Thyrotropic Feedback Control: Evidence for an Additional Ultrashort Feedback Loop from Fractal Analysis

THYROTROPICFEEDBACKCONTROL: EVIDENCE
FORANADDITIONALULTRASHORTFEEDBACK
LOOPFROMFRACTAL ANALYSIS
J.W. DIETRICH
Abteilung InnereMedizin I, Medizinische Klinik und Poliklinik,
Universit�tsklinikumUlm, Ulm, Germany
A.TESCHE
Chirurgische Klinik, Klinikum, Campus Innenstadt,
Ludwig-Maximilian-University of Munich, Munich, Germany
C. R. PICKARDT
Medizinische Klinik, Klinikum, Campus Innenstadt,
Ludwig-Maximilian-University of Munich, Munich, Germany
U.MITZDORF
Institut fˇr Medizinische Psychologie,
Ludwig-Maximilian-University of Munich, Munich, Germany
More than 70 years after the discovery of the pituitary�thyroid feedback
control mechanism, a classical endocrine regulation system, most of its
parameters have been identified. However, the regulation of its central com-
ponent in the pituitary gland, probably responsible for pulsatile release of
thyrotropin (TSH), remains obscure. In order to infer its structure from the
system’s behavior, four different pituitary models were created and compared
regarding their fractal properties. Based on the simplest model showing
Address correspondence to Dr. Johannes W. Dietrich, M. D., Sektion Endokrinologie,
Abteilung Innere Medizin I, Medizinische Klinik und Poliklinik, Universita¨tsklinikum
Ulm, Robert-Koch-Str. 8, D-89081 Ulm, F. R. Germany. E-mail: johannes.dietrich@
medizin.uni-ulm.de
Cybernetics and Systems: An InternationalJournal, 35: 315�331, 2004
Copyright#Taylor & Francis Inc.
ISSN: 0196-9722 print/1087-6553 online
DOI: 10.1080/01969720490443354
315

noncompetitive inhibition of TSH release by thyroid hormones—a physio-
logically plausible correlation—one alternative model added stochastic
stimulation by central signals and another added an additional intrapituitary
feedback loop, whereas the fourth model combined both effects. This latter
model combining noncompetitive inhibition with the two additional effects
showed the same fractal dimensions as in vivo time series, whereas the simpler
models yielded significantly lower time-series complexity. These results
suggest that both stochastic stimulation and ultrashort loop feedback are
involved in the generation of TSH pulses in the human pituitary.
INTRODUCTION
Pulsatile release of hormones is common in endocrine systems, and is
achieved by combining analog signal encoding with amplitude or fre-
quency modulation. Pulsatility contributes to reliable information
transfer. Furthermore, oscillating hormone levels help to prevent desen-
sitization of target cells that would otherwise be caused by down-
regulation of specific receptors. The pituitary�thyroid feedback control
(thyrotropic feedback control) involves two classes of hormones, the
peptide hormones thyroliberin (TRH) and thyrotropin (TSH) and two
thyroid hormones (T4 or thyroxine and T3 or triiodothyronine, Figure 1).
Although little is known about the temporal patterns of TRH levels in the
portal system of the pituitary stalk, the release of TSH into blood plasma
is known to occur in a pulse-like manner. Being similar to other signaling
pathways based on peptide hormones, the thyrotropic information
transfer occurs via amplitude modulation of the TSH level. Faster
oscillations with a rate of 5 to 20 per 24 h are superimposed on a
circadian rhythm with maximum TSH levels early in the morning.
The mechanism causing the fast TSH oscillations is unknown. The
previously favored hypothesis assuming a pulsatile input of TRH at the
pituitary yielding corresponding TSH pulses has been disproved by
Samuels et al. (1993), who showed that subjects receiving constant high
doses of TRH still exhibited TSH levels with significant pulses. Until now
TSH patterns were mainly classified by comparatively simple measures
like amplitude and rate. More sophisticated approaches using methods
from nonlinear systems science to measure the complexity of the signal
patterns have been applied to other endocrine control systems, for
example, to the release of PTH in the calcium phosphate homeostasis
(Prank et al. 1994).
316 J. W. DIETRICH ET AL.

Thyroid hormones play a key role in controlling the activity of
growth, differentiation, and metabolism. Nevertheless, the physiology of
the thyrotropic feedback control and the factors influencing its behavior
are only partly understood. Previous models of pituitary�thyroid feed-
back control were implemented in a ‘‘behaviorally isomorphic’’ way
using different classes of equations (linear, logarithmic, exponential, or
polynomial), their parameters optimized to yield behavior resembling
that of a living organism (Danziger and Elmergreen 1956; Roston 1959;
Norwich and Reiter 1965; DiStefano 1969; Saratchandran et al. 1976;
Wilkin et al. 1977; Cohen 1990; Li et al. 1995). Even though these models
propose possible alternative ways in which the system might be realized,
this approach also exposes the models to charges of being arbitrary.
Figure 1. Overview of the pituitary�thyroid feedback control. Black lines indicate known
relations, gray lines possible additional effects. TRH: TSH releasing hormone (thyrotropin);
TSH: thyroid stimulating hormone; T4: thyroxine; FT4: free T4: T3: triiodothyronine; FT3:
free T3.
THYROTROPIC FEEDBACK CONTROL 317

Exhaustive functional investigations of the human pituitary in vivo
are practically impossible. The objective of this study, therefore, was to
develop a parametrically isomorphic simulative approach for gathering
information about the structure of pituitary information processing from
the system’s behavior.
METHODS
TheModel
In order to elucidate the unknown mechanism of pulsatile TSH release,
we created a set of physiologically consistent models (Table 1). Where
empirically determined input�output relations were available, all models
shared the same parametrically isomorphic basis. Modifications have
been implemented at the level of the pituitary gland, whose dynamic
properties are not yet well characterized.
The system was analyzed in two ways: First, the equations were
solved analytically to obtain instant solutions of the mean equifinal
hormone levels. In a second step, a computer simulation was generated to
obtain time series of the respective hormone levels. The simulation
program was developed in Pascal on an Apple Macintosh workstation.
The model was based on two principal mechanisms of biological
information transfer, the Michaelis�Menten�Hill kinetics and the
Analog Signal memory with Intrinsic Adjustment (ASIA) element,
supplemented by several feedback loops for the binding of hormones to
plasma proteins.
Michaelis�Menten�Hill kinetics are known to determine the beha-
vior of enzymatic conversion processes and receptor-mediated signal
transduction systems (Figure 2). The subsystems respond with
ya ¼
Gxe
Dþ xe
ð1Þ
to an input signal xe, where G is the maximum possible response of the
transduction element and D is the input signal yielding half of the
maximum response G.
The temporal behavior of the system’s variables was modeled with
ASIA elements that essentially consist of a variable stimulating its own
degradation with
318 J. W. DIETRICH ET AL.

dy
dt
¼ axðtÞ � byðtÞ ð2Þ
in a first-order linear feedback loop (Dietrich 2000), where y denotes the
output signal, a is the input gain factor, and b is a gain factor for output
extinction. In the equifinal state the subsystem’s behavior will converge to
y1 ¼
axðtÞ
b ð3Þ
with a first-order time constant of
t1 ¼
1
b : ð4Þ
Binding of thyroid hormones to plasma proteins was simulated in a
zeroth-order linear feedback loop according to the mass action law with
½HF� ¼ ½HT� � K½P�½HF� ð5Þ
where ½HF� denotes the concentration of the free hormone, ½HT� the total
hormone level, K a binding constant, and ½P� the concentration of the
respective plasma protein (e.g., TBG). In equilibrium, a level of
½HF� ¼
½HT�
1þ K½P� ð6Þ
will result.
Figure 2. The Michaelis�Menten�Hill kinetics.
THYROTROPIC FEEDBACK CONTROL 319

For each level of signal transfer the respective equations were map-
ped to values taken from empirical studies (Tables 2�4).
Obviously, information processing at the pituitary level occurs in a
more complex way than it does in the thyroid gland and its target tissues.
Due to the paucity of empirical input�output relations, we modeled four
distinct subsystems differing in the temporal pattern of TRH release into
the hypothalamopituitary portal vessels as well as in the presence or
absence of an ultrashort feedback loop connecting level and release of
pituitary TSH (Figure 3). Common to all four models was the assump-
tion of a noncompetitive inhibition of TSH release by receptor-bound
triiodothyronine ð½T3�RÞ in the form of
Table 1. Characteristics of the four variants of the pituitary model
Version TRH level Ultrashort feedback
1 CV Omitted
2 CV and LGN Omitted
3 CV Present
4 CV and LGN Present
CV¼ circadian variation, LGN¼ log-normal Gaussian noise.
Table 2. Numerical implementation of the Michaelis�Menten�Hill kinetics
Symbol Explanation Value
GH Secretion capacity of the pituitary 817 mU/s
DH Damping constant (EC50) of TRH at the
pituitary
47 nmol/l
GT Secretion capacity of thyroid gland 3.4 pmol/s
DT Damping constant (EC50) of TSH at the
thyroid gland
2.75 mU/1
GD1 Maximum activity of type I deiodinase 28 nmol/s
KM1 Dissociation constant of 50-deiodinase I 500 nmol/1
GD2 Maximum activity of type II deiodinase 4.3 fmol/s
KM2 Dissociation constant of 50-deiodinase II 1 nmol/1
GR Maximum gain of TRb receptors 1 mol/s
DR EC50 for central T3 100 pmol/1
SS Brake constant of TSH ultrashort feedback 100 1/mU
DS EC50 for TSH at the pituitary 50 mU/1
Empirically determined values from D’Angelo et al. (1976), Dumont and Vassart (1995),
Greenspan (1997), Lazar and Chin (1990), Okuno et al. (1979). van Doorn et al. (1985),
Visser et al. (1983), and from our own data (Dietrich 2002).
320 J. W. DIETRICH ET AL.

d½TSH�
dt
¼ aSGH½TRH�OðDH þ ½TRH�OÞð1 þ LS½T3�RÞ
� bS½TSH� ð7Þ
where ½TRH�O denotes the TRH level in the pituitary stalk vessels; see
Tables 2 and 3 for an explanation of other symbols. Further variants 3
and 4 of the pituitary model include an ultrashort feedback mechanism of
TSH in the pituitary interstitium ½TSH�Z on its own release according to
d½TSH�
dt
¼ aSGH½TRH�OðDH þ ½TRH�OÞð1 þ LS½T3�RÞZ
� bS½TSH� ð8Þ
with
Z ¼ 1 þ SS½TSH�z
DS þ ½TSH�z
� �
: ð9Þ
Table 3. Parameterization of ASIA elements
aR Dilution factor for peripheral TRH 0.4 l-1
bR Clearance exponent for TRH 2.3 e-3 s-1
aS Dilution factor for TSH 0.4 l-1
bS Clearance exponent for TSH 2.3 e-4 s-1
aT Dilution factor for T4 0.1 l-1
bT Clearance exponent for T4 1.1 e-6 s-1
a31 Dilution factor for peripheral T3 2.6 e-2 l-1
b31 Clearance exponent for T3P 8 e-6 s-1
a32 Dilution factor for central T3 1.3 e5 l-1
b32 Clearance exponent for central T3 8.3 e-4 s-1
aS2 Dilution factor for pituitary TSH 2.6 e5 l-1
bS2 Clearance exponent for central TSH 140 s-1
Empirical values from Benvenga and Robbins (1998), Duntas et al. (1990), Greenspan
(1997), Grußendorf (1988), Odell et al. (1967), Oppenheimer et al. (1967).
Table 4. Dissociation constants of hormonic binding
K30 Dissociation constant T3-TBG 2 e9 l/mol
K31 Dissociation constant T3-IBS 2 e9 l/mol
K41 Dissociation constant T4-TBG 2 e10 l/mol
K42 Dissociation constant T4-TBPA 2 e8 l/mol
Values from Li et al. (1995).
THYROTROPIC FEEDBACK CONTROL 321

Pituitary models 1 and 3 assume a portal TRH level that is—except for
circadian variation—constant, whereas versions 2 and 4 implement
additional stochastic variations of the TRH level in the hypothalamo-
pituitary vessels. To be congruent with observations made with other
peptide hormones, the TRH fluctuations were simulated by means of a
Gaussian random generator delivering a log-normal distribution (Spaniol
and Hoff 1995).
Fractal Dimensioning
In order to compare simulated to real-life time series, recordings made
from volunteers by Brabant et al. (1990), Greenspan et al. (1986), and
Samuels et al. (1990) were digitized and processed by two programs for
calculating the fractal dimensions of the signal patterns.
The first measure of complexity used was the fractal capacity
dimension D0. This approach covers the graphical representation of the
Figure 3. Different versions of the pituitary model.
322 J. W. DIETRICH ET AL.

time series with squares of successively varied border length s using the
mesh-counting theorem. For each length it counts the number of squares,
NðsÞ, covering the curve. With
D0 ¼ lim
s!0
logNðsÞ
logð1=sÞ ; ð10Þ
the capacity dimension can be calculated and compared for real and
simulated time series.
By means of a second approach to determine the data’s complexity,
the so-called correlation dimension D2 (Loistl and Betz 1996) was
calculated.
After embedding the time series x1; x2; x3; . . . ; xN into the m-dimen-
sional vector
Qi ¼ ðxi; xiþp; xiþ2p; . . . ; xiþ½m�1�pÞ; ð11Þ
the local density
niðeÞ ¼
1
N
XN
j¼1
u0ðe � kQj �QikÞ ð12Þ
as the relative number of neighbor points of an attractor point Qi whose
distance is smaller than e results with the Heaviside function
u0ðxÞ ¼
0; x < 0
1; x > 0:
ð13Þ
Subsequently, by averaging over several reference points the correlation
integral
CðeÞ ¼ 1
M2
XM
i;j¼1
i 6¼j
u0ðe � kQj �QikÞ; ð14Þ
as the number of correlated vectors normalized over the number of
possible vector pairs M2, could be calculated.
THYROTROPIC FEEDBACK CONTROL 323

For each embedding dimension, formally similar to the definition of
the capacity dimension, a specific local correlation dimension D2 can be
obtained from
D2 ¼ lime!0
logCðeÞ
log e : ð15Þ
The first maximum of the local correlation dimensions D2, arranged by
increasing embedding dimension m, was regarded as a global correlation
dimension of the time series.
Eight real time series adopted from Brabant et al. (1990), Greenspan
et al. (1986), and Samuels et al. (1990) were respectively compared with
eight time series generated from each pituitary model.
The capacity dimension was calculated with the Fractal Dimension
Calculator 1.5 by Paul Bourke (Astrophysics and Supercomputing
Centre, Swimburne University of Technology, Hawthorn, Melbourne,
Australia, available from http://astronomy.swin.edu.au/pbourke/
fractals/fracdim/).
Correlation and embedding dimensions were calculated with the
application C(D2) (J. W. Dietrich, University of Munich, Germany,
available from http://link.medion.med.uni-muenchen.de/cybermed/
nonlin/cd2/).
RESULTS
All four models showed the same results for equifinal hormone levels as
those obtained by analytically solving the model equations for TSH, FT4,
and FT3. The equation system is solved via a cubic equation as casus
irreducibilis with three mathematically real solutions. Only solution 1 is
Table 5. Solutions for the equilibrium levels of the simulated hormone
levels
Parameter Solution 1 Solution 2 Solution 3
TSH 1.8 mU/l 7 1.2 mU/l 7 1.2 mU/l
FT4 1.4 ng/dl 7 2.4 ng/dl 7 2.4 ng/dl
FT3 3.5 pg/ml 7 6.0 pg/ml 7 6.0 pg/ml
324 J. W. DIETRICH ET AL.

realizable in a biological context; the other two results are negative
(Table 5).
Obviously, the simulated parameters are located within known
reference regions for healthy individuals.
The differences between the four variants are disclosed in the
comparison of the time series delivered by the computer simulations
(Figure 4). Fractal properties are implied by the four variants as shown in
Table 6 and Figure 5.
As revealed by all dimension measures, pituitary models 1, 2, and 3
exhibit significantly lower complexity than real time series, whereas the
fractal behavior of model 4 is comparable to that of empirical data
(except for a smaller variance of simulated time series for the capacity
dimension).
Figure 4. The behavior of the four versions of the pituitary model (time series over 24 hr
simulated time).
THYROTROPIC FEEDBACK CONTROL 325

DISCUSSION
The existence of a feedback loop interconnecting the pituitary and
thyroid gland has been known for decades (Aron 1929, Crew and
Wiesner 1930). Nevertheless, the algorithms of information processing
inside the pituitary remained unclear. The inhibiting effect of TSH on its
Figure 5. Fractal dimensions of the four pituitary models compared with empirical data.
Table 6. Fractal properties of the models and empirical time series
Mean dimensions D0 D2 m
Empirical 1.20 1.75 19.63
Model 1 0.96** 0.76** 1.00**
Model 2 1.04** 0.77** 1.00**
Model 3 0.99** 0.74** 1.13**
Model 4 1.18 1.91 20.14
D0: Capacity dimension, D2: correlation dimension, m: embedding
dimension,**: p < 0,001, t-test for independent samples, comparison
of empirical and simulated time series
326 J. W. DIETRICH ET AL.

Figure 6. Information processing structure of the overall system according to version 4 of
the pituitary model. [T3�P, [FT3�P, [T3�Z, [T3�N and [T3�R: concentrations of peripheral, free
peripheral, total intracellular, free intracellular, and receptor bound T3, respectively
(adapted, with permission, from Dietrich [2002]).
THYROTROPIC FEEDBACK CONTROL 327

own release has been observed in animals (Kakita and Odell 1986; Kakita
et al. 1984). There is some controversy whether or not this kind of
‘‘ultrashort feedback’’ exists in humans, although Prummel et al. (1997)
found TSH receptors in human pituitary tissue.
Like other peptide hormones, TSH is secreted episodically. Since
TRH pulses have been ruled out as the cause of these rhythms, the
location and nature of the pulse generator remain obscure.
Apart from the mechanisms occurring in the central organs, the
physiology of thyroid regulation seems to be well characterized. There-
fore, it was possible to develop a model relying predominantly on
empirically defined input�output relations (again except for pituitary
regulation). This parametrically isomorphic model could then be used to
test different variants for the as yet unknown information processing
within the pituitary gland.
In the form of Michaelis�Menten�Hill kinetics with one additional
noncompetitive inhibitory site, the first pituitary model was physiologi-
cally plausible and relatively simple. Alternative models added stochastic
stimulation by TRH and/or an ultrashort feedback loop inhibiting the
TSH release by interstitial thyrotropin in the pituitary.
Although all variants yielded the same equilibrium hormone levels,
their behavior over time was different. All versions failed to reach the
complexity of real time series, with the exception of the fourth model.
It may appear to be trivial to observe that the rising complexity
within an information-processing structure parallels the increasing com-
plexity of the time series. Nevertheless, the fact that simulated time series
from model 4 show dimensions nearly identical to real time series sup-
ports the hypothesis that they may be caused by isomorphic processes.
Certainly, the system’s behavior in vivo will be influenced by additional
factors, an assumption that is supported, for example, by the larger
standard deviation of natural capacity and correlation dimensions com-
pared with simulated data.
The results of our simulations suggest that regulation of thyroid
activity might be more complex than simple noncompetitive inhibition of
the TRH-mediated activation of TSH release. Together with the identi-
fication of TSH receptors in the pituitary tissue (Prummel et al. 1997,
2000; Brokken et al. 2001), our results support the hypothesis that an
ultrashort feedback loop in the pituitary gland may also play a role in
human physiology (Figure 6).
328 J. W. DIETRICH ET AL.

When inspecting the simulated time series (Figure 4) it is striking to
note that the amplitudes of the TSH pulses increase when the circadian
rhythms yield a maximum of the basal TSH activity. This observation
can also be made with empirical data, although this effect has hitherto
rarely been described (e.g., by Adriaanse et al. 1993).
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