Calculating sample entropy from isometric torque signals: methodological considerations and recommendations

Abstract

We investigated the effect of different sampling frequencies, input parameters and observation times for sample entropy (SaEn) calculated on torque data recorded from a submaximal isometric contraction. Forty-six participants performed sustained isometric knee flexion at 20% of their maximal contraction level and torque data was sampled at 1,000 Hz for 180 s. Power spectral analysis was used to determine the appropriate sampling frequency. The time series were downsampled to 750, 500, 250, 100, 50, and 25 Hz to investigate the effect of different sampling frequency. Relative parameter consistency was investigated using combinations of vector lengths of two and three and tolerance limits of 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, and 0.4, and data lengths between 500 and 18,000 data points. The effect of different observations times was evaluated using Bland-Altman plot for observations times between 5 and 90 s. SaEn increased at sampling frequencies below 100 Hz and was unaltered above 250 Hz. In agreement with the power spectral analysis, this advocates for a sampling frequency between 100 and 250 Hz. Relative consistency was observed across the tested parameters and at least 30 s of observation time was required for a valid calculation of SaEn from torque data.

Keywords: motor control; muscle contraction; nonlinear analysis; regularity; time series.

FIGURE 1

Experimental setup.

FIGURE 2

Power spectral density of the torque signals for each participant. Frequencies between 5.5 and 18.5 Hz and powers between 850 and 1,550 have been omitted.

FIGURE 3

Sample entropy of the time series with six different sampling frequencies for (A) the fixed observation time of 180 s and (B) the fixed number of 4,500 data points. * indicates significant decrease in sample entropy with increment in sampling frequency.

FIGURE 4

(A) Sample entropy of the time series sampled at 100 Hz for an observation time of 180 s with m = 2 or 3 and r = 0.10, 0.15, 0.20, 0.25, 0.30, 0.35 or 0.40. * indicates significant decrease in sample entropy with increase in r for a given m. $ indicates significant difference between m for a given r. (B) Sample entropy of the time series sampled at 100 Hz, with m = 2 and r = 0.2 and data lengths between 500 and 18,000 data points. A indicates significant different sample entropy from the time series with 500 data point and b indicates significant different sample entropy from the time series with 1,500 data point.

FIGURE 5

Bland-Altman plot of the difference in sample entropy between the first and second window of the time series against the average of the sample entropy from the two time series for the five different observation times. Solid horizontal line indicates sample entropy bias and dashed lines indicate upper and lower limits of agreement.