Modeling the hypothalamus–pituitary–adrenal system: homeostasis by interacting positive and negative feedback |
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Authors: | Matthias Conrad Christian Hubold Bernd Fischer Achim Peters |
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Institution: | (1) Department of Mathematics and Computer Science, Emory University, 400 Dowman Drive E429, Atlanta, GA 30033, USA;(2) Medical Clinic 1, University of Lübeck, Ratzeburger Allee 160, 23538 Lübeck, Germany;(3) Institute of Mathematics, University of Lübeck, Wallstrasse 40, 23560 Lübeck, Germany |
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Abstract: | 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. |
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Keywords: | Physiological modeling Parameter estimation Physiological system Stress system Hypothalamus– pituitary– adrenal system Homeostasis |
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