Stability of a general delay differential model of the hypothalamo- pituitary-adrenocortical system

International Journal of Bifurcation and Chaos

Volumn 16, Issue 10, 2006, Pages 3079-3085

  Savić, Danka ^a   Jelić, Smiljana ^a   Burić, Nikola ^b  

^a UNIVERSITY OF BELGRADE   (Serbia)

^b UNIVERSITY OF BELGRADE   (Serbia)

Author keywords

Circadian rhythm; DDE; Hypothalamo pituitary adrenocortical (HPA) axis; Roushe's theorem; Stability analysis

Indexed keywords

ASYMPTOTIC STABILITY; CONVERGENCE OF NUMERICAL METHODS; LINEAR EQUATIONS; MATHEMATICAL MODELS; THEOREM PROVING;

CIRCADIAN OSCILLATIONS; DELAY DIFFERENTIAL MODEL; HYPOTHALAMO- PITUITARY-ADRENOCORTICAL SYSTEM; ROUSHE'S THEOREM; STABILITY ANALYSIS;

DELAY CIRCUITS;

EID: 33845547295     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127406016665     Document Type: Article

References (41)

1. Albrecht, U. [2002] "Regulation of mammalian circadian clock genes," J. Appl. Physiol. 92, 1348-1355.
2. Axelrod, J. [1984] "The relationship between the stress hormones, catecholamines, ACTH and glucocorticoids," in Stress - The Role of Catecholamines and Other Neurotransmitters, Vol. 1, eds. Usdin, E., Kvetnansky, R. & Axelrod, J. (Gordon and Breach Sci. Publishers, NY), pp. 3-13.
3. Axelrod, J. & Terry, D. R. [1984] "Stress hormones: Their interaction and regulation," Science 224, 452-459.
4. Baker, C. T. H., Bocharov, G. A. & Rihan, F. A. [1999] "A report on the use of delay differential equations in numerical modelling in the biosciences," Numer. Anal. Rep. 343, University of Manchester, Department of Mathematics.
5. Balsalobre, A., Brown, S. A., Marcacci, L., Tronche, F., Kellendonk, C., Reichardt, H. M., Schutz, G. & Schibler, U. [2000] "Resetting of circadian time in peripheral tissues by glucocorticoid signaling," Science 289, 2344-2347.
6. Barden, N., Reul, J. M. H. M. & Holsboer, F. [1995] "Do antidepressants stabilize mood through actions on the HPA system?" Trends Neurosci. 18, 6-10.
7. Berry, H. [2003] "Chaos in a bienzymatic cyclic model with two autocatalytic loops," Chaos Solit. Fract. 18, 1001-1014.
8. Brown, E. N., Meehan, P. M. &; Dempster, A. P. [2001] "A stochastic differential equation model of diurnal cortisol patterns," Am. J. Physiol. Endocrinol. Metab. 280, E450-E461.
9. Chrousos, G. P. & Gold, P. W. [1992] "The concepts of stress and stress system disorders," JAMA 267, 1244-1252.
10. Chrousos, G. P. [1998] "Ultradian, circadian, and stress-related hypothalamic-pituitary-adrenal axis activity - a dynamic digital-to-analog modulation," Endocrinology 139, 437-440.
11. Dinan, T. G. [1996] "Serotonin and the regulation of hypothalamic-pituitary-adrenal axis function," Life Sci. 58, 1683-1694.
12. Dokoumetzidis, A., Iliadis, A. &: Macheras, P. [2002] "Nonlinear dynamics in clinical pharmacology: The paradigm of cortisol secretion and suppression," Br. J. Clin. Pharmacol. 54, 21-29.
13. Feldman, S. & Weidenfeld, J. [1996] "Involvement of amygdalar alpha adrenoceptors in hypothalamo-pituitary-adrenocortical responses," Neuroendocrin. 7, 3055-3057.
14. Folk, G. E. & Long, J. P. [1988] "Serotonin as a neuro-trasmitter: A review," Comp. Biochem. Physiol. C 91, 251-257.
15. Gonzalez-Heydrich, J., Steingard, R. J. & Kohane, I. [1994] "A computer simulation of the hypothalamo-pituitary-adrenal axis," in Eighteenth Ann. Proc. Symp. Computer Applications in Medical Care (SCAMC), p. 1010.
16. Gonzalez-Heydrich, J., Steingard, R. J., Putnam, F., Beardslee, W. & Kohane, I. S. [1999] "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, 227-238.
17. Gopalsamy, K. [1992] Stability and Oscillations in Delay Differential Equations in Population Dynamics (Kluwer Academic Publishers, Netherlands).
18. Gray, P. & Scott, S. K. [1990] "Local stability analysis and Hopf bifurcation for n variables," in Chemical Oscillations and Instabilities (Clarendon Press, Oxford), p. 355.
19. Herman, J. P. & Cullinan, W. E. [1997] "Neurocircuitry of stress: Central control of the hypothalamopituitary-adrenocortical axis," Trends Neurosci. 20, 78-84.
20. Ilias, I., Vgontzas, A. N., Provata, A. & Mastorakos, G. [2002] "Complexity and non-linear description of diurnal cortisol and growth hormone secretory patterns before and after sleep deprivation," Endocr. Regul. 36, 63-72.
21. Jacobs, B. L. [1994] "Serotonin, motor activity and depression-related disorders," Amer. Sci. 82, 456-463.
22. Klerman, E. B., Rimmer, D. W., Dijk, D., Kronauer, R. E., Rizzo III, J. F. & Czeisler, C. A. [1998] "Nonphotic entrainment of the human circadian pacemaker," Am. J. Physiol. 274 (Regulatory Integrative Comp. Physiol. 43), R991-R996.
23. Lenbury, Y. & Pacheenburawana, P. [1991] "Modelling fluctuation phenomena in the plasma cortisol secretion system in normal man," Biosystems 26, 117-125.
24. Liu, B. Z. & Deng, G. M. [1991] "An improved mathematical model of hormone secretion in the hypothalamo-pituitary-gonadal axis in man," J. Theor. Biol. 150, 51-58.
25. Londergan, C. H. & Peacock-López, E. [1998] "Dynamic model of hormonal systems coupled by negative feedback," Biophys. Chem. 73, 85-107.
26. Miller, W. L. & Tyrrell, J. B. [1995] "The adrenal cortex," in Endocrinology and Metabolism, eds. Felig, P., Baxter, J. D. & Frohman, L. A. (McGraw-Hill, NY), p. 555.
27. Molitch, M. E. [1995] "Neurondocrinology," in Endocrinology and Metabolism, eds. Felig, P., Baxter, J. D. & Frohman, L. A. (McGraw-Hill, NY), p. 258.
28. Mulatero, P., Panarelli, M., Schiavone, D., Rossi, A., Mengozzi, G., Kenyon, C. J., Chiandussi, L., Veglio, F. [1997] "Impaired cortisol binding to glucocorticoid receptors in hypertensive patients," Hypertension 30, 1274-1278.
29. Murray, J. D. [1977] Lectures on Nonlinear-Differential-Equation Models in Biology (Clarendon Press, Oxford), Chap. 4.8.
30. Murray, J. D. [1993] Mathematical Biology, 2nd edition (Springer-Verlag, Berlin).
31. Paunovic, V. R. & Babinski, T. [1995] Biological Psychiatry 1: The Molecular Basis of Mental Processes, Belgrad, Faculty of Medicine, University of Belgrade (in Serbian).
32. Rohatagi, S., Bye, A., Mackie, A. E. & Derendorf, H. [1996] "Mathematical modeling of cortisol circadian rhythm and cortisol suppression," E. J. Pharmacol. Sci. 4, 341-350.
33. Savic, D. & Gajic, S. [1998] "How strong is the stress spring? - stability analysis of the mathematical model of the stress response mechanism," Iugoslav Physiol. Pharmacol. Acta 34, 231-236.
34. Savic, D., Knezevic, G. & Opacic, G. [2000] "A mathematical model of stress reaction: Individual differences in threshold and duration," Psychobiol. 28, 581-592.
35. Savic, D. & Jelic, S. [2005] "A mathematical model of the hypothalamo-pituitary-adrenocortical system and its stability analysis," Chaos Solit. Fract. 26, 427-436.
36. Titchmarch, E. C. [1939] Theory of Functions, 2nd edition (Oxford University Press).
37. Tsigos, C. & Chrousos, G. P. [2002] "Hypothalamic-pituitary- adrenal axis, neuroendocrine factors and stress," J. Psychosom. Res. 53, 865-871.
38. van der Kolk, B. A. [1996] "The body keeps the score: Approaches to the psychobiology of posttraumatic stress disorder," in Traumatic Stress: The Effects of Overwhelming Experience on Mind, Body, and Society, eds. van der Kolk, B. A., McFarlane, A. C. & Weisaeth, L. (Guilford Press, NY), pp. 214-241.
39. Veldhuis, J. D., Iranmanesh, A., Naftolowitz, D., Tatham, N., Cassidy, F. & Carroll, B. J. [2001] "Corticotropin secretory dynamics in humans under low glucocorticoid feedback," J. Clin. Endocrinol. Metab. 86, 5554-5563.
40. Wang, Y., Ke, C. & Brown, M. B. [2003] "Shape invariant modelling of circadian rhythms with random effects and smoothing spline ANOVA decompositions," Biometrics 59, 804-812.
41. Yehuda, R., Teicher, M. H., Trestman, R. L., Levengood, R. A. & Siever, L. J. [1996] "Cortisol regulation in posttraumatic stress disorder and major depression: A chronobiological analysis," Biol. Psychiatry 40, 79-88.