Characterizing the distribution of anisotropic micro-structural environments with diffusion-weighted imaging (DIAMOND).

Diffusion-weighted imaging (DWI) enables investigation of the brain microstructure by probing natural barriers to diffusion in tissues. In this work, we propose a novel generative model of the DW signal based on considerations of the tissue microstructure that gives rise to the diffusion attenuation. We consider that the DW signal can be described as the sum of a large number of individual homogeneous spin packets, each of them undergoing local 3-D Gaussian diffusion represented by a diffusion tensor. We consider that each voxel contains a number of large scale microstructural environments and describe each of them via a matrix-variate Gamma distribution of spin packets. Our novel model of DIstribution of Anisotropic MicrOstructural eNvironments in DWI (DIAMOND) is derived from first principles. It enables characterization of the extra-cellular space, of each individual white matter fascicle in each voxel and provides a novel measure of the microstructure heterogeneity. We determine the number of fascicles at each voxel with a novel model selection framework based upon the minimization of the generalization error. We evaluate our approach with numerous in-vivo experiments, with cross-testing and with pathological DW-MRI. We show that DIAMOND may provide novel biomarkers that captures the tissue integrity.