# A Hypothalamic-Pituitary-Adrenal System Model: Figure 5

#### 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, and it runs to reproduce figure 5 from the paper. In order to reproduce figure 5, equation 7 was discarded and the variables were defined explicitly as described in the legend for figure 5. An equation was also added describing the SCN periodic input to PVN. The model must be run for roughly 1 day before it stabilizes.

#### 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. |