Knee Abduction Moment Is Predicted by Lower Gluteus Medius Force and Larger Vertical and Lateral Ground Reaction Forces during Drop Vertical Jump in Female Athletes

Abstract

Prospective knee abduction moments measured during the drop vertical jump task identify those at increased risk for anterior cruciate ligament injury. The purpose of this study was to determine which muscle forces and frontal plane biomechanical features contribute to large knee abduction moments. Thirteen young female athletes performed three drop vertical jump trials. Subject-specific musculoskeletal models and electromyography-informed simulations were developed to calculate the frontal plane biomechanics and lower limb muscle forces. The relationships between knee abduction moment and frontal plane biomechanics were examined. Knee abduction moment was positively correlated to vertical (R = 0.522, P < 0.001) and lateral ground reaction forces (R = 0.395, P = 0.016), hip adduction angle (R = 0.358, P < 0.023) and lateral pelvic tilt (R = 0.311, P = 0.061). A multiple regression showed that knee abduction moment was predicted by reduced gluteus medius force and increased vertical and lateral ground reaction forces (P < 0.001, R2 = 0.640). Hip adduction is indicative of lateral pelvic shift during landing. The coupled hip adduction and lateral pelvic tilt were associated to the increased vertical and lateral ground reaction forces, propagating into higher knee abduction moments. These biomechanical features are associated with ACL injury and may be limited in a landing with increased activation of the gluteus medius. Targeted neuromuscular training to control the frontal pelvic and hip motion may help to avoid injurious ground reaction forces and consequent knee abduction moment and ACL injury risk.

1. Introduction

Anterior cruciate ligament (ACL) tear is a serious sports injury. Approximately 250,000 ACL injuries occur each year in the United States (Johnson and Warner, 1993). While ACL reconstruction is the gold-standard procedure for athletes who return to sport after ACL injury, only 33–78% of young, reconstructed athletes are able to return to the same level of participation post-injury within a year (Ardern et al., 2011; Arundale et al., 2018; Geffroy et al., 2018). Especially, female athletes have a higher rate of ACL injury compared to male athletes (Stanley et al., 2016). Therefore, effective injury prevention and rehabilitation programs for female athletes are required to reduce ACL injury (Hewett and Bates, 2017). Females show larger external knee abduction moment measured in vivo during the drop vertical jump (DVJ) task relative to males (Ford et al., 2010), and the external knee abduction moment is a predictive factor of ACL injury in female athletes (Hewett et al., 2005). Externally applied knee abduction moment has also been identified as an injurious load as it induces anterior tibial translation (Bates et al., 2019; Matsumoto, 1990; Navacchia et al., 2019a; Ueno et al., 2019). Therefore, external knee abduction moment in female athletes is a targeted risk factor to be reduced in prevention programs (Sugimoto et al., 2015).

Knee abduction moment was correlated to lateral trunk tilt angle during side step cutting and single leg landing task (Dempsey et al., 2012; Jamison et al., 2012). The potential to decrease external knee abduction moment during landing by means of muscle activation has been shown with surface electromyography (EMG), but it is still controversial (Brown et al., 2014; Jamison et al., 2013; Palmieri-Smith et al., 2009). The relationships between net joint moment and EMG may be different among subjects because each subject may have different cross-sectional-area, firing rate and recruitment of motor units in a muscle to generate a joint torque. Unlike EMG data, musculoskeletal modeling provides muscle force magnitudes consistent with the joint moments calculated via inverse dynamics. A previous study reported that the force exerted by hip muscles, including the gluteus medius, gluteus maximus and piriformis, estimated with a static optimization method, primarily opposed the knee abduction moment during side-step-cutting (Maniar et al., 2018).

Musculoskeletal modeling is used to estimate muscle forces based on in vivo marker-based kinematics and ground reaction force (Laughlin et al., 2011; Maniar et al., 2018; Mokhtarzadeh et al., 2013; Navacchia et al., 2017, 2016; Ueno et al., 2017). However, the commonly used static optimization method is inadequate to estimate antagonist muscle activation during a co-contraction (Pizzolato et al., 2015). Novel approaches that use subject-specific EMG signals as inputs to the muscle force prediction, can now be utilized to estimate muscle forces consistent with subject-specific muscle activity (Afschrift et al., 2018; Pizzolato et al., 2015).

Direct collocation is a method to solve optimal control problems that has been recently used in biomechanics applications (De Groote et al., 2016). This technique discretizes and approximates continuous data using polynomial splines, which allows to simulate the dynamic equations of motion by solving all time frames simultaneously (Kelly, 2017). Consequently, muscle activations estimates are more consistent with muscle physiology compared to the static optimization method, as they account for the excitation-activation dynamics (De Groote et al., 2009). In addition, direct collocation requires shorter computational times compared to sequential shooting-based dynamic optimization approaches (De Groote et al., 2016; Kelly, 2017; Porsa et al., 2016). Furthermore, informing the objective function with subject-specific EMG data allow for an estimation of more physiological muscle co-contractions with respect to non-EMG-informed methods that minimize muscle activation (Navacchia et al., 2019b). An elevated co-contraction is produced by increased muscle forces in both agonist and antagonist forces compared to static optimization. This fact may provide different conclusions on the relationship between knee abduction moment and muscle forces compared to static optimization (Maniar et al., 2018).

Since hip muscles are the primary controllers of the trunk and hip position in a closed kinetic chain motion (Frank et al., 2013; Kim et al., 2016), higher hip abductor muscle activation are hypothesized to decrease the knee abduction moment during DVJ. Therefore, the purpose of this study was to determine the relationships between the knee abduction moment and lower limb muscle force during DVJ using an EMG-informed musculoskeletal model. Concurrently, the relationship between the knee abduction moment and frontal plane biomechanics, including vertical and lateral ground reaction force, hip adduction moment and trunk and hip kinematics were investigated, as a previous study indicated that those biomechanics variables might be related to the increased knee abduction moment during asymmetrical landing (Hewett and Myer, 2011). The hypothesis tested was that the knee abduction moment would be negatively correlated to the hip abductor muscle force and positively correlated to the vertical ground reaction force, lateral ground reaction force and lateral trunk lean.

2. Methods

2.1. Experimental data collection

Thirteen young female athletes (age 15.6 ± 1.6 years, heights 169.8 ± 5.6 cm, mass 62.6 ± 5.2 kg) participated in this study. Each participant performed three DVJ trials. The participants were instructed to drop off from a 30-cm-high box onto two force plates (AMTI, Watertown, MA) and immediately perform a maximum vertical jump. Institutional review board approval and informed consent was obtained before the conduction of the study.

Thirty-five reflective markers were placed bilaterally on the shoulder, elbow, wrist, anterior superior iliac spine, greater trochanter, thigh, medial and lateral knee, tibial tubercle, shank, distal shank, medial and lateral ankle, heel, dorsal surface of the midfoot, lateral foot (fifth metatarsal), toe (between second and third metatarsals) and sacrum. Marker trajectories were collected using a motion capture system (EVaRT v5, Motion Analysis Corporation, Santa Rosa, CA) with ten digital cameras (Eagle cameras; Motion Analysis Corporation, Santa Rosa, CA) sampled at 240 Hz. Ground reaction forces were synchronously recorded at 1,200 Hz with the two force plates. Both kinematic and ground reaction force data were low-pass filtered using a zero-lag fourth order Butterworth filter at 12Hz and 50 Hz, respectively. The cut-off frequency for kinematics was chosen to be twice the cut-off frequency determined with a spectral analysis for gait (Winter, 2009), in order to account for the dynamic nature of a DVJ. The filtering cut-off frequency for the ground reaction force was determined by performing a spectral analysis, which aimed to retain 99% of the information present in the data and keep the data unaffected (Winter, 2009). The spectral analysis resulted in an average of 19.5 ± 8.2, 44.6 ± 36.7, 143.4 ± 59.3 Hz for the vertical, medio-lateral and antero-posterior components, respectively. Since the medio-lateral component of the ground reaction force was considered of importance for this study, as it influences the knee abduction moment, 50 Hz was chosen for the cut-off frequency of the ground reaction force. This value is also consistent with a previous report that a 50 Hz cut-off frequency for the ground reaction force was adequate to assess the impulsive knee abduction moment immediately after initial contact (IC) with the ground (Roewer et al., 2014). IC was defined as the time frame at which a ground force larger than 10 N was recorded.

Surface EMG data for the right leg were measured using a telemetry surface EMG system (TeleMyo 2400, Noraxon, Scottsdale, AZ) at a sampling rate of 1,200Hz. The electrodes were placed on biceps femoris, semitendinosus, rectus femoris, vastus lateralis, vastus medialis, gastrocnemius medialis, hip adductors, and gluteus medius of each leg of the participants. Electrode placement was determined using previously described protocols (Boling et al., 2006; Cram et al., 1998; Ford et al., 2011). The raw experimental EMG data were band-pass filtered using a zero-lag eighth order Butterworth filter with cutoff frequencies of 10 and 400 Hz, then full wave rectified and low-pass filtered using a zero-lag second order Butterworth filter with a cutoff frequency of 6 Hz. Finally, processed EMG data were normalized to peak EMG magnitudes from the subject across all the motor activities performed during data collection, which included maximum voluntary contractions and DVJ from different drop heights (15 and 45 cm) (Martelli et al., 2015).

2.4. Musculoskeletal models

A previously developed and validated generic musculoskeletal model (Rajagopal et al., 2016) was scaled to subject body size and weight based on marker data collected during the static trial. Knee abduction/adduction and internal/external rotation were added as independent degrees of freedom to the generic model, since female athletes exhibit large knee rotations in the frontal and coronal planes during DVJ (Ford et al., 2003; Hewett et al., 2005). In addition, quadratus femoris, gemellus and obturator were added according to a previous musculoskeletal model focused on hip musculature (https://simtk.org/projects/hip_muscles). In addition, piriformis path was modified based on a previous study (Vaarbakken et al., 2014) to generate hip external rotation torque. The maximum isometric force of each muscle was increased by 20% to enable the muscles to generate the required joint torques during landing, as previously done in other studies (Laughlin et al., 2011; Mokhtarzadeh et al., 2013). The scaled models were used to perform inverse kinematics, inverse dynamics, muscle analysis and the EMG-informed direct collocation using GPOPS-II optimal control software (Patterson and Rao, 2012) (Fig. 1). GPOPS-II is a MATLAB program that transcribes the dynamic optimization problem to a non-linear problem using a Legendre-Guass-Radau quadrature collocation method. Inverse kinematics, inverse dynamics and muscle analysis were performed in OpenSim (Delp et al., 2007) using marker and ground reaction force data for the three DVJ trials collected for each subject to derive joint angles, net torques, moment arms and musculotendon lengths during DVJ. Joint torques, moment arms and musculotendon lengths were used as inputs to an optimization to solve the muscle redundancy problem (Afschrift et al., 2018; De Groote et al., 2016, 2009). A previously described objective function was modified as follows to track subject-specific experimentally measured EMG signals, similarly to Afschrift et al. (2018):

$$J={\int }_{t_0}^{t_f}\left(\sum _{i=1}^m{a}_i^2+w_1\sum _{i=1}^m{v}_i^2+w_2\sum _{k=1}^K{a}_{Tk}^2+\sum _{j=1}^{m_{EMc}}{w}_3{\left(s_j{\widehat{a}}_j-a_j\right)}^2\right)dt$$

Fig. 1:

Workflow of the study to estimate muscle forces for the drop vertical jump trial using an electromyography-informed optimization. A generic model was scaled to subject size and mass using anthropometric data. Marker position data from motion analysis was used to perform an inverse kinematics analysis and obtain the joint kinematics data. Inverse dynamics was performed with joint angles and ground reaction force (GRF) data to calculate the net joint torques required by each subject to perform the motor task. Moment arms and musculotendon lengths were obtained from the muscle analysis tool in OpenSim using joint kinematics data as input. An EMG-informed direct collocation was performed to estimate muscle forces using kinematics, kinetics, muscle geometry data and electromyography (EMG) data as inputs. In the objective function, the error between each EMG signal and the corresponding muscle activation estimate was minimized (see the Methods section for a more complete version of the objective functions). Acronyms: IC = initial contact.

where the integral time window (t₀,t_f) goes from 150 ms before impact with the ground (IC – 150) to 300 ms after impact (IC + 300), m is the number of muscles in the model, a_i and v_i are the activation and its time derivative of muscle i (0 ≤ a_i ≤ 1), respectively. w₁ = 0.01 is a weighting factor, k is the number of degrees of freedom, a_TK is the activation level of the ideal actuator k ( −1 ≤ a_TK ≤ 1), w₂ = 100 is a weighting factor penalizing the use of the ideal actuators, m_EMG = 11 is the number of muscles tracking EMG data, ${\widehat{a}}_j$ is the normalized EMG profile to be tracked by muscle j delayed by 40 ms to represent the electromechanical delay between muscle excitation and activation (Corcos et al., 1992; De Ste Croix et al., 2015; Zhou et al., 1996). w₃ = 1000 is a weighting factor, and s_j is a scaling factor and an optimization variable used to impose similarity only in shape (not in magnitude) between the normalized-delayed EMG profiles and predicted muscle activations (Afschrift et al., 2018), since errors in EMG measurement and normalization may limit the reliability of the profile magnitude (De Luca, 1997; Sartori et al., 2014). Minimum values of optimal torques that satisfy the optimization were assigned to the ideal actuators except for knee ab/adduction and internal/external rotation: a maximum torque of 1 Nm was used for ankle plantar/dorsiflexion, knee flexion/extension, hip flexion/extension, and hip ab/adduction and 50 Nm was used for hip internal/external rotation, whereas 10,000 Nm was used for knee ab/adduction, and knee internal/external rotation. The ideal actuator k could, therefore, generate a torque

$$T_k=a_{Tk}{T}_K^{max}$$

where $T_K^{max}$ is its maximum torque. Larger maximum torques were chosen for the two secondary rotations of the knee (abduction/adduction and internal/external) because their net joint torque is mostly explained by the contribution of unmodeled components, such as tibiofemoral contact and ligaments (Engel et al., 2015; Grood et al., 1981). The muscles in the model assigned to tracking each EMG signal are presented in Tab. 1.

Table 1:

Assignment of EMG data to model muscles for the EMG-informed optimization.

EMG Profile	Muscle model
Biceps femoris	Biceps femoris long head
Semitendinosus	Semitendinosus, semimembranosus
Rectus femoris	Rectus femoris
Vastus lateralis	Vastus lateralis
Vastus medialis	Vastus medialis
Gastrocnemius medialis	Gastrocnemius medialis
Hip adductors	Adductor longus and glacius
Gluteus medius	Gluteus medius 1,2,3

2.5. Output variables

The outcomes of interest were peak values for external knee abduction moment, muscle forces, vertical and lateral ground reaction forces, external hip adduction moment and frontal plane trunk and hip kinematics during the landing phase (Tab. 2). Non-normalized values were used for consistency with a previous study that reported that non-normalized knee abduction moment during DVJ predicted ACL injury (Hewett et al., 2005). Only right side outcome variables were used in this study since the EMG data was recorded only for the right leg. The landing phase was defined as the time window from IC to maximum knee flexion. The first landing of DVJ was used because a previous study found that ACL injury is linked with the knee abduction moment occurring during the first landing of DVJ, which is larger compared to the second landing of DVJ and a drop landing task without subsequent jump (Bates et al., 2013; Hewett et al., 2005; Ishida et al., 2018). As for trunk kinematics, the lateral pelvic tilt and lateral lumbar bending were defined as the frontal plane rotation of the pelvis with respect to the global coordinate system and the frontal plane rotation relative to the pelvis. Muscles were grouped according to their function, consistent with a prior approach (Tab. 3) (Maniar et al., 2018).

Table 2:

Mean, standard deviations (SD) and 95 % confidence intervals of mean for outcome variables.

Variables	Mean	SD	Lower 95 %	Upper 95%
Knee abduction moment (Nm)	32.0	11.0	28.4	35.7
Vertical ground reaction force (N)	1073.2	221.3	999.4	1147.0
Lateral ground reaction force (N)	0.864	10.3	− 2.58	4.31
Lateral pelvic tilt (deg)	0.984	2.32	0.211	1.76
Lateral lumber bending (deg)	2.66	3.49	1.50	3.82
Hip adduction (deg)	− 0.699	4.62	− 2.24	0.842
Hip adduction moment (Nm)	33.9	12.3	29.8	38.0
Functional muscle groups (N)
Hip adductors	1005.4	471.9	848.0	1162.7
Ankle dorsi flexors	376.7	190.4	313.2	440.2
Gluteus maximus	1890.8	298.8	1791.2	1990.4
Gluteus medius	783.7	191.3	719.9	847.5
Gluteus minimus	339.6	392.5	208.7	470.5
Iliopsoas	1424.3	358.4	1301.8	1540.8
Medial hamstrings	1013.5	385.8	884.9	1142.1
Vasti	6296.7	1157.0	5910.9	6682.5
Individual muscles (N)
Biceps femoris long head	270.6	101.8	973.9	1293.3
Biceps femoris short head	204.6	101.8	170.7	238.6
Rectus femoris	1133.6	479.1	973.9	1293.3
Gastrocnemius medialis	969.5	269.3	879.7	1059.3
Gastrocnemius lateralis	379.2	207.8	309.9	448.5
Soleus	3385.9	800.1	3119.2	3652.7
Tibialis posterior	385.3	429.3	242.2	528.4
Tensor fascia latae	55.5	35.9	43.5	67.5
Sartorius	144.5	66.0	122.5	166.5
Gracilis	73.7	32.3	62.9	84.5
Flexor Digitorum Longus	48.3	47.7	32.4	64.2
Flexor Hallucis Longus	179.7	215.7	251.6	107.8
Peroneous brevis	99.1	128.4	56.3	141.9
Peroneous longus	257.2	284.2	162.5	352.0
Piriformis	676.0	305.8	574.0	777.9
Quadratus femoris	286.0	128.1	243.3	328.8
Gemellus	0.539	0.855	0.254	0.824
Obturator	95.1	89.5	65.2	125.0

Table 3:

Functional groups of musculotendinous actuators

Functional group	Muscles	Musculotendinous actuators*
Hip adductors	Adductor brevis Adductor longus Adductor magnus	addbrev addlong addmagProx addmagMid addmagDist addmagIsch
Ankle dorsi flexors	Extensor digitorum longus Extensor hallucis longus Tibialis anterior	edl ehl tibant
Gluteus maximus	Gluteus maximus	glmax1 glmax2 glmax3
Gluteus medius	Gluteus medius	glmed1 glmed2 glmed3
Gluteus minimus	Gluteus minimus	glmin1 glmin2 glmin3
Iliopsoas	Iliacus Psoas major	iliacus psoas
Medial hamstrings	Semimembranosus Semitendinosus	semimem semiten
Vasti	Vastus Intermedius Vastus Lateralis Vastus Medialis	vasint vaslat vasmed

^*Actuator names taken from the generic musculoskeletal model (Rajagopal et al., 2016).

2.6. Statistical analysis

Correlations between the output variables were determined using Pearson’s product correlation coefficients. In addition, the correlation between right-left difference in hip adduction angle and right-left difference in vertical ground reaction force was analyzed to determine if asymmetrical landing induced larger vertical ground reaction force on one side. Subsequently, a stepwise multiple regression analysis was used to develop the regression model that predicts knee abduction moment using the kinematic and kinetic variables. The best fit model was selected with forward direction stepwise minimum Bayesian Information Criterion. The relative importance of each predictor was assessed with the absolute values of standardized coefficients. Statistical significance was set at P < 0.05 for all analyses, which were performed with JMP Pro (v 14: SAS Institute Inc., Cary, NC).

3. Results

The knee abduction moment was positively correlated to the vertical ground reaction force (R = 0.522, P < 0.001), lateral ground reaction force (R = 0.395, P = 0.016) and hip adduction angle (R = 0.358, P < 0.023), and partially correlated with lateral pelvic tilt (R = 0.311, P = 0.061) (Supplemental Tab. 1). The significant correlation was not detected between knee abduction moment and gluteus medius force (R = - 0.234, P < 0.164) whereas some muscle forces correlated to the knee abduction moment (Supplemental Tab. 1). Between the variables correlated to the knee abduction moment, hip adduction angle was correlated to the vertical ground reaction force (R = 0.481, P = 0.003), whereas lateral pelvic tilt was correlated to the lateral ground reaction force (R = 0.332, P = 0.045) (Supplemental Tab. 2). The right-left difference in hip adduction angle was positively correlated to the right-left difference in vertical ground reaction force (R = 0.368, P = 0.025) (Fig. 2).

Fig. 2:

Scatter plot of right-left difference in hip adduction versus right-left difference in vertical ground reaction force. Positive values of hip adduction difference indicate that the right hip presented a larger adduction than the left hip, which indicates an asymmetric landing strategy with a pelvic shift towards the right leg. Positive values of ground reaction force indicate that the right leg presented a larger ground reaction force than the left leg.

Multiple regression analysis showed that the knee abduction moment was predicted by lower gluteus medius force and higher vertical and lateral ground reaction forces (P < 0.001, R2 = 0.640). The regression model for knee abduction moment was

$$\text{Knee}\text{abduction moment}=9.828-\text{0}.020\times \text{Gluteus medius force}+\text{0}.035\times \text{Vertical ground reaction force}+\text{0}.500\text{×}\text{Lateral ground reaction force}$$

The P values for the variables included in the regression model were P = 0.154 (intercept), P = 0.003 (gluteus medius force), P < 0.001 (vertical ground reaction force), and P < 0.001 (lateral ground reaction force). The absolute values of standardized coefficients were 9.2 (gluteus medius force), 14.5 (vertical ground reaction force) and 11.4 (lateral ground reaction force). A representative trial with high knee abduction moment demonstrated lower gluteus medius force and higher vertical and lateral ground reaction forces, hip adduction and lateral pelvic tilt, whereas a low knee abduction moment trial demonstrated opposite patterns on these variables to high knee abduction moment trial (Fig. 3).

Fig. 3:

A waveform comparison of frontal plane biomechanics between representative trials with high (red) and low (blue) knee abduction moment. Acronyms: KAM = knee abduction moment.

4. Discussion

The purpose of the present study was to investigate the relationships between the knee abduction moment and frontal plane biomechanical variables and lower limb muscle force during DVJ in female athletes. The present study showed that the peak knee abduction moment was positively correlated to the peak vertical and lateral ground reaction forces, hip adduction angle and lateral pelvic tilt. Furthermore, a significant regression model indicated that peak knee abduction moment was predicted by lower peak gluteus medius force and higher peak vertical and lateral ground reaction force, with higher impact from ground reaction forces, which supported the a priori hypothesis tested. The simulations predicted muscle activations consistent with EMG data, as demonstrated by the large significant correlations between them (Supplemental Fig. 1).

The present study showed that a larger gluteus medius force predicted lower knee abduction moments during DVJ based on the regression. Although the gluteus medius force did not significantly correlate to the knee abduction moment, the gluteus medius force was significantly included in the multiple regression model based on the minimum Bayesian information criterion and multicollinearity was not detected using the variance inflation factor (1.11, 1.05 and 1.10 for vertical ground reaction force, lateral ground reaction force and gluteus medius force, respectively). This indicated that the regression model was valid (Hair et al., 2013). A previous study reported that the gluteus medius force accelerates the center-of-mass medially during gait (Pandy et al., 2010), which suggests that the gluteus medius force should have a mechanical relationship with the lateral ground reaction force. However, since the acceleration and ground reaction force are a function of muscle forces, gravity, residual forces, centrifugal, Coriolis, and inertial forces, the linear relationships between the gluteus medius force and lateral ground reaction force could be concealed by the contribution of other factors. Hewett et al. (Hewett et al., 2005) prospectively predicted ACL injury with peak knee abduction moment during DVJ. Although the results of the present study do not prove causation, the significant relationship between gluteus medius force and knee abduction moment reveal a potential connection between them. This result was consistent with a previous report that identified gluteus muscle force opposed the knee abduction moment during a side step cutting task (Maniar et al., 2018).

With regard to the relationships between the biomechanical variables, hip adduction and lateral pelvic tilt were correlated to the vertical and lateral ground reaction forces, respectively. Higher vertical ground reaction force was observed during trials with larger hip adduction angle. This finding is related to the finding that subjects landed asymmetrically with larger body weight on one leg, which shifted the pelvis to the same side and increased hip adduction angle (Fig. 2). These biomechanical features may explain the larger lateral trunk lean of female athletes at the time of ACL injury that was reported in a video analysis (Hewett et al., 2009), which is the proposed theory of mechanical connection between trunk, hip, knee and ACL injury in female athletes (Hewett and Myer, 2011). A possible interpretation of these results is that hip adduction and lateral pelvic tilt might increase the vertical and lateral ground reaction force, which, in turn, would result in higher knee abduction moments (Fig. 3). However, as this study is limited to identifying any cause and effect relationship, further investigation is necessary to demonstrate this interpretation.

The relationships between outcome variables were examined using peak values, even though the peaks did not always occur at the same time. Using the peak values was motivated by the intention of the authors to evaluate the biomechanical factors and to inform a training protocol in clinical settings, which are often based on peak values, as they are more readily quantifiable (Di Stasi et al., 2013; Myer et al., 2010). However, to ensure that the significant relationships were not limited to peak values, an analysis that used the outcome values at the time of peak abduction moment was conducted and reported as Supplemental data.

Biceps femoris short head, gastrocnemius lateralis, hip adductors and ankle dorsi flexors were negatively correlated to the knee abduction moment and the vertical or lateral ground reaction forces. Since the large ideal actuator was assigned on knee ab/adduction, those muscles were not used to track the knee abduction moment during the optimization process. Time of peak force in biceps femoris short head and dorsi flexors was immediately before IC, whereas the time of peak force in gastrocnemius lateralis and hip adductors occurred immediately after IC and in the later phase, respectively. Therefore, biceps femoris short head and dorsi flexors activated to prepare for landing, while gastrocnemius lateralis contributed to absorption of the ground reaction forces. The negative correlation between the hip adductors force and the knee abduction moment and lateral ground reaction force might derive from the co-activation of hip adductors and abductors needed to provide hip joint stability. A previous study showed that hip adductors contribute to accelerate the center-of-mass laterally (Pandy et al., 2010),which appears to contrast the results of this study. However, since the net hip abduction torque is positive during the landing phase, an activation of the hip adductors will inevitably cause a higher coactivation of the hip abductors to counteract it, which could in turn produce the negative correlations observed in the present study.

This study presents some limitations. First, the effect of lower limb muscle forces around the knee may be decreased since higher ideal torque on knee abduction/adduction was applied to keep the model physiologically. Previous studies indicated that co-contraction of quadriceps and hamstrings, activation of gracilis and tensor fascia lata contributed to muscular absorption of the external knee abduction moment (Lloyd et al., 2005; Lloyd and Buchanan, 2001). The effect of co-contraction of quadriceps and hamstrings on the knee abduction moment should be investigated in the future using a more detailed musculoskeletal model, including ligaments and contact between knee articular surfaces. Second, a limitation of our EMG-informed method is that EMG data was not available for every muscle (e.g. deeper muscles). Therefore, their activation was only driven by the component of the objective function that minimizes muscle activity. Third, the factors that increase the gluteus medius activation were not investigated. To understand the contribution of neuromuscular control on the knee abduction moment more clearly, future musculoskeletal modeling on the effect of strengthening and neuromuscular training on the knee abduction moment and recruitment of the hip abductor muscle is required.

The relationships between the knee abduction moment, muscle forces and frontal plane biomechanics were quantified using EMG-informed musculoskeletal simulations. The knee abduction moment was predicted by lower gluteus medius force and higher vertical and lateral ground reaction force during drop vertical jump. Controlling the frontal plane pelvic position during landing may help to avoid injurious ground reaction forces and consequent knee abduction moment.