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Hypothalamus–Pituitary–Thyroid Feedback Control: Implications of Mathematical Modeling and Consequences for Thyrotropin (TSH) and Free Thyroxine (FT4) Reference Ranges

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Abstract

The components of thyrotropic feedback control are well established in mainstream physiology and endocrinology, but their relation to the whole system’s integrated behavior remains only partly understood. Most modeling research seeks to derive a generalized model for universal application across all individuals. We show how parameterizable models, based on the principles of control theory, tailored to the individual, can fill these gaps. We develop a system network describing the closed-loop behavior of the hypothalamus–pituitary (HP)–thyroid interaction and the set point targeted by the control system at equilibrium. The stability of this system is defined by using loop gain conditions. Defined points of homeostasis of the hypothalamus–pituitary–thyroid (HPT) feedback loop found at the intersections of the HP and thyroid transfer functions at the boundaries of normal reference ranges were evaluated by loop gain calculations. At equilibrium, the feedback control approaches a point defined in both dimensions by a [TSH]–[FT4] coordinate for which the loop gain is greater than unity. This model describes the emergence of homeostasis of the HPT axis from characteristic curves of HP and thyroid, thus supporting the validity of the translation between physiological knowledge and clinical reference ranges.

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Authors and Affiliations

  1. Electronic Engineering, Oterlekerweg 4, 1841 GP , Stompetoren, The Netherlands

    Simon L. Goede

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

    Melvin Khee-Shing Leow

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

    Jan W. A. Smit

  4. Endocrinology and Diabetes Department, Medical Hospital I, Bergmannsheil University Hospitals, Ruhr University of Bochum, 44789 Bochum, NRW, Germany

    Harald H. Klein

  5. Laboratory XU44, Medical Hospital I, Bergmannsheil University Hospitals, Ruhr University of Bochum, 44789 Bochum, NRW, Germany

    Johannes W. Dietrich

Authors
  1. Simon L. Goede
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  2. Melvin Khee-Shing Leow
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  3. Jan W. A. Smit
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  4. Harald H. Klein
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  5. Johannes W. Dietrich
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Correspondence to Simon L. Goede.

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Goede, S.L., Leow, M.KS., Smit, J.W.A. et al. Hypothalamus–Pituitary–Thyroid Feedback Control: Implications of Mathematical Modeling and Consequences for Thyrotropin (TSH) and Free Thyroxine (FT4) Reference Ranges. Bull Math Biol 76, 1270–1287 (2014). https://doi.org/10.1007/s11538-014-9955-5

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  • DOI: https://doi.org/10.1007/s11538-014-9955-5

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