Elbow Flexion and Extension Strength Relative to Body or Muscle Size in Children


Medicine & Science in Sports & Exercise: November 2004 - Volume 36 - Issue 11 - pp 1977-1984
Applied Sciences: Physical Fitness and Performance

Purpose: The purpose of this study was to examine gender- and age-related differences in elbow flexion and extension strength in children, when linear size measurements and actual measurements of muscle size were used as explanatory variables in a multilevel model.

Methods: Thirty-seven children participated in a 3-yr longitudinal study (18 boys and 19 girls). The average age ± SD at the first test occasion was 13.0 ± 0.3 yr. Stature, arm length, isokinetic concentric and isometric elbow extension and flexion torques, and MRI-determined elbow flexor and extensor muscle cross-sectional areas (CSAs) were assessed annually. Multilevel modeling was used to describe the relationship between the measured torques and body/muscle size variables, incorporating age, age by gender, and gender as additional explanatory variables.

Results: When muscle CSA was included in the static and dynamic torque multilevel models, gender differences in strength were nonsignificant. In contrast, use of stature or arm length alone, suggested gender differences in strength that could not be explained by differences in body size. All torque measures were best explained by inclusion of muscle CSA and a linear dimension in the models. Age also explained additional variance in torque, but the influence of age was action and muscle specific.

Conclusion: Use of only linear dimensions rather than muscle CSA to account for differences in size may have clouded our understanding of strength development in children.

1Department of Sport and Exercise Science, University of Portsmouth, Portsmouth, UNITED KINGDOM; 2School of Sport and Health Sciences, University of Exeter, Exeter, UNITED KINGDOM; and 3Somerset MRI Centre, Bridgwater, Somerset, UNITED KINGDOM.

Address for correspondence: Dr. Neil Armstrong, The Children’s Health and Exercise Research Centre, School of Sport and Health Sciences, University of Exeter, St Luke’s Campus, Heavitree Road, Exeter, EX1 2LU, UK; Email: N.Armstrong@exeter.ac.uk.

Submitted for publication August 2003.

Accepted for publication July 2004.

This study was supported by a grant from the Darlington Trust.

Article Outline

Differences in upper body strength between boys and girls become most apparent during and following the male adolescent growth spurt. During this time, higher velocities of growth are observed in both stature and body mass in males compared to females (8). The development of lean body mass in relation to total body mass, and the relative distribution of muscle tissue within the body, is also known to differ between genders (17). Overall accretion of muscle is superior in males, with a higher proportion distributed in the upper body compared to females (26).

Despite these recognized gender differences in upper extremity muscle and strength development, the exact mechanisms underpinning strength differences are not understood. Given that skeletal muscle is responsible for the generation of force, which, acting via the skeletal system will result in muscular torques, the link between muscle development and “strength” would be expected to be significant. Therefore, unsurprisingly, significant correlations between elbow flexion and extension strength and muscle cross-sectional area, fat-free mass, and lean upper limb volume have been observed (3,11,23).

The uncertainty resides in the degree to which muscle size accounts for differences in strength. If differences in strength persist despite consideration of muscle size, other factors may be sought to further explain strength variation. For example, differences in muscle quality and/or levels of neural drive could partly explain differences in the ability to generate force per unit of cross-sectional area (specific tension).

Our understanding of gender- and age-related differences in strength may have been clouded by the use of global body size measures (such as stature, mass and lean body mass) and local linear dimensions (such as limb segment length), as opposed to direct measurement of muscle size to adjust strength measures (21,22,24). To consider differences in muscle size, cross-sectional areas (CSA) of nonweight-bearing muscles are often assumed to be proportional to the square of a linear dimension (stature, segment length), based on the theory of geometric similarity described by Asmussen (1). A linear dimension cubed is deemed to reflect development of weight-bearing muscles (21,22). However, although growth of the long bones and weight bearing activities are mechanical factors known to stimulate muscle development, global size measures may not parallel localized segmental growth and maturation (7,17). In addition, it is uncertain whether even limb segment lengths can be deemed to reflect local muscle growth. Round et al. (24) suggested that instead of stature, the length of the humerus may be a more appropriate variable to include in models when examining biceps development. However, in contrast to the use of limb lengths, only direct measurement of muscle size would be expected to be able to identify differential growth of synergist muscle groups, such as elbow flexors versus extensors.

There are no known longitudinal studies that have simultaneously tracked static and dynamic elbow strength changes and muscle size changes (using direct measurement) across childhood and adolescence. Cross-sectional studies (14), for example, have examined elbow flexor and extensor strength and CSA. However, the measurement of muscle CSA at a single site may or may not effect conclusions with regard to the role of muscle size in strength capability (6). Cross-sectional studies can also only characterize average developmental patterns displayed by children differing in age, gender, and maturity. They cannot describe the variation in the timing and magnitude of changes that occurs between and within individuals in growth and performance (25).

Multilevel modeling is a technique that can be applied to longitudinal data to examine the contribution of explanatory variables (i.e., gender, age, and maturity) to a performance variable, once differences in body size have been taken into account (21,24,28). With this approach, both the mean population response, across individuals and/or test occasions, and the variation of individual responses, around the mean curve, can be assessed (28). Unlike many statistical repeated measures analyses, multilevel modeling allows for unbalanced data sets (resulting, for example, from dropout or missed measurements over the course of a longitudinal study) and also unequal times between observations. As summarized by Goldstein et al. (9), this form of analysis enables us to “combine data from individuals with very different measurement patterns, some of whom may only have been measured once and some who have been measured several times at irregular intervals.” Multilevel modeling would therefore enable interpretation of gender- and age-related differences in strength after adjustment for the effects of body or muscle size.

The aim of this longitudinal study was to assess the ability of linear and muscle size measurements to explain gender- and age-related differences in static and dynamic strength. It was hypothesized that gender- and age-related differences in static and dynamic elbow flexion and extension strength would be reduced following adjustment of torques for muscle size, compared to adjustment using only linear size measures.

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Thirty-seven children (18 boys and 19 girls, all recruited from local secondary schools) volunteered to participate in a 3-yr longitudinal study. Following institutional ethical approval, written informed consent was provided by all of the children and a parent or guardian, after details of the study had been explained in a year assembly and subsequently in a letter sent home. The average age ± SD at the start of the study was 13.0 ± 0.3 yr. Subject numbers and characteristics at each test occasion are presented in Table 1. Seventeen boys and 14 girls completed all 3 yr of the study, one boy and four girls completed two yr of the study, and one girl only attended one of the test occasions. The data presented in Table 1 only include details of the children for which magnetic resonance imaging (MRI) scans were analyzed. Dropout and availability for MRI scanning meant that the children included in the analyses varied from year to year. Nine boys and eight girls were scanned every year, eight boys and six girls missed one scanning session, and one boy and five girls were only scanned on one occasion.

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Once a year for 3 yr, the children visited the laboratory for the determination of elbow flexor and extensor isokinetic (concentric) and isometric strength. Stature, body mass, and upper arm length (distance between the superior aspect of the acromian process and the olecranon process (18)) were also examined on this occasion. Stature and body mass were measured according to the techniques described by Weiner and Lourie (27), using a Holtain stadiometer (Crymych, Dyfed, UK) and calibrated beam scales (Weylux, UK), respectively. Upper arm length was measured with the subject standing and positioned according to the guidelines presented by Martin et al. (18), using a Harpenden anthropometer configured as a sliding beam caliper (Crymych, Dyfed, UK).

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Strength assessment.

Elbow flexion and extension strength tests were performed on a Biodex System 3 isokinetic dynamometer. Two different attachments were used depending on the length of the forearm and hand segment. The adult shoulder/elbow adapter, or the wrist adapter, was connected to the shoulder/elbow attachment for the children with longer and shorter limb lengths, respectively. Subjects were positioned with their upper arm placed on a limb support and resting approximately horizontally. The axis of rotation of the dynamometer was aligned with the lateral epicondyle of the humerus, while the elbow was flexed to approximately 1.57 rad. The joint range of motion was set to 1.75 rad, with zero representing elbow extension (forearm horizontal). The forearm was in a neutral (semipronated) position for all tests. Only the dominant arm (the limb associated with writing) was examined, with all subjects identified as right-hand dominant during the process of recruitment. Straps were used to stabilize the body during testing. Two shoulder straps, crossing over in front of the body, were used to hold the shoulders and trunk against the chair back. Hip movement was restricted by a waist strap, and the upper arm was secured to the limb support pad with a strap positioned superior to the cubital fossa.

The strength tests completed were three maximal voluntary concentric-concentric flexion and extension actions at 0.52 rad·s−1, and two maximal voluntary isometric actions at 1.57 rad (elbow flexion) and 0.17 rad (elbow extension), respectively. The children were habituated to the strength tests during the initial visit to the laboratory. This involved demonstration and practice of all actions until maximal efforts resulted in visually repeatable torque curves, and a torque plateau during isometric actions. Subjects were instructed to “push away” (elbow extension) or “pull toward” them (elbow flexion), and to keep the torque line displayed on the Biodex monitor “as high and as straight as possible” (isometric actions). For the isokinetic actions, subjects were instructed to move the dynamometer lever arm “as hard and as fast as possible.” After the practice period, the children rested for a minimum of 2 h before performing the actual recorded strength tests.

The isokinetic and isometric strength tests were separated by a minimum of 2 min rest, and always initiated from 1.75 rad of elbow flexion. Thirty seconds of rest were given between the two isometric actions of the same muscle group. The order of testing of the isometric actions was randomized, with a 30-s rest period separating flexion and extension actions. Verbal encouragement was provided throughout the isokinetic and isometric tests. All of the strength tests and arm length measures were performed by the same examiner over the 3-yr study period. All dynamic torque data were filtered, windowed, and gravity corrected. The peak torque across the three isokinetic concentric repetitions and the maximum isometric torque occurring on the torque plateau were used in subsequent analyses.

The reliability of the strength and arm length measurements was assessed on 10 boys (mean ± SD: age, 9.8 ± 0.2 yr; mass, 39.0 ± 11.2 kg; stature, 1.44 ± 0.07 m). All procedures, which were identical to the current study, were completed on two occasions separated by approximately one week.

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Assessment of muscle CSA.

In addition to completion of the strength tests, the children visited a private MRI facility for the determination of elbow flexor and extensor muscle CSA. The average time between completion of the strength tests and the date of scanning was 3–4 wk. Subjects lay supine with arms resting extended and by their sides, within the whole body core of a magnetic resonance imager (Philips 0.5-T Powertrak 1000 system). Ten axial slices (T1 turbo spin echo; echo time, 14 ms; repetition time, 794 ms; field of view, 300 mm; matrix, 192 × 256; slice thickness, 12 mm) were taken along the length of the arm up to the head of the humerus, with the initial slice positioned through the medial and lateral epicondyles of the humerus. The slice gap varied between and within subjects across test occasions to limit the slice number to 10.

An infrared mouse and gridded mouse mat were used to trace around the borders of the biceps, brachialis, brachioradialis, pronator teres, and triceps muscles for each 12-mm axial slice. The Philips Gyroview package calculated the area enclosed by each trace. This represented the muscle CSA in a given slice. Total elbow flexor CSA was estimated by summing biceps, brachialis, brachioradialis, and pronator teres CSAs in each slice. The maximal total elbow flexor CSA across the slices was used to represent the elbow flexor CSA. Similarly, the maximal CSA of the triceps across slices was deemed to represent elbow extensor CSA. The reliability of the MRI scan analysis for estimation of muscle CSA was assessed by performing these complete analyses 10 times for one subject. Since there were 10 scans per subject, this represented approximately 100 analyses of the muscle CSAs.

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Statistical analyses


The typical error of measurement expressed as a coefficient of variation was used to estimate the reliability of the arm length and static and dynamic torque measures (10). The reliability of the muscle CSA measurements was estimated by calculating the coefficient of variation after 10 trials (SD/mean × 100).

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Multilevel modeling.

MlwiN Multilevel modeling software (12) was used to examine the relationship between isometric and isokinetic concentric flexion and extension torques and explanatory variables. This enabled significant explanatory variables to be identified, and also the variation between individuals (level-2 variation) and within individuals between test occasions (level-1 variation) to be quantified where appropriate. The model that was explored initially was based upon that derived by Nevill and Holder (21):

where k is an exponent, α is the intercept term, b is the age parameter, ϵ represents the multiplicative error term, and the “i” and “j” subscripts represent level-1 and level-2 variation, respectively.

The model was linearized using log transformation so that the regression parameters could be solved:

The model parameters can either be fixed, or set to vary randomly at level 1, level 2, or level 1 and 2. A fixed parameter estimate represents the mean population response, while random terms describe the variation about this mean response. If an explanatory variable is allowed to vary randomly, variation in the slope of individual lines is provided. All of the parameters were initially fixed except the constant (intercept term, α) and the age parameter (denoted by the “j” subscript), which were allowed to vary randomly at level 2 (between subjects). The multiplicative error term (ϵ) also varied randomly both between test occasions (as denoted by the “i” level-1 subscript) and level 2. Age was centered on the mean age across test occasions, 14.1 yr. Additional explanatory variables entered into the models were gender, and an age by gender (age × gender) interaction. Gender was entered as an indicator variable, where boys = 0 and girls = 1. This allowed the girls’ parameter estimate to vary around the baseline estimate of the boys. The age by gender interaction enabled examination of whether the development of torque with age differed between boys and girls once body size had been taken into account.

Separate models using stature (Model 1), arm length (Model 2), and muscle CSA (Model 3) size variables enabled comparison of gender- and age-related torque development following adjustment for these measures. In the fourth model, all of the size parameters, along with age, gender, and interaction effects were entered to explore which combination of variables significantly enhanced explanation of static and dynamic torque variance. The significance of each explanatory variable was determined from both examination of the parameter estimate and its associated standard error, and the loglikelihood (5). If the parameter estimate exceeded its standard error by a factor of two, it was significantly different from zero (P < 0.05). However, the addition of the explanatory variable to the model must also cause a significant change in the loglikelihood—also known as the deviance statistic. The smaller the loglikelihood, the better the model fit and, therefore, the prediction of the torque measurements. If explanatory variables are entered into a model one at a time, the decrease in −2·loglikelihood must exceed 3.84 (the chi-square critical value for 1 degree of freedom) to be significant at the level P < 0.05. If the fixed parameter estimate for the age explanatory variable was significant, the level-2 random variation was then examined to determine its significance. If an explanatory variable did not significantly contribute to the prediction of the torque measure, it was removed from the model.

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Subject characteristics.

All body size, muscle size, and torque measures at each test occasion are presented for boys and girls in Table 1.

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The typical errors of measurement expressed as coefficients of variation were 1.1% (arm length), 14.5% (concentric elbow flexion), 15.2% (concentric elbow extension), 6.6% (isometric elbow flexion at 1.57 rad), and 13.1% (isometric elbow extension at 0.17 rad). These reliability estimates yielded error in the arm length measurement of ±0.3 cm, and error in the torque measurements ranging from ±1 N·m to ±4 N·m. Coefficients of variation for the muscle CSA measurements did not exceed 3.3% (total elbow flexor CSA) and 1.9% (elbow extensor CSA).

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Gender-related differences in strength.

Tables 2, 3 and 5 illustrate that gender differences in isokinetic concentric elbow flexion and extension torque and isometric elbow extension torque are apparent when only stature or arm length alone is used to control for body size (Models 1 and 2). In addition, a significant age × gender interaction was obtained in the isokinetic concentric elbow flexion models after adjustment of the torques for stature or arm length (Table 2, Models 1 and 2). All significant gender effects became nonsignificant when measurements of muscle size were incorporated into the multilevel models (Tables 2, 3 and 5, Models 3 and 4). In contrast to the other strength measures, gender and the age × gender interaction were nonsignificant explanatory variables in Models 1 and 2 for isometric elbow flexion torque development (Table 4).

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Age-related differences in strength.

Age did not significantly enhance the explanation of torque above the variance explained by the body size measures for isokinetic concentric elbow extension torque or isometric elbow flexion torque (Tables 3 and 4, Models 1–4). For the remaining torque measurements (Tables 2 and 5), age was a significant explanatory variable in all models, and the inclusion of CSA (Models 3 and 4) did not reduce the significance of age (ratio of age parameter estimate to its standard error).

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Comparison of torque models.

For all models there was level-1 and level-2 “random” variation for the constant (intercept) term. Compared to the variation in Models 1–3, the level-1 and/or level-2 variation in Model 4 was lower. Model 3 did not consistently lead to a reduction in the level-1 or -2 variance across the torque measures. When age was allowed to vary randomly at level 2, no significant variation was observed between individuals in the growth rates.

Adjustment of isokinetic torques using muscle CSA (Tables 2 and 3, Model 3) improved the fit of the multilevel models (as represented by the smaller −2·loglikelihood value), compared to use of stature or arm length. This was not the case for the isometric models. In fact, when only muscle CSA was used to adjust isometric elbow flexion torque, the fit was inferior to the models using stature or arm length (Table 4, Models 1–3). All torques were best explained when muscle CSA and a linear measure were included in the model (Model 4).

The variables that explained a significant amount of torque variance (Model 4) were action and muscle specific. Along with muscle CSA, stature improved the explanation of all torques, with the exception of isometric elbow flexion, where arm length rendered stature nonsignificant. Age enhanced the explanation of isokinetic elbow flexion and isometric elbow extension torques, but not isokinetic elbow extension or isometric elbow flexion torque.

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The results of this study demonstrate that interpretations of gender differences in torque differ when actual measures of muscle CSA, as opposed to linear measures, are used to adjust elbow flexion and extension torques. All significant gender and age × gender effects were rendered nonsignificant when muscle size was entered into the torque models. The significance of the age explanatory variable was not influenced by the body size measure included in the multilevel models.

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Gender differences in the development of isokinetic torque relative to body or muscle size.

Models 1 and 2 in Tables 2 and 3 indicate that differences in stature or arm length, or inferred muscle size based on linear dimension (2), were not sufficient to explain gender differences and gender interaction effects (the latter effect was only significant for concentric isokinetic elbow flexion). Thus other factors would be sought to explain the lower strength capability of the girls relative to the boys. In contrast, when muscle CSA was used to predict these dynamic torque measures, all significant gender and age × gender interaction effects were rendered nonsignificant. This suggested that gender differences in concentric isokinetic strength are primarily the result of variation in the amount of contractile material. There are no longitudinal studies reporting concentric isokinetic elbow torque and muscle CSA data for both boys and girls with which to compare the findings of this study. However, the results highlight that use of linear dimensions alone may provide a different interpretation of gender differences in concentric isokinetic strength, compared to examination of actual muscle size.

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Gender differences in the development of isometric torque relative to body or muscle size.

Similar to the isokinetic torque models, the finding that differences in isometric extension torque persist after adjustment for stature or arm length would suggest that factors other than size differences contribute to the difference in isometric strength between boys and girls (Table 5, Models 1 and 2). Gender effects were nonsignificant for all models for isometric elbow flexion torque (Table 4). This latter finding contrasts with the results of Round et al. (24), who also used multilevel modeling to examine the development of isometric elbow flexion strength in 100 boys and girls aged between 8 and 17 yr. When stature and body mass were taken into account, significant gender and age × gender interaction parameter estimates were obtained. It should be emphasized that although Round et al. (24) also examined isometric elbow flexion with the elbow in 1.57 rad of flexion, the test equipment (custom-made dynamometer vs Biodex isokinetic dynamometer) and the forearm position (supinated vs neutral) limits direct comparison of study findings. In addition, these authors also included body mass in their model, which may alter the data interpretation because of possible collinearity between mass and stature (2). The use of body mass to explain development of the elbow musculature should also be questioned.

Round et al. (24) hypothesized that testosterone may be an additional factor contributing to the remaining gender difference in strength. However, when this hormone was incorporated into the multilevel model, significant gender differences in strength were still apparent. It was concluded that “the large upper limb girdle and the resultant disproportionate strength of the biceps in males (in relation to body size) may be seen, therefore, as another example of a secondary sexual characteristic.” This finding led Round et al. to suggest that part of the reason for the unexplained gender differences in strength (once size had been considered) may have been the use of stature rather than upper arm length (which would be the local skeletal measurement). In the current study, however, the predictors of torque were the same regardless of whether stature or upper arm length were used in the multilevel models (Tables 2 to 5 in comparison with Models 1 and 2).

The fact that boys were stronger than girls after differences in stature and mass were considered led Round et al. (24) to suggest that boys are able to produce more force or torque per unit size compared to girls. This finding is supported by other studies that have used global size measures to correct arm strength. For example, Kemper et al. (15) described how after 12 yr of age, arm pull strength per unit of body mass was lower in girls compared to boys. Parker et al. (22) used allometric scaling to examine the relationship between changes in stature and changes in isometric flexion strength in a cross-sectional study, examining children aged 5 to 17 yr. After 13 yr of age, the stature exponents for boys were greater than for the girls (2.93 and 1.49, respectively). This would indicate that for a given increase in size, strength increases more in boys than in girls. However, cross-sectional studies that have directly assessed muscle CSA and strength in boys and girls and adult males and females do not support the notion that males are stronger per unit of muscle size (11,13). This discrepancy may reflect the differential growth of limb segments relative to stature, and the fact that growth of the long bones is not the only stimulus for muscle growth. For example, hormones such as testosterone, insulin-like growth factor-1, and growth hormone may promote muscle growth by direct action on skeletal muscle androgen receptors, or indirect action via neurotransmitters or interactions with other hormones (19). Muscle function (antigravity/gravity assisted) and exercise intensity also influence muscle fiber hypertrophy (17). In the present study, the mean torque and muscle cross-sectional area data suggest differences in torque per CSA between boys and girls, particularly at test occasion 3 (Table 1). However, this interpretation is based on the cross-sectional treatment of longitudinal data. The multilevel models illustrated that gender differences in torques were completely explained by differences in muscle size.

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Age and isometric and isokinetic torque development in children.

Once differences in muscle CSA had been accounted for, age explained a significant amount of additional variance for isometric elbow extension and isokinetic elbow flexion torques. None of the age terms were negative, indicating a positive effect of age on torque development in both boys and girls. This is in contrast to the findings of Round et al. (24), who observed a negative age term for the girls, suggesting that as girls got older, they became weaker relative to body size. This may be explained by the fact that the body mass and stature terms used in their models do not allow for changes in body composition to be considered. The greater increase in percentage body fat with age in girls compared to boys would therefore explain the negative age term.

Since maturation was not assessed in the current study, it is possible that the significance of age may partly reflect shared variance with maturation. Age has, however, been observed to exert an effect on strength independently from stage of maturity (4). Asmussen (1) suggested that maturation of the CNS with age may cause improvement of static and dynamic motor skill performance; however, the exact mechanisms by which CNS maturation influences strength development with age remain to be elucidated.

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Optimal predictors of isometric and isokinetic torque development in children.

Although the modeling of strength using linear dimensions alone yielded a different interpretation of gender differences in torque, the inclusion of a linear dimension in addition to muscle CSA enhanced the explanation of torque variance (Tables 2–5, Model 4). The mechanism by which linear dimensions influence joint torque is unclear. Stature or segment lengths have been deemed to crudely reflect differences in moment arm lengths (3). Since moment arm lengths (along with muscular force) contribute to joint torque, any relationship between muscle moment arms and linear dimensions may enhance torque prediction. However, anthropometric predictors of moment arms lengths may be muscle-specific, and the relationships between these measures remain to be elucidated (20). It is uncertain why the global linear dimension (stature) was superior to arm length in predicting torque in three of the four “optimal variable” models (Model 4). This requires further study.

The −2·loglikelihood values indicated that the isometric models were not predicted as well as the isokinetic models, implying that more specific variables may need to be included in the isometric analyses. These factors may relate to motor unit activation, musculotendinous stiffness, blood flow dynamics, and maturation (16,29).

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This study has highlighted the limitations of using only global and local linear size measures to adjust strength data during childhood and adolescence. When actual measurements of muscle CSA are used to model strength changes, gender differences in strength during growth and maturation are removed. This suggests that the greater strength capability of boys is primarily caused by their greater muscle development. The significance of age as an explanatory variable differed between muscle group (flexors vs extensors) and strength test (isometric vs slow isokinetic concentric). Inclusion of muscle CSA as opposed to linear size measures did not influence the significance of the age effect. All elbow flexion and extension torques were best predicted by inclusion of muscle CSA and a linear size measure (stature of arm length) in the multilevel model.

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