Epilepsies as dynamical diseases of brain systems: basic models of the transition between normal and epileptic activity

Neural mass modeling of slow-fast dynamics of seizure initiation and abortion

Epilepsy is a dynamic and complex neurological disease affecting about 1% of the worldwide population, among which 30% of the patients are drug-resistant. Epilepsy is characterized by recurrent episodes of paroxysmal neural discharges (the so-called seizures), which manifest themselves through a large-amplitude rhythmic activity observed in depth-EEG recordings, in particular in local field potentials (LFPs). The signature characterizing the transition to seizures involves complex oscillatory patterns, which could serve as a marker to prevent seizure initiation by triggering appropriate therapeutic neurostimulation methods. To investigate such protocols, neurophysiological lumped-parameter models at the mesoscopic scale, namely neural mass models, are powerful tools that not only mimic the LFP signals but also give insights on the neural mechanisms related to different stages of seizures. Here, we analyze the multiple time-scale dynamics of a neural mass model and explain the underlying structure of the complex oscillations observed before seizure initiation. We investigate population-specific effects of the stimulation and the dependence of stimulation parameters on synaptic timescales. In particular, we show that intermediate stimulation frequencies (>20 Hz) can abort seizures if the timescale difference is pronounced. Those results have the potential in the design of therapeutic brain stimulation protocols based on the neurophysiological properties of tissue.

Validation of virtual resection on intraoperative interictal data acquired during epilepsy surgery

OBJECTIVE

A 'Virtual resection' consists of computationally simulating the effect of an actual resection on the brain. We validated two functional connectivity based virtual resection methods with the actual connectivity measured using post-resection intraoperative recordings.

METHODS

A non-linear association index was applied to pre-resection recordings from 11 extra-temporal focal epilepsy patients. We computed two virtual resection strategies: first, a 'naive' one obtained by simply removing from the connectivity matrix the electrodes that were resected; second, a virtual resection with partialization accounting for the influence of resected electrodes on not-resected electrodes. We validated the virtual resections with two analysis: 1) We tested with a Kolmogorov-Smirnov test if the distributions of connectivity values after the virtual resections differed from the actual post-resection connectivity distribution; 2) we tested if the overall effect of the resection measured by contrasting pre-resection and post-resection connectivity values is detectable with the virtual resection approach using a Kolmogorv-Smirnov test.

RESULTS

The estimation of post-resection connectivity values did not succeed for both methods. In the second analysis, the naive method failed completely to detect the effect found between pre-resection and post-resection connectivity distributions, while the partialization method agreed with post-resection measurements in detecting a drop connectivity compared to pre-resection recordings.

CONCLUSION

Our findings suggest that the partialization technique is superior to the naive method in detecting the overall effect after the resection.

SIGNIFICANCE

We pointed out how a realistic validation based on actual post-resection recordings reveals that virtual resection methods are not yet mature to inform the clinical decision-making.

Neurostimulation stabilizes spiking neural networks by disrupting seizure-like oscillatory transitions

An improved understanding of the mechanisms underlying neuromodulatory approaches to mitigate seizure onset is needed to identify clinical targets for the treatment of epilepsy. Using a Wilson–Cowan-motivated network of inhibitory and excitatory populations, we examined the role played by intrinsic and extrinsic stimuli on the network’s predisposition to sudden transitions into oscillatory dynamics, similar to the transition to the seizure state. Our joint computational and mathematical analyses revealed that such stimuli, be they noisy or periodic in nature, exert a stabilizing influence on network responses, disrupting the development of such oscillations. Based on a combination of numerical simulations and mean-field analyses, our results suggest that high variance and/or high frequency stimulation waveforms can prevent multi-stability, a mathematical harbinger of sudden changes in network dynamics. By tuning the neurons’ responses to input, stimuli stabilize network dynamics away from these transitions. Furthermore, our research shows that such stabilization of neural activity occurs through a selective recruitment of inhibitory cells, providing a theoretical undergird for the known key role these cells play in both the healthy and diseased brain. Taken together, these findings provide new vistas on neuromodulatory approaches to stabilize neural microcircuit activity.

Recurrence quantification analysis of dynamic brain networks

Evidence suggests that brain network dynamics are a key determinant of brain function and dysfunction. Here we propose a new framework to assess the dynamics of brain networks based on recurrence analysis. Our framework uses recurrence plots and recurrence quantification analysis to characterize dynamic networks. For resting-state magnetoencephalographic dynamic functional networks (dFNs), we have found that functional networks recur more quickly in people with epilepsy than in healthy controls. This suggests that recurrence of dFNs may be used as a biomarker of epilepsy. For stereo electroencephalography data, we have found that dFNs involved in epileptic seizures emerge before seizure onset, and recurrence analysis allows us to detect seizures. We further observe distinct dFNs before and after seizures, which may inform neurostimulation strategies to prevent seizures. Our framework can also be used for understanding dFNs in healthy brain function and in other neurological disorders besides epilepsy.

Seizure forecasting and cyclic control of seizures

Epilepsy is a unique neurologic condition characterized by recurrent seizures, where causes, underlying biomarkers, triggers, and patterns differ across individuals. The unpredictability of seizures can heighten fear and anxiety in people with epilepsy, making it difficult to take part in day-to-day activities. Epilepsy researchers have prioritized developing seizure prediction algorithms to combat episodic seizures for decades, but the utility and effectiveness of prediction algorithms has not been investigated thoroughly in clinical settings. In contrast, seizure forecasts, which theoretically provide the probability of a seizure at any time (as opposed to predicting the next seizure occurrence), may be more feasible. Many advances have been made over the past decade in the field of seizure forecasting, including improvements in algorithms as a result of machine learning and exploration of non-EEG-based measures of seizure susceptibility, such as physiological biomarkers, behavioral changes, environmental drivers, and cyclic seizure patterns. For example, recent work investigating periodicities in individual seizure patterns has determined that more than 90% of people have circadian rhythms in their seizures, and many also experience multiday, weekly, or longer cycles. Other potential indicators of seizure susceptibility include stress levels, heart rate, and sleep quality, all of which have the potential to be captured noninvasively over long time scales. There are many possible applications of a seizure-forecasting device, including improving quality of life for people with epilepsy, guiding treatment plans and medication titration, optimizing presurgical monitoring, and focusing scientific research. To realize this potential, it is vital to better understand the user requirements of a seizure-forecasting device, continue to advance forecasting algorithms, and design clear guidelines for prospective clinical trials of seizure forecasting.

A taxonomy of seizure dynamotypes

Seizures are a disruption of normal brain activity present across a vast range of species and conditions. We introduce an organizing principle that leads to the first objective Taxonomy of Seizure Dynamics (TSD) based on bifurcation theory. The ‘dynamotype’ of a seizure is the dynamic composition that defines its observable characteristics, including how it starts, evolves and ends. Analyzing over 2000 focal-onset seizures from multiple centers, we find evidence of all 16 dynamotypes predicted in TSD. We demonstrate that patients’ dynamotypes evolve during their lifetime and display complex but systematic variations including hierarchy (certain types are more common), non-bijectivity (a patient may display multiple types) and pairing preference (multiple types may occur during one seizure). TSD provides a way to stratify patients in complement to present clinical classifications, a language to describe the most critical features of seizure dynamics, and a framework to guide future research focused on dynamical properties.

Epileptic seizures have been recognized for centuries. But it was only in the 1930s that it was realized that seizures are the result of out-of-control electrical activity in the brain. By placing electrodes on the scalp, doctors can identify when and where in the brain a seizure begins. But they cannot tell much about how the seizure behaves, that is, how it starts, stops or spreads to other areas. This makes it difficult to control and prevent seizures. It also helps explain why almost a third of patients with epilepsy continue to have seizures despite being on medication.

Saggio, Crisp et al. have now approached this problem from a new angle using methods adapted from physics and engineering. In these fields, “dynamics research” has been used with great success to predict and control the behavior of complex systems like electrical power grids. Saggio, Crisp et al. reasoned that applying the same approach to the brain would reveal the dynamics of seizures and that such information could then be used to categorize seizures into groups with similar properties. This would in effect create for seizures what the periodic table is for the elements.

Applying the dynamics research method to seizure data from more than a hundred patients from across the world revealed 16 types of seizure dynamics. These “dynamotypes” had distinct characteristics. Some were more common than others, and some tended to occur together. Individual patients showed different dynamotypes over time. By constructing a way to classify seizures based on the relationships between the dynamotypes, Saggio, Crisp et al. provide a new tool for clinicians and researchers studying epilepsy.

Previous clinical tools have focused on the physical symptoms of a seizure (referred to as the phenotype) or its potential genetic causes (genotype). The current approach complements these tools by adding the dynamotype: how seizures start, spread and stop in the brain. This approach has the potential to lead to new branches of research and better understanding and treatment of seizures.

Identification of global and local states during seizures using quantitative functional connectivity and recurrence plot analysis

INTRODUCTION

As a dynamical system, the brain constantly modulates its state and epileptic seizures have been hypothesized to be low dimensional periodic states of the brain. With this assumption, seizures have previously been investigated to identify patterns of these recurrent states; however, these attempts have generated conflicting results. These discrepant observations led us to reconsider the dynamic of state transitions during seizures.

METHODS

Using intracerebral recordings of 17 refractory epilepsy patients assessed prior to surgery, we studied ictal states with several state-of-the-art methods in order to investigate their dynamics. Global states were identified based on distinct functional connectivity measures in the time domain, frequency domain, and phase-space. We further investigated the state transitions in different brain regions locally using a univariate measure based on dynamical system analysis named the Recurrence Plot (RP).

RESULTS

For the ictal period, we detected lower global state transition rates compared to pre- and post-ictal periods (p < 0.05 for seizure-free (SF) and p > 0.05 for non-seizure-free (NSF) groups post-surgery); however, the structure of RPs pointed towards higher state transition rates in some regions like the seizure-onset-zone (p < 0.001 for SF and p > 0.05 for NSF group). Moreover, a direct comparison of state transition dynamics between SF and NSF patients revealed different patterns for local state transitions between SF and NSF patients (p < 0.05 for seizure-onset-zone while p > 0.05 for other regions) and no significant difference in global state transition rates (p > 0.05).

CONCLUSION

Our findings pointed to distinct dynamics for state transitions at different spatial scales. While the pattern of global state transitions led to the conclusion that the brain changes state less frequently during ictal activity, locally, it experienced a higher rate of state transition. Furthermore, our results for different patterns of state transitions in the seizure-onset-zone between SF and NSF patients could have a practical application in predicting surgical outcome.

Epileptic Seizures: Glia-Neuron Interactions For Better or For Worse

Investigations of the mechanisms generating epileptic seizures have primarily focused on neurons. However, more systemic research of brain circuits has highlighted an important role of non-neuronal cells such as glia in the genesis and spreading of generalized seizures in the brain.

The Role of Excitability and Network Structure in the Emergence of Focal and Generalized Seizures

Epileptic seizures are generally classified as either focal or generalized. It had been traditionally assumed that focal seizures imply localized brain abnormalities, whereas generalized seizures involve widespread brain pathologies. However, recent evidence suggests that large-scale brain networks are involved in the generation of focal seizures, and generalized seizures can originate in localized brain regions. Herein we study how network structure and tissue heterogeneities underpin the emergence of focal and widespread seizure dynamics. Mathematical modeling of seizure emergence in brain networks enables the clarification of the characteristics responsible for focal and generalized seizures. We consider neural mass network dynamics of seizure generation in exemplar synthetic networks and we measure the variance in ictogenicity across the network. Ictogenicity is defined as the involvement of network nodes in seizure activity, and its variance is used to quantify whether seizure patterns are focal or widespread across the network. We address both the influence of network structure and different excitability distributions across the network on the ictogenic variance. We find that this variance depends on both network structure and excitability distribution. High variance, i.e., localized seizure activity, is observed in networks highly heterogeneous with regard to the distribution of connections or excitabilities. However, networks that are both heterogeneous in their structure and excitability can underlie the emergence of generalized seizures, depending on the interplay between structure and excitability. Thus, our results imply that the emergence of focal and generalized seizures is underpinned by an interplay between network structure and excitability distribution.

Differences Between Interictal and Ictal Generalized Spike-Wave Discharges in Childhood Absence Epilepsy: A MEG Study

Purpose: To investigate the differences between interictal and ictal generalized spike-wave discharges (GSWDs) for insights on how epileptic activity propagates and the physiopathological mechanisms underlying childhood absence epilepsy (CAE).

Methods: Twenty-five patients with CAE were studied using magnetoencephalography (MEG). MEG data were digitized at 6,000 Hz during the interictal and ictal GSWDs. GSWDs were analyzed at both neural magnetic source levels and functional connectivity (FC) in multifrequency bands: delta (1–4 Hz), theta (4–8 Hz), alpha (8–12 Hz), beta (12–30 Hz), gamma (30–80 Hz), ripple (80–250 Hz), and fast ripple (250–500 Hz). Brain FC was studied with the posterior cingulate cortex/precuneus (PCC/pC) as the seed region.

Results: The magnetic source of interictal GSWDs mainly locates in the PCC/pC region at 4–8 and 8–12 Hz, while that of ictal GSWDs mainly locates in the medial frontal cortex (MFC) at 80–250 Hz. There were statistically significant differences between interictal and ictal GSWDs (p < 0.05). The FC network involving the PCC/pC showed strong connections in the anterior-posterior pathways (mainly with the frontal cortex) at 80–250 Hz during ictal GSWDs, while the interictal GSWDs FC were mostly limited to the posterior cortex region. There was no significant difference in the magnetic source strength among interictal and ictal GSWDs at all bandwidths.

Conclusions: There are significant disparities in the source localization and FC between interictal and ictal GSWDs. Low-frequency activation in the PCC/pC during inhibition of seizures possibly relates to the maintenance of consciousness during interictal GSWDs. High-frequency oscillations (HFOs) of the MFC during CAE may associate with the inducing or occurrence of GSWDs. Weakened network connections may be in favor of preventing overexcitability and relates to the termination of GSWDs.

Effect of Repetitive Transcranial Magnetic Stimulation on Seizure Frequency and Epileptiform Discharges in Drug-Resistant Epilepsy: A Meta-Analysis

Background and Purpose

The role of low-frequency repetitive transcranial stimulation (rTMS) in drug-resistant epilepsy (DRE) has been conflicting and inconclusive in previous clinical trials. This meta-analysis evaluated the efficacy of rTMS on seizure frequency and epileptiform discharges in DRE.

Methods

A standard meta-analysis protocol was registered in the International Prospective Register of Ongoing Systematic Reviews (PROSPERO: CRD42018088544). After performing a comprehensive literature search using specific keywords in MEDLINE, the Cochrane database, and the International Clinical Trial Registry Platform (ICTRP), reviewers assessed the eligibility and extracted data from seven relevant clinical trials. Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) guidelines were followed in the selection, analysis, and reporting of findings. A random-effects model was used to estimate the effect size as the mean difference in seizure frequency and interictal epileptiform discharges between the groups. Quality assessment was performed using a risk-of-bias assessment tool, and a meta-regression was used to identify the variables that probably influenced the effect size.

Results

The random-effects model analysis revealed a pooled effect size of −5.96 (95% CI= −8.98 to −2.94), significantly favoring rTMS stimulation (p=0.0001) over the control group with regard to seizure frequency. The overall effect size for interictal epileptiform discharges also significantly favored rTMS stimulation (p<0.0001), with an overall effect size of −9.36 (95% CI=−13.24 to −5.47). In the meta-regression, the seizure frequency worsened by 2.00±0.98 (mean±SD, p=0.042) for each week-long lengthening of the posttreatment follow-up period, suggesting that rTMS exerts only a short-term effect.

Conclusions

This meta-analysis shows that rTMS exerts a significant beneficial effect on DRE by reducing both the seizure frequency and interictal epileptiform discharges. However, the meta-regression revealed only an ephemeral effect of rTMS.

Inhibitory Network Bistability Explains Increased Interneuronal Activity Prior to Seizure Onset

Recent experimental literature has revealed that GABAergic interneurons exhibit increased activity prior to seizure onset, alongside additional evidence that such activity is synchronous and may arise abruptly. These findings have led some to hypothesize that this interneuronal activity may serve a causal role in driving the sudden change in brain activity that heralds seizure onset. However, the mechanisms predisposing an inhibitory network toward increased activity, specifically prior to ictogenesis, without a permanent change to inputs to the system remain unknown. We address this question by comparing simulated inhibitory networks containing control interneurons and networks containing hyperexcitable interneurons modeled to mimic treatment with 4-Aminopyridine (4-AP), an agent commonly used to model seizures in vivo and in vitro. Our in silico study demonstrates that model inhibitory networks with 4-AP interneurons are more prone than their control counterparts to exist in a bistable state in which asynchronously firing networks can abruptly transition into synchrony driven by a brief perturbation. This transition into synchrony brings about a corresponding increase in overall firing rate. We further show that perturbations driving this transition could arise in vivo from background excitatory synaptic activity in the cortex. Thus, we propose that bistability explains the increase in interneuron activity observed experimentally prior to seizure via a transition from incoherent to coherent dynamics. Moreover, bistability explains why inhibitory networks containing hyperexcitable interneurons are more vulnerable to this change in dynamics, and how such networks can undergo a transition without a permanent change in the drive. We note that while our comparisons are between networks of control and ictogenic neurons, the conclusions drawn specifically relate to the unusual dynamics that arise prior to seizure, and not seizure onset itself. However, providing a mechanistic explanation for this phenomenon specifically in a pro-ictogenic setting generates experimentally testable hypotheses regarding the role of inhibitory neurons in pre-ictal neural dynamics, and motivates further computational research into mechanisms underlying a newly hypothesized multi-step pathway to seizure initiated by inhibition.

Excitation and Inhibition Balance Underlying Epileptiform Activity

OBJECTIVE

The phenomenon of postictal generalized EEG suppression state (PGES) - a period with suppressed activity following seizure termination and has been found to be associated with sudden unexpected death in epilepsy - remains poorly understood. This article aims to examine the how the balance of excitation and inhibition (E/I balance) affect the dynamics of seizure and PGES.

METHODS

A network of 1000 Izhikevich model neurons was developed and only the strengths of synaptic connections were adjusted to recreate the dynamics observed in recordings of seizure and PGES from human patients.

RESULTS

A rapid rise followed by a slow decay of dominant frequency was observed in iEEG recordings of ictal periods and reproduced in the simulated local field potential by changing the E/I balance of the model network. The rate of this dominant frequency evolution was quantified by a single measure, β, which was found to have a significant rank correlation with the duration of PGES in iEEG data and the rate of E/I balance shift in the model. Significance and Conclusion: (i) highlighting the importance of E/I balance in the dynamics of seizure and PGES; (ii) suggesting the measure, β, as a marker for PGES and the shift in E/I balance as a neural correlate for this marker.

Imaging epilepsy in larval zebrafish

Our understanding of the genetic aetiology of paediatric epilepsies has grown substantially over the last decade. However, in order to translate improved diagnostics to personalised treatments, there is an urgent need to link molecular pathophysiology in epilepsy to whole-brain dynamics in seizures. Zebrafish have emerged as a promising new animal model for epileptic seizure disorders, with particular relevance for genetic and developmental epilepsies. As a novel model organism for epilepsy research they combine key advantages: the small size of larval zebrafish allows high throughput in vivo experiments; the availability of advanced genetic tools allows targeted modification to model specific human genetic disorders (including genetic epilepsies) in a vertebrate system; and optical access to the entire central nervous system has provided the basis for advanced microscopy technologies to image structure and function in the intact larval zebrafish brain. There is a growing body of literature describing and characterising features of epileptic seizures and epilepsy in larval zebrafish. Recently genetically encoded calcium indicators have been used to investigate the neurobiological basis of these seizures with light microscopy. This approach offers a unique window into the multiscale dynamics of epileptic seizures, capturing both whole-brain dynamics and single-cell behaviour concurrently. At the same time, linking observations made using calcium imaging in the larval zebrafish brain back to an understanding of epileptic seizures largely derived from cortical electrophysiological recordings in human patients and mammalian animal models is non-trivial. In this review we briefly illustrate the state of the art of epilepsy research in zebrafish with particular focus on calcium imaging of epileptic seizures in the larval zebrafish. We illustrate the utility of a dynamic systems perspective on the epileptic brain for providing a principled approach to linking observations across species and identifying those features of brain dynamics that are most relevant to epilepsy. In the following section we survey the literature for imaging features associated with epilepsy and epileptic seizures and link these to observations made from humans and other more traditional animal models. We conclude by identifying the key challenges still facing epilepsy research in the larval zebrafish and indicate strategies for future research to address these and integrate more directly with the themes and questions that emerge from investigating epilepsy in other model systems and human patients.

Seizure prediction and intervention

Epilepsy treatment is challenging due to a lack of essential diagnostic tools, including methods for reliable seizure detection in the ambulatory setting, to assess seizure risk over time and to monitor treatment efficacy. This lack of objective diagnostics constitutes a significant barrier to better treatments, raises methodological concerns about the antiseizure medication evaluation process and, to patients, is a main issue contributing to the disease burden. Recent years have seen rapid progress towards better diagnostics that meet these needs of epilepsy patients and clinicians. Availability of comprehensive data and the rise of more powerful computational analysis methods have driven progress in this area. Here, we provide an overview on data- and theory-driven approaches aimed at identifying methods to reliably detect and forecast seizures as well as to monitor brain excitability and treatment efficacy in epilepsy. We provide a particular account on neural criticality, the hypothesis that cortical networks may be poised in a critical state at the boundary between different types of dynamics, and discuss its role in informing diagnostics to track cortex excitability and seizure risk in recent experiments. With the further expansion of digitalization in medicine, tele-medicine and long-term, ambulatory monitoring, these computationally based methods may gain more relevance in epilepsy in the future. This article is part of the special issue entitled 'New Epilepsy Therapies for the 21st Century - From Antiseizure Drugs to Prevention, Modification and Cure of Epilepsy'.

Magnetoencephalography imaging of high frequency oscillations strengthens presurgical localization and outcome prediction

In patients with medically refractory epilepsy, resective surgery is the mainstay of therapy to achieve seizure freedom. However, ∼20-50% of cases have intractable seizures post-surgery due to the imprecise determination of epileptogenic zone. Recent intracranial studies suggest that high frequency oscillations between 80 and 200 Hz could serve as one of the consistent epileptogenicity biomarkers for localization of the epileptogenic zone. However, these high frequency oscillations are not adopted in the clinical setting because of difficult non-invasive detection. Here, we investigated non-invasive detection and localization of high frequency oscillations and its clinical utility in accurate pre-surgical assessment and post-surgical outcome prediction. We prospectively recruited 52 patients with medically refractory epilepsy who underwent standard pre-surgical workup including magnetoencephalography (MEG) followed by resective surgery after determination of the epileptogenic zone. The post-surgical outcome was assessed after 22.14 ± 10.05 months. Interictal epileptic spikes were expertly identified, and interictal epileptic oscillations across the neural activity frequency spectrum from 8 to 200 Hz were localized using adaptive spatial filtering methods. Localization results were compared with epileptogenic zone and resected cortex for congruence assessment and validated against the clinical outcome. The concordance rate of high frequency oscillations sources (80-200 Hz) with the presumed epileptogenic zone and the resected cortex were 75.0% and 78.8%, respectively, which is superior to that of other frequency bands and standard dipole fitting methods. High frequency oscillation sources corresponding with the resected cortex, had the best sensitivity of 78.0%, positive predictive value of 100% and an accuracy of 78.84% to predict the patient's surgical outcome, among all other frequency bands. If high frequency oscillation sources were spatially congruent with resected cortex, patients had an odds ratio of 5.67 and 82.4% probability of achieving a favourable surgical outcome. If high frequency oscillations sources were discordant with the epileptogenic zone or resection area, patient has an odds ratio of 0.18 and only 14.3% probability of achieving good outcome, and mostly tended to have an unfavourable outcome (χ2 = 5.22; P = 0.02; φ = -0.317). In receiver operating characteristic curve analyses, only sources of high-frequency oscillations demonstrated the best sensitivity and specificity profile in determining the patient's surgical outcome with area under the curve of 0.76, whereas other frequency bands indicate a poor predictive performance. Our study is the first non-invasive study to detect high frequency oscillations, address the efficacy of high frequency oscillations over the different neural oscillatory frequencies, localize them and clinically validate them with the post-surgical outcome in patients with medically refractory epilepsy. The evidence presented in the current study supports the fact that HFOs might significantly improve the presurgical assessment, and post-surgical outcome prediction, where it could widely be used in a clinical setting as a non-invasive biomarker.

Acute Focal Seizures Start As Local Synchronizations of Neuronal Ensembles

Understanding seizure formation and spread remains a critical goal of epilepsy research. We used fast in vivo two-photon calcium imaging in male mouse neocortex to reconstruct, with single-cell resolution, the dynamics of acute (4-aminopyridine) focal cortical seizures as they originate within a spatially confined seizure initiation site (intrafocal region), and subsequently propagate into neighboring cortical areas (extrafocal region). We find that seizures originate as local neuronal ensembles within the initiation site. This abnormal hyperactivity engages increasingly larger areas in a saltatory fashion until it breaks into neighboring cortex, where it proceeds smoothly and is then detected electrophysiologically (LFP). Interestingly, PV inhibitory interneurons have spatially heterogeneous activity in intrafocal and extrafocal territories, ruling out a simple role of inhibition in seizure formation and spread. We propose a two-step model for the progression of focal seizures, where neuronal ensembles activate first, generating a microseizure, followed by widespread neural activation in a traveling wave through neighboring cortex during macroseizures.SIGNIFICANCE STATEMENT We have used calcium imaging in mouse sensory cortex in vivo to reconstruct the onset of focal seizures elicited by local injection of the chemoconvulsant 4-aminopyridine. We demonstrate at cellular resolution that acute focal seizures originate as increasingly synchronized local neuronal ensembles. Because of its spatial confinement, this process may at first be undetectable even by nearby LFP electrodes. Further, we establish spatial footprints of local neural subtype activity that correspond to consecutive steps of seizure microprogression. Such footprints could facilitate determining the recording location (e.g., inside/outside an epileptogenic focus) in high-resolution studies, even in the absence of a priori knowledge about where exactly a seizure started.

Unified dynamics of interictal events and absence seizures

The dynamics of interictal events between absence seizures and their relationship to seizures themselves are investigated by employing a neural field model of the corticothalamic system. Interictal events are modeled as being due to transient parameter excursions beyond the seizure threshold, in the present case by sufficiently temporally varying the connection strength between the cerebral cortex and the thalamus. Increasing connection strength drives the system into ∼3-Hz seizure oscillations via a supercritical Hopf bifurcation once the linear instability threshold is passed. Depending on the time course of the excursion above threshold, different interictal activity event dynamics are seen in the time series of corticothalamic fields. These resemble experimental interictal time series observed via electroencephalography. It is found that the morphology of these events depends on the magnitude and duration of the excursion above threshold. For a large-amplitude excursion of short duration, events resemble interictal spikes, where one large spike is seen, followed by small damped oscillations. For a short excursion with long duration, events like observed interictal periodic sharp waves are seen. When both amplitude and duration above threshold are large, seizure oscillations are seen. Using these outcomes, proximity to seizure can be estimated and tracked.

Unified analysis of global and focal aspects of absence epilepsy via neural field theory of the corticothalamic system

Absence epilepsy is characterized by a sudden paroxysmal loss of consciousness accompanied by oscillatory activity propagating over many brain areas. Although primary generalized absence seizures are supported by the global corticothalamic system, converging experimental evidence supports a focal theory of absence epilepsy. Here a physiology-based corticothalamic model is investigated with spatial heterogeneity due to focal epilepsy to unify global and focal aspects of absence epilepsy. Numeric and analytic calculations are employed to investigate the emergent spatiotemporal dynamics as well as their underlying dynamical mechanisms. They can be categorized into three scenarios: suppressed epilepsy, focal seizures, or generalized seizures, as summarized from a phase diagram vs focal width and characteristic axon range. The corresponding temporal frequencies and spatial extents of cortical waves in generalized seizures and focal seizures agree well with experimental observations of global and focal aspects of absence epilepsy, respectively. The emergence of the spatiotemporal dynamics corresponding to focal seizures provides a biophysical explanation of the temporally higher frequency but spatially more localized cortical waves observed in genetic rat models that display characteristics of human absence epilepsy. Predictions are also presented for further experimental test.

Seizure prediction - ready for a new era

Epilepsy is a common disorder characterized by recurrent seizures. An overwhelming majority of people with epilepsy regard the unpredictability of seizures as a major issue. More than 30 years of international effort have been devoted to the prediction of seizures, aiming to remove the burden of unpredictability and to couple novel, time-specific treatment to seizure prediction technology. A highly influential review published in 2007 concluded that insufficient evidence indicated that seizures could be predicted. Since then, several advances have been made, including successful prospective seizure prediction using intracranial EEG in a small number of people in a trial of a real-time seizure prediction device. In this Review, we examine advances in the field, including EEG databases, seizure prediction competitions, the prospective trial mentioned and advances in our understanding of the mechanisms of seizures. We argue that these advances, together with statistical evaluations, set the stage for a resurgence in efforts towards the development of seizure prediction methodologies. We propose new avenues of investigation involving a synergy between mechanisms, models, data, devices and algorithms and refine the existing guidelines for the development of seizure prediction technology to instigate development of a solution that removes the burden of the unpredictability of seizures.

Plasticity facilitates pattern selection of networks of chemical oscillations

Rotating wave synchronization patterns are explored with a ring of 20 electrochemical oscillators during nickel electrodissolution in sulfuric acid. With desynchronized initial states, coupling alone yields predominance of nonrotating solutions, i.e., in-phase synchronization. An experimental technique is presented in which, through a combination of temporary alterations in topology, the application of global feedback provides rotational solutions. With phase repulsive global feedback, the in-phase synchronization is destabilized and a rotating wave is obtained. This feedback induced rotating wave can be employed to establish an initial condition for the rotating wave with coupling only. Higher order rotating solutions with 2, 3, and 4 waves corotating around the ring are observed, where the initial conditions are generated by temporary network rewiring to a structure with 2, 3, and 4 loops, respectively, and by global feedback. The experimental observations are supported by numerical simulations with a phase model. The results indicate that while network plasticity is thought to be significant in the operation of neural systems, it can also play a role in pattern selection of chemical systems.

Oscillations in cortico-basal ganglia circuits: implications for Parkinson’s disease and other neurologic and psychiatric conditions

Cortico-basal ganglia circuits are thought to play a crucial role in the selection and control of motor behaviors and have also been implicated in the processing of motivational content and in higher cognitive functions. During the last two decades, electrophysiological recordings in basal ganglia circuits have shown that several disease conditions are associated with specific changes in the temporal patterns of neuronal activity. In particular, synchronized oscillations have been a frequent finding suggesting that excessive synchronization of neuronal activity may be a pathophysiological mechanism involved in a wide range of neurologic and psychiatric conditions. We here review the experimental support for this hypothesis primarily in relation to Parkinson’s disease but also in relation to dystonia, essential tremor, epilepsy, and psychosis/schizophrenia.

Robust closed-loop control of spike-and-wave discharges in a thalamocortical computational model of absence epilepsy

In this paper, we investigate the abatement of spike-and-wave discharges in a thalamocortical model using a closed-loop brain stimulation method. We first explore the complex states and various transitions in the thalamocortical computational model of absence epilepsy by using bifurcation analysis. We demonstrate that the Hopf and double cycle bifurcations are the key dynamical mechanisms of the experimental observed bidirectional communications during absence seizures through top-down cortical excitation and thalamic feedforward inhibition. Then, we formulate the abatement of epileptic seizures to a closed-loop tracking control problem. Finally, we propose a neural network based sliding mode feedback control system to drive the dynamics of pathological cortical area to track the desired normal background activities. The control system is robust to uncertainties and disturbances, and its stability is guaranteed by Lyapunov stability theorem. Our results suggest that the seizure abatement can be modeled as a tracking control problem and solved by a robust closed-loop control method, which provides a promising brain stimulation strategy.

Non-Linear Dynamical Analysis of Resting Tremor for Demand-Driven Deep Brain Stimulation

Parkinson's Disease (PD) is currently the second most common neurodegenerative disease. One of the most characteristic symptoms of PD is resting tremor. Local Field Potentials (LFPs) have been widely studied to investigate deviations from the typical patterns of healthy brain activity. However, the inherent dynamics of the Sub-Thalamic Nucleus (STN) LFPs and their spatiotemporal dynamics have not been well characterized. In this work, we study the non-linear dynamical behaviour of STN-LFPs of Parkinsonian patients using ε -recurrence networks. RNs are a non-linear analysis tool that encodes the geometric information of the underlying system, which can be characterised (for example, using graph theoretical measures) to extract information on the geometric properties of the attractor. Results show that the activity of the STN becomes more non-linear during the tremor episodes and that ε -recurrence network analysis is a suitable method to distinguish the transitions between movement conditions, anticipating the onset of the tremor, with the potential for application in a demand-driven deep brain stimulation system.

The role that choice of model plays in predictions for epilepsy surgery

Mathematical modelling has been widely used to predict the effects of perturbations to brain networks. An important example is epilepsy surgery, where the perturbation in question is the removal of brain tissue in order to render the patient free of seizures. Different dynamical models have been proposed to represent transitions to ictal states in this context. However, our choice of which mathematical model to use to address this question relies on making assumptions regarding the mechanism that defines the transition from background to the seizure state. Since these mechanisms are unknown, it is important to understand how predictions from alternative dynamical descriptions compare. Herein we evaluate to what extent three different dynamical models provide consistent predictions for the effect of removing nodes from networks. We show that for small, directed, connected networks the three considered models provide consistent predictions. For larger networks, predictions are shown to be less consistent. However consistency is higher in networks that have sufficiently large differences in ictogenicity between nodes. We further demonstrate that heterogeneity in ictogenicity across nodes correlates with variability in the number of connections for each node.

Dynamic origin of spike and wave discharges in the brain

Spike and wave discharges are the main electrographic characteristic of a number of epileptic brain disorders including childhood absence epilepsy and photosensitive epilepsy. The basic dynamic mechanism that underlies the occurrence of these abnormal electrical patterns in the brain is not well understood. The current paper aims to provide a dynamic explanation for features and generation mechanism of spike and wave discharges in the brain. The main proposition of this study is that epileptic seizures could be interpreted as a resonance phenomenon rather than a limit cycle behavior. To shows this, a revised version of Jansen-Rit neural mass model is employed. The system can switch between monostable and bistable regimes, which are considered in this paper as wake and sleep states of the brain, respectively. In particular, it is shown that, in monostable region, the model can depict the alpha rhythm and alpha rhythm suppression due to mental activity. Frequency responses of the model near the bistable regime demonstrate that high amplitude harmonic excitation may lead to spike and wave like oscillations. Based on the computational results and the concept of stochastic resonance, a model for absence epilepsy is presented which can simulate spontaneous transitions between ictal and interictal states. Finally, it is shown that spike and wave discharges during epileptic seizures can be explained as a resonance phenomenon in a nonlinear system.

A Straw Can Break a Neural Network's Back and Lead to Seizures-But Only When Delivered at the Right Time

Loss of Neuronal Network Resilience Precedes Seizures and Determines the Ictogenic Nature of Interictal Synaptic Perturbations

Chang WC, Kudlacek J, Hlinka J, et al. Nat Neurosci. 2018; 21(12):1742-1752. doi:10.1038/s41593-018-0278-y. PMID: 30482946.

The mechanism of seizure emergence and the role of brief interictal epileptiform discharges (IEDs) in seizure generation are 2 of the most important unresolved issues in modern epilepsy research. We found that the transition to seizure is not a sudden phenomenon, but is instead a slow process that is characterized by the progressive loss of neuronal network resilience. From a dynamical perspective, the slow transition is governed by the principles of critical slowing, a robust natural phenomenon that is observable in systems characterized by transitions between dynamical regimes. In epilepsy, this process is modulated by synchronous synaptic input from IEDs. The IEDs are external perturbations that produce phasic changes in the slow transition process and exert opposing effects on the dynamics of a seizure-generating network, causing either antiseizure or proseizure effects. We found that the multifaceted nature of IEDs is defined by the dynamical state of the network at the moment of the discharge occurrence.

Patient-Specific Seizure Detection Using Nonlinear Dynamics and Nullclines

Nonlinear dynamics has recently been extensively used to study epilepsy due to the complex nature of the neuronal systems. This study presents a novel method that characterizes the dynamic behavior of pediatric seizure events and introduces a systematic approach to locate the nullclines on the phase space when the governing differential equations are unknown. Nullclines represent the locus of points in the solution space where the components of the velocity vectors are zero. A simulation study over 5 benchmark nonlinear systems with well-known differential equations in three-dimensional exhibits the characterization efficiency and accuracy of the proposed approach that is solely based on the reconstructed solution trajectory. Due to their unique characteristics in the nonlinear dynamics of epilepsy, discriminative features can be extracted based on the nullclines concept. Using a limited training data (only 25% of each EEG record) in order to mimic the real-world clinical practice, the proposed approach achieves 91.15% average sensitivity and 95.16% average specificity over the benchmark CHB-MIT dataset. Together with an elegant computational efficiency, the proposed approach can, therefore, be an automatic and reliable solution for patient-specific seizure detection in long EEG recordings.

Automated epileptic seizure detection based on break of excitation/inhibition balance

Physiological models are attractive for seizure detection, as their parameters are related to physiological meanings. We propose an algorithm to early detect epileptic seizures based on automatic estimation of average synaptic gains (excitatory Ae, slow and fast inhibitory B and G) by combining clinical data with a neural mass model. Three indices (Ae/B, Ae/G and Ae/(B + G)), all related to excitation/inhibition balance, were calculated and used as cues to detect seizures. A simple thresholding method was employed. We evaluated the algorithm against the manual scoring of a human expert on intracranial EEG samples from 23 patients suffering from different types of epilepsy. Best performance was achieved using Ae/(B + G) as a cue, i.e. excitation/(slow + fast) inhibition, on temporal lobe epilepsy (TLE) patients. A leave-one-out cross-validation showed that the algorithm achieved 92.98% sensitivity for TLE patients. The median false positive rate was 0.16 per hour, and median detection delay was 14.5 s. Of interest, the threshold values determined by a leave-one-out cross-validation did nearly not vary among TLE patients, suggesting a general excitation/inhibition balance baseline in TLE patients. The same approach could be used with other types of epilepsy by adapting the neural mass model to these types.

Outgrowing seizures in Childhood Absence Epilepsy: time delays and bistability

We formulate a conductance-based model for a 3-neuron motif associated with Childhood Absence Epilepsy (CAE). The motif consists of neurons from the thalamic relay (TC) and reticular nuclei (RT) and the cortex (CT). We focus on a genetic defect common to the mouse homolog of CAE which is associated with loss of GABA_A receptors on the TC neuron, and the fact that myelination of axons as children age can increase the conduction velocity between neurons. We show the combination of low GABA_A mediated inhibition of TC neurons and the long corticothalamic loop delay gives rise to a variety of complex dynamics in the motif, including bistability. This bistability disappears as the corticothalamic conduction delay shortens even though GABA_A activity remains impaired. Thus the combination of deficient GABA_A activity and changing axonal myelination in the corticothalamic loop may be sufficient to account for the clinical course of CAE.

Computer modelling of connectivity change suggests epileptogenesis mechanisms in idiopathic generalised epilepsy

Patients with idiopathic generalised epilepsy (IGE) typically have normal conventional magnetic resonance imaging (MRI), hence diagnosis based on MRI is challenging. Anatomical abnormalities underlying brain dysfunctions in IGE are unclear and their relation to the pathomechanisms of epileptogenesis is poorly understood.

In this study, we applied connectometry, an advanced quantitative neuroimaging technique for investigating localised changes in white-matter tissues in vivo. Analysing white matter structures of 32 subjects we incorporated our in vivo findings in a computational model of seizure dynamics to suggest a plausible mechanism of epileptogenesis.

Patients with IGE have significant bilateral alterations in major white-matter fascicles. In the cingulum, fornix, and superior longitudinal fasciculus, tract integrity is compromised, whereas in specific parts of tracts between thalamus and the precentral gyrus, tract integrity is enhanced in patients. Combining these alterations in a logistic regression model, we computed the decision boundary that discriminated patients and controls. The computational model, informed with the findings on the tract abnormalities, specifically highlighted the importance of enhanced cortico-reticular connections along with impaired cortico-cortical connections in inducing pathological seizure-like dynamics.

We emphasise taking directionality of brain connectivity into consideration towards understanding the pathological mechanisms; this is possible by combining neuroimaging and computational modelling. Our imaging evidence of structural alterations suggest the loss of cortico-cortical and enhancement of cortico-thalamic fibre integrity in IGE. We further suggest that impaired connectivity from cortical regions to the thalamic reticular nucleus offers a therapeutic target for selectively modifying the brain circuit for reversing the mechanisms leading to epileptogenesis.

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Significant focal alterations along major white-matter fascicles in IGE patients are characterised.

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Increased white matter integrity found in thalamo-cortical connections.

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Decreased white matter integrity found in cortico-cortical connections.

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Disease mechanism is investigated by combining the neuroimaging findings with a dynamical model of seizure activity.

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Model implicates cortical projections to the thalamic reticular nucleus in IGE.

Loss of neuronal network resilience precedes seizures and determines the ictogenic nature of interictal synaptic perturbations

The mechanism of seizure emergence and the role of brief interictal epileptiform discharges (IEDs) in seizure generation are two of the most important unresolved issues in modern epilepsy research. We found that the transition to seizure is not a sudden phenomenon, but is instead a slow process that is characterized by the progressive loss of neuronal network resilience. From a dynamical perspective, the slow transition is governed by the principles of critical slowing, a robust natural phenomenon that is observable in systems characterized by transitions between dynamical regimes. In epilepsy, this process is modulated by synchronous synaptic input from IEDs. IEDs are external perturbations that produce phasic changes in the slow transition process and exert opposing effects on the dynamics of a seizure-generating network, causing either anti-seizure or pro-seizure effects. We found that the multifaceted nature of IEDs is defined by the dynamical state of the network at the moment of the discharge occurrence.

Simulation Study of Intermittent Axonal Block and Desynchronization Effect Induced by High-Frequency Stimulation of Electrical Pulses

Deep brain stimulation (DBS) has been successfully used in treating neural disorders in brain, such as Parkinson’s disease and epilepsy. However, the precise mechanisms of DBS remain unclear. Regular DBS therapy utilizes high-frequency stimulation (HFS) of electrical pulses. Among all of neuronal elements, axons are mostly inclined to be activated by electrical pulses. Therefore, the response of axons may play an important role in DBS treatment. To study the axonal responses during HFS, we developed a computational model of myelinated axon to simulate sequences of action potentials generated in single and multiple axons (an axon bundle) by stimulations. The stimulations are applied extracellularly by a point source of current pulses with a frequency of 50–200 Hz. Additionally, our model takes into account the accumulation of potassium ions in the peri-axonal spaces. Results show that the increase of extracellular potassium generates intermittent depolarization block in the axons during HFS. Under the state of alternate block and recovery, axons fire action potentials at a rate far lower than the frequency of stimulation pulses. In addition, the degree of axonal block is highly related to the distance between the axons and the stimulation point. The differences in the degree of block for individual axons in a bundle result in desynchronized firing among the axons. Stimulations with higher frequency and/or greater intensity can induce axonal block faster and increase the desynchronization effect on axonal firing. Presumably, the desynchronized axonal activity induced by HFS could generate asynchronous activity in the population of target neurons downstream thereby suppressing over-synchronized firing of neurons in pathological conditions. The desynchronization effect generated by intermittent activation of axons may be crucial for DBS therapy. The present study provides new insights into the mechanisms of DBS, which is significant for advancing the application of DBS.

Deep brain stimulation probing performance is enhanced by pairing stimulus with epileptic seizure

The unpredictability of spontaneous and recurrent seizures significantly impairs the quality of life of patients with epilepsy. Probing neural network excitability with deep brain electrical stimulation (DBS) has shown promising results predicting pathological shifts in brain states. This work presents a proof-of-principal that active electroencephalographic (EEG) probing, as a seizure predictive tool, is enhanced by pairing DBS and the electrographic seizure itself. The ictogenic model used consisted of inducing seizures by continuous intravenous infusion of pentylenetetrazol (PTZ - 2.5 mg/ml/min) while a probing DBS was delivered to the thalamus (TH) or amygdaloid complex to detect changes prior to seizure onset. Cortical electrophysiological recordings were performed before, during, and after PTZ infusion. Thalamic DBS probing, but not amygdaloid, was able to predict seizure onset without any observable proconvulsant effects. However, previously pairing amygdaloid DBS and epileptic polyspike discharges (day-1) elicited distinct preictal cortically recorded evoked response (CRER) (day-2) when compared with control groups that received the same amount of electrical pulses at different moments of the ictogenic progress at day-1. In conclusion, our results have demonstrated that the pairing strategy potentiated the detection of an altered brain state prior to the seizure onset. The EEG probing enhancement method opens many possibilities for both diagnosis and treatment of epilepsy.

Axonal Stimulations With a Higher Frequency Generate More Randomness in Neuronal Firing Rather Than Increase Firing Rates in Rat Hippocampus

Deep brain stimulation (DBS) has been used for treating many brain disorders. Clinical applications of DBS commonly require high-frequency stimulations (HFS, ∼100 Hz) of electrical pulses to obtain therapeutic efficacy. It is not clear whether the electrical energy of HFS functions other than generating firing of action potentials in neuronal elements. To address the question, we investigated the reactions of downstream neurons to pulse sequences with a frequency in the range 50-200 Hz at afferent axon fibers in the hippocampal CA1 region of anesthetized rats. The results show that the mean rates of neuronal firing induced by axonal HFS were similar even for an up to fourfold difference (200:50) in the number and thereby in the energy of electrical pulses delivered. However, HFS with a higher pulse frequency (100 or 200 Hz) generated more randomness in the firing pattern of neurons than a lower pulse frequency (50 Hz), which were quantitatively evaluated by the significant changes of two indexes, namely, the peak coefficients and the duty ratios of excitatory phase of neuronal firing, induced by different frequencies (50-200 Hz). The findings indicate that a large portion of the HFS energy might function to generate a desynchronization effect through a possible mechanism of intermittent depolarization block of neuronal membranes. The present study addresses the demand of high frequency for generating HFS-induced desynchronization in neuronal activity, which may play important roles in DBS therapy.

Improving cognitive task in kindled rats by using low frequency stimulation during epileptogenesis

Numerous studies indicate that one of the bad effects of epilepsy is cognitive impairment. In this study we focused on the effect of LFS as a potential anticonvulsant agent, during epileptogenesis on cognitive impairments induced by amygdala kindling in rat. Twenty-one adult rats were divided into 3 groups including control (n = 7), kindled (n = 7), and Kindled+LFS (KLFS) (n = 7). Animals in the kindled group received kindling stimulation in a rapid kindling manner (a 3 s train of 50 Hz monophasic pulses of 1 ms duration, 12 times a day) in amygdala whereas control animals had no stimulation. Four packages of LFS (each package consisting of 200 monophasic square pulses, 0.1 ms pulse duration at 1 Hz) were applied daily after termination of kindling stimulation in KLFS group. Spatial memory of all animals was tested using radial arm maze after termination of stimulation on acquisition trial days and 14 days after the final acquisition trial test. Epileptogenesis process significantly increased working and reference memory error compared to control groups whereas application of LFS immediately after kindling stimulation prevented this impairment in 8 arm radial maze and there was no significant difference between KLS and control groups. Our results indicated that application of LFS during kindling acquisition suppresses memory impairment in epileptogenesis by kindling stimulation.

Seizure pathways: A model-based investigation

We present the results of a model inversion algorithm for electrocorticography (ECoG) data recorded during epileptic seizures. The states and parameters of neural mass models were tracked during a total of over 3000 seizures from twelve patients with focal epilepsy. These models provide an estimate of the effective connectivity within intracortical circuits over the time course of seizures. Observing the dynamics of effective connectivity provides insight into mechanisms of seizures. Estimation of patients seizure dynamics revealed: 1) a highly stereotyped pattern of evolution for each patient, 2) distinct sub-groups of onset mechanisms amongst patients, and 3) different offset mechanisms for long and short seizures. Stereotypical dynamics suggest that, once initiated, seizures follow a deterministic path through the parameter space of a neural model. Furthermore, distinct sub-populations of patients were identified based on characteristic motifs in the dynamics at seizure onset. There were also distinct patterns between long and short duration seizures that were related to seizure offset. Understanding how these different patterns of seizure evolution arise may provide new insights into brain function and guide treatment for epilepsy, since specific therapies may have preferential effects on the various parameters that could potentially be individualized. Methods that unite computational models with data provide a powerful means to generate testable hypotheses for further experimental research. This work provides a demonstration that the hidden connectivity parameters of a neural mass model can be dynamically inferred from data. Our results underscore the power of theoretical models to inform epilepsy management. It is our hope that this work guides further efforts to apply computational models to clinical data.

Activity patterns with silent states in a heterogeneous network of gap-junction coupled Huber-Braun model neurons

A mathematical model of a network of nearest neighbor gap-junction coupled neurons has been used to examine the impact of neuronal heterogeneity on the networks' activity during increasing coupling strength. Heterogeneity has been introduced by Huber-Braun model neurons with randomization of the temperature as a scaling factor. This leads to neurons of an enormous diversity of impulse pattern, including burst discharges, chaotic activity, and two different types of tonic firing-all of them experimentally observed in the peripheral as well as central nervous system. When the network is composed of all these types of neurons, randomly selected, a particular phenomenon can be observed. At a certain coupling strength, the network goes into a completely silent state. Examination of voltage traces and inter-spike intervals of individual neurons suggests that all neurons, irrespective of their original pattern, go through a well-known bifurcation scenario, resembling those of single neurons especially on external current injection. All the originally spontaneously firing neurons can achieve constant membrane potentials at which all intrinsic and gap-junction currents are balanced. With limited diversity, i.e., taking out neurons of specific patterns from the lower and upper temperature range, spontaneous firing can be reinstalled with further increasing coupling strength, especially when the tonic firing regimes are missing. Reinstalled firing develops from slowly increasing subthreshold oscillations leading to tonic firing activity with already fairly well synchronized action potentials, while the subthreshold potentials can still be significantly different. Full in phase synchronization is not achieved. Additional studies are needed elucidating the underlying mechanisms and the conditions under which such particular transitions can appear.

A neural mass model to predict electrical stimulation evoked responses in human and non-human primate brain

OBJECTIVE

Deep brain stimulation (DBS) is a valuable tool for ameliorating drug resistant pathologies such as movement disorders and epilepsy. DBS is also being considered for complex neuro-psychiatric disorders, which are characterized by high variability in symptoms and slow responses that hinder DBS setting optimization. The objective of this work was to develop an in silico platform to examine the effects of electrical stimulation in regions neighboring a stimulated brain region.

APPROACH

We used the Jansen-Rit neural mass model of single and coupled nodes to simulate the response to a train of electrical current pulses at different frequencies (10-160 Hz) of the local field potential recorded in the amygdala and cortical structures in human subjects and a non-human primate.

RESULTS

We found that using a single node model, the evoked responses could be accurately modeled following a narrow range of stimulation frequencies. Including a second coupled node increased the range of stimulation frequencies whose evoked responses could be efficiently modeled. Furthermore, in a chronic recording from a non-human primate, features of the in vivo evoked response remained consistent for several weeks, suggesting that model re-parameterization for chronic stimulation protocols would be infrequent.

SIGNIFICANCE

Using a model of neural population activity, we reproduced the evoked response to cortical and subcortical stimulation in human and non-human primate. This modeling framework provides an environment to explore, safely and rapidly, a wide range of stimulation settings not possible in human brain stimulation studies. The model can be trained on a limited dataset of stimulation responses to develop an optimal stimulation strategy for an individual patient.

Seizure evolution can be characterized as path through synaptic gain space of a neural mass model

Physiologically based models could facilitate better understanding of mechanisms underlying epileptic seizures. In this paper, we attempt to reveal the dynamic evolution of intracranial EEG activity during epileptic seizures based on synaptic gain identification procedure of a neural mass model. The distribution of average excitatory, slow and fast inhibitory synaptic gain in the parameter space and their temporal evolution, i.e., the path through the model parameter space, were analyzed in thirty seizures from ten temporal lobe epileptic patients. Results showed that the synaptic gain values located roughly on a plane before seizure onset, dispersed during seizure and returned to the plane when seizure terminated. Cluster analysis was performed on seizure paths and demonstrated consistency in synaptic gain evolution across different seizures from the individual patient. Furthermore, two patient groups were identified, each one corresponding to a specific synaptic gain evolution in the parameter space during a seizure. Results were validated by a bootstrapping approach based on comparison with random paths. The differences in the path revealed variations in EEG dynamics for patients despite showing identical seizure onset pattern. Our approach may have the potential to classify the epileptic patients into subgroups based on different mechanisms revealed by subtle changes in synaptic gains and further enable more robust decisions regarding treatment strategy.

How stimulation frequency and intensity impact on the long-lasting effects of coordinated reset stimulation

Several brain diseases are characterized by abnormally strong neuronal synchrony. Coordinated Reset (CR) stimulation was computationally designed to specifically counteract abnormal neuronal synchronization processes by desynchronization. In the presence of spike-timing-dependent plasticity (STDP) this may lead to a decrease of synaptic excitatory weights and ultimately to an anti-kindling, i.e. unlearning of abnormal synaptic connectivity and abnormal neuronal synchrony. The long-lasting desynchronizing impact of CR stimulation has been verified in pre-clinical and clinical proof of concept studies. However, as yet it is unclear how to optimally choose the CR stimulation frequency, i.e. the repetition rate at which the CR stimuli are delivered. This work presents the first computational study on the dependence of the acute and long-term outcome on the CR stimulation frequency in neuronal networks with STDP. For this purpose, CR stimulation was applied with Rapidly Varying Sequences (RVS) as well as with Slowly Varying Sequences (SVS) in a wide range of stimulation frequencies and intensities. Our findings demonstrate that acute desynchronization, achieved during stimulation, does not necessarily lead to long-term desynchronization after cessation of stimulation. By comparing the long-term effects of the two different CR protocols, the RVS CR stimulation turned out to be more robust against variations of the stimulation frequency. However, SVS CR stimulation can obtain stronger anti-kindling effects. We revealed specific parameter ranges that are favorable for long-term desynchronization. For instance, RVS CR stimulation at weak intensities and with stimulation frequencies in the range of the neuronal firing rates turned out to be effective and robust, in particular, if no closed loop adaptation of stimulation parameters is (technically) available. From a clinical standpoint, this may be relevant in the context of both invasive as well as non-invasive CR stimulation.

Degenerate time-dependent network dynamics anticipate seizures in human epileptic brain

Epileptic seizures are known to follow specific changes in brain dynamics. While some algorithms can nowadays robustly detect these changes, a clear understanding of the mechanism by which these alterations occur and generate seizures is still lacking. Here, we provide crossvalidated evidence that such changes are initiated by an alteration of physiological network state dynamics. Specifically, our analysis of long intracranial electroencephalography (iEEG) recordings from a group of 10 patients identifies a critical phase of a few hours in which time-dependent network states become less variable ("degenerate"), and this phase is followed by a global functional connectivity reduction before seizure onset. This critical phase is characterized by an abnormal occurrence of highly correlated network instances and is shown to be particularly associated with the activity of the resected regions in patients with validated postsurgical outcome. Our approach characterizes preseizure network dynamics as a cascade of 2 sequential events providing new insights into seizure prediction and control.

Understanding and predicting the generation of seizures in epileptic patients is fundamental to improving the quality of life of the more than 1% of the world population who suffer from this illness. Although seizure prediction has made important advances over the last decade, there is a lack of understanding of the common principles explaining the transitions that brain activity undergoes before a seizure. In this study, we characterized this transition from a novel perspective grounded on the mathematical analysis of continuous recordings inside the brains of epileptic patients over several days using depth electrodes. We show that the critical period preceding a seizure unfolds in a two-stage process. It begins with a phase of several hours when the highly correlated activity in the preceding days is altered, and it proceeds with a second, shorter phase of decrease in global connectivity before the seizure onset. Furthermore, our analysis reveals that these global alterations are more locally manifested in areas that are selected for surgical treatment. Our study suggests that preseizure activity might follow global stereotyped dynamics that could be targeted and modulated to prevent epileptic seizures.

Localization of Epileptogenic Zone With the Correction of Pathological Networks

Patients with focal drug-resistant epilepsy are potential candidates for surgery. Stereo-electroencephalograph (SEEG) is often considered as the “gold standard” to identify the epileptogenic zone (EZ) that accounts for the onset and propagation of epileptiform discharges. However, visual analysis of SEEG still prevails in clinical practice. In addition, epilepsy is increasingly understood to be the result of network disorder, but the specific organization of the epileptic network is still unclear. Therefore, it is necessary to quantitatively localize the EZ and investigate the nature of epileptogenic networks. In this study, intracranial recordings from 10 patients were analyzed through adaptive directed transfer function, and the out-degree of effective network was selected as the principal indicator to localize the epileptogenic area. Furthermore, a coupled neuronal population model was used to qualitatively simulate electrical activity in the brain. By removing individual populations, virtual surgery adjusting the network organization could be performed. Results suggested that the accuracy and detection rate of the EZ localization were 82.86 and 85.29%, respectively. In addition, the same stage shared a relatively stable connectivity pattern, while the patterns changed with transition to different processes. Meanwhile, eight cases of simulations indicated that networks in the ictal stage were more likely to generate rhythmic spikes. This indicated the existence of epileptogenic networks, which could enhance local excitability and facilitate synchronization. The removal of the EZ could correct these pathological networks and reduce the amount of spikes by at least 75%. This might be one reason why accurate resection could reduce or even suppress seizures. This study provides novel insights into epilepsy and surgical treatments from the network perspective.

Classifying dynamic transitions in high dimensional neural mass models: A random forest approach

Neural mass models (NMMs) are increasingly used to uncover the large-scale mechanisms of brain rhythms in health and disease. The dynamics of these models is dependent upon the choice of parameters, and therefore it is crucial to be able to understand how dynamics change when parameters are varied. Despite being considered low dimensional in comparison to micro-scale, neuronal network models, with regards to understanding the relationship between parameters and dynamics, NMMs are still prohibitively high dimensional for classical approaches such as numerical continuation. Therefore, we need alternative methods to characterise dynamics of NMMs in high dimensional parameter spaces. Here, we introduce a statistical framework that enables the efficient exploration of the relationship between model parameters and selected features of the simulated, emergent model dynamics of NMMs. We combine the classical machine learning approaches of trees and random forests to enable studying the effect that varying multiple parameters has on the dynamics of a model. The method proceeds by using simulations to transform the mathematical model into a database. This database is then used to partition parameter space with respect to dynamic features of interest, using random forests. This allows us to rapidly explore dynamics in high dimensional parameter space, capture the approximate location of qualitative transitions in dynamics and assess the relative importance of all parameters in the model in all dimensions simultaneously. We apply this method to a commonly used NMM in the context of transitions to seizure dynamics. We find that the inhibitory sub-system is most crucial for the generation of seizure dynamics, confirm and expand previous findings regarding the ratio of excitation and inhibition, and demonstrate that previously overlooked parameters can have a significant impact on model dynamics. We advocate the use of this method in future to constrain high dimensional parameter spaces enabling more efficient, person-specific, model calibration.

Epileptic Seizure Detection in Long-Term EEG Recordings by Using Wavelet-Based Directed Transfer Function

GOAL

The accurate automatic detection of epileptic seizures is very important in long-term electroencephalogram (EEG) recordings. In this study, the wavelet decomposition and the directed transfer function (DTF) algorithm were combined to present a novel wavelet-based directed transfer function (WDTF) method for the patient-specific seizure detection.

METHODS

First, five subbands were extracted from 19-channel EEG signals by using wavelet decomposition in a sliding window. Second, the information flow characteristics of five subbands and full frequency band of EEG signals were calculated by the DTF method. The intensity of the outflow information was then used to reduce the feature dimensionality. Finally, all features were combined to identify interictal and ictal EEG segments by the support vector machine classifier.

RESULTS

By using fivefold cross validation, the proposed method had achieved excellent performance with the average accuracy of 99.4%, the average selectivity of 91.1%, the average sensitivity of 92.1%, the average specificity of 99.5%, and the average detection rate of 95.8%.

CONCLUSION

The WDTF method is able to enhance seizure detection results in long-term EEG recordings of focal epilepsy patients.

SIGNIFICANCE

This study may lead to the development of seizure detection system with high performance, thus reducing the workload of epileptologists and facilitating to take corresponding steps promptly after the seizure onset. The high-frequency activity in the epilepsy brain may be of great importance for investigating the pathological mechanism and treatment of seizure.

Characterisation of ictal and interictal states of epilepsy: A system dynamic approach of principal dynamic modes analysis

Epilepsy is a brain disorder characterised by the recurrent and unpredictable interruptions of normal brain function, called epileptic seizures. The present study attempts to derive new diagnostic indices which may delineate between ictal and interictal states of epilepsy. To achieve this, the nonlinear modeling approach of global principal dynamic modes (PDMs) is adopted to examine the functional connectivity of the temporal and frontal lobes with the occipital brain segment using an ensemble of paediatric EEGs having the presence of epileptic seizure. The distinct spectral characteristics of global PDMs are found to be in line with the neural rhythms of brain dynamics. Moreover, we find that the linear trends of associated nonlinear functions (ANFs) associated with the 2nd and 4th global PDMs (representing delta, theta and alpha bands) of Fp1–F3 may differentiate between ictal and interictal states of epilepsy. These findings suggest that global PDMs and their associated ANFs may offer potential utility as diagnostic neural measures for ictal and interictal states of epilepsy.