Correlation-based Method for Measuring the Duration of Motor Unit

Action Potentials

Armando Malanda

, Ignacio Rodríguez

, Luis Gila

, Iñaki García-Gurtubay

, Javier Navallas

and Javier Rodríguez

Department of Electric and Electronic Engineering, Universidad Pública de Navarra, Pamplona, Spain

Economics Department, Universidad de Navarra, Pamplona, Spain

Department of Neurophysiology, Complejo Hospitalario de Navarra, Pamplona, Spain

Keywords: MUAP, Duration, Electromyography, Correlation.

Abstract: We present a novel automatic method for measuring the duration of motor unit action potentials (MUAPs)

and compare it with two state-of-the-art automatic duration methods on normal and pathological MUAPs. To

this end we analyzed 313 EMG recordings from normal and pathological muscles during slight contractions.

A “gold standard” of the duration positions (start and end markers) was obtained for each MUAP from the

manual measurements determined by two expert electromyographists. The results of the novel method were

compared to those obtained by the two automatic methods using the “gold standard” duration measures for

the different groups of normal and pathological MUAPs. Several statistical tests were applied and showed

that the novel method provided closer duration positions to the “gold standard” and fewer gross aberrant errors

than those obtained by the two other methods in the four MUAP groups, being significantly different in many

of the cases.

1 INTRODUCTION

The motor unit (MU) is the functional unit for the

voluntary activation of the muscle. It comprises a

motor-neuron and the muscle fibres (MFs) innervated

by it. The order for contraction of these MFs comes

from the spinal cord and ultimately from the brain as

a train of action potentials traveling along the motor

unit. When they reach the muscle fibres highly

synchronized action potentials are generated in these

fibres and they travel towards the tendons producing

the contraction of the fibres. The potential wave

observed by an electrode near the MU is called motor

unit action potential (MUAP) and is dependent of the

structure and function of the whole MU. Analysis of

the MUAP is a central aspect of needle EMG studies

and is applied for diagnosis in clinical

neurophysiology practice.

The MUAP waveform is quantitatively

characterized by several parameters of which

duration is an essential one, as the rest of parameters

are measured within the MUAP time span defined by

its duration (Stalberg et al., 1986). MUAP duration is

related to the number of muscle fibres in the MU and

to the temporal dispersion of the activation times of

the fibres and their conduction velocities (Stalberg et

al., 1996).

The MUAP onset is usually an abrupt takeoff due

to the muscle fibre depolarization. However the offset

is more difficult to determine as the final phase of the

potential returns to the baseline (BL) very slowly and

asymptotically without a distinct end point (Sonoo

and Stalberg, 1993). It has been demonstrated in real

electromyographic (EMG) recordings and simulation

studies that the extinction of the action potentials

continues for over 20 ms after the main spike of the

MUAP (Lateva and McGill, 1998; Dumitru and King,

1999; Dumitru et al., 1999). Real routine EMG

signals almost invariably show slow baseline (BL)

fluctuations and other noise such that it is very

difficult to distinguish the full extension of the final

portion of the MUAP. This work is devoted to the

“clinical MUAP duration”, i.e., that which can be

observed in routine neurophysiological practice and

which has clinical meaning, as opposed to the

“physiologic MUAP duration” (Dumitru and King,

1999; Dumitru et al., 1999), which lasts until the

repolarization is entirely completed.

Measuring MUAP duration presents hard intrinsic

difficulties, so much that manual duration

Malanda, A., Rodríguez, I., Gila, L., García-Gurtubay, I., Navallas, J. and Rodríguez, J.

Correlation-based Method for Measuring the Duration of Motor Unit Action Potentials.

DOI: 10.5220/0005648301290136

In Proceedings of the 9th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2016) - Volume 4: BIOSIGNALS, pages 129-136

ISBN: 978-989-758-170-0

129

measurement has been previously described as “an

arbitrary task” (Sonoo, 2002) and low degrees of

reliability of manual duration markers have been

reported (Stalberg et al. 1986; Nandedkar et al., 1988;

Chu et al., 2003; Takehara et al., 2004b; Rodríguez et

al., 2007a). A number of automatic algorithms have

been designed to overcome the limitations of the

subjective assessment of MUAP duration (Stalberg et

al., 1986; Nandedkar et al., 1995). These were

eventually implemented in available commercial

EMG acquisition systems. But, as reported by several

authors (Bischoff et al., 1994; Stalberg et al., 1995;

Takehara et al., 2004a), conventional automatic

algorithms imply the necessity of continuous visual

supervision and frequent manual readjustments of the

duration markers. These methods fail to estimate

correctly the duration measurement mainly because

of the presence of noise and fluctuations in the BL and

other potentials, all of them being unfortunately

common in routine EMG signals.

Apart from the previous (conventional)

approaches, a different automatic duration

measurement method based on the wavelet

transforms was presented more recently (Rodríguez

et al., 2010; Rodríguez et al., 2012). In a comparative

study, this duration algorithm outperformed the

results of conventional methods over normal and

pathological signals. However, recent works are still

using conventional methods to measure MUAP

duration (Ghosh et al., 2014; Matur et al., 2014),

sometimes applying manual corrections (Jian et al.,

2015).

In this paper we present a novel duration

algorithm based on correlation. In biological systems

some physiological situations generate a train of

potentials or a quasi-periodic repetition of certain

waveforms. This is the case of MUAP trains in

voluntary or artificially-induced contractions of

skeletal muscles, the P, QRS and T complexes in the

ECG, the S1 and S2 sounds in the phonocardiogram,

or the spike-and-wave complexes in the EEG of

epileptic patients. If the physiological and recording

conditions stay stable during a certain period of time

in these situations, the potentials that can be recorded

will include a deterministic component, that can be

considered basically unaltered throughout this time,

and a stochastic component, i.e., noise and artifacts of

different origins which may include biological

potentials from other sources different from the ones

of interest. According to this, the correlation between

two waveforms of a train will be high. Moreover the

correlation between corresponding segments (i.e., the

initial upraise, the central spike, the final portion,

etc.), of two different waveforms of the train will also

be large.

On the other hand, the correlation between signal

periods in which these repetitive waveforms are

absent will be much lower. This is the central idea

behind our new MUAP duration estimation method:

to determine the potential duration regarding the time

extension in which it presents high correlation with

other potentials in the train.

In this work we present this novel algorithm, and

compare it to a well-known conventional automatic

duration method and to the more recent wavelet-

based approach over signals extracted from normal

and pathological muscles.

2 MATERIAL

We analyzed 313 recordings containing a 5 seconds

long EMG signal during slight voluntary

contractions: 68 signals from 14 normal deltoid

muscles, 105 from muscles with myopathies, 27 from

chronic neurogenic muscles, and 72 from subacute

neurogenic muscles. All these signals were recorded

from eight different muscles and exhibited definite

changes of characteristic pathologies. These signals

were acquired with a Medelec Synergy Mobile

electromyograph (Oxford Instruments Medical, Inc.),

using concentric needle electrodes (type DCN37;

diameter = 0.46 mm, recording area = 0.07 mm2;

Medtronic). The filter setting was 3 Hz to 10 kHz

with a sampling rate of 20 kHz and 16-bit analogue-

to-digital conversion. The digitized signals were

stored on the hard disk of a PC computer and further

analysis was performed off-line.

The multi-MUAP procedure of an automatic

decomposition method was used to extract MUAPs

from the continuous EMG signals (Florestal et al.,

2006). Epochs of 50 or 100 ms containing discharges

(potentials) of the same MUAP train were obtained.

The maximal negative peak of the MUAP was

centred on 40% of the length of the window epoch (at

20 or 40 ms corresponding to 50 or 100 ms epoch

window). A 100 ms epoch window was only used in

8 MUAPs from chronic and subacute neurogenic

muscles, as in these cases a 50 ms epoch was not

sufficient to visualize the whole MUAP.

Next, the waveforms of the isolated discharges of

each MUAP train were aligned in the time axis by

maximum correlation (Proakis and Manolakis, 1996;

Campos et al., 2000) and in the voltage axis by

euclidean distance minimization (the MUAP

discharges are ordered in accordance to their

euclidean distance to the average of MUAP

discharges) (Navallas et al., 2006). Besides,

BIOSIGNALS 2016 - 9th International Conference on Bio-inspired Systems and Signal Processing

130

interactive tools were implemented to visualize the

set of the extracted discharges in raster and

superimposed modes in order to discard manually

undesirable ones. The MUAP waveform was finally

obtained using a novel method of sample estimation

based on a sliding window algorithm (Malanda et al.,

2008).

Figure 1: MUAP discharges (grey) and MUAP

representative waveform (black) obtained using a sliding

window algorithm.

This method optimizes the MUAP waveform

extraction procedure and can be applied in the

presence of low or high superposition of discharges

from other MUs (Fig. 1).

Well defined waveforms (avoiding

superimpositions, gross baseline fluctuations and

secondary potentials) of 3 to 10 (mean 9.9 and

standard deviation (SD) 0.7) discharges were selected

for each studied MUAP. All the selected MUAP

waveforms were well-defined above baseline (BL)

activity and had a “rise-time” < 1 ms (most of them

less than 500 μs). A total of 295 MUAPs were

accepted for analysis: 68 from normal deltoid

muscles, 124 from myopathic muscles, 20 from

chronic neurogenic muscles and 83 from subacute

neurogenic muscles.

Figure 2: Example of determination of the gold standard of

the duration markers positions (GSP) from six manual

marker positions for the end point (continuous vertical

lines). The GSP (x) is calculated as the mean position of the

three closest manual marker positions.

Notice that in relation to the number of analyzed

signals, the number of extracted MUAPs is reduced.

One of the reasons of this reduction is related to the

extraction process. In spite of the efficiency of the

described automatic methods for selection, alignment

and cleaning of the discharges, all the processes were

supervised and final selection were carried out

manually for ensuring the acceptation of

representative and distortion free MUAP waveforms.

3 METHODS

3.1 Determination of the Gold Standard

Duration Marker Positions

The high variability in the manual placement of

duration markers requires first to define the best

manual position among a set of several

measurements. Therefore, a method was devised by

the authors to find the “most likely” MUAP start and

end points. Over the whole set of MUAPs extracted

from the 313 recordings, two experienced

electromyographists (LGU and IGG) made each of

them three measurements of the duration, each

measurement separated by at least two weeks. To

perform this task they were provided with a software

interactive tool (designed in Matlab

) that showed

the MUAP waveform and the set of the extracted

discharges in raster and superimposed modes. The

sensitivity scale was fixed at 100 μV/cm and the

sweep speed at 10 ms/cm to place the duration

markers. From the six manually marked positions for

the start or end markers, the “most likely” placement

was the mean point of the three closest positions

using a probabilistic procedure (Fig. 2) as explained

on a previous paper (Rodríguez et al., 2007a). This

was considered our gold standard position (GSP).

Among all the MUAPs extracted from the 313

recordings, we decided to select those MUAPs with a

high degree of agreement in the duration markers

manually placed. Therefore, MUAPs with a

maximum range of variation of 1 ms among all the

six manual placements for the start and also for the

end markers were selected. The mean and SD

obtained from the range of the three closest markers

were 0.02 and 0.05 ms for the start marker and 0.1

and 0.1 ms for the end marker. This confirms the GSP

markers as consistent estimates of the MUAP start

and end points. Fig. 2 illustrates the GSP

determination procedure.

Correlation-based Method for Measuring the Duration of Motor Unit Action Potentials

131

3.2 Automatic Methods for the

Measurement of MUAP Duration

Our proposed based-correlation method (CM) was

compared with two automatic methods for the

measurement of MUAP duration were used: a well-

known conventional method (Nandedkar et al., 1995),

and the wavelet-based method (WM) previously

mentioned (Rodríguez et al., 2010). The conventional

method and the WM were directly applied to the

representative MUAP waveforms (only 1 potential),

while the CM used the whole set of discharges of the

MUAP train (from 3 to 10 discharges).

3.2.1 Conventional Automatic Method

The conventional automatic method is detailed in

(Nandedkar et al., 1995), and we call it Nandedkar’s

method, NM. In NM, MUAPs are automatically

isolated, identified and classified using a multi-

MUAP system. In the referenced work from 50 to 65

discharges are extracted for each MUAP and its

representative waveform is obtained using median

averaging. To find the MUAP start and end markers

NM calculates the BL first, as the average of the first

5 ms of the window epoch. Once the BL is subtracted,

NM begins its search from the maximum MUAP

peak. From this point, the start and end markers are

calculated using thresholds related to the area under

the MUAP and to the amplitude sample values.

3.2.2 Wavelet Method

This MUAP duration estimation method was based

on the discrete wavelet transform (DWT) (Rodríguez

et al., 2007a; Rodríguez et al., 2007b; Rodríguez et

al., 2010; Rodríguez et al., 2012). In the DWT scales,

the peaks related to MUAP peaks are identified and

amplitude and slope thresholds are used to determine

MUAP start and end points. Besides, high frequency

noise and BL fluctuations can be put aside, so that BL

estimation is not necessary.

3.2.3 Correlation Method

As explained before, the time span of a set of

discharges from a MUAP train will be obtained so

that different segments of the potentials in the set will

be highly correlated to the corresponding segments in

other discharges in the set. The first thing to do is to

align the set of potentials in the time and amplitude

axes. Each potential in the train is time aligned to the

average potential by use of the standard technique of

cross correlation maximization (Proakis and

Manolakis, 1996). As for the amplitude alignment,

we simply add a constant amplitude to each potential

so that its Euclidean distance to the mean (i.e. the

average of all the potentials in the MUAP train) is

minimized.

After this, a sliding window of a certain

length (Lw) is moved along the complete length of

these discharges (50 or 100 ms in our case), with hops

of a given time length (h). We will call x

to the i-th

discharges in the set as seen by the sliding window in

its j-th hop (Fig. 3).

The correlation coefficient (CC) between every

pair of segments in a given hop will be computed

(Matlab corrcoef function, which implements the

standard algorithm was used) and the average among

the CC of the different pairs will be obtained. This

will be repeated for every j-th hop, yielding a curve

of segment correlation along the complete interval

under study (50 or 100 ms in our case) (Fig. 4). This

curve usually has its maximum near the time

occurrence of the MUAP central spike, around which

a ‘plateau’ appears. Some ms at either side of the

maximum point, the curve normally declines rapidly.

To search the MUAP start marker, we will set a

threshold (Th1) and find the time instant when,

moving from the maximum peak to the left (towards

the initial part of the discharges), the correlation curve

goes below this threshold. This is tentatively our

MUAP start marker. To make the detection more

robust we will still move further to the left inspecting

if there is a second peak higher than Th2, in which

case, from this point we repeat again the search of the

point where the curves goes down below Th1 and

finally set there the MUAP start marker (Fig 4). To

obtain the MUAP end marker we repeat all this

operation, but moving from the maximum peak to the

right (towards the final part of the potentials). To

increase flexibility, different sets of parameters (Th1,

Th2, Lw and h) can be used for the detection of the

initial and the marker.

In our study, for the start marker we empirically

set Th1 and Th2 to 0.06 and 0.5, respectively, and Lw

and h to 1 and 0.1 ms, respectively. For the end

marker, Th1 and Th2 were set to 0.05 and 0.5,

respectively, and Lw and h to 2.5 and 0.25 ms,

respectively. Those values were set by visual

inspection, not by computer simulations.

3.2.4 Statistical Analysis

To assess the accuracy of the automatic methods for

MUAP duration measurement three statistical

comparative tests were performed for each method:

(a) Comparison of bias and precision. To measure the

performance of both methods, the mean and the SD

of the relative differences to the GSP were computed

BIOSIGNALS 2016 - 9th International Conference on Bio-inspired Systems and Signal Processing

132

for the start and end markers. The mean is related to

the bias of a method around the GSP and the SD is

related to its precision. The results of the methods in

each group of MUAPs were compared using a

Student’s t test.

Figure 3: MUAP potentials presented in raster mode.

Sliding window for selection is shown. (Time axis is given

in samples and amplitude axis in Volts).

Figure 4: shows how the CM calculates the start and end

markers. (Time axis is given in samples and amplitude axis

in Volts).

(b) Calculation of the EMSE values. The mean of the

differences between the automatic marker position

(considering both start and end markers) and the GSP

(i.e., the bias of each method) and the standard

deviation (SD) of such differences (the precision)

were calculated. Then we calculated the estimated

mean square error (EMSE) of the differences as

follows:

enddendd

startdstartd

mean

meanEMSE

var





(1)

with mean

d,start

and var

d,start

being the square mean

and the variance, respectively, of the differences

between the start marker position of the method and

the start GSP for each MUAP group; and mean

d,end

and var

d,end

are equivalent measures for the end

marker. We also obtained the global EMSE value for

all the different MUAP groups using the next

equation:

TSSCC

MMNNG

NNEMSENEMSE

NEMSENEMSEEMSE

(











(2)

where EMSE

, EMSE

and EMSE

are the

results for the normal, myopathic, chronic neurogenic

and subacute neurogenic potentials, respectively, and

, N

and N

are the number of MUAPs of the

four different groups considered for the study, and N

is the total number of MUAPs from all the groups put

together.

the absolute difference between the GSP and the

automatic marker position was greater than 5 ms was

counted for each method. Such cases can be generally

considered as gross errors. The proportions of gross

errors corresponding to each method were compared

using the Chi-square test.

4 RESULTS

4.1 Comparison of Bias and Precision

The mean and the SD of the differences (bias and

precision, respectively) between the start and end

marker positions and GSPs of the three automatic

methods are respectively given in Tables 1 and 2.

Asterisks are shown to indicate significant

differences between any method and the CM.

Table 1: Differences between GSP and the start marker

positions assigned by NM and CM for the different MUAP

groups. Mean/SD (ms).* = p<0.05 (Student’s t test).

Chr=Chronic. Subac=Subacute.

MUAPs/Method NM WM CM

Normal -1.4/1.2* -0.3/1.3 -0.1/0.8

Myopathic -1.2/1.0* -0.5/1.1* 0.0/0.5

Chr. neurogenic 1.6/6.7 0.7/2.3* 0.0/0.5

Subac. neurogenic -1.3/1.4* -0.4/1.6 -0.1/0.9

Table 1 shows the results for the start marker

positions. It can be appreciated that the CM is the less

biased and the most precise method placing the start

marker, as it has simultaneously the lowest mean and

the lowest SD of differences to the GSP for all the

five MUAP groups. The CM presents significant

differences against NM in all the MUAP groups

100 200 300 400 500 600 700 800 900 1000

-1.5

-1

-0.5

0.5

1.5

2.5

x 10

-3

j-th hop

i-th

potential

h

0 200 400 600 800 100 0

-0 .2

0.2

0.4

0.6

0.8

1.2

0 200 400 600 800 100 0

-2

-1 .5

-1

-0 .5

0.5

x 1 0

-3

Th2

Th1

Correlation curve

MUAP discharges

Inic marker

End marker

MUAP duration

Correlation-based Method for Measuring the Duration of Motor Unit Action Potentials

133

except for the chronic neurogenic MUAPs. On the

other hand, the CM shows significant differences

against the WM in myopathic and chronic neurogenic

MUAPs.

Table 2: Differences between GSP and the end marker

positions assigned by NM and CM for the different MUAP

groups. Mean/SD (ms).* = p<0.05 (Student’s t test).

Chr=Chronic. Subac=Subacute.

MUAPs/Method NM WM CM

Normal 3.1/3.1* -0.1/3.5 -0.7/2.4

Myopathic 4.4/2.9* 0.6/2.6* -0.7/1.9

Chr. neurogenic 6.5/10.6* 1.4/7.6 -3.5/7.5

Subac. neurogenic 4..3/4.2* 0.8/4.0* -0.7/3.3

In Table 2, the results for the end marker positions

are shown. It can be appreciated that the CM presents

significant differences against the NM in all the

MUAP groups. Comparing to the WM, the CM

exhibits significant differences in myopathic and

subacute neurogenic MUAPs, with more precision

(lower SD).

From inspection of the two tables, we can notice

that in chronic neurogenic MUAPs, the bias of the

methods is higher and the precision is lower than in

other groups. This is probably a consequence of the

rare characteristics of the analysed signals, which are

the longest MUAPs and frequently present

polyphasia.

It can also be appreciated from these tables that

end marker placements present higher mean and SD

in absolute value than the start markers, which

indicates that it is more difficult for the automatic

methods to place the end markers than the start

markers.

4.2 Calculation of the EMSE Values

Table 3 shows the EMSE values of the three methods

for the four different MUAP groups and the global

EMSE. As it can be appreciated, the CM presents the

lowest EMSE in all the cases, except for the chronic

neurogenic MUAPs.

Table 3: EMSE values of NM and CM for the different

MUAP groups and EMSE

. Chr=Chronic.

Subac=Subacute.

MUAPs/Method NM WM CM

Normal 10.4 12.4 3.4

Myopathic 15.3 4.2 2.1

Chr. neurogenic 98.5 32.1 33.1

Subac. neurogenic 19.9 9.5 5.9

Total (EMSE

) 21.5 8.6 5.0

4.3 Rate of Gross Errors

The rate of gross errors for the start and end markers

of the three duration methods for the four different

MUAP groups are shown in Tables 4 and 5,

respectively.

For the start and end markers, the CM presents the

lowest rate of gross errors in all cases. Significant

differences were found between CM and the rest in

chronic neurogenic MUAPs for the start marker. For

the end marker, the CM showed significant

differences in normal, myopathic and subacute

neurogenic MUAPs against the NM, and in myopathic

MUAPs against the WM.

Table 4: Rate of automatic start marker placements in %

with differences to the GSP greater than 5 ms for NM and

CM and different MUAP groups.* = p<0.01 (Chi-square

test) Chr=Chronic. Subac=Subacute.

MUAPs/Method NM WM CM

Normal 0.0 2.9 0.0

Myopathic 1.6 0.8 0.0

Chr. neurogenic 6.9* 10.3* 0.0

Subac. neurogenic 3.6 3.6 1.2

Table 5: Rate of automatic end marker placements with

differences to the GSP greater than 5 ms for NM and CM

and different MUAP groups.* = p<0.01 (Chi-square test)

Chr=Chronic. Subac=Subacute.

MUAPs/Method NM WM CM

Normal 29.4* 11.8 7.4

Myopathic 39.5* 9.7* 3.2

Chr. neurogenic 37.9 27.6 13.8

Subac. neurogenic 42.2* 9.6 9.6

4.4 Visual Assessment

Some examples of the NM and the CM over normal

and the different pathological MUAP groups are

shown in Figure 5.

Normal MUAPs can have small or medium

amplitude (Fig. 5.a). Polyphasic serrated myopathic

MUAP is more difficult to measure (Fig. 5.b).

Chronic poten tials can have great amplitude and also

large duration (Fig. 5.c).

Finally, subacute neurogenic MUAPs can have

multiple turns and be polyphasic too (Fig. 5.d). In all

these cases the CM achieves the best results.

4.5 Computational Cost

The CPU times in ms (mean/SD) for the Matlab

implementation of the three algorithms (NM, WM

and CM) were 0.26/0.6, 5.1/2.4 and 513.3/101.4 ms,

BIOSIGNALS 2016 - 9th International Conference on Bio-inspired Systems and Signal Processing

134

Figure 5: Examples of duration measurements of NM and CM on normal (a), myopathic (b), chronic neurogenic (c) and

subacute neurogenic (d) MUAPs. GSP are in crosses.

respectively. Therefore they are all fast enough for

any real-time application.

5 DISCUSSION

MUAP duration is a very important, yet elusive,

parameter in quantitative EMG, as it gives relevant

information about the MU generating the MUAP (the

number of fibres) and is also critical for the estimation

of other MUAP waveform parameters. In this paper

we have presented an automatic procedure to obtain

MUAP duration markers with high agreement with

the markers obtained by expert neurophysiologists in

normal and pathological signals.

The novel approach provides more accurate

duration marker placements and fewer gross aberrant

errors for normal and pathological MUAPs than the

other two tested methods. This, together with its

simplicity and low computational cost makes it a very

valuable tool for quantitative analysis of MUAPs,

reducing the requirement for electromyographists’

manual intervention. Moreover, real-time

implementations in a clinical setting could reduce

exploration time and patient discomfort.

Future works will focus on computational

approaches aimed to obtain optimum values for the

CM parameters.

ACKNOWLEDGEMENTS

This work has been supported by the Spanish

Ministry of Education, Culture and Sport, under the

TEC2014-58947-R project.

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