Analysis of Lacker's Model with an Ageing Factor for the Control of Ovulation and Polycystic Ovary Syndrome

In the present paper, we develop an extensive theoretical analysis of the deterministic model for the control of ovulation in mammals proposed by Mariana et al., (1994), which is an extension of Lacker's model. Mariana et al. incorporated an age decaying factor in follicle maturity, and kept follicle growth law as Lacker first proposed. However, they produced only some numerical examples simulating the new advantages of their model. As a result of the present analysis, we propose an alternative understanding of folliclegenesis, pre-ovulatory follicle selection in mammals, and polycystic ovary syndrome (PCOS) in women. In particular, a minimum oestradiol threshold level required for initial follicular growth is obtained. Relative values of follicle size and age necessary for its development are also determined. We prove that the model controls pre-ovulatory follicle selection rate at a local level. The model is shown to be globally unstable and fails to regulate the selection process. Finally, a discussion on how these results bring new insight to possible causes for PCOS is given.