The effect of mathematical modelling on critical velocity

Terry J. Housh, Joel T. Cramer, Anthony J. Bull, Glen O. Johnson, Dona J. Housh

Research output: Contribution to journalArticlepeer-review

47 Scopus citations


The purpose of this investigation was to examine the effects of mathematical modeling on critical velocity (CV) estimates and the oxygen consumption (VO2), heart rate (HR), and plasma lactate values that corresponded to the five CV estimates. Ten male subjects performed a maximal, incremental treadmil test to determine maximal VO2, and four randomly ordered treadmill runs for the estimation of CV. Two linear, two nonlinear, and one exponential mathematical models were used to estimate CV. Regression analyses were used to determine the VO2, HR, and plasma lactate values that corresponded to the five CV estimates from the relationships for VO2, HR, and plasma lactate versus running velocity from the maximal, incremental test. The nonlinear, three-component model (Nonlinear-3) resulted in a mean CV that was significantly (P<0.05) less than the mean values derived from the other four models, and was the lowest CV estimate for each subject. The percent of maximal VO2, HR, and plasma lactate values that corresponded to the Nonlinear-3 model were 89%, 93%, and 63%, respectively. These findings indicate that CV estimates differ by as much as 20% depending upon the model used to determine the characteristics of the velocity/time relationship. Future studies are needed to determine which model provides the most valid estimate of the demarcation point between heavy and severe exercise.

Original languageEnglish (US)
Pages (from-to)469-475
Number of pages7
JournalEuropean Journal of Applied Physiology
Issue number5
StatePublished - May 2001


  • Cycle ergometry
  • Heart rate
  • Lactate
  • Mathematical modeling
  • Oxygen consumption

ASJC Scopus subject areas

  • Orthopedics and Sports Medicine
  • Public Health, Environmental and Occupational Health
  • Physiology (medical)

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