INTRODUCTION

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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 three-dimensional 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 pixel-by-pixel 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, high-resolution studies of the functional anatomy of tissues.

The goal of the present study is thus to test the fundamental hypothesis in MR fiber-orientation 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 FIBER-ORIENTATION MAPPING

To refine the methodology and for the sake of completeness, we include the theoretical basis of MR fiber-orientation 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 three-dimensional random-walk model that the diffusion signal attenuation in a spin-echo experiment at time of echo t = TE is given by

(1)

where  is a math integration dummy variable, , , and  denote the principal axes of diffusion, D is the diffusivity, G is the time-varying magnetic field gradient, and  is the spin gyromagnetic constant. Equation 1 indicates that the attenuation from diffusion-encoding gradient pulses can be independently evaluated, provided that stationary spins are refocused [i.e., G()d = 0] immediately before and after the pulses. Consequently, the attenuation due to the imaging (spatial-encoding) gradients can be factored out and treated as a constant, and the cross terms between the imaging and diffusion-encoding gradients are eliminated. For simplicity, G shall denote only the diffusion-encoding gradient in the following sections.

In the case when the diffusion-encoding gradients in different axes are identical in timing and differ only in their relative amplitude, the encoding gradient vector G = [G(t),G(t),G(t)]^T can be written as G = (g, g, g)^TG(t) where T is a transpose operation in linear algebra. Expressing

(2)

the signal attenuation equation reduces to

(3)

where D denotes diagonal matrix. From the convention in one-dimensional diffusion analysis, the scalar u^T · D · u is equivalent to the apparent (time-averaged) diffusion coefficient (ADC), and ² [G()d]²dt is the diffusion weighting factor for each encoding gradient used. In the general case when the laboratory x-y-z coordinate system is different from the principal diffusion system, the laboratory gradient vector g can be mapped into the -- system via a linear transformation, u = Eg (E is an orthonormal matrix). The ADC then becomes

(4)

The center term corresponds to the apparent diffusion tensor D

(5)

The elements of the tensor can be selectively weighted in the MR signal by choosing the appropriate diffusion-encoding direction g = (g_x, g_y, g_z)^T. For example, using only the x gradient [i.e., g = (1,0,0)^T] yields ADC = D_xx. According to Eq. 5, the eigenvalues and eigenvectors of the diffusion tensor represent the diffusivities and orientations, respectively, of the principal diffusion axes.

	METHODS

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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 10-mm-long, 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 1.8-cm-diameter, 3.0-cm-long plastic cylinder (cut from a 20-ml syringe) filled with Ringer solution.

View larger version (31K): [in this window] [in a new window]   Fig. 1.   A schematic showing location and orientation of tissue sample on right ventricle (RV). The rectangular myocardial sample was excised mostly parallel to the left anterior descending coronary artery and had a size of 1.7 × 2.0 × 0.55 cm. The 3 circles on the epicardial surface indicate positions of the registration reference markers.

MR diffusion tensor imaging. Imaging experiments were conducted on an Oxford 7.1-T instrument (20°C bore temperature) interfaced with an Omega console (General Electric NMR Instrument, Fremont, CA). The sample was placed inside a 2.1-cm-diameter loop-gap radio frequency (RF) coil. Using the reference markers to locate slice positions, we acquired multislice (4 slices, 1.5-mm slice thickness, 2.0-mm slice-to-slice separation) images (30-mm field of view, 128 × 64 zero-filled to 128 × 128 matrix size, 1-s repetition time between 90° RF pulses, 50-ms time to echo, 4 averages) containing a short-axis view of the myocardium using a modified spin-echo pulse sequence as shown in Fig. 2. Anisotropic diffusion was encoded using bipolar half-sine gradient pulses ( = 7 ms,  = 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 positive-negative 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 diffusion-weighted images was acquired in ~3.5 h.

View larger version (52K): [in this window] [in a new window]   Fig. 2.   A modified spin-echo pulse sequence for generating cross term-free diffusion-weighted images. Modifications include placing imaging phase and read-dephase gradient pulses immediately before the readout pulse, and using bipolar, half-sine gradient pulses (shaded regions) to encode diffusion. The diffusion weighting factor is 82G22(  /4)/2 for each encoding gradient used. G is gradient pulse amplitude,  is gradient pulse width,  is pulse separaton,  is spin gyromagnetic ratio, RF is radio frequency, and Gx, Gy, and Gz are gradients in x, y, and z directions. See THEORY: MR FIBER-ORIENTATION MAPPING for details.

Histological correlation. Immediately after MRI data acquisition, the tissue block was removed from the holder and pinned to corkboard using four stainless steel T-pins (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, 6-µm thickness) were made. Sections at each 0.5-mm interval through the wall were slide-mounted and stained with hematoxylin and eosin.

(6)

	RESULTS

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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 × 10³ mm²/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 short-axis view, three-dimensional 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 midwall-epicardial half of the tissue block.

View larger version (34K): [in this window] [in a new window]   Fig. 3.   Representative short-axis views of the 3 diffusion tensor eigenvectors determined by magnetic resonance imaging (MRI). Vectors shown in A, B, and C correspond to eigenvectors of largest, middle, and smallest diffusion tensor eigenvalues, respectively, taken from MRI image slice closest to base of heart. Eigenvectors are drawn as 3-dimensional unit vectors at their pixel locations and are viewed from an elevated perspective [epicardium (Epi) toward endocardium (Endo)] as illustrated by axes shown at bottom of C.

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 _mri and _hist were compared. The random errors in the measurements of _mri and _hist were estimated to be 5.6 and 6.5°, respectively. The graphs in Fig. 5 show the transmural change of _mri and _hist at the four locations marked in Fig. 4 (sites a, b, c, and d). At each site, both _mri and _hist exhibit the classical counterclockwise rotation with depth.

View larger version (165K): [in this window] [in a new window]   View larger version (142K): [in this window] [in a new window]   Fig. 4.   Photographs of histological sections with superimposed fiber directions (dark lines) obtained from MR diffusion tensor imaging. The slices were obtained at depths (from epicardial surface) of 2.0 mm (A) and 4.5 mm (B). Locations of registration markers are denoted by black-outlined circles. Additional holes in tissue block (e.g., in A) were created by steel pins used during fixation. Sites where histology fiber angles at all depths were quantitatively measured and compared with MRI results are represented by asterisks in A. Sites a, b, c, and d are locations where data in Fig. 5 were obtained.

View larger version (23K): [in this window] [in a new window]   Fig. 5.   Fiber orientation determined from MRI and histology as a function of depth at 4 locations in tissue block. A-D correspond to sites a-d, respectively, from Fig. 4A. A right-handed convention, with +90° pointing toward base of heart, was used. The classical counterclockwise rotation of fiber orientation from epicardium to endocardium is evident at all sites with both methods.

Histograms summarizing the fiber angle difference and the correlation coefficient analyses are presented in Figs. 6 and 7, respectively. The distribution of d of all measurements in all planes reveals an average of 2.30 ± 0.98° (average ± SE, n = 239, P < 0.02 by Student's t-test to the zero-mean hypothesis), with an SD of 15.3°. The average correlation coefficient and P_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 _mri and _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 _mri and _hist are comparable, in terms of offsets and relative amplitudes of the curves.

View larger version (53K): [in this window] [in a new window]   Fig. 6.   Histogram of difference in fiber orientation angle measured by MRI and histology (d = hist  mri). Number of comparisons (n), mean difference (), and SD () are included. Data were taken from the locations marked with asterisks in Fig. 4A, in all section slice depths. Isolated points compromised by obvious histological artifacts were omitted.

View larger version (34K): [in this window] [in a new window]   Fig. 7.   Histogram of linear correlation coefficient (r) between MRI and histology fiber orientations as functions of depth. Data were based on the 24 measurement sites marked with asterisks in Fig. 4A.

	DISCUSSION

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To our knowledge, the present study demonstrates for the first time that high-resolution MR fiber-orientation 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. Point-by-point 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 average P_r (probability of false-positive 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 _mri and _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 fiber-orientation 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 ( in Fig. 2) is limited by the use of bipolar diffusion gradients (especially in conjunction with slice-selective 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 diffusion-weighted 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 (29-31), 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, high-resolution 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 pace-mapping strategy and MR diffusion-weighted 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 three-dimensional, noninvasive means to elucidate tissue architecture, particularly in evaluating myocardial structural changes that are linked to electrical or mechanical dysfunction.