Analysis of the heart-torso conductivity parameters recovery inverse problem in cardiac electrophysiology ECG modelling

Abstract

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Global Lipschitz stability of multiple space dependent ionic parameters for the MEA/hiPSC-CM assays

“…The paper [26] shows the stability of the identification of a reaction parameter in the Mitchell-Schaeffer model for the monodomain system. The paper [4] prove a stability estimate for both heart and torso conductivity parameters. The approach used in all the works cited uses Carleman estimates.…”

“…Let us first give regularity results on the solution of system (1a)-(1h) completed by (4). These results can be proved using the existence and uniqueness result from [33] and thanks to successive energy estimates on the solution and its derivatives with respect to time and using elliptic energy estimates.…”

Carleman estimates and some inverse problems for the coupled quantitative thermoacoustic equations by partial boundary layer data. Part II: Some inverse problems

“…For the development of this approach, there are many works. We refer to some of them (e.g., [7–38], and the references therein). The main advantages of this approach concern the finite number of observations required, the obtention of stability inequalities between the coefficient to be reconstructed, and the observation data.…”