Numerical Study on the Mathematical Model of the Cardiac Electrical Conduction

The most vicious ventricular arrhythmias are thought to underlie the majority of sudden cardiac death. Computer simulations based on complex mathematical models have been widely used to reveal their mechanisms. To solve these models with high accuracy and less computing time consumption are what people look for. In this paper a new numerical method was studied to integrate the cardiac electrical conduction model. The time splitting method was used to solve the reaction-diffusion equations for the developed two-dimensional tissue. The second-order Runge-Kutta method with adaptive time step was applied to solve the action potential of each single cell. The perturbation finite difference (PFD) method was first studied to use in the cardiac electrical conduction to solve the partial differential equation (PDE). Its discretization processes and finial scheme were described in detail in this paper. By computing and comparing, we found PFD method had good numerical stability, higher accuracy than the conventional five-point centered difference (CD) method. The precision could be improved without obvious increasing the computing time, implying its reliability and feasibility in the simulation studies of the cardiac electrical activities.