Regulation of ovulation number in mammals. A follicle interaction law that controls maturation

Abstract

The assumption that developing follicles communicate through circulating hormones has been used to obtain a class of interaction laws that describe follicle growth. A specific member of this class has been shown to control ovulation number. Although all interacting follicles obey the same growth law and are given initial maturities that are chosen at random from a uniform distribution, ovulatory and atretic follicles emerge. Changing the parameters in the growth law can alter the most probable ovulation number values, anovulatory states are also admitted as possible solutions of the growth law. The behavior of the model is examined for interacting follicle populations of different size. Methods are suggested for identifying growth laws in particular mammals. These can be used to test the model from experimental data.

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

“…Contrary to the extensive analysis of Lacker's model available in the literature (Lacker, 1981;Akin and Lacker, 1984;Lacker et al, 1987;Lacker and Akin, 1988;Lacker and Percus, 1991;Chivez-Ross et al, 1997), there is no theoretical analysis for this model. Mariana et al only presented some numerical examples in order to show that their model is able to reflect the basic features of control of ovulation and its new advantages.…”

“…In the early eighties, Lacker was the first to publish a mathematical model reflecting the dynamics of many growing follicles during the follicular phase of the menstrual cycle (Lacker, 1981). Many assumptions are made about the complex pituitary-ovary system and follicular development in order to obtain a suitable and manageable system of ordinary differential equations.…”

Modelling Perspectives on Aging: Can Mathematics Help us Stay Young?

“…Some modelling of follicular dynamics dates back to Lacker (1981Lacker ( , 1988, who modelled interactions of growing follicles, estrogen, LH, and FSH. For analytical tractability, Lacker assumed that follicles have identical responses and follow identical growth laws.…”

A model for the production of ovarian hormones during the menstrual cycle

“…We refer to this time period as the growth follicle stage (see Figure 1). We do not try to model the follicle selection process, but models have been developed, e.g., see Lacker and Peskin [1981], Lacker et al [1987], and ChavezRoss et al [1997]. During the growth follicle stage, F SH reaches a maximum and secondary follicles begin to atrophy.…”