https://doi.org/10.1140/epjs/s11734-024-01336-7
Regular Article
Firing rate model for brain rhythms controlled by astrocytes
Lobachevsky State University of Nizhny Novgorod, 23 Prospekt Gagarina, 603950, Nizhny Novgorod, Russia
d
tatiana.levanova@itmm.unn.ru
Received:
21
April
2024
Accepted:
7
September
2024
Published online:
23
September
2024
We propose a new firing rate model of brain rhythms governed by astrocytes. This theoretical framework describes how astrocytes can regulate neuronal activity and contribute to the generation of brain rhythms. The model describes at the population level the interactions between two large groups of excitatory and inhibitory neurons. The excitatory population is governed by astrocytes via a so-called tripartite synapse. This approach allows us to describe how the interactions between different groups of neurons and astrocytes can give rise to various patterns of synchronized activity and transitions between them. Using analysis of the vector field and special structure of our equations that allows reduction of the original 5-dimensional system to only two equations, we obtain coordinates of the equilibrium state. Two-parameter numerical bifurcation analysis combined with method of maximal Lyapunov exponent charts on different planes of control parameters of the system under study allows us to find regions in the parameter space that correspond to different patterns of population activity. One-parameter analysis of the dependence of firing rates of both populations on astrocytic influence on synaptic connections reveals that astrocytic modulation can lead to a change in the period and amplitude of oscillations in the populations of neurons.
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