We present a modified bidomain model, derived with homogenization technique from assumption of existence of diffusive inclusions in the cardiac tissue. The diffusive inclusions represent regions without electrically active myocytes, e.g. fat, fibrosis etc. These regions are of scale $\varepsilon$, such that $d \ll \varepsilon \ll L$, where $d$ represents the scale of one myocyte and $L$ represents the tissue scale. Using the semigroup approach, we proved the existence and uniqueness of the solution for the mesoscale model, and using two-scale convergence we derived the limit problem, namely the modified bidomain model.
We present the application of this model to a rat heart. Starting from high resolution (HR) MRI, geometry is built and meshed using image processing techniques and software MUSIC. We perform the simulations on the mesh of 20 million tetrahedra. We used the C++ based software, CEPS, and we added the functionality in order to perform simulations for modified bidomain model. We use the Mitchell-Schaeffer ionic model, which we fit to the rat heart epicardium ionic model. We perform a study on the effects of tissue heterogeneities induced with diffusive inclusions on the velocity and shape of the depolarization wavefront. We study several test cases with different geometries for diffusive inclusions, and we find that both are affected.