Mathematical modelling of retinal metabolism

Age-related macular degeneration and diabetic retinopathy, in which the cells at the back of the eye degrade due to age and diabetes respectively, are prevalent causes of vision loss in adults. We formulate mathematical models of retinal metabolic regulation to investigate defects that may be responsible for pathology. Continuum PDE models are developed to test whether rod photoreceptors, light detecting cells in the eye, may regulate their energy demand by adapting their length under light and dark conditions. These models assume photoreceptor length depends on the availability of nutrients, such as oxygen, which diffuse and are consumed within the photoreceptor. Our results suggest that the length is limited by oxygen and phosphocreatine shuttle-derived ATP under dark and light conditions respectively. Parameter sensitivity analysis indicates that lowered mitochondrial efficiency due to ageing may be responsible for the damage to and death of photoreceptors that are characteristic of age-related macular degeneration. In the latter part of this thesis we shift our focus to the inner retina and examine how metabolite levels in the tissue surrounding the neurons (highly sensitive, excitable cells that transmit electrical signals) are regulated by glial cells. For instance, stimulated neurons activate their neighbours via the release of the neurotransmitter glutamate, while glial cells regulate neuronal activity via glutamate uptake. Diabetes produces large fluctuations in blood glucose levels, and eventually results in neuronal cell death, causing vision loss. We generate an ODE model for the exchange of key metabolites between neurons and surrounding cells. Using numerical and analytical techniques, we use the model to show that the fluctuations in blood glucose and metabolic changes associated with diabetes may result in abnormally high glutamate levels in the inner retina, which could lead to neuronal damage via excitotoxicity (unregulated neuronal stimulation)