The validation of new phase-dependent gait stability measures: a modelling approach

Identification of individuals at risk of falling is important when designing fall prevention methods. Current stability measures that estimate gait stability and robustness appear limited in predicting falls in older adults. Inspired by recent findings of phase-dependent local stability changes within a gait cycle, we used compass-walker models to test several phase-dependent stability metrics for their usefulness to predict gait robustness. These metrics are closely related to the often-employed maximum finite-time Lyapunov exponent and maximum Floquet multiplier. They entail linearizing the system in a rotating hypersurface orthogonal to the period-one solution, and estimating the local divergence rate of the swing phases and the foot strikes. We correlated the metrics with the gait robustness of two compass walker models with either point or circular feet to estimate their prediction accuracy. To also test for the metrics' invariance under coordinate transform, we represented the point-feet walker in both Euler-Lagrange and Hamiltonian canonical form. Our simulations revealed that for most of the metrics, correlations differ between models and also change under coordinate transforms, severely limiting the prediction accuracy of gait robustness. The only exception that consistently correlated with gait robustness is the divergence of foot strikes. These results admit challenges of using phase-dependent stability metrics as objective measure to quantify gait robustness.