Abstract
Thyroid disorders are common and often require lifelong hormone replacement. Treating thyroid disorders involves a fascinating and troublesome delay, in which it takes many weeks for serum thyroid-stimulating hormone (TSH) concentration to normalize after thyroid hormones return to normal. This delay challenges attempts to stabilize thyroid hormones in millions of patients. Despite its importance, the physiological mechanism for the delay is unclear. Here, we present data on hormone delays from Israeli medical records spanning 46 million life-years and develop a mathematical model for dynamic compensation in the thyroid axis, which explains the delays. The delays are due to a feedback mechanism in which peripheral thyroid hormones and TSH control the growth of the thyroid and pituitary glands; enlarged or atrophied glands take many weeks to recover upon treatment due to the slow turnover of the tissues. The model explains why thyroid disorders such as Hashimoto’s thyroiditis and Graves’ disease have both subclinical and clinical states and explains the complex inverse relation between TSH and thyroid hormones. The present model may guide approaches to dynamically adjust the treatment of thyroid disorders.
Synopsis
A new mathematical model for the thyroid axis shows that slow changes in thyrotroph mass are responsible for hormone delays in the treatment of thyroid disorders.
- The thyroid axis displays delays in which TSH levels are abnormal long after thyroid hormone T4 normalizes.
- Mathematical modeling of gland mass dynamics shows that changes in thyrotroph mass explain this delay.
- Gland mass changes also explain the transition from subclinical to clinical thyroid disorders and the complex inverse relation between TSH and thyroid hormones.
Discussion
This study provides evidence from large-scale medical records for thyroid hysteresis and for a three-regime relationship between TSH and T4, and an explanation of these effects by a model of gland-mass changes in the thyroid axis. The model framework clarifies the dynamics of thyroid disorders on the timescale of months. It explains the phenomena of delays and hysteresis based on changes in pituitary thyrotroph mass during chronic conditions, because such mass changes take many weeks to recover upon treatment. The model also explains the three-regime relation between TSH and T4 in terms of failed dynamic compensation when gland-masses approach their carrying capacity, leading to hyperthyroidism or hypothyroidism.
The gland-mass model also explains the existence of subclinical thyroid disorders, in which TSH is abnormal but T3 and T4 levels are normal, and how these subclinical disorders transition into clinical ones. Subclinical disorders exist because the glands change their mass to fully compensate for disrupted thyroid function. This is an example of the general principle of dynamic compensation (Karin et al, 2016). In Hashimoto’s thyroiditis, the transition from subclinical to clinical disease occurs when the autoimmune killing rate is so high that thyrotroph mass approaches its carrying capacity, and can no longer compensate by increased TSH secretion for the loss of thyroid function. Such a carrying capacity might be due to the confined anatomical position of the pituitary, together with the need for other pituitary cell types. Some experimental reports show a fivefold increase in pituitary volume in hypothyroidism (Khawaja, 2006), while others show a milder increase. The thyrotroph carrying capacity requires further study; it may not result in observable volume growth if carrying capacity is imposed by other cell types. Alternatively, a low level of thyroid hormones may be required for thyrotroph proliferation, in addition to their effect on other pituitary cell types (Friedrichsen et al, 2004).
An additional explanation of subclinical disorders was provided by Dietrich and colleagues, in a model without dynamic compensation (Dietrich et al, 2012). Subclinical hypothyroidism resulted from the nonlinear shape of the involved nullclines. However, in the Dietrich model the range of subclinical hypothyroidism was rather small. In a model with dynamic compensation, this effect occurs over a much larger range of parameters, potentially reflecting the high prevalence of subclinical hypothyroidism. Both mechanisms can coexist.
In the case of Graves’ disease, the model predicts that the pituitary thyrotroph mass shrinks in order to make less TSH and compensate for the autoantibody activation of TSH receptors. Such a degeneration of thyrotroph mass is seen in pituitary histological samples (Scheithauer et al, 1992). This dynamic compensation fails when the antibody effect rises across a threshold at which thyrotroph mass drops near zero, resulting in clinical hyperthyroidism. We predict such a transition also in the case of toxic thyroid nodules. An alternative or complementary explanation for the delay in Graves’ disease is the stimulation of an ultra-short negative feedback loop in which TSH receptor autoantibodies stimulate TSH receptors in the pituitary to inhibit TSH secretion (Prummel et al, 2004).
The present model for thyroid disorders provides a basis for the observed three-regime “log-linear” TSH–T4 relation. The two extreme regimes correspond to clinical hypothyroidism (Hashimoto’s thyroiditis and iodine deficiency) and clinical hypothyroidism (Graves’ disease and toxic nodules). The middle regime corresponds to compensated thyroid hormones, composed of a distribution of thyroid set points within a healthy population. The mean slope of the middle region can be explained in the model by two types of effects (i) fast timescale effects such as individual differences in the production and removal rates of hormones, and (ii) slow timescale effects such as differences in the growth and removal rates of the endocrine cells, as may occur during aging. Both sources of variation provide similar predictions for the mid-regime slope and may both occur physiologically.
The model also explains compensation and its breakdown in the case of goiter due to iodine deficiency. Fast timescale compensation occurs by increased avidity to iodine and other physiological processes. On the slow timescale, once these fast compensation processes have saturated, the model indicates that the thyroid and thyrotroph functional masses both grow, as clinically observed (Marine & Kimball, 1917; Mariotti & Beck-Peccoz, 2000). Thyroid hormones remain normal until both thyroid and thyrotroph masses approach their carrying capacities. When these carrying capacities are reached, thyroid hormone levels drop to clinical hypothyroidism. This transition to clinical condition occurs when the parameter
in the model, the maximal thyroid hormone secretion rate per thyrocyte, drops below a critical value.
It would be important to measure thyrotroph and thyrocyte masses as well as TSH levels as a function of time after thyroid perturbations in humans and rodents (Pohlenz et al, 1999; Nolan et al, 2004; Turgeon et al, 2017) in order to test the model predictions, such as delays in thyrotroph mass increase after an initial TSH rise. For example, Turgeon et al show a reduction in T4 and an elevation of TSH in mice under low iodine diet. It would be interesting to measure the delay in TSH normalization after returning to normal iodine diet and test whether high TSH levels correlate with increased thyrotroph mass.
The dynamic compensation mechanism by changes in mass in equations (4) and (5) is an example of a more general feedback-control strategy known in engineering as integral feedback, as in the pioneering work of El-Samad and Khammash (El-Samad et al, 2002; Alon, 2019). When the glands are far from their carrying capacity, equations (4) and (5) guarantee that steady state can only be achieved at certain values of TH and TSH, namely and
. These set points are independent of all of the fast timescale parameters in equations (1–3). Therefore, changes in hormone production and degradation parameters, such as changes in iodine supply, are expected to be compensated. On the long timescale of weeks-months, TH and TSH are guaranteed to reach a set point that is defined only by the proliferation and death rate of the thyrocytes and thyrotrophs, respectively.
This compensation explains, at least in part, how an individual’s set point of TSH and TH is kept within a relatively limited range (Andersen et al, 2002; Wartofsky & Dickey, 2005), even in face of sizable changes in the parameters. For example, iodine nutritional intake can drop or exceed the recommended level by an order of magnitude before there is a clinical effect (Trumbo et al, 2001; National Research Council et al, 2005). The model also predicts full compensation, after a transient of a few months, for moderate changes in hypothalamic input such as temperature and nutritional states. Compensation should also occur to changes in blood volume, which can be described as changes in the hormone secretion parameters (Karin et al, 2016). The model can explore changes during gestation. Interestingly, the finding of coordinated P and T volumes changes (Otani et al, 2021) sets constraints on which parameter group might change during gestation (Appendix Supplementary Text).
The present study focused on the dynamics of free T4; future work can address the dynamics of free T3 (FT3) concentration. Dietrich and colleagues observed increased FT3 concentration and increased calculated deiodinase capacity (SPINA-GD) in beginning hypothyroidism, but this was dependent on the amount of thyroid tissue (Hoermann et al, 2014, 2015a, 2016; Midgley et al, 2015). Therefore, it may be mediated by dynamic compensation.
The complex dynamics and hysteresis of thyroid hormones challenge the treatment of thyroid disorders, especially in a fraction of the population where the dynamics seem not to easily converge (Dietrich, 2015). The present model might, therefore, guide future studies on improved treatment. One way that the model might help is to provide estimates of the effective thyrotroph mass of a patient, the “hidden variable” at the root of hysteresis. This is perhaps analogous to the benefits in the field of diabetes gained by estimates of insulin resistance and beta-cell function from insulin and glucose test results using models such as HOMA (Matthews et al, 1985). Such a formula for thyroid total function was developed by Dietrich et al (Dietrich et al, 2016). The present study suggests a formula for relative pituitary thyrotroph mass based on TRH tests. One can, therefore, envisage using the present model, perhaps together with additional measurements, to design optimal treatment over time for returning a given patient to the euthyroid condition. For example, estimating thyrotroph mass accumulation rate during treatment in Graves’ disease can help to predict the time to recovery and thus help to choose between a conservative to an ablative approach for treatment.
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