A Whole-Life Model for Hormonal Regulation of the Reproductive Cycle of Women with Applications to Age-Induced and Pathological Changes in the Cycle

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Using state-of-the-art mathematical modeling, this research project aims to understand the norm and pathology of the female reproductive cycle.Changes in patterns of the secretion of one to six or more different hormones alter the normal female physiology. For example, some 6-9% of adult women have the disorder known as polycystic ovarian syndrome PCOS) making it the most common of all endocrinopathies. PCOS has a profound adverse impact on the health of many women since it commonly causes infertility, is associated with unhealthy body composition, and increases key risk factors for Type 2 diabetes and cardiovascular disease. The menopause transition is another example of changes in hormones secretion with resulting symptoms that might be mild, moderate or severe and lead to significant medical intervention. To study cycle abnormalities in a mathematical setting, this project will develop a model for a woman's reproductive life span. Using data sets from three consecutive age groups, three submodels will be integrated into one whole-life model represented by a system of delay differential equations with some slowly varying time-dependent coefficients. The resulting model will be the first endocrine system model which encompasses three time scales (days, months and years), with possible ensuing mathematical difficulties. For such systems, techniques for parameter identification and parameter sensitivity will be developed. The tools of dynamical systems such as stability, bifurcation and perturbation theories will be used to study model behavior.Mathematical simulations will be used to investigate cycle abnormalities due to polycystic ovarian syndrome (PCOS) and to the menopause transition. These studies may help to identify subtle hormonal changes in the aging process and to predict optimal types, doses and durations of hormonal therapies for young and aging women. In turn, given the broad consensus that hormone therapies be used at lowest doses for the shortest intervals necessary to achieve specifc therapeutic aims, the impact of these studies on women's health could be beneficial. A key ingredient for understanding PCOS is the relationship between the endocrine (hormone) system and the glucoregulatory (blood sugar) system.A working model incorporating the hormonal imbalances of PCOS may illuminate the connections between excess androgens, insulin resistance and PCOS. Thus, in addition to applications to the treatment of infertility and menopause, this work may also advance our understanding of diabetes and metabolic disorders, the incidence of which has increased dramatically in recent years.