Effective suppression of beta oscillation in Parkinsonian state via a noisy direct delayed feedback control scheme*

This work explores the function of the noisy direct delayed feedback (NDDF) control strategy in suppressing the pathological oscillations in the basal ganglia (BG) with Parkinson's disease (PD). Deep brain stimulation (DBS) alleviates the PD state fantastically. However, due to its unclear mechanism and open-loop characteristic, it is challenging to further improve its effects with lower energy expenditure. The noise stimulus performs competitively in alleviating the PD state theoretically, but it cannot adapt to the neural condition timely and automatically due to its open-loop control scheme. The direct delayed feedback (DDF) control strategy is able to disturb excessive synchronous effectively. Therefore, the NDDF control strategy is proposed and researched based on a BG computational model, which can reflect the intrinsic properties of the BG neurons and their connections with thalamic neurons. Simulation results show that the NDDF control strategy with optimal parameters is effective in removing the pathological beta oscillations. By comparison, we find the NDDF control strategy performs more excellent than DDF in alleviating PD state. Additionally, we define the multiple-NDDF control strategy and find that the multiple-NDDF with appropriate parameters performs better than NDDF. The obtained results contribute to the cure for PD symptoms by optimizing the noise-induced improvement of the BG dysfunction.