Stability Analysis of the Respiratory Control System During Sleep

  • Zbignlew L. Topor
  • Konstantinon Vasilakos
  • John E. Remmers
Conference paper
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 551)


Chemoreflex control of breathing during sleep consists of two negative feedback loops with delays depending on the controlled variables (PaCO 2 and PaO 2). The peripheral chemoreceptor (PCR) loop operates with short delay and the central chemoreceptor (CCR) loop operates with long delay (see Figure 1). Periodic breathing, indicative of instability in the control system, is commonly seen during sleep in premature infants, in patients with heart failure, and during exposure to high altitude. These periodicities appear to relate to the operation of the two chemoreflex loops.


Cerebral Blood Flow Negative Feedback Loop Ventilatory Response Central Sleep Apnea Congestive Heart Failure Patient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Belair J., Stability of a differential-delay equation with two time lags, in: Proceedings of the Canadian Mathematical Society: 1986 Seminar on oscillation, bifurcation, and chaos, Langford W. and A. Mingarelli, ed., AMS, 1987.Google Scholar
  2. 2.
    Chemiack N. S., C. von Euler, I. Homma and F. F. Kao, Experimentally induced Cheyne-Stokes breathing, Respir. Physiol. 37 (1979), 185–200.CrossRefGoogle Scholar
  3. 3.
    Cunningham D. J. C., Integrative aspects of the regulation of breathing: a personal view, Widdicombe J. G. Editor, “Respiratory physiology”, UK: Butterworths, London, p 303–369, 1974.Google Scholar
  4. 4.
    Fortune J. B., D. Bock, A. M. Kupinski, H. H. Stratton, D. M. Shah and P. J. Feustel, Human cerebrovascular response to oxygen and carbon dioxide as determined by internal carotid artery duplex scanning, The J. of Trauma 32(5) (1992), 618–628.CrossRefGoogle Scholar
  5. 5.
    Grodins F. S., J. Buell and A. J. Bart, Mathematical analysis and digital simulation of the respiratory control system, J. Appl. Physiol. 22(2) (1967), 260–276.PubMedGoogle Scholar
  6. 6.
    Hale J. K. and W. Huang, Global geometry of the stable regions for two delay differential equations, J. Math. Anal. Appl. 178 (1993), 344–362.CrossRefGoogle Scholar
  7. 7.
    Khoo M. C. K., R. E. Kronauer, K. P. Strohl and A. S. Slutsky, Factors inducing periodic breathing in humans: a general model. J. Appl. Physiol. 53(3): (1982), 644–659.PubMedGoogle Scholar
  8. 8.
    Kiely D. G., R. I. Cargill and B. J. Lipworth, Effects of hypercapnia on hemodynamic, inotropic, lusitropic, and electrophysiologic indices in humans, Chest 109(5) (1996), 1215–1221.CrossRefPubMedGoogle Scholar
  9. 9.
    Lloyd B. B., M. G. M. Jukes and D. J. C. Cunningham, The interactions between hypoxia and other ventilatory stimuli, Quart. J. Exp. Physiol. 43 (1958), 214–221.PubMedGoogle Scholar
  10. 10.
    Nielsen M. and H. Smith, Studies on the regulation of respiration in acute hypoxia, Acta Physiol. Scand. 24 (1952), 293–313.CrossRefPubMedGoogle Scholar
  11. 11.
    Olszowka A. J. and L. E. Farhi, A system of digital computer subroutines for blood gas calculations, Respir. Physiol. 4 (1968), 270–280.CrossRefPubMedGoogle Scholar
  12. 12.
    Phillips B. A., J. W. McConelly and M. D. Smith, The effects of hypoxemia on cardiac output. A dose-response curve, Chest 93(3) (1988), 471–475.CrossRefPubMedGoogle Scholar
  13. 13.
    Poulin M. J., P. J. Liang and P. A. Robbins, Dynamics of the cerebral blood flow response to step changes in end-tidal PCO 2 and PO 2 in humans, J. Appl. Physiol. 81(3) (1996), 1084–95.PubMedGoogle Scholar
  14. 14.
    Poulin M. J. and P. A. Robbins, Indices of flow and cross-sectional area of the middle cerebral artery using Doppler ultrasound during hypoxia and hypercapnia in humans, Stroke 27 (1996), 2244–2250.PubMedGoogle Scholar
  15. 15.
    Serebrovskaya T. V., Comparison of respiratory and circulatory human responses to progressive hypoxia and hypercapnia, Respiration 59 (1992), 35–41.CrossRefGoogle Scholar
  16. 16.
    Severinghaus J. W., Proposed standard determination of ventilatory responses to hypoxia and hypercapnia in man, Chest 70(1) (1976), 129–131.CrossRefPubMedGoogle Scholar
  17. 17.
    Topor Z. L., Investigation of the human respiratory control system by computer modeling and system identification techniques, Ph.D. Thesis University of Calgary, 1999.Google Scholar
  18. 18.
    Topor Z. L., M. Pawlicki and J. E. Remmers, A computational model of the human respiratory control system: responses to hypoxia and hypercapnia, Ann. Biomed. Eng. (in review).Google Scholar
  19. 19.
    Topor Z. L., L. Johannson, J. Kasprzyk and J. E. Remmers, Dynamic ventilatory response to CO2 in congestive heart failure patients with and without central sleep apnea, J. Appl. Physiol. 91 (2001), 408–416.PubMedGoogle Scholar
  20. 20.
    Young D. L., F. L. Eldridge and C. S. Poon, Integration-differentiation and gating of carotid afferent traffic that shapes the respiratory pattern, J. Appl. Physiol. 94 (2002), 1213–1229.PubMedGoogle Scholar

Copyright information

© Kluwer Academic/Plenum Publishers, New York 2004

Authors and Affiliations

  • Zbignlew L. Topor
    • 1
  • Konstantinon Vasilakos
    • 1
  • John E. Remmers
    • 1
  1. 1.Department of PhysiologyUniversity of CalgaryCalgaryCanada

Personalised recommendations