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Ionic parameters identification of an inverse problem of strongly coupled PDE's system in cardiac electrophysiology using Carleman estimates

Abstract : In this paper, we consider an inverse problem of determining multiple ionic parameters of a 2 × 2 strongly coupled parabolic-elliptic reaction-diffusion system arising in cardiac electrophysiology modelling. We use the bidomain model coupled to an ODE system and we consider a general formalism of physiologicaly-detailed cellular membrane models to describe the ionic exchanges at the microscopic level. Our main result is the uniqueness and a Lipschitz stability estimate of the ion channels con-ductance parameters of the model using subboundary observations over an interval of time. The key ingredients are a global Carleman-type estimate with a suitable observations acting on a part of the boundary.
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https://hal.inria.fr/hal-01923862
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Submitted on : Thursday, November 15, 2018 - 3:04:19 PM
Last modification on : Tuesday, October 22, 2019 - 12:00:41 PM

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Yassine Abidi, Mourad Bellassoued, Moncef Mahjoub, Nejib Zemzemi. Ionic parameters identification of an inverse problem of strongly coupled PDE's system in cardiac electrophysiology using Carleman estimates. Mathematical Modelling of Natural Phenomena, EDP Sciences, 2019, Mathematical Modelling in Cardiology, 14 (2), ⟨10.1051/mmnp/2018060⟩. ⟨hal-01923862⟩

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