An Efficient Staggered Scheme for Solving the Poromechanics Problem of Quasi-Static Cardiac Perfusion

Abstract

The ventricles can be considered a type of poroelastic material, where the mass and pressure of the interstitial fluid, along with the displacement of the skeleton, are the three primary physical quantities of interest. Based on the free energy function of the poroelastic material, we propose a simplified model that requires only two fields to be directly solved, with another quantity obtained through post-processing. To solve this model, we first discretize the equations with the backward Euler scheme and finite element method, leading to a nonlinear system of equations, which can be solved using the Newton method in a monolithic way. For computational efficiency, we proposed a staggered scheme, where the large nonlinear system is divided into two smaller independent systems, and each only solves for one field using the Newton method. The numerical results showed the staggered scheme is more efficient than the monolithic scheme and that the two schemes achieve the same results, and are also in good agreement with those reported in the literature. Finally, we applied the staggered scheme to ventricular myocardial perfusion models and obtained the blood perfusion patterns in the myocardium during the cardiac systole.