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A layer potential approach to inverse problems in brain imaging

hal.structure.identifierAnalyse fonctionnelle pour la conception et l'analyse de systèmes [FACTAS]
dc.contributor.authorASENSIO, Paul
dc.contributor.authorBADIER, Jean-Michel
hal.structure.identifierAnalyse fonctionnelle pour la conception et l'analyse de systèmes [FACTAS]
dc.contributor.authorLEBLOND, Juliette
hal.structure.identifierCentre de Mathématiques Appliquées [CMA]
dc.contributor.authorMARMORAT, Jean-Paul
hal.structure.identifierAnalyse fonctionnelle pour la conception et l'analyse de systèmes [FACTAS]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorNEMAIRE, Masimba
dc.date.accessioned2024-04-04T02:31:53Z
dc.date.available2024-04-04T02:31:53Z
dc.date.created2023
dc.date.issued2023-02
dc.identifier.issn0928-0219
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190338
dc.description.abstractEnWe study the inverse source (primary current) localisation problem using the electrical potential measured point-wise inside the head with stereo-ElectroEncephaloGraphy (sEEG), the electrical potential measured point-wise on the scalp with ElectroEncephaloGraphy (EEG) or the magnetic flux density measured point-wise outside the head with MagnetoEncephaloGraphy (MEG). We present a method that works on a wide range of models of primary currents, in particular we give details for primary currents that are assumed to be smooth vector-fields that are supported on and normally oriented to the grey/white matter interface. Irrespective of the data used we need to understand the transmission of the electric potential associated with a recovered source through the head hence we solve the cortical mapping problem. To ensure that the electric potential and normal currents are continuous in the head, the electric potential is expressed as a linear combination of double layer potentials and the magnetic flux density is expressed as a linear combination of single layer potentials. Numerically, we solve the problems on meshed surfaces of the grey/white matter interface, cortical surface, skull and scalp. A main feature of the numerical approach we take is that on the meshed surfaces we can compute the double and single layer potentials exactly and at arbitrary points. Because we study the transmission of the electric potential in head irrespective of the modality used, this enables the coupling of electric and magnetic data in the source recovery problem. We provide numerical examples of the source recovery and inverse cortical mapping using synthetic data.
dc.language.isoen
dc.publisherDe Gruyter
dc.rights.urihttp://creativecommons.org/licenses/by/
dc.subject.eninverse problems
dc.subject.enlayer potentials
dc.subject.enEEG
dc.subject.enMEG
dc.subject.ensEEG
dc.title.enA layer potential approach to inverse problems in brain imaging
dc.typeArticle de revue
dc.identifier.doi10.1515/jiip-2023-0041
dc.subject.halMathématiques [math]
bordeaux.journalJournal of Inverse and Ill-posed Problems
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03977724
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03977724v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Inverse%20and%20Ill-posed%20Problems&rft.date=2023-02&rft.eissn=0928-0219&rft.issn=0928-0219&rft.au=ASENSIO,%20Paul&BADIER,%20Jean-Michel&LEBLOND,%20Juliette&MARMORAT,%20Jean-Paul&NEMAIRE,%20Masimba&rft.genre=article


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