Spectral analysis and the interference EMGN.B. Jones, B.Sc, M.Eng., D.Phil., C.Eng., M.I.E.E., and P.J.A. Lago, M.Sc, D.Phil.

Indexing terms: Biomedical engineering, Instrumentation and measuring science, Signal processing

Abstract: A comparison between the features observable in the spectrum of the interference EMG and in thespectrum of the turning points of the interference EMG is made. Explanations of these features are presented,and the two methods are compared. In particular, evidence is presented which indicates that it is easier toinfer the shapes of the action potentials from the turning-points spectrum, provided that synchronisation canbe accounted for.

1 Introduction

The performance of a muscle can be monitored by observingits ability to produce force and the electrical activity (EMG)associated with the production of this force. In advancedneuromuscular disease disruption of both EMG and forceproduction can be clearly seen. However, in the early stages ofdisease, and with certain types of patients, careful examinationof the EMG is required to provide a diagnosis. The examinationusually includes the monitoring of individual motor-unitaction potentials to estimate size, duration and shape, parti-cularly the number of phases or lobes associated with eachaction potential. This type of examination requires considerableco-operation from the patient, and also is only useful whenlow force levels are being considered. Those motor unitswhich are recruited at higher force levels are not easilyobserved in this way as the action potentials begin to overlapand interfere when the activity is high.

The interference EMG produced by the overlappingof action potentials is of interest in myoelectric control,sports medicine, ergonomics and some branches of physiology,as well as in neurology, as it is the type of signal observed inmost moderate to high levels of contraction when large,robust electrodes are used.

It seems intuitively reasonable that, given a long enoughrecord of EMG, the information about action potential shapeshould be available, and that it may also be possible to deduceother parameters of the contraction, such as the averagefiring frequency of motor units and the degree of synchron-isation between different motor units.

It has long been hoped that the interference EMG can beinterpreted with the confidence of the ECG, thus allowingreasonably precise assessment of the state of neuromuscularsystems in addition to the heart. There are several approachesto this problem which involve a variety of signal-processingtechniques. This paper concentrates on the use of spectralanalysis, and is an attempt to summarise the present stateof understanding and to indicate some possible new directionsfor progress.

2 Direct spectral analysis of the interference EMG

The interference EMG is often said to resemble randomnoise, and therefore to be well suited to power/spectral-density analysis. Although the nature of the signal is toocomplex to be regarded as deterministic, there are certainfeatures about it which can be seen by trained observers.First, the signal is not symmetrical (the amplitude probability-density distribution is skewed) and there are almost always

Paper 2245 A, first received 20th September and in revised form 19thOctober 1982Dr. Jones is with the Graduate Division of Biomedical Engineering,University of Sussex, Brighton BN19QT, England. Mr. Lago is withthe Grupo de Matematica Aplicada, Universidade do Porto, 4000 Porto,Portugal

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periodically recurring features (spikes). The occurrence ofperiodicity and grouping of spikes seems to increase withfatigue.

2.1 Features of the EMG spectrumAn interference EMG record of the type under considerationis typically as shown in Fig. 1, and its spectrum, althoughstrongly influenced by the geometric property of the electrode,is of the typical form shown in Fig. 2.

On top of the underlying shape, there are narrow low-frequency peaks, and, in addition, the underlying shape it-self is known to change with increased contraction force and,particularly, with fatigue.

For moderate levels of contraction a narrow peak can oftenbe detected above the fluctuations in the region of 15 Hz andoften also at twice this frequency. The frequency at which thepeaks occur increases, and the peaks spread and become less

Fig. 1 Typical surface electrode EMG; maximal voluntary con-traction, flexor digitorum

frequency.Hz250

Fig. 2 Typical EMG power-density spectrum; spectrum of 32seconds of EMG shown in Fig. 1Resolution 1.5 Hz, 32 averages in frequency domain, Hanning window,FFT length 256 points, linear scale

0143-702X182/090673 + 06 $01.50/0 673

distinct as the force of contraction is increased [1]. Anexample of these phenomena is shown in Fig. 3. Experi-mentally it has been observed that as constant moderate orhigh levels of contraction are sustained until fatigue sets inthe overall EMG spectrum tends to skew towards the lowfrequencies. This tends to be true whatever level of con-traction is chosen and whatever muscle is being examined[2 -5 ] .

The shape of the EMG spectrum is also known to differfor different levels of contraction when fatigue is not present.The effects of changing the contraction level does not,however, appear to be consistent in the way that fatiguechanges are induced [4,5] , although there is often a tendencyfor the spectrum to skew towards the higher frequenciesas the contraction level increases.

increasingcontraction

level

10 40frequency,Hz

256

Fig. 3 Power-density spectrum of surface EMG; tibialis anteriorwith increasing contraction level on logarithmic scale

Increasing the contraction level is known to increase thefrequency at which at which the low-frequency peaks occur.An increase of force of seven times increases the peak fre-quency by a factor of about two in some of the experimentalresults reported [1].

Other features observable in the EMG spectrum are the so-called 'dips' in the mid-frequency region [6, 7 ] . These dipsare observed with both needle [6] and surface [7] electrodes,and are seen to retain their general shape and relative positionin the spectrum as it skews due to changes in contractionlevel or fatigue.

2.2 Explanations and interpretations of the EMG spectrumThe physiological processes involved in muscle contractionare complex, and any attempt to describe them mathemati-cally will be subject to error. It is also true to say that theshape of the components of the EMG, the so called 'motorunit action potentials' (MUAPs), depend on the type andpositioning of the electrodes. Any attempt to interpret theEMG will always be limited by these considerations.

The basic mechanism for the generation of MUAPs whenobserved by differential electrodes is well described by deLuca [8]. It is clear from his description, as well as fromdetailed examination of EMG traces [9], that there are severaldifferent MUAP shapes involved in an interference EMG record.

It is, however, possible to propose some form of 'average'MUAP which reflects the basic properties of the muscle asa whole, and which is meaningful when the type of electrodeis known. This average MUAP can then be considered as theimpulse response of a linear filter being stimulated by animpulse train which is the equivalent of the pooled activity ofthe motoneurons. If the statistics of this impulse train areknown the spectrum can be interpreted. In particular, if thetrain can be considered to be Poisson [10], then the spectrumis the square of the modulus of the Fourier transform ofthe average MUAP [15]. Such an interpretation would beboth mathematically convenient and clinically important asit would allow the identification of action potential anomaliesat moderate and high contraction levels.

An elaboration of this idea would entail the propositionsthat there were several different MUAP shapes involved,each elicited by its own train of impulses. This would allowthe spectral shape to be interpreted as a sum of componentspectra, but would not allow the MUAPs, or even the com-ponent spectra, to be deduced from the EMG spectrum.

The general shape of the spectrum can be used as indirectevidence of the existence of polyphasic action potential asthese tend to be of shorter than average duration, leadingto more high-frequency components in the spectrum. How-ever, this effect is of a secondary nature, and can be confusedby other secondary effects, such as changes in conductionvelocity and by anatomical variations.

Even if the concept of an 'average action potential' h{t) isacceptable, it has been shown that the pooled pulse traindriving it cannot, in general, be of the renewal Poisson type.It has also been shown that the spectral density is proportionalto

\H(joS)\2 1 +Fjjd)

l-F(jcS)= \H\2<P

where FQ'cS) is the Fourier transform of /(?); the interspikeinterval probability distribution of the renewal processcharacterises each motor unit [16].

For a Gaussian distribution <£ has the forms shown in Fig.4. The initial peak in this spectrum, which corresponds to theaverage firing frequency, is equivalent to the low-freqencypeak in the EMG spectrum already referred to. The shiftin this peak is due to an increase in average firing frequency

(A

1'

20 40 60frequency, Hz

80 100

20 40 60 80frequency, Hz b

100

Fig. 4 Normalised modifying functions for Gaussian interspikeinterval distributiona One motor unit; mean 50 ms, standard deviation 6.3 ms6 Fifty motor units; means 40—60 ms uniformly distributed, standarddeviations 4.6—8 ms uniformly distributed

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as the force increases, and its spreading is due to increasingvariance about the mean firing frequency as a result ofrecruitment.

Other distributions can be considered, and the appropriatespectra computed. In particular, experimental data of firingfrequencies can be used to verify the model. One particularlyinteresting set of empirical data has been produced on thehuman deltoid [11] for which the Weibull distribution isfound to be a good approximation to f(t). These data includeboth the effect of contraction level and contraction time(fatigue) on the firing statistics.

The effect of firing-time statistics is, as for the Gaussianapproximation, largely a low-frequency attenuation, and againshows that only very low levels of contraction can be con-sidered as appropriate for the Poisson model. These data onmotor neuron firing statistics, when examined in detail,show that the effect of prolonged contraction time is just theopposite. The use of a Weibull distribution to model the firingstatistics does not, however, predict the low-frequency peakwhich is currently observed in the deltoid spectrum [ 1 ] ;nor does such a model predict the contrary spectral shiftssometimes associated with moderate to high nonfatiguingcontractions.

Further energy transfer to the lower frequencies due tosynchronisation is considered as a process separate from thatof changes in the firing-time statistics.

If two needle electrodes are inserted into a muscle suf-ficiently far apart that it can be assumed there are no musclefibres which produce signals in both electrodes, it has beenshown that both the cross-correlation function and thecoherence spectrum of the two EMGs are very small duringweak nonfatiguing contractions. However, both for moderateloads and for fatiguing contractions there is evidence ofsynchronous activity [12], and the resulting effect on thespectrum can counteract that due to changing firing statistics.

Under these circumstances the cross-correlation function isobserved to be symmetrical and to have a peak at the origin,and the coherence spectrum is observed to decrease withfrequency (after an initial rise) and also to increase withfatigue.

A reasonable explanation for these phenomena can beoffered by proposing that the motor units synchronise ingroups such that the action potentials arising from membersof any one group are related by pure time delays.

These time delays are considered to be random functionsof time to explain both the consistency of spectral shape atdifferent points in the muscle and direct observation ofchanging firing order within a group of synchronised motorunits. Furthermore, the variation of the time delays needsto be assumed to have strong positive serial correlation tomaintain consistency with experimental data regarding therenewal nature of the spike trains.

1.0;

200frequency, Hz

400

Fig. 5 Examples of spectral modifying functions arising whenpulse train is made up from groups of synchronised pulses ratherthan from independent single pulses

Starting point of groups is a Gaussian renewal process

It should be noted that a certain number of motor unitsmust be assumed never to synchronise, otherwise the coherencywould tend to unity, which is not observed. Also, the effect oflow-frequency tissue noise and other forms of low-frequencynoise reduces the observed coherency at low frequenciesto near zero. Tissue noise and amplifier noise are known tohave the appropriate low-frequency characteristics [13].

Finally, the dips in the EMG spectrum are thought to bemanifestations of the predominant action potential shape inthe EMG. The fact that their position and shape go throughsmooth transitions is taken to indicate [7] that, during pro-longed forceful contractions, no switching of fibres orrecruiting of new fibres occurs.

3 Spectral analysis of interference EMG turning-pointsequence

Attempts to disentangle the interacting effects of changes infiring statistics, action potential shape and synchronisationhave not only led to the general conclusion that it cannotbe done easily via direct spectral analysis, but have in theprocess led to a better understanding of the mechanismsinvolved, and have indicated that the predominant factor isthe relative timing of the significant features in the record.

The times of the first peaks of a particular MUAP traindefine the firing statistics, and the relative timings of sub-sequent peaks are related to the shape of these waves. Astudy of the point process associated with the peaks in theinterference EMG is therefore an attractive alternative todirect spectral analysis of the record.

The interference EMG is characterised by a sequence ofalternating maxima and minima. A consecutive maximumand minimum is regarded as defining 'an event' which isarbitrarily allocated the same time as the maximum. Onlymaxima and minima differing by more than some prescribed'peak discrimination factor' [14], are recognised. Theassociated point process is regarded as a sequence of zerosand ones allocated to the nearest time marker, typicallyseparated by 0.25 ms. An FFT algorithm is used to estimatethe spectral density of the sequence of zeros and ones.

3.1 Features of the EMG turning-point spectrumIt has already been shown [16] that the normalised spectraldensity of trains of single pulses with those statisticalcharacteristics associated with the occurrence of EMG actionpotentials are heavily dependent on the assumed firing-timedistribution for frequencies below about 80 Hz. For higherfrequencies, however, these spectra are almost flat and can,in all realistic situations, be assumed to be unity above 100 Hz.For frequencies between 10 Hz and 100 Hz the spectrum ofthe pulse train is either nearly unity or fluctuates in such away as to be nearly unity on average.

If each action potental is marked by a time-locked burstof pulses such as that associated with a multiphasic potential,instead of the single pulse of a biphasic potential, the pulse-train spectrum can be shown by theoretical considerations[17] to be modified by a function with the general shapeillustrated in Fig. 5. This shows amplification at the low-frequency end (below about 70 Hz) and attenuation in themidband (about 100—300 Hz, depending on the action po-tential shape), a result which has been reproduced bysimulation.

The difference between the spectral shape when multi-phasic rather than biphasic action potentials are involvedcan be quantified by means of flatness coefficients. Onepossible coefficient y is the difference between the ratio of theaverage power per hertz in the bands 10 to 100 Hz and 110to 200 Hz and unity. Using this measure, a completely flat

IEEPROC, Vol. 129, Pt. A, No. 9, DECEMBER 1982 675

spectrum gives 7 = 0. Low-frequency amplification gives7 > 0 and low-frequency attenuation gives 7 < 0.

Simulation studies have shown that for EMG models withGaussian renewal statistics [18], or indeed other experimentallyestimated renewal models [9, 19], 7 is in the range 0 to— 0.15 for biphasic action potentials of the type used byParker and Scott [15], illustrated in Fig. 6A; this has a turning-point spectrum as shown in Fig. 6B. It can also be shown[17] that negative correlation between adjacent intervals[20, 21] is unlikely to cause an increase in 7 above zero.Simulation and theoretical considerations have also shownthat the effect of rejecting events because of too much overlapof action potentials makes 7 more negative.

Fig. 6 A Model biphasic action potential, after Parker and Scott [15]

a> 3 1

•2 2

200 400 600frequency, Hz

800 1000

Fig. 6B Typical EMG turning point for action potential shown inFig. 6A with Gaussian renewal spike statistics

When differential electrodes are used the basic MUAPis triphasic, of the type shown in Fig. la. A simulated inter-ference EMG based on these action potentials results in aturning-point spectrum as shown in Fig. 8a, which is sub-stantially tlat for frequencies above 200 Hz. A shortmultiphasic MUAP, as shown in Fig. 1b, which can be regardedas representing those found in certain myopathics, gives arecognisably different spectrum with low-frequency ampli-fication and a midband dip, as shown in Fig. Sb. A compositeaction potential representing the early stages of neurogenesisresults in a spectrum as shown in Fig. 8c. These sim-ulations, based on the three MUAPs illustrated in Fig. 7,were taken from recently suggested models for this purpose[22], provided turning-point spectra as shown in Fig. 8.

Many neuromuscular disease states exhibit mixtures ofdifferent normal and pathological MUAPs. Fig. 9 shows aturning-point spectrum arising from an equal mixture ofaction potentials of the types shown in Fig. la and b.

In all these simulations attempts have been made toincrease the realism by using Gaussian interspike statistics[18] and providing random variations of both amplitude andduration.

Fig. 7 Models of action potentials, after Maranzana, Fingini andFabro [22]

a Normal b Myopathic c Initial neurogenic

200 400 600 1000

frequency, Hz

200 400 600frequency, Hz

800b

1000

200 400 600frequency, Hz

800 1000

Fig. 8 EMG turning points spectra, derived from simulations usingaction potentials given by Figs. 7a-c, respectively

200 400 600frequency.Hz

800 1000

Fig. 9 EMG turning points spectrum derived from simulationusing 50% of action potentials of Fig. 7a and 50% ofFig. 7 b

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3.2 Explanations and interpretations of EMG turning-point spectrum

Several different models of the pooled motor neuron pulsetrains have been assumed or deduced from experimental data[10, 11, 18-21]. The spectra of these pulse trains differonly at low frequencies, and are all essentially flat at otherfrequencies. If these pulse trains provide the basis for a trainof MUAPs in an interference EMG then much of the infor-mation in the original pulse train is available in the sequenceof turning points. Simple constituent MUAPs, in particular,will provide rather similar spectra to those of the pooledmotor neuron pulse train itself, even when loss due to MUAPoverlap is accounted for. The low-frequency enhancementand mid-frequency attenuation characteristic of multiphasicMUAPs arises from the fact that the turning-point sequenceis made up of groups of spikes separated by gaps. This pro-vides contributions to the spectrum which are predominantlyat the high and low frequencies.

The differences between the predominantly flat spectrumarising from simple constituent MUAPs, particularly biphasictypes, and triphasic and multiphasic MUAPs allow simplediscriminators to be considered, such as the flatness coefficient7 already referred to. This coefficient can be used to discri-minate between those interference EMGs which contain ahigh proportion of polyphasic action potentials and thosewhich are predominantly constituted of biphasics, providingthe degree of synchronisation of motor units can be keptconstant or allowed for in some way. The coefficient 7 focuseson the low-frequency region of the spectrum only. The use of

100frequency, Hz

200

8 c

2 2

II100

frequency, Hz200

Fig. 10 Changes in EMG turning points spectrum with contractiontimea Contraction time = 0 min b Contraction time = 3 min

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other features of the EMG turning-point spectral densityfor a more complete characterisation of the degree and ofthe type of polyphasic potentials is clearly suggested by thesimulation results present herein, and will be the subjectof further investigation.

If the time delays between synchronised motor units stayconstant the effect of synchronisation of biphasic actionpotentials on the turning-point spectrum is indistinguishablefrom the effect of multiphasic action potentials.

Fig. 10 gives experimental data (human brachii biceps)showing spectral changes with contraction time, and theassociated changes in 7 are shown in Fig. 11. It is reasonableto postulate at this point that the initial finite value of 7represents an underlying percentage of polyphasic potentials,and that any subsequent increase represents synchronisationor increased incidence of polyphasic potentials broughton by fatigue.

1.0

y

0.5

o

-

//

f

1

_^s

2 3time, min

Fig. 11 Changes in spectral flatness coefficient y with contractiontime

More complex action potentials, such as shown in Fig. 7c,provide an additional feature — a mid-frequency hump arisingfrom the changing frequency of spikes within each group.A simple flatness discriminator is not therefore suitable whenthe interference EMG is suspected of having components ofthis nature and should be interpreted directly.

An important property of the turning-point spectral analysisis illustrated by Fig. 9, in that mixtures of MUAPs can beidentified as producing a mixture of the features of theelementary spectra.

All the spectra so far investigated also show a significantspike at the average firing frequency, thus retaining one of thefew important pieces of information which is available fromthe spectrum of the EMG itself under favourable conditions.

4 Conclusion and comment

The evidence available suggests that direct spectral analysisof the interference EMG is of limited use, and that the majorobjective of extracting the main features of the constituentMUAPs is unobtainable.

However, this type of data reduction, when carefully used,does often allow for an estimation to be made of the averagefiring frequency and the dispersion of firing rates about thisaverage. The way in which this average rate and the dispersionchange with force level and fatigue can also be observed.

The use of EMG turning-point spectral analysis is a muchmore recent idea, and there is not much experience available,particularly with real data. However, the indications are thatthe data associated with the average firing frequency can beseen at least as well as for direct analysis, and that evidenceof action potential shape is visible in a frequency rangeseparated from that which is most influenced by the firing

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statistics. Difficulties still exist in separating the effects ofpolyphasic action potentials from synchronisation of simpleaction potentials, but the technique seems promising as aprocedure complementary to the spectral analysis of theEMG itself. An attractive feature of the normalised turning-point spectrum is that when polyphasics potentials andsynchronisation are not significant the curve is simple. Inparticular, it is flat and about unity for frequencies above200 Hz irrespective of the electrodes used and of the fibreconduction velocity. No such standard exists for the EMGspectrum.

Finally, it should be pointed out that spectral analysisof a 0—1 sequence is a rapid procedure which can be madeeven faster by the use of Walsh spectra instead of Fourierspectra. Early experiments with this procedure indicate thatthere is some loss of resolution, but the essential features ofthe spectra are still easily visible.

5 Acknowledgments

The authors would like to acknowledge the support of theINIC, the Fundacao Calouste Gulbenkian and the SouthEast Thames Regional Health Authority.

6 References

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2 KADEFORS, E.K., KAISER, E., and PETERSEN, I.: 'Dynamicspectrum analysis of myoelectric potentials with special referenceto muscle fatigue', Electromyography, 1968, 8, pp. 39-74

3 JOHANSSON, S., LARSSON, L.E., and ORTHENGREN, R.: 'Anautomated method for the frequency analysis of myoelectricsignals evaluated by an investigation of the spectral changes followingstrong sustained contractions', Med. & Biol. Eng., 1970, 8, pp.257-264

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5 FAY, D.F., JONES, N.B., and PORTER, N.H.: 'Spectral analysisof the myoelectric activity of the pelvic floor during voluntarycontractions', ibid., 1976,16, pp. 525-551

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suring motor unit action potential duration by means of surfaceelectrode EMG', ibid., 1978,18, pp. 45-56

7 LINDST6M, L., MAGNUSSON, R., and PETERSEN, I.: 'Muscularfatigue and action potential conduction velocity changes studiedwith frequency analysis of EMG signals', Electromyography, 1970,4, pp. 341-356

8 DE LUC A, C.J.: 'Towards understanding the EMG signal' in BAS-MAJIAN, J.V. (Ed.): 'Muscles alive' (4th Edn., Williams & Wilkins,Baltimore, 1978), pp. 53-78

9 LE FEVER, D.S., and DE LUCA, C.J.: 'A procedure for decom-posing the myoelectric signal into its constituent action potentials',IEEE Trans., 1982, BME-29, pp. 149-164

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11 DE LUCA, C.J., and FORREST, W.J.: 'Some properties of motorunit action potential trains recorded during constant force isometriccontractions in man', Kybernetik, 1973,12, pp. 160-168

12 PEARSON, R.S., and MISHIN, L.N.: 'Auto- and cross-correlationanalysis of the electrical activity of muscles', Med. & Biol. Eng.,1964, 2, pp. 155-159

13 HAYES, K.J.: 'Wave analysis of tissue noise and muscle actionpotentials', J. Appl. Physiol., 1960,15, 749-752

14 JONES, N.B., LISTER, P.F., LAGO, P.J.A., and RESTIVO, F.J.de O.: 'Microcomputer-based electromyographic signal analysis',Med. & Biol. Eng. & Comput., 1982, 20, (5), pp. 649-652

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16 LAGO, P.J., and JONES, N.B.: 'Effect of motor-unit firing timestatistics on EMG spectra', Med. & Biol. Eng. & Comput., 1977,15, pp. 648-655

17 LAGO, P.J., and JONES, N.B.: 'Turning points spectral analysisof the interference myoelectric activity', ibid., 1983, 21, (to bepublished)

18 CLAMANN, H.P.: 'Statistical analysis of motor unit firing patternsin human skeletal muscle', Biophys. J., 1969, 9, pp. 1233—1251

19 SHIAVI, R., and NEGIN, M.: 'Stochastic properties of motor-neouron activity and the effect of muscular length', Cybernetics,1975,19, pp. 231-237

20 PEARSON, R.S., and KUDINA, L.P.: 'Discharge frequency anddischarge pattern of human motor units during voluntary con-traction of muscle', Electroencephalogr. & Clin. Neurophysiol.,1972, 32, pp. 471-483

21 KRANZ, H., and BAUMGARTNER, G.: 'Human alpha motorneurone discharge, a statistical analysis', Brain Res., 1974, 67,pp. 324-329

22 MARANZANA FIGINI, M., and FABBRO, M.: 'A simulationmodel for the study of EMG signals in normal and pathologicalconditions', Electroencephalogr. & Clin. Neurophysiol., 1981,52, pp. 378-381

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