Numerical Algorithms
Numerical Algorithms
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DOI：
10.1117/3.975277.ch6
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发表时间：
2019-01
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影响因子：
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通讯作者：
Marcell Schweitzer;Denis Duesseldorf
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文献类型：
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作者：
Marcell Schweitzer;Denis Duesseldorf
心脏模拟通常通过数值求解双域或单域方程来进行。在这些模拟中，大部分的计算工作量都用于计算由心肌细胞模型产生的常微分方程系统的时间积分。对于这种时间积分，公认的首选方法是Rush-Larsen （RL）方法，该方法根据门控方程和非门控方程对心肌细胞模型进行划分，分别用指数欧拉法和正演欧拉法进行处理。RL方法的划分策略基于J. W. Moore和F. Ramon先前的工作[关于膜动作电位的Hodgkin和Huxley方程的数值积分]，J. Theor。生物学报，45,No. 1, 249-273 (1974; doi: 10.1016/0022-5193(74)90054-x)]，主要区别在于Moore-Ramon （MR）方法将非门控方程与Heun方法(一种两阶段二阶显式龙格-库塔（ERK2）方法相结合。虽然RL方法比MR方法每一步的计算成本更低，但它不应该是一个既定的结论，即RL更有效。在本文中，我们证明了MR方法在效率方面通常优于RL方法。此外，基于相同的划分策略，提出了两种新的数值方法，分别将非门控方程与其他ERK2方法和多阶段一阶Runge-Kutta-Chebyshev方法相结合。我们表明，RL方法在36个测试的细胞模型中有34个优于RL方法。
Cardiac simulations are often performed by numerically solving the bidomain or monodomain equations. In these simulations, much of the computational workload is devoted to the time integration of the systems of ordinary differential equations that arise from the myocardial cell models. For such time integration, a well-established top choice is the Rush-Larsen (RL) method, which partitions the myocardial cell models according to the gating and non-gating equations and treats them with the exponential Euler method and the forward Euler method, respectively. The partitioning strategy of the RL method is based on previous work by J. W. Moore and F. Ramon [“On numerical integration of the Hodgkin and Huxley equations for a membrane action potential”, J. Theor. Biol. 45, No. 1, 249–273 (1974; doi: 10.1016/0022-5193(74)90054-x)], with the main difference being that the Moore-Ramon (MR) method integrates the non-gating equations with Heun’s method, a two-stage, second-order explicit Runge-Kutta (ERK2) method. Although the RL method is less computationally expensive per step than the MR method, it should not be a foregone conclusion that the RL is more efficient. In this paper, we demonstrate that in the MR method typically outperforms the RL method in terms of efficiency. Furthermore, two new families of numerical methods are proposed based on the same partitioning strategy but integrating the non-gating equations with other ERK2 methods and multi-stage, first-order Runge-Kutta-Chebyshev methods, respectively. We show that the RL method is outperformed on 34 out of 36 cell models tested.