## 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 6.2.1 and 6.2.2 ) which are directly connected to this problem, there are a number of additional problems such as finding the events of interest in the recorded signal (section 6.2.3 ), or jointly modeling multimodal signals by studying generative models (section 6.2.4 ). Some of the tools described in this sub-theme are distributed in the opensource library OpenMEEG (see section 5.1 ).

#### Inverse problems of MEG and EEG

Participants : Maureen Clerc, Alexandre Gramfort [Parietal project-team] , Théodore Papadopoulo, Juliette Leblond [APICS project-team, INRIA] , Jean-Paul Marmorat [APICS project-team, INRIA] .

Investigating on brain activity with EEG or MEG measurements requires the solution of ill-posed inverse problems, whose solution implies regularization. Source models for EEG and MEG can be either distributed dipoles or isolated dipoles. In distributed models, the relationship between sources and measurements is linear, but the problem is underconstrained because thousands of putative positions for the cortical activity must be handled at the same time. In isolated dipole models, on the contrary, there are less unknowns than measurements, but the relationship between sources and measurements is more complex.

We are pursuing our collaboration with the APICS project-team, on rational approximation for source localization, when the sources are modeled as isolated dipoles. The force of the method is to provide a good and stable estimation of the number of sources and of their positions and moments. It requires the knowledge of the potential on the inner skull surface, provided by a Cortical Mapping method [2] . Cortical Mapping and rational approximation techniques are now being combined, leading to a dipolar source localization directly from scalp electrode measurements [56] .

We are involved in an ANR grant on Multimodal Neuroimaging of Rapid Brain Processes in the Human Visual System (ViMAGINE). An initial step in the exploration of the Human Visual System has been to perform retinotopy, i.e. determine the subject-dependent mapping linking positions in the visual field to the positions of the associated activity in the low-level visual cortex [57] . Since brain activity is not static, but varies in time, the regularization of the inverse problem should take time into account. A new approach has been proposed to track cortical activity with spatio-temporal constraints, and its implementation uses graph-cuts for computational efficiency [18] . This spatio-temporal regularization is a post-processing which is applied to a minimum-norm inverse problem.

#### Forward models for MEG and EEG

Participants : Maureen Clerc, Alexandre Gramfort [Parietal project-team] , Emmanuel Olivi, Théodore Papadopoulo, Sylvain Vallaghé [Laboratoire Jean Kuntzmann] .

Most methods for the inverse source problem in electroencephalography (EEG) and magnetoencephalography (MEG) use a lead field as an input. The lead field is the function which relates any source in the brain to its measurements at the sensors. Its computation requires solving a forward problem.

The inverse source localization problem of EEG and MEG strongly depends on the quality of the forward solution. The information required to specify the forward problem are the geometrical and physiological description of the head, in terms of its electrical conductivity.

Appropriate computational methods are compulsory for solving the M/EEG forward problem: either by surface-based Boundary Element Methods (BEM) or volume-based Finite Element or Finite Difference Methods. Until recently, the state of the art in BEM consisted in using a double-layer formulation [62] , with an accuracy improvement provided by the isolated Skull Approach [64] . We have proposed a new, symmetric BEM [67] which improves over the state of the art in terms of accuracy. This has been implemented within OpenMEEG which we continue to push through the community [18] , [22] .

Finite Element Methods (FEM) are also being studied for M/EEG because of their ability to account for anisotropic media. The cumbersome meshing procedure associated to the FEM should be alleviated with our recent development of the Implicit Mesh FEM [10] ,[44] . It is quite tempting to combine the Boundary Element Method and FEM in an hybrid model that would exploit each model for its strengths (Symmetric BEM for its accuracy for tissues having an isotropic homogeneous conductivity, FEM for its ability to deal with anisotropy) to provide even better forward problems [41] , [42] .

For complex geometries, there is no analytical formula of the lead field. The common approach is to numerically compute the value of the lead field for a finite number of point sources (dipoles). There are several drawbacks: the model of the source space is fixed (a set of dipoles) and the computation can be expensive for as much as 10000 dipoles. The common idea to bypass these problems is to compute the lead field from a sensor point of view. We use the adjoint method to derive general EEG and MEG sensor-based lead field equations [9] . Within a simple framework, we provide a complete review of the explicit lead field equations, and we are able to extend these equations to non-pointlike sensors [23] .

#### Single trial analysis and Brain Computer Interfaces

Participants : Maureen Clerc, Théodore Papadopoulo, Joan Fruitet, Alexandre Gramfort [Laboratoire Jean Kuntzmann] , Antoine Saillenfest, Renaud Keriven [ENPC] , Christian Bénar [INSERM U751, La Timone] , Bruno Torrésani [LATP, CMI, Université de Provence] .

Extracting information from multi-trial MEG or EEG recordings is challenging because of the very low signal-to-noise ratio (SNR), and because of the inherent variability of brain responses. The problem of low SNR is commonly tackled by averaging multiple repetitions of the recordings, also called trials, but the variability of response across trials leads to biased results and limits interpretability.

We have explored a data-driven way of decoding the variability of neural responses, which makes use of graph representations. First, a manifold learning algorithm based on a graph Laplacian offers an efficient way of ordering trials with respect to the response variability, under the condition that this variability itself depends on a single parameter. Second, the estimation of the variability is formulated as a combinatorial optimization that can be solved very efficiently using graph cuts. We have applied this method to the problem of latency estimation, on P300 oddball experiments [16] .

For Brain Computer Interfaces (BCI), a challenge is to extract from ongoing EEG information that is specific, and to use it to control an interface. In the ANR project Co-Adapt, we are studying an error potential that is generated by a central region of the brain, when a BCI user perceives that the system is producing an error. Detecting this error potential online could help improve the BCI, by bringing more information into the system. Antoine Saillenfest's Master's thesis was devoted to developing an experimental setup controlling the error potentials produced by the experimental subjects and to analyzing the measurements in order to detect trials in which there is an error. We have pursued our work on source localization for BCI, by comparing several inverse source reconstruction methods for their efficiency in preprocessing the signal before classification [32] .

#### Unified generative source models

Participants : Maureen Clerc, Théodore Papadopoulo, Nicole Voges, Habib Benali [Laboratoire d'Imagerie Fonctionnelle, INSERM U678, Faculté de Médecine, Univ Paris 6 / Hôpital Pitié-Salpêtrière] , Solenna Blanchard [INSERM U642, Rennes] , Christian Bénar [INSERM U751, Faculté de Médecine, La Timone, Marseille] , Olivier David [INSERM U594, Grenoble] , Fabrice Wendling [INSERM U642, Rennes] .

The models of source activities usually differ with various image modalities such as M/EEG, fMRI or optical imaging (OI). This is mostly due to the fact that these modalities deal with differing views of the functioning brain (different physical phenomena, different spatial or temporal scales). Various models cope with either the metabolic [61] , [80] or the electrophysiologic [65] aspects of brain function. It is quite tempting to couple these two kinds of models into a unified neural-mass computational model that can explain a broad variety of measurements obtained with different image modalities. To be efficient, such a model should have a limited number of parameters while keeping its expressiveness, and be computationally tractable. The paper [12] is a first exploration of such models. This model has been used to investigate the linearity of the metabolic response using epileptic spikes [49] , [47] .