A delay-differential equation model of the feedback-controlled hypothalamus-pituitary-adrenal axis in humans

Math Med Biol. 2005 Mar;22(1):15-33. doi: 10.1093/imammb/dqh020.


The present work develops and analyses a model system of delay-differential equations which describes the core dynamics of the stress-responsive hypothalamus-pituitary-adrenal axis. This neuroendocrine ensemble exhibits prominent pulsatile secretory patterns governed by nonlinear and time-delayed feedforward and feedback signal interchanges. Formulation and subsequent bifurcation analysis of the model provide a qualitative and mathematical frame work for a better understanding of the delayed responsive mechanisms as well as the dynamic variations in different pathological situations.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Adrenocorticotropic Hormone / physiology
  • Computer Simulation
  • Corticotropin-Releasing Hormone / physiology
  • Feedback / physiology
  • Humans
  • Hydrocortisone / metabolism
  • Hypothalamo-Hypophyseal System / physiology*
  • Models, Biological*
  • Nonlinear Dynamics
  • Pituitary-Adrenal System / physiology*


  • Adrenocorticotropic Hormone
  • Corticotropin-Releasing Hormone
  • Hydrocortisone