A mathematical model of the hypothalamo-pituitary-adrenocortical system and its stability analysis

It is commonly assumed that the hypothalamo-pituitary-adrenocortical (HPA) axis generates oscillations, because a regular daily rhythm of its component hormones is observed. We offer another plausible explanation of the origin of its circadian oscillations: HPA just responds to an independent external pacemaker (from the suprachiazmatic nucleus, SCN). Five versions (with and without time delay) of a qualitative non-phenomenological mathematical model of the HPA axis as a feedback mechanism are constructed wherein all the terms in the equations are introduced according to the rules of chemical kinetics, i.e. are physicochemically interpretable. The dynamics of the HPA axis model was examined using linear stability analysis. The results show stability of this system, meaning that it does not generate diurnal oscillations. Computer simulation based on this model shows oscillations that are system’s response to an external pulsing activator (SCN) implying that the observed time-periodic pattern does not have to be an intrinsic property of the HPA axis.