Parameter-robust Multiphysics Algorithms for Biot Model with Application in Brain Edema Simulation

TL;DR

This paper introduces two parameter-robust numerical algorithms for the Biot model, reformulated as multiphysics problems, and applies them to simulate brain edema, revealing how key parameters influence brain swelling and intracranial pressure.

Contribution

The paper develops novel, parameter-robust algorithms for the Biot model using a multiphysics reformulation and demonstrates their effectiveness in brain edema simulations.

Findings

Permeability significantly affects intracranial pressure and tissue deformation.

Young's modulus and Poisson ratio influence swelling speed but not maximum ICP.

Algorithms are robust across a range of physical parameters.

Abstract

In this paper, we develop two parameter-robust numerical algorithms for Biot model and applied the algorithms in brain edema simulations. By introducing an intermediate variable, we derive a multiphysics reformulation of the Biot model. Based on the reformulation, the Biot model is viewed as a generalized Stokes subproblem combining with a reaction-diffusion subproblem. Solving the two subproblems together or separately will lead to a coupled or a decoupled algorithm. We conduct extensive numerical experiments to show that the two algorithms are robust with respect to the physics parameters. The algorithms are applied to study the brain swelling caused by abnormal accumulation of cerebrospinal fluid in injured areas. The effects of key physics parameters on brain swelling are carefully investigated. It is observe that the permeability has the greatest effect on intracranial pressure (ICP) and tissue deformation; the Young's modulus and the Poisson ratio will not affect the maximum ICP too much but will affect the tissue deformation and the developing speed of brain swelling.