Tissues with regularly ordered microstructure, such as skeletal muscle, spine, tongue, heart, and cerebral white matter, exhibit anisotropic water diffusion due to the alignment of the diffusion compartments in the tissue (1–7). The direction of preferred diffusion, and hence the direction of preferred orientation in the tissue, can be resolved with a method called magnetic resonance (MR) diffusion tensor imaging (DTI) (7), which measures the apparent water self-diffusion tensor under the assumption of Gaussian diffusion. Based on the eigenstructure of the measured diffusion tensor, it is possible to infer the orientation of the diffusion compartments within the voxel so that, for example, the major eigenvector of the diffusion tensor parallels the mean fiber orientation (7), and the minor eigenvector parallels the normal to the mean plane of fiber dispersion (8).

The tensor model is incapable, however, of resolving multiple fiber orientations within an individual voxel. This shortcoming of the tensor model stems from the fact that the tensor possesses only a single orientational maximum, i.e., the major eigenvalue of the diffusion tensor (9, 10). At the millimeter-scale resolution typical of DTI, the volume of cerebral white matter containing such intravoxel orientational heterogeneity (IVOH) may be considerable given the widespread divergence and convergence of fascicles (11–13). The abundance of IVOH at the millimeter scale can be further appreciated by considering the ubiquity of oblate (pancake-shaped) diffusion tensors in DTI, a hypothesized indicator of IVOH (3, 4, 8).

Given the obstacle that IVOH (particularly fiber crossing (14–16)) poses to white matter tractography algorithms (14–20), we sought to determine whether high angular resolution, high *b*-value diffusion gradient sampling could resolve such intravoxel heterogeneity (9). High *b*-values were employed because at the lower *b*-values conventionally employed by DTI there is insufficient contrast between the fast-diffusion component of one fiber and the slow-diffusion component of another fiber to effectively resolve the two fibers (10). Using high angular resolution, high *b-*value diffusion gradient sampling, we were able to detect diffusion signals with multiple, discrete maxima/minima as a function of gradient orientation, indicating the presence of multiple underlying fiber populations. Such IVOH has recently been hypothesized (3, 8) to manifest in DTI in the form of oblate diffusion tensors, i.e., diffusion tensors in which the first eigenvalue is comparable to the second, and both are much larger than the third. Here, we found that the non-Gaussianity of the observed diffusion signal (a measure of disagreement with the tensor model) increased with an increase in the oblateness of the measured diffusion tensor. This finding provides preliminary support for the hypothesis that oblate diffusion tensors in DTI arise from IVOH.

The detection of multimodal diffusion signals indicates the presence of IVOH, but it does not resolve the underlying directions of enhanced diffusion. To do so, the diffusion signal was modeled as arising from a discrete mixture of Gaussian diffusion processes in slow exchange (a mixture of tensors). The distribution of tensors within each voxel was solved for using a gradient descent algorithm, which revealed multiple intravoxel fiber orientations corresponding to known fiber anatomy, and consistent with the neighboring fiber anatomy.