A nash game algorithm for the solution of coupled conductivity identification and data completion in cardiac electrophysiology

Autor: Rabeb Chamekh, Moez Kallel, Nejib Zemzemi, Abderrahmane Habbal
Přispěvatelé: Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis] (LR-LAMSIN-ENIT), Ecole Nationale d'Ingénieurs de Tunis (ENIT), Université de Tunis El Manar (UTM)-Université de Tunis El Manar (UTM), Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Analysis and Control of Unsteady Models for Engineering Sciences (ACUMES), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], This work has been supported by EPICARD cooperative research program, funded by INRIA inter-national laboratory LIRIMA. The LAMSIN researcher’s work is supported on a regular basis by the Tunisian Ministryof Higher Education, Scientific Research and Technology. This s, LIRIMA, Epicard, ANR-10-IAHU-0004,LIRYC,L'Institut de Rythmologie et modélisation Cardiaque(2010), Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest
Jazyk: angličtina
Rok vydání: 2019
Předmět:
0209 industrial biotechnology
Computer science
[SDV.IB.IMA]Life Sciences [q-bio]/Bioengineering/Imaging
02 engineering and technology
01 natural sciences
Data completion
Dirichlet distribution
symbols.namesake
020901 industrial engineering & automation
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
0101 mathematics
Nash algorithm
Applied Mathematics
Inverse problem
[INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
010101 applied mathematics
Parameter identification problem
Elliptic operator
Identification (information)
Mathematics Subject Classification
Modeling and Simulation
symbols
Mathematics Subject Classification. 35J25
35N05
91A80

Identifiability
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Algorithm
Game theory
Conductivity identification
Zdroj: Mathematical Modelling of Natural Phenomena
Mathematical Modelling of Natural Phenomena, 2019, Mathematical modelling in cardiology, 14 (2), pp.15. ⟨10.1051/mmnp/2018059⟩
Mathematical Modelling of Natural Phenomena, EDP Sciences, 2019, Mathematical modelling in cardiology, 14 (2), pp.15. ⟨10.1051/mmnp/2018059⟩
ISSN: 0973-5348
1760-6101
DOI: 10.1051/mmnp/2018059⟩
Popis: International audience; We consider the identification problem of the conductivity coefficient for an elliptic operator using an incomplete over specified measures on the surface. Our purpose is to introduce an original method based on a game theory approach, and design a new algorithm for the simultaneous identification of conductivity coefficient and data completion process. We define three players with three corresponding criteria. The two first players use Dirichlet and Neumann strategies to solve the completion problem, while the third one uses the conductivity coefficient as strategy, and uses a cost which basically relies on an identifiability theorem. In our work, the numerical experiments seek the development of this algorithm for the electrocardiography imaging inverse problem, dealing with in-homogeneities in the torso domain. Furthermore, in our approach, the conductivity coefficients are known only by an approximate values. we conduct numerical experiments on a 2D torso case including noisy measurements. Results illustrate the ability of our computational approach to tackle the difficult problem of joint identification and data completion. Mathematics Subject Classification. 35J25, 35N05, 91A80. The dates will be set by the publisher.
Databáze: OpenAIRE
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