A novel fractional operator-based model for Parkinson’s disease: Analyzing abnormal beta-oscillation and the influence of synaptic parameters

Abstract

With the aggravation of the global aging trend, Parkinson’s disease has become a hot spot of scientific research all over the world. Abnormal β-oscillation in the basal ganglia region is considered to be a major inducement of Parkinson’s disease. In this paper, a new and more complete Parkinson’s model based on fractional operators is proposed to study the oscillation behavior of the basal ganglia region. The correctness of this new fractional model is validated by the simulation of Nambu and Tachibana’s experiment [A. Nambu, Y. Tachibana, Mechanism of parkinsonian neuronal oscillations in the primate basal ganglia: some considerations based on our recent work, Front. Syst. Neurosci., 8:74, 2014]. Then we carry out the Hopf bifurcation analysis of the fractional model and derive the critical conditions for periodic oscillation. The influence of important parameters on the oscillation behavior of the system is analyzed by numerical simulations. It is found that proper control of synaptic transmission delay and synaptic connection strength can improve the abnormal β-oscillation behavior in the basal ganglia region effectively. In addition, the fractional Parkinson’s model in this paper provides more flexibility for model fitting and parameter estimation. The choice of the fractional order α plays a crucial role in the analysis of system oscillation.