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Article

Biomechanical Symmetry during Drop Jump Landing and Takeoff in Adolescent Athletes Following Recent Anterior Cruciate Ligament Reconstruction

by
Eva M. Ciccodicola
1,*,
Nicole M. Mueske
1,
Mia J. Katzel
1,
Curtis D. VandenBerg
1,2,
James Lee Pace
3 and
Tishya A. L. Wren
1,2
1
Children’s Hospital Los Angeles, Los Angeles, CA 90027, USA
2
Department of Orthopaedic Surgery, University of Southern California, Los Angeles, CA 90007, USA
3
Connecticut Children’s Medical Center, Hartford, CT 06106, USA
*
Author to whom correspondence should be addressed.
Symmetry 2021, 13(4), 639; https://doi.org/10.3390/sym13040639
Submission received: 15 March 2021 / Revised: 2 April 2021 / Accepted: 9 April 2021 / Published: 10 April 2021
(This article belongs to the Special Issue Symmetry and Biomechanics)

Abstract

:
This study investigated asymmetry between lower extremities during the landing and takeoff phases of a vertical drop jump (VDJ) in adolescent athletes following anterior cruciate ligament reconstruction (ACLR) and examined if performance was affected by reducing jump height. Thirty-three athletes who underwent ACLR and were referred for 3D biomechanical assessment before returning to play (mean age 15.9, SD 1.3 years; 16/33 female; mean time since surgery 7.4, SD 1.2 months) completed the VDJ while kinematics and kinetics were collected using motion capture. Lower extremity symmetry was compared between phases using paired t-tests. Jump height was calculated to measure performance. Asymmetries in ankle inversion, ankle adduction, knee adduction, hip adduction, hip adduction moment, and hip rotation moment were observed in both phases. Asymmetry was also observed in both phases for sagittal moments and power integrals at the knee and ankle and total power integral, with the magnitude of asymmetry being smaller during takeoff for power absorption/generation. Jump height was related to power generation integrals during takeoff but not to the asymmetry of power generation. Since asymmetries are translated from landing through takeoff, rehabilitation should address both phases to decrease injury risk and maximize performance after return to play.

1. Introduction

Anterior cruciate ligament (ACL) injuries have become increasingly common in adolescent athletes in the past two decades with the number of ACL tears increasing by 2.3% per year in youth 6 to 18 years of age [1,2]. This increase has been influenced by a greater number of adolescents participating in organized, high-level sports [1]. Studies have found a number of biomechanical factors, such as dynamic knee valgus and greater side to side knee abduction moment asymmetry, that contribute to a higher risk of sustaining an ACL injury [1,3,4,5]. Surgical reconstruction of the ACL is the preferred treatment to allow for patients to return to their prior level of activity [6,7]. McCollugh et al. found that 63% of high school athletes did return to their sport following ACL reconstruction (ACLR). However, just 43% of athletes who returned to sport felt that they were playing at their pre-injury level of performance [8]. Research has shown that athletes returning to sport after ACLR have an increased risk of sustaining a new injury to both the ipsilateral and contralateral limbs and developing early onset osteoarthritis (OA) in the reconstructed knee even with successful surgery [9,10].
Due to this increased risk of sustaining a second ACL injury, there is much debate over the objective clinical criteria used to determine when an adolescent athlete should be allowed to return to sport following ACLR [5,10,11,12,13]. Some of the commonly used return to sport measures include time since surgery, movement analysis, and the strength and range of motion symmetry between limbs [5,14]. In addition, physical performance tests that include hopping and jumping are also often used clinically to examine knee stability and return to sport readiness [5,14,15].
The vertical drop jump (VDJ) test is one such measure commonly used as it mimics a deceleration task often seen in sport and is a way to assess limb symmetry during a single movement [11,16,17]. In addition, it has been shown that uninjured adolescents perform a VDJ task with only slight asymmetries, supporting that biomechanical symmetry is an appropriate goal for return to sport testing [18]. The landing phase of this task has been extensively researched as this is the point when most non-contact ACL injuries are thought to occur [19,20,21]. Research has shown that poor biomechanics are present in patients following ACLR in tasks such as the VDJ landing [11,19,22]. Mueske et al. found that there is decreased energy absorption, decreased sagittal plane external flexion moments at the knee and ankle, and decreased peak dorsiflexion angle during the landing phase in adolescent athletes who had undergone ACLR compared to their uninvolved side [23]. Dynamic valgus, reduced active shock absorption, and decreased flexion of the lower extremity seen during the landing phase of the VDJ task have been associated with an increased risk for ACL injury [20,24,25,26].
The takeoff phase of the VDJ task has been less researched as it is normally used as a performance-based measure [27,28]. Little is known about the takeoff phase and how it relates to between limb symmetry following ACLR. Currently, no study has examined the biomechanical strategies utilized during both the landing and takeoff phases in the VDJ task and their implications in rehabilitation following ACLR. The purpose of this study was to investigate the occurrence and degree of asymmetries of kinetics and kinematics between the lower extremities during the landing and takeoff phases of a VDJ task in adolescent athletes following recent ACLR. We hypothesized that asymmetries seen in the landing phase will carry over to the takeoff phase, which will likely lead to decreased performance from a reduced jump height.

2. Materials and Methods

This retrospective study examined data from patients 13 to 18 years old who were seen in the Motion and Sports Analysis Laboratory between March 2015 and February 2018 for 3D biomechanical assessment following unilateral ACLR for a non-contact injury (Table 1). Patients were excluded from the study if they had a history of other serious lower extremity injury, previous ACL injury, were unable to complete the VDJ, or had missing motion analysis data during VDJ landing and takeoff. Patients had not yet been cleared for return to full activity at the time of testing. Data were accessed retrospectively under either a waiver of consent or signed consent approved by the Children’s Hospital Los Angeles Institutional Review Board.
Data collection was performed by two experienced pediatric physical therapists who had specialized training in sports biomechanical assessment and motion analysis. Anthropometric measurements were obtained using standard clinical procedures, and a VDJ was performed as part of a more extensive biomechanical testing protocol [29]. Prior to all biomechanical testing, the subject warmed up with approximately 5 min of treadmill running. For the VDJ task, participants were instructed to drop off a 41 cm box, land with each foot on a different force plate, and then jump straight up as high as possible, landing back on the same force plates to keep the jump vertical (Figure 1). Following two to three practice trials, three trials for data collection were performed, and all trials with useable data (a minimum of two per subject) were averaged for further analysis [30].
Three-dimensional lower extremity motion analysis data were recorded during the VDJ using an 8 to 10 camera motion capture system at 120 Hz (Nexus 2, Vicon Motion Systems Ltd., Oxford, UK) and two analog force plates at 2400 Hz (AMTI OR6-5, Advanced Medical Terminology, Inc., Watertown, MA, USA). An experienced physical therapist placed markers on the participant’s trunk, pelvis, and lower extremities following a custom 6-degree of freedom (DOF) model [30]. Marker trajectories were filtered using a Woltring filter with a mean squared error of 10 mm2. Force plate data were filtered using a 16 Hz Butterworth filter.
Kinematic and kinetic measures were calculated during the landing and takeoff phases of the VDJ task. The landing phase was defined as the first initial contact to sacral marker velocity change of vertical direction, and the takeoff phase was defined as sacral marker velocity change of vertical direction to foot off. Kinematics were calculated based on segment orientations determined by 6DOF segment optimization in Visual3D (C-Motion, Inc., Germantown, MD, USA), and kinetics were calculated using inverse dynamics in the same software. Average joint angles, external moments and power in the sagittal, frontal and transverse planes were collected and used to calculate limb symmetry as the surgical limb minus the contralateral limb. Positive values indicate flexion, adduction, and internal rotation of the hip and knee and dorsiflexion, adduction, and inversion of the ankle, along with the corresponding external moments. The power integral was calculated during landing as the integral of power absorption (negative values) over the landing phase. Similarly, the power integral was calculated during takeoff as the integral of power generation (positive values) over the takeoff phase. In both cases, the integral is reported as a positive value indicating energy absorption during landing and energy generation during takeoff.
Jump height (Hjump) was calculated as a measure of performance using the impulse-momentum method based on the integral of vertical ground reaction force (GRF) from peak knee flexion (PKF) to foot off [31].
Equation (1):
H j u m p = v t a k e o f f 2 2 g ,
where g is the acceleration due to gravity and takeoff velocity is
Equation (2):
v t a k e o f f = P K F f o o t o f f ( F G R F m g ) d t ,
where FGRF is the total (left + right) vertical GRF, and m is subject mass.
Difference between limbs (significance of asymmetry) during each phase and difference in magnitude of asymmetry between the landing and takeoff phases were evaluated using paired t-tests. The relationship of jump height to power generation integral at each joint and in total was evaluated using Pearson’s correlation. Pearson’s correlation was also used to examine the relationship between jump height and asymmetry of power generation. All statistical analysis was performed in Stata (version 14, StataCorp LLC, College Station, TX, USA) with a significance level of 0.05.

3. Results

Thirty-three patients (16 female; mean age 15.9, standard deviation (SD) 1.3 years) met the eligibility criteria and were included in this study (Table 1). Their mean time since surgery was 7.4 months (range 6 to 10 months). All patients had autograft reconstructions, 13 with hamstring tendon, 13 with patellar tendon, 6 with quadriceps tendon, and 1 with iliotibial band.
Kinematics and Kinetics:
In the frontal and transverse planes, significant asymmetry was observed, with the surgical limb having higher values during both landing and takeoff for ankle inversion, knee adduction, ankle adduction, and hip rotation (Table 2). The hip was less abducted on the surgical side during both landing and takeoff, but the difference only reached statistical significance during landing. The hip adduction moment and ankle adduction moment were significantly lower on the surgical side during both landing and takeoff. Knee and hip rotation moment were lower on the surgical side during both landing and takeoff, but the difference only reached statistical significance during landing. The magnitude of asymmetry was greater during landing than during takeoff for hip abduction angle and moment, ankle adduction moment, and hip rotation moment.
In the sagittal plane, asymmetry was observed during both landing and takeoff for ankle, knee, and hip angles, ankle and knee flexion moments, ankle and knee power integrals, and total power integral. Angles, moments, and power integrals were lower for the surgical compared with the contralateral side. The magnitude of asymmetry was greater during landing than during takeoff for ankle and knee angles and moments and the power integral at all joints and in total. At the hip, flexion moments were higher for the surgical limb during both landing and takeoff, but the difference was only statistically significant during landing (Figure 2).
Jump Height:
Jump height, as a measure of performance, was significantly related to the power generation integral during takeoff at all joints and in total regardless of limb injury status (p ≤ 0.05) (Table 3). However, jump height was not related to asymmetry of the power integral at any joint or in total (p ≥ 0.52).

4. Discussion

Reduced active shock absorption and decreased flexion of the lower extremity seen during the landing of jumping or cutting tasks are factors that have been associated with an increased risk for obtaining an ACL injury [24,26,32]. The current study found that asymmetries in shock absorption occurred during the landing phase of the VDJ for the ankle and knee, and that energy absorption during landing was lower overall on the surgical limb compared to the contralateral side. This decreased energy absorption could contribute to inadequate shock absorption at the knee joint which has been shown to be one risk factor associated with ACL injury during landing and cutting tasks [33,34].
Previous studies have shown that between limb asymmetries are often seen as the surgical limb offloading to the contralateral limb during the landing phase of the VDJ task, though specific asymmetric strategies differ by study [12,26,35,36]. Our study found decreased energy absorption on the surgical limb during landing which is consistent with previous research [12,23,37]. This is often thought to be a protective compensation while the surgical knee is still recovering. We also found that the surgical limb had higher values for ankle inversion, ankle adduction and hip rotation moment compared to the contralateral limb in both the landing and takeoff phases. Increased hip internal rotation angles are one of the main components of dynamic limb valgus which has been well documented as a risk factor for initial and subsequent ACL tears [3,11,21]. However, contrary to other research which has shown increased knee abduction moment as a risk factor for ACL injury, we found increased knee adduction moments on the surgical limb. This could indicate that these subjects have further protective offloading of their surgical knee which is seen clinically and has been documented in previous research, highlighting the importance of training the patient to appropriately and symmetrically load the knees in rehabilitation following ACLR [38,39]. In addition, this persistent offloading of the surgical limb shifts the load and increases the demand on the contralateral side, leading to potential overloading and contributing to the high rate of contralateral injuries following an initial ACL tear [9]. As this was not the focus of our paper, this finding deserves further investigation such as separating the groups into male and female subjects to examine if there is a sex difference or including strength or electromyography data to further examine clinical rehabilitation measures.
An avoidance of active shock absorption may suggest that the patient continues to be apprehensive and protecting the reconstructed knee or does not have adequate strength to eccentrically control their landing. Consistent with previous research, we also found asymmetries for ankle and knee flexion moments during the landing phase for the surgical limb compared to the contralateral limb [23,26,40,41]. This reduced knee flexion moment further contributes to decreased shock absorption upon landing and can cause the knee to be more at risk to reinjury since the joint experiences more shear stress and resultant ACL tears when it is in a more extended position [19]. In addition, research has shown that in this timeframe following ACLR patients with patella or quadriceps tendon grafts have more sagittal plane deficits and slower recovery of symmetry than those with hamstring tendon grafts [19]. Disruption of the knee extensor mechanism and eccentric knee flexion control of the knee could be a factor in decreased knee flexion moments seen in these patients. Increasing active shock absorption during landing tasks is an important component of rehabilitation and return to sport training following an ACL tear to decrease the chance of reinjury and osteoarthritis development of the surgically reconstructed knee and maximize performance of athletic tasks.
We also found that patients had decreased energy generation on the surgical limb during takeoff illustrating that offloading strategies persist in this phase of the VDJ task. While asymmetries carry over from landing to takeoff, the magnitude of asymmetry of energy transfer appears to be attenuated during takeoff. If not properly addressed during rehabilitation, offloading strategies and compensations can persist leading to weakness on the ACLR limb and can also increase patients’ long-term risk for OA in the reconstructed knee by hindering normal cartilage production [33,34,42]. This persistent weakness can also lead to reduced performance and may contribute to some patients stating they do not achieve their preinjury level of play. The resolution of avoidance strategies and the resulting improved lower extremity symmetry as a criterion for return to sport clearance could produce a sounder assessment and a more confident return to sport decision and reduce the risk of subsequent ACL injuries to the ipsilateral and contralateral side. The specific metrics of these strategies can be captured with motion analysis and shows the importance of this type of assessment in a clinical setting [19].
Previous research has typically used the takeoff phase of the VDJ tasks as a performance metric based off either jump height or flight time [27,28,43]. We found that jump height was significantly related to the power generation integral during takeoff at all joints. However, asymmetry of the power integral between limbs was not found to be related to jump height or performance of the task. Asymmetry may not have a large impact on an athlete’s performance, and other research has shown that kinematic asymmetry has no effect on running efficiency or energy expenditure [44].
The limitations of our study include the retrospective design and limited sample size. Due to the relatively small sample size, the male and female participants were not analyzed separately, despite some evidence for biomechanical differences between the sexes [45]. The biomechanical model used a single segment foot and therefore did not model separate hindfoot and forefoot or midfoot motion. Following the common convention in motion analysis, we refer to the joint connecting the shank and foot as the ankle. In this context, ankle adduction is equivalent to ankle rotation in the transverse plane. Also, patients were between 6 to 10 months post-surgery and were not yet cleared for return to sport, which may limit generalizability to other patient populations. Because the patients in this study had not yet been cleared to return to full activity at the time of testing, they would be expected to continue to improve over time in terms of lower extremity symmetry and deviations from normal landing and takeoff biomechanics [19].

5. Conclusions

Similar sagittal, frontal, and transverse plane asymmetries were present during both the landing and takeoff phases of the VDJ task. Because asymmetries are translated from the landing through the takeoff phase, specifically in energy absorption to generation, this may give early insight as to why some athletes do not return to their preinjury level of play and are at higher risk of sustaining a future ACL injury. Though we did not find a significant relationship between asymmetries and performance, we found that jump height was significantly related to power generation which will not be maximized if one side produces less than maximal output. Targeting asymmetry and focusing on both landing and takeoff mechanics during rehabilitation may help to decrease the rate of injuries and maximize performance. Because premature return to sport may put athletes at an increased risk for future injury, further research is needed to establish more comprehensive, objective return-to-sport criteria for adolescents post ACLR that can effectively show biomechanical deficits.

Author Contributions

The authors made the following contributions: Conceptualization, E.M.C. and N.M.M.; methodology, E.M.C., N.M.M. and T.A.L.W.; validation, N.M.M. and T.A.L.W.; formal analysis, N.M.M. and T.A.L.W.; investigation, M.J.K.; resources, C.D.V. and J.L.P.; data curation, E.M.C., N.M.M. and T.A.L.W.; writing—original draft preparation, E.M.C.; writing—review and editing, E.M.C., N.M.M., M.J.K., C.D.V., J.L.P. and T.A.L.W.; visualization, E.M.C., N.M.M. and T.A.L.W.; supervision, N.M.M. and T.A.L.W.; project administration, E.M.C., N.M.M. and T.A.L.W. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

The study was conducted according to the guidelines of the Declaration of Helsinki, and approved by the Institutional Review Board (or Ethics Committee) of Children’s Hospital Los Angeles (protocol code #CHLA-14-00194 and 6/11/2014 of approval).

Informed Consent Statement

Informed consent was obtained from all subjects involved in the study.

Data Availability Statement

Data is contained within the article.

Acknowledgments

The authors would like to thank our Sports Motion Lab team—Bitte Healy.

Conflicts of Interest

One author is a consultant for Arthex and Ceterix; neither company was involved in any aspect of this study. The remaining authors have no conflicts of interest to declare.

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Figure 1. Vertical drop jump task performance.
Figure 1. Vertical drop jump task performance.
Symmetry 13 00639 g001
Figure 2. Asymmetry of kinematics and kinetics (difference between operated side and contralateral side).
Figure 2. Asymmetry of kinematics and kinetics (difference between operated side and contralateral side).
Symmetry 13 00639 g002
Table 1. Participant characteristics (N = 33).
Table 1. Participant characteristics (N = 33).
CharacteristicValue
Sex
Female16 (48%)
Male17 (52%)
Age (years)15.9 (1.3)
Height (cm)170.2 (10.4)
Weight (kg)69.6 (17.4)
BMI (kg/m2)24.0 (5.4)
Time since surgery (months)7.4 (1.2)
Graft type (all autograph)
Hamstring tendon13 (39%)
Patella tendon13 (39%)
Quadriceps tendon6 (18%)
Iliotibial band1 (3%)
Surgical side
Left22 (67%)
Right11 (33%)
Meniscal involvement *
None18 (56%)
Repair13 (24%)
Menisectomy3 (9%)
Single sport19 (59%)
Multiple Sports14 (41%)
Continuous variables are reported as mean (SD). Categorical variables are reported as N (%). * 1 subject had both repair and menisectomy.
Table 2. Kinematics and kinetics of the reconstructed and contralateral limbs during vertical drop jump (VDJ) landing and takeoff.
Table 2. Kinematics and kinetics of the reconstructed and contralateral limbs during vertical drop jump (VDJ) landing and takeoff.
Landing Takeoff
Injured, Mean (SD)Contralateral, Mean (SD)Asymmetry, Mean (SE)pInjured, Mean (SD)Contralateral, Mean (SD)Asymmetry, Mean (SE)pP Asymmetry TO vs. Landing
FRONTAL PLANE
Ankle inversion9.3 (4.5)7.3 (4.2)2.0 (0.7)0.0110.9 (4.5)9.0 (4.2)1.8 (0.7)0.010.61
Knee adduction8.8 (7.1)3.4 (6.5)5.4 (1.1)<0.00017.6 (7.0)2.7 (6.2)5.0 (1.1)0.00010.22
Hip adduction−8.2 (8.1)−11.1 (6.8)2.9 (1.3)0.04−7.8 (7.5)−9.1 (6.5)1.3 (1.1)0.260.02
Ankle inversion moment0.03 (0.06)0.05 (0.08)−0.02 (0.01)0.200.09 (0.06)0.10 (0.08)−0.01 (0.01)0.340.47
Knee adduction moment−0.17 (0.18)−0.22 (0.25)0.05 (0.04)0.18−0.10 (0.13)−0.14 (0.19)0.04 (0.03)0.160.69
Hip adduction moment−0.11 (0.22)0.20 (0.21)−0.31 (0.05)<0.0001−0.02 (0.21)0.20 (0.20)−0.22 (0.04)<0.00010.0001
TRANSVERSE PLANE
Ankle adduction3.4 (4.5)1.3 (5.2)2.2 (0.9)0.022.9 (4.7)0.9 (4.9)2.0 (0.9)0.020.63
Knee rotation−10.6 (10.3)−9.5 (9.0)−1.0 (1.4)0.47−12.8 (9.3)−11.7 (8.6)−1.1 (1.2)0.370.87
Hip rotation12.1 (7.9)4.2 (6.7)7.9 (1.2)<0.000111.3 (8.4)3.5 (7.5)7.8 (1.2)<0.00010.86
Ankle adduction moment0.11 (0.06)0.15 (0.06)−0.04 (0.01)0.0020.16 (0.06)0.18 (0.07)−0.02 (0.01)0.030.02
Knee rotation moment0.001 (0.04)0.03 (0.07)−0.03 (0.01)0.050.01 (0.04)0.03 (0.05)−0.02 (0.01)0.130.21
Hip rotation moment0.03 (0.11)−0.04 (0.11)0.07 (0.02)0.001−0.02 (0.10)−0.05 (0.10)0.02 (0.02)0.120.003
SAGITTAL PLANE
Ankle dorsiflexion17.2 (5.7)22.1 (5.2)−4.9 (0.8)<0.000115.0 (5.5)18.6 (5.9)−3.5 (0.6)<0.00010.006
Knee flexion85.5 (13.0)88.8 (11.9)−3.3 (0.7)0.000179.3 (12.2)81.5 (11.7)−2.1 (0.5)0.00010.02
Hip flexion84.9 (11.7)82.6 (12.0)2.4 (0.7)0.00177.5 (11.1)75.3 (11.0)2.2 (0.6)0.00090.61
Ankle dorsiflexion moment0.65 (0.17)0.84 (0.27)−0.19 (0.04)0.00020.74 (0.19)0.84 (0.23)−0.11 (0.03)0.00020.03
Knee flexion moment0.84 (0.34)1.40 (0.36)−0.56 (0.09)<0.00010.70 (0.27)1.00 (0.24)−0.30 (0.05)<0.0001<0.0001
Hip flexion moment1.05 (0.19)1.01 (0.34)0.05 (0.06)0.441.10 (0.23)1.03 (0.24)0.06 (0.03)0.040.76
Power integral ankle0.51 (0.14)0.83 (0.32)−0.32 (0.05)<0.00010.78 (0.19)0.97 (0.23)−0.19 (0.03)<0.00010.005
Power integral knee1.10 (0.52)2.07 (0.54)−0.97 (0.13)<0.00011.03 (0.46)1.55 (0.38)−0.52 (0.07)<0.0001<0.0001
Power integral hip0.98 (0.24)1.02 (0.40)−0.05 (0.06)0.461.17 (0.36)1.17 (0.38)0.002 (0.03)0.940.01
Power integral total2.59 (0.65)3.92 (0.95)−1.33 (0.21)<0.00012.98 (0.80)3.68 (0.80)−0.70 (0.09)<0.00010.0002
External moments are reported. Angles are in units of degrees, moments in Nm/kg, and power integral in J/kg.
Table 3. Correlation of jump height to power generation integral (AUC) during takeoff.
Table 3. Correlation of jump height to power generation integral (AUC) during takeoff.
Surgical Contralateral Asymmetry
RpRpRp
Ankle power integral0.400.020.410.02−0.120.52
Knee power integral0.340.050.500.003−0.090.63
Hip power integral0.500.0030.450.0090.050.77
Power integral total0.510.0020.570.0005−0.020.90
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Ciccodicola, E.M.; Mueske, N.M.; Katzel, M.J.; VandenBerg, C.D.; Pace, J.L.; Wren, T.A.L. Biomechanical Symmetry during Drop Jump Landing and Takeoff in Adolescent Athletes Following Recent Anterior Cruciate Ligament Reconstruction. Symmetry 2021, 13, 639. https://doi.org/10.3390/sym13040639

AMA Style

Ciccodicola EM, Mueske NM, Katzel MJ, VandenBerg CD, Pace JL, Wren TAL. Biomechanical Symmetry during Drop Jump Landing and Takeoff in Adolescent Athletes Following Recent Anterior Cruciate Ligament Reconstruction. Symmetry. 2021; 13(4):639. https://doi.org/10.3390/sym13040639

Chicago/Turabian Style

Ciccodicola, Eva M., Nicole M. Mueske, Mia J. Katzel, Curtis D. VandenBerg, James Lee Pace, and Tishya A. L. Wren. 2021. "Biomechanical Symmetry during Drop Jump Landing and Takeoff in Adolescent Athletes Following Recent Anterior Cruciate Ligament Reconstruction" Symmetry 13, no. 4: 639. https://doi.org/10.3390/sym13040639

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