Control of breathing: Two types of delays studied in an integrated model of the respiratory system

Respiratory Physiology and Neurobiology

Volumn 170, Issue 1, 2010, Pages 103-112

  Ben Tal, Alona ^a   Smith, Jeffrey C ^b  

^a MASSEY UNIVERSITY   (New Zealand)

^b NATIONAL INSTITUTE OF NEUROLOGICAL DISORDERS AND STROKE   (United States)

Author keywords

Apnea; Brainstem; Feedback regulation; Hypercapnia; Hypoxia; Respiration

Indexed keywords

CARBON DIOXIDE;

ARTICLE; BLOOD FLOW VELOCITY; BRAIN STEM; CARBON DIOXIDE BREATHING; CHEMORECEPTOR; FEEDBACK SYSTEM; GAS EXCHANGE; GAS TRANSPORT; HYPERCAPNIA; HYPOXIA; MATHEMATICAL MODEL; PRIORITY JOURNAL; RESPIRATION CONTROL; RESPIRATORY SYSTEM;

ANIMALS; ANOXIA; HUMANS; HYPERCAPNIA; MODELS, BIOLOGICAL; MODELS, THEORETICAL; NONLINEAR DYNAMICS; REACTION TIME; RESPIRATION; RESPIRATORY SYSTEM; TIME FACTORS;

EID: 74849105195     PISSN: 15699048     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.resp.2009.10.008     Document Type: Article

References (33)

1. Batzel J.J., Kappel F., Schneditz D., and Tran H.T. Cardiovascular & Respiratory Systems: Modeling, Analysis & Control (Frontiers in Applied Mathematics) (2006), SIAM
2. Batzel J.J., and Tran H.T. Modeling instability in the control system for human respiration: applications to infant non-REM sleep. Appl. Math. Comput. 110 (2000) 1-51
3. Ben-Tal A. Simplified models for gas exchange in the human lungs. J. Theor. Biol. 238 (2006) 474-495
4. Ben-Tal A., and Smith J.C. A model for control of breathing in mammals: coupling neural dynamics to peripheral gas exchange and transport. J. Theor. Biol. 251 (2008) 480-497
5. Comroe J.H. Physiology of Respiration. 2nd edition (1974), Year Book Medical Publishers, Inc.
6. Driver R.D. Ordinary and Delay Differential Equations (1977), Springer-Verlag
7. Eldridge F.L. The North Carolina respiratory model. A multipurpose model for studying the control of breathing. In: Khoo M.C.K. (Ed). Bioengineering Approaches to Pulmonary Physiology and Medicine (1996), Plenum Press, New York 25-49
8. Engelberg S. A Mathematical Introduction to Control Theory (2005), Imperial College Press
9. Feldman J.L., and Del Negro C.A. Looking for inspiration: new perspectives on respiratory rhythm. Nat. Rev. Neurosci. 7 (2006) 232-241
10. Feldman J.L., Mitchell G.S., and Nattie E.E. Breathing: rhythmicity, plasticity, chemosensitivity. Ann. Rev. Neurosci. 26 (2003) 239-266
11. Fowler A.C., and Kalamangalam G.P. Periodic breathing at high altitude. IMA J. Math. Appl. Med. 19 (2002) 293-313
12. Grodins F.S., Buell J., and Bart A.J. Mathematical analysis and digital simulation of the respiratory control system. J. Appl. Physiol. 22 2 (1967) 260-276
13. Jordan A.S., Catcheside P.G., Orr R.S., O'Donoghue F.J., Saunders N.A., and McEvoy R.D. Ventilatory decline after hypoxia and hypercapnia is not different between healthy young men and women. J. Appl. Physiol. 88 (2000) 3-9
14. Kellogg R.H. Central chemical regulation of respiration. In: Fenn W.O., and Rahn H. (Eds). Handbook of Physiology, Respiration vol. I (1964), American Physiological Society, Washington, DC 507-534
15. Khoo M.C.K. Physiological Control Systems. Analysis, Simulation, and Estimation (2000), IEEE Press
16. Khoo M.C., Kronauer R.E., Strohl K.P., and Slutsky A.S. Factors inducing periodic breathing in humans: a general model. J. Appl. Physiol. 53 3 (1982) 644-659
17. Khoo M.C.K., and Yamashiro S.M. Models of control of breathing. In: Chang H.A., and Paiva M. (Eds). Respiratory Physiology: An Analytical Approach (1989), Mercer Dekker, New York 799-829
18. Kolmanovskii V., and Myshkis A. Applied Theory of Functional Differential Equations (1992), Kluwer Academic Publishing
19. Lange R.L., Horgan J.D., Botticelli J.T., Tsagaris T., Carlisle R.P., and Kuida H. Pulmonary to arterial circulatory transfer function: importance in respiratory control. J. Appl. Physiol. 21 4 (1966) 1281-1291
20. Lu K., Clark Jr. J.W., Ghorbel F.H., Ware D.L., Zwischenberger J.B., and Bidani A. Whole-body gas exchange in human predicted by a cardiopulmonary model. Cardiovasc. Eng. 3 1 (2002) 1-19
21. MacDonald N. Biological Delay Systems: Linear Stability Theory (1989), Cambridge University Press
22. Mackey M.C., and Glass L. Oscillation and chaos in physiological control systems. Science 197 (1977) 287-289
23. Milhorn Jr. H.T. The Application of Control Theory to Physiological Systems (1966), W. B. Saunders Company
24. Milhorn Jr. H.T., and Guyton A.C. An analog computer analysis of Cheyne-Stokes breathing. J. Appl. Physiol. 20 2 (1965) 328-333
25. Ponte J., and Purves M.J. J. Appl. Physiol. 37 5 (1974) 635-647
26. Quaranta A.J., D'Alonzo G.E., and Krachman S.L. Cheyne-Stokes respiration during sleep in congestive heart failure. Chest 111 (1997) 467-473
27. Rubin J.E., Shevtsova N.A., Ermentrout G.B., Smith J.C., and Rybak I.A. Multiple rhythmic states in a model of the respiratory CPG. J. Neurophysiol. 101 (2009) 2146-2165
28. Smith J.C., Abdala A.P.L., Koizumi H., Rybak I.A., and Paton J.F.R. Spatial and functional architecture of the mammalian brainstem respiratory network: a hierarchy of three oscillatory mechanisms. J. Neurophysiol. 98 (2007) 3370-3387
29. Smith J.C., Butera R.J., Koshiya N., Negro C.D., Wilson C.G., and Johnson S.M. Respiratory rhythm generation in neonatal and adult mammals: the hybrid pacemaker-network model. Respir. Physiol. Neurobiol. 122 (2000) 131-147
30. Smith J.C., Ellenberger H.H., Ballanyi K., Richter D.W., and Feldman J.L. Pre-Bötzinger complex: a brainstem region that may generate respiratory rhythm in mammals. Science 254 (1991) 726-729
31. Tawhai M., and Ben-Tal A. Multiscale modelling for the lung physiome. Cardiovasc. Eng. 4 1 (2004) 19-26
32. Topor Z.L., Vasilakos K., Younes M., and Remmers J.E. Model based analysis of sleep disordered breathing in congestive heart failure. Respir. Physiol. Neurobiol. 155 (2007) 82-92
33. Ursino M., Magosso E., and Avanzolini G. An integrated model of the human ventilatory control system: the response to hypercapnia. Clin. Physiol. 21 4 (2001) 447-464