Numerical Modelling of the Brain Poromechanics by High-Order Discontinuous Galerkin Methods

TL;DR

This paper develops a high-order discontinuous Galerkin numerical method for simulating brain poromechanics based on the MPET model, enabling detailed, multi-scale analysis of brain fluid dynamics.

Contribution

It introduces a novel high-order DG method for MPET equations with stability and error analysis, applied to realistic brain geometries.

Findings

Validated the method with convergence tests on brain slice mesh

Achieved accurate simulations of brain perfusion in 3D patient-specific models

Demonstrated the method's potential for detailed brain fluid flow analysis

Abstract

We introduce and analyze a discontinuous Galerkin method for the numerical modelling of the equations of Multiple-Network Poroelastic Theory (MPET) in the dynamic formulation. The MPET model can comprehensively describe functional changes in the brain considering multiple scales of fluids. Concerning the spatial discretization, we employ a high-order discontinuous Galerkin method on polygonal and polyhedral grids and we derive stability and a priori error estimates. The temporal discretization is based on a coupling between a Newmark $\beta$-method for the momentum equation and a $\theta$-method for the pressure equations. After the presentation of some verification numerical tests, we perform a convergence analysis using an agglomerated mesh of a geometry of a brain slice. Finally we present a simulation in a three dimensional patient-specific brain reconstructed from magnetic resonance images. The model presented in this paper can be regarded as a preliminary attempt to model the perfusion in the brain.