Variability in the secretion of corticotropin-releasing hormone, adrenocorticotropic hormone and cortisol and understandability of the hypothalamic-pituitary-adrenal axis dynamics--a mathematical study based on clinical evidence

Abstract

In this article, we have developed a simple mathematical model that captures the vital mechanisms of the hypothalamic-pituitary-adrenal (HPA) axis self-regulatory activities. For this, a system of three-component non-linear delay differential equations has been proposed and analysed to observe the ultradian and circadian variabilities of the hormone secretion of the HPA axis in normal subjects. Our analysis reveals that a feedback mechanism is sufficient to show the ultradian variability of the hormone secretion pattern but fails to show the circadian variability. A central nervous system-driven pulse generator coupled with the primary feedback mechanism can exhibit the ultradian as well as circadian variability in the hormone secretion of the HPA axis. The model can also predict different dynamics of the normal HPA axis following physiological changes (viz. adrenalectomy and hypophysectomy) and pathological changes (viz. infusion of different hormones).

Predictive modeling of the hypothalamic-pituitary-adrenal (HPA) axis response to acute and chronic stress

“…Bifurcation analysis was used to predict the response of the HPA axis to chronic stress. Model predictions were compared with experimental findings reported in the literature and relevance for pharmacotherapy with glucocorticoids was discussed.Key words: HPA axis, Stress, Cortisol, Predictive modeling, Circadian and ultradian rhythmicity acteristic frequencies: ultradian oscillations, with a period of 20-120 min [4-6] superimposed on circadian oscillations, with a period of about 24 h. The importance of circadian rhythms for adequate functioning of the HPA axis has been recognized for years [7, 8]; in addition, new experimental [9-15] and theoretical [16][17][18][19][20][21][22][23][24][25][26][27] results offer enough evidence to support the indispensable roles of ultradian oscillatory dynamics of HPA hormones levels for normal physiology. Since ultradian and circadian oscillations operate on different time scales, their effects are manifested in different biological realms.…”

“…acteristic frequencies: ultradian oscillations, with a period of 20-120 min [4][5][6] superimposed on circadian oscillations, with a period of about 24 h. The importance of circadian rhythms for adequate functioning of the HPA axis has been recognized for years [7,8]; in addition, new experimental [9][10][11][12][13][14][15] and theoretical [16][17][18][19][20][21][22][23][24][25][26][27] results offer enough evidence to support the indispensable roles of ultradian oscillatory dynamics of HPA hormones levels for normal physiology. Since ultradian and circadian oscillations operate on different time scales, their effects are manifested in different biological realms.…”

Transcriptional implications of ultradian glucocorticoid secretion in homeostasis and in the acute stress response

“…Several prior models have been published in an attempt to investigate ultradian rhythms in HPA axis function, particularly with respect to the mechanistic origins of ultradian rhythms. These prior studies consider the origin of ultradian rhythms as due to either discrete bursting (21,22) or an unstable fixed point driving oscillatory dynamics (2,20,24,28,40,50). The latter class of models rely on either unphysical parameter values or time delays to induce oscillations, as illustrated by Vinther et al (49).…”

“…In contrast to ultradian rhythms, which are largely assumed to arise due to dynamics internal to the HPA axis, circadian rhythms are typically viewed as a centrally mediated external signal that drives 24 h variability in glucocorticoid secretion (38). For this reason, prior models that have considered this issue typically drive a model parameter by an imposed sinusoid with a 24 h period (2,20,24,49,50). This has previously been applied to the HPA axis model in Eq.…”

Theory-Driven Models for Correcting Fight or Flight" Imbalance in Gulf War Illness"

“…If however, the perturbation is of significant strength and duration, the system may abandon its normal operating regime and instead be drawn into the basin of attraction of a new alternate resting state. Knowledge of the system dynamics can allow us to map these different regimes and several mathematical models of the HPA exist [18][19][20][21][22][23][24][25][26].…”