Chávez-Ross, María Alexandra; (1999) Follicle selection dynamics in the mammalian ovary. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The main objective of this thesis is to develop and analyse mathematical models of the regulation of the ovulation cycle in mammals. Specifically, we are interested in understanding the mechanisms that control the number of follicles ovulated in each cycle. In humans, a failure of such control mechanisms can lead to Polycystic Ovary Syndrome (PCOS), which accounts for a substantial fraction of all cases of anovulatory infertility found in women of reproductive age. Although treatment is available, it is highly desirable to improve it. Thus, a better understanding of the selection process of the ovulatory follicle is still required. The thesis begins with a biological description of the terminal phase of the ovarian cycle. This provides the necessary background for the understanding and formulation of the mathematical models presented in later chapters. Next, a review of existing models found in the literature is given and their relevance to the regulation process is analysed. Of these, the one due to Lacker (also referred as the symmetric model) is the best understood in terms of the control of ovulation and PCO. It is given by a system of non-linear differential equations and assumes the same growth rate for each follicle. This assumption is biologically implausible and leads the model to exhibit unrealistic behaviour in some cases. A non symmetric generalisation is therefore developed and Lacker's theoretical analysis of the symmetric model is extended to this case. The non-symmetric model exhibits behavior which more closely reflects that observed in PCO. The thesis then goes on to present a theoretical and numerical analysis of another version of the symmetric model which has been proposed by Mariana et al. This incorporates a variable representing the ageing of the follicle in the same framework as that of Lacker's original model. Finally, all of the above models use a somewhat arbitrary function to describe a follicle's sensitivity to hormonal stimulation. In order to provide a more biologically motivated basis for our analysis we therefore develop a model in terms of the gonadotropic receptors of follicular cells. It is believed that the degree of sensitivity of a follicle to pituitary hormones is one of the factors determining its selection. This model is studied using numerical techniques, since its mathematical structure is too complicated to allow a theoretical analysis. Tentative conclusions underlying the mechanisms that select the ovulatory follicle are given in terms of the different models described in this thesis. Some of these are rather speculative due to the greatly simplified nature of the models in comparison to the real biological system. Nevertheless, since the behaviour of the models is qualitatively consistent with the results obtained from experimental data, they provide useful insights into the mechanisms that control the ovulation number in mammals.

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