Generating mechanism of pathological beta oscillations in STN-GPe circuit model: A bifurcation study

Parkinson’s disease(PD)is characterized by pathological spontaneous beta oscillations(13 Hz-35 Hz)often observed in basal ganglia(BG)composed of subthalamic nucleus(STN)and globus pallidus(GPe)populations.From the viewpoint of dynamics,the spontaneous oscillations are related to limit cycle oscillations in a nonlinear system;here we employ the bifurcation analysis method to elucidate the generating mechanism of the pathological spontaneous beta oscillations underlined by coupling strengths and intrinsic properties of the STN-GPe circuit model.The results reveal that the increase of inter-coupling strength between STN and GPe populations induces the beta oscillations to be generated spontaneously,and causes the oscillation frequency to decrease.However,the increase of intra-coupling(self-feedback)strength of GPe can prevent the model from generating the oscillations,and dramatically increase the oscillation frequency.We further provide a theoretical explanation for the role played by the inter-coupling strength of GPe population in the generation and regulation of the oscillations.Furthermore,our study reveals that the intra-coupling strength of the GPe population provides a switching mechanism on the generation of the abnormal beta oscillations:for small value of the intra-coupling strength,STN population plays a dominant role in inducing the beta oscillations;while for its large value,the GPe population mainly determines the generation of this oscillation.