Dynamical Analyses on Beta Oscillations in a STN-GPE-GPI Model of Parkinson’s Disease

Exploring the behaviors of beta oscillations in the basal ganglia is helpful to understand the mechanism of Parkinson’s disease. Studies have shown that the external and internal segments (GPe, GPi) of the globus pallidus receive different intensities of signals from the striatum in Parkinson’s disease and play different roles in the production of beta oscillations, but the relevant mechanism still remains unclear. Based on a model of the subthalamic nucleus (STN) and globus pallidus (GP), we propose an extended STN-GPe-GPi model and analyze the dynamical behaviors of beta oscillations in this model. The stability condition is obtained through theoretical analyses, and the generation of beta oscillations by the inputs from the cortex and striatum is further considered. The influence of some parameters related to GPi on its firing rate oscillations is discussed. The results obtained in this paper are expected to play a guiding role in the medical treatment of Parkinson’s disease.