Localizing epileptic seizure onsets with Granger causality

Seizure onset zone (SOZ) identification using effective brain connectivity of epileptogenic networks

Objective. To demonstrate the capability of utilizing graph feature-based supervised machine learning (ML) algorithm on intracranial electroencephalogram recordings for the identification of seizure onset zones (SOZs) in individuals with drug-resistant epilepsy.Approach. Utilizing three model-free measures of effective connectivity (EC)-directed information, mutual information-guided Granger causality index (MI-GCI), and frequency-domain convergent cross-mapping (FD-CCM) - directed graphs are generated. Graph centrality measures at different sparsity are used as the classifier's features.Main results. The centrality features achieve high accuracies exceeding 90% in distinguishing SOZ electrodes from non-SOZ electrodes. Notably, a sparse graph representation with just ten features and simple ML models effectively achieves such performance. The study identifies FD-CCM centrality measures as particularly significant, with a mean AUC of 0.93, outperforming prior literature. The FD-CCM-based graph modeling also highlights elevated centrality measures among SOZ electrodes, emphasizing heightened activity relative to non-SOZ electrodes during ictogenesis.Significance. This research not only underscores the efficacy of automated SOZ identification but also illuminates the potential of specific EC measures in enhancing discriminative power within the context of epilepsy research.

Explosive transitions in coupled Lorenz oscillators

We study the transition to synchronization in an ensemble of chaotic oscillators that are interacting on a star network. These oscillators possess an invariant symmetry and we study emergent behavior by introducing the timescale variations in the dynamics of the nodes and the hub. If the coupling preserves the symmetry, the ensemble exhibits consecutive explosive transitions, each one associated with a hysteresis. The first transition is the explosive synchronization from a desynchronized state to a synchronized state which occurs discontinuously with the formation of intermediate clusters. These clusters appear because of the driving-induced multistability and the resulting attractors exhibit intermittent synchrony (antisynchrony). The second transition is the explosive death that occurs as a result of stabilization of the stable fixed points. However, if the symmetry is not preserved, the system again makes a first-order transition from an oscillatory state to death, namely, an explosive death. These transitions are studied with the help of the master stability functions, Lyapunov exponents, and the stability analysis.

A Stable EEG Epilepsy Network Spans From Infraslow to Ripple and From Interictal to Ictus

PURPOSE

To characterize the epilepsy network as reflected in intracranial electroencephalography (iEEG) across the full spectrum of iEEG frequencies and different phases of epilepsy, using a single, conceptually straightforward mathematical measure.

METHODS

The authors applied the spectral Granger causality techniques to intracranial electroencephalography recordings and computed contact-by-contact inward, outward, and total causal flow across frequencies and seizure phases in a selected group of three patients with well-defined, nonlesional seizure foci and prolonged responses to invasive procedures. One seizure and one interictal sample were analyzed per subject.

RESULTS

A prominent intracranial electroencephalography network was identified by Granger causality at both high and low frequencies. This network persists during the preictal and interictal phases of epilepsy and closely matches the visible seizure onset. The causal inflow network corresponded to seizure onset electrode contacts in 8 of 12 conditions, including ripple, infraslow, preictal, and interictal phases of epilepsy. Its most striking feature is the consistent dominance of causal inflow rather than outflow in the vicinity of the seizure onset zone.

CONCLUSIONS

Findings of this study indicate that a stable intracranial electroencephalography epilepsy network persists, and it can be characterized by a single Granger causality measure from infraslow to ripple frequencies and from the interictal to the immediate preictal phases of epilepsy.

Explosive synchronization in a turbulent reactive flow system

The occurrence of abrupt dynamical transitions in the macroscopic state of a system has received growing attention. We present experimental evidence for abrupt transition via explosive synchronization in a real-world complex system, namely, a turbulent reactive flow system. In contrast to the paradigmatic continuous transition to a synchronized state from an initially desynchronized state, the system exhibits a discontinuous synchronization transition with a hysteresis. We consider the fluctuating heat release rate from the turbulent flames at each spatial location as locally coupled oscillators that are coupled to the global acoustic field in the confined system. We analyze the synchronization between these two subsystems during the transition to a state of oscillatory instability and discover that explosive synchronization occurs at the onset of oscillatory instability. Further, we explore the underlying mechanism of interaction between the subsystems and construct a mathematical model of the same.

Tiered synchronization in Kuramoto oscillators with adaptive higher-order interactions

Phase transitions widely occur in natural systems. Incorporation of higher-order interactions in coupled dynamics is known to cause first-order phase transition to synchronization in an otherwise smooth second-order in the presence of only pairwise interactions. Here, we discover that adaptation in higher-order interactions restores the second-order phase transition in the former setup and notably produces additional bifurcation referred as tiered synchronization as a consequence of combination of super-critical pitchfork and two saddle node bifurcations. The Ott-Antonsen manifold underlines the interplay of higher-order interactions and adaptation in instigating tiered synchronization, as well as provides complete description of all (un)stable states. These results would be important in comprehending dynamics of real-world systems with inherent higher-order interactions and adaptation through feedback coupling.

Catalytic feed-forward explosive synchronization in multilayer networks

Inhibitory couplings are crucial for the normal functioning of many real-world complex systems. Inhibition in one layer has been shown to induce explosive synchronization in another excitatory (or positive) layer of duplex networks. By extending this framework to multiplex networks, this article shows that inhibition in a single layer can act as a catalyst, leading to explosive synchronization transitions in the rest of the layers feed-forwarded through intermediate layer(s). Considering a multiplex network of coupled Kuramoto oscillators, we demonstrate that the characteristics of the transition emergent in a layer can be entirely controlled by the intra-layer coupling of other layers and the multiplexing strengths. The results presented here are essential to fathom the synchronization behavior of coupled dynamical units in multi-layer systems possessing inhibitory coupling in one of its layers, representing the importance of multiplexing.

Inhibition-induced explosive synchronization in multiplex networks

To date, explosive synchronization (ES) in a network is shown to be originated from considering either degree-frequency correlation, frequency-coupling strength correlation, inertia, or adaptively controlled phase oscillators. Here we show that ES is a generic phenomenon and can occur in any network by multiplexing it with an appropriate layer without even considering any prerequisite for the emergence of ES. We devise a technique which leads to the occurrence of ES with hysteresis loop in a network upon its multiplexing with a negatively coupled (or inhibitory) layer. The impact of various structural properties of positively coupled (or excitatory) and inhibitory layers along with the strength of multiplexing in gaining control over the induced ES transition is discussed. Analytical prediction for the spread of phase distribution of each layer is provided, which is in good agreement with the numerical assessment. This investigation is a step forward in highlighting the importance of multiplex framework not only in bringing phenomena which are not possible in an isolated network but also in providing more structural control over the induced phenomena.

Synchronization transition in Sakaguchi-Kuramoto model on complex networks with partial degree-frequency correlation

We investigate transition to synchronization in the Sakaguchi-Kuramoto (SK) model on complex networks analytically as well as numerically. Natural frequencies of a percentage (f) of higher degree nodes of the network are assumed to be correlated with their degrees and that of the remaining nodes are drawn from some standard distribution, namely, Lorentz distribution. The effects of variation of f and phase frustration parameter α on transition to synchronization are investigated in detail. Self-consistent equations involving critical coupling strength (λ_c) and group angular velocity (Ω_c) at the onset of synchronization have been derived analytically in the thermodynamic limit. For the detailed investigation, we considered the SK model on scale-free (SF) as well as Erdős-Rényi (ER) networks. Interestingly, explosive synchronization (ES) has been observed in both networks for different ranges of values of α and f. For SF networks, as the value of f is set within 10%≤f≤70%, the range of the values of α for existence of the ES is greatly enhanced compared to the fully degree-frequency correlated case when scaling exponent γ<3. ES is also observed in SF networks with γ>3, which is never observed in fully degree-frequency correlated environment. On the other hand, for random networks, ES observed is in a narrow window of α when the value of f is taken within 30%≤f≤50%. In all the cases, critical coupling strengths for transition to synchronization computed from the analytically derived self-consistent equations show a very good agreement with the numerical results. Finally, we observe ES in the metabolic network of the roundworm Caenorhabditis elegans in partially degree-frequency correlated environment.

Exact explosive synchronization transitions in Kuramoto oscillators with time-delayed coupling

Synchronization commonly occurs in many natural and man-made systems, from neurons in the brain to cardiac cells to power grids to Josephson junction arrays. Transitions to or out of synchrony for coupled oscillators depend on several factors, such as individual frequencies, coupling, interaction time delays and network structure-function relation. Here, using a generalized Kuramoto model of time-delay coupled phase oscillators with frequency-weighted coupling, we study the stability of incoherent and coherent states and the transitions to or out of explosive (abrupt, first-order like) phase synchronization. We analytically derive the exact formulas for the critical coupling strengths at different time delays in both directions of increasing (forward) and decreasing (backward) coupling strengths. We find that time-delay does not affect the transition for the backward direction but can shift the transition for the forward direction of increasing coupling strength. These results provide valuable insights into our understanding of dynamical mechanisms for explosive synchronization in presence of often unavoidable time delays present in many physical and biological systems.

Reliability of EEG Interactions Differs between Measures and Is Specific for Neurological Diseases

Alterations of interaction (connectivity) of the EEG reflect pathological processes in patients with neurologic disorders. Nevertheless, it is questionable whether these patterns are reliable over time in different measures of interaction and whether this reliability of the measures is the same across different patient populations. In order to address this topic we examined 22 patients with mild cognitive impairment, five patients with subjective cognitive complaints, six patients with right-lateralized temporal lobe epilepsy, seven patients with left lateralized temporal lobe epilepsy, and 20 healthy controls. We calculated 14 measures of interaction from two EEG-recordings separated by 2 weeks. In order to characterize test-retest reliability, we correlated these measures for each group and compared the correlations between measures and between groups. We found that both measures of interaction as well as groups differed from each other in terms of reliability. The strongest correlation coefficients were found for spectrum, coherence, and full frequency directed transfer function (average rho > 0.9). In the delta (2–4 Hz) range, reliability was lower for mild cognitive impairment compared to healthy controls and left lateralized temporal lobe epilepsy. In the beta (13–30 Hz), gamma (31–80 Hz), and high gamma (81–125 Hz) frequency ranges we found decreased reliability in subjective cognitive complaints compared to mild cognitive impairment. In the gamma and high gamma range we found increased reliability in left lateralized temporal lobe epilepsy patients compared to healthy controls. Our results emphasize the importance of documenting reliability of measures of interaction, which may vary considerably between measures, but also between patient populations. We suggest that studies claiming clinical usefulness of measures of interaction should provide information on the reliability of the results. In addition, differences between patient groups in reliability of interactions in the EEG indicate the potential of reliability to serve as a new biomarker for pathological memory decline as well as for epilepsy. While the brain concert of information flow is generally variable, high reliability, and thus, low variability may reflect abnormal firing patterns.

When two wrongs make a right: synchronized neuronal bursting from combined electrical and inhibitory coupling

Synchronized cortical activities in the central nervous systems of mammals are crucial for sensory perception, coordination and locomotory function. The neuronal mechanisms that generate synchronous synaptic inputs in the neocortex are far from being fully understood. In this paper, we study the emergence of synchronization in networks of bursting neurons as a highly non-trivial, combined effect of electrical and inhibitory connections. We report a counterintuitive find that combined electrical and inhibitory coupling can synergistically induce robust synchronization in a range of parameters where electrical coupling alone promotes anti-phase spiking and inhibition induces anti-phase bursting. We reveal the underlying mechanism, which uses a balance between hidden properties of electrical and inhibitory coupling to act together to synchronize neuronal bursting. We show that this balance is controlled by the duty cycle of the self-coupled system which governs the synchronized bursting rhythm.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'.

A small change in neuronal network topology can induce explosive synchronization transition and activity propagation in the entire network

We here study explosive synchronization transitions and network activity propagation in networks of coupled neurons to provide a new understanding of the relationship between network topology and explosive dynamical transitions as in epileptic seizures and their propagations in the brain. We model local network motifs and configurations of coupled neurons and analyze the activity propagations between a group of active neurons to their inactive neuron neighbors in a variety of network configurations. We find that neuronal activity propagation is limited to local regions when network is highly clustered with modular structures as in the normal brain networks. When the network cluster structure is slightly changed, the activity propagates to the entire network, which is reminiscent of epileptic seizure propagation in the brain. Finally, we analyze intracranial electroencephalography (IEEG) recordings of a seizure episode from a epilepsy patient and uncover that explosive synchronization-like transition occurs around the clinically defined onset of seizure. These findings may provide a possible mechanism for the recurrence of epileptic seizures, which are known to be the results of aberrant neuronal network structure and/or function in the brain.

Noninvasive Electromagnetic Source Imaging and Granger Causality Analysis: An Electrophysiological Connectome (eConnectome) Approach

OBJECTIVE

Combined source-imaging techniques and directional connectivity analysis can provide useful information about the underlying brain networks in a noninvasive fashion. Source-imaging techniques have been used successfully to either determine the source of activity or to extract source time-courses for Granger causality analysis, previously. In this work, we utilize source-imaging algorithms to both find the network nodes [regions of interest (ROI)] and then extract the activation time series for further Granger causality analysis. The aim of this work is to find network nodes objectively from noninvasive electromagnetic signals, extract activation time-courses, and apply Granger analysis on the extracted series to study brain networks under realistic conditions.

METHODS

Source-imaging methods are used to identify network nodes and extract time-courses and then Granger causality analysis is applied to delineate the directional functional connectivity of underlying brain networks. Computer simulations studies where the underlying network (nodes and connectivity pattern) is known were performed; additionally, this approach has been evaluated in partial epilepsy patients to study epilepsy networks from interictal and ictal signals recorded by EEG and/or Magnetoencephalography (MEG).

RESULTS

Localization errors of network nodes are less than 5 mm and normalized connectivity errors of ∼20% in estimating underlying brain networks in simulation studies. Additionally, two focal epilepsy patients were studied and the identified nodes driving the epileptic network were concordant with clinical findings from intracranial recordings or surgical resection.

CONCLUSION

Our study indicates that combined source-imaging algorithms with Granger causality analysis can identify underlying networks precisely (both in terms of network nodes location and internodal connectivity).

SIGNIFICANCE

The combined source imaging and Granger analysis technique is an effective tool for studying normal or pathological brain conditions.

The salience network dynamics in perceptual decision-making

Recent neuroimaging studies have demonstrated that the network consisting of the right anterior insula (rAI), left anterior insula (lAI) and dorsal anterior cingulate cortex (dACC) is activated in sensory stimulus-guided goal-directed behaviors. This network is often known as the salience network (SN). When and how a sensory signal enters and organizes within SN before reaching the central executive network including the prefrontal cortices is still a mystery. Previous electrophysiological studies focused on individual nodes of SN, either on dACC or rAI, have reports of conflicting findings of the earliest cortical activity within the network. Functional magnetic resonance imaging (fMRI) studies are not able to answer these questions in the time-scales of human sensory perception and decision-making. Here, using clear and noisy face-house image categorization tasks and human scalp electroencephalography (EEG) recordings combined with source reconstruction techniques, we study when and how oscillatory activity organizes SN during a perceptual decision. We uncovered that the beta-band (13-30Hz) oscillations bound SN, became most active around 100ms after the stimulus onset and the rAI acted as a main outflow hub within SN for easier decision making task. The SN activities (Granger causality measures) were negatively correlated with the decision response time (decision difficulty). These findings suggest that the SN activity precedes the executive control in mediating sensory and cognitive processing to arrive at visual perceptual decisions.

Self-organized correlations lead to explosive synchronization

Very recently, a first-order phase transition, named explosive synchronization (ES), has attracted great attention due to its remarkable novelty in theory and significant impact in applications. However, so far, all observations of ES have been associated with various correlation constraints on system parameters, which restrict its generality and applications. Here we consider heterogeneous networks around Hopf bifurcation point described by chemical reaction-diffusion systems and also by their reduced order parameter versions, the complex Ginzburg-Landau equations, and demonstrate that explosive synchronization can appear as an emergent feature of oscillatory networks, and the restrictions on specific parameter correlations used so far for ES can be lifted entirely. Theoretical analyses and numerical simulations show with a perfect agreement that explosive synchronization can appear in networks with nodes having identical natural frequencies, and necessary correlation conditions for ES can be realized in a self-organized manner by network evolution.

Explosive synchronization in adaptive and multilayer networks

At this time, explosive synchronization (ES) of networked oscillators is thought of as being rooted in the setting of specific microscopic correlation features between the natural frequencies of the oscillators and their effective coupling strengths. We show that ES is, in fact, far more general and can occur in adaptive and multilayer networks in the absence of such correlation properties. We first report evidence of ES for single-layer networks where a fraction f of the nodes have links adaptively controlled by a local order parameter, and we then extend the study to a variety of two-layer networks with a fraction f of their nodes coupled with each other by means of dependency links. In the latter case, we give evidence of ES regardless of the differences in the frequency distribution, in the topology of connections between the layers, or both. Finally, we provide a rigorous, analytical treatment to properly ground all of the observed scenarios and to advance the understanding of the actual mechanisms at the basis of ES in real-world systems.

Dynamic directed interictal connectivity in left and right temporal lobe epilepsy

OBJECTIVE

There is increasing evidence that epileptic activity involves widespread brain networks rather than single sources and that these networks contribute to interictal brain dysfunction. We investigated the fast-varying behavior of epileptic networks during interictal spikes in right and left temporal lobe epilepsy (RTLE and LTLE) at a whole-brain scale using directed connectivity.

METHODS

In 16 patients, 8 with LTLE and 8 with RTLE, we estimated the electrical source activity in 82 cortical regions of interest (ROIs) using high-density electroencephalography (EEG), individual head models, and a distributed linear inverse solution. A multivariate, time-varying, and frequency-resolved Granger-causal modeling (weighted Partial Directed Coherence) was applied to the source signal of all ROIs. A nonparametric statistical test assessed differences between spike and baseline epochs. Connectivity results between RTLE and LTLE were compared between RTLE and LTLE and with neuropsychological impairments.

RESULTS

Ipsilateral anterior temporal structures were identified as key drivers for both groups, concordant with the epileptogenic zone estimated invasively. We observed an increase in outflow from the key driver already before the spike. There were also important temporal and extratemporal ipsilateral drivers in both conditions, and contralateral only in RTLE. A different network pattern between LTLE and RTLE was found: in RTLE there was a much more prominent ipsilateral to contralateral pattern than in LTLE. Half of the RTLE patients but none of the LTLE patients had neuropsychological deficits consistent with contralateral temporal lobe dysfunction, suggesting a relationship between connectivity changes and cognitive deficits.

SIGNIFICANCE

The different patterns of time-varying connectivity in LTLE and RTLE suggest that they are not symmetrical entities, in line with our neuropsychological results. The highest outflow region was concordant with invasive validation of the epileptogenic zone. This enhanced characterization of dynamic connectivity patterns could better explain cognitive deficits and help the management of epilepsy surgery candidates.

Application of high-frequency Granger causality to analysis of epileptic seizures and surgical decision making

OBJECTIVE

In recent decades intracranial EEG (iEEG) recordings using increasing numbers of electrodes, higher sampling rates, and a variety of visual and quantitative analyses have indicated the presence of widespread, high frequency ictal and preictal oscillations (HFOs) associated with regions of seizure onset. Seizure freedom has been correlated with removal of brain regions generating pathologic HFOs. However, quantitative analysis of preictal HFOs has seldom been applied to the clinical problem of planning the surgical resection. We performed Granger causality (GC) analysis of iEEG recordings to analyze features of preictal seizure networks and to aid in surgical decision making.

METHODS

Ten retrospective and two prospective patients were chosen on the basis of individually stereotyped seizure patterns by visual criteria. Prospective patients were selected, additionally, for failure of those criteria to resolve apparent multilobar ictal onsets. iEEG was recorded at 500 or 1,000 Hz, using up to 128 surface and depth electrodes. Preictal and early ictal GC from individual electrodes was characterized by the strength of causal outflow, spatial distribution, and hierarchical causal relationships.

RESULTS

In all patients we found significant, widespread preictal GC network activity at peak frequencies from 80 to 250 Hz, beginning 2-42 s before visible electrographic onset. In the two prospective patients, GC source/sink comparisons supported the exclusion of early ictal regions that were not the dominant causal sources, and contributed to planning of more limited surgical resections. Both patients have a class 1 outcome at 1 year.

SIGNIFICANCE

GC analysis of iEEG has the potential to increase understanding of preictal network activity, and to help improve surgical outcomes in cases of otherwise ambiguous iEEG onset.

Functional brain connectivity from EEG in epilepsy: seizure prediction and epileptogenic focus localization

Today, neuroimaging techniques are frequently used to investigate the integration of functionally specialized brain regions in a network. Functional connectivity, which quantifies the statistical dependencies among the dynamics of simultaneously recorded signals, allows to infer the dynamical interactions of segregated brain regions. In this review we discuss how the functional connectivity patterns obtained from intracranial and scalp electroencephalographic (EEG) recordings reveal information about the dynamics of the epileptic brain and can be used to predict upcoming seizures and to localize the seizure onset zone. The added value of extracting information that is not visibly identifiable in the EEG data using functional connectivity analysis is stressed. Despite the fact that many studies have showed promising results, we must conclude that functional connectivity analysis has not made its way into clinical practice yet.

Ictal propagation of high frequency activity is recapitulated in interictal recordings: effective connectivity of epileptogenic networks recorded with intracranial EEG

Seizures are increasingly understood to arise from epileptogenic networks across which ictal activity is propagated and sustained. In patients undergoing invasive monitoring for epilepsy surgery, high frequency oscillations have been observed within the seizure onset zone during both ictal and interictal intervals. We hypothesized that the patterns by which high frequency activity is propagated would help elucidate epileptogenic networks and thereby identify network nodes relevant for surgical planning. Intracranial EEG recordings were analyzed with a multivariate autoregressive modeling technique (short-time direct directed transfer function--SdDTF), based on the concept of Granger causality, to estimate the directionality and intensity of propagation of high frequency activity (70-175 Hz) during ictal and interictal recordings. These analyses revealed prominent divergence and convergence of high frequency activity propagation at sites identified by epileptologists as part of the ictal onset zone. In contrast, relatively little propagation of this activity was observed among the other analyzed sites. This pattern was observed in both subdural and depth electrode recordings of patients with focal ictal onset, but not in patients with a widely distributed ictal onset. In patients with focal ictal onsets, the patterns of propagation recorded during pre-ictal (up to 5 min immediately preceding ictal onset) and interictal (more than 24h before and after seizures) intervals were very similar to those recorded during seizures. The ability to characterize epileptogenic networks from interictal recordings could have important clinical implications for epilepsy surgery planning by reducing the need for prolonged invasive monitoring to record spontaneous seizures.

Explosive synchronization as a process of explosive percolation in dynamical phase space

Explosive synchronization and explosive percolation are currently two independent phenomena occurring in complex networks, where the former takes place in dynamical phase space while the latter in configuration space. It has been revealed that the mechanism of EP can be explained by the Achlioptas process, where the formation of a giant component is controlled by a suppressive rule. We here introduce an equivalent suppressive rule for ES. Before the critical point of ES, the suppressive rule induces the presence of multiple, small sized, synchronized clusters, while inducing the abrupt formation of a giant cluster of synchronized oscillators at the critical coupling strength. We also show how the explosive character of ES degrades into a second-order phase transition when the suppressive rule is broken. These results suggest that our suppressive rule can be considered as a dynamical counterpart of the Achlioptas process, indicating that ES and EP can be unified into a same framework.