  We study the homogenization of a novel microscopic tridomain system, allowing
for a more detailed analysis of the properties of cardiac conduction than the
classical bidomain and monodomain models. In (Acta Appl.Math. 179 (2022)
1--35), we detail this model in which gap junctions are considered as the
connections between adjacent cells in cardiac muscle and could serve as
alternative or supporting pathways for cell-to-cell electrical signal
propagation. Departing from this microscopic cellular model, we apply the
periodic unfolding method to derive the macroscopic tridomain model. Several
difficulties prevent the application of unfolding homogenization results,
including the degenerate temporal structure of the tridomain equations and a
nonlinear dynamic boundary condition on the cellular membrane. To prove the
convergence of the nonlinear terms, especially those defined on the microscopic
interface, we use the boundary unfolding operator and a Kolmogorov--Riesz
compactness's result.
