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LETTER TO THE EDITOR
The aim of this study was to critically examine the influence of body size on maximal oxygen uptake (
O2 max) in boys and men using body mass (BM), estimated fat-free mass (FFM), and estimated lower leg muscle volume (Vol) as the separate scaling variables. O2 max and an in vivo measurement of Vol were assessed in 15 boys and 14 men. The FFM was estimated after percentage body fat had been predicted from population-specific skinfold measurements. By using nonlinear allometric modeling, common body size exponents for BM, FFM, and Vol were calculated. The point estimates for the size exponent (95% confidence interval) from the separate allometric models were: BM 0.79 (0.53–1.06), FFM 1.00 (0.78–1.22), and Vol 0.64 (0.40–0.88). For the boys, substantial residual size correlations were observed for O2 max/BM0.79 and O2 max/FFM1.00, indicating that these variables did not correctly partition out the influence of body size. In contrast, scaling by Vol0.64 led to no residual size correlation in boys or men. Scaling by BM is confounded by heterogeneity of body composition and potentially substantial differences in the mass exponent between boys and men. The FFM is precluded as an index of involved musculature because Vol did not represent a constant proportion of FFM [Vol
FFM1.45 (95% confidence interval, 1.13–1.77)] in the boys (unlike the men). We conclude that Vol, as an indicator of the involved muscle mass, is the most valid allometric denominator for the scaling of O2 max in a sample of boys and men heterogeneous for body size and composition.
Scaling maximum oxygen uptake using lower leg muscle volume provides further insight into the pitfalls of whole body-mass power laws
To the Editor: We should like to congratulate Tolfrey et al. (4) for their recent article promoting the use of lower leg muscle volume (Vol), rather than either body mass (BM) or fat-free mass (FFM), as a more appropriate body size dimension to scale maximal oxygen uptake (O2 max) in boys and men. These results confirm the findings of a number of previous studies (1, 3, 5) that also report the utility of leg muscle dimensions as more appropriate body-size dimension to scale O2 max.
However, in their discussion, we feel the authors may have overlooked an important insight that can be gained from their results. The power function relationship between O2 max and BM has been the source of much controversy among biologists and physiologists for many years. Various studies have reported mass exponents greater than the anticipated "surface-area" exponent 0.67, often closer to 0.75 originally identified by Kleiber (2). Since then, numerous authors have attempted to explain these inflated exponents using a variety of different theories but, as yet, without consensus. Tolfrey et al. (4) also report "inflated" mass exponents (0.96 for boys, 0.73 for men, and 0.79 combined) closer to 0.75 and certainly greater than 0.67. However, when the analysis was repeated, incorporating Vol rather than BM, the analysis identified the exponents (0.62 for boys; 0.65 for men and 0.64 combined) much closer to the theoretical surface-area law parameter (0.67). These results provide a valuable insight as to why body size dimensions that more accurately reflect musculature are better able to reflect the anticipated surface-area law and hence are likely to be more appropriate variables to scale O2 max. This interpretation supports the findings reported earlier by Nevill et al. (3), who also identified an inflated mass exponent of 0.75 when scaling the O2 max of 119 professional soccer players. The study confirmed that the larger individuals have disproportionately greater leg muscle girths. When the analysis was repeated incorporating the calf and thigh muscle girths rather than BM as predictor variables, not only did the analysis explain significantly more of the variance in O2 max, but the girth exponents confirmed a surface-area law. Taken in combination, these studies by Tolfrey at al. and Nevill et al. highlight the pitfalls of fitting body-mass power laws and suggest using leg muscle dimensions as a more appropriate way to scale or normalize metabolic variables such as O2 max for individuals of different body sizes.
We would like to offer a note of caution, however, with Tolfrey et al.'s (4) evidence. The authors choose Vol rather than BM or FFM to scale O2 max, on the basis of "substantial residual size correlations" observed for the common (boys and men) power functions O2 max/BM0.79 and O2 max/FFM1.00, indicating that BM and FFM did not correctly partition out the influence of body size in a sample of 15 boys. What the authors have demonstrated is that, certainly in the case of BM, the common power functions provide an inadequate fit for just the boys' data alone (although the authors do test for equality of mass exponents and report no significant differences, this test will be underpowered given the sample sizes available). We also note an inconstancy in using the parameters a and c in the equation for O2 max and the subsequent description (taking antilogs of the coefficient a and the construction of the group coefficient a+c) reported in the discussion in the section entitled Allometric modeling procedures. If the authors had explored the boys' power function O2 max/BM0.96, the "substantial residual size correlation" is likely to disappear. The rationale given for choosing Vol rather than BM or FFM to scale O2 max may be a statistical artifact caused by fitting the wrong model to a subgroup (the boys) of the combined sample and have little to do with the underlying physiology as suggested Tolfrey et al.
REFERENCES
Roger Holder2
2Department of Primary Care and General Practice
University of Birmingham
Birmingham, United Kingdom
Goran Markovic3
3Faculty of Kinesiology
University of Zagreb
Zagreb, Croatia
Nevill et al. question the evidence supporting our choice of lower leg muscle volume as the most appropriate scaling denominator in this study. We are happy to lay this critique to rest. First, as we articulated clearly, we did not choose muscle volume solely on the basis of the residual size correlations for the mass and fat-free mass power function ratios in boys. However, a conditio sine qua non of scaling using a common size exponent is that there is no substantial correlation between Y/Xb and X for either boys or men. Of course, if we scale using the separate group-specific mass exponent of 0.96 for boys, this residual size correlation disappears, although Nevill et al. have clearly missed the main point here. It is, in part, heterogeneity of body composition that results in the common mass exponent providing an inadequate fit for boys. Nevill et al. sustain that, although we tested for equality of regression slopes, our study is not powered to detect differences in the separate mass exponents between boys and men. Indeed, this issue was discussed in our paper since we stated that "... this test is obviously influenced by sample size, and the difference may be real and important. Hence, the common group exponent for body mass appears less robust than for the other two body size variables." Again, this underscores one of the central issues: that body mass may be an inadequate proxy for the metabolically active muscle mass. Furthermore, as we demonstrated clearly, fat-free mass is also inadequate in this respect because the active muscle mass does not represent a constant proportion of fat-free mass in boys.
Nevill et al. suggest that our evidence for rejecting body mass and fat-free mass as appropriate scaling denominators is based on "fitting the wrong model to a subgroup" of boys. What they have once again failed to appreciate is that the underlying anatomy and physiology helps to explain what they describe erroneously as "statistical artifact." The flaw in their specious critique is exposed if the same logic is applied to the scaling by fat-free mass. Here, both the common and group-specific size exponents were essentially equivalent, yet there was still a residual size correlation in boys, for reasons clearly explained in the paper. Body mass and fat-free mass are inadequate scaling denominators for developing boys because they are not a good proxy for the skeletal muscle sink for the oxygen passing through the lungs during maximal exercise. Lower leg muscle volume provides a common group exponent that results in no residual size correlation in either boys or men and may serve as a better indicator of the involved muscle mass.
REFERENCES
Alan M. Batterham
Centre for Food, Physical Activity, and Obesity Research
School of Health and Social Care
University of Teesside
Middlesbrough, United Kingdom
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