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 R(2) 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.

Figure 1. Ankle moment vs. relative angle curve for a representative subject walking at 1.75 m/s.

Letters a-f on the graph correspond to the poses schematically shown during a typical walking cycle (top, schematic timing is adapted from [69]). Quasi-stiffness is calculated based on the slope of the best-line fit to the moment-angle curve of b-c for the dorsi-flexion (), c-d for the dual-flexion (), and d-e for the plantar-flexion () phases of the progression period (b-e). The area enclosed by the graph represents the propulsion work of the ankle (). The joint excursion in each phase is the difference between the ankle relative angle at the onset and end of that phase (i.e. , and

Figure 2. Ankle quasi-stiffnesses (N.m/rad) in dorsi-flexion (top-left), dual-flexion (top-right), and plantar-flexion (bottom-left) phases, and propulsive work (J) in stance (bottom-tight) plotted against gait speed for subject 10 as an example.

The circles indicate the experimental value and the diamonds are the predictions of the general-form models of Table 2.

Figure 3. Ankle quasi-stiffnesses (N.m/rad) in dorsi-flexion (top-left), dual-flexion (top-right), and plantar-flexion (bottom-left) phases, and propulsive work (J) in stance (bottom-tight) plotted for different subjects walking at a speed closest to the preferred gait speed.

The experimental values are shown by circles, the predictions of the general-form models by diamonds, and the stature-based models with squares. To avoid suppressing the rest of the data, the arrows are included on the top-right graph to indicate the values that are dramatically higher than the rest of the data.