Diffusion tensor imaging (DTI) is widely used for structural characterization of the heart. One metric, the fractional anisotropy (FA), describes the macroscopic average of the microscopic diffusion tensors. While this is sensitive to tissue anisotropy, FA is also influenced by orientation dispersion. In the heart, a transmural variation in helix angle of the cardiomyocytes is observed¹, along with the presence of multiple cell populations in regions such as the intersection of the left and right ventricles (LV and RV), and the apex². Both situations give rise to a decrease in FA due to the orientation dispersion of cells within a voxel. In contrast, the double diffusion encoding (DDE) method enables measurement of the microscopic FA (µFA) that describes the underlying anisotropy insensitive to orientation dispersion^3,4. We propose µFA as a more robust measure of cardiomyocyte integrity in the heart than FA, and assess this with simulations and ex vivo MRI.

3D Monte Carlo simulations of diffusion were performed along a 1D transmural profile in the simulated LV wall. Cardiomyocytes were simulated as impermeable cylinders with diameters of 10 μm using the Camino software^5,6. These were arranged in a parallel manner within sheets. Sheets were then layered across the myocardial wall, with a similar range of helix angles (α) as reported by Streeter, et al¹. The helix angle distribution is described below, where s = normalized wall thickness. Simulated free diffusivity was set to 1.0e^-3 mm²/s and diffusion timings were similar to those in the ex vivo MRI experiments.

$$\alpha=90^\circ \times \frac{{log(1-s) - log(s)}}{\parallel log(1-s)-log(s) \parallel}$$

One heart was excised from a female Sprague-Dawley rat, fixed in 4% paraformaldehyde and embedded in a tube of 1% agarose gel for MRI. Imaging was performed on a 4.7 T preclinical scanner (Agilent Technologies, Santa Clara, CA) with a 12 cm bore using a transmit-receive quadrature coil. DDE and DTI data were acquired with a 2D spin echo double pulsed field gradient (dPFG) sequence with bipolar diffusion encoding. The DDE parameters were: TR/TE = 3000/30 ms, matrix = 96 x 96, in-plane resolution = 0.17 mm, slice thickness = 2 mm, #B0 images = 3, #DW images = 72 with gradient direction pairs arranged for rotationally invariant sampling³, δ = 4 ms, Δ = 5 ms, mixing time, τ = 13 ms, b-value = 2,000 s/mm², acquisition time = 6 h. The DTI parameters differed from the DDE as follows: #DW images = 12, b-value = 1,000 s/mm². FA and µFA were calculated in the simulated and experimental data³ using custom code in Matlab (Mathworks, Natick, USA).

Figure 1A illustrates the helix angles across a 1D profile in the simulated LV wall. Figure 1B shows the FA and µFA across the same profile. We find that FA was consistently lower than µFA, particularly in regions where the rate of change in helix angle was greatest. In contrast, µFA was consistent across the full LV wall thickness. Figures 2A and 2B depict the FA and µFA maps in a mid-myocardial short axis slice of an ex vivo rat heart. We found that FA = 0.31 ± 0.07 and µFA = 0.34 ± 0.05 across the entire slice. Lower FA was observed particularly where the LV and RV intersect. This heterogeneity was not seen in the µFA data. Figure 3A shows that the helix angle profile across the lateral wall of the LV is approximately linear. The corresponding FA was lower than µFA (Figure 3B), consistent with the sensitivity of FA to orientation dispersion. The shapes of the FA and µFA were similar, suggesting a transmural variation in intrinsic diffusion anisotropy.The simulations show that FA is sensitive to transmural variation in helix angle (dα/ds), and is consistently underestimated relative to the µFA. On the other hand, µFA is stable and consistent with the simulated diffusion anisotropy. A wide range of dα/ds have been described in the literature, ranging from non-linear to almost linear behavior. This is dependent on species⁷ and contraction state². The experimental data show that dα/ds was predominantly linear across the LV wall, and explains the indistinct transmural variation in FA. However, FA was lower in regions where the LV and RV wall intersect, as is consistent with the presence of multiple cell populations. µFA was generally higher and more homogeneous than FA as might be expected in healthy myocardium. We have demonstrated a technique for measuring intrinsic diffusion anisotropy in the heart that is insensitive to the macroscopic orientation dispersion effects that confound DTI measurements.