Approximate entropy based on attempted steady isometric contractions with the ankle dorsal- and plantarflexors: Reliability and optimal sampling frequency

Abstract

The aim of this study was to (1) examine the test–retest reliability of approximate entropy (ApEn) calculated for torque time-series from attempted steady isometric contractions performed at two different days, and (2) examine the significance of the sampling frequency for the ApEn values. Eighteen healthy young subjects (13 ± 3 years, mean ± 1 S.D.) performed attempted steady isometric submaximal contractions with the ankle dorsal- and plantarflexors at two different days. Relative (ICC 3.1) and absolute (standard error of measurement [S.E.M.], and S.E.M.%) test–retest reliability was assessed for the ApEn values calculated for torque time-series down-sampled to 30 and 100 Hz, respectively. The relative reliability was generally moderate (0.360 ≤ ICC 3.1 ≤ 0.897), with an absolute reliability (S.E.M.%) of 6–14%. The mean ApEn values varied considerably depending on the applied down-sampling frequency (5–200 Hz). When ApEn was used to quantify structure in the torque time-series, the relative and absolute reliability of steady isometric contractions with the ankle proved to be good in healthy young subjects. We propose that an optimal time-series down-sampling frequency exists for ApEn calculations, which will increase the sensitivity for biological system-changes, reduce adverse effects of random noise, and ensure that biological information in the signal is preserved. We recommend estimating this frequency using a variable high-pass filter-method for frequency analysis. Based on this method, the optimized time-series down-sampling frequency was around 30 Hz for the isometric contractions performed with the ankle in the present study.