On the performance of an implicit-explicit Runge-Kutta method in models of cardiac electrical activity

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.