On the calculation of sample entropy using continuous and discrete human gait data.

Andrew Arnold,William Denton,Jennifer Yentes,John McCamley,Peter Raffalt

doi:10.3390/e20100764

Abstract

Sample entropy (SE) has relative consistency using biologically-derived, discrete data >500 data points. For certain populations, collecting this quantity is not feasible and continuous data has been used. The effect of using continuous versus discrete data on SE is unknown, nor are the relative effects of sampling rate and input parameters m (comparison vector length) and r (tolerance). Eleven subjects walked for 10-minutes and continuous joint angles (480 Hz) were calculated for each lower-extremity joint. Data were downsampled (240, 120, 60 Hz) and discrete range-of-motion was calculated. SE was quantified for angles and range-of-motion at all sampling rates and multiple combinations of parameters. A differential relationship between joints was observed between range-of-motion and joint angles. Range-of-motion SE showed no difference; whereas, joint angle SE significantly decreased from ankle to knee to hip. To confirm findings from biological data, continuous signals with manipulations to frequency, amplitude, and both were generated and underwent similar analysis to the biological data. In general, changes to m, r, and sampling rate had a greater effect on continuous compared to discrete data. Discrete data was robust to sampling rate and m. It is recommended that different data types not be compared and discrete data be used for SE.

Highlights

Measures of entropy have become increasingly popular as a means to describe the predictability of a signal
Joint angles data were compared separately to range of motion data data
If the entropy of the dynamics within a cycle are of interest, it is recommended that careful consideration be given to sampling rate and input parameters, as results could be due to a parameter artifact and not a true finding

Summary

Introduction

Measures of entropy have become increasingly popular as a means to describe the predictability of a signal. Approximate entropy was introduced as a measure of regularity useful in differentiating periodic, deterministic, and chaotic signals [1]. This measure was originally developed on QRS intervals of heart rate data from the electrocardiogram [2] and has since been widely used for the assessment of heart rate variability [3,4,5,6,7,8,9]. The application of entropy measures to human gait data (e.g., joint angles and stride characteristics) provides valuable information of the movement dynamics executed by the human motor control system [18,19].

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