Modeling the hypothalamus-pituitary-adrenal system: homeostasis by interacting positive and negative feedback
M. Conrad and C. Hubold and B. Fischer and A. Peters
Journal of Biological Physics  35  149 -- 162  (2009)

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 which constitute a principle of homeostasis and include only substantial 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 which 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 of the system is investigated. We show that, under mild conditions, the systems has always a well-defined set-point which reflects the clinical situation to be modeled. Finally, the computed parameter may be interpreted from a physiological point of view and thereby gaining connoting insights in diseases like depression, obesity, or diabetes.