Convex Hull Area in Triaxial Mechanomyography during Functional

Electrical Stimulation

Guilherme N. Nogueira-Neto

1,3

, Eddy Krueger

, Eduardo M. Scheeren

Vera L. S. N. Button

and Percy Nohama

1,2,3

PPGTS, Pontifícia Universidade Católica do Paraná, Imaculada Conceição St 1155, Curitiba, PR, Brazil

CPGEI, Universidade Tecnológica Federal do Paraná, Sete de Setembro Ave 3165, Curitiba, PR, Brazil

CEB, Universidade Estadual de Campinas, Cidade Universitária “Zeferino Vaz”, Campinas, SP, Brazil

Keywords: Convex Hull, Triaxial Mechanomyography, Functional Electrical Stimulation.

Abstract: This study employed the convex hull in the analysis of triaxial mechanomyography (MMG) to determine

hull area variations along prolonged muscle contractions elicited by functional electrical stimulation (FES).

Closed-loop FES systems may need real-time adjustments in control parameters. Such systems may need to

process small sample sets. The convex hull area can be applied to small sample sets and it does not suffer

with non-stationarities. The MMG sensor used a triaxial accelerometer and the acquired samples were pro-

jected onto all planes. The hull determined the smallest convex polygon surrounding all points and its area

was computed. Four spinal cord injured volunteers participated in the experiment. The quadriceps femoral

muscle was stimulated in order to cause a full knee extension. FES parameters: 1 kHz pulse frequency and a

20 Hz burst frequency. Adjustments in the stimuli amplitude were controlled by a technician to sustain the

extension. The results showed that the convex hull area decreased over time. Since the polygons are related

to MMG amplitude, decreasing areas were related to muscle fatigue. The convex hull area can be a candi-

date to follow muscle fatigue during FES-elicited contractions and analysis of short length epochs.

1 INTRODUCTION

Functional electrical stimulation (FES) allows the

production of real muscle contractions that are artifi-

cially elicited by means of electric charges applied to

paralyzed muscles (Bajd et al., 1981, Langlois et al.,

2010). In addition to easing locomotion problems,

the electrical current applied to a spinal cord injured

subject brings physiological and biomechanical

benefits to the subject’s health (Peng et al., 2011).

During FES sessions, monitoring muscle

response to the electrical stimuli is a way of

investigating the evolution of muscle condition.

Mechanomyography (MMG) is a technique that

registers muscle vibrations and can help investigate

mechanical and physiological properties of

contracting muscles. Stokes and Cooper (1992)

reported that MMG is related to force production

whereas Petitjean et al. (1998) stated that evoked

MMG amplitude is a good index of motor unit

recruitment. MMG can also be used to observe

muscle fatigue installation, as a force suppressor

phenomenon, during FES programs performed in

rehabilitation protocols (Gobbo et al., 2006). Triaxial

MMG uses a 3D accelerometer that registers muscle

vibration in three orthogonal directions

simultaneously. It was already employed in the study

of muscle fatigue installation or neuronal adaptation

during FES (Nogueira-Neto et al., 2011), in which 1

s epochs of MMG signals were analyzed. However,

in closed-loop control of FES systems using MMG

parameters, updating the control strategy may

require epochs less than 1 s long. Using such epochs,

spectral (such as mean frequency and spectral

kurtosis) and temporal parameters (like those that

require constant signal variance) can be

contaminated by non-stationarity effects and this

becomes a problem for signal analysis and

classification (Fong et al., 2011) because parameters

have limited discriminatory power (Xie et al., 2009).

So, it is necessary to investigate techniques that can

also be applied to short epochs in neural control

systems.

Triaxial MMG allows the projection of a single

coordinate (defined by the values of each

acceleration axes) onto three representational planes

251

N. Nogueira-Neto G., Krueger E., M. Scheeren E., L. S. N. Button V. and Nohama P..

Convex Hull Area in Triaxial Mechanomyography during Functional Electrical Stimulation.

DOI: 10.5220/0004806702510256

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2014), pages 251-256

ISBN: 978-989-758-011-6

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

(XY – XZ – YZ). In the space defined by the

vibratory axes, Graham’s convex hull algorithm

(Graham, 1972) can identify the smallest convex

polygon that encloses all points in a plane. The

scattered plot of the coordinates represents the

spatial distribution of muscle vibrations. After

determining such polygon, its area can be computed

and it is closely related to the amplitude of MMG

signals in these directions. The area computation is

independent of the number of points (related to the

triaxial MMG epoch duration) and, thus, non-

stationarity issues do not limit the discriminatory

power of signal descriptors. The validation of the

convex hull area as signal analysis technique can

provide a new method to investigate bi- or triaxial

MMG during epochs less than 1s long during

closed-loop FES.

As long as FES is continuously applied to

paralyzed muscles, the installation of muscle fatigue

and neuronal adaptation can change the muscle

vibratory response (Jailani and Tokhi, 2012). Since

no previous work was found using convex hull and

bi- or triaxial MMG for muscle condition analysis

during FES, we propose to investigate whether the

convex hull area of planar finite MMG coordinates

set can identify changes in muscle condition during

knee maximum extension evoked by prolonged FES

application.

2 METHODS

2.1 Volunteers

The data were obtained from four male spinal cord

injured volunteers submitted to FES. The experiment

was approved by the research ethics committee of

Pontifícia Universidade Católica do Paraná (letter of

approval 2416/08). Participants were instructed

about the protocol and, after signing an informed

consent term, trichotomy and skin cleaning were

performed previous to the positioning of MMG

sensor and FES electrodes. Figure 1 shows the ex-

perimental setup for the subjects, sensors and elec-

trodes during the protocol.

2.2 Functional Electrical Stimulator

A multichannel functional electrical stimulator was

used to excite the quadriceps femoral muscle. The

FES waveform was a rectangular wave with pulse

frequency of 1 kHz, because it is preferable so as to

cause a forceful motor response (Ward and Robert-

son, 1998), and a 20 Hz, 6% duty cycle burst fre-

quency. A low duty cycle allows efficient contrac-

tions with less undesired metabolic effects. A low

burst frequency, preferably below 70 Hz, may post-

pone muscle fatigue installation and avoid tetanic

contractions being 20 Hz the limit before reaching

muscle fasciculation (Petrofsky, 2004). The stimula-

tor worked in open-loop and a technician changed

the stimuli amplitude as required.

Figure 1: Experimental setup. FES elicited extension from

30 (rest) up to 0 (full extension). MMG sensor was

placed over the quadriceps muscle belly. The electrogoni-

ometer registered the angle of the knee. FES electrodes:

over the femoral triangle and the suprapatellar region.

2.3 Acquisition System

The developed MMG instrumentation used a Free-

scale MMA7260Q MEMS triaxial accelerometer

(13x18mm, 0.94 g, 800 mV/G sensitivity at 1.5 G

[G, gravitational acceleration] – see Figure 2 for axis

orientation). The electronic circuits allowed 10x

amplification. A LabVIEW program was responsible

for the acquisition, pre-conditioning and processing

of all signals. The acquisition hardware was a com-

mercial Data Translation DT300 board working on a

sampling rate of 1 kHz. The conditioning phase

prepared for analysis the first 30 s after the knee

angle reached maximum extension.

2.4 Experimental Protocol

The participant’s left lower limb was initially posi-

tioned at 30º of the maximum knee extension (0º).

FES caused the knee to fully extend. The manual

adjustments in FES amplitude performed by the

technician sustained the extension between 3º e 0º.

2.5 Convex Hull Processing

Each ordinate pair





1, 1



;



2, 2



;...;



, 



 represents a point

in a plane. Figure 3 shows the dispersion of 1000

BIOSIGNALS2014-InternationalConferenceonBio-inspiredSystemsandSignalProcessing

252

ordinate pairs of a triaxial MMG signal, but only for

X and Y axes.

The hull was computed based in the algorithm

proposed by Graham (1972) with small

modifications. The routine determines the convex

hull  of an ordinate pairs set  

0,1,..., in the plane, where  depends on

the epoch length. At every 1 s epoch, a vector  was

processed to find the external points that define

.

Basically, the process can be defined in three

phases: (i) identify the point with the smallest

ordinate, i. e., the pivot point; (ii) compute the

angles of all other pairs in relation to the pivot,

resulting in a vector of angles sorted in ascending

order and (iii) use the cross product to determine the

angle formed by two line segments defined at every

consecutive three pairs. In the case of a negative

cross product, the intermediate pair is discarded for

it is an internal point.

Figure 2: Orientation of MMG sensor’s axes. Solid in red:

perspective of the limb segment representing the thigh.

Directions: Z – antero-posterior; X – lateral, and Y –

longitudinal.

Figure 3: Dispersion of 1000 ordinate pairs from a 1 s

triaxial MMG signal. Pairs were linked with black solid

lines. The orange contour represents the convex hull.

The last phase is repeated successively and

recurrently until no point in discarded from the

current . Finally, the routine determines the

area of .

2.6 Statistical Analysis

The area in each plane was normalized as a percent

of mean area. Linear determination coefficients (R

)

were computed to investigate how much a regression

line expresses the evolution of the area of FC(S)

along the extension maintenance.

3 RESULTS

Figure 4 shows the convex hull area at every epoch.

All curves presented a gradual decrease in the values

of . One can note that for some volunteer data

(e.g., Patients A and C) there are variations in the

trend of area values of different planes.

Table 1 shows the linear determination

coefficients (R

) for all curves. Data imply the

existence of strong linear correlation in the trends,

except for Patient C. All regressive line slopes were

negative, evidencing a decline in the trend (–0.0171

to –0.069).

Table 1: Determination coefficients of regression lines.

Patient XY XZ YZ

A 0.8404 0.9145 0.8831

B 0.9184 0.8245 0.9397

C 0.2642 0.324 0.6338

D 0.9605 0.9438 0.9527

4 DISCUSSION

The contracting muscle vibrates when sufficiently

excited by FES, and the MMG captures the muscle

lateral oscillation in three orthogonal directions.

Each axes pair delimited a plane and Figure 4 shows

that the area of  presented a gradual reduction

in all defined planes during the contraction.

Around the hull areas of Patient C, at instant 25

s, there is a transient in all planes. Incautious

placement of sensors was avoided as well as the

patients did not hit the leads during the experiment.

A possible explanation would be that this event is a

result of the recruitment of new motor units during

the evoked task. The recruitment of motor units

while applying FES can follow a non-obvious

pattern of sequencing, depending on muscle fiber

types (Gregory and Bickel, 2005). Therefore, the

ConvexHullAreainTriaxialMechanomyographyduringFunctionalElectricalStimulation

253

muscle of Patient C can be more responsive to

variations in FES amplitude and this responsiveness

lead to greater oscillations in the triaxial MMG axes.

After the transient, however, the area of 

diminished again, revealing a decreasing trend in

MMG amplitude but less pronounced in the XZ

plane, the transversal plane. The observed overall

decrease is consistent with the findings of other

researchers. Progressive decreases in MMG

amplitude were observed in fatiguing isometric

contractions of the erector spinae muscle (Yoshitake

et al., 2001). The integrated amplitude of rectus

femoris MMG response also decreased with force

production (Stokes and Dalton, 1991) that indicates

that motor unit recruitment decreases with the

installation of muscle fatigue and it could explain

the reduction in the hull area.

The main motivation for using computational

geometry was the possibility of employing analysis

with short length epochs without non-stationarity

problems. Its algorithm can be easily incorporated in

microcontroller units employed in closed-loop FES

systems with a low computational cost and capable

of providing real time efficiency (Yun-Hui, 1999).

The use of epochs less than 1 s in length is not

recommended for analysis of electromyographic

(EMG) parameters (Beck et al., 2005), as well as for

biomechanical data during dynamic contractions

(Schwartz et al., 2012) due to stationarity issues.

Wavelet analysis is a recommended technique to

study non-stationary signals (Rioul and Vetterli,

1991). Alternative to the complex hull analysis is

principal component analysis (PCA), an statistical

method that explains the covariance of multivariate

signals by means of a small set of components and is

less susceptible to outliers (Hubert and Rousseeuw,

2005).

The relationship between eccentric and

concentric muscle contractions was studied with

decomposition of MMG and EMG signals in

principal components (Qi et al., 2011). This work

focused in convex hull because microcontroller-

based closed-loop FES control systems need short

response times and this implied the use of short

length epochs what could eventually impair the

results with PCA (Osborne and Costello, 2004).

Nevertheless, PCA had been already used in real-

time control systems (Chapin et al., 1999) and robust

PCA algorithms may be computed really fast

(Hubert and Rousseeuw, 2005).

The reduction in the hull area can occur due to

the attenuation in the amplitude of MMG signals in

any axis. Generally, a monoaxial sensor registers the

signal in the muscle normal direction and does not

Figure 4: Convex hull area (in V

) vs. epoch.

acquire vibrations in other directions (Akataki et al.,

1999). Therefore, triaxial accelerometry favors the

investigation of what is happening in vibration

planes.

While a technique under study, data

normalization is non-problematic, because absolute

values can depend on volunteer, FES parameters and

hardware/software amplification stages. A limitation

of this technique is intrinsic to the method. The area

enclosed by the hull does not represent the area of

the polygon exactly defined by the pairs in the plane.

However, the hull determination can be

compromised if outliers are present in the samples.

The number of subjects investigated was small

because not all volunteers could hold an artificially

sustained contraction for as long as 30 s.

Investigating MMG spectral parameters in

voluntary isometric contractions, Tarata et al. (2001)

observed a decrease in the MMG mean spectrum

frequency for biceps and brachioradialis muscles. In

studies previously published (Nogueira-Neto et al.,

BIOSIGNALS2014-InternationalConferenceonBio-inspiredSystemsandSignalProcessing

254

2011) using FES and a spinal cord injured person,

we have also found that the mean frequency

decreases during the periods of extension

maintenance. Therefore, the results presented in this

paper are consistent with studies already published

and show that this technique can be useful in

following the evolution of FES-elicited muscle

contraction. Convex hull area, despise its limitations,

can be a promising candidate as a parameter

indicating muscle fatigue in closed-loop FES control

systems.

5 CONCLUSIONS

In this study, we proposed the use of a computational

geometry technique known as the convex hull of a

finite set of planar points in the analysis of triaxial

mechanomyography signals. During an open chain

contraction and maximum knee extension evoked by

functional electrical stimulation, the convex hull

showed that its area reduced in all planes in a space

defined by the three axes of the mechanomyography

sensor. This reduction in the convex hull area was

related to a decrease in force production due to sup-

pressive performance phenomena like muscle fa-

tigue.

ACKNOWLEDGEMENTS

The authors thank CNPq, SETI-PR, CAPES e

FINEP for the financial support.

REFERENCES

Akataki, K., Mita, K. & Itoh, Y. 1999. Relationship Be-

tween Mechanomyogram And Force During Voluntary

Contractions Reinvestigated Using Spectral Decompo-

sition. European Journal Of Applied Physiology, 80,

173-9.

Bajd, T., Kralj, A., Sega, J., Turk, R., Benko, H. & Stro-

jnik, P. 1981. Use Of A Two-Channel Functional Elec-

trical Stimulator To Stand Paraplegic Patients. Physi-

cal Therapy, 61, 526-27.

Beck, T. W., Housh, T. J., Johnson, G. O., Weir, J. P.,

Cramer, J. T., Coburn, J. W. & Malek, M. H. 2005.

Comparison Of Fourier And Wavelet Transform Pro-

cedures For Examining The Mechanomyographic And

Electromyographic Frequency Domain Responses

During Fatiguing Isokinetic Muscle Actions Of The

Biceps Brachii. Journal Of Electromyography And Ki-

nesiology, 15, 190-9.

Chapin, J., Moxon, K., Markowitz, R. & Nicolelis, M.

1999. Real-Time Control Of A Robot Arm Using Sim-

ultaneously Recorded Neurons In The Motor Cortex.

Nature Neuroscience, 2, 664-70.

Fong, S., Hang, Y., Mohammed, S. & Fiaidhi, J. 2011.

Stream-Based Biomedical Classification Algorithms

For Analyzing Biosignals. Journal Of Information

Processing Systems, 7, 717-32.

Gobbo, M., Cè, E., Diemont, B., Esposito, F. & Orizio, C.

2006. Torque And Surface Mechanomyogram Parallel

Reduction During Fatiguing Stimulation In Human

Muscles. European Journal Of Applied Physiology,

97, 9-15.

Graham, R. L. 1972. An Efficient Algorithm For Deter-

mining The Convex Hull Of A Finite Planar Set. In-

formation Processing Letters, 1, 132-3.

Gregory, C. M. & Bickel, C. S. 2005. Recruitment Patterns

In Human Skeletal Muscle During Electrical Stimula-

tion. Physical Therapy, 85, 358-64.

Hubert, M. & Rousseeuw, P. J. 2005. Robpca: A New

Approach To Robust Principal Component Analysis.

Technometrics, 47, 64-79.

Jailani, R. & Tokhi, M. O. 2012. The Effect Of Functional

Electrical Stimulation (Fes) On Paraplegic Muscle Fa-

tigue. Ieee 8th International Colloquium On Signal

Processing And Its Applications (Cspa). Shah Alam,

Selangor, Malaysia: Ieee.

Langlois, P. J., Demosthenous, A., Pachnis, I. & Donald-

son, N. 2010. High-Power Integrated Stimulator Out-

put Stages With Floating Discharge Over A Wide Volt-

age Range For Nerve Stimulation. Ieee Transactions

On Biomedical Circuits And Systems, 4, 39-48.

Nogueira-Neto, G. N., Krueger, E., Scheeren, E. M., No-

hama, P. & Button, V. L. S. 2011. Estimulação Elétrica

Funcional Aplicada Em Cadeia Aberta - Um Estudo

De Caso Com Monitoração Mecanomiográfica. 5th

Latin American Congress Of Biomedical Engineering.

Havana: Ifmbe.

Osborne, J. W. & Costello, A. B. 2004. Sample Size And

Subject To Item Ratio In Principal Components Anal-

ysis. Practical Assessment, Research & Evaluation, 9,

Peng, C.-W., Chen, S.-C., Lai, C.-H., Chen, C.-J., Chen,

C.-C., Mizrahi, J. & Handa, Y. 2011. Review: Clinical

Benefits Of Functional Electrical Stimulation Cycling

Exercise For Subjects With Central Neurological Im-

pairments. Journal Of Medical And Biological Engi-

neering, 31, 1-11.

Petitjean, M., Maton, B. & Fourment, A. 1998. Summation

Of Elementary Phonomyograms During Isometric

Twitches In Humans. European Journal Of Applied

Physiology, 77, 527-35.

Petrofsky, J. S. 2004. Electrical Stimulation: Neurophysio-

logical Basis And Application. Basic And Applied My-

ology, 14, 205-13.

Qi, L., Wakeling, J. M., Green, A., Lambrecht, K. & Fer-

guson-Pell, M. 2011. Spectral Properties Of Electro-

myographic And Mechanomyographic Signals During

Isometric Ramp And Step Contractions In Biceps Bra-

ConvexHullAreainTriaxialMechanomyographyduringFunctionalElectricalStimulation

255

chii. Journal Of Electromyography And Kinesiology,

21, 128-35.

Rioul, O. & Vetterli, M. 1991. Wavelets And Signal Pro-

cessing. Ieee Signal Processing Magazine, 8, 14-38.

Schwartz, F. P., De Oliveira Nascimento, F. A., Bottaro,

M. & Celes, R. S. 2012. Análise Da Estacionariedade

Do Sinal De Eletromiografia De Superfície Nas Fases

Do Exercício Isocinético De Extensão Do Joelho. Re-

vista Brasileira De Engenharia Biomédica, 28, 44-52.

Stokes, M. J. & Cooper, R. G. 1992. Muscle Sounds Dur-

ing Voluntary And Stimulated Contractions Of The

Human Adductor Pollicis Muscle. Journal Of Applied

Physiology, 72, 1908-13.

Stokes, M. J. & Dalton, P. A. 1991. Acoustic Myography

For Investigating Human Skeletal Muscle Fatigue.

Journal Of Applied Physiology, 71, 1422-26.

Tarata, M., Spaepen, A. & Puers, R. 2001. The Accel-

erometer Mmg Measurement Approach, In Monitoring

The Muscular Fatigue. Measurement Science Review,

1, 47-50.

Ward, A. R. & Robertson, V. J. 1998. Variation In Torque

Production With Frequency Using Medium Frequency

Alternating Current. Archives Of Physical Medicine

And Rehabilitation, 79, 1399-1404.

Xie, H.-B., Zheng, Y.-P. & Guo, J.-Y. 2009. Classification

Of The Mechanomyogram Signal Using A Wavelet

Packet Transform And Singular Value Decomposition

For Multifunction Prosthesis Control. Physiological

Measurement, 30, 441-57.

Yoshitake, Y., Ue, H., Miyazaki, M. & Moritani, T. 2001.

Assessment Of Lower-Back Muscle Fatigue Using

Electromyography, Mechanomyography, And Near-

Infrared Spectroscopy. European Journal Of Applied

Physiology, 84, 174-9.

Yun-Hui, L. 1999. Qualitative Test And Force Optimiza-

tion Of 3-D Frictional Form-Closure Grasps Using

Linear Programming. Ieee Transactions On Robotics

And Automation, 15, 163-73.

BIOSIGNALS2014-InternationalConferenceonBio-inspiredSystemsandSignalProcessing

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