Ankle Joint Angle Influences Relative Torque Fluctuation during Isometric Plantar Flexion

The purpose of this study was to investigate the influence of changes in muscle length on the torque fluctuations and on related oscillations in muscle activity during voluntary isometric contractions of ankle plantar flexor muscles. Eleven healthy individuals were asked to perform voluntary isometric contractions of ankle muscles at five different contraction intensities from 10% to 70% of maximum voluntary isometric contraction (MVIC) and at three different muscle lengths, implemented by changing the ankle joint angle (plantar flexion of 26°-shorter muscle length; plantar flexion of 10°-neutral muscle length; dorsiflexion of 3°-longer muscle length). Surface electromyogram (EMG) signals were recorded from the skin surface over the triceps surae muscles, and rectified-and-smoothed EMG (rsEMG) were estimated to assess the oscillations in muscle activity. The absolute torque fluctuations (quantified by the standard deviation) were significantly higher during moderate-to-high contractions at the longer muscle length. Absolute torque fluctuations were found to be a linear function of torque output regardless of muscle length. In contrast, the relative torque fluctuations (quantified by the coefficient of variation) were higher at the shorter muscle length. However, both absolute and relative oscillations in muscle activities remained relatively consistent at different ankle joint angles for all plantar flexors. These findings suggest that the torque steadiness may be affected by not only muscle activities, but also by muscle length-dependent mechanical properties. This study provides more insights that muscle mechanics should be considered when explaining the steadiness in force output.


Introduction
Force (or torque) fluctuations in the low-frequency (<1 Hz) band are well-known to arise during voluntary sustained isometric contractions in human skeletal muscles [1]. Such fluctuations, often quantified by standard deviation (SD) or coefficient of variation (CoV), appear to be a useful biomarker to help us understand motor performance. For example, greater force fluctuations have been observed in individuals in aging [2][3][4], musculoskeletal injuries [5,6] and neurophysiology disorders [3], demonstrating significant correlation with motor function [1,7]. Accordingly, a systematic investigation into underlying mechanisms of force fluctuations is essential for understanding motor activities and for improving motor control ability in broad clinical populations.
Force fluctuations were found to be closely related to variability in the recruitment and rate-coding properties of the motor units [8]. Both experimental and simulation studies demonstrated a linear increase of SD for force (F SD ) with increasing voluntary isometric contraction level [9]. Such increase in F SD can be explained by the presence of

Experimental Protocol
Plantar flexion contractions with the right leg were performed at three ankle joint angles: ankle joint angles at 87°, at 100°, and at 116° (the angle between shank and sole of foot), corresponding to longer, neutral, and shorter muscle lengths, respectively. Each configuration was set by adjusting the foot-plate position. At each ankle joint angle, three MVICs were performed, and the averaged value of these was used to estimate the target submaximal contraction torque. Each subject was asked to perform isometric contractions at 10%, 20%, 30%, 50%, and 70% MVIC. Visual feedback was provided in real time involving reaching the target level from rest state (5-10 s) and then maintaining at the target level ± 3% MVIC for at least 6 s. Each contraction level was repeated three times. To minimize the effects from systematic muscle fatigue, the orders of the ankle joint angles and target contraction levels were randomized, and at least a 30 s break was provided between trials.

Data Analysis
The torque signals were low-pass filtered using a fourth-order Butterworth filter with a cutoff frequency at 6 Hz. Raw EMG signals were band-pass filtered using a fourth-order Butterworth filter with a passband of 20-450 Hz. The filtered EMG signals were then rectified and smoothed by applying a fourth-order Butterworth filter with a cutoff frequency of 2 Hz (hereafter called rsEMG).
To determine a representative stable measure of the variability of muscle contractions for each trial, a 4 s segment in the middle of each sustained contraction was chosen by calculating the minimum standard deviation in the filtered torque signals. Using this time segment, both absolute and relative variability for the filtered torque signals were quantified as SD and as the CoV, respectively. Hereafter, absolute and relative variability for torque is called TSD and TCoV. CoV was defined as the ratio of SD to the mean torque value of the segment. Both absolute and relative variability values for the rsEMG of each plantar flexor (MGSD, LGSD, and SOLSD; MGCoV, LGCoV, and SOLCoV) were calculated to examine the oscillations in muscle activities. Figure 2 shows representative detrended torque trials and rsEMG signals from a representative subject.

Experimental Protocol
Plantar flexion contractions with the right leg were performed at three ankle joint angles: ankle joint angles at 87 • , at 100 • , and at 116 • (the angle between shank and sole of foot), corresponding to longer, neutral, and shorter muscle lengths, respectively. Each configuration was set by adjusting the foot-plate position. At each ankle joint angle, three MVICs were performed, and the averaged value of these was used to estimate the target submaximal contraction torque. Each subject was asked to perform isometric contractions at 10%, 20%, 30%, 50%, and 70% MVIC. Visual feedback was provided in real time involving reaching the target level from rest state (5-10 s) and then maintaining at the target level ± 3% MVIC for at least 6 s. Each contraction level was repeated three times. To minimize the effects from systematic muscle fatigue, the orders of the ankle joint angles and target contraction levels were randomized, and at least a 30 s break was provided between trials.

Data Analysis
The torque signals were low-pass filtered using a fourth-order Butterworth filter with a cutoff frequency at 6 Hz. Raw EMG signals were band-pass filtered using a fourthorder Butterworth filter with a passband of 20-450 Hz. The filtered EMG signals were then rectified and smoothed by applying a fourth-order Butterworth filter with a cutoff frequency of 2 Hz (hereafter called rsEMG).
To determine a representative stable measure of the variability of muscle contractions for each trial, a 4 s segment in the middle of each sustained contraction was chosen by calculating the minimum standard deviation in the filtered torque signals. Using this time segment, both absolute and relative variability for the filtered torque signals were quantified as SD and as the CoV, respectively. Hereafter, absolute and relative variability for torque is called T SD and T CoV . CoV was defined as the ratio of SD to the mean torque value of the segment. Both absolute and relative variability values for the rsEMG of each plantar flexor (MG SD , LG SD , and SOL SD ; MG CoV , LG CoV , and SOL CoV ) were calculated to examine the oscillations in muscle activities. Figure 2 shows representative detrended torque trials and rsEMG signals from a representative subject.

Statistical Analysis
A Kolmogorov-Smirnov test was performed to assess the normality of the data for each test. Since the normality test on the major outcomes rejected the null hypothesis, a log transformation was applied. Given the evaluation of their skewness and kurtosis after log transformation, the data distributions were acceptable to conduct recommended parametric tests [21]. Thus, a two-way, repeated-measures ANOVA was performed to examine the differences in the log-transformed torque measurement outcomes (T SD and T CoV ) and oscillations of muscle activities at the five contraction levels and three ankle joint angles via the SPSS (IBM Corp., Armonk, NY, USA) with a significance level (α) of 0.05. When necessary, post hoc pairwise multiple comparisons with Bonferroni correction were used. In any case the sphericity assumption was violated, Greenhouse-Geisser would be used instead.

Statistical Analysis
A Kolmogorov-Smirnov test was performed to assess the normality of the data for each test. Since the normality test on the major outcomes rejected the null hypothesis, a log transformation was applied. Given the evaluation of their skewness and kurtosis after log transformation, the data distributions were acceptable to conduct recommended parametric tests [21]. Thus, a two-way, repeated-measures ANOVA was performed to examine the differences in the log-transformed torque measurement outcomes (TSD and TCoV) and oscillations of muscle activities at the five contraction levels and three ankle joint angles via the SPSS (IBM Corp., Armonk, NY, USA) with a significance level (α) of 0.05. When necessary, post hoc pairwise multiple comparisons with Bonferroni correction were used. In any case the sphericity assumption was violated, Greenhouse-Geisser would be used instead.
Stepwise regression analysis was applied to test what is the more dominant contributor to the changes in TCoV with contraction levels and ankle joint angles. To determine the dominant muscle that contributes to the changes in torque variability with contraction levels, the data were collapsed across the contraction levels, and the stepwise regression analysis was conducted at each ankle joint angle. When determining the dominant muscle that contributes to the changes in torque variability with the ankle joint angle at each contraction level, the data were collapsed across the ankle joint angles, and the analysis was conducted at each contraction level. Stepwise regression analysis was applied to test what is the more dominant contributor to the changes in T CoV with contraction levels and ankle joint angles. To determine the dominant muscle that contributes to the changes in torque variability with contraction levels, the data were collapsed across the contraction levels, and the stepwise regression analysis was conducted at each ankle joint angle. When determining the dominant muscle that contributes to the changes in torque variability with the ankle joint angle at each contraction level, the data were collapsed across the ankle joint angles, and the analysis was conducted at each contraction level.

Absolute Variability for Torque
The ANOVA analysis revealed significant main effects from both the contraction level (F (4, 40) = 142.458, p < 0.001) and ankle angle (F (2, 20) = 6.547, p = 0.006) on T SD . No significant interaction was also found between the contraction level and ankle angle (F (8, 80) = 1.325, p = 0.243). As shown in Figure 3a, further analysis suggested that T SD at the longer muscle length was observed to be significantly larger than that at the shorter muscle length when the contraction level is at 30% (d z = 0.274, p = 0.026), 50% (d z = 0.420, p = 0.029) and 70% MVIC (d z = 0.414, p = 0.006). As shown in Figure 3b, T SD increases linearly with the actual plantar flexion torque regardless of muscle length.

Absolute Variability for rsEMG
The average MGSD, LGSD, and SOLSD at different contraction levels and ankle angles are presented in Table 1

Absolute Variability for rsEMG
The average MG SD , LG SD , and SOL SD at different contraction levels and ankle angles are presented in Table 1

Relative Variability for Torque
The statistical analysis suggested a significant main effect from the contraction level (F (4, 40) = 8.037, p < 0.001) and ankle joint angle (F (2, 20) = 11.177, p < 0.001) on T CoV , but there was no significant effect from the interaction between the contraction level and ankle joint angle (F (8, 80) = 1.536, p = 0.158). As shown in Figure 4a, T CoV at the ankle joint angle of 116 • was significantly higher than that at the other two ankle joint angles at the contraction of 10% MVIC (Shorter vs. Longer: d z = 0.724, p = 0.031; Shorter vs. Neutral: d z = 0.743, p = 0.039) and 20% MVIC (Shorter vs. Longer: d z = 0.734, p < 0.001; Shorter vs. Neutral: d z = 0.818, p < 0.001). As shown in Figure 4b, T CoV at ankle joint angle of 116 • tends to be the highest at the same plantar flexion torque compared with the other two ankle joint angles.

Relative Variability for Torque
The statistical analysis suggested a significant main effect from the contraction level (F (4, 40) = 8.037, p < 0.001) and ankle joint angle (F (2, 20) = 11.177, p < 0.001) on TCoV, but there was no significant effect from the interaction between the contraction level and ankle joint angle (F (8, 80) = 1.536, p = 0.158). As shown in Figure 4a, TCoV at the ankle joint angle of 116° was significantly higher than that at the other two ankle joint angles at the contraction of 10% MVIC (Shorter vs. Longer: dz = 0.724, p = 0.031; Shorter vs. Neutral: dz = 0.743, p = 0.039) and 20% MVIC (Shorter vs. Longer: dz = 0.734, p < 0.001; Shorter vs. Neutral: dz = 0.818, p < 0.001). As shown in Figure 4b, TCoV at ankle joint angle of 116° tends to be the highest at the same plantar flexion torque compared with the other two ankle joint angles.

Relative Variability for rsEMG
The average MGCoV, LGCoV, and SOLCoV at each ankle angle are presented in Table 2. It shows a significant effect from the ankle joint angle (F (2, 20) = 5.915, p = 0.010) with a significant reduction in SOLCoV at 20% and 70% MVIC when the ankle angle is changed from 116° to 87°, and a reduction at 30% MVIC when it is changed from 100° to 87°.

Relative Variability for rsEMG
The average MG CoV , LG CoV , and SOL CoV at each ankle angle are presented in Table 2.

Contributions from Relative Variability of rsEMG to the Resultant Relative Torque Variability
It appears that individual muscle contributions to T CoV may be different at different ankle joint angles ( Table 3). The stepwise regression model revealed that the MG CoV contribution to T CoV was significant at all tested ankle angles. The LG CoV significantly contributed to T CoV at both the neutral and shorter muscle lengths, whereas the SOL CoV contribution was significant only at the longer muscle length. Table 3. Stepwise regression model to identify possible predictors of the relative variability for torque (T CoV ) out of the relative variabilities for EMG burst (MG CoV , LG CoV , and SOL CoV ) across the contraction levels at each ankle joint angle. Data are shown as the estimated coefficient ±95% confidence interval. The significant predictors are in boldface type and the most important variable is highlighted. * p < 0.05. ** p < 0.001.

MG
LG SOL Longer * 0.14 ± 0.08 0.04 ± 0.07 * 0. 18  When considering the individual muscle contributions to T CoV at different contraction intensities (Table 4), MG CoV seems to be a more dominant contributor compared to the other two muscles, as supported by its significant contribution to T CoV from 20 to 70% MVIC. The contribution of both LG CoV and SOL CoV to T CoV was significant only at 30 and 50% MVIC. Interestingly, T CoV at 10% MVIC was not explained significantly by any of triceps surae.

Discussion
The main findings of this study are as follows: (1) absolute torque variability (T SD ) increased linearly with increasing the contraction level, and a significantly higher T SD was observed during moderate-to-high submaximal contractions (i.e., 30-70% MVIC) at the longer muscle length compared to the shorter muscle length, while the oscillations in muscle activities (absolute variability for rsEMG of each muscle-MG SD , LG SD , and SOL SD ) remained relatively constant at different ankle joint angles; (2) T SD was found to be linearly increased with actual torque output regardless of ankle joint angles; (3) relative torque variability (T CoV ) was found to be significantly higher during low submaximal contractions (i.e., 10-20% MVIC) at the shorter muscle length compared to the other two muscle lengths, but it appears that there is no significant effect of ankle joint angle on T CoV during moderate-to-high submaximal contractions; and (4) the stepwise regression models suggested that among triceps surae, the MG may play an important role to control the steadiness of plantar flexion torque.
T SD increased monotonically with contraction level at each ankle joint angle, as supported by previous findings [22]. This linear increment with contraction level of T SD may be explained by the presence of the signal-dependent noise (SDN) model, which assumes that there is noise from the motor command and that the amount of noise scales with the magnitude of motor command [10]. Our study further emphasized that the presence of SDN may also hold in a joint with multiple synergists. Studies have demonstrated that T SD is highly correlated with the low-frequency oscillations in the common neural drive, which can be quantified via cumulative spike trains or rsEMG of the target muscles [12][13][14]. This assertion can also be supported by our findings that MG SD , LG SD , and SOL SD increase monotonically with the contraction level ( Table 1).
The significantly larger T SD was found at the longest muscle length during the moderate-to-high contractions (i.e., 30-70% MVIC). Since there are no significant effects from the ankle joint angle on the oscillations in muscle activities (Table 1), it suggests that the significant changes in T SD at the longer muscle length is not likely affected by oscillations in common neural drive; instead, T SD appears to be a linear function of actual torque output (Figure 3b), which further implies that the increment in T SD at the longer muscle during moderate-to-high contractions may result from the higher torque output linked to the length-tension function [23][24][25], while the lack of significant differences in T SD at lower contractions may be due to the fact that the actual torque output in that range across the muscle lengths is similar. This may suggest that absolute torque variability is a function of actual torque output regardless of muscle mechanics.
Our results revealed that at all ankle joint angles, T CoV decreased from a higher value and remained constant afterwards with significance detected at both the neutral (100 • ) and shorter muscle length (116 • ), in agreement with previous findings [9]. There are no clear underlying mechanisms for this yet, but it is plausible that such nonlinear relationships can be explained, in part, by motor unit mechanics (i.e., firing patterns and contractile properties), as supported by the previous finding, which demonstrated a significant correlation between CoV for motor unit discharge rate and T CoV at low contraction intensities of the first dorsal interosseous muscles in older individuals [7]. Given that the influence of variability in discharge rate of a single motor unit is almost attenuated by convolution of motoneuron spike trains with motor unit twitches and summation of twitch forces, motor unit discharge variability may affect the steadiness in force output only at low contraction levels. At higher force levels thereafter, the more fused contractions due to more active motor units and their increased firing rates would result in higher absolute but lower relative force variability. However, rsEMG has limitations to provide information regarding an individual MU firing characteristics. To better understand the association between the firing characteristics and force variability, further studies are needed.
T CoV at low contraction levels (i.e., 10-20% MVIC) was significantly higher at the shorter muscle length (Figure 4a). Indeed, to generate the comparable forces at the shorter muscle length, it is most likely that more active motor units (MUs) are recruited and/or higher firing rates of the active MUs are required [19], leading to a more fused status and thus a smaller T CoV . The potential underlying mechanisms may involve the changes in twitch properties of the activated MUs (i.e., decreased half-relaxation time) but with a relatively constant firing rate at the shorter muscle length [15], which may lead to less fused status and thus a higher T CoV . Another possible mechanism may be related to the inhibited transmission of the low-frequency oscillations in force signals at the shorter muscle length while the muscle is under high slack (i.e., 10-20% MVIC). The lack of significance in the changes of T CoV at moderate-to-high contractions (i.e., 30-70% MVIC in Figure 4a) may be due to the fact that muscle slack uptake occurs while the muscle is with high active tension and thus can limit the effects from changes in muscle length at moderate-to-high contractions. As demonstrated in Table 3, the lack of contribution from any of triceps surae on T CoV at 10% MVIC may further suggest that the relative torque variability at low contractions can be highly affected by muscle mechanics instead of muscle activation.
Future studies are required to better understand the potential effects of length-dependent mechanisms on force variability, which have received less attention so far.
Some animal studies demonstrated direct evidence on selective recruitment of different types of motor units, particularly in synergistic muscles [26]. It is then possible that SOL may be recruited first and contribute predominantly to ankle torque generation, thus affecting the changes in torque variability at low contraction levels. However, different from animal models, MG is a mixed muscle containing at least 40% slow-twitch fibers in humans [27]. Our results (Tables 3 and 4) suggested that MG muscle may play an important role to control the steadiness of plantar flexion torque among triceps surae. Moreover, T CoV at low contraction levels (i.e., 10% MVIC) among different ankle angles was not explained significantly by any of triceps surae, which may provide indirect evidence that torque variability can be highly affected by muscle mechanics instead of by muscle activation strategy at a low contraction level, and thus the potential effects from the recruitment order among triceps surae on the different torque variabilities at different ankle angles may be limited.
Several studies indicated that most of the variability in the force signal during the steady contractions can be explained by fluctuations in the common modulation of the motor unit discharge rate, with low-frequency oscillations over time, indicated by rsEMG [13,28]. It has been proposed to use force variability as a potential measurement approach to evaluate motor function in clinical populations (i.e., stroke survivors) [13,28]. Our study suggested that not only the potential changes in motor function, but also the changes in muscle mechanics, can impact the changes in force variability. Considering that muscle mechanics disorders (i.e., muscle stiffness) can also be highly impacted in individuals with neurological disorders, care should be taken when explaining the changes in force steadiness in clinical populations. Further studies would be needed to understand the relative contribution from changes in muscle mechanics and motor function to the steadiness of the resultant force output.
There are several limitations in our study. Previous research has demonstrated that tibialis anterior (TA) muscle contracts simultaneously [29,30] to maintain the joint stability during isometric contractions. However, our further evaluation on the activation status of the TA muscle shows that the RMS EMG of TA was significantly smaller when compared with MG and LG; moreover, its amplitude was less than 4% of the RMS EMG of TA collected during maximum dorsiflexion, suggesting that the effects from the antagonist on the plantar flexion torque variability may be negligible. We also have limitations on the manipulations of changes in the ankle joint angle due to the constraints of our setup. Our results only demonstrated a significant difference in T CoV between the shorter and the longer/neutral muscle length but lack an observable difference when comparing between the neutral and longer muscle length. This may be due to the small interval of changes in the ankle joint angles. Another limitation is that the targeted population in this study only involves young individuals. Considering that aging and neurological impairment (i.e., stroke survivors) also affect the steadiness of force output [2,3,31] as well as mechanical properties of the muscle-tendon unit [32], it would be interesting to investigate the relative contribution of changes in the mechanical properties to the force variability in different populations. Lastly, it is possible that the higher T CoV observed at the shorter muscle length during lower contractions (10-20% MVIC) can be affected by the smaller torque output at a shorter muscle length. However, considering that the average torque value during 20% MVIC at a longer muscle length (12.9 N m) is comparable to that during 30% MVIC at a shorter muscle length (12.1 N m), our further evaluation suggested that T CoV at the shorter muscle length was~20% greater compared to the longer muscle length. T CoV -torque relation also illustrated that T CoV at the shorter muscle length is likely higher at a given, comparable torque output (Figure 4b). Future studies are necessary to examine torque fluctuations at the matched actual torque.

Conclusions
This study demonstrated that the absolute torque variability increased during modest submaximal contractions at a longer muscle length, whereas the relative torque variability increased during low submaximal contractions at a shorter muscle length. These findings suggest that the torque steadiness may be affected by both neural drive and muscle mechanics. Future studies are needed to better describe how these neuromuscular properties can influence the variability of force output.

Institutional Review Board Statement:
The study was conducted in accordance with the Declaration of Helsinki and approved by the Institutional Review Board (or Ethics Committee) of Northwestern University (Approval code: STU00206371; Approval date: 02/07/2018).

Informed Consent Statement:
Informed consent was obtained from all subjects involved in the study.

Data Availability Statement:
The data that support the findings of this study are available from the corresponding author upon reasonable request.