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

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.

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.

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.

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.

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.