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Longitudinal analysis of scaling V˙O2 for differences in body size during puberty: the Muscatine Study


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Medicine& Science in Sports & Exercise: September 1998 - Volume 30 - Issue 9 - p 1436-1444
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Increases in absolute V˙O2 (mL·min−1) are heavily influenced by change in body size. As a result, controlling for the effects of changing body size in growing children is critical to understanding the relative contributions of other factors including gender, maturation, habitual physical activity, and functional cardiorespiratory improvements to changes in V˙O2. The assumption is that once V˙O2 has been appropriately adjusted for body size any remaining difference in V˙O2 should help to explain differences in other independent variables (12). To this end, the conventional (ratio) approach to controlling or "normalizing" V˙O2 for body size has been to describe V˙O2 per kilogram of body mass (mL·kg −1·min−1). Always controversial (2,8), criticisms of this method have recently increased (1,4,9,14,21,22). These critiques most often recommend the use of allometric scaling exponents to partition out more appropriately and thoroughly body size differences in V˙O2. Frequently, body mass to the 0.67 (2/3) power, predicted from the theory of geometric similarity, is recommended. This theory proposes that V˙O2 in individuals of different sizes but similar dimensions is proportional to the cross-sectional area of muscle which is, correspondingly, proportional to body mass to the 0.67 power (2,21). In practice, the application of scaling models to pediatric data sets has generally but not always resulted in exponents less than unity supporting criticisms of the conventional ratio method by demonstrating that increases in V˙O2 are less than proportional to one-to-one changes in body size (3,13,14,16). However, the theoretical exponent of 0.67 has not been universally reported (3,13,16,22). In 1994, Nevill (11) proposed that observed exponents different from 0.67 are artifacts of allometric models that do not control for the heterogeneity in the proportion of muscle mass to body size among study subjects. The hypothesis is that the dependent variable (V˙O2) in the model is greatly influenced(confounded) by the amount of available muscle mass (11). Interested readers are referred to Rowland (15) and Nevill et al. (12) for discussions of the theoretical and statistical procedures of allometric scaling methods applied to V˙O2.

In this paper, using allometric scaling methods, we examine the relationship between peak and submaximal V˙O2 to body mass and fat-free body mass (FFM) in children and adolescents. To address the disproportionate increase in muscle mass with increasing body size expected in sexually maturing boys and the disproportionate increase in fat mass with increasing body size expected in sexually maturing girls, and the heterogeneity in the proportion of muscle mass to body size because of normal differences in body composition among children, we consider additional factors (height, body fatness, and sexual maturation) within scaling models. We also examine how different scaling models influence the interpretation of the relationship between body size and V˙O2 and the precision of the body size parameter estimate. Our objective is to identify the most parsimonious and appropriate model for partitioning out the influence of body size on V˙O2 among maturing children and adolescents. Our initial hypothesis was that the most parsimonious model would support the theory of geometric similarity.


Subjects. The Muscatine Study is a longitudinal, population-based investigation of cardiovascular disease risk factors in children, young adults, and selected family groups from Muscatine, IA. From a large (N = 925) cross-sectional echocardiographic screening of Muscatine school children, 150 subjects thought to be prepubertal based on age were identified. Initial contact was made through information mailed to the parents of each child and a phone call to the parents by a Muscatine study staff member. Nineteen parents reported that their child had begun pubertal development, and one parent declined participation for a child. Informed consent was secured from 130 subjects and their parents. Based on a physician's physical examination, four of the 130 subjects were judged to have begun significant secondary sex characteristic development (greater than stage 2 using the criteria of Tanner) (20). Consequently, 126 subjects, all stage 1 or 2 using the criteria of Tanner for secondary sex characteristic development, were enrolled in this present study. Sixty-one boys, ages 8 to 12 yr, and 62 girls, ages 7 to 11 yr, attempted all baseline research procedures. At year five, 53 boys and 57 girls attempted all research procedures (87% of the initial cohort). Enrolled children were within the expected ranges for weight, height, and resting BP, suggesting that the sample was representative of normal children in this age range. All children were Caucasian. Protocol requirements established by the University of Iowa's Human Subjects Review Committee, including written permission from subjects and their parents, were satisfied before data collection.

Procedures. Body composition, peak V˙O2, submaximal V˙O2, and sexual maturation were measured yearly for 5 yr. Sexual maturation was measured each spring. Approximately 3 months after the spring examination, body composition and V˙O2 were measured. The same protocols and equipment were used throughout this 5-yr study.

Sexual maturation. Pediatricians conducted a general physical examination of each subject including the rating of breast and pubic hair development in girls and genital and pubic hair development in boys according to the criteria of Tanner (20).

Body composition. Height was measured without shoes to the nearest 0.1 cm using the IOWA anthropometric plane and square (University of Iowa Department of Medical Engineering, Iowa City, IA). Weight was measured to the nearest 0.1 kg using a Seca 770 digital metric scale(Columbia, MD) calibrated daily with standardized weights. Skinfolds were taken on the right side of the body at six sites (tricep, bicep, subscapular, abdominal, suprailiac, and calf) using a Lange caliper (Cambridge Scientific Industries, Cambridge, MA). Two measurements were taken alternately at each site and averaged (6). If the measurements varied by more than 1 mm, additional measurements were taken until the difference was less than 1 mm. All anthropometric measurements were obtained by field staff members who attend yearly formal training sessions.

The sum of the six skinfolds (Sum SF) was used to operationally define body fatness. Fat-free body mass (FFM) was estimated from skinfolds using equations developed by Slaughter et al. (17,18). These equations account for the changing relationship of skinfold measures to the maturation-dependent density variations in FFM. Our laboratory SEEs for FFM range from 1.5 kg to 1.8 kg for the Slaughter equations (7). The validity correlations for the Slaughter equations range from r = 0.98 to 0.99 for FFM (7).

Peak and submaximal VO2. Open circuit spirometry using the Medgraphics System CPX metabolic cart (Medical Graphics Corp, St. Paul, MN) was used to measure V˙O2. Before testing, the pneumotachograph was calibrated to within ± 4 mL·s−1. Known reference gases were used to calibrate the system analyzers to within ± 0.03%. Heart rate (HR) was measured from a Burdick electrocardiograph single channel recorder (Milton, WI). A Siemens Elema electromechanically braked cycle ergometer (Siemens Systems, Coralville, IA) provided incremental workloads. The protocol for the graded exercise test consisted of a 1-min warm-up, three 3-min submaximal stages followed by a series of 30-s stages ("ramps") until exhaustion.

The highest V˙O2 was described as peak V˙O2 providing the subject could no longer maintain a pedal cadence of at least 40 rev·min−1 and had a respiratory exchange ratio (RER) of > 1.0 or was within 95% of his/her predicted maximal HR. Peak V˙O2 was calculated by averaging all breath-by-breath data during the last 30-s ramp. Peak HR, peak mechanical power, and peak RER were also recorded. Submaximal V˙O2 was calculated by averaging all breath-by-breath data during the last two 30-s periods of stage two. All subjects were in steady-state aerobic metabolism at this time (<50 mL O2 difference between the two 30-s periods). Using this protocol, we previously reported laboratory reliability correlations ranging from r = 0.91 to 0.99 for these submaximal and peak exercise variables (5). Our reliability correlation for peak V˙O2 was r= 0.96 (5).

Statistical analysis. Means ± SD and proportions were used to characterize the data across the five study years for boys and girls. To ensure adequate cell size, subjects in late and postpuberty were grouped together. Pearson product-moment correlation coefficients were estimated to characterize the linear association between body mass, V˙O2 and adjusted V˙O2. Allometric scaling was used to determine appropriate scaling factors that would allow "normalization" of V˙O2 for body size. Allometric equations take the general form y = axb, where the values for a and b are obtained from a least-squares linear regression analysis of logarithmic transformations of the dependent variable (in this study, V˙O2) and the independent variable(s), yielding, for example, the simple model ln(V˙O2) = ln a + b ln(body mass). We also considered multivariate allometric models that included, in addition, ln(height) or ln(body fatness) or ln(sexual maturation). These multivariate models were extensions of the univariate body size model to include the additional independent variables. The generalized estimating equation (GEE) method (10,23) was used to examine all associations between ln(V˙O2) and ln(body mass, FFM, height, body fatness, and sexual maturation). This method adjusts for the repeated-measures nature of the data (up to five annual measurements for each subject) in the regression analysis and allowed us to obtain unbiased estimates of the SE for the parameter estimates. Models were first examined sorted by gender and sexual maturation. Next, models were examined sorted by gender, but allowing ln(sexual maturation) to enter as an independent variable. Both independence (which assumes that repeated observation for a subject over time are independent) and exchangeable (which assumes that the correlation is constant between any two observation times) working correlation models were considered. There was little difference in the parameter estimates or the SEs between the two models, and the results from assuming an independent correlation model are presented. Finally, using methods suggested by Nevill et al. (12), body size parameter estimates for boys and girls were examined together allowing for separate constant multipliers (intercept) but a common power function parameter(slope). The SAS/IML macro GEE1 (19) was used for model fitting. A P-value <0.05 was considered to be statistically significant in all of the reported analyses.


Subject characteristics by study year are presented in Table 1. Mean body mass and FFM increased each year for boys and girls. Table 2 shows the yearly distribution (percentage) of boys in each stage of genital development and the distribution of girls in each stage of breast development. At the beginning of the study, all study subjects were either prepubertal or in early puberty. By year five, all study subjects had advanced at least one stage in genital or breast development. Most of the study subjects were in late or postpuberty.

Description of subjects by gender, years 1 through 5 (mean + SD).
Description of sexual maturation by gender, years 1 through 5 (%).

Table 3 presents peak and submaximal exercise responses by study year. When described in absolute terms (mL·min−1), mean peak V˙O2 improved throughout the observational period in boys. When described in relative terms using the ratio method to adjust for body size (mL·kg−1·min−1), mean peak V˙O2 decreased slightly between years two and three and then remained unchanged between years three and five. In girls, mean peak V˙O2(mL·min−1) improved until year four and remained unchanged in year five, while mean peak V˙O2 described as mL·kg−1·min−1 remained unchanged from years one to four and then decreased in year five. During the entire study, for both boys and girls, there were strong positive associations between body mass and absolute peak V˙O2 (mL·min−1) with Pearson product-moment correlations ranging from r = 0.62 to 0.78, P< 0.0005. Concurrently, strong inverse associations existed between body mass and peak V˙O2 adjusted for body mass using the ratio method (mL·kg−1·min−1) with correlations ranging from −0.72 to −0.48, P < 0.0005. Appropriate adjustment of peak V˙O2 for body mass should result in correlations between body mass and adjusted peak V˙O2 which are not significantly different from zero. These findings indicate that the ratio method over adjusted the data and underestimated the aerobic fitness levels of heavier boys and girls.

Description of peak and submaximal exercise values by gender, years 1 through 5 (mean + SD).

Gender and sexual maturation-specific model fitting.Tables 4 through 7 present fitted models with allometric scaling of V˙O2 as a function of body size sorted by sexual maturation and gender. Within each model, there were few meaningful differences between the peak- and submaximally-scaled exponent parameters, intercepts, or standard errors. Within most models, the confidence intervals for peak- and submaximally-scaled body size parameters overlapped, indicating no statistical difference. Theoretically, submaximal V˙O2 is more stable and more reproducible than peak V˙O2 because it is less likely to be influenced by motivation, fitness level, and training(14).

Body size scaling models for peak V˙O2 and submaximal V˙O2 for prepubescent boys (N = 110) and girls (N = 62).
Body size scaling models for peak V˙O2 and submaximal V˙O2 for early pubescent boys (N = 59) and girls (N = 85).
Body mass scaling models for peak V˙O2 and submaximal V˙O2 for mid-pubescent boys (N= 30) and girls (N = 62).
Body size scaling models for peak V˙O2 and submaximal V˙O2 for late and post-pubescent boys (N = 57) and girls (N = 60).

In the univariate models, body size parameters appeared stable across puberty for boys with values ranging from 0.41 to 0.56 for body mass(Model 1) and 0.76 to 0.94 for FFM (Model 4). However, for girls body size parameters appeared markedly greater during early puberty. Figures 1 and 2 illustrate these univariate models using exponents derived from allometric scaling submaximal data and using exponents derived from allometric scaling peak data. When height and body size (body mass or FFM) were modeled together (Models 2 and 5), the height parameter was generally not statistically significant. When sum of SF and body size were modeled together (Models 3 and 6), the sum of SF parameter was generally statistically significant for models that included body mass and not significant in models that included FFM.

Figure 1
Figure 1:
Scaling parameters for body size for boys across sexual maturation levels (N= 259).
Figure 2
Figure 2:
Scaling parameters for body size for girls across sexual maturation levels (N = 292).

To test the "goodness of fit" of our models, we examined Pearson correlations between adjusted peak V˙O2 and actual body mass (in models that used body mass as the body size parameter) and between adjusted peak V˙O2 and actual FFM (in models that used FFM as the body size parameter). We adjusted our peak V˙O2 data two ways, using exponents derived from scaling submaximal and using exponents derived from scaling peak data. Across almost all sexual maturation categories, correlations were not statistically different from zero (i.e., data suggest that these gender- and sexual maturation-specific, univariate models successfully partitioned out the influence of body size on peak V˙O2). The exceptions were pre- and mid-pubescent girls where peak V˙O2 adjusted for FFM using the parameters derived from scaling submaximal data was significantly associated with actual FFM (P< 0.05, r 64 0.25).

Multivariate model fitting using body size and sexual maturation. Results of allometric scaling using body size and sexual maturation in the same model are presented in Table 8. Log transformed sexual maturation was not significant for boys or girls when FFM was used as the body size parameter (regardless of whether exponents were derived from scaling submaximal or peak data). These results indicate that after adjusting for the effects of body size using FFM, sexual maturation, per se, does not influence the association between FFM and V˙O2. However, when body mass was used as the body size parameter, sexual maturation was significant for boys in models derived from scaling submaximal and peak data and in girls in the model derived from scaling peak data. These results indicate that the relationship between body mass and V˙O2 changes with changing sexual maturation in boys (and possibly in girls, at least when parameters are derived from scaling peak data). We subsequently estimated a common exponent across sexual maturation levels in models in which sexual maturation was not significant (Table 9). For boys, the FFM parameters were 0.82 (95% CI = 0.74 to 0.90) derived from scaling submaximal data and 0.91 (95% CI = 0.83 to 0.99) derived from scaling peak data. For girls, the FFM parameters were 0.71 (95% CI = 0.61 to 0.81) from submaximal data and 0.87 (95% CI = 0.77 to 0.97) from peak data. The body mass parameter was 0.51 (CI = 0.43 to 0.59) from submaximal data for girls.

Body size and sexual maturation scaling models for peak V˙O2 and submaximal V˙O2 for boys (N= 259) and girls (N = 272).
Body size scaling models V˙O2 for boys (N = 259) and girls(N = 272).

Correlations between adjusted peak V˙O2 (adjusted using the FFM parameter of 0.82 and the FFM parameter of 0.91) and actual FFM were not significantly different from zero across all sexual maturation categories for girls. Likewise, for girls correlations between adjusted peak V˙O2 (adjusted using the FFM parameter of 0.87) and actual FFM were not significantly different from zero. Nonsignificant correlations also existed for girls between adjusted peak V˙O2 (adjusted using the body mass parameter of 0.51) and actual body mass. However correlations between adjusted peak V˙O2(adjusted using the FFM parameter of 0.71 derived from scaling submaximal data) were significantly associated with FFM in girls in pre-, early-, and mid-puberty (r ≃ 0.25). A comparison of peak V˙O2 adjusted for body size using these scaling parameters and the traditional (ratio) method is presented in Figures 3 and 4.

Figure 3
Figure 3:
Peak V˙O2 adjusted for body size for boys across sexual maturation levels (N = 259).
Figure 4
Figure 4:
Peak V˙O2 adjusted for body size for girls across sexual maturation levels (N = 292).

Finally, using methods suggested by Nevill et al. (12), we tried to identify a common exponent for FFM for both boys and girls. Using this approach, our parameter estimate for FFM was 0.78 (CI = 0.72 to 0.84) using parameters derived from scaling submaximal data and 0.89 (CI = 0.83 to 0.95) using parameters derived from scaling peak data. However, in both models, there were significant gender and FFM interaction effects that suggested that there was no common exponent for boys and girls.


The use of a longitudinal design and the generalized estimating equation method allowed us to examine various scaling models for "normalizing" V˙O2 in the same growing children during a period of rapid maturation and changes in body composition. This approach avoided limitations inherent in cross-sectional designs and provided adequate statistical power for the regression analysis, a component of allometric scaling. In our study several univariate and multivariate models successfully adjusted V˙O2 when study subjects were sorted by sexual maturation and gender, an approach that reduced the heterogeneity within groups (11). When sexual maturation levels were examined together, univariate modeling for boys indicated an exponent of FFM (0.82) or FFM(0.91) could be used to successfully partition out the effects of body size on V˙O2. With this approach for girls, the FFM exponent of 0.87 partitioned out the effects of body size across all sexual maturation categories. These exponents are statistically different from the theoretically proposed exponent of 0.67 and from each other. This latter observation indicates that the relationship between changing V˙O2 and changing body size during sexual maturation differs between boys and girls.

When height was considered as a covariate in our gender- and sexual maturation-specific models, the body size exponent deviated widely across sexual maturation levels and the SEE increased for both boys and girls. These results indicate that height, as an additional parameter, created instability in the estimate of the relationship between body mass and V˙O2. This was surprising since Welsman et al. (22) and Nevill (11) both suggest that height can be used when scaling body size to address possible disproportionate increases in muscle mass with increasing body size. It may be that our exercise mode, cycle ergometry, made height an unnecessary and perhaps an unreliable covariate for modeling, particularly since our test bicycle was adjusted for each child's arm length, leg length, and sitting height to minimize variation in pedal efficiently among children(5). In addition, Astrand and Rodahl (2) have proposed that body proportions between children and adults are essentially the same by 10 yr of age. Therefore, it may be that after age 10 an increasing proportion of muscle mass cannot be adequately addressed by the inclusion of height in allometric scaling models. (The mean age of our study subjects at the beginning of our study was 10.3 yr). This conclusion is at least partially supported by our results which demonstrate that height was not statistically significant in almost all of our models.

When body fatness was considered as a covariate in the gender- and sexual maturation-specific models, the body mass exponent increased for boys and for girls. The increase in the body mass exponent with the introduction of body fatness as a second parameter has also been observed by Vanderburgh et al. who have suggested that "when the effect of lean body mass is considered in allometric scaling the body mass exponent increases probably due to the effect that excess fat mass has on increasing body mass with no increase in V˙O2max" (21, p. 83). In these multivariate models, the body fatness exponent was negative, i.e., the greater the body fat the smaller the predicted increase in V˙O2. In models using FFM as the body size parameter, body fatness almost never entered as statistically significant, suggesting that once the effects of body size are addressed by normalizing V˙O2 for FFM, body fatness does not add to the model (or influence the relationship between the V˙O2 and FFM).

We could find no published reports examining the effect of sexual maturation to body mass exponents in children and adolescents although investigators have speculated that changes in body composition during puberty might result in different associations between body size and V˙O2(14). Our data indicate that sexual maturation influenced the association between body mass and V˙O2 in boys regardless of when scaling submaximal or peak data. In girls sexual maturation influenced the association between body mass and V˙O2 when scaling parameters were derived from peak data. However, entering FFM, rather than body mass, produced nonsignificant associations between sexual maturation and V˙O2 for both submaximally- and peak-derived scaling parameters, therefore controlling for the confounding of sexual maturation in the V˙O2 to body size relationship. These results suggest that FFM can be used to address the disproportionate increase in muscle mass with increasing body size that occurs in maturing boys. When viewed from a population perspective, sexual maturation signals changes in body composition that appear to influence the relation-ship between body size and V˙O2; therefore, sexual maturation might also be used (as a covariate) to address disproportionate increases in muscle mass in maturing boys. However, since sexual maturation does not serve as a reliable indicator of body composition changes in an individual child, it seems more appropriate to address the heterogeneity in the proportion of muscle mass to body size by scaling V˙O2 using FFM parameters rather than markers of maturation. In the end, we see no advantage to our multivariate models when compared with our univariate models for normalizing V˙O2 for body size.

Finally, the use of FFM to normalize V˙O2 is more appropriate for research questions examining physiologic changes during growth and maturation rather than questions examining endurance performance in weight-bearing activities (15). During endurance performance, the weight load added by excessive (nonmetabolically active) body mass (i.e., body fat) would negatively influence endurance fitness. However, normalizing V˙O2 for FFM would not provide an index of endurance fitness (peak V˙O2) that would account for this effect. In addition, normalizing V˙O2 for FFM and ignoring the burden of fat mass would probably result in an index of endurance fitness that does not predict endurance performance (15). Issues of measurement validity may also limit the use of FFM as a scaling parameter for body size.

In summary, in a relatively large sample of circumpubertal children followed for 5 yr, adjusting peak V˙O2 for FFM using allometric scaling produced exponents for body mass that were greater than the proposed exponent of 0.67 and statistically different between boys and girls. In our study, the univariate models that scaled FFM appeared most appropriate for maturing girls and boys. Our inability to scale body mass for boys indicates that it is necessary to address the disproportionate increase in muscle mass with increasing body size in maturing boys.


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