Respiratory control and the onset of periodic breathing

Mathematical Modelling of Natural Phenomena

Volumn 9, Issue 1, 2014, Pages 39-57

  Pujo Menjouet, L ^a   Fowler, A C ^a  

^a UNIVERSITY OF LIMERICK   (Ireland)

Author keywords

Cheyne Stokes respiration; Delay equation; Periodic breathing; Respiratory control

Indexed keywords

EID: 84893912572     PISSN: 09735348     EISSN: 17606101     Source Type: Journal    
DOI: 10.1051/mmnp/20149104     Document Type: Article

References (27)

1. J. J. Batzel, H. T. Tran. Modeling instability in the control system for human respiration: applications to infant non-REM sleep. Appl. Math. Comput. 110 (2000a), 1-51.
2. J. J. Batzel, H. T. Tran. Stability of the human respiratory control system. I. Analysis of a two-dimensional delay state-space model. J. Math. Biol. 41 (2000b), 45-79.
3. J. J. Batzel, H. T. Tran. Stability of the human respiratory control system. II. Analysis of a three-dimensional delay state-space model. J. Math. Biol. 41 (2000c), 80-102.
4. A. Ben-tal, J. C. Smith. Control of breathing: two types of delays studied in an integrated model of the respiratory system. Respir. Physiol. Neurobiol. 170 (2010), 103-112.
5. D. W. Carley, D. C. Shannon. A minimal mathematical model of human periodic breathing. J. Appl. Physiol. 65 (1988), 1400-1409.
6. J. A. Cheyne. A case of apoplexy in which the fleshy part of the heart was converted into fat. Dublin Hosp. Rep. 2 (1818), 216-219.
7. F. Dong, W. F. Langford. Models of Cheyne-Stokes respiration with cardiovascular pathologies. J. Math. Biol. 57 (2008), 497-519.
8. A. ElHefnawy, G. M. Saidel, E. N. Bruce, N. S. Cherniack Stability analysis of CO2 control of ventilation. J. Appl. Physiol. 69 (1990), 498-503.
9. A. C. Fowler, G. P. Kalamangalam, G. C. Kember. A mathematical analysis of the Grodins model of respiratory control. IMA J. Math. Appl. Med. Biol. 10 (1993), 249-280.
10. A. C. Fowler, G. P. Kalamangalam. The role of the central chemoreceptor in causing periodic breathing. IMA J. Math. Appl. Med. Biol. 17 (2000), 147-167. (Pubitemid 30648949)
11. A. C. Fowler, G. P. Kalamangalam. Periodic breathing at high altitude. IMA J. Math. Appl. Med. Biol. 19 (2003), 293-313. (Pubitemid 36722198)
12. A. C. Fowler, R. E. M. Rickaby, E. W. Wolff. Exploration of a simple model for ice ages. Int. J. Geomath. 4 (2013), 227-297.
13. D. P. Francis, K. Wilson, L. C. Davies, A. J. S. Coats, M. Piepoli. Quantitative general theory for periodic breathing in chronic heart failure and its clinical implications. Circulation 102 (2000), 2, 214-221.
14. F. S. Grodins, J. Buell, A. J. Bart. Mathematical analysis and digital simulation of the respiratory control system. J. Appl. Physiol. 22 (1967), 260-276.
15. A. C. Guyton, J. W. Crowell, J. W. Moore. Basic oscillating mechanism of Cheyne-Stokes breathing. Amer. J. Physiol. 187 (1956), 395-398.
16. A. C. Guyton, J. E. Hall Textbook of medical physiology, 11th ed. Elsevier, Pennsylvania, 2006.
17. M. C. K. Khoo, R. E. Kronauer, K. P. Strohl, A. S. Slutsky. Factors inducing periodic breathing in humans: a general model. J. Appl. Physiol. 53 (1982), 644-659. (Pubitemid 12027236)
18. M. H. Kryger, T. Millar. Cheyne-Stokes respiration: stability of interacting systems in heart failure. Chaos 1 (1991), 265-269.
19. G.-S. Longobardo, B. Gothe, N. S. Cherniack. Factors affecting respiratory system stability. Ann. Biomed. Engng. 17 (1989), 377-396. (Pubitemid 19188601)
20. M. C. Mackey, L. Glass. Oscillations and chaos in physiological control systems. Science 197 (1977), 287-289. (Pubitemid 8130447)
21. C. H. Manisty, K. Willson, R. Wensel, Z. I. Whinnett, J. E. Davies, W. L. G. Oldfield, J. Mayet, D. P. Francis. Development of respiratory control instability in heart failure: a novel approach to dissect the pathophysiological mechanisms. J. Physiol. 577 (2006), 387-401. (Pubitemid 44698263)
22. N. K. Martin, E. A. Gaffney, R. A. Gatenby, R. J. Gillies, I. F. Robey, P. K. Maini. A mathematical model of tumour and blood pHe regulation: The HCO3-/CO2 buffering system. Math. Biosci. 230 (2011), 1-11.
23. J. D. Murray Mathematical biology. Springer-Verlag, Berlin, (2003).
24. W. Stokes The disease of the heart and the aorta. Hodges and Smith, Dublin, Ireland, (1854).
25. M. P. Ward, J. S. Milledge and J. B. West High altitude medicine and physiology, 3rd ed. Arnold, London, (2000).
26. J. B. West Respiratory physiology-the essentials, 4th ed. Williams and Wilkins, Baltimore, (1990).
27. J. B. West, R. M. Peters, G. K. H. Aksnes, J. S. Milledge, R. B. Schoene. Nocturnal periodic breathing at 6300 and 8050 m. J. Appl. Physiol. 61 (1986), 280-287. (Pubitemid 16055689)