Model number


A delay-differential equation model of the feedback/feedforward-controlled hypothalamus-pituitary-adrenal axis in humans. Lenbury and Pornsawad, 2005 paper.


 (abstract) 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.

Model converted from original cellML and updated to reproduce Figure 3 of Lenbury and Pornsawad, 2005 paper.

fig 1


The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.

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 (Primary) Lenbury, Yongwimon and Pornsawad, Pornsarp;  A delay-differential equation 
 model of the feedback-controlled hypothalamus-pituitary-adrenal axis in humans.  
 Mathematical Medicine and Biology 22: 15-33,2005,pubmed:15716298

Key terms
adrenal cortex
anterior pituitary
hpa axis

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The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

Model development and archiving support at https://www.imagwiki.nibib.nih.gov/physiome provided by the following grants: NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.