Modiz Corinna, Körner Andreas
Institute of Analysis and Scientific Computing, TU Wien, Wiedner Hauptstraße 8, 1040, Vienna, Austria.
J Math Biol. 2024 Dec 18;90(1):9. doi: 10.1007/s00285-024-02176-8.
The HPT complex, consisting of the hypothalamus, pituitary and thyroid, functions as a regulated system controlled by the respective hormones. This system maintains an intrinsic equilibrium, called the set point, which is unique to each individual. In order to optimize the treatment of thyroid patients and understand the dynamics of the system, a validated theoretical representation of this set point is required. Therefore, the research field of mathematical modeling of the HPT complex is significant as it provides insights into the interactions between hormones and the determination of this endogenous equilibrium. In literature, two mathematical approaches are presented for the theoretical determination of the set point in addition to a time-dependent model. The two approaches are based on the maximum curvature of the pituitary response function and the optimal gain factor in the representation of the HPT complex as a closed feedback system. This paper demonstrates that all hormone curves described by the model converge to the derived set point with increasing time. This result establishes a clear correlation between the physiological equilibrium described by the set point and the mathematical equilibrium with respect to autonomous systems of differential equations. It thus substantiates the validity of the theoretical set point approaches.
由下丘脑、垂体和甲状腺组成的下丘脑-垂体-甲状腺（HPT）复合体，作为一个由各自激素控制的调节系统发挥作用。该系统维持着一种内在平衡，称为设定点，每个个体的设定点都是独特的。为了优化甲状腺疾病患者的治疗并了解该系统的动态变化，需要一个经过验证的关于这个设定点的理论模型。因此，HPT复合体的数学建模研究领域具有重要意义，因为它能深入了解激素之间的相互作用以及这种内源性平衡的确定。在文献中，除了一个时间依赖模型外，还提出了两种用于理论确定设定点的数学方法。这两种方法分别基于垂体反应函数的最大曲率以及将HPT复合体表示为一个封闭反馈系统时的最优增益因子。本文证明，随着时间的增加，模型描述的所有激素曲线都收敛到推导得出的设定点。这一结果在设定点所描述的生理平衡与关于微分方程自治系统的数学平衡之间建立了明确的关联。因此，这证实了理论设定点方法的有效性。
