Minisymposium at the AMAM conference, Nice (France), Feb 10-13 2003
Coordinator: Maureen Clerc +33 (0)4 92 38 77 35
"Basic modeling and estimation of generators from the electro and magnetoencephalogram. "
Sylvain Baillet (CNRS, CHU Pitié-Salpêtrière) , joint work with Line Garnero, Cognitive Neuroscience & Brain Imaging Laboratory, Hôpital de la Salpêtrière, 47, blvd de l'hopital - 75651 Paris Cedex 13 - France
Abstract: Electroencephalography (EEG) and Magnetoencephalography (MEG) are two non-invasive techniques which are sensitive to cortical electrophysiological activity. Characterization and imaging of their generators may contribute to a better understanding of the dynamics of neural activations across the cortex in the millisecond time range. Though the corresponding inverse problem is ill-posed, reasonable a priori modeling of basic properties of the expected neural source assemblies can be introduced as regularization features of the source estimation process. We will introduce some of the basic forward and inverse approaches used in the MEG/EEG imaging community and illustrate the techniques with examples of experimental protocols from cognitive neurophychology and clinical research in epilepsy.
"Solving the direct EEG-MEG problem with the Symmetric Boundary Element Method"
Maureen Clerc (CERMICS, ENPC), joint work with Renaud Keriven (CERMICS, ENPC), Jan Kybic (INRIA), Théo Papadopoulo (INRIA), Olivier Faugeras (INRIA), members of the Odyssée Project
Abstract: This talk addresses the "direct EEG problem": the calculation of the electric potential on the scalp for a known configuration of sources, assuming piecewise constant tissue conductivities. The potential is the solution of a Poisson equation, which, under a piecewise constant head conductivity model, can be solved using a Boundary Element Method. All previous Boundary Element solutions to this problem have used the same integral formulation, based on a double layer potential. In this talk we introduce a new symmetric formulation which combines single and double layer potentials. Numerical experiments show that our new Boundary Element solution is significantly more accurate than the classical Boundary Element results reported in the litterature.
"Identification of dipoles in EEG-MEG"
Tuong Ha-Duong (UTC Compiègne)
Abstract: We discuss in this talk the mathematical problem of identifying the primary sources in the brain from the measurements of the electric field at the surface of the head (EEG) or the magnetic field around the head (MEG). We assume that the head is made up of disjoint coated domains (scalp, skull, cerebrospinal fluid and brain), in each of which the conductivity is constant, and that the support of the cerebral current is in the innermost one (the cortex). Otherwise the geometry of these domains can be arbitrary. We show that, in general, these exterior measurements do not permit to determine uniquely distributed currents. However, for mono or dipole sources, this uniqueness is true, and in this case, we give an algorithm to determine the number, locations and moments of the dipoles.
"Sources identification using meromorphic approximation"
Juliette Leblond (Miaou Project, INRIA), joint work with A. Ben Abda, L. Baratchart, F. Ben Hassen, J.-P. Marmorat
Abstract: We approach the inverse problem of determining pointwise conductivity defaults of a solution to Laplace equation from boundary data. In both 2D and 3D cases, we show how this issue can be expressed as a rational or meromorphic approximation problem with constrained poles. This provides the basis of a constructive test to establish the presence of sources in the domain (brain) and to to localize them, as singularities (analyticity defaults) of some function of the complex variable.