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Mathematical Medicine and Biology Advance Access originally published online on March 14, 2008
Mathematical Medicine and Biology 2008 25(1):37-63; doi:10.1093/imammb/dqn003
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

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

N. Bairagi{dagger}

Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700 032, India

Samrat Chatterjee{ddagger} and J. Chattopadhyay§

Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata 700 108, India
{dagger} Email: nbairagi{at}math.jdvu.ac.in
{ddagger} Email: samrat_ct{at}rediffmail.com

§ Corresponding auhor. Email: joydev{at}isical.ac.in

Received on September 4, 2006. Revised on October 19, 2007. Accepted on December 13, 2007.

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).

Keywords: hypothalamic-pituitary-adrenal axis; corticotropin-releasing hormone; adrenocorticotropic hormone; cortisol; ultradian and circadian variability; delay; local stability


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