Evaluating kinetic symmetry during loaded and unloaded jumping across multiple rehabilitation phases in ACLR patients

Abstract

Background

The rehabilitation of patients following anterior cruciate ligament reconstruction (ACLR) requires objective assessments that can identify between-limb asymmetries in jump performance to guide return-to-play (RTP) decisions. This study investigated kinetic asymmetries in ACLR patients using loaded and unloaded vertical jumping across multiple rehabilitation phases to assess neuromuscular recovery and readiness for RTP.

Methods

Participants (ACLR, n = 18; 14 males and 4 females; ages 20 ± 2.46 years) completed unilateral countermovement jumps (CMJ_UL), unilateral drop jumps (DJ_UL), and loaded squat jumps (SJ) on dual force plates during phases 3 (~ 16 weeks), and 4 (~ 20 weeks) of rehabilitation. Metrics including reactive strength index (RSI), jump height (JH), and force-velocity (FV) profiles analysed for inter-limb asymmetries. Statistical analyses included statistical parametric mapping to evaluate between-limb differences in the force-time waveforms and repeated measures ANOVAs for jumping-based metrics with standardised effect sizes (Cohen’s d) calculated for key pairwise comparisons of the between-limb differences.

Results

Significant between-limb asymmetries were observed throughout key phases of the force-time waveform in both CMJ_UL and DJ_UL tests (p < 0.001), with moderate-to-large effect sizes for RSI (d = 1.32–1.41) and JH (d = 1.53–2.01) across both phases. Force asymmetries persisted in the propulsive phases of CMJ_UL and DJ_UL and loaded SJ trials revealed substantial force production asymmetries (mean asymmetry angle > 25%, p < 0.001) at higher velocities. Correlation analyses showed strong associations between RSI and JH in CMJ_UL and DJ_UL (r = 0.70–0.89).

Conclusions

Jump analyses provide valuable insights regarding neuromuscular recovery in ACLR patients, revealing significant and persistent asymmetries through late rehabilitation phases. These findings highlight the importance of phase-specific, targeted interventions to address neuromuscular deficits and support safe RTP decisions.

Background

Recent recommendations pertaining to anterior cruciate ligament reconstruction (ACLR) emphasize the importance of integrating functionally relevant assessments, such as vertical jumping, within return-to-play (RTP) protocols [1]. Such evaluations, based on the assumption of their applicability to real-world performances, aimed to distinguish between the capabilities of injured- and uninjured limbs, correlating with actual sports outcomes [2, 3]. Nevertheless, the effectiveness of certain functional RTP assessments and the metrics associated with them, have been subject to scrutiny on the basis that individuals can pass some tests (e.g., single leg hop test for distance), while failing other tests (e.g., quadriceps strength limb symmetry index) [4, 5]. This highlights the need for objective, practical, and sensitive assessments that can detect and quantify residual functional deficits, especially in sporting environments where balanced decision-making on performance outcomes is crucial.

A critical aspect of rehabilitation following ACLR is the assessment of lower limb function and neuromuscular control, for which jump analyses have become indispensable tools [6]. Assessments such as the unilateral countermovement jump (CMJ_UL), unilateral drop jumps (DJ_UL), and squat jumps (SJ) provide insights into an athlete’s force generation capacity, landing control, and limb symmetry which indicate readiness for sport-specific activities [7–9]. Although jump tests are widely used in ACLR research, most studies report only discrete outcome measures (0D variables), such as jump height, peak force, impulse, or momentum, which describes what the athlete achieved during the jump. Far fewer studies examine the continuous force-time waveform (1D analysis), which provides insight into how the movement was executed[10–13].. Analysing the full force-time curve offers a more detailed understanding of compensatory movement strategies that may not be visible in isolated performance metrics [14].

Moreover, details concerning these strategy-level differences, particularly during braking, amortization, and propulsion phases, remain under-investigated in ACLR cohorts and represent an important gap in the literature. More specifically, a deeper understanding of the movement strategies employed by ACLR patients can be gained through an appraisal of the asymmetry present during functionally relevant tasks such as vertical jumping which is known to challenge the knee to a greater extent compared to horizontal jumping [15]. Additionally, evaluations of asymmetry provide a quantifiable measure that delineates the deviation in limb mechanics between the injured and uninjured limbs during jump testing which can then be tracked longitudinally.

In this line, assessments that incorporate jumping, such as the CMJ, serve as a fundamental measure of the explosive capacity of the lower extremities of an individual [16]. By assessing both the concentric and eccentric phases of the jump, clinicians can gauge the functional symmetry between the injured- and uninjured limbs, as well as overall power outputs [7, 8]. Information related to symmetry is particularly relevant in the latter stages of rehabilitation when decisions regarding the intensification of training loads and the initiation of sport-specific drills are made. The role of the CMJ in measuring explosive capacity makes it a pivotal part of determining the capability of an athlete to perform high-intensity athletic activities [17]. Similarly, the drop jump (DJ) emphasizes the plyometric and reactive strength capabilities of an individual, characterized by a rapid transition from a high-elevation fall to a jump [18]. The efficiency of this movement reflects the integrity of the neuromuscular system and its ability to withstand sudden, high-impact forces similar to those experienced in competitive sports environments [19]. Monitoring DJ performance can guide clinicians in customizing plyometric training interventions to address specific deficits and prevent re-injury upon RTP, thereby making it essential for assessing reactive strength and neuromuscular response in dynamic situations [8].

In contrast, the SJ focuses almost exclusively on concentric leg strength by eliminating the pre-stretch or countermovement phase thereby isolating the athlete’s ability to generate force from a static position [20]. The SJ provides a clear overview of muscular strength independent of plyometric ability and is particularly useful in the later stages of rehabilitation when assessing raw concentric strength. Moreover, the strength component of the SJ can, at least in principle, be amplified by incorporating progressive loading to provide a more holistic overview of the interaction between the strength and movement velocity of an individual [21]. No previous research, at least to our knowledge, has investigated the use of the loaded SJ in evaluating the force-velocity profile of ACLR patients and how these performances compare to more traditional jump assessments such as the CMJ and DJ within a rehabilitation setting.

By integrating these jump analyses into the ACLR rehabilitation protocol, clinicians can potentially optimize recovery trajectories, mitigate the risk of re-injury, and ultimately support athletes in achieving their goal of a safe and confident RTP. This comprehensive evaluation facilitates informed, data-driven decisions about when and how to safely advance the rehabilitation process and establishes objective criteria for RTP, ensuring that athletes meet established benchmarks for strength, symmetry, and neuromuscular control before resuming competitive activities.

Subsequently, the primary objectives of this study were to: (i) assess 1D between-limb force asymmetries during the CMJ and DJ tests across consecutive rehabilitation phases (ii) evaluate the 1D force-time characteristics and asymmetries during loaded SJ testing during the fourth phase of rehabilitation (iii) analyse 0D between-limb differences in reactive strength indices (RSI), peak force (PF), and JH during the CMJ and DJ across consecutive rehabilitation phases, (iv) quantify the force-velocity profiles from loaded SJ assessments, identifying performance variability to refine rehabilitative strategies, and (v) evaluate the relationship between key loaded (SJ) and unloaded (CMJ, DJ) jump parameters.

Based on current evidence of persistent neuromuscular deficits following ACLR, we hypothesised that patients would demonstrate significant inter-limb asymmetries in CMJ_UL and DJ_UL metrics (e.g., peak force, jump height, and reactive strength index) during the mid-to-late stages of rehabilitation. We additionally anticipated that these asymmetries would be more evident in tasks with higher stretch-shortening cycle demands (e.g., DJ_UL) and would persist throughout the rehabilitation process despite overall improvements in performance. Furthermore, we expected that the force-velocity characteristics derived from bilateral loaded SJ’s would offer supplementary insights into overall force and velocity capacities of the lower limbs, and that these parameters would demonstrate significant correlations with essential unilateral jump metrics.

Methods

Setting

The study was conducted in controlled clinical environments at the North-West University of Potchefstroom, South Africa, Center for health and Human Performance (CHHP) and Physical Activity, Sport and Recreation (PhASRec). This arrangement provided a standard space for the implementation of jump assessments on calibrated dual force plate system, enabling reliable data capture and ensuring measuring accuracy.

Participants

The study consisted of a repeated measures design whereby the same participants were assessed recurrently at each phase of rehabilitation. A minimum sample size of 15 participants was calculated using the following input parameters: (i) expected effect size (f) of 0.25, (i) 5% type-1 error rate, (iii) 20% type-2 error rate, (iv) 6 repeated measures, and (v) repeated measures correlation of at least 0.6 [22]. Participants in the ACLR group were eligible for inclusion if they were between 14 and 30 years old, had undergone a reconstruction of the anterior cruciate ligament and fell within 16–24 weeks post-surgery at the time of testing. Only phase 3 (~ 16 weeks) and phase 4 (~ 20 weeks) were included because these phases represent the transition to higher-intensity plyometrics and sport-specific loading, where jump-based asymmetry can be safely and meaningfully administered. Rehabilitation phases were established in advance according to the elapsed time since surgery. Participants were assessed at these specific time intervals solely if they were considered clinically prepared by the treating clinician to safely execute maximal effort unilateral and loaded jumping tasks. This method guaranteed that testing was conducted at uniform postoperative intervals while considering individual readiness and safety. Individuals were excluded if they presented with: (i) current chronic or acute knee conditions that could alter movement mechanics, such as patellofemoral pain or iliotibial band syndrome; (ii) any current or recent (≤ 6 months) lower-limb musculoskeletal injuries, including ankle sprains, hip labral pathology, or hamstring or quadriceps strains.

Prior to data collection, written informed consent was obtained from all adult participants who voluntarily agreed to take part. For those younger than 18 years, assent was secured alongside parental or guardian consent. The study adhered to the ethical standards of the Declaration of Helsinki and received approval 1from the Health Research Ethics Committee of the Faculty of Health Sciences (ethics number: NWU-00335-21-A1) and the regional Department of Health.

Measuring instruments and equipment

Jump testing was performed using a dual Hawkin Dynamics force plate system (3rd Generation, model 0486; Westbrook, Maine, USA). Peak force values were adjusted for bodyweight, which was recorded on the force plates during a one-second static interval immediately prior to each measurement.

Procedures

Unilateral jump testing

The method previously described by Jordan et al. [7] for testing participants with ACLR as well as healthy individuals was adopted in this study. Both CMJ_UL and DJ_UL testing was undertaken during phase three and four testing. The standardised protocol, used across sessions and phases to ensure consistency, included a 10-minute light-to moderate intensity (Borg RPE 9–13) warm-up on a cycle ergometer followed by light dynamic stretching of lower limb musculature that included the quadriceps, hamstrings, gluteals, hip flexors, and plantar flexors. The participants were cued to step onto the dual force plates and were instructed to stand still so that the force plate system could accurately record the participant’s weight in newtons. The participants were asked to place their hands on their hips (akimbo) and were cued to remain as still as possible on the force plates prior to initiating the jump. The participant then initiated a countermovement and attempted to jump as high as possible while maintaining their hands akimbo. Participants were instructed to initiate the CMJ_UL and land on each leg individually on separate attempts. The participants were cued to stabilise as quickly as possible on landing and to remain still for 5-seconds once stabilized.

Hopper et al. [23] had found high test-retest reliability for the CMJ_UL in patients with ACLR (ICC = 0.86–0.97). The uninvolved limb was tested first during each attempt whereby the knee of the non-jumping leg was kept at approximately 90° and hands remained akimbo throughout the trial [24]. The uninvolved limb was tested first to ensure participant safety, to allow familiarisation with the movement task before loading the reconstructed limb. This order is consistent with established ACLR jump-testing protocols. A total of five successful CMJ_UL trials were performed with each trial being separated by 60-seconds. Unsuccessful trials (e.g., loss of balance, stepping off force plate early, removing hands from hips) were discarded and participants were asked to repeat the trial.

After completion of the CMJ_UL, another 5-minute rest interval was given to each participant followed by a DJ_UL test described by Bosco et al. [25]. The participants were set-up behind the force plates on an elevated platform (0.15 m) with hands akimbo, a height chosen to provide a controlled level of eccentric loading appropriate for individuals in the mid-to-late stages of ACLR rehabilitation while minimising excessive ground reaction forces associated with higher drop heights, consistent with protocols used in previous ACLR research [26]. The participants were cued to step off the platform with minimal vertical displacement (i.e., ‘fall’ rather than ‘step’) and to land on the force plates with minimal contact time, followed by a rapid transition into a maximal jump, and finally to stabilize as quickly as possible on landing for a period of 5-seconds. A total of five successful unilateral DJ_UL trials were performed for each limb with a 1-minute rest between each DJ_UL. Unsuccessful trials (e.g., loss of balance, stepping off force plate early, stepping off the box with too much vertical displacement rather than ‘falling’) were discarded and participants were asked to repeat the trial.

The force-time data of all jumps were obtained from the force plates and exported to Matlab (version 2021b, The MathWorks, MA, USA) for processing whereby the ground reaction force data were smoothed using a low-pass zero lag Butterworth filter (fourth-order) with a cutoff frequency of 50 Hz. The CMJ was divided into three phases: (i) unweighting phase: defined from movement onset to the instant when force returns to body weight, (ii) braking phase: defined from peak negative centre-of-mass [CoM] to peak negative CoM displacement, and (iii) propulsive phase: defined from positive CoM velocity to take-off [27]. The DJ was divided into two phases that also consisted of a (i) braking phase: defined as the time between the peak negative CoM velocity and lowest vertical CoM position, and (ii) propulsive phase: defined from lowest vertical CoM position to take-off [28]. Jump height was calculated using the impulse-momentum method [29], whereas RSI and RSI-modified (RSI_m) were calculated as the ratio of JH (numerator: DJ or flight time: CMJ) to ground contact time (denominator; DJ or time-to-takeoff: CMJ) respectively [30]. Jump data were time-normalised such that comparisons could be made across all participants (CMJ: movement initiation to take-off; DJ: touch-down to take-off), and all trials for a given jump were ensemble averaged for analysis. The order of tests followed a fixed progression from CMJ_UL to DJ_UL and finally the loaded SJ.

Force-velocity (FV) parameters

Force- velocity (FV) profiling was performed during phase 4 (~ 20 weeks) of rehabilitation only, as this phase represents a stage at which loaded squat jumping can be safely and meaningfully administered following ACLR. The testing protocol developed by Samozino et al. [21] was used in the present study to determine the force-velocity relationship. Participants were positioned on dual force plates with each leg on a separate platform. Participants were instructed to perform a series of SJ of which the starting position was determined during anthropometric measurement. A series of loaded SJ’s were then performed with weight for each jump calculated as a percentage of the participant’s body mass. For this study, loading increments corresponding to 0%, 20%, 40% and 60% of body mass were used. A barbell was loaded with weight plates on a squat rack where after it was positioned on the participants’ back. In the unloaded condition, the participant was set-up with arms akimbo. Participants then instructed to squat down to the predetermined optimal position (as close to 90° as possible). The participants then had to stabilize in this position for at least 1-second before a maximal effort jump was performed. Participants were cued to apply downward pressure on the barbell during the loaded jumps and maintain an upright chest. They were cued to touch down with a similar leg position as in the take-off (i.e., extended legs with plantar flexed feet) and then move into the squatted position as soon as possible after ground contact to accommodate shock absorption and lower impact. Failure to adhere to these requirements resulted in a failed attempt and the trial was repeated. Two attempts at each weight were performed and the highest recorded jump retained for analysis, resulting in four data points to construct the FV relationship (0%, 20%, 40% and 60% body mass). Three minutes of recovery time were allotted between each SJ trial to allow for optimal performance. Kinetics were recorded for each attempt and retained for analysis. From these data the FV relationship for each individual was determined using least squares linear regression. The quality of the FV fit was evaluated using the coefficient of determination (R²), with all individual profiles demonstrating a strong linear fit. Subsequently, the maximal theoretical force (F_0; N.kg^{− 1}) and velocity (v₀; m.s^{− 1}) were established through extrapolation and corresponded to the intercepts of the force and velocity axes respectively [31].

Asymmetry

Rehabilitation after ACLR seeks to restore strength and coordination symmetry between limbs; therefore, asymmetry was quantified using the asymmetry angle (AA) [15], considered a robust measure:

To facilitate the interpretation of AA in comparison to more conventional measures of asymmetry, the relationship between AA and three key asymmetry indices (see Parkinson et al. [32]) for peak force has been provided in Fig. 1 as well as their respective conversion equations. The reconstructed limb was coded as the injured limb and the opposite limb as the uninjured limb. Asymmetry values were expressed such that positive values reflected greater performance in the uninjured limb. Limb dominance was not considered in the analysis.

Fig. 1.

Conversion between asymmetry angle and more conventional asymmetry scores. Black solid lines represent the regression line, and dots are coloured based on the jump type (i.e., salmon = CMJ; teal = DJ). Asymmetry calculations are derived from Parkinson et al. [32]. Note: AA Asymmetry angle

Statistical analysis

Primary outcome measures were determined in advance as the inter-limb asymmetry in peak force, jump height (JH), and reactive strength index (RSI), as these metrics are commonly utilised to assess neuromuscular performance and readiness for RTS following ACLR. Secondary outcomes encompassed, FV profile parameters (F₀ and V₀), waveform-based asymmetry across the force-time curve, and correlation analyses between loaded and unloaded jump metrics. These were regarded as exploratory and aimed to offer mechanistic and contextual insights into jump performance and compensation strategies.

All statistical analyses were completed using the R programming language (R Core Team, version 2022.04.01, RStudio, Posit Software PBC, URL: https://posit.co/download/rstudio-desktop/), and Python (Spyder IDE, version 6.1.0, URL: https://Spyder-IDE.org). Data were evaluated for normality using the Shapiro-Wilk test and accepted as being normally distributed when the p-value exceeded the alpha-threshold of 0.05.

For the first- and second objectives we evaluated the asymmetry (using AA) between the limbs across each time point during the jump to assess the magnitude of the asymmetry present for the different jumping tasks. The force-time waveforms of each limb were temporally normalized from 0% to 100% of a given jump (i.e., from movement initiation to take-off) and evaluated using a one-dimensional statistical parametric mapping (SPM), two tailed paired t-test that resulted in a continuous SPM{t} curve [13]. The SPM analyses are based on random field theory which describes the probabilistic behaviour of random curves and accounts for the smoothness of the data and is used to set a critical threshold (α = 0.05). If the SPM{t} curves exceeded the critical threshold, the waveforms were deemed to be significantly different between the two limbs at these specific time nodes [13, 33]. For the third objective we conducted a 2-way repeated measures ANOVA (afex package: DV = limb*phase + error(ID/(limb*phase); where DV = dependent variable, IV = independent variable) to evaluate the mean differences of a dependent variable (e.g., JH, RSI) across two within-subject factors (limb [injured vs. uninjured], phase [e.g., phase 3 vs. phase 4]). Partial eta squared (PES; η_p²) served as the measure of the effect size, and the sphericity assumption was evaluated using Mauchly’s test of sphericity. For instances where sphericity was violated the Greenhouse-Geisser correction was implemented (afex package). Post-hoc comparisons were conducted (emmeans package) where pairwise contrasts were adjusted using the Holm correction to minimise the type-1 error rate. The standardised effect size was computed as Cohen’s d (effectsize package) and interpreted as follows: trivial: <0.2; small: 0.2–0.6; moderate: 0.6–1.2; and large: > 1.2 [34]. For the fourth objective we used least squares linear regression to evaluate the relationship between load and maximal take-off velocity to derive the maximal theoretical force (F₀) and velocity (v₀) [31]. Finally, the fifth objective incorporated an exploratory correlation analysis (correlation package) to evaluate the relationship between key metrics from loaded and unloaded jumping. More specifically, the Spearman Rank correlation coefficient was used and adjusted for multiple comparisons using the Holm correction. The absolute magnitude of the coefficients were interpreted as follows: negligible: 0.00–0.10.00.10; weak: 0.10–0.39; moderate: 0.40–0.69; strong: 0.70–0.89; and very strong: 0.90–1.00.90.00 [35].

Results

The data from 18 ACLR participants (males/females = 14/4; age: 20.17 ± 2.46 years; height: 1.77 ± 0.07 m; mass: 85.30 ± 16.47 kg) across several rehabilitation phases are presented below. Also see Table 1 for demographics, injury characteristics, and surgical details.

Table 1.

Participant demographic, anthropometric, activity-history, and surgical characteristics

Variable	ACLR (n = 18)
Age (years)	20.17 ± 2.46 [range = 14–26]
Height (m)	1.77 ± 0.07
Activity history, n	Rugby = 12 Soccer = 2 Hockey = 2 Netball = 2
Limb Dominance	Left = 1 Right = 17
Involved Side	Left = 12 Right = 6
Isolated ACL injury, n	14
Meniscal injury, n	3
Medial Collateral Ligament injury, n	1
Injury mechanism
Contact, n  Non-contact, n	6 12
Graft type
Hamstring tendon, n  Quadriceps tendon, n  BPTB, n	11 6 1

Impact of injury on CMJ_UL and DJ_UL jump phases

An analysis of asymmetries associated with the force-time characteristics of the CMJ_UL revealed distinct patterns of force application across the sub-phases of the jump (see top two panels of Fig. 2). More specifically, the top two panels of Fig. 2 show the mean across all participants during the CMJ as a function of a given rehabilitation phase. Substantial asymmetries were present at the latter portion of the unweighting phase that tends to compound towards the end of the propulsive phase (AA: 10–15%, p < 0.001) during all rehabilitation phases.

Fig. 2.

Mean CMJ and DJ force-time plots of the injured and uninjured limbs of ACLR patients. Data are shown for the injured (solid line) and uninjured (dotted line) limb during the CMJ (top two panels) and DJ (bottom two panels). The magnitude of the asymmetry between limbs is indicated by the specific colour; vertical blue shaded areas represent the regions of the force-time trace that are statistically significant. Note: CMJ Countermovement jump, DJ Drop jump

Similarly, an examination of the force-time asymmetries during the DJ_UL highlight distinctive force application patterns throughout the various stages of the jump (see bottom two panels of Fig. 2). More specifically, the bottom two panels of Fig. 2 present the mean force-time data for all participants as a function of a given rehabilitation phase during the rebound phase of the DJ The magnitudes of the asymmetry tend to change towards the end of the braking phase and beginning of the propulsive phase that coincides with the amortization phase of the typical DJ (AA: 4–10%, p < 0.001). The asymmetries tend to again compound towards the end of the propulsive phase in preparation for take-off.

Propulsive force asymmetry during loaded SJ at varying intensities

The force-time curves for the SJ are highlighted in Fig. 3. A consistent pattern is observable across all four loading conditions with the uninjured limb being loaded considerably more throughout the propulsive phase. A notable degree of asymmetry is evident beyond the mid-portion of the normalized propulsive phase which is intensified prior to take-off where maximal movement velocity would be observed (AA: > 25%, p < 0.001).

Fig. 3.

Mean force-time plots of the injured and uninjured limbs of ACLR patients during the loaded bilateral squat jump. Mean data are shown for the injured (solid line) and uninjured (dotted line) limb during each trial. Note: the magnitude of the asymmetry between limbs is indicated by the specific colour. Note: BW Body weight

Assessment of between-limb asymmetries in CMJ_UL performance parameters

The mean between-limb differences (M_diff) for RSIm, PF, and JH across rehabilitation phases for the CMJ_UL are presented in Fig. 4. There was evidence for within-limb differences across the phases regarding jumping height (F = 6.70, η_p² = 0.28, p = 0.019) and RSIm (F = 7.13, η_p² = 0.30, p = 0.016), but not peak force (p > 0.05). Moderate-to-large between-limb differences were observable for each metric that tend to persist into the latter phases (all η_p² > 0.33, p < 0.005).

Fig. 4.

Between-limb differences for each participant during each phase of rehabilitation for the CMJ_UL test. Individual data points are shown for jump height (Panel A), peak force (Panel B) and RSIm (Panel C). The magnitude of the differences between limbs is indicated by the specific colour; horizontal black lines represent the mean. The inferential statistics associated for the between-limb differences (M_diff with 95%CI) for each phase are shown at the top of each panel. The inferential statistics for each main effect and interaction effect are shown in the caption of each panel. Note: M_diff Mean difference,d Cohen’s d

Assessment of between-limb asymmetries in DJ_UL performance parameters

The mean between-limb differences (M_diff) for RSI, PF, and JH across rehabilitation phases for the DJ_UL are presented in Fig. 5. There was insufficient evidence for within-limb differences across the phases for the metrics of interest (all η_p² < 0.13, p > 0.132) implying fairly consistent performances. However, moderate-to-large between-limb differences were observable for the JH, PF and RSI within the rehabilitation phases (all η_p² > 0.34, p < 0.009), with more variability being evident for PF.

Fig. 5.

Between-limb differences for each participant during each phase of rehabilitation for the DJ_UL test. Individual data points are shown for jump height (Panel A), peak force (Panel B) and RSI (Panel C). The magnitude of the differences between limbs is indicated by the specific colour; horizontal black lines represent the mean. The inferential statistics associated for the between-limb differences (M_diff with 95%CI) for each phase are shown at the top of each panel. The inferential statistics for each main effect and interaction effect are shown in the caption of each panel. Note: M_diffMean differencedCohen’s d

Force-velocity relationship in late-stage rehabilitation

The force-velocity profile measured during phase 4 of ACLR rehabilitation was assessed using loaded SJ of 14 participants (lost to follow-up: n = 2; incomplete data: n = 2) (see Fig. 6A). The associations between FV parameters (F₀ and v₀) and key parameters from unloaded jumps (CMJ and DJ) were investigated using an exploratory correlation analysis, the results of which are presented in Fig. 6B (bilateral) and C (unilateral).

Fig. 6.

Force-velocity profile and correlation analysis. Panel A shows the FV relationship from the bilateral squat jump during phase 4 of rehabilitation. Individual data points are shown for each participant (black lines) and the overall group mean (red line). Panel B shows the correlation results between key parameters from the bilateral CMJ, DJ and SJ. Note: F₀ Maximal force, v₀ Maximal speed, RSI_DJ RSI during DJ, JH_DJ Jump height during drop jump, RSIm_CMJ Modified RSI during CMJ, JH_CMJ Jump height during CMJ. Panel C shows the correlation results between key parameters from the CMJ, DJ, and SJ. Note: F₀ Maximal force, v₀ = Maximal speed; RSIm_DJ^UL Modified RSI from uninjured limb (UL) during drop jump (DJ), JH_DJ^UL Jump height from UL during DJ; RSIm_DJ^IL Modified RSI from injured limb (IL) during DJ, JH_DJ^UL Jump height from IL during DJ, RSI_CMJ^UL RSI from UL during CMJ, JH_CMJ^UL Jump height from UL during CMJ, RSI_CMJ^IL RSI from IL during CMJ, JH_CMJ^IL Jump height from IL during CMJ

From the bilateral analysis, it is evident that F₀ exhibited strong positive associations with JH from the CMJ (r = 0.82, p < 0.01) RSI from the DJ (r = 0.73, p < 0.01). The v₀ metric demonstrated a strong negative association with RSIm from the CMJ (r = −0.71, p < 0.01), but not any other metrics (all r < −0.24, p > 0.05).

Discussion

The purpose of this study was to enhance the understanding of ACLR rehabilitation by incorporating diverse jumping analyses to assess neuromuscular control and compensation strategies across multiple rehabilitation phases. Our study contributes novel insights into the application of composite jump analyses within the sample of ACLR patients evaluated by showing: (i) persistent asymmetries in force production within the force-time domain for both CMJ_UL and DJ_UL across two phases of ACLR rehabilitation, (ii) substantial between-leg force asymmetries (AA = 4%−10%) prior to the braking phase and shortly before take-off of the CMJ (in phase 4) and prior to, during, and after the amortization phase of the DJ that are compounded before to take-off, (iii) consistent asymmetry magnitudes across all four loading conditions during the SJ, with notably large asymmetries (AA > 25%) towards the latter part of the propulsive phase, (iv) moderate-to-large between-limb differences for key jump-related metrics such as RSI and JH that persisted across rehabilitation phases, and (v) weak-to-strong associations between loaded (F₀, v₀) and unloaded (RSI, JH, PF) jump metrics. These findings should be interpreted as exploratory descriptions of asymmetry patterns within this cohort rather than definitive indicators of RTP readiness or recovery status.

In this study the vertical CMJ, DJ and SJ were selected due to how they uniquely challenge the different aspects of lower limb function, specifically with respect to the knee joint. Although the triple extension of jumping movements require contributions from hip, knee, and ankle joints, vertical jumping in particular requires a greater knee contribution compared to horizontal jumping [36]. The CMJ is primarily used to assess explosive lower body impulse and joint coordination [16] as well as uncover potential asymmetries in limb performance during dynamic movement which may be indicative of inter-limb compensation strategies common in the ACLR patient [37]. When compared to other stretch-shortening cycle activities like CMJ, the DJ requires a higher impulse which is coupled with larger impact forces due to increased eccentric load, thereby making it a useful tool for evaluating ACLR patients in later stages of rehabilitation [18]. The DJ is utilized to quantify the quickness and reactivity of an athlete in the transition from impact absorption to propulsion which is encapsulated in the reactive strength index (RSI) [38]. As such, apart from asymmetry, clinicians should monitor between-limb metrics such as jump height and RSI when seeking to restore athletic performances [39]. The SJ is typically used to assess the explosive capacity of the lower body without the advantage of the stretch-shortening cycle therefore evaluating concentric strength [39]. Incrementally loading the SJ allows for the calculation of a F-v profile enabling insights into velocity-based rehabilitation post-ACLR [40]. Each jump type therefore offers distinctive insights into asymmetries that may persist after ACLR and may offer information relevant to later rehabilitation planning, although their application to RTP decision-making requires validation in larger cohort.

Research has shown that the CMJ_UL effectively distinguishes between ACLR individuals and healthy controls based on performance metrics such as JH, limb symmetry index (LSI), and peak power (PP), which are critical for assessing rehabilitation status [8, 24]. Vertical jump tests, including the CMJ_UL and DJ_UL, reveal significant asymmetries in discrete performance and kinetic metrics at RTP, emphasizing the importance of restoring both symmetry and absolute performance metrics [8]. Our study is the first to show that, by mapping the AA onto the force-time curves, we were able to detect varying asymmetries across specific phases of all jump types, such as the amortization phase, which is commonly problematic within ACLR patients [41]. Our results corroborate previous research by showing that around six months post-operatively when more aggressive protocols indicate possible RTP, significant asymmetries were still present for all jump types assessed [42]. More importantly, we show that an appraisal of asymmetry across the entire force-time curve likely provides more meaningful insights regarding jumping-based compensation strategies compared to discrete analyses alone.

Additionally, we show that in Phase 3 (~ 20 weeks), significant asymmetries were detected in the CMJ_UL, especially during the unweighting and propulsion phases, with the injured limb showing AA from < 4% to 25% (see Fig. 2) which corresponds to conventional asymmetry scores of < 8.8–45% (see Fig. 1, index 9). The asymmetry is relevant as a difference between 10% − 15% are typically considered clinically significant [43, 44]. These asymmetries persisted into Phase 4 (~ 24 weeks) (see Fig. 2) with key metrics including RSI_m, PF and JH further illustrating these asymmetries (see Fig. 4).

In ACL populations, asymmetries exceeding 10–15% are considered significant and are associated with altered movement patterns and increased risk of reinjury upon return to sport. This study revealed that multiple force-based and reactive measurements exceeded established clinical thresholds (10–15%) during the recovery phases. These asymmetries may have therapeutic relevance even when they do not reach statistical significance, although this interpretation requires confirmation in larger, sport-specific samples. The findings emphasise the need of evaluating both the extent and distribution of asymmetry, rather than solely concentrating on statistical significance, in the assessment of jump performance during ACLR rehabilitation.

When compared to normative data, JH performance of participants in our study (Phase 3: injured limb = 0.07 m ± 0.04, uninjured limb = 0.12 m ± 0.04,; Phase 4: injured limb = 0.09 m ± 0.04, uninjured limb = 0.13 m ± 0.03) is similar to that of recreational athletes at RTP (injured limb = 0.11 m ± 0.04, uninjured limb = 0.13 m ± 0.03) but falls short of the performance seen in injured professional athletes at RTP (injured limb = 0.14 m ± 0.03, uninjured limb = 0.16 m ± 0.03) and in uninjured controls (0.17 m ± 0.04) [11]. Notably, the group data indicated persistent asymmetries, suggesting variability in individual recovery rates. Variability in lower extremity function of the recovering limb is common in post-ACLR cohorts and has been observed in hop and muscle power test [45]. Our novel method of mapping the AA onto the force-time curve may therefore provide greater utility for detecting divergent recovery trajectories of individuals when compared to the group means.

The DJ_UL data revealed similar patterns, with notable asymmetries persistent during the amortization and late propulsive phases (AA: 4% - 10%) (see Fig. 2). The recommendation that plyometric exercise prescription be included during the latter phases of ACLR rehabilitation is therefore warranted to correct these asymmetries and potentially mitigate re-injury [46]. Aligned with the present approach is the finding that PF as a discrete metric did not show statistically significant between-limb differences when evaluating jump performance (see Fig. 5). This observation aligns with previous research indicating that impulse and RSI, rather than PF, are likely better predictors of performance in ACLR cohorts [47]. More specifically, the RSI reflects the efficiency of the amortization phase in plyometric movements, with a shorter amortization phase leading to a higher RSI, indicating better explosive strength. Essentially, a quicker transition from eccentric to concentric phases enhances RSI, which correlates with improved athletic performance [48]. In comparison to normative data, RSI values of participants in our study (Phase 3: injured limb = 0.14 ± 0.08, uninjured limb = 0.24 ± 0.1, Phase 4: injured limb = 0.15 ± 0.1, uninjured limb = 0.25 ± 0.13) were considerably lower than those of recreational (injured limb = 0.29 ± 0.12, uninjured limb = 0.37 ± 0.14), professional (injured limb = 0.38 ± 012, uninjured 0.47 ± 0.14) and professional controls (0.58 ± 0.13). Considering that a minimum RSI for DJ_UL of 0.5 is suggested before discharging athletes, our data indicate that at ~ 24 weeks post-ACLR almost none of the participants in our cohort would have met this standard even for the uninjured limb [8]. Such a finding would indicate specific areas requiring attention for subsequent rehabilitation programming in preparation for RTP.

Moreover, such disparities underscore the challenge of achieving full recovery to pre-injury levels, especially in terms of explosiveness and reactive strength. The lower RSI values observed in our participants, suggest that even after extensive rehabilitation, ACLR patients may not regain the reactive strength necessary for high-level athletic performance. These findings reinforce the importance of setting realistic RTP goals based on an individual’s specific context and athletic demands. Additionally, the persistent asymmetries in force production suggest that these asymmetries are likely due to neuromuscular deficiencies that endure after the initial injury [49]. The more pronounced asymmetries during the unweighting and propulsive phases of the CMJ_UL and during the braking and amortization phases of the DJ_UL could be attributed to impaired muscle coordination and timing, especially in the quadriceps and hamstrings [49]. These muscles are essential for generating propulsive forces and absorbing impact forces at the knee, and their compromised function in the injured limb may, at least partially, explain the observed asymmetries. The extent to which these mechanisms can be targeted during rehabilitation to restore strength and neuromuscular control within reasonable timeframes would require further research.

Although unloaded jump tests (e.g., CMJ and DJ) are functionally appropriate for ACLR, no previous research has explored the magnitude of the asymmetry during loaded jumping and whether the force-velocity relationship provides any useful insights in ACLR patients in preparation for RTP. Including velocity-based prescription and training has been suggested for the later stages of ACLR rehabilitation as most strengthening protocols neglect targeting force capabilities at higher velocities, which is necessary for optimal performance at RTP [40]. Incorporating SJ testing with incremental loads and calculating a F-v profile within our study helps to fill this gap in the literature. Our study shows that within the SJ trials (see Fig. 3) a 25% AA force production asymmetry was consistently present in the injured limb before take-off, where the quadriceps, hamstrings, and ankle plantar flexors must generate maximum force for propulsion [8, 50–52]. Such a large asymmetry (25% AA) underlines the compromised status of the involved muscle groups, indicating that motor control strategies require specific attention, especially under loaded conditions. Subsequently we sought to evaluate whether a correlation analysis (see Fig. 6B and C) would shed light into relationships between key jumping-based performance parameters. Strong correlations between RSIm_CMJ and RSI_DJ, as well as between JH_CMJ and JH_DJ, suggest that either CMJ_UL or DJ_UL can be used to assess reactive strength. In unilateral tasks, both limbs displayed consistent performance patterns with strong correlations between RSI and JH underscoring the importance of the amortization phase to effective jump performance. Moderate-to-strong correlations were observed between F₀, RSI_DJ, and JH_CMJ suggesting that maximal force is associated with performance during explosive movements. The v₀ metric generally showed weak-to-strong negative associations with unloaded jumping metrics implying that maximal velocity contributes to a much lesser extent to unloaded jumping performances, at least within ACLR patients. The extent to which loaded jumping metrics correspond to other performance metrics or are modifiable through targeted rehabilitation is presently unclear and would require further research.

The results of this study have several implications for clinicians involved in ACLR rehabilitation. The consistent asymmetries observed across different jump types suggest that a comprehensive assessment of jump performance, including both loaded and unloaded conditions, should be part of the rehabilitation process. Clinicians should consider incorporating velocity-based training and plyometric exercises, particularly in the later stages of rehabilitation, to address the force production deficits and improve reactive strength [40]. Furthermore, the weak-to-strong correlations between F₀ and other jump metrics indicate that focusing on maximizing force production alone may be an important consideration although it is unclear to what extent this transfers to force-time performances. Furthermore, the persistent asymmetries across all jump types observed in this study highlight important considerations for clinical practice, particularly in the context of RTP decisions. Despite meeting traditional discharge criteria, athletes often exhibit asymmetries in both concentric and eccentric phases of jump tasks [12]. These asymmetries represent underlying neuromuscular deficits that could predispose athletes to re-injury if not addressed. Clinicians should likely prioritize regular and individualized assessments of jump performance especially RSI and JH to monitor these asymmetries and adjust rehabilitation protocols accordingly [53]. Interventions, such as plyometric exercises and velocity-based training during the latter stages of rehabilitation, may be necessary to correct these imbalances and optimize RTP readiness [40, 46].

This study provides insights into ACLR rehabilitation, but it is not without limitations. The small sample size and the specific population studied (i.e., club level athletes) may limit the generalizability of the findings to other groups, such as elite athletes or individuals with different rehabilitation protocols. Subsequently, these findings should not be construed as ‘established rehabilitation thresholds’ or causal mechanisms. Instead, the study offers preliminary insights into the manifestation of asymmetry across various jump tasks during the intermediate phase of rehabilitation. These findings establish a basis for future hypothesis-driven research but necessitate validation in larger, sport-specific populations prior to informing RTS criteria or clinical guidelines. Moreover, clinicians can integrate these findings by adding CMJ_UL, DJ_UL, and progressively loaded SJ assessments to mid-to late-stage rehabilitation testing batteries. In this cohort, JH, RSI, and phase-specific asymmetry within the force-time curve were most sensitive to between-limb variations and may help 'diagnose' neuromuscular impairments. Before becoming RTP criteria, these variables should be validated in larger, sport-specific cohorts. The study did not include a healthy control group, preventing direct comparison of asymmetry magnitudes to normative or non-injured patterns. The rehabilitation content and training exposure between participants were not standardised or monitored, and differences in rehabilitation quality or training load may have influenced recovery trajectories. Potential heterogeneity in surgical graft type or concomitant injuries was not controlled for and may contribute to variability in performance outcomes. Additionally, longitudinal studies that track recovery over a longer period could provide further insights into the time course of neuromuscular recovery and the effectiveness of different rehabilitation strategies. Future investigations could include analyses on joint kinetics and kinematics, such as knee extension and abduction moments, which may elucidate joint-level loading and compensatory mechanisms not identified by ground reaction force-based measures. The current sample included a limited number of female participants which may also limit, at least partially, the generalisability of the findings. Finally, the current analysis focused on jumping-based metrics, therefore the extent to which these performances are linked to other tests within a traditional ACLR testing battery would also require further research.

Conclusion

This study demonstrated that significant asymmetries and differences in jump performance persist between limbs throughout ACLR rehabilitation. These findings highlight the importance of individualized rehabilitation programs that focus on correcting specific neuromuscular deficits and ensuring athlete\s meet objective performance benchmarks before RTP. By addressing these persistent asymmetries, clinicians can help reduce the risk of re-injury and support athletes in achieving a successful and confident return to sport.

Abbreviations

0D

Zero-dimensional

1D

One-dimensional

AA

Asymmetry angle

ACLR

Anterior cruciate ligament reconstruction

CHHP

Centre for Health and Human Performance

CMJ_UL

Unilateral countermovement jumps

CoM

Centre-of-Mass

DJ_UL

Unilateral drop jumps

DoH

Department of Health

FV

Force-velocity

ICC

Intraclass correlation coefficient

JH

Jump height

JH_CMJ

Countermovement jump, jump height

JH_DJ

Drop jump, jump height

LSI

Limb symmetry index

M_diff

Mean difference

m.s⁻¹

Meters per second

N·kg⁻¹

Newton per kilogram

NWU

North-West University

PF

Peak force

PhASRec

Physical Activity, Sport, and Recreation

PP

Peak power

RSI

Reactive strength index

RSI_DJ

Drop jump reactive strength index

RSIm

Reactive strength index modified

RSIm_CMJ

Countermovement jump modified reactive strength index

RTP

Return-to-play

SJ

Loaded squat jumps

USA

United States of America

Authors’ contributions

JPJ, MK, MvA: Conceptualization, Investigation, Methodology, Writing–review and editing. MK: Formal Analysis, Writing–review and editing.

Funding

The author(s) state that this work did not receive any form of financial assistance for the research, writing, or publication of the article.

Data availability

The data set for the study is freely available at the Harvard Dataverse and can be accessed via the following link: 10.7910/DVN/0TYLFC.

Declarations

Ethics approval and consent to participate

All adult participants provided written informed consent before data collection and chose to take part voluntarily. In cases where individuals were younger than 18 years, assent was obtained in addition to parental or guardian consent. The research adhered to the ethical standards of the Declaration of Helsinki and received clearance from the Health Research Ethics Committee of the Faculty of Health Sciences (ethics number: NWU-00335-21-A1) as well as approval from the regional Department of Health.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.