On the identification of multiple space dependent ionic parameters in cardiac electrophysiology modelling. (31st January 2018)

• Record Type: Journal Article
• Authors: Abidi, Yassine; Bellassoued, Mourad; Mahjoub, Moncef; Zemzemi, Nejib
• Is Part Of: Inverse problems. Volume 34:Number 3(2018:Mar.)
• Publication Date: 2018-01-31
• Subjects: Lipschitz stability estimate -- Carleman estimate -- cardiac electrophysiology modelling -- monodomain system -- Hodgkin–Huxley model -- ionic parameters identification; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aaa72e
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this paper, we consider the inverse problem of space dependent multiple ionic parameters identification in cardiac electrophysiology modelling from a set of observations. We use the monodomain system known as a state-of-the-art model in cardiac electrophysiology and we consider a general Hodgkin–Huxley formalism to describe the ionic exchanges at the microscopic level. This formalism covers many physiological transmembrane potential models including those in cardiac electrophysiology. Our main result is the proof of the uniqueness and a Lipschitz stability estimate of ion channels conductance parameters based on some observations on an arbitrary subdomain. The key idea is a Carleman estimate for a parabolic operator with multiple coefficients and an ordinary differential equation system.