Estimation of Muscle fatigue during cyclic contractions using source separation

techniques

Ganesh R. Naik, Dinesh K. Kumar, Katherine Wheeler, Sridhar P. Arjunan

School of Electrical and Computer Engineering

RMIT Univerisity

Melbourne, Australia

Email: ganesh.naik@rmit.edu.au

Abstract—Previous research studies have reported that spec-tral compression of the surface Electromyogram (SEMG)towards lower frequencies is associated with onset of localizedmuscle fatigue. One reason for this spectral compression hasbeen attributed to motor unit synchronization in literature.According to this, motor units are pseudo randomly ex-cited during muscle contraction, and the recruitment patternchanges during the onset of muscle fatigue, such that the firingof motor units becomes more synchronized. While this theoryis widely accepted, there is little experimental proof of the phe-nomenon. This paper has used source dependence propertiesand measures developed in research related to independentcomponent analysis (ICA) to test for synchronization. Thispaper has also determined that the global matrix can be usedas a measure for estimating localized muscle fatigue duringcyclic movements.

Keywords-Surface EMG; Muscle fatigue; Source separation;ICA;

I. INTRODUCTION

Muscle fibers are organized in the muscle into motor

units, with a single motor unit consisting of a motor neuron

and muscle fibers innervated by this neuron. Contraction of

muscle fibers is associated with action potentials and these

cause measurable changes of the electrical potential at the

surface of the body. The recording of the electrical potential

from the surface is surface electromyogram (sEMG). The

combination of muscle fiber action potential from all muscle

fibers of a motor unit is the motor unit action potential

(MUAP). The amplitude of the MUAP depends upon the

types, sizes and number of muscle fibers in the motor unit.

SEMG is the result of the interferential summation of all

MUAPs in the recording field. These potentials are non-

linearly attenuated by cutaneous tissue between the muscle

and the surface electrode. This attenuation is frequency

dependent [1], [2]. Despite the complex nature of the signal,

the SEMG can be used to identify level of muscle contrac-

tion,neuromuscular diseases, abnormal muscle activity and

muscle fatigue.

Muscle fatigue is the state of the muscle when the ability

of a skeletal muscle to contract or produce force is highly

diminished. The causes of fatigue vary, and can be located

anywhere in the neuromuscular path between the brain

and the muscle itself. Local muscle fatigue occurs when

the neuro stimulation path is intact, but the ability of the

muscle to produce force is reduced. The known causes

of local muscle fatigue vary, and depend on the level of

muscle activity and the muscle fiber types present. Localized

muscle fatigue generally results after sustained or intense

contractions.

Numerous researchers have studied muscle fatigue and

the effect of muscle fatigue on the SEMG signal. The

predominant effects of fatigue on the SEMG during high

level contractions are (i) an increase in the signal ampli-

tude and (ii) compression of the spectrum towards lower

frequencies. Well-studied and accepted features of the sEMG

signal for fatigue assessment include amplitude features

[3](Root mean square (RMS) and integrated EMG (iEMG))

or spectral features (mean or median frequency (MDF) or

power spectral density (PSD)) [4]. These general trends

can be partly explained by understanding the physiological

effects of local muscle fatigue.

Firstly, fatigue results in the slowing of the average

action potential conduction velocity due to a buildup of

the byproduct lactic acid. This has been considered to be

the predominant cause of the spectral compression of the

SEMG towards lower frequencies [5]. Secondly, an increase

in the muscle cell hyper polarization time due to the onset

of localized muscle fatigue changes the shape of the action

potential. The general effect of this is a slight displacement

towards lower frequencies.

The other impact of sustained contraction leads to the

recruitment of muscle fibres usually active only during rapid

contractions. The recruitment of these larger muscle fibres

results in an increase in the average SEMG amplitude.

Finally, muscle fatigue can affect motor unit recruitment pat-

terns [6], [7]. Recruitment changes and motor units appear

to become synchronized with the onset of localized muscle

fatigue. This increased synchronicity of motor unit firing

also results in a spectrum shift towards lower frequencies.

However, the total effect of this increase in synchronicity is

not known and warrants further investigation.

Modeling studies have found that the spectral shift to

lower frequencies (and the related drop in MDF) is coun-

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tered by a reduction in the conduction velocity (CV) [7].

During low-level bicep voluntary contractions, MF also

drops, but the CV remains the same. With the onset of

fatigue, the motor unit firing patterns become significantly

more synchronous (firing at almost the same time). In the

fatigue state, the central drive to a muscle has to increase,

leading to synaptic input that is common to more than one

neuron. This leads to increased synchronicity. Kleine et al

[6] posits that changes in the firing pattern, particularly

synchronization, must be responsible for the spectral shift to

lower frequencies not attributable to a conduction velocity

change.

While widely accepted, there appears to be lack of di-

rect evidence of the synchronization of motor units during

localized muscle fatigue [8]. Further, the effects of such syn-

chronization on the sEMG signal are not yet confirmed, with

signal dependence [9], recurrence quantification analysis [8]

and cross correlation of motor unit pairs [10] all reported as

methods of quantifying motor unit synchronisation.

Recent experimental studies on synchronicity have fo-

cussed on constant force, isometric contractions of the bicep

[8]–[10]. In order to be applicable in real world scenarios,

an understanding of the changes in synchronicity, and the

effect of these changes on the SEMG during dynamic or

cyclic movements must also be sought.

During dynamic contractions, the frequency content of

the SEMG changes continually due to the modulation of the

muscle force and the relative displacement of muscle force

with respect to the underlying muscle fibers. Therefore, fre-

quency analysis techniques for stationary techniques are not

suitable. Bonato et al [11] detailed time-frequency analysis

techniques for assessing local muscle fatigue during cyclic

contractions. An alternative to such complex techniques

would be to investigate features of the SEMG signal which

are not dependent on the frequency content of the signal.

It has recently been demonstrated [9] that there exists

motor unit synchronization due to the onset of fatigue

demonstrated with channel dependence. If synchronicity is

due to an increase in the central drive to a muscle, then

the hypothesis that this would lead to an increase in motor

unit dependence appears sound. In the non-fatigued state,

motor units will fire pseudo-randomly, such that sEMG

recorded from two recording sites should be independent

from each other. This was confirmed using experimental

isometric contraction data.

Further, it was shown that as local muscle fatigue in-

creased, the dependence of the recorded signals on each

other also increased [9]. This paper reports the research

that attempts to characterize the effects of fatigue during

cyclic movements (repeated supination and pronation of the

forearm) of the human arm using Independent Component

Analysis (ICA) techniques.

II. THEORY

A. ICA theory

Independent Component Analysis (ICA) is an iterative

technique used to estimate statistically independent source

signals s(t) = [s1(t), ....,sn(t)]Tfrom a given set of their

linear mixtures x(t) = [x1(t), ....,xn(t)]. If the mixing processis assumed to be linear, it can be expressed as

x(t) = As(t) (1)

where A is an N ×M scalar matrix representing the

unknown mixing coefficients. A is referred to as the transfer

or mixing matrix. The goal of ICA is to find a linear

transformation W of the dependent sensor signals x(t) thatmakes the outputs as independent as possible:

s(t) =Wx(t) =WAs(t) (2)

where s(t) is an estimate of the sources. The sources are

exactly recovered whenW is the inverse of A subject to order

permutation and scale change. Since both, the sources and

the mixing coefficients are unknown, it is impossible either

to determine the variances or the order of the independent

components.

The product of the mixing matrix, A, with the estimated

unmixing matrix, W , is the global matrix, G. After sorting

the order ambiguity between the mixing and unmixing

matrix, under ideal conditions, this global matrix, G should

be a unity matrix and the determinant of this should be

unity [12], [13]. However, if the recordings are not all

independent, the determinant of this matrix is no longer unity

and is close to zero. This can be used as an indicator of the

dependence of the input to the system.

One shortcoming of the above is that this requires prior

knowledge of the mixing matrix, which in real situations is

not possible. To estimate G, one option is to use sub-band

ICA.

B. Sub-band ICA

Sub-band ICA is an extension of ICA. It assumes that

each source is represented as the sum of some independent

sub components and dependent sub components, which have

different frequency bands. Wide-band source signals are a

linear decomposition of several narrow-band sub compo-

nents s(t) = s1(t)+ ....+ sn(t). Such decomposition can be

modeled in the time, frequency or time frequency domains

using any suitable linear transform.

We obtain a set of un-mixing or separating matrices:

W1,W2, ....,Wn where W1 is the un-mixing matrix for sensor

data x1(t) and Wn is the un-mixing matrix for sensor data

xn(t). If the specific sub-components of interest are mutuallyindependent for at least two sub-bands, or more generally

two subsets of multi-band, such as for the sub band ‘p’ and

sub band ‘q’, then the global matrix

Gpq =Wp×W−1q = P (3)

226210218218

will be a sparse generalized permutation matrix P with

special structure with only one non-zero (or strongly domi-

nating) element in each row and each column [14].

III. METHODOLOGY

A. SEMG Recording Equipment

Surface electromyogram (SEMG) signals were recorded

using BIOPAC 100 (California, USA), a proprietary SEMG

acquisition system. Prior to placing the electrodes the par-

ticipants’ skin was cleaned using mild soap. The following

parameters were used during the recording:

• Preamplifier Gain: 2000

• Low Pass Filter: 500Hz

• High Pass Filter: 10Hz

• Notch Filter: 50dB@50Hz

• Sampling frequency: 1500

Two-channel SEMG were recorded from biceps muscles

using surface electrodes during isometric contractions.

B. Experimental Protocol

Four healthy volunteer subjects participated in the trial.

The experimental protocol was approved by the Human

Ethics Committee of RMIT University. Electrode pairs were

placed longitudinally, and the two pairs of electrodes were

placed such that each pair was on either side of the midline

of the biceps muscle (medial and lateral belly) Each subject

performed repeated cyclic contraction using fixed standard

load. The load was chosen to be close to 75% maximum

voluntary contraction. The SEMG was recorded throughout

the experiment until the subject complained of muscle

fatigue. The typical time period of each recording was 180

seconds.

C. Data Analysis

Firstly, the following three data subsets(as shown in

Figure 1) were extracted for analysis:

1) During the beginning of the cyclic experiment (Where

it is assumed that the muscle unit firings are indepen-

dent from each other)

2) In the middle of the cyclic experiment. The intent here

was to test the trend of independency and dependency

3) At the final stages of the cyclic experiment to test the

quality of the source separation and the muscle fatigue

levels.

The three SEMG subsets were analyzed using ICA tech-

niques to detect localized muscle fatigue. This was done

using two signal processing techniques.

1) Preliminary analysis using RMS: Initially the FastICA

MATLAB software was used to separate the sources. This is

a known application of ICA, used to reduce crosstalk prior to

calculating the amplitude features (RMS). The RMS values

were computed for all three described data subsets.

2) Global matrix analysis: The determinant of global

matrix generated using ICA is used as an indicator for iden-

tifying the muscle fatigue. This analysis was also performed

for the three different conditions.

IV. RESULTS AND OBSERVATIONS

The results of the data analysis are tabulated in Tables

I and II. Table I shows the RMS values of SEMG (2

channels) for the initial, middle and final segments of the

cyclic contraction data after source separation using ICA.

Table II shows the value of the determinant of the global

matrix, calculated to determine the dependency and the

independency properties using ICA.

From Table I and Figure 2, it is evident that the RMS of

both channels increases as a result of the onset of muscle

fatigue. This confirms that onset of muscle fatigue results in

the recruitment of larger and faster motor units. However,

these do not shed any light regarding the dependency or

synchronicity behaviour of the motor units due to the onset

of localised muscle fatigue.

Table IRMS OF THE ICA SEPARATED SOURCES

Subject Beginning data Middle data End data

Ch 1 Ch 2 Ch 1 Ch 2 Ch 1 Ch 2

1 1.001 1.142 1.289 1.217 1.419 1.415

2 1.125 1.115 1.201 1.300 1.402 1.456

3 1.210 1.206 1.210 1.194 1.414 1.443

4 1.110 1.191 1.3014 1.1967 1.434 1.476

Mean 1.112 1.164 1.250 1.227 1.417 1.448

It is posited here that the model of motor unit syn-

chronicity during fatigue can be tested by determining the

dependence of the recorded signals. In order to confirm the

dependant properties of sources as explained in theory, a

Global matrix was computed.

The determinant of the global matrix is an indicator of the

dependence of the sources. If the sources are independent,

the determinant value is close to unity, whereas when there

is dependence between the sources, this value becomes close

to zero [15] .

• Independency Results (Before Fatigue: Beginning data)

G=

(

0.8418 −0.0100

−0.0755 1.0862

)

det(G) = 0.9135

• Dependency Results (Middle data)

G=

(

0.8763 0.0210

−0.6743 0.0130

)

det(G) = 0.0256

• Double dependency Results (After Fatigue: End data)

G=

(

0.0236 −0.0202

0.0057 0.0362

)

227211219219

0 0.5 1 1.5 2

x 105

−1.5

−1

−0.5

0

0.5

1

1.5

Two ChanneCyclic Fatigue data

0 0.5 1 1.5 2

x 105

−3

−2

−1

0

1

2

3

Beginning

data

Middle

data

Final stage

cyclic data

Figure 1. Plot showing the three SEMG subsets (beginning, middle and end) during cyclic contractions.

det(G) = 0.00096

Table IIDETERMINANT OF GLOBAL MATRIX FOR ICA SEPARATED SOURCES

FOR DIFFERENT ITERATIONS

Independency Dependency Double Dependency

0.9135 0.0256 0.00096

0.8905 0.0228 0.00090

0.9549 0.0231 0.00094

0.9015 0.0198 0.00089

0.8998 0.0267 0.00092

0.9106 0.0184 0.00088

0.9213 0.0229 0.00095

0.8978 0.0212 0.00091

0.9325 0.0205 0.00089

Mean = 0.9136 0.0223 0.00092

From Table II and Figure 3, it is observed that the

determinant of the global matrix for all subjects is close to

unity before fatigue and this moves closer to zero once the

subject becomes fatigued. This shows that when the muscle

is not fatigued, the motor units are firing independently and

when the muscle is fatigued, the motor units are dependant

and therefore more synchronized.

V. DISCUSSION AND CONCLUSION

Many research groups have reported a link between sEMG

spectrum (or median frequency) and fatigue. Fatigue has

been associated with a spectral shift towards lower frequen-

cies. However, it has been reported that that MF does not

change significantly with muscle fatigue at low contraction

levels [16]. Modeling studies have shown that unlike high

level of muscle contraction of the biceps, during low-level

bicep voluntary contractions, the motor unit conduction

velocity does not reduce. In the fatigue state, the central

drive to a muscle has to increase, leading to synaptic input

that is common to more than one neuron. This has been

explained in literature based on increased synchronicity in

the motor unit firing patterns.

From literature it is known that the human bicep muscle

recruits additional muscle fibers as force increases, up to

around 88% MVC. Above 88% MVC, the frequency of

motor unit firing increases to allow muscle force output to

modulate up to the maximal contraction force [17]. However,

both an increase in motor unit firing rate and an increase in

the number of active motor units can increase the signal

amplitude (measured by RMS of sEMG).

After the onset of muscle fatigue, increased effort is

required to sustain the same force level; a point which is

reflected in the uniform increase in RMS values. This paper

confirms these known results. However, this RMS increase

does not contribute to the practical knowledge regarding

motor unit synchronization.

The work presented here has tested the motor unit syn-

chronization model by associating synchronicity with de-

228212220220

1 2 3 41

1.1

1.2

1.3

1.4

1.5

CH

1− R

MS

1 2 3 41.1

1.2

1.3

1.4

1.5

Subjects

Ch

2− R

MS

Beginning During End

Figure 2. RMS of the separated sources for three subsets of cyclic data.

1 2 3 4 5 6 7 8 90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Iterations

Det

erm

inan

t

Independency Dependency Double Dependency

Figure 3. Determinant values of global matrix for Independency, Dependency and Double dependency

pendence between motor units which are the sources of

MUAP. During non-fatigued state, the motor units appear

to work independently and this ensures smooth contraction.

SEMG taken from two channels should therefore reveal

independence from each other. This is confirmed from

the values of the determinants calculated using the global

matrix.

The determinant of the global matrix calculated after the

onset of muscle fatigue shows dependence between the two

channels. These results support the contention that motor

unit synchronicity increases in the fatigued state.

This work confirms the dependency between the differ-

ent channels. Work reported in this paper has determined

that determinant of the Global matrix associated with the

recordings can be used to determine the onset of muscle

fatigue even when the contraction is cyclic. This is important

because during cyclic contraction, it is difficult to obtain sta-

tionary features of sEMG that may be useful for determining

the onset of muscle fatigue.

The Global matrices showed a strong correlation between

fatigue and the matrix determinants. It is concluded by

this study that the correctness of the proposed motor unit

synchronization model to explain muscle fatigue. This paper

also reports that this fundamental property relating to muscle

229213221221

fatigue may be a used as an indicator for muscle fatigue.

However, the implementation of this would need to be

considered for real time applications.

ACKNOWLEDGMENT

The authors would like to acknowledge and thank Vivek

Yadav for collecting and providing the data for this research

study.

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