Coupling of numerical methods for the forward problem in Magneto- and Electro-Encephalography

Emmanuel Olivi 1
1 ATHENA - Computational Imaging of the Central Nervous System
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : Electro- and Magneto-Encephalography are precious tools for studying brain activity, notably due to their time resolution and their non invasive nature. Acquisitions are done on the exterior of the head (scalp electrodes for EEG, and magnetometers for MEG); in order to recover the sources responsible of the measured signal, an inverse problem must be solved, for which accurate solutions of the forward problem must be available. This requires a good modeling of the head tissues, and an appropriate representation of this electrophysiological model within numerical methods such as the BEM or FEM. In this thesis we focus on this dual problem of modeling and numerical resolution, notably to handle the skull region which must often be considered anisotropic or highly inhomogeneous in clinical applications, and for the white matter anisotropy which surrounds the sources in the brain. In this thesis we first see the common numerical solvers for solving the forward problem, and expose their strengths and weaknesses. Then, a dual point of view for solving the forward problem using any numerical method is exposed; which is the adjoint method of our forward problem. Its application within a BEM framework is given. Later using a domain decomposition (DD) framework, we present different coupling procedures of the main methods BEM and FEM, in order to get both methods advantages regarding the resolution of the forward problem (notably for handling the skull). This is done within a DD framework, which appears to be interesting in many points. Finally, we propose a new method for dealing with locally anisotropic or inhomogeneous conductivities using a BEM.
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Emmanuel Olivi. Coupling of numerical methods for the forward problem in Magneto- and Electro-Encephalography. Numerical Analysis [cs.NA]. Université Nice Sophia Antipolis, 2011. English. ⟨tel-00838707⟩

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