Estimation of Quasi-Stiffness and Propulsive Work of the Human Ankle in the Stance Phase of Walking

Abstract

Characterizing the quasi-stiffness and work of lower extremity joints is critical for evaluating human locomotion and designing assistive devices such as prostheses and orthoses intended to emulate the biological behavior of human legs. This work aims to establish statistical models that allow us to predict the ankle quasi-stiffness and net mechanical work for adults walking on level ground. During the stance phase of walking, the ankle joint propels the body through three distinctive phases of nearly constant stiffness known as the quasi-stiffness of each phase. Using a generic equation for the ankle moment obtained through an inverse dynamics analysis, we identify key independent parameters needed to predict ankle quasi-stiffness and propulsive work and also the functional form of each correlation. These parameters include gait speed, ankle excursion, and subject height and weight. Based on the identified form of the correlation and key variables, we applied linear regression on experimental walking data for 216 gait trials across 26 subjects (speeds from 0.75–2.63 m/s) to obtain statistical models of varying complexity. The most general forms of the statistical models include all the key parameters and have an R2 of 75% to 81% in the prediction of the ankle quasi-stiffnesses and propulsive work. The most specific models include only subject height and weight and could predict the ankle quasi-stiffnesses and work for optimal walking speed with average error of 13% to 30%. We discuss how these models provide a useful framework and foundation for designing subject- and gait-specific prosthetic and exoskeletal devices designed to emulate biological ankle function during level ground walking.

Effect of static foot posture on the dynamic stiffness of foot joints during walking

“…Calculated joint moments were normalized to body-weight, consistently with previous publications [4], [5], and were low-pass filtered with a 4 th -order Butterworth filter and cut-off frequency of 50 Hz.…”

“…Analysis of the foot joints dynamics during gait can help understanding the development of these injuries [3]. Different works undertook this analysis by looking at the dynamic joint stiffness [4], [5], defined as the ratio between the external moment applied to the joint and the joint angle, at a specific time, assessed while performing activities that require muscle activation, such as walking. This stiffness combines the effect of muscle forces, inertia and deformation of soft tissue, and was already applied to the ankle in the sagittal plane with different purposes [4], [6], [7].…”

Novel Method to Evaluate Angular Stiffness of Prosthetic Feet From Linear Compression Tests

“…Ankle quasistiffness data from normal walking has been estimated as roughly 3.5-17.3 N-m/deg [7] or 3.5-24.4 N-m/deg [8] during different phases of gait. The angular stiffness values estimated here (7.9-29.1 N-m/deg) span a similar range.…”

“…Mechanical testing could, in principle, measure stiffness directly, but it is nontrivial to produce pure rotations for comparison against measured moments and to control for the variations in induced external force. The most common approximation is to estimate ankle "quasistiffness" from ankle torque versus moment plots measured with gait analysis [7,8]. However, this technique does not isolate the properties of a foot prosthesis, because the ankle moment measurements include confounding effects due to fluctuating ground reaction forces and the unique gait behaviors of different subjects.…”

Ankle mechanics during sidestep cutting implicates need for 2-degrees of freedom powered ankle-foot prostheses

“…Powered prosthesis controllers are currently designed based on ankle moment-angle relationships that are averaged across a study population (e.g., Shamaei et al [23]) rather than ankle impedance. Rouse et al developed a platform capable of applying moment perturbations during the foot-flat stance phase in sagittal plane [24][25].…”