An Information-Theoretic Framework to Map the Spatiotemporal Dynamics of the Scalp Electroencephalogram

Rehabilitation Modulates High-Order Interactions Among Large-Scale Brain Networks in Subacute Stroke

The recovery of motor functions after stroke is fostered by the functional integration of large-scale brain networks, including the motor network (MN) and high-order cognitive controls networks, such as the default mode (DMN) and executive control (ECN) networks. In this paper, electroencephalography signals are used to investigate interactions among these three resting state networks (RSNs) in subacute stroke patients after motor rehabilitation. A novel metric, the O-information rate (OIR), is used to quantify the balance between redundancy and synergy in the complex high-order interactions among RSNs, as well as its causal decomposition to identify the direction of information flow. The paper also employs conditional spectral Granger causality to assess pairwise directed functional connectivity between RSNs. After rehabilitation, a synergy increase among these RSNs is found, especially driven by MN. From the pairwise description, a reduced directed functional connectivity towards MN is enhanced after treatment. Besides, inter-network connectivity changes are associated with motor recovery, for which the mediation role of ECN seems to play a relevant role, both from pairwise and high-order interactions perspective.

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.

Entropy Could Quantify Brain Activation Induced by Mechanical Impedance-Restrained Active Arm Motion: A Functional NIRS Study

Brain activation has been used to understand brain-level events associated with cognitive tasks or physical tasks. As a quantitative measure for brain activation, we propose entropy in place of signal amplitude and beta value, which are widely used, but sometimes criticized for their limitations and shortcomings as such measures. To investigate the relevance of our proposition, we provided 22 subjects with physical stimuli through elbow extension-flexion motions by using our exoskeleton robot, measured brain activation in terms of entropy, signal amplitude, and beta value; and compared entropy with the other two. The results show that entropy is superior, in that its change appeared in limited, well established, motor areas, while signal amplitude and beta value changes appeared in a widespread fashion, contradicting the modularity theory. Entropy can predict increase in brain activation with task duration, while the other two cannot. When stimuli shifted from the rest state to the task state, entropy exhibited a similar increase as the other two did. Although entropy showed only a part of the phenomenon induced by task strength, it showed superiority by showing a decrease in brain activation that the other two did not show. Moreover, entropy was capable of identifying the physiologically important location.

Coupling feature extraction method of resting state EEG Signals from amnestic mild cognitive impairment with type 2 diabetes mellitus based on weight permutation conditional mutual information

This study aimed to find a good coupling feature extraction method to effectively analyze resting state EEG signals (rsEEG) of amnestic mild cognitive impairment(aMCI) with type 2 diabetes mellitus(T2DM) and normal control (NC) with T2DM. A method of EEG signal coupling feature extraction based on weight permutation conditional mutual information (WPCMI) was proposed in this research. With the WPCMI method, coupling feature strength of two time series in Alpha1, Alpha2, Beta1, Beta2 and Gamma bands for aMCI with T2DM and NC with T2DM could be extracted respectively. Then selected three frequency bands coupling feature matrix with the help of multi-spectral image transformation method to map it as spectral image characteristics. And finally classified these characteristics through the convolution neural network method(CNN). For aMCI with T2DM and NC with T2DM, the highest classification accuracy of 96%, 95%, 95% could be achieved respectively in the combination of three frequency bands (Alpha1, Alpha2, Gamma), (Beta1, Beta2 and Gamma) and (Alpha2, Beta1, Beta2). This WPCMI method highlighted the coupling dynamic characteristics of EEG signals, and its classification performance was better than all previous methods in aMCI with T2DM diagnosis field. WPCMI method could be used as an effective biomarker to distinguish EEG signals of aMCI with T2DM and NC with T2DM. The coupling feature extraction method used in this paper provided a new perspective for the EEG analysis of aMCI with T2DM.

Estimating Conditional Transfer Entropy in Time Series Using Mutual Information and Nonlinear Prediction

We propose a new estimator to measure directed dependencies in time series. The dimensionality of data is first reduced using a new non-uniform embedding technique, where the variables are ranked according to a weighted sum of the amount of new information and improvement of the prediction accuracy provided by the variables. Then, using a greedy approach, the most informative subsets are selected in an iterative way. The algorithm terminates, when the highest ranked variable is not able to significantly improve the accuracy of the prediction as compared to that obtained using the existing selected subsets. In a simulation study, we compare our estimator to existing state-of-the-art methods at different data lengths and directed dependencies strengths. It is demonstrated that the proposed estimator has a significantly higher accuracy than that of existing methods, especially for the difficult case, where the data are highly correlated and coupled. Moreover, we show its false detection of directed dependencies due to instantaneous couplings effect is lower than that of existing measures. We also show applicability of the proposed estimator on real intracranial electroencephalography data.

A Framework to Assess the Information Dynamics of Source EEG Activity and Its Application to Epileptic Brain Networks

This study introduces a framework for the information-theoretic analysis of brain functional connectivity performed at the level of electroencephalogram (EEG) sources. The framework combines the use of common spatial patterns to select the EEG components which maximize the variance between two experimental conditions, simultaneous implementation of vector autoregressive modeling (VAR) with independent component analysis to describe the joint source dynamics and their projection to the scalp, and computation of information dynamics measures (information storage, information transfer, statistically significant network links) from the source VAR parameters. The proposed framework was tested on simulated EEGs obtained mixing source signals generated under different coupling conditions, showing its ability to retrieve source information dynamics from the scalp signals. Then, it was applied to investigate scalp and source brain connectivity in a group of children manifesting episodes of focal and generalized epilepsy; the analysis was performed on EEG signals lasting 5 s, collected in two consecutive windows preceding and one window following each ictal episode. Our results show that generalized seizures are associated with a significant decrease from pre-ictal to post-ictal periods of the information stored in the signals and of the information transferred among them, reflecting reduced self-predictability and causal connectivity at the level of both scalp and source brain dynamics. On the contrary, in the case of focal seizures the scalp EEG activity was not discriminated across conditions by any information measure, while source analysis revealed a tendency of the measures of information transfer to increase just before seizures and to decrease just after seizures. These results suggest that focal epileptic seizures are associated with a reorganization of the topology of EEG brain networks which is only visible analyzing connectivity among the brain sources. Our findings emphasize the importance of EEG modeling approaches able to deal with the adverse effects of volume conduction on brain connectivity analysis, and their potential relevance to the development of strategies for prediction and clinical treatment of epilepsy.

Evaluation of synchronization measures for capturing the lagged synchronization between EEG channels: A cognitive task recognition approach

During cognitive, perceptual and sensory tasks, connectivity profile changes across different regions of the brain. Variations of such connectivity patterns between different cognitive tasks can be evaluated using pairwise synchronization measures applied to electrophysiological signals, such as electroencephalography (EEG). However, connectivity-based task recognition approaches achieving viable recognition performance have been lacking from the literature. By using several synchronization measures, we identify time lags between channel pairs during different cognitive tasks. We employed mutual information, cross correntropy, cross correlation, phase locking value, cosine similarity and nonlinear interdependence measures. In the training phase, for each type of cognitive task, we identify the time lags that maximize the average synchronization between channel pairs. These lags are used to calculate pairwise synchronization values with which we construct the train and test feature vectors for recognition of the cognitive task carried out using Fisher's linear discriminant (FLD) analysis. We tested our framework in a motor imagery activity recognition scenario on PhysioNet Motor Movement/Imagery and BCI Competition-III Ⅳa datasets. For PhysioNet dataset, average performance results ranging between % 51 and % 61 across 20 subjects. For BCI Competition-Ⅲ dataset, we achieve an average recognition performance of % 76 which is above the minimum reliable communication rate (% 70). We achieved an average accuracy over the minimum reliable communication rate on the BCI Competition-Ⅲ dataset. Performance levels were lower on the PhysioNet dataset. These results indicate that a viable task recognition system is achievable using pairwise synchronization measures evaluated at the proper task specific lags.

MAXENT3D_PID: An Estimator for the Maximum-Entropy Trivariate Partial Information Decomposition

Partial information decomposition (PID) separates the contributions of sources about a target into unique, redundant, and synergistic components of information. In essence, PID answers the question of “who knows what” of a system of random variables and hence has applications to a wide spectrum of fields ranging from social to biological sciences. The paper presents MaxEnt3D_Pid, an algorithm that computes the PID of three sources, based on a recently-proposed maximum entropy measure, using convex optimization (cone programming). We describe the algorithm and its associated software utilization and report the results of various experiments assessing its accuracy. Moreover, the paper shows that a hierarchy of bivariate and trivariate PID allows obtaining the finer quantities of the trivariate partial information measure.

Identification of Hidden Sources by Estimating Instantaneous Causality in High-Dimensional Biomedical Time Series

The study of connectivity patterns of a system’s variables, such as multi-channel electroencephalograms (EEG), is of utmost importance towards a better understanding of its internal evolutionary mechanisms. Here, the problem of estimating the connectivity network from multivariate time series in the presence of prominent unobserved variables is addressed. The causality measure of partial mutual information from mixed embedding (PMIME), designed to estimate direct lag-causal effects in the presence of many observed variables, is adapted to estimate also zero-lag effects, the so-called instantaneous causality. We term the proposed advanced method, PMIME0. The estimation of instantaneous causality by PMIME0 is a signature of the presence of hidden source in the observed system, as demonstrated analytically in a toy model. It is further demonstrated that the PMIME0 identifies the true instantaneous with great accuracy in a variety of high-dimensional dynamical systems. The method is applied to EEG data with epileptiform discharges (EDs), and the results imply a strong impact of unobserved confounders during the EDs. This finding comes as a possible explanation for the increased levels of causality during epileptic seizures estimated by some measures affected by the presence of a common source.

Estimating coupling strength between multivariate neural series with multivariate permutation conditional mutual information

Recently, coupling between groups of neurons or different brain regions has been widely studied to provide insights into underlying mechanisms of brain functions. To comprehensively understand the effect of such coupling, it is necessary to accurately extract the coupling strength information among multivariate neural signals from the whole brain. This study proposed a new method named multivariate permutation conditional mutual information (MPCMI) to quantitatively estimate the coupling strength of multivariate neural signals (MNS). The performance of the MPCMI method was validated on the simulated MNS generated by multi-channel neural mass model (MNMM). The coupling strength feature of simulated MNS extracted by MPCMI showed better performance compared with standard methods, such as permutation conditional mutual information (PCMI), multivariate Granger causality (MVGC), and Granger causality analysis (GCA). Furthermore, the MPCMI was applied to estimate the coupling strengths of two-channel resting-state electroencephalographic (rsEEG) signals from different brain regions of 19 patients with amnestic mild cognitive impairment (aMCI) with type 2 diabetes mellitus (T2DM) and 20 normal control (NC) with T2DM in Alpha1 and Alpha2 frequency bands. Empirical results showed that the MPCMI could effectively extract the coupling strength features that were significantly different between the aMCI and the NC. Hence, the proposed MPCMI method could be an effective estimate of coupling strengths of MNS, and might be a viable biomarker for clinical applications.

The Identity of Information: How Deterministic Dependencies Constrain Information Synergy and Redundancy

Understanding how different information sources together transmit information is crucial in many domains. For example, understanding the neural code requires characterizing how different neurons contribute unique, redundant, or synergistic pieces of information about sensory or behavioral variables. Williams and Beer (2010) proposed a partial information decomposition (PID) that separates the mutual information that a set of sources contains about a set of targets into nonnegative terms interpretable as these pieces. Quantifying redundancy requires assigning an identity to different information pieces, to assess when information is common across sources. Harder et al. (2013) proposed an identity axiom that imposes necessary conditions to quantify qualitatively common information. However, Bertschinger et al. (2012) showed that, in a counterexample with deterministic target-source dependencies, the identity axiom is incompatible with ensuring PID nonnegativity. Here, we study systematically the consequences of information identity criteria that assign identity based on associations between target and source variables resulting from deterministic dependencies. We show how these criteria are related to the identity axiom and to previously proposed redundancy measures, and we characterize how they lead to negative PID terms. This constitutes a further step to more explicitly address the role of information identity in the quantification of redundancy. The implications for studying neural coding are discussed.

Comparison of connectivity analyses for resting state EEG data

OBJECTIVE

In the present work, a nonlinear measure (transfer entropy, TE) was used in a multivariate approach for the analysis of effective connectivity in high density resting state EEG data in eyes open and eyes closed. Advantages of the multivariate approach in comparison to the bivariate one were tested. Moreover, the multivariate TE was compared to an effective linear measure, i.e. directed transfer function (DTF). Finally, the existence of a relationship between the information transfer and the level of brain synchronization as measured by phase synchronization value (PLV) was investigated.

APPROACH

The comparison between the connectivity measures, i.e. bivariate versus multivariate TE, TE versus DTF, TE versus PLV, was performed by means of statistical analysis of indexes based on graph theory.

MAIN RESULTS

The multivariate approach is less sensitive to false indirect connections with respect to the bivariate estimates. The multivariate TE differentiated better between eyes closed and eyes open conditions compared to DTF. Moreover, the multivariate TE evidenced non-linear phenomena in information transfer, which are not evidenced by the use of DTF. We also showed that the target of information flow, in particular the frontal region, is an area of greater brain synchronization.

SIGNIFICANCE

Comparison of different connectivity analysis methods pointed to the advantages of nonlinear methods, and indicated a relationship existing between the flow of information and the level of synchronization of the brain.

The Power of Connecting Dots: Advanced Techniques to Evaluate Brain Functional Connectivity in Humans

Brain functional connectivity estimation allows us to depict patterns of cerebral activity not understandable otherwise with the standard brain imaging techniques such as functional magnetic resonance imaging (fMRI) as well as electro or magnetoencephalography (hr-EEG, MEG). This special issue of the IEEE Transactions on Biomedical Engineering reports a range of methodological innovations toward the estimation of functional connectivity from brain activity data, with emphasis on neuroelectric and hemodynamic imaging modalities. Functional connectivity methodologies enable "connecting of the dots" derived from brain activity observations over multiple distributed sites, as depicted by such fMRI and hr-EEG/MEG devices.