Nonlinear dynamics of heart rate and oxygen uptake in exhaustive 10,000 m runs: influence of constant vs. freely paced

J Physiol Sci. 2006 Feb;56(1):103-11. doi: 10.2170/physiolsci.r2028.


We hypothesized that a freely paced 10,000 m running race would induce a smaller physiological strain (heart rate and oxygen uptake) compared with one performed at the same average speed but with an imposed constant pace. Furthermore, we analyzed the scaling properties with a wavelet transform algorithm computed log2 (wavelet transform energy) vs. log2 (scale) to get slope alpha, which is the scaling exponent, a measure of the irregularity of a time series. HR was sampled beat by beat and V2O, breath by breath. The enforced constant pace run elicited a significantly higher mean VO2 value (53 +/- 4 vs. 48 +/- 5 ml kg(-1) min(-1), P < 0.001), HR (169 +/- 13 vs. 165 +/- 14 bpm, P < 0.01), and blood lactate concentration (6.6 +/- 0.9 vs. 7.5 +/- 1 mM, P < 0.001) than the freely paced run. HR and VO2 signals showed a scaling behavior, which means that the signals have a similar irregularity (a self-similarity) whatever the scale of analysis may be, in both constant and free-paced 10,000 m runs. The scaling exponent was not significantly different according to the type of run (free vs. constant, P > 0.05) and the signal (HR vs. VO2, P > 0.05). The higher metabolic cost of constant vs. free paced run did not affect the self-similarity of HR and VO2, in either run. The HR signal only kept its scaling behavior only with a distance run, no matter the type of run (free or constant). The results suggest that the larger degree of pace variation in freely paced races may be an intentionally chosen strategy designed to minimize the physiological strain during severe exercise and to prevent a premature termination of effort, even if the variability of the heart rate and VO2, are comparable in an enforced constant vs. a freely paced run and if HR keeps the same variability until the arrival.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Adult
  • Fatigue / physiopathology
  • Heart Rate / physiology*
  • Humans
  • Lactates / blood
  • Linear Models
  • Mathematics
  • Nonlinear Dynamics*
  • Oxygen Consumption / physiology*
  • Physical Endurance / physiology*
  • Running / physiology*
  • Time Factors


  • Lactates