Anterior cruciate ligament (ACL) injury is very common during sport activities including skiing, basketball, and soccer, and more than 70% of ACL ruptures are caused by a noncontact mechanism (17). Although a noncontact ACL injury is known to occur often during landing or deceleration before a change of direction, the mechanism of noncontact ACL injury is not well understood (17,32,35). Several studies have suggested the following potential mechanisms of noncontact ACL injury: large anterior tibial translation by excessive quadriceps contraction (11), valgus loading (13,19,24), tibial internal rotation moment (22,26), combined valgus and tibial rotation (28,32), and femoral intercondylar notch impingement (20,32). These proposed mechanisms have been formulated from observations of complex three-dimensional knee motion in three planes (sagittal, frontal, and transverse planes) at the time of injury. Although previous studies have considerably enhanced our understanding of the motions associated with ACL injury, the injury mechanism remains unclear. One reason for this is that ACL strain or ACL forces have not been measured or estimated during actual injury causing conditions.
Recently, knee valgus moment and internal tibial rotation moment have been individually studied as possible ACL injury mechanisms. Through two-dimensional video analysis, an apparent valgus collapse has been observed during ACL injury events (32). A prospective study has shown that female athletes who subsequently ruptured the ACL performed jump landing tasks with significantly higher valgus moments than female athletes who did not rupture their ACL (19). Bone contusions in the lateral femoral condyle and the posterolateral region of the tibial plateau observed in magnetic resonance (MR) images of patients without accompanying bone contusions in the medial femoral condyle or medial tibial plateau after ACL injury are consistent with the hypothesis that both high valgus loading and tibial internal rotation may be associated with ACL injury (29,31). Because these bone contusions may be caused by large tibiofemoral impact forces at the time of ACL rupture, the location of the bone contusion may indicate the location of peak tibiofemoral contact force. Therefore, it would be worthwhile to investigate the location of the peak contact force occurring in the tibial plateau during landing. Furthermore, in vivo study of subjects performing landing maneuvers has shown that valgus and tibial internal rotation occur (40). Thus, investigating ACL strain and/or knee joint motion caused by knee valgus and tibial internal rotation moments during landing maneuvers would be important to understand ACL injury mechanisms.
Cadaver studies have shown that combined tibial internal rotation moment and valgus moment significantly increase forces in the ACL (13,22). However, previous cadaver studies were often conducted while limiting some degrees of freedom or applying low levels of loading to investigate the static or quasistatic characteristics of the knee joint without the shear forces that occur during landing. Thus, they may not be sufficient for predicting the dynamic response of the knee joint when the ACL rupture occurs. Dynamic three-dimensional simulation studies offer an attractive alternative because we are able to apply and predict responses to a wider array of complex dynamic joint loading scenario, apply physiological loads, and allow unconstrained motion.
The recent development and validation of specimen-specific knee models for single-leg landing have made it possible to predict the effect of various loading configurations on ACL strain during dynamic single-leg landing (36,37). It has been suggested that valgus moment at the knee joint does increase ACL strain, but the physiological level of isolated valgus moment observed in vivo motions alone may not be sufficient to rupture the ACL (38). However, predictions of ACL strain under physiological levels of combined valgus and internal rotation moment during dynamic landing have not been studied using a model validated for the estimation of ACL strain.
The purpose of this study was to test the influence of combined valgus and tibial internal rotation moment on ACL strain during single-leg landing using a dynamic three-dimensional simulation model driven by in vivo human loading data. We tested the following hypotheses: the combination of the valgus and internal rotation moments observed during single-leg landing produces a higher ACL strain than either moment applied individually, the combined rotational moments at the physiological levels observed could theoretically increase strain in the ACL high enough to rupture the ACL, and the location of the peak contact force on the tibial plateau was at the posterior-lateral side for combined loading.
We applied a previously developed dynamic knee simulation model to predict ACL strains. The model is three-dimensional, specimen-specific, and driven by applied forces. The model was validated for prediction of ACL anteromedial bundle strain against previous cadaveric experiment data (37) by applying the same dynamic vertical impact loads as in the cadaver experiment. These loads were chosen to simulate single-leg landing. The simulation's ACL strain prediction showed good correspondence to the measured strain in the cadaver, with <16% difference for peak ACL anteromedial bundle strain and very similar knee flexion motion through the applied load cycle (Pearson correlation coefficient of 0.983) (37). In this study, physiological levels of valgus moments and tibial internal rotation moment (normalized based on the subject's body weight × height) observed from in vivo studies were rescaled to an average-sized person (height = 1.75 m, body mass = 76.5 kg) and applied to investigate the influence of those combined moments on ACL strain during dynamic single-leg landing.
The development and validation of this knee model to predict ACL strain during landing have been described in detail by Shin et al. (37); thus, only a brief description is given here. The knee model was created using sagittal MR images (GE 3D spoiled-gradient-recalled-echo (SPGR), 1.5 T, field of view (FOV) = 140 × 140 mm, matrix = 256 × 256, slice thickness = 1.5 mm) of a cadaveric knee (Fig. 1). MR images were segmented and imported into dynamic motion simulation software (MSC.ADAMS; MSC.Software, Santa Ana, CA). This knee model includes nonlinear elastic ligament bundles (the ACL, the posterior cruciate ligament (PCL), the medial collateral ligament (MCL), the lateral collateral ligament (LCL), posterior capsules, and the patellar ligament) with properties from published data (1,45,46). The ligaments were formulated as nonlinear springs with toe and linear regions (37) and pretensions (5,34). The origins and insertions of the ACL and PCL were determined based on segmented MR images. Two functional bundles of the ACL and PCL were identified in the reconstructed geometries as previously quantified (18), and the centroids of each region were determined to be the insertion points. The MCL, LCL, and posterior capsule were placed over the appropriate anatomic bony landmarks (15,37,46). The patellar ligament was modeled by medial and lateral bundles and placed based between the patellar apex and tibial tuberosity as viewed in the MR image. The contact forces at the cartilage-to-cartilage articulation were defined using a penalty regulation of normal contact force constraints (21), whose algorithm was implemented in the MSC.ADAMS solver, with previously reported cartilage properties (30,33). The location of the center of pressure of the tibiofemoral contact force was calculated in the MSC.ADAMS solver and displayed on the tibial plateau at each simulation step. The passive characteristics of the knee model were tested under various conditions, including valgus rotational stiffness, internal rotation stiffness, and passive flexion movement to ensure proper tibiofemoral behavior (36,37).
To simulate the motion of a single-leg landing, a simulated landing apparatus was created using commercial software (MSC.ADAMS) on the knee model with the same geometric configuration using the same cadaver knee specimen (Fig. 2) as in a previously described cadaver experiment (42,43). Three musculotendinous groups (the quadriceps, the medial/lateral hamstrings, and the medial/lateral gastrocnemius) were modeled as linear tension springs with the same pretension and stiffness used in the experiment to provide the appropriate tension to hold the initial knee flexion angle at 25° before impact load and to simulate eccentric contraction in the quadriceps as done in the physical experiment (42). The proximal femur was connected to the mounting apparatus through a spherical joint and linear slide, allowing free rotation analogous to a hip joint and vertical motion. The distal tibia was connected to a spherical joint, functioning like an ankle joint. This complete model and apparatus were previously tested to validate the model for predicting ACL strain during landing against the physical experiment, in which a differential variable reluctance transducer was attached to the ACL to measure strain (37).
A range of valgus moments from 0 to 65 N·m was chosen to characterize the response of the ACL to the reported range of valgus moments (3,39). Within this range, based on the dynamic profile and magnitude of valgus moment from a previous in vivo study of a run-to-cut landing maneuver (8) and normalized to an average-sized person (height = 1.75 m, weight = 750 N), we identified four physiological levels of valgus moment indicative of landing technique. Neutral lander, valgus lander, and varus lander groups were classified based on the angle between the shank and the thigh during the weight acceptance phase. Thus, four physiological levels of valgus moment were determined as follows: minimum valgus moment of neutral landers (0 N·m), average valgus moment of neutral landers (8 N·m), average valgus moment of valgus landers (24 N·m), and maximum valgus moment of valgus landers (51 N·m). Two additional values (55 and 65 N·m) were added to represent the entire range with six possible values of valgus moment.
Similarly, we chose a range of peak tibial internal rotation moment values (0-30 N·m) to encompass the range of moments experienced in vivo from a previous study (3). Again, we chose four characteristic physiological levels of peak internal rotation moments to simulate the normal range of in vivo tibial internal rotation moments due to the ground reaction force from a previous landing experiment using 25 subjects with no history of musculoskeletal injury after providing informed consent (9). The profile and magnitude of tibial internal rotation moment for these 25 subjects were normalized by body weight and height, then averaged, then rescaled to an average-sized person (height = 1.75 m, weight = 750 N). The four characteristic levels of null (0 N·m), minimum (3.6 N·m), average (11.5 N·m), and maximum (25.9 N·m) value of peak internal rotation moment during single-leg landing were determined from this previous data set and applied to the knee model. Three additional values (18, 23, and 30 N·m) were added to represent the entire range with seven possible values of internal rotation moment.
All combinations of the six values of valgus and seven values of internal rotation moment were parametrically varied to determine an ACL strain response surface. These combinations generated 42 cases of combined valgus and internal rotation moments for simulation input.
The combined valgus moment, internal rotation moment, and vertical impact force resulting from the external forces acting on the leg were simultaneously applied with an initial knee flexion angle of 25° (Fig. 2). A dynamic vertical impact force with a peak value of 1300 N was applied at the top of the femoral axis of the thigh to simulate landing motions. This value was chosen to match the experimental study (42) and is approximately equal to two body weights. This value was within the range observed in the in vivo study. The dynamic simulations were conducted using an implicit method (GSTIFF integrator (16)) built in the MSC.ADAMS solver. In response to the applied loading, the model calculated knee kinematics and ACL strain during each simulation (Fig. 2). It should be noted that only a vertical force, a valgus moment, and a tibial internal rotation moment were applied, but because the knee was unconstrained, motions in all six degrees of freedom were possible.
The estimated peak strains in the anteromedial bundle of the ACL under the various combinations of valgus moment and internal rotational moment are illustrated as a three-dimensional response surface (Fig. 3). The peak strains in the posterolateral bundle were generally smaller but followed a similar trend. The peak strain in the ACL increased nonlinearly when either the applied valgus moment or the internal tibial rotation moment was increased in the model. When valgus moment or internal rotation moment was applied individually (without the other rotation moment), neither caused ACL strain higher than 0.077, and the effect of each moment reached a plateau at or near the maximum level observed in vivo. However, when applied in combination, the two rotational moments had a much larger effect, and estimated strain in the ACL consistently increased over 0.077 when one of the rotational moments was held at a high level and the other moment was applied at any level greater than 0.
The estimated peak strain in the anteromedial bundle of the ACL under the combination of maximum valgus (51 N·m) and maximum internal tibial rotation moment (25.9 N·m) observed from in vivo experiments was 0.105 during simulated single-leg landing (Fig. 3).
The estimated peak contact force on the tibia occurred at the posterior-lateral side of the tibial cartilage when the combined maximum valgus moment, maximum tibial internal rotation moment, and vertical impact were applied (Figs. 4A and C: loading case 1). When the maximum level of valgus moment was applied with no tibial internal rotational moment, the center of pressure of the peak contact force occurred close to the midline of the tibial anterior-posterior axis (Figs. 4B and C: loading case 2).
This simulation study demonstrated that combined valgus moment and tibial internal rotation moment on the knee joint during single-leg landing motion significantly increased the peak strain in the ACL. The predicted peak strain in the ACL due to the combined physiological maximum valgus (51 N·m) and internal rotational moment (25.9 N·m) was 0.105, which lies within the reported range for ACL rupture of 0.09-0.15 (6,27). The predicted peak strain in the ACL increased even higher over the reported threshold for ligament failure when the combined loads were increased to levels one might reasonably expect in full-speed game situations (i.e., not in a motion analysis laboratory), as high as 0.115 under combined internal rotation moment (25.9 N·m; maximum value from our previous in vivo laboratory study) and valgus moment (65 N·m; 30% above maximum value from our previous in vivo laboratory study).
The results of this study showed that the effect of combined rotation moments on ACL strain is more distinctive than the effect of either rotation moment acting in isolation. Applying either rotation moment caused a nonlinear increase in the ACL strain. The predicted peak strain in the ACL increased by 27% (absolute increase = 0.015 mm·mm−1) when the applied peak internal tibial rotation moment increased from 0 to 25.9 N·m (the maximum value observed from our previous in vivo study) with vertical impact force but no valgus moment applied. Similarly, the predicted peak strain in the ACL increased by 34% (absolute increase = 0.019 mm·mm−1) when the applied peak valgus moment increased from 0 to 51 N·m (the maximum value observed from our previous in vivo study) with vertical impact force but no tibial internal rotation moment applied. Neither of these maximum applied moments created strains high enough to expect injury, and the plateaus of strain at the highest moment levels suggest that merely increasing the rotation moments in isolation further might not be enough to cause ACL rupture. However, when applied in combination, the two rotation moments had a much larger effect, and the sensitivity of ACL strain to increases in either quantity was much higher when the other was held at a high level (Fig. 3). These results suggest that subjects whose typical valgus and internal rotation moments are both high may be at greater risk because ACL strain is more sensitive to perturbations in the applied moments at those levels, as shown by the steepest slope of the surface when valgus moment is between 24 and 51 N·m and internal rotation moment is between 11.5 and 25.9 N·m. One possible explanation for this predicted phenomenon is that, with internal rotation, the ACL is more horizontal and thus will have less resistance to a valgus moment. Therefore, combining the internal rotation with valgus moment will produce a geometric nonlinearity that is greater than the effect of applying these moments independently.
Although we used values for rotational moments from laboratory studies of preplanned cutting maneuvers, it is important to note that, during unanticipated game situations, the moments experienced by the knee may be considerably larger. McLean et al. (25) reported that athletes performing a sidestepping maneuver increased their peak knee valgus angle and moment when a defensive opponent was present. Besier et al. (3) reported that peak valgus moments can double for subjects during unanticipated movement compared with preplanned maneuvers. Those perturbations to either rotational moment may increase strain in the ACL further and thereby increase risk of noncontact ACL injury. Our results are also consistent with the observed gender difference in ACL injury incidence in soccer and basketball (2) because, typically, females have been observed to experience higher valgus moments and tibial internal rotation moments than males (25,39).
Another interesting finding of this study was that the predicted center of pressure of the peak tibiofemoral contact force occurred at the posterior-lateral region of the tibial cartilage when combined valgus moment and tibial internal rotational moment were applied during single-leg landing. It is clear that the tibiofemoral contact location moved posteriorly when the tibia was internally rotated with the location of femur fixed (Fig. 5). This predicted posterolateral contact location on the tibial plateau agrees with the locations of bone contusions or bone marrow edema that have often been observed in acute ACL-injured patients examined by MR imaging in previous studies (29,31). However, when the maximum valgus and vertical impact loading were applied (without tibial internal rotation moment), the peak contact force occurred in the midlateral region of the tibial plateau. This finding supports the hypothesis that isolated valgus moment (i.e., without any tibial internal rotation moment) is less likely to cause ACL rupture (38) compared with combined tibial internal rotation and valgus moments because bone contusions usually have been observed in the posterolateral region of the tibial plateau.
One of the greatest advantages of this model is the fact that it allows unconstrained knee kinematics rather than only allowing a subset of knee joint motion. Previous cadaveric and simulation studies have most often constrained flexion, extension, or tibial axial rotation (11,13,22,24). It has been reported that the relative contributions of the ACL to the knee kinematics vary depending on the constraints applied by the testing devices (44). Thus, the unconstrained knee joint used in this study seems to be the most appropriate for predicting the subtle changes in ACL strain during a dynamic motion. The increased ACL strain due to valgus moment in this study was much higher than in previous studies where axial rotation was constrained (12,23). Similarly, when flexion angle is fixed, the addition of valgus moment to internal rotation moment does not seem to significantly increase ACL strain (22). However, it has been observed that ACL forces significantly increases in response to valgus loading when axial rotation was unconstrained (13). These differences in the observed effects of valgus and internal rotation moments on ACL strain between our study and other studies (11-13,22-24) are most likely due to the different degrees of freedom allowed, different methods to support specimens, and different simulated motions.
The results from this study should be considered in light of the fact that our knee modeling method was initially developed to ensure proper passive tibiofemoral behavior, including passive flexion and rotational stiffness of the knee joint (5,36,41). On the basis of the knowledge that our model recreated passive tibiofemoral characteristics correctly, we assumed that the knee model should predict the kinematics of landing motion correctly. This assumption was supported by the fact that our validation comparisons showed good correspondence in ACL strain during single-leg landing. These results give confidence that the model should predict changes in ACL strain with the application of additional rotational loading correctly. Given the good agreement between our model, the cadaver knee it was generated from, and literature data on passive knee characteristics, we elected not to perform a systematic analysis of the sensitivity of peak ACL strain to variations in model parameters.
One potential limitation of this study is that, in real sport activities, the total combined loading applied to the knee joint may include other forces such as impingement forces or medial-lateral forces. Previous studies have suggested that, at 25° of flexion, impingement of the ACL on the intercondylar notch is not a concern (14,42,43). We are unaware of any studies examining the influence of medial-lateral forces on the ACL. However, the purpose of this study was to evaluate the influence of combined valgus and tibial internal rotation moment on ACL strain during landing because these two moments have been repeatedly observed in in vivo studies. Thus, understanding the influence of combined valgus and tibial internal rotation moment on the ACL strain provides valuable insight into ACL injury mechanisms.
It should be noted that the initial angle may have an influence on ACL strain because the anteromedial bundle of the ACL seems to be strained more in an extended position. The average knee flexion angle at foot strike has previously been reported as 23° for landing from a jump motion (10). In addition, many previous studies have reported that the ACL is strained between 15° and 30°. For example, cadaver studies have shown that, at 30° of knee flexion, the ACL represents 85% of the total capsular and ligamentous resistance (7). Fleming et al. (12) used 20° of flexion during in vivo testing to study the effect of weight bearing and external loading on ACL strain. Beynnon and Fleming (4) reported in vivo ACL strains at 30° of flexion. Thus, the cadaver experimental apparatus was designed holding the initial knee flexion of 25° to simulate landing motion (42). Our knee simulation model was designed to replicate all conditions as closely as possible to the cadaver apparatus (42). Therefore, the initial condition of 25° flexion from the experimental apparatus was recreated in the simulation model.
Another limitation of this study is that the knee model was created using the geometric information of one knee specimen, so one must take care in overapplying its results generally to all knees. It is certainly possible that another knee could respond very differently to the same variations in applied loads. To calculate an individual's ACL strain accurately, it would be ideal to generate different subject-specific models with their subject-specific tissue properties and to apply subject-specific loads. However, this model was created using the anatomy of an average-sized male based on the bicondylar width and inspected for malalignment or radiographic deformity. The height-of-patella ratio of this knee (Blackburne-Peel index = 0.94, Insall-Salvati index = 1.1) indicates normal patellofemoral movement (37). Thus, the results from this study should be generally applicable to the normal movement of an average-sized knee joint without bony deformities. Unlike previous simulation studies where a single generic model is generated from averaged anatomical data that may not represent any real specimen and whose results cannot be directly validated, this model represents a real individual of average size, and it has the distinct advantage of being directly validated against experimental results. Although some subtle differences may occur in anatomy and motions between individuals, the general trend of the influence of combined valgus and internal rotation moments on ACL strain should be preserved.
In conclusion, this study has shown that combined valgus and internal rotation moments increase strain in the ACL more than either alone. The combination of valgus and internal rotation moments that occur in vivo during landing can cause ACL strains that may be high enough to cause ACL injury. This predicted high ACL strain and contact force location in this study suggest that combined valgus and tibial internal rotational moments during landing motion are relevant to the rupture of the ACL.
Partial funding from the National Institutes of Health grant R01-AR39421 and the Sogang University Research grant 200910041.01 is greatly acknowledged. This research was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (2010-0005704).
The authors have no conflict of interest with respect to any material in the article.
The results from the present study do not constitute endorsement by the American College of Sports Medicine.
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