Asymptotic Analysis of the Static Bidomain Model

In this talk, I present a formal asymptotic analysis of the static bidomain model, focusing on a domain containing a thin sheet where the intra-cellular conductivity scales with the square of the sheet’s thickness. In particular, I outline the asymptotic analysis by considering an asymptotic expansion of the intra- and extra-cellular potentials in a nonlinear context. This allows us to determine transmission conditions at the interface at any order. The asymptotic expansion is proven by deriving estimates of the H1 and L2 norms of the errors of an expansion with a given number of terms. The study is validated by numerical convergence tests and numerical simulations are proposed in the context of cardiac arrhythmias applications, specifically for ablation techniques to isolate the pathologies.