基于心室动作电位的三维心肌组织模型算法研究

Algorithm Study on the Three-dimensional Cardiac Tissue Based on the Model of Ventricular Action Potential

心肌电折返是引起心律失常的重要因素之一,它会导致心动过速(VT)乃至室颤(VF)的发生,从而引起心源性猝死。随着计算机仿真在定量电生理研究中的广泛应用,迫切需要建立三维心肌组织实验平台。本文就这种组织模型的数值解方法进行了研究。文中利用Luo-Rudy 1991心室肌细胞模型结合扩散方程形成三维组织模型,利用算子分裂法求其数值解。分别采用ADI格式和七点差分格式求解描述电扩布的偏微分方程,边界条件采用二阶精度的离散格式。实验结果表明,以上两种格式均可成功地解算出细胞膜电位的变化以及电兴奋的活动,且具有良好的稳定性。但ADI格式可较大幅度地缩短计算时间。因此ADI格式下增加时间步长以提高计算效率的方法更具优势。

Cardiac reentry is one of the important factors to induce arrhythmias. It could lead to ventricular tachycardia（VT） or even fibrillation（VF）,resulting in sudden cardiac death.With the wide use of computer in the quantitative study of electrophysiology,the three-dimensional virtual heart for simulations needs to be developed imminently in computer.In this paper,numerical algorithm of the model was studied.The three-dimensional model was constructed by integrating Luo-Rudy 1991 ventricular cell model and diffusion equation.The operator splitting method was employed to solve the model.The alternate direction iterative（ADI） format and seven-point centered difference method were used for the partial differential equation.And the discrete format with second-order accuracy was taken for the boundary conditions.The results showed that the ADI format and seven-point centered difference method both could successfully figure out the membrane potential and electrical activities with good numerical stability.However,computing consumption could be greatly reduced with the ADI format,implying that the ADI method with large time step was more powerful in numerical simulations.