Mathematical models are used to estimate physiological parameters which are otherwise inaccessible to measurement. When applied to tracer kinetic data obtained in positron tomographic studies, these methods allow for the quantitative analysis of regional metabolic rates in the human brain during life. Dopamine, a neurotransmitter in the mammalian central nervous system, is synthesized by the action of aromatic amino acid decarboxylase on L-dihydroxyphenylalanine (L-dopa). A fluorinated analogue of L-dopa, 6-[18F]fluoro-L-dopa, is used as a tracer in positron tomography to study the nigrostriatal dopaminergic system. Although this tracer has been in use in man for over ten years, a definitive method of quantitative analysis has not yet emerged. The comparison of quantitative results obtained by this approach has been confounded by the diversity of mathematical modelling techniques employed. These techniques range from simple graphical analyses, which yield a single rate constant for the entire system, to complex compartmental approaches, which may not present a unique solution. The goal of this research has been to develop an approach to quantitative analysis which is both informative and mathematically justifiable. Compartmental models of increasing complexity have been evaluated by statistical methods (F-test) to determine the simplest model which adequately fits the data. This strict methodological approach indicates that a two-compartment, three-parameter model produces the best fit, in a statistical sense, to the measured data. This data has also been analyzed by a simple graphical method to yield an influx constant for the system. The influx constant has also been calculated, for comparison, from the results of the compartmental analysis. The two methods were found to be in excellent agreement; both responded predictably to physiological perturbations of the system. While the compartmental method yielded a more informative analysis of the system, the graphically determined influx constant was found to be less sensitive to measurement errors. It is recommended that these two methods be applied in parallel, such that the comparison of results may serve as an internal measure of the integrity of the analysis. / Thesis / Master of Science (MS)