标题： 细胞外-膜-细胞内模型的解析解 显示英文标题

标题： Analytical solutions for the Extracellular-Membrane-Intracellular model

摘要： 细胞外-膜-细胞内（EMI）模型是一种用于心脏电生理模拟的新数学框架。 与传统的单域和双域模型相比，EMI 模型能够更详细地描述心脏的电活动，这可能使其更适合于理解病理条件下心脏的电动力学。 本文推导并验证了 EMI 模型的若干解析解。 具体来说，我们在极坐标下得到了单个二维细胞的一组解，在球坐标下得到了一对耦合三维细胞的一组解。 我们还引入了笛卡尔坐标下 N 个三维细胞的人为解。 为了验证这些解析解，我们使用了结合算子分裂的 mortar 有限元法进行了数值实验。 结果表明，这些解析解可以有效地验证 EMI 模型数值模拟的准确性。 显示英文摘要

摘要： The Extracellular-Membrane-Intracellular (EMI) model is a novel mathematical framework for cardiac electrophysiology simulations. The EMI model provides a more detailed description of the heart's electrical activity compared to traditional monodomain and bidomain models, potentially making it better-suited for understanding the electrical dynamics of the heart under pathological conditions. In this paper, we derive and verify several analytical solutions for the EMI model. Specifically, we obtain a family of solutions for a single two-dimensional cell in polar coordinates and for a pair of coupled three-dimensional cells in spherical coordinates. We also introduce a manufactured solution for N three-dimensional cells in Cartesian coordinates. To verify the analytical solutions, we conduct numerical experiments using the mortar finite element method combined with operator splitting. The results demonstrate that the analytical solutions are effective for verifying the accuracy of numerical simulations of the EMI model.