**The Relationship between Population T4/TSH Set Point Data and T4/TSH Physiology**

Stephen Paul Fitzgerald en Nigel Geoffrey Bean

*Abstract*

**Context.**

Population studies of the distribution of T4/TSH set points suggest a more complex inverse relationship between T4 and TSH than that suggested by physiological studies.

The reasons for the similarities and differences between the curves describing these relationships are unresolved.

**Methods.**

We subjected the curve, derived from empiric data, describing the TSH suppression response to T4, and the more mathematically derived curve describing the T4 response to TSH, to the different possible models of population variation.

The implied consequences of these in terms of generating a population distribution of T4/TSH equilibrium points (a “population curve”) were generated and compared to the empiric population curve.

The physiological responses to primary hypothyroidism and hyperthyroidism were incorporated into the analysis.

**Conclusions.**

Though the population curve shows a similarly inverse relationship, it is describing a different relationship than the curve describing the suppression of TSH by T4.

The population curve is consistent with the physiological studies of the TSH response to T4 and implies a greater interindividual variation in the positive thyroid T4 response to TSH than in the central inhibitory TSH response to T4.

The population curve in the dysthyroid states is consistent with known physiological responses to these states.

Figure 1:

Comparison of 2 representations of the population distribution of T4/TSH (the population curve) with the T4/TSH physiological relationship as described in individuals (the TSH curve).

http://www.hindawi.com/journals/jtr/2016/6351473/fig1/

Figure 2:

(a) The TSH curve, (b, c) the T4 curve (on different axes, approx. 41), and (d) the location of the T4/TSH set point.

http://www.hindawi.com/journals/jtr/2016/6351473/fig2/

Figure 3:

The generation of the T4/TSH set points in a population. The circles represent the different potential set points of different individuals (generated as per Figure 2) that are lying on the intersection points of their individual T4 and TSH curves.

http://www.hindawi.com/journals/jtr/2016/6351473/fig3/

Figure 4:

(a) shows a population in which interindividual T4 curve variation is greater than interindividual TSH curve variation (the extreme example of only one TSH curve intersecting with multiple T4 curves is shown), (b) shows the converse, one T4 curve intersecting with multiple TSH curves, and (c) shows a population in which T4 and TSH curve variation are similar (there are multiple T4 and multiple TSH curves and more intersection points).

In these graphs the intersection points are marked by circles of different sizes to indicate a typical distribution of the curves and the larger circles indicate that more individuals are expected to lie in the centre of the range as compared to the extremities. The lines of best fit (thick red lines) are drawn such that the differences in the possible slopes of the lines of best fit (the different population curves) are apparent.

http://www.hindawi.com/journals/jtr/2016/6351473/fig4/

Figure 5:

The generation of a population T4/TSH relationship by nonrandom associations between the physiological curves.

In this example there is a hypothetical association between insensitive thyroids and sensitive pituitaries (this might occur by evolution to minimise T4 variation).

The sizes of the circles, as in Figure 4, are proportionate to the number of individuals in the population with T4/TSH levels at that point. The line of best fit has a small negative slope.

http://www.hindawi.com/journals/jtr/2016/6351473/fig5/

Figure 6:

The effect of vertical shifts in the TSH curves, induced by primary thyroid dysfunction, on the points of intersection of the physiological curves.

On account of these changes the T4 curves in the hypothyroid and hyperthyroid ranges do not intersect with the extensions of the TSH curves of the normal range (these extensions are shown as dashed lines) and therefore the slope of the population curve increases.

The extensions of the TSH curves into the normal range from the regions of thyroid dysfunction are also shown as dashed lines to indicate that they do not normally exist in this range. The red line is the population curve as per Hadlow et al. [4].

http://www.hindawi.com/journals/jtr/2016/6351473/fig6/

**5. Conclusion**

In summary, this work offers a resynthesis of the empiric data concerning the T4/TSH relationship, demonstrating that the previously derived individual physiological data and population set point data refer to different relationships, which are compatible with each other, and that therefore the former needs no revision on account of the latter.

The similarities and differences previously noted are readily explained by population variations in physiology and by the known physiological responses to primary thyroid dysfunction.

In turn the population data imply a particular pattern of interindividual variation of thyroid and pituitary physiology.

This clarification and simplification of the T4/TSH relationship, apart from having intrinsic value, may contribute to the further understanding of thyroid physiology and in particular the understanding of thyroid regulation.