A principal component analysis approach to correcting the knee flexion axis during gait

Abstract

Accurate and precise knee flexion axis identification is critical for prescribing and assessing tibial and femoral derotation osteotemies, but is highly prone to marker misplacement-induced error. The purpose of this study was to develop an efficient algorithm for post hoc correction of the knee flexion axis and test its efficacy relative to other established algorithms. Gait data were collected on twelve healthy subjects using standard marker placement as well as intentionally misplaced lateral knee markers. The efficacy of the algorithm was assessed by quantifying the reduction in knee angle errors. Crosstalk error was quantified from the coefficient of determination (r2) between knee flexion and adduction angles. Mean rotation offset error (αo) was quantified from the knee and hip rotation kinematics across the gait cycle. The principal component analysis (PCA)-based algorithm significantly reduced r2 (p<0.001) and caused αo,knee to converge toward 11.9±8.0 degrees of external rotation, demonstrating improved certainty of the knee kinematics. The within-subject standard deviation of αo,hip between marker placements was reduced from 13.5±1.5 to 0.7±0.2 degrees (p<0.001), demonstrating improved precision of the knee kinematics. The PCA-based algorithm performed at levels comparable to a knee abduction-adduction minimization algorithm (Baker et al., 1999) and better than a null space algorithm (Schwartz and Rozumalski, 2005) for this healthy subject population.

Knee Angles and Axes Crosstalk Correction In Gait, Cycling, and Elliptical Training Exercises

“…These results reinforce previous findings that PCA can reduce crosstalk errors in G which was also seen in other studies on crosstalk correction in G [1,2]. However, a novel finding of the present study was the use of PCA to calculate the G PCA corrected axes.…”

“…This study didn't reduce the AA variability and the range in G was not as much as previous studies where markers were intentionally misplaced to create crosstalk which resulted in large AA angles pre-PCA correction [1,2]. For one study, the lateral knee marker was intentionally placed anterior and posterior of the appropriate location and calculated pre-PCA G AA ranges of ~17 and ~23 degrees, for anterior and posterior, respectively [1].…”

“…Previous studies that performed PCA to correct G data didn't calculate the corrected axes [1,2]. Thus, custom MATLAB code was developed to determine the axes from the PCA corrected angles.…”

“…More recently, a post hoc correction method has been studied which uses PCA to correct for crosstalk [1,2] and has shown to be less susceptible to marker placement errors than a null space algorithm [46] and comparable to a knee AA minimization algorithm [10]. Implementing PCA requires no hardware setup which reduces the required time for experiments and utilizes a computationally efficient statistical algorithm that is available to anyone.…”

“…This study addresses two limitations of previous studies that have used PCA to reduce crosstalk errors. First, previous studies that have used PCA have focused on reducing crosstalk errors as evidenced by reduced FE-AA correlations [1,2] only in G studies and have not considered whether PCA is effective in reducing crosstalk errors for other exercises such as cycling (C) and elliptical training (E).…”