1 INTRODUCTION

Anterior cruciate ligament (ACL) injury is a well-known risk factor for knee osteoarthritis.1 Degenerative changes associated with osteoarthritis are observed in both the tibiofemoral-joint (TFJ) and patellofemoral-joint (PFJ) in up to 90% of young adults within 10 years of ACL injury, irrespective of surgical ACL reconstruction (ACLR) or nonoperative management.2, 3 The mechanobiological processes associated with the initiation and progression of knee osteoarthritis post-ACLR are still unclear, but altered movement patterns and mechanical loading within the joint are thought to play critical roles.4-7

Considerable differences between the ACLR limb compared to the contralateral limb and/or uninjured controls in joint kinematics and moments have been observed for tasks, such as walking,8 running,9, 10 single-leg drop landing11 and forward hop-landing.12-15 The most evident and consistent differences for the ACLR limb are in the sagittal plane,8 including a lower peak knee flexion angle and peak external knee flexion moment,8 and increased overall leg stiffness.12 These differences are apparent from 6 months after ACLR,7, 13 but persist for at least another 8 years,16 suggesting lower-limb biomechanical function never fully recovers.

Diminished loading may be a salient biomechanical feature following ACLR. Compared to uninjured knees, lower PFJ contact forces post-ACLR have been found during running,9, 10 while lower TFJ compressive forces were reported for walking,7, 17 running, and side-stepping.17 Furthermore, lower TFJ anterior shear forces, but greater TFJ compressive forces, were observed in the ACLR knee during drop-landings,11 indicating a possible task-dependency of loading following ACLR. While many studies have investigated joint kinematics and moments after ACLR, only a few studies have explicitly reported knee-joint forces. Most notably, very few investigations of PFJ contact forces have been undertaken, even though the PFJ frequently displays rapid early cartilage loss and radiographic changes after ACLR.18-20

The single-leg forward hop-for-distance is a challenging but routine task to evaluate function after ACLR, and to assess readiness for return to sport.21 It is an effective surrogate for explosive/ballistic sagittal-plane movements commonly undertaken during sport, and may reflect the upper limits of lower-limb joint loading experienced. During the landing phase of this task, individuals must coordinate their trunk and lower-limb muscles to arrest their forward motion while simultaneously resisting collapse due to gravity.12 The landing phase imparts sudden high-impact loading on the lower-limb, with rapidly applied ground forces rising to more than double the magnitude experienced at take-off.22 Peak PFJ reaction forces during landing may be as high as 8.6 body weights (BW) in uninjured individuals,23 but TFJ loading has not been reported to our knowledge. Moreover, PFJ loading during a forward hopping task following ACLR remains unexplored. Thus, understanding knee-joint loading during high impact tasks after ACLR may yield new insights into the risk of reinjury and the development of posttraumatic osteoarthritis.

Our objective was to quantify the reaction forces and impulses in the ACLR knee during the landing phase of a forward hop for individuals 12–24 months postoperatively, and to compare results with those from uninjured controls. We hypothesised that peak compressive forces, as well as compressive impulses, in the PFJ and TFJ following ACLR would be lower than in uninjured controls.

2 METHODS 2.1 Study design

Case-control study (Level of Evidence III).

2.2 Study participants

Sixty-six adults 12–24 months following ACLR and 33 uninjured controls were included. Experimental data from these cohorts were used previously,12 with one additional participant in each group for the present study. Participants with ACLR were part of a larger cohort () of consecutively eligible patients with a primary hamstring-tendon autograft ACLR from one of two orthopaedic surgeons.21, 24, 25 At the time data collection, participants were aged 18–50 years and were involved in physical activity 1–3 times per week (Tegner activity scale ≥4). The study was approved by the University of Melbourne Human Research Ethics Committee (ID: 1136167). Exclusion criteria were previous injury or surgery to the contralateral knee, grade III injury to other knee ligaments, subsequent injury or surgery to the ACLR knee, or any other condition affecting physical function. Sports involvement was assessed using the Sports Activity Classification.26 Quadriceps strength was measured as the maximum isometric knee extension moment, with participants seated at 90° hip flexion and 60° knee flexion, using a KinCom dynamometer (Chattecx Corp.).27 Objective knee function was assessed using hop-for-distance and side-hop tasks, while patient-reported function was assessed with the Cincinnati knee rating scale.28

2.3 Biomechanical data collection

The detailed experimental procedure was recently published.6, 12 Briefly, biomechanical testing was undertaken at the Movement Research Laboratory, Centre for Health, Exercise and Sports Medicine, University of Melbourne. Participants walked forwards three steps in time with a metronome set at 100 beats per minute and performed a single forward hop, taking off and landing on the same leg. The ACLR group hopped using their reconstructed leg, while controls used their right leg. Hop distance was standardised (with marks on the floor) to equal 100% of the participant's leg length (i.e., from greater trochanter to the floor). Participants were barefoot and folded their arms across their chest. A trial was deemed successful if the participant landed on their mark, and comfortably maintained their balance for at least 2 s after foot-strike. A maximum of 10 trials were attempted, but the number of successful trials varied between participants, ranging from 4 to 7 (median: 5). No participants reported any knee pain while undertaking the task.

During each hop trial, the spatial trajectories of 32 retro-reflective markers placed on the torso, pelvis, and both lower-limbs of the participants29 were collected using a 12-camera Vicon motion analysis system (Oxford Metrics) at 120 Hz. A static standing trial was recorded initially, to determine participant anthropometry for subsequent musculoskeletal modelling. For this purpose, an additional eight markers were placed on the lower-limb which were removed before undertaking dynamic trials. A single force plate (AMTI Watertown) was used to measure ground reaction force (GRF) data at 1080 Hz. Kinematic and GRF data were filtered at 15 Hz using a fourth-order, zero-lag, recursive Butterworth filter.

2.4 Musculoskeletal modeling

Musculoskeletal modelling was undertaken using OpenSim 4.030 via the API in MATLAB (The Mathworks Inc.). For each participant, a whole-body three-dimensional musculoskeletal model was created by scaling the inertial properties and musculotendon geometry of a reference model, adapted from Arnold et al.,31 using anatomical measurements estimated from the static trial. The reference model consisted of 14 rigid segments, 23 degrees-of-freedom and 94 Hill-type muscle-tendon units. The head, arms, and torso were combined into a single rigid body, articulating with the pelvis via a ball-and-socket. Each hip-joint was modelled as a ball-and-socket, and each knee, ankle and subtalar-joint was modelled as a hinge. For each leg, the motions of each tibia and patella relative to the femur were prescribed with respect to the knee flexion angle, and a passive inelastic patellar tendon articulated with the tibia and patella. The metatarsophalangeal joints, modelled as hinges, were locked at the reference position.

Joint angles were calculated using inverse kinematics, which minimised the sum-of-squares of distances between experimental marker trajectories and the equivalent virtual markers on the model.32 Joint moments were calculated using inverse dynamics. Muscle forces were estimated from joint moments using static optimisation, by minimizing the sum-of-squares of activations subject to constraints imposed by each muscle's force-length-velocity properties.33

2.5 PFJ forces A simple model of the PFJ was implemented in MATLAB to calculate PFJ reaction forces. A full mathematical description of the model is presented in Sritharan et al.10 Briefly, it consisted of a rigid patella, and the three-dimensional musculotendon geometry of the vastus laterialis, vastus intermedius, vastus medialis, rectus femoris and the patellar tendon derived directly from each participant's OpenSim model. For each trial, at each time step, the instantaneous vasti and rectus femoris forces were applied to the patella (Figure 1A), acting along each respective muscle's instantaneous line-of-action, calculated from the OpenSim model's instantaneous pose. The sum of these muscle force vectors is the quadriceps force, FQ. Subsequently, the three-dimensional patellar tendon force vector, FPT, was calculated by equating the components of the quadriceps force and patellar tendon force tangent to the surface of the femur at that time step. Finally, by assuming negligible patellar mass and zero sliding friction of the patella along the trochlear groove, the net PFJ reaction force vector, FPFJ, is simply equal and opposite to the sum of the quadriceps and patella tendon forces: (1)Where is the component of the net PFJ reaction force perpendicular to the surface of the femur at that time step, and is the component acting mediolaterally. The magnitude of the PFJ compressive force experienced by the patella acting against the surface of the trochlear groove is the Euclidian norm of the x- and z-components of the net PFJ reaction force: (2) (A) Schematic diagram of the model used to calculate patellofemoral-joint (PFJ) reaction forces. The vector sum of the vastus medius, vastus intermedius, vastus lateralis and rectus femoris muscle forces, which have magnitudes , , , , respectively, is the quadriceps force vector, which has magnitude . The three-dimensional quadriceps force vector and the position and orientation of the patella in space are used to calculate the three-dimensional patella tendon force vector, which has magnitude . Using static equilibrium, and assuming zero friction (setting the component of the net PFJ reaction force acting tangent to the femur surface in the sagittal-plane to zero, i.e., ), the non-zero components of the net PFJ reaction force are the component acting normal to the instantaneous surface of the femur, and the component acting mediolaterally, which have magnitudes and , respectively. (B) Schematic diagram of the tibial plateau model used to calculate tibiofemoral-joint (TFJ) compartment forces. and are the known magnitudes of the TFJ compressive force and frontal-plane reaction moment, respectively, acting at the knee-joint centre, point A. and are the magnitudes of the unknown medial and lateral compartment forces acting at their respective centres-of-pressure, points O and B. and are the distances from O to A and B, respectively. is the magnitude of the net moment acting about O, due to and 2.6 TFJ forces and medial/lateral compartment forces

For each trial, the TFJ reaction forces and moments were calculated at each time step by applying the joint angles, muscle forces, the GRFs, and the calculated patellar tendon forces, to the musculoskeletal model, and solving for the instantaneous three-dimensional joint reaction forces and moments. The three-dimensional TFJ reaction force and reaction moment together represent the net loads borne by the knee, that balance the forces and moments applied by the knee-spanning muscles and external loads. For this study, the component of the net TFJ reaction force acting axially along the tibia was defined as the TFJ compressive force, while the fore-aft component with respect to the tibia was defined as the TFJ anterior shear force.

The TFJ compressive force was further partitioned into medial and lateral tibiofemoral compartment forces, given by F MED  and F LAT , respectively, by considering a simple force-moment balance in the frontal-plane (Figure 1B). Firstly, we calculated the sum of reaction moments in the frontal-plane about the lateral compartment centre-of-pressure (point O), , which has magnitude: (3)Where and are the magnitudes of the frontal-plane TFJ reaction moment and the TFJ compressive force, respectively; and is the horizontal distance from point O to the knee-joint centre (point A). Assuming static equilibrium, , acting at the medial tibiofemoral compartment centre-of-pressure (point B), produces a moment about O that balances . The magnitude of is therefore: (4)Where is the horizontal distance from points O to B. Finally, the magnitude of is simply given by: (5)

The medial and lateral compartment centres-of-pressure were assumed to always be located at the midpoint of the medial and lateral tibial plateaus in the frontal-plane, respectively. Reference dimensions for each plateau were obtained from Yoshioka et al.,34 and scaled to each participant's anthropometry.

2.7 Data analysis

Demographic differences between the ACLR and uninjured control groups were compared using Welch's t tests, Mann–Whitney U tests or χ 2 tests, as appropriate based on distribution of data. We analysed biomechanical data from the landing phase only, defined as the time period from foot-strike to peak knee flexion angle, because the lower-limb experiences the greatest loading during this phase.22 The impulse of each joint force of interest, that is, the PFJ and TFJ compressive forces, the TFJ anterior shear force, and the medial and lateral compartment forces, was defined as the time integral of that force over the landing phase.

Group means (with standard deviations), mean differences (with 95% confidence intervals), as well as Cohen's d effect sizes were calculated for peak joint angles, joint moments, quadriceps forces, knee-joint reaction force peaks and impulses, as well as the timing of their respective peaks. For each variable, the group mean peak values were obtained by first calculating mean peak values for each participant (by averaging the discrete peak values from that participant's successful trials), and then averaging these participant means for each group.

All biomechanical variables were normally distributed and analysed using Welch's t tests with significance set a priori at . Between-group differences in body weight were accounted for by expressing knee-joint reaction force peaks and impulses in normalised units (body weights, BW, and body weight-seconds, BWs, respectively). All analyses were undertaken in RStudio (RStudio, Inc.) using R v4.0.2.

3 RESULTS

The ACLR group was tested 17 ± 3 months post-ACLR, were, on average, 2 years older, significantly heavier and had inferior self-reported and objective knee function (Table 1). More than two-thirds of the participants from each group were involved in Level I or II sport at the time of testing. There was no between-group difference in quadriceps strength.

Table 1. Participant characteristics ACLR (n = 66) Control (n = 33) p Agea, years 28 ± 6 26 ± 5 0.050 Body mass, kg 78 ± 15 70 ± 12 0.005 Height, m 1.75 ± 0.10 1.71 ± 0.08 0.044 Maximum hop distance, m 1.20 ± 0.23 1.32 ± 0.28 0.038 Leg length, m (% of max hop distance) 0.88 ± 0.06 (76%) 0.86 ± 0.04 (68%) 0.052 Womenb, n (% of participants in group) 24 (36%) 16 (48%) 0.247 Quadriceps strengthc, Nm/kg 1.84 ± 0.71 2.00 ± 0.67 0.291 Time after ACLR surgery, months 17 ± 3 - - Concomitant partial meniscectomy, n (%) 24 (36%) - - Level I/II sports participationb,d, b,d, n (%) 46 (69%) 22 (66%) 0.759 Tegner activity scalee, /10 6 (3) 6 (4) 0.958 Knee function and hop performance Cincinnati knee rating scalee, % 90 (14) 100 (0) <0.001 Hop for distance LSIe, % 96 (12) 102 (7) <0.001 Side hop LSIe, % 90 (38) 106 (25) <0.001 Landing phase timef, s 0.18 ± 0.04 0.18 ± 0.03 0.366 Note: Unless indicated otherwise below, values are presented as mean ± standard deviation with p values calculated using Welch's t test. Significance levels for all tests were set a priori at α = 0.05. Abbreviations: ACLR, anterior cruciate ligament reconstruction; LSI, limb symmetry index; n, number of participants.

Peak values for knee flexion angle, internal knee extension moment, quadriceps force and external knee adduction moment were all lower in the ACLR group (Table 2). There were no between-group differences in the timing of each peak, except for the knee adduction moment, with controls peaking slightly later (Table 2; Figure 2). The ACLR group had a smaller knee flexion angle at initial contact, but a similar range of motion (Figure 2A).

Table 2. Differences in peak knee-joint biomechanical variables between ACLR and control groups during the landing phase Mean ± SD p d ACLR Control Mean diff (95% CI) Knee flexion angle (degrees) 59 ± 8 64 ± 10 −6 (−10, −2) 0.002 −0.67 Internal knee extension moment (%BW*HT) 18.24 ± 2.70 21.86 ± 4.34 −3.63 (−5.29, −1.97) <0.001 −1.09 External knee adduction moment (%BW*HT) 4.65 ± 1.95 6.01 ± 1.76 −1.36 (−2.16, −0.56) 0.001 −0.72 Quadriceps force (BW) 8.56 ± 1.44 10.60 ± 2.45 −2.02 (−2.95, −1.09) <0.001 −1.10 Knee-joint reaction forces (BW) PFJ compressive 8.56 ± 1.64 10.80 ± 2.81 −2.24 (−3.31, −1.18) <0.001 −1.07 TFJ anterior shear 1.35 ± 0.43 1.25 ± 0.32 0.10 (−0.06, 0.27) 0.229 0.26 TFJ compressive 9.35 ± 1.02 10.10 ± 1.19 −0.74 (−1.20, −0.28) 0.002 −0.69 Medial compartment 5.31 ± 0.71 6.08 ± 0.77 −0.76 (−1.08, −0.44) <0.001 −1.05 Lateral compartment 4.44 ± 0.69 4.48 ± 0.63 −0.04 (−0.31, 0.23) 0.765 −0.06 Knee-joint reaction impulse (BWs) PFJ compressive 0.76 ± 0.17 0.89 ± 0.26 −0.13 (−0.23, −0.03) 0.012 −0.64 TFJ anterior shear 0.13 ± 0.07 0.12 ± 0.03 0.02 (−0.01, 0.04) 0.230 0.26 TFJ compressive 1.21 ± 0.26 1.26 ± 0.19 −0.04 (−0.15, 0.06) 0.385 −0.19 Medial compartment 0.73 ± 0.16 0.79 ± 0.14 −0.06 (−0.12, 0.00) 0.068 −0.38 Lateral compartment 0.48 ± 0.14 0.46 ± 0.07 0.02 (−0.02, 0.06) 0.365 0.16 Time of peak (% of landing phase) External knee adduction moment 56 ± 15 62 ± 12 −6 (−12, −0) 0.038 −0.45 Quadriceps force 56 ± 9 58 ± 8 −2 (−6, 2) 0.280 −0.23 PFJ compressive force 62 ± 11 64 ± 9 −2 (−6, 3) 0.476 −0.15 TFJ anterior shear force 39 ± 9 40 ± 6 −1 (−5, 2) 0.416 −0.17 TFJ compressive force 48 ± 11 49 ± 8 −1 (−5, 3) 0.588 −0.10 Medial compartment force 59 ± 15 60 ± 11 −1 (−6, 4) 0.661 −0.08 Lateral compartment force 43 ± 11 43 ± 8 0 (−3, 4) 0.836 0.04 Note: Quadriceps force is the sum of vastus medialis, vastus intermedius, vastus lateralis and rectus femoris muscle forces. p Values were calculated using Welch's t tests with significance set a priori at α = 0.05. Significant differences are shown in bold. Effect sizes were calculated using Cohen's d. Abbreviations: %BW × HT, percentage of body weight × subject height; ACLR, anterior cruciate ligament reconstruction; BW, body weights; BWs, body weights-seconds; CI, confidence interval; PFJ, patellofemoral-joint; TFJ, tibiofemoral-joint.