- Email: [email protected]
Uncovering chaotic structure in mechanomyography signals of fatigue biceps brachii muscle
ARTICLE IN PRESS Journal of Biomechanics 43 (2010) 1224–1226
Contents lists available at ScienceDirect
Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com
Short communication
Uncovering chaotic structure in mechanomyography signals of fatigue biceps brachii muscle Hong-Bo Xie a,c,n, Jing-Yi Guo a, Yong-Ping Zheng a,b a
Department of Health Technology and Informatics, The Hong Kong Polytechnic University, Hong Kong Research Institute of Innovative Products and Technologies, The Hong Kong Polytechnic University, Hong Kong c Department of Biomedical Engineering, Jiangsu University, Zhenjiang, PR China b
a r t i c l e in f o
a b s t r a c t
Article history: Accepted 27 November 2009
The mechanomyography (MMG) signal reflects mechanical properties of limb muscles that undergo complex phenomena in different functional states. We undertook the study of the chaotic nature of MMG signals by referring to recent developments in the field of nonlinear dynamics. MMG signals were measured from the biceps brachii muscle of 5 subjects during fatigue of isometric contraction at 80% maximal voluntary contraction (MVC) level. Deterministic chaotic character was detected in all data by using the Volterra–Wiener–Korenberg model and noise titration approach. The noise limit, a power indicator of the chaos of fatigue MMG signals, was 22.20 78.73. Furthermore, we studied the nonlinear dynamic features of MMG signals by computing their correlation dimension D2, which was 3.35 7 0.36 across subjects. These results indicate that MMG is a high-dimensional chaotic signal and support the use of the theory of nonlinear dynamics for analysis and modeling of fatigue MMG signals. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Muscle Mechanomyography Nonlinearity Chaos Noise titration Correlation dimension
1. Introduction
2. Methods
The mechanomyography signal records and quantifies lowfrequency lateral oscillations of active skeletal muscle. These oscillations reflect the ‘‘mechanical counterpart’’ of the motor unit electrical activity measured by EMG (Orizio, 1993). The present methods used for MMG analysis are most commonly based on the assumption that the signal is a linear stochastic process; thus temporal and frequency spectrum characteristics are used (Esposito et al., 1998; Madeleine et al., 2006; Yasushi et al., 2004). Recently, wavelet and other linear time–frequency representation methods have also been suggested for analyzing MMG signals (Xie et al., 2009). Although these techniques do characterize MMG signals, nonlinear techniques may be needed to ascertain the characteristics of MMG signals and to fully characterize their pattern. To our knowledge, few investigators have thus far examined the nonlinear nature of MMG. Thus, the present study aimed to investigate the fatigue MMG signals during static contraction by applying nonlinear dynamic analysis methods. In this study, some recent developments in the field of nonlinear dynamics were employed with the aim of detecting and locating determinism and nonlinearity in the system governing the time behavior of fatigue MMG signals.
2.1. MMG data sets
n Corresponding author at:. Department of Health Technology and Informatics, The Hong Kong Polytechnic University, Hong Kong. Tel.: + 86 852 27667664; fax: + 86 852 23624365. E-mail addresses: [email protected] (H.-B. Xie), [email protected] (Y.-P. Zheng).
0021-9290/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2009.11.035
The experiment were conducted on five healthy human subjects (mean age=29.473.6 yr, mean mass=71.6714.8 kg, mean height=1.7670.06 m). None had a history of any neuromuscular disorder and they gave informed consent to the present experimental procedure that had been approved by the University Ethics Committee. The subjects visited the laboratory two times (a familiarization and a main testing session), 3 days apart at the same time under the same environmental conditions. During the first (familiarization) session, subjects practiced isometric maximal and submaximal voluntary contractions. During the second session, the accelerometer (EGAS-FS-10-VO5, Entran Inc., Fairfield, NJ) was placed on longitudinally abraded, clean skin under the thickest point of the biceps brachii. It was fixed to the skin using double adhesive tape. After appropriate warm-up, the maximum voluntary contraction (MVC) of elbow flexion of each subject was estimated by performing three maximal efforts using a Cybex machine (Cybex Norm Testing and Rehabilitation System, Cybex Norm Int. Inc., Ronkonkoma, USA). Each MVC lasted 5 s, with 3-min rest intervals between repetitions. Following a 15-min break, the subject was asked to perform an elbow flexion against the lever arm to 80% of the maximal voluntary contraction. The visual feedback of the force showed on the screen and the verbal encouragement were provided to maintain the target force. The test was stopped when the force dropped to approximately 70% of the MVC, indicating that the muscle was exhausted (Dimitrova et al., 2009). The gain of the MMG signal was 5000 with a 5– 250 Hz bandwidth. Signals from the sensor were acquired at 500 Hz and stored in a computer. The stationary segment in the fatigue state with 1000 points was selected for further nonlinear analysis.
2.2. Nonlinear analysis The proposed framework for MMG analysis in the present work consisted of three logical steps, i.e., the Volterra–Wiener–Korenberg (VWK) model approach for
ARTICLE IN PRESS H.-B. Xie et al. / Journal of Biomechanics 43 (2010) 1224–1226 nonlinear detection (Barahona and Poon, 1996), numerical titration method for chaos detection (Poon and Barahona, 2001), and Gaussian kernel method for correlation dimension estimation (Diks, 1996). In brief, several VWK series are first generated, with different degrees of nonlinearity d and embedding dimension k, to
0 linear nonlinear
produce a family of linear and nonlinear polynomial autoregressive models. The best linear model is obtained by adjusting the k value with d = 1 to minimize the Akaike information theoretic criterion C(r). The best nonlinear model is obtained by sequentially increasing k values with d 41. A parametric F-test was applied to reject the hypothesis that nonlinear modes are not better than linear models if C(r)lin 4 C(r)nl in the statistical sense. If the null hypothesis is rejected, the titration process itself can be started (Poon and Barahona, 2001). White noise of incrementally increasing SD is added to the time series until the null hypothesis can no longer be rejected. This defines a noise limit (NL), which when above 0, indicates chaos and provides an estimate of its intensity. All codes of the detection procedures were designed and implemented using Matlab software (Version 7.0, MathWorks, Inc., MA, USA).
C (r)
-0.5
1225
-1
3. Results and discussion -1.5 50
100
150
200
Number of terms (r) Fig. 1. Linear and nonlinear model fits using the Volterra–Wiener–Korenberg series for the representive MMG signal acquired from subject 2. The information criterion C(r) indicates that dopt 41. Similarly, the F-test rejects the null hypothesis and demonstrates the nonlinear component is significant.
0
Linear Nonlinear
C (r)
9% noise -0.5 -1 0
50
100 150 Number of terms (r)
0
Linear Nonlinear
18% noise C (r)
200
-0.5 -1 0
50
100
150
200
Number of terms (r) 0
Linear Nonlinear
C (r)
27% noise -0.2 -0.4
0
50
100
150
200
Number of terms (r) Fig. 2. The information criterion C(r) vs. number of terms r plots for the MMG signal of subject 2 when added noise was (a) 9%, (b) 18%, and (c) 27%. The statistical comparison of the linear and the nonlinear models still rejects the hypothesis of their identity when the MMG is added with noise, indicating the chaos in fatigue MMG signals.
4 Correlation dimension (D2)
0
The VWK model method was first applied to the MMG sequences to test nonlinearity. In all subjects, C(r) vs. number of terms r were analyzed for both linear and nonlinear models with variation of the parameters k and d. Fig. 1 shows a typical C(r) vs. r plots for the MMG signal taken from subject 2. The plots for other subjects were similar, i.e., Clin(r) was significantly larger than Cnl(r) by F-test. In all the cases, the null hypothesis of linearity was rejected using the F-test. This finding indicates that the analyzed MMG signals were all nonlinear. Then, according to the chaotic titration method, we added white noise to the MMG signal until the VWK nonlinear identification method could not detect the nonlinearity. Titration of each MMG signal was performed with an increment of 1% noise at every step. Fig. 2(a–c) show C(r) vs. r plots for the MMG signal shown in Fig. 1 for 9%, 18%, and 27% noise additions, respectively. The highest noise limit values obtained in each subject are listed in Table 1. The noise limit yielded by the noise titration procedure for each data set was above zero, depicting a sufficient condition for chaos in the fatigue MMG signals. Fig. 3 shows the plot of the correlation dimension vs. varying embedding dimension based on the segment of MMG data taken from subject 2. When the embedding dimension m was increased, the correlation dimension D2 first rose and then entered a relative flat range with slight fluctuation. The average value and
3 2 1 0 -1 0
5
10
15
20
Embedding dimension (m) Fig. 3. The measurement of MMG (subject 2) correlation dimension D2 as a function of the embedding dimension m.
Table 1 The noise limit values found by using the noise titration procedure in five subjects. Subjects
Noise limit (%)
Embedding dimension k
Nonlinear degree d
Correlation dimension D2 (Mean 7 Std)
1 2 3 4 5 Mean 7 Std
16 27 12 34 22 22.207 8.73
6 6 6 6 6
4 4 4 4,5 5
3.43 70.19 3.84 70.23 3.04 70.16 3.50 70.25 2.95 70.17 3.35 70.36
ARTICLE IN PRESS 1226
H.-B. Xie et al. / Journal of Biomechanics 43 (2010) 1224–1226
corresponding standard deviation were obtained over the flat part, i.e., m= 8–19 for subject 2, giving D2 =3.84 70.23. This measurement indicates that the mechanical activity of the muscle within this segment of MMG can be described by 3–4 active degrees of freedom. Hence, the dynamical behavior of the muscle’s mechanical activity is most likely to originate from the high-dimensional chaos. The average of D2 of other subjects is obtained over m=7–19 for subject 3 and 5, m =8–19 for subject 1 and 4. The results are shown in Table 1. The mean and standard deviation of the correlation dimension across five subjects were 3.35 and 0.36, respectively. Application of MMG signals for assessment of muscular effort is useful for evaluation of muscular fatigue in order to prevent work-related musculoskeletal disorders (Kassolik et al., 2009), diagnosis of neuromuscular diseases (Marusiak et al., 2009), and establish physical therapy or rehabilitation programs (Gorelick, 2006). Our results advocate the use of the theory of nonlinear dynamics for analysis and modeling of fatigue MMG. Combining the surrogate data method with chaotic invariants may be potentially applied to differentiate the muscle states in the future work (Ocak, 2009; Schreiber and Schmitz, 2000).
Conflict of interest None of the authors have any conflict of interest in this study.
Acknowledgements We would like to thank Prof. C.S. Poon for offering the Matlab code of noise titration. This work was partially supported by the Hong Kong Research Grant Council (PolyU 5331/06E), The Hong Kong Polytechnic University (1-BB69), The Jiangsu Natural Science Foundation (BK2009198), and Jiangsu University (07JDG40), PRC.
References Barahona, M., Poon, C., 1996. Detection of nonlinear dynamics in short, noisy time series. Nature 381, 215–217. Diks, C., 1996. Estimating invariants of noisy attractors. Physics Review E 53, R4263–R4266. Dimitrova, N.A., Arabadzhiev, T.I., Hogrel, J.-Y., Dimitrov, G.V., 2009. Fatigue analysis of interference EMG signals obtained from biceps brachii during isometric voluntary contraction at various force levels. Journal of Electromyography and Kinesiology 19, 252–258. Esposito, F., Orizio, C., Veicsteinas, A., 1998. Electromyogram and mechanomyogram changes in fresh and fatigued muscle during sustained contraction in men. European Journal of Applied Physiology And Occupational Physiology 78 6, 494–501. Gorelick, M., 2006. Location of injury site in chronic low back pain patients: an electromyographic and mechanomyographic analysis, Ph.D. Thesis. University of Wollongong, Australia. Kassolik, K., Jasko´lska, A., Kisiel-Sajewicz, K., Marusiak, J., Kawczyn´ski, A., Jasko´lski, A., 2009. Tensegrity principle in massage demonstrated by electro- and mechanomyography. Journal of Bodywork and Movement Therapies 13, 164–170. Madeleine, P., Ge, H.Y., Jasko´lska, A., Farina, D., Jasko´lski, A., Arendt-Nielsen, A., 2006. Spectral moments of mechanomyographic signals recorded with accelerometer and microphone during sustained fatiguing contractions. Medical and Biological Engineering and Computing 44 (4), 290–297. Marusiak, J., Jasko´lska, A., Kisiel-Sajewicz, K., Yue, G.H., Jasko´lski, A., 2009. EMG and MMG activities of agonist and antagonist muscles in Parkinson’s disease patients during absolute submaximal load holding. Journal of Electromyography and Kinesiology 19, 903–914. Ocak, H., 2009. Automatic detection of epileptic seizures in EEG using discrete wavelet transform and approximate entropy. Expert Systems with Applications 36, 2027–2036. Orizio, C., 1993. Muscle sound: bases for the introduction of a mechanomyographic signal in muscle studies. Critical Review of Biomedical Engineering 21, 201–243. Poon, C., Barahona, M., 2001. Titration of chaos with added noise. Proceedings of the National Academy of Sciences 98, 7107–7112. Schreiber, T., Schmitz, A., 2000. Surrogate time series. Physica D 142, 227–244. Xie, H.B., Zheng, Y.P., Guo, J.Y., 2009. Classification of the mechanomyogram signal using a wavelet packet transform and singular value decomposition for multifunction prosthesis control. Physiological Measurement 30, 441–457. Yasushi, I., Kumi, A., Katsumi, M., Makoto, W., Kunihiko, I., 2004. Time–frequency analysis of mechanomyogram during sustained contractions with muscle fatigue. Systems and Computers in Japan 35 (1), 26–36.
Contents lists available at ScienceDirect
Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com
Short communication
Uncovering chaotic structure in mechanomyography signals of fatigue biceps brachii muscle Hong-Bo Xie a,c,n, Jing-Yi Guo a, Yong-Ping Zheng a,b a
Department of Health Technology and Informatics, The Hong Kong Polytechnic University, Hong Kong Research Institute of Innovative Products and Technologies, The Hong Kong Polytechnic University, Hong Kong c Department of Biomedical Engineering, Jiangsu University, Zhenjiang, PR China b
a r t i c l e in f o
a b s t r a c t
Article history: Accepted 27 November 2009
The mechanomyography (MMG) signal reflects mechanical properties of limb muscles that undergo complex phenomena in different functional states. We undertook the study of the chaotic nature of MMG signals by referring to recent developments in the field of nonlinear dynamics. MMG signals were measured from the biceps brachii muscle of 5 subjects during fatigue of isometric contraction at 80% maximal voluntary contraction (MVC) level. Deterministic chaotic character was detected in all data by using the Volterra–Wiener–Korenberg model and noise titration approach. The noise limit, a power indicator of the chaos of fatigue MMG signals, was 22.20 78.73. Furthermore, we studied the nonlinear dynamic features of MMG signals by computing their correlation dimension D2, which was 3.35 7 0.36 across subjects. These results indicate that MMG is a high-dimensional chaotic signal and support the use of the theory of nonlinear dynamics for analysis and modeling of fatigue MMG signals. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Muscle Mechanomyography Nonlinearity Chaos Noise titration Correlation dimension
1. Introduction
2. Methods
The mechanomyography signal records and quantifies lowfrequency lateral oscillations of active skeletal muscle. These oscillations reflect the ‘‘mechanical counterpart’’ of the motor unit electrical activity measured by EMG (Orizio, 1993). The present methods used for MMG analysis are most commonly based on the assumption that the signal is a linear stochastic process; thus temporal and frequency spectrum characteristics are used (Esposito et al., 1998; Madeleine et al., 2006; Yasushi et al., 2004). Recently, wavelet and other linear time–frequency representation methods have also been suggested for analyzing MMG signals (Xie et al., 2009). Although these techniques do characterize MMG signals, nonlinear techniques may be needed to ascertain the characteristics of MMG signals and to fully characterize their pattern. To our knowledge, few investigators have thus far examined the nonlinear nature of MMG. Thus, the present study aimed to investigate the fatigue MMG signals during static contraction by applying nonlinear dynamic analysis methods. In this study, some recent developments in the field of nonlinear dynamics were employed with the aim of detecting and locating determinism and nonlinearity in the system governing the time behavior of fatigue MMG signals.
2.1. MMG data sets
n Corresponding author at:. Department of Health Technology and Informatics, The Hong Kong Polytechnic University, Hong Kong. Tel.: + 86 852 27667664; fax: + 86 852 23624365. E-mail addresses: [email protected] (H.-B. Xie), [email protected] (Y.-P. Zheng).
0021-9290/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2009.11.035
The experiment were conducted on five healthy human subjects (mean age=29.473.6 yr, mean mass=71.6714.8 kg, mean height=1.7670.06 m). None had a history of any neuromuscular disorder and they gave informed consent to the present experimental procedure that had been approved by the University Ethics Committee. The subjects visited the laboratory two times (a familiarization and a main testing session), 3 days apart at the same time under the same environmental conditions. During the first (familiarization) session, subjects practiced isometric maximal and submaximal voluntary contractions. During the second session, the accelerometer (EGAS-FS-10-VO5, Entran Inc., Fairfield, NJ) was placed on longitudinally abraded, clean skin under the thickest point of the biceps brachii. It was fixed to the skin using double adhesive tape. After appropriate warm-up, the maximum voluntary contraction (MVC) of elbow flexion of each subject was estimated by performing three maximal efforts using a Cybex machine (Cybex Norm Testing and Rehabilitation System, Cybex Norm Int. Inc., Ronkonkoma, USA). Each MVC lasted 5 s, with 3-min rest intervals between repetitions. Following a 15-min break, the subject was asked to perform an elbow flexion against the lever arm to 80% of the maximal voluntary contraction. The visual feedback of the force showed on the screen and the verbal encouragement were provided to maintain the target force. The test was stopped when the force dropped to approximately 70% of the MVC, indicating that the muscle was exhausted (Dimitrova et al., 2009). The gain of the MMG signal was 5000 with a 5– 250 Hz bandwidth. Signals from the sensor were acquired at 500 Hz and stored in a computer. The stationary segment in the fatigue state with 1000 points was selected for further nonlinear analysis.
2.2. Nonlinear analysis The proposed framework for MMG analysis in the present work consisted of three logical steps, i.e., the Volterra–Wiener–Korenberg (VWK) model approach for
ARTICLE IN PRESS H.-B. Xie et al. / Journal of Biomechanics 43 (2010) 1224–1226 nonlinear detection (Barahona and Poon, 1996), numerical titration method for chaos detection (Poon and Barahona, 2001), and Gaussian kernel method for correlation dimension estimation (Diks, 1996). In brief, several VWK series are first generated, with different degrees of nonlinearity d and embedding dimension k, to
0 linear nonlinear
produce a family of linear and nonlinear polynomial autoregressive models. The best linear model is obtained by adjusting the k value with d = 1 to minimize the Akaike information theoretic criterion C(r). The best nonlinear model is obtained by sequentially increasing k values with d 41. A parametric F-test was applied to reject the hypothesis that nonlinear modes are not better than linear models if C(r)lin 4 C(r)nl in the statistical sense. If the null hypothesis is rejected, the titration process itself can be started (Poon and Barahona, 2001). White noise of incrementally increasing SD is added to the time series until the null hypothesis can no longer be rejected. This defines a noise limit (NL), which when above 0, indicates chaos and provides an estimate of its intensity. All codes of the detection procedures were designed and implemented using Matlab software (Version 7.0, MathWorks, Inc., MA, USA).
C (r)
-0.5
1225
-1
3. Results and discussion -1.5 50
100
150
200
Number of terms (r) Fig. 1. Linear and nonlinear model fits using the Volterra–Wiener–Korenberg series for the representive MMG signal acquired from subject 2. The information criterion C(r) indicates that dopt 41. Similarly, the F-test rejects the null hypothesis and demonstrates the nonlinear component is significant.
0
Linear Nonlinear
C (r)
9% noise -0.5 -1 0
50
100 150 Number of terms (r)
0
Linear Nonlinear
18% noise C (r)
200
-0.5 -1 0
50
100
150
200
Number of terms (r) 0
Linear Nonlinear
C (r)
27% noise -0.2 -0.4
0
50
100
150
200
Number of terms (r) Fig. 2. The information criterion C(r) vs. number of terms r plots for the MMG signal of subject 2 when added noise was (a) 9%, (b) 18%, and (c) 27%. The statistical comparison of the linear and the nonlinear models still rejects the hypothesis of their identity when the MMG is added with noise, indicating the chaos in fatigue MMG signals.
4 Correlation dimension (D2)
0
The VWK model method was first applied to the MMG sequences to test nonlinearity. In all subjects, C(r) vs. number of terms r were analyzed for both linear and nonlinear models with variation of the parameters k and d. Fig. 1 shows a typical C(r) vs. r plots for the MMG signal taken from subject 2. The plots for other subjects were similar, i.e., Clin(r) was significantly larger than Cnl(r) by F-test. In all the cases, the null hypothesis of linearity was rejected using the F-test. This finding indicates that the analyzed MMG signals were all nonlinear. Then, according to the chaotic titration method, we added white noise to the MMG signal until the VWK nonlinear identification method could not detect the nonlinearity. Titration of each MMG signal was performed with an increment of 1% noise at every step. Fig. 2(a–c) show C(r) vs. r plots for the MMG signal shown in Fig. 1 for 9%, 18%, and 27% noise additions, respectively. The highest noise limit values obtained in each subject are listed in Table 1. The noise limit yielded by the noise titration procedure for each data set was above zero, depicting a sufficient condition for chaos in the fatigue MMG signals. Fig. 3 shows the plot of the correlation dimension vs. varying embedding dimension based on the segment of MMG data taken from subject 2. When the embedding dimension m was increased, the correlation dimension D2 first rose and then entered a relative flat range with slight fluctuation. The average value and
3 2 1 0 -1 0
5
10
15
20
Embedding dimension (m) Fig. 3. The measurement of MMG (subject 2) correlation dimension D2 as a function of the embedding dimension m.
Table 1 The noise limit values found by using the noise titration procedure in five subjects. Subjects
Noise limit (%)
Embedding dimension k
Nonlinear degree d
Correlation dimension D2 (Mean 7 Std)
1 2 3 4 5 Mean 7 Std
16 27 12 34 22 22.207 8.73
6 6 6 6 6
4 4 4 4,5 5
3.43 70.19 3.84 70.23 3.04 70.16 3.50 70.25 2.95 70.17 3.35 70.36
ARTICLE IN PRESS 1226
H.-B. Xie et al. / Journal of Biomechanics 43 (2010) 1224–1226
corresponding standard deviation were obtained over the flat part, i.e., m= 8–19 for subject 2, giving D2 =3.84 70.23. This measurement indicates that the mechanical activity of the muscle within this segment of MMG can be described by 3–4 active degrees of freedom. Hence, the dynamical behavior of the muscle’s mechanical activity is most likely to originate from the high-dimensional chaos. The average of D2 of other subjects is obtained over m=7–19 for subject 3 and 5, m =8–19 for subject 1 and 4. The results are shown in Table 1. The mean and standard deviation of the correlation dimension across five subjects were 3.35 and 0.36, respectively. Application of MMG signals for assessment of muscular effort is useful for evaluation of muscular fatigue in order to prevent work-related musculoskeletal disorders (Kassolik et al., 2009), diagnosis of neuromuscular diseases (Marusiak et al., 2009), and establish physical therapy or rehabilitation programs (Gorelick, 2006). Our results advocate the use of the theory of nonlinear dynamics for analysis and modeling of fatigue MMG. Combining the surrogate data method with chaotic invariants may be potentially applied to differentiate the muscle states in the future work (Ocak, 2009; Schreiber and Schmitz, 2000).
Conflict of interest None of the authors have any conflict of interest in this study.
Acknowledgements We would like to thank Prof. C.S. Poon for offering the Matlab code of noise titration. This work was partially supported by the Hong Kong Research Grant Council (PolyU 5331/06E), The Hong Kong Polytechnic University (1-BB69), The Jiangsu Natural Science Foundation (BK2009198), and Jiangsu University (07JDG40), PRC.
References Barahona, M., Poon, C., 1996. Detection of nonlinear dynamics in short, noisy time series. Nature 381, 215–217. Diks, C., 1996. Estimating invariants of noisy attractors. Physics Review E 53, R4263–R4266. Dimitrova, N.A., Arabadzhiev, T.I., Hogrel, J.-Y., Dimitrov, G.V., 2009. Fatigue analysis of interference EMG signals obtained from biceps brachii during isometric voluntary contraction at various force levels. Journal of Electromyography and Kinesiology 19, 252–258. Esposito, F., Orizio, C., Veicsteinas, A., 1998. Electromyogram and mechanomyogram changes in fresh and fatigued muscle during sustained contraction in men. European Journal of Applied Physiology And Occupational Physiology 78 6, 494–501. Gorelick, M., 2006. Location of injury site in chronic low back pain patients: an electromyographic and mechanomyographic analysis, Ph.D. Thesis. University of Wollongong, Australia. Kassolik, K., Jasko´lska, A., Kisiel-Sajewicz, K., Marusiak, J., Kawczyn´ski, A., Jasko´lski, A., 2009. Tensegrity principle in massage demonstrated by electro- and mechanomyography. Journal of Bodywork and Movement Therapies 13, 164–170. Madeleine, P., Ge, H.Y., Jasko´lska, A., Farina, D., Jasko´lski, A., Arendt-Nielsen, A., 2006. Spectral moments of mechanomyographic signals recorded with accelerometer and microphone during sustained fatiguing contractions. Medical and Biological Engineering and Computing 44 (4), 290–297. Marusiak, J., Jasko´lska, A., Kisiel-Sajewicz, K., Yue, G.H., Jasko´lski, A., 2009. EMG and MMG activities of agonist and antagonist muscles in Parkinson’s disease patients during absolute submaximal load holding. Journal of Electromyography and Kinesiology 19, 903–914. Ocak, H., 2009. Automatic detection of epileptic seizures in EEG using discrete wavelet transform and approximate entropy. Expert Systems with Applications 36, 2027–2036. Orizio, C., 1993. Muscle sound: bases for the introduction of a mechanomyographic signal in muscle studies. Critical Review of Biomedical Engineering 21, 201–243. Poon, C., Barahona, M., 2001. Titration of chaos with added noise. Proceedings of the National Academy of Sciences 98, 7107–7112. Schreiber, T., Schmitz, A., 2000. Surrogate time series. Physica D 142, 227–244. Xie, H.B., Zheng, Y.P., Guo, J.Y., 2009. Classification of the mechanomyogram signal using a wavelet packet transform and singular value decomposition for multifunction prosthesis control. Physiological Measurement 30, 441–457. Yasushi, I., Kumi, A., Katsumi, M., Makoto, W., Kunihiko, I., 2004. Time–frequency analysis of mechanomyogram during sustained contractions with muscle fatigue. Systems and Computers in Japan 35 (1), 26–36.