Fourier Analysis of the Vertical Ground Reaction Force During Walking: Applications for Quantifying Differences in Gait Strategies

Abstract

Time series biomechanical data inform our understanding of normal gait mechanics and pathomechanics. This study examines the utility of different quantitative methods to distinguish vertical ground reaction forces (VGRFs) from experimentally distinct gait strategies. The goals of this study are to compare measures of VGRF data—using the shape factor method and a Fourier series-based analysis—to (1) describe how these methods reflect and distinguish gait patterns and (2) determine which Fourier series coefficients discriminate normal walking, with a relatively stiff-legged gait, from compliant walking, using deep knee flexion and limited vertical oscillation. This study includes a reanalysis of previously presented VGRF data. We applied the shape factor method and fit 3- to 8-term Fourier series to zero-padded VGRF data. We compared VGRF renderings using Euclidean L2 distances and correlations stratified by gait strategy. Euclidean L2 distances improved with additional harmonics, with limited improvement after the seventh term. Euclidean L2 distances were greater in shape factor versus Fourier series renderings. In the 8 harmonic model, amplitudes of 9 Fourier coefficients—which contribute to VGRF features including peak and local minimum amplitudes and limb loading rates—were different between normal and compliant walking. The results suggest that Fourier series-based methods distinguish between gait strategies.