Anisotropy in high-resolution diffusion-weighted MRI and anomalous diffusion

It is shown below that complex diffusion anisotropy observed in diffusion-weighted MRI can be fully accounted for by allowing for non-locality of the spatial operator in the diffusion equation. The anisotropy is represented by a distribution over directions on a sphere. It allows recognition of fiber tracts crossing at arbitrary angles. A simple generalization of the Stejskal-Tanner equation for the determination of the ODF is presented. Furthermore, an explicit solution of the Bloch-Torrey equation for an anisotropic time-fractional diffusion equation is obtained in terms of a generalized Mittag-Leffler type function.