Quantification of self-diffusion process in brain white matter tracts via numerical PDE simulation

Diffusion MRI (DMRI) signal is characterized by the self-diffusion propagation profile within the brain white matters. Despite previous efforts on quantification of this physical phenomenon in the literature, most existing methods suffer from a number of constraints which severely limit the extent of their practical applicability. In this work, we relax these limitations to a large degree by addressing the solution of the self-diffusion process in its most general partial differential equation (PDE) form. Specifically, we develop an approach based on the finite element method (FEM) to obtain numerical self-diffusion solution in multi-compartments models of the white matters. Besides, due to sensitivity of the DMRI signal to the average self-diffusion process, we provide a formulation for this process of a voxel in terms of microstructure parameters of white matters. Several simulation results based on the proposed FEM method are given to demonstrate its flexibility and accuracy.