  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.
