Theoretical electroencephalogram stationary spectrum for a white-noise-driven cortex: evidence for a general anesthetic-induced phase transition

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.

Modelling cortical network dynamics

We have investigated the theoretical constraints of the interactions between coupled cortical columns. Each cortical column consists of a set of neural populations where each population is modelled as a neural mass. The existence of semi-stable states within a cortical column is dependent on the type of interaction between the neuronal populations, i.e., the form of the synaptic kernels. Current-to-current coupling has been shown, in contrast to potential-to-current coupling, to create semi-stable states within a cortical column. The interaction between semi-stable states of the cortical columns is studied where we derive the dynamics for the collected activity. For small excitations the dynamics follow the Kuramoto model; however, in contrast to previous work we derive coupled equations between phase and amplitude dynamics with the possibility of defining connectivity as a stationary and dynamic variable. The turbulent flow of phase dynamics which occurs in networks of Kuramoto oscillators would indicate turbulent changes in dynamic connectivity for coupled cortical columns which is something that has been recorded in epileptic seizures. We used the results we derived to estimate a seizure propagation model which allowed for inversions using the Laplace assumption (Dynamic Causal Modelling). The seizure propagation model was trialed on simulated data, and future work will investigate the estimation of the connectivity matrix from empirical data. This model can be used to predict changes in seizure evolution after virtual changes in the connectivity network, something that could be of clinical use when applied to epilepsy surgical cases.

Analysis two types of K complexes on the human EEG based on classical continuous wavelet transform

In our work, we compare EEG time-frequency features for two types of K-complexes detected in volunteers performing the monotonous psychomotor test with their eyes closed. Type I K-complexes preceded spontaneous awakenings, while after type II K-complexes, subjects continued to sleep at least for 10 s after. The total number of K-complexes in the group of 18 volunteers was 646, of which of which type I K-complexes was 150 and type II K-complexes was 496. Time-frequency analysis was performed using continuous wavelet transform. EEG wavelet spectral power was averaged upon several brain zones for each of the classical frequency ranges (slow wave, δ, θ, α, β₁, β₂, γ bands). The low-frequency oscillatory activity ( δ-band) preceding type I K-complexes was asymmetrical and most prominent in the left hemisphere. Statistically significant differences were obtained by averaging over the left and right hemispheres, as well as projections of the motor area of the brain, p<0.05. The maximal differences between the types I and II of K-complexes were demonstrated in δ-, θ-bands in the occipital and posterior temporal regions. The high amplitude of the motor cortex projection response in β₂-band, [20;30] Hz, related to the sensory-motor modality of task in monotonous psychomotor test. The δ-oscillatory activity preceding type I K-complexes was asymmetrical and most prominent in the left hemisphere may be due to the important role of the left hemisphere in spontaneous awakening from sleep during monotonous work, which is an interesting issue for future research.

Discrete spectral eigenmode-resonance network of brain dynamics and connectivity

The problem of finding a compact natural representation of brain dynamics and connectivity is addressed using an expansion in terms of physical spatial eigenmodes and their frequency resonances. It is demonstrated that this discrete expansion via the system transfer function enables linear and nonlinear dynamics to be analyzed in compact form in terms of natural dynamic "atoms," each of which is a frequency resonance of an eigenmode. Because these modal resonances are determined by the system dynamics, not the investigator, they are privileged over widely used phenomenological patterns, and obviate the need for artificial discretizations and thresholding in coordinate space. It is shown that modal resonances participate as nodes of a discrete spectral network, are noninteracting in the linear regime, but are linked nonlinearly by wave-wave coalescence and decay processes. The modal resonance formulation is shown to be capable of speeding numerical calculations of strongly nonlinear interactions. Recent work in brain dynamics, especially based on neural field theory (NFT) approaches, allows eigenmodes and their resonances to be estimated from data without assuming a specific brain model. This means that dynamic equations can be inferred using system identification methods from control theory, rather than being assumed, and resonances can be interpreted as control-systems data filters. The results link brain activity and connectivity with control-systems functions such as prediction and attention via gain control and can also be linked to specific NFT predictions if desired, thereby providing a convenient bridge between physiologically based theories and experiment. Amplitudes of modes and resonances can also be tracked to provide a more direct and temporally localized representation of the dynamics than correlations and covariances, which are widely used in the field. By synthesizing many different lines of research, this work provides a way to link quantitative electrophysiological and imaging measurements, connectivity, brain dynamics, and function. This underlines the need to move between coordinate and spectral representations as required. Moreover, standard theoretical-physics approaches and mathematical methods can be used in place of ad hoc statistical measures such as those based on graph theory of artificially discretized and decimated networks, which are highly prone to selection effects and artifacts.

Neural Field Theory of Evoked Response Sequences and Mismatch Negativity With Adaptation

Physiologically based neural field theory of the corticothalamic system is used to calculate the responses evoked by trains of auditory stimuli that correspond to different cortical locations via the tonotopic map. The results are shown to account for standard and deviant evoked responses to frequent and rare stimuli, respectively, in the auditory oddball paradigms widely used in human cognitive studies, and the so-called mismatch negativity between them. It also reproduces a wide range of other effects and variants, including the mechanism by which a change in standard responses relative to deviants can develop through adaptation, different responses when two deviants are presented in a row or a standard is presented after two deviants, relaxation of standard responses back to deviant form after a stimulus-free period, and more complex sequences. Some cases are identified in which adaptation does not account for the whole difference between standard and deviant responses. The results thus provide a systematic means to determine how much of the response is due to adaptation in the system comprising the primary auditory cortex and medial geniculate nucleus, and how much requires involvement of higher-level processing.

Computational Models in Electroencephalography

Computational models lie at the intersection of basic neuroscience and healthcare applications because they allow researchers to test hypotheses in silico and predict the outcome of experiments and interactions that are very hard to test in reality. Yet, what is meant by “computational model” is understood in many different ways by researchers in different fields of neuroscience and psychology, hindering communication and collaboration. In this review, we point out the state of the art of computational modeling in Electroencephalography (EEG) and outline how these models can be used to integrate findings from electrophysiology, network-level models, and behavior. On the one hand, computational models serve to investigate the mechanisms that generate brain activity, for example measured with EEG, such as the transient emergence of oscillations at different frequency bands and/or with different spatial topographies. On the other hand, computational models serve to design experiments and test hypotheses in silico. The final purpose of computational models of EEG is to obtain a comprehensive understanding of the mechanisms that underlie the EEG signal. This is crucial for an accurate interpretation of EEG measurements that may ultimately serve in the development of novel clinical applications.

Noise induced quiescence of epileptic spike generation in patients with epilepsy

Clinical scalp electroencephalographic recordings from patients with epilepsy are distinguished by the presence of epileptic discharges i.e. spikes or sharp waves. These often occur randomly on a background of fluctuating potentials. The spike rate varies between different brain states (sleep and awake) and patients. Epileptogenic tissue and regions near these often show increased spike rates in comparison to other cortical regions. Several studies have shown a relation between spike rate and background activity although the underlying reason for this is still poorly understood. Both these processes, spike occurrence and background activity show evidence of being at least partly stochastic processes. In this study we show that epileptic discharges seen on scalp electroencephalographic recordings and background activity are driven at least partly by a common biological noise. Furthermore, our results indicate noise induced quiescence of spike generation which, in analogy with computational models of spiking, indicate spikes to be generated by transitions between semi-stable states of the brain, similar to the generation of epileptic seizure activity. The deepened physiological understanding of spike generation in epilepsy that this study provides could be useful in the electrophysiological assessment of different therapies for epilepsy including the effect of different drugs or electrical stimulation.

Analysis of the Hindriks and van Putten model for propofol anesthesia: Limitations and extensions

We present a detailed analysis of the Hindriks and van Putten thalamocortical mean-field model for propofol anesthesia [NeuroImage 60(23), 2012]. The Hindriks and van Putten (HvP) model predicts increases in delta and alpha power for moderate (up to 130%) prolongation of GABA_A inhibitory response, corresponding to light anesthetic sedation. Our analysis reveals that, for deeper anesthetic effect, the model exhibits an unexpected abrupt jump in cortical activity from a low-firing state to an extremely high-firing stable state (∼250 spikes/s), and remains locked there even at GABA_A prolongations as high as 300% which would be expected to induce full comatose suppression of all firing activity. We demonstrate that this unphysiological behavior can be completely suppressed with appropriate tuning of the parameters controlling the sigmoidal functions that map soma voltage to firing rate for the excitatory and inhibitory neural populations, coupled with elimination of the putative population-dependent anesthetic efficacies introduced in the HvP model. The modifications reported here constrain the anesthetized brain activity into a biologically plausible range in which the cortex now has access to a moderate-firing state ("awake") and a low-firing ("anesthetized") state such that the brain can transition from "awake" to "anesthetized" states at a critical level of drug concentration. The modified HvP model predicts a drug-effect hysteresis in which the drug concentration required for induction is larger than that at emergence. In addition, the revised model shows a decrease in the intensity and frequency of alpha-band fluctuations, transitioning to delta-band dominance, with deepening anesthesia. These predicted drug concentration-dependent changes in EEG dynamics are consistent with clinical reports.

Cognitive Analytics for Rapid Stress Relief in Humans Using EEG Based Analysis of Tratak Sadhana (Meditation)

The article reports the effect of Tratak Sadhana (meditation) on humans using electroencephalograph (EEG) signals. EEG represents the brain activities in the form of electrical signals. Due to non-stationary nature of the EEG signals, nonlinear parameters like approximate entropy, wavelet entropy and Higuchi' fractal dimensions are used to assess the variations in EEG rest as well as during Tratak Sadhana, i.e. at a rest state with eyes closed and during Tratak meditation. EEG signals are captured using EPOC Emotive EEG sensor. The sensor has 14 electrodes covering human scalp. Results shows that new practitioners can also achieve a rapid meditative state as compared to other meditation techniques. Further, the Big Data perspective of the present study is discussed. The present study shows that Tratak Sadhana meditation is an effective tool for rapid stress relief in humans.

Brain-wave equation incorporating axodendritic connectivity

We introduce an integral model of a two-dimensional neural field that includes a third dimension representing space along a dendritic tree that can incorporate realistic patterns of axodendritic connectivity. For natural choices of this connectivity we show how to construct an equivalent brain-wave partial differential equation that allows for efficient numerical simulation of the model. This is used to highlight the effects that passive dendritic properties can have on the speed and shape of large scale traveling cortical waves.

Regional entropy of functional imaging signals varies differently in sensory and cognitive systems during propofol-modulated loss and return of behavioral responsiveness

The level and richness of consciousness depend on information integration in the brain. Altered interregional functional interactions may indicate disrupted information integration during anesthetic-induced unconsciousness. How anesthetics modulate the amount of information in various brain regions has received less attention. Here, we propose a novel approach to quantify regional information content in the brain by the entropy of the principal components of regional blood oxygen-dependent imaging signals during graded propofol sedation. Fifteen healthy individuals underwent resting-state scans in wakeful baseline, light sedation (conscious), deep sedation (unconscious), and recovery (conscious). Light sedation characterized by lethargic behavioral responses was associated with global reduction of entropy in the brain. Deep sedation with completely suppressed overt responsiveness was associated with further reductions of entropy in sensory (primary and higher sensory plus orbital prefrontal cortices) but not high-order cognitive (dorsal and medial prefrontal, cingulate, parietotemporal cortices and hippocampal areas) systems. Upon recovery of responsiveness, entropy was restored in the sensory but not in high-order cognitive systems. These findings provide novel evidence for a reduction of information content of the brain as a potential systems-level mechanism of reduced consciousness during propofol anesthesia. The differential changes of entropy in the sensory and high-order cognitive systems associated with losing and regaining overt responsiveness are consistent with the notion of "disconnected consciousness", in which a complete sensory-motor disconnection from the environment occurs with preserved internal mentation.

Spinodal decomposition in a mean-field model of the cortex: Emergence of hexagonally symmetric activation patterns

Spinodal decomposition is a well-known pattern-forming mechanism in metallurgic alloys, semiconductor crystals, and colloidal gels. In metallurgy, if a heated sample of a homogeneous Zn-Al alloy is suddenly quenched below a critical temperature, then the sample can spontaneously precipitate into inhomogenous textures of Zn- and Al-rich regions with significantly altered material properties such as ductility and hardness. Here we report on our recent discovery that a two-dimensional model of the human cortex with inhibitory diffusion can, under particular homogeneous initial conditions, exhibit a form of nonconserved spinodal decomposition in which regions of the cortex self-organize into hexagonally distributed binary patches of activity and inactivity. Fine-scale patterns precipitate rapidly, and then the dynamics slows to render coarser-scale shapes which can ripen into a range of slowly evolving patterns including mazelike labyrinths, hexagonal islands and continents, nucleating "mitotic cells" which grow to a critical size then subdivide, and inverse nucleations in which quiescent islands are surrounded by a sea of activity. One interesting class of activity coalesces into a soliton-like narrow ribbon of depolarization that traverses the cortex at ∼4cm/s. We speculate that this may correspond to the thus far unexplained interictal waves of cortical activation that precede grand-mal seizure in an epileptic event. We note that spinodal decomposition is quite distinct from the Turing mechanism for symmetry breaking in cortex investigated in earlier work by the authors [Steyn-Ross et al., Phys. Rev. E 76, 011916 (2007)PLEEE81539-375510.1103/PhysRevE.76.011916].

NFTsim: Theory and Simulation of Multiscale Neural Field Dynamics

A user ready, portable, documented software package, NFTsim, is presented to facilitate numerical simulations of a wide range of brain systems using continuum neural field modeling. NFTsim enables users to simulate key aspects of brain activity at multiple scales. At the microscopic scale, it incorporates characteristics of local interactions between cells, neurotransmitter effects, synaptodendritic delays and feedbacks. At the mesoscopic scale, it incorporates information about medium to large scale axonal ranges of fibers, which are essential to model dissipative wave transmission and to produce synchronous oscillations and associated cross-correlation patterns as observed in local field potential recordings of active tissue. At the scale of the whole brain, NFTsim allows for the inclusion of long range pathways, such as thalamocortical projections, when generating macroscopic activity fields. The multiscale nature of the neural activity produced by NFTsim has the potential to enable the modeling of resulting quantities measurable via various neuroimaging techniques. In this work, we give a comprehensive description of the design and implementation of the software. Due to its modularity and flexibility, NFTsim enables the systematic study of an unlimited number of neural systems with multiple neural populations under a unified framework and allows for direct comparison with analytic and experimental predictions. The code is written in C++ and bundled with Matlab routines for a rapid quantitative analysis and visualization of the outputs. The output of NFTsim is stored in plain text file enabling users to select from a broad range of tools for offline analysis. This software enables a wide and convenient use of powerful physiologically-based neural field approaches to brain modeling. NFTsim is distributed under the Apache 2.0 license.

Anesthesia modifies subthreshold critical slowing down in a stochastic Hodgkin-Huxley-like model with inhibitory synaptic input

The dynamics of a stochastic type-I Hodgkin-Huxley-like point neuron model exposed to inhibitory synaptic noise are investigated as a function of distance from spiking threshold and the inhibitory influence of the general anesthetic agent propofol. The model is biologically motivated and includes the effects of intrinsic ion-channel noise via a stochastic differential equation description as well as inhibitory synaptic noise modeled as multiple Poisson-distributed impulse trains with saturating response functions. The effect of propofol on these synapses is incorporated through this drug's principal influence on fast inhibitory neurotransmission mediated by γ-aminobutyric acid (GABA) type-A receptors via reduction of the synaptic response decay rate. As the neuron model approaches spiking threshold from below, we track membrane voltage fluctuation statistics of numerically simulated stochastic trajectories. We find that for a given distance from spiking threshold, increasing the magnitude of anesthetic-induced inhibition is associated with augmented signatures of critical slowing: fluctuation amplitudes and correlation times grow as spectral power is increasingly focused at 0 Hz. Furthermore, as a function of distance from threshold, anesthesia significantly modifies the power-law exponents for variance and correlation time divergences observable in stochastic trajectories. Compared to the inverse square root power-law scaling of these quantities anticipated for the saddle-node bifurcation of type-I neurons in the absence of anesthesia, increasing anesthetic-induced inhibition results in an observable exponent <-0.5 for variance and >-0.5 for correlation time divergences. However, these behaviors eventually break down as distance from threshold goes to zero with both the variance and correlation time converging to common values independent of anesthesia. Compared to the case of no synaptic input, linearization of an approximating multivariate Ornstein-Uhlenbeck model reveals these effects to be the consequence of an additional slow eigenvalue associated with synaptic activity that competes with those of the underlying point neuron in a manner that depends on distance from spiking threshold.

The effect of inhibition on the existence of traveling wave solutions for a neural field model of human seizure termination

In this paper we study the influence of inhibition on an activity-based neural field model consisting of an excitatory population with a linear adaptation term that directly regulates the activity of the excitatory population. Such a model has been used to replicate traveling wave data as observed in high density local field potential recordings (González-Ramírez et al. PLoS Computational Biology, 11(2), e1004065, 2015). In this work, we show that by adding an inhibitory population to this model we can still replicate wave properties as observed in human clinical data preceding seizure termination, but the parameter range over which such waves exist becomes more restricted. This restriction depends on the strength of the inhibition and the timescale at which the inhibition acts. In particular, if inhibition acts on a slower timescale relative to excitation then it is possible to still replicate traveling wave patterns as observed in the clinical data even with a relatively strong effect of inhibition. However, if inhibition acts on the same timescale as the excitation, or faster, then traveling wave patterns with the desired characteristics cease to exist when the inhibition becomes sufficiently strong.

Development and validation of brain target controlled infusion of propofol in mice

Mechanisms through which anesthetics disrupt neuronal activity are incompletely understood. In order to study anesthetic mechanisms in the intact brain, tight control over anesthetic pharmacology in a genetically and neurophysiologically accessible animal model is essential. Here, we developed a pharmacokinetic model that quantitatively describes propofol distribution into and elimination out of the brain. To develop the model, we used jugular venous catheters to infuse propofol in mice and measured propofol concentration in serial timed brain and blood samples using high performance liquid chromatography (HPLC). We then used adaptive fitting procedures to find parameters of a three compartment pharmacokinetic model such that all measurements collected in the blood and in the brain across different infusion schemes are fit by a single model. The purpose of the model was to develop target controlled infusion (TCI) capable of maintaining constant brain propofol concentration at the desired level. We validated the model for two different targeted concentrations in independent cohorts of experiments not used for model fitting. The predictions made by the model were unbiased, and the measured brain concentration was indistinguishable from the targeted concentration. We also verified that at the targeted concentration, state of anesthesia evidenced by slowing of the electroencephalogram and behavioral unresponsiveness was attained. Thus, we developed a useful tool for performing experiments necessitating use of anesthetics and for the investigation of mechanisms of action of propofol in mice.

A stochastic basis for neural inertia in emergence from general anaesthesia

BACKGROUND

Transitions into and out of the anaesthetised state exhibit resistance to state transitions known as neural inertia. As a consequence, emergence from anaesthesia occurs at a consistently lower anaesthetic concentration than induction. Motivated by stochastic switching between discrete activity patterns observed at constant anaesthetic concentration, we investigated the consequences of such switching for neural inertia.

METHODS

We simulated stochastic switching in MATLAB as Brownian motion on an energy landscape or equivalently as a discrete Markov process. Effects of anaesthetics were modelled as changing stability of the awake and the anaesthetised states. Simulation results were compared with re-analysed neural inertia data from mice and Drosophila.

RESULTS

Diffusion on a two-well energy landscape gives rise to hysteresis. With additive noise, hysteresis collapses. This collapse occurs over a mixing time that is independent from pharmacokinetics. The two-well potential gives rise to the leftward shift for the emergence dose-response curve. Yet, from in vivo data, ΔEC₅₀ and Δ Hill slope are strongly negatively correlated (R²=0.45, P<1.7×10^-15). This correlation is not explained by a two-well potential. The extension of the diffusion model to a Markov process with 10 states (three awake, seven unconscious) reproduces both the left shift and the shallower Hill slope for emergence.

CONCLUSIONS

Stochastic state switching accounts for all known features of neural inertia. More than two states are required to explain the consistent increase observed in variability of recovery from general anaesthesia. This model predicts that hysteresis should collapse with a time scale independent of anaesthetic drug pharmacokinetics.

Metastability of Neuronal Dynamics during General Anesthesia: Time for a Change in Our Assumptions?

There is strong evidence that anesthetics have stereotypical effects on brain state, so that a given anesthetic appears to have a signature in the electroencephalogram (EEG), which may vary with dose. This can be usefully interpreted as the anesthetic determining an attractor in the phase space of the brain. How brain activity shifts between these attractors in time remains understudied, as most studies implicitly assume a one-to-one relationship between drug dose and attractor features by assuming stationarity over the analysis interval and analyzing data segments of several minutes in length. Yet data in rats anesthetized with isoflurane suggests that, at anesthetic levels consistent with surgical anesthesia, brain activity alternates between multiple attractors, often spending on the order of 10 min in one activity pattern before shifting to another. Moreover, the probability of these jumps between attractors changes with anesthetic concentration. This suggests the hypothesis that brain state is metastable during anesthesia: though it appears at equilibrium on short timescales (on the order of seconds to a few minutes), longer intervals show shifting behavior. Compelling evidence for metastability in rats anesthetized with isoflurane is reviewed, but so far only suggestive hints of metastability in brain states exist with other anesthetics or in other species. Explicit testing of metastability during anesthesia will require experiments with longer acquisition intervals and carefully designed analytic approaches; some of the implications of these constraints are reviewed for typical spectral analysis approaches. If metastability exists during anesthesia, it implies degeneracy in the relationship between brain state and effect site concentration, as there is not a one-to-one mapping between the two. This degeneracy could explain some of the reported difficulty in using brain activity monitors to titrate drug dose to prevent awareness during anesthesia and should force a rethinking of the notion of depth of anesthesia as a single dimension. Finally, explicit incorporation of knowledge of the dynamics of the brain during anesthesia could offer better depth of anesthesia monitoring.

Multistability in the corticothalamic system

Neural field theory of the corticothalamic system is used to analyze the properties of its steady-state solutions, including their linear stability, in the parameter space of synaptic couplings for physiological parameter ranges representing normal arousal waking states in adult humans. The independent connections of the corticothalamic model define an eight-dimensional parameter space, while specific combinations of these connections parameterize intracortical, corticothalamic, and intrathalamic loops. Multistable regions are systematically identified and the existence of up to five steady-state solutions is confirmed, up to three of which are linearly stable. A key determinant for the existence of five steady states is found to be the number of nonzero connections. This finding had not been previously proposed as the determining factor of high multiplicities of multistability in mesoscopic models of the brain. In the corticothalamic model presented here, multistability occurs when the intrathalamic loop is present (i.e., the reticular nucleus inhibits the relay nuclei), and when the net synaptic effect of the intracortical loop is inhibitory. The signature of these additional waking states is an overall increased level of thalamic activity. It is argued that the additional steady states found may represent hyperarousal states which occur when the corticothalamic projections do not attenuate the activity of the cortex.

Relationship of Topology, Multiscale Phase Synchronization, and State Transitions in Human Brain Networks

How the brain reconstitutes consciousness and cognition after a major perturbation like general anesthesia is an important question with significant neuroscientific and clinical implications. Recent empirical studies in animals and humans suggest that the recovery of consciousness after anesthesia is not random but ordered. Emergence patterns have been classified as progressive and abrupt transitions from anesthesia to consciousness, with associated differences in duration and electroencephalogram (EEG) properties. We hypothesized that the progressive and abrupt emergence patterns from the unconscious state are associated with, respectively, continuous and discontinuous synchronization transitions in functional brain networks. The discontinuous transition is explainable with the concept of explosive synchronization, which has been studied almost exclusively in network science. We used the Kuramato model, a simple oscillatory network model, to simulate progressive and abrupt transitions in anatomical human brain networks acquired from diffusion tensor imaging (DTI) of 82 brain regions. To facilitate explosive synchronization, distinct frequencies for hub nodes with a large frequency disassortativity (i.e., higher frequency nodes linking with lower frequency nodes, or vice versa) were applied to the brain network. In this simulation study, we demonstrated that both progressive and abrupt transitions follow distinct synchronization processes at the individual node, cluster, and global network levels. The characteristic synchronization patterns of brain regions that are “progressive and earlier” or “abrupt but delayed” account for previously reported behavioral responses of gradual and abrupt emergence from the unconscious state. The characteristic network synchronization processes observed at different scales provide new insights into how regional brain functions are reconstituted during progressive and abrupt emergence from the unconscious state. This theoretical approach also offers a principled explanation of how the brain reconstitutes consciousness and cognitive functions after physiologic (sleep), pharmacologic (anesthesia), and pathologic (coma) perturbations.

Anesthetic action on the transmission delay between cortex and thalamus explains the beta-buzz observed under propofol anesthesia

In recent years, more and more surgeries under general anesthesia have been performed with the assistance of electroencephalogram (EEG) monitors. An increase in anesthetic concentration leads to characteristic changes in the power spectra of the EEG. Although tracking the anesthetic-induced changes in EEG rhythms can be employed to estimate the depth of anesthesia, their precise underlying mechanisms are still unknown. A prominent feature in the EEG of some patients is the emergence of a strong power peak in the β-frequency band, which moves to the α-frequency band while increasing the anesthetic concentration. This feature is called the beta-buzz. In the present study, we use a thalamo-cortical neural population feedback model to reproduce observed characteristic features in frontal EEG power obtained experimentally during propofol general anesthesia, such as this beta-buzz. First, we find that the spectral power peak in the α- and δ-frequency ranges depend on the decay rate constant of excitatory and inhibitory synapses, but the anesthetic action on synapses does not explain the beta-buzz. Moreover, considering the action of propofol on the transmission delay between cortex and thalamus, the model reveals that the beta-buzz may result from a prolongation of the transmission delay by increasing propofol concentration. A corresponding relationship between transmission delay and anesthetic blood concentration is derived. Finally, an analytical stability study demonstrates that increasing propofol concentration moves the systems resting state towards its stability threshold.

Pattern recognition of spectral entropy features for detection of alcoholic and control visual ERP's in multichannel EEGs

This paper presents a novel ranking method to select spectral entropy (SE) features that discriminate alcoholic and control visual event-related potentials (ERP'S) in gamma sub-band (30-55 Hz) derived from a 64-channel electroencephalogram (EEG) recording. The ranking is based on a t test statistic that rejects the null hypothesis that the group means of SE values in alcoholics and controls are identical. The SE features with high ranks are indicative of maximal separation between their group means. Various sizes of top ranked feature subsets are evaluated by applying principal component analysis (PCA) and k-nearest neighbor (k-NN) classification. Even though ranking does not influence the performance of classifier significantly with the selection of all 61 active channels, the classification efficiency is directly proportional to the number of principal components (pc). The effect of ranking and PCA on classification is predominantly observed with reduced feature subsets of (N = 25, 15) top ranked features. Results indicate that for N = 25, proposed ranking method improves the k-NN classification accuracy from 91 to 93.87% as the number of pcs increases from 5 to 25. With same number of pcs, the k-NN classifier responds with accuracies of 84.42-91.54% with non-ranked features. Similarly for N = 15 and number of pcs varying from 5 to 15, ranking enhances k-NN detection accuracies from 88.9 to 93.08% as compared to 86.75-91.96% without ranking. This shows that the detection accuracy is increased by 6.5 and 2.8%, respectively, for N = 25, whereas it enhances by 2.2 and 1%, respectively, for N = 15 in comparison with non-ranked features. In the proposed t test ranking method for feature selection, the pcs of only top ranked feature candidates take part in classification process and hence provide better generalization.

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.

Extensions to a manifold learning framework for time-series analysis on dynamic manifolds in bioelectric signals

This paper addresses the challenge of extracting meaningful information from measured bioelectric signals generated by complex, large scale physiological systems such as the brain or the heart. We focus on a combination of the well-known Laplacian eigenmaps machine learning approach with dynamical systems ideas to analyze emergent dynamic behaviors. The method reconstructs the abstract dynamical system phase-space geometry of the embedded measurements and tracks changes in physiological conditions or activities through changes in that geometry. It is geared to extract information from the joint behavior of time traces obtained from large sensor arrays, such as those used in multiple-electrode ECG and EEG, and explore the geometrical structure of the low dimensional embedding of moving time windows of those joint snapshots. Our main contribution is a method for mapping vectors from the phase space to the data domain. We present cases to evaluate the methods, including a synthetic example using the chaotic Lorenz system, several sets of cardiac measurements from both canine and human hearts, and measurements from a human brain.

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.

Functional and Topological Conditions for Explosive Synchronization Develop in Human Brain Networks with the Onset of Anesthetic-Induced Unconsciousness

Sleep, anesthesia, and coma share a number of neural features but the recovery profiles are radically different. To understand the mechanisms of reversibility of unconsciousness at the network level, we studied the conditions for gradual and abrupt transitions in conscious and anesthetized states. We hypothesized that the conditions for explosive synchronization (ES) in human brain networks would be present in the anesthetized brain just over the threshold of unconsciousness. To test this hypothesis, functional brain networks were constructed from multi-channel electroencephalogram (EEG) recordings in seven healthy subjects across conscious, unconscious, and recovery states. We analyzed four variables that are involved in facilitating ES in generic, non-biological networks: (1) correlation between node degree and frequency, (2) disassortativity (i.e., the tendency of highly-connected nodes to link with less-connected nodes, or vice versa), (3) frequency difference of coupled nodes, and (4) an inequality relationship between local and global network properties, which is referred to as the suppressive rule. We observed that the four network conditions for ES were satisfied in the unconscious state. Conditions for ES in the human brain suggest a potential mechanism for rapid recovery from the lightly-anesthetized state. This study demonstrates for the first time that the network conditions for ES, formerly shown in generic networks only, are present in empirically-derived functional brain networks. Further investigations with deep anesthesia, sleep, and coma could provide insight into the underlying causes of variability in recovery profiles of these unconscious states.

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.

A Mechanistic Neural Field Theory of How Anesthesia Suppresses Consciousness: Synaptic Drive Dynamics, Bifurcations, Attractors, and Partial State Equipartitioning

With the advances in biochemistry, molecular biology, and neurochemistry there has been impressive progress in understanding the molecular properties of anesthetic agents. However, there has been little focus on how the molecular properties of anesthetic agents lead to the observed macroscopic property that defines the anesthetic state, that is, lack of responsiveness to noxious stimuli. In this paper, we use dynamical system theory to develop a mechanistic mean field model for neural activity to study the abrupt transition from consciousness to unconsciousness as the concentration of the anesthetic agent increases. The proposed synaptic drive firing-rate model predicts the conscious-unconscious transition as the applied anesthetic concentration increases, where excitatory neural activity is characterized by a Poincaré-Andronov-Hopf bifurcation with the awake state transitioning to a stable limit cycle and then subsequently to an asymptotically stable unconscious equilibrium state. Furthermore, we address the more general question of synchronization and partial state equipartitioning of neural activity without mean field assumptions. This is done by focusing on a postulated subset of inhibitory neurons that are not themselves connected to other inhibitory neurons. Finally, several numerical experiments are presented to illustrate the different aspects of the proposed theory.

Percolation Model of Sensory Transmission and Loss of Consciousness Under General Anesthesia

Neurons communicate with each other dynamically; how such communications lead to consciousness remains unclear. Here, we present a theoretical model to understand the dynamic nature of sensory activity and information integration in a hierarchical network, in which edges are stochastically defined by a single parameter p representing the percolation probability of information transmission. We validate the model by comparing the transmitted and original signal distributions, and we show that a basic version of this model can reproduce key spectral features clinically observed in electroencephalographic recordings of transitions from conscious to unconscious brain activities during general anesthesia. As p decreases, a steep divergence of the transmitted signal from the original was observed, along with a loss of signal synchrony and a sharp increase in information entropy in a critical manner; this resembles the precipitous loss of consciousness during anesthesia. The model offers mechanistic insights into the emergence of information integration from a stochastic process, laying the foundation for understanding the origin of cognition.

How the cortico-thalamic feedback affects the EEG power spectrum over frontal and occipital regions during propofol-induced sedation

Increasing concentrations of the anaesthetic agent propofol initially induces sedation before achieving full general anaesthesia. During this state of anaesthesia, the observed specific changes in electroencephalographic (EEG) rhythms comprise increased activity in the δ- (0.5-4 Hz) and α- (8-13 Hz) frequency bands over the frontal region, but increased δ- and decreased α-activity over the occipital region. It is known that the cortex, the thalamus, and the thalamo-cortical feedback loop contribute to some degree to the propofol-induced changes in the EEG power spectrum. However the precise role of each structure to the dynamics of the EEG is unknown. In this paper we apply a thalamo-cortical neuronal population model to reproduce the power spectrum changes in EEG during propofol-induced anaesthesia sedation. The model reproduces the power spectrum features observed experimentally both in frontal and occipital electrodes. Moreover, a detailed analysis of the model indicates the importance of multiple resting states in brain activity. The work suggests that the α-activity originates from the cortico-thalamic relay interaction, whereas the emergence of δ-activity results from the full cortico-reticular-relay-cortical feedback loop with a prominent enforced thalamic reticular-relay interaction. This model suggests an important role for synaptic GABAergic receptors at relay neurons and, more generally, for the thalamus in the generation of both the δ- and the α- EEG patterns that are seen during propofol anaesthesia sedation.

Measuring effects of different noises in a model using ISI-distance methods

This paper examines the effects of current and conductance noises in a minimal Hodgkin–Huxley type model of a cold receptor neuron. Current noise enters the membrane equation directly while conductance noise is propagated through the activation variables. Compared with common used interspike interval method, ISI-distance is a simple complementary approach to measure the different effects of current and conductance noises. ISI-distance extracts information from the interspike intervals by evaluating the ratio of instantaneous firing rates, which is parameter-free, time scale-independent and easy to visualize. Simulation results show that the most significant differences between different noise implementations in a pacemaker-like tonic firing regime at the transition to chaotic burst discharges.

Fractional Diffusion Based Modelling and Prediction of Human Brain Response to External Stimuli

Human brain response is the result of the overall ability of the brain in analyzing different internal and external stimuli and thus making the proper decisions. During the last decades scientists have discovered more about this phenomenon and proposed some models based on computational, biological, or neuropsychological methods. Despite some advances in studies related to this area of the brain research, there were fewer efforts which have been done on the mathematical modeling of the human brain response to external stimuli. This research is devoted to the modeling and prediction of the human EEG signal, as an alert state of overall human brain activity monitoring, upon receiving external stimuli, based on fractional diffusion equations. The results of this modeling show very good agreement with the real human EEG signal and thus this model can be used for many types of applications such as prediction of seizure onset in patient with epilepsy.

Noise-induced precursors of state transitions in the stochastic Wilson-cowan model

The Wilson-Cowan neural field equations describe the dynamical behavior of a 1-D continuum of excitatory and inhibitory cortical neural aggregates, using a pair of coupled integro-differential equations. Here we use bifurcation theory and small-noise linear stochastics to study the range of a phase transitions-sudden qualitative changes in the state of a dynamical system emerging from a bifurcation-accessible to the Wilson-Cowan network. Specifically, we examine saddle-node, Hopf, Turing, and Turing-Hopf instabilities. We introduce stochasticity by adding small-amplitude spatio-temporal white noise, and analyze the resulting subthreshold fluctuations using an Ornstein-Uhlenbeck linearization. This analysis predicts divergent changes in correlation and spectral characteristics of neural activity during close approach to bifurcation from below. We validate these theoretical predictions using numerical simulations. The results demonstrate the role of noise in the emergence of critically slowed precursors in both space and time, and suggest that these early-warning signals are a universal feature of a neural system close to bifurcation. In particular, these precursor signals are likely to have neurobiological significance as early warnings of impending state change in the cortex. We support this claim with an analysis of the in vitro local field potentials recorded from slices of mouse-brain tissue. We show that in the period leading up to emergence of spontaneous seizure-like events, the mouse field potentials show a characteristic spectral focusing toward lower frequencies concomitant with a growth in fluctuation variance, consistent with critical slowing near a bifurcation point. This observation of biological criticality has clear implications regarding the feasibility of seizure prediction.

Emergence of spatially heterogeneous burst suppression in a neural field model of electrocortical activity

Burst suppression in the electroencephalogram (EEG) is a well-described phenomenon that occurs during deep anesthesia, as well as in a variety of congenital and acquired brain insults. Classically it is thought of as spatially synchronous, quasi-periodic bursts of high amplitude EEG separated by low amplitude activity. However, its characterization as a “global brain state” has been challenged by recent results obtained with intracranial electrocortigraphy. Not only does it appear that burst suppression activity is highly asynchronous across cortex, but also that it may occur in isolated regions of circumscribed spatial extent. Here we outline a realistic neural field model for burst suppression by adding a slow process of synaptic resource depletion and recovery, which is able to reproduce qualitatively the empirically observed features during general anesthesia at the whole cortex level. Simulations reveal heterogeneous bursting over the model cortex and complex spatiotemporal dynamics during simulated anesthetic action, and provide forward predictions of neuroimaging signals for subsequent empirical comparisons and more detailed characterization. Because burst suppression corresponds to a dynamical end-point of brain activity, theoretically accounting for its spatiotemporal emergence will vitally contribute to efforts aimed at clarifying whether a common physiological trajectory is induced by the actions of general anesthetic agents. We have taken a first step in this direction by showing that a neural field model can qualitatively match recent experimental data that indicate spatial differentiation of burst suppression activity across cortex.

Spin-glass model predicts metastable brain states that diminish in anesthesia

Patterns of resting state connectivity change dynamically and may represent modes of cognitive information processing. The diversity of connectivity patterns (global brain states) reflects the information capacity of the brain and determines the state of consciousness. In this work, computer simulation was used to explore the repertoire of global brain states as a function of cortical activation level. We implemented a modified spin glass model to describe UP/DOWN state transitions of neuronal populations at a mesoscopic scale based on resting state BOLD fMRI data. Resting state fMRI was recorded in 20 participants and mapped to 10,000 cortical regions (sites) defined on a group-aligned cortical surface map. Each site represented the population activity of a ~20 mm(2) area of the cortex. Cross-correlation matrices of the mapped BOLD time courses of the set of sites were calculated and averaged across subjects. In the model, each cortical site was allowed to interact with the 16 other sites that had the highest pair-wise correlation values. All sites stochastically transitioned between UP and DOWN states under the net influence of their 16 pairs. The probability of local state transitions was controlled by a single parameter T corresponding to the level of global cortical activation. To estimate the number of distinct global states, first we ran 10,000 simulations at T = 0. Simulations were started from random configurations that converged to one of several distinct patterns. Using hierarchical clustering, at 99% similarity, close to 300 distinct states were found. At intermediate T, metastable state configurations were formed suggesting critical behavior with a sharp increase in the number of metastable states at an optimal T. Both reduced activation (anesthesia, sleep) and increased activation (hyper-activation) moved the system away from equilibrium, presumably incompatible with conscious mentation. During equilibrium, the diversity of large-scale brain states was maximum, compatible with maximum information capacity-a presumed condition of consciousness.

Anesthetic action on extra-synaptic receptors: effects in neural population models of EEG activity

The role of extra-synaptic receptors in the regulation of excitation and inhibition in the brain has attracted increasing attention. Because activity in the extra-synaptic receptors plays a role in regulating the level of excitation and inhibition in the brain, they may be important in determining the level of consciousness. This paper reviews briefly the literature on extra-synaptic GABA and NMDA receptors and their affinity to anesthetic drugs. We propose a neural population model that illustrates how the effect of the anesthetic drug propofol on GABAergic extra-synaptic receptors results in changes in neural population activity and the electroencephalogram (EEG). Our results show that increased tonic inhibition in inhibitory cortical neurons cause a dramatic increase in the power of both δ− and α− bands. Conversely, the effects of increased tonic inhibition in cortical excitatory neurons and thalamic relay neurons have the opposite effect and decrease the power in these bands. The increased δ-activity is in accord with observed data for deepening propofol anesthesia; but is absolutely dependent on the inclusion of extrasynaptic (tonic) GABA action in the model.

Critical role for resource constraints in neural models

Criticality has emerged as a leading dynamical candidate for healthy and pathological neuronal activity. At the heart of criticality in neural systems is the need for parameters to be tuned to specific values or for the existence of self-organizing mechanisms. Existing models lack precise physiological descriptions for how the brain maintains its tuning near a critical point. In this paper we argue that a key ingredient missing from the field is a formulation of reciprocal coupling between neural activity and metabolic resources. We propose that the constraint of optimizing the balance between energy use and activity plays a major role in tuning brain states to lie near criticality. Important recent findings aligned with our viewpoint have emerged from analyses of disorders that involve severe metabolic disturbances and alter scale-free properties of brain dynamics, including burst suppression. Moreover, we argue that average shapes of neuronal avalanches are a signature of scale-free activity that offers sharper insights into underlying mechanisms than afforded by traditional analyses of avalanche statistics.

Emergence from general anesthesia and the sleep-manifold

The electroencephalogram (EEG) during the re-establishment of consciousness after general anesthesia and surgery varies starkly between patients. Can the EEG during this emergence period provide a means of estimating the underlying biological processes underpinning the return of consciousness? Can we use a model to infer these biological processes from the EEG patterns? A frontal EEG was recorded from 84 patients. Ten patients were chosen for state-space analysis. Five showed archetypal emergences; which consisted of a progressive decrease in alpha power and increase peak alpha frequency before return of responsiveness. The five non-archetypal emergences showed almost no spectral EEG changes (even as the volatile general anesthetic decreased) and then an abrupt return of responsiveness. We used Bayesian methods to estimate the likelihood of an EEG pattern corresponding to the position of the patient on a 2-dimensional manifold in a state space of excitatory connection strength vs. change in intrinsic resting neuronal membrane conductivity. We could thus visualize the trajectory of each patient in the state-space during their emergence period. The patients who followed an archetypal emergence displayed a very consistent pattern; consisting of progressive increase in conductivity, and a temporary period of increased connection strength before return of responsiveness. The non-archetypal emergence trajectories remained fixed in a region of phase space characterized by a relatively high conductivity and low connection strength throughout emergence. This unexpected progressive increase in conductivity during archetypal emergence may be due to an abating of the surgical stimulus during this period. Periods of high connection strength could represent forays into dissociated consciousness, but the model suggests all patients reposition near the fold in the state space to take advantage of bi-stable cortical dynamics before transitioning to consciousness.

Integrating neuroinformatics tools in TheVirtualBrain

TheVirtualBrain (TVB) is a neuroinformatics Python package representing the convergence of clinical, systems, and theoretical neuroscience in the analysis, visualization and modeling of neural and neuroimaging dynamics. TVB is composed of a flexible simulator for neural dynamics measured across scales from local populations to large-scale dynamics measured by electroencephalography (EEG), magnetoencephalography (MEG) and functional magnetic resonance imaging (fMRI), and core analytic and visualization functions, all accessible through a web browser user interface. A datatype system modeling neuroscientific data ties together these pieces with persistent data storage, based on a combination of SQL and HDF5. These datatypes combine with adapters allowing TVB to integrate other algorithms or computational systems. TVB provides infrastructure for multiple projects and multiple users, possibly participating under multiple roles. For example, a clinician might import patient data to identify several potential lesion points in the patient's connectome. A modeler, working on the same project, tests these points for viability through whole brain simulation, based on the patient's connectome, and subsequent analysis of dynamical features. TVB also drives research forward: the simulator itself represents the culmination of several simulation frameworks in the modeling literature. The availability of the numerical methods, set of neural mass models and forward solutions allows for the construction of a wide range of brain-scale simulation scenarios. This paper briefly outlines the history and motivation for TVB, describing the framework and simulator, giving usage examples in the web UI and Python scripting.

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.

Neural masses and fields in dynamic causal modeling

Dynamic causal modeling (DCM) provides a framework for the analysis of effective connectivity among neuronal subpopulations that subtend invasive (electrocorticograms and local field potentials) and non-invasive (electroencephalography and magnetoencephalography) electrophysiological responses. This paper reviews the suite of neuronal population models including neural masses, fields and conductance-based models that are used in DCM. These models are expressed in terms of sets of differential equations that allow one to model the synaptic underpinnings of connectivity. We describe early developments using neural mass models, where convolution-based dynamics are used to generate responses in laminar-specific populations of excitatory and inhibitory cells. We show that these models, though resting on only two simple transforms, can recapitulate the characteristics of both evoked and spectral responses observed empirically. Using an identical neuronal architecture, we show that a set of conductance based models-that consider the dynamics of specific ion-channels-present a richer space of responses; owing to non-linear interactions between conductances and membrane potentials. We propose that conductance-based models may be more appropriate when spectra present with multiple resonances. Finally, we outline a third class of models, where each neuronal subpopulation is treated as a field; in other words, as a manifold on the cortical surface. By explicitly accounting for the spatial propagation of cortical activity through partial differential equations (PDEs), we show that the topology of connectivity-through local lateral interactions among cortical layers-may be inferred, even in the absence of spatially resolved data. We also show that these models allow for a detailed analysis of structure-function relationships in the cortex. Our review highlights the relationship among these models and how the hypothesis asked of empirical data suggests an appropriate model class.

The anesthetic propofol shifts the frequency of maximum spectral power in EEG during general anesthesia: analytical insights from a linear model

The work introduces a linear neural population model that allows to derive analytically the power spectrum subjected to the concentration of the anesthetic propofol. The analytical study of the power spectrum of the systems activity gives conditions on how the frequency of maximum power in experimental electroencephalographic (EEG) changes dependent on the propofol concentration. In this context, we explain the anesthetic-induced power increase in neural activity by an oscillatory instability and derive conditions under which the power peak shifts to larger frequencies as observed experimentally in EEG. Moreover the work predicts that the power increase only occurs while the frequency of maximum power increases. Numerically simulations of the systems activity complement the analytical results.

Neural field theory of plasticity in the cerebral cortex

A generalized timing-dependent plasticity rule is incorporated into a recent neural field theory to explore synaptic plasticity in the cerebral cortex, with both excitatory and inhibitory populations included. Analysis in the time and frequency domains reveals that cortical network behavior gives rise to a saddle-node bifurcation and resonant frequencies, including a gamma-band resonance. These system resonances constrain cortical synaptic dynamics and divide it into four classes, which depend on the type of synaptic plasticity window. Depending on the dynamical class, synaptic strengths can either have a stable fixed point, or can diverge in the absence of a separate saturation mechanism. Parameter exploration shows that time-asymmetric plasticity windows, which are signatures of spike-timing dependent plasticity, enable the richest variety of synaptic dynamics to occur. In particular, we predict a zone in parameter space which may allow brains to attain the marginal stability phenomena observed experimentally, although additional regulatory mechanisms may be required to maintain these parameters.

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.