Abstract The monodomain model is a common description for explaining the electrical activity of the heart. The model is nonlinear and consists of an ODE system that describes electrochemical reactions in the cardiac cells and a parabolic PDE that express the diffusion of the electrical signal. FEM approaches for the numerical solution of the monodomain equations can be classified into those that simultaneously update the state variables with respect to time by solving a coupled system and those that perform the temporal update in a decoupled manner. While coupled strategies are known to yield more accurate results, they so far have not been applied to physiological cell models due to their enormous memory requirements and computational times. In this paper, we tackle these challenges and suggest a novel computational strategy, that exploits the sparsity of local matrices in the assembly of global FEM matrices and hence features optimal usage of memory. We demonstrate the practicability of our coupled approach by employing three popular physiological cell models (Luo-Rudy phase-I, Ten Tusscher 2006 and O’Hara-Rudy 2011) and compare it with a commonly used decoupled strategy. Qualitatively different results obtained for the simulation of cardiac reentry underline the potential relevance of our work for future studies of cardiac pathology.

中文翻译：

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用于模拟心波传播的具有最佳内存使用的耦合单域求解器

摘要 单域模型是解释心脏电活动的常用描述。该模型是非线性的，由描述心肌细胞中电化学反应的 ODE 系统和表示电信号扩散的抛物线 PDE 组成。用于单域方程数值求解的 FEM 方法可以分为通过求解耦合系统同时更新状态变量的方法和以解耦方式执行时间更新的方法。虽然已知耦合策略可以产生更准确的结果，但由于其巨大的内存需求和计算时间，它们迄今为止尚未应用于生理细胞模型。在本文中，我们解决了这些挑战并提出了一种新颖的计算策略，它利用全局 FEM 矩阵组装中局部矩阵的稀疏性，因此具有内存的最佳使用。我们通过采用三种流行的生理细胞模型（Luo-Rudy phase-I、Ten Tusscher 2006 和 O'Hara-Rudy 2011）来证明我们的耦合方法的实用性，并将其与常用的解耦策略进行比较。为模拟心脏折返获得的定性不同结果强调了我们的工作与未来心脏病学研究的潜在相关性。