Abstract
Entropic half-life (ENT½) and statistical persistence decay (SPD) was recently introduced as measures of time dependency in stride time intervals during walking. The present study investigated the effect of data length on ENT½ and SPD and additionally applied these measures to stride length and stride speed intervals. First, stride times were collected from subjects during one hour of treadmill walking. ENT½ and SPD were calculated from a range of stride numbers between 250 and 2500. Secondly, stride times, stride lengths and stride speeds were collected from subjects during 16 min of treadmill walking. ENT½ and SPD were calculated from the stride times, stride lengths and stride speeds. The ENT½ values reached a plateau between 1000 and 2500 strides whereas the SPD increased linearly with the number of included strides. This suggests that ENT½ can be compared if 1000 strides or more are included, but only SPD obtained from same number of strides should be compared. The ENT½ and SPD of the stride times were significantly longer compared to that of the stride lengths and stride speeds. This indicates that the time dependency is greater in the motor control of stride time compared to that of stride lengths and stride speeds.
Highlights
A key feature of human walking is the time dependency in the stride-to-stride fluctuation of stride time (ST), stride length (SL) and stride speed (SS) (Hausdorff et al, 1995; Hausdorff et al, 1996; Terrier and Deriaz, 2011, 2012; Terrier et al, 2005)
In addition to ENT1⁄2, we introduced statistical persistence decay (SPD) which is based on the same rescaling method and applies detrended fluctuation analysis (DFA) to estimate the deterioration of statistical persistence over time in a time series
Increased with increase in strides and the post hoc test revealed a general pattern of a significant increase in SPD when the analyzed number of strides was increased with 750 strides (Fig. 2)
Summary
A key feature of human walking is the time dependency in the stride-to-stride fluctuation of stride time (ST), stride length (SL) and stride speed (SS) (Hausdorff et al, 1995; Hausdorff et al, 1996; Terrier and Deriaz, 2011, 2012; Terrier et al, 2005). Several studies have characterized this time dependency using entropy measures and detrended fluctuation analysis (DFA) to improve the fundamental understanding of walking motor control as well as describing the impairment induced by various diseases (Afsar et al, 2016; Alkjaer et al, 2015; Gates and Dingwell, 2007; Hausdorff, 2009; Hausdorff et al, 1997; Kaipust et al, 2012). DFA returns a scaling exponent describing the degree of statistical persistence or anti-persistence in a time series. While both methods quantify different characteristics of the time dependency in a time series, they do not return an output on an interpretable physiological or physical time scale.
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