Estimation of tri-axial walking ground reaction forces of left and right foot from total forces in real-life environments

This is the final version of the article. Available from MDPI via the DOI in this record.Continuous monitoring of natural human gait in real-life environments is essential in many applications including disease monitoring, rehabilitation, and professional sports. Wearable inertial measurement units are successfully used to measure body kinematics in real-life environments and to estimate total walking ground reaction forces GRF(t) using equations of motion. However, for inverse dynamics and clinical gait analysis, the GRF(t) of each foot is required separately. Using an experimental dataset of 1243 tri-axial separate-foot GRF(t) time histories measured by the authors across eight years, this study proposes the ‘Twin Polynomial Method’ (TPM) to estimate the tri-axial left and right foot GRF(t) signals from the total GRF(t) signals. For each gait cycle, TPM fits polynomials of degree five, eight, and nine to the known single-support part of the left and right foot vertical, anterior-posterior, and medial-lateral GRF(t) signals, respectively, to extrapolate the unknown double-support parts of the corresponding GRF(t) signals. Validation of the proposed method both with force plate measurements (gold standard) in the laboratory, and in real-life environment showed a peak-to-peak normalized root mean square error of less than 2.5%, 6.5% and 7.5% for the estimated GRF(t) signals in the vertical, anterior-posterior and medial-lateral directions, respectively. These values show considerable improvement compared with the currently available GRF(t) decomposition methods in the literature.The authors acknowledge the financial support provided by the UK Engineering and Physical Sciences Research Council (EPSRC) for the following research grants: Frontier Engineering Grant EP/K03877X/1 (Modelling complex and partially identified engineering problems: Application to the individualized multiscale simulation of the musculoskeletal system); and Platform Grant EP/G061130/2 (Dynamic performance of large civil engineering structures: an integrated approach to management, design and assessment)

Three-Dimensional Decomposition of Ground-Reaction Forces Under Both Feet During Gait Using Parametric Curve Modeling

RÉSUMÉ Introduction: La mesure tridimensionnelle des forces de réaction au sol (FRS-3D) est un élément important de l'analyse de la démarche. En effet, lors de l'évaluation fonctionnelle des patients en réadaptation, cette mesure permet de calculer les centres de pression, les paramètres spatio-temporels ainsi que les couples articulaires. Pour obtenir les FRS-3D sur plusieurs cycles de marche, l’utilisation de longues plateformes est nécessaire. Cependant, les systèmes de mesure de ce type posent un problème puisqu'ils fournissent uniquement une résultante des FRS-3D pour les deux pieds combinés. En plus, aucune méthode n'a précédemment été validée sur un nombre raisonnablement élevé de participants. Objectif: Cette étude vise à développer une méthode automatisée en utilisant des courbes paramétriques en forme de « S » pour augmenter la précision de la décomposition des FRS-3D pendant les phases de double-appui, aux profils gauche et droit et ceci, le long des axes tridimensionnels X, Y et Z. Méthodes: Trente adultes en bonne santé, âgés en moyenne de 24.8 ans (écart-type (ÉT) : 3.1 ans), dont 17 hommes, et ayant en moyenne un poids de 70.6 kg (ÉT : 11.4), ont marché naturellement, à pieds-nus, sur un plancher équipé de plateformes de force séparées. La méthode de modélisation de la décomposition de forces a été appliquée aux FRS-3D en considérant différentes fonctions paramétriques telles qu'une fonction polynomiale du 3ième ordre, une sinusoïde et des sinusoïdes sigmoïdes. Pour valider cette méthode, les valeurs de FRS-3D décomposées ont été comparées à celles des FRS-3D enregistrées par plateformes de forces indépendantes et ceci pour chacun des sujets de l'étude. Une erreur globale est calculée en comparant la norme des valeurs de FRS-3D décomposées à celle de FRS-3D enregistrées par les----------ABSTRACT Introduction: Three-dimensional ground reaction forces (3D-GRF) measurement is an important aspect of gait analysis to compute centers of pressure, spatial-temporal parameters and joint torques for functional evaluation in rehabilitation. To obtain these 3D-GRF on several gait cycles, a long measurement platform is required. However, the difficulty of such measurement systems arise from the fact that the unique force platform provides the resultant of GRF for the two feet combined. Therefore, one needs to decompose the 3D-GRF into components under each foot. Indeed, both feet are placed on the same force platform, which solely provides the global resultant of left and right foot together. Furthermore, no method has been previously validated on reasonable number of participants. Objective: This study aims to develop an automatic method using s-type parametric curve modeling to increase the accuracy of decomposition of 3D-GRF during double stance into left and right profiles and along X, Y and Z axes. Methods: Thirty healthy adults (age: 24.8 (Standard Deviation (SD): 3.1) years, 17 males, weight: 70.6 (SD: 11.4) kg) walked naturally barefoot on a floor equipped with separate force platforms. The decomposition modeling method was applied to global 3D-GRF using different parametric curve functions as in 3rd order polynomial, sine and sine-sigmoid functions. To validate this method, the decomposed 3D-GRF was compared to the 3D-GRF independently recorded for each subject. A global error is calculated based on global GRF, which is the comparison between the decomposed global 3D-GRF and recorded global 3D-GRF. The global 3D-GRF is obtained by computing the square root of the sum of the second exponential of GRF along each axis