Modèles numériques personnalisés de la fibrillation auriculaire

Abstract : Atrial arrhythmias are a major pathology in cardiology, and their study is alarge research topic. To study them, many mathematical models of the actionpotential propagation in atria have been developed. Most of those generic models can be used to reproduce typical activation sequences of the atria. Such models may have an experimental or even clinical interest, for example in helping the location of arrhythmic foci or in the analysis of treatment failures for these arrhythmias. Nevertheless, to achieve this goal, it isnecessary to be able to adjust the model at best, based on experimental orclinical data. Data assimilation, a mathematical discipline in which we seek to optimally combine theory and observations, is then a good candidate for the customization of action potential propagation models.In this thesis, we propose to study different data assimilation methods-- sequential and variational -- in order to adjust action potential propagation model on electroanatomical data. More precisely, we are interested in two possible applications of data assimilation: state estimation and parameter estimation.First, we study a state observer which is able to correct the simulatedpropagation front localization based on the observed front localization. Thisobserver is then used to complete an activation map obtained during a clinical procedure.Then, this observer is combined with a reduced order Kalman filterin order to estimate the conductivity parameters of the action potentialpropagation model. A study of the joint state-parameter estimationstrategy is then realized to see how the method behaves faced with modelingerrors. The method is then tested on a clinically acquired dataset.Then, we look at variational data assimilation methods that allow the estimation of spatially distributed parameters. Several minimization problems, allowing to estimate a conductivity parameter distributed in space, are then introduced and analyzed. We then show that the discretization of these minimization problems, in order to obtain numerical methods of resolution, can be complex. A numerical method is then implemented for one of the studied minimization problems, and three 1D test cases are analyzed.Finally, we demonstrate the existence of a minimum for one of the studiedobjective function based on functional analysis results from theliterature.
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Antoine Gerard. Modèles numériques personnalisés de la fibrillation auriculaire. Modélisation et simulation. Université de Bordeaux, 2019. Français. ⟨NNT : 2019BORD0120⟩. ⟨tel-02297510⟩

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