Download an activation-recruitment scheme for use in - Research

J. B,omechan,cs
Pnnted
Vol
0021-9290192
25. No. 12. pp 1467 -1476. 1992.
Pergamon
m Great Britain
S500t.00
Press Ltd
AN ACTIVATION-RECRUITMENT
SCHEME FOR USE IN
MUSCLE MODELING
DAVID
A. HAWKINS*? and M. L. HULL~
*Biomechanics Laboratory, University of Wisconsin-Madison, 2000 Observatory Drive, Madison,
WI 53706. U.S.A. and IDepartment of Mechanical Engineering, University of California at Davis.
Davis, CA 95616, U.S.A.
Abstract-The derivation of a new activation-recruitment scheme and the results of a study designed to test
its validity are presented. The activation scheme utilizes input data of processed surface EMG signals.
muscle composition, muscle architecture, and experimentally determined activation coefficients. In the
derivation, the relationship between muscle activation and muscle fiber recruitment was considered. In the
experimental study, triceps muscle force was determined for isometric elbow extension tasks varying in
intensity from 10 to 100% of a maximum voluntary contraction (MVC) using both a muscle model that
incorporates the activation scheme, and inverse dynamics techniques. The forces calculated using the two
methods were compared statistically. The modeled triceps force was not significantly different from the
experimental results determined using inverse dynamics techniques for average activation levels greater than
25% of MVC. but was significantly different for activation levels less than 25% of MVC. These results lend
support for use of the activation-recruitment scheme for moderate to large activation levels, and suggest
that factors in addition to fiber recruitment play a role in force regulation at lower activation levels,
INTRODUCTION
Two of the greatest hindrances to predicting muscle
forces in uino are the inability to determine (1) the
relationship between electromyography (EMG) data
and the level of muscle activation and (2) the relationships between the activation level and both the number of active motor units and the force generated per
motor unit (or fiber). Many attempts have been made
to derive expressions to predict muscle force based on
muscle activation information. These include direct
relationships between recorded electromyography
data and muscle force (Zuniga and Simons, 1969;
Gottlieb and Agarwal, 1971; Bigland-Ritchie, 1981)
and muscle models incorporating activation parameters (Coggshall and Bekey, 1970; Stern, 1974;
Zahalak et al., 1976; Hatze, 1981; Baildon and Chapman, 1983; Caldwell and Chapman, 1989). Despite
these efforts, there does not exist a robust and widely
accepted method for determining either muscle activation or muscle force based on electromyography data.
Therefore, the objectives of this study were to
(1) develop an activation-recruitment
scheme for
converting EMG data into muscle modeling activation variable values and (2) to test the validity of this
scheme.
METHODS
Actitation-recruitment
scheme
Most muscle model derivations incorporate an
activation variable which is used either to modify the
force calculated based on muscle kinematics or to
Received in~nafform 8 May 1992.
f Author to whom correspondence should be addressed.
determine the number of active motor units or fibers
contributing to the force. The activation scheme presented here utilizes the input data of processed surface
EMG signals, muscle composition, muscle architecture, and the experimentally determined activation
coefficients to calculate the activation variable values
used in the muscle models of a form similar to that
given in equation (1):
F,=
i
(hi)
(F,j)
cos
@,
(1)
i=l
where
F, =
nai =
Fri =
Q=
muscle force (N),
number of activated fibers of a given type i.
force generated by each fiber type (N),
fiber angle of pennation (deg).
In equation (1) the force generated by a muscle is
expressed as the summed force of all the active fibers
within each fiber pool, adjusted for fiber orientation.
In this type of muscle model, muscles are assumed to
be composed of three fiber pools (SO-slow-twitch
oxidative, FOG-fast-twitch oxidative glycolytic, FGfast-twitch glycolytic). Activation characteristics affect
the number of active fibers (nai) within each fiber pool
and, possibly, the fiber force (Fu).
The activation scheme presented below provides a
methodology for determining ‘n,,’ based on EMG data
while making some assumptions about the relationship between fiber force and activation characteristics.
It was assumed that the amplitude of the processed
EMG signal (e) is proportional to the level of muscle
activation and, hence, the number of active fibers
within the muscle. Further, to be consistent with the
three-fiber-type muscle model, it was assumed that the
number of fibers per motor unit within a specific fiber
1467
D. A. HAWKINS and M. L. HULL
1468
pool, and the amplitude of the action potential propagated along each of these fibers, are the same, but not
necessarily the same as those from another fiber pool.
Thus, increases in muscle activation causing recruitment of a motor unit from one fiber pool may have a
different effect on the processed EMG signal compared to an increase in activation that causes recruitment of a motor unit from a different fiber pool. The
final assumntion made was that fibers from each
motor unit -are equally distributed throughout the
cross-sectional area of the muscle so that changes in
the EMG signal created by motor unit recruitment are
not the result of differences in impedance. Based on
these assumptions, the processed EMG signal amplitude may be expressed as
e= f
Ci (r&i)*
(2)
areai
area,
area,
ST
ST
=6.10x lo-’ (cm’) (Costill et al., 1976),
= 7.12 x 10m5 (cm2) (Costill et al., 1976),
=7.12 x 10m5 (cm2) (Costill et al., 1976),
= fiber specific tension (N cm - 2),
=22.5 NcmV2 (Fitts, 1990, personal communication).
Expressing the change in force as a percentage of the
maximum muscle force
9
(AF~F,,,)loo=(loo/F,,,)C(An,,)(F,,)
+(An,z)
(F,,)
where
F
mnx= pcsa (ST) cos cb
pcsa = muscle
(cm2).
V-n)1~0sQ>(5)
+ (4)
(N),
physiological
(6)
cross-sectional
area
i=l
Dividing equation (5) by equation (3) yields
@FnJJFmJ~=(loo/F,,)C(An,l)(F,l)
+@n,,W,,) + @n,,)(F,,)l cm@
Ae
Cl (An,,)+C,tAn,,)+C,(An,,)
where
e = processed and normalized EMG signal amplitude (percentage of maximum),
nai=number of active fibers within a specific fiber
pool,
Ci = activation scheme constants which account for
differences in fiber pool innervation ratios and
variations in the amplitude of the action potential propagated along the fiber.
Therefore, the change in the processed EMG signal
may be expressed as a function of the change in the
number of active fibers within each fiber pool, as given
in equation (3).
Ae= Cl (An,,) + C2 (Ana2)+ C, (An.&.
(3)
To complete the activation scheme derivation, the
activation scheme constants were determined. These
constants were determined experimentally by relating
changes in muscle force (AF,,,) to changes in the
processed EMG signal amplitude (de). Muscle force is
regulated by changes in either the number of active
fibers (recruitment) or the force generated per fiber
(rate coding). It was assumed that for large limb
muscles, rate coding plays only a minor role in force
gradation compared to fiber recruitment. Based on
this assumption and the assumptions that the fibers
were activated while near their rest length, the contraction was isometric, and that the fiber force was
constant after recruitment, the following relation applies:
(7)
If the muscle composition is known, then the experimental results (relating the percentage change in force
to the percentage change in the processed EMG signal
amplitude) may be used in conjunction with equation
(7) to solve for the coefficients C,, C, and C,. For
example, if predominately SO fibers are activated,
then changes in the force result from changes in the
number of active SO fibers.
(AF,,,/F,,,nx)l~
(l~/F,,,XAn,J
(F,i) cos Q
Ae
=
Ci(Au,i)
.
(8)
Solving for Ci,
C,=(l00/F,,,)(F,,)cos~/lK,,
(9)
where
K L= experimentally
If predominately
(AF,JF,,JlOO
Ale
determined (AFJF,,JlOO/Ae.
FOG fibers are activated, then
WWF,,3
=
(Aus2)(Ftr) cos@
C2 (An,&
* (10)
Solving for C2,
C,
= W’WmJ
V,,)
~0s
Q/K,,
(11)
where
K, =experimentally
And if predominately
determined (AF,,,/F,,&lOO/Ae.
FG fibers are activated, then
AF,=C(An,,)(F,,)+(An,,)(F,,)
+ (Ad
(Ff3)l~0s@,
Solving for C,,
(4)
C3 =(100/F,,,)(F,,)cos~)/K,
where
Fn
area,
= (area3 (ST) (N),
= fiber cross-sectional
(13)
where
area (cm2),
K, = experimentally
determined (AF,,,/F,,JlOO/Ae.
Activation-recruitment scheme for muscle modeling
For a heterogeneous muscle, equations (8)-(13) are
valid as long as the experimental values (K,, K,, K3)
correspond to activation levels causing fiber recruitment from only one fiber pool. An illustration of these
ideas is given in Fig. 1, with normalized EMG amplitude shown along the horizontal axis and normalized
force along the vertical axis. The slopes (K ,, K1, and
K3) are determined by calculating the best-fit lines for
these data over three regions of normalized EMG. The
three regions are selected such that changes in the
EMG signal are believed to be caused exclusively by
recruitment of only one fiber type.
To make the activation scheme continuous, it is
necessary to know explicitly the EMG amplitudes
$
5
a
P
r'
ec2= lOO-pcsa(pct,)(ST,)cos(D/[K,(F,,,)]
= 100-pct,/(K,).
(IS)
Values for ‘n,,’ can now be defined from equation (3):
for 0 <e < ccl,
for ec2<e<lOO,
na2=n2,
z 1;
=40-
Solving for ‘ec2’ yields
na3=o,
na3= (e-ecZ)/C,,
pCti = percentage of the muscle pcsa composed
of ‘P-type fibers.
60-
K, = pcsa (pct,NST,)cos 4/( lOO-ec2)(F,,,).
na3- -4
where
E
Similarly, if ‘ec2’ represents the activation level when
FG fibers begin to be recruited, then
na2= (e-ecl)/C,,
x (ST) cos @/(eel-0) (F,,,),
6
04)
na2- -0,
=n1,
K, =(AF,,,/JF,,,)lOO/Ae=pcsa(pct,)
60
ecl=pcsa(pct,)(ST)cos@/[K,(F,,,)]
n,, =elC,,
corresponding to the onset of recruitment from each
fiber pool. SO fibers are recruited for EMG amplitudes greater than zero. The EMG amplitudes when
FOG and FG fibers are first recruited are determined
based on knowledge of the muscle composition, specific tension, physiological cross-sectional area and the
experimental coefficients. For example, the slope K, of
normalized force versus normalized EMG is valid for
EMG amplitudes less than that amplitude which
causes all SO fibers to be recruited. Letting ccl represent the EMG amplitude at which all SO fibers become
active, then
i
E
Solving for ‘ccl’ yields
%l
4, =nl,
‘Z
1469
for ccl <e < ec2,
(16)
An example of one possible recruitment scheme
resulting from these procedures is illustrated in Fig. 2,
with normalized EMG signal amplitude shown along
the horizontal axis and the number of active fibers
within each fiber pool along the vertical axis. SO fibers
are recruited first, followed by FOG, and lastly by FG.
The EMG amplitudes ‘ccl’ and ‘ec2’ represent the
transition from recruitment of one fiber type to
another.
Methodology for determining normalized muscle EMG
The determination of an appropriate normalizing
factor for surface EMG data is not an easy task. The
EMG signal recorded using surface electrodes may be
influenced by the length and velocity of the muscle if
such factors alter either the impedance or the location
of motor units relative to the electrodes. In addition, it
is not a trivial task to define an activity that will elicit a
maximum EMG signal that may be used to normalize
other EMG signals. However, a new procedure for
determining a normalized EMG signal was developed
for just this purpose.
70-
302010
./
f
/
0
P
9
Kl
l
-/,
0.
10
,
20
,
30
,
,
40
50
, ,
60
70
,
,
60
90
'$
"2 -
6
"3-
/
l
/
l
100
EMG amplitude (% of maximum)
Fig. 1. An example of the results that might be obtained
using an experimental
approach to determine the activation
constants
(K,, K,, and KJ. Normalized
EMG is shown
along the horizontal
axis and normalized
force along the
vertical. Slopes (K,, K,, and K,) are determined
by calculating the best-fit lines for experimental
data obtained for
three activation
regions corresponding
to fiber recruitment
from only one fiber pool.
ii
is
-.-.-.-.
e-a-o-0
“I_
w_,+/++;+;;;:j
-/
f--*-*--*-*-*--*
0
10 20 30 40
50
60
70
60
90
100
EMG amplitude (Yo of maximum)
-o- na, -+- na2 -*- na3
Fig. 2. An example of one possible recruitment
sequence
resulting from the modeled activation scheme. Normalized
EMG is shown along the horizontal axis and the number of
active fibers within each fiber pool along the vertical. SO
fibers are recruited first followed by FOG and lastly by FG.
1470
HAWKINS and
D. A.
male volunteers between the ages of 22 and 41 (mean
age, weight, and height being 27.6 yr, 736 N and
1.78 m, respectively) participated in this study. All the
subjects were in good physical condition. The test
protocol was explained to each subject prior to the
experiment and they were given the opportunity to
stop the testing at any time.
In this study, the triceps brachii (TB) force was
determined, using both the muscle model [equation
(l)] and another direct approach based on rigid-body
dynamics, as subjects performed isometric elbow extension efforts varying in intensity from 10 to 100% of
a maximum voluntary contraction (MVC). To determine TB force based on either approach required
information specific to that approach. The procedures
utilized to obtain this information are discussed
below.
One objective of the test procedure was to position
the subject such that only the TB muscle would
contribute to elbow torque during the elbow extension
test protocols described below. To achieve this objective, the subject reclined in a specially designed chair
with his right upper arm directed posterior to the torso
and supported by a wooden brace (see Fig. 3). This
arm position was selected based on pilot work which
indicated that this position isolated the elbow joint
and prevented other structures from contributing to
the torque recorded by the Cybex machine.
Signals from three sources were recorded to determine TB muscle force using both the muscle model
and the second direct approach. A Cybex dynamometer provided a-voltage output proportional to the
elbow torque. Two EMG circuits provided the remaining signals recorded. The Cybex output was also
The determination of the EMG normalizing factor
involved four steps. In the first step of the procedure,
the specific muscles to be studied were identified along
with the joints they spanned. The second step required
identification of the segment kinematics produced by
the subject during the activity studied. The subject
performed the activity or task of interest while appropriate data (i.e. film, video, or goniometer, and EMG)
were recorded to allow the determination of segment
kinematics and periods of muscle activity. During
periods of muscle activity, the kinematics of the joints
the muscles of interest spanned were identified. In step
three, to account for changes in the EMG signal
created by changes in the impedance caused by the
limb kinematics, maximum-effort exercises were performed by the subject while maintaining similar limb
kinematics to those recorded for the movement in
question. Several exercises were tried, to determine
which one elicited the maximum EMG signal for each
of the muscles considered. In step four, a maximum
EMG value was determined by calculating an average
root-mean-square (RMS) EMG from the maximumeffort exercises. The maximum RMS EMG value was
subsequently used to normalize instantaneous RMS
EMG values determined for the movement task being
studied to give the normalized EMG signal amplitude
(e). This procedure yielded instantaneous EMG amplitudes which were used in the activation scheme to
determine kp;.
Experimental
M. L. HULL
verification
An experimental study was conducted to test the
validity of the activation scheme presented above. Ten
Data acquisition
computer
EMG cables
A
r-h-
Signalconditioningcircuit
Interface panel
Potentiometer
cable\
2
Cybex con1
A[-
dynamometer “‘““?“”
Torque output
I
I
\
1
oscilloscope
Fig. 3. The subjSct/equipment setup used in the elbow extension study.Elbow moments were determined
from data recorded using a Cybex dynamometer. The levels of triceps brachii activation were recorded using
surface electrodes.
1471
Activation-recruitment scheme for muscle modeling
input to an oscilloscope, which provided feedback to
the subject and identified the level of torque being
generated as a function of his maximum value. Cybex
dynamometer
and EMG amplifier outputs were
sampled at loo0 Hz and converted to digital signals
using a Metrabyte A/D converter. These signals were
then processed using specially designed software to
determine joint torques and normalized TB EMG
amplitudes.
Triceps brachii force (Fmode,)was calculated using
the activation scheme and the muscle model [equation
(l)]. Model input quantities (i.e. muscle composition
and pennation angle at rest length) were taken from
the literature and ‘pcsa’ values calculated. Triceps
brachii pennation angles and muscle composition
were assumed to be similar among the subjects. The
average data for these values were taken from the
work of Amis et al. (1979) and are shown in Table 1.
Since all subjects generated different levels of torque,
and accurate measures of muscle physiological crosssectional areas (pcsa) were not obtainable, pcsa values
were determined based on individual maximum TB
force calculated using equation (6) for the elbow flexed
to 75”. It was assumed that the medial and lateral
heads had similar ‘pcsa’, while the long head was 1,386
times larger (Amis et al., 1979). It was assumed that
optimal muscle length for the TB muscle occurs at a
joint angle of 75” of flexion.
The activation scheme used to estimate the number
of active fibers within each fiber pool required as input
the TB EMG amplitudes. These values were determined using surface electrodes and appropriate amplification and signal processing. Prior to attaching the
electrodes to the skin covering the TB, the posterior
portion of the subject’s upper arm was shaved and
lightly abraded to remove dead skin. Three Ag-AgC1
surface electrodes (supplied by In Vivo Metric) were
then secured to the skin covering the lateral and
medial heads of the TB muscles. The electrodes had an
outer diameter of 12.5 mm, with a sensor diameter of
6mm. The electrodes were applied to the skin with a
center-to-center spacing of approximately 2.5 cm. The
middle electrode was used as a ground (or reference)
electrode. Prior to digital sampling of each EMG
signal, the signal was amplified and filtered. Muscle
action potentials were amplified and high-pass-filtered
with a small signal conditioning circuit located within
1Ocm of the electrode sensing elements. The signal
conditioning circuit incorporated an amplifier with a
gain of approximately 850, and an RC high-pass-filter
with a cutoff frequency set to 33 Hz. Further processing involved the calculation of an average rootmean-square (RMS) EMG value as previously discussed. The average RMS EMG values were normalized with respect to similar values determined for
maximum efforts.
To determine whether the three heads of the TB
(medial, lateral, and long) acted independently or
together during the elbow extension tasks studied, a
preliminary study was conducted. In this study, EMG
signals from all three heads of the TB were recorded as
a subject performed isometric elbow extension tasks of
varying intensities. Paired r-test statistical analyses
were performed on combinations of TB EMG data
consisting of the medial and long heads, lateral and
long heads, and medial and lateral heads. The results
from these analyses indicated that there were no
significant differences between the activation levels of
the medial and long heads (p=O.20), but that there
were significant differences between the lateral and
both the medial and long heads (p = 0.002 and 0.0007,
respectively). Therefore, to reduce the amount of data
collected, only the medial and lateral heads were
monitored and the long-head activation was assumed
to be similar to that of the medial head.
The modeled force-EMG relationship was evaluated over the entire range of effort levels. With the
elbow at 75’ of flexion the subject was instructed to
provide a maximum isometric effort, while monitoring
the maximum Cybex dynamometer voltage output as
displayed on an oscilloscope. The data from three
trials were then recorded at the following effort levels:
10, 20, 30, 40, 50, 60, 70, 80, 90 and 100% of the
maximum torque. The subject was asked to perform
isometric efforts to maintain the oscilloscope trace at
different levels corresponding to the above-mentioned
percentages of the maximum efforts. Data were
sampled for 0.5s and averaged for each trial. EMG
data were normalized with respect to values determined for the maximum effort trials. Activation
scheme coefficients were determined based on the
procedures outlined previously, with the exception
Table 1. Quantities used to describe the triceps brachii design. Architecture data were
taken from Amis et al. (1979), and composition data from Johnson et al. (1973). These data
were used as input to the muscle model
Triceps brachii muscle
Medial head
Structure
Pennation angle (deg)
SO fibers (% by area)
FOG fibers (% by area)
FG fibers (% by area)
Unipennate/couples
13.2
33.0
35.0
32.0
Lateral head
Unipennate/couples
11.9
33.0
35.0
32.0
Long head
Bipennate
15.7
33.0
35.0
32.0
D. A. HAWKINS
and M. L. HULL
1472
that an average EMG value was utilized. The average
EMG was defined as
average EMG = [EMGmcdial(pcsamsdis3
+ EMGlatcral(PCsalntcral)
+
EMGlonptPCSalon~l/PCsatotsl,
(17)
where
EMG,,,,,,
= average normalized RMS EMG for
the medial triceps brachii,
EMG,.w =average normalized RMS EMG for
the lateral triceps brachii,
EMG,,,,
= average normalized RMS EMG for
the long triceps brachii,
pcsa,_,ia, =pcsa of the medial triceps brachii
(cm2),
pcsalstcrPl = pcsa of the lateral triceps brachii (cm2),
=pcsa of the long triceps brachii (cm2),
I=aloog
= total pcsa of triceps brachii (cm2).
pcsaI.,.l
Recall, that an experimental approach was needed
to determine the activation constants (K r, K,, KS). K i
represented the ratio of the change in normalized
muscle force to the change in normalized EMG for
effort levels causing recruitment of SO fibers. K, and
Ks were defined similarly, with the exception that they
pertained to effort levels causing recruitment of FOG
and FG fibers, respectively. To determine these ratios
for this study, both ‘Fcybex) and the average EMG
[equation (17)] were determined for each effort level
tested. Linear regression analyses were performed to
determine the equations that described best ‘F,ybex) as
a function of average EMG for three effort level
ranges. Each effort level range was considered to cause
recruitment of one fiber type only. Effort level ranges
analyzed were O-25, 3565, and 75-100% of MVC.
The slopes of the lines determined for each of these
ranges were taken as K,, K,, and K,, respectively. To
assess how well these constants described the experimental data, the correlation coefficients were calculated for each regression equation. Activation constants were utilized to determine the activation scheme
coefficients (C,, C,, C,) as expressed in equations
(9)-(13), and activation/fiber recruitment transitions
(ccl and ec2) as expressed in equations (14) and (15).
In the second approach used to determine TB
muscle force, rigid-body dynamic analysis techniques
were used in conjunction with Cybex torque data to
calculate TB force (Fcybcx) directly. A free-body diagram of the lower arm is shown in Fig. 4. The
equations describing the rotational dynamics of this
segment are given in equation (18):
(Fcybcr)(rr) +(sw) (CGL) (cos 0) - (Tcybcr)= Iu,
(18)
where
F cybsx
=
rT
=
triceps brachii force determined from Cybex torque (N),
triceps brachii moment arm length (cm),
it
CGL
-+I
Fig. 4. Free-body diagram of the forearm. See text for
symbol definitions and the derivation used to determine
triceps brachii force.
=bwer arm plus hand segment weight (N),
SW
CGL =distance to center of gravity of combined
lower arm and hand from elbow joint
center (cm),
=angle of lower arm relative to horizontal
0
(deg),
T cJbcl =cybex Torque (N cm),
= combined lower arm and hand moment of
I
inertia about elbow joint center (kg cm2),
= lower arm angular acceleration (rad s- 2).
a,
In the derivation of equation (18), it was assumed that
the TB muscle generated the majority of elbow extension torque. All tests conducted in this study were
isometric; hence, la, was set equal to zero. Equation
(18) may be rearranged, expressing TB muscle force as
a function of the other parameters as shown in equation (19):
F cybcx= [~yt.c. -SW (CGL) cos @l/r,.
WI
Variables appearing on the right hand side of
equation (19) were determined either experimentally
or from previously published data. ‘Tcybcx’was determined from the output of the Cybex dynamometer. An
average torque was determined for a 5OOms interval
for each trial. The joint angle (0) was maintained at
75” of flexion. Triceps brachii moment arm data (rT)
were taken from the work of Amis et al. (1979) (see
Table 2). The combined forearm plus hand weight (SW)
and center of gravity location were determined from
subject anthropometries and the work of Plagenhoef
(1983).
The Cybex machine was calibrated prior to each
day of testing and the calibration information was
confirmed at the end of testing. The linearity of the
Cybex torque calibration was always very good
(T> 0.99).
The validity of the activation scheme utilized in the
muscle model was tested by comparing Fmode, to
F cybcx.The results from the subject sample (n= 10)
were pooled and analyzed using a two-sided paired
t-test statistical analysis procedure. In general, the null
hypothesis tested was
(Fcybex- Fmo~c,)= 0.
(20)
Activation-recruitment
scheme for muscle modeling
1473
Table 2. Triceps brachii moment arm lengths and the amount muscle lengths change as a
function of elbow flexion angle. Full extension is represented as an angle of 0”. Moment
arm lengths were taken from the work of Amis et al. (1979). Changes in muscle length
represent the increase in muscle length as the arm is flexed from full extension to the
specified angle. These data were taken from four cadaver specimens as discussed in the
text. Also indicated are standard deviations for the muscle length change data
Joint angle (deg)
10
30
60
75
90
115
Moment arm length (cm) of
triceps (Amis et al., 1979)
2.40
2.58
2.10
2.10
1.97
1.70
Mean change in triceps
muscle-tendon length with
flexion from full extension (cm)
(from skeletons n = 4)
0.7
1.4
2.1
2.9
3.4
3.8
Standard deviation of length
change estimates
0.2
0.6
0.3
0.1
0.2
0.5
hypothesis was rejected (p < 0.001). For average EMG
amplitudes greater than 25% of maximum, the null
hypothesis was not rejected (p = 0.47) and the power of
the test was found to be -0.94. These results lend
support to the activation scheme used in the model for
intermediate and large EMG amplitudes, but not for
small amplitudes.
Bi
0
II
10 20
30
I
1111
40
50
60
70
80
I
90
I
loo
DISCUSSION
EMG amplitude (% of maximum)
+ Fcybex
l
Fmodel
Fig. 5. A comparison of the experimental and modeled
triceps brachii force as a function of average EMG amplitude
for a single subject. For EMG amplitudes below 25% of
maximum, the model underestimated the force. For EMG
amplitudes above 25% of maximum there were no significant
differences between the model force predictions and the
experimental forces.
The null hypothesis was rejected for p-values less than
0.05.
RESULTS
Based on the calculated slopes of the three regions
of the normalized force-EMG curve, it was determined that the activation scheme constants K2 and K,
were the same and smaller than K,. Activation constants were found to be
K, = 1.1756,
K,=K3=0.6779.
(21)
The correlation coefficients determined for the equations incorporating the above constants were 0.70 and
0.63, respectively. An example result of Fcybcx and
F modc,as a function of average activation level for a
single subject is shown in Fig. 5.
The difference between model and experimental
data depended on the average EMG amplitude. For
small amplitudes
(e<25%
of maximum)
the null
Because of the research and clinical importance of
predicting individual muscle forces and the current
limitations in determining muscle activation levels
which affect this force, a new activation recruitment
scheme was derived. This scheme may be used in
conjunction with surface electromyography to predict
the number of active muscle fibers, which is one
important variable in fiber-based muscle models.
The derivation
of the activation-recruitment
scheme depended on several assumptions. Some of
these assumptions dealt with the relationships between a recorded EMG signal amplitude, the number
of active fibers (n,,), and the amplitude of action
potentials propagated along these fibers. Formulating
this relationship was based on an understanding of the
properties of the EMG signal. The electromyogram is
the electrical manifestation of the neuromuscular activation associated with a contracting muscle. It is a
complicated signal which is affected by the anatomical
and physiological properties of the muscles, the control scheme of the peripheral nervous system, as well
as the characteristics of the instrumentation
used to
detect it. The signal develops when an action potential
of sufficient magnitude propagates down a motoneuron. All the muscle fibers associated with that
motoneuron are activated, resulting in the propagation of an action potential along the length of each
fiber. In general, depolarization of the muscle fibers of
one motor unit overlap in time with those of other
motor units. Hence, the resultant signal present at a
1474
D. A. HAWKINSand
detection site constitutes a spatial-temporal
superposition of the contributions of all individual action
potentials and is random in nature (Basmajian and
DeLuca, 1985). Because the EMG signal is a superposition of individual action potentials, the signal
detected by a particular electrode installation will be
affected primarily by changes in the number of active
fibers and the amplitude of the action potential created by each fiber. This result occurs provided that
fibers from any single motor unit are distributed
evenly throughout the muscle cross-sectional area so
that changes in the EMG signal are not the result of
differences in impedance. Evidence to support this
idea has been found in both human studies (Johnson
et al., 1973) and cat studies (Burke and Tsairis, 1973).
Based on the three-fiber-type muscle model, it was
also assumed that the amplitude of the action potential and the motor unit innervation ratio are the same
for motor units within a specific fiber pool. Burke and
Tsairis (1973) examined the medial gastrocnemius
muscle of cats and found that the fiber cross-sectional
areas were different between fiber types, with mean
values being 1734,2890, and 5290pm’ for SO, FOG,
and FG fibers, respectively. Olson et al. (1968) studied
the triceps surae muscle of cats and showed that the
fiber diameter influences the recorded EMG amplitude. Data from these two studies support the assumption that different fiber types elicit different EMG
amplitudes. A review article by Buchthal and Schmalbruch (1980) gives further support for the assumptions
stated above and also provides evidence that different
motor units have different innervation ratios. Therefore, based on the results from previous studies, activation scheme constants (C,) were defined to account for
the effects that innervation ratio and action potential
amplitude have on the EMG amplitude. Through
these constants the processed EMG signal was modeled as increasing in a piecewise linear fashion with
increases in the number of active fibers as expressed by
equation (2).
To select an EMG signal processing technique
which would yield an amplitude that satisfied the
assumed linear relationship mentioned above, previously described techniques were scrutinized. Over
the past several years, several techniques have been
used to process EMG signals. Some of these techniques have included rectification, smoothing of a
rectified signal, averaging of a rectified signal, integration of a rectified signal, spike counting, root-meansquare, and power spectral density analysis. For a
detailed discussion of each of these techniques, refer to
Basmajian and DeLuca (1985). Basmajian and DeLuca
recommended that the RMS technique be used because they believe it provides more information about
muscle activation compared to other methods. They
reported that the RMS method is unaffected by the
cancellation due to motor unit action potential train
superposition, which does affect other processing techniques involving rectification. This method was selec-
M. L. HULL
ted based on the idea that motor unit action potential
cancellation might degrade the desired linearity.
Another assumption was that fiber recruitment
provided the primary means of muscle force regulation with rate coding playing only a minor role. The
two primary means of force gradation are fiber recruitment and rate coding. The first method, fiber recruitment, takes place in a predictable manner. The size
principle put forth by Henneman et al. (1965) states
that motor units are recruited in a rank order, dependent on the size of their motoneuron. Large motoneurons have higher activation thresholds for recruitment.
Several studies have confirmed this general principle
and indicate that slow-twitch fibers are recruited first,
followed by FOG, and lastly FG (Henneman et al.,
1974; Budingen and Freund, 1976; DeLuca et al., 1982;
Armstrong and Laughlin, 1985; Zajac and Faden,
1985). Slow-twitch fibers tend to be smaller and are
innervated by neurons of a smaller size than the larger
fast-twitch fibers. Thus, slow-twitch motor units have
slower conduction velocities and lower activation
level thresholds.
Kanosue et al. (1979) tested the brachialis muscles in
human subjects and found that recruitment was the
major source of force gradation for effort levels up to
70% of maximum voluntary contraction (MVC). For
the deltoid muscle, DeLuca et al. (1982) showed that
recruitment was responsible for force gradation for
activation levels between 40 and 80% of MVC.
Hennig and Lomo (1987) investigated fast and slow
motor units of cat muscles. In contrast to the results
given above, they suggested that fiber recruitment is
the primary means of force gradation for SO and FG
motor units, but that FOG fibers are recruited at
frequencies less than optimal, thus allowing rate coding to contribute to force gradation for these fibers.
Although a review of the literature does not reveal a
single relationship between force gradation within a
specific fiber pool and recruitment/rate coding interactions, it does suggest that the principle mechanism
for force gradation by large limb muscles is recruitment.
Several other assumptions stemmed from the assumption inherent in fiber-based muscle models that
the muscle can be considered to be composed of three
specific fiber types. To be consistent with this assumption, the activation threshold and innervation ratio of
motor units within a given fiber pool were assumed to
be similar. In reality, a continuum probably exists for
both the amplitude of the action potential propagated
along the fiber and the innervation ratio. The use of
specific values for each fiber pool represents a tradeoff
between model complexity and predictive accuracy.
The validity of the activation-recruitment
scheme
was tested using an experimental elbow extension
protocol and comparing the modeled TB force to the
force calculated using inverse dynamics techniques. In
addition to the assumptions stated above, several
other assumptions were required for utilization of the
Activation-recruitment
muscle model in this application. The TB composition, pennation angle, and rest length were assumed to
be similar among subjects. These values probably
varied between subjects; however, the statistical analysis procedures were designed to account for these
intrasubject variations.
Triceps brachii rest length was assumed to occur
when the joint was flexed to 75” of flexion. This
assumption stemmed from the belief that the body
matches the full range of the force-length relationship
to the full range of joint motion. For example, the full
range of elbow flexion is around 140”. For a range of
motion of 140’, the TB length changes by 5 cm
(extrapolating from data presented in row 2 of Table 2
discussed below). Thus, to match the force-length
curve to the full range of motion requires that rest
length occurs when the muscle length is 2.5 cm greater
than that at full extension. Again referring to Table 2,
this length occurs for a joint flexion angle near 75”.
To utilize the inverse dynamics technique for determining TB force it was assumed that only the TB
contributed to the joint torque. This was considered a
valid assumption due to the smaller pcsa and the less
advantageous line of action of other muscles crossing
the elbow. In addition, the arm position depicted in
Fig. 3 was selected based on pilot work which indicated that this position prevented other structures
from contributing to the torque recorded by the Cybex
machine during the elbow extension effort. Additionally, during pilot studies, the EMG amplitude of
the biceps brachii was recorded as subjects performed
maximum-effort elbow extension tasks. The results
showed the biceps brachii to be activated less than 5%
of MVC.
The final assumptions in the experimental protocol
were that the average EMG amp: rude in the range
O-25% of MVC, 35-65’~ of MVC, and 75-100% of
MVC represented recruitment of only SO, FOG, and
FG fibers, respectively. If the rank order of recruitment ideas of Henneman et al. (1974) are correct, then
these assumptions seem reasonable for an average TB
composed of 33% SO fibers, 35% FOG fibers and
72% FG fibers (Table 1).
Despite
the assumptions
inherent
in the
activation-recruitment
derivation and testing protocols, the force-EMG results lend support to the use
of the activation scheme presented here for moderate
to large EMG amplitudes, but not for small amplitudes. Recall from the activation scheme derivation
that force gradation may be regulated by either increasing the number of active fibers, or increasing the
force generated by active fibers by increasing the
stimulation frequency (i.e. rate coding). In the model
derivation it was assumed that rate coding was only a
minor factor in force gradation of large limb muscles.
11appears from the results of this study that this is an
inappropriate assumption for low activation levels.
These data suggest that for low activation
(indicative of SO fibers generating the observed
1475
scheme for muscle modeling
levels
force),
motor unit recruitment does not act alone to increase
the force. It may be that a large percentage of the
overall number of SO motor units have low activation
thresholds, hence being recruited at low activation
levels. Upon initial recruitment, these fibers may be
stimulated at a frequency which does not cause the
fibers to generate their maximum force. The large
number of initial motor units recruited could cause the
actual muscle force to be higher than that predicted by
the muscle model. Indeed, this is the response that was
observed. This response suggests that motor unit
recruitment is the major mode of force gradation for
activation levels causing the activation of FOG and
FG fibers, but not of SO fibers. Thus, the activation
scheme used in the muscle model provides accurate
results for activation levels causing recruitment of
FOG and FG fibers, but causes the muscle force to be
underestimated when only SO fibers are active.
Because the results suggest that rate coding may act
to regulate muscle force at low activation levels, it is
useful to consider how the effects of this phenomenon
might be included in the model. Rate coding effects
can be accounted for in the muscle force calculations
by either (1) adding an offset value for the number of
active fibers at low activation levels, or (2) performing
additional processing of the EMG signal and including an additional variable in the muscle model derivation. The EMG signal could be processed using
Fourier transforms to determine the frequency content of the signal. Since rate coding affects fiber force,
an additional variable and relationship could be added to define ‘Fl; in the muscle model derivation.
The value of the activation-recruitment
scheme
presented here lies in its mathematical formulation
[equation (3)]. This equation is based on the fundamental principles which relate the processed EMG
signal to the number of active muscle fibers through
constants (C,). These constants represent the effects
due to tissue impedance and the amplitude of the
propagated action potential, which depends on the
fiber diameter. In this study these constants were
specified after determining experimental constants
(Ki). The need to determine the experimental constants required that changes in muscle force for given
changes in the processed EMG signal be obtainable
for the muscle to be studied. Ideally, it is desirable to
determine the constants Ci independently of the experimental constants. This appears feasible, pending
results from further research designed to identify the
individual effects that tissue impedance and fiber
diameter have on these constants.
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