A computational method for the covariance matrix associated with extracellular diffusivity on disordered models of cylindrical brain axons

Abstract

This study developed a method to approximate the covariance matrix associated with the simulation of water molecular diffusion inside the brain tissue. The computation implements the Discontinuous Galerkin method of the diffusion equation. A physically consistent numerical flux is applied to model the interaction between the axon walls and extracellular regions. This numerical flux yields an efficient GPU-CUDA implementation. We consider the two-dimensional case of high axon pack density, valid, for instance, in the brain's corpus callosum region.

Keywords

• extracellular diffusivity
• covariance matrix
• numerical flux
• discontinuous galerkin