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The cardiac bidomain model and homogenization

  • * Corresponding author: Erik Grandelius

    * Corresponding author: Erik Grandelius 

This work was supported by the Research Council of Norway (project 250674/F20)

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  • 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.

    Mathematics Subject Classification: Primary: 35K57, 35B27; Secondary: 35K65, 92C30.


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  • Figure 1.  The rescaled sets $ \Omega_i^{\varepsilon} $, $ \Omega_e^{\varepsilon} $, $ \Gamma^{\varepsilon} $ (left) and the unit cell $ Y $ (right)

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