DIAMOND: a novel biophysical diffusion model that characterizes the distribution of anisotropic micro-structural environments with DWI

Theory. We propose a novel biophysical model of the diffusion signal. Inspired by the ADC approach of [1], we consider measurements of the signal arising from a large number of individual homogeneous spin packets within a voxel. However, in contrast to the 1D model of [1], we model the 3-D Gaussian diffusion of each homogeneous spin packet with a full diffusion tensor , capturing the 3-D structure of the local restriction to diffusion. Furthermore, we consider that each voxel is composed of large scale microstructural environments (LSME) (or compartments) (Fig 1a), and that each compartment has in turn some degree of heterogeneity (Fig 1b) and is therefore described by a continuous distribution of homogeneous spin packets. More precisely, each LSME composition is described with a matrix-variate Gamma distribution of spin packets, which is a peak-shaped probability distribution defined over the space of tensors. This leads to the following description of the signal formation: