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

该研究项目利用最先进的数学模型，旨在了解女性生殖周期的规范和病理。一至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，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产生了深远的不利影响，因为它通常会导致不孕，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。更年期过渡是激素分泌变化的另一个例子，其导致的症状可能是轻度，中度或重度，并导致显著的医疗干预。为了在数学环境中研究周期异常，该项目将开发一个妇女生殖寿命的模型。使用来自三个连续年龄组的数据集，三个子模型将被整合成一个终生模型，该模型由具有一些缓慢变化的随时间变化的系数的延迟微分方程系统表示。由此产生的模型将是第一个内分泌系统模型，其中包括三个时间尺度（天，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。动力系统的工具，如稳定性，分叉和扰动理论将被用来研究模型的行为。数学模拟将被用来调查周期异常由于多囊卵巢综合征（PCOS）和更年期过渡。这些研究可能有助于确定衰老过程中微妙的激素变化，并预测年轻和老年女性激素治疗的最佳类型，剂量和持续时间。反过来，鉴于广泛的共识，即激素治疗应在最低剂量下使用，以最短的间隔达到特定的治疗目的，这些研究对妇女健康的影响可能是有益的。内分泌（激素）系统和血糖（血糖）系统的关系是理解PCOS的关键因素，结合PCOS的激素失衡的工作模型可以阐明雄激素过多、胰岛素抵抗和PCOS之间的联系。因此，除了应用于治疗不孕症和更年期，这项工作也可能促进我们对糖尿病和代谢紊乱的理解，近年来其发病率急剧增加。

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.