A model of oxygen uptake kinetics in response to exercise: Including a means of calculating oxygen demand/deficit/debt

Bulletin of Mathematical Biology

Volumn 67, Issue 5, 2005, Pages 989-1015

  Stirling, J R ^a,b   Zakynthinaki, M S ^a   Saltin, B ^c  

^a UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

^b UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^c Rigshospitalet   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

OXYGEN;

ALGORITHM; ARTICLE; BIOLOGICAL MODEL; EXERCISE; HUMAN; KINETICS; METABOLISM; OXYGEN CONSUMPTION; PHYSIOLOGY; SPORT;

ALGORITHMS; EXERCISE; HUMANS; KINETICS; MODELS, BIOLOGICAL; OXYGEN; OXYGEN CONSUMPTION; SPORTS;

EID: 21444444547     PISSN: 00928240     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.bulm.2004.12.005     Document Type: Article

References (86)

1. P.O. Astrand, and B. Saltin Oxygen uptake during the first minutes of heavy muscular exercise J. Appl. Physiol. 16 6 1961 971 976
2. P.O. Astrand, K. Rodahl, H.A. Dahl, and S.B. Stromme Textbook of Work Physiology: Physiological Bases of Exercise 2003 Human Kinetics Champaign, IL
3. J. Bangsbo Physiological factors associated with efficiency in high intensity exercise Sports Med. 22 5 1996 299 305
4. J. Bangsbo Oxygen deficit: A measure of the anaerobic energy production during intense exercise? Can. J. Appl. Physiol. 21 5 1996 350 363
5. J. Bangsbo Quantification of anaerobic energy production during intense exercise Med. Sci. Sports Exerc. 30 1 1998 47 52
6. J. Bangsbo, P. Krustrup, J. Gonzalez-Alonso, R. Bonshel, and B. Saltin Muscle oxygen kinetics at onset of intense dynamic exercise in humans Am. J. Physiol. Regul. Integr. Comp. Physiol. 279 2000 R899 R906
7. 2 kinetics during heavy exercise Med. Sci. Sports Exerc. 26 11 1994 1327 1334
8. T.J. Barstow, and P.A. Mole Simulation of pulmonary oxygen uptake during exercise in humans J. Appl. Physiol. 63 1987 2253 2261
9. T.J. Barstow, and P.A. Mole Linear and nonlinear characteristics of oxygen uptake kinetics during heavy exercise J. Appl. Physiol. 71 6 1991 2099 2106
10. 2 deficit as related to exercise intensity and blood lactate J. Appl. Physiol. 75 1993 755 762
11. 2 deficit in heavy exercise J. Appl. Physiol. 88 2000 1407 1412
12. O. Bernard, F. Maddio, S. Ouattara, C. Jimenez, A. Charpenet, B. Melin, and J. Bittel Influence of the oxygen uptake slow component on the energy cost of high-intensity submaximal treadmill running in humans Eur. J. Appl. Physiol. 78 1998 578 585
13. 2 slow component and performance in endurance sports Brit. J. Sports Med. 34 2 2000 83 85
14. V.L. Billat Interval training for performance: A scientific and empirical practice. Special recommendations for middle and long distance running. Part I: Aerobic interval training Sports Med. 31 1 2001 13 31
15. V.L. Billat Interval training for performance: A scientific and empirical practice. Special recommendations for middle and long distance running. Part II: Anaerobic interval training Sports Med. 31 12 2001 75 90
16. V.L. Billat, L. Mille-Hamard, A. Demarle, and J. Koralsztein Effect of training in humans on off- and on-transient oxygen uptake kinetics after severe exhausting intensity runs Eur. J. Appl. Physiol. 87 2002 496 505
17. 2max on oxygen kinetics during an all-out severe run in humans J. Sports Med. Phys. Fitness 40 2000 185 194
18. 2 slow component dependent upon progressive recruitment of fast-twitch fibres in trained runners J. Appl. Physiol. 90 2001 2212 2220
19. G.A. Brooks, and G.A. Gaesser End points of lactate and glucose metabolism after exhausting exercise J. Appl. Physiol.: Respirat. Environ. Exerc. Physiol. 49 1980 1057 1069
20. G.A. Brooks, K.J. Hittelman, J.A. Faulkner, and R.E. Beyer Temperature, skeletal muscle mitochondrial functions, and oxygen debt Am. J. Physiol. 220 1971 1053 1059
21. R. Casaburi, T.J. Barstow, T. Robinson, and K. Wasserman Influence of work rate on ventilatory and gas exchange kinetics J. Appl. Physiol. 67 1989 547 555
22. R. Casaburi, J. Daly, J.E. Hansen, and R.M. Effros Abrupt changes in mixed venous blood gas composition after the onset of exercise J. Appl. Physiol. 67 1989 1106 1112
23. D. Costill, J. Kovaleski, D. Porter, J. Kirwan, R. Fielding, and D. King Energy expenditure during front crawl swimming: Predicting success in middle distance events Int. J. Sports Med. 6 4 1985 266 270
24. E.F. Coyle, M.T. Hamilton, J.G. Alonso, S.J. Montain, and J.L. Ivy Carbohydrate metabolism during intense exercise when hyperglycemic J. Appl. Physiol. 70 1991 834 840
25. C.T. Davies, P.E. Di Prampero, and P. Cerretelli Kinetics of the cardiac output and respiratory gas exchange during exercise and recovery J. Appl. Physiol. 32 1972 618 625
26. 2 uptake and heart rate kinetics during severe exercise J. Appl. Physiol. 81 6 1996 2500 2508
27. G.A. Gaesser, and G.A. Brooks Metabolic bases of excess post-exercise oxygen consumption: A review Med. Sci. Sports Exerc. 16 1984 29 43
28. G.A. Gaesser, and D.C. Poole The slow component of oxygen uptake in humans Exerc. Sport Sci. Rev. 24 1996 35 70
29. J. Guckenheimer, and P. Holmes Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields 1983 Springer-Verlag
30. M.T. Hamilton, J.G. Alonso, S.J. Montain, and E.F. Coyle Fluid replacement and glucose infusion during exercise prevents cardiovascular drift J. Appl. Physiol. 71 1991 871 877
31. P. Harris Lactic acid and the phlogiston debt Cardiovasc. Res. 3 1969 381 390
32. D.W. Hill, and C.S. Ferguson A physiological description of critical speed Eur. J. Physiol. Occup. Physiol. 79 3 1999 290 293
33. A.V. Hill, and L. Lupton Muscular exercise, lactic acid and the supply and utilization of oxygen Q. J. Med. 16 1923 135 171
34. 2 response to the onset of severe intensity exercise Can. J. Appl. Physiol. 26 4 2001 350 355
35. 2max Med. Sci. Sports Exerc. 34 4 2002 709 714
36. 2 consumption during prolonged exercise J. Appl. Physiol. 64 1988 753 758
37. H. Kantz, and T. Schreiber Nonlinear Time Series Analysis 1999 Cambridge University Press Cambridge
38. J. Karlsson, and B. Saltin Lactate, ATP and CrP in working muscles during exhausting exercise in man J. Appl. Physiol. 29 1970 598 602
39. C.A. Kindig, P. McDonough, H.H. Erickson, and D.C. Poole Effect of L-NAME on oxygen uptake kinetics during heavy-intensity exercise in the horse J. Appl. Physiol. 91 2001 891 896
40. S. Koga Breath-by-breath gas exchange kinetics during constant load work Ann. Physiol. Anthropol. 9 2 1990 163 166
41. A. Krogh, and J. Lindhard The regulation of respiration and circulation during the initial stages of muscular work J. Physiol. (Lond) 47 1913 112 136
42. Krogh, A., Lindhard, J., 1919-1920. The changes in respiration at the transition from work to rest. J. Physiol. (Lond) 53, 431-437
43. I. Lamarra, B.J. Whipp, S.A. Ward, and K. Wasserman Effect of interbreath fluctuations on characterizing exercise gas exchange kinetics J. Appl. Physiol. 62 1987 2003 2012
44. 2 recovery kinetics in the horse following moderate, heavy and severe exercise J. Appl. Physiol. 86 1999 1170 1177
45. 2 kinetics in the horse during moderate and heavy exercise J. Appl. Physiol. 83 1997 1235 1241
46. D. Linnarsson Dynamics of pulmonary gas exchange and heart rate changes at start and end of exercise Acta Physiol. Scand. Suppl. 415 1974 1 68
47. 2 kinetics in heavy submaximal exercise by hyperoxia and prior high-intensity exercise J. Appl. Physiol. 83 4 1997 1318 1325
48. A. Mader Glycolysis and oxidative phosphorylation as a function of cytosolic phosphorylation state and power output of the muscle cell Eur. J. Appl. Physiol. 88 4-5 2003 317 338
49. R. Margaria, F. Mangili, F. Cuttica, and P. Cerretelli The kinetics of the oxygen consumption at the onset of muscular exercise in man Ergonomics 8 1965 49 54
50. D.E. Martin, and P.N. Coe Better Training for Distance Runners 1997 Human Kinetics Champaign, IL
51. 2 deficit J. Appl. Physiol. 64 1988 50 60
52. O. Meyerhof Die Energieumwandlungen im Muskel. II. Das Schicksal der Milchsäure in der Erholungsperiode des Muskels Arch. Ges. Physiol. 182 1920 284 317
53. 2 recovery curve Eur. J. Appl. Physiol. Occup. Physiol. 47 4 1981 385 391
54. T. Noakes Lore of Running. Discover the Science and Spirit of Running 4th edition 2003 Human Kinetics Champaign, IL
55. 2 uptake kinetics during high-intensity exercise in trained and untrained prepubertal children Int. J. Sports Med. 21 2000 31 36
56. F. Ozyener, H.B. Rossiter, S.A. Ward, and B.J. Whipp Influence of exercise intensity on the on- and off-transient kinetics of pulmonary oxygen uptake in humans J. Appl. Physiol. 53 3 2001 891 902
57. D.H. Paterson, and B.J. Whipp Asymmetries of oxygen uptake transients at the on- and offset of heavy exercise in humans J. Physiol. (Lond) 443 1991 575 586
58. 2 Med. Sci. Sports Exerc. 26 11 1994 1335 1340
59. 2 slow component: Physiological and functional significance Med. Sci. Sport Exerc. 26 11 1994 1354 1358
60. C.R. Potter, D.J. Childs, W. Houghton, and N. Armstrong Breath-to-breath noise in the ventilatory and gas exchange responses of children to exercise Eur. J. Appl. Physiol. Occup. Physiol. 80 2 1999 118 124
61. W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery Numerical Recipes in C: The Art of Scientific Computing 2nd edition 1993 Cambridge University Press Cambridge
62. L. Puente-Maestu, J.B. Abad, R. Godoy, J.M. Pérez-Parra, J.M. Gubillo, and B.J. Whipp Breath-by-breath fluctuations of pulmonary gas exchange and ventilation in COPD patients Eur. J. Appl. Physiol. 87 2002 535 541
63. J.M. Ren, S. Broderg, and K. Sahlin Oxygen deficit is not affected by the rate of transition from rest to submaximal exercise Acta Physiol. Scand. 135 1989 545 548
64. F.A. Rodriguez Maximal oxygen uptake and cardiorespiratory response to maximal 400 m free swimming, running and cycling tests in competitive swimmers J. Sports Med. Phys. Fitness. 40 2 2000 87 95
65. F.A. Rodriguez, and A. Mader Energy metabolism during 400 m and 100 m crawl swimming: Computer simulation based on free swimming measurement J.C. Chatard Biomechanics and Medicine in Swimming IX 2003 Publications de l'Universite de Saint-Etienne Saint-Etienne 373 378
66. F.A. Rodriguez, K.L. Keskinen, O.P. Keskinen, and M. Malvela Oxygen uptake kinetics during free swimming: A pilot study J.C. Chatard Biomechanics and Medicine in Swimming IX 2003 Publications de l'Universite de Saint-Etienne Saint-Etienne 379 384
67. 31P-magnetic resonance spectroscopy and parameter estimation of metabolic responses to exercise in humans J. Physiol. 528 2 2000 359 369
68. Saltin, B., 1987. The physiological and biochemical basis of aerobic and anaerobic capacities in man; effect of training and range of adaption. In: Maehlum, S., Nilsson, S., Renstrom, P., (Eds.), An Update in Sports Medicine: Proceedings from the Second Scandinavian Conference in Sports Medicine. pp. 16-59
69. B. Saltin Anaerobic capacity: Past, present and prospective A. Taylor P.D. Gollmack Biochemistry of Exercise VII 1990 Human Kinetics Champaign, IL 387 412
70. B. Saltin, A.P. Gagge, U. Bergh, and J.A.J. Stolwigk Body temperatures and sweating during exhaustive exercise J. Appl. Physiol. 32 2 1972 635 643
71. B. Saltin, C.K. Kim, N. Terrados, H. Larsen, J. Svendenhag, and C.J. Rolf Morphology, enzyme activities and buffer capacity in leg muscles of Kenyan and Scandinavian runners Scand. J. Med. Sports 5 1995 222 230
72. B. Saltin, H. Larsen, W. Terrados, J. Bangsbo, T. Bak, C.K. Kim, J. Svedenhag, and C.J. Rolf Aerobic exercise capacity at sea level and at altitude in Kenyan boys, junior and senior runners compared with Scandinavian runners Scand. J. Med. Sports 5 1995 209 221
73. 2 uptake for recovery Med. Sci. Sports 2 1970 177 186
74. J.R. Stirling Transport and bifurcation in a non-area preserving 2 dimensional map with applications to the discharge of pollution in an estuarine flow Physica D 144 2000 169 193
75. J.R. Stirling Nonlinear dynamics, transport and the patchiness of clouds of pollution in an estuarine fluid flow Discrete Contin. Dyn. Syst., Ser. B 3 2 2003 263 284
76. Stirling, J.R., Zakynthinaki, M.S., 2004. Mathematical modelling of the physiological response to exercise (translated into Polish). Sport Wyczynowy bimonthly periodical (submitted for publication)
77. J.R. Stirling, and M.S. Zakynthinaki Stability and the maintenance of balance following a perturbation from quiet stance Chaos 14 1 2004 96 105
78. K. Wasserman, B.J. Whipp, and J. Castagna Cadriodynamic hyperpnea: Hyperpnea secondary to cardiac output increase J. Appl. Physiol. 36 1974 457 464
79. K. Wasserman, J.E. Hansen, D.Y. Sue, R. Casaburi, and B.J. Whipp Principles of Exercise Testing and Interpretation, Including Pathophysiology and Clinical Applications third ed 1999 Lippincott Williams and Wilkins
80. M.L. Weissman, P.W. Jones, A. Oren, N. Lammarra, B.J. Whipp, and K. Wasserman Cardiac output increase and gas exchange at the start of exercise J. Appl. Physiol. 52 1982 236 244
81. A. Weltman The Blood Lactate Response to Exercise (Current Issues in Exercise Science) 1995 Human Kinetics Champaign, IL
82. 2 uptake kinetics during heavy exercise Medi. Sci. Sports Exerc. 26 11 1994 1319 1326
83. B.J. Whipp, and K. Wasserman Oxygen uptake kinetics for various intensities of constant load work J. Appl. Physiol. 33 1972 351 356
84. B.J. Whipp, H.B. Rossiter, and S.A. Ward Exertional oxygen uptake kinetics: A stamen or stamina? Biochem. Soc. Trans. 2002 237 247
85. H.C. Xing, J.E. Cochrane, Y. Yamamoto, and R.L. Hughson Frequency domain analysis of ventilation and gas exchange kinetics in hypoxic exercise J. Appl. Physiol. 71 6 1991 2394 2401
86. Zakynthinaki, M.S., Stirling, J.R., 2004. Smoothing of physiological time series data using Fourier filtering: Application to the heart rate response to exercise (submitted for publication)