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 frontal-plane 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 MoSML discards crucial step-to-step dynamics. We present a framework unifying the inverted pendulum with Goal-Equivalent Manifold (GEM) analyses. We identify in the pendulum’s center-of-mass dynamics constant-MoSML manifolds, including one candidate “stability GEM” signifying the goal to maintain some constant MoSML∗. We used this framework to assess step-to-step MoSML dynamics of humans walking in destabilizing environments. While goal-relevant deviations were readily corrected, people did not exploit equifinality by allowing deviations to persist along this GEM. Thus, maintaining a constant MoSML∗ is inconsistent with observed step-to-step fluctuations in center-of-mass states. Conversely, the extent to which participants regulated fluctuations in mediolateral foot placements strongly predicted their regulation of center-of-mass fluctuations. Thus, center-of-mass dynamics may arise indirectly as a consequence of regulating mediolateral foot placements. To help resolve the paradox caused by averaging MoSML, we present a new statistic, Probability of Instability (PoIL), used here to predict lateral instability likelihood. Participants exhibited increased PoIL when destabilized (p = 9.45 × 10−34), despite exhibiting larger (“more stable”) average MoSML (p = 1.70 × 10−15). Thus, PoIL correctly captured people’s increased risk of losing lateral balance, whereas average MoSML did not. PoIL also helps explain why people’s average MoSML increased in destabilizing contexts.