modeling the dynamics of thyroid … the dynamics of thyroid hormones and related disorders by oylum...

MODELING THE DYNAMICS OF THYROID HORMONES AND RELATED

DISORDERS

by

Oylum Seker

B.S., Industrial Engineering, Bogazici University, 2009

Submitted to the Institute for Graduate Studies in

Science and Engineering in partial fulfillment of

the requirements for the degree of

Master of Science

Graduate Program in Industrial Engineering

Bogazici University

2012

ii

MODELING THE DYNAMICS OF THYROID HORMONES AND RELATED

DISORDERS

APPROVED BY:

Prof. Yaman Barlas . . . . . . . . . . . . . . . . . . .

(Thesis Supervisor)

Assist. Prof. Gonenc Yucel . . . . . . . . . . . . . . . . . . .

Assoc. Prof. Ata Akın . . . . . . . . . . . . . . . . . . .

DATE OF APPROVAL: 17.09.2012

iii

ACKNOWLEDGEMENTS

First and foremost, I would like to express my sincere and immense gratitude to Prof.

Yaman Barlas, my thesis supervisor, for his guidance, patience and support throughout this

study. Anything that I could have humbly learnt and hopefully continue to learn from him

as an excellent professor, as an intellectual, and as a friend have been and will be

invaluable assets to me.

I would like to thank to Assist. Prof. Gönenç Yücel and Assoc. Prof. Ata Akın for

taking part in my thesis committee and providing valuable comments, which I surely will

benefit in my future research.

I wish to extend my sincere thanks and appreciation to Prof. Faruk Alagöl for readily

offering his vast knowledge and experience about thyroid, and for his deep interest in this

study.

I am grateful to Nükhet Barlas, who inspired the onset of this work, for kindly

sharing her personal blood test results to support this study.

I would like to express my gratitude to Prof. Çetin Önsel for being so kind to answer

my exhaustive questions about thyroid.

I wish to express special acknowledgements to my colleagues at SESDYN

Laboratory. I would like to thank to Nisa Önsel for her sympathetic, soothing and warm

companion, to Onur Özgün for kindly offering his never-ending help and support on all the

otherwise unsolvable methodological and technological issues, to M. Emre Keskin for

genially answering my endless questions about every single topic in industrial engineering

courses, and finally to Can Sücüllü for cheering us up with his improvised shows.

iv

I owe my special thanks to O. Kaan Drağan for his irreplaceable friendship and

sympathy, and for patiently being my one and only voluntary therapist.

Lastly, I wish to thank to Google and to some undisclosed third parties which

generously provided me numerous papers and books about the subject of my study.

v

ABSTRACT

MODELING THE DYNAMICS OF THYROID HORMONES AND

RELATED DISORDERS

In this study, a dynamic simulation model for thyroid hormone system is constructed.

The objective of this work is to first generate the dynamics of the hormones involved in

thyroid hormone system in healthy body, and then to adapt the model to portray the

dynamics of certain common thyroid disorders. The ultimate aim is to provide a platform

for scenario analysis to support medical education, training and research, without risking

patients’ health. Initially, the model structure is tested by standard structure validity tests.

After the validation part, four common thyroid disorders are simulated. Firstly, Graves’

disease, the most common source of hyperthyroidism, is addressed. Goiter formation,

effect of iodine availability on the severity of the disease, and increased T3/T4 –a

commonly used diagnostic measure in hyperthyroidism– are all well captured by the

model. Other typical behaviour of hormones and glands are also well mimicked by

simulations. Secondly, iodine deficiency, one prevailing cause of hypothyroidism, is

discussed for two different levels of daily iodine intake. The model was able to depict all

the characteristic changes including the goiter formation and increase in T3/T4 in these

two scenarios, both independently and comparatively. Thirdly, the transient inhibitory

effect of excessive iodine intake on thyroid gland is discussed. The model is able to

demonstrate the enlargement in thyroid volume and the mild decline in thyroid hormones.

Lastly, a condition called subacute thyroiditis, a common disorder in which thyroid gland

is exposed to inflammation, is analysed. The typical triphasic clinical course of subacute

thyroiditis, comprised of thyrotoxicosis, hypothyroidism and normal thyroid functioning is

well represented by the model. In conclusion, with respect to both qualitative and

quantitative information in literature, and interviews with the medical doctors, the model

exhibits an acceptable degree of validity and is able to cover a wide range of thyroid-

related disorders.

vi

ÖZET

TİROİT HORMONLARININ VE İLGİLİ HASTALIKLARIN

DİNAMİKLERİNİN MODELLENMESİ

Bu çalışmada, tiroit hormon sistemi için dinamik bir benzetim modeli kurulmuştur.

Çalışmanın amacı, öncelikle sağlıklı vücutta tiroit hormon sisteminin işleyişinde rol alan

hormonların dinamiğini üretmek ve ardından yaygın görülen bazı tiroid rahatsızlıklarının

dinamiklerinin gösterilebilmesi için modeli uyarlamaktır. Nihai amaç, hastaların hayatını

tehlikeye atmaksızın tıbbi eğitim, çalışma ve araştırmayı senaryo analizleriyle

destekleyecek bir ortam sunmaktır. Öncelikle, modelin yapısı standart geçerlilik testleri ile

analiz edilmiştir. Geçerleme safhası bittikten sonra, yaygın görülen dört tane tiroid

hastalığının benzetimi yapılmıştır. İlk olarak, hipertiroidizmin sık görülen sebeplerinden

biri olan Graves’ hastalığı ele alınmıştır. Model, guatr oluşumunu, mevcut iyot miktarının

hastalığın şiddetine etkisini, bu hastalığın teşhisinde sıklıkla kullanılan artmış T3/T4

oranını ve diğer hormon ve bezlerin tipik davranışlarını tutarlı bir biçimde

sergileyebilmiştir. İkinci olarak, hipotiroidizmin sıkça görülen sebeplerinden biri olan iyot

eksikliği iki farklı günlük iyot alımı seviyesi için incelenmiştir. İki iyot alım seviyesinde

guatr oluşumu ve T3/T4 oranındaki değişimler gibi tipik göstergeler hem karşılaştırmalı

hem de bağımsız olarak model tarafından üretilebilmiştir. Üçüncü olarak, aşırı iyot

alımının geçici kısıtlayıcı etkileri ele alınmış, tiroit hacmindeki büyüme ve tiroit

hormonlarındaki hafif düşüş elde edilebilmiştir. Son olarak, tiroit bezinin iltihaplanması

sonucu ortaya çıkan subakut tiroidit adlı hastalık analiz edilmiştir. Model, hastalığın

tirotoksikoz, hipotiroidizm ve ardından normal işleyişin kazanılmasından oluşan üç

aşamalı tipik klinik gidişatını başarılı bir biçimde yansıtabilmiştir. Sonuç olarak, literatürde

yer alan nitel ve nicel bilgiler ile tıp doktorlarlarıyla yapılan görüşmelerin ışığında,

modelin makul seviyede geçerli olduğu ve geniş yelpazedeki tiroit hormon hastalıklarını

kapsayabildiği söylenebilir.

vii

TABLE OF CONTENTS

ACKNOWLEDGEMENTS .................................................................................................. iii

ABSTRACT ........................................................................................................................... v

ÖZET .................................................................................................................................... vi

LIST OF FIGURES .............................................................................................................. ix

LIST OF ACRONYMS/ABBREVIATIONS ....................................................................... ix

1. INTRODUCTION ............................................................................................................. 1

2. LITERATURE REVIEW AND RESEARCH OBJECTIVE ............................................ 4

3. RESEARCH METHODOLOGY ...................................................................................... 7

4. OVERVIEW OF THE MODEL ...................................................................................... 10

5. DESCRIPTION OF THE MODEL ................................................................................. 13

5.1. Hypothalamus Sector ............................................................................................... 13

5.1.1. Background Information ................................................................................ 13

5.1.2. Fundamental Approach and Assumptions ..................................................... 15

5.1.3. Description of the Structure ........................................................................... 18

5.2. Pituitary Sector ......................................................................................................... 25




5.3. Thyroid Sector .......................................................................................................... 31




5.4. Iodine Sector ............................................................................................................ 52



6. VALIDATION AND ANALYSIS OF THE MODEL .................................................... 58

6.1. Equilibrium Behaviour ............................................................................................. 59

viii

6.2. Base Run .................................................................................................................. 59

6.3. TRH Injection Test ................................................................................................... 61

6.4. Ten-Fold Increase in T4 Secretion for One Hour .................................................... 62

6.5. Zero T4 Secretion for One Hour .............................................................................. 65

6.6. Hypophysectomy ..................................................................................................... 67

7. THYROID DISORDERS ................................................................................................ 70

7.1. Graves’ Disease ........................................................................................................ 70

7.1.1. Graves’ Disease with Normal Daily Iodine Intake ........................................ 71

7.1.2. Graves’ Disease with Relatively High Daily Iodine Intake ........................... 76

7.2. Iodine Deficiency ..................................................................................................... 79

7.2.1. Severe Iodine Deficiency ............................................................................... 80

7.2.2. Moderate Iodine Deficiency ........................................................................... 86

7.3. Iodine Excess ........................................................................................................... 89

7.4. Subacute Thyroiditis ................................................................................................ 95

8. CONCLUSION .............................................................................................................. 103

APPENDIX: Model Equations .......................................................................................... 105

REFERENCES .................................................................................................................. 118

ix

LIST OF FIGURES

Figure 1.1. Basic structure of the thyroid hormone system. ............................................. 2

Figure 3.1. Stock-flow diagram of a simple population model. ....................................... 9

Figure 4.1. Simplified causal loop diagram of the model. .............................................. 11

Figure 5.1. Stock-flow diagram of the hypothalamus sector. ......................................... 19

Figure 5.2. Effect of thyroid hormones on TRH secretion. ............................................ 20

Figure 5.3. Graphical function for the effect of capacity on TRH secretion. ................. 22

Figure 5.4. Graphical function for the effect of implied TRH secretion on hypothalamus

weight. .......................................................................................................... 23

Figure 5.5. Graphical function for effect on hypothalamic adjustment time. ................. 25

Figure 5.6. Stock-flow diagram of the pituitary sector. .................................................. 28

Figure 5.7. Graphical function for the effect of TRH on TSH secretion. ....................... 30

Figure 5.8. Graphical function for the effect of thyroid hormones on TSH secretion. ... 30

Figure 5.9. Stock-flow diagram of the thyroid sector. .................................................... 36

Figure 5.10. Graphical function for the effect of thyroid hormone store capacity. .......... 38

Figure 5.11. The graphical function for the effect of TSH on thyroid hormone secretion.

..................................................................................................................... 39

Figure 5.12. Graphical function for the effect of iodine on thyroid capacity. .................. 40

Figure 5.13. Graphical function for the effect of preferential T3 synthesis on reduction in

T3 synthesis. ................................................................................................ 47

Figure 5.14. Graphical function for the effect of T3 concentration on peripheral

conversion. ................................................................................................... 49

Figure 5.15. Graphical function for the effect of thyroid stimulation on T3 secretion

fraction. ........................................................................................................ 51

Figure 5.16. Graphical function for the fraction of T3 secretion. .................................... 52

Figure 5.17. Stock-flow diagram of the iodine sector. .................................................... 54

Figure 5.18. Graphical function for desired trapping fraction. ........................................ 55

Figure 5.19. Graphical function for the effect of TSH on iodide trapping. ..................... 56

x

Figure 5.20. Graphical function for the effect of thyroid weight on iodide trapping. ..... 56

Figure 5.21. Simplified stock-flow diagram of the model. .............................................. 57

Figure 6.1. T3 (left top), T4 (right top), TRH (lower left), and TSH (lower right)

concentrations at equilibrium. ...................................................................... 59

Figure 6.2. T4 concentration in base run. ....................................................................... 60

Figure 6.3. T3 concentration in base run. ....................................................................... 60

Figure 6.4. TSH concentration in base run. .................................................................... 60

Figure 6.5. TRH concentration in base run. .................................................................... 61

Figure 6.6. Average TSH concentration of six normal subjects when 25 µg TRH is

injected at t=0 (Snyder and Utiger, 1972).................................................... 62

Figure 6.7. TSH concentration when 25 µg TRH is injected at t=0. .............................. 62

Figure 6.8. T4 concentration when its secretion is increased ten-fold for one hour. ...... 63

Figure 6.9. T3 concentration when T4 secretion is increased ten-fold for one hour. ..... 63

Figure 6.10. TRH concentration when T4 secretion is increased ten-fold for one hour. . 64

Figure 6.11. TSH concentration when T4 secretion is increased ten-fold for one hour. .. 64

Figure 6.12. T4 concentration when T4 secretion is stopped for one hour. ..................... 65

Figure 6.13. T3 concentration when T4 secretion is stopped for one hour. ..................... 66

Figure 6.14. TSH concentration when T4 secretion is stopped for one hour. .................. 66

Figure 6.15. T3 concentration in case of hypophysectomy. ............................................. 67

Figure 6.16. TRH concentration in case of hypophysectomy. .......................................... 67

Figure 6.17. Thyroid weight in case of hypophysectomy. ................................................ 68

Figure 6.18. Hypothalamus weight in case of hypophysectomy. ..................................... 69

Figure 7.1. T3 concentration in Graves’ disease with normal iodine intake. ................. 71

Figure 7.2. T4 concentration in Graves’ disease with normal iodine intake. ................. 72

Figure 7.3. Iodine in thyroid in Graves’ disease with normal iodine intake. .................. 73

Figure 7.4. T3 to T4 ratio in Graves’ disease with normal iodine intake. ...................... 73

Figure 7.5. TRH concentration in Graves’ disease with normal iodine intake. .............. 74

Figure 7.6. TSH concentration in Graves’ disease with normal iodine intake. .............. 74

Figure 7.7. Thyroid weight in Graves’ disease with normal iodine intake. .................... 75

Figure 7.8. Hypothalamus weight in Graves’ disease with normal iodine intake. ......... 75

xi

Figure 7.9. Pituitary weight in Graves' disease with normal iodine intake. .................. 76

Figure 7.10. T3 concentration in Graves’ disease with relatively high iodine intake. .... 77

Figure 7.11. Iodine in thyroid in Graves’ disease with relatively high iodine intake. ..... 77

Figure 7.12. T3 to T4 ratio in Graves’ disease with relatively high iodine intake. ......... 78

Figure 7.13. TSH concentration in Graves’ disease with relatively high iodine intake. . 78

Figure 7.14. Thyroid weight in Graves’ disease with relatively high iodine intake. ....... 79

Figure 7.15. Pituitary weight in Graves’ disease with relatively high iodine intake. ...... 79

Figure 7.16. T3 concentration when daily iodine intake is 30 µg. .................................. 81


Figure 7.18. T3 to T4 ratio when daily iodine intake is 30 µg. ....................................... 82

Figure 7.19. Iodine in thyroid when daily iodine intake is 30 µg. ................................... 82

Figure 7.20. T3 store when daily iodine intake is 30 µg. ................................................ 83


Figure 7.22. TSH concentration when daily iodine intake is 30 µg. ............................... 84

Figure 7.23. Thyroid weight when daily iodine intake is 30 µg. ..................................... 84

Figure 7.24. Hypothalamus weight when daily iodine intake is 30 µg. .......................... 85

Figure 7.25. Pituitary weight when daily iodine intake is 30 µg. .................................... 85



Figure 7.28. T3 to T4 ratio when daily iodine intake is 50 µg. ....................................... 87


Figure 7.30. TSH concentration when daily iodine intake is 50 µg. ............................... 88

Figure 7.31. Thyroid weight when daily iodine intake is 50 µg. ..................................... 89

Figure 7.32. Average free T4 concentration of ten subjects receiving 27 mg iodine

supplementation for 28 days (Namba et al., 1993). ..................................... 90

Figure 7.33. Free T4 concentration (in pmol/l) in case of 27 mg iodine supplementation

for 28 days. .................................................................................................. 91

Figure 7.34. T3 concentration in case of 27 mg iodine supplementation for 28 days. ..... 91

Figure 7.35. Average TSH concentration of ten subjects receiving 27 mg iodine


xii

Figure 7.36. TSH concentration in case of 27 mg iodine supplementation for 28 days. .. 92

Figure 7.37. Average thyroid volume (as % of normal volume) of ten subjects receiving

27 mg iodine supplementation for 28 days (Namba et al., 1993). ............... 93

Figure 7.38. Thyroid weight in case of 27 mg iodine supplementation for 28 days. ....... 94

Figure 7.39. Average serum iodine levels of ten subjects receiving 27 mg iodine


Figure 7.40. Iodine in blood in case of 27 mg iodine supplementation for 28 days. ........ 95

Figure 7.41. Modified structure of thyroid sector for subacute thyroiditis. ...................... 97

Figure 7.42. Modified structure of iodine sector for subacute thyroiditis. ....................... 98

Figure 7.43. The assumed course of inflammation status in subacute thyroiditis. ......... 100

Figure 7.44. TSH and T4 concentrations in subacute thyroiditis. .................................. 100

Figure 7.45. Data from a patient with subacute thyroiditis (Lazarus, 2009). ................. 101

Figure 7.46. Data from a patient with subacute thyroiditis (secondary axis: TSH). ...... 101

Figure 7.47. T3 to T4 ratio in subacute thyroiditis. ........................................................ 102

xiii

LIST OF ACRONYMS/ABBREVIATIONS

abs absorption

adj adjustment

avail availability

cap capacity

chg change

clear clearance

conc concentration

cons consumption

conv conversion

deiod deiodination

del delay

des desired

disc discrepancy

eff effect

excr excretion

fr fraction

gr graphical function

hypo hypothalamus (or hypothalamic)

imp implied

peri peripheral

pit pituitary

pos possible

pot potential

pref preferential

prod productivity

recov recovery

red reduction

xiv

rest restricted

restor restoration

stim stimulation

thres threshold

thy thyroid (or thyroidal)

trap trapping

wt weight

AT Adjustment Time

HAT Adjustment Time for Hypothalamus

PAT Adjustment Time for Pituitary

TAT Adjustment Time for Thyroid

TH Thyroid Hormones

TRH Thyrotropin Releasing Hormone

TSH Thyroid Stimulating Hormone

1

1. INTRODUCTION

There are mainly two systems in the regulation of the functions of the body: (1) the

nervous system, and (2) the endocrine system, or the hormonal system. In this study, a

hormonal system will be of interest. For the lexical meaning, the word “hormone” is

derived from the Greek word hormaein, which means to excite, arouse or stir up. As for

the biological implication, a hormone is a chemical substance responsible for conveying

messages to target cells. They are secreted by a cell or gland, and act as means of

communication among the parts of the body. Through the actions of hormones, the

endocrine system exerts physiological control on metabolic functions of the body.

Therefore, endocrine system plays a vital role in the regulation, integration and

coordination of various physiological processes (Rhoades and Bell, 2009).

A crucial point in the functioning of endocrine system is to preserve the internal

balance, or homeostasis, in the body. This is where feedback loops come into play.

Feedback loops are the principal regulators of the endocrine system. They adjust the

amount of hormones released by the gland and keep them at a desired level in order to

guarantee a healthy maintenance of bodily functions.

As far as the order of feedback loops is concerned, different forms of hormonal

regulation exist. Rather than the systems that operate under the control of a single feedback

loop, the ones involving higher order, complex feedback loops have more interesting

dynamics to study. Production and release of thyroid hormones, which comprises the main

focus in this study, is controlled by such higher order negative (balancing, compensating)

feedback loops.

Three tiers are involved in thyroid hormone system. First tier is the hypothalamus,

second is the pituitary gland, and the third one is the thyroid gland (Kronenberg et al.,

2008). Firstly, the hypothalamus secretes thyrotropin-releasing hormone (TRH) which

2

prompts the production of thyroid-stimulating hormone (TSH) from the pituitary. Then,

TSH stimulates the thyroid gland. Upon stimulation, production and release of thyroid

hormones, which are triiodothyronine (T3) and thyroxine (T4), is triggered. After T3 and

T4 are secreted from the thyroid, they circulate in blood and reach their target tissues

(Guyton and Hall, 2006; Kronenberg et al., 2008; Rhoades and Bell, 2009). Eventually,

concentration of thyroid hormones in blood creates a double-armed negative feedback

effect. That is, thyroid hormones in blood affect negatively both the hypothalamus and the

pituitary, and consequently control the secretion of TRH and TSH to keep the thyroid

hormone concentrations at a constant desired level. Pictorially, the basic structure of the

thyroid hormone system looks as in Figure 1.1.

Figure 1.1. Basic structure of the thyroid hormone system.

The thyroid hormones play key roles in the regulation of bodily functions. They

govern the pace of metabolic functions of cells in the body by enhancing the rate of oxygen

consumption, utilization of fats, carbohydrates and proteins by the cells. In this respect, the

thyroid gland undertakes a managerial role in the regulation of metabolic functions;

Hypothalamus

Pituitary

Thyroid

TRH

TIER I

TIER II

TIER III

TSH

T3 and T4

Peripheral Tissues

-

-

3

depending on the intensity of hormone signals from the thyroid, the rate of metabolism in

the body is adjusted.

The prevalence of thyroid diseases is quite high and misdiagnosis of these diseases is

not uncommon. Since these hormones affect virtually every part of the body and regulate

some vital functions, it is important to gain an insight into the structure of this hormonal

system, the interplay between the constituent components of the system, and the dynamics

of the hormones involved under related disorders.

In the following chapter, systems-theoretic research in the modelling of thyroid

hormone system will be briefly reviewed and the research objective of this modelling study

will be described. Then, the research methodology and the rationale behind it will be

concisely explained. In the remaining chapters, the system dynamics model will be

elucidated, validity test results will be presented, and the dynamics of some well-known

disorders of thyroid hormone system will be generated and discussed.

4

2. LITERATURE REVIEW AND RESEARCH OBJECTIVE

Modelling of physiological systems has aroused considerable interest over the past

several decades. That physiological systems, in particular endocrine systems, are capable

of preserving their internal balance through the actions of feedback mechanisms connects

them to technological feedback control systems that are widely studied in engineering

fields, in the sense that their regulation abides essentially to the same principles. The

formidable complexity and large number of interactions inherent within and among

endocrine systems introduce problems of quantification that well fit to the tremendous

abilities of computers, and that (verbal) language mostly fails to suffice, whereas

modelling and simulation succeeds for both simple and complex systems, as pointed in one

of the early works of DiStefano and Chang (1971) on simulation of thyroid hormone

dynamics.

A number of studies have been conducted in which engineering principles are

applied to model the thyroid hormone system at various levels of complexity, from various

aspects, and with different research objectives. One prominent name in these studies is

Joseph J. DiStefano III. There has been a number of pioneering researches conducted by

DiStefano and colleagues to model the thyroid system with a systems-theoretical approach

and integrate it with experimental data. Some of these studies deal with hypotheses about

the underlying feedback structure (DiStefano, 1969; DiStefano and Stear, 1968), some with

parameter estimation for thyroid hormone secretion, distribution, binding, conversion and

metabolism (DiStefano and Chang, 1971; DiStefano and Mori, 1969; Wilson et al., 1977),

some with the mathematical models for secretory output of thyroid hormones in response

to TSH input (DiStefano, 1969), and some with the prescription of thyroid hormones in

hypothyroidism and after thyroidectomy (Mak and DiStefano, 1977; Eisenberg et al.,

2007; Ben-Shachar et al., 2012).

5

There are also other thyroid-related quantitative modelling studies that adopt a

systemic perspective. In the work of Khee and Leow (2007), a mathematical model is

proposed for pituitary-thyroid interaction that aims to provide a better understanding of the

sensitivity of the pituitary to the feedback effect of thyroid hormones in the context of

thyroid hormone excess and deficiency. Another work conducted by Liu et al. (1994)

proposes a new mathematical model for the secretory system of hypothalamo-pituitary-

thyroid axis by revising and improving the previous two works by Liu and Peng (1990)

and Liu and Liu (1992) which takes into account the interactions of the hormones in the

axis and the binding characteristics of hormones to proteins in plasma and tissues. Lastly,

the work of Degon et al. (2008) uses recent molecular-level and clinical observations to

develop a computational thyroid model which captures the known aspects of thyroid

physiology and uses it to evaluate the competing hypotheses related to the Wolff-Chaikoff

escape.

Unlike many others, our modelling study integrates all four aspects involved in the

control of thyroid hormone system; namely the hypothalamus, pituitary, thyroid, and the

essential ingredient iodine. The main focus is to depict the major macro-level causal

relationships among these four components that strive for the homeostatic regulation of the

system, rather than concentrating on the intracellular pathways and micro-level molecular

mechanisms. The model combines sufficiently many aspects involved in the regulation of

thyroid hormone system, and thus is able to cover a wide range of conditions (like

hyperthyroidism, hypothyroidism, thyroiditis, goiter, etc.) and illustrate the associated

overall descriptive behaviours of key variables in the system.

The main goal of modelling physiological systems is to provide a platform to

conduct experiments and subsequently propose policies, without any necessity to rehearse

on humans. This study aims at modelling the thyroid system to capture the dynamics of

thyroid hormones and some related diseases in order to facilitate the recognition of these

disorders. Initial goal is to develop a system dynamics model as a valid representation of

the underlying structure of thyroid hormone system so as to illustrate the dynamics of key

stimulating and thyroid hormones in healthy body. The next purpose is to modify the

6

model to represent some well-known thyroid disorders. The final goal is to capture the

typical course of behaviour of the key hormones under these disorders, hence to hopefully

offer a platform for the recognition of these disorders and for scenario analysis to assist

medical education, training and research.

7

3. RESEARCH METHODOLOGY

This study aims at modelling the thyroid hormone system to portray the dynamics of

key hormones under healthy and diseased states, particularly by stressing the role of

functional feedback mechanisms involved. Being composed of a tripartite regulatory

mechanism, the smooth functioning of thyroid hormone system can be disturbed by the

malfunctioning of any of the constituent subsystems, either due to purely internal motives,

or anomaly of essential external inputs to the system. The fact that thyroid hormone system

operates under not a simple first order but a dual feedback control, the existence of two

different thyroid hormones, one of them largely depending on the production of the other

and requiring a more sensitive modulation, and the role of iodine intake render the problem

complex enough that our intuition mostly remains incapable. The assistance of

mathematical or simulation modelling may well provide a deep insight into the structure of

the system and the behaviour of key variables under related disorders, and contribute to

medical training and research.

System dynamics methodology is an efficient tool to enhance the understanding of

the behaviour of complex, large-scale systems and study their underlying structures. The

idea is to address an issue by adopting a holistic approach, which essentially states that a

system is more than the sum of its individual constituent parts and cannot be fully

understood in terms of the properties of individual elements in isolation. So, this approach

puts a particular emphasis to the causal relationships between the constituents of the

system. In other words, it is the internal structure of a system which drives the system

behaviour. The structure can be defined as the totality of relationships that exist between

system variables and the behaviour of a system is essentially the operation of its internal

structure over time (Barlas, 2002). Once a proper and valid model structure is constructed,

the behaviour that the system would generate under various schemes can be experimented

via simulation runs, and a broad appreciation can be developed about the system as a

whole.

8

The fact that feedback relationships largely prevail in the regulation of endocrine

systems makes this engineering discipline a natural choice in such modelling studies. As

far as the dominant roles of accumulations, feedbacks, nonlinearities and time delays

inherent in the system of interest are concerned, system dynamics methodology is very

suitable for quantitative behavioural analysis of the disorders of thyroid system.

One important feature of system dynamics approach is that it particularly emphasizes

the importance of causal relations as opposed to mere statistical correlations (Barlas,

2002). It aims at developing an understanding of the overall dynamic behaviour of the

system of concern, rather than concentrating on the point prediction of the future values of

the variables involved. In this respect, it becomes an appropriate tool in the modelling of

physiological systems, for it is usually the collection of the overall pattern of the key

variables, rather than their precise point values, which characterizes a particular condition.

In system dynamics methodology, two central concepts are used in modelling. The

first one is stocks, which represent the accumulations in a system. Stocks can be used in

the conceptualization of a wide range of notions, from physical to information entities.

Some examples for stock variables can be inventory, population, knowledge level, etc. The

stocks are changed merely via their flows; that is, the net flow into a stock corresponds to

the rate of change of that stock. Examples of flow variables related to the above stock

examples can be production, sales, births, deaths, learning, forgetting, etc. (Barlas, 2002).

A stock variable and its flows together correspond to a first order differential (or

difference) equation, the stock being the system variable and the flows being the rates of

change over time.

The mathematical description of a system only entails the stocks and flows actually.

However, for the sake of clarity, a third type of variable is also used in system dynamics

which is called converter, or auxiliary variable. Converters are used to explicitly define

some intermediate parameters or variables, and thus can be constants or functions of stocks

and/or flows.

9

In model diagrams, stocks are represented by rectangular boxes, and flows by valves

on arrows that point into or out of the stock. If the arrowhead of the flow point into the

stock, that flow is called an “inflow”, and if it points out, then it is named “outflow”.

Clouds symbolize the sources and sinks for the flows if they originate from or discharge

outside the boundary of the model, and they do not induce any capacity constraint on the

related flow (Sterman, 2000). An example stock-flow diagram of a simple population

model is shown in Figure 3.1.

Figure 3.1. Stock-flow diagram of a simple population model.

Population(t) = Population(t - dt) + (birth rate – death rate) × dt (3.1)

birth rate = birth fraction × Population (3.2)

death rate = death fraction × Population (3.3)

In this simple model, the stock variable is Population. The inflow to the stock is birth

rate and the outflow death rate; that is, the birth rate tends to increase and death rate tends

to decrease the population from its present value. birth fraction and death fraction are

auxiliary variables. The arrows that connect the variables show the causal relationships

between the variables. The variable on the head of the arrow is defined as a function of the

variable (or the parameter) on the tail of the arrow.

Population

birth rate death rate

birth fractiondeath fraction

10

4. OVERVIEW OF THE MODEL

The levels of all the hormones in thyroid hormone system are controlled by the

properly operating feedback loops between the components of the system as it is the case

in most other physiological systems to preserve a stable functioning. In thyroid hormone

system, two fundamental feedback loops operate on hypothalamus-pituitary-thyroid and

pituitary-thyroid axes. Both of these loops operate to keep the thyroid hormones T3 and T4

at their normal levels.

The overall model basically consists of four subdivisions: the hypothalamus, the

pituitary, the thyroid, and the iodine. Hypothalamus and pituitary sectors are basically the

same in terms of their qualitative structure; they involve one gland, its related hormone,

and relationships that have an effect on the gland and hormone. Thyroid sector, however,

involves one gland, related two hormones, the stores of the two hormones, and all the

means and links that affect the functioning of the sector. Lastly, the iodine sector, where

iodine is the main rate-limiting ingredient in the synthesis of thyroid hormones, involves

the iodine levels in blood and in the thyroid gland, and the relevant measures.

A simplified causal loop diagram depicting the main variables in the model together

with the key feedback loops is provided in Figure 4.1. A “+” sign on the head of an arrow

indicates a positive causal relationship between the variable on the tail and the variable on

the head of the arrow, and conversely a “−” sign a negative causality. A positive causal

link means that a change in the variable on the tail of the arrow (cause) induces a change in

the variable on the head of the arrow (effect) in the same direction by an amount more than

what it would have been otherwise. Conversely, a negative causal link means that a change

in the cause prompts a change in the variable on the head of the arrow in the opposite

direction by an amount more than what it would have been otherwise.

11

Figure 4.1. Simplified causal loop diagram of the model.

The 1st and 2

nd loops demonstrate the negative feedback mechanism on

hypothalamus-pituitary-thyroid axis and pituitary-thyroid axis respectively. The hormones

involved in these loops are TRH, TSH and T3 and T4. These two main feedback loops

represent the short-term hormone control mechanisms in the body. In addition to the short-

term effects, some delayed effects on the weights of hypothalamus, pituitary and thyroid

gland may be observed. The 3rd

, 4th

and 5th

loops display these delayed feedback effects

TRH secretion

TSH secretion

T3 and T4

secretion

Free T3 and T4 in

Blood

Desired

hypothalamus

weight+

Desired

pituitary

weight

+

Desiredthyroidweight

+

1

2

3

4

5

+

+

+

Hypothalamus

Weight

+

Pituitary

Weight

+

Thyroid

Weight

+

TSH

TRH

T3 and T4

+

Implied TRH

secretion

-+

+

Implied TSH

secretion

+

+

+

-

Implied T3 and T4

secretion

+

++

12

between the weight of one particular gland and the subsequent hormone secretions in the

related axis.

The model will be elucidated in detail in the next chapter; but, briefly the rationale

behind the model is as follows: The amount of a hormone secreted basically depends on

two factors; the capacity of the gland and the implied secretion rate. The capacity of the

gland is mainly imposed by the weight of the gland. The implied secretion rate is

determined by the relative amounts of stimulating hormone and inhibitory hormone, if any,

and this happens without a delay. However, changes in gland weight take place in time.

First, the body “decides” on a desired gland weight with a delay by continually considering

the induced levels of hormone demand, which actually is the implied secretion rate of that

gland. According to this target level, gland weight might be altered in the long run.

13

5. DESCRIPTION OF THE MODEL

5.1. Hypothalamus Sector

5.1.1. Background Information

Hypothalamus, a key regulator of homeostasis, is a small region of the brain located

above the brain stem. It is the central element in the regulation of endocrine function due to

its connections with the pituitary gland, which is the master gland of the endocrine system

(Rhoades and Bell, 2009). The hypothalamus synthesizes and secretes unique releasing and

inhibitory hormones which coordinate the production and secretion of hormones from

anterior pituitary, which is one of the two lobes of the pituitary gland (Melmed, 2002). The

weight of the hypothalamus in adult human is about 4000 mg (Bhagavan, 2002). The

hypothalamus secretes various hormones that affect the anterior pituitary hormones, one of

them being the TRH. TRH is synthesized and secreted by the parvicellular neurons of the

paraventricular cells (PVNparv) and the periventricular nucleus (PeriVN).

TRH is a hypothalamic hormone which principally stimulates the synthesis and

release of TSH. The connection between the hormones of the hypothalamus and the

anterior pituitary is enabled via minute blood vessels called hypothalamic-hypophysial

portal vessels. Through these portal vessels, TRH is transported to the anterior pituitary to

trigger the secretion of TSH. The rate of TRH secretion is mainly determined by the level

of free thyroid hormone levels in blood. Some portion of free T3 and T4 molecules

impinges upon hypothalamic cells and couples with the receptors on these cells (Bhagavan,

2002; Rhoades and Bell, 2009; Guyton and Hall, 2006; Werner et al., 2005). The amount

of thyroid hormone-receptor complexes is the main determinant of the rate of TRH

secretion. As aforementioned, the levels of thyroid hormones in blood negatively affect

TRH secretion. So, as the amount of thyroid hormone-receptor complexes increase on the

14

cells of the hypothalamus, the TRH output will decrease, and vice versa. In short, the rate

of TRH secretion is inversely proportional to the amount of thyroid hormones in blood.

There are two factors that affect the concentration of a hormone in blood; secretion

of that hormone and rate of removal from blood (Guyton and Hall, 2006). As most other

hormones do, TRH is cleared from the body with a certain half-life, where half-life is the

time it takes for half of the amount of a hormone to be cleared from blood in our context.

TRH has a half-life of 6.2 minutes (Motta, 1991).

In short term, changes in TRH secretion rate occur as the levels of thyroid hormones

in blood dictate. However, there might be cases where the stimulation persists at far below

or far above the baseline values. Relying upon the fact that a hormone, which provokes or

inhibits the activity of a gland, can also affect its weight over the long term in certain cases

(Donovan, 1966; Melmed, 2002; Guyton and Hall, 2006), thyroid hormones can also

influence the weight of the hypothalamus. There is not direct evidence that the weight of

the TRH-secreting section of the hypothalamus can be altered according to the circulating

thyroid hormone levels. However, there is evidence that the number of cells that secrete

CRH, which is a hypothalamic hormone analogous to TRH in the regulation of

hypothalamus-pituitary-adrenal (HPA) axis, substantially decline in subjects who

externally receive the hormones that inhibit its secretion (Erkut et al., 1998). Extrapolating

all this information to our case, the weight of the hypothalamus is taken as a variable

quantity.

First, if the magnitude of stimuli from thyroid hormones is persistently far above the

standard levels, it means that the secretory capacity of hypothalamus is consistently

underutilized. In such cases, the specific portions of hypothalamus, which are in charge of

the TRH secretion, would shrink not to retain the redundant capacity in vain. Second, if

thyroid hormones constantly circulate at considerably below normal concentrations, i.e. if

hypothalamus is persistently understimulated, then the hypothalamus would continually

operate at above-normal levels, and thereby expand to adjust its capacity. So, it adjusts its

capacity in the direction that the current needs of the body necessitate.

15

5.1.2. Fundamental Approach and Assumptions

Plasma levels of hormones normally fluctuate throughout the day or from one day to

another because of neurological, psychological, environmental, or similar factors. Though

these fluctuations and the features that influence them might count for some practical

purposes like prescribing the right dose of a drug for a patient, the primary aim of the study

is not to observe the dynamics of diurnal variations of the hormones in the body but rather

to represent the long-term dynamics of the important elements involved in thyroid

hormone system under certain conditions. Thus, the time unit of this study is taken to be

one day, the base values of the variables are taken to be an average value in the model, and

possible variations in hormone levels and neurological, psychological, environmental or

similar other effects are considered to be outside the scope of this study.

The circulating levels of all the hormones in this model are assumed to act according

to set point theory. Here, the set points of the hormones are defined to be their absolute

total quantity in blood. Though it might appear to be erroneous at first sight to take the

absolute quantities of hormones in blood as their set points rather than their concentrations,

it is not so because the blood or plasma volume cannot be too variable. Albeit so, it

wouldn’t still hurt our assumption since this study does not encompass cases where the

changes in the volumes of the fluid, which hormones float in, constitute the problem of

interest.

Secretion rates of hormones are commonly found in some mass unit (like µg, ng etc.)

per unit time. Since the net change in the value of a stock variable is the integral of the net

flow to the stock over time, the units of the flows of a stock is the unit of the stock divided

by the time unit of the model. Therefore, defining the levels of hormones in terms of their

absolute quantities renders it possible to use the secretion rates in their typically defined

units.

When the hypothalamic neurons are excited to secrete releasing hormones, that

hormone is discharged into the hypophysial portal circulation. As mentioned before, this

16

portal system is composed of small blood vessels that link the hypothalamus and the

anterior pituitary. The releasing hormones have only a small distance to travel in order to

communicate with their target cells. Thus, it is enough to release just the quantity of

hormone to the portal circulation to regulate the anterior pituitary hormone in this nearly

isolated communication space. Hence, releasing hormones of hypothalamus circulate in

almost undetectable amounts in systemic blood (Rhoades and Bell, 2009).

Throughout the literature survey, secretion rate of TRH could not be found explicitly

because hypothalamic-hypophyseal portal blood is an extremely difficult area to obtain

blood samples in humans (Rhoades and Bell, 2009). Furthermore, direct measurement of

the secretion rate of a hormone is quite a challenging task. Hence, secretion rates are

commonly inferred from the blood concentration of the hormone and its clearance rate. For

the case of TRH, related literature states that it also circulates in the cerebrospinal fluid

(CSF), which is a serumlike fluid that essentially circulates through the ventricles of the

brain. Firstly, the value for concentration of TRH in CSF, which is stated to range between

65-290 pg/ml (Werner et al., 2005) and taken approximately as 200 pg/ml, is assumed as

its concentration in portal vessels. Secondly, the volume of plasma in these portal vessels is

assumed to be 10 ml. According to these two assumptions, the normal absolute quantity of

TRH in portal vessels is calculated as 2 ng in the model.

The weight of the hypothalamus as a whole is 4000 mg, as mentioned in the previous

section. The percentage of the TRH secreting cells, however, could not be found explicitly

in literature. Thus, it is assumed that 1% of the hypothalamic cells are in charge of TRH

secretion. So, the related weight is taken as 40 mg in the model.

In general, hormones are cleared from the blood with some specific rate. Not only

the hypothalamus sector but the whole model also works according to this principle; the

clearance of each hormone from plasma occurs with respect to a certain fraction, which is

called the “clearance fraction” (clear fr) in the model. In literature, half-lives are

commonly used to quantify the clearance rate of a hormone. Thus, removal of hormones

from blood (or the related fluid) is assumed to follow a first order exponential decay in the

17

model, and the respective clearance fractions are calculated from their half-lives using the

following equation:

clearance fraction = ln2 / th (5.1)

where stands for the half-life in days. So, the clearance fractions are in units of .

There are mainly three determinants of the magnitude of hormonal response of a

target tissue; concentration of the hormone, sensitivity of the target cells, and number of

functional target cells. The sensitivity of a target cell primarily depends on the number of

its operational receptors, the affinity of the receptors for the hormone, and the capacity to

amplify the post-receptor activities.

Firstly, it is the binding of the hormone molecule to its specific receptor which gives

rise to cellular response. And, the probability that a hormone molecule encounters a

receptor molecule is induced by the abundance of both the hormone and the molecule. The

availability of hormone receptors can be altered by the stimulating hormone itself or by

another hormone. For instance, it is stated that T3 decreases the sensitivity of the TSH-

secreting anterior pituitary cells to TRH (Goodman, 2009). Secondly, affinity is a measure

of the tightness of binding or the likelihood of an encounter between a hormone and its

receptor that result in binding. Some sources suggest that binding of a hormone to its

receptor affects the affinity of unoccupied receptors. Thirdly, the post-receptor capacity of

a target cell implies how well the cell can react to a unit magnitude of stimuli (Goodman,

2009; Rhoades and Bell, 2009). The first two ingredients of sensitivity and the

circumstances that alter them are not explicitly included in the model, and are considered

out of the scope of this study. The third one, however, is implicitly counted by allowing the

intensity of hormonal stimulation to alter the secretory rates of the target cells to a certain

extent.

18

The number of target cells is also not explicitly incorporated in the model; the

weights of the glands are used as an indicator instead. As the weight of a gland increases,

the competence or the capacity to respond to hormonal stimuli increases too. So, only the

concentration of the hormone, the weight of the related gland or tissue, and the capacity of

cells (more precisely, the capacity of a unit weight of gland or tissue) are assumed to

dictate the response of the target tissue.

One last remark is that when using the term hypothalamus weight, the weight of the

relevant portion of the hypothalamus, i.e. the weight of the section responsible for TRH

release, will be assumed.

5.1.3. Description of the Structure

The structure constructed in this sector aims to depict the first tier in the regulation of

the thyroid hormone system. As mentioned before, the hypothalamus and the related

releasing hormone TRH are the top-level controllers of the negative feedback mechanism

in the functioning of thyroid hormone system. TRH plays a chief role in the functioning of

hypothalamic–pituitary–thyroid axis (HPT-axis) as the only positive effector of TSH

secretion from the pituitary, TSH being the only direct positive stimulant of thyroid

hormone synthesis and secretion.

The stock-flow diagram of the sector is given in Figure 5.1. The sector involves two

main stock variables; Hypo Wt (hypothalamus weight) and TRH.

To begin with TRH, the only inflow to this stock is its secretion rate, and the only

outflow from TRH is its clearance rate. The secretion rate of TRH is determined according

to both the levels of the thyroid hormones in blood and current capability of the

hypothalamus. But, before figuring out the actual TRH secretion from the hypothalamus,

implied TRH secretion (imp TRH sec) is calculated. This implied secretion merely contains

the effect of thyroid hormone concentration on secretion as if the hypothalamus has infinite

capacity to secrete. That is, the implied secretion is a measure of how much TRH secretion

19

thyroid hormones would dictate regardless of the short-term secretory capability of the

hypothalamus. Then, this implied secretion rate is exposed to the capacity restrictions of

the hypothalamus and as much TRH as the capacity permits is secreted. It is calculated

according to Equation 5.2 and 5.3.

Figure 5.1. Stock-flow diagram of the hypothalamus sector.

free T4 inblood

TRH

Hypo Wt

TRH sec rate TRH clearrate

Hypo wt chg

ratio of TH tonormal TH

normal TH

normal TRHsec

eff of cap onTRH sec

des hypo wtHAT

TRH clear fr

normal hypowt

MW of T4

gr for eff of impTRH sec on hypo wt

eff of imp TRH secon hypo wt

free T3 inblood

MW of T3

total free T3molecules

total free T4molecules

total free T3&T4molecules

imp TRH sec

smth imp TRHsec

ratio of smth impTRH sec to normal

log ratio of THto normal

gr for eff of THon TRH sec

eff of TH onTRH sec

gr for hypocap

ratio of imp TRHsec to hypo cap

normal hypoprod

hypo cap

ratio of des hypowt to hypo wt gr for eff on

HAT

20

imp hypo sec = normal TRH sec × eff of TH on TRH sec (5.2)

eff of TH on TRH sec = f (log(total TH / normal TH)) (5.3)

where f (log(total TH / normal TH)) is defined as in Figure 5.2.

Figure 5.2. Effect of thyroid hormones on TRH secretion.

When the thyroid hormone levels stay at their neutral values, the implied TRH

secretion remains at the normal secretion value. However, when the circulating levels of

thyroid hormones are disturbed from their set points, i.e. if the ratio of total circulating

unbound thyroid hormones to the normal is different than one, the implied TRH secretion

will be altered in the opposite direction of the shift in the thyroid hormone levels, as the

negative feedback regulation necessitates.

The work of Goodman (2009) suggests that the magnitude of the biological response

of a target cell can be explained as a function of the logarithm of the concentration of the

effector hormone. Thus, the logarithm of the ratio of hormone levels relative to the normal

levels is used in the model when quantifying the hormonal effect on the response of the

target tissue. So, not directly the ratio of circulating thyroid hormones to normal but the

logarithm of it is used as an input to the graphical effect function shown in Figure 5.2.

1-1.1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8

10

0

2

3

4

5

6

7

8

9

log ratio TH to normal

eff

of

TH

on

TR

H s

ec

21

According to the graphical function in Figure 5.2, if the thyroid hormone levels are

far above their baseline values, the TRH secretion falls to considerably low values, though

not to zero. The reason why hormone secretion does not reset is that most hormone-

secreting tissues exhibit minimal (basal) secretion in the absence of stimulatory signals, as

suggested by the related literature (Negi, 2009). The resistance of the hypothalamus not to

reset but to remain at some basal secretion values are achieved via the nonzero right

endpoint of the graphical function.

The last step in the determination of TRH secretion is to expose the implied secretion

rate to the capacity restrictions of the hypothalamus. The secretory capacity of

hypothalamus is an upper bound to the total amount of TRH that can be maximally

secreted daily. The way this capacity is defined is shown in Equation 5.4.

hypo cap = Hypo Wt × normal hypo prod × 10 (5.4)

Two main ingredients are involved in the definition of hypothalamic capacity; the

normal productivity of the hypothalamus and the weight of the hypothalamus. The term

productivity implies the production or release amount per unit weight. The normal

productivity is defined to be the amount of TRH that one unit weight of the hypothalamus

secretes under normal physiological conditions, and is a constant. This normal productivity

is then multiplied with ten because it is assumed that one unit weight of the hypothalamus

is capable of secreting ten times the normal amount maximally. And so, the overall

capacity of the hypothalamus is defined as the product of the maximal secretory capacity

of a unit weight with the current hypothalamus weight.

TRH sec rate = eff of cap on hypo prod × hypo cap (5.5)

eff of cap on TRH sec = f (imp TRH sec / hypo cap) (5.6)

where f (imp TRH sec / hypo cap) is defined as in Figure 5.3.

22

Figure 5.3. Graphical function for the effect of capacity on TRH secretion.

Equations 5.5 and 5.6 depict how the actual TRH secretion computed as a function of

the capacity and implied secretion. According to the graphical function shown in Figure

5.3, when the implied secretion operates appreciably away from the capacity of

hypothalamus, the capacity constraint does not become binding and the actual secretion

equals to the implied. But, as the implied levels tend to push the capacity limit, a littler

fraction of the implied secretion is allowed to realize. The secretory capacity of

hypothalamus is fully utilized only if the implied secretion considerably exceeds the

capacity. So, the extent at which the falls in thyroid hormone levels immediately influence

the TRH secretion is confined to the short-term adaptation competence of the hypothalamic

cells. If somehow a very high level of TRH secretion is demanded, the hypothalamus

would only secrete as much as its existing capacity permits. So, this means that when

necessary, the hypothalamus would utilize its maximum capacity to meet high TRH

requests immediately, but may not suffice to conform the “orders” in short term.

The formulations for the calculation of the TRH secretion provide some flexibility in

the short run. As explained in section 5.1.1, the weight of the hypothalamus can change in

conditions where it is persistently forced to over- or underfunction. In the model, this

phenomenon is constructed as such: First, implied secretion rate is calculated. This implied

23

secretion may or may not actualize depending on the capacity limits. However, it is

important to retain this piece of information because it tells how much the secretion would

have been if there were no restrictions on it. This information does not immediately show

its effect on the weight of the hypothalamus, and that’s what is meant by the term

“persistent”. Generally, hormone-secreting tissues in a way accommodate themselves to

the needs of the body after some time. That is, these tissues do not opt for weight

adjustment in case of transient and drastic shifts from the baseline values, and usually

show some inertia against weight changes. For this reason, the implied secretion levels are

smoothed with a third order information delay structure in the model, where the overall

delay duration is chosen to be 20 days. Smoothing provides a defence mechanism to

preserve the normal weight against transient switches in secretion rates. Yet, smoothing is

the first step. The second step is to check whether the smoothed implied secretion rates

exceed some limits. This is done to ensure that the hypothalamus indeed functions at levels

appreciably away from normals, and there is need for modifications in the weight. Thus,

the weight of the hypothalamus is affected only if the smoothed implied secretion values

relative to the normal values surpass some threshold values. The graphical function

depicting this effect is shown in Figure 5.4.

Figure 5.4. Graphical function for the effect of implied TRH secretion on hypothalamus

weight.

120 1 2 3 4 5 6 7 8 9 10 11

3.7

0

1

2

3

ratio of smth imp TRH sec to normal

eff

of

imp T

RH

sec

on h

ypo w

t

24

The input to this graphical function is the ratio of smoothed implied TRH secretion

to the normal TRH secretion, and the output turns out to be some coefficient to be

multiplied with the normal hypothalamus weight to figure the desired hypothalamus

weight. The desired hypothalamus weight constitutes a target for the current hypothalamus

weight. Gradually, the hypothalamus converges to that target value. Convergence to the

target value is facilitated through the classical stock adjustment formulation, which is

shown in Equation 5.8.

des hypo wt = normal hypo wt × eff of imp TRH sec on hypo wt (5.7)

Hypo wt chg = (des hypo wt −Hypo Wt) / HAT (5.8)

The above equation is the formula for the flow of the stock that stands for the

hypothalamus size. The adjustment time is a measure of how fast the hormone-secreting

tissue tends to correct the difference between the target and current value. The adjustment

time for hypothalamic weight change (HAT) is not a constant; it changes according to the

ratio of the desired hypothalamus weight to the current hypothalamus weight (ratio of des

hypo wt to hypo wt). It is not very reasonable to set the speed to correct the discrepancy

regardless of the magnitude of that discrepancy. The variable ratio of des hypo wt to hypo

wt is used as a measure of convergence speed of the hypothalamus to reach the desired

level. If the desired weight is too high relative to the current weight, then it should take

more time for the hypothalamus to adjust itself to the desired weight. In a sense, the current

weight is regarded like the capacity of hypothalamus that determines the rapidity of

approaching the desired level. Thus, as ratio of des hypo wt to hypo wt increases, the

adjustment time increases too. The graphical function for HAT is shown in Figure 5.5.

Ultimately, depending on the level of thyroid hormones in blood, and the capacity of

the hypothalamus, a certain amount of TRH is released into the portal circulation to

interact with the thyrotrophs in the anterior pituitary and trigger TSH secretion.

25

Figure 5.5. Graphical function for effect on hypothalamic adjustment time.

5.2. Pituitary Sector


The pituitary gland, or alternatively called hypophysis, is a complex endocrine organ

positioned in the sella turcica, a bony cavity at the base of the brain, and is linked to the

hypothalamus by a stalk (Guyton and Hall, 2006). The weight of this gland is

approximately 600 milligrams in adult human (Donovan, 1966; Sodeman and Sodeman,

1985; Kronenberg et al., 2008; Guyton and Hall, 2006). The pituitary secretes many

hormones, which take part in various physiological processes by either acting directly on

the target cells, or stimulating other endocrine glands to secrete hormones leading to

alterations in body function. The human pituitary is comprised of two morphologically and

functionally distinct glands that are connected to the hypothalamus. These two glands are

called the neurohypophysis and the adenohypophysis, also known as the anterior pituitary.

The anterior lobe of the pituitary comprises 75% of the pituitary gland. The cells of the

anterior lobe secrete six different hormones, and a distinct specialized cluster of cells

secretes each of these hormones. TSH is one of the hormones that the anterior pituitary is

in charge of synthesizing and secreting, and the cells specialized for TSH are called

51 1.5 2 2.5 3 3.5 4 4.5

250

30

100

150

200

ratio of des hypo wt to hypo wt

eff

on

HA

T

26

thyrotrophs. The thyrotrophs, i.e. TSH-secreting cells, compose 5% of the anterior

pituitary cells (Bhagavan, 2002; Guyton and Hall, 2006; Kronenberg et al., 2008; Rhoades

and Bell, 2009).

TSH, also known as thyrotropin, is the principal regulator of thyroid hormone

synthesis and secretion for it is the eventual messenger in the stimulation of the thyroid

gland. As noted earlier, TRH plays the major role in the positive regulation of TSH

secretion. Upon secretion, TRH reaches the anterior pituitary through the portal blood

system, impinges upon the thyrotrophs, and binds to specific receptors on these cells.

Binding of TRH with its receptors on thyrotrophs activates a number of intracellular

mechanisms which ultimately lead to TSH release. However, it is not only TRH that

influences the rate of TSH secretion, but also the levels of thyroid hormones in blood.

Thyroid hormones exert a suppressive, negative feedback effect on the thyrotrophs to

prevent the oversecretion of TSH, as opposed to the augmenting effect of TRH. Some

portion of circulating free thyroid hormones binds with the unique thyroid hormone

receptors, TR’s, on the thyrotrophs, and exerts a suppressive effect on TSH release. This

means that an increase in circulating thyroid hormone concentrations would lead to a

reduction in the rate of TSH secretion; and a decrease would result in a rise in TSH

secretion. Consequently, the magnitude of TSH secretion is induced by the opposing

signals to the anterior pituitary, one by TRH and the other by the thyroid hormones

(Bhagavan, 2002; Guyton and Hall, 2006).

The time it takes for the contrasting effects of TRH and thyroid hormones on TSH

release to be revealed are different indeed. TRH elicits a prompt release of TSH within

minutes (~15 minutes), while the inhibitory effect of thyroid hormones becomes evident

after several hours (Bhagavan, 2002). Still, the time lag between the effect of TRH and

thyroid hormones on TSH does not make much difference because the time unit of our

model is one day and all these occur within a day anyway. Upon stimulation of the anterior

pituitary by TRH, TSH is released into the circulation.

27

TSH is typically measured in “microunits” (µU) or “milliunits” (mU). Normal range

for TSH secretion rate is 40-150 µU/day, and for circulating TSH in plasma 0.3-4 µU/ml

(Kronenberg et al., 2008; Oertli and Udelsman, 2007). And, the half-life of TSH is about

one hour (Negi, 2009).

It is stated that long-standing hypothyroidism may lead to pituitary enlargement

(Melmed, 2002), and increasing the negative feedback by any mechanism may result in

atrophy of the thyrotrophs (Tucker, 1999). In other words, prolonged overstimulation may

lead to expansion in pituitary size, and conversely sustained understimulation to shrinkage.


In this study, when speaking of changes in the weight of the pituitary, it will always

be referred to the thyrotrophs, i.e. cells that secrete the TSH. The assumptions about the

sensitivity of target cells explained in hypothalamus sector are valid for the pituitary too.

As aforesaid, the set points for the levels of hormones in blood are taken to be the

absolute quantities of the hormones rather than their concentrations. This is simply done by

multiplying the relative concentration of the hormone with the total plasma volume. In this

model, plasma volume is taken as 3 litres (Rhoades, 2009). This approach is qualitatively

and quantitatively valid both for TSH and the two thyroid hormones.


The structure of this sector is nearly the same as that of the hypothalamus sector.

Two main stock variables are involved; TSH and Pituitary Weight (see the stock-flow

diagram in Figure 5.6). The distinction is that TSH secretion has two effectors as opposed

to thyroid hormones being the single effector of TRH secretion. Here, it is not only the

circulating thyroid hormones that act on the secretion rate of TSH, but also TRH from

hypothalamus. As mentioned earlier, the functioning of the thyroid hormone system is

governed by a double-armed negative feedback mechanism. So, both the stimulant effect

28

of TRH and the inhibitory effect of thyroid hormones ought to be taken into account when

figuring the rate of TSH secretion. The impact of these two factors is formulated as the

product of two distinct effect functions. The one that counts for thyroid hormone inhibition

is a decreasing function, and the one for TRH is an increasing one.

Figure 5.6. Stock-flow diagram of the pituitary sector.

The work of Guyton and Hall (2006) states that when the blood flow in portal vessels

from hypothalamus to pituitary is completely hindered, TSH secretion rate diminishes

TSH

Pit Wt

TSH sec rate TSH clear rate

Pit wt chg

ratio of TRH

to normal

normalTRH

normalTSH sec

des pit wt

PAT

TSH clear fr

normal

pit wt

thres grfor pit

eff of smth imp

TRH on pit wt

eff of TH on

TSH sec

gr for eff of TH

on TSH sec

imp TSH sec

smth imp

TSH sec

ratio of smthimp TSH sec

to normal

log ratio of

TH to normal

log ratio of

TRH to normal

gr for eff of TRH

on TSH sec

eff of TRH on

TSH secgr for pit cap

eff of cap on

TSH sec

ratio of imp TSH

sec to pit cap

normal pit

prod pit cap<TRH>

ratio of des pit wt

to pit wt

gr for eff on

PAT

29

substantially but isn’t cut back to zero, remains at basal levels. The qualitative and

quantitative structure of Equation 5.9 is constructed based on this statement. First, it is

ensured that the graphical function for the effect of TRH on TSH secretion does not

become zero, but yields a considerably small value when TRH stimulus is non-existent.

Second, from this statement it can be inferred that the prerequisite for significant TSH

secretion is TRH stimulation; low levels of thyroid hormones alone wouldn’t help enhance

TSH secretion. Thus, effect of thyroid hormones should in a way depend on TRH effect; it

should not be allowed to act independently. The dependency is provided by the

multiplicative formulation. By enforcing the graphical function for thyroid hormone effect

to yield the value one for all subnormal levels of thyroid hormones, they are only allowed

to abate the existing stimulatory impact of TRH on TSH secretion.

The implied secretion rates are calculated as a function of the logarithm of the ratio

of the stimulant or inhibitory hormone level to its normal level, as in the hypothalamus

sector. Here again, implied secretion is computed before the actual. The calculation of

implied secretion includes both the effect of thyroid hormones and TRH, and excludes the

capacity restriction.

imp TSH sec = eff of TRH on TSH sec × eff of TH on TSH sec × normal TSH sec (5.9)

eff of TRH on TSH sec = f (log(TRH / normal TRH) ) (5.10)

eff of TH on TSH sec = f (log(total TH / normal TH)) (5.11)

where f (log(total TH / normal TH)) and f (log(TRH / normal TRH)) are defined as in

Figure 5.7 and Figure 5.8.

And, in the exact same manner as in the hypothalamus sector, the implied secretion

rate is constrained with capacity limit according to the following set of equations:

30

TSH sec rate = eff of cap on TSH sec × pit cap (5.12)

eff of cap on TSH sec = f (imp TSH sec / pit cap) (5.13)

Figure 5.7. Graphical function for the effect of TRH on TSH secretion.

Figure 5.8. Graphical function for the effect of thyroid hormones on TSH secretion.

Variations in secretion amounts happen in a very short while, almost immediately

(Melmed, 2002). In the long run, the pituitary may adjust its weight in case over- or

understimulation lingers for a sufficiently long period of time, in the same fashion as the

1.1-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8

10.1

0

2

3

4

5

6

7

8

9

log ratio TRH to normal

eff

of

TR

H o

n T

SH

sec

10 0.2 0.4 0.6 0.8

1

0

0.2

0.4

0.6

0.8

log ratio TH to normal

eff

of

TH

on T

SH

sec

31

hypothalamus does. Here again, the implied secretion rates are smoothed via a third order

information delay structure with a delay time of 20 days. In the same manner as clarified in

section 3.1.3, the ratio of these smoothed values to its normal is filtered through a graphical

function. Using the output of that function, a desired weight is calculated at every step.

As mentioned before, the weight of the entire pituitary gland is around 600 mg, and

the anterior lobe constitutes 75% of it. So, the anterior lobe weighs 450 mg. Since the

TSH-secreting cells compose 5% of the anterior lobe, the normal weight of the pituitary is

taken as 22.5 mg. The normal secretion rate of TSH is set to nearly 110 mU/day, and

circulating TSH levels, i.e. the value of the stock, to 6.6 mU (i.e., 2.2 mU/l or µU/ml).

5.3. Thyroid Sector


Thyroid hormones are the primary regulators of metabolic functions in the body, and

almost all cells of the body are regularly subjected to the actions of thyroid hormones.

They are vital for proper development and differentiation of the cells of the human body,

and their deficiency result in serious or even life-threatening diseases.

The human thyroid gland, located just below the larynx, is one of the largest

endocrine glands, and is comprised of two lobes attached to either side of and anterior to

the trachea. The thyroid gland in a healthy adult normally weighs about 20 grams. The

gland is composed of spherical follicles filled with a gel-like substance called colloid, and

surrounded by follicular cells (alternatively called thyrocytes). The primary ingredient of

colloid is a large protein called thyroglobulin, which is the site where the thyroid hormones

are formed and stored (Guyton and Hall, 2006; Rhoades and Bell, 2009).

The synthesis and secretion of thyroid hormones initiates upon the stimulation of the

thyroid by TSH. Binding of TSH with TSH receptors on follicular cells triggers a series of

intracellular functions in these cells to synthesize and release thyroid hormones. For the

32

synthesis of thyroid hormones, iodide is indispensable. So, the first step in the formation of

these hormones is the uptake of available iodide into follicular cells. There, iodide is

converted into an active form called iodine, which is the constituent part of thyroid

hormones. Then, iodine attaches to tyrosine residues within thyroglobulin molecules. This

process, i.e. binding of iodine to tyrosine residues within thyroglobulin, is called

organification. Coupling of one iodine atom with a tyrosine molecule creates

monoiodotyrosine (MIT). When MIT is iodized once more, a diiodotyrosine (DIT)

molecule is formed. So, tyrosine is first iodized to monoiodotyrosine and then to

diiodotyrosine. And, thyroid hormones are formed from these two kinds of molecules.

When one MIT and one DIT molecule couples, one molecule of triiodothyronine, T3, is

formed; and when two DIT’s come together, one molecule of thyroxine, T4, is created

(Bhagavan, 2002; Guyton and Hall, 2006; Rhoades and Bell, 2009). So, formation of one

unit of T4 necessitates double the amount of iodine used for the production of one unit of

T3. The molecular weights of T3 and T4 are 651 and 777 Da, respectively (Bhagavan,

2002), where Da (Dalton) is a unit commonly used to measure mass on atomic or

molecular scale, and has a value of about 1.66054 × 10-24

g (Raymond, 2009).

After being synthesized, thyroid hormones reside in thyroglobulins, unless cleaved

from them on demand. Stimulation of thyroid glandular cells by TSH not only promotes

the synthesis of thyroid hormones, but also the secretion of them. In fact, the most rapid

impact of TSH stimulation on the thyroid is the initiation of breakdown of thyroglobulin,

which results in the secretion of T3 and T4 within half an hour. For this to happen,

follicular cells engulf bits of the colloid, internalizes the colloid droplet into the cells,

disintegrates it by the help of enzymes, allow the hormones to discharge from the storage

element thyroglobulin, and release them into the blood circulation. So, TSH stimulation

simultaneously activates all the secretory mechanisms of thyroid glandular cells, but the

fastest among them is the secretion process. Though synthesis requires a relatively longer

time compared to the secretion process, it still happens within one day under normal

conditions (Guyton and Hall, 2006; Werner et al., 2005; Rhoades and Bell, 2009).

33

One unique characteristic of thyroid gland, in contrast to most endocrine glands, is

that it has a considerably large capacity to store thyroid hormones in itself. In literature, it

is stated that the thyroid gland is able to store approximately two months’ supply of thyroid

hormones in it. Thus, if synthesis of thyroid hormone ceases, the physiologic effects may

not be recognized for about two months (Molina, 2004; Guyton and Hall, 2006;

Kronenberg et al., 2008). In a sense, these stores serve as buffers to guard against sudden

and transient dysfunctions in the thyroid system and thus helps preserve the healthy state of

the body.

Normally, T4 constitutes 93% of the thyroid hormones released daily from the

thyroid gland, and only 7% is T3. The functions of these two hormones are qualitatively

the same; however, they differ from each other in terms of rapidity and intensity of action.

T3 is said to be physiologically active form of the thyroid hormones (Guyton and Hall,

2006; Rhoades and Bell, 2009). T4 can only be synthesized in the thyroid gland and is the

major secretory product of the thyroid gland. The normal production and secretion rate of

T4 from the thyroid is approximately 90 µg/day. On the other hand, only 20% of T3 is

produced directly by the thyroid; the rest is generated by enzymatic removal of one iodine

atom (deiodination) of T4 molecules in peripheral tissues. The production rate of T3,

including the peripheral conversions, is 35 µg/day (Braunwald et al., 2001; Bhagavan,

2002).

Upon stimulation by TSH, T3 and T4 are released into the blood stream. Most of the

T3 and T4 molecules become bound to plasma proteins, only less than 1% of them

circulate in free form. Normally, the range for total plasma concentration is 4-11 µg/dl for

T4, and 75-220 ng/dl for T3. Specifically, 0.02% of T4 and 0.3% of T3 circulates in

unbound form. Merely the free portion of the hormones is biologically active and able to

interact with target cells (Rhoades and Bell, 2009). And so, it is the circulating free

hormones that feed back to the hypothalamus and pituitary to reduce the secretion of TRH

and TSH (Bhagavan, 2002; Rhoades and Bell, 2009).

34

In general, hormones are “cleared” from the plasma by various means involving

metabolic destruction by the tissues, binding with the tissues, excretion by the liver into the

bile, and excretion by the kidneys into the urine (Guyton and Hall, 2006). For our case, it

was recognized early that T4 and T3 were dispersed widely into tissues in addition to the

blood (Hays, 2009). It is stated that about 40% of plasma T4 is converted to T3 and about

40% to reverse triiodothyronine (rT3), which is a metabolically inactive form. The half-life

of T4 in the bloodstream is approximately 7 days, whereas that of circulating T3 is about 1

day (Rhoades and Bell, 2009).

Like the hypothalamus and pituitary, the weight of thyroid gland may also be altered

under certain circumstances. The work of Vassart and Dumont (1992) asserts that

hypophysectomy, hypopituitarism, or an isolated TSH deficiency, i.e. the conditions that

clearly abate the thyroid function, leads to thyroid atrophy. Conversely, chronic stimulation

of the thyroid for some reason is stated to enhance thyroid growth.


The stock variables for the blood levels of thyroid hormones represent the total

circulating amount of them, both bound and unbound (free). Bound and unbound hormones

are in a dynamic equilibrium with each other. However, only the free portion is

biologically active. So, it is merely the small unbound portion of thyroid hormones that is

able to diffuse into peripheral tissues, induce metabolic effects, and that undergoes

deiodination or degradation. When free hormones disperse out of the blood stream, the

equilibrium is disturbed. Thus, the carrier proteins free additional thyroid hormones until

the equilibrium state is restored (Kronenberg et al., 2008; Rhoades and Bell, 2009; Martini,

2007). As far as the scope and the objective of this study are concerned, this process is not

explicitly modeled. Instead, for each case, e.g. diffusion of the hormone into peripheral

tissues, conversion into some other form etc., it is simply assumed that some fraction of the

total circulating thyroid hormones leave the blood stream and diffuse into relevant parts of

the body.

35

Related literature suggests that under certain physiological or pathological conditions

the total circulating hormone content and amount of plasma transport proteins may change,

while the free hormone concentration may remain relatively normal. In the model,

however, the quantity of each thyroid hormone that is unbound is assumed some given

constant fraction of total circulating hormones.

As mentioned earlier, under certain circumstances the weight of the thyroid may

change. There are studies, however, where the volume of the thyroid is measured rather

than its weight (probably because volume measurement does not require the ablation of the

gland as in the assessment of the weight). It is assumed that changes in the volume of the

thyroid go parallel with the changes in the weight. These two notions will be used

interchangeably when necessary.


This sector tries to illustrate the structure of the third and last tier in the control of

thyroid hormone system. The stock-flow diagram of thyroid sector is given in Figure 5.9. It

involves five main stock variables; Thy Wt (thyroid weight), T4 Store, T3 Store, T4 in

Blood and T3 in Blood.

As mentioned before, the thyroid synthesizes and secretes two hormones, T3 and T4.

The structures that represent the mechanisms in the synthetic and secretory regulation of

T3 and T4 are quite similar, though not the same. To begin with T4, there are two stocks

and their associated flows that involve the main measures about T4 in the model. The stock

variable named T4 in Blood represents the overall amount, both bound and unbound, of

circulating T4 in blood. It is subject to a single inflow, and four different outflows. The

single inflow to this stock is the secretion rate of T4. Under normal conditions, T4

secretion rate is set to 90 µg/day.

36

Figure 5.9. Stock-flow diagram of the thyroid sector.

T4 in Blood

T4 clear rate

Thy Wt

Thy wt chg

des thy wt

ratio of TSHto normal

normalTSH normal

TH sec

pot TH sec

TAT

normal

thy wt

T4clear fr

gr for eff ofimp TH secon thy wt

eff of impTH sec on

thy wt

T4 StoreT4 syn rate T4 sec rate

des T4 store

T3 in Blood

T3 clear rateT3 Store

T3 sec rateT3 syn rate

T3 clear fr

Abs rateof T3 bytissues

Convrate to

rT3


des T3 store

thy cap

T4 store adj

disc from

des T4 store

disc from

des T3 store

T3 storeadj

normal Iin thy

ratio of I in thy to

thres

eff of I onthy cap

pot T4 sec

pot T3 sec

pot totalI cons

pot I consfor T4

pot I consfor T3

normalT4 to T3conv fr

T4 to T3conv fr

des T4 syn

des T3 syn

gr for eff of

I on cap

pot T4 synpot T3 syn T3 from

deiod ofT4

T4 to T3

conv rate

normal T3

in blood

gr for effof T3 onperi conv

eff of T3 conc

on peri conv

ratio of T3

to normal

fr of T3 sec

fr ofT4 sec

normalratio of T3

to T4

disc btw pot TH syn

and I rest TH syn

pot total Icons

under Icap rest

ratio of cap rest I

cons to pot

pot TH syn

eff of pref T3syn on red in

T3 syn

gr for eff of

pref T3 syn

ratio of disc btwI rest syn andtotal pot syn to

total pot syn

ratio ofT3 to T4

pos T4sec

gr for THstore cap

eff of T4store cap

ratio ofpos to pot

T4 sec

pos T3 sec

eff of T3

store cap

ratio ofpos to pot

T3 sec

pos I cons

ratio ofpot to pos

I cons

gr for Istorecap

eff of thyI cap

imp TH sec

smth imp TH sec

ratio ofsmth impTH sec to

normal

log ratioof TSH

gr for effof TSH

on TH sec

eff ofTSH onTH sec

gr for

thy capeff of capon TH sec

ratio of impTH sec to

thy cap

normal thy

prod

short smth imp

TH sec

eff ofthy stimon T3 fr

gr forthy stimon T3 fr

ratio ofshort smthimp TH secto normal

eff of thycap on T4

syn

ratio ofdes T4 syn

to cap

thy syn capfor T4

thy syn cap

for T3

eff of thycap onT3 syn

ratio ofdes T3

syn to cap

<TSH>

<thy cap>

<normalTH sec>

<gr forthy cap>

<I in Thy>

<pot THsec>

<gr for

thy cap>

<gr for TH

store cap>

<I in Thy>

<imp TH sec>

ratio of des thy wt

to thy wt

gr for eff

on TAT

disc btw potT3 syn and Irest T3 syn

<fr ofT3 sec>

<fr of T4 sec>

<fr of T4sec>

<fr ofT3 sec>

total normal TH

store

AT forstore restor

<disc btw pot TH syn

and I rest TH syn>

<fr of

T3 sec>

<pot TH syn><T3 syn

rate>

<thy syn cap

for T4>

pot fr ofT3 sec

gr for fr

of T3 sec

total free T3

molecules

total free T4

molecules

I inhib thres

37

As the stock-flow diagram reveals, the amount of T4 to be secreted is withdrawn

from the T4 Store stock. In general, it is not very reasonable to let the outflow of a stock to

act independent from the value of that stock. And also, the body does not utilize its

resources regardless of its present status. The thyroid hormone stores are high when

compared to the daily normal requirements. The work of Bürgi (2010) suggests that when

thyroid hormone synthesis is obstructed somehow, hormone secretion diminishes only

after significant amount of the stores is depleted, which takes several weeks in human.

Considering this proposition, it is assumed that there has to be some limit to the amount of

thyroid hormones that could maximally be withdrawn and secreted from these stores

within a day. This limit is based on the current level of the stores in the model. If the

demand dictated by the hormonal stimuli somehow exceeds or is sufficiently close to the

amount of hormone that the target tissue is willing to maximally release, it would adjust its

sensitivity according to its existing state and respond as a function of both the imposed

requirements and its current status. As the stores diminish, the amount that the gland would

be willing to release declines too. So, the potential rate of T4 secretion is constrained by an

effect function which counts for the capacity of hormone stores. The equation for T4

secretion rate is formulated as shown in Equation 5.14.

T4 sec rate = pot T4 sec × eff of T4 store cap (5.14)

eff of T4 store cap = f (pos T4 sec / pot T4 sec) (5.15)

where f (pos T4 sec / pot T4 sec) is defined as in Figure 5.10.

The input to the graphical effect function in Figure 5.10 is the ratio of possible T4

secretion (pos T4 sec) to potential T4 section (pot T4 sec) where possible T4 secretion is

computed by multiplying some coefficient with the current value of T4 store. Possible T4

secretion means that given the current value of T4 store, the thyroid would avoid to release

more than a certain fraction of its supplies, as explained in the preceding paragraph. This

fraction is selected to be 0.15 in the model. According to this graphical function, the entire

38

potential amount is allowed for secretion if it is not sufficiently close to the upper limit, i.e.

possible secretion. But as the potential value tends toward this maximum possible, the

thyroid becomes reluctant to push its limits, and releases the whole possible amount only

when fairly more than the maximum possible is desired. Consistent with the findings

suggested by Bürgi (2010), when daily demands are approximately at normal levels, the

constraint on daily secretion imposed by possible T4 secretion does not become a binding

one in the model until an appreciable portion of stores is exhausted.

Figure 5.10. Graphical function for the effect of thyroid hormone store capacity.

The second factor that participates in the calculation of T4 secretion is the potential

T4 secretion (pot T4 sec). It is some target amount for T4 secretion rate and is calculated

using Equation 5.16.

pot T4 sec = pot TH sec × fr of T4 sec (5.16)

pot TH sec = eff of cap on TH sec × thy cap (5.17)

To begin with the first element in the equation, potential thyroid hormone secretion

(pot TH sec) is some raw value for total thyroid hormone secretion not yet exposed to

hormone store limitation. It is calculated in the same way as the TRH and TSH secretions

1.50 0.2 0.4 0.6 0.8 1 1.2 1.4

1

0

0.2

0.4

0.6

0.8

ratio of pos to pot T4 sec

eff

of

TH

sto

re c

ap

39

have been; that is, by subjecting the implied total thyroid hormone secretion to the effect of

thyroid capacity. Here, since some additional constraints exist to possibly limit this rate

further, it is attributed to a potential value rather than actual.

imp TH sec = normal TH sec × eff of TSH on TH sec (5.18)

eff of TSH on TH sec = f (log(TSH / normal TSH)) (5.19)

where f (log(TSH / normal TSH)) is depicted in Figure 5.11.

Figure 5.11. The graphical function for the effect of TSH on thyroid hormone secretion.

The calculation of the potential thyroid hormone secretion is done by constraining

the implied thyroid hormone secretion with thyroid capacity, as just mentioned, but the

capacity of the thyroid is computed in a slightly modified way in this case (see Equation

5.20). First, as in the previous two sectors, ten times the normal thyroid productivity is

multiplied with the weight of the thyroid to find the maximal amount for secretion or

synthesis that the thyroid is capable of. Then, this term is further multiplied with the effect

of iodide on thyroid capacity (eff of I on thy cap) to count for the mild impairment in

thyroidal secretion in high intrathyroidal iodide concentrations. There are a number of

1.1-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8

10.1

0

2

3

4

5

6

7

8

9

log ratio TSH to normal

eff

of

TS

H o

n T

H s

ec

40

studies where high doses of iodine are administered to subjects for a short period of time,

and mild but significant decreases in serum T3 and T4 levels and increase in TSH levels

are observed (Vagenakis et al., 1973; Gardner et al., 1988; Paul et al., 1988; Philippou et

al., 1992; Georgitis et al., 1993; Namba et al., 1993; Lemar et al., 1995; McKonigal et al.,

2000). The decrease in thyroid hormone concentrations is attributed to high intrathyroidal

iodine concentrations. So, depending on the concentration, intrathyroidal iodine

concentration may contract the capacity of the thyroid.

thy cap = normal thy prod × Thy Wt × 10 × eff of I on thy cap (5.20)

eff of I on thy cap = f (I in Thy / I inhib thres) (5.21)

where f(I in Thy / I inhib thres) is defined as in Figure 5.12.

Figure 5.12. Graphical function for the effect of iodine on thyroid capacity.

According to the graphical function in Figure 5.12, as the iodine concentration within

the gland tends to the threshold value, the capacity of the thyroid declines. But the real

inhibitory effect takes place when the iodine levels surpass the threshold value because

only then the total capacity of the thyroid falls below the value that is necessitated for

normal hormone production. As the iodine levels exceed the threshold more, the inhibitory

1.50.9 1 1.1 1.2 1.3 1.4

1

0.085

0.2

0.4

0.6

0.8

ratio of I in thy to thres

eff

of

I on t

hy c

ap

41

effect on thyroid capacity rises too. To find the inhibitory threshold, firstly the thyroidal

iodine levels are smoothed with a third order information delay structure using a delay time

of 30 days, and then multiplied by 1.1. Then, the maximum of this value and 400 will be

assigned to I inhib thres because it is assumed that this threshold cannot fall below 400 µg.

The graphical function for the effect of capacity on thyroid hormone secretion (eff of

cap on TH sec) is not explicitly shown because it is the same as the ones in the previous

two sectors.

To figure only the amount of T4 secretion out of the total thyroid hormone secretion,

the potential total secretion is multiplied with the fraction of T4 secretion (fr of T4 sec). As

mentioned before, a specific fraction of secretion is reserved for each of the two thyroid

hormones. Normally, this fraction is approximately 93% (90/97) for T4 in the model.

However, it is not a constant and can be altered under certain conditions. The way this

fraction is revised will be elucidated later in this section.

As explained in section 5.3.1, the majority of T3 is obtained via deiodination of T4

molecules. Under normal conditions, the glandular secretion of T3 comprises only 20% of

the total T3 release. So, of the daily 35 µg T3 secretion, 28 µg is acquired through the

conversion of T4 to T3. The outflow named T4 to T3 conv rate serves for this purpose. As

is the fraction of T4 productivity for secretion, the fraction of T4 to be deiodinated is

variable too. The conditions under which this fraction changes will be clarified later in this

section.

Other two outflows from T4 in Blood are conversion rate to rT3 (Conv rate to rT3)

and (Abs rate of T4 by tissues). The values of these flows are computed by multiplying the

current stock value with some constant fraction. Normally, 32 µg of T4 is assumed to be

deiodinated into rT3, which comprises about 36% of the daily T4 secretion. The last

outflow, called T4 clear rate, stands for the rate of (renal) clearance of T4 (with the half-

life of 7 days) from the blood.

42

The flows into and from the stock variable for the level of T3 in blood resemble to

those of T4 in blood. There are four flows that influence the level of T3 in blood. The first

inflow to T3 in blood is its secretion rate. T3 secretion rate is formulated in the same

manner as T4 secretion rate. The fraction of secretion for T3 is taken approximately 7%

(7/97) under normal conditions. This fraction may vary under certain circumstances, as

does the fraction of productivity for T4.

The second inflow to T3 in Blood is the rate of deiodination of T4 into T3. The

reason why the related outflow from T4 doesn’t directly enter into T3 in Blood stock is that

some numerical adjustment was required to account for the mass change due to departure

of iodine atoms from T4 molecules in the conversion process. As mentioned in T4 case,

the value of the outflow named Abs rate of T3 by tissues is calculated by multiplying some

coefficient with the stock value. Lastly, T3 clearance rate (T3 clear rate) is the renal

clearance rate of T3 from the blood (with a half-life of 1 day). So, the only difference from

T4 is that T3 in blood does not have an outflow analogous to the rate of conversion of T4

to rT3; all other flows are qualitatively the same as those of T4 in Blood.

As mentioned in detail in section 3.3.1, the thyroid has the capacity to store

appreciable amounts of preformed thyroid hormones. The two stocks in the model, T4

Store and T3 Store, stand for these hormone stores. Normally, these stocks contain two

months’ supply of thyroid hormones. The set point is 5400 µg for T4 store, and 420 µg for

T3 store. The only inflow to these stocks is the synthesis rate of the related hormone. To

determine the synthesis rate of either thyroid hormone, a desired synthesis rate is

calculated at first. The classical stock adjustment formulation is used when constructing

the equation for desired synthesis rate. The associated equations for T3 are shown in

Equations 5.22 - 5.24. The related equations for T4 are of the same form as T3, and

therefore will not be shown explicitly anew.

The first ingredient in desired T3 synthesis is its secretion rate which acts to

replenish the usual daily release rate from the stores. The second term is the stock

adjustment term that helps close the gap between the desired and the current level of the

43

store. So, if the T3 store were valued below the desired level, then this formulation would

not only compensate for the regular daily losses but also for the gap between the normal

and current stock value. Conversely, if the stock levels were sufficiently above the desired

levels, then the adjustment term would take a negative value to facilitate the convergence

to normal stock values.

des T3 syn rate = T3 sec rate + pot T3 store adj (5.22)

pot T3 store adj = disc from des T3 store / AT for store restor (5.23)

disc from des T3 store = des T3 store − T3 Store (5.24)

The desired levels of hormone stores are not constant; they change according to the

changes in the secretory fractions of thyroid hormones. In literature, it is stated that

intrathyroidal fractions of hormone stores are in concordance with the fractional secretion

rates of T3 and T4 from the thyroid when preferential secretion of T3 is the case (Brent,

2010). Thus, the total normal amount of hormone store within the thyroid (5820 μg) is

multiplied by the related secretory fraction to figure the desired level for that hormone

store.

des T4 store = (total normal TH store) × fr of T4 sec (5.25)

des T3 store = (total normal TH store) × fr of T3 sec (5.26)

In cases where hormone stores are above their desired level, it is possible for the

desired synthesis rate to take negative values. Though it is conceptually not illogical for a

“desired” quantity to take a negative value, a negative actual synthesis rate is neither

plausible nor possible. In other words, the gland wouldn’t freely discharge its excessive

content just to get rid of it. Hence, when subjecting this desired value to some capacity

constraints, the maximum of this desired value and zero will be taken. Lastly, as mentioned

earlier, the adjustment time for store restoration (AT for store restor) is an indicator of how

fast the gland is thought to be likely to close the gap between the target and current stock

value, and is taken as 30 days here.

44

After the desired synthesis rate is set, it is firstly filtered through some capacity

constraint, as done in the determination of secretion rates of thyroid hormones. This

capacity is an upper bound for synthesis rate of T4 that the thyroid gland is thought to be

capable of, as it was for the secretion rates. One should note that reducing the capacity of

the thyroid only in extremely high concentrations of iodine does not mean that the cases

where the intraglandular quantity of iodine itself doesn’t suffice to meet the requirements

for the synthesis of hormones are ignored. The potential synthesis rate will be further

constrained at the time when the iodine availability is checked. The corresponding set of

equations involved in the calculation of the potential synthesis is depicted below.

pot T3 syn rate = thy syn cap for T3 × eff of thy cap on T3 syn (5.27)

thy syn cap for T3 = thy cap × fr of T3 sec (5.28)

eff of thy cap on T3 syn = f (max{des T3 syn , 0} / thy syn cap for T3) (5.29)

As Equation 5.26 reveals, by multiplying the fraction of T3 secretion with the total

capacity, the relevant portion of thyroidal capacity reserved for T3 synthesis (thy syn cap

for T3) is taken to restrain the (nonnegative) desired amount of T3 synthesis. And, the

nominator of the input to the effect of thyroid capacity on T3 synthesis is taken as the

maximum of the desired T3 synthesis and zero in order to be able to discard negative

synthesis rates. The graphical function for this capacity effect is the same as the others,

and thus not presented over again.

The last step that needs to be taken before deciding on the actual synthesis rates is to

check the iodine availability. If the iodine demand for thyroid hormone synthesis cannot be

fully met, the available amount of iodine is redistributed for the synthesis of two thyroid

hormones not according to the former fractions but rather in favor of T3.

The maintenance of normal levels of T3 in the body is of primary importance for its

being the biologically active form, i.e. the one that is utilized by the cells, of thyroid

hormones. So, the deficiency of T3 becomes more of an issue as compared to that of T4,

45

and necessitates effective balancing mechanisms to guard against life-threatening

situations. Related literature suggests that unless the impairment of thyroid hormone

production is severe, T3 levels in blood remain within normal limits (Werner et al., 2005).

Thus, the measurement of blood T3 levels does not provide differentiating information in

the diagnosis of hypothyroidism.

It is stated that numerous intrathyroidal and extrathyroidal mechanisms act in concert

in order to retain T3 availability. Within the thyroid gland, both the secretion and synthesis

of T3 is favored to T4. Moreover, peripheral conversion of T4 to T3 increases in the

hypothyroid state. So, at the expense of decreasing the circulating T4 concentrations, the

mentioned compensatory mechanisms operate to preserve normal, healthy T3 levels

(Brent, 2010; Werner et al., 2005; Greenstein and Wood, 2011). One of the most common

causes of hypothyroidism is iodine deficiency. So, if an implication of iodine deficiency is

detected during the availability check, synthesis of T3 will be favored. But the point where

iodine availability checked is not the only one where T3 is favored; the preferential T3

synthesis will again become a current issue when the secretory fractions of thyroid

hormones are revised.

After determining the potential synthesis rate, the amount of iodine necessitated is

calculated by simply multiplying that amount with the weight percentage of iodine in T3

molecule. The same procedure that is explained up to this point is applied for determining

T4 synthesis rate too. So, at this point, the total amount of iodine required for total

potential thyroid hormone synthesis is at hand. To check the adequacy of iodine supplies,

the overall amount of necessary iodine is compared to the possible amount. If consumption

of this potential quantity is not fully permitted, the fractions of productivity reserved for

each hormone is revised in favor of T3 to mitigate the vital implications of iodine

deficiency.

The rationale behind the constrained utilization of intraglandular hormone stores is

extrapolated to the consumption of iodine stores too. The first step to examine the

availability of iodine supplies is to send the ratio of the potential iodine consumption (pot

46

total I cons) to the maximum possible amount (pos I cons) to a graphical effect function as

input. The graphical function is the same as the functions that stand for the effect of

hormone store capacities, and thus is not shown explicitly. The maximum possible amount

of daily iodine consumption is presumably set as 15% of the existing intrathyroidal iodine

stock. The value that this function yields is then multiplied with the maximum permissible

amount to obtain the potential iodine consumption under iodine restriction (pot total I cons

under I cap rest), as illustrated in Equation 5.30.

pot total I cons under I cap rest = pos I cons × eff of thy I cap (5.30)

If the potential iodine consumption lies decently below the maximum tolerable

amount, then all the iodine demanded can be delivered. As the sought quantity approaches

to the limit, the gland tends to act more economical and agrees to give the daily maximum

only when fairly higher quantities are requested. This kind of control on the outflow of the

stock is also implemented in the thyroid hormone stores, as explained before.

Following the determination of accessible quantity of iodine, the synthesis rate

allocated to each hormone is to be revised. For this purpose, the discrepancy between the

synthesis with the permitted amount of iodine and the potential synthesis is calculated.

Then, this discrepancy is divided to the value of potential synthesis rate (ratio of disc btw I

rest TH syn and pot TH syn to pot TH syn). In the model, this ratio is regarded as an

indicator of the severity of iodine deficiency, and thus the potential hypothyroidism. A

graphical effect function is defined that uses this ratio as input (see Figure 5.13).

The decreasing function in Figure 5.13 is used to attenuate the amount that will be

subtracted from the potential T3 synthesis due to iodine availability constraint. If the

preferential synthesis of T3 were not the case, the potential synthesis rates of each

hormone would be multiplied with ratio of cap rest I cons to pot to find the actual

synthesis rates. Since T3 is the critical hormone, in cases where the iodine supply is a

binding constraint, the reduction in T3 synthesis should be relatively smaller than that of

47

T4. The function eff of pref T3 syn on red in T3 syn is created to decrease the quantity that

is subtracted from the potential T3 synthesis rate. Because the value that the function in

Figure 5.13 yields ranges from one to zero, the resultant fraction declines as the

discrepancy increases, i.e. as the consumable quantity of iodine declines.

Figure 5.13. Graphical function for the effect of preferential T3 synthesis on reduction in

T3 synthesis.

When correcting the shares of production rates for T3 and T4, two conditions must

be satisfied. First, the synthesis rate of the hormone under iodine restriction should not

exceed its potential synthesis rate. Second, the revised synthesis rate should not go beyond

the total potential synthesis rate. Subtracting some fraction of the discrepancy from the

total potential synthesis rate is enough to satisfy the first condition, but not the second one.

The second situation can happen when the total iodine-constrained synthesis rate is below

the initial one necessitated by T3. The denominator of Equation 5.31 helps hinder this

situation.

The nominator of Equation 5.31 will always be less than or equal to the potential T3

synthesis rate (which is the rate not yet confined to iodine adequacy). And, the

denominator of the equation can take a value greater than one when the second condition

explained above is active. So, as the allowable total synthesis rate approaches to zero, the

10 0.2 0.4 0.6 0.8

1

0

0.2

0.4

0.6

0.8

ratio of disc btw I rest TH syn and pot TH syn to pot TH syn

eff

of

pre

f T

3 s

yn o

n r

ed i

n T

3 s

yn

48

nominator of the ratio within the maximum operator and the nominator of the equation

tend to cancel out each other. Thereby, the resultant synthesis rate is prevented to exceed

the feasible rate.

synTH rest I and synTH pot btw disc - synTH pot

synT3 pot

synT3 in red on synT3 pref of eff synT3 rest I and synT3 pot btw disc synT3 pot

= rate synT3

,1max

(5.31)

Since T4 is the secondary hormone in the calculations, its synthesis rate is just the

remaining of the total permissible synthesis rate. The related equation is shown below.

T4 syn rate = pot TH syn − disc btw pot TH syn and I rest TH syn − T3 syn rate (5.32)

One should note that after checking the possible amount, altering the potential

synthesis rates in favor of T3 does not hurt the initial principle of obtaining a feasible

amount of thyroidal iodine to be consumed because less iodine is required for unit T3

synthesis as compared to T4. So, the ultimate amount of iodine expended will always be

less than or equal to the quantity that is found to be feasible after the availability check.

Another mechanism that operates to preserve T3 availability is the adaptability of the

conversion fraction of T4 to T3. To ensure the T3 availability, this fraction increases to

some extent in hypothyroid state. The fraction is adjusted as a function of the circulating

T3 levels relative to its set point. The related graphical effect function is illustrated in

Figure 5.14. As the ratio of currently circulating T3 levels to the normal levels decrease,

the value that the function yields increases and then saturates after some point. This means,

if the T3 level falls below its set point, the rate of conversion rises to compensate for the

gap.

49

Figure 5.14. Graphical function for the effect of T3 concentration on peripheral

conversion.

As mentioned earlier in this section, fractions of T3 and T4 secretion are not

constant. The modifications in these fractions are done in three phases. Firstly, circulating

T3 and T4 levels don’t necessarily differ from their set points with the same proportion.

Thus, it is thought that it wouldn’t be very reasonable to allocate the total secretion rate

regardless of the individual differences from the set points by using just some constant

fractions. For this purpose, the overall thyroidal secretion is distributed inversely

proportional (because thyroid hormones feed back negatively) to the ratio of the related

hormone to its normal value. Equation 5.33 shows how the formulation for this first part is

derived. For ease of demonstration, variable name x is used for the fraction of T3 secretion

not yet undergone the second and third steps.

As mentioned earlier in this section, 7/97 and 90/97 are the normal thyroidal

secretion fractions of T3 and T4, respectively. This first part of the formulation does not

explicitly lead to preferential secretion of T3 in hypothyroid state; it just fairly distributes.

After redistributing the fractions according to the individual deviations of two

hormones from their set points, the second step is to consider the effect of the level of

thyroid stimulation on the fractions. Normally, T3 of thyroidal origin comprises 20% of

10 0.2 0.4 0.6 0.8

1.7

0

0.4

0.8

1.2

ratio of T3 to normal

eff

of

T3 c

onc

on p

eri

conv

50

total T3 production in the body. However, related literature reports that in patients with

thyroid hyperfunction or hypofunction, a relatively higher fraction of the total T3 is

delivered by the thyroid (Laurberg, 1984; Brent, 2008; Brent, 2010). Equation 5.34 shows

the second step in the calculation of fraction of T3 secretion.

T4 to T3 of ratio normal90

7T4 to T3 of ratio

T4 to T3 of ratio normal90

7

x

T4 to T3 of ratio normal

T4 to T3 of ratio

x

T4 to T3 of ratio

T4 to T3 of ratio normal90/97

7/97

x1

x

90

71

1 (5.33)

fr T3 on thy stim of eff

T4 to T3 of ratio normal + T4 to T3 of ratio

T4 to T3 of ratio normal

= secT3 of fr pot

90

790

7

(5.34)

The findings about preferential synthesis and secretion of T3 in hypothyroid state

were previously mentioned in this section. Besides, it has been documented that in the

thyroids of patients with Graves’ disease, a common source of hyperthyroidism, T3/T4 was

consistently higher and was not due to iodine deficiency (Izumi and Larsen, 1977), and that

thyroidal secretion of T3 rises from approximately 20% to 30% in Graves’ disease (Brent,

2008). The common point for cases where thyroidal secretion of T3 is relatively higher

compared to the normal physiological conditions is that the thyroid is overstimulated.

Depending on the capability of the thyroid, this hyperstimulation may result in

hyperthyroidism or hypothyroidism, but the “potential demand” that the thyroid faces is

51

high in either case. In this respect, the ratio of implied thyroidal secretion to the normal can

be taken as an indicator of stimulation level. But, it is thought that sudden shifts in the

level of thyroid stimulation should not alter these fractions instantaneously; persistence in

hyperstimulation must be sought. Thus, the smoothed version of this ratio rather than its

instantaneous value is allowed to affect these fractions. Smoothing is achieved through a

third order information delay structure with a delay time of 10 days.

Figure 5.15. Graphical function for the effect of thyroid stimulation on T3 secretion

fraction.

Lastly, the fraction of T3 secretion is calculated as a function the potential value for

this fraction. This final step is performed to prevent fr of T3 sec from exceeding the value

one in potential (unrealistically) extreme cases because of multiplication with the

coefficient that the effect of thyroid stimulation yields. The related graphical function is

shown in Figure 5.16.

The above mentioned mechanism directly counts for preferential T3 secretion. In

addition, as aforementioned, the synthesis fractions are also modified in favor of T3 in

cases of iodine deficiency. Hence, when that is the case, T3 stores will surely persist

longer than T4 stores and availability of hormone supplies won’t easily become a binding

constraint on T3 release, which in fact is an indirect reference to preferential secretion too.

51 1.5 2 2.5 3 3.5 4 4.5

2.5

1

1.5

2

ratio of short smth imp TH sec to normal

eff

of

thy s

tim

on T

3 f

r

52

Figure 5.16. Graphical function for the fraction of T3 secretion.

As the hypothalamus and pituitary do, the thyroid can change its weight under

certain circumstances. The structure related to thyroid weight adjustments functions in the

same manner as in the previous two sectors. So, the stock that stands for the weight of the

thyroid is subjected to a single adjustment flow. This adjustment flow is formulated in the

same way as the adjustment flow of the hypothalamus and pituitary, and thus will not be

explained anew.

5.4. Iodine Sector


Iodine is a requisite substrate for the synthesis of thyroid hormones. It is present in

foods usually as iodide, which is the inorganic form of iodine. Iodide is available in the

form of iodized table salt, and also various kinds of food exist which are rich in iodide; e.g.

seafood, kelp, spinach, soybeans, garlic etc. After being ingested, iodide is absorbed nearly

completely in the stomach and duodenum. Related literature suggests that the absorption of

dietary iodide is greater than 90% in healthy adults (Zimmermann, 2009). The absorbed

iodide then diffuses in blood. Iodide is cleared from circulation mainly by the thyroid and

1.10.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08

1

0.9

0.92

0.94

0.96

0.98

pot fr of T3 sec

fr o

f T

3 s

ec

53

kidney. The clearance of circulating iodide by the thyroid is called iodide trapping. Within

the thyroid gland, iodides are converted into an oxidized form of iodine. Once iodides

undergo oxidation process, they are ready to participate in the production of thyroid

hormones (Guyton and Hall, 2006).

Due to its vital role in the functioning of the whole body, the thyroid gland is

equipped with buffers to preserve the healthy state in case thyroid function is somehow

impaired. As mentioned before, the thyroid reserves a considerably large amount of

preformed thyroid hormones in it which is available for secretion on demand. Besides the

hormone stocks, the thyroid gland has a large iodine supply which allows to maintain

thyroid hormone synthesis in lack of iodine intake for some time. That is, in case of

inadequate iodine intake, hormone synthesis persists until the available iodine stores has

been depleted, unless, of course, the thyroid itself dysfunctions. In literature, it is stated

that the normal dietary iodine intake is 150 µg/day, and the amount of intrathyroidal iodine

stores range from 10 to 20 milligrams (Van Vliet and Polak, 2007).

Iodide uptake from the circulation into the thyroid is primarily controlled by TSH

(Guyton and Hall, 2006; Nyström et al., 2011). The rate of iodide trapping by the thyroid is

altered depending on the magnitude of TSH stimulation; if TSH signals increase, amount

of iodide trapped also rises, and if the stimuli decline, iodide trapping diminishes too. In

addition to this, related literature postulates that the thyroid is able to “sense” its iodine

content and adjust its sensitivity to TSH stimulation (Yadav, 2008). So, the intrathyroidal

iodine supply can be autoregulated by an internal feedback mechanism which controls the

intraglandular utilization of iodine and the thyroid response to TSH stimulation (Bhagavan,

2002).


The iodine sector is composed of three stocks. Two of these stocks have real physical

counterparts in the body, but the third one serves as an intermediate step in the calculation

of iodide trapping rate. The stock-flow diagram of this sector is depicted in Figure 5.17.

54

Figure 5.17. Stock-flow diagram of the iodine sector.

As can be seen in Figure 5.17, the stock Iodine in Blood is altered via two inflows

and two outflows. The first inflow to the stock is the absorbed portion of dietary iodine (I

abs rate), and the retained iodine from the deiodination or peripheral catabolism of thyroid

hormones (I from deiod) is the second one. The normal dietary iodine intake is taken as

150 µg and the absorption fraction as 95%. The outflow Excretion of I represents the renal

clearance of plasma iodine, and Trap rate the rate of clearance of iodide by the thyroid.

The thyroid can accommodate itself to the current iodine status of the body. If there

is inadequate iodine intake, then the thyroid traps a higher percentage of iodine, and vice

versa. Since the impact of TSH on synthetic and secretory activities of the thyroid is

I in Blood

I abs rate I excr

normal I in thy

excr fr

ratio of thy I conc

to normal

I in Thy

Trap rate

I cons

gr for eff of

TSH on I trap

eff of TSH on I

trapping

I from deiod

Pot Trap Fr

chg in trap fr

disc

Del for trap fr

des trap fr

gr for destrap fr

I cons for T3

I cons for T4

I intakeabs fr of I

eff of thy wt

on I trap

gr for effof thy wton I trap log ratio of

TSH tonormal

I from T4 in tissues

I from T3 in tissues

I from T3 convI from rT3

retained I

55

evident within a short period of time as mentioned earlier, in the model TSH exerts its

effect on iodide trapping rate instantaneously too. But, in case intrathyroidal iodine

concentration is not at its normal, the adaptation of the trapping rate is assumed to occur

with one-day delay. The stock Pot Trap Fr serves for this purpose. First, a desired trapping

fraction is calculated as a function of the ratio of current intrathyroidal iodine content to

the normal (see Figure 5.18). According to this desired fraction, the value of the

adjustment flow to the stock is revised (as in the adjustment flows of gland weights). But,

the value of the stock is some raw value for trapping fraction and is not yet exposed to the

effect of TSH stimuli. Equation 5.35 shows the formulation for trapping rate (Trap rate).

Figure 5.18. Graphical function for desired trapping fraction.

Trap rate = Pot Trap Fr × I in Blood × eff of TSH on I trap × eff of thy wt on trap cap

(5.35)

According to Equation 5.35, the trapping fraction is either amplified or contracted

depending on the magnitude of TSH stimuli. TSH and intrathyroidal regulatory

mechanisms alter the trapping fraction to a certain extent. In addition to these two factors,

it is stated that the enlargement of the thyroid to raises its capacity to accumulate iodide

from the blood (Rhoades and Bell, 2009). Bearing this in mind, the potential trapping

fraction is further multiplied with an effect function (eff of thy wt on trap cap) that aims at

50 0.5 1 1.5 2 2.5 3 3.5 4 4.5

0.5

0

0.1

0.2

0.3

0.4

ratio of thy I conc to normal

des

tra

p f

r

56

depicting the dependency of trapping capacity on the weight of the thyroid. The graphical

function is depicted in Figure 5.20.

Figure 5.19. Graphical function for the effect of TSH on iodide trapping.

Figure 5.20. Graphical function for the effect of thyroid weight on iodide trapping.

Lastly, the outflow I cons represents the total iodine loss from available stores due to

its usage in thyroid hormone synthesis and is simply the sum of the iodine consumptions

necessitated by T3 synthesis rate and T4 synthesis rate.

1-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8

1.4

0

0.2

0.4

0.6

0.8

1

1.2

log ratio of TSH to normal

gr

for

eff

of

TS

H o

n I

tra

p

30 0.5 1 1.5 2 2.5

1.3

0

0.2

0.4

0.6

0.8

1

Thy Wt / normal thy wt

gr

for

eff

of

thy w

t on I

tra

p

57

To summarize this chapter, a simplified stock flow diagram of the whole model is

given in Figure 5.21.

Figure 5.21. Simplified stock-flow diagram of the model.

T4 in BloodT4 clear

rate

Thy WtThy

wt chgdes

thy wt

eff of TSHon TH sec

impTH sec

TSH

Pit Wt

TSHsec rate

TSHclear rate

Pit wtchg

imp TSH sec

eff of TRHon TSH sec

des pit wt

T4clear fr

TSHclear fr

TRH

Hypo Wt

TRHsec rate

TRHclear rate

Hypowt chg

imp TRH sec

eff of TH onTRH sec

des hypowt

TRH clear fr

T4 StoreT4 syn rate T4 sec rate

T3 in Blood

T3 clearrate

T3 Store

T3 sec rateT3 syn rate

T4 to T3conv rate

T3clear fr


Convrate torT3


eff of TH onTSH sec

des T4store

des T3store

I in Blood

I in Thy

I absrate

Trap rate

I cons

I consfor T3

I consfor T4

I fromdeiod

pos I cons

hypo cap pit cap

thy cap

pot total I cons

eff of prefT3 syn on

red in T3 syn

pot T3 syn

pot T4 syn

<thy cap>

<thy cap>

fr of T3 sec

fr of T4 sec

<T4 in Blood>

<T3 in Blood>

<T3 syn rate>

<T4 syn rate> <fr of T3 sec>

<imp TH sec><thy cap>

I intake

<TSH>

<Thy Wt>

pot TH syn

ratio of caprest I cons

to pot

<pot T3 syn>

<I in Thy>

58

6. VALIDATION AND ANALYSIS OF THE MODEL

Model validation is a procedure to check if the model is able to adequately illustrate

the real problem, as far as the purpose of the modelling study is concerned. Model validity

is tested both in structural and behavioural aspects, structural being of primary importance

in system dynamics models. So, the logical course of model validation is first to test the

validity of the structure, and then begin to check the behaviour accuracy. Structural

validity tests check if the structure of the model is able to satisfactorily reflect the actual

relations that exist in the real system. Once the model succeeds in the structural tests and

sufficient confidence is established in the model structure, behaviour validity tests are

implemented to check if the dynamic behaviours produced by the model can sufficiently

reflect the real patterns of concern (Barlas, 2002; Barlas 1996).

The validity check, especially the structural one, is in fact continuously achieved

during the development of the model, and should not be perceived as a completely isolated

phase. In this study, a significant portion of structural validation has been done during the

process of model construction. It is done by verifying the structure both with the existing

information in literature and through the interviews with medical doctors. The aim of this

chapter is to represent the outputs of the simulations conducted under certain scenarios to

further check the structural validity of the model that is described in the preceding chapter.

The model is simulated using Vensim software. As mentioned before, the time unit

of the model is one day. The time horizon of the simulations is selected long enough to

observe the system behaviour evidently, ranging from a few days to several years. For all

the simulation runs, a sufficiently small time step is selected (DT=1/128).

59

6.1. Equilibrium Behaviour

When all the variables are initially set to their equilibrium (normal) levels, all

hormones stay constant at their equilibrium values, as expected.

Figure 6.1. T3 (left top), T4 (right top), TRH (lower left), and TSH (lower right)

concentrations at equilibrium.

6.2. Base Run

Here, the initial value of T4 in blood is set to three times its normal value (720 µg).

All the other variables are set to their normal values initially.

Firstly, since T4 is above its equilibrium value initially, it gradually decays to restore

the equilibrium value and stabilizes there. It takes a few days for T4 to converge to the

equilibrium value because its half-life is seven days. Secondly, since T3 is largely obtained

via the deiodination of T4, T3 concentration also rises with the initial shift in T4.

0.2

0.175

0.15

0.125

0.1

0 1 2 3 4 5

Time (Day)

mic

rogr

ams/

dL

10

9

8

7

6

0 1 2 3 4 5

Time (Day)m

icro

gram

s/dL

3

2.5

2

1.5

1

0 1 2 3 4 5

Time (Day)

mic

roun

its/m

l

0.3

0.25

0.2

0.15

0.1

0 1 2 3 4 5

Time (Day)

nano

gram

s/m

l

60

Figure 6.2. T4 concentration in base run.

Figure 6.3. T3 concentration in base run.

Figure 6.4. TSH concentration in base run.

30

22.5

15

7.5

0

0 0.60 1.20 1.80 2.40 3 3.60

Time (Day)

mic

rogra

ms/

dL

0.4

0.3

0.2

0.1

0

0 0.60 1.20 1.80 2.40 3 3.60

Time (Day)

mic

rog

ram

s/d

L

3

2.25

1.5

0.75

0

0 0.60 1.20 1.80 2.40 3 3.60

Time (Day)

mic

rou

nits/

ml

61

Due to the negative feedback effect of thyroid hormones on the release of TRH and

TSH, their concentrations decline too. As thyroid hormones converge to the equilibrium,

TSH and TRH restore their normal levels (see Figure 6.4 and Figure 6.5).

Figure 6.5. TRH concentration in base run.

6.3. TRH Injection Test

In the work of Snyder and Utiger (1972), a TRH stimulation test is performed on six

normal healthy subjects. 25 µg TRH is injected to each of the six subjects at t=0, and blood

samples are collected to measure the TSH levels in blood (see Figure 6.6).

To replicate this test, all the variables are set to their equilibrium levels initially, and

25 µg TRH is assumed to be injected at t=0. For the model output to be comparable to real

data, only the first three-hour portion of the simulation run is displayed in Figure 6.7.

Comparing the two graphs in Figure 6.6 and Figure 6.7, it can be said that the overall

behaviour and even the value of the peak point of TSH from the model highly matches

with those of real data. The time of the hormone to reach its maximum takes somewhat

longer in the model; but since the time unit of the model is one day and relatively long-

term dynamics of hormones are the point of interest in this study, this slight difference

does not hurt the validity of the model.

0.24

0.18

0.12

0.06

0

0 0.60 1.20 1.80 2.40 3 3.60

Time (Day)

nan

og

ram

s/m

l

62

Figure 6.6. Average TSH concentration of six normal subjects when 25 µg TRH is injected

at t=0 (Snyder and Utiger, 1972).

Figure 6.7. TSH concentration when 25 µg TRH is injected at t=0.

6.4. Ten-Fold Increase in T4 Secretion for One Hour

In literature, it is stated that if T4 secretion were increased ten-fold for one hour, we

would expect the total T4 concentration in blood to increase by 12% (Goodman, 2009).

20

15

10

5

0

0 0.019 0.038 0.058 0.077 0.096 0.115

Time (Day)

mic

rounits/

ml

63

Here, it is assumed that from t=0 to t=1/24, T4 secretion rate is ten times its normal value,

i.e. 900 µg. After t=1/24, no external intervention is applied on T4 secretion. The

behaviour of T4 under this scenario is shown in Figure 6.8.

Figure 6.8. T4 concentration when its secretion is increased ten-fold for one hour.

Figure 6.9. T3 concentration when T4 secretion is increased ten-fold for one hour.

Increasing the T4 secretion for one hour causes T4 levels to rise until the end of the

first hour, as expected. The amount of increase in T4 in the model outputs is about 13%

which is quite consistent with the data in literature. Since no component of the system is

9.5

9

8.5

8

7.5

0 0.20 0.40 0.60 0.80 1 1.20 1.40

Time (Day)

mic

rogra

ms/

dL

0.17

0.165

0.16

0.155

0.15

0 0.20 0.40 0.60 0.80 1 1.20 1.40

Time (Day)

mic

rog

ram

s/d

L

64

interfered with after the first day, T4 levels start to decrease thereafter, and reach

equilibrium in about one day.

Under this scenario, it is not only T4 whose value is disturbed from equilibrium. A

significant portion of T3 in the body is formed via conversion of T4 to T3. Because of this,

T3 levels also rise in this case. But after a very short while, it drops to values that are

below the baseline values to compensate for the high circulating T4 and then returns

almost to normal at the end of the first day (see Figure 6.9).

Figure 6.10. TRH concentration when T4 secretion is increased ten-fold for one hour.

Figure 6.11. TSH concentration when T4 secretion is increased ten-fold for one hour.

0.22

0.195

0.17

0.145

0.12

0 0.20 0.40 0.60 0.80 1 1.20 1.40

Time (Day)

nan

og

ram

s/m

l

2.5

2

1.5

1

0.5

0 0.20 0.40 0.60 0.80 1 1.20 1.40

Time (Day)

mic

rounits/

ml

65

As a result of negative feedback effect of thyroid hormones on both the

hypothalamus and pituitary, TRH and TSH levels decline. As seen in Figure 6.10 and

Figure 6.11, TRH and TSH levels in the body first decline and then rise so as to enable the

body to restore the equilibrium state.

6.5. Zero T4 Secretion for One Hour

The work of Goodman (2009) suggests that if T4 secretion were stopped for one

hour, we would expect its concentration to decrease by only 1%. So, in this scenario, the

secretion rate of T4 is set to zero for one hour at t=0, and after one hour the model is left to

operate by its own.

Figure 6.12. T4 concentration when T4 secretion is stopped for one hour.

As the secretion rate of T4 cannot be modulated with the feedback loops for the first

hour, its concentration rises initially inevitably. As the external intervention ceases,

circulating T4 levels quickly restore to normal levels. The lowermost point in T4

concentration shown in Figure 6.12 gives a 1.45% reduction in T4 concentration.

As in the previous scenario, the change in T3 concentration goes parallel with the

change in T4 concentration as the primary source of circulating T3 is the deiodination of

8.050

8

7.95

7.9

7.85

0 0.20 0.40 0.60 0.80 1 1.20 1.40

Time (Day)

mic

rogra

ms/

dL

66

T4 to form T3. Since a number of mechanisms work in concert to preserve the T3

availability in body, it starts to rise to values that are above normal and returns to normal

values as T4 stabilizes (see Figure 6.13).

Figure 6.13. T3 concentration when T4 secretion is stopped for one hour.

TRH and TSH concentrations show qualitatively the same behaviour in this scenario.

Thus, only TSH is pictorially shown in Figure 6.14. As expected, TSH initially rises to

compensate for the decline in thyroid hormone levels, and then gradually reaches the

equilibrium.

Figure 6.14. TSH concentration when T4 secretion is stopped for one hour.

0.17

0.169

0.168

0.167

0.166

0 0.20 0.40 0.60 0.80 1 1.20 1.40

Time (Day)

mic

rog

ram

s/d

L

2.4

2.345

2.29

2.235

2.18

0 0.20 0.40 0.60 0.80 1 1.20 1.40

Time (Day)

mic

rounits/

ml

67

6.6. Hypophysectomy

Hypophysectomy, as stated before, means the complete removal of the pituitary

gland. In reality, a person cannot survive long in the absence of such a critical gland

without any therapeutic intervention. However, for the sake of the validation of the model,

we assume that the person continues to live.

Figure 6.15. T3 concentration in case of hypophysectomy.

Figure 6.16. TRH concentration in case of hypophysectomy.

0.2

0.15

0.1

0.05

0

0 6 12 18 24 30 36 42 48 54 60

Time (Day)

mic

rogra

ms/

dL

2.4

1.8

1.2

0.6

0

0 6 12 18 24 30 36 42 48 54 60

Time (Day)

nan

ogra

ms/

ml

68

Since the pituitary is completely removed, no TSH exists in the body. And since

there is no TSH in the body, only minimal amounts of thyroid hormones are secreted. Low

levels of thyroid hormones in blood cause TRH secretion to rise. However, since the

medium of communication between the hypothalamus and the thyroid gland is no longer

present, thyroid hormones in blood continue to drop. The behaviours of circulating T3 and

T4 in this scenario are qualitatively the same; thus, only that of T3 is shown pictorially in

Figure 6.15.

The work of Smith (1930) suggests that the thyroids of rats start to regress in weight

soon after hypophysectomy, evident in ten days and pronounced in thirty days. The

diminution in the weights of the rat thyroids is observed to be usually about by half or even

more. A similar work conducted by White (1933) investigates the effect of

hypophysectomy on rabbits and shows that the average shrinkage in the thyroids is 30% in

male rabbits, and 20% in females.

Figure 6.17. Thyroid weight in case of hypophysectomy.

The simulation outputs regarding the thyroid weight is consistent with the findings in

literature explained above. Since low levels of thyroid hormones persist because of the

absence of pituitary gland, the hypothalamus persistently over-functions due to scantiness

of inhibition by thyroid hormones. This, in turn, leads to an increase in the weight of the

21

18.5

16

13.5

11

0 20 40 60 80 100 120 140 160 180 200

Time (Day)

gra

ms

69

hypothalamus, which turns out to be about three-fold in our case (see Figure 6.18). The

opposite is seen in thyroid gland. Since no TSH exists in the body, thyroid gland is no

longer stimulated. Due to prolonged “idling”, the gland shrinks (Donovan, 1966; Melmed,

2002). As seen in Figure 6.17, the weight of the thyroid is contracted almost by half. The

time scale of the output graphs for thyroid weight and hypothalamus weight is taken as 200

days in order to be able to evidently depict the changes in the sizes.

Figure 6.18. Hypothalamus weight in case of hypophysectomy.

130

105

80

55

30

0 20 40 60 80 100 120 140 160 180 200

Time (Day)

mg

70

7. THYROID DISORDERS

Once the model is believed to be structurally and behaviourally valid, the last step is

to analyse the model via simulation experiments. In this chapter, the model will be

simulated under some common thyroid-related disorders, and the dynamics of the key

variables will be illustrated.

7.1. Graves’ Disease

Graves’ disease is an autoimmune disease which causes excessive thyroid hormone

production. It affects approximately 0.5% of population and counts for the 50 to 80% of

cases of hyperthyroidism (Bürgi, 2010). This disorder is caused by thyroid-stimulating

immunoglobulins, TSIs, which are proteins that mimic the actions of TSH, bind to the

receptors on thyroid cells and stimulate the production of thyroid hormones. In Graves’

disease, TSH and TRH concentrations are less than normal, and often essentially zero. It is

the negative feedback effect of the elevated concentrations of circulating thyroid hormones

that results in low levels of TRH and TSH. Yet, thyroid hormones cannot feed back to

inhibit excessive TSI stimulation. Thus, despite the scarcity of TRH and TSH,

oversecretion of thyroid hormones persists, for independently acting TSIs continue to

trigger the formation and secretion of thyroid hormones. Due to prolonged overstimulation,

the thyroid enlarges and forms a specific type of goiter, called diffuse toxic goiter (Guyton

and Hall, 2006; Rhoades and Bell, 2009).

In this section, the outputs of two simulation runs will be presented. Firstly, the daily

iodine intake will be assumed normal, i.e. 150 µg. Secondly, the iodine intake will be set to

400 µg/day. In these two cases, the amount of TSIs will be kept at the same level. For the

outputs to be comparable, the horizontal and vertical scales of the graphs will be retained

throughout the two runs (except for the graph of thyroidal iodine).

71

7.1.1. Graves’ Disease with Normal Daily Iodine Intake

Here, the daily iodine intake is set to 150 µg, and the values of all the variables are

initially set to their equilibrium levels.

In this scenario, the thyroid hormone concentrations rise with the stimulatory effect

of TSIs, and persistently stay elevated since the negative feedback loop is interrupted

because of the independently acting agents. However, at approximately halfway of the

simulation run, the thyroid hormones start to drop and stabilize at a level above the normal.

The reason behind this that the TSIs demand more than what the thyroid gland can

synthesize using only the given daily iodine intake. So, consumption rate the iodine

exceeds the rate of uptake which leads to the gradual exhaustion of thyroidal iodine stores.

Yet, the drop in thyroid hormone concentrations is not immediately followed by that. After

the depletion of these stores, the preformed hormone stores are used to meet the residuary

demand of TSIs that the thyroidal synthesis rate cannot fulfil.

Figure 7.1. T3 concentration in Graves’ disease with normal iodine intake.

Related literature suggests that in hyperthyroid patients taking drugs that block

thyroid hormone synthesis stores of thyroid hormones are more rapidly depleted, and the

therapeutic effect of these drugs may require several weeks to become evident (Carruthers

0.6

0.45

0.3

0.15

0

0 28 56 84 112 140 168 196 224 252 280

Time (Day)

mic

rogra

ms/

dL

72

et al., 2000). So, if thyroid hormone synthesis is blocked or reduced for some reason, the

hormone stores are depleted before the severity of the disease attenuates. Consistent with

these findings, when both iodine and preformed hormone stores are exhausted in the

simulation, the thyroid hormones start to decline to a level still higher than normal and

stabilize there.

As an example to the levels of hormones in patients with Graves’ disease, a clinical

case has been illustrated in which a 35-year-old woman with this disease presented with

very high T4 concentration (total T4: 320 nmol/l, normal range: 70–150 nmol/l) and

suppressed serum TSH concentration (<0.05 mU/l, normal range: 0.5–4.0 mU/l) (Nussey

and Whitehead, 2001). Consistent with this case, T4 concentration is rises maximally to

three times the normal value (before being suppressed by the above-mentioned

constraints).

Figure 7.2. T4 concentration in Graves’ disease with normal iodine intake.

The amount of iodine in the thyroid in euthyroid individuals is suggested to normally

vary between about 3 and 20 mg. In hyperthyroidism due to Graves’ disease, the amount of

iodine in the thyroid is suggested to be low, rarely above 3 mg (Nyström et al., 2011). As

illustrated in Figure 7.3, the thyroidal iodine drops to very low levels in Graves’ disease (to

about 600 µg).

28

21

14

7

0

0 28 56 84 112 140 168 196 224 252 280

Time (Day)

mic

rog

ram

s/d

L

73

Figure 7.3. Iodine in thyroid in Graves’ disease with normal iodine intake.

One characteristic feature of Graves’ disease is that T3/T4 is high compared to

normal physiological conditions. As depicted in Figure 7.4, the ratio of serum T3 to T4

ratio rises above normal value (which is 0.0208 in the model) with the introduction of

TSIs, and climbs further with the increase in TSH and depletion of iodine stores.

Figure 7.4. T3 to T4 ratio in Graves’ disease with normal iodine intake.

As one might expect, TRH and TSH concentrations fall to very low values because

of the inhibitory effect of elevated thyroid hormones. Since measurement of TRH

concentrations is impossible, only TSH concentrations are available numerically. Albeit so,

16,000

12,000

8,000

4,000

0

0 42 84 126 168 210 252

Time (Day)

mic

rog

ram

s

0.03

0.0275

0.025

0.0225

0.02

0 42 84 126 168 210 252

Time (Day)

74

the output graphs for both TRH and TSH are presented here in order to demonstrate their

general course of behaviour.

Figure 7.5. TRH concentration in Graves’ disease with normal iodine intake.

In the first phase of the simulation run (when the stores are not yet exhausted), the

minimal value of TSH concentration is approximately 0.028 µU/ml, quite consistent with

the data given above where TSH concentration was found to be <0.05 µU/ml.

Figure 7.6. TSH concentration in Graves’ disease with normal iodine intake.

0.2

0.15

0.1

0.05

0

0 28 56 84 112 140 168 196 224 252 280

Time (Day)

nan

ogra

ms/

ml

2.4

1.8

1.2

0.6

0

0 28 56 84 112 140 168 196 224 252 280

Time (Day)

mic

rou

nits/

ml

75

One common finding about Graves’ disease is thyroid gland growth due to

overstimulation (Melmed and Conn, 2005). When the patient with Graves’ disease whose

hormone concentrations were given above was examined, it is realized that she had

moderate diffuse goiter. As Figure 7.7 reveals, the thyroid enlarges to a certain extent in

Graves’ disease (note that the time scale of the graphs for gland weights is longer).

Figure 7.7. Thyroid weight in Graves’ disease with normal iodine intake.

Figure 7.8. Hypothalamus weight in Graves’ disease with normal iodine intake.

Finally, the weights of the hypothalamus and pituitary regress as a result of the low

TRH and high thyroid hormones, respectively. The relative remission in the atrophy results

23

22.25

21.5

20.75

20

0 50 100 150 200 250 300 350

Time (Day)

gra

ms

40

36

32

28

24

0 50 100 150 200 250 300 350

Time (Day)

mg

76

from the relative decrease in thyroid hormones and rise in TRH and TSH following the

hormone store depletion.

Figure 7.9. Pituitary weight in Graves' disease with normal iodine intake.

7.1.2. Graves’ Disease with Relatively High Daily Iodine Intake

All other things being the same as the previous scenario, the iodine intake is set to

400 µg/day here, and the model is simulated again. This experiment is done to show the

behaviour of the system when the iodine is no longer a binding constraint for the synthesis

of thyroid hormones in Graves’ disease.

For the sake of brevity, not every single output of the previous case will be shown;

only the descriptive ones will be selectively presented in this scenario.

With the increase in daily iodine intake, no shift in thyroid hormone concentrations is

observed in the middle of the run (see Figure 7.10). As implied by the stable behaviour of

T3 throughout the run, the thyroidal iodine stores do not get depleted in this case because

the increased daily iodine intake suffices to meet the demand imposed by the TSIs.

30

22.5

15

7.5

0

0 50 100 150 200 250 300 350

Time (Day)

mg

77

Figure 7.10. T3 concentration in Graves’ disease with relatively high iodine intake.

Figure 7.11. Iodine in thyroid in Graves’ disease with relatively high iodine intake.

Figure 7.12 shows the ratio of T3 to T4 for this scenario. Because of overstimulation

of the thyroid, the ratio of T3 to T4 is higher than normal in this case too. As opposed to

the previous case, no further shift can be witnessed here because TSH levels do not show a

relative increase and thus do not cause the ratio to grow any further.

As depicted in Figure 7.13, TSH concentration ultimately stabilizes at a subnormal

level (0.028 µU/ml).

0.6

0.45

0.3

0.15

0

0 28 56 84 112 140 168 196 224 252 280

Time (Day)

mic

rogra

ms/

dL

16,000

15,500

15,000

14,500

14,000

0 42 84 126 168 210 252

Time (Day)

mic

rog

ram

s

78

Figure 7.12. T3 to T4 ratio in Graves’ disease with relatively high iodine intake.

Figure 7.13. TSH concentration in Graves’ disease with relatively high iodine intake.

Finally, the weights of the thyroid and pituitary are depicted in Figure 7.14 and

Figure 7.15. The time scales of these graphs are again longer than the previous ones (the

same as the time scales of the graphs of gland weights in the previous section) in order to

be able to depict the complete behaviour evidently. The convergence of the thyroid to the

ultimate value is smoother in this case. As for the pituitary, no remission in the atrophy can

be observed since no change in neither the thyroid hormones nor TRH occurs once they

stabilize.

0.03

0.0275

0.025

0.0225

0.02

0 42 84 126 168 210 252

Time (Day)

2.5

1.875

1.25

0.625

0

0 50 100 150 200 250 300 350

Time (Day)

mic

rou

nit

s/m

l

79

To summarize, it can be said that the availability of iodine may well augment the

severity of Graves’ disease depending on the amount of TSIs.

Figure 7.14. Thyroid weight in Graves’ disease with relatively high iodine intake.

Figure 7.15. Pituitary weight in Graves’ disease with relatively high iodine intake.

7.2. Iodine Deficiency

Iodine deficiency is a common cause of hypothyroidism. Though eradicated in many

regions of the world with salt iodization, it still is one prevailing cause of hypothyroidism.

23

22.25

21.5

20.75

20

0 50 100 150 200 250 300 350

Time (Day)

gra

ms

30

22.5

15

7.5

0

0 50 100 150 200 250 300 350

Time (Day)

mg

80

Approximately 30% of the world population is encountered with iodine deficiency, about

half of them with goiter (Goldman and Hatch, 2000).

Lack of iodine, which is an indispensable ingredient for thyroid hormone synthesis

as mentioned earlier, hinders the production of thyroid hormones. Consequently, since no

or little thyroid hormone is available to inhibit the production of TSH, excessive amounts

of TSH is secreted. Excessive TSH overstimulates the thyroid gland. But, because of

scarcity of iodide, formation of T3 and T4 does not occur and consequently TSH secretion

cannot be suppressed. In the long run, since the overstimulation by TSH lingers, the

thyroid gland grows larger. Enlarged thyroid gland due to iodine deficiency is called

endemic colloid goiter (Guyton and Hall, 2006).

In this section, the outputs of two simulation runs will be presented; severe iodine

deficiency and moderate iodine deficiency. In the first case, the daily iodine intake will

assumed to be 30 µg. And in the second case, the iodine intake will be increased to 50

µg/day. In both cases, the model is run for 800 days. For the outputs to be comparable, the

horizontal and vertical scales of the graphs will be retained throughout the two runs.

7.2.1. Severe Iodine Deficiency

Here, the daily iodine intake is set to 30 µg by leaving all the other variables at their

normal values initially.

In the initial phase of the run, the concentrations of hormones persevere at their

normal equilibrium levels since the body utilizes the iodine and hormone stores before the

implications of iodine deficiency become apparent. Except for thyroidal iodine, variables

stay at their set-points for a long while. To be able to explicitly demonstrate the dynamics

of the variables, the interval from t=350 to t=750 will be shown in all the output graphs but

the thyroidal iodine.

81

Figure 7.16. T3 concentration when daily iodine intake is 30 µg.


Evidence in literature suggests that serum thyroid hormone levels change in a

characteristic pattern with iodine deficiency, typically showing a low T4 and a normal or

increased serum T3 concentration (Braverman, 2003). It is stated that T3 concentrations

also decline, but not until hypothyroidism, or the iodine deficiency is severe (Werner et al.,

2005; Brent, 2010). In this case, i.e. when iodine intake is 30 µg/day, the body fails to

maintain the serum T3 levels at normal levels. When the equilibrium state is disturbed with

the depletion of iodine and then hormone stores, T3 levels rise above the normal levels for

0.27

0.23

0.19

0.15

0.11

350 390 430 470 510 550 590 630 670 710 750

Time (Day)

mic

rogra

ms/

dL

10

7.5

5

2.5

0

350 390 430 470 510 550 590 630 670 710 750

Time (Day)

mic

rog

ram

s/d

L

82

a short while but cannot survive there with the given level of iodide. So, it falls to a

subnormal level and stabilizes there (see Figure 7.16).

As mentioned above, the impact of iodine deficiency on T4 concentrations is more

drastic. The proportional decrease in T4 is much more than that of T3 (see Figure 7.16 and

Figure 7.17). As a consequence, the ratio of serum T3 to T4 is elevated in iodine

deficiency (see Figure 7.18).

Figure 7.18. T3 to T4 ratio when daily iodine intake is 30 µg.

Figure 7.19. Iodine in thyroid when daily iodine intake is 30 µg.

0.16

0.12

0.08

0.04

0

350 410 470 530 590 650 710

Time (Day)

15,000

11,250

7,500

3,750

0

0 100 200 300 400 500 600 700

Time (Day)

mic

rog

ram

s

83

If iodine intake diminishes, hormone secretion remains constant until available stores

of the mineral are depleted (Garrison and Somer, 1995). Consistent with this statement, in

the model, the effects of iodine deficiency become apparent shortly after the depletion of

these stores. The time lag between the depletion of iodine stores results from the fact that

the thyroid makes use of the preformed hormone stores, and is able to release sufficient

amount of thyroid hormones in that interval before a significant portion of these stores are

consumed. Figure 7.19 depicts the dynamics of thyroidal iodine (note that the horizontal

scale begins from t=0).

Figure 7.20. T3 store when daily iodine intake is 30 µg.


440

360

280

200

120

350 390 430 470 510 550 590 630 670 710 750

Time (Day)

mic

rogra

ms

6,000

4,500

3,000

1,500

0

350 410 470 530 590 650 710

Time (Day)

mic

rog

ram

s

84

As mentioned before, both the synthesis and secretion of T3 is favoured in

hypothyroid state. Hence, the degree of diminution in T3 reserves is less severe than that of

T4 (see Figure 7.20 and Figure 7.21). One should note that the decrease in hormone stores

shows itself after thyroidal iodine is considerably emptied.

Figure 7.22. TSH concentration when daily iodine intake is 30 µg.

Figure 7.23. Thyroid weight when daily iodine intake is 30 µg.

As the nature of the negative feedback necessitates, TSH concentrations rise in

parallel with the diminishment in thyroid hormones, as presented in Figure 7.22. Since the

24

18

12

6

0

350 390 430 470 510 550 590 630 670 710 750

Time (Day)

mic

rou

nits/

ml

62

51

40

29

18

350 390 430 470 510 550 590 630 670 710 750

Time (Day)

gra

ms

85

behaviour of TRH is qualitatively the same as that of TSH, the related output graph is not

shown separately in this case.

The last thing to mention is the alterations in the weights of the glands. The thyroid

gland starts to be stimulated more than normally when the thyroid hormone levels drop and

TSH levels rise subsequently. As seen in Figure 7.23, the weight of the thyroid increases to

about three times its normal weight.

Figure 7.24. Hypothalamus weight when daily iodine intake is 30 µg.

Figure 7.25. Pituitary weight when daily iodine intake is 30 µg.

44

42.75

41.5

40.25

39

350 410 470 530 590 650 710

Time (Day)

mg

48

41

34

27

20

350 390 430 470 510 550 590 630 670 710 750

Time (Day)

mg

86

In parallel with the persistent drop in thyroid hormones and rise in TRH and TSH,

both the hypothalamus and the pituitary also grow in size (see Figure 7.24 and Figure

7.25).

7.2.2. Moderate Iodine Deficiency

In this case, the daily iodine intake is set to 50 µg. Again, for the sake of brevity, not

all the outputs shown in the severe deficiency case, but only some descriptive ones will be

selected and presented.



0.27

0.23

0.19

0.15

0.11

350 390 430 470 510 550 590 630 670 710 750

Time (Day)

mic

rogra

ms/

dL

10

7.5

5

2.5

0

350 390 430 470 510 550 590 630 670 710 750

Time (Day)

mic

rog

ram

s/d

L

87

It was previously explained that unless the iodine deficiency is severe, the

characteristic pattern of serum thyroid hormones is normal or elevated T3, and low T4

concentrations. In the case where iodine intake was 30 µg/day, T3 levels couldn’t hold on

to the normal levels and dropped below the set point. Here however, since the deficiency is

not as severe, T3 succeeds to stabilize at a level above the normal. The diminution in the

severity is reflected to T4 concentration too; it becomes stable at a level higher than the

previous case.

Figure 7.28. T3 to T4 ratio when daily iodine intake is 50 µg.

Though milder than the previous case, 50 µg iodine intake is still inadequate and

causes insufficient synthesis and secretion of thyroid hormones. So, the hypothyroid state

still exists and therefore T3/T4 is higher than normal in this case. As can be observed in

Figure 7.28, this ratio starts to rise with the decrease in thyroid hormone concentrations but

stabilizes at a point which is smaller than the one in the 50 µg-case. So, it can be said that

this ratio is proportional to the severity of the deficiency.

Another important thing to note is that the implications of the deficiency become

evident later than the previous case for the relatively higher intake of iodine helps the pre-

existing stores to bear longer here. Also, the hormone stores equilibrate at a higher level as

compared to the previous case (see Figure 7.29).

0.16

0.12

0.08

0.04

0

350 410 470 530 590 650 710

Time (Day)

88


Upon the depletion of hormone stores, TSH concentration starts to rise to

compensate for the thyroid hormone deficiency (see Figure 7.30).

Figure 7.30. TSH concentration when daily iodine intake is 50 µg.

The behaviours of the weights of the glands are basically the same as in the previous

case; the only difference is that they stabilize at a lower level in this case. As a

representative one, only the graph for thyroid weight is shown in Figure 7.31.

440

360

280

200

120

350 390 430 470 510 550 590 630 670 710 750

Time (Day)

mic

rogra

ms

6,000

4,500

3,000

1,500

0

350 410 470 530 590 650 710

Time (Day)

mic

rog

ram

s

89

Figure 7.31. Thyroid weight when daily iodine intake is 50 µg.

7.3. Iodine Excess

As mentioned earlier, sufficient iodine intake is crucial for the maintenance of

healthy thyroid functioning and severe iodine deficiency obstruct thyroid hormone

production and induces goiter formation. Interestingly, functioning of the thyroid is also

impaired when the dietary iodine intake is far above the physiological needs.

It is postulated that identical iodine excess may cause hyperthyroidism in some

persons and hypothyroidism in others (Bürgi, 2010). Iodine-induced hyperthyroidism is

suggested to happen often due to the autonomy in thyroid function, because of some

therapeutic intervention for some pre-existing thyroid disease, or as a result of the disease

itself. In this study, the effects of iodine excess on thyroids with prior pathological

conditions are considered out of scope; only the impacts on normal thyroids will be of

interest.

A number of studies are conducted to demonstrate the inhibitory effect of excessive

iodine intake on thyroids of healthy subjects, as mentioned before. In one of such studies,

Namba et al. (1993) investigate the effect of 27 mg iodine administration to ten normal

male volunteers on thyroid function and volume. Thyroid volume was measured before

62

51

40

29

18

350 390 430 470 510 550 590 630 670 710 750

Time (Day)

gra

ms

90

treatment, on the day of the last treatment, and 1 month after the treatment. It is found that

there was a significant rise in serum TSH levels, with a small decline in serum free T4

concentration during iodide administration; the values remained within the normal range

except for two subjects. The volume of the thyroid gland is found to be significantly

enlarged after 28 days of iodide intake. And it is stated that when iodide was discontinued,

thyroid volume and function returned to baseline levels within one month for all subjects.

Here, it is assumed that 27 mg iodine is supplemented for 28 days starting at t=0. As

in all the previous scenarios, the variables are initially set to their equilibrium levels. For

the model outputs to be comparable to real data graphs, the model is simulated for 56 days.

Figure 7.32. Average free T4 concentration of ten subjects receiving 27 mg iodine

supplementation for 28 days (Namba et al., 1993).

The average free T4 levels of the ten subjects are depicted in Figure 7.34. T4 levels

decline after the introduction of excessive iodine supplementation and start to rise soon

before the withdrawal of the iodine supplementation. The dynamics of free T4 in the

simulation run is demonstrated in Figure 7.33 and is highly consistent with that of the real

data (note that the horizontal scales do not linearly increase).

91

Figure 7.33. Free T4 concentration (in pmol/l) in case of 27 mg iodine supplementation for

28 days.

Figure 7.34. T3 concentration in case of 27 mg iodine supplementation for 28 days.

The behaviour of T3 is shown in Figure 7.34. As opposed to T4, the rising trend in

T3 concentration becomes apparent in T3 after about t=7. The early improvement of T3 is

a consequence of the mechanisms that operate to preserve T3 availability in body. These

mechanisms even lead to elevated T3 levels transiently, to compensate for the subnormal

levels of T4. So, consistent with the findings of Namba et al., the concentrations of both

T3 and T4 return to normal within one month after the discontinuation of iodine

supplementation.

0.19

0.1775

0.165

0.1525

0.14

0 8 16 24 32 40 48 56

Time (Day)

mic

rogra

ms/

dL

92

Figure 7.35. Average TSH concentration of ten subjects receiving 27 mg iodine


Figure 7.36. TSH concentration in case of 27 mg iodine supplementation for 28 days.

In concordance with the lowered levels of thyroid hormones, the average TSH

concentration of the subjects increases (see Figure 7.35), and restores the normal level

within one month after the excessive iodine intake is stopped. The model output shown in

Figure 7.36 matches well with the dynamics of the real data (note that the horizontal scales

do not linearly increase). The maximum level that the average TSH of the subjects reaches

93

is about 2-2.5 times the normal levels, whereas that of the simulation model is a bit higher,

about three times the normal level.

It was mentioned earlier that the changes in the weight of the thyroid will be

presumably accompanied by the changes in the volume of the thyroid. The average thyroid

volume of ten subjects measured before, during and one month after the supplementation is

shown in Figure 7.37. Since only three data points are available, the data is not exactly

comparable to the model output.

Though not significantly different, the average thyroid volume of the ten subjects is

slightly higher than the volume before the supplementation. In our simulation run, the

weight of the thyroid gland does not restore to normal as much as the average thyroid

volume of the subjects does after one month (at t=56), but it does so in about three to four

months (which is not explicitly shown here).

Figure 7.37. Average thyroid volume (as % of normal volume) of ten subjects receiving 27

mg iodine supplementation for 28 days (Namba et al., 1993).

94

Figure 7.38. Thyroid weight in case of 27 mg iodine supplementation for 28 days.

Lastly, serum iodine levels of the subjects remain elevated until the iodine

supplementation is discontinued. After the cessation of excessive iodine intake (day 28),

the serum iodine starts to drop. The related data and simulation output are depicted in

Figure 7.39 and Figure 7.40. The units of the real data and the model output are different;

but the overall dynamics of the two match well.

Figure 7.39. Average serum iodine levels of ten subjects receiving 27 mg iodine


25

23.5

22

20.5

19

0 8 16 24 32 40 48 56

Time (Day)

gra

ms

95

Figure 7.40. Iodine in blood in case of 27 mg iodine supplementation for 28 days.

7.4. Subacute Thyroiditis

The term thyroiditis refers to the inflammation of the thyroid gland. Inflammation is

the response of tissues to harmful stimuli, and can be caused by viral infections or

autoimmune processes. Here, we are not interested in the causes of the inflammation, but

rather in the consequences of it.

Inflamed cells of the thyroid lose their secretory and synthetic abilities. Moreover,

the inflammatory reaction within the gland causes the follicles to lose their integrity by

disrupting them and results in the release of preformed hormones and iodine into the

peripheral circulation (Grossman, 1998, Werner et al., 2005). The release of the preformed

hormones is not a controlled discharge like the secretion process, but rather a leakage.

The inflammatory reaction in the thyroid gland might be temporary or persistent. In

this section, an instance of temporary thyroiditis, namely subacute thyroiditis, will be of

interest. Subacute thyroiditis is the most common reason of the painful thyroid gland and

may account for up to 5% of clinical thyroid abnormalities. In subacute thyroiditis, the

thyroid gland is exposed to a transient course of inflammation, which usually lasts several

weeks and then ameliorates.

96

Subacute thyroiditis demonstrates a triphasic clinical course of thyrotoxicosis,

hypothyroidism and restoration of normal thyroid functioning. Thyrotoxicosis, which

means an excess of thyroid hormones in the body, is a result of destruction of thyroid cells

and uncontrolled release of hormone stores into the circulation. Since thyroid cells cannot

synthesize hormones during the inflammation phase and leakage of preformed hormones

persist due to inflammation, hormone stores get depleted after some time. As a result,

hypothyroidism is observed. As the name suggests, hypothyroidism is a condition in which

too little thyroid hormone is circulating throughout the body. After the inflammation

subsides, levels of circulating hormones restore their normal levels and hormone stores are

replenished gradually (Van den Berghe, 2008; Grossman, 1998).

In the model, the notion of inflammation is quantified by using a stock which is

allowed to vary between zero and one. The name of that stock is Inflammation Status.

Inflammation Status being one means that the gland is completely inflamed, and being zero

means that the gland is functioning properly. In a sense, this variable gives the inflamed

proportion of the gland.

In this case, two separate sources of thyroid hormone release exist; secretion by the

normally functioning cells, and leakage from the inflamed cells. Having defined the

inflammation status stock as the percentage of dysfunctioning gland, some distinction will

be made for the utilization of hormone stores for secretion and leakage purposes. If some

portion of the thyroid is inflamed, then that portion should leak out thyroid hormones

according to the amount of preformed thyroid hormones covered by that portion, but not

secrete any because it is not capable of doing it yet. Conversely, recovered or healthy

portion of the gland should only be in charge of secreting, not leaking, and be allowed to

consume the amount of preformed hormones that they “own”. For this purpose, three new

stocks are defined in the model; two of them for the thyroid hormones, and one for

thyroidal iodine. For all three substructures, the rationale behind is the same. To begin with

the thyroid hormones, these stocks serve as the amount of hormone stores that the inflamed

portion of the gland encapsulates. And, the old stocks for hormone stores stand for the

amount of hormone stores enveloped by the recovered portion. Two things count for the

97

loss from the new stocks; one is the leakage of hormones, the other is the transition from

the coverage area of inflamed cells to the healthy ones with the recovery of those inflamed

cells. The modified portion of stock flow diagram and related equations for T3 are shown

in Figure 7.41.

Figure 7.41. Modified structure of thyroid sector for subacute thyroiditis.

Recov of T3 cont portion = Leaking T4 Store × Recov rate (7.1)

T3 leak = Leaking T3 Store × 0.02 (7.2)

T4 in Blood

T4 clear rate

T4 Store

T4 syn rate T4 sec rate

T3 in Blood

T3 clear rate

T3 Store

T3 sec rateT3 syn rateAbs

rate ofT3 bytissues

Convrate to

rT3


Inflammation

Status

T3 fromdeiod of

T4

T4 to T3

conv rate

Leaking T3

Store T3 leakRecov ofT3 contportion

Leaking T4

StoreT4 leakRecov of

T4 contportion

Recov rate

98

As the above equations reveal, a certain fraction of preformed hormones that are

covered by the inflamed portion of cells leak out of the gland into the circulation, and some

fraction of preformed hormones flows into the regular hormone store stock with the

recovery of inflamed cells. Also, since only healthy cells are capable of synthesizing, the

newly synthesized thyroid hormones flow into the regular hormone store and do not get

mixed with the hormones enclosed by the inflamed portion.

Figure 7.42. Modified structure of iodine sector for subacute thyroiditis.

The iodine sector is modified in the same manner as explained above so as to

distinguish the portion of intrathyroidal iodine that is to be consumed for synthetic

purposes and that leaks out of the gland into the blood. The old stock for the thyroidal

I in Blood

I abs rate

I excr

I in Thy

Trap

rate

I cons

I from

deiod

Leaking I

I leak

Recov of cells

Inflammation

StatusRecov rate

99

iodine stands for the amount of iodine to be consumed in a controlled manner, and the new

one for iodine enclosed by the inflamed cells (see Figure 7.42).

There are few last remarks that have to be mentioned to fully elucidate the revised

structure of the model under subacute thyroiditis. Firstly, the stock for thyroid weight (Thy

Wt) represents not the whole but the properly functioning part of the gland (i.e. not

exposed to inflammatory reaction). Secondly, it is assumed that the gland cannot expand in

size during the course of the simulation run. Having zeroed the weight adjustments in the

thyroid, the only inflow to Thy Wt becomes the recovery of the inflamed portions of the

gland (Recov of inflamed thy).

Recov of inflamed thy = 20 × Recov rate (7.3)

Since the gland is completely inflamed at the beginning, the normal weight of the

thyroid is multiplied with the rate of recovery of inflammation to figure the correspondent

recovery in thyroid weight (see Equation 7.3). Thirdly, the capacity of one unit weight of

the properly functioning part of the gland is taken as one fourth of the normal capacity, i.e.

2.5 times the normal productivity level. The second and third assumptions are related to

the idea that the cells that newly recover from the inflammatory reaction may not perform

as well as in the healthy state, at least over the course of the simulation run. Lastly, the

effect of iodine on thyroid capacity is not taken into account in this case because the

presumed mechanism of impairment for iodine in healthy subjects may not be the same in

an inflamed gland.

Having done all the modifications in model structure and parameters, the model is

run for 150 days assuming a course of inflammation status as depicted in Figure 7.43. The

simulation output showing the TSH and T4 concentrations are shown in Figure 7.44.

Figure 7.45 and Figure 7.46 shows the real data from patients with subacute thyroiditis.

100

Figure 7.43. The assumed course of inflammation status in subacute thyroiditis.

Figure 7.44. TSH and T4 concentrations in subacute thyroiditis.

The curves depicting FTI and TSH levels in Figure 7.45 are the ones that we

basically compare our results to. The curve showing TG levels is commonly used as an

indicator for thyroid damage. TG being high implies that the thyroid gland is damaged

(Rubin, 2006). In this case, it returns to normal range (shaded region) near the end of the

time horizon. This is consistent with our presumed Inflammation Status for this case. FTI

is an indicator of free T4 levels in blood, but not the direct amount of it. In the model

output shown in Figure 7.44, the total T4 level is shown. Since the real data uses a

1

0.75

0.5

0.25

0

0 20 40 60 80 100 120 140

Time (Day)

20

10

10

5

0

0

0 20 40 60 80 100 120 140

Time (Day)

TSH conc : Current

T4 conc : Current

101

different measure for T4 levels in blood, the output of out model is numerically not

comparable to the real data. In subacute thyroiditis, not the behaviour or the course, but the

levels of hormones may show variability from patient to patient. So, even if the units did

match, it would not be very reasonable to try to exactly match to the data points of only

one patient. And, since the ultimate aim of this study is not point prediction, it can be said

that the model gives reasonable results by matching the typical dynamical behaviour.

Figure 7.45. Data from a patient with subacute thyroiditis (Lazarus, 2009).

Figure 7.46. Data from a patient with subacute thyroiditis (secondary axis: TSH).

TSH

FT4

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0

1

2

3

4

5

6

102

The name FT4 in Figure 7.46 refers to the free T4 concentration. Though not as

obvious as the data shown in Figure 7.45, the overall course of behaviour that TSH and

FT4 follows is essentially the same. The patient first presents with very low TSH and

elevated FT4 values. With the decline in FT4 concentrations, TSH rises and then stabilizes

(except for the last data point) at a normal level.

Lastly, the work of Werner et al. (2005) states that in the thyrotoxic phase of

subacute thyroiditis, the T3 to T4 ratio is lower than in Graves' thyrotoxicosis. Since the

reason behind the thyrotoxic phase is the uncontrolled leakage of preformed hormones, the

effect of thyroidal stimulation on the preferential secretion of T3 is non-existent in this

case. Therefore, the ratio of T3 to T4 is lower in the thyrotoxic phase of subacute

thyroiditis, as can be seen in Figure 7.47.

Figure 7.47. T3 to T4 ratio in subacute thyroiditis.

0.03

0.0275

0.025

0.0225

0.02

0 20 40 60 80 100 120 140

Time (Day)

103

8. CONCLUSION

In this study, a model for the thyroid hormone dynamics is constructed. Thyroid

hormones are the primary regulators of metabolic functions in the body, and disorders

related to thyroid hormone system are commonly seen. The aim of this study is first to

model the dynamics of the thyroid hormones and the stimulating hormones in healthy

body, then to adapt the model to portray some common abnormalities/disorders, finally to

capture the characteristic dynamics of the hormones involved under these circumstances

and to provide a platform to test possible scenarios.

For model validation, standard model structure and behaviour validity tests have

been applied. In this study, validity tests are illustrated by four runs to demonstrate the

consistency of the model outputs with the information in literature. First, the equilibrium

behaviour is shown to depict the equilibrium state in the body under normal conditions.

Then, the equilibrium state is disturbed with the administration of TRH and the outputs are

compared to the real data. Thereafter, the model is run under two scenarios where the

secretion rate of T4 is increased ten-fold and zeroed for one hour. The outputs are highly

consistent with the numerical data suggested by the related literature. Finally, the effects of

hypophysectomy, the complete removal of the pituitary gland, are shown. The behaviour

of the model under all these scenarios reasonably matches the qualitative and quantitative

data in literature.

After the validation tests, four different conditions related to the thyroid are

addressed. Firstly, Graves’ disease, the most common cause of hyperthyroidism, is

addressed in two different levels of iodine intake. In Graves’ disease; the formation of

goiter, effect of iodine availability on the severity of the disease, and other typical changes

in hormones and glands are well mimicked by the model. Increased T3/T4, which is often

used as a diagnostic criterion in Graves’ disease, is also captured by the simulations.

Secondly, iodine deficiency, one prevailing cause of hypothyroidism, is discussed for two

104

different levels of daily iodine intake. The model was able to depict all the characteristic

changes including the goiter formation and increase in T3/T4 in these two scenarios, both

independently and comparatively. Thirdly, the transient inhibitory effect of excessive

iodine intake on thyroid gland is discussed. The increase in thyroid volume and the mild

decline in thyroid hormones are captured well. Lastly, a disorder called subacute

thyroiditis is analysed. Subacute thyroiditis is a common disorder in which thyroid gland is

exposed to inflammation. The model is shown to reproduce well the behaviour of

hormones during the typical triphasic clinical course of subacute thyroiditis, composed of

thyrotoxicosis, hypothyroidism and normal thyroid functioning.

As far as the information in literature and interviews with the medical doctors are

concerned, the model structure exhibits a reasonable degree of validity. As future work,

more real data can be collected, parameters can be adjusted to reflect more precisely

quantitative and qualitative real data, and some extensions in the model structure can be

done to be able to model medical interventions and drug therapy.

105

APPENDIX: MODEL EQUATIONS

abs fr of I = 0.95 {dimensionless}

Abs rate of T3 by tissues = T3 in Blood × (35 − 5 × LN(2)) / 5 {µg / day}

Abs rate of T4 by tissues = T4 in Blood × ((5334 − 7440 × LN(2)) / 217) / 240 {µg / day}

AT for store restor = 30 {day}

chg in trap fr = disc / del for trapping fr {dimensionless}

Conv rate to rT3 = T4 in Blood × 32 / 240 {µg / day}

del for trapping fr = 1 {day}

des hypo wt = normal hypo wt × eff of imp TRH sec on hypo wt {mg}

des pit wt = normal pit wt × eff of imp TSH sec on pit wt {mg}

des T3 store = total normal TH store × fr of T3 sec {µg}

des T3 syn = T3 sec rate + T3 store adj {µg / day}

des T4 store = total normal TH store × fr of T4 sec {µg}

des T4 syn = T4 sec rate + T4 store adj {µg / day}

des thy wt = normal thy wt × eff of imp TH sec on thy wt {g}

des trap fr = LOOKUP EXTRAPOLATE(gr for des trap fr, ratio of thy I conc to normal)

{dimensionless}

disc = des trap fr − Pot Trap Fr {dimensionless}

disc btw pot T3 syn and I rest T3 syn = pot T3 syn × (1 − ratio of cap rest I cons to pot)

{µg / day}

disc btw pot TH syn and I rest TH syn = pot TH syn × (1 − ratio of cap rest I cons to pot)

{µg / day}

disc from des T3 store = des T3 store − T3 Store {µg}

disc from des T4 store = des T4 store − T4 Store {µg}

eff of cap on TH sec = LOOKUP EXTRAPOLATE(gr for thy cap, ratio of imp TH sec to

thy cap) {dimensionless}

eff of cap on TRH sec = LOOKUP EXTRAPOLATE(gr for hypo cap, ratio of imp TRH

sec to hypo cap) {dimensionless}

106

eff of cap on TSH sec = LOOKUP EXTRAPOLATE(gr for pit cap, ratio of imp TSH sec

to pit cap) {dimensionless}

eff of I on thy cap = LOOKUP EXTRAPOLATE(gr for eff of I on thy cap, ratio of I in thy

to thres) {dimensionless}

eff of imp TH sec on thy wt = LOOKUP EXTRAPOLATE(gr for imp TH sec on thy wt,

ratio of smth imp TH sec to normal) {dimensionless}

eff of imp TRH sec on hypo wt = LOOKUP EXTRAPOLATE(gr for eff of imp TRH sec

on hypo wt, ratio of smth imp TRH sec to normal) {dimensionless}

eff of imp TSH sec on pit wt = LOOKUP EXTRAPOLATE(gr for eff of imp TSH sec on

pit wt, ratio of smth imp TSH sec to normal) {dimensionless}

eff of pref T3 syn on red in T3 syn = LOOKUP EXTRAPOLATE(gr for eff of pref T3 syn

on red in T3 syn, ratio of disc btw I rest TH syn and pot TH syn to pot TH syn)

{dimensionless}

eff of T3 conc on peri conv = LOOKUP EXTRAPOLATE(gr for eff of T3 on peri conv,

ratio of T3 to normal) {dimensionless}

eff of T3 store cap = LOOKUP EXTRAPOLATE(gr for eff of TH store cap, ratio of pos to

pot T3 sec) {dimensionless}

eff of T4 store cap = LOOKUP EXTRAPOLATE(gr for eff of TH store cap, ratio of pos to

pot T4 sec) {dimensionless}

eff of TH on TRH sec = LOOKUP EXTRAPOLATE(gr for eff of TH on TRH sec, log

ratio of TH to normal) {dimensionless}

eff of TH on TSH sec = LOOKUP EXTRAPOLATE(gr for eff of TH on TSH sec, log

ratio of TH to normal) {dimensionless}

eff of thy cap on T3 syn = LOOKUP EXTRAPOLATE(gr for thy cap, ratio of des T3 syn

to cap) {dimensionless}

eff of thy cap on T4 syn = LOOKUP EXTRAPOLATE(gr for thy cap, ratio of des T4 syn

to cap) {dimensionless}

eff of thy I cap = LOOKUP EXTRAPOLATE(gr for I store cap, ratio of pot to pos I cons)

{dimensionless}

107

eff of thy stim on T3 fr = LOOKUP EXTRAPOLATE(gr for eff of thy stim on TH fr, ratio

of short smth imp TH sec to normal) {dimensionless}

eff of thy wt on I trap = LOOKUP EXTRAPOLATE(gr for eff of thy wt on I trap, Thy Wt

/ 20) {dimensionless}

eff of TRH on TSH sec = LOOKUP EXTRAPOLATE(gr for eff of TRH on TSH sec, log

ratio of TRH to normal) {dimensionless}

eff of TSH on I trapping = LOOKUP EXTRAPOLATE(gr for eff of TSH on I trap, log

ratio of TSH to normal) {dimensionless}

eff of TSH on TH sec = LOOKUP EXTRAPOLATE(gr for eff of TSH on TH sec, log

ratio of TSH to normal) {dimensionless}

excr fr = 103.358 / 150 {1 / day}

fr of T3 sec = LOOKUP EXTRAPOLATE(gr for T3 sec fr, pot fr of T3 sec)

{dimensionless}

fr of T4 sec = 1 − pot fr of T3 sec{dimensionless}

free T3 in blood = 0.003 × T3 in Blood {µg}

free T4 in blood = T4 in Blood × 0.0002{µg}

gr for des trap fr = ([(0, 0) − (5, 0.6)], (0, 0.5), (0.1, 0.5), (0.386965, 0.491429), (0.661914,

0.47619), (0.824847, 0.460952), (1, 0.419131), (1.16208, 0.329825), (1.22324, 0.245614),

(1.2844, 0.154386), (1.43731, 0.0877193), (1.67006, 0.0333333), (1.96538, 0.0152381),

(2.27088, 0.0104762), (2.59674, 0.00761904), (2.99389, 0.0057143), (3.5336, 0.001),

(4.95927, 0.0005), (5, 0.0005)) {dimensionless}

gr for eff of I on thy cap = ([(0.9, 0) − (1.5, 1)], (0.9, 1), (0.91, 1), (0.920183, 0.964912),

(0.925662, 0.866667), (0.936697, 0.70614), (0.958656, 0.447619), (0.970876, 0.319048),

(0.977064, 0.263158), (0.98554, 0.195238), (0.997248, 0.140351), (1.01009, 0.098),

(1.02661, 0.0894737), (1.05596, 0.087), (1.09817, 0.086), (1.49, 0.085), (1.5, 0.085))

{dimensionless}

gr for eff of imp TRH sec on hypo wt = ([(0, 0) − (1, 4)], (0.02, 0.3), (0.021, 0.3),

(0.030581, 0.403509), (0.04058, 0.5316), (0.0814664, 0.723809), (0.224033, 0.8),

(0.366972, 0.9), (0.550459, 1), (0.733198, 1), (1, 1), (2, 1), (4.86762, 1.02857), (5.23014,

1.06667), (5.74338, 1.08571), (6.13442, 1.12381), (6.5499, 1.21905), (6.89206, 1.29524),

108

(7.18534, 1.37143), (7.55193, 1.48571), (7.96741, 1.58095), (8.28513, 1.69524), (8.77393,

1.90476), (9.28717, 2.15238), (9.75153, 2.4381), (10.1181, 2.7619), (10.3381, 3.00952),

(10.6558, 3.29524), (10.9491, 3.46667), (11.3157, 3.65714), (11.7067, 3.69524), (12, 3.7))

{dimensionless}

gr for eff of imp TSH sec on pit wt = ( [(0, 0) − (12, 4)], (0.02, 0.3), (0.021, 0.3),

(0.030581, 0.403509), (0.04058, 0.5316), (0.0814664, 0.723809), (0.224033, 0.8),

(0.366972, 0.9), (0.550459, 1), (0.733198, 1), (1, 1), (2, 1), (4.86762, 1.02857), (5.23014,

1.06667), (5.74338, 1.08571), (6.13442, 1.12381), (6.5499, 1.21905), (6.89206, 1.29524),

(7.18534, 1.37143), (7.55193, 1.48571), (7.96741, 1.58095), (8.28513, 1.69524), (8.77393,

1.90476), (9.28717, 2.15238), (9.75153, 2.4381), (10.1181, 2.7619), (10.3381, 3.00952),

(10.6558, 3.29524), (10.9491, 3.46667), (11.3157, 3.65714), (11.7067, 3.69524), (12, 3.7))

{dimensionless}

gr for eff of pref T3 syn on red in T3 syn = ([(0, 0) − 1, 1)], (0, 1), (0.0001, 1), (0.0203666,

0.980952), (0.0305499, 0.966667), (0.0610998, 0.909524), (0.0916497, 0.838095),

(0.120163, 0.766667), (0.167006, 0.661905), (0.211813, 0.566667), (0.258656, 0.490476),

(0.297352, 0.438095), (0.329939, 0.4), (0.372709, 0.352381), (0.423625, 0.3), (0.484725,

0.252381), (0.560081, 0.195238), (0.623218, 0.147619), (0.672098, 0.114286), (0.729124,

0.0857143), (0.784114, 0.0619048), (0.828921, 0.047619), (0.881874, 0.0285714),

(0.936864, 0.0190476), (0.9999, 0), (1, 0)) {dimensionless}

gr for eff of T3 on peri conv = ([(0, 0.8) − (1, 1.7)], (0.0112016, 1.64762), (0.0492872,

1.648), (0.0940937, 1.64333), (0.147862, 1.62714), (0.199389, 1.58667), (0.264358, 1.53),

(0.329328, 1.47333), (0.387576, 1.41905), (0.445825, 1.36), (0.501833, 1.31143),

(0.55112, 1.26286), (0.613849, 1.20619), (0.676578, 1.14952), (0.737067, 1.10095),

(0.802037, 1.06333), (0.858045, 1.03619), (0.923014, 1.01333), (0.9999, 1), (1, 1))

{dimensionless}

gr for eff of TH on TRH sec = ([(−1.1, 0) − (1, 10)], (−1.09572, 10), (−1.04012, 9.90476),

(−0.997248, 9.7807), (−0.952294, 9.69298), (−0.900917, 9.38597), (− 0.860489, 9.14286),

( − 0.813442, 8.7619), (−0.759633, 8.42105), (−0.693686, 7.71429), (−0.629532,

7.04762), (−0.566972, 6.31579), (−0.451376, 5.13158), (−0.393578, 4.51754),

(−0.284404, 3.50877), (−0.200917, 2.7193), (−0.143119, 2.2807), (−0.0660551, 1.53509),

109

(0, 1), (0.0174312, 0.868421), (0.0366972, 0.719298), (0.0489297, 0.574561), (0.0733945,

0.434211), (0.0948012, 0.315789), (0.134557, 0.22807), (0.180428, 0.153509), (0.248624,

0.118421), (0.33211, 0.100877), (0.440367, 0.0833333), (0.577982, 0.0701754),

(0.730887, 0.0657895), (0.852294, 0.0614035), (0.922936, 0.0570175), (0.999, 0.05), (1,

0.05)) {dimensionless}

gr for eff of TH on TSH sec = ( [(0, 0) − (1, 1)], (0, 1), (0.0001, 1), (0.0366972, 0.982456),

(0.0519878, 0.969298), (0.0642202, 0.938596), (0.0764526, 0.903509), (0.088685,

0.850877), (0.0997963, 0.780952), (0.110092, 0.70614), (0.124236, 0.609524), (0.140673,

0.508772), (0.16208, 0.403509), (0.186544, 0.320175), (0.2263, 0.223684), (0.262997,

0.166667), (0.308868, 0.131579), (0.389002, 0.104762), (0.468432, 0.0857143),

(0.553517, 0.0745614), (0.629969, 0.0657895), (0.691131, 0.064), (0.776758, 0.063),

(0.83792, 0.0622), (0.902141, 0.0614035), (0.941896, 0.0570175), (0.99, 0.05), (1, 0.05))

{dimensionless}

gr for eff of TH store cap = ([(0, 0) − (1.5, 1)], (0, 0), (0.75, 0.75), (0.876147, 0.833333),

(0.947047, 0.87619), (1.00509, 0.919048), (1.05092, 0.942857), (1.09633, 0.960526),

(1.14679, 0.97807), (1.23, 1), (1.5, 1)) {dimensionless}

gr for eff of thy stim on TH fr([(1, 0) − (5, 2.5)], (1, 1), (1.001, 1), (1.1, 1.02), (1.39144,

1.0636), (1.67278, 1.12939), (1.96636, 1.18421), (2.3211, 1.27193), (2.54128, 1.34868),

(2.85933, 1.45833), (3.16514, 1.57895), (3.39755, 1.72149), (3.62997, 1.84211), (3.80122,

1.95175), (3.99694, 2.08333), (4.14373, 2.20395), (4.30275, 2.2807), (4.47401, 2.35746),

(4.64526, 2.42325), (4.823, 2.47368), (4.999, 2.5), (5, 2.5)) {dimensionless}

gr for eff of thy wt on I trap = ([(0, 0) − (3, 1.5)], (0, 0), (1e−005, 0), (0.0651731,

0.0285714), (0.126273, 0.0714285), (0.207739, 0.142857), (0.274949, 0.228571),

(0.360489, 0.333333), (0.427699, 0.428571), (0.519348, 0.580952), (0.629328, 0.71426),

(0.761711, 0.814286), (0.849287, 0.895238), (1, 1), (1.16701, 1.05714), (1.33198, 1.1),

(1.5096, 1.13571), (1.71079, 1.16429), (2.01629, 1.20714), (2.389, 1.25), (2.66395,

1.27143), (2.99, 1.3), (3, 1.3)) {dimensionless}

gr for eff of TRH on TSH sec = ([(−1, 0) − (1.1, 10.1)], (−1, 0.05), (−0.999, 0.05),

(−0.790428, 0.053), (−0.640733, 0.058), (−0.550917, 0.065), (− 0.478208, 0.0714286), (−

0.428135, 0.0833333), (−0.379205, 0.0921053), (−0.324159, 0.122807), (−0.272171,

110

0.153509), (−0.223242, 0.201754), (−0.180428, 0.245614), (−0.140673, 0.311404),

(−0.100917, 0.403509), (−0.0733945 , 0.517544), (−0.0519878, 0.614035), (−0.0366972,

0.697368), (−0.0244648, 0.77193), (−0.0152905, 0.855263), (−0.00917431, 0.934211), (0,

1), (0.053211, 1.44737), (0.111009, 1.92982), (0.194495, 2.67544), (0.244603, 3.27048),

(0.308758, 3.94381), (0.355804, 4.56905), (0.406422, 5.30702), (0.449898, 6.1081),

(0.492668, 6.68524), (0.526884, 7.18857), (0.573931, 7.77143), (0.629532, 8.36857),

(0.680855, 8.84), (0.732179, 9.27714), (0.766395, 9.47476), (0.804888, 9.61905),

(0.864766, 9.81143), (0.924644, 9.90762), (0.984521, 10.027), (1.09572, 10.1))

{dimensionless}

gr for eff of TSH on I trap = ([( − 1, 0) − (1, 1.5)], ( − 1, 0.02), ( − 0.9999, 0.02), ( −

0.885947, 0.0357143), ( − 0.751527, 0.0785714), ( − 0.649695, 0.15), ( − 0.551935,

0.257143), ( − 0.412844, 0.440789), ( − 0.29052, 0.598684), ( − 0.155963, 0.776316), (0,

1), (0.120163, 1.1), (0.211009, 1.16429), (0.340122, 1.22143), (0.462322, 1.27143),

(0.565749, 1.308), (0.669725, 1.341), (0.828746, 1.38), (0.9999, 1.4), (1, 1.4))

{dimensionless}

gr for eff of TSH on TH sec = ( [( − 1, 0) − (1.1, 10.1)], (−1, 0.05), (−0.999, 0.05),

(−0.790428, 0.053), (−0.640733, 0.058), (−0.550917, 0.065), (−0.478208, 0.0714286),

(−0.426884, 0.0904762), (−0.37556, 0.119048), (−0.327902, 0.144285), (−0.277189,

0.190476), (−0.23442, 0.228571), (−0.195927, 0.271429), (−0.161711, 0.338095),

(−0.131772, 0.419048), (−0.098778, 0.52381 ), (−0.0761711, 0.614286), (−0.0633401,

0.68), (−0.0498981, 0.761905), (−0.0291243, 0.847619), (−0.0162933, 0.92381), (0, 1),

(0.0606924, 1.34286), (0.129124, 1.77143), (0.214664, 2.38095), (0.278819, 3.06),

(0.334419, 3.64286), (0.381466, 4.46857), (0.419959, 5.24571), (0.462729, 6.02286),

(0.492668, 6.68524), (0.526884, 7.18857), (0.573931, 7.77143), (0.629532, 8.36857),

(0.680855, 8.84), (0.732179, 9.27714), (0.766395, 9.47476), (0.804888, 9.61905),

(0.864766, 9.81143), (0.924644, 9.90762), (0.984521, 10.027), (1.09572, 10.1))

{dimensionless}

gr for eff on HAT = ([(1, 30) − (5, 250)], (1, 30), (1.1, 30), (1.33028, 35.0877), (1.62385,

49.2982), (1.81957, 62.1053), (2.00306, 79.2105), (2.13761, 95.614), (2.27217, 113.684),

(2.3945, 137.632), (2.66361, 178.158), (2.84709, 200.263), (3.11621, 218.684), (3.45872,

111

228.816), (3.75229, 236.184), (4.10703, 242.632), (4.42508, 245.395), (5, 250))

{dimensionless}

gr for eff on PAT = ([(1, 30) − (5, 250)], (1, 30), (1.1, 30), (1.33028, 35.0877), (1.62385,

49.2982), (1.81957, 62.1053), (2.00306, 79.2105), (2.13761, 95.614), (2.27217, 113.684),

(2.3945, 137.632), (2.66361, 178.158), (2.84709, 200.263), (3.11621, 218.684), (3.45872,

228.816), (3.75229, 236.184), (4.10703, 242.632), (4.42508, 245.395), (5, 250))

{dimensionless}

gr for eff on TAT = ([(1, 30) − (5, 250)], (1, 30), (1.1, 30), (1.33028, 35.0877), (1.62385,

49.2982), (1.81957, 62.1053), (2.00306, 79.2105), (2.13761, 95.614), (2.27217, 113.684),

(2.3945, 137.632), (2.66361, 178.158), (2.84709, 200.263), (3.11621, 218.684), (3.45872,

228.816), (3.75229, 236.184), (4.10703, 242.632), (4.42508, 245.395), (5, 250))

{dimensionless}

gr for hypo cap = ([(0, 0) − (1.5, 1)], (0, 0), (0.75, 0.75), (0.855397, 0.838095), (0.934827,

0.9), (0.986762, 0.92381), (1.02953, 0.947619), (1.06925, 0.961905), (1.11813, 0.980952),

(1.23, 1), (1.5, 1)) {dimensionless}

gr for I store cap([(0, 0) − (1.1, 1)], (0, 0), (1e − 005, 0), (0.5, 0.5), (0.7, 0.7), (0.806517,

0.780952), (0.907332, 0.87619), (0.943177, 0.914286), (0.976782, 0.942857), (1.01039,

0.971429), (1.05, 1), (1.1, 1)) {dimensionless}

gr for imp TH sec on thy wt = ([(0, 0) − (12, 4)], (0.02, 0.3), (0.021, 0.3), (0.030581,

0.403509), (0.04058, 0.5316), (0.0814664, 0.723809), (0.224033, 0.8), (0.366972, 0.9),

(0.550459, 1), (0.733198, 1), (1, 1), (1.5, 1), (2.7156, 1.07), (3.52294, 1.19298), (4.55046,

1.36842), (5.50459, 1.54386), (6.45872, 1.73684), (7.52294, 2.03509), (8.51376, 2.40351),

(9.43119, 2.73684), (9.87156, 2.96491), (10.2018, 3.12281), (10.6055, 3.31579), (10.9725,

3.54386), (11.3157, 3.65714), (11.7067, 3.69524), (12, 3.7)) {dimensionless}

gr for pit cap = ([(0, 0) − (1.5, 1)], (0, 0), (0.75, 0.75), (0.855397, 0.838095), (0.934827,

0.9), (0.986762, 0.92381), (1.02953, 0.947619), (1.06925, 0.961905), (1.11813, 0.980952),

(1.23, 1), (1.5, 1)) {dimensionless}

gr for T3 sec fr = ([(0.9, 0.9) − (1.1, 1)], (0.9, 0.9), (0.97, 0.97), (0.97844, 0.976754),

(0.988685, 0.982456), (1.00153, 0.988596), (1.01437, 0.991667), (1.02477, 0.99386),

(1.04434, 0.99693), (1.07, 1), (1.1, 1)) {dimensionless}

112

gr for thy cap = ([(0, 0) − (1.5, 1)], (0, 0), (0.75, 0.75), (0.855397, 0.838095), (0.934827,

0.9), (0.986762, 0.92381), (1.02953, 0.947619), (1.06925, 0.961905), (1.11813, 0.980952),

(1.23, 1), (1.5, 1)) {dimensionless}

HAT = LOOKUP EXTRAPOLATE(gr for eff on HAT, ratio of des hypo wt to hypo wt)

{days}

hypo cap = Hypo Wt × normal hypo prod × 10 {ng / day}

Hypo Wt = INTEG (Hypo wt chg, 40) {mg}

Hypo wt chg = (des hypo wt − Hypo Wt) / HAT {mg / day}

I abs rate = I intake × abs fr of I {µg / day}

I cons = I cons for T3+I cons for T4 {µg / day}

I cons for T3 = T3 syn rate × 3 × 126.904 / 651 {µg / day}

I cons for T4 = T4 syn rate × 4 × 126.904 / 777 {µg / day}

I excr = I in Blood × excr fr {µg / day}

I from deiod = 0.8 × retained I {µg / day}

I from rT3 = (126.904 / 777) × Conv rate to rT3 {µg / day}

I from T3 conv = (126.904 / 777) × T4 to T3 conv rate {µg / day}

I from T3 in tissues = 3 × (126.904 / 651) × Abs rate of T3 by tissues {µg / day}

I from T4 in tissues = 4 × (126.904 / 777) × Abs rate of T4 by tissues {µg / day}

I in Blood = INTEG (I abs rate+I from deiod − I excr − Trap rate, 150) {µg}

I in Thy = INTEG (Trap rate − I cons, 15000) {µg}

I inhib thres = MAX(SMOOTH3I( I in Thy, 30, 15000 ) × 1.1, 400) {µg}

I intake = 150 {µg / day}

imp TH sec = normal TH sec × eff of TSH on TH sec {µg / day}

imp TRH sec = normal TRH sec × eff of TH on TRH sec {ng / day}

imp TSH sec = eff of TRH on TSH sec × eff of TH on TSH sec × normal TSH sec {mU /

day}

log ratio of TH to normal = LOG(ratio of TH to normal TH, 10) {dimensionless}

log ratio of TRH to normal = LOG( ratio of TRH to normal, 10 ) {dimensionless}

log ratio of TSH to normal = LOG(ratio of TSH to normal, 10) {dimensionless}

MW of T3 = 651 × 1.66054 × 10^( − 18) {µg}

113

MW of T4 = 777 × 1.66054 × 10^( − 18) {µg}

normal amount of T3 mol = 1.38759e+013 {dimensionless}

normal amount of T4 mol = 3.72024e+013 {dimensionless}

normal hypo prod = 24 × (LN(2) / (6.2 / 60)) × 2 / 40 {ng / day / mg}

normal hypo wt = 40 {mg}

normal I in thy = 15000 {µg}

normal pit prod = 24 × 6.6 × LN(2) / 22.5 {mU / day / mg}

normal pit wt = 22.5 {mg}

normal ratio of T3 to T4 = normal amount of T3 mol / normal amount of T4 mol

{dimensionless}

normal T3 in blood = 5 {µg}

normal T4 to T3 conv fr = (28 / 240) × 777 / 651 {dimensionless}

normal TH = 5.10783e+013 {dimensionless}

normal TH sec = 97 {µg / day}

normal thy prod = 97 / 20 {µg / day / g}

normal thy wt = 20 {mg}

normal TRH = 2 {ng}

normal TRH sec = 24 × (LN(2) / (6.2 / 60)) × 2 {ng / day}

normal TSH = 6.6 {mU}

normal TSH sec = 24 × 6.6 × LN(2) {mU / day}

PAT = LOOKUP EXTRAPOLATE(gr for eff on PAT, ratio of des pit wt to pit wt) {day}

pit cap = normal pit prod × Pit Wt × 10 {mU / day}

Pit Wt = INTEG (Pit wt chg, 22.5) {mg }

Pit wt chg = (des pit wt − Pit Wt) / PAT {mg / day}

pos I cons = I in Thy × 0.15 {µg / day}

pos T3 sec = T3 Store × 0.15 {µg / day}

pos T4 sec = T4 Store × 0.15 {µg / day}

pot fr of T3 sec = (normal ratio of T3 to T4 × 7 / 90) / (ratio of T3 to T4 + normal ratio of

T3 to T4 × 7 / 90) × eff of thy stim on T3 fr {dimensionless}

pot I cons for T3 = pot T3 syn × 3 × 126.904 / 651 {µg / day}

114

pot I cons for T4 = pot T4 syn × 4 × 126.904 / 777 {µg / day}

pot T3 sec = pot TH sec × fr of T3 sec {µg / day}

pot T3 syn = eff of thy cap on T3 syn × thy syn cap for T3 {µg / day}

pot T4 sec = pot TH sec × fr of T4 sec {µg / day}

pot T4 syn = eff of thy cap on T4 syn × thy syn cap for T4 {µg / day}

pot TH sec = eff of cap on TH sec × thy cap {µg / day}

pot TH syn = pot T3 syn+pot T4 syn {µg / day}

pot total I cons = pot I cons for T3 + pot I cons for T4 {µg / day}

pot total I cons under I cap rest = pos I cons × eff of thy I cap {µg / day}

Pot Trap Fr = INTEG (chg in trap fr, (62.8697 / 150)) {1 / day}

ratio of cap rest I cons to pot = pot total I cons under I cap rest / pot total I cons

{dimensionless}

ratio of des hypo wt to hypo wt = des hypo wt / Hypo Wt {dimensionless}

ratio of des pit wt to pit wt = des pit wt / Pit Wt {dimensionless}

ratio of des T3 syn to cap = MAX( des T3 syn , 0) / thy syn cap for T3 {dimensionless}

ratio of des T4 syn to cap = MAX( des T4 syn , 0) / thy syn cap for T4 {dimensionless}

ratio of des thy wt to thy wt = des thy wt / Thy Wt {dimensionless}

ratio of disc btw I rest TH syn and pot TH syn to pot TH syn = 1 − ratio of cap rest I cons

to pot {dimensionless}

ratio of I in thy to thres = I in Thy / I inhib thres {dimensionless}

ratio of imp TH sec to thy cap = imp TH sec / thy cap {dimensionless}

ratio of imp TRH sec to hypo cap = imp TRH sec / hypo cap {dimensionless}

ratio of imp TSH sec to pit cap = imp TSH sec / pit cap {dimensionless}

ratio of pos to pot T3 sec = pos T3 sec / pot T3 sec {dimensionless}

ratio of pos to pot T4 sec = pos T4 sec / pot T4 sec {dimensionless}

ratio of pot to pos I cons = pot total I cons / pos I cons {dimensionless}

ratio of short smth imp TH sec to normal = short smth imp TH sec / normal TH sec

{dimensionless}

ratio of smth imp TH sec to normal = smth imp TH sec / normal TH sec {dimensionless}

115

ratio of smth imp TRH sec to normal = smth imp TRH sec / normal TRH sec

{dimensionless}

ratio of smth imp TSH sec to normal = smth imp TSH sec / normal TSH sec

{dimensionless}

ratio of T3 to normal = T3 in Blood / normal T3 in blood {dimensionless}

ratio of T3 to T4 = total free T3 molecules / total free T4 molecules {dimensionless}

ratio of TH to normal TH = "total free T3&T4 molecules" / normal TH {dimensionless}

ratio of thy I conc to normal = I in Thy / normal I in thy {dimensionless}

ratio of TRH to normal = TRH / normal TRH {dimensionless}

ratio of TSH to normal = TSH / normal TSH {dimensionless}

retained I = I from rT3+I from T3 in tissues+I from T4 in tissues+I from T3 conv {µg /

day}

short smth imp TH sec = SMOOTH3I( imp TH sec, 10, 97 ) {µg / day}

smth imp TH sec = SMOOTH3I( imp TH sec, 20, 97 ) {µg / day}

smth imp TRH sec = SMOOTH3I(imp TRH sec, 20, 24 × (LN(2) / (6.2 / 60)) × 2) {ng /

day}

smth imp TSH sec = SMOOTH3I( imp TSH sec, 20, 24 × 6.6 × LN(2) ) {mU / day}

T3 clear fr = LN(2) / 1 {1day}

T3 clear rate = T3 in Blood × T3 clear fr {µg / day}

T3 conc = T3 in Blood / 30 {µg / dL}

T3 from deiod of T4 = T4 to T3 conv rate × 651 / 777 {µg / day}

T3 in Blood = INTEG (T3 from deiod of T4+T3 sec rate − Abs rate of T3 by tissues − T3

clear rate, 5) {µg}

T3 sec rate = pot T3 sec × eff of T3 store cap {µg / day}

T3 Store = INTEG (T3 syn rate − T3 sec rate,420) {µg}

T3 store adj = disc from des T3 store / AT for store restor {µg / day}

T3 syn rate = (pot T3 syn − disc btw pot T3 syn and I rest T3 syn × eff of pref T3 syn on

red in T3 syn) / MAX(1, (pot T3 syn / MAX(1e − 005,(pot TH syn − disc btw pot TH syn

and I rest TH syn)))) {µg / day}

T4 clear fr = LN( 2 ) / (7) {1 / day}

116

T4 clear rate = T4 in Blood × T4 clear fr {µg / day}

T4 conc = T4 in Blood / 30 {µg / dL}

T4 in Blood = INTEG (T4 sec rate − Abs rate of T4 by tissues − Conv rate to rT3 − T4

clear rate − T4 to T3 conv rate, 240) {µg}

T4 sec rate = pot T4 sec × eff of T4 store cap {µg / day}

T4 Store = INTEG (T4 syn rate − T4 sec rate, 5400) {µg}

T4 store adj = disc from des T4 store / AT for store restor {µg / day}

T4 syn rate = pot TH syn − disc btw pot TH syn and I rest TH syn − T3 syn rate {µg /

day}

T4 to T3 conv fr = eff of T3 conc on peri conv × normal T4 to T3 conv fr {1 / day}

T4 to T3 conv rate = T4 in Blood × T4 to T3 conv fr {µg / day}

TAT = LOOKUP EXTRAPOLATE(gr for eff on TAT, ratio of des thy wt to thy wt) {day}

thy cap = normal thy prod × Thy Wt × 10 × eff of I on thy cap {µg / day}

thy syn cap for T3 = thy cap × fr of T3 sec {µg / day}

thy syn cap for T4 = thy cap × fr of T4 sec {µg / day}

Thy Wt = INTEG (Thy wt chg, 20) {g}

total free T3 molecules = free T3 in blood / MW of T3 {dimensionless}

"total free T3&T4 molecules" = total free T3 molecules+total free T4

molecules{dimensionless}

total free T4 molecules = free T4 in blood / MW of T4{dimensionless}

total normal TH store = 5400 + 420 {µg}

Trap rate = Pot Trap Fr × I in Blood × eff of TSH on I trapping × eff of thy wt on I trap

{µg / day}

TRH = INTEG (TRH sec rate − TRH clear rate, 2) {ng}

TRH clear fr = LN(2) / (6.2 / (60 × 24)) {1 / day}

TRH clear rate = TRH × TRH clear fr {ng / day}

TRH conc = TRH / 10 {ng / ml}

TRH sec rate = eff of cap on TRH sec × hypo cap {ng / day}

TSH = INTEG (TSH sec rate − TSH clear rate, 6.6) {mU}

TSH clear fr = 24 × LN(2) {1 / day}

117

TSH clear rate = TSH × TSH clear fr {mU / day}

TSH conc = TSH / 3 {µU / ml}

TSH sec rate = eff of cap on TSH sec × pit cap {mU / day}

118

REFERENCES

Barlas, Y., 2002, “System Dynamics: Systemic Feedback Modeling for Policy Analysis”,

In Knowledge for Sustainable Development - An Insight into the Encyclopedia of Life

Support Systems, UNESCO-EOLSS Publishers, Paris, France; Oxford, UK, pp. 1131-

1175.

Barlas, Y., 1996, “Formal Aspects of Model Validity and Validation in System

Dynamics”, System Dynamics Review, Vol. 12, No. 3, pp. 183-210.

Ben-Shachar, R., M. Eisenberg, S. A. Huang, and J. J. DiStefano III, 2012, “Simulation of

Post-Thyroidectomy Treatment Alternatives for Triiodothyronine or Thyroxine

Replacement in Pediatric Thyroid Cancer Patients”, Thyroid, Vol. 22, No. 6, pp. 595-

603.

Bhagavan, N. V., 2002, Medical Biochemistry (4th edn), Harcourt/Academic Press, San

Diego.

Braunwald, E., A. S. Fauci, D. L. Kasper, S. L. Hauser, D. L. Longo, and J. L. Jameson

(eds), 2001, Harrison’s Principles of Internal Medicine (15th edn), McGraw-Hill, New

York.

Braverman, L. E., 2003, Diseases of the Thyroid (2nd edn), Humana Press, New Jersey.

Brent, G. A., 2008, “Graves’ Disease”, The New England Journal of Medicine, Vol. 358,

pp. 2594-2605.

Brent, G. A., 2010, Thyroid Function Testing, Springer, New York.

119

Bürgi, H., 2010, “Iodine Excess”, Best Practice & Research Clinical Endocrinology &

Metabolism, Vol. 24, pp. 107-115.

Brown, J. H. U., and D. S. Gann (eds), 1973, Engineering Principles in Physiology,

Academic Press, New York.

Carruthers, S. G., B. B. Hoffman, K. L. Melmon, and D. W. Nierenberg (eds), 2000,

Melmon and Morrelli’s Clinical Pharmacology: Basic Principles in Therapeutics,

McGraw Hill, USA.

Conn P. M. (ed), 2008, Neuroscience in medicine. Humana Press, USA.

Dayan, C. M., and G. H. Daniels, 1996, “Chronic Autoimmune Thyroiditis”, The New

England Journal of Medicine, Vol. 335, No. 2, pp. 99-108.

Degon, M., S. R. Chipkin, C. V. Hollot, R. T. Zoeller, and Y. Chait, 2008, “A

Computational Model of the Human Thyroid”, Mathematical Biosciences, Vol. 212,

No. 1, pp. 22-53.

DiStefano III, J. J., and E. B. Stear, 1968, “Neuroendocrine Control of Thyroid Secretion

in Living Systems: A Feedback Control System Model”, Bulletin of Mathematical

Biology, Vol. 30, No. 1, pp. 3-26.

DiStefano III, J. J., 1969, “A Model of the Normal Thyroid Hormone Glandular Secretion

Mechanism”, Journal of Theoretical Biology, Vol. 22, No. 3, pp. 412-417.

DiStefano III, J. J., 1969, “Hypothalamic and Rate Feedback in the Thyroid Hormone

Regulation System: An Hypothesis”, Bulletin of Mathematical Biology, Vol. 31, No. 2,

pp. 233-246.

120

DiStefano III, J. J., and R. F. Chang, 1971, “Computer Simulation of Thyroid Hormone

Binding, Distribution, and Disposal Dynamics in Man”, American Journal Physiology,

Vol. 221, No. 5, pp. 1529-1544.

DiStefano III, J. J., and F. Mori, 1977, “Parameter Identifiability and Experiment Design:

Thyroid Hormone Metabolism Parameters”, AJP - Regulatory, Integrative and

Comparative Physiology, Vol. 233, No. 3, pp. 134-144.

Donovan, B. T., 1966, The Pituitary Gland, Volume 2. University of California Press,

California.

Eisenberg, M., M. Samuels, and J. J. DiStefano III, 2006, “L-T4 Bioequivalence and

Hormone Replacement Studies via Feedback Control Simulations”, Thyroid, Vol. 16,

No. 12, pp. 1279-1292.

Erkut, Z. A., C. Pool, and D. F. Swaab, 1998, “Glucocorticoids Suppress Corticotropin-

Releasing Hormone and Vasopressin Expression in Human Hypothalamic Neurons”,

The Journal of Clinical Endocrinology & Metabolism, Vol. 83, No. 6, pp. 2066-2073.

Gardner D. F., R. M. Centor, and R. D. Utiger, 1988, “Effect of Low Dose Oral Iodide

Supplementation on Thyroid Function in Normal Men”, Clinical Endocrinology

(Oxford), Vol. 28, pp. 283–288.

Garrison, R., and E. Somer, 1995, The Nutrition Desk Reference, Keats Publishing, USA.

Georgitis W. J., M. T. McDermott, and G. S. Kidd, 1993, “An Iodine Load from Water-

Purification Tablets Alters Thyroid Function in Humans”, Military Medicine, Vol. 158,

No. 12, pp. 794-7.

Goldman, M. B., and M. C. Hatch, 2000, Women and Health, Academic Press, USA.

121

Goodman, H. M., 2009, Basic Medical Endocrinology (4th edn), Academic Press, China.

Greenstein, B., and D. Wood, 2011, The Endocrine System at a Glance (3rd edn), Wiley-

Blackwell.

Grossman, A. (ed), 1998, Clinical Endocrinology (2nd edn), Blackwell Science, United

Kingdom.

Guyton, A. C., and J. E. Hall., 2006, Textbook of Medical Physiology, W.B. Saunders

Company, Philadelphia.

Hays, M., 2009, “Mathematical Models of Human Iodine Metabolism, Including

Assessment of Human Total Body Iodine Content”, In: Comprehensive Handbook of

Iodine, edited by V. R. Preedy, G. N. Burrow and R. R. Watson, Academic Press,

USA.

Izumi, M., and P. R. Larsen, 1977, “Triiodothyronine, Thyroxine, and Iodine in Purified

Thyroglobulin from Patients with Graves' Disease”, The Journal of Clinical

Investigation, Vol. 59, No. 6, pp. 1105-1112.

Khee, M., and S. Leow, 2007, “A Mathematical Model of Pituitary–Thyroid Interaction to

Provide an Insight into the Nature of the Thyrotropin–Thyroid Hormone Relationship”,

Journal of Theoretical Biology, Vol. 248, No. 2, pp. 275-287.

Kronenberg H. M., S. Melmed, K.S. Polonsky, and P. R. Larsen, 2008, Williams Textbook

of Endocrinology, Saunders, Philadelphia.

Laurberg, P., 1984, “Mechanisms Governing the Relative Proportions of Thyroxine and

3,5,3’-Triiodothyronine in Thyroid Secretion”, Metabolism, Vol. 33, No. 4, pp. 379-

392.

122

Lazarus, J. H., 2009. “Acute and Subacute Thyroiditis”. In The Thyroid and Its Diseases.

Available: http://www.thyroidmanager.org/Chapter19/19-frame.htm.

LeMar H. J., Georgitis W. J., and McDermott M. T., 1995, “Thyroid Adaptation to

Chronic Tetraglycine Hydroperiodide water purification tablet use”, The Journal of

Clinical Endocrinology and Metabolism, Vol. 80, pp. 220–223.

Liu, B. Z., and J. H. Peng, 1990, “A Mathematical Model of Hypothalamo-Pituitary-

Thyroid Axis”, Acta Biophysica Sinica, Vol. 6, pp. 431-437.

Liu, Y. W., and B. Z. Liu, 1992, “An Improved Mathematical Model of Hypothalamo-

Pituitary-Thyroid Axis”, Progress in Biochemistry and Biophysics, Vol. 6 pp. 439-443.

Liu, Y. W., B. Z. Liu, J. Xie, and Y. X. Liu, 1994, “An Improved Mathematical Model of

Hypothalamo-Pituitary-Thyroid Axis”, Mathematical and Computer Modelling, Vol.

19, No. 9, pp. 81-90.

Mak, P. H., and J. J. DiStefano III, 1977, “Optimal Control Policies for

the Prescription of Thyroid Hormones”, Mathematical Biosciences, Vol. 42, No. 3-4,

pp. 159-186.

Martini, F. H., 2007, Fundamentals of Anatomy and Physiology, Pearson, Philippines.

McMonigal K. A., L. E. Braverman, J. T. Dunn, J. B. Stanbury, M. L. Wear, P. B. Hamm,

R. L. Sauer, R. D. Billica, and S. L. Pool, 2000, “Thyroid Function Changes Related to

Use of Iodinated Water in The U.S. Space Program”, Aviation Space and

Environmental Medicine, Vol. 71, No. 11, pp. 1120-5.

Melmed, S., 2002, The Pituitary, Blackwell Science, Cambridge.

123

Melmed, S., and P. M. Conn, 2005, Endocrinology: Basic and Clinical Principles,

Humana Press, New Jersey.

Molina, P. E., 2004, Endocrine Physiology, McGraw-Hill Professional, USA.

Motta, M., 1991, Brain Endocrinology, Raven Press, New York.

Namba H., S. Yamashita, H. Kimura, N. Yokoyama, T. Usa, A. Otsuru, M. Izumi, and S.

Nagataki, 1993, “Evidence of Thyroid Volume Increase in Normal Subjects Receiving

Excess Iodide”, The Journal of Clinical Endocrinology & Metabolism, Vol. 76, pp.

605–608.

Negi, C. S., 2009, Introduction to Endocrinology, PHI Learning, New Delhi.

Nussey, S., and S. Whitehead, 2001. Endocrinology: An Integrated Approach, Oxford,

London.

Nyström, E., G. E. B. Berg, S. K. G. Jansson, O. Torring, and S. V. Valdemarsson, 2011,

Thyroid Disease in Adults, Springer, Berlin.

Oertli, D., and R. Udelsman (eds), 2007, Surgery of the Thyroid and Parathyroid Glands,

Springer, Berlin.

Paul, T., B. Meyers, R. J. Witorsch, S. Pino, S. Chipkin, S. H. Ingbar, and L. E.

Braverman, 1988, “The Effect of Small Increases in Dietary Iodine on Thyroid Function

in Euthyroid Subjects”, Metabolism, Vol. 37, pp. 121–124.

Philippou G., D. A. Koutras, G. Piperingos, A. Souvatzoglou, and S. D. Moulopoulos,

1992, “The Effect of Iodide on Serum Thyroid Hormone Levels in Normal Persons, in

Hyperthyroid Patients, and in Hypothyroid Patients on Thyroxine Replacement”,

Clinical Endocrinology (Oxford), Vol.36, pp. 573–578.

124

Raymond, K. W., 2009, General Organic and Biological Chemistry, Wiley, USA.

Rhoades, R. A., and D. R., Bell, 2009, Medical Physiology: Principles for Clinical

Medicine (3rd edn), Lippincott Williams & Wilkins, Philadelphia.

Rubin, A. L., 2006, Thyroid for Dummies (2nd edn), Wiley, New Jersey.

Smith, P. E., 1930, “Hypophysectomy and a Replacement Therapy in the Rat”, American

Journal of Anatomy, Vol. 45, No. 2, pp. 205-273.

Sodeman, W. A., and T. M. Sodeman, 1985, Pathologic Physiology: Mechanisms of

Disease, Saunders, Philadelphia.

Stanbury, J. B., A. E. Ermans, P. Bourdoux, C. Todd, E. Oken, R. Tonglet, G. Vidor, L. E.

Braverman, and G. Medeiros-Neto, 1998, “Iodine-Induced Hyperthyroidism:

Occurrence and Epidemiology”, Thyroid, Vol. 8, No. 1, pp. 83-100.

Synder, P. J., and R. D. Utiger, 1972. “Inhibition of Thyrotropin Response to Thyrotropin-

Releasing Hormone by Small Quantities of Thyroid Hormones”, The Journal of

Clinical Investigation, Vol. 51, pp. 2077-2084.

Thapar, K., K. Kovacs, B. W. Scheithauer, and R. V. Lloyd, 2001. Diagnosis and

Management of Pituitary Tumors, Humana Press, New Jersey.

Tucker, M. J., 1999, “Pituitary Toxicology: Direct Toxicity, Secondary Changes and Effects

on Distal Target Tissues”, In: Endocrine and Hormonal Toxicology, edited by P. W.

Harvey, K. C. Rush and A. Cockburn, Wiley, England.

Van den Berghe, G., 2008, Acute Endocrinology: From Cause to Consequence, Humana

Press, New York.

125

Vagenakis A. G., P. Downs, L. E. Braverman, A. Burger, and S. H. Ingbar, 1973, “Control

of Thyroid Hormone Secretion in Normal Subjects Receiving Excess Iodides”, The

Journal of Clinical Investigation, Vol. 52, pp. 528–532.

Vassart, G., and J. E. Dumont, 1992, “The Thyrotropin Receptor and the Regulation of

Thyrocyte Function and Growth”, Endocrine Reviews, Vol. 13, No. 3, pp. 596-611.

Van Vliet, G., and M. Polak, 2007, Thyroid Gland Development and Function, Karger,

Switzerland.

Werner, S. C., S. H. Ingbar, L. E. Braverman, and R. D. Utiger, 2005, Werner & Ingbar’s

The Thyroid: A Fundamental and Clinical Text, Lippincott Williams & Wilkins,

Philadelphia.

White, W. E., 1933, “The Effect of Hypophysectomy on the Rabbit”, In: Proceedings of

the Royal Society of London, Vol. 114, No. 786, pp. 64-79.

Wilson, K. C., J. J. DiStefano III, D. A. Fisher, and J. Sack, 1977, “System Analysis and

Estimation of Key Parameters of Thyroid Hormone Metabolism in Sheep”, Annals of

Biomedical Engineering, Vol. 5, No. 1, pp. 70-84.

Yadav, M., 2008, Mammalian Endocrinology, Discovery Publishing House, New Delhi.

Zimmermann, M. B., 2009, “Iodine Deficiency”, Endocrine Reviews, Vol. 30, No. 4, pp.

376-408.

modeling the dynamics of thyroid … the dynamics of thyroid hormones and related disorders by oylum...

Documents