PRINCIPAL COMPONENT ANALYSIS OF A SINGLE LEG SQUAT

Abstract

INTRODUCTION

Single leg squat (SLS) is a clinical test that is useful in assessing the biomechanical performance of the lower limb. In particular, SLS may provide indicators of muscle strength and balance of a patient [1]. In order to measure the movements present in the single leg squat, a motion capture system is typically used in conjunction with a set of reflective markers. This use of motion capture enables the study of the kinetics and kinematics of the squat for the chosen sample population.

Since the use of motion capture in recording the SLS results in a continuous dataset, it is helpful to compress the data to compare the results. Principal component analysis (PCA) is a technique that may be used to reduce the dimensionality in a given dataset so fewer comparisons need to be made. In addition, by interpreting these principal components, any significant differences found can be related back to the biomechanics of the squat. Therefore, the main objective of this study is to run PCA on the SLS data, and look for kinematic differences between the injured and non-injured populations. A secondary objective is to interpret the principal components to find a meaning for any differences found.

METHODS

The SLS was performed by 50 subjects with intra-articular knee injuries and 50 healthy controls (age: 21.3±2.9, BMI: 24.4±3.7). Each subject performed 3 trials consisting of 5 squats to approximately 45° knee flexion each.  The data was collected using a motion capture system (Motion Analysis, Santa Rosa, CA) at a sampling frequency of 240 Hz. The 3D motion capture data was imported into MATLAB, and the knee FE angle was computed according to [2]. For each subject, the squat that reached closest to 45° knee flexion was chosen for the PCA.

PCA was computed on the knee flexion angles of all subjects with respect to time. The resulting principal components (PCs) represent the variation between subjects accounted for by each time point. The first 3 principal components were selected for further analysis, in order to account for 95% of the total variance in the data.

In order to determine the meaning of the selected PCs, patient waveforms corresponding to the highest and lowest 5% of PC scores were compared and interpreted, according to Deluzio [3]. The subject data was reduced to 3 dimensions by plotting the FE angle along the selected PC axes. To study the difference between the injured and non-injured subjects, a student t-test was performed on the PC scores for each of the three components, with p value at 0.05.

RESULTS

High values along the first PC axis were found to correspond to a leftward shift in the subject waveform. A high second PC was found to correspond to a more gradual FE curve, and a high third PC corresponded to a larger downward slope compared to the upward component. When performing a t-test, the PC 1 values for the non-injured group were found to be statically lower (p < 0.0164) than the injured group. No significant difference was noticed along the PC 2 or PC 3 axes.

DISCUSSION AND CONCLUSIONS

The interpretation of the first PC was taken to be the shift in time of the squat from the average pattern. Based on the results of the t-test, the non-injured group shows a lower PC 1. Based on the interpretation above, the non-injured group appears to spend a larger proportion of the total time in the downward portion of the squat when compared to the non-injured group. This may indicate a deficiency in controlling the flexion descent for subjects suffering from knee injury, which may in turn indicate a possibility for future therapeutic intervention.