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

Model Structure

The hypothalamus-pituitary-adrenal (HPA) axis is an essential stress-responsive component which initiates and co-ordinates physiological responses to both internal and external stresses, including disease and sleep deprivation. These stimuli are initially detected by the central nervous system, and are fed into the HPA axis via the hypothalamus. The hypothalamus responds by synthesising and secreting corticotropin-releasing hormone (CRH), which acts directly on the anterior pituitary to stimulate the production and release of corticotropin (ACTH). ACTH binds to a specific cell surface receptor expressed by the cells of the adrenal cortex and cortisol is released as a result of this ACTH-binding. Finally, cortisol can have negative feedback effects on various components of the HPA axis, including CRH release from the hypothalamus and ACTH secretion from the anterior pituitary. All of these steps in the hormone cascade system are summarised schematically in the diagram below.

In the paper described here, Lenbury and Pornsawad propose mathematical model incorporating time delays and negative feedback loops to describe the kinetics of the hormone cascade in the HPA axis. They build further on the earlier HPA axis model of Lenbury and Pacheenburawana (published in 1991, and also described in CellML in the model repository), presenting a physiologically realistic, but relatively simple, mathematical representation of the hormone cascade.

Schematic diagram of the hypothalamus-pituitary-adrenal (HPA) axis. Stimulatory and inhibitory paths are indicated by the arrows and + or - signs respectively. CRH represents corticotropin-releasing hormone and ACTH represents corticotropin.

The complete original paper reference is cited below:

A delay-differential equation model of the feedback-controlled hypothalamus-pituitary-adrenal axis in humans, Yongwimon Lenbury and Pornsarp Pornsawad, 2005, Mathematical Medicine and Biology , 22, 15-33. (A PDF version of the article is available to journal subscribers on the Mathematical Medicine and Biology website.) PubMed ID: 15716298

It should be noted that in its current form, the CellML description of the this model is unable to perfectly capture the simulation results of the published model, this is due to the time delays which are difficult to describe in the CellML code.