ABIDI, Yassine; MAHJOUB, Moncef; ZEMZEMI, Nejib

Métadonnées

Licence d’utilisation du document

ABIDI, Yassine
Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis] [LR-LAMSIN-ENIT]

MAHJOUB, Moncef
Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis] [LR-LAMSIN-ENIT]

ZEMZEMI, Nejib
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]

Langue

Document de travail - Pré-publication

Résumé en anglais

In this work, we present an optimal control formulation for the bidomain model in order to estimate maximal conductance parameters in cardiac electrophysiology multiscale modelling. We consider a general Hodgkin-Huxley formalism to describe the ionic exchanges at the microscopic level. We treat the desired parameters as control variables in a cost function minimizing the gap between the measured and the computed transmembrane potentials. First, we establish the existence of an optimal control solution and we formally derive the optimality system. Second, we propose a strategy for solving the estimation problem for both single and multiple parameters cases. Our algorithm is based on a gradient descent method, where the gradient is obtained by solving an adjoint problem. Both the state and the adjoint problems are solved using the finite element method. Numerical simulations for single and multiple conductances estimations show the capability of this approach to identify the values of sodium, calcium and potassium ion channels conductances of the Luo Rudy phase I model.< Réduire

Mots clés en anglais

Optimal control with PDE constraints

Bidomain model

Physiological ionic model

Maximal conductance parameters

URI

https://oskar-bordeaux.fr/handle/20.500.12278/192737

Project ANR

L'Institut de Rythmologie et modélisation Cardiaque - ANR-10-IAHU-0004

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251