发表机构
University of Pavia（帕维亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明Kirchhoff网络模型（KNM）的适定性，并利用最小移动与Γ-收敛框架，证明当网格尺寸趋于零时KNM解收敛到心脏电生理双域模型。
AI 中文摘要
本文研究了心脏电生理学中的双域模型与Jäger和Tveito最近提出的Kirchhoff网络模型（KNM）之间的联系。在KNM中，心脏组织的每个细胞被表示为离散网络中的一个节点，心脏中电势的动态由节点上的常微分方程组描述。我们首先研究KNM的适定性，然后证明：当节点位于规则格子的顶点且网格尺寸ε趋于零时，在适当的子序列意义下，细胞尺寸为ε的KNM系统的解收敛到双域模型的解。关于收敛性，我们采用Pennacchio、Savaré和Colli Franzone在2005年《心脏电活动多尺度建模》中提出的框架，该框架基于（a）通过半隐式欧拉格式对双域和ε-KNM系统的演化方程进行时间离散化，（b）将时间离散解识别为最小移动格式的极值点，以及（c）最小移动泛函的Γ-收敛。
英文摘要
In this work, we study the connection between the bidomain model of cardiac electrophysiology and the Kirchhoff Network model (KNM), that was recently introduced by Jäger and Tveito. In the KNM, each cell of the cardiac tissue is represented as a node in a discrete network and the dynamics of the electric potentials in the heart are described by a system of ordinary differential equations on the nodes. We first study the well-posedness of the KNM and then prove that, when the nodes are situated on the vertices of a regular lattice and the mesh size $\varepsilon$ tends to zero, the solutions of the KNM system at cell-size $\varepsilon$ converge to the solution of the bidomain model, along appropriate subsequences. Regarding the convergence, we adopt the framework presented by Pennacchio, Savaré, and Colli Franzone in "Multiscale modeling for the electrical activity of the heart", 2005, which is based on (a) the time-discretization of the evolution equations of the bidomain and $\varepsilon$-KNM systems via a semi-implicit Euler scheme, (b) the identification of the time-discrete solutions as extremal points of a Minimizing Movement scheme, and (c) the $Γ$-convergence of the Minimizing Movements functionals.
Comments26 pages, submitted
