Ionic parameters identification of an inverse problem of strongly coupled PDE's system in cardiac electrophysiology using Carleman estimates - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Mathematical Modelling of Natural Phenomena Year : 2019

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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Dates and versions

hal-01923862 , version 1 (15-11-2018)

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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, 2019, Mathematical Modelling in Cardiology, 14 (2), ⟨10.1051/mmnp/2018060⟩. ⟨hal-01923862⟩
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