ABSTRACT

Children perform cyclic motor tasks less efficiently than adults; however, the mechanisms underlying such differences are not fully understood. One mechanism that may contribute to these age-related differences is a differential contribution of muscles and tendons to a given muscle–tendon unit (MTU) excursion. The aims of this study were to (i) compare muscle and tendon excursion between children and adults performing vertical hopping, and (ii) determine whether children and adults choose a hopping frequency that maximizes movement efficiency, based on the utilization of energy-saving mechanisms. Twelve children (8.8±0.3 years) and 12 adults (26.0±2.1 years) performed 20 s of two-legged hopping at a self-selected frequency and at 1.33, 2.00, 2.67 and 3.33 Hz. Gastrocnemius medialis MTU excursion was estimated from kinematic data and muscle and tendon excursions were derived using a combination of 3D-motion capture and ultrasonography. Optimum hopping frequency was determined as the frequency that maximized surrogate measures of elastic energy storage potential of the tendon and minimized muscle excursion. Adults presented a significantly greater potential for elastic energy storage in combination with lower muscle excursion than children at their self-selected frequency, suggesting that children do not utilize these energy-saving mechanisms as effectively as adults. However, tendon elastic energy storage was maximized and muscle excursion minimized at the preferred frequency in both children and adults, indicating that children may select their preferred hopping frequency based on the same criteria as adults. These findings increase our understanding of the mechanisms contributing to the higher energy cost of movement performance in children, and have implications for the interpretation of age-related differences in complex task performance.

INTRODUCTION

Locomotor efficiency is influenced by a number of biomechanical and physiological mechanisms, including basal metabolic rate (Rowland and Green, 1988), inter- and intra-muscular coordination (Ballaz et al., 2010), mechanical muscular efficiency (Roberts and Scales, 2002) and the reutilization of stored elastic energy (Fukunaga et al., 2001). In ‘bouncing’ activities such as running and hopping (Cavagna et al., 1977), efficient locomotion is thought to be achieved by capitalizing on the system's energy storage–recovery mechanism (Cavagna et al., 1964). This mechanism is dependent upon the dynamic interaction of the in-series muscle and tendon, which is governed by the mechanical properties of the tendon and needs to be matched by appropriately timed and dosed muscle activations (Lichtwark and Wilson, 2005). It has been suggested that, during certain modes of locomotion, an optimum tendon stiffness allows the associated muscle fascicles to operate around their optimum force-producing length and at a low shortening velocity (Roberts and Scales, 2002), whilst the tendons lengthen and shorten considerably to allow for the muscle–tendon unit (MTU) length changes needed to meet the task requirements (Biewener et al., 1998; Witvrouw et al., 2007). The energy-saving implications of this partnership are twofold. First, the energy cost of producing mechanical work due to muscular contraction is directly related to the extent of muscle length change; therefore, the cost of tension development is relatively small for muscle fibres working at near-zero velocities (Hill, 1938). This is particularly advantageous for muscles operating close to their optimum length on the length–tension curve, as this further reduces the muscular contribution to the task by maximizing the muscle's force output for a given amount of neural activation. Second, the resistance provided by the contractile and passive elastic elements of the muscle during loading permits the tendon to behave like a spring to maximize energy conservation by capitalizing on the elastic stretch–recoil mechanism (Fukunaga et al., 2001). Previous studies have estimated that ∼6% of the total energy requirement of walking and ∼35% of that of running can be attributed to elastic energy storage and recoil of the Achilles tendon alone (Ker et al., 1987; Maganaris and Paul, 2002), demonstrating the importance of this mechanism.

Children demonstrate a higher metabolic cost of movement than adults (Schepens et al., 2004). Differences in a number of biomechanical, neurological and physiological mechanisms between children and adults have been identified as contributing to this greater energy cost (Rowland, 1996). The interaction between muscle mechanics and tendon deformation could also contribute to children's higher energy cost of movement, but has yet to be examined. Many of the mechanical and morphological properties of the muscle (Morse et al., 2008; O'Brien et al., 2010b) and tendon (O'Brien et al., 2010a; Waugh et al., 2012) change as a result of childhood growth; children are not only weaker but also have more compliant tendons as a result of dimensional and micro-structural differences that develop with maturation. As a result, it is possible that the ratio between muscle strength and tendon stiffness – which is normally well matched in adults (Muraoka et al., 2005; Waugh et al., 2012) – changes throughout childhood (Mersmann et al., 2014). Whilst compliant tendons store more elastic potential energy than stiff tendons under the same relative loading conditions (Cavagna et al., 1964; Ker et al., 1988), the associated muscle must undergo a greater length change as the tendon resists more of the stretch, unless different muscle activation strategies are used (Hoffrén et al., 2012; Lichtwark and Wilson, 2005). It is therefore possible that the differential development of muscle (both contractile and passive elements) and tendon mechanical properties during childhood would affect energy-saving mechanisms, which could impact on movement efficiency. The overall goal of this study was therefore to investigate dynamic muscle and tendon behaviours in children with a view to understanding the role of previously observed age-related differences in mechanical muscle–tendon properties in movement efficiency. The first specific aim was to determine whether age-related differences in muscle–tendon interaction exist between children and adults performing vertical hopping at a self-selected frequency, an exercise involving stretch–shortening cycles (SSCs). Based on differences in key muscle and tendon parameters, we hypothesized that energy-saving mechanisms would be less effectual in children than in adults.

Another relevant factor within the context of energy-saving mechanisms during SSC activities is the movement frequency. During bouncing activities, the human body can be modelled as a mass–spring system (Blickhan, 1989; Farley et al., 1991), the natural frequency of which is determined by its stiffness. It has been suggested that muscles act energetically optimally when their frequency of force application (i.e. movement frequency) matches the system's natural frequency (Sakuma et al., 2011; Takeshita et al., 2006) to cause resonance (greatest oscillation amplitude for least input effort). This also allows the tendon to behave as the primary spring to conserve energy and minimize metabolic expenditure (Cavanagh and Williams, 1982; Farley et al., 1991). As the elastic properties of muscles and tendons differ considerably between children and adults, the natural frequency of SSC movements may be expected to change during childhood with the increase in body mass associated with developmental growth. It is therefore of interest to identify whether children select a SSC frequency that coincides with the MTU resonant frequency. The second specific aim was therefore to determine whether children and adults choose a hopping frequency that maximizes muscle–tendon energy-saving mechanisms by examining muscle–tendon interactions and excursions at different hopping frequencies. As both young children (Jeng et al., 1997) and adults (Holt et al., 1991) demonstrate the ability to choose locomotive frequencies that minimize their physiological cost, we hypothesized that both children and adults would exhibit the greatest tendon excursion and lowest muscle excursion velocities at their self-selected hopping frequencies. Given that the natural frequency of a mass–spring system is dependent upon spring stiffness and mass, and considering that body mass to elastic tissue stiffness ratios differ between children and adults (Schepens et al., 1998), we also hypothesized differences in the preferred SSC frequency between these two populations.

MATERIALS AND METHODS

Ethical approval and participant information

Twelve children (5 boys and 7 girls, age 8.8±0.3 years, mass 31.4±8.8 kg, height 1.37±0.06 m) were recruited from a local school to participate in this study. Twelve adults (5 men, 7 women, age 26.0±2.1 years, mass 69.9±13.6 kg, height 1.72±0.09 m) provided an adult population for comparison purposes. All participants attended the laboratory on a single occasion for testing. Informed written assent and consent were provided by the children and their guardians, respectively. Adult participants provided informed written consent. Physical activity readiness questionnaires were completed for each child by their guardians to ensure all children were physically capable of participating in the study and to provide an indication of their current physical activity levels. All participants were required to be free from known orthopaedic, neuromuscular and musculoskeletal pathologies and were not involved in competitive sports. The biological immaturity of the child participants was confirmed using the regression equations of Mirwald et al. (2002). This study was approved by the institutional Ethics Committee, and the research was conducted in accordance with the guidelines set out in the Declaration of Helsinki.

Hopping protocol

Participants were instructed to carry out two-legged unshod vertical hopping with their hands placed on their hips at a freely chosen frequency (subsequently referred to as ‘preferred’ frequency). This trial was followed by hopping trials at four specific frequencies set by a metronome (1.33, 2.00, 2.67 and 3.33 Hz). These trials were randomized, with each trial separated by a 2 min rest. Hopping at the preferred frequency was always performed first to avoid the potential influence of the set frequency trials influencing the freely chosen frequency. Each trial was completed on a force platform (Kistler Instruments, Winterthur, Switzerland) for a 20 s period to allow for constant-frequency hopping to be captured. Ground reaction forces (GRFs) from the force platform were sampled at 1000 Hz and converted from analog signals via integrated amplifiers and software (Bioware v4.0, Kistler) to provide a digital output.

Reflective markers placed on the fifth metatarsal, proximal calcaneus (reference for Achilles insertion), lateral malleolus, lateral femoral epicondyle (reference for gastrocnemius origin), greater trochanter and ultrasound probe handle were tracked using a passive 3D motion capture system (Cortex v1.1, Motion Analysis, Santa Rosa, CA, USA). Marker coordinates were sampled at 100 Hz and were smoothed using a low-pass, zero-lag Butterworth filter at 7 Hz prior to down-sampling.

Determination of muscle–tendon junction position

B-mode ultrasonography was used to image the gastrocnemius medialis (GM) muscle–tendon junction (MTJ) in the sagittal plane. The position of the GM MTJ was visualized 1–2 cm medial to the inter-muscular septum separating the two gastrocnemius heads with a 45 mm linear array probe (Megas GPX, Esaote, Italy; 10 MHz transducer scanning). Once the scanning probe was orientated to clearly display both the separation between the aponeuroses of the GM and soleus muscles as well as the GM MTJ, the ultrasound probe was secured to the skin surface using a custom-made foam cast and combination of zinc oxide tape and elasticated bandages. Ultrasound images were digitally captured at 50 frames s−1 (ADVC-55, Grass Valley, France). The 2D position of the GM MTJ was manually identified in each frame (Peak MOTUS digitizing software, Vicon, Oxford, UK). An echo-absorptive strip placed on the skin and visible on the ultrasound display was used to identify probe movement relative to the skin and enabled probe movement to be accounted for in calculations of tendon length (Fig. 1B). Position data were low-pass filtered using a fourth-order, zero-lag Butterworth filter with a 5 Hz cut-off frequency.

Fig. 1.

Experimental setup for measuring muscle–tendon unit (MTU) and tendon length changes. (A) MTU length changes were estimated from 3D motion capture marker coordinates (open circles). MTJ location was made in reference to the ultrasound scanning interface mid-line. Echoabsorptive tape provided a reference for probe movement relative to the skin. (B) Schematic diagram of the transformation of the 2D ultrasound reference frame (x2, z2) into the 3D motion capture reference system (x1, z1) using the coordinates of the scanning interface mid-line in each reference system.

Fig. 1.

Experimental setup for measuring muscle–tendon unit (MTU) and tendon length changes. (A) MTU length changes were estimated from 3D motion capture marker coordinates (open circles). MTJ location was made in reference to the ultrasound scanning interface mid-line. Echoabsorptive tape provided a reference for probe movement relative to the skin. (B) Schematic diagram of the transformation of the 2D ultrasound reference frame (x2, z2) into the 3D motion capture reference system (x1, z1) using the coordinates of the scanning interface mid-line in each reference system.

3D marker coordinates and ultrasound video data were collected synchronously through the motion capture system using an analog trigger sent to both devices (Stimulator DS7A, Digitimer Ltd, Hertfordshire, UK). Using the coordinates of two reflective markers positioned along the mid-line of the ultrasonography probe handle face (perpendicular to the scanning interface) whose centroids were located at known distances from the probe scanning interface, it was possible to extrapolate a 3D coordinate to represent the centre of the probe scanning interface, using the assumption that the markers and probe were a rigid body. As this coordinate is analogous to the mid-point of the ultrasound image x-axis (Fig. 1A), and the angle of the ultrasound image relative to the 3D motion capture reference frame is represented by the markers on the ultrasound probe handle, the ultrasound imaging plane could then be transformed into the 3D motion capture reference system using trigonometry and the law of cosines (Fig. 1B). This transformation allowed the position of the GM MTJ to be estimated within the 3D motion capture reference frame.

Calculation of muscle–tendon dynamics and descriptive hopping characteristics

Reference muscle, tendon and MTU lengths were calculated using the methods detailed below during quiet standing prior to each hopping trial. GM MTU length was defined as the distance from the origin of the GM to the insertion of the Achilles tendon. MTU excursion with respect to the reference position was derived from regression equations provided by Grieve et al. (1978) using subject-specific ankle and knee joint angles calculated from the filtered 3D marker coordinates. Tendon length was calculated as the linear distance between the calcaneus marker and the MTJ coordinates, and GM muscle belly length was calculated by subtracting tendon length from MTU length.

GRF data were synchronized with the motion capture data by identifying specific events within the hopping cycle (Lichtwark et al., 2007). GRF onset during the landing phase of each hop was defined as the point at which vertical force exceeded 2 standard deviations above the baseline; baseline was determined by averaging the force signal over a 100 ms period during the hop flight phase prior to landing. GRF onset by foot contact was defined as the point at which the vertical velocity of the 5th metatarsal marker switched from negative to positive. This method of synchronization was compared against hopping trials where an analog trigger signal (Digitimer, Welwyn Garden City, UK) was sent to all data-collecting equipment, and proved to be a reliable predictor for initial foot–ground contact.

One hop cycle was defined as the time between GRF onset during landing from one hop and the GRF onset of the subsequent hop after the corresponding flight phase. The average cycle duration of 10 consecutive hops was calculated to determine hopping frequency, ground contact and flight times, leg stiffness and mass–spring likeness in each trial. To describe mass–spring likeness, Pearson's correlation coefficients were computed between vertical centre of mass (COM) displacement (obtained by double integration of the ratio between vertical GRF and body mass) and the vertical component of the GRF during the ground contact phase. Absolute leg stiffness was derived as the ratio between peak GRF and the lowest COM position during the ground contact phase. To account for differences in body size, leg stiffness was normalized to body weight and leg length to provide a dimensionless measure. The ground contact phases (defined as the time between force onset and force offset) of six consecutive hops were used to average the differential muscle–tendon excursions as a function of MTU length change using a custom-written program (Matlab, Mathworks, Natick, MA, USA). Muscle, tendon and MTU excursions were normalized to shank length (measured from lateral femoral epicondyle to lateral malleolus). The area under the muscle and tendon's excursion–time curve was calculated in an effort to compare relative muscle–tendon contributions to MTU length change between groups and across frequencies. Based on the assumption that in-series muscle and tendon experience the same forces, these measures can be assumed to indicate the tendon's capacity for storing and releasing elastic energy and the muscle's mechanical contributions to the task. Muscle and tendon lengthening and shortening velocities were calculated from normalized excursions with respect to ground contact time; mean lengthening velocity was calculated as the average negative velocity, whilst mean shortening velocity was calculated as the average positive velocity.

Data analysis

All data were analysed using SPSS statistical software (IBM SPSS v22.0, IBM Corp., Armonk, NY, USA). To test the first hypothesis, we performed a MANOVA with group as the independent variable and preferred hopping frequency muscle and tendon excursion and muscle excursion velocities (shortening and lengthening) as the dependent variables. In case of significance, post hoc t-tests were performed for each dependent variable. To test the second hypothesis, we performed two MANOVAs (one for each age group) with hopping frequency as the independent variable. Dependent variables were the same as above. In case of significance, follow-up univariate ANOVA were performed with Bonferroni-corrected paired t-tests to locate the differences. In addition, we also performed a MANOVA with Bonferroni-corrected follow up t-tests to describe differences in descriptive hopping characteristics (frequency, mass–spring likeness, absolute and dimensionless leg stiffness, ground contact and flight times, hopping height to stature ratio) between children and adults at each hopping frequency.

RESULTS

Children and adults hopped at preferred frequencies of 2.39±0.21 and 2.17±0.41 Hz, respectively, which were not significantly different (P=0.177). Regarding the first hypothesis, that differences in muscle–tendon interaction and muscle velocity profiles would exist between children and adults hopping at their preferred frequency, a significant group effect was found (MANOVA Wilks' lambda=0.572; F3,20=4.985, P=0.01). Follow-up univariate tests indicated that muscle length changes relative to MTU length change were larger and relative tendon length changes were smaller in children when compared with adults (P=0.001; Figs 2 and 3A). Muscle shortening and lengthening velocities at this frequency did not differ between groups (P=0.764 and P=0.967, respectively; Table 1).

Fig. 2.

Relativemuscle–tendon contributions to MTU length change across frequencies. The areas under the tendon and muscle excursion curves are expressed as a percentage of the area under the MTU excursion curve. Data represent means±s.e.m (grey bars). Pref., preferred frequency. *P<0.05.

Fig. 2.

Relativemuscle–tendon contributions to MTU length change across frequencies. The areas under the tendon and muscle excursion curves are expressed as a percentage of the area under the MTU excursion curve. Data represent means±s.e.m (grey bars). Pref., preferred frequency. *P<0.05.

Fig. 3.

Normalized excursion and velocity profiles of MTU, tendon and muscle during two-legged hopping at different frequencies. Subjects hopped at 1.33, 2.00, 2.67 and 3.33 Hz and at their preferred frequency. (A) Excursion and (B) velocity profiles. MTU, solid line; tendon, long-dash line; and muscle, short-dash line.

Fig. 3.

Normalized excursion and velocity profiles of MTU, tendon and muscle during two-legged hopping at different frequencies. Subjects hopped at 1.33, 2.00, 2.67 and 3.33 Hz and at their preferred frequency. (A) Excursion and (B) velocity profiles. MTU, solid line; tendon, long-dash line; and muscle, short-dash line.

Table 1.

Peak muscle–tendon unit (MTU), tendon and muscle excursions and muscle shortening and lengthening velocities during the ground contact phase of hopping at different frequencies.

Peak muscle–tendon unit (MTU), tendon and muscle excursions and muscle shortening and lengthening velocities during the ground contact phase of hopping at different frequencies.
Peak muscle–tendon unit (MTU), tendon and muscle excursions and muscle shortening and lengthening velocities during the ground contact phase of hopping at different frequencies.

Regarding the second hypothesis, that children and adults choose a hopping frequency that maximizes tendon rather than muscle length change, the main effect for hopping frequency was significant for adults (Wilks' lambda=0.706; F4,8=4.585, P=0.004). Follow-up univariate ANOVA performed for each dependent variable of the adult data set revealed that the frequency effect was significant for all dependent variables (P=0.001–0.012). Bonferroni-corrected post hoc t-tests revealed that tendon excursion was greatest at the preferred hopping frequency and was significantly greater than that exhibited during 1.33 and 3.33 Hz hopping (P=0.025 and 0.042, respectively; Fig. 2). Correspondingly, muscle excursion was least at the preferred frequency and significantly greater at 1.33 and 3.33 Hz. Mean muscle shortening and lengthening excursion velocities were smallest at the preferred hopping frequency; however, only muscle lengthening velocity differed significantly between conditions: lengthening velocity at the preferred frequency was significantly lower than at 1.33 Hz (P=0.009) and tended to be greater at 1.33 Hz than at 2.67 and 3.33 Hz (P=0.077 and P=0.068, respectively; Fig. 3, Table 1). For children, the MANOVA did not achieve statistical significance (Wilks' lambda=0.646; F4,8=1.796, P=0.057); however, there was a clear tendency for muscle excursion to be smallest and tendon excursion to be largest during the preferred frequencies compared with the other frequencies (Fig. 2).

A significant effect of group was found for each MANOVA performed on the descriptive hopping characteristics at other frequencies. Descriptive hopping characteristics (means±s.d.) and statistical differences found in follow-up tests are given in Table 2. Both groups achieved hopping frequencies within 5% of that required for the metronome-set frequencies and were not statistically different for any hopping frequency between groups (P=0.480–0.897). Ground contact and flight times decreased with increasing hopping frequency; with the exception of adult flight time being significantly longer than that of children at 1.33 Hz (P=0.034), neither were statistically different between children and adults (P=0.054–0.672 and P=0.08–0.621, respectively). Similarly, there were no significant differences in hopping height normalized to subject height for any frequency examined (P=0.183–0.759). With the exception of 1.33 Hz, both children and adults behaved as mass–spring systems during preferred, 2.00, 2.67 and 3.33 Hz hopping, although adults more so at most frequencies (P=0.004–0.079). Both groups demonstrated similar normalized leg stiffness for preferred and 2.00 Hz hopping conditions (P=0.286 and 0.067, respectively), but children demonstrated significantly lower stiffness values for hopping at 1.33, 2.67 and 3.33 Hz (P<0.003).

Table 2.

Hopping frequency, ground contact and flight time, stature-normalized hopping height, absolute and body weight-normalized leg stiffness and mass–spring likeness

Hopping frequency, ground contact and flight time, stature-normalized hopping height, absolute and body weight-normalized leg stiffness and mass–spring likeness
Hopping frequency, ground contact and flight time, stature-normalized hopping height, absolute and body weight-normalized leg stiffness and mass–spring likeness

DISCUSSION

To our knowledge, this study is the first to examine MTU function and muscle–tendon interactions during a SSC task in pre-pubertal children, and it provides novel insights into possible mechanical contributions of the muscle and tendon to movement efficiency. Our results let us speculate that age-related differences in muscle–tendon behaviour could contribute to previously observed differences in movement efficiency between children and adults (Schepens et al., 2004). The first aim of the present study was to compare MTU behaviour during preferred-frequency hopping between children and adults. In agreement with our first hypothesis, tendon excursion was smaller in children than in adults relative to overall MTU excursion, suggesting that a greater proportion of MTU excursion was accomplished through excursion of the muscle belly.

Several neural and mechanical mechanisms could explain these results. First, muscular strength increases faster than tendon stiffness during growth (Waugh et al., 2012). As the differential lengthening of muscle and tendon is governed by their respective stiffnesses, the greater increase in muscle strength versus tendon stiffness observed from childhood to adulthood is likely to have affected muscle–tendon interaction during hopping. Second, children are clearly able to develop the submaximal muscular forces required to perform hopping; however, our results may imply that they do not (volitionally or otherwise) produce enough force to maintain a near-isometric muscular contraction. Several neural factors should be considered with respect to this finding. For example, it is possible that stretching their relatively stiffer tendons would require a larger relative muscle activation than in adults and would increase the metabolic cost of the task. Impaired tendon excursion would also result in less tendon recoil force. This may impact on recoil velocity (Nagano et al., 2004) and therefore hopping performance, although our findings demonstrate that normalized hopping height was not statistically different between children and adults for preferred frequency (Table 2). In addition, children demonstrate slower maximum rates of force development (Waugh et al., 2013), which may reduce their capability of generating sufficient muscular tension in the required time to fully resist length change and stretch the tendon optimally. If this were the case, the muscle would undergo a greater length change during the braking phase of ground contact, which (i) compromises the energy-storing potential of the tendon, and (ii) increases the requirement for active force production during the concentric phase of the hop. Even if the muscle acts as a spring under these conditions, the current evidence suggests that muscle has a higher hysteresis than tendon (Best et al., 1994; Finni et al., 2013), so children will be required to increase muscular force production to generate additional mechanical work, and their movement will be more costly as a result.

Alternatively, children may use different neural activation patterns to complete the same task. It has been demonstrated both computationally (Ettema, 2001; Lichtwark and Wilson, 2005) and experimentally (Hoffrén et al., 2012; Sano et al., 2013) that tendons with different mechanical properties may require different muscle activation strategies to achieve similar levels of efficiency. Moreover, previous studies have shown lower agonist and higher antagonist muscle activities in pre-pubertal children than in post-pubertal children and adults (Lloyd et al., 2012) during the pre-activation, braking and propulsive phases of jumping activities. Age-related differences in neural control strategies may be reflective of neurophysiological differences and suggest that developmental factors may contribute to the neural regulation of leg stiffness in SSC activities with age. Muscle recruitment patterns and activation strategies in relation to movement efficiency were not examined here and should be explicitly examined in future.

A number of mechanical factors should also be considered when interpreting our results. During the ground contact phase, passive strain forces from in-parallel (parallel elastic component, PEC; e.g. fascia, perimysium) and in-series (series elastic component, SEC; e.g. aponeurosis, titin) connective tissues may have contributed to force production in children and adults, as has been suggested during adult walking (Whittington et al., 2008), and provided an additional source of elastic energy recovery as well as augmenting the behaviour of the muscle–tendon complex in vivo. As muscle lengthening was greater in children than in adults, one might speculate that passive forces could have been greater than in adults, although this assumes that the mechanical and force–length properties of the active and passive elements are the same between children and adults. This is unlikely given the lower absolute tendon stiffness of children (Waugh et al., 2012). Passive stiffness is not well related to tendon stiffness in adults (Kubo et al., 2001) and varies significantly between individuals; thus, without subject-specific force–length relationships we cannot verify its impact here (Abellaneda et al., 2009). Muscular connective tissue and architectural properties also influence muscle mechanics by constraining muscle bulging to particular axes (Randhawa et al., 2013). For example, shorter and less pennate GM fascicles in children (O'Brien et al., 2010b) would increase the architectural gearing ratio of their MTU and negatively affect the muscle's length–tension relationship (Azizi et al., 2008). Differences in neural and muscular characteristics between children and adults may therefore result in different gearing. Future research should investigate this speculation explicitly.

Finally, we chose to allow participants to hop at their preferred frequency without controlling for additional characteristics such as hopping height or kinematics. Interestingly, we found flight time at the preferred frequency did not differ significantly between children and adults (P=0.080), which was reflected in their similar normalized hopping heights (P=0.393). Moreover, leg stiffness normalized to body weight and leg length were the same (P=0.286). It is therefore unlikely that different hopping characteristics contributed to observed differences in muscle–tendon function in the present study.

The second aim of the present study was to determine whether children and adults select movement frequencies that maximize their energy-saving mechanisms. In support of our second hypothesis, we found that both children and adults performed two-legged hopping at a movement frequency that resulted in the greatest proportion of MTU length change being completed by the tendon (67% and 93% for children and adults, respectively), indicating that both groups selected a hopping frequency that best coincided with their MTU resonant frequency. Accordingly, muscle belly excursion was minimized at this frequency, reducing the amount of positive work performed by the contractile elements of the muscle, as well as the excursion velocity (see Table 1). This behaviour is likely to enhance force production potential by allowing the muscle to work within a more favourable region of its force–velocity (and potentially force–length) relationship, although elastic energy storage and recoil by PEC elements would be limited. Qualitative analysis of the muscle and tendon excursion profiles at the set frequencies (Fig. 3A) further illustrates the potential energetic benefit of hopping at the preferred frequency. In addition, the muscle–tendon excursion profiles at preferred frequency and higher are uni-modal. Bimodal muscle–tendon excursion traces seen at the lower frequencies indicate that the body did not behave like a Hookean mass–spring system, possibly in an attempt to avoid excessive COM excursion (Taylor, 1985), and this may be associated with energy dissipation during landing (Farley et al., 1991). To compensate for this energy loss, muscular mechanical work would need to be done on the system during the propulsive phase of the hop to maintain the energetic requirements of the movement, making the activity energetically costly. These mechanisms, and the fact that increased tissue stretch has a substantial impact on elastic energy storage, lead us to speculate that both children and adults choose a hopping frequency that minimizes energy cost during dynamic movements (Lichtwark and Wilson, 2008). This is in keeping with evidence that children choose a walking speed that minimizes metabolic energy expenditure (Jeng et al., 1997).

Several limitations should be highlighted regarding the methods used in the present study. Firstly, when inferring tendon elastic energy storage from the area under the excursion–time curve, we assumed in-series muscle and tendon experience the same forces. However, in dynamic contexts, potential force contributions from PEC means this may not be the case; thus, our surrogate measures of elastic energy storage should be interpreted with some caution. Secondly, two 3D markers were positioned on the handle of the ultrasound probe. Whilst these allowed an estimation of the probe position in 3D space, this is insufficient for detecting probe rotation about its own axis. As the probe was housed in a semi-rigid holder and fixed securely to the skin, we are confident that errors introduced to the measurement of MTJ movement by possible probe rotation were minimal. This is supported by the fact that the echoabsorptive strip positioned on the skin did not move when the ultrasound videos were viewed post hoc, and the MTJ and visible fascicles remained clearly within the ultrasound scanning plane. The use of a straight-line approach for estimating tendon length may have under-estimated tendon length because of the significant curve of the Achilles tendon near its insertion with the calcaneus. Subsequently, calculated tendon excursions (strains) may be over-estimated (Stosic and Finni, 2011). We have assumed that any errors associated with this approach are systematic and therefore the relationships and differences found in this study are maintained.

Lastly, there are also limitations associated with using equations provided by Grieve et al. (1978) for estimating MTU and tendon excursion from joint angle changes. The extent of MTU excursion is a result of the angular displacement of a joint and the moment arm length over which the MTU acts (Fukunaga et al., 1996). Whilst the equations provided for estimating MTU excursion are normalized for leg length, they inherently assume that moment arm length scales linearly to leg length. The data for these equations were derived from adult cadavers; thus, their appropriateness for use in children is questionable, given that leg length is a poor predictor of moment arm length in this population (Waugh et al., 2011). We performed a sensitivity analysis of this effect by re-estimating MTU length change based on the individual Achilles tendon moment arms for our subjects by means of reversing the tendon excursion method (moment arm lengths known from a previous study; Waugh et al., 2011). We then re-calculated all of our dependent variables based on these new MTU lengths and re-performed the statistical analysis. Across all subjects and conditions, the statistical results remained the same (obtained P-values were slightly smaller). Whilst our alternative method of estimating MTU length changes based on individual moment arms has its own limitations, this sensitivity analysis suggests that our statistical results are robust.

In summary, the present data provide an important insight into the mechanical contributions to movement efficiency in pre-pubertal children. Differences in muscle–tendon dynamics were found between children and adults when hopping at their preferred frequency, whereby whole MTU length change was accomplished with relatively greater muscle excursion in children. This indicates that children do not utilize their energy-saving mechanisms as effectively as adults. However, children and adults appear to choose movement frequencies that maximize the elastic energy storage potential of the tendon and minimize the mechanical work due to muscle contraction during hopping, indicating that children utilize energy-saving mechanisms to the best of their potential. These results add to our understanding of the potential mechanisms underpinning the higher energy cost of movement performance in children, and have implications for the interpretation of age-related differences in the performance of complex motor tasks.

Acknowledgements

We would like to express thanks to Ros Hancell and classes 4B and 4C of Ravenor Primary School for their collaboration and compliance with this study.

Footnotes

Author contributions

Conceptualization, Methodology, Formal Analysis and Writing: C.W., T.K., A.B.; Investigation and Data Curation: C.W.; Supervision and Funding Acquisition: T.K., A.B.

Funding

This work was supported by the Engineering and Physical Sciences Research Council (EP/ E013007/1).

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Competing interests

The authors declare no competing or financial interests.