dissertationWe develop mathematical models relating measured biological markers to how animals process nutrients and toxins. Our models track molecules as they are ingested, transformed through metabolic processes, and excreted, and relate measurements of biological markers to these processes. We focus on specific problems of practical interest. We begin by developing a model of acetaminophen metabolism and use our model to estimate outcome of acetaminophen overdose patients. Acetaminophen overdose increasingly occurs as a result of chronic use. We analyze the dynamics of chronic use and find threshold dynamics that result from the structure of acetaminophen metabolism. We next study animal nitrogen metabolism. Nitrogen stable isotope ratios in consumer tissue are used by ecologists to estimate diet and trophic dynamics, but feedbacks between diet and physiology complicate the relationship between diet and the nitrogen isotope ratio of consumer tissue. We develop a model of animal nitrogen metabolism to study the influence of diet on stable nitrogen isotope ratios of consumer tissue. Finally, hair is often measured to understand how animals process nutrients and toxins because organic and inorganic substances are incorporated into hair, remaining inert for long periods of time. We develop a model based on the known physiology of hair growth to describe the signal averaging caused by bundling multiple hairs for segmental analysis
