Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, U.S.A.
Int J Numer Method Biomed Eng. 2013 Oct;29(10):1104-33. doi: 10.1002/cnm.2565. Epub 2013 Jun 24.
Computational modeling of the human heart allows us to predict how chemical, electrical, and mechanical fields interact throughout a cardiac cycle. Pharmacological treatment of cardiac disease has advanced significantly over the past decades, yet it remains unclear how the local biochemistry of an individual heart cell translates into global cardiac function. Here, we propose a novel, unified strategy to simulate excitable biological systems across three biological scales. To discretize the governing chemical, electrical, and mechanical equations in space, we propose a monolithic finite element scheme. We apply a highly efficient and inherently modular global-local split, in which the deformation and the transmembrane potential are introduced globally as nodal degrees of freedom, whereas the chemical state variables are treated locally as internal variables. To ensure unconditional algorithmic stability, we apply an implicit backward Euler finite difference scheme to discretize the resulting system in time. To increase algorithmic robustness and guarantee optimal quadratic convergence, we suggest an incremental iterative Newton-Raphson scheme. The proposed algorithm allows us to simulate the interaction of chemical, electrical, and mechanical fields during a representative cardiac cycle on a patient-specific geometry, robust and stable, with calculation times on the order of 4 days on a standard desktop computer.
人类心脏的计算建模使我们能够预测化学、电气和机械场如何在整个心动周期中相互作用。在过去几十年中，心脏疾病的药物治疗取得了重大进展，但仍不清楚个体心脏细胞的局部生物化学如何转化为整体心脏功能。在这里，我们提出了一种新颖的、统一的策略，可以跨三个生物学尺度模拟兴奋生物系统。为了在空间上离散控制化学、电气和机械方程，我们提出了一种整体有限元方案。我们应用了一种高效且固有的模块化全局-局部分裂，其中变形和跨膜电势作为节点自由度全局引入，而化学状态变量则作为内部变量局部处理。为了确保无条件算法稳定性，我们应用隐式向后 Euler 有限差分方案对所得系统进行时间离散化。为了提高算法鲁棒性并保证最优二次收敛性，我们建议使用增量迭代牛顿-拉普森方案。所提出的算法允许我们在特定于患者的几何形状上模拟代表心动周期期间化学、电气和机械场的相互作用，计算时间稳定，计算时间在标准台式计算机上约为 4 天。
