Thyrotropic
Feedback Control
Mathematical
models of the pituitarythyroid axis:
In 1940, eleven years after the discovery of the thyrotropic hormone TSH by Aron in the year 1929, W. T. Salter postulated the existence of a control loop linking the pituitary and thyroid gland. This idea was inspired by the recent description of the two gonadotropic feedback control loops. Only a few years later, Astwood and Hoskins could reveal both the existence and the pathophysological relevance of this thyrotropic feedback control system. In 1968, Panda and Turner succeeded in a quantitative description ot the interdependence of thyroxine and TSH levels, but the first mathematical models of the feedback loop had already been developed up to 12 years earlier.
Over the years, these models were increasingly improved. As a consequence of this continued evolution, some of the newest models [Dietrich 2001, Dietrich et al. 2004 and Eisenberg et al. 2010] are also suitable for medical decision making.
Today, modelling of thyrotropic feedback control is faced with the challenge of newly discovered complexities in the information processing structure, e. g. Ultrashort feedback control of TSH secretion (KakitaLabordeOdell loop and BrokkenWiersingaPrummel loop) and longfeedback of iodothyronines on hypothalamic TRH release (FeketeLechan loop).
For a more comprehensive review of mathematical models of thyroid homeostasis see Dietrich et al. 2012.
A
selection of historic and modern models:
Model

Year

Transfer
characteristics

Information
processing structure

Danziger and Elmergreen

1956

linear

phenomenological

Roston

1959

linear
with basal secretion

phenomenological

Norwich and Reiter

1965

linear

phenomenological

DiStefano
and Stear

1968

linear
with basal secretion

phenomenological,
partly parametrically isomorphic

DiStefano

1969

linear
with basal secretion

phenomenological,
partly parametrically isomorphic

DiStefano
et al.

1975

N/A

parametrically
isomorphic

Saratchandran
et al.

1976

logarithmic
/ linear

phenomenological,
partly parametrically isomorphic

Seif 
1977 
logarithmic / linear 
phenomenological, partly parametrically isomorphic 
Wilkin

1977

limit
elements

phenomenological,
partly parametrically isomorphic

Cohen

1990

exponential

phenomenological

Li
et al.

1995

complex
polynoms

phenomenological,
partly parametrically isomorphic

Dietrich
et al.

1997

MichealisMenten
kinetics and linear elements

partly
parametrically isomorphic (Model 2 
see
below)

Dietrich
et al.

1997

MiMeNoCoDi
model

parametrically
isomorphic (Model 7.1  see
below )

Dietrich
et al.

1998

MiMeNoCoDi
model

parametrically
isomorphic (Model 9  see
below )

Dietrich
et al.

2001

MiMeNoCoDi
model

parametrically
isomorphic (Model 10  see
below )

Degon
et al.

2005

based on compartment and flux analysis

parametrically
isomorphic, but intrathyroidal kinetics
only

Leow 
2007 
Second order Bernoulli differential equations with hysteresis,
inverse exponental power law of TSH response 
partly parametrically isomorphic 
Eisenberg et al.

2010

Based on DiStefanos models from 1968, 1969 and 1975

parametrically
isomorphic

Versions
of nonlinear models based on or related to the
MiMeNoCoDI
model:
Version

Comment

1

MichaelisMenten
kinetics in pituitary and thyroid gland
(II1997)

2

Introduction
of time constants, plasma protein binding also
for T3 (II1997, presented at ETA
'97)

3

MichaelisMenten
kinetics for 5'Dejodinase

4

Type
I and Type II 5'Dejodinase
differentiated

5

Feedback
term changed (abandoned again,
VIII1997)

6

Feedback
term corrected (VIII1997)

7

Non
competitive quotient inhibition in form of
vtype allostery, plasma protein binding for T3
addressed in a more differentiated manner
(VIII1997)

7.1

Changed
name conventions (XI1997, presented in the
colloqium of endocrine methods, university of
Munich)

8

Ultrashort
feedback in anterior pituitary introduced
(IV1998)

9

Ultrashort
feedback now covering MichaelisMenten kinetics
(V1998, presented at Symposium Gentianum
1999)

9.1

Changed
name conventions, disturbances better addressed
in simulation (IV1999)

10

Intracellular
binding substrate introduced (presented at
EMCSR
2002,
published with LogosVerlag
and in CBS)

11

Introduction
of Longfeedback at TRH site
(planned)
