Sundnes J, Wall S, Osnes H, Thorvaldsen T, McCulloch A D
a Simula Research Laboratory, Lysaker, Norway/Department of Informatics , University of Oslo , Oslo , Norway.
Comput Methods Biomech Biomed Engin. 2014;17(6):604-15. doi: 10.1080/10255842.2012.704368. Epub 2012 Jul 16.
Mathematical models of cardiac electro-mechanics typically consist of three tightly coupled parts: systems of ordinary differential equations describing electro-chemical reactions and cross-bridge dynamics in the muscle cells, a system of partial differential equations modelling the propagation of the electrical activation through the tissue and a nonlinear elasticity problem describing the mechanical deformations of the heart muscle. The complexity of the mathematical model motivates numerical methods based on operator splitting, but simple explicit splitting schemes have been shown to give severe stability problems for realistic models of cardiac electro-mechanical coupling. The stability may be improved by adopting semi-implicit schemes, but these give rise to challenges in updating and linearising the active tension. In this paper we present an operator splitting framework for strongly coupled electro-mechanical simulations and discuss alternative strategies for updating and linearising the active stress component. Numerical experiments demonstrate considerable performance increases from an update method based on a generalised Rush-Larsen scheme and a consistent linearisation of active stress based on the first elasticity tensor.
描述肌肉细胞中电化学反应和横桥动力学的常微分方程组、模拟电激活在组织中传播的偏微分方程组以及描述心肌机械变形的非线性弹性问题。数学模型的复杂性促使人们采用基于算子分裂的数值方法，但已证明简单的显式分裂格式对于实际的心脏电机械耦合模型会产生严重的稳定性问题。采用半隐式格式可以提高稳定性，但这在更新和线性化主动张力方面带来了挑战。在本文中，我们提出了一个用于强耦合电机械模拟的算子分裂框架，并讨论了更新和线性化主动应力分量的替代策略。数值实验表明，基于广义拉什 - 拉森格式的更新方法和基于第一弹性张量的主动应力一致线性化方法可显著提高性能。
