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

Chaos, Solitons and Fractals

Volumn 26, Issue 2, 2005, Pages 427-436

  Savić, Danka ^a   Jelić, Smiljana ^a  

^a UNIVERSITY OF BELGRADE   (Serbia)

Author keywords

[No Author keywords available]

Indexed keywords

BRAIN; CHAOS THEORY; COMPUTER SIMULATION; FEEDBACK; FUNCTIONS; MATHEMATICAL MODELS; NEUROLOGY; PACEMAKERS; REACTION KINETICS; SYSTEM STABILITY; TISSUE;

FEEDBACH MECHANISMS; HYPOTHALAMO-PITUITARY-ADRENOCORTICAL (HPA) SYSTEM; STABILITY ANALYSIS; SUPRACHIAZMATIC NUCLEUS (SCN);

PHYSIOLOGICAL MODELS;

EID: 18544374277     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2005.01.013     Document Type: Article

References (37)

1. E.B. Klerman, D.W. Rimmer, D. Dijk, R.E. Kronauer, J.F. Rizzo III, and C.A. Czeisler Nonphotic entrainment of the human circadian pacemaker Am J Physiol 274 1998 (Regulatory Integrative Comp Physiol 43):R991-6
2. U. Albrecht Regulation of mammalian circadian clock genes J Appl Physiol 92 2002 1348 1355
3. W.L. Miller, and J.B. Tyrrell The adrenal cortex P. Felig J.D. Baxter L.A. Frohman Endocrinology and metabolism 1995 McGraw-Hill, Inc. New York 618
4. A. Balsalobre, S.A. Brown, L. Marcacci, F. Tronche, C. Kellendonk, and H.M. Reichardt Resetting of circadian time in peripheral tissues by glucocorticoid signaling Science 289 2000 2344 2347
5. C. Tsigos, and G.P. Chrousos Hypothalamic-pituitary-adrenal axis, neuroendocrine factors and stress J Psychosom Res 53 2002 865 871
6. J.P. Herman, and W.E. Cullinan Neurocircuitry of stress: central control of the hypothalamo-pituitary-adrenocortical axis Trends Neurosci 20 1997 78 84
7. G.P. Chrousos, and P.W. Gold The concepts of stress and stress system disorders JAMA 267 1992 1244 1252
8. J. Axelrod, and D.R. Terry Stress hormones: Their interaction and regulation Science 224 1984 452 459
9. T.G. Dinan Serotonin and the regulation of hypothalamic-pituitary-adrenal axis function Life Sci 58 1996 1683 1694
10. G.E. Folk, and J.P. Long Serotonin as a neurotrasmitter: a review Comp Biochem Physiol 91C 1988 251 257
11. B.A. van der Kolk The body keeps the score: approaches to the psychobiology of posttraumatic stress disorder B.A. van der Kolk A.C. McFarlane L. Weisaeth Traumatic stress: the effects of overwhelming experience on mind body and society 1996 Guilford Press New York 214 241
12. J. Axelrod The relationship between the stress hormones, catecholamines, ACTH and glucocorticoids E. Usdin R. Kvetnansky J. Axelrod Stress-the role of catecholamines and other neurotransmitters vol. 1 1984 Gordon and Breach Sci. Publishers New York 3 13
13. S. Feldman, and J. Weidenfeld Involvement of amygdalar alpha adrenoceptors in hypothalamo-pituitary-adrenocortical responses Neuroendocrin 7 1996 3055 3057
14. N. Barden, J.M.H.M. Reul, and F. Holsboer Do antidepressants stabilize mood through actions on the HPA system? Trends Neurosci 18 1995 6 10
15. B.L. Jacobs Serotonin, motor activity and depression-related disorders Am Sci 82 1994 456 463
16. Paunovic VR, Babinski T. Biological psychiatry 1: The molecular basis of mental processes. Faculty of Medicine, University of Belgrade, Belgrade, 1995 [Serbian]
17. J.D. Murray Lectures on nonlinear-differential-equation models in biology 1977 Clarendon Press Oxford [chapter 4.8]
18. B.Z. Liu, and G.M. Deng An improved mathematical model of hormone secretion in the hypothalamo-pituitary-gonadal axis in man J Theor Biol 150 1991 51 58
19. Gonzalez-Heydrich J, Steingard RJ, Kohane I. A computer simulation of the hypothalamo-pituitary-adrenal axis. In: Eighteenth annual proceedings of the symposium for computer applications in medical care (SCAMC), 1994. p. 1010
20. Y. Lenbury, and P. Pacheenburawana Modelling fluctuation phenomena in the plasma cortisol secretion system in normal man Biosystems 26 1991 117 125
21. Wang Y, Ke C, Brown MB. Shape invariant modelling of Circadian rhythms with random effects and smoothing spline ANOVA decompositions. Technical Report, 2002; No. 386, Department of Statistics and Applied Probability, UCSB (Pending review)
22. R. Yehuda, M.H. Teicher, R.L. Trestman, R.A. Levengood, and L.J. Siever Cortisol regulation in posttraumatic stress disorder and major depression: a chronobiological analysis Biol Psychiatry 40 1996 79 88
23. J.D. Veldhuis, A. Iranmanesh, D. Naftolowitz, N. Tatham, F. Cassidy, and B.J. Carroll Corticotropin secretary dynamics in humans under low glucocorticoid feedback J Clin Endocrinol Metab 86 2001 5554 5563
24. E.N. Brown, P.M. Meehan, and A.P. Dempster A stochastic differential equation model of diurnal cortisol patterns Am J Physiol Endocrinol Metab 280 2001 E450 E461
25. A. Dokoumetzidis, A. Iliadis, and P. Macheras Nonlinear dynamics in clinical pharmacology: the paradigm of cortisol secretion and suppression Br J Clin Pharmacol 54 2002 21 29
26. S. Rohatagi, A. Bye, A.E. Mackie, and H. Derendorf Mathematical modeling of cortisol circadian rhythm and cortisol suppression E J Pharmacol Sci 4 1996 341 350
27. J. Gonzalez-Heydrich, R.J. Steingard, F. Putnam, W. Beardslee, and I.S. Kohane Using 'off the shelf', computer programs to mine additional insights from published data: diurnal variation in potency of ACTH stimulation of cortisol secretion revealed Comp Met Prog Biomed 58 1999 227 238
28. C.H. Londergan, and E. Peacock-López Dynamic model of hormonal systems coupled by negative feedback Biophys Chem 73 1-2 1998 85 107
29. I. Ilias, A.N. Vgontzas, A. Provata, and G. Mastorakos Complexity and non-linear description of diurnal cortisol and growth hormone secretary patternsbefore and after sleep deprivation Endocr Regul 36 2002 63 72
30. H. Berry Chaos in a bienzymatic cyclic model with two autocatalytic loops Chaos, Solitons & Fractals 18 2003 1001 1014
31. D. Savic, G. Knezevic, and G. Opacic A mathematical model of stress reaction: individual differences in threshold and duration Psychobiology 28 2000 581 592
32. D. Savic, and S. Gajic How strong is the stress spring?-Stability analysis of the mathematical model of the stress response mechanism Iugoslav Physiol Pharmacol Acta 34 1 1998 231 236
33. J.D. Murray Mathematical biology 2nd ed 1993 Springer-Verlag Berlin
34. Baker CTH, Bocharov GA, Rihan FA. A report on the use of delay differential equations in numerical modelling in the biosciences. Numerical Analyses Report No. 343, 1999; Department of Mathematics, University of Manchester
35. M.E. Molitch Neurondocrinology P. Felig J.D. Baxter L.A. Frohman Endocrinology and metabolism 1995 McGraw-Hill Inc New York 258
36. P. Gray, and S.K. Scott Local stability analysis and Hopf bifurcation for n variables Chemical oscillations and instabilities 1990 Clarendon Press Oxford 355
37. G.P. Chrousos Ultradian, circadian, and stress-related hypothalamic-pituitary-adrenal axis activity-a dynamic digital-to-analog modulation Endocrinology 139 2 1998 437 440