The cardiac bidomain model and homogenization

2018/11/19 by Erik Grandelius, Kenneth H. Karlsen, Grandelius, Erik +1
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1811.07524

openalex publication_date 2018/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a rather simple proof of a homogenization result for the bidomain model of cardiac electrophysiology. Departing from a microscopic cellular model, we apply the theory of two-scale convergence to derive the bidomain model. To allow for some relevant nonlinear membrane models, we make essential use of the boundary unfolding operator. There are several complications preventing the application of standard homogenization results, including the degenerate temporal structure of the bidomain equations and a nonlinear dynamic boundary condition on an oscillating surface.

Citations

• A quantitative description of membrane current and its application to conduction and excitation in nerve

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