Comparison of algorithms for estimation of EMG variables during voluntary isometric contractions

Comparison of algorithms for estimation of EMG variables during voluntary isometric contractions
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  Journal of Electromyography and Kinesiology 10 (2000) 337– Comparison of algorithms for estimation of EMG variables duringvoluntary isometric contractions Dario Farina  a, b , Roberto Merletti  a,* a Centro di Bioingegneria, Department of Electronics, Politecnico di Torino, Torino, Italy b  De´  partement d’Automatique et Informatique applique´ e, Ecole Centrale de Nantes, Nantes, France Abstract Many algorithms have been described in the literature for estimating amplitude, frequency variables and conduction velocity of the surface EMG signal detected during voluntary contractions. They have been used in different application areas for the noninvasive assessment of muscle functions. Although many studies have focused on the comparison of different methods for infor-mation extraction from surface EMG signals, they have been carried out under different conditions and a complete comparison isnot available. It is the purpose of this paper to briefly review the most frequently used algorithms for EMG variable estimation,compare them using computer generated as well as real signals and outline the advantages and drawbacks of each. In particularthe paper focuses on the issue of EMG amplitude estimation with and without pre-whitening of the signal, mean and medianfrequency estimation with periodogram and autoregressive based algorithms both in stationary and non-stationary conditions, delayestimation for the calculation of muscle fiber conduction velocity.  ©  2000 Elsevier Science Ltd. All rights reserved. Keywords:  Electromyography; Muscle fatigue; Whitening filters; AR modeling; Conduction velocity 1. Introduction The surface EMG signal detected during a voluntarymuscle contraction is a realization of a non-stationarystochastic process. Any variable of the signal, computedover a given time interval, is intrinsically an estimate of the true value of that variable with an associated varianceand bias which depend on the window length and on theestimator used. A specific feature of the signal may infact be indicated by a number of different estimators.For example, amplitude may be indicated by the averagerectified value or the root mean square value while spec-tral features may be indicated by the mean spectral fre-quency or the median spectral frequency. Different esti-mators of the same feature usually have differentproperties. Some may show lower variance, otherslarger, some may be more sensitive to noise andothers less.It is the purpose of this work to give indications aboutthe variability of EMG variable estimations related to * Corresponding author. Tel.:  + 39-011-5644137/4330476; fax:  + 39-011-5644099/4330404.  E-mail address: (R. Merletti). 1050-6411/00/$ - see front matter  ©  2000 Elsevier Science Ltd. All rights reserved.PII: S1050-6411(00)00025-0 the processing techniques adopted, and to clarify thepros and cons of the different approaches used for timeand spectral description of the EMG signal. 1.1. Some definitions A feature of the EMG signal is a distinct quality orcharacteristic of the signal that can be observed ordescribed qualitatively, such as being large or small, fastor slow, spiky or smooth. A variable of the EMG signalis the value of a physical quantity that can be computed,reported and transmitted in numerical form and that canchange as a function of time, such as a voltage, a fre-quency, a velocity, a delay, etc. A variable is estimatedfrom a finite length time interval referred to as an epoch.A parameter of the EMG is either a stable variable ora value of the physical or mathematical model ideallyassociated to the EMG generation or detection processes,such as the length and depth of a fiber, the electrodesurface or the interelectrode distance, the coefficients of an autoregressive model, etc. 1.2. EMG variables It is known that the EMG spectrum changes during asustained contraction due to fatigue because the signal  338  D. Farina, R. Merletti / Journal of Electromyography and Kinesiology 10 (2000) 337–349 is not stationary [8,9,11,15,23,24,26,32,35]. The changeis usually quantified by monitoring amplitude and spec-tral variables as well as conduction velocity.The most commonly used estimators of amplitude fea-tures are the average rectified value (ARV) and the rootmean square value (RMS) which are usually computedwithout any pre-processing of the data by the followingequations in the numerical domain:ARV  1  N    N i  1   x i   RMS    1  N    N i  1  x 2 i where  x i  are the signal samples, and  N   the number of samples in the epoch considered.Spectral variables commonly used are the mean(centroid) and the median frequency (MNF and MDF)[8,32] defined by the following equations in the numeri-cal domain:  f  mean    M i  1  f  i P i   M i  1 P i   f  med i  1 P i     M i   f  med P i  12   M i  1 P i where  P i  is the  i th line of the power spectrum and  M   isthe highest harmonic considered. These two variablesprovide some basic information about the spectrum of the signal and its changes versus time. They coincide if the spectrum is symmetric with respect to its center linewhile they differ if the spectrum is skewed. A tail in thehigh frequency region implies that MNF is higher thanMDF. A constant ratio  f  mean  /   f  med  versus time impliesspectral scaling without shape change while a change inthis ratio implies a change of spectral skewness or shape.It can be shown that the standard deviation of MDF istheoretically higher than that of MNF by a factor 1.253[2]. Other factors may increase this ratio which is usuallyhigher than the theoretical prediction. However, it canalso be shown that MDF estimates are less affected byrandom noise [46] (expecially if the noise is in the highfrequency band of the EMG spectrum) and more affectedby fatigue (since the spectrum becomes more skewedwith fatigue). Because of these pros and cons andbecause of the additional information that is carried jointly by the two variables, researchers often use bothin their reports.In order to estimate muscle fiber conduction velocity(CV) two quantities must be measured: the interelectrodedistance and the delay between the two detected signals.A meaningful measure of interelectrode distance impliesthat the electrodes must be thin and aligned in the direc-tion of the muscle fibers. The last requirement may notbe easy to meet in pennated muscles. A meaningful mea-sure of delay implies that the two signals are identicaland time shifted. In this case the delay between peaks,valleys or zero crossings is the same. Unfortunately, thisis rarely the case and it is therefore necessary to agreeon the “best” definition of delay between two signalsthat are not identical. The concept of delay between twosignals that are very different is meaningless: it is there-fore also necessary to agree on a “degree of similarity”that makes the estimate of delay (whatever its definition)acceptable. The problem has been addressed in otherfields of research and the approach that is generallyaccepted is the following: the delay between two similarbut not identical signals is the time shift that must beapplied to one of the signals to minimize the meansquare error with the other [4,30]. This time shift is thesame that maximizes the crosscorrelation function (CCF)between the two signals. The maximum of the nor-malized CCF is adopted as the indicator of shape simi-larity. 1.3. Phenomenological EMG models In order to test performances of algorithms designedto extract information from the EMG signal it is neces-sary to have synthetic signals generated by models. Sim-ple models based on the generation of filtered whitegaussian noise have been used to simulate stochastic pro-cesses with known expected spectra [27,31,34,44]. Themodel proposed by Shwedyk et al. [44] is described inFig. 1.The expression of the expected spectrum has twoparameters  f  h  and  f  l  that allow changes to the shape of the spectrum. Non stationarity may be generated bychanging these parameters during time. The first moment(mean frequency) can be computed analytically [12]:  f  mean  2  f  h p a  +1 a  − 1   2 a  2 a  2 − 1ln a   1  a   being the ratio  f  l  /   f  h .In the following this model will be used to simulatestationary and non-stationary stochastic processes. Thesampling frequency will always be 1024 Hz. 1.4. Physical EMG models In order to test algorithms developed for estimatingmuscle fiber CV, a description of the EMG signal whichtakes into account the physical properties of the EMGgeneration system is necessary. Several physical EMGgeneration models have been described in the past. Wewill use in this paper the model recently proposed byFarina and Merletti [13] which describes the volumeconductor as an asitropic layered medium (muscle, fatand skin layers) and can take into account the end plateand the end of fiber effects, and electrode shape and size.  339  D. Farina, R. Merletti / Journal of Electromyography and Kinesiology 10 (2000) 337–349 Fig. 1. Simulation of EMG signals by filtering white gaussian noise. (a) Examples of expected spectra obtained from the equation indicated onthe right for different values of the two parameters  f  h  and  f  l . (b,c) Two simulated signals obtained by filtering white gaussian noise with the inverseFourier transform of the square root of   P (  f  ). 2. Amplitude features and their estimators It can be shown that the variance of estimation of ARV and RMS is higher in the case of correlatedsamples with respect to the case of uncorrelatedsequences [6]. This observation leads to the idea of de-correlating the samples before applying the amplitudeestimators [5,6,18,45]. The problem of whitening a sig-nal is an estimation problem. The signal is supposed tobe the output of a linear filter with white noise as input;in this case, by inverting the transfer function of the fil-ter, the input white noise is obtained from the availablesignal. If the signal is not generated by the estimatedmodel, the output of the whitening filter will have apower spectral density “approximately” white [21,28].The problem is closely related to the parametric spectralestimation which will be investigated in further detailbelow. For the moment let’s assume that the signal gen-eration filter is an all pole filter (autoregressive model);in this case the whitening filter would be an all zerofilter. The problem of estimation of the filter parametersis the same as that found in parametric spectral esti-mation.The usefulness of a pre-whitening filter has beeninvestigated for real signals in the literature [5,6,45].The results obtained with simulated signals arepresented in Fig. 2. 1000 realizations of the same station-ary stochastic process have been generated by the modeldescribed in Fig. 1 with parameters set in order to have  f  mean = 80 Hz. The whitening filter of different orders hasbeen estimated from a single 2 s long realization(calibration signal). In Fig. 2 the coefficient of variation(standard deviation over the mean of the estimation) of  Fig. 2. Coefficient of variation of amplitude estimators as a functionof the window length for different orders of the whitening filter. Theresults obtained from raw signals are also shown. 1000 realizations of the same stochastic process have been used to compute each of thepoints depicted. the estimates of ARV and RMS is shown for differentepoch lengths and orders  p  of the whitening filter. It isevident that the filter order is not critical: orders higherthan 3 lead to comparable results. For any epoch lengthwhitening considerably improves the estimation,resulting in a decrement of the coefficient of variationof about 54%. As predicted theoretically, RMS is a betterestimator with respect to ARV if the amplitude distri-bution of the signal is gaussian. Note that ARV wouldbe better in the case of Laplacian distribution [7]. Inany case the difference is minimal and not relevant forpractical applications.Fig. 3 shows ARV as a function of time for a 10 scontraction at 20% MVC for a raw and a pre-whitened  340  D. Farina, R. Merletti / Journal of Electromyography and Kinesiology 10 (2000) 337–349 Fig. 3. ARV normalized with respect to the mean value and com-puted from a real signal (sampling frequency 1024 Hz) detected duringa voluntary contraction of the biceps brachii muscle at 20% MVC witha sliding window of 250 ms and high degree of overlapping betweenepochs. The estimations obtained with and without pre-whitening of the signal are shown.Fig. 4. Comparison between the expected spectrum of a stochastic process generated with the model of Fig. 1 (solid lines) and the estimatedspectra obtained using an AR model with different orders  p  (dashed lines). The estimated MNF and MDF are indicated. signal. The whitening filter (of order 5) has been com-puted from a 2 s contraction of the same subject, at thesame contraction level, in the same experimental session.The decrease in the variance of estimation is evident andis approximately the same as predicted by the simula-tions.It can be concluded that pre-whitening reduces con-siderably the variance of the most commonly usedamplitude estimators, and it is fast since very low orderfilters can be implemented. An order higher than 5 wouldnot improve the performance although it would increasethe computational effort. On the other hand the necessityof a calibration contraction may be a drawback in practi-cal applications. 3. Spectral features and their estimators The power spectral density (PSD) of a wide sensestationary stochastic process is defined as the Fouriertransform of its autocorrelation function. It can be esti-mated by different methods; the most commonly used isthe periodogram, which is the square of the absolutevalue of the Fourier transform of the signal divided by  341  D. Farina, R. Merletti / Journal of Electromyography and Kinesiology 10 (2000) 337–349 the signal length. In this way the standard deviation of the PSD estimate at each frequency is equal to 100% of the expected value and may be reduced by smoothing(moving average of nearby lines) or by averaging spectraof nearby epochs under the assumption of stationarityover these epochs [21].A different approach for PSD estimation is based onthe methods referred to as modern, parametric ormodel-based.The theoretical basis for the parametric approach isthe assumption that the signal is a realization of a stoch-astic process described by a mathematical model. Themodel is a filter that has white noise as input. The para-meters of the model can be estimated from the avail-able data.One of the most powerful models is the so-calledARMA (autoregressive moving average) model. In theARMA model each sample  x n  of the signal is describedas a linear combination of   p  past outputs and  q + 1 presentand past inputs:  x n    pk   1 a k   x n − k    ql  0 b l u n − l where  u n  is the white input sequence [21,28].If   a i = 0 (for  i = 1, … ,  p ) the model is called MA (movingaverage) and if   b i = 0 (for  i = 0, … , q ) the model is calledAR (autoregressive). MA and AR models are specialcases of the ARMA model. In the following, attentionwill be focused on the AR model. This has been by farthe most widely used for spectral estimation.A few studies in the literature report EMG analysisby parametric methods [10,29,34,37]. The model chosenfor the estimation is usually the AR with an orderbetween 4 and 11. As in the case of the periodogrambased methods, MNF and MDF are often considered,however any of the estimated model parameters can beused to monitor changes in the spectrum.The problem of spectral estimation is thus convertedin the problem of estimation of a finite number of modelparameters (from which derives the name of parametricmethods). In this paper the method used for estimatingthe AR parameters will always be the one proposed byBurg [21].An additional problem with respect to traditional per-iodogram based methods is the choice of the order of the model (number of parameters). If the estimatedmodel order is too small, the spectrum appears excess-ively smooth due to incorrect assumptions on the gener-ator model, while if it is too large the variance increasesand peaks that are not present in the real spectrum aregenerated as artifacts [21,28,37]. The model order  p  canbe estimated from the data available using one of severalcriteria proposed in the literature. Akaike [1] has pro-vided two criteria, the final prediction error (FPE) andthe Akaike information criterion (AIC); a third method Fig. 5. Square root of the mean square error of MNF estimation asa function of the order of the AR model for different window lengths.The plots are normalized with respect to the maximum value of theMSE which is reached for a model order equal to 3.Fig. 6. Square root of the mean square error of (a) MNF and (b)MDF estimation as a function of the window length for differentmodel orders.
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