Interrogating the origin and behavior of magnetic resonance diffusion tensor scalar parameters in the myocardium

Myocardial microstructure plays an important role in sustaining the orchestrated beating motion of the heart. Several microstructural components, including myocytes and auxiliary cells, extracellular space, and blood vessels provide the infrastructure for normal heart function, including excitation propagation, myocyte contraction, delivery of oxygen and nutrients, and removing byproduct wastes. Cardiac diseases cause deleterious changes to some or all of these microstructural components in the detrimental process of cardiac remodeling. Since heart failure is among the leading causes of death in the world, new and novel tools to noninvasively characterize heart microstructure are needed for monitoring and staging of cardiac disease. In this regards, diffusion magnetic resonance imaging (MRI) provides a promising framework to probe and quantify tissue microstructure without the need for exogenous contrast agent. As diffusion in 3-dimensional space is characterized by the diffusion tensor, MR diffusion tensor imaging (DTI) is being used to noninvasively measure anisotropic diffusion, and thus the magnitude and spatial orientation of microstructural organization of tissues, including the heart. However, even though in vivo cardiac DTI has become more clinically available, to date the origin and behavior of different microstructural components on the measured DTI signal remain to be explicitly specified. The presented studies in this work demonstrate that DTI can be used as a noninvasive and contrast-free imaging modality to characterize myocyte size and density, extracellular collagen content, and the directional magnitude of blood flow. The identified applications are expected to provide metrics to enable physicians to detect, quantify, and stage different microstructural components during progression of cardiac disease.

INTERROGATING THE ORIGIN AND BEHAVIOR OF MAGNETIC RESONANCE DIFFUSION TENSOR SCALAR PARAMETERS IN THE MYOCARDIUM by Osama Mahmoud Abdullah A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Bioengineering The University of Utah May 2016 Copyright © Osama Mahmoud Abdullah 2016 All Rights Reserved The Uni v e r s i t y of Utah Graduat e School STATEMENT OF DISSERTATION APPROVAL The dissertation of Osama Mahmoud Abdullah has been approved by the following supervisory committee members: Edward W. Hsu Chair 3/10/2016 Date Approved Edward Victor Rebok Di Bella Member 3/9/2016 Date Approved Robert S. MacLeod Member 3/9/2016 Date Approved Frank Sachse Member 3/9/2016 Date Approved Kurt H. Albertine Member 3/9/2016 Date Approved and by Patrick A. Tresco Chair/Dean of the Department/College/School o f ________________ Bioengineering and by David B. Kieda, Dean of The Graduate School. ABSTRACT Myocardial microstructure plays an important role in sustaining the orchestrated beating motion of the heart. Several microstructural components, including myocytes and auxiliary cells, extracellular space, and blood vessels provide the infrastructure for normal heart function, including excitation propagation, myocyte contraction, delivery of oxygen and nutrients, and removing byproduct wastes. Cardiac diseases cause deleterious changes to some or all of these microstructural components in the detrimental process of cardiac remodeling. Since heart failure is among the leading causes of death in the world, new and novel tools to noninvasively characterize heart microstructure are needed for monitoring and staging of cardiac disease. In this regards, diffusion magnetic resonance imaging (MRI) provides a promising framework to probe and quantify tissue microstructure without the need for exogenous contrast agent. As diffusion in 3­dimensional space is characterized by the diffusion tensor, MR diffusion tensor imaging (DTI) is being used to noninvasively measure anisotropic diffusion, and thus the magnitude and spatial orientation of microstructural organization of tissues, including the heart. However, even though in vivo cardiac DTI has become more clinically available, to date the origin and behavior of different microstructural components on the measured DTI signal remain to be explicitly specified. The presented studies in this work demonstrate that DTI can be used as a noninvasive and contrast-free imaging modality to characterize myocyte size and density, extracellular collagen content, and the directional magnitude of blood flow. The identified applications are expected to provide metrics to enable physicians to detect, quantify, and stage different microstructural components during progression of cardiac disease. iv To my parents, daughter and wife. ABSTRACT........................................................................................................................... iii LIST OF TABLES..................................................................................................................ix LIST OF FIGURES.................................................................................................................x ACKNOWLEDGEMENTS..................................................................................................xii CHAPTERS 1. INTRODUCTION.............................................................................................................. 1 1.1 Overview.......................................................................................................................1 1.2 References.....................................................................................................................7 2. BACKGROUND.............................................................................................................. 16 2.1 Introduction..................................................................................................................16 2.2 Earlier Observations of Cardiac Fiber Structure.......................................................18 2.3 Basics of Diffusion MRI............................................................................................ 20 2.4 MRI of Anisotropic Diffusion................................................................................... 22 2.5 DTI Assessment of Myocardial Structure................................................................26 2.6 Validation of DTI for Myocardial Fiber Orientation Mapping.............................. 27 2.7 Sheet Structure Mapping via DTI..............................................................................28 2.8 DTI as a Function of the Cardiac Cycle.................................................................... 29 2.9 Cardiac DTI in the Mammalian Species................................................................... 30 2.10 Applications in Cardiac Pathology..........................................................................32 2.11 Applications in Small Animals................................................................................35 2.12 Technical Consideration for In Vivo DTI in Small Animals................................ 36 2.13 Conclusion................................................................................................................ 39 2.14 References..................................................................................................................39 3. CHARACTERIZATION OF DIFFUSE FIBROSIS IN THE FAILING HUMAN HEART VIA DIFFUSION TENSOR IMAGING AND QUANTITATIVE HISTOLOGICAL..................................................................................................................47 TABLE OF CONTENTS 3.1 Abstract.......................................................................................................................47 3.2 Introduction..................................................................................................................48 3.3 Methods........................................................................................................................52 3.3.1 Study Population and Specimen Collection.......................................................52 3.3.2 MRI Acquisition and Analysis............................................................................52 3.3.3 Histology: Whole-Field Digital Microscopy.................................................... 54 3.3.4 Statistical Analysis...............................................................................................55 3.3.5 Computational Compartmental Analysis...........................................................55 3.4 Results.........................................................................................................................58 3.4.1 DTI ........................................................................................................................ 58 3.4.2 Collagen Evaluation and DTI-Histology Correlation.......................................59 3.4.3 Computational Compartmental Analysis...........................................................60 3.5 Discussion....................................................................................................................63 3.6 References....................................................................................................................67 ORIENTATION DEPENDENCE OF MICROCIRCULATION-INDUCED DIFFUSION SIGNAL IN ANISOTROPIC TISSUES ............................................................................74 4.1 Abstract.......................................................................................................................74 4.2 Introduction..................................................................................................................75 4.3 Theory.........................................................................................................................77 4.3.1 Effects of Flow in Single and Multiple Tubes.................................................. 77 4.3.2 Special Multitube Systems..................................................................................78 4.3.3 Generalized Multitube Systems in Tissues........................................................79 4.4 Methods........................................................................................................................83 4.4.1 Flow in Organized Tissues..................................................................................83 4.4.2 Realistic Tissue Model....................................................................................... 84 4.4.3 MR Signal Simulation........................................................................................ 85 4.4.4 Data Analysis.......................................................................................................86 4.4.5 Isolated Heart Preparation................................................................................... 86 4.4.6 MRI Acquisition..................................................................................................88 4.4.7 Data Analysis.......................................................................................................88 4.5 Results.........................................................................................................................90 4.6 Discussion....................................................................................................................97 4.7 References..................................................................................................................101 DIFFUSION TENSOR IMAGING AND HISTOLOGY OF DEVELOPING HEARTS............................................................................................................................. 105 5.1 Abstract...................................................................................................................... 105 5.2 Introduction............................................................................................................... 106 vii CONCLUDING REMARKS............................................................................................. 135 6.1 Abstract......................................................................................................................135 6.2 Future Directions......................................................................................................137 6.3 References..................................................................................................................142 viii LIST OF TABLES 3.1 Baseline characteristics of the 14 patients with chronic HF due to idiopathic dilated cardiomyopathy, and 5 normal donors..................................................................................53 3.2 DTI and quantitative collagen measurements obtained from control and failing hearts.......................................................................................................................................58 3.3 Correlation between DTI scalar parameters and total collagen from histology................................................................................................................................. 61 4.1 Microcirculation parameters in simulated case of perfectly aligned tubes..................82 5.1 Left ventricular group-averaged DTI scalar and orientation parameters of developing hearts.................................................................................................................................... 117 5.2 Right ventricular group-averaged DTI scalar and orientation parameters of developing hearts................................................................................................................. 118 5.3 Group-averaged bi-compartment scalar DTI parameters from the left ventricles of developing hearts................................................................................................................. 122 5.4 Quantitative confocal microscopy measurements of developing hearts....................123 LIST OF FIGURES 2.1 Pulsed field gradient preparation as proposed by Stejskal and Tanner.......................21 2.2 Anisotropic diffusion contrast in a perfused guinea pig heart......................................23 2.3 DTI scalar parameters obtained from a healthy fixed human heart............................. 27 2.4 Validation of DTI fiber orientation mapping against histology.................................. 28 2.5 DTI orientation parameters at different cardiac states................................................. 31 2.6 Myocardial fiber orientation mapping in different species..........................................32 2.7 Fiber orientation mapping and tractography of fixed mouse and rat hearts................36 3.1 Representative DTI scalar maps from healthy and failing heart specimens................59 3.2 Histological evaluation of control and failing heart cores............................................60 3.3 Monte Carlo computer simulation of DTI scalar parameters as function of collagen content................................................................................................................................... 61 3.4 Quantitative correlation between experimental DTI scalar parameters and collagen content.................................................................................................................................... 62 4.1 Numerical simulations of flow-induced MR signal attenuation...................................81 4.2 Orientation dependence of IVIM parameters on the angle between flow and capillary direction................................................................................................................................90 4.3 Orientation dependence of tissue IVIM parameters in numerical analysis of same laminar flow in capillary networks of varying degrees of anisotropy...............................91 4.4 MRI of a representative isolated perfused heart............................................................92 4.5 Experimental diffusion-weighted signal intensities in a representative isolated heart.........................................................................................................................................93 4.6 Anisotropy of experimentally observed IVIM parameters in isolated perfused hearts...................................................................................................................................... 94 4.7 Arterial spin labeling MRI of a representative isolated heart.......................................95 4.8 Scatter plot between arterial spin labeling and input aortic pressure measurements in perfused hearts........................................................................................................................95 4.9 Scatter plot between diffusion MRI and arterial spin labeling in perfused hearts 96 5.1 Representative gross pictures and DTI maps of developing lamb hearts..................116 5.2 Groups averaged DTI scalar bar-graphs taken from regions of interest in the fixed developing hearts................................................................................................................. 116 5.3 Group-averaged histograms of myocardial fiber and sheet orientation populations...........................................................................................................................118 5.4 Normalized diffusion-induced signal attenuation in regions of interest longitudinal and transverse to myofibers.................................................................................................119 5.5 Representative maps obtained from bi-compartment DTI of developing hearts.................................................................................................................................... 122 5.6 Confocal images from representative developing hearts............................................123 5.7 Scatter plots of DTI scalar parameters and confocal microscopy.............................. 124 xi ACKNOWLEDGEMENTS As any person who is fortunate enough to have wonderful parents, my parents gave their finest to raise their family during peace and war. My father's mission for me was to complete the highest academic degree, PhD, and here I am writing these words in honoring his long-time dream. My mother's love, strength, and intellect could not come at better times during the ordeals we went through in the chaotic Middle East. No words of appreciation can fulfill a fraction of a fraction of what my parents deserve. Next I have to acknowledge my previous mentor, Dr. Shadi Othamn, who did not quit on me when the University of Illinois at Chicago (UIC) rejected my Masters application. He made the case that despite not having a prestigious GPA or GRE scores; I should be given a chance. Without that chance, I would not be able to fulfill my father's dream today. Finally, I would like to acknowledge my PhD advisor, Dr. Edward W Hsu, not only as a boss, but as a wise man, a friend, and a mentor. During the past 9 years working with Dr. Hsu, I learned to think differently, I learned to look deeper, and search smarter. Rather than thinking about what I can do now, I learned to go after what is needed to solve a problem, even if it means going after the unchartered or the undiscovered. I enjoyed every single hour with Dr. Hsu, especially the tough moments when I had to defend my ideas. Now that my PhD training is coming to an end, I feel more confident, wiser, and somewhat more patient to life's struggles. CHAPTER 1 INTRODUCTION 1.1 Overview The highly coordinated functional behaviors of the heart are mediated by the distinctive organizations of its microstructural constituents. Elongated myocytes are stacked together, forming the myocardial fiber structure [1], [2], which is supported by a predominantly collagen-rich extracellular matrix (ECM) that forms secondary sheet structures [3], [4]. Myocardial torsion [13]-[17] and shear [18] during ventricular contraction have been directly attributed to the fiber and sheet structures, respectively. These structures, in turn, are often subject to alterations at both microscopic (e.g., fibrosis and fiber disarray) and macroscopic (fiber structural remodeling) scales in response to diseases like hypertrophic cardiomyopathy or changes in the cardiac environment such as elevated ventricular afterloads from hypertension [19]-[23]. Although these seminal studies have been instrumental in the current understanding of the structures and structure-function relationships of the heart, the utility of myocardial structural information in detecting, staging and monitoring under therapy of heart diseases and potentially recovery heavily depends on the ability to evaluate the structures in a subject-specific, noninvasive, and longitudinal manner, which is precluded by conventional histological examinations. Therefore, noninvasive imaging tools to characterize myocardial structural parameters in disease and during normal development are critically needed. Diffusion tensor imaging (DTI) [5] has emerged as the method of choice for noninvasive quantifications of myocardial structures. Diffusion, which is characterized by the Brownian motion of water molecules, in the presence of applied magnetic field gradient results in attenuation of the MRI signal that closely follows the tissue's microenvironment. The principal direction of diffusion anisotropy (i.e., the DTI primary eigenvector) has been directly correlated to the myocardial fiber orientation [24]-[26], and used to characterize the fiber structure of hearts in humans [27], [28], small [24], [29], [30], and large animals [31]. Besides alterations in the myocardial fiber orientation that are thought to be part of the compensatory responses [32], changes in the scalar DTI quantities, such as fractional anisotropy (FA), and the mean diffusivity reflecting the underlying microstructural remodeling have been observed in ischemia, post infarction, hypertrophic cardiomyopathy and heart failure [20], [30], [33]-[39]. Although the feasibility has long been demonstrated [27], [40], [41], recent advances in both gradient hardware and imaging technologies have made in vivo cardiac DTI more widely used [39], [41]-[47]. Cardiac DTI has been utilized to evaluate the structural remodeling associated with cardiac pathologies of both ischemic and nonischemic origins. Studies of ischemic injury have reported a reduction in the degree of diffusion anisotropy coupled with an increase of water diffusivity in the infarct zone [33], [35], [36], [48]. Additionally, DTI has been utilized in assessing nonischemic cardiac disease, such as dyssynchronous HF [49], hypertrophic cardiomyopathy [50], and dilated cardiomyopathy [51]. Besides 2 changes in the fiber orientation, the diseased myocardium (e.g., hypertrophy or dilated cardiomyopathy) is generally found to have decreased diffusion anisotropy [50], [51] and increased water diffusivity [51]. Although the latter changes suggest that microscopic environment for water diffusion has become less restrictive, and can be associated with myocardial fibrosis, the exact relationships between myocardial fibrosis and the DTI parameters remain yet to be determined. Since heterogeneity of the microenvironment is the norm and not the exception in tissues, including the heart, the origin and behavior of the observed DTI changes during cardiac remodeling remain poorly understood. In this regards compartmental exchange models provide a promising framework to approximate the behavior of the diffusion MRI signal arising from a heterogeneous microscopic environment [52], [53], which is to be expected of, for example, the fibrotic myocardium. In the so-called fast-exchange situation, water spins spend much shorter time in the compartments than the temporal-length scale of their molecular dynamics. Then the MRI parameters (e.g., relaxation rate and diffusion constants) of the aggregate system behave like the fractional volume-weighted sum of the same parameters of the individual compartments. Conversely under the slow-exchange limit, the overall MRI signal is simply the proportional superposition of the signals from the individual compartments, as if the latter are completely independent. Bi-compartmental slow exchange models have been used to describe the MRI diffusion signal, including DTI, observed in the myocardium [11], [12]. Therefore, utilizing compartmental exchange models to model clinically relevant myocardial structures offers a promising framework to demonstrate the clinical utility of cardiac DTI. Diffuse myocardial fibrosis is one of the key structural biomarkers for staging and 3 treatment planning of the failing heart [54]-[56]. Myocardial fibrosis has been classified into reparative or reactive [57]. In myocardial infarction (MI), fibrotic scar forms as macroscopic patches of collagen following myocyte necrosis to protect the myocardium from rupturing, and is thus called reparative fibrosis. On the other hand, collagen that develops in the remote zone to infarcts or in nonischemic cardiac disease (such as dilated cardiomyopathy or cardiac hypertrophy) manifests as microscopic collagen depositions in the interstitial space and is termed reactive or diffuse fibrosis. Diffuse fibrosis is known to increase ventricular stiffness that can lead to pump dysfunction [57], [58], and has been suggested to play a bigger role in structural remodeling in ischemic disease than the fibrotic scarring itself [59]. Tissue biopsy and histology remain the primary methods for quantifying structural remodeling in HF for staging and treatment planning of the disease [54], [56]. However, the invasive and laborious nature of the histological procedures presents a practical limitation on the number of sites and time points that can be performed. Other MRI techniques have already been used to characterize myocardial fibrosis in diseased hearts. MRI-based spin-lattice (T1) mapping has been proposed to infer myocardial collagen content via quantifying the T1 difference between pre- and post-contrast administration in the myocardium [60]. However, since many heart failure patients also suffer from kidney disease, there has been some concern on the use of gadopentate dimeglumine agents in patients with renal failure [61]. Hence, it is desirable to explore alternative contrast-free techniques to complement or replace Tl-mapping for detecting and quantifying diffused fibrosis. Translating studies of cardiac DTI to the in vivo domain generally encounters additional challenges due to cardiac bulk motion and capillary blood flow effects. 4 5 Promising techniques have already been developed to tackle the bulk motion problem [41], [43], [46], but microcirculation effects in cardiac DTI have not been fully characterized. The diffusion signal can be described as the statistical average of phase dispersions associated with spin displacements. For isotropic systems with Gaussian-distributed Brownian motion, the signal is an exponentially decaying function of the spin motility and the encoding diffusion sensitivity (aka, 6-value). The same behavior also applies to ordered tissues, except the rate of signal decay depends also on the relative direction of the encoding gradient. In heterogeneous systems that contain spin populations with different motilities, depending on the rate of compartmental exchange, the signal is modeled as either a single exponential function with weighted decay constant or superposition of separate exponential functions [12], [53], [62]. Since blood flow in capillaries also results in translational dispersion of water molecules, theories such as the intravoxel incoherent motion (IVIM) have been proposed for characterizing microcirculation using similar diffusion-weighted imaging methodology [63], [64]. A key assumption in IVIM theory is that the capillary network consists of identical but randomly oriented straight segments, with blood changing segments rapidly while transiting through the network. In tissues, the MR signal is usually modeled as a bi­exponential function to separate the slower extravascular diffusion from the faster flow-mediated component, whose decay constant is referred to as the pseudo diffusion coefficient (D*). Because of the assumption of random capillary orientation, it is unclear whether the classical IVIM theory can be directly applied to the myocardium, where the capillary network is both organized and oriented mostly parallel to the myofibers [12], [65]-[67]. Thus, unlike DWI and DTI in ordered tissues, the relationship between IVIM and microcirculation-mediated diffusion signal and organized capillary networks is not completely understood. Another clinically relevant component to better characterize myocardial remodeling is myocyte size and density. During fetal development, myocyte division (hyperplasia) is the primary mechanism for cardiac growth, whereas myocyte growth (hypertrophy) becomes the main mechanism for cardiac adaptation, for example, in response to increased systemic or pulmonary resistance [58], [68]-[71]. The preterm ovine model [72] offers unique opportunity to study cardiac adaptation in normal development (e.g., myocyte growth) and in disease (e.g., pulmonary hypertension) [73]. Although costly and laborious, the fetal ovine model is frequently used in investigations of cardiovascular and lung diseases because it recapitulates human conditions with fetuses of similar size to human as well as tolerating chronic instrumentation and experimental interventions [70], [74]. Therefore, the fetal lamb hearts at different gestational ages provide an ideal model to establish the utility of DTI to characterize myocyte size and density changes, provided that histological validation is provided. Taken together, this dissertation aims to establish and validate the role of cardiac DTI in characterizing clinically relevant myocardial structures, including diffuse fibrosis, microcirculation flow speed and volume, and myocyte size and density. Chapter 2 summarizes the latest advances in mapping myocardial microstructure with DTI technology. It starts with a brief history of alternative methods to characterize myocardial microstructure, followed by an overview of the main concepts of diffusion MRI, and provides a literature review of cardiac DTI and its applications in animals and humans. 6 7 Chapter 3 evaluates cardiac modeling in excised heart specimens from end-stage heart failure (HF) patients. In this chapter the effects of increased myocardial fibrosis on cardiac DTI will be established, which is an important milestone because the degree of diffuse fibrosis has been used as a marker for staging and planning of HF treatment [54], [56]. Further, the effect of diffuse fibrosis will be directly incorporated into the DTI signal equation using compartmental exchange models. In Chapter 4, a novel theoretical framework will be introduced to describe the DTI signal equation in the presence of coherent spin motion due to organized capillary flow. The theory will be subsequently validated both numerically and experimentally, with myocardial blood flow verified via independent arterial spin labeling MRI. This chapter will provide a critically lacking theory for the effects of organized microcirculation effects, which is an important step toward the eventual use of cardiac DTI clinically. In Chapter 5, the effect of myocyte increase in size and density on the DTI signal will be characterized in an animal model of fetal myocardial development. The chapter will complement previous chapters by describing the additional effect of increased myocyte size and density in myocardial tissue on the DTI signal. 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Albertine, "Progress in understanding the pathogenesis of BPD using the baboon and sheep models," Semin. Perinatol., vol. 37, no. 2, pp. 60-68, 2013. CHAPTER 2 BACKGROUND1 2.1 Introduction The intricate organization of the cardiac microstructure is a key determinant in the remarkably orchestrated atrial and ventricular activities. For example, each cardiac myocyte conducts an electrical impulse, contracts at the appropriate moment, at the right speed, and to the necessary extent [1]. The arrangement of the ventricular myocytes is involved in coordinating systolic contraction, in such ways that the efficiencies of blood ejection and fiber strain distribution are maximized [2]. Because electrical impulses propagate faster parallel to the main axis of cardiomyocytes than perpendicular to them [3], mapping myofiber orientation is an essential element for understanding the structural-functional relationship not only in the normal heart, but also in disease conditions. Over time, several conceptual and theoretical models have been proposed for different aspects of the heart incorporating progressively sophisticated interpretations of fiber structures made available by advancing technologies [4] (and references therein). Examples in cardiac biomechanics included constitutive modeling of tissue as an elastic 1 © 2015 Bentham Science Publishers, reprinted, with permission, from: Abdullah OM, Gomez AD, Welsh CL, Hsu EW. Mapping Myocardial Fiber Structure using Diffusion Tensor Imaging. material [5] and holistic understanding of the heart as a pump [1,6,7]. Experimental observations, like mechanical testing of myocardial tissue have shown that mechanical properties are dependent of tissue microstructure, in particular, fiber orientation, lamination (i.e., sheet-like formation of fibers) and the associated arrangement of the extracellular matrix. To reach physiologically relevant results from the application of these models, both, information on tissue geometry and anisotropic tissue properties are necessary [8]. Similar requirements are related to modeling of cardiac tissue electrophysiology [9], including simulation of electrical propagation. It is well established that electrical conductivities of cardiac tissues are anisotropic [3,10] and that those are determined by tissue microstructure, in particular, the local orientation [11] and apparent laminar structure of cardiac fibers [12]. In general, anisotropic description of tissue properties is a crucial component for electro-mechanical modeling of the heart [13]. Electro-mechanical applications require the integrative modeling of electrical activation, force development, and mechanical deformation based on anisotropic tissue properties. Likewise, anisotropic cardiac tissue properties have been used to produce comprehensive models seeking to provide explanations for the basic mechanisms for ventricular contraction, expansion, and torsion [14], or to explain the nature of myocardial fiber arrangement [15,16]. By quantifying the effects on the translational motility of water molecules exerted by the microscopic environment, magnetic resonance diffusion tensor imaging (MR-DTI, or DTI for short) [17] has emerged as a unique, noninvasive and nondestructive alternative to histology for characterizing myocardial tissue microstructure. DTI yields information on the diffusion anisotropy, in terms of both its direction and magnitude, 17 18 which can be used to elucidate the nature of the organization, geometry and content of the tissue. In this chapter, we will provide the basics of DTI theory, and summarize the latest progress that has been reported in relating the radiological findings provided by DTI to the known structural changes in cardiac disease, such ischemic or non-ischemic heart failure. 2.2 Earlier Observations of Cardiac Fiber Structure Structural observations have been associated with fundamental changes in our understanding of the heart as an organ from the early days of the study of anatomy and physiology. An early example came about in 1664, when Niels Stensen published comparative observations between dissections of cardiac and skeletal muscle tissues, both which resembled each other by their fibrous appearance, thus allowing the identification of the heart as a muscle [18]. As more detailed observations became documented, the fundamental tool used to identify transmural variations of myocardial tissue orientation i.e., gross dissection of excised hearts (Lower et al. [19]), became insufficient for microstructural analysis and was aided by microscopes [20,21]. Ever since, analysis of cardiac microstructure in terms of fiber organization is often linked to the available technology. Histological sections provided quantifiable investigations that allowed modeling of the heart, so that fiber orientation could be modeled and predicted by a mathematical formula, and to explain quantifiable differences between man and other species [11,22­24]. Specifically, Streeter and others observed that the sub-epicardial layer contains myofibers pointing "downward" toward the apex. The sub-endocardial layer contains myofibers pointing "upwards" toward the base of the heart. And the mid-wall fibers run circumferentially parallel to the heart equator. This unique fiber orientation patterns provided the basis to coin the term "double helical fiber structure" of the heart [22]. The sub-endocardial layer was assigned a positive helix angle, which is referred to as the right handed fibers (RHF). The sub-epicardial layer was assigned a negative helix angle, and referred to as the left handed fibers (LHF). And the mid-wall layer was referred to as the circumferential fibers (CF), because the fibers in this layer mostly run parallel to the cardiac short axis. Cardiac modeling and the development of structure-function theories continues to be an active area of research today [4], and the adoption of a comprehensive heart model is still controversial [1,6,7,16]. The introduction of digital image processing permitted more comprehensive analysis of histology, which sometimes included the use of volumetric statistics [25-28]. Likewise, more sophisticated optical methods like electron microscopy were later used to observe intermediate structures like myocardial sheets [12], and more recently, subcellular organization with the use of confocal microscopy [29]. The advent of radiological imaging has allowed noninvasive and nondestructive quantification of the myocardial fiber structure, which is highly desirable for preserving valuable samples or for evaluating the tissue in vivo. Specific techniques include X-ray diffraction [30,31], contrast-enhanced computer tomography [32] and MRI. The latter, stands alone in terms of soft tissue sensitivity and safety considerations, and can provide fiber orientation information via either susceptibility mapping [33] or diffusion tensor imaging (DTI) [34-38]. Recent technological advances like in vivo DTI [39-42] hold the potential to not only improve the general understanding of cardiac structure and function, 19 20 but also to provide subject-specific modeling of normal and diseased hearts. 2.3 Basics of Diffusion MRI Diffusion is the random displacement of water molecules due to their thermal energy, also referred to as Brownian motion. It is important to distinguish diffusion from other transport mechanisms such as coherent blood flow in vessels. In a statistical sense, the average displacement along a given axis in space, (r), of diffusing water molecules is related to the diffusion coefficient, D (in mm2/s), via the Einstein's equation: <r) = y[2DA (2.1) where A is the diffusion time. The diffusion coefficient D is typically slower in biological tissues compared to free water due to the obstructions imposed by tissue microstructure (e.g., cell membranes, fibers, etc.). The effect of diffusion on the magnetic resonance signal has been observed and quantified well before the invention of the MRI scanner [43,44]. Stejskal and Tanner proposed the pulsed-field-gradient (PFG) preparation to measure diffusion [45]. In the PFG preparation shown in Fig. 2.1, suppose a unit MRI signal (called "spin") at an initial position rx experiences a short diffusion-weighting gradient pulse, and the same spin randomly moves to location r2 at some duration A (referred to as diffusion time) later when it experiences a second gradient pulse of equal amplitude but opposite polarity to the first. The net phase 0 net imparted on the spin will be proportional to its relative displacement (r2 - rx) given by: 0net = - Y G ■ (r2 - 7l) 5 (2.2) where y is the gyromagnetic ratio for the spin (hydrogen for most DTI applications), G and S are the amplitude and widths of the diffusion encoding gradient pulses, 21 A G A <--- > V < Figure 2.1. Pulsed field gradient preparation as proposed by Stejskal and Tanner [45]. respectively. Note that the direction of G dictates the axis in which diffusion motion is measured - for example, Gx will encode water displacements in the x direction only. The Brownian translational motion of spins due to diffusion is a random process that is subject to the conditional probability density function P specified by a normal distribution with a standard deviation indicated by Eq. (2.1). The detected MRI signal after PFG preparation can be obtained by calculating the expected value of the phase dispersion for an ensemble of spins over the probability density function according to: where IQ is the diffusion-independent image intensity. The solution of the above equation for isotropic case can be expressed as [45]: (2.3) (2.4) Equation (2.4) is often rewritten as with b = y 2G2S2 ^ . Equation (2.5) conveniently separates the exponent into an intrinsic tissue property term, D, and a single parameter, the so-called diffusion-weighting b factor (typically expressed in units of s/mm2), that combines all the MRI prescription variables. Equation (2.5) states that the effect of diffusion manifests as attenuation of the image intensity, which behaves inverse-exponentially with respect to both the diffusivity and the applied diffusion encoding gradient parameters. 2.4 MRI of Anisotropic Diffusion Diffusion in an anisotropic medium will manifest in directionally dependent Brownian motion. Axons, ligaments, and muscle fibers are all example of anisotropic tissues, which impose a preferential direction for diffusing water molecules, where, one would intuitively expect that water diffusion will be more free and faster along the direction of the fibers but is more hindered and slower across the fibers. The orientation-dependent behavior gives rise to the anisotropic diffusion property probed in DTI. In a PFG preparation, when the diffusion encoding gradient is applied parallel to the fibers, the image intensity I in Eq. (2.5) will contain higher diffusion contribution than in the case when the encoding gradient is applied perpendicular to the fibers. Higher diffusion contribution in certain direction translates to higher attenuation in signal intensity. Figure 2.2 illustrates the anisotropic diffusion behavior in a perfused guinea pig heart. Figure 2.2a is an anatomical image without diffusion weighting, while Fig. 2.2b and 2.2c are diffusion-weighted images showing different contrasts due to the different diffusion 22 / = /0 exp(- bD) (5) 23 . > s J 4 • m * m / a % b C Figure 2.2. Anisotropic diffusion contrast in a perfused guinea pig heart. (a) anatomical gradient-echo image without diffusion weighting. Diffusion-weighted image (b = 500 s/mm2) with diffusion encoding gradient applied in left-right direction (b), and in-out of page (c). encoding direction in each case. Anisotropic diffusion in 3D space cannot be fully characterized by a single diffusion coefficient. Instead, a tensor, appropriately called diffusion tensor, is required [17]. The MRI signal of spins diffusing in an anisotropic medium can be explained by considering the special case where the principal axes of diffusion of certain anisotropic tissue have diffusivities D! , D2, and D3 along the three orthogonal principal directions (in descending order), and that diffusion is encoded along the same direction as the principal diffusivities via the diffusion encoding gradients G(t). If the encoding gradients have identical timings and only differ in their directions, then G(t) can be written as: ^ i( O' G( 0 = G2( 0 = u -|| G ( ^ | = u2 G3(t) M3. l|G( Oil (2.7) where u is a unit vector defining the direction of the encoding gradients (which coincides with principal diffusion axis). Following the notation of Eq. (2.4), the signal intensity satisfies 24 where the effective diffusivity can be defined as: De = u T • DA • u. Now let us generalize the special case introduced in Eq. (2.6) and (2.7) when the diffusion encoding gradients direction g does not coincide with the principal diffusion axis, the former can be translated to the principal diffusion axis via a rotation matrix R, such that: u = Rg. Then, Eq. (2.7) becomes: where D = RT • DA • R corresponds to the diffusion tensor. The diffusion tensor is a magnitude and another 3 describing the principal direction of diffusion. Although Eq. (2.8) provides a convenient and intuitive link between the MRI signal and the principal diffusion directions, it does not take into account the effect of the co-called gradient cross terms [17]. A more general expression for the diffusion tensor formalism can be written as: where x, y, z represent the laboratory frame of reference. In Eq. (2.9), the diffusion tensor can be written in a matrix form as: / = /0 exp(- b g TRT • DA • R g ) = /0 exp(- b g T • D • g ) (2.8) symmetric, 2nd rank tensor, containing 6 independent elements, 3 describing the (2.10) And bij is the b-matrix [17] which can be calculated according to: 25 b = y2 TE f , (2.11) and G is an arbitrary time-varying diffusion-weighting vector of any orientation: G(t) - [Gx(t), Gy (t), Gz(t)] (2.12) Regardless on whether Eq. (2.8) or (2.9) is used, the typical DTI experiment consists of acquiring series of diffusion-weighted MRI scans with diffusion encoding gradients encoded along at least six non-collinear directions. Estimation of the diffusion tensor is usually performed on pixel-by-pixel basis, via appropriate curve fitting of the observed signals to the signal attenuation equation. The estimated diffusion tensor in Eq. (2.10) bears little use for inferring the tissue microstructure, since the relevant information is embedded in the tensor elements. Hence, the concept of "diffusion ellipsoid" has been proposed [17] to simplify the interpretation of the diffusion tensor. The diffusion ellipsoid is a 3-dimensional representation of the displacement profile covered in space by diffusing molecules during the diffusion time A [46]. The principal axes of the diffusion ellipsoid can be calculated by performing eigenvalue decomposition of Eq. (2.10) where the diffusion tensor gets converted into a product between a diagonal matrix of its eigenvalues (D! , D2, and D3) and transformation (or rotation) matrix consisting of its eigenvectors (ex, e2, and e3). The eigenvalues and the eigenvectors of the diffusion tensor correspond to the diffusivities as observed along the principal axes of diffusion ellipsoid and the orientations of its axes, respectively. The central premise of DTI is that the direction in which water diffusion is the fastest, which is the eigenvector of the largest diffusion tensor eigenvalue, coincides with the local tissue fiber orientation. To make the derived eigenvalues from the diffusion tensor more intuitive, the diffusion 26 tensor eigenvalues are commonly used to compute the mean diffusivity (MD) and fractional anisotropy (FA) index, given by: where D1, D2, D3 represent the eigenvalues of the DT matrix (in descending order). Mathematically, the MD is proportional to the average diffusion in the 3 principal axes. FA measures the fraction of the diffusion tensor that can be ascribed to anisotropic diffusion [46]. FA varies between 0 (isotropic diffusion) and 1 (infinite anisotropy). Lower FA values can be found in isotropic media (e.g., gray matter in the brain), whereas progressively higher FA reflects higher diffusion anisotropy (e.g., brain white matter). In practice, MD and FA have the feature of being rotationally invariant, i.e., do not depend on the orientations of the diffusion principal axes. This renders FA and MD as a convenient quantitative metrics that capture the overall magnitude of diffusion and the degree of diffusion anisotropy, respectively. Figure 2.3 shows MD and FA pixel maps of a healthy human heart specimen. The anisotropy and orientation of cardiomyocytes make the heart an excellent candidate for diffusion MRI techniques. Indeed, the first report documenting cardiac fiber mapping using DTI was published soon after DTI was introduced by Basser et al. [17]. In 1994, Garrido et al. [34] reported the detection of the known myocardial helical pattern in perfused rat heart by DTI, demonstrating the potential for utilizing DTI as a nondestructive technique to characterize the 3-dimensional myocardial fiber architecture. MD = (£>! + D2 + D3 )/3 (2.13) FA = 3 {D1 - MD)2 + (Dz - MD)2 + (D3 - MD)2 (2.14) £>! + Df + Df 2.5 DTI Assessment of Myocardial Structure 27 x 1 0 J mm2/s Figure 2.3. Pixel maps of Fractional Anisotropy (left) and Mean Diffusivity (right) obtained from a healthy human heart specimen. 2.6 Validation of DTI for Myocardial Fiber Orientation Mapping As stated above, the main premise in DTI mapping of myocardial fiber structure is that the direction of fastest observed water diffusion (i.e., the primary eigenvector of the diffusion tensor) coincides with local fiber orientation. Histological correlation studies performed in freshly excised [36], perfused [37], and formalin fixed [38] myocardium provided strong support for the premise. Hsu et al. [36] correlated local fiber angle measurements obtained from DTI and histology, on a pixel-by-pixel basis, in a freshly excised specimen from the right ventricle of dog heart as shown in Fig. 2.4. Expanding on Hsu's study, Scollan et al. [37] used a perfused rabbit heart model to quantify and correlate DTI fiber orientation mapping with histology. Not only Scollan's study reaffirmed the findings by Hsu - that primary eigenvector obtained from DTI correlates closely with histological measures in the left ventricle, but they also demonstrated this correlation when the heart was perfused at physiologic conditions. Holmes et al. subsequently correlated the principal eigenvector obtained from DTI to histology in fixed rabbit hearts and reported less than 4o difference between fiber angles 28 Figure 2.4. Validating DTI fiber mapping against histology. Fiber orientation obtained from DTI and histology show excellent agreement across the myocardial wall. Figure modified from Hsu et al. [36]; with permission. measured from DTI and histology. The latter two studies suggest that neither physiologic perfusion nor tissue fixation adversely impacted the accuracy of fiber orientation mapping using DTI. 2.7 Sheet Structure Mapping via DTI In 1995, LeGrice et al. [12] proposed that the ventricular myocardium is further organized into laminar substructures, referred to as sheets, or "sheetlets" as they do not form continuous structure traversing the whole heart [47]. The sheetlet planes are approximately 4-5 cardiomyocyte thick, with the myocytes in each sheet tightly coupled with a collagen network, while the adjacent sheets loosely connected to allow for slippage [12, 48]. However, because the initial study was performed on fixed myocardium which was susceptible to artifacts (e.g., shrinkage) related to the preparation, the existence of laminar structure (or sheets) has been debated by some researchers [1]. Nevertheless, several cardiac DTI reports have linked the tertiary (smallest) eigenvector of the DTI matrix to the normal of the sheet plane [37,47-49]. Scollan et al. [37] suggested that the secondary and tertiary eigenvector of the diffusion tensor form a systematic pattern similar to the sheet structure proposed by Le Grice [12]. Scollan suggested that the sheet planes lay horizontally in the LV mid-wall and become more vertically oriented at the epicardium and endocardium. Tseng et al. [48] utilized optical images of inked prints obtained directly from the cut face of bovine heart specimens. The authors claimed that their inking method allows for DTI fiber mapping and the cleavage orientations in fresh specimens to be acquired under identical conditions, which minimizes the possibility of alterations of the tissue integrity between modalities (optical vs. DTI). Together, although the supporting evidence is not as direct and unequivocal as the case of fiber orientation, results of cardiac DTI studies to date are consistent with the notion that the secondary and tertiary diffusion tensor eigenvectors respectively correspond to the orientation and the normal to the myocardial sheets. 2.8 DTI as a Function of the Cardiac Cycle It is accepted that blood is ejected by the heart mainly via the contraction of its cardiomyocytes. However, the increase in cardiomyocyte diameter during contraction accounts for only 20% of the observed systolic wall thickening [12], which suggests that the dynamically changing hierarchical organization of the myocardium also plays an important role. DTI can provide unique insights on the states of the fiber and sheet rearrangement during contraction. Although different groups attempted to conduct DTI at 29 different points in the cardiac cycle [40, 50, 51], probably the most comprehensive investigation of myofiber rearrangement dynamics using DTI so far was the report by Hales et al. [47]. The authors imaged the same perfused heart (of a normal rat) at relaxed and contracted states. As shown in Fig. 2.5, the authors reported higher right-handed fibers percentage (in the endocardial wall) and lower left-handed fibers percentage (in the epicardial wall) in contracture state. They also suggested that the sheet angles follow a similar pattern of that demonstrated by Scollan [37] - in which the sheet planes at relaxed state lays parallel to the equatorial axis in the mid-wall, and become vertically orientated at the epi- and endocardial walls. Further, they also showed that the sheet angles rearrangement follows an accordion-like behavior in contracture state, in which the sheet planes become more vertically orientated (especially in the mid-wall) at contracture as shown in Fig. 2.5b. This study elegantly proposed a mechanism in which an accordion­like rearrangement of sheets combined with inter-sheet slippage can contribute to ventricular deformation, including centripetal wall-thickening (i.e., toward the center of the LV cavity) and baso-apical shortening. 2.9 Cardiac DTI in the Mammalian Species To date, DTI has been used to characterize the fiber structure of normal hearts in several small and large animal species, including mouse, rat, rabbit, sheep, dog, in addition to human [34,51-54]. Despite differences in mammalian hearts, the general myocardial fiber architecture detected by DTI displays high degree of general similarity among different species, albeit there also exist important differences. 30 31 Figure 2.5. Helix angle maps of relaxed (A) and contracted states (C). Helix angles are represented by the colorbar. Color-coded rectangles on the right represent profiles of sheet arrangement in the transmural direction (taken from the white-bars) in relaxed (B) and contracted states (D). The sheet angles in B and D were calculated as the planes perpendicular to the smallest eigenvector obtained from the diffusion tensor. Obtained from Hales et al. [47]; with permission. Healy et al. [55] compared the helix angle between mouse, rabbit and sheep. As shown in Fig. 2.6, although all three species showed the well-known counterclockwise rotation of the fiber helix angle in the LV, the range of endocardial to epicardial helix angle was significantly different among the species. The structural differences exist among hearts at least from animals of different sizes, suggesting caution is needed when extrapolating myocardial structures from one species to another in, for example, myocardial functional modeling studies. 32 90 60 30 0 -30 -60 -90 Figure 2.6. Myocardial fiber orientation in mouse (A,D), rabbit (B, E), and sheep (C,F). Top row shows cylindrical rods rendering of the fiber structure, while the bottom row show the color-coded helix angle map on pixel-by-pixel basis in short axis configuration. The colorbar on the left reports angles in degrees. Despite similarities of helix angle across species, significant differences exist in the range of fiber rotation from endocardium to epicardium. Figure obtained from Healy et al. [55]; with permission. 2.10 Applications in Cardiac Pathology DTI has also been utilized to study cardiac pathologies in humans and animals for ischemic and non-ischemic cardiac disease, both in vivo and ex vivo [56-63]. The main parameters that have been reported are the scalar DTI parameters (especially FA and MD), and myocardial fiber orientation (helix and sheet angles). For ischemic disease in animal models and humans, nearly all studies reported a decrease in FA and increase in MD in the infarcted myocardium compared to remote, unaffected normal regions of the same heart or to healthy control group [57, 59-62]. One infarcted mouse heart study reported the opposite trend in the infarct zone (i.e., lower MD and higher FA in infarct zone depending on heart extraction time post myocardial infarction) [64]. The known helical pattern in the infarct and remote zones retains its general behavior (i.e., endocardium has positive right-handed helix fiber angles, denoted as RHF, and the epicardium has negative left-handed helix fiber angles, denoted as LHF). Most studies reported higher fiber angular deviation in the infarct compared to remote zone or in normal subjects. The fiber angular deviation was defined as the standard deviation of the helix angles in selected ROIs and used as a metric for the local fiber disarray. For example, a rat infarct model by Chen et al. [56] reported higher angular deviation in the infarcted myocardium and correlated the measurements from DTI with histology. Chen's finding was supported by Wu et al. [59] who reported in an infarcted porcine model higher angular deviation and lower helix angle range (defined as sub­endocardial minus sub-epicardial helix angle) in the infarct zone. Another study by Wu et al. [61] of infarcted porcine model reported lower RHF and higher LHF in the infarct and remote zones, which the authors referred to as "left-handed shift of fibers around the infarct zone". In vivo DTI in human patients with acute myocardial infarction [58] and a follow up study on chronic infarct [60] was performed on the same subjects. In these human studies, the RHF percentage was decreased while the LHF increased in the infarct zone. Interestingly, these studies also reported that the opposite trend occur in the remote zone (i.e., increase in RHF and reduction in LHF in remote zone) [58], which is contrary to the porcine heart infarct study (in the remote zone) [61]. The authors hypothesized that compensatory responses affected the RHF and LHF in the remote and infarct zones such that the overall (LHF+RHF)/CF (where CF refers to mid-wall circumferential fibers percentage) would remain constant [58]. Collectively, a major finding [58,60,61] is that 33 the sub-endocardial RHF is implicated in the remodeling and healing process in the infarcted heart, and this notion was supported by non-DTI studies (e.g., [65]). Recently, Mekkaoui et al. [62] expanded on the conventional region-of-interest-based analyses by utilizing statistical approach to characterize the 3D helical fiber architecture in the full left ventricle. Mekkaoui utilized tractography-based helix angle classification and introduced the tractography coherence index, and applied this approach to study normal human, normal rat, and normal and infarcted sheep hearts [62]. Since this approach eliminated the subjectivity of selecting ROIs in heart, and treated the heart fiber structure as a continuum, to date this study seems to be the most robust study for fiber angle analysis in the heart. In the infarcted sheep myocardium, Mekkaoui [62] confirmed some of the finding reported in the previous ischemic human studies [59, 61], in which the LHF decreased in the remote zone, and he also showed that remodeling in the remote zone implicate all layers (endocardium, epicardium, and mid-wall). DTI has also been applied to study cardiac remodeling in the non-ischemic heart disease, such as the dyssynchronous heart failure [57], and in hypertrophic cardiomyopathy [63]. Helm et al. [57] used a canine heart model of dyssynchronous heart failure and performed 3D DTI acquisition on the excised specimens. In diseased hearts, they reported regional reduction in wall thickness (septal, anterior, and posterior), but not in the lateral wall. They showed that the regional differences in the wall thickness were associated with rearrangement of sheet angles, whereas the septal wall became more vertically oriented compared to the lateral wall. The authors hypothesized that vertically oriented sheet angles could explain the reduction of wall thickness in the septal wall. Because electrical propagation in myocytes favors the direction along the main fibers axis 34 35 [3], the authors speculated that vertically-oriented sheet angles may be responsible for hindering the transmural electrical propagation, which may explain the observed dyssynchrony in certain segments of the diseased hearts. In a study of hypertrophic cardiomyopathy by Tseng et al. [63], the authors performed in vivo DTI and strain imaging on human patients. They reported reduced fractional anisotropy and increased fiber disarray, which interestingly correlated with reduction in functional parameters (e.g., fiber and cross fiber strains). The authors then concluded that myofiber disarray in hypertrophic cardiomyopathy is correlated with abnormalities of both passive and active myocardial function [63]. 2.11 Applications in Small Animals Mapping the 3D myocardial fiber architecture can be performed routinely and in a relatively short time, at least compared to reconstructing a 3D volume from 2D histological dissection. However, compared to many other MRI techniques, DTI is inherently challenging due to the prolonged scan time and its low SNR (from diffusion encoding via signal attenuation). In the small animals (e.g. mouse), the challenges are exacerbated by the small imaging voxel size necessary to provide the anatomical details and, in the case of in vivo imaging, constraints imposed by the specific physiology (e.g., high heart rate) of the animals. Nonetheless, state-of-the-art dedicated small animal MRI scanners equipped with high performance gradient sets are capable of producing high-quality DTI fiber maps in several hours. Figure 2.7 shows 3D heart reconstruction from a mouse (right) and a rat (left), with the two images demonstrating one of the many possibilities to visualize the fiber structure in the heart. The simplest way to visualize the fiber orientation is by using the definition of the helix angle proposed by Streeter [11]. 36 Figure 2.7. Left: color-coded helix angle map in mouse heart (resolution 100 y.m isotropic, 12 diffusion gradient directions, scan time 9 hours). The colorbar on the left represent the helix angle value for each imaging voxel (in degrees). Right: Myocardial fiber mapping using DTI-tractography in a rat heart (resolution 150 pern isotropic, 12 diffusion gradient directions, scan time 16 hours.) Image on right is courtesy of Dr. Grant Gullberg from Berkeley National Lab. The helix angle can be obtained from each imaging voxel by projecting the principal eigenvector of the diffusion tensor onto the tangential plane and then taking the angle between this projection and the horizontal (or equatorial) axis. Each angle can be assigned a different false color depending on its value as shown in the colorbar in Fig. 2.7. An alternative way to visualize fiber structure is by generating "tractography" [66] streamlines connecting principal eigenvectors of neighboring voxels as shown in the right panel of Fig. 2.7. 2.12 Technical Consideration for In Vivo DTI in Small Animals Despite challenges arising from the beating motion of the heart and the sensitivity of diffusion-encoding to strain-memory effect [36, 68], in vivo cardiac DTI has been shown feasible, at least in humans [36, 40-42, 61, 68]. Moreover, although additional challenges exist, the feasibility of in vivo cardiac DTI in the mouse has been demonstrated by recent reports, where diffusivity and fiber orientation information is used to characterize cardiac remodeling associated with ischemia and hypertrophy [69, 79]. Besides constraints imposed by scan time, resolution and SNR common to all DTI experiments, in vivo cardiac DTI in general face few additional challenges stem from the unique physiology of the heart. First, compared to other organs, the heart undergoes large and relatively periodic beating motion, which can cause pronounced ghosting and streaking artifacts along the phase encoding axis of an MR image. Although these motion artifacts can be greatly reduced by employing gated acquisitions (e.g., dual cardiac and ventilation-gated MRI), the heightened sensitivity of diffusion MRI to motion leaves very little room for uncorrected instrument imperfections, such as errors in gradients calibration or uncompensated eddy current effects. Second, to reduce the effects of bulk motion while providing sufficient degree of diffusion encoding, in vivo cardiac DTI is often performed using narrow diffusion encoding pulses across not one but two cardiac cycles using stimulated echo-based pulse sequences [35]. The contraction and expansion of the myocardium between the diffusion encoding gradient pulses can lead to erroneous estimates of diffusion induced by strain-memory effects [36, 68, 71], since tissue strain alters the relative displacements and phases of spins from which diffusion is encoded. Depending on the nature of the strain, if uncorrected, the effect can be either over- or under-estimation of the diffusion measurements. Because cardiac strain can be separately quantified via, for example, phase-contrast methods, one solution is to subtract its effects and produce corrected fiber orientation measurements from in vivo cardiac DTI data [67]. A second solution, based on the fact that the strain effects are dependent on the average strain across the cardiac 37 cycle, is to obtain strain-free in vivo cardiac DTI measurements by selecting the right timing delay in the cardiac-gated acquisition where the average strain is already zero [70]. Instead of working with myocardial strain, an alternative approach is to employ bipolar diffusion encoding gradient pulses, where spin phases are not left un-refocused across the cardiac cycle, which has been shown effective in minimizing the contribution of strain in in vivo cardiac DTI measurements [40, 41]. The main drawback of the approach is the reduced diffusion-weighting b-value that can be achieved using shortened diffusion times. Obviously the practical utility of bipolar gradient pulses depends on whether the required hardware, specifically whether high-performance gradients (in terms of both amplitude and slew rate), exists. Recently, advanced gradient hardware, capable of up to 300 mT/m for human brain imaging and 1500 mT/m in mouse systems as of the current writing, has been introduced. The latter has been credited for the feasibility of in vivo cardiac DTI in mice, where the fast heart rate of the animal (300-600 bpm) makes it all but impossible to conduct DTI without extremely large and narrow diffusion encoding pulses. Because the feasibility hinges on the availability of high-performance gradient systems relative to the animal heart rate, and that the performance of a gradient system in turn depends greatly on its size, the feasibility of in vivo cardiac DTI in other-size small animals (e.g., rats) remains to be demonstrated. Besides strain, another physiologic source that can complicate in vivo cardiac DTI is perfusion. Perfusion (in this case blood flow in the capillary bed) has long been known for causing additional spin phase dispersion and leading to overestimated diffusion coefficients via the so called intravoxel incoherent motion effect [71] in highly 38 39 vascularized organs such as the liver [72]. Because the capillary flow is faster than the diffusion of water, the flow-mediated perfusion effects can be eliminated from diffusion measurements by employing sufficiently high (b > 200 s/mm2) diffusion weighting. The perfusion dependence of diffusion MRI has been theorized [73,74] and recently empirically demonstrated in vivo [75] and for the perfused heart [76]. Combined, it is clear that the specific physiologies of the beating heart add technical challenges that need to be addressed for performing in vivo cardiac DTI. Technological advances have made most the known issues tractable, but there remains room for improvement. Until then, caution is warranted in interpreting in vivo cardiac DTI results. 2.13 Conclusion Cardiac DTI has gained momentum in recent years. Advances in gradient hardware and motion compensation strategies allowed the acquisition of high quality DTI data in fixed and live, beating hearts. 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Relationship of MRI delayed contrast enhancement to irreversible injury, infarct age, and contractile function. Circulation. 1999;1992-2002. [78] Messroghli D, Nordmeyer S, Dietrich T, Dirsch O, Kaschina E, Savvatis K, et al. Assessment of diffuse myocardial fibrosis in rats using small animal look-locker inversion recovery (salli) t1 mapping. Circulation Cardiovascular Imaging. 2011 Sep 14;4(6):636-40. CHAPTER 3 CHARACTERIZATION OF DIFFUSE FIBROSIS IN THE FAILING HUMAN HEART VIA DIFFUSION TENSOR IMAGING AND QUANTITATIVE HISTOLOGICAL VALIDATION 1 3.1 Abstract Non-invasive imaging techniques are highly desirable as an alternative to conventional biopsy for characterizing remodeling of tissues associated with disease progression, including end-stage heart failure. Cardiac diffusion tensor imaging (DTI) has become an established method for characterizing myocardial microstructure. However, the relationships between diffuse myocardial fibrosis, which is a key biomarker for staging and treatment planning of the failing heart, and measured DTI parameters have yet to be systematically investigated. In this study, DTI was performed on left ventricular specimens collected from patients with chronic end-stage heart failure due to idiopathic dilated cardiomyopathy (n=14) and from normal donors (n=5). Scalar DTI parameters, including fractional anisotropy (FA), mean (MD), primary (D1), secondary (D2), and 1 © 2014 Wiley Periodicals, Inc. Reprinted, with permission, from. Abdullah OM, Drakos SG, Diakos NA, Wever-Pinzon O, Kfoury AG, Stehlik J, Selzman CH, Reid BB, Brunisholz K, Verma DR, Myrick C, Sachse FB, Li DY, Hsu EW. Characterization Of Diffuse Fibrosis In The Failing Human Heart Via Diffusion Tensor Imaging And Quantitative Histological Validation. NMR in Biomedicine. DOI 10.1002/nbm.3200 tertiary (D3) diffusivities, were correlated to collagen content measured by digital microscopy. Compared to hearts from normal subjects, the FA in failing hearts decreased by 22%, whereas the MD, D2 and D3 increased by 12%, 14%, and 24%, respectively (P < 0.01). No significant change was detected for D1 between the two groups. Furthermore, significant correlation was observed between the DTI scalar indices and quantitative histological measurements of collagen (i.e., fibrosis). Pearson's correlation coefficient (r) between collagen content and either FA, MD, D2, and D3 was -0.51, 0.59, 0.56 and 0.62 (P < 0.05), respectively. The correlation between D1 and collagen content was not significant (r = 0.46, P = 0.05). Computational modeling analysis indicated that the behaviors of the DTI parameters as a function of the degree of fibrosis were well explained by compartmental exchange between myocardial and collagenous tissues. Combined, these findings suggest that scalar DTI parameters can be used as metrics for noninvasive quantification of diffuse fibrosis in failing hearts. 3.2 Introduction End stage heart failure (HF) is a major public health problem with high mortality, morbidity and cost to the healthcare systems in the US and Europe [1], [2]. The disease is characterized by adverse changes in cardiac structure and function as a result of mechanical, neurohormonal, and cardiorenal factors [3]. One of the main factors leading to HF is the development of pathological myocardial fibrosis. Abnormally high collagen content adversely impacts the mechanical [4] and electrical [5] behaviors of the myocardium, and has been linked to increased risk of ventricular and atrial tachyarrhythmias and sudden cardiac death [6]. Myocardial fibrosis has been classified into reparative or reactive [7]. In 48 myocardial infarction (MI), fibrotic scar forms as macroscopic patches of collagen following myocytes necrosis to protect the myocardium from rupturing, and is thus called reparative fibrosis. On the other hand, collagen that develops in the remote zone to infarcts or in non-ischemic cardiac disease (such as dilated cardiomyopathy or cardiac hypertrophy) manifests as microscopic collagen depositions in the interstitial space and is termed reactive or diffuse fibrosis. Diffuse fibrosis is known to increase ventricular stiffness and leads to pump dysfunction [7], [8], and has been suggested to play a more detrimental role in structural remodeling in ischemic disease than the fibrotic scarring [9]. To date, tissue biopsy and histology remain the goldstandard method for quantifying structural remodeling in HF for staging and treatment planning of the disease [10], [11]. However, the invasive and laborious nature of the histological procedures presents a practical limitation on the number of sites and time points that can be practically performed. Hence, non-invasive imaging techniques for quantifying myocardial diffuse fibrosis are highly desirable. Magnetic resonance diffusion tensor imaging (MR-DTI, or DTI for short), which captures the dependence of tissue water diffusion on the molecular environment [12], has emerged as an established, non-invasive alternative to histology for characterizing myocardial tissue microstructure. Technically, DTI yields a second-rank, symmetric matrix that describes both the direction and magnitude of the diffusion anisotropy, which can in turn be used to infer the underlying tissue organization, geometry and content. For example, the direction in which diffusion is the fastest (i.e., the eigenvector of the largest diffusion tensor eigenvalue) has been found to coincide with the local fiber orientation in freshly excised [13], perfused [14], and formalin-fixed [15] myocardium. Moreover, the 49 eigenvector of the second diffusion tensor eigenvalue has been associated with the orientation of myocardial sheet structure [16]. So far, DTI has been used to characterize the structures of normal hearts in a variety of small and large animal models [17]-[21], in addition to humans [22]. Diffusion tensor imaging has also been utilized to evaluate the structural remodeling associated with cardiac pathologies of both ischemic and non-ischemic origins. Studies of ischemic injury have reported a reduction in the degree of diffusion anisotropy coupled with an increase of water diffusivity in the infarct zone [23]-[26]. Additionally, DTI has been utilized in assessing nonischemic cardiac disease, such as dyssynchronous HF [27], hypertrophic cardiomyopathy [28], and dilated cardiomyopathy [29]. Besides changes in the fiber orientation, the diseased myocardium (e.g., hypertrophy or dilated cardiomyopathy) is generally found to have decreased diffusion anisotropy [28], [29] and increased water diffusivity [29]. Although the latter changes suggest that microscopic environment for water diffusion has become less restrictive, and can be associated with myocardial fibrosis, the exact relationships between myocardial fibrosis and the DTI parameters remain yet to be determined. Beyond the empirical observations, to better understand the origin and predict the behavior of the relationship, it is also useful to explore the biophysical basis of dependence of the measured DTI indices on myocardial collagen content. Compartmental exchange models have been used to approximate the behavior of the MRI signal arising from a heterogeneous microscopic environment [30], [31], which is to be expected of the fibrotic myocardium. In the so-called fast-exchange situation, water spins spend much shorter time in the compartments than the temporal-length scale of their molecular 50 51 dynamics. Then the MRI parameters (e.g., relaxation rate and diffusion constants) of the aggregate system behave like the fractional volume-weighted sum of the same parameters of the individual compartments. Conversely, under the slow-exchange limit, the overall MRI signal is simply the proportional superposition of the signals from the individual compartments, as if the latter are completely independent. Bi-compartmental slow exchange models have been used to describe the MRI diffusion signal, including DTI, observed in the myocardium [32], [33]. Although it is unclear whether the behavior of the fibrotic myocardium is better described by the fast or slow-exchange model, either mechanism provides a possible starting point to explain the role in which diffuse fibrosis contributes to the MRI signal of the diseased myocardium. Taken together, the present study aims to quantify the relationship between the DTI parameters and diffuse fibrosis, and to explore the biophysical explanations of the relationships. While fiber orientation remodeling associated with heart diseases has been examined in previous studies [27], [28], the current work focuses on the scalar DTI parameters. To reduce measurement subjectivity, histological examination of the myocardium is performed using state-of-the-art, whole-field digital microscopy for comprehensive endocardium-to-epicardium evaluation, followed by quantitative image analysis [34]. Findings of the current study are expected to be important for assessing the utility of DTI, and to pave the way for the technique to be used in eventual in vivo studies on HF patients. 3.3.1 Study Population and Specimen Collection The study was approved by the Institutional Review Board at the University of Utah. The study group comprised 14 patients with chronic end-stage HF due to idiopathic dilated cardiomyopathy who required implantation of a left ventricular assist device (LVAD) for either bridge to heart transplantation or destination therapy in 2010. All patients met the medical policy guideline of the New York Heart Association (NYHA) class IIIb/IV for HF. The control group consisted of five donors whose hearts were determined to be functionally and structurally normal but were not suitable for transplantation due to non-cardiac reasons. Heart specimens were collected at the time of LVAD implantation by excising approximately a 1 x 1 x 1 cm3 transmural plug from the left ventricular apex. The normal hearts were collected as intact specimens. All specimens were fixed in 10% buffered formalin for at least 24 h prior to further examination. Demographic, clinical, echocardiographic, hemodynamic and laboratory data were collected 48-72 h prior to surgery and tissue collection. The collected information from patients with end-stage HF and from normal donors is shown in Table 3.1. HF in the diseased group was confirmed by the left ventricle ejection fraction, which was almost four times lower than that of the normal group. All subjects with HF had non­ischemic cardiomyopathies and are expected to have predominantly diffuse fibrosis. 3.3.2 MRI Acquisition and Analysis MRI experiments were conducted on a Bruker 7.0 T horizontal bore MRI scanner (Bruker Biospin, Ettlinegn, Germany) interfaced with 12.0 cm-diameter actively shielded gradient insert (BGA12S) capable of producing magnetic field gradients of up to 600 52 3.3 Methods 53 Table 3.1 - Baseline characteristics of the 14 patients with chronic HF due to idiopathic dilated cardiomyopathy, and 5 normal donors. Parameter HF Patients (N=14) Normal Donor (N=5) Age, years 52 ± 14.8 21 ± 3.6 Male gender 84% 60% HF etiology IDC 100% n/a ICMP 0% n/a NYHA class II 6% n/a III 47% n/a IV 47% n/a LVEF, % 16 ± 6.1 62 ± 6 LVEDD, cm 6.8 ± 0.99 4.1 ± 0.41 LVESD, cm 6.2 ± 1.0 2.7 ± 0.32 RAP, mm Hg 12 ± 5.9 7 ± 3.1 PASP, mmHg 49 ±13.5 - MPAP, mm Hg 34 ± 9.9 - PCWP, mm Hg 22 ± 10.0 7.2 ± 1.6 PVR, Woods units 4.1 ± 3.2 - CI, LPM/m2 1.8 ± 0.7 3.5 ± 0.5 mT/m. Each heart specimens was placed in a sealed container filled with susceptibility matching fluid (Fomblin, Solvay Solexis, NJ, USA). A combination of a linear volume coil (72 mm ID) for signal transmission and a quadrature surface coil (25 mm diameter) for signal reception were used to acquire the DTI datasets. DTI acquisition was performed using a standard multi-slice diffusion-weighted spin echo sequence with the following imaging parameters: TR/TE 2000/30 ms; matrix size, 64 x 64; in-plane resolution, 1.5 mm; four transverse slices; thickness, 1.0 mm. Diffusion was encoded along a set of 12 optimized gradient directions [35], using a pair of trapezoidal gradient pulses [rise time, 0.25 ms; duration (<3), 4.00 ms; separation (A), 10.00 ms] equivalent to a nominal b-value of 1500 s/mm2. The average signal-to-noise ratio for the non-diffusion-weighted image (B0) was 80. The total scan time for each specimen was approximately 28 min. Post-processing computation was performed using custom-codes written in Matlab (Version R2010a, Mathworks, MA) as described previously [12]. Briefly, diffusion tensors were estimated on a pixel-by-pixel basis from the MR diffusion images and diagonalized to yield the 3 eigenvalues (D1, D2 and D3, in sorted descending order and commonly referred to as primary, secondary, and tertiary diffusivities, respectively) and eigenvectors, which are equivalent to the speeds and principal axes of diffusion, respectively. The diffusion tensor eigenvalues were in turn used to obtain the mean diffusivity (MD) and fractional anisotropy (FA), which represent the magnitude of diffusion and degree of anisotropy, respectively, and are commonly used scalar indices for characterizing tissue microstructure [36]. MD and FA were reported as averages over the entire myocardial area on all 4 image slices for each specimen. The average area of the selected ROIs across all samples was 3.16 ± 0.32 cm2 (n = 19, mean ± SEM). To determine the underlying source of observed changes in the MD or FA, averages of the principal diffusivity terms D1, D2, and D3 were similarly obtained. 3.3.3 Histology: Whole-Field Digital Microscopy For histology, the specimens were dehydrated in progressively higher concentrations of alcohol, cleared through xylene and embedded in paraffin. Each specimen was cut into 4 ^m-thick sections and mounted on glass slides. It was then evaluated on a whole-field basis spanning the entire myocardial wall (epicardium to endocardium) using a ScanScope XT digital histopathology system equipped with the ImageScope 10.0 image analysis software (Aperio Technologies, CA) as described 54 previously [34]. Quantitative histological measurements to quantify diffuse fibrosis percentage in the heart specimen were conducted using Masson's trichrome stain for collagen content evaluation. The collagen content was automatically quantified by identifying, counting and expressing the number of blue-staining pixels as a percentage of the total tissue area [34]. Because of the relatively low spatial resolution of the DTI scans (1.5 mm), which was insufficient to directly visualize the interstitial content, the degree of diffuse fibrosis was approximated by the total collagen detected on the whole histological slide (endocardium to epicardium). 3.3.4 Statistical Analysis Statistical analysis was performed using GraphPad Prism (Version 5.0a, GraphPad Software Inc., CA). Variables were reported as mean and standard error of the mean (SEM). All parameters measured in the current study, including both DTI and histological indices, were compared between the failing and normal control groups using two-tailed unpaired t-tests. A P-value less than 0.05 was considered to be statistically significant. Correlation between DTI and histological indices was determined by evaluating the Pearson's correlation coefficients (r) for all pairings of MRI and histology parameters. 3.3.5 Computational Compartmental Analysis Computational simulations were performed as a means to explain the behavior of the DTI experiment in the myocardium with varying amount of fibrosis. Monte Carlo simulations of DTI parameters that would have been measured in standard DTI experiments were conducted assuming that the diffusion signal originated from either fast 55 or slow compartmental exchange between myocardial and collagenous tissues. As a first approximation, the myocardium was assumed to consist of the normal myocardial and collagen (i.e., non-fibrous and fibrous) compartments, with the former lumping together myocytes and supporting cells, and normal interstitial and vascular spaces in a single compartment. For fast-exchange, the MRI signal intensity l f ast for the j th diffusion encoding gradient direction g j was modeled after a two-compartment MR diffusion equation [37] adapted for DTI, l f aSt = e x p ( -b g ! ■ [(1 - f ') Dmyo + f 'Dcol\ • ), (3.1) where Dmyo and Dcol denoted the diffusion tensors for the myocardial and collagen compartments, respectively, and b is the scalar diffusion encoding sensitivity. Similarly, the slow-exchange signal equation followed one given previously [33], I jlow = (1 - f ') exp ( - b g ! • Dmyo • g ; ) + f ' ex p (- b g J • Dcol • g j ). (3.2) In both Eq. (3.1) and (3.2), the adjusted fractional volume f ', given as / ' = 1 - y , (3.3) was used instead of the nominal fractional volume f for the collagen compartment size in order to account for the small but non-negligible level of collagen content / 0 intrinsically found in the normal myocardium. The mean principal diffusivities determined for the experimental control group in the current study (or D1, D2 and D3 of 0.88, 0.64 and 0.51 x10-3 mm2/s, respectively) were used to construct the diagonal Dmyo. The mean collagen content for the same group (7%) was used as f 0. Because DTI parameters for the collagenous compartment were not directly measured in the current study, diffusion properties previously reported [38], [39] 56 for collagenous tissues (or 1.2 x10-3 mm2/s each D1, D2 and D3) were used for the diagonal Dcol. As a result of the rather low anisotropy of diffusion in collagenous tissues, with FA reported in the 0.05-0.12 range [39], [40], Dcol was assumed to be isotropic. To avoid the directional dependence of measurement accuracy inherent in each set of encoding gradient directions [35], the diagonal Dmyo was randomly rotated in 3D space and used in Eqs. [1] and [2] to estimate the diffusion signal intensities under simulated but same experimental conditions (e.g., diffusion-encoding directions and b-value) employed in the current study. Moreover, for evaluating the impact of image noise, Gaussian noise comparable to that found in the experimental data (i.e., SNR of 80) was added to the signal intensities, which were then used to compute the scalar DTI parameters, including D1, D2, D3, and FA, of the fibrotic myocardium. In this fashion, DTI parameters under fast and slow compartmental exchange were separately obtained 1000 times and averaged for each level of collagen content (i.e., f ) over the range seen in the current study (4% to 32%). To compare the simulation results to experimental data, the slopes of the simulated DTI profiles (D1, D2, D3, and FA) as a function of collagen content were obtained, and compared to the slope of the linear regression line obtained from the experimental data. Slopes were normalized to units of percentage change per unit of collagen fraction percentage, with the average collagen percentage of the control group taken as the baseline. 57 The quantified and ROI-averaged values of the DTI parameters for the normal control and HF groups are detailed in Table 3.2. Consistent with the qualitative observations, the FA in HF specimens was on average 22% lower than normal specimens (0.21 ± 0.01 vs. 0.27 ± 0.02). In contrast, MD of the HF specimens was 12% higher than normal samples (0.76 ± 0.02 vs. 0.68 ± 0.01 x10-3 mm2/s). MR images and DTI-derived FA and MD maps obtained from ^-representative normal and HF myocardial samples are shown in Fig. 3.1. Qualitatively, compared to the normal control, lower FA and higher diffusivities were observed in the failing myocardium. Together, the trends of MD and FA suggest that water motility is both higher and less anisotropic in HF than normal myocardial tissues. 58 3.4 Results 3.4.1 DTI Table 3.2. DTI and quantitative collagen measurements obtained from control and failing hearts. FA (fractional anisotropy), MD (mean diffusivity), D1 (primary diffusivity), D2 (secondary diffusivity), and D3 (tertiary diffusivity). DTI and collagen FA MD Dj D2 D3 Collagen 10-3 mm2/s 10-3 mm2/s 10-3 mm2/s 10-3 mm2/s (%) Control (n=5) 0.27±0.02 0.68±0.01 0.88±0.02 0.64±0.01 0.51±0.02 7.1±1.1 Failing (n=14) 0.21±0.01 0.76±0.02 0.93±0.02 0.73±0.02 0.63±0.02 19.4±2.0 P <0.01 <0.01 0.13 <0.01 <0.01 <0.01 59 Figure 3.1. Representative DTI scalar maps from control and failing heart cores. The top panel shows a MR image without diffusion weighting (B0), FA, MD, Di, D2, and D3 maps for normal (a-f), whereas the lower panel shows the failing core (g-l). A transverse view is shown, with the endocardium located at the top. The pericardial fat visible in the B0 image (white arrows in a and g) was segmented out in the DTI processing step. The DTI parameters are shown in falsecolor according to the colorbars, and all diffusivities had the same color scaling with units of 10-3 mm2/s. 3.4.2 Collagen Evaluation and DTI-Histology Correlation Representative trichrome sections from control and HF myocardial samples are shown in Fig. 3.2. Compared to the control specimen (Fig. 3.2a), the HF slide (Fig. 3.2b) contains conspicuously higher content of the blue-staining interstitial collagen. Quantitative collagen content measurements are summarized in Table 3.2. The total collagen content, used as the metric of fibrosis, is nearly 3 times higher in HF than in normal myocardium (19.4 ± 2.0 versus 7.1 ± 1.1 percent area). The level of collagen intrinsic in the normal myocardium is in agreement with the ~4-5% reported by a previous study [34]. The relationships between different DTI parameters and the total collagen content are shown as scatter plots in Fig. 3.3. Qualitatively, from the scatter of the data points around the fitted lines, there appears to be more variability in D1 and FA, 60 a b Figure 3.2. Histological evaluation of control and failing heart cores. Masson's trichrome histological images of collagen content (20x magnification, collagen stains in blue) from a representative control (a) and failing (b) heart cores. The black arrow in (a) points to perivascular collagen, which was included as part of the total collagen calculation reported in this study. compared to D2 and D3. The observation is consistent with the Pearson's correlation coefficients between individual DTI parameters and total collagen content, which are listed in Table 3.3. Among the pairings examined, significant correlations were found between the collagen content (or fibrosis) and FA (r = -0.51), MD (0.59), D2 (0.56), and D3 (0.62). The correlation between D1 and collagen was relatively weaker (r = 0.46), and was not significant (P = 0.05). 3.4.3 Computational Compartmental Analysis Plots of the Monte Carlo simulated DTI scalar parameters (D1, D2, D3, and FA) vs. collagen percentages are shown in Fig. 3.4. Overall, simulation results obtained using fast and slow exchange models were in close agreement with the experimental data regression line. Both exchange models indicate that all DTI diffusivities would increase, whereas the FA would decrease, as the percent collagen content is increased. 61 E E b 'x r = 0.46 P = 0.05 0 10 20 30 40 Total Collagen (%) EE CO b CM Q 1.2 - 0 .8 « Total Collagen (%) b 0.56 ^ 0.01 r= 0.62 E E ro Q Total Collagen (%) 0.4- <LL. 0.2' r= -0.51 P = 0.03 10 20 30 Total Collagen (%) 40 Figure 3.3 Quantitative correlation between DTI scalar parameters and collagen content. Scatter plots