Vigmond Edward J, Aguel Felipe, Trayanova Natalia A
Department of Electrical and Computer Engineering, University of Calgary, 2500 University Dr. NW, Calgary, AB T2N 1N4, Canada.
IEEE Trans Biomed Eng. 2002 Nov;49(11):1260-9. doi: 10.1109/TBME.2002.804597.
The bidomain equations are the most complete description of cardiac electrical activity. Their numerical solution is, however, computationally demanding, especially in three dimensions, because of the fine temporal and spatial sampling required. This paper methodically examines computational performance when solving the bidomain equations. Several techniques to speed up this computation are examined in this paper. The first step was to recast the equations into a parabolic part and an elliptic part. The parabolic part was solved by either the finite-element method (FEM) or the interconnected cable model model (ICCM). The elliptic equation was solved by FEM on a coarser grid than the parabolic problem and at a reduced frequency. The performance of iterative and direct linear equation system solvers was analyzed as well as the scalability and parallelizability of each method. Results indicate that the ICCM was twice as fast as the FEM for solving the parabolic problem, but when the total problem was considered, this resulted in only a 20% decrease in computation time. The elliptic problem could be solved on a coarser grid at one-quarter of the frequency at which the parabolic problem was solved and still maintain reasonable accuracy. Direct methods were faster than iterative methods by at least 50% when a good estimate of the extracellular potential was required. Parallelization over four processors was efficient only when the model comprised at least 500,000 nodes. Thus, it was possible to speed up solution of the bidomain equations by an order of magnitude with a slight decrease in accuracy.
双域方程是对心脏电活动最完整的描述。然而，由于需要精细的时间和空间采样，其数值解在计算上要求很高，尤其是在三维情况下。本文系统地研究了求解双域方程时的计算性能。本文研究了几种加速这种计算的技术。第一步是将方程重铸为抛物型部分和椭圆型部分。抛物型部分通过有限元法（FEM）或互连电缆模型（ICCM）求解。椭圆型方程在比抛物型问题更粗的网格上并以降低的频率通过有限元法求解。分析了迭代和直接线性方程组求解器的性能以及每种方法的可扩展性和并行性。结果表明，在求解抛物型问题时，ICCM的速度是FEM的两倍，但在考虑整个问题时，这仅导致计算时间减少20%。椭圆型问题可以在比求解抛物型问题的频率低四分之一的粗网格上求解，并且仍然保持合理的精度。当需要对细胞外电位进行良好估计时，直接方法比迭代方法至少快50%。只有当模型包含至少500,000个节点时，在四个处理器上进行并行化才是有效的。因此，有可能在精度略有下降的情况下将双域方程的求解速度提高一个数量级。
