Theta-Nested Gamma Oscillations in Next Generation Neural Mass Models

Abstract

Theta-nested gamma oscillations have been reported in many areas of the brain and are believed to represent a fundamental mechanism to transfer information across spatial and temporal scales. In a series of recent experiments in vitro it has been possible to replicate with an optogenetic theta frequency stimulation several features of cross-frequency coupling (CFC) among theta and gamma rhythms observed in behaving animals. In order to reproduce the main findings of these experiments we have considered a new class of neural mass models able to reproduce exactly the macroscopic dynamics of spiking neural networks. In this framework, we have examined two setups able to support collective gamma oscillations: namely, the pyramidal interneuronal network gamma (PING) and the interneuronal network gamma (ING). In both setups we observe the emergence of theta-nested gamma oscillations by driving the system with a sinusoidal theta-forcing in proximity of a Hopf bifurcation. These mixed rhythms always display phase amplitude coupling. However, two different types of nested oscillations can be identified: one characterized by a perfect phase locking between theta and gamma rhythms, corresponding to an overall periodic behavior; another one where the locking is imperfect and the dynamics is quasi-periodic or even chaotic. From our analysis it emerges that the locked states are more frequent in the ING setup. In agreement with the experiments, we find theta-nested gamma oscillations for forcing frequencies in the range [1:10] Hz, whose amplitudes grow proportionally to the forcing intensity and which are clearly modulated by the theta phase. Furthermore, analogously to the experiments, the gamma power and the frequency of the gamma-power peak increase with the forcing amplitude. At variance with experimental findings, the gamma-power peak does not shift to higher frequencies by increasing the theta frequency. This effect can be obtained, in our model, only by incrementing, at the same time, also the stimulation power. An effect achieved by increasing the amplitude either of the noise or of the forcing term proportionally to the theta frequency. On the basis of our analysis both the PING and the ING mechanism give rise to theta-nested gamma oscillations with almost identical features.

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

“…This new generation of neural mass models has been recently used to describe the emergence of collective oscillations in fully coupled networks (Devalle et al, 2017 ; Laing, 2017 ; Coombes and Byrne, 2019 ; Dumont and Gutkin, 2019 ) and in balanced sparse networks (di Volo and Torcini, 2018 ). Furthermore, it has been successfully employed to reveal the mechanisms at the basis of theta-nested gamma oscillations (Ceni et al, 2020 ; Segneri et al, 2020 ) and the coexistence of slow and fast gamma oscillations (Bi et al, 2020 ). Finally, it has been recently applied to modeling electrical synapses (Montbrió and Pazó, 2020 ), working memory (Taher et al, 2020 ), the influence of transcranial magnetic stimulation on brain dynamics (Byrne et al, 2020 ), and brain resting state activity (Rabuffo et al, 2020 ).…”

A reduction methodology for fluctuation driven population dynamics

“…In particu-lar, this formulation has allowed to derive a closed lowdimensional set of macroscopic equations describing exactly the evolution of the population firing rate and of the mean membrane potential [21]. In the very last years the Montbrió-Pazó-Roxin (MPR) model [21] is emerging as a representative of a new generation of neural mass models able to successfuly capture relevant aspects of neural dynamics [22][23][24][25][26][27][28][29][30][31][32][33].…”

Gamma Entrainment Improves Synchronization Deficits in Dementia Patients

“…This interaction involves feedback loops between excitatory and inhibitory populations in the hippocampus, through which PCs induce theta cycles in the interneurons, which in turn send inhibitory signals to the PCs as gamma cycles. Theta-gamma coupled oscillations can thus be described by a pyramidal interneuronal network gamma (PING) model 49 , which describes the interaction of the theta and gamma oscillatory activities. One arresting idea triggered by the cyclic nature of theta-gamma interactions suggested by the PING model is that both gamma stimulations 23 , as in our study, and theta stimulations 47,[49][50][51][52] be employed to increase the coupling strength and even the gamma power.…”

“…Theta-gamma coupled oscillations can thus be described by a pyramidal interneuronal network gamma (PING) model 49 , which describes the interaction of the theta and gamma oscillatory activities. One arresting idea triggered by the cyclic nature of theta-gamma interactions suggested by the PING model is that both gamma stimulations 23 , as in our study, and theta stimulations 47,[49][50][51][52] be employed to increase the coupling strength and even the gamma power. More generally, the premise of the PING model motivates that any stimulating intervention in the excitatory-inhibitory feedback loop can be used to trigger the cyclic circuit no matter if the stimulant is in the theta or gamma bands.…”