Fast Approximation of EEG Forward Problem and Application to Tissue Conductivity Estimation

Bioelectric source analysis in the human brain from scalp electroencephalography (EEG) signals is sensitive to the conductivity of the different head tissues. Conductivity values are subject dependent, so non-invasive methods for conductivity estimation are necessary to fine tune the EEG models. To do so, the EEG forward problem solution (so-called lead field matrix) must be computed for a large number of conductivity configurations. Computing one lead field requires a matrix inversion which is computationally intensive for realistic head models. Thus, the required time for computing a large number of lead fields can become impractical. In this work, we propose to approximate the lead field matrix for a set of conductivity configurations, using the exact solution only for a small set of basis points in the conductivity space. Our approach accelerates the computing time, while controlling the approximation error. Our method is tested for brain and skull conductivity estimation , with simulated and measured EEG data, corresponding to evoked somato-sensory potentials. This test demonstrates that the used approximation does not introduce any bias and runs significantly faster than if exact lead field were to be computed.Comment: Copyright (c) 2019 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to [email protected]

Motion Analysis of 3D Rigid Curves from Monocular Image Sequences

Cette thèse s'attaque au problème difficile de la détermination du mouvement et de la structure d'une scène à partir de séquences d'images dans le cas particulier où celle-ci est constituée d'une courbe rigide. L'intérêt de ce problème est à la fois théorique et pratique~: en effet, même si la situation qui nous occupe peut sembler caricaturale, il importe de bien comprendre ce qui se passe dans ce cas qui constitue, en quelque sorte, la situation générique à laquelle on est confronté. Car calculer le mouvement à partir des contours pose des problèmes. Le premier d'entre eux est le problème dit de l'ouverture~: en un point de contour seule la composante normale du champ de mouvement image peut être récupérée. Face à ce problème, les chercheurs ont développé deux stratégies~: soit on (d'une certaine manière) la composante du champ de mouvement manquante, soit on utilise des informations différentielles d'ordre supérieur. C'est cette dernière voie que nous explorons dans le cas des courbes rigides. Nous nous sommes tout particulièrement attaché à n'utiliser que l'information génériquement disponible à partir des images. Les équations liant le torseur cinématique associé au mouvement 3D aux mesures images sont étudiées en détail. Un algorithme marchant avec des séquences tests synthétiques et réelles a été implémenté. La mise en oeuvre de celui-ci a nécessité la mise au point de méthodes de calcul pour les dérivées (jusqu'à l'ordre 2) qui sont nécessaires. Un des principaux enseignements que l'on a pu tirer de ces expériences est que si le calcul du mouvement sur la base de l'observation d'un unique contour est possible, il est cependant indispensable de prendre en compte certaines contraintes (dites contraintes de visibilités) qui imposent à la solution de vérifier la propriété que la courbe 3D correspondante est totalement devant la caméra

Le cerveau dans tous ses états. Des sciences cognitives au diagnostic : entretien avec Stéphane Lehéricy propos recueillis par Dominique Chouchan

Article suivi par un entretien "des sciences cognitives au diagnostic" avec Stéphane Lehéricy directeur du Centre de neuro-imagerie de recherche (CENIR) du CHU Pitié Salpêtrière et professeur dans le service de neuroradiologie de ce CHU. Propos recueillis par Dominique ChouchanNational audienceChacun de nos quelque 100 milliards de neurones peut communiquer avec des milliers d'autres : autant dire qu'à ce jour, le cerveau est pour l'essentiel terra incognita. On sait qu'il comporte des aires spécialisées (dans la vision, la marche, les émotions...) dites corticales, qui constituent la matière grise. Celles-ci s'échangent des messages, électriques notamment, au travers de fibres nerveuses, la substance blanche. La compréhension de l'anatomie du cerveau (structure spatiale) et de sa réponse à des stimuli (approche temporelle) vont donc de pair. Aujourd'hui, nous disposons de techniques de mesure et d'imagerie performantes. Mais encore faut-il interpréter les données obtenues. Un défi qui nécessite d'étroites collaborations entre mathématiciens, informaticiens, spécialistes des neurosciences et médecins

An embedding for EEG signals learned using a triplet loss

Neurophysiological time series recordings like the electroencephalogram (EEG) or local field potentials are obtained from multiple sensors. They can be decoded by machine learning models in order to estimate the ongoing brain state of a patient or healthy user. In a brain-computer interface (BCI), this decoded brain state information can be used with minimal time delay to either control an application, e.g., for communication or for rehabilitation after stroke, or to passively monitor the ongoing brain state of the subject, e.g., in a demanding work environment. A specific challenge in such decoding tasks is posed by the small dataset sizes in BCI compared to other domains of machine learning like computer vision or natural language processing. A possibility to tackle classification or regression problems in BCI despite small training data sets is through transfer learning, which utilizes data from other sessions, subjects or even datasets to train a model. In this exploratory study, we propose novel domain-specific embeddings for neurophysiological data. Our approach is based on metric learning and builds upon the recently proposed ladder loss. Using embeddings allowed us to benefit, both from the good generalisation abilities and robustness of deep learning and from the fast training of classical machine learning models for subject-specific calibration. In offline analyses using EEG data of 14 subjects, we tested the embeddings' feasibility and compared their efficiency with state-of-the-art deep learning models and conventional machine learning pipelines. In summary, we propose the use of metric learning to obtain pre-trained embeddings of EEG-BCI data as a means to incorporate domain knowledge and to reach competitive performance on novel subjects with minimal calibration requirements.Comment: 23 pages, 11 figures, 5 appendix pages, 6 appendix figures, work conducted in 2020-2021 during an ARPE (https://ens-paris-saclay.fr/en/masters/ens-paris-saclay-degree/year-pre-doctoral-research-abroad-arpe

Topography-Time-Frequency Atomic Decomposition for Event-Related M/EEG Signals.

International audienceWe present a method for decomposing MEG or EEG data (channel x time x 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). 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 is an extension of the matching pursuit procedure. The method is evaluated on a simulated dataset presenting both low-frequency evoked potentials and high-frequency oscillatory activity. We show that the method is able to recover well both low-frequency and high-frequency simulated activities. There was however cross-talk across some recovered components due to the correlation introduced in the simulation

Structural connectivity to reconstruct brain activation and effective connectivity between brain regions

International audienceUnderstanding how brain regions interact to perform a specific task is very challenging. EEG and MEG are two non-invasive imaging modalities that allow the measurement of brain activation with high temporal resolution. Several works in EEG/MEG source reconstruction show that estimating brain activation can be improved by considering spatio-temporal constraints but only few of them use structural information to do so. In this work, we present a source reconstruction algorithm that uses brain structural connectivity, estimated from diffusion MRI (dMRI), to constrain the EEG/MEG source reconstruction. Contrarily to most source reconstruction methods which reconstruct activation for each time instant, the proposed method estimates an initial reconstruction for the first time instants and a multivariate autoregressive model that explains the data in further time instants. This au-toregressive model can be thought as an estimation of the effective connectivity between brain regions. We called this algorithm iterative Source and Dynamics reconstruction (iSDR). This paper presents the overall iSDR approach and how the proposed model is optimized to obtain both brain activation and brain region interactions. The accuracy of our method is demonstrated using synthetic data in which it shows a good capability to reconstruct both activation and connectivity. iSDR is also tested with real data obtained from [dataset] (face recognition task). The results are in phase with other works published with the same data and others that used different imaging modalities with the same task showing that the choice of using an autoregressive model gives relevant results

Jitter-Adaptive Dictionary Learning - Application to Multi-Trial Neuroelectric Signals

Dictionary Learning has proven to be a powerful tool for many image processing tasks, where atoms are typically defined on small image patches. As a drawback, the dictionary only encodes basic structures. In addition, this approach treats patches of different locations in one single set, which means a loss of information when features are well-aligned across signals. This is the case, for instance, in multi-trial magneto- or electroencephalography (M/EEG). Learning the dictionary on the entire signals could make use of the alignement and reveal higher-level features. In this case, however, small missalignements or phase variations of features would not be compensated for. In this paper, we propose an extension to the common dictionary learning framework to overcome these limitations by allowing atoms to adapt their position across signals. The method is validated on simulated and real neuroelectric data.Comment: 9 pages, 5 figures, minor correction

Quantitative comparisons of forward problems in MEEG.

This document gives comparisons between several methods that solve the forward problem in MEEG by comparing their precision on a 3-layer spherical model. These methods are based on finite elements which either use surfacic meshes with triangles, volumic meshes with tetrahedra, or implicit elements deduced from levelsets

An empirical evaluation of free BEM solvers for M/EEG forward modeling

International audienceNeuroimaging with magneto and electroencephalography (M/EEG) requires to compute the forward problem. It consists in predicting what is measured by MEG or EEG sensors due to a configuration of current generators within the head. When considering realistic head models, the equations derived from Maxwell equations can only be solved numerically. The Boundary Element Method is a standard approach to address this problem. However, different mathematical and computational variants exist within this class of BEM solvers. At least two BEM formulations exist for M/EEG forward modeling [Geselowitz 1967, Kybic et al. 2005]. Also implementation details vary between the different software packages (e.g. the precision of the numerical integrations). In order to investigate the influence of such differences, we have conducted a numerical experiment that evaluates the precision of different freely available BEM solvers. The BEM solvers are tested for EEG forward modeling with head models consisting of three nested shells. Multiple dipoles are located at different distances from the inner shell supposed to model the inner skull. To quantify the precision of the solvers we consider sphere models for which analytical solutions exist. Random sphere models are obtained by triangulating points randomly sampled over the spheres. We test and compare the accuracy of the BEM solvers on multiple random sphere models with different numbers of vertices on each interface. We also provide the computation times of the different solvers. The implementations tested are: OpenMEEG, SimBio [Zanow et al. 1995], Helsinki BEM [Stenroos et al. 2007], Dipoli [Oostendorp et al. 1989] and BEMCP [Phillips 2000] (Dipoli and BEMCP are available via Fieldtrip or SPM). Results show that OpenMEEG provides the best accuracy, followed by SimBio and dipoli which give comparable results. Finally, BEMCP and Helsinki BEM provide rather limited precisions