A multiple-inhibin model of the human menstrual cycle

Inhibin is one of several hormones which collectively regulate the human female reproductive endocrine system. In recent years, physiologists have been able to separately assay two forms of inhibin. We begin by discussing the physiology and endocrinology that underlie the menstrual cycle. Then, we fit an existing delay differential equation model of the human menstrual cycle to new data describing average hormone levels of young women throughout the menstrual cycle. Next, we consider the existence and stability of equilibrium and periodic solutions, analyze bifurcations, and perform a sensitivity analysis. We compare and contrast these results to previously published results based on the same model but a different data set. Because the introduction of exogenous hormones, whether pharmacological or environmental, can have significant effects on the menstrual cycle, we model the effects of these external hormones. Next, we introduce an expanded model that more fully accounts for the actions of both forms of inhibin. We optimize the parameters to fit the data, then discuss the equilibrium and periodic solutions, bifurcations, and sensitivity for this new model and parameter set. Next, we use the model to consider the effects of exogenous pharmacological hormones. Finally, we discuss the effects on the menstrual cycle of age-related hormone production changes that occur during the peri-menopausal years. This leads to a second parameter set, with only a few variations from the first one, for which the model approximates the monthly hormonal fluctuations for a woman around age 40. In closing, we discuss future possibilities for this line of research.