Model and Analysis for the Onset of Parkinsonian Firing Patterns in a Simplified Basal Ganglia

Abstract

Parkinson’s disease (PD) is a degenerative neurological disease that disrupts the movement cycle in the basal ganglia. As the disease progresses, dopamine depletion leads to changes to how the basal ganglia functions as well as the appearance of abnormal beta oscillations. There is much debate on just exactly how these connection strengths change and just how the oscillations emerge. One leading hypothesis claims that the oscillations develop in the globus pallidus external, subthalamic nucleus, and globus pallidus internal loop. We introduce a mathematical model that calculates the average firing rates of this loop while still accounting for the larger closed loop of the entire basal ganglia system. This model is constructed such that physiologically realistic results can be obtained while not sacrificing the use of analytic methods. Because of this, it is possible to determine how the change in the connection strengths can drive the necessary changes in firing rates seen in recordings and account for the generation of trademark beta oscillations of PD without relying on highly specific time delays, stochastic approaches, or numerical approximations. Additionally, we find that the entire cortico-basal ganglia-thalamo-cortical loop is essential for abnormal oscillations to originate.