Modeling sparse connectivity between underlying brain sources for EEG/MEG

📝 Abstract

We propose a novel technique to assess functional brain connectivity in EEG/MEG signals. Our method, called Sparsely-Connected Sources Analysis (SCSA), can overcome the problem of volume conduction by modeling neural data innovatively with the following ingredients: (a) the EEG is assumed to be a linear mixture of correlated sources following a multivariate autoregressive (MVAR) model, (b) the demixing is estimated jointly with the source MVAR parameters, (c) overfitting is avoided by using the Group Lasso penalty. This approach allows to extract the appropriate level cross-talk between the extracted sources and in this manner we obtain a sparse data-driven model of functional connectivity. We demonstrate the usefulness of SCSA with simulated data, and compare to a number of existing algorithms with excellent results.

💡 Analysis

We propose a novel technique to assess functional brain connectivity in EEG/MEG signals. Our method, called Sparsely-Connected Sources Analysis (SCSA), can overcome the problem of volume conduction by modeling neural data innovatively with the following ingredients: (a) the EEG is assumed to be a linear mixture of correlated sources following a multivariate autoregressive (MVAR) model, (b) the demixing is estimated jointly with the source MVAR parameters, (c) overfitting is avoided by using the Group Lasso penalty. This approach allows to extract the appropriate level cross-talk between the extracted sources and in this manner we obtain a sparse data-driven model of functional connectivity. We demonstrate the usefulness of SCSA with simulated data, and compare to a number of existing algorithms with excellent results.

📄 Content

1 Modeling sparse connectivity between underlying brain sources for EEG/MEG Stefan Haufe, Ryota Tomioka, Guido Nolte, Klaus-Robert M¨uller and Motoaki Kawanabe Abstract—We propose a novel technique to assess functional brain connectivity in EEG/MEG signals. Our method, called Sparsely-Connected Sources Analysis (SCSA), can overcome the problem of volume conduction by modeling neural data innova- tively with the following ingredients: (a) the EEG is assumed to be a linear mixture of correlated sources following a multivariate autoregressive (MVAR) model, (b) the demixing is estimated jointly with the source MVAR parameters, (c) overfitting is avoided by using the Group Lasso penalty. This approach allows to extract the appropriate level cross-talk between the extracted sources and in this manner we obtain a sparse data-driven model of functional connectivity. We demonstrate the usefulness of SCSA with simulated data, and compare to a number of existing algorithms with excellent results. I. INTRODUCTION A. Functional brain connectivity The analysis of neural connectivity plays a crucial role for understanding the general functioning of the brain. In the past two decades such analysis has become possible thanks to tremendous progress that has been made in the fields of neuroimaging and mathematical modeling. Today, a multiplicity of imaging modalities exists, allowing to monitor brain dynamics at different spatial and temporal scales. Given multiple simultaneously-recorded time-series reflect- ing neural activity in different brain regions, a functional (task- related) connection (sometimes also called information flow or (causal) interaction in this paper) between two regions is com- monly inferred, if a significant time-lagged influence between the corresponding time-series is found. Different measures have been proposed for quantifying this influence, most of them being formulated either in terms of the cross-spectrum (e.g., coherence, phase slope index [1]) or an autoregressive models (e.g., Granger causality [2], directed transfer function [3], partial directed coherence [4], [5]). B. Volume conduction problem in EEG and MEG In electroencephalography (EEG) and magnetoencephalog- raphy (MEG), sensors are placed outside the head and the problem of volume conduction arises. That is, rather than measuring activity of only one brain site, each sensor captures a linear superposition of signals from all over the brain. This mixing introduces instantaneous correlations in the data, which can cause traditional analyses to detect spurious connectivity [6]. S. Haufe and K.-R. M¨uller are with the Berlin Institute of Technology, Germany. R. Tomioka is with the University of Tokyo, Japan. G. Nolte and M. Kawanabe are with Fraunhofer Institute FIRST, Berlin, Germany. C. Existing source connectivity analyses Only recently, methods have been brought up, which qualify for EEG/MEG connectivity analysis, since they account for volume conduction effects. These methods can roughly be divided as follows. One type of methods aims at providing meaningful connec- tivity estimates between sensors. The idea here is, that only the real part of the cross-spectrum and related quantities is affected by instantaneous effects. Thus, by using only the imaginary part, many traditional coupling measures can be made robust against volume-conduction [1], [6]. Another group of methods attempts to invert the mixing process in order to apply standard measures to the obtained source estimates. These methods can be further divided into (i) source-localization approaches (where sources are obtained as solutions to the EEG/MEG inverse problem), (ii) methods using statistical assumptions, and (iii) combined methods. The first approach is pursued, for example, in [7], [8]. Methods in the second category can be appealing, since they avoid finding an explicit inversion of the physical forward model. Instead, both the sources and the (de-)mixing transformation are estimated. To make such decomposition unique, assump- tions have to be formulated, the choice of which is not so straightforward. We will now briefly review some possibilities for such assumptions. Principal component analysis (PCA) and independent com- ponent analysis (ICA) are the most prominent linear decom- position techniques for multivariate data. Unfortunately, these methods contradict either with the goal of EEG/MEG connec- tivity analysis (assumption of independent sources in ICA1) or even with the physics underlying EEG/MEG generation (as- sumption of orthogonal loadings in PCA). Nevertheless, both concepts have been successfully used in more sophisticated ways to find meaningful EEG/MEG decompositions. For example, an interesting use of ICA is proposed in [10]. The authors of this paper do not assume independence of the source traces, but rather argue that this property holds for the residuals of an MVAR model if no instantaneous correlations in the data exist. Hence, in their MVARICA approach

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