# Jelic, Cupic, Kolar-Anic, 2005

#### Model Status

This CellML model runs in PCEnv and OpenCell, but not in COR because the free variable (time) is dimensionless. The units are consistent throughout, but it does not reproduce the published results. It is a faithful reproduction of the paper equations (eqns 5-8), where all reaction constants are defined by equations, but the CellML model does not precisely reproduce the figures in the paper because to do this the reaction constants have to be defined explicitly (the parameter values are listed in the figure legends). Such CellML models have been created (called Fig4 and Fig5) and they exist in this workspace.

#### Model Structure

ABSTRACT: Mathematical modeling has proven to be valuable in understanding of the complex biological systems dynamics. In the present report we have developed an initial model of the hypothalamic-pituitary-adrenal system self-regulatory activity. A four-dimensional non-linear differential equation model of the hormone secretion was formulated and used to analyze plasma cortisol levels in humans. The aim of this work was to explore in greater detail the role of this system in normal, homeostatic, conditions, since it is the first and unavoidable step in further understanding of the role of this complex neuroendocrine system in pathophysiological conditions. Neither the underlying mechanisms nor the physiological significance of this system are fully understood yet.

The original paper reference is cited below:

Mathematical modeling of the hypothalamic-pituitary-adrenal system activity, Smiljana Jelic, Zeljko Cupic, and Ljiljana Kolar-Anic, 2005, *Mathematical Biosciences*, 197, pp173-187. PubMed ID: 16112688

A schematic diagram of the hypothalamic-pituitary-adrenal system. Corticotrophin-releasing hormone (CRH) and arginin-vasopressin (AVP) stimulate adrenocorticotropin (ACTH) secretion from the pituitary, followed by cortisol secretion from the adrenal cortex. GR represents a glucocorticoid receptor and MR denotes a mineralocorticoid receptor. + represents a postive feedback loop while - represents a negative feedback loop. |