Numerical resolution of the inverse source problem for EEG using the quasi-reversibility method

Marion Darbas (1) , Juliette Leblond (2) , Jean-Paul Marmorat (3) , Pierre-Henri Tournier (4, 5)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 FACTAS - Analyse fonctionnelle pour la conception et l'analyse de systèmes
3 CMA - Centre de Mathématiques Appliquées
4 ALPINES - Algorithms and parallel tools for integrated numerical simulations
5 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

The paper concerns the numerical resolution of the inverse source problem for electroencephalography (EEG). We propose an approach which is able to take into account some heterogeneity properties (namely a varying electrical conductivity) of the head tissues, in particular of the skull layer. It combines two consecutive steps: (i) a data completion procedure from the scalp to the cortex using the quasi-reversibility (QR) method, (ii) a source estimation method from these cortical transmitted data within the brain (modeled as sphere), developed in the software tool FindSources3D (FS3D). Numerical simulations in the case of the multi-layered spherical head model illustrate both the promising and limiting features of the approach.

Keywords: Inverse problems; elliptic PDE; quasi-reversibility; best constrained approximation; brain imaging (EEG)

Domains: Mathematics [math]

Marion Darbas, Juliette Leblond, Jean-Paul Marmorat, Pierre-Henri Tournier. Numerical resolution of the inverse source problem for EEG using the quasi-reversibility method. Inverse Problems, 2023, 39 (11), pp.115003. ⟨10.1088/1361-6420/acf9c6⟩. ⟨hal-03880526v2⟩