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DYNAMIC BEHAVIOR OF A DELAY-DIFFERENTIAL EQUATION MODEL FOR THE HORMONAL REGULATION OF THE MENSTRUAL CYCLE
Clark, L. H., P. M. Schlosser, AND J. F. Selgrade. DYNAMIC BEHAVIOR OF A DELAY-DIFFERENTIAL EQUATION MODEL FOR THE HORMONAL REGULATION OF THE MENSTRUAL CYCLE. Presented at Joint Mathematics Meetings, Phoenix, AZ, January 7-10, 2004.
During the menstrual cycle, pituitary hormones stimulate the growth and development of ovarian follicles and the release of an ovum to be fertilized. The ovarian follicles secrete hormones during the cycle that regulate the production of the pituitary hormones creating positive and negative feedback loops. This behavior can be modeled mathematically using delay differential equations. The model presented in this work describes the normal cycling of five hormones important in this regulation process. Using Hopf bifurcation theory, the model is shown to have two asymptotically stable periodic solutions for the same parameter set, a normal cycle that fits experimental data found in the literature and an abnormal cycle that resembles a menstrual cycle disorder called polycystic ovarian syndrome (PCOS). The model is used to simulate external hormone therapies that perturb the abnormal cycle into the normal cycle. The model is also used to simulate menstrual cycle disruption by exposing the normal cycle to exogenous estrogen. Such simulations may be useful in exploring the impact of hormonally active substances on normally and abnormally cycling women. (This abstract does not reflect EPA policy.)