Neuronal synchrony and critical bistability: Mechanistic biomarkers for localizing the epileptogenic network.

OBJECTIVE: Postsurgical seizure freedom in drug-resistant epilepsy (DRE) patients varies from 30% to 80%, implying that in many cases the current approaches fail to fully map the epileptogenic zone (EZ). We aimed to advance a novel approach to better characterize epileptogenicity and investigate whether the EZ encompasses a broader epileptogenic network (EpiNet) beyond the seizure zone (SZ) that exhibits seizure activity. METHODS: We first used computational modeling to test putative complex systems-driven and systems neuroscience-driven mechanistic biomarkers for epileptogenicity. We then used these biomarkers to extract features from resting-state stereoelectroencephalograms recorded from DRE patients and trained supervised classifiers to localize the SZ against gold standard clinical localization. To further explore the prevalence of pathological features in an extended brain network outside of the clinically identified SZ, we also used unsupervised classification. RESULTS: Supervised SZ classification trained on individual features achieved accuracies of .6-.7 area under the receiver operating characteristic curve (AUC). Combining all criticality and synchrony features further improved the AUC to .85. Unsupervised classification discovered an EpiNet-like cluster of brain regions, in which 51% of brain regions were outside of the SZ. Brain regions in the EpiNet-like cluster engaged in interareal hypersynchrony and locally exhibited high-amplitude bistability and excessive inhibition, which was strikingly similar to the high seizure risk regime revealed by our computational modeling. SIGNIFICANCE: The finding that combining biomarkers improves SZ localization accuracy indicates that the novel mechanistic biomarkers for epileptogenicity employed here yield synergistic information. On the other hand, the discovery of SZ-like brain dynamics outside of the clinically defined SZ provides empirical evidence of an extended pathophysiological EpiNet.

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.

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.

Comparison of Methods to Identify Modules in Noisy or Incomplete Brain Networks.

Community structure, or "modularity," is a fundamentally important aspect in the organization of structural and functional brain networks, but their identification with community detection methods is confounded by noisy or missing connections. Although several methods have been used to account for missing data, the performance of these methods has not been compared quantitatively so far. In this study, we compared four different approaches to account for missing connections when identifying modules in binary and weighted networks using both Louvain and Infomap community detection algorithms. The four methods are "zeros," "row-column mean," "common neighbors," and "consensus clustering." Using Lancichinetti-Fortunato-Radicchi benchmark-simulated binary and weighted networks, we find that "zeros," "row-column mean," and "common neighbors" approaches perform well with both Louvain and Infomap, whereas "consensus clustering" performs well with Louvain but not Infomap. A similar pattern of results was observed with empirical networks from stereotactical electroencephalography data, except that "consensus clustering" outperforms other approaches on weighted networks with Louvain. Based on these results, we recommend any of the four methods when using Louvain on binary networks, whereas "consensus clustering" is superior with Louvain clustering of weighted networks. When using Infomap, "zeros" or "common neighbors" should be used for both binary and weighted networks. These findings provide a basis to accounting for noisy or missing connections when identifying modules in brain networks.

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.

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.

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.

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.

Gamma Oscillations Underlie the Maintenance of Feature-Specific Information and the Contents of Visual Working Memory.

Visual working memory (VWM) sustains information online as integrated object representations. Neuronal mechanisms supporting the maintenance of feature-specific information have remained unidentified. Synchronized oscillations in the gamma band (30-120 Hz) characterize VWM retention and predict task performance, but whether these oscillations are specific to memorized features and VWM contents or underlie general executive VWM functions is not known. In the present study, we investigated whether gamma oscillations reflect the maintenance of feature-specific information in VWM. Concurrent magneto- and electroencephalography was recorded while subjects memorized different object features or feature conjunctions in identical VWM experiments. Using a data-driven source analysis approach, we show that the strength, load-dependence, and source topographies of gamma oscillations in the visual cortex differentiate these memorized features. Load-dependence of gamma oscillations in feature-specific visual and prefrontal areas also predicts VWM accuracy. Furthermore, corroborating the hypothesis that gamma oscillations support the perceptual binding of feature-specific neuronal assemblies, we also show that VWM for color-location conjunctions is associated with stronger gamma oscillations than that for these features separately. Gamma oscillations hence support the maintenance of feature-specific information and reflect VWM contents. The results also suggest that gamma oscillations contribute to feature binding in the formation of memory representations.