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Section: New Results
Numerical methods for cardiac electrophysiology
Participants : Muriel Boulakia, Miguel Ángel Fernández Varela, Jean-Frédéric Gerbeau, Vincent Martin, Elisa Schenone.
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[32] : We consider the problem of estimating some parameters of a model of electrocardiograms from the data of the Einthoven leads. The direct model is based on the bidomain equations in the heart and a Poisson equation in the torso. To keep the computational time reasonable, the evaluation of the direct problem is approximated with a reduced order model based on Proper Orthogonal Decomposition.The optimization problem is solved using an evolutionary algorithm. Numerical tests show that, with noisy synthetic data, the proposed procedure allows to recover ionic parameters and initial activation regions with a fair accuracy.
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[34] and [48] : In presence of a high magnetic field, the blood flow in the aorta induces an electrical potential which is responsible for an increase of the -wave in the electrocardiogram (ECG). This phenomenon may perturb ECG-gated imaging. The aim of this numerical study is to reproduce this experimental observation through computer simulations. The proposed model consists of three components: magnetohydrodynamics (MHD) in the aorta, bidomain equations in the heart and electrical diffusion in the rest of the body. These models are strongly coupled together and solved with finite elements.
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[38] : We present an overview of our works about electrocardiogram numerical simulations.
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[45] : A reduced-order model based on Proper Orthogonal Decomposition is proposed for the bidomain equations of cardiac electrophysiology. Its accuracy is assessed through electrocardiograms in various configurations, including myocardium infarctions and long-time simulations. We show in particular that a restitution curve can efficiently be approximated by this approach. The reduced-order model is then used in an inverse problem solved by an evolutionary algorithm. Some attempts are presented to identify infarction locations from synthetic electrocardiograms.