The EMG signal represents the superposition of motor unit action potentials from activated motor units and is commonly assessed to identify characteristics, such as firing rates of individual units (1) or recruitment of populations of units (2). Within an individual muscle, more generalized features of activity, such as the time of onset and offset and the magnitude of each burst, can also be determined from fluctuations in the intensity envelope of the EMG recorded during activities such as cycling. Additionally, the coordination of multiple muscles within each limb can also be assessed and has been shown to be a key determinate to cycling performance (3).
However, the structure (temporal organization of variability) within the EMG signal may also contain information on the challenge posed by a movement task and give us new insight to the motor control strategies that govern the muscles to meet these challenges. One way to determine the structure of a signal is to calculate its entropy (4), and for EMG signals this can be done using a particular approach termed sample entropy. Sample entropy (5) identifies how often small segments of data (with m sample points) from a signal would be identified within the signal (within a specified tolerance) compared to segments that contained one more (m + 1) sample point. A low value of sample entropy reflects a high degree of structure in the signal, with higher sample entropy reflecting a more chaotic structure. This approach was further developed (6) and has been used to quantify the rate at which signal structure decays within EMG signals (7) using a measure termed the entropic half-life (EnHL). Calculation of EnHL involves resampling the original EMG signal at increasingly larger time steps, to identify the time-scale at which structure in the signal is lost as the resampled signal transitions to containing random fluctuations.
Muscle activity during cycling varies with both cadence and power (3,8–15). When increasing the pedaling cadence the burst duration decreases (8) but not as much as the cycle duration, and so the duty cycle increases. All EMG signals recorded during cycling have structure reflecting the neuromuscular control of their motor units, and a theoretical analysis of the factors that shape surface EMG signals and their effect on EnHL predicted that EMG signals at the fastest cadences (short burst durations and longer duty cycles) would result in shorter EnHL (7). However, this is contrary to the view that high-cadence cycling represents a demanding task that would result in greater, or more persistent, structure to the neuromuscular control strategy. Whether EMG signal structure during cycling reflects structure to the neuromuscular control strategy is therefore not clear. We therefore aim to address this gap in knowledge by investigating structure of raw EMG, EMG intensity and muscle coordination patterns and how EnHL changes in response to cycling demand. Below we provide a rationale for why each signal may be expected to be structured and the physiological responses to the cycling demand that may influence that structure.
Within the raw EMG each motor unit action potential occurs at a distinct time and leaves characteristic spectral components in the EMG signal (16). If the variability in the EMG signal is organized over time (i.e., it is structured) the action potential shapes, amplitudes and the relative phase between different motor units potentials’ would be expected to influence the characteristics of the structure. As motor unit recruitment responds to the mechanical demands of cycling (17), changes in raw EMG signal structure would be predicted to occur in response to altered cycling mechanical demands.
The EMG intensity provides an envelope of the signal, smoothing out some of the time-dependent fluctuations from the raw EMG signal. It is therefore possible that EMG intensities from individual muscles may be more structured (i.e., fewer random fluctuations) than the raw EMG. This may mean that burst parameters within each muscle, such as burst duration and duty cycle, are the main factors influencing the individual EnHL. Cycling at higher cadences results in decreased burst duration (8), and higher duty cycles, that has led to predictions of shorter EnHL (7). These predictions have yet to be tested on experimental data.
Muscle coordination patterns that consist of the EMG intensities from many different muscles may show greater variability due to the higher-dimensionality of the additional muscles, and so the EnHL for coordination may be shorter than for the individual muscles as the more variable structure of the coordination may dissipate over shorter time scales. Entropic half-lives from such multi-muscle coordination patterns may reflect the net response of the neuromuscular system and may therefore provide insight into the structure of variability of muscle recruitment patterns tolerated by the nervous system for different task demands. Enders et al. (18) showed an increase in EnHL from 9 to 16 ms between 150 and 300 W power conditions for cycling at 90 rpm However, it is not known if this finding can be generalized across a range of cycling conditions particularly as the variability in and composition of the muscle coordination during cycling depends in a complex and nonlinear fashion on both the power output and the cadence (8).
The purpose of this study was thus to explore the EnHL from the level of the raw EMG signal through to multi-muscle coordination patterns during cycling. We address the question of whether the EnHL at these different signal levels vary with the opposing demands of the cycling task (high power output and cadence), or with EMG parameters (burst duration and duty cycle).
The entropic half-life, EnHL, was determined from a large cycling data set that has been described in a previous study (15). In brief, nine club to national level racing cyclists pedaled on an indoor ergometer at a range of cadences (60, 80, 100, 120, and 140 rpm) at a low and fixed crank torque of 6.5 N·m, and also cycled at a range of crank torques (12.9, 25.1, 32.4 and 39.9 N·m) at the low cadence of 60 rpm Cyclists pedaled for 5 to 10 s to reach a steady-state speed, and then data were recorded for a further 30 s for each trial. The cycle conditions were presented in a random order, and repeated in three blocks to minimize bias due to increasing fatigue and body temperature. A total of 6804 pedal cycles were analyzed (9 subjects × 3 blocks × 9 conditions × 28 cycles per condition). Pedaling cadence was maintained using visual feedback, and independently recorded with a pedal switch; post analysis showed it was on average 1.3 rpm higher than the target velocity, and varied with a standard deviation of only 1.1 rpm within each trial; there was a slight increase in variability in pedal cadence at the higher cadences, with the 140 rpm trials having standard deviations of 1.8 rpm. A 45-s rest period was given between each condition. Each participant gave written informed consent in accordance with the Simon Fraser University’s policy on research using human subjects.
Bipolar Ag/AgCl surface EMG electrodes (10 mm diameter, 21 mm interelectrode distance) were placed in the center of the muscle bellies of the tibialis anterior, medial gastrocnemius, lateral gastrocnemius, soleus, vastus medialis, rectus femoris, vastus lateralis, biceps femoris long head, semitendinosus, and gluteus maximus of the left leg and surface EMG was recorded at 2000 Hz. A pedal switch allowed the time of top-dead center to be identified.
The entropic half-life, EnHL, was calculated for each signal using the following procedure. Initially, the EnHL was calculated from the raw EMG signals (as directly recorded from the EMG amplifiers). These signals were filtered (Butterworth, high-pass with 10 Hz cutoff) and standardized to have a mean of zero and standard deviation of one. The SampEn was calculated using a freely available software package (19). SampEn(m, r, N) quantifies the regularity of a time series of length N, reflecting the conditional probability that two sequences of m consecutive data points, similar to one another within a tolerance (r), will remain similar when a consecutive data point is added (20). Values of m = 0 and m = 1, were recorded with r = 0.2 for a range of reshape-scales from 1 ms to 1 s (6). For each reshape-scale, the SampEn for m = 1 was normalized to the corresponding SampEn for m = 0 (which can be interpreted as the negative logarithm of the probability of a match of length one (19)): this stage is computationally faster but equivalent to normalizing to the random permutation of the signal as described by Enders and co-workers (18). EnHL is the time-scale at which the normalized SampEn (from across the reshape-scales) reached a value of 0.5 (18), indicating the time-scale that the time series transitioned from ordered to random structure. It therefore provides a measure of the persistence of structure in the EMG intensity envelopes from each individual muscle.
The intensity envelope for the EMG signals was calculated for each muscle, using an EMG-specific wavelet analysis (21), where each wavelet k had a center frequency fc(k), and the sum of the intensities ik over the frequency band 11 to 432 Hz (1 ≤ k ≤ 10) generated the total intensity that was a close approximation to the power within the EMG signal. The mean frequency fm for the EMG intensity (16) was:
The EMG intensities for each muscle and trial were mean normalized and each intensity trace was resampled at 1000 Hz. The burst durations for the normalized EMG intensities were taken as the duration that the intensity was greater than 5% of the maximum for each pedal cycle, and the duty cycle was the proportion of this burst duration relative to the period of each pedal cycle. The mean frequencies of the EMG intensities were calculated for each pedal cycle. Entropic half-lives were calculated for the EMG intensities in the same manner as describe above for the raw EMG signals.
The muscle coordination patterns were quantified by principal component analysis. For each cycling trial the coordination patterns for each time instant were generated from the normalized EMG intensities for all ten muscles, and placed in an P × N matrix A (P = 10 muscles, N is number of time points for 28 pedal cycles at the 1000 Hz sample rate). The mean intensity vector (mean intensity for each muscle in A) was subtracted from A, from which the covariance matrix B was calculated. The principal components (PC) of A were described by Eigen analysis of B: the PC loading scores were calculated from ξ′A, where ξ′ are the transpose of the Eigen vectors of B and were ordered into decreasing Eigen values. The loading scores for the first six PC explained 91% of the variance within matrix B, and were used as signals for the EnHL analysis, as above, providing a measure of the persistence of structure in the multi-muscle coordination patterns.
The EnHL was additionally calculated for phase-randomized surrogates (18) of the raw EMG signals and the EMG intensity envelopes for each muscle and each trial. Phase-randomized surrogate signals have the same power spectrum and autocorrelation as the original signal; however, the structure encoded in the phase is removed. The process of phase-randomization removes structure due to the bursting patterns of the EMG, due to regularity of firing or synchronization of the motor units, and from the shape of the individual motor unit action potentials (Fig. 1). Thus, the surrogate signals can be used as reference values for signals with no structure (18).
The factors influencing the EnHL values were tested using mixed model analyses of covariance (Minitab version 16; State College, PA): cadence, power, burst duration, duty cycle and EMG intensity were included as covariates, and subject was a random factor. ANCOVA were evaluated for the EnHL for the raw EMG and for the EMG intensities, and these used the muscle as an additional factor and muscle–power, cadence–power, and muscle–cadence as interaction terms. A third ANCOVA was evaluated for the EnHL for PC loading scores, and this used the PC number as an additional factor, and PC number–power, cadence–power and PC number–cadence as interaction terms. For this ANCOVA, the burst duration, duty cycle and EMG intensity values used as covariates were taken as the mean values across the 10 muscles. Statistical effects were deemed significant at P < 0.05, and data are reported as mean ± standard error of the mean.
The cycling conditions encompassed a range of powers, of which a set was at a low cadence of 60 rpm but at increasing crank torques, whereas a second set was at a low crank torque but with increasing cadence. There was a general increase in EMG intensity for each muscle with power, with greater EMG intensities occurring for the higher-cadence conditions for each given power (Fig. 2A). There was a cadence-specific effect on the burst durations with shorter burst durations occurring for faster cycling cadences (Fig. 2B). There was a general but small increase in duty cycle with power for all muscles (Fig. 2C).
The mean EnHL for each muscle for the phase-randomized surrogate EMG ranged between 5.23 ± 0.04 and 9.05 ± 0.05 ms (N = 269). These EnHL showed a strong negative correlation with the mean frequency of the EMG intensities (r2 = 0.94; Fig. 3A), with even higher correlations occurring (r2 = 0.98) when the EnHL for the phase-randomized surrogate EMG intensities were correlated against the period of the mean frequencies (1 / mean frequency) of the EMG intensities.
The mean EnHL for each muscle for the raw EMG were typically greater than their phase-randomized values and ranged between 1.32 ± 0.10 and 45.64 ± 5.50 ms (N = 28) for the least demanding condition of 60 rpm at 35 W. The mean EnHL for each muscle for the raw EMG showed a general decrease at the higher cadences when the torque was held constant (Fig. 4A). As the torque increased for the low cadence conditions there was an increase in EnHL for the raw EMG signals for vastus medialis, rectus femoris, vastus lateralis, and gluteus maximus, with a decrease for the remaining muscles (Fig. 4B). The EnHL for each muscle for the raw EMG neither correlated with the EnHL for the phase-randomized raw EMG (0.01 < r2 < 0.15), nor with the mean frequency of the EMG intensities (0.01 < r2 < 0.10; Fig. 3B).
The EnHL for the EMG intensities ranged between 20.26 ± 1.40 and 36.70 ± 1.67 ms (N = 28) for the least demanding condition of 60 rpm at 35 W. There was a general decrease in the EnHL to values between 17.98 ± 0.59 and 24.16 ± 0.38 ms as power output increased for both the increasing torque and increasing cadence conditions, with the EnHL being more sensitive to changes in cadence than crank torque (Fig. 5). However, the exception to this was the quadriceps muscles that increased their EnHL for the increasing torque conditions to reach their maxima, between 32.81 ± 1.80 and 35.71 ± 1.44 ms, at the 260 W power. The ANCOVA showed that decreases in EnHL were significantly associated with increases in both cadence and power, and the EnHL showed a significant negative association with EMG intensity and duty cycle, and a positive association with burst duration (Table 1). The mean EnHL for the EMG intensities for each muscle was greater than the mean EnHL for the intensities of the phase-randomized surrogate EMG and correlated with neither the mean frequencies of the EMG intensities (r2 < 0.01), nor with the EnHL for the intensities of the phase-randomized signals (r2 < 0.01).
The EnHL for the PC loading scores describing the muscle coordination patterns were shorter than the EnHL for the EMG intensities for the individual muscles (Fig. 6). The EnHL for the muscle coordination patterns ranged between 14.81 ± 1.22 and 21.80 ± 1.81 ms (N = 28) for the least demanding condition of 60 rpm at 35 W. The ANCOVA (Table 1) showed significant interaction effects PC number, with the higher PCs resulting in lower EnHL (Fig. 5A). The EnHL increased with burst duration, and a significant interaction between PC number–cadence showed a greater cadence dependence for the higher PCs (Fig. 6A).
Is there information in the EMG signal related to EnHL?
The entropic half-life analysis in this study shows that there is persistent and nonrandom structure in all levels of the EMG signals analyzed, indicating that further investigation of structure in EMG is warranted. The phase of a signal has been shown to contain important information (22). At the level of the raw EMG, this may reflect the shapes of the motor unit action potentials, variability (or lack off) in the firing rates of the motor units and coherence between different motor units. The raw EMG signals typically had longer EnHL than their phase-randomized surrogates (Fig. 3), so there is information in the phase properties of the EMG. The EnHL for the phase-randomized signals correlated with the mean frequency of the EMG and is of similar time scale to the period of that mean frequency. This suggests that the fundamental presence of voltage fluctuations (from the motor unit action potentials that make up the raw EMG) that occur at distinct times and with distinct frequency properties, manifest as time-dependent structure to the phase within that signal. Each motor unit action potential occurs at a distinct time and leaves characteristic spectral components in the surface EMG signal (16), and these can also be resolved using time-frequency signal processing techniques, such as wavelet analysis (21,23). The raw EMG had more persistent structure (longer EnHL) than the phase-randomized surrogate signals, but these EnHL no longer correlated with the mean frequency of the EMG (Fig. 3B). Thus the additional structure within the raw EMG derived from other features that are likely to include variability in the discharge of individual motor units (24,25), synchronicity between motor units (26) and activation-deactivation burst duration and duty cycle. This persistent structure and thus information in the raw EMG (Fig. 4) was also found in the individual muscle EMG intensity envelopes (Fig. 5) and in the multimuscle coordination patterns (Fig. 6), although the timescale over which structure persisted and the changes in response to cycling demand differed. The factors that may cause these differences are therefore considered below.
Why does EnHL differ between the EMG signals analyzed?
The raw surface EMG signals are the superposition of motor unit action potentials in the underlying muscle. Frequency information in the raw signal is strongly correlated with EnHL, even when the EMG is phase-randomized, and this information reflects the time-varying voltage fluctuations of the constituent motor unit action potentials. The raw EMG signals and the EMG intensities additionally contain phase-related information seen by their EnHL being longer than their phase-randomized surrogates. The EMG signals are the convolution of the firing statistics and the time-varying properties of the individual motor unit action potentials, and so additional information in the EnHL for the EMG intensities likely derives from the structure and variability in the firing. This structure is related to the discharge of individual motor units and synchronicity between motor units, both of which vary with activation levels and the proficiency for doing tasks. Although the EnHL for the EMG intensities was related to the burst durations for the EMG, they were considerably shorter than for those burst durations, and so fluctuations in the firing statistics are more rapid than each burst of activity. The EnHL values from the EMG intensities of individual muscles were generally longer than those for the raw signals, likely reflecting smoothing out some of the time-dependent fluctuations in the raw EMG when the envelope of the signal is calculated. This means that burst parameters, such as duration and duty cycle, may dominate the structure of the EMG intensity signal and indeed ANCOVA revealed a negative associations between EnHL and duty cycle, and a positive association between EnHL and burst duration (Table 1); and this is consistent with changes in EnHL that were simulated across this physiological range (7). It is these changes in burst duration that appear to play the major role in affecting the EnHL in these EMG intensities. It is of note that the burst durations (177.4–526.8 ms) were an order of magnitude greater than the EnHL values (15.7–36.7 ms; Fig. 5), and thus the reason for the reduced EnHL is probably not limited by the actual burst duration. In the quadriceps muscles, however, there were longer EnHL in the raw EMG than in the EMG intensities in some cycling conditions. Structure persisted over longer periods within the raw signals from these muscles when compared to others (Fig. 4), and this structure must have been related to time-dependent fluctuations in the raw EMG that were removed when the intensity envelope was calculated. The significance of these differences is difficult to determine from the data available from this study, but it is interesting to note that these muscles were the only ones in which significant changes in EnHL occurred between cycling conditions (greater EnHL associated with increasing torque conditions). It could be suggested that differences in motor unit (e.g., size, spatial distribution) and muscle anatomical (e.g., size, fiber pennation angle) features could combine to influence the raw EMG signals and hence EnHL. However, similar EnHL values occurred across all muscles for some of the cycling conditions (e.g., Fig. 4), suggesting that the raw EMG signal properties altered in response to task demand. Important time-varying differences in the neuromuscular drive across individual muscles may therefore occur in response to task demands. These may reflect differences in the neuromuscular control required to elicit different mechanical roles of each muscle over the time course of a task (e.g., power production, force transfer), the dynamics of which warrant further investigation. No muscle works in isolation, however, and as such, it is valuable to consider the amalgamated responses of multiple muscles to task demand. Here, this was done by combining the intensity traces into multi-muscle coordination patterns, quantified by their PC loading scores, which resulted in EnHL that were shorter than the EnHL for the individual muscles. This was as expected, because the more muscles that are amalgamated into coordination patterns the more ways in which those patterns can vary, or the greater the chance the signal structure will dissipate. The EnHL for the coordination calculated from this study are generally longer than those reported by Enders et al. (18); however, the calculated EnHL are sensitive to the filter cutoff frequencies used before the sample entropy analysis: in this study the data were low-pass filtered with a 10 Hz cutoff due to the pedal cadences reaching 140 rpm, as opposed to the Enders et al. (18) study where 2.5 Hz was used related to the cadence of 90 rpm.
Why does EnHL differ across cycling conditions?
Variability is a ubiquitous and fundamental characteristic of human movement (27), however variability may decrease with task constraints such as maximizing power output or pedaling velocity. Previous studies have shown that the dimensionality of muscle coordination patterns reduces for pedaling at greater power outputs (18,28), and the variability of the muscle coordination patterns reduces at high cadences (8). However, the approaches used in those studies did not consider the temporal organization of variability that can be studied using the EnHL approach. Specifically, by analyzing the structure of signals over the time course of the whole trial EnHL includes consideration of how one pedal cycle impacts subsequent cycles (i.e., effects of the order of data points across multiple pedal cycles is conserved in the analysis). The EnHL for the EMG intensities for the quadriceps muscles increased with power output for the low cadence, with increasing torque conditions. However, the EnHL for the remaining muscles, and for the increasing cadence conditions, showed general decreases with both power and cadence (Fig. 5). Although the average variability of muscle coordination decreases with greater task demand (8,18,28), the data presented here suggest that the time-dependent structure of these coordination patterns has greater variability during more challenging movement tasks. The shorter EnHL recorded may reflect greater interference, or more frequent adjustments, from the central nervous system or may suggest that during more challenging tasks the nervous system was more tolerant of time-varying fluctuations in coordination patterns; as has been suggested for postural balance tasks (29,30). Further assessment of the temporal structure of variation in muscle coordination patterns and changes in response to task demand are therefore warranted.
Previously, the EnHL for muscle coordination patterns has been shown to increase for cycling at higher power output (18). The muscle coordination patterns were calculated from the time-varying EMG intensities from seven lower extremity muscles that included three of the quadriceps, and it was found that the principal coordination pattern for the high-power condition was dominated by signal from the rectus femoris (18). In our current study, the rectus femoris was one of the muscles that showed an increase in EnHL as crank torque increased (Fig. 5B). However, the coordination patterns determined here contain signals from 10 muscles, of which the majority did not show increases in EnHL with power (Fig. 5). Furthermore, due to the large number of different conditions that we tested, we calculated a common set of principal coordination patterns across all conditions: although such patterns are influenced by the variability in the EMG intensity from the rectus femoris, the other muscles still have substantial contribution across all principal patterns that are identified (8) and these muscles showed decreasing EnHL with increased power output. These methodological differences explain the finding in this study that the EnHL for the muscle coordination patterns did not increase with the increasing power (at a fixed cadence) conditions.
It is possible that the EnHL (for both individual muscles and for the coordination between muscles) would have showed greater increases related to the increased demands of cycling at higher power outputs than those tested in this study. It should be noted that the highest power tested in this study (260 W) is considerably less than the maximum powers that can be achieved by competitive cyclists (of over 1000 W; (31)) and so may have only been of limited challenge to the cyclists tested. Additionally, the relative intensities of the cycle conditions were not normalized to the maximum power achievable by each participant, and so the relative demands of the conditions may also vary between the cyclists tested.
We therefore conclude that there is structure at all levels of the EMG signals analyzed here, with the persistence of this structure differing between muscles and in response to cycling task demand. Differences in structure relate to the underlying motor unit recruitment patterns and interact with the EMG burst parameters. Further work is, however, required to determine the functional significance of the changes found here and to improve understanding of neuromuscular control of time-dependent changes in muscle recruitment during dynamic tasks.
The authors thank Tamara Horn for assistance during the original data collection.
There are no professional relationships with companies or manufacturers to disclose for all authors. This research was supported by the Natural Sciences and Engineering Research Council of Canada. The results of the present study do not constitute endorsement by the American College of Sports Medicine. The authors declare that the results of the study are presented clearly, honestly, and without fabrication, falsification, or inappropriate data manipulation.
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