Dal Hüsnü, Göktepe Serdar, Kaliske Michael, Kuhl Ellen
Institute for Structural Analysis, Technische Universität Dresden, Dresden D-01062, Germany.
Comput Methods Biomech Biomed Engin. 2012;15(6):645-56. doi: 10.1080/10255842.2011.554410. Epub 2011 May 24.
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 Φ(i)-Φ(e) and the extracellular potential Φ(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.
这项工作介绍了一种用于心脏电生理双域方程组的新型、无条件稳定且完全耦合的有限元方法。跨膜电位Φ(i)-Φ(e)和细胞外电位Φ(e)被视为独立变量。为此，通过传统的等参伽辽金方法将各自的反应扩散方程转化为弱形式。由此产生的非线性残差方程组被一致地线性化。该方法得到一组对称方程组，与传统求解算法相比，显著减少了计算时间。所提出的方法本质上是模块化的，可以与跨细胞膜的唯象模型或离子模型相结合。通过具有代表性的数值例子展示了该方法的效率及其与简化单域模型相比的计算成本。
