An efficient parallel numerical method for large-scale computational models of cardiac electrophysiology

Electrophysiological models have been widely used in the researches of electrical activities of cardiac tissue. It is always recognized as a computational challenge to solve these large-scale computational models with reliable accuracy and less time consumption. In this paper, a modified explicit finite difference method with a high accuracy for large-scale parallel computation was studied, which is absolute stable to make larger time steps can be achieved. Then a new global method for treatment of no-flux boundary conditions is proposed, which can automatic handle without tracking, especially convenient for parallel computing. By computing and comparing, the methods proposed has a higher accuracy than traditional difference methods (e.g. conventional seven-point centered difference (CD)) and conventional boundary treatment, moreover, in the reasonable error range, a maximum time step of 0.1ms could be used, and the time cost for stimulating 400ms is cut to 6.08 hours contrasting to 33.89 hours of CD method, implying it is a reliable, efficient and feasible parallel method, which is practical and promising for simulation research of the cardiac electrical activities.