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How to identify the physiological parameters and run the optimal race. (English) Zbl 1343.92093

Summary: This paper shows how a system of ordinary differential equations describing the evolution of the anaerobic energy, the oxygen uptake, the propulsive force and the velocity of a runner accurately describes pacing strategy. We find a protocol to identify the physiological parameters needed in the model using numerical simulations and time splits measurements for an 80m and a 1600m race. The velocity curve of the simulations is very close to the experimental one. This model could allow to study the influence of training and improving some specific parameters for the pacing strategy.

MSC:

92C30 Physiology (general)
92C40 Biochemistry, molecular biology

Software:

Bocop
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Full Text: DOI

References:

[1] Aftalion, A.; Bonnans, J. F., Optimization of running strategies based on anaerobic energy and variations of velocity, SIAM Journal on Applied Mathematics, 74, 5, 1615-1636 (2014) · Zbl 1307.49002 · doi:10.1137/130932697
[2] Behncke, H., A mathematical model for the force and energetics in competitive running, Journal of mathematical biology, 31, 8, 853-878 (1993) · Zbl 0782.92007 · doi:10.1007/BF00168050
[3] Bonnans, F.; Grelard, V.; Martinon, P., Bocop, the optimal control solver, open source toolbox for optimal control problems, URL http://bocop.org (2011)
[4] Hanon, C.; Leveque, J-M.; Thomas, C.; Vivier, L., Pacing Strategy and \(\dot{VO2}\) Kinetics during a 1500-m Race, International journal of sports medicine, 29, 3, 206-211 (2008) · doi:10.1055/s-2007-965109
[5] Hanon, C.; Thomas, C., Effects of optimal pacing strategies for 400-, 800-, and 1500-m races on the \(\dot{VO2}\) response, Journal of sports sciences, 29, 9, 905-912 (2011) · doi:10.1080/02640414.2011.562232
[6] Keller, J. B., A theory of competitive running, Physics today, 43 p. pp. (1973)
[7] Keller, J. B., Optimal velocity in a race, American Mathematical Monthly, 474-480 (1974) · Zbl 0288.49010 · doi:10.1080/00029890.1974.11993589
[8] Maroński, R., Minimum-time running and swimming: an optimal control approach, Journal of biomechanics, 29, 2, 245-249 (1996) · doi:10.1016/0021-9290(95)00041-0
[9] Morton, R. H., A 3-parameter critical power model, Ergonomics, 39, 4, 611-619 (1996) · doi:10.1080/00140139608964484
[10] Morton, R. H., The critical power and related whole-body bioenergetic models, European journal of applied physiology, 96, 4, 339-354 (2006) · doi:10.1007/s00421-005-0088-2
[11] Peronnet, F.; Massicote, D., Table of nonprotein respiratory quotient: an update., Can J Sport Sci, 9, 16-23 (1991)
[12] Pitcher, A. B., Optimal strategies for a two-runner model of middle-distance running, SIAM Journal on Applied Mathematics, 70, 4, 1032-1046 (2009) · Zbl 1195.49049 · doi:10.1137/090749384
[13] Quinn, M., The effects of wind and altitude in the 400-m sprint, Journal of sports sciences, 22, 11-12, 1073-1081 (2004) · doi:10.1080/02640410410001730016
[14] Thiel, C.; Foster, C.; Banzer, W.; De Koning, J., Pacing in Olympic track races: competitive tactics versus best performance strategy, Journal of sports sciences, 30, 11, 1107-1115 (2012) · doi:10.1080/02640414.2012.701759
[15] Tucker, R.; Lambert, M. I.; Noakes, T. D., An analysis of pacing strategies during men’s world-record performances in track athletics, International journal of sports physiology and performance, 1, 3, 233 p. pp. (2006) · doi:10.1123/ijspp.1.3.233
[16] Tucker, R.; Noakes, T. D., The physiological regulation of pacing strategy during exercise: a critical review, British journal of sports medicine, 43, 6, e1-e1 (2009) · doi:10.1136/bjsm.2009.057562
[17] Ward-Smith, A. J., A mathematical theory of running, based on the first law of thermodynamics, and its application to the performance of world-class athletes, Journal of biomechanics, 18, 5, 337-349 (1985) · doi:10.1016/0021-9290(85)90289-1
[18] Woodside, W., The optimal strategy for running a race (a mathematical model for world records from 50 m to 275 km), Mathematical and computer modelling, 15, 10, 1-12 (1991) · Zbl 0800.00016 · doi:10.1016/0895-7177(91)90086-M
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