An integrative smoothed particle hydrodynamics framework for modeling cardiac function

Mathematical modeling of cardiac function can provide augmented simulation-based diagnosis tool 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 an unified meshless approach for total heart modeling, herein we propose an integrative smoothed particle hydrodynamics (SPH) framework 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 quasi-steady-state (QSS) solver , anisotropic SPH-diffusion discretization and total Lagrangian SPH formulation, are introduced and exploited for dealing with the fundamental challenges of developing integrative SPH framework for simulating cardiac function, namely, (i) the correct capturing of the stiff dynamics of the transmembrane potential and the gating variables , (ii) the stable predicting of the large deformations and the strongly anisotropic behavior of the myocardium, and (iii) the proper coupling of electrophysiology and tissue mechanics for electromechanical feedback. A set of numerical examples demonstrate the effectiveness and robustness of the present SPH framework, and render it a potential and powerful alternative that can augment current lines of total cardiac modeling and clinical applications.