Math. Model. Nat. Phenom.
Volume 14, Number 2, 2019
Mathematical modelling in cardiology
|Number of page(s)||24|
|Published online||15 February 2019|
Ionic parameters identification of an inverse problem of strongly coupled PDE’s system in cardiac electrophysiology using Carleman estimates
Tunis El Manar University, ENIT-LAMSIN, BP 37,
1002 Tunis, Tunisia.
2 INRIA, Bordeaux Sud-Ouest, 200 Avenue de la vielle Tour, 33405 Talence Cedex, France.
3 IHU LIRYC, Electrophysiology and Heart Modeling Institute, Pessac, France.
* Corresponding author: firstname.lastname@example.org
Accepted: 2 October 2018
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 modeling. We use the bidomain model coupled to an ordinary differential equation (ODE) system and we consider a general formalism of physiologically 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 conductance 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.
Mathematics Subject Classification: 35Q92 / 34A55
Key words: Lipschitz stability estimate / Carleman estimate / cardiac electrophysiology / bidomain system / physiological ionic model / ionic parameters
© EDP Sciences, 2019
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