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Contribution à l'amélioration du modèle de source dans la méthode des éléments finis pour la résolution du problème direct en électroencéphalographie

Abstract : Understanding the brain functions is one of the major challenges of neuroscience. To apprehend this organ in vivo many devices are developed, among them the electroencephalography (EEG). EEG measures directly and noninvasively the brain signals with high time resolution. The electrical activation of a region in the brain is modeled by a current dipole. The main objective of the EEG is monitoring the brain activity during a specific task and the location/reconstruction of the dipole sources within the brain. It is used both in practice and in research in neuroscience. The source’s localization process consists of solving an inverse problem that requires models of the solution of the direct or forward problem. The forward problem is the prediction of the electric potential on the scalp from a distribution sources in the brain. The accuracy of the source’s localization depends largely on the performance of the forward problem’s solution, which is related to the accuracy of the head model, the source model and the related method used to solve the forward problem.Currently in practice for reasons of computational simplicity and speed, EEG codes use mainly the multilayered spherical head model or the boundary element method for solving the forward problem. Improving the EEG’s source localization requires the use of more realistic head models which take into account more parameters such as inhomogeneity and anisotropy of the tissues. For these reasons the finite element method (FEM) is best suited and attracted the attention of many researchers. Nevertheless, with the FEM discretization, the sources may bring a numerical singularity; this negatively impacts the solution of the forward problem. To treat this problem some techniques such as the direct method, the subtraction method and the method of Saint-Venant are developed. However, all these methods show numerical instabilities in the case from sources close to the interfaces of brain tissue. To remedy these instabilities a modification was made on the Saint-Venant’s method.The report provides an overview on brain activity, a reminder of the FEM, its application for solving the forward problem in EEG, processing to treat the numerical singularity of the source and the instability near interfaces using the modified method of the Saint-Venant. We validate the results of the modified Venant’s method in models of multilayered spherical head and models with real geometries. Finally, we will test this approach in tools and software currently used in practice for locating areas activated in the brain and shows the improvements that can be made using the method of modified Saint-Venant.
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Submitted on : Wednesday, November 30, 2016 - 10:58:10 AM
Last modification on : Friday, May 29, 2020 - 3:57:33 PM
Document(s) archivé(s) le : Monday, March 27, 2017 - 8:10:01 AM


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  • HAL Id : tel-01400335, version 2


Takfarinas Medani. Contribution à l'amélioration du modèle de source dans la méthode des éléments finis pour la résolution du problème direct en électroencéphalographie. Electronique. Université Pierre et Marie Curie - Paris VI, 2016. Français. ⟨NNT : 2016PA066166⟩. ⟨tel-01400335v2⟩



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