Whole-brain simulation of interictal epileptic discharges for patient-specific interpretation of interictal SEEG data.

In patients with refractory epilepsy, the clinical interpretation of stereoelectroencephalographic (SEEG) signals is crucial to delineate the epileptogenic network that should be targeted by surgery. We propose a pipeline of patient-specific computational modeling of interictal epileptic activity to improve the definition of regions of interest. Comparison between the computationally defined regions of interest and the resected region confirmed the efficiency of the pipeline. This result suggests that computational modeling can be used to reconstruct signals and aid clinical interpretation.

Modification of brain conductivity in human focal epilepsy: A model-based estimation from stereoelectroencephalography.

OBJECTIVE: We have developed a novel method for estimating brain tissue electrical conductivity using low-intensity pulse stereoelectroencephalography (SEEG) stimulation coupled with biophysical modeling. We evaluated the hypothesis that brain conductivity is correlated with the degree of epileptogenicity in patients with drug-resistant focal epilepsy. METHODS: We used bipolar low-intensity biphasic pulse stimulation (.2 mA) followed by a postprocessing pipeline for estimating brain conductivity. This processing is based on biophysical modeling of the electrical potential induced in brain tissue between the stimulated contacts in response to pulse stimulation. We estimated the degree of epileptogenicity using a semi-automatic method quantifying the dynamic of fast discharge at seizure onset: the epileptogenicity index (EI). We also investigated how the location of stimulation within specific anatomical brain regions or within lesional tissue impacts brain conductivity. RESULTS: We performed 1034 stimulations of 511 bipolar channels in 16 patients. We found that brain conductivity was lower in the epileptogenic zone (EZ; unpaired median difference = .064, p < .001) and inversely correlated with the epileptogenic index value (p < .001, Spearman rho = -.32). Conductivity values were also influenced by anatomical site, location within lesion, and delay between SEEG electrode implantation and stimulation, and had significant interpatient variability. Mixed model multivariate analysis showed that conductivity is significantly associated with EI (F = 13.45, p < .001), anatomical regions (F = 5.586, p < .001), delay since implantation (F = 14.71, p = .003), and age at SEEG (F = 6.591, p = .027), but not with the type of lesion (F = .372, p = .773) or the delay since last seizure (F = 1.592, p = .235). SIGNIFICANCE: We provide a novel model-based method for estimating brain conductivity from SEEG low-intensity pulse stimulations. The brain tissue conductivity is lower in EZ as compared to non-EZ. Conductivity also varies significantly across anatomical brain regions. Involved pathophysiological processes may include changes in the extracellular space (especially volume or tortuosity) in epileptic tissue.

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.

Tuning Microelectrodes' Impedance to Improve Fast Ripples Recording.

Epilepsy is a chronic neurological disorder characterized by recurrent seizures resulting from abnormal neuronal hyperexcitability. In the case of pharmacoresistant epilepsy requiring resection surgery, the identification of the Epileptogenic Zone (EZ) is critical. Fast Ripples (FRs; 200-600 Hz) are one of the promising biomarkers that can aid in EZ delineation. However, recording FRs requires physically small electrodes. These microelectrodes suffer from high impedance, which significantly impacts FRs' observability and detection. In this study, we investigated the potential of a conductive polymer coating to enhance FR observability. We employed biophysical modeling to compare two types of microelectrodes: Gold (Au) and Au coated with the conductive polymer poly(3,4-ethylenedioxythiophene)-poly(styrene sulfonate) (Au/PEDOT:PSS). These electrodes were then implanted into the CA1 hippocampal neural network of epileptic mice to record FRs during epileptogenesis. The results showed that the polymer-coated electrodes had a two-order lower impedance as well as a higher transfer function amplitude and cut-off frequency. Consequently, FRs recorded with the PEDOT:PSS-coated microelectrode yielded significantly higher signal energy compared to the uncoated one. The PEDOT:PSS coating improved the observability of the recorded FRs and thus their detection. This work paves the way for the development of signal-specific microelectrode designs that allow for better targeting of pathological biomarkers.

Spontaneous fast-ultradian dynamics of polymorphic interictal events in drug-resistant focal epilepsy.

OBJECTIVE: We studied the rate dynamics of interictal events occurring over fast-ultradian time scales, as commonly examined in clinics to guide surgical planning in epilepsy. METHODS: Stereo-electroencephalography (SEEG) traces of 35 patients with good surgical outcome (Engel I) were analyzed. For this we developed a general data mining method aimed at clustering the plethora of transient waveform shapes including interictal epileptiform discharges (IEDs) and assessed the temporal fluctuations in the capability of mapping the epileptogenic zone (EZ) of each type of event. RESULTS: We found that the fast-ultradian dynamics of the IED rate may effectively impair the precision of EZ identification, and appear to occur spontaneously, that is, not triggered by or exclusively associated with a particular cognitive task, wakefulness, sleep, seizure occurrence, post-ictal state, or antiepileptic drug withdrawal. Propagation of IEDs from the EZ to the propagation zone (PZ) could explain the observed fast-ultradian fluctuations in a reduced fraction of the analyzed patients, suggesting that other factors like the excitability of the epileptogenic tissue could play a more relevant role. A novel link was found between the fast-ultradian dynamics of the overall rate of polymorphic events and the rate of specific IEDs subtypes. We exploited this feature to estimate in each patient the 5 min interictal epoch for near-optimal EZ and resected-zone (RZ) localization. This approach produces at the population level a better EZ/RZ classification when compared to both (1) the whole time series available in each patient (p = .084 for EZ, p < .001 for RZ, Wilcoxon signed-rank test) and (2) 5 min epochs sampled randomly from the interictal recordings of each patient (p < .05 for EZ, p < .001 for RZ, 105 random samplings). SIGNIFICANCE: Our results highlight the relevance of the fast-ultradian IED dynamics in mapping the EZ, and show how this dynamics can be estimated prospectively to inform surgical planning in epilepsy.

Biophysical modeling of the electric field magnitude and distribution induced by electrical stimulation with intracerebral electrodes.

Intracranial electrodes are used clinically for diagnostic or therapeutic purposes, notably in drug-refractory epilepsy (DRE) among others. Visualization and quantification of the energy delivered through such electrodes is key to understanding how the resulting electric fields modulate neuronal excitability, i.e. the ratio between excitation and inhibition. Quantifying the electric field induced by electrical stimulation in a patient-specific manner is challenging, because these electric fields depend on a number of factors: electrode trajectory with respect to folded brain anatomy, biophysical (electrical conductivity / permittivity) properties of brain tissue and stimulation parameters such as electrode contacts position and intensity. Here, we aimed to evaluate various biophysical models for characterizing the electric fields induced by electrical stimulation in DRE patients undergoing stereoelectroencephalography (SEEG) recordings in the context of pre-surgical evaluation. This stimulation was performed with multiple-contact intracranial electrodes used in routine clinical practice. We introduced realistic 3D models of electrode geometry and trajectory in the neocortex. For the electrodes, we compared point (0D) and line (1D) sources approximations. For brain tissue, we considered three configurations of increasing complexity: a 6-layer spherical model, a toy model with a sulcus representation, replicating results from previous approaches; and went beyond the state-of-the-art by using a realistic head model geometry. Electrode geometry influenced the electric field distribution at close distances (∼3 mm) from the electrode axis. For larger distances, the volume conductor geometry and electrical conductivity dominated electric field distribution. These results are the first step towards accurate and computationally tractable patient-specific models of electric fields induced by neuromodulation and neurostimulation procedures.

Spherical harmonics representation of the steady-state membrane potential shift induced by tDCS in realistic neuron models.

Objective.We provide a systematic framework for quantifying the effect of externally applied weak electric fields on realistic neuron compartment models as captured by physiologically relevant quantities such as the membrane potential or transmembrane current as a function of the orientation of the field.Approach.We define a response function as the steady-state change of the membrane potential induced by a canonical external field of 1 V m-1as a function of its orientation. We estimate the function values through simulations employing reconstructions of the rat somatosensory cortex from the Blue Brain Project. The response of different cell types is simulated using the NEURON simulation environment. We represent and analyze the angular response as an expansion in spherical harmonics.Main results.We report membrane perturbation values comparable to those in the literature, extend them to different cell types, and provide their profiles as spherical harmonic coefficients. We show that at rest, responses are dominated by their dipole terms (ℓ=1), in agreement with experimental findings and compartment theory. Indeed, we show analytically that for a passive cell, only the dipole term is nonzero. However, while minor, other terms are relevant for states different from resting. In particular, we show howℓ=0andℓ=2terms can modify the function to induce asymmetries in the response.Significance.This work provides a practical framework for the representation of the effects of weak electric fields on different neuron types and their main regions-an important milestone for developing micro- and mesoscale models and optimizing brain stimulation solutions.

Towards a mesoscale physical modeling framework for stereotactic-EEG recordings.

Objective.Stereotactic-electroencephalography (SEEG) and scalp EEG recordings can be modeled using mesoscale neural mass population models (NMMs). However, the relationship between those mathematical models and the physics of the measurements is unclear. In addition, it is challenging to represent SEEG data by combining NMMs and volume conductor models due to the intermediate spatial scale represented by these measurements.Approach.We provide a framework combining the multi-compartmental modeling formalism and a detailed geometrical model to simulate the transmembrane currents that appear in layer 3, 5 and 6 pyramidal cells due to a synaptic input. With this approach, it is possible to realistically simulate the current source density (CSD) depth profile inside a cortical patch due to inputs localized into a single cortical layer and the induced voltage measured by two SEEG contacts using a volume conductor model. Based on this approach, we built a framework to connect the activity of a NMM with a volume conductor model and we simulated an example of SEEG signal as a proof of concept.Main results.CSD depends strongly on the distribution of the synaptic inputs onto the different cortical layers and the equivalent current dipole strengths display substantial differences (of up to a factor of four in magnitude in our example). Thus, the inputs coming from different neural populations do not contribute equally to the electrophysiological recordings. A direct consequence of this is that the raw output of NMMs is not a good proxy for electrical recordings. We also show that the simplest CSD model that can accurately reproduce SEEG measurements can be constructed from discrete monopolar sources (one per cortical layer).Significance.Our results highlight the importance of including a physical model in NMMs to represent measurements. We provide a framework connecting microscale neuron models with the neural mass formalism and with physical models of the measurement process that can improve the accuracy of predicted electrophysiological recordings.

Signal processing and computational modeling for interpretation of SEEG-recorded interictal epileptiform discharges in epileptogenic and non-epileptogenic zones.

Objective.In partial epilepsies, interictal epileptiform discharges (IEDs) are paroxysmal events observed in epileptogenic zone (EZ) and non-epileptogenic zone (NEZ). IEDs' generation and recurrence are subject to different hypotheses: they appear through glutamatergic and gamma-aminobutyric acidergic (GABAergic) processes; they may trigger seizures or prevent seizure propagation. This paper focuses on a specific class of IEDs, spike-waves (SWs), characterized by a short-duration spike followed by a longer duration wave, both of the same polarity. Signal analysis and neurophysiological mathematical models are used to interpret puzzling IED generation.Approach.Interictal activity was recorded by intracranial stereo-electroencephalography (SEEG) electrodes in five different patients. SEEG experts identified the epileptic and non-epileptic zones in which IEDs were detected. After quantifying spatial and temporal features of the detected IEDs, the most significant features for classifying epileptic and non-epileptic zones were determined. A neurophysiologically-plausible mathematical model was then introduced to simulate the IEDs and understand the underlying differences observed in epileptic and non-epileptic zone IEDs.Main results.Two classes of SWs were identified according to subtle differences in morphology and timing of the spike and wave component. Results showed that type-1 SWs were generated in epileptogenic regions also involved at seizure onset, while type-2 SWs were produced in the propagation or non-involved areas. The modeling study indicated that synaptic kinetics, cortical organization, and network interactions determined the morphology of the simulated SEEG signals. Modeling results suggested that the IED morphologies were linked to the degree of preserved inhibition.Significance.This work contributes to the understanding of different mechanisms generating IEDs in epileptic networks. The combination of signal analysis and computational models provides an efficient framework for exploring IEDs in partial epilepsies and classifying EZ and NEZ.

Transcranial current stimulation in epilepsy: A systematic review of the fundamental and clinical aspects.

Purpose: Transcranial electrical current stimulation (tES or tCS, as it is sometimes referred to) has been proposed as non-invasive therapy for pharmacoresistant epilepsy. This technique, which includes direct current (tDCS) and alternating current (tACS) stimulation involves the application of weak currents across the cortex to change cortical excitability. Although clinical trials have demonstrated the therapeutic efficacy of tES, its specific effects on epileptic brain activity are poorly understood. We sought to summarize the clinical and fundamental effects underlying the application of tES in epilepsy. Methods: A systematic review was performed in accordance with the PRISMA guidelines. A database search was performed in PUBMED, MEDLINE, Web of Science and Cochrane CENTRAL for articles corresponding to the keywords "epilepsy AND (transcranial current stimulation OR transcranial electrical stimulation)". Results: A total of 56 studies were included in this review. Through these records, we show that tDCS and tACS epileptic patients are safe and clinically relevant techniques for epilepsy. Recent articles reported changes of functional connectivity in epileptic patients after tDCS. We argue that tDCS may act by affecting brain networks, rather than simply modifying local activity in the targeted area. To explain the mechanisms of tES, various cellular effects have been identified. Among them, reduced cell loss, mossy fiber sprouting, and hippocampal BDNF protein levels. Brain modeling and human studies highlight the influence of individual brain anatomy and physiology on the electric field distribution. Computational models may optimize the stimulation parameters and bring new therapeutic perspectives. Conclusion: Both tDCS and tACS are promising techniques for epilepsy patients. Although the clinical effects of tDCS have been repeatedly assessed, only one clinical trial has involved a consistent number of epileptic patients and little knowledge is present about the clinical outcome of tACS. To fill this gap, multicenter studies on tES in epileptic patients are needed involving novel methods such as personalized stimulation protocols based on computational modeling. Furthermore, there is a need for more in vivo studies replicating the tES parameters applied in patients. Finally, there is a lack of clinical studies investigating changes in intracranial epileptiform discharges during tES application, which could clarify the nature of tES-related local and network dynamics in epilepsy.

Interictal Functional Connectivity in Focal Refractory Epilepsies Investigated by Intracranial EEG.

Introduction: Focal epilepsies are diseases of neuronal excitability affecting macroscopic networks of cortical and subcortical neural structures. These networks ("epileptogenic networks") can generate pathological electrophysiological activities during seizures, and also between seizures (interictal period). Many works attempt to describe these networks by using quantification methods, particularly based on the estimation of statistical relationships between signals produced by brain regions, namely functional connectivity (FC). Results: FC has been shown to be greatly altered during seizures and in the immediate peri-ictal period. An increasing number of studies have shown that FC is also altered during the interictal period depending on the degree of epileptogenicity of the structures. Furthermore, connectivity values could be correlated with other clinical variables including surgical outcome. Significance: This leads to a conceptual change and to consider epileptic areas as both hyperexcitable and abnormally connected. These data open the door to the use of interictal FC as a marker of epileptogenicity and as a complementary tool for predicting the effect of surgery. Aim: In this article, we review the available data concerning interictal FC estimated from intracranial electroencephalograhy (EEG) in focal epilepsies and discuss it in the light of data obtained from other modalities (EEG imaging) and modeling studies.

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.

Spatio-temporal dynamics of large-scale electrophysiological networks during cognitive action control in healthy controls and Parkinson's disease patients.

Among the cognitive symptoms that are associated with Parkinson's disease (PD), alterations in cognitive action control (CAC) are commonly reported in patients. CAC enables the suppression of an automatic action, in favor of a goal-directed one. The implementation of CAC is time-resolved and arguably associated with dynamic changes in functional brain networks. However, the electrophysiological functional networks involved, their dynamic changes, and how these changes are affected by PD, still remain unknown. In this study, to address this gap of knowledge, 10 PD patients and 10 healthy controls (HC) underwent a Simon task while high-density electroencephalography (HD-EEG) was recorded. Source-level dynamic connectivity matrices were estimated using the phase-locking value in the beta (12-25 Hz) and gamma (30-45 Hz) frequency bands. Temporal independent component analyses were used as a dimension reduction tool to isolate the task-related brain network states. Typical microstate metrics were quantified to investigate the presence of these states at the subject-level. Our results first confirmed that PD patients experienced difficulties in inhibiting automatic responses during the task. At the group-level, we found three functional network states in the beta band that involved fronto-temporal, temporo-cingulate and fronto-frontal connections with typical CAC-related prefrontal and cingulate nodes (e.g., inferior frontal cortex). The presence of these networks did not differ between PD patients and HC when analyzing microstates metrics, and no robust correlations with behavior were found. In the gamma band, five networks were found, including one fronto-temporal network that was identical to the one found in the beta band. These networks also included CAC-related nodes previously identified in different neuroimaging modalities. Similarly to the beta networks, no subject-level differences were found between PD patients and HC. Interestingly, in both frequency bands, the dominant network at the subject-level was never the one that was the most durably modulated by the task. Altogether, this study identified the dynamic functional brain networks observed during CAC, but did not highlight PD-related changes in these networks that might explain behavioral changes. Although other new methods might be needed to investigate the presence of task-related networks at the subject-level, this study still highlights that task-based dynamic functional connectivity is a promising approach in understanding the cognitive dysfunctions observed in PD and beyond.

Stereo-EEG based personalized multichannel transcranial direct current stimulation in drug-resistant epilepsy.

OBJECTIVE: In epilepsy, multichannel transcranial direct electrical stimulation (tDCS) is applied to decrease cortical activity through the delivery of weak currents using several scalp electrodes. We investigated the long-term effects of personalized, multisession, stereotactic-EEG (SEEG)-targeted multichannel tDCS on seizure frequency (SF) and functional connectivity (Fc) as measured by EEG in patients with drug-resistant epilepsy (DRE). METHODS: Ten patients suffering from DRE were recruited. Multichannel tDCS (Starstim, Neuroelectrics) was applied during three cycles (one cycle every 2 months) of stimulation. Each cycle consisted of five consecutive days where patients received tDCS daily in two 20 min sessions separated by 20 min. The montages were personalized to target epileptogenic area of each patient as defined by SEEG recordings. SF during and after treatment was compared with baseline. Fc changes were analysed using scalp EEG recordings. RESULTS: After the last tDCS session, five patients experienced a SF decrease of 50% or more compared with baseline (R: responders, average SF decrease of 74%). We estimated Fc changes between cycles and across R and non-responder (NR) patients. R presented a significant decrease in Fc (p < 0.05) at the third session in alpha and beta frequency bands compared to the first one. CONCLUSIONS: Multichannel tDCS guided by SEEG is a promising therapeutic approach. Significant response was associated with a decrease of Fc after three stimulation cycles. SIGNIFICANCE: Such results suggest that tDCS-induced functional plasticity changes that may underlie the clinical response.

Modeling implanted metals in electrical stimulation applications.

Objective. Metal implants impact the dosimetry assessment in electrical stimulation techniques. Therefore, they need to be included in numerical models. While currents in the body are ionic, metals only allow electron transport. In fact, charge transfer between tissues and metals requires electric fields to drive electrochemical reactions at the interface. Thus, metal implants may act as insulators or as conductors depending on the scenario. The aim of this paper is to provide a theoretical argument that guides the choice of the correct representation of metal implants in electrical models while considering the electrochemical nature of the problemApproach.We built a simple model of a metal implant exposed to a homogeneous electric field of various magnitudes. The same geometry was solved using two different models: a purely electric one (with different conductivities for the implant), and an electrochemical one. As an example of application, we also modeled a transcranial electrical stimulation (tES) treatment in a realistic head model with a skull plate using a high and low conductivity value for the plate.Main results. Metal implants generally act as electric insulators when exposed to electric fields up to around 100 V m-1and they only resemble a perfect conductor for fields in the order of 1000 V m-1and above. The results are independent of the implant's metal, but they depend on its geometry. tES modeling with implants incorrectly treated as conductors can lead to errors of 50% or more in the estimation of the induced fieldsSignificance.Metal implants can be accurately represented by a simple electrical model of constant conductivity, but an incorrect model choice can lead to large errors in the dosimetry assessment. Our results can be used to guide the selection of the most appropriate model in each scenario.

Mean-Field Modeling of Brain-Scale Dynamics for the Evaluation of EEG Source-Space Networks.

Understanding the dynamics of brain-scale functional networks at rest and during cognitive tasks is the subject of intense research efforts to unveil fundamental principles of brain functions. To estimate these large-scale brain networks, the emergent method called "electroencephalography (EEG) source connectivity" has generated increasing interest in the network neuroscience community, due to its ability to identify cortical brain networks with satisfactory spatio-temporal resolution, while reducing mixing and volume conduction effects. However, no consensus has been reached yet regarding a unified EEG source connectivity pipeline, and several methodological issues have to be carefully accounted to avoid pitfalls. Thus, a validation toolbox that provides flexible "ground truth" models is needed for an objective methods/parameters evaluation and, thereby an optimization of the EEG source connectivity pipeline. In this paper, we show how a recently developed large-scale model of brain-scale activity, named COALIA, can provide to some extent such ground truth by providing realistic simulations of source-level and scalp-level activity. Using a bottom-up approach, the model bridges cortical micro-circuitry and large-scale network dynamics. Here, we provide an example of the potential use of COALIA to analyze, in the context of epileptiform activity, the effect of three key factors involved in the "EEG source connectivity" pipeline: (i) EEG sensors density, (ii) algorithm used to solve the inverse problem, and (iii) functional connectivity measure. Results showed that a high electrode density (at least 64 channels) is required to accurately estimate cortical networks. Regarding the inverse solution/connectivity measure combination, the best performance at high electrode density was obtained using the weighted minimum norm estimate (wMNE) combined with the weighted phase lag index (wPLI). Although those results are specific to the considered aforementioned context (epileptiform activity), we believe that this model-based approach can be successfully applied to other experimental questions/contexts. We aim at presenting a proof-of-concept of the interest of COALIA in the network neuroscience field, and its potential use in optimizing the EEG source-space network estimation pipeline.

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.

Long term evolution of fast ripples during epileptogenesis.

Objective.Fast ripples (FRs) have received considerable attention in the last decade since they represent an electrophysiological biomarker of the epileptogenic zone (EZ). However, the real dynamics underlying the occurrence, amplitude, and time-frequency content of FRs generation during epileptogenesis are still not well understood. This work aims at characterizing and explaining the evolution of these features.Approach.Intracortical electroencephalographic signals recorded in a kainate mouse model of temporal lobe epilepsy were processed in order to compute specific FR features. Then realistic physiologically based computational modeling was employed to explore the different elements that can explain the mechanisms of epileptogenesis and simulate the recorded FR in the early and late latent period.Main results.Results indicated that continuous changes of FR features are mainly portrayed by the epileptic (pathological) tissue size and synaptic properties. Furthermore, the microelectrodes characteristics were found to dramatically affect the observability and spectral/temporal content of FRs. Consequently, FRs evolution seems to mirror the continuous pathophysiological mechanism changes that occur during epileptogenesis as long as the microelectrode properties are taken into account.Significance.Our study suggests that FRs can account for the pathophysiological changes which might explain the EZ generation and evolution and can contribute in the treatment plan of pharmaco-resistant epilepsies.

In silico model reveals the key role of GABA in KCNT1-epilepsy in infancy with migrating focal seizures.

OBJECTIVE: This study was undertaken to investigate how gain of function (GOF) of slack channel due to a KCNT1 pathogenic variant induces abnormal neuronal cortical network activity and generates specific electroencephalographic (EEG) patterns of epilepsy in infancy with migrating focal seizures. METHODS: We used detailed microscopic computational models of neurons to explore the impact of GOF of slack channel (explicitly coded) on each subtype of neurons and on a cortical micronetwork. Then, we adapted a thalamocortical macroscopic model considering results obtained in detailed models and immature properties related to epileptic brain in infancy. Finally, we compared simulated EEGs resulting from the macroscopic model with interictal and ictal patterns of affected individuals using our previously reported EEG markers. RESULTS: The pathogenic variants of KCNT1 strongly decreased the firing rate properties of γ-aminobutyric acidergic (GABAergic) interneurons and, to a lesser extent, those of pyramidal cells. This change led to hyperexcitability with increased synchronization in a cortical micronetwork. At the macroscopic scale, introducing slack GOF effect resulted in epilepsy of infancy with migrating focal seizures (EIMFS) EEG interictal patterns. Increased excitation-to-inhibition ratio triggered seizure, but we had to add dynamic depolarizing GABA between somatostatin-positive interneurons and pyramidal cells to obtain migrating seizure. The simulated migrating seizures were close to EIMFS seizures, with similar values regarding the delay between the different ictal activities (one of the specific EEG markers of migrating focal seizures due to KCNT1 pathogenic variants). SIGNIFICANCE: This study illustrates the interest of biomathematical models to explore pathophysiological mechanisms bridging the gap between the functional effect of gene pathogenic variants and specific EEG phenotype. Such models can be complementary to in vitro cellular and animal models. This multiscale approach provides an in silico framework that can be further used to identify candidate innovative therapies.

Design of optimal multi-site brain stimulation protocols via neuro-inspired epilepsy models for abatement of interictal discharges.

Objective. Electrical brain stimulation is recognized as a promising therapeutic approach for treating brain disorders such as epilepsy. However, the use of this technique is still largely empirical, since stimulation parameters and targets are chosen using a trial-and-error approach. Therefore, there is a pressing need to design optimal, rationale-based multi-site brain stimulation protocols to control epileptiform activity.Approach. Here, we developed biologically-inspired models of brain activity receiving stimulation at two levels of description (single- and multi-population epileptogenic networks). First, we used bifurcation analysis to determine optimal parameters able to abort epileptiform patterns. Second, we present a graph-theory based method to classify network populations in an epileptogenic network based on their contribution to seizure generation and propagation. Main results. The best therapeutic effects (i.e. reduction of epileptiform discharges duration and occurrence rate) were obtained by the specific targeting of populations with the highest eigenvector centrality values. The timing of stimulation was also found to be critical in seizure abortion impact.Significance. Overall, our results provide a proof-of-concept that using network neuroscience combined with physiology-based computational models of brain activity can provide an effective method for the rational design of brain stimulation protocols in epilepsy.