Quantifying Nonlinear Ankle Quasi-Stiffness During Level and Sloped Walking

Natural ankle quasi-stiffness describes the joint's resistance to motion during loading in gait, which is informative for the design of biomimetic devices (eg, prostheses, orthoses, and exoskeletons). Ankle quasi-stiffness is typically quantified as the slope of the moment-angle curve using a linear approximation. Yet, recent studies during level-ground walking reveal that the human ankle displays a nonlinear behavior, in that the ankle stiffens with greater dorsiflexion. However, little is known regarding the nonlinear behavior when walking on slopes. Here, we aimed to quantify natural ankle quasi-stiffness during level and sloped walking. Twelve healthy young adults walked barefoot on an instrumented treadmill at 1.25 m/s at 5 slopes: decline (-10°, -5°), level (0°), and incline (5°, 10°). Linear, quadratic, and cubic polynomial regressions were computed on ankle moment-angle data during the loading phase. Adjusted R2 values evaluated the goodness of fit. During the decline and level conditions, cubic regression best predicted the moment-angle relationship (adjusted R2 > .975). During inclines, quadratic models best predicted the moment-angle relationship, although the goodness of fit was low (adjusted R2 < .444). Such models were especially poor for the incline 10° condition, revealing that a spring-like measure of ankle quasi-stiffness is not a sufficient summary for the ankle's behavior on steep inclines. Our results suggest that the human ankle exhibits nonlinear quasi-stiffness across level and sloped walking, with decline and level conditions being quantifiable by polynomial regression models. These findings may inform the design of biomimetic devices that can adapt to varying terrain.