Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

Lumped versus distributed thermoregulatory control: Results from a three-dimensional dynamic model

  • 71 Accesses

  • 13 Citations


In this study we use a three-dimensional model of the human thermal system, the spatial grid of which is 0.5 ... 1.0 cm. The model is based on wellknown physical heat-transfer equations, and all parameters of the passive system have definite physical values. According to the number of substantially different areas and organs, 54 spatially different values are attributed to each physical parameter. Compatibility of simulation and experiment was achieved solely on the basis of physical considerations and physiological basic data. The equations were solved using a modification of the alternating direction implicit method. On the basis of this complex description of the passive system close to reality, various lumped and distributed parameter control equations were tested for control of metabolic heat production, blood flow and sweat production. The simplest control equations delivering results on closed-loop control compatible with experimental evidence were determined. It was concluded that it is essential to take into account the spatial distribution of heat production, blood flow and sweat production, and that at least for control of shivering, distributed controller gains different from the pattern of distribution of muscle tissue are required. For sweat production this is not so obvious, so that for simulation of sweating control after homogeneous heat load a lumped parameter control may be justified. Based on these conclusions threedimensional temperature profiles for cold and heat load and the dynamics for changes of the environmental conditions were computed. In view of the exact simulation of the passive system and the compatibility with experimentally attainable variables there is good evidence that those values extrapolated by the simulation are adequately determined. The model may be used both for further analysis of the real thermoregulatory mechanisms and for special applications in environmental and clinical health care.

This is a preview of subscription content, log in to check access.


  1. Bazett HC, McGlone G (1927) Temperature gradients in the tissues in man. Am J Physiol 82:415–451

  2. Brück K, Hensel H (1953) Wärmedurchgang und Innentemperaturen der menschlichen Extremitäten. Pflügers Arch257:70–86

  3. Buse M, Werner J (1985a) ADI-Verfahren zur Lösung von Wärmeleitungsproblemen in allgemeinen dreidimensionalen Körpern. PARS-Mitt 3:75–84

  4. Buse M, Werner J (1985b) Heat balance of the human body: influence of variations of locally distributed parameters. J Theor Biol 114:34–51

  5. Buse M, Werner J (1989) Closed-loop control of human body temperature: Results from a one-dimensional model. Biol Cybern 61:467–475

  6. Golenhofen K (1963) Zur Topographie der Muskelaktivität bei Kältebelastung des Menschen. Arch Phys Ther 15:435–438

  7. Golenhofen K (1965) Das Reaktionsmuster der menschlichen Muskulatur im Rahmen der Thermoregulation. Pflügers Arch 285:124–146

  8. Hayward JS, Eckerson JD, Collis ML (1977) Thermoregulatory heat production in man: prediction equation based on skin and core temperatures. J Appl Physiol 42:377–384

  9. Heising M, Werner J (1987) Control of sweating in man after work-induced thermal load and symmetrically applied cooling. Eur J Appl Physiol 56:608–614

  10. Hertzman AB, Randall WC (1948) Regional differences in the basal and maximal rates of blood flow in the skin. J Appl Physiol 1:234–241

  11. Hertzman AB, Randall WC (1952) Regional rates of evaporation from the skin at various environmental temperatures. J Appl Physiol 5:153–161

  12. Jiji LM, Weinbaum S, Lemons DE (1984) Theory and experiment for the effect of vascular microstructure on surface tissue heat transfer. II. Model formulation and solution. IEEE Trans Biomed Eng 106:331–341

  13. Kelterbaum J, Werner J, Schön H (1977) Makroskopische Topographic des menschlichen Körpers: Gewinnung der Rohdaten und deren EDV-gerechte Aufarbeitung in einer Datenbank. EDV Med Biol 4:123–128

  14. Kuznetz LH (1979) A two dimensional transient mathematical model of human thermoregulation. Am J Physiol237:266–277

  15. Pennes HH (1948) Analysis of tissue and arterial blood temperature in the resting human forearm. J Appl Physiol 1:93–122

  16. Stolwijk JAJ (1970) Mathematical model of thermoregulation. In: Hardy DJ, Gagge AP, Stolwijk JAJ (eds) Physiological and behavioral temperature regulation. Thomas, Springfield Ill, pp 703–721

  17. Stolwijk JAJ, Hardy JD (1966) Temperature regulation in man — a theoretical study. Pflügers Arch 291:129–162

  18. Werner J (1975) Zur Temperaturregelung des menschlichen Körpers. Ein mathematisches Modell mit verteilten Parametern und ortsabhängigen Variablen. Biol Cybern 17:53–63

  19. Werner J (1977) Mathematical treatment of structure and function of the human thermoregulatory system. Biol Cybern 25:93–101

  20. Werner J (1980) The concept of regulation for human body temperature. J Therm Biol 5:77–82

  21. Werner J (1984) Regelung der menschlichen Körpertemperatur. De Gruyter, Berlin New York

  22. Werner J (1989) Thermoregulatory models: recent research, current applications and future development. Scand J Work Environ Health (in press)

  23. Werner J, Buse M (1988) Temperature profiles with respect to inhomogeneity and geometry of the human body. J Appl Physiol 65:1110–1118

  24. Werner J, Heising M (1989) The drive local sweating rate at rest and exercise. In: Mercer JB (ed) Thermal Physiology. Elsevier, Amsterdam (in press)

  25. Werner J, Reents T (1980) A contribution to the topography of temperature regulation in man. Eur J Appl Physiol 45:87–94

  26. Werner J, Heising M, Rautenberg W, Leimann K (1985) Dynamics and topography of human temperature regulation in response to thermal and work load. Eur J Appl Physiol53:353–358

  27. Wissler EH (1961) Steady state temperature distribution in man. J Appl Physiol 16:734–740

  28. Wissler EH (1964) A mathematical model of the human thermal system. Bull Math Biophys 26:147–166

  29. Wissler EH (1985) Mathematical simulation of human thermal behaviour using whole body models. In: Shitzer A, Eberhart RC (eds) Heat transfer in medicine and biology. Plenum Press, New York, pp 325–374

  30. Wissler EH (1988) A review of human thermal models. In: Mekjavic IB, Banister EW, Morrison JB (eds) Environmental ergonomics. Taylor & Francis, New York London, pp 267–285

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Werner, J., Buse, M. & Foegen, A. Lumped versus distributed thermoregulatory control: Results from a three-dimensional dynamic model. Biol. Cybern. 62, 63–73 (1989).

Download citation


  • Heat Production
  • Heat Load
  • Control Equation
  • Implicit Method
  • Controller Gain