Connexin36 knockout mice display increased sensitivity to pentylenetetrazol-induced seizure-like behaviors

Large-scale synchronous firing of neurons during seizures is modulated by electrotonic coupling between neurons via gap junctions. To explore roles for connexin36 (Cx36) gap junctions in seizures, we examined the seizure threshold of connexin36 knockout (Cx36KO) mice using a pentylenetetrazol (PTZ) model

Forced patterns near a Turing-Hopf bifurcation

We study time-periodic forcing of spatially-extended patterns near a Turing-Hopf bifurcation point. A symmetry-based normal form analysis yields several predictions, including that (i) weak forcing near the intrinsic Hopf frequency enhances or suppresses the Turing amplitude by an amount that scales quadratically with the forcing strength, and (ii) the strongest effect is seen for forcing that is detuned from the Hopf frequency. To apply our results to specific models, we perform a perturbation analysis on general two-component reaction-diffusion systems, which reveals whether the forcing suppresses or enhances the spatial pattern. For the suppressing case, our results explain features of previous experiments on the CDIMA chemical reaction. However, we also find examples of the enhancing case, which has not yet been observed in experiment. Numerical simulations verify the predicted dependence on the forcing parameters.Comment: 4 pages, 4 figure

A neuronal network model of interictal and recurrent ictal activity

We propose a neuronal network model which undergoes a saddle-node bifurcation on an invariant circle as the mechanism of the transition from the interictal to the ictal (seizure) state. In the vicinity of this transition, the model captures important dynamical features of both interictal and ictal states. We study the nature of interictal spikes and early warnings of the transition predicted by this model. We further demonstrate that recurrent seizures emerge due to the interaction between two networks.Comment: 9 pages, 7 figure

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

Studying the effects of thalamic interneurons in a thalamocortical neural mass model

Neural mass models of the thalamocortical circuitry are often used to mimic brain activity during sleep and wakefulness as observed in scalp electroencephalogram (EEG) signals [1]. It is understood that alpha rhythms (8-13 Hz) dominate the EEG power-spectra in the resting-state [2] as well as the period immediately before sleep [3]. Literature review shows that the thalamic interneurons (IN) are often ignored in thalamocortical population models; the emphasis is on the connections between the thalamo cortical relay (TCR) and the thalamic reticular nucleus (TRN). In this work, we look into the effects of the IN cell population on the behaviour of an existing thalamocortical model containing the TCR and TRN cell populations [4]. A schematic of the extended model used in this work is shown in Fig.1. The model equations are solved in Matlab using the Runge-Kutta method of the 4th/5th order. The model shows high sensitivity to the forward and reverse rates of reactions during synaptic transmission as well as on the membrane conductance of the cell populations. The input to the model is a white noise signal simulating conditions of resting state with eyes closed, a condition well known to be associated with dominant alpha band oscillations in EEG e.g. [5]. Thus, the model parameters are calibrated to obtain a set of basal parameter values when the model oscillates with a dominant frequency within the alpha band. The time series plots and the power spectra of the model output are compared with those when the IN cell population is disconnected from the circuit (by setting the inhibitory connectivity parameter from the IN to the TCR to zero). We observe (Fig. 2 inset) a significant difference in time series output of the TRN cell population with and without the IN cell population in the model; this in spite of the IN having no direct connectivity to and from the TRN cell population (Fig. 1). A comparison of the power spectra behaviour of the model output within the delta (1-3.5Hz), theta (3.75-7.5Hz), alpha (7.75-13.5Hz) and beta (13.75-30.5Hz) bands is shown in Fig. 2. Disconnecting the IN cell population shows a significant drop in the alpha band power and the dominant frequency of oscillation now lies within the theta band. An overall ‘slowing’ (left-side shift) of the power spectra is observed with an increase within the delta and theta bands and a decrease in the alpha and beta bands. Such a slowing of EEG is a signature of slow wave sleep in healthy individuals, and this suggests that the IN cell population may be centrally involved in the phase transition to slow wave sleep [6]. It is also characteristic of the waking EEG in Alzheimer’s disease, and may help us to understand the role of the IN cell population in modulating TCR and TRN cell behaviour in pathological brain conditions

Approach to the semiconductor cavity QED in high-Q regimes with q-deformed boson

The high density Frenkel exciton which interacts with a single mode microcavity field is dealed with in the framework of the q-deformed boson. It is shown that the q-defomation of bosonic commutation relations is satisfied naturally by the exciton operators when the low density limit is deviated. An analytical expression of the physical spectrum for the exciton is given by using of the dressed states of the cavity field and the exciton. We also give the numerical study and compare the theoretical results with the experimental resultsComment: 6 pages, 2 figure

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

Linear amplifiers with phase-sensitive noise

We present a model for a linear amplifier which adds phase-dependent noise to the input signal. This is achieved by preparing the internal modes of the amplifier in a squeezed vacuum. Such a scheme could be used to amplify a squeezed-signal quadrature with reduced added noise compared with conventional schemes. The model discussed could be realized as nondegenerate parametric amplification

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