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Is phase-dependent stability related to phase-dependent gait robustness?

Predicting gait robustness is useful for targeting interventions to prevent falls. A first step towards this is to properly quantify gait robustness. However, this step already comes with challenges, as humans can withstand different magnitudes of perturbations at different phases in a gait cycle. Earlier, we showed using a simple model that phase-dependent stability measures are limited to predict gait robustness. However, phase-dependent stability measures might relate to phase-dependent gait robustness. To study this, we simulated a ‘simple’ walker model that walks stably and periodically. We applied push and pull perturbations to the stance or swing leg at each phase of the single stance phase and evaluated how phase-dependent stability measures correlate with phase-dependent gait robustness. The latter was quantified via the maximum energy deviation induced by a perturbation that the walker could withstand without falling within 50 steps. Phase-dependent stability measures were obtained, after linearizing the system in a rotating hypersurface perpendicular to the periodic trajectory, via the maximum and the sum of the eigenvalues of the reduced Jacobian matrix, i.e., the trajectory-normal divergence rate. We did not find any strong association between phase-dependent stability measures and phase-dependent robustness. Combining this with our previous assessment of gait robustness, we conclude that phase-dependent stability does not allow for predicting gait robustness, let alone predicting fall risk.