Cardiac arrhythmias are increasingly being treated using ablation procedures. Development of fast electrophysiological models and estimation of parameters related to conduction pathologies can aid in the investigation of better treatment strategies during Radio-frequency ablations. We present a fast electrophysiological model incorporating anisotropy of the cardiac tissue. A global-local estimation procedure is also outlined to estimate a hidden parameter (apparent electrical conductivity) present in the model. The proposed model is tested on synthetic and real data derived using XMR imaging. We demonstrate a qualitative match between the estimated conductivity parameter and possible pathology locations. This approach opens up possibilities to directly integrate modelling in the intervention room.