Stability of a General Delay Differential Model of the Hypothalamo-Pituitary-Adrenocortical System

Most of the systems in an organism (human included) function in a regular daily rhythm. Hypothalamo-pituitary-adrenocortical (HPA) axis, although mostly known for its role in stress response, probably has a role in conveying rhythmic signals from the major pacemaker, suprachiazmatic nucleus (SCN), to the periphery. A general qualitative nonphenomenological mathematical model of the HPA axis is constructed and its dynamics is examined using linear stability analysis and Roushe's theorem. The results show that this system is asymptotically stable, i.e. it does not generate circadian oscillations, but only responds to the external pacemaker.

[1]  Steven A. Brown,et al.  Resetting of circadian time in peripheral tissues by glucocorticoid signaling. , 2000, Science.

[2]  Goran Opacic,et al.  A mathematical model of stress reaction: Individual differences in threshold and duration , 2000, Psychobiology.

[3]  Panos Macheras,et al.  Nonlinear dynamics in clinical pharmacology: the paradigm of cortisol secretion and suppression. , 2002, British journal of clinical pharmacology.

[4]  E N Brown,et al.  A stochastic differential equation model of diurnal cortisol patterns. , 2001, American journal of physiology. Endocrinology and metabolism.

[5]  E. Peacock-López,et al.  Dynamic model of hormonal systems coupled by negative feedback. , 1998, Biophysical chemistry.

[6]  B. Carroll,et al.  Corticotropin secretory dynamics in humans under low glucocorticoid feedback. , 2001, The Journal of clinical endocrinology and metabolism.

[7]  J. Herman,et al.  Neurocircuitry of stress: central control of the hypothalamo–pituitary–adrenocortical axis , 1997, Trends in Neurosciences.

[8]  Larry J. Siever,et al.  Cortisol regulation in posttraumatic stress disorder and major depression: A chronobiological analysis , 1996, Biological Psychiatry.

[9]  U. Albrecht.  Functional Genomics of Sleep and Circadian Rhythm Invited Review: Regulation of mammalian circadian clock genes , 2002 .

[10]  H. Berry.  Chaos in a bienzymatic cyclic model with two autocatalytic loops , 2003 .

[11]  J. Axelrod,et al.  Stress hormones: their interaction and regulation. , 1984, Science.

[12]  Lawrence Stark.  Stability and Oscillations , 1968 .

[13]  F. Holsboer,et al.  Do antidepressants stabilize mood through actions on the hypothalamic-pituitary-adrenocortical system? , 1995, Trends in Neurosciences.

[14]  F. Veglio,et al.  Impaired cortisol binding to glucocorticoid receptors in hypertensive patients. , 1997, Hypertension.

[15]  H. Derendorf,et al.  Mathematical modeling of cortisol circadian rhythm and cortisol suppression , 1996 .

[16]  I S Kohane,et al.  Using 'off the shelf', computer programs to mine additional insights from published data: diurnal variation in potency of ACTH stimulation of cortisol secretion revealed. , 1999, Computer methods and programs in biomedicine.

[17]  T. Dinan,et al.  Serotonin and the regulation of hypothalamic-pituitary-adrenal axis function. , 1996, Life sciences.

[18]  J. P. Long,et al.  Serotonin as a neurotransmitter: a review. , 1988, Comparative biochemistry and physiology. C, Comparative pharmacology and toxicology.

[19]  Modelling fluctuation phenomena in the plasma cortisol secretion system in normal man. , 1991, Bio Systems.

[20]  G. Chrousos,et al.  The concepts of stress and stress system disorders. Overview of physical and behavioral homeostasis. , 1992, JAMA.

[21]  Danka Savic,et al.  A mathematical model of the hypothalamo-pituitary-adrenocortical system and its stability analysis , 2005 .

[22]  B. Jacobs.  Serotonin, Motor Activity and Depression-Related Disorders , 1994 .

[23]  Yuedong Wang,et al.  Shape‐Invariant Modeling of Circadian Rhythms with Random Effects and Smoothing Spline ANOVA Decompositions , 2003, Biometrics.

[24]  Liu Bingzheng,et al.  An improved mathematical model of hormone secretion in the hypothalamo-pituitary-gonadal axis in man. , 1991 .

[25]  Ioannis Ilias,et al.  Complexity and non-linear description of diurnal cortisol and growth hormone secretory patterns before and after sleep deprivation. , 2002, Endocrine regulations.

[26]  C. Tsigos,et al.  Hypothalamic-pituitary-adrenal axis, neuroendocrine factors and stress. , 2002, Journal of psychosomatic research.

[27]  G. Chrousos.  Editorial: Ultradian, Circadian, and Stress-Related Hypothalamic-Pituitary-Adrenal Axis Activity-A Dynamic Digital-to-Analog Modulation. , 1998, Endocrinology.