Titre

Line, Surface, and Volume Integral Equations for the Electromagnetic Modelling of the Electroencephalography Forward Problem

Auteur(s)

PILLAIN Axelle1,2

Type de document

Thèse

Source

Th. doct. : Sciences de l'Ingénieur, Institut Mines-Télécom-Télécom Bretagne-UEB, UMR CNRS 6285 - Télécom Bretagne - Université de Bretagne Occidentale - Université de Bretagne Sud - ENSTA Bretagne - Ecole Nationale d'ingénieurs de Brest, october 2016

Année

2016

Résumé

Electroencephalography (EEG) is a very useful tool for characterizing epileptic sources. Brain source imaging with EEG necessitates to solve the so-called EEG inverse problem. Its solution depends on the solution of the EEG forward problem that provides from known current sources the potential measured at the electrodes positions. For realistic head shapes, this problem can be solved with different numerical techniques. In particular surface integral equations necessitates to discretize only the interfaces between the brain compartments. However, the existing formulations do not take into account the anisotropy of the media. The work presented in this thesis introduces two new integral formulations to tackle this weakness. An indirect formulation that can handle brain anisotropies is proposed. It is discretized with basis functions conform to the mapping properties of the involved operators. The effect of this mixed discretization on brain source reconstruction is also studied. The second formulation focuses on the white matter fiber anisotropy. Obtaining the solution to the obtained numerical system rapidly is also highly desirable. The work is hence complemented with a proof of the preconditioning effect of Calderon strategies for multilayered media. The proposed theorem is applied in the context of solving the EEG forward problem. A Calderon preconditioner is also introduced for the wire electric field integral equation. Finally, preliminary results on the impact of a fast direct solver in solving the EEG forward problem are presented.

Labos

1 : MO(TB) - Dépt. Micro-Ondes (Institut Mines-Télécom-Télécom Bretagne-UEB)
2 : Lab-STICC(TB) - Laboratoire en sciences et technologies de l'information, de la communication et de la connaissance (UMR CNRS 6285 - Télécom Bretagne - Université de Bretagne Occidentale - Université de Bretagne Sud - ENSTA Bretagne - Ecole Nationale d'ingénieurs de Brest)

Mots clés

EEG, Boundary Element Method, Forward Problem, Integral Equations, Preconditioning

Référence

17783

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