Analyses of conditions for generating beta oscillations in the Cortex-Subthalamic Nucleus-Globus Pallidus model

Analyzing the conditions for generating beta oscillation in basal ganglia plays a key role in understanding the mechanism of Parkinson's disease (PD). In this paper, we consider a Cortex-STN-GPe model, which consists of the external segment of globus pallidus (GPe), subthalamic nucleus (STN) and cortex including excitatory and inhibitory neurons. We obtain the stability boundary conditions for the model through theoretical analyses, and discuss the influence of two inputs to cortex and GPe on oscillations by numerical simulation. Our results reveal that the model can oscillate for large connection weight between STN and GPe, much larger input to the cortex, and most input values to the GPe. Furthermore, the effects of parameters in the cortical circuit on the amplitude and frequency of the beta oscillation are analyzed. We show that larger delay and larger firing rate of excitatory and inhibitory neurons in the cortex make the model oscillate easily. We hope that our results will be helpful for further understanding the mechanisms of beta oscillations in the treatment of Parkinson's disease and may apply to some studies of neural oscillations.