Reduced models in cardiac electrophysiology. Applications to the inverse problem

This Master Thesis is the result of a six month internship in the REO group of the Insitut Nationale de Recherche Informatique et Automatique (INRIA) of Rocquencourt - Paris (France), under the supervision of Jean-Frédéric Gerbeau and Muriel Boulakia. This work aim is the application of the Proper Orthogonal Decomposition (POD) as a reduced model technique in cardiac electrophysiology. The main features used to solve and treat this problem are the bi-domain model, the Mitchell and Schaeffer ionic model and the Electrocardiogram (ECG). Particularly, we focused on two medical studies: myocardial transmural infarction and accelerated beats. In both cases we numerically solved the problem with a complete model and with a reduced one and we faced with an inverse problem. In the study of the myocardial infarction we are aimed to find the infarcted area starting from a simulated ECG, applying a genetic algorithm. In the case of the simulation of a long sequence of accelerated beats, the solutions and the corresponding ECG are used to build the so-called restitution curve. Once obtained the restitution curve, i.e. a relationship between the two main phases of a cardiac beat, we applied some theoretical results in order to estimate some parameters of the ionic model. Dealing with this last part, here is presented a preliminary study useful for future work.