Dynamical role of pedunculopntine nucleus stimulation on controlling Parkinson’s disease

Parkinson’s disease (PD) is considered to be associated with the abnormal activities of the cortex–thalamus and basal ganglia. Besides these nuclei, anatomical evidence indicates that the pedunculopontine nucleus (PPN) also plays a crucial role in the modulation of PD, yet relevant biophysical mechanisms are not completely explained. In this paper, on the basis of a biophysical mean-field model, a new network model for PPN is established. The connection parameters between the PPN and other nuclei are determined from experimental data. Preliminary analysis indicates that although stimulating PPN has little effect on the firing rate of the system, the impact of PPN on the firing pattern is significant. According to the nature of the oscillatory activity in PD and the complexity of PPN control over PD, two kinds of origin of parkinsonian oscillations are studied. The parkinsonian oscillation activities can be controlled and modulated by the direct projection from the PPN to the subthalamic nucleus (STN), and may successfully alleviate akinesia. Moreover, the dynamical bifurcation mechanisms underlying these transitions are analyzed. With the increasing of these parameters, the system produces a supercritical Hopf bifurcation from the unstable equilibrium state to the stable state, but it returns to the unstable state again as the parameters become large enough. More importantly, when a stimulus is added to the PPN, the oscillation can be suppressed at the beginning, but as the stimulation parameter gradually increases, it is excited again. The obtained results can be helpful to understand the PPN stimulation in treating Parkinson patients, and provide a theoretical basis for future clinical studies.