Finite element methods for large-strain poroelasticity/chemotaxis models simulating the formation of myocardial oedema

TL;DR

This paper introduces a novel finite element approach for simulating large-strain poroelasticity coupled with chemotaxis, modeling myocardial oedema formation through interactions of flow, deformation, and immune response.

Contribution

It presents a new coupled poroelasticity-diffusion model and a five-field finite element scheme with stability analysis and preconditioning strategies.

Findings

Model effectively simulates myocardial oedema formation.

Finite element scheme demonstrates stability and accuracy.

Computational tests validate the model's properties.

Abstract

In this paper we propose a novel coupled poroelasticity-diffusion model for the formation of extracellular oedema and infectious myocarditis valid in large deformations, manifested as an interaction between interstitial flow and the immune-driven dynamics between leukocytes and pathogens. The governing partial differential equations are formulated in terms of skeleton displacement, fluid pressure, Lagrangian porosity, and the concentrations of pathogens and leukocytes. A five-field finite element scheme is proposed for the numerical approximation of the problem, and we provide the stability analysis for a simplified system emanating from linearisation. We also discuss the construction of an adequate, Schur complement based, nested preconditioner. The produced computational tests exemplify the properties of the new model and of the finite element schemes.