Thyroid UK

A Novel Minimal Mathematical Model of the Hypothalamus-Pituitary-Thyroid Axis Validated for Individualized Clinical Applications

A Novel Minimal Mathematical Model of the Hypothalamus-Pituitary-Thyroid Axis Validated for Individualized Clinical Applications

On the one hand, we keep getting told that medics know exactly how to get our doses right. Simple, isn't it? And "they" know all about how it works. (Sorry - can't be bothered to carry on with the usual stuff we all know.)

On the other hand we read an abstract which is able to say:

"... each H [hypothalamus] P [pituitary] characteristic curve being uniquely defined for each individual akin to a fingerprint..."

In case you do not know who "Dietrich JW" is, have a look here:


Math Biosci. 2014 Jan 27. pii: S0025-5564(14)00006-6. doi: 10.1016/j.mbs.2014.01.001. [Epub ahead of print]

A Novel Minimal Mathematical Model of the Hypothalamus-Pituitary-Thyroid Axis Validated for Individualized Clinical Applications.

Goede SL1, Leow MK2, Smit JW3, Dietrich JW4.

Author information

1Electronic Engineering, Private Research and Consultancy Oterlekerweg 4, 1841 GP Stompetoren, The Netherlands. Electronic address:

2Singapore Institute for Clinical Sciences, Brenner Centre for Molecular Medicine, A∗STAR; Tan Tock Seng Hospital; National University of Singapore; Duke-NUS Graduate Medical School Singapore. Electronic address:

3Department of General Internal Medicine of Radboud University Nijmegen Medical Centre, Postbus 9101, 6500 HB Nijmegen, The Netherlands. Electronic address:

4Laboratory XU44; Medical Hospital I Bergmannsheil University Hospitals Ruhr University of Bochum D-44789 Bochum, NRW, Germany. Electronic address:


The hypothalamus-pituitary-thyroid (HPT) axis represents a complex, non-linear thyroid hormone system in vertebrates governed by numerous variables. The common modeling approach until now aims at a comprehensive inclusion of all known physiological influences. In contrast, we develop a parsimonious mathematical model that integrates the hypothalamus-pituitary (HP) complex as an endocrinologic unit based on a parameterized negative exponential function between free thyroxine (FT4) as stimulus and thyrotropin (thyroid stimulating hormone, TSH) as response. Model validation with clinical data obtained from geographically different hospitals revealed a goodness-of-fit largely ranging between 90% <R2 < 99%, each HP characteristic curve being uniquely defined for each individual akin to a fingerprint. Specifically, the HP model represents the afferent feedback limb of the HPT axis while the efferent limb is mathematically depicted by TSH input to the thyroid gland which responds by secreting T4 as its chief output. The complete HPT axis thus forms a closed loop system with negative feedback resulting in an equilibrium state or homeostasis under defined conditions illustrated by the intersection of the HP and thyroid response characteristics. In this treatise, we demonstrate how this mathematical approach facilitates homeostatic set points computation for personalized dosing of thyroid medications of patients to individualized euthyroid states.

Copyright © 2014. Published by Elsevier Inc.


Clinical validation, Individualized therapeutic target, Logarithmic-linear relationship, Negative exponential, Parameterization

PMID: 24480737 [PubMed - as supplied by publisher]


8 Replies

This group of people are without doubt the premier theoretical cybernetic researchers around. Johannes Dietrich will be one of the coauthors in our upcoming clinical trial publication. He is in full intellectual flow at the moment and I personally am breathless at his rate of uncovering new concepts by computer modelling. It's too bad that there is a gaping intellectual void between such people, cell biologists as opposed to the diagnostic thyroid socalled gurus at the "sharp end" of the scale from theory to practice and who are frankly 10-20 years behind the times.


It is patently obvious that the traditional ways of guesstimating doses for treatment are very crude.

Often the one that gets me is the treatment of those who have been hyper and, whether by surgery or pharmacy, get pitched headlong into severe hypothyroidism.

At present we don't even have a half-way sensible approach to starting people on, say, levothyroxine when they are hypothyroid (i.e. not attempting full replacement as might be done after total thyroidectomy). The actual doses we see reported here vary from 25 to 125, but with little rationale, and almost no science.

I strongly believe that computer modelling is the only way to go - both in developing models to identify and explain what happens, and, in time, to manage treatment.

All too often the medics' approaches are more akin to paracetamol - one for a mild headache, two if it is worse.



What happened to Treating Symptoms? Being prescribed the amount of thyroid hormone based on a mathematical formula may not be any better than the average NHS GP doing a 'thumb suck' (as they do right now). And this is based on the assumption that blood tests done are accurate! Furthermore, if you've been hypothyroid for any length of time, your thyroid is probably not functioning at all anymore - so the HP characteristic curve would be invalid!!


I think you misunderstand the work. What it does is to indicate the optimal balance between FT4 and TSH (really the sum of FT4 and FT3 versus TSH) that will most nearly satisfy a patient's unique situation and setpoints to assist normalization. So this is a target to aim at by dosing. The method is used to monitor dosing and finding an optimal point. Steady changes in dosing, measuring the TSH and thyroid hormones at each change, produces the curves that when they intersect indicate the best target to aim at. Of course intelligent diagnosis will include patient symptoms. But there is a proviso here. The appearance of a patient feeling well on T4 or NDT or anything else is not a guarantee that they are well or on optimal therapy. They can feel splendid on an overdose (the effect of T4/3 on the brain from an external dose is like a drug hit). One has to be careful that overdosing isn't happening, but in being careful not to go the other way and underdose. That is what this paper is all about - getting a method to produce a patient-unique target and see what happens then. Blood tests aren't accurate between producers, but they are usually precise within a particular test from a particular source. So long as you stick to one test, then comparisons are quite valid and meaningful.


I don't pretend to understand it at the same level as diogenes.

The authors are immensely bright people who are unlikely to miss any such issues.

The last comment in the article says:

It remains for future studies to assess if such a methodology will prove superior to current heuristic therapeutic paradigms and facilitates a more accurate, targeted treatment based on HPT axis physiology, and most importantly, if it improves patients’ clinical outcomes and quality of life.

I suggest that shows clear evidence of awareness of many aspects of the disease and its treatment. Indeed, the very inclusion within a research paper of such a strong comment about quality of life is rare and comes across to me very positively.

In my own case, I have now felt significantly over-dosed on two occasions. It has crept up on me without any change in dose. I also feel that I have suffered two significant troughs of hypothyroidism - again without changes of dose. I have detested both feelings and would do an awful lot to avoid them. But it is so very difficult to get it right from either a symptomatic direction or from a blood test direction. I end up thinking that maybe the time between starting to be over-dosed and then suddenly realising that I actually was over-dosed did indeed feel pretty good much of the time.



Why are they using TSH as part of the criteria for assessing the dosages? From what I can gather about the criticisms surrounding the incorrect treatment of hypothyroid people, is the use of TSH as a valid marker of thyroid hormone 'repleteness'. Nor does this take into account T2 and T1.

But it still means that doctors never even look at the patient - they will just plug in some numbers and tell the patient 'The formula says you are taking enough / too much / too little'. Doctors are already technocrats, not healers.


I don't believe that TSH has to be forever ignored simply because the current practices surrounding it are poor.

If we suggest that TSH simply has to be in range, that is a very poor approach. It should be cast into the pit.

If we suggest that changes in TSH can be analysed and correlated against the levels of thyroid hormones calibrated in and for an individual then it might well have a useful role as an indicator.

I'd rather have a decent formula for dosing than what currently happens. After all, we often see people being prescribed only exact multiple of 25mcg, and the same amount very day. That is, adjustments are made in increments of 175mcg a week. Which, in something of such extraordinary impact at minuscule doses, is far too rough and ready. And all too typically, adjustments are not followed up by appropriate testing.



Yes, you have the argument perfectly. TSH is not a panacea, it's a useful guide but as a guide has to be treated with both caution and respect. And it cannot act as a standalone but only in conjunction of WHAT EFFECT A GIVEN TSH HAS ON STIMULATION OF AN INDIVIDUAL'S THYROID TO PRODUCE A CORRESPONDING INCREMENT OF T4 AND T3.


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