Weighted and directed interactions in evolving large-scale epileptic brain networks

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.

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.

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.

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.

Brain functional network modeling and analysis based on fMRI: a systematic review

In recent years, the number of patients with neurodegenerative diseases (i.e., Alzheimer's disease, Parkinson's disease, mild cognitive impairment) and mental disorders (i.e., depression, anxiety and schizophrenia) have increased dramatically. Researchers have found that complex network analysis can reveal the topology of brain functional networks, such as small-world, scale-free, etc. In the study of brain diseases, it has been found that these topologies have undergoed abnormal changes in different degrees. Therefore, the research of brain functional networks can not only provide a new perspective for understanding the pathological mechanism of neurological and psychiatric diseases, but also provide assistance for the early diagnosis. Focusing on the study of human brain functional networks, this paper reviews the research results in recent years. First, this paper introduces the background of the study of brain functional networks under complex network theory and the important role of topological properties in the study of brain diseases. Second, the paper describes how to construct a brain functional network using neural image data. Third, the common methods of functional network analysis, including network structure analysis and disease classification, are introduced. Fourth, the role of brain functional networks in pathological study, analysis and diagnosis of brain functional diseases is studied. Finally, the paper summarizes the existing studies of brain functional networks and points out the problems and future research directions.

Astroglial Glutamine Synthetase and the Pathogenesis of Mesial Temporal Lobe Epilepsy

The enzyme glutamine synthetase (GS), also referred to as glutamate ammonia ligase, is abundant in astrocytes and catalyzes the conversion of ammonia and glutamate to glutamine. Deficiency or dysfunction of astrocytic GS in discrete brain regions have been associated with several types of epilepsy, including medically-intractable mesial temporal lobe epilepsy (MTLE), neocortical epilepsies, and glioblastoma-associated epilepsy. Moreover, experimental inhibition or deletion of GS in the entorhinal-hippocampal territory of laboratory animals causes an MTLE-like syndrome characterized by spontaneous, recurrent hippocampal-onset seizures, loss of hippocampal neurons, and in some cases comorbid depressive-like features. The goal of this review is to summarize and discuss the possible roles of astroglial GS in the pathogenesis of epilepsy.

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.

The Human Organism as an Integrated Interaction Network: Recent Conceptual and Methodological Challenges

The field of Network Physiology aims to advance our understanding of how physiological systems and sub-systems interact to generate a variety of behaviors and distinct physiological states, to optimize the organism's functioning, and to maintain health. Within this framework, which considers the human organism as an integrated network, vertices are associated with organs while edges represent time-varying interactions between vertices. Likewise, vertices may represent networks on smaller spatial scales leading to a complex mixture of interacting homogeneous and inhomogeneous networks of networks. Lacking adequate analytic tools and a theoretical framework to probe interactions within and among diverse physiological systems, current approaches focus on inferring properties of time-varying interactions-namely strength, direction, and functional form-from time-locked recordings of physiological observables. To this end, a variety of bivariate or, in general, multivariate time-series-analysis techniques, which are derived from diverse mathematical and physical concepts, are employed and the resulting time-dependent networks can then be further characterized with methods from network theory. Despite the many promising new developments, there are still problems that evade from a satisfactory solution. Here we address several important challenges that could aid in finding new perspectives and inspire the development of theoretic and analytical concepts to deal with these challenges and in studying the complex interactions between physiological systems.

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.

Association of Seizure Spread With Surgical Failure in Epilepsy

Importance

Seizures recur in as many as half of patients who undergo surgery for drug-resistant temporal lobe epilepsy (TLE). Understanding why TLE is resistant to surgery in some patients may reveal insights into epileptogenic networks and direct new therapies to improve outcomes.

Objective

To characterize features of surgically refractory TLE.

Design, Setting, and Participants

Medical records from a comprehensive epilepsy center were retrospectively reviewed for 131 patients who received a standard anteromedial temporal resection by a single surgeon from January 1, 2000, to December 31, 2015. Thirteen patients were excluded for having less than 1 year of follow-up. Patients at the highest risk for seizure recurrence were identified. Intracranial electroencephalogram (iEEG) analyses generated 3-dimensional seizure spread representations and quantified rapid seizure spread. The final analyses of seizure outcome and follow-up data were performed in June 2017.

Main Outcomes and Measures

The Engel class seizure outcome following surgery was evaluated for all patients, defining seizure recurrence as Engel class II or greater. Intracranial recordings of neocortical grids/strips and depth electrodes were analyzed visually for seizure spread. Fast β power was projected onto reconstructions of patients' brain magnetic resonance imaging scans to visualize spread patterns and was quantified to compare power within vs outside resective margins.

Results

Of 118 patients with 1 year of follow-up or more (mean [SD], 6.5 [4.6] years), 66 (55.9%) were women and 52 (44.1%) were men (median age, 39 years [range, 4-66 years]). The cumulative probability of continuous Engel class I seizure freedom since surgery at postoperative year 10 and afterward was 65.6%, with 92% of recurrences in years 1 to 3. Multivariable statistical analyses found that the selection for iEEG study was the most reliable predictor of seizure recurrence, with a mixed-effects model estimating that the Engel score in the iEEG cohort was higher by a mean (SD) of 1.1 (0.33) (P = .001). In patients with iEEG results, rapid seizure spread in less than 10 seconds was associated with recurrence (hazard ratio, 5.99; 95% CI, 1.7-21.1; P < .01). In the first 10 seconds of seizures, fast β power activity outside the resective margins in the lateral temporal cortex was significantly greater in patients whose seizures recurred compared with patients who were seizure-free (mean [SEM], 137.5% [16.8%] vs 93.4% [4.6%]; P < .05).

Conclusions and significance

Rapid seizure spread outside anteromedial temporal resection resective margins plays a significant role in the surgical failure of drug-resistant TLE. Seizure control after epilepsy surgery might be improved by investigating areas of early spread as candidates for resection or neuromodulation.

Pilot Study of An Intracranial Electroencephalography Biomarker of Depressive Symptoms in Epilepsy

OBJECTIVES

Adult patients with epilepsy have an increased prevalence of major depressive disorder (MDD). Intracranial EEG (iEEG) captured during extended inpatient monitoring of patients with treatment-resistant epilepsy offers a particularly promising method to study MDD networks in epilepsy.

METHODS

The authors used 24 hours of resting-state iEEG to examine the neural activity patterns within corticolimbic structures that reflected the presence of depressive symptoms in 13 adults with medication-refractory epilepsy. Principal component analysis was performed on the z-scored mean relative power in five standard frequency bands averaged across electrodes within a region.

RESULTS

Principal component 3 was a statistically significant predictor of the presence of depressive symptoms (R²=0.35, p=0.014). A balanced logistic classifier model using principal component 3 alone correctly classified 78% of patients as belonging to the group with a high burden of depressive symptoms or a control group with minimal depressive symptoms (sensitivity, 75%; specificity, 80%; area under the curve=0.8, leave-one-out cross validation). Classification was dependent on beta power throughout the corticolimbic network and low-frequency cingulate power.

CONCLUSIONS

These finding suggest, for the first time, that neural features across circuits involved in epilepsy may distinguish patients who have depressive symptoms from those who do not. Larger studies are required to validate these findings and to assess their diagnostic utility in MDD.

Astrocytes and Glutamine Synthetase in Epileptogenesis

The cellular, molecular, and metabolic mechanisms that underlie the development of mesial temporal lobe epilepsy are incompletely understood. Here we review the role of astrocytes in epilepsy development (a.k.a. epileptogenesis), particularly astrocyte pathologies related to: aquaporin 4, the inwardly rectifying potassium channel Kir4.1, monocarboxylate transporters MCT1 and MCT2, excitatory amino acid transporters EAAT1 and EAAT2, and glutamine synthetase. We propose that inhibition, dysfunction or loss of astrocytic glutamine synthetase is an important causative factor for some epilepsies, particularly mesial temporal lobe epilepsy and glioblastoma-associated epilepsy. We postulate that the regulatory mechanisms of glutamine synthetase as well as the downstream effects of glutamine synthetase dysfunction, represent attractive, new targets for antiepileptogenic interventions. Currently, no antiepileptogenic therapies are available for human use. The discovery of such interventions is important as it will fundamentally change the way we approach epilepsy by preventing the disease from ever becoming manifest after an epileptogenic insult to the brain.

Connectivity strength, time lag structure and the epilepsy network in resting-state fMRI

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Stereo-encephalography informed high-resolution functional connectome analysis on the nodal and whole brain levels identifies consistent patterns of altered correlation strength and altered time lag architecture in epilepsy patients compared to controls.

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Specific patterns of altered connectivity include:.○

broadly distributed increased strength of correlation between the seizure onset node and the remainder of the brain.

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decreased time lag within the seizure onset node.

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globally increased time lag throughout all regions of the brain not involved in seizure onset or propagation.

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Comparing the topographic distribution of findings against a functional atlas, all resting state networks were involved to a variable degree. These local and whole brain findings presented here lead us to propose the network steal hypothesis as a possible mechanistic explanation for the non-seizure clinical manifestations of epilepsy.

The relationship between the epilepsy network, intrinsic brain networks and hypersynchrony in epilepsy remains incompletely understood. To converge upon a synthesized understanding of these features, we studied two elements of functional connectivity in epilepsy: correlation and time lag structure using resting state fMRI data from both SEEG-defined epileptic brain regions and whole-brain fMRI analysis. Functional connectivity (FC) was analyzed in 15 patients with epilepsy and 36 controls. Correlation strength and time lag were selected to investigate the magnitude of and temporal interdependency across brain regions. Zone-based analysis was carried out investigating directed correlation strength and time lag between both SEEG-defined nodes of the epilepsy network and between the epileptogenic zone and all other brain regions. Findings were compared between patients and controls and against a functional atlas. FC analysis on the nodal and whole brain levels identifies consistent patterns of altered correlation strength and altered time lag architecture in epilepsy patients compared to controls. These patterns include 1) broadly distributed increased strength of correlation between the seizure onset node and the remainder of the brain, 2) decreased time lag within the seizure onset node, and 3) globally increased time lag throughout all regions of the brain not involved in seizure onset or propagation. Comparing the topographic distribution of findings against a functional atlas, all resting state networks were involved to a variable degree. These local and whole brain findings presented here lead us to propose the network steal hypothesis as a possible mechanistic explanation for the non-seizure clinical manifestations of epilepsy.

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.

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

Knowing when, where, and how seizures are initiated in large-scale epileptic brain networks remains a widely unsolved problem. Seizure precursors – changes in brain dynamics predictive of an impending seizure – can now be identified well ahead of clinical manifestations, but either the seizure onset zone or remote brain areas are reported as network nodes from which seizure precursors emerge. We aimed to shed more light on the role of constituents of evolving epileptic networks that recurrently transit into and out of seizures. We constructed such networks from more than 3200 hours of continuous intracranial electroencephalograms recorded in 38 patients with medication refractory epilepsy. We succeeded in singling out predictive edges and predictive nodes. Their particular characteristics, namely edge weight respectively node centrality (a fundamental concept of network theory), from the pre-ictal periods of 78 out of 97 seizures differed significantly from the characteristics seen during inter-ictal periods. The vast majority of predictive nodes were connected by most of the predictive edges, but these nodes never played a central role in the evolving epileptic networks. Interestingly, predictive nodes were entirely associated with brain regions deemed unaffected by the focal epileptic process. We propose a network mechanism for a transition into the pre-seizure state, which puts into perspective the role of the seizure onset zone in this transition and highlights the necessity to reassess current concepts for seizure generation and seizure prevention.

Inferring directed networks using a rank-based connectivity measure

Inferring the topology of a network using the knowledge of the signals of each of the interacting units is key to understanding real-world systems. One way to address this problem is using data-driven methods like cross-correlation or mutual information. However, these measures lack the ability to distinguish the direction of coupling. Here, we use a rank-based nonlinear interdependence measure originally developed for pairs of signals. This measure not only allows one to measure the strength but also the direction of the coupling. Our results for a system of coupled Lorenz dynamics show that we are able to consistently infer the underlying network for a subrange of the coupling strength and link density. Furthermore, we report that the addition of dynamical noise can benefit the reconstruction. Finally, we show an application to multichannel electroencephalographic recordings from an epilepsy patient.

Traceability and dynamical resistance of precursor of extreme events

Extreme events occur in a variety of natural, technical, and societal systems and often have catastrophic consequences. Their low-probability, high-impact nature has recently triggered research into improving our understanding of generating mechanisms, providing early warnings as well as developing control strategies. For the latter to be effective, knowledge about dynamical resistance of a system prior to an extreme event is of utmost importance. Here we introduce a novel time-series-based and non-perturbative approach to efficiently monitor dynamical resistance and apply it to high-resolution observations of brain activities from 43 subjects with uncontrollable epileptic seizures. We gain surprising insights into pre-seizure dynamical resistance of brains that also provide important clues for success or failure of measures for seizure prevention. The novel resistance monitoring perspective advances our understanding of precursor dynamics in complex spatio-temporal systems with potential applications in refining control strategies.

Localization of the Epileptogenic Zone Using Interictal MEG and Machine Learning in a Large Cohort of Drug-Resistant Epilepsy Patients

Objective: Epilepsy surgery results in seizure freedom in the majority of drug-resistant patients. To improve surgery outcome we studied whether MEG metrics combined with machine learning can improve localization of the epileptogenic zone, thereby enhancing the chance of seizure freedom.

Methods: Presurgical interictal MEG recordings of 94 patients (64 seizure-free >1y post-surgery) were analyzed to extract four metrics in source space: delta power, low-to-high-frequency power ratio, functional connectivity (phase lag index), and minimum spanning tree betweenness centrality. At the group level, we estimated the overlap of the resection area with the five highest values for each metric and determined whether this overlap differed between surgery outcomes. At the individual level, those metrics were used in machine learning classifiers (linear support vector machine (SVM) and random forest) to distinguish between resection and non-resection areas and between surgery outcome groups.

Results: The highest values, for all metrics, overlapped with the resection area in more than half of the patients, but the overlap did not differ between surgery outcome groups. The classifiers distinguished the resection areas from non-resection areas with 59.94% accuracy (95% confidence interval: 59.67–60.22%) for SVM and 60.34% (59.98–60.71%) for random forest, but could not differentiate seizure-free from not seizure-free patients [43.77% accuracy (42.08–45.45%) for SVM and 49.03% (47.25–50.82%) for random forest].

Significance: All four metrics localized the resection area but did not distinguish between surgery outcome groups, demonstrating that metrics derived from interictal MEG correspond to expert consensus based on several presurgical evaluation modalities, but do not yet localize the epileptogenic zone. Metrics should be improved such that they correspond to the resection area in seizure-free patients but not in patients with persistent seizures. It is important to test such localization strategies at an individual level, for example by using machine learning or individualized models, since surgery is individually tailored.

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.

Impact of type of intracranial EEG sensors on link strengths of evolving functional brain networks

Objective and Approach: Investigating properties of evolving functional brain networks has become a valuable tool to characterize the complex dynamics of the epileptic brain. Such networks are usually derived from electroencephalograms (EEG) recorded with sensors implanted chronically into deeper structures of the brain and/or placed onto the cortex. It is still unclear, however, whether the use of different sensors for an identification of network nodes affects properties of functional brain networks. We address this question by investigating properties of links of such networks that we characterize by assessing interactions in multi-sensor, multi-day EEG data recorded from 49 epilepsy patients during presurgical evaluation. These data allow us to study the impact of different types of sensors together with the impact of various physiologic and pathophysiologic activities on the properties of links.

MAIN RESULTS

We observe that different types of sensors differently impact on spatial means and temporal fluctuations of link strengths. Moreover, the impact depends on the relative anatomical location of sensors with respect to location and extent of sources of the prevailing activities.

SIGNIFICANCE

Type and location of sensors should be considered when constructing networks.

States and traits of neural irregularity in the age-varying human brain

Sensory representations, and thus human percepts, of the physical world are susceptible to fluctuations in brain state or “neural irregularity”. Furthermore, aging brains display altered levels of neural irregularity. We here show that a single, within-trial, information-theoretic measure (weighted permutation entropy) captures neural irregularity in the human electroencephalogram as a proxy for both, trait-like differences between individuals of varying age, and state-like fluctuations that bias perceptual decisions. First, the overall level of neural irregularity increased with participants’ age, paralleled by a decrease in variability over time, likely indexing age-related changes at structural and functional levels of brain activity. Second, states of higher neural irregularity were associated with optimized sensory encoding and a subsequently increased probability of choosing the first of two physically identical stimuli to be higher in pitch. In sum, neural irregularity not only characterizes behaviourally relevant brain states, but also can identify trait-like changes that come with age.

Surrogate-assisted identification of influences of network construction on evolving weighted functional networks

We aim at identifying factors that may affect the characteristics of evolving weighted networks derived from empirical observations. To this end, we employ various chains of analysis that are often used in field studies for a data-driven derivation and characterization of such networks. As an example, we consider fully connected, weighted functional brain networks before, during, and after epileptic seizures that we derive from multichannel electroencephalographic data recorded from epilepsy patients. For these evolving networks, we estimate clustering coefficient and average shortest path length in a time-resolved manner. Lastly, we make use of surrogate concepts that we apply at various levels of the chain of analysis to assess to what extent network characteristics are dominated by properties of the electroencephalographic recordings and/or the evolving weighted networks, which may be accessible more easily. We observe that characteristics are differently affected by the unavoidable referencing of the electroencephalographic recording, by the time-series-analysis technique used to derive the properties of network links, and whether or not networks were normalized. Importantly, for the majority of analysis settings, we observe temporal evolutions of network characteristics to merely reflect the temporal evolutions of mean interaction strengths. Such a property of the data may be accessible more easily, which would render the weighted network approach-as used here-as an overly complicated description of simple aspects of the data.

Network Inference and Maximum Entropy Estimation on Information Diagrams

Maximum entropy estimation is of broad interest for inferring properties of systems across many disciplines. Using a recently introduced technique for estimating the maximum entropy of a set of random discrete variables when conditioning on bivariate mutual informations and univariate entropies, we show how this can be used to estimate the direct network connectivity between interacting units from observed activity. As a generic example, we consider phase oscillators and show that our approach is typically superior to simply using the mutual information. In addition, we propose a nonparametric formulation of connected informations, used to test the explanatory power of a network description in general. We give an illustrative example showing how this agrees with the existing parametric formulation, and demonstrate its applicability and advantages for resting-state human brain networks, for which we also discuss its direct effective connectivity. Finally, we generalize to continuous random variables and vastly expand the types of information-theoretic quantities one can condition on. This allows us to establish significant advantages of this approach over existing ones. Not only does our method perform favorably in the undersampled regime, where existing methods fail, but it also can be dramatically less computationally expensive as the cardinality of the variables increases.