Section: New Results

MEG, EEG

ECoG

Participants : Maureen Clerc, Analisa Pascarella [CNR-IAC Roma] , Michele Piana [University of Genova] .

Electrocorticography (ECoG) measures the distribution of the electrical potentials on the cortex produced by the neural currents. A full interpretation of ECoG data requires solving the ill-posed inverse problem of reconstructing the spatio-temporal distribution of the neural currents. This study addresses the ECoG source modeling developing a beamformer method. New method: We computed the lead-field matrix by using a novel routine provided by the OpenMEEG software. We performed an analysis of the numerical stability of the ECoG inverse problem by computing the condition number of the lead-field matrix for different configurations of the electrodes grid. We applied a Linear Constraint Minimum Variance (LCMV) beamformer to both synthetic data and a set of real measurements recorded during a rapid visual categorization task. For all considered grids the condition number indicates that the ECoG inverse problem is mildly ill-conditioned. For realistic SNR we found a good performance of the LCMV algorithm for both localization and waveforms reconstruction. Comparison with existing method: The flow of information reconstructed by analyzing real data seems consistent with both invasive monkey electrophysiology studies and non-invasive (MEG and fMRI) human studies. Despite a growing interest from the neuroscientific community, solving the ECoG inverse problem has not quite yet reached the level of systematicity found for EEG and MEG. Starting from an analysis of the numerical stability of the problem we considered the most widely utilized method for modeling neurophysiological data based on the beamformer method in the hope to establish benchmarks for future studies.

This work has been published in [18].

Conductivity estimation

Participants : Maureen Clerc, Christos Papageorgakis, Juliette Leblond [APICS project-team] , Jean-Paul Marmorat [CMA Ecole des Mines Paritech] .

Considering a geometry made of three concentric spherical nested layers, each with constant homogeneous conductivity, we establish a uniqueness result in inverse conductivity estimation, from partial boundary data in presence of a known source term. We make use of spherical harmonics and linear algebra computations, that also provide us with stability results and a robust reconstruction algorithm. As an application to electroencephalography (EEG), in a spherical 3-layer head model (brain, skull, scalp), we numerically estimate the skull conductivity from available data (electrical potential at electrodes locations on the scalp, vanishing current flux) and given pointwise dipolar sources in the brain. This work was supported by the Région Provence-Alpes-Côte d'Azur, France, and BESA GmbH, Germany.

This work has been published in [14] and [29].

Efficient lead field computation a la Reduced Basis Methods

Participants : Kostiantyn Maksymenko, Maureen Clerc, Théodore Papadopoulo.

Bioelectric source analysis in the human brain from scalp electroencephalography (EEG) signals is sensitive to geometry and conductivity properties of the different head tissues. These conductivities can vary a lot across subjects so non-invasive methods of conductivity estimation are required. To achieve this, we should have a possibility to compute a forward EEG problem solution for a large number of conductivity configurations. We propose a method of approximation of these solutions using a relatively small number of basis points, which will allow us to dramatically decrease required computing time.