Decoupling Axial and Radial Tissue Heterogeneity in Diffusion Compartment Imaging

Diffusion compartment imaging (DCI) characterizes tissues in vivo by separately modeling the diffusion signal arising from a finite number of large scale microstructural environments in each voxel, also referred to as compartments. The DIAMOND model has recently been proposed to characterize the 3-D diffusivity of each compartment using a statistical distribution of diffusion tensors. It enabled the evaluation of compartment-specific diffusion characteristics while also accounting for the intra-compartment heterogeneity. In its original formulation, however, DIAMOND could only describe symmetric heterogeneity, while tissue heterogeneity likely differs along and perpendicular to the orientation of the fascicles. In this work we propose a new statistical distribution model able to decouple axial and radial heterogeneity of each compartment in each voxel. We derive the corresponding analytical expression of the diffusion attenuated signal and evaluate this new approach with both numerical simulations and in vivo data. We show that the heterogeneity arising from white matter fascicles is anisotropic and that the shape of the distribution is sensitive to changes in axonal dispersion and axonal radius heterogeneity. We demonstrate that decoupling the modeling of axial and radial heterogeneity has a substantial impact of the estimated heterogeneity, enables improved estimation of other model parameters and enables improved signal prediction. Our distribution model characterizes not only the orientation of each white matter fascicle but also their diffusivities; it may enable unprecedented characterization of the brain development and of brain disease and injury.