Differential equation models for the hormonal regulation of the menstrual cycle.

摘要

There are growing concerns about the effects of environmental substances on the sexual endocrine system. It is believed that estrogenic substances may disrupt the sexual endocrine system. Such a disruption might have a profound effect on the menstrual cycle. Therefore, mathematical models that accurately predict the serum levels of hormones that control the menstrual cycle would be useful tools in evaluating the effects of environmental substances.;The human menstrual cycle is controlled by the pituitary hormones, luteinizing hormone (LH) and follicle-stimulating hormone (FSH), and the ovarian hormones, estradiol (E2), progesterone (P4), and inhibin (Ih). The pituitary hormones stimulate the growth of ovarian follicles that secrete hormones and work to produce a fertilized ovum. The mathematical models to be presented in this work predict the blood levels of these five hormones as they interact to regulate and maintain the menstrual cycle.;The unmerged model has a pituitary component and an ovarian component consisting of linear systems of ordinary differential equations. The pituitary systems describe the synthesis, release, and clearance of LH and FSH during the menstrual cycle, based on their response to E2, P4 and Ih. The ovarian system describes the roles of FSH and LH in the development of ovarian follicles and the production of E2, P4 and Ih during the menstrual cycle. The merged model is formed by merging the pituitary and ovarian systems together, creating a nonlinear system of delay differential equations.;The merged system is shown to have two stable periodic solutions for the same parameter set, a large amplitude solution that fits data found in the literature for normally cycling women and a small amplitude solution arising from Hopf bifurcation in the system parameters. The small amplitude cycle possesses many similarities to the menstrual cycle disorder referred to as polycystic ovarian syndrome. Hormonal treatments for this abnormality are simulated and the large amplitude cycle fitting the data for normally cycling women is successfully recovered.