Evaluation of the Performance of Different Numerical Methods in Cardiac Electrophysiology Simulations

This paper presents a comprehensive evaluation of the performance of different numerical methods in cardiac electrophysiological simulations, including the Explicit Euler (EE) Method, Implicit Euler (IE) Method, Trapezoidal Rule (TR), and the Fourth-Order Runge-Kutta (RK4) Method within the framework of one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) models of the human ventricles. Simulation accuracy was investigated for varying the time step (h) for different tissue scales and complexities. It was shown that, as the dimension of the model increased, the upper limit of h for acceptable simulation accuracy (h<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ul</inf>) gradually decreased. However, the difference in h<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ul</inf> among the methods was small. As the h or the tissue dimension increased, the EE method showed greater computational error compared to other methods. The experiment results also showed that the amplitude of the external stimulation pulse current, the size of the spatial range of tissue receiving stimuli, the spatial dimension of the tissue models, as well as the diffusion coefficient of the model, also affected simulation accuracy. The present study discusses the influence of numerical methods on the accuracy of cardiac simulations, providing insights for choosing optimal numerical methods for cardiac simulations.