IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 51, NO. 9, SEPTEMBER 2004
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Blind Separation of Linear Instantaneous Mixtures of Nonstationary Surface Myoelectric Signals Dario Farina*, Member, IEEE, Cédric Févotte, Christian Doncarli, and Roberto Merletti, Member, IEEE
Abstract—Electromyographic (EMG) recordings detected over the skin may be mixtures of signals generated by different active muscles due to the phenomena related to volume conduction. Separation of the sources is necessary when single muscle activity has to be detected. Signals generated by different muscles may be considered uncorrelated but in general overlap in time and frequency. Under certain assumptions, mixtures of surface EMG signals can be considered as linear instantaneous but no a priori information about the mixing matrix is available when different muscles are active. In this study, we applied blind source separation (BSS) methods to separate the signals generated by two active muscles during a force-varying task. As the signals are non stationary, an algorithm based on spatial time-frequency distributions was applied on simulated and experimental EMG signals. The experimental signals were collected from the flexor carpi radialis and the pronator teres muscles which could be activated selectively for wrist flexion and rotation, respectively. From the simulations, correlation coefficients between the reference and reconstructed sources were higher than 0.85 for signals largely overlapping both in time and frequency and for signal-to-noise ratios as low as 5 dB. The Choi–Williams and Bessel kernels, in this case, performed better than the Wigner–Ville one. Moreover, the selection of time-frequency points for the procedure of joint diagonalization used in the BSS algorithm significantly influenced the results. For the experimental signals, the interference of the other source in each reconstructed source was significantly attenuated by the application of the BSS method. The ratio between root-mean-square values of the signals from the two sources detected over one of the muscles increased from (mean standard 1 04 to 4 51 1 37 and from 1 55 0 46 deviation) 2 33 to 2 72 0 65 for wrist flexion and rotation, respectively. This increment was statistically significant. It was concluded that the BSS approach applied is promising for the separation of surface EMG signals, with applications ranging from muscle assessment to detection of muscle activation intervals, and to the control of myoelectric prostheses. Index Terms—Blind source separation, selectivity, surface electromyography.
I. INTRODUCTION
B
LIND SOURCE separation (BSS) consists of recovering a set of signals (sources) of which only mixtures are available (observations). Neither the structure of the mixtures nor the source signals are known. The aim is to identify and decouple the mixtures [4]. Surface electromyographic (EMG) signals are
Manuscript received July 23, 2003; revised January 16, 2004. This work was supported by the European Shared Cost Project “Neuromuscular assessment in the Elderly Worker” (NEW) (Contract QLRT-2000-00 139) and by the COFIN MIUR project “Surface EMG techniques for the assessment of muscle activity during dynamic contractions of the lower limb” (Contract 2 002 093 459 003). Asterisk indicates corresponding author. *D. Farina is with the Centro di Bioingegneria, Dipartimento di Elettronica, Politecnico di Torino, Torino 10129, Italy (e-mail:
[email protected]). C. Févotte and C. Doncarli are with the IRCCyN, École Centrale de Nantes, Nantes, France. R. Merletti is with the Centro di Bioingegneria, Dipartimento di Elettronica, Politecnico di Torino, Torino 10129, Italy (e-mail:
[email protected]). Digital Object Identifier 10.1109/TBME.2004.828048
the resultant of the electrical activity of the muscle fibers active during a muscle contraction. When two or more muscles close to each other are concomitantly active, the EMG signals detected over the skin are mixtures of contributions generated by all the active muscles. Indeed, the electric potential distribution generated by an intracellular action potential covers a large region over the skin due to the blurring effect (basically a low pass filtering) of the tissues separating the sources (the muscle fibers) and the recording electrodes [20]. The detection system has poor spatial selectivity, and thus it is often impossible to distinguish, from the interference EMG signal detected from a group of closely located muscles, the activity of the individual muscles. Separation of these activities is important in many applications, such as the control of prostheses [18], [19], the assessment of muscle coordination [24], or the reduction of crosstalk [9]. The EMG signals generated by different muscles may overlap in the time and frequency domain, thus classic linear filtering approaches cannot be applied for the purpose of source separation. Moreover, no a priori information about the relative activation of different muscles is available. The signals may be generated in short bursts and may change their spectral characteristics over time, for example because of fatigue. In general, they are mixtures of nonstationary, wide-band signals. The signal generated by each motor unit (MU) is detected by an electrode system and is filtered by a transfer function which depends on the distance between the source and the detection point and on the conductivities of the tissues interposed. In specific cases, it is possible to roughly approximate this complex convolutive mixture model with a simpler linear instantaneous mixture model (see Section II). In this case, the surface potentials of all the MUs belonging to a muscle are scaled in amplitude by the same (unknown, depending on the electrode location) amount when detected over the skin. This assumption is rather strong and is approximated in specific cases, which will be analyzed in the present study. A situation in which the assumption of linear instantaneous mixtures may be valid within reasonable approximations is that of small muscles located close to each other. In the case of small muscles, indeed, the MUs are concentrated in small regions, thus their action potentials are all affected almost (but not exactly) in the same way by the tissues interposed between the muscle and the detection points. Assuming a linear instantaneous mixture, the degree of attenuation of the source signal depends on the thickness and conductivity of the subcutaneous layers, on the depth of the source, and on the distance between detection systems. Thus, it is not possible to have a priori information on the attenuation factor.
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The few previous studies that aimed at applying BSS approaches to surface EMG signals did not provide any validation of the performance and did not discuss the assumptions and limitations of the proposed methods [17]. Linear instantaneous mixtures of nonstationary surface EMG signals were considered in the present work which focuses on a systematic evaluation of the separability of surface EMG signals generated by different muscles without any a priori information about the sources. An approach based on spatial time-frequency distributions (STFDs) will be applied to separate both simulated and experimental nonstationary surface EMG signals. The simulation analysis will give indications on the selection of the algorithm parameters while the experimental approach will provide information on the performance of the method in practice. The experimental part of the work will show that the methods proposed may significantly increase the selectivity of the recording and markedly improve the detection of single muscle activity from a group of closely located muscles. II. METHODS A. BSS Method The following linear instantaneous signal model is adopted in : the following, for
time-frequency locations for the joint diagonalization [13], [16]. It has been shown that methods based on second-order statistics perform better on nonstationary and/or colored noise signals with respect to higher order statistics approaches [14] since they explicitly exploit the time and/or frequency diversity contained in the sources, whereas high-order statistics methods assume the sources to be independently and identically distributed sequences (for simplifying the calculations), and thus do not use the time and/or frequency information. As many BSS methods, the method proceeds in two steps: 1) estimation of a “spatial whitening matrix” and 2) estimation of the “missing rotation matrix”. 1) Step 1—Whitening: Spatial whitening consists in finding of size such that a matrix (3) where denotes the complex conjugate transpose of a matrix, denotes the identity matrix of size , and is an unknown positive definite diagonal matrix. can be computed from the sample covariance The matrix matrix of the observations, provided that the sample covariance matrix of the sources is close to diagonal. Indeed, with (4)
(1) where is the vector of size containing the mixtures (called the observations), is the vector of size containing is the full rank mixing matrix of size the sources, with (this implies that the number of sources should is the be not larger than the number of observations), and additive noise vector of equal power on each observation. The sources are modeled as the realizations of zero mean nonstationary mutually uncorrelated random processes. The noise is assumed to be an independent and identically distributed random process, independent of the sources and with , where denotes the identity matrix of size covariance . This assumption implies that the noise sequences on each observation are mutually uncorrelated and of same power . The overall objective of BSS is to obtain an estimate of , up to the standard BSS indeterminacies on ordering and scale is known, the (and phase in the complex case) [1]. Once sources are estimated as (2) where denotes the Moore–Penrose pseudoinverse of a matrix is a matrix with only one nonzero entry per row and and columns aimed at modeling the BSS indeterminancies. The method we will describe in the following was first proposed by Belouchrani and Amin [1]. It is based on the joint diagonalization of STFD matrices of the observations for several time-frequency locations (and after spatial whitening). With respect to [1], our description of the method is based on a stochastic interpretation of the original method, which is necessary when dealing with stochastic processes. Moreover, we will apply a recently proposed procedure for the selection of the
and with the assumptions made on noise, we obtain (5) With and can be computed from the . An estimate of the eigenvalues and eigenvectors of noise variance is the average of the - smallest eigenvalues . Moreover, given the largest eigenvalues , of of , a spatial corresponding to the eigenvectors is built as whitening matrix (6) 2) Step 2—Rotation: Defining , by definiis a unitary square matrix of dimension . It can tion of be shown that [28] (7) Thus, the matrix , equal to up to the diagonal matrix (which models BSS scale indeterminacy), can be recovered from and . At this step, is assumed to be known and we will focus on the estimation of . The matrix can be obtained by a procedure of diagonalization of matrices obtained by the spatial time-frequency representation of the observations, as described in [2]. With respect to [2], we will report in the following a more general interpretation of the spatial time-frequency representation of the whitened observations which has direct impact on the possible criteria for the selection of time-frequency points for the procedure of joint diagonalization. be the covariance of Let the spatial Wigner–Ville spectrum the sources and (SWVS) of . For time-continuous signals, the SWVS is the
FARINA et al.: BLIND SEPARATION OF LINEAR INSTANTANEOUS MIXTURES OF NONSTATIONARY SURFACE MYOELECTRIC SIGNALS
Fourier transform of the covariance with respect to the lag . For time-discrete signals it is defined as
(8) For a given time-frequency location is a square matrix of size whose diagonal entries contain the auto Wigner–Ville spectra of the observations, whereas nondiagonal is entries contain cross Wigner–Ville spectra. Since is diagonal . diagonal From (1) and the assumptions on noise, we obtain (9) Defining the following “whitened and denoised SWVS matrices”: (10) from (9), we obtain (11) and are diagonal, and since is unitary, Since diagonalizes for any . Then, can be estiwith dismated from the eigenvectors of any matrix tinct eigenvalues, up to column permutations and sign changes (and phase shift in the complex case), which correspond to BSS indeterminacies. At this step, we can theoretically compute and thus recover . We have to, however, deal with the estimation of the SWVS of the observations in practice. The SWVS can be interpreted as (12) where fined by
is the spatial Wigner–Ville distribution, de-
(13) Thus, the spatial Wigner–Ville distribution is a rough approximation of the SWVS based on the only available realization of the observations. It is shown [27] that smoothing the spatial Wigner–Ville distribution in time and frequency, i.e., using Cohen’s class STFDs [5], yield better estimators of the SWVS. For a given normalized smoothing kernel , the STFD is defined as (14) Thus, with using the estimate
, given the estimates and of , (11) becomes
, and
(15)
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where (16) In practice, to compute , instead of diagonalizing a single for a single time-frequency location , matrix from the joint diagoit is rather suggested to compute , nalization of several matrices corresponding to several time-frequency locations . As was widely discussed in [1] and [2], joint diagonalization provides a better estimate since an “average eigenstructure” of the whole set of is computed. Furthermore, joint diagonalization does not require that all the matrices have distinct eigenvalues. The way the time-frequency locations for the matrices to be joint diagonalized are selected is an important and nontrivial issue. 3) Selection of the Matrices to be Joint Diagonalized: Since is only an estimate of , in practice is not diagonal for any time-frequency location (though, is diagonal for any ). Thus, it is not in theory, , corresponding possible to diagonalize any matrix to any location . Prior to joint diagonalizing the set , it is necessary to find blindly, that is from the observations only, a set of time-frequency locations for which is actually diagonal. Various time-frequency location selection criteria have been proposed in the literature. In [2], it is suggested that the matrices selected for the joint diagonalization should be chosen as those of “highest power in the - domain”. The following relations hold (with (15) and being unitary): (17) (18) denotes the sum of the diagonal elements of a where trace matrix and denotes the Frobenius matrix norm. From (17) and (18), in [3] the following criterion for selecting the matrices to be joint diagonalized is proposed:
(19)
where is an arbitrary threshold. Another approach is to select the time-frequency locations where is diagonal with only one nonzero term on the diagonal [13], [16]. This criterion is based on the observation that, in practice, most of the matrices which are diagonal have indeed only one nonzero term. This can be simply explained by considering that if two sources share the same freat the same time , then the cross time-frequency quency is likely to distribution between the sources at location be nonzero. This suggests that it is necessary to select time-frequency locations for which only one source is active [13].
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Fig. 1. Example of surface EMG signal simulated during a variable force contraction. (a) Locations of the centers of the simulated MUs in a nonhomogeneous, anisotropic volume conductor are indicated by black circles. The MU territories depends on the number of fibers in each MU and are not shown, for clarity. (b) Simulated force profile and the computed activations of the active MUs (vertical bars). (c) Simulated signal. (d) Power spectrum (periodogram estimation over the entire burst) of the simulated signal.
A diagonal matrix with only one nonzero entry on the diagonal is referred to as a single auto-term matrix. Such matrices have obviously one nonzero eigenvalue. Since the eigenare the same as those of (with (15) values of is unitary), the source single auto-term locations and since can be detected as those where has a dominant eigenvalue. This leads to the following selection criterion:
(20) denotes the set of eigenvalues of where and where is close to zero. The source separation performance according to the selection procedures based on (19) and (20) are compared on simulated and experimental surface EMG signals. To overcome the problem and , a fixed number of of choosing the thresholds time-frequency locations corresponding to the highest values
and will be chosen, and the evolution of of source separation performance with respect to the number of selected time-frequency locations will be studied. B. Simulation Model The BSS approach described above has been mainly tested in the past on multicomponent sources (sum of frequency modulated signals). There are no extensive validations on wide-band signals and no indications about the comparison of different kernels, selection of time-frequency points, number of points for joint diagonalization, and effect of additive noise. To address these issues in simulated conditions, we used a structure-based surface EMG signal-generation model [7]. The tissues separating the muscle fibers and the surface electrodes are layered parallel planes which describe the muscle (anisotropic), the fat (isotropic; 3 mm thick, in this study), and the skin (isotropic; 1 mm thick) layers [Fig. 1(a)]. Thus, the volume conductor is a nonhomogeneous, anisotropic medium. The sources of signal are the intracellular action potentials which travel [Gaussian distribution of the conduction velocities
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Fig. 2. Examples of simulated force profiles with the corresponding surface EMG signals and power spectral densities. The force profiles of the two simulated muscles have a Gaussian shape and are temporally overlapped. The frequency content of the signals from the two muscles is almost the same. (a) First case simulated (later indicated as DYN1). The first burst (source 1) has a peak force corresponding to 20% MVC and is located at 400 ms with an SD of 130 ms. The second burst reaches a force of 15% MVC, is located at 550 ms, and has an SD of 100 ms. (b) Second case simulated (DYN2). The first burst reaches 35% MVC, is located at 400 ms, and has an SD of 130 ms. The second burst corresponds to 15% MVC peak force, has location at 450 ms, and SD of 100 ms.
with mean 4 m/s and standard deviation (SD) 0.3 m/s] along finite-length muscle fibers (65 mm semi-fiber length in this study) from the end plates toward the tendon junctions. A MU is comprised of a number of muscle fibers (uniform distribution of the number of muscle fibers in the range 50–800) which are innervated by the same motoneuron. The MU action potentials are generated as the summation of the action potentials produced by the fibers belonging to the MU (circular MU territories with 20 fibers/mm ). A MU is recruited when the force developed by the muscle exceeds a given threshold which is typical of each unit (recruitment threshold). The recruitment threshold function has been simulated as proposed by Fuglevand et al. [15] (see also [8]). After the force exceeds the recruitment threshold, the firing rate of the MU increases linearly with force (0.3 pps/%MVC, in this study). Given the force profile, the complete interference EMG signal is generated by computing, at each instant of time, the number of active MUs and their instantaneous firing rates according to the force level. The position of a firing is finally determined by adding a Gaussian variability (20% of the inter-spike interval, in this study) to the computed mean position.
Nonstationary surface EMG signals were simulated as produced by Gaussian force profiles. A representative synthetic EMG signal is reported in Fig. 1 together with the activation instants of the active MUs. A situation with two muscles has been simulated for testing the BSS algorithm. The signals from the two muscles are detected by either three or five single differential systems (10 mm inter-electrode distance, electrodes 1 5 mm), two of them located over the two muscles and the remaining in between the muscles. The muscle territories have been defined as in Fig. 1(a). The detection systems were placed between the innervation zone and one of the tendon regions of the simulated MUs. The signal generated by each muscle and detected over the same muscle was computed by the surface EMG generation model. The signals generated by a muscle and detected between the two muscles or over the second muscle were obtained by scaling the amplitude of the signal detected directly over the muscle. The scaling factor was computed on the basis of an inverse linear relationship with the distance between the center of the muscle and the detection point [26]. Other choices for the rate of decrease of amplitude with distance could be selected
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Fig. 3. (a) The isometric brace used for the experimental part of this study. The hand is fixed at the brace with the forearm blocked. Two movements were requested to the subjects, one of wrist flexion (black arrows) and the other of wrist rotation (white arrows). Two torque meters are placed at the two sides of the hand. The torque meters record independent forces and are fixed to bars which do not move. The two systems recording forces are mechanically independent. (b) The locations of the three adhesive arrays over the two muscles in one of the subjects analyzed.
but this issue is not critical for the results shown in this study. The simulated signals were thus ideal linear instantaneous mixtures of surface EMG signals. Two cases were simulated, corresponding to two muscles active during short intervals of time. The time intervals of activity of the two muscles partially overlapped and their frequency bandwidths almost completely overlapped. The two cases are represented in Fig. 2. C. Experimental Protocol The main issue in testing BSS algorithms on experimental surface EMG signals is that the sources are not known. This determines difficulties in objectively evaluating performance. Given the assumptions done in this work (i.e., linear instantaneous mixtures), it was of paramount importance to design an experimental protocol with which the performance of the algorithm could be objectively evaluated. The experimental protocol considered two muscles, the flexor carpi radialis and the pronator teres. These muscles could be controlled rather selectively by the subjects, thus it was possible to produce contractions in which only one muscle was active at a time. In particular, the flexor carpi radialis produced wrist flexions and the pronator teres wrist rotations. The two muscles are closely placed. The contractions were cyclic with flexions and rotations during which (presumably only) one of the two muscles was active at a time. The forces produced during flexion and rotations were recorded separately and provided as a feedback to the subjects. It was thus known a priori in which intervals of time one muscle was active and the other not.
1) Subjects: Eight healthy male volunteers (age, mean years; height: cm; weight: kg) participated in the study. The study was approved by the Local Ethics Committee and written informed consent was obtained from all subjects prior to inclusion. 2) Surface EMG Recordings: Surface EMG signals were detected with three linear adhesive arrays (model ELSCH008, SPES Medica, Salerno, Italy) of four electrodes (1 5 mm) with 10-mm inter-electrode distance, in single differential configuration [23]. Each array provided three single differential signals. The arrays were connected to a multichannel surface EMG amplifier (LISiN-SEMA Elettronica, Torino, Italy). The EMG signals were amplified, band-pass filtered ( -dB bandwidth, 10–500 Hz), sampled at 2048 Hz, and converted in digital data by a 12-bit A/D converter. Before placement of the arrays, the skin was slightly abraded with abrasive paste and the muscles of interest were identified by palpation in a few test contractions of flexion and rotation of the wrist. The arrays were placed parallel to each other in the direction of the muscle fibers [Fig. 3(b)]. One array was located over the pronator teres muscle, the second over the flexor carpi radialis and the third in between the two muscles [Fig. 3(b)]. The transverse distance between adjacent arrays was approximately 10 mm. For each array, only the central single differential signal of the three available pairs was used for further analysis in this study. The BSS method was then applied to the three observations (without any other information) but we were able to record approximations of the reference sources (the observations given by the arrays located directly over the two muscles) and the time in-
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Fig. 4. Examples of signals detected over the two investigated muscles during cyclic flexion/rotation of the wrist. A cyclic task, consisting of 3-s flexion at 50% MVC, 1-s rest, 3-s rotation at 50% MVC, and 1-s rest was performed. The recorded force signals are also reported. Note that, although the exerted force is very selective for the two muscles, surface EMG signals from both muscles are recorded at the two sensors. It is not possible to recognize, from the recorded signals, the activities of the muscles involved in each movement. For validating performance, the first reference source was obtained by considering the parts of the signal detected over the flexor carpi radialis muscle in the intervals with flexion force larger than 15% MVC, while the second reference source corresponded to the signals detected over the pronator teres muscle in the intervals of time with rotation force higher than 15% MVC. The first and second reference sources in two of the intervals of time considered are indicated by dotted and dashed lines, respectively. The signals detected at the first sensor and generated by the second source, and vice versa, are indicated in grey for two intervals of time. The ratio between rms values of the signals generated by the first and the second source and detected at the first sensor is an indication of the selectivity of the recording. In all cases, the experimental results are reported as obtained by processing the entire signals (100 s long).
tervals (given by the force records) in which they were present. Thus, the sources did not overlap in time. In this case, separation of sources is in principle obviously easy. However, the information on the time intervals of activation of the two muscles was not taken into account by the separation algorithm because it processed the signals in batch. Thus, we were able to assess the performance of the algorithm through its ability to reduce the other source contribution in the time intervals where one reconstructed source was supposed to be inactive. 3) General Procedures: Wrist flexion and rotation forces were measured with a modular isometric brace which incorporates two independent torque meters, one on each side (model TR11, CCT Transducers, Torino, Italy) [Fig. 3(a)]. The dominant hand was fixed at the brace with the arm 90 flexed and the forearm fully extended. The forearm was fixed at the brace with straps. The distal part of the hand palm touched a bar connected to the first force sensor [Fig. 3(a)]. Flexing the wrist determined the recording of a force signal from this sensor but did not cause any recording from the second sensor. The proximal part of the palm touched a bar connected to the second torque sensor which recorded forces related to wrist rotation. The subjects were instructed to perform only flexions and rotations and to be as se-
lective as possible with respect to the force produced. The force signals from the two sensors were filtered with a band-pass filter (cut-off frequency 80 Hz), sampled at 2048 Hz, and acquired after 12-bit A/D conversion. The two force signals were shown to the subject on an oscilloscope, during all contractions, to provide feedback of the performance. For both flexion and rotation, the subject was asked to produce two preliminary 3–4 s long maximal voluntary contractions (MVCs) separated by a 2-min rest and was encouraged to exceed the previously reached maximum level. Visual torque feedback was given to the subject when exerting the MVCs. The maximum of the two MVCs was assumed as reference. After the MVC assessment for each movement, a 5-min rest was given to the subject. After the MVC measurement, the subjects performed two variable force isometric exercises, cyclically flexing and rotating the wrist for 100 s. Five minutes of rest were given to the subject between the two exercises. The first exercise consisted of a cycle with: 1) 3 s of flexion at 50% MVC; 2) 1 s of rest; 3) 3 s of rotation at 50% MVC; and 4) 1 s of rest (Fig. 4). The cycle, lasting 8 s, was repeated for 100 s. The second exercise consisted of a cycle, 4 s long, with: 1) 2 s of flexion at 50%
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Fig. 5. Examples of experimental signals recorded from the three locations over the two muscles. A cyclic task, consisting of 3-s flexion at 50% MVC, 1-s rest, 3-s rotation at 50% MVC, and 1-s rest was performed. The two sources are detected by three sensors and the mixtures can be approximated as linear instantaneous, as shown on the right. The entire recording lasts 100 s. Note the different amplitude scales for the three plots on the right.
MVC and 2) 2 s of rotation at 50% MVC, repeated for 100 s. The subjects were asked to perform flexion and rotation as selectively as possible by using the force feedback information. Fig. 5 shows the three detected EMG signals during an exercise.
D. Signal Analysis 1) Synthetic Signals: The BSS algorithm described above was applied to simulated signals evaluating the effect of the following factors: 1) the kernel for the STFD; 2) the criterion for the selection of the time-frequency points for joint diagonalization; 3) the number of time-frequency points; 4) the SNR; and 5) the number of sensors. ), The Wigner–Ville, Choi–Williams (with and Bessel kernels [5] were compared. The time-frequency points for joint diagonalization were 10, 100, or 1000, and were selected: 1) randomly; 2) with the criterion proposed by Belouchrani et al. [3] (19); and 3) with the single auto-term criterion [13], [16] (20). In the simulations, SNR varied between 0 and 20 dB, at steps of 5 dB, and three or five sensors were simulated. Fig. 6 reports the selection of time-frequency points according to the single auto-term criterion for simulated signals. For each SNR, 50 simulations were performed. In addition to the different noise signal realizations, for each of the 50 simulations, the locations of the MUs within the muscle were randomly selected. Moreover, the inter-pulse interval variability introduced additional differences among the signals generated in
Fig. 6. Representation of the criterion based on single auto-terms (20) for the selection of the time-frequency points for joint diagonalization. Three simulated signal mixtures (case DYN1 with 20-dB SNR, see Fig. 2) are considered for the calculation of the STFDs. In particular, the function C [t; f ], defined in (20), is shown. The time-frequency points corresponding to high values of C [t; f ] represent the locations in the time frequency plane where the two sources are maximally separated (see also Fig. 2).
the 50 simulations. In each condition, the results will be provided as mean and SD over the 50 simulations. 2) Experimental Signals: On the basis of the results from simulations (see below), the experimental signals were analyzed by the BSS approach described above with Choi–Williams
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Fig. 7. Example of separation of sources from three mixtures with SNR 20 dB. The simulated case corresponds to DYN2 (Fig. 2). The Choi–Williams kernel with 10 (t; f ) points selected by the single auto-term criterion [13], [16] for joint diagonalization was chosen for the source separation. The three mixtures are shown on the left while the reference (white lines) and reconstructed (solid black lines) sources are shown on the right.
kernel and with selection of 10 points based on the single auto-term criterion [13], [16] (20). The entire signal recordings (100 s) were processed by the BSS algorithm without any information except for the number of sources to be separated. To limit computational time, the time resolution in the STFDs was fixed to 97 ms and the frequency resolution was 2 Hz. Thus, the cross time-frequency representations of the entire signals recorded (100 s) had a size of 1024*256 points. Increasing resolution did not lead to significant improvement of performance. The reference and reconstructed sources could be identified from the activation intervals of the muscles. Each source was identified as detected over the active muscle on the basis of the force exerted (Fig. 4). A threshold of 15% MVC on the force signal was applied to identify the intervals of activity of the two muscles. The reconstructed sources were compared with the signals detected over each muscle in the intervals of selective activation of the specific muscle (Fig. 4). Thus, the reference sources were considered the signals detected over the two muscles in the intervals of force production by the specific muscle. All the indexes computed to assess performance were obtained by comparison with the reference sources, as defined above. As noted above, the reference sources were available for performance analysis since separation of the sources could be simply performed on the basis of the force signals and the sources did
not overlap in time. It should again be stressed that this information was not used by the BSS algorithm which was applied to the entire 100-s recordings. The main aim of the experimental validation of performance was to validate the approximation of linear instantaneous mixtures in specific recording conditions. The mean frequency (MNF) of the power spectral density of the reference and reconstructed sources was computed over time to assess changes in the frequency content of the signals, reflecting fatigue [22]. The ratio between root-mean-square (rms) values of the reconstructed and reference source with respect to the other source detected at the same sensor was used as performance index. In addition, the correlation coefficient between the reference and reconstructed source was computed. III. RESULTS A. Simulated Signals Fig. 7 reports an example of source separation from three simulated EMG signal mixtures with 20-dB SNR. There was no significant difference among performance of the Bessel and ) kernels. In some conChoi–Williams (with ditions, the Wigner–Ville kernel resulted in slightly worse results. Performance in simulated signals were evaluated by the cross-correlation coefficient between the reference and the reconstructed sources. Since there was no significant difference
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TABLE I CROSS-CORRELATION COEFFICIENTS (MEAN SD) BETWEEN THE ORIGINAL AND RECONSTRUCTED SOURCE WITH THE APPLICATION OF THE BSS APPROACH ON SIMULATED SIGNALS. RESULTS FROM TWO KERNELS, THREE NUMBERS OF TIME-FREQUENCY POINTS, THREE CRITERIA FOR THE SELECTION OF THE POINTS, AND TWO SNRs ARE REPORTED. DYN1 AND DYN2 REFER TO THE TWO CASES SIMULATED (SEE FIG. 2), “WV” STANDS FOR WIGNER-VILLE KERNEL, “CW1” STANDS FOR CHOI-WILLIAMS KERNEL WITH = 1, “RAND” STANDS FOR RANDOM SELECTION OF THE (t; f ) POINTS, “BEL” FOR SELECTION OF THE (t; f ) POINTS ACCORDING TO BELOUCHRANI et al. [3], AND “SAT” ACCORDING TO THE SINGLE AUTO-TERM CRITERION (20), [13], [16]. THE BEST PERFORMANCE IS OBTAINED BY THE CHOI–WILLIAMS KERNEL AND THE SINGLE AUTO-TERM SELECTION OF THE (t; f ) POINTS (INDICATED BY GREY)
6
between performance related to the first and the second source reconstruction, only results for the first source will be reported. Table I shows the cross-correlation coefficient between the first original and reconstructed source for the case of three sensors. The results with five sensors were slightly better, as expected, and will not be reported. Results with the Wigner–Ville ) kernels are reported for two and Choi–Williams (with point selection, and three numSNRs, the three criteria of bers of points for the joint diagonalization (10, 100, and 1000). Choi–Williams kernel performed slightly better than the Wigner–Ville one, especially for the simulation case DYN2 points based on (Fig. 2). Moreover, the selection of the criterion (20) provided in general the best performance. With Choi–Williams kernel and single auto-term criterion, the results were only slightly affected by the number of points which can be limited, saving computational time. As was expected, the second simulation case (DYN2, see Fig. 2) led to poorer performance with respect to the first and larger noise determined lower correlation coefficients between the original and reconstructed sources. It has to be noted, however, that large temporal overlapping (DYN2) was not critical and decreased performance only slightly (Table I). With the Choi–Williams kernel and the single auto-term criterion for points, in all conditions, the average the selection of the correlation coefficient was greater than 0.85 for SNR as low as locations is selected, the 5 dB. When a large number of results of the BSS method using any selection criteria are very similar. This is due to the fact that as long as “enough” diagonal are selected, the influence of the nondiagonal matrices selected matrices is smoothed by the joint-diagonalization procedure. Nevertheless, the results obtained with 1000 randomly chosen points may be achieved with only 10 points selected
according to the single auto-term criterion. This decreases the computation cost of the joint-diagonalization part. The same analysis was performed for 0- and 20-dB SNR (results not shown). With 20-dB SNR, the Choi–Williams or Bessel kernel, and single auto-term criterion, the correlation coefficient was on average higher than 0.98 in the two simulated conditions (DYN1 and DYN2). The results with Wigner–Ville kernel were similar while the performance decreased significantly with the point selection instead of the Belouchrani method [3] for single auto-term criterion (average correlation coefficient higher than 0.86 versus 0.98). With 0-dB SNR, the Choi–Williams kernel, and the single auto-term criterion, the cross-correlation coefficient was always higher than 0.70. B. Experimental Signals All subjects were able to selectively exert flexion and rotation forces in the defined intervals of time. The average flexion (rotation) force level during rotation (flexion) was lower than 1% MVC in all cases. The cross-correlation between signals generated during rotation and flexion was not significantly different from zero for all the three observations, indicating that the hypothesis of uncorrelated sources could be applied to the signals generated by the two investigated muscles. After BSS, the cross-correlation between the first reference source (flexor carpi radialis) and its reconstruction was (mean SD, over all subjects and the two contraction types, ) , while for the second . source (pronator teres) it was The initial MNF value of the flexor carpi radialis and pronator teres muscles (reference sources) was Hz and Hz, respectively. After source separation,
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MNF initial values were Hz and Hz for the two muscles, respectively. There was no statistical difference (student t-test for dependent samples) between MNF initial values in the reference and reconstructed sources. The rate of decrease of MNF was, for the two reference sources ), (mean SD, over all subjects and the two exercises, Hz/s and Hz/s, indicating that the signals changed spectral content during time. The two reconstructed sources led to MNF rate of change of Hz/s and Hz/s, respectively. The rates of decrease of MNF were not significantly different between the reference and reconstructed sources. The correlation coefficient and the similar trends in MNF of the reference and reconstructed sources indicate that the hypothesis of linear instantaneous mixtures was met in the experimental recordings. In the case of linear instantaneous mixtures, almost perfect reconstruction of the reference sources in the present experimental analysis was expected. A more useful indicator of the performance of the method on experimental signals is the ability of reduce the influence of the second source from recordings over the two muscles. between rms values of the referThe average ratio ence source and of the other source activity detected at the first while it increased to after sensor was BSS. For the second source, the ratio increased from to . In both cases of flexion and rotation, the increase in rms ratio with respect to the original condition was statistically significant (Student t-test for dependent samples), indicating a significant improvement of selectivity. Fig. 8 shows an example of source separation for experimental signals. IV. DISCUSSION This study provides validation of a specific BSS method for the separation of surface EMG signals generated by different muscles. It indicates the limitations, the proper choices of the parameters, and the areas of applications of the method. In other works in which BSS methods have been used for surface EMG signal analysis, BSS was simply applied to experimental signals without any validation neither for the experimental case nor in simulation [17]. The present work shows that the applied BSS approach may be used in practical situations for separating surface EMG signals generated by different closely located muscles. However, limitations of this approach, both related to the basic assumptions and to the performance achieved, are still important and need further investigation. The BSS approach is particularly suited for the separation of surface EMG signals generated by different muscles. Indeed, in this case, no a priori information is available about the mixture matrix and the sources. Moreover, no assumptions can be made on the frequency content of the sources which in general have bandwidths largely overlapped. In some cases it is impossible, with surface EMG measures, to separate the activities of closely located muscles, due to the poor selectivity of the recording (see Fig. 4, for example). In this work, we applied a BSS approach to surface EMG signals and validated the performance by both simulations and experimental signals. For this purpose, a model for the description
Fig. 8. Example of signals recorded from the sensors located over the flexor carpi radialis and the pronator teres muscles during cyclic wrist flexion/rotation (black lines). A cyclic task, consisting of 2-s flexion at 50% MVC and 2-s rotation at 50% MVC is shown. The entire recording lasts 100 s, of which approximately 8 s are shown for clarity. The results shown correspond to the application of the BSS approach to the entire recordings of 100 s. A threshold has been applied to the force signal related to flexion (upper traces) and rotation (lower traces) and the intervals of time in which these forces exceed 15% MVC are shown (limited by dashed lines). The intervals defined by the force signals are those during which the flexor carpi radialis and the pronator teres muscles are active. From the original signals, it is clear that large contributions from the activation of the pronator teres (in the first case) and the flexor carpi radialis (in the second case) during rotation and flexion are present in the two recordings. After source separation, the relative amplitude of the second source in the reconstructed signals (grey lines) significantly decreases in both cases.
of MU control strategies during a force-varying task was implemented and applied together with a structure-based model for the generation of single MU action potentials. The simulations well represented the generation system but did not indicate if the assumption of linear instantaneous mixtures was met in experimental cases. Indeed, ideal linear instantaneous mixtures were generated in simulation. The experimental protocol allowed objective validation of the method in practical conditions. It was shown that the method can, to some degree, separate the activity of sources which are mixed in an approximately linear instantaneous manner. However, source separation was not perfectly reached, as it was shown, e.g., in Fig. 8. The ref-
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erence source was reconstructed accurately (correlation coefficients higher than 0.9), indicating that the assumption of linear instantaneous mixtures was approximately met, but the other source detected at the same sensor was not completely removed. The attenuation of the second source was, in any case, significant, with an average improvement of approximately twice, which is relevant in the applications (see Fig. 8, for example). In general experimental conditions, besides the fact that the assumption of linear instantaneous mixtures is only an approximation, there are also other issues which may affect the basic hypotheses of the BSS approach. For example, the MUs of different muscles may show a certain degree of synchronization during synergic activity [17] and this may affect the hypotheses of uncorrelated sources. In the experimental part of this work, we used simple detection systems with rather large inter-electrode distance. Higher selectivity of the recording could be reached by more complex systems [6], [25] and/or by decreasing inter-electrode distance [20], [21]. The relative decrease of signal amplitude with 5-mm displacement of the electrodes was, for example, found significantly higher when highly selective systems (e.g., the Laplacian [6]) were used with respect to the single differential detection in the tibialis anterior, upper trapezius, and biceps brachii muscle [10], [11]. Improvement of selectivity by using spatial filters more complex than the single differential one depends on the anatomy and may vary on a subject by subject and muscle by muscle basis [12]. The combined use of selective detection systems and of the BSS approach applied in this work may determine significantly higher selectivity than with the BSS alone. Thus, advanced detection systems and signal processing methods may allow almost complete separation of signals generated by very close muscles as those investigated in this work. This study was not focused on the combination of selective detection systems and BSS approaches, but rather dealt with the applicability of the BSS approach and on its performance. Future work will address the improvement in performance by the combined use of highly selective spatial filters and BSS approaches. The spatial filter may be applied either before or after source separation, depending on how well the filtered signals approximate the assumptions of the BSS approach. The present study focused, both for the simulations and for the experimental part, on the analysis of two muscle activities. However, the derivation of the method reported in the Section II is clearly applicable to any number of sources, with the only limitation being that the number of detected signals (observations) should be larger than the number of sources. The objective validation of performance imposed the analysis of particularly simple cases, especially in the experimental situation, but the approach can be extended to muscle groups with more than two muscles. The method proposed is limited to linear instantaneous mixtures and this may have partly determined the poorer performance in the experimental case with respect to the simulations (compare, e.g., Figs. 7 and 8). It should be stressed that, due to the limitation of dealing with linear instantaneous mixtures, the application of the method proposed in this study is limited to specific conditions and does not include the general issue of separating any type of cross-talk signals. For sources located far from each other, crosstalk signals have indeed properties
different from those of signals located close to the source [9] and certainly the linear instantaneous mixture approximation does not hold. The application proposed in this study considered small muscles close and running parallel to each other. The muscles selected for the experimental part of this study are an example of such muscle groups. In this case, the assumption of linear instantaneous mixtures is at least approximated (Fig. 5). Besides its limitations, in the conditions analyzed, the method provided a relevant improvement in source separation, indicating promising applications. V. CONCLUSION A BSS approach was applied to nonstationary simulated and experimental surface EMG signals. It was shown that, within the limitations of linear instantaneous mixtures, the approach may have interesting applications for the separation of signal sources which could not be distinguished otherwise. Together with the design of selective detection systems, the method presented may lead to satisfactory separation of the activities of small muscles placed close to each other. The limitation of dealing with linear instantaneous mixtures, instead of the more general convolutive ones, has to be addressed and possibly overcome in future studies. ACKNOWLEDGMENT The authors are sincerely grateful to F. Lebrun for the useful help in running some of the simulations reported in this study and to R. Bergamo who contributed in designing the experimental protocol. REFERENCES [1] A. Belouchrani, K. Abed-Meraim, J. F. Cardoso, and E. Moulines, “A blind source separation technique using second-order statistics,” IEEE Trans. Signal Processing, vol. 45, pp. 434–443, Feb. 1997. [2] A. Belouchrani and M. G. Amin, “Blind source separation based on time-frequency signal representations,” IEEE Trans. Signal Processing, vol. 46, pp. 2888–2897, Nov. 1998. [3] A. Belouchrani, K. Abed-Meraim, M. G. Amin, and A. Zoubir, “Jointantidiagonalization for blind source separation,” in Proc. ICASSP, vol. 5, 2001, pp. 2789–2792. [4] J. F. Cardoso, “Blind signal separation: Statistical principles,” Proc. IEEE, vol. 9, pp. 2009–2025, 1998. [5] L. Cohen, Time-Frequency Analysis, ser. Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1995. [6] C. Disselhorst-Klug, J. Silny, and G. Rau, “Improvement of spatial resolution in surface-EMG: A theoretical and experimental comparison of different spatial filters,” IEEE Trans. Biomed. Eng., vol. 44, pp. 567–574, July 1997. [7] D. Farina and R. Merletti, “A novel approach for precise simulation of the EMG signal detected by surface electrodes,” IEEE Trans. Biomed. Eng., vol. 48, pp. 637–646, Dec. 2001. [8] D. Farina, M. Fosci, and R. Merletti, “Motor unit recruitment strategies investigated by surface EMG variables,” J. Appl. Physiol., vol. 92, pp. 235–247, 2002. [9] D. Farina, R. Merletti, B. Indino, M. Nazzaro, and M. Pozzo, “Cross-talk between knee extensor muscles. Experimental and model results,” Muscle & Nerve, vol. 26, pp. 681–95, 2002. [10] D. Farina, L. Arendt-Nielsen, R. Merletti, B. Indino, and T. GravenNielsen, “Selectivity of spatial filters for surface EMG detection from the tibialis anterior muscle,” IEEE Trans. Biomed. Eng., vol. 50, pp. 354–364, Mar. 2003. [11] D. Farina, E. Schulte, R. Merletti, G. Rau, and C. Disselhorst-Klug, “Single motor unit analysis from spatially filtered surface EMG signals—Part I: Spatial selectivity,” Med. Biol. Eng. Comput., vol. 41, pp. 330–337, 2003.
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[12] D. Farina, L. Mesin, S. Martina, and R. Merletti, “Comparison of spatial filter selectivity in surface myoelectric signal detection—Influence of the volume conductor model,” Med. Biol. Eng. Comput., vol. 42, pp. 114–120, 2004. [13] C. Févotte and C. Doncarli, “Two contributions to blind source separation using time-frequency distributions,” IEEE Signal Processing Lett., vol. 11, pp. 386–389, Mar. 2004. [14] C. Févotte, “Approche temps-fréquence pour la séparation aveugle de sources nonstationnaires (Time-frequency approach for blind separation of nonstationary sources),” Ph.D. dissertation, Ecole Centrale de Nantes, Nantes, France, 2003. [15] A. J. Fuglevand, D. A. Winter, and A. E. Patla, “Models of recruitment and rate coding organization in motor unit pools,” J. Neurophysiol., vol. 70, pp. 2470–2488, 1993. [16] A. Holobar, C. Févotte, C. Doncarli, and D. Zazula, “Single autoterms selection for blind source separation in time-frequency plane,” in Proc. EUSIPCO, Toulouse, France. [17] J. M. Kilner, S. N. Baker, and R. N. Lemon, “A novel algorithm to reduce electrical cross-talk between surface EMG recordings and its application to the measurement of short-term synchronization in humans,” J. Physiol., vol. 538, pp. 919–930. [18] T. A. Kuiken, N. S. Stoykov, M. Popovic, M. Lowery, and A. Taflove, “Finite element modeling of electromagnetic signal propagation in a phantom arm,” IEEE Trans. Neural Syst. Rehabil. Eng., vol. 9, pp. 346–354, Dec. 2001. [19] U. Kuruganti, B. Hudgins, and R. N. Scott, “Two-channel enhancement of a multifunction control scheme,” IEEE Trans. Biomed. Eng., vol. 42, pp. 109–111, Jan. 1995. [20] L. Lindstrom and R. Magnusson, “Interpretation of myoelectric power spectra: A model and its applications,” Proc. IEEE, vol. 65, pp. 653–662, 1977. [21] M. M. Lowery, N. S. Stoykov, and T. A. Kuiken, “Independence of myoelectric control signals examined using a surface EMG model,” IEEE Trans. Biomed. Eng., vol. 50, pp. 789–793, June 2003. [22] R. Merletti, M. Knaflitz, and C. J. De Luca, “Myoelectric manifestations of fatigue in voluntary and electrically elicited contractions,” J. Appl. Physiol., vol. 69, pp. 1810–1820, 1990. [23] R. Merletti, D. Farina, and M. Gazzoni, “The linear electrode array: A useful tool with many applications,” J. Electromyogr. Kinesiol., vol. 13, pp. 37–47, 2003. [24] J. Perry, Gait Analysis. Normal and Pathological Function. Thorofare, NJ: Slack, Inc., 1992. [25] G. Rau, C. Disselhorst-Klug, and J. Silny, “Noninvasive approach to motor unit characterization: Muscle structure, membrane dynamics and neuronal control,” J. Biomechan., vol. 30, pp. 441–446, 1997. [26] K. Roeleveld, D. F. Stegeman, H. M. Vingerhoets, and M. J. Zwarts, “How inter-electrode distance and motor unit depth influence surface potentials,” SENIAM Deliverable, vol. 5, pp. 55–59, 1997b. [27] A. M. Sayeed and D. L. Jones, “Optimal kernels for nonstationary spectral estimation,” IEEE Trans. Signal Processing, vol. 43, pp. 478–491, Feb. 1995. [28] L. Tong, R. Liu, V. Soon, and Y. F. Huang, “Indeterminacy and identifiability of blind identification,” IEEE Trans. Circuits Syst., vol. 21, pp. 499–509, May 1991.
Dario Farina (M’01) graduated in summa cum laude in electronics engineering from Politecnico di Torino, Torino, Italy, in February 1998. In 2001 he received the Ph.D. degree in electronics engineering from Politecnico di Torino and from the Ecole Centrale de Nantes, Nantes, France. In 1999-2004, he taught courses in Electronics and Mathematics at Politecnico di Torino and in 2002-2004 he was Research Assistant Professor at the same university. Currently, he is Associate Professor in Biomedical Engineering at the Faculty of Engineering and Science, Department of Health Science and Technology of Aalborg University, Aalborg, Denmark. He acts as referee for many scientific international journals and is on the Editorial Board of the Journal of Electromyography and Kinesiology. His main research interests are in the areas of signal processing applied to biomedical signals, modeling of biological systems, and basic and applied physiology of the neuromuscular system. In these fields he has published approximately 60 peer-reviewed papers in International Journals, 80 conference abstracts, and more than 10 book chapters. Dr. Farina is a Registered Professional Engineer.
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Cédric Févotte was born in Laxou, France, in 1977 and has lived in Tunisia, Senegal, and Madagascar until 1995. He graduated from the École Centrale de Nantes, Nantes, France, in 2000 and received the Doctorat d’Automatique et Informatique Appliquée from Ecole Centrale and the University of Nantes, Nantes, France, in 2003. Since November 2003, he has been a Research Associate with the Signal Processing Laboratory, Cambridge University, Cambridge, U.K. His current research interests are statistical signal processing and time-frequency signal representations with application to blind-source separation.
Christian Doncarli graduated in electrical engineering from the Ecole Nationale Supérieure dee Mécanique, Nantes, France, in 1971 and received the Ph.D. degree in signal processing from the Universite de Nantes, Nantes, France, in 1976. He is currently a Professor of Signal Processing with the Ecole Centrale de Nantes. His research interests concern decision problems (classification, detection, blind-source separation), especially in transformed domains like time frequency or time scales. His application domains are biomedical and audio signals.
Roberto Merletti (S’71–M’72) graduated in electronics engineering from the Politecnico di Torino, Torino, Italy, and received the M.S. and Ph.D. degrees in biomedical engineering from The Ohio State University, Columbus. Since 1984, he has been an Associate Professor of Biomedical Instrumentation at the Department of Electronics, Politecnico di Torino. From 1989 to 1994, he was an Associate Professor at the Department of Biomedical Engineering and a Research Associate at the Neuromuscular Research Center, both at Boston University, Boston, MA. In 1996, he founded the Laboratory for Neuromuscular System Engineering at the Politecnico di Torino, where he is currently the Director. He is the Coordinator of a project sponsored by the European Community and of a project sponsored by the European Space Agency. His research focuses on detection, processing, and interpretation of surface EMG, and on electrical stimulation and neuromuscular control.
