Hoerman et al (Ref.1) have developed a mathematical model with 14 different parameters that influence the HPT axis (hypothalamus – pituitary – thyroid axis). I will describe the effects in the following.

There are different parameters which can change the hormones in this mathematical model.

S1 is an input signal with an effect on TRH. As seen in the description above, changes in S1 affect the other hormones as well. The article describes how this knowledge can be used in combination with different parameters.

The first part of the above presentation describes the three different equilibrium solutions for s1=1, 0.1 and 10 and the second part describes the time-dependent solution.

You need not be good at mathematics to see the connection between the used equations and the conceptual drawing of the HPT axis (Ref.1). What is important is the complexity – and flexibility compared to a fixed TSH value as the understanding of the HPT axis.

The first part of the second presentation describes the three different equilibrium solutions for k134 =1, 0.1 and 10 and the second part describes the time-dependent solution.

This is theoretical and only serves as an example of how the hormones are changed by the parameter. K134 is the negative feedback of FT4 and FT3 onto TRH (upstream, repressing).

Finally the a1 parameter ( a1 is the TRH elimination rate constant):

Look at equation 1.1:

We have looked at the effects of s1, k134 and a1 on TRH and the other hormones.

One thing to observe is the FT3 and FT4 curves. In the plot left is shown what the authors call “The perfect homeostasis”. Here the two curves follow each other with a certain distance. In the plots above this pattern is disrupted. We will get back to these observations later.

Hoermann R, Pekker MJ, Midgley JEM, Larisch R and Dietrich JW (2022) Principles of Endocrine Regulation: Reconciling Tensions Between Robustness in Performance and Adaptation to Change. Front. Endocrinol. 13:825107. doi: 10.3389/fendo.2022.825107 https://www.frontiersin.org/articles/10.3389/fendo.2022.825107/full