Reinecke Isabel, Deuflhard Peter
Zuse Institute Berlin, Department of Numerical Analysis and Modelling, Research Group Computational Drug Design, Takustrasse 7, 14195 Berlin, Germany.
J Theor Biol. 2007 Jul 21;247(2):303-30. doi: 10.1016/j.jtbi.2007.03.011. Epub 2007 Mar 14.
Despite the fact that more than 100 million women worldwide use birth control pills and that half of the world's population is concerned, the menstrual cycle has so far received comparatively little attention in the field of mathematical modeling. The term menstrual cycle comprises the processes of the control system in the female body that, under healthy circumstances, lead to ovulation at regular intervals, thus making reproduction possible. If this is not the case or ovulation is not desired, the question arises how this control system can be influenced, for example, by hormonal treatments. In order to be able to cover a vast range of external manipulations, the mathematical model must comprise the main components where the processes belonging to the menstrual cycle occur, as well as their interrelations. A system of differential equations serves as the mathematical model, describing the dynamics of hormones, enzymes, receptors, and follicular phases. Since the processes take place in different parts of the body and influence each other with a certain delay, passing over to delay differential equations is deemed a reasonable step. The pulsatile release of the gonadotropin-releasing hormone (GnRH) is controlled by a complex neural network. We choose to model the pulse time points of this GnRH pulse generator by a stochastic process. Focus in this paper is on the model development. This rather elaborate mathematical model is the basis for a detailed analysis and could be helpful for possible drug design.
尽管全球有超过1亿女性使用避孕药，且全球一半人口都对此有所关注，但月经周期在数学建模领域迄今受到的关注相对较少。月经周期这一术语涵盖了女性体内控制系统的过程，在健康情况下，该系统会导致定期排卵，从而使生殖成为可能。如果情况并非如此或不希望排卵，就会出现如何影响这个控制系统的问题，例如通过激素治疗。为了能够涵盖广泛的外部操纵，数学模型必须包括月经周期相关过程发生的主要组成部分及其相互关系。一个微分方程系统作为数学模型，描述激素、酶、受体和卵泡期的动态变化。由于这些过程发生在身体的不同部位且相互影响存在一定延迟，采用延迟微分方程被认为是合理的步骤。促性腺激素释放激素（GnRH）的脉冲式释放由一个复杂的神经网络控制。我们选择通过一个随机过程对这个GnRH脉冲发生器的脉冲时间点进行建模。本文重点在于模型开发。这个相当精细的数学模型是详细分析的基础，可能有助于药物设计。
