Global Lipschitz stability of multiple space dependent ionic parameters for the MEA/hiPSC-CM assays. (1st January 2023)

• Record Type: Journal Article
• Authors: Ammar, Hamza; Mahjoub, Moncef; Zemzemi, Nejib
• Is Part Of: Inverse problems. Volume 39:Number 1(2023)
• Publication Date: 2023-01-01
• Subjects: parameter identification -- inverse problem -- reaction–diffusion equations -- Carleman estimate -- uniqueness -- stability result; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aca70d
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this paper, we consider an inverse problem of determining two space dependent ionic parameters of a strongly coupled parabolic-elliptic reaction–diffusion system arising in cardiac electrophysiology modeling when simulating drugs action with multi-electrode array/human induced pluripotent stem cells-cardiomyocytes assays. We use the bidomain model coupled to an ordinary differential equation and we consider the classical phenomenological model in cardiac electrophysiology of FitzHugh–Nagumo to describe the ionic exchanges at the microscopic level. Our main result is the uniqueness and a Lipschitz stability estimate for two ionic parameters ( k, γ ) of the model using sub-boundary observations over an interval of time. The key ingredients are a global Carleman-type estimates with a suitable observations acting on a part of the boundary.