Table 1.
Subject Characteristics [15].
Fig 1.
Schematic of Multiscale Entropy Calculation.
(A) After the original EMG signal is bandpass filtered at 20–300 Hz, it is coarse grained to extract dynamics at different time scales. (B) Sample entropy (SampEn) is calculated from each coarse grained signal. For each pattern of m points in the signal (template example: ×-■), places in other parts of the signal where the template is seen are identified within tolerance r. SampEn is calculated as the negative natural log (-ln) of the conditional probability that the pattern of m+1 points (×-■-○) will match if that the pattern of m points (×-■) did match. In other words, after the signal matched the first two parts of the pattern ×-■, this is the probability that pattern match will complete, ×-■-○. The number of ×-■ matches are compared to the number of complete pattern (×-■-○) matches. Higher SampEn indicates that the signal is less predictable, and thus more irregular. (C) Multiscale view of the signal is derived by examining sample entropy of the EMG at each of the coarse-grained time scales. Complexity index CI is defined as the area under the curve. Higher CI indicates that the signal has unpredictable dynamics over a wide range of time scales, and thus more complex.
Fig 2.
Effect of EMG duty factor on the Multiscale Entropy of Simulated EMG.
Increasing EMG duty factor of EMG signals increased the SampEn of the EMG signal at the smaller timescales. This is because the signal is smoother on average in the short timescales, since the quiescent portions become very predictable as templates will match very often. In real EMG signals, EMG duty factor could confound the observed complexity differences between two signals.
Fig 3.
(A) RMS amplitude histogram. The EMG signal was divided into 25-ms portions and the root-mean-square (RMS) amplitude was calculated. Amplitude histogram is shown in (A). The 1st percentile was used to assume that this EMG activity is when the muscle is quiescent or “Off.” “On” was defined as 3× the RMS amplitude. (B) Sample EMG signal denoted with On/Off times. “On” portion is marked in dark blue; “Off” portion is marked in grey. This method identifies phasic bursts as “On” relative to the quiescent “Off” periods.
Fig 4.
Age and Walking Speed Effects on the Complexity Index.
The (unadjusted) complexity index CI are shown for vastus lateralis, biceps femoris, gastrocnemius, and tibialis anterior muscles as a function of the age group and walking speed. Error bars indicate standard deviation. CI decreased slightly with increasing walking speed in the proximal muscles. P-values are shown in the plot. Significant (p<0.05) pairwise Tukey-Kramer post-hoc tests are indicated with an asterisk (*). In vastus lateralis and biceps femoris, the two slow speeds were significantly different from the two fast speeds. After covariate adjustment with EMG duty factor, age-group differences were no longer present in biceps femoris (p = 0.06), but became noticeable in tibialis anterior (p<0.0001).
Fig 5.
Age and Walking Speed Effects on EMG duty factor.
The fraction of the time that vastus lateralis, biceps femoris, gastrocnemius, and tibialis anterior muscles as “on” within a gait cycle is plotted as a function of the age group and walking speed. Error bars indicate standard deviation. Older adults exhibited higher EMG duty factor than young adults except in tibialis anterior. Statistically significant P-values are shown in the plot.
Table 2.
Complexity Index Comparisons across m = 2–3 and r = 0.01–0.35 SD with and without Covariate Adjustment.
Fig 6.
Age and Timescale Effects on the Sample Entropy.
Sample entropy of the EMG signals for vastus lateralis, biceps femoris, gastrocnemius, and tibialis anterior were calculated for timescales 4–40 (27–270 Hz) after successive coarse-graining. The timescales and corresponding frequencies are shown on the abscissa of the plots. Error bars indicate standard deviations. SampEn values in general become smaller at larger timescales. Age-related differences are more noticeable at small timescales. Older adults exhibited lower SampEn values in the proximal muscles, and higher values in the gastrocnemius. Significant age-related differences (main effect of age) at α = 0.001 (≈ 0.05/37 scales tested) are shown with the dot (∙) above each timescale. Plotted mean and standard deviation values were pooled across walking speeds.
Fig 7.
Age and Timescale Effects on Sample Entropy stratified by Speed.
Sample entropy values are shown stratified by walking speed. Although the main effect of walking speed was present as shown in Fig 4, the trends between walking speeds are similar. The asterisk (*) denotes significant age-related differences as determined using Welch’s t-test (unequal variances, 2-tail). Compared to Fig 6, the age differences are not statistically significant except with gastrocnemius due to the less powerful t-test and the smaller sample size.