Size exponents for scaling maximal oxygen uptake in over 6500 humans: a systematic review and meta-analysis

Lorenzo Lolli, Alan M. Batterham, Kathryn L. Weston, Greg Atkinson

Research output: Contribution to journalReview articlepeer-review

38 Citations (Scopus)


Background: Maximal oxygen uptake (V ˙ O 2max) is conventionally normalized to body size as a simple ratio or using an allometric exponent < 1. Nevertheless, the most appropriate body size variable to use for scaling and the value of the exponent are still enigmatic. Studies tend to be based on small samples and can, therefore, lack precision. Objective: The objective of this systematic review was to provide a quantitative synthesis of reported static allometric exponents used for scaling V ˙ O 2max to whole body mass and fat-free mass. Methods: Eight electronic databases (CINAHL, Cochrane Central Register of Controlled Trials, EMBASE, MEDLINE, PubMed, Scopus, SPORTDiscus and Web of Science) were searched for relevant studies published up to January 2016. Search terms included ‘oxygen uptake’, ‘cardiorespiratory fitness’, ‘V ˙ O 2max’, ‘V ˙ O 2peak’, ‘scaling’ and all interchangeable terms. Inclusion criteria included human cardiorespiratory fitness data; cross-sectional study designs; an empirical derivation of the exponent; reported precision statistics; and reported information regarding participant sex, age and sports background, V ˙ O 2max protocol, whole body composition protocol and line-fitting methods. A random-effects model was used to quantify weighted pooled exponents and 95% confidence limits (Cls). Heterogeneity was quantified with the tau-statistic (τ). Meta-regression was used to quantify the impact of selected moderator variables on the exponent effect size. A 95% prediction interval was calculated to quantify the likely range of true fat-free mass exponents in similar future studies, with this distribution used to estimate the probability that an exponent would be above theorised universal values of 23and34. Results: Thirty-six studies, involving 6514 participants, met the eligibility criteria. Whole body mass and fat-free mass were used as the scaling denominator in 27 and 15 studies, respectively. The pooled allometric exponent (95% Cls) was found to be 0.70 (0.64 to 0.76) for whole body mass and 0.90 (0.83 to 0.96) for fat-free mass. The between-study heterogeneity was greater for whole body mass (τ = ±0.15) than for fat-free mass (τ = ±0.11). Participant sex explained 30% of the between-study variability in the whole body mass exponent, but the influence on the fat-free mass exponent was trivial. The whole body mass exponent of 0.52 (0.40 to 0.64) for females was substantially lower than the 0.76 (0.70 to 0.83) for males, whereas the fat-free mass exponent was similar for both sexes. The effects of all other moderators were trivial. The 95% PI for fat-free mass ranged from 0.68 to 1.12. The estimated probability of a true fat-free mass exponent in a future study being greater than 23or34 power scaling is 0.98 (very likely) and 0.92 (likely), respectively. Conclusions: In this quantitative synthesis of published studies involving over 6500 humans, the whole body mass exponent was found to be spuriously low and prone to substantial heterogeneity. We conclude that the scaling of V ˙ O 2max in humans is consistent with the allometric cascade model with an estimated prediction interval for the fat-free mass exponent not likely to be consistent with the 23and34 power laws.

Original languageEnglish
Pages (from-to)1405-1419
Number of pages15
JournalSports Medicine
Issue number7
Early online date6 Jan 2017
Publication statusPublished - 1 Jul 2017


  • scaling
  • oxygen


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