Stability results for the parameter identification inverse problem in cardiac electrophysiology. (20th September 2016)

• Record Type: Journal Article
• Authors: Lassoued, Jamila; Mahjoub, Moncef; Zemzemi, Néjib
• Is Part Of: Inverse problems. Volume 32:Number 11(2016:Nov.)
• Publication Date: 2016-09-20
• Subjects: parameter identification -- carleman inequality -- stability result -- monodomain system -- Mitchell–Schaeffer model -- ionic parameters; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/11/115002
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this paper we prove a stability estimate of the parameter identification problem in cardiac electrophysiology modeling. We use the monodomain model which is a reaction diffusion parabolic equation where the reaction term is obtained by solving an ordinary differential equation (ODE). We are interested in proving the stability of the identification of the parameter τ in, which is the parameter that multiplies the cubic term in the reaction term. The proof of the result is based on a new Carleman-type estimate for both partial differential equation (PDE) and ODE problems. As a consequence of the stability result we prove the uniqueness of the parameter τ in giving some observations of both state variables at a given time t 0 in the whole domain and in the PDE variable in a non empty open subset w 0 of the domain.