Ankle joint torque is the product of the applied muscle force and the length of the Achilles tendon moment arm (ATMA). Accordingly, this structural attribute is of great importance in joint torque development (Piazza et al., 2011; Baxter et al., 2012; Baxter and Piazza, 2014). The resting ATMA length is genetically determined (Raichlen et al., 2011), but the dynamic ATMA length changes with ankle joint angular displacement (Fath et al., 2013; Deforth et al., 2019), which in turn may modify the mechanical capability of the plantarflexor muscles (Dick et al., 2017; Monte et al., 2021). Several studies have investigated how length changes in ATMA during joint rotation influence muscle output (Nagano and Komura, 2003; Harkness-Armstrong et al., 2020; Monte et al., 2021). In a model simulation, Nagano and Komura (2003) reported that a longer ATMA generated higher joint torque during eccentric contraction (<120 deg∙s^-1), while during concentric contraction, higher joint torque was produced with a shorter ATMA compared to a longer ATMA. In contrast to these results, Baxter and Piazza (Baxter and Piazza, 2014) reported greater maximal ankle torque with a longer ATMA during both isometric and isokinetic contractions. In the latter study, the volume of the plantarflexor muscles was also assessed, showing only a moderate correlation with both isometric and isokinetic peak ankle joint torque, indicating that the muscle volume alone may not be a major influencing factor in joint torque development.

A few studies have attempted to explore the influence of ATMA on the bilateral hopping task. During hopping, the ankle joint absorbs and generates the largest amount of power among the lower limb joints, and the movement occurs mainly in the vertical direction (Farris and Sawicki, 2012). Werkhoven and Piazza (2017b) found that a higher jumping height in a single-joint jumping task can be achieved with a longer heel length, which could indirectly indicate a positive connection between jumping height and a longer ATMA. Kenyan runners possess a longer ATMA (Kunimasa et al., 2014) and hop higher (Sano et al., 2013) compared to Japanese long-distance runners. However, the connection between these variables was not investigated, thus we cannot conclude that superior hopping performance is related to a longer ATMA.

In addition to ATMA, the external moment arm and the ratio of ATMA to the external moment arm have been shown to influence the functional role of the ankle, which primarily operates as a spring during hopping (Monte et al., 2021). Therefore, the ratio of ATMA to the lever arm length (external moment arm) can reflect the effective mechanical advantage (Harkness-Armstrong et al., 2020; Monte et al., 2021), which can explain the magnitude of force production required to achieve hopping height.

Ankle joint torque also depends on the activation of the plantarflexor muscles and their force generation capacity, which is closely related to the muscles’ structural characteristics. Generally, larger muscle size (i.e., volume, mass, anatomical cross-sectional area, etc.) is associated with greater force output in the plantarflexor muscles (Bamman et al., 2000; Baxter and Piazza, 2014), which presumably could lead to a greater hopping height. In addition to muscle characteristics, tendon properties could also influence hopping performance (Lamontagne and Kennedy, 2013). Collectively, triceps surae muscle mass, plantarflexor strength capacity, and the ATMA all contribute to hopping performance. However, considering that the dynamic length changes of the ATMA seem to influence ankle joint function and force generation capacity, it is important to explore how muscle dimensions are linked to joint torque in relation to changes in ATMA length. Exploring the connection between interindividual variation in human lower leg muscles and foot structure with hopping performance will improve our understanding of the mechanisms behind the association of structural and functional indices and may provide better insight into the determinants of hopping performance. Therefore, the purpose of this study was to test for correlations between lower leg and foot structural measures such as muscle mass, cross-sectional area and ATMA length and the mechanical characteristics of hopping such as hopping height, ground reaction force and ankle joint kinematics measured during an ankle thrusted bilateral hopping task. Given that ankle joint moment is the product of muscle force and muscle moment arm, we hypothesized that individuals with a longer ATMA would be able to produce higher ankle joint moments that accelerate the center of mass of the whole-body therefore, achieve greater hopping height.

The average hopping height was 21.8 ± 4.1 cm. The mean resting length of the ATMA, as measured from the MRI images, was 4.91 ± 0.63 cm (Table 1.). The dynamic length changes of the ATMA during hopping are presented in Figure 2. The minimum length (4.50 ± 0.72 cm) occurred at the midpoint of the jump, around the peak ankle dorsiflexion, while the maximum length (6.08 ± 0.74 cm) (23.6% longer compared to the resting length) was reached at the moment of takeoff. Participants landed with a plantarflexed ankle position (12.13 ± 7.75°) and a slightly flexed knee (171.30 ± 8.04°), resulting in a 9.04% ± 0.06% (5.37 ± 0.71 cm) longer ATMA than the resting length (Figure 3). The reliability test demonstrated excellent agreement between the analysts for each muscle and tendon (ICC >0.97, see in Supplementary Material). The mean and SD values of the plantar flexor muscle tendon unit properties in Table 2. SOL volume was 51.16% of the total triceps sure while MG was 30.44%, and LG was 18.41% respectively. The detailed correlation analysis results are presented in Figure 4 and in the Supplementary Material. None of the morphological parameters (such as volume, cross-sectional area (CSA), and total CSA (tCSA) of the plantarflexor muscle-tendon unit showed any correlation with hopping height. Isometric force was only associated with the length, volume, and mass of the medial gastrocnemius (MG) muscle (Figure 4). Normalized and absolute ATMA length was only correlated with peak ground reaction force (GRF) during hopping. However, there was a correlation between absolute ATMA length and the total mass of the triceps surae muscle group, and it also correlated with peak GRF. Peak GRF was also associated with the MG, lateral gastrocnemius (LG), soleus (SOL), and the total mass of the triceps surae muscles, as well as with hopping height and isometric force. However, when GRF was normalized to body mass, these connections disappeared. Foot length and gear ratio showed negative correlations with most of the muscle characteristic variables.

The aim of this study was to investigate correlations between lower leg and foot structural measures and hopping performance. Our initial hypothesis, suggesting a correlation between hopping height and ATMA length, was not supported. However, it appears that ATMA is associated with mechanical and morphological parameters that serve as strong indicators of improved hopping performance. Interestingly, none of the structural parameters of the plantarflexor muscles showed a correlation with hopping height.

Our results indicate that the length of the ATMA, whether at rest or during hopping, is not a strong predictor of hopping height (Figure 4). This finding holds true regardless of the applied normalization methods, suggesting that ATMA length may not be a useful indicator of ankle muscle function during hopping. In this study, we used a bilateral hopping technique, similar to previous experiments (Hobara et al., 2007; 2008; Sano et al., 2013), and the hopping height achieved by our participants were consistent with earlier reports (Hobara et al., 2007; 2008; Sano et al., 2013; Kovács et al., 2021a). The mean ATMA length of 4.91 cm observed in our study aligns with findings reported in the existing literature (Fath et al., 2010; Baxter and Piazza, 2014; Deforth et al., 2019; Kovács et al., 2021b), as do the measured and calculated morphological parameters of the plantarflexor muscle tendon unit (Friederich and Brand, 1990; Fukunaga et al., 1992; Baxter and Piazza, 2014; Kovács et al., 2020).

Previous studies have provided conflicting findings regarding the role of ATMA on hopping performance. Watanabe et al. (2008) demonstrated that volleyball players with shorter ATMA were able to achieve higher hops compared to distance runners, although no correlation was observed. In cases where the hop was performed as a static jump (only pushing off from the ground), heel length showed a strong correlation with hop height, suggesting that a longer ATMA may be advantageous for superior hopping performance. In our recent study (2021a), we did not find a direct correlation between ATMA and hopping height. However, it is worth noting that in that study, ATMA length was estimated using a photograph based method, which is considered less accurate (Fath et al., 2010) and may limit the interpretation of the results. On the other hand, we did find a correlation between ATMA length and both absolute and body weight normalized peak ground reaction force (Figure 4). A longer ATMA should, by definition, allow for greater generation of plantarflexor moment with a given muscle force. However, the role of ATMA in determining ankle joint strength may require consideration of the mechanical advantage. Monte et al. (2021) investigated the role of the external moment arm and the ratio between the external to internal moment arm length (effective mechanical advantage) on hopping performance, suggesting that the ankle can adapt its leverage and mechanical function in response to different mechanical demands. In our study, we were unable to directly determine the length of the external moment arm, so we used foot length as a structural indicator, which may reflect the length of the external moment arm. However, neither foot length nor gear ratio showed any association with hopping height (Figure 4). Both ATMA and external moment arm length undergo significant changes during hopping (Monte et al., 2021), indicating that variations in length can modulate muscle-tendon interaction. Furthermore, we observed that longer foot was paired with smaller muscle mass for each muscle and in combination, as well as with thinner and shorter Achilles tendon. Similarly, we found that gear ratio exhibited similar correlations with these variables and showed a negative correlation with peak GRF (Figure 4).

Surprisingly, we did not find any relationship between muscle characteristics (such as muscle mass and ACSA and hopping performance (Figure 4). This contradicts previous reports that have demonstrated a strong connection between spatial parameters of the muscle (such as volume, mass, and ACSA) and maximal isometric and isokinetic plantarflexor strength (Bamman et al., 2000; Baxter and Piazza, 2014). Additionally, studies have shown that interindividual variation in triceps surae muscle volume can account for a significant variance in maximal plantarflexor torque (Gadeberg et al., 1999; Bamman et al., 2000; Baxter and Piazza, 2014). Based on these findings, it was reasonable to assume that larger muscle size would result in greater maximal force, which, in turn, could lead to a higher hopping height. However, contrary to our initial assumption, we could not confirm a connection between muscle size and maximal isometric force or between maximal isometric force and hopping height in our study.

Additionally, maximal hops require maximal effort, indicating that a stronger plantarflexor muscle is likely to result in higher hops. It is worth noting that the ground contact time (i.e., muscle contraction time) during hopping is shorter compared to activities such as running (Kovács et al., 2021b), jumping (Lamontagne and Kennedy, 2013; Kovács et al., 2023), or isolated isokinetic or isometric contractions in dynamometric measurements (Baxter and Piazza, 2014). This suggests that factors beyond muscle’s anatomical attributes and muscle strength, such as movement control and coordination, may contribute to the variability in hopping performance. During the push-off phase of hopping, the ATMA increases with plantarflexion, which likely facilitates tendon recoil (Farris et al., 2016). This, in turn, allows for the release of elastic energy and an increase in mechanical force output (Astley and Roberts, 2014). It has been suggested that the elastic function of the plantarflexor muscle-tendon unit is the primary source of mechanical power during hopping (Monte et al., 2021). Consequently, the mechanical characteristics of the tendon and the effective utilization of the stored strain energy within the tendon may play a more crucial role in repetitive hopping than the structural parameters of the lower leg. The major difference in our protocol compared to previous studies is that during hopping, muscles operate under a stretch shortening cycle type of contraction in oppose to only isometric or isokinetic contractile conditions (Nagano and Komura, 2003; Van Werkhoven and Piazza, 2013; Werkhoven and Piazza, 2017b; Baxter and Piazza, 2018), which can explain the different outcome. In our earlier study where we used the same task to investigate the connection between ATMA and hopping performance (Kovács et al., 2021a) but we found no direct link between hopping height and ATMA length. On the other hand, ATMA was related to peak GRF and rate of force development indicating an indirect role in muscle force production.

Our study has several methodological limitations that should be addressed. Firstly, the chosen task of repetitive bilateral hopping focused primarily on ankle thrust movement emphasizing ankle joint propulsion. However, it is important to note that knee and hip joint movements were not constrained, resulting in some degree of knee joint rotation. This may have influenced hopping performance and should be taken into consideration when interpreting the results. To mitigate this effect, hops were visually checked by an experimenter, and trials with notable knee movement were repeated. The estimation of dynamic ATMA length was performed using a polynomial model based on previous reports (Werkhoven and Piazza, 2017a). However, it is important to acknowledge that this method may not precisely represent the participants’ actual dynamic ATMA length. Nevertheless, we corrected the dynamic length using each participant’s resting ATMA length measured from MRI images, which is considered the “gold standard” method for estimating ATMA length (Fath et al., 2010). Additionally, the resting ATMA length was estimated using a two-dimensional analysis, neglecting rotations out of the plane of the image. This limitation could be overcome by implementing a more comprehensive three-dimensional determination of the moment arm. Furthermore, the inclusion of physiological cross-sectional area as a predictor of muscle force generation capacity would have allowed for a more comprehensive analysis. However, due to the lack of proper ultrasound equipment and the inability to visualize and calculate muscle fascicles, physiological cross-sectional area could not be included in the study. Incorporating this parameter would have provided a more accurate assessment of muscle force generation capacity. Lastly, male and female participants were pooled into a single group to increase the generalizability within our dataset and create a broader spectrum of the investigated variables. While there was no reason to assume that the relationships between the variables differed by gender, it is important to acknowledge this pooling of participants as a potential limitation.

In conclusion, the findings of this study suggest that longer ATMA does not lead to superior performance in a hopping task. Surprisingly, maximal isometric plantarflexion force and muscle size did not show a correlation with repetitive bilateral hopping performance. These results imply that the mechanical properties of the tendon and the efficient utilization of stored strain energy within the tendon may play a more significant role in repetitive hopping than the structural parameters of the lower leg.