On the use of approximate entropy and sample entropy with centre of pressure time-series

• Published in: Journal of neuroengineering and rehabilitation Vol. 15; no. 1; pp. 116 - 15
• Main Authors: Montesinos, Luis, Castaldo, Rossana, Pecchia, Leandro
• Format: Journal Article
• Language: English
• Published: London BioMed Central 12.12.2018; BioMed Central Ltd; BMC
• Subjects: Adult; Adults; Aged; Algorithms; Approximate entropy; Balance; Biomedical and Life Sciences; Biomedical Engineering and Bioengineering; Biomedicine; Centre of pressure; Computer Simulation; Entropy; Entropy (Thermodynamics); Falls; Female; Human balance; Humans; Male; Mathematical analysis; Middle Aged; Models, Biological; Neurology; Neurosciences; Older people; Parameter sensitivity; Physiology; Postural Balance - physiology; Postural control; Posture; Posturography; Pressure; Rehabilitation Medicine; Sample entropy; Senses; Time series; Time series analysis; Variance analysis; Young Adult; Young adults; Singapore; Approximate entropy; Sample entropy; Posturography; Postural control; Human balance; Centre of pressure
• ISSN: 1743-0003; 1743-0003
• DOI: 10.1186/s12984-018-0465-9

Background Approximate entropy (ApEn) and sample entropy (SampEn) have been previously used to quantify the regularity in centre of pressure (COP) time-series in different experimental groups and/or conditions. ApEn and SampEn are very sensitive to their input parameters: m (subseries length), r (tolerance) and N (data length). Yet, the effects of changing those parameters have been scarcely investigated in the analysis of COP time-series. This study aimed to investigate the effects of changing parameters m , r and N on ApEn and SampEn values in COP time-series, as well as the ability of these entropy measures to discriminate between groups. Methods A public dataset of COP time-series was used. ApEn and SampEn were calculated for m  = {2, 3, 4, 5}, r  = {0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5} and N  = {600, 1200} (30 and 60 s, respectively). Subjects were stratified in young adults (age < 60, n  = 85), and older adults (age ≥ 60) with ( n  = 18) and without ( n  = 56) falls in the last year. The effects of changing parameters m , r and N on ApEn and SampEn were investigated with a three-way ANOVA. The ability of ApEn and SampEn to discriminate between groups was investigated with a mixed ANOVA (within-subject factors: m , r and N ; between-subject factor: group). Specific combinations of m , r and N producing significant differences between groups were identified using the Tukey’s honest significant difference procedure. Results A significant three-way interaction between m , r and N confirmed the sensitivity of ApEn and SampEn to the input parameters. SampEn showed a higher consistency and ability to discriminate between groups than ApEn. Significant differences between groups were mostly observed in longer ( N  = 1200) COP time-series in the anterior-posterior direction. Those differences were observed for specific combinations of m and r , highlighting the importance of an adequate selection of input parameters. Conclusions Future studies should favour SampEn over ApEn and longer time-series (≥ 60 s) over shorter ones (e.g. 30 s). The use of parameter combinations such as SampEn (m = {4, 5}, r = {0.25, 0.3, 0.35}) is recommended.