Predicting VO_2max Using Lung Function and Three-Dimensional (3D) Allometry Provides New Insights into the Allometric Cascade (M^0.75)

Alan M Nevill¹, Matthew Wyon², Jonathan Myers^{3

4}, Matthew P Harber⁵, Ross Arena⁶, Tony D Myers⁷, Leonard A Kaminsky⁸

Affiliations

¹ Faculty of Education, Health and Wellbeing, University of Wolverhampton, Walsall Campus, Gorway Road, Walsall, WS1 3BD, UK. a.m.nevill@wlv.ac.uk.
² Faculty of Education, Health and Wellbeing, University of Wolverhampton, Walsall Campus, Gorway Road, Walsall, WS1 3BD, UK.
³ Division of Cardiology, VA Palo Alto Health Care System, Palo Alto, CA, USA.
⁴ Stanford University, Stanford, CA, USA.
⁵ Health Sciences, Taylor University, Upland, IN, USA.
⁶ Department of Physical Therapy, College of Applied Sciences, University of Illinois at Chicago, Chicago, IL, USA.
⁷ Sport and Health, Newman University, Birmingham, UK.
⁸ Fisher Institute of Health and Well-Being and Clinical Exercise Physiology Laboratory, Ball State University, Muncie, IN, USA.

PMID: 40223039
DOI: 10.1007/s40279-025-02208-3

Predicting VO_2max Using Lung Function and Three-Dimensional (3D) Allometry Provides New Insights into the Allometric Cascade (M^0.75)

Alan M Nevill et al. Sports Med. 2025 Jul.

. 2025 Jul;55(7):1757-1767.

doi: 10.1007/s40279-025-02208-3. Epub 2025 Apr 13.

Authors

Alan M Nevill¹, Matthew Wyon², Jonathan Myers^{3

4}, Matthew P Harber⁵, Ross Arena⁶, Tony D Myers⁷, Leonard A Kaminsky⁸

Affiliations

¹ Faculty of Education, Health and Wellbeing, University of Wolverhampton, Walsall Campus, Gorway Road, Walsall, WS1 3BD, UK. a.m.nevill@wlv.ac.uk.
² Faculty of Education, Health and Wellbeing, University of Wolverhampton, Walsall Campus, Gorway Road, Walsall, WS1 3BD, UK.
³ Division of Cardiology, VA Palo Alto Health Care System, Palo Alto, CA, USA.
⁴ Stanford University, Stanford, CA, USA.
⁵ Health Sciences, Taylor University, Upland, IN, USA.
⁶ Department of Physical Therapy, College of Applied Sciences, University of Illinois at Chicago, Chicago, IL, USA.
⁷ Sport and Health, Newman University, Birmingham, UK.
⁸ Fisher Institute of Health and Well-Being and Clinical Exercise Physiology Laboratory, Ball State University, Muncie, IN, USA.

PMID: 40223039
DOI: 10.1007/s40279-025-02208-3

Abstract

Background: Using directly measured cardiorespiratory fitness (i.e. VO_2max) in epidemiological/population studies is rare due to practicality issues. As such, predicting VO_2max is an attractive alternative. Most equations that predict VO_2max adopt additive rather than multiplicative models despite evidence that the latter provides superior fits and more biologically interpretable models. Furthermore, incorporating some but not all confounding variables may lead to inflated mass exponents (∝ M^0.75) as in the allometric cascade.

Objective: Hence, the purpose of the current study was to develop multiplicative, allometric models to predict VO_2max incorporating most well-known, but some less well-known confounding variables (FVC, forced vital capacity; FEV₁, forced expiratory volume in 1 s) that might provide a more dimensionally valid model (∝ M^2/3) originally proposed by Astrand and Rodahl.

Methods: We adopted the following three-dimensional multiplicative allometric model for VO_2max (l⋅min^-1) = M^k1·HT^k2·WC^k3·exp(a + b·age + c·age² + d·%fat)·ε, (M, body mass; HT, height; WC, waist circumference; %fat, percentage body fat). Model comparisons (goodness-of-fit) between the allometric and equivalent additive models was assessed using the Akaike information criterion plus residual diagnostics. Note that the intercept term 'a' was allowed to vary for categorical fixed factors such as sex and physical inactivity.

Results: Analyses revealed that significant predictors of VO_2max were physical inactivity, M, WC, age², %fat, plus FVC, FEV₁. The body-mass exponent was k₁ = 0.695 (M^0.695), approximately∝M^2/3. However, the calculated effect-sizes identified age² and physical inactivity, not mass, as the strongest predictors of VO_2max. The quality-of-fit of the allometric models were superior to equivalent additive models.

Conclusions: Results provide compelling evidence that multiplicative allometric models incorporating FVC and FEV₁ are dimensionally and theoretically superior at predicting VO_2max(l⋅min^-1) compared with additive models. If FVC and FEV₁ are unavailable, a satisfactory model was obtained simply by using HT as a surrogate.

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Conflict of interest statement

Declarations. Funding: No financial support was received when conducting this study, or for the preparation or publication of this manuscript. Conflict of Interest: There were no conflicts of interest for specific or individual authors. Ethics Approval: Participating CPX laboratories were responsible for obtaining local institutional review board approval for inclusion in FRIEND, providing documentation that they were authorised to submit deidentified, coded data to the coordinating centre at Ball State University, which then forwarded these data to the core CPX laboratory housed at the University of Illinois, Chicago. Institutional review board approval for the core CPX laboratory was also obtained at the University of Illinois, Chicago. Data Sharing Statement: Access to the FRIENDS database is possible at www.cardiology.org . Author Contributions: Alan M. Nevill—Lead author; substantial contribution of the intellectual content of the manuscript including statistical analysis and interpretation of the data. Matthew Wyon—Substantial contribution drafting and revising intellectual content of the manuscript including interpretation of the data, formatting the manuscript, final approval of submitted version. Jonathan Myers—Substantial contribution revising intellectual content of the manuscript including interpretation of the data, final approval of submitted version. Matthew P. Harber—Substantial contribution revising intellectual content of the manuscript including interpretation of the data, final approval of submitted version. Ross Arena—Substantial contribution revising intellectual content of the manuscript including interpretation of the data, final approval of submitted version. Tony D. Myers—Substantial contribution revising intellectual content of the manuscript including analysis and preparation of figures and tables, final approval of submitted version. Leonard A. Kaminsky—Substantial contribution revising intellectual content of the manuscript including interpretation of the data, access to dataset, final approval of submitted version.

References

1. Ross R, Blair SN, Arena R, Church TS, Després J-P, Franklin BA, et al. Importance of assessing cardiorespiratory fitness in clinical practice: a case for fitness as a clinical vital sign: a scientific statement from the American Heart Association. Circulation. 2016;134(24):e653–99. - DOI - PubMed
1. Harber MP, Myers J, Bonikowske AR, Muntaner-Mas A, Molina-Garcia P, Arena R, et al. Assessing cardiorespiratory fitness in clinical and community settings: lessons and advancements in the 100th year anniversary of VO_2max. Prog Cardiovasc Dis. 2024;83:36–42. - DOI - PubMed
1. Myers J, Kaminsky LA, Lima R, Christle JW, Ashley E, Arena R. A reference equation for normal standards for VO_2max: analysis from the Fitness Registry and the Importance of Exercise National Database (FRIEND Registry). Prog Cardiovasc Dis. 2017;60:21–9. - DOI - PubMed
1. Nevill AM, Myers J, Kaminsky LA, Arena R. Improving reference equations for cardiorespiratory fitness using multiplicative allometric rather than additive linear models: data from the Fitness Registry and the Importance of Exercise National Database Registry. Prog Cardiovasc Dis. 2019;62(6):515–21. - DOI - PubMed
1. Leger LA, Mercier D, Gadoury C, Lambert J. The multistage 20 metre shuttle run test for aerobic fitness. J Sports Sci. 1988;6(2):93–101. - DOI - PubMed

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Predicting VO_2max Using Lung Function and Three-Dimensional (3D) Allometry Provides New Insights into the Allometric Cascade (M^0.75)

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Predicting VO_2max Using Lung Function and Three-Dimensional (3D) Allometry Provides New Insights into the Allometric Cascade (M^0.75)

Authors

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Abstract

Conflict of interest statement

References

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