Approximate and Sample Entropy of the Center of Pressure During Unperturbed Tandem Standing: Effect of Altering the Tolerance Window - Jayla Wesley; Samhita Rhodes; David W. Zeitler; Gordon Alderink (Applied Sciences, 2025)
Approximate entropy (ApEn) and sample entropy (SampEn) are statistical indices designed to quantify the regularity or predictability of time-series data. Although ApEn has been a prominent choice in analyzing non-linear data, it is currently unclear which method and parameter selection combination is optimal for its application in biomechanics. This research aimed to examine the differences between ApEn and SampEn related to center-of-pressure (COP) data during tandem standing balance tasks, while also changing the tolerance window, r. Six participants completed five, 30 s trials, feet-together and tandem standing with eyes open and eyes closed. COP data (fs = 60 Hz, downsampled from 1200 Hz) from ground reaction force platforms were collected. ApEn and SampEn were calculated using a constant vector length, i.e., m = 2, but differing values of r (tolerance window). For each of the participants, four separate one-way analysis of variance analyses (ANOVA) were conducted for ApEn and SampEn along the anterior–posterior (AP) and medial–lateral (ML) axes. Dunnett’s intervals were applied to the one-way ANOVA analyses to determine which tandem conditions differed significantly from the baseline condition. ApEn and SampEn provided comparable results in the predictability of patterns for different stability conditions, with increasing instability, i.e., tandem eyes closed postures, being associated with greater unpredictability. The selection of r had a relatively consistent effect on mean ApEn and SampEn values across r = 0.15 × SD to r = 0.25 × SD, where both entropy methods tended to decrease as r increased. Mean SampEn values were generally lower than ApEn values. The results suggest that both ApEn and SampEn indices demonstrated relative consistency and were equally effective in quantifying the level of the center-of-pressure signal regularity during quiet tandem standing postural balance tests.