## Section: New Results

### Brain functional imaging using MEG/EEG

The work depicted in this sub-theme concerns various aspects related to the problem of estimating the sources in the brain corresponding to some given activity. Besides the forward and inverse EEG/MEG problems (see sections 6.4.4 – 6.4.8 ) which are directly connected to this problem, there are a number of additionnal problems such as finding the events of interest in the recorded signal (sections 6.4.2 and 6.4.3 ), applying the reconstruction methods developped in the project to the problem of retinotopy (section 6.4.9 ) or providing a simple user interface to promote those in the clinical environment (section 5.4 ). Finally, the same set of tools can also be applied to model nerve stimulation (see section 6.1.9 ).

#### Combinatorial optimization and applications to EEG

Participants : Mickael Pechaud, Renaud Keriven, Théo Papadopoulo, Jean-Michel Badie.

An important issue in electroencephalographiy (EEG) experiments is to measure accurately the three dimensional (3D) positions of the electrodes. A system is proposed where these positions are automatically estimated from several images using computer vision techniques. Yet, only a set of undifferentiated points are recovered this way and remains the problem of labeling them, i.e. of finding which electrode corresponds to each point. A fast and robust solution is designed to this latter problem based on combinatorial optimization. A specific energy is minimized with a modified version of the Loopy Belief Propagation algorithm. Experiments on real data show that a manual labeling of two or three electrodes only is sufficient to get the complete labeling of a 64 electrodes cap in less than 10 seconds.

This work has been presented in [Oops!] , [Oops!] .

#### Single-Trial MEG and EEG analysis

Participants : Maureen Clerc, Theo Papadopoulo, Christian Bénar [ INSERM U751 ] .

##### Non-linear fit of time frequency atoms

In [Oops!] we introduce a new method for estimating single-trial magneto- or electro-encephalography (M/EEG), based on a non-linear fit of time-frequency atoms. The method can be applied for transient activity (e.g. event-related potentials) as well as for oscillatory activity (e.g. gamma bursts), and for both evoked or induced activity. In order to benefit from all the structure present in the data, the method accounts for (i) spatial structure of the data via multivariate decomposition, (ii) time-frequency structure via atomic decomposition and (iii) reproducibility across trials via a constraint on parameter dispersion. Moreover, a novel iterative method is introduced for estimating the initial time-frequency atoms used in the non-linear fit. Numerical experiments show that the method is robust to low signal-to-noise conditions, and that the introduction of the constraint on parameter dispersion significantly improves the quality of the fit.

##### Decomposition of signals

In [Oops!] presents a method for decomposing MEG or EEG data (channel × time × trials) into a set of atoms with fixed spatial and time-frequency signatures. The spatial part (i.e., topography) is obtained by independent component analysis (ICA), in order to separate activities that overlap at the sensor level. We propose a frequency prewhitening procedure as a pre-processing step before ICA, which gives access to high frequency activity. The time-frequency part is obtained with a novel iterative procedure, which bears similarities with the matching pursuit procedure, but with an extension to data organized in trials. The method is evaluated on a simulated dataset consisting of several simulated components, presenting both low-frequency evoked potentials and high-frequency oscillatory activity, with added noise correlated in time and space. We show that the method is able to recover well both low-frequency and high-frequency simulated activities. There was however some cross-talk across recovered components.

#### Dimensionality reduction

Participants : Alexandre Gramfort, Maureen Clerc.

Magneto-encephalography (MEG) and electro-encephalograhy (EEG) experiments provide huge amounts of data and lead to the manipulations of high dimensional objects like time series or topographies. In the past, essentially in the last decade, various methods for extracting the structure in complex data have been developed and successfully exploited for visualization or classification purposes. [Oops!] proposes to use one of these methods, the Laplacian eigenmaps, on EEG data and prove that it provides an powerful approach to visualize and understand the underlying structure of evoked potentials or multitrial time series.

#### Cortical Mapping

Participants : Maureen Clerc, Jan Kybic [ Czech Technical University ] .

Inverse Problems article, accepted for publication, put on HAL [Oops!] . The Laplace-Cauchy problem of propagating Dirichlet and Neumann data from a portion to the rest of the boundary is an ill-posed inverse problem. Many regularizing algorithms have been recently proposed, in order to stabilize the solution with respect to noisy or incomplete data. Our main application is in electro-encephalography (EEG) where potential measurements available at part of the scalp are used to reconstruct the potential and the current on the inner skull surface. This problem, known as cortical mapping, and other applications — in fields such as nondestructive testing, or biomedical engineering — require to solve the problem in realistic, three-dimensional geometry. The goal of this article is to present a new boundary element based method for solving the Laplace-Cauchy problem in three dimensions, in a multilayer geometry. We validate the method experimentally on simulated data.

#### Quantitative comparisons of forward problem in EEG

Participants : Emmanuel Olivi [ Odyssée and Geometrica ] , Théo Papadopoulo, Mariette Yvinec [ Geometrica ] , Maureen Clerc.

[Oops!] gives comparisons between several methods that solve the forward problem in EEG by comparing their relative precision on a 3-layer spherical model of the head and then on a realistic model. These methods are based on finite element methods which either use surfacic meshes with triangles, volumic meshes with tetrahedra, or implicit elements deduced by levelsets.

This work has been funded by the INRIA Color MedMesh action.

#### Implicit Meshing for Finite Element Methods using Levelsets

Participants : Théo Papadopoulo, Sylvain Vallaghé.

Finite Element methods (FEM) usually require a mesh to describe the geometric domain on which the computations are occuring. These meshes must have several properties: 1) they must approximate the geometrical domain accurately, 2) they must have good numerical properties, and 3) they must be small enough so that the computations take a reasonable amount of time. These goals are somewhat contradictory and in many cases such as biomedical images – and particularly in the case of the head –, even though the geometric domains can effectively be extracted, eg from Magnetic Resonance Images (MRI), the generation of such meshes is quite difficult.

The paper [Oops!] describes a technique that bypasses this mesh generation step going directly from a description by levelsets of the interfaces separating the various domains to the matrix associated to the FEM method. Using the levelsets description is quite convenient as it is already used by many segmentation tools.

The technique is illustrated on spherical and realistic geometries for the Electroencephalography (EEG) direct problem.

#### Conductivity estimation

Participants : Maureen Clerc, Sylvain Vallaghé, Jean-Michel Badier [ INSERM U751 ] .

[Oops!] proposes a new method for
*in vivo* conductivity estimation of head tissues in the case of a realistic piecewise constant model. Unlike classical electrical impedance tomography methods, for which the conductivity is inferred from a current injection on the scalp, we use an evoked source inside the brain that
comes from a somatosensory experiment. The resulting uncertainty with respect to the source is then balanced by strong constraints: we assume the source to be a single dipole located in the cortex, with orientation normal to the cortical surface. Using only EEG data, we are then able to
estimate conductivity values, using the MUSIC method to recover the position of the source. Results on simulations show robustness to noise, and the applicability of the method is demonstrated on real data.

The accuracy of EEG forward models partially depends on the head tissue conductivites. Some methods have been proposed to estimate these conductivities. They are all based on the idea of imposing the electrical source in the head, and considering the conductivities as the only unknowns. Although the conductivity models are becoming more and more complex, it is not clear in the literature whether it is really possible to estimate the conductivities of all the head tissues. [Oops!] presents the limits of conductivity estimation for the common three-layer model (brain, skull, scalp), with and without skull anisotropy.

#### Neural mass model parameter identification for MEG/EEG

Participants : Olivier Faugeras, Jan Kybic [ Czech Technical University ] , Théo Papadopoulo, Maureen Clerc.

This work was partially supported by the Barrande grant "Brain Multimodal Imagery" and the Fondation d'Entreprise EADS.

Electroencephalography (EEG) and magnetoencephalography (MEG) have excellent time resolution. However, the poor spatial resolution and small number of sensors do not permit to reconstruct a general spatial activation pattern. Moreover, the low signal to noise ratio (SNR) makes accurate reconstruction of a time course also challenging. [Oops!] therefore proposes to use constrained reconstruction, modeling the relevant part of the brain using a neural mass model: There is a small number of zones that are considered as entities, neurons within a zone are assumed to be activated simultaneously. The location and spatial extend of the zones as well as the inter-zonal connection pattern can be determined from functional MRI (fMRI), diffusion tensor MRI (DTMRI), and other anatomical and brain mapping observation techniques. The observation model is linear, its deterministic part is known from EEG/MEG forward modeling, the statistics of the stochastic part can be estimated. The dynamics of the neural model is described by a moderate number of parameters that can be estimated from the recorded EEG/MEG data. We explicitly model the long-distance communication delays. Our parameters have physiological meaning and their plausible range is known. Since the problem is highly nonlinear, a quasi-Newton optimization method with random sampling and automatic success evaluation is used. The actual connection topology can be identified from several possibilities. The method was tested on synthetic data as well as on true MEG somatosensory-evoked potential (SEP) data.

#### Estimation of cortical activity from MEG with retinotopic maps

Participants : Maureen Clerc, Alexandre Gramfort, Benoît Cottereau [ LENA ] , Sylvain Baillet [ LENA ] , Bertrand Thirion [ INRIA-CEA ] , Jean Lorenceau [ LENA ] , Théo Papadopoulo, Olivier Faugeras.

This work was partially supported by the Fondation d'Entreprise EADS.

Detection of activity from the primary visual cortex is a difficult challenge to magneto-encephalography (MEG) source imaging techniques: the geometry of the visual cortex is intricate, with structured visual field maps extending deep within the calcarine fissure. This questions the very sensitivity of MEG to the corresponding neural responses of visual stimuli and the usage of MEG source imaging for innovative retinotopic explorations. In this context, [Oops!] , [Oops!] compare two imaging models of MEG generators in realistic simulations of activations within the visual cortex. Localization and spatial extent of neural activity in the visual cortex were extracted from retinotopic maps obtained in fMRI.We prove that the suggested approaches are robust and succeed in accurately recovering the activation patterns with satisfactory match with fMRI results. These results suggest that fast retinotopic exploration of the visual cortex could be obtained from MEG as a complementary alternative to more standard fMRI approaches. The excellent time resolution of MEG imaging further opens interesting perspectives on the temporal and spectral processes sustained by the human visual system.