Precursors of seizures due to specific spatial-temporal modifications of evolving large-scale epileptic brain networks

Time-series-analysis-based detection of critical transitions in real-world non-autonomous systems

Real-world non-autonomous systems are open, out-of-equilibrium systems that evolve in and are driven by temporally varying environments. Such systems can show multiple timescale and transient dynamics together with transitions to very different and, at times, even disastrous dynamical regimes. Since such critical transitions disrupt the systems' intended or desired functionality, it is crucial to understand the underlying mechanisms, to identify precursors of such transitions, and to reliably detect them in time series of suitable system observables to enable forecasts. This review critically assesses the various steps of investigation involved in time-series-analysis-based detection of critical transitions in real-world non-autonomous systems: from the data recording to evaluating the reliability of offline and online detections. It will highlight pros and cons to stimulate further developments, which would be necessary to advance understanding and forecasting nonlinear behavior such as critical transitions in complex systems.

The time-evolving epileptic brain network: concepts, definitions, accomplishments, perspectives

Epilepsy is now considered a network disease that affects the brain across multiple levels of spatial and temporal scales. The paradigm shift from an epileptic focus-a discrete cortical area from which seizures originate-to a widespread epileptic network-spanning lobes and hemispheres-considerably advanced our understanding of epilepsy and continues to influence both research and clinical treatment of this multi-faceted high-impact neurological disorder. The epileptic network, however, is not static but evolves in time which requires novel approaches for an in-depth characterization. In this review, we discuss conceptual basics of network theory and critically examine state-of-the-art recording techniques and analysis tools used to assess and characterize a time-evolving human epileptic brain network. We give an account on current shortcomings and highlight potential developments towards an improved clinical management of epilepsy.

EEG epilepsy seizure prediction: the post-processing stage as a chronology

Almost one-third of epileptic patients fail to achieve seizure control through anti-epileptic drug administration. In the scarcity of completely controlling a patient's epilepsy, seizure prediction plays a significant role in clinical management and providing new therapeutic options such as warning or intervention devices. Seizure prediction algorithms aim to identify the preictal period that Electroencephalogram (EEG) signals can capture. However, this period is associated with substantial heterogeneity, varying among patients or even between seizures from the same patient. The present work proposes a patient-specific seizure prediction algorithm using post-processing techniques to explore the existence of a set of chronological events of brain activity that precedes epileptic seizures. The study was conducted with 37 patients with Temporal Lobe Epilepsy (TLE) from the EPILEPSIAE database. The designed methodology combines univariate linear features with a classifier based on Support Vector Machines (SVM) and two post-processing techniques to handle pre-seizure temporality in an easily explainable way, employing knowledge from network theory. In the Chronological Firing Power approach, we considered the preictal as a sequence of three brain activity events separated in time. In the Cumulative Firing Power approach, we assumed the preictal period as a sequence of three overlapping events. These methodologies were compared with a control approach based on the typical machine learning pipeline. We considered a Seizure Prediction horizon (SPH) of 5 mins and analyzed several values for the Seizure Occurrence Period (SOP) duration, between 10 and 55 mins. Our results showed that the Cumulative Firing Power approach may improve the seizure prediction performance. This new strategy performed above chance for 62% of patients, whereas the control approach only validated 49% of its models.

Seizure forecasting: Where do we stand?

A lot of mileage has been made recently on the long and winding road toward seizure forecasting. Here we briefly review some selected milestones passed along the way, which were discussed at the International Conference for Technology and Analysis of Seizures-ICTALS 2022-convened at the University of Bern, Switzerland. Major impetus was gained recently from wearable and implantable devices that record not only electroencephalography, but also data on motor behavior, acoustic signals, and various signals of the autonomic nervous system. This multimodal monitoring can be performed for ultralong timescales covering months or years. Accordingly, features and metrics extracted from these data now assess seizure dynamics with a greater degree of completeness. Most prominently, this has allowed the confirmation of the long-suspected cyclical nature of interictal epileptiform activity, seizure risk, and seizures. The timescales cover daily, multi-day, and yearly cycles. Progress has also been fueled by approaches originating from the interdisciplinary field of network science. Considering epilepsy as a large-scale network disorder yielded novel perspectives on the pre-ictal dynamics of the evolving epileptic brain. In addition to discrete predictions that a seizure will take place in a specified prediction horizon, the community broadened the scope to probabilistic forecasts of a seizure risk evolving continuously in time. This shift of gears triggered the incorporation of additional metrics to quantify the performance of forecasting algorithms, which should be compared to the chance performance of constrained stochastic null models. An imminent task of utmost importance is to find optimal ways to communicate the output of seizure-forecasting algorithms to patients, caretakers, and clinicians, so that they can have socioeconomic impact and improve patients' well-being.

Impact of biological rhythms on the importance hierarchy of constituents in time-dependent functional brain networks

Biological rhythms are natural, endogenous cycles with period lengths ranging from less than 24 h (ultradian rhythms) to more than 24 h (infradian rhythms). The impact of the circadian rhythm (approximately 24 h) and ultradian rhythms on spectral characteristics of electroencephalographic (EEG) signals has been investigated for more than half a century. Yet, only little is known on how biological rhythms influence the properties of EEG-derived evolving functional brain networks. Here, we derive such networks from multiday, multichannel EEG recordings and use different centrality concepts to assess the time-varying importance hierarchy of the networks' vertices and edges as well as the various aspects of their structural integration in the network. We observe strong circadian and ultradian influences that highlight distinct subnetworks in the evolving functional brain networks. Our findings indicate the existence of a vital and fundamental subnetwork that is rather generally involved in ongoing brain activities during wakefulness and sleep.

Epileptic-network-based prediction and control of seizures in humans

Epilepsy is now conceptualized as a network disease. The epileptic brain network comprises structurally and functionally connected cortical and subcortical brain regions - spanning lobes and hemispheres -, whose connections and dynamics evolve in time. With this concept, focal and generalized seizures as well as other related pathophysiological phenomena are thought to emerge from, spread via, and be terminated by network vertices and edges that also generate and sustain normal, physiological brain dynamics. Research over the last years has advanced concepts and techniques to identify and characterize the evolving epileptic brain network and its constituents on various spatial and temporal scales. Network-based approaches further our understanding of how seizures emerge from the evolving epileptic brain network, and they provide both novel insights into pre-seizure dynamics and important clues for success or failure of measures for network-based seizure control and prevention. In this review, we summarize the current state of knowledge and address several important challenges that would need to be addressed to move network-based prediction and control of seizures closer to clinical translation.

Ordinal methods for a characterization of evolving functional brain networks

Ordinal time series analysis is based on the idea to map time series to ordinal patterns, i.e., order relations between the values of a time series and not the values themselves, as introduced in 2002 by C. Bandt and B. Pompe. Despite a resulting loss of information, this approach captures meaningful information about the temporal structure of the underlying system dynamics as well as about properties of interactions between coupled systems. This-together with its conceptual simplicity and robustness against measurement noise-makes ordinal time series analysis well suited to improve characterization of the still poorly understood spatiotemporal dynamics of the human brain. This minireview briefly summarizes the state-of-the-art of uni- and bivariate ordinal time-series-analysis techniques together with applications in the neurosciences. It will highlight current limitations to stimulate further developments, which would be necessary to advance characterization of evolving functional brain networks.

Stimulation-related modifications of evolving functional brain networks in unresponsive wakefulness

Recent advances in neurophysiological brain network analysis have demonstrated novel potential for diagnosis and prognosis of disorders of consciousness. While most progress has been achieved on the population-sample level, time-economic and easy-to-apply personalized solutions are missing. This prospective controlled study combined EEG recordings, basal stimulation, and daily behavioral assessment as applied routinely during complex early rehabilitation treatment. We investigated global characteristics of EEG-derived evolving functional brain networks during the repeated (3–6 weeks apart) evaluation of brain dynamics at rest as well as during and after multisensory stimulation in ten patients who were diagnosed with an unresponsive wakefulness syndrome (UWS). The age-corrected average clustering coefficient C* allowed to discriminate between individual patients at first (three patients) and second assessment (all patients). Clinically, only two patients changed from UWS to minimally conscious state. Of note, most patients presented with significant changes of C* due to stimulations, along with treatment, and with an increasing temporal distance to injury. These changes tended towards the levels of nine healthy controls. Our approach allowed to monitor both, short-term effects of individual therapy sessions and possibly long-term recovery. Future studies will need to assess its full potential for disease monitoring and control of individualized treatment decisions.

Sequential Semiology of Seizures and Brain Perfusion Patterns in Patients with Drug-Resistant Focal Epilepsies: A Perspective from Neural Networks

Ictal semiology and brain single-photon emission computed tomography have been performed in approaching the epileptogenic zone in drug-resistant focal epilepsies. The authors aim to describe the brain structures involved in the ictal and interictal epileptogenic network from sequential semiology and brain perfusion quantitative patterns analysis. A sequential representation of seizures was performed (n = 15). A two-level analysis (individual and global) was carried out for the analysis of brain perfusion quantification and estimating network structures from the perfusion indexes. Most of the subjects started with focal seizures without impaired consciousness, followed by staring, automatisms, language impairments and evolution to a bilateral tonic-clonic seizure (temporal lobe and posterior quadrant epilepsy). Frontal lobe epilepsy seizures continued with upper limb clonus and evolution to bilateral tonic-clonic. The perfusion index of the epileptogenic zone ranged between 0.439-1.362 (mesial and lateral structures), 0.826-1.266 in dorsolateral frontal structures and 0.678-1.507 in the occipital gyrus. The interictal epileptogenic network proposed involved the brainstem and other subcortical structures. For the ictal state, it included the rectus gyrus, putamen and cuneus. The proposed methodology provides information about the brain structures in the neural networks in patients with drug-resistant focal epilepsies.

Perspectives on Understanding Aberrant Brain Networks in Epilepsy

Epilepsy is a neurological disorder affecting approximately 70 million people worldwide. It is characterized by seizures that are complex aberrant dynamical events typically treated with drugs and surgery. Unfortunately, not all patients become seizure-free, and there is an opportunity for novel approaches to treat epilepsy using a network view of the brain. The traditional seizure focus theory presumed that seizures originated within a discrete cortical area with subsequent recruitment of adjacent cortices with seizure progression. However, a more recent view challenges this concept, suggesting that epilepsy is a network disease, and both focal and generalized seizures arise from aberrant activity in a distributed network. Changes in the anatomical configuration or widespread neural activities spanning lobes and hemispheres could make the brain more susceptible to seizures. In this perspective paper, we summarize the current state of knowledge, address several important challenges that could further improve our understanding of the human brain in epilepsy, and invite novel studies addressing these challenges.

A straightforward edge centrality concept derived from generalizing degree and strength

Vertex degree—the number of edges that are incident to a vertex—is a fundamental concept in network theory. It is the historically first and conceptually simplest centrality concept to rate the importance of a vertex for a network’s structure and dynamics. Unlike many other centrality concepts, for which joint metrics have been proposed for both vertices and edges, by now there is no concept for an edge centrality analogous to vertex degree. Here, we propose such a concept—termed nearest-neighbor edge centrality—and demonstrate its suitability for a non-redundant identification of central edges in paradigmatic network models as well as in real-world networks from various scientific domains.

Electrodermal Activity Biofeedback Alters Evolving Functional Brain Networks in People With Epilepsy, but in a Non-specific Manner

There is evidence that biofeedback of electrodermal activity (EDA) can reduce seizure frequency in people with epilepsy. Prior studies have linked EDA biofeedback to a diffuse brain activation as a potential functional mechanism. Here, we investigated whether short-term EDA biofeedback alters EEG-derived large-scale functional brain networks in people with epilepsy. In this prospective controlled trial, thirty participants were quasi-randomly assigned to one of three biofeedback conditions (arousal, sham, or relaxation) and performed a single, 30-min biofeedback training while undergoing continuous EEG recordings. Based on the EEG, we derived evolving functional brain networks and examined their topological, robustness, and stability properties over time. Potential effects on attentional-executive functions and mood were monitored via a neuropsychological assessment and subjective self-ratings. Participants assigned to the relaxation group seemed to be most successful in meeting the task requirements for this specific control condition (i.e., decreasing EDA). Participants in the sham group were more successful in increasing EDA than participants in the arousal group. However, only the arousal biofeedback training was associated with a prolonged robustness-enhancing effect on networks. Effects on other network properties were mostly unspecific for the different groups. None of the biofeedback conditions affected attentional-executive functions or subjective behavioral measures. Our results suggest that global characteristics of evolving functional brain networks are modified by EDA biofeedback. Some alterations persisted after the single training session; however, the effects were largely unspecific across the different biofeedback protocols. Further research should address changes of local network characteristics and whether multiple training sessions will result in more specific network modifications.

More Than Spikes: On the Added Value of Non-linear Intracranial EEG Analysis for Surgery Planning in Temporal Lobe Epilepsy

Epilepsy surgery can be a very effective therapy in medication refractory patients. During patient evaluation intracranial EEG is analyzed by clinical experts to identify the brain tissue generating epileptiform events. Quantitative EEG analysis increasingly complements this approach in research settings, but not yet in clinical routine. We investigate the correspondence between epileptiform events and a specific quantitative EEG marker. We analyzed 99 preictal epochs of multichannel intracranial EEG of 40 patients with mixed etiologies. Time and channel of occurrence of epileptiform events (spikes, slow waves, sharp waves, fast oscillations) were annotated by a human expert and non-linear excess interrelations were calculated as a quantitative EEG marker. We assessed whether the visually identified preictal events predicted channels that belonged to the seizure onset zone, that were later resected or that showed strong non-linear interrelations. We also investigated whether the seizure onset zone or the resection were predicted by channels with strong non-linear interrelations. In patients with temporal lobe epilepsy (32 of 40), epileptic spikes and the seizure onset zone predicted the resected brain tissue much better in patients with favorable seizure control after surgery than in unfavorable outcomes. Beyond that, our analysis did not reveal any significant associations with epileptiform EEG events. Specifically, none of the epileptiform event types did predict non-linear interrelations. In contrast, channels with strong non-linear excess EEG interrelations predicted the resected channels better in patients with temporal lobe epilepsy and favorable outcome. Also in the small number of patients with seizure onset in the frontal and parietal lobes, no association between epileptiform events and channels with strong non-linear excess EEG interrelations was detectable. In contrast to patients with temporal seizure onset, EEG channels with strong non-linear excess interrelations did neither predict the seizure onset zone nor the resection of these patients or allow separation between patients with favorable and unfavorable seizure control. Our study indicates that non-linear excess EEG interrelations are not strictly associated with epileptiform events, which are one key concept of current clinical EEG assessment. Rather, they may provide information relevant for surgery planning in temporal lobe epilepsy. Our study suggests to incorporate quantitative EEG analysis in the workup of clinical cases. We make the EEG epochs and expert annotations publicly available in anonymized form to foster similar analyses for other quantitative EEG methods.

Network connectivity predicts effectiveness of responsive neurostimulation in focal epilepsy

Responsive neurostimulation is a promising treatment for drug-resistant focal epilepsy; however, clinical outcomes are highly variable across individuals. The therapeutic mechanism of responsive neurostimulation likely involves modulatory effects on brain networks; however, with no known biomarkers that predict clinical response, patient selection remains empiric. This study aimed to determine whether functional brain connectivity measured non-invasively prior to device implantation predicts clinical response to responsive neurostimulation therapy. Resting-state magnetoencephalography was obtained in 31 participants with subsequent responsive neurostimulation device implantation between 15 August 2014 and 1 October 2020. Functional connectivity was computed across multiple spatial scales (global, hemispheric, and lobar) using pre-implantation magnetoencephalography and normalized to maps of healthy controls. Normalized functional connectivity was investigated as a predictor of clinical response, defined as percent change in self-reported seizure frequency in the most recent year of clinic visits relative to pre-responsive neurostimulation baseline. Area under the receiver operating characteristic curve quantified the performance of functional connectivity in predicting responders (≥50% reduction in seizure frequency) and non-responders (<50%). Leave-one-out cross-validation was furthermore performed to characterize model performance. The relationship between seizure frequency reduction and frequency-specific functional connectivity was further assessed as a continuous measure. Across participants, stimulation was enabled for a median duration of 52.2 (interquartile range, 27.0-62.3) months. Demographics, seizure characteristics, and responsive neurostimulation lead configurations were matched across 22 responders and 9 non-responders. Global functional connectivity in the alpha and beta bands were lower in non-responders as compared with responders (alpha, p_fdr < 0.001; beta, p_fdr < 0.001). The classification of responsive neurostimulation outcome was improved by combining feature inputs; the best model incorporated four features (i.e. mean and dispersion of alpha and beta bands) and yielded an area under the receiver operating characteristic curve of 0.970 (0.919-1.00). The leave-one-out cross-validation analysis of this four-feature model yielded a sensitivity of 86.3%, specificity of 77.8%, positive predictive value of 90.5%, and negative predictive value of 70%. Global functional connectivity in alpha band correlated with seizure frequency reduction (alpha, P = 0.010). Global functional connectivity predicted responder status more strongly, as compared with hemispheric predictors. Lobar functional connectivity was not a predictor. These findings suggest that non-invasive functional connectivity may be a candidate personalized biomarker that has the potential to predict responsive neurostimulation effectiveness and to identify patients most likely to benefit from responsive neurostimulation therapy. Follow-up large-cohort, prospective studies are required to validate this biomarker. These findings furthermore support an emerging view that the therapeutic mechanism of responsive neurostimulation involves network-level effects in the brain.

Impact of Transcutaneous Auricular Vagus Nerve Stimulation on Large-Scale Functional Brain Networks: From Local to Global

Transcutaneous auricular vagus nerve stimulation (taVNS) is a novel non-invasive brain stimulation technique considered as a potential supplementary treatment option for a wide range of diseases. Although first promising findings were obtained so far, the exact mode of action of taVNS is not fully understood yet. We recently developed an examination schedule to probe for immediate taVNS-induced modifications of large-scale epileptic brain networks. With this schedule, we observed short-term taVNS to have a topology-modifying, robustness- and stability-enhancing immediate effect on large-scale functional brain networks from subjects with focal epilepsies. We here expand on this study and investigate the impact of short-term taVNS on various local and global characteristics of large-scale evolving functional brain networks from a group of 30 subjects with and without central nervous system diseases. Our findings point to differential, at first glance counterintuitive, taVNS-mediated alterations of local and global topological network characteristics that result in a reconfiguration of networks and a modification of their stability and robustness properties. We propose a model of a stimulation-related stretching and compression of evolving functional brain networks that may help to better understand the mode of action of taVNS.

Transcutaneous auricular vagus nerve stimulation induces stabilizing modifications in large-scale functional brain networks: towards understanding the effects of taVNS in subjects with epilepsy

Transcutaneous auricular vagus nerve stimulation (taVNS) is a novel non-invasive brain stimulation technique considered as a potential supplementary treatment option for subjects with refractory epilepsy. Its exact mechanism of action is not yet fully understood. We developed an examination schedule to probe for immediate taVNS-induced modifications of large-scale epileptic brain networks and accompanying changes of cognition and behaviour. In this prospective trial, we applied short-term (1 h) taVNS to 14 subjects with epilepsy during a continuous 3-h EEG recording which was embedded in two standardized neuropsychological assessments. From these EEG, we derived evolving epileptic brain networks and tracked important topological, robustness, and stability properties of networks over time. In the majority of investigated subjects, taVNS induced measurable and persisting modifications in network properties that point to a more resilient epileptic brain network without negatively impacting cognition, behaviour, or mood. The stimulation was well tolerated and the usability of the device was rated good. Short-term taVNS has a topology-modifying, robustness- and stability-enhancing immediate effect on large-scale epileptic brain networks. It has no detrimental effects on cognition and behaviour. Translation into clinical practice requires further studies to detail knowledge about the exact mechanisms by which taVNS prevents or inhibits seizures.

Criticality, Connectivity, and Neural Disorder: A Multifaceted Approach to Neural Computation

It has been hypothesized that the brain optimizes its capacity for computation by self-organizing to a critical point. The dynamical state of criticality is achieved by striking a balance such that activity can effectively spread through the network without overwhelming it and is commonly identified in neuronal networks by observing the behavior of cascades of network activity termed "neuronal avalanches." The dynamic activity that occurs in neuronal networks is closely intertwined with how the elements of the network are connected and how they influence each other's functional activity. In this review, we highlight how studying criticality with a broad perspective that integrates concepts from physics, experimental and theoretical neuroscience, and computer science can provide a greater understanding of the mechanisms that drive networks to criticality and how their disruption may manifest in different disorders. First, integrating graph theory into experimental studies on criticality, as is becoming more common in theoretical and modeling studies, would provide insight into the kinds of network structures that support criticality in networks of biological neurons. Furthermore, plasticity mechanisms play a crucial role in shaping these neural structures, both in terms of homeostatic maintenance and learning. Both network structures and plasticity have been studied fairly extensively in theoretical models, but much work remains to bridge the gap between theoretical and experimental findings. Finally, information theoretical approaches can tie in more concrete evidence of a network's computational capabilities. Approaching neural dynamics with all these facets in mind has the potential to provide a greater understanding of what goes wrong in neural disorders. Criticality analysis therefore holds potential to identify disruptions to healthy dynamics, granted that robust methods and approaches are considered.

Chance and risk in epilepsy

PURPOSE OF REVIEW

Epilepsy is a dynamical disorder of the brain characterized by sudden, seemingly unpredictable transitions to the ictal state. When and how these transitions occur remain unresolved questions in neurology.

RECENT FINDINGS

Modelling work based on dynamical systems theory proposed that a slow control parameter is necessary to explain the transition between interictal and ictal states. Recently, converging evidence from chronic EEG datasets unravelled the existence of cycles of epileptic brain activity at multiple timescales - circadian, multidien (over multiple days) and circannual - which could reflect cyclical changes in a slow control parameter. This temporal structure of epilepsy has theoretical implications and argues against the conception of seizures as completely random events. The practical significance of cycles in epilepsy is highlighted by their predictive value in computational models for seizure forecasting.

SUMMARY

The canonical randomness of seizures is being reconsidered in light of cycles of brain activity discovered through chronic EEG. This paradigm shift motivates development of next-generation devices to track more closely fluctuations in epileptic brain activity that determine time-varying seizure risk.

Reconfiguration of human evolving large-scale epileptic brain networks prior to seizures: an evaluation with node centralities

Previous research has indicated that temporal changes of centrality of specific nodes in human evolving large-scale epileptic brain networks carry information predictive of impending seizures. Centrality is a fundamental network-theoretical concept that allows one to assess the role a node plays in a network. This concept allows for various interpretations, which is reflected in a number of centrality indices. Here we aim to achieve a more general understanding of local and global network reconfigurations during the pre-seizure period as indicated by changes of different node centrality indices. To this end, we investigate—in a time-resolved manner—evolving large-scale epileptic brain networks that we derived from multi-day, multi-electrode intracranial electroencephalograpic recordings from a large but inhomogeneous group of subjects with pharmacoresistant epilepsies with different anatomical origins. We estimate multiple centrality indices to assess the various roles the nodes play while the networks transit from the seizure-free to the pre-seizure period. Our findings allow us to formulate several major scenarios for the reconfiguration of an evolving epileptic brain network prior to seizures, which indicate that there is likely not a single network mechanism underlying seizure generation. Rather, local and global aspects of the pre-seizure network reconfiguration affect virtually all network constituents, from the various brain regions to the functional connections between them.

Von Interaktionen zu Interaktionsnetzwerken: Zeitabhängige funktionelle Netzwerke am Beispiel der Epilepsie

Das menschliche Gehirn ist ein komplexes Netzwerk aus interagierenden nichtstationären Subsystemen (Netzwerk von Netzwerken), deren komplizierte räumlich-zeitliche Dynamiken bis heute nur unzureichend verstanden sind. Dabei versprechen aktuelle Entwicklungen im Bereich der Zeitreihenanalyse sowie der Theorie komplexer Netzwerke neue und verbesserte Einblicke in die Dynamiken von Hirnnetzwerken auf verschiedenen räumlich-zeitlichen Skalen. Wir geben einen Überblick über diese Entwicklungen und besprechen am Beispiel zeitabhängiger epileptischer Hirnnetzwerke Fortschritte im Verständnis von Hirndynamiken, die über multiple Skalen hinweg variieren.

Identifying edges that facilitate the generation of extreme events in networked dynamical systems

The collective dynamics of complex networks of FitzHugh-Nagumo units exhibits rare and recurrent events of high amplitude (extreme events) that are preceded by so-called proto-events during which a certain fraction of the units become excited. Although it is well known that a sufficiently large fraction of excited units is required to turn a proto-event into an extreme event, it is not yet clear how the other units are being recruited into the final generation of an extreme event. Addressing this question and mimicking typical experimental situations, we investigate the centrality of edges in time-dependent interaction networks. We derived these networks from time series of the units' dynamics employing a widely used bivariate analysis technique. Using our recently proposed edge-centrality concepts together with an edge-based network decomposition technique, we observe that the recruitment is primarily facilitated by sets of certain edges that have no equivalent in the underlying topology. Our finding might aid to improve the understanding of generation of extreme events in natural networked dynamical systems.

Controversies on the network theory of epilepsy: Debates held during the ICTALS 2019 conference

Debates on six controversial topics on the network theory of epilepsy were held during two debate sessions, as part of the International Conference for Technology and Analysis of Seizures, 2019 (ICTALS 2019) convened at the University of Exeter, UK, September 2-5 2019. The debate topics were (1) From pathologic to physiologic: is the epileptic network part of an existing large-scale brain network? (2) Are micro scale recordings pertinent for defining the epileptic network? (3) From seconds to years: do we need all temporal scales to define an epileptic network? (4) Is it necessary to fully define the epileptic network to control it? (5) Is controlling seizures sufficient to control the epileptic network? (6) Does the epileptic network want to be controlled? This article, written by the organizing committee for the debate sessions and the debaters, summarizes the arguments presented during the debates on these six topics.

Linear and nonlinear interrelations show fundamentally distinct network structure in preictal intracranial EEG of epilepsy patients

Resection of the seizure generating tissue can be highly beneficial in patients with drug-resistant epilepsy. However, only about half of all patients undergoing surgery get permanently and completely seizure free. Investigating the dependences between intracranial EEG signals adds a multivariate perspective largely unavailable to visual EEG analysis, which is the current clinical practice. We examined linear and nonlinear interrelations between intracranial EEG signals regarding their spatial distribution and network characteristics. The analyzed signals were recorded immediately before clinical seizure onset in epilepsy patients who received a standardized electrode implantation targeting the mesiotemporal structures. The linear interrelation networks were predominantly locally connected and highly reproducible between patients. In contrast, the nonlinear networks had a clearly centralized structure, which was specific for the individual pathology. The nonlinear interrelations were overrepresented in the focal hemisphere and in patients with no or only rare seizures after surgery specifically in the resected tissue. Connections to the outside were predominantly nonlinear. In all patients without worthwhile improvement after resective treatment, tissue producing strong nonlinear interrelations was left untouched by surgery. Our findings indicate that linear and nonlinear interrelations play fundamentally different roles in preictal intracranial EEG. Moreover, they suggest nonlinear signal interrelations to be a marker of epileptogenic tissue and not a characteristic of the mesiotemporal structures. Our results corroborate the network-based nature of epilepsy and suggest the application of network analysis to support the planning of resective epilepsy surgery.

No evidence for critical slowing down prior to human epileptic seizures

There is an ongoing debate whether generic early warning signals for critical transitions exist that can be applied across diverse systems. The human epileptic brain is often considered as a prototypical system, given the devastating and, at times, even life-threatening nature of the extreme event epileptic seizure. More than three decades of international effort has successfully identified predictors of imminent seizures. However, the suitability of typically applied early warning indicators for critical slowing down, namely, variance and lag-1 autocorrelation, for indexing seizure susceptibility is still controversially discussed. Here, we investigated long-term, multichannel recordings of brain dynamics from 28 subjects with epilepsy. Using a surrogate-based evaluation procedure of sensitivity and specificity of time-resolved estimates of early warning indicators, we found no evidence for critical slowing down prior to 105 epileptic seizures.