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Cardiac Imaging |
1 From the Department of Radiology, National Taiwan University Medical College, Laser Medical Research Center, Taipei, Taiwan (W.Y.I.T.); and the Department of Radiology, NMR Center, Massachusetts General Hospital-East, Bldg 149, 13th St, Charlestown, MA 02129 (T.G.R., R.M.W., T.J.B., V.J.W). Received July 16, 1999; revision requested August 17; revision received October 7; accepted October 25. Supported by National Institutes of Health 1RO1-HL56737 grant (V.J.W., W.Y.I.T.), the American Heart Association Established Investigator Grant 9740208N (V.J.W.), and grants from the New York Cardiac Center and the Sol Goldman Charitable Trust (V.J.W.). Address correspondence to V.J.W. (e-mail: van@nmr.mgh.harvard.edu).
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
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MATERIALS AND METHODS: Images of fiber shortening for midventricular short-axis sections were acquired in eight healthy subjects. Fiber orientation maps obtained by means of diffusion-sensitive MR imaging were coregistered with systolic strain maps obtained by means of velocity-sensitive MR imaging. Fiber shortening was quantified by use of the component of systolic strain in the fiber direction.
RESULTS: The results were reproducible among subjects and were consistent with published values. MR imaging of myocardial fibers showed axisymmetric progression of fiber angles from -90° epicardially to +90° endocardially, with maxima near 0°. Fiber shortening (mean, 0.12 ± 0.01 [SD]) was more uniform than radial, circumferential, longitudinal, or cross-fiber strain or any principal strain. Fiber orientation coincided with the direction of maximum contraction epicardially, with that of minimum contraction endocardially, and varied between these extremes linearly with wall depth (r = 0.6).
CONCLUSION: Registered diffusion and strain MR imaging can be used quantitatively to map fiber orientation and its relations to myocardial deformation in humans.
Index terms: Heart, function, 51.91, 51.92 • Heart, MR, 51.121411, 51.121416, 51.12144 • Magnetic resonance (MR), diffusion study, 51.12144 • Magnetic resonance (MR), phase imaging, 51.121411, 51.121416 • Myocardium, MR, 511.121411, 511.121416, 511.12144
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
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The present study had three aims: first, to define an MR imaging methodology to obtain registered images of myocardial structure and function and derive from them quantitative maps of myocardial fiber shortening and related parameters; second, to validate this method in a series of healthy subjects by means of showing reproducibility and agreement with published values obtained by using conventional methods; and third, to show that MR imaging affords improved recognition of general characteristics of cardiac function.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
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The image acquisition and reconstruction procedure is as follows: (a) Acquire an MR movie of myocardial two-dimensional (2D) strain rates. (b) Compute from the strain-rate movie the optimum cardiac phase delay 
for diffusion MR imaging. (c) At t = , acquire an image of the cardiac diffusion tensor D and a registered image of the myocardial 3D strain-rate tensor S'(). (d) By using the image of 3D strain rate S'() and the strainrate movie, compute the tensor image of net systolic 3D strain Ssys. (e) Compute from the tensor images D and Ssys myocardial fiber shortening and associated quantities.
The details concerning computation of optimum cardiac phase delay in step b and of the net systolic strain in step d are given in the Appendix.
MR Imaging Acquisitions
Eight healthy volunteers (six men, two women; age range, 26–40 years) without previous history of heart disease were recruited. Each subject provided written informed consent, which was approved by the hospital human study committee. All experiments were performed with a 1.5-T MR imager (Signa; GE Medical Systems, Milwaukee, Wis) with Instascan echo-planar imaging. After electrocardiographic leads were applied, a 15 x 28-cm rectangular receive-only radio-frequency surface coil was positioned precordially, and the subject was put in the magnet lying in a 45° left anterior oblique orientation.
To suppress the effects of respiratory motion, all of the images were acquired at the end of expiration by using synchronized breathing. With imaging electrocardiographically triggered to every fifth heartbeat, subjects were requested to take a breath after the sound of each imaging pulse, then passively exhale, await the next image acquisition, and repeat. The resultant respiratory rate was within normal limits and could be sustained comfortably for many minutes. Both diffusion and strain-rate images were spatially encoded by using single-shot echo-planar imaging with a 20 x 40-cm field of view and a 64 x 128 image matrix, with a resultant in-plane resolution of 3 x 3 mm.
After a sagittal T1-weighted study was performed to establish left ventricular location and axis, a midventricular short-axis section was defined for the studies of myocardial strain rate (a 2D strain-rate movie to determine , followed by 3D strain-rate tensor imaging at t = ) and the registered study of myocardial diffusion. Registration of the diffusion image and the strain-rate image required temporal alignment among three corresponding components of the respective images: (a) section-selection for section registration, (b) diffusion and velocity encoding pulses for registration of architecture and function, and (c) readout period for in-plane registration. The registered pulse sequences of diffusion and strain rate are illustrated in Figure 1. To ensure coregistration, the same phase-encoding direction and readout direction were used in diffusion and strain-rate imaging sequences.
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xi is the differential between pixels adjacent in the xi direction. The strain-rate image obtained with use of Equation (2) has spatial resolution identical to that of the original velocity-sensitive phase-contrast images. Images of 2D strain rates were computed by using velocity-sensitive data for a single section, whereas 3D strain rates required velocity-sensitive data for two contiguous sections offset in the through-plane, or z direction, to define z components of strain.
Strain-rate MR imaging data were acquired by using a single-shot spin-echo echo-planar imaging sequence augmented by velocity-encoding bipolar gradient pulses. Velocity-encoding gradient pulses were applied with amplitude |gv| = 10 mT · m-1 and pulse duration v = 6 msec for a velocity sensitivity |kv| 
130 radian · m-1, with tetrahedral orientations corresponding to the nonopposed corners of a cube (8). Velocity sensitivity was selected to yield myocardial phase shifts that had differentials that did not exceed 
/2 radians per 3-mm voxel at peak ejection rate. A movie of 2D strain rates was acquired with a 3.0-mm section thickness, progressive cardiac delay of 30 msec, four velocity encoding directions, one signal acquired, one section, a repetition time of five R-R intervals with synchronized breathing, and an echo time of 48 msec, for an imaging time of 7–9 minutes.
After determination of the optimum time delay t = (Appendix), an image of the 3D strain-rate tensor field S'() was acquired at this same section by using two contiguous 3.0-mm sections with opposite 1.5-mm offsets from the section center. For this acquisition, we used four velocity-encoding directions, four signals acquired, two sections, and a repetition time of five R-R intervals for an imaging time of about 2 minutes, which typically yielded a signal-to-noise ratio of at least 40:1 for strain rates. This corresponded to a root-mean-square error of approximately 11° in the principal thickening direction and of approximately 13° in the principal shortening direction.
Diffusion MR Imaging
Diffusion tensor MR imaging reconstructs the symmetric diffusion tensor at each location in an MR image. It is based on the diffusion-dependent reduction in the MR signal intensity that results from the application of a reversible spatial modulation of magnetization by a pair of temporally separated magnetic gradient pulses of opposite signs (9). The measured signal intensities are related to the diffusion tensor D by
is the diffusion time; and kD is the gradient-induced spatial modulation of magnetization produced in a time D << . By measuring this attenuation for spatial modulations in six directions and an image of null gradient (kD 0), we computed the diffusion tensor at each pixel by using standard algebraic inversion of Equation (3) (10).
In the present study, a double-gated stimulated-echo pulse sequence was used to acquire diffusion tensor MR images at the required time delay t = with 6.0-mm section thickness. Diffusion-sensitizing gradient pulses were applied in six nonopposed edge-centers of a cube, |1,±1,0|, |0,1,±1|, and |±1,0,1|, and were of amplitude |gD| = 10 mT · m-1 duration D = 8.6 msec, which corresponded to a spatial modulation
being the proton gyromagnetic ratio, and diffusion sensitivity b = 
|kD|2 d
|kD|2 420 sec · mm-2, given a diffusion time 800 msec (one R-R interval). With 16 signals acquired and a repetition time of five R-R intervals, the total acquisition time was approximately 7.5 minutes. With 75% k-space readout and an echo time of 48 msec, the net signal-to-noise ratio was 45:1 for the nonattenuated diffusion image (b 0 sec/mm2) and 25:1 for the attenuated (b 420 sec/mm2) images, which corresponded to a root-mean-square error in the direction of principal diffusion of approximately 8°.
Strains in Local Fiber and Cardiac Coordinates
Strain components of interest were computed by transforming the strain tensor Ssys from the lab frame |x, y, z| into local cardiac coordinates or local fiber coordinates by using
For each short-axis section, local fiber orientation f was defined as the first eigenvector of the diffusion tensor d1 with sign assigned to produce a counterclockwise orientation relative to the ventricular centroid
is the gradient of the polar angle about the left ventricular centroid. In each section, a ventricular axis L was defined as the direction about which the fiber orientations have maximum symmetry, specifically, as the vector L that maximized the net axial contribution
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Statistics
For each strain component in each subject, the mean and SD for the left ventricle in the imaged section were computed. The mean for each subject and the mean and SD for all subjects together were then computed for every averaged strain component to evaluate the intersubject variability. To study spatial uniformity of fiber shortening, we computed 95% variance ratio CIs of normal strains with respect to fiber shortening. In addition, linear regression of fiber shortening and of other normal strains against wall depth was performed. The resultant slopes and residuals indicating transmural variability and local variability, respectively, were compared among strain components.
Geometric relations between fibers and principal shortening strains were studied by computing the regression slopes, intercepts, and correlation coefficients between fiber helix angles and helix angles of principal shortening directions. The angles between fibers and directions of principal thickening also were analyzed in terms of the mean and SD.
In this study, MR data acquisition was performed by T.G.R. and W.Y.I.T. together, and data analysis was performed by both W.Y.I.T. and V.J.W.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
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The means and SDs of cardiac strain components within and among subjects are plotted in Figure 4b. Despite the large variance within each strain component in each subject, the intersubject variance of the component means was small.
In Figure 5, the strain tensor field Ssys is graphically rendered with boxes so that 3D patterns of the strain tensor field orientation are appreciated easily. We see that the direction of principal thickening was predominantly radial. The lengths of two principal shortenings were unequal, and the skew of the greater shortening corresponded to myocardial twist. Furthermore, the shortenings were seen to rotate about the thickening direction from epi- to endocardium, with greatest shortening longitudinal more epicardially and circumferential more endocardially.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
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Advantages of MR imaging are illustrated in the trabecular myocardium. Histologic studies of myocardial fiber architecture were initially equivocal about the trabecular zones but ultimately showed trabecular regions to contain fiber angles in a range of +70° to +90° and also showed that this contribution substantially improved the overall symmetry of the ventricular fiber angle graph (11). MR imaging results, conversely, indicated that trabecular and compact myocardium were equally accessible. MR imaging immediately obtains a full and symmetric fiber angle graph. Furthermore, images of fiber orientation show a uniform progression of fiber angles across the interface between trabecular and compact myocardium, which is direct evidence of the structural unity of compact and noncompact myocardium.
Fiber Shortening
In the present study, mean fiber shortening in healthy human subjects was 0.12 ± 0.01. This is smaller than the shortening of 0.15 reported by MacGowan et al (17). In that study, fiber shortening was computed by using strain measurements obtained by means of MR imaging tagging in vivo in conjunction with fiber orientations determined in unrelated autopsy specimens. Although the variability of fiber angles among autopsy specimens was small, it is still unclear to what extent these angles faithfully represent fiber geometry in situ. Their endocardial fiber angles were approximately +70°, which is substantially less than the +90° of our in vivo results. As shown in Figure 8, in vivo imaging shows endocardial fiber angles up to +90°, at which point they are orthogonal to the direction of maximum shortening. Therefore, calculation of fiber shortening by using fiber angles less than +90° would lead to overestimation of shortening by an amount cos(20°)-2 1.13, or about half of the noted disparity.
The hypothesis that myocardial fiber shortening is transmurally uniform was proposed by Arts et al (18) and subsequently was derived as an optimum solution to a general model of myocardial fiber orientation and function (19). This hypothesis has been supported by experimental observations in the dog, including those of Waldman et al (2), who found fiber shortenings in the inner and outer walls of 0.06 ± 0.06 and 0.09 ± 0.04, respectively, by using radiopaque marker strain measurement and postmortem histologic examination for fiber architecture. Rademakers et al (20), using MR imaging tagging and postmortem histologic examination, found shortening in the endocardium and epicardium of 0.09 ± 0.10 and 0.06 ± 0.11, respectively. Bloomgarden et al (21), using MR imaging tagging and published histologic examination results, found fiber shortenings of 0.12 and 0.13, respectively, in the inner and outer halves of the ventricular wall.
To our knowledge, the present quantitative analysis of the uniformity of fiber shortening and its relation to other strain components has not been reported previously. Its results show that variance ratios of strain components are all substantially greater than 1, as compared with those of fiber shortening. Results of analysis of transmural profiles further showed that fiber shortening had the narrowest distribution and smallest transmural gradient among all strain components (Tables 1, 2), which verifies that fiber shortening is the most uniform of all cardiac strain components.
Cross-Fiber Shortening
Cross-fiber shortening in normal human hearts was 0.10 ± 0.03 and had the largest variance ratio with respect to fiber shortening (Table 1). The reason for the large variance in cross-fiber shortening was mainly because it had a steep transmural gradient, with 0.05 ± 0.02 at the epicardium and 0.20 ± 0.02 at the endocardium (Fig 7). This prominent transmural gradient was found previously in canine and human studies. In canine left ventricles, cross-fiber shortening in the outer and the inner walls, respectively, were reported to be 0.04 ± 0.04 and 0.17 ± 0.03 by Waldman et al (2), 0.006 ± 0.082 and 0.251 ± 0.103 by Rademakers et al (20), and 0.09 and 0.22 by Bloomgarden et al (21). In healthy human subjects, MacGowan et al (17) found a similar transmural trend: 0.08 ± 0.01 and 0.26 ± 0.01 in the areas beneath the epicardium and beneath the endocardium, respectively.
Advantages of Measuring Myocardial Strains in Local Fiber Coordinates
Having characterized transmural patterns of fiber and cross-fiber shortening, advantages of transforming the strain tensor from local cardiac coordinates to local fiber coordinates becomes evident. Whereas circumferential and longitudinal strains both showed transmural variations, fiber and cross-fiber strains took the opposite modes of shortening patterns across the wall: Fiber shortening was virtually constant, whereas cross-fiber shortening showed a steep gradient (Table 2). With these two drastically different transmural patterns as norms, it is easy to detect any deviation from these two standard patterns in diseased hearts.
Another advantage of transforming the strain tensor into local fiber coordinates is that two different myocardial functions can be separated. Fiber shortening indicates myocardial contractility, whereas cross-fiber shortening is believed to reflect a dynamic rearrangement of the myocardial sheet structure to facilitate systolic wall thickening (15). Different cardiac disease states may have different effects on these two functions (22); these changes would not be shown clearly in local cardiac coordinates.
The present MR imaging method demonstrated its capability to provide images of fiber orientation and myocardial strains with identical cardiac configurations in identical physiologic conditions; it directly mapped the fiber shortening and its relation to local wall deformation with anatomic details not previously available. This imaging capability should be of particular value in the study of disease in which the characterization of regional abnormalities and their change over time in the living individual is essential (23). Furthermore, for disease detection and characterization, conventional cardiac coordinates and corresponding strain components are likely to become equivocal, since anatomic distortions affect these geometry-based coordinates. Fiber shortening and related functional parameters, however, should be less affected by these distortions, and they thus better reflect disease location and severity.
Fiber and Principal Shortening
Since clarification by Streeter (11) of the basic helical geometry of myocardial fiber orientations, several explanations of its functional significance have been offered (18,20). Arts et al (1) emphasized the capacity of helical fiber orientations to make fiber stress and fiber strain transmurally more uniform and constructed a model in which observed patterns of structure and function emerged purely through local feedback. Teleologically, this uniformity may facilitate physiologic tuning by means of concomitant uniformity of cellular workload, of local tissue perfusion, and of myocyte metabolism and morphology (24–26). Waldman et al (2) and Rademakers et al (20) suggested that the helical fiber geometry serves to transmit fiber contraction from the outer to the inner wall through the connective tissue network and produces the remarkable cross-fiber shortening in the inner wall that in turn generates substantial radial thickening. Present MR imaging findings in humans support both of these views, as well as their mutual synergy.
As was noted earlier, MR imaging demonstrated the change with transmural depth of fiber orientation from the direction of maximum to that of minimum shortening. This arrangement allowed principal shortening to increase with wall depth while the fibers, by rotating away from the direction of greatest shortening, continued to shorten by constant amounts. MR imaging showed that this rotation was linear with transmural depth (Fig 8, bottom) and that it exhausted the meaningful angular ranges of fiber orientation and of its relation to shortening, with fiber orientation rotating anatomically 180° relative to the heart wall even as it rotated 90° relative to the direction of maximum shortening. We see therefore that the observed fiber geometry in healthy humans accomplishes an equipartition of fibers across the entire range of relevant states. This condition of pushing to possible limits lends new support to the hypothesis that fiber geometry and its relation to myocardial 3D strain are objects of close physiologic optimization (27).
Technical Considerations
Multisection ventricular coverage from apex to base is constrained currently by the inherently low signal-to-noise ratio of present cardiac diffusion MR imaging methodology and consequent long imaging times. This study presents myocardial structure-function relations only at the midventricular level, and information concerning more apical or basal regions is lacking. In the future, imaging speed may be increased by replacing synchronized breathing with one of the automated MR imaging methods now being developed for respiratory artifact suppression (28). Acquisition economies also may be obtainable by use of intersecting sections in the cardiac long axis.
Present methodology for identification of optimum cardiac phase delay to acquire accurate diffusion data incurs certain systematic errors, as described previously (3). Among these are potential inaccuracies in the assumed linearity between myocardial strain and the observed diffusion, and sweet-spot localization errors arising from R-R variability or errors of myocardial tracking in the present sampling strategy. Within the range of normal cardiac function, we estimated that these systematic errors led to diffusion error of 15% or less, or uncertainty in fiber direction of 5° or less.
In the present study, acquisition of accurate diffusion images with minimum strain effects depended on cardiac synchrony. Application of this method to disease would be expected to be less accurate owing to mechanical dyssynergy. Partial relief from this problem may result from the fact that dyssynergic walls are most often hypokinetic and so would have reduced strains and correspondingly reduced measurement errors. Furthermore, new MR imaging pulse sequences that provide cardiac diffusion MR imaging completely free of myocardial strain effects have been proposed (29). Methods such as this would provide accurate maps of myocardial fiber architecture in the normal or the diseased heart and at any point in the cardiac cycle.
MR imaging of diffusion and strain makes possible quantitative noninvasive imaging of myocardial fiber shortening and its relation to local myocardial deformation in healthy human subjects. This method addresses the problems of in vivo access and of metric distortion that hindered prior attempts to relate myocardial structure and function. Present data confirm key quantitative features of fiber shortening previously established invasively in animal models and indirectly in humans; but as image data, MR imaging resolves these measurements with anatomic details not previously available. Recognition of robust regularities in myocardial fiber architecture and function with the present method may provide new insight into myocardial design and furnish new normative parameters to facilitate evaluation of myocardial dysfunction.
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APPENDIX |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
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D - <S>D - D<S>, where angle brackets denote the time-average during the diffusion encoding time of one cardiac cycle, U is the time-dependent material stretch tensor, and S is the corresponding strain tensor. To have a more intuitive picture of the sweet spot, consider a measurement of diffusion in a rubber band that we deform cyclically. Diffusion encoding and decoding gradient pulses are applied at the same phase of the deformation cycle to eliminate signal dropout owing to bulk motion. If these pulses are applied when the band is shortest, then the subsequent stretching of the band also will stretch the phase modulation inscribed on it and lead to a reduction of the phase modulation. As this phase modulation is reduced during the diffusion time, the diffusion-induced signal attenuation will be less than it would have been had there been no stretching, and measured diffusion would appear smaller than expected. Conversely, if diffusion encoding is applied when the band is maximally stretched, the apparent diffusion will be larger than expected. In general, the deviation of the apparent diffusion from the true diffusion is proportional to the time integral of the strain curve during a full cycle (3). This deviation varies periodically from positive to negative, and the sweet spots are the time points when the deviation crosses zero. Diffusion measurement at the sweet spots is therefore free of strain effects.
In each subject, sweet-spot location was determined by analyzing the mean radial strain, a robust and easily measured scalar index of strain state, as described (3). From the strain-rate movie, we measured the time-course of the mean radial strain rate S'rr(), where the radial was defined by the ventricular centroid and the underscore denotes the mean over ventricular pixels. This was integrated numerically to construct a scalar function F(t) that varies linearly with the mean radial strain
when the myocardium occupied its mean strain state were then the solutions of
during one cardiac cycle. A typical curve F(t) and its relation to is shown in Figure A1. The normal cardiac cycle contains two time points that satisfy Equation (A2), one in midejection and the other in rapid filling. In this work, we always used the that occurs in midsystole to match the cardiac configuration of strain images acquired in systole.
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is equal to the integral of the strain rates
refers to the time of end systole. Synchrony of strain rates implies S'(t1) L(t2) = S'(t2) L(t1), for L(t) any linear functional of strain rate and any times t1 and t2. Setting L(t) = S'rr() and t1 = , one obtains
expresses net systolic strains relative to cardiac configuration at t = .
According to standard practice, we computed net systolic strain relative to cardiac configuration at end-diastole Ssys by change of coordinates Ssys = U S U for
to end-diastole in image coordinates.
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FOOTNOTES |
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Author contributions: Guarantors of integrity of entire study, W.Y.I.T., V.J.W., R.M.W.; study concepts and design, W.Y.I.T., V.J.W., T.J.B.; definition of intellectual content, W.Y.I.T., V.J.W.; literature research, W.Y.I.T.; clinical studies, W.Y.I.T., T.G.R., V.J.W.; experimental studies, W.Y.I.T., T.G.R., V.J.W.; data acquisition, T.G.R., W.Y.I.T.; data analysis, W.Y.I.T., V.J.W.; statistical analysis, W.Y.I.T.; manuscript preparation, W.Y.I.T.; manuscript editing, V.J.W., R.M.W., T.J.B.; manuscript review, V.J.W., T.G.R., R.M.W., T.J.B.
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
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parallels the long axis of the left ventricle L. The radial axis r points away from the ventricular centroid and perpendicular to 
, Sfx, and Sxr^ denote shear strains in fiber-radial, fiber-cross-fiber, and cross-fiber-radial planes, respectively. (a) Schematic shows that the maximum root-mean-square error of strain measurement at each pixel estimated from MR noise is about 0.02 and is indicated by the width of a small rectangle in the gray-level bar. See text for a detailed description of individual strain patterns. (b) Graph shows summary plot of strain components in the fiber coordinates with the same symbols used in 
