Eur. Phys. J. B (2023) 96: 94
https://doi.org/10.1140/epjb/s10051-023-00565-4

Regular Article - Statistical and Nonlinear Physics

Kinetic analysis of spike and wave discharge in a neural mass model

College of Science, North China University of Technology, 100144, Beijing, China

^a wangzhihui@ncut.edu.cn

Received: 30 April 2023
Accepted: 28 June 2023
Published online: 11 July 2023

Abstract

In the brain, feedforward inhibition is a fundamental regulator of balancing neural excitation and inhibition, and its dysfunction may cause epilepsy. In this paper, we investigate the influence of feedforward inhibition on absence seizures and its dynamical mechanisms based on a neural mass model. On the one hand, pyramidal neurons (PY), fast kinetic interneurons ($I_{\mathit{fast}}$) and slow kinetic interneurons ($I_{\mathit{slow}}$) form two feedforward inhibition pathways, which are the PY–$I_{\mathit{fast}}$–$I_{\mathit{slow}}$ pathway and the PY–$I_{\mathit{slow}}$–$I_{\mathit{fast}}$ pathway, respectively. When changing the synaptic strength in different pathways, the system shows simple oscillation state, spike and wave discharge (SWD), and multi-spike and wave discharge (m-SWD). On the other hand, the one-parameter bifurcation analysis reveals that the system develops fold bifurcations, Hopf bifurcations, fold bifurcations on limit cycle, and period doubling bifurcations when state transitions occur. In particular, when the system is in the bistable region, the dynamic state of this region is closely related to the stable limit cycle and stable fixed point. Therefore, feedforward inhibition pathways are indeed involved in the regulation of absence seizures, excitatory connections in both feedforward inhibition pathways are more effective than the inhibitory connections in the control of absence seizures. More interestingly, the feedforward inhibition pathway PY–$I_{\mathit{slow}}$–$I_{\mathit{fast}}$ has a stronger regulation of absence seizures than PY–$I_{\mathit{fast}}$–$I_{\mathit{slow}}$. These results provide a theoretical basis for a more detailed understanding of the underlying mechanisms of neurological disorders.