On the reconstruction of cavities in a nonlinear model arising from cardiac electrophysiology

In this paper, we deal with the problem of determining perfectly insulating regions (cavities) from one boundary measurement in a nonlinear elliptic equation arising from cardiac electrophysiology. Based on the results obtained in [9] we propose a new reconstruction algorithm based on $\mathrm{\Gamma }$-convergence. The relevance and applicability of this approach are then shown through several numerical experiments.