Can greater muscularity in larger individuals resolve the 3/4 power-law controversy when modelling maximum oxygen uptake?

Abstract

Summary. Background: The power function relationship, MR ¼ aÁm b , between metabolic rate (MR) and body mass m has been the source of much controversy amongst biologists for many years. Various studies have reported mass exponents (b) greater than the anticipated 'surface-area' exponent 0.67, often closer to 0.75 originally identified by Kleiber. Aim: The study aimed to provide a biological explanation for these 'inflated' exponents when modelling maximum oxygen uptake ( _ V VO 2 max), based on the observations from this and previous studies that larger individuals develop disproportionately more muscle mass in the arms and legs. Research design and subjects: A cross-sectional study of 119 professional soccer players from Croatia aged 18-34 was carried out. Results: Here we confirm that the power function relationship between _ V VO 2 max and body mass of the professional soccer players results in an 'inflated' mass exponent of 0.75 (95% confidence interval from 0.56 to 0.93), but also the larger soccer players have disproportionately greater leg muscle girths. When the analysis was repeated incorporating the calf and thigh muscle girths rather than body mass as predictor variables, the analysis not only explained significantly more of the variance in _ V VO 2 max, but the sum of the exponents confirmed a surface-area law. Conclusions: These findings confirm the pitfalls of fitting body-mass power laws and suggest using muscle-girth methodology as a more appropriate way to scale or normalize metabolic variables such as _ V VO 2 max for individuals of different body sizes. IntroductionAn enduring mystery that has challenged biologists and physiologists alike for over a century is how metabolic rate (MR) is related to body size (see Voit 1901, cited by Kleiber 1987. Larger mammals expend more energy than smaller mammals due to the greater energy cost of metabolism and locomotion. However, if energy expenditure is expressed as a simple ratio standard, per unit body mass, smaller mammals consume more energy per unit body mass than larger mammals. A theoretical explanation for these observations is based on the assumption that energy expenditure obeys the surface-area law (Schmidt-Nielsen 1984, Weibel 2002.Assuming that mammals are geometrically similar to each other, individual body components (e.g. homologous muscles, hearts, lungs) should have masses proportional to body mass (m), cross-sectional or surface areas proportional to m 0.67 and linear dimensions (L), such as heights or limb girths, proportional to L ¼ m 0.33 . Under such circumstances, if energy expenditure obeys the surface-area law, then MR should be proportional to m 0.67 (or L 2 ).

Modeling Physiological and Anthropometric Variables Known to Vary with Body Size and Other Confounding Variables

“…The ANCOVA analyses reported by Nevill et al (2004a) not only confirmed that the power function relationship between VO 2 max and body mass alone resulted in an \inflated" mass exponent of 0.75 (although we acknowledge that the 95% confidence interval, from 0.56-0.93, does encompass the surface-area law exponent of 0.67), but also confirmed that the larger soccer players had disproportionately greater leg muscle girths. When the analysis was repeated incorporating calf and thigh muscle girths together with stature (rather than body mass) as predictor variables, the analysis not only explained significantly more of the variance in VO 2 max compared with body mass alone (using the adjusted R 2 to account for the different number of fitted parameters), but the sum of the exponents confirmed a surface-area law.…”

“…The new methodology of adopting and combining muscle girths and stature measurements as covariates (Nevill et al, 2004a) has some similarities to the approach proposed by Darveau et al (2002). Darveau et al (2002) advocated combining a weighted sum of mass exponents, each estimated from a diverse range of control sites or processes known to contribute to metabolic pathways.…”

“…Under these circumstances, more flexible allometric models may be required, such as the gamma function model mentioned earlier, that can accommodate an observed initial rise and subsequent decline in variables with excessive body mass (e.g., FEV 1 and weightlifting performance). If, on the other hand, the dependent variable fails to demonstrate a subsequent fall with excessive body mass, an alternative solution, suggested by Nevill et al (2004a) when scaling the _ VO 2 max of Croatian professional soccer players, is to adopt muscle-girth methodology as a more appropriate way to scale or normalize metabolic variables such as _ VO 2 max for individuals of different body sizes.…”

Novos horizontes para a normalização da aptidão cardiorrespiratória em crianças: Quebrando o paradigma

“…Therefore, the active muscle mass during exercise may be an even more appropriate variable to normalize VO 2max 13 . Similarly, other studies have used MV to normalize VO 2max , since MV better represents the active muscle mass during exercise 8,11,12 . Welsman et al 11 found that VO 2max and power were higher among boys compared to girls using body mass, whereas no significant difference was found between sexes when data were normalized by MV using either ratio or allometric scaling.…”

“…Some studies have used muscle volume (MV), free fat mass (FFM), total muscle mass or lower limb muscle mass as normalizing variables in the attempt to adjust for differences in body dimensions 6,8,11,12 . These variables were chosen to reflect the reality that under maximal intensity exercise, 90% of blood flow and VO 2 are allocated to ATP synthesis during muscle contraction.…”