Influence of periodic diffusive inclusions on the bidomain model

We present a new mathematical model of the electric activity of the heart. In the standard bidomainmodel we can distinguish the intra- and the extracellular space with different conductivities for excitablecells and the fibrotic tissue around them. The main drawback is that it assumes the existence of excitablecells everywhere in the heart, while it is known that there exist non small regions where fibroblasts takeplace. The fibroblasts are equally distributed and since they are non excitable cells, they can beconsidered as a diffusive part. Hence we extend the standard bidomain model as follows: we assumethat we have periodic alternation of the healthy tissue (linear bidomain model) and fibrotic extracellularspace (diffusive part). We use homogenisation techniques to derive our macroscopic partial differentialequations. Interestingly, we obtain again a bidomain type model with modified conductivities thatinvolve the volume fraction of the diffusive domain. Preliminary numerical experiments will concludeon the influence of these diffusive inclusions