Department of Mathematics and Biomathematics Program, North Carolina State University, Raleigh, NC 27695-8205, USA.
Math Biosci. 2010 Jun;225(2):108-14. doi: 10.1016/j.mbs.2010.02.004. Epub 2010 Feb 26.
A model for hormonal control of the menstrual cycle with 13 ordinary differential equations and 41 parameters is presented. Important changes in model behavior result from variations in two of the most sensitive parameters. One parameter represents the level of estradiol sufficient for significant synthesis of luteinizing hormone, which causes ovulation. By studying bifurcation diagrams in this parameter, an interval of parameter values is observed for which a unique stable periodic solution exists and it represent an ovulatory cycle. The other parameter measures mass transfer between the first two stages of ovarian development and is indicative of healthy follicular growth. Changes in this parameter affect the uniqueness interval defined with respect to the first parameter. Hopf, saddle-node and transcritical bifurcations are examined. To attain a normal ovulatory menstrual cycle in this model, a balance must be maintained between healthy development of the follicles and flexibility in estradiol levels needed to produce the surge in luteinizing hormone.
提出了一个具有 13 个常微分方程和 41 个参数的激素控制月经周期模型。模型行为的重要变化源于两个最敏感参数中的两个参数的变化。一个参数表示足以显著合成促黄体生成素（LH）的雌二醇水平，而 LH 又会导致排卵。通过研究该参数的分岔图，可以观察到一个参数值区间，在此区间内存在唯一稳定的周期解，代表排卵周期。另一个参数衡量卵巢发育前两个阶段之间的质量转移，表明卵泡生长健康。该参数的变化会影响相对于第一个参数定义的唯一性区间。检查了 Hopf、鞍结和叉形分岔。在这个模型中，要实现正常的排卵月经周期，就必须在卵泡的健康发育和产生黄体生成素激增所需的雌二醇水平的灵活性之间保持平衡。
