**3. Results**

## **3.1. Surrogate testing**

The results of the discriminant statistics (see Appendix-Shuffled Surrogate Tests of EMG). for each muscle and algorithm are shown in Table. 1. For all subjects, muscles, and gait cycle, the results of three different surrogate tests rejected the null hypotheses of equal or more deter‐ minism in surrogate data compared to the original data (φ > 2 and p< 5% ). The rejection of this null hypothesis indicated significant change in the nonlinear behavior of the surrogate signals (i.e. reduction of determinism) compared to the collected EMG signals which justified the application of higher order nonlinear data analysis techniques such as RQA to investigate the underlying dynamical pattern of the EMG signals specifically in SYNERGOS.

In Fig.2(a) an example of soleus EMG activity obtained during a single gait cycle (right heel strike to right heel strike) is depicted. Soleus contributes to the ankle planterflexion during body propulsion in stance phase of the gait. Muscle activity dramatically increases during midstance and peaks during the terminal stance phase with a rapid decrease in muscle activity in the pre-swing phase. The muscle remains fairly quiet during the swing phase of gait. Fig. 2(b) displays the recurrence plot (RP) of the soleus activity in which recurrent points are positioned along several parallel diagonal recurrent lines demonstrating the existence of a specific deterministic muscular activity in the soleus during the gait cycle. Fig.2(c) represents the randomized shuffling of the EMG signal using surrogate testing algorithms. The RP of the shuffled data are presented in Fig.2(d). No particular deterministic pattern can be recognized by observing several recurrent points scattered on the plot as these points do not generate long diagonal recurrent lines that would indicate determinism of the signal. The analyses of the original and surrogate signals also confirmed the results displayed in Fig.2(b) and Fig.2 (d). The reduction in % DET and increase in ApEn indicates that the surrogate data follows different dynamical patterns than the original EMG signal therefore the EMG signal included nonlinear behaviors (i.e. determinism) that were altered by the randomization of the original signal.


**Table 1.** The values of surrogate testing for three different algorithms; φ*ApEn* and φ*%DET* represents the value of statistics calculated from ApEn and % DET of the EMG signals and surrogate data series. (Fourier transform (FT), Iterated amplitude adjusted Fourier transform (IAAFT), rectus femoris (RF), tibialis anterior (TA), lateral gastrocnemius (GA), soleus (SO), vastus medialis (VM), and biceps femoris (BF))

#### **3.2. SYNERGOS analysis**

The SYNERGOS indices during walking, running, and the whole protocol are summarized in table2.


As expected, the changes in the gait mode (walking vs. running) altered the activation of muscles contributing to gait. Fig.3 shows the normalized EMG activities in one of the subjects whose SYNERGOS indices increased significantly from 2.58% during the slowest walking speed to 41.56% during the fastest running speed indicating an increase in cooperation among

tected by decreasing % DET and increasing ApEn verified the nonlinear dynamics of the EMG signal.

**Figure 2.** (a) The neuromuscular activities of soleus muscle during a gait cycle are depicted by EMG activities in in which soleus is mostly active during the propulsion of body during stance phase while showing little activity during swing phase. (b) The Recurrence plots (RP) generated based on the original data is shown in the graph (a) indicating the existence of a specific pattern in the soleus activity during the gait cycle. This pattern is depicted by several recur‐ rent points located along particular diagonal lines which are parallel to the main diagonal line (see Appendix-RQA formulation). The outcome of the RQA also verified the existence of the aforementioned pattern (% REC = 1.98; % DET = 51.80, radius=2.86, ApEn=0.72). Figure (c) contains the randomized shuffled data of the signal shown in 1(a). Figure (d) is the RP of the randomized signal which shows no significant determinism in the shuffled data. The time delayed dimensional data in RP are randomly scattered around the main diagonal line and the recurrent points are positioned along very short length. In addition, the outcome of RQA has shown significant reduction in determinism in the randomized data (% REC = 1.99 radius=8.70, ApEn=1.46). The drastic drop in the determinism of the signal de‐

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multiple muscles.

**Table 2.** The SYNERGOS indices averaged across all subjects and during walking, running, and the full protocol. The average index increased significantly during running compared to walking.

shuffled data are presented in Fig.2(d). No particular deterministic pattern can be recognized by observing several recurrent points scattered on the plot as these points do not generate long diagonal recurrent lines that would indicate determinism of the signal. The analyses of the original and surrogate signals also confirmed the results displayed in Fig.2(b) and Fig.2 (d). The reduction in % DET and increase in ApEn indicates that the surrogate data follows different dynamical patterns than the original EMG signal therefore the EMG signal included nonlinear behaviors (i.e. determinism) that were altered by the randomization of the original

**SO GA TA VA RF BF**

Mean 37.54 37.02 24.76 38.99 30.46 27.35 SD 6.52 7.12 7.30 7.81 7.00 3.42

Mean 454.65 518.50 344.20 292.60 42.17 213.00 SD 165.09 93.84 111.21 89.51 26.36 68.31

Mean 42.16 40.60 32.22 43.79 24.18 25.61 SD 7.43 7.38 12.72 8.92 5.82 4.83

Mean 61.26 94.09 232.65 22.43 69.42 48.27 SD 23.08 57.94 46.55 8.34 26.57 9.20

Mean 16.63 14.77 18.56 12.47 17.22 15.78 SD 4.16 4.70 6.01 4.59 4.44 1.45

Mean 49.24 66.33 53.88 25.84 35.58 11.03 SD 4.95 22.98 41.35 23.47 11.35 4.57

**Table 1.** The values of surrogate testing for three different algorithms; φ*ApEn* and φ*%DET* represents the value of statistics calculated from ApEn and % DET of the EMG signals and surrogate data series. (Fourier transform (FT), Iterated amplitude adjusted Fourier transform (IAAFT), rectus femoris (RF), tibialis anterior (TA), lateral gastrocnemius

The SYNERGOS indices during walking, running, and the whole protocol are summarized in

**Condition Average SD** Walking 17.61 11.57 Running 33.86 10.89 Overall 25.71 13.76

**Table 2.** The SYNERGOS indices averaged across all subjects and during walking, running, and the full protocol. The

signal.

Time Shuffled

FT

IAAFT

table2.

φ*ApEn*

140 Electrodiagnosis in New Frontiers of Clinical Research

φ*%DET*

φ*ApEn*

φ*%DET*

φ*ApEn*

φ*%DET*

**3.2. SYNERGOS analysis**

(GA), soleus (SO), vastus medialis (VM), and biceps femoris (BF))

average index increased significantly during running compared to walking.

**Figure 2.** (a) The neuromuscular activities of soleus muscle during a gait cycle are depicted by EMG activities in in which soleus is mostly active during the propulsion of body during stance phase while showing little activity during swing phase. (b) The Recurrence plots (RP) generated based on the original data is shown in the graph (a) indicating the existence of a specific pattern in the soleus activity during the gait cycle. This pattern is depicted by several recur‐ rent points located along particular diagonal lines which are parallel to the main diagonal line (see Appendix-RQA formulation). The outcome of the RQA also verified the existence of the aforementioned pattern (% REC = 1.98; % DET = 51.80, radius=2.86, ApEn=0.72). Figure (c) contains the randomized shuffled data of the signal shown in 1(a). Figure (d) is the RP of the randomized signal which shows no significant determinism in the shuffled data. The time delayed dimensional data in RP are randomly scattered around the main diagonal line and the recurrent points are positioned along very short length. In addition, the outcome of RQA has shown significant reduction in determinism in the randomized data (% REC = 1.99 radius=8.70, ApEn=1.46). The drastic drop in the determinism of the signal de‐ tected by decreasing % DET and increasing ApEn verified the nonlinear dynamics of the EMG signal.

As expected, the changes in the gait mode (walking vs. running) altered the activation of muscles contributing to gait. Fig.3 shows the normalized EMG activities in one of the subjects whose SYNERGOS indices increased significantly from 2.58% during the slowest walking speed to 41.56% during the fastest running speed indicating an increase in cooperation among multiple muscles.

This change was detected by a significant alteration in the SYNERGOS index with the index being significantly greater during running than during walking (F(1,382.149) = 54.067, p <0.001) suggesting increased muscle multiple coactivity during more vigorous movements. In addition, the hypothesis that SYNEGOS could detect changes in MMA associated with slight increases of 0.045 m/s in gait speed was confirmed (F(1,382.537)= 675.85, p< 0.001). A significant interaction effect of gait speed and movement pattern ( F(1,382.082) = 48.075, p <0.001) was also detected indicating that increases in SYNERGOS values occurred at a lower rate during increases in running speed than during increases in walking speed. A high degree of reliability was detected during both walking (ICC=0.92, SEm=3.14) and running (ICC=0.91, SEm=2.71).

SYNERGOS run = 32.84 ± 2.71). Furthermore, the fitted slopes for increases in the SYNERGOS index during walking (slope = 18.30) and running (slope=15.35) were significantly (p<0.001)

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**Figure 4.** The shaded area indicates the 95% CI of the SYNERGOS index for each gait speed. The vertical dotted line indicates the average walk to run transition speed. The linear fit model for walk and run are shown by solid line while the extrapolation of the linear fit model into the opposite gait pattern was shown by dotted lines for the SYNERGOS indices. In both walking and running conditions the SYNERGOS indices increased consistently in response to increas‐ ing gait speed. The index had larger absolute values (>20) during running, indicating greater magnitude and activa‐ tion of muscle activity, but the slope for walking (slope = 18.30) was significantly (p<0.001) higher than the slope in running condition (slope=15.35) indicating a greater rate of change in MMA when increasing walking speed relative

We have introduced a new analysis method, SYNERGOS that provides an index for quanti‐ fying the state of muscle multiple coactivation during a given movement task and demon‐ strated that it could successfully discriminate between muscle coactivation patterns associated with changing gait mode and speed as a particular combination of the % DET for multiple muscles. As mentioned previously a SYNERGOS index of 100 would represent 100% contrac‐ tion and simultaneous activation of all measured muscles. Such a possibility is extremely unlikely when considering any voluntary contraction but definitely would not occur during

Several studies investigated the effect of increasing gait speed on the neuromuscular activities of the lower extremities [22, 44-49]. These studies reported increasing average and peak EMG voltage associated with increasing speed in the soleus, gastrocnemius, tibialis anterior, vastus

different.

to increasing running speed.

a dynamic movement as rigidity would result.

**4.1. SYNERGOS considerations**

**4. Discussion**

**Figure 3.** The EMG activity of the lower extremity muscles in soleus (SO), gastrocnemius (GA), tibialis anterior (TA), vastus medialis (VM), rectus femoris (RF), and biceps femoris (BF) comparing walking and running stage. The data are time normalized using a linear length normalization method to convert different each gait cycle into equally scaled units (each unit represents 1% of gait cycle). A gait cycle was defined as the duration between right heel strike and the next right heel strike (gait cycle = 100% of scaled unit). For demonstration purposes, the amplitude for each mus‐ cle was normalized to the maximum EMG obtained during the data collection. This maximum was always reached during running.

Fig.4 displays the 95% confidence intervals (95% CI) of SYNERGOS index across all subjects for each of the gait speeds. In addition, the final fitted model slopes both during walk and run in the SYNERGOS indices across treadmill speeds (solid lines) is depicted. The model consis‐ tently increased in response to increasing gait speed and had larger absolute values during running, indicating greater magnitude and coactivation (SYNERGOS walk 16.517 ± 3.14 vs. SYNERGOS run = 32.84 ± 2.71). Furthermore, the fitted slopes for increases in the SYNERGOS index during walking (slope = 18.30) and running (slope=15.35) were significantly (p<0.001) different.

**Figure 4.** The shaded area indicates the 95% CI of the SYNERGOS index for each gait speed. The vertical dotted line indicates the average walk to run transition speed. The linear fit model for walk and run are shown by solid line while the extrapolation of the linear fit model into the opposite gait pattern was shown by dotted lines for the SYNERGOS indices. In both walking and running conditions the SYNERGOS indices increased consistently in response to increas‐ ing gait speed. The index had larger absolute values (>20) during running, indicating greater magnitude and activa‐ tion of muscle activity, but the slope for walking (slope = 18.30) was significantly (p<0.001) higher than the slope in running condition (slope=15.35) indicating a greater rate of change in MMA when increasing walking speed relative to increasing running speed.
