A Model for the Production of Ovarian Hormones during the Menstrual Cycle

In this study, a mathematical model is developed for the production of the ovarian hormones (estradiol, progesterone, and inhibin) with input functions which represent blood levels of the gonadotropin hormones (luteinizing hormone and follicle stimulating hormone). A 9-dimensional system of linear, nonautonomous, ordinary differential equations tracks the capacities of 9 stages of the ovary to synthesize hormones. The model predicts blood levels of these ovarian hormones which match reasonably well data in the literature collected from normally cycling women. In addition, given input functions fitting the data for the gonadotropin hormones and of a fixed period, the system of differential equations is shown to have a globally asymptotically stable solution with the same period. This model will be merged with a similar model for the gonadotropin hormones to obtain a nonlinear system with delay describing the concentrations of five hormones important for regulation and maintenance of the menstrual cycle. Such a model may be useful for predicting the effects of hormonally active environmental substances on the menstrual cycle.