Effect of kinematics on ground reaction force during single-leg jump landing in children: a causal decomposition approach in jumpers and non-jumpers

Participants

Twenty-five children complied with the inclusion criteria, as follows: (i) regular practice of volleyball (n = 8) or gymnastics (n = 6) for at least one year (jumpers group) or no practice of any structured sport in their leisure time (n = 11, non-jumpers); (ii) no injuries in the 6 months prior to the tests; and (iii) have body mass index below 25 kg/m². For the jumpers group, the minimum duration of sports practice was set at 1 year and they trained at least twice a week. No differences in age, body mass index or % of body fat between the jumpers and non-jumpers (control group) were found (Table 1). The study was approved by the University Valencia Ethics Committee (H1446557620395) and the parents of the participants gave their written informed consent. Some of the data given here have been used in a previous article (Estevan et al., 2020), which addressed a different research question using another data analysis method.

Apparatus

VGRF and joint angles data of the lower limb during landing were acquired using a nine-camera motion capture system (Oqus, 240 Hz; Qualisys, Gothenburg, Sweden) synchronized with a force plate (9281CA, 1,200 Hz; Kistler, Winterthur, Switzerland). Reflective markers were securely positioned to define segments (Estevan et al., 2020). Data from the markers were processed by Visual 3D software (C-Motion, Germantown, MD, USA).

Procedure

After a standardized individual warmup (including familiarization), the barefoot participants performed 10 single-leg landings from a height of 25 cm onto the force plate, keeping their hands on their hips during the task (Fig. 1A). The take-off platform was located 5 cm behind the force platform. The dominant leg was the one used for landing (kicking preference). The child, acting on their own decision, took a step with the ground leg, landing on the force platform. All children were encouraged to land on one leg while maintaining stability for 10 s. The free leg was kept in the rear with the knee flexed 90° approximately. The trials were video recorded to reject those who started jumping instead of stepping or the free knee was not flexed around 90°. The trials started preferably between 1–3 s after the research assistant gave the appropriate signal and a rest interval of 1–2 min was allowed between the trials.

Signal processing and causal interaction assessment

The data from 10 single-leg landing tests were used for further analysis. VGRF data were smoothed with a fourth-order 75 Hz low-pass Butterworth filter (Blackburn et al., 2016), and the same filter was applied to the sagittal hip, knee and ankle joint angle to preserve the dynamic consistency between signals (Tomescu et al., 2018) (Fig. 1B). Jump landing signals (i.e., landing cycle) were determined based on a threshold VGRF value of 15 N to the maximum knee flexion on the dominant lower limb. The causal interaction between the sagittal joint kinematics and VGRF on the landing cycle was assessed by ensemble empirical mode decomposition (EEMD) and time series instantaneous phase dependence in bi-directional causality, using the Yang methodology (Yang, Peng & Huang, 2018). The code for its calculation can be downloaded from the study by Yang, Peng & Huang (2018). EEMD with adapted additive noise was used to obtain the intrinsic mode functions (IMFs). Unlike wavelet decomposition or Fourier transform, EEMD is a self-adaptive and data-driven technique that does not need a pre-set basis function (Chan et al., 2014; Peng et al., 2021). Based on previous methodology, white noise was added to enhance the separability of IMFs during decomposition (Chan et al., 2014; Cruz-Montecinos et al., 2022). Briefly, in each landing test, the EEMD was used to obtain a finite number of IMFs and identify the instantaneous phase coherence between paired IMFs. The noise level with the lowest root-mean-square was selected for further analysis by EEMD. This step is critical to avoiding spurious causal detection resulting from the poor separation of a given signal. Based on Yang’s methodology, the relative causal strength (RCS) was then quantified as the relative ratio of absolute strength between IMFs (Yang, Peng & Huang, 2018). The maximal RCS was utilized to evaluate both the intensity and the direction of the causal relationships between the sagittal joint angles and the VGRF. An RCS ratio of 0.5 suggests an absence of causality, whereas ratios close to 0 or 1 indicate a strong causal influence of the corresponding IMFs in the bidirectional interactions (Yang, Peng & Huang, 2018). In our case, it indicates a strong causal influence between the kinematic data and VGRF (e.g., from kinematics to VGRF or vice versa). For example, an RCS close to 1 between the sagittal joint angles and VGRF suggests that changes in joint kinematics are significantly impacting the forces transmitted through the foot during landing (kinematic → VGRF). Figures 1B and 1C show the kinematic and kinetic signals, and the selected IMFs with higher RCS based on the landing cycle, respectively. The median IMF frequency was used to characterize the frequency of IMFs selected for the sagittal joint kinematics and VGRF.

Statistical analysis

All the data were analyzed on SPSS (IBM, Armonk, NY, USA). A p-value of <0.05 was considered statistically significant. Normality was assessed using the Shapiro-Wilk test. Age, body mass, and body mass index showed non-normal distributions. The RCS of the hip in the non-jumpers group and the median frequency of the IMF for ankle kinematics also exhibited non-normal distributions. The chi-squared test was used to compare the distribution of the direction of causality between joints and groups. To compare the RCS and the median frequency of the IMFs selected between joints and groups, a mixed ANOVA (joints × groups) were applied, followed by pairwise comparisons with Bonferroni correction. A p-value of <0.05 was considered statistically significant. Even though the hip RCS and median frequency of the IMF for ankle kinematics in the non-jumpers group were not normally distributed, the mixed ANOVA assumptions were met. Mauchly’s test confirmed sphericity (p = 0.792 and p = 0.977), and Levene’s test showed equal variances for both RCS and median frequency (p > 0.05). Finally, the effect sizes were calculated for all variables. For ANOVA, partial eta squared (η²p) was used to interpret effect sizes, categorized as follows: trivial (η²p < 0.01), small (0.01 ≤ η²p < 0.06), moderate (0.06 ≤ η²p < 0.14), and large (η²p ≥ 0.14). For normally distributed variables, Cohen’s d was used: trivial (d < 0.2), small (0.2 ≤ d < 0.5), moderate (0.5 ≤ d < 0.8), and large (d ≥ 0.8). For non-normally distributed variables, the Rank Biserial Correlation (r) was used: trivial (r < 0.1), small (0.1 ≤ r < 0.3), moderate (0.3 ≤ r < 0.5), and large (r ≥ 0.5). For categorical variables, Cramér’s V was used: trivial (v < 0.1), small (0.1 ≤ v < 0.3), moderate (0.3 ≤ v < 0.5), and large (v ≥ 0.5).

Direction of causality

There were no differences between groups in the direction of causality (hip p = 0.399, v = 0.17; knee p = 0.366, v = 0.18; ankle, p = 0.191, v = 0.26) (Fig. 2A). The direction of causality from kinematics to VGRF (i.e., kinematics → VGRF) was observed in 92% of participants in the ankle joint, 88% in the hip joint and 96% for knee joint (Fig. 2A). The consistency in the direction of causality (average of 92%), along with the high RCS value (average of 0.83), confirms the influence of kinematics on VGRF.

Strength of causality

For RCS, the mixed ANOVA showed a main significant effect of joint factor (F_(2,46) = 6.30, p = 0.004, η²p = 0.22), with no differences between the groups (F_(1,23) = 0.42, p = 0.524, η²p = 0.02). A significant interaction between joint × group (F_(2,46) = 3.60, p = 0.035, η²p = 0.14) was found. The post-hoc analysis showed that the RCS from hip-to-VGRF was higher than ankle-to-VGRF (p = 0.004, d = 0.91) in the control group, while no differences were observed between RCS joints in the jumpers group (p > 0.05). Notably, the jumpers group had higher ankle-to-VGRF RCS compared to non-jumpers ((p = 0.017, d = 1.03); Fig. 2B). For all post-hoc comparisons and effect size see Table S1. Overall, these results indicate that non-jumping children use the hip more to modulate reaction forces during landing, while jumping children rely more on the ankle joint compared to non-jumpers to regulate these forces.

Characteristics of IMF selected

The median IMF frequency selected from joint kinematics was found between 16–17 Hz and between 17–21 Hz from VGRF. The mixed ANOVA for IMFs from kinematics and VGRF showed a non-significant main effect for joint (F_(2,46) = 0.09, p = 0.916, η²p = 0.01 and F_(2,46) = 1.42, p = 0.251, η²p = 0.06, respectively), non-significant main effect for group (F_(1,23) = 0.04, p = 0.842, η²p = 0.01 and F_(1,23) = 0.31, p = 0.586, η²p = 0.01, respectively), and non-significant joint x group interaction effect (F_(2,46) = 1.07, p = 0.352, η²p = 0.04 and F_(2,46) = 0.57, p = 0.569, η²p = 0.02, respectively).

Practical implications

These findings could lead to training programs which adjust landing strategies to minimize lower limb injuries and improve motor function in young athletes. Understanding the causes and effects of joint kinematics and VGRF allows the creation of specific training programs to optimize landing strategies and decrease the risk of injuries. Promoting a greater range of ankle motion could help lower VGRF, thereby reducing injury risk by enhancing shock absorption (Taylor et al., 2022; Tait et al., 2022; Xu et al., 2024). By improving both ankle flexibility and strength, athletes may decrease the risk of overload and soft tissue injuries (Hopper et al., 2017; Martinez et al., 2022; Maniar et al., 2022). According to our results, ankle movement seems to be more relevant for jumpers, while hip movement is more significant for non-jumpers in managing landing forces. Therefore, prioritizing ankle strengthening for jumpers and hip strengthening for non-jumpers appears to be an approach that could potentially optimize the modulation of reaction forces during landing. As indicated in Fig. 3, progression in training could involve transitioning to integrated ankle and hip strengthening as the landing technique improves. Furthermore, the increased causal interaction from hip kinematics to VGRF, compared to ankle kinematics to VGRF, may indicate an improvement in landing technique based on athletes’ progress. However, future studies are needed to corroborate these assumptions in longitudinal research. Additionally, future studies could be conducted to understand the effect of neuromuscular training (e.g., plyometric and joint-specific strengthening programs) on the causal interaction between kinematics and kinetics in non-jumper and jumper young athletes (Hopper et al., 2017). Furthermore, future studies are needed to understand the effect of training programs and different types of feedback to determine whether these interventions can modify the causal interaction between kinematic and kinetic forces (Prapavessis & McNair, 1999; Aerts et al., 2013), particularly at the ankle joint, in order to restore more normal patterns of force absorption and reduce the occurrence of repeated micro-trauma to ankle structures, especially in children with a history of ankle injuries (e.g., ankle sprain or restricted dorsiflexion) (Caulfield & Garrett, 2004; Taylor et al., 2022).

Unlike linear approaches, nonlinear methods, such as causal empirical decomposition, provide a more specific approach based on the physical nature (i.e., nonlinear and non-stationary data) of the kinetic and kinematic signals during landing. It has been reported that the lower extremity coordination presents a non-linear interaction during the landing phase (Yeow, Lee & Goh, 2011). Our study suggests that non-linear analysis based on causal decomposition is a valuable method for assessing the direction and strength of causal interactions between kinematics and kinetics in biomechanical landing research. It may also contribute to the study of other motor tasks.

Our study has several limitations that should be considered: (i) the landing strategy was assessed from a single height. The VGRF peaks and eccentric muscle work by the lower extremity joints may increase with increased landing heights (Zhang et al., 2008). (ii) It was not possible to associate the results obtained with training load experience or to evaluate the effect of jumping practice as a pre- and post-methodology. Future longitudinal studies are needed to investigate the effect of jump training on causal relationships between kinematics and VGRF. (iii) The muscle activity during the landing task was not collected; therefore, it is not possible to determine if there was a different neuromuscular strategy associated with the differences observed. (iv) The maturity offset was not assessed in our study. With maturation, male adolescent athletes report increased vertical jump height and lower landing forces, whereas female athletes have not (Quatman et al., 2006). Future research should consider maturation-related variables such as bone structure, muscle mass, and tendon mechanical properties to better understand the implications of maturity and jump training on the causal interaction between joint kinematics and VGRF (Werkhausen et al., 2018). (v) Due to the relatively small size of our sample, it was not possible to differentiate between jumping sports and their interaction with sex. Therefore, these results should be taken with caution and cannot be extrapolated to other sports. Future studies will be required to confirm our results using different landing heights and comparing other sports. Finally, the causal empirical decomposition approach has some limitations that should be considered. Adding noise during the EEMD process, while necessary to improve the separability and orthogonality of the IMFs and to control spurious correlations (Yang, Peng & Huang, 2018, 2022), may introduce challenges in interpreting the results (Chang, Munch & Hsieh, 2022). However, in our data, the direction of causality was robustly determined in 92% of cases. Future research should explore the development of enhanced methods to improve the understanding of causal interactions in biomechanics.