Abstract
The purpose of this project was to make progress towards a mean-field model of reward-related activity in the superior colliculus of rats. As such, this thesis contains an amount of information on different functions of and processes within the superior colliculus, as well as a step-by-step formulation of the model so far (with mathematical derivations) and a brief overview of the sort of output it can produce, to allow an uninitiated researcher to get up-to-speed on the work so far. The model presented is a low-dimensional mean field reduction of an all-to-all coupled theta-neuron model, with a global maximum synaptic conductance parameter that varies according to population activity and synchrony. To approximate a neuronal population with both increases and decreases in coupling strength, two reduced networks, one weakened, the other strengthened, are coupled together and their outputs averaged. Stimulus presentation and subsequent reward (signal) are simulated as depolarising input current pulses and a dopamine trace. The model is far from ideal, so the discussion is focused around pitfalls that anyone intending to continue this research should be advised to avoid, as well as other potential further (or even completely different) avenues to explore.