Finite Element Methods for Large-Strain Poroelasticity/Chemotaxis Models Simulating the Formation of Myocardial Oedema

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.

Automated summary

In this paper, we propose a novel coupled poroelasticity-diffusion model that considers the formation process of extracellular edema and infectious myocarditis under large deformations. The model takes into account the interaction between interstitial flow and the immune-driven dynamics between leukocytes and pathogens. A numerical approximation scheme using five-field finite element method is developed and stability analysis is conducted. The computational tests demonstrate the properties of the model and finite element schemes.