Spiteri Raymond J, Dean Ryan C
Department of Computer Science University of Saskatchewan, Saskatoon, Saskatchewan S7N 5A9, Canada.
IEEE Trans Biomed Eng. 2008 May;55(5):1488-95. doi: 10.1109/TBME.2007.914677.
Mathematical models of electric activity in cardiac tissue are becoming increasingly powerful tools in the study of cardiac arrhythmias. Considered here are mathematical models based on ordinary differential equations (ODEs) that describe the ionic currents at the myocardial cell level. Generating an efficient numerical solution of these ODEs is a challenging task, and, in fact, the physiological accuracy of tissue-scale models is often limited by the efficiency of the numerical solution process. In this paper, we examine the efficiency of the numerical solution of four cardiac electrophysiological models using implicit--explicit Runge-Kutta (IMEX-RK) splitting methods. We find that variable step-size implementations of IMEX-RK methods (ARK3 and ARK5) that take advantage of Jacobian structure clearly outperform the methods commonly used in practice.
心脏组织电活动的数学模型正日益成为研究心律失常的有力工具。这里考虑的是基于常微分方程（ODEs）的数学模型，这些方程描述了心肌细胞水平的离子电流。生成这些ODEs的有效数值解是一项具有挑战性的任务，事实上，组织尺度模型的生理准确性常常受到数值求解过程效率的限制。在本文中，我们使用隐式 - 显式龙格 - 库塔（IMEX - RK）分裂方法研究了四种心脏电生理模型的数值解效率。我们发现，利用雅可比结构的IMEX - RK方法（ARK3和ARK5）的变步长实现明显优于实际中常用的方法。
