 1)B for k < 0. The pattern spectrum of a binary image f , in terms of a structuring element B, is given by: )+ + +f ◦ kB − f ◦ (k + 1)B +, + + k≥0 + (59) Pf ;B (k) = +dk (f ; B)+ = + +f • |k| B − f • (|k| − 1)B +, k ≤ 0 where f =

f (x, y),

f (x, y) ≥ 0.

(60)

x,y

We note that in the limit, as k → ∞, we have that the resulting image f ◦ kB − f ◦ (k + 1) B converges to the zero image. Also, we note that with increasing values of k, f ◦ kB is a subset of the original image. For k ≥ 0, we may thus normalize the Pattern Spectrum by dividing by the norm of the original image f . Similarly, as k → ∞, f • kB converges to N M max f (x, y), where it is assumed that the image is of size N by M. Hence, for k < 0, we can normalize the pattern spectrum by dividing by N M max f (x, y) − f . Thus, to eliminate undesired variations, all the pattern spectra were normalized. As mentioned earlier the pattern spectra were computed for three binary images, corresponding to low, middle, and high image intensity values. 5. Classiﬁcation Techniques 5.1. The KNN Classiﬁer The statistical pattern recognition K Nearest Neighbour (KNN) classiﬁer was applied for classifying carotid plaques into two groups (asymptomatic and symptomatic). In the

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KNN algorithm in order to classify a new pattern, its k nearest neighbours from the training set are identiﬁed. The new pattern is classiﬁed to the most frequent class among its neighbours based on a similarity measure that is usually the Euclidean distance. In this work the KNN carotid plaque classiﬁcation system was implemented for values of k = 1, 3, 5, 7 and 9 using for input the eight texture feature sets and morphology features described above. Because in this work the number of patterns per class was unequal, a bias was created in favor of the class with a larger number of members. In order to alleviate the above bias, the number of patterns for each class in the k nearest neighbors was multiplied with a correction factor. The correction factor was computed as the total number of patterns, (i.e. 336) divided by the number of members of each class. Thus, the class with a smaller number of members was given a greater weight in the classiﬁcation process [67]. 5.2. The PNN Classiﬁer A Probabilistic Neural Network (PNN) classiﬁer was used for developing classiﬁcation models for the problem under study. The PNN falls within the category of nearestneighbor classiﬁers [68,69]. For a given vector wto be classiﬁed, an activation ai is computed for each of the two classes of plaques (i = 1, . . . , 2). The activation ai is deﬁned (i) to be the total distance of wfrom each of the Mi prototype feature vectors xj that belong to the i-th class: ai =

Mi

(i) T (i) w − xj , exp −β w − xj

(61)

j =1

where β is a smoothing factor. The normalized activations a˜ i = ai / N i=1 ai provide a conﬁdence estimate for the hypothesis that wbelongs to class i. We then classify w into the class that yields the highest conﬁdence. An important advantage of the PNN is that it provides conﬁdence estimates for our classiﬁcation decision. Also, to avoid dependence on the smoothing factor β, the value of β was set to the one that yielded the minimum misclassiﬁcation error on the training set. 5.3. The SVM Classiﬁer The Support Vector Machine (SVM) was also used for developing classiﬁcation models for the problem. The method is initially based on nonlinear mapping of initial data set using a function ϕ(.) and then the identiﬁcation of a hyperplane which is able to achieve the separation of two categories of data. The PNN network performance is compared to an SVM classiﬁer with Gaussian Radial Basis Function (RBF) kernels. Details about the implementation of the SVM algorithm used can be found in [70,71]. 5.4. Feature Selection A popular way to reduce the dimensionality of a feature vector is Principal Component Analysis (PCA) [72]. This method can be used in cases when the input features vector is large but the components of this vector are highly correlated. After applying PCA, the data set is represented by a reduced number of uncorrelated features while retaining most

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263

of its information content. In this study feature sets were reduced to smaller dimension sets by using only the components which contributed for 98% of the variance in the data set. Another way to select features that have the highest discriminatory power, is to compute the distance between the two classes of each feature as: |m1 − m2 | , dis = σ12 + σ22

(62)

where m1 and m2 are the mean values and σ 1 and σ 2 are the standard deviations of the two classes [74]. Best features are considered to be the ones with the greatest distance. 5.5. Cross Validation The leave-one-out estimate was used for validating the classiﬁcation models. This method calculates the error or the classiﬁcations score by using n − 1 samples in the training set and testing or evaluating the performance of the classiﬁer on the remaining sample. In the experiments carried out in this study, this was repeated for 336 subsets of size 335, dataset 1, for developing the KNN models and for 274 subsets of size 273, dataset 2, for developing the PNN and SVM models. It is known that for large n, this method is computationally expensive; however, it is approximately unbiased, at the expense of an increase in the variance of the estimator [69].

6. Results 6.1. Texture Features A dataset of 336 ultrasound carotid images (199 Asymptomatic and 137 Symptomatic) was examined. Eight different feature sets (a total of 54 features) were extracted from each manually segmented plaque as described in Section 2.5. The results obtained through the feature selection techniques as described in Section 5.4 are presented in Table 3. For each group the mean and standard deviation were computed. Furthermore the distance between the two classes was computed as given in Section 5.4 and the features were ordered according to their interclass distance. The best features were those with the greatest distance. Finally the signiﬁcant difference of each class for all features using the t-test hypothesis testing was computed (1 deﬁnes signiﬁcant difference and 0 no signiﬁcant difference). Best texture features as presented in Table 3 were found to be the Inverse Difference Moment of SGLDM (mean) with average and standard deviation values for the symptomatic plaques 0.439 ± 0144 and for the asymptomatic plaques 0.305 ± 0.136, the median from the SF with 17.04 ± 14.42 and 35.16 ± 23.12, the Sum Average of the SGLDM (mean) with 61.45 ± 27.19 and 93.89 ± 43.42 and the Entropy of the SGLDM (mean) with 6.06 ± 1.43 and 7.21 ± 1.3 for the symptomatic and asymptomatic plaques respectively. Box plots illustrating median, lower and upper quartiles for each feature and conﬁdence intervals are shown in Fig. 4.

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Table 3. Statistical analysis of 54 texture features computed from the 336 (199 symptomatic and 137 asymptomatic) ultrasound images of carotid atherosclerotic plaques of dataset 1. For each feature the mean and standard deviation were computed (i) for the symptomatic group, and (ii) for the asymptomatic group. The distance between the symptomatic and the asymptomatic groups was computed as described in Eq. (62) and their rank order according to their interclass distance is given.

Nr

Texture Feature

Asymptomatic

Symptomatic

Distance |m −m | dis = 1 2

Mean M1

Std σ1

Mean M2

Std σ2

52.49 35.16 53.49 2.03 8.69

23.08 23.12 16.52 1.10 7.52

36.20 17.04 51.39 2.67 11.80

16.53 14.42 16.59 1.06 7.85

0.574 0.665 0.090 0.419 0.286

6 2 43 15 28

1 1 0 1 1

σ12 + σ22

Rank Sign. Order Diff.

Statistical Features (SF) 1 2 3 4 5

Mean Median Stand. Deviation Skewness Kurtosis

Spatial Gray Level Dependence Matrices (SGLDM) – Mean values 6

Angular second moment

0.0316

0.0838

0.0890

0.1231

0.385

20

1

7 8 9 10 11 12

Contrast Correlation Sum of squares: variance Inverse difference moment Sum average Sum variance

753.3 0.772 2110.2 0.305 93.892 7687.3

218.6 0.104 979.2 0.136 43.418 3833.9

728.9 0.739 1806.2 0.439 61.452 6495.8

207.6 0.112 834.7 0.144 27.185 3257.5

0.081 0.218 0.2362 0.676 0.633 0.237

45 34 32 1 3 31

0 1 1 1 1 1

13 14 15 16 17

Sum entropy Entropy Difference variance Difference entropy Information measures

5.082 7.210 657.5 2.768 −0.371

0.805 1.295 187.2 0.411 0.035

4.390 6.061 659.7 2.436 −0.391

0.943 1.427 186.4 0.409 0.040

0.558 0.597 0.009 0.573 0.375

8 4 52 7 21

1 1 0 1 1

18

of correlation

0.974

0.024

0.962

0.031

0.308

27

1

Spatial Gray Level Dependence Matrices (SGLDM) – Range of values 19

Angular second moment

0.0029

0.0040

0.0063

0.0059

0.474

12

1

20 21 22 23 24

Contrast Correlation Sum of squares: variance Inverse difference moment Sum average

688.1 0.247 863.6 0.120 10.68

249.4 0.132 1083.4 0.031 12.11

721.7 0.309 929.8 0.116 10.65

241.8 0.144 1120.2 0.037 11.76

0.097 0.320 0.043 0.090 0.002

41 25 49 42 53

0 1 0 0 0

25 26 27 28 29 30

Sum variance Sum entropy Entropy Difference variance Difference entropy Information measures

4127.6 0.034 0.454 586.6 0.601 0.121

4437.3 0.017 0.127 215.6 0.114 0.026

4433.5 0.033 0.375 643.5 0.560 0.131

4577.7 0.019 0.158 213.7 0.125 0.030

0.048 0.027 0.386 0.188 0.244 0.263

48 51 19 38 30 29

0 0 1 1 1 1

31

of correlation

0.022

0.016

0.031

0.022

0.322

24

1

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265

Table 3. (Continued.)

Nr

Texture Feature

Asymptomatic

Symptomatic

Mean M1

Std σ1

Mean M2

Std σ2

Distance |m −m | dis = 1 2

σ12 + σ22

Rank Sign. Order Diff.

Gray Level Difference Statistics (GLDS) 32 33

Contrast Angular second moment (Energy)

748.7 0.120

215.5 0.086

724.7 0.191

204.3 0.113

0.081 0.501

44 10

0 1

34 35

Entropy Mean

2.792 9.163

0.417 2.300

2.453 7.791

0.413 1.773

0.579 0.473

5 13

1 1

Neighborhood Gray Tone Difference Matrix (NGTDM) 36

Coarseness

18.55

13.46

9.32

10.57

0.540

9

1

37 38 39 40

Contrast Busyness Complexity Strength

0.231 0.0002 82355 952810

0.119 0.0007 47656 591776

0.165 0.0004 77010 1176290

0.141 0.0009 47304 873763

0.358 0.173 0.080 0.212

22 40 46 36

1 1 0 1

6.38 38.35 0.687 2.35

2.45 5.97 0.055 0.09

7.77 37.78 0.684 2.39

2.60 5.54 0.061 0.10

0.388 0.071 0.034 0.318

18 47 50 26

1 0 0 1

Statistical Feature Matrix (SFM) 41 42 43 44

Coarseness Contrast Periodicity Roughness

Laws Texture Energy Measures (TEM) 45

LL – texture energy from LL kernel

131686 48047

105327

43246

0.408

16

1

46

EE – texture energy from EE kernel SS – texture energy from SS kernel LE – average texture energy from LE and EL kernels ES – average texture energy from ES and SE kernels LS – average texture energy from LS and SL kernels

911.8

323.8

729.1

290.9

0.420

14

1

99.16

29.46

99.21

32.24

0.001

54

0

8572.3

3017.7

6653

2453.4

0.494

11

1

270.57

83.62

246.03

82.90

0.2085

37

1

1945.9

596.3

1633.1

521.3

0.395

17

1

0.062 0.061 0.032 0.028

0.334 0.324 0.249 0.211

0.064 0.068 0.031 0.026

0.338 0.222 0.175 0.216

23 33 39 35

1 0 1 1

47 48

49

50

Fractal Dimension Texture Analysis (FDTA) 51 52 53 54

H1 H2 H3 H4

0.364 0.345 0.257 0.203

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Figure 4. Boxplots of the features a) SGLDM(mean) Inverse different moment(10), b) SF-Median(2), c) SGLDM(mean) – Sum Average(11) and d) SGLDM(mean) – Entropy(14) for the 1) symptomatic and 2) asymptomatic plaques. (The numbers in brackets denote the serial feature number as listed in Table 3. The notched box shows the median, lower and upper quartiles and conﬁdence interval around the median for each feature. The dotted line connects the nearest observations within 1.5 of the inter-quartile range (IQR) of the lower and upper quartiles. Crosses (+) indicate possible outliers with values beyond the ends of the 1.5 × IQR.

Typical examples of cropped asymptomatic and symptomatic plaques are shown in Fig. 3. The results for the best texture features are also displayed under each plaque. 6.2. Morphology Features The mean morphological pattern spectra that gave the best classiﬁcation results are summarized in Figs 6, 7 and 8. For plaque image regions with low image intensity, we compute the mean cumulative distribution functions (cdf ) for the openings, which constitute the positive part of the pattern spectrum, (Fig. 5a) and the closings, for the negative part of the spectrum, (Fig. 5b). For plaque image regions with image intensity in the middle range, we show the mean probability density function for the closings in Fig. 5c. The spectra are plotted against the radius (in mm) of the circular structural element that was used. From Fig. 5b we see that the mean symptomatic (close) cdf is above the mean asymptomatic cdf . We say that the symptomatic cdf is stochastically larger than the asymptomatic cdf . This implies that dark regions in the symptomatic cases were somewhat closer together, leaving smaller “holes” between the dark regions. Another impor-

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a.

267

b.

c. Figure 5. a) Mean cumulative distribution function (cdf ) plots for images thresholded at a low threshold, for the openings. The asymptomatic plot is plotted with a solid line, while the symptomatic plot is plotted with a dotted line. b) Mean cumulative distribution function (cdf ) plots for images thresholded at a low threshold, for the closings. The asymptomatic plot is plotted with a solid line, while the symptomatic plot is plotted with a dotted line. c) Mean probability density function (pdf ) plots for images thresholded at the middle range, for the closings. The asymptomatic plot is plotted with a solid line, while the symptomatic plot is plotted with a dotted line.

tant feature of this ﬁgure is that all the “holes” were found to be of a diameter that is less than 3.6 mm (3.6 mm = 2*1.8 mm). From Fig. 5b, we see that the mean cumulative distribution functions for the (open) cdf s are very close between the symptomatic and asymptomatic cases. From the graph intersections around 1mm and 3.6 mm, we infer that the dark regions in the symptomatic plaques have shown increased presence within these two sizes. From Fig. 5c, we can see that the mean (close) probability density function for the asymptomatic plaques lies well above the symptomatic plaques for radii in the neighbourhood of 1mm. This implies that mid-range intensity regions below 2 mm diameter (2 mm = 2*1 mm) showed a stronger presence in the asymptomatic cases. 6.3. Classiﬁcation Models 6.3.1. Classiﬁcation Results Using the KNN Classiﬁer In order to investigate the ability of the feature sets to discriminate asymptomatic from symptomatic images, we have used a KNN classiﬁer for k = 3, 5, 7, 9, 11. Table 4 shows the detailed results for all feature sets. The diagnostic Yield (DY) (indicates the percentage of the correct classiﬁed plaques) of the classiﬁer was computed for the dataset 1, 336

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Table 4. Diagnostic Yield (DY) using the K-nearest neighbor (KNN) for the classiﬁcation of two classes of plaques (for 199 symptomatic and 137 asymptomatic plaques) for the SF, SGLDM mean, SGLDM range, GLDS, NGTDM, TEM and FDTA feature sets. Window Feature set

Size

k=3

k=5

k=7

k=9

k = 11

Average

DY%

DY%

DY%

DY%

DY%

DY%

1 2

SF SGLDM (mean)

62.5 66.1

64.9 63.7

57.7 64.6

61.3 62.5

62.5 63.4

61.8 64.0

3 4 5 6 7 8

SGLDM (range) GLDS NGTDM SFM TEM FDTA

56.8 61.3 58.3 61.6 65.8 62.2

61.0 62.8 63.4 61.0 64.6 59.8

60.4 60.7 63.7 61.0 65.8 51.8

64.3 58.9 62.8 58.9 68.2 56.5

62.5 61.0 63.7 60.7 67.9 59.5

61.0 61.0 62.4 60.7 66.4 58.0

9

All 54 features

Average

64.0

67.9

64.6

66.1

67.3

66.0

62.1

63.2

61.1

62.2

63.2

62.4

plaques (199 asymptomatic and 137 symptomatic). The leave one out method as mentioned in subsection 5.5 was used in order to validate the classiﬁer. The classiﬁer was applied separately on each one of the eight different texture feature sets and for all the feature sets together. The highest individual diagnostic yield was achieved with k = 9 and 11 which shows the need to consider a large number of neighbors because of the overlap of the two classes. Best feature sets were in average for all k the TEM and the SGLDM (mean) with average DY, for all k, 66.4% and 64% respectively. Individually TEM achieved the best results from all other algorithms. Furthermore, morphological features as mentioned in Section 4 were applied using a KNN classiﬁer. The detailed results for this test are shown in Table 5. The diagnostic yield of the classiﬁer was computed on the same data set 336 plaques (199 asymptomatic and 137 symptomatic). The leave one out method was used in order to validate the classiﬁer. In addition for this case and because of the structure of the feature sets, Principal Component Analysis (PCA) was used, and the components accounting for 98% of the variance were used in order to reduce the dimensionality of the feature sets. The average diagnostic yield for k = 7 was computed for the three different levels of morphology and for each one of the feature sets. The overall results were not as good as for the texture analysis results. The best individual result were by cdf close 57% for pattern spectra from “high images” with PCA, 56.4% for pattern spectra from “high images” without PCA and 56% for pattern spectra from “medium images” with PCA. 6.3.2. Classiﬁcation Results Using the PNN and SVM Classiﬁers In order to ﬁnd a better classiﬁcation scheme we also used two other classiﬁers, the Probabilistic Neural Network (PNN) and the Support Vector Machine (SVM). The dataset 2 of 274 manually cropped ultrasound plaque images was used (137 Asymptomatic and 137 symptomatic). Principal Component Analysis (PCA) was again used as a method for dimensionality reduction. This was applied in order to retain only those components that contributed 98% to the variance of the data set. For each one of the algorithms and for each one of the texture and morphology feature sets the classiﬁers were evaluated with and without PCA analysis. Results from all classiﬁers and image texture sets are presented in Table 6.

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269

Table 5. Average diagnostic yield (DY) of the K-nearest neighbor (KNN) leave-one-out classiﬁer system with k = 7 for the morphology features. The diagnostic yield is given for the three image gray levels and when the three image gray levels were combined Vs when all features obtained by the morphology algorithm were used and when these were reduced using PCA (98%). DY%

DY%

Low Image

All 100 features

PCA (98%) features

Pdf_open

45.1

52.2

Cdf_open Pdf_close Cdf_close

54.9 52.2 50.4

52.2 54.6 50.1

Medium Image

All 100 features

PCA (98%) features

Pdf_open Cdf_open Pdf_close Cdf_close

55.2 51.3 46.3 54.9

54.0 52.8 45.7 56.0

High Image

All 100 features

PCA (98%) features

Pdf_open Cdf_open Pdf_close

56.1 60.5 48.1

56.1 63.9 48.1

Cdf_close

56.4

57.0

Table 6. Diagnostic Yield (DY) using the Probabilistic neural Nets (PNN) and the Support Vector Machine (SVM) classiﬁers, for the classiﬁcation of two classes of plaque (for 137 symptomatic and 137 asymptomatic plaques) for the SF, SGLDM mean, SGLDM range, GLDS, NGTDM, TEM and FDTA feature sets. Compared to that of KNN for k = 9. Texture Analysis Algorithms – Classiﬁcation results KNN (k = 9) Texture Features

PNN

SVM (RBF kernel function )

DY%

DY%

Original

Original

Using PCA (98%)

DY% Original

Using PCA (98%)

SF SGLDM(mean) SGLDM(range) GLDS NGTDM

61.3 62.5 64.3 58.9 62.8

65.3 71.2 61.0 60.6 55.8

65.3 70.8 62.4 60.6 55.8

69.3 69.7 64.6 65.0 68.3

70.1 68.6 64.2 65.0 67.9

SFM TEM FDTA All 54 features

58.9 68.2 56.5 66.1

54.4 61.0 59.5 55.5

54.4 58.4 59.5 59.9

58.4 69.3 61.3 69.7

58.4 67.5 62.4 64.2

SF & NGTDM SF & SGLDM(mean)

62.5 63.7

62.8 66.8

62.4 68.6

71.2 68.6

69.3 65.7

SF & SGLDM(mean)& TEM & NGTDM

66.4

65.3

64.2

70.8

70.1

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Table 7. Diagnostic Yield (DY) using the Probabilistic neural Nets (PNN) and the Support Vector Machine (SVM) classiﬁers, for the classiﬁcation of two classes of plaque (for 137 symptomatic and 137 asymptomatic plaques) for the Morphology feature sets. Compared to trhat of KNN k = 7. Morphology – Classiﬁcation results Morphology features

KNN (k = 7) DY%

PNN DY%

SVM (RBF kernel function) DY%

Original

Using PCA (98%)

Original

Using PCA (98%)

Using PCA (98%)

pdf_open cdf_open pdf_close cdf_close Medium Image

45.1 54.9 52.2 50.4

52.2 52.2 54.6 50.1

54.7 54.7 59.8 50.7

56.9 59.4 58.7 52.2

62.7 63.8 61.6 63.8

pdf_open cdf_open pdf_close cdf_close

55.2 51.3 46.3 54.9

54.0 52.8 45.7 56.0

60.5 58.3 55.8 58.0

53.3 58.3 62.3 58.3

52.2 63.0 67.4 62.7

Low image

High Image pdf_open

56.1

56.1

54.7

48.6

58.3

cdf_open pdf_close cdf_close

60.5 48.1 56.4

63.9 48.1 57.0

55.4 53.3 52.9

53.6 57.3 58.7

53.6 62.0 54.7

Results using PNN and SVM classiﬁers were signiﬁcantly improved, compared to those of KNN. For the PNN classiﬁer; the highest DY of 71.2% was achieved using the SGLDM (mean) set without PCA, while SF gave a DY only up to 65.3 %. The combination of all 54 features did not improve the best DY. For the SVM classiﬁer; the highest DY was achieved using SF after PCA analysis, DY 70.1%. The use of SGLDM(mean) achieved results up to 69.7%. The use of all 54 features gave 69.7%. The combination of SF and NGTDM gave the same results as the SGLDM(mean) with the previous classiﬁer 71.2%. Morphology features for low, medium and high images, as described in Section 4, were used in order to classify images using PNN and SVM classiﬁers. The dimensionality of the features vector was reduced using PCA to account for 98% of the total variance. Table 7 illustrates the results from all classiﬁers and morphology sets. The use of PNN and SVM classiﬁers could signiﬁcantly improve results, compared to those of morphology features through KNN, but again, results were not as high as for the texture analysis features. For the PNN classiﬁer, the highest diagnostic yield of 62.3% was achieved using the left part of the pattern spectra (close) from the mid intensity images with PCA. For the SVM classiﬁer, the highest DY was achieved for the same pattern spectra as for PNN with a DY of 67.4%. After investigating each one of the categories (texture and morphology) individually, we have selected the best of the features and combined them in order to investigate ways to improve classiﬁcation results. Table 8 tabulates the results from this section. The Combination of texture features SGLDM(mean) and the left part of the pattern spectra

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Table 8. Diagnostic Yield (DY) using the Probabilistic neural Nets (PNN) and the Support Vector Machine (SVM) classiﬁers, for the classiﬁcation of two classes of plaque (for 137 symptomatic and 137 asymptomatic plaques) using combination of texture and morphology feature sets. Combination Morphology & Texture – Classiﬁcation results Features

PNN DY%

SVM (RBF kernel function) DY%

SGLDM(mean)+med_pdf_close PCA 2%

63.9

70.1

SGLDM(mean)+ med_cdf_open PCA 2%

63.9

67.5

SF+med_pdf_close PCA 2%

63.5

67.2

SF+low_cdf_close PCA 2%

58.8

66.4

SF+NGTDM+med_pdf_close PCA 2%

65.7

70.1

SF+SGLDM(mean) +NGTDM+med_pdf_close PCA 2%

61.0

70.8

(close) from the mid intensity images with PCA, using a PNN classiﬁer gave 63.9%, not improving the previous results achieved with texture analysis algorithms. On the other hand, the combination of texture features SF, SGLDM(mean), NGTDM and the same pattern spectra with PCA, using an SVM classiﬁer gave one of the best results with a DY of 70.8%. 7. Conclusions and Suggestions for Future Work In this work the use of image texture and morphology analysis algorithms is investigated in order to classify ultrasound carotid plaques. The results using several classiﬁers are very promising and can be used in order to create a system, which can be used for computer assisted identiﬁcation of patients with asymptomatic carotid stenosis at risk of stroke. The results in this study are comparable with previous work carried out with different datatasets [50–53]. The Haralick SGLDM texture features gave best results in both studies whereas the statistical feature gray scale median (GSM) proved again a good and simple descriptor for plaque instability. Morphological features help us understand the inter-relations among different intensity regions. We have examined morphological results from dark, mid-range, and high intensity regions. We have found that there was signiﬁcant overlap between the pattern spectra coming from symptomatic and asymptomatic plaques. Furthermore, as we expected, probability density function (pdf ) estimates were visually veriﬁed to be noisier than cumulative distribution function estimates. For larger morphological components, the pdf started to drop, and the variance in the estimates increased signiﬁcantly. Thus, most of the discriminating power was concentrated in the smaller components, around a radius of 1mm. Currently two randomised controlled studies (ACAS, ACST) [76] have demonstrated that carotid endarterectomy in asymptomatic individuals with stenosis greater than 60– 70% reduces the risk of stroke from 2% per year to 1% per year. The implication is that

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approximately 100 operations need to be performed to prevent one stroke. This carries a high ﬁnancial burden for any health care system. A method based on image analysis of ultrasound images of carotid plaques that can differentiate between the stable plaques that tend to remain asymptomatic and the unstable ones that eventually produce symptoms has the potential to reﬁne the indications for surgery and spare many patients from an unnecessary costly operation which itself carries a 2.7–3.1% risk of stroke. The principal steps of such a method which will strife to identify plaques with increased risk for stroke should consist of the following generic steps: A. Training of the System Step 1: Image acquisition and preprocessing. Acquire ultrasound images of symptomatic and asymptomatic carotid plaques to comprise the system training set. Standardize images using blood and adventitia as reference points, standardize image resolution, and segment manually the plaque region. Step 2: Feature extraction. Extract from the segmented plaque images of the training set, the n different texture feature sets described above. Step 3: Training of the PNN and SVM classiﬁers. Train a PNN and or an SVM classiﬁer for the feature sets that gave the best results. B. Classiﬁcation of a New Plaque Step 4: Feature extraction for a new plaque. In order to classify a new carotid plaque image, repeat steps 1 and 2 and calculate the different feature sets for the new plaque image. Step 5: Input the feature sets to the trained classiﬁers and compute the conﬁdence measures. Input each one the feature sets to its corresponding, previously trained classiﬁer and classify the plaque as symptomatic or asymptomatic as described above.

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Plaque Imaging: Pixel to Molecular Level J.S. Suri et al. (Eds.) IOS Press, 2005 © 2005 The authors. All rights reserved.

On the Assessment of Texture Feature Descriptors in Intravascular Ultrasound Images: A Boosting Approach to a Feasible Plaque Classiﬁcation Oriol PUJOL and Petia RADEVA Centre de Visió per Computador, Ediﬁci O, Campus UAB, 08193 Bellaterra, Barcelona, Spain Abstract. Intravascular ultrasound images represent a unique tool to guide interventional coronary procedures, this technique allows to supervise the crosssectional locations of the vessel morphology and to provide quantitative and qualitative information about the causes and severity of coronary diseases. At the moment, the automatic extraction of this kind of information is performed without taking into account the basic signal principles that guide the process of image generation. In this chapter, we overview the main physical principles and factors that affect the IVUS generation; we propose a simple physics-based approach for IVUS image simulation that is deﬁned as a discrete representation of the tissue by individual scatterrers elements with given spatial distribution and backscattering differential cross sections. In order to generate the physical model that allows to construct synthetic IVUS images, we analyze the process of pulse emission, transmission and reception of the ultrasound signal as well as its interaction with the different tissues scatterrers of the simulated artery. In order to obtain the 3D synthetic image sequences we involve the dynamic behavior of the heart/arteries and the catheter movement in the image generation model. Having an image formation model allows to study rhe physics parameters that participate during the image generation and to achieve a better understanding and robust interpreting of IVUS image structures. Moreover, this model allows to comprehend, simulate and solve several limitations of IVUS sequences, to extract important image parameters to be taken into account when developing robust image processing algorithms as well as to construct wide synthetic image sequence databases in order to validate different image processing techniques.

1. Introduction Myocardial infarction, sudden cardiac death and unstable angina as a consequence of coronary thrombosis developed as a result of a ruptured vulnerable or an eroded atherosclerotic plaque. Plaque rupture or endothelial erosion with subsequent thrombosis formation are the most frequent cause of acute coronary syndromes. A study reported a high correlation between multiple plaque ruptures in acute coronary syndrome (ACS) patients. Another study shows that plaque ruptures occur not only in this case but in pa-

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Figure 1. Typical IVUS image presenting different kind of tissues.

tients with stable angina or asymptotic ischemia too. Moreover, there are studies showing plaque rupture in patients with non-cardiac death. Hence, it is not clear why some plaque ruptures in coronary arteries of patients lead to severe consequences meanwhile other remain asymptomatic and heal. To understand the mechanisms of plaque destabilization and guide a pharmacological treatment, it is of high interest to image the fragile part of the atheromatous plaque and to differentiate between low-risk and high-risk plaques. The composition and structure of the vessel change with age, hypertension, diabetes mellitus and many other factors. Until this moment, it is feasible to discriminate different morphological structures of the vessel as calcium deposits, fatty, fatty ﬁbrous and ﬁbrous materials. Although from several decades investigators recognized that noninvasive imaging of coronary calcium might be useful to identify patients with unsuspected coronary artery disease, until the advance of high-resolution techniques little success has been achieved. Today, it is well-known that coronary calcium is a result of a complex, regulated and active process similar to bone formation that is related and at the same time different from atherosclerosis. On the other hand, it is not completely clear what the vulnerable plaque is. The common researcher opinion is that a vulnerable plaque consists of: lipid core, ﬁbrous cap, presence of inﬂammatory cells and is affected by the vessel remodelling and its 3D morphology. Still a complete morphological, mechanical and chemical information is necessary in order to characterize the vulnerable plaque in a robust way. Coronary angiography has been so far the gold standard to assess the severity of obstructive luminal narrowing. Furthermore it serves as a decision tool to direct therapeutical procedures (as PTCA). By coronary angiography the lumen boundaries can be assessed, but no information is provided about plaque burden, plaque delineation and plaque components. The predictive power of occurrence of myocardial infarction is rather low since 70 angiographically normal, and only a minority occur where there was severe stenosis. Other studies have afﬁrmed, that the culprit lesion prior to a myocardial infarction has, in 48–78 a stenosis smaller than 50 detected by angiography, but can be well assessed pathologically. IVUS displays the morphology and histological properties of a cross-section of a vessel [1]. Figure 1 shows a good example of IVUS image. It is generally accepted that the different kind of plaque tissues distinguishable in IVUS images is threefold: Calcium formation is characterized by a very high echoreﬂectivity and absorbtion of the emitted pulse from the transducer. This behavior produces a deep shadowing effect behind cal-

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cium plaques. In the ﬁgure, calcium formation can be seen at three o’clock and from ﬁve to seven o’clock. Fibrous plaque has medium echoreﬂectivity resembling that of the adventitia. This tissue has a good transmission coefﬁcient allowing the pulse to travel through the tissue, and therefore, providing a wider range of visualization. This kind of tissue can be observed from three o’clock to ﬁve o’clock. Soft plaque or Fibro-Fatty plaque is the less echoreﬂective of the three kind of tissues. It also has good transmission coefﬁcient allowing to see what is behind this kind of plaque. Observing the ﬁgure, a soft plaque conﬁguration is displayed from seven o’clock to three o’clock. There are two lines of research to describe the vessel morphology and detect plaques in IVUS images: by textural image analysis, radio-frequency analysis of IVUS data and elastograms. Textural analysis is the most close to the physician “exercises” during IVUS analysis as a decision is taken on morphological analysis of image sequence. Visual textural analysis is a difﬁcult, subjective and time-consuming process highly depending on the specialist. Therefore, there is an increasing interest of the medical community in developing automatic tissue characterization procedures of IVUS images. This is accentuated because the procedure for tissue classiﬁcation by physicians implies the manual analysis of IVUS images frequently necessary to be done online during the therapeutical procedure. The problem of automatic tissue characterization has been widely studied in different medical ﬁelds. The unreliability of gray level only methods to achieve good discrimination among the different kind of tissues force us to use more complex measures, usually based on texture analysis. Texture analysis has played a prominent role in computer vision to solve tissue characterization problems in medical imaging [2–9]. Several researching groups have reported different approximations to characterize the tissue of intravascular ultrasound image. Vandenberg et al., in [10], base their contribution on reducing the noise of the image, to have a clear representation of the tissues. The noise reduction is achieved by averaging sets of images when the least variance in diameter of the IVUS occurs. At the end, a fuzzy logic based expert is set to discriminate among the tissues. Nailon et al. devote several efforts to IVUS tissue characterization. In [11] they use classic Haralick texture statistics to discriminate among tissues. In [12] the author proposes the use of co-occurrence matrices texture analysis and fractal texture analysis to characterize intravascular tissue. Thirteen features plus fractal dimension derived from Brownian motion are used for this task. The conclusion shows that fractal dimension is unable to discriminate between calcium and ﬁbrous plaque but helps in ﬁbrous versus lipidic plaque. On the other hand, co-occurrence matrices are well suited for the overall classiﬁcation. In [13], it is stated that the discriminative power of fractal dimension is poor when trying to separate ﬁbrotic tissue, lipidic tissue and foam cells. The method used is based on fractal dimension estimation techniques (box-counting, brownian motion and frequency domain). Spencer et al. in [14], center their work on spectral analysis. Different features are compared: mean power, maximum power, Spectral Slope and 0 Hz interception. The work concludes with the 0 Hz spectral slope as the most discriminative feature. Dixon et al. in [15], use co-occurrence matrices and discriminant analysis to evaluate the different kind of tissues in IVUS images.

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Ahmed et al. [16] uses a radial transform and correlation for pattern matching. The features used are higher order statistics such as kurtosis, skewness, and up to four order cumulants, C4 . The results provided appear to have fairly good visual recognition rate. The work of de Korte et al. [17] opens a new proposal based in assessing the local strain of the atherosclerotic vessel wall to identify different plaque components. This line of work is based on estimating the radial strain by performing cross-correlation analysis on pairs of IVUS at a certain intra-coronary pressure. This very promising technique, is called elastography, and is still in development. Probably, one of the most interesting work in this ﬁeld is the one provided by Zhang, Sonka et al. [18]. This work is much more complex trying to evaluate the full morphology of the vessel. Detecting the plaque and adventitia borders and characterizing the different kind of tissues, the tissue discrimination is done using a combination of well-known techniques previously reported in the literature as: co-occurrence matrices and fractal dimension from brownian motion, and adding two more strategies to the amalgam of features: run-length measures and radial proﬁle. The experiments assess the accuracy of the method quantitatively. Most of the literature found in the tissue characterization matters use texture features, being co-occurrence matrices the most popular of all feature extractors. Further work has been done trying to use other kind of texture feature extractors and IVUS images, and although not speciﬁcally centered on tissue characterization, the usage of different texture features in plaque border assessment is reported, that can be easily extrapolated to tissue characterization. In [19], derivative of gaussian, wavelets, co-occurrence matrices, Gabor ﬁlters and cumulative moments are evaluated and used to classify blood from plaque. The work highlights the discriminative power of co-occurrence matrices, derivatives of gaussian and cumulative moments. Other works such as [20] provide some hints on how to achieve a fast framework based on local binary patterns and fast highperformance classiﬁers. This last line of investigation overcomes one of the most significant drawbacks of the texture based tissue characterization systems, the speed. Texture descriptors are inherently slow to be computed. With the proposal of the feature extractor based on local binary patterns a good discriminative power is ensured as well as a fast technique for tissue characterization. Whatever method we use in the tissue characterization task, we follow an underlying main methodology. First, we need to extract some features describing the tissue variations. This ﬁrst step is critical since the features chosen have to be able to describe each kind of tissue in a unique way so that it can not be confused with another one. In this category of feature extraction we should consider the co-occurrence matrix measures, statistical descriptors, local binary patterns, etc. The second step is the classiﬁcation of the extracted features. Depending on the complexity of the feature data some methods will ﬁt better than others. In most cases, high dimensional spaces are generated, so we should consider the use of dimensionality reduction methods such as Principal component analysis or Fisher linear discriminant analysis. Either a dimensionality reduction process is needed or not, this step will require a classiﬁcation procedure. This procedures can be supervised, if we provide samples of each tissue to be classiﬁed so that the system “knows” a priori what the tissues are, or unsupervised, if we allow the system to try to ﬁnd which are the different kind of tissues by itself. In this category we can ﬁnd clustering methods for unsupervised classiﬁcation and, for supervised classiﬁcation, methods like maximum likelihood, nearest neighbors, support vector machines, and the center of

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our current analysis adaptative boosting. In particular, adaptative boosting techniques allow to deal with high dimensional spaces by using an intelligent feature selection process while training the classiﬁer. The following sections are devoted to describe: First, the texture methods we are using in our study. Second, we introduce the Adaboost classiﬁcation process. And third, we describe the result of using such techniques and for plaque characterization.

2. Feature Spaces The ﬁrst issue when dealing with complex real problems, such as tissue characterization, is to create a representation of the data we are analyzing. The representation of the data is usually a more compact version of the original samples, for the problem to be analytically feasible. While centering in some aspects of the original samples, we restrict ourselves to that kind of features, and expect them to fully describe the problem. Though not always happens. Plaque recognition is usually approached as a texture discrimination problem. This focuses our work, in the analysis of the variability, size, granularity of the original tissue samples. Several texture representations are available in literature. We will focus our study on two different kind of texture descriptors. The ﬁrst class of texture descriptors are formally acknowledged as fully representative and highly discriminant sets. In this class we place co-occurrence matrices descriptors [22] and a bank of ﬁlters approach based on derivatives of gaussian [24]. The second class, is less recognized since the techniques are relatively new. This class comprehend descriptors characterized by its low complexity and therefore fast computationally. This gain in speed, however has a cost, the lost in accuracy of the description. In this category we are placing, cumulative moments [23] and local binary patterns [28]. Those sets include examples of the two most important lines of work when dealing with texture, the statistical approach (co-occurrence matrices measures and cumulative moments) and the kernel-based approach (bank of ﬁlters and local binary patterns). The ﬁrst line of work are concerned with density estimation techniques or parameters. The second line of work centers on sampled forms of analytic functions. In this sense, the local binary patterns approach is the less conventional of the methods, but we have chosen to include it in the kernel-based approach for sake of simplicity. 2.1. Co-Occurrence Matrix Approach Co-occurrence matrices were ideated in 1963 by Julesz [29]. They were created as tools for texture segregation using second order related statistics. They have been used in image processing, as texture descriptors with very successful results [22]. In the cooccurrence method, the relative frequencies of gray level pairs of pixels at certain relative displacement are computed and sorted in a matrix, the co-occurrence matrix P. The co-occurrence matrix can be thought of as an estimate of the joint probability density function of gray-level pairs in an image. For G gray levels in the image, P will be of size G × G. If G is large, the number of pixel pairs contributing to each element, pi,j in P is low, and the statistical signiﬁcance poor. On the other hand if the number of gray levels is low, much of the texture information may be lost in the image quantization. The element values in the matrix, when normalized, are bounded by [0, 1], and the sum of all element values is equal to 1.

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Figure 2. Co-occurrence matrix creation explanation diagram.

P (i, j, D, θ ) = P I (l, m) = i and I (l + D cos(θ ), m + D sin(θ )) = j

(1)

where I (l, m) is the image at pixel (l, m), D is the distance between pixels and θ is the angle. It has been proved by other researchers [30,21] that the nearest neighbor pairs at distance D at orientations θ = {00 , 450 , 900 , 1350 } are the minimum set needed to describe the texture second-order statistic measures. Figure 2 provides a graphical explanation of the co-occurrence method. It is based on a discrete approximation of the probability density function of the occurrences of the appearance of two pixels of certain gray levels at a certain distance with a ﬁxed angle. In practice, this is done using a matrix with as much ﬁles and columns as the gray levels. This matrix is the co-occurrence matrix, and is ﬁlled adding one to the cell pointed by the gray levels of the pixels pair located at a certain distance D with angle θ . This matrix is still difﬁcult to deal with, and the data it contains is usually sparse. Therefore, a description of the matrix shape and information is useful for reducing the complexity and dimensionality of the problem. The most important measures that characterize the co-occurrence matrices are: Energy, Entropy, Inverse Difference Moment (IDM), Shade, Inertia and Promenance. [30] Let us introduce some notation for the deﬁnition of the features: P (i, j ) is the (i, j )th element of a normalized co-occurrence matrix. Px (i) =

P (i, j )

j

Py (j ) =

i

P (i, j )

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μx =

i P (i, j ) = iPx (i) = E{i} i

j

i

j

i

j

j P (i, j ) = j Py (j ) = E{j } μy = With the above notation, the features can be written as follow: P (i, j )2 Energy = i,j

Entropy = −

P (i, j )logP (i, j )

i,j

IDM =

i,j

Shade =

1 P (i, j ) 1 + (i − j )2 (i + j − μx − μy )3 P (i, j )

i,j

Inertia =

(i − j )2 P (i, j )

i,j

Promenance =

(i + j − μx − μy )4 P (i, j )

i,j

As a result of the co-occurrence matrices descriptors extraction process, we have a set of values (one for each descriptor) for each pixel in a certain plaque and for a certain orientation. As we are using four orientations, the ﬁnal feature vector will contain 24 features per pixel. 2.2. Derivatives of Gaussian Derivatives of gaussian refers to a ﬁlter bank in which the transference function of each ﬁlter is one of the directional derivatives of the 2-D gaussian function. This alone, would only provide information of the orientation, size and complexity of the region we are ﬁltering. Since, we aim for a more accurate description of the texture, scale can be introduced to handle image structures in a consistent manner. This texture descriptor is a particularization of the linear scale-space representation proposed in [24,34]. The basic idea is to embed the original signal into a one-parameter (scale) family of gradually smoothed signals, in which ﬁne scale details are successively suppressed. It can be shown that the Gaussian kernel and its derivatives are one of the possible smoothing kernels for such scale-space. The Gaussian kernel is well-suited for deﬁning a space-scale because of its linearity and spatial shift invariance, and the notion that structures at coarse scales should be related to structures at ﬁner scales in a well-behaved manner (new structures are not created by the smoothing method). Scale-space representation is a special type of multiscale representation that comprises a continuous scale parameter and preserves the same spatial sampling at all scales. Formally, the linear-space representation of a continuous signal is constructed as follows. Let f : N → represent any given signal. Then, the scale-space representation L : N × R+ → is deﬁned by L(·; 0) = f so that:

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L(·; t) = g(·; t) ∗ f

283

(2)

where t ∈ + is the scale parameter, and g : N xR+ {0} → is the Gaussian kernel. In arbitrary dimensions, it is written as:

1 1 2 −x T x/(2t) − N i=1 xi /(2t) , x ∈ Re N , x ∈ e = e (3) i (2πt)N/2 (2πt)N/2 √ The square root of the scale parameter, σ = (t), is the standard deviation of the kernel g, and is a natural measure of spatial scale in the smoothed signal at scale t. From this scale-space representation, multi-scale spatial derivatives can be deﬁned by

g(x; t) =

Lx n (·; t) = ∂x n L(·; t) = gx n (·; t) ∗ f,

(4)

where gx n denotes a derivative of some order n. The main idea behind the construction of this scale-space representation is that the ﬁne scale information should be suppressed with increasing values of the scale parameter. Intuitively, √ when convolving a signal by a Gaussian kernel with standard det, the effect of this operation is to suppress most of the structures viation σ = in the signal with a characteristic length less than σ . Different directional derivatives can be used to extract orientation related structural features at different scales. It is shown in the literature [35] that a possible complete set of directional derivatives are 2 , ∂ 2 , ∂ 3 , ∂ 3 , ∂ 3 , ∂ 3 ]. So our feature vector will consist on the ∂ n = [∂0 , ∂90 , ∂02 , ∂60 120 0 45 90 135 directional derivatives, including the zero-derivative, for each of the n scales desired: (5) F = {∂ n , Gn }, n ∈ 2.3. Cumulative Local Moments Cumulative Local Moments is a simple approach to moment calculation. Geometric moments have been used effectively for texture segmentation in many different application domains [23]. In addition, other kind of moments have been proposed, Zernique moments, Legendre moments, etc. By deﬁnition, any set of parameters obtained by projecting an image onto a 2D polynomial basis is called moments. Then, since different sets of polynomials up to the same order deﬁne the same subspace, any complete set of moments up to given order can be obtained from any other set of moments up to the same order. The computation of some of these sets of moments leads to very long processing times, so in this section a particular fast computed moment set has been chosen. This set of moments are known as the accumulation local moments. Two kind of accumulation local moments can be computed, direct accumulation and reverse accumulation. Since direct accumulation is more sensitive to round off errors and small perturbations in the input data [31], the reverse accumulation moments are used. The reverse accumulation moment of order (k − 1, l − 1) of matrix Iab is the value of Iab [1, 1] after bottom-up accumulating its column k times (i.e., after applying k times the assignment Iab [a − i, j ] ← Iab [a − i, j ] + Iab [a − i + 1, j ], for i = 0 to a − 1, and for j = 1 to b), and accumulating the resulting ﬁrst row from right to left l times (i.e., after applying l times the assignment Iab [1, b − j ] ← Iab [1, b − j ] + Iab [1, b − j + 1], for j = 1 to b − 1). The reverse accumulation moment matrix is deﬁned so that Rmn [k.l] is the reverse accumulation moment of order (k − 1, l − 1).

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Consider the matrix in the following example, ⎛ ⎞ 012 ⎝1 1 1⎠ 423 According to the deﬁnition, its reverse accumulation moment of order (1,2) requires two column accumulations, ⎞ ⎛ ⎛ ⎞ 14 9 13 546 ⎝ 5 3 4 ⎠ and ⎝ 9 5 7 ⎠ 423 4 2 3 and three right to left accumulation of the ﬁrst row 36 22 13 and 71 35 13 and 119 48 13 Then it is said that the reverse accumulation moment of order (1,2) of the former matrix is 119. The set of moments alone are not sufﬁcient to obtain good texture features in certain images. Some iso-second order texture pairs which are pre-attentively discriminable by humans, would have the same average energy over ﬁnite regions. However, their distribution would be different for the different textures. One solution suggested by Caelli is to introduce a nonlinear transducer that maps moments to texture features [32]. Several functions have been proposed in literature: logistic, sigmoidal, power function or absolute deviation of feature vectors from the mean [23]. The function we have chosen is the hyperbolic tangent function, which is logistic in shape. Using the accumulation moments image Im , and a non linear operator |tanh(σ (Im − I m )| an ‘average’ is performed throughout the region of interest. The parameter σ controls the shape of the logistic function. Therefore each textural feature will be the result of the application of the non-linear operator to the computed moments. If n = k · l moments are computed over the image, then the dimension of the feature vector will be n. Hence, a n-dimensional point is associated with each pixel of the image. 2.4. Local Binary Patterns Local Binary Patterns [28] is a feature extraction operator used for detecting “uniform” local binary patterns at circular neighborhoods of any quantization of the angular space and at any spatial resolution. The operator is derived based on a circularly symmetric neighbor set of P members on a circle of radius R. It is denoted by LBPPriu2 ,R . Parameter P controls the quantization of the angular space, and R determines the spatial resolution of the operator. Figure 3 shows typical neighborhood sets. To achieve gray-scale invariance, the gray value of the center pixel (gc ) is subtracted from the gray values of the circularly symmetric neighborhood gp (p = 0, 1, . . . , P − 1) and assigned a 1 value if the difference is positive and 0 if negative.

1 if x ≥ 0 s(x) = 0 otherwise

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Figure 3. Typical neighbors (Top-Left) P = 4, R = 1.0 (Top-Right) P = 8, R = 1.0 (Bottom-Left) P = 12, R = 1.5 (Bottom-Right) P = 16, R = 2.0.

By assigning a binomial factor 2p for each value obtained, we transform the neighborhood into a single value. This value is the LBPR,P : LBPR,P =

P

s(gp − gc ) · 2p

p=0

To achieve rotation invariance the pattern set is rotated as many times as necessary to achieve a maximal number of the most signiﬁcant bits, starting always from the same pixel. The last stage of the operator consists on keeping the information of “uniform” patterns while ﬁltering the rest. This is achieved using a transition count function U . U is a function which counts the number of transitions 0/1, 1/0 while we move over the neighborhood. U (LBPP ,R ) = s(gP −1 − gc ) − s(g0 − gc ) +

P −1

s(gp − gc ) − s(gp−1 − gc )

p=1

Therefore,

LBPriu2 P ,R =

LBPri P ,R P +1

if U (LBPP ,R ) ≤ 2 otherwise

Therefore, local binary patterns look for the longest chain of homogeneous-valued pixels given a circular sampled neighborhood. This description is gray level independent since it just binarize the neighborhood pixel value according to the central pixel value. However, we can be further improve this description by ﬁnding the local variance of the neighborhood set in gray level.

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Figure 4. Block diagram of the AdaBoost procedure.

3. Adaboost Classiﬁcation Process At this point, we have a set of features that represent each instance of the problem. In our particular case, they are samples of plaque. Each sample of plaque has a feature vector associated, that contains useful information about this plaque. The feature vector describes a multi-dimensional space. Therefore, for each pixel we have a n-dimensional point in the feature space, where n is the number of features. This set of data is the input to the classiﬁcation process. The Adaboost process is a supervised learning and classiﬁcation tool, since we know exactly the classes we are seeking. Adaboost is created as a method for combining simple classiﬁers to obtain a very accurate decision. Roughly, it is an iterative assembling process in which each each classiﬁer is devoted to ﬁnd a good division of the sub-set of points formed by the samples that are more difﬁcult classiﬁed up to that point. In particular Adaboost is a shortening for Adaptative Boosting (AdaBoost), and is widely recognized as one of the most accurate processes for high accuracy classiﬁcation. 3.1. AdaBoost Procedure Adaptative Boosting (AdaBoost) is an arcing method that allows the designer to keep adding “weak” classiﬁers until some desired low training error has been achieved [41,42]. At each step of the proces, a weight is assigned to each of the feature points. These weights measure how accurate the feature point is being classiﬁed at that stage. If it is accurately classiﬁed, then its probability of being used in subsequent learners is reduced, or emphasized otherwise. This way, AdaBoost focuses on difﬁcult training points at each stage. The classiﬁcation result is a linear combination of the “weak” classiﬁers. The weight of each classiﬁer is proportional to the amount of data that classiﬁes in a correct way. Figure 4 shows a diagram of the general process of boosting. The adaboost process uses weights that modify the probability density function of the appearance of each sam-

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ple data point. This fact can be troublesome, since we need to ﬁnd classiﬁers that allow weighing the samples points. Another possibility is to resampled the data set according to the weights of each feature data. The new set of feature points are inputs of the new classiﬁer to be added to the process. Although, this last method is more general is unadvisable to use it, since after several iterations, the training set can be trimmed to very little data points. Therefore, it hinders the classiﬁcation process. As an additional feature AdaBoost is capable of performing a feature selection process while training. In order to perform both tasks, feature selection and classiﬁcation process, a weak learning algorithm is designed to select the single features which best separate the different classes. That is, one classiﬁer is trained for each feature, determining the optimal classiﬁcation function (so that the minimum number of feature points is misclassiﬁed). And then, the most accurate classiﬁer-feature pair is stored at that stage of the process. If feature selection is not desired, the weak classiﬁer focuses on all the features at a time. The general algorithm is described as follows:

• Determine a supervised set of feature points {xi , ci } where ci = {−1, 1} is the class associated to each of the features classes. 1 , 2l1 for ci = {−1, 1} respectively, where • Initialize weights w1,i = 2m m and l are the number of feature points for each class. • For t = 1..T : ∗ Normalize weights wt,i wt,i ← n j =1 wt,i so that wt is a probability distribution. ∗ For each feature, j train a classiﬁer, hj which is restricted to using a single feature. The error is evaluated with respect to wt , j = i wi |hj (xi ) − ci |. ∗ Choose the classiﬁer, ht with the lowest error t . ∗ Update the weights: wt+1,i = wt,i βtei where ei = 1 for each well-classiﬁed feature and ei = 0 otherwise. t . Calculate parameter αt = − log(βt ). βt = 1− t • The ﬁnal “strong” classiﬁer is:

T 1 t=1 αt ht (x) ≥ 0 h(x) = 0 otherwise

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Therefore, the strong classiﬁer is the ensemble of a series of simple classiﬁers (“weak”). Parameter αt is the weighting factor of each of the classiﬁers. The loop ends whether the classiﬁcation error of a “weak” classiﬁer is over 0.5, the estimated error for the whole “strong” classiﬁer is lower than a given error rate or if we achieve the desired number of “weaks”. The ﬁnal classiﬁcation is the result of the weighted classiﬁcations of the “weaks”. The process is designed so that if h(x) > 0, then pixel x belongs to one of the classes. 3.2. Behavior of the Adaboost Procedure Analyzing the Adaboost process, we can ﬁgure out the error rate behavior when adding new “weak” classiﬁers. As we have described in the former section, the probability of each sample to be used in a “weak” classiﬁer raises if it has been misclassiﬁed up to that moment by the “strong” classiﬁer. So if

we want to add a classiﬁer ht+1 (x), we take the misclassiﬁed points according h(x) = Tt=1 αt ht (x) and raise its probability in t + 1. As the set with higher probability is composed by the difﬁcult data points, the “weak” classiﬁer will easily fail in assigning the correct label to each sample. This fact, tells us that the error rate will increase the more classiﬁers we add. This is true for the transient time. To further understand the behavior of the stationary time, we will now describe the behavior of the “strong” classiﬁer error rate. One of the conditions that stop the process is the fact that the “weak” classiﬁer must perform better than the random guess. That is, we always want the error rate of the “weak” classiﬁer to be under 0.5. If this condition is granted at each step, it means that although the “weak” is focusing on the most difﬁcult data set, it still manages to ﬁnd a usable solution. This translates in the fact that some misclassiﬁed points will now be correctly assigned to the true label. This, of course, is decreasing the error rate of the compound of “weaks”. This is true up to the point that if no other stop condition is met, the error rate tends asymptotically to zero. Resuming the “weak” classiﬁcation error rate in the stationary stage. It is expected that the classiﬁer will be able to classify correctly at least one of the samples. If this happens, the error will be better than random guess, though tending to 0.5. Otherwise, the “weak” can not be used to train the “strong” classiﬁer and the process will end. Figure 5 shows the evolution of the error rates for the training and the test feature points. Figure 5(a) shows the test error rate. One can observe, that the overall error has a decreasing tendency as more “weak” classiﬁers are added to the process. Figure 5(b) shows the error evolution of each of the “weak” classiﬁers. The ﬁgure illustrates how the error increases as more “weak” classiﬁers are added. Figure 5(c) shows the error rate of the system response on the training data. As it is expected, the error rate decreases to very low values. This, however does not ensure a test classiﬁcation error of such accuracy. One question arises at this point. What will happen with the test error rate? The answer is not simple. While we expect the test error rate to decrease in the same way as the training error rate does, one can not guarantee this behavior. However, we realize that if the training set is meaningful, in the sense that it correctly represents the problem, the test error rate should decrease according with the “strong” error rate. But we also must take into account that we have a ﬁnite amount of samples, and therefore, the “weak” classiﬁers could try to distinguish among not representative and conﬂictive points due to the sampling. This fact can lead to overtraining stages, in which, though the training is

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Figure 5. Error rates associated to the AdaBoost process. (a) Test error rate. (b) “Weak” single classiﬁcation error (c) Strong classiﬁcation. error. on the training data.

correctly classiﬁed, as it is not a good representation of the reality, the test samples are misclassiﬁed. 3.3. The Role of the “Weak” Classiﬁer The weak classiﬁer has a very important role in the procedure. Different approaches can be used, however it is relatively interesting to center our attention in low time-consuming classiﬁers. The ﬁrst and the most straight forward approach to a “weak” is the perceptron. The perceptron is constituted by a weighed sum of the inputs and an adaptative threshold function. This scheme is easy to embed in the adaboost process since it relies on the weights to make the classiﬁcation. Another approach to be taken in consideration is to model the feature points as Gaussian distributions. This allows us to deﬁne a simple scheme by simply calculating the weighed mean and weighed covariance of the classes at each step of the process: j j j 2 μi,t = wi,t xi i,t = wi,t xi − μi,t j

for each xi point in class Cj . Wi,j are the weights for each data point. If feature selection is desired, this scheme is highly constrained to the N features of the N-dimensional feature space. If N is not enough large, the procedure could not improve its performance. Therefore we propose another classiﬁer for relatively low dimensional spaces (2 magnitude orders). Because the selection of a single feature for each of the classiﬁers is quite a hard constraint, we can look for the most signiﬁcant pair of features which discriminates better the different classes. For each pair of features of our space we use linear discriminant analysis to ﬁnd the transformation which leads to the most discriminant axis. We chose the pair of features with the lowest error. We can describe this “weak” classiﬁer as follows.

1 if pj Wjt x < pj θj h(x) = 0 otherwise where pj and θj are the parity and threshold parameters and Wj is deﬁned as follows: Wj = j−1 (μ−1,j − μ1,j )

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which is the canonical variate. Wj is the principal axis of the solution of the linear discriminant analysis system which maximizes J (W ) =

W t SB W , W t SW W

t where SB is the between-class scatter SB = C i=1 Ni (μi − μ)(μi − μ) and SW is the

C

within-class scatterSW = i=1 x∈Ci (x − μi )(x − μi )t , where μ is the mean value of the whole data, C is the number of classes and Ni is the number of samples in class i. Another approach to a “weak” classiﬁer relies on the use of the ROC curves. The ROC curves show the amount of false positives and false negatives for each possible parameter of the classiﬁer. In particular, if we use a threshold value, it shows the curves for each threshold value. At this point, the optimal threshold value is the minimum of the sum of both curves. This is the optimal trade-off between the misclassiﬁcation in both classes. This process can be done for each feature using a feature selection plus classiﬁcation process. This is the approach we have used in this article. In general, the weak classiﬁer, hj (x) consists of a feature fj , if the feature extraction process is desired, and the parameters of the classiﬁer j . Those parameters are a threshold θj , a parity pj and Wj , a classiﬁer trained by linear discriminant analysis. Although the threshold separates the two classes it is not enough to identify which class is in either side of the threshold. Therefore a parameter pj (parity) is needed to indicate the direction of the inequality sign when classifying:

1 if pj fj (x) < pj θj hj (x) = 0 otherwise Both, the feature extraction and the classiﬁcation processes, are the central parts of any classiﬁcation system. We will use the framework explained in the former sections in order to classify exhaustively the plaque in the IVUS image.

4. Results and Conclusions The assessment of the classiﬁcation process is presented in this section. First, the database building and experimental settings are introduced. Then, a discrimination classiﬁcation reference for methodology comparison is shown. After the reference, we are explaining the multiple pair-wise problems and the results of their classiﬁcation. We ﬁnish this section showing the characteristic curves of the behavior of the Adaboost process. 4.1. Experimental Settings and Database Building One of the main problems in the IVUS scientiﬁc community is the lack of a standard reference set for validation of the IVUS tissue classiﬁcation. Regarding this matter, we have devoted a great amount of time in collaboration with expert physicians to create a database with ten thousand samples of each of the four tissues acknowledged by experts, soft tissue, ﬁbrous tissue, mixed tissue and calcium. Those samples have been extracted from 20 different patients, using a nombre del aparatito y megaherz de funcionamiento y otras caracteristicas tecnicas chachis :P. Using this database, several texture descriptors have been selected.

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Table 1. Computational complexity and performance for each set. Feature Set

Computational Complexity

Discriminative Power

Filter bank Co-occurrence set LBP Cumulative Moments

High High Low Low

High High High Average

Table 2. Error rate for each plaque pair, using the different tissue descriptors. Plaque pair

BOF

COOC25

COOC38

LBP

MOM

Fibrous vs Calcium Soft vs Calcium Mixed vs Calcium Soft vs Fibrous Fibrous vs Mixed

35.18% 25.30% 29.64% 34.83% 44.56%

24.55% 10.07% 18.51% 35.81% 47.68%

23.84% 9.94% 17.83% 34.57% 49.84%

48.53% 42.97% 46.55% 48.46% 49.91%

46.43% 44.10% 46.14% 47.67% 49.70%

Soft vs Mixed

42.73%

40.30%

49.36%

46.94%

47.87%

Particularly, we have chosen • A derivatives of gaussian ﬁlter bank, up to the third derivative. A ﬁve level multi-resolution framework is used, with scales {0.2, 0.5, 1, 2, 4}. For each scale, a set of directional derivatives is extracted. Particularly, this set is ∂ n = 2 , ∂ 2 , ∂ 3 , ∂ 3 , ∂ 3 , ∂ 3 ], where the subindex points the direction [∂0 , ∂90 , ∂02 , ∂60 120 0 45 90 135 of the partial derivative in degrees. To this set we also include the zero-derivative image, that is a smoothed version at the corresponding level of the original image. • A set of descriptors of the co-occurrence matrices at angles {0, 45, 90, 135} with neighborhoods of 11 × 11 pixels and distance for the co-occurrence pair of D = 2 and a 17 × 17 pixels neighborhood with a distance of D = 3. • A tissue description set based on local binary patterns and local variance, using radius 1 with 8 samples, radius 2 with 16 samples and radius 3 with 24 samples. • A feature space based on cumulative moments, with moments up to (9, 9). All these feature spaces are well-known and well-suited spaces for texture description. They usually differ from each other in terms of computational complexity and discriminative power. Table 1 shows how the performance of each feature set. Regarding the Adaboost procedure, we use a composition of 500 classiﬁers in the original feature space, for each description set. 4.2. Discrimination Reference To compare the performance of the boosting method we have selected a well-known classiﬁer, Fisher Linear Discriminant Analysis. The results of this classiﬁer is our groundtruth, to which we will refer in order to compare the results of the Adaboost technique. Table 2 shows the test error rate for each pair of plaques. Having a look at the ﬁgures, the table reveals that there are some sets with a great amount of overlapping samples. This is particularly true in the discrimination between mixed tissue and soft or ﬁbrous tissue, since mixed tissue implies an ill-deﬁned mixture of both ﬁbrous and soft tissues. We can also see that some feature spaces tend to perform better for our problem than others. In fact, co-occurrence matrices descriptors (COOC25, COOC38) and derivatives

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Feature Set BOF COOC25 COOC38 LBP MOM

Initial Error 33.13% 20.90% 20.67% 24.76% 43.62%

Final Error 13.09% 13.74% 11.04% 21.81% 38.04%

(a)

(b) Figure 6. Examples of the ﬁbrous tissue (a) and the calcium plaque (b).

Feature Set BOF COOC25 COOC38 LBP MOM

Initial Error 17.75% 9.81% 8.88% 15.31% 45.49%

Final Error 5.80% 7.27% 4.29% 14.68% 33.00%

(a)

(b) Figure 7. Examples of the soft tissue (a) and the calcium plaque (b).

of gaussian ﬁlter bank (BOF), outperform clearly the low complexity descriptors, Local Binary Patterns (LBP) and Cumulative Moments (MOM). This means that both feature spaces, describe better the tissue properties than the other two. However, this fact could have been easily predicted from Table 1, since there is always a trade-off between complexity and performance. 4.3. The Fibrous vs Calcium Problem The characterization of the calcium tissue seems to be the less difﬁcult one since the calcium tissue has a very high echo-reﬂectivity and homogeneity. On the other hand, ﬁbrous plaque is also high reﬂective, but have much more rugosity. Figure 6 shows an example of the ﬁbrous plaque Fig. 6(a) and the calcium plaque Fig. 6(b). The table from Fig. 6 shows the results for this test. As expected the initial error in the overall feature space of the best performing sets and the error using discriminant analysis are quite close to each other. However, the Adaboost procedure reﬁnes the classiﬁcation thus increasing the recognition rates to an average of 88%. Unexpectedly, LBP has a relative good performance, close to 80%, making it an ideal candidate if we aim for fast processing. 4.4. The Soft vs Calcium Problem This problem is by far the most simple one since the plaques we are distinguishing are the more different kind of plaques. In particular, the soft tissue has low echo-reﬂectivity and high granularity, while the calcium plaque is just the opposite. Figure 7 shows an example of the ﬁbrous plaque Fig. 7(a) and the calcium plaque Fig. 7(b). The former statement is conﬁrmed by the table shown in Fig. 7. That shows

O. Pujol and P. Radeva / On the Assessment of Texture Feature Descriptors

Feature Set BOF COOC25 COOC38 LBP MOM

Initial Error 26.29% 16.36% 15.91% 20.54% 44.16%

Final Error 9.79% 12.44% 7.46% 19.15% 35.75%

293

(a)

(b) Figure 8. Examples of the mixed tissue (a) and the calcium plaque (b).

the ﬁgures for the error rate in this problem. Again, the recognition rate of the high complexity spaces is pretty high, and further increased by the Adaboost process, up to an average over 95%. Three important remarks can be made looking at the ﬁgures. First, there is a huge improvement in performance using derivatives of gaussian (BOF), of about 12%. Second, LBP still has pretty good results, over 85%. Third, and the most surprising, MOM still performs bad in this stage. Looking at the reference Table 2 we can see that there is a huge improvement in LBP performance and BOF performance. LBP lowers its error rate by 30% and BOF lowers its error rate by 20%. 4.5. The Mixed vs Calcium Problem Since the behavior of the soft and ﬁbrous plaque against calcium tissue is fairly good, we expect this problem to be an “average” of the above ones. Figure 8 shows an example of the mixed plaque Fig. 8(a) and the calcium plaque Fig. 8(b). Certainly, this is what happens, the results are not as good as the soft versus calcium problem, (see table in Fig. 8) but are better than the ﬁbrous versus calcium one. This is logical if we recall that the mixed tissue is a combination of both ﬁbrous tissue and lipid tissue in an interleaved way. At this stage, we have clearly a good vision of what is the performance of each feature space as well as the inﬂuence of the adaboost process in the problem. BOF and COOC38 performs the best after adaboost, granting high recognition rates. COOC25 seems to perform the worst of the trio formed by the high complexity classiﬁers. If we compare this results to the ones obtained using FLD, BOF lowers its error rate by 20%, and COOC38 by 10%. 4.6. The Soft vs Fibrous Problem One of the most interesting and less obvious problems is the soft vs ﬁbrous problem. In this case, both plaques has a good amount of texture involved in them (high granularity). Although, there is a difference in the reﬂectivity of the transducer pulse. Figure 9 shows an example of the soft plaque Fig. 9(a) and the ﬁbrous plaque Fig. 9(b). Table in Fig. 9 shows the performance of the Adaboost procedure when applied to this problem. We can conclude from the ﬁgures, that in this case, the Adaboost process does not help much. This fact, seems to show that the way data is distributed in the feature spaces is clearly entwined. This fact, hinders the process of the combination of classiﬁers, since, presumingly, each weak classiﬁer is focusing on a really low amount of bad strong classiﬁed data. In this case, the comparison of the results with the reference of Fisher, improves the recognition rate by 10%.

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Feature Set BOF COOC25 COOC38 LBP MOM

Initial Error 28.63% 27.58% 26.57% 31.62% 44.41%

Final Error 26.41% 27.53% 25.98% 30.93% 38.43%

(a)

(b) Figure 9. Examples of the soft tissue (a) and the ﬁbrous plaque (b).

Feature Set BOF COOC25 COOC38 LBP MOM

Initial Error 37.74% 39.99% 39.40% 41.31% 43.42%

Final Error 36.28% 37.33% 35.65% 40.90% 40.92%

(a)

(b) Figure 10. Examples of the ﬁbrous tissue (a) and the mixed plaque (b).

4.7. The Fibrous vs Mixed Problem This problem and the soft vs mixed problems are by far the most complex ones. The ﬁbrous and the mixed plaques really resemble each other in terms of local distribution features. The difference between both is simply the spatial overall distribution of the tissues. Most of the methods we have tried are purely local, and therefore are destined to fail in this problem. In fact, we have seen that the mixed label is also the most disagreeable of the plaques among the experts labelling. However, we also attach the results for this two problems. Figure 10 shows an example of the ﬁbrous plaque Fig. 10(a) and the mixed plaque Fig. 10(b). Table in Fig. 10 shows the error rates for this problem. 4.8. The Soft vs Mixed Problem In the same way than the former case. The soft versus mixed plaque problem is ill-posed from the local texture point of view. Figure 10 shows an example of the soft plaque Fig. 10(a) and the mixed plaque Fig. 10(b) Table in Fig. 11 show the results for this case. It is remarkable the fact that COOC38 is able to distinguish both plaques with an average recognition rate of over 70%. This is due to the fact that COOC38 uses a 17 × 17 neighborhood and therefore is susceptible to pick up the spatial distribution of the entwined ﬁbrous and soft plaques. The ﬁbrous vs. mixed and soft vs. mixed using linear discriminant analysis can not be made, since the results show that the decision is nearly random (recognition rates of about 55%). However, using adaboost the problem seems to have a weak solution, that is, a solution of nearly 70% of recognition.

O. Pujol and P. Radeva / On the Assessment of Texture Feature Descriptors

Feature Set BOF COOC25 COOC38 LBP MOM

Initial Error 40.44% 37.72% 35.42% 39.35% 46.45%

Final Error 37.36% 33.09% 29.29% 39.01% 41.26%

295

(a)

(b) Figure 11. Examples of the soft tissue (a) and the mixed plaque (b).

4.9. Characteristic Curves As stated in the adaboost description section, the error rate of the weak classiﬁers increases at each iteration (every time we add a classiﬁer) due to the fact that it has to classify the previously erroneous classiﬁed data (the errors of the combination of weak classiﬁers up to this moment). The other characteristic of this process is that the overall error rate on the training data tends to zero as the number of weak classiﬁers increases. This fact does not imply that the test classiﬁcation error also tends to zero. In fact, it has been shown, and we will see in the ﬁgures, that it can worsens or keep nearly constant. Figure 12 shows some examples of the characteristic behavior of the adaboost process. Figures 12(a) and 12(b) refer to the behavior of the derivatives of gaussian in front of the soft-calcium and mixed-calcium problems respectively. Figure 12(c) shows the error curves for the accumulation moments in front of the ﬁbrous-calcium problem. Figure 12(d) shows the aforementioned constant behavior of the test error rate although the training error rate clearly decreases. This ﬁgure refers to the co-occurrence 2, 5 when characterizing soft versus ﬁbrous plaque. Figures 12(e) and 12(f) show co-occurrence matrix descriptors for parameters (3, 8) in front of the problems soft-calcium and softmixed plaque, respectively.

5. Discussion and Conclusions The ﬁrst conclusion that arises from the experiments is the beneﬁcial inﬂuence that has the adaboost procedure in the classiﬁcation of the plaque. Thus, rendering it to a very good classiﬁer if we aim for plaque characterization. However, although adaboost is a very high performance classiﬁer, the results show that plaque characterization based only on texture can not be made accurately if we want recognition rates over 85%. Furthermore, the most different kind of tissue, calcium is easily identiﬁed even without context information, with an overall accuracy of over 95%. However, mixed plaques are really difﬁcult to distinguish. This points out that if we want to classify mixed plaques texture descriptors alone are not suitable for the task. Regarding the feature spaces, co-occurrence matrices descriptors performs better than the rest, closely followed by the bank of ﬁlters approach. Local binary patterns is the third in recognition rate. Several aspects have to be taken into account when judging the results. First of all, regarding the database. The data included in the database is widely variable and from a good amount of different patients. Analyzing the plaques, we have seen that different

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(a)

(b)

(c)

(d)

(e)

(f)

Figure 12. Examples of the characteristic curves for the adaboost process. (a) BOF in soft-calcium problem. (b) BOF in mixed-calcium problem. (c) MOM in ﬁbrous-calcium problem. (d) COOC25 in soft-ﬁbrous problem. (e) COOC38 in soft-calcium problem. (f) COOC38 in soft-mixed problem.

plaques from different patients can be quite different among each other, although they are grouped under the same label. It is surprising how, some plaques labelled as different can resemble to each other. This fact, also seems to point out that more information must be taken into account when dealing with plaque characterization. We have seen that physicians heavily rely on the context information, and the location of the plaque. Therefore, the results presented here are useful as a guideline of the performance of the classiﬁers but they are by no means a criterion to avoid the less accurate feature descriptors. In particular, we can see from the study that MOM based classiﬁers lead to low recognition rates. However, the performance of the MOM classiﬁer is deceiving. While it provides bad results as a feature space, we have seen that using contextual information

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297

Figure 13. Illustration of how the local classiﬁcation of tissue can be deceiving.

(a)

(b)

(c) Figure 14. Adaboost overtraining and fake-plaque effect. (a) Original image. (b) 50 classiﬁers. (c) 500 classiﬁers.

most of the misclassiﬁed data can be seen as speckle noise caused by the decision of the classiﬁer. That means that in the context of an IVUS image, the misclassiﬁed data points are scattered and can be re-classiﬁed taking into account neighboring plaques, since more of then are in isolated groups of two or three pixels. If this is done accurate results can be extracted from them. This reinforces the idea shown at the previous paragraph, the analysis of the contextual information can easily improve the recognition rate of the methods. Figure 13 shows an example of how the local information can not be enough for a good classiﬁcation. In fact, if we look at the top images, we can see that both images are quite similar and we probably will classify them as some kind of plaque, in particular as ﬁbrous plaque. However if we look at the original images we can see that one is in fact a tissue plaque, but the other it is neither a tissue, it is part of the blood pool (lumen). The effect of the previous casuistic can lead to undesirable situations such as the one showed in Fig. 14. This ﬁgure is a simpliﬁcation of the tissue problem. In particular, this is a blood vs tissue classiﬁcation, but it will serve to easily understand some concepts. The ﬁgure is an example of two effects. On one hand, the ﬁnal recognition rate is low because of the fake-plaque effect, as mentioned in the former paragraph. On the other hand, this is a classical example of an overtrained classiﬁer. Figure 14(b) shows the

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classiﬁer results in a middle stage of learning. Figure 14(c) shows the ﬁnal result. As we can see, as the blood is relatively different from the blood expected, and because the last group of classiﬁers added in the adaboost process are more focused on very few samples of the training data, they can degrade the ﬁnal classiﬁcation result if the particularities of the training data do not coincide with the ones of the test set. This effect lead us to create a new kind of classiﬁcation process, currently under development, that takes into account the particular test set to infer context information and therefore adapt the classiﬁcation process to the particularities of the test set.

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[19] Pujol, O. and Radeva, P., Automatic segmentation of lumen in intravascular ultrasound images: An evaluation of texture feature extractors, Proceedings for IBERAMIA 2002, pp. 159–168, 2002. [20] Pujol, O. and Radeva, P., Near real time plaque segmentation of ivus, Proceedings of Computers in Cardiology, pp. 159–168, 2003. [21] Randen, T. and Husoy, J.H., Filtering for texture classiﬁcation: A comparative study, Pattern Recognition, Vol. 21, No. 4, pp. 291–310, 1999. [22] Haralick, R., Shanmugam, K. and Dinstein, I., Textural features for image classiﬁcation, IEEE Trans. System, Man, Cybernetics, Vol. 3, pp. 610–621, 1973. [23] Tuceryan, M., Moment based texture segmentation, Pattern Recognition Letters, Vol. 15, pp. 659–668, 1994. [24] Lindeberg, T., Scale-Space Theory in Computer Vision, Kluwer Academic Publishers, 1994. [25] Jain, A. and Farrokhnia, F., Unsupervised texture segmentation using gabor ﬁlters, Systems, Man and Cybernetics, 1990. Conference Proceedings, pp. 14–19, 1990. [26] Mallat, S., A theory for multiresolution signal decomposition: The wavelet representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 11, No. 7, pp. 674–694, 1989. [27] Mandelbrot, B., The Fractal Geometry of Nature, W.H. Freeman and Co. New York, 1983. [28] Ojala, T., Pietikainen, M. and Maenpaa, T., Multiresolution gray-scale and rotation invariant texture classiﬁcation with local binary patterns, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 24, No. 7, pp. 971–987, 2002. [29] Julesz, B., Visual pattern discrimination, IRE Transactions on Information Theory, Vol. IT-8, pp. 84–92, 1962. [30] Ohanian, P. and Dubes, R., Performance evaluation for four classes of textural features, Pattern Recognition, Vol. 25, No. 8, pp. 819–833, 1992. [31] Martinez, J. and Thomas, F., Efﬁcient computation of local geometric moments, IEEE Trans. Image Processing, Vol. 11, No. 9, pp. 1102–1111, 2002. [32] Caelli, T. and Oguztoreli, M.N., Some tasks and signal dependent rules for spatial vision, Spatial Vision, No. 2, pp. 295–315, 1987. [33] Chaudhuri, B. and Sarkar, N., Texture segmentation using fractal dimension, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 17, No. 1, pp. 72–77, 1995. [34] Lindeberg, T., Scale-space theory: A basic tool for analysing structures at different scales, Journal of Applied Statistics, Vol. 21, No. 2, pp. 225–270, 1994. [35] Rao, R. and Ballard, D., Natural basis functions and topographic memory for face recognition, Proceedings of International Joint Conference on Artiﬁcial Intelligence, pp. 10–17, 1995. [36] Lumbreras, F., PhD Thesis: Segmentation, Classiﬁcation and Modelization of Textures by means of Multiresolution Descomposition Techniques, CVC, UAB, 2001. [37] Jain, A. and Farrokhnia, F., A multi-channel ﬁltering approach to texture segmentation, Computer Vision and Pattern Recognition, 1991. Proceedings CVPR ’91, pp. 364–370, 1991. [38] Fukunaga, K., Introduction to statistical pattern recognition, Academic Press, 1971. [39] Duda, R. and Hart, P., Pattern Classiﬁcation, Willey-Interscience, 2001. Second Edition. [40] Belhumeur, P., Eigenfaces vs ﬁsherfaces: Recognition using class speciﬁc linear projection, IEEE Pattern Analysis and Machine Intelligence, Vol. 19, No. 7, pp. 711–720, 1997. [41] Schapire, R. E., The boosting approach to machine learning. an overview, MSRI Workshop on Nonlinear Estimation and Classiﬁcation, 2002. [42] Viola, P. and Jones, M., Rapid object detection using a boosted cascade of simple features, Conference on Computer Vision and Pattern Recognition, pp. 511–518, 2001. [43] Sonka, M. and Zhang, X., Segmentation of intravascular ultrasound images: A knowledge-based approach, IEEE Transactions on Medical Imaging, Vol. 17, No. 6, pp. 889–899, 1998. [44] von Birgelen, C., Computerized assessment of coronary lumen and atherosclerotic plaque dimensions in three-dimensional intravascular ultrasound correlated with histomorphometry, Amer. J. Cardiology, Vol. 78, pp. 1202–1209, 1996. [45] Klingensmith, J., Shekhar, R., and Vince, D., Evaluation of three-dimensional segmentation algorithms for identiﬁcation of luminal and medial-adventitial borders in intravascular ultrasound images, IEEE Trans. on Medical Imaging, Vol. 19, No. 10, pp. 996–1011, 2000. [46] McInerney, T. and Terzopoulos, D., Deformable models in medical images analysis: a survey, Medical Image Analysis, Vol. 1, No. 2, pp. 91–108, 1996.

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Plaque Imaging: Pixel to Molecular Level J.S. Suri et al. (Eds.) IOS Press, 2005 © 2005 The authors. All rights reserved.

Real-Time Plaque Characterization and Visualization with Spectral Analysis of Intravascular Ultrasound Data Anuja NAIR, Jon D. KLINGENSMITH and D. Geoffrey VINCE Cleveland Clinic Foundation, Cleveland, OH Abstract. Coronary artery disease is the number one cause of death in the United States and the Western world, and approximately 250,000 affected people die per year without ever being admitted to a hospital. One of the main reasons of such a high death-rate without any diagnosis is that more than 50 or heart-attacks) occur in pa- tients with no prior history of known heart disease or symptoms. Coronary artery disease leads to the occlusion of arteries that are vital in providing nutrients to the heart muscles. The disease develops by progressive accumulation or formation of “plaque” within an artery. Certain types of plaques could occlude blood ﬂow and yet might be “stable”. These plaques usually have a high ﬁbrous content, and are known as hard plaques. On the other hand, “unstable” or “soft” plaques might not cause much occlusion but could be vulnerable to rupture. Rupture of such plaques could lead to total or partial occlusion in arteries resulting in sudden cardiac death or heart-attack. In fact, 68 coronary arteries are less than 50. Intravascular ultrasound (IVUS) is a minimally invasive imaging modality that provides cross-section images of arteries in real-time, allowing visualization of atherosclerotic plaques in vivo. In standard IVUS gray-scale images, calciﬁed regions of plaque and dense ﬁbrous components generally reﬂect ultrasound energy well and thus appear bright and homogeneous on IVUS images. Conversely, regions of low echo reﬂectance in IVUS images are usually labeled “soft” or “mixed” plaque. However, this visual interpretation has been demonstrated to be very inconsistent in accurately determining plaque composition and does not allow real-time assessment of quantitative plaque constituents. Spectral analysis of the backscattered radiofrequency (RF) ultrasound signals allows detailed assessment of plaque composition. Advanced mathematical techniques can be employed to extract spectral information from these RF data to determine composition. The spectral content or signature of RF data reﬂected from tissue depends on density, compressibility, concentration, size, etc. A combination of spectral parameters were used to develop statistical classiﬁcation schemes for analysis of in vivo IVUS data in real-time. The clinical data acquisition system is ECG gated and the analysis software developed by our group reconstructs IVUS gray-scale images from the acquired RF data. A combination of spectral parameters and active contour models is used for real-time 3D plaque segmentation followed by computation of color-coded tissue maps for each image cross-section and longitudinal views of the entire vessel. The “ﬂy-through” mode allows one to visualize the complete length of the artery internally with the histology components at the lumen surface. In addition, vessel and plaque metrics such as areas and volumes of individual plaque components (collagen, ﬁbro-lipid, calcium, lipid-core) are also available. Keywords. Intravascular ultrasound, radiofrequency backscatter, spectral analysis, color plaque maps, 3-D reconstruction

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Atherosclerosis results in a majority of ischemic events, making it a leading cause of death. The clinical manifestations of human coronary atherosclerosis extend from an asymptomatic state and stable angina to acute coronary events such as myocardial infarction (MI), unstable angina, and sudden cardiac death [1]. Additionally, atherosclerosis is known to exist in two forms, stable or hard plaque and unstable or soft plaque. ‘Stable’ plaques are characterized by a ﬁbrous cap that is thick relative to the volume of lipid and necrosis. The ﬁbrous matrix is rich in collagen and smooth muscle cells (SMCs), hence hardening or stabilizing the plaque. In the case of soft plaques, particular geometrical features such as a thin ﬁbrous cap and a large necrotic core with high lipid content cause regions of increased circumferential stress in the ﬁbrous cap, making it ‘unstable’ and prone to rupture [2,3]. Current diagnostic tools do not allow adequate in vivo identiﬁcation and characterization of plaques. Intravascular ultrasound (IVUS) provides two dimensional cross-sectional views of the vessel, hence accurate information on vessel morphology. IVUS backscattered signals have the potential to provide real-time in vivo plaque composition via spectral analysis, wherein a combination of spectral parameters can be employed collectively to characterize spectra. Statistical techniques can further be used to determine patterns in the parameters pertaining to various plaque components. Such techniques make real-time analysis of IVUS data conceivable, enabling plaque characterization and further increasing the utility of IVUS. This chapter discusses the principles of ultrasound that are exploited in combination with spectral analysis for plaque characterization. Finally, it provides a brief overview of the software we have developed to classify plaques in real-time with IVUS. The clinical data acquisition system is electrocardiogram (ECG) gated and the developed analysis software reconstructs IVUS gray-scale images from the acquired radio-frequency (RF) data. A combination of spectral parameters and active contour models is used for real-time three-dimensional plaque segmentation followed by computation of color-coded tissue maps for each image cross-section and longitudinal views of the entire vessel. The “ﬂy-through” mode allows one to visualize the complete length of the artery internally with the histology components at the lumen surface. In addition, vessel and plaque metrics such as areas and volumes of individual plaque components (collagen, ﬁbro-lipid, calcium, lipid/necroticcore) are also available.

Vulnerable Plaques Clinical data has shown that the amount of stenosis may not affect plaque stability. In fact, 68% of MIs occur as a result of plaques that are less than 50% occluded [4]. Therefore, atherosclerotic plaque stability is related to histologic composition. Vulnerable plaques are dominated by a large lipidic/necrotic core with microcalciﬁcations and a relatively thin ﬁbrous cap with reduced collagen content, sparse SMCs and increased macrophage and mast cell densities and activity [2,3,5]. Recent studies have reported that rupture prone lesions typically have ﬁbrous caps that are < 65 :m in thickness [6]. Furthermore, there is evidence that associates vulnerability of plaques to compensatory enlargement in coronary arteries [7,8]. Compensatory enlargement, also known as positive remodeling, is the growth of the vessel wall outwards, such that the intimal thickening does not cause immediate lumen occlusion. Figure 1 displays examples of coronary arteries with some of these features. The ultrasound analysis techniques, that we have de-

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Figure 1. (A) MOVAT pentachrome histology of a ruptured plaque. The arrow indicates the thin ﬁbrous cap. Note that if the vessel wall was extrapolated, the size of this lesion would be insigniﬁcant and unobvious when visualized with traditional imaging modalities like angiography. (B) Artery section displaying a typical vulnerable plaque, with a thin cap (arrow) and a large lipidic/necrotic core (*). Positive remodeling (growth of plaque outside the dotted line) is also evidenced and is often associated with plaque vulnerability.

veloped, provide plaque characterization and detect indications of positive remodeling, both of which can potentially be used to identify these rupture prone lesions.

Imaging Modalities For more than forty years, contrast angiography has served as the principal imaging modality to assess the anatomic severity of coronary artery disease. Recently, scientiﬁc analysis has revealed many deﬁciencies inherent in angiographic methods [9]. An angiogram provides a two-dimensional silhouette of a three-dimensional structure. Many different lumen sizes and shapes can yield the same silhouette via angiography. Moreover, the angle of the angiographic view can misrepresent the degree of stenosis, thus either over- or under-estimating the extent of disease. Due to the drawbacks with angiography, MRI and CT have received much interest recently as alternative non-invasive techniques. OCT, thermography and near infrared spectroscopy are all emerging intravascular technologies that are catheter based and may or may not require physical contact with the plaque surface to acquire information. Other chapters in this book will discuss some of these techniques. The potential of IVUS to quantify the structure and geometry of normal and atherosclerotic coronary arteries is well documented [9,10]. Initial studies suggest that the three-layer appearance of the normal arterial wall that is seen in most adults is formed by; (I) the echogenic lumen/intimal interface; (II) the echolucent zone that represents the media, and (III) the echogenic outer adventitial region of connective and adipose tissue, as illustrated in Fig. 2 [10]. Current IVUS catheters, which are as small as 0.9 mm in diameter, permit the interrogation of most areas of the human coronary vasculature. In addition, spatial resolution is on the order of 100–120 :m radially and 200–250 :m circumferentially [11]. IVUS clinical systems are designed to be portable, the procedure is safe, relatively inexpensive and images can be acquired at the rate of 30 frames per second. In IVUS images, atherosclerotic segments exhibit both abnormal thickening and increased and/or inhomogeneous echogenicity within the intimal layer. Presumably, the

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Figure 2. An intravascular ultrasound image of a human left anterior descending coronay artery ex vivo. The image was reconstructed from IVUS backscatter and clearly portrays the three vessel wall structure of these mechanical arteries. I – intima; II – media; and III – adventitia.

Figure 3. Intravascular ultrasound images of diseased human coronary arteries, ex vivo. (A) Calciﬁed plaque distinguished by high echogenicity followed by a shadow (arrow); (B) Arrow indicates an echolucent region representative of lipid laden necrotic core.

more echogenic plaques represent areas of greater intimal ﬁbrosis, with increase in specular reﬂections and shadowing of underlying structures indicative of plaques containing calciﬁcations (visible in Fig. 3A). Less echogenic atherosclerotic plaques are thought to include fewer ﬁbrotic elements and/or more lipidic elements (Fig. 3B). In fact, many of the studies evaluating the efﬁcacy of IVUS images in determining plaque composition have been limited by their reliance on digitizing videotape. This process has major limitations as stated by Vince et al. [12] and the perception of the scattering, or texture in images, which is important for tissue characterization, is also adversely affected [13]. More recent studies have realized the importance of gaining access to the raw ultrasound back-scattered signals (Fig. 4) [14–19]. Spectral analysis of the unprocessed ultrasound signals allows a more detailed interrogation of various vessel components than image analysis. The rest of this chapter will focus on underlying ultrasound principles and the corresponding spectral content of IVUS backscatter for plaque characterization. We will discuss various techniques that

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Figure 4. An intravascular ultrasound (IVUS) A-scan acquired by imaging a human left anterior decending coronary artery ex vivo, with a 30 MHz IVUS catheter and digitized at 100 MHZ. The dotted line shows the absence of any echoes (barring noise) as the ultrasound wave travels through the lumen. The solid arrow indicates the echoes from the three vessel wall structure of the artery, including the atherosclerotic plaque. In clinical IVUS consoles, 240, 256 or 512 such A-scans form one image.

can be used to obtain the spectra and highlight their advantages and disadvantages for analysis of IVUS backscatter data. Further, we will discuss certain statistical techniques that provide accurate plaque characterization in conjunction with spectral analysis and discuss how these have been implemented in software for automated real-time determination of plaque composition.

Ultrasound The ﬁrst instance of cardiac imaging with ultrasound was perhaps the development of echocardiography by Elder in the early 1950s [20]. Like other ultrasound research in that period, medical diagnosis suffered from poor ultrasound transducer design, inadequate signal ampliﬁcation, and absence of log compression for image display [13]. As a result, the images could be interpreted to detect major tissue interfaces but lacked information about soft tissue texture. With the pulse-echo mode of operation, a single ultrasound beam is transmitted in tissue and the resulting echoes that “bounce” off the different interfaces are acquired. The distance between these echoes is indicative of the size of the tissue structures and their amplitudes can be further analyzed to determine the type of tissue or its make-up. Without log-compression, only the high intensity echoes can be visualized and no information regarding the tissue itself is available in the images. After the improvement in ultrasound backscatter processing techniques to include log-compression, the usage of medical ultrasound and its development increased tremendously [13,21]. Sound energy propagates through media like a wave and is therefore subject to laws of wave motion. Since the propagation is also dependant on the medium the sound energy transverses, any changes to the original wave are implicative of the properties of that medium. Therefore, by studying these changes, one can reasonably derive conclusions about any such media. It is important to understand the underlying principles of ultrasound waves in order to extract information from them.

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Figure 5. Generation of an ultrasonic pulse of wavelength λ by the intravascular ultrasound transducer. These transducers are either single elements that are mechanically rotated or multi-element phased arrays.

Wave Propagation The pulse-echo mode of ultrasound imaging is the most common method of visualizing tissues, and is also the modus operandi with IVUS. The ultrasound transducer is excited with a certain voltage, which makes it oscillate and produce an ultrasound pulse. This is characteristic of piezoelectric materials. The echos of the original ultrasound wave that are reﬂected or scattered back by the media to the transducer, are converted to an electrical signal, called the backscatter. Figure 5 is an illustration of ultrasound wave propagation after being transmitted by a transducer. An ultrasound pulse is sent out into the tissue to be imaged in the radial direction. The backscatter is acquired by the transducer with typically 256 or 512 such A-scans (backscattered signals) forming one IVUS image in the clinically available consoles. It is the analysis of these A-scans that holds potential for tissue characterization. Ultrasound propagation in general is approximated as a compression or longitudinal wave for simplicity [22]. The fundamental one-dimensional equation of wave motion (for elastic media) derived from Newton’s and Hooke’s Law states that, ∂P ∂u = −ρ ∂z ∂t

(1)

∂u 1 ∂P =− ∂z E ∂t

(2)

and,

where z is the direction of sound propagation, u is the particle velocity, P is the pressure in the medium, E is the Young’s modulus of the medium and ρ its density [22,23]. Differentiating these two equations with respect to z and time t, respectively, gives the speed of sound c in the medium to be:

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Figure 6. Reﬂection and refraction of the ultrasound wave at a tissue interface can be approximated by the plane wave Snell’s law from optics.

0 c=

1 κρ

(3)

with κ = 1/E, being the compressibility of the surrounding medium. Also, c = λf

(4)

where, λ = the wavelength and f = frequency of ultrasound. This simple representation of sound wave propagation demonstrates how backscattered signals acquired with ultrasound medical systems are attributed to the intervening tissue properties they are reﬂected from, namely density and compressibility. The RF backscattered signals are composed of two types of echoes that can also be seen in ultrasound gray-scale images [13,24]. 1. Specular reﬂections from tissue interfaces. The reﬂections and refractions from an interface are governed by a relationship between the angles of incidence, reﬂection and refraction and the acoustic impedances (Zi ) of the two tissues such that, pr Z2 cos θi − Z1 cos θt = pi Z2 cos θi + Z1 cos θt

(5)

2Z2 cos θi pt = pi Z2 cos θi + Z1 cos θt

(6)

and

where pr /pi and pt /pi are the pressures due to reﬂection and transmission, respectively at the tissue interface [13]. Figure 6 explains the angles in equations (5) and (6), and the characteristic impedance is given by: Zi = ρi ci i = 1, 2 for the two tissues at the interface.

(7)

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In addition, in ultrasound systems where the same transducer is also the receiver for the backscatter (such as the current IVUS catheters), detection of specular reﬂections are highly dependant on the angle of incidence. If the angle is large, the reﬂected wave will not be detected, only reﬂections off perpendicular interfaces and those with small angles are received. 2. Diffusely scattered echoes from tissue microstructure, that could include cells and other sub-cellular components. These are due to a phenomena of scattering from structures smaller in dimension than the wavelength of ultrasound, often called Rayleigh scattering [22]. These are very low amplitude reﬂections in many directions and are independent of the angle of incidence [13,25]. In addition, since the scattering is in many directions, only a small amount is reﬂected back to the ultrasound transducer and given their low amplitude in comparison to specular reﬂections, they are very often attributed to noise in the backscattered signals. Detailed studies have demonstrated that ultrasound attenuation due to diffuse scattering is small [26,27]. However, this phenomena (observed as ‘speckle’ in the log compressed gray-scale ultrasound images) is considered important for discerning soft tissue detail and may vary for different tissues [26].

Ultrasound-Tissue Interactions Sound attenuation in tissue is a result of the phenomena of absorption and diffuse scattering. The attenuated amplitude of an ultrasound wave propagating in the z direction is: Az = A0 e −μz

(8)

where A0 is the peak value at z = 0 and μ is the attenuation coefﬁcient in nepers per centimeter given by: μ=

2ηω 2 3ρc 3

(9)

where η is the viscosity of the medium and ω = 2πf is the frequency of the wave. Absorption The dominant part of ultrasound attenuation in tissue results from absorption. The speciﬁc absorption due to different macromolecules varies signiﬁcantly and is related to the structure of the biological macromolecule, its hydration level, and can vary with heat denaturation and pH [27]. Energy is lost through absorption by two main processes: 1) classical absorption which is due to the viscosity of the medium and, 2) the relaxation process. Classical absorption is caused by the frictional losses to the ultrasound wave in the medium, and in general increases with the square of the ultrasound frequency. The relaxation process is characterized by an absorption peak at a particular frequency and is negligible elsewhere [13]. However, this effect is very small when the tissue relaxation time is much smaller than the wave period. If this time is almost equal to the wave period, the molecule may not return to equilibrium before another compression wave arises. Alternatively, if the frequency of ultrasound is very high, the molecule may not

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be able to follow wave motion and as a result the process will not occur. The relaxation times of tissue overlap, thus making the overall absorption almost linearly dependant on the frequency of ultrasound [28]. Scattering Many researchers have analyzed and attempted to model ultrasound scattering in various tissues [22–25,29]. In general, it has been noted that the amplitude of the backscatter is dependant on the density, size and spacing of scatterers, the homogeneity or heterogeneity of the scatterer type, their acoustic impedance differences, water content and distribution and the frequency of ultrasound. The most common assumptions made for modeling diffuse scatter of ultrasound are thus based on simplifying these factors.

Acoustic Properties of Tissues Spectral techniques mentioned later in this chapter can be used to calculate certain acoustic properties of tissues, like relative acoustic impedance (equation (7)) or the attenuation coefﬁcient (equation (9)). Prior knowledge of such tissue properties is a tremendous help in classiﬁcation of RF data. To date, no detailed studies have been performed for atherosclerosis, probably due to lack of adequate analysis techniques for the shorttime and stochastic IVUS RF signals. However, many studies have documented the trends in acoustic attenuation and speed of sound in various gross human organs and tissues [30]. An important aspect that was highlighted is that there is signiﬁcant overlap in acoustic properties of gross human tissues, indicating the difﬁculty of tissue characterization at the molecular level for small structures (like artery walls). However, there were a few studies where scanning acoustic microscopy (SAM) was used to determine a few key properties of vascular tissues, since SAM allows very high frequency ultrasound evaluation of tissue microstructure [31,32]. These studies reported the range of speed of sound in vascular wall to be between 1500–1760 m/s. The speed of sound was found to be1568 m/s through normal intima, 1760 m/s through calciﬁed plaques, 1677 m/s in ﬁbrous or stable plaques, and 1526 m/s in lipidic regions. Current IVUS systems do not allow speed of sound calculations with such accuracy, therefore limiting this evaluation to ex vivo analysis with other equipment like SAM. The next section of this chapter explores mathematical techniques for IVUS data analysis that can provide detailed classiﬁcation of atherosclerotic components in vivo (more speciﬁcally, to identify ﬁbrous, ﬁbro-lipidic, necrotic/lipidic cores and regions of calciﬁcations in plaques).

Plaque Characterization The following properties of tissue are important for understanding ultrasonic wave propagation, specular reﬂections, absorption and diffuse scattering: • • • •

density, compressibility, viscosity, size of scatterers,

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• spacing of the scatterers, • homogeneity or heterogeneity of the media, and • the different acoustic impedances of the media. The backscattered signals that can be acquired and analyzed thus contain information regarding all these properties at the macroscopic and microscopic level. Also, a large part of the attenuation could be attributed to diffuse scattering since the size of scatterers within an atherosclerotic plaque are usually smaller than the wavelength of current commercially available IVUS systems. Many techniques have been developed to analyze either ultrasound images or the backscattered signals to attain reasonable classiﬁcation of tissues. In our approach, we used ex vivo plaque IVUS data with corresponding histology as the gold-standard to build a database of regions of interest (ROIs). These ROIs are homogeneous for a particular plaque component and the IVUS backscatter from each such ROI can be further examined for “spectral signatures.” The following section explains what these signatures are and how they can be calculated. Furthermore, statistics can be used to devise classiﬁcation rules with an extensive database of spectral signatures of representative plaque components (see section on Statistical Classiﬁcation Trees).

Spectral Analysis Spectral analysis of backscattered ultrasound data has demonstrated the ability to characterize tissue [17–19,33–38]. Various aspects of this procedure are examined here. First of all, the ability of spectral parameters (e.g., slope, mid-band ﬁt and y-intercept) to classify plaque composition is discussed. Next, various spectral algorithms are discussed to evaluate the advantages of a parametric approach over the classic Fourier techniques. Spectral Parameters As noted above, the amplitude of the RF backscatter of ultrasound systems is dependant on the density, concentration, size and spacing of scatterers, the homogeneity or heterogeneity of the scatterer type, their acoustic impedance differences, water content and distribution and the frequency of ultrasound. Some earlier studies (for example, those by Lizzi et al. [36] and O’Donnell [39,40]) laid out the basis for a theoretical framework pertaining to RF data analysis. The results from these studies, of analyzing spectral parameters (Fig. 7), indicated that the slope, y-intercept, and mid-band ﬁt (MBF) are representative of different tissue structures, sizes, and intervening attenuation. Intercept and MBF are also indicative of the ultrasound scatterer concentration [35]. MBF has not been extensively studied for IVUS data, although it has been for ultrasonic tissue characterization for other tissues [35,37,38]. Another parameter that has been examined extensively is integrated backscatter, and it aims to provide a crude estimation of the backscatter coefﬁcient given by: fmax 1 PSD(f )df (10) Integrated Backscatter = fmax − fmin fmin where, fmin − fmax is the bandwidth for analysis [33,41]. The averaged spectrum representing a homogenous ROI is approximated by statistical least squares regression ﬁt and then employed to compute various parameters after normalization (see Fig. 7).

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Figure 7. Computation of spectral parameters from the normalized spectra. The average spectrum from an ROI is normalized by subtracting from it the spectra calculated by imaging a perfect reﬂector (plexiglas). Spectral parameters are calculated using the normalized spectra within the bandwidth of 17–42 MHz (for 30 MHz intravascular ultrasound data). The database of parameters is then used to compute classiﬁcation trees for plaque characterization. 1: y-intercept; 2: minimum power; 3: mid-band ﬁt; 4: maximum power; 5 and 6: frequencies at minimum and maximum powers, respectively; 7 (not shown): slope of the regression line; and 8 (not shown): integrated backscatter.

The main spectral parameters analyzed are thus, slope (indicative of scatterer size and intervening attenuation), y-intercept (indicative of acoustic impedance and scatterer concentration, mid-band ﬁt (indicative of scatterer size, concentration and intervening attenuation) and integrated backscatter (a crude measure of the amount of backscattered energy). In addition to these, more parameters can be recorded from the normalized and raw data spectrum for appropriate pattern recognition (such as maximum power and corresponding frequency, minimum power and corresponding frequency). Many IVUS RF studies to date have been limited to the use of Fourier techniques to extract such parameters from the RF data spectra [17–19]. Although the fast Fourier transform (FFT) is computationally efﬁcient, it does not perform well with short and sparse data (such as IVUS RF) since the model is based on sinusoids [42,43]. The Welch periodogram, another classic spectral technique, is a modiﬁed FFT algorithm calculated by windowing a data record in a certain number of segments and overlapping those segments by a speciﬁed number of samples [44]. It aims to stabilize the spectrum to some extent by statistical averaging (Fig. 8) but requires data windowing which suffers from a trade-off between resolution and reduction of leakage in side-lobes. In contrast, autore-

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Figure 8. Comparison of spectrum computed with three spectral techniques. The autoregressive model does not display side lobes in the power spectrum for short time, stochastic, intravascular ultrasound data.

gressive (AR) modeling of sparse short-time data can produce high resolution in spectra without side lobes (Fig. 8) and does not require data windowing [43,45]. Therefore, assuming an AR model for the IVUS RF data could improve accuracy in estimation of spectral parameters. Traditional Fourier Techniques Computational efﬁciency is a signiﬁcant advantage with the classic approaches to calculation of power spectra. The power spectral density (PSD) estimate is directly proportional to the power of sinusoid processes and they make excellent models for certain applications where the signals can be estimated as a sum of harmonically related sinusoids [42,43]. The performance of classic spectral estimates at any given frequency ‘f’ can be characterized by the stability-time-bandwidth product inequality, which states that: S T f >1, where S is the stability factor (ratio of the variance of spectral estimates to the mean spectral estimate). S should be minimum for a stable solution to the spectra, and this can be achieved by increasing pf. But any increase in pf results in reduction of resolution in the frequency domain, a tradeoff that both the classic Fourier and Welch techniques suffer from [44]. In addition, strong side-lobes typically suppress the weak signal main-lobe response, as illustrated in Fig. 8.

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Autoregressive Models A parametric approach to IVUS data modeling is desirable due to the improved frequency resolution achieved for the spectral estimates [43,46]. AR modeling of data assumes the process is an autoregression of order p driven by the white noise process e[n], described by Marple as [43]: x[n] = −

p

a[k]x[n − k] + e[n]

(11)

k=1

where the sequence x[n] is a linear regression on itself with the AR coefﬁcients a[k]. The present value is thus represented as a weighted sum of past values in addition to a noise term e[n] of variance σ 2 (MSE). According to the Yule-Walker equations, the AR PSD may be written as: σ2 PAR [f ] = 2

p 1 + k=1 a[k] exp[−j 2πf kt]

(12)

where {a1 , a2 , . . . , ap , σ 2 } is required to estimate the PSD [42,46]. This is also called the all-pole model, since the only frequency dependence is in the denominator. Alternatively, PAR [f ] =

∞

rxx [n] exp[−j 2πf nt]

(13)

n=−∞

where

⎧ ⎪ ⎨Rxx [n], for |n| ≤ p p rxx [n] =

⎪ ⎩− ap [k]rxx [n − k],

for |n| > p

(14)

k=1

and Rxx is the autocovariance function [42]. It can be observed from (14) that the AR PSD preserves the known lags and recursively extends the lags beyond the window with an inﬁnite extrapolation of the autocovariance function rather than windowing it to zero, thus not exhibiting the side-lobes common with the traditional Fourier methods [42,43,46]. Also, the implied extrapolation results in high resolution of the spectral estimates that cannot be achieved by the more classic approaches for calculating spectra [43,44]. In most cases, a decrease in record length (essential for analysis of short homogeneous segments of a plaque) would result in a lower signal-to-noise ratio and increased perturbations. This leads to an unstable system that requires regularization. In the AR approach, regularization is achieved by determining a suitable model order, which effectively separates the signal from the white noise in equation (11). With diffuse ultrasonic scattering there might be little or no distinction between noise and diffuse backscatter that is actually representative of the tissue it is reﬂected from. Therefore, for characterizing atherosclerosis, it might be important to select an AR order large enough to include some of this “useful” noise. There are many techniques mentioned in the literature for determining a suitable AR order for a process, but most of these tend to underestimate the order for very short record lengths [43].

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The Levinson-Durbin Algorithm The Yule-Walker equations in (14) provide a simple method to determine the AR coefﬁcients since only p equations need to be solved to obtain values for {a1 , a2 , . . . , ap }, and then the value of σ 2 can be computed by solving only one additional equation. Furthermore, in (14), the set of equations requiring the least number of lags of the autocorrelation functions is for k = 1, 2, . . . , p, and can be expressed in matrix format with σ 2 incorporated, to give: ⎤ ⎡ ⎤ ⎡ 2⎤ ⎡ 1 Rxx (0) Rxx (1) . . . Rxx (−p) σ ⎢ ⎥ ⎢ ⎥ ⎢ Rxx (−1) Rxx (0) ⎥ a . . . R (−p + 1) 0 xx ⎥ ⎢ 1⎥ ⎢ ⎥ ⎢ (15) ⎥ ⎢ .. ⎥ = ⎢ .. ⎥ ⎢ .. .. .. ⎦ ⎣. ⎦ ⎣. ⎦ ⎣. . . ap Rxx (p) Rxx (p − 1) . . . Rxx (0) 0 from which the AR parameters and σ 2 can be calculated [42,46]. The Levinson-Durbin algorithm is an efﬁcient technique for solving equation (15) and allows interpretation of some fundamental properties of the AR process [42,47]. The algorithm recursively computes the AR parameters in sets with increasing order number p to give {a11 , σ12 }, {a21 , a22 , σ22 }, . . . , {ap1 , ap2 , . . . , app , σp2 }. Since order is not known a priori, the algorithm can be used to generate successively higher order AR models, until the error σp2 is reduced to a desirable level. This level is selected when, in the recursive algorithm, variance of the excitation noise (σ 2 ) is constant for a model order equal to or greater than a suitable order of the AR process [42,47]. Additionally, it has been noted that due to diffuse scattering of sound in highly heterogeneous tissue, some noise components in the backscatter might be of importance for tissue characterization. Therefore, one can examine the trend in the decrease of σ 2 for increasing model orders and estimate a suitable model order such that the value of σ 2 reaches a plateau [48]. Other Techniques for Order Determination There are a few criteria commonly used in literature to determine the order of an AR model [43,45]. All of these use the MSE in addition to a cost function. The MSE decreases while the cost function increases with increasing model order. Thus when the two are combined, the overall criteria exhibits a minimum at a particular order number, which is assumed to be an acceptable order for the process. For example: +p+1 2 • Final Prediction Error (FPE) = N N −p−1 σ (p) where N is the data length in the window of analysis. The AR order is selected such that the FPE is a minimum. • Akaike’s Information Criterion (AIC) = N ln[σ (p)2 ] + 2p, which was interpreted by Kay and Marple [42]. The second term in the equation above represents the penalty for using higher orders that do not reduce the prediction error variance substantially. However, AIC could be statistically inconsistent in some cases since the probability of error in choosing the correct order does not converge to 0 as N 6 4 [43]. • Minimum Description Length (MDL) = N ln[σ (p)2 ] + p ln N, is a variation of AIC, and the second term here (p ln N ) increases both with N and with p. Hence,

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it provides statistical consistency to the outcome that can be lacking with use of the AIC method [43]. Other techniques used for order determination (ﬁrst zero crossing, residual variance, criterion autoregressive transfer function) are built on principles similar to the three mentioned above. However, most of these techniques are known to underestimate the order of AR processes of short record lengths and are not used in our research [43]. Statistical Classiﬁcation Trees Tree-based modeling or classiﬁcation is an exploratory technique of data-mining for discovering structure in data and can be used to devise prediction rules from multivariate data. Classiﬁcation trees comprise a collection of such prediction rules that are determined by a procedure called recursive partitioning. At each node in a tree, unclassiﬁed data are separated based on one variable (spectral parameter) that displays maximum separation at the 95% conﬁdence level. Various criteria may be used for the split at each node [49]. The Classiﬁcation and Regression Trees (CART) procedure was described initially by Breiman et al. [50], and has been used signiﬁcantly since then [49]. CART is based on the notion of ‘node impurity,’ splitting data at each node into two classes. The decrease in impurity of data at each node is thus used as the measure for making a split. CART recovers the ‘maximal binary tree,’ which has very few cases (ROIs) in the most homogeneous terminal nodes. This is done by one split using deviance as the criteria, and then an‘honest size tree’ is computed by pruning via ten-fold cross-validation [49,51]. The data splitting criteria, based on node impurity, uses the ‘Gini index of heterogeneity,’ deﬁned by Mola and Siciliano as: i(t) = 1 −

J

Pt2 (j )

(16)

j =1

where, Pt (j ) is the proportion of all cases in class j at a node [49]. The impurity measures at sub-nodes from i(t) are then subtracted from the Gini index to obtain the ‘decrease in impurity.’ The best split is that which maximizes this decrease. It was recently concluded in a study that classiﬁcation trees would be well suited for medical data (with multiple outcomes), and that they have the best combinations of error rates and computational efﬁciency [51]. At each pass in a tree, unclassiﬁed data are separated based on one spectral parameter. The split results in two groups, which are internally most homogeneous and externally most heterogeneous. Studies have proven the advantage of these trees in plaque characterization as opposed to analyzing the separation of data by linear regression techniques [52,53]. The classiﬁcation trees are typically built with 75% of the data and then cross-validated by resolving the type of plaque in the remaining 25% of the test data. The outcomes of these predictions are compared to the known pathologies for each ROI to obtain the corresponding sensitivity and speciﬁcity of the classiﬁcation: Sensitivity =

True Positive Decisions Decisions Actually Positive

(17)

Speciﬁcity =

True Negative Decisions . Decisions Actually Negative

(18)

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Recently, classiﬁcation results were reported for a database of 88 plaque sections from 51 ex vivo human left anterior descending coronary arteries imaged with 30 MHz central frequency IVUS [53]. In this database, ROIs were selected from corresponding histology sections for ﬁbrous (n = 101), ﬁbro-lipidic (n = 56), calciﬁed (n = 50) and necrotic-core (n = 70) areas. The tree calculated from the AR tissue spectra classiﬁed ﬁbrous, ﬁbro-lipidic, calciﬁed and calciﬁed-necrotic regions with high predictive accuracies of 90.4%, 92.8%, 90.9% and 89.5%, respectively for the training data and 79.7%, 81.2%, 92.8% and 85.5%, respectively for the test data. The corresponding results for the tree with the Welch PSD were 88.9%, 92.3%, 91.8%, and 86.5% for training and 66.7%, 76.8%, 82.6% and 72.5% for test data, respectively. Predictive accuracy can be calculated by combining the sensitivity and speciﬁcity for a test outcome. It is the sum of all correct decisions divided by the total number of decisions. The test data results clearly demonstrate how the AR analysis is better suited to IVUS RF data. In another study, we optimized the AR models by regularizing the estimates so that the pseudo-histology tissue maps were of increased spatial accuracy [48]. The techniques developed here have been implemented in custom built software [54].

In Vivo Plaque Characterization The previous sections of this chapter have examined how spectral analysis can be used to extract tissue related information from IVUS RF backscattered data. An outline of the procedure we developed is: • acquire ex vivo IVUS data and the corresponding histology which is the goldstandard, • select homogeneous ROIs on the histology representing a particular plaque component and ﬁnd the matching RF data from those ROIs in the IVUS data (we have developed software for quantitative and accurate ROI selection) [52], • calculate and normalize the spectra from the ROIs with appropriate AR models followed by estimation of eight spectral parameters, • develop non-linear regression (or classiﬁcation) trees with multiple spectral and depth related parameters, and • ﬁnally implement the trees in software for automated classiﬁcation of in vivo data. Figure 9 displays an example IVUS image with corresponding histology and the calculated color tissue-map. The analysis software is currently undergoing clinical evaluation at various sites. A custom designed ECG-gated RF data acquisition system is used for acquiring clinical IVUS pullback data. The electronics monitor the patient’s ECG signal and trigger the analog-to-digital converter card to acquire A-scans representing an IVUS image when the peak of an R-wave is detected [54]. The software also incorporates semi-automated three-dimensional segmentation of the lumen-plaque and media-adventitia interfaces after IVUS image reconstruction. These techniques involve a combination of spectral parameters and active contour models and have been extensively validated on clinical data [55,56]. Brieﬂy, a surface template is built automatically via a two-dimensional automated edge-detection algorithm and by preliminary assessment of spectral content of plaque versus blood. The surface is warped, under the inﬂuences of forces based on the

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Figure 9. Plaque characterization with intravascular ultrasound (IVUS) backscatter. A) An IVUS gray-scale image reconstructed from IVUS radio-frequency signals, B) predicted tissue-map of the plaque after segmentation, and C) the corresponding MOVAT pentachrome stain histology section (gold-standard). The presence of calcium is apparent in the IVUS image, due to the high echogenicity and the shadow behind. No conclusion can be made regarding the rest of the plaque from the IVUS image. However, the color-coded tissue map (gray = media; green = ﬁbrous; yellow = ﬁbro-lipidic; white = calcium; and red = lipid/necrotic core) illustrates the plaque components well in comparison to the true histology (green = ﬁbrous; red = ﬁbrin, muscle; black = nuclei and elastin ﬁbers; bluish-purple stain = calcium).

Figure 10. Example intravascular ultrasound images with (A) reconstructed and scan-converted image; (B) same image with segmented borders and (C) three-dimensional reconstruction of the vessel with the luminal (light blue) and medial-adventitial (dark blue) borders.

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Figure 11. Three-dimensional surface rendering of Virtual Histology™with intravascular ultrasound (IVUS) pullback data in a human coronary artery. The plaque composition is depicted in color on the luminal surface of a human left anterior descending coronary artery, over a length of 56 mm. Green is ﬁbrous tissue, yellow is ﬁbro-lipidic, red is lipid/necrotic core and white represents calciﬁcations.

image data and the continuity of the surface model until it converges on the borders of interest [55]. Both the lumen-plaque and media-adventitia borders are thus detected and are illustrated in an example in Fig. 10. A volumetric data set of histologic composition is hence available by applying the above principles to the RF data from each end-diastolic image in the sequences resulting from the ECG-gated pullbacks. After plaque segmentation, the lumen surface can be color-coded according to the histologic components, allowing a unique ﬂy-through visualization of the inside of the coronary lumen, where the color of the inside of the arterial wall denotes the most superﬁcial histologic feature (see Fig. 11). The volumetric data-set also provides quantitative assessment of both arterial geometry and composition [54]. Plots of lumen, vessel and plaque cross-sectional area versus image slice number can be created for geometric assessment and identiﬁcation of positive remodeling. Also, the characterized plaques can be subdivided into areas of histologic components and plotted versus image slice number, creating a volumetric assessment of plaque composition which was previously unavailable (see Fig. 12). The system has signiﬁcant clinical potential since it has the ability to provide analyzed volumetric IVUS RF data. Increasing evidence has shown that positive remodeling and plaque composition are two factors related to the likelihood of acute coronary syndromes, both of which can be detected by the software described above [7]. Also, ex vivo studies on human coronary arteries have demonstrated that positively remodeled plaques have greater lipid content, inﬂammation and macrophage count than plaques that do not exhibit positive remodeling [8]. Hence, the analysis of three-dimensional plaque composition and geometry has the unique potential for identiﬁcation of vulnerable plaques. Further, these tools could help elucidate relationship of plaque vulnerability with geometry in vivo, potentially providing insights into plaque rupture that were previously un-

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Figure 12. An example output from the custom-engineered software for quantitative analysis of plaque components along the length of an artery.

available, in addition to the potential usage in the clinical monitoring of plaque burden over time.

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Plaque Imaging: Pixel to Molecular Level J.S. Suri et al. (Eds.) IOS Press, 2005 © 2005 The authors. All rights reserved.

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Coronary Plaque Analysis by Multimodality Fusion Andreas WAHLE 1 and Milan SONKA The University of Iowa Electrical and Computer Engineering Abstract. Imaging of the coronary arteries is usually performed by X-ray contrast angiography or intravascular ultrasound (IVUS). Angiography provides information about the vessel lumen and its geometry. IVUS offers more detailed information that also includes the vascular wall. The chapter describes these two imaging modalities and their geometrically correct fusion yielding a 3-D and/or 4-D representation of the coronary geometry and morphology. The image-derived information is used for assessment of coronary function and plaque severity, blood ﬂow related indices are determined using computational ﬂuid dynamics. Detailed description of the methodology is followed by validation and clinical studies. Keywords. Cardiovascular disease, coronary arteries, hemodynamics, vascular morphology, data fusion, biplane angiography, intravascular ultrasound

1. Introduction Coronary atherosclerosis remains a major cause of death in the U.S. [6] and other industrialized countries. Treatment of local coronary artery stenoses usually involves dilatation of the vessel lumen by percutaneous transluminal coronary angioplasty (PTCA) and stent placement [7]. In this procedure, a stainless steel stent mounted on an angioplasty balloon is inserted into the vessel lumen and inﬂated, thus widening the obstructed area by compressing plaque and expanding the media-adventitial border. Despite a successful initial procedure, 20–30% of patients return with clinical symptoms and sequelae due to neointimal formation with a previously placed stent, resulting in in-stent restenosis [8]. As one option to reduce the incidence of repeat restenosis, intravascular brachytherapy with either beta (β) or gamma (γ ) radiation has shown to be effective after repeat balloon dilation [9–11]. Despite coronary interventions being routine procedures, understanding the mechanisms of plaque development in coronary arteries and the role of hemodynamics and vessel geometry is of utmost importance to predict areas of future plaque development. It has been shown that plaque development depends on the vessel geometry [12]. The vessel geometry has an impact on the coronary hemodynamics, thus a number of 1 Corresponding Author: Andreas Wahle, The University of Iowa, Department of Electrical and Computer Engineering, 3320 Seamans Center, Iowa City, IA 52242, U.S.A. Tel.: +1 319 384 0773; Fax: +1 319 335 6028; E-mail: [email protected]; parts of this chapter were reprinted with permission from [1–5].

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(a)

(b)

(c)

(d)

Figure 1. Development and treatment of a stenosis: (a) normal vessel; (b) outward remodeling; (c) lumen narrowing; (d) after PTCA and stenting, the lumen has been restored, plaque either redistributed or compressed.

experimental and computational simulation studies have been reported on the ﬂuid mechanics in arteries [13,14]. In turn, the wall shear stress induces a reaction of the endothelial layer, thus causing remodeling [15]. Figure 1 illustrates the process from diffuse accumulation of plaque over compensatory remodeling (i.e., plaque accumulation without luminal narrowing) to the ﬁnal stenosis, and after treatment. For the beforementioned reasons, accurate assessments of stenoses and diffuse alterations are indispensable in diagnosis and treatment of coronary artery disease. For a number of decades, quantitative coronary analysis from selective contrast angiography (QCA) represented the state of the art in clinical applications. Several computer-based systems for quantiﬁcation of local lesions have been developed during this time and are still wide-spread in clinical use [7,16–21]. However, it became apparent that systems based on a single projection could not provide reliable data in the common cases of foreshortening or overlapping. Consequently, there was an extension from the projection-based 2-D measurements into the 3-D space. Spatial reconstructions from biplane angiograms evolved as important tools for morphological analyses of vessel trees in both coronary and cerebral domains [22–29]. From the known imaging geometry and based on the epipolar constraint, any point visible in both projections can be spatially reconstructed by retracing the projection rays back to the point of their intersection. High-level systems allow accurate volumetric measurements and an indirect assessment of diffuse alterations from the morphological relationships between the vessels within the arterial tree [30–32]. A major drawback of many of these systems is their assumption of elliptical cross-sections. Binary reconstruction methods, which allow the modeling of free-shaped contours from densitometric proﬁles, are well-established in ventricle analyses [33]. However, due to the limited resolution of angiography they are rarely used to assess smaller vessels like coronary or cerebral arteries [34–36]. As proposed in [37], the geometrically derived elliptical shape may serve as a basis for binary reconstruction methods to reﬁne the crosssectional contour. The major problem with X-ray angiography is its inherent inability to depict the plaque; only the contrast-ﬁlled lumen can be visualized. Thus, any data of plaque extent and progression has to be obtained indirectly from the vessel lumen [7,31,32].

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(1) (4)

(2)

(5)

(3)

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(a)

(b)

Figure 2. Intravascular ultrasound images of a patient’s right coronary artery with in-stent restenosis after PTCA and β-radiation treatment: (a) unstented vessel segment, (b) segment with stent; (1) media/adventitia interface, (2) lumen/plaque interface, (3) 2.9F imaging catheter, (4) stent struts, (5) plaque accumulation from in-stent restenosis, (6) plaque compressed during PTCA.

41RAO

35LAO

(a)

(b)

Figure 3. Biplane angiographic images in (a) right anterior oblique and (b) left anterior oblique views of the artery depicted in Fig. 2, showing the IVUS catheter before the pullback start.

Another modality, intravascular ultrasound (IVUS), was introduced carrying the promise to overcome the shortcomings of angiography. By inserting into the vessel a catheter with an ultrasonic transducer in its tip, the cross-sectional shape of the lumen can be visualized and quantiﬁed (Fig. 2), and the thickness and composition of the vessel wall and plaque can be determined [7,38–45]. Acquisitions in 3-D are possible by pulling the catheter tip back during imaging, thus generating a series of images at different locations (Fig. 3). A new problem arose: IVUS itself does not provide any information about the location of a speciﬁc image or about its spatial orientation. Common systems simply perform a straight stacking of adjacent frames, completely neglecting the inﬂuence of the vessel curvature (Fig. 4, see also [45–47]). This paper describes a comprehensive system for fusion of both modalities, i.e., combining the geometrical information as obtained from biplane angiography with the volumetric data derived from intravascular ultrasound. The catheter path is extracted and

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Compression

(a)

Expansion

Tortuous Vessel with Catheter

Axial Twisting

(b) Figure 4. Problems of the conventional reconstruction methods that use a straight stacking of the IVUS frames without consideration of the vessel curvature; (a) theory, (b) example of a longitudinal slice through the frame stack.

reconstructed from the biplane angiograms and used to map the IVUS images to their locations (Figs 5–7). Aside from the localization of the individual IVUS frames in 3-D, the estimation of their spatial orientations is of major importance. Examples of previous work performed in this area include Laban et al. [48], Evans et al. [49], Pellot et al. [50], and Shekhar et al. [51]. Our approach incorporates several well-established algorithms for vessel detection in angiograms, for geometrical 3-D reconstruction, and for IVUS segmentation. It includes a novel method for the estimation of the frame orientation, which ﬁrst determines the relative relations between adjacent IVUS frames and then optimizes the absolute orientation of the entire frame set.1 The methods have been validated in computer and phantom models, as well as in in-vitro studies. Figure 8 shows the processing steps for the angiographic images (described in Section 2) and the IVUS data (Section 3), which are performed in parallel. Their output is then used for the actual fusion process (Section 4). The in-vitro and in-vivo validation of the fusion system is described in Section 5, followed by a couple of application examples in Section 6. A brief discussion and conclusions are given at the end of this chapter.

1 Parts of the fusion methodology are protected by U.S. patent # 6,148,095.

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a)

325

b)

Figure 5. Biplane angiograms of a coronary artery in a cadaveric pig heart; (a) frontal and (b) lateral projections, with inserted IVUS catheter (arrows indicate the location of the transducer at the tip of catheter core).

Figure 6. Image fusion between angiography and IVUS facilitates a geometrically correct assignment of the IVUS images to the vessel segment in both 3-D locations and orientations.

#174

#63 #0

Figure 7. Result of the fusion between the IVUS set from Fig. 2 and the angiograms in Fig. 3 from a posterior view; some IVUS frames have been inserted for illustration of the mapping process (frame numbering in direction of the IVUS pullback).

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Angiography

Ultrasound

Angiogram Acquisition

IVUS Acquisition

Fusion Image Rectification Geometry Estimation

Extraction of Catheter Path 3-D Trajectory Reconstruction

Cross-Section Segmentation

3-D Matching of IVUS Frames

Estimation of Relative Twist 3-D Mapping of Contours

Estimation of Absolute Orient. Visualization or Quantification

Figure 8. Parallel processing pipelines of the angiograms and the IVUS images, followed by the steps of image fusion.

2. Biplane Angiography 2.1. Acquisition and Preprocessing The ﬁrst step in angiographic processing consists of the acquisition and digitization of the images. Many modern angiographic devices provide digital output in standardized formats, and the role of the 35 mm cine ﬁlm as major archiving medium diminishes. The DICOM standard2 provides the means for storage and interchange of the angiographic data [7]. It is well-known from conventional QCA that the imaging process introduces numerous geometrical distortions on angiograms which need to be rectiﬁed [19,53]. In addition, the elimination of distorting axial rotations and shifts is required for 3-D reconstruction purposes [54,55]. For more sophisticated diagnostics, e.g., volumetric measurements on the vessel lumen, the highest accuracy in image rectiﬁcation is required. For the fusion approach, we only need a 3-D description of the catheter path, while the cross-sectional data are obtained from IVUS. Since calibration procedures are mostly unacceptable in clinical routine, we are using an 8-point dewarping method that provides sufﬁcient accuracy without the need of separately imaging a rectiﬁcation grid [56]. The eight lead markers can simply be mounted on the image intensiﬁers and are visible in all angiograms (Fig. 9). 2 DICOM is the registered trademark of the National Electrical Manufacturers Association for its standards publications relating to digital communications of medical information [52].

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(a)

327

(b)

Figure 9. Original angiograms of the calibration ball in (a) frontal and (b) lateral projection; after dewarping of the images using the eight markers, the nails at the poles of the ball may be used for biplane calibration.

Z-Axis

Image Intensifier

n

tio

jec

Pro

Second Angle

Ax is

DI

Distances

First Angle

Origin

I

DS

X-Axis

Offset Iso Axis

X-Ray Source

Figure 10. The ﬁve degrees of freedom per X-ray system that have to be considered by the geometric model.

2.2. Geometry Estimation The exact assessment of the imaging geometry is essential for an accurate 3-D reconstruction from biplane angiograms. It is therefore necessary to have a precise description of the imaging geometry (Fig. 10). Two contradictory concepts of geometry estimation exist. Purely analytical methods calculate the imaging geometry directly from the gantry parameters [22,24]. On the other hand, purely empirical methods use phantoms with known locations of reference points or establish the geometry from the vessel system itself by following the branches [25,26]. While the analytical approach cannot

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consider the tolerances within a gantry system, the empirical approach is prone to errors from geometrically insufﬁcient or inaccurately identiﬁed reference points. A comprehensive hybrid approach exists that combines both the analytical assessment of the imaging geometry serving as an initial geometry estimate with the empirical method for reﬁning the initial geometry using a set of reference points [31,32]. To completely identify the imaging geometry for a biplane angiographic system using such a hybrid approach, the following parameters must be available for each angiographic image pair: the gantry type, the rotation and angulation angles, the size of the image intensiﬁers, as well as the distances from the X-ray focus to the image intensiﬁer entrance ﬁelds. The gantries are classiﬁed into three different motion patterns [22,32,57] for the determination of the correct gantry positioning according to rotation and angulation angles. The primary axis of a type I equipment is on the side of the patient, while it is along the patient axis for type II, and on top of the patient for type III. A typical example of a type I gantry is the B I A NGIOSKOP C from Siemens, consisting of a pair of C/L-arm combinations; for type II the PolyD IAGNOST C, a head-mounted parallelogram architecture, along with the L-ARC, a double C-arm mounted on the ceiling, from Philips; the lateral system of the Siemens HICOR is an example for type III and consists of a single C-arm mounted on the ceiling. For the measurement of absolute dimensions, a calibration object must be either available in the angiograms or imaged separately using the same gantry settings. For example, for phantom studies we use a wooden ball of known size (83.5 mm in diameter, Fig. 9) with two nails as markers. The outer tips of the nails provide a known distance in 3-D space and can thus be used for absolute calibration of the scene. In-vivo, catheter markers are preferred over the very common use of the catheter diameter, since they provide a larger calibration distance and are not inﬂuenced by contrast dye ﬁlling or differences in exposure parameters. Some catheters provide 2–3 markers in 20 mm distance along their distal end, thus allowing accurate calibration even if the catheter does not appear straight in the images. Comprehensive comparisons between 2-D and 3-D calibrations as well as the use of different calibration objects were presented in [32]. 2.2.1. Coordinate Systems Standard biplane angiographic equipment consists of two X-ray systems having a common coordinate system. The isocentric geometry model assumes a ﬁxed rotational origin of both systems, the isocenter [22]. Due to the inﬂuence of the gravitation and instabilities of the gantry itself, this assumption is idealistic. In practice, it cannot be assumed that the projection axes intersect at the isocenter, and the distance between the two projection axes must be considered in the geometric model (Fig. 10). Devices which combine both imaging systems in the same gantry (G-arm [29]) provide a better stability, but are restrictive in terms of imaging options. The fact of an uncertain isocenter lead to the introduction of the iso-axis geometry model [31,32]. Aside from the 3-D world and the 2-D image coordinate systems, for which the points are indicated as [xwc , ywc , zwc ] and [uic , vic ], respectively, an intermediate 3-D coordinate system [xxc , yxc , zxc ] can be deﬁned that is ﬁxed to the respective X-ray system. The zxc axis corresponds to the projection axis, while xxc and yxc deﬁne the orientation of the image plane. With these deﬁnitions, the projection of a point in 3-D to an image can be mathematically described, and vice versa the projection ray from an X-ray source A to any image point B determined:

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[xxc , yxc , zxc ] = [xwc , ywc , zwc ] + Ip · Rp [uic , vic ] = [xxc , yxc ] ·

DSp + DIp

329

(1)

sp · (DSp + zxc )

(2)

Ap = [ 0, 0, −DSp ]xc Bp (uic , vic ) = (uic · sp ), (vic · sp ), DIp xc

(3) (4)

The angulation is deﬁned by a rotation matrix R as derived in [32]. The gantry shifts result in a vector I perpendicular to the projection axis; their point of intersection deﬁnes the distances DS to the X-ray source and DI to the corresponding image intensiﬁer. The last parameter is the height s of the image intensiﬁer. For each projection p, a separate parameter set is given. 2.2.2. The Epipolar Constraint The concept of the epipolar constraint serves as the basis for the geometrical 3-D reconstruction of any given point identiﬁable in both 2-D views. While the imaging process results in unique projections of a point, the reverse is ambiguous. Due to the loss of one dimension, only one ray per projection can be reconstructed that traversed the object point during imaging. The ray q(t) with 0 ≤ t ≤ 1 of a projected point [u, v] in view p is then: qxc (tp , uic , vic ) = Ap + tp · Bp (uic , vic ) − Ap (5) qwc (tp , uic , vic ) = qxc (tp , uic , vic ) · R−1 p − Ip

(6)

This ambiguity can be solved as follows: For two projections, the set of points {A1 , A2 , B1 , B2 } deﬁnes a plane, the epipolar plane. The object point P must lie within this plane since there must be a solution for t1 and t2 that deﬁnes the same point, i.e., the intersection point of the two rays which is identical to P. It seems to be rather straightforward to solve the set of four equations, however, it usually happens that slight errors are introduced when ﬁnding the 3-D locations for Ap and Bp . The deﬁnition of a generalized intersection point is used to solve this problem [23,32,58]. For both projections, a point Qp on ray qp is searched, for which their distance is minimal. The weighted means of these points approximates the desired object point P as shown in Fig. 11. This reconstruction error can be used for the reﬁnement of the assumed imaging geometry. The set of parameters representing the gantry geometry is initialized with the data obtainable from the gantry settings; default values are assumed for unknown parameters. From a given set of reference points (e.g., branches or surgical clamps), the reconstruction errors are determined following the epipolar constraint and analyzed for systematics. Then, the parameter set is optimized to obtain the solution of minimum reconstruction error over all reference points in a least-square sense [31,32]. 2.3. 3-D Reconstruction of the IVUS Trajectory The angiograms show the IVUS transducer in its most distal location, i.e., immediately before the pullback starts. In the 2-D images, three points are marked: a uniquely identiﬁable reference point for the geometry reﬁnement, the distal location of the IVUS trans-

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X-Ray Sources A1

A2

Q2

P Q1 B2

B1

Image Intensifiers Figure 11. Theory of 3-D reconstruction of a point from its known locations in biplane angiograms using the generalized intersection point.

ducer (start point), and the vessel ostium (end point). Arbitrary intermediate points following the catheter between its endpoints are set for further guidance. The catheter is usually visible as a local maximum along the vessel proﬁles (Fig. 5) and can thus be extracted using common approaches of dynamic programming or heuristic graph search [59,60]. Our algorithm is based on dynamic programming and allows free manipulation of the regions of interest (ROIs), which are derived from Catmull-Rom splines [61] through the guide points. In the same process, the two edges of the vessel lumen outline are extracted as well, which serve as reference for establishment of the absolute frame orientation as presented in Section 4.3.4. While the start and end points each create only one ray per projection, the vessel segment they enclose creates intersecting ray bundles, where the corresponding ray pairs have to be found. A cost matrix is generated, which contains the distances of the rays for each pair (i, j ) of segment elements by calculating the minimum distances Q1 (i) − Q2 (j ). Parker et al. developed a method in which the elements are discretely assigned and reconstructed [62], which was further reﬁned by bilinear interpolation and for the application of restrains later [31,32,58]. Our algorithm works well even in difﬁcult orientations of the vessel [32,58]. However, while the initial algorithm that was developed for the reconstruction of entire vessel trees required a number of corresponding guide points uniquely identiﬁed in both angiograms (e.g., vessel branches), the input for this modiﬁed approach consists only of the two points. Thus, the algorithm had to be optimized to handle large vessel segments.

3. Intravascular Ultrasound 3.1. Acquisition and Preprocessing Currently, there are two major kinds of IVUS devices available, mechanically driven catheters and solid-state devices. Mechanically driven catheters consist of a ﬂexible sheath, a core which contains the transducer in its tip, and an external motor which ro-

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tates the core. Solid-state devices generate images from a transducer array and do not contain any moving parts. The sheathed design of mechanically driven catheters has the major advantage of a stable pullback path, since only the core is moving in the direction of the pullback and the sheath remains in its position. There are common artifacts associated with the mechanical devices, mostly caused by bending of the catheter or other types of friction [46,63,64]. One way to avoid these distortions is to place the motor close to the tip, thus reducing inﬂuences of the path between the imaging machine and the transducer [40]. Solid-state transducers can avoid distortions from friction effects almost completely, but lack the guiding sheath. To ensure a constant-speed pullback, automated devices are recommended. For in-vivo studies, ECG-gating and/or respiratory control is required as well [65]. 3.2. Segmentation A detailed overview of the common 2-D and 3-D segmentation and reconstruction systems was recently presented in [7]. Well-known approaches include the segmentation method of Herrington et al. [38] based on simulated annealing, and the 3-D segmentation of Li et al. [39], which performs longitudinal as well as cross-sectional semi-automatic contour detection based on a minimum cost algorithm. A validation of volumetric quantiﬁcations on straight vessels and a feasibility study of the latter algorithm in clinical applications were performed by von Birgelen et al. [42,43]. A recent review article on IVUS segmentation and quantitative evaluation can be found in [45]. We were initially using the well-validated segmentation algorithm previously described in [41,44], which is based on a graph-search approach within a given elliptical region of interest (ROI). This ROI is automatically adapted from frame to frame. Within each image, the contours indicating the lumen/plaque and media/adventitia borders. In addition, the plaque composition can be determined for extended analysis. The entire process is automated, except for the speciﬁcation of the ROI in the ﬁrst image, but may be interrupted and manually corrected at any stage. The segmented contour lists are kept in 2-D polar coordinates (v, φ). Over time, there has been an accumulation of both manually traced IVUS data sets and IVUS data sets that have been semi-automatically segmented with manual corrections applied. These data sets can be used to learn what pixels the human observer most often chooses for border pixels. Although the presence of noise, speckle, and artifacts tends to confuse automated methods, human tracers are still able to correctly segment the vast majority of images. This fact motivated the design of a cost function that consists of terms that were learned from experience, in addition to those that were derived analytically from the data being analyzed [66]. In order to perform this learning step, a window is passed over a set of training images. Within the window, a pattern is examined. For each pattern that contains a border pixel, the system increments an accumulator entry corresponding to that border pattern. An accumulator entry exists for every possible pattern, subject to normalization and quantization (to allow for image variation and memory conservation, respectively). Following this process, the accumulator can be thought of as containing the likelihood of each pattern being a border pattern. After the training stage is complete, the learned information can be used to score an image that is to be analyzed. In the same way that the accumulator was created in the training step, patterns are examined in the image. Then, a cost image is generated by

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assigning a likelihood value to the pixel based on the value found in the accumulator for the same pattern. This process results in costs for both the luminal and medial-adventitial borders. In effect, the process eliminates the need of deﬁning an initial region of interest (ROI) and also provides one term for a cost function that may be used for segmentation. This is similar to the process in which a human observer ﬁrst recognizes a scene (in this case an IVUS image) and then directs his or her attention to the important region in the image based on the image content. One may think of the scoring process described above as performing a process in which the automated segmentation system learns what the human observer deems as the most important region of the image and then directs its attention at that region. To use this scoring method to achieve a segmentation of an image, a multiresolution approach that also mimics human vision is employed. For example, in a picture of two people shaking hands, the attention of the human observer is ﬁrst drawn to the clasped hands in the image. The region of the hands has been recognized by the human as the most important region in this type of image after having seen similar scenes and having learned their content in prior experiences. In doing so, the eye works at a very low resolution. Once the observer’s concentration has ﬁxed on the hands, higher resolution information is included in the analysis of the scene and smaller eye movements move to investigate nearby features in high resolution. The automated system implements this approach by ﬁrst scoring a low resolution version of the image to be analyzed. Then, a dynamic programming routine ﬁnds the optimal luminal and medial-adventitial borders based on the assigned likelihoods. Next, the borders are used to guide the search in a higher resolution image. The search space is reduced as the resolution increases, in a manner consistent with how human eye movements decrease as they process images in higher resolution. The higher resolution image is rescored as before, and image features such as edge strength and the presence of ultrasound echoes are included in the cost function. This process is repeated over a number of images (in practice 4 different resolutions were used) until the highest (original) image resolution is reached and segmented (Fig. 12).

4. Fusion of Angiography and IVUS 4.1. Outline of the Fusion Process It is a well-known problem that the conventional straight stacking of the IVUS pixel and segmentation data does not deliver geometrically correct results [45–47]. Thus, this approach is not acceptable for the complex analyses presented later in this chapter. Figure 4 shows the typical effects of the stacking: Due to neglecting the vessel curvature, portions of the vessel volume may be either over- or underestimated, depending on which side of the vessel they are located; since the vessel torsion is not considered, the axial rotation (twist) of the catheter leads to a wrong relation of radial segments between different images. As shown in Section 4.3.1, curvature and torsion of an idealized catheter can be expressed using the Frenet-Serret formulas, and are a function of the pullback path of the transducer. The vessel course is determined from the biplane angiograms, thus for each IVUS frame, its location can be determined. It must be kept in mind that the course of the catheter is not identical with the course of the vessel [67], but the correct assignment of

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Figure 12. Result of the border detection in two patient in-vivo IVUS images; the lumen/plaque and media/adventitia borders have been correctly identiﬁed with the fully automated segmentation approach, except for a few localized mismatches.

the IVUS data in 3-D yields correct results even if the frames are oblique to the vessel. Since a constant angiographic supervision of the pullback as proposed in [49–51] may not be applicable in clinical cases, the location of a speciﬁc frame is directly determined from its time-stamp and the pullback speed. The estimation of the absolute orientation of the IVUS frames in 3-D is a challenging problem. While Evans et al. [49] neglected axial catheter rotations completely, the iterative methods of Pellot et al. [50] and Shekhar et al. [51] both used a local match of each individual IVUS frame with the angiographic outline. Pellot, however, reﬁned the preliminary contour by using the densitometric proﬁles and a-priori information as input for a combination of Markov random ﬁelds and adapted simulated annealing [37,50]. In contrast to determining the orientation individually for each frame, constraints from the Frenet-Serret formulas can be used to determine the twist between the frames. Laban et al. [48] implemented the Frenet-Serret formulas directly, using a Fourier function to approximate the catheter path. This function satisﬁed the requirement of a third-order derivative as implied by the rules. However, the Frenet-Serret formulas can only deliver the relations between adjacent images relative to each other. What remains to be determined is the absolute orientation of the set of frames, which Laban performed iteratively by backprojection of the segmented contours and visual matching of the IVUS data in the angiograms.

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We have developed a non-iterative approach for the determination of the absolute orientation, which combines the analytical calculation of the catheter twist based upon the Frenet-Serret formulas with a global optimization of the absolute frame orientation over the entire frame set. 4.2. Localization of IVUS Frames on 3-D Path Our approach uses the length determination as described in [31,32] for assigning the IVUS frames along the catheter path. In contrast to a vessel, which is of variable diameter and stiffness, the catheter has constant physical properties, which simplify the length measurement. An arbitrary downsampling rate can be speciﬁed, resulting in the assignment of a ﬁxed number of images per millimeter pullback. In the current version, a constant pullback speed is assumed, since landmarks for synchronization are frequently not available or may be unreliable [56]. If such landmarks (e.g. clips) are available, the speed between adjacent synchronization points is assumed to be constant. For the invivo case, ECG-gated image acquisition in combination with a constant pullback have to be synchronized with the heart phase, which is subject to certain variabilities. Thus, the acquired frames would no longer be equidistant. This has actually been observed in the in-vivo patient data acquired thus far; even in patients with normal heart rhythm, the heart rate may ﬂuctuate over the pullback time of up to 4 min. Therefore, our algorithm is currently being extended to consider non-uniform distances between adjacent frames. 4.3. Catheter Curvature and Torsion 4.3.1. The Frenet-Serret Formulas According to a fundamental theorem of differential geometry, a space curve with nonzero curvature is determined up to an Euclidean transformation by its curvature and torsion [68]. Let c : [0, 1] → R3 , c(s) = [x(s), y(s), z(s)] be the pullback path of the transducer as a function of the arc length s. The local behavior of the space curve c may be described by the Frenet frame, a righthanded trihedron of three orthonormal vectors t (tangent), n (normal), and b (binormal). The Frenet-Serret formulas express the local change of the Frenet frame in terms of the frame itself: t (s) = +κ(s) n(s)

(7)

n (s) = −κ(s) t(s) + τ (s) b(s)

(8)

b (s) = −τ (s) n(s)

(9)

where the prime denotes the derivative with respect to arc length s. The curvature κ and respectively, as the Frenet the torsion τ are the angular velocities of the vectors t and b, frame is moved along c according to s. They calculate to: + + (10) κ(s) = + c (s) + 2 τ (s) = det c (s), c (s), c (s) κ 2 (s) (11) Based upon this theory, we have developed an analytical catheter model as well as a sequential triangulation method for determination of catheter curvature and torsion during the pullback.

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t i /2

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Ci

−ωi Ci - 1

+ωi t i /2

ϑi

Figure 13. Deﬁnition of the generalized torsion-free joint with three degrees of freedom.

4.3.2. Analytical Model of the Catheter The behavior of an imaging catheter was estimated analytically, resulting in the following geometrical model: We assume that the catheter consists of a chain of generalized joints, which are torsion-free (i.e., do not introduce any other axial rotation on bending than speciﬁed by the Frenet-Serret formulas). Each joint performs a relative transformation, resulting in an absolute position and orientation after applying all transformations on an initial position of the transducer. Furthermore, some constraints are given. The imaged frame is always perpendicular to the catheter axis, and the initial axial orientation is ﬁxed (i.e., no axial twist is applied). Thus, three parameters are given for each of these joints. The length t describes the distance of the end-points when the joint is straight, an angle ϑ gives the amount of bending at this joint, and a second angle ω speciﬁes the axis of rotation. A non-discrete version of this model can be derived for t → 0, yielding an inﬁnite number of joints within the chain. As shown in Fig. 13, the catheter segment between two adjacent points Ci−1 and Ci can be described by the following transformations, considering that each point is associated with both location and orientation: 1. the previous location is translated by ti /2; 2. the orientation is axially rotated by +ωi ; 3. the orientation is rotated by ϑi around a ﬁxed axis local to the current orientation (i.e., the rotation axis was affected by the previous axial rotation); 4. the axial rotation is compensated by applying −ωi ; 5. the location is translated by another ti /2. Equations (12)–(14) show the resulting transformation matrices using homogeneous coordinates. 3x y z 4 , , (12) C0 = [x, y, z, h] = h h h Ci = Ci−1 · M(ϑi , ωi , ti ) = C0 ·

i 5

M(ϑj , ωj , tj )

j =1

(13)

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frame 0

frame 1

P1 n0

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α0

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n1

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n2 α2

P4

Figure 14. Sequential triangulation method for estimation of the relative catheter twist.

M(ϑ, ω, t) = ⎡ ⎤ cos ϑ − sin ϑ sin ω − sin ϑ cos ω 0 ⎢ sin ϑ sin ω cos ϑ sin2 ω + cos2 ω (cos ϑ − 1) sin ω cos ω 0 ⎥ ⎥ ⎢ ⎣ sin ϑ cos ω (cos ϑ − 1) sin ω cos ω cos ϑ cos2 ω + sin2 ω 0 ⎦ t − 2t sin ϑ sin ω − 2t sin ϑ cos ω 1 2 (cos ϑ + 1)

(14)

The local curvature κi in joint i is directly related to ϑi , while the local torsion τi depends on the difference ωi between bending directions ωi and ωi−1 of adjacent joints. 4.3.3. Estimation of the Relative Twist In accordance with the catheter model described in the previous section, a sequential triangulation method is used to determine the relative twist between adjacent IVUS frames (Fig. 14). This can be considered as a discrete approximation of the Frenet-Serret formulas where the local torsion τi is calculated as the angle between the normal vectors of two adjacent triangles in the reconstructed pullback polygon. Each frame is deﬁned by the location of its center and a local 2-D coordinate system. For time instances i and i +1, both frames are located halfway between three consecutive points Pi , Pi+1 , Pi+2 so that: Si = (Pi + Pi+1 )/2

(15)

Si+1 = (Pi+1 + Pi+2 )/2

(16)

The frames are perpendicular to the tangent vectors: ti = Pi+1 − Pi

(17)

ti+1 = Pi+2 − Pi+1

(18)

The center of the circumscribed circle of the triangle as deﬁned by: Ti = (Pi , Pi+1 , Pi+2 )

(19)

is determined as the intersection of the perpendicular bisectors of the tangent vectors ti and ti+1 . The orientation of frame i + 1 is determined by rotating frame i by the enclosed angle αi (which reﬂects the local curvature κi ) around the normal vector: ni = ti × ti+1

(20)

of the triangle Ti . Finally, the center of frame i + 1 is shifted to point Si+1 . In the special case of the collinearity of (Pi , Pi+1 , Pi+2 ), the circle has an inﬁnite radius, i.e., κi = 0, and thus no twisting takes place.

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Vessel Lumen

Sheath Transducer IVUS Frames

Figure 15. Bending of the imaging catheter within the vessel due to vessel curvature, seeking position of minimum energy, and associated out-of-center position in IVUS images. First Frame with Axes

Catheter Path

Reference Plane

Figure 16. Reference plane for speciﬁcation of the initial orientation; the horizontal axis of the ﬁrst IVUS frame is aligned parallel to the plane.

4.3.4. Estimation of the Absolute Orientation After establishing the relative orientation changes between the frames, the absolute orientation in 3-D remains ambiguous. This problem is comparable to ﬁtting a sock on a leg [48]: While the leg (catheter path) is stable, the sock (axial orientation of the frame set, while retaining the known spatial relationships between adjacent frames) can be freely rotated around the leg, but ﬁts optimally only in one orientation. Our method uses the bending behavior of the imaging catheter as a reference, which is expected to fall in the position of minimum energy within the vessel [67]. This results in an out-of-center position of the catheter relative to the inner lumen, which is visible in both angiographic and IVUS data (Fig. 15). Based on this out-of-center position, a correction angle can be calculated. First, the segmented IVUS lumen contour is mapped into 3-D using an initial orientation. In general, this initial orientation is arbitrary. However, to ensure a well-deﬁned orientation to begin from, the uic axis of the ﬁrst frame is aligned with a reference plane (Fig. 16). This plane is generated by bilinear regression from the catheter path data and is thus the plane of best approximation in a least square sense. For each frame location, the angiographic outline is reconstructed as an elliptical contour as described in [31,32], and mapped onto the IVUS frame at the respective transducer location (Fig. 17). For both angiographic and IVUS outlines, 3-D out-of-center vectors are generated from the contour center to the catheter position: = pcath − pcenter a

(21)

= mcath − mcentroid v

(22)

is derived from the angiographic reconstruction of the catheter point pcath and where a is derived from the mapped IVUS frame center mcath the ellipse center pcenter , and v

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IVUS Frame with Contour

μ

Centroid

Cath

ϕ

Center Angiographic Outline

Figure 17. Out-of-center strength μ and error angle ϕ for estimation of the absolute orientation.

indicating the catheter location and the centroid mcentroid of the contour. For each frame i, the out-of-center strength μi and a signed error angle ϕi with respect to the initial orientation can be calculated: + + i+ (23) μi = + v i i , v ϕi = a (24) Within a moving window of arbitrary but ﬁxed width w, a statistical analysis is performed. For nf frames, nw = nf − (w − 1) window locations exist. For each window location k, the summed out-of-center strength μk , the weighted mean ϕ k , and the weighted standard deviation σ (ϕk ) of the difference angle are calculated: μk =

k+(w−1)

μi

(25)

i=k

1 ϕk = μk 1 σ (ϕk ) = μk 2

k+(w−1)

μi ϕi

(26)

2 μi ϕi − ϕ k

(27)

i=k k+(w−1) i=k

From these values, a reliability weight is calculated for each location of the moving window, giving higher weight to locations with high out-of-center strength (i.e., locations with increased signiﬁcance for the estimation of the correction angle), and limiting those with a high standard deviation of the difference angle function (i.e., locations showing distortions in either angiographic or IVUS lumen outlines): rk =

μk σ (ϕk )

(28)

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339

A single correction angle ϕ corr is determined and applied to all IVUS frames relative to the initial orientation: r =

n w −1

rk

(29)

k=0

ϕ corr =

nw −1 1 rk ϕ k r

(30)

k=0

4.4. 3-D Mapping of the IVUS Data The frames generated during the previous steps may be used in many ways: For a fast visualization, which does not even require a full segmentation of the IVUS data beyond the lumen borders, the pixel data are mapped into the frames; furthermore, the segmented contour and plaque composition information can be mapped into 3-D space as well by locating their corresponding pixels. The points of the segmented and mapped IVUS contours can be connected to a surface model by triangulation and then be displayed, e.g., by using the standardized Virtual Reality Modeling Language (VRML) with a respective viewer. A voxel cube of pre-deﬁned size can be generated and used as input for common volume-oriented systems. Therefore, the 3-D space is divided into cubic voxels. After assigning a speciﬁc IVUS pixel to its 2-D coordinates, and mapping into 3-D space, the corresponding voxel can be determined. Depending on the size of the cube, it may occur that two or more IVUS pixels share the same voxel, or that a single IVUS pixel extends over more than one voxel. The resolution of the voxel cube depends on several factors. The basic limitation is the resolution of the image data (both angiographic and IVUS), as well as the distance between the frames. Furthermore, the dimensions of the voxel cube are restricted by computer performance and memory. Typical sizes are 380×380×380 voxels, e.g., allowing a resolution around 150–180 μm for a curved vessel segment of 100–120 mm length, or of 50 μm for assessing a local lesion of 12–15 mm length. Since the conventionally used minimum-intensity projections (MIP) did no show adequate results for a direct rendering of the voxel cube, we developed the energy-complement projection as presented in [69].

5. Validation 5.1. Description of Validation Setups 5.1.1. Validations in Phantoms In a computer simulation, two helical pullbacks of two full revolutions were deﬁned by two concentric 3-D polygons within a unit cube of arbitrary units (a.u.). The number of line segments per polygon was varied between 8 and 128 to study the error introduced by sampling. Both helical pullbacks had the same displacement per revolution (0.4 a.u.), but one helix had twice the diameter (0.8 a.u.) of the other. The twist predicted by the laws of differential geometry served as an independent standard. The unit-speed helix

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35mm

35mm

10mm 10mm

15mm

20mm

20mm

15mm

Figure 18. Nail plate for veriﬁcation of unsystematic twists.

⎤ a cos sl β(s) = ⎣ a sin sl ⎦ b sl ⎡

with l =

a 2 + b2

(31)

(32)

has a constant torsion τ (s) = b/ l 2 , where 2a is the diameter of the helix, 2πb is the height per revolution and 2πl the arc length per revolution. Applied to the computersimulated pullbacks, this results in an overall torsion of 56.6◦ per revolution for the wide helix (0.8 a.u. diameter, 0.4 a.u. height/revol.) and 109.2◦ for the narrow helix (0.4 a.u. diameter, 0.4 a.u. height/revol.). To conﬁrm the twist behavior suggested by the computer simulation in an experimental setup, two helical vessel phantoms were built, details of which are described in [67]. An important test is the veriﬁcation of the assumption of a torsion-free catheter. If this assumption is correct, the orientation of the IVUS image should remain constant if the catheter is moved and bent within a stable plane. For this purpose, we supplied a wooden plate with guide nails (Fig. 18). Because the wood does not deliver a sufﬁcient ultrasonic echo, its top surface was covered with an aluminum foil. Furthermore, the plate was submerged in a water bath, and the path of the catheter between the motor unit and the beginning of the plate was ﬁxed during imaging. In this speciﬁc experiment, the pullback was performed with the automatic pullback device to eliminate any inﬂuence from the manual handling of the catheter. Three setups were imaged: (a) the catheter was straight along the plate, (b) the catheter was slightly bent over the upper restraint point, and (c) the catheter was bent in a double-S shape using the three lower nails. In each pullback, the axial rotations of the images were analyzed. 5.1.2. Cadaveric Pig Hearts The right coronary arteries of two fresh cadaveric pig hearts were supplied with eight straight clips each, allowing a proper identiﬁcation in both angiographic and IVUS images (Figs 19, 20). The vessels were catheterized and pressurized with 0.9% saline at about 100 mmHg. Each pig heart was immersed into a cylindrical container (100×200 mm), which was ﬁlled with water at body temperature. The IVUS catheter was inserted into the coronary artery and advanced into position under ﬂuoroscopic con-

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341

Vessel Pericardium Catheter

ak Pe

Myocardium

Clip

Figure 19. Generation of the echo caused by a paper clip.

(a)

(b)

(c)

Figure 20. Cadaveric pig heart with clips; (a) frontal and (b) lateral angiographic images, (c) IVUS image with peak.

trol with help of a guidewire, which was removed afterwards. Diluted contrast agent was injected into the coronary artery and biplane angiograms of the pig heart were recorded for 3–5 seconds on cine ﬁlm, showing the transducer in its distal location. The IVUS catheter was pulled back manually at approximately constant speed of 1.0 mm/s. Three pullbacks per heart were recorded over a length of 110–130 mm, resulting in approximately 3400 images per pullback. In one of the hearts, the most proximal clip could not be reached in two of three pullbacks and this marker was therefore discarded from the analysis. From the angiograms, both the catheter path and the catheter clips were reconstructed and retained in separate 3-D models. The clips were also used for the imaging geometry reﬁnement. For each clip, its closest distance to the catheter was determined in order to generate a 3-D vector indicating the expected orientation of the IVUS peak. Between adjacent clips, the actual pullback speed was estimated from the reconstruction and the IVUS time-stamps, and the location errors were corrected. The peaks were mapped into 3-D space in accordance with the calculated twist, and the angular errors between the mapped peaks and those previously reconstructed from the angiograms were calculated. The absolute orientation was corrected to minimize the mean angular error over all peaks within a pullback.

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In a third cadaveric pig heart without clips, the complete fusion was performed including IVUS segmentation (Figs 4b, 5). The absolute orientation was determined both interactively and by our algorithm. Afterwards, the resulting vessel surfaces as well as the catheter path were reprojected into the angiograms and visually compared with the lumen proﬁles. 5.1.3. In-Vivo Validation The accuracy of the prototypic fully automated IVUS segmentation system was validated by comparison to 10 manually-segmented IVUS pullbacks with a total of 1581 images. The automated segmentation results, prior to any manual editing, were then compared against the gold standard, i.e., the segmentations performed by an experienced observer. For the purpose of in-vivo validation of the overall fusion system, three patients with stable coronary artery disease undergoing coronary revascularization and stent placement in native coronary arteries were imaged as part of their clinical procedure [2]. The developed data fusion method was applied to vascular segments of interest in the left anterior descending, left circumﬂex, and right coronary arteries with 40, 64, and 77 mm in length, respectively. The angiograms were acquired at a biplane Siemens HICOR cath-lab with DICOM output on CD-R. IVUS imaging was performed after advancing the transducer 5 mm past the target segment into the distal vessel. The IVUS images were obtained using sheathed 2.9 F and 3.2 F 30 MHz catheters (Boston Scientiﬁc, San Jose, CA). The motorized pullback device was activated for 8 s (4 mm, speed 0.5 mm/s) to straighten the catheter core within the vessel. Two pairs of biplane angiograms were acquired in different angulations with the IVUS catheter inserted in the distal location. One of the angiographic pairs was used in the data fusion, the other pair was used for validation. Since no reliable independent standard exists for patients, only limited quantitative validation was possible in-vivo and results were mainly assessed qualitatively. 5.2. Validation Results 5.2.1. Validations in Phantoms In the analysis of the helical phantoms, the method overestimated the analytically derived torsion by less than 3% if the helices are approximated by polygons of 16 or more line segments per revolutions, and the overestimation is less than 1% for polygons with 24 or more line segments. As the catheter was pulled back in the actual helical phantoms, the IVUS image of the half tube and the cylinder wall rotated continuously in a clockwise direction as predicted by our catheter twist model for helical pullbacks. The measured catheter twist per revolution was overestimated by our catheter twist model by 9.1% for the short helix and 12.6% for the long helix; normalized by the length of the pullback the observed overestimation was 0.87% and 1.0% per cm, respectively [67]. In the phantom study using the nail plate, the catheter showed no signiﬁcant twisting (<3◦ ) during pullback in the straight setup. On slight curvature with weak restraint (approx. 32◦ around the upper nail), no effects caused by bending were detected. The axial orientation between images in the center of the segments proximal and distal to the nail differed by less than 1◦ . Thus, the catheter behaved as expected. However, when using the three lower nails and a stronger restraint, signiﬁcant twisting was observed. Figure 21 shows the echoes at the most proximal nail, where the catheter is bent by approx. 50◦ along a segment of 15 mm. Theoretically, the orienta-

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(a)

(b)

343

(c)

Figure 21. Distortions due to bending; IVUS images (a) 8 mm distal from, (b) closest to, and (c) 8 mm proximal from an outer nail.

tion of the echo should remain constant at all locations despite of the bending. In this extreme example, the echo covered a radial segment of 57◦ . The difference of the orientation between the distal and the proximal end-points of the curve was 9◦ , where the proximal echo moved counter-clockwise compared to the distal one. In addition to the clockwise rotation, non-uniform rotational distortions (NURDs) could be identiﬁed, indicating varying rotational velocity of the catheter core. The enclosed angle of the foil echoes left and right to the catheter should always be 180◦ . However, at the closest distance to the nail, the enclosed angle was as low as 115◦ . The mentioned effects could be measured at the other two nails as well, although in less strength (clockwise rotations of 42◦ at the distal and 19◦ at the center nail). For the NURD effects, the enclosed angle at the center nail was increased, while it was decreased at the outer nails. A further distortion could be recognized when saline was ﬂushed into the catheter. The short increase of the pressure within the catheter introduced a clockwise axial rotation by up to 70◦ during the ﬂush. 5.2.2. Clips Analysis All pullbacks were performed manually in the cadaveric pig hearts. From the 40 segments between adjacent clips over all three pullbacks in each heart, the real speed was calculated as 1.14 mm/s with a standard deviation of 0.34 mm/s, ranging 0.55–2.33 mm/s. For 45 clips, the orientations of the angiographically reconstructed peak vectors and those mapped from IVUS were compared. The RMS error of the predicted frame orientations over all six pullbacks was 21.96◦ with a standard deviation of 4.87◦ . In comparison, the mathematical analysis of the pullback trajectory revealed that the catheter was twisting up to 60◦ . After adjustment of the absolute orientation to minimize the overall mean matching error, and generation of the voxel cube, the visual results showed a good correspondence (Fig. 22). We performed further evaluations on this data set to identify the possible sources for the mapping errors. We compared the reproducibility of the manual pullbacks from the relative 2-D twist between images of adjacent clips, resulting in an acceptable RMS error of 5.01◦ over all 39 pairs. However, the maximum of 27.5◦ showed that local tolerances might be quite high. The major reasons for the remaining errors are most likely caused by the effects described in Section 5.2.1.

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a)

b)

Figure 22. Maximum intensity projections of the clips in (a) frontal and (b) lateral orientation, compare the reconstructions with the corresponding angiograms shown in Fig. 20a, b; the clip echoes have been enhanced in the IVUS images before reconstruction for better visibility.

5.2.3. Complete Fusion Cycle The reconstruction from the third pig heart showed a good performance for both angiographic and IVUS parts. The comparison of the projected segmentation results with the lumen proﬁles visible in the angiograms showed a good match. Slight tolerances could be identiﬁed, which were obviously caused by localization errors due to the manual pullback. Since these tolerances distorted the results of the absolute orientation determination, the erroneous segments were manually discarded. This caused a change of 33.6◦ in absolute frame orientation compared to the unmodiﬁed calculation. In result, there was no visible difference between the interactively matched and calculated frame orientation. 5.2.4. In-Vivo Validation In the 10 pullbacks used to validate the IVUS segmentation system, results show a mean border positioning error of 0.15 ± 0.16 mm for the luminal border and 0.11 ± 0.14 mm for the medial-adventitial border. The maximum error for both contours was 1.1 mm. Figure 12 shows two examples of IVUS frames with fully automated contours displayed. As can be seen, the contours were in general detected correctly, and only minor manual adjustments would have to be performed. In all three in-vivo cases used for validation of the overall fusion approach, our method successfully determined the geometrically correct coronary vessel representation. Figures 23–25 show the results for the left circumﬂex artery. For all data sets, VRML scenes were created (Fig. 25), 3-D data cubes were constructed and reprojected at angles corresponding to the second pair of biplane angiograms which were not used for data fusion (Fig. 24). The 2-D data were quantitatively analyzed to approximate the IVUS reconstruction accuracy by comparison of the ﬁnal result with the initial orientation of the IVUS frames. Fig. 24 shows the reconstructed 3-D cube and the functions for μ and ϕ as deﬁned in Eqs. (23)–(24), as well as the total reliability weight as deﬁned in Eq. (28), for the artery presented in Fig. 23. For this vessel, the analysis of the 2-D projections in frontal angulation showed a centerline mismatch in object level of 0.73 ± 0.35 mm (max. 1.5 mm) after establishing the absolute orientation, compared with 1.91 ± 0.90 mm (max. 3.6 mm) in the initial orientation.

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(a)

(b)

345

(c)

Figure 23. Angiograms of a left circumﬂex artery in a patient heart using (a) 30◦ right and (b) 60◦ left anterior oblique projections, with catheter inserted and the vessel lumen outline detected; (c) automated detection of the lumen border in one of the IVUS images; note the out-of-center position of the catheter.

(a)

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Figure 24. Frontal projection through the voxel cube with catheter centerline and detected plaque borders previously marked in the 2-D IVUS images; (a) in initial orientation of the frames; (b) after application of the absolute orientation algorithm; (c) independent angiogram in frontal projection for comparison; (d) length μ of the out-of-center vector for each IVUS image; (e) local correction angle ϕ determined from initial orientation; (f) resulting weighting function μk /σ (ϕk ) of the correction angles with a window width of 5 mm. Side branches were not included in the segmentation process, thus the vessel is modeled as a tube.

6. Clinical Applications and Results 6.1. 3-D vs. 4-D Modeling While the in-vitro applications presented thus far are all based on a static 3-D model, invivo modeling requires to also consider that the heart is in constant movement. Therefore, the 3-D model resulting from the fusion process needs to be extended into 4-D (specifically, 3-D plus time, where time relates to any given heart phase). The raw image data from angiography and IVUS can be split into n sets of different heart phases [0 · · · n−1], where the ECG signal is used to assign each angiogram or frame to its respective heart phase [70]. The complete in-vivo sequence of steps therefore reads as follows: 1. Acquire IVUS and angiographic data and sort them by the heart phase; 2. segment IVUS and angiographic data for the lumen and other features; 3. determine the 3-D location for each point of the vessel lumen in each considered heart phase;

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Figure 25. Interactive VRML visualization of the geometrically correct reconstructed vessel shown in Fig. 23.

4. use the fusion system to create a 3-D model for each heart phase; 5. if desired, interpolate intermediate heart phases using cubic splines. In general, the 4-D data set is created from the complete set of 3-D models. However, there are certain assumptions that can be made when reconstructing the same object over time that beneﬁt the process. The segmentation of the IVUS frames is done phase by phase; after all the regions of interests have been derived from one phase, they can be used as initial guess for the next phase, whose frames are basically next to the ones segmented before. Thus, only slight adjustments may be necessary, and the overall process of IVUS segmentation may be reduced substantially. A further aspect where the close relation between the phases beneﬁts the process is the determination of the absolute orientation. It can be assumed safely that, from phase to phase, only slight rotations of the overall frame set should occur; therefore, the parameters of the absolute orientation analysis over all phases can be utilized to tie the phases with each other. Since the initial orientation is derived from a reference plane determined by bilinear regression from the catheter path as described in Section 4.3.4, the initial orientations and therefore all correction angles are connected with each other across the phases. This results in a more stable statistical basis for determination of the correction angle. 6.2. Computational Hemodynamics From observations in curved-tube experiments [70] and the compensatory remodeling effects [15], it is commonly hypothesized that plaque accumulation is associated with locations of low wall shear stress along the boundaries of the vessel lumen. For our computational-ﬂuid dynamics (CFD) simulations of blood ﬂow through the coronary vessels, we employ a ﬁnite-volume CFD code (U2 RANS), which was developed at the University of Iowa, Iowa Institute of Hydraulic Research [71]. The U2 RANS code has the capability of simulating steady and unsteady laminar and turbulent ﬂows and allows speciﬁcation of moving boundaries as well as pre-speciﬁed arterial motion. Unstructured

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Figure 26. Extraction of the IVUS catheter path (dotted line) and the lumen from one of the angiograms used for the fusion process; the inset shows the tetrahedral mesh of the lumen after 3-D fusion.

tetrahedral meshes were employed to represent the lumen and created using a commercial grid generation software (Gambit 1.3.2, Fluent Inc., Lebanon NH, USA). Figure 26 shows an example of the mesh in the stenotic region of a right coronary artery, Fig. 27 the resulting shear-stress distribution. A validation of the CFD system was presented in [70]. To perform CFD in 4-D cases, thin-plate splines are used to interconnect the mesh points between the different heart phases. Since the CFD algorithm is beyond the scope of this chapter, the interested reader may look into the results, e.g.: of a reproducibility study published in [72], reporting a good correlation of multiple pullbacks in 10 coronary arteries (r > 0.91, p < 0.0001); and into the longitudinal studies reported in [73], in which plaque development was monitored over a period of six months in a limited set of patients. It could be shown that indeed there is a relationship between shear-stress distribution and the progression of plaque. Recent studies demonstrated that the compensatory enlargement (remodeling) of the artery also coincides with low shear stress, as long as no vessel narrowing occurs [74]. These results emphasize the importance of CFD simulations in coronary arteries. 6.3. Plaque Development and Vessel Geometry The CFD analyses described in Section 6.2 are computationally expensive, yet able to accurately consider the most complex vessel geometries. In a related study, we attempted to directly correlate circumferential plaque distribution with the geometry of the vessel [4]. As can be seen in Figs 28a, 28b, it is a common observation that plaque tends to accumulate on the inner bend of a curved vessel (inner curvature) rather than on the outer

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(a)

(b)

Figure 27. Result of the CFD simulation using the U2 RANS system: (a) color-coded visualization of the vessel shown in Fig. 26, where red color indicates high, and blue color low shear stress, (b) zooms into the stenotic region.

bend (outer curvature). Thus, our aim was to identify the frequency of vessel regions for which high plaque accumulation coincides with locations at the inner curvature of the vessel and vice versa. The plaque thickness is determined with respect to the vessel centerline as the distance between the two contours (Fig. 28c). We deﬁned a curvature index that combines the magnitude of the local curvature with the circumferential position of a speciﬁc contour point [4]: 1. determine the local curvature at each frame; 2. determine the curvature indices for each circumferential point within that frame. The local curvature of the frame is determined in analogy to the catheter twisting (Section 4.3.1) using the Frenet set of equations. Since vessel torsion is not considered here, we are mainly interested in the curvature κ and the direction of the curvature indicated by its normal n. With c(s) specifying the point [x(s), y(s), z(s)] of centerline c at location s, c (s) = t (s) = κ(s) n(s) + + κ(s) = + c (s) +

(33)

n(s) = c (s) / κ(s)

(35)

(34)

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(a)

(b)

(c)

(d)

(e)

Figure 28. Morphology/geometry analysis: (a) part of the original angiogram; (b) 3-D model in the same view, note that the left circumﬂex branch has not been modeled; (c) plaque distribution; (d) local curvature; (e) classiﬁcation results of the left anterior descending branch distal of the bifurcation.

The normal vector n(s) always points towards the origin of the radius of curvature, thus indicating the inner curvature on the circumference. Complementarily, κ(s) is a measure of the magnitude of the curvature. To combine the magnitude and direction of the curvature, thereby differentiating between inner and outer curvature, we deﬁned a scalar curvature index κidx (s, i) for each point i at the frame location s (Fig. 29a). A positive κidx (s, i) indicates inner curvature, a negative index outer curvature, and an index close to zero applies for points on the sides of the curved vessel segment, i.e., perpendicular to n(s). The maximum (most positive) curvature index and the minimum (most negative) curvature index depend directly on the magnitude of the curvature κ(s) for that frame. The circumferential position of the vertex point indicating the inner curvature is obtained by projecting the unit normal vector n(s) on the respective frame s. To determine the circumferential position of the i-th point relative to the inner curvature reference point, a vector v(s, i) is deﬁned from the centroid c(s) to the i-th point of the lumen contour f(s, i) of the IVUS frame at location s. Finally, κidx (s, i) can be obtained using the dot product: v(s, i) = f(s, i) − c(s) v(s, i) κidx (s, i) = κ(s) n(s) · v (s, i)

(36) (37)

A. Wahle and M. Sonka / Coronary Plaque Analysis by Multimodality Fusion

−κ

κidx = 0

n

0

Ratio (r) of Rai +Rbo

350

Curvature Threshold (T ) [◦ /cm]

+κ (a)

(b)

Figure 29. (a) deﬁnition of the circumferential curvature index κidx derived from the local curvature κ and the projected normal vector n for a speciﬁc IVUS frame; (b) with increasing curvature threshold T , ratio r of vertices for which the hypothesis holds increases as well; the standard deviation (bars) also increases with T .

Figure 28d shows the resulting curvature indices in red for κidx (s, i) > 0 and blue for κidx (s, i) < 0. To categorize each vertex point according to its respective plaque thickness and curvature index, four regions Rxy were deﬁned. The subscript x distinguishes between a (“above average”) and b (“below average”) for the relative plaque thickness, whereas y is set to i (“inner curvature”) for κidx (s, i) ≥ 0 and to o (“outer curvature”) for κidx (s, i) < 0. Thus, four regions Rai , Rao , Rbi , and Rbo are obtained. It is also necessary to deﬁne a ﬁfth region Rn for “neutral” to indicate regions of low curvature that are excluded to prevent incorporating small perturbations in the results. A vertex point is categorized as Rn if its curvature index is below a speciﬁed curvature threshold T (i.e., |κidx (s, i)| < T ). Figure 28e shows the resulting regions of the segment distal to the branch: Red color combines inner curvature with above-average circumferential plaque distribution (Rai ), and blue color combines outer curvature with below-average plaque accumulation (Rbo ), thus in accordance with the observation. Yellow (Rbi ) and magenta (Rao ) are the respective opposite regions, and green marks areas of Rn excluded due to low local curvature. Satisfying the inequality Rai + Rbo ≥ Rao + Rbi indicates that more plaque is accumulating along the inner curvature as compared to the outer curvature, thus supporting the hypothesis that plaque accumulation is circumferentially higher at the inner curvature. This can also be expressed as a ratio r=

Rai + Rbo Rai + Rao + Rbi + Rbo

(38)

with r ≥ 0.5 implying that the hypothesis holds. The analysis was performed on 39 in-vivo pullbacks in 37 human coronary vessel segments from 31 patients that were routinely imaged at the University of Iowa Hospitals and Clinics or Brigham & Women’s Hospital. The fusion process described in Section 4 was performed for 14 right coronary arteries, 13 left anterior descending arteries, and 10 left circumﬂex arteries, with pullback lengths ranging from 41.9 mm to 122.5 mm. The ratio r was determined for 12 different curvature thresholds T , which were empirically selected as a function of the maximum curvature over all pullbacks. Thus, 468 rvalues were calculated in total. Over 39 pullbacks, 10.2% (for T = 2.31◦ /cm) to 78.3% (for T = 22.94◦ /cm) of the vertex points were excluded and assigned to the region Rn .

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Furthermore, vessel portions located in branches, or areas for which strong calciﬁcations or dense plaque prevented an accurate segmentation of the borders, were excluded from the analysis. Separate sets of calculations were performed, in which stented areas were either included in or excluded from the analysis. The hypothesis held for r ≥ 0.5 in 367 (78.4%) of the 468 calculations with stented areas included, and in 349 (74.6%) of 468 calculations with stented areas excluded. In 29 of 37 vessel segments, the hypothesis held for at least half of the thresholds (i.e., r ≥ 0.5 was true for at least 6 of the 12 T -values for each of these vessel segments). In 6 of 37 vessel segments (16.2%), r ≥ 0.5 was not satisﬁed for any threshold T . Consistently, r ≥ 0.5 held for the averages over all vessel segments, which is statistically signiﬁcant for all T (p < 0.001), and r increased along with T (Fig. 29b). Another observation is that the standard deviation of r over all 39 pullbacks increased from 0.109 (T = 2.31◦ /cm) to 0.183 (T = 22.94◦ /cm, with stents), in accordance with the observation that r frequently decreases with increasing T in segments with overall low r-ratios. The comparison of the r-value distribution in calculations that included stented areas vs. those in which stented areas were excluded showed no statistical difference (p > 0.20 for T ≥ 6.86◦ /cm). 6.4. Simulation of Interventional Procedures As mentioned in the introduction to this chapter, in-stent restenosis is a major factor in 20–30% of patients returning with clinical symptoms after a successful initial procedure. Intravascular brachytherapy is conventionally used to reduce the risk of repeat restenosis. A comprehensive tutorial-style review can be found in [75]. The typical approach involves a catheter that is delivered to the treatment site within the stented region. A train of β-seeds or a γ -wire is sent to the treatment site, where it dwells for a calculated period of time, before it is retracted and the catheter withdrawn. The radiation dose diminishes as a function of distance from the source train [76,77]. Towards both ends of the source train, fall-off zones are present where subtherapeutic doses may be delivered. The studies described here are based on the Novoste Beta-Cath system utilizing the Strontium/Yttrium (90 Sr/Y) β-isotope. In a 30–40 mm train, 12–16 sealed radiation sources are provided. The application time is usually determined from source activity and the angiographically estimated vessel diameter. Conventionally, a simpliﬁed model is used, assuming a straight vessel with the catheter centered and a constant-diameter circular cross section. However, the irradiation pattern of the sources is complex [77]. Furthermore, vessel shape, curvature, and catheter location have a substantial impact on the actual dose delivered [76,78], but are not considered in the current models of dose delivery. The primary aim of this study was therefore to compare intravascular-brachytherapy dosing models using three-dimensional (3-D) computer simulations in an effort to estimate the inﬂuence of vessel shape and catheter position on dose distribution. To assess errors in delivered doses following the conventionally used dosing schemes, the actual differences in predicted dose distribution between a simpliﬁed tubular model and a geometrically correct 3-D model were quantiﬁed. The characteristics of the Novoste Beta-Cath β-radiation catheter used for brachytherapy at the University of Iowa Hospitals and Clinics were modeled from previously reported experiments on dose distribution. A one-dimensional distance function has been employed to simulate the dose fall-off, based on data from Soares, Halpern, and Wang for 90 Sr/Y radionuclides [77]. Their comprehensive data have been condensed to obtain a

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sufﬁciently accurate dose estimate with reasonable computational effort. For each source i, the dose in Gray (Gy) for any point p in a distance of dpi was determined as follows: Di (dpi ) =

C · Ai · t · g(dpi ) dpi 2

with g(d) = a0 + a1 ·d + a2 ·d 2 + a3 ·d 3 + a4 ·d 4 Di (dpi ) Dp =

(39) (40) (41)

i

where C is a dose rate constant speciﬁc for the brachytherapy device; Ai is the activity of the source in giga-Becquerels (GBq), with usually the same Ai for all i within a train; t is the application time in seconds; and g(d) is a radial dose function with polynomial coefﬁcients a0 to a4 derived from experimental results. The polynome has been validated for a range 0.75 mm ≤ dpi ≤ 9.0 mm. The minimum results from the diameter of the delivery catheter (5F = 1.6 mm). For distances above 9.0 mm, the dose was assumed to be zero. The total dose Dp for point p was determined as the sum of the individual doses delivered from all sources i. The simulation was performed in computer-generated models based on a torus with varying radius and out-of-center location of the brachytherapy catheter. In such phantoms of 50 mm length with a shape corresponding to a 60–180◦ segment of a respectively sized torus, the average dose in 2 mm depth was decreased by 2.70–7.48% at the outer curvature and increased by 2.95–9.70% at the inner curvature as compared to a straight phantom. The experiments also showed that the dose delivered by a non-centered catheter substantially deviates from the dose distribution of a centered catheter. When introducing just a 1 mm offset to the catheter location, the dose is roughly doubled at the closer and halved at the farther side [3]. In-vivo, dose calculations were performed in 10 vessel segments of 8 patients, using our fusion method to generate 3-D end-diastolic models. These data were compared to a simpliﬁed tubular model reﬂecting common assumptions of conventional dosing schemes. As shown in Fig. 30, plaque and media tissues were modeled as a structured grid with a ﬁxed number of layers and radial elements. For each of the resulting measurement points, the dose received from each source was determined using the distance function, and the overall dose summed up over all sources. The resulting estimates for the dose distribution in one of the patients is shown in Figs 31, 32. While the differences in dose estimates were largest in the right coronary arteries, there were also substantial differences in the left anterior descending and left circumﬂex arteries [3]. In general, the simpliﬁed model yielded signiﬁcantly lower estimates of the delivered radiation and the dose variability as compared to a geometrically correct model (p < 0.001). The estimated dose was on average 8.76% lower at the lumen/plaque and 6.52% lower at the media/adventitia interfaces (simpliﬁed tubular model relative to geometrically correct model). The differences in dose estimates between the two models were signiﬁcantly higher in the right coronary artery as compared to the left coronary artery (p < 0.001). 7. Discussion and Conclusions The methods for data fusion between biplane angiography and IVUS presented in this chapter yields new perspectives in studying the development of plaque in the process of

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Lumen Plaque Interpolated Layers Media Adventitia

Figure 30. For brachytherapy analysis, the volume between lumen/plaque and media/adventitia contours is ﬁlled with a structured radial grid of 72 circumferential points; two intermediate layers are determined by linear interpolation along the radial axes, dose estimates are determined at each intersection of a layer with a radial grid line.

coronary atherosclerosis, and allows a better quantitative assessment of the results from interventional procedures than either modality alone can deliver. The geometrically correct 3-D and 4-D models have been applied in the calculation of wall shear stresses, in the determination of geometric and morphologic vessel parameters, and in the veriﬁcation of treatment results. Obviously, more application areas are yet to be discovered. As demonstrated in the validations, our fusion methods showed a good overall performance. While the automated pullback used for the phantom showed a good stability of the pullback speed, the manual pullback performed in the pig hearts was subject to several distortions. If a constant pullback speed is assumed, this leads to signiﬁcant errors in the matching of the estimated locations of the frames, and thus to miscalculations of the local axial twist as well. The high variance in the pullback speed proved that the manual pullback is not acceptable for high-quality assessments such as 3-D reconstructions and volumetric quantiﬁcations. On the other hand, these artifacts are avoidable with moderate effort, e.g., by using a motorized pullback device. Therefore, only a fully automated IVUS pullback without any manual intervention is employed for our in-vivo acquisition protocol. Currently, the algorithm assumes a stable path of the catheter during pullback. While this is true for sheathed catheters, the tip of an unsheathed catheter will probably not follow the path as derived from the angiographic images depicting the transducer in its distal position. Thus, the approach presented here is limited to sheathed catheters. For in-vivo applications, problems with ECG and respiratory gatings occur, and nonuniform distances between adjacent frames have to be considered. These items need to be addressed by future developments.

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(a)

(b) Figure 31. Brachytherapy evaluation on the in-vivo example introduced in Figs 2, 3, 7; dose distribution (a) at the innermost layer, (b) at the outermost layer; each marker represents one of the 72 circumferential grid points per contour and 134 contours over the 60 mm irradiated segment with a prescribed dose, assuming a 4 mm diameter with centered catheter, was 18.4 Gy in 2 mm distance from the source train.

The matching of the clip peaks showed a good estimation of the orientations of the frames, but uncovered some limitations as well. Mechanically driven imaging catheters are sensitive to bending and external forces. Friction effects may introduce a phase shift, resulting in an artiﬁcial axial rotation of the images. Changing the pressure in the catheter, e.g., by a routine saline ﬂush, introduces similar effects. In-vivo, the slight pressure changes introduced by blood ﬂow are unlikely to affect the catheter core inside the sheath. The detected phase shifts consist of both local and additive components. The local component causes a rotation that is present only at the restraint point itself, while the additive component affects the entire catheter core distal to the restraint point. For the catheters we used, these effects resulted always in a clockwise rotation of the echoes. However, the NURD effects depend on the direction of bending. With future extensions to the method for establishing the absolute orientation of the frames, friction points can be identiﬁed from inconsistencies in the angle function ϕ, thus creating multiple correction angles for the speciﬁc vessel segments.

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Figure 32. Dose distribution in simpliﬁed tubular model derived from the 3-D geometrically correct model by straightening of the vessel and centering of the catheter; due to the circular shape, all points within a contour receive the same dose.

The clinical application is still ongoing, and many of the results presented in Section 6 have to be considered preliminary. Nevertheless, important results have already been obtained, and our research continues into the direction of analyzing the interdependencies between vessel geometry, coronary hemodynamics, and plaque development. Acknowledgments The software system for coronary angiography and IVUS fusion was developed and applied at the University of Iowa during the last decade with a number of internal and external collaborators involved; therefore, the contributions of the following colleagues are gratefully acknowledged. — For their contributions to the fusion system: Mark E. Olszewski, Steven C. Mitchell, Sharan D. Ramaswamy, and Sarah C. Vigmostad, all with the University of Iowa; Guido P. M. Prause, now with MeVis, Bremen, Germany; and Rubén Medina, Universidad de Los Andes, Mérida, Venezuela. For his help with the in-vitro phantom and pig studies: Steven C. DeJong, University of Iowa. For their work on computational hemodynamics: Krishnan B. Chandran and Yong-Gen Lai, University of Iowa; Peter H. Stone and Charles L. Feldman, Brigham & Women’s Hospital; and A. Ümit Co¸skun, Northeastern University, Boston. For their contributions to the intravascular-brachytherapy study: Sanford L. Meeks and Edward C. Pennington, University of Iowa. We would also like to thank our clinical partners for the acquisition of the patient data used in this project, and for important discussions: James D. Rossen, Theresa M. H. Brennan, Kathleen C. Braddy, James M. Fox, and John M. Buatti, all with the University of Iowa; John J. Lopez, University of Chicago; and Clemens von Birgelen, University Hospital Essen, Germany. Financial support was granted by the German Research Society (DFG, Pr 507/1-2 and Wa 1280/1-1) and the National Institutes of Health (NIH, R01 HL63373).

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Plaque Imaging: Pixel to Molecular Level J.S. Suri et al. (Eds.) IOS Press, 2005 © 2005 The authors. All rights reserved.

Imaging of Plaque Cellular Activity with Contrast Enhanced MRI William KERWIN University of Washington, Seattle, WA Abstract. A new horizon in imaging of atherosclerotic plaque is the use of contrast enhancing agents to investigate molecular and cellular markers. This chapter reviews the state of the art in contrast-enhanced imaging of atherosclerotic plaque. Topics include enhancement characteristics of different plaque tissues, modeling of dynamic contrast-enhanced MRI, and targeted contrast agents. For each topic, speciﬁc techniques for image acquisition and post-processing are presented. Quantitative results are summarized for experiments conducted with histological validation. Finally, potential applications of these techniques in detecting vulnerable lesions and in drug development are discussed. Keywords. MRI contrast agents, gadolinium, USPIO, atherosclerosis, carotid artery, kinetic modeling, inﬂammation, neovasculature, permeability, macrophage

1. Introduction Magnetic resonance imaging is generally thought of as a macroscopic imaging modality. In plaque imaging, the ability of MRI to provide high resolution depictions of the vessel lumen, outer wall boundary and plaque substructures is well established (see “MRI Plaque tissue characterization and assessment of plaque stability”). Such information, however, tells only part of the story of the plaque. Microscopic processes, such as inﬁltration of macrophages, can have profound effects on disease progression. Fortunately, MRI offers the ability to assess such processes through the use of injected contrast agents. The development of contrast agents for MRI is a rapidly expanding area, with most agents utilizing gadolinium and its ability to shorten MR relaxation times T1 and T2. In T1-weighted images, regions with accumulation of the agent are characteristically brighter and in T2-weighted images, high concentration regions appear darker. Chelates of gadolinium including Gd-DTPA are currently available for clinical use and were initially approved for applications in detecting lesions of the central nervous system. Experimental uses under investigation include MR angiography (MRA) and MRI of atherosclerosis. Techniques exist in these areas for ﬁrst pass imaging in which the agent is restricted to the blood stream, late phase enhancement in which the agent has diffused into the extracellular space of the tissue, and dynamic imaging in which the transfer from the blood stream to the tissue is observed over time. While the established MRI contrast agents have proven valuable in many medical applications, they also have some drawbacks. Their rapid diffusion into the tissue hinders

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MRA and dynamic uses because very rapid imaging becomes necessary to observe agent characteristics before tissue uptake. This has led to the development of experimental gadolinium agents with higher molecular weights to inhibit diffusion and of agents that bind to blood products such as albumin and thus remain within the blood pool [1–3]. The ability to develop gadolinium agents that bind to speciﬁc receptors also overcomes the non-speciﬁc enhancement associated with standard gadolinium agents. In plaque imaging, agents have been proposed that bind to thrombus and factors that promote angiogenesis [4–6]. This permits cell or protein speciﬁc enhancement to occur in a manner akin to nuclear medicine. In addition to gadolinium agents, one further contrast modifying compound investigated for plaque imaging is ultrasmall particles of superparamagnetic iron oxide (USPIOs) [7,8]. These particles are taken up by macrophages and induce signal reductions via susceptibility effects. Thus, USPIOs may be valuable for detecting plaque inﬂammation characterized by macrophage inﬁltration. This chapter reviews the state of the art in contrast-enhanced MRI of atherosclerosis. It begins with a section describing observed late-phase enhancement characteristics and their association with tissue types. The bulk of the chapter will discuss the challenges and quantitative advantages of dynamic contrast-enhanced imaging of plaque. Then a brief overview will be presented of tissue-speciﬁc agents such as USPIOs that target speciﬁc plaque features. These topics are illustrated with a variety of case studies. In all cases, subjects provided informed consent and the studies were approved by the institutional review boards. The chapter will close with a discussion of the comparative merits of each of these techniques.

2. Late-Phase Plaque Enhancement The observation of enhancing regions in plaque after injection of a contrast agent was ﬁrst reported in animals by Lin et al. [9] and in humans by Aoki et al. [10]. The dominant feature noted was a bright rim attributed to growth of the vaso vasorum in the adventitia (Fig. 1a). Others noted patchy enhancement within the plaque itself (Fig. 1b) [11,12]. This led investigators including Weiss et al. [13], Yuan et al. [12] and Wasserman et al. [11], to consider whether CE-MRI provides unique information regarding plaque composition and vulnerability. 2.1. Imaging Techniques CE-MRI of atherosclerosis using gadolinium agents requires special considerations in the method of image acquisition. Most importantly, the proximity of the large vessel lumen, with its high concentration can lead to difﬁculties in interpretation of the images if care is not taken to suppress the blood signal. Typically, two options are available, spatial saturation bands and double inversion recovery (DIR). Both techniques, rely on dephasing of the net magnetization of the blood outside of the image plane and subsequent inﬂow of the dephased blood. The DIR technique generally provides better suppression of the blood signal because suppression is applied over a broader area and more time is allowed for inﬂow of suppressed blood. In CE-MRI, this advantage becomes even greater as the rapid recovery from spatial saturation due to T1 shortening further undermines that technique.

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(a)

(b)

Figure 1. Contrast enhancement in carotid atherosclerosis: a) pre-contrast DIR image of the common carotid artery and b) post-contrast DIR image with arrows pointing to regions of enhancement in the artery wall.

pre-contrast

3 minutes

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Figure 2. The INCQIR method applied to the carotid artery showing a sequence of INCQIR images of the common carotid artery (arrow) beginning with pre-contrast image and showing images at 3 minute intervals following injection of a Gadolinium contrast agent. Note consistent suppression of vessel lumen (black region at vessel center).

One problem that arises in DIR imaging is that the timing of the inversion must be carefully set relative to the T1 of the blood for optimal suppression. However, the T1 of the blood depends on the unknown concentration of the contrast agent. To overcome this issue, Yarnykh and Yuan [14] proposed the quadruple inversion recovery (QIR) technique, which adds a second double inversion recovery pulse set to the sequence. This leads to perfect suppression for two values of T1 and nearly perfect suppression over a wide range of T1 vales. This technique is also useful for exploring enhancement characteristics at different delay times after injection (Fig. 2), a method known as incremental QIR (INCQIR) [15].

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* *

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Figure 3. Two different enhancement characteristics observed by INCQIR imaging. Images show the change in absolute enhancement between 3 minutes and 15 minutes after injection of a Gadolinium contrast agent. Gray represents constant enhancement over time, white represents early enhancement followed by rapid washout, and black represents a slow rise in enhancement with a late peak. a) Result from images shown in Fig. 2 showing little change within the carotid artery wall (arrow). b) An example of an artery (white arrow) with strong early phase enhancement (black arrows) adjacent to the lumens (asterisks) of the internal and external carotid arteries.

To image at different delay times using traditional DIR approaches, the inversion time must be carefully altered according to the expected concentration of contrast agent in the blood, which is difﬁcult to determine. Furthermore, changing the inversion time alters the signal from the tissue itself [14]. With QIR, on the other hand, blood suppression is achieved across a wide range of contrast agent concentrations allowing the same sequence parameters to be used at all delay times. This, in turn permits the changing signal intensities due to contrast agent concentrations to be examined without confounding intensity changes caused by changes in sequence parameters. For the most part, investigations of enhancement at different time points show minimal impact of the delay on the enhancement pattern. For example, Fig. 2a shows a plaque that was imaged every 3 minutes for a total of 15 minutes after contrast agent injection. The images are quite similar over time as can be conﬁrmed by examining the change in absolute enhancement over time (Fig. 3a). This shows the change in signal intensity at 15 minutes subtracted from the change in signal intensity at 3 minutes. The fact that the artery wall is a near-uniform gray indicates that little change in enhancement occurred in the intervening time. The importance of the INCQIR technique may, nevertheless, lie in examining the highly important luminal layer of the atherosclerotic plaque. An example is shown in Fig. 3b in which bright regions adjacent to the lumen indicate an initial high enhancement at 3 minutes that is signiﬁcantly reduced by 15 minutes. Several cases have been observed in which such rapidly changing intensities occur adjacent to the lumen. These changes are attributed to rapid wash in/out of contrast agent from the vessel lumen. This rapid exchange implies a highly permeable ﬁbrous cap, likely consisting of loose matrix and possibly in danger of rupture. 2.2. Tissue Speciﬁc Characteristics Utilizing the DIR and QIR techniques, several researchers have uncovered tantalizing links between enhancement and plaque characteristics. Yuan et al. [12] and Wasserman et al. [11] both found higher enhancement associated with ﬁbrous tissue, suggesting that

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CE-MRI might be valuable for assessing the status of the ﬁbrous cap, a key component of plaque stability. Yuan et al. also found the highest enhancement associated with areas of dense neovasculature, which are thought to contribute to plaque destabilization [16,17]. Weiss et al. [13] found an association between high enhancement and serum markers of inﬂammation, suggesting CE-MRI might be valuable for evaluating plaque inﬂammation. Inﬂammation plays a critical role in plaque initiation, progression, and disruption and represents an emerging target in the treatment of atherosclerosis. To further explore the links between enhancement and tissue types, 18 patients scheduled for endarterectomy were enrolled in an MRI study. The protocol was identical to that used in [12]. After acquiring pre and post contrast images at a total of 76 locations within these subjects, an expert reviewer placed matched regions of interest (ROIs) on both sets of images corresponding to uniform-appearing structures within the plaques. For each matched set of ROIs, the percent enhancement was computed. Following carotid endarterectomy, the specimens were formalin ﬁxed, decalciﬁed, and embedded in parafﬁn. Sections (10 mm thick) corresponding to the image locations were identiﬁed after staining with Hematoxylin & Eosin and Mallory’s Trichrome. The sections were then independently evaluated by a reviewer who was unaware of the imaging results and categorized the tissue types within each cross-section using the following histopathological classiﬁcation scheme [18,19]: 1. Necrotic core: a disorganized mass of lipid material, cholesterol clefts and cellular debris, and variable amounts of blood and blood products. 2. Calciﬁcation: present in varying forms, from speckled, ﬁne calciﬁcation to regions of dense calciﬁcation. 3. Matrix: a mixture of collagen and proteoglycan ground substance produced by ﬁbroblasts and smooth muscle cells. Numbers of macrophages and lymphocytes may be present along with calciﬁcation in a variety of forms and amounts. 4. Neovasculature I (NV I): one to four microvessels per high power ﬁeld (200X) measuring under 0.02mm in diameter. 5. Neovasculature II (NV II): ﬁve or more microvessels under 0.02 mm in diameter per high power ﬁeld (200X) or any number of microvessels measuring greater than 0.02 mm in diameter per high power ﬁeld. Comparison between histology and MRI enhancement was performed on a quadrant basis (N = 198). Each location was divided into four quadrants and for each quadrant, the percent enhancement of any ROI within the quadrant was recorded. Also, for each quadrant the set of tissues present in histology was recorded. This facilitated the search for a link between a speciﬁc level of enhancement and the presence of certain tissue types in the vicinity. Table 1 summarizes the signal enhancement in MRI quadrants with and without speciﬁed histological features. Only neovasculature II showed a statistically signiﬁcant association with hyper-enhancement. Speciﬁcally, when neovasculature II was present, the mean percent increase was 109% ± 52% versus 51% ± 52% when it was absent (p = 0.002). The 109% average enhancement associated with neovasculature II was also the highest of all tissue components evaluated. Although marginal in terms of statistical signiﬁcance, the presence of loose matrix was also associated with a higher level of enhancement (79% versus 57%) and a necrotic core was associated with a lower level of enhancement (55% versus 79%). Because inﬂammatory cells such as macrophages are

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Table 1. Correlations between different model parameters for blood supply in 18 carotid artery plaques.

tissue Matrix Necrotic Core Calciﬁcation NV I NV II

percent enhancement present absent 79 ± 54 (N = 86) 55 ± 48 (N = 102) 69 ± 55 (N = 49) 54 ± 42 (N = 56) 109 ± 52 (N = 54)

57 ± 52 (N = 112) 79 ± 57 (N = 96) 66 ± 54 (N = 149) 71 ± 57 (N = 142) 51 ± 46 (N = 144)

p-value p = 0.07 p = 0.19 p = 0.51 p = 0.43 p = 0.002

associated with neovasculature and loose matrix [19,20], these ﬁndings suggest areas of strong enhancement may also be indicative of inﬂammation.

3. Dynamic Imaging of Plaque Enhancement Although late phase enhancement has been shown to provide additional information for characterizing plaque composition, the major contributions of CE-MRI were expected to be in quantiﬁcation and identiﬁcation of inﬂammation. Because quantitative measurements of late phase enhancement are dependent on factors such as dose, scanner parameters, and timing, researchers turn to dynamic contrast-enhanced (DCE) MRI for quantitative studies. In DCE-MRI, the time course of enhancement assists in characterizing tissue by showing not just what enhances but also how it enhances. For example, both neovasculature and loose matrix have strong enhancement in late phase images; these two tissues can be distinguished in dynamic images because loose matrix should enhance more slowly because it relies on diffusion of the contrast agent from the blood, rather than direct connection to the vascular system. Quantitative characterizations are then possible via kinetic modeling of contrast agent uptake. 3.1. Imaging Techniques Quantitative DCE-MRI utilizes multiple image acquisitions over the course of contrast agent injection. It requires a sequence that provides rapid imaging to capture the changing enhancement patterns as the agent distributes through the vascular system and into the tissues. Additionally, the sequence must not suppress the blood signal, which then serves as an indicator of agent concentration in the blood. A typical imaging technique is a 2D spoiled gradient-recalled echo (SPGR) T1-weighted sequence with parameters: TR = 100 ms, TE = 3.5 ms, ﬂip = 60◦ , thickness = 3mm, gap = 1 mm, ﬁeld-ofview = 16×12 cm, matrix = 256×144. Blood saturation bands are placed above and below each block of image locations to induce a T1 recovery for measurement of signal increases due to contrast agent concentration in the blood. Each acquisition is repeated 10 or more times, with a repetition interval on the order of 15 sec. Coincident with the second image in the sequence, a standard dose (0.1 mmol/kg) of a Gadolinium-based contrast agent is injected at a rate of 2 ml/sec via power injector. Examples of the resulting sequence of images are depicted in Fig. 4.

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Figure 4. DCE-MRI of carotid atherosclerosis before contrast agent arrival (pre) and at 15 second intervals following bolus arrival. The lumen is marked by an “X” and the outer wall is marked by arrows in the second frame. Note patient motion relative to the ﬁxed “X” and generally poor delineation of the vessel boundaries.

3.2. Image Processing One challenge in DCE-MRI is that quantitative kinetic modeling of enhancement requires exact registration of the images in the sequence. However, patient motion during the scan occurs. Even small shifts on the order of 1 mm can have dramatic consequences since the pixel size is well under 1 mm and the entire vessel is often less than 1 cm in diameter. To combat patient motion in DCE-MRI of atherosclerosis, the Kalman Filtering Registration and Smoothing (KFRS) algorithm was proposed [21]. This technique is essentially an estimation theoretic approach to the problem, modeling enhancement and motion stochastically and seeking the linear minimum mean square error (LMMSE) estimate of the true sequence of images. The stochastic model assumes that the true signal from a given image pixel will vary over time according to the equation

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Mj = Mj −1 + Bj ,

367

(1)

where Mj is the signal in the j th time frame and Bj is the incremental change in intensity due to contrast agent dynamics. Bj is assumed to be zero-mean Gaussian with variance σB2 . Additionally, the received signal will be corrupted by noise so that the acquired value at time j is given by I j = Mj + η j ,

(2)

where ηj is zero-mean Gaussian noise with variance ση2 . Finally, the image is assumed to be compromised by patient motion so that the pixel value at multidimensional position x is Ij (x) = Mj (x − dj ) + ηj (x),

(3)

where Mj (x) is the pixel intensity that would have been obtained in the absence of motion, dj is the displacement of the tissue at time frame j , and ηj (x) is the noise associated with the pixel. The displacement dj is assumed to be a uniform random variable with a maximum magnitude of D. The goal is then to estimate M1 (x), . . . , MN (x) given the sequence of corrupted intensities I1 (x − d1 ), . . . , IN (x − dN ), where N is the number of images in the sequence. Estimation of the true image sequence is performed recursively in the KFRS algo6j −1|j −1 of Mj −1 based on observations up to rithm. Assume that we have an estimate M time j − 1. Then, the estimate of Mj can be made based on this estimate and the observation Ij at time j . First, the displacement is determined by ﬁnding the value of dˆ j that minimizes 6j −1|j −1 (x) 2 . Ij (x + dj ) − M (4) x

We chose this method because it can be shown to be the maximum a posteriori esti6j −1|j −1 (x). To minimize Eq. (4) we ﬁnd mate given the model and assuming Mj (x) = M its minimum value over a user speciﬁed range of whole-pixel displacements (nominally ±5 pixels in each dimension). Then, a quadratic patch is ﬁt to the 3 × 3 set of values centered on that minimum and the minimum of the quadratic patch is taken as the displacement estimate to subpixel accuracy. This displacement is corrected in the image using the shift theorem of the Fourier transform, which requires forward and reverse Fourier transformation of the region of interest. Use of the shift theorem avoids interpolation artifacts, particularly generation of smoothed, spatially-correlated noise Once the displacement is determined, the true image is estimated by Kalman ﬁltering using the recursive equations 6j −1|j −1 + gj Ij − M 6j −1|j −1 , 6j |j = M (5) M 61|1 = I1 . The term gj is the Kalman gain calculated using beginning with M gj =

j −1 + σB2

j −1 + σB2 + ση2 j = (1 − gj ) j −1 + σB2 .

(6) (7)

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6j |j . The resulting estimate can The term j is the mean square error in the estimate M then be fed back into the registration algorithm to eliminate displacement in the image at time j + 1 and so on. The estimate obtained via this combination of registration and Kalman ﬁlter is unfortunately not the desired LMMSE estimate, which should incorporate future images as well as past and present ones. As a result the amount of noise attenuation varies de61|1 has pending on the number of prior images in the sequence and the ﬁrst estimate M no noise attenuation at all. To compute the full LMMSE estimate and achieve more consistent noise attenuation for all time frames, a second “smoothing” pass is made through the data. We derive the smoothing solution by noting that the LMMSE estimate given all N images in the sequence can be written 6j |j + R 6j , 6j = M M

(8)

that is, as the sum of the ﬁltered estimate plus the LMMSE estimate of the residual error 6j |j . Rj = Mj − M

(9)

A recursive formula for calculating the LMMSE estimate of the residual error is 6j = R

j j + σB2

6j +1 + R

j j + σB2

+ ση2

6j |j . Ij +1 − M

(10)

6N = 0, because the N th estimate from We initialize these recursive calculations with R the Kalman ﬁlter already incorporates all available time frames. Combined use of the ﬁltering and smoothing equations, permits the LMMSE estimate to be obtained for each pixel at each time frame in two passes through the sequence. By comparison, standard techniques for computing LMMSE estimates would require the equivalent of N passes through the data. The only pieces of information required to implement the KFRS algorithm are the variances of the stochastic processes. The variance ση2 is estimated by computing the variance of a region outside the body and dividing by 0.655. This scale factor arises from the Rician nature of noise in MR images (see [22]). The variance σB2 is estimated by calculating the variation in the average brightness of the vessel lumen over the time sequence. Figure 5 shows typical results of the KFRS algorithm. 3.3. Kinetic Modeling Once the sequence of DCE-MRI images has been acquired and registered, it must be mathematically analyzed to glean the biologically relevant information from the time course of enhancement. The biological information accessible in this way consists of various measurements related to tissue permeability and blood supply. The measurements are extracted by ﬁtting a prior model of the contrast agent kinetics to the observed brightness variations. These kinetic models are usually cast in continuous time, requiring parametric curves to ﬁrst be ﬁt to the observed data points. Alternatively, discrete time kinetic models have also been proposed [23,24].

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Figure 5. Effect of KFRS algorithm on DCE-MRI of carotid atherosclerosis. The same image sequence shown in Fig. 4 shows improved delineation of vessel boundaries and elimination of vessel motion relative to the “X” after application of the KFRS algorithm.

Continuous Kinetic Models. In kinetic modeling of contrast agent uptake, measurements are taken over time of blood plasma concentration Cp (t) and tissue concentration Ct (t). In DCE-MRI, the change in signal intensity is sometimes used in lieu of concentration or, for greater accuracy, the change in longitudinal relaxation rate R1 is used [25]. These measurements are then used to estimate the model parameters by optimal curve ﬁtting of the selected model. One possibility is a two-compartment model of contrast agent kinetics, such as that illustrated in Fig. 6. The total tissue concentration is given by C t = v p Cp + v e Ce where Ce is the concentration in the EES, and vp and ve are the respective partial volumes of plasma and EES. The change in EES concentration over time is dictated by

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tissue Cp vp

kep

Ce ve

Figure 6. Two-compartment model of contrast agent exchange: The total concentration in a volume of tissue is determined by a partial volume of plasma vp , a partial volume of extravascular extracellular space ve and their respective concentrations Cp and Ce . Dynamic interchange of contrast agent is determined by the rate constant kep .

C˙ e = kep (Cp − Ce ) where kep is the transfer rate of contrast agent between plasma and EES. Further complexity can be introduced to the model by assuming different exchange rates from plasma to EES and from EES back to plasma. Unfortunately, even if matching transfer rates are assumed, parameter estimates for the two-compartment model can be unstable, an issue of “global identiﬁability” [26]. For example, if Ct (t) is similar in shape to Cp (t), this can be accounted for by setting vp = Ct /Cp , by making kep very large and setting ve = Ct /Cp , or any combination of these. Small changes in the observed data can thus lead to large changes in the estimated parameters. This phenomenon is illustrated in Fig. 7 for simulated data based on the twocompartment model. The data in this example are well modeled by two radically different solutions. Therefore, care must be taken to ensure this model is applied in situations with high signal-to-noise ratios, where model instabilities have less impact, or in situations where unstable solutions, such as that depicted in Fig. 7, are unlikely. Otherwise, further simpliﬁcation of the model is warranted. One simpliﬁcation employed by Patlak [27] assumes that the movement of contrast agent from the tissue back to the plasma is negligible. The result is a linear model of contrast agent dynamics that depends only on vp and the term K trans = ve kep according to Ct (t) = vp + K trans Cp (t)

t 0

Cp (τ )dτ . Cp (t)

(11)

This model will be valid if the transfer rate from EES to plasma is slow compared to the time span of the observations.

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1 0.9 0.8

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Figure 7. Example of instability in the two-compartment model: The blood curve is the solid line and samples from a voxel are represented by squares. Equally good ﬁts to the data are obtained with the parameters vp = 0.5, ve = 0 (dashed line) and with the parameters vp = 0, ve = 0.5, kep = 0.25 sec−1 (dotted line).

For situations where this is not true, an alternative assumption employed by Tofts is that vp is negligible [28]. This leads to the general differential equation governing contrast agent uptake Ct . (12) C˙ t = K trans Cp − ve The physiological deﬁnition of K trans relates to blood ﬂow, capillary surface area, and permeability, making it a good indicator of blood supply [29]. The solution to Eq. (12) is t Cp (τ )e−kep (t−τ ) dτ. (13) Ct (t) = K trans 0

If Cp (t) is known, the parameters kep , K trans and ve = K trans /kep can be extracted. Typically, the blood concentration is periodically sampled and ﬁtted with a multi-exponential curve to approximate Cp (t) [25]. Discrete Kinetic Model. Because DCE-MRI data is obtained at discrete time points, a discrete model of contrast agent kinetics may be more appropriate than the continuous models outlined above. This is particularly true when the images are equally spaced in time by an amount T . A basic two-parameter discrete model is Ct [n] = rCt [n − 1] + uCp [n],

(14)

where Ct [n] is the tissue concentration at time tn , Cp [n] is the corresponding plasma concentration and r and u are model parameters.

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To estimate the values of r and u in the discrete model, the sum of squared differences (SSD) is minimized between the observations and the model. For the discrete model, the SSD is given by SSD =

N

7 Ct [n] −

n=1

n

82 r

n−k

uCp [k]

k=1

where N is the total number of observation times. Setting the derivative of the SSD with respect to u to 0 yields the optimal value of u for any value of r, which is

N

n n−k C [k] p n=1 Ct [n] k=1 r u=

.

N n n−k C [k] 2 p n=1 k=1 r Optimization can therefore be accomplished by searching for the value of r and its corresponding u that generate the smallest SSD. To ﬁnd this minimum, the parameter r is stepped over its physical range from 0 to 1 (see below) and for each value of r, the optimal value of u is computed. Then, for each of these pairs (u,r), the SSD is computed and the pair that produces the overall minimum is identiﬁed. From here, the absolute minimum is found by gradient descent on r. In this model, the term rCt [n − 1] indicates to what extent contrast agent that has entered the tissue remains in the tissue. Speciﬁcally, the parameter r is the fraction of contrast agent that is retained within the volume from one time frame to the next, which will depend heavily on the transfer rate of contrast agent between blood and tissue. The term uCp [n] indicates to what extent the tissue concentration depends on the current blood concentration. Speciﬁcally, the parameter u is the fractional amount of contrast agent uptake within one time interval and is therefore a rough indication of the blood supply to the tissue. Given these interpretations, r and u can be used to indicate the general behavior of the contrast agent in the tissue, making them “semi-quantitative” indicators of kinetics [30]. Meaningful comparison of both r and u across subjects requires that T be the same for all cases. An attractive aspect of the parameters r and u is that they must occupy a very speciﬁc range. First, r must lie between 0 and 1. Otherwise, the model predicts the non-physical solution that the amount retained or washed out is greater than the amount previously present. Likewise, u should also be between 0 and 1. Otherwise, the tissue concentration will immediately exceed the plasma concentration, which implies diffusion against a concentration gradient. A ﬁnal constraint is derived by considering a hypothetical case of constant plasma concentration. In this event, the equilibrium concentration is Ct =

u Cp . 1−r

(15)

If we assume that tissue concentration cannot exceed the constant plasma concentration at equilibrium — which would imply diffusion against a concentration gradient — we ﬁnd that u < 1 − r. Based on these arguments, the values of u and r must lie within the triangle depicted in Fig. 8. Although, the interpretation of r and u discussed above provides some insight into tissue kinetics, truly quantitative physiological parameters, such as those in the twocompartment model, are preferable. In fact, the discrete model parameters can be used

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373

1 u

0 0

r

1

Figure 8. Triangular domain of allowed values for u and r.

to estimate the parameters of the two-compartment model, speciﬁcally vp and ve . If the time span of the experiment is long enough for the plasma and tissue concentrations to reach a state of near-equilibrium, the two compartments will have equal concentrations. This equilibrium condition implies that Ce = Cp so that Ct = (vp + ve )Cp . Equating this to the equilibrium condition of the discrete model from Eq. (15) yields (vp + ve ) ≈

u , 1−r

(16)

which establishes the necessary relationship for the two models to agree in the later time frames. A second relationship between the model parameters can be established at the initial time frame. According to the discrete model, the fractional concentration uptake in the ﬁrst time frame is u and the portion remaining in the second time frame is ru. If T is shorter than kep , then virtually no reﬂux from the EES to the plasma will have occurred in this short time. Thus, ru represents the portion entering the EES in the ﬁrst time interval and (1 − r)u will represent the portion remaining within the plasma (i.e. vp ). Combining this with Eq. (16) yields vp ≈ (1 − r)u 2r − r 2 ve ≈ u. 1−r

(17) (18)

To facilitate the accuracy of these relationships, the observations should span a long duration and the interval between observations should be on the order of the time constant of tracer exchange or smaller. These same requirements should be met for accurate ﬁtting of any kinetic model. The advantage of the discrete model is that the model does not encounter instabilities such as that depicted in Fig. 7 because it uses only two parameters instead of three. In addition, this illustrates an advantage of the discrete model over both

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the Tofts model and the Patlak model. The former can estimate ve but not vp , whereas the latter can estimate vp but not ve . With the discrete model, both partial volumes can be estimated. Performance Comparisons. To compare the performance of the discrete model to the continuous two-parameter alternatives, data were simulated using the two-compartment model. The plasma concentration was assumed to follow a single exponential decay characterized by a rate parameter m so that Cp (t) = e−mt

(19)

where an initial concentration of unity was utilized. According to the two-compartment model, the tissue concentration is then given by Ct (t) = vp e−mt + ve

kep −mt e − e−kep t . kep − m

Speciﬁcation of m, vp , ve , and kep permits a complete spectrum of models for simulation. The Tofts model can also be simulated by setting vp = 0. The values of Cp (t) and Ct (t) were sampled at regular intervals of T for a total of 10 samples. To eliminate T as a further parameter to specify, m and kep were entered in terms of T . The results could then be scaled for any absolute value of T . Based on samples from the simulated concentration curves, the optimal parameters were found for the Tofts, Patlak, and discrete models. For the Tofts and Patlak models, the actual plasma curve from Eq. (19) was used. In normal use, this curve would have to be estimated from sampled data as well. Figure 9 demonstrates the ability of the discrete model to estimate vp given data simulated by the two-compartment model with a wide range of user-deﬁned parameters. The value of vp was determined using Eq. (17). Curves are shown for plasma concentrations that decay very slowly (m = 0.01/T ) and very rapidly (m = 1/T ). Similarly, high and low values of ve and kep are included. In general, the curves lie close to the line of unity indicating that the estimate of vp is reasonable. The worst performance (diamond and square in plot) comes for a large value of ve and slow transfer between plasma and EES, for which vp was underestimated by as much as 50%. The poor performance is attributed to the failure of the tissue concentration to reach a state of near equilibrium in the later samples. If the experiment had run longer, better performance is expected. For comparison, the performance of the Patlak-based model is also shown in Fig. 9 for the same simulated data. This model overestimated vp by as much as 350% for large ve and fast transfer. This overestimation is caused because the fast transfer rate violates the central assumption of the Patlak approach that reﬂux can be neglected. Figure 10 demonstrates the ability of the discrete model to estimate ve given data simulated by the two-compartment model with a wide range of parameters. The value of ve was determined using Eq. (18). Curves are again shown for plasma concentrations that decay very slowly and very rapidly, high and low values of kep and, in this case, two values of vp . As with the estimates of vp , the estimates of ve lie close to the line of unity indicating reasonably good estimates. In contrast, the Tofts model results (also shown in Fig. 10) show gross errors in ve when vp is large.

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0.6

0.5

estimated v

p

0.4

0.3

0.2

0.1

0 0

0.1

0.2

0.3 actual v

0.4

0.5

0.6

0.4

0.5

0.6

p

(a) 0.6

0.5

estimated v

p

0.4

0.3

0.2

0.1

0 0

0.1

0.2

0.3 actual v

p

(b) Figure 9. Estimates of vp given data simulated by the two-compartment model: a) discrete model and b) Patlak model. The curves correspond to: ve = 0.05, kep = 0.2/T , m = 1/T (circle); ve = 0.05, kep = 0.2/T , m = 0.01/T (x); ve = 0.05, kep = 0.5/T , m = 1/T (plus); ve = 0.05, kep = 0.5/T , m = 0.01/T (asterisk); ve = 0.4, kep = 0.2/T , m = 1/T (square); ve = 0.4, kep = 0.2/T , m = 0.01/T (diamond); ve = 0.4, kep = 0.5/T , m = 1/T (downward triangle); ve = 0.4, kep = 0.5/T , m = 0.01/T (upward triangle).

3.4. DCE-MRI of Carotid Atherosclerosis Figure 11 illustrates the application of the discrete kinetic model to an advanced atherosclerotic plaque. The color-coded values of vp are shown to be high in the lumen (as expected since the lumen is 100% blood) and moderately high in the shoulder region indicating dense neovasculature there. Throughout the plaque, the values of ve are shown to be high suggesting signiﬁcant extravascular space consistent with loose ﬁbrous matrix and/or inﬂammation.

376

W. Kerwin / Imaging of Plaque Cellular Activity 0.6

0.5

estimated v

e

0.4

0.3

0.2

0.1

0 0

0.1

0.2

0.3 actual v

0.4

0.5

0.6

0.4

0.5

0.6

e

(a) 0.6

0.5

estimated v

e

0.4

0.3

0.2

0.1

0 0

0.1

0.2

0.3 actual v

e

(b) Figure 10. Estimates of ve given data simulated by the two-compartment model: a) discrete model and b) Tofts model. The curves correspond to: vp = 0.05, kep = 0.2/T , m = 1/T (circle); vp = 0.05, kep = 0.2/T , m = 0.01/T (x); vp = 0.05, kep = 0.5/T , m = 1/T (plus); vp = 0.05, kep = 0.5/T , m = 0.01/T (asterisk); vp = 0.4, kep = 0.2/T , m = 1/T (square); vp = 0.4, kep = 0.2/T , m = 0.01/T (diamond); vp = 0.4, kep = 0.5/T , m = 1/T (downward triangle); vp = 0.4, kep = 0.5/T , m = 0.01/T (upward triangle).

One question that arises is which of the kinetic models described above is best for modeling atherosclerotic plaque dynamics. Although the above comparison of kinetic models illustrates the trade offs between methods, the model chosen proves to have relatively minor implications for analyzing plaque. This fact is illustrated by the following comparisons of the models based on images of 18 patients with advanced carotid atherosclerosis. For each subject, slice level averages of the kinetic parameters were obtained for two locations along each artery.

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800

Blood

700

P L

signal intensity

600

500

400

Plaque 300

200

100 1

3

5

7

9

11

time frame

(a)

(b)

0.50

1.50

0.00

0.00

−0.50

−1.50

(c)

(d)

Figure 11. Discrete modeling of DCE-MRI of the carotid artery: a) boundaries of the lumen (L) and plaque (P); b) time course of signal intensity for the lumen and plaque where the ﬁrst time frame is pre-contrast and the remaining time frames are at 15 second intervals after bolus arrival; c) Color coded blood volume showing 100% for the lumen and pockets of moderate blood volume in the plaque; d) Color coded EES volume showing large EES throughout plaque, likely indicative of inﬂammation.

Comparison of the model parameters obtained by each model (Table 2) indicates that vp (Patlak), vp (2-comp), vp (discrete), and K trans (Tofts) are highly correlated, where the model used is indicated in parentheses. The strong association of K trans (Tofts) with vp from other models is not surprising since K trans (Tofts) is generally considered an indicator of blood supply [29]. Similar correlations were observed between K trans (Patlak), K trans (2-comp), ve (discrete), and ve (Tofts) (Table 3), which can be interpreted as tissue permeability factors. Based on these interrelationships, we conclude that all models provide similar measurements of blood supply and permeability. We illustrate the biological signiﬁcance of these model parameters using the discrete kinetic model to estimate vp and ve . For the same 18 subjects used in the model comparison, specimens of the plaques were obtained after endarterectomy surgery. Cross sections corresponding to the image planes were obtained for each specimen and immunohistochemically analyzed using ulex (neovasculature), HAM56 (macrophages) and CD-45 (leukocytes). These tissue components were then quantiﬁed as fVA (average area of neovessels per unit plaque area), fMA (average area of macrophages per unit plaque area) and fNL (number of leukocytes per unit plaque area). We found the statistically signiﬁcant correlations:

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W. Kerwin / Imaging of Plaque Cellular Activity Table 2. Correlations between different model parameters for blood supply in 18 carotid artery plaques. vp (Patlak)

vp (2-comp)

vp (discrete)

K trans (Tofts)

1 0.978 0.817 0.872

1 0.852 0.898

1 0.994

1

vp (Patlak) vp (2-comp) vp (discrete) K trans (Tofts)

Table 3. Correlations between different model parameters for permeability in 18 carotid artery plaques.

K trans (Patlak) K trans (2-comp) ve (discrete) ve (Tofts)

K trans (Patlak)

K trans (2-comp)

ve (discrete)

ve (Tofts)

1 0.756 0.759 0.793

1 0.634 0.607

1 0.854

1

• vp (discrete) vs. fVA: r = 0.45 (p = 0.03) • ve (discrete) vs. fMA: r = 0.50 (p = 0.02) • ve (discrete) vs. fNL: r = 0.50 (p = 0.02) This analysis indicates that vp and ve can be used as indicators of blood supply and inﬂammatory cell content, respectively, in atherosclerotic plaque. In other work, the Patlak model proved to have somewhat higher overall associations with these histological parameters. Speciﬁcally, in one study, the correlation between vp (Patlak) and fVA was r = 0.76 (p = 0.0003) and the correlation between K trans (Patlak) and fMA was r = 0.74 (p = 0.0005) [31]. In an earlier study, the correlation between vp (Patlak) and fVA was r = 0.80 (p = 0.001) [32]. 4. Targeted Contrast Agents Up to now, the small molecular weight gadolinium contrast agents described in the preceding have been the workhorses of contrast-enhanced MRI. The next generation of contrast agents promises to usher in a new era of contrast-enhanced MRI wherein speciﬁc tissue receptors, interaction with cell types, and different pharmacokinetic behavior are employed in tailoring agents to speciﬁc diseases [33]. Detection of the vulnerable atherosclerotic plaque is one of the foremost targets of these disease-speciﬁc agents. 4.1. Blood Pool Agents One focus of the new agents is the burgeoning area of contrast-enhanced MR angiography (MRA). Although the ability of commonly available contrast agents to generate high blood signal in time-of-ﬂight imaging has shown great promise for MRA, the rapid distribution of the agents into the extravascular space limits the lumen contrast improvement. Several agents are nearing clinical availability for MRA based on maintaining the agents within the blood pool.

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One of these agents is MS-325 (Epix Medical), which binds to albumin with an 80%–96% bound fraction in human plasma and exhibits a six to ten-fold higher relaxivity effect than Gd-DTPA [1]. The intravascular conﬁnement of albumin prevents bound MS-325 from diffusing into the extravascular space. In combination with the higher relaxivity effects, this makes MS-325 an excellent agent for MRA in both ﬁrst-pass and steady-state acquisitions [2]. Conﬁnement to the blood pool also enables MS-325 to potentially gauge tissue blood volume [34]. Measuring permeability of the agent into the extravascular space is also conceivable, but the different pharmacokinetics of bound and unbound forms complicates the analysis [35]. Another blood pool agent is P792 (Guerbet), which is a macromolecular Gadolinium chelate that is predominately restricted to the blood stream by its large size. Experiments suggest that P792 may have larger maximal effects on relaxivity than MS-325 in MRA experiments [36]. P792 has also been shown to be useful in kinetic modeling of DCE-MRI, where the slow transfer of the large molecule reduces the need for rapid imaging [37]. 4.2. Molecular Imaging Agents Perhaps the most promising but also most distant application of contrast agents in imaging of atherosclerosis is agents that bind to and thus enhance speciﬁc molecular receptors. In 2001, Flacke et al. described a method for generating nanoparticles with greater than 50,000 Gadolinium atoms per nanoparticle and high avidity for ﬁbrin [4]. These ligand-targeted nanoparticles were shown to form a thin layer over the surface of clots in scanning electron micrographs which resulted in high enhancement of clots in vitro and in dogs. Winter et al. demonstrated a nearly two-fold increased reduction in relaxivity for a similar ﬁbrin-targeted agent based on a different Gadolinium formulation [5]. These agents may one day be used for early detection of clot material – a potential sign of vulnerable plaque – within entire vascular beds. Another target of molecular contrast agents in the investigation of atherosclerosis is factors inﬂuencing angiogenesis. Angiogenesis is signiﬁcant because the resulting neovasculature may contribute to plaque progression through intraplaque hemorrhage and to plaque disruption through inﬂammatory processes. Winter et al. proposed such an agent with roughly 90,000 gadolinium atoms per particle that targeted the αv β3 -integrin, which is expressed in the vascular wall and is associated with angiogenesis [6]. In cholesterol fed rabbits, the aorta wall showed greater enhancement with this agent than in rabbits fed a control diet. Histological analysis conﬁrmed a signiﬁcant expansion of the adventitial vasa vasorum of the cholesterol fed rabbits compared to the controls. Finally, an agent that is not targeted at atherosclerosis but has an apparent afﬁnity for plaque is Gadoﬂuorine (Schering AG), which is a gadolinium-based agent with a perﬂuorinated side chain [38]. The effect of the hydrophobic side chain is to induce the molecules to aggregate in solution, forming large micelles with multiple gadolinium atoms. In the blood stream, the micelles remain in the plasma for long durations making Gadoﬂuorine a potential blood pool agent. Additionally, the hydrophobic side chain is lipophilic which may explain the observed afﬁnity of the agent for plaque. In WHHL rabbits, Gadoﬂuorine was found to remain within plaques several days after administration, a sufﬁcient time for its elimination from the blood pool. MRI showed distinct enhancement of such plaque regions with a strong association with regions staining with Sudan red (i.e. lipids) in subsequent histological analysis [38].

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4.3. USPIOs A major alternative to gadolinium based agents are ultrasmall particles of superparamagnetic iron oxides (USPIOs). USPIOs (e.g. Sinerem, Guerbet) suspended in solution and injected into patients at low concentrations result in positive contrast on T1-weighted images [39]. Their relaxation effects have the ability to enhance blood in MRA with results similar to those obtained with P792 [36]. Of greater value is the propensity of macrophages to phagocytose the USPIOs leading to a macrophage speciﬁc agent [8]. Allowing for sufﬁcient time for macrophage uptake – usually at least 24 hours – T2* – weighted images show signiﬁcant signal reduction due to susceptibility effects of the USPIOs [40]. In experiments with human carotid endarterectomy subjects, Kooi et al. showed that macrophages within plaques were positive for iron in histological and electron microscopy evaluations of endarterectomy specimens [7]. In MRI of corresponding locations, signiﬁcant signal reductions were observed.

5. Conclusion The prospect of developing contrast agents that highlight speciﬁc features of atherosclerotic plaque such as macrophages, neovasculature or ﬁbrin is certainly an exciting development in imaging of atherosclerosis. These tools provide the potential for visualizing the plaque features associated with rupture and clinical events. MRI with targeted contrast agents may one day be used to assess the stability of individual plaques based on their enhancement characteristics. Alternatively, the ability to image enhancement over broad regions suggests that agents speciﬁc to plaque features could be used in screening exams to assess overall plaque burden. To date, however, results with targeted agents are preliminary and such applications will require extensive efﬁcacy and safety studies, likely making their wide-scale use a decade or more away. In the nearer term, the mainstays of contrast enhanced MRI of plaque will be currently approved chelates of gadolinium, USPIOs, and blood pool agents nearing approval. A disadvantage of USPIOs is the need to wait a day or more after injection for macrophage uptake, which means pre and post contrast images must be obtained on separate days. This imposition may limit their applicability, although their strong association with macrophages makes them a powerful tool within certain applications. Basic gadolinium agents, on the other hand, result in nearly instantaneous enhancement allowing pre and post contrast images to be acquired within the same session. Over time, a shift away from small molecular weight agents and toward blood pool agents is expected, owing to the better performance in MRA and dynamic applications. Although standard gadolinium agents produce nonspeciﬁc enhancement, they still provide considerable useful information for gauging atherosclerotic plaque. Contrastenhanced T1-weighted images can serve as additional weightings in a comprehensive multi-contrast evaluation of plaque composition. Wasserman et al. showed that in such a role, contrast-enhanced images provide similar information to T2-weighted images with higher contrast-to-noise ratios [11]. The further facilitation of MRA by contrast agents presents an opportunity for combined angiographic and contrast-enhanced plaque assessment of diseased vessels. The ability of DCE-MRI to extract quantitative physiological parameters is also an exciting development in plaque imaging. Kinetic modeling of the entire plaque distills

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plaque characteristics to a single quantity, akin to measuring stenosis. In combination with stenosis, this information could lead to clinical decisions being made on the paired data. Of course, large scale studies are need to assess the clinical relevance of the contrast enhancement data. At present, the most sought after feature to detect by contrast-enhanced MRI is inﬂammation, characterized by macrophage inﬁltration into the vessel wall and plaque. Additionally, inﬂammation is commonly associated with neovasculature which provides nutrition to the inﬂammatory cells, is induced by vascular growth factors expressed by the cells [41], and provides a pathway for further inﬂammatory inﬁltration [20]. The interest in inﬂammation stems from the fact that inﬂammatory cells contribute to both plaque initiation and destabilization [42]. Inﬂammation is a natural target for contrastenhanced MRI because the increased blood supply and permeability associated with inﬂammation provides a signiﬁcant pathway for agent entry and because macrophages are established targets of tissue-speciﬁc agents. Potential future targets of contrast agents in atherosclerosis are many and varied, with ﬁbrous matrix molecules such as proteoglycan an attractive option, given their implications for cap stability. In terms of clinical and preclinical applications of contrast-enhanced MRI of atherosclerosis, the ﬁrst use is likely to emerge in drug development. For example, the effectiveness of pharmaceutical agents targeting plaque inﬂammation could be judged based on their measured effects on contrast enhancement characteristics. Ultimately, the hope is to develop techniques based on contrast-enhanced MRI that provide a risk assessment for individual plaques. This information could then be used by the clinician in deciding the course of treatment. The material presented in this chapter was based largely on experience in the human carotid artery. While the carotid represents a clinically important vessel, the ultimate hope is to extend these techniques for use on plaques in other vessels. Currently such applications are difﬁcult because other clinically signiﬁcant vessels, most notably the coronary arteries, are smaller, less superﬁcially located, or undergoing greater motion than the carotid arteries. Although imaging of plaque in the aorta and coronary arteries has been demonstrated, further technological advances are needed to make it clinically feasible. In the near term, the clinical beneﬁt of this technique for vessels other than the carotid artery is most likely to come from therapies shown to have positive effects in carotid plaque that have a similar effect throughout the vascular system. References [1] RB Lauffer, DJ Parmelee, SU Dunham, HS Ouellet, RP Dolan, S Witte, TJ McMurry, and RC Walovitch. Ms-325: albumin-targeted contrast agent for mr angiography. Radiol, 207:529–538, 1998. [2] TM Grist, FR Korosec, DC Peters, S Witte, RC Walovitch, RP Dolan, WE Bridson, EK Yucel, and CA Mistretta. Steady-state and dynamic mr angiography with ms-325: initial experience in humans. Radiol, 207:539–544, 1998. [3] M Port, C Corot, I Raynal, A Dencausse, M Schaefer, D Rousseaux, C Simonot, L Devoldere, J Lin, M Foulon, P Bourrinet, B Bonnemain, and D Meyer. P792: a rapid clearance blood pool agent for magnetic resonance imaging: preliminary results. MAGMA, 12:121–127, 2001. [4] S Flacke, S Fischer, MJ Scott, RJ Fuhrhop, JS Allen, M McLean, P Winter, GA Sicard, PJ Gaffney, SA Wickline, and GM Lanza. Novel mri contrast agent for molecular imaging of ﬁbrin: implications for detecting vulnerable plaques. Circulation, 104:1280–1285, 2001. [5] PM Winter, SD Caruthers Sand, X Yu, SK Song, J Chen, B Miller, JW Bulte, JD Robertson, PJ Gaffney, SA Wickline, and GM Lanza. Improved molecular imaging contrast agent for detection of human thrombus. Magn Reson Med, 50:411–416, 2003.

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[27] CS Patlak. Graphical evaluation of blood-to-brain transfer constants from multiple-time uptake data. J Cereb Blood Flow Metab, 3:1–7, 1983. [28] PS Tofts and AG Kermode. Measurement of the blood-brain barrier permeability and leakage space using dynamic MR imaging. 1. fundamental concepts. Magn Reson Med, 17:357–367, 1991. [29] PS Tofts, G Brix, DL Buckley, JL Evelhoch, E Henderson, MV Knopp, HBW Larsson, TY Lee, NA Mayr, GJM Parker, RE Port, and J Taylor an RM Weisskopff. Estimating kinetic parameters from dynamic contrast-enhanced T1-weighted MRI of a diffusable tracer: standardized quantities and symbols. J Magn Reson Imaging, 10:223–232, 1999. [30] AR Padhani. Dynamic contrast-enhanced mri in clinical oncology: Current status and future directions. J Magn Reson Imaging, 16:407–422, 2002. [31] WS Kerwin, M Ferguson, K O’Brien, T Hatsukami, and C Yuan. Quantitative detection of inﬂammation in carotid atherosclerosis by dynamic contrast enhanced magnetic resonance imaging. J Amer Coll Cardiol, 43:534A, 2004. [32] W Kerwin, A Hooker, M Spilker, P Vicini, M Ferguson, T Hatsukami, and C Yuan. Quantitative magnetic resonance imaging analysis of neovasculature volume in carotid atherosclerotic plaque. Circulation, 107:851–856, 2003. [33] HJ Weinmann, W Ebert, B Misselwitz, and H Schmitt-Willich. Tissue-speciﬁc mr contrast agents. Eur J Radiol, 46:33–44, 2003. [34] MH Krause, KK Kwong, J Xiong, ES Gragoudas, and LH Young. Mri of blood volume with ms 325 in experimental choroidal melanoma. Magn Reson Imaging, 21:725–732, 2003. [35] K Turetschek, E Floyd, T Helbich, TP Roberts, DM Shames, MF Wendland, WO Carter, and RC Brasch. Mri assessment of microvascular characteristics in experimental breast tumors using a new blood pool contrast agent (ms-325) with correlations to histopathology. J Magn Reson Imaging, 14:237–242, 2001. [36] C Corot, X Violas, P Robert, G Gagneur, and M Port. Comparison of different types of blood pool agents (p792, ms325, uspio) in a rabbit mr angiography-like protocol. Invest Radiol, 38:311–319, 2003. [37] C Pradel, N Siauve, G Bruneteau, O Clement, C de Bazelaire, F Frouin, SR Wedge, JL Tessier, PH Robert, G Frija, and CA Cuenod CA. Reduced capillary perfusion and permeability in human tumour xenografts treated with the vegf signalling inhibitor zd4190: an in vivo assessment using dynamic mr imaging and macromolecular contrast media. Magn Reson Imaging, 21:845–851, 2003. [38] J Barkhausen, W Ebert, C Heyer, JF Debatin, and HJ Weinmann. Detection of atherosclerotic plaque with gadoﬂuorine-enhanced magnetic resonance imaging. Circulation, 108:605–609, 2003. [39] C Chambon, O Clement, A Le Blanche, E Schouman-Claeys, and G Frija. Superparamagnetic iron oxides as positive mr contrast agents: in vitro and in vivo evidence. Magn Reson Imaging, 11:509–519, 1993. [40] SG Ruehm, C Corot, P Vogt, S Kolb, and JF Debatin. Magnetic resonance imaging of atherosclerotic plaque with ultrasmall superparamagnetic particles of iron oxide in hyperlipidemic rabbits. Circulation, 103:415–422, 2001. [41] YX Chen, Y Nakashima, K Tanaka, S Shiraishi, K Nakagawa, and K Sueishi. Immunohistochemical expression of vascular endothelial growth factor/vascular permeability factor in atherosclerotic intimas of human coronary arteries. Arteriosler Thromb Vasc Biol, 19:131–139, 1999. [42] P Libby. Inﬂammation in atherosclerosis. Nature, 420:868–874, 2002.

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Inter- and Intra-Observer Variability Assessment of in Vivo Carotid Plaque Burden Quantiﬁcation Using Multi-Contrast Dark Blood MR Images Shaoxiong ZHANG, Jasjit S. SURI, Olivier SALVADO, Yiping CHEN, Frank K. WACKER, David L. WILSON, Jeffrey L. DUERK and Jonathan S. LEWIN Case Western Reserve University, Cleveland, OH Abstract. The chapter presents the research to test the hypotheses that (1) vessel wall volume measurements from dark blood MR images with multiple contrastweightings (T1W, T2W and PDW) are highly reproducible, and that (2) the intraobserver and inter-observer variability of carotid wall volume measurements will be less than those obtained with maximum wall area (MaxWA) measurements. Methods: Sixteen patients (aged 72 ± 7years) with carotid stenosis documented by duplex ultrasound were recruited for the study. Dark blood T1W, PDW and T2W MR images were used to measure carotid wall volume and MaxWA by two independent observers for inter-observer and intra-observer variability assessment. Results: The intra-observer absolute difference of carotid wall volume for T1W, T2W and PDW images were 67.3 ± 47.5 mm3 (2.3 ± 1.8%), 63.2 ± 52.2 mm3 (2.0 ± 1.3%), and 69.8 ± 45.2 mm3 (2.4 ± 1.7%) respectively. The inter-observer absolute difference of carotid wall volume for T1W, T2W and PDW images were 103.5 ± 141.8 mm3 (3.0 ± 3.1%), 95.9 ± 102.1 mm3 (3.1 ± 2.6%), and 132.1 ± 87.8 mm3 (4.3 ± 2.7%) respectively. The intra-observer absolute difference of carotid MaxWA for T1W, T2W and PDW images were 6.9 ± 5.0 mm2 (4.2 ± 2.9%), 5.1 ± 4.2 mm2 (3.1 ± 2.3%) and 7.5 ± 4.7 mm2 (4.2 ± 2.7%) respectively. The inter-observer absolute difference of carotid MaxWA for T1W, T2W and PDW images were 9.5 ± 4.2 mm2 (5.8 ± 2.3%), 6.4 ± 6.1 mm2 (3.8 ± 3.1%) and 10.8 ± 7.3 mm2 (6.1 ± 3.7%) respectively. Both intra- and inter-observer variability in carotid volume measurement tend to be smaller than that in carotid MaxWA measurement with intraclass correlation coefﬁcients ranged 0.932 to 0.987 for volume measurement and 0.822 to 0.946 for MaxWA measurement. Keywords. Atherosclerotic disease, image quality rating, image segmentation, carotid boundary tracing, wall volume, maximum wall area, evaluation, intraobserver, inter-observer variability assessment, statistical analysis

Background Atherosclerotic disease of the carotid artery is the leading cause of stroke. For all ischemic stroke, it was shown that the highest early recurrent strokerate was found in

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those with large-artery atherosclerotic disease (1). The risk of stroke from carotid artery stenosis progressively increases with the increasing degree of stenosis; however the degree of stenosis does not completely explain stroke risk. Moderate carotid artery stenosis is associated with stroke, though not quite as strongly as high-grade stenosis (2,3). Increasingly investigators are exploring the relationship between atherosclerotic clinical outcomes and plaque burden and composition (4–6). Atherosclerosis is a systemic disease of the vessel wall, which primarily involves medium to large arteries including the carotid artery, the coronary arteries and the aorta. Thus, direct in vivo visualization of the vessel wall would be extremely meaningful in understanding atherosclerotic disease. Over the last decade, MRI has emerged as a potential leading in vivo imaging modality for atherosclerotic plaque characterization (7–12). While many MR methods have been advocated for vessel wall analysis, black blood high-resolution MRI techniques with multiple contrast weightings have been shown to be not only useful for atherosclerotic tissue characterization (12–14) but also for vessel wall area measurement (15–18) (a known direct measure of plaque burden). Vessel wall area measurement allows monitoring of regression and progression of atherosclerosis. The importance of plaque burden quantiﬁcation should not be underemphasized. Quantiﬁcation during disease progression and after therapeutic intervention may improve our knowledge of the natural history of disease and lead to improved therapeutic strategies. A reliable quantitative method is necessary to precisely assess atherosclerotic plaque burden. Maximum wall area (MaxWA) has been used as a reproducible parameter to assess plaque burden (17), however, the accuracy and reproducibility of direct vessel wall volume measurement remains unclear when compared to other measures like MaxWA. This study was performed to test the hypotheses that (1) vessel wall volume measurements from dark blood images with multiple contrast-weightings (T1W, T2W and PDW) are highly reproducible, and that (2) the intra-observer variability and interobserver variability of carotid wall volume measurements will be less than those obtained when using MaxWA measurements. If vessel wall volume measurement on MRI images is reproducible, this method could be useful for monitoring the changes in carotid plaque burden and the response of plaque burden to pharmacological therapies.

Methods Patient Population Sixteen patients (14 males and 2 females, aged 72 ± 7 years) with carotid stenosis documented by duplex ultrasound were recruited for the study. Informed consent was obtained from all subjects under a protocol approved by the institutional review board for human investigation. MR Examination All MR scans were conducted on a 1.5 T system (Magnetom Sonata. Siemens Medical Solutions, Erlangen, Germany) with a custom-built phased array coil to improve the local image signal-to-noise ratio. Patients were positioned supine on the scanner

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table. After axial, sagittal and coronal localizer images were acquired; a set of double oblique localizer imagers was then acquired to monitor the phased array coil position and to roughly identify the carotid artery bifurcation. Then, a transaxial threedimensional (3D) multiple overlapping thin slab angiography(MOTSA) sequence with TR/TE/ﬂip angle/partition thickness = 20 ms/3.4 ms/25◦ /1.0 mm, was used to locate the exact level of the carotid bifurcation. Dark blood images were then obtained using ECG-triggered double inversion recovery (DIR) turbo spin echo sequences. The imaging parameters (TR/TE/TI/NSA/thickness/FOV) were as follows: T1W: 1R-R/7.1 ms/ 500 ms/2/3 mm/13 cm; PDW: 2R-R/7.1 ms/600 ms/2/3 mm/13 cm; T2W: 2R-R/68 ms/ 600 ms/2/3 mm/13 cm. Fat saturation was applied for all dark blood images. The in plane resolution was 0.51× 0.51 mm2 . Image Quality Rating and Atherosclerotic Plaque Classiﬁcation An image quality rating, on a scale of 1–5, was used to rate all three series of images (1 being the poorest; 5 representing the highest) based on image information content, image artifacts and overall signal-to-noise level. A single rating was assigned to each image from each series of images. If an image received a rating of 2 or less in any series (T1W, T2W and PDW), images from the same location from the other series were discard from review. Atherosclerotic plaque classiﬁcation for each patient was determined according to a recently reported modiﬁed AHA classiﬁcation for MRI (14). Image Segmentation and Carotid Boundary Tracing The carotid lumen and outer wall boundaries were manually segmented on a freestanding image processing station (MR View, Siemens, Erlangen, Germany). The outer vessel wall boundary was deﬁned as the vessel wall-perivascular soft tissue interface. The wall area was deﬁned as the area calculated by subtracting the lumen area from the outer wall boundary area. Operators manually placed initial points onto the lumen and outer wall boundaries to measure carotid artery cross-sectional area. Boundaries were automatically determined by the workstation; once the boundaries were deﬁned, the area was automatically calculated. Segmentation of the lumen and outer wall boundary was performed on each image set independently by two observers who were blinded to the measurement results obtained on other image contrast weighted data sets. Wall Volume and Maximum Wall Area Evaluation MaxWA was deﬁned as the largest area measured from the distal common carotid, the bifurcation, and the internal carotid artery wall. Wall volume was deﬁned as the sum of each section volume, which was deﬁned as the wall area from each slice multiplied by the slice thickness. Intra-Observer and Inter-Observer Variability Assessment The measurements from two observers were used to assess the inter-observer variability. To assess the intra-observer variability, measurement of each image data set was repeated at a different time by a single observer, again blinded from all other measurements. The average time between measurements was 3 weeks.

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Figure 1. Bright blood signal on TOF image is satisfactory suppressed on DIR T1W, PDW and T2W images with dark lumens. Arrows indicate type VIII plaque (ﬁbrotic plaque without lipid core) in the left common carotid artery.

Statistical Analysis All measurement data from T1W, T2W and PDW images were exported to an Excel 2000 spread sheet for calculations of absolute differences, both on the original scale (mm2 for MaxWA and mm3 for carotid volume measurement) and as a percentage. For each MaxWA measurement, the absolute difference in area for both inter-observer measurements and intra-observer measurements was divided by the section mean area and multiplied by 100% to convert it to a percentage. For each carotid artery volume measurement, the absolute difference in area for both inter-observer measurements and intraobserver measurements was divided by the mean volume of the measured vessel wall and multiplied by 100% to convert it to a percentage. Paired t-tests for inter- and intraobserver measurements on the three contrast-weightings were then performed. P < 0.05 is used to deﬁne a signiﬁcant difference between pairs. Intra-observer and inter-observer agreement was calculated using the intraclass correlation coefﬁcients (ICC) (SPSS 11.0).

Results Three different contrast weightings, T1, T2 and PD, were successfully acquired in all subjects with satisfactory ﬂow signal suppression (Fig. 1). Images from one patient were used for the training session to ensure consistency between the two readers on the criteria to deﬁne the lumen and outer wall boundaries. Four hundred and fourteen images from one hundred and thirty-eight locations (3 contrast weightings × 138 locations) from the remaining 15 patients were available for this study. Thirty-six images corresponding to 12 locations were discarded due to image quality rating of 2 or less.

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Figure 2. Intra-observer variability in carotid wall volume and MaxWA measurements. Measurement differences were small on both carotid wall volume and MaxWA measurements with smaller difference in volume measurement (<2.4%) than that in MaxWA measurement (<4.4%).

Type III disease was identiﬁed in 3 cases. Type IV–V disease was identiﬁed in 5 cases. Type VI disease was identiﬁed in 2 cases. Type VII disease was found in 4 cases while type VIII lesions were found in 2 cases (Fig. 1). Measurement on Maximum Wall Area The mean carotid MaxWA for T1W, PDW and T2W images were 86.9 mm2 , 84.8 mm2 and 80.2 mm2 respectively. The intra- and inter-observer absolute difference of carotid MaxWA for T1W, PDW and T2W images were summarized in Tables 1 and 2. No statistically signiﬁcant difference was noted for both the intra-observer and inter-observer measurements. The variation of inter-observer measurement is slightly larger than that of intra-observer measurement. Measurement on Carotid Wall Volume The mean carotid wall volumes for T1W, PDW and T2W images were 1622.6 mm3 , 1561.3 mm3 and 1452.8 mm3 respectively. The intra- and inter-observer absolute differences of carotid wall volume for T1W, PDW and T2W images were summarized in Tables 1 and 2. No statistically signiﬁcant difference was identiﬁed for both the intraobserver and inter-observer measurements. As evidenced in MaxWA quantiﬁcation, the variation of inter-observer measurement is slightly larger than that of intra-observer measurement in carotid artery wall volume quantiﬁcation. Comparison of Inter- and Intra-Observer Measurements and Comparison of Maximum Wall Area and Carotid Wall Volume Measurement As indicated in Figs 2 and 3, the difference for inter-observer measurements is larger than that for intra-observer measurements. The percentile of the mean of the absolute dif-

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389

Figure 3. Inter-observer variability in carotid wall volume and MaxWA measurements. Measurement differences were small on both carotid wall volume and MaxWA measurements with smaller difference in volume measurement (<4.3%) than that in MaxWA measurement (<6.1%).

ference in volume measurements is smaller than that in MaxWA measurements for both intra- and inter-observer evaluation. As shown in Tables 1 and 2, intraclass correlation coefﬁcients for carotid wall volume measurement in both inter- and intra-observer evaluation are higher than those for carotid MaxWA measurements, which suggest that carotid wall volume measurements yield stronger correlation for both inter- and intra-observer measurements than MaxWA measurement do.

Discussion High resolution MRI is recognized as a powerful tool in atherosclerotic plaque characterization and vessel wall visualization (19–25). Previous studies have demonstrated the usefulness of cross-section vessel wall area measurement in assessing atherosclerotic plaque burden (26–28). Among many methods that have been explored, MaxWA measurement has been shown as a reliable method for in vivo plaque burden quantiﬁcation, as compared to ex vivo plaque cross-section area measurement (17). However, the usefulness of vessel wall volume measurement for plaque burden quantiﬁcation remains to be determined. In this study, the advantages of vessel wall volume measurement over MaxWA measurement was investigated by evaluating the intra- and inter-observer variability on carotid wall volume and MaxWA measurements.

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S. Zhang et al. / Inter- and Intra-Observer Variability Assessment Table 1. The intra-observer difference of measurements on carotid wall volume and MaxWA.

Unit

mm3 mm3 mm3 mm2 mm2 mm2

Contrast Volume T1 T2 PD MaxWA T1 T2 PD

ICC

P value

Absolute Mean

Difference SD

Percent of Absolute Difference Mean SD

0.987 0.981

0.062 0.571

67.3 63.2

47.5 52.2

2.3% 2.0%

1.8% 1.3%

0.981

0.261

69.8

45.2

2.4%

1.7%

0.935 0.946 0.897

0.054 0.074 0.759

6.9 5.1 7.5

5.0 4.2 4.7

4.2% 3.1% 4.4%

2.9% 2.3% 2.7%

Note: ICC = intraclass correlation coefﬁcients.

Table 2. The inter-observer difference of measurements on carotid wall volume and MaxWA. Unit

mm3

Contrast Volume T1

ICC

P value

Absolute Mean

Difference SD

Percent of Absolute Difference Mean SD

0.932

0.054

103.5

141.8

3.0%

3.1%

0.950 0.934

0.086 0.050

95.9 132.1

102.1 87.8

3.1% 4.3%

2.6% 2.7%

mm2 mm2

T2 PD MaxWA T1 T2

0.908 0.901

0.119 0.531

9.5 6.4

4.2 6.1

5.8% 3.8%

2.3% 3.1%

mm2

PD

0.822

0.210

10.8

7.3

6.1%

3.7%

mm3 mm3

To assess the impact of medical interventions on atherosclerosis, it is critical to identify a reliable method that can highly reproducibly measure the plaque burden. Our results showed that both MaxWA and carotid wall volume measurements are highly reproducible. The variability of both MaxWA and carotid wall volume measurements are small without statistically signiﬁcant differrence. The absolute mean differences in carotid wall volume measurement are less than 69.8 mm3 or 2.4% for the intraobserver, and 132.1 mm3 or 4.3% for the inter-observer. The absolute mean differences in carotid MaxWA measurement are less than 7.5 mm2 or 4.4% for the intra-observer, and 10.8 mm2 or 6.1% for the inter-observer (Tables 1, 2). Both inter- and intra-observer measurements on either carotid wall volume or MaxWA are highly correlated as evidenced by high intraclass correlation coefﬁcient R value as shown in Tables 1 and 2. Furthermore, in the present study, our results support the hypothesis that the intra-observer variability and inter-observer variability of carotid wall volume measurements will be better than those of the MaxWA measurements. Speciﬁcally, we found that the variation of carotid wall volume measurement is smaller than that of carotid MaxWA measurement from three different contrast weighted images on either inter- or intra- observer evalutation (Tables 1, 2; Figs 1, 2). Using two standard deviations to cover an expected 95% of differences, the carotid wall volume measurement would differ by 5.9% for interobserver measurement, by 9.7% for inter-observer measurement; the carotid MaxWA would differ by 10% for inter-observer measurement, by 13.5% for inter-observer measurement There are many possible reasons that carotid volume measurement are supe-

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rior to MaxWA measurements. First, more locations were included in carotid volume measurements than from MaxWA which is obtained from a single location. Thus the measurement error from a single location on volume assessment has been minimized. Second, MaxWA may not be measured from the same location since it is the maximum area among common carotid, bifurcation and internal carotid artery regardless of the physical location. Carotid volume, however, was obtained from matched volumes, thus minimizing the potential misregistration errors. Since different observers conducted measurements on the identical image sets one could hope that their measurements would be the same, or alternatively, the interobserver variability should be similar to the intra-observer variability. The observation that inter-observer variability was higher than intra-observer variability in this study suggests that either more extensive training should be provided to the different observers, or the same patient should be evaluated by the same observer in order to more reliably monitor changes in the atherosclerotic plaque burden. It was reported that Multi-spectrum dark blood MR images were used to measure carotid plaque area, in which T1W images were acquired with a DIR technique while T2W and PDW images were acquired using non-DIR fast spin echo sequences (18). When T2W and PDW images were acquired using non-DIR technique, the ﬂow artifacts within lumen may cause difﬁculty in determining the exact lumen boundary and further impact the accuracy in the measurement of carotid wall volume and MaxWA. Thus TOF MRA may be used as a reference in recognizing the true lumen boundary under these circumstances (18). In this study, lumen boundaries on T2W and PDW images were clearly demonstrated with satisfactory ﬂow suppression by a DIR technique. Thus, TOF images were not used as a reference. In addition to T1W images, DIR techniques should be used with T2W and PDW images due to their efﬁcacy in the ﬂow signal suppression. Lumen boundary segmentation is quite simple and reliable except for calciﬁcation on the plaque surface that is adjacent to lumen. However, the outer wall boundary visualization is a major obstacle to precise measurement in some cases. Contrast enhanced MRI may be useful not only for plaque characterization (29,30) but also for outer wall boundary deﬁnition. Akio has demonstrate that Gd-DTPA based contrast agent can induce rim-like enhancement of vessel wall (31,32), which would be helpful in identifying the carotid outer wall boundary in patients in whom the carotid outer wall is not well visualized on non-contrast dark blood MR images. Currently, DIR methods are essentiall single slice techniques. Thus, the scan time is relatively long. Scan coverage was limited at 10 slices due to scan time considerations,. With combination DIR and multi-slice techniques, larger scan coverage would be expected in the near future. Finally, according to our results, regardless of intra- or inter-observer assessment, one can reliably detect 9.7% changes in carotid wall volume and 13.5% changes in carotid maximum wall area measurement, which may be set as a cut-point for potential clinical application in monitoring atherosclerosis regression or progression after medical intervention (pharmacology therapy).

Limitation Plaque burden for this study was deﬁned as the vessel wall volume due to the inability to segment the exact plaque contour. Direct measurement of plaque volume would be

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possible in the near future with further improvements in both spatial resolution and SNR that could result from catheter-based intra-vascular coils (33).

Conclusion Both carotid wall volume and MaxWA measurements are highly reproducible as shown by intra-and inter-observer investigation in this study. Arterial wall volume measurement may provide a more accurate measure of plaque burden when compared to MaxWA measurements. The observation that inter-observer variability was higher than intra-observer variability suggests that either more extensive training should be provided to the different observers, or that the same patient should be evaluated by the same observer in order to more reliably monitor atherosclerotic plaque regression or progression.

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Three-Dimensional Volume Registration of Carotid MR Images Baowei FEI a , Jasjit S. SURI b and David L. WILSON a a Case Western Reserve University, Cleveland, OH, USA b Fischer Imaging Corporation, Denver, CO, USA Abstract. This chapter describes automatic three-dimensional registration techniques for magnetic resonance images of carotid vessels. The immediate applications include atherosclerotic plaque characterization and plaque burden quantiﬁcation vector-based segmentation using dark blood MR images having multiple contrast weightings (proton density (PD), T1, and T2). Another application is the measurement of disease progression and regression with drug trials. A normalized mutual information registration algorithm is applied to compensate movements between image acquisitions. PD, T1, and T2 images were acquired from patients and volunteers and then matched for image analysis. Visualization methods such as contour overlap showed that vessels well aligned after registration. Distance measurements from the landmarks indicated that the registration method worked well with an error of less than 1-mm. Keywords. Image registration, mutual information, non-rigid registration, dark blood MR image, carotid plaque classiﬁcation

1. Introduction Atherosclerotic disease of the carotid artery is the leading cause of stroke [1]. Magnetic resonance imaging (MRI) has emerged as a potential leading in vivo imaging modality for atherosclerotic plaque characterization [2,3]. Black blood high-resolution MRI techniques with multiple contrast weightings (proton density (PD), T1, and T2) have been shown to be useful for atherosclerotic plaque characterization and plaque burden assessment [4]. Quantiﬁcation during disease progression and after therapeutic intervention may improve our knowledge of the natural history of the disease and lead to improved therapeutic strategies. However, the spatial location mismatching of different scans from serial examination will impair the accuracy of quantiﬁed analysis of atherosclerotic disease using MRI. Image registration has the potential to improve the quantiﬁcation and characterization [5]. Combination of multiple images such as PD, T1, and T2 could verify lesions and provide more information for diagnosis and treatment. Further, registration of serial examinations can follow up the progression and regression of diseases [6]. There are a very large number of 3D registration applications in MR vascular imaging, including: registration of proton density, T1-weighted, and T2-weighted images for tissue typing;

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registration for vascular progression/regression studies; and registration for subtraction processing to increase conspicuity of imaging agents. We review the literatures on vascular image registration in the next paragraphs. Chillet et al. developed a method for forming vascular atlases using vascular distance maps and a vascular model-to-image registration method [7]. Blood vessels were extracted from data using a tubular object segmentation method. A subject’s vascular network model was chosen as a template, and its vascular distance map (DM) image was computed. Each of the remaining vascular network models was registered with the DM template using a vascular model-to-image afﬁne registration method. Chan et al. presented a multi-modal three-dimensional (3D) vascular registration algorithm, which transforms the 3D-3D registration problem into a multiple twodimensional (2D)-3D vascular registration problem [8]. Along each orthogonal axis, a projected 2D image from a segmented binary 3D ﬂoating volume was compared with maximum intensity projection (MIP) image of the reference volume. Stewart et al. introduced a dual-bootstrap iterative closest point (Dual-Bootstrap ICP) registration method for retinal registration [9]. The approach starts from one or more initial, low-order estimates that are accurate in small image regions, called bootstrap regions. In registering retinal image pairs, Dual-Bootstrap ICP is initialized by automatically matching individual vascular landmarks, and it aligns images based on detected blood vessel centerlines. Hipwell et al. proposed a registration method for aligning 3D magnetic resonance angiography (MRA) with 2-D X-ray digital subtraction angiograms (DSA) [10]. The method was developed from an algorithm to register computed tomography (CT) volumes to X-ray images based on intensity matching of digitally reconstructed radiographs (DRRs). To make the DSA and DRR more similar, they transformed MRA images and computed the similarity between the transformed MRA images and the DSA images. Aylward et al. developed a method for rigidly aligning images of tubes for the registration evaluation of 3D images of human vasculature [11]. The method aligned a source image with a target image by registering a model of the tubes in the source image directly with the target image. Time can be spent to extract an accurate model of the tubes in the source image. The registration method was built upon the principles of a tubular object segmentation work that combines dynamic-scale central ridge traversal with radius estimation. Bullitt et al. proposed a semiautomatic method of 3D-2D vascular registration [12]. The objective was to help guide endovascular procedures by allowing interpretation of each digital subtraction angiographic (DSA) image in terms of pre-created, connected 3D vessel trees that were created from MRA images. Zana et al. presented an algorithm for temporal and/or multimodal registration of retinal images based on point correspondences [13]. The algorithm was applied to the registration of ﬂuorescein images (obtained after a ﬂuorescein dye injection) with green images (green ﬁlter of a color image). The vascular tree was ﬁrst detected in each type of images and bifurcation points were labeled with surrounding vessel orientations. An angle-based invariant was then computed in order to give a probability for two points to match. A Bayesian Hough transform was used to sort the transformations with their respective likelihoods. An afﬁne estimate was computed for most likely transformations. Hamilton et al. used major blood vessels for the registration of pelvic CT and SPECT [14]. Vessels were segmented from the image datasets by outlining them on

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transverse planar slices using a mouse-based drawing tool. Stacking the transverse outlines provides a 3D representation of vascular structures. Registration was performed by matching the surfaces of the segmented volumes. Beier et al. introduced an image registration procedure for an enhanced visualization of the contrast agent. Object displacements were detected by analyses of image deformations in local regions [15]. Motion patterns were used to compute a synthetic mask of maximum congruence with the contrast medium image. Mask images were used in the subsequent subtraction processing. Although there are many other methods such as anatomical point, line, or surfacebased registration methods [16–22], we will focus on gray scale-based registration techniques because they do not require segmentation and because they are useful for nonrigid registration [23–36]. In many cases, rigid body registration of a volume of interest will be sufﬁcient because patients should move little between image acquisitions. Gray-scale, rigid body, mutual information registration has been used successfully in many applications for same modality and cross-modality registration [23,27,29,30]. We recently developed and used a mutual information algorithm with special features that added robustness to register MR images of abdominal organs such as the liver and prostate [24–28,37]. Registration quality was rigorously evaluated using a large variety of qualitative and quantities techniques. We also used mutual information and created a fast and accurate slice-to-volume registration algorithm for applications in interventional-MR-guided thermal ablation of prostate cancer [25–27], a method with obvious applicability to vascular MR interventions [38]. In other cases, non-rigid registration may be required. Schemes have been suggested for brain [39–41], breast [42–44], a variety of other organs [24,45–47], and excised tissue [48]. We have created a non-rigid registration algorithm for the prostate and pelvis [28,49,50]. An interactive method where an operator sets initial control points that are optimized by the computer [28] could be extended to provide a platform for non-rigid registration experiments on vascular MR images. A recent automated non-rigid scheme [50] is very robust and accurate for MR prostate images. In this study, we perform registration experiments for MR images from patients with carotid stenosis and health volunteers. We will demonstrate the mutual information image registration algorithm for the carotid MR images. We will discuss the potential application of a deformable image registration method for vascular MR image volumes.

2. Materials and Methods A. Registration Algorithm We are investigating voxel-based methods for automatic 3D registration because they do not depend on possibly inaccurate image segmentation and because they can be extended to non-rigid registration [23,25,27,28]. We used normalized mutual information (NMI) as the similarity measures in our registration because they are robust and suitable for multi-modality image registration [23]. Suppose one image R is the reference, and the other F is ﬂoating. NMI is given by the following equation [23].

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NMI(R, F ) = where H (R) = −

2MI (R, F ) H (R) + H (F )

pR (r) log pR (r),

H (F ) = −

r

MI(R, F ) =

397

r,f

pF (f ) log pF (f )

f

pRF (r, f ) log

pRF (r, f ) . pR (r) · pF (f )

The joint probability pRF (r, f ) and the marginal probabilities pR (r) of the reference image and pF (f ) of the ﬂoating image, can be estimated from the normalized joint intensity histograms. When two images are geometrically aligned, NMI is maximal. The ﬂow chart of the registration algorithm follows. 1. Set an initial transformation parameters 2. Optimize similarity (NMI) between the reference and reformatted MR volumes 1) Transform the initial reformatted volume and interpolate to get a new reformatted volume 2) Calculate similarity (NMI) between the reference and the new reformatted MR volumes 3) Repeat 1) and 2) until meeting the function tolerance or the maximum iteration number We used rigid body transformation (three translations and three angles) and trilinear interpolation. For optimization, we use the downhill simplex method of Nelder and Mead [51]. Optimization of alignment ends either when the maximum number of NMI calculations is reached (typically 500) or the fractional change in NMI is smaller than a tolerance (typically 0.0001). Our very ﬁrst initial guesses are all zeros for the 3 displacements and 3 angles. B. Image Acquisitions All MR scans were conducted on a 1.5 T system (Magnetom Sonata, Siemens Medical Solutions, Erlangen, Germany) with a custom-built phased array coil to improve the local image signal-to-noise ratio. Patients were positioned supine on the scanner table. After axial, sagittal and coronal localizer images were acquired; a set of double oblique localizer images was then acquired to monitor the phased array coil position and to roughly identify the carotid artery bifurcation. A transverse three-dimensional (3D) multiple overlapping thin slab angiography(MOTSA) sequence with TR/TE/ﬂip/partition thickness of 20 ms/3.4 ms/25◦ /1 mm, was used to locate the exact level of the carotid bifurcation. Dark blood images were then obtained using ECG-triggered double inversion recovery (DIR) turbo spin echo sequences. The imaging parameters (TR/TE/TI/NSA/thickness/FOV) were as follows: 1R-R/7.1 ms/500 ms/2/3 mm/13 cm (T1), 2R-R/7.1 ms/600 ms/2/3 mm/13 cm (PD), 2R-R/68 ms/600 ms/2/3 mm/13 cm (T2). Fat saturation was applied for all dark blood images. The in plane resolution was 0.51×0.51 mm2 . We acquired PD, T1, and T2 images from one patient P1 and two volunteers S1 and S2.

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C. Registration Experiments We have nine pairs of volumes for registration experiments. For each subject, we have PD, T1 and T2 image volumes. We used PD as the reference image and we registered T1 and T2 with PD. We also matched T2 with T1 to test the registration algorithm. There are three registration experiments for each subject. We performed two registration trials for volunteers S1 and S2. In total, we conducted 15 registration experiments, three for the patient P1 and three for each of the volunteers S1 and S2. D. Registration Evaluation We used visual inspections to evaluate the registration. We used RegViz, a program written in IDL (Interactive Data Language, Research System Inc., Boulder, CO) and created in our laboratory for visualizing and analyzing registered image volumes. First, we manually segmented carotid vessel walls in image slices and copied them to corresponding slices. This enabled visual determination of the overlap of vessel walls over the entire volume. Second, color overlay displays were used to evaluate overlap of structures. One image was rendered in gray and the other in the “hot-iron” color scheme available in IDL. To visualize potential differences, it was quite useful to interactively change the contribution of each image using the transparency scale. Third, we used a sector display, which divided the reference and registered images into rectangular sectors and created an output image by alternating sectors from the two input images. Even subtle shifts of edges would be clearly seen. We evaluated registration of the vessels by measuring the displacement of the landmarks following registration. We used the left and right bifurcations as the landmarks. To measure displacements, we navigated transverse, coronal, and sagittal MR images sliceby-slice to search bifurcations in both reference and registered volumes. Using consistent rules and magniﬁed images, a radiologist used a cursor to identify unique features on both images. The 3D locations for each landmark were recorded and 3D distance between corresponding landmarks is computed.

3. Results A. Visual Inspection We determined the quality of vessel registration by visually examining all image slices of registered volume pairs using one or more of the methods found in RegViz. A typical example is shown in Fig. 1 where the contour overlap is excellent and probably within the manual segmentation error. Other transverse images were also well aligned indicating that the registration was successful in three dimensions. Other visual inspection techniques such as color overlay (Fig. 2) also demonstrate excellent registration.

B. Assessments of Bifurcations Following registration, we measured 3D distances between corresponding bifurcations. Registration results are shown in Table 1. The average error across the three subjects

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Figure 1. Contour overlap for registration evaluation of MR images of carotid vessels. The top images from left to right are proton density (PD), T1, and T2 images, respectively. Both T1 and T2 images were registered with the PD image. The rectangular regions are magniﬁed and displayed at the bottom. The carotid vessel walls were manually segmented from the PD image (left) and copied to the T1 (center) and T2 images (right). The contour overlaps at the bottom shows that the vessel boundaries from PD well aligned with those in T1 and T2 images. Images are from Volunteer S1.

Figure 2. Surface rendering and transparent display. Image on the left (red) is the surface rendering of the bifurcation. Carotid artery images were acquired from a patient using proton density MR imaging. Image at the center (blue) is the same bifurcation from T1-weighted MR images. Image on the right is the transparent display. The red is from proton density images and the blue is from T1 images. The color display shows excellent registration of the bifurcation.

with 15 registration experiments is only 1.09 ± 0.42 mm. The isotropic voxel size of the volumes is 0.51 mm. The measured error reported for NMI registration is probably overestimated due to landmark location error.

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B. Fei et al. / Three-Dimensional Volume Registration of Carotid MR Images Table 1. Displacement of Bifurcations Mean (Standard Deviation) in mm. PD-T1

PD-T2

T1-T2

Left bifurcation

1.04 (0.63)

1.49 (0.56)

1.02 (0.27)

Right bifurcation

0.97 (0.34)

1.04 (0.24)

0.98 (0.31)

Figure 3. MR carotid images with large head movement. Images at the top were acquired when the subject’s head was at the normal center position. Images at the center were acquired when the subject moved his head to the left side. Images at the bottom were acquired when the subject moved his head to the right. Images from left to right panels are proton density (PD), T1, and T2 images, respectively. The same ﬁeld of view (FOV) was used to acquire these images. Multiple two-dimensional images were acquired. Images are from the slice No. 2.

C. Implementation Issues The algorithm was quite robust for nine volume pairs in this study. Each call to the Simplex optimization resulted in 120 to 250 NMI evaluations before the tolerance (0.0001) was reached. The time for a single registration, typically 5 minutes for the volumes with 256 × 256 × 59-voxels on a Pentium IV, 1.8GHz CPU, with 1Gbytes of memory, could probably be greatly improved with optimized C code rather than IDL.

4. Discussion A. Patient Movement and Deformation In this study, the rigid body registration works well because we kept patients in the same position during imaging experiments and because we minimized the patient movement between imaging acquisitions. Normally, patients’ heads are at the center position during imaging acquisitions. For extreme cases, patients may move his head to one side, either left or right side. Figures 3–5 show images acquired from a healthy volunteer who was

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Figure 4. MR carotid images with large head movement. See the legend of Fig. 3 for detail. Images are from the slice No. 6.

Figure 5. MR carotid images with large head movement. See the legend of Fig. 3 for details. Images are from the slice No. 10.

asked to move his head between image acquisitions. In these cases, we observed large movement and deformation in the simulated imaging experiments. We anticipate that rigid body registration may not work in this situation. In the next section, we discuss the ability of non-rigid registration to express this deformation. Non rigid registration studies are reported for the brain [52,53], for the breast [54–56], for a variety of other organs [57–60], for excised tissue [61], and for the prostate [62]. Voxel based methods, particularly those based upon mutual information, are robust, require no segmentation that can be prone to error, are highly accurate for

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Figure 6. Flow chart of the warping registration algorithm. Following rigid body registration, N control points are selected in both the reference and ﬂoating volumes. A small cubic volume of interest (VOI) is centered on each control point. Optimization is performed by varying the x, y, and z locations of the ﬂoating VOI until the mutual information between corresponding voxels is maximized. Each control point is optimized independently, and then the optimized control points are used to establish a three-dimensional thin plate spline transformation for the entire volume.

brain registration [63], and are suitable for abdominal registration where there can be deformation [64]. We are discussing voxel-based non-rigid registration for the potential application in the vascular imaging. B. Non-Rigid Registration Algorithm Figure 6 outlines a non-rigid body registration method that has been successfully applied to the prostate and pelvic MR images [28]. We brieﬂy describe the algorithm because it has the potential for the vascular image registration. The non-rigid registration algorithm includes three major steps: control point selection, control point optimization, and thin plate spline warping. Prior to non-rigid registration, we perform rigid body registration as reported in Section 2. Again, the unchanging volume is the reference, and the one to be warped is ﬂoating. The manual selection of CP’s is an important step. We used home-made software for visualizing and analyzing image volumes. Following rigid body registration, the aligned two volumes are displayed in two rows slice-by-slice. Images can be transverse, coronal, or sagittal slices. It is quite straightforward to ﬁnd corresponding features at the vascular structures. We normally select control points (CP’s) using recognizable organ features such as corners and intersections of edges because of their unique positions. Corresponding CP’s in the two volumes are placed using a cursor, and sometimes they are in different image slices. The 3D coordinates are automatically stored in a ﬁle. Because of the optimization that occurs later, the correspondence can be up to 15 mm or ≈ 10 voxels in error. The next step of the non-rigid algorithm (Fig. 6) is the CP optimization. We deﬁne a small cubic volume of interest (VOI) centered at each CP. The VOI can be 16, 32, 48 or

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64 voxels on a side. As reported later, the selection of VOI size depends on the amount of warping required. A simplex optimization algorithm varies the x, y, and z transformation parameters of the ﬂoating VOI until the mutual information with the reference VOI is optimized. Each control point is optimized independently and the 3D coordinates of the optimal CP’s are recorded. The ﬁnal major step is to warp the ﬂoating volume using the corresponding optimal CP’s coordinates to establish a three-dimensional thin-plate spline (TPS) transformation [65,66]. We now brieﬂy go through the three computing steps for the TPS transformation. First, let P1 = (x1 , y1 , z1 ), P2 = (x2 , y2 , z2 ), . . . , Pn = (xn , yn , zn ) be n control points in the image coordinate of the reference volume. Write rij = |Pi − Pj | for the distance between point i and j . We deﬁne matrices: ⎤ ⎡ 1 x1 y1 z1 ⎢ 1 x2 y2 z2 ⎥ ⎥ P =⎢ ⎣· · · · · · · · · · · ·⎦, n × 4; 1 xn yn zn ⎡ ⎤ 0 r12 r13 · · · r1n ⎢r21 0 r23 · · · r2n ⎥ ⎥ K=⎢ ⎣ · · · · · · · · · · · · · · · ⎦, n × n; rn1 rn2 rn3 · · · 0 and

L=

K P , (n + 4) × (n + 4); PT O

where T is the matrix transpose operator and O is a 4 × 4 matrix of zero. Second, let Q1 = (u1 , v1 , w1 ), Q2 = (u2 , v2 , w2 ), . . . , Qn = (un , vn , wn ) be n correspondingcontrol points in the image coordinate of the ﬂoating volume. We get matrices: ⎤ ⎡ u1 u2 · · · un V = ⎣ v1 v2 · · · vn ⎦, 3 × n, w1 w2 · · · wn Y − (V | 0

0

0

0)T ,

3 × (n + 4),

and deﬁne the vector W = (w1 , w2 , . . . , wn ) and the coefﬁcients α1 , αx , αy , and αz by the equation L−1 Y = (W | α1

αu

αv

αw )T .

Third, use the elements of L−1 Y to deﬁne a function f (u , v , w ) everywhere in the entire volume:

f (u , v , w ) = α1 + αu u + αv v + αw w +

n

wi Pi − (u, v, w).

i=0

Thus any voxel (ui , vi , wi ) in the ﬂoating volume is transformed to a new coordinate (u i , vi , wi ) and a warped volume can be obtained by trilinear interpolation.

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Figure 7. Control point selection when images are acquired in the treatment and diagnostic positions. Image (a) is from the reference volume acquired in the treatment position with legs raised. Image (b) is to be warped and is from the volume acquired in the diagnostic position with the subject supine on the table. Transverse slices best show the deformations, especially at the legs. As described in the text, control points indicated by the white dots are selected around the pelvic surface and the prostate. Each control point is located at one voxel but displayed much bigger for better visualization.

Additional algorithm details are now described. For both VOI optimization and rigid body registration, we use trilinear interpolation. Optimization of similarity ends either when the maximum number of calculations is reached (typically 500) or the fractional change in the similarity function is smaller than a tolerance (typically 0.001). We use IDL as the programming language. Some rules follow for strategic placement of CP’s. For registration of treatment and diagnostic image volumes, most CP’s were selected using transverse slices because they best showed the pelvic displacement when moving the legs to the treatment position (Fig. 7). About 25 CP pairs were placed near edge and point features having recognizable correspondence on each of 5–8 transverse slices with a z interval of ≈ 8 mm, covering the entire pelvic region. Additionally, we placed about 25 CP’s from sagittal slices because they provided other structures that can be missed in the transverse images. It was also important to include CP’s from organs other than the prostate because they constrained warps. We always placed CP’s at critical regions such as the prostate center, pelvic surface, bladder border, and rectal walls. In Fig. 8, we compare warping and rigid body registration for a typical volume pair in the treatment and diagnostic positions. Following warping registration, the prostate boundary overlap is excellent (Fig. 8e) and probably within the manual segmentation error. Similar results were obtained in other transverse slices throughout the prostate. The prostate 3D centroid calculated from segmented images displaced by only 0.6 mm, or 0.4 voxels, following warping. Following rigid body registration, the prostate was misaligned with a displacement to the posterior of ≈ 3.4 mm when in the treatment position

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Figure 8. volumes acquired in the treatment and diagnostic positions. Image (a) is from the reference volume acquired in the treatment position, and the prostate is manually segmented. Images in the left and right columns are from the ﬂoating volume acquired in the diagnostic position following rigid body and warping registration, respectively. To show potential mismatch, the prostate contour from the reference in (a) is copied to (b) and (c) and magniﬁed as the dashed contours in (d) and (e). The 3 mm movement of the prostate to the posterior is corrected with warping (e) but not rigid body registration (d). Pelvic boundaries manually segmented from the reference show signiﬁcant misalignment with rigid body (f) that is greatly improved with warping (g).

(Fig. 8d), as previously reported by us [25]. Using rigid body registration, there is significant misalignment throughout large regions in the pelvis (Fig. 8f) that is greatly reduced with warping (Fig. 8g). Note that warping even allows the outer surfaces to match well. Other visualization methods such as two-color overlays and difference images, quickly show matching of structures without segmentation but do not reproduce well on a printed page. We also examined the effect of conditions such as bladder and rectal ﬁlling that might change from one imaging session to the next. In Fig. 9, we compare warping and rigid body registration for a volume pair with one-week between imaging sessions. One volume is with an empty bladder and the other is with a relatively full bladder. There is also a difference in rectal ﬁlling. Warping registration closely aligns the prostate (Fig. 9e) while rigid body does not (Fig. 9d). In addition, rigid body registration does not align the bladder and parts of the rectum (Fig. 9f). With warping, the bladder closely matches the reference, and the rectum is better aligned (Fig. 9g). Other visualization methods showed excellent alignment of internal and surface edges.

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Figure 9. Comparison of rigid body and warping registration for volumes acquired with an interval of one week between imaging sessions. The reference image (a) with a manually segmented prostate was acquired later with an empty bladder (vertical arrow) and partial rectal ﬁlling (horizontal arrow). Images in the left and right columns are from the ﬂoating volume acquired earlier following rigid body and warping registration, respectively. To show potential mismatch, contours from the reference are shown on images following registration, as described in Fig. 8. The full bladder in (d) has pushed the prostate, shown by the continuous curve, in the caudal direction. After warping, prostate contours match closely (e). The bladder, rectum, and other organs closely align following warping (g). With rigid body (f), proceeding from left to right, the front of the pelvis, the bladder (arrow), and the rectum are all misaligned.

When vascular MR images are acquired at different positions (see Figs 3–5), the non-rigid image registration algorithm may work better than the rigid method. We are performing registration experiments to compare the two methods for the carotid artery. C. Registration of MR to Histology All automated segmentation and classiﬁcation strategies are to be validated against manual methods and against registered digitized histology as a gold standard. Histological validation requires experimental and computer techniques to enable registration of histological and MR images (Fig. 10). We developed a special tissue slicing apparatus, created a special 3D registration scheme using ﬁducial needles, used various stains to high-

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Figure 10. MR images and registered histological image. MR images were obtained from a fresh (< 1 hour) iliac artery taken from a human cadaver. The specimen was placed in to a custom-built birdcage phase-array coil to obtain high-resolution MR images and imaged in a 1.5T human MR system. The MR in plane resolution was 0.25×0.25 mm. Histological slides were prepared and imaged on a microscope system having a motorized stage and tiling software. Images were registered to produce the images shown here. Features in the MR images correspond to tissue types deﬁnitively identiﬁed in histology.

light features of interest, created non-rigid registration to correct for deformations and tears in histology images, and determined overall errors on the order of one MRI voxel in acceptable data sets [67,68]. We are investigating methods to perform registration of MR to histology for carotid MR images.

5. Conclusion We have developed an automatic volume registration algorithm for multiple contrast weighted MR images of carotid vessels. Our internal measures showed the registration is quite robust and accurate. It will probably be a useful tool for many applications of interest in vascular imaging. We also propose a non-rigid body registration for the potential application in vascular imaging.

References [1] Petty, G.W., Brown, R.D., Whisnant, J.P., Sicks, J.D., O’Fallon, W.M., and Wiebers, D.O., Ischemic stroke subtypes – A population-based study of functional outcome, survival, and recurrence, Stroke, Vol. 31, No. 5, pp. 1062–1068, 2000. [2] Fayad, Z.A. and Fuster, V., Clinical imaging of the high-risk or vulnerable atherosclerotic plaque, Circulation Research, Vol. 89, No. 4, pp. 305–316, 2001. [3] Yuan, C., Mitsumori, L.M., Beach, K.W., and Maravilla, K.R., Carotid atherosclerotic plaque: Noninvasive MR characterization and identiﬁcation of vulnerable lesions, Radiology, Vol. 221, No. 2, pp. 285–299, 2001.

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Plaque Imaging: Pixel to Molecular Level J.S. Suri et al. (Eds.) IOS Press, 2005 © 2005 The authors. All rights reserved.

Characterization of Shear Stress on the Wall of the Carotid Artery Using Magnetic Resonance Imaging and Computational Fluid Dynamics Peter YIM a , Kevin DeMARCO a , Marcelo A. CASTRO b and Juan CEBRAL b a UMDNJ-Robert Wood Johnson Medical School, New Brunswick, NJ, USA b SCS-George Mason University, Fairfax, VA, USA Abstract. Considerable evidence has emerged that adverse blood ﬂow patterns are a major factor in the onset of atherosclerotic disease and may play a role in disease progression. This chapter reviews a technique, referred to as vascular computational ﬂuid dynamics (CFD), for characterizing blood ﬂow patterns in large arteries from magnetic resonance angiography (MRA) and velocity-encoded phasecontrast magnetic resonance (PC MR) imaging. In vascular CFD, hemodynamic conditions are modeled by the ﬁnite-element method with ﬂow is governed by the incompressible Navier-Stokes equations. Construction of the vascular CFD models is a multi-step process. Critical aspects of the methodology are described in detail including surface reconstruction, construction of the volumetric mesh, imposition of boundary conditions and solution of the ﬁnite element model. In vitro and in vivo experimentation is discussed that demonstrates, in a preliminary manner, the validity of the methodology. Flow models are presented for carotid arteries with a wide range of atherosclerotic disease. Keywords. Carotid artery, magnetic resonance angiography, phase-contrast magnetic resonance imaging, computational ﬂuid dynamics, shear stress

1. Introduction Atherosclerotic disease of the carotid artery is a leading cause of stroke [1]. Atherosclerotic plaque in the carotid artery obstructs blood ﬂow to the brain and stimulates the formation of thrombo-emboli that occlude downstream vessels. The risk of stroke from carotid artery stenosis progressively increases with increasing degree of stenosis. For moderate stenosis (30–70%) in patients with history of transient ischemic attack (TIA), the 5-year risk of stroke is 4% [2]. For severe stenosis of 70–99% the 5-year risk of stroke is 13% [3]. Endarterectomy, or surgical removal of the plaque, is indicated for severe stenoses. Presumably, atherosclerotic plaque produces thrombo-emboli by similar mechanisms in the carotid and coronary arteries. In the coronary arteries, thrombo-emboli that

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cause heart attacks are precipitated principally by plaque rupture [4] and by plaque erosion [5,6]. Plaque rupture exposes the ﬂowing blood to extra-vascular tissue that is highly thrombogenic, including collagen and cholesterol [7]. Plaque rupture is due to both the presence of high mechanical stress on the plaque [8,9] and to a long-term process of thinning of the ﬁbrous cap possibly caused by inﬂammation [10]. Plaque erosion is the process of stripping of the endothelial cell lining of the vessel. This phenomena is estimated to occur in 25% of cases of sudden cardiac death [5]. Similarly to plaque rupture, plaque erosion exposes the ﬂowing blood to thrombogenic material within the ﬁbrous cap. Since the erosion occurs at the thickest point of the plaque, the erosion is likely related to shear stress from blood ﬂow. Similar processes may occur in the carotid artery. There is evidence that plaque rupture is not solely responsible for transient ischemic attacks (TIA’s) or stroke from plaques of the carotid artery. For example the occurrence of plaque rupture is only mildly larger in symptomatic patients than asymptomatic patients (77% vs 60%) [11]. Another possible mechanism for formation of thrombo-emboli in the carotid artery is via disturbed ﬂow distal to the stenosis [12]. In stenosed vessels, in the region immediately distal to the stenosis, there are ﬂow disturbances that presumably cause high spatial gradients of shear stress [13,14] and temporal variation of ﬂow directionality [15]. While in normal vessels, the endothelial cells are highly aligned with one another and with the direction of ﬂow [16] distinct abnormalities in the endothelium of the vessels occur distal to stenoses [17]. Distal to stenoses endothelial cells are poorly aligned, “giant” endothelial cells are present [18] and endothelial cells undergo apoptosis [19]. These abnormalities could predispose this region to the formation of thrombo-emboli. Clinical experience also suggests that ﬂow disturbance at stenoses could be a factor in progression of atherosclerosis or thrombogenesis. The presence of audible turbulence or bruits distal to high-grade stenoses is associated with the risk of stroke or TIA. However, the presence of bruits does not indicate a higher risk than other that associated with other high-grade stenoses [20]. Quantitative ﬂow imaging has demonstrated ﬂow is depressed in symptomatic carotid arteries relative to the contralateral arteries [21]. While this association between plaque instability and ﬂow may be incidental, it is entirely consistent with the hypothesis that hemodynamic phenomena play a role in the destabilization of atherosclerotic plaque. Shear stress is difﬁcult to measure in vivo and methodology for doing so the focus of our research. However, qualitative assessment of shear stress due to blood ﬂow has been made in coronary and carotid stenoses and compared with rates of stroke and heart attack. Angiograms taken prior to acute myocardial infarction were analyzed from 84 patients. Stenoses responsible for the current infarction were found to have a signiﬁcantly steeper outﬂow angles and were found to be signiﬁcantly more symmetrical [22]. These geometric factors could be associated with undesirable mechanical stress. Angiograms of 948 patients with high-grade stenoses from the European Carotid Surgery Trial were analyzed. Post-stenotic vessel diameter was measured in all angiograms. Those patients with post-stenotic narrowing were found to have an 8% 5-year risk of stroke versus a 25% 5-year risk for patients without narrowing [23]. The authors of that study speculate that widened internal carotid arteries have, on average, higher ﬂow rates. According to that hypothesis, higher ﬂow rates through a given grade of stenosis produce a greater risk of stroke. Findings in coronary artery disease also suggest that hemodynamic conditions have considerable importance relative to disease progression. Studies of restenosis after

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stenting of the coronary artery have found that the pressure gradient across the stent in the coronary artery are predictive of restenosis [24]. Given the functional signiﬁcance of shear stress on normal arteries and the possible role shear stress plays in thrombogenesis and plaque progression, we speculate that shear stress and other hemodynamic conditions at stenoses of the carotid artery may be associated with destabilization of atherosclerotic plaque or disease progression. However, direct measurement of shear stress on the arterial wall at the carotid bifurcation is problematic. Methodology for directly measuring shear stress in the common carotid artery [25–27] cannot be reliably used at the carotid bifurcation or stenoses due to complications in the ﬂow patterns. Reports of the use of direct measurement of PC MR to measure wall shear stress in regions prone to formation of atherosclerotic plaque have not been validated in physical ﬂow-through models or in vivo to the best of our knowledge. Such models assume linear velocity proﬁles in the vicinity of the vessel wall that is not justiﬁed based on well established ﬂuid dynamics principles. Given the difﬁculty in making direct measurements of the shear rate of the blood at the wall of the artery, an alternative approach has been developed by ourselves and others [29–31] for estimating the shear rate from realistic computational ﬂuid dynamics (CFD) models. These models incorporate direct measurements made on the vessel of interest. One approach includes black-blood magnetic resonance angiography (MRA) to deﬁne the vessel shape and phase-contrast magnetic resonance (PC MR) imaging to obtain a cross-sectional view of the blood velocity within the vessel [28,29]. A similar approach has been taken by Cebral et al [56] which makes use of contrast-enhanced MRA to deﬁne the vessel shape. Another similar approach has been proposed by Long et al using timeof-ﬂight MRA. Augst et al. [32] have proposed the use of three-dimensional ultrasound to determine the vessel shape and Doppler ultrasound to obtain blood-ﬂow conditions. Any of these approaches could be applied to the carotid arteries. The relative accuracy of these various approaches has, to the best of our knowledge, not be determined. In many ways, however, the computational schemes underlying each of these approaches is similar. Namely, a ﬁnite-element volumetric mesh is constructed from angiography. Construction of the ﬁnite-element mesh begins with the use of semi-automated methods for segmentation of the angiography. Flow conditions are imposed at inﬂow and outﬂow locations based on PC MR or Doppler ultrasound. The focus of this chapter will be to describe the computational methodology for characterization of shear stress on the wall of the carotid artery. Signiﬁcant attention will be given to validation of the vascular CFD models. The description will emphasize the use of contrast-enhanced magnetic resonance angiography and PC MR since that is where our experience lies.

2. Magnetic Resonance Angiography At our institution, the protocol for acquisition of contrast-enhanced MRA is described below. MRA is obtained on a General Electric 1.5T EXCITE system using a neurovascular array coil. The MRA protocol includes intravenous injection of a Gadolinium chelate contrast media with the image acquisition synchronized with the arterial phase of the circulation. The timing of the acquisition was established using a test bolus of Gd Chelate injected intravenously. The enhancement pattern of the common carotid is shown in Fig. 1. The delay time from the contrast injection to the peak enhancement of the com-

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Figure 1. Maximum intensity projections of contrast-enhanced MRA images.

mon carotid is used as the delay time in the acquisition of the MRA. Images were acquired in the coronal orientation with the Spoiled Gradient Recall Echo (SPGR) with elliptical-centric sampling at a native resolution of 0.5 × 0.5 × 0.6 mm. Magnetic resonance angiography (MRA) has recently undergone rapid development. The introduction of the use of contrast agents in MRA has allowed for the depiction of the arterial lumen independently of ﬂow conditions within the vessel [33,34]. Previous MRA methodologies were dependent on blood ﬂow to produce blood-tissue contrast and were thus susceptible to artifacts due to slow or reverse ﬂow [35]. The use of contrast agents in MRA also minimized problems with loss of blood-tissue contrast that is prone to occur at stenoses due to “spin dephasing” [26]. For MRA using contrast media, or contrast-enhanced MRA, the image acquisition must be synchronized the arrival of the contrast media in the arteries of interest. Several reliable methods have been developed for synchronization including the use of a test bolus and real-time bolus detection [36].

3. Phase-Contrast Magnetic Resonance Imaging Magnetic resonance (MR) ﬂow quantiﬁcation has also recently become a viable methodology [37,38]. MR ﬂow quantiﬁcation is obtained by cine phase-contrast (PC) MR that provides a measure of tissue velocity at each point in the ﬁeld of the image. Typically, PC images are obtained with temporal resolution of 30 msec and 1–3-mm spatial in-plane resolution. Arterial ﬂow can be derived by integration of the velocities from PC MR images over the region of the artery. The accuracy of the ﬂow measurement depends on the accuracy of the delineation of the cross sectional area of the vessel in the PC MR images. Schemes for doing such delineation include manual segmentation [39] and thresholding of the magnitude, or anatomical, component of the PC image [40]. Accuracy of the PC

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Figure 2. Phase-contrast MR of the common carotid artery.

MR velocity measurement is also dependent on the type of ﬂow pattern being measured. Where inhomogeneities of the tissue velocity exist within the region of a pixel, the velocity measured by PC MR is close to the average velocity. That assumption is valid as long as inhomogeneities in tissue velocity are not extreme [41,42]. Flow quantiﬁcation using PC MR is thus primarily applicable to regions of vessels where the velocity proﬁle is smooth. Thus, PC MR properly applies to ﬂow quantiﬁcation only in relatively large vessels and and in regions without ﬂow disturbances. The protocol we have designed for acquisition of PC MR of the carotid is the following: Velocity encoded phase-contrast (PC) MR is obtained using the Fastcard pulse sequence with the acquisition gated to the cardiac cycle by PC MR. The velocity-encoding gradient is applied in the through-plane direction and with a magnitude of 150 cm/sec. PC MR are acquired at a location that transected the common carotid arteries and a location that transected the internal carotid artery. The images are acquired with a 15 cm ﬁeld-of-view, a 256 × 196 acquisition matrix and a 5-mm slice-thickness. The PC MR is acquired for between 25 and 40 phases of the cardiac cycle. The time series of the PC MR is shown in Fig. 2. The ﬂow is derived from the PC MR using a region-of-interest manually drawn around the cross-section of the vessel. The manual contour is drawn based on the vessel cross-section at peak-systole. The same contour is then propagated to all other time frames. Flow in the vessel at any time point is then the sum of the velocity-encoded phases within the ROI multiplied by the pixel area. The ﬂow waveform derived from the PC MR is shown in Fig. 2.

4. Vascular Surface Reconstruction The ﬁrst step in the construction of vascular CFD models is segmentation of the vessel lumen from MRA. Simplistic methods for construction of the mesh of the vessel surface have been found to be inadequate. These include manual contouring of the surface and iso-intensity surface reconstruction [43]. The ﬁrst, manual contouring, is time

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consuming and subjective. The second, iso-intensity surface reconstruction is unreliable since vessels in MRA are inhomogeneous in intensity. The inhomogeneity is arises from magnetic-ﬁeld inhomogeneities, inhomogeneous coverage of the ﬁeld of view by the transmit and receive radio-frequency (RF) coils and from the magnetic-spin dephasing artifact [44]. Two deformable model methods for reconstruction of the lumenal surface of the carotid arteries will be described. The deformable model is a method for reconstruction of a surface from a 3D image. Deformable models generate a realistic surface of an object in an image given an approximation of the desired surface. The initial surface is transformed to align with image edges that correspond to object boundaries. The transformation of the surface, which is non-rigid, is subject to constraints that smooth the surface. Usually, the surface of the deformable model is represented as a triangulated mesh. Typically, the transformation of the surface is governed by a mechanical analogy in which “forces” act on vertices of the surface mesh. The image force on a vertex pulls the vertex towards points in the domain of the image with higher gradient magnitude. The internal forces on a vertex resist bending and stretching of the surface. Meshing of the surface of the deformable model implicitly dictates the overall shape of the object to be reconstructed. Large-scale modiﬁcations of a surface mesh entail distortions of the mesh that are resisted by smoothing forces. Thus, a deformable modes are, by design, only be applicable to a certain structure or organ. More general methodologies have been proposed [45,46] in which the surface is “topologically adaptive” that allow for large-scale changes in the surface to occur. In principle these approaches minimize the need for user-interaction. However, when an accurate initialization of a surface is available, deformable models with ﬁxed or a priori meshes are more reliable methods of surface reconstruction. We have proposed two deformable models that are particularly suitable for vascular image analysis that rely on an a priori meshing. The Tubular Deformable Model (TDM) [47] is based on a cylindrical mesh and the Isosurface Deformable Model (IDM) [48,49] is based on the mesh generated by the Marching Cubes isosurface algorithm. Both are described below. The TDM is based on a cylindrical mesh. The mesh is initialized in an interactive manner as follows. First, the axis of the vessel is deﬁned manually by identifying points along the center of the vessel. A smoothed axis with even spacing of the axial points is generated from the picked points by b-spline interpolation. A cylindrical coordinate system is then established based on the interpolated axis. Vertices of the deformable model mesh are located at each axial position and each of 16 circumferential positions. Given this coordinate system, the shape of a vessel is described by the radial location of each vertex which is a discrete function R(a, φ) where a is the axial location and φ is the circumferential position. Vertices are constrained to deform only in the radial direction. The surface reconstruction is obtained by energy minimization where the energy function is: Etotal = Eimage + Ebending

(1)

The component of the energy derived from the image is minimized by a force that pushes the vertices towards peaks in the gradient magnitude image: (2) Fimage (i) = k1 rˆi · ∇ ∇I (xi )rˆi

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where rˆi is the radial direction, I is the image intensity function, k1 is a constant, and xi is the position of a given vertex. The bending component of the energy function is minimized by a force on each vertex that displaces the vertex towards a location with a radius that is the mean of its neighbors: Fbend (i) = k2

1 (Rj ) − Ri rˆi n

(3)

j ∈N

where n is the number of neighbors of the vertex, N is the set of neighbors, k2 is a constant, and Rm is the radial location of the mth vertex. The deformable model is described in greater detail elsewhere including the description of a robust method for construction of a cylindrical coordinate system based on a curvilinear axis [50]. The TDM is appropriate for vascular surface reconstruction in several respects. • Cylindrical meshing will reproduce a wide range of normal and pathologic vascular shapes without undue mesh distortion. • The TDM is unbiased with respect to vessel diameter. In principal, vessel diameter should be neither exaggerated nor diminished in the surface reconstructed by the TDM • The TDM is remains effective in the presence of venous contamination or of other high-intensity objects nearby to the arteries. The TDM was validated using images of a physical phantom of the carotid bifurcation. The bifurcation was reconstructed by superimposing the surfaces obtained by independently reconstructing the surface of the common carotid artery and its continuation along each branch of the bifurcation. The physical phantom was constructed from glass with realistic dimension of 8.0 mm, 7.0 mm of the common and internal carotid arteries respectively. An MR volumetric image was obtained of the phantom immersed in a glycerol-water solution. The image was obtained with a 1.5T system using a spin-echo pulse sequence with a voxel resolution of 0.31 × 0.31 × 1.0 mm. The ratio of the smoothing parameters of the TDM, k2 : k1 is 7.0 × 103 cm−1 . A cross-sectional image of the phantom and the reconstructed surface are shown in Fig. 3 (top). The accuracy of the TDM was evaluated in terms of vessel diameter. The radius of each reconstructed vessel segment was computed based on the assumption of a circular cross-sectional area using the formula, A = π r 2 using the polygonal cross-sectional area generated by the TDM. An average radius for each vessel segment was obtained by averaging the radius for 10 successive points along the axis. Vessel radii of the common and internal carotid arteries determined from the TDM were accurate to within 0.1 mm. This validation study suggests that under optimal imaging conditions TDM can reconstruct a vascular surface such as the carotid artery bifurcation with a high degree of precision. Qualitative evaluation of the TDM was carried out with MRA from a normal subject and from a subject with carotid artery disease. MRA for both studies was obtained by contrast enhancement on 1.5T system with the Spoiled Gradient Recalled Echo (SPGR) sequence. The ratio of the smoothing parameters of the TDM, k2 : k1 is 7.0 × 103 cm−1 (the same as for the phantom study). A maximum intensity projection (MIP) of a subject with mild carotid artery disease and the surface reconstructed by the TDM are shown in Fig. 3 (bottom). As desired, the TDM surface reconstruction of the normal carotid artery has a normal appearance and stenosis is apparent in the surface of

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Figure 3. Surface reconstruction of a carotid bifurcation phantom (left) and of a carotid artery from MRA (right).

the diseased carotid artery. The degree of stenosis apparent in the surface is slightly less than is apparent in the MIP. An alternative to the TDM has been developed that requires less user interaction. This algorithm is known as the Isosurface Deformable Model (IDM) [51]. The mesh of the IDM is the isosurface of the MRA. The isosurface is generated by the Marching Cubes algorithm in an interactive manner. The iso-intensity value is chosen by trialand-error until the surface has a realistic appearance. The isosurface then serves as a deformable model of the vessel. The model is deformed by energy minimization. The energy function is composed of a term derived from the image and smoothing terms: Etotal = Eimage + Estretch + Ebend

(4)

The image energy term Eimage is minimized by a force acting on each vertex as follows: image

Fj

= cimage nˆ j · (∇||∇I (xj )||) nˆ j

(5)

where cimage is a constant, nˆ j is a unit normal vector to the surface at the location of the vertex, I () is the image intensity function, and xj is the location of the j th vertex. The stretch energy term Estretch is minimized by a force that attracts a vertex the adjacent vertices with a force proportional to an in-plane displacement between the vertices. The in-plane displacement between two vertices is the component of the displacement in the plane tangent to the surface, Pj . Out-of-plane components are excluded in this formulation of the stretch force since out-of-plane components produce an artifactual contraction of the surface, particularly in regions with high curvature. The stretch force is thus deﬁned as follows: = cstretch projPj xj (n) − xj (n) (6) Fstretch jj The function projPj (u) is the orthogonal projection of a vector u onto the plane, Pj . The bending energy term Ebend is minimized by a moment that rotates triangles of the surface so as to reduce differences between the unit normal vectors of adjacent triangles: neighbors

Mk = cbend nˆ k × nˆ k

(7)

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Figure 4. Surface reconstruction of stenosed renal artery from MRA and measurement of degree of stenosis from conventional angiography. neighbors

nˆ k is the unit vector normal to a given triangle, nˆ k is the unit vector that is the average of the unit normal vectors of the adjacent triangles. The deformation process is then governed by: image total stretch lj k × Mk T xj = Fj + Fj + (8) k∈N

where lj k is the moment arm from the j th vertex to the center of mass of the k th triangle and T is the time step, and N is the set of triangles associated with a given vertex. The constants cimage , cstretch , and cbend are determined by trial and error. The IDM algorithm is advantageous over the TDM for vascular surface reconstruction when image quality is sufﬁcient for the generation of realistic isosurface models. The IDM was applied to 4 carotid arteries with atherosclerotic disease in three highresolution (approximately 0.5 × 0.5 × 1.2 mm) contrast enhanced MRAs (Gd-DTPA). The appearance of the carotid arteries reconstructed by the IDM was qualitatively similar to the appearance of the arteries on conventional digital subtraction angiography (DSA) (see Fig. 4) and the degree of stenosis measured from the IDM was highly correlated with the degree of stenosis as measured by DSA (r2 = 0.9101). 5. Construction of Finite Element Mesh Once the surface has been reconstructed using a deformable model as explained in Section 4, the model is further processed. The ultimate surface must be a watertight maniford [52], i.e. contain no holes, gaps, self-intersections, overlapping triangles, topological defects, etc. If arterial branches have been reconstructed independently using for instance a TDM along each branch, they are merged using an adaptive volumetric technique [53]. For this purpose, a background grid of tetrahedral elements is constructed covering the entire computational domain, and the signed distance from each point to the closest surface model is computed. In order to increase the resolution of the procedure, the background grid is adaptively reﬁned close to the surface of the models using a clas-

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sical h-reﬁnement algorithm [54]. The merged surface is then obtained by extraction of the zero-level iso-surface of the signed distance map. Typically, two to four levels of reﬁnement are sufﬁcient. Corrections to the IDM surface may also be necessary including the removal of self-intersections, holes and protrusions from small branches. The surface is then smoothed using an algorithm developed by Taubin [55]. This algorithm which is very simple, fast, and does not shrink the model, acts as a low pass ﬁlter eliminating the high frequency noise present in the triangulation. The model is then cut perpendicularly to the vessel axis at the locations where boundary condition will be applied. If desired, the boundaries are extruded in the direction of the vessel axis in order to minimize the inﬂuence that idealized boundary conditions might have on the ﬂow ﬁeld in the regions of interest [56]. The surface triangulation is then optimized using edge collapses to eliminate very small or very distorted elements [52]. Diagonal swaps are performed to improve the inner angles of adjacent triangles, i.e. minimize the maximum interior angle [52,57]. Although the resulting model is a high quality watertight triangulation with the correct topology, it may not have the appropriate element size distribution for a CFD calculation. Therefore, it is only used as a geometrical deﬁnition of the computational domain during the ﬁnite element grid generation process. An advancing front grid generation technique [58–60] is used to ﬁrst create a new surface triangulation with the desired element size distribution. During this process, newly created points are placed on the original surface by linear interpolation [61]. Topological constraints are used to avoid connections between different but close arterial branches [52]. Surface features present in the original triangulation are automatically detected and preserved in the ﬁnal mesh [52,61]. In contrast to many commercial grid generators, this method does not require an analytical representation of the computational domain, it operates directly on the discrete data, i.e. triangulation. Once the surface grid has been re-triangulated, an advancing front method is used to ﬁll the interior of the model with tetrahedral elements [58,60]. The element size distribution is speciﬁed by the user using sources, i.e. analytical functions of the distance to source points, lines or triangles, and adaptive background grids [62]. In the latter approach the resolution is automatically increased by adaptively reﬁning the background grid in regions of high surface curvature. Adaptive background grids provide a robust method for the speciﬁcation of appropriate element sizes based on the dimensions of anatomical structures, and require no user intervention. In a post-processing step, the tetrahedral mesh is optimized using edge collapses and diagonal swaps. Typical meshes used for ﬁnite element simulations of carotid artery hemodynamics contain between 1 to 3 million tetrahedral elements. 6. Blood Flow Modeling Blood ﬂow is mathematically modeled by the unsteady Navier-Stokes equations for an incompressible ﬂuid in three dimensions [63,64]. The conservation of mass and momentum can be expressed as: ∇ ·v=0 ∂v + v · ∇v = ∇ · σ + f ρ ∂t

(9) (10)

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where ρ is the density, v is the velocity ﬁeld, σ is the stress tensor, and f are the external or body forces such as gravity. The stress tensor can be written as: σij = −p δij + τij

(11)

where p is the pressure, δij the unit tensor, and τij is the deviatoric stress tensor, which is assumed to be a linear function of the strain-rate tensor: τij =

1 μ ij 2

with μ the viscosity and the strain-rate tensor deﬁned as: ∂vj 1 ∂vi . + ij = 2 ∂xj ∂xi

(12)

(13)

In order to close the system of equations, a constitutive law must be provided to compute the local viscosity of the ﬂuid. Although the stress/strain-rate relationship is in general a tensor relation, it is usually expressed as an algebraic equation of the form: τ = μ γ˙

(14)

where the strain-rate is deﬁned as the second invariant of the strain-rate tensor, which for incompressible ﬂuids yields (using Einstein’s summation convention): √ (15) γ˙ = 2 ij ij . The simplest rheological model is a Newtonian ﬂuid which assumes a constant viscosity: μ = μ0 . In this case, the momentum equation reduces to: ∂v + v · ∇v = −∇p + μ∇ 2 v + f. ρ (16) ∂t Typical values used for blood are ρ = 1.105 g/cm3 and μ = 0.04 dynes/cm. Some analytical solutions of the Naiver-Stokes equations in cylindrical pipes are useful for implementing boundary conditions and for comparison to numerical results,and are reproduced here. The simplest solution is that of the fully developed steady ﬂow of an incompressible Newtonian ﬂuid, i.e. Poiseuille ﬂow [63]: v=

p 2 (a − r 2 )z 4μL

(17)

where p is the applied pressure difference, L the length of the pipe, a its radius, and (z) the axial direction. The volume ﬂow through a cross-section of the pipe can be computed from the velocity proﬁle: a v(r)rdr (18) Q = 2π 0

which in this case yields: Q=

p πa 4 . 8μL

(19)

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If now the applied pressure gradient is allowed to vary in time in a sinusoidal manner: ∂p = −P eiωt ∂z

(20)

and the solution of the Navier-Stokes equation is assumed of the form: v(r, t) = V (r)eiωt z

(21)

then the velocity proﬁle is (Womersley [65]): iP J0 (βr/a) 1− V (r) = − ωρ J0 (β)

(22)

where J0 are the Bessel functions of the ﬁrst kind with complex argument β = i 3/2 α

(23)

with the Womersley number deﬁned as: ω α=a ν

(24)

and the kinematic viscosity: ν=

μ . ρ

(25)

Inserting this velocity proﬁle into equation 18 yields the volume ﬂow: iπP a 2 2J1 (β) iωt 1− e Q=− ωρ βJ0 (β)

(26)

These formulas can be used to calculate the pulsatile velocity proﬁle for a given timedependent volume ﬂow curve. Performing a Fourier decomposition of the ﬂow curve: Q(t) =

N

Qn einωt

(27)

n=0

the velocity proﬁle can be expressed as [66]: ! J0 (βn r/a) " N 9 r :2 2Q0 Qn 1 − J0 (βn ) v(r, t) = 1− + einωt a πa 2 πa 2 1 − 2J1 (βn ) n=1 βn J0 (βn ) where

βn = i

3/2

αn = i

3/2

a

nω . ν

(28)

(29)

This formula is widely used to impose pulsatile velocity boundary conditions from ﬂow measurements, for instance using phase-contrast MR [56,67,68]. While the Newtonian model of blood viscosity can be used to approximate the behavior of blood, more accurate models have been developed that more accurately re-

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ﬂect the nature of blood as a suspension of particles (red blood cells) in an aqueous medium (Plasma). Blood is neither homogeneous nor Newtonian and its rheological properties are mainly dependent on the Hematocrit, or the volume fraction of red blood cells in the blood. One of the most commonly used non-Newtonian ﬂuid models used for blood is the model of Casson [63], which assumes a stress/strain-rate relation of the form: √ √ √ τ = τ0 + μ0 γ˙ (30) where τ0 is the yield stress and μ0 the Newtonian viscosity. The existence of a yield stress implies that blood requires a ﬁnite stress before it begins to ﬂow, a fact that has been observed experimentally. Comparing equations 14 and 30, the apparent viscosity ca be written as: 2 τ0 √ + μ0 . (31) μ= γ˙ Since this expression diverges as the strain-rate becomes zero, it is typically modiﬁed in the following way: ⎤2 ⎡0 −mγ˙ 1 − e √ + μ0 ⎦ (32) μ = ⎣ τ0 γ˙ where the parameter m controls the maximum viscosity obtained when γ˙ tends to zero: √ √ 2 μmax = lim μ = τ0 m + μ0 (33) γ˙ →0

Typical values used for blood are: τ0 = 0.04 dyne/cm2 , μ0 = 0.04 dyne s/cm and m = 100. The steady ﬂow of a Casson ﬂuid in a rigid cylindrical pipe can also be computed analytically. In this case, the ﬂow ﬁeld is divided into to regions: a core or plug region with a ﬂat velocity proﬁle, and an outer region with a non-ﬂat proﬁle:

v(r)z, r ≥ rp (34) v= vp z, r ≤ rp where rp = 2τ0 /P is the radius of the core region, P = −∂p/∂z is the pressure gradient. The plug velocity is P 8 1 a 2 + 2rp a − (35) rp a 3 − rp2 vp = 4μ0 3 3 and the velocity proﬁle in the outer region is given by: P 8 1 2 2 3 r + 2rp r − v(r) = vp − rp r − rp 4μ0 3 3

(36)

Finally, deﬁning x = rp /a, the volume ﬂow computed using equation 18 can be written as:

P. Yim et al. / Characterization of Shear Stress on the Wall of the Carotid Artery

Q=

P πa 4 8μ

16 1 4 1 − x 1/2 + x − x 4 7 3 21

425

(37)

which reduces to Poiseuille ﬂow (Eq. 19) in the absence of yield stresses (τ0 = 0).

7. Physiologic Boundary Conditions As mentioned in the previous section, the ﬁnite-element solution can be obtained provided that the ﬂow-rate is known at inﬂow and outﬂow locations. In the approach described here, the ﬂow rates are derived from phase-contrast MR imaging as described in Section 3. Time-dependent ﬂow rates in each of the arterial branches included in the model are obtained by integration of the measured velocity proﬁle over the vessel crosssection. The region of integration is either manually drawn on cross-sectional views or via threshold segmentation of the magnitude images. Each curve is then decomposed into Fourier modes (equation 27) and the velocity proﬁle is computed from the Womersley solution (equation 28). These proﬁles are mapped to the vessel boundary using an algorithm that maps the surface mesh of the boundary to a circle [69]. In models with n arterial branches, velocity boundary conditions are prescribed in n − 1 branches while in the remainder branch traction-free boundary conditions are imposed [69]. Vessel wall compliance is an important effect that may alter the local carotid artery hemodynamics. Fluid-solid interaction algorithm have been applied to the study of these effects on the ﬂow patterns [70]. This approach requires the coupling of ﬂow solvers that can deal with dynamic moving meshes with solid solvers capable of modeling the vessel deformation with the correct material characteristics. Several simpliﬁed structural models ranging from independent ring models to more complicated membrane and 3D models of the vessel wall and its complex material behavior have been investigated [71]. However, the main problem remains the proper characterization of the arterial wall, i.e. the values of local material properties such as modulus of elasticity, wall thickness, etc. Better imaging techniques to quantify the mechanical behavior of the vessel wall are needed. In addition, coupled ﬂuid-solid models require the speciﬁcation of proper pressure boundary conditions, i.e. the pressure waveform that drives the motion of the arterial wall, which is difﬁcult to measure non-invasively [68]. Furthermore, the solution of the coupled ﬂuid-solid system of equations is about an order of magnitude more computationally expensive than non-compliant models. For these reasons, the discussion will be restricted to models that assume rigid walls. Although different authors have argued that vessel compliance is only a second order effect, especially in diseased arteries that become stiffer, we believe that compliant models should be further studied and the ﬂuidsolid interaction algorithms need to be made more robust and faster before using them in clinical studies. No-slip boundary conditions are applied at the vessel walls, i.e. the ﬂuid velocity is equal to the velocity of the wall, which under the assumption of rigid vessel walls becomes v = 0. Since the vessel walls are actually compliant, instantaneous ﬂows measured in the ICA and ECA do not add up to the instantaneous ﬂow measured in the CCA. Due to mass conservation, the volume ﬂux computed over a closed region enclosing the CCA, ICA and ECA must equate to zero:

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;

v · n dA =

CCA

v · n dA +

+

wall

I CA

v · n dA +

ECA

v · n dA

v · n dA = 0.

(38)

Therefore, since the velocity at the vessel wall is not zero the instantaneous ﬂow through the CCA cannot be equated to that of the ICA and the ECA. If the arterial walls are assumed rigid, then there is an ambiguity in the speciﬁcation of ﬂow boundary conditions from the measured ﬂow rates. For instance, if one prescribes the measured ﬂows in the CCA and the ECA one would obtain QI CA = QCCA − QECA in the ICA, which in general may be different from the measured ﬂow rate through the ICA. Other alternatives include modifying the ﬂows in the ICA and ECA that to obtain the same instantaneous ﬂow division, but that add to the instantaneous ﬂow through the CCA: Q CCA = QCCA ,

Q I CA QI CA = , Q CCA = Q I CA + Q ECA . QECA QECA

(39)

Since we are mostly interested in the hemodynamics in the ICA, we prescribe QCCA and QECA = QCCA − QI CA from the measured curves. Traction-free boundary conditions are imposed in the ICA, to let the ﬂow adjust itself to the measured value while not affecting secondary ﬂows. The choice of ﬂow boundary conditions may be important to accurately quantify the hemodynamic forces on the atherosclerotic plaque. This issue is obviously resolved if compliant vessel models are used. Further investigation is warranted.

8. Finite Element Methods Over the years, several numerical schemes have been used to solve the incompressible Navier-Stokes equations 10,9 [72–74]. What sets incompressible ﬂow solvers apart from compressible ﬂow solvers is that the pressure is not obtained from an equation of state but from the divergence constraint. In other words, the pressure establishes itself instantaneously and must therefore be integrated implicitly [75]. The equation for the pressure can be found by taking the divergence of the momentum equation 10: ∇ 2 p = −∇ · (v · ∇v)

(40)

The hyperbolic character of the advection operator (second term on left hand side of equation 10) and the elliptic character of the pressure-Poisson equation (40) have led to a number of so-called projection schemes. Our methodology is based on this approach and will be described in detail below. The basic idea of fractional step or pressure projection methods is to predict ﬁrst a velocity ﬁeld from the current ﬂow variables without taking into account the divergence constraint. In a second step, the divergence constraint is enforced by solving a Poisson equation (40) for the pressure. An explicit scheme is composed of the following stages [76]: Advective-diffusive prediction: vn → v∗ 1 − ∇μ · ∇ (v∗ − vn ) + vn · ∇vn + ∇p n = ∇μ · ∇vn . (41) t

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427

Pressure correction: p n → p n+1 ∇ · vn+1 = 0

(42)

vn+1 − v∗ + ∇(p n+1 − p n ) = 0 t

(43)

which results in a Poisson equation for the pressure: ∇ · v∗ ∇ 2 p n+1 − p n = . t

(44)

Velocity correction: v∗ → vn+1 vn+1 = v∗ − t ∇(p n+1 − p n ).

(45)

It is well known that a straightforward Galerkin ﬁnite element approximation of the advection terms leads to unstable numerical schemes. Therefore, the equations are discretized in space using an edge-based upwind ﬁnite element approximation [76,77]. The discretized momentum equation is solved using a generalized minimal residual (GMRES) solver, while a diagonal preconditioned conjugate gradient solver is used for the pressure Poisson equation [78]. Explicit integration of the advective terms implies that information can only travel at most one element per timestep. In order to allow for faster transfer of information and larger timesteps, the advective terms have to be integrated implicitly. In this case, equation 41 becomes [76]: 1 + v∗ · ∇ − ∇μ · ∇ (v∗ − vn ) + vn · ∇vn + ∇p n = ∇μ · ∇vn (46) t which results in a non-symmetric system of equations of the form: A · v = r.

(47)

This system can be written as: A · v = (L + D + U) · v = r

(48)

where L, D, U denote the lower, diagonal and upper diagonal entries of A. This system is solved using a Lower-Upper Symmetric Gauss-Seidel (LU-SGS) relaxation scheme: (L + D) · D−1 · (D + U) · v = r.

(49)

This relaxation scheme has been optimized over the years, resulting in very efﬁcient matrix free solvers [80,81]. Although this scheme can substantially accelerate the convergence of steady state problems, the timestep is still constrained for unsteady problems. The result is that for typical hemodynamics simulations several tens or hundreds of thousands of timesteps are required per cardiac cycle. The alternative is to use fully implicit time integration schemes. The simplest such schemes can be written in the following form [76,82]: vθ − vn + vθ · ∇vθ + ∇p θ = ∇μ · ∇vθ θ t

(50)

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∇ · vθ = 0

(51)

when θ = 1 the ﬁrst order backward Euler scheme is recovered, while for θ = 0.5 the second order Cranck-Nicholson scheme is obtained. Moving the ﬁrst term to the right hand side, this scheme can be interpreted as the steady-state solution of the pseudo-time system: ∂vθ vθ − vn + vθ · ∇vθ + ∇p θ = ∇μ · ∇vθ − . ∂τ θ t

(52)

This equation has the same form as the original Navier-Stokes equation 10 but with a source term on the right hand side. The solution is then advanced by solving a steadystate problem in pseudo-time τ at each timestep. The steady-state problems are solved using the implicit advection projection scheme described above. An alternative fully implicit ﬁnite element formulation that yields stable solutions for arbitrary timesteps can be written as [82]: 1 n+1,i (v , w) − (vn , w) + (vn+θ,i−1 · ∇Vn+θ,i , w) + (ν∇vn+θ,i , ∇w) t − (p n+1,i−1 , ∇ · w) + τ [vn+θ,i−1 · ∇vn+θ,i − αn+θ,i−1 ], vn+θ,i−1 · ∇w = (σ n+θ,i−1 · n, w) + (fn+θ , w)

(53)

t (∇p n+1,i − ∇p n+1,i−1 , ∇q) + τ [∇p n+1,i − αξ n+1,i−1 ], ∇q = −(∇ · vn+1,i , q)

(54)

where i is the subiteration level, w and q are the ﬁnite element test functions, σ the deviatoric stress tensor, (a, b) denotes the L2 inner product taken over the computational domain , is the boundary of the domain and n its outer normal. The local critical timestep or stabilization parameter τ is computed from the element Courant-FriedrichLevy (CFL) condition: τ=

h2 2|v|h + 4ν

(55)

where h is the element size. The projected terms and ξ deﬁned as (n+θ,i , w) = (vn+θ,i · ∇vn+θ,i , w)

(56)

(ξ n+1,i , w) = (∇p n+1,i , w)

(57)

are treated explicitly using a lumped approximation of the mass matrix. A pressure switch of the form α =1−

∇p − ξ ∇p + ξ

(58)

was added to the ﬁnite element formulation in order to reduce the order of the scheme in regions where the pressure gradient is not smooth. This term becomes important in bio-ﬂuid applications involving higher Reynolds numbers. The discretized momentum

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equation 53 is solved using a GMRES algorithm, while the pressure equation 54 is solved using an Incomplete Lower-Upper (ILU) preconditioned conjugate gradient solver [78]. The algorithm is iterated until convergence in each timestep. These schemes have been implemented into our in-house software FEFLO [79]. This software has been extensively optimized, vectorized, and parallelized for both distributed and shared memory architectures. Currently, a typical run of approximately 1.3 million elements takes about 15 hours per cardiac cycle on a PC with a 3.0 GHz Pentium4 processor and 2GB of RAM. The same run takes approximately 5 hours on 8 1.3 GHz Itanium processors of a Silicon Graphics Altix running in shared memory mode. A speedup of about 1.9 is observed from 8 to 16 processors of this same supercomputer.

9. Validation Validation and evaluation of the ﬁnite element models is of fundamental importance. Studies have been conducted in vitro and in vivo to validate CFD modeling. In vitro models can provide very detailed ﬂow information useful for validation of computational models. In contrast, validation with in vivo data is difﬁcult because there is no gold standard for measuring ﬂows. In spite of these limitations, we have tried to compare the results obtained with our numerical models to in vivo measurements of blood ﬂow velocities [83]. In this section, validation studies performed with in vitro as well as in vivo data are presented. The rigid-wall CFD model has been quantitatively evaluated in a physical glass ﬂowthrough model of the carotid artery bifurcation with stenosis [84], in a physical glass ﬂow-through model of the abdominal aorta [85] and renal artery with stenosis and for two normal carotid arteries based on MR imaging. These studies are described in detail below. 9.1. Prediction of Velocity Proﬁles in Glass Model A physical ﬂow-through model of the carotid bifurcation was constructed using the glass model described above and shown in Fig. 5 (bottom left). A 2 : 3 glycerol-water solution was circulated at a constant rate through the model. A experimental setup is shown in Fig. 5 (top left). Velocity-encoded PC MR images were obtained at 5 axial slice-planes along the vessel. The location of the slice planes are shown in the ﬁgure. Flow rates in the common and internal carotid artery segments were obtained from the PC MR images at the most proximal and most distal slice planes respectively. The vessel geometry was obtained as described previously in using Tubular Deformable Model. A velocity proﬁle at an intermediate location was predicted by the CFD model and compared with a velocity proﬁle measured by PC MC. The location of the intermediate slice plane is shown in Fig. 5. The peak velocity in this slice plane predicted by the CFD model was 77 cm/sec while the peak velocity from PC MR was 84 cm/sec. The location of the peak velocity was similar in the predicted and measured velocity proﬁle of 51◦ degrees and 61◦ respectively, from horizontal. The corresponding velocity proﬁles from PC MR and vascular CFD are shown in Fig. 5 (right).

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51 deg

61 deg

Figure 5. Experimental setup and glass model of carotid artery bifurcation (top). Comparison of velocity proﬁles from PC-MR and vascular CFD (bottom).

9.2. Prediction of Differential Pressure in Glass Model CFD modeling was also validated using a renal-artery physical ﬂow-through model. The vessel model was constructed from glass and is shown in Fig. 6 (top right). A glycerolwater solution with a viscosity of 3.5 cP was circulated at a constant rate through the model. Outﬂow from the renal artery segment and the aortic segment was measured with ultrasonic ﬂow probes (Transonic Systems, Ithaca, NY). The ﬂow rate through the renal artery was 10.7 cc/sec. The differential pressure between locations proximal and distal to the stenosis was measured by Validyne transducers from ports on the glass model indicated in Fig. 6 (top left). A computed tomography (CT) image of the vessel model was acquired with the Bone-Plus CT at a resolution of 0.24 × 0.24 × 0.63 mm. The surface of the vessel was reconstructed by the IDM. The ﬂuid dynamics were modeled with a range of mesh resolutions. The lowest resolution mesh had 7.7×105 elements while the highest had 2.2×106 elements. The differential pressure measured by transducer was 12.1 mmHg. The differential pressure between the same transducer locations, as predicted by the CFD models, was dependent on the mesh resolution but asymptotically approached the measured

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Figure 6. Experimental setup and glass model of the abdominal aorta and renal artery (top). Glass model of aorta and stenosed renal artery.

value as the mesh resolution increased. For the highest mesh resolution, the differential pressure was predicted to be 14.1 mmHg that represents a 16% error. Thus, the use of high-resolution meshes is certainly warranted although additional computational expense is entailed. While these results were obtained with a model of the renal artery, they are likely to apply to modeling of the carotid bifurcation as well. A realistic pulsatile ﬂow was also imposed on the renal physical ﬂow through phantom. Prediction of the peak pressure gradient across the stenosis by CFD was 9% greater than the direct transducer measurement of the pressure gradient. A cross-section of the relative pressures in the ﬂow-through model is shown in Fig. 6 (bottom left). A comparison of the predicted and measured pressure gradients is shown in Fig. 6 (bottom right). 9.3. Prediction of Velocity Proﬁle A model of the right carotid artery of a normal volunteer was reconstructed from contrastenhanced MRA images using the TDM followed by surface merging and processing. Phase-contrast MR images were obtained at several locations along the carotid artery. A ﬁnite element mesh with uniform element size distribution was generated and a pulsatile ﬂow calculation was performed. Flow rates were prescribed at the outlets of the ICA and ECA and traction free conditions were speciﬁed at the CCA. A maximum intensity projection (MIP) of the MRA and the reconstructed model are shown in Fig. 7. Even though the MRA contained the veins as well, the TDM was able to successfully reconstruct the carotid artery.

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Figure 7. Validation of velocity proﬁles.

Comparisons of the computed and measured velocity proﬁles just proximal and distal of the carotid bifurcation are presented in Fig. 7. Two time frames are shown for the slice through the CCA and three for the bifurcation. These images show a very good agreement between the CFD model and the PC-MR measurements. The difference in the velocity magnitude between the CFD and PC-MR proﬁles is due to the assumption of rigid walls and the choice of boundary conditions. Note that this difference is larger in the CCA because the ﬂow in the CCA is larger in the CFD model than the actual measurement: QCCA (CFD) = QICA (PCMR) + QECA (PCMR) > QCCA (PCMR). This difference can be made smaller by different choices of boundary conditions, or by using compliant vessel wall models. 9.4. Prediction of Peak Velocity A model of the left carotid artery of a patient with atherosclerosis was reconstructed from contrast-enhanced MRA images. The MIP of the MRA images and the reconstructed model are shown in Fig. 8. In this case, the patient had an occluded right carotid artery and a normal left carotid artery. Flow rates in the CCA, ICA and ECA were measured with phase-contrast MR and the peak velocity in the bulb region was measured with Doppler ultrasound (DUS). A CFD simulation was performed imposing ﬂow rates measured with PC-MR in the CCA and ICA. Traction-free boundary conditions were prescribed in the ECA. Although the PC-MR images were quite noisy, the CFD and PC-MR velocity proﬁles in the region of the bifurcation are in good agreement (see Fig. 8). A comparison of the peak velocity in the bulb region obtained with the CFD model and measured with DUS is shown in Fig. 8. The DUS velocity waveform was obtained from the envolvent of the ultrasound spectrum and averaged over several cardiac cycles. Figure 8 shows a very good agreement between the CFD and DUS peak velocities.

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Figure 8. Validation of peak velocity and proﬁles.

Figure 9. Reconstructed anatomical models.

10. Examples In this section we present examples of ﬁnite element models of carotid artery hemodynamics in patients with different degrees of atherosclerotic disease. Patient-speciﬁc models were constructed for each of these arteries as described before. The reconstructed vascular models are shown in Fig. 9. These models correspond to carotid arteries with the following degrees of atherosclerotic disease: a) normal, b) nor-

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Figure 10. Details of ﬁnite element grids.

Table 1. Summary of hemodynamic calculations. No.

p (mmHg)

peak mean WSS (dyne/cm2 )

Disease

a

12.0

50.0

Normal

b

2.0

100.0

Normal - contralateral occlusion

c

5.0

40.0

Mild

d

10.0

30.0

Moderate

e

18.0

200.0

Severe

f

20.0

200.0

Severe - kink

mal with occluded contralateral internal carotid artery, c) mild stenosis, d) moderate stenosis, e) severe stenosis, f) severe stenosis. Tubular deformable models followed by surface merging were used in the ﬁrst three cases (a,b,c) and iso-surface deformable models were used in the last three cases (d,e,f). The ﬁnite element grids generated for each of these models are shown in Fig. 10. Blood ﬂow analyses were conducted in each of these models for two cardiac cycles. In a post-processing stage, hemodynamic quantities such as peak pressure drop (pressure difference between the CCA inlet and the ICA outlet at peak systole) and mean or timeaveraged wall shear stress (WSS) magnitude were calculated. The results are summarized in Table 1. Visualizations of the computed peak pressure drops, are presented in Fig. 11. A slight pressure increase can be observed at the apex of the bifurcation and increased pressure drops across stenoses can be clearly seen. Visualizations of the distribution of mean WSS are shown in Fig. 12. Regions with increased WSS include, arterial stenoses, the apex of the carotid bifurcation, and outer surface of vessels with high curvature. Low WSS are observed in the bulb region of healthy carotid arteries. The oscillatory shear index (OSI) provides a measure of the angular change of the shear force during the cardiac cycle [56]: || 1 1− (59) OSI = 2 < |f| >

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Figure 11. Peak pressure distributions.

where f = τ · n is the tangential force per unit area, n is the normal to the vessel surface, and <> denotes time average over the cardiac cycle. Regions with elevated values of OSI indicate that the direction of the shear force changes signiﬁcantly over the cardiac cycle. These changes are thought to possibly lead to endothelial cell damage and development or progression of the atherosclerotic disease. However, one must be cautious because the OSI does not account for the magnitude of the shear force, in other words, the shear force may be changing in direction signiﬁcantly (high OSI), but its magnitude may be very low. Visualizations of the OSI distribution (Fig. 13) indicate that high levels of OSI are encountered near the bulb, where the ﬂow recirculates, or at the bifurcation apex, where the ﬂow divides. More complex distributions of OSI observed in stenosed vessels may be indicative of disturbed or turbulent ﬂow patterns. The effects of the non-Newtonian properties of blood are illustrated in Fig. 14. A model of a healthy carotid artery was analyzed both with a Newtonian approximation and the Casson model. As shown in the ﬁgure, differences of the order of 10% to 20% in the distribution of the mean wall shear stress magnitude can be observed in the region of the bulb. Further investigation is needed to determine the importance of nonNewtonian effects for varying degrees of atherosclerotic disease. Incorporating non-

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Figure 12. Mean wall shear stress distributions.

Newtonian models into a CFD solver is very simple and the computing time is only slightly affected (it increases by about 10%). In addition, estimating a priori the regions where non-Newtonian effects may be important is difﬁcult because it requires knowledge of the time varying ﬂowﬁeld, and in particular the regions of low ﬂow and low shear. For these reasons, we favor the use of non-Newtonian models in all calculations. When using such models, one must be careful with the initial conditions used to initialize the ﬂowﬁeld. If the ﬂow starts from zero, the initial non-Newtonian viscosity would be maximum, and it may take several cardiac cycles to adjust to the correct values. Alternatively, the ﬂowﬁeld can be initialized from a simulation performed using a Newtonian model for an entire cardiac cycle or from a steady run using the initial values of the ﬂow rates. Finally, the complex ﬂow patterns computed for patients with carotid artery disease, are visualized in Fig. 15. These visualizations were produced by cutting the computational domain along a surface that follows the axis of each arterial branch [86]. Velocity magnitudes on these cuts were plotted at ﬁve instants during the cardiac cycle. Several important ﬂow characteristics can be observed. These include: high speed jets at arter-

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Figure 13. Distributions of oscillatory shear index.

Figure 14. Non-Newtonian effects on the wall shear stress distribution.

ial stenoses, ﬂow recirculation zones in the bulb, highly skewed velocity proﬁles in regions of high curvature, and unstable velocity patterns distal of severe stenoses. Note that ﬂow impingement correspond with regions of increased pressure, and regions of highly skewed velocity proﬁles with increased wall shear stress.

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Figure 15. Visualization of ﬂow patterns for cases with atherosclerotic disease.

11. Discussion Progress in characterization of hemodynamic conditions in the carotid artery has been substantial. Namely, a comprehensive computational process has been assembled to perform vascular CFD analysis. The reliability of that methodology has been established, on a preliminary basis, in a diverse set of experiments. However, several legitimate concerns must still be addressed before vascular CFD analysis can be used on a routine basis and without signiﬁcant technical expertise. A primary concern is the high computational complexity (computing time) of vascular CFD analysis. The computational schemes described in this chapter for obtaining the ﬁnite-element solution are speciﬁcally geared towards reduction of the computational complexity. These schemes now permit the computation of the ﬁnite-element solution of the carotid artery hemodynamics in less than 12 hours on a consumer PC that is a remarkable performance considering that such analysis was only recently relegated to supercomputers. However, such the delay currently in-

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volved in performing vascular CFD analysis is probably unacceptable in a clinical setting. Perhaps of even greater concern is that vascular CFD analysis requires expert supervision, for example, for ensuring that the correct segmentation of the vessel has been obtained and for identifying and truncating inﬂow and outﬂow locations. Of the greatest concern still, is whether the CFD analysis can accurately assess the hemodynamic conditions in the carotid artery in a consistent manner. The accuracy of vascular CFD analysis might be compromised by any of a variety of factors including inaccuracy of the vessel segmentation, inaccuracy of the ﬂow quantiﬁcation and the inaccuracy of the simplifying assumptions of the ﬂuid-dynamics modeling. In spite of these technical concerns, it is now appropriate to begin consideration for the use of vascular CFD analysis in the clinical setting. Ultimately, CFD analysis could take its place, along with other imaging methods, in the evaluation of carotid artery disease.

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[66] Taylor,C.A., Hughes, T.J.R., and Zarins, C.K., Finite Element Modeling of Blood Flow in Arteries. Comput. Methods Appl. Mech. Engrg., 158, 155–196, 1998. [67] Milner,J.S., Moore, J.A., Rutt, B.K., and Steinman, D.A., Hemodynamics of human carotid artery bifurcations: computational studies in models reconstructed from magnetic resonance imaging of normal subjects. J. Vasc. Surg. 28, 143–156, 1998. [68] Zhao, S.Z., Xu, X.Y., Hughes, A.D., Thom, S.A., Stanton, A.V., Ariff, B., and Long, Q., Blood Flow and Vessel Mechanics in a Physiologically Realistic Model of a Human Carotid Arterial Bifurcation. J. Biomech. 33, 975–984, 2000. [69] Cebral, J.R., Castro, M.A., Soto, O., Löhner, R., and Alperin, N., Blood-ﬂow models of the circle of Willis from magnetic resonance data. Journal of Engineering Mathematics, 47, 369–386, 2003. [70] Cebral, J.R., Yim, P.J., Löhner, R., Soto, O., Marcos, H., and Choyke, P.L., New Methods for Computational Fluid Dynamics of Carotid Artery From Magnetic Resosnance Angiography, Proc. SPIE Medical Imaging, Vol. 4321, paper No. 22, San Diego, California, February 2001. [71] Quarteroni, A., Tuveri, M., and Veneziani, A., Computational vascular ﬂuid dynamics: problems, models and methods. Report EPFL/DMA 11.98, 1998. [72] Thomaset, F., Implementation of ﬁnite element methods for Navier-Stokes equations. Springer-Verlag, 1981. [73] Gunsburger, M.D., and Nicolaides, R. (eds.), Incompressible Computational Fluid Dynamics: Trends and Advances. Cambridge University Press, 1993. [74] Hafez, M.M. (ed.), Numerical Simulation of Incompressible Flows. World Scientiﬁc, 2003. [75] Löhner, R., Applied CFD Techniques, John Wiley & Sons, New York, 2001. [76] Löhner, R., Yang, C., Cebral, J.R., Soto, O., Camelli, F., and Waltz, J., Improving the speed and accuracy of projection-type incompressible ﬂow solvers. AIAA-03-3991-CP, 2003. [77] Löhner, R., Yang, C., Oñate, E., and Idelssohn, S., An unstructured grid-based, parallel free surface solver. Appl. Num. Math., 31, 271–293, 1999. [78] Saad, Y., Iterative methods for sparse linear systems. Boston: PWS Pub. Co., 1996. [79] Löhner, R., Yang, C., Cebral, J.R., Soto, O., Camelli, F., Baum, J.D, Luo, H., Mestreau, E. and Shadov, D., Advances in FEFLO, AIAA-02-1024, 2002. [80] Luo, H., Baum, J.D., and Löhner, R., A fast matrix-free implicit method for compressible ﬂows on unstructured grids. J. Comp. Phys., 146, 664–690, 1998. [81] Sharov, D., Luo, H., Baum, J.D., and Löhner, R., Implementation of unstructured grid GMRES+LU-SGS method on shared-memory, cache-based parallel computers. AIAA-00-0927, 2000. [82] Soto, O., Löhner, R., Cebral, J.R., and Codina, R., A Time-Accurate Implicit Monolithic Finite Element Scheme for Incompressible Flow Problems, Proc. ECCOMAS CFD, Swansea, UK, September 2001. [83] Cebral, J.R., Putman, C., Pergolizzi, R., and Burgess, J.E., Patient-Speciﬁc Modeling of Atherosclerotic Carotid Arteries from Multi-Modality Image Data, Proc. IMECE’03, Washington DC, Nov. 16–24, 2003. [84] Estimation of Mechanical Stress on the Carotid Artery, Yim, P.J., Cebral, J., Löhner, R., Ho, V., Choyke, P.L., Annals of Biomedical Engineering, vol. 29, Supplement 1, Page S-77. [85] “Measurement of pressure drops at arterial stenoses from MR imaging” Abstract Book, Joint Meeting of the Biomedical Engineering Society and the IEEE Engineering in Medicine and Biology Society, Houston, Texas, (October 23–26, 2002), Yim, P.J. Cebral, J.R., Weaver, A., Lutz, R., Vasbinder, G.B.C., Choyke, P.L. p. 223. [86] Cebral, J.R., and Löhner, R., Flow Visualization On Unstructured Grids Using Geometrical Cuts, Vortex Detection and Shock Surfaces, AIAA-01-0915, 2001.

Plaque Imaging: Pixel to Molecular Level J.S. Suri et al. (Eds.) IOS Press, 2005 © 2005 The authors. All rights reserved.

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Numerical Modeling of Coronary Drug Eluting Stents Rosaire MONGRAIN a , Richard LEASK a , Jean BRUNETTE b , Iam FAIK a , Neil BULMAN-FELEMING a and T. NGUYEN a a McGill University, McGill, Canada b Université de Montréal, Montreal, Quebec, Canada Abstract. One of the principal therapies considered for the control of in-stent restenosis is the use of drug loaded polymer-coated stents for local delivery. We present two-dimensional and three-dimensional numerical models to study local delivery of drug eluting stents. The impact of various stent and ﬂow parameters on the concentration distribution in the wall are investigated including the effect of the strut size, coating thickness, strut inter-distance and strut embedment in the vascular wall, blood ﬂowing speed and the respective diffusion coefﬁcients in the blood, wall and polymer. We also present criteria to assess the drug delivery efﬁciency based of the concept of the therapeutic window which aims at an spatial homogeneous concentration distribution and we introduce the variables to assess the amount of drug delivered in the wall. The results suggest that advection have a much stronger effect compared to diffusion in the blood media and that drug diffusivity in the arterial wall and in the polymer coating signiﬁcantly affects the drug distribution. It is also shown that fully-embedded struts provide better spatial drug concentration uniformity after a short period of time and the half-embedded struts have a better temporal uniformity. Keywords. Drug eluting stent, numerical models, drug concentration, delivery efﬁciency

Introduction The success of coronary artery stenting has improved over the last decade. In stent restenosis has gone from approximately 40% at six months in the 1990s to around 10% at the turn of the century following the initial procedure1−4 . A number of promising methods for preventing restenosis have been investigated including systemic drug delivery5 , brachytherapy4 , local drug delivery6 , and targeted gene therapy7−9 . These therapies are meant to inhibit neointimal hyperplasia by altering the cellular growth response in the tissues surrounding the stent. In this chapter we will discuss some of the modeling tools developed to study drug delivery by drug eluting stents. In order to successfully prevent restenosis, drug eluting stents must deliver a therapeutic drug dose evenly through the treatment region for a deﬁned duration. Favorable results have come from animal trials in porcine models6,10 , unfortunately information about the dose distribution over time is difﬁcult to obtain from

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investigations of this nature. Moreover, porcine models of drug-eluting stents concentrate on measuring the degree of restenosis rather than drug concentrations in the tissue of interest. Clinical studies have shown impressive results with sirolimus-eluting stents even in complex disease vessels11−15 , however failure of the target vessel still occur in up to 10% in the ﬁrst year. Numerical modeling of local delivery may help to identify some of the sources of these shortcomings and further optimize treatment. Current tissue transport models can be divided into two broad groups: porous medium models16,17 and diffusive models with various convective mechanisms incorporated into an effective diffusivity18,19 . These models use measured diffusivities and various porous model parameters in simulating transient drug delivery, often considering the multiphase structures of the arterial tissue. Results from the two basic models provide adequate agreement (ie. within the same order of magnitude) of drug delivery seen in vivo. Reﬁnements to these models can be considered higher-order adjustments which will result in successive increases model accuracy, ultimately leading to more precise dose distribution in the arterial tissues. However tissue anisotropy and the complexity of shape and composition in actual pathological vessels could easily overshadow these higher-order model improvements. In this chapter, we present a relatively simple model for stent designers and cardiologists to study the inﬂuence of stent geometry, stent conﬁgurations, eluting polymer coating thickness and initial doses. With this in mind, we present a purely diffusive ﬁnite element model with appropriate boundary conditions, and focus our interest on representing some realistic geometric scenarios likely to arise following stent implantation. The numerical model is veriﬁed by comparing the impact of heparin-like (hydrophilic) and taxol-like (hydrophobic) diffusivities on drug concentration homogeneity distribution. The numerical tools developed can be used to: determine dose and dose-rate delivery for optimal therapy, compare dose delivery characteristics of polymer coated stent and quantify the effects of blood velocity, relative diffusion constants, coating thickness, inter-strut spacing, and strut apposition on dose delivery.

1. 2D Model of Drug Delivery The pharmacokinetic modeling of drug delivery from a polymer coated stent is a very complex problem. The complex three-dimensional geometry and structure of an atherosclerotic vessel with a stent are difﬁcult to simulate. In addition, the polymer coating is relatively thin which makes numerical mesh generation difﬁcult. The dispersion of the molecule is a multiphysics problem involving pulsatile ﬂuid ﬂow and mass transfer. In this section we present a very simple 2D steady ﬂow model with rigid walls and a homogeneous wall structure to model drug delivery. In Section 3 we generalize the model in three-dimension and subsequently present an anatomically correct atherosclerotic vessel reconstructed from Intravascular Ultrasound (IVUS) image data. The proposed models (2D and 3D) are a simpliﬁcation of the pharmacokinetics occurring in the context of arterial treatment. We assume homogeneous isotropic (nonporous) media. This means that the molecule transport due to transmural pressure gradient is neglected. The structures are assumed to be rigid and the ﬂow steady. Similar models to investigate blood ﬂow dynamics in stents have previously been proposed20,21 .

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445

Figure 1. Description of the pharmacokinetic model around a single strut.

1.1. 2D Model Description The dispersion of the drug is modeled using the 2D advection-diffusion equation in the vessel lumen coupled to the Navier-Stokes equations and as a purely diffusive process in the arterial wall. It is assumed that the removal of drug at the outer radius (adventitial side) of the vessel is complete due to clearance by the vasa vasorum and lymphatic drainage, and therefore, modeled as a Dirichlet boundary condition. The model is illustrated in Fig. 1 and described with the following set of equations: ρ(u · ∇)u = −∇p + μ∇ 2 u ∇ ·u=0 ∂C + (u · ∇)C = DL ∇ 2 C ∂t ∂C = Dp ∇ 2 C ∂t ∂C = Dw ∇ 2 C ∂t

(1a) (1b) (1c) (1d) (1e)

where u is the blood velocity (m/s), C is the local drug concentration (Kg/m3 ), p the blood pressure (Pa), ρ the blood density (kg/m3 ), μ the blood dynamic viscosity (Pa.s) and DL ,Dp , Dw are the diffusion constants of the drug molecule in the lumen, the polymer and the arterial wall respectively (m2 /s). 1.2. Model Geometry The approach is illustrated with a simple helicoid stent geometry composed of a circular wire (similar to the CardioCoilT M stent from Medtronic) Fig. 2b. As a ﬁrst approach, we consider a 2D representation of the symmetric plane along the axis of the stent (Fig. 2a). The dimensions adopted for this model are: • • • •

15 struts, 0.15 mm in diameter and located 0.7 mm center to center apart Polymer Coating Thickness = 0.005 mm Diameter of the artery = 3 mm Arterial wall thickness = 0.4 mm

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Figure 2. A) Successive ring conﬁguration corresponding to the 2D model B) Representation of the corresponding coil stent with the strut characteristics.

Figure 3. A) Typical mesh and B) a zoom of the mesh in between two struts (bottom), point 1 and 2 denote the location of where concentration levels were measured (see text).

1.3. Mesh Generation A ﬁnite element mesh was generated for the above conﬁgurations with quadrilateral linear elements using a combination of the pave and map schemes available in FIDAP (Fluent, USA). Smaller elements in the vicinity of the struts were used to better capture the physics in this region. This was accomplished by pre-meshing the sides and by creating boundary layers around the struts. A typical mesh is illustrated in Fig. 3. 1.4. Physical Parameters and Boundary Conditions From the governing equations, the principal physical model parameters are the mechanical properties of the blood, the properties of the coronary blood ﬂow, the diffusivity of the drug molecule in the three continuum media and the initial concentration of the drug in the polymer coating. Blood properties used in this analysis are: density ρ = 1.057 g/cm3 and viscosity μ = 3.5 10−2 Poise. Physiological coronary blood ﬂow rates vary between 0.5 and 1 cm3 /s, assuming fully developed ﬂow condition at the inlet, this results in a maximum velocity (Vmax located at the center of the vessel) between 14 and 28 cm/s for an artery of 0.3 cm in diameter. The ﬂow is considered laminar and fully developed hence the radial velocity distribution in the inlet is set to be parabolic:

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447

Table 1. Summary of the boundary conditions. Boundary

Condition

Inlet

Parabolic velocity Proﬁle and Concentration: C = 0

Endothelium

Velocity: Vx = 0 and Vy = 0

Advantitia

Concentration: C = 0

Axis of symmetry

Velocity: Vy = 0

V(R) = Vmax 1 −

R Ra

2 (2)

where R is the radial position and Ra the inner radius of the artery. The values of the diffusion constants of the drug in blood (DL ), in the polymer (Dp) and in the arterial wall (Dw) are unknown and depend mainly on the characteristics of the drug molecule and the type of the material properties of the polymer and vessel wall. Their range covers a wide spectrum, and hence their effect is studied for different orders of magnitude varying between hydrophobic and hydrophilic molecules. Molecule transport due to the transmural pressure gradient is neglected. This means that we consider the arterial wall and the polymer as non-porous media and thus all mass transport mechanisms are lumped into a single effective diffusion coefﬁcient. A no-slip boundary condition is imposed at the solid walls (endothelium, stent struts). The concentration in the polymer is normalized so that the initial concentration is set to unity (Co = 1). This allows subsequent local concentrations in the polymer to be expressed directly as fractions of the initial concentration. Coronary arteries contain vasa vasorum and a lymphatic system which exchange bioﬂuids within the vessel. This drainage establishes the boundary condition for the drug concentration at the outer limit of the arterial wall. Two extreme conditions are possible; 1) the molecule is completely washed away (C = 0 at the boundary) or 2) a saturation is achieved and the mass ﬂux is zero (dC/dn = 0). As mentioned earlier, in these simulations it is assumed that there is complete removal at the outer limits of the artery wall (C = 0). The boundary conditions are summarized in Table 1. 1.5. Assessment of Drug Delivery Efﬁciency Two dimensional contour plots are a good way to visualize the distribution of drug concentration. In addition, numerical measures for comparing dose delivery between models were developed;

C dA

• The mean value of the concentration in the polymer ( dA ). • The local concentrations at point 1 and 2, Fig. 3. A is located at 250 microns from the endothelium directly facing the strut and B is in-between two struts. • The dose homogeneity index (DHI). • The remaining mass percentage (RMP). We deﬁne the DHI as the coefﬁcient of variation, CV, of the concentration at each nodal point within the therapeutic region. A simple rectangular therapeutic region was considered with a depth of 200 μm into the arterial wall and a length of 17 mm (which extended beyond the ﬁrst and last struts by 65 μm). The area taken up by the stent and

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Figure 4. Illustration of 2D concentration distribution.

polymer are excluded from the calculation since these areas do not reﬂect on the success of local delivery. The mathematical form of the DHI is given as: M,N σC 1 Cij =√ −1 . DHI = CV ther.reg. = C C MN i,j

(3)

The lower the DHI the more homogeneous is the concentration distribution. The efﬁciency of drug transport to the vascular wall is measured with the Remaining Mass Percentage (RMP). The RMP is deﬁned simply as the percentage of combined drug mass remaining in the stent and arterial wall after a speciﬁed time interval following stent implantation (the rest is lost in the blood stream). The value is given by:

Atotal i,j Cij dxi dyj = Cij (4) RMP = C0 Apolymer Apolymer i,j

When the dxi and dyj are made equal (by interpolation on a regular grid) there is no need for individual element weighting and the expression is simpliﬁed to the sum of all concentrations in the domain multiplied by the ratio of areas. The RMP provides a simple means of estimating initial concentrations necessary in achieving therapeutic dosages over a speciﬁed time period. It also offers a means of evaluating temporal dose distribution behavior, and its complement (1-RMP) indicates the fraction of initial mass removed from the system.

2. Effect of Model Variables on 2D Drug Delivery 2.1. Effect of Blood Velocity We ﬁrst analyzed the effect of blood velocity on the drug diffusion rate and distribution patterns. The effect of blood velocity on the concentration patterns of the drug in the arterial wall was investigated at different steady ﬂow velocities within the range of physiological coronary blood ﬂow (with ﬂow velocity varying between 10−3 to 28 cm/s). For these cases, the model assumes the stent struts to be half embedded with diffusion constants: Dw = 10−14 m2 /s, Dp = 10−13 m2 /s, DL = 10−9 m2 /s. An illustration of typical 2D concentration distribution distributions is shown in Fig. 4. The concentration results at different ﬂow velocities are summarized in Table 2. Variations in blood velocity have a negligible effect on the relaxation time of the drug from the polymer as evaluated by the mean concentration in the polymer after one, two and three days. We also note that the local concentration in the arterial wall and hence the distribution pattern of the drug is not signiﬁcantly affected by the variations in blood velocity for the entire range of diffusion coefﬁcients.

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449

Table 2. Effect of blood velocity on the mean normalized concentration in the polymer and in the vascular wall. Mean Normalized Concentration in Polymer

Mean Normalized Concentration in point 1 (See Fig. 3)

Maximum Velocity (mm/s)

1day

2days

3days

1day

2days

3days

280

8.30E-02

2.57E-02

1.20E-02

4.97E-02

3.86E-02

2.35E-02

200

8.30E-02

2.57E-02

1.20E-02

4.97E-02

3.86E-02

2.35E-02

140

8.30E-02

2.57E-02

1.20E-02

4.97E-02

3.86E-02

2.35E-02

10

8.30E-02

2.57E-02

1.20E-02

4.97E-02

3.86E-02

2.35E-02

1

8.30E-02

2.57E-01

1.20E-02

4.97E-02

3.86E-02

2.35E-02

1.00E-03

8.56E-02

2.67E-02

1.25E-02

5.00E-02

3.91E-02

2.39E-02

Figure 5. Final concentration in the polymer as a function of blood diffusion coefﬁcient after 1 day, 2 days and 3 days.

2.2. Effect of the Drug Molecule Diffusion Coefﬁcient in the Blood (DL ) The mean concentration of the drug molecule in the polymer after one, two and three days was evaluated for different values of the diffusion constant of the molecule in the blood (with DL varying between 10−12 to 10−6 m2 /s)which covers the range of diffusion constants between hydrophobic and hydrophilic molecules. The diffusion constants of the polymer and wall were ﬁxed (Dw = Dp = 10−13 m2 /s). These values implicitly assumes that the drug molecule diffuses equally in all solid media. The results displayed in Fig. 5, show that the value of the mean concentration is unaffected by six orders of magnitude variation in the blood diffusion constant. 2.3. Effect of the Drug Molecule Diffusion Coefﬁcient in the Polymer (Dp ) and in the arterial wall (Dw ) In the previous sections, we have shown little dependence of the concentration distribution on the blood ﬂow velocity and on the diffusion coefﬁcient in the blood. In this

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Figure 6. Mean concentration remaining in the polymer after 1 day , 2 days and 3 days for different arterial wall diffusion coefﬁcients.

section we investigate the effect of the relative values of the diffusion coefﬁcients in the vascular wall (Dw ) and in the polymer coating (Dp ). To assess the effect of the different combinations of these two diffusion constants, we again evaluate both the mean concentration in the polymer and the ratio of the total concentration in the arterial wall to the C dA initial total concentration in the polymer: dA . The results are summarized in Table 3 and Figs 6a and 6b. Figure 6 presents the amount of the drug left in the polymer with time. Table 3 shows how much of this drug is accumulated in the arterial wall; the rest being washed away in the lumen and the outer radius of the model or still in the polymer. These results show a strong dependence of the drug release time and drug accumulation on both the drug diffusivity in the polymer and in the arterial wall. We can also note that better accumulation and homogeneity are achieved for lower values of the two diffusion constant (hydrophobic range). 2.4. Effect of Coating Thickness To investigate the effect of polymer thickness on the tissue drug concentration, the diffusion coefﬁcients were ﬁxed (Dp = Dw = 10−13 m2 /s) and blood advection was ignored (see Section 2.1). Thicknesses of 5, 10 and 15 μm were investigated for heparin-like diffusion coefﬁcients. The time period used for these simulations was the 3 day duration of the previous sections. DHI results show similar homogeneities for the three poly-

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451

Table 3. Effect of the relative values of Dw and Dp on the percentage of concentration in the arterial wall. Concentration (%) in Arterial Wall Dw

Dp

1day

2days

3days

1.00E-12

1.00E-12

3.66

0.27

0.02

1.00E-12

1.00E-13

5.43

5.87

5.42

1.00E-12

1.00E-14

5.24

18.76

7.09

1.00E-13

1.00E-12

11.04

5.73

3.02

1.00E-13

1.00E-13

26.28

18.95

12.32

1.00E-13

1.00E-14

23.51

22.09

17.32

1.00E-14

1.00E-12

4.94

3.28

2.62

1.00E-14

1.00E-13

18.95

18.66

17.20

1.00E-14

1.00E-14

21.91

27.19

29.51

Figure 7. Left: Concentration distribution (for two successive square struts) with a 5 μm coating (DHI = 0.65, RMP = 1.1%) Right: Concentration distribution (for two successive square struts) with a 15 μm coating (DHI = 0.73, RMP = 2.2%).

Figure 8. Top: Concentration distribution (shown around three successive struts for solid polymeric strut, Solid Stent: DHI = 1.344, RMP = 2.31% Bottom: Concentration distribution (coating thickness10 μm): DHI = 0.844, RMP = 0.73%.

mer layer thicknesses, with DHIs of 0.65, 0.66 and 0.73 for 5, 10 and 15 μm thickness. The remaining mass percentages (RMP) for the different layer thickness were; 1.1% for 5 μm, 1.5% for 10 μm and 2.2% for 15 μm. This suggests that in order to achieve the same drug retention in a 5 μm coating as a 15 μm coating, approximately twice the initial drug mass would need to be loaded within the polymer. Figure 7 illustrates the results for the 5 μm and the 15 μm thickness coatings. Although twice the drug remains in the system with the thickest coating, the distribution is less uniform.

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R. Mongrain et al. / Numerical Modeling of Coronary Drug Eluting Stents

Figure 9. Effect of inter strut spacing on drug concentration homogeneity (Top). Effect of inter strut spacing on remaining amount of drug in the wall (Bottom).

We also investigated the effect of having the entire stent made of drug eluting polymer and compared it with the 10 μm coating. The solid polymer stent has a slower elution rate and therefore a higher RMP but has a less even distribution of drug in the tissue. This suggests a coated approach with a higher initial dose of drug would provide good homogeneity of drug delivery and longer residence times. 2.5. Inter Strut Distance The impact of inter strut spacing on the concentration distribution was also investigated. Figure 9 summarizes the results. The homogeneity (DHI) of drug delivery increases with inter-strut spacing and the amount of drug remaining in the wall and coating (RMP) decreases as the inter-strut spacing increases due to changes in the spatial concentration gradient. As a result we conclude that the closer the struts, the more favorable the outcome. However there is a trade off, as increased stent contact area increases endothelial cell damage and the risk of inﬂammation and thrombosis. 2.6. Strut Embedment In the previous sections, we have shown that the physical variables that have the most inﬂuence on the concentration of distribution in the vascular wall are the relative values of the diffusion coefﬁcients of the drug molecule in the wall and in the polymer (Dw, Dp). In this section, we investigate the impact of the strut embedment due to angioplasty for a given set of Dw, Dp. Different strut embedment conﬁgurations were compared on the basis of the uniformity of the drug concentration distribution over the arterial wall as well as the uniformity

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453

Figure 10. Drug concentration distribution for the half embedded, non-embedded strut and fully embedded conﬁgurations. Table 4. Homogeneity indices and remaining mass percentages for four strut apposition scenarios. Apposition Scenario

DHI

RMP (%)

Completely embedded

0.74

2.2

Half embedded

0.66

1.5

Contacting

0.79

1.2

over time for Dw = Dp = 10−13 m2 /s. Again the objective in drug eluting-stent design and deployment is to achieve a uniform spatial and temporal distribution of the drug molecule. Using this model, three strut apposition conﬁgurations were investigated; no strut embedment, half-embedded struts and fully embedded struts. Figure 10 displays the general behaviour of the drug concentration distribution for all three conﬁgurations. The RPM is strongly affected by the degree of embedment. Interestingly, there seems to be an opposite DHI results for coated/solid (although coated is almost constant). Overall, the best concentration distribution is found with the fully embedded struts. However, again a balance between embedment and tissue injury should also be taken into account. The homogeneity parameters DHI and remaining mass percentage RMP as summarized in the following table.

3. 3D Dose Concentration Computations In this section, we present recent developments for modeling the pharmacokinetics of drug eluting stents in 3D. The complex 3D geometry requires the use of a Computer Assisted Design (CAD) program and a dedicated numerical mesh generation software to properly represent the artery and stent. The physics (blood ﬂow and mass transport) is modeled with the same set of equations as in the 2D approach. The same concentration distribution criteria (DHI, RMP) are used to assess the drug dispersion. In addition, the surface contact area is calculated as a measure of endothelial disruption and resulting potential adverse biological response.

454

R. Mongrain et al. / Numerical Modeling of Coronary Drug Eluting Stents

Figure 11. The Symbiotech stent and solid model.

Figure 12. 3D Stent strut geometry and numerical mesh.

Figure 13. 3D Wall shear stress distribution.

3.1. 3D Basic Geometry Numerical Model The 3D stent geometry of the Symbiotech stent (Laval, Qc) was generated using the CAD software Pro-Engineer (PTC, USA). Figure 12 shows the actual stent and its 3D CAD representation. The stent is shown in a 3.1 mm expanded conﬁguration. The total stent length is 1.5 cm, the strut width is 63.5 μm and the modeled polymer coating thickness is 5 μm. 3.2. 3D Domain Discretization and Numerical Model For the 3D model, the discretization was carried out using ICEM-CFD (ANSYS, USA) with tetrahedral elements. Grid independence tests indicated that mesh element side lengths of 2.5 μm surrounding the polymer layer to 25 μm in the outer regions resulted in a favourable computation time/result agreement compromise. Figure 13 shows a magniﬁed view near the strut of the solid model and local mesh used for simulation.

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455

Coupled 3D Navier-Stokes and Advection-Diffusion equations were applied in the vessel lumen. The polymer coating and arterial wall were considered purely diffusive regions. Blood is considered an incompressible Newtonian ﬂuid of density ρ = 1.05 g/cm3 and dynamic viscosity μ = 0.035 Poise (g/cm.s). ρ( u · ∇) u = −∇p + μ∇ 2 u

(5a)

∇·u=0

(5b)

Ct + ( u · ∇)C = Dlumen ∇ C 2

Ct = Dpolymer ∇ 2 C

(5c) Ct = Dartery ∇ 2 C.

(5d)

For comparison purposes, the same diffusivities used in 2D for hydrophilic and hydrophobic drug molecules, arterial wall, polymer coating and pathological tissues were implemented. Concentrations at the outer limit of the arterial wall and lumen inlet are set to zero for all time. At the outer wall limit this condition is meant to approximate the effect of dilution resulting from transport of mass from the vasa vasorum and lymphatic drainage. At the inlet concentrations due to dilution in blood will effectively be zero. No-slip velocity conditions are imposed on the polymer coating and arterial wall. Drug loading of the stent is represented as an initial concentration of 1.0 in the polymer. 3.3. 3D Velocity and Shear Stress Computation As mentioned in the introduction, non-physiological values of wall shear stress (WSS) are considered by some groups as a potential factor in the development of in-stent restenosis 20,21 . The 3D characterization of WSS and of ﬂow patterns in a stented artery is therefore necessary to understand the phenomenon and to better design the next generation of stents. Indeed, 3D simulations of the stent allow us to investigate the global WSS distribution that cannot be obtained by simple 2D analyses. This is especially true for stents with complex shapes and for the description of the circumferential intra-struts WSS distribution. In the following ﬁgure we show recent 3D computations of the shear stress obtained from the velocity. We notice relatively high shear stress values at the struts (24.5 Pa) adjacent to a relatively low shear level in between the struts (1.4 Pa). This proximity of alternating shear stress levels could be involved in the pathogenesis of in-stent restenosis. In the following ﬁgure we show a preliminary 3D concentration distribution in the vascular wall and the corresponding remaining mass percentage (RMP) calculated over a period of one week. We propose an additional design criterion to take into account the biological response of the stent which we simply measure with the contact area of the stent with the vascular wall (this implicitly assumes a proportionality between the area of contact of the foreign body with the wall and the biological response). The area of contact index (ACI) is thus simply deﬁned as the area of contact of the stent over the area of the cylinder deﬁned by the stent length and circumference (this means that the ACI varies between 0 and 1). Finally, we combine all the design criteria into a single design efﬁciency criterion DE with the following weighted average:

456

R. Mongrain et al. / Numerical Modeling of Coronary Drug Eluting Stents

Figure 14. 3D drug concentration distribution computation.

Figure 15. Left column: Modeled stent, middle column: corresponding numerical mesh, right column: summary of the dose distribution design efﬁciency criteria results.

7 DE = α

DH I −1 −1 DH Imin

8

+β

with α + β + γ = 1

F MP F MPmax

7

+γ

ACI −1

8

−1 ACImin

(6)

This means that DE varies between 0 (worst design) to 1 (best theoretical design) in terms of drug concentration homogeneity (DHI), remaining mass in the vascular wall (RMP) and biological response through contact area (ACI). We present in the following ﬁgure the analyses that were done for three different stent designs (Symbiotech, Cardiocoil and Palmaz). In these computations the values for αsgβ and γ were set to 0.5, 0.2 and 0.3 respectively to give more importance to the homogeneity equal to the combined effects of the remaining mass and area of contact. We note that in terms of the remaining mass percentage, the Palmaz stent appears to be the best. In terms of area of contact, the coil stent seems to perform best. Ongoing work includes the extension of the models to simulate the diffusion of the molecule into pathologic vessel structures taking into account the effect of the vascular matrix, lipid, ﬁbrotic and calciﬁc pools. These structures are reconstructed from Intravascular Ultrasound (IVUS) using manual segmentation as illustrated in Fig. 16.

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457

Figure 16. Left to right: IVUS manual segmentation for the lumen and internal plaque structures; 3D CAD reconstruction of the lumen (gray), external elastic membrane (wireframe) and inclusions and Sent inserted in the 3D reconstructed pathologic wall structure.

The corresponding concentration computations are underway and should reveal how the drug transports through and in between the different plaque internal structures (matrix, lipid pools, ﬁbrotic pools, calciﬁc pools).

Discussion and Conclusions Although the success of coronary stenting has improved over the last decade, in-stent restenosis is still a common cause of stent failure. Numerical modeling of drug eluting stents present several advantages and have the potential to optimize stent design before testing in animals, therefore limiting costly experimental studies. In this chapter we presented some numerical tools to help assess and design drug eluting stents. We ﬁrst showed that, for a simpliﬁed 2D model, changes in the blood velocity in the range of coronary blood ﬂow do not signiﬁcantly inﬂuence the rate of diffusion of the drug molecule from the polymer or its local concentration in the arterial wall. This suggests that the transport forces in the blood are mainly governed by advection while diffusion effects are negligible (Peclet number of the order 105 ). For the same reason, the results show little inﬂuence of the variability of the drug molecule diffusivity in the blood over several orders of magnitude on the total rate of diffusion from the polymer. The constants of diffusion of the drug molecule in the polymer and in the arterial wall were then shown to be the major parameters affecting the physiological transport of the drug after stent deployment. The evaluation of the drug distribution, more speciﬁcally its global homogeneity (spatial and temporal) over the arterial wall in a stent based delivery system is an important step to ensure that the drug will have the desired therapeutic effect. Previous studies have investigated the effect of different stent design parameters on speciﬁc aspects of the spatial distribution and have shown that circumferential and longitudinal strut spacing, signiﬁcantly affects drug homogeneity18,19 . However, to the best of our knowledge, there are no numerical studies in literature concerning strut embedment. We have also shown that the essence of the 3D physics is recovered using 2D numerical models through the use of the introduced design efﬁciency drug delivery parameters, DHI, RMP and ACI allowing us to investigate the stent design in 2D before involved 3D computations. A method was presented to analyse the 3D distribution of a molecule for local delivery using realistic stent and vessel wall structures. The method allows visualization of the homogeneity of the 3D distribution of the molecule achieved in the vascular wall. It also provides a quantitative comparison of delivery efﬁciency in time

458

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after stent implantation for various molecules and stent geometries. Such a tool is complementary to current animal investigations in assessing the efﬁciency of a given coated stent conﬁguration.

References [1] Carrozza, J. P., Jr., Kuntz, R. K., Schatz, R. A., Leon, M., Goldberg, S., Savage, M. et al., Inter-series differences in the restenosis rate of Palmaz-Schatz coronary stent placement: differences in demographics and post-procedure lumen diameter. Cathet. Cardiovasc. Diagn., Vol. 31, pp. 173–8, 1994. [2] Lau, K. W., Ding, Z. P., Johan, A., Kwok, V., Lim, Y. L., Angiographic restenosis rate in patients with chronic total occlusions and subtotal stenoses after initially successful intracoronary stent placement. Am. J. Cardiol., vol. 83, pp. 963–10, 1999. [3] Schiele, F., Meneveau, N., Vuillemenot, A., Zhang, D. D., Gupta, S., Mercier, M. et al., Impact of intravascular ultrasound guidance in stent deployment on 6-month restenosis rate: a multicenter, randomized study comparing two strategies–with and without intravascular ultrasound guidance. RESIST Study Group. REStenosis after Ivus guided STenting. J. Am. Coll. Cardiol., vol. 32, pp. 320–8, 1998. [4] Schiele, T. M., Pollinger, B., Kantlehner, R., Rieber, J., Konig, A., Seelig, V. et al., Evolution of angiographic restenosis rate and late lumen loss after intracoronary beta radiation for in-stent restenotic lesions. Am. J. Cardiol., vol. 93, pp. 836–42, 2004. [5] Kubota, Y., Kichikawa, K., Uchida, H., Maeda, M., Nishimine, K., Makutani, S. et al., Pharmacologic treatment of intimal hyperplasia after metallic stent placement in the peripheral arteries. An experimental study. Invest Radiol., vol. 30, pp. 532–7, 1995. [6] Suzuki, T., Kopia, G., Hayashi, S., Bailey, L. R., Llanos, G., Wilensky, R. et al., Stent-based delivery of sirolimus reduces neointimal formation in a porcine coronary model. Circulation, vol. 104, pp. 1188–93, 2001. [7] Akyurek, L. M., Nallamshetty, S., Aoki, K., San, H., Yang, Z. Y., Nabel, G. J. et al., Coexpression of guanylate kinase with thymidine kinase enhances prodrug cell killing in vitro and suppresses vascular smooth muscle cell proliferation in vivo. Mol. Ther., vol. 3, pp. 779–86, 2001. [8] Hedman, M., Hartikainen, J., Syvanne, M., Stjernvall, J., Hedman, A., Kivela, A. et al., Safety and feasibility of catheter-based local intracoronary vascular endothelial growth factor gene transfer in the prevention of postangioplasty and in-stent restenosis and in the treatment of chronic myocardial ischemia: phase II results of the Kuopio Angiogenesis Trial (KAT). Circulation, vol. 107, pp. 2677–83, 2003. [9] Kipshidze, N., Moses, J., Shankar, L. R., Leon, M., Perspectives on antisense therapy for the prevention of restenosis. Curr. Opin. Mol. Ther., vol. 3, pp. 265–77, 2001. [10] Farb, A., Heller, P. F., Shroff, S., Cheng, L., Kolodgie, F. D., Carter, A. J. et al., Pathological analysis of local delivery of paclitaxel via a polymer-coated stent. Circulation, vol. 104, pp. 473–9, 2001. [11] Fattori, R., Piva, T., Drug-eluting stents in vascular intervention. Lancet, vol. 361, pp. 247–9, 2003. [12] Holmes, D. R., Jr., Leon, M. B., Moses, J. W., Popma, J. J., Cutlip, D., Fitzgerald, P. J. et al., Analysis of 1-year clinical outcomes in the SIRIUS trial: a randomized trial of a sirolimus-eluting stent versus a standard stent in patients at high risk for coronary restenosis. Circulation, vol. 109, pp. 634–40, 2004. [13] Lemos, P. A., Serruys, P. W., van Domburg, R. T., Saia, F., Arampatzis, C. A., Hoye, A. et al., Unrestricted utilization of sirolimus-eluting stents compared with conventional bare stent implantation in the “real world”: the Rapamycin-Eluting Stent Evaluated At Rotterdam Cardiology Hospital (RESEARCH) registry. Circulation, vol. 109, pp. 190–5, 2004. [14] Morice, M. C., Serruys, P. W., Sousa, J. E., Fajadet, J., Ban, H. E., Perin, M. et al., A randomized comparison of a sirolimus-eluting stent with a standard stent for coronary revascularization. N. Engl. J. Med., vol. 346, pp. 1773–80, 2002. [15] Schampaert, E., Cohen, E. A., Schluter, M., Reeves, F., Traboulsi, M., Title, L. M. et al., The Canadian study of the sirolimus-eluting stent in the treatment of patients with long de novo lesions in small native coronary arteries (C-SIRIUS). J. Am. Coll. Cardiol., vol. 43, pp. 1110–5, 2004. [16] Huang, Z. J., Tarbell, J. M., Numerical simulation of mass transfer in porous media of blood vessel walls. Am. J. Physiol, vol. 273, pp. H464–H477, 1997. [17] Qiu, Y., Tarbell, J. M., Numerical simulation of oxygen mass transfer in a compliant curved tube model of a coronary artery. Ann. Biomed. Eng, vol. 28, pp. 26–38, 2000.

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[18] Hwang, C. W., Wu, D., Edelman, E. R., Physiological transport forces govern drug distribution for stentbased delivery. Circulation, vol. 104, pp. 600–5, 2001. [19] Lovich, M. A., Philbrook, M., Sawyer, S., Weselcouch, E., Edelman, E. R., Arterial heparin deposition: role of diffusion, convection, and extravascular space. Am. J. Physiol, vol. 275, pp. H2236–H2242, 1998. [20] LaDisa, J. F., Jr., Guler, I., Olson, L. E., Hettrick, D. A., Kersten, J. R., Warltier, D. C. et al., Threedimensional computational ﬂuid dynamics modeling of alterations in coronary wall shear stress produced by stent implantation. Ann. Biomed. Eng, vol. 31, pp. 972–80, 2003. [21] Wentzel, J. J., Whelan, D. M., van der Giessen, W. J., van Beusekom, H. M., Andhyiswara, I., Serruys, P. W. et al., Coronary stent implantation changes 3-D vessel geometry and 3-D shear stress distribution. J. Biomech., vol. 33, pp. 1287–95, 2000.

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Author Index Amores, J. Baldewsing, R.A. Bertrand, O.F. Bischof, H. Brunette, J. Budoff, M.J. Bulman-Feleming, N. Cai, J. Castro, M.A. Cebral, J. Chakareksi, J. Chen, Y. Christodoulou, C.I. de Korte, C.L. DeMarco, K. Duerk, J.L. Elbischger, P.J. Faik, I. Fei, B. Fox, M.D. Galaz, R. Griffin, M. Hatsukami, T.S. Holzapfel, G.A. Joshi, A. Kakkos, S. Kerwin, W. Klingensmith, J.D. Kyriacou, E. Lara-Montalvo, R. Laxminarayan, S. Leask, R. Lewin, J.S.

26 75 130 97 130, 443 148 443 55 412 412 208 384 241 75 412 384 97 443 394 1 130 241 55 97 130 241 360 300 241 208 1 130, 443 384

Li, C. Macione, J. Mastik, F. Mongrain, R. Nair, A. Nguyen, T. Nicolaides, A. Pattichis, C.S. Pattichis, M.S. Pedersen, P. Pujol, O. Radeva, P. Ranga, A. Regitnig, P. Rumberger, J. Salvado, O. Schaar, J.A. Serruys, P.W. Shinbane, J.S. Sonka, M. Suri, J.S. Tardif, J.-C. van der Steen, A.F.W. Vince, D.G. Wacker, F.K. Wahle, A. Wilson, D.L. Wu, D. Yang, Z. Yim, P. Yuan, C. Zhang, S.

1 1 75 130, 443 300 443 241 1, 241 241 208 276 26, 276 130 97 182 384 75 75 148 321 1, 384, 394 130 75 300 384 321 384, 394 1 1 412 55 384

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