Modeling the influence of body size onV˙o_{2 peak}: effects of model choice and body composition

Abstract

This study examined the bivariate relationship between peak oxygen uptake (V(O2) peak); l/min) and body size in adult men (n = 1,314, age 17-66 yr), using both "simple" and "full" iterative nonlinear allometric models. The simple model was described by V(O2) peak = M(b) (or FFM(b)) exp(c SR-PA) exp(a + d age) epsilon (where M is body mass in kg; FFM is fat-free mass in kg; SR-PA is self-reported physical activity; epsilon is a multiplicative error term; and exp indicates natural antilogarithms). The full model was described by V(O2) peak = M(b) (or FFM(b)) exp(c SR-PA) exp(a + d age) + e (epsilon), where e is a permitted Y-intercept term. The M exponent obtained from simple allometry was 0.65 [95% confidence interval (CI), 0.59-0.71], suggestive of a curvilinear relationship constrained to pass through the origin. This "zero Y-intercept" assumption was examined via the full allometric model, which revealed an M exponent of 1.00 (95% CI, 0.7-1.31), together with a positive Y-intercept term (e) of 1.13 (95% CI, 0.54-1.73). The FFM exponents were not significantly different from unity in either the simple or full allometric models. It appears that the curvilinearity of the simple allometric model (using total M) is fictitious and is due to the inappropriate forcing of the regression line through the origin. Utilizing FFM as the body-size variable revealed a linear relationship between body size and V(O2) peak, irrespective of model choice. We conclude that the population mass exponent for V(O2) peak is close to unity.

Modelling the influence of fat-free mass and physical activity on the decline in maximal oxygen uptake with age in older humans

“…In the past, several investigations have used power function analysis to derive a population body mass exponent (Rogers et al 1995;Welsman et al 1996;Heil, 1997). In agreement with several others (Davies et al 1995;Vanderburgh & Katch, 1996;Batterham et al 1999) the exponent for FFM in this study was not significantly different from one. However, the use of ratio scaling is only statistically justified when (1) the regression line between ýOµ,max and BM (or FFM) passes through the origin and (2) the coefficient of variation for BM (or FFM) divided by the coefficient of variation for ýOµ,max equals the correlation coefficient (r) between the two variables (Tanner, 1949;Toth et al 1993;Rogers et al 1995).…”

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

“…A number of authors (Albrecht et al, 1993;Batterham et al, 1999b) proposed an alternative \full allometric" model, Y ¼ a + bX k (compared to the simple allometric model, Y¼ bX k ), to adjust variables for differences in body size in morphometrics. For example, Batterham et al (1999b) compared the simple allometric model (Eq.…”

“…For example, Batterham et al (1999b) compared the simple allometric model (Eq. 1) with the equivalent \full" allometric model by introducing an additional intercept term \e," as follows…”

Body Mass Bias in Exercise Physiology

“…Some studies have indicated deviation from theoretical for the body mass exponent for expressing VO 2max . Batterham et al (1999) found that, in a sample of 1314 adult men, although the body mass exponent was 0.65, the fat-free mass exponent was not different from 1.0. Since body fat is essentially metabolically inert, and fat-free mass is the body compartment largely responsible for generating oxygen consumption, then body composition was a confounder in leading to the spurious conclusion that the 0.65 body mass exponent matched the theoretically expected value of 2/3.…”