Work

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

Year: 2025

Type: article

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.

Source: International Journal for Numerical Methods in Biomedical Engineering

DOI: 10.1002/cnm.70030

Authors: Xuan Wang, Li Cai, Pengfei Ma, Hao Gao

Institutions: Northwestern Polytechnical University, University of Glasgow

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: bronze

Funders: British Heart Foundation, National Natural Science Foundation of China, Engineering and Physical Sciences Research Council

Awards: A modelling study of right ventricular function in repaired tetralogy of Fallot for predicting outcome and impact of pulmonary valve replacement, G1615827359, G1793616496, G2519137040, SofTMech with MIT and POLIMI (SofTMechMP)