Zhang Hong, Ming Lequn, Jin Yinbin, Li Mingjun, Zhang Zhenxi, Lin Yang
School of Electrical Engineering, Xi'an Jiaotong University, Xi'an 710049, China.
Sheng Wu Yi Xue Gong Cheng Xue Za Zhi. 2010 Feb;27(1):1-5.
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.
心脏折返是诱发心律失常的重要因素之一。它可导致室性心动过速（VT）甚至颤动（VF），从而引发心源性猝死。随着计算机在电生理定量研究中的广泛应用，迫切需要在计算机中开发用于模拟的三维虚拟心脏。本文研究了该模型的数值算法。通过整合Luo-Rudy 1991心室细胞模型和扩散方程构建了三维模型。采用算子分裂法求解该模型。对偏微分方程使用交替方向迭代（ADI）格式和七点中心差分法，对边界条件采用二阶精度的离散格式。结果表明，ADI格式和七点中心差分法均能成功求解膜电位和电活动，具有良好的数值稳定性。然而，ADI格式可大大降低计算量，这意味着大时间步长的ADI方法在数值模拟中更具优势。
