Complex nonlinear dynamics of bursting of thalamic neurons related to Parkinson's disease

Parkinson's disease is associated with bursting of the thalamic (TC) neuron, which receives the inhibitory synaptic current of the basal ganglia composed of multiple nuclei; deep brain stimulation (DBS) applied to the basal ganglia can eliminate the bursting to recover to the normal state. In this paper, the complex nonlinear dynamics for the appearance and disappearance of the bursting are obtained in a widely used theoretical model of a neuronal network. First, through a bifurcation analysis, isolated TC neurons exhibit paradoxical bursting induced from the resting state by enhanced inhibitory effect, which is different from the common view that the enhanced inhibitory effect should suppress the electrical behaviors. Second, the mechanism for the appearance of bursting is obtained by analyzing the electrical activities of the basal ganglia. The inhibitory synaptic current from the external segment of the globus pallidus (GPe) induces a reduced firing rate of the subthalamic nucleus (STN); then, an excitatory synaptic current from the STN induces the bursting behaviors of the GPe. The excitatory current of STN neurons and the inhibitory current of the GPe cause bursting behaviors of the internal segment of the globus pallidus (GPi), thus resulting in an enhanced inhibition from the GPi to the TC, which can induce the paradoxical bursting similar to the isolated TC neurons. Third, the cause for the disappearance of paradoxical bursting is acquired.The high frequency pulses of DBS induces enhanced firing activity of the STN and GPe neurons and enhanced inhibitory synaptic current from the GPe to the GPi, resulting in a reduced inhibitory effect from the GPi to the TC, which can eliminate the paradoxical bursting. Finally, the fast-slow dynamics of the paradoxical bursting of isolated TC neurons are acquired, which is related to the saddle-node and saddle-homoclinic orbit bifurcations of the fast subsystem of the TC neuron model. The results provide theoretical support for understanding the mechanism of Parkinson's disease and treatment methods such as DBS.