Journal of Biological Physics

, Volume 35, Issue 2, pp 149–162

Modeling the hypothalamus–pituitary–adrenal system: homeostasis by interacting positive and negative feedback


    • Department of Mathematics and Computer ScienceEmory University
  • Christian Hubold
    • Medical Clinic 1University of Lübeck
  • Bernd Fischer
    • Institute of MathematicsUniversity of Lübeck
  • Achim Peters
    • Medical Clinic 1University of Lübeck
Original Paper

DOI: 10.1007/s10867-009-9134-3

Cite this article as:
Conrad, M., Hubold, C., Fischer, B. et al. J Biol Phys (2009) 35: 149. doi:10.1007/s10867-009-9134-3


The hypothalamus–pituitary–adrenal (HPA) system is closely related to stress and the restoration of homeostasis. This system is stimulated in the second half of the night, decreases its activity in the daytime, and reaches the homeostatic level during the late evening. In this paper, we derive and discuss a novel model for the HPA system. It is based on three simple rules that constitute a principle of homeostasis and include only the most substantive physiological elements. In contrast to other models, its main components include, apart from the conventional negative feedback ingredient, a positive feedback loop. To validate the model, we present a parameter estimation procedure that enables one to adapt the model to clinical observations. Using this methodology, we are able to show that the novel model is capable of simulating clinical trials. Furthermore, the stationary state of the system is investigated. We show that, under mild conditions, the system always has a well-defined set-point, which reflects the clinical situation to be modeled. Finally, the computed parameters may be interpreted from a physiological point of view, thereby leading to insights about diseases like depression, obesity, or diabetes.


Physiological modelingParameter estimationPhysiological systemStress systemHypothalamus–pituitary–adrenal systemHomeostasis

Copyright information

© Springer Science + Business Media B.V. 2009