Continuous Wavelet Transform Analysis of Surface Electromyography for Muscle Fatigue Assessment on the Elbow Joint Motion

Studying muscle fatigue plays an important role in preventing the risks associated with musculoskeletal disorders. The effect of elbow-joint angle on time-frequency parameters during a repetitive motion provides valuable information in finding the most accurate position of the angle causing muscle fatigue. Therefore, the purpose of this study is to analyze the effect of muscle fatigue on the spectral and time-frequency domain parameters derived from electromyography (EMG) signals using the Continuous Wavelet Transform (CWT). Four male participants were recruited to perform a repetitive motion (flexion and extension movements) from a non-fatigue to fatigue condition. EMG signals were recorded from the biceps muscle. The recorded EMG signals were then analyzed offline using the complex Morlet wavelet. The time-frequency domain data were analyzed using the time-averaged wavelet spectrum (TAWS) and the Scale-Average Wavelet Power (SAWP) parameters. The spectral domain data were analyzed using the Instantaneous Mean Frequency (IMNF) and the Instantaneous Mean Power Spectrum (IMNP) parameters. The index of muscle fatigue was observed by calculating the increase of the IMNP and the decrease of the IMNF parameters. After performing a repetitive motion from non-fatigue to fatigue condition, the average of the IMNF value decreased by 15.69 % and the average of the IMNP values increased by 84 %, respectively. This study suggests that the reliable frequency band to detect muscle fatigue is 31.10–36.19 Hz with linear regression parameters of 0.979 mV 2·Hz−1 and 0.0095 mV 2·Hz−1 for R and slope, respectively.


Introduction
In everyday life, when the limb performs an intensive repetitive motion, the muscle can experience muscle fatigue.The muscle fatigue is a condition in which the muscle cannot sustain the force on the given certain task.Muscle fatigue can provide a useful information which needs to be considered in the area of ergonomic, robotic exoskeleton based on EMG control, and sport.Furthermore, the muscle fatigue can be used to prevent the muscle disorder.Several techniques have been used to determine the muscle fatigue, and analyzing the EMG signals are widely used to indicate the muscle fatigue [1].When the muscle is in the fatigue condition, it is proved that the spectral parameters (frequency and amplitude) of the EMG signal will change [1].Basmajian and De Luca had reported the results of their study, where during constant force contraction, the amplitude of the EMG signal increased and both mean and median frequency shifted to the lower values [1].Generally, a conventional method to measure the spectral parameters of the EMG signal is by utilizing the Fast Fourier Transform (FFT) method.In this case, the EMG signal, however, is assumed to be in the stationary condition which the muscle fatigue is determined by performing constant force or isometric contraction [2] on the subject's limb.Determination of the muscle fatigue in the dynamic motion of the limb is closely related to daily activities.During the dynamic motion, the muscle length changes [1] in accordance with the limb joint angle, and for this issue, the nonstationary characteristic of the EMG signal increases [3].
The studies that addressed the muscle fatigue in the dynamic contraction have been conducted by several previous researchers.Gonzales et al. determined the muscle fatigue during a repetitive motion on the knee using the mean and variance of instantaneous frequency based on Choi-William distribution [4].Chowdhury et al. used Discrete Wavelet Transform (DWT) to determine the muscle fatigue on the neck and shoulder during a repetitive motion [5].In their study, the changes in the spectral parameter were observed by calculating the DWT coefficients.Karthick and Ramakrishnan proposed a method to observe the progression of the muscle fatigue during the elbow motion in the flexion and extension [6] by utilizing the time-frequency distribution.Triwiyanto et al. proposed the DWT analysis of the EMG signal to conclude which level of decomposition is mostly determined for the muscle fatigue in the dynamic motion [7].The models used in the previous studies have not discussed the relationship between the elbow joint angle and the time-frequency parameters when the muscle was in the fatigue condition.
It is obvious that the EMG signals have the nonstationary characteristic which means that the frequency of the EMG signal changes by the time.In this case, the EMG signals analysis using the CWT becomes the most suitable method compared to the FFT.Therefore, to address the limitations that have been mentioned in the previous studies, a new method needs to be presented for investigating the relationship between the elbow joint angle, and the spectral and time-frequency parameters of the EMG signal when the muscle is in the non-fatigue and fatigue condition.The purpose of this study is to analyze the effect of the muscle fatigue on the spectral and time-frequency parameters using the CWT.The specific objectives of the study are: • to calculate the linear regression parameters, • to investigate the effect of the elbow joint angle on the time-frequency parameters in the non-fatigue and fatigue condition, and • to test the significant difference of the power spectrum density between non-fatigue and fatigue conditions.

Theoretical Background
Wavelet analysis is a method to decompose the signal into several parts of the signal based on wavelet basis function.A wavelet function, ψ τ,s (t), is built based on a mother wavelet function composed of scaling and translation parameters.In this case, s refers to scaling parameter related to the frequency of the signal and τ is translation parameter.The wavelet function is written as follows [8]: The Continuous Wavelet Transform (CWT) of the signal, x(t), is written as follows [8]: The CWT function on Eq. ( 2) is composed of the scaling, translation, wavelet function ψ t−τ s , and the signal x(t).In order to analyze the EMG signal, the function x(t) in Eq. ( 2) can be substituted by the EMG signals.In this study, the Morlet mother wavelet was used to implement the CWT.The complex-Morlet mother wavelet is defined as follows [8]: where f 0 indicates the Morlet frequency constant (f 0 = 0.849).
The local Power Spectrum Density (PSD) of the CWT for a certain scale range is measured using the Scaled-Average Wavelet Power (SAWP), as shown in Eq. (4) [9]: where s 1 and s 2 indicate the ranges of the CWT scale, C δ indicates the coefficient of the mother wavelet, δ s is the increment of the scale, δ τ is the time translation of the mother wavelet and W n is the CWT coefficient.The global scale PSD is measured for all ranges of the scale.A local PSD for the short period of time is measured using the Time-Averaged Wavelet Spectrum (TAWS) described as follows [9]: where W n is the CWT coefficient, and n and N are the specific time range to average the CWT coefficients.

Participants
Four healthy male volunteers (age: 22.4±3.2years old, weight: 65.4 ± 5.6 kg, height: 169 ± 4.2 cm) who had no history of the muscular disorder were recruited in this study.Before the data collection, the subjects were recommended not to do any hard work that could harm the elbow joint.Furthermore, the subjects were given the explanation how to do the movements of flexion and extension and told any potential risks that might occur during the experiment.

Participants
To implement the proposed method, four healthy male participants with no history of muscular disorder (age: 22.4±3.2years old, weight: 65.45±5.67kg) were recruited for this study after giving informed consent.Before the data collection process, the participants were recommended not to do any hard work especially anything that could potentially harm the elbow joint.The participants were instructed on how to perform the flexion and extension movements and were informed about any potential risk that could be involved in carrying out these motions.

Equipment
In this study, the EMG signal was collected using one channel EMG system consists of pre-amplifier, band pass filter with the cut-off frequency of 20 and 500 Hz, adjustable gain amplifier and summing amplifier.The EMG signal was collected using three surface electrodes (Ag/AgCl, size: 57 × 48 mm, Ambu, Bluesensor R, Malaysia).Two electrodes were placed on biceps muscle and one electrode was placed on hand as a common ground electrode.An exoskeleton frame was used to synchronize the elbow joint motion (Fig. 1).The elbow joint angle was collected using a linear potentiometer.One kilogram of the load was placed on the edge of the exoskeleton frame.

Data Collection
The EMG signal covers frequency in the range of 0 to 500 Hz, while the range of the dominant frequency falls between 50 and 150 Hz [10].The EMG signal and elbow joint position were collected with a sampling frequency of 1000 Hz [11] and [12].The choice of this sampling frequency was in accordance with the Nyquist rule [13].Furthermore, the application program developed using Borland Delphi Professional (Version 7.0, Borland Software Corporation, Scotts Valley, California, USA) was used to acquire the EMG signal and CWT analysis.
During the flexion and extension motion from 0 to 120 degrees, the EMG signal and the elbow joint angle were recorded for off-line data analysis.In the data collection process, subjects were instructed to perform repetitive motion until they were perceived in fatigue conditions.The condition was indicated by the subject's elbow that could not perform the flexion and extension movements.

Data Processing
The EMG signal and angle data were processed offline using the Borland Delphi Professional (Version 7.0, Borland Software Corporation, Scotts Valley, California, USA), see Fig. 2. Four cycles of flexion and extension motion assigned by T1, T5, T10, and T15 were selected from the EMG data.The T1, T5, T10, and T15 were the cycles that were measured in the first minute, fifth minute, tenth minute, and last minute, respectively.T1 would be assumed as a time location of the non-fatigue condition and T15 denoted as a time location of the fatigue condition.Each cycle of motion was analysed using the CWT.In this study, the CWT implementation used the complex Morlet wavelet which was widely accepted in the EMG analysis [14], [15] and [16].The coefficients of the CWT were calculated with the scale of 100 with the delta scale (δ s ) of 0.002.The mother wavelet was shifted with the total translation (τ total ) of 360.The delta translation (δ τ ) is calculated as follows: where f s is the frequency sampling in Hz, N is the number of the sample point and τ total is the number of total translation.The following time-frequency and spectral parameters were calculated: • Scale-Average Wavelet Power (SAWP) is the average of PSD for the specific range of the scale band.In this study, the scales range to be analysed was from 0.002 to 0.052.The scales were divided into 10 bands in which each band has the scale length of 0.005.These ten bands were denoted by the 1 st to 10 th bands (for example, the 1 st band had the scale range of 0.002 to 0.007).The SAWS was calculated based on Eq. ( 4).
• Time-Average Wavelet Spectrum (TAWS) is the average of PSD for the specific length of the translation.In this study, the number of translation was 360.If the translation length was 20, the number of the TAWS was 18.The TAWS is calculated based on Eq. ( 5).
• Instantaneous Mean Frequency (IMNF) [6] is calculated to obtain the mean power of frequency at an instant time.The IMNF is formulated as follows: where f 1 denotes the lowest frequency and f 2 denotes the highest frequency and |CW T | is the absolute of the CWT coefficients.The f 1 and f 2 were determined based on the frequency range of the processed EMG signal (f 1 = 20 Hz and f 2 = 500 Hz).
• Instantaneous Mean Power (IMNP) is the mean of PSD at an instant time [6].
where N indicates the number of scale and |CW T | indicates the absolute of the CWT coefficients.

Statistical Analysis
Muscle fatigue affected the spectral and time-frequency parameters of the EMG signal.The significant difference of the parameters was examined using the one way single factor ANOVA with the confidence level of 95 % for T1, T5, T10 and T15 cycle.The effect of the muscle fatigue was significantly indicated by p-value.
If the p-value is less than 0.05, then it indicates that the muscle fatigue has significantly affected.

Results and Discussion
In consideration to the purpose of the study, the change in the spectral parameters (the frequency and magni-       tude of power spectrum) was analyzed using the CWT.In the non-fatigue condition (Fig. 3), the averages of the IMNF and IMNP for all of the scale and time are 70.37 ± 10.16 Hz and 0.0165 ± 0.0094 mV 2 , respec-tively.After a repeated flexion and extension movements, the muscle will be in the fatigue condition and the magnitude of the power spectrum increased significantly.Thus, the contour of the wavelet power is wider compared to that in the non-fatigue condition, see Fig. 4(b).Therefore, the averages of the spectral parameters also changed.The averages of the IMNF and IMNP for all of the scale and time in the fatigue condition are 60.83 ± 13.95 Hz and 0.1039 ± 0.084 mV 2 , respectively.The average of the IMNF decreased by 15.69 % and the average of the IMNP increased by 84.14 %.These results, i.e. the decrease of the frequency and the increase of the power, are in line with the previous study conducted by Basmajian and De Luca [1].Similar results were also observed by Karthick and Krishnan which showed that the IMNF and IMDF of EMG signal decrease from non-fatigue to fatigue condition [6].
The Global Wavelet Spectrum (GWS) was calculated based on the average of the PSD for the total time range of 2 seconds as shown in Fig. 5. Figure 5 shows that the highest magnitude of the global wavelet spectrum was in the center of scales: 0.017 (58.54 Hz), 0.0175 (56.87 Hz), 0.0185 (53.8 Hz), and 0.020 (49.76 Hz) for the time of T1, T5, T10 and T15, respectively.The GWS in the scale range of 0.002 to 0.008 showed a consistent increase from non-fatigue (T1) to fatigue condition (T15).The time of T1 shows the lowest magnitude of the GWS.It was the first cycle of the EMG measurement (at first minute) and was assumed as a non-fatigue condition.It was followed by T5, T10, and T15.For all of the scale, T15 had the highest GWS.The average of PSD from T1 to T15 increased significantly (p < 0.05) about 84.17 %.It was also observed in Fig. 5 in which the frequency changed to lower frequency by 10.48 %, from non-fatigue to fatigue condition.This phenomenon was in line with the Basmajian and de Luca's report.In their study on the assessment of the muscle fatigue, the frequency changed to the lower value and the amplitude increased significantly [1].
The Time-Averaged Wavelet Spectrum (TAWS) and the Scale-Averaged Wavelet Spectrum (SAWS) was calculated to find the specific time location of the spectral parameters.

Time-Averaged Wavelet Spectrum
Time-Averaged Wavelet Spectrum (TAWS) is calculated according to Eq. ( 5).The TAWS was calculated for a specific range of time, which was aimed to find the specific time and frequency location related to the elbow joint angle and the muscle fatigue condition.In order to perform the TAWS calculation, the 2 seconds period of the cycle was divided into 18 ranges of time.
The TAWS increased significantly (p-value < 0.05) from T1 to T5, T1 to T10 and T1 to T15.This highest PSD was related to the elbow-joint angle at 108 • to 110 • .The similar finding has also been reported by Chowdhury and Nimbarte.They observed the significant increase of PSD in the frequency band of 23-46 Hz and 46-93 Hz [17].that there was no relationship between the elbow joint angle and power or EMG amplitude [3].This difference was due to the different technique in analyzing the EMG signals.They observed the relationship between the elbow joint angle and EMG amplitude using the amplitude-based parameters.

Scale-Averaged Wavelet Power
The Scale-Averaged Wavelet Power (SAWP) feature is calculated using Eq. ( 4).SAWP is used to test the fluctuation of PSD in the time series for specific frequency bands.By using this feature, the dominant PSD can be found in the specific time and elbow joint angle.In order to perform this calculation, the frequency was divided into ten frequency bands including    angle of 97 • -110 • ). Figure 16 shows that the PSD of the SAWP, in the fatigue condition, were found at several locations from 0.6 to 1.2 seconds.In this case, we could not use this band (58.54-79.62Hz) to localize the muscle fatigue in the certain time and angle.As shown in Fig. 12, Fig. 13, Fig. 14, Fig. 15, Fig. 16 and Fig. 17, each frequency band has different SAWP.The reliable frequency band, that could be effectively used to detect the muscle fatigue, was determined using the determination coefficient (R 2 ) of linear regression calculated from the average of SAWP for all the time.The linear regressions parameters (Slope, R 2 , and Intercept) were calculated using the average of the SAWP for T1, T5, T10, and T15.In the frequency band of 31.10-36.19Hz, the R 2 shows the highest value (0.979), see Tab. 1.The positive value in the R 2 indicated that the PSD magnitude increased linearly by the time.These results are similar to Karthick and Ramakrishnan's finding [6].In their study, they used the IMNP to observe the effect of the muscle fatigue and obtained R 2 = 0.57 and slope = 0.0039 mV 2 • Hz −1 .The increase of the PSD magnitude in this band was also similar to Chowdury and Nimbrate's finding.They found that in the frequency range of 23-46 Hz and 46-93 Hz, the magnitude of the power spectrum increased significantly.
Tab. 1: The summary of linear regression parameters for all the frequency bands.

Conclusion
This study investigated the effect of muscle fatigue quantitatively on the spectral and time-frequency parameters of the EMG signal using CWT.It was found that when the muscle was in the fatigue condition, the spectral parameters of the EMG signal changed.The average of the IMNF decreased by 15.69 % and the average of the IMNP increased by 84.14 %.The optimum fatigue detection was located at the time range of 1.006 to 1.111 seconds related to the elbow joint angle in the range of 108

Fig. 2 :
Fig. 2: The illustration of the EMG data processing.Four cycles of the EMG signal indicated by T1, T5, T10, and T15 was analyzed using the CWT.The black line is the EMG signal and the red line is the elbow joint angle.
The EMG signal during the flexion and extension motion with the motion period of 2 seconds (the black line is the EMG signal and the red line is the elbow joint angle).
The global wavelet spectrum.

Fig. 3 :
Fig. 3: The typical example of one cycle of the flexion and extension motion which was measured at the first cycle (T1) in the non-fatigue condition.
The global wavelet spectrum.

Fig. 4 :
Fig. 4: The typical cycle of flexion and extension motion which was measured in the last cycle (T15) in the fatigue condition.

Fig. 5 :
Fig. 5: The global wavelet spectrum for the 2 second duration.

Figure 12 ,Fig. 13 :Fig. 14 :Fig. 15 :
Figure 12, Fig. 13, Fig. 14, Fig. 15 and Fig.17show that the SAWP with the maximum PSD, in the fatigue condition (T15), was mostly found in the flexion motion at the time range of 0.8 to 1.03 seconds (at the

Freq. (Hz)
(b) The contour of the CWT coefficients.