Hyperbolic Modeling of Subthalamic Nucleus Cells to Investigate the Effect of Dopamine Depletion

To investigate how different types of neurons can produce well-known spiking patterns, a new computationally efficient model is proposed in this paper. This model can help realize the neuronal interconnection issues. The model can demonstrate various neuronal behaviors observed in vivo through simple parameter modification. The behaviors include tonic and phasic spiking, tonic and phasic bursting, class 1 and class 2 excitability, rebound spike, rebound burst, subthreshold oscillation, and accommodated spiking along with inhibition neuron responses. Here, we investigate the neuronal spiking patterns in Parkinson's disease through our proposed model. Abnormal pattern of subthalamic nucleus in Parkinson's disease can be studied through variations in the shape and frequency of firing patterns. Our proposed model introduces mathematical equations, where these patterns can be derived and clearly differentiated from one another. The irregular and arrhythmic behaviors of subthalamic nucleus firing pattern under normal conditions can easily be transformed to those caused by Parkinson's disease through simple parameter modifications in the proposed model. This model can explicitly show the change of neuronal activity patterns in Parkinson's disease, which may eventually lead to effective treatment with deep brain stimulation devices.