A model and analysis for the onset and progression of Parkinson's disease

Abstract

With this, the model is extended to include the entire cortico-basal ganglia-thalamo-cortical loop. This Full Model, is able to adequately account for the firing rates of six nuclei populations, using the same framework developed for the three population model. Additionally, these firing rates are shown to be consistent with the experimental firing rate data and tests done on individual basal ganglia connections. Again, using the tractability of the model it is shown how parameter-regions of stability can be found between four key connections. Mapping the progression of PD through these stability regions, insight can be gained on the order in which the disease takes root.

Parkinson's disease (PD) is a degenerative neurological disease that disrupts the movement cycle in the basal ganglia. As the disease progresses, the neurotransmitter, dopamine, becomes depleted. This depletion leads to changes in connection strengths between the seven nuclei in the basal ganglia as well as the appearance of abnormal beta oscillations. Though data is plentiful in rodents and nonhuman primates there is much debate on just exactly how these connection strengths change and just how the oscillations emerge as the disease progresses. One leading hypothesis claims that the oscillations develop in the the globus pallidus external (GPe), subthalamic nucleus (STN), and globus pallidus internal (GPi) loop. We introduce a mathematical model that calculates the firing rates of the loop created between the GPe, STN, and, GPi. This model is formulated in such a way that the neuron firing rates are accounted for yet the model is tractable enough to allow analytic methods to be used. 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. The analysis also shows how the trademark beta oscillations of PD arise as the connection strengths change.