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Integral Formulations for the EEG Problem

Jan Kybic 1 Maureen Clerc Toufic Abboud Olivier Faugeras Renaud  Keriven Théodore Papadopoulo
1 ODYSSEE - Computer and biological vision
DI-ENS - Département d'informatique de l'École normale supérieure, CRISAM - Inria Sophia Antipolis - Méditerranée , ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
Abstract : The forward electro-encephalography (EEG) problem involves finding a potential V from the Poisson equation (V)=f, in which f represents electrical sources in the brain, and the conductivity of the head tissues. In the piecewise constant conductivity head model, this can be accomplished by the Boundary Element Method (BEM) using a suitable integral formulation. Most previous work is based on the same integral formulation, based on a double-lay- er potential. In this article we detail several alternative possibilities. We present a dual approach which involves a single-layer potential. Finally, we propose a symmetric formulation, which combines single and double-layer potentials, and which is new to the field of EEG, although it has been applied to other problems in electromagnetism. The three methods have been evaluated numerically using a semi-realistic geometry with known analytical solution, and the symmetric method achieves a significantly higher accuracy.
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Submitted on : Tuesday, May 23, 2006 - 6:57:42 PM
Last modification on : Tuesday, September 22, 2020 - 3:58:25 AM
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  • HAL Id : inria-00071852, version 1



Jan Kybic, Maureen Clerc, Toufic Abboud, Olivier Faugeras, Renaud  Keriven, et al.. Integral Formulations for the EEG Problem. RR-4735, INRIA. 2003. ⟨inria-00071852⟩



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