| Summary: | Oscillations between various populations of neurons are common and well documented. However, there are oscillations that can emerge within networks of neurons that are pathological and highly detrimental to the normal functioning of the brain. This thesis is concerned with modelling the transition from healthy network states to the pathological oscillatory states in two different brain disorders; epilepsy and Parkinson’s disease (PD). To study these transitions, existing computational methods for modelling large systems of interacting populations of neurons are used and new tools are developed. The first half of this thesis explores the evidence for the dynamic evolution of focal epilepsy using bifurcation analysis of a neural mass model, and relating these bifurcations to specific features of clinical data recordings in the time-domain. These findings are used to map out the evolution of seizures based on features of segments of the clinically recorded electroencephalograms. The similarity of seizure evolution within patients is tested. Statistically significant similarities were found between the evolutions of seizures from the same patient. In the latter half of the thesis a way of creating firing rate models is described, in which the value of the membrane time constant is dependent on the activity of afferent populations. This method is applied to modelling the basal ganglia (BG). The hypothesis that the BG are responsible for selection in the primate brain is tested and confirmed. The model is then used to investigate the development of PD. It was found that the loss of dopaminergic innervation caused a failure of selection capability but did not directly give rise to the beta oscillations ubiquitous in PD. Network connection strength changes that are seen in PD cause the model to regain selection functionality but lead to a beta frequency resting state oscillation, as is the case in real PD.
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