A poroelastic model valid in large strains with applications to perfusion in cardiac modeling

Dominique Chapelle (1) , Jacques Sainte-Marie (1) , Jean-Frédéric Gerbeau (2) , Irene Vignon-Clementel (2)

1 MACS - Modeling, analysis and control in computational structural dynamics
2 REO - Numerical simulation of biological flows

This paper is motivated by the modeling of blood flows through the beating myocardium, namely cardiac perfusion. As in other works, perfusion is modeled here as a flow through a poroelastic medium. The main contribution of this study is the derivation of a general poroelastic model valid for a nearly incompressible medium which experiences finite deformations. A numerical procedure is proposed to iteratively solve the porous flow and the nonlinear poroviscoelastic problems. Three-dimensional numerical experiments are presented to illustrate the model. The first test cases consist of typical poroelastic configurations: swelling and complete drainage. Finally, a simulation of cardiac perfusion is presented in an idealized left ventricle embedded with active fibers. Results show the complex temporal and spatial interactions of the muscle and blood, reproducing several key phenomena observed in cardiac perfusion.

Mots clés: Porous media; Large deformation; Incompressibility limit; Cardiac perfusion; Biomechanics

Domaines: Biomécanique [physics.med-ph]; Biomécanique [physics.med-ph]; Analyse numérique [math.NA]

Dominique Chapelle, Jacques Sainte-Marie, Jean-Frédéric Gerbeau, Irene Vignon-Clementel. A poroelastic model valid in large strains with applications to perfusion in cardiac modeling. Computational Mechanics, 2010, 46 (1), pp.91-101. ⟨10.1007/s00466-009-0452-x⟩. ⟨inria-00542672⟩