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.

Critical-like Brain Dynamics in a Continuum from Second- to First-Order Phase Transition.

The classic brain criticality hypothesis postulates that the brain benefits from operating near a continuous second-order phase transition. Slow feedback regulation of neuronal activity could, however, lead to a discontinuous first-order transition and thereby bistable activity. Observations of bistability in awake brain activity have nonetheless remained scarce and its functional significance unclear. Moreover, there is no empirical evidence to support the hypothesis that the human brain could flexibly operate near either a first- or second-order phase transition despite such a continuum being common in models. Here, using computational modeling, we found bistable synchronization dynamics to emerge through elevated positive feedback and occur exclusively in a regimen of critical-like dynamics. We then assessed bistability in vivo with resting-state MEG in healthy adults (7 females, 11 males) and stereo-electroencephalography in epilepsy patients (28 females, 36 males). This analysis revealed that a large fraction of the neocortices exhibited varying degrees of bistability in neuronal oscillations from 3 to 200 Hz. In line with our modeling results, the neuronal bistability was positively correlated with classic assessment of brain criticality across narrow-band frequencies. Excessive bistability was predictive of epileptic pathophysiology in the patients, whereas moderate bistability was positively correlated with task performance in the healthy subjects. These empirical findings thus reveal the human brain as a one-of-a-kind complex system that exhibits critical-like dynamics in a continuum between continuous and discontinuous phase transitions.SIGNIFICANCE STATEMENT In the model, while synchrony per se was controlled by connectivity, increasing positive local feedback led to gradually emerging bistable synchrony with scale-free dynamics, suggesting a continuum between second- and first-order phase transitions in synchrony dynamics inside a critical-like regimen. In resting-state MEG and SEEG, bistability of ongoing neuronal oscillations was pervasive across brain areas and frequency bands and was observed only with concurring critical-like dynamics as the modeling predicted. As evidence for functional relevance, moderate bistability was positively correlated with executive functioning in the healthy subjects, and excessive bistability was associated with epileptic pathophysiology. These findings show that critical-like neuronal dynamics in vivo involves both continuous and discontinuous phase transitions in a frequency-, neuroanatomy-, and state-dependent manner.

Brain criticality predicts individual levels of inter-areal synchronization in human electrophysiological data.

Neuronal oscillations and their synchronization between brain areas are fundamental for healthy brain function. Yet, synchronization levels exhibit large inter-individual variability that is associated with behavioral variability. We test whether individual synchronization levels are predicted by individual brain states along an extended regime of critical-like dynamics - the Griffiths phase (GP). We use computational modelling to assess how synchronization is dependent on brain criticality indexed by long-range temporal correlations (LRTCs). We analyze LRTCs and synchronization of oscillations from resting-state magnetoencephalography and stereo-electroencephalography data. Synchronization and LRTCs are both positively linearly and quadratically correlated among healthy subjects, while in epileptogenic areas they are negatively linearly correlated. These results show that variability in synchronization levels is explained by the individual position along the GP with healthy brain areas operating in its subcritical and epileptogenic areas in its supercritical side. We suggest that the GP is fundamental for brain function allowing individual variability while retaining functional advantages of criticality.

Genetic polymorphisms in COMT and BDNF influence synchronization dynamics of human neuronal oscillations.

Neuronal oscillations, their inter-areal synchronization, and scale-free dynamics constitute fundamental mechanisms for cognition by regulating communication in neuronal networks. These oscillatory dynamics have large inter-individual variability that is partly heritable. We hypothesized that this variability could be partially explained by genetic polymorphisms in neuromodulatory genes. We recorded resting-state magnetoencephalography (MEG) from 82 healthy participants and investigated whether oscillation dynamics were influenced by genetic polymorphisms in catechol-O-methyltransferase (COMT) Val158Met and brain-derived neurotrophic factor (BDNF) Val66Met. Both COMT and BDNF polymorphisms influenced local oscillation amplitudes and their long-range temporal correlations (LRTCs), while only BDNF polymorphism affected the strength of large-scale synchronization. Our findings demonstrate that COMT and BDNF genetic polymorphisms contribute to inter-individual variability in neuronal oscillation dynamics. Comparison of these results to computational modeling of near-critical synchronization dynamics further suggested that COMT and BDNF polymorphisms influenced local oscillations by modulating the excitation-inhibition balance according to the brain criticality framework.

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.

Hyperedge bundling: Data, source code, and precautions to modeling-accuracy bias to synchrony estimates.

It has not been well documented that MEG/EEG functional connectivity graphs estimated with zero-lag-free interaction metrics are severely confounded by a multitude of spurious interactions (SI), i.e., the false-positive "ghosts" of true interactions [1], [2]. These SI are caused by the multivariate linear mixing between sources, and thus they pose a severe challenge to the validity of connectivity analysis. Due to the complex nature of signal mixing and the SI problem, there is a need to intuitively demonstrate how the SI are discovered and how they can be attenuated using a novel approach that we termed hyperedge bundling. Here we provide a dataset with software with which the readers can perform simulations in order to better understand the theory and the solution to SI. We include the supplementary material of [1] that is not directly relevant to the hyperedge bundling per se but reflects important properties of the MEG source model and the functional connectivity graphs. For example, the gyri of dorsal-lateral cortices are the most accurately modeled areas; the sulci of inferior temporal, frontal and the insula have the least modeling accuracy. Importantly, we found the interaction estimates are heavily biased by the modeling accuracy between regions, which means the estimates cannot be straightforwardly interpreted as the coupling between brain regions. This raise a red flag that the conventional method of thresholding graphs by estimate values is rather suboptimal: because the measured topology of the graph reflects the geometric property of source-model instead of the cortical interactions under investigation.

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

Inter-areal functional connectivity (FC), neuronal synchronization in particular, is thought to constitute a key systems-level mechanism for coordination of neuronal processing and communication between brain regions. Evidence to support this hypothesis has been gained largely using invasive electrophysiological approaches. In humans, neuronal activity can be non-invasively recorded only with magneto- and electroencephalography (MEG/EEG), which have been used to assess FC networks with high temporal resolution and whole-scalp coverage. However, even in source-reconstructed MEG/EEG data, signal mixing, or "source leakage", is a significant confounder for FC analyses and network localization. Signal mixing leads to two distinct kinds of false-positive observations: artificial interactions (AI) caused directly by mixing and spurious interactions (SI) arising indirectly from the spread of signals from true interacting sources to nearby false loci. To date, several interaction metrics have been developed to solve the AI problem, but the SI problem has remained largely intractable in MEG/EEG all-to-all source connectivity studies. Here, we advance a novel approach for correcting SIs in FC analyses using source-reconstructed MEG/EEG data. Our approach is to bundle observed FC connections into hyperedges by their adjacency in signal mixing. Using realistic simulations, we show here that bundling yields hyperedges with good separability of true positives and little loss in the true positive rate. Hyperedge bundling thus significantly decreases graph noise by minimizing the false-positive to true-positive ratio. Finally, we demonstrate the advantage of edge bundling in the visualization of large-scale cortical networks with real MEG data. We propose that hypergraphs yielded by bundling represent well the set of true cortical interactions that are detectable and dissociable in MEG/EEG connectivity analysis.

Cross-frequency synchronization connects networks of fast and slow oscillations during visual working memory maintenance.

Neuronal activity in sensory and fronto-parietal (FP) areas underlies the representation and attentional control, respectively, of sensory information maintained in visual working memory (VWM). Within these regions, beta/gamma phase-synchronization supports the integration of sensory functions, while synchronization in theta/alpha bands supports the regulation of attentional functions. A key challenge is to understand which mechanisms integrate neuronal processing across these distinct frequencies and thereby the sensory and attentional functions. We investigated whether such integration could be achieved by cross-frequency phase synchrony (CFS). Using concurrent magneto- and electroencephalography, we found that CFS was load-dependently enhanced between theta and alpha-gamma and between alpha and beta-gamma oscillations during VWM maintenance among visual, FP, and dorsal attention (DA) systems. CFS also connected the hubs of within-frequency-synchronized networks and its strength predicted individual VWM capacity. We propose that CFS integrates processing among synchronized neuronal networks from theta to gamma frequencies to link sensory and attentional functions.

Phase transfer entropy: a novel phase-based measure for directed connectivity in networks coupled by oscillatory interactions.

We introduce here phase transfer entropy (Phase TE) as a measure of directed connectivity among neuronal oscillations. Phase TE quantifies the transfer entropy between phase time-series extracted from neuronal signals by filtering for instance. To validate the measure, we used coupled Neuronal Mass Models to both evaluate the characteristics of Phase TE and compare its performance with that of a real-valued TE implementation. We showed that Phase TE detects the strength and direction of connectivity even in the presence of such amounts of noise and linear mixing that typically characterize MEG and EEG recordings. Phase TE performed well across a wide range of analysis lags and sample sizes. Comparisons between Phase TE and real-valued TE estimates showed that Phase TE is more robust to nuisance parameters and considerably more efficient computationally. In addition, Phase TE accurately untangled bidirectional frequency band specific interaction patterns that confounded real-valued TE. Finally, we found that surrogate data can be used to construct appropriate null-hypothesis distributions and to estimate statistical significance of Phase TE. These results hence suggest that Phase TE is well suited for the estimation of directed phase-based connectivity in large-scale investigations of the human functional connectome.

Intra- and inter-frequency brain network structure in health and schizophrenia.

Empirical studies over the past two decades have provided support for the hypothesis that schizophrenia is characterized by altered connectivity patterns in functional brain networks. These alterations have been proposed as genetically mediated diagnostic biomarkers and are thought to underlie altered cognitive functions such as working memory. However, the nature of this dysconnectivity remains far from understood. In this study, we perform an extensive analysis of functional connectivity patterns extracted from MEG data in 14 subjects with schizophrenia and 14 healthy controls during a 2-back working memory task. We investigate uni-, bi- and multivariate properties of sensor time series by computing wavelet entropy of and correlation between time series, and by constructing binary networks of functional connectivity both within and between classical frequency bands ([Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]). Networks are based on the mutual information between wavelet time series, and estimated for each trial window separately, enabling us to consider both network topology and network dynamics. We observed significant decreases in time series entropy and significant increases in functional connectivity in the schizophrenia group in comparison to the healthy controls and identified an inverse relationship between these measures across both subjects and sensors that varied over frequency bands and was more pronounced in controls than in patients. The topological organization of connectivity was altered in schizophrenia specifically in high frequency [Formula: see text] and [Formula: see text] band networks as well as in the [Formula: see text]-[Formula: see text] cross-frequency networks. Network topology varied over trials to a greater extent in patients than in controls, suggesting disease-associated alterations in dynamic network properties of brain function. Our results identify signatures of aberrant neurophysiological behavior in schizophrenia across uni-, bi- and multivariate scales and lay the groundwork for further clinical studies that might lead to the discovery of new intermediate phenotypes.

Measuring information-transfer delays.

In complex networks such as gene networks, traffic systems or brain circuits it is important to understand how long it takes for the different parts of the network to effectively influence one another. In the brain, for example, axonal delays between brain areas can amount to several tens of milliseconds, adding an intrinsic component to any timing-based processing of information. Inferring neural interaction delays is thus needed to interpret the information transfer revealed by any analysis of directed interactions across brain structures. However, a robust estimation of interaction delays from neural activity faces several challenges if modeling assumptions on interaction mechanisms are wrong or cannot be made. Here, we propose a robust estimator for neuronal interaction delays rooted in an information-theoretic framework, which allows a model-free exploration of interactions. In particular, we extend transfer entropy to account for delayed source-target interactions, while crucially retaining the conditioning on the embedded target state at the immediately previous time step. We prove that this particular extension is indeed guaranteed to identify interaction delays between two coupled systems and is the only relevant option in keeping with Wiener's principle of causality. We demonstrate the performance of our approach in detecting interaction delays on finite data by numerical simulations of stochastic and deterministic processes, as well as on local field potential recordings. We also show the ability of the extended transfer entropy to detect the presence of multiple delays, as well as feedback loops. While evaluated on neuroscience data, we expect the estimator to be useful in other fields dealing with network dynamics.