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MULTIPLE STABLE PERIODIC SOLUTIONS IN A MODEL FOR THE HORMONAL REGULATION OF THE MENSTRUAL CYCLE
Citation:
CLARK, L. H., P. M. Schlosser, AND J. F. Selgrade. MULTIPLE STABLE PERIODIC SOLUTIONS IN A MODEL FOR THE HORMONAL REGULATION OF THE MENSTRUAL CYCLE. BULLETIN OF MATHEMATICAL BIOLOGY. Elsevier Science Ltd, New York, NY, 65(1):157-73, (2003).
Impact/Purpose:
To determine the sensitivity of a mathematical model for predicting the blood levels of pituitary hormones
Description:
ABSTRACT
The pituitary hormones, luteinizing hormone (LH) and follicle-stimulating hormone (FSH), and the ovarian hormones, estradiol (E2), progesterone (P4), and inhibin (Ih), are five hormones important for the regulation and maintenance of the human menstrual cycle. The pituitary hormones stimulate the growth of ovarian follicles which secrete E2, P4, and Ih and work to produce a fertilized ovum. The mathematical model to be presented in this work predicts reasonably accurate blood levels of these five hormones as observed in the literature for normally cycling women. An analysis of how sensitive the model is to small perturbations will be presented. The model system of delay differential equations is shown to have two asymptotically stable periodic solutions for the same parameter set, a normal cycle and an abnormal cycle. Bifurcations giving rise to these solutions are discussed. Numerical simulations of exogenous estrogen and progesterone exposure show that the abnormal cycle can be perturbed into the normal cycle, and vice versa. Therefore, the model can be a useful tool in examining the effects of hormonally active substances on the endocrine system and in evaluating the effectiveness of hormonal therapies on abnormal menstrual cycles.