Using mathematics to mitigate blindness
This talk will provide a brief overview of my mathematical research in photoreceptor degeneration and vitality at both the cellular and molecular level as well as the interactions and feedback mechanisms within and between these levels. Mathematical modeling has been used to study diverse biological topics ranging from protein folding to cell interactions to interacting populations of humans but has only recently been used to study photoreceptor degeneration, which occurs in age-related macular degeneration (AMD) and retinitis pigmentosa (RP). There are many different maladies that can result in blindness but the ones that result from photoreceptor degeneration pose the biggest threat as there is no cure. Computer (in silico) experiments in this area have given researchers invaluable insights to mitigate blindness and, in some cases, re-directed experimental research. My mathematical models, often developed in collaboration with wetlab researchers or their data, investigate experimentally observed photoreceptor death and rescue in retinal degeneration and the complex interrelated metabolic pathways in cones. Dynamical systems, optimal control, uncertainty and sensitivity analysis together with in silico experiments are used to analyze these systems of nonlinear differential equations. This work highlights the delicate balance of many aspects of the photoreceptor system including the inter-dependent and inter-connected feedback processes modulated by and affecting cone’s metabolism. My work provides a framework for future physiological investigations potentially leading to long-term targeted multi-faceted interventions and therapies.