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Dynamic Stability of Gait Cycles as a Function of Speed and System Constraints

Ugo H. Buzzi and Beverly D. Ulrich

The purpose of this study was to examine the dynamic stability of two groups of children with different dynamic resources in changing contexts. The stability of the lower extremity segments of preadolescent children (8–10 years old) with and without Down syndrome (DS) was evaluated as children walked on a motorized treadmill at varying speeds. Tools from nonlinear dynamics, maximum Lyapunov exponent, and approximate entropy were used to assess the behavioral stability of segmental angular displacements of the thigh, shank, and foot. Our results suggest that children with DS show decreased dynamic stability during walking in all segments and that this might be a consequence of inherently different subsystem constraints between these groups. Differences between groups also varied, though not uniformly, with speed, suggesting that inherent differences could further constrain the behavioral response to changing task demands.

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Lyapunov Exponent and Surrogation Analysis of Patterns of Variability: Profiles in New Walkers With and Without Down Syndrome

Beth A. Smith, Nick Stergiou, and Beverly D. Ulrich

In previous studies we found that preadolescents with Down syndrome (DS) produce higher amounts of variability (Smith et al., 2007) and larger Lyapunov exponent (LyE) values (indicating more instability) during walking than their peers with typical development (TD) (Buzzi & Ulrich, 2004). Here we use nonlinear methods to examine the patterns that characterize gait variability as it emerges, in toddlers with TD and with DS, rather than after years of practice. We calculated Lyapunov exponent (LyE) values to assess stability of leg trajectories. We also tested the use of 3 algorithms for surrogation analysis to investigate mathematical periodicity of toddlers’ strides. Results show that toddlers’ LyE values were not different between groups or with practice and strides of both groups become more periodic with practice. The underlying control strategies are not different between groups at this point in developmental time, although control strategies do diverge between the groups by preadolescence.