Reduced Order Models, Forward and Inverse Problems in Cardiac Electrophysiology

Abstract : This PhD thesis is dedicated to the investigation of the forward and the inverse problem of cardiac electrophysiology. Since the equations that describe the electrical activity of the heart can be very demanding from a computational point of view, a particular attention is paid to the reduced order methods and to their application to the electrophysiology models. First, we introduce the mathematical and numerical models of electrophysiology and we implement them to provide for simulations that are validated against various qualitative and quantitative criteria found in the medical literature. Since our model takes into account atria and ventricles, we are able to reproduce full cycle Electrocardiograms (ECG) in healthy configurations and also in the case of several pathologies. Then, several reduced order methods are investigated for the resolution of the electrophysiology equations. The Proper orthogonal Decomposition (POD) method is applied for the discretization of the electrophysiology equations in several configurations, as for instance the simulation of a myocardial infarction. Also, the method is used in order to solve some parameters identification problems such as the identification of an infarcted zone using the Electrocardiogram measures and for the efficient simulation of restitution curves. To circumvent some limitations of the POD method, a new reduced order method based on the Approximated Lax Pairs (ALP) is investigated. This method is applied to the forward and inverse problems. Finally, a new reduced order algorithm is proposed, based on the ALP and the Discrete Empirical Interpolation methods. This new approach significantly improves the efficiency of the original ALP algorithm and allow us to consider more complex models used in electrophysiology.
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Submitted on : Tuesday, December 9, 2014 - 5:19:28 PM
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Elisa Schenone. Reduced Order Models, Forward and Inverse Problems in Cardiac Electrophysiology. General Mathematics [math.GM]. Université Pierre et Marie Curie - Paris VI, 2014. English. ⟨NNT : 2014PA066447⟩. ⟨tel-01092945⟩

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