Simulation of excitation contraction coupling in ventricular cardiac myocytes

心律失常和纤颤是心源性死亡的主要原因之一。它们可能来自细胞水平上的交替和其他致心律失常过程。Ca~(2+)动力学参与了其中的多种过程。该项目将通过模拟心室肌细胞的兴奋收缩偶联(ECC)来研究细胞的心律失常过程，这些过程部分已知，但远未完全了解，特别是在它们的相互作用中。在细胞内数千个微小的二分裂隙中，膜刺激被转化为钙信号。该问题的大时空范围要求采用多尺度技术，用准静态格林函数描述裂隙内的浓度梯度，并用有限元方法(FEMS)模拟整体反应扩散过程。裂隙的离子通道将在分子状态细节上模拟为随机过程。膜电位动力学将因细胞类型和物种而异。我们将开发针对该问题的随机-确定性混合时间步长管理。块体过程中空间和时间尺度的范围要求有限元具有时空自适应性。我们将开发允许两者使用的算法。高阶线性隐式Runge-Kutta方法将被应用于时间步长管理的挑战。该问题的规模需要在多个CPU上进行高性能计算，包括适当开发的负载平衡方法。

Arrhythmias and fibrillation are among the prime causes of cardiac death. They may arise from alternans and other arrhythmogenic processes on cell level. Ca2+ dynamics are involved in a variety of them. The project will investigate cellular arrhythmogenic processes, which are known in part but far from completely understood especially in their interaction, by simulating excitation contraction coupling (ECC) in ventricular cardiac myocytes. Membrane excitation is translated into a Ca2+ signal in thousands of tiny dyadic clefts inside the cell. The problem's large range of space and time scales requires a multi-scale technique, which describes the concentration gradients in the clefts by quasi-static Green's functions, and simulates the bulk reaction-diffusion processes with finite element methods (FEMs). The cleft's ion channels will be modeled in molecular state detail as stochastic processes. Membrane potential dynamics will be cell type and species specific. We will develop hybrid stochastic-deterministic time step management specified to the problem. The range of space and time scales in the bulk processes requires spatial and temporal adaptivity of the FEM. We will develop algorithms allowing for the use of both. Higher order linearly implicit Runge-Kutta methods will be applied to meet the time step management challenges. The size of the problem requires high performance computing on many CPUs involving appropriately developed load balancing methods.