Stepping boundary of external force-controlled perturbations of varying durations: Comparison of experimental data and model simulations

Abstract

This study investigated the stepping boundary – the force that can be resisted without stepping – for force-controlled perturbations of different durations. Twenty-two healthy young adults (19–37 years old) were instructed to try not to step in response to 86 different force/time combinations of forward waist-pulls. The forces at which 50% of subjects stepped (F50) were identified for each tested perturbation durations. Results showed that F50 decreased hyperbolically when the perturbation’s duration increased and converged toward a constant value (about 10%BW) for longer perturbations (over 1500 ms). The effect of perturbation duration was critical for the shortest perturbations (less than 1 s).In parallel, a simple function was proposed to estimate this stepping boundary. Considering the dynamics of a linear inverted pendulum + foot model and simple balance recovery reactions, we could express the maximum pulling force that can be withstood without stepping as a simple function of the perturbation duration. When used with values of the main model parameters determined experimentally, this function replicated adequately the experimental results.This study demonstrates for the first time that perturbation duration has a major influence on the outcomes of compliant perturbations such as force-controlled pulls. The stepping boundary corresponds to a constant perturbation force-duration product and is largely explained by only two parameters: the reaction time and the displacement of the center of pressure within the functional base of support. Future work should investigate pathological populations and additional parameters characterizing the perturbation time-profile such as the time derivative of the perturbation.