Statistical precision and sensitivity of measures of dynamic gait stability

Recently, two methods for quantifying a system's dynamic stability have been applied to human locomotion: local stability (quantified by finite time maximum Lyapunov exponents, lambda(S-stride) and lambda(L-stride)) and orbital stability (quantified as maximum Floquet multipliers, MaxFm). Thus far, however, it has remained unclear how many data points are required to obtain precise estimates of these measures during walking, and to what extent these estimates are sensitive to changes in walking behaviour. To resolve these issues, we collected long data series of healthy subjects (n=9) walking on a treadmill in three conditions (normal walking at 0.83 m/s (3 km/h) and 1.38 m/s (5 km/h), and walking at 1.38 m/s (5 km/h) while performing a Stroop dual task). Data series from 0.83 and 1.38 m/s trials were submitted to a bootstrap procedure and paired t-tests for samples of different data series lengths were performed between 0.83 and 1.38 m/s and between 1.38 m/s with and without Stroop task. Longer data series led to more precise estimates for lambda(S-stride), lambda(L-stride), and MaxFm. All variables showed an effect of data series length. Thus, when estimating and comparing these variables across conditions, data series covering an equal number of strides should be analysed. lambda(S-stride), lambda(L-stride), and MaxFm were sensitive to the change in walking speed while only lambda(S-stride) and MaxFm were sensitive enough to capture the modulations of walking induced by the Stroop task. Still, these modulations could only be detected when using a substantial number of strides (>150).