Nonlinear net ankle quasi-stiffness reduces error and changes with speed but not load carried

Abstract

Background: Natural ankle quasi-stiffness (NAS) is a key metric used to personalize orthotic and prosthetic ankle-foot devices. NAS has traditionally been defined as the average slope (i.e. linear regression) of the net ankle moment vs. ankle angle curve during stance. However, NAS appears to have nonlinear characteristics. Characterizing nonlinear NAS across a wide range of tasks will enable us to incorporate these attributes into future orthotic and prosthetic ankle-foot device designs.

Research question: Does nonlinear NAS change across multiple intensities of walking, running, and load carriage tasks?

Methods: This observational study examined 22 young, healthy individuals as they walked, ran, and walked while carrying a load at three intensities (speed or load). Linear, quadratic, and cubic regressions were done on the net ankle moment vs. ankle angle curve over three phases of stance: impact, loading, and push-off. RMSE between regressions and measured data were computed to determine regression accuracy, and multilevel linear models (MLMs) were used to determine significant differences between coefficients across intensities.

Results: Quadratic and cubic regressions of NAS had significantly lower RMSE than linear NAS for all phases of stance. Because of diminishing reductions in RMSE between quadratic and cubic regressions, only quadratic regression coefficients were further analyzed. Most first (linear) and second (nonlinear) order coefficients of quadratic regressions exhibited clear trends with respect to changes in walking or running speed, but not to increases in load.

Significance: This was the first study to our knowledge to thoroughly characterize nonlinear NAS across multiple gait tasks and intensities. This study provides an advanced understanding of the characteristics of nonlinear NAS for the design of future prosthetic and orthotic ankle-foot devices.

Keywords: Dynamic ankle stiffness; Load carriage; Natural ankle quasi-stiffness; Running; Walking.