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We study the homogenization of a novel microscopic tridomain system, allowingfor a more detailed analysis of the properties of cardiac conduction than theclassical bidomain and monodomain models. In (Acta Appl.Math. 179 (2022)1--35), we detail this model in which gap junctions are considered as theconnections between adjacent cells in cardiac muscle and could serve asalternative or supporting pathways for cell-to-cell electrical signalpropagation. Departing from this microscopic cellular model, we apply theperiodic unfolding method to derive the macroscopic tridomain model. Severaldifficulties prevent the application of unfolding homogenization results,including the degenerate temporal structure of the tridomain equations and anonlinear dynamic boundary condition on the cellular membrane. To prove theconvergence of the nonlinear terms, especially those defined on the microscopicinterface, we use the boundary unfolding operator and a Kolmogorov--Rieszcompactness's result.

asymptotic analysis

Microscopic tridomain model of electrical activity in the heart with  dynamical gap junctions. Part 2 -- Derivation of the macroscopic tridomain  model by unfolding homogenization method