Abstract
Functional properties of the myocardium are mediated by the tissue structure. Consequently, proper physiological studies and modeling necessitate a precise knowledge of the fiber orientation. Magnetic resonance (MR) diffusion tensor imaging techniques have been used as a nondestructive means to characterize tissue fiber structure; however, the descriptions so far have been mostly qualitative. This study presents a direct, quantitative comparison of highresolution MR fiber mapping and histology measurements in a block of excised canine myocardium. Results show an excellent correspondence of the measured fiber angles not only on a pointbypoint basis (average difference of −2.30 ± 0.98°, n = 239) but also in the transmural rotation of the helix angles (average correlation coefficient of 0.942 ± 0.008 with average falsepositive probability of 0.004 ± 0.001, n = 24). These data strongly support the hypothesis that the eigenvector of the largest MR diffusion tensor eigenvalue coincides with the orientation of the local myocardial fibers and underscore the potential of MR imaging as a noninvasive, threedimensional modality to characterize tissue fiber architecture.
 magnetic resonance imaging
 diffusion tensor
 anisotropic diffusion
functional properties of tissues are highly dependent on the tissue structure. Although the exact biophysical mechanisms are not fully understood, the nonuniformity and rotational anisotropy of fiber structure in the heart play important roles in both its electrical and mechanical performance. Myocardial architecture is known to affect the initiation and maintenance of reentrant arrhythmias (6,9) and also the mechanical coupling associated with systolic wall thickness changes (17, 34). In most cases, the alteration in fiber structure is a dynamic process that accompanies healing or remodeling. For example, during healing of an infarcted region, the fibers arrange themselves in a parallel orientation and are usually not aligned with the fibers outside the border zone (32). The fibers can be packed tightly or separated by edema, and the regions can exhibit increased fibrosis. The overall changes produce abrupt transitions in the tissue structure and material properties that may facilitate mechanical failure (1) or conduction anomalies, particularly in regions of depressed excitability (37).
Characterization and identification of subtle changes in fiber architecture at submillimeter resolution have been challenging, as standard histological techniques are destructive and require special tissue preparation (e.g., fixation and sectioning). As a result, little information is available regarding the threedimensional fiber architecture associated with a given pathology. Magnetic resonance (MR) diffusion tensor imaging has recently been proposed as a method to noninvasively map fiber structure (4). The technique, in general, involves a pixelbypixel estimation of the eigenvectors of the diffusion tensor (a 3 × 3 symmetrical matrix) from multiple MR images with diffusion encoded in at least six directions. The procedure can be simplified if, for example, cylindrical symmetry of diffusion is established in the sample (7, 12). In addition to applications in studying the brain (5, 23, 24) and a variety of musculature (4, 7, 12,33), the MR technique has been used to characterize fiber organization in the myocardium (10, 25). In most cases, the results were qualitatively consistent with the gross tissue fiber orientation; however, none has been rigorously correlated to histology or other established measures of fiber orientation. A direct correlation is required to determine the accuracy of the MR methodology and to establish the validity of MR data in quantitative, highresolution studies of the functional anatomy of tissues.
The goal of the present study is thus to test the fundamental hypothesis in MR fiberorientation mapping via diffusion tensor measurements: the eigenvector corresponding to the largest eigenvalue of the calculated diffusion tensor coincides with the fiber orientation. In this, fiber orientation is measured using both MR imaging (MRI) and conventional histological techniques in the same block of excised myocardium, and the results are quantitatively compared at multiple sites.
THEORY: MR FIBERORIENTATION MAPPING
To refine the methodology and for the sake of completeness, we include the theoretical basis of MR fiberorientation mapping.
Nuclear magnetic dipoles (or spins) precess about the axis of an applied magnetic field at a frequency proportional to the magnitude of the field. Random translational motion such as diffusion in the presence of a magnetic field gradient causes an irreversible loss of precession coherence, resulting in an attenuation of the MR signal. Because gradients are used to encode both spatial and diffusion information, accurate quantitation of diffusion necessitates accounting for the effects of all gradient pulses, including cross terms (14, 20) describing interactive effects between different gradient pulses. Expressions for the signal attenuation due to anisotropic diffusion for an arbitrary gradient waveform have been reported previously, using a diffusion tensor notation (3, 28). Although this generalized formalism is particularly useful for analyzing pulse sequences that have significant cross terms between gradient pulses, they are relatively complicated to calculate (e.g., must be reevaluated when an imaging parameter, such as time to echo or field of view, is changed) and often require approximation using numerical methods.
Alternatively, it has been shown (12) by using a threedimensional randomwalk model that the diffusion signal attenuation in a spinecho experiment at time of echo t = TE is given by
In the case when the diffusionencoding gradients in different axes are identical in timing and differ only in their relative amplitude, the encoding gradient vector G = [G
_{ξ}(t),G
_{η}(t),G
_{ζ}(t)]^{T}can be written as G = (g
_{ξ}, g
_{η}, g
_{ζ})^{T}
G(t) where T is a transpose operation in linear algebra. Expressing
METHODS
Myocardial sample preparation.
All animal procedures were approved by the Duke University Institutional Animal Care and Use Committee. The heart of a mongrel dog (26 kg) was isolated, thoroughly rinsed, and maintained in chilled Ringer solution. A block of myocardium (1.7 × 2.0 cm) oriented parallel to the left anterior descending coronary artery was excised from the free wall of the right ventricle, as shown schematically in Fig. 1. Three 10mmlong, thin plastic tubing segments were inserted through the tissue block perpendicular to the epicardium, in a triangular pattern, to serve as reference markers for registration. The edge nearest the base of the heart was painted with alcian blue dye for identification. The tissue block was then encased in a 1.8cmdiameter, 3.0cmlong plastic cylinder (cut from a 20ml syringe) filled with Ringer solution.
MR diffusion tensor imaging.
Imaging experiments were conducted on an Oxford 7.1T instrument (20°C bore temperature) interfaced with an Omega console (General Electric NMR Instrument, Fremont, CA). The sample was placed inside a 2.1cmdiameter loopgap radio frequency (RF) coil. Using the reference markers to locate slice positions, we acquired multislice (4 slices, 1.5mm slice thickness, 2.0mm slicetoslice separation) images (30mm field of view, 128 × 64 zerofilled to 128 × 128 matrix size, 1s repetition time between 90° RF pulses, 50ms time to echo, 4 averages) containing a shortaxis view of the myocardium using a modified spinecho pulse sequence as shown in Fig.2. Anisotropic diffusion was encoded using bipolar halfsine gradient pulses (δ = 7 ms, Δ = 12 ms) placed on either side of the 180° RF pulses, in each of six directions g ^{T}∈ [(1,1,0), (0,1,1), (1,0,1), (−1,1,0), (0,−1,1), (1,0,−1)], with gradient amplitudes of 3, −3, 10, −10, 20, −20, 25, and −25 G/cm in each direction. Pairwise positivenegative diffusion gradient amplitudes were used to eliminate inadvertent cross terms between diffusion and static background gradients (which should be distinguished from those associated with spatial encoding gradient pulses) by taking the geometric mean (square root of the sum of squares) of the image intensities (21). A total of 48 diffusionweighted images was acquired in ∼3.5 h.
Geometricmean images were calculated for each pair of images obtained with the same amplitude but opposite polarities of diffusion gradients. The elements of the diffusion tensor were estimated on a pixelbypixel basis over the tissue region according to Eqs.35 , using a customcoded multivariate nonlinear leastsquares curvefitting algorithm. The eigenvalues and eigenvectors of the diffusion tensor were subsequently calculated and visualized using MATLAB (MathWorks, Natick, MA) and AVS (Advanced Visual Systems, Waltham, MA). The eigenvalues were sorted, and the means and SDs of both original and normalized (pixelwise to the largest eigenvalue) values were determined over all fitted pixels. The eigenvectors were displayed as threedimensional unit vectors in their pixel locations. To make the viewing plane consistent with that of histological measurements, we transformed the fiber angles (i.e., eigenvector of the largest eigenvalue) and displayed them in planes parallel to the epicardium.
Histological correlation.
Immediately after MRI data acquisition, the tissue block was removed from the holder and pinned to corkboard using four stainless steel Tpins (Labelon; 1 in each corner) to minimize tissue deformation during fixation. A gap was left between the tissue and corkboard so fixative could penetrate from all sides of the sample. Digital photographs were taken of the pinned block from directly above the epicardium. The block was then placed, epicardial side down, inside a large container filled with 10% buffered Formalin and left undisturbed for 24 h. Subsequently, the tissue was removed from the corkboard and placed in a container of fresh Formalin for another 24 h. After the tissue was embedded in paraffin wax, serial sections (parallel to the epicardial surface, 6μm thickness) were made. Sections at each 0.5mm interval through the wall were slidemounted and stained with hematoxylin and eosin.
Each stained tissue section was digitized using a highresolution microscopy slide scanner [Polaroid, with a scan resolution of 1,375 dots per inch (dpi)]. Scanned sections were converted to 8bit grayscale images using imageprocessing software (Signal Analytics, Vienna, VA). To ensure alignment of the serial sections, we registered the section images with each other in software using the reference markers. Images were then calibrated using the measured distance between reference marks to determine the appropriate scaling (i.e., number of pixels/μm). A rectilinear grid (1.0mm spacing) was overlaid on each section image within the three reference holes. Histology fiber angles (α_{hist}) were measured on four rows (corresponding to the no. of MRI image slices) and, to avoid tissue borders that were prone to histological artifact, on six columns of points near the center. The convention for α_{hist} was the same as that used by Streeter and Basset (31) in describing the helix angle of fiber orientation viewed from the epicardium; for example, +90° (righthanded system) denoted the direction toward the base of the heart.
The MRI data (i.e., eigenvectors of the largest eigenvalues, projected onto a plane parallel to the epicardium) were registered, overlaid directly onto the corresponding histology section images, and converted to angular form (α_{mri}). The SDs of α_{mri} and α_{hist} over a region of relatively uniform fiber orientation were used as an upperbound estimate of the measurement random errors. The α_{mri} and α_{hist} at respective (or closest) measurement points were compared by calculating the difference between the angles, d
_{α}= α_{hist} − α_{mri}, for all points in all planes. To examine the transmural rotation of fiber orientation, we graphed α_{mri} and α_{hist} for each measurement point separately as functions of depth from the epicardium, and the linear (Pearson’s) correlation coefficient rwas determined for the pair of curves. The significance of the coefficient P_{r}
(the probability that the observed rhad occurred by chance alone) was estimated according to intended meaning: according to Eq. 6 in Ref. 2
RESULTS
The average sorted MR diffusion tensor eigenvalues (in descending order) were found to be 0.94 ± 0.28, 0.74 ± 0.27, and 0.63 ± 0.24 × 10^{−3}mm^{2}/s (mean ± SD,n = 8,384 each). When the values were pixelwise normalized to the largest eigenvalue, the second and third eigenvalues were 0.785 ± 0.081 and 0.664 ± 0.095, respectively. The SD, as a percentage of the mean, is reduced dramatically by the normalization, indicating that the eigenvalues (i.e., diffusivities) are relatively heterogeneous within the excised block of myocardium.
Representative shortaxis view, threedimensional plots of the three diffusion tensor eigenvectors (from the MR image slice nearest to the base, viewed from an elevated angle) are shown in Fig.3. A counterclockwise transmural rotation is evident in the eigenvector of the largest eigenvalue. Although the behavior of the transverse (i.e., 2nd and 3rd) eigenvectors is less systematic than that of the first, a consistent organization is discernible, particularly in the midwallepicardial half of the tissue block.
Two representative histology section slice images, overlaid with MRI fiber angles, at different depths (2.0 ± 0.5 and 4.5 ± 0.5 mm) from the epicardium are displayed in Fig.4. Because MRI data were acquired in transmural (i.e., short axis) planes, they represent four rows of vectors on the images. The asterisks on the images correspond to the locations where α_{mri} and α_{hist} were compared. The random errors in the measurements of α_{mri} and α_{hist} were estimated to be 5.6 and 6.5°, respectively. The graphs in Fig.5 show the transmural change of α_{mri} and α_{hist} at the four locations marked in Fig. 4 (sites a,b, c, and d). At each site, both α_{mri} and α_{hist} exhibit the classical counterclockwise rotation with depth.
Histograms summarizing the fiber angle difference and the correlation coefficient analyses are presented in Figs.6 and 7, respectively. The distribution ofd _{α} of all measurements in all planes reveals an average of −2.30 ± 0.98° (average ± SE, n = 239,P < 0.02 by Student’sttest to the zeromean hypothesis), with an SD of 15.3°. The average correlation coefficient andP_{r} of the fiber angles as functions of depth among the 24 measurement sites are 0.942 ± 0.008 and 0.004 ± 0.001, respectively. The average means of the individual α_{mri} and α_{hist} curves are found to be 65.7 ± 1.4 and 62.9 ± 1.8° (average ± SE,n = 24,P > 0.10), and their average SDs are 36.1 ± 1.3 and 38.4 ± 1.2° (P > 0.10), respectively. Although these average values carry little physical significance, they indicate that the transmural behaviors of α_{mri} and α_{hist} are comparable, in terms of offsets and relative amplitudes of the curves.
DISCUSSION
To our knowledge, the present study demonstrates for the first time that highresolution MR fiberorientation mapping can be directly and quantitatively compared with results from standard histological techniques. The results in general show an excellent correlation between the two methods. Pointbypoint comparisons of angles revealed a low (albeit significant) average difference of −2.3 ± 1.0°, and analysis of transmural fiber rotation showed an average correlation coefficient of 0.942 ± 0.008 and an averageP_{r} (probability of falsepositive correlation) of 0.004 ± 0.001. These data strongly support the hypothesis that the eigenvector of the largest diffusion tensor eigenvalue is parallel to the local fiber orientation.
Although these results are promising for the use of MRI in characterizing tissue fiber orientation, several factors can be identified in the present study that may adversely affect the correlation. First, each α_{mri}and α_{hist} measurement has an uncertainty of ∼6° due to random error. Second, although the tissue block was pinned during fixation, visual inspection of the sample revealed that small degrees of shrinkage and deformation had occurred in the tissue block. The shrinkage is evident by the small discrepancy in the areas spanned by the MR and histology section images in Fig. 4. The histology sections close to the epicardium reveal that deformation caused the microtome blade angle not to be perfectly parallel to the entire epicardial surface. Furthermore, there may have been some internal deformation (e.g., transverse shear) within the tissue block. Although the degrees of shrinkage and deformation were not quantified, the empirical close correlation between MR and histological measurements indicates that their combined effects are small.
Because magnetic field gradients are used to encode both diffusion and spatial information, the accuracy of MR fiberorientation mapping critically depends on the ability to separate the effects of individual encoding gradients and cross terms between different gradients. The present study differs from previously reported MR diffusion tensor imaging techniques in that cross terms are eliminated or minimized by modifications in the pulse sequence, rather than by providing additional terms in the quantitation of signal attenuation. Although this approach may not impact on the accuracy of MR diffusion tensor mapping, it provides an easier and more direct measure of anisotropic diffusion. For example, the diffusion weighting factor scales directly with the square of the diffusion encoding gradient amplitude, independent of changes in the imaging parameters. Moreover, the estimated diffusion coefficient in an arbitrary diffusion encoding direction corresponds directly to the sum of the diffusivities in the principal axes of diffusion, weighted by the squares of directional cosines (i.e., cosines of the angles between the encoding direction and the principal axes) (12). However, the allowable diffusion time (Δ in Fig. 2) is limited by the use of bipolar diffusion gradients (especially in conjunction with sliceselective refocusing RF pulses), which may reduce the dynamic range of the diffusion weighting factor.
Analysis of the eigenvalues reveals that the transverse (i.e., 2nd and 3rd) eigenvalues are appreciably smaller than the largest eigenvalue, with the average normalized eigenvalues more than 2.5 SDs below unity. The existence of a preferred direction of diffusion, combined with the behavior of its eigenvector, supports the assumption that the largest eigenvalue of the diffusion tensor corresponds to the diffusivity along muscle fibers. However, the difference between the normalized transverse eigenvalues (0.785 ± 0.081 vs. 0.664 ± 0.095) is relatively small. Although it is possible that the apparent difference in the transverse eigenvalues reflects a consequence of sorting, their respective eigenvectors (Fig. 3), particularly those close to the epicardium, exhibit some form of organization, suggesting that there may be a physical correlation between the transverse eigenvalues (and eigenvectors) and myocardial tissue structure. It has been suggested recently (16) that ventricular myocardium possesses three distinct material property axes (i.e., orthotropic with respect to the long axis of the fibers), which may have implications for characterizing electrophysiological and mechanical properties of the tissue. With improved accuracy (e.g., by acquiring more data points for the diffusion tensor calculation), MRI may provide some insight into the anatomic basis for these proposed transversely orthotropic material properties.
The present study underscores the potential of MR diffusion tensor imaging as a nondestructive means to determine myocardial fiber architecture without requiring tissue fixation, albeit current technical difficulties of diffusionweighted MRI associated with motion may limit the applications to studying arrested or in vitro heart preparations. Although myocardial fiber angle has been measured quantitatively in intact hearts (2931), fiber directions at more than a few sites in both right and left ventricles have been reported only once (22). A particular difficulty of the methods employed in these studies was in accurately reconstructing fiber structure in regions where it changed rapidly or was discontinuous. The noninvasive, highresolution MR approach is better suited for estimating the fiber architecture not only in these regions but also in areas subject to injury where myocardial infarction or remodeling have altered the local tissue structure (8, 13, 18), creating a region of anisotropic collagenous scar (35, 36). Alternatively, fiber structural information has recently been obtained using an electrophysiological approach, where maps of the electrical activity over a small epicardial region recorded during pacing (from the surface and in the wall) reveal both the surface and intramural fiber orientation (19). Comparative studies using the pacemapping strategy and MR diffusionweighted imaging may help us better understand the strengths and drawbacks of these techniques, as well as further elucidate the link between tissue architecture and material properties of the myocardium. Finally, the MR technique may also be used in evaluating the structure of atrial myocardium, which has not been described as completely (in a mathematical sense) as has been done for the ventricles (15). However, a detailed description of the atrial geometry and fiber architecture is very much desirable, as electrophysiological recordings from the atria have shown that their complex structure plays a role in atrial conduction patterns (26, 27) and likely contributes to the genesis and maintenance of atrial arrhythmias (11).
In summary, fiber orientation was measured using both MR diffusion tensor imaging and conventional histological techniques. Direct, quantitative comparisons revealed an excellent correlation of measurements. The data support the hypothesis that the eigenvector of the largest diffusion tensor eigenvalue corresponds to the local fiber orientation. The results highlight the utility and validity of the MR diffusion tensor imaging methodology as a threedimensional, noninvasive means to elucidate tissue architecture, particularly in evaluating myocardial structural changes that are linked to electrical or mechanical dysfunction.
Acknowledgments
The authors gratefully acknowledge the support and advice of Dr. G. A. Johnson and Dr. P. Basser and the technical and editorial assistance of E. DixonTulloch and E. Fitzsimons.
Footnotes

Address for reprint requests: E. W. Hsu, Center for In Vivo Microscopy, Duke Univ. Medical Center, DUMC Box 3302, Durham, NC 27710.

This work was funded in part by National Institutes of Health Grant P41RR05959, National Science Foundation (NSF) Engineering Research Center Grant CDR8622201, and NSF Grant BCS93–09181.
 Copyright © 1998 the American Physiological Society