Millions of degrees of freedom are often required to accurately represent the electrophysiology of the myocardium due to the presence of discretization effects. This study seeks to explore the influence of temporal and spatial discretization on the simulation of cardiac electrophysiology in conjunction with changes in modeling choices. Several finite element analyses are performed to examine how discretization affects solution time, conduction velocity and electrical excitation. Discretization effects are considered along with changes in the electrophysiology model and solution approach. Two action potential models are considered: the Aliev‐Panfilov model and the ten Tusscher‐Noble‐Noble‐Panfilov model. The solution approaches consist of two time integration schemes and different treatments for solving the local system of ordinary differential equations. The efficiency and stability of the calculation approaches are demonstrated to be dependent on the action potential model. The dependency of the conduction velocity on the element size and time step is shown to be different for changes in material parameters. Finally, the discrepancies between the wave propagation in coarse and fine meshes are analyzed based on the temporal evolution of the transmembrane potential at a node and its neighboring Gauss points. Insight obtained from this study can be used to suggest new methods to improve the efficiency of simulations in cardiac electrophysiology.

中文翻译：

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时空离散化对心脏电生理影响的数值研究

由于存在离散化效应，通常需要数百万个自由度才能准确表示心肌的电生理。本研究旨在结合建模选择的变化，探索时空离散化对心脏电生理模拟的影响。执行多项有限元分析以检查离散化如何影响求解时间、传导速度和电激励。随着电生理模型和求解方法的变化，考虑了离散化效应。考虑了两种动作电位模型：Aliev-Panfilov 模型和十个 Tusscher-Noble-Noble-Panfilov 模型。求解方法包括用于求解局部常微分方程组的两种时间积分方案和不同的处理方法。计算方法的效率和稳定性被证明取决于动作电位模型。传导速度对单元尺寸和时间步长的依赖性显示为随着材料参数的变化而不同。最后，基于节点处跨膜电位及其相邻高斯点的时间演变，分析了粗网格和细网格中波传播之间的差异。从这项研究中获得的见解可用于提出新方法，以提高心脏电生理学模拟的效率。计算方法的效率和稳定性被证明取决于动作电位模型。传导速度对单元尺寸和时间步长的依赖性显示为随着材料参数的变化而不同。最后，基于节点处跨膜电位及其相邻高斯点的时间演变，分析了粗网格和细网格中波传播之间的差异。从这项研究中获得的见解可用于提出新方法，以提高心脏电生理学模拟的效率。计算方法的效率和稳定性被证明取决于动作电位模型。传导速度对单元尺寸和时间步长的依赖性显示为随着材料参数的变化而不同。最后，基于节点处跨膜电位及其相邻高斯点的时间演变，分析了粗网格和细网格中波传播之间的差异。从这项研究中获得的见解可用于提出新方法，以提高心脏电生理学模拟的效率。基于节点处跨膜电位及其相邻高斯点的时间演变，分析了粗网格和细网格中波传播之间的差异。从这项研究中获得的见解可用于提出新方法，以提高心脏电生理学模拟的效率。基于节点处跨膜电位及其相邻高斯点的时间演变，分析了粗网格和细网格中波传播之间的差异。从这项研究中获得的见解可用于提出新方法，以提高心脏电生理学模拟的效率。