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

这项研究利用最先进的数学模型，旨在了解女性生殖周期的正常和病理。一到六种或更多不同激素分泌模式的变化会改变正常的女性生理。例如，大约6%-9%的成年女性患有多囊卵巢综合征(PCOS)，使其成为所有内分泌疾病中最常见的。多囊卵巢综合征对许多妇女的健康有深远的不利影响，因为它通常导致不孕不育，与不健康的身体成分有关，并增加了2型糖尿病和心血管疾病的关键风险因素。更年期过渡是荷尔蒙分泌变化的另一个例子，其结果可能是轻微、中度或严重的症状，并导致重大的医疗干预。为了在数学环境中研究周期异常，这个项目将开发一个女性生殖寿命的模型。利用来自三个连续年龄组的数据集，将三个子模型集成到一个由具有一些缓慢变化的时变系数的延迟微分方程组表示的终身模型中。由此产生的模型将是第一个内分泌系统模型，它包括三个时间尺度(日、月和年)，可能随之而来的数学困难。对于这样的系统，将开发参数识别和参数灵敏度的技术。将使用动力学系统的工具，如稳定性、分叉和微扰理论来研究模型的行为。数学模拟将用于研究由于多囊卵巢综合征(PCOS)和更年期转变而导致的周期异常。这些研究可能有助于识别衰老过程中微妙的荷尔蒙变化，并预测年轻和老年女性荷尔蒙疗法的最佳类型、剂量和持续时间。反过来，考虑到广泛的共识，即激素治疗应在实现特定治疗目标所需的最短时间内以最低剂量使用，这些研究对妇女健康的影响可能是有益的。了解多囊卵巢综合征的一个关键因素是内分泌(激素)系统和血糖调节系统之间的关系。一个包含多囊卵巢综合征激素失衡的工作模型可能解释过多雄激素、胰岛素抵抗和多囊卵巢综合征之间的联系。因此，除了应用于不孕不育和更年期的治疗外，这项工作还可能增进我们对糖尿病和代谢紊乱的了解，近年来糖尿病和代谢紊乱的发病率急剧上升。

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.