Mixed-norm estimates for the M/EEG inverse problem using accelerated gradient methods

International audienceMagneto- and electroencephalography (M/EEG) measure the electromagnetic fields produced by the neural electrical currents. Given a conductor model for the head, and the distribution of source currents in the brain, Maxwell's equations allow one to compute the ensuing M/EEG signals. Given the actual M/EEG measurements and the solution of this forward problem, one can localize, in space and in time, the brain regions that have produced the recorded data. However, due to the physics of the problem, the limited number of sensors compared to the number of possible source locations, and measurement noise, this inverse problem is ill-posed. Consequently, additional constraints are needed. Classical inverse solvers, often called minimum norm estimates (MNE), promote source estimates with a small ℓ(2) norm. Here, we consider a more general class of priors based on mixed norms. Such norms have the ability to structure the prior in order to incorporate some additional assumptions about the sources. We refer to such solvers as mixed-norm estimates (MxNE). In the context of M/EEG, MxNE can promote spatially focal sources with smooth temporal estimates with a two-level ℓ(1)/ℓ(2) mixed-norm, while a three-level mixed-norm can be used to promote spatially non-overlapping sources between different experimental conditions. In order to efficiently solve the optimization problems of MxNE, we introduce fast first-order iterative schemes that for the ℓ(1)/ℓ(2) norm give solutions in a few seconds making such a prior as convenient as the simple MNE. Furthermore, thanks to the convexity of the optimization problem, we can provide optimality conditions that guarantee global convergence. The utility of the methods is demonstrated both with simulations and experimental MEG data

Sparse algorithms for EEG source localization

Source localization using EEG is important in diagnosing various physiological and psychiatric diseases related to the brain. The high temporal resolution of EEG helps medical professionals assess the internal physiology of the brain in a more informative way. The internal sources are obtained from EEG by an inversion process. The number of sources in the brain outnumbers the number of measurements. In this article, a comprehensive review of the state of the art sparse source localization methods in this field is presented. A recently developed method, certainty based reduced sparse solution (CARSS), is implemented and is examined. A vast comparative study is performed using a sixty four channel setup involving two source spaces. The first source space has 5004 sources and the other has 2004 sources. Four test cases with one, three, five, and seven simulated active sources are considered. Two noise levels are also being added to the noiseless data. The CARSS is also evaluated. The results are examined. A real EEG study is also attempted.Comment: Published in Medical & Biological Engineering & Computing, Springer on Oct 02, 202

Development of a Group Dynamic Functional Connectivity Pipeline for Magnetoencephalography Data and its Application to the Human Face Processing Network

Since its inception, functional neuroimaging has focused on identifying sources of neural activity. Recently, interest has turned to the analysis of connectivity between neural sources in dynamic brain networks. This new interest calls for the development of appropriate investigative techniques. A problem occurs in connectivity studies when the differing networks of individually analyzed subjects must be reconciled. One solution, the estimation of group models, has become common in fMRI, but is largely untried with electromagnetic data. Additionally, the assumption of stationarity has crept into the field, precluding the analysis of dynamic systems. Group extensions are applied to the sparse irMxNE localizer of MNE-Python. Spectral estimation requires individual source trials, and a multivariate multiple regression procedure is established to accomplish this based on the irMxNE output. A program based on the Fieldtrip software is created to estimate conditional Granger causality spectra in the time-frequency domain based on these trials. End-to-end simulations support the correctness of the pipeline with single and multiple subjects. Group-irMxNE makes no attempt to generalize a solution between subjects with clearly distinct patterns of source connectivity, but shows signs of doing so when subjects patterns of activity are similar. The pipeline is applied to MEG data from the facial emotion protocol in an attempt to validate the Adolphs model. Both irMxNE and Group-irMxNE place numerous sources during post-stimulus periods of high evoked power but neglect those of low power. This identifies a conflict between power-based localizations and information-centric processing models. It is also noted that neural processing is more diffuse than the neatly specified Adolphs model indicates. Individual and group results generally support early processing in the occipital, parietal, and temporal regions, but later stage frontal localizations are missing. The morphing of individual subjects\u27 brain topology to a common source-space is currently inoperable in MNE. MEG data is therefore co-registered directly onto an average brain, resulting in loss of accuracy. For this as well as reasons related to uneven power and computational limitations, the early stages of the Adolphs model are only generally validated. Encouraging results indicate that actual non-stationary group connectivity estimates are produced however

Reconstruction de l'activité corticale à partir de données MEG à l'aide de réseaux cérébraux et de délais de transmission estimés à partir d'IRMd

White matter fibers transfer information between brain regions with delays that are observable with magnetoencephalography and electroencephalography (M/EEG) due to their millisecond temporal resolution. We can represent the brain as a graph where nodes are the cortical sources or areas and edges are the physical connections between them: either local (between adjacent vertices on the cortical mesh) or non-local (long-range white matter fibers). Long-range anatomical connections can be obtained with diffusion MRI (dMRI) tractography which yields a set of streamlines representing white matter fiber bundles. Given the streamlines’ lengths and the information conduction speed, transmission delays can be estimated for each connection. dMRI can thus give an insight into interaction delays of the macroscopicbrain network.Localizing and recovering electrical activity of the brain from M/EEG measurements is known as the M/EEG inverse problem. Generally, there are more unknowns (brain sources) than the number of sensors, so the solution is non-unique and the problem ill-posed. To obtain a unique solution, prior constraints on the characteristics of source distributions are needed. Traditional linear inverse methods deploy different constraints which can favour solutions with minimum norm, impose smoothness constraints in space and/or time along the cortical surface, etc. Yet, structural connectivity is rarely considered and transmission delays almost always neglected.The first contribution of this thesis consists of a multimodal preprocessing pipeline used to integrate structural MRI, dMRI and MEG data into a same framework, and of a simulation procedure of source-level brain activity that was used as a synthetic dataset to validate the proposed reconstruction approaches.In the second contribution, we proposed a new framework to solve the M/EEG inverse problem called Connectivity-Informed M/EEG Inverse Problem (CIMIP), where prior transmission delays supported by dMRI were included to enforce temporal smoothness between time courses of connected sources. This was done by incorporating a Laplacian operator into the regularization, that operates on a time-dependent connectivity graph. Nonetheless, some limitations of the CIMIP approach arised, mainly due to the nature of the Laplacian, which acts on the whole graph, favours smooth solutions across all connections, for all delays, and it is agnostic to directionality.In this thesis, we aimed to investigate patterns of brain activity during visuomotor tasks, during which only a few regions typically get significantly activated, as shown by previous studies. This led us to our third contribution, an extension of the CIMIP approach that addresses the aforementioned limitations, named CIMIP_OML (“Optimal Masked Laplacian”). We restricted the full source space network (the whole cortical mesh) to a network of regions of interest and tried to find how the information is transferred between its nodes. To describe the interactions between nodes in a directed graph, we used the concept of network motifs. We proposed an algorithm that (1) searches for an optimal network motif – an optimal pattern of interaction between different regions and (2) reconstructs source activity given the found motif. Promising results are shown for both simulated and real MEG data for a visuomotor task and compared with 3 different state-of-the-art reconstruction methods.To conclude, we tackled a difficult problem of exploiting delays supported by dMRI for the reconstruction of brain activity, while also considering the directionality in the information transfer, and provided new insights into the complex patterns of brain activity.Les fibres de la matière blanche permettent le transfert d’information dans le cerveau avec des délais observables en Magnétoencéphalographie et Électroencéphalographie (M/EEG) grâce à leur haute résolution temporelle. Le cerveau peut être représenté comme un graphe où les nœuds sont les régions corticales et les liens sont les connexions physiques entre celles-ci: soit locales (entre sommets adjacents sur le maillage cortical), soit non locales (fibres de la matière blanche). Les connexions non-locales peuvent être reconstruites avec la tractographie de l’IRM de diffusion (IRMd) qui génère un ensemble de courbes («streamlines») représentant des fibres de la matière blanche. Sachant les longueurs des fibres et la vitesse de conduction de l’information, les délais de transmission peuvent être estimés. L’IRMd peut donc donner un aperçu des délais d’interaction du réseau cérébral macroscopique.La localisation et la reconstruction de l’activité électrique cérébrale à partir des mesures M/EEG est un problème inverse. En général, il y a plus d’inconnues (sources cérébrales) que de capteurs. La solution n’est donc pas unique et le problème est dit mal posé. Pour obtenir une solution unique, des hypothèses sur les caractéristiques des distributions de sources sont requises. Les méthodes inverses linéaires traditionnelles utilisent différentes hypothèses qui peuvent favoriser des solutions de norme minimale, imposer des contraintes de lissage dans l’espace et/ou dans le temps, etc. Pourtant, la connectivité structurelle est rarement prise en compte et les délais de transmission sont presque toujours négligés.La première contribution de cette thèse est un pipeline de prétraitement multimodal utilisé pour l’intégration des données d’IRM, IRMd et MEG dans un même cadre, et d’une méthode de simulation de l’activité corticale qui a été utilisée comme jeu de données synthétiques pour valider les approches de reconstruction proposées. Nous proposons également une nouvelle approche pour résoudre le problème inverse M/EEG appelée «Problème Inverse M/EEG Informé par la Connectivité» (CIMIP pour Connectivity-Informed M/EEG Inverse Problem), où des délais de transmission provenant de l’IRMd sont inclus pour renforcer le lissage temporel entre les décours des sources connectées. Pour cela, un opérateur Laplacien, basé sur un graphe de connectivité en fonction du temps, a été intégré dans la régularisation. Cependant, certaines limites de l’approche CIMIP sont apparues en raison de la nature du Laplacien qui agit sur le graphe entier et favorise les solutions lisses sur toutes les connexions, pour tous les délais, et indépendamment de la directionnalité.Lors de tâches visuo-motrices, seules quelques régions sont généralement activées significativement. Notre troisième contribution est une extension de CIMIP pour ce type de tâches qui répond aux limitations susmentionnées, nommée CIMIP_OML («Optimal Masked Laplacian») ou Laplacien Masqué Optimal. Nous essayons de trouver comment l’information est transférée entre les nœuds d’un sous-réseau de régions d’intérêt du réseau complet de l’espace des sources. Pour décrire les interactions entre nœuds dans un graphe orienté, nous utilisons le concept de motifs de réseau. Nous proposons un algorithme qui 1) cherche un motif de réseau optimal- un modèle optimal d’interaction entre régions et 2) reconstruit l’activité corticale avec le motif trouvé. Des résultats prometteurs sont présentés pour des données MEG simulées et réelles (tâche visuo-motrice) et comparés avec 3 méthodes de l’état de l’art. Pour conclure, nous avons abordé un problème difficile d’exploitation des délais de l’IRMd lors l’estimation de l’activité corticale en tenant compte de la directionalité du transfert d’information, fournissant ainsi de nouvelles perspectives sur les patterns complexes de l’activité cérébrale

Bayesian Modeling and Estimation Techniques for the Analysis of Neuroimaging Data

Brain function is hallmarked by its adaptivity and robustness, arising from underlying neural activity that admits well-structured representations in the temporal, spatial, or spectral domains. While neuroimaging techniques such as Electroencephalography (EEG) and magnetoencephalography (MEG) can record rapid neural dynamics at high temporal resolutions, they face several signal processing challenges that hinder their full utilization in capturing these characteristics of neural activity. The objective of this dissertation is to devise statistical modeling and estimation methodologies that account for the dynamic and structured representations of neural activity and to demonstrate their utility in application to experimentally-recorded data. The first part of this dissertation concerns spectral analysis of neural data. In order to capture the non-stationarities involved in neural oscillations, we integrate multitaper spectral analysis and state-space modeling in a Bayesian estimation setting. We also present a multitaper spectral analysis method tailored for spike trains that captures the non-linearities involved in neuronal spiking. We apply our proposed algorithms to both EEG and spike recordings, which reveal significant gains in spectral resolution and noise reduction. In the second part, we investigate cortical encoding of speech as manifested in MEG responses. These responses are often modeled via a linear filter, referred to as the temporal response function (TRF). While the TRFs estimated from the sensor-level MEG data have been widely studied, their cortical origins are not fully understood. We define the new notion of Neuro-Current Response Functions (NCRFs) for simultaneously determining the TRFs and their cortical distribution. We develop an efficient algorithm for NCRF estimation and apply it to MEG data, which provides new insights into the cortical dynamics underlying speech processing. Finally, in the third part, we consider the inference of Granger causal (GC) influences in high-dimensional time series models with sparse coupling. We consider a canonical sparse bivariate autoregressive model and define a new statistic for inferring GC influences, which we refer to as the LASSO-based Granger Causal (LGC) statistic. We establish non-asymptotic guarantees for robust identification of GC influences via the LGC statistic. Applications to simulated and real data demonstrate the utility of the LGC statistic in robust GC identification