Gating-enhanced IMEX splitting methods for cardiac monodomain simulation
Gating-enhanced IMEX splitting methods for cardiac monodomain simulation
复制标题
用于心脏单域模拟的门控增强 IMEX 分裂方法
作者：
K. R. Green;R. Spiteri
可兴奋心脏组织中的电活动可以用所谓的单域模型来模拟。单域模型是一个基于连续介质的多尺度模型，它由描述细胞尺度上的电活动的非线性常微分方程组和描述组织尺度上的电传播的半线性抛物型偏微分方程组成。模拟单域模型的标准“基于比例”的分裂方法是分割组织和细胞模型，对每个模型应用不同的积分器。通常，组织模型用隐式时间积分方法模拟，细胞模型用显式或显式指数模型模拟。我们证明，当细胞模型是刚性的时，隐式-显式(IMEX)线性多步法或Runge-Kutta方法应用于这种分裂可能具有较差的稳定性。我们提出了一种新的“门控增强型”IMEX分裂，它隐含地将组织变量和(通常是刚性的)细胞模型门控变量一起处理。在各种一维和二维实验中，测量了使用这两种分裂的14种不同IMEX方法的性能。低增量开销与门控增强型分裂的显著改进的稳定性相结合，被证明导致用刚性的人类心内膜细胞的Tusscher-Panfilov模型模拟单域模型的性能提高了大约四倍。
The electrical activity in excitable cardiac tissue can be simulated using the so-called monodomain model. The monodomain model is a continuum-based multi-scale model that consists of non-linear ordinary differential equations describing the electrical activity at the cellular scale along with a semi-linear parabolic partial differential equation describing electrical propagation at the tissue scale. The standard “scale-based” splitting method for simulating the monodomain model is to split the tissue and cell models, applying different integrators to each. Typically, the tissue model is simulated with an implicit time-integration method, and the cell model is simulated with an explicit or explicit-exponential one. We demonstrate that the application of implicit-explicit (IMEX) linear multistep or Runge–Kutta methods to this splitting can have poor stability properties when the cell model is stiff. We propose a novel “gating-enhanced” IMEX splitting that treats the tissue variable and the (typically stiff) cell model gating variables together implicitly. The performance of 14 different IMEX methods using both splittings is measured in a variety of one- and two-dimensional experiments. The low incremental overhead combined with the substantially improved stability of the gating-enhanced splitting is shown to result in a performance increase of approximately a factor of four for simulations of the monodomain model with the stiff ten Tusscher–Panfilov model of human endocardial cells.
DOI：
10.1080/10618562.2011.575368
发表时间：
2011-01-01
影响因子：
1.3
作者：
Vos, Peter E. J.;Eskilsson, Claes;Sherwin, Spencer J.
通讯作者：
Sherwin, Spencer J.