Computational modeling of high-frequency oscillations at the onset of neocortical partial seizures: From ‘altered structure’ to ‘dysfunction’

Network effects of traumatic brain injury: from infra slow to high frequency oscillations and seizures

Traumatic brain injury (TBI) can have a multitude of effects on neural functioning. In extreme cases, TBI can lead to seizures both immediately following the injury as well as persistent epilepsy over years to a lifetime. However, mechanisms of neural dysfunctioning after TBI remain poorly understood. To address these questions, we analyzed human and animal data and we developed a biophysical network model implementing effects of ion concentration dynamics and homeostatic synaptic plasticity to test effects of TBI on the brain network dynamics. We focus on three primary phenomena that have been reported in vivo after TBI: an increase in infra slow oscillations (<0.1 Hz), increase in Delta power (1 - 4 Hz), and the emergence of broadband Gamma bursts (30 - 100 Hz). Using computational network model, we show that the infra slow oscillations can be directly attributed to extracellular potassium dynamics, while the increase in Delta power and occurrence of Gamma bursts are related to the increase in strength of synaptic weights from homeostatic synaptic scaling triggered by trauma. We also show that the buildup of Gamma bursts in the injured region can lead to seizure-like events that propagate across the entire network; seizures can then be initiated in previously healthy regions. This study brings greater understanding of the network effects of TBI and how they can lead to epileptic activity. This lays the foundation to begin investigating how injured networks can be healed and seizures prevented.

Transition to seizure in focal epilepsy: From SEEG phenomenology to underlying mechanisms

OBJECTIVE

For the pre-surgical evaluation of patients with drug-resistant focal epilepsy, stereo-electroencephalographic (SEEG) signals are routinely recorded to identify the epileptogenic zone network (EZN). This network consists of remote brain regions involved in seizure initiation. However, the pathophysiological mechanisms underlying typical SEEG patterns that occur during the transition from interictal to ictal activity in distant brain nodes of the EZN remain poorly understood. The primary aim is to identify and explain these mechanisms using a novel physiologically-plausible model of the EZN.

METHODS

We analyzed SEEG signals recorded from the EZN in 10 patients during the transition from interictal to ictal activity. This transition consisted of a sequence of periods during which SEEG signals from distant neocortical regions showed stereotypical patterns of activity: sustained preictal spiking activity preceding a fast activity occurring at seizure onset, followed by the ictal activity. Spectral content and non-linear correlation of SEEG signals were analyzed. In addition, we developed a novel neuro-inspired computational model consisting of bidirectionally coupled neuronal populations.

RESULTS

The proposed model captured the essential characteristics of the patient signals, including the quasi-synchronous onset of rapid discharges in distant interconnected epileptogenic zones. Statistical analysis confirmed the dynamic correlation/de-decorrelation pattern observed in the patient signals and accurately reproduced in the simulated signals.

SIGNIFICANCE

This study provides insight into the abnormal dynamic changes in glutamatergic and γ-aminobutyric acid (GABA)ergic synaptic transmission that occur during the transition to seizures. The results strongly support the hypothesis that bidirectional connections between distant neuronal populations of the EZN (from pyramidal cells to vaso-intestinal peptide-positive interneurons) play a key role in this transition, while parvalbumin-positive interneurons intervene in the emergence of rapid discharges at seizure onset.

Spike-spindle coupling during sleep and its mechanism explanation in childhood focal epilepsy

Childhood focal epilepsy (CFE) is a serious neurological disorder characterized by epileptic seizures arising from a focal or multi-focal zone of the brain in clinics. During non-rapid eye movement (NREM) sleep stage, epileptiform discharges become frequent, and sleep spindles are generated through local interaction between thalamic neurons for CFE patients. Recent research has shown that epileptiform spikes significantly induce spindle oscillations within 1 s (say, spike-spindle coupling) during NREM sleep in focal epilepsy, which might damage cognitive function of epilepsy patients. However, the temporal interaction mechanism between spikes and spindles is lack of understanding. In this paper, we first develop a new thalamocortical model of CFE (CFE-TCM) by integrating M-type potassium current, persistent sodium current and NMDAR current into Costa model, where the three types of currents are important for modulating the excitability of thalamocortical system. Then we demonstrate in simulations that: (1) the temporal spike-spindle coupling oscillatory patterns do exist in real CFE-EEGs recorded in clinics; (2) the constructed model CFE-TCM has a capacity of generating spike-spindle coupling discharges, and the corresponding statistical results are consistent with those obtained from real EEGs; (3) the spike-spindle coupling discharges are mediated by the strength of long-range thalamus-cortex connections where the excitable projection from thalamocortical neuron in thalamus to pyramidal neuron in cortex takes a great role. The obtained results reveal that pathological spike-spindle coupling may be a potential marker of thalamocortical circuit dysfunction, which will provide a possible treatment strategy for disease progression and cognition impairment in focal epilepsy.

Is High-Frequency Activity at Seizure Onset Inhibitory? A Stereoelectroencephalographic Study of Motor Cortex Seizures

OBJECTIVE

In the era of stereoelectroencephalography (SEEG), many studies have been devoted to understanding the role of interictal high-frequency oscillations. High-frequency activity (HFA) at seizure onset has been identified as a marker of epileptogenic zone. We address the physiological significance of ictal HFAs and their relation to clinical semiology.

METHODS

We retrospectively identified patients with pure focal primary motor epilepsy. We selected only patients in whom SEEG electrodes were optimally placed in the motor cortex as confirmed by electrical stimulation. Based on these narrow inclusion criteria, we extensively studied 5 patients (3 males and 2 females, mean age = 22.4 years) using time-frequency analysis and time correlation with motor signs onset.

RESULTS

A total of 157 analyzable seizures were recorded in 5 subjects. The first 2 subjects had tonic or clonic semiology with rare secondary generalization. Subject 3 had atonic onset followed by clonic hand/arm flexion. Subject 4 had clusters of tonic and atonic facial movements. Subject 5 had upper extremity tonic movements. The median frequency of the fast activity extracted from the Epileptogenic Zone Fingerprint pipeline in the first 4 subjects was 76 Hz (interquartile range = 21.9Hz). Positive motor signs did not occur concomitantly with high gamma activity developing in the motor cortex. Motor signs began at the end of HFAs.

INTERPRETATION

This study supports the hypothesis of an inhibitory effect of ictal HFAs. The frequency range in the gamma band was associated with the direction of the clinical output effect. Changes from inhibitory to excitatory effect occurred when discharge frequency dropped to low gamma or beta. ANN NEUROL 2024;95:1127-1137.

Multiscale neuro-inspired models for interpretation of EEG signals in patients with epilepsy

OBJECTIVE

The aim is to gain insight into the pathophysiological mechanisms underlying interictal epileptiform discharges observed in electroencephalographic (EEG) and stereo-EEG (SEEG, depth electrodes) recordings performed during pre-surgical evaluation of patients with drug-resistant epilepsy.

METHODS

We developed novel neuro-inspired computational models of the human cerebral cortex at three different levels of description: i) microscale (detailed neuron models), ii) mesoscale (neuronal mass models) and iii) macroscale (whole brain models). Although conceptually different, micro- and mesoscale models share some similar features, such as the typology of neurons (pyramidal cells and three types of interneurons), their spatial arrangement in cortical layers, and their synaptic connectivity (excitatory and inhibitory). The whole brain model consists of a large-scale network of interconnected neuronal masses, with connectivity based on the human connectome.

RESULTS

For these three levels of description, the fine-tuning of free parameters and the quantitative comparison with real data allowed us to reproduce interictal epileptiform discharges with a high degree of fidelity and to formulate hypotheses about the cell- and network-related mechanisms underlying the generation of fast ripples and SEEG-recorded epileptic spikes and spike-waves.

CONCLUSIONS

The proposed models provide valuable insights into the pathophysiological mechanisms underlying the generation of epileptic events. The knowledge gained from these models effectively complements the clinical analysis of SEEG data collected during the evaluation of patients with epilepsy.

SIGNIFICANCE

These models are likely to play a key role in the mechanistic interpretation of epileptiform activity.

A physical neural mass model framework for the analysis of oscillatory generators from laminar electrophysiological recordings

Cortical function emerges from the interactions of multi-scale networks that may be studied at a high level using neural mass models (NMM) that represent the mean activity of large numbers of neurons. Here, we provide first a new framework called laminar NMM, or LaNMM for short, where we combine conduction physics with NMMs to simulate electrophysiological measurements. Then, we employ this framework to infer the location of oscillatory generators from laminar-resolved data collected from the prefrontal cortex in the macaque monkey. We define a minimal model capable of generating coupled slow and fast oscillations, and we optimize LaNMM-specific parameters to fit multi-contact recordings. We rank the candidate models using an optimization function that evaluates the match between the functional connectivity (FC) of the model and data, where FC is defined by the covariance between bipolar voltage measurements at different cortical depths. The family of best solutions reproduces the FC of the observed electrophysiology by selecting locations of pyramidal cells and their synapses that result in the generation of fast activity at superficial layers and slow activity across most depths, in line with recent literature proposals. In closing, we discuss how this hybrid modeling framework can be more generally used to infer cortical circuitry.

Comparison between an exact and a heuristic neural mass model with second-order synapses

Neural mass models (NMMs) are designed to reproduce the collective dynamics of neuronal populations. A common framework for NMMs assumes heuristically that the output firing rate of a neural population can be described by a static nonlinear transfer function (NMM1). However, a recent exact mean-field theory for quadratic integrate-and-fire (QIF) neurons challenges this view by showing that the mean firing rate is not a static function of the neuronal state but follows two coupled nonlinear differential equations (NMM2). Here we analyze and compare these two descriptions in the presence of second-order synaptic dynamics. First, we derive the mathematical equivalence between the two models in the infinitely slow synapse limit, i.e., we show that NMM1 is an approximation of NMM2 in this regime. Next, we evaluate the applicability of this limit in the context of realistic physiological parameter values by analyzing the dynamics of models with inhibitory or excitatory synapses. We show that NMM1 fails to reproduce important dynamical features of the exact model, such as the self-sustained oscillations of an inhibitory interneuron QIF network. Furthermore, in the exact model but not in the limit one, stimulation of a pyramidal cell population induces resonant oscillatory activity whose peak frequency and amplitude increase with the self-coupling gain and the external excitatory input. This may play a role in the enhanced response of densely connected networks to weak uniform inputs, such as the electric fields produced by noninvasive brain stimulation.

A mean-field model of glutamate and GABA synaptic dynamics for functional MRS

Advances in functional magnetic resonance spectroscopy (fMRS) have enabled the quantification of activity-dependent changes in neurotransmitter concentrations in vivo. However, the physiological basis of the large changes in GABA and glutamate observed by fMRS (>10%) over short time scales of less than a minute remain unclear as such changes cannot be accounted for by known synthesis or degradation metabolic pathways. Instead, it has been hypothesized that fMRS detects shifts in neurotransmitter concentrations as they cycle from presynaptic vesicles, where they are largely invisible, to extracellular and cytosolic pools, where they are detectable. The present paper uses a computational modelling approach to demonstrate the viability of this hypothesis. A new mean-field model of the neural mechanisms generating the fMRS signal in a cortical voxel is derived. The proposed macroscopic mean-field model is based on a microscopic description of the neurotransmitter dynamics at the level of the synapse. Specifically, GABA and glutamate are assumed to cycle between three metabolic pools: packaged in the vesicles; active in the synaptic cleft; and undergoing recycling and repackaging in the astrocytic or neuronal cytosol. Computational simulations from the model are used to generate predicted changes in GABA and glutamate concentrations in response to different types of stimuli including pain, vision, and electric current stimulation. The predicted changes in the extracellular and cytosolic pools corresponded to those reported in empirical fMRS data. Furthermore, the model predicts a selective control mechanism of the GABA/glutamate relationship, whereby inhibitory stimulation reduces both neurotransmitters, whereas excitatory stimulation increases glutamate and decreases GABA. The proposed model bridges between neural dynamics and fMRS and provides a mechanistic account for the activity-dependent changes in the glutamate and GABA fMRS signals. Lastly, these results indicate that echo-time may be an important timing parameter that can be leveraged to maximise fMRS experimental outcomes.

A personalizable autonomous neural mass model of epileptic seizures

Work in the last two decades has shown that neural mass models (NMM) can realistically reproduce and explain epileptic seizure transitions as recorded by electrophysiological methods (EEG, SEEG). In previous work, advances were achieved by increasing excitation and heuristically varying network inhibitory coupling parameters in the models. Based on these early studies, we provide a laminar NMM capable of realistically reproducing the electrical activity recorded by SEEG in the epileptogenic zone during interictal to ictal states. With the exception of the external noise input into the pyramidal cell population, the model dynamics are autonomous. By setting the system at a point close to bifurcation, seizure-like transitions are generated, including pre-ictal spikes, low voltage fast activity, and ictal rhythmic activity. A novel element in the model is a physiologically motivated algorithm for chloride dynamics: the gain of GABAergic post-synaptic potentials is modulated by the pathological accumulation of chloride in pyramidal cells due to high inhibitory input and/or dysfunctional chloride transport. In addition, in order to simulate SEEG signals for comparison with real seizure recordings, the NMM is embedded first in a layered model of the neocortex and then in a realistic physical model. We compare modeling results with data from four epilepsy patient cases. By including key pathophysiological mechanisms, the proposed framework captures succinctly the electrophysiological phenomenology observed in ictal states, paving the way for robust personalization methods based on NMMs.

Canard solutions in neural mass models: consequences on critical regimes

Mathematical models at multiple temporal and spatial scales can unveil the fundamental mechanisms of critical transitions in brain activities. Neural mass models (NMMs) consider the average temporal dynamics of interconnected neuronal subpopulations without explicitly representing the underlying cellular activity. The mesoscopic level offered by the neural mass formulation has been used to model electroencephalographic (EEG) recordings and to investigate various cerebral mechanisms, such as the generation of physiological and pathological brain activities. In this work, we consider a NMM widely accepted in the context of epilepsy, which includes four interacting neuronal subpopulations with different synaptic kinetics. Due to the resulting three-time-scale structure, the model yields complex oscillations of relaxation and bursting types. By applying the principles of geometric singular perturbation theory, we unveil the existence of the canard solutions and detail how they organize the complex oscillations and excitability properties of the model. In particular, we show that boundaries between pathological epileptic discharges and physiological background activity are determined by the canard solutions. Finally we report the existence of canard-mediated small-amplitude frequency-specific oscillations in simulated local field potentials for decreased inhibition conditions. Interestingly, such oscillations are actually observed in intracerebral EEG signals recorded in epileptic patients during pre-ictal periods, close to seizure onsets.

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.

COALIA: A Computational Model of Human EEG for Consciousness Research

Understanding the origin of the main physiological processes involved in consciousness is a major challenge of contemporary neuroscience, with crucial implications for the study of Disorders of Consciousness (DOC). The difficulties in achieving this task include the considerable quantity of experimental data in this field, along with the non-intuitive, nonlinear nature of neuronal dynamics. One possibility of integrating the main results from the experimental literature into a cohesive framework, while accounting for nonlinear brain dynamics, is the use of physiologically-inspired computational models. In this study, we present a physiologically-grounded computational model, attempting to account for the main micro-circuits identified in the human cortex, while including the specificities of each neuronal type. More specifically, the model accounts for thalamo-cortical (vertical) regulation of cortico-cortical (horizontal) connectivity, which is a central mechanism for brain information integration and processing. The distinct neuronal assemblies communicate through feedforward and feedback excitatory and inhibitory synaptic connections implemented in a template brain accounting for long-range connectome. The EEG generated by this physiologically-based simulated brain is validated through comparison with brain rhythms recorded in humans in two states of consciousness (wakefulness, sleep). Using the model, it is possible to reproduce the local disynaptic disinhibition of basket cells (fast GABAergic inhibition) and glutamatergic pyramidal neurons through long-range activation of vasoactive intestinal-peptide (VIP) interneurons that induced inhibition of somatostatin positive (SST) interneurons. The model (COALIA) predicts that the strength and dynamics of the thalamic output on the cortex control the local and long-range cortical processing of information. Furthermore, the model reproduces and explains clinical results regarding the complexity of transcranial magnetic stimulation TMS-evoked EEG responses in DOC patients and healthy volunteers, through a modulation of thalamo-cortical connectivity that governs the level of cortico-cortical communication. This new model provides a quantitative framework to accelerate the study of the physiological mechanisms involved in the emergence, maintenance and disruption (sleep, anesthesia, DOC) of consciousness.

Ictal networks of temporal lobe epilepsy: views from high-frequency oscillations in stereoelectroencephalography

OBJECTIVE

In this study, the authors investigated high-frequency oscillation (HFO) networks during seizures in order to determine how HFOs spread from the focal cerebral cortex and become synchronized across various areas of the brain.

METHODS

All data were obtained from stereoelectroencephalography (SEEG) signals in patients with drug-resistant temporal lobe epilepsy (TLE). The authors calculated intercontact cross-coefficients between all pairs of contacts to construct HFO networks in 20 seizures that occurred in 5 patients. They then calculated HFO network topology metrics (i.e., network density and component size) after normalizing seizure duration data by dividing each seizure into 10 intervals of equal length (labeled I1-I10).

RESULTS

From the perspective of the dynamic topologies of cortical and subcortical HFO networks, the authors observed a significant increase in network density during intervals I5-I10. A significant increase was also observed in overall energy during intervals I3-I8. The results of subnetwork analysis revealed that the number of components continuously decreased following the onset of seizures, and those results were statistically significant during intervals I3-I10. Furthermore, the majority of nodes were connected to a single dominant component during the propagation of seizures, and the percentage of nodes within the largest component grew significantly until seizure termination.

CONCLUSIONS

The consistent topological changes that the authors observed suggest that TLE is affected by common epileptogenic patterns. Indeed, the findings help to elucidate the epileptogenic network that characterizes TLE, which may be of interest to researchers and physicians working to improve treatment modalities for epilepsy, including resection, cortical stimulation, and neuromodulation treatments that are responsive to network topologies.

Pathological responses to single-pulse electrical stimuli in epilepsy: The role of feedforward inhibition

Delineation of epileptogenic cortex in focal epilepsy patients may profit from single‐pulse electrical stimulation during intracranial EEG recordings. Single‐pulse electrical stimulation evokes early and delayed responses. Early responses represent connectivity. Delayed responses are a biomarker for epileptogenic cortex, but up till now, the precise mechanism generating delayed responses remains elusive. We used a data‐driven modelling approach to study early and delayed responses. We hypothesized that delayed responses represent indirect responses triggered by early response activity and investigated this for 11 patients. Using two coupled neural masses, we modelled early and delayed responses by combining simulations and bifurcation analysis. An important feature of the model is the inclusion of feedforward inhibitory connections. The waveform of early responses can be explained by feedforward inhibition. Delayed responses can be viewed as second‐order responses in the early response network which appear when input to a neural mass falls below a threshold forcing it temporarily to a spiking state. The combination of the threshold with noisy background input explains the typical stochastic appearance of delayed responses. The intrinsic excitability of a neural mass and the strength of its input influence the probability at which delayed responses to occur. Our work gives a theoretical basis for the use of delayed responses as a biomarker for the epileptogenic zone, confirming earlier clinical observations. The combination of early responses revealing effective connectivity, and delayed responses showing intrinsic excitability, makes single‐pulse electrical stimulation an interesting tool to obtain data for computational models of epilepsy surgery.

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.

Adaptation and Inhibition Control Pathological Synchronization in a Model of Focal Epileptic Seizure

Pharmacoresistant epilepsy is a common neurological disorder in which increased neuronal intrinsic excitability and synaptic excitation lead to pathologically synchronous behavior in the brain. In the majority of experimental and theoretical epilepsy models, epilepsy is associated with reduced inhibition in the pathological neural circuits, yet effects of intrinsic excitability are usually not explicitly analyzed. Here we present a novel neural mass model that includes intrinsic excitability in the form of spike-frequency adaptation in the excitatory population. We validated our model using local field potential (LFP) data recorded from human hippocampal/subicular slices. We found that synaptic conductances and slow adaptation in the excitatory population both play essential roles for generating seizures and pre-ictal oscillations. Using bifurcation analysis, we found that transitions towards seizure and back to the resting state take place via Andronov-Hopf bifurcations. These simulations therefore suggest that single neuron adaptation as well as synaptic inhibition are responsible for orchestrating seizure dynamics and transition towards the epileptic state.

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.

Mechanisms underlying different onset patterns of focal seizures

Focal seizures are episodes of pathological brain activity that appear to arise from a localised area of the brain. The onset patterns of focal seizure activity have been studied intensively, and they have largely been distinguished into two types-low amplitude fast oscillations (LAF), or high amplitude spikes (HAS). Here we explore whether these two patterns arise from fundamentally different mechanisms. Here, we use a previously established computational model of neocortical tissue, and validate it as an adequate model using clinical recordings of focal seizures. We then reproduce the two onset patterns in their most defining properties and investigate the possible mechanisms underlying the different focal seizure onset patterns in the model. We show that the two patterns are associated with different mechanisms at the spatial scale of a single ECoG electrode. The LAF onset is initiated by independent patches of localised activity, which slowly invade the surrounding tissue and coalesce over time. In contrast, the HAS onset is a global, systemic transition to a coexisting seizure state triggered by a local event. We find that such a global transition is enabled by an increase in the excitability of the "healthy" surrounding tissue, which by itself does not generate seizures, but can support seizure activity when incited. In our simulations, the difference in surrounding tissue excitability also offers a simple explanation of the clinically reported difference in surgical outcomes. Finally, we demonstrate in the model how changes in tissue excitability could be elucidated, in principle, using active stimulation. Taken together, our modelling results suggest that the excitability of the tissue surrounding the seizure core may play a determining role in the seizure onset pattern, as well as in the surgical outcome.

A Phase-Locked Loop Epilepsy Network Emulator

Most seizure forecasting employs statistical learning techniques that lack a representation of the network interactions that give rise to seizures. We present an epilepsy network emulator (ENE) that uses a network of interconnected phase-locked loops (PLLs) to model synchronous, circuit-level oscillations between electrocorticography (ECoG) electrodes. Using ECoG data from a canine-epilepsy model (Davis et al. 2011) and a physiological entropy measure (approximate entropy or ApEn, Pincus 1995), we demonstrate the entropy of the emulator phases increases dramatically during ictal periods across all ECoG recording sites and across all animals in the sample. Further, this increase precedes the observable voltage spikes that characterize seizure activity in the ECoG data. These results suggest that the ENE is sensitive to phase-domain information in the neural circuits measured by ECoG and that an increase in the entropy of this measure coincides with increasing likelihood of seizure activity. Understanding this unpredictable phase-domain electrical activity present in ECoG recordings may provide a target for seizure detection and feedback control.

Dynamic changes of depolarizing GABA in a computational model of epileptogenic brain: Insight for Dravet syndrome

Abnormal reemergence of depolarizing GABAA current during postnatal brain maturation may play a major role in paediatric epilepsies, Dravet syndrome (DS) being among the most severe. To study the impact of depolarizing GABA onto distinct patterns of EEG activity, we extended a neural mass model as follows: one sub-population of pyramidal cells was added as well as two sub-populations of interacting interneurons, perisomatic-projecting interneurons (basket-like) with fast synaptic kinetics GABAA (fast, I1) and dendritic-projecting interneurons with slow synaptic kinetics GABAA (slow, I2). Basket-like cells were interconnected to reproduce mutual inhibition mechanisms (I1➔I1). The firing rate of interneurons was adapted to mimic the genetic alteration of voltage gated sodium channels found in DS patients, SCN1A(+/-). We implemented the "dynamic depolarizing GABAA" mediated post-synaptic potential in the model, as some studies reported that the chloride reversal potential can switch from negative to more positive value depending on interneuron activity. The "shunting inhibition" promoted by GABAA receptor activation was also implemented. We found that increasing the proportion of depolarizing GABAA mediated IPSP (I1➔I1 and I1➔P) only (i.e., other parameters left unchanged) was sufficient to sequentially switch the EEG activity from background to (1) interictal isolated polymorphic epileptic spikes, (2) fast onset activity, (3) seizure like activity and (4) seizure termination. The interictal and ictal EEG patterns observed in 4 DS patients were reproduced by the model via tuning the amount of depolarizing GABAA postsynaptic potential. Finally, we implemented the modes of action of benzodiazepines and stiripentol, two drugs recommended in DS. Both drugs blocked seizure-like activity, partially and dose-dependently when applied separately, completely and with a synergic effect when combined, as has been observed in DS patients. This computational modeling study constitutes an innovative approach to better define the role of depolarizing GABA in infantile onset epilepsy and opens the way for new therapeutic hypotheses, especially in Dravet syndrome.

Analysis and Enhancements of a Prolific Macroscopic Model of Epilepsy

Macroscopic models of epilepsy can deliver surprisingly realistic EEG simulations. In the present study, a prolific series of models is evaluated with regard to theoretical and computational concerns, and enhancements are developed. Specifically, we analyze three aspects of the models: (1) Using dynamical systems analysis, we demonstrate and explain the presence of direct current potentials in the simulated EEG that were previously undocumented. (2) We explain how the system was not ideally formulated for numerical integration of stochastic differential equations. A reformulated system is developed to support proper methodology. (3) We explain an unreported contradiction in the published model specification regarding the use of a mathematical reduction method. We then use the method to reduce the number of equations and further improve the computational efficiency. The intent of our critique is to enhance the evolution of macroscopic modeling of epilepsy and assist others who wish to explore this exciting class of models further.

A New Computational Model for Neuro-Glio-Vascular Coupling: Astrocyte Activation Can Explain Cerebral Blood Flow Nonlinear Response to Interictal Events

Developing a clear understanding of the relationship between cerebral blood flow (CBF) response and neuronal activity is of significant importance because CBF increase is essential to the health of neurons, for instance through oxygen supply. This relationship can be investigated by analyzing multimodal (fMRI, PET, laser Doppler…) recordings. However, the important number of intermediate (non-observable) variables involved in the underlying neurovascular coupling makes the discovery of mechanisms all the more difficult from the sole multimodal data. We present a new computational model developed at the population scale (voxel) with physiologically relevant but simple equations to facilitate the interpretation of regional multimodal recordings. This model links neuronal activity to regional CBF dynamics through neuro-glio-vascular coupling. This coupling involves a population of glial cells called astrocytes via their role in neurotransmitter (glutamate and GABA) recycling and their impact on neighboring vessels. In epilepsy, neuronal networks generate epileptiform discharges, leading to variations in astrocytic and CBF dynamics. In this study, we took advantage of these large variations in neuronal activity magnitude to test the capacity of our model to reproduce experimental data. We compared simulations from our model with isolated epileptiform events, which were obtained in vivo by simultaneous local field potential and laser Doppler recordings in rats after local bicuculline injection. We showed a predominant neuronal contribution for low level discharges and a significant astrocytic contribution for higher level discharges. Besides, neuronal contribution to CBF was linear while astrocytic contribution was nonlinear. Results thus indicate that the relationship between neuronal activity and CBF magnitudes can be nonlinear for isolated events and that this nonlinearity is due to astrocytic activity, highlighting the importance of astrocytes in the interpretation of regional recordings.

Role of multiple-scale modeling of epilepsy in seizure forecasting

Over the past three decades, a number of seizure prediction, or forecasting, methods have been developed. Although major achievements were accomplished regarding the statistical evaluation of proposed algorithms, it is recognized that further progress is still necessary for clinical application in patients. The lack of physiological motivation can partly explain this limitation. Therefore, a natural question is raised: can computational models of epilepsy be used to improve these methods? Here, we review the literature on the multiple-scale neural modeling of epilepsy and the use of such models to infer physiologic changes underlying epilepsy and epileptic seizures. The authors argue how these methods can be applied to advance the state-of-the-art in seizure forecasting.

Future of seizure prediction and intervention: closing the loop

The ultimate goal of epilepsy therapies is to provide seizure control for all patients while eliminating side effects. Improved specificity of intervention through on-demand approaches may overcome many of the limitations of current intervention strategies. This article reviews the progress in seizure prediction and detection, potential new therapies to provide improved specificity, and devices to achieve these ends. Specifically, we discuss (1) potential signal modalities and algorithms for seizure detection and prediction, (2) closed-loop intervention approaches, and (3) hardware for implementing these algorithms and interventions. Seizure prediction and therapies maximize efficacy, whereas minimizing side effects through improved specificity may represent the future of epilepsy treatments.

Sensing-enabled hippocampal deep brain stimulation in idiopathic nonhuman primate epilepsy

Epilepsy is a debilitating condition affecting 1% of the population worldwide. Medications fail to control seizures in at least 30% of patients, and deep brain stimulation (DBS) is a promising alternative treatment. A modified clinical DBS hardware platform was recently described (PC+S) allowing long-term recording of electrical brain activity such that effects of DBS on neural networks can be examined. This study reports the first use of this device to characterize idiopathic epilepsy and assess the effects of stimulation in a nonhuman primate (NHP). Clinical DBS electrodes were implanted in the hippocampus of an epileptic NHP bilaterally, and baseline local field potential (LFP) recordings were collected for seizure characterization with the PC+S. Real-time automatic detection of ictal events was demonstrated and validated by concurrent visual observation of seizure behavior. Seizures consisted of large-amplitude 8- to 25-Hz oscillations originating from the right hemisphere and quickly generalizing, with an average occurrence of 0.71 ± 0.15 seizures/day. Various stimulation parameters resulted in suppression of LFP activity or in seizure induction during stimulation under ketamine anesthesia. Chronic stimulation in the awake animal was studied to evaluate how seizure activity was affected by stimulation configurations that suppressed broadband LFPs in acute experiments. This is the first electrophysiological characterization of epilepsy using a next-generation clinical DBS system that offers the ability to record and analyze neural signals from a chronically implanted stimulating electrode. These results will direct further development of this technology and ultimately provide insight into therapeutic mechanisms of DBS for epilepsy.

A Neural Mass Model with Direct and Indirect Excitatory Feedback Loops: Identification of Bifurcations and Temporal Dynamics

Neural mass modeling is a part of computational neuroscience that was developed to study the general behavior of a neuronal population. This type of mesoscopic model is able to generate output signals that are comparable to experimental data, such as electroencephalograms. Classically, neural mass models consider two interconnected populations: excitatory pyramidal cells and inhibitory interneurons. However, many authors have included an excitatory feedback on the pyramidal cell population. Two distinct approaches have been developed: a direct feedback on the main pyramidal cell population and an indirect feedback via a secondary pyramidal cell population. In this letter, we propose a new neural mass model that couples these two approaches. We perform a detailed bifurcation analysis and present a glossary of dynamical behaviors and associated time series. Our study reveals that the model is able to generate particular realistic time series that were never pointed out in either simulated or experimental data. Finally, we aim to evaluate the effect of balance between both excitatory feedbacks on the dynamical behavior of the model. For this purpose, we compute the codimension 2 bifurcation diagrams of the system to establish a map of the repartition of dynamical behaviors in a direct versus indirect feedback parameter space. A perspective of this work is, from a given temporal series, to estimate the parameter value range, especially in terms of direct versus indirect excitatory feedback.

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.

Transcranial current brain stimulation (tCS): models and technologies

In this paper, we provide a broad overview of models and technologies pertaining to transcranial current brain stimulation (tCS), a family of related noninvasive techniques including direct current (tDCS), alternating current (tACS), and random noise current stimulation (tRNS). These techniques are based on the delivery of weak currents through the scalp (with electrode current intensity to area ratios of about 0.3-5 A/m2) at low frequencies (typically < 1 kHz) resulting in weak electric fields in the brain (with amplitudes of about 0.2-2 V/m). Here we review the biophysics and simulation of noninvasive, current-controlled generation of electric fields in the human brain and the models for the interaction of these electric fields with neurons, including a survey of in vitro and in vivo related studies. Finally, we outline directions for future fundamental and technological research.

Modulation of epileptic activity by deep brain stimulation: a model-based study of frequency-dependent effects

A number of studies showed that deep brain stimulation (DBS) can modulate the activity in the epileptic brain and that a decrease of seizures can be achieved in “responding” patients. In most of these studies, the choice of stimulation parameters is critical to obtain desired clinical effects. In particular, the stimulation frequency is a key parameter that is difficult to tune. A reason is that our knowledge about the frequency-dependant mechanisms according to which DBS indirectly impacts the dynamics of pathological neuronal systems located in the neocortex is still limited. We address this issue using both computational modeling and intracerebral EEG (iEEG) data. We developed a macroscopic (neural mass) model of the thalamocortical network. In line with already-existing models, it includes interconnected neocortical pyramidal cells and interneurons, thalamocortical cells and reticular neurons. The novelty was to introduce, in the thalamic compartment, the biophysical effects of direct stimulation. Regarding clinical data, we used a quite unique data set recorded in a patient (drug-resistant epilepsy) with a focal cortical dysplasia (FCD). In this patient, DBS strongly reduced the sustained epileptic activity of the FCD for low-frequency (LFS, < 2 Hz) and high-frequency stimulation (HFS, > 70 Hz) while intermediate-frequency stimulation (IFS, around 50 Hz) had no effect. Signal processing, clustering, and optimization techniques allowed us to identify the necessary conditions for reproducing, in the model, the observed frequency-dependent stimulation effects. Key elements which explain the suppression of epileptic activity in the FCD include: (a) feed-forward inhibition and synaptic short-term depression of thalamocortical connections at LFS, and (b) inhibition of the thalamic output at HFS. Conversely, modeling results indicate that IFS favors thalamic oscillations and entrains epileptic dynamics.

Neural mass modeling of power-line magnetic fields effects on brain activity

Neural mass models are an appropriate framework to study brain activity, combining a high degree of biological realism while being mathematically tractable. These models have been used, with a certain success, to simulate brain electric (electroencephalography, EEG) and metabolic (functional magnetic resonance imaging, fMRI) activity. However, concrete applications of neural mass models have remained limited to date. Motivated by experimental results obtained in humans, we propose in this paper a neural mass model designed to study the interaction between power-line magnetic fields (MFs) (60 Hz in North America) and brain activity. The model includes pyramidal cells; dendrite-projecting, slow GABAergic neurons; soma-projecting, fast GABAergic neurons; and glutamatergic interneurons. A simple phenomenological model of interaction between the induced electric field and neuron membranes is also considered, along with a model of post-synaptic calcium concentration and associated changes in synaptic weights Simulated EEG signals are produced in a simple protocol, both in the absence and presence of a 60 Hz MF. These results are discussed based on results obtained previously in humans. Notably, results highlight that (1) EEG alpha (8-12 Hz) power can be modulated by weak membrane depolarizations induced by the exposure; (2) the level of input noise has a significant impact on EEG power modulation; and (3) the threshold value in MF flux density resulting in a significant effect on the EEG depends on the type of neuronal populations modulated by the MF exposure. Results obtained from the model shed new light on the effects of power-line MFs on brain activity, and will provide guidance in future human experiments. This may represent a valuable contribution to international regulation agencies setting guidelines on MF values to which the general public and workers can be exposed.

From oscillatory transcranial current stimulation to scalp EEG changes: a biophysical and physiological modeling study

Both biophysical and neurophysiological aspects need to be considered to assess the impact of electric fields induced by transcranial current stimulation (tCS) on the cerebral cortex and the subsequent effects occurring on scalp EEG. The objective of this work was to elaborate a global model allowing for the simulation of scalp EEG signals under tCS. In our integrated modeling approach, realistic meshes of the head tissues and of the stimulation electrodes were first built to map the generated electric field distribution on the cortical surface. Secondly, source activities at various cortical macro-regions were generated by means of a computational model of neuronal populations. The model parameters were adjusted so that populations generated an oscillating activity around 10 Hz resembling typical EEG alpha activity. In order to account for tCS effects and following current biophysical models, the calculated component of the electric field normal to the cortex was used to locally influence the activity of neuronal populations. Lastly, EEG under both spontaneous and tACS-stimulated (transcranial sinunoidal tCS from 4 to 16 Hz) brain activity was simulated at the level of scalp electrodes by solving the forward problem in the aforementioned realistic head model. Under the 10 Hz-tACS condition, a significant increase in alpha power occurred in simulated scalp EEG signals as compared to the no-stimulation condition. This increase involved most channels bilaterally, was more pronounced on posterior electrodes and was only significant for tACS frequencies from 8 to 12 Hz. The immediate effects of tACS in the model agreed with the post-tACS results previously reported in real subjects. Moreover, additional information was also brought by the model at other electrode positions or stimulation frequency. This suggests that our modeling approach can be used to compare, interpret and predict changes occurring on EEG with respect to parameters used in specific stimulation configurations.

Interictal spikes, fast ripples and seizures in partial epilepsies--combining multi-level computational models with experimental data

Epileptic seizures, epileptic spikes and high-frequency oscillations (HFOs) are recognized as three electrophysiological markers of epileptogenic neuronal systems. It can be reasonably hypothesized that distinct (hyper)excitability mechanisms underlie these electrophysiological signatures. The question is 'What are these mechanisms?'. Solving this difficult question would considerably help our understanding of epileptogenic processes and would also advance our interpretation of electrophysiological signals. In this paper, we show how computational models of brain epileptic activity can be used to address this issue. With a special emphasis on the hippocampal activity recorded in various experimental models (in vivo and in vitro) as well as in epileptic patients, we confront results and insights we can get from computational models lying at two different levels of description, namely macroscopic (neural mass) and microscopic (detailed network of neurons). At each level, we show how spikes, seizures and HFOs can (or cannot) be generated depending on the model features. The replication of observed signals, the prediction of possible mechanisms as well as their experimental validation are described and discussed; as are the advantages and limitations of the two modelling approaches.

Phase space approach for modeling of epileptic dynamics

Epileptic electroencephalography recordings can be described in terms of four prototypic wave forms: fast sinusoidal oscillations, large slow waves, fast spiking, and spike waves. On the macroscopic level, these wave forms have been modeled by different mechanistic models which share canonical features. Here we derive a minimal model of excitatory and inhibitory processes with features common to all previous models. We can infer that at least three interacting processes are required to support the prototypic epileptic dynamics. Based on a separation of time scales we analyze the model in terms of interacting manifolds in phase space. This allows qualitative reverse engineering of all epileptic wave forms and transitions between them. We propose this method as a complement to traditional approaches to modeling epileptiform rhythms.

High-frequency oscillations as a new biomarker in epilepsy

The discovery that electroencephalography (EEG) contains useful information at frequencies above the traditional 80Hz limit has had a profound impact on our understanding of brain function. In epilepsy, high-frequency oscillations (HFOs, >80Hz) have proven particularly important and useful. This literature review describes the morphology, clinical meaning, and pathophysiology of epileptic HFOs. To record HFOs, the intracranial EEG needs to be sampled at least at 2,000Hz. The oscillatory events can be visualized by applying a high-pass filter and increasing the time and amplitude scales, or EEG time-frequency maps can show the amount of high-frequency activity. HFOs appear excellent markers for the epileptogenic zone. In patients with focal epilepsy who can benefit from surgery, invasive EEG is often required to identify the epileptic cortex, but current information is sometimes inadequate. Removal of brain tissue generating HFOs has been related to better postsurgical outcome than removing the seizure onset zone, indicating that HFOs may mark cortex that needs to be removed to achieve seizure control. The pathophysiology of epileptic HFOs is challenging, probably involving populations of neurons firing asynchronously. They differ from physiological HFOs in not being paced by rhythmic inhibitory activity and in their possible origin from population spikes. Their link to the epileptogenic zone argues that their study will teach us much about the pathophysiology of epileptogenesis and ictogenesis. HFOs show promise for improving surgical outcome and accelerating intracranial EEG investigations. Their potential needs to be assessed by future research.

Mechanisms of physiological and epileptic HFO generation

High frequency oscillations (HFO) have a variety of characteristics: band-limited or broad-band, transient burst-like phenomenon or steady-state. HFOs may be encountered under physiological or under pathological conditions (pHFO). Here we review the underlying mechanisms of oscillations, at the level of cells and networks, investigated in a variety of experimental in vitro and in vivo models. Diverse mechanisms are described, from intrinsic membrane oscillations to network processes involving different types of synaptic interactions, gap junctions and ephaptic coupling. HFOs with similar frequency ranges can differ considerably in their physiological mechanisms. The fact that in most cases the combination of intrinsic neuronal membrane oscillations and synaptic circuits are necessary to sustain network oscillations is emphasized. Evidence for pathological HFOs, particularly fast ripples, in experimental models of epilepsy and in human epileptic patients is scrutinized. The underlying mechanisms of fast ripples are examined both in the light of animal observations, in vivo and in vitro, and in epileptic patients, with emphasis on single cell dynamics. Experimental observations and computational modeling have led to hypotheses for these mechanisms, several of which are considered here, namely the role of out-of-phase firing in neuronal clusters, the importance of strong excitatory AMPA-synaptic currents and recurrent inhibitory connectivity in combination with the fast time scales of IPSPs, ephaptic coupling and the contribution of interneuronal coupling through gap junctions. The statistical behaviour of fast ripple events can provide useful information on the underlying mechanism and can help to further improve classification of the diverse forms of HFOs.

Recording and analysis techniques for high-frequency oscillations

In recent years, new recording technologies have advanced such that, at high temporal and spatial resolutions, high-frequency oscillations (HFO) can be recorded in human partial epilepsy. However, because of the deluge of multichannel data generated by these experiments, achieving the full potential of parallel neuronal recordings depends on the development of new data mining techniques to extract meaningful information relating to time, frequency and space. Here, we aim to bridge this gap by focusing on up-to-date recording techniques for measurement of HFO and new analysis tools for their quantitative assessment. In particular, we emphasize how these methods can be applied, what property might be inferred from neuronal signals, and potentially productive future directions.

Ictal high-gamma oscillation (60-99 Hz) in intracranial electroencephalography and postoperative seizure outcome in neocortical epilepsy

OBJECTIVE

High-gamma oscillations (HGOs) (60-99 Hz) have been suggested to correlate with seizure onset zones and seizure outcomes. We investigated the correlation between the extent of removal of ictal HGO generating areas and postoperative seizure outcome in neocortical epilepsy (NE).

METHODS

Twenty three patients with medically intractable NE underwent chronic intracranial electroencephalography (iEEG) using subdural electrodes. Ictal HGOs and superimposed undersampled ripples within ±3 s of video-iEEG ictal onset were extracted by wavelet clustering and thresholding. Cluster epileptogenicity indices (CEIs) were calculated. The temporal analysis window was locked to the timing of the maximum CEI wavecluster. Root mean square amplitudes, cross-correlation synchronies and the local focus indices within the temporal window were calculated.

RESULTS

Percentages of resected maximum CEI waveclusters and HGO zones with high standardised amplitudes (>3), high cross-correlation synchronies (>0.9) and high local focus indices (>2) were significantly higher in the seizure-free group compared to the not seizure-free group (p=0.036, p=0.018, and p=0.026, respectively).

CONCLUSIONS

The automatic quantitative ictal HGO analysis may be effective in delineating the epileptogenic zone.

SIGNIFICANCE

HGO analysis may be helpful for improving post-resection seizure outcome in NE in the future.

Effects of transcranial Direct Current Stimulation (tDCS) on cortical activity: a computational modeling study

Although it is well-admitted that transcranial Direct Current Stimulation (tDCS) allows for interacting with brain endogenous rhythms, the exact mechanisms by which externally-applied fields modulate the activity of neurons remain elusive. In this study a novel computational model (a neural mass model including subpopulations of pyramidal cells and inhibitory interneurons mediating synaptic currents with either slow or fast kinetics) of the cerebral cortex was elaborated to investigate the local effects of tDCS on neuronal populations based on an in-vivo experimental study. Model parameters were adjusted to reproduce evoked potentials (EPs) recorded from the somatosensory cortex of the rabbit in response to air-puffs applied on the whiskers. EPs were simulated under control condition (no tDCS) as well as under anodal and cathodal tDCS fields. Results first revealed that a feed-forward inhibition mechanism must be included in the model for accurate simulation of actual EPs (peaks and latencies). Interestingly, results revealed that externally-applied fields are also likely to affect interneurons. Indeed, when interneurons get polarized then the characteristics of simulated EPs become closer to those of real EPs. In particular, under anodal tDCS condition, more realistic EPs could be obtained when pyramidal cells were depolarized and, simultaneously, slow (resp. fast) interneurons became de- (resp. hyper-) polarized. Geometrical characteristics of interneurons might provide some explanations for this effect.

Scaling effects and spatio-temporal multilevel dynamics in epileptic seizures

Epileptic seizures are one of the most well-known dysfunctions of the nervous system. During a seizure, a highly synchronized behavior of neural activity is observed that can cause symptoms ranging from mild sensual malfunctions to the complete loss of body control. In this paper, we aim to contribute towards a better understanding of the dynamical systems phenomena that cause seizures. Based on data analysis and modelling, seizure dynamics can be identified to possess multiple spatial scales and on each spatial scale also multiple time scales. At each scale, we reach several novel insights. On the smallest spatial scale we consider single model neurons and investigate early-warning signs of spiking. This introduces the theory of critical transitions to excitable systems. For clusters of neurons (or neuronal regions) we use patient data and find oscillatory behavior and new scaling laws near the seizure onset. These scalings lead to substantiate the conjecture obtained from mean-field models that a Hopf bifurcation could be involved near seizure onset. On the largest spatial scale we introduce a measure based on phase-locking intervals and wavelets into seizure modelling. It is used to resolve synchronization between different regions in the brain and identifies time-shifted scaling laws at different wavelet scales. We also compare our wavelet-based multiscale approach with maximum linear cross-correlation and mean-phase coherence measures.

Towards a model-based integration of co-registered electroencephalography/functional magnetic resonance imaging data with realistic neural population meshes

Brain activity can be measured with several non-invasive neuroimaging modalities, but each modality has inherent limitations with respect to resolution, contrast and interpretability. It is hoped that multimodal integration will address these limitations by using the complementary features of already available data. However, purely statistical integration can prove problematic owing to the disparate signal sources. As an alternative, we propose here an advanced neural population model implemented on an anatomically sound cortical mesh with freely adjustable connectivity, which features proper signal expression through a realistic head model for the electroencephalogram (EEG), as well as a haemodynamic model for functional magnetic resonance imaging based on blood oxygen level dependent contrast (fMRI BOLD). It hence allows simultaneous and realistic predictions of EEG and fMRI BOLD from the same underlying model of neural activity. As proof of principle, we investigate here the influence on simulated brain activity of strengthening visual connectivity. In the future we plan to fit multimodal data with this neural population model. This promises novel, model-based insights into the brain's activity in sleep, rest and task conditions.