Network bistability mediates spontaneous transitions between normal and pathological brain states

GABA-Induced Seizure-Like Events Caused by Multi-ionic Interactive Dynamics

Experimental evidence showed that an increase in intracellular chloride concentration [Formula: see text] caused by gamma-aminobutyric acid (GABA) input can promote epileptic firing activity, but the actual mechanisms remain elusive. Here in this theoretical work, we show that influx of chloride and concomitant bicarbonate ion [Formula: see text] efflux upon GABA receptor activation can induce epileptic firing activity by transition of GABA from inhibition to excitation. We analyzed the intrinsic property of neuron firing states as a function of [Formula: see text] We found that as [Formula: see text] increases, the system exhibits a saddle-node bifurcation, above which the neuron exhibits a spectrum of intensive firing, periodic bursting interrupted by depolarization block (DB) state, and eventually a stable DB through a Hopf bifurcation. We demonstrate that only GABA stimuli together with [Formula: see text] efflux can switch GABA's effect to excitation which leads to a series of seizure-like events (SLEs). Exposure to a low [Formula: see text] can drive neurons with high concentrations of [Formula: see text] downward to lower levels of [Formula: see text], during which it could also trigger SLEs depending on the exchange rate with the bath. Our analysis and simulation results show how the competition between GABA stimuli-induced accumulation of [Formula: see text] and [Formula: see text] application-induced decrease of [Formula: see text] regulates the neuron firing activity, which helps to understand the fundamental ionic dynamics of SLE.

Cholinergic modulation supports dynamic switching of resting state networks through selective DMN suppression

Brain activity during the resting state is widely used to examine brain organization, cognition and alterations in disease states. While it is known that neuromodulation and the state of alertness impact resting-state activity, neural mechanisms behind such modulation of resting-state activity are unknown. In this work, we used a computational model to demonstrate that change in excitability and recurrent connections, due to cholinergic modulation, impacts resting-state activity. The results of such modulation in the model match closely with experimental work on direct cholinergic modulation of Default Mode Network (DMN) in rodents. We further extended our study to the human connectome derived from diffusion-weighted MRI. In human resting-state simulations, an increase in cholinergic input resulted in a brain-wide reduction of functional connectivity. Furthermore, selective cholinergic modulation of DMN closely captured experimentally observed transitions between the baseline resting state and states with suppressed DMN fluctuations associated with attention to external tasks. Our study thus provides insight into potential neural mechanisms for the effects of cholinergic neuromodulation on resting-state activity and its dynamics.

Bursting Dynamics Based on the Persistent Na+ and Na+/K+ Pump Currents: A Dynamic Clamp Approach

Life-supporting rhythmic motor functions like heart-beating in invertebrates and breathing in vertebrates require an indefatigable generation of a robust rhythm by specialized oscillatory circuits, central pattern generators (CPGs). These CPGs should be sufficiently flexible to adjust to environmental changes and behavioral goals. Continuous self-sustained operation of bursting neurons requires intracellular Na+ concentration to remain in a functional range and to have checks and balances of the Na+ fluxes met on a cycle-to-cycle basis during bursting. We hypothesize that at a high excitability state, the interaction of the Na+/K+ pump current, Ipump, and persistent Na+ current, INaP, produces a mechanism supporting functional bursting. INaP is a low voltage-activated inward current that initiates and supports the bursting phase. This current does not inactivate and is a significant source of Na+ influx. Ipump is an outward current activated by [Na+]i and is the major source of Na+ efflux. Both currents are active and counteract each other between and during bursts. We apply a combination of electrophysiology, computational modeling, and dynamic clamp to investigate the role of Ipump and INaP in the leech heartbeat CPG interneurons (HN neurons). Applying dynamic clamp to introduce additional Ipump and INaP into the dynamics of living synaptically isolated HN neurons in real time, we show that their joint increase produces transition into a new bursting regime characterized by higher spike frequency and larger amplitude of the membrane potential oscillations. Further increase of Ipump speeds up this rhythm by shortening burst duration (BD) and interburst interval (IBI).

Non-convulsive status epilepticus possibly induced by a rapid correction of severe hyperkalemia: a case report and literature review

BACKGROUND

Patients with chronic kidney disease frequently develop neurological complications including confusion and altered consciousness. Non-convulsive status epilepticus, which is characterized by a change in behavior and/or mental process accompanied by epileptiform discharges on electroencephalogram in the absence of convulsive seizures, is one of the overlooked causes of altered consciousness. The incidence and precise pathophysiological mechanism of non-convulsive status epilepticus in patients with kidney disease, and especially in patients with electrolyte disturbances, remains unknown. We recently treated an older patient with chronic kidney disease and severe hyperkalemia in whom non-convulsive status epilepticus developed following a correction of severe hyperkalemia.

CASE PRESENTATION

An 82-year-old male was admitted to our hospital at midnight because of weakness of all four limbs (Day 1). He underwent urgent hemodialysis for severe hyperkalemia (9.84 mEq/L) and his serum potassium concentration decreased to 4.97 mEq/L. He regained full consciousness and his limb weakness improved on the morning of Day 2, but he became confused in the evening. Electroencephalogram revealed repeated low-voltage ictal discharges in the right occipital region and a diagnosis of non-convulsive status epilepticus was made. Following medication with fosphenytoin and phenytoin, the patient became fully alert and orientated on Day 8.

CONCLUSION

We speculate that a rapid correction of hyperkalemia was the possible cause of non-convulsive status epilepticus development. To our knowledge, this is the first report of non-convulsive status epilepticus from a potassium abnormality. We described a case of this condition in detail and summarized 78 previous case reports of non-convulsive status epilepticus with kidney disease or electrolyte disturbances.

Ligand-gated mechanisms leading to ictogenesis in focal epileptic disorders

We review here the neuronal mechanisms that cause seizures in focal epileptic disorders and, specifically, those involving limbic structures that are known to be implicated in human mesial temporal lobe epilepsy. In both epileptic patients and animal models, the initiation of focal seizures - which are most often characterized by a low-voltage fast onset EEG pattern - is presumably dependent on the synchronous firing of GABA-releasing interneurons that, by activating post-synaptic GABA_A receptors, cause large increases in extracellular [K⁺] through the activation of the co-transporter KCC2. A similar mechanism may contribute to seizure maintenance; accordingly, inhibiting KCC2 activity transforms seizure activity into a continuous pattern of short-lasting epileptiform discharges. It has also been found that interactions between different areas of the limbic system modulate seizure occurrence by controlling extracellular [K⁺] homeostasis. In line with this view, low-frequency electrical or optogenetic activation of limbic networks restrain seizure generation, an effect that may also involve the activation of GABA_B receptors and activity-dependent changes in epileptiform synchronization. Overall, these findings highlight the paradoxical role of GABA_A signaling in both focal seizure generation and maintenance, emphasize the efficacy of low-frequency activation in abating seizures, and provide experimental evidence explaining the poor efficacy of antiepileptic drugs designed to augment GABAergic function in controlling seizures in focal epileptic disorders.

Transition behavior of the seizure dynamics modulated by the astrocyte inositol triphosphate noise

Epilepsy is a neurological disorder with recurrent seizures, which convey complex dynamical characteristics including chaos and randomness. Until now, the underlying mechanism has not been fully elucidated, especially the bistable property beneath the epileptic random induction phenomena in certain conditions. Inspired by the recent finding that astrocyte GTPase-activating protein (G-protein)-coupled receptors could be involved in stochastic epileptic seizures, we proposed a neuron-astrocyte network model, incorporating the noise of the astrocytic second messenger, inositol triphosphate (IP3) that is modulated by G-protein-coupled receptor activation. Based on this model, we have statistically analyzed the transitions of epileptic seizures by performing repeatable simulation trials. Our simulation results show that the increase in the IP3 noise intensity induces depolarization-block epileptic seizures together with an increase in neuronal firing frequency, consistent with corresponding experiments. Meanwhile, the bistable states of the seizure dynamics were present under certain noise intensities, during which the neuronal firing pattern switches between regular sparse spiking and epileptic seizure states. This random presence of epileptic seizures is absent when the noise intensity continues to increase, accompanying with an increase in the epileptic depolarization block duration. The simulation results also shed light on the fact that calcium signals in astrocytes play significant roles in the pattern formations of the epileptic seizure. Our results provide a potential pathway for understanding the epileptic randomness in certain conditions.

GABAA signaling, focal epileptiform synchronization and epileptogenesis

Under physiological conditions, neuronal network synchronization leads to different oscillatory EEG patterns that are associated with specific behavioral and cognitive functions. Excessive synchronization can, however, lead to focal or generalized epileptiform activities. It is indeed well established that in both epileptic patients and animal models, focal epileptiform EEG patterns are characterized by interictal and ictal (seizure) discharges. Over the last three decades, employing in vitro and in vivo recording techniques, several experimental studies have firmly identified a paradoxical role of GABA_A signaling in generating interictal discharges, and in initiating—and perhaps sustaining—focal seizures. Here, we will review these experiments and we will extend our appraisal to evidence suggesting that GABA_A signaling may also contribute to epileptogenesis, i.e., the development of plastic changes in brain excitability that leads to the chronic epileptic condition. Overall, we anticipate that this information should provide the rationale for developing new specific pharmacological treatments for patients presenting with focal epileptic disorders such as mesial temporal lobe epilepsy (MTLE).

Electroencephalography complexity in resting and task states in adults with attention-deficit/hyperactivity disorder

Analysing EEG complexity could provide insight into neural connectivity underlying attention-deficit/hyperactivity disorder symptoms. EEG complexity was calculated through multiscale entropy and compared between adults with attention-deficit/hyperactivity disorder and their peers during resting and go/nogo task states. Multiscale entropy change from the resting state to the task state was also examined as an index of the brain’s ability to change from a resting to an active state. Thirty unmedicated adults with attention-deficit/hyperactivity disorder were compared with 30 match-paired healthy peers on the multiscale entropy in the resting and task states as well as their multiscale entropy change. Results showed differences in multiscale entropy between individuals with attention-deficit/hyperactivity disorder and their peers during the resting state as well as the task state. The multiscale entropy measured from the comparison group was larger than that from the attention-deficit/hyperactivity disorder group in the resting state, whereas the reverse pattern was found during the task state. Our most robust finding showed that the multiscale entropy change from individuals with attention-deficit/hyperactivity disorder was smaller than that from their peers, specifically at frontal sites. Interestingly, individuals without attention-deficit/hyperactivity disorder performed better with decreasing multiscale entropy changes, demonstrating higher accuracy, faster reaction time and less variability in their reaction times. These data suggest that multiscale entropy could not only provide insight into neural connectivity differences between adults with attention-deficit/hyperactivity disorder and their peers but also into their behavioural performance.

Control of epileptic seizures by electrical stimulation: a model-based study

High frequency electrical stimulation of brain is commonly used in research experiments and clinical trials as a modern tool for control of epileptic seizures. However, the mechanistic basis by which periodic external stimuli alter the brain state is not well understood. This study provides a computational insight into the mechanism of seizure suppression by high frequency stimulation (HFS). In particular, a modified version of the Jansen-Rit neural mass model is employed, in which EEG signals can be considered as the input. The proposed model reproduces seizure-like activity in the output during the ictal period of the input signal. By applying a control signal to the model, a wide range of stimulation amplitudes and frequencies are systematically explored. Simulation results reveal that HFS can effectively suppress the seizure-like activity. Our results suggest that HFS has the ability of shifting the operating state of neural populations away from a critical condition. Furthermore, a closed-loop control strategy is proposed in this paper. The main objective has been to considerably reduce the control effort needed for blocking abnormal activity of the brain. Such an energy reduction could be of practical importance, to reduce possible side effects and increase battery life for implanted neurostimulators.

Neural recruitment by ephaptic coupling in epilepsy

OBJECTIVE

One of the challenges in treating patients with drug-resistant epilepsy is that the mechanisms of seizures are unknown. Most current interventions are based on the assumption that epileptic activity recruits neurons and progresses by synaptic transmission. However, several experimental studies have shown that neural activity in rodent hippocampi can propagate independently of synaptic transmission. Recent studies suggest these waves are self-propagating by electric field (ephaptic) coupling. In this study, we tested the hypothesis that neural recruitment during seizures can occur by electric field coupling.

METHODS

4-Aminopyridine was used in both in vivo and in vitro preparation to trigger seizures or epileptiform activity. A transection was made in the in vivo hippocampus and in vitro hippocampal and cortical slices to study whether the induced seizure activity can recruit neurons across the gap. A computational model was built to test whether ephaptic coupling alone can account for neural recruitment across the transection. The model prediction was further validated by in vitro experiments.

RESULTS

Experimental results show that electric fields generated by seizure-like activity in the hippocampus both in vitro and in vivo can recruit neurons locally and through a transection of the tissue. The computational model suggests that the neural recruitment across the transection is mediated by electric field coupling. With in vitro experiments, we show that a dielectric material can block the recruitment of epileptiform activity across a transection, and that the electric fields measured within the gap are similar to those predicted by model simulations. Furthermore, this nonsynaptic neural recruitment is also observed in cortical slices, suggesting that this effect is robust in brain tissue.

SIGNIFICANCE

These results indicate that ephaptic coupling, a nonsynaptic mechanism, can underlie neural recruitment by a small electric field generated by seizure activity and could explain the low success rate of surgical transections in epilepsy patients.

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.

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.

Analysis of stochastic fluctuations in responsiveness is a critical step toward personalized anesthesia

Traditionally, drug dosing is based on a concentration-response relationship estimated in a population. Yet, in specific individuals, decisions based on the population-level effects frequently result in over or under-dosing. Here, we interrogate the relationship between population-based and individual-based responses to anesthetics in mice and zebrafish. The anesthetic state was assessed by quantifying responses to simple stimuli. Individual responses dynamically fluctuated at a fixed drug concentration. These fluctuations exhibited resistance to state transitions. Drug sensitivity varied dramatically across individuals in both species. The amount of noise driving transitions between states, in contrast, was highly conserved in vertebrates separated by 400 million years of evolution. Individual differences in anesthetic sensitivity and stochastic fluctuations in responsiveness complicate the ability to appropriately dose anesthetics to each individual. Identifying the biological substrate of noise, however, may spur novel therapies, assure consistent drug responses, and encourage the shift from population-based to personalized medicine.

Every year, millions of patients undergo general anesthesia for complex or life-saving surgeries. In the vast majority of cases, the drugs work as intended. But a minority of patients take longer than expected to regain consciousness after anesthetic, and a few wake up during the surgery itself. It is unclear what causes these unintended events.

When choosing an anesthetic dose for each patient, physicians rely on data from large clinical studies. These studies expose many patients to different doses of an anesthetic drug. At higher doses, fewer and fewer patients remain conscious. This enables physicians to identify the dose at which an average person will lose consciousness. But this approach ignores the difference between the response of an individual and that of the population as a whole. At the population level, the likelihood of a patient being awake decreases smoothly as the concentration of anesthetic increases. But within that population, each individual patient can only ever show a binary response: awake or not awake.

To compare anesthetic effects on individuals versus populations, McKinstry-Wu, Wasilczuk et al. exposed mice to a commonly used anesthetic called isoflurane. During prolonged exposure to a constant dose of the drug, each mouse was sometimes unconscious and sometimes awake. These fluctuations in responsiveness seemed to occur at random. Exposing zebrafish to propofol, an anesthetic that works via a different mechanism, had a similar effect.

Notably, the responses of both species to anesthesia showed a phenomenon known as inertia. If an individual was unresponsive at one point in time, they were likely to still be unresponsive when assessed again after three minutes. The amount of inertia was similar in mice and zebrafish. This suggests that the mechanism responsible for inertia has remained unchanged over more than 400 million years of evolution.

The results reveal similarities between how individuals respond to anesthetics and how individual anesthetic molecules act on cells. When a molecule binds to its receptor protein on a cell, the receptor fluctuates spontaneously between active and inactive states. Studying how individuals respond to drugs could thus provide clues to how the drugs themselves work. Future studies should explore the biological basis of fluctuations in anesthetic responses. Understanding how these arise will help us tailor anesthetics to individual patients.

Multistable properties of human subthalamic nucleus neurons in Parkinson's disease

Behaviors are realized through concerted activity in neural circuits. This activity results from a combination of neural connectivity and the properties of the involved neurons. By studying the activity of neurons in the human subthalamic nucleus during surgery for Parkinson’s disease, we report that these neurons have multiple stable states, and that brief electrical stimuli can lead to transitions between states. We thus suggest that these neurons function as finite state machines. The different states could influence the function of key motor circuits of the basal ganglia, and thus knowledge of these states in disease or in response to treatment could help to define new treatment strategies for people with movement disorders.

To understand the function and dysfunction of neural circuits, it is necessary to understand the properties of the neurons participating in the behavior, the connectivity between these neurons, and the neuromodulatory status of the circuits at the time they are producing the behavior. Such knowledge of human neural circuits is difficult, at best, to obtain. Here, we study firing properties of human subthalamic neurons, using microelectrode recordings and microstimulation during awake surgery for Parkinson’s disease. We demonstrate that low-amplitude, brief trains of microstimulation can lead to persistent changes in neuronal firing behavior including switching between firing rates, entering silent periods, or firing several bursts then entering a silent period. We suggest that these multistable states reflect properties of finite state machines and could have implications for the function of circuits involving the subthalamic nucleus. Furthermore, understanding these states could lead to therapeutic strategies aimed at regulating the transitions between states.

Computational Analysis of Insulin-Glucagon Signalling Network: Implications of Bistability to Metabolic Homeostasis and Disease states

Insulin and glucagon control plasma macronutrient homeostasis through their signalling network composed of multiple feedback and crosstalk interactions. To understand how these interactions contribute to metabolic homeostasis and disease states, we analysed the steady state response of metabolic regulation (catabolic or anabolic) with respect to structural and input perturbations in the integrated signalling network, for varying levels of plasma glucose. Structural perturbations revealed: the positive feedback of AKT on IRS is responsible for the bistability in anabolic zone (glucose >5.5 mmol); the positive feedback of calcium on cAMP is responsible for ensuring ultrasensitive response in catabolic zone (glucose <4.5 mmol); the crosstalk between AKT and PDE3 is responsible for efficient catabolic response under low glucose condition; the crosstalk between DAG and PKC regulates the span of anabolic bistable region with respect to plasma glucose levels. The macronutrient perturbations revealed: varying plasma amino acids and fatty acids from normal to high levels gradually shifted the bistable response towards higher glucose range, eventually making the response catabolic or unresponsive to increasing glucose levels. The analysis reveals that certain macronutrient composition may be more conducive to homeostasis than others. The network perturbations that may contribute to disease states such as diabetes, obesity and cancer are discussed.

Ionic and synaptic mechanisms of seizure generation and epileptogenesis

The biophysical mechanisms underlying epileptogenesis and the generation of seizures remain to be better understood. Among many factors triggering epileptogenesis are traumatic brain injury breaking normal synaptic homeostasis and genetic mutations disrupting ionic concentration homeostasis. Impairments in these mechanisms, as seen in various brain diseases, may push the brain network to a pathological state characterized by increased susceptibility to unprovoked seizures. Here, we review recent computational studies exploring the roles of ionic concentration dynamics in the generation, maintenance, and termination of seizures. We further discuss how ionic and synaptic homeostatic mechanisms may give rise to conditions which prime brain networks to exhibit recurrent spontaneous seizures and epilepsy.

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.

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.

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.

The promise and perils of causal circuit manipulations

The development of increasingly sophisticated methods for recording and manipulating neural activity is revolutionizing neuroscience. By probing how activity patterns in different types of neurons and circuits contribute to behavior, these tools can help inform mechanistic models of brain function and explain the roles of distinct circuit elements. However, in systems where functions are distributed over large networks, interpreting causality experiments can be challenging. Here we review common assumptions underlying circuit manipulations in behaving animals and discuss the strengths and limitations of different approaches.

Slow moving neural source in the epileptic hippocampus can mimic progression of human seizures

Fast and slow neural waves have been observed to propagate in the human brain during seizures. Yet the nature of these waves is difficult to study in a surgical setting. Here, we report an observation of two different traveling waves propagating in the in-vitro epileptic hippocampus at speeds similar to those in the human brain. A fast traveling spike and a slow moving wave were recorded simultaneously with a genetically encoded voltage sensitive fluorescent protein (VSFP Butterfly 1.2) and a high speed camera. The results of this study indicate that the fast traveling spike is NMDA-sensitive but the slow moving wave is not. Image analysis and model simulation demonstrate that the slow moving wave is moving slowly, generating the fast traveling spike and is, therefore, a moving source of the epileptiform activity. This slow moving wave is associated with a propagating neural calcium wave detected with calcium dye (OGB-1) but is independent of NMDA receptors, not related to ATP release, and much faster than those previously recorded potassium waves. Computer modeling suggests that the slow moving wave can propagate by the ephaptic effect like epileptiform activity. These findings provide an alternative explanation for slow propagation seizure wavefronts associated with fast propagating spikes.

Low-to-High Cross-Frequency Coupling in the Electrical Rhythms as Biomarker for Hyperexcitable Neuroglial Networks of the Brain

OBJECTIVE

One of the features used in the study of hyperexcitablility is high-frequency oscillations (HFOs, >80 Hz). HFOs have been reported in the electrical rhythms of the brain's neuroglial networks under physiological and pathological conditions. Cross-frequency coupling (CFC) of HFOs with low-frequency rhythms was used to identify pathologic HFOs in the epileptogenic zones of epileptic patients and as a biomarker for the severity of seizure-like events in genetically modified rodent models. We describe a model to replicate reported CFC features extracted from recorded local field potentials (LFPs) representing network properties.

METHODS

This study deals with a four-unit neuroglial cellular network model where each unit incorporates pyramidal cells, interneurons, and astrocytes. Three different pathways of hyperexcitability generation-Na - ATPase pump, glial potassium clearance, and potassium afterhyperpolarization channel-were used to generate LFPs. Changes in excitability, average spontaneous electrical discharge (SED) duration, and CFC were then measured and analyzed.

RESULTS

Each parameter caused an increase in network excitability and the consequent lengthening of the SED duration. Short SEDs showed CFC between HFOs and theta oscillations (4-8 Hz), but in longer SEDs the low frequency changed to the delta range (1-4 Hz).

CONCLUSION

Longer duration SEDs exhibit CFC features similar to those reported by our team.

SIGNIFICANCE

First, Identifying the exponential relationship between network excitability and SED durations; second, highlighting the importance of glia in hyperexcitability (as they relate to extracellular potassium); and third, elucidation of the biophysical basis for CFC coupling features.

Interneuronal Network Activity at the Onset of Seizure-Like Events in Entorhinal Cortex Slices

The onset of focal seizures in humans and in different animal models of focal epilepsy correlates with reduction of neuronal firing and enhanced interneuronal network activity. Whether this phenomenon contributes to seizure generation is still unclear. We used the in vitro entorhinal cortex slices bathed in 4-aminopirydine (4-AP) as an experimental paradigm model to evaluate the correlation between interneuronal GABAergic network activity and seizure-like events. Epileptiform discharges were recorded in layer V-VI pyramidal neurons and fast-spiking interneurons in slices from male and female mice and in the isolated female guinea pig brain preparation during perfusion with 4-AP. We observed that 90% of seizure-like events recorded in principal cells were preceded by outward currents coupled with extracellular potassium shifts, abolished by pharmacological blockade of GABA_A receptors. Potassium elevations associated to GABA_A receptor-mediated population events were confirmed in the entorhinal cortex of the in vitro isolated whole guinea pig brain. Fast-rising and sustained extracellular potassium increases associated to interneuronal network activity consistently preceded the initiation of seizure-like events. We conclude that in the 4-AP seizure model, interneuronal network activity occurs before 4-AP-induced seizures and therefore supports a role of interneuron activity in focal seizure generation.SIGNIFICANCE STATEMENT The paper focuses on the mechanisms of ictogenesis, a topic that requires a step beyond the simplistic view that seizures, and epilepsy, are due to an increase of excitatory network activity. Focal temporal lobe seizures in humans and in several experimental epilepsies likely correlate with a prevalent activation of interneurons. The potassium channel blocker 4-aminopyridine reliably induces seizure-like events in temporal lobe structures. Herein, we show that a majority of seizures in the entorhinal cortex starts with interneuronal network activity accompanied by a fast and sustained increase in extracellular potassium. Our new findings reinforce and add a new piece of evidence to the proposal that limbic seizures can be supported by GABAergic hyperactivity.

Criticality in the brain: A synthesis of neurobiology, models and cognition

Cognitive function requires the coordination of neural activity across many scales, from neurons and circuits to large-scale networks. As such, it is unlikely that an explanatory framework focused upon any single scale will yield a comprehensive theory of brain activity and cognitive function. Modelling and analysis methods for neuroscience should aim to accommodate multiscale phenomena. Emerging research now suggests that multi-scale processes in the brain arise from so-called critical phenomena that occur very broadly in the natural world. Criticality arises in complex systems perched between order and disorder, and is marked by fluctuations that do not have any privileged spatial or temporal scale. We review the core nature of criticality, the evidence supporting its role in neural systems and its explanatory potential in brain health and disease.

Prediction of the Seizure Suppression Effect by Electrical Stimulation via a Computational Modeling Approach

In this paper, we identified factors that can affect seizure suppression via electrical stimulation by an integrative study based on experimental and computational approach. Preferentially, we analyzed the characteristics of seizure-like events (SLEs) using our previous in vitro experimental data. The results were analyzed in two groups classified according to the size of the effective region, in which the SLE was able to be completely suppressed by local stimulation. However, no significant differences were found between these two groups in terms of signal features or propagation characteristics (i.e., propagation delays, frequency spectrum, and phase synchrony). Thus, we further investigated important factors using a computational model that was capable of evaluating specific influences on effective region size. In the proposed model, signal transmission between neurons was based on two different mechanisms: synaptic transmission and the electrical field effect. We were able to induce SLEs having similar characteristics with differentially weighted adjustments for the two transmission methods in various noise environments. Although the SLEs had similar characteristics, their suppression effects differed. First of all, the suppression effect occurred only locally where directly received the stimulation effect in the high noise environment, but it occurred in the entire network in the low noise environment. Interestingly, in the same noise environment, the suppression effect was different depending on SLE propagation mechanism; only a local suppression effect was observed when the influence of the electrical field transmission was very weak, whereas a global effect was observed with a stronger electrical field effect. These results indicate that neuronal activities synchronized by a strong electrical field effect respond more sensitively to partial changes in the entire network. In addition, the proposed model was able to predict that stimulation of a seizure focus region is more effective for suppression. In conclusion, we confirmed the possibility of a computational model as a simulation tool to analyze the efficacy of deep brain stimulation (DBS) and investigated the key factors that determine the size of an effective region in seizure suppression via electrical stimulation.

The influence of depolarization block on seizure-like activity in networks of excitatory and inhibitory neurons

The inhibitory restraint necessary to suppress aberrant activity can fail when inhibitory neurons cease to generate action potentials as they enter depolarization block. We investigate possible bifurcation structures that arise at the onset of seizure-like activity resulting from depolarization block in inhibitory neurons. Networks of conductance-based excitatory and inhibitory neurons are simulated to characterize different types of transitions to the seizure state, and a mean field model is developed to verify the generality of the observed phenomena of excitatory-inhibitory dynamics. Specifically, the inhibitory population's activation function in the Wilson-Cowan model is modified to be non-monotonic to reflect that inhibitory neurons enter depolarization block given strong input. We find that a physiological state and a seizure state can coexist, where the seizure state is characterized by high excitatory and low inhibitory firing rate. Bifurcation analysis of the mean field model reveals that a transition to the seizure state may occur via a saddle-node bifurcation or a homoclinic bifurcation. We explain the hysteresis observed in network simulations using these two bifurcation types. We also demonstrate that extracellular potassium concentration affects the depolarization block threshold; the consequent changes in bifurcation structure enable the network to produce the tonic to clonic phase transition observed in biological epileptic networks.

Astrocytic modulation of neuronal excitability through K+ spatial buffering

The human brain contains two major cell populations, neurons and glia. While neurons are electrically excitable and capable of discharging short voltage pulses known as action potentials, glial cells are not. However, astrocytes, the prevailing subtype of glia in the cortex, are highly connected and can modulate the excitability of neurons by changing the concentration of potassium ions in the extracellular environment, a process called K⁺ clearance. During the past decade, astrocytes have been the focus of much research, mainly due to their close association with synapses and their modulatory impact on neuronal activity. It has been shown that astrocytes play an essential role in normal brain function including: nitrosative regulation of synaptic release in the neocortex, synaptogenesis, synaptic transmission and plasticity. Here, we discuss the role of astrocytes in network modulation through their K⁺ clearance capabilities, a theory that was first raised 50 years ago by Orkand and Kuffler. We will discuss the functional alterations in astrocytic activity that leads to aberrant modulation of network oscillations and synchronous activity.

Synaptic Conductances during Interictal Discharges in Pyramidal Neurons of Rat Entorhinal Cortex

In epilepsy, the balance of excitation and inhibition underlying the basis of neural network activity shifts, resulting in neuronal network hyperexcitability and recurrent seizure-associated discharges. Mechanisms involved in ictal and interictal events are not fully understood, in particular, because of controversial data regarding the dynamics of excitatory and inhibitory synaptic conductances. In the present study, we estimated AMPAR-, NMDAR-, and GABA_A R-mediated conductances during two distinct types of interictal discharge (IID) in pyramidal neurons of rat entorhinal cortex in cortico-hippocampal slices. Repetitively emerging seizure-like events and IIDs were recorded in high extracellular potassium, 4-aminopyridine, and reduced magnesium-containing solution. An original procedure for estimating synaptic conductance during IIDs was based on the differences among the current-voltage characteristics of the synaptic components. The synaptic conductance dynamics obtained revealed that the first type of IID is determined by activity of GABA_A R channels with depolarized reversal potential. The second type of IID is determined by the interplay between excitation and inhibition, with early AMPAR and prolonged depolarized GABA_A R and NMDAR-mediated components. The study then validated the contribution of these components to IIDs by intracellular pharmacological isolation. These data provide new insights into the mechanisms of seizures generation, development, and cessation.

Interaction between synaptic inhibition and glial-potassium dynamics leads to diverse seizure transition modes in biophysical models of human focal seizures

How focal seizures initiate and evolve in human neocortex remains a fundamental problem in neuroscience. Here, we use biophysical neuronal network models of neocortical patches to study how the interaction between inhibition and extracellular potassium ([K (+)] o ) dynamics may contribute to different types of focal seizures. Three main types of propagated focal seizures observed in recent intracortical microelectrode recordings in humans were modelled: seizures characterized by sustained (∼30-60 Hz) gamma local field potential (LFP) oscillations; seizures where the onset in the propagated site consisted of LFP spikes that later evolved into rhythmic (∼2-3 Hz) spike-wave complexes (SWCs); and seizures where a brief stage of low-amplitude fast-oscillation (∼10-20 Hz) LFPs preceded the SWC activity. Our findings are fourfold: (1) The interaction between elevated [K (+)] o (due to abnormal potassium buffering by glial cells) and the strength of synaptic inhibition plays a predominant role in shaping these three types of seizures. (2) Strengthening of inhibition leads to the onset of sustained narrowband gamma seizures. (3) Transition into SWC seizures is obtained either by the weakening of inhibitory synapses, or by a transient strengthening followed by an inhibitory breakdown (e.g. GABA depletion). This reduction or breakdown of inhibition among fast-spiking (FS) inhibitory interneurons increases their spiking activity and leads them eventually into depolarization block. Ictal spike-wave discharges in the model are then sustained solely by pyramidal neurons. (4) FS cell dynamics are also critical for seizures where the evolution into SWC activity is preceded by low-amplitude fast oscillations. Different levels of elevated [K (+)] o were important for transitions into and maintenance of sustained gamma oscillations and SWC discharges. Overall, our modelling study predicts that the interaction between inhibitory interneurons and [K (+)] o glial buffering under abnormal conditions may explain different types of ictal transitions and dynamics during propagated seizures in human focal epilepsy.

Effects of astrocytic mechanisms on neuronal hyperexcitability

While originally astrocytes have been thought to only act as support to neurons, recent studies have implicated them in multiple active roles, including the ability to moderate or alter neuronal firing patterns and to possibly be involved in both the prevention and propagation of epileptic seizures. In this study we propose a new model to incorporate pyramidal cells and interneurons (a common neural circuit in CA3 hippocampal slices) as well as a model of astrocyte. As both potassium and calcium ions have been shown to potentially affect neuronal hyperexcitability, the astrocytic model has both mechanisms--the clearance of potassium through potassium channels (such as KIR, KDR and sodium-potassium pump), and the influence of astrocyte in the synapse (forming the tripartite synapse with calcium-glutamate interactions). Preliminary findings of the model results show that when potassium conductances in the astrocyte are decreased, it results in the accumulation of extracellular potassium, leading to both spontaneous discharges and depolarization block, while the alteration of normal calcium response in the astrocyte can lead to just hyperexcitable conditions without the depolarization block.

Computational modeling of epileptiform activities in medial temporal lobe epilepsy combined with in vitro experiments

In this paper, we propose a comprehensive computational model that is able to reproduce three epileptiform activities. The model targets a hippocampal formation that is known to be an important lesion in medial temporal lobe epilepsy. It consists of four sub-networks consisting of excitatory and inhibitory neurons and well-known signal pathways, with consideration of propagation delay. The three epileptiform activities involve fast and slow interictal discharge and ictal discharge, and those activities can be induced in vitro by application of 4-Aminopyridine in entorhinal cortex combined hippocampal slices. We model the three epileptiform activities upon previously reported biological mechanisms and verify the simulation results by comparing them with in vitro experimental data obtained using a microelectrode array. We use the results of Granger causality analysis of recorded data to set input gains of signal pathways in the model, so that the compatibility between the computational and experimental models can be improved. The proposed model can be expanded to evaluate the suppression effect of epileptiform activities due to new treatment methods.

Modeling of Age-Dependent Epileptogenesis by Differential Homeostatic Synaptic Scaling

Homeostatic synaptic plasticity (HSP) has been implicated in the development of hyperexcitability and epileptic seizures following traumatic brain injury (TBI). Our in vivo experimental studies in cats revealed that the severity of TBI-mediated epileptogenesis depends on the age of the animal. To characterize mechanisms of these differences, we studied the properties of the TBI-induced epileptogenesis in a biophysically realistic cortical network model with dynamic ion concentrations. After deafferentation, which was induced by dissection of the afferent inputs, there was a reduction of the network activity and upregulation of excitatory connections leading to spontaneous spike-and-wave type seizures. When axonal sprouting was implemented, the seizure threshold increased in the model of young but not the older animals, which had slower or unidirectional homeostatic processes. Our study suggests that age-related changes in the HSP mechanisms are sufficient to explain the difference in the likelihood of seizure onset in young versus older animals. Significance statement: Traumatic brain injury (TBI) is one of the leading causes of intractable epilepsy. Likelihood of developing epilepsy and seizures following severe brain trauma has been shown to increase with age. Specific mechanisms of TBI-related epileptogenesis and how these mechanisms are affected by age remain to be understood. We test a hypothesis that the failure of homeostatic synaptic regulation, a slow negative feedback mechanism that maintains neural activity within a physiological range through activity-dependent modulation of synaptic strength, in older animals may augment TBI-induced epileptogenesis. Our results provide new insight into understanding this debilitating disorder and may lead to novel avenues for the development of effective treatments of TBI-induced epilepsy.

Ion dynamics during seizures

Changes in membrane voltage brought about by ion fluxes through voltage and transmitter-gated channels represent the basis of neural activity. As such, electrochemical gradients across the membrane determine the direction and driving force for the flow of ions and are therefore crucial in setting the properties of synaptic transmission and signal propagation. Ion concentration gradients are established by a variety of mechanisms, including specialized transporter proteins. However, transmembrane gradients can be affected by ionic fluxes through channels during periods of elevated neural activity, which in turn are predicted to influence the properties of on-going synaptic transmission. Such activity-induced changes to ion concentration gradients are a feature of both physiological and pathological neural processes. An epileptic seizure is an example of severely perturbed neural activity, which is accompanied by pronounced changes in intracellular and extracellular ion concentrations. Appreciating the factors that contribute to these ion dynamics is critical if we are to understand how a seizure event evolves and is sustained and terminated by neural tissue. Indeed, this issue is of significant clinical importance as status epilepticus—a type of seizure that does not stop of its own accord—is a life-threatening medical emergency. In this review we explore how the transmembrane concentration gradient of the six major ions (K⁺, Na⁺, Cl⁻, Ca²⁺, H⁺and HCO3−) is altered during an epileptic seizure. We will first examine each ion individually, before describing how multiple interacting mechanisms between ions might contribute to concentration changes and whether these act to prolong or terminate epileptic activity. In doing so, we will consider how the availability of experimental techniques has both advanced and restricted our ability to study these phenomena.

Slow Spatial Recruitment of Neocortex during Secondarily Generalized Seizures and Its Relation to Surgical Outcome

Understanding the spatiotemporal dynamics of brain activity is crucial for inferring the underlying synaptic and nonsynaptic mechanisms of brain dysfunction. Focal seizures with secondary generalization are traditionally considered to begin in a limited spatial region and spread to connected areas, which can include both pathological and normal brain tissue. The mechanisms underlying this spread are important to our understanding of seizures and to improve therapies for surgical intervention. Here we study the properties of seizure recruitment-how electrical brain activity transitions to large voltage fluctuations characteristic of spike-and-wave seizures. We do so using invasive subdural electrode arrays from a population of 16 patients with pharmacoresistant epilepsy. We find an average delay of ∼30 s for a broad area of cortex (8 × 8 cm) to be recruited into the seizure, at an estimated speed of ∼4 mm/s. The spatiotemporal characteristics of recruitment reveal two categories of patients: one in which seizure recruitment of neighboring cortical regions follows a spatially organized pattern consistent from seizure to seizure, and a second group without consistent spatial organization of activity during recruitment. The consistent, organized recruitment correlates with a more regular, compared with small-world, connectivity pattern in simulation and successful surgical treatment of epilepsy. We propose that an improved understanding of how the seizure recruits brain regions into large amplitude voltage fluctuations provides novel information to improve surgical treatment of epilepsy and highlights the slow spread of massive local activity across a vast extent of cortex during seizure.

Possible Mechanisms Underlying the Therapeutic Effects of Transcranial Magnetic Stimulation

Transcranial magnetic stimulation (TMS) is an effective method used to diagnose and treat many neurological disorders. Although repetitive TMS (rTMS) has been used to treat a variety of serious pathological conditions including stroke, depression, Parkinson’s disease, epilepsy, pain, and migraines, the pathophysiological mechanisms underlying the effects of long-term TMS remain unclear. In the present review, the effects of rTMS on neurotransmitters and synaptic plasticity are described, including the classic interpretations of TMS effects on synaptic plasticity via long-term potentiation and long-term depression. We also discuss the effects of rTMS on the genetic apparatus of neurons, glial cells, and the prevention of neuronal death. The neurotrophic effects of rTMS on dendritic growth and sprouting and neurotrophic factors are described, including change in brain-derived neurotrophic factor concentration under the influence of rTMS. Also, non-classical effects of TMS related to biophysical effects of magnetic fields are described, including the quantum effects, the magnetic spin effects, genetic magnetoreception, the macromolecular effects of TMS, and the electromagnetic theory of consciousness. Finally, we discuss possible interpretations of TMS effects according to dynamical systems theory. Evidence suggests that a rTMS-induced magnetic field should be considered a separate physical factor that can be impactful at the subatomic level and that rTMS is capable of significantly altering the reactivity of molecules (radicals). It is thought that these factors underlie the therapeutic benefits of therapy with TMS. Future research on these mechanisms will be instrumental to the development of more powerful and reliable TMS treatment protocols.

Possible Mechanisms Underlying the Therapeutic Effects of Transcranial Magnetic Stimulation

Transcranial magnetic stimulation (TMS) is an effective method used to diagnose and treat many neurological disorders. Although repetitive TMS (rTMS) has been used to treat a variety of serious pathological conditions including stroke, depression, Parkinson's disease, epilepsy, pain, and migraines, the pathophysiological mechanisms underlying the effects of long-term TMS remain unclear. In the present review, the effects of rTMS on neurotransmitters and synaptic plasticity are described, including the classic interpretations of TMS effects on synaptic plasticity via long-term potentiation and long-term depression. We also discuss the effects of rTMS on the genetic apparatus of neurons, glial cells, and the prevention of neuronal death. The neurotrophic effects of rTMS on dendritic growth and sprouting and neurotrophic factors are described, including change in brain-derived neurotrophic factor concentration under the influence of rTMS. Also, non-classical effects of TMS related to biophysical effects of magnetic fields are described, including the quantum effects, the magnetic spin effects, genetic magnetoreception, the macromolecular effects of TMS, and the electromagnetic theory of consciousness. Finally, we discuss possible interpretations of TMS effects according to dynamical systems theory. Evidence suggests that a rTMS-induced magnetic field should be considered a separate physical factor that can be impactful at the subatomic level and that rTMS is capable of significantly altering the reactivity of molecules (radicals). It is thought that these factors underlie the therapeutic benefits of therapy with TMS. Future research on these mechanisms will be instrumental to the development of more powerful and reliable TMS treatment protocols.

Characterising seizures in anti-NMDA-receptor encephalitis with dynamic causal modelling

We characterised the pathophysiology of seizure onset in terms of slow fluctuations in synaptic efficacy using EEG in patients with anti-N-methyl-d-aspartate receptor (NMDA-R) encephalitis. EEG recordings were obtained from two female patients with anti-NMDA-R encephalitis with recurrent partial seizures (ages 19 and 31). Focal electrographic seizure activity was localised using an empirical Bayes beamformer. The spectral density of reconstructed source activity was then characterised with dynamic causal modelling (DCM). Eight models were compared for each patient, to evaluate the relative contribution of changes in intrinsic (excitatory and inhibitory) connectivity and endogenous afferent input. Bayesian model comparison established a role for changes in both excitatory and inhibitory connectivity during seizure activity (in addition to changes in the exogenous input). Seizures in both patients were associated with a sequence of changes in inhibitory and excitatory connectivity; a transient increase in inhibitory connectivity followed by a transient increase in excitatory connectivity and a final peak of excitatory–inhibitory balance at seizure offset. These systematic fluctuations in excitatory and inhibitory gain may be characteristic of (anti NMDA-R encephalitis) seizures. We present these results as a case study and replication to motivate analyses of larger patient cohorts, to see whether our findings generalise and further characterise the mechanisms of seizure activity in anti-NMDA-R encephalitis.

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We characterised seizures in patient with anti-NMDA-R encephalitis using EEG.

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Dynamic causal modelling was used to estimate causes of seizure activity.

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Characteristic variation of excitatory–inhibitory balance during seizure activity.

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This variation was seen for seizures within and between patients.

The spacing principle for unlearning abnormal neuronal synchrony

Desynchronizing stimulation techniques were developed to specifically counteract abnormal neuronal synchronization relevant to several neurological and psychiatric disorders. The goal of our approach is to achieve an anti-kindling, where the affected neural networks unlearn abnormal synaptic connectivity and, hence, abnormal neuronal synchrony, by means of desynchronizing stimulation, in particular, Coordinated Reset (CR) stimulation. As known from neuroscience, psychology and education, learning effects can be enhanced by means of the spacing principle, i.e. by delivering repeated stimuli spaced by pauses as opposed to delivering a massed stimulus (in a single long stimulation session). To illustrate that the spacing principle may boost the anti-kindling effect of CR neuromodulation, in this computational study we carry this approach to extremes. To this end, we deliver spaced CR neuromodulation at particularly weak intensities which render permanently delivered CR neuromodulation ineffective. Intriguingly, spaced CR neuromodulation at these particularly weak intensities effectively induces an anti-kindling. In fact, the spacing principle enables the neuronal population to successively hop from one attractor to another one, finally approaching attractors characterized by down-regulated synaptic connectivity and synchrony. Our computational results might open up novel opportunities to effectively induce sustained desynchronization at particularly weak stimulation intensities, thereby avoiding side effects, e.g., in the case of deep brain stimulation.

Electrogenic properties of the Na⁺/K⁺ ATPase control transitions between normal and pathological brain states

Ionic concentrations fluctuate significantly during epileptic seizures. In this study, using a combination of in vitro electrophysiology, computer modeling, and dynamical systems analysis, we demonstrate that changes in the potassium and sodium intra- and extracellular ion concentrations ([K(+)] and [Na(+)], respectively) during seizure affect the neuron dynamics by modulating the outward Na(+)/K(+) pump current. First, we show that an increase of the outward Na(+)/K(+) pump current mediates termination of seizures when there is a progressive increase in the intracellular [Na(+)]. Second, we show that the Na(+)/K(+) pump current is crucial in maintaining the stability of the physiological network state; a reduction of this current leads to the onset of seizures via a positive-feedback loop. We then present a novel dynamical mechanism for bursting in neurons with a reduced Na(+)/K(+) pump. Overall, our study demonstrates the profound role of the current mediated by Na(+)/K(+) ATPase on the stability of neuronal dynamics that was previously unknown.

A computational study of stimulus driven epileptic seizure abatement

Active brain stimulation to abate epileptic seizures has shown mixed success. In spike-wave (SW) seizures, where the seizure and background state were proposed to coexist, single-pulse stimulations have been suggested to be able to terminate the seizure prematurely. However, several factors can impact success in such a bistable setting. The factors contributing to this have not been fully investigated on a theoretical and mechanistic basis. Our aim is to elucidate mechanisms that influence the success of single-pulse stimulation in noise-induced SW seizures. In this work, we study a neural population model of SW seizures that allows the reconstruction of the basin of attraction of the background activity as a four dimensional geometric object. For the deterministic (noise-free) case, we show how the success of response to stimuli depends on the amplitude and phase of the SW cycle, in addition to the direction of the stimulus in state space. In the case of spontaneous noise-induced seizures, the basin becomes probabilistic introducing some degree of uncertainty to the stimulation outcome while maintaining qualitative features of the noise-free case. Additionally, due to the different time scales involved in SW generation, there is substantial variation between SW cycles, implying that there may not be a fixed set of optimal stimulation parameters for SW seizures. In contrast, the model suggests an adaptive approach to find optimal stimulation parameters patient-specifically, based on real-time estimation of the position in state space. We discuss how the modelling work can be exploited to rationally design a successful stimulation protocol for the abatement of SW seizures using real-time SW detection.

Dynamic mechanisms of neocortical focal seizure onset

Recent experimental and clinical studies have provided diverse insight into the mechanisms of human focal seizure initiation and propagation. Often these findings exist at different scales of observation, and are not reconciled into a common understanding. Here we develop a new, multiscale mathematical model of cortical electric activity with realistic mesoscopic connectivity. Relating the model dynamics to experimental and clinical findings leads us to propose three classes of dynamical mechanisms for the onset of focal seizures in a unified framework. These three classes are: (i) globally induced focal seizures; (ii) globally supported focal seizures; (iii) locally induced focal seizures. Using model simulations we illustrate these onset mechanisms and show how the three classes can be distinguished. Specifically, we find that although all focal seizures typically appear to arise from localised tissue, the mechanisms of onset could be due to either localised processes or processes on a larger spatial scale. We conclude that although focal seizures might have different patient-specific aetiologies and electrographic signatures, our model suggests that dynamically they can still be classified in a clinically useful way. Additionally, this novel classification according to the dynamical mechanisms is able to resolve some of the previously conflicting experimental and clinical findings.

According to the WHO fact sheet, epilepsy is a neurological disorder affecting about 50 million people worldwide. Even today 30% of epilepsy patients do not respond well to drug therapies. Neocortical focal epilepsy is a particular type of epilepsy in which drug treatments fail and surgical success rate is low. Hence, research is essential to improve the treatment of this type of epilepsy. Recent advances in brain recording methods have led to new observations regarding the nature of neocortical focal epilepsy. However, some of the observations appear to be contradictory. Here, we develop a computational modelling framework that can explain the different observations as different aspects of possible mechanisms that can all lead to seizure onset. Specifically, we classify three main conditions under which focal seizure onset can happen. This classification is clinically important, as our model predicts different treatment strategies for each class. We conclude that focal seizures are diverse, not only in their electrographic appearance and aetiology, but also in their onset mechanism. Combined multiscale recordings as well as stimulation studies are required to elucidate the onset mechanism in each patient. Our work provides the first classification of possible onset mechanism.

Elevated serotonergic signaling amplifies synaptic noise and facilitates the emergence of epileptiform network oscillations

Serotonin fibers densely innervate the cortical sheath to regulate neuronal excitability, but its role in shaping network dynamics remains undetermined. We show that serotonin provides an excitatory tone to cortical neurons in the form of spontaneous synaptic noise through 5-HT3 receptors, which is persistent and can be augmented using fluoxetine, a selective serotonin re-uptake inhibitor. Augmented serotonin signaling also increases cortical network activity by enhancing synaptic excitation through activation of 5-HT2 receptors. This in turn facilitates the emergence of epileptiform network oscillations (10-16 Hz) known as fast runs. A computational model of cortical dynamics demonstrates that these two combined mechanisms, increased background synaptic noise and enhanced synaptic excitation, are sufficient to replicate the emergence fast runs and their statistics. Consistent with these findings, we show that blocking 5-HT2 receptors in vivo significantly raises the threshold for convulsant-induced seizures.

The influence of ion concentrations on the dynamic behavior of the Hodgkin-Huxley model-based cortical network

Action potentials (APs) in the form of very short pulses arise when the cell is excited by any internal or external stimulus exceeding the critical threshold of the membrane. During AP generation, the membrane potential completes its natural cycle through typical phases that can be formatted by ion channels, gates and ion concentrations, as well as the synaptic excitation rate. On the basis of the Hodgkin-Huxley cell model, a cortical network consistent with the real anatomic structure is realized with randomly interrelated small population of neurons to simulate a cerebral cortex segment. Using this model, we investigated the effects of Na(+) and K(+) ion concentrations on the outcome of this network in terms of regularity, phase locking, and synchronization. The results suggested that Na(+) concentration does slightly affect the amplitude but not considerably affects the other parameters specified by depolarization and repolarization. K(+) concentration significantly influences the form, regularity, and synchrony of the network-generated APs. No previous study dealing directly with the effects of both Na(+) and K(+) ion concentrations on regularity and synchronization of the simulated cortical network-generated APs, allowing for the comparison of results obtained using our methods, was encountered in the literature. The results, however, were consistent with those obtained through studies concerning resonance and synchronization from another perspective and with the information revealed through physiological and pharmacological experiments concerning changing ion concentrations or blocking ion channels. Our results demonstrated that the regularity and reliability of brain functions have a strong relationship with cellular ion concentrations, and suggested the management of the dynamic behavior of the cellular network with ion concentrations.

Fragility in dynamic networks: application to neural networks in the epileptic cortex

Epilepsy is a network phenomenon characterized by atypical activity at the neuronal and population levels during seizures, including tonic spiking, increased heterogeneity in spiking rates, and synchronization. The etiology of epilepsy is unclear, but a common theme among proposed mechanisms is that structural connectivity between neurons is altered. It is hypothesized that epilepsy arises not from random changes in connectivity, but from specific structural changes to the most fragile nodes or neurons in the network. In this letter, the minimum energy perturbation on functional connectivity required to destabilize linear networks is derived. Perturbation results are then applied to a probabilistic nonlinear neural network model that operates at a stable fixed point. That is, if a small stimulus is applied to the network, the activation probabilities of each neuron respond transiently but eventually recover to their baseline values. When the perturbed network is destabilized, the activation probabilities shift to larger or smaller values or oscillate when a small stimulus is applied. Finally, the structural modifications to the neural network that achieve the functional perturbation are derived. Simulations of the unperturbed and perturbed networks qualitatively reflect neuronal activity observed in epilepsy patients, suggesting that the changes in network dynamics due to destabilizing perturbations, including the emergence of an unstable manifold or a stable limit cycle, may be indicative of neuronal or population dynamics during seizure. That is, the epileptic cortex is always on the brink of instability and minute changes in the synaptic weights associated with the most fragile node can suddenly destabilize the network to cause seizures. Finally, the theory developed here and its interpretation of epileptic networks enables the design of a straightforward feedback controller that first detects when the network has destabilized and then applies linear state feedback control to steer the network back to its stable state.