Journal of Biological Physics

, Volume 35, Issue 2, pp 149–162 | Cite as

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

  • Matthias ConradEmail author
  • Christian Hubold
  • Bernd Fischer
  • Achim Peters
Original Paper


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 modeling Parameter estimation Physiological system Stress system Hypothalamus–pituitary–adrenal system Homeostasis 



This work was supported by grants (Clinical Research Group KFO-126) from the German Research Foundation.


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Copyright information

© Springer Science + Business Media B.V. 2009

Authors and Affiliations

  • Matthias Conrad
    • 1
    Email author
  • Christian Hubold
    • 2
  • Bernd Fischer
    • 3
  • Achim Peters
    • 2
  1. 1.Department of Mathematics and Computer ScienceEmory UniversityAtlantaUSA
  2. 2.Medical Clinic 1University of LübeckLübeckGermany
  3. 3.Institute of MathematicsUniversity of LübeckLübeckGermany

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