二维心室肌中动作电位传导的数值算法研究

Numerical Algorithm for Conduction of Action Potential in Two-Dimensional Cardiac Ventricle Tissue

为了进一步探讨求解二维心室肌中动作电位传导方程的方法,采用时间分裂法将求解过程分为两步,第一步用时间步长自适应算法求解每个细胞的动作电位,第二步用交替方向隐式法或五点差分法对偏微分方程进行数值积分.仿真结果表明,在保证数值算法的稳定性和精度上,时间分裂法和时间步长自适应算法起着重要的作用.采用了时间分裂算法和时间步长自适应算法后,在计算精度上,用交替方向隐式法略高于用五点差分法去积分偏微分方程,在计算耗时上,五点差分法是交替方向隐式法的70%.

To further investigate the numerical algorithm for conduction of action potential in two-dimensional cardiac tissue, the solving procedure is divided into two steps by using the time splitting method. In the first step, the adaptive time step method is applied to solve the action potential for every single cell. In the second step, the alternating direction implicit method (ADI) or the five-point difference method is employed to integrate the partial differential equations (PDE's). Simulation results show that the time splitting and adaptive time step methods play an important role in ensuring the stability and accuracy. Once the time splitting and adaptive time step methods are adopted, the integration accuracy of the PDE's with the ADI method shows slightly higher than that of five-point difference method, and the computation time of the five-point difference method approaches to 70% of that of the ADI method.