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Differences in Cutting Knee Mechanics Based on Principal Components Analysis


Medicine & Science in Sports & Exercise: April 2009 - Volume 41 - Issue 4 - p 867-878
doi: 10.1249/MSS.0b013e31818f8743
Applied Sciences

Purpose: The increased number of women participating in sports has led to a higher knee injury rate in women compared with men. Analysis of injury risk is limited to identification of discrete-dependent variables, but analysis of the entire waveform using principal components analysis (PCA) may provide greater insight. The purpose of this study was to examine gender differences in cutting knee mechanics using PCA and to compare these findings to those based on traditional discrete measures.

Methods: Sixteen male and 17 female recreational athletes were recruited to perform unanticipated run and cutting tasks. Three-dimensional joint dynamics were recorded, and discrete variables were extracted. PCA analyses were also performed on the angle and moment waveforms in all three planes. The PCA used an eigenvalue analysis on the data covariance matrix. Gender differences in the principal component (PC) scores generated by the PCA were assessed using a MANOVA (P < 0.05).

Results: On the basis of the discrete variables, flexion range of motion for females was less than for males. From the PCA analysis, females were less internally rotated during late stance and exhibited a relatively greater peak adduction moment that was not apparent in the original time series. This peak moment correlated with a greater abduction oscillation during early stance. There was also less variability for females in the sagittal and frontal plane moment PC.

Conclusions: The PCA analysis did not significantly detect the decreased flexion, but PCA did reveal gender differences in movement patterns and variability that were not apparent in the discrete variables. The results of this study demonstrate the potential of PCA to provide deeper understand of movement dynamics that may help in detecting injury risk factors.

Neuromechanics Laboratory, Department of Human Movement Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI

Address for correspondence: Kristian M. O'Connor, Ph.D., Department of Human Movement Sciences, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI 53201l; E-mail:

Submitted for publication August 2007.

Accepted for publication September 2008.

Over the past 30 yr, there has been a great increase in the number of female athletes in many team sports such as basketball, volleyball, and soccer (1). Parallel to this phenomenon, there has been an increase in the number of injuries, particularly to the anterior cruciate ligament (ACL) for female athletes. These injuries occur at a rate between two and seven times greater for females than for males (7). ACL injuries have been found to be very common in noncontact situations (4) and occur in sports with changes in direction (cutting maneuvers), landing, and rapid stops. Boden et al. (4) reported that the deceleration phase during a cutting maneuver was one of the most common maneuvers linked to ACL injury (38 of 71 injuries).

In some cases, performing these activities appears to place the knee in positions that increase the risk of ACL rupture (14). In vitro studies showed that the strain in the ACL is positively correlated with knee abduction and extension (18,20). In the sagittal plane, additional ACL strain may have been caused by the augmented patellar tendon angle, which consequently increases the anterior shear force (18). Appropriate neuromuscular control is required to avoid extreme joint positions, and female athletes tend to display joint mechanics during cutting that may increase the risk of injury (27,33). In particular, some of these studies have reported that females flex less (25), abduct more (23), and experience a greater peak internal adduction moment at the knee as compared with males (22). These gender differences are also consistent with the findings of Hewett et al. (14) who reported that subsequently injured females athletes exhibited less flexion and greater abduction during a two-leg drop jump (14). Increased ACL loading has also been observed when internal rotation forces are applied to the tibia (18,20), and excessive rotation has been identified as commonly occurring during noncontact ACL injuries (4).

Although studies of cutting mechanics have reached consensus on the importance of frontal plane dynamics, the role of sagittal and transverse plane mechanics remains unclear. For instance, some studies have reported less knee flexion for females (19,25) whereas others have not (10,24,27). Aside from inherent limitations in estimating bone movement from surface markers (especially in the transverse plane) (17), the inconsistencies may be in part due to differences in a priori assumptions these studies made regarding dependent variables. Although some authors have reported peak values from the entire stance phase (23,24), others have focused on early stance (2,5). Arguments can be made in support of either approach based on previous work. For example, the ACL is under greatest tension when the knee is flexed less than 40° (20,27), and the rate of loading is greatest during early stance. On the other hand, reporting the overall peak moment (which occurs generally at midstance) could be important because it represents the period of likely greatest joint loading. Additionally, there may not be a logical peak value for a joint angle or moment during early stance, leading to different data reduction approaches, including average values across the phase (3) or reporting values at a specific temporal event (5). These differences in data reporting may be one of the reasons why inconsistent conclusions have been reached, particularly regarding gender differences. It should also be noted that differences in testing protocol and subjects demographics may also be part of these inconsistencies. An analysis technique that can remove the challenges of a priori identification of dependent variables may provide a broader understanding of differences in movement dynamics between males and females.

Principal components analysis (PCA) provides a means to accomplish this goal. PCA is a multivariate analysis technique that extracts orthogonal common sources of variation in a data set (15) and assumes that a data set can be reduced to a few common modes of variation (29). Landry et al. (16) recently analyzed lower extremity mechanics during unanticipated cutting using PCA. They reported gender differences in frontal plane knee moments with this technique, with the males exhibiting a greater peak abduction moment during early stance. Although demonstrating that the PCA technique was sensitive enough to detect gender differences, Landry et al. (16) did not explore how the PCA analysis related to traditional discrete measures. From this same research group, Wrigley et al. (36) demonstrated that a PCA approach could discriminate low-back injury risk whereas a discrete parameter-based approach could not. A strength of the PCA analysis technique is that it allows for a more holistic approach to assessing a movement pattern and may have great potential to be a powerful discriminator for athletic injury risk.

Most research to date has focused on identifying possible injury risk factors through assessment of mean data with the assumption that discrete values are clinically important (e.g., peak adduction moment). Another approach has been to look at injury risk through the prism of movement variability. Greater variability can be viewed as increasing the risk of injury because trial-to-trial dynamics may be more likely to approach the threshold for injury (24). McLean et al. (24) reported greater transverse plane variability in females compared with males, which may support this view. In a more recent article, McLean et al. (25) replicated this result for internal rotation and also reported greater frontal plane knee intertrial variability for females. Alternatively, some have argued that greater variability may be a healthy trait (12,13). For running overuse injuries, it has been proposed that low stride-to-stride coordination variability increases injury risk (12,13). A similar approach has been applied to the traumatic injury model, where it is hypothesized that greater intertrial variability represents more robust neuromuscular control that allows an individual to safely adapt to unanticipated events, such as landing on an uneven surface (28). In support of this theory, Pollard et al. (28) reported that females exhibited decreased variability in coupling patterns of the lower extremity during an unanticipated cut as compared with males. These divergent conclusions were reached with different analysis techniques (discrete joint variables vs interlimb coupling), but one potentially important difference between these studies is the use of an unanticipated cutting maneuver by Pollard et al. (28). Unanticipated cutting has been suggested as a model that may approximate the neuromuscular response of an athlete responding to a game stimulus (2). However, this assumption has yet to be validated. The average mechanics of an unanticipated cutting maneuver have been shown to differ from an anticipated cut (2), and perhaps movement variability is equally affected. Pollard et al. (28) examined the variability of joint coupling for this task and reported decreased variability in selected couplings for females. PCA also has great potential to address this question because the technique is designed to extract common modes of variability from a data set and can partition variability into random and deterministic components (6).

It has been established that during sidestep cutting, the knee experiences a valgus load and torsion and that these motions put the joint in a risky position for ligament injuries. Traditional parameter-based approaches to quantifying gender differences in lower extremity mechanics are subject to the restrictions of a priori establishment of perceived relevant variables. A multivariate approach through PCA has potential to elucidate differences not detected with parameter-based analyses. PCA may provide a unique perspective into the role of intertrial variability during a cutting maneuver. Further, examination of movement variability as a risk factor for injury generally cannot separate random from structured sources of variation. PCA has the potential to advance our knowledge of injury risk factors by identifying differences in cutting mechanics across the entire stance phase, and it also provides a powerful tool to examine movement variability. Therefore, the purposes of this study were to quantify gender differences in cutting knee mechanics using PCA, to compare these results to traditional measures, and to examine joint dynamics variability using both approaches.

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Sixteen recreationally active males (22.7 ± 2.7 yr, 86.1 ± 13.5 kg, 1.81 ± 0.08 m) and 17 recreationally active females (20.9 ± 1.5 yr, 62.9 ± 5.9 kg, 1.68 ± 0.06 m) volunteered to participate in this study. A power analysis was based on pilot data to detect a 2° kinematic difference in the frontal plane with an alpha of 0.05% and 80% power. Withrow et al. (34) associated ∼2° of increased valgus motion with increased ACL strain. Thirty total subjects were sufficient to detect this difference, although additional subjects were collected to assure adequate sample size if technical difficulties were detected during postprocessing (e.g., marker plate movement). A background questionnaire was used to screen for health status, and an informed consent form were read and signed by all volunteers before the beginning of the study. The protocol was approved by the university institutional review board. Volunteers were accepted in the study if they had not suffered an ACL injury and had been free of any other injury within the previous 6 months that could interfere with normal movements. Subjects were also asked how many years they had competed (if any) in competitive team sports. Males participated 11.4 ± 3.4 yr, and females participated 6.4 ± 4.0 yr.

Participants wore standard laboratory footwear (Saucony Jazz). Trajectories of light-reflecting markers were collected at 200 Hz with a seven-camera Motion Analysis Eagle System (Santa Rosa, CA). Synchronously, ground reaction forces were collected at 1000 Hz with an AMTI OR6-5 force plate (Watertown, MA). Running speed was monitored through two gates 2.5-m apart positioned along the runway just before the athlete reached the force plate.

There were two sessions for this study. During the first session, subjects practiced the required tasks until they could comfortably complete the 45° unanticipated cutting maneuver. All cuts were performed on the subject's dominant leg, which was determined from the subject's preferred jumping leg. The approach speed of the subjects was controlled to be 4.5-5.0 m·s−1, and subjects were presented with a visual stimulus to continue running straight ahead, stop quickly, or side cut 45°. The chosen speed was similar to that of McLean et al. (23) (4.5-5.5 m·s−1) but was more constrained to avoid introduction of excessive trial to trial variability associated with speed. The visual stimulus was triggered by the first timing gate that was ∼3m before reaching the force plate. Subjects were instructed to run straight ahead and to react to the visual stimulus when presented. If presented with a cutting stimulus, subjects were instructed to cut to the side after a 1-m-wide path oriented at 45° to the line of progression. The timing of presentation was adjusted by the experimenter during practice trials to minimize the time available to react while allowing the subject enough time to successfully perform the task. This led to a challenging task where generally ∼25-30 trials were completed to capture the 15 successful trials.

The testing session was scheduled within 1 wk of the practice session. After a 5-min jogging warm-up, 24 skin markers were placed on the participants. Markers used exclusively for the standing calibration trial (calibration markers) included the left and right iliac crests and greater trochanters and stance leg lateral and medial femoral epicondyles, lateral and medial malleoli, and first and fifth metatarsal heads. Additional tracking markers were placed on the left and right anterosuperior iliac spines, the sacrum, the two four-marker plates attached to elastic Velcro straps on the thigh and shank segments, and a marker triad secured on the heel counter of the shoe. A 2-s standing calibration trial was recorded. Calibration markers were removed after standing calibration trial completion. Each participant then completed five cutting trials. To capture these trials, subjects completed a total of 15 successful trials where there were also five each of running and stopping commands randomly interspersed with the cutting commands. These trials were considered valid only if the stance foot was entirely on the force plate and if the subject stayed within a 1-m wide path after the cut (defined by the width of the running platform).

Data reduction was implemented with Visual3D (v3.89; C-Motion, Inc., Rockville, MD). The raw three-dimensional coordinate data of all markers were filtered using a fourth-order, zero lag, recursive Butterworth filter with a cutoff frequency of 12 Hz. This was consistent with the 10- to 15-Hz range that has been used by previous studies for analyzing cutting maneuvers (3). Right-handed Cartesian local coordinate systems for the pelvis, thigh, shank, and foot segments of the support leg were defined to describe position and orientation of each segment. Three-dimensional Cardan knee angles were calculated using a joint coordinate system approach (11). Joint centers were given by the midpoint between the medial and the lateral calibration markers for the knee and the ankle joints. The hip joint center was estimated as 25% of the distance from the ipsolateral to the contralateral greater trochanter (30). Body segment parameters were estimated from Dempster (9), and joint kinetics were calculated using a Newton-Euler approach. Joint moments were reported in the distal segment coordinate system and were normalized by subject height multiplied by body mass. The beginning and the end of the support phase of cutting were determined by the instant when the vertical GRF exceeded and fell below 20 N, respectively. Processed data were time normalized to 101 data points, and all joint angles were reported relative to the static standing position. Discrete measures extracted as dependent variables included the knee touchdown angle (TD), the range of motion (ROM), and the peak moment. The sagittal, the frontal, and the transverse ROM measures represent flexion, abduction, and internal rotation from TD to peak. The peak internal net joint moments represent extension, adduction, and internal rotation.

PCA was used to identify dominant modes of variation within the three-dimensional knee angle and moment waveforms. The PCA approach used for this study was based on the methods of Wrigley et al. (36). Matrices for each of the six moment and angle waveforms were created, where the trials populated n rows and the time-normalized 101 data points populated p columns in an

matrix. Out of a possible 165 trials (33 subjects × 5 trials), n = 153 trials were used for analysis yielding six X 153×101 matrices. Twelve trials were discarded due to technical difficulties. PCA was performed through an eigenvalue analysis of the covariance matrix S 101×101, which yielded the eigenvectors (U 101×101) and eigenvalues (L 1×101) (15). The eigenvector matrix U 101×101 contains the coefficients for each of the 101 principal components (PC) that were extracted, and the eigenvalue matrix L 1×101 contains the relative contribution of each PC to the total variation. The PC scores (Z 153×101) for each of the 153 individual time series were calculated by multiplying each individual trial's variation about the overall mean with the transpose of the eigenvector matrix (equation 1), where

is the mean waveform of all 153 trials.

A SCREE analysis was performed that retained only those PC that contributed modes of variation greater than an equivalently sized input matrix of randomly generated numbers (15,36). To assess how well the retained PC represented the original input data, the Q-statistic was calculated, which is the sum of squares of the residuals between the individual trial and the reconstructed curve based on the retained PC. A Q-critical value () was calculated based on an alpha level of 0.05 and a t-distribution (15). Reconstructed trials with a Q-statistic lower than indicated that the original data were adequately represented.

PCA also provided a unique way to investigate movement variability. First, correlations (rji) were calculated between the ith PC and the jth time sample, where sj is the SD at a given time in the input time series,

rji2 provides the percent variance explained across time for a given PC. Summing the variance explained across time provides the ability to separate the overall variation in the data into random and deterministic components. The variance not explained by the retained PC represents random contributions such as those due to random measurement error or random biological sources. Additionally, by including all 153 trials in the PCA, a measure of within-subject variability can be obtained by calculating the SD of the five trial (or in some cases four) scores for each subject. All calculations were performed with Matlab (v6.5, Mathworks, Inc.).

To assess whether the overall cutting task demands were similar for each gender, the stance time and the peak ground reaction forces were compared using independent t-tests. The discrete variables (TD angle, ROM, and peak moment) were also assessed between genders with independent t-tests. These were performed for each variable on the subjects' five-trial means and the intertrial SD. To assess gender differences for the PC, a one-way between-groups multivariate analysis of variance was performed on each waveform for both mean and intertrial variability. A MANOVA was performed for each of the six angle and moment time series. These six MANOVA were performed on the five-trial mean PC scores and also on the intertrial SD, for a total of 12 MANOVA analyses. Gender was the independent variable. The mean (SD) scores of each gender for the retained PC served as the dependent variables. The assumption of equality of variances was assessed with Box's test of equality of covariance matrices, and equality of error variances for significant effects were assessed with Levene's test of equality of error variances. If these assumptions were met, significant effects were analyzed with Bonferroni-adjusted pairwise comparisons. Significance for all tests was set at P < 0.05, and all statistical analyses were performed using SPSS (v13.0, SPSS, Inc.). Effect sizes for independent t-tests (d) and for MANOVA (η p 2) were reported.

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Discrete variables

There were no differences in stance times or peak ground reaction forces between genders. The mean (SD) stance times were 265 (50) and 230 (25) ms for males and females, respectively. The peak ground reaction forces were 1.36 (0.28) and 1.19 (0.32) body weight (BW) in the anterior-posterior direction (braking force), 1.03 (0.50) and 0.97 (0.35) BW in the mediolateral direction, and 3.34 (0.72) and 3.30 (0.73) BW in the vertical direction for males and females. Group mean time series for angles and moments in each plane are presented (Fig. 1). The mean TD angles, the ranges of motion, and the peak moments listed in Table 1 have been previously reported (26). Only the mean sagittal plane ROM was significantly different between genders, where the males experienced greater knee flexion than females. There were no differences between genders for the intertrial variability for any of these variables (Table 1).





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Four to seven PC were retained based on the SCREE analysis for the six waveforms (Table 2). Between 85% and 100% of the total variance was explained by the retained PC. Waveforms were reconstructed using the scores and coefficients of the retained PC for each of the joint variables, and the first three PC are presented for each waveform (Figs. 2 and 3). Each PC panel contains the combined group mean curve of the original data (thin line), and the +/− curves represent the effect of 1 SD of the between-subjects z-score variability (genders combined). This representation is similar to that proposed by Ramsay and Silverman (29) and used by Ryan et al. (31), who portrayed the effect of a PC about the mean curve by adding and subtracting a multiple of the PC coefficients. Additionally, these panels contain the mean male and female PC effects for that PC. When compared with Q-critical (, α = 0.05), Q-statistics revealed that 94%-95% of the original 153 kinematic waveforms were adequately described by the reconstructed waveforms (Table 2). For the kinetic data, 94% of the sagittal plane individual waveforms were adequately reconstructed, but only 45% of the frontal plane and none of the transverse plane waveforms were adequately described by the retained PC. The inability to adequately reconstruct any of the transverse plane kinetic waveforms suggests that individual trials are highly sensitive to random trial-to-trial variation contained in the 15% of variance not explained by the retained PC. Similarly, the low success in reconstructing the frontal plane waveforms is related to the 9% of variance unexplained by the retained PC. Of the six waveforms, these two had the lowest percentage of variance explained and reflects greater random variation of the individual waveforms.







Examination of the first three PC of each variable demonstrates the primary modes of variation extracted. Kinematic results are presented in Figure 2. Assigning qualitative meaning to the PC was accomplished through visual inspection of the results (Figs. 2 and 3). These descriptions reflect the patterns observed in the +/− curves of each plane, combined with the variance explained represented in the bottom rows of Figures 2 and 3. The +/− curves can be used to understand the functional meaning of a particular PC. As noted by Wrigley et al. (36), PC generally explain one of three different sources of variance: differences in overall amplitude, differences in relative amplitudes with the waveform (e.g., relative magnitudes of two peaks), or differences in timing. For the sagittal plane knee angle, the first principal component (PC1) identified the greatest source of variation from 35% to end of stance and characterized differences in peak knee flexion during stance. PC2 primarily extracted difference in the rate of knee flexion between 10% and 50% of stance. PC3 primarily identified variation in contact angle (<10% stance). The temporal differences and magnitudes of the relative contributions of each PC can be observed in the bottom panel of Figure 2. The first three PC each explained variation at progressively earlier phases of stance. For the frontal plane, PC1 described an overall offset of the kinematic patterns from the mean, whereas PC2 captured variation in the first of the two minimum angles that occurred during early (<25%) stance. PC3 described the relative dominance of the first and the second peaks. In the transverse plane, PC1 describes the offset from the mean. PC2 explains variation in the TD and the timing to peak internal rotation. PC3 describes the timing of the initiation of knee external rotation during late stance and the final position at takeoff.

Kinetic variables are presented in Figure 3. In the sagittal plane, PC1 described variation in the peak moment at midstance, whereas PC2 described the timing of the peak and the rate of increase and PC3 described the relative magnitude of the moment at midstance versus the end of stance. In the frontal plane, PC1 primarily described variation about the mean during mid to late stance, whereas PC2 described variation in the peak adduction moment that occurred during early (<25%) stance. PC3 in the frontal plane explained variation shortly after heel strike and characterizes variation in the rate of increase in the adduction moment. In the transverse plane, PC1 described variation in the moment during mid to late stance, whereas PC2 described shifts from a dominant first peak to a dominant second peak internal rotation moment. PC3 extracted variation of a peak internal rotation moment occurring during early stance.

None of the MANOVA analyses violated the assumption of equal covariance matrices. For the six MANOVA examining mean scores for the waveforms between genders, only the transverse plane angle and the frontal plane moment reported a significant gender effect (Table 3). Levene's tests indicated no violations of variance equality assumptions; therefore, comparisons of the individual PC for the transverse angle and the frontal moment were performed with an independent t-test for each retained PC (Table 4). For the transverse angle, the practical meaning of the difference in scores is highlighted in Figure 2. The significant gender difference for PC3 reflects difference at takeoff, with the males more internally rotated. For the frontal moment, PC2 and PC3 differed between genders. PC2 indicates that females exhibited a greater peak adduction moment than the males when viewed in isolation from other sources of variation. PC3 indicated that the males reached the peak moment sooner with a greater rate of loading and unloading than the females.





The MANOVA results for the intertrial variability indicated significant gender differences for the sagittal and the frontal plane moments. For all significant PC differences, the males exhibited greater variability. For the sagittal plane moments, PC3 indicates greater variability for males in the relative magnitude of the peak moment versus the moment at takeoff, whereas PC6 and PC7 describe variability during early and late stance (not displayed). In the frontal plane, there was greater intertrial variability for PC1 and PC4. This indicates greater variability for males during midstance (PC1) and immediately after heel strike (PC4; not displayed).

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The purpose of this study was to use PCA to examine knee mechanics for males and females during an unanticipated cutting maneuver. It was hypothesized that this approach would identify gender differences not readily apparent when examining discrete dependent variables. It was also believed that PCA would provide a novel approach to examining the role of movement variability. The results of this study indicated that PCA could identify waveform differences between genders that would not necessarily be detected using traditional approaches. In this study, TD, ROM, and peak moments were chosen as exemplar variables based on previous literature. Although the traditional approach detected greater flexion ROM for males, the PCA approach did not. However, the PCA analysis identified some waveform differences during early stance and late stance that were not detected by the traditional approaches. More importantly, the frontal plane mechanics were significantly different in ways that are consistent with the current theories regarding increased injury risk. Further, the within-subjects variability indicated that females were less variable in the primary loading patterns in the sagittal and the frontal planes, although it is unclear whether this can be attributed directly to gender or to other factors.

The overall joint dynamics patterns replicate those observed previously for cutting (2,23,24,27,33). In the sagittal plane, the decreased ROM for females observed in the current study was also observed by McLean et al. (23) as a reduction in peak knee flexion. However, the waveform analysis did not detect a significant MANOVA main effect for gender. When a post hoc analysis was performed, the P value for PC1 was 0.02, which suggested that females did flex less than males. The current frontal kinematic patterns are remarkably similar to McLean et al. (23). Those authors noted a high-frequency oscillation during early stance not previously reported, and this same oscillation was present in the current study. McLean et al. (23) postulated that this is a likely mechanical response to the frontal plane moment created by the ground reaction force. In addition, they reported significantly greater peak knee abduction for females. In contrast, the current study did not report a significant TD or ROM difference. In the transverse plane, the pattern of internal rotation is similar to other studies (23,27,33).

Similar to the waveform results for the sagittal plane angle, the frontal plane angle MANOVA did not detect a significant gender effect. However, there was a trend (P = 0.02) for PC2, with females exhibiting greater knee valgus patterns during the oscillation of early stance. This high-frequency oscillation in the frontal plane may be clinically important. During early stance, there is an impulsive load applied that will generate a flexion and valgus moment about the knee. The kinematic and ACL load effects of this type of loading were confirmed by Withrow et al. (34), who reported greater ACL strain and knee abduction motion when an impulsive external force was applied to cadaver limbs. The kinematic response in that study also appears to match the oscillation observed during early stance by McLean et al. (23) and the current study. The difference in frontal moment PC2 suggests that a greater impulsive load was applied to the knee for females. Analysis of the peak ground reaction forces in each plane did not reveal any significant gender differences. However, the effect of the ground reaction force on knee moments is also affected by subtleties in the center of pressure and orientation of the body segments, which will change the moment arm about the knee. A full examination of the ground reaction force influence on the knee was beyond the scope of the current study, but the PCA results suggest a relationship between the frontal plane knee kinematics and kinetics.

To examine the relationship between the frontal plane angles and moments, a post hoc analysis was performed correlating subject mean PC scores between these two waveforms (Table 5). In addition, correlations were performed for the subject mean TD and ROM with the peak adduction moments. Interestingly, there were moderate correlations between most of the paired PC (e.g., PC1 to PC1, PC2 to PC2). As can be observed in the variation explained panels of Figures 2 and 3, the frontal moment PC1 explained the most variation from 25% of stance to toe-off, as does the frontal angle PC1. For all but PC3, the periods of the greatest variance explained matched for each pair, which explains why the variance explained for the PC3 pair is zero. PCA is a multivariate mathematical technique that only identifies dominant modes of variation within a data set. The fact that the PCA extracted nearly identical sources of variation in the two waveforms suggests that this may be a powerful new way to investigate kinetic/kinematic relationships. For PC2 in particular, this supports the cadaver study by Withrow et al. (34) that an impulsive moment during early stance causes rapid abduction of the knee. The r 2 value of 0.24 when subject means were evaluated for PC2 demonstrates a moderate correlation between the peak knee moment and the magnitude of this oscillation across subjects. In contrast, correlations of subject mean TD and ROM with peak adduction moments only yielded r 2 values of 0.10 and 0.13. A further analysis was performed where the PC2 pairing for individual trials of each subject was correlated, which yielded an average of r 2 of 0.47 ± 0.36 for all subjects. When within-subject correlations were performed on the discrete measure, the average r 2 was 0.34 ± 0.3 (TD) and 0.32 ± 0.28 (ROM), which are slightly greater but comparable to values reported by McLean et al. (22). On the basis of these results, there appears to be a relatively strong relationship between the frontal plane loading during early stance and the amount of rapid abduction observed. Given ACL strain results of Withrow et al. (34), this observation suggests potential for greater ACL strain among females. This result demonstrates a promising application of PCA, and the use of this technique in a longitudinal study may enhance the discriminative power to detect increased injury risk.



Subtle shifts in kinematic and kinetic inputs can have a large effect on joint moment calculations, particularly in the frontal and the transverse planes. Only half of the frontal plane moment waveforms were adequately represented by the retained PC, and none of the transverse plane waveform could be adequately reconstructed. Of previous studies that have used PCA to examine biomechanical waveforms (8,16,21,36), only Wrigley et al. (36) included the Q-statistic to quantify the reconstructive ability of the retained PC. In that study, the retained PC accounted for most of the variance (>95%), and most of the individual waveforms (>92%) were adequately represented. This provided strong evidence that an appropriate number of PC were retained based on the SCREE analysis. The Q-statistic can be considered analogous to a threshold established for a traditional residual analysis to determine filter cutoff frequencies. Overfiltering leads to unacceptable residuals, analogous to retaining too few PC. In the current study, the relatively low variance explained for the frontal (91%) and the transverse (85%) plane moments suggests that individual waveforms are less likely to be adequately represented by the retained PC, which was confirmed by the Q-statistic. This, however, should not affect the previously discussed clinical significance of the retained frontal plane PC because the Q-statistic tests the ability to fully reconstruct an original waveform from its PC. The variance explained by the retained frontal plane PC exists in the data set regardless of whether the original waveform can be fully reconstructed. The main implication of the Q-statistic results for these waveforms suggests that there is a relatively large nondeterministic component to these waveforms in addition to the structure identified by the retained PC.

When comparing studies characterizing cutting performance and injury risk, there are several potential confounding factors. The current study did not control for years of playing experience, and there is some evidence to suggest that experience level can influence task performance (24,32), although these studies only reported differences in joint kinetics (32) and within-subject variability (24). For the current data set, experience was not a significant covariate when comparing mean kinematic and kinetic data between groups (26). The demands of the task can also affect cutting dynamics. The use of an unanticipated cutting maneuver has also been suggested as a more "realistic" task because it has been shown to elicit more extreme mechanical and neuromuscular responses (2). However, it is interesting to note that there was large agreement between the kinematic patterns observed in the current study and those of McLean et al. (23) because the two studies used comparable approach velocities (4.5-5.0 m·s−1 current study; 4.5-5.5 m·s−1 McLean et al. 23) whereas McLean et al. (23) used an anticipated task. The kinematic similarities of these two studies indicate that the approach velocity may be a more important factor. Some studies have used slow jogging speeds of 3-3.5 m·s−1 (2,16), whereas others have used higher velocities of 5.5-7.0 m·s−1 (27,33). Unfortunately, it is difficult to make direct comparisons between these studies to understand velocity effects because these studies also differ in subjects' experience, use of anticipation, and other methodological differences such as how joint moments are reported.

These confounding factors are important to consider in comparing the current results to those of Landry et al. (16). The two studies share a common goal to investigate gender differences in lower extremity mechanics during an unanticipated cutting maneuver using PCA. In comparing knee kinematics, Landry et al. (16) only reported sagittal plane angles. Similar to the current results, PC1 extracted magnitude differences in the data set but they did not find a significant gender difference. For knee moments, Landry et al. (16) only reported a possible gender difference (P = 0.06) in one PC in the frontal plane (PC3). They reported that the PC related to the magnitude during early stance, which is the same as the PC results for the current study. The current study, however, did find a significant gender difference for PC3 in the same direction suggested by Landry et al. (16). Although Landry et al. (16) did not report all of their knee PCA results, the modes of variation they identified for the sagittal plane angle and the frontal plane moment match the results of the current study. This lends confidence that PCA is robust in identifying similar modes of variation across studies despite differences in subject populations and data collection protocols. Approach velocity is likely the most significant methodological difference. Landry et al. (16) used a 3.5-m·s−1 approach velocity that was considerably slower than the current study. The lack of significant knee differences in the study of Landry et al. (16) may be a direct result of this low-approach velocity. The task demands on both groups may have been low enough so as not to allow for discrimination between groups.

Unlike the studies by McLean et al. (23,24), the current study did not detect significant differences in intertrial variability for discrete kinematic or kinetic variables. A primary difference in the current study was the use of the unanticipated cutting maneuver, which may explain the discrepancy. Interestingly, evaluating the intertrial variability of the waveform scores identified significant variability differences in sagittal and frontal plane moments, with males exhibiting greater variability in all significantly different PC than females. McLean et al. (24) reported a negative relationship between playing experience and kinematic variability. Their results would predict greater variability for females in the current study, but the opposite was observed. It is possible that the lesser relative task demands for males may have allowed greater freedom to alter their movement patterns. The same approach velocities were used to remove a substantial source of variation, but in doing so it may have created differences in relative task demands. Although further work needs to be done to understand the clinical significance of variability, the results of this study demonstrate that PCA has great potential to identify variability differences not readily observed from traditional discrete variables.

Although the results of this study provide a clear indication that PCA can be a valuable and an effective tool to detect group differences in joint mechanics, there is one major limitation. Statistical testing of the PC scores identified gender differences, but the values of the scores themselves do not have intuitive meaning, which makes it difficult to discuss absolute differences between curves. Perhaps the greatest strength of this analysis approach may be to determine an optimal set of discrete variables that can be used for future analyses. For instance, Deluzio et al. (8) compared PCA to discrete measures gait parameters affected by knee osteoarthritis and found that the traditional discrete measures characterized the waveform differences relatively well. On the other hand, Wrigley et al. (35) found that the chosen discrete measures were not adequate to detect low back pain risk factors. The results of the current study indicate agreement between the two approaches for some measures but not for all. The ROM and the peak moment measures, in particular, did not adequately describe the frontal plane kinematics and kinetics. These results suggest that discrete kinematic measures of early stance are important, such as a mean or a peak angle during the first ∼20% of stance, as some have reported (5,27). The frontal plane kinetics PCA results, on the other hand, suggest that discrete measures would not be able to extract the differences observed in this study. Further work needs to be done to determine whether the significant PCA differences have clinical significance, but the results seem consistent with risk factors and loading patterns noted by others (14,34). In summary, PCA has great potential to inform decisions regarding discrete parameters that best characterize clinically relevant function.

Knee mechanics differences between males and females for an unanticipated cutting maneuver were assessed with traditional discrete variables and with a waveform analysis using PCA. Although the traditional discrete measures were able to detect a significant difference in flexion ROM and the PCA analysis was not, the PCA analysis identified potentially clinically important differences in frontal plane mechanics not detected by the discrete measures. The PCA analysis also highlighted a linkage between the frontal plane moment and the kinematics that was not obvious from the discrete measure. In addition, the traditional analysis did not detect any gender differences in intertrial variability, whereas the waveform analysis found that males were more variable in both the sagittal and the frontal plane moments. Although to date unproven, it has been suggested that movement variability is important for robust responses to perturbations. The decreased variability for females based on PCA suggests that this analysis technique may be useful in prospective studies to better understand the link between movement variability and injury risk. The results of this study indicate that this analysis approach can yield greater insight into injury mechanisms, not only for ACL injury but potentially for other injuries as well.

The authors would like to thank the University of Wisconsin-Milwaukee Graduate School Research Committee for its financial support of this project. The authors would also like to thank Sarika Monteiro, Ian Hoelker, Richard Deklotz, and Carl Johnson for their invaluable assistance.

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