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. 2003 Dec 1;330(1-2):53-60.
doi: 10.1016/j.physa.2003.08.022. Epub 2003 Sep 21.

Multiscale entropy analysis of human gait dynamics

M Costa  1   2 , C-K Peng  1 , Ary L Goldberger  1 , Jeffrey M Hausdorff  3   4
Affiliations

Multiscale entropy analysis of human gait dynamics

M Costa et al. Physica A. .

Abstract

We compare the complexity of human gait time series from healthy subjects under different conditions. Using the recently developed multiscale entropy algorithm, which provides a way to measure complexity over a range of scales, we observe that normal spontaneous walking has the highest complexity when compared to slow and fast walking and also to walking paced by a metronome. These findings have implications for modeling locomotor control and for quantifying gait dynamics in physiologic and pathologic states.

Keywords: Complexity; Human gait; Locomotion; Multiscale entropy; Neural control.

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Figures

Fig. 1.
Fig. 1.
Schematic illustration of the coarse-graining procedure for scales 2 and 3.
Fig. 2.
Fig. 2.
Representative stride interval time series obtained from a healthy subject who walked freely and in time to a metronome at slow, normal (usual) and fast rates. The last two time series are examples of randomized surrogate time series. They were generated by shuffling the values of the normal walking rate time series presented here.
Fig. 3.
Fig. 3.
(a) MSE analysis of Gaussian distributed white noise (mean zero, variance one) and 1/f noise. On the y-axis, the value of SampEn [4] for the coarse-grained time series is plotted. Original time series have 3 × 104 data points. The value of parameters m and r, defined in Ref. [7] are 2 and 0.15, respectively. The scale factor specifies the number of data points averaged to obtain each element of the coarse-grained time series. Symbols represent results of simulations and dotted lines represent analytic results. SampEn for coarse-grained white noise time series is analytically calculated by the expression: − ln∫−∞+∞12(τ/2π)[erf((x+r)/(2/τ))−erf((x−r)/(2/τ))]e−(1/2)x2τ dx (for any m ⩾ 1). τ and erf refer to the scale factor and to the error function, respectively. For 1/f noise time series, the analytic value of SampEn is a constant. Adapted from Ref [3]. (b) MSE analysis of a Guassian distributed white noise time series and 20 corresponding shuffled time series. The symbols refer to mean values of sample entropy (SampEn) for all time series and the broken lines to mean values ±SD. MSE curves for all time series should coincide with the analytic solution obtained for uncorrelated random noise. This is the case for scale one; but for larger scales, the dispersion of values around the analytic solution progressively increases due to the shortening of the length of the coarse-grained time series. To quantify these finite size effects, we calculated the area between the upper and lower curves, δ = 0.36. Two MSE curves were then considered significantly different if the area between them was > δ.
Fig. 4.
Fig. 4.
(a-d) MSE analysis of unconstrained walking time series derived from healthy subjects who walked for 1 h at slow, normal and fast rates (original time series), and of the corresponding surrogate shuffled time series. Curves represent lines connecting mean values of sample entropy (SampEn). The differences between mean MSE curves for physiologic and surrogate time series are all statistically significant. In all cases, physiologic time series are assigned higher entropy values than surrogate time series at larger scales. These results indicate that physiologic time series are more complex than surrogate ones. In addition, panel(d) shows that normal free walking dynamics are more complex than fast free walking dynamics, which in turn are more complex than slow free walking.
Fig. 5.
Fig. 5.
(a-d) MSE analysis of metronomically paced walking time series obtained from healthy subjects who walked at slow, normal and fast rates for 30 min, and of the corresponding surrogate time series. There is no qualitative difference between MSE curves corresponding to physiologic and surrogate time series. In all cases, the values of entropy monotonically decrease with the scale factor similar to white noise time series (Fig. 3), which indicates that all time series share a common random underlying dynamics.
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