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




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Barnafi Wittwer, Nicolás Alejandro
Gómez Vargas, Bryan Andrés
Lourenço, Wesley De Jesus
Reis, Ruy Freitas
Rocha, Bernardo Martins
Lobosco, Marcelo
Ruiz Baier, Ricardo
Weber dos Santos, Rodrigo

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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.


Palabras clave

Poroelasticity, Finite-strain regime, Cardiac applications, Oedema formation, Finite element discretisation, DIFFUSION, SIMULATION MODELS, CARDIOVASCULAR DISEASES