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

Jian Jin,Sjoerd M Bruijn,Andreas Daffertshofer,Jaap H Van Dieën,Dinant Kistemaker

doi:10.1098/rsos.201122

Abstract

Identification of individuals at risk of falling is important when designing fall prevention methods. Current measures that estimate gait stability and robustness appear limited in predicting falls in older adults. Inspired by recent findings on changes in phase-dependent local stability within a gait cycle, we devised several phase-dependent stability measures and tested for their usefulness to predict gait robustness in compass walker models. These measures are closely related to the often-employed maximum finite-time Lyapunov exponent and maximum Floquet multiplier that both assess a system's response to infinitesimal perturbations. As such, they entail linearizing the system, but this is realized in a rotating hypersurface orthogonal to the period-one solution followed by estimating the trajectory-normal divergence rate of the swing phases and the foot strikes. We correlated the measures with gait robustness, i.e. the largest perturbation a walker can handle, in two compass walker models with either point or circular feet to estimate their prediction accuracy. To also test for the dependence of the measures under state space transform, we represented the point feet walker in both Euler–Lagrange and Hamiltonian canonical form. Our simulations revealed that for most of the measures their correlation with gait robustness differs between models and between different state space forms. In particular, the latter may jeopardize many stability measures' predictive capacity for gait robustness. The only exception that consistently displayed strong correlations is the divergence of foot strike. Our results admit challenges of using phase-dependent stability measures as objective means to estimate the risk of falling.

Highlights

Falling is a major threat, especially for older adults
In order to evaluate how well these phase-dependent stability measures and the local divergence exponent predict gait robustness, we correlated them with gait robustness (= maximum perturbation the model could handle), given our sets of parameter combinations
Before selecting our correlation measure, the general rubric for a ‘good correlation’ maintains that (i) for a given stability measure value, there should be a small variation in the corresponding gait robustness; (ii) a monotonic increasing stability measure should be able to predict a monotonic increasing or decreasing gait robustness

Summary

Introduction

Falling is a major threat, especially for older adults. About one-third of all adults older than 65 years fall at least once per year, often with serious injuries and fractures as consequences [1]. Lockhart & Liu [6] and Toebes et al [7] suggested that the local divergence exponent may allow for discriminating fallers from non-fallers, with accuracy of 80% at best [8]. 80% accuracy is a fair achievement in view of the complexity of the dynamics involved in human walking, it may still lead to a large number of false positives ( predicted fallers that are not prone to fall) and—arguably worse—false negatives ( predicted non-fallers that are prone to fall) of the elderly population. A higher accuracy in fall prediction is of great importance

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Discussion

Conclusion