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Impact of Knee Modeling Approach on Indicators and Classification of Anterior Cruciate Ligament Injury Risk


Medicine & Science in Sports & Exercise: July 2014 - Volume 46 - Issue 7 - p 1269–1276
doi: 10.1249/MSS.0000000000000236

Introduction The aim of this study was to determine whether using a direct kinematic (DK) or inverse kinematic (IK) modeling approach could influence the estimation of knee joint kinematics, kinetics, and ACL injury risk classification during unanticipated side cutting.

Methods The three-dimensional motion and force data of 34 amateur Australian rules footballers conducting unanticipated side-cutting maneuvers were collected. The model used during the DK modeling approach was an eight-segment lower body model with the hip, knee, and ankle free to move in six degrees of freedom. During the IK modeling approach, the same eight-segment model was used; however, translational constraints were imposed on the hip, knee, and ankle joints. The similarity between kinematic and kinetic waveforms was evaluated using the root mean square difference (RMSD) and the one-dimensional statistical parametric mapping (SPM1D). The classification of an athlete’s ACL injury risk was determined by correlating their peak knee moments with a predefined injury risk threshold.

Results The greatest RMSD occurred in the frontal plane joint angles (RMSD = 10.86°) and moments (RMSD = 0.67 ± 0.18 N·m·kg−1), which were also shown to be significantly different throughout the stance phase in the SPM1D analysis. Both DK and IK modeling approaches classified the same athletes as being at risk of ACL injury.

Conclusions The choice of a DK or an IK modeling approach affected frontal plane estimates of knee joint angles and peak knee moments during the weight acceptance phase of unanticipated side cutting. However, both modeling approaches were similar in their classification of an athlete’s ACL injury risk.

Supplemental digital content is available in the text.

1School of Sport and Exercise Sciences, Liverpool John Moores University, Liverpool, UNITED KINGDOM; and 2School of Sport Science, Exercise and Health, University of Western Australia, Perth, AUSTRALIA

Address for correspondence: Mark Robinson, Tom Reilly Building, Byrom Street Campus, Liverpool, Merseyside, L3 3AF, United Kingdom; E-mail:

Submitted for publication May 2013.

Accepted for publication November 2013.

Supplemental digital content is available for this article. Direct URL citations appear in the printed text and are provided in the HTML and PDF versions of this article on the journal’s Web site (

Biomechanical models are frequently used to estimate knee loading and to describe lower limb kinematics during dynamic sporting tasks (10,29). To generate model kinematics experimentally, reflective markers are placed onto specific anatomical landmarks, and their three-dimensional trajectories are recorded during a dynamic task. These marker trajectories can then be used to generate the kinematics of the model either directly (the direct kinematic [DK] modeling approach) or using an inverse approach via optimization (9,24) where the generalized coordinates (kinematics) of a rigid skeletal model with predefined joint constraints (rotational and/or translational) are adjusted to “best fit” the marker data (the inverse kinematic [IK] modeling approach). Arguments have been made for the use of both DK (7) and IK modeling approaches (24), but little research is available directly comparing both methods.

Joint kinematics is the measurement of two segmental coordinate systems with respect to each other (6). During the DK modeling approach (4), a static trial is used to define participant-specific joint centers, which are then used to define segments, joint axes, and segmental coordinate systems. The location of participant-specific joint centers are stored virtually and relative to external kinematic markers placed over the skin of the participant. During dynamic time-varying trials, participant-specific joint centers are derived directly from these external skin-mounted kinematic markers, and joint kinematics are calculated. With the DK modeling approach, segments are linked implicitly by anatomical constraints and can move freely about three rotational and three translational degrees of freedom (DoF), which prevents the propagation of errors from one segment to another. The primary limitation of the DK modeling approach is that soft tissue artifact is inherently present in the external skin mounted kinematic marker data (3), which can cause errors in joint center identification and, in turn, estimates in participant-specific kinematic estimates. During dynamic movements characterized by high accelerations like side cutting, the influence of soft tissue artifact is apparent, likely influencing the accuracy and/or reliability of joint kinematic and kinetic estimates.

The IK modeling approach also uses a static trial to define a rigid skeletal model’s segment lengths and joint axes; however, assumptions about the skeletal model’s available DoF are chosen a priori (9). Unlike the DK modeling approach, which calculates joint centers and kinematics directly from external skin-mounted markers, the joint coordinates (kinematics) of the rigid skeletal model are optimally adjusted to “best fit” the kinematic marker data. This is thought to minimize the effect of soft tissue artifact (23). In the lower limbs, and the knee specifically, rotational DoF are generally chosen a priori to suit specific research questions (e.g., 3 DoF [14] and 1 DoF [16]), although it is not known to what extent constraining knee translations might influence knee joint kinematics and kinetic estimates, which could subsequently affect the clinical interpretation of these data such as the classification of an athlete’s risk of ACL injury in sport (4,18,32).

Both DK and IK modeling approaches have been used to investigate the mechanisms of noncontact ACL injury during side cutting (e.g., DK = 39, 10, 34, 13; IK = 29, 27, 28, 20, 14). These studies all quantify knee kinematics and kinetics in the context of ACL injury risk, yet it is not known to what extent the choice of modeling approach influences the clinical interpretation of this data or whether the choice of modeling approach affects the classification of an individual’s ACL injury risk. Recently, attempts have been made to standardize side-cutting methodology, specifically knee axis definition (36), data filtering (22), and approach speed (39) to improve the utility of side cutting for the assessment of ACL injury risk.

The purpose of this study was to determine whether using a DK or an IK modeling approach influenced the estimation of knee joint kinematics, kinetics, and ACL injury risk classification during unanticipated side cutting. If the modeling approach affects an athlete’s ACL injury risk classification, then it becomes an important methodological decision for screening protocols interested in identifying “at risk” athletes.

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The participants used in this investigation were a subset of the sample of Donnelly et al. (13). Thirty-four male amateur Australian rules footballers (mean age = 21.2 ± 3.1 yr, height = 1.84 ± 0.09 m, mass = 82.1 ± 10.4 kg) free from self-reported joint disorders or previous orthopedic surgery provided their written informed consent to perform side cutting while biomechanical data were collected. The experimental procedures performed were approved by the University of Western Australia’s Human Research Ethics Committee.

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Participants performed a variety of dynamic tasks similar to those during which the occurrence of ACL injuries have been reported (21). These included anticipated and unanticipated straight running, crossover-cutting, and side-cutting maneuvers with their preferred stance limb (13). For this study, three unanticipated side-cutting maneuvers per participant were analyzed. The unanticipated cue was provided by an arrow which was displayed on a computer screen when participants triggered a set of timing gates placed 1.5 m from the force platform. The arrow pointed either left, right, or upward, which indicated the direction in which the participant should travel and inherently the task they should perform, for example, a left pointing arrow would require a right legged side cut and a right pointing arrow a right legged crossover cut if the preferred leg was the right, a preferred left leg would make the tasks opposite. For a trial to be successful, participants were required to follow a black line on the floor at 45° to the initial direction of travel and to have an average (approach) velocity between 4.5 and 5.5 m·s−1 as calculated from the anterior superior iliac spine marker. A minimum of 60 s rest was given between each trial. Each participant’s side-cutting trials were captured at 250 Hz using retroreflective markers (Vicon MX, Vicon Peak, Oxford Metrics, UK) with simultaneous recording of ground reaction force (GRF) data at 2000 Hz (Advanced Mechanical Technology, Watertown, MA). Static calibration and functional knee and hip joint trials were recorded separately.

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Model creation

For the DK modeling approach, a six DoF model was adapted for the current data set from the UWA model previously described by Dempsey et al. (10) using Visual3D (v.4.83; C-motion, Germantown, MD). The model was composed of eight segments, including the trunk, pelvis, thighs, shanks, and feet. Segments were created based on cadaver segmental data (11) and represented as geometric volumes (17). Segmental coordinate systems were described according to the UWA model with functional methods used to calculate subject-specific hip joint centers and knee joint axes and a calibration rig to define the anatomical frame of the foot (5). The length, mass, and inertial properties of each segment were scaled to each subject’s total body mass and joint center positions using Visual3D. The local coordinate systems of the trunk, pelvis, thigh, shank, and foot were obtained from a static trial.

The IK modeling approach used the same segment definitions and anthropometry as the DK method, except translational joint constraints were applied to the hip, knee, and ankle joints. The pelvis was assigned six DoF relative to the global coordinate system, and the trunk segment was given three rotational DoF relative to the pelvis, which in total allowed the model 18 DoF. The pose at each frame was calculated with the default setting within Visual3D, which performs a weighted least-squares global optimization using a Levenberg–Marquardt algorithm. The thorax, pelvis, and foot were given a weight factor of 4, whereas the shank was given a weight factor of 3 and the thigh a weight factor of 2.

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Data reduction and analysis

Following recent recommendations (39), the variables whole-body center of mass velocity at touchdown and toe-off, approach angle, exit angle, and stance time were calculated. The two horizontal components of the whole-body center of mass velocity vector were used to calculate the magnitude of the whole-body center of mass velocity at touchdown and toe-off. The same velocity components were also used to calculate the angulation of the vector at touchdown (approach angle) and toe-off (exit angle). These variables together are used to describe the execution of the unanticipated side-cutting tasks (Table 1).



The kinematic and GRF data were both low-pass filtered at 18 Hz using a fourth-order Butterworth filter (22). Touchdown and take-off events were created when the vertical GRF rose above and fell less than 20 N, respectively. The weight acceptance phase was defined as from touchdown to the first trough after the passive peak in the vertical GRF (10). Joint angles and moments were calculated in Visual3D for the entire stance phase using inverse dynamics. External moments, that is, moments due to the environment acting against musculoskeletal structures, are reported throughout. All kinetic data were normalized to body mass. The following discrete variables were calculated during the weight acceptance phase of stance as they have been shown to be associated with ACL injury risk (12): knee flexion range of motion, mean flexion, internal rotation range of motion, mean rotation angle, peak flexion moment, peak knee abduction moment, and peak internal rotation moment. Knee flexion angle at the instance of touchdown was also calculated. A root mean square difference (RMSD) was calculated over the whole stance phase for the knee angles and moments to estimate the similarity of the curves (30).

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Statistical analysis

Statistical analyses of discrete variables were compared using two-tailed paired t-tests (α = 0.05) in SPSS (SPSS v.20; SPSS Inc., Chicago, IL). The open-source one-dimensional statistical parametric mapping package (SPM1D [33]) was used to compare the mean angle and moment waveforms in Python (Python 2.7.2; Enthought Python Distribution, Austin, TX). The scalar test statistic SPM {t} was computed at each point in the time series, forming a statistical parametric map. Alpha was set at 0.0083, which was α = 0.05 corrected for six comparisons. The temporal smoothness based on the average temporal gradient was then estimated using random field theory (33). Significance was achieved when the value of the test statistic exceeded the threshold above which only 0.83% of the data would be expected to reach had the test statistic trajectory resulted from an equally smooth random process. The probability values were then calculated for specific suprathreshold regions that could have resulted from an equally smooth random process.

To determine whether the modeling approach (IK vs DK) affected the clinical classification of an athlete’s ACL injury risk, a Spearman’s ρ was calculated for the peak knee moments during weight acceptance (22). The peak frontal plane knee moments in the IK model were positively skewed, so these data were square-root-transformed to meet the assumption of normality. An injury risk threshold was calculated based on injury rate data from Finch et al. (15), who found that from a sample of 321 Australian Rules football players, 5.5% experienced ligament injury. Assuming that their sample adequately represented the population, the threshold on the normal distribution curve below which 94.5% of the population fell was the mean +1.6 SD. Any participants above this threshold we subsequently refer to as “at risk.”

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The discrete variables knee flexion angle at touchdown, mean flexion, mean rotation, and internal rotation range of motion during weight acceptance were all significantly different between models (P < 0.01, Table 2). The peak flexion and abduction moments during weight acceptance were significantly (P < 0.01) greater when calculated using the DK modeling approach.



The mean knee angle curves showed <5° RMSD in the sagittal plane and <8° RMSD in the transverse plane (Figs. 1A and 1C). The greatest RMSD was in the frontal plane (10.86° ± 3.40°); the mean IK curve stayed in adduction throughout stance whereas the DK method was in abduction (Fig. 1B).



The SPM1D analysis of the angle data found significant differences in all three planes (Figs. 1D–1F). The IK modeling approach showed significantly more knee flexion from 0% to 75% (P < 0.001) of the stance phase. The frontal plane angle curves were completely dissimilar throughout the stance phase (P < 0.001) with the DK approach in abduction and the IK approach in adduction. In the transverse plane, the DK modeling approach showed significantly more internal rotation than the IK modeling approach at 7%–38% (P < 0.001) and 44%–63% (P = 0.002) and significantly more external rotation at 95%–100% of the stance phase (P = 0.004).

Both the sagittal and the transverse plane mean knee moment curves showed minor differences between the two models with RMSD values of 0.24 ± 0.08 N·m·kg−1 and 0.11 ± 0.04 N·m·kg−1, respectively (Figs. 2A and 2C). The frontal plane mean knee moment curves were more varied; an RMSD of 0.67 ± 0.18 N·m·kg−1 reflected a difference in magnitude during weight acceptance and also the transition into an external adduction moment in the IK model versus the maintenance of an external abduction moment in the DK model (Fig. 2B).



The SPM1D analysis of the moment data also found significant differences in all three planes (Figs. 2D–2F). In the sagittal plane, there were significant differences at five separate instances in the stance phase (8%–15%, 23%–33%, 55%–68%, 78%–89%, and 95%–100%, all P < 0.001), although the differences in moment magnitude were small. In the frontal plane, the DK abduction moment was significantly (P < 0.001) greater from 10% to 87% of the stance phase (Fig. 2E) and significantly smaller than the IK abduction moment at 0%–5% (P = 0.001). In the transverse plane, there was a significantly greater external rotation moment at 1%–7% and 30%–50% of the stance phase (both P < 0.001) in the DK versus IK modeling approach.

Spearman’s rank correlation for the peak knee moments (Fig. 3) showed a good to strong correlation between the two models in all planes (ρ = 0.842–0.903). Both models classified the same subjects as “at risk” in the frontal and transverse plane (based on [15]), but in the sagittal plane, two subjects were on the borderline of being deemed “at risk” by the IK model but not by the DK model.



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The purpose of this study was to determine whether using a DK or an IK modeling approach influenced the estimation of knee joint kinematics, kinetics, and ACL injury risk classification during unanticipated side cutting. Although the analysis of discrete and continuous kinematic and kinetic variables showed statistical differences between modeling approaches, classification of an athlete’s ACL injury risk was unaffected.

As the same experimental marker data and model anthropometry were used to estimate knee kinematics and kinetics data during both modeling approaches, the observed differences are likely associated with the modeling principles. Specifically, in the DK modeling approach, the influence of soft tissue artifact on joint center estimates and segment definitions, and in the IK modeling approach, a priori restrictions imposed on joint translations. Although significant differences were found for all angles and moments, the frontal plane knee angle and moment estimates were most sensitive to the modeling approach used and likely the most meaningful results. Frontal plane knee moments are deemed important biomechanical variables for understanding the mechanisms of ACL injury (knee abduction moment [19]) and/or knee osteoarthritis development and progression (knee adduction moments in varus-aligned patients [1]). The difference of 0.52 N·m·kg−1 in the peak knee abduction moment is perhaps of most concern as this variable is used for ACL injury risk classification (4,18,32).

The difference in frontal plane knee moments observed between modeling approaches is likely a downstream effect resulting from differences in frontal plane knee kinematics, which differed by up to 15° throughout stance. Results showed that during stance, the DK model was biased toward abduction and the IK model was biased toward adduction. Using simplified mechanical principles, a large knee abduction angle during the weight acceptance phase of unanticipated side cutting would increase the perpendicular distance between the knee joint center and the GRF vector passing laterally to it. The result would be an elevated peak knee abduction moment. The opposite would be true if the perpendicular distance between the knee joint center and the GRF vector were reduced (27). This may in part explain why the DK kinematic modeling approach produced larger peak abduction knee moments (0.52 N·m·kg−1) than the IK modeling approach, as an abducted knee angle would position the knee joint more medially relative to the GRF during unanticipated sidestepping.

Previous research has shown that frontal and transverse plane knee joint kinematics are less reliable measures when compared with sagittal plane kinematics (8,25,35). The present study revealed a large amount of between-subject variability in both the frontal and transverse knee kinematics (Figs. 1B and 1C). Moreover, the two modeling approaches described completely inverse estimates of frontal plane joint angles (DK, abduction; IK, adduction) during weight acceptance and throughout the stance phase. The existing literature shows little consensus on frontal plane knee motion. Some studies that used a DK modeling approach showed comparable results to our DK frontal plane angle (34,37), but another’s results more closely resembled our IK angle (38). The comparison with IK studies was also inconsistent as one study’s results resembled our IK frontal plane angle (20), yet another’s results more closely matched our DK angle (30). This variability between studies seems to reflect poorly on the accuracy and meaningfulness of this measurement. We show that modeling approach is one likely cause of frontal plane angle discrepancies, yet other factors such as soft tissue artifact, knee axis definition (36), and marker misplacement are also likely to contribute. Until the validity of using skin mounted markers to measure the frontal plane knee angle is established, this variable should be interpreted with caution.

As the DK and IK modeling approaches estimated inverse frontal plane knee angles, it is prudent to consider which approach might best represent the true underlying bony motion. Unfortunately, no “gold standard” measures of bone motion such as those using bone pins (e.g., 6,35) have specifically examined side cutting. However, an alternative study (31) used biplanar videoradiography, arguably a suitable gold standard, to examine a jump-cut maneuver which, like a side cut, is designed to induce ACL loading. Miranda et al. (31) compared knee kinematics from a DK modeling approach to bone kinematics estimated from biplanar videoradiography and CT scans. Their DK data showed a similar knee abduction profile to ours, except for ∼5° offset toward neutral. Their bone kinematics showed ∼5° adduction during stance, similar to our IK results. As the IK method matched the bone movement most closely, and with earlier comments in mind, one could speculate that the DK method may calculate larger mean peak abduction moments during the weight acceptance phase of an unanticipated side cut compared with the IK modeling approach.

Research has shown that the frontal plane range of motion of the knee is approximately ±5° (2). Restricting a model’s frontal plane knee motion to ±5° and therefore closer to the likely anatomical range might increase confidence in frontal plane knee kinematics. Unfortunately, such limits could not be set in Visual3D (software that can includes OpenSim [9]). To consider the effect of applying a frontal plane rotational constraint, knee joint angles and moments were recalculated using a 2DoF IK knee model restricted to zero frontal plane motion, instead of 3DoF. The magnitude of knee loading in all planes closely followed the 3DoF IK modeling approach (see Figure, Supplementary Digital Content 1,, 2 DoF IK model results). These results would suggest that there is perhaps some merit in recommending an IK modeling approach using either a 3DoF knee with a limited range of motion or even a 2DoF knee, neither of which are an option with a DK model, so that confidence in the kinematics and kinetics calculated during side cutting can be increased.

Although arguments can be made for the IK method on the basis of allowed joint motion, the strong correlations between the DK and the IK modeling approaches would suggest that injury risk classification is not affected. The peak knee abduction moment, the strongest predictor of ACL injury risk (18), had two participants identified as “at risk” by both modeling approaches. The borderline cases identified in the sagittal plane moment by the IK modeling approach are of lesser concern as this variable is unlikely to cause an ACL injury during side cutting (26). As the correlations between the IK and the DK modeling approach estimates of peak flexion, abduction and internal rotation moments were strong (ρ = 0.842–0.903), the specific location of the injury risk threshold is unlikely to affect the classification of “at risk” athletes between modeling approaches. The observed differences in magnitude of the frontal plane kinematics and kinetics between modeling approaches, however, indicate that caution should be used if attempting to compare data between studies. Moreover, other relevant differences including ∼5° differences in the sagittal and transverse plane angles can impose significant elongation of the ACL (40), or be a greater kinematic difference than was induced by fatigue (37), respectively.

This study has several limitations; for instance, it remained focused on the knee without considering the ankle and hip joints, which are also known to be sensitive to modeling approach (7) and influence knee joint loading (27,29). The results of this study are side-cutting specific, and so the transferability to other dynamic tasks such as drop vertical jumping, which has also received considerable investigation in relation to ACL injury risk, is unknown. In addition, many studies have examined the reliability of the DK (for a review during gait, see [25]), but not the IK modeling approach. To use the IK modeling approach for clinically relevant research, the inter- and intrasubject reliability of this method as well as the sensitivity of the IK method to alternative joint constraints and segment weightings should be investigated. Finally, because of a lack of ACL-specific data, the selected injury threshold applied to ligament injuries in general and not ACL injury per se. An ACL injury threshold would have resulted in a threshold further away from the mean moving some of those identified as “at risk” toward lesser risk.

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The DK and the IK modeling approaches showed significant kinematic and kinetic differences during the weight acceptance phase of unanticipated side cutting, which were most prominent in the frontal plane. This has important consequences for the investigation of ACL injury mechanisms and in the comparison of frontal plane kinematics and kinetics measures between laboratories using different modeling approaches. Despite differences in kinematic and kinetic estimates between the DK and the IK modeling approaches, their estimates of peak knee moments were still strongly correlated, providing the same injury risk classification.

Dr. Cyril J. Donnelly thanks the Australian National Health and Medical Research Council (grant no. 400937 to Prof. C. Finch, Prof. D. Lloyd, and Prof. B. Elliott) and the Western Australian Medical Health and Research Infrastructure Fund (Prof. D. Lloyd) for funding and providing data for this investigation. Jessica Tsao would like to acknowledge the US–UK Fulbright Commission for funding her studies.

The authors declare no conflict of interest.

The results of the present study do not constitute endorsement by the American College of Sports Medicine.

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© 2014 American College of Sports Medicine