Poisson-distributed noise induces cortical γ-activity: explanation of γ-enhancement by anaesthetics ketamine and propofol

Abstract

Additive noise is known to affect the stability of nonlinear systems. To understand better the role of additive noise in neural systems, we investigate the impact of additive noise on a random neural network of excitatory and inhibitory neurons. Here we hypothesize that the noise originates from the ascending reticular activating system (ARAS). Coherence resonance in the γ-frequency range emerges for intermediate noise levels while the network exhibits non-coherent activity at low and high noise levels. The analytical study of a corresponding mean-field model system explains the resonance effect by a noise-induced phase transition via a saddle-node bifurcation. An analytical study of the linear mean-field systems response to additive noise reveals that the coherent state exhibits a quasi-cycle in the γ-frequency range whose spectral properties are tuned by the additive noise. To illustrate the importance of the work, we show that the quasi-cycle explains γ-enhancement under impact of the anaesthetics ketamine and propofol as a destabilizing effect of the coherent state.

Mathematical Model Insights into EEG Origin under Transcranial Direct Current Stimulation (tDCS) in the Context of Psychosis

“…Simultaneously, a constant input in these cortical layers is applied. As demonstrated in previous studies [ 60 , 64 ], the synchronous impact on both input and transfer function steepness is a direct result of a modulation by Poisson spiking activity in the ensemble, cf. the Appendix A.2 .…”

“…To gain these insights, the neural model considers recent hypotheses on how tDCS affects synapses and neuronal populations. For instance, we assume that tDCS induces an intrinsic Poisson-noise activity in single neurons that represents a modulated input current and transfer function in the population [ 64 ]. This allows to describe the well-known modulated excitability by short-duration tDCS.…”

“…For short stimulus periods, no plasticity effect occurs. Anodal tDCS induces an increased input current I and increased variances and [ 60 , 64 ]. This results from the fact that biological neuron populations exhibit Poisson-like firing rate statistics, i.e., the mean and variance of their firing activity is proportional to each other.…”

Additive Noise-Induced System Evolution (ANISE)

“…Recently, Powanwe and Longtin [48] have described experimentally observed neural burst activity as an additive noise-controlled process and Powanwe and Longtin [49] have provided conditions under which two additive noisedriven biological systems share optimally their information. Moreover, previous theoretical neural population studies have demonstrated that additive noise can explain intermittent frequency transitions observed in experimental resting state electroencephalographic data [50], dynamical switches between two frequency bands induced by opening and closing eyes in humans [51], and the enhancement of spectral power in the γ -frequency under the anesthetic ketamine [52].…”

“…For completeness, it is important to mention quasi-cycle activity [52][53][54][55]. Mathematically, this is the linear response of a deterministically stable system to additive noise below a Hopf bifurcation.…”