decomposition of multiunit electromyographic signals

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 46, NO. 6, JUNE 1999 685

Decomposition of MultiunitElectromyographic Signals

Jianjun Fang,* Gyan C. Agarwal,Fellow, IEEE, and Bhagwan T. Shahani

Abstract—We have developed a comprehensive technique toidentify single motor unit (SMU) potentials and to decomposeoverlapped electromyographic (EMG) signals into their con-stituent SMU potentials. This technique is based on one-channelEMG recordings and is easily implemented for many clinicalEMG tests. There are several distinct features of our technique:1) it measures waveform similarity of SMU potentials in thewavelet domain, which gives this technique significant advantagesover other techniques; 2) it classifies spikes based on the nearestneighboring algorithm, which is less sensitive to waveform vari-ation; 3) it can effectively separate compound potentials basedon a maximum signal energy deduction algorithm, which isfast and relatively reliable; and 4) it also utilizes the informa-tion on discharge regularities of SMU’s to help correct possibledecomposition errors. The performance of this technique hasbeen evaluated by using simulated EMG signals composed ofup to eight different discharging SMU’s corrupted with whitenoise, and also by using real EMG signals recorded at levelsup to 50% maximum voluntary contraction. We believe thatit is a very useful technique to study SMU discharge patternsand recruitment of motor units in patients with neuromusculardisorders in clinical EMG laboratories.

Index Terms—Constituent motor unit (MU) potential train,electromyographic (EMG) signal decomposition, single motorunit (SMU) potentials.

I. INTRODUCTION

STUDIES of the behavior of single motor unit (SMU)potentials and the underlying physiological functions of

human motor system are of significant importance to bothclinicians and basic researchers. These studies mainly dependon the analysis of SMU activities, which are normally recordedby a needle electrode inserted in a muscle. However, it isinevitable that more than one SMU potential will be registeredat same time overlapping with each other during muscularcontraction, especially with a strong effort. Therefore, a suc-cessful study of SMU discharge properties relies on correctlydecomposing multiunit EMG signals into their constituentSMU potential trains. At present, many types of decompositiontechniques are available. The window discriminator is one

Manuscript received November 27, 1997; revised January 8, 1999.Asteriskindicates corresponding author.

*J. Fang was with the Department of Rehabilitation Medicine and Restora-tive Medical Sciences, University of Illinois at Chicago. He is currently withthe Information Processing Research Lab, Motorola Inc., Schaumburg, IL60196 USA (e-mail: [email protected] or [email protected]).

G. C. Agarwal is with the Department of Electrical Engineering andComputer Science, University of Illinois at Chicago, Chicago, IL 60607 USA.

B. T. Shahani is with the Department of Rehabilitation Medicine andRestorative Medical Sciences, University of Illinois at Chicago, Chicago, IL60612 USA.

Publisher Item Identifier S 0018-9294(99)03984-1.

of the earliest techniques developed for EMG signal decom-position. It classifies different MU potentials based on theiramplitude partitioned by a group of preset thresholds [1].The matched filter, on the other hand, utilizes the informationof the entire waveform to recognize a MU potential. In thiscase, a set of desired waveforms is designated as templates tomatch with waveforms of MU potentials detected. This type ofclassifier is based on a set of decision rules that maximizesaposterioriprobability of the correct classification. Therefore, itis widely adopted for classification of multiunit EMG signals[2]–[4], and is currently considered as the main technique formultiunit EMG signal analysis [5]–[9]. As a variation of thetime domain concept of matched filter technique, McGillet al.[10] suggested a different way to perform template matchingbased on coefficients of the Fourier transform in the frequencydomain. Stashuket al. [11] proposed a similar method toidentify MU potentials based on power spectrum matching.

For those multiunit EMG recordings that do not containmany active SMU potentials and features of their wave-forms distinguish with each other, a technique known asfeature extraction has been introduced. According to thistechnique, a MU potential can be described by features of itswaveform, such as peak-to-peak amplitude, rise time, peak-to-peak duration, etc. These features are then compiled into avector referred to as a feature vector, which also representsa spike in the feature space. Since similar waveforms areof similar features, the feature points corresponding to thesame SMU are most likely located close to each other in thefeature space. Therefore, classification for this type of MUpotentials can be achieved by establishing a set of optimaldiscriminatory boundaries to partition the feature space [12].These discriminatory boundaries are usually determined basedon statistical decision theory [13].

In recent years, neural networks have also been used toclassify MU potentials [14]–[17]. One of the most importantproperties of a neural network is its learning ability. It is wellknown that neural networks are capable of learning patternsof an arbitrary nature. This property makes neural networksuseful in cases where little prior description of a SMU potentialis available. However, in many cases, the information aboutSMU potentials is not completely unknown, therefore, theadvantage of neural network technique may not necessarily besuperior over that of the matched filter technique. Furthermore,the neural network technique is usually very time-consuming,especially by using serial type of computing algorithms.

Superimposition of MU potentials is another important issuein decomposition of multiunit EMG signals. Due to lack of

0018–9294/99$10.00 1999 IEEE

686 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 46, NO. 6, JUNE 1999

efficient separation techniques, studies are often limited tolow force levels to avoid difficulties of separating compoundSMU potentials. In many clinical applications, separation ofcompound MU potentials is not as important as extraction ofmorphological features of MU potentials [18]. Therefore, insuch cases the compound MU potentials are simply ignored[19]. At present, the most frequently used method to handlesuperposition problem is a technique based on an exhaustivesearch scheme performed in the time domain. This techniqueexamines all possible combinations of templates and theirwaveform shifts in each possible time location to determine thebest template match [5], [20]–[23]. Obviously, any exhaustivesearch technique is usually very time-consuming and is nor-mally applicable only when the number of available templatesis small.

LeFever and DeLuca [20] developed a decomposition tech-nique based on multiple channel EMG recordings to increasethe power of identification during strong muscle contraction.This technique is very useful for research purposes; however,its cumbersome recording procedures and the dependence onsophisticated data analysis limits its usefulness for clinicalEMG tests.

In our study, we developed a different decomposition tech-nique, which has many advantages over previously describeddecomposition techniques. First, the identification algorithm inour technique is based on spectrum matching in the waveletdomain. The spectrum matching technique is sometimes con-sidered to be more effective than the waveform matchingtechnique in the time domain, especially when the inter-ference is induced by low-frequency baseline drift or byhigh-frequency noise. In both cases, the interference onlyaffects two marginal portions of the frequency spectrum. How-ever, previously described spectrum-matching techniques [11]are based on the Fourier spectrum, which normally requiresadditional windowing to eliminate truncation errors becauseof the rectangular data window for each spike potential. Withtime-frequency analysis like the wavelet transform, windowfiltering becomes unnecessary. Moreover, the interference ofwhite noise, which affects the entire spectrum and makesthe Fourier transform vulnerable, can be easily denoised withsoft-thresholding method. It has been shown that the wavelettransform method achieves a maximum number of vanishingmoments; therefore, a substantial degree of separation betweensignals and noise can be obtained by the wavelet transform.Second, the separation of superimposed SMU potentials in ourtechnique is based on a series of peel-off schemes in which atemplate with proper waveform shift is determined and thenremoved from the superimposed SMU potential one at a time.Our algorithm is somewhat similar to that described by Etawiland Stashuk [24]. However, the shift of the template to bepeeled off in our algorithm is determined by the maximumcorrelation between the residual signal and the template [25],rather than determined by the peak of the residual signal. Inour algorithm, adjustments are also made in each sequentialstep to reduce possible separation errors. Our technique hasbeen tested by using both simulated and real EMG signals.The performance of this technique has been satisfactory inboth aspects of speed and accuracy. We believe that with the

advancement of computer technology this new technique maybe easily implemented in future laboratory EMG machines tostudy SMU discharge patterns and recruitment order in patientswith neuromuscular disorders.

In Section II, we will describe the procedures of our de-composition algorithms. To facilitate the understanding of ouralgorithms, we will present a decomposition example in con-junction with the descriptions of our algorithms. In Section III,we use simulated and real EMG signals to evaluate theperformance of our algorithms. In Section IV, we will presentevaluation results for both simulated and real EMG signals. InSection V we then show an example of decomposition on asegment of real EMG signal based on our technique. Finally, inSection VI we discuss some technical aspects of EMG signaldecomposition.

II. DECOMPOSITION ALGORITHMS

EMG signal decomposition is a complicated task and isusually conducted in multiple stages. To start with, signalfiltering may be required to enhance the quality of EMGsignals, and signal detection may be need to detect the presenceof spike potentials. Since SMU’s discharge repetitively, itis essential for any EMG signal decomposition techniqueto identify the spikes originating from the same SMU’s.Furthermore, a spike may be a SMU potential or a compoundpotential, which results from temporal overlapping of multipleSMU potentials. Therefore, an EMG signal decompositiontechnique should be able to distinguish each SMU potentialand use it as a template potential to separate compoundpotentials. Finally, the decomposition result may not be error-free. Thus the incorporation of human decision is very helpfulfor detection and correction of possible decomposition errors.The decomposition technique we have developed consists ofthe following four separate modules, each of which handlesthe aspects described above.

Spike Detection and Signal Denoising:The EMG signal isa continuous recording of muscular potentials [Fig. 1(A)]. Itusually represents the overlapped muscle action potentials ofdifferent SMU’s. Each muscle action potential is normallyreferred to as a spike. The purpose of spike detection isto capture these spikes and to break down the continuousvoltage recording into a sequence of isolated spike poten-tials [Fig. 2(A)]. Our spike detection algorithm is based onan amplitude detection scheme, where a threshold cursor isusually set by an operator visually at a level to distinguishspike potentials from recording noise. During data scanning,detection of a spike is acknowledged if the amplitude of theEMG signal crosses the preset cursor. A segment of the EMGsignal containing the triggering potential will be sampled andused to represent a spike. At the end of data scanning, the EMGsegments that do not contain any spikes are treated as noisesegments, and are used to estimate the standard deviation ofthe noise.

In cases when noise interference cannot be neglected, asignal denoising procedure will be used. In this procedure, weassume that the recorded EMG data is a linear summationof an unknown, noise-free EMG signal and a Gaussian

FANG et al.: DECOMPOSITION OF MULTIUNIT EMG SIGNALS 687

Fig. 1. An example of denoising process based on the soft thresholdingtechnique in wavelet domain. (A) A segment of simulated EMG signalcorrupted with 10-dB Gaussian white noise. (B) The denoised version of(A). (C) and (D) are the enlarged portions of (A) and (B) indicated byQ,respectively. The threshold shown in (D) is used for signal detection duringdetection procedure.

white noise process , i.e.,

(1)

where . It has been proven [26] that withoutany knowledge of , the estimation of can be achievedfrom the EMG signal in a min–max sense based on asoft-thresholding technique in the wavelet domain. Accordingto this technique, the wavelet coefficients of are evaluatedas

(2)

where and are the wavelet coefficients ofand respectively, at scale index , and time

index . The optimal threshold is then determined as

(3)

where is the total number of samples of , and is thestandard deviation of noise estimated from noise seg-ments. Thus the estimate of based on the soft-thresholdingtechnique is calculated as

ifif (4)

Therefore, an estimate of the unknown EMG signal isthe inverse wavelet transform of . An example of signaldenoising based on the wavelet soft-thresholding technique isshown in Fig. 1(C) and (D), where the white noise was greatlysuppressed without significantly altering the waveform of eachspike potential.

The denoised EMG signal will then undergo the similarspike detection process once more using the same thresholdcursor. However, at this time each spike will be acquired withits largest peak aligned at center and stored in a temporary datamemory in the order of its occurrence [Fig. 2(A)]. The size of

Fig. 2. A graphic illustration of detection and classification procedures of ourEMG signal decomposition algorithm. (A) The spikes detected by the triggerlevel shown in Fig. 1(D). The sequential order of spike raster from left to rightrepresents the order of detection. (B) The similarity measures from the spikeraster in (A). Each vertical line represents the similarity measure of a pairof closely resembled spikes in each step. A discriminatory threshold is usedto group spikes together based on similarity measures. (C) The rearrangedspike raster based on the similarity measure in (B). (D) Superimposition ofthe spikes of each group bounded by two consecutive threshold crossings.The time scale for each spike segment is 5.33 ms. Triangles indicate thecandidates of SMU templates.

each spike segment is 64 sample points. At the sampling rate of12 kHz, 64 samples correspond to a duration of 5.33 ms, whichnormally covers the major portion of most SMU potentials. Ifa spike is less than 1.5 ms away from the previous one, thesecond spike will not be registered as an independent spike.Instead, it is considered as an extra phase of the previous spike.At the end of data scanning, all stored spike segments arealigned with their peak at the center, and assembled together toform a two-dimensional (2-D) matrix denoted as SPIKE, whichhas 64 columns and rows, where is the total number ofspikes detected. The time elapsed from the beginning of therecording to the center of each spike segment is also registeredin a separated one-dimensional (1-D) array

(5)

Spike Classification:A spike detected is either a SMUpotential or a compound potential. The purpose of spikeclassification is to identify the SMU potentials that originatefrom the same SMU’s and then to distinguish these SMUpotentials from compound potentials. Since spikes are storedin the order of detection, adjacent spikes in the matrix SPIKEmay not necessarily be the spikes belonging to the sameSMU. Therefore, the first task of spike classification is torearrange spikes so that similar spikes are placed next to eachother. The similarity measure is a distance measure similarto other spectrum matching techniques [10], [11]. However,our similarity measure is defined in the wavelet domain.Wavelet transform is a time-frequency analysis [27]. For atime sequence, , where andis a positive integer, the corresponding wavelet transform can


Fig. 3. An example of similarity measure based on wavelet coefficients. (A) A segment of SMU potential. (B) Another segment of SMU potential fromthe same SMU in (A), however, contaminated by some low-frequency noise. (C) Superimposition of potentials in (A) and (B). It shows a significantwaveform variation in time domain. (D) Comparison of wavelet coefficients for (A) (black) and (B) (white). It shows that their coefficients are matchedvery well if lower scales (scales one and two) are skipped.

be double indexed as

(6)

where is wavelet scale, reflecting the frequency informationof and is translation index, indicating the waveformshifting in time. Therefore, the wavelet spectrum of a spikedescribes not only frequency components of the spike butalso their time locations. Thus, waveform matching in thewavelet domain preserves the best properties of matched filtertechniques in both the time and the frequency domains. Inour technique we used the second order Daubechies waveletbasis [27], whose waveform has the biphasic feature similar tomost spikes. This type of wavelet basis is also orthogonal andcompactly supported. However, other similar types of waveletbasis are also applicable.

The similarity measure we use to evaluate the resemblanceof a pair of spikes and is defined as

(7)

where is the wavelet transform of spike. Accordingto this definition, the similarity measure represents themaximum difference of corresponding wavelet coefficientsbetween spike and , excluding the scales below three toeliminate low-frequency interference (Fig. 3).

The spike classification process, on the other hand, isbased on the nearest neighbor algorithm, which is a recur-sive procedure to rearrange the spikes by placing the mostsimilar spikes next to each other [12]. At first, a spike isselected at random from the matrix SPIKE. The algorithmthen searches for the most similar spike to the previouslyselected spike among the rest of the spikes in the matrix.The newly found spike is placed next to the previous onefollowing which another spike similar to the one just foundis searched, excluding the ones that have already been re-arranged. This process is a recursive procedure that iteratesuntil all spikes in the matrix are rearranged. At the end of therecursive process, all rearranged spikes are linked in a waysuch that every two consecutive spikes are the most similarspikes at the corresponding recursive step. In other words, thenearest neighboring algorithm transforms the 2-D similaritymatrix into a 1-D array that its elements are linked basedon the closest similarity [Fig. 2(B)–(C)]. Thus, by introducinga threshold, the spikes between two consecutive thresholdcrossings can be grouped together.

Determination of the discriminatory threshold is very crit-ical. Generally speaking, lower discriminatory levels maygenerate extra number of groups and tend to increase typeI error, which mistakenly classifies the spikes belonging to thesame SMU into different groups. Higher discriminatory levels,on the other hand, may generate less number of groups andincrease type II error, which fails to distinguish the spikes ofdifferent SMU’s. In our algorithm, a proper threshold level isdetermined by compromising two factors.

1) The minimum time interval of a pair of spikes in the samegroup: The upper limit of the discriminatory threshold isrestricted by the minimum interval values, which is setat 25 ms. A threshold cannot be placed above the levelthat the property of the refractory period is violated.


2) The minimum number of groups:The lower limit of thediscriminatory threshold should be placed at the levelthat generates the least number of groups.

Therefore, the threshold is determined at the level that pro-duces a minimum number of groups without violating theproperty of refractory period.

The final task of spike classification is to identify the groupsthat represent the spikes of SMU’s, and to select them astemplates. Identification of templates mainly relies on thenumber of spikes in a group, which indicates the number ofrepetitions of a spike. Therefore, a group containing morespikes has a higher chance to be selected as a template.Five groups in our example [marked by triangular symbolsin Fig. 2(D)] were selected as the templates. The waveformof each template was represented by average spike waveformof the corresponding group.

Spike Separation:For a given compound potential ,the purpose of spike separation is 1) to identify a particularcombination of templates among all possible combinationsof templates, ; and 2) to locate the proper shift fortemplates in such that the corresponding squared error

has the minimum value. In mathematical notation

(8)

where represents the th template shiftedsampling intervals to the right. If we denote the templatesselected in as winning templates among all templates in

and

(9)

and their shifts as optimal shifts, the solutionfor will then be the collection of winning templates andtheir optimal shifts

(10)

In case of templates and 64 samples for each template, thesearching ranges for each winning template and its optimalshift will be and , respectively.The number of possible combinations in solution spacetherefore, is

To avoid such a time consuming searching scheme, we useda different technique to search for the minimum square errorthrough a series of 1-D solution , where

(11)

Then, the solution at the th step is of a chainstructure as

(12)

and

(13)

In other words, the final solution is built upon a series of1-D solutions, each of which only searches in 1-D spacefor a single template and its optimal shift that result in alocal minimum square error at the corresponding step (Fig. 4).It can be shown (Appendix) that the optimal shift of a 1-D solution for the minimum square error is the shift thatyields maximum cross correlation, and the winning templateis the template that yields the minimum square error at itsoptimal shift. In each of 1-D searching steps, the compoundpotential will be subsequently subtracted by the winningtemplate at its optimal shift (Fig. 4). After each 1-D searching,the proceeding winning templates will be excluded fromsubsequent searches. This type of search scheme has shownmany favorable properties.

1) This technique is very fast. It takes only a fraction oftime required by the exhaustive searching technique.

2) If the compound potential is composed of only one dom-inant potential, meaning that the overlapping portions ofwaveforms are relatively away from the centers of eachother, the solution by this technique is identical to thatof the exhaustive searching technique. However, it canbe achieved in a much shorter time.

3) Within each subsequent searching step, this techniqueguarantees a maximum energy deduction in each step.

4) The sequential searching process terminates at the stepthat the sequential minimal square error starts to in-crease. In this case, the energy of the residual signalbecomes smaller than the energy of any remainingtemplate (Appendix). Therefore, the residual signal isno longer a possible combination of the remainingtemplates if no severe phase cancellation occurs.

In the example shown in Fig. 4, the separation procedurestopped at Step 3 since the current minimum square errorbecame larger than that in the previous step. Therefore, twowinning templates were identified and the summation of thesetemplates at their optimal shifts matched very well with thecompound potential.

Due to the substitution of sequential searching, some un-desired features may be introduced. For example, the 1-D solution at each sequential step becomes dependent onthe solutions in previous steps. Therefore, any errors in theprevious steps will have cumulative effect on the later steps.Furthermore, the interaction of other overlapping potentialsmay influence the correct detection of the optimal shift ofeach template. Thus, the final solution using sequentialsearch may not coincide with the solution determined bythe exhaustive searching method. In order to improve the finalsolution, we modify our 1-D search scheme to an adjustable1-D search scheme, in which the th solution isdetermined in two separate stages. In the first stage, the 1-Dsolution at the th step is calculated based onthe previous described search scheme An intermediatesolution is then constructed as

(14)

In the second stage, is determined by adjusting theoptimal shifts of the intermediate solution in order to


Fig. 4. An example of separation procedure. At beginning, a compound potential indicated by an arrow in Fig. 2(D) is used to correlate with each of thefive templates identified. Each template will be shifted based on the location of the corresponding maximum correlation. Residual signals will be obtainedby subtraction of the compound signal from each of shifted templates. The signal energy will be calculated. The residual signal with smallest signal energywill be identified (triangular symbol), and used as the new compound potential for further separation in the same fashion. The separation process stopsif the smallest signal energy becomes larger than that of the preceding step. The templates that are selected in previous steps will be excluded from thelater steps. The final separation result is composed by the collection of all shifted templates in previous steps. The summation of all previously identifiedtemplates at proper shift is shown with the original compound potential in the superimposed fashion.

achieve a lower square error value

(15)

where are the adjustments of theintermediate optimal shifts respectively. The typical rangeof adjustment is from 3– 3 sampling intervals.

After a final separation result for each spike is obtained,the spike will be dissolved into its composite template,and the corresponding discharge time will be updated.For example, if the separation result of theth spike is

, then the th spike can bedecomposed as an overlapping oftemplates:and the discharge time can be expanded into

(16)

This separation procedure is applied to each ofspikesdetected in spike detection. At the end, all spikes can berepresented by templates

(17)

and the firing timetable of each template potential can beresolved from time array as

......

...(18)

where is the total number of discharges of SMU, respectively [Fig. 5(C)].

Confirmation: At the end of the separation procedure, allEMG signals are basically decomposed. However, it is in-evitable that some decomposition errors may be introducedduring previous procedures. For example, spikes originatingfrom the same SMU may be classified into multiple groups,or some spikes may be misclassified. Due to the complicatednature of these decomposition errors, human decision becomesnecessary in reduction of the decomposition errors. The con-firmation procedure in this case is dedicated entirely for thispurpose.

During the confirmation procedure, identification of possibledecomposition errors mainly relies on two types of infor-mation: similarity between the original and the reconstructedEMG recordings [Fig. 5(A) and (B)], and the firing pattern ofeach SMU template [Fig. 5(C)]. First, the absolute value of thedifferential signal between the original and the reconstructed


Fig. 5. Comparison of original EMG signal and the reconstructed EMGsignal based on our decomposition algorithm during confirmation. (A) Thedenoised segment of simulated EMG signal shown in Fig. 1(B). (B) Thereconstructed EMG signal before confirmation. (C) The firing patterns offive previously identified SMU’s and their waveforms. The duration of eachtemplate is 5.33 ms. (D) and (E) are the enlarged portions indicated byQ in(A) and (B), respectively. The decomposition result coincides with the knownresult that is indicated by the short solid lines below the time-axis.

EMG signals are compared with the level of the thresholddetermined during spike detection. An analysis program willmark any significant differential signal whose amplitude isgreater than the threshold level determined during signaldetection. Second, in each SMU discharge train, any pair ofspikes whose interspike interval I locates outside the range of

will be considered asan irregular firing interval and also marked for the operator totake further actions and are the mean and standarddeviation of the firing intervals of the SMU train, respectively,and the range is the 95% confidence interval). Any interspikeinterval whose value is 100% larger or 50% less than thepreceding interval will also be marked for further inspection.The markers for potential decomposition errors will be re-evaluated following each human intervention. Many editingtools, such as spike deletion, insertion, and selection, are alsoincluded in our software package to increase processing speed.

In this example, the reconstructed EMG signal comparedwell with the original simulated EMG signal [Fig. 5(D), and5(E)], and the decomposition result matched correctly withthe known result [Fig. 5(C)].

III. EVALUATION OF THE PERFORMANCE

The usefulness of an algorithm depends very much on itsperformance. In this study, we used two different types ofsignals to evaluate our decomposition algorithm. One typeof signal was simulated EMG recordings generated by acomputer. The other type of signal was actual EMG recordingsrecorded at different voluntary contraction levels.

1) Evaluation Using Simulated EMG Signals:The perfor-mance of the algorithm evaluated by simulated EMG signalshas many advantages over the real EMG data. First, thesimulated EMG data provides a known solution, which the

result of the decomposition algorithm can be compared to.Second, simulation provides a tractable environment to testeach component of the proposed technique separately andindependently. For example, the level of noise and the shapeof the SMU potentials can be easily controlled in simulationconditions. In this study, the performance of our algorithm wasevaluated by 35 segments of simulated EMG signals. These35 segments of simulated recordings were divided into sevengroups with five segments in each group. Within the samegroup, EMG recordings were simulated by superimpositionof the same number of independent SMU discharge trainsranging from 2–8. Firing intervals of each SMU discharge trainwas randomized by a Gaussian distribution with given meanintervals and standard deviations. The mean firing intervals ofthe 175 independent SMU discharge trains generated rangedfrom 70–170 ms. The standard deviations of their firingintervals ranged from 8–25 ms. Each segment of the simulatedEMG recordings was 10-s long and corrupted with Gaussianwhite noise at the level of 10-dB signal-to-noise ratio. Thewaveform of each SMU potential, , was simulatedby summation of three terms of a Gaussian probability densityfunction [28] described as

where

(19)

represents the time variable;, , and are parametersdetermining the shape of This method provides arelatively simple way to generate a variety of shapes of SMUpotentials by selecting different parameter matrices

(20)

In this study, values of ’s and ’s were randomized byGaussian distribution with means and standard deviations at20 1 mV ms and 0 0.5 ms, respectively. The valueof was randomized by uniform distribution ranging from0.1–1.0 ms.

2) Evaluation with Real EMG Signals:It is important toevaluate the performance of our algorithm with real EMGsignals, which gives the ultimate test of our algorithm in thereal-life setting. In this study, EMG recordings were acquiredfrom 3 different levels of voluntary contraction at 10%, 30%,and 50% of maximum voluntary contraction (MVC) level,respectively. At each contraction level, five segments of EMGsignals each with a duration of 10 s were collected. The total 15segments of real EMG signals were recorded from biceps andextensor digitorum communis muscles in two normal subjects.During recordings, each subject’s arm was immobilized withVelcro straps so that the co-contractions of other muscleswere minimized. The maximum voluntary contraction level foreach tested muscle was measured and the corresponding targetcontraction levels were displayed on an oscilloscope to providevisual cues. Each subject was instructed to perform a sustained


TABLE IPERFORMANCE BASED ON SIMULATED EMG RECORDINGS

isometric voluntary muscle contraction to match the displayedtarget contraction level. The tension of muscle contractionwas sensed with a TC-2000-50LBS load cell manufactured byKulite. The force signal was magnified with a bridge amplifierwhose frequency band was set at 0–1 kHz.

The muscle activity, on the other hand, was recorded bya concentric EMG needle electrode (25-mm length, 0.33-mm diameter, TECA) inserted into the appropriate muscle.A ground electrode (TECA 32-mm diameter stainless steeldisc) applied with commercial electrode paste was taped ontothe skin near the needle insertion site. The needle electrodewas moved in several directions in each muscle to collectdischarging potentials from different groups of SMU’s. TheEMG signals were amplified and filtered by a TECA Sapphireelectromyograph in one-channel mode. The bandpass filter ofthe recording channel was set at 100 Hz–5 kHz. The filteredand amplified EMG signal was stored onto a digital audiotape by a TEAC RD-120TE tape recorder and downloadedto the computer hard disk via a direct data transfer system.The downloaded data was sampled at 12 kHz with 16-bitresolution.

IV. RESULTS

Evaluations of our algorithm based on simulated EMGsignals and real EMG signals recorded from two normal sub-jects are presented in Tables I and II, respectively. Evaluationcriteria were mainly emphasized on the speed and accuracyof the EMG decomposition. In data analysis, we used aDell 200 MHz Pentium desktop computer for all performanceevaluations. For simulated EMG signals, our algorithm was

able to decompose every SMU potential from all simulatedEMG signals. Final decomposition results were then comparedwith known solutions. The average time required by ouralgorithm to correctly decompose a 10-s-long data segmentranged from 3.3–59.4 min depending on the number of activeSMU’s involved. The average decomposition time beforeconfirmation procedure ranged from 1.7–18.4 min; whereasthe average time for the confirmation procedure ranged from1.6–41.0 min. Misidentification of spikes was observed in mosttrials before the final confirmation. The average error rateincreased from 0.7% with two active SMU’s to 5.6% witheight active SMU’s. The increasing error rate may be related tothe increasing overlapping rate of spikes in the simulated EMGsignals with higher number of active SMU’s. For example,the average overlapping rate was 9.5% with only two activeSMU’s. The average overlapping rate increased significantlyto almost 50% when the number of active SMU’s was eight.

In evaluation with real EMG signals, the average total timerequired for 10-s data ranged from 21.2–31.2 min dependingon the contraction level. The average processing time beforeconfirmation procedure increased from 7.2–12.4 min parallelto the increase in the level of muscle contraction. The timefor the confirmation procedure increased as well. The errorrate, however, could not be assessed for real EMG signalsdue to unknown solutions. Therefore, only the proportion ofspikes modified by the operator is listed in Table II. Thepercentage of modifications increased from 4.2%–7.3% alongwith the percentage of MVC, which was coincided well withthe increase of spike overlapping rate. The firing statisticsof the decomposed SMU trains at different levels are alsosummarized in Table II. The mean interspike intervals of the


TABLE IIPERFORMANCE BASED ON REAL EMG RECORDINGS

Fig. 6. An example of decomposition on a segment of real EMG signalrecorded during isometric ramp contraction. (A) The actual EMG recordingwith duration of 6.5 s. (B) The reconstructed EMG signal based on thedecomposition result. (C) Nine SMU potentials identified from the EMGsignal. (D) The resulting SMU discharge patterns for each SMU identified. (E)and (F) are the enlarged portions denoted byQ in (A) and (B), respectively.

decomposed SMU trains decreased consistently from 102.1 to89.6 ms as the contraction level increased from 10–50% MVC.The standard error of the mean interspike intervals decreasedas well.

V. A DECOMPOSITIONEXAMPLE OF REAL EMG SIGNAL

A segment of 6.5-s-long real EMG recording [Fig. 6(A)]was acquired from a biceps muscle of a normal subject duringan isometric ramp contraction, which increased from 0%–30%of maximum voluntary contraction. The experimental setup

and data acquisition was the same as that described earlier.Interference of white noise for this segment of EMG signal wasminimal so that the optional denoising procedure was skipped.During spike detection, a total of 413 spikes were detected.These spikes were classified based on their similarities. Forthis particular segment, 163 groups resulted from 413 detectedspikes. Among which, only 11 groups contained more thanfour spikes. Waveform analysis showed that two pairs of the 11groups were just the shifted version of each other. Therefore,the remaining nine groups were identified as SMU templates[Fig. 6(C)]. These nine templates were then used in signalseparation procedure to search for the composition of eachcompound potential. The discharge patterns associated withthese nine templates after confirmation is shown in Fig. 6(D).It took approximately 11 min to complete the first threeprocedures, and approximately 19 min for confirmation. Afterconfirmation, the 413 spikes detected were resolved into 472SMU spikes, 9.7% of which were manually modified. MostSMU spikes modified were due to superimposition of smallspikes (Templates 1 and 2) on top of much larger spikes.Two segments of enlarged portion of the original and thereconstructed EMG signal are shown in Fig. 6(E) and (F),respectively. The rectified differential EMG signal betweenthe original and reconstructed EMG signals was found wellbelow the threshold used in spike detection. Furthermore, thedischarge intervals of all nine decomposed SMU trains wererelatively regular. Their mean firing intervals ranged from69.9–238.8 ms. The minimum and maximum intervals were40.9 and 333.1 ms, respectively. Based on these statistics, thedecomposition result of this segment of EMG signal could beverified with a fairly good degree of certainty.

VI. DISCUSSION

A. Wavelet Scale Elimination

According to the definition of similarity measure, thewavelet coefficients below scale three are ignored. The rationalis to eliminate the interference of low-frequency noise. For the


Fig. 7. An example of utilization of information of SMU firing pattern in confirmation procedure. (A) A segment of original EMG signals. (B) The waveformsof eight identified template potentials. (C1) The reconstructed EMG signal based on the result before confirmation. (D1) The decomposition result before theconfirmation procedure. Lettersa; b; andc indicate the potential decomposition errors due to irregular discharge patterns. (C2) The reconstructed EMG signalbased on the revised decomposition result. (D2) The decomposition errors are corrected by exchanging the misidentified spikes (dotted lines) between SMUfour and five indicated by arrows, and by inserting an additional spike of SMU six at location marked by the triangular symbol. The decomposition results(the vertical lines pointed upwards) coincide with the known solution (the vertical lines pointed downwards). The vertical scale of (B) is one half of(A).

second-order of Daubechies wavelet, the frequency response ofthe wavelet bases below scale three has bandpass frequenciesfrom 0–300 Hz. Therefore, the low frequency noise can beeffectively eliminated. The effect of such scale eliminationon similarity measure can be observed in Fig. 3, where spike(B) is contaminated by the low frequency noise. This type ofcontamination significantly alters the waveform configurationof spike (B) from that of spike (A). However, such waveformalteration can be easily captured by wavelet coefficientsin lower scales, therefore, can be easily isolated by scaleelimination during spectrum matching in wavelet domain.

B. Types of Decomposition Errors

Our technique is designed for decomposition of multiunitEMG signals with extensive degree of waveform superimpo-sition, which may not be suitable for on-line analysis. Ourentire decomposition process is basically conducted under thecontrol of a computer program we developed in C language.However, due to the complicated nature of waveform super-imposition, human decision becomes necessary in reduction ofthe decomposition error. A typical example of the confirmationprocedure is shown in Fig. 7, where a segment of simulatedEMG signal [Fig. 7(A)] was composed of eight different SMUpotentials [Fig. 7(B)]. The decomposition results obtained byour algorithm before confirmation are shown in Fig. 7(C1) and

(D1). From a morphological point of view, the reconstructedEMG signal was very close to the original EMG signal. How-ever, the result suggested that SMU four and five dischargedin an irregular manner [indicated by and , respectively,in Fig. 7(D1)]. The advisory information provided by thecomputer implicated a possible mistake on SMU four sincethe spike at time was too close to its preceding one. Inthe meantime, the spike of SMU five at timewas too farfrom its previous one. A detail examination revealed smalldifferences between the reconstructed EMG signal and theoriginal signal at places marked by arrows in Fig. 7(C1).This type of misclassification error was clearly caused bythe close resemblance between SMU potentials four and five[Fig. 7(B)]. The error was corrected during confirmation byexchanging the misidentified spikes of SMU four and five attime and , respectively [Fig. 7(D2)].

Another type of error occurs due to the inability of detectingsmall spikes superimposed with much larger spikes. Theexample of such an error is illustrated in Fig. 7(D1) indicatedwithin bracket , where no spike of SMU six was detected foran extended period of time. Reexamination of the constructedEMG signal indicated that the error of misdetection mighthappen at the place marked by an arrow above bracketin Fig. 7(C1). After inserting a spike into the spike train ofSMU six at the location indicated by a triangular symbol[Fig. 7(D2)], the corresponding portion of the reconstructed


EMG signal [Fig. 7(C2)] matched much better with the orig-inal EMG signal [Fig. 7(A)].

C. Needle Movement

Waveform variation of SMU potentials during the course ofrecording is usually considered as a problem in EMG signaldecomposition. It is believed that the waveform variation iscaused by movement of the needle electrode. Based on ourexperience, waveform of SMU potentials may not be alteredin an evenly paced manner. Instead, it mutates in a stepwisefashion. Therefore, an adaptive method to track the waveformvariation may not work very well. With our technique, thesmall waveform variation has very little effect on the finaldecomposition result. It is because our classification techniqueis based on the nearest neighboring algorithm. As long as thewaveform of one SMU potential does not vary too much toresemble another SMU potential, the classification procedureis still able to correctly distinguish its spikes from others. Incase of significant waveform variation, the mutated templatepotentials are often recognized as different template poten-tials. This type of error can be easily corrected by mergingthem together at a later stage based on discharge continuityand mutual exclusiveness. Another way to circumvent thewaveform variation is to break EMG signals into a series ofshort segments and decompose each of these short segmentsseparately, assuming that within each segment the variationof waveforms is minimal. Our experience indicates that thesegmentation of EMG signals in 10-s periods can significantlyreduce decomposition errors caused by waveform variation.Besides, the decomposition speed is usually faster in process-ing a series of shorter segments than one longer segment.

D. Motor Unit Recruitment

It is known that number of MU’s recruited increases withthe increase of voluntary muscular contraction. The decompo-sition results in Fig. 6 illustrated nicely about such orderlyrecruitment pattern. Detailed analysis indicated that duringrecruitment SMU’s started with an initial unstable dischargephase before firing steadily. It was interesting to notice that themean firing frequency of SMU’s in Fig. 6(D) did not alwaysincrease with the order of recruitment. However, the result inTable II indicated that on average the mean firing frequencyof SMU’s increased with increasing voluntary contraction.

Since the number of MU increases with the voluntarycontraction, the number of SMU potentials registered by aneedle electrode increases. Therefore, EMG signal decom-position becomes more difficult and more time-consuming.In order to study the SMU’s at higher end of recruitment,many practical ways can be used. In this study, we purposelymanipulated the recording location of a needle electrodeto avoid registration of large amount of SMU potentialsin strong voluntary contractions (Table II). During strongvoluntary contraction, an attempt to decompose every SMUpotential registered may not be practical. The spikes with smallamplitude are of similar waveform configuration, and are oftenobscured by large spikes. Significant amount of decompositionerrors may result due to misidentification of these small spikes.

An effective way to circumvent such a problem is to increasethe detection threshold in signal-detection procedure so thatthe small spikes are considered as noise. During confirmation,the operator can also discard similar templates that causesignificant misclassification errors.

E. Feature Extraction from MU Potentials

During data recording, we set the lower bandpass frequencyat 100 Hz to reduce the interference of low frequency noise.However, such operation can usually cause severe waveformdistortion of MU potentials, which contains very importantinformation for clinical diagnosis. A possible technique torecover the original waveform of MU potentials is to recordthe wide-band EMG signal, which can then be processed bya digital bandpass filter and used for EMG decomposition.At the end of decomposition, the original shape of eachSMU potential can be recuperated from the wide-band EMGsignal using spike triggered averaging technique. In the similarfashion, the satellite potentials can also be retrieved.

In conclusion, we have demonstrated that our new techniqueis accurate, reliable, and relatively fast, and may prove to bea useful method to study SMU discharge patterns and recruit-ment order in normal subjects and patients with neuromusculardisorders.

APPENDIX

Maximum Energy Deduction:Given templates, and a spike signal , where

for and

We denote as a residual signal of the spike atthe th iteration, obviously . The square errorbetween a shifted template and at the thiteration can be described as

Therefore

In other words, at each iteration step, the unused templatescompete with each other to obtain the minimal square error.Since is equivalent to the residual signal of next iterationstep, by selecting the winning template at the shift associated to


the maximum correlation, the energy deduction from previousiteration step will be maximum.

Termination Criterion: In vector notation, we letand

. Therefore, the square error can be described as

so that by rotating the winning template with an angle ofto coincide with the minimal square error can

be achieved and expressed as

Since , we have

If , then . In other words, when thelocal minimal square error at each step starts to increase, theminimum energy of remaining templates is at least twice theenergy of the residual signal. Therefore, it is impossible thatany of the remaining templates can be used to produce theresidual signal if there is no phase cancellation .Thus, the iteration should be terminated. It is because thatfurther separation may otherwise result in unreliable decompo-sition if severe phase cancellation occurs among the remainingtemplates.

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Jianjun Fang received the B.S. degree in electri-cal engineering from Guangxi University, Nanning,China, in 1982, the M.S. degree in biomedical engi-neering from Boston University, MA, in 1988, andthe Ph.D. degree in electrical engineering and com-puter science from University of Illinois, Chicago(UIC) in 1998.

From 1997 to 1998, he had his post-doctoraltraining at the Sensory Motor Performance Programat the Rehabilitation Institute of Chicago. He wasworking in the Department of Neurology, Massa-

chusetts General Hospital from 1988 to 1992 as an Assistant BiomedicalEngineer. He later moved to UIC as a Research Engineer until he received thePh.D. degree. He is now working at Motorola’s Chicago Corporate ResearchLaboratories in Schaumburg, IL.


Gyan C. Agarwal (S’61–M’65–SM’76–F’86)received the B.Sc. degree in mathematics andphysics from Agra University, Agra, India, in1957, the B.E. degree with Honors in electricalengineering from University of Roorkee, Roorkee,India, in 1960, and the M.S.E.E. and the Ph.D.degrees in electrical engineering from PurdueUniversity, West Lafayette, IN, in 1962 and 1965,respectively.

He has been with the University of Illinoisat Chicago since 1965 as an Assistant Professor

(1965–1969), Associated Professor (1969–1973), and currently as Professor(since 1973) and Director of Graduate Studies (since 1991) in the departmentof electrical engineering and computer science. He was Consulting Editor oftheJournal of Motor Behavior(1981–1992). He has been an Associate Editorof the Journal of Electromyography and Kinesiologysince 1994.

Dr. Agarwal is a Fellow of the AAAS, Founding Fellow of the AIMBE,and member of the Society for Neuroscience. He was Associate Editor ofthe IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING (1988–1996). He wasTechnical Program Chair for the 19th Annual International Conference of theIEEE Engineering in Medicine and Biology Society, Chicago, IL, 1997.

Bhagwan T. Shahanireceived the M.B.B.S. degreefrom Bombay University, Bombay, India, in 1962and the Ph.D. degree in clinical neuroscience fromOxford University, Oxford, U.K., in 1970.

He joined the staff at the Massachusetts GeneralHospital, Harvard Medical School, Boston, in 1970and remained there until 1992, first as the Directorof Clinical EMG and Motor Control Laboratoriesand then as the Director of Clinical Neurophysiol-ogy Laboratories. In 1992, he moved to Universityof Illinois at Chicago (UIC) as the Chairman of the

Department of Rehabilitation Medicine and Restorative Medical Sciences.He is currently Professor of Neurology and of Rehabilitation Medicine andRestorative Medical Sciences at UIC.

decomposition of multiunit electromyographic signals

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