用于心脏干细胞单层多电极阵列仿真的二阶IMEX时间步进方法
Second-Order IMEX Time-Stepping Methods for Efficient Bidomain Multi-Electrode Array Simulations of Cardiac Stem Cell Monolayers
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中文总结 AI 辅助
本研究提出用于心脏干细胞单层MEA仿真的二阶IMEX时间步进方法，在固定计算成本下将误差降低2-3个数量级，显著提升精度-成本比。
中文摘要 AI 辅助
多电极阵列（MEA）通过记录细胞外场电位，能够实现对人诱导多能干细胞来源的心肌细胞（hiPSC-CMs）的组织水平电生理研究。近期的计算模型通过将详细的电极描述与Bidomain框架（一个与刚性离子模型耦合的非线性偏微分方程抛物-椭圆系统）相结合，改进了MEA仿真。标准数值策略依赖于算子分裂技术，将偏微分方程和常微分方程部分解耦。在大多数实现中，离子子系统被显式处理，而扩散算子被隐式处理，导致一阶隐式-显式（IMEX）时间离散化。尽管计算上方便，但这种方法限制了时间精度，并可能降低大规模仿真的效率。在本工作中，我们研究了在基于Strang的算子分裂中的高阶IMEX龙格-库塔格式，特别针对hiPSC-CMs单层的MEA模型进行了定制。通过使用非常小的时间步长获得的高保真参考解，比较了一阶和二阶格式的计算成本和全局误差。在固定计算成本下，二阶格式实现的误差比一阶方法小2-3个数量级。这些结果表明，高阶IMEX积分显著提高了MEA仿真的精度-成本比，为大规模电生理研究提供了一种实用且可靠的方法。
英文摘要
Multi-electrode Arrays (MEAs) enable tissue-level electrophysiological studies of human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) by recording extracellular field potentials. Recent computational models have improved MEA simulations by coupling detailed electrode descriptions with the Bidomain framework, a parabolic-elliptic system of nonlinear PDEs coupled with a stiff ionic model. The standard numerical strategy relies on operator splitting techniques that decouple the PDE and ODE components. In most implementations, the ionic subsystem is treated explicitly while the diffusive operator is handled implicitly, resulting in a first-order implicit-explicit (IMEX) time discretization. Although computationally convenient, this approach limits temporal accuracy and may reduce efficiency in large-scale simulations. In this work, we investigate higher-order IMEX Runge-Kutta schemes within a Strang-based operator splitting, specifically tailored for the MEA model of hiPSC-CMs monolayers. First- and second-order schemes are compared in terms of computational cost and global error against a high-fidelity reference solution obtained with a very small time step. For a fixed computational cost, the second-order schemes achieve errors that are 2-3 orders of magnitude smaller than those of the first-order method. These results demonstrate that higher-order IMEX integration significantly improves the accuracy-to-cost ratio of MEA simulations, providing a practical and reliable approach for large-scale electrophysiological studies.
发表机构
- Politecnico di Milano（米兰理工大学）
- Università della Svizzera Italiana（瑞士意大利语大学）
- University of Pavia（帕维亚大学）
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