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Towards the modelling of the Purkinje/ myocardium coupled problem: A well-posedness analysis

Saloua Aouadi 1 Wajih Mbarki 1 Nejib Zemzemi 2
2 CARMEN - Modélisation et calculs pour l'électrophysiologie cardiaque
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest, IHU-LIRYC
Abstract : The Purkinje network is the specialized conduction system in the heart. It ensures the physiological spread of the electrical wave in the ventricles. In this work, in an insulated heart framework, we model the free running Purkinje system, using the monodomain equation. The intra-myocardium part of the Purkinje fiber is coupled to the ventricular tissue using the bidomain equation. The coupling is performed through the extracellular potential. We discretize the problem in time using a semi-implicit scheme. Then, we write a variational formulation of the semi discrete problem in a non standard weighted Sobolev functional spaces. We prove the existence and uniqueness of the solution of the Purkinje/myocardium semi-discretized problem. We discretize in space by the finite element P 1 − Lagrange and conduct some numerical tests showing the anterograde and retrograde propagation of the electrical wave between the tissue and the Purkinje fibers.
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Submitted on : Thursday, November 15, 2018 - 2:25:03 PM
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Saloua Aouadi, Wajih Mbarki, Nejib Zemzemi. Towards the modelling of the Purkinje/ myocardium coupled problem: A well-posedness analysis. Journal of Computational and Applied Mathematics, Elsevier, 2019, ⟨10.1016/j.cam.2018.10.024⟩. ⟨hal-01923779⟩

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