A fully implicit finite element method for bidomain models of cardiac electrophysiology
A fully implicit finite element method for bidomain models of cardiac electrophysiology
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DOI：
10.1080/10255842.2011.554410
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发表时间：
2012-01-01
影响因子：
1.6
通讯作者：
Kuhl, Ellen
中科院分区：
文献类型：
--
作者：
Dal, Huesnue;Goktepe, Serdar;Kuhl, Ellen
介绍了一种新的，无条件稳定的和完全耦合的有限元方法的心脏电生理学的bidomain方程组。将跨膜电位phi（i）- phi（e）和细胞外电位phi（e）作为自变量处理。为此，相应的反应扩散方程重铸成弱形式，通过传统的等参伽辽金方法。由此产生的非线性残差方程组一致线性化。该方法的结果在一个对称的方程组，这减少了计算时间显着相比，传统的解决方案的算法。所提出的方法本质上是模块化的，可以与跨细胞膜的现象学或离子模型相结合。通过有代表性的数值算例，证明了该方法的有效性及其相对于简化单域模型的计算成本的比较。
This work introduces a novel, unconditionally stable and fully coupled finite element method for the bidomain system of equations of cardiac electrophysiology. The transmembrane potential phi(i) - phi(e) and the extracellular potential phi(e) are treated as independent variables. To this end, the respective reaction-diffusion equations are recast into weak forms via a conventional isoparametric Galerkin approach. The resultant nonlinear set of residual equations is consistently linearised. The method results in a symmetric set of equations, which reduces the computational time significantly compared to the conventional solution algorithms. The proposed method is inherently modular and can be combined with phenomenological or ionic models across the cell membrane. The efficiency of the method and the comparison of its computational cost with respect to the simplified monodomain models are demonstrated through representative numerical examples.