Hoermann Rudolf, Pekker Mark J, Midgley John E M, Dietrich Johannes W
Department for Nuclear Medicine, Klinikum Lüdenscheid, 113 Andersons Road, Yandina QLD 4561, Australia.
Mathematical Sciences Department, University of Alabama, Huntsville, AL, USA.
Ther Adv Endocrinol Metab. 2023 Mar 14;14:20420188231158163. doi: 10.1177/20420188231158163. eCollection 2023.
Thyroid hormones are controlled by the hypothalamic-pituitary-thyroid (HPT) axis through a complex network of regulatory loops, involving the hormones TRH, TSH, FT4, and FT3. The relationship between TSH and FT4 is widely used for diagnosing thyroid diseases. However, mechanisms of FT3 homeostasis are not well understood.
We used mathematical modelling to further examine mechanisms that exist in the HPT axis regulation for protecting circulating FT3 levels.
A mathematical model consisting of a system of four coupled first-order parameterized non-linear ordinary differential equations (ODEs) was developed, accounting for the interdependencies between the hormones in the HPT axis regulation. While TRH and TSH feed forward to the pituitary and thyroid, respectively, FT4 and FT3 feed backward to both the pituitary and hypothalamus. Stable equilibrium solutions of the ODE system express homeostasis for a particular variable, such as FT3, if this variable stays in a narrow range while certain other parameter(s) and system variable(s) may vary substantially.
The model predicts that (1) TSH-feedforward protects FT3 levels if the FT4 production rate declines and (2) combined negative feedback by FT4 and FT3 on both TSH and TRH production rates keeps FT3 levels insensitive to moderate changes in FT4 production rates and FT4 levels. The optimum FT4 and FT3 feedback and TRH and TSH-feedforward ranges that preserve FT3 homeostasis were found by numerical continuation analysis. Model predictions were in close agreement with clinical studies and individual patient examples of hypothyroidism and hyperthyroidism.
These findings further extend the concept of HPT axis regulation beyond TSH and FT4 to integrate the more active sister hormone FT3 and mechanisms of FT3 homeostasis. Disruption of homeostatic mechanisms leads to disease. This provides a perspective for novel testable concepts in clinical studies to therapeutically target the disruptive mechanisms.
甲状腺激素由下丘脑 - 垂体 - 甲状腺(HPT)轴通过复杂的调节环路网络进行控制,涉及促甲状腺激素释放激素(TRH)、促甲状腺激素(TSH)、游离甲状腺素(FT4)和游离三碘甲状腺原氨酸(FT3)等激素。TSH与FT4之间的关系被广泛用于诊断甲状腺疾病。然而,FT3体内稳态的机制尚未完全明确。
我们运用数学建模进一步研究HPT轴调节中存在的保护循环FT3水平的机制。
构建了一个由四个耦合的一阶参数化非线性常微分方程(ODE)组成的数学模型,该模型考虑了HPT轴调节中激素之间的相互依存关系。TRH和TSH分别正向作用于垂体和甲状腺,而FT4和FT3则反向作用于垂体和下丘脑。如果某个特定变量(如FT3)在其他某些参数和系统变量可能大幅变化的情况下仍保持在狭窄范围内,那么ODE系统的稳定平衡解就表示该变量处于稳态。
该模型预测:(1)如果FT4生成率下降,TSH正向作用可保护FT3水平;(2)FT4和FT3对TSH和TRH生成率的联合负反馈使FT3水平对FT4生成率和FT4水平的适度变化不敏感。通过数值延拓分析找到了维持FT3稳态的最佳FT4和FT3反馈以及TRH和TSH正向作用范围。模型预测与甲状腺功能减退和甲状腺功能亢进的临床研究及个体患者实例密切相符。
这些发现进一步扩展了HPT轴调节的概念,从TSH和FT4扩展到整合更具活性的姊妹激素FT3以及FT3体内稳态机制。体内稳态机制的破坏会导致疾病。这为临床研究中针对破坏机制进行治疗的新的可测试概念提供了一个视角。