Assortative mixing in functional brain networks during epileptic seizures

Altered White-Matter Functional Network in Children with Idiopathic Generalized Epilepsy

RATIONALE AND OBJECTIVES

The white matter (WM) functional network changes offers insights into the potential pathological mechanisms of certain diseases, the alterations of WM functional network in idiopathic generalized epilepsy (IGE) remain unclear. We aimed to explore the topological characteristics changes of WM functional network in childhood IGE using resting-state functional Magnetic resonance imaging (MRI) and T1-weighted images.

METHODS

A total of 84 children (42 IGE and 42 matched healthy controls) were included in this study. Functional and structural MRI data were acquired to construct a WM functional network. Group differences in the global and regional topological characteristics were assessed by graph theory and the correlations with clinical and neuropsychological scores were analyzed. A support vector machine algorithm model was employed to classify individuals with IGE using WM functional connectivity as features, and the model's accuracy was evaluated using leave-one-out cross-validation.

RESULTS

In IGE group, at the network level, the WM functional network exhibited increased assortativity; at the nodal level, 17 nodes presented nodal disturbances in WM functional network, and nodal disturbances of 11 nodes were correlated with cognitive performance scores, disease duration and age of onset. The classification model achieved the 72.6% accuracy, 0.746 area under the curve, 69.1% sensitivity, 76.2% specificity.

CONCLUSION

Our study demonstrated that the WM functional network topological properties changes in childhood IGE, which were associated with cognitive function, and WM functional network may help clinical classification for childhood IGE. These findings provide novel information for understanding the pathogenesis of IGE and suggest that the WM function network might be qualified as potential biomarkers.

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.

Altered Metabolic Networks in Mesial Temporal Lobe Epilepsy with Focal to Bilateral Seizures

This study was designed to identify whether the metabolic network changes in mesial temporal lobe epilepsy (MTLE) patients with focal to bilateral tonic-clonic seizures (FBTCS) differ from changes in patients without FBTCS. This retrospective analysis enrolled 30 healthy controls and 54 total MTLE patients, of whom 27 had FBTCS. Fluorodeoxyglucose positron emission tomography (FDG-PET) data and graph theoretical analyses were used to examine metabolic connectivity. The differences in metabolic networks between the three groups were compared. Significant changes in both local and global network topology were evident in FBTCS+ patients as compared to healthy controls, with a lower assortative coefficient and altered betweenness centrality in 15 brain regions. While global network measures did not differ significantly when comparing FBTCS- patients to healthy controls, alterations in betweenness centrality were evident in 13 brain regions. Significantly altered betweenness centrality was also observed in four brain regions when comparing patients with and without FBTCS. The study revealed greater metabolic network abnormalities in MTLE patients with FBTCS as compared to FBTCS- patients, indicating the existence of distinct epileptogenic networks. These findings can provide insight into the pathophysiological basis of FBTCS.

Differences in functional network between focal onset nonconvulsive status epilepticus and toxic metabolic encephalopathy: application to machine learning models for differential diagnosis

We aimed to compare network properties between focal-onset nonconvulsive status epilepticus (NCSE) and toxic/metabolic encephalopathy (TME) during periods of periodic discharge using graph theoretical analysis, and to evaluate the applicability of graph measures as markers for the differential diagnosis between focal-onset NCSE and TME, using machine learning algorithms. Electroencephalography (EEG) data from 50 focal-onset NCSE and 44 TMEs were analyzed. Epochs with nonictal periodic discharges were selected, and the coherence in each frequency band was analyzed. Graph theoretical analysis was performed to compare brain network properties between the groups. Eight different traditional machine learning methods were implemented to evaluate the utility of graph theoretical measures as input features to discriminate between the two conditions. The average degree (in delta, alpha, beta, and gamma bands), strength (in delta band), global efficiency (in delta and alpha bands), local efficiency (in delta band), clustering coefficient (in delta band), and transitivity (in delta band) were higher in TME than in NCSE. TME showed lower modularity (in delta band) and assortativity (in alpha, beta, and gamma bands) than NCSE. Machine learning algorithms based on EEG global graph measures classified NCSE and TME with high accuracy, and gradient boosting was the most accurate classification model with an area under the receiver operating characteristics curve of 0.904. Our findings on differences in network properties may provide novel insights that graph measures reflecting the network properties could be quantitative markers for the differential diagnosis between focal-onset NCSE and TME.

Structural brain network analysis in occipital lobe epilepsy

BACKGROUND

This study aimed to analyze the structural brain network in patients with occipital lobe epilepsy (OLE) and investigate the differences in structural brain networks between patients with OLE and healthy controls.

METHODS

Patients with OLE and healthy controls with normal brain MRI findings were enrolled. They underwent diffusion tensor imaging using a 3.0T MRI scanner, and we computed the network measures of global and local structural networks in patients with OLE and healthy controls using the DSI studio program. We compared network measures between the groups.

RESULTS

We enrolled 23 patients with OLE and 42 healthy controls. There were significant differences in the global structural network between patients with OLE and healthy controls. The assortativity coefficient (-0.0864 vs. -0.0814, p = 0.0214), mean clustering coefficient (0.0061 vs. 0.0064, p = 0.0203), global efficiency (0.0315 vs. 0.0353, p = 0.0086), and small-worldness index (0.0001 vs. 0.0001, p = 0.0175) were lower, whereas the characteristic path length (59.2724 vs. 53.4684, p = 0.0120) was higher in patients with OLE than those in the healthy controls. There were several nodes beyond the occipital lobe that showed significant differences in the local structural network between the groups. In addition, the assortativity coefficient was negatively correlated with the duration of epilepsy (r=-0.676, p = 0.001).

A perturbation-based approach to identifying potentially superfluous network constituents

Constructing networks from empirical time-series data is often faced with the as yet unsolved issue of how to avoid potentially superfluous network constituents. Such constituents can result, e.g., from spatial and temporal oversampling of the system's dynamics, and neglecting them can lead to severe misinterpretations of network characteristics ranging from global to local scale. We derive a perturbation-based method to identify potentially superfluous network constituents that makes use of vertex and edge centrality concepts. We investigate the suitability of our approach through analyses of weighted small-world, scale-free, random, and complete networks.

Complex network of eye movements during rapid automatized naming

Introduction

Although the method of visualizing eye-tracking data as a time-series might enhance performance in the understanding of gaze behavior, it has not yet been thoroughly examined in the context of rapid automated naming (RAN).

Methods

This study attempted, for the first time, to measure gaze behavior during RAN from the perspective of network-domain, which constructed a complex network [referred to as gaze-time-series-based complex network (GCN)] from gaze time-series. Hence, without designating regions of interest, the features of gaze behavior during RAN were extracted by computing topological parameters of GCN. A sample of 98 children (52 males, aged 11.50 ± 0.28 years) was studied. Nine topological parameters (i.e., average degree, network diameter, characteristic path length, clustering coefficient, global efficiency, assortativity coefficient, modularity, community number, and small-worldness) were computed.

Results

Findings showed that GCN in each RAN task was assortative and possessed “small-world” and community architecture. Additionally, observations regarding the influence of RAN task types included that: (i) five topological parameters (i.e., average degree, clustering coefficient, assortativity coefficient, modularity, and community number) could reflect the difference between tasks N-num (i.e., naming of numbers) and N-cha (i.e., naming of Chinese characters); (ii) there was only one topological parameter (i.e., network diameter) which could reflect the difference between tasks N-obj (i.e., naming of objects) and N-col (i.e., naming of colors); and (iii) when compared to GCN in alphanumeric RAN, GCN in non-alphanumeric RAN may have higher average degree, global efficiency, and small-worldness, but lower network diameter, characteristic path length, clustering coefficient, and modularity. Findings also illustrated that most of these topological parameters were largely independent of traditional eye-movement metrics.

Discussion

This article revealed the architecture and topological parameters of GCN as well as the influence of task types on them, and thus brought some new insights into the understanding of RAN from the perspective of complex network.

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.

Saccades and presaccadic stimulus repetition alter cortical network topology and dynamics: evidence from EEG and graph theoretical analysis

Parietal and frontal cortex are involved in saccade generation, and their output signals modify visual signals throughout cortex. Local signals associated with these interactions are well described, but their large-scale progression and network dynamics are unknown. Here, we combined source localized electroencephalography (EEG) and graph theory analysis (GTA) to understand how saccades and presaccadic visual stimuli interactively alter cortical network dynamics in humans. Twenty-one participants viewed 1-3 vertical/horizontal grids, followed by grid with the opposite orientation just before a horizontal saccade or continued fixation. EEG signals from the presaccadic interval (or equivalent fixation period) were used for analysis. Source localization-through-time revealed a rapid frontoparietal progression of presaccadic motor signals and stimulus-motor interactions, with additional band-specific modulations in several frontoparietal regions. GTA analysis revealed a saccade-specific functional network with major hubs in inferior parietal cortex (alpha) and the frontal eye fields (beta), and major saccade-repetition interactions in left prefrontal (theta) and supramarginal gyrus (gamma). This network showed enhanced segregation, integration, synchronization, and complexity (compared with fixation), whereas stimulus repetition interactions reduced synchronization and complexity. These cortical results demonstrate a widespread influence of saccades on both regional and network dynamics, likely responsible for both the motor and perceptual aspects of saccades.

Network structure from a characterization of interactions in complex systems

Many natural and man-made complex dynamical systems can be represented by networks with vertices representing system units and edges the coupling between vertices. If edges of such a structural network are inaccessible, a widely used approach is to identify them with interactions between vertices, thereby setting up a functional network. However, it is an unsolved issue if and to what extent important properties of a functional network on the global and the local scale match those of the corresponding structural network. We address this issue by deriving functional networks from characterizing interactions in paradigmatic oscillator networks with widely-used time-series-analysis techniques for various factors that alter the collective network dynamics. Surprisingly, we find that particularly key constituents of functional networks—as identified with betweenness and eigenvector centrality—coincide with ground truth to a high degree, while global topological and spectral properties—clustering coefficient, average shortest path length, assortativity, and synchronizability—clearly deviate. We obtain similar concurrences for an empirical network. Our findings are of relevance for various scientific fields and call for conceptual and methodological refinements to further our understanding of the relationship between structure and function of complex dynamical systems.

Altered grey matter integrity and network vulnerability relate to epilepsy occurrence in patients with multiple sclerosis

BACKGROUND

To investigate the relevance of compartmentalized grey matter (GM) pathology and network reorganization in MS patients with concomitant epilepsy.

METHODS

From 3T MRI scans of 30 MS patients with epilepsy (MSE; age 41±15 years, 21 females, disease duration 8±6 years, median Expanded Disability Status Scale (EDSS) 3), 60 MS patients without epilepsy (MS; age 41±12 years, 35 females, disease duration 6±4 years, EDSS 2), and 60 healthy subjects (HS; age 40±13 years, 27 females) regional volumes of GM lesions and of cortical, subcortical, and hippocampal structures were quantified. Network topology and vulnerability were modeled within the graph theoretical framework. The receiver operating characteristic (ROC) analysis was applied to assess the accuracy of GM pathology measures to discriminate between MSE and MS patients.

RESULTS

Higher lesion volumes within the hippocampus, mesiotemporal cortex, and amygdala were detected in MSE compared to MS (all p<0.05). MSE displayed lower cortical volumes mainly in temporal and parietal areas compared to MS and HS (all p<0.05). Lower volumes of hippocampal tail and presubiculum were identified in both MSE and MS patients compared to HS (all p<0.05). Network topology in MSE was characterized by higher transitivity and assortativity, and higher vulnerability compared to MS and HS (all p<0.05). Hippocampal lesion volume yielded the highest accuracy (area under the ROC curve 0.80 [0.67-0.91]) in discriminating between MSE and MS patients.

CONCLUSIONS

High lesion load, altered integrity of mesiotemporal GM structures, and network reorganization are associated with a greater propensity of epilepsy occurrence in MS.

Modifications of Functional Human Brain Networks by Transcutaneous Auricular Vagus Nerve Stimulation: Impact of Time of Day

Transcutaneous auricular vagus nerve stimulation (taVNS) is a novel non-invasive treatment option for different diseases and symptoms, such as epilepsy or depression. Its mechanism of action, however, is still not fully understood. We investigated short-term taVNS-induced changes of local and global properties of EEG-derived, evolving functional brain networks from eighteen subjects who underwent two 1 h stimulation phases (morning and afternoon) during continuous EEG-recording. In the majority of subjects, taVNS induced measurable modifications of network properties. Network alterations induced by stimulation in the afternoon were clearly more pronounced than those induced by stimulation in the morning. Alterations mostly affected the networks’ topology and stability properties. On the local network scale, no clear-cut spatial stimulation-related patterns could be discerned. Our findings indicate that the possible impact of diurnal influences on taVNS-induced network modifications would need to be considered for future research and clinical studies of this non-pharmaceutical intervention approach.

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.

Glymphatic system function in patients with newly diagnosed focal epilepsy

INTRODUCTION

The aim of this study was to analyze the glymphatic system function and its relationship with clinical characteristics, global diffusion tensor imaging (DTI) parameters, and global structural connectivity in treatment-naïve patients with newly diagnosed focal epilepsy.

METHODS

This retrospective single-center study investigated patients with focal epilepsy and healthy controls. All participants underwent routine brain magnetic resonance imaging and DTI. DTI analysis along the perivascular space (DTI-ALPS) was used to evaluate glymphatic system function. We also calculated the measures of global DTI parameters, including whole-brain fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD), and radial diffusivity (RD), and performed a graph theoretical network analysis to measure global structural connectivity.

RESULTS

A total of 109 patients with focal epilepsy and 88 healthy controls were analyzed. There were no significant differences in the DTI-ALPS index (1.67 vs. 1.68, p = 0.861) between the groups. However, statistically significant associations were found between the DTI-ALPS index and age (r = -0.242, p = 0.01), FA (r = 0.257, p = 0.007), MD (r = -0.469, p < 0.001), AD (r = -0.303, p = 0.001), RD (r = -0.434, p < 0.001), and the assortative coefficient (r = 0.230, p = 0.016) in patients with focal epilepsy.

CONCLUSION

The main finding of this study is that DTI-ALPS index is significantly correlated with global DTI parameters and structural connectivity measures of the brain in patients with focal epilepsy. In addition, DTI-ALPS index decreases with age in these patients. We conclude that the DTI-ALPS index can be used to investigate glymphatic system function in patients with focal epilepsy.

Brain networks in migraine with and without aura: An exploratory arterial spin labeling MRI study

OBJECTIVES

The aim of this exploratory study was to investigate the underlying pathomechanisms of migraine with aura (MA) and migraine without aura (MO) in the interictal phase using a connectivity analysis.

METHODS

We prospectively enrolled patients who were newly diagnosed with migraine. All patients underwent brain MRI, including diffusion tensor imaging and arterial spin labeling perfusion MRI. We analyzed the differences between patients with MA and those with MO in structural connectivity based on diffusion tensor imaging and functional connectivity based on arterial spin labeling perfusion MRI using a graph theoretical analysis.

RESULTS

We enrolled 58 patients with migraine (11 patients with MA and 47 patients with MO). There were no differences between patients with MA and those with MO in the network measures of global structural connectivity. However, differences in global functional connectivity were found between the two groups. The assortative coefficient was lower in patients with MA than in those with MO (-0.050 vs. -0.012, p = .017). There were no differences in local structural and functional connectivity between patients with MA and those with MO.

CONCLUSION

We found differences in global functional connectivity between patients with MO and those with MA. The study of MA and MO using a connectivity analysis may shed light on migraine pathophysiology. We suggest it is worthwhile to investigate if changes in functional connectivity may serve as novel biomarkers in MA. In this regard, ASL MRI appears to be valuable in the context of network analysis, but further studies are needed to confirm our findings.

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.

Synchrony and Complexity in State-Related EEG Networks: An Application of Spectral Graph Theory

The brain may be considered as a synchronized dynamic network with several coherent dynamical units. However, concerns remain whether synchronizability is a stable state in the brain networks. If so, which index can best reveal the synchronizability in brain networks? To answer these questions, we tested the application of the spectral graph theory and the Shannon entropy as alternative approaches in neuroimaging. We specifically tested the alpha rhythm in the resting-state eye closed (rsEC) and the resting-state eye open (rsEO) conditions, a well-studied classical example of synchrony in neuroimaging EEG. Since the synchronizability of alpha rhythm is more stable during the rsEC than the rsEO, we hypothesized that our suggested spectral graph theory indices (as reliable measures to interpret the synchronizability of brain signals) should exhibit higher values in the rsEC than the rsEO condition. We performed two separate analyses of two different datasets (as elementary and confirmatory studies). Based on the results of both studies and in agreement with our hypothesis, the spectral graph indices revealed higher stability of synchronizability in the rsEC condition. The k-mean analysis indicated that the spectral graph indices can distinguish the rsEC and rsEO conditions by considering the synchronizability of brain networks. We also computed correlations among the spectral indices, the Shannon entropy, and the topological indices of brain networks, as well as random networks. Correlation analysis indicated that although the spectral and the topological properties of random networks are completely independent, these features are significantly correlated with each other in brain networks. Furthermore, we found that complexity in the investigated brain networks is inversely related to the stability of synchronizability. In conclusion, we revealed that the spectral graph theory approach can be reliably applied to study the stability of synchronizability of state-related brain networks.

Predicting the antiepileptic drug response by brain connectivity in newly diagnosed focal epilepsy

OBJECTIVE

Growing evidence has suggested that epilepsy is a disease with alterations in brain connectivity. The aim of this study was to investigate whether the changes in brain connectivity can predict the response to an antiepileptic drug (AED) in patients with a newly diagnosed focal epilepsy of unknown etiology.

METHODS

This observational study was independently performed at two tertiary hospitals (Group A and B). Thirty-eight patients with newly diagnosed focal epilepsy of unknown etiology were enrolled in Group A and 46 patients in Group B. We divided these patients into two groups according to their seizure control after AED treatment: AED good and poor responders. We defined the AED good responders as those in whom had seizure free for at least the last 6 months while AED poor responders who were not. All of the subjects underwent diffusion tensor imaging, and graph theoretical analysis was applied to reveal the brain connectivity. We investigated the difference in the clinical characteristics and network measurements between the two groups.

RESULTS

Of the network measures, the assortativity coefficient in the AED good responders was significantly higher than that in the AED poor responders in both Groups A and B (- 0.0239 vs. - 0.0473, p = 0.0110 in Group A; 0.0173 vs. - 0.0180, p = 0.0024 in Group B). The Kaplan-Meier survival analysis revealed that the time to failure to retain the first AED was significantly longer in the patients with assortative networks (assortativity coefficient > 0) than in those with disassortative networks (assortativity coefficient < 0) in Group B.

CONCLUSION

We demonstrated that the assortativity coefficient differed between patients with newly diagnosed focal epilepsy of unknown etiology according to their AED responses, which suggests that the changes in brain connectivity could be a biomarker for predicting the responses to AED.

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.

Cascading failures in scale-free interdependent networks

Large cascades are a common occurrence in many natural and engineered complex systems. In this paper we explore the propagation of cascades across networks using realistic network topologies, such as heterogeneous degree distributions, as well as intra- and interlayer degree correlations. We find that three properties, scale-free degree distribution, internal network assortativity, and cross-network hub-to-hub connections, are all necessary components to significantly reduce the size of large cascades in the Bak-Tang-Wiesenfeld sandpile model. We demonstrate that correlations present in the structure of the multilayer network influence the dynamical cascading process and can prevent failures from spreading across connected layers. These findings highlight the importance of internal and cross-network topology in optimizing robustness of interconnected systems.

Discordant attributes of structural and functional brain connectivity in a two-layer multiplex network

Several studies have suggested that functional connectivity (FC) is constrained by the underlying structural connectivity (SC) and mutually correlated. However, not many studies have focused on differences in the network organization of SC and FC, and on how these differences may inform us about their mutual interaction. To explore this issue, we adopt a multi-layer framework, with SC and FC, constructed using Magnetic Resonance Imaging (MRI) data from the Human Connectome Project, forming a two-layer multiplex network. In particular, we examine node strength assortativity within and between the SC and FC layer. We find that, in general, SC is organized assortatively, indicating brain regions are on average connected to other brain regions with similar node strengths. On the other hand, FC shows disassortative mixing. This discrepancy is apparent also among individual resting-state networks within SC and FC. In addition, these patterns show lateralization, with disassortative mixing within FC subnetworks mainly driven from the left hemisphere. We discuss our findings in the context of robustness to structural failure, and we suggest that discordant and lateralized patterns of associativity in SC and FC may provide clues to understand laterality of some neurological dysfunctions and recovery.

Expanding Brain-Computer Interfaces for Controlling Epilepsy Networks: Novel Thalamic Responsive Neurostimulation in Refractory Epilepsy

Seizures have traditionally been considered hypersynchronous excitatory events and epilepsy has been separated into focal and generalized epilepsy based largely on the spatial distribution of brain regions involved at seizure onset. Epilepsy, however, is increasingly recognized as a complex network disorder that may be distributed and dynamic. Responsive neurostimulation (RNS) is a recent technology that utilizes intracranial electroencephalography (EEG) to detect seizures and delivers stimulation to cortical and subcortical brain structures for seizure control. RNS has particular significance in the clinical treatment of medically refractory epilepsy and brain–computer interfaces in epilepsy. Closed loop RNS represents an important step forward to understand and target nodes in the seizure network. The thalamus is a central network node within several functional networks and regulates input to the cortex; clinically, several thalamic nuclei are safe and feasible targets. We highlight the network theory of epilepsy, potential targets for neuromodulation in epilepsy and the first reported use of RNS as a first generation brain–computer interface to detect and stimulate the centromedian intralaminar thalamic nucleus in a patient with bilateral cortical onset of seizures. We propose that advances in network analysis and neuromodulatory techniques using brain–computer interfaces will significantly improve outcomes in patients with epilepsy. There are numerous avenues of future direction in brain–computer interface devices including multi-modal sensors, flexible electrode arrays, multi-site targeting, and wireless communication.

Network dynamics in the healthy and epileptic developing brain

Electroencephalography (EEG) allows recording of cortical activity at high temporal resolution. EEG recordings can be summarized along different dimensions using network-level quantitative measures, such as channel-to-channel correlation, or band power distributions across channels. These reveal network patterns that unfold over a range of different timescales and can be tracked dynamically. Here we describe the dynamics of network state transitions in EEG recordings of spontaneous brain activity in normally developing infants and infants with severe early infantile epileptic encephalopathies (n = 8, age: 1–8 months). We describe differences in measures of EEG dynamics derived from band power, and correlation-based summaries of network-wide brain activity. We further show that EEGs from different patient groups and controls may be distinguishable on a small set of the novel quantitative measures introduced here, which describe dynamic network state switching. Quantitative measures related to the sharpness of switching from one correlation pattern to another show the largest differences between groups. These findings reveal that the early epileptic encephalopathies are associated with characteristic dynamic features at the network level. Quantitative network-based analyses like the one presented here may in the future inform the clinical use of quantitative EEG for diagnosis.

Transition to reconstructibility in weakly coupled networks

Across scientific disciplines, thresholded pairwise measures of statistical dependence between time series are taken as proxies for the interactions between the dynamical units of a network. Yet such correlation measures often fail to reflect the underlying physical interactions accurately. Here we systematically study the problem of reconstructing direct physical interaction networks from thresholding correlations. We explicate how local common cause and relay structures, heterogeneous in-degrees and non-local structural properties of the network generally hinder reconstructibility. However, in the limit of weak coupling strengths we prove that stationary systems with dynamics close to a given operating point transition to universal reconstructiblity across all network topologies.

Dynamical properties of LFPs from mice with unilateral injection of TeNT

Local field potential (LFP) recordings were performed from the visual cortex (V1) of a focal epilepsy mouse model. Epilepsy was induced by a unilateral injection of the synaptic blocker tetanus neurotoxin (TeNT). LFP signals were simultaneously recorded from V1 of both hemispheres of each animal under acute and chronic conditions (i.e. during and after the period of TeNT action). All data were analysed by using nonlinear time series methods. Suitable values of the lag time and embedding dimension for phase space reconstruction were estimated by employing well-known methods. The results showed that lag times are sensitive to the presence of TeNT. Interestingly, TeNT promoted an increase in the level of linear and nonlinear correlation of LFP signals. The values of the embedding dimension failed to show any dependence on the presence of the neurotoxin. However, a local nonlinear prediction method showed that the presence of TeNT increases the predictability, quantified by the normalized prediction error, of the neural recordings. From a neurophysiological point of view, the above results suggest that TeNT injected in one hemisphere strongly impacts the local electrical activity of the neural populations in the opposite hemisphere. We hypothesize that this could arise from a qualitative and quantitative alteration of the transmission properties of the callosal fibers.

New Insights on Temporal Lobe Epilepsy Based on Plasticity-Related Network Changes and High-Order Statistics

Epilepsy is a disorder of the brain characterized by the predisposition to generate recurrent unprovoked seizures, which involves reshaping of neuronal circuitries based on intense neuronal activity. In this review, we first detailed the regulation of plasticity-associated genes, such as ARC, GAP-43, PSD-95, synapsin, and synaptophysin. Indeed, reshaping of neuronal connectivity after the primary, acute epileptogenesis event increases the excitability of the temporal lobe. Herein, we also discussed the heterogeneity of neuronal populations regarding the number of synaptic connections, which in the theoretical field is commonly referred as degree. Employing integrate-and-fire neuronal model, we determined that in addition to increased synaptic strength, degree correlations might play essential and unsuspected roles in the control of network activity. Indeed, assortativity, which can be described as a condition where high-degree correlations are observed, increases the excitability of neural networks. In this review, we summarized recent topics in the field, and data were discussed according to newly developed or unusual tools, as provided by mathematical graph analysis and high-order statistics. With this, we were able to present new foundations for the pathological activity observed in temporal lobe epilepsy.

Modeling the network dynamics of pulse-coupled neurons

We derive a mean-field approximation for the macroscopic dynamics of large networks of pulse-coupled theta neurons in order to study the effects of different network degree distributions and degree correlations (assortativity). Using the ansatz of Ott and Antonsen [Chaos 18, 037113 (2008)], we obtain a reduced system of ordinary differential equations describing the mean-field dynamics, with significantly lower dimensionality compared with the complete set of dynamical equations for the system. We find that, for sufficiently large networks and degrees, the dynamical behavior of the reduced system agrees well with that of the full network. This dimensional reduction allows for an efficient characterization of system phase transitions and attractors. For networks with tightly peaked degree distributions, the macroscopic behavior closely resembles that of fully connected networks previously studied by others. In contrast, networks with highly skewed degree distributions exhibit different macroscopic dynamics due to the emergence of degree dependent behavior of different oscillators. For nonassortative networks (i.e., networks without degree correlations), we observe the presence of a synchronously firing phase that can be suppressed by the presence of either assortativity or disassortativity in the network. We show that the results derived here can be used to analyze the effects of network topology on macroscopic behavior in neuronal networks in a computationally efficient fashion.

Predictive modeling of EEG time series for evaluating surgery targets in epilepsy patients

During the last 20 years, predictive modeling in epilepsy research has largely been concerned with the prediction of seizure events, whereas the inference of effective brain targets for resective surgery has received surprisingly little attention. In this exploratory pilot study, we describe a distributional clustering framework for the modeling of multivariate time series and use it to predict the effects of brain surgery in epilepsy patients. By analyzing the intracranial EEG, we demonstrate how patients who became seizure free after surgery are clearly distinguished from those who did not. More specifically, for 5 out of 7 patients who obtained seizure freedom (= Engel class I) our method predicts the specific collection of brain areas that got actually resected during surgery to yield a markedly lower posterior probability for the seizure related clusters, when compared to the resection of random or empty collections. Conversely, for 4 out of 5 Engel class III/IV patients who still suffer from postsurgical seizures, performance of the actually resected collection is not significantly better than performances displayed by random or empty collections. As the number of possible collections ranges into billions and more, this is a substantial contribution to a problem that today is still solved by visual EEG inspection. Apart from epilepsy research, our clustering methodology is also of general interest for the analysis of multivariate time series and as a generative model for temporally evolving functional networks in the neurosciences and beyond. Hum Brain Mapp 38:2509-2531, 2017. © 2017 Wiley Periodicals, Inc.

Random matrix theory for analyzing the brain functional network in attention deficit hyperactivity disorder

Attention deficit hyperactivity disorder (ADHD) is the most common childhood neuropsychiatric disorder and affects approximately 6-7% of children worldwide. Here, we investigate the statistical properties of undirected and directed brain functional networks in ADHD patients based on random matrix theory (RMT), in which the undirected functional connectivity is constructed based on correlation coefficient and the directed functional connectivity is measured based on cross-correlation coefficient and mutual information. We first analyze the functional connectivity and the eigenvalues of the brain functional network. We find that ADHD patients have increased undirected functional connectivity, reflecting a higher degree of linear dependence between regions, and increased directed functional connectivity, indicating stronger causality and more transmission of information among brain regions. More importantly, we explore the randomness of the undirected and directed functional networks using RMT. We find that for ADHD patients, the undirected functional network is more orderly than that for normal subjects, which indicates an abnormal increase in undirected functional connectivity. In addition, we find that the directed functional networks are more random, which reveals greater disorder in causality and more chaotic information flow among brain regions in ADHD patients. Our results not only further confirm the efficacy of RMT in characterizing the intrinsic properties of brain functional networks but also provide insights into the possibilities RMT offers for improving clinical diagnoses and treatment evaluations for ADHD patients.

Which Brain Regions are Important for Seizure Dynamics in Epileptic Networks? Influence of Link Identification and EEG Recording Montage on Node Centralities

Nodes in large-scale epileptic networks that are crucial for seizure facilitation and termination can be regarded as potential targets for individualized focal therapies. Graph-theoretical approaches based on centrality concepts can help to identify such important nodes, however, they may be influenced by the way networks are derived from empirical data. Here we investigate evolving functional epileptic brain networks during 82 focal seizures with different anatomical onset locations that we derive from multichannel intracranial electroencephalographic recordings from 51 patients. We demonstrate how the various methodological steps (from the recording montage via node and link inference to the assessment of node centralities) affect importance estimation and discuss their impact on the interpretability of findings in the context of pathophysiological aspects of seizure dynamics.

Reflex seizures, traits, and epilepsies: from physiology to pathology

Epileptic seizures are generally unpredictable and arise spontaneously. Patients often report non-specific triggers such as stress or sleep deprivation, but only rarely do seizures occur as a reflex event, in which they are objectively and consistently modulated, precipitated, or inhibited by external sensory stimuli or specific cognitive processes. The seizures triggered by such stimuli and processes in susceptible individuals can have different latencies. Once seizure-suppressing mechanisms fail and a critical mass (the so-called tipping point) of cortical activation is reached, reflex seizures stereotypically manifest with common motor features independent of the physiological network involved. The complexity of stimuli increases from simple sensory to complex cognitive-emotional with increasing age of onset. The topography of physiological networks involved follows the posterior-to-anterior trajectory of brain development, reflecting age-related changes in brain excitability. Reflex seizures and traits probably represent the extremes of a continuum, and understanding of their underlying mechanisms might help to elucidate the transition of normal physiological function to paroxysmal epileptic activity.

Disrupted Ipsilateral Network Connectivity in Temporal Lobe Epilepsy

OBJECTIVE

The current practice under which patients with refractory epilepsy are surgically treated is based mainly on the identification of specific cortical areas, mainly the epileptogenic zone, which is believed to be responsible for generation of seizures. A better understanding of the whole epileptic network and its components and properties is required before more effective and less invasive therapies can be developed. The aim of the present study was to partially characterize the evolution of the functional network during the preictal-ictal transition in partial seizures in patients with temporal lobe epilepsy (TLE).

METHODS

Scalp and foramen ovale (FOE) recordings from twenty-two TLE patients were analyzed under the complex network perspective. The density of links, average path length, average clustering coefficient, and modularity were calculated during the preictal and the ictal stages. Both linear-Pearson correlation-and non-linear-phase synchronization-measures were used as proxies of functional connectivity between the electrode locations areas. The transition from one stage to the other was evaluated in the whole network and in the mesial sub-networks. The results were compared with a voltage-dependent measure, namely, the spectral entropy.

RESULTS

Changes in the global functional network during the transition from the preictal to the ictal stage show, in the linear case, that in sixteen cases (72.7%) the density of the links increased during the seizure, with a decrease in the average path length in fifteen cases (68.1%). There was also a preictal and ictal imbalance in functional connectivity during both stages (77.2% to 86.3%). The SE dropped during the seizure in 95.4% of the cases, but did not show any tendency towards lateralization. When using the nonlinear measure of functional connectivity, the phase synchronization, similar results were obtained.

CONCLUSIONS

In TLE patients, the transition to the ictal stage is accompanied by increasing global synchronization and a more ordered spectral content of the signals, indicated by lower spectral entropy. The interictal connectivity imbalance (lower ipsilateral connectivity) is sustained during the seizure, irrespective of any appreciable imbalance in the spectral entropy of the mesial recordings.

Termination patterns of complex partial seizures: An intracranial EEG study

PURPOSE

While seizure onset patterns have been the subject of many reports, there have been few studies of seizure termination. In this study we report the incidence of synchronous and asynchronous termination patterns of partial seizures recorded with intracranial arrays.

METHODS

Data were collected from patients with intractable complex partial seizures undergoing presurgical evaluations with intracranial electrodes. Patients with seizures originating from mesial temporal and neocortical regions were grouped into three groups based on patterns of seizure termination: synchronous only (So), asynchronous only (Ao), or mixed (S/A, with both synchronous and asynchronous termination patterns).

RESULTS

88% of the patients in the MT group had seizures with a synchronous pattern of termination exclusively (38%) or mixed (50%). 82% of the NC group had seizures with synchronous pattern of termination exclusively (52%) or mixed (30%). In the NC group, there was a significant difference of the range of seizure durations between So and Ao groups, with Ao exhibiting higher variability. Seizures with synchronous termination had low variability in both groups.

CONCLUSIONS

Synchronous seizure termination is a common pattern for complex partials seizures of both mesial temporal or neocortical onset. This may reflect stereotyped network behavior or dynamics at the seizure focus.

Time-dependent degree-degree correlations in epileptic brain networks: from assortative to dissortative mixing

We investigate the long-term evolution of degree-degree correlations (assortativity) in functional brain networks from epilepsy patients. Functional networks are derived from continuous multi-day, multi-channel electroencephalographic data, which capture a wide range of physiological and pathophysiological activities. In contrast to previous studies which all reported functional brain networks to be assortative on average, even in case of various neurological and neurodegenerative disorders, we observe large fluctuations in time-resolved degree-degree correlations ranging from assortative to dissortative mixing. Moreover, in some patients these fluctuations exhibit some periodic temporal structure which can be attributed, to a large extent, to daily rhythms. Relevant aspects of the epileptic process, particularly possible pre-seizure alterations, contribute marginally to the observed long-term fluctuations. Our findings suggest that physiological and pathophysiological activity may modify functional brain networks in a different and process-specific way. We evaluate factors that possibly influence the long-term evolution of degree-degree correlations.

Dynamics on networks: the role of local dynamics and global networks on the emergence of hypersynchronous neural activity

Graph theory has evolved into a useful tool for studying complex brain networks inferred from a variety of measures of neural activity, including fMRI, DTI, MEG and EEG. In the study of neurological disorders, recent work has discovered differences in the structure of graphs inferred from patient and control cohorts. However, most of these studies pursue a purely observational approach; identifying correlations between properties of graphs and the cohort which they describe, without consideration of the underlying mechanisms. To move beyond this necessitates the development of computational modeling approaches to appropriately interpret network interactions and the alterations in brain dynamics they permit, which in the field of complexity sciences is known as dynamics on networks. In this study we describe the development and application of this framework using modular networks of Kuramoto oscillators. We use this framework to understand functional networks inferred from resting state EEG recordings of a cohort of 35 adults with heterogeneous idiopathic generalized epilepsies and 40 healthy adult controls. Taking emergent synchrony across the global network as a proxy for seizures, our study finds that the critical strength of coupling required to synchronize the global network is significantly decreased for the epilepsy cohort for functional networks inferred from both theta (3-6 Hz) and low-alpha (6-9 Hz) bands. We further identify left frontal regions as a potential driver of seizure activity within these networks. We also explore the ability of our method to identify individuals with epilepsy, observing up to 80% predictive power through use of receiver operating characteristic analysis. Collectively these findings demonstrate that a computer model based analysis of routine clinical EEG provides significant additional information beyond standard clinical interpretation, which should ultimately enable a more appropriate mechanistic stratification of people with epilepsy leading to improved diagnostics and therapeutics.

Clinical correlates of graph theory findings in temporal lobe epilepsy

PURPOSE

Temporal lobe epilepsy (TLE) is considered a brain network disorder, additionally representing the most common form of pharmaco-resistant epilepsy in adults. There is increasing evidence that seizures in TLE arise from abnormal epileptogenic networks, which extend beyond the clinico-radiologically determined epileptogenic zone and may contribute to the failure rate of 30-50% following epilepsy surgery. Graph theory allows for a network-based representation of TLE brain networks using several neuroimaging and electrophysiologic modalities, and has potential to provide clinicians with clinically useful biomarkers for diagnostic and prognostic purposes.

METHODS

We performed a review of the current state of graph theory findings in TLE as they pertain to localization of the epileptogenic zone, prediction of pre- and post-surgical seizure frequency and cognitive performance, and monitoring cognitive decline in TLE.

RESULTS

Although different neuroimaging and electrophysiologic modalities have yielded occasionally conflicting results, several potential biomarkers have been characterized for identifying the epileptogenic zone, pre-/post-surgical seizure prediction, and assessing cognitive performance. For localization, graph theory measures of centrality have shown the most potential, including betweenness centrality, outdegree, and graph index complexity, whereas for prediction of seizure frequency, measures of synchronizability have shown the most potential. The utility of clustering coefficient and characteristic path length for assessing cognitive performance in TLE is also discussed.

CONCLUSIONS

Future studies integrating data from multiple modalities and testing predictive models are needed to clarify findings and develop graph theory for its clinical utility.

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.

Incidental and intentional learning of verbal episodic material differentially modifies functional brain networks

Learning- and memory-related processes are thought to result from dynamic interactions in large-scale brain networks that include lateral and mesial structures of the temporal lobes. We investigate the impact of incidental and intentional learning of verbal episodic material on functional brain networks that we derive from scalp-EEG recorded continuously from 33 subjects during a neuropsychological test schedule. Analyzing the networks' global statistical properties we observe that intentional but not incidental learning leads to a significantly increased clustering coefficient, and the average shortest path length remains unaffected. Moreover, network modifications correlate with subsequent recall performance: the more pronounced the modifications of the clustering coefficient, the higher the recall performance. Our findings provide novel insights into the relationship between topological aspects of functional brain networks and higher cognitive functions.