Study On The Generating And Suppressing Mechanisms Of Abnormal Oscillations In Parkinson’s Disease Using Bifurcation Theory

Parkinson’s disease(PD)is a common chronic neurodegenerative disease,which mainly occurs in the middle and old age,and seriously affects the quality of life of patients and their families.Until now,the etiology and the treatment mechanism of Parkinson’s disease have not been fully elucidated,but it is generally believed that Parkinson’s disease mainly occurs in the cortex-basal ganglia(BG)-thalamus neural circuit model.Previous studies have shown that abnormal beta rhythm oscillation(13-35Hz)in the BG is a typical characteristic in patients and animal models of Parkinson’s disease.In the BG nuclei,the excitatory subthalamic nucleus(STN)and the inhibitory external globus pallidus(GPe)are interconnected to form a negative feedback circuit,which is a typical neural circuit that produces abnormal beta oscillation.In this paper,bifurcation theory and simulation analysis methods are used to elucidate the generation and suppression mechanism of abnormal spontaneous beta oscillations in the STN-GPe feedback circuit model at the level of neural mass.Studies have shown that the STN-GPe neural circuit is the origin of Parkinson’s abnormal beta oscillation.Simulation analysis suggested that increased coupling connection in the model can induce the generation of Parkinson’s oscillation and enhance the oscillation frequency.There are different types of coupling connections in the STN-GPe model,whether they play the same role in the generation of Parkinson’s oscillation and the regulation of the frequency remains to be further clarified.In addition,the existing research is mainly through simulation analysis,but the specific dynamic regulation mechanism is still not very clear.The study based on bifurcation in this paper show that increased coupling connections between STN and GPe can lead to the generation of Parkinson’s oscillation and reduce oscillation frequency,but increased the self-feedback strength of the GPe can suppress the generation of Parkinson’s oscillation and enhance the oscillation frequency.Furthermore,the self-feedback strength of the GPe also plays a switching role in the generation of beta oscillation and frequency regulation.For small values of the self-feedback strength of the GPe,the STN plays a dominant role in the generation of beta oscillation,while for large values of the self-feedback strength of the GPe,the GPe exert a predominant role in the generation of beta oscillation.Increased the parameters of the STN neural mass reduce the frequency of limit cycle oscillation,while increased the parameters of the GPe neural mass can cause the increase of the frequency of limit cycle oscillation.In the STN-GPe neural circuit,STN and GPe also receive inputs from cortex and striatum,the structure is the result of the brain’s own evolution.Therefore,it is worth exploring how inputs from cortex and striatum play a role in the production and frequency regulation of Parkinson’s beta oscillation.By bifurcation and simulation studies,it is found that both the inputs of cortex and striatum could suppress the generation of abnormal beta oscillation in the model and the beta rhythmic oscillation induced by the increase of coupling connections.Moreover,when the two inputs act simultaneously on the STN-GPe model,the greater the cortical input to STN,the lower the striatal input to GPe needed to inhibit such oscillations,and vice versa.Relatice to the regulation of Parkinson’s oscillation by a single cortical or striatum input,dual input is more conducive to suppressing the generation of Parkinson’s beta oscillation in the model.Closed-loop control is a promising regulation method for Deep Brain Stimulation(DBS)of Parkinson’s oscillations.The existing studies mainly focus on the single closed-loop control,but the study on the dual closed-loop control of Parkinson’s oscillations is still lacking,and the specific kinetic regulation mechanism is not very clear.Therefore,in this paper,the STN-GPe neural circuit model is used to study the dual closed-loop control scheme of Parkinson’s oscillations based on proportional controller.The bifurcation and simulation results show that the closed-loop control of STN or GPe can effectively suppress the generation of Parkinson’s oscillations;Moreover,dual closed-loop control is better than single closed-loop control.The dual closed-loop control proposed in our study is a novel regulation scheme,providing a reference for the study of dual closed-loop control of abnormal neural oscillations.The model,theoretical methods,and research results in this paper can provide a basis for the study of the pathogenesis and inhibition mechanism of Parkinson’s disease,and can also provide a reference for the clinical application of DBS in the treatment of Parkinson’s disease.