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.

中文翻译：

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用于模拟心脏功能的综合平滑粒子流体动力学框架

心脏功能的数学建模可以提供增强的基于仿真的诊断工具，以补充和扩展人类对心脏病的理解，心脏病是全球最常见的死亡原因。作为开发用于全心脏建模的统一无网格方法的现实起点，本文提出了一种综合平滑粒子流体动力学 (SPH) 框架，用于解决心脏功能的主要方面的模拟，包括心脏电生理学、被动机械反应和机电耦合。为此，几种算法，例如，结合准稳态 (QSS) 求解器、各向异性 SPH 扩散离散化和总拉格朗日 SPH 公式的逐个反应分解法，被引入和利用来应对开发用于模拟心脏功能的综合 SPH 框架的基本挑战，即（i）正确捕获跨膜电位和门控变量的刚性动力学，（ii）稳定预测大变形和心肌的强各向异性行为，以及 (iii) 电生理学和组织力学的正确耦合，用于机电反馈。一组数值示例证明了当前 SPH 框架的有效性和稳健性，并使其成为一种潜在且强大的替代方案，可以增强当前的总心脏建模和临床应用。(i) 正确捕获跨膜电位和门控变量的刚性动力学，(ii) 稳定预测心肌的大变形和强各向异性行为，以及 (iii) 电生理学和组织力学的适当耦合用于机电反馈。一组数值示例证明了当前 SPH 框架的有效性和稳健性，并使其成为一种潜在且强大的替代方案，可以增强当前的总心脏建模和临床应用。(i) 正确捕获跨膜电位和门控变量的刚性动力学，(ii) 稳定预测心肌的大变形和强各向异性行为，以及 (iii) 电生理学和组织力学的适当耦合用于机电反馈。一组数值示例证明了当前 SPH 框架的有效性和稳健性，并使其成为一种潜在且强大的替代方案，可以增强当前的总心脏建模和临床应用。