Actually, muscle strength norms are mostly expressed in relation to chronological age [14]. However, as pointed out by Rauch et al. [2], chronological age may be a poor variable to account for muscle strength because physical development, hence body size, is a substantial determinant of strength. To overcome the limited value of chronological age for reliably predicting strength, several predictive equations have been developed using additional variables, e.g. weight, height, body mass index (BMI) and sex [3,4,15]. Again, these predictive models mainly concern grip strength.

Even for other muscle functions, strength values are generally presented as linear forces in kg or N. However, the actions of flexor and extensor muscles around joints generally result in angular movements. Thus, it seems more appropriate to measure flexion and extension torques rather than linear forces. Torque is computed as the product between the length of the lever arm (the distance between the rotation axis and the application point of the force) and the force generated perpendicularly to this lever arm. In children, torque measurement is particularly relevant because lever arm length increases during growth [4].

Fifty-six children attended a second testing session to evaluate a possible learning effect. The median time between the two sessions was 42days (2 – 85). No learning effect was detected: the differences between the results at the first and second visits were not significant for any of the muscle functions tested (all p>0.05). Figure ​Figure11 presents Bland-Altman plots for each muscle function for both non-dominant and dominant hand sides. The differences between visit 1 and visit 2 plotted versus the mean torque for visit 1 and 2 were normally distributed and no trends were identified concerning the mean test and retest measures. The mean strength, the mean and SD of the differences between visit 1 and visit 2, the SEM, the relative SEM, the ICC and the 95%CI for ICC for each muscle function are shown in Table ​Table2.2. The relative SEM was about 10 to 15% depending on the muscle function. As the results obtained during the two sessions were not significantly different, the values recorded during the first visit were used to compute the predictive equations.

The strength values for handgrip (p<0.001), elbow flexion (p<0.001), knee flexion (p=0.044) and knee extension (p<0.001) were all greater for the dominant than the contralateral side. This was not the case for elbow extension although a trend was observed (p=0.245). The same was true for each sex separately, except for knee flexion for which only boys presented a greater strength on the dominant hand side (p=0.020).

The characteristics of the predictive model based on height, sex and age for the log transform of MVIC are given in Table ​Table33 for each muscle function. As an alternative model, exponential regression may also be used to predict MVIC with height as the single explanatory variable (Table ​(Table4).4). Figure ​Figure22 presents the strength measured for the different muscle functions as a function of height, which was the most significant explanatory variable for strength as assessed by multiple linear regression. The strength for all muscle functions did not differ between girls and boys of the same height. Both types of model gave similar adjusted coefficients of determination (see Tables3 and ​and4)4) although the Akaike information criteria were slightly better for the model based on height, sex and age.

In previous studies, grip strength has been more extensively studied than other muscle functions. The strength values we report here are consistent with previous work in paediatrics for handgrip [2] and for other muscle functions tested by handheld dynamometry [4]. Child muscle strength has rarely been reported as torque, although torque is a more appropriate measure than linear force. Indeed, for the same torque, generated by the muscle during a maximal contraction for instance, the linear force depends on the length of the lever arm, defined as the distance between the application point of force and the rotation axis of the joint. Measuring the torque rather than linear force is therefore particularly important for longitudinal studies involving growing children.

The literature provides evidence of substantial inter-individual variability concerning strength expressed with respect to the age. A significant part of this variability may be due to differences in height among children in a given age class. Indeed, Niempoog et al. [15] recently indicated that “chronological age alone does not reflect the pubertal stage that leads to different physical performance”. Height was found to be strongly correlated to grip strength in several studies [15,17]. Our study suggests that height is a major explanatory variable also for strength of muscle functions other than handgrip and is in line with Parker et al. [18]. The strong correlations between the different muscle functions are a clue to a global effect of stature on the whole body muscle strength. We found that girls and boys cannot be overall distinguished according to strength when related to height, at least before 17years of age. A strong relationship between muscle strength and height has previously been reported for pre-pubertal boys and girls [4,19] Also, the study of Newman et al. [20], implies that grip strength is similar in boys and girls under, approximately, 160cm of height. Thus below 160cm, norms for girls and boys appear to be the same when using height as the single explanatory variable. Sartorio et al. [21] observed that “gender differences disappeared when grip strength is normalized for fat free mass in children from 5 to 15”. Since height is closely correlated to lean body mass [22,23], it is not surprising that height explains a large part of the variability between individuals. Interestingly, the relationship between strength and height was accurately described by an exponential model, consistent with the observation that "lean body mass is an exponential function of height" [22].

The exponential model was also applied to linear force. Compared to torque-height relations, the mean adjusted R² decreased from 0.825 ±0.035 down to 0.686 ±0.080 due to a larger inter-individual variability that can probably be explained by a lever arm effect.

We found that the dominant hand side was significantly stronger than non-dominant hand side for both sexes for handgrip, elbow flexion (in accordance for both sexes with Bäckman et al. [6]) and knee extension (only for boys in the same study). Concerning knee flexion, we found that only boys were stronger on the dominant hand side, in contrast with Bäckman et al. [6] who found this result only for girls. However, the effect of dominance for this muscle function was weak: in our study, the difference between the two sides was only 1Nm for a mean strength of about 40Nm.

Results did not differ between the test session and the retest session. It suggests that the QMT method can be used immediately, without preliminary training, for children in clinical trials. However, a habituation session may be useful to accustom children to the assessment procedures and make them feel confident with the evaluator.

ICCs are relative measures of reliability that have been used in many studies. They are generally good to excellent, as in the present study, particularly because the range of the measures is generally large. However, the assessment of reliability should not be limited to the use of ICC. Standard error of measurements (SEM) is a measure of agreement and serves as an index of absolute reliability; it has been much less widely used for evaluations of the performance of strength assessment techniques. The SEM for handgrip strength was about 20N in our study, while Moleenar et al. [24] reported a SEM of about 11N. The difference may be due to the larger age range, hence the larger range of strengths, of the children in our study. Indeed, when normalized to the mean of the measurements, the relative SEMs for the two studies are similar (10% and 9%, respectively). Meldrum et al. [25] used the same QMT measurement system with adults, and the standard error of the difference between test and retest reported can be used to compute the relative SEM: the relative SEM was between 3.9 and 12.8% in adults, to be compared to 9.8 to 15.1% for children in our study. This suggests lower reliability of strength measurement in children than adults possibly due to their poorer concentration or motivation through successive visits. However, strength measurement reliability has not yet been formally compared between children and adults.

As underlined by Jaric [26] in the field of sports medicine, "the primary goal of strength testing has often been to assess the objective value of muscle function independent of possible confounding factors". This is all the more true in the clinical field when the aim is to evaluate neuromuscular involvement in a disease. Moreover, when considering children, early or late maturation needs to be taken into account due to the direct link between body stature and muscle strength. This connection seems also to apply to adults as recently demonstrated by the close relationship between hand circumference, as an indicator of body stature, and grip strength [27].

In this study, we used a paediatric population aged from 5 to 17years to develop models to predict handgrip strength and elbow and knee flexion and extension torque. Several authors have reported strong correlations between strength and height and have proposed models linking the two variables [2,17,19]. Similarly, Van den Beld et al. [3] observed that "height proved to be a better predictor for handgrip strength than age in children aged 4–11years".

Our paediatric population counted a rather small number of children and was not necessarily representative of the general population of French children. Reliability was assessed by several indicators. First, there are limitations to using ICC, particularly its interpretation when the data include large inter-individual variability, which is the case for groups of children covering a wide range of growth/maturation stages. In such situations, ICC is only a rough indicator of reproducibility. Second, standard error of measurement (SEM) was used to quantify absolute agreement between test and retest values. Although our results indicate a satisfactory reproducibility between test and re-test results, some children were clearly less motivated during the second evaluation visit than the first. This behaviour could have led to an overestimation of the SEM. This also indicates that evaluation sessions for children should not be complicated, boring or long such that motivation and attention are maintained.