Biomechanical asymmetry during side-cutting is associated with lower limb muscle strength after anterior cruciate ligament reconstruction

Abstract

Objective

The relationship between muscle function recovery and biomechanical alterations after anterior cruciate ligament reconstruction (ACLR) during high-risk movements remains unclear. This study aimed to investigate lower-limb muscle strength across multiple angular velocities (concentric and eccentric contractions) and knee biomechanics during side-cutting at 9 months post-ACLR, and to explore their association.

Methods

Thirty-six participants (21 males, 15 females) at 9 months post-ACLR completed three-dimensional motion analysis during side-cutting and isokinetic strength testing (concentric: 60, 180, 300°/s; eccentric: 60°/s). Paired t-tests analyzed interlimb differences; Spearman’s correlation assessed limb symmetry index (LSI) correlations.

Results

The reconstructed limb demonstrated reduced peak knee flexion angle (P < 0.001, Cohen’s d = 0.91), extension moment (P < 0.001, Cohen’s d = 1.05), and vertical ground reaction force (P = 0.011, Cohen’s d = 0.45), alongside increased external rotation angle (P = 0.035, Cohen’s d = 0.37). Concentric quadriceps strength was weaker at 60°/s (P = 0.010, Cohen’s d = 0.46), 180°/s (P = 0.001, Cohen’s d = 0.58) and 300°/s (P = 0.001, Cohen’s d = 0.62), concentric hamstring strength was also reduced at 300°/s (P = 0.037, Cohen’s d = 0.36). Knee flexion angles showed a strong positive correlation with concentric quadriceps strength at 180°/s (r = 0.512, P = 0.001), while external rotation angles correlated moderately negatively with both concentric quadriceps strength and concentric hamstring strength at 300°/s (r = -0.410, P = 0.013; r = །0.467, P = 0.004). At the vGRF peak, the extension moment correlated positively with eccentric quadriceps (r = 0.377, P = 0.023) and hamstring strength (r = 0.364, P = 0.029) at 60°/s.

Conclusion

At nine months post ACLR, persistent interlimb asymmetries in side-cutting biomechanics and thigh muscle strength were observed, with moderate correlations between them, particularly at medium to high angular velocities. These findings suggest moving beyond maximal strength training in rehabilitation. Incorporating velocity-specific and eccentric training, together with isokinetic strength assessment at velocities such as 180°/s and 300°/s in return-to-sport criteria, may help reduce reinjury risk.

Introduction

Anterior cruciate ligament (ACL) injuries typically occur during non-contact sports maneuvers such as landing from a jump, deceleration, and side-cutting [1]. Anterior cruciate ligament reconstruction (ACLR) is the primary treatment for ACL injuries and can restore knee joint stability [2]. However, return-to-sport (RTS) rates remain suboptimal. After ACLR, only 55% of athletes return to competitive sports [3], and the risk of secondary injury remains elevated, between 5.4% and 27.8% [4]. This persistent risk highlights the potential importance of addressing underlying biomechanical and strength deficits, as targeted training has been shown to mitigate such risks in related contexts [5].

Among various high-risk sports movements, the side-cutting task, which requires rapid deceleration, change of direction, and acceleration, can generate substantial multiplanar knee joint forces and moments, placing greater demands on joint stability and muscle tensile strength [6]. Shi et al. [7] found that one year after ACLR, the reconstructed limb exhibited abnormal biomechanics during side-cutting compared with the contralateral limb and healthy controls.

Notably, a relationship exists between muscle strength and lower limb biomechanical function [8, 9]. Studies have shown that patients with greater quadriceps strength symmetry demonstrate better functional performance than those with reduced symmetry [10]. Ren and Huang [11] also reported a correlation between muscle strength symmetry and gait biomechanics symmetry one year after ACLR. However, most current research focuses on daily activities such as walking or jumping [9, 11, 12], and muscle strength assessments are often limited to isometric contractions or single- velocity (e.g., 60°/s) concentric contractions [11, 13]. Existing evidence suggests [14] that peak torque output typically occurs at angular velocities between 0 and 60°/s, yet improvements in maximal strength do not consistently lead to increases in sprinting speed or jumping height [15]. This indicates that for such movements, assessment across multiple angular velocities may be more critical. Consequently, the relationship between biomechanics during high-risk movements and lower limb muscle strength across multiple contraction types and velocities remains incompletely understood.

The 9-month postoperative period is a critical window for RTS decisions [16]. Research indicates [17] that delaying RTS within the first nine months after surgery is associated with a substantially reduced risk of secondary injury (51% decrease per month delayed). Similarly, Beischer et al. [18] demonstrated that the incidence of graft rupture was seven times greater in patients who returned to sport at nine months post-ACLR compared to those who delayed their return. Underlying biomechanical abnormalities may be a significant factor in secondary injuries. Thomson et al. [19] observed significant biomechanical asymmetries in the reconstructed limb during running among male soccer players who returned to sport within 9 months after surgery, whereas no such asymmetries were noted in those who returned after 9 months. Therefore, systematically investigating the relationship between side-cutting biomechanics and lower limb muscle strength is crucial for identifying specific deficits and developing targeted rehabilitation strategies.

Accordingly, the objectives of this study were: (1) to analyze lower limb biomechanical parameters during side-cutting in ACLR patients; (2) to compare the muscle strength of the quadriceps and hamstrings between the reconstructed and contralateral limbs during concentric contractions at 60°/s, 180°/s, and 300°/s and eccentric contractions at 60°/s; and (3) to explore the correlations between lower limb muscle strength and side-cutting biomechanics. We hypothesized that significant biomechanical alterations and muscle strength deficits would exist after ACLR. We also hypothesized that a unique association would exist between lower limb muscle strength and knee biomechanics during side-cutting.

Methods

Participants

The inclusion criteria for patients were as follows: (1) being at 9 months after primary ACL reconstruction with a hamstring tendon autograft; (2) had a pre-injury Tegner Activity Scale score [20] > 5; (3) completion of a standardized postoperative rehabilitation protocol in the hospital; and (4) recovered a normal range of joint motion, with no swelling and effusion. Patients were excluded if they (1) had concomitant injuries to other ligaments of the knee joint; (2) had a history of surgery or skeletal muscle system injury on the contralateral knee; (3) were unable to complete the follow-up testing sessions. Sample size was determined a priori using G*Power 3.1 software. Based on previous research showing moderate correlations (r = 0.40) between strength asymmetry and biomechanical parameters [11] , with α = 0.05 and power (1-β) = 0.80, a minimum sample of 34 participants was required for correlation analysis. We recruited 36 participants to account for potential data loss. Post-hoc power analysis: With n = 36 and observed correlation coefficients ranging from r = 0.329 to r = 0.512, the achieved power ranges from 0.68 to 0.95 for detecting these correlations at α = 0.05. The study appears adequately powered for medium-to-large correlations but may be underpowered for detecting small correlations. All patients signed informed consent forms. This study was approved by the Medical Ethics Committee of Peking University Third Hospital.

Data collection

Isokinetic strength testing

Muscle strength was assessed using an isokinetic dynamometer (Con-Trex MJ, Physiomed Elektromedizin AG, Schnaittach, Germany; Version MK2m) with data acquisition at 256 Hz. The reliability and validity of this system for knee strength assessment have been previously established [21]. Prior to testing, the participants completed a standardized 5–10 min warm-up and stretching protocol, starting with 5 min of low intensity cycling on a stationary bicycle, followed by a series of dynamic stretches targeting the major muscle groups of the lower limbs [22]. One to two practice trials were conducted before formal testing to familiarize patients with the testing procedure and force generation patterns, with 90-second rest intervals between trials. To reduce potential kinesiophobia in participants during testing, this study was designed to test the contralateral limb first, followed by the reconstructed limb. The testing protocol included concentric and eccentric strength of the quadriceps and hamstrings at 60°/s, as well as concentric strength of both muscle groups at 180°/s and 300°/s. The range of motion for isokinetic testing was set at 20°-90°of knee flexion. Patients were instructed to perform 5 maximal knee extension and flexion movements as rapidly and forcefully as possible. The mean isokinetic peak torque (Nm) was calculated and normalized to the body mass (Nm/kg). Each test was separated by a 3 min rest interval.

Three-dimensional motion test

A modified Plug-in-Gait full-body marker set was used. Passive reflective markers were at the shoulder, anterior superior iliac spine (ASIS), posterior superior iliac spine (PSIS), mid-thigh (50% of thigh length), distal lateral third of thigh, lateral and medial femoral condyles, proximal and distal thirds of tibia, distal lateral third of the tibia, lateral and medial malleoli, calcaneus, and first, second, and fifth metatarsophalangeal joints. A Vicon motion capture system (Vicon Motion Systems Ltd, Oxford, UK; Version: v2.2) with 12 high-speed infrared cameras was used to collect three-dimensional kinematic data during side-cutting maneuvers at a sampling frequency of 100 Hz [23]. Two force plates (Advanced Mechanical Technology, Watertown, MA, USA; Version BP400600) simultaneously recorded ground reaction forces at 1000 Hz. Kinematic and kinetic data were synchronized using an analog-to-digital converter (AMTI GEN5, Advanced Mechanical Technology, USA). For the side-cutting task, patients performed a 4-step maximal sprint approach, landed with the test leg on one force plate, and then executed a rapid 45° cutting maneuver to the contralateral side, followed by maximal sprinting. Three successful side-cutting trials were collected, and the average of these trials was used for analysis. During testing, the contralateral limb was assessed first, followed by the reconstructed limb. Five trials were performed per limb, with a minimum of three valid trials retained for each limb per participant. A trial was considered successful if the participant completed the task as instructed and the researchers collected all required kinematic and kinetic data. The entire process was completed without reports of pain.

Observation indicators

The primary outcome measures were: (1) peak concentric knee extension and flexion strength at 60°/s, 180°/s, 300°/s, as well as peak eccentric knee extension and flexion strength at 60°/s; (2) peak knee joint angles and moments during the stance phase; and (3) knee joint angles and moments during the peak posterior ground reaction force (pGRF) and vertical ground reaction force (vGRF) (Fig. 1).

Fig. 1.

Mean GRF patterns during the side-cutting stance phase (n=36). Solid lines represent the group mean; the shaded area represents ±1 standard deviation.GRF, ground reaction force; vGRF, vertical ground reaction force; BS, body mass

In addition to the aforementioned data, we further analyzed the correlation between the limb symmetry index (LSI) of side-cutting biomechanics parameters and the isokinetic strength LSI in ACLR patients. The LSI was calculated for both biomechanical parameters and thigh muscle strength [17].

LSI=(reconstructed limb / contralateral limb) *100%.

Data reduction

The raw marker trajectories were smoothed using a 4th-order low-pass Butterworth filter with an estimated optimal cutoff frequency of 10 Hz [24], and subsequently exported in C3D format. After importing this file into Visual 3D software (C-Motion, USA; version 6.01.0), the derived kinematic and kinetic data were filtered using low-pass filters with cutoff frequencies of 12 Hz and 100 Hz, respectively, in accordance with recommendations for human gait analysis.

Knee joint angles were calculated as Cardan angles of a distal segment reference frame relative to the proximal segment reference frame in order of (1) flexion-extension (2), adduction -abduction, and (3) internal -external rotation. Joint moments were calculated using an inverse dynamic approach and transferred into the distal segment reference frame. The joint moments presented in this study represent net internal moments. Initial contact (IC) was defined as the first point at which the vGRF exceeded 10 N. Toe-off (TO) was subsequently determined as the point at which the vGRF dropped below the 10 N threshold following IC. GRF were normalized to body mass (BS). Joint moments were normalized to the product of body mass and body height (BS·BH). The entire stance phase of the side-cutting task was time-normalized to 101 discrete data points corresponding to 0–100% of the stance phase.

Statistical analysis

Statistical analysis was performed using SPSS 25.0 software. The Shapiro-Wilk test was used to assess data normality. Normally distributed continuous data were presented as mean ± standard deviation (x̄ ± s) and analyzed using paired samples t-tests. Non-normally distributed continuous data were expressed as median (interquartile range) [M (Q1, Q3)] and analyzed using Wilcoxon signed-rank tests. For all statistically significant comparisons, effect sizes were calculated and reported using Cohen’s d. It was classified as follows: no (< 0.2), small (0.20–0.49), medium (0.5–0.79), and large (≥ 0.8) effect [25].

For the correlation analyses between isokinetic strength LSI and side-cutting biomechanical parameter LSI, Spearman’s rank correlation coefficient was employed, as the relevant variables were not normally distributed. The assumption of a monotonic relationship for Spearman correlations was verified through visual inspection of scatterplots. Given the exploratory nature of conducting multiple correlations across different biomechanical and strength parameters, uncorrected P-values are reported. We acknowledge that a strict correction for multiple comparisons (e.g., Bonferroni correction, with α = 0.05/number of tests) would be overly conservative for this hypothesis‑generating research. Therefore, correlations with P-values between 0.01 and 0.05 should be interpreted with appropriate caution. The thresholds for the correlation coefficient (r) were as follows: 0–0.1, trivial; 0.1–0.3, weak; 0.3–0.5, moderate; >0.5, strong. Additionally, the coefficient of determination (r²) was calculated to quantify the proportion of variation between variables that can be explained by their relationship. All tests were two-tailed.

Results

A total of 36 patients ultimately met the criteria and were included in this study. All participant characteristics are shown in Table 1.

Table 1.

Participant Characteristics ^a

Characteristic	ACLR Group, Mean ± SD/%
Age, y	33.40 ± 6.70
Sex (male/female)	21(58.33%) / 15(41.67%)
Body mass, kg	74.50 ± 12.60
Body height, cm	172.90 ± 7.90
BMI, kg/m2	24.70 ± 2.80
Time since surgery, mo	9.45 ± 0.55

^aACLR anterior cruciate ligament reconstruction, BMI Body Mass Index

Knee biomechanics

During the entire stance phase, the reconstructed limb showed significantly reduced peak flexion angle (P < 0.001, Cohen’s d = 0.91) and extension moment (P < 0.001, Cohen’s d = 1.05) but demonstrated greater external rotation angle (P = 0.035, Cohen’s d = 0.37) than the contralateral limb. The reconstructed limb demonstrated a significantly lower peak vGRF than the contralateral limb (P = 0.011, Cohen’s d = 0.45). No significant difference was found in the peak pGRF between limbs; no significant differences were observed in the coronal plane angles or moments. (Table 2)

Table 2.

Maximum knee joint angles and moments during the stance phase

Items	reconstructed limb Mean ± SD	contralateral limb Mean ± SD	P values	Effect Size (Cohen’s d)	95%CI
Peak values
Peak flexion angle (°)	46.475 ± 6.029	51.920 ± 7.208	< 0.001*	0.91	-7.479, །3.411
Peak adduction angle (°)	0.092 ± 4.438	0.138 ± 3.923	0.937	0.01	-1.233, 1.140
Peak external rotation angle (°)	9.993 ± 5.577	8.195 ± 4.514	0.035*	0.37	0.137,3.459
Peak extension moment (BS·BH)	0.118 ± 0.043	0.170 ± 0.035	< 0.001*	1.05	-0.069,།0.035
Peak abduction moment (BS·BH)	0.028 ± 0.034	0.034 ± 0.030	0.374	0.16	-0.018, 0.007
Peak external rotation moment (BS·BH)	0.007 ± 0.028	0.003 ± 0.010	0.388	0.15	-0.005, 0.013
Peak pGRF (BS)	0.240 ± 0.122	0.237 ± 0.119	0.448	0.02	-0.044, 0.050
Peak vGRF (BS)	1.981 ± 0.278	2.096 ± 0.297	0.011	0.45	-0.202, །0.028

^*P < 0.050, BS body mass, BH body height, BS·BH body mass multiplied by body height

At the peak of the pGRF, the reconstructed limb demonstrated a greater external rotation angle (P = 0.032, Cohen’s d = 0.37) and a reduced knee extension moment (P = 0.014, Cohen’s d = 0.43). At the vGRF peak, it exhibited a smaller knee flexion angle (P < 0.001, Cohen’s d = 0.62) and reduced extension moment (P < 0.001, Cohen’s d = 0.78) (Table 3).

Table 3.

Knee joint angles and moments at the peak of GRF

Items	reconstructed limb Mean ± SD	contralateral limb Mean ± SD	P values	Effect Size (Cohen’s d)	95%CI
at the peak pGRF
Knee flexion angle (°)	31.870 ± 5.812	32.670 ± 6.359	0.289	0.18	-2.389, 0.734
Knee external rotation angle (°)	8.313 ± 5.758	6.394 ± 5.095	0.032*	0.37	0.179, 3.660
Knee extension moment (BS·BH)	0.054 ± 0.027	0.068 ± 0.031	0.014*	0.43	-0.03,།0.003
Knee external rotation moment (BS·BH)	0.001 ± 0.002	0.001 ± 0.003	0.509	0.11	-0.001, 0.002
at the peak vGRF
Knee flexion angle (°)	43.023 ± 6.448	48.028 ± 8.550	< 0.001*	0.62	-7.756, །2.253
Knee external rotation angle (°)	4.793 ± 5.232	3.077 ± 4.891	0.057	0.33	-0.053, 3.486
Knee extension moment (BS·BH)	0.110 ± 0.040	0.149 ± 0.040	< 0.001*	0.78	-0.056,།0.022
external rotation moment (BS·BH)	0.002 ± 0.006	0.003 ± 0.007	0.642	0.08	-0.003, 0.002

BS body mass, BH body height

BS·BH body mass multiplied by body height

pGRF peak posterior ground reaction force

vGRF peak vertical ground reaction force

^*P < 0.050

Isokinetic strength of the thigh

Compared with the contralateral limb, the reconstructed limb had significantly weaker Qc at 60°/s, 180°/s, and 300°/s (P = 0.010, Cohen’s d = 0.46; P = 0.001,Cohen’s d = 0.58; P = 0.001, Cohen’s d = 0.62), and weaker concentric hamstring strength (Hc) at 300°/s (P = 0.037,Cohen’s d = 0.36) (Table 4).

Table 4.

Peak Isokinetic Quadriceps and Hamstring Strength

Variable	reconstructed limb Mean ± SD	contralateral limb Mean ± SD	P values	Effect Size (Cohen’s d)	95%CI
Qc (60°/s), Nm/kg	1.417 ± 0.548	1.616 ± 0.477	0.010*	0.46	-0.347, །0.051
Hc (60°/s), Nm/kg	1.004 ± 0.350	0.981 ± 0.282	0.430	0.13	-0.035, 0.082
Qc (180°/s), Nm/kg	1.154 ± 0.437	1.363 ± 0.382	0.001*	0.58	-0.332, །0.087
Hc (180°/s), Nm/kg	0.789 ± 0.263	0.825 ± 0.234	0.108	0.28	-0.080, 0.008
Qc (300°/s), Nm/kg	1.003 ± 0.370	1.181 ± 0.252	0.001*	0.62	-0.276, །0.081
Hc (300°/s), Nm/kg	0.708 ± 0.239	0.751 ± 0.210	0.037*	0.36	-0.084, །0.003
Qe (60°/s), Nm/kg	1.762 ± 0.633	1.860 ± 0.585	0.227	0.21	-0.258, 0.063
He (60°/s), Nm/kg	1.173 ± 0.443	1.209 ± 0.381	0.475	0.12	-0.137, 0.065

Hc concentric hamstring strength

He eccentric hamstring strength

Qc concentric quadriceps strength

Qe eccentric quadriceps strength

^*P < 0.050

Correlation analysis between isokinetic strength LSI and side-cutting LSI

The peak knee flexion angle showed moderate positive correlations with Qc at 180°/s and 300°/s (r = 0.392, P = 0.018, r² = 0.154; r = 0.371, P = 0.026, r² = 0.138) (Fig. 2); the knee adduction angle, by contrast, exhibited a moderate positive correlation with Qc at 60°/s (r = 0.438, P = 0.008, r² = 0.192) (Fig. 2).

Fig. 2.

Correlation Analysis Between Thigh Isokinetic Strength LSI and Knee Biomechanics LSI at 9 Months after ACLR. ^*P < 0.050; Qc, concentric quadriceps strength. No adjustment for multiple comparisons was applied, as described in the Methods section

At the peak pGRF, the knee flexion angle exhibited correlations of varying magnitudes with isokinetic muscle strength across different angular velocities: it showed a strong positive correlation with Qc at 180°/s (r = 0.512, P = 0.001, r² = 0.262) and a moderate positive correlation with Hc at 180°/s (r = 0.460, P = 0.005, r² = 0.212). The knee external rotation angle was moderately negatively correlated with both Qc at 300°/s (r =-0.410, P = 0.013, r² = 0.168) and Hc at 300°/s (r =།0.467, P = 0.004, r² = 0.218). Additionally, the knee extension moment displayed a moderate positive correlation with Qc at 60°/s (r = 0.375, P = 0.024, r² = 0.141) and 300°/s (r = 0.372, P = 0.026, r² = 0.138). (Table 5).

Table 5.

The correlation between knee biomechanics LSI at the peak GRF and LSI of thigh isokinetic strength

Variable	Variable	P values	r	r 2
at the pGRF
flexion angle (°)	60°/ s Hc	0.007*	0.443	0.196
	180°/ s Qc	0.001*	0.512	0.262
	180°/ s Hc	0.005*	0.460	0.212
	300°/ s Qc	0.008*	0.434	0.188
external rotation angle (°)	180°/ s Hc	0.039*	-0.345	0.119
	300°/ s Qc	0.013*	-0.410	0.168
	300°/ s Hc	0.004*	-0.467	0.218
extension moment (BS·BH)	60°/ s Qc	0.024*	0.375	0.141
	300°/ s Qc	0.026*	0.372	0.138
at the vGRF
flexion angle (°)	300°/ s Qc	0.046*	0.335	0.112
external rotation angle (°)	300°/ s Qc	0.007*	-0.441	0.195
extension moment (BS·BH)	60°/ s Qc	0.005*	0.456	0.208
	180°/ s Qc	0.005*	0.458	0.215
	300°/ s Qc	0.010*	0.425	0.181
	60°/ s Qe	0.023*	0.377	0.142
	60°/ s He	0.029*	0.364	0.133

No adjustment for multiple comparisons was applied, as described in the Methods section

Hc concentric hamstring strength

He eccentric hamstring strength

Qc concentric quadriceps strength

Qe eccentric quadriceps strength

pGRF peak posterior ground reaction force

vGRF peak vertical ground reaction force

^*P < 0.050, BS body mass, BH body height, BS·BH body mass multiplied by body height

At the peak vGRF, the knee flexion angle and external rotation angle exhibited a moderate positive correlation and a moderate negative correlation, respectively, with Qc at 300°/s (r = 0.335, P = 0.046, r² = 0.112; r = -0.441, P = 0.007, r² = 0.195). The knee extension moment was moderately correlated with Qc across multiple angular velocities; additionally, it showed a moderate positive correlation with Qe (r = 0.377, P = 0.023, r² = 0.142) and He at 60°/s (r = 0.364, P = 0.029, r² = 0.133). (Table 5).

Discussion

Main finding of the study

Patients after anterior cruciate ligament reconstruction (ACLR) often show abnormal movement patterns and muscle weakness, but the relationship between interlimb biomechanical asymmetries and multi-velocity muscle strength deficits during side-cutting at the critical 9-month postoperative stage remains unclear. Clarifying this relationship is essential for designing targeted rehabilitation strategies. This study therefore aimed to systematically evaluate knee biomechanics and isokinetic strength during side-cutting 9 months after ACLR and to explore their correlations.

The main findings partially supported our hypotheses. Not only were there significant interlimb asymmetries in knee biomechanics and muscle strength during side-cutting after ACLR, but moderate correlations between the muscle strength LSI and biomechanics were also observed, particularly at medium-to-high angular velocities (180°/s and 300°/s). Future clinical practice should integrate multi-velocity and eccentric strength training into rehabilitation and establish return-to-sport criteria that assess both muscle strength across velocities and movement quality, enabling a more comprehensive system for making rehabilitation decisions.

Biomechanical differences in bilateral lower extremity side-cutting after ACLR surgery

Decreases in the knee flexion angle and extension moment are common compensations after ACLR, often stemming from quadriceps weakness, deficits in neuromuscular control, and impaired knee function [26, 27]. Similar biomechanical compensations have been documented in other clinical populations with lower limb dysfunction. Lemos et al. [28] demonstrated that ACL injured athletes show altered quadriceps force fluctuation patterns during maximal isometric contractions, which correlates with functional performance deficits, suggesting that motor control alterations may underlie the kinematic changes observed during dynamic tasks. These abnormal biomechanics may lead to aberrant cartilage loading [29, 30], thereby increasing the risk of subsequent knee osteoarthritis [31]. Furthermore, an increased external rotation angle is a particularly critical finding. Another contradictory claim [7] suggests that although ACL reconstruction can partially restore the sagittal plane stability of the knee, its effectiveness in controlling tibial rotation during high-demand activities remains limited. Residual abnormal tibial rotation after surgery may lead to the establishment of aberrant movement patterns [32]. Such prolonged abnormal mechanical loading not only may increase the risk of reinjury [33] but may also accelerate degenerative changes in intra-articular sot tissues, ultimately contributing to the development and progression of post-traumatic osteoarthritis [34] . In conclusion, the biomechanical abnormalities observed during side-cutting underscore the necessity of restoring dynamic knee stability and establishing correct movement patterns after ACLR, with the aim of reducing the risk of reinjury upon return to sports.

The difference in isokinetic muscle strength of both thighs after ACLR surgery

Thigh muscle weakness is common after anterior cruciate ligament reconstruction (ACLR) and increases the risk [17] of reinjury [35]. One year after ACLR, knee extensor strength decreases by approximately 10%, and knee flexor strength decreases by 5–7% compared with that of the contralateral limb [36]. Notably, the recovery trajectory of muscle strength following ACLR may be non-linear, with some studies suggesting continued improvements beyond 9 months. Migliorini et al. [37] conducted systematic reviews of various ACL reconstruction techniques in different populations, consistently emphasizing the importance of comprehensive rehabilitation protocols that address both structural and functional restoration. The present study reported similar results. Schmitt et al. [38] found that participants with reduced quadriceps strength demonstrated aberrant landing patterns during a drop vertical jump maneuver upon return to sport after ACLR. A decrease in muscle strength may be related to postoperative muscle atrophy, a reduction in motor unit recruitment [39], and altered sensory input, which includes an increase in pain-related signals alongside a decrease in proprioceptive feedback due to inflammation and effusion [40]. It is crucial to note that hamstring muscle strength deficiency is equally significant [41]. In intense dynamic movements, the coactivation of the hamstrings is crucial for ensuring dynamic knee stability and preventing excessive ACL shear forces [42]. This suggests that when assessing recovery and making decisions about returning to sports, equal attention should be given to the functional recovery of both the quadriceps and hamstrings.

Kinematic asymmetry of the knee joint is associated with muscle strength asymmetry of the thigh

Correlation analysis of knee kinematics revealed strong to moderate positive correlations between sagittal plane parameters and concentric thigh muscle strength (at 60°/s, 180°/s, and 300°/s). Notably, the knee flexion angle showed a strong positive correlation with Qc at 180°/s, and a moderate positive correlation with both Hc at 180°/s and Qc at 300°/s, which reflect the demand for different force outputs during distinct phases of the side-cutting maneuver. Palmieri-Smith et al. [8] reported that patients with reduced quadriceps strength demonstrated greater movement asymmetries at the knee in the sagittal plane when they returned to sport. However, some studies have found [43] that even when quadriceps strength symmetry is achieved, abnormal lower limb biomechanics may persist, which aligns with the findings of the present study. The development of maximal strength serves as the foundation for power production. However, as athletic proficiency increases, the efficacy of relying solely on maximal strength training to increase power in high-velocity movements such as sprinting and jumping plateaus considerably [44]. This suggests that solely increasing maximal muscle strength may be insufficient to optimize performance in high-load activities for patients after ACLR. Velocity-based resistance training (VBT) may be an effective alternative rehabilitation strategy [45]. The importance of velocity-specific training is further supported by recent research in athletic populations. Pedrosa et al. [46] examined muscle swelling responses to different training protocols and found that training adaptations may be influenced by the training status of individuals, with more trained individuals potentially requiring higher velocities or novel stimuli to generate adaptation. This suggests that as ACLR patients progress through rehabilitation, progressive introduction of higher-velocity training may be necessary to continue driving improvements in neuromuscular function. Current evidence shows [47] that VBT leads to superior improvements in strength, jump, and sprint performance compared with traditional 1RM (one repetition maximum) based resistance training.

Another important finding of this study was that the knee external rotation angle showed moderate negative correlations with both Qc and Hc at 180°/s and 300°/s. These findings indicate that patients with greater strength deficits at faster angular velocities demonstrate increased external rotation on the reconstructed side during side-cutting. The underlying mechanism may be that high-velocity movements place extreme demands on the rapid recruitment and coordination capacity of the neuromuscular system [48]. During dynamic movements, the quadriceps serve a protective function by acting as shock absorbers, effectively reducing impact on the lower limbs, while the hamstrings generate a posterior shear force at the tibia, which helps reduce ACL loading. The coordinated action of both muscle groups ensures knee joint stability, thereby supporting participation in various sports activities [49]. However, it is important to note that [50] previous studies have consistently shown that the recovery of explosive muscle function lags behind that of muscle strength. Therefore, even if a patient’s maximal strength is adequate, a deficit in the rate of force development (RFD) may impair the ability to rapidly initiate effective cocontraction of the quadriceps and hamstrings to stabilize the knee during fast movements. A report indicates that [51] electromyographic delay increases after ACLR, particularly in the medial hamstring muscle group. This may be associated with reduced force production rate in the hamstrings and delayed periarticular muscular stabilization. Therefore, this finding suggests that assessing peak strength alone is insufficient to fully capture neuromuscular recovery after ACLR. It may be critical to incorporate muscle strength evaluation across different angular velocities to comprehensively assess postoperative neuromuscular functional restoration.

Asymmetry in the knee extension moment is correlated with asymmetry in thigh muscle strength

The knee extension moment was moderately correlated with concentric thigh muscle strength across multiple angular velocities (at 60°/s, 180°/s, and 300°/s), which was consistent with our expectations. Previous ACLR studies have similarly observed reduced knee extension moments across various movement patterns, including walking, running, and jumping [52–54], suggesting that this kinetic deficit is common and persistent. Notably, this extensor strength deficiency can trigger compensatory movement strategies. Research has demonstrated [55] that ACLR patients frequently adopt increased trunk flexion during landing tasks to compensate for knee extensor weakness, albeit at the cost of significantly compromised postural stability, underscoring the critical importance of improving extension moment capacity.

Furthermore, a key finding was that a moderate correlation was observed between the knee extension moment at the peak vGRF and both Qe and He at 60°/s. This association may be related to the specific movement pattern occurring during this phase of the task. Eccentric contractions are generally used to decelerate, brake, or absorb energy [56]. Notably, during side-cutting maneuvers, eccentric contractions effectively absorb potential energy generated by the motion, and part of this absorbed energy can be reused to enhance movement explosiveness [57]. This finding further underscores the importance of eccentric control capacity in maintaining dynamic knee stability and movement efficiency during high-risk, high-load sports tasks. Critically, key metrics for assessing this capacity, such as bilateral symmetry indices, have been shown to vary significantly across different sports [58]. This highlights the need for sport-specific normative data when interpreting isokinetic strength results and designing return-to-sport protocols.

Limitations

This study has several limitations. First, its cross-sectional design precludes causal inference. Second, the lack of a healthy control group limits contextualization of the observed deficits. Third, the absence of follow-up over the long term prevents linking the biomechanical findings to reinjury outcomes. Fourth, potential selection bias exists as we included only patients who completed a standardized rehabilitation protocol, and the lack of sport-specific subgroup analyses limits generalizability across athletic populations. Fifth, as only hamstring tendon autografts were included, the findings may not generalize to other graft types (e.g., BPTB or quadriceps tendon). Sixth, the standardized testing sequence (contralateral limb followed by reconstructed limb) may have introduced order effects, such as practice or fatigue, that could affect between-limb comparisons. Finally, although the inclusion criterion was 9 months post-ACLR, variability in the actual postoperative time (9.45 ± 0.55 months) may have introduced heterogeneity in recovery status. Future studies comparing different graft types are warranted.

Clinical implications

The observed correlations between strength asymmetry and biomechanics were weak to moderate (r = 0.335 to 0.512), explaining approximately 11% to 26% of the variance. This indicates that while strength deficits are a meaningful and modifiable contributor to aberrant movement, a substantial portion (74% to 89%) of the variance is attributable to other factors (e.g., neuromuscular control, movement strategy). Therefore, integrating strength assessment with dynamic movement analysis may be beneficial within a comprehensive, multifactorial return-to-sport evaluation. This approach aligns with the broader evidence-based principle that multifaceted, individualized rehabilitation strategies yield superior outcomes [59].

Conclusion

At nine months post-ACLR, patients presented with interlimb asymmetries in lower extremity side-cutting biomechanics and thigh muscle strength. These biomechanical asymmetries demonstrated moderate correlations with thigh muscle strength asymmetries, with the strongest associations evident at medium and high angular velocities.

Therefore, clinicians should consider incorporating velocity-based training, explosive strength training, and eccentric control training into the rehabilitation protocol after ACLR. Moreover, isokinetic strength assessments across multiple angular velocities (180°/ s, 300°/ s) should be incorporated into the RTS criteria to refine the evaluation system and reduce the risk of reinjury.

Abbreviations

ACL

Anterior Cruciate Ligament

ACLR

Anterior Cruciate Ligament Reconstruction

RTS

Return-to-Sport

LSI

Limb Symmetry Index

BS

Body mass

BH

Body Height

BS·BH

Body Mass Multiplied by Body Height

GRF

ground reaction force

pGRF

Posterior Ground Reaction Force

vGRF

Vertical Ground Reaction Force

Hc

Concentric Hamstring Strength

He

Eccentric Hamstring Strength

Qc

Concentric Quadriceps Strength

Qe

Eccentric Quadriceps Strength

Authors’ contributions

Mingxuan Gao and Xialin Ge contributed equally to this work. M.X.G. and X.L.G. participated in the design of the study and drafted the manuscript. L.T.S. and Y.M.T. provided assistance for data acquisition and analysis. Y.F.A. and S.R. conceived of the study and performed manuscript review. All authors read and approved the final manuscript.

Funding

The authors gratefully acknowledge financial support from the National Natural Science Foundation of China (Joint Fund for Regional Innovation and Development, U23A20471), the Beijing Natural Science Foundation grant (L241073), and General Project of Sports Medicine Technology Innovation Program of the General Administration of Sport of China (2025-19).

Data availability

Data supporting the findings of this study are not publicly available due to restrictions imposed by patient confidentiality and privacy laws. However, the data is available from the corresponding author upon reasonable request.

Declarations

Ethics approval and consent to participate

This study was conducted according to the guidelines of the Declaration of Helsinki and approved by the Peking University Third Hospital Medical Science Research Ethics Committee (Approval Code: M20250039; Approval Date: 2 April 2025). Written informed consent was obtained from all individual participants included in the study.

Consent for publication

Written informed consent for publication was obtained from all participants.

Competing interests

The authors declare no competing interests.