Spectral analysis of muscular sound during isometric contraction of biceps brachii CLAUDIO MARISA
ORIZIO, RENZA PERINI, BERTRAND MARANZANA FIGINI, AND ARSENIO
DIEMONT, VEICSTEINAS
Istituto di Fisiologia Umana, Dipartimento di Scienze Biomediche e Biotecnologie, Universitk di Brescia, 25124 Brescia; and Centro di Teoria dei Sistemi, Dipartimento di Elettronica, Politecnico di Milano, 20138 Milan, Italy
ORIZIO, CLAUDIO, RENZA PERINI, BERTRANDDIEMONT, MARISA MARANZANA FIGINI, AND ARSENIO VEICSTEINAS. Spectral analysis of muscular sound during isometric contraction of biceps bra&ii. J. Appl. Physiol. 68(2): 508-512, 1990.-The frequency content of muscular sound (MS), detected by placing a contact sensor transducer over the belly of the biceps brachii during 10 isometric contractions of 4 s each [lo-100% of maximal voluntary contraction (MVC)] in seven sedentary men, was analyzed by the maximum entropy spectral estimation and the fast Fourier transform methods. With increasing %MVC, the power spectrum of the MS enlarges and tends to be multimodal beyond 30% MVC. Independent of the method, the mean frequency is -11 Hz at the lower tasks, and then it increases up to 15 Hz at 80% MVC and to 22 Hz at 100% MVC. When the effort is increased the relative power in the 15 to 45-Hz bandwidth (range of firing rate of the motor units with fast-twitch fibers) from 20% reaches 55% of the power in the 6- to 45-Hz bandwidth (firing rate range of motor units with slow- and fast-twitch fibers). Our results obtained by the two different modeling approaches confirm the reliability of the sound signal. Moreover, it appears that from the MS the motor unit activation pattern can be retrieved. motor unit activation
pattern;
recruitment;
exertion
WHEN MUSCLE CONTRACTSa low rumbling noise is detectable at its surface. This phenomenon was described in the last century and named muscular sound (MS) (15, 22). More recently the interest in MS has been renewed. Nevertheless its nature is still not well defined. Data from isolated frog muscle suggested that the source of MS might be the “brief shock wave” caused by the stepwise change in radius of the activated fibers (5) or by the “gross lateral movement of the central region of the muscle” when stimulated (2,10). Studies on human muscle have indicated that the possible factors implied in MS generation could be the pressure waves generated by dimensional changes, i.e., lateral expansion of the activated fibers (l2), the physiological tremor (20), the actomyosin cross-bridge cycling (19), and the oscillations due to the pulling on the elastic-connective tissue at each step of contraction (21). The frequency content of the MS was also studied in the last century and roughly estimated to be between 25 and 40 Hz (15, 22). However, the recent availability of valuable tools, such as sensors capable of transducing 508
0161-7567/90
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MS into an electrical signal (Sound MyoGram, SMG), and of rapid spectral analysis algorithms has provided a more accurate means of defining the frequency content of the SMG. The most relevant frequency parameters found during isometric contraction of human biceps brachii were reported to be between 10 and 25 Hz (9, 1921). The wide range of frequency values observed probably depends on the not well-defined and comparable contraction intensities and on the different signal-processing techniques adopted by the different authors. The growing interest in MS, the uncertain data reported in the literature, and the lack of a systematic analysis of the SMG in the frequency domain during isometric exercise in the whole range of contraction intensity have prompted the present study. However, the final aim is to verify whether the frequency content of SMG reflects the motor unit (MU) activation pattern at the different levels of isometric effort. To check the influence of the computation algorithms on the estimation of the power spectrum frequency parameters, two spectral analysis methods, fast Fourier transform (FFT) and the maximum entropy spectral estimation (MESE), were adopted. SUBJECTSAND METHODS
After being fully informed about the experimental procedure, a group of seven healthy young males [age, 21-25 yr; body wt, 63-73 kg; maximal voluntary contraction of the elbow flexors (MVC), 300-360 N] volunteered for the study. Each subject was asked to isometrically contract the biceps brachii muscle of his preferential arm, which was kept in an adjustable anatomically shaped stirrup constructed so as to maintain a constant angle of 115" between arm and forearm (18). The output force was recorded by a load cell (Interface S-M 1000, linear from 0 to 1,000 N) strapped to the subject’s wrist, which was kept halfway between pronation and supination. The applied force was displayed on a monitor to provide the necessary visual feedback to the subject. The MS was detected at the belly of the biceps brachii by a contact sensor transducer (Hewlett-Packard model 21050 A; bandwidth, 0.02-2,000 Hz) and then amplified
0 1990 the American
Physiological
Society
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SPECTRAL
ANALYSIS
by the Hewlett Packard 8802A medium gain amplifier and filtered (bandwidth, 2-100 Hz). After analog-to-digital conversion (Burr-Brown PCI2OK) the SMG was sampled (256 points/s) and stored on an IBM-AT personal computer for further processing. The results are given as means t SE. The statistical differences between the various groups of data are estimated by the t test and are considered significant for P < 0.05. Spectral Analysis
The power spectrum density distribution (PSD) was estimated by the MESE and by the FFT methods. With both methods the upper limit of the power spectrum estimation was 128 Hz. lMESE method. The Burg algorithm was used (6). The recursive technique describes the signal y(t) by means of an autoregressive (AR) model (4,8) YW = -[aley(t
- 1) + azay(t - 2)
+ %-Y(t - p)] + e(t) where y(t) is the current value of the signal at time t, ap are the AR parameters, e(t) is the estimation error, and p is the order of the model. The AR parameters were estimated by a least square fitting. The optimal order of the model, which indicates the most parsimonious model (16), was estimated by three criteria and was defined as the middle one of the three separately selected ones. Increasing the model order (MO) from the optimal one, the figure of merit reduces up to a MO of ~20, indicating an improvement in the relationship between signal characteristics and the MO. In this range the MO related to the biggest drop in the behavior of the figure of merit was selected. This procedure was adopted to estimate a more detailed PSD (9) FFT method. The FFT with a Papoulis window (14) was applied to the same data. From the PSDs, calculated by both MESE and FFT, the mean frequency (MF) and distribution of the power in adjoining 5-Hz-wide frequency bands were obtained. +
l
l
l
aI,
l
l
l
9
EXPERIMENTAL
PROCEDURE
After determining the maximal voluntary contraction (MVC), i.e., the strongest of three maximal contractions lasting 3 s each, the subject trained himself daily for 1 wk on the laboratory apparatus to learn how to keep the output force constant at different levels of effort. During the experimental session the subject performed, in a randomized sequence, 10 isometric contractions from 10 to 100% MVC, each lasting 4 s. To avoid transient phenomena the middle 2 s of the 4-s exercise were processed. Between one task and the next a rest period of 5 min was allowed. During this time the subject kept his arm in the stirrup with the transducer in place. The muscular sound variability was estimated both intra- and interindividually. For this purpose SMG was recorded at 20% MVC in I) one subject during 1 min of
OF MUSCULAR
509
SOUND
sustained contraction (epochs of 2 s out of every 6 s of activity were stored) and in 2) all the subjects during the 4-s trials performed on two different days. RESULTS
During the contraction the output force was maintained constant within &5% of the target value. Whenever one of the trials showed a greater variability, the whole series from 10 to 100% MVC was repeated. In Fig. 1 the digitized SMG signals from 10 to 100% MVC for a typical subject are presented. It can be noted that the amplitude of the signal increases up to 80% MVC and then decreases. Signal Repeatability
In Table 1 the individual and the average values of the mean frequency computed by MESE and FFT for each epoch of 2 s during the 1 min of sustained contraction at 20% MVC are reported. No significant differences among the different epochs nor between MESE and FFT values are observed. In Table 2 the individual mean frequency calculated with the two spectral analysis methods in all subjects on the two different days are reported together with the group average values. The correlation and determination
f 1200 rv 200.
6oo nV
t 1200
l v
f 1200
lV
r
50 FIG. 1. Sound myogram signal of 2-s epochs after analog-to-digital conversion during isometric contraction of biceps brachii from 10 to 100% MVC in a representative subject. Gain in lo-50% MVC is double that in 60-100% MVC range.
TABLE
1. SMG mean frequency Mean
Frequency
Epoch MESE
1 2 3 4 5 6 7 8 9 10
10.7 11.8 11.8
FFT
10.1
11.4 11.9 12.1 10.3
11.2 10.3 9.3 9.6 11.7
12.0 10.7 9.7 9.9 12.0
10.3
11.0
Means t SE 10.68kO.29 11.lt0.29 Values are mean frequency (Hz) of SMG recorded during 1 min (10 epochs) of sustained contraction at 20% MVC.
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510
SPECTRAL
MESE
Subj No.
Day
1 2 3 4 5 6 7 Means
t, SE
FFT
1
Day 2
8.8 12.5 10.0 10.1 10.4 10.5 11.8 10.59t0.46
8.3 11.2 10.9 11.0 11.0 10.9 12.1 10.7720.44
Mean frequency (Hz) all subjects at 20% MVC.
of SMG
Day
20
30
40
0
was recorded
10
20
30
FIG.
IO
2. Normalized power spectra by MESE and FFT in lo-100%
20
30
2
8.9 11.7 11.5 11.5 12.3 11.6 12.7 11.46k0.46 days
in
F.F.T.
40 Hz
of signal reported MVC range.
M.E.S.E.
0
Day
on 2 different
x M.V.C.
Hz
mated
1
9.5 13.1 10.9 11.0 11.7 11.1 12.9 11.46k0.47
M.E.S.E.
10
OF
2. Test-retest SMG mean frequency
TABLE
0
ANALYSIS
40
0
10
Hz FIG. 3. Average spectra (MESE Each spectrum is mean of individual 7) at each contraction intensity.
% M.V.C.
20
30
in Fig. 1 esti-
F.F.T.
40
MUSCULAR
SOUND
increasing intensity of contraction the SMG spectrum shifts toward the higher frequencies and enlarges. When MESE spectra are considered it is possible to identify, starting from 30% MVC, two frequency ranges in which the power is distributed. This tendency toward multimodality is clearer beyond 70% MVC. The FFT spectra present a more detailed morphology. Even here as the intensity of contraction increases a change in the spectra from uni- to multimodality occurs. Independently of the subject and the spectral analysis method used, the first peak of the multimodal PSD lies in the 6- to 11-Hz bandwidth. This is the same bandwidth of the unimodal PSD peak frequency. In Fig. 4 the average values of the MF calculated by both MESE and FFT are given as a function of %MVC. At each value on the x-axis the MF computed by FFT is -1 Hz higher than that computed by MESE. The MF increases with %MVC but not in a unique fashion. Up to 20% MVC the MF remains practically constant at -11 Hz, and then an increase of -1 Hz per 10% MVC occurs up to 80% MVC. Beyond 80% MVC the MF increases steeply up to -22 Hz at 100% MVC. The power content of the spectra was always negligible beyond 45 Hz. The average values of the relative power calculated in adjoining ~-HZ bandwidths, from 0 to 45 Hz, are reported in Table 3 for each effort level. As the contraction level increases the power is distributed in a wider range of frequencies and is shifted to higherfrequency bands. The larger power content is retrievable in the 5- to lo-Hz band below 40% MVC and in the loto 15-Hz band for contraction levels higher than 50% MVC. The power shift toward the higher frequencies with increasing %MVC was also analyzed by considering the relative weight of the power content in the bandwidth 15-45 Hz [high frequencies, (HF), frequency rate bandwidth of MUs with fast-twitch fibers] in respect to the 6-45 Hz (frequency rate bandwidth of MUs with slow+ fast-twitch fibers) for reasons described in the DISCUSSION. In Fig. 5 the average values of the HF% as a function of %MVC are reported. A slight increase in the HF% occurs up to 60% MVC, after which a well-defined
Hz
and FFT) from 10 to 100% MVC. normalized power spectrum (n =
25 -
coefficients between the mean frequencies of the two days were 0.772 and 0.595 (P < 0.05) for MESE and 0.803 and 0.646 (P < 0.05) for FFT values, respectively. The paired t test applied to the same data showed no statistical difference between the MF calculated on the two different days.
20 -
Power Spectrum Estimation
In Fig. 2 the normalized power spectra estimated by both MESE and FFT are reported for each level of contraction intensity in a representative subject. The average spectrum, calculated from seven individual spectra at each contraction level, is shown in Fig. 3. A rapid inspection of Figs. 2 and 3 indicates that with
10 -
5L 0
a a Y Y '
1 20
& 9
& P
a aP P
L 1 L 40 60 80 % M.V.C. FIG. 4. Average values (&SE, n = 7) of mean frequency by MESE (0) and FFT (0) methods as function of %MVC.
A Y
I I
4 100 calculated
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511
SPECTRAL ANALYSIS OF MUSCULAR SOUND TABLE 3. Relative power
spectrum
distribution
5-10 Hz
O-5 Hz
lo-15 Hz
X-20
Hz
20-25 Hz
25-30 Hz
30-35 Hz
35-40 Hz
40-45 Hz
%MVC MESE
FFT
MESE
FFT
MESE
FFT
MESE
FFT
10 20 30 40 50 60 70 80 90 100
MESE
FFT
MESE
FFT
MESE
18t3.3 16t2.7 46~3.5 4lk3.0 2Ozk2.7 2522.6 8k2.0 9H.9 3kO.4 3t0.5 220.4 2kO.4 220.4 17t2.6 18t2.8 43t3.7 3923.7 21t2.4 23t2.6 8kO.9 10kl.2 4kO.6 4kO.6 2t0.4 2t0.4 lkO.1 15k2.9 14~3.0 3921.9 36t2.9 28~2.7 30t3.0 lOtl.7 12kl.9 4kO.8 4k0.6 2t0.3 2t0.3 lkO.1 9tl.7 8kl.8 36k2.7 3lk2.1 3324.0 38k2.7 13t2.6 14t2.1 420.8 4kO.9 2tO.l 2kO.3 2t0.3 7tl.4 5tl.O 2922.8 25t2.8 41t4.8 4424.5 1222.0 15t2.3 4tl.l 4tl.O 220.2 220.3 2t0.3 5t0.7 4t0.8 22tl.8 19tl.2 46t4.7 46t4.8 1423.6 16k3.4 5tl.O 6tl.4 3t0.3 220.8 2kO.3 5tl.O 4kl.0 2324.8 2024.1 35k5.9 37t5.4 24t5.5 2625.6 620.9 721.0 2kO.5 3-0.5 lt0.2 5tl.4 5tl.5 23t2.6 20t2.6 3326.1 34k5.8 211k3.6 2223.3 822.3 9t2.3 4t0.5 4-r-0.5 2kO.4 5kO.7 3-e0.9 23k2.9 20t3.1 3023.6 3124.3 19k4.5 2Ok4.2 9kl.4 921.4 6t0.6 6t0.7 320.5 4tl.5 3kl.0 17k4.2 16k4.3 29t6.1 27t5.6 13k2.9 16k3.3 5kl.0 620.8 6kl.4 6tl.2 7kl.7 Values are means t SE for 7 subjects. For each intensity of contraction relative power content of adjacent
60 -
50 -
40 HF%
30 -
1 1 P P
20 -
101
’
0
1
20
.
I
40
% 5. Average values (GE, n Hz bandwidth (HF%) in respect bandwidth calculated by MESE (0) FIG.
increment practically
.
1
1
1
60
80
100
M.V.C. = 7) of relative power in 15- to 45to power content in 6- to 45-Hz and FFT (0) as function of %MVC.
is observed. The trend of HF% vs. %MVC is the same for MESE and FFT calculated data.
DISCUSSION
Although recent years have brought about a renewed interest in the study of MS, a comparison of results is difficult, if not impossible, because of diverse experimental designs that have not employed well-known, reproducible, easy to measure physiological conditions nor similar signal-processing techniques. To overcome this pitfall a full range of isometric contraction (lo-100% MVC) has been investigated, and two algorithms (MESE and FFT) commonly adopted for spectral analysis have been applied to the recorded MS. These two spectral analysis methods are based on different modeling approaches. The MESE method is considered applicable whenever the frequency content of an investigated signal is scarcely known, as is the case of SMG. In fact MESE predicts the autocorrelation function (ACF) of the signal beyond the limited range of the data. The principle used for this prediction is that the spectral estimate must be the most random; i.e., it must have the maximum entropy of any power spectrum that is consistent with the sample values of the ACF. As a result no new information is added by the prediction process.
FFT
2t0.4 lkO.2 lt0.1 2t0.3 2kO.5 2t0.2 MO.2 2t0.4 3t0.5 721.7
MESE
MO.3 MO.2 120.2 lk0.3 lt0.2 2kO.6 MO.3 MO.3 2kO.5 7t2.3
~-HZbands
FFT
020.3 MO.2 lt0.1 MO.5 lt0.2 2t0.6 MO.4 120.2 2kO.4 8t2.5
MESE
020.3 lt0.2 lt0.2 Ot0.2 lt0.2 120.2 Ot0.2 lrt0.2 120.2 3kO.6
FFT
Ot0.2 l&O.2 lk0.2 020.2 lt0.2 lk0.3 Ot0.3 lt0.2 l&O.2 3kO.6
is reported.
In a previous study (9), our group chose the MF as that parameter into which the frequency information of the power spectrum could be compressed because of its robustness and its independence of the algorithm. This is not always true for the median and peak frequencies. The present study confirms the previous data and shows that both MESE and FFT yield an absolutely similar MF. The repeatability of the sound during isometric contractions at 20% MVC was verified using the MF. This level of effort can be easily developed and maintained without involving fatigue at least during the first 10 min of exercise (1). This allowed a comparison of several MF values obtained during the 1 min of sustained contraction and of the values recorded on different days. The stability of the MF in different trials, both with the MESE and the FFT method, ensures that the SMG is a reproducible signal, as was pointed out previously (9, 18). The SMG power spectrum as the level of contraction increases shows a shift toward the higher frequencies and enlarges, presenting a multimodal distribution. The MF is related to the %MVC in a not unique fashion. In fact, MF is practically constant up to 20% MVC. It then increases, with two different relationships from 20 to 80% and from 80 to 100% MVC. Other authors (19, 20) have reported that at increasing contraction levels the peak frequency does not change. However the narrow range of contraction intensities investigated (up to -50% MVC) and the different experimental design employed by these authors could explain this discrepancy in the dynamics of the two frequency parameters. The similarity of our values of MF with those of the MU firing rate, as detected by an intramuscular electrode at different intensities of contraction (17), supports the hypothesis that the “lateral expansion” of the activated fibers is one of the possible sources of MS and that the MS is the “mechanical counterpart” of the electrical activity of the muscle fiber (12). In addition to the reported consistency between MF of the MS and MU firing rate, the shift of the power spectrum toward higher frequencies and its clear multimodality at the highest intensities of contraction suggest that the MU activation pattern of the biceps brachii could be retrieved. To verify this hypothesis a detailed analysis of the SMG spectrum was performed on the basis of the physiological characteristics of the investigated muscle.
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512
SPECTRAL
ANALYSIS
The biceps brachii is composed of a well-balanced population of slow- and fast-twitch fibers. MU recruitment is used to generate the initial 70-80% of the maximal voluntary force by engaging MUs with progressively higher firing rates. The remaining 20-30% of MVC is developed only by increasing the firing rate (11, 23). No MUs with fast-twitch fibers are activated for exercise intensities below 30% MVC (13). During voluntary contraction the lowest reported firing rate is 6 Hz, which is attributed to the MUs with slow-twitch fibers (ll), and the highest is -40 Hz (3). The MUs with fast-twitch fibers have a lower limit at 15 Hz (7, 11). Based on this experimental evidence, the ratio between the power in the high-frequency band of the spectrum (15-45 Hz) and the power in the whole range of the firing rate of MU (6-45 Hz) was calculated to estimate the contribution of the fast-twitch fibers in MS generation. The trend of the resulting HF% vs. %MVC seems to reflect the previously reported MU activatio n pattern. In fact, it increases with contraction intensity and a much steeper relationship is clearly observed beyond 60% MVC, reflecting the dominance of the frequency code in the force generation. At these contraction levels the high firing frequency of the MUs could determine a fusionlike situation in which the dimensional change of the activated muscle fibers may be greatly reduced. This would lead in turn to a reduction of the generated pressure wave detectable at the muscle surface as MS. This assumption is supported by the evidence of a reduction of the sound amplitude signal shown in Fig. 1 and of the integrated SMG at the highest effort levels previously reported (18). Further support is provided by data from isolated frog muscle, in which the same relationship between stimulation frequency rate and sound amplitude is described (10). The presence of a little residual power below 6 Hz suggests that other sources, in addition to the lateral expansion of the activated fibers, must be taken into account in the overall evaluation of the physiological information contained in MS. In conclusion it appears that the SMG spectrum analysis is unaffected by the algorithm artifacts. As a consequence the SMG can be considered a reliable and noninvasive tool to study the mechanism of muscular contraction. In particular the SMG frequency analysis provides information about the MU activation pattern. The relevance of the sound in the description of the basic muscular contraction mechanisms should be proven by future investigations on different muscles and different pathophysiological situations. This work was supported by Consiglio Roma, Italy, by Minister0 della Pubblica Universitario Lombardia Orientale, Italy.
Nazionale Istruzione,
delle Italy,
Ricerche, and Ente
OF
MUSCULAR
SOUND
Address for reprint requests: A. Veicsteinas, Umana, Dipartimento di Scienze Biomediche Valsabbina, 19, 25124 Brescia, Italy. Received
27 February
1989; accepted
in final
Istituto di Fisiologia e Biotecnologie, Via form
28 September
1989.
REFERENCES 1. ASTRAND, P. O., AND R. RODAHL. Textbook of World Physiology. New York: McGraw-Hill, 1986, p. 115-116. 2. BARRY, D. T. Acoustic signals from frog skeletal muscle. Biophys. J. 51: 769-773,1987. 3. BELLEMARE, F., J. J. WOODS, R. JOHANSSON, AND B. BIGLANDRITCHIE. Motor-unit discharge rates in maximal voluntary contractions of three human muscles. J. Neurophysiol. 50: 1380-1392, 1983. BOX, G. E. P., AND G. M. JENKINS. Time Series Analysis. San Francisco, CA: Holden-Day, 1970. BROZOVICH, F. V., AND G. H. POLLACK. Muscle contraction generates discrete sound bursts. Biophys. J. 41: 35-40, 1983. BURG, J. P. Maximum Entropy Spectral Analysis (PhD dissertation). Stanford, CA: Stanford University, 1975. BURKE, R. E. Motor units: anatomy, physiology, and functional organization. In: Handbook of Physiology. The Nervous System. Motor Control. Bethesda, MD: Am. Physiol. Sot., 1981, sect. 1, vol. II, part 1, chapt. 10, p. 345-422. 8. CHILDERS, D. G. (Editor). Modern Spectrum Analysis. New York: IEEE, 1978. 9. DIEMONT, B., M. MARANZANA FIGINI, C. ORIZIO, R. PERINI, AND A. VEICSTEINAS. Spectral analysis of muscular sound at low and high contraction level. Int. J. Biomed. Comp. 23: 161-175, 1988. 10. FRANGIONI, J. V., T. S. KWAN-GETT, L. E. DOBRUNZ, AND T. A. MCMAHON. The mechanism of low-frequency sound production in muscle. Biophys. J. 51: 775-783, 1987. 11. FREUND, H. J. Motor unit and muscle activity in voluntary motor control. Physiol. Reu. 63: 387-436, 1983. 12. GORDON, G., AND A. H. S. HOLBOURN. The sounds from single motor units in a contracting muscle. J. Physiol. Land. 107: 456464,1948. 13. GYDIKOV, A., AND D. KOSAROV. Some features of different motor units in human biceps brachii. Pfluegers Arch. 347: 75-88, 1974. 14. HARRIS, F. J. On the use of windows for harmonic analysis with the discrete Fourier Transform. IEEE Proc. 66: 51-83, 1978. 15. HELMHOLTZ, H. L. F. Ueber den Muskelton. Monatsber. Dtsch. Akad. Wiss. Berl. 5: 307-310, 1864. 16. MARANZANA FIGINI, M., R. MOLINARI, AND G. SOMMARIVA. The parametrization of the electromyographic signal: an approach based on simulated EMG signal. Electromyogr. Clin. Neurophysiol. 24: 47-65, 1984. 17. MORITANI, T., AND M. MURO. Motor unit activity and surface electromyogram power spectrum during increasing force of contraction. Eur. J. Appl. Physiol. Occup. Physiol. 56: 260-265, 1987. 18. ORIZIO, C., R. PERINI, AND A. VEICSTEINAS. Muscular sound and force relationship during isometric contraction in man. Eur. J. Appl. Physiol. Occup. Physiol. 58: 528-533, 1989. 19. OSTER, G. Muscle sounds. Sci. Am. 250: 108-114,1984. 20. OSTER, G., AND J. S. JAFFE. Low frequency sounds from sustained contraction of human skeletal muscle. Biophys. J. 30: 119-128, 1980. B. A., K. C. MYLREA, E. LONSDALE, AND L. Z. STERN. 21. RHATIGAN, Investigation of sounds produced by healthy and diseased human muscular contraction. IEEE Trans. Biomed. Eng. 33: 967-971, 1986. 22. WOLLASTON, W. H. On the duration of muscle action. Philos. Trans. R. Sot. Land. B. Biol. Sci. l-5, 1810. 23. ZHOU, B. H., R. BARATTA, AND M. SOLOMONOW. Manipulation of muscle force with various firing rate and recruitment control strategies. IEEE Trans. Biomed. Eng. 34: 128-139, 1987.
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ORIZIO, RENZA PERINI, BERTRAND MARANZANA FIGINI, AND ARSENIO
DIEMONT, VEICSTEINAS
Istituto di Fisiologia Umana, Dipartimento di Scienze Biomediche e Biotecnologie, Universitk di Brescia, 25124 Brescia; and Centro di Teoria dei Sistemi, Dipartimento di Elettronica, Politecnico di Milano, 20138 Milan, Italy
ORIZIO, CLAUDIO, RENZA PERINI, BERTRANDDIEMONT, MARISA MARANZANA FIGINI, AND ARSENIO VEICSTEINAS. Spectral analysis of muscular sound during isometric contraction of biceps bra&ii. J. Appl. Physiol. 68(2): 508-512, 1990.-The frequency content of muscular sound (MS), detected by placing a contact sensor transducer over the belly of the biceps brachii during 10 isometric contractions of 4 s each [lo-100% of maximal voluntary contraction (MVC)] in seven sedentary men, was analyzed by the maximum entropy spectral estimation and the fast Fourier transform methods. With increasing %MVC, the power spectrum of the MS enlarges and tends to be multimodal beyond 30% MVC. Independent of the method, the mean frequency is -11 Hz at the lower tasks, and then it increases up to 15 Hz at 80% MVC and to 22 Hz at 100% MVC. When the effort is increased the relative power in the 15 to 45-Hz bandwidth (range of firing rate of the motor units with fast-twitch fibers) from 20% reaches 55% of the power in the 6- to 45-Hz bandwidth (firing rate range of motor units with slow- and fast-twitch fibers). Our results obtained by the two different modeling approaches confirm the reliability of the sound signal. Moreover, it appears that from the MS the motor unit activation pattern can be retrieved. motor unit activation
pattern;
recruitment;
exertion
WHEN MUSCLE CONTRACTSa low rumbling noise is detectable at its surface. This phenomenon was described in the last century and named muscular sound (MS) (15, 22). More recently the interest in MS has been renewed. Nevertheless its nature is still not well defined. Data from isolated frog muscle suggested that the source of MS might be the “brief shock wave” caused by the stepwise change in radius of the activated fibers (5) or by the “gross lateral movement of the central region of the muscle” when stimulated (2,10). Studies on human muscle have indicated that the possible factors implied in MS generation could be the pressure waves generated by dimensional changes, i.e., lateral expansion of the activated fibers (l2), the physiological tremor (20), the actomyosin cross-bridge cycling (19), and the oscillations due to the pulling on the elastic-connective tissue at each step of contraction (21). The frequency content of the MS was also studied in the last century and roughly estimated to be between 25 and 40 Hz (15, 22). However, the recent availability of valuable tools, such as sensors capable of transducing 508
0161-7567/90
$1.50 Copyright
MS into an electrical signal (Sound MyoGram, SMG), and of rapid spectral analysis algorithms has provided a more accurate means of defining the frequency content of the SMG. The most relevant frequency parameters found during isometric contraction of human biceps brachii were reported to be between 10 and 25 Hz (9, 1921). The wide range of frequency values observed probably depends on the not well-defined and comparable contraction intensities and on the different signal-processing techniques adopted by the different authors. The growing interest in MS, the uncertain data reported in the literature, and the lack of a systematic analysis of the SMG in the frequency domain during isometric exercise in the whole range of contraction intensity have prompted the present study. However, the final aim is to verify whether the frequency content of SMG reflects the motor unit (MU) activation pattern at the different levels of isometric effort. To check the influence of the computation algorithms on the estimation of the power spectrum frequency parameters, two spectral analysis methods, fast Fourier transform (FFT) and the maximum entropy spectral estimation (MESE), were adopted. SUBJECTSAND METHODS
After being fully informed about the experimental procedure, a group of seven healthy young males [age, 21-25 yr; body wt, 63-73 kg; maximal voluntary contraction of the elbow flexors (MVC), 300-360 N] volunteered for the study. Each subject was asked to isometrically contract the biceps brachii muscle of his preferential arm, which was kept in an adjustable anatomically shaped stirrup constructed so as to maintain a constant angle of 115" between arm and forearm (18). The output force was recorded by a load cell (Interface S-M 1000, linear from 0 to 1,000 N) strapped to the subject’s wrist, which was kept halfway between pronation and supination. The applied force was displayed on a monitor to provide the necessary visual feedback to the subject. The MS was detected at the belly of the biceps brachii by a contact sensor transducer (Hewlett-Packard model 21050 A; bandwidth, 0.02-2,000 Hz) and then amplified
0 1990 the American
Physiological
Society
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SPECTRAL
ANALYSIS
by the Hewlett Packard 8802A medium gain amplifier and filtered (bandwidth, 2-100 Hz). After analog-to-digital conversion (Burr-Brown PCI2OK) the SMG was sampled (256 points/s) and stored on an IBM-AT personal computer for further processing. The results are given as means t SE. The statistical differences between the various groups of data are estimated by the t test and are considered significant for P < 0.05. Spectral Analysis
The power spectrum density distribution (PSD) was estimated by the MESE and by the FFT methods. With both methods the upper limit of the power spectrum estimation was 128 Hz. lMESE method. The Burg algorithm was used (6). The recursive technique describes the signal y(t) by means of an autoregressive (AR) model (4,8) YW = -[aley(t
- 1) + azay(t - 2)
+ %-Y(t - p)] + e(t) where y(t) is the current value of the signal at time t, ap are the AR parameters, e(t) is the estimation error, and p is the order of the model. The AR parameters were estimated by a least square fitting. The optimal order of the model, which indicates the most parsimonious model (16), was estimated by three criteria and was defined as the middle one of the three separately selected ones. Increasing the model order (MO) from the optimal one, the figure of merit reduces up to a MO of ~20, indicating an improvement in the relationship between signal characteristics and the MO. In this range the MO related to the biggest drop in the behavior of the figure of merit was selected. This procedure was adopted to estimate a more detailed PSD (9) FFT method. The FFT with a Papoulis window (14) was applied to the same data. From the PSDs, calculated by both MESE and FFT, the mean frequency (MF) and distribution of the power in adjoining 5-Hz-wide frequency bands were obtained. +
l
l
l
aI,
l
l
l
9
EXPERIMENTAL
PROCEDURE
After determining the maximal voluntary contraction (MVC), i.e., the strongest of three maximal contractions lasting 3 s each, the subject trained himself daily for 1 wk on the laboratory apparatus to learn how to keep the output force constant at different levels of effort. During the experimental session the subject performed, in a randomized sequence, 10 isometric contractions from 10 to 100% MVC, each lasting 4 s. To avoid transient phenomena the middle 2 s of the 4-s exercise were processed. Between one task and the next a rest period of 5 min was allowed. During this time the subject kept his arm in the stirrup with the transducer in place. The muscular sound variability was estimated both intra- and interindividually. For this purpose SMG was recorded at 20% MVC in I) one subject during 1 min of
OF MUSCULAR
509
SOUND
sustained contraction (epochs of 2 s out of every 6 s of activity were stored) and in 2) all the subjects during the 4-s trials performed on two different days. RESULTS
During the contraction the output force was maintained constant within &5% of the target value. Whenever one of the trials showed a greater variability, the whole series from 10 to 100% MVC was repeated. In Fig. 1 the digitized SMG signals from 10 to 100% MVC for a typical subject are presented. It can be noted that the amplitude of the signal increases up to 80% MVC and then decreases. Signal Repeatability
In Table 1 the individual and the average values of the mean frequency computed by MESE and FFT for each epoch of 2 s during the 1 min of sustained contraction at 20% MVC are reported. No significant differences among the different epochs nor between MESE and FFT values are observed. In Table 2 the individual mean frequency calculated with the two spectral analysis methods in all subjects on the two different days are reported together with the group average values. The correlation and determination
f 1200 rv 200.
6oo nV
t 1200
l v
f 1200
lV
r
50 FIG. 1. Sound myogram signal of 2-s epochs after analog-to-digital conversion during isometric contraction of biceps brachii from 10 to 100% MVC in a representative subject. Gain in lo-50% MVC is double that in 60-100% MVC range.
TABLE
1. SMG mean frequency Mean
Frequency
Epoch MESE
1 2 3 4 5 6 7 8 9 10
10.7 11.8 11.8
FFT
10.1
11.4 11.9 12.1 10.3
11.2 10.3 9.3 9.6 11.7
12.0 10.7 9.7 9.9 12.0
10.3
11.0
Means t SE 10.68kO.29 11.lt0.29 Values are mean frequency (Hz) of SMG recorded during 1 min (10 epochs) of sustained contraction at 20% MVC.
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510
SPECTRAL
MESE
Subj No.
Day
1 2 3 4 5 6 7 Means
t, SE
FFT
1
Day 2
8.8 12.5 10.0 10.1 10.4 10.5 11.8 10.59t0.46
8.3 11.2 10.9 11.0 11.0 10.9 12.1 10.7720.44
Mean frequency (Hz) all subjects at 20% MVC.
of SMG
Day
20
30
40
0
was recorded
10
20
30
FIG.
IO
2. Normalized power spectra by MESE and FFT in lo-100%
20
30
2
8.9 11.7 11.5 11.5 12.3 11.6 12.7 11.46k0.46 days
in
F.F.T.
40 Hz
of signal reported MVC range.
M.E.S.E.
0
Day
on 2 different
x M.V.C.
Hz
mated
1
9.5 13.1 10.9 11.0 11.7 11.1 12.9 11.46k0.47
M.E.S.E.
10
OF
2. Test-retest SMG mean frequency
TABLE
0
ANALYSIS
40
0
10
Hz FIG. 3. Average spectra (MESE Each spectrum is mean of individual 7) at each contraction intensity.
% M.V.C.
20
30
in Fig. 1 esti-
F.F.T.
40
MUSCULAR
SOUND
increasing intensity of contraction the SMG spectrum shifts toward the higher frequencies and enlarges. When MESE spectra are considered it is possible to identify, starting from 30% MVC, two frequency ranges in which the power is distributed. This tendency toward multimodality is clearer beyond 70% MVC. The FFT spectra present a more detailed morphology. Even here as the intensity of contraction increases a change in the spectra from uni- to multimodality occurs. Independently of the subject and the spectral analysis method used, the first peak of the multimodal PSD lies in the 6- to 11-Hz bandwidth. This is the same bandwidth of the unimodal PSD peak frequency. In Fig. 4 the average values of the MF calculated by both MESE and FFT are given as a function of %MVC. At each value on the x-axis the MF computed by FFT is -1 Hz higher than that computed by MESE. The MF increases with %MVC but not in a unique fashion. Up to 20% MVC the MF remains practically constant at -11 Hz, and then an increase of -1 Hz per 10% MVC occurs up to 80% MVC. Beyond 80% MVC the MF increases steeply up to -22 Hz at 100% MVC. The power content of the spectra was always negligible beyond 45 Hz. The average values of the relative power calculated in adjoining ~-HZ bandwidths, from 0 to 45 Hz, are reported in Table 3 for each effort level. As the contraction level increases the power is distributed in a wider range of frequencies and is shifted to higherfrequency bands. The larger power content is retrievable in the 5- to lo-Hz band below 40% MVC and in the loto 15-Hz band for contraction levels higher than 50% MVC. The power shift toward the higher frequencies with increasing %MVC was also analyzed by considering the relative weight of the power content in the bandwidth 15-45 Hz [high frequencies, (HF), frequency rate bandwidth of MUs with fast-twitch fibers] in respect to the 6-45 Hz (frequency rate bandwidth of MUs with slow+ fast-twitch fibers) for reasons described in the DISCUSSION. In Fig. 5 the average values of the HF% as a function of %MVC are reported. A slight increase in the HF% occurs up to 60% MVC, after which a well-defined
Hz
and FFT) from 10 to 100% MVC. normalized power spectrum (n =
25 -
coefficients between the mean frequencies of the two days were 0.772 and 0.595 (P < 0.05) for MESE and 0.803 and 0.646 (P < 0.05) for FFT values, respectively. The paired t test applied to the same data showed no statistical difference between the MF calculated on the two different days.
20 -
Power Spectrum Estimation
In Fig. 2 the normalized power spectra estimated by both MESE and FFT are reported for each level of contraction intensity in a representative subject. The average spectrum, calculated from seven individual spectra at each contraction level, is shown in Fig. 3. A rapid inspection of Figs. 2 and 3 indicates that with
10 -
5L 0
a a Y Y '
1 20
& 9
& P
a aP P
L 1 L 40 60 80 % M.V.C. FIG. 4. Average values (&SE, n = 7) of mean frequency by MESE (0) and FFT (0) methods as function of %MVC.
A Y
I I
4 100 calculated
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511
SPECTRAL ANALYSIS OF MUSCULAR SOUND TABLE 3. Relative power
spectrum
distribution
5-10 Hz
O-5 Hz
lo-15 Hz
X-20
Hz
20-25 Hz
25-30 Hz
30-35 Hz
35-40 Hz
40-45 Hz
%MVC MESE
FFT
MESE
FFT
MESE
FFT
MESE
FFT
10 20 30 40 50 60 70 80 90 100
MESE
FFT
MESE
FFT
MESE
18t3.3 16t2.7 46~3.5 4lk3.0 2Ozk2.7 2522.6 8k2.0 9H.9 3kO.4 3t0.5 220.4 2kO.4 220.4 17t2.6 18t2.8 43t3.7 3923.7 21t2.4 23t2.6 8kO.9 10kl.2 4kO.6 4kO.6 2t0.4 2t0.4 lkO.1 15k2.9 14~3.0 3921.9 36t2.9 28~2.7 30t3.0 lOtl.7 12kl.9 4kO.8 4k0.6 2t0.3 2t0.3 lkO.1 9tl.7 8kl.8 36k2.7 3lk2.1 3324.0 38k2.7 13t2.6 14t2.1 420.8 4kO.9 2tO.l 2kO.3 2t0.3 7tl.4 5tl.O 2922.8 25t2.8 41t4.8 4424.5 1222.0 15t2.3 4tl.l 4tl.O 220.2 220.3 2t0.3 5t0.7 4t0.8 22tl.8 19tl.2 46t4.7 46t4.8 1423.6 16k3.4 5tl.O 6tl.4 3t0.3 220.8 2kO.3 5tl.O 4kl.0 2324.8 2024.1 35k5.9 37t5.4 24t5.5 2625.6 620.9 721.0 2kO.5 3-0.5 lt0.2 5tl.4 5tl.5 23t2.6 20t2.6 3326.1 34k5.8 211k3.6 2223.3 822.3 9t2.3 4t0.5 4-r-0.5 2kO.4 5kO.7 3-e0.9 23k2.9 20t3.1 3023.6 3124.3 19k4.5 2Ok4.2 9kl.4 921.4 6t0.6 6t0.7 320.5 4tl.5 3kl.0 17k4.2 16k4.3 29t6.1 27t5.6 13k2.9 16k3.3 5kl.0 620.8 6kl.4 6tl.2 7kl.7 Values are means t SE for 7 subjects. For each intensity of contraction relative power content of adjacent
60 -
50 -
40 HF%
30 -
1 1 P P
20 -
101
’
0
1
20
.
I
40
% 5. Average values (GE, n Hz bandwidth (HF%) in respect bandwidth calculated by MESE (0) FIG.
increment practically
.
1
1
1
60
80
100
M.V.C. = 7) of relative power in 15- to 45to power content in 6- to 45-Hz and FFT (0) as function of %MVC.
is observed. The trend of HF% vs. %MVC is the same for MESE and FFT calculated data.
DISCUSSION
Although recent years have brought about a renewed interest in the study of MS, a comparison of results is difficult, if not impossible, because of diverse experimental designs that have not employed well-known, reproducible, easy to measure physiological conditions nor similar signal-processing techniques. To overcome this pitfall a full range of isometric contraction (lo-100% MVC) has been investigated, and two algorithms (MESE and FFT) commonly adopted for spectral analysis have been applied to the recorded MS. These two spectral analysis methods are based on different modeling approaches. The MESE method is considered applicable whenever the frequency content of an investigated signal is scarcely known, as is the case of SMG. In fact MESE predicts the autocorrelation function (ACF) of the signal beyond the limited range of the data. The principle used for this prediction is that the spectral estimate must be the most random; i.e., it must have the maximum entropy of any power spectrum that is consistent with the sample values of the ACF. As a result no new information is added by the prediction process.
FFT
2t0.4 lkO.2 lt0.1 2t0.3 2kO.5 2t0.2 MO.2 2t0.4 3t0.5 721.7
MESE
MO.3 MO.2 120.2 lk0.3 lt0.2 2kO.6 MO.3 MO.3 2kO.5 7t2.3
~-HZbands
FFT
020.3 MO.2 lt0.1 MO.5 lt0.2 2t0.6 MO.4 120.2 2kO.4 8t2.5
MESE
020.3 lt0.2 lt0.2 Ot0.2 lt0.2 120.2 Ot0.2 lrt0.2 120.2 3kO.6
FFT
Ot0.2 l&O.2 lk0.2 020.2 lt0.2 lk0.3 Ot0.3 lt0.2 l&O.2 3kO.6
is reported.
In a previous study (9), our group chose the MF as that parameter into which the frequency information of the power spectrum could be compressed because of its robustness and its independence of the algorithm. This is not always true for the median and peak frequencies. The present study confirms the previous data and shows that both MESE and FFT yield an absolutely similar MF. The repeatability of the sound during isometric contractions at 20% MVC was verified using the MF. This level of effort can be easily developed and maintained without involving fatigue at least during the first 10 min of exercise (1). This allowed a comparison of several MF values obtained during the 1 min of sustained contraction and of the values recorded on different days. The stability of the MF in different trials, both with the MESE and the FFT method, ensures that the SMG is a reproducible signal, as was pointed out previously (9, 18). The SMG power spectrum as the level of contraction increases shows a shift toward the higher frequencies and enlarges, presenting a multimodal distribution. The MF is related to the %MVC in a not unique fashion. In fact, MF is practically constant up to 20% MVC. It then increases, with two different relationships from 20 to 80% and from 80 to 100% MVC. Other authors (19, 20) have reported that at increasing contraction levels the peak frequency does not change. However the narrow range of contraction intensities investigated (up to -50% MVC) and the different experimental design employed by these authors could explain this discrepancy in the dynamics of the two frequency parameters. The similarity of our values of MF with those of the MU firing rate, as detected by an intramuscular electrode at different intensities of contraction (17), supports the hypothesis that the “lateral expansion” of the activated fibers is one of the possible sources of MS and that the MS is the “mechanical counterpart” of the electrical activity of the muscle fiber (12). In addition to the reported consistency between MF of the MS and MU firing rate, the shift of the power spectrum toward higher frequencies and its clear multimodality at the highest intensities of contraction suggest that the MU activation pattern of the biceps brachii could be retrieved. To verify this hypothesis a detailed analysis of the SMG spectrum was performed on the basis of the physiological characteristics of the investigated muscle.
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512
SPECTRAL
ANALYSIS
The biceps brachii is composed of a well-balanced population of slow- and fast-twitch fibers. MU recruitment is used to generate the initial 70-80% of the maximal voluntary force by engaging MUs with progressively higher firing rates. The remaining 20-30% of MVC is developed only by increasing the firing rate (11, 23). No MUs with fast-twitch fibers are activated for exercise intensities below 30% MVC (13). During voluntary contraction the lowest reported firing rate is 6 Hz, which is attributed to the MUs with slow-twitch fibers (ll), and the highest is -40 Hz (3). The MUs with fast-twitch fibers have a lower limit at 15 Hz (7, 11). Based on this experimental evidence, the ratio between the power in the high-frequency band of the spectrum (15-45 Hz) and the power in the whole range of the firing rate of MU (6-45 Hz) was calculated to estimate the contribution of the fast-twitch fibers in MS generation. The trend of the resulting HF% vs. %MVC seems to reflect the previously reported MU activatio n pattern. In fact, it increases with contraction intensity and a much steeper relationship is clearly observed beyond 60% MVC, reflecting the dominance of the frequency code in the force generation. At these contraction levels the high firing frequency of the MUs could determine a fusionlike situation in which the dimensional change of the activated muscle fibers may be greatly reduced. This would lead in turn to a reduction of the generated pressure wave detectable at the muscle surface as MS. This assumption is supported by the evidence of a reduction of the sound amplitude signal shown in Fig. 1 and of the integrated SMG at the highest effort levels previously reported (18). Further support is provided by data from isolated frog muscle, in which the same relationship between stimulation frequency rate and sound amplitude is described (10). The presence of a little residual power below 6 Hz suggests that other sources, in addition to the lateral expansion of the activated fibers, must be taken into account in the overall evaluation of the physiological information contained in MS. In conclusion it appears that the SMG spectrum analysis is unaffected by the algorithm artifacts. As a consequence the SMG can be considered a reliable and noninvasive tool to study the mechanism of muscular contraction. In particular the SMG frequency analysis provides information about the MU activation pattern. The relevance of the sound in the description of the basic muscular contraction mechanisms should be proven by future investigations on different muscles and different pathophysiological situations. This work was supported by Consiglio Roma, Italy, by Minister0 della Pubblica Universitario Lombardia Orientale, Italy.
Nazionale Istruzione,
delle Italy,
Ricerche, and Ente
OF
MUSCULAR
SOUND
Address for reprint requests: A. Veicsteinas, Umana, Dipartimento di Scienze Biomediche Valsabbina, 19, 25124 Brescia, Italy. Received
27 February
1989; accepted
in final
Istituto di Fisiologia e Biotecnologie, Via form
28 September
1989.
REFERENCES 1. ASTRAND, P. O., AND R. RODAHL. Textbook of World Physiology. New York: McGraw-Hill, 1986, p. 115-116. 2. BARRY, D. T. Acoustic signals from frog skeletal muscle. Biophys. J. 51: 769-773,1987. 3. BELLEMARE, F., J. J. WOODS, R. JOHANSSON, AND B. BIGLANDRITCHIE. Motor-unit discharge rates in maximal voluntary contractions of three human muscles. J. Neurophysiol. 50: 1380-1392, 1983. BOX, G. E. P., AND G. M. JENKINS. Time Series Analysis. San Francisco, CA: Holden-Day, 1970. BROZOVICH, F. V., AND G. H. POLLACK. Muscle contraction generates discrete sound bursts. Biophys. J. 41: 35-40, 1983. BURG, J. P. Maximum Entropy Spectral Analysis (PhD dissertation). Stanford, CA: Stanford University, 1975. BURKE, R. E. Motor units: anatomy, physiology, and functional organization. In: Handbook of Physiology. The Nervous System. Motor Control. Bethesda, MD: Am. Physiol. Sot., 1981, sect. 1, vol. II, part 1, chapt. 10, p. 345-422. 8. CHILDERS, D. G. (Editor). Modern Spectrum Analysis. New York: IEEE, 1978. 9. DIEMONT, B., M. MARANZANA FIGINI, C. ORIZIO, R. PERINI, AND A. VEICSTEINAS. Spectral analysis of muscular sound at low and high contraction level. Int. J. Biomed. Comp. 23: 161-175, 1988. 10. FRANGIONI, J. V., T. S. KWAN-GETT, L. E. DOBRUNZ, AND T. A. MCMAHON. The mechanism of low-frequency sound production in muscle. Biophys. J. 51: 775-783, 1987. 11. FREUND, H. J. Motor unit and muscle activity in voluntary motor control. Physiol. Reu. 63: 387-436, 1983. 12. GORDON, G., AND A. H. S. HOLBOURN. The sounds from single motor units in a contracting muscle. J. Physiol. Land. 107: 456464,1948. 13. GYDIKOV, A., AND D. KOSAROV. Some features of different motor units in human biceps brachii. Pfluegers Arch. 347: 75-88, 1974. 14. HARRIS, F. J. On the use of windows for harmonic analysis with the discrete Fourier Transform. IEEE Proc. 66: 51-83, 1978. 15. HELMHOLTZ, H. L. F. Ueber den Muskelton. Monatsber. Dtsch. Akad. Wiss. Berl. 5: 307-310, 1864. 16. MARANZANA FIGINI, M., R. MOLINARI, AND G. SOMMARIVA. The parametrization of the electromyographic signal: an approach based on simulated EMG signal. Electromyogr. Clin. Neurophysiol. 24: 47-65, 1984. 17. MORITANI, T., AND M. MURO. Motor unit activity and surface electromyogram power spectrum during increasing force of contraction. Eur. J. Appl. Physiol. Occup. Physiol. 56: 260-265, 1987. 18. ORIZIO, C., R. PERINI, AND A. VEICSTEINAS. Muscular sound and force relationship during isometric contraction in man. Eur. J. Appl. Physiol. Occup. Physiol. 58: 528-533, 1989. 19. OSTER, G. Muscle sounds. Sci. Am. 250: 108-114,1984. 20. OSTER, G., AND J. S. JAFFE. Low frequency sounds from sustained contraction of human skeletal muscle. Biophys. J. 30: 119-128, 1980. B. A., K. C. MYLREA, E. LONSDALE, AND L. Z. STERN. 21. RHATIGAN, Investigation of sounds produced by healthy and diseased human muscular contraction. IEEE Trans. Biomed. Eng. 33: 967-971, 1986. 22. WOLLASTON, W. H. On the duration of muscle action. Philos. Trans. R. Sot. Land. B. Biol. Sci. l-5, 1810. 23. ZHOU, B. H., R. BARATTA, AND M. SOLOMONOW. Manipulation of muscle force with various firing rate and recruitment control strategies. IEEE Trans. Biomed. Eng. 34: 128-139, 1987.
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