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Journal of Theoretical Medicine
Volume 3, Issue 4, Pages 247-270

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

1Centre for Nonlinear Dynamics and its Applications, University College London, Gower Street, London, WC1E 6BT, UK
2Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, V6T 1Z2, Canada

Received 3 May 2000; Accepted 15 January 2001

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.