Effect of parameter selection on entropy calculation for long walking trials

It is sometimes difficult to obtain uninterrupted data sets that are long enough to perform nonlinear analysis, especially in pathological populations. It is currently unclear as to how many data points are needed for reliable entropy analysis. The aims of this study were to determine the effect of changing parameter values of m, r, and N on entropy calculations for long gait data sets using two different modes of walking (i.e., overground versus treadmill). Fourteen young adults walked overground and on a treadmill at their preferred walking speed for one-hour while step time was collected via heel switches. Approximate (ApEn) and sample entropy (SampEn) were calculated using multiple parameter combinations of m, N, and r. Further, r was tested under two cases r*standard deviation and r constant. ApEn differed depending on the combination of r, m, and N. ApEn demonstrated relative consistency except when m = 2 and the smallest r values used (rSD = 0.015*SD, 0.20*SD; rConstant = 0 and 0.003). For SampEn, as r increased, SampEn decreased. When r was constant, SampEn demonstrated excellent relative consistency for all combinations of r, m, and N. When r constant was used, overground walking was more regular than treadmill. However, treadmill walking was found to be more regular when using rSD for both ApEn and SampEn. For greatest relative consistency of step time data, it was best to use a constant r value and SampEn. When using entropy, several r values must be examined and reported to ensure that results are not an artifact of parameter choice.