Numerical Computation For Conduction Of Action Potential In Two-Dimensional Cardiac Ventricle Tissue

In the process of using difference method to solve the PDE, perturbation finite difference (PFD) method was put forward by Z. Gao in 1990s. In the PFD, both the differentials and non-differential terms in the differential equation are discretized, and the coefficients of the power series are determined by means of eliminating the truncation error of the corresponding modified scheme, then the high accurate difference scheme is obtained. And that method is different from the adding base point method and impact method from importing derivatives of higher order.In this paper, we use this numerical method and adopt operator splitting method to simulate the conduction model of action potential in two-dimensional cardiac ventricle tissue,the conduction model of the action potential in two-dimensional cardiac ventricle tissue is denoted by one reaction-diffusion equation with a series of ODE describing ionic channels of cell, at the same time,we adopt the compact alternate direct implicit difference(CADID) method to simulate that model,compar-ing these value results,get some conlusions. The present investigation shows that PFD scheme space discretization with Euler time discretization can obtain the same numerical accuracy as that of central difference space discretization with fourth-order Runge-Kutta time discretization in this problem,and the computation time for PFD being only one fourth of central difference method.This paper consists of seven chapters. In the second section, we present the theoretical basis of electrophysiology and the advance in heart electrophysiology. In the third section,we introduce the conduction model of action potential in two-dimensional cardiac ventricle tissue. In the fourth section, we obtain the PFD scheme for the equations of this model,and do value stability analysis. In the fifth part, we obtain the CADID scheme for the model,and do the value stability analysis. In the sixth part,we give the numerical result of these numerical method for this model. In the end of the paper, we draw a conclusion of this work and make some comments on the prospect of simulating this model.