Abstract
In this chapter we discuss various approaches to mathematical and computational modelling of the basal ganglia, particularly in the context of their most common pathology: Parkinson’s disease (PD). The chapter begins with a review of the basal ganglia and PD, which briefly describes the anatomical structure and connectivity as well as typical dynamics of neuronal activity which is mostly oscillatory. Also we provide a short review of computational models of the basal ganglia and PD. These reviews pay particular attention to the modelling of deep brain stimulation: a successful treatment for PD whose mechanism remains unknown. Following that, we present two different models that aim to demonstrate a physiological role of oscillations in the basal ganglia in the context of action selection. Through computational simulation and mathematical analysis of these models we demonstrate that a regime of partial activity synchronization can be considered as a potential mechanism for the action selection.
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