Approximate entropy (ApEn) and sample entropy (SampEn) are mathematical algorithms created to measure the repeatability or predictability within a time series. Both algorithms are extremely sensitive to their input parameters: m (length of the data segment being compared), r (similarity criterion), and N (length of data). There is no established consensus on parameter selection in short data sets, especially for biological data. Therefore, the purpose of this research was to examine the robustness of these two entropy algorithms by exploring the effect of changing parameter values on short data sets. Data with known theoretical entropy qualities as well as experimental data from both healthy young and older adults was utilized. Our results demonstrate that both ApEn and SampEn are extremely sensitive to parameter choices, especially for very short data sets, N ≤ 200. We suggest using N larger than 200, an m of 2 and examine several r values before selecting your parameters. Extreme caution should be used when choosing parameters for experimental studies with both algorithms. Based on our current findings, it appears that SampEn is more reliable for short data sets. SampEn was less sensitive to changes in data length and demonstrated fewer problems with relative consistency.

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BackgroundChronic obstructive pulmonary disease (COPD) is characterized by the frequent association of disease outside the lung. The objective of this study was to determine the presence of biomechanical gait abnormalities in COPD patients compared to healthy controls while well rested and without rest.MethodsPatients with COPD (N = 17) and aged-matched, healthy controls (N = 21) walked at their self-selected pace down a 10-meter walkway while biomechanical gait variables were collected. A one-minute rest was given between each of the five collected trials to prevent tiredness (REST condition). Patients with COPD then walked at a self-selected pace on a treadmill until the onset of self-reported breathlessness or leg tiredness. Subjects immediately underwent gait analysis with no rest between each of the five collected trials (NO REST condition). Statistical models with and without covariates age, gender, and smoking history were used.ResultsAfter adjusting for covariates, COPD patients demonstrated more ankle power absorption in mid-stance (P = 0.006) than controls during both conditions. Both groups during NO REST demonstrated increased gait speed (P = 0.04), stride length (P = 0.03), and peak hip flexion (P = 0.04) with decreased plantarflexion moment (P = 0.04) and increased knee power absorption (P = 0.04) as compared to REST. A significant interaction revealed that peak ankle dorsiflexion moment was maintained from REST to NO REST for COPD but increased for controls (P < 0.01). Stratifying by disease severity did not alter these findings, except that step width decreased in NO REST as compared to REST (P = 0.01). Standardized effect sizes of significant effects varied from 0.5 to 0.98.ConclusionsPatients with COPD appear to demonstrate biomechanical gait changes at the ankle as compared to healthy controls. This was seen not only in increased peak ankle power absorption during no rest but was also demonstrated by a lack of increase in peak ankle dorsiflexion moment from the REST to the NO REST condition as compared to the healthy controls. Furthermore, a wider step width has been associated with fall risk and this could account for the increased incidence of falls in patients with COPD.

Patients with COPD walk with increased duration of time between steps, and this timing is more variable than that of control subjects. They also walk with a narrower step width in which the variability of the step widths from step to step is decreased. Changes in these parameters have been related to increased risk of falling in aging research. This provides a mechanism that could explain the increased prevalence of falls in patients with COPD.

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