An integrative smoothed particle hydrodynamics method for modeling cardiac function

Abstract

Mathematical modeling of cardiac function can provide augmented simulation-based diagnosis tools for complementing and extending human understanding of cardiac diseases, which represent the most common cause of worldwide death. As the realistic starting-point for developing a unified meshless approach for total heart modeling, in this paper we propose an integrative smoothed particle hydrodynamics (SPH) method for addressing the simulation of the principle aspects of cardiac function, including cardiac electrophysiology, passive mechanical response and electromechanical coupling. To that end, several algorithms, e.g. splitting reaction-by-reaction method combined with a quasi-steady-state (QSS) solver, as well as anisotropic SPH-diffusion discretization and total Lagrangian SPH formulation, are introduced for dealing with the fundamental challenges of developing an integrative SPH method for simulating cardiac function, including, (i) the correct capture of the stiff dynamics of the transmembrane potential and the gating variables, (ii) the stable prediction of the large deformations and the strongly anisotropic behavior of the myocardium, and (iii) a proper coupling between the electrophysiology and tissue mechanics for the electromechanical feedback. A set of numerical examples demonstrate the effectiveness and robustness of the present SPH method, and render it a potential and powerful alternative that can augment the current lines of total cardiac modeling and clinical applications.