Connectivity Analysis in EEG Data: A Tutorial Review of the State of the Art and Emerging Trends

Understanding how different areas of the human brain communicate with each other is a crucial issue in neuroscience. The concepts of structural, functional and effective connectivity have been widely exploited to describe the human connectome, consisting of brain networks, their structural connections and functional interactions. Despite high-spatial-resolution imaging techniques such as functional magnetic resonance imaging (fMRI) being widely used to map this complex network of multiple interactions, electroencephalographic (EEG) recordings claim high temporal resolution and are thus perfectly suitable to describe either spatially distributed and temporally dynamic patterns of neural activation and connectivity. In this work, we provide a technical account and a categorization of the most-used data-driven approaches to assess brain-functional connectivity, intended as the study of the statistical dependencies between the recorded EEG signals. Different pairwise and multivariate, as well as directed and non-directed connectivity metrics are discussed with a pros-cons approach, in the time, frequency, and information-theoretic domains. The establishment of conceptual and mathematical relationships between metrics from these three frameworks, and the discussion of novel methodological approaches, will allow the reader to go deep into the problem of inferring functional connectivity in complex networks. Furthermore, emerging trends for the description of extended forms of connectivity (e.g., high-order interactions) are also discussed, along with graph-theory tools exploring the topological properties of the network of connections provided by the proposed metrics. Applications to EEG data are reviewed. In addition, the importance of source localization, and the impacts of signal acquisition and pre-processing techniques (e.g., filtering, source localization, and artifact rejection) on the connectivity estimates are recognized and discussed. By going through this review, the reader could delve deeply into the entire process of EEG pre-processing and analysis for the study of brain functional connectivity and learning, thereby exploiting novel methodologies and approaches to the problem of inferring connectivity within complex networks

Analysis of EEG signals using complex brain networks

The human brain is so complex that two mega projects, the Human Brain Project and the BRAIN Initiative project, are under way in the hope of answering important questions for peoples' health and wellbeing. Complex networks become powerful tools for studying brain function due to the fact that network topologies on real-world systems share small world properties. Examples of these networks are the Internet, biological networks, social networks, climate networks and complex brain networks. Complex brain networks in real time biomedical signal processing applications are limited because some graph algorithms (such as graph isomorphism), cannot be solved in polynomial time. In addition, they are hard to use in single-channel EEG applications, such as clinic applications in sleep scoring and depth of anaesthesia monitoring. The first contribution of this research is to present two novel algorithms and two graph models. A fast weighted horizontal visibility algorithm (FWHVA) overcoming the speed limitations for constructing a graph from a time series is presented. Experimental results show that the FWHVA can be 3.8 times faster than the Fast Fourier Transfer (FFT) algorithm when input signals exceed 4000 data points. A linear time graph isomorphism algorithm (HVGI) can determine the isomorphism of two horizontal visibility graphs (HVGs) in a linear time domain. This is an efficient way to measure the synchronized index between two time series. Difference visibility graphs (DVGs) inherit the advantages of horizontal visibility graphs. They are noise-robust, and they overcome a pitfall of visibility graphs (VG): that the degree distribution (DD) doesn't satisfy a pure power-law. Jump visibility graphs (JVGs) enhance brain graphs allowing the processing of non-stationary biomedical signals. This research shows that the DD of JVGs always satisfies a power-lower if the input signals are purely non-stationary. The second highlight of this work is the study of three clinical biomedical signals: alcoholic, epileptic and sleep EEGs. Based on a synchronization likelihood and maximal weighted matching method, this work finds that the processing repeated stimuli and unrepeated stimuli in the controlled drinkers is larger than that in the alcoholics. Seizure detections based on epileptic EEGs have also been investigated with three graph features: graph entropy of VGs, mean strength of HVGs, and mean degrees of JVGs. All of these features can achieve 100% accuracy in seizure identification and differentiation from healthy EEG signals. Sleep EEGs are evaluated based on VG and DVG methods. It is shown that the complex brain networks exhibit more small world structure during deep sleep. Based on DVG methods, the accuracy peaks at 88:9% in a 5-state sleep stage classification from 14; 943 segments from single-channel EEGs. This study also introduces two weighted complex network approaches to analyse the nonlinear EEG signals. A weighted horizontal visibility graph (WHVG) is proposed to enhance noise-robustness properties. Tested with two Chaos signals and an epileptic EEG database, the research shows that the mean strength of the WHVG is more stable and noise-robust than those features from FFT and entropy. Maximal weighted matching algorithms have been applied to evaluate the difference in complex brain networks of alcoholics and controlled drinkers. The last contribution of this dissertation is to develop an unsupervised classifier for biomedical signal pattern recognition. A Multi-Scale Means (MSK-Means) algorithm is proposed for solving the subject-dependent biomedical signals classification issue. Using JVG features from the epileptic EEG database, the MSK-Means algorithm is 4:7% higher in identifying seizures than those by the K-means algorithm and achieves 92:3% accuracy for localizing the epileptogenic zone. The findings suggest that the outcome of this thesis can improve the performance of complex brain networks for biomedical signal processing and nonlinear time series analysis

Quantitative Methods For Guiding Epilepsy Surgery From Intracranial Eeg

Despite advances in intracranial EEG (iEEG) technique, technology and neuroimaging, patients today are no more likely to achieve seizure freedom after epilepsy surgery than they were 20 years ago. These poor outcomes are in part due to the difficulty and subjectivity associated with interpreting iEEG recordings, and have led to widespread interest in developing quantitative methods to localize the epileptogenic zone. Approaches to computational iEEG analysis vary widely, spanning studies of both seizures and interictal periods, and encompassing a range of techniques including electrographic signal analysis and graph theory. However, many current methods often fail to generalize to new data and are sensitive to differences in pathology and electrode placement. Indeed, none have completed prospective clinical trials. In this dissertation, I develop and validate tools for guiding epilepsy surgery through the quantitative analysis of intracranial EEG. Specifically, I leverage methods from graph theory for mapping network synchronizability to predict surgical outcome from ictal recordings, and also investigate the effects of sampling bias on network models. Finally, I construct a normative intracranial EEG atlas as a framework for objectively identifying patterns of abnormal neural activity and connectivity. Overall, the methods and results of this dissertation support the implementation of quantitative iEEG analysis in epilepsy surgical evaluation

Coherence analysis: Methods, solutions and problems

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.A coherence function is a measure of the correlation of two signals and may be used as a measure for functional relationship between brain areas. In studying functional relationships, referenced EEG (REEG) coherence analysis yields important new aspects of brain activities, which complement the data obtained by power spectral analysis. However, REEG-based coherence tends to show a false high value due to volume conduction from un correlated sources (VCUS). Existing signal processing methods address this issue using a Fourier coherence function of scalp Laplacian. Although this method has been proved useful to reveal correlation between EEG signals with minimum VCUS effects, it only provides frequency-domain analysis. Since EEG signals are highly non-stationary, it is more appropriate to use time-frequency methods for coherence analysis of scalp Laplacian. Thus this research applies the wavelet transform on coherence analysis of scalp Laplacian. To verify our technique, already recorded EEG data of event related potentials were obtained from a study of two large groups of alcoholic and abstinent alcoholic subjects, performing visual picture-recognition tasks. The proposed coherence method successfully detected time-frequency correlation between EEG signals with minimum VCUS effects. It showed significant spatial specificity and revealed detailed coherence patterns. Some new important results regarding time-frequency characteristics of VCUS effects on wavelet and short-time Fourier transform (STFT) coherence analysis of REEG signals were deduced. The proposed coherence method was also compared to a conventional wavelet coherence method of REEG signals in the study of coherence difference between coherences of alcoholic and abstinent alcoholic EEG signals. Results of this study provided substantial evidence that VCUS effects are not additive and therefore can not be ignored in comparison of different brain states between groups of subjects

Dynamic correlations in ongoing neuronal oscillations in humans - perspectives on brain function and its disorders

This Thesis is involved with neuronal oscillations in the human brain and their coordination across time, space and frequency. The aim of the Thesis was to quantify correlations in neuronal oscillations over these dimensions, and to elucidate their significance in cognitive processing and brain disorders. Magnetoencephalographic (MEG) recordings of major depression patients revealed that long-range temporal correlations (LRTC) were decreased, compared to control subjects, in the 5 Hz oscillations in a manner that was dependent on the degree of the disorder. While studying epileptic patients, on the other hand, it was found that the LRTC in neuronal oscillations recorded intracranially with electroencephalography (EEG) were strengthened in the seizure initiation region. A novel approach to map spatial correlations between cortical regions was developed. The method is based on parcellating the cortex to patches and estimating phase synchrony between all patches. Mapping synchrony from inverse-modelled MEG / EEG data revealed wide-spread phase synchronization during a visual working memory task. Furthermore, the network architectures of task-related synchrony were found to be segregated over frequency. Cross-frequency interactions were investigated with analyses of nested brain activity in data recorded with full-bandwidth EEG during a somatosensory detection task. According to these data, the phase of ongoing infra-slow fluctuations (ISF), which were discovered in the frequency band of 0.01-0.1 Hz, was correlated with the amplitude of faster > 1 Hz neuronal oscillations. Strikingly, the behavioral detection performance displayed similar dependency on the ISFs as the > 1 Hz neuronal oscillations. The studies composing this Thesis showed that correlations in neuronal oscillations are functionally related to brain disorders and cognitive processing. Such correlations are suggested to reveal the coordination of neuronal oscillations across time, space and frequency. The results contribute to system-level understanding of brain function