Neural field model of seizure-like activity in isolated cortex

Epileptiform discharges on an isolated cortex are explored using neural field theory. A neural field model of the isolated cortex is used that consists of three neural populations, excitatory, inhibitory, and excitatory bursting. Mechanisms by which an isolated cortex gives rise to seizure-like waveforms thought to underly pathological EEG waveforms on the deafferented cortex are explored. It is shown that the model reproduces similar time series and oscillatory frequencies for paroxysmal discharges when compared with physiological recordings both during acute and chronic deafferentation states. Furthermore, within our model ictal activity arises from perturbations to steady-states very close to the dynamical system’s instability boundary; hence, these are distinct from corticothalamic seizures observed in the model for the intact brain which involved limit-cycle dynamics. The results are applied to experiments in deafferented cats.     

Constrained brain volume in an efficient coding model explains the fraction of excitatory and inhibitory neurons in sensory cortices

The number of neurons in mammalian cortex varies by multiple orders of magnitude across different species. In contrast, the ratio of excitatory to inhibitory neurons (E:I ratio) varies in a much smaller range, from 3:1 to 9:1 and remains roughly constant for different sensory areas within a species. Despite this structure being important for understanding the function of neural circuits, the reason for this consistency is not yet understood. While recent models of vision based on the efficient coding hypothesis show that increasing the number of both excitatory and inhibitory cells improves stimulus representation, the two cannot increase simultaneously due to constraints on brain volume. In this work, we implement an efficient coding model of vision under a constraint on the volume (using number of neurons as a surrogate) while varying the E:I ratio. We show that the performance of the model is optimal at biologically observed E:I ratios under several metrics. We argue that this happens due to trade-offs between the computational accuracy and the representation capacity for natural stimuli. Further, we make experimentally testable predictions that 1) the optimal E:I ratio should be higher for species with a higher sparsity in the neural activity and 2) the character of inhibitory synaptic distributions and firing rates should change depending on E:I ratio. Our findings, which are supported by our new preliminary analyses of publicly available data, provide the first quantitative and testable hypothesis based on optimal coding models for the distribution of excitatory and inhibitory neural types in the mammalian sensory cortices.     

Travelling waves and EEG patterns during epileptic seizure: analysis with an integrate-and-fire neural network

Epilepsy is characterized by paradoxical patterns of neural activity. They may cause different types of electroencephalogram (EEG), which dynamically change in shape and frequency content during the temporal evolution of seizure. It is generally assumed that these epileptic patterns may originate in a network of strongly interconnected neurons, when excitation dominates over inhibition. The aim of this work is to use a neural network composed of 50 x 50 integrate-and-fire neurons to analyse which parameter alterations, at the level of synapse topology, may induce network instability and epileptic-like discharges, and to study the corresponding spatio-temporal characteristics of electrical activity in the network. We assume that a small group of central neurons is stimulated by a depolarizing current (epileptic focus) and that neurons are connected via a Mexican-hat topology of synapses. A signal representative of cortical EEG (ECoG) is simulated by summing the membrane potential changes of all neurons. A sensitivity analysis on the parameters describing the synapse topology shows that an increase in the strength and in spatial extension of excitatory vs. inhibitory synapses may cause the occurrence of travelling waves, which propagate along the network. These propagating waves may cause EEG patterns with different shape and frequency, depending on the particular parameter set used during the simulations. The resulting model EEG signals include irregular rhythms with large amplitude and a wide frequency content, low-amplitude high-frequency rapid discharges, isolated or repeated bursts, and low-frequency quasi-sinusoidal patterns. A slow progressive temporal variation in a single parameter may cause the transition from one pattern to another, thus generating a highly non-stationary signal which resembles that observed during ECoG measurements. These results may help to elucidate the mechanisms at the basis of some epileptic discharges, and to relate rapid changes in EEG patterns with the underlying alterations at the network level.     

A Realistic Neural Mass Model of the Cortex with Laminar-Specific Connections and Synaptic Plasticity – Evaluation with Auditory Habituation

In this work we propose a biologically realistic local cortical circuit model (LCCM), based on neural masses, that incorporates important aspects of the functional organization of the brain that have not been covered by previous models: (1) activity dependent plasticity of excitatory synaptic couplings via depleting and recycling of neurotransmitters and (2) realistic inter-laminar dynamics via laminar-specific distribution of and connections between neural populations. The potential of the LCCM was demonstrated by accounting for the process of auditory habituation. The model parameters were specified using Bayesian inference. It was found that: (1) besides the major serial excitatory information pathway (layer 4 to layer 2/3 to layer 5/6), there exists a parallel “short-cut” pathway (layer 4 to layer 5/6), (2) the excitatory signal flow from the pyramidal cells to the inhibitory interneurons seems to be more intra-laminar while, in contrast, the inhibitory signal flow from inhibitory interneurons to the pyramidal cells seems to be both intra- and inter-laminar, and (3) the habituation rates of the connections are unsymmetrical: forward connections (from layer 4 to layer 2/3) are more strongly habituated than backward connections (from Layer 5/6 to layer 4). Our evaluation demonstrates that the novel features of the LCCM are of crucial importance for mechanistic explanations of brain function. The incorporation of these features into a mass model makes them applicable to modeling based on macroscopic data (like EEG or MEG), which are usually available in human experiments. Our LCCM is therefore a valuable building block for future realistic models of human cognitive function.     

A model of event-related EEG synchronization changes in beta and gamma frequency bands

During preparation, execution and recovery from simple movements, the EEG power spectrum undergoes a sequence of changes. The power in the beta band (13-25 Hz) decreases during preparation and execution of movement, but during recovery it reaches a level higher than that in the reference period (not affected by the event). These effects are known as event-related beta desynchronization and beta rebound. The power in the gamma band (>30 Hz) increases significantly just before the onset of the movement. This effect is known as event-related gamma synchronization. There are numerous observations concerning these effects but the underlying physiological mechanisms and functional role are not clear. We propose a lumped computational model of a cortical circuit. The model consists only of a pyramidal and an interneuronal population. Each population represents averaged properties of constituting neurons. The output of the model represents a local field potential, with a power spectrum peak either in the beta or in the gamma band. The model elucidates the mechanisms of transition between slower and faster rhythms, gamma synchronization and beta desynchronization and rebound effects. The sufficient conditions to observe the effects in the model are changes of the external excitation level and of the connection strength between excitatory and inhibitory populations attributed to short-time plasticity. The present model presents the role of the pyramidal neurons to interneuron connection in the oscillatory behavior of the two populations. We conclude that the pronounced facilitation of the pyramidal to fast spiking interneuron connections, initiated by robust excitation of the motor cortex neurons, may be essential for the effect of beta rebound. Further experiments concerning short-time plasticity during behavioral tasks would be of great value in studies of functional local cortical circuits.     

Spike suppression in a local cortical circuit induced by transcranial magnetic stimulation

Transcranial magnetic stimulation (TMS) noninvasively interferes with human cortical function, and is widely used as an effective technique for probing causal links between neural activity and cognitive function. However, the physiological mechanisms underlying TMS-induced effects on neural activity remain unclear. We examined the mechanism by which TMS disrupts neural activity in a local circuit in early visual cortex using a computational model consisting of conductance-based spiking neurons with excitatory and inhibitory synaptic connections. We found that single-pulse TMS suppressed spiking activity in a local circuit model, disrupting the population response. Spike suppression was observed when TMS was applied to the local circuit within a limited time window after the local circuit received sensory afferent input, as observed in experiments investigating suppression of visual perception with TMS targeting early visual cortex. Quantitative analyses revealed that the magnitude of suppression was significantly larger for synaptically-connected neurons than for isolated individual neurons, suggesting that intracortical inhibitory synaptic coupling also plays an important role in TMS-induced suppression. A conventional local circuit model of early visual cortex explained only the early period of visual suppression observed in experiments. However, models either involving strong recurrent excitatory synaptic connections or sustained excitatory input were able to reproduce the late period of visual suppression. These results suggest that TMS targeting early visual cortex disrupts functionally distinct neural signals, possibly corresponding to feedforward and recurrent information processing, by imposing inhibitory effects through intracortical inhibitory synaptic connections.     

Dynamic Excitatory and Inhibitory Gain Modulation Can Produce Flexible,Robust and Optimal Decision-making

Behavioural and neurophysiological studies in primates have increasingly shown the involvement of urgency signals during the temporal integration of sensory evidence in perceptual decision-making. Neuronal correlates of such signals have been found in the parietal cortex, and in separate studies, demonstrated attention-induced gain modulation of both excitatory and inhibitory neurons. Although previous computational models of decision-making have incorporated gain modulation, their abstract forms do not permit an understanding of the contribution of inhibitory gain modulation. Thus, the effects of co-modulating both excitatory and inhibitory neuronal gains on decision-making dynamics and behavioural performance remain unclear. In this work, we incorporate time-dependent co-modulation of the gains of both excitatory and inhibitory neurons into our previous biologically based decision circuit model. We base our computational study in the context of two classic motion-discrimination tasks performed in animals. Our model shows that by simultaneously increasing the gains of both excitatory and inhibitory neurons, a variety of the observed dynamic neuronal firing activities can be replicated. In particular, the model can exhibit winner-take-all decision-making behaviour with higher firing rates and within a significantly more robust model parameter range. It also exhibits short-tailed reaction time distributions even when operating near a dynamical bifurcation point. The model further shows that neuronal gain modulation can compensate for weaker recurrent excitation in a decision neural circuit, and support decision formation and storage. Higher neuronal gain is also suggested in the more cognitively demanding reaction time than in the fixed delay version of the task. Using the exact temporal delays from the animal experiments, fast recruitment of gain co-modulation is shown to maximize reward rate, with a timescale that is surprisingly near the experimentally fitted value. Our work provides insights into the simultaneous and rapid modulation of excitatory and inhibitory neuronal gains, which enables flexible, robust, and optimal decision-making.     

A geometric model of orientation tuning dynamics in visual neurons]

A geometrical model for the dynamics of orientation tuning of visual neurones was proposed, which makes it possible to study the dynamics of configuration, localization, and weight of excitatory and inhibitory subzones of the receptive field. The model reproduces typical patterns of orientation tuning dynamics, observed in neurophysiological experiments on cat visual cortex neurones. The parameters of the model (size and mutual position of excitatory and inhibitory zones of the receptive field, their weight, and dynamics type) were estimated that correspond to the main types of orientation tuning dynamics in natural conditions. It is shown that selective and acute tuning of neurones can be formed and/or sharpened by intracotrical inhibition, while the dynamics of preferred orientation is due to changes in the geometry of the inhibitory subzone of the receptive field.     

A Pharmacokinetics-Neural Mass Model (PK-NMM) for the Simulation of EEG Activity during Propofol Anesthesia

Modeling the effects of anesthetic drugs on brain activity is very helpful in understanding anesthesia mechanisms. The aim of this study was to set up a combined model to relate actual drug levels to EEG dynamics and behavioral states during propofol-induced anesthesia. We proposed a new combined theoretical model based on a pharmacokinetics (PK) model and a neural mass model (NMM), which we termed PK-NMM—with the aim of simulating electroencephalogram (EEG) activity during propofol-induced general anesthesia. The PK model was used to derive propofol effect-site drug concentrations (C _eff) based on the actual drug infusion regimen. The NMM model took C _eff as the control parameter to produce simulated EEG-like (sEEG) data. For comparison, we used real prefrontal EEG (rEEG) data of nine volunteers undergoing propofol anesthesia from a previous experiment. To see how well the sEEG could describe the dynamic changes of neural activity during anesthesia, the rEEG data and the sEEG data were compared with respect to: power-frequency plots; nonlinear exponent (permutation entropy (PE)); and bispectral SynchFastSlow (SFS) parameters. We found that the PK-NMM model was able to reproduce anesthesia EEG-like signals based on the estimated drug concentration and patients’ condition. The frequency spectrum indicated that the frequency power peak of the sEEG moved towards the low frequency band as anesthesia deepened. Different anesthetic states could be differentiated by the PE index. The correlation coefficient of PE was 0.80±0.13 (mean±standard deviation) between rEEG and sEEG for all subjects. Additionally, SFS could track the depth of anesthesia and the SFS of rEEG and sEEG were highly correlated with a correlation coefficient of 0.77±0.13. The PK-NMM model could simulate EEG activity and might be a useful tool for understanding the action of propofol on brain activity.     

Long-term plasticity at inhibitory synapses

Experience-dependent modifications of neural circuits and function are believed to heavily depend on changes in synaptic efficacy such as LTP/LTD. Hence, much effort has been devoted to elucidating the mechanisms underlying these forms of synaptic plasticity. Although most of this work has focused on excitatory synapses, it is now clear that diverse mechanisms of long-term inhibitory plasticity have evolved to provide additional flexibility to neural circuits. By changing the excitatory/inhibitory balance, GABAergic plasticity can regulate excitability, neural circuit function and ultimately, contribute to learning and memory, and neural circuit refinement. Here we discuss recent advancements in our understanding of the mechanisms and functional relevance of GABAergic inhibitory synaptic plasticity.     

Analysis of stability of neural network with inhibitory neurons

Phase coding in a neural network composed of neural oscillators with inhibitory neurons was studied based on the theory of stochastic phase dynamics. We found that with increasing the coupling coefficients of inhibitory neural oscillators, the firing density in excitatory population transits to a critical state. In this case, when we increase the inhibitory coupling, the firing density will come into dynamic balance again and tend to a fixed value gradually. According to the phenomenon, in the paper we found parameter regions to exhibit those different population states, called dividing zones including flat fading zone, rapid fading zone and critical zone. Based on the dividing zones we can choose the number ratio between inhibitory neurons and excitatory neurons in the neural network, and estimate the coupling action of inhibitory population and excitatory population. Our research also shows that the balance value, enabling the firing density to reach the dynamic balance, does not depend on initial conditions. In addition, the critical value in critical state is only related to the number ratio between inhibitory neurons and excitatory neurons, but is independent of inhibitory coupling and excitatory coupling.     

Cortical Network Models of Firing Rates in the Resting and Active States Predict BOLD Responses

Measurements of blood oxygenation level dependent (BOLD) signals have produced some surprising observations. One is that their amplitude is proportional to the entire activity in a region of interest and not just the fluctuations in this activity. Another is that during sleep and anesthesia the average BOLD correlations between regions of interest decline as the activity declines. Mechanistic explanations of these phenomena are described here using a cortical network model consisting of modules with excitatory and inhibitory neurons, taken as regions of cortical interest, each receiving excitatory inputs from outside the network, taken as subcortical driving inputs in addition to extrinsic (intermodular) connections, such as provided by associational fibers. The model shows that the standard deviation of the firing rate is proportional to the mean frequency of the firing when the extrinsic connections are decreased, so that the mean BOLD signal is proportional to both as is observed experimentally. The model also shows that if these extrinsic connections are decreased or the frequency of firing reaching the network from the subcortical driving inputs is decreased, or both decline, there is a decrease in the mean firing rate in the modules accompanied by decreases in the mean BOLD correlations between the modules, consistent with the observed changes during NREM sleep and under anesthesia. Finally, the model explains why a transient increase in the BOLD signal in a cortical area, due to a transient subcortical input, gives rises to responses throughout the cortex as observed, with these responses mediated by the extrinsic (intermodular) connections.     

Multi-dimensional modulations of α and γ cortical dynamics following mindfulness-based cognitive therapy in Major Depressive Disorder

To illuminate candidate neural working mechanisms of Mindfulness-Based Cognitive Therapy (MBCT) in the treatment of recurrent depressive disorder, parallel to the potential interplays between modulations in electro-cortical dynamics and depressive symptom severity and self-compassionate experience. Linear and nonlinear α and γ EEG oscillatory dynamics were examined concomitant to an affective Go/NoGo paradigm, pre-to-post MBCT or natural wait-list, in 51 recurrent depressive patients. Specific EEG variables investigated were; (1) induced event-related (de-) synchronisation (ERD/ERS), (2) evoked power, and (3) inter-/intra-hemispheric coherence. Secondary clinical measures included depressive severity and experiences of self-compassion. MBCT significantly downregulated α and γ power, reflecting increased cortical excitability. Enhanced α-desynchronisation/ERD was observed for negative material opposed to attenuated α-ERD towards positively valenced stimuli, suggesting activation of neural networks usually hypoactive in depression, related to positive emotion regulation. MBCT-related increase in left-intra-hemispheric α-coherence of the fronto-parietal circuit aligned with these synchronisation dynamics. Ameliorated depressive severity and increased self-compassionate experience pre-to-post MBCT correlated with α-ERD change. The multi-dimensional neural mechanisms of MBCT pertain to task-specific linear and non-linear neural synchronisation and connectivity network dynamics. We propose MBCT-related modulations in differing cortical oscillatory bands have discrete excitatory (enacting positive emotionality) and inhibitory (disengaging from negative material) effects, where mediation in the α and γ bands relates to the former.     

An extended first approximation model for the amygdaloid kindling phenomenon

A first approximation model, which accounts for the strongest phenomena defining kindling is suggested. It is based on an excitatory-inhibitory coupling of neural aggregates, to which a self-stimulation element for the excitatory aggregate was added. The functional linking hypothesis views the representation of kindling as a process of gradual transition through structural changes from a stable system to a system showing stability for small perturbations and an oscillatory orbit for larger perturbations, to a purely oscillatory system. The anatomical linking hypothesis views the excitatory aggregate as representing the hypothalamus, the inhibitory aggregate as representing the hippocampal-septal-preoptic complex, and the selfstimulating element of the excitatory aggregate as representing the amygdaloid-pyriform complex. The model was realized on a digital computer with graphic capabilities and showed good qualitative agreement with the experimental data related to kindling. In addition, the use of the model for generating new experiments is discussed.     

Coupled Van der Pol oscillators — A model of excitatory and inhibitory neural interactions

A system of mutually coupled Van der Pol equations is derived from an extended version of the Wilson and Cowan model for the dynamics of a number of excitatory and inhibitory neural subsets. In the lowest order of approximation, interactions between excitatory and inhibitory subsets appear as linear elastic coupling, while those within and between excitatory and excitatory subsets appear as nonlinear frictional coupling. The case of two coupled oscillators is investigated by the method of averaging and the stability conditions for two mode oscillations are obtained. Internal resonance is also discussed briefly in the case of identical oscillators.     

Activity dependent degeneration explains hub vulnerability in Alzheimer's disease

Brain connectivity studies have revealed that highly connected 'hub' regions are particularly vulnerable to Alzheimer pathology: they show marked amyloid-β deposition at an early stage. Recently, excessive local neuronal activity has been shown to increase amyloid deposition. In this study we use a computational model to test the hypothesis that hub regions possess the highest level of activity and that hub vulnerability in Alzheimer's disease is due to this feature. Cortical brain regions were modeled as neural masses, each describing the average activity (spike density and spectral power) of a large number of interconnected excitatory and inhibitory neurons. The large-scale network consisted of 78 neural masses, connected according to a human DTI-based cortical topology. Spike density and spectral power were positively correlated with structural and functional node degrees, confirming the high activity of hub regions, also offering a possible explanation for high resting state Default Mode Network activity. 'Activity dependent degeneration' (ADD) was simulated by lowering synaptic strength as a function of the spike density of the main excitatory neurons, and compared to random degeneration. Resulting structural and functional network changes were assessed with graph theoretical analysis. Effects of ADD included oscillatory slowing, loss of spectral power and long-range synchronization, hub vulnerability, and disrupted functional network topology. Observed transient increases in spike density and functional connectivity match reports in Mild Cognitive Impairment (MCI) patients, and may not be compensatory but pathological. In conclusion, the assumption of excessive neuronal activity leading to degeneration provides a possible explanation for hub vulnerability in Alzheimer's disease, supported by the observed relation between connectivity and activity and the reproduction of several neurophysiologic hallmarks. The insight that neuronal activity might play a causal role in Alzheimer's disease can have implications for early detection and interventional strategies.     

EEG markers of upright posture in healthy individuals

The EEG spectral-coherence parameters were analyzed in 10 healthy individuals (mean age, 22 ± 0.67 years) at different steps of verticalization, from the lying position to the sitting and standing positions. The maximal changes in all EEG parameters were revealed when the upright posture was maintained in the absence of visual control. Under these conditions, a power increase for the fast EEG components (the ??- and ??-bands) was observed, as was an additional increase when the conditions of maintaining the upright posture were complicated. According to the results of the EEG??s coherent analysis, human verticalization revealed a specific increase for most of the EEG rhythm ranges in the right hemisphere, especially in the frontocentral and occipitoparietal regions, as well as for the interhemispheric coherences for these leads reflecting the involvement of both cortical and subcortical structures in these processes. When the posture maintenance conditions were complicated, an additional coherence increase in the fast EEG bands (the ??-rhythm) was observed in the frontal cortical regions, which was evidence of the increase in the executive functions under these conditions.     

Changes in inhibitory CA1 network in dual pathology model of epilepsy

The combination of two precipitating factors appears to be more and more recognized in patients with temporal lobe epilepsy. Using a two-hit rat model, with a neonatal freeze lesion mimicking a focal cortical malformation combined with hyperthermia-induced seizures mimicking febrile seizures, we have previously reported an increase of inhibition in CA1 pyramidal cells at P20. Here, we investigated the changes affecting excitatory and inhibitory drive onto CA1 interneurons to better define the changes in CA1 inhibitory networks and their paradoxical role in epileptogenesis, using electrophysiological recordings in CA1 hippocampus from rat pups (16–20 d old). We investigated interneurons in CA1 hippocampal area located in stratum oriens (Or) and at the border of strata lacunosum and moleculare (L-M). Our results revealed an increase of the excitatory drive to both types of interneurons with no change in the inhibitory drive. The mechanisms underlying the increase of excitatory synaptic currents (EPSCs) in both types of interneurons are different. In Or interneurons, the amplitude of spontaneous and miniature EPSCs increased, while their frequency was not affected suggesting changes at the post-synaptic level. In L-M interneurons, the frequency of spontaneous EPSCs increases, but the amplitude is not affected. Analyses of miniature EPSCs showed no changes in both their frequency and amplitude. We concluded that L-M interneurons increase in excitatory drive is due to a change in Shaffer collateral axon excitability. The changes described here in CA1 inhibitory network may actually contribute to the epileptogenicity observed in this dual pathology model by increasing pyramidal cell synchronization.     

Synchronization and sensitivity enhancement of the Hodgkin-Huxley neurons due to inhibitory inputs

Recent experimental results imply that inhibitory postsynaptic potentials can play a functional role in realizing synchronization of neuronal firing in the brain. In order to examine the relation between inhibition and synchronous firing of neurons theoretically, we analyze possible effects of synchronization and sensitivity enhancement caused by inhibitory inputs to neurons with a biologically realistic model of the Hodgkin-Huxley equations. The result shows that, after an inhibitory spike, the firing probability of a single postsynaptic neuron exposed to random excitatory background activity oscillates with time. The oscillation of the firing probability can be related to synchronous firing of neurons receiving an inhibitory spike simultaneously. Further, we show that when an inhibitory spike input precedes an excitatory spike input, the presence of such preceding inhibition raises the firing probability peak of the neuron after the excitatory input. The result indicates that an inhibitory spike input can enhance the sensitivity of the postsynaptic neuron to the following excitatory spike input. Two neural network models based on these effects on postsynaptic neurons caused by inhibitory inputs are proposed to demonstrate possible mechanisms of detecting particular spatiotemporal spike patterns. Received: 15 April 1999 /Accepted in revised form: 25 November 1999     

A Dynamic Neural Field Model of Mesoscopic Cortical Activity Captured with Voltage-Sensitive Dye Imaging

A neural field model is presented that captures the essential non-linear characteristics of activity dynamics across several millimeters of visual cortex in response to local flashed and moving stimuli. We account for physiological data obtained by voltage-sensitive dye (VSD) imaging which reports mesoscopic population activity at high spatio-temporal resolution. Stimulation included a single flashed square, a single flashed bar, the line-motion paradigm – for which psychophysical studies showed that flashing a square briefly before a bar produces sensation of illusory motion within the bar – and moving squares controls. We consider a two-layer neural field (NF) model describing an excitatory and an inhibitory layer of neurons as a coupled system of non-linear integro-differential equations. Under the assumption that the aggregated activity of both layers is reflected by VSD imaging, our phenomenological model quantitatively accounts for the observed spatio-temporal activity patterns. Moreover, the model generalizes to novel similar stimuli as it matches activity evoked by moving squares of different speeds. Our results indicate that feedback from higher brain areas is not required to produce motion patterns in the case of the illusory line-motion paradigm. Physiological interpretation of the model suggests that a considerable fraction of the VSD signal may be due to inhibitory activity, supporting the notion that balanced intra-layer cortical interactions between inhibitory and excitatory populations play a major role in shaping dynamic stimulus representations in the early visual cortex.