Lacker's model: control of follicular growth and ovulation in domestic species

Lacker (1981) and Lacker & Akin (1988) developed a mathematical model of follicular maturation and ovulation; this model of only four parameters accounts for a large number of results obtained over the past decade or more on the control of follicular growth and ovulation in mammals. It establishes a single law of maturation for each follicle which describes the interactions between growing follicles. The function put forward is sufficient to explain the constancy of the number of ovulations or large follicles in a female as well as the variability of this number among strains or species and for either induced or spontaneous ovulators. According to the model, the number of ovulations or large follicles lies between two limits that are themselves simple functions of two parameters of the model. Moreover, Lacker's model exhibits interesting characteristics in agreement with results obtained by physiologists: in particular, it predicts that the number of ovulating or large follicles is independent of:

1. the total number of maturing follicles,
2. the process of recruitment of newly maturing follicles towards the terminal maturation (Poisson or other),
3. the form of the LH or FSH secretion curves as functions of the systemic level of oestradiol. The model further predicts that
4. selection and dominance of follicles result from the feedback between the ovary and the hypophysis through the interactions between follicles; these interactions are expressed by the maturation function of the model.
5. recovery from atresia is possible for a follicle: from decreasing, the rate of secretion of oestradiol may increase.
6. the revised model suggests a renewal of follicles during the sexual cycle, as “waves of follicular growth”.

Lacker's model is a model of strict dominance; it maintains a hierarchy of the follicles as soon as they start their final maturation to the ovulations as that is observed in bird or reptile ovary. Such a strict hierarchy is possible but it is probably not a general situation in all mammals. We therefore modified the maturing function of the follicle in order to make it compatible with the observations of physiologists: follicles always interact as in the initial model but they individually become old, the hierarchy of follicles can be modified with time and the largest follicles do not indefinitely grow as in the initial model.