## Abstract

The orientation of MRI-measured diffusion tensor in the myocardium has been directly correlated to the tissue fiber direction and widely characterized. However, the scalar anisotropy indexes have mostly been assumed to be uniform throughout the myocardial wall. The present study examines the fractional anisotropy (FA) as a function of transmural depth and circumferential and longitudinal locations in the normal sheep cardiac left ventricle. Results indicate that FA remains relatively constant from the epicardium to the midwall and then decreases (25.7%) steadily toward the endocardium. The decrease of FA corresponds to 7.9% and 12.9% increases in the secondary and tertiary diffusion tensor diffusivities, respectively. The transmural location of the FA transition coincides with the location where myocardial fibers run exactly circumferentially. There is also a significant difference in the midwall-endocardium FA slope between the septum and the posterior or lateral left ventricular free wall. These findings are consistent with the cellular microstructure from histological studies of the myocardium and suggest a role for MR diffusion tensor imaging in characterization of not only fiber orientation but, also, other tissue parameters, such as the extracellular volume fraction.

- fractional anisotropy
- left ventricle
- extracellular volume fraction
- cardiac electrophysiology and biomechanics

cellular microstructure and arrangement of the myocardium are known to have a profound impact on its electrical (10, 37) and mechanical properties (1, 44). Early histological studies (27, 31, 45), although labor intensive, destructive, and prone to tissue-processing artifacts, have provided important insights into the myocardial structure, including the distinctive counterclockwise transmural rotation of the ventricular myocardial fiber orientation. By probing the tissue microstructure via its influence on the molecular diffusion of water, MR diffusion tensor imaging (DTI) (3) has emerged as a convenient and reliable alternative for characterization of the three-dimensional (3D) structure of the myocardium (23, 38).

In 3D space, the MRI-measured diffusion tensor is a symmetrical 3 × 3 matrix; its eigenvalues and eigenvectors represent the motilities along the principal axes of water translational diffusion and their spatial orientations, respectively. The diffusion tensor eigenvectors have been linked to the orientation of myocardial microstructure. For example, the primary diffusion tensor eigenvector (i.e., which corresponds to the largest eigenvalue) has been directly correlated to the myocardial fiber orientation (23), and the tertiary eigenvector (pertaining to the smallest eigenvalue) has been taken as the plane normal to the myocardial laminar structure (38). Meanwhile, the diffusion tensor eigenvalues, which are often aggregated into single scalar indexes for easier quantification of the degree of diffusion anisotropy, are generally considered to reflect the underlying cellular composition (e.g., white matter myelination) and organization (cell packing density) (3).

Besides in vivo studies in humans (13, 49), DTI has been used to characterize in vitro or ex vivo hearts in several species, including goat (15), dog (20), sheep (47), rabbit (18), rat (7, 8), and mouse (25), and applied to the study of myocardial structures as functions of cardiac contractile state (7) and remodeling associated with infarction (8, 47), hypertrophy (18), and dyssynchronous heart failure (20). These studies have focused primarily on the measurement and analysis of spatial variations of the myocardial fiber and sheet structures obtained from the orientation information in the diffusion tensor. In contrast, the scalar quantities, including the diffusivities and anisotropy indexes, have simplistically been assumed to be homogeneous throughout the myocardium (7, 15, 20, 25, 47), and the validity of this assumption remains largely untested.

Transmural variations of myocardial microstructure have been documented in several histological studies. A transmural gradient of myocyte dimensions has been observed in the rat left ventricle (LV), with the largest and smallest cell volume and cross-sectional area found in the endocardium and epicardium, respectively (5). In a dog heart study (27), a progressive decrease in the relative proportion of myocytes from the epicardium to the endocardium was accompanied by an increase in the volume fraction occupied by extracellular space. Transmural differences in connective tissue concentration have been reported in dog (50) and mouse (32) hearts, as well as cell types and distribution in different (e.g., canine, rabbit, and human) hearts (39, 48). Since MR diffusion and DTI measurements are highly sensitive to the underlying tissue structure, the above-described evidence of structural heterogeneity suggests that DTI scalar quantities are also likely heterogeneous in the myocardium.

The hypothesis of the present study is that structural heterogeneity of the myocardium gives rise to measurable differences in DTI diffusion anisotropy. Without loss of generality, the DTI-derived fractional anisotropy (FA) index (34), a commonly used rotationally invariant index of diffusion anisotropy, as well as the diffusion tensor eigenvalues, are examined as functions of LV wall depth and circumferential and longitudinal locations. The observations are explained in terms of a biophysical model of diffusion and correlated to the known cellular structure, including fiber orientation, of the myocardium. Since the goal of the present study is to point out that DTI may generate more information about functional significance than is currently utilized, analyses of the fiber or sheet structure orientations are not included to avoid repetition of previous studies.

## METHODS

### Specimen Preparation

Specimens were obtained from a separate study (47). Briefly, under a protocol approved by the University of California, San Francisco, Institutional Animal Care and Use Committee, intact hearts (*n* = 4) from normal adult castrated male Dorsett sheep were excised, fixed under retrograde perfusion, and stored in formalin. The average time between specimen harvest and imaging was 4 ± 1 wk.

### Diffusion Tensor Imaging

Imaging experiments were conducted on a 2.0-T MRI instrument (Oxford Instruments, Oxford, UK) interfaced to a Signa console (Epic 5X, General Electric Medical Systems, Milwaukee, WI). The intact heart was placed inside a custom-built 10-cm-diameter loop-gap radio-frequency coil, with the cardiac long axis parallel to the coil axis. A standard diffusion-weighted spin-echo pulse sequence was used to acquire 3D volume images (field of view = 10 × 10 × 10 cm, TR = 500 ms, TE = 27.3 ms, and no. of averages = 1). Diffusion encoding was performed using a pair of half-sine gradient pulses (10.0 ms wide, 15.0 ms separation, and 18.0 g/cm gradient amplitude, which corresponds to a diffusion-weighting *b* value of 1,175 s/mm^{2}). A reduced encoding DTI methodology (22) was employed to reduce the scan time without proportional loss in measurement accuracy. Each DTI dataset consisted of a fully encoded 128 × 128 × 128 (readout × phase × slice) matrix-size *b* ≈ 0 (or *b*_{0}) and 12 reduced encoded (128 × 64 × 64) diffusion-weighted images sensitized in each of an optimized set of 12 directions (33). The acquisition time for each complete DTI dataset was ∼9.1 h.

Reduced encoded diffusion-weighted images were reconstructed to 128 × 128 × 128 matrix size (equivalent to an isotropic resolution of 0.78 mm) by reduced-encoding imaging via a generalized series reconstruction (RIGR) algorithm (28), with the *b*_{0} image used as the constraining reference. Diffusion tensors were estimated by nonlinear least-squares curve fitting and diagonalized on a pixel-by-pixel basis, as described previously (25). The FA for each pixel was also computed.

### Data Analysis

#### Anatomic coordinate system.

To provide consistent and objective placement of the measurement regions of interest, the following semiautomated procedures were used to define a prolate spheroid-based coordinate system (31) on each LV. *1*) Since the imaging and cardiac short-axis planes were not necessarily parallel, which resulted in elliptical, rather than circular (15), LV cross sections on the image slices, points (10 per plane) were manually selected on the epicardial boundary and fitted to an ellipse on nine equally spaced planes spanning approximately the middle 75% of the LV volume. *2*) The long axis of the LV was determined by linear regression of the centers of the fitted ellipses (7, 15), and the entire volume of the heart was rotated as a rigid body, such that the LV long axis coincides with the imaging slice axis. Cubic interpolation was used for all image (including diffusion tensor eigenvalue and FA maps) rotations, and the diffusion tensor eigenvector fields were rotated accordingly by nearest-neighbor interpolation. *3*) Because the volume rotation resulted in new epicardial boundaries in the imaging slice planes, *steps 1* and *2* were repeated until the LV long axes between iterations differed by < 3°.

Whereas the smooth shape and image contrast of the LV epicardial boundary make it relatively easy to delineate, the presence of the papillary muscle and trabeculations has been a significant source of variation in manual definition of the endocardial boundary (7, 25, 47). For the present study, the papillary muscle and trabeculations were observed within regions of the LV where the fiber helix angle [i.e., the angle of inclination of the primary diffusion tensor eigenvector from the imaging slice plane (25)] exceeded 50°. To reduce the subjectivity in defining the boundary and excluding papillary muscles, 10 points with fiber helix angle of 50° were selected and used to fit an inner ellipse to approximate the LV endocardial border. Subsequently, the local LV myocardial wall thickness (i.e., the distance between the fitted epicardial and endocardial boundaries) was used to obtain the normalized transmural depth (0.0 and 1.0 at the epicardium and endocardium, respectively) along radial trajectories that passed through the LV central long axis (Fig. 1*A*). The corresponding FA map of the same slice is displayed in Fig. 1*B*.

#### Region-of-interest measurements.

The short-axis slice with the largest cross-sectional area was taken to be the LV hemispherical plane. Regions of interest were selected on five equally spaced short-axis slices (1 above, 1 at, and 3 below the hemispherical plane). The gap between the slices was equal to one-fifth of the distance between the hemisphere plane and the cardiac apex, and the slices were labeled S1–S5 in sequential order according to their proximity to the base (Fig. 1*C*). Within each slice and along the LV circumference, four 20° sectors (Fig. 1*D*) were defined at orthogonal locations corresponding to the septal, posterior, lateral, and anterior regions of the LV, where the septal region is located in the middle of the two right ventricle (RV) fusion sites. Within each sector, the mean FA profile as a function of normalized transmural depth was computed from the anisotropy indexes at the same transmural depth along 10 radial trajectories evenly spanning the sector. In total, 80 transmural FA profiles (4 sectors per slice and 5 slices per heart) were obtained from 4 hearts. In a similar manner, the transmural profiles of primary, secondary, tertiary, and mean diffusivities (i.e., diffusion tensor eigenvalues) and primary eigenvector helix angle were obtained. To determine whether any change in the FA was caused by alterations in the diffusion tensor characteristics or by differences of goodness of fit in tensor computation, the uncertainty in the multivariate curve fitting was quantified by a normalized magnitude of diffusion tensor errors (NMTE) (6) derived from the corresponding standard error covariance matrix, which was also analyzed and plotted as a function of the transmural depth.

#### Statistical analysis and transmural profile modeling.

As a first step to quantify the transmural trend of the FA, all 80 profiles were pooled and analyzed as a single group. To reduce statistical false results originating from excessive comparisons, each FA profile was divided into four equal zones labeled Z1–Z4 starting at the epicardium (Fig. 2*A*). The mean FA values of all 80 profiles across the 4 zones were compared by one-way ANOVA and post hoc Tukey-Kramer tests. Similarly, transmural trends of the primary (*D*_{1}), secondary (*D*_{2}), tertiary (*D*_{3}), and mean (*D*_{av}) diffusion tensor diffusivities were examined. Unless otherwise noted, values are means ± SD, and *P* < 0.05 was considered statistically significant.

Because the FA remained relatively constant from the epicardium to the ventricular midwall and then decreased steadily from the midwall to the endocardium, individual FA transmural profiles were empirically fitted to a step-ramp function (Fig. 2*B*) (1) where *x* is the normalized transmural depth, *y* is the FA value, *y*_{0} is the intercept of *y* at *x* = 0 (i.e., FA at the epicardium), *m* is the slope, and *x*_{0} is the depth of transition. Parameters of the step-ramp function, *x*_{0}, *y*_{0}, *m*, and *R*^{2} (for goodness of fit) were determined by least-squares regression. Each fitted step-ramp parameter (*x*_{0}, *y*_{0}, or *m*) as a function of longitudinal slice and circumferential sector was compared by two-way ANOVA and subsequent Tukey-Kramer tests to examine regional variations of the value and trend of the FA.

To determine whether a correlation exists between the observed trend of the FA and fiber orientation, locations where the fiber orientation helix angle is zero (i.e., myocardial fibers run exactly circumferentially) were determined by linear regression of the helix angle profile. The zero-helix angle location was chosen, since the myocardium on either side exhibits quite different material strain during LV contraction (11, 46). The locations, in terms of normalized transmural depth, were compared with the transition points (*x*_{0}) of the FA profiles by paired Student's *t*-test.

## RESULTS

In Fig. 3*A*, FA profiles obtained for all sectors, slices, and specimens (*n* = 80) are plotted as functions of the normalized transmural depth and overlaid with a bar graph of the FA (mean ± SD) in each of the quartile transmural zones. The FA profiles and the bar graph demonstrate a conspicuous decreasing trend of FA from the epicardium toward the endocardium. FA values for the four zones, starting from the epicardium, are 0.35 ± 0.05, 0.35 ± 0.04, 0.32 ± 0.05, and 0.27 ± 0.06 (mean ± SD, *n* = 80). One-way ANOVA (Table 1) across the four zones for all profiles reveals a significant difference (*P* < 10^{−6}) among the mean FA values. Subsequent Tukey-Kramer tests (Table 1) reveal that the mean FA in Z1 and Z2 are each significantly larger than the mean FA in Z3 and Z4, and the mean FA in Z3 is significantly larger than that in Z4. Mean FA values in Z1 and Z2 are not statistically different.

The individual profiles for *D*_{1}, *D*_{2}, *D*_{3}, *D*_{av}, and NMTE are overlaid with bar graphs of the corresponding zone-averaged values in Fig. 3, *B–F*. The averaged values in zones Z1, Z2, Z3, and Z4 are 1.27 ± 0.13, 1.28 ± 0.13, 1.26 ± 0.01, and 1.24 ± 0.15 × 10^{−3} mm^{2}/s (mean ± SD, *n* = 80) for *D*_{1}, 0.83 ± 0.14, 0.83 ± 0.14, 0.85 ± 0.13, and 0.89 ± 0.14 × 10^{−3} mm^{2}/s for *D*_{2}, 0.64 ± 0.11, 0.64 ± 0.10, 0.67 ± 0.11, and 0.72 ± 0.13 × 10^{−3} mm^{2}/s for *D*_{3}, 0.91 ± 0.12, 0.92 ± 0.12, 0.93 ± 0.12, and 0.95 ± 0.13 × 10^{−3} mm^{2}/s for *D*_{av}, and 0.023 ± 0.008, 0.022 ± 0.007, 0.022 ± 0.006, and 0.022 ± 0.005 for NMTE.

One-way ANOVA (Table 1) on the four zones indicates significant differences in *D*_{2} (*P* = 0.015) and *D*_{3} (*P* = 10^{−5}), but not *D*_{1} (*P* = 0.24), *D*_{av} (*P* = 0.24), and NMTE (*P* = 0.94). Post hoc Tukey-Kramer tests (Table 1) indicate significantly higher *D*_{2} in Z4 than in Z1 and Z2 and significantly higher *D*_{3} in Z4 than in all other zones. As a group, averaged FA of 80 profiles decreases 25.7% from the epicardium to the endocardium, and *D*_{2} and *D*_{3} increase by 7.9% and 12.9%, respectively, over the same length.

Fitting the transmural FA profiles to step-ramp functions and pooling results from all 80 profiles yield averaged intercept, slope, and transition depth of 0.35 ± 0.01, −0.21 ± 0.09, and 0.48 ± 0.05 (mean ± SD), respectively. Moreover, an average *R*^{2} of 0.86 ± 0.10 was obtained, indicating that the fitting quality was reasonably good.

The fitted FA slope, intercept, and transition point, averaged in each sector as functions of circumferential and slice locations, are tabulated in Tables 2, 3, and 4, respectively. Two-way ANOVA for the fitted slope (data not shown) reveals a significant difference among circumferential locations (*P* < 0.003) but not among longitudinal slices (*P* > 0.5). Post hoc comparisons reveal significant differences between the mean slope in the septal region (−0.12 ± 0.02, mean ± SD, *n* = 20) and posterior (−0.26 ± 0.08) and lateral (−0.29 ± 0.07) regions. For the intercept, no significant variation was found among different circumferential or slice locations (*P* > 0.9 in either case). Similarly, no significant dependence was observed for the transition point with respect to circumferential or longitudinal slice locations (*P* > 0.3). In the analyses of all three fitted parameters, interactions between the two variables, circumferential and longitudinal slice locations, are insignificant (*P* > 0.2), which indicates that these two variables are independent.

For the comparison of the zero-fiber orientation helix angle and FA profile transition points, paired Student's *t*-test reveals no significant difference between the two groups (*P* > 0.5). The zero-helix angle for fiber orientation occurs on average at a normalized transmural depth of 0.47 ± 0.06 (mean ± SD, *n* = 80) compared with the average FA profile transition point of 0.48 ± 0.05. Conversely, the average corresponding fiber orientation helix angle at all FA profile transition points is −1 ± 6° (*n* = 80).

## DISCUSSION

### Transmural Heterogeneity of Diffusion Anisotropy

The results reveal heterogeneity in the scalar DTI parameters across the LV myocardial wall. Although the biophysical mechanisms linking the MRI diffusion (and diffusion tensor) measurements to the underlying tissue structure are not perfectly understood, intuitively, the diffusion properties are a function of the intrinsic diffusivities and relative volumes of the intra- and extracellular spaces, including restriction of the water molecular motility imposed by the cellular arrangement (21, 26). Since the DTI primary eigenvector has been correlated to the local myocardial fiber orientation (23, 38), the generally constant primary diffusion tensor eigenvalue (or diffusivity) is consistent with a previous report of no significant difference in myocyte length between transmural LV regions within several animal species (5). The increases in secondary and tertiary DTI diffusivities, which may have been due to reduced restricted diffusion transverse to the myocyte axis, are also in agreement with past histological studies that reported an increase in myocyte cross-sectional radius (∼9.6%) (5) from the epicardium to the endocardium and a decrease in myocyte density accompanied by an increase in extracellular volume fraction (from 0.12 at the epicardium to 0.25 at the endocardium) (27).

Quantitative relationships, both analytic and computer simulation based, between MRI diffusion characteristics and cellular structure have been proposed (26, 43). For example, via the effective medium theory (40), the water diffusivity (*D*_{eff}) of a tissue with cylindrical cells can be related to the cell radius (α), membrane permeability (κ), and extracellular volume fraction (φ) as follows (26) (2) where *x* = (κα*D*_{int}c_{int})/(κα + *D*_{int}c_{int}), c_{eff} = φc_{ext} + (1 − φ)c_{int}, *D*_{int} and *D*_{ext} are the intrinsic intra- and extracellular diffusion coefficients, and c_{int} and c_{ext} are the intra- and extracellular water concentrations. With the use of typical values reported in the literature, κ *=* 10 × 10^{−2} mm/s, *D*_{ext} = 2.5 × 10^{−3} mm^{2}/s, *D*_{int} = 0.7 × 10^{−3} mm^{2}/s (21), c_{ext} = 0.9, c_{int} = 0.7 (26), and α = 10.0 μm (30) at the epicardium and 11.0 μm at endocardium, which corresponds to a 9.6% increase (5), the effective diffusivity transverse to the myocyte axis (based on the geometric mean of the measured DTI secondary and tertiary eigenvalues) at the epicardium (0.75 × 10^{−3} mm^{2}/s) and endocardium (0.83 × 10^{−3} mm^{2}/s) would correspond to extracellular volume fractions of 0.24 and 0.28, respectively, or a 18% increase transmurally. These values are in general agreement with extracellular volume fractions of 0.26–0.28 previously reported for the whole heart (9, 12) but are somewhat higher than the regional measurement of 0.12 for the epicardium (27). Although the above-mentioned computations and volume fraction measurements necessarily depend on the assumptions incorporated (e.g., *D*_{int}, *D*_{ext}, and κ, which were based on in vitro measurements and used here only as a 1st approximation) and experimental technique employed, they demonstrate the plausibility of obtaining quantitative tissue microstructural information (in this case, extracellular volume fraction) from scalar DTI measurements.

In addition to differences in the cellular characteristics (e.g., myocyte size, density, and extracellular space), a second possible explanation for the transmural heterogeneity of the FA is the existence of “complex” tissue structure, such as bifurcating sheet structures in the subendocardium (19). Because of the greater complexity of these structures (i.e., multiple populations of tissues with different cellular properties, including fiber or sheet orientations), longer diffusion time is likely required for water molecules experiencing different subregions of the tissue to become well mixed. Consequently, along with reduced FA, a poorer diffusion tensor goodness of fit is also expected. The results of the NMTE analysis (Fig. 3*F*) reveal that the quality of the tensor estimation remains constant across the ventricular wall. This suggests that the decrease in FA at the endocardium more likely reflects differences in myocyte organization than the presence of complex tissue structure.

Throughout the myocardial wall, the average values of the diffusion tensor eigenvalues, in descending order, are 1.27 ± 0.15 for *D*_{1}, 0.87 ± 0.16 for *D*_{2}, and 0.68 ± 0.14 × 10^{−3} mm^{2}/s for *D*_{3} (mean ± SD, *n* = 1,306,626). The corresponding *D*_{av} is 0.94 ± 0.15 × 10^{−3} mm^{2}/s, and the mean FA is 0.32 ± 0.07. These values are in good agreement with the values reported previously (8, 13, 15, 25, 38). However, only averaged values have been reported in the literature, because those values were considered to be uniform throughout the heart.

### Methodological Considerations

Because DTI measurements are sensitive to changes in tissue microstructure and imaging conditions (particularly signal-to-noise ratio), interpretation of the present results needs to take into account effects of fixation and image noise on the diffusion anisotropy. Similar to alterations in the relaxation times, the MRI apparent diffusivity has been found to decrease significantly as a result of the macromolecular cross-linking associated with fixation, at least for brain tissues (41, 42). However, the changes must have been proportional in all directions (with respect to the tissue structural orientation), such that the principal or preferred axes of diffusion and the relative degree of anisotropy (e.g., FA) are preserved (17, 41, 42). Results in the present study are based on the behavior of FA, an index of anisotropy, and trends of the diffusivity across the myocardial wall. Consequently, although the individual diffusivity measurements may have been lowered by fixation, the observations reported in FA and transmural relative changes in diffusivity (e.g., higher *D*_{2} and *D*_{3} in endocardium than epicardium) likely remain unaffected.

In DTI, it is known that image noise can cause significant bias, by means of overestimation, in the FA of tissue and that the degree of bias is disproportionately larger in tissues such as the myocardium, which have lower intrinsic FA (2, 4, 34). In the present study, the signal-to-noise ratio was measured and found not to be significantly different for the inner and outer halves of the LV in all specimens (data not shown). Moreover, if image noise were a significant factor, it would have caused higher artificial inflation of FA in the endocardium, which has lower intrinsic FA, than in the epicardium and presented only a situation for false-negative observation of transmural difference. Therefore, although image noise likely impacted the accuracy of the current FA measurements similar to all DTI studies, if there is any effect, the observed transmural differences in the FA (i.e., significantly smaller in the endocardium) and transverse diffusivities are likely reflective of the underlying tissue microstructure and represent a lower-limit estimation of the true difference.

### Implications for Cardiac Electrophysiological and Biomechanical Modeling

Studies of cardiac electrophysiology (14, 29) and biomechanics (30, 36), although based on computational anatomic models of the myocardium (31, 45), largely incorporated only the transmural rotation of the fiber orientation and implicitly assumed that material properties of the myocardium are uniform. The present study indicates that not only can these anatomic models be made more robust by incorporating, for example, the varying extracellular volume fraction across the myocardial wall but, also, the tissue microstructural information can possibly be inferred from scalar DTI measurements. Moreover, if different properties are to be assumed for the epicardium and endocardium, the zero-helix angle location (i.e., where the FA transitions from constant to steady decrease) could serve as a convenient criterion for segmenting the tissues.

Cardiac electrophysiological studies have shown that the anisotropic spread of excitation and the potential distribution are greatly affected by the myocyte architecture and the anisotropy ratios of the intra- and extracellular conductivities (14, 29), where the conductivity coefficients are assumed to be constant throughout the myocardial tissue (i.e., the anisotropy of the tissue is uniform). However, there has been evidence of heterogeneity in the transmural conductivity (35, 51), which can be, for example, explained by a heterogeneous gap junction expression (35), but there could also be a change in extracellular space transmurally. The present findings reinforce the necessity to incorporate transmural heterogeneity in cardiac electrophysiological modeling (e.g., by extending the model to heterogeneous conductivity coefficients across the myocardial wall).

The passive mechanical properties of the myocardium are influenced by alterations in myocyte size and function as well as changes in the amount, distribution, and interactions of different types of extracellular collagen matrix (24). In modeling the cardiac mechanics and identifying functional forms and parameters of the constitutive equations, the transmural and regional inhomogeneities of the material properties are usually ignored, and these material parameters are considered constant throughout the heart (11, 30). However, certain model studies have provided evidence against this assumption (46), which again can possibly be improved by incorporating material parameters (e.g., fiber and cross-fiber stiffness) that vary transmurally (16) to reduce the disagreement between experimental measurements and mechanical modeling.

### Summary

Diffusion anisotropy as measured by MR-DTI in the fixed sheep myocardium remained relatively constant from the epicardium to the midwall and then decreased steadily toward the endocardium. The transmural location of the transition coincides with the location where myocardial fibers run exactly circumferentially. There is also a significant difference in the midwall-endocardium FA slope between circumferential regions of the LV. These results are generally consistent with the known cellular microstructure from reported histological studies of the myocardium. Findings of the present study reinforce the need to incorporate transmural variations in the myocardial microstructure in modeling cardiac electrophysiology and biomechanics and suggest that, besides fiber orientation information, additional tissue microstructure parameters such as the extracellular volume fraction can possibly be inferred from MR-DTI measurements.

## GRANTS

This study was supported by Whitaker Foundation Research Grant RG-01-0438 and National Institutes of Health Grants P41 RR-005959 (Y. Jiang and E. W. Hsu), R01-HL-77921 (J. M. Guccione), and R01-HL-63348 (M. B. Ratcliffe).

## Footnotes

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- Copyright © 2007 by the American Physiological Society