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Inverse ECG problem using the factorization method

hal.structure.identifierModélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
dc.contributor.authorZEMZEMI, Nejib
hal.structure.identifierModélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
dc.contributor.authorBOUYSSIER, Julien
dc.date.accessioned2024-04-04T03:19:02Z
dc.date.available2024-04-04T03:19:02Z
dc.date.conference2014-05-07
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194466
dc.description.abstractEnInverse Problem in Electrocardiography viaFactorization Method of Boundary ValueProblemsJulien Bouyssier, Nejib Zemzemi, Jacques Henry,CARMEN team, Inria Bordeaux Sud-Ouest200 avenue de la vieille tour, 33405 Talence CedexElectrocardiographic Imaging (ECGI) is a new imaging technique thatnoninvasively images cardiac electrical activity on the heart surface. InECGI, a multi-electrode vest records body-surface potential maps (BSPMs);then, using geometrical information from CT-scans and a mathematical al-gorithm, electrical potentials, electrograms and isochrones are reconstructedon the heart surface. The reconstruction of cardiac activity from BSPMs isan ill-posed inverse problem. In this work, we present an approach basedon an invariant embedding method: the factorization method of boundaryvalues problems [1, 2]. The idea is to embed the initial problem into a familyof similar problems on subdomains bounded by a moving boundary from thetorso skin to the epicardium surface. For the direct problem this method pro-Inverse Problem in Electrocardiography via FactorizationMethod of Boundary Value Problems :How reconstruct epicardial potential maps from measurements of the torso ?Julien Bouyssier, Nejib Zemzemi, Jacques Henryjulien.bouyssier@inria.fr, nejib.zemzemi@inria.fr, jacques.henry@inria.frMotivation and goalSolve the inverse problem in electrocardiography frommeasurements of the torso.factorizationmethod to compute epicardial potential maps.simplified presentation of the method by considering acylindrical geometry of our problem.Conclusions and perspectivesConclusions :Direct optimal estimation of t and ! before using any discretisation :=# Analyse ill-posedness and propose a better regularization and discretizationEquations for P and Q depend only of the geometry :=# Not necessary to repeat resolution at every time step of cardiac cyclePerspectives :Apply the method to 3D case where the moving boundary S will be a deformed surface :=# First : model of spheres=# Then : realistic geometries : how compute 3D surfaces ? + numerical cost ?. This method calculates Neumman-Dirichlet and Dirichlet-Neumannoperators on the moving boundary using Riccati equations. Mathematicalanalysis allows to write an optimal estimation of the epicardial potentialbased on a quadratic criterion. The analysis of the of the inverse problemill-posedness allows to compare different regularisation terms and choose abetter one. For numerical simulations we first construct a synthetical databased on the ECG solver [3]. The electrical potential on the torso boundaryis then extracts from the forward solution to be used as an input of the in-verse problem. The first obtained results using this method in 3D show thatwe can capture the wave front. Whereas the amplitude of theinverse problem solution is too low compared to the forward solution.References[1] Jacques Henry and Angel Manuel Ramos , La methode de factorisationdes problemes aux limites, book (in preparation), (2013)[2] Fadhel Jday, Completion de donnees frontieres : la methode de plonge-ment invariant, PHD thesis, (2012)[3] Nejib Zemzemi, Etude theorique et numerique de l'activite electrique ducoeur: Applications aux electrocardiogrammes, PHD thesis, (2009)2
dc.language.isoen
dc.title.enInverse ECG problem using the factorization method
dc.typeCommunication dans un congrès
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.conference.titlePICOF'2014
bordeaux.countryTN
bordeaux.conference.cityHammamet
bordeaux.peerReviewedoui
hal.identifierhal-01114023
hal.version1
hal.invitednon
hal.proceedingsnon
hal.conference.organizerLAMSIN
hal.conference.end2014-05-09
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01114023v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=ZEMZEMI,%20Nejib&BOUYSSIER,%20Julien&rft.genre=unknown


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