Symmetry Analysis of Amputee Gait Based on Body Center of Mass Trajectory and Discrete Fourier Transform

Abstract

The calculation of symmetry in amputee gait is a valuable tool to assess the functional aspects of lower limb prostheses and how it impacts the overall gait mechanics. This paper analyzes the vertical trajectory of the body center of mass (CoM) of a group formed by transfemoral amputees and non-amputees to quantitatively compare the symmetry level of this parameter for both cases. A decomposition of the vertical CoM into discrete Fourier series (DFS) components is performed for each subject’s CoM trajectory to identify the main components of each pattern. A DFS-based index is then calculated to quantify the CoM symmetry level. The obtained results show that the CoM displays different patterns along a gait cycle for each amputee, which differ from the sine-wave shape obtained in the non-amputee case. The CoM magnitude spectrum also reveals more coefficients for the amputee waveforms. The different CoM trajectories found in the studied subjects can be thought as the manifestation of developed compensatory mechanisms, which lead to gait asymmetries. The presence of odd components in the magnitude spectrum is related to the asymmetric behavior of the CoM trajectory, given the fact that this signal is an even function for a non-amputee gait. The DFS-based index reflects this fact due to the high value obtained for the non-amputee reference, in comparison to the low values for each amputee.

Speed-dependent modulations of asymmetric center of body mass trajectory in the gait of above-knee amputee subjects

“…We employed Fourier series expansion to examine how walking speed affects the asymmetry of CoM trajectories [ Supplementary Figure S1 ( 20 , 24 )]. The mediolateral CoM trajectories can be well represented by a the first harmonic ( , Supplementary Figure S2 ).…”

“…However, it is generally incorrect to assume that CoM trajectories are symmetric. Asymmetric CoM trajectories have been observed in amputee subjects ( 20 ). Patients with knee osteoarthritis demonstrate different accelerations of CoM movements in gait compared to healthy controls, indicating asymmetric CoM positions ( 21 ).…”

“…Leveraging this valuable open dataset, we aim to elucidate the speed-dependent modulations of asymmetric CoM trajectories in individuals with above-knee amputations. We employ Fourier series expansion, enabling the assessment of periodic curves, including asymmetrical CoM trajectories, and facilitating the analysis of the functional impact of speed-dependent modulations [( 20 , 24 ), Supplementary Figure S1 ].…”

Система Для Визначення Особливостей Ходи У Пацієнтів З Транстибіальною Ампутацією

“…Вчасне виявлення відхилень ходи у пацієнтів з ампутаціями забезпечує найскоріший процес реабілітації та попереджує виникнення таких дегенеративних уражень опорно-рухового апарату як остеопенія та остеопороз [2,3,4].…”

A Novel Algorithm for Automatic Estimation of Gait Parameters Using Lower-Body Kinematics

“…Lastly, gait symmetry is an important parameter in am-putee gait indicating gait quality [39]. It measures the amount of divergence between the left and right leg.…”