  In this paper we consider the monodomain model of cardiac electrophysiology.
After an analysis of the well-posedness of the model, we determine an
asymptotic expansion of the perturbed potential due to the presence of small
conductivity inhomogeneities (modeling small ischemic regions in the cardiac
tissue) and use it to detect the anomalies from partial boundary measurements.
This is done by determining the topological gradient of a suitable boundary
misfit functional. The robustness of the algorithm is confirmed by several
numerical experiments.
