Nonparametric decomposition of electromyographic wavelet spectra during concentric and eccentric muscle actions.
The advent of the modern day digital computer has greatly improved the ability to perform frequency analysis of biological signals. With surface electromyographic (EMG) signals, the traditional method for frequency analysis involves a Fourier Transform to generate a power spectrum, followed by calculation of the center frequency (i.e., mean or median). Advantages of this method include simplicity and the fact that the center frequency generally tracks changes in spectral power. For example, several studies [1,10,14] have found that during sustained or repeated muscle actions, the surface EMG signal demonstrates a decrease in high frequency power and an increase in low frequency power. As a result, there is a fairly predictable decrease in EMG center frequency that reflects a fatigue-related decline in the muscle's ability to produce maximal force, even though force production may remain stable during a submaximal muscle action.
The recent development of a wavelet-based technique, however, has provided another method for examining changes in spectral shape. Specifically, von Tscharner and Goepfert  created a parametric spectral decomposition procedure in which the EMG wavelet spectrum is decomposed into a set of generating spectra (g_spectra). It was theorized  that any given wavelet spectrum could be accurately represented by a linear combination of two or more g_spectra. In many cases, the two g_spectra are similar in shape, but occupy different bandwidths (i.e., a high frequency bandwidth and a low frequency bandwidth). Thus, decomposition of the measured EMG wavelet spectra into the g_spectra provides a set of contributing weights (Cweights) that reflect the relative contributions of the high-and low-frequency g_spectra to the measured EMG wavelet spectra. Wavelet spectra that have more power at high frequencies will have a larger weight on the high frequency gspectrum than on the low frequency g spectrum. In contrast, those with more power at low frequencies will have a larger weight on the low frequency g spectrum than on the high frequency gspectrum. This technique of decomposing EMG spectra into g_spectra is very sensitive, and the results can be analyzed with parametric statistics. von Tscharner and Goepfert  hypothesized that the high frequency and low frequency g_spectra reflected the contributions of "fast" and "slow" muscle fibers to the measured EMG wavelet spectrum, respectively. It was emphasized, however, that the fast and slow terminology was not necessarily indicative of the twitch properties of the fibers, but was instead reflective of their contributions to the overall shape of the spectrum . No previous investigations have used spectral decomposition methods to determine if there are differences between the wavelet spectra generated during concentric versus eccentric muscle actions. Thus, the purposes of this study were twofold: (1) to determine the accuracy of a nonparametric spectral decomposition procedure for decomposing EMG wavelet spectra, and (2) to compare the shapes of the EMG wavelet spectra from concentric versus eccentric muscle actions. We hypothesize that the nonparametric spectral decomposition will accurately decompose the EMG wavelet spectra. In addition, the concentric and eccentric muscle actions will have EMG wavelet spectra with differing shapes that reflect the unique motor control strategies used during the two types of muscle actions.
Fourteen men (mean [+ or -] SD age = 23.3 [+ or -] 2.8 yrs; height = 179.9 [+ or -] 6.7 cm; mass = 85.1 [+ or -] 15.2 kg) volunteered to participate in this investigation. The study was approved by the University Institutional Review Board for Human Subjects, and all subjects completed a pre-exercise health status questionnaire and signed an informed consent form prior to testing. In addition, all subjects were experienced in weight training (mean [+ or -] SD training experience = 5.1 [+ or -] 4.0 yrs).
All subjects were tested for unilateral one repetition maximum (1-RM) dynamic constant external resistance (DCER) strength of the dominant (based on throwing preference) forearm flexors while seated in a chair. The concentric and eccentric phases of each muscle action were both 3-sec in duration, with a 1-sec isometric hold between these phases when the forearm was fully flexed. The investigator provided verbal commands to the subject to aid in achieving the desired speed for each phase of the movement. A repetition was considered successful if the subject moved the plate-loaded dumbbell throughout the entire range of motion at the desired cadence. Prior to the 1-RM assessment, the subjects performed a warm-up of five DCER muscle actions with a weight that they perceived to be 50% of their maximum. The weight on the dumbbell was then progressively increased until the subject could no longer perform a single repetition at the desired cadence. Two minutes of rest were allowed between all 1-RM attempts. After the 1-RM was established, the subjects performed nine separate DCER muscle actions with 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, and 90% of the 1-RM. These submaximal muscle actions were performed in a random order with two minute rest periods.
A bipolar surface EMG signal was detected from the biceps brachii during each DCER muscle action. The electrode arrangement (nickel-plated, circular, 10 mm diameter, 20 mm interelectrode distance, Jari Electrode Supply, Gilroy CA) was placed on the skin over the belly of the biceps brachii muscle. Prior to placing the electrodes over the muscle, the skin was shaved, carefully abraded with sandpaper, and cleansed with rubbing alcohol. During each muscle action, the EMG signal was sampled at 2,000 samples/second with a 24-bit analog-to-digital converter (cDAQ 9172, National Instruments, Austin TX) and stored in a personal computer (Dell Optiplex 755, Dell Computers, Inc., Round Rock TX) for subsequent analyses. The 24-bit precision provided by the analog-to-digital converter gives adequate resolution for surface EMG signals without the need for additional amplification. In addition, the analog-to-digital converter incorporates an anti-alias low-pass filter with a cut-off frequency that is set to exactly 1/2 of the sampling rate. Thus, in the present study, the anti-alias filter was set with a cut-off frequency of 1,000 Hz.
All EMG signals were digitally band-pass filtered (zero-lag, fourth order Butterworth) with cutoff frequencies of 10 and 500 Hz. One second portions of the EMG signals for the concentric and eccentric muscle actions were then selected for subsequent analyses. These 1-sec portions corresponded to the middle 30[degrees] of the range of motion for each phase of the movement. The EMG signals were then processed with the wavelet analysis described by von Tscharner . This analysis provides the optimal combination of time and frequency resolution for EMG signals. This is accomplished with a filter bank of eleven nonlinearly scaled wavelets that extract the intensity (which is analogous to power) of the EMG signal in different frequency bands. The result is a two dimensional matrix of data known as an intensity pattern that reflects the time locations and frequency distributions where the intensity in the EMG signal is greatest. The intensity pattern itself contains a great deal of information and has been used in previous studies to examine gender differences in muscle activation during running  and the mechanisms underlying fatigue during low intensity cycling . In the present study, however, the information contained in the EMG intensity pattern was consolidated into a wavelet spectrum by averaging the EMG intensity values across all time points in each wavelet band. As a result, the wavelet spectrum is similar in shape to the power spectrum from the Fourier Transform. The wavelet spectrum then served as the input for the spectral decomposition.
The wavelet spectra for each subject and %1-RM during both the concentric and eccentric phases were first normalized to have equal total energy. For each %1-RM, the spectra from each subject and muscle action type (concentric versus eccentric) were stacked side-by-side into a matrix known as the Data matrix that served as the input for the spectral decomposition. Thus, for each %1-RM, the Data matrix contains 11 rows (one row for each wavelet band) and 28 columns (one for each subject and muscle action type). A separate spectral decomposition was then performed for each %1-RM in a manner similar to that described by von Tscharner and Goepfert . An important difference, however, is that von Tscharner and Goepfert  used a parametric spectral decomposition, whereas in the present study the decomposition was nonparametric. In both procedures, the spectra in the Data matrix are decomposed into a set of g_spectra. With the parametric decomposition, it is assumed that the g_spectra can be modeled by a specific function, whereas with the nonparametric decomposition, the g_spectra do not have to conform to a function and are generated by a linear combination of the eigenvectors . The result of the nonparametric spectral decomposition is a set of two g_spectra (a high frequency spectrum and a low frequency spectrum). In turn, every wavelet spectrum in the Data matrix can be reconstructed by a linear combination of the two g_spectra weighted by the Cweights. The accuracy of this decomposition is determined by the percentage of the variance in the original Data matrix that can be explained by the two g_spectra. Appendix A provides the details of the nonparametric spectral decomposition.
t-tests and Classification
For each %1-RM, two separate paired-samples t-tests were performed to determine if there were significant mean differences between the concentric and eccentric muscle actions for C_weights on both the high frequency and low frequency g_spectra. In addition, a Fisher's Linear Discriminant Analysis procedure was used to determine the accuracy with which the C_weights from the high frequency and low frequency g_spectra could be classified into their respective concentric and eccentric muscle action groups. A Binomial Test was used at each %1-RM to determine if the classification was significantly better than random. An alpha level of 0.05 was used for each of these tests.
Table 1 shows the accuracy for the nonparametric spectral decomposition at each %1-RM. Figure 1 demonstrates the high frequency and low frequency g_spectra at each %1-RM. Notice that the general shapes of the g_spectra were similar across percentages of the 1-RM, with the only major difference being the locations of the peaks of the g_spectra. Figure 2 shows the averaged (across subjects) EMG wavelet spectra for the concentric and eccentric muscle actions at each %1-RM. Notice that the general shapes of the spectra were the same at all %1-RM, but the spectra for the concentric muscle actions were always shifted very slightly toward higher frequencies relative to those from the eccentric muscle actions. Table 2 shows the mean [+ or -] SD C_weights on the high frequency and low frequency g_spectra for the concentric and eccentric muscle actions at each %1-RM. The results from the paired-samples t-tests indicated that the mean C_weights on the high frequency g_spectra were significantly greater during the concentric than the eccentric muscle actions at all %1-RM except 10% 1-RM. In addition, the C_weights on the low frequency g_spectra were significantly lower during the concentric than the eccentric muscle actions at all %1-RM except 10% 1-RM. Finally, Table 3 shows that the classification of the wavelet spectra into their respective concentric versus eccentric categories was significantly better than random at all %1-RM. At an alpha level of 0.05, the Binomial Test required at least 19 of the 28 spectra to be classified correctly for the classification to be considered significantly better than random.
An important finding from this study was that the wavelet spectra could be decomposed into the high frequency and low frequency g_spectra with accuracy that was always greater than 92% and very similar to the accuracy obtained with a principal components analysis. Thus, the g_spectra provided a valid set of axes into which the measured EMG wavelet spectra could be decomposed. And, unlike the principal components, which are often difficult to interpret, the information provided by the g_spectra has physiological relevance, as these spectra are similar in shape to those measured from skeletal muscle.
Recently, von Tscharner and Nigg  and Farina  discussed whether or not the surface EMG power spectrum could be used to provide information regarding motor unit recruitment and muscle fiber type composition. The argument put forth by von Tscharner and Nigg  was that motor unit recruitment occurs in a task-dependent fashion (i.e., different motor units are recruited for different tasks), and that changes in
this recruitment pattern can cause changes in the shape of the EMG power spectrum. The counter argument was that many factors can affect the shape of the EMG power spectrum (e.g., thickness of the subcutaneous adipose tissue, location of the active motor units in the muscle, inconsistent differences between the conduction velocities of fast-twitch versus slow-twitch muscle fibers, etc.), and it is therefore not appropriate to infer motor control strategies from it under most conditions . This discussion engaged several other top scientists that provided their own viewpoints . It is important to point out that previous studies [12,13] have suggested that the normal order of motor unit recruitment (i.e., low-threshold motor units first, high-threshold motor units last) may be reversed during eccentric muscle actions. Other investigations have reported decreased levels of muscle activation , reduced recruitment thresholds [15,16], and lower motor unit firing rates  for eccentric muscle actions when compared to concentric and/or isometric muscle actions. The results from the present study neither confirm nor deny that these phenomena may exist. They do, however, demonstrate consistent differences in spectral shape between eccentric and concentric muscle actions (Figure 2).
Thus, an important question is what could be causing these differences? There are two possibilities: (a) differences in muscle length, and/or (b) differences in motor control strategies. It has been argued  that changes in the lengths of the active fibers beneath the recording electrodes could affect conduction velocity and also the shape of the EMG power spectrum. It is important to point out, however, that the EMG wavelet spectra in the present study were always measured from the middle 30[degrees] of the range of motion. Thus, muscle length should have been the same, or at least very similar during the concentric and eccentric phases of the movement. We feel that a more plausible explanation is that concentric muscle actions are controlled by a different motor control strategy than eccentric muscle actions. Huber et al  recently reported differences between the EMG spectra of elite endurance-trained versus elite sprint-trained athletes. Specifically, the spectra from the endurance-trained athletes were higher frequency than those from the sprint-trained athletes. This finding was particularly interesting because it is exactly opposite of what would be expected from conventional fiber type-based explanations of EMG frequency, where fast-twitch fibers would have higher frequency EMG spectra than slow-twitch fibers. It was hypothesized, however, that perhaps the strength-trained athletes had improved the ability to synchronize motor unit firings, which would increase the relative power in the low-frequency portion of the EMG spectrum . It is not possible to determine whether or not this same mechanism affected the EMG power spectra in the present investigation. However, recent studies [3,4] have reported increased motor unit synchronization after eccentric exercise. Thus, it is certainly possible that the differences between the spectra from the concentric and eccentric muscle actions in the present investigation were due to differences in motor unit synchronization. In addition, Linnamo et al.  provided evidence that there may be selective activation of fast-twitch motor units for the biceps brachii during eccentric, when compared to concentric muscle actions, which provides further support for the contention that the two contractions use different motor control strategies. This topic should be the focus of future studies that use both indwelling and surface EMG to examine motor control strategies and differences in the shape of the EMG spectrum during concentric versus eccentric muscle actions.
As acknowledged by von Tscharner and Goepfert , changes and/or differences in the shape of the surface EMG power spectrum are not always reflected in the center frequency value. For example, an increase in EMG center frequency could be due to greater high frequency power, lower low frequency power, or a combination of both. Similarly, comparable increases or decreases in both high frequency and low frequency power can change the shape of the EMG power spectrum without affecting its center frequency. Thus, there is a need for the development of methods capable of tracking changes in spectral shape, rather than just center frequency. The g_spectra fulfill this need nicely, while still providing values that can be analyzed with parametric statistics.
It is important to point out that even though the g_spectra explained over 92% of the variance in the wavelet spectra, they did not account for all of it. The use of additional support vectors would allow for three or maybe even four g_spectra that would increase the proportion of the variance that could be accounted for to near 100%. An obvious consideration, however, is at what point does the use of additional g_spectra provide diminishing returns, and would the additional g_spectra give relevant information? Developing a thorough understanding of the information provided by just two g_spectra is important. As stated previously, von Tscharner and Goepfert  hypothesized that the high frequency and low frequency g_spectra reflected the contributions of fast and slow muscle fibers to the power spectrum, respectively. Furthermore, as shown in Figure 1, the high frequency and low frequency g_spectra overlapped to some degree at every %1-RM. Thus, decomposition of the power spectrum cannot always be done effectively by separating it into non-overlapping high frequency and low frequency components.
The results from this study also showed that the concentric portion of the range of motion demonstrated an EMG wavelet spectrum that was dominated by intensity at higher frequencies than the corresponding spectrum for the eccentric portion of the range of motion. This finding is supported by the mean differences between the concentric and eccentric phases for the C_weights on both the high frequency and low frequency g_spectra (Table 2), as well as the relatively high classification rates at all %1-RM. Although the exact cause(s) for these differences is unclear, we hypothesize that it may reflect differences in the motor control strategies used for concentric versus eccentric muscle actions. Since the same absolute load was used throughout the movement, muscle activation should have been lower during the eccentric portion of the range of motion than during the concentric phase . This alone, however, cannot account for all the differences between the concentric and eccentric phases because the wavelet spectra were all normalized to have the same total intensity. Nonetheless, it is still difficult to identify the differences in motor control strategies that could have caused the uniquely shaped spectra. Perhaps the concentric and eccentric muscle actions used a different group of fibers. Or, it is possible that the two movements required different recruitment and/or firing rate patterns. Again, it would be difficult to pinpoint the mechanism causing these differences. We can conclude, however, that there were distinct differences in spectral shape that cannot be explained simply by different muscle activation levels, since all spectra were normalized to have equal total power.
In summary, the results from this study showed that the nonparametric spectral decomposition was a valid method for decomposing EMG wavelet spectra. The high frequency and low frequency g_spectra were able to explain at least 92% of the variance in the EMG wavelet spectra. It may be necessary, however, for future studies to use three g_spectra. In doing so, the investigator must always strike a balance between decomposition accuracy and complexity. Using more than two g_spectra improves accuracy, but the results quickly become difficult to interpret. In addition, the concentric portion of the range of motion was characterized by significantly more high frequency power than the eccentric phase, which resulted in excellent separability of the spectra from the two phases. The exact cause(s) for these differences is unclear, but may be related to differences in motor control strategies. Future studies should apply the nonparametric spectral decomposition to EMG data from different types of muscle actions and examine its sensitivity to various types of interventions.
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A parametric version of the spectral decomposition has been described previously . In this appendix, we will focus on the procedures required for the nonparametric spectral decomposition. von Tscharner and Goepfert  discussed the fact that with the parametric spectral decomposition, the generating spectra (g_spectra) can be simulated by the following function:
[phi](f) = exp [([-f/cf] + 1 + ln (f/cf)) x mode]
where f is frequency, cf is center frequency, and mode is a parameter that can change the overall shape of the spectrum. With the nonparametric spectral decomposition, however, this function is not used, and the g_spectra are instead created with the eigenvectors from a principal components analysis. Specifically, each of the two g_spectra are modeled as a linear combination of the first two principal components with the following requirements:
1. The variability of the measured EMG wavelet spectra minus the variability of those spectra reconstructed from the g_spectra must be minimal.
2. The weights with which the high frequency and low frequency g_spectra contribute to the measured EMG wavelet spectra must always be positive, since all spectra must be a linear combination of the two g_spectra.
3. The difference between the mean frequencies of the two g_spectra must be as large as possible.
As discussed by von Tscharner and Goepfert , the g_spectra were optimized with the solve block function "Minerr" of the MathCad programming language. Specifically, this function returns the values for the high- and low-frequency g_spectra such that they explain as much of the variance in the measured EMG wavelet spectra as possible. The result is the best possible combination of g_spectra for explaining the variance in the measured data. It should be emphasized that programming languages other than MathCad can be used, as long as they provide some type of function that will minimize error variance based on a set of user-defined input criteria. Once the g_spectra have been calculated, the contributing weights (C_weights) can be determined with the following equation, as described by von Tscharner and Goepfert :
C_weights = [([g_spectra.sup.T] x g_spectra).sup.-1] x [g_spectra.sup.T] x Data
where Data is a matrix formed by placing the measured EMG wavelet spectra side-by-side. The C_weights reflect the contributions of the high frequency and low frequency g_spectra to each of the measured EMG wavelet spectra in the Data matrix. Thus, after decomposition into the g_spectra, each of the measured EMG wavelet spectra in the Data matrix can be reconstructed with the following equation:
Data_reconstructed = g_spectra x C_weights
The accuracy of the decomposition can then be determined by calculating the percentage of the variance in the Data matrix that can be explained by Data_reconstructed.
Travis W. Beck (1), Matt S. Stock (2), and Jason M. DeFreitas (1)
(1) Biophysics Laboratory, University of Oklahoma, Department of Health and Exercise Science, Norman, Oklahoma and (2) Texas Tech University, Department of Health, Exercise and Sport Sciences, Lubbock, Texas
Travis W. Beck
University of Oklahoma
Department of Health and Exercise Science
110 Huston Huffman Center
Norman, OK 73019-6081
Phone: (405) 325-1378
Fax: (405) 325-0594
Table 1. Accuracy rates (%) for the principal components analysis and nonparametric spectral decomposition at each percentage of the one repetition maximum (1-RM). Each value reflects the percentage of the variance in the wavelet spectra that can be explained by the principal components and generating spectra (g_spectra). %1-RM 10 20 30 40 50 Principal Components 95.7 95.9 96.6 96.3 96.5 Generating Spectra 92.7 93.9 94.8 94.2 94.5 %1-RM 60 70 80 90 100 Principal Components 96.7 96.1 96.8 96.8 96.5 Generating Spectra 94.5 93.9 94.7 95.1 94.3 Table 2. Mean [+ or -] SD contributing weights (C_weights) on the high frequency and low frequency generating spectra (g_spectra) for the concentric and eccentric muscle actions at each percentage of the one repetition maximum (1-RM). The p-values for the paired-samples t-tests are shown in the last row. * Denotes a statistically significant difference between the concentric and eccentric muscle actions. High Frequency g_spectra %1-RM 10 20 30 40 Concentric Mean 0.052 0.096 0.137 0.128 SD 0.088 0.076 0.061 0.082 Eccentric Mean -0.052 0.096 -0.137 -0.128 SD 0.164 0.078 0.104 0.103 p = 0.068 p < 0.05 * p < 0.05 * p < 0.05 * High Frequency g_spectra %1-RM 50 60 70 80 Concentric Mean 0.119 0.114 0.125 0.119 SD 0.091 0.073 0.092 0.084 Eccentric Mean -0.119 -0.114 -0.125 -0.119 SD 0.083 0.089 0.102 0.101 p < 0.05 * p < 0.05 * p < 0.05 * p < 0.05 * High Frequency g_spectra %1-RM 90 100 Concentric Mean 0.153 0.154 SD 0.095 0.109 Eccentric Mean -0.153 -0.154 SD 0.136 0.136 p < 0.05 * p < 0.05 * Low Frequency g_spectra %1-RM 10 20 30 40 Concentric Mean -0.028 -0.059 -0.108 -0.117 SD 0.089 0.089 0.064 0.082 Eccentric Mean 0.028 0.059 0.108 0.117 SD 0.170 0.086 0.092 0.107 p = 0.210 p < 0.05 * p < 0.05 * p < 0.05 * Low Frequency g_spectra %1-RM 50 60 70 80 Concentric Mean -0.113 -0.111 -0.094 -0.118 SD 0.093 0.071 0.090 0.082 Eccentric Mean 0.113 0.111 0.094 0.118 SD 0.083 0.104 0.105 0.098 p < 0.05 * p < 0.05 * p < 0.05 * p < 0.05 * Low Frequency g_spectra %1-RM 90 100 Concentric Mean -0.129 -0.131 SD 0.113 0.121 Eccentric Mean 0.129 0.131 SD 0.112 0.118 p < 0.05 * p < 0.05 * Table 3. Classification accuracy for the electromyographic (EMG) wavelet spectra during the concentric versus eccentric muscle actions at each % of the one repetition maximum (1-RM). %1-RM 10% 20% 30% 40% 50% Correct 19 25 27 27 26 Total Cases 28 28 28 28 28 % Correct 67.9 89.3 96.4 96.4 92.9 60% 70% 80% 90% 100% Correct 26 27 25 25 24 Total Cases 28 28 28 28 28 % Correct 92.9 96.4 89.3 89.3 85.7
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|Author:||Beck, Travis W.; Stock, Matt S.; DeFreitas, Jason M.|
|Publication:||Clinical Kinesiology: Journal of the American Kinesiotherapy Association|
|Date:||Jun 22, 2013|
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