Modeling sparse connectivity between underlying brain sources for EEG/MEG

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.Comment: 9 pages, 6 figure

Independent EEG Sources Are Dipolar

Independent component analysis (ICA) and blind source separation (BSS) methods are increasingly used to separate individual brain and non-brain source signals mixed by volume conduction in electroencephalographic (EEG) and other electrophysiological recordings. We compared results of decomposing thirteen 71-channel human scalp EEG datasets by 22 ICA and BSS algorithms, assessing the pairwise mutual information (PMI) in scalp channel pairs, the remaining PMI in component pairs, the overall mutual information reduction (MIR) effected by each decomposition, and decomposition ‘dipolarity’ defined as the number of component scalp maps matching the projection of a single equivalent dipole with less than a given residual variance. The least well-performing algorithm was principal component analysis (PCA); best performing were AMICA and other likelihood/mutual information based ICA methods. Though these and other commonly-used decomposition methods returned many similar components, across 18 ICA/BSS algorithms mean dipolarity varied linearly with both MIR and with PMI remaining between the resulting component time courses, a result compatible with an interpretation of many maximally independent EEG components as being volume-conducted projections of partially-synchronous local cortical field activity within single compact cortical domains. To encourage further method comparisons, the data and software used to prepare the results have been made available (http://sccn.ucsd.edu/wiki/BSSComparison)

Independent component analysis on spectral domain

Independent component analysis (ICA) is an effective data-driven method for blind source separation. It has been successfully applied to separate source signals of interest from their mixtures. Most existing ICA procedures are carried out by relying solely on the estimation of the marginal density functions, either parametrically or nonparametrically. In many applications, correlation structures within each source also play an important role besides the marginal distributions. One important example is functional magnetic resonance imaging (fMRI) analysis where the brain-function-related signals are temporally correlated. In this thesis, we propose two novel ICA algorithms that fully exploit the correlation structures within the source signals through spectral density estimation. Our methodology development is two-fold: 1) ICA for auto-correlated sources via parametric spectral density estimation (cICA-YW); 2) ICA for sources with mixed spectra via nonparametric spectral density estimation and atom detection (cICA-LSP). The cICA-YW focuses on the sources with autocorrelation and is implemented using spectral density functions from frequently used time series models such as autoregressive moving average (ARMA) processes. The time series parameters and the mixing matrix are estimated via maximizing the Whittle likelihood function. We illustrate the performance of the proposed method through extensive simulation studies and a real fMRI application. The numerical results indicate that our approach outperforms several popular methods including the most widely used fastICA algorithm. We also establish the sampling properties of the proposed method. For the cICA-LSP, we consider the case of sources with possibly mixed spectra, where ARMA estimates are often unstable. Specifically, we propose to estimate the spectral density functions and the line spectra of the source signals using cubic splines and indicator functions, respectively. The mixed spectra and the mixing matrix are estimated via maximizing the Whittle likelihood function. We illustrate the performance of the proposed method through extensive simulation studies.Doctor of Philosoph

Statistical Analysis of EEG Phase Shift Events

This thesis develops statistical methods for the identification, and analysis of phase shift events, i.e. sudden changes in the timing relationship between coupled oscillators. Phase shifts events occur in many complex systems but here the primary interest is the analysis of electroencephalogram (EEG) recordings where they have been identified as markers of information transmission in the brain; as a secondary example we analyze systems of weakly coupled Rossler attractors. The main result, found in Chapter 2, is a novel method for estimating neural connectivity from EEG recordings based on spatio-temporal patterns of phase shift events. Phase shift events are modelled as a multivariate point process, and the ideas of Granger causality are used to motivate a directed measure of connectivity. The method is demonstrated on EEG recordings from 18 participants during three task conditions; resting, visual vigilance and auditory vigilance. Likelihood ratios are used to test the hypothesis of no Granger causal interaction between signals, and network patterns are analyzed using graph theory. In Chapter 3 the problem of phase shift identification is formulated as a change point in the instantaneous phase. Two estimators are considered, based on the cumulative summation and the instantaneous phase derivative. Block bootstrapping techniques are used to capture the dependency structure in the signals and determine critical values for shift identification. Estimators are evaluated both on their accuracy, and temporal resolution. Finally, detailed simulation studies are performed using realistic head models to investigate the effect of volume conduction (linear spread of electrical activity at the scalp) on phase shift analysis. Specifically, Chapter 4 investigates the effect of volume conduction on the analysis, in order to understand the limitations of the phase shift Granger causality method. Chapter 5 then investigates an approach for reducing the effect of volume conduction by using EEG source reconstruction techniques to estimate neural source activity and then identifying phase shifts with-in the brain directly from the reconstructed sources. The primary impact is the novel method for estimating neural connectivity. Each chapter investigates a different aspect of EEG phase analysis, and together they form a complete package for estimation and interpretation of neural connectivity. Two other areas of impact are in statistical change point analysis, and behavioural psychology