Rethinking Margin of Stability: Incorporating Step-To-Step Regulation to Resolve the Paradox

Abstract

Derived from inverted pendulum dynamics, mediolateral Margin of Stability (MoSML) is a mechanically-grounded measure of instantaneous stability. However, average MoSML measures yield paradoxical results. Gait pathologies or perturbations often induce larger (supposedly "more stable") average MoSML, despite clearly destabilizing factors. However, people do not walk "on average" - they walk (and sometimes lose balance) one step at a time. We assert the paradox arises because averaging discards step-to-step dynamics. We present a framework unifying the inverted pendulum with Goal-Equivalent Manifold (GEM) analyses. We identify in the pendulums center-of-mass dynamics constant-MoSML manifolds, including one candidate "stability GEM" signifying the goal to maintain some constant [Formula]. We used this framework to assess step-to-step MoSML dynamics of humans walking in destabilizing environments. While goal-relevant deviations were readily corrected, humans did not exploit equifinality by allowing deviations to persist along this GEM. Thus, maintaining a constant [Formula] is inconsistent with observed step-to-step fluctuations in center-of-mass states. Conversely, the extent to which participants regulated fluctuations in foot placements strongly predicted regulation of center-of-mass fluctuations. Thus, center-of-mass dynamics may arise indirectly as a consequence of regulating mediolateral foot placements. To resolve the paradox caused by averaging MoSML, we present a new statistic, Probability of Instability (PoIL), to predict instability likelihood. Participants exhibited increased PoIL when destabilized (p = 9.45x10-34), despite exhibiting larger ("more stable") average MoSML (p = 1.70x10-15). Thus, PoIL correctly captured peoples increased risk of losing lateral balance, whereas average MoSML did not. PoIL also explains why peoples average MoSML increased in destabilizing contexts.