Control effects of stimulus paradigms on characteristic firings of parkinsonism

Experimental studies have shown that neuron population located in the basal ganglia of parkinsonian primates can exhibit characteristic firings with certain firing rates differing from normal brain activities. Motivated by recent experimental findings, we investigate the effects of various stimulation paradigms on the firing rates of parkinsonism based on the proposed dynamical models. Our results show that the closed-loop deep brain stimulation is superior in ameliorating the firing behaviors of the parkinsonism, and other control strategies have similar effects according to the observation of electrophysiological experiments. In addition, in conformity to physiological experiments, we found that there exists optimal delay of input in the closed-loop GPtrain|M1 paradigm, where more normal behaviors can be obtained. More interestingly, we observed that W-shaped curves of the firing rates always appear as stimulus delay varies. We furthermore verify the robustness of the obtained results by studying three pallidal discharge rates of the parkinsonism based on the conductance-based model, as well as the integrate-and-fire-or-burst model. Finally, we show that short-term plasticity can improve the firing rates and optimize the control effects on parkinsonism. Our conclusions may give more theoretical insight into Parkinson's disease studies.