Bifurcation analysis of a menstrual cycle model reveals multiple mechanisms linking testosterone and classical PCOS.

A system of 16 differential equations is described which models hormonal regulation of the menstrual cycle focusing on the effects of the androgen testosterone (T) on follicular development and on the synthesis of luteinizing hormone (LH) in the pituitary. Model simulations indicate two stable menstrual cycles - one cycle fitting data in the literature for normal women and the other cycle being anovulatory because of no LH surge. Bifurcations with respect to sensitive model parameters illustrate various characteristics of polycystic ovarian syndrome (PCOS), a leading cause of female infertility. For example, varying one parameter retards the growth of preantral follicles and produces a "stockpiling" of these small follicles as observed in the literature for some PCOS women. Modifying another parameter increases the stimulatory effect of T on LH synthesis resulting in reduced follicular development and anovulation. In addition, the model illustrates how anovulatory and hyperandrogenic cycles which are characteristic of PCOS can be reproduced by perturbing both pituitary sensitivity to T and the follicular production of T. Thus, this model suggests that for some women androgenic activity at the levels of both the pituitary and the ovaries may contribute to the etiology of PCOS.

Modeling endocrine control of the pituitary-ovarian axis: androgenic influence and chaotic dynamics.

Mathematical models of the hypothalamus-pituitary-ovarian axis in women were first developed by Schlosser and Selgrade in 1999, with subsequent models of Harris-Clark et al. (Bull. Math. Biol. 65(1):157-173, 2003) and Pasteur and Selgrade (Understanding the dynamics of biological systems: lessons learned from integrative systems biology, Springer, London, pp. 38-58, 2011). These models produce periodic in-silico representation of luteinizing hormone (LH), follicle stimulating hormone (FSH), estradiol (E2), progesterone (P4), inhibin A (InhA), and inhibin B (InhB). Polycystic ovarian syndrome (PCOS), a leading cause of cycle irregularities, is seen as primarily a hyper-androgenic disorder. Therefore, including androgens into the model is necessary to produce simulations relevant to women with PCOS. Because testosterone (T) is the dominant female androgen, we focus our efforts on modeling pituitary feedback and inter-ovarian follicular growth properties as functions of circulating total T levels. Optimized parameters simultaneously simulate LH, FSH, E2, P4, InhA, and InhB levels of Welt et al. (J. Clin. Endocrinol. Metab. 84(1):105-111, 1999) and total T levels of Sinha-Hikim et al. (J. Clin. Endocrinol. Metab. 83(4):1312-1318, 1998). The resulting model is a system of 16 ordinary differential equations, with at least one stable periodic solution. Maciel et al. (J. Clin. Endocrinol. Metab. 89(11):5321-5327, 2004) hypothesized that retarded early follicle growth resulting in "stockpiling" of preantral follicles contributes to PCOS etiology. We present our investigations of this hypothesis and show that varying a follicular growth parameter produces preantral stockpiling and a period-doubling cascade resulting in apparent chaotic menstrual cycle behavior. The new model may allow investigators to study possible interventions returning acyclic patients to regular cycles and guide developments of individualized treatments for PCOS patients.