Summary The corticothalamic Compact Model with time delay proposed by Kim and Robinson is analyzed focusing on the resting EEG, which can be described by the linear version of the model with white‐noise input, under the assumption of spatial homogeneity and temporal steadiness. After discussing the availability and restriction of the model by comparing to the original Pre‐Compact Model, a data analysis method for the resting EEG using the model is presented. The experimental results analyzed by the method suggest that the eye‐closed state compared to the eye‐open state would be characterized by enhanced corticothalamic feedback and depressed cortical excitation. The validity of the Reduced Equations derived in our previous paper is also investigated for the resting EEG, concluding that the Reduced Equations would be available with some restriction for the resting EEG, although the center manifold theory on which the Reduced Equations are based is justified at the edge of linear stability in principle.
Background: Pharmacotherapeutic options supporting the treatment of alcohol dependence are recommended and available but underutilized, partly due to questions about efficacy. Nalmefene, a μ-opioid receptor antagonist and partial kappa receptor agonist, is recommended for reduction of alcohol consumption, but evidence about its effectiveness has been equivocal; identifying factors which predict response will help optimize treatment. Methods: The alcohol deprivation effect paradigm is a tightly controlled procedure comprising repeated deprivation and reintroduction phases, leading to increased preference for alcohol; reintroduction approximates relapse. Using a digital drinkometer system measuring high-resolution drinking behavior, we examined the effects of nalmefene on relapse drinking behavior in alcohol addicted rats. We also tested whether drinking behavior in the relapse phase prior to nalmefene administration predicted treatment response. We further examined whether longitudinal drinking behavior and locomotor activity predicted treatment response. Results: Our results showed that nalmefene (0.3 mg/kg) reduced relapse-like consumption significantly (∼20%) compared to vehicle on the first 2 days of alcohol reintroduction. Examining the first 6 h of a preceded treatment-free relapse episode revealed drinking patterns clustering the rats into responders (reduction of >40%, n = 17) and non-responders (reduction of <40%, n = 7) to subsequent nalmefene treatment. During the first 6 h of the preceding relapse phase, responders consumed more alcohol than non-responders; the amount of alcohol consumed during each drinking approach was larger but frequency of drinking did not differ. Longitudinal drinking behavior and locomotor activity did not significantly predict response. Conclusion: Our results suggest that nalmefene reduces alcohol intake during a relapse-like situation but effectiveness can differ greatly at the individual level. However, who responds may be informed by examining drinking profiles and rats that show high drinking levels prior to treatment are more likely to respond to nalmefene.
Gamma oscillations of the local field potential are organized by collective dynamics of numerous neurons and have many functional roles in cognition and/or attention. To mathematically and physiologically analyse relationships between individual inhibitory neurons and macroscopic oscillations, we derive a modification of the theta model, which possesses voltage-dependent dynamics with appropriate synaptic interactions. Bifurcation analysis of the corresponding Fokker-Planck equation (FPE) enables us to consider how synaptic interactions organize collective oscillations. We also develop the adjoint method (infinitesimal phase resetting curve) for simultaneous equations consisting of ordinary differential equations representing synaptic dynamics and a partial differential equation for determining the probability distribution of the membrane potential. This method provides a macroscopic phase response function (PRF), which gives insights into how it is modulated by external perturbation or internal changes of parameters. We investigate the effects of synaptic time constants and shunting inhibition on these gamma oscillations. The sensitivity of rising and decaying time constants is analysed in the oscillatory parameter regions; we find that these sensitivities are not largely dependent on rate of synaptic coupling but, rather, on current and noise intensity. Analyses of shunting inhibition reveal that it can affect both promotion and elimination of gamma oscillations. When the macroscopic oscillation is far from the bifurcation, shunting promotes the gamma oscillations and the PRF becomes flatter as the reversal potential of the synapse increases, indicating the insensitivity of gamma oscillations to perturbations. By contrast, when the macroscopic oscillation is near the bifurcation, shunting eliminates gamma oscillations and a stable firing state appears. More interestingly, under appropriate balance of parameters, two branches of bifurcation are found in our analysis of the FPE. In this case, shunting inhibition can effect both promotion and elimination of the gamma oscillation depending only on the reversal potential.
Summary Objectives: This study aimed to describe a robust method with high time resolution for estimating the cortico-thalamo-cortical (CTC) loop strength and the delay when using a scalp electroencephalography (EEG) and to illustrate its applicability for analyzing the wake-sleep transition. Methods: The basic framework for the proposed method is the parallel use of a physiological model and a parametric phenomenological model: a neural field theory (NFT) of the corticothalamic system and an autoregressive (AR) model. The AR model is a “stochastic” model that shortens the time taken to extract spectral features and is also a “linear” model that is free from the local-minimum problem. From the relationship between the transfer function of the AR model and the transfer function of the NFT in the low frequency limit, we successfully derived a direct expression of CTC loop strength and the loop delay using AR coefficients. Results: Using this method to analyze sleep-EEG data, we were able to clearly track the wake-to-sleep transition, as the estimated CTC loop strength (c 2) decreased to almost zero. We also found that the c 2-distribution during nocturnal sleep is clearly bimodal in nature, which can be well approximated by the superposition of two Gaussian distributions that correspond to sleep and wake states, respectively. The estimated loop delay distributed ∼0.08 s, which agrees well with the previously reported value estimated by other methods, confirming the validity of our method. Conclusions: A robust method with high time resolution was developed for estimating the cortico-thalamo-cortical loop strength and the delay when using a scalp electroencephalography. This method can contribute not only to detecting the wake-sleep transition, but also to further understanding of the transition, where the cortico-thalamo-cortical loop is thought to play an important role.
The corticothalamic Compact Model with time delay proposed by Kim and Robinson is successfully reduced to a real Ginzburg-Landau equation in the vicinity of pitchfork bifurcation point, using center manifold theory for functional differential equations and perturbation theory of week interactions. Broad agreement between the predictions with the reduced equation and corresponding numerical results with the original equation are confirmed in transient analysis of single-body and two-body problem, with emphasis that a “projection to the center subspace” is essential. Furthermore, analogies with Ginzburg-Landau theory of phase transition and with theory developed by Benayoun et al. of neural avalanches are pointed out.
