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Respiratory Control and the Onset of PeriodicBreathing

Published online by Cambridge University Press:  07 February 2014

A. C. Fowler
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Abstract

We analyse a reduced version of the Grodins et al. control model [14] of respiration involving only CO2, andshow that it can be dramatically simplified by the use of judicious approximations. Inparticular, we show that the conceptual basis of the popular model of Mackey and Glass[20] is at odds with the important transportprocesses of the Grodins model. Despite this, a realistic approximation of the Grodinsmodel yields a Mackey-Glass type model with almost the same criterion for the onset ofCheyne-Stokes breathing.

While the reduced Grodins model does apparently provide a realistic mechanism forinstability, consideration of the buffering effect of the blood-brain barrier appears tomake it unlikely. We conclude that a realistic physiological model of Grodins type toexplain Cheyne–Stokes breathing is not yet in place, and raise the question whether thebicarbonate buffering system has a rôle to play.

Keywords

periodic breathingrespiratory controlCheyne-Stokes respirationdelay equation
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 1: Issue dedicated to Michael Mackey , 2014 , pp. 39 - 57
Copyright
© EDP Sciences, 2014

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References

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