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The retina is the ocular tissue responsible for the detection of light. Its extensive demand for oxygen, coupled with a concomitant elevated supply, renders this tissue prone to both hypoxia and hyperoxia. In this thesis, we construct mathematical models of the retina, formulated as systems of reaction-diffusion equations, investigating its oxygen-related dynamics in healthy and diseased states. In the healthy state, we model the oxygen distribution across the human retina, examining the efficacy of the protein neuroglobin in the prevention of hypoxia. It has been suggested that neuroglobin could prevent hypoxia, either by transporting oxygen from regions where it is rich to those where it is poor, or by storing oxygen during periods of diminished supply or increased uptake. Numerical solutions demonstrate that neuroglobin may be effective in preventing or alleviating hypoxia via oxygen transport, but that its capacity for oxygen storage is essentially negligible, whilst asymptotic analysis reveals that, contrary to the prevailing assumption, neuroglobin's oxygen affinity is near optimal for oxygen transport. A further asymptotic analysis justifies the common approximation of a piecewise constant oxygen uptake across the retina, placing existing models upon a stronger theoretical foundation. In the diseased state, we explore the effect of hyperoxia upon the progression of the inherited retinal diseases, known collectively as retinitis pigmentosa. Both numerical solutions and asymptotic analyses show that this mechanism may replicate many of the patterns of retinal degeneration seen in vivo, but that others are inaccessible to it, demonstrating both the strengths and weaknesses of the oxygen toxicity hypothesis. It is shown that the wave speed of hyperoxic degeneration is negatively correlated with the local photoreceptor density, high density regions acting as a barrier to the spread of photoreceptor loss. The effects of capillary degeneration and treatment with antioxidants or trophic factors are also investigated, demonstrating that each has the potential to delay, halt or partially reverse photoreceptor loss. In addition to answering questions that are not accessible to experimental investigation, these models generate a number of experimentally testable predictions, forming the first loop in what has the potential to be a fruitful experimental/modelling cycle.

A growing body of evidence shows that presynaptic nerve terminals throughout the nervous system are vulnerable to a range of traumatic, toxic and disease-related neurodegenerative stimuli. The aim of this study was to further characterise this vulnerability by examining the response of mouse α-motor nerve terminals at the neuromuscular junction (NMJ) to hypoxia-reperfusion injury. To address this aim, a novel model system was generated in which ex vivo skeletal muscle preparations could be maintained in an hypoxic environment, at an O2 concentration below in vivo normoxic values (<0.25% O2), for 2hr followed by 2hr reperfusion (2H-2R). Using this model system combined with quantitative assessment of immunohistological preparations as well as some ultrastructural observations, I present evidence to show that α-motor nerve terminals are rapidly and selectively vulnerable to hypoxia-reperfusion injury with no apparent perturbations to postsynaptic endplates or muscle fibres. I show that the severity of α-motor nerve terminal pathology is age and muscle type/location dependent: in 8-12wk old mice, nerve terminals in fast-twitch lumbrical muscles are more vulnerable than predominantly slow-twitch transversus abdominis and triangularis sterni. In 5-6 week old mice however, there is an age dependent increase in vulnerability of α-motor nerve terminals from the predominantly slow-twitch muscles while the fast-twitch lumbricals remained unaffected by age. The functional, morphological and ultrastructural pathology observed in α-motor nerve terminals following 2H-2R is indicative of selective and ongoing nerve terminal disassembly but, occurs via a mechanism distinct from Wallerian degeneration, as the neuroprotective slow Wallerian degeneration (Wlds) gene did not protect nerve terminals from these pathological changes. I also provide provisional evidence to show that 1A/II muscle spindle afferents and γ-motor nerve terminals are more resistant to hypoxia-reperfusion injury compared with α-motor nerve terminals. In addition to this, I also report preliminary finding that indicate that the oxygen storing protein, neuroglobin, maybe expressed at the mouse NMJ and report the difficulties of using mice that express yellow fluorescent protein (YFP) in their neurons for repeat/live imaging studies. Overall, these data show that the model of hypoxia-reperfusion injury developed in this study is robust and repeatable, that it induces rapid, quantitative changes in α-motor nerve terminals and that it can be used to further examine the mechanisms regulating nerve terminal vulnerability in response to hypoxia-reperfusion injuries. These findings have clinical implications for the use of surgical tourniquets and in the aetiology of many neurodegenerative diseases and neuropathic sequelae where mechanisms relating to hypoxia and hypoxia-reperfusion injury have been implicated.