AOUADI, Saloua; MBARKI, Wajih; ZEMZEMI, Nejib

doi:10.1016/j.cam.2018.10.024

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AOUADI, Saloua
Université de Tunis El Manar [UTM]

MBARKI, Wajih
Université de Tunis El Manar [UTM]

ZEMZEMI, Nejib
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]

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Journal of Computational and Applied Mathematics. 2019

Elsevier

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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.< Leer menos

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Semi-implicit scheme

Monodomain/bidomain

Purkinje/myocardium

Discrete problem

Weighted Sobolev spaces

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

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