Abstract
The influence of gender, growth, and maturation on peak O_{2} consumption (V˙o _{2 peak}) in 11–13 yr olds were examined by using multilevel regression modeling. Subjects were 119 boys and 115 girls, aged 11.2 ± 0.4 (SD) yr at the onset of the study. Sexual maturation was classified according to Tanner's indexes of pubic hair.V˙o _{2 peak} was determined annually for 3 yr. The initial model identified body mass and stature as significant explanatory variables, with an additional positive effect for age and incremental effects for stage of maturation. A significant gender difference was apparent with lower values for girls, and an agebygender interaction indicated a progressive divergence in boys' and girls'V˙o _{2 peak}. Subsequent incorporation of the sum of two skinfold thicknesses into the model negated stature effects, reduced the gender term, and explained much of the observed maturity effects. The body mass exponent almost doubled, but the agebygender interaction term was consistent with the initial model.
 aerobic fitness
 growth
 maturation
 multilevel modeling
 gender
aerobic fitness serves as a functional index of the pulmonary, cardiovascular, and hematologic components of oxygen delivery and the oxidative mechanisms of the exercising muscles. Peak oxygen uptake (V˙o _{2 peak}), the highest oxygen uptake elicited during an exercise test to exhaustion, is recognized as the best single indicator of young people's aerobic fitness (4). However,V˙o _{2 peak} is highly correlated with body size, and, for the effects of chronological age, maturation, and gender onV˙o _{2 peak} to be elucidated, the confounding influence of body size must be accounted for. Inappropriate analyses have clouded our understanding of growth and maturational changes inV˙o _{2 peak} (4, 5).
Although always controversial (32), the expression ofV˙o _{2 peak} in simple ratio to body mass to account for body size differences has been, and to a large extent remains (20), the method of choice for normalizingV˙o _{2 peak} data. However, the recent literature reflects a resurgence of interest in issues concerning the validity of ratio scaling and the discussion of alternative means for controlling for body size differences. There is accumulating evidence to refute the validity of conventional ratio methods derived from both convincing theoretical and statistical arguments and empirical evidence that demonstrates the failure of per body mass ratios to produce a sizeindependent exercise variable (4,5). Scaling techniques based on allometric principles have been shown to produce sizefree performance measures when applied to data derived from young people, have yielded mass exponents less than the value of 1.0 assumed by the simple ratio method, and in crosssectional studies have produced results that challenge conventional interpretations of the growth and maturation ofV˙o _{2 peak} (7,34).
The application of allometric techniques to the interpretation of longitudinal data is not straightforward and may provide an incomplete interpretation of the performance measure under investigation. Two recent studies (15, 27) have employed an ontogenetic allometric approach (19), in which individual body mass exponents are calculated from each subject's longitudinal body massV˙o _{2 peak} regression relationship. Individual values may be averaged subsequently to describe, for example, gender or maturityspecific group exponents. This approach has been criticized on the basis that the interpretation of withinindividual and betweengroup responses requires a statistically inefficient twostage process (25). Moreover, as the longitudinal analysis centers on describing the body massV˙o _{2 peak}relationship, limited information is gained regarding the nature or magnitude of the pattern of change in aerobic fitness.
Two studies have applied one or both of the theoretically proposed mass exponents of 0.67 and 0.75 (28) to examine the longitudinal tracking of and agerelated changes inV˙o _{2 peak} (21, 27). Although individual crosssectional studies in large, homogeneous subject populations have derived mass exponents approximating these values (1, 7), there is considerable evidence to show that exponents are highly sample specific (5), often deviating markedly from theoretical expectations, particularly in small samples. Although producing results that may better reflect underlying changes, the application of a theoretical exponent may not provide an accurate representation of true longitudinal changes within a given subject group.
Few longitudinal studies have considered the influence of covariates other than body mass despite indications from crosssectional studies in both adults and young people that factors such as stature and body fatness may be significant independent predictors (20, 24). Neither has the separate influence of age vs. maturity on the growth ofV˙o _{2 peak} been elucidated comprehensively, in part because of the limitations of traditional analytic techniques.
Multilevel regression modeling (18) is a statistical technique that enables a flexible and sensitive interpretation of longitudinal data while avoiding many of the pitfalls associated with the analyses described above. In contrast to traditional analytic approaches, multilevel modeling not only describes the underlying population mean response but also recognizes and describes variation around the group mean. Furthermore, both the number of observations per individual and the temporal spacing of the observations may vary within a multilevel analysis as individual growth trajectories are modeled.
In a reanalysis of the data from a longitudinal study ofV˙o _{2 peak} in young elite athletes (12), Nevill et al. (25) used an allometric approach within a multilevel regression analysis to demonstrate age and, in boys, maturational, influences onV˙o _{2 peak} that were over and above those explained by the overall increase in body size. Unfortunately, the participation of boys and girls in different sports precluded a detailed examination of differential growth between the genders. The present study sought to extend our understanding of the development of aerobic fitness by using a multilevel regression modeling approach to interpret chronological age, gender, and maturityassociated changes inV˙o _{2 peak} in a healthy, untrained population of subjects tested for three consecutive years, commencing at a mean age of 11.2 yr.
METHODS
Subjects.
All of the children in year 6 (age 10–11 yr) of the 15 state schools in the city of Exeter, United Kingdom, were invited to participate in a longitudinal study of physical activity patterns, physiological responses to exercise, and body composition. Some 745 children (70% of those eligible) volunteered, and written consent was obtained from both the children and their parents and/or guardians. The project received ethical approval from the Exeter District Health Authority Ethical Committee. In an attempt to detect sample bias, the stature and body mass of the volunteers were compared with the stature and body mass of those who declined to participate. No significant difference (P > 0.05) was detected in either gender. Twentyfive percent of the eligible children in each school were randomly selected from those who volunteered. Previous publications have described theV˙o _{2 peak} of boys and girls who were prepubertal in the first year of the project (1) and analyzed crosssectional changes inV˙o _{2 peak} by maturity group by using data from the second year of the project (7). The present study involves a longitudinal analysis of the development ofV˙o _{2 peak} during the first 3 yr of the study. The subject sample thus comprises those young people who satisfactorily completed theV˙o _{2 peak} test and associated anthropometric measures and for whom maturity assessments were available. Subject numbers for year 1 are n = 119 boys, n = 115 girls;year 2,n = 94 boys,n = 88 girls; andyear 3,n = 93 boys,n = 81 girls. There were no significant differences (P > 0.05) between those who failed to return for a subsequent test occasion and the rest of the group on key measures including stature, body mass, skinfold thicknesses, hemoglobin concentration, andV˙o _{2 peak}.
Experimental methods.
Age was computed from date of birth and date of examination. Anthropometric apparatus was calibrated according to the manufacturers' instructions. Stature was measured by using a Holtain stadiometer (Holtain, Crymych, Dyfed, UK), body mass was determined by using Avery beam balance scales (Avery, Birmingham, UK), and skinfold thickness over the triceps and subscapular regions was measured by using Holtain skinfold calipers (Holtain) according to the techniques described by Weiner and Lourie (33). Sexual maturity was visually assessed by using Tanner's indexes for pubic hair development (31). Anthropometric and maturity measures were taken once on each measurement occasion due to time and ethical restrictions. However, the same trained research team made the anthropometric measures and the same trained research nurse made the maturity assessments throughout the duration of the study. Blood hemoglobin concentration was determined from duplicate fingertip blood samples. Blood samples were immediately assayed by using a HemoCue Photometer (Clandon Scientific, Farnborough, UK), which was calibrated against a control cuvette before each measurement.
The children had visited the laboratory on several occasions and were habituated to both the general environment and the experimental procedures. After a 3min warmup at 1.67 m/s (6 km/h),V˙o _{2 peak} was determined during an incremental treadmill running test on a motorized treadmill (Woodway, Cranlea Medical, Birmingham, UK). Belt speed was increased to 1.94 m/s (7 km/h, year 1) or 2.22 m/s (8 km/h, years 2 and 3) for the initial stage and then increased by 0.28 m/s (1 km/h) for each 3min stage until a speed of 2.78 m/s (10 km/h) was reached. Subsequently, belt speed was held constant, and the gradient was increased by 2.5% each stage for further increments. A 1min rest period separated the exercise stages. The test was continued to voluntary exhaustion. If the young person showed signs of intense exertion (hyperpnea, facial flushing, unsteady gait, sweating) and if his or her heart rate had reached a value within 5% of agepredicted maximum or the respiratory exchange ratio was at least 1.0, theV˙o _{2 peak} attained was accepted as a maximal index. All subjects included in this paper satisfied these criteria on all test occasions.
Throughout the test expired gases were monitored continuously by using an Oxycon Sigma online gasanalysis system (Cranlea Medical), which was calibrated before each test by using gases of verified concentration. Heart rate was monitored by using an electrocardiograph (Rigel, Morden, UK).
Statistical methods.
Descriptive statistics (means and SDs) for anthropometric variables, blood hemoglobin concentration, andV˙o _{2 peak} were computed for subjects on the first test occasion. Gender differences within each year of the study were calculated by using analysis of variance.
Factors associated with the longitudinal development ofV˙o _{2 peak}(gender and maturity), adjusted for differences in anthropometric measures and age, were investigated by using the multilevel modeling program MLwiN (17). Multilevel modeling is an extension of multiple regression, which is appropriate for analyzing hierarchically structured data. In longitudinal data sets the hierarchy can be seen as the repeatedmeasurement occasions (defined as level 1 units), grouped within the individual subject (defined as the level 2 unit).
Multilevel modeling is preferable to traditional analytic approaches (e.g., repeatedmeasures analysis of variance) for longitudinal data as, in addition to describing the population mean response, this method recognizes and describes variation around the mean at both levels. For example, at level 2, individuals are allowed to have their own growth rates, which vary randomly around the underlying population response and, at level 1, each individual's observed measurements may vary around his or her own growth trajectory. Furthermore, in contrast to traditional methods that require a complete longitudinal data set, both the number of observations per individual and the temporal spacing of the observations may vary within a multilevel analysis as individual growth trajectories can be modeled.
In this study a multiplicative, allometric approach was adopted on the basis of the model proposed by Nevill and associates (25) as follows
This model can be linearized by logarithmic transformation and multilevel regression analysis on log_{e}(y) used to solve for the unknown parameters. Once transformed, the equation above becomes
As demonstrated for crosssectional data (34), this multiplicative, allometric modeling approach has been shown to be theoretically and statistically superior for longitudinal analyses (25) to an additive, polynomial model (12) as the former accommodates the skewness and heteroscedasticity that often characterize sizerelated exercise performance data (34).
RESULTS
The subjects' physical characteristics in each year of the study are presented in Table 1. There were no significant (P > 0.05) gender differences in age, body mass, stature, or hemoglobin concentration at any point of measurement. Boys had significantly higher (P < 0.001)V˙o _{2 peak} than did girls on each measurement occasion. The sum of skinfolds for boys was significantly lower (P < 0.05) than that for girls on the first two measurement occasions.
The results of the initial modeling ofV˙o _{2 peak} over the three measurement occasions are presented in Table2. In this model, mass and stature proved to be significant covariates with exponents of 0.48 ± (SE) 0.03 and 0.81 ± 0.12, respectively. There was a significant positive effect for age that was larger for boys than girls, as indicated by the significant agebygender interaction term that would be deducted from the age term for the girls. A small but significant term for age squared was also identified for both genders, although girls'V˙o _{2 peak} was shown to be significantly lower than that for boys' as reflected by the negative term for gender (−0.15 ± 0.01). In addition to these anthropometric, age, and gender effects, there was an incremental effect of maturation that was consistent for boys and girls. The maturitybygender effects investigated are not included in Table 2 as they were nonsignificant throughout all models.
These fixed estimates describe the population mean response, whereas the random parameters describe variation around this response at bothlevel 1 (within individuals) and atlevel 2 (between individuals); i.e., these parameters reflect the variance that remains unaccounted for by the fixed part of the model. Within model 1 there was significant random variation atlevel 2 for age, reflecting differential individual growth rates inV˙o _{2 peak}. Allowing each individual his or her own mass exponent proved unnecessary as there was no random variation between individuals around the fixed (mean) parameter.
The independent effect of introducing the sum of two skinfold thicknesses into the model was examined, with the results summarized in Table 2, model 2. The addition of skinfolds to the baseline model rendered the stature and age squared terms nonsignificant and reduced the magnitude of the gender term, whereas the mass exponent was almost doubled to a value of 0.86 ± 0.03. Inclusion of skinfolds also explained much of the observed maturity effects, with the parameter estimates for maturitystages 3–5 almost halved. Furthermore, the addition of this measure of body fatness explained a considerable proportion of the remaining level 2 (betweenindividuals) variance associated with the constant in model 1; i.e., the estimate was reduced from 0.0042 ± 0.0005 to 0.0029 ± 0.0004.
Blood hemoglobin concentration was introduced as an additional explanatory variable, but a nonsignificant parameter estimate was obtained.
DISCUSSION
The V˙o _{2 peak} data in liters per minute are in accordance with the extant literature (4). The present data, however, offer further insights into the growth ofV˙o _{2 peak}, with body size appropriately accounted for. The conventional interpretation of V˙o _{2 peak}“corrected” for body mass (ml ⋅ kg^{−1} ⋅ min^{−1}) is that, during the teen years, boys' values remain remarkably consistent, whereas girls' values progressively decline (4). However, although it has been argued that there is no need to abandon the use of the abovementioned unit of measure to normalizeV˙o _{2 peak} for body size (29), the recent literature reflects a growing awareness of the theoretical and statistical limitations of this approach (4, 20).
There is increasing empirical evidence to refute the assumption that scalingV˙o _{2 peak} to a mass exponent of 1.0 produces a sizefree variable (1, 7, 21, 34), and theoretical arguments based on considerations of geometric similarity or surface law predict thatV˙o _{2 peak} should scale to mass raised to the power 0.67 (28). Nevertheless, whenV˙o _{2 peak} is modeled in subject groups heterogeneous for factors such as body size and age, several studies have reported mass exponents close to the power 0.75 (20). The numeric value of an alternative “universal” or “true” mass exponent for normalizingV˙o _{2 peak} has therefore been the focus of much debate in exercise science (5), but few studies have considered the likelihood that the value of the mass exponent is dependent on not only sample size (4, 5) and homogeneity (20) but also the effect of other confounding covariates. For example, with stature included as an additional covariate the value of the mass exponent has been reduced in several data sets (20, 34). Conversely, inclusion of a measure of body fatness tends to raise the value of the mass exponent (21). The present study demonstrates these effects clearly. When, for illustrative purposes, the data in the present study were analyzed with mass as the sole body size variable, a mass exponent of 0.67 ± (SE) 0.03 was obtained, reflecting the values reported in crosssectional investigations of these children at prepuberty (1) and 12 yr of age (7). The value of the mass exponent decreased to 0.48 ± 0.03 with the addition of stature (model 1) and increased to 0.86 ± 0.03 when a measure of body fatness was incorporated (model 2), illustrating the interdependence of covariates and supporting the view that a lack of statistical control over known covariates is a factor underlying the variability in reported mass exponents (20). These findings also illustrate that it is inappropriate to assume that scaling to either the traditional per body mass ratio or to one of the theoretical mass exponents (i.e., 0.67 or 0.75) will control adequately for body size differences in children and adolescents.
Welsman et al. (34) used loglinear analysis of covariance to partition out body size fromV˙o _{2 peak} in groups of preteen and teenage boys and girls and adult men and women. These data challenged the conventional interpretation ofV˙o _{2 peak} during growth by demonstrating thatV˙o _{2 peak} increases progressively in boys from prepuberty through puberty into adulthood, whereas in girls increases are observed from prepuberty into puberty with no significant decline into adulthood (34). Subsequently, the same group examined the relationship between maturation andV˙o _{2 peak}, with body mass controlled by using allometry (7). Twelveyearold boys and girls were classified into maturity stages 1–4 (31), and the results demonstrated significant increases inV˙o _{2 peak}across maturity stages that were over and above the changes attributable to increased body mass alone (7). These maturational effects had been masked in previous crosssectional studies by the use of the ratio standard (ml ⋅ kg^{−1} ⋅ min^{−1}) to partition out bodysize effects (10, 17). The present study has sought to further clarify age, growth, and maturity effects onV˙o _{2 peak} in boys and girls studied longitudinally by using appropriate multilevel regression modeling techniques.
Most longitudinal studies have analyzed age, growth, or maturityassociated changes inV˙o _{2 peak} by correcting data for a single bodysize indicator within each analysis, usually body mass (15, 27) or anthropometrically predicted lean body mass (21,27). However, a more comprehensive understanding of developmental changes in V˙o _{2 peak}should ideally investigate simultaneously the influence of other known covariates. For example, despite valid concerns regarding issues of collinearity among covariates (11), stature has been shown to be a significant, independent predictor ofV˙o _{2 peak} in both adults and young people when incorporated alongside mass in an allometric analysis (20, 25, 34). This was confirmed in the baseline model presented here (Table 2, model 1) with a significant exponent for stature of 0.78 ± 0.12.
The addition of the sum of two skinfolds (Table 2,model 2) to the baseline model made the terms for both stature and age squared redundant. Incorporating this measure of body fatness also explained a large proportion of the observed maturity effects, with the magnitude of the effect increasing with progression through maturational stages. A similar effect was observed when the development of mean power obtained during a Wingate Anaerobic Test in 12–13 yr olds from the present population (9) was modeled. In the present study, differences in skinfold thickness also explained part of the gender difference observed in addition to a considerable proportion of the residual betweenindividual variance (level 2).
Studies investigating age, growth, and maturational changes in the body massV˙o _{2 peak}relationship by using ontogenetic allometry (15, 27) have noted extreme variability in individual mass exponents with, for example, values ranging from 0.18 to 1.74 in one study (27). The flexibility of the multilevel modeling procedure used in the present study enables the underlying mean response to be described while concurrently allowing individuals to have their own mass exponent. The need for this was examined by fitting a random component for mass atlevel 2 of the analysis (i.e., between individuals). When this was done, however, the model failed to converge, indicating that the fixed (mean) parameter adequately described this population. Individual variation in overall growth rates was evident, as indicated by the significant random variance at level 2 associated with the age term. The variability in overall rates of change inV˙o _{2 peak} during the 3 yr of this study is clearly evident from the individual growth trajectories illustrated in Fig. 1.
The data from the first year of the study support evidence of gender differences in V˙o _{2 peak}at age 11 yr (4). In fact, a significant gender difference inV˙o _{2 peak} was demonstrated even when prepubescent girls (n = 53) and boys (n = 111) were compared, and with this subsample there was no significant gender difference in skinfold thicknesses (1). Explanations for girls' lowerV˙o _{2 peak} at a young age are speculative but the lower values may be due to a lower exercise stroke volume than in boys. Boys have consistently demonstrated higher stroke volumes than girls at the same submaximal oxygen uptake or exercise intensity, although differences have been small and in some cases statistically insignificant (26). Comparative data at V˙o _{2 peak} appear to be limited to one published study (23), which, by using carbon dioxide rebreathing, reported boys' stroke index to be 15% higher than those in girls at 9–10 yr of age and 5% higher at 11–12 yr of age. However, recent work by Rowland (26), using Doppler echocardiography, provides supportive data, with 12yrold boys reported to have 13% higher maximal stroke indexes relative to lean body mass than similarly aged girls.
The results of the multilevel regression models examined here confirm previous crosssectional indications (34) in showing increases in sizerelated V˙o _{2 peak} that contrast with conventional interpretation ofV˙o _{2 peak}during growth (4). Furthermore, the significant agebygender interaction term in the present data set indicates a progressive divergence in boys' and girls' values over the age range examined. The increasing gender difference inV˙o _{2 peak} during childhood and adolescence has been attributed to the greater accumulation of body fat in relation to body mass in girls, boys' higher hemoglobin concentration, and girls' lower levels of habitual physical activity (4).
The addition of the sum of skinfold thicknesses to the baseline model reduced the magnitude of the gender term. This may be reflective of boys' relatively greater increase in muscle mass, which would not only facilitate the use of oxygen during exercise but may also supplement the venous return to the heart and therefore augment stroke volume, through the peripheral muscle pump (6, 26).
During puberty there is a marked increase in hemoglobin concentration and hence oxygencarrying capacity in boys, whereas girls' values plateau (16). It might therefore be expected that differences in hemoglobin levels between boys and girls would be a contributory factor to the observed gender difference inV˙o _{2 peak}, and this has been demonstrated with 14 and 15 yr olds (10). Hemoglobin levels were determined routinely in the present study at each laboratory visit, but, when investigated as an additional explanatory variable, a nonsignificant parameter estimate was obtained with these 11–13 yr olds. This is not an unexpected finding given the minimal change in hemoglobin concentration across the 3 yr of observation in both boys and girls (see Table 1).
Boys have been consistently demonstrated to have higher levels of habitual physical activity than girls, but the evidence relating habitual physical activity toV˙o _{2 peak} is conflicting (5). In parallel studies the physical activity patterns of the present children were monitored over 3 days, using continuous heart rate monitoring, and no significant relationships were detected betweenV˙o _{2 peak} and heart rate indicators of level of physical activity in either the first (3) or second year (8) of the study. In a multilevel regression analysis of the 3yr heart rate data,V˙o _{2 peak} was examined as an additional explanatory variable, but a nonsignificant parameter estimate was obtained (2). Habitual physical activity is unlikely to influence children's and adolescents'V˙o _{2 peak}because such activity typically lacks the intensity and duration sufficient to improve aerobic fitness (5).
In the exercise sciences, maturity is usually assessed by using indicators of skeletal, somatic, or sexual maturity. Although no single assessment gives a complete description of the tempo of maturation, there is a high concordance among the aforementioned indicators (13). Previous studies have revealed that skeletal age adds little to the description of physiological variables yielded by chronological age and body size (30). Beunen and Malina (14) reviewed the literature concerningV˙o _{2 peak} and the adolescent growth spurt, commented that the available data should be interpreted with caution, and concluded that the evidence suggests a spurt in V˙o _{2 peak} in boys that reaches a maximum gain at the time of peak height velocity, but secure data are insufficient to offer any generalization for girls. Few longitudinal studies have investigated the influence of maturity, independent of body size, onV˙o _{2 peak}. BaxterJones et al. (12) used an additive polynominal model within a multilevel regression structure. They assessed maturity by using secondary sexual characteristics (31) and reported that, in athletic boys, there was a significant increase inV˙o _{2 peak} toward the end of puberty that was in direct contrast to the nonsignificant increase in V˙o _{2 peak}found in athletic girls during this time. The authors attributed this additional increase inV˙o _{2 peak} partially to the boys' trained status. Using stature velocity as an indicator of maturity status and analysis of covariance to control for body mass, Malina et al. (22) observed similar results with children from a sports school. In the present study of untrained boys and girls, maturity positively affectedV˙o _{2 peak} in both genders, and an additional effect of chronological age indicated the importance of incorporating both age and maturity into analyses ofV˙o _{2 peak} during growth and maturation.
In summary, the multilevel modeling approach has revealed age, gender, and maturity effects, independent of body size, on theV˙o _{2 peak} of untrained boys and girls. These effects may have been masked in previous studies by the inappropriate use ofV˙o _{2 peak} in ratio to body mass and/or the failure to consider the impact of covariates other than body mass. Physiological explanations for these effects cannot be established fully by the present data set, but it appears that gender, age, and maturity differences in the increase in fatfree mass relative to body mass are the predominant influences on the differential growth of boys' and girls'V˙o _{2 peak} in 11–13 yr olds.
Acknowledgments
We gratefully acknowledge the technical assistance of Jenny Frost, Alison Husband, and Sue Vooght.
Footnotes

Address for reprint requests and other correspondence: N. Armstrong, Children's Health and Exercise Research Centre, Univ. of Exeter, Heavitree Rd., Exeter, EX1 2LU, UK (Email: N.Armstrong{at}exeter.ac.uk).

The work was supported by the British Heart Foundation and the Healthy Heart Research Trust. Alan Nevill is with the School of Human Sciences, Liverpool John Moores University, Liverpool, UK.

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 Copyright © 1999 the American Physiological Society