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Estimation and Application of
EMG Amplitude During
Dynamic Contractions
Processing Nonstationary EMG for Applications in Prosthesis
Control, Biofeedback, and Joint Torque Estimation
Wthey conduct electrical activity (ac-
hen skeletal muscle fibers contract,
Edward A. Clancy1, Stéphane Bouchard2,
Denis Rancourt2
1
Department of Electrical and Computer Engineering
and Department of Biomedical Engineering,
Worcester Polytechnic Institute
2
Department of Mechanical Engineering,
Laval University
November/December 2001
tion potentials, APs) that can be measured
by electrodes affixed to the surface of the
skin above the muscle. As the APs pass by
the electrodes, spikes of electrical activity
are observed and pulses of muscle fiber
contractions are produced. Small functional groups of muscle fibers, termed
motor units (MUs), contract synchronously, resulting in a motor unit action potential (MUAP). To sustain force, an MU
is repeatedly activated by the central nervous system several times per second. The
repetition, or average, firing rate is often
between 5 and 30 times per second (or
faster) [1]. During most voluntary muscle
contraction, however, a sufficiently large
number of MUs contract (generally
asynchronously) and a random electrical
interference pattern is observed by surface electrodes. In the absence of muscle
fatigue (a condition that will not be discussed in this report), increased firing rate
and/or increases in the number of active
MUs result in both increased muscle tension and an interference pattern with
higher power. Studied as a whole (i.e.,
without decomposing the individual action potentialsa separate and important
study topic) the overall magnitude of the
electrical activity found at the skin surface
provides insight into muscle effort. The
magnitude of the electrical activity is
commonly referred to as the amplitude of
the electromyogram (EMG). This amplitude has been used, for example, as the
control input to upper-limb prostheses
(myoelectrically controlled elbows [19],
wrists, and hands), in biofeedback applications, in ergonomic assessment, and to
estimate the torque produced about a joint
[2, 9, 15, 23].
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Although an MU is activated repeatedly, the interval between successive activations is not fixed. Rather, the
physiology “fires” an MU at nonperiodic
time intervals (with some average firing
rate). The interval lengths can be well
modeled as a random process with a mean
value equal to the average time between
firings. In addition, the number and identity of MUs active at any time is controlled. Thus, stochastic process models
have been used to model the recorded
EMG. Some of these models superimpose
the random firing of individual MUs to
form a composite recorded EMG (e.g., [1,
25]). Alternatively, “functional” models
are based on the observed interference
signal without specific regard to the underlying physiologic processes of individual MU firings. In this case, the observed
interference pattern is modeled directly as
a Gaussian (e.g., [10, 17, 18]) or
Laplacian [10] random process. The functional modeling style will be developed
exclusively herein. Further, because the
strength of muscle contraction is varied in
many of these applications, EMG amplitude is generally a time-varying parameter. As will be discussed below, timevarying EMG amplitudes cause the stochastic models to be nonstationary.
If the EMG signal is modeled mathematically as a random process, then EMG
amplitude can more formally be defined as
the time-varying standard deviation of the
random process. Then, optimal estimation
techniques can be used to best estimate
EMG amplitude from a sample of the
EMG. This style of formal EMG modeling
has led to progressive iterative improvement in EMG amplitude estimates over the
past 25 or more years, with a concomitant
increase in the number of signal details in0739-5175/01/$10.00©2001IEEE
47
There are at least two
fundamental
difficulties in relating
surface EMG
amplitude directly to
the tension produced
by individual muscles.
cluded in the random process model. The
majority of this article will describe the
present “state of the art” in EMG modeling
and amplitude estimation. Emphasis will
be placed on the impact of the
nonstationary nature of the signal on the
details of the estimation technique. Estimates of EMG amplitude can be used directly in such applications as the control
input to upper-limb prostheses, biofeedback, and ergonomic assessment.
Once a dynamic EMG amplitude estimate is available, a common application is
to relate the EMG amplitude to the dynamic mechanical activity of the muscle. It
would be ideal to relate surface EMG amplitude directly to the tension produced by
wi
Htime(ejω)
individual muscles. However, there are at
least two fundamental difficulties in doing
so. First, classical EMG recorded at the
surface of the skin can contain “cross talk.”
That is, EMG from muscles other than that
which the experimenter intends to record
may be included in the signal. Cross talk is
a difficult problem with no immediate,
simple solution. Second, relating EMG to
individual muscle tension requires independent verification via direct mechanical
measurement of individual muscle tension.
At present, there is no practical (and perhaps not any) method for reliably making
such measurements in situ. Because of
these fundamental limitations, several efforts have focused on relating surface
EMG amplitude to joint torque. First, cross
talk, if it exists, may not be as problematic.
Certain cross-talk contributions are automatically removed from the estimated
torque, even if they cannot be removed
from the individual muscle tension contributions (c.f., [3, pp. 343-345]). Second, net
torque about a joint can, in many cases, be
reasonably (or even easily) verified via direct mechanical measurement. The second
portion of this article will present preliminary results of a recent study of relating
EMG amplitude to joint torque during
force-varying contractions.
Model of the Surface EMG
Functional models of the EMG seek to
capture the observed stochastic behavior
of the EMG signal without including the
complexity that would be involved in
modeling the activity of each individual
MU. A complete model in this style for a
single channel of EMG is shown in Fig. 1.
ri
ni
si
Zero Mean, WSS, Shaping Filter
CE, White
Process of Unit
Intensity
Σ
mi
vi
EMG
Amplitude
Zero Mean,
WSS, CE,
Additive Noise
Process
Measured
Surface
EMG
1. Mathematical model of a single channel of the surface EMG. A zero-mean,
wide-sense stationary (WSS), correlation-ergodic (CE), white process of unit intensity
wi (i is the sample index) passes through the stable, causal, inversely stable, linear,
time-invariant shaping filter H ( e jω ). It is then multiplied by the EMG amplitude s i
and added to the zero-mean, WSS, CE, Gaussian noise process v i to form the measured surface EMG m i . The processes wi and v i are assumed to be uncorrelated with
each other and the EMG amplitude. Muscle contraction is nonfatiguing.
48
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This model produces a measured surface
EMG (m i ) with statistical properties similar to real EMG. The model develops surface EMG from a zero-mean, wide-sense
stationary (WSS), correlation-ergodic
(CE), white process of unit intensity. The
white process is passed through a time-invariant shaping filter, which accounts for
the spectral shaping in the measured
EMG. The output of the shaping filter is
multiplied by the time-varying EMG amplitude (s i ). All changes in the signal variance of the noise-free EMG (ri ) are
attributed to changes in the EMG amplitude. Because EMG is invariably observed in the presence of measurement
noise, an additive Gaussian noise source
(v i ) is included in the model. This noise
source is much broader-band than the
noise-free EMG (represented by ri ). The
white process (wi) is frequently assumed
to be Gaussian distributed, although other
distribution assumptions are possible
[10]. As can be seen by this mathematical
model, EMG amplitude is defined as the
standard deviation of the EMG (observed
in the presence of additive noise). This
standard deviation is time varying (hence,
the process is nonstationary) because
EMG amplitude is a function of time.
Note that multiple-channel EMG models
also exist for the purpose of estimating
EMG amplitude. In these models, it is assumed that several electrodes can be
placed over different regions of the same
muscle to simultaneously monitor the
electrical activity of different muscle fibers. In this case, all electrodes contribute
to the one amplitude estimate.
EMG Amplitude Estimation
During Dynamic Conditions
Given the above EMG model, EMG
amplitude estimation becomes the problem of estimating the time-varying standard deviation of a colored random
process in the presence of additive noise.
An optimal closed-form analytic solution for achieving this goal has yet to be
derived. (See [4, 11] for a brief historical
perspective of research work in this
area.) However, piece-wise solutions
(i.e., those in which individual processing steps are optimal) exist. The most
common of these solutions is shown in
block diagram form in Fig. 2. The figure
shows the cascade of six sequential processing stages to form a general processor for EMG amplitude estimation. The
six stages are 1) noise and interference attenuation/filtering, 2) whitening, 3) mulNovember/December 2001
tiple-channel combination (including
gain scaling), 4) demodulation, 5)
smoothing, and 6) relinearization. Noise
and interference attenuation/filtering is
used to reject motion artifacts, power line
interference, etc.—common noise
sources that have been omitted from the
EMG model shown in Fig. 1. Because
successive EMG samples are necessarily
acquired at or above the Nyquist rate,
neighboring EMG samples are correlated. [Physiologically, the correlation
between neighboring EMG samples is a
consequence of the limited signal bandwidth (modeled by the shaping filter in
Fig. 1). The limited signal bandwidth reflects the actual biological generation of
EMG and the lowpass filtering effects of
the tissues as the signal propagates from
its source to the measurement apparatus.]
Unfortunately, correlated samples confound optimal statistical estimation
problems, such as estimation of a standard deviation (i.e., the EMG amplitude
estimation problem). Decorrelation (that
is, whitening) makes the samples statistically uncorrelated and increases the “statistical bandwidth.” Thereafter, the
detection algorithm treats each sample as
independent. Multiple-channel combination is used to combine the information
from several electrode recordings made
over the same muscle. Demodulation
rectifies the whitened EMG and then
raises the result to a power [either one for
mean-absolute-value (MAV) processing
or two for root-mean-square (RMS) processing]. Smoothing filters the signal, increasing the signal-to-noise ratio, albeit
at the expense of adding bias error to the
estimate. Finally, relinearization inverts
the power law applied during the demodulation stage, returning the signal to units
of EMG amplitude.
Two issues are important to point out
when using this processing scheme.
First, five of the six steps are relatively
independent of each other. (The demodulation and relinearization steps must be
inverses of each other, thus they are completely dependent.) Therefore, the processing steps can generally be considered
separately. Second, it turns out that dynamics in the EMG only have a significant influence on processing decisions in
the smoothing step. This article will review these six processing steps with an
emphasis on the smoothing step. Additional details of these steps can be found
elsewhere [5-8, 10-11].
November/December 2001
EMG Amplitude Estimation
Processing Steps
The goal of the first processing stage
is to eliminate noise and interference
(e.g., motion artifact, power-line interference) that are acquired along with the
“true” EMG. Of course, it should be mentioned that the most successful treatment
of these unwanted signal sources is to
minimize their contribution to the measured signal samples via, for example,
proper skin preparation prior to electrode
placement and the use of active electrodes. The frequency content of motion
artifact is typically below 10-20 Hz. The
general approach to motion artifact reduction is to high-pass filter the EMG
with a cutoff frequency of approximately
20 Hz. Little “true” signal power is lost,
however most motion artifact is rejected.
For attenuating power-line interference,
the most straightforward technique is to
apply a narrow fixed-notch filter to EMG
at the power-line fundamental frequency
and its first few harmonics. Notch filtering, however, removes “true” signal as
well as power-line components. Most remaining techniques fall under the category of adaptive filters, the most well
known being that of Widrow et al. [24].
They describe an adaptive interference
cancellation method in which a reference
input (a signal correlated with the
power-line interference) is adaptively
filtered and subtracted from the corrupted signal, giving an estimate of the
true signal. This method can be applied
for interference reduction wherever a ref-
The goal of the first
processing stage is
to eliminate noise
and interference
(e.g., motion
artifact, power-line
interference) that are
acquired along with
the “true” EMG.
erence “noise” signal (in this case, the
power line) can be obtained simultaneously with the corrupted signal. Additional discussion of motion artifact and
power-line interference attenuation can
be found in [11].
After attenuation of motion artifact
and power-line interference, the signal is
treated as though it were free of these arti-
m1(t) Noise
Reject/
Filter
Whiten
Detect
•d
m2(t) Noise
Reject/
Filter
Whiten
Detect
•d
m3(t) Noise
Reject/
Filter
Whiten
m4(t) Noise
Reject/
Filter
Whiten
..
.
Spatial
Uncorrelate
and Gain
Normalize
..
.
Detect
•d
Smooth
∧
Relinearize s(t)
(•)1/d
..
.
Detect
•d
2. Cascade of processing stages used to form an EMG amplitude estimate. The acquired EMG m1 , i through m L , i are all assumed to be from bipolar electrodes
placed over the same muscle. The EMG amplitude estimate is s i . In the “Detect”
and “Relinearize” stages, d = 1 for MAV processing and d = 2 for RMS processing.
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49
facts (although an additive background
noise remains). Next, in stage two, the signal is whitened, typically via software signal processing algorithms. A whitening
filter is formed by first estimating the
power spectral density (PSD) of the “true”
(i.e., noise-free) EMG and, in one case
discussed below, the accompanying additive noise. Then, the inverse of the square
root of the “true” PSD is the shape of the
whitening filter. At least three general
methods to achieve whitening have been
described in the literature. First, for constant-force, constant-posture, nonfatiguing contractions, it is common to whiten
using a moving average filter (determined
by the “true” PSD). (See [7, 16] for details.) Second, contrary to the functional
Table 1. Degrees of freedom constant “g” for several different
EMG processors. This constant is determined by the statistical
bandwidth of the EMG, the number of EMG channels,
and the detector type (see [5] for details).
EMG Processor
Degrees of
Freedom
Constant “g”
(Hz)
Detector
Whitened vs.
Unwhitened
Number of
EMG Channels
Mean-Absolute-Value (MAV)
Unwhitened
1
263
Mean-Absolute-Value (MAV)
Unwhitened
4
546.5
Mean-Absolute-Value (MAV)
Whitened
1
639
Mean-Absolute-Value (MAV)
Whitened
4
1427
Root-Mean-Square (RMS)
Unwhitened
1
234.5
Root-Mean-Square (RMS)
Unwhitened
4
463.5
Root-Mean-Square (RMS)
Whitened
1
617.5
800
Optimal Window Length (ms)
700
Noncausal, Quadratic Model
600
500
400
300
200
100
Causal, Linear Model
0
0
0.5
1
1.5
2
2.5
3
EMG Amplitude / [EMG Amplitude Derivative]
3. Theoretical optimal smoothing window lengths. Dotted graph is for noncausal
processing. For this plot, the X-axis is the ratio of EMG amplitude to EMG amplitude second derivative magnitude (in units of seconds squared). The solid graph is
for causal processing. For this plot, the X-axis is the ratio of EMG amplitude to
EMG amplitude first derivative magnitude (in units of seconds). For both graphs,
the constant g is set to 500/s.
50
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EMG model given above, some research
has assumed that the PSD of the EMG can
v a ry (i. e . , th e s h a p in g f i l t e r i s
time-varying), and thus the whitening filter must vary as well. In this case, the PSD
model is continuously updated, and thus
the whitening filter is time adaptive
[13-14]. Historically, both of these methods have ignored that fact that EMG is invariably observed in the presence of
additive broadband noise, as modeled in
Fig. 1. Hence, when EMG amplitude is
small relative to the noise (at lower contraction levels), the above techniques may
fail. Thus, a third technique was recently
developed that adapts the whitening
scheme based on the PSD of both the
“true” EMG and the additive noise [6].
This technique incorporates a noise attenuation stage that adaptively filters the signal based on the relative strength of the
signal versus the noise. EMG is effectively whitened over all contraction levels. Formally, the adaptive noise
attenuation is a nonstationary filter. But,
because the filter has a short time constant, EMG amplitude is relatively constant over the duration of time during
which data are passing through the filter.
Hence, the processing is considered stationary for the filter duration, even though
the filter shape is continuously updated
(quasi-stationary).
After the whitening stage, the signal is
assumed to be noise-free and temporally
uncorrelated. When multiple channels
have been recorded from the same muscle, they are next combined in the third
processing step. Formally, the spatial correlation between channels must be accounted for when combining channels [7,
17]. However, in practice, simple gain
normalizing of the channels (to account
for the fact that the signal strength can
vary from one recording site to the other)
is sufficient (at least for up to four electrodes [7]). Thus, channel combination is
accomplished by gain normalizing the
multiple signals.
The standard deviation of the “true”
EMG is now the common standard deviation of these signals. In order to estimate
this standard deviation from the EMG
samples, some form of nonlinearity must
be applied to the signals. In general, the
nonlinearity consists of taking the absolute value of each sample, then raising
each sample to a power. This operation is
the fourth processing stage—demodulation. Whatever power is selected in this
stage also specifies the relinearization opNovember/December 2001
eration in the sixth processing stage. The
two most common powers are one (MAV
processing) and two (RMS processing).
Theoretically, Hogan and Mann [17]
have shown that RMS processing is optimal if EMG is Gaussian distributed, and
Clancy and Hogan [10] have shown that
MAV processing is optimal if EMG is
Laplacian distributed. Using EMG from
biceps and triceps muscles, Clancy and
Hogan found that the observed densities
fell in between the theoretic Gaussian
and Laplacian densities. On average, the
Gaussian density was the better fit. For
amplitude estimation, MAV processing
had a higher SNR than RMS processing,
but only by 2.0-6.5%. These results suggest that forming EMG amplitude estimates via either RMS or MAV processing
is nearly indistinguishable.
The Smoothing Step
 s2
⋅  2Ave
 (s ) Ave



1/ 5
where N is the window length (samples),
2
is
f is the sampling frequency (Hz), s Ave
the average value of the square of EMG
amplitude, and (s 2 ) Ave is the average
value of the square of the second derivative of EMG amplitude. The quantities
November/December 2001
2
 s Ave

⋅

1/ 3  2
g
 ( s ) Ave 
1
1/ 3
where ( s 2 ) Ave is the average value of the
square of the first derivative of EMG amplitude. Figure 3 shows an example plot
used to select the optimal window length.
Note that several studies have attempted
to improve the amplitude estimate by dynamically adapting the window length to
the local characteristics of the EMG (e.g.,
[5, 12, 21]). In direct comparison to the
best fixed-length smoother, these adaptive smoothers have found little or no advantage for generic applications, with a
few exceptions.
The six steps described above produce a state-of-the-art estimate of EMG
amplitude. Note that in all of the above,
selection of the window length was discussed in view of optimizing the amplitude estimate only. For applications such
as EMG-torque estimation (discussed
below), the amplitude estimate is the input to an ensuing procedure (e.g., EMG
amplitude to torque modeling). In these
cases, smoothing may be skipped en-
mE1,i
mE2,i
mE L
Extensor
EMG
Amplitude
Estimator
∧
sE
E,i
tirely (leaving all of the smoothing to the
ensuing application), or the smoothing
parameters may be dictated by the requirements of the application.
Preliminary Results of Relating
EMG Amplitude to Joint Torque
During Dynamic Conditions
As mentioned above, a common application of EMG amplitude is to estimate
torque about a joint. Preliminary results of
a first investigation to do so with advanced EMG amplitude estimators and
dynamic contractions will now be described. To adequately estimate joint
torque, both agonist and antagonist muscles must be monitored [9]. If multiple-channel EMG recordings are made
from both the agonist and antagonist muscle groups, then EMG-torque estimation
can be organized as shown in Fig. 4. In the
figure, all flexion torque is attributed to
one “composite” agonist muscle, and all
extension torque is attributed to one
“composite” antagonist muscle. Although
individual muscle group tensions (TE and
TF ) are internal states of the model, only
the net joint torque contributes to model
error. Note that more general model representations exist; e.g., the more generic
two-input ( s F , s E ), one-output (TExt ) system is also common.
For this investigation, linear models of
the EMG amplitude to torque relationship
were studied during constant-posture contraction about the elbow. Linear models
would likely capture much of the system
dynamics (c.f. the EMG-torque investigations of Gottlieb and Agarwal [15] and
Extensor
EMG
Amplitude to
Torque
Estimator
TE
−
TExt
Σ
mF1,i
mF2,i
mFL
…
 72 
N Noncausal = f  
g 
1/ 5
N Causal = f
…
What remains to be described is the
fifth processing step—smoothing. Initially, the demodulated samples from each
sample index are averaged across L channels. A single demodulated signal results.
Then, several demodulated samples are
averaged in time to form one amplitude
estimate. A sliding time window selects
the demodulated samples for each successive amplitude estimate, thereby forming
an averaging filter. Because EMG amplitude is changing during contraction, an
appropriate smoothing window length
over which the signal is quasi-stationary
must be selected [5, 12, 20-21]. In doing
so, it is found that variance (random) errors in the EMG amplitude estimate are
diminished with a long smoothing window; however, bias (deterministic) errors
in tracking the signal of interest are diminished with a short smoothing window.
Clancy [5, see Appendix] derived a
method for optimal selection of a fixed
window length. Different results were derived for causal and noncausal (midpoint
moving average) processing. For
noncausal processing, the optimal window length was found to be:
2
and (s 2 ) Ave take different values for
s Ave
different tasks. The constant g is related to
the number of statistical degrees of freedom in the data, determined by the statistical bandwidth of the EMG, the number of
EMG channels, and the detector type (see
[5] for details). Table 1 shows the value of
g det e rm in e d e x p e r im e n ta lly b y
St-Amant et al. [22] for eight different
processors. For causal processing, the optimal window length was found to be:
Flexor
EMG
Amplitude
Estimator
F,i
∧
sF
Flexor
EMG
Amplitude to
Torque
Estimator
TF
+
4. Net torque about the joint (TExt ) equals the flexor muscles torque contribution
(TF ) minus the extensor muscles torque contribution (TE ). The flexor muscles
torque contribution is a function of the flexor EMG amplitude (s F ), which is estimated from the flexion electrode EMG samples (m F1 , i through m FL , i , where L F is
F
the number of flexion channels). The extensor muscles torque contribution is
similarly estimated.
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51
Thelen et al. [23]). Appropriate nonlinear
models can be incorporated in the future,
as necessary.
Methods
The EMG and torque data used in this
study are a portion of the data obtained during an experiment examining constant-posture exertions about the elbow,
described in detail in [6]. Briefly, subjects
(16) were firmly seated in the chair of an
exercise machine (Biodex Medical Systems, Shirley, NY, U.S.A.) and their right
wrist rigidly secured to the chair arm. They
were asked to exert dynamically varying
elbow torque (motion bandwidth of 1 Hz)
indicated by a visual feedback signal
shown to them on a computer screen, for
periods of 30 s at a maximum of 50% of
their maximum voluntary contraction
(MVC). The contraction patterns were random in nature, requiring equal durations of
flexion and extension contraction on average. Eight EMG surface electrodes (Liberty Technology model MYO115,
Hopkinton, MA, U.S.A.) were placed on
the subject’s right arm (four over the biceps
and four over the triceps muscles) for acquisition of two four-channel EMG signal
sets. The location of the four biceps electrodes is depicted in Fig. 5.
EMG-torque processing was performed offline, with a portion of the acquired data from each subject serving as
a training set for the model, and the remaining data serving as the test set. Only
test set results are reported. To investigate the influence of advanced EMG algorithms—in particular, multiplechannel processing and the adaptive
whitening technique of [6]—four different EMG processors were used (each
processor was used to produce a flexion
and an extension EMG amplitude estimate for each trial). Processor 1 was the
single-channel technique, without whitening. Processor 2 was the four-channel
technique, without whitening. Processor 3 was the single-channel technique,
with whitening. Processor 4 was the
four-channel technique, with whitening.
The smoothing stage was effectively
omitted from amplitude estimate processing since the optimal smoothing for
torque estimation is inherently solved for
in the system-identification process.
Two different system-identification
models were examined. Model 1 was an
output error (OE) model that incorporated
the operating point (mean values of the inputs and the outputs) into the identification
process. This model estimated the complete joint torque. Model 2 was an OE
model that operated on the data after all
mean values were removed (“AC model”).
This model only estimated the dynamic
portion of joint torque. In all, a total of
eight processor-model combinations were
reported. For each combination, a range of
model orders was also investigated. Results were expressed as the percent variance accounted for (%VAF), a
time-domain error measure equal to
100 ⋅ PError
,
%VAF = 100 −
PTrue
where PError is the total power in the
torque estimate error and PTrue is the total
power in the true torque. Additional details of the system identification are available in [2].
EMG 3
Subject 21, File 69, %VAF = 89.5
EMG 2
EMG 1
Anterior
EMG 0
Torque (Percent of Maximum Contraction)
100
50
0
−50
−100
5. Drawing showing the location of the
four biceps electrode-amplifiers on the
right arm of a subject. The two contacts
of each electrode-amplifier were oriented
along the muscle’s long axis, the presumed direction of action potential conduction. Each electrode-amplifier had a
pair of 4-mm-diameter, stainless steel,
hemispherical contacts separated by 15
mm (center to center). The distance between adjacent electrode-amplifiers was
approximately 1.75 cm (center to center).
52
0
5
10
15
20
25
30
Time (Seconds)
6. The measured torque (solid line) and the corresponding EMG-torque estimate
(dotted line) are plotted versus time into the trial. EMG were processed using the
four-channel technique, with whitening. The EMG-torque modeling technique was
the OE model that incorporated the operating point into the identification process.
The model numerator order was five and denominator order was six. A positive-valued torque denotes extension, a negative-valued torque denotes flexion.
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November/December 2001
Experimental Results
and Discussion
Only preliminary results are presently
available, with accompanying statistical
analysis yet to be completed. Figure 6 is a
time-series plot representative of the results for the four-channel, whitened EMG
amplitude estimation technique using the
OE modeling method that incorporated
the operating point into the identification
process. The model numerator order was
five and the denominator order was six.
Table 2 lists summary results from the
eight processor-model combinations. The
%VAF listed is that corresponding to the
maximum average value of all the model
orders tested. This model order is also
listed in each cell.
Average torque estimation performance using whitened EMG processors
was better than unwhitened processors,
and using four-channel processors it was
better than single-channel processors.
These results are consistent with results
from a previous experiment using
nondynamic contractions [9]. In addition,
the combination of whitening and multiple channels provided the best performance. This result is expected since both
whitening and multiple-channel EMG
amplitude estimation reduce the noise
variance of EMG amplitude. Their combination provides a cumulative benefit [8].
Hence, the input to the system identification process has less noise.
The “AC Model” was investigated
since it is common in system identification studies to separately model the ac and
dc characteristics of a system. Doing so
removes the influence of the system’s operating point (the dc component of the signals) on the system’s dynamics (the ac
components of the signal). Of course, after estimating the ac response, a complete
response is found by combining the estimated ac and dc responses. Only the ac
portion of the response was studied here.
For OE processing, the ac models all had a
higher average %VAF than the full
model. Since the dc component can more
accurately be modeled with a nonlinear
model [9], it may be worthwhile in the future to consider nonlinear dynamical system models. One such system would be to
combine a dc model (e.g., [9]) with the ac
models reported above. Many other options are available.
Table 2 also lists the number of nonconvergent trials for each of the reported
%VAFs. There were a total of 80 trials
available per cell (16 subjects times five
November/December 2001
training set trials per subject). For these
trials, the system identification algorithms were unable to find a global minimum solution for the model parameters.
In these cases, no test result is reported
for that trial-processor-model combination. As can be seen from the table, nonconvergence was less of a problem with
the ac model. There are several issues related to nonconvergence that warrant further investigation in this EMG-torque
application, including: selecting a contraction bandwidth that sufficiently excites the system to be identified,
appropriate model order selection, appropriate selection of an initial solution
in the OE model, duration of the training
contraction, and the extent of co-contraction exhibited by the subjects.
Summary
The sections above have described an
EMG amplitude estimator and an initial
application of this estimator to the
EMG-torque problem. The amplitude estimator consists of six stages. In the first
stage, motion artifact and power-line interference are attenuated. Motion artifact
is typically removed with a highpass filter. Elimination of power-line noise is
more difficult. Commercial systems tend
to use notch filters, accepting the concomitant loss of “true” signal power in exchange for simplicity and robustness.
Adaptive methods may be preferable,
however, to preserve more “true” signal
power. In stage two, the signal is whitened. One fixed whitening technique and
two adaptive whitening methods were described. For low-amplitude levels, the
adaptive whitening technique that includes adaptive noise cancellation may be
necessary. In stage three, multiple EMG
channels (all overlying the same muscle)
are combined. For most applications, simple gain normalization is all that is required. Stage four rectifies the signal and
then applies the power law required to demodulate the signal. In stage six, the inverse of the power law is applied to
relinearize the signal. Direct comparison
of MAV (first power) to RMS (second
power) processing demonstrates little
difference between the two. Therefore,
unless there is reason to believe that the
EMG density departs strongly from that
found in the existing studies, RMS and
MAV processing are essentially identical. In stage five, the demodulated samples are averaged across all channels and
then smoothed (time averaged) to reduce
the variance of the amplitude estimate,
but at the expense of increasing the bias.
For best performance, the window length
that best trades off variance and bias error is selected.
The advanced EMG processing was
next applied to dynamic EMG-torque estimation about the elbow joint. Results
showed that improved EMG amplitude
estimates led to improved EMG-torque
estimates. An initial comparison of different system-identification techniques
and model orders was reported. It is expected that these advanced processing
and identification algorithms will also
improve performance in other EMG applications, including myoelectrically
controlled prostheses, biofeedback, and
ergonomic assessment.
Table 2. EMG-torque estimation results for the 1-Hz bandwidth trials for
the four EMG processors and the two modeling techniques, in %VAF.
Each result cell lists 1) %VAF: the mean ± standard deviation percent variance accounted for (%VAF), 2) the model order, and 3) nonconvergent trials: the number of contraction trials (out of 80 total) omitted from the
%VAF result because the training model did not converge. Symbol nb is
the numerator model order and symbol nf is the denominator model order.
Model
EMG Processor
Single
Channel
Multiple
Channel
Single
Channel
Whitened
Multiple
Channel
Whitened
OE
%VAF
n b / nf
Nonconvergent Trials
75.7 ± 20.2
6/4
20
82.0 ± 14.2
4/4
16
81.7 ± 12.7
5/3
19
85.4 ± 11.1
5/6
20
OE (AC Model)
%VAF
n b / nf
Nonconvergent Trials
81.5 ± 15.6
½
6
84.8 ± 13.6
2/2
8
84.7 ± 13.4
4/2
7
87.2 ± 12.4
6/2
6
IEEE ENGINEERING IN MEDICINE AND BIOLOGY
53
Edward (Ted) A.
Clancy received the
B.S. degree from
Worcester Polytechnic Institute (WPI)
and the S.M. and
Ph.D. degrees from
the Massachusetts Institute of Technology,
all in electrical engineering. He spent 12
years in industry as an engineer and research scientist for medical instrumentation and analysis companies interested in
EMG, EEG, ECG, blood pressure, and
ergonomics, and as a radar engineer at
Raytheon Company. He is an associate
professor in the Department of Electrical
and Computer Engineering and the Department of Biomedical Engineering at
WPI. He is interested in signal processing, stochastic estimation, and system
identification, particularly as applied to
problems in medical engineering and human rehabilitation. (www.wpi.edu/~ted,
www.ece.wpi.edu/Research/csp2)
Stéphane Bouchard
received the B.Sc. degree in mechanical engineering in 1998
from Laval University, PQ, Canada. He
received the M.Sc.A.
in mechanical engineering (with a concentration in bioengineering) at the same
university in 2001. His thesis subject was
the dynamic relationship between biceps-triceps EMG and the torque produced during constant-angle contraction
of the elbow. His principal interests include system identification, control, signal processing, modeling, real-time
programming, and data acquisition. Currently, he is working in the aerospace industry for MDS Aero Support Corp., ON,
Canada.
Denis Rancourt received the B.Sc degree
in mechanical engineering in 1986 from
Laval University, PQ,
Canada. He received
the M.Sc.A. in mechanical engineering
at École Polytechnique de Montréal in 1989, and the Ph.D.
degree in mechanical engineering at the
Massachusetts Institute of Technology in
1995. He holds an associate professor appointment in mechanical engineering at
54
Laval University and is director of the bioengineering laboratory in the same department. He is currently on sabbatical
leave at the Euros R&D department, a
French orthopaedic designer and manufacturer. His interests cover tissue engineering, human factors, design, modeling, and control of physical systems,
with an emphasis on the musculo-skeletal system and orthopaedic implants.
(www.gmc.ulaval.ca/labos/bioing/)
Address for Correspondence: Edward
(Ted) A. Clancy, Department of Electrical
and Computer Engineering, Worcester
Polytechnic Institute, 100 Institute Road,
Worcester, MA 01609. Tel: +1 508 831
5778. Fax: +1 508 831 5491. E-mail:
[email protected].
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November/December 2001