THYROTROPIC FEEDBACK CONTROL: EVIDENCE FOR AN ADDITIONAL ULTRASHORT FEEDBACK LOOP FROM FRACTAL ANALYSIS

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1 Cybernetics and Systems: An International Journal, 35: , 2004 Copyright #Taylor & Francis Inc. ISSN: print/ online DOI: / THYROTROPIC FEEDBACK CONTROL: EVIDENCE FOR AN ADDITIONAL ULTRASHORT FEEDBACK LOOP FROM FRACTAL ANALYSIS J. W. DIETRICH Abteilung Innere Medizin I, Medizinische Klinik und Poliklinik, UniversitÌtsklinikum Ulm, 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 component 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, Universitätsklinikum Ulm, Robert-Koch-Str. 8, D Ulm, F. R. Germany. johannes.dietrich@ medizin.uni-ulm.de 315

2 316 J. W. DIETRICH ET AL. noncompetitive inhibition of TSH release by thyroid hormones a physiologically 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 frequency modulation. Pulsatility contributes to reliable information transfer. Furthermore, oscillating hormone levels help to prevent desensitization of target cells that would otherwise be caused by downregulation 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 (T 4 or thyroxine and T 3 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).

3 THYROTROPIC FEEDBACK CONTROL 317 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; T 4 : thyroxine; FT 4 : free T 4 :T 3 : triiodothyronine; FT 3 : free T 3. 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 feedback 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.

4 318 J. W. DIETRICH ET AL. 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 The Model 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 behavior of enzymatic conversion processes and receptor-mediated signal transduction systems (Figure 2). The subsystems respond with y a ¼ Gx e D þ x e ð1þ to an input signal x e, 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

5 THYROTROPIC FEEDBACK CONTROL 319 Figure 2. The Michaelis Menten Hill kinetics. 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 y 1 ¼ axðtþ b ð3þ with a first-order time constant of t 1 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 ½H F Š¼½H T Š K½PŠ½H F Š ð5þ where ½H F Š denotes the concentration of the free hormone, ½H T Š the total hormone level, K a binding constant, and ½PŠ the concentration of the respective plasma protein (e.g., TBG). In equilibrium, a level of ½H F Š¼ ½H TŠ 1 þ K½PŠ ð6þ will result.

6 320 J. W. DIETRICH ET AL. 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 CV ¼ circadian variation, LGN ¼ log-normal Gaussian noise. For each level of signal transfer the respective equations were mapped 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 assumption of a noncompetitive inhibition of TSH release by receptor-bound triiodothyronine ð½t 3 Š R Þ in the form of Table 2. Numerical implementation of the Michaelis Menten Hill kinetics Symbol Explanation Value G H Secretion capacity of the pituitary 817 mu/s D H Damping constant (EC 50 ) of TRH at the 47 nmol/l pituitary G T Secretion capacity of thyroid gland 3.4 pmol/s D T Damping constant (EC 50 ) of TSH at the 2.75 mu/1 thyroid gland G D1 Maximum activity of type I deiodinase 28 nmol/s K M1 Dissociation constant of 5 0 -deiodinase I 500 nmol/1 G D2 Maximum activity of type II deiodinase 4.3 fmol/s K M2 Dissociation constant of 5 0 -deiodinase II 1 nmol/1 G R Maximum gain of TRb receptors 1 mol/s D R EC 50 for central T3 100 pmol/1 S S Brake constant of TSH ultrashort feedback 100 1/mU D S EC 50 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).

7 THYROTROPIC FEEDBACK CONTROL 321 Table 3. Parameterization of ASIA elements a R Dilution factor for peripheral TRH 0.4 l-1 b R Clearance exponent for TRH 2.3 e-3 s-1 a S Dilution factor for TSH 0.4 l-1 b S Clearance exponent for TSH 2.3 e-4 s-1 a T Dilution factor for T l-1 b T Clearance exponent for T e-6 s-1 a 31 Dilution factor for peripheral T e-2 l-1 b 31 Clearance exponent for T 3 P 8 e-6 s-1 a 32 Dilution factor for central T e5 l-1 b 32 Clearance exponent for central T e-4 s-1 a S2 Dilution factor for pituitary TSH 2.6 e5 l-1 b S2 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). d½tshš a S G H ½TRHŠ ¼ O dt ðd H þ½trhš O Þð1 þ L S ½T 3 Š R Þ b S½TSHŠ ð7þ where ½TRHŠ 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 ½TSHŠ Z on its own release according to d½tshš dt ¼ a S G H ½TRHŠ O ðd H þ½trhš O Þð1 þ L S ½T 3 Š R ÞZ b S½TSHŠ ð8þ with Z ¼ 1 þ S S½TSHŠ z : ð9þ D S þ½tshš z Table 4. Dissociation constants of hormonic binding K 30 Dissociation constant T 3 -TBG 2 e9 l/mol K 31 Dissociation constant T 3 -IBS 2 e9 l/mol K 41 Dissociation constant T 4 -TBG 2 e10 l/mol K 42 Dissociation constant T 4 -TBPA 2 e8 l/mol Values from Li et al. (1995).

8 322 J. W. DIETRICH ET AL. Figure 3. Different versions of the pituitary model. 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 hypothalamopituitary 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 D 0. This approach covers the graphical representation of the

9 THYROTROPIC FEEDBACK CONTROL 323 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 D 0 ¼ lim s!0 log NðsÞ 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 D 2 (Loistl and Betz 1996) was calculated. After embedding the time series x 1 ; x 2 ; x 3 ;...; x N into the m-dimensional vector Q i ¼ðx i ; x iþp ; x iþ2p ;...; x iþ½m 1Š pþ; ð11þ the local density n i ðeþ ¼ 1 N X N j¼1 u 0 ðe kq j Q i kþ ð12þ as the relative number of neighbor points of an attractor point Q i whose distance is smaller than e results with the Heaviside function u 0 ðxþ ¼ 0; x < 0 1; x > 0: ð13þ Subsequently, by averaging over several reference points the correlation integral CðeÞ ¼ 1 M 2 X M i;j¼1 i6¼j u 0 ðe kq j Q i kþ; ð14þ as the number of correlated vectors normalized over the number of possible vector pairs M 2, could be calculated.

10 324 J. W. DIETRICH ET AL. For each embedding dimension, formally similar to the definition of the capacity dimension, a specific local correlation dimension D 2 can be obtained from log CðeÞ D 2 ¼ lim : ð15þ e!0 log e The first maximum of the local correlation dimensions D 2, 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 fractals/fracdim/). Correlation and embedding dimensions were calculated with the application C(D2) (J. W. Dietrich, University of Munich, Germany, available from 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, FT 4, and FT 3. 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 mu/l mu/l FT ng/dl ng/dl ng/dl FT pg/ml pg/ml pg/ml

11 THYROTROPIC FEEDBACK CONTROL 325 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).

12 326 J. W. DIETRICH ET AL. Table 6. Fractal properties of the models and empirical time series Mean dimensions D 0 D 2 m Empirical Model ** 0.76** 1.00** Model ** 0.77** 1.00** Model ** 0.74** 1.13** Model D 0 : Capacity dimension, D 2 : correlation dimension, m: embedding dimension,**: p < 0,001, t-test for independent samples, comparison of empirical and simulated time series 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.

13 THYROTROPIC FEEDBACK CONTROL 327 Figure 6. Information processing structure of the overall system according to version 4 of the pituitary model. [T 3 Š P,[FT 3 Š P,[T 3 Š Z,[T 3 Š N and [T 3 Š R : concentrations of peripheral, free peripheral, total intracellular, free intracellular, and receptor bound T 3, respectively (adapted, with permission, from Dietrich [2002]).

14 328 J. W. DIETRICH ET AL. 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. Therefore, 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 physiologically 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 complexity of the time series. Nevertheless, the fact that simulated time series from model 4 show dimensions nearly identical to real time series supports 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 compared 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 identification 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).

15 THYROTROPIC FEEDBACK CONTROL 329 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). REFERENCES Adriaanse, R., Brabant, G., Endert, E., and Wiersinga, W. M Pulsatile thyrotropin release in patients with untreated pituitary disease. Journal of Clinical Endocrinology and Metabolism, 77(1): Aron, M Action de la pre hypophyse sur la thyroide chez le cobaye. Comptes Rendus des Se ances de la Socie te de Biologie, 102: Benvenga, S., and Robbins, J Thyroid hormone efflux from monolayer cultures of human fibroblasts and hepatocytes. Effect of lipoproteins and other thyroxine transport proteins. Endocrinology, 139(10): Brabant, G., Prank, K., Ranft, U., Bergmann, P., Schuermeyer, T., Hesch, R. D., and von zur Muhlen, A Circadian and pulsatile TSH secretion under physiological and pathophysiological conditions. Hormone and Metabolic Research Supplement, 23: Brokken, L. J. S., Scheenhart, J. W. C., Wiersinga, W. M., and Prummel, M. F Suppression of serum TSH by Graves ig: Evidence for a functional pituitary TSH receptor. Journal of Clinical Endocrinology and Metabolism, 86(10): Cohen, J. L Thyroid-stimulation hormone and its disorders. In Principles and practice of endocrinology and metabolism, pp , edited by K. L. Becker. Philadelphia: J. B. Lippincolt Company. Crew, F. A. E., and Wiesner, B. P On the existence of a fourth hormone, thyreotropic in nature, of the anterior pituitary. British Medical Journal, 1(April 26): D Angelo, S. A., Paul, D. H., Wall, N. R., and Lombardi, D. M Pituitary thyrotropin (TSH) rebound phenomenon and kinetics of secretion in the goitrous rat: Differential effects of thyroxine on synthesis and release of TSH. Endocrinology, 99(4): Danziger, L., and Elmergreen, G. L The thyroid-pituitary homecostatic mechanism. Bulletin of Mathematical Biophysics, 18:1 13. Dietrich, J. W Signal storage in metabolic pathways: The ASIA element. Kybernetik, 1(3):1 9. Dietrich, J. W. Der Hypophysen-Schilddrusen-Regelkreis. Entwicklung and klinische Anwendung eines nichtlinearen Modells. Spektrum medizinischer Forschung, ed. F. Schardt. Vol. 2. (Berlin: Logos-Verlag, 2002).

16 330 J. W. DIETRICH ET AL. DiStefano, J. J A model of the normal thyroid hormone glandular secretion metabolism. Journal of Theoretical Biology, Dumont, J. E., and Vassart, G Thyroid regulation. In Endocrinology, edited by DeGroot. W. B. Saunders. Duntas, L., Keck, F. S., Rosenthal, J., Wolf, Ch., Loss, U., and Pfeiffer, E. F Single-compartment model analysis of thyrotropin-releasing hormone kinetics in hyper- and hypothyroid patients. Klinische Wochenschrift, 68: Greenspan, F. S The thyroid gland. In Basic & Clinical Endocrinology, pp , edited by F. S. Greenspan and G. J. Strewler. Stamford, CT: Appleton & Lange. Greenspan, S. L., Klibanski, A., Schoenfeld, D., and Ridgway, E. C Pulsatile secretion of thyrotropin in man. Journal of Clinical Endocrinology and Metabolism, 63(3): Grubendorf, M Metabolismus der Schilddru senhormone, 1st ed. Stuttgart, New York: Thieme. Kakita, T., and Odell, W. D Pituitary gland: One site of ultrashort-feedback regulation for control of thyrotropin. American Journal of Physiology, 250(2 Pt 1):E Kakita, T., Laborde, N. P., and Odell, W. D Autoregulatory control of thyrotropin in rabbits. Endocrinology, 114(6): Lazar, M. A., and Chin, W. W Nuclear thyroid hormone receptors. Journal of Clinical Investigation, 86(Dec.): Li, G., Liu, B., and Liu, Y A dynamical model of the pulsatile secretion of the hypothalamo-pituitary-thyroid axis. Biosystems, 35(1): Loistl, O., and Betz, I Chaostheorie, 3rd ed. Munich, Vienna: R. Oldenbourg. Norwich, K. H., and Reiter, R Homeostatic control of thyroxin concentration expressed by a set of linear differential equations. Bulletin of Mathematical Biophysics, 27: Odell, W. D., Utiger, R. D., Wilber, J. F., and Condliffe, P. G Estimation of the secretion rate of thyrotropin in man. Journal of Clinical Investigation, 46(6): Okuno, A., Teguchi, T., Nukayama, K., and Takomoto, M Kinetic analysis of plasma TSH dynamics after TRH stimulation. Hormone and Metabolic Research, 11: Oppenheimer, J. H., Bernstein, G., and Hasen, J Estimation of rapidly exchangeable cellular thyroxine from the plasma disappearance curves of simultaneously administered thyroxine-131i and albumin 125I. Journal of Clinical Investigation, 46(5): Prank, K., Harms, H., Dammig, M., Brabant, G., Mitschke, F., and Hesch, R. D Is there low-dimensional chaos in pulsatile secretion of parathyroid

17 THYROTROPIC FEEDBACK CONTROL 331 hormone in normal human subjects? American Journal of Physiology, 266(4 pt 1):E Prummel, M. F., Méduri, G., and Loosfeldt, H Human anterior pituitary contains a TSH-receptor. Journal of Endocrinological Investigation, 20(5 Suppl.):27. Prummel, M. F., Brokken, L. J. S., Me duri, G., Misrahi, M., Bakker, O., and Wiersinga, W. M Expression of the thyroid-stimulating hormone receptor in the folliculo-stellate cells of the human anterior pituitary. Journal of Clinical Endocrinology and Metabolism, 85(11): Roston, S Mathematical represention of some endocrinological systems. Bulletin of Mathematical Biophysics, 21: Samuels, M. H., Veldhuis, J. D., Henry, P., and Ridgway, E. C Pathophysiology of pulsatile and copulsatile release of thyroid-stimulating hormone, luteinizing hormone, follicle-stimulating hormone, and alphasubunit. Journal of Clinical Endocrinology and Metabolism, 71(2): Samuels, M. H., Henry, P., Luther, M., and Ridgway, E. C Pulsatile TSH secretion during 48-hour continuous TRH infusions. Thyroid, 3(3): Saratchandran, P., Carson, E. R., and Reeve, J An improved mathematical model of human thyroid hormone regulation. Clinical Endocrinology, 5: Spaniol, O., and Hoff, S Ereignisorientierte Simulation, 1st ed., vol. 7, edited by B. Mahr, A. Schill, and G. Vossen. Bonn, Albany, Belmont: International Thomson Publishing. van Doorn, J., Roelfsema, F., and van der Heide, D Concentrations of thyroxine and 3,5,3 0 -triiodothyronine at 34 different sites in euthyroid rats as determined by an isotopic equilibrium technique. Endocrinology, 117(3): Visser, T. J., Kuplun, M. M., Leonard, J. L., and Larsen, P. R Evidence for two pathways of iodothyronine 5 0 -deiodination in rat pituitary that differ in kinetics, propylthiouracil sensitivity, and response to hypothyroidism. Journal of Clinical Investigation, 71(4): Wilkin, T. J., Storey, B. E., Isles, T. E., Crooks, J., and Swanson Beck, J High TSH concentrations in euthyroidism : Explanation based on controlloop theory. British Medical Journal, 1(16 April):