Hyperedge bundling: A practical solution to spurious interactions in MEG/EEG source connectivity analyses

The effects of spatial leakage correction on the reliability of EEG-based functional connectivity networks

Electroencephalography (EEG) functional connectivity (FC) estimates are confounded by the volume conduction problem. This effect can be greatly reduced by applying FC measures insensitive to instantaneous, zero-lag dependencies (corrected measures). However, numerous studies showed that FC measures sensitive to volume conduction (uncorrected measures) exhibit higher reliability and higher subject-level identifiability. We tested how source reconstruction contributed to the reliability difference of EEG FC measures on a large (n = 201) resting-state data set testing eight FC measures (including corrected and uncorrected measures). We showed that the high reliability of uncorrected FC measures in resting state partly stems from source reconstruction: idiosyncratic noise patterns define a baseline resting-state functional network that explains a significant portion of the reliability of uncorrected FC measures. This effect remained valid for template head model-based, as well as individual head model-based source reconstruction. Based on our findings we made suggestions how to best use spatial leakage corrected and uncorrected FC measures depending on the main goals of the study.

Rhythmicity of neuronal oscillations delineates their cortical and spectral architecture

Neuronal oscillations are commonly analyzed with power spectral methods that quantify signal amplitude, but not rhythmicity or 'oscillatoriness' per se. Here we introduce a new approach, the phase-autocorrelation function (pACF), for the direct quantification of rhythmicity. We applied pACF to human intracerebral stereoelectroencephalography (SEEG) and magnetoencephalography (MEG) data and uncovered a spectrally and anatomically fine-grained cortical architecture in the rhythmicity of single- and multi-frequency neuronal oscillations. Evidencing the functional significance of rhythmicity, we found it to be a prerequisite for long-range synchronization in resting-state networks and to be dynamically modulated during event-related processing. We also extended the pACF approach to measure 'burstiness' of oscillatory processes and characterized regions with stable and bursty oscillations. These findings show that rhythmicity is double-dissociable from amplitude and constitutes a functionally relevant and dynamic characteristic of neuronal oscillations.

Characterization of Second-Order Mixing Effects in Reconstructed Cross-Spectra of Random Neural Fields

Functional connectivity in electroencephalography (EEG) and magnetoencephalography (MEG) data is commonly assessed by using measures that are insensitive to instantaneously interacting sources and as such would not give rise to false positive interactions caused by instantaneous mixing of true source signals (first-order mixing). Recent studies, however, have drawn attention to the fact that such measures are still susceptible to instantaneous mixing from lagged sources (i.e. second-order mixing) and that this can lead to a large number of false positive interactions. In this study we relate first- and second-order mixing effects on the cross-spectra of reconstructed source activity to the properties of the resolution operators that are used for the reconstruction. We derive two identities that relate first- and second-order mixing effects to the transformation properties of measurement and source configurations and exploit them to establish several basic properties of signal mixing. First, we provide a characterization of the configurations that are maximally and minimally sensitive to second-order mixing. It turns out that second-order mixing effects are maximal when the measurement locations are far apart and the sources coincide with the measurement locations. Second, we provide a description of second-order mixing effects in the vicinity of the measurement locations in terms of the local geometry of the point-spread functions of the resolution operator. Third, we derive a version of Lagrange's identity for cross-talk functions that establishes the existence of a trade-off between the magnitude of first- and second-order mixing effects. It also shows that, whereas the magnitude of first-order mixing is determined by the inner product of cross-talk functions, the magnitude of second-order mixing is determined by a generalized cross-product of cross-talk functions (the wedge product) which leads to an intuitive geometric understanding of the trade-off. All results are derived within the general framework of random neural fields on cortical manifolds.

A recurrent Hopfield network for estimating meso-scale effective connectivity in MEG

The architecture of communication within the brain, represented by the human connectome, has gained a paramount role in the neuroscience community. Several features of this communication, e.g., the frequency content, spatial topology, and temporal dynamics are currently well established. However, identifying generative models providing the underlying patterns of inhibition/excitation is very challenging. To address this issue, we present a novel generative model to estimate large-scale effective connectivity from MEG. The dynamic evolution of this model is determined by a recurrent Hopfield neural network with asymmetric connections, and thus denoted Recurrent Hopfield Mass Model (RHoMM). Since RHoMM must be applied to binary neurons, it is suitable for analyzing Band Limited Power (BLP) dynamics following a binarization process. We trained RHoMM to predict the MEG dynamics through a gradient descent minimization and we validated it in two steps. First, we showed a significant agreement between the similarity of the effective connectivity patterns and that of the interregional BLP correlation, demonstrating RHoMM's ability to capture individual variability of BLP dynamics. Second, we showed that the simulated BLP correlation connectomes, obtained from RHoMM evolutions of BLP, preserved some important topological features, e.g, the centrality of the real data, assuring the reliability of RHoMM. Compared to other biophysical models, RHoMM is based on recurrent Hopfield neural networks, thus, it has the advantage of being data-driven, less demanding in terms of hyperparameters and scalable to encompass large-scale system interactions. These features are promising for investigating the dynamics of inhibition/excitation at different spatial scales.

Strengthening of alpha synchronization is a neural correlate of cognitive transfer

Cognitive training can lead to improvements in both task-specific strategies and general capacities, such as visuo-spatial working memory (VSWM). The latter emerge slowly and linearly throughout training, in contrast to strategy where changes typically occur within the first days of training. Changes in strategy and capacity have not been separated in prior neuroimaging studies. Here, we used a within-participants design with dense temporal sampling to capture the time dynamics of neural mechanisms associated with change in capacity. In four participants, neural activity was recorded with magnetoencephalography on seven occasions over two months of visuo-spatial working memory training. During scanning, the participants performed a trained visuo-spatial working memory task, a transfer task, and a control task. First, we extracted an individual visuo-spatial working memory-load-dependent synchronization network for each participant. Next, we identified linear changes over time in the network, congruent with the temporal dynamics of capacity change. Three out of four participants showed a gradual strengthening of alpha synchronization. Strengthening of the same connections was also found in the transfer task but not in the control task. This suggests that cognitive transfer occurs through slow, gradual strengthening of alpha synchronization between cortical regions that are vital for both the trained task and the transfer task.

Enhanced behavioral performance through interareal gamma and beta synchronization

Cognitive functioning requires coordination between brain areas. Between visual areas, feedforward gamma synchronization improves behavioral performance. Here, we investigate whether similar principles hold across brain regions and frequency bands, using simultaneous electrocorticographic recordings from 15 areas of two macaque monkeys during performance of a selective attention task. Short behavioral reaction times (RTs), suggesting efficient interareal communication, occurred when occipital areas V1, V2, V4, and DP showed gamma synchronization, and fronto-central areas S1, 5, F1, F2, and F4 showed beta synchronization. For both area clusters and corresponding frequency bands, deviations from the typically observed phase relations increased RTs. Across clusters and frequency bands, good phase relations occurred in a correlated manner specifically when they processed the behaviorally relevant stimulus. Furthermore, the fronto-central cluster exerted a beta-band influence onto the occipital cluster whose strength predicted short RTs. These results suggest that local gamma and beta synchronization and their inter-regional coordination jointly improve behavioral performance.

Identifying good practices for detecting inter-regional linear functional connectivity from EEG

Aggregating voxel-level statistical dependencies between multivariate time series is an important intermediate step when characterising functional connectivity (FC) between larger brain regions. However, there are numerous ways in which voxel-level data can be aggregated into inter-regional FC, and the advantages of each of these approaches are currently unclear. In this study we generate ground-truth data and compare the performances of various pipelines that estimate directed and undirected linear phase-to-phase FC between regions. We test the ability of several existing and novel FC analysis pipelines to identify the true regions within which connectivity was simulated. We test various inverse modelling algorithms, strategies to aggregate time series within regions, and connectivity metrics. Furthermore, we investigate the influence of the number of interactions, the signal-to-noise ratio, the noise mix, the interaction time delay, and the number of active sources per region on the ability of detecting phase-to-phase FC. Throughout all simulated scenarios, lowest performance is obtained with pipelines involving the absolute value of coherency. Further, the combination of dynamic imaging of coherent sources (DICS) beamforming with directed FC metrics that aggregate information across multiple frequencies leads to unsatisfactory results. Pipelines that show promising results with our simulated pseudo-EEG data involve the following steps: (1) Source projection using the linearly-constrained minimum variance (LCMV) beamformer. (2) Principal component analysis (PCA) using the same fixed number of components within every region. (3) Calculation of the multivariate interaction measure (MIM) for every region pair to assess undirected phase-to-phase FC, or calculation of time-reversed Granger Causality (TRGC) to assess directed phase-to-phase FC. We formulate recommendations based on these results that may increase the validity of future experimental connectivity studies. We further introduce the free ROIconnect plugin for the EEGLAB toolbox that includes the recommended methods and pipelines that are presented here. We show an exemplary application of the best performing pipeline to the analysis of EEG data recorded during motor imagery.

Structural basis of envelope and phase intrinsic coupling modes in the cerebral cortex

Intrinsic coupling modes (ICMs) can be observed in ongoing brain activity at multiple spatial and temporal scales. Two families of ICMs can be distinguished: phase and envelope ICMs. The principles that shape these ICMs remain partly elusive, in particular their relation to the underlying brain structure. Here we explored structure-function relationships in the ferret brain between ICMs quantified from ongoing brain activity recorded with chronically implanted micro-ECoG arrays and structural connectivity (SC) obtained from high-resolution diffusion MRI tractography. Large-scale computational models were used to explore the ability to predict both types of ICMs. Importantly, all investigations were conducted with ICM measures that are sensitive or insensitive to volume conduction effects. The results show that both types of ICMs are significantly related to SC, except for phase ICMs when using measures removing zero-lag coupling. The correlation between SC and ICMs increases with increasing frequency which is accompanied by reduced delays. Computational models produced results that were highly dependent on the specific parameter settings. The most consistent predictions were derived from measures solely based on SC. Overall, the results demonstrate that patterns of cortical functional coupling as reflected in both phase and envelope ICMs are both related, albeit to different degrees, to the underlying structural connectivity in the cerebral cortex.

Brain-wide network analysis of resting-state neuromagnetic data

The present study performed a brain-wide network analysis of resting-state magnetoencephalograms recorded from 53 healthy participants to visualize elaborate brain maps of phase- and amplitude-derived graph-theory metrics at different frequencies. To achieve this, we conducted a vertex-wise computation of threshold-independent graph metrics by combining proportional thresholding and a conjunction analysis and applied them to a correlation analysis of age and brain networks. Source power showed a frequency-dependent cortical distribution. Threshold-independent graph metrics derived from phase- and amplitude-based connectivity showed similar or different distributions depending on frequency. Vertex-wise age-brain correlation maps revealed that source power at the beta band and the amplitude-based degree at the alpha band changed with age in local regions. The present results indicate that a brain-wide analysis of neuromagnetic data has the potential to reveal neurophysiological network features in the human brain in a resting state.

Enhanced Behavioral Performance through Interareal Gamma and Beta Synchronization

Cognitive functioning requires coordination between brain areas. Between visual areas, feedforward gamma synchronization improves behavioral performance. Here, we investigate whether similar principles hold across brain regions and frequency bands, using simultaneous local field potential recordings from 15 areas during performance of a selective attention task. Short behavioral reaction times (RTs), an index of efficient interareal communication, occurred when occipital areas V1, V2, V4, DP showed gamma synchronization, and fronto-central areas S1, 5, F1, F2, F4 showed beta synchronization. For both area clusters and corresponding frequency bands, deviations from the typically observed phase relations increased RTs. Across clusters and frequency bands, good phase relations occurred in a correlated manner specifically when they processed the behaviorally relevant stimulus. Furthermore, the fronto-central cluster exerted a beta-band influence onto the occipital cluster whose strength predicted short RTs. These results suggest that local gamma and beta synchronization and their inter-regional coordination jointly improve behavioral performance.

Multistage classification identifies altered cortical phase- and amplitude-coupling in Multiple Sclerosis

Distinguishing groups of subjects or experimental conditions in a high-dimensional feature space is a common goal in modern neuroimaging studies. Successful classification depends on the selection of relevant features as not every neuronal signal component or parameter is informative about the research question at hand. Here, we developed a novel unsupervised multistage analysis approach that combines dimensionality reduction, bootstrap aggregating and multivariate classification to select relevant neuronal features. We tested the approach by identifying changes of brain-wide electrophysiological coupling in Multiple Sclerosis. Multiple Sclerosis is a demyelinating disease of the central nervous system that can result in cognitive decline and physical disability. However, related changes in large-scale brain interactions remain poorly understood and corresponding non-invasive biomarkers are sparse. We thus compared brain-wide phase- and amplitude-coupling of frequency specific neuronal activity in relapsing-remitting Multiple Sclerosis patients (n = 17) and healthy controls (n = 17) using magnetoencephalography. Changes in this dataset included both, increased and decreased phase- and amplitude-coupling in wide-spread, bilateral neuronal networks across a broad range of frequencies. These changes allowed to successfully classify patients and controls with an accuracy of 84%. Furthermore, classification confidence predicted behavioral scores of disease severity. In sum, our results unravel systematic changes of large-scale phase- and amplitude coupling in Multiple Sclerosis. Furthermore, our results establish a new analysis approach to efficiently contrast high-dimensional neuroimaging data between experimental groups or conditions.

EEG functional connectivity analysis in the source space

There is a growing interest in using electroencephalography (EEG) and source modeling to investigate functional interactions among cortical processes, particularly when dealing with pediatric populations. This paper introduces two pipelines that have been recently used to conduct EEG FC analysis in the cortical source space. The analytic streams of these pipelines can be summarized into the following steps: 1) cortical source reconstruction of high-density EEG data using realistic magnetic resonance imaging (MRI) models created with age-appropriate MRI templates; 2) segmentation of reconstructed source activities into brain regions of interest; and 3) estimation of FC in age-related frequency bands using robust EEG FC measures, such as weighted phase lag index and orthogonalized power envelope correlation. In this paper we demonstrate the two pipelines with resting-state EEG data collected from children at 12 and 36 months of age. We also discuss the advantages and limitations of the methods/techniques integrated into the pipelines. Given there is a need in the research community for open-access analytic toolkits that can be used for pediatric EEG data, programs and codes used for the current analysis are made available to the public.

Edge-centric analysis of stroke patients: An alternative approach for biomarkers of lesion recovery

Most neuroimaging studies of post-stroke recovery rely on analyses derived from standard node-centric functional connectivity to map the distributed effects in stroke patients. Here, given the importance of nonlocal and diffuse damage, we use an edge-centric approach to functional connectivity in order to provide an alternative description of the effects of this disorder. These techniques allow for the rendering of metrics such as normalized entropy, which describes the diversity of edge communities at each node. Moreover, the approach enables the identification of high amplitude co-fluctuations in fMRI time series. We found that normalized entropy is associated with stroke lesion severity and continually increases across the time of patients' recovery. Furthermore, high amplitude co-fluctuations not only relate to the lesion severity but are also associated with patients' level of recovery. The current study is the first edge-centric application for a clinical population in a longitudinal dataset and demonstrates how a different perspective for functional data analysis can further characterize topographic modulations of brain dynamics.

Neural Networks for Directed Connectivity Estimation in Source-Reconstructed EEG Data

Directed connectivity between brain sources identified from scalp electroencephalography (EEG) can shed light on the brain’s information flows and provide a biomarker of neurological disorders. However, as volume conductance results in scalp activity being a mix of activities originating from multiple sources, the correct interpretation of their connectivity is a formidable challenge despite source localization being applied with some success. Traditional connectivity approaches rely on statistical assumptions that usually do not hold for EEG, calling for a model-free approach. We investigated several types of Artificial Neural Networks in estimating Directed Connectivity between Reconstructed EEG Sources and assessed their accuracy with respect to several ground truths. We show that a Long Short-Term Memory neural network with Non-Uniform Embedding yields the most promising results due to its relative robustness to differing dipole locations. We conclude that certain network architectures can compete with the already established methods for brain connectivity analysis.

Harmoni: a Method for Eliminating Spurious Interactions due to the Harmonic Components in Neuronal Data

Cross-frequency synchronization (CFS) has been proposed as a mechanism for integrating spatially and spectrally distributed information in the brain. However, investigating CFS in Magneto- and Electroencephalography (MEG/EEG) is hampered by the presence of spurious neuronal interactions due to the non-sinusoidal waveshape of brain oscillations. Such waveshape gives rise to the presence of oscillatory harmonics mimicking genuine neuronal oscillations. Until recently, however, there has been no methodology for removing these harmonics from neuronal data. In order to address this long-standing challenge, we introduce a novel method (called HARMOnic miNImization - Harmoni) that removes the signal components which can be harmonics of a non-sinusoidal signal. Harmoni's working principle is based on the presence of CFS between harmonic components and the fundamental component of a non-sinusoidal signal. We extensively tested Harmoni in realistic EEG simulations. The simulated couplings between the source signals represented genuine and spurious CFS and within-frequency phase synchronization. Using diverse evaluation criteria, including ROC analyses, we showed that the within- and cross-frequency spurious interactions are suppressed significantly, while the genuine activities are not affected. Additionally, we applied Harmoni to real resting-state EEG data revealing intricate remote connectivity patterns which are usually masked by the spurious connections. Given the ubiquity of non-sinusoidal neuronal oscillations in electrophysiological recordings, Harmoni is expected to facilitate novel insights into genuine neuronal interactions in various research fields, and can also serve as a steppingstone towards the development of further signal processing methods aiming at refining within- and cross-frequency synchronization in electrophysiological recordings.

Brain rhythms define distinct interaction networks with differential dependence on anatomy

Cognitive functions are subserved by rhythmic neuronal synchronization across widely distributed brain areas. In 105 area pairs, we investigated functional connectivity (FC) through coherence, power correlation, and Granger causality (GC) in the theta, beta, high-beta, and gamma rhythms. Between rhythms, spatial FC patterns were largely independent. Thus, the rhythms defined distinct interaction networks. Importantly, networks of coherence and GC were not explained by the spatial distributions of the strengths of the rhythms. Those networks, particularly the GC networks, contained clear modules, with typically one dominant rhythm per module. To understand how this distinctiveness and modularity arises on a common anatomical backbone, we correlated, across 91 area pairs, the metrics of functional interaction with those of anatomical projection strength. Anatomy was primarily related to coherence and GC, with the largest effect sizes for GC. The correlation differed markedly between rhythms, being less pronounced for the beta and strongest for the gamma rhythm.

Source space reduction for eLORETA

Objective.We introduce Sparse exact low resolution electromagnetic tomography (eLORETA), a novel method for estimating a nonparametric solution to the source localization problem. Its goal is to generate a sparser solution compared to other source localization methods including eLORETA while benefitting from the latter's superior source localization accuracy.Approach.Sparse eLORETA starts by reducing the source space of the Lead Field Matrix using structured sparse Bayesian learning from which a Reduced Lead Field Matrix is constructed, which is used as input to eLORETA.Main results.With Sparse eLORETA, source sparsity can be traded against signal fidelity; the proposed optimum is shown to yield a much sparser solution than eLORETA's with only a slight loss in signal fidelity.Significance.When pursuing a data-driven approach, for cases where it is difficult to choose specific regions of interest, or when subsequently a connectivity analysis is performed, source space reduction could prove beneficial.

Principles and open questions in functional brain network reconstruction

Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network representation involves often covert theoretical assumptions and methodological choices which affect the way networks are reconstructed from experimental data, and ultimately the resulting network properties and their interpretation. Here, we review some fundamental conceptual underpinnings and technical issues associated with brain network reconstruction, and discuss how their mutual influence concurs in clarifying the organization of brain function.

Electrophysiological Signatures of Hierarchical Learning

Human perception and learning is thought to rely on a hierarchical generative model that is continuously updated via precision-weighted prediction errors (pwPEs). However, the neural basis of such cognitive process and how it unfolds during decision-making remain poorly understood. To investigate this question, we combined a hierarchical Bayesian model (i.e., Hierarchical Gaussian Filter [HGF]) with electroencephalography (EEG), while participants performed a probabilistic reversal learning task in alternatingly stable and volatile environments. Behaviorally, the HGF fitted significantly better than two control, nonhierarchical, models. Neurally, low-level and high-level pwPEs were independently encoded by the P300 component. Low-level pwPEs were reflected in the theta (4-8 Hz) frequency band, but high-level pwPEs were not. Furthermore, the expressions of high-level pwPEs were stronger for participants with better HGF fit. These results indicate that the brain employs hierarchical learning and encodes both low- and high-level learning signals separately and adaptively.

Dyconnmap: Dynamic connectome mapping-A neuroimaging python module

Despite recent progress in the analysis of neuroimaging data sets, our comprehension of the main mechanisms and principles which govern human brain cognition and function remains incomplete. Network neuroscience makes substantial efforts to manipulate these challenges and provide real answers. For the last decade, researchers have been modelling brain structure and function via a graph or network that comprises brain regions that are either anatomically connected via tracts or functionally via a more extensive repertoire of functional associations. Network neuroscience is a relatively new multidisciplinary scientific avenue of the study of complex systems by pursuing novel ways to analyze, map, store and model the essential elements and their interactions in complex neurobiological systems, particularly the human brain, the most complex system in nature. Due to a rapid expansion of neuroimaging data sets' size and complexity, it is essential to propose and adopt new empirical tools to track dynamic patterns between neurons and brain areas and create comprehensive maps. In recent years, there is a rapid growth of scientific interest in moving functional neuroimaging analysis beyond simplified group or time‐averaged approaches and sophisticated algorithms that can capture the time‐varying properties of functional connectivity. We describe algorithms and network metrics that can capture the dynamic evolution of functional connectivity under this perspective. We adopt the word ‘chronnectome’ (integration of the Greek word ‘Chronos’, which means time, and connectome) to describe this specific branch of network neuroscience that explores how mutually informed brain activity correlates across time and brain space in a functional way. We also describe how good temporal mining of temporally evolved dynamic functional networks could give rise to the detection of specific brain states over which our brain evolved. This characteristic supports our complex human mind. The temporal evolution of these brain states and well‐known network metrics could give rise to new analytic trends. Functional brain networks could also increase the multi‐faced nature of the dynamic networks revealing complementary information. Finally, we describe a python module (https://github.com/makism/dyconnmap) which accompanies this article and contains a collection of dynamic complex network analytics and measures and demonstrates its great promise for the study of a healthy subject's repeated fMRI scans.

Magnetoencephalography: physics, techniques, and applications in the basic and clinical neurosciences

Magnetoencephalography (MEG) is a technique used to measure the magnetic fields generated from neuronal activity in the brain. MEG has a high temporal resolution on the order of milliseconds and provides a more direct measure of brain activity when compared with hemodynamic-based neuroimaging methods such as magnetic resonance imaging and positron emission tomography. The current review focuses on basic features of MEG such as the instrumentation and the physics that are integral to the signals that can be measured, and the principles of source localization techniques, particularly the physics of beamforming and the techniques that are used to localize the signal of interest. In addition, we review several metrics that can be used to assess functional coupling in MEG and describe the advantages and disadvantages of each approach. Lastly, we discuss the current and future applications of MEG.

Lag-invariant detection of interactions in spatially-extended systems using linear inverse modeling

Measurements on physical systems result from the systems' activity being converted into sensor measurements by a forward model. In a number of cases, inversion of the forward model is extremely sensitive to perturbations such as sensor noise or numerical errors in the forward model. Regularization is then required, which introduces bias in the reconstruction of the systems' activity. One domain in which this is particularly problematic is the reconstruction of interactions in spatially-extended complex systems such as the human brain. Brain interactions can be reconstructed from non-invasive measurements such as electroencephalography (EEG) or magnetoencephalography (MEG), whose forward models are linear and instantaneous, but have large null-spaces and high condition numbers. This leads to incomplete unmixing of the forward models and hence to spurious interactions. This motivated the development of interaction measures that are exclusively sensitive to lagged, i.e. delayed interactions. The drawback of such measures is that they only detect interactions that have sufficiently large lags and this introduces bias in reconstructed brain networks. We introduce three estimators for linear interactions in spatially-extended systems that are uniformly sensitive to all lags. We derive some basic properties of and relationships between the estimators and evaluate their performance using numerical simulations from a simple benchmark model.

Functional connectivity of EEG is subject-specific, associated with phenotype, and different from fMRI

A variety of psychiatric, behavioral and cognitive phenotypes have been linked to brain ''functional connectivity'' -- the pattern of correlation observed between different brain regions. Most commonly assessed using functional magnetic resonance imaging (fMRI), here, we investigate the connectivity-phenotype associations with functional connectivity measured with electroencephalography (EEG), using phase-coupling. We analyzed data from the publicly available Healthy Brain Network Biobank. This database compiles a growing sample of children and adolescents, currently encompassing 1657 individuals. Among a variety of assessment instruments we focus on ten phenotypic and additional demographic measures that capture most of the variance in this sample. The largest effect sizes are found for age and sex for both fMRI and EEG. We replicate previous findings of an association of Intelligence Quotient (IQ) and Attention Deficit Hyperactivity Disorder (ADHD) with the pattern of fMRI functional connectivity. We also find an association with socioeconomic status, anxiety and the Child Behavior Checklist Score. For EEG we find a significant connectivity-phenotype relationship with IQ. The actual spatial patterns of functional connectivity are quite different between fMRI and source-space EEG. However, within EEG we observe clusters of functional connectivity that are consistent across frequency bands. Additionally we analyzed reproducibility of functional connectivity. We compare connectivity obtained with different tasks, including resting state, a video and a visual flicker task. For both EEG and fMRI the variation between tasks was smaller than the variability observed between subjects. We also found an increase of reliability with increasing frequency of the EEG, and increased sampling duration. We conclude that, while the patterns of functional connectivity are distinct between fMRI and phase-coupling of EEG, they are nonetheless similar in their robustness to the task, and similar in that idiosyncratic patterns of connectivity predict individual phenotypes.

Frequency-dependent functional connectivity in resting state networks

Functional magnetic resonance imaging studies have documented the resting human brain to be functionally organized in multiple large‐scale networks, called resting‐state networks (RSNs). Other brain imaging techniques, such as electroencephalography (EEG) and magnetoencephalography (MEG), have been used for investigating the electrophysiological basis of RSNs. To date, it is largely unclear how neural oscillations measured with EEG and MEG are related to functional connectivity in the resting state. In addition, it remains to be elucidated whether and how the observed neural oscillations are related to the spatial distribution of the network nodes over the cortex. To address these questions, we examined frequency‐dependent functional connectivity between the main nodes of several RSNs, spanning large part of the cortex. We estimated connectivity using band‐limited power correlations from high‐density EEG data collected in healthy participants. We observed that functional interactions within RSNs are characterized by a specific combination of neuronal oscillations in the alpha (8–13 Hz), beta (13–30 Hz), and gamma (30–80 Hz) bands, which highly depend on the position of the network nodes. This finding may contribute to a better understanding of the mechanisms through which neural oscillations support functional connectivity in the brain.

Decoding Analysis of Alpha Oscillation Networks on Maintaining Driver Alertness

The countermeasure of driver fatigue is valuable for reducing the risk of accidents caused by vigilance failure during prolonged driving. Listening to the radio (RADIO) has been proven to be a relatively effective “in-car” countermeasure. However, the connectivity analysis, which can be used to investigate its alerting effect, is subject to the issue of signal mixing. In this study, we propose a novel framework based on clustering and entropy to improve the performance of the connectivity analysis to reveal the effect of RADIO to maintain driver alertness. Regardless of reducing signal mixing, we introduce clustering algorithm to classify the functional connections with their nodes into different categories to mine the effective information of the alerting effect. Differential entropy (DE) is employed to measure the information content in different brain regions after clustering. Compared with the Louvain-based community detection method, the proposed method shows more superior ability to present RADIO effectin confused functional connection matrices. Our experimental results reveal that the active connection clusters distinguished by the proposed method gradually move from frontal region to parieto-occipital regionwith the progress of fatigue, consistent with the alpha energy changes in these two brain areas. The active class of the clusters in parieto-occipital region significantly decreases and the most active clusters remain in the frontal region when RADIO is taken. The estimation results of DE confirm the significant change (p < 0.05) of information content due to the cluster movements. Hence, preventing the movement of the active clusters from frontal region to parieto-occipital region may correlate with maintaining driver alertness. The revelation of alerting effect is helpful for the targeted upgrade of fatigue countermeasures.

Spectral and Anatomical Patterns of Large-Scale Synchronization Predict Human Attentional Capacity

The capacity of visual attention determines how many visual objects may be perceived at any moment. This capacity can be investigated with multiple object tracking (MOT) tasks, which have shown that it varies greatly between individuals. The neuronal mechanisms underlying capacity limits have remained poorly understood. Phase synchronization of cortical oscillations coordinates neuronal communication within the fronto-parietal attention network and between the visual regions during endogenous visual attention. We tested a hypothesis that attentional capacity is predicted by the strength of pretarget synchronization within attention-related cortical regions. We recorded cortical activity with magneto- and electroencephalography (M/EEG) while measuring attentional capacity with MOT tasks and identified large-scale synchronized networks from source-reconstructed M/EEG data. Individual attentional capacity was correlated with load-dependent strengthening of theta (3–8 Hz), alpha (8–10 Hz), and gamma-band (30–120 Hz) synchronization that connected the visual cortex with posterior parietal and prefrontal cortices. Individual memory capacity was also preceded by crossfrequency phase–phase and phase–amplitude coupling of alpha oscillation phase with beta and gamma oscillations. Our results show that good attentional capacity is preceded by efficient dynamic functional coupling and decoupling within brain regions and across frequencies, which may enable efficient communication and routing of information between sensory and attentional systems.

Genuine cross-frequency coupling networks in human resting-state electrophysiological recordings

Phase synchronization of neuronal oscillations in specific frequency bands coordinates anatomically distributed neuronal processing and communication. Typically, oscillations and synchronization take place concurrently in many distinct frequencies, which serve separate computational roles in cognitive functions. While within-frequency phase synchronization has been studied extensively, less is known about the mechanisms that govern neuronal processing distributed across frequencies and brain regions. Such integration of processing between frequencies could be achieved via cross-frequency coupling (CFC), either by phase–amplitude coupling (PAC) or by n:m-cross–frequency phase synchrony (CFS). So far, studies have mostly focused on local CFC in individual brain regions, whereas the presence and functional organization of CFC between brain areas have remained largely unknown. We posit that interareal CFC may be essential for large-scale coordination of neuronal activity and investigate here whether genuine CFC networks are present in human resting-state (RS) brain activity. To assess the functional organization of CFC networks, we identified brain-wide CFC networks at mesoscale resolution from stereoelectroencephalography (SEEG) and at macroscale resolution from source-reconstructed magnetoencephalography (MEG) data. We developed a novel, to our knowledge, graph-theoretical method to distinguish genuine CFC from spurious CFC that may arise from nonsinusoidal signals ubiquitous in neuronal activity. We show that genuine interareal CFC is present in human RS activity in both SEEG and MEG data. Both CFS and PAC networks coupled theta and alpha oscillations with higher frequencies in large-scale networks connecting anterior and posterior brain regions. CFS and PAC networks had distinct spectral patterns and opposing distribution of low- and high-frequency network hubs, implying that they constitute distinct CFC mechanisms. The strength of CFS networks was also predictive of cognitive performance in a separate neuropsychological assessment. In conclusion, these results provide evidence for interareal CFS and PAC being 2 distinct mechanisms for coupling oscillations across frequencies in large-scale brain networks.

Genuine interareal cross-frequency coupling (CFC) can be identified from human resting state activity using magnetoencephalography, stereoelectroencephalography, and novel network approaches. CFC couples slow theta and alpha oscillations to faster oscillations across brain regions.

Mapping critical hubs of receptive and expressive language using MEG: A comparison against fMRI

The complexity of the widespread language network makes it challenging for accurate localization and lateralization. Using large-scale connectivity and graph-theoretical analyses of task-based magnetoencephalography (MEG), we aimed to provide robust representations of receptive and expressive language processes, comparable with spatial profiles of corresponding functional magnetic resonance imaging (fMRI). We examined MEG and fMRI data from 12 healthy young adults (age 20-37 years) completing covert auditory word-recognition task (WRT) and covert auditory verb-generation task (VGT). For MEG language mapping, broadband (3-30 Hz) beamformer sources were estimated, voxel-level connectivity was quantified using phase locking value, and highly connected hubs were characterized using eigenvector centrality graph measure. fMRI data were analyzed using a classic general linear model approach. A laterality index (LI) was computed for 20 language-specific frontotemporal regions for both MEG and fMRI. MEG network analysis showed bilateral and symmetrically distributed hubs within the left and right superior temporal gyrus (STG) during WRT and predominant hubs in left inferior prefrontal gyrus (IFG) during VGT. MEG and fMRI localization maps showed high correlation values within frontotemporal regions during WRT and VGT (r = 0.63, 0.74, q < 0.05, respectively). Despite good concordance in localization, notable discordances were observed in lateralization between MEG and fMRI. During WRT, MEG favored a left-hemispheric dominance of left STG (LI = 0.25 ± 0.22) whereas fMRI supported a bilateral representation of STG (LI = 0.08 ± 0.2). Laterality of MEG and fMRI during VGT consistently showed a strong asymmetry in left IFG regions (MEG-LI = 0.45 ± 0.35 and fMRI-LI = 0.46 ± 0.13). Our results demonstrate the utility of a large-scale connectivity and graph theoretical analyses for robust identification of language-specific regions. MEG hubs are in great agreement with the literature in revealing with canonical and extra-canonical language sites, thus providing additional support for the underlying topological organization of receptive and expressive language cortices. Discordances in lateralization may emphasize the need for multimodal integration of MEG and fMRI to obtain an excellent predictive value in a heterogeneous healthy population and patients with neurosurgical conditions.

Increased segregation of functional networks in developing brains

A growing literature conceptualises typical brain development from a network perspective. However, largely due to technical and methodological challenges inherent in paediatric functional neuroimaging, there remains an important gap in our knowledge regarding the typical development of functional brain networks in "preschool" childhood (i.e., children younger than 6 years of age). In this study, we recorded brain oscillatory activity using age-appropriate magnetoencephalography in 24 children, including 14 preschool children aged from 4 to 6 years and 10 school children aged from 7 to 12 years. We compared the topology of the resting-state brain networks in these children, estimated using minimum spanning tree (MST) constructed from phase synchrony between beamformer-reconstructed time-series, with that of 24 adults. Our results show that during childhood the MST topology shifts from a star-like (centralised) toward a more line-like (de-centralised) configuration, indicating the functional brain networks become increasingly segregated. In addition, the increasing global network segregation is frequency-independent and accompanied by decreases in centrality (or connectedness) of cortical regions with age, especially in areas of the default mode network. We propose a heuristic MST model of "network space", which posits a clear developmental trajectory for the emergence of complex brain networks. Our results not only revealed topological reorganisation of functional networks across multiple temporal and spatial scales in childhood, but also fill a gap in the literature regarding neurophysiological mechanisms of functional brain maturation during the preschool years of childhood.

Electrophysiological Brain Connectivity: Theory and Implementation

We review the theory and algorithms of electrophysiological brain connectivity analysis. This tutorial is aimed at providing an introduction to brain functional connectivity from electrophysiological signals, including electroencephalography (EEG), magnetoencephalography (MEG), electrocorticography (ECoG), stereoelectroencephalography (SEEG). Various connectivity estimators are discussed, and algorithms introduced. Important issues for estimating and mapping brain functional connectivity with electrophysiology are discussed.

Quantifying the Effect of Demixing Approaches on Directed Connectivity Estimated Between Reconstructed EEG Sources

Electrical activity recorded on the scalp using electroencephalography (EEG) results from the mixing of signals originating from different regions of the brain as well as from artifactual sources. In order to investigate the role of distinct brain areas in a given experiment, the signal recorded on the sensors is typically projected back into the brain (source reconstruction) using algorithms that address the so-called EEG "inverse problem". Once the activity of sources located inside of the brain has been reconstructed, it is often desirable to study the statistical dependencies among them, in particular to quantify directional dynamical interactions between brain areas. Unfortunately, even when performing source reconstruction, the superposition of signals that is due to the propagation of activity from sources to sensors cannot be completely undone, resulting in potentially biased estimates of directional functional connectivity. Here we perform a set of simulations involving interacting sources to quantify source connectivity estimation performance as a function of the location of the sources, their distance to each other, the noise level, the source reconstruction algorithm, and the connectivity estimator. The generated source activity was projected onto the scalp and projected back to the cortical level using two source reconstruction algorithms, linearly constrained minimum variance beamforming and 'Exact' low-resolution tomography (eLORETA). In source space, directed connectivity was estimated using multi-variate Granger causality and time-reversed Granger causality, and compared with the imposed ground truth. Our results demonstrate that all considered factors significantly affect the connectivity estimation performance.

Dynamic large-scale network synchronization from perception to action

Sensory-guided actions entail the processing of sensory information, generation of perceptual decisions, and the generation of appropriate actions. Neuronal activity underlying these processes is distributed into sensory, fronto-parietal, and motor brain areas, respectively. How the neuronal processing is coordinated across these brain areas to support functions from perception to action remains unknown. We investigated whether phase synchronization in large-scale networks coordinate these processes. We recorded human cortical activity with magnetoencephalography (MEG) during a task in which weak somatosensory stimuli remained unperceived or were perceived. We then assessed dynamic evolution of phase synchronization in large-scale networks from source-reconstructed MEG data by using advanced analysis approaches combined with graph theory. Here we show that perceiving and reporting of weak somatosensory stimuli is correlated with sustained strengthening of large-scale synchrony concurrently in delta/theta (3-7 Hz) and gamma (40-60 Hz) frequency bands. In a data-driven network localization, we found this synchronization to dynamically connect the task-relevant, that is, the fronto-parietal, sensory, and motor systems. The strength and temporal pattern of interareal synchronization were also correlated with the response times. These data thus show that key brain areas underlying perception, decision-making, and actions are transiently connected by large-scale dynamic phase synchronization in the delta/theta and gamma bands.

Phase locking value revisited: teaching new tricks to an old dog

OBJECTIVE

Despite the increase in calculation power over the last few decades, the estimation of brain connectivity is still a tedious task. The high computational cost of the algorithms escalates with the square of the number of signals evaluated, usually in the range of thousands. In this work we propose a re-formulation of a widely used algorithm that allows the estimation of whole brain connectivity in much smaller times.

APPROACH

We start from the original implementation of phase locking value (PLV) and re-formulated it in a computationally very efficient way. What is more, this formulation stresses its strong similarity with coherence, which we used to introduce two new metrics insensitive to zero lag synchronization: the imaginary part of PLV (iPLV) and its corrected counterpart (ciPLV).

MAIN RESULTS

The new implementation of PLV avoids some highly CPU-expensive operations and achieves a 100-fold speedup over the original algorithm. The new derived metrics were highly robust in the presence of volume conduction. Moreover, ciPLV proved capable of ignoring zero-lag connectivity, while correctly estimating nonzero-lag connectivity.

SIGNIFICANCE

Our implementation of PLV makes it possible to calculate whole-brain connectivity in much shorter times. The results of the simulations using ciPLV suggest that this metric is ideal to measure synchronization in the presence of volume conduction or source leakage effects.

How to Build a Functional Connectomic Biomarker for Mild Cognitive Impairment From Source Reconstructed MEG Resting-State Activity: The Combination of ROI Representation and Connectivity Estimator Matters

Our work aimed to demonstrate the combination of machine learning and graph theory for the designing of a connectomic biomarker for mild cognitive impairment (MCI) subjects using eyes-closed neuromagnetic recordings. The whole analysis based on source-reconstructed neuromagnetic activity. As ROI representation, we employed the principal component analysis (PCA) and centroid approaches. As representative bi-variate connectivity estimators for the estimation of intra and cross-frequency interactions, we adopted the phase locking value (PLV), the imaginary part (iPLV) and the correlation of the envelope (CorrEnv). Both intra and cross-frequency interactions (CFC) have been estimated with the three connectivity estimators within the seven frequency bands (intra-frequency) and in pairs (CFC), correspondingly. We demonstrated how different versions of functional connectivity graphs single-layer (SL-FCG) and multi-layer (ML-FCG) can give us a different view of the functional interactions across the brain areas. Finally, we applied machine learning techniques with main scope to build a reliable connectomic biomarker by analyzing both SL-FCG and ML-FCG in two different options: as a whole unit using a tensorial extraction algorithm and as single pair-wise coupling estimations. We concluded that edge-weighed feature selection strategy outperformed the tensorial treatment of SL-FCG and ML-FCG. The highest classification performance was obtained with the centroid ROI representation and edge-weighted analysis of the SL-FCG reaching the 98% for the CorrEnv in α1:α2 and 94% for the iPLV in α2. Classification performance based on the multi-layer participation coefficient, a multiplexity index reached 52% for iPLV and 52% for CorrEnv. Selected functional connections that build the multivariate connectomic biomarker in the edge-weighted scenario are located in default-mode, fronto-parietal, and cingulo-opercular network. Our analysis supports the notion of analyzing FCG simultaneously in intra and cross-frequency whole brain interactions with various connectivity estimators in beamformed recordings.

Ghost interactions in MEG/EEG source space: A note of caution on inter-areal coupling measures

When combined with source modeling, magneto- (MEG) and electroencephalography (EEG) can be used to study long-range interactions among cortical processes non-invasively. Estimation of such inter-areal connectivity is nevertheless hindered by instantaneous field spread and volume conduction, which artificially introduce linear correlations and impair source separability in cortical current estimates. To overcome the inflating effects of linear source mixing inherent to standard interaction measures, alternative phase- and amplitude-correlation based connectivity measures, such as imaginary coherence and orthogonalized amplitude correlation have been proposed. Being by definition insensitive to zero-lag correlations, these techniques have become increasingly popular in the identification of correlations that cannot be attributed to field spread or volume conduction. We show here, however, that while these measures are immune to the direct effects of linear mixing, they may still reveal large numbers of spurious false positive connections through field spread in the vicinity of true interactions. This fundamental problem affects both region-of-interest-based analyses and all-to-all connectome mappings. Most importantly, beyond defining and illustrating the problem of spurious, or "ghost" interactions, we provide a rigorous quantification of this effect through extensive simulations. Additionally, we further show that signal mixing also significantly limits the separability of neuronal phase and amplitude correlations. We conclude that spurious correlations must be carefully considered in connectivity analyses in MEG/EEG source space even when using measures that are immune to zero-lag correlations.

Network Entropy for the Sequence Analysis of Functional Connectivity Graphs of the Brain

Dynamic representation of functional brain networks involved in the sequence analysis of functional connectivity graphs of the brain (FCGB) gains advances in uncovering evolved interaction mechanisms. However, most of the networks, even the event-related ones, are highly heterogeneous due to spurious interactions, which bring challenges to revealing the change patterns of interactive information in the complex dynamic process. In this paper, we propose a network entropy (NE) method to measure connectivity uncertainty of FCGB sequences to alleviate the spurious interaction problem in dynamic network analysis to realize associations with different events during a complex cognitive task. The proposed dynamic analysis approach calculated the adjacency matrices from ongoing electroencephalpgram (EEG) in a sliding time-window to form the FCGB sequences. The probability distribution of Shannon entropy was replaced by the connection sequence distribution to measure the uncertainty of FCGB constituting NE. Without averaging, we used time frequency transform of the NE of FCGB sequences to analyze the event-related changes in oscillatory activity in the single-trial traces during the complex cognitive process of driving. Finally, the results of a verification experiment showed that the NE of the FCGB sequences has a certain time-locked performance for different events related to driver fatigue in a prolonged driving task. The time errors between the extracted time of high-power NE and the recorded time of event occurrence were distributed within the range [−30 s, 30 s] and 90.1% of the time errors were distributed within the range [−10 s, 10 s]. The high correlation (r = 0.99997, p < 0.001) between the timing characteristics of the two types of signals indicates that the NE can reflect the actual dynamic interaction states of brain. Thus, the method may have potential implications for cognitive studies and for the detection of physiological states.