Oscillatory Neural Models of the Basal Ganglia for Action Selection in Healthy and Parkinsonian Cases

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.