Dynamical analysis of a mean firing rate model in Parkinson's disease

The generation of pathological oscillations in Parkinson's disease(PD) is closely linked to the synchronous evolution of neuronal populations within the basal ganglia. Given the advantages of average firing rate models in describing large scale neural dynamics, this paper proposes an extended model that enhances biological plausibility, building upon a previous basal ganglia circuit model. We incorporated the cortex, thalamus and Pedunculopontine Nucleus(PPN) into the basal ganglia model.We calculated the phase locked value and differences in β-band energy proportions across different nuclei, and conducted lesion simulations to validate the biological plausibility of the model. We also introduced two distinct types of dopaminergic parameters into the model to simulate their effects on synapses and, consequently, on network oscillations; the results indicate that relative changes in these parameters may be more likely to induce oscillations than changes in any single value alone. We also investigated the influence of time constants on network activity and found that, whether under normal conditions or in a state of mild dopamine deficiency, the population response rate of the PPN affects the magnitude of oscillation frequencies within the basal ganglia. Furthermore, we conducted a dynamical analysis of synaptic connection delays and weights, discovering that they can induce a transition of the system from a normal state to a pathological oscillatory state. Finally, we performed Morris and Sobol sensitivity analyses to quantitatively assess the influence of various network parameters on oscillatory activity. Through this analysis, we identified the connection strength between the cortex and the thalamic basal nuclei, the bidirectional connection strength of the subthalamic nucleus (STN)-the external segment of the globus pallidus (GPe) loop, and the connection delays in the basal ganglia, the cortico-thalamic system, and the PPN; these parameters play a crucial role in the generation of pathological activity and the regulation of oscillation frequency. These findings provide theoretical guidance for a deeper understanding of the underlying mechanisms of Parkinson's disease and for the alleviation of PD symptoms.