A Simplified Mathematical Model and Simulations of the Hypophysis-Ovarian Endocrine Control System

摘要

The dynamic relationship between the follicle stimulating hormone of the hypophysis and the estrogenic hormone of the ovaries is investigated. A mather matical model for this system is proposed, which unlike previous models, includet the growing follicle as an explicit part of the model. The size of this estrogen-producing follicle is postulated as a determining factor in the periodicity of the system. Simulation of this simplified piece-wise linear model yields solutions which are persistent and periodic. In addition, the results are in good agreement with known physiological data. The results also suggest that the modeling approach is extremely useful in understanding the changes in the system's behavior caused by alterations in its parameters, whether produced by disease or therapeutic measures.