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

Keywords

Advanced Numerical Methods for Scientific Computing
Living Systems and Precision Medicine
Code:
63/2022
Title:
Numerical Modelling of the Brain Poromechanics by High-Order Discontinuous Galerkin Methods
Date:
Wednesday 5th October 2022
Author(s):
Corti, M.; Antonietti, P.F.; Dede', L.; Quarteroni, A.
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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.
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Mathematical Models and Methods in Applied Sciences 33(08) (2023), 1577-1609