Mechanisms of seizure propagation in a cortical model

A General, Noise-Driven Mechanism for the 1/f-Like Behavior of Neural Field Spectra

Consistent observations across recording modalities, experiments, and neural systems find neural field spectra with 1/f-like scaling, eliciting many alternative theories to explain this universal phenomenon. We show that a general dynamical system with stochastic drive and minimal assumptions generates 1/f-like spectra consistent with the range of values observed in vivo without requiring a specific biological mechanism or collective critical behavior.

Advanced Modeling and Signal Processing Methods in Brain-Computer Interfaces Based on a Vector of Cyclic Rhythmically Connected Random Processes

In this study is substantiated the new mathematical model of vector of electroencephalographic signals, registered under the conditions of multiple repetitions of the mental control influences of brain-computer interface operator, in the form of a vector of cyclic rhythmically connected random processes, which, due to taking into account the stochasticity and cyclicity, the variability and commonality of the rhythm of the investigated signals have a number of advantages over the known models. This new model opens the way for the study of multidimensional distribution functions; initial, central, and mixed moment functions of higher order such as for each electroencephalographic signal separately; as well as for their respective compatible probabilistic characteristics, among which the most informative characteristics can be selected. This provides an increase in accuracy in the detection (classification) of mental control influences of the brain-computer interface operators. Based on the developed mathematical model, the statistical processing methods of vector of electroencephalographic signals are substantiated, which consist of statistical evaluation of its probabilistic characteristics and make it possible to conduct an effective joint statistical estimation of the probability characteristics of electroencephalographic signals. This provides the basis for coordinated integration of information from different sensors. The use of moment functions of higher order and their spectral images in the frequency domain, as informative characteristics in brain-computer interface systems, are substantiated. Their significant sensitivity to the mental controlling influence of the brain-computer interface operator is experimentally established. The application of Bessel's inequality to the problems of reducing the dimensions (from 500 to 20 numbers) of the vectors of informative features makes it possible to significantly reduce the computational complexity of the algorithms for the functioning of brain-computer interface systems. Namely, we experimentally established that only the first 20 values of the Fourier transform of the estimation of moment functions of higher-order electroencephalographic signals are sufficient to form the vector of informative features in brain-computer interface systems, because these spectral components make up at least 95% of the total energy of the corresponding statistical estimate of the moment functions of higher-order electroencephalographic signals.

Patient-Specific Network Connectivity Combined With a Next Generation Neural Mass Model to Test Clinical Hypothesis of Seizure Propagation

Dynamics underlying epileptic seizures span multiple scales in space and time, therefore, understanding seizure mechanisms requires identifying the relations between seizure components within and across these scales, together with the analysis of their dynamical repertoire. In this view, mathematical models have been developed, ranging from single neuron to neural population. In this study, we consider a neural mass model able to exactly reproduce the dynamics of heterogeneous spiking neural networks. We combine mathematical modeling with structural information from non invasive brain imaging, thus building large-scale brain network models to explore emergent dynamics and test the clinical hypothesis. We provide a comprehensive study on the effect of external drives on neuronal networks exhibiting multistability, in order to investigate the role played by the neuroanatomical connectivity matrices in shaping the emergent dynamics. In particular, we systematically investigate the conditions under which the network displays a transition from a low activity regime to a high activity state, which we identify with a seizure-like event. This approach allows us to study the biophysical parameters and variables leading to multiple recruitment events at the network level. We further exploit topological network measures in order to explain the differences and the analogies among the subjects and their brain regions, in showing recruitment events at different parameter values. We demonstrate, along with the example of diffusion-weighted magnetic resonance imaging (dMRI) connectomes of 20 healthy subjects and 15 epileptic patients, that individual variations in structural connectivity, when linked with mathematical dynamic models, have the capacity to explain changes in spatiotemporal organization of brain dynamics, as observed in network-based brain disorders. In particular, for epileptic patients, by means of the integration of the clinical hypotheses on the epileptogenic zone (EZ), i.e., the local network where highly synchronous seizures originate, we have identified the sequence of recruitment events and discussed their links with the topological properties of the specific connectomes. The predictions made on the basis of the implemented set of exact mean-field equations turn out to be in line with the clinical pre-surgical evaluation on recruited secondary networks.

Transient neocortical gamma oscillations induced by neuronal response modulation

In this paper a mean field model of spatio-temporal electroencephalographic activity in the neocortex is used to computationally study the emergence of neocortical gamma oscillations as a result of neuronal response modulation. It is shown using a numerical bifurcation analysis that gamma oscillations emerge robustly in the solutions of the model and transition to beta oscillations through coordinated modulation of the responsiveness of inhibitory and excitatory neuronal populations. The spatio-temporal pattern of the propagation of these oscillations across the neocortex is illustrated by solving the equations of the model using a finite element software package. Thereby, it is shown that the gamma oscillations remain localized to the regions of neuronal modulation. Moreover, it is discussed that the inherent spatial averaging effect of commonly used electrocortical measurement techniques can significantly alter the amplitude and pattern of fast oscillations in neocortical recordings, and hence can potentially affect physiological interpretations of these recordings.

Model-based robust suppression of epileptic seizures without sensory measurements

Uncontrolled seizures may lead to irreversible damages in the brain and various limitations in the patient's life. There exist experimental studies to stabilize the patient seizures. However, the experimental setups have many sensory devices to measure the dynamics of the brain cortex. These equipments prevent to produce small portable stabilizers for patients in everyday life. Recently, a comprehensive cortex model is introduced to apply model-based observers and controllers. However, this cortex model can be uncertain and have time-varying parameters. Therefore, in this paper, a robust Takagi-Sugeno (TS) controller and observer are designed to suppress the epileptic seizures without sensory measurements. The unavailable sensory measurements are provided by the designed nonlinear observer. The exponential convergence of the observer and controller is satisfied by the feedback parameter design using linear matrix inequalities. In addition, TS fuzzy observer-controller design has been compared with the conventional PID method in terms of control performance and design problem. The numerical computations show that the epileptic seizures are more effectively suppressed by the TS fuzzy observer-based controller under uncertain membrane potential dynamics.

A Computational Study of a Spatiotemporal Mean Field Model Capturing the Emergence of Alpha and Gamma Rhythmic Activity in the Neocortex

In this paper, we analyze the spatiotemporal mean field model developed by Liley et al. in order to advance our understanding of the wide effects of pharmacological agents and anesthetics. Specifically, we use the spatiotemporal mean field model for capturing the electrical activity in the neocortex to computationally study the emergence of α - and γ -band rhythmic activity in the brain. We show that α oscillations in the solutions of the model appear globally across the neocortex, whereas γ oscillations can emerge locally as a result of a bifurcation in the dynamics of the model. We solve the dynamic equations of the model using a finite element solver package and show that our results verify the predictions made by bifurcation analysis.

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.

Multivariate regression methods for estimating velocity of ictal discharges from human microelectrode recordings

OBJECTIVE

Epileptiform discharges, an electrophysiological hallmark of seizures, can propagate across cortical tissue in a manner similar to traveling waves. Recent work has focused attention on the origination and propagation patterns of these discharges, yielding important clues to their source location and mechanism of travel. However, systematic studies of methods for measuring propagation are lacking.

APPROACH

We analyzed epileptiform discharges in microelectrode array recordings of human seizures. The array records multiunit activity and local field potentials at 400 micron spatial resolution, from a small cortical site free of obstructions. We evaluated several computationally efficient statistical methods for calculating traveling wave velocity, benchmarking them to analyses of associated neuronal burst firing.

MAIN RESULTS

Over 90% of discharges met statistical criteria for propagation across the sampled cortical territory. Detection rate, direction and speed estimates derived from a multiunit estimator were compared to four field potential-based estimators: negative peak, maximum descent, high gamma power, and cross-correlation. Interestingly, the methods that were computationally simplest and most efficient (negative peak and maximal descent) offer non-inferior results in predicting neuronal traveling wave velocities compared to the other two, more complex methods. Moreover, the negative peak and maximal descent methods proved to be more robust against reduced spatial sampling challenges. Using least absolute deviation in place of least squares error minimized the impact of outliers, and reduced the discrepancies between local field potential-based and multiunit estimators.

SIGNIFICANCE

Our findings suggest that ictal epileptiform discharges typically take the form of exceptionally strong, rapidly traveling waves, with propagation detectable across millimeter distances. The sequential activation of neurons in space can be inferred from clinically-observable EEG data, with a variety of straightforward computation methods available. This opens possibilities for systematic assessments of ictal discharge propagation in clinical and research settings.

Suppression of epileptic seizures via Anderson localization

Here we show that brain seizures can be effectively suppressed through random modulation of the brain medium. We use an established mesoscale cortical model in the form of a system of coupled stochastic partial differential equations. We show that by temporal and spatial randomization of parameters governing the firing rates of the excitatory and inhibitory neuron populations, seizure waves can be significantly suppressed. We find that the attenuation is the most effective when applied to the mean threshold potential. The proposed technique can serve as a non-invasive paradigm to mitigate epileptic seizures without knowing the location of the epileptic foci.

From individual spiking neurons to population behavior: Systematic elimination of short-wavelength spatial modes

Mean-field models of the brain approximate spiking dynamics by assuming that each neuron responds to its neighbors via a naive spatial average that neglects local fluctuations and correlations in firing activity. In this paper we address this issue by introducing a rigorous formalism to enable spatial coarse-graining of spiking dynamics, scaling from the microscopic level of a single type 1 (integrator) neuron to a macroscopic assembly of spiking neurons that are interconnected by chemical synapses and nearest-neighbor gap junctions. Spiking behavior at the single-neuron scale ℓ≈10μm is described by Wilson's two-variable conductance-based equations [H. R. Wilson, J. Theor. Biol. 200, 375 (1999)], driven by fields of incoming neural activity from neighboring neurons. We map these equations to a coarser spatial resolution of grid length Bℓ, with B≫1 being the blocking ratio linking micro and macro scales. Our method systematically eliminates high-frequency (short-wavelength) spatial modes q(->) in favor of low-frequency spatial modes Q(->) using an adiabatic elimination procedure that has been shown to be equivalent to the path-integral coarse graining applied to renormalization group theory of critical phenomena. This bottom-up neural regridding allows us to track the percolation of synaptic and ion-channel noise from the single neuron up to the scale of macroscopic population-average variables. Anticipated applications of neural regridding include extraction of the current-to-firing-rate transfer function, investigation of fluctuation criticality near phase-transition tipping points, determination of spatial scaling laws for avalanche events, and prediction of the spatial extent of self-organized macrocolumnar structures. As a first-order exemplar of the method, we recover nonlinear corrections for a coarse-grained Wilson spiking neuron embedded in a network of identical diffusively coupled neurons whose chemical synapses have been disabled. Intriguingly, we find that reblocking transforms the original type 1 Wilson integrator into a type 2 resonator whose spike-rate transfer function exhibits abrupt spiking onset with near-vertical takeoff and chaotic dynamics just above threshold.

Closed-loop feedback control and bifurcation analysis of epileptiform activity via optogenetic stimulation in a mathematical model of human cortex

Optogenetics provides a method of neuron stimulation that has high spatial, temporal, and cell-type specificity. Here we present a model of optogenetic feedback control that targets the inhibitory population, which expresses light-sensitive channelrhodopsin-2 channels, in a mean-field model of undifferentiated cortex that is driven to seizures. The inhibitory population is illuminated with an intensity that is a function of electrode measurements obtained via the cortical model. We test the efficacy of this control method on seizurelike activity observed in two parameter spaces of the cortical model that most closely correspond to seizures observed in patients. We also compare the effect of closed-loop and open-loop control on seizurelike activity using a less-complicated ordinary differential equation model of the undifferentiated cortex in parameter space. Seizurelike activity is successfully suppressed in both parameter planes using optimal illumination intensities less likely to have adverse effects on cortical tissue.

Predicting Surgery Targets in Temporal Lobe Epilepsy through Structural Connectome Based Simulations

Temporal lobe epilepsy (TLE) is a prevalent neurological disorder resulting in disruptive seizures. In the case of drug resistant epilepsy resective surgery is often considered. This is a procedure hampered by unpredictable success rates, with many patients continuing to have seizures even after surgery. In this study we apply a computational model of epilepsy to patient specific structural connectivity derived from diffusion tensor imaging (DTI) of 22 individuals with left TLE and 39 healthy controls. We validate the model by examining patient-control differences in simulated seizure onset time and network location. We then investigate the potential of the model for surgery prediction by performing in silico surgical resections, removing nodes from patient networks and comparing seizure likelihood post-surgery to pre-surgery simulations. We find that, first, patients tend to transit from non-epileptic to epileptic states more often than controls in the model. Second, regions in the left hemisphere (particularly within temporal and subcortical regions) that are known to be involved in TLE are the most frequent starting points for seizures in patients in the model. In addition, our analysis also implicates regions in the contralateral and frontal locations which may play a role in seizure spreading or surgery resistance. Finally, the model predicts that patient-specific surgery (resection areas chosen on an individual, model-prompted, basis and not following a predefined procedure) may lead to better outcomes than the currently used routine clinical procedure. Taken together this work provides a first step towards patient specific computational modelling of epilepsy surgery in order to inform treatment strategies in individuals.

Temporal lobe epilepsy (TLE) is a disorder characterised by unpredictable seizures, where surgical removal of brain tissue is often the final treatment option. In roughly 30% of cases surgery procedures are unsuccessful at preventing future seizures. This paper shows the application of a computational model which uses patient derived brain connectivity to predict the success rates of surgery in people with TLE. We consider the brains of 22 patients as networks, with brain regions as nodes and the white matter connections between them as edges. The brain network is unique to each subject and produced from brain imaging scans of 22 patients and 39 controls. Seizures are simulated before and after surgery, where surgery in the model is the removal of nodes from the network. The model successfully identifies regions known to be involved in TLE, and its predicted success rates for surgery are close to the results found in reality. The model additionally provides patient specific recommendations for surgical procedures, which in simulations show improved results compared to standard surgery in every case. This is a first step towards designing personalised surgery procedures in order to improve surgery success rates.

Optogenetic induced epileptiform activity in a model human cortex

Background

Cortical stimulation plays an important role in the study of epileptic seizures. We present a numerical simulation of stimulation using optogenetic channels expressed by excitatory cells in a mean field model of the human cortex.

Findings

Depolarising excitatory cells in a patch of model cortex using Channelrhodpsin-2 (ChR2) ion channels, we are able to hyper-excite a normally functioning cortex and mimic seizure activity. The temporal characteristics of optogenetic channels, and the ability to control the frequency of synchronous activity using these properties are also demonstrated.

Conclusions

Optogenetics is a powerful stimulation technique with high spatial, temporal and cell-type specificity, and would be invaluable in studying seizures and other brain disorders and functions.

Permittivity coupling across brain regions determines seizure recruitment in partial epilepsy

Brain regions generating seizures in patients with refractory partial epilepsy are referred to as the epileptogenic zone (EZ). During a seizure, paroxysmal activity is not restricted to the EZ, but may recruit other brain regions and propagate activity through large brain networks, which comprise brain regions that are not necessarily epileptogenic. The identification of the EZ is crucial for candidates for neurosurgery and requires unambiguous criteria that evaluate the degree of epileptogenicity of brain regions. To obtain such criteria and investigate the mechanisms of seizure recruitment and propagation, we develop a mathematical framework of coupled neural populations, which can interact via signaling through a slow permittivity variable. The permittivity variable captures effects evolving on slow timescales, including extracellular ionic concentrations and energy metabolism, with time delays of up to seconds as observed clinically. Our analyses provide a set of indices quantifying the degree of epileptogenicity and predict conditions, under which seizures propagate to nonepileptogenic brain regions, explaining the responses to intracerebral electric stimulation in epileptogenic and nonepileptogenic areas. In conjunction, our results provide guidance in the presurgical evaluation of epileptogenicity based on electrographic signatures in intracerebral electroencephalograms.

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

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

Modern concepts of seizure modeling

Seizures are complex phenomena spanning multiple spatial and temporal scales, from ion dynamics to communication between brain regions, from milliseconds (spikes) to days (interseizure intervals). Because of the existence of such multiple scales, the experimental evaluation of the mechanisms underlying the initiation, propagation, and termination of epileptic seizures is a difficult problem. Theoretical models and numerical simulations provide new tools to investigate seizure mechanisms at multiple scales. In this chapter, we review different theoretical approaches and their contributions to our understanding of seizure mechanisms.

A probabilistic framework for a physiological representation of dynamically evolving sleep state

This work presents a probabilistic method for mapping human sleep electroencephalogram (EEG) signals onto a state space based on a biologically plausible mathematical model of the cortex. From a noninvasive EEG signal, this method produces physiologically meaningful pathways of the cortical state over a night of sleep. We propose ways in which these pathways offer insights into sleep-related conditions, functions, and complex pathologies. To address explicitly the noisiness of the EEG signal and the stochastic nature of the mathematical model, we use a probabilistic Bayesian framework to map each EEG epoch to a distribution of likelihoods over all model sleep states. We show that the mapping produced from human data robustly separates rapid eye movement sleep (REM) from slow wave sleep (SWS). A Hidden Markov Model (HMM) is incorporated to improve the path results using the prior knowledge that cortical physiology has temporal continuity.

Open loop optogenetic control of simulated cortical epileptiform activity

We present a model for the use of open loop optogenetic control to inhibit epileptiform activity in a meso scale model of the human cortex. The meso scale cortical model first developed by Liley et al. (2001) is extended to two dimensions and the nature of the seizure waves is studied. We adapt to the meso scale a 4 state functional model of Channelrhodopsin-2 (ChR2) ion channels. The effects of pulsed and constant illumination on the conductance of these ion channels is presented. The inhibitory cell population is targeted for the application of open loop control. Seizure waves are successfully suppressed and the inherent properties of the optogenetic channels ensures charge balance in the cortex, protecting it from damage.

Mechanisms of seizure propagation in 2-dimensional centre-surround recurrent networks

Understanding how seizures spread throughout the brain is an important problem in the treatment of epilepsy, especially for implantable devices that aim to avert focal seizures before they spread to, and overwhelm, the rest of the brain. This paper presents an analysis of the speed of propagation in a computational model of seizure-like activity in a 2-dimensional recurrent network of integrate-and-fire neurons containing both excitatory and inhibitory populations and having a difference of Gaussians connectivity structure, an approximation to that observed in cerebral cortex. In the same computational model network, alternative mechanisms are explored in order to simulate the range of seizure-like activity propagation speeds (0.1-100 mm/s) observed in two animal-slice-based models of epilepsy: (1) low extracellular [Formula: see text], which creates excess excitation and (2) introduction of gamma-aminobutyric acid (GABA) antagonists, which reduce inhibition. Moreover, two alternative connection topologies are considered: excitation broader than inhibition, and inhibition broader than excitation. It was found that the empirically observed range of propagation velocities can be obtained for both connection topologies. For the case of the GABA antagonist model simulation, consistent with other studies, it was found that there is an effective threshold in the degree of inhibition below which waves begin to propagate. For the case of the low extracellular [Formula: see text] model simulation, it was found that activity-dependent reductions in inhibition provide a potential explanation for the emergence of slowly propagating waves. This was simulated as a depression of inhibitory synapses, but it may also be achieved by other mechanisms. This work provides a localised network understanding of the propagation of seizures in 2-dimensional centre-surround networks that can be tested empirically.

Computational modeling of epilepsy for an experimental neurologist

Computational modeling can be a powerful tool for an experimentalist, providing a rigorous mathematical model of the system you are studying. This can be valuable in testing your hypotheses and developing experimental protocols prior to experimenting. This paper reviews models of seizures and epilepsy at different scales, including cellular, network, cortical region, and brain scales by looking at how they have been used in conjunction with experimental data. At each scale, models with different levels of abstraction, the extraction of physiological detail, are presented. Varying levels of detail are necessary in different situations. Physiologically realistic models are valuable surrogates for experimental systems because, unlike in an experiment, every parameter can be changed and every variable can be observed. Abstract models are useful in determining essential parameters of a system, allowing the experimentalist to extract principles that explain the relationship between mechanisms and the behavior of the system. Modeling is becoming easier with the emergence of platforms dedicated to neuronal modeling and databases of models that can be downloaded. Modeling will never be a replacement for animal and clinical experiments, but it should be a starting point in designing experiments and understanding their results.

A continuous mapping of sleep states through association of EEG with a mesoscale cortical model

Here we show that a mathematical model of the human sleep cycle can be used to obtain a detailed description of electroencephalogram (EEG) sleep stages, and we discuss how this analysis may aid in the prediction and prevention of seizures during sleep. The association between EEG data and the cortical model is found via locally linear embedding (LLE), a method of dimensionality reduction. We first show that LLE can distinguish between traditional sleep stages when applied to EEG data. It reliably separates REM and non-REM sleep and maps the EEG data to a low-dimensional output space where the sleep state changes smoothly over time. We also incorporate the concept of strongly connected components and use this as a method of automatic outlier rejection for EEG data. Then, by using LLE on a hybrid data set containing both sleep EEG and signals generated from the mesoscale cortical model, we quantify the relationship between the data and the mathematical model. This enables us to take any sample of sleep EEG data and associate it with a position among the continuous range of sleep states provided by the model; we can thus infer a trajectory of states as the subject sleeps. Lastly, we show that this method gives consistent results for various subjects over a full night of sleep and can be done in real time.

A model of feedback control for the charge-balanced suppression of epileptic seizures

Here we present several refinements to a model of feedback control for the suppression of epileptic seizures. We utilize a stochastic partial differential equation (SPDE) model of the human cortex. First, we verify the strong convergence of numerical solutions to this model, paying special attention to the sharp spatial changes that occur at electrode edges. This allows us to choose appropriate step sizes for our simulations; because the spatial step size must be small relative to the size of an electrode in order to resolve its electrical behavior, we are able to include a more detailed electrode profile in the simulation. Then, based on evidence that the mean soma potential is not the variable most closely related to the measurement of a cortical surface electrode, we develop a new model for this. The model is based on the currents flowing in the cortex and is used for a simulation of feedback control. The simulation utilizes a new control algorithm incorporating the total integral of the applied electrical potential. Not only does this succeed in suppressing the seizure-like oscillations, but it guarantees that the applied signal will be charge-balanced and therefore unlikely to cause cortical damage.

Complexity evolution in epileptic seizure

The present paper concentrates on neural complexity generated during the phase transition in epileptic seizure. Epileptic seizures represent a sudden and transient change in the synchronized firing of neuronal brain ensembles. The proposed model treats the brain as an excitable medium for the propagation of waves of electrical activity with a level of abstraction encompassing underlying variables into a number of discrete states. The analysis presented here provides support for the notion of dynamical phase transition in the sequence of chaos --> complexity --> order during the progress of epilepsy. Evolving cellular automata and quantifying it using Langton parameter shows critical value or highest complexity at the onset of seizure phenomenon.

Population based models of cortical drug response: insights from anaesthesia

A great explanatory gap lies between the molecular pharmacology of psychoactive agents and the neurophysiological changes they induce, as recorded by neuroimaging modalities. Causally relating the cellular actions of psychoactive compounds to their influence on population activity is experimentally challenging. Recent developments in the dynamical modelling of neural tissue have attempted to span this explanatory gap between microscopic targets and their macroscopic neurophysiological effects via a range of biologically plausible dynamical models of cortical tissue. Such theoretical models allow exploration of neural dynamics, in particular their modification by drug action. The ability to theoretically bridge scales is due to a biologically plausible averaging of cortical tissue properties. In the resulting macroscopic neural field, individual neurons need not be explicitly represented (as in neural networks). The following paper aims to provide a non-technical introduction to the mean field population modelling of drug action and its recent successes in modelling anaesthesia.