# Intraindividual allometric development of aerobic power in 8- to 16-year-old boys

BEUNEN, G., A. D. G. BAXTER-JONES, R. L. MIRWALD, M. THOMIS, J. LEFEVRE, R. M. MALINA, and D. A. BAILEY. Intraindividual allometric development of aerobic power in 8- to 16-year-old boys. *Med. Sci. Sports Exerc.*, Vol. 33, No. 3, pp. 503–510, 2002.

Purpose The aims of this study are two-fold: first, to analyze intraindividual allometric development of aerobic power of 73 boys followed at annual intervals from 8 to 16 yr, and second, to relate scaled aerobic power with level of habitual physical activity and biological maturity status.

Methods Peak V̇O_{2} (treadmill), height, and body mass were measured. Biological maturity was based on age at peak height velocity (PHV) and level of physical activity was based on five assessments between 11 and 15 yr and at 17 yr. Interindividual and intraindividual allometric coefficients were calculated. Multilevel modeling was applied to verify if maturity status and activity explain a significant proportion of peak V̇O_{2} after controlling for other explanatory characteristics.

Results At most age levels, interindividual allometry coefficients for body mass exceed k = 0.750. Intraindividual coefficients of peak V̇O_{2} by body mass vary widely and range from k′ = 0.555 to k′ = 1.178. Late maturing boys have smaller k′ coefficients than early maturing boys.

Conclusion Peak V̇O_{2} is largely explained by body mass, but activity level and its interaction with maturity status contribute independently to peak V̇O_{2} even after adjusting for body mass.

Department of Sport and Movement Sciences, Faculty of Physical Education and Physiotherapy, Katholieke Universiteit Leuven, Leuven, BELGIUM; College of Kinesiology, University of Saskatchewan, Saskatoon, Saskatchewan, CANADA; Department of Kinesiology, Michigan State University, East Lansing, MI; and Department of Human Movement Studies, University of Queensland, Brisbane, AUSTRALIA

Submitted for publication February 2001.

Accepted for publication June 2001.

Cross-sectional studies of children and adolescents (excluding trained children) demonstrate that peak oxygen uptake (peak V̇O_{2}) increases almost linearly with age between 7 and 16 yr in both sexes, but nearly twice as much in boys than in girls. Relative to body mass, aerobic power remains fairly constant with age in boys but decreases in girls (^{2}). The use of relative aerobic power expressed as a ratio of body mass has been criticized, especially when changes associated with growth and maturation should be controlled (^{4–6,16,17,22,26,30,31,33,34}). When working with children and adolescents, cross-sectional designs are useful for studying population characteristics at several age levels, but they are poor designs to study individual patterns and variations associated with tempo and timing of growth and maturation (^{8,19}).

Longitudinal studies incorporating tests of aerobic power are limited (^{2,19}). Longitudinal data from Canada, Germany, Norway, and The Netherlands that span adolescence indicate a linear increase in absolute peak V̇O_{2} with age, but a steeper increase near the time of maximum growth in height during the adolescent spurt, about 12 yr in girls and about 14 yr in boys. When individual values of aerobic power are aligned on the age at peak height velocity (PHV), a spurt in V̇O_{2} coincident with PHV is evident in Canadian youths of both sexes (^{21}). When aerobic power is expressed per unit body mass in boys, the ratio is stable until 2 yr before PHV and then declines, whereas the ratio declines from 3 yr before PHV in girls (^{21}).

There is a need for analyses of longitudinal data that considers individual developmental patterns in aerobic power with mathematically correct adjustment for the simultaneous increases in body dimensions and biological maturation. Paterson et al. (^{24}), Sjodin and Svedenhag (^{29}), and Beunen et al. (^{10}) have used intraindividual or ontogenetic allometry (k′) (^{13}) to describe changes in relative or scaled oxygen uptake during adolescence. The mean ontogenetic allometry exponent for body mass was 1.19 ± 0.14 for peak V̇O_{2} in 18 athletic boys 11–15 yr of age (^{24}). In eight trained adolescent boys (runners), the mean ontogenetic allometry coefficient for body mass relative to peak V̇O_{2} (k′ = 1.01 ± 0.04) was significantly higher than the coefficient for four untrained adolescent boys (k′ = 0.78 ± 0.07) (^{29}). Among active boys 11–14 yr old, ontogenetic scaling factors varied with maturity status and were higher in early and average maturing than in late maturing active boys of the same age. In active girls 11–14 yr of age, the increase in peak V̇O_{2} was not related to the increase in either body mass or height in the majority of subjects (^{10}). When peak V̇O_{2} was allometrically scaled as a function of fat-free mass (FFM) in a 5-yr follow-up study of 126 children (mean age, 10.3 yr at study entry), the effects of maturation on the relationship between peak V̇O_{2} and body size differed between boys and girls (^{15}). The exponent of FFM was influenced by stage of sexual maturity in boys, but not in girls.

Multilevel analysis (^{11}) is another appropriate method with which to analyze longitudinal data. Additive and multiplicative (proportional) multilevel models have been used in the analysis of V̇O_{2} of 453 boys and girls participating in gymnastics, soccer, swimming, and tennis (^{7,23}). After controlling for age, height, and body mass, V̇O_{2max} significantly increased with pubertal status in boys. Girls showed a similar pattern; however, the significant increase in V̇O_{2max} as a function of stage of puberty apparent in boys was not evident. With a multiplicative “allometric” model, there was a better fit, and V̇O_{2max} developed approximately proportionally to mass, with k′ ranging between 0.66 and 0.69, and with a highly significant age parameter indicating that aerobic power of boys and girls increased at a greater proportion of their body size at the age of 12 yr. This was explained as a function of training status (^{23}), but it was difficult to specifically quantify a training factor, given the different demands of the four sports considered. In British adolescents 11–13 yr old, body mass and stature were the most important explanatory variables of peak oxygen uptake with additional relatively small effects of age and sexual maturity status (^{4}). When skinfolds were introduced in the multilevel model, stature was no longer a significant explanatory variable, sex differences were reduced, and much of the maturity effect was also accounted for. The aims of the present study are, therefore, to analyze intraindividual allometric development of aerobic power in a representative sample of boys followed longitudinally on an annual basis from 8–16 yr, and to relate scaled aerobic power with estimated level of habitual physical activity and with biological maturity status.

## METHODS

### Design.

Subjects consisted of 73 boys from the Saskatchewan Growth and Development Study (SGDS), which started with 207 7-yr-old boys who were randomly selected on a stratified socioeconomic basis from the elementary school system in the city of Saskatoon, Saskatchewan, Canada. Written informed consent was obtained from the city of Saskatoon, the parents, and the subjects, and the SGDS was approved by the University of Saskatchewan Human Research Ethics Committee. The subjects were not exposed to any special program of physical activity or systematic training other than the yearly tests and school physical education, or their self-selected participation in sports or physical activity. Subjects were tested annually over a 9-yr period. Some subjects were missing at certain years, others did not meet the criteria for the exercise test, and a number withdrew from the study. The observations for 7 yr of age were not included in the analysis of the exercise data to allow the subjects to familiarize themselves with the test protocol and equipment. The development of aerobic power of these subjects has been previously described (^{21}).

### Measurements.

The exercise test was performed on a treadmill with minute-to-minute data collection during 5 min of standing before exercise, followed by continuous exercise to exhaustion with the treadmill at 0% grade. The speed was increased stepwise: 3 min at 4.8 km·h^{−1}, 3 min at 9.6 km·h^{−1}, 3 min at 14.4 km·h^{−1}, and if necessary, at 19.2 km·h^{−1} until exhaustion. At the end of the test, a 10-min standing recovery was taken. Rail holding was only permitted just before and after speed changes. Heart rate was monitored by means of a chest lead electrocardiogram. Subjects were required to breath through a two-way valve with a large inner diameter. The minute ventilation was measured on the intake by a high-speed dry gas meter (Parkinson-Cowan CD4, Parkinson Cowan, Berkshire, England). Expired air was collected in a three-way rotating Douglas bag system. The oxygen content of the expired air was measured by a rapid response analyser (Beckman model E2) and carbon dioxide content was measured by an infrared carbon dioxide analyzer (from 8 to 12 yr with a Godart Capnograph and from 13 to 16 with a Beckman model 215A). The details of the protocol and specific procedures are described in Mirwald and Bailey (^{21}).

Although the treadmill protocol used in the Saskatchewan study met the criteria of a maximal aerobic power test, not all the subjects tested ran to exhaustion at each occasion. Under the assumption that a heart rate of ≥ 200 bpm indicates maximal effort, subjects were drawn at each age who met this criterion. Several respiratory and cardiovascular variables were measured at submaximal and maximal workloads on each subject. A stepwise multiple regression procedure using anthropometric and cardiovascular variables was then applied to develop age- and workload-specific regression equations for peak V̇O_{2}. The absolute prediction error was < 5% at every age level. The prediction equation was also cross-validated on a subgroup of 14 boys who were not part of the study, but who were tested on two separate occasions. There were no significant differences between observed and predicted peak V̇O_{2} values. The absolute error between observed and predicted values was 5%. On the basis of these procedures, the multiple regressions were acceptable as a suitable means of predicting maximal aerobic power in individuals who did not meet the heart rate criterion. Of the total number of 747 maximal aerobic power tests, 34% were predicted using the procedures described above.

Height was measured with a fixed stadiometer to the nearest millimeter using a free-standing technique with the head in Frankfort horizontal plane. Body mass was recorded to the nearest 0.1 kg with the subject attired only in a swim suit. Maturity status was determined on the basis of the age at PHV. The Preece-Baines model I (^{25}) growth function was fitted to the height data for individual boys to estimate age at PHV. The height records of 10 boys were not appropriately fitted by the model, reducing the final sample to 73 boys (^{21}).

For the multilevel analysis, a continuous measure of maturity, labeled maturity age at the time of measurement, was generated. It is the age at which V̇O_{2} was measured in decimal years from the age at PHV derived from the Preece-Baines model I. The growth curve for V̇O_{2} for each boy was aligned on his own age at PHV (i.e., V̇O_{2} years before and after PHV). The effect of maturity (i.e., age at PHV) was adjusted for the time of measurement of V̇O_{2}. This is achieved by noting how far the individual was from maturity at the time of measurement of V̇O_{2} (i.e., age or time in decimal years from age at PHV). Thus, a maturity age of −1.0 indicates that the subject was measured 1 yr before maturity or PHV; a maturity age of 0 indicates that the subject was measured at the time of maturity; and maturity age of +1.0 indicates that the subject was measured 1 yr after maturity. V̇O_{2} was thus adjusted for the time before and after age at PHV to provide an estimate of maturity.

During the course of the study, five assessments of physical activity were made. At 11 yr, the child and parents completed activity questionnaires, and at 12 yr, the child’s school teacher also assessed his physical activity. At 13, 14, and 15 yr, each boy completed a sport participation inventory. A paper-and-pencil inventory developed for use in this study was administered to assess sports patterns (number and type of sport). Besides number and types of competitive organized sports, recreational and leisure time activities were also listed. A weighted score was subsequently assigned to each of these and used for further classification. Two years after the study, subjects present on the last examination were interviewed by the high school physical education teacher and also completed a questionnaire. Boys were classified as habitually active (*N* = 14) or inactive (*N* = 12) if they were classified, respectively, as active or inactive in four of the five previous assessments and at the follow-up. Those who were neither active nor inactive were considered average in level of habitual physical activity (*N* = 47). A more detailed description of the procedures is reported by Mirwald and Bailey (^{21}).

### Statistical analyses.

Sample statistics and regression equations were calculated using the SAS (^{28}) package (SAS Institute, Cary, NC). Static (interindividual) allometric coefficients (k) were calculated for peak V̇O_{2} and body mass at each age level. Static allometric coefficients reflect the dimensional relationship between peak V̇O_{2} and body mass at a given age. They are not identical with ontogenetic coefficients, which reflect proportional changes in peak V̇O_{2} relative to body mass over time. Following Gould (^{13}), intraindividual or ontogenetic allometric coefficients (k′) were also calculated for each subject. An allometric regression was performed for each subject on the double logarithmic transformation of peak V̇O_{2} and body mass. Furthermore, the slopes of different bivariate structural relationships and their confidence intervals were obtained following procedures described by Jolicoeur and Heusner (^{16}).

In order to make maximal use of the longitudinal data, a multilevel (a random coefficient model) modeling approach was used (^{11,12}). Multilevel modeling is an extension of ordinary multiple regression where data have a hierarchical or clustered structure. A hierarchy consists of units grouped at different levels; such data hierarchies are neither accidental nor ignorable. Repeated aerobic power measures are an example of hierarchically structured data. The assessments are clustered within individuals and represent the level 2 units; the measurement occasions are level 1 units. Thus, when individuals are measured on more than one occasion, two levels of variability account for a single individual’s departure from their fitted growth trajectory (level 1) and the underlying population response (level 2). In contrast to traditional methods, complete longitudinal data on all individuals are not necessary. The number of observations per individual and the temporal spacing of the observations are allowed to vary within the analysis ^{11}).

The model used shows a complex level 2 variation (random variables) that allows each child to have his own intercept and slope. Fitting a curve to a subject’s repeated measurements is the only way of extracting the maximum information about an individual’s growth from measurement data, since there is very wide variation among children in growth parameters at any age and in the velocity of these parameters from one age to the next; thus, it is essential that any modeling procedure used incorporates this feature. The random coefficient model is one such model, where level 1 regression coefficients are treated as random variables at the second level. The two levels of random variation in the model mark the model as multilevel. In common with previous studies, we adopted a multiplicative allometric approach to describe developmental changes in aerobic power (y = peak V̇O_{2}, in L·min^{−1}) (^{4,23}) as follows: Y = mass^{k1}·exp (a_{J} + b_{J}·maturity age) ε_{ij}, where all the parameters were fixed with the exception of the constant (intercept term) and maturity age parameters “a” and “b” that were allowed to vary randomly from child to child (level 2), and the multiplicative error ratio, ε, that was used to describe the error variance between visit occasions (level 1). Subscripts i and j denote random variations at levels 1 and 2, respectively.

Log-transformation linearizes the model and multilevel regression analysis on log_{e}(peak V̇O_{2}) is used to estimate the unknown parameters. The transformed log-linear multilevel regression model becomes log_{e}(peak V̇O_{2}) = k_{1}·log_{e}(mass) + a_{J} + b_{J}·maturity age + log_{e}(ε_{ij}).

Initially, a null model was fitted, which contained only a response variable and no explanatory variables other than an intercept. The null model was used as a baseline for the estimation of explained versus unexplained variances in comparison with more elaborate models. In the traditional regression model, the within and between variances of a null model serve as the criterion for estimation of the multiple R^{2}. However, for models with random slopes, there are two R^{2}s and thus the use of R^{2} to interpret goodness of fit is not appropriate. Goodness of fit of multilevel models is measured by the deviance between two models measured using the maximum log likelihood criterion. The difference in deviance between two nested models has a chi-square distribution and this is compared with the degrees of freedom lost, to determine if one model is a significant improvement over the other. In this way, explanatory variables are added to the models and are retained if deviance improves and/or if the variances at level 1 and level 2 are reduced. Covariates are accepted as significant if the estimated mean is greater than twice the standard error of the estimate (SEE). If the retention criteria are not met, then the explanatory variable is discarded. In this way, explanatory additional variables were investigated. Physical activity was incorporated into the fixed part of the model as two categorical factors. The inactive physical activity group was used as the baseline parameter with which the performance of other physical activity groups (active and average) were compared, i.e., allowed to deviate from the constant baseline (“inactive-average” and “inactive-active” variables). To allow different growth rates to be associated with the physical activity groupings, the product of maturity age and physical activity group variables were introduced as additional predictor variables (i.e., by introducing “maturity age × inactive-average” and “maturity age × inactive-active” terms).

## RESULTS

### Interindividual allometric analysis.

Concomitant with the increase in size and body mass, peak V̇O_{2} increases from 1.45 L·min^{−1} at 8 yr to 3.03 L·min^{−1} at 16 yr (Table 1). Interindividual variation ranges from 0.26 L·min^{−1} at 8 yr to about 0.60 L·min^{−1} at 14–16 yr, or, in relation to the average, the coefficient of variation ranges from 18% to 20%. Point estimates of the linear regression coefficients and of the major axis were calculated together with their confidence limits (*P* = 0.01). As proposed by Jolicoeur and Heusner (^{16}), these confidence intervals were used to test for differences between slopes. Static or interindividual allometry coefficients (k) derived from the linear regression of the double logarithmic transformation of peak V̇O_{2} and body mass (point estimates in Table 2) are lowest (k = 0.644) at 12 yr and highest (k = 0.929) at 15 yr. The regression coefficients (point estimates) are significantly higher at 8 yr and 14–16 yr, than at 9–13 yr. The point estimates at 8 yr and at 14–16 yr are higher than the upper limits of the confidence interval at 9–13 yr, and the point estimates at 9–12 yr are lower than the lower limits at 8 yr and 14–16 yr. The point estimates derived from the linear regression, assuming no error term in the measurement of body mass, differ considerably from the point estimates derived from the major axis, assuming that both body mass and peak V̇O_{2} have equal error variance. Biologically, this is a more realistic assumption than assuming that body mass and/or peak V̇O_{2} are measured without error. The point estimates of the linear regression fall below the lower limit of the k-coefficients for the major axis. Under the assumption that both body mass and peak V̇O_{2} have equal error variance, the allometry coefficients vary between k = 0.777 at 12 yr and k = 1.220 at 16 yr. The upper and lower limits indicate the 99% confidence limits of the k-coefficients. For the major axis approach, the lower limits of the allometry coefficients surpass k = 0.750 in all age categories, except at 11 and 12 yr. Under the assumption that the error variance in peak V̇O_{2} is two times the error variance in body mass, the point estimates vary between k = 0.719 at 12 yr and k = 1.270 at 16 yr (data not shown in Table 2).

### Intraindividual allometric analysis.

The linear regression of the double logarithmic transformation of peak V̇O_{2} and body mass calculated for each individual separately shows a very good fit in most of the cases. The adjusted determination coefficient (R^{2}) exceeds 0.85 in 77% of the subjects, and is below 0.65 in only one boy.

The intraindividual allometry coefficients (k′) of peak V̇O_{2} by body mass vary widely. They range from k′ = 0.555 to k′ = 1.178, with a mean of k′ = 0.855 and SD = 0.143.

### Multilevel Model.

Table 3 summarizes the results from the multilevel model of log-transformed peak V̇O_{2} (L·min^{−1}) with maturity age. At level 1, the significant within-individual variation for peak V̇O_{2} (0.0082 > 2 × SEE) indicates that the fitted explanatory variable does not fit perfectly. The level 2 random parameters show that individuals differ in the fitted peak V̇O_{2} at PHV, maturity age zero (intercept, 0.0031 > 2 × SEE), and in the rate of gain in peak V̇O_{2} (slope, 0.00004 > 2 × SEE). The two were not correlated and the correlation was thus removed from the model. After each explanatory variable was adjusted for other explanatory variables (Table 3, fixed variables) log body mass, activity levels, and maturity age activity level interactions were all significant predictors of peak V̇O_{2}. When the interaction terms were added to the model, the explanatory variable maturity age became nonsignificant and was removed. The allometric coefficient for body mass is k′ = 0.779 (SEE = 0.028). When maturity age is removed from the model (i.e., its interaction with physical activity group), the body mass coefficient rises to k′ = 0.855 (SEE = 0.014).

The inactive physical activity group was chosen as the reference of comparison for the average and active groups. The results indicate that physical activity had a significant independent effect on peak V̇O_{2} when the confounding effect of body mass is controlled. The results (Table 3) indicate that this is a graded effect that is also related to maturity age. When comparing the three groups, both average and active groups add a significant positive contribution to the prediction of peak V̇O_{2}, with the coefficient for the active group (0.120 (SEE = 0.026)) being roughly twice that of the average group (0.067 (SEE = 0.022)). When other confounders were controlled, the two interaction terms were both negative (Table 3). As maturity age is a continuous variable centered about PHV, at PHV maturity age will equal zero, before PHV maturity age is negative, and after PHV maturity age is positive. The physical activity variables are dummy variables set at 0 or 1, with the inactive group serving as the baseline. Thus, before PHV for an individual in the average or active group, the interaction term will add an additional positive value to predicted peak V̇O_{2} because a negative regression coefficient multiplied by a negative maturity age yields a positive value. Before PHV, these positive values are declining. At PHV, this term equals zero and, therefore, does not affect the prediction of peak V̇O_{2}. After PHV, when maturity age is positive and the interaction coefficient is negative, peak V̇O_{2} of the average and active groups declines relative to the inactive baseline group. The three physical activity groups’ growth of peak V̇O_{2} are illustrated in Figure 1. The interaction effects are clearly seen, where differences between the groups are smallest around PHV.

## DISCUSSION

Average peak V̇O_{2} values for this longitudinal sample of boys fall well within the range of values reported for different populations as summarized by Armstrong and Welsman (^{2}). The development of peak V̇O_{2} from childhood through adolescence in the Saskatchewan sample has been described previously (^{21}). In summary, absolute peak V̇O_{2} increases significantly with age and follows a growth curve that has a pattern similar to that for stature. The growth curve for peak V̇O_{2} is accurately described with the Preece-Baines model I (^{25}) and shows a well-defined adolescent growth spurt. At takeoff (10.6 yr), peak V̇O_{2} is 1.88 L·min^{−1} with a velocity of 0.14 L·min^{−1}·yr^{−1}. At peak velocity (14.3 yr), peak V̇O_{2} is 2.75 L·min^{−1} with a velocity of 0.53 L·min^{−1}·yr^{−1}. The adult value of peak V̇O_{2} is estimated at 3.39 L·min^{−1}. Thus, at takeoff, nearly 56% of estimated adult peak V̇O_{2} is attained, and at peak velocity, about 81% of estimated adult peak V̇O_{2} is attained. Maximum velocity in peak V̇O_{2} is reached at the same time as PHV (^{21}). The estimated adult peak V̇O_{2} is derived from the parameters of the Preece-Baines growth model (^{25}).

When yearly velocities are calculated from the means of peak V̇O_{2} in Table 1, it is clear that cross-sectional analyses, even of longitudinal data, fail to reveal the underlying characteristics of the developmental process of individual adolescents. Between 13 and 14 yr, and between 14 and 15 yr, the mean increases are, respectively, 0.36 L·min^{−1}·yr^{−1} and 0.21 L·min^{−1}·yr^{−1}, which are considerably less than 0.528 L·min^{−1}·yr^{−1} obtained from analyses of individual growth curves.

Static allometry coefficients are reported most often in the exercise physiology literature (^{5,6,26,27}). Allometry coefficients derived from the linear regression (Table 2) are similar to those for a sample of active Polish boys followed from 11–14 yr (^{10}). In the total sample of Saskatchewan boys, coefficients increase from k = 0.696 at 11 yr to k = 0.921 at 14 yr, whereas in the active Polish boys they increase from k = 0.516 to k = 1.026 over the same age interval. With the exception of k = 0.516, the coefficients for Polish boys are within the confidence limits of the coefficients for Saskatchewan boys at the corresponding ages.

It is often assumed, and commonly overlooked in linear regression, that the variable to which the other is regressed is measured without error. This would imply that there are no errors or no biological fluctuations in the measurement of body mass or height. This assumption does not hold. As shown by Jolicoeur and Heusner (^{16}), other indicators of the association between two measurements in which assumptions about measurement errors in both variables are made need to be considered. The point estimates and confidence limits of the major axis through the ellipse encompassing the bivariate distribution of the logarithmically transformed peak V̇O_{2} and body mass are given in Table 2. In the major axis, it is assumed that both body mass and peak V̇O_{2} have the same error variance. Static allometric coefficients for Saskatchewan boys 8–16 yr exceed the hypothetical coefficient of k = 0.67, implying that the geometric similarity and surface law hold true for peak V̇O_{2} (^{14}). The static allometric coefficients also exceed the hypothetical k = 0.75, implying that elastic criteria impose limits on oxygen consumption and metabolic rate (^{20}). The point estimates of the k-coefficients vary between k = 0.777 and k = 1.466. The hypothetical k = 0.75 (implying elastic similarity) cannot be rejected at only 11 and 12 yr, since this value is within the confidence limits at these ages. This means that in boys 8–10 yr and 13–16 yr, peak V̇O_{2} is higher than expected from the hypothetical laws of geometric or elastic similarity, (i.e., heavier boys have higher peak V̇O_{2} values than predicted from body mass under both hypothetical laws). These results are consistent with a corresponding analysis of 11- to 14-yr-old active Polish boys (^{10}). It can be argued that the true error variance in V̇O_{2} peak is larger than the true error variance in body mass. If it is assumed that the error variance of the logarithmic transformed peak V̇O_{2} is twice the error variance of the logarithmic transformed body mass, the k-coefficient varies between k = 0.719 at 12 yr and k = 1.270 at 8 yr. At 8 yr and at 13–16 yr, the lower limit of these coefficients is again higher than expected from laws of both geometric and elastic similarity.

For ontogenetic allometry, the linear regression of the logarithmic transformation of peak V̇O_{2} on body mass shows a very good fit. Coefficients of determination (R^{2}) in the majority of the subjects are above 0.85. This also implies that the allometry coefficients of the linear regressions can be used to compare them with the hypothetical values (k = 0.67 or k = 0.75), since the bivariate distribution is closely aligned around the line of identity. Consequently, the slopes of the different axes that can be calculated under different assumptions regarding error variance become more identical.

Individual ontogenetic coefficients for body mass vary considerably, ranging from k′ = 0.555 to k′ = 1.178, with a mean of k′ = 0.855. Somewhat less than 90% of the boys have an allometry coefficient less than k′ = 1.00. This indicates that the traditional approach of dividing V̇O_{2} by body mass has limitations. As stressed by Günther (^{14}), adjustment or scaling factors should be based on calculations for the sample under study and not on some hypothetical value, since this will lead to incorrect adjustments or scaling. Furthermore, on the average, individual values of peak V̇O_{2} increase more than would be expected from the hypothetical laws of geometric or elastic similarity. The variability in the ontogenetic coefficients reflect individual differences in tempo and timing of the adolescent growth spurt in body dimensions, body composition, heart, lung, and muscle. Also, the development of the O_{2} delivery and utilization systems probably interferes, but these changes have not yet been satisfactory addressed during the growth spurt (^{19}).

By adopting the multiplicative allometric model within a multilevel structure, a one-stage allometric analysis that is able to incorporate all covariates simultaneously is achieved (Table 3). It also allows each individual in the sample to have his own individual body mass exponent. In the present analysis, the confounding effects of maturity were controlled by aligning peak V̇O_{2} on age from peak height velocity (maturity age) rather than chronological age. When maturity age was removed from the fixed part of the model, the average mass exponent was k′ = 0.855 (SE = 0.014), which was the same as the mean of individual ontogenetic coefficients.

However, when maturity age was included in the fixed model, as an interaction with physical activity grouping, it had a significant independent effect and reduced the average mass exponent for the sample to k′ = 0.78, which was slightly higher than that observed in a group of boys undergoing systematic training (k′ = 0.69) (^{23}). This independent effect of maturity is consistent with results from cross-sectional (^{1}) and longitudinal (^{4}) analyses. In a previous study of young boys (8–19 yr of age) involved in systematic training before puberty (^{7,23}), sexual maturity had a significant independent effect on the prediction of peak V̇O_{2}. This independent effect of sexual maturity was not seen in girls (^{7,23}). Recently, a study of 11- to 13-yr-old boys and girls not undergoing systematic training confirmed the finding in boys but refuted the results in girls (^{4}). Comparisons between models are problematic given the fact that in the training group the sexes were modeled separately (^{7,23}). Both studies used stage of sexual maturity as the indicator of biological maturity, which permits only an approximate classification of maturity, since only five discrete stages are identified (^{19}). Maturity age as used in the present study provides a continuous and probably more accurate indicator of biological maturity (^{8}), and thus better synchronization of the changes in peak V̇O_{2} than with use of stages of a secondary sex characteristic. It may be inferred that this maturity effect is associated with higher hemoglobin concentration and greater muscle mass observed in adolescent boys as they progress through the growth spurt (^{19}).

In the multilevel analysis, physical activity also had a significant independent effect on aerobic power when growth and maturity were statistically controlled. The results suggested a graded effect for physical activity. When the least active or inactive group was compared with the active group, the latter had significantly higher levels of aerobic power. There also was a significant difference between the average activity and inactive groups, but the difference was smaller. Although these effects were found to increase before and after PHV, at all stages of maturation the active boys had significantly greater peak V̇O_{2} than the average active boys, who in turn had significantly greater peak V̇O_{2} than the inactive boys. Note that the activity groups were based on five assessments during the course of the study and one assessment at follow-up at 17 yr. Boys who consistently stayed active or inactive were grouped in these respective categories. At 13, 14, and 15 yr, sport participation, including organized, recreational, and leisure time activities, was used as an indicator of physical activity.

Although it has often been suggested that habitual physical activity is unlikely to influence peak V̇O_{2} in children because such activity typically lacks the intensity and duration sufficient to improve aerobic fitness (^{3}), evidence does in fact show a significant association between aerobic fitness and level of physical activity in adolescent boys. For example, a longitudinal study of teenagers from The Netherlands found that active boys and girls had significantly higher peak V̇O_{2} per unit body mass than inactive youth (^{32}). Since the difference was present at the start of the study (13 yr of age), self-selection rather than physical activity level may have contributed to the differences. When the sample was divided into sport participants or nonparticipants, the former had higher aerobic fitness, which did not change systematically with age, supporting the hypothesis that youngsters are more active because they have high aerobic fitness rather than the reverse (^{32}). Furthermore, participation in organized youth sports represented more than 20% of estimated total daily energy expenditure and 55% of estimated energy expenditure in moderate to vigorous activity by adolescent boys (^{18}). Finally, the activity classification as used in the present study led to a clear differentiation in peak V̇O_{2} values and also gains in peak V̇O_{2} during male adolescence (^{21}). These observations provide substantial support to the validity of the activity classification used in this study.

When incorporated into the multilevel analysis, physical activity had a significant independent effect on peak V̇O_{2} over and above effects associated with growth and maturation. In the present study, boys who were classified as inactive had peak V̇O_{2} values that were 49 mL·min^{−1} and 100 mL·min^{−1} less than boys classified as average and active, respectively. This contrasts the suggestion that peak V̇O_{2} was not independently affected by physical activity as estimated by heart rate indicators (^{4}). However, heart rate was monitored only over 3 d. In contrast, the present study as well as the study of Dutch adolescents used estimates of habitual physical activity and/or sport participation over more extended periods of time.

Available longitudinal data provide a unique resource, especially when advances in methods of analysis and/or novel questions emerge. The present study falls into this category. This study provides additional information on the development of aerobic power during male adolescence and adds to studies using the multilevel approach (^{4,7,15,23}). The present analysis has three unique features. First, the whole adolescent period is covered, 8–16 yr, using complete longitudinal data of a sufficiently large sample of nonathletic boys. Second, a powerful indicator of biological maturity (i.e., age at PHV, mathematically derived from individually fitted growth records) was used to align the peak V̇O_{2} data. Third, an indicator of physical activity based on five assessments was also introduced in the model.

In conclusion, this study demonstrates that individual growth patterns in scaled peak V̇O_{2} show considerable variation. Peak V̇O_{2} increases proportionally to body mass to the power k′ = 0.855 (or k′ = 0.78 when adjusted for biological maturity). When the confounding influence of body weight on peak V̇O_{2} is accounted for, level of habitual physical activity and its interaction with biological maturity significantly affects peak V̇O_{2} development.

Address for correspondence: Gaston Beunen, Ph.D., Department of Sport and Movement Sciences, Faculty of Physical Education and Physiotherapy, K.U. Leuven, Tervuursevest 101, B3001 Leuven, Belgium; E-mail: gaston.beunen@flok.kuleuven.ac.be.

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**Keywords:**

AEROBIC POWER; OXYGEN UPTAKE; ALLOMETRY; PHYSICAL ACTIVITY; GROWTH SPURT; ADOLESCENCE; PUBERTY; LONGITUDINAL STUDY