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具有时滞的帕金森模型的振荡动力学分析

OSCILLATION DYNAMICS ANALYSIS OF PARKINSON'S MODEL WITH TIME DELAY

  • 摘要: 研究大脑基底神经节中产生异常β振荡的起源有助于分析帕金森病的致病机理. 本文系统地研究了改进的皮质−基底神经节(E-I-STN-GPe-GPi)共振模型的振荡动力学. 首先, 通过Routh-Hurwitz准则和稳定性理论获得了该模型局部平衡点处的稳定性与Hopf分岔发生的条件, 并且推导出该共振模型存在Hopf分岔的时滞参数范围. 研究发现, 增加突触传输时滞能够使模型产生Hopf分岔, 并且诱导β振荡的产生, 使系统在健康和帕金森病这两个状态之间相互转换. 其次, 揭示了β振荡的产生与丘脑底核相关的突触连接强度有关. 数值模拟发现, 当丘脑底核同时受到兴奋性神经元集群和苍白球外侧较强的促进作用时, 丘脑底核产生振荡. 最后, 分析了与苍白球内侧有关的参数对其产生振荡的影响, 研究结果发现, 当较小的苍白球外侧突触连接强度和较大的突触传输时滞共同作用时, 苍白球内侧更容易发生振荡, 且振幅越来越大. 希望本文对E-I-STN-GPe-GPi共振模型的动力学特征的研究有助于人们理解帕金森病的致病机理和揭示帕金森病异常β振荡的来源.

     

    Abstract: The study of the origin of abnormal beta oscillations generated in the basal ganglia of the brain can help analyze the pathogenesis of Parkinson's disease. In this paper, the oscillatory dynamics of a modified cortico-basal ganglia (E-I-STN-GPe-GPi) resonance model is systematically investigated. First, the conditions for the stability of the model at the local equilibrium point and the occurrence of Hopf bifurcation are obtained by the Routh-Hurwitz criterion and stability theory, and the range of time delay parameters for the existence of Hopf bifurcation in this resonant model is derived. It was found that increasing the time delay of synaptic transmission could generate Hopf bifurcation in the model and induce beta oscillations, allowing the system to switch between the healthy and Parkinson's disease states.Second, it was revealed that the generation of beta oscillations is related to the strength of synaptic connections associated with the subthalamic nucleus. From the results of numerical simulations, it can be seen that when the subthalamic nucleus is subjected to both excitatory neuronal clusters and stronger facilitation of the globus pallidus external, oscillations are generated. Finally, the effect of GPi-related parameters on its generation of oscillations was analyzed by numerical simulations, and our results revealed that when smaller GPe synaptic connection strengths and larger synaptic transmission time delay are combined, they are more likely to make GPi oscillate with increasing amplitude. It is hoped that the results of this paper can provide some reference for the study of the mechanism of Parkinson's disease.It is hoped that the study of the dynamics characteristics of the E-I-STN-GPe-GPi resonance model in this paper will help us understand the pathogenesis of Parkinson's disease and reveal the origin of abnormal beta oscillations in Parkinson's disease.

     

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