Computational framework of neuronal-astrocytic network within the basal ganglia-thalamic circuits associated with Parkinson's disease.

Parkinson's disease is the neurodegenerative disorder which involves both neurons and non-neurons, and whose symptoms are usually represented by the error index and synchronization index in the computational study. This paper combines with the classical basal ganglia-thalamic network model and tripartite synapse model to explore the internal effects of astrocytes on the Parkinson's disease. The model simulates the firing patterns of the Parkinsonian state and healthy state, verifies the feasibility of the neural-glial model. The results show that the rate of production for IP $_3^{}$ modulate the frequency and amplitude of slow inward current for subthalamic nucleus, globus pallidus externa and interna in two modes. Increasing the rate of production for IP $_3^{}$ of subthalamic nucleus and globus pallidus externa can decrease the error index and presumably alleviate the Parkinson's disease. Increasing the rate of production for IP $_3^{}$ of globus pallidus externa and adjusting the rate of production for IP $_3^{}$ of subthalamic nucleus can result in the desynchronization of network in a regular way. These obtained results emphasize the effect of neurons (especially subthalamic nucleus and globus pallidus externa), astrocytes and their interaction on the Parkinson's disease. It enriches the evidence of involvement of astrocyte in Parkinson's disease, and proposes some cognitive points to the alleviation of Parkinson's disease.