Exp Brain Res (1992) 91:509-519
Experimental
BrainResearch
9 Springer-Verlag1992
Effects of weak antagonist
on fast elbow flexion movements in man
M. Margaret Wierzbicka and Allen W. Wiegner
Spinal Cord Injury Service, Brockton/WestRoxburyVA Medical Center, i400 VFW Parkway, Boston, MA 02132, USA and Department
of Neurology, Harvard Medical School, Boston, MA 02132, USA
Received October 4, 1991 / Accepted May 12, 1992
Summary. By using a mathematical model and experiments involving electrical simulation of antagonistic
muscles, we have formed the hypothesis (Wierzbicka
et al. 1986) that in one-joint movements the antagonist
muscle not only provides braking torque but also controis movement time. To get additional experimental
support for this hypothesis, we studied elbow flexion
movements performed by patients with spinal cord injury at the C 5 6 level who had relatively normal strength
in their biceps muscle and little or no voluntary control
of the triceps. Seven quadriplegic patients and six control
subjects performed elbow flexion movements of 10~, 20~,
and 30~ "as fast and accurately as possible". Despite
the lack of antagonist, patients used the same "pulse
height" strategy as control subjects to scale their responses with movement amplitude. However, patients'
movement time was on average twice that of control
subjects, and durations of both accelerative and decelerative phases of movement were increased. Movement
speed and acceleration were reduced to 20-50% of the
corresponding values of control subjects. Patients tended
to overshoot the target to a larger extent than control
subjects, particularly 10~ targets, with nearly twice the
error. We performed the same experiments using an external torque motor to assist the weak triceps. When
a constant extensor torque of 2.5 or 5 Nm was provided
by the motor, patients were able to move faster, and
movement accuracy improved to within the normal
range. These results provide direct evidence that the lack
of an antagonist has an important effect on completion
time and accuracy of fast goal-directed movements.
Key words: Voluntary movements - Antagonist muscle
- Quadriplegia - Human
Correspondence to:
M. Margaret Wierzbicka
Introduction
It is obvious why we need our triceps muscle, the primary elbow extensor, to extend our arm and reach overhead, but it is more difficult to ascertain the full role
of the extensor muscle in controlling fast flexion movements. This problem has been widely investigated by
examining relatively simple goal-directed movements or
isometric contractions at one joint. Studies of movements under different load conditions have supported
the hypothesis that the antagonist muscle provides the
torque necessary to brake a rapid movement on reaching
a target (Lestienne 1979; Flament et al. 1984; Meinck
et al. 1984; Stein et al. 1988). However, it has also been
shown that antagonist torque often exceeds the level
needed for braking (Karst and Hasan 1987).
A number of quantitative studies have been performed to relate parameters of the antagonist electromyogram (EMG) burst, such as size and timing, to parameters of movement trajectories (displacement, velocity, acceleration) under varied task conditions. Attempts
to correlate the antagonist EMG burst size to single
kinematic parameters have shown inconsistent results,
indicating that the underlying relationship is not simple
(Hallett and Marsden 1979; Brown and Cooke 1981;
Hoffman and Strick 1990). Marsden et al. (1983) showed
that the antagonist EMG burst is a function of two
kinematic parameters, the amplitude and the speed of
movement, and varies in a nonlinear fashion with joint
rotation angle. The direct effect of the antagonist on
a movement is difficult to assess because the recorded
motion of the arm is a complex integrated function of
the activation of both agonist and antagonist muscles.
Furthermore, the antagonist is usually activated when
the limb is already moving, invoking the different muscle
mechanics involved in "lengthening'' or eccentric contractions. In view of the above limitations on assessing
the role of the antagonist in voluntary movements, exploratory studies of antagonist function have been undertaken using mathematical models (Hannaford and
510
S t a r k 1985) a n d also electrical s t i m u l a t i o n ( W i e r z b i c k a
et al. 1986).
The present study of elbow flexions in quadriplegics
p r o v i d e s a u n i q u e o p p o r t u n i t y to assess flexor f u n c t i o n
separately, an assessment that could not be made on
t h e basis o f v o l u n t a r y e f f o r t i n n o r m a l subjects. P a t i e n t s
w i t h a cervical s p i n a l c o r d i n j u r y a t the C 5 - 6 m o t o r
level t y p i c a l l y h a v e m i n i m a l loss o f s t r e n g t h i n t h e b i c e p s
muscle, may have some wrist extensor strength, and have
little o r n o v o l u n t a r y c o n t r o l o f their triceps m u s c l e .
Q u a n t i t a t i v e e v a l u a t i o n o f m o t o r deficits i n these p a t i e n t s c a n h e l p to c l a r i f y s o m e f u n d a m e n t a l issues reg a r d i n g a n t a g o n i s t f u n c t i o n . I n p a r t i c u l a r , will a l a c k
o f a n t a g o n i s t : (1) i n c r e a s e m o v e m e n t t i m e i n q u a d r i p l e g ic p a t i e n t s in c o m p a r i s o n w i t h c o n t r o l s u b j e c t s w h e n
m o v e m e n t s o f d i f f e r e n t a m p l i t u d e s are p e r f o r m e d " a s
fast a n d a c c u r a t e l y as p o s s i b l e " ; (2) affect the a c c u r a c y
o f m o v e m e n t s to a t a r g e t , after a n e q u i v a l e n t a m o u n t
o f p r a c t i c e i n p a t i e n t s a n d c o n t r o l s u b j e c t s ; (3) r e s u l t
in a different pattern of agonist muscle activation from
t h a t u s e d b y c o n t r o l s u b j e c t s to p r o d u c e fast m o v e m e n t s
o f d i f f e r e n t a m p l i t u d e ? I n a d d i t i o n , we e x a m i n e d t h e
effect o f a n " a r t i f i c i a l t r i c e p s " (a c o n s t a n t e x t e n s o r
t o r q u e p r o v i d e d at t h e e l b o w j o i n t b y a n e x t e r n a l t o r q u e
m o t o r ) o n the t i m i n g a n d a c c u r a c y o f m o v e m e n t s p r o duced by patients.
Materials
and methods
We studied elbow flexion movements in six quadriplegic patients
(average age 40) and six control subjects (average age 34). For
the purposes of this study we selected quadriplegics with injuries
at the C 5-6 level with relatively normal biceps function and little
or no voluntary control of triceps (Table 1). One additional subject
(number 7) was studied twice: 9 months after the injury, when
the triceps strength had recovered from 1/51 to 4/5 (measured as
10 Nm); and 21 months after the injury, when the triceps strength
was 5/5 (36 Nm). Because a somewhat different protocol was used
the first time subject 7 was studied, the movement-time data have
been included in Fig. 5, but the other data from this patient have
not been averaged with those of other subjects.
During the experiment, subjects were seated in a chair (or their
personal wheelchair) with their right arm supported on a table
at shoulder height, the forearm, wrist, and hand strapped to the
lever arm of a torque motor mounted below the table, its vertical
motor shaft coaxial with the elbow. Subjects viewed an oscilloscope
which displayed two horizontal lines, one with initial and then
final target levels and the other showing the subject's measured
elbow angle. The subjects were instructed to align their position
with the initial target line at the beginning for each trial and then
move "as fast and accurately as possible" to the final target position when the target line shifted. The starting and final target position were controlled by the experimenter at the computer console.
Subjects were also asked to refrain from correcting their movements once initiated.
Flexion movements of 10~ 20~ and 30~ were performed in
blocks of ten trials at each distance in semirandomized order. Final
target position was maintained at an angle of 60~ at the elbow
joint for all movements; starting position ranged from 70 to 90~
to obtain the desired distance of each movement. More extended
(beyond 90~) starting positions were unreachable by patients with
no triceps function. All subjects were allowed a period of practice
x Clinical motor grading scale: 0/5 = n o n e ; 1/5 =trace; 2/5 = p o o r ;
3/5 = fair; 4/5 = good; 5/5 = normal.
TaMe 1. Patient data
Patient
Age
(years)
1
2
3
4
5
6
7
7
Time
since
injury
(years)
45
1
64
35
21
38
38
31
32
36
13
0.3
20
16
0.8
1.8
Biceps
strength
Triceps
strength
(Nm)
(Nm)
33
4/5*
51
37
27
61
59
56
Triceps
tendon
reflex
0
-
0
1.5
0.2
7
4
10
36
+
+
+
+
* Not measured; clinical assessment
at the start of each experimental condition (0-, 2.5-, and 5-Nm
extensor torque), with frequent coaching from the investigators
to increase their speed and accuracy, until improvement in their
movement times was no longer seen. Five additional practice trials
were given each time the distance was changed. Patients performed
the first block of trials at each distance without the external torque
motor. During the second and third sets of 30 trials, 2.5 and 5 Nm,
respectively, of constant extensor torque was provided by the motor, and patients flexed against this torque. The motor was left
on continuously throughout each block of 10 trials (unless the
subject requested an extra period of rest). Control subjects also
performed a block of 30 ~ trials with a "slower, still accurate"
instruction. The torque motor was not energized in experiments
with control subjects after preliminary measurements in two subjects indicated that it had little effect on their movement parameters
(e.g., movement time 186_+ 10 ms with torque, 179__ 9 ms without
torque).
The angular position of the arm was recorded with a potentiometer attached to the motor shaft. EMG activity of biceps and
triceps muscles was recorded with surface electrodes (Liberty Mutual MYO-111 with a --3-dB bandwidth of 120~500 Hz), which
were relatively immune to motion artifacts. Data acquisition began
when the target shifted to its final position; position and two channels of EMG were sampled for 2 s at a rate of 1 kHz and were
stored on a Compaq Deskpro 386/20 computer equipped with a
Metrabyte DAS-20 data acquisition board. One second of position
and EMG data, starting 100 ms prior to movement onset, was
stored in a computer file for further off-line processing.
Maximum voluntary contractile strength was measured by having subjects pull (biceps) or push (triceps) against a fixed load
cell while in a posture similar to that used for the movement studies.
Strength was averaged over a 2-s period.
Key kinematic parameters such as peak displacement, velocity,
and acceleration; movement time; and duration of accelerative and
decelerative phases were evaluated automatically according to predefined criteria. The onset of the movement was defined as when
acceleration reached 5% of its maximum. Movement time was defined as the time from movement onset to peak displacement (the
point at which velocity returned to 1% of its maximum). Velocity
and acceleration trajectories were calculated by numerical differentiation of the position data. Gaussian smoothing (standard deviation, SD = 9; Abeles 1982) was applied after each subsequent differentiation. Errors in subjects' performance were measured as the
difference between actual peak displacement and position of the
intended target, and were expressed as a percentage of the target
amplitude. Constant errors (mean percentage overshoot) and variable errors (SD of within-subject constant errors) were evaluated
for each subject. EMG signals were rectified and smoothed (Gaussian filter, SD = 2) before manual evaluation of the burst duration
and area.
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Time (ms)
Fig. 1. Fast movements of 10% 20~ and 30~ produced by a C5-6
quadriplegic without physiological triceps (patient 1). Averaged displacement, velocity, and acceleration at each target distance
Results
i
AntQgonist
i
200
300
Time (ms)
i
400
i
500
T
600
Fig. 2. Fast movements of 10~ 20~ and 30~ produced by a control
subject showing averaged displacement (top) and acceleration (middle) at each target distance. Superimposed averaged, rectified biceps and triceps EMG at each distance (bottom). In this example,
biceps burst area increases with distance and triceps burst area
decreases with distance
Comparison of patients" movement with those
of control subjects
Muscle strength
Maximum biceps strength in control subjects ranged
from 66 to 91 N m with a mean of 78 N m ; triceps
strength ranged from 26 to 66 N m with a mean of
39 Nm. Table 1 shows that patients' biceps strength was
about half that of the control group, which may reflect
the patients' injury, difficulty in transferring their maximal biceps effort to the apparatus because of their lack
of trunk stability, or weakness secondary to lack of exercise against the triceps. Three patients had essentially
no triceps strength, three had a small fraction of normal
strength, and patient 7 returned to normal strength between the first and second test sessions. The last column
of Table 1 indicates whether a palpable triceps tendon
jerk could be elicited during examination by a neurologist.
Kinematics. Figure I shows averaged (n = 10) trajectories
of fast elbow flexion movements to the three targets
produced by a quadriplegic patient with no physiological
triceps (patient I in Table 1). A consistent feature of
each patient's movements to different targets was that
the overall shape of the trajectories was similar, with
a small increase in movement time in larger movements.
Similar scaling of movement profiles to the different targets was observed in control subjects (Fig. 2), although
movement times varied less with target distance.
Movement-time parameters for control subjects and
patients are compared in Fig. 3 and kinematic parameters in Fig. 4. Patients' movement time, on average (all
subjects and distances), was twice that of control subjects and roughly inversely related to the preserved voluntary strength of the triceps muscle (compare Table 1
and Fig. 5). Interestingly, not only was the decelerative
phase of the movements extended (on average, by a fac-
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Target (deg)
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Target (deg)
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Fig. 3. Movement time parameters of patients and control subjects
plotted versus target distance. Different open symbols are used
for each patient. Dashed lines indicate mean values for the patient
group, solM lines with filled circles show means -t-SD of control
subjects
Fig. 4. Kinematic parameters of movements plotted versus target
distance. Different open symbols are used for each patient. Dashed
lines indicate mean values for the patient group, solid lines with
filled circles show means _+SD of control subjects
tor o f 2.8), as could be expected from the weaker braking
torque involved, but also the duration of the accelerative
phase was increased (on average, 1.6 times) in comparison with control subjects (Fig. 3).
Peak velocity of patients' movements was reduced
on average (all distances) by a factor of 2; patients were
apparently forced to modulate the velocity of their
movements according to their ability to recruit braking
torque to halt the movement. Peak acceleration was reduced by a factor of 3 and peak deceleration by a factor
of 5 (Fig. 4), with the result that the acceleration profiles
of patients' movements did not attain the symmetry
characteristic of controls' fast movements (Fig. 2). Even
those patients with no active antagonist were able to
plan movements which stopped near the desired target
by relying on the passive viscoelastic torque acting at
the elbow joint, but movement speed was greatly reduced.
Errors. Constant errors (mean percentage overshoot)
and variable errors (SD of within-subject constant errors) of patients and control subjects, expressed as a
percentage of target amplitude, are shown in Table 2.
Positive constant errors indicate that control subjects
overshot the target, on average, at all movement distances. Patients had the most difficulty in controlling
the amplitude of smaller movements (10~ as both their
constant and variable errors were nearly twice those of
control subjects; these differences were statistically significant (Table 2). At 20 ~ the constant error of patients
was comparable with that of controls, but the variable
error o f their efforts, reflected in the SD, remained statistically greater (P < 0.01). At 30 ~ the differences between
controls and patients did not reach statistical significance at the 0.05 level. However, when control subjects
performed 30 ~ movements at a speed comparable with
that of the patient group (movement time 361 +_86 ms),
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Patient No
i
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i
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6
i
7
Fig. 5. Patients' average movement time (all trials) for movements
without torque (filled circle) and with 2.5-Nm (open triangle) or
5-Nm (plus) external torque. Patient numbering as in Table 1. Solid
and dashed lines are mean and mean +2 SD, respectively, of control subjects
their constant error decreased and was significantly less
than that of the patient group at the same distance (P <
0.01).
Electromyogram. Averaged surface E M G recorded from
flexor and extensor muscles is shown in Fig. 6 for movements made by patient 1, as shown in Fig. 1. The agonist
muscle was activated in a clearly defined burst of approximately 100 ms duration, with burst area proportionally adjusted to the distance (Fig. 7). An antagonist
burst was not seen, since this patient could not voluntarily activate his triceps, nor was an extensor stretch reflex
present during clinical examination. A low level of E M G
activity recorded by the triceps electrode paralleled biceps activity and was most likely volume-conducted biceps E M G (cross talk). A second agonist burst in patient
1 (Fig. 8) was seen in 21 of 30 trials and occurred 454_+
41 ms after movement onset, near the time of peak displacement (443+37 ms). Similar E M G patterns were
seen in the other two patients with functionally absent
triceps.
In patients with some triceps strength, one produced
a triphasic E M G pattern (consisting of two agonist
bursts separated by a relative silent period in the agonist,
Table 2. Movement errors
Percentage
error
during which the antagonist burst occurs), one a biphasic pattern (no second agonist burst), and the third a
biphasic pattern followed by cocontraction of agonist
and antagonist. A m o n g control subjects, E M G patterns
ranged from triphasic (Fig. 2) to biphasic with substantial cocontraction. A summary of selected E M G parameters from l0 ~ and 30 ~ movements is given in Table 3
(data from 20 ~ movements are not included since one
patient failed to complete these trials). First agonist
burst duration in all patients was like that of control
subjects making fast movements, and did not show the
increased duration characteristic of controls' slower
movements. First agonist burst area showed comparable
scaling in controls and patients. In patients with a functional but weak triceps, the width of the antagonist burst
was increased in a manner similar to that o f control
subjects making slower movements, perhaps as an accommodation to the weakness of the muscle. Antagonist
burst area appeared to change little with movement distance in both patients and controls. However, because
of the unknown spatial distribution of the remaining
active fibers within each paretic triceps muscle, and the
corresponding unknown impact on the shape of the
E M G - force relation, quantitative measures of triceps
E M G magnitude in patients are approximate.
Thus, both patients and control subjects scaled the
amplitude of the first agonist E M G burst, which had
relatively constant duration, with distance to produce
fast m o t o r responses. However, there were substantial
qualitative and quantitative differences in the kinematics
of the responses o f patients and control subjects. The
lack of a strong antagonist resulted in asymmetry of
the accelerative and decelerative phases of patients'
movements, with a substantially prolonged decelerative
phase (Fig. 1), in contrast to the approximately symmetric acceleration profiles of the fast m o t o r responses of
control subjects (Fig. 2).
Comparison of patients' movements
with and without triceps support
Kinematics. Figure 9 shows the effect of the amplitude
of artificial extensor torque on movement time, acceleration time, and deceleration time in patient 1. In this
10~ movements
Constant
Patients, 0 Nm
Patients, 2.5Nm
Patients, 5.0Nm
Controls, fast
Controls, slower
20~ movements
Variable Constant
40_+13" 30_+11'
28-+10
20_+ 5
19-+14
13_+ 3
23_+ 7
15_+ 3
18_+6
13-+7
11_+6
17_+8
30~ movements
Variable Constant
Variable
17_+3"
14-+5
12_+4
9_+3
11_+3
13_+3
9_+2
9_+5
84- 2
14_+ 9**
15_+ 9
10-+10
8_+ 6
3 _+ 3
All errors expressed as mean 4-SD. Constant error is percentage overshoot; variable error
is within-subject variability of measured constant error; SD indicates across-subjects variability of both evaluated errors
* Differs from fast movements of controls (P < 0.05, Newman-Keuls test)
** Differs from slower movements of controls (P < 0.05, Newman-Keuls test)
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Fig. 6. Averaged, rectified EMG recorded from biceps (left) and triceps (right) during fast movements of 10~ (top), 20~ (middle), and
30~ (bottom) by patient 1. Antagonist spike seen in one trial at 20~ appeared to be noise
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Fig. 8. Single trial showing two bursts of biceps EMG (top) and
displacement (bottom) from 10~ movement by patient 1
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Target (deg)
Fig. 7. First agonist E M G burst (AGI) area and duration plotted
versus target distance for patient I
p a t i e n t w i t h no p h y s i o l o g i c a l l y significant a n t a g o n i s t ,
m o v e m e n t t i m e was r e d u c e d (on average, all distances)
f r o m 446 to 310 m s w h e n 2.5 N m o f e x t e n s o r t o r q u e
was p r o v i d e d b y the m o t o r . F u r t h e r r e d u c t i o n o f the
m o v e m e n t time (to 279 ms) was o b t a i n e d w h e n e x t e n s o r
t o r q u e was i n c r e a s e d to 5 N m . E x t e r n a l t o r q u e r e d u c e d
n o t o n l y m o v e m e n t t i m e b u t also the d u r a t i o n s o f b o t h
the accelerative a n d d e c e l e r a t i v e p h a s e s o f m o v e m e n t
515
Table 3. S u m m a r y o f E M G data
Distance
Controls
(" f a s t " )
Controls
(" slower")
Patients
(" fast")
M o v e m e n t time (ms)
10 ~
30 ~
171
182
336
333
381
Agonist duration (ms)
10 ~
30 ~
93
92
165
101
105
Agonist area (% o f 30 ~ fast)
10 ~
30 ~
46
(100)
28
64
(100)
A n t a g o n i s t duration (ms)
10 ~
30 ~
122
132
162
193
201
A n t a g o n i s t area ( % o f 30 ~ fast)
10 ~
30 ~
108
(100)
28
84
000)
Selected electromyogram ( E M G ) parameters. Values are medians o f individual subject
means, n = 6, except for patient antagonist data where n = 3. E M G burst areas are normalized for each subject by dividing by the E M G area seen in 30 ~ fast m o v e m e n t s and expressing
the ratio as a percentage; thus 30 ~ fast m o v e m e n t s are defined as 100%
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i
I
i
I
i
I
500
I0
-2000
400
.,e-
oc 300
C
O
4O
"4--
O
200
-1000
@
O
I~
U
100
0
i
0
i
1 0
i
i
20
i
i
30
i
i
40
Target (deg)
Fig. 9. M o v e m e n t time p a r a m e t e r s in patient 1 before and after
implementation o f "artificial triceps". Open diamonds represent
average values in m o v e m e n t s with no external torque;filled triangles, 2.5-Nm constant extensor t o r q u e ; and filled diamonds, 5-Nm
torque
i
I0
20
Torge! (deg)
i
!
30
4O
Fig. 10. Kinematic p a r a m e t e r s o f m o v e m e n t s by patient I before
and after i m p l e m e n t a t i o n o f "artificial triceps". Open diamonds
represent average values in m o v e m e n t s with no external torque;
filled triangles, 2.5-Nm c o n s t a n t extensor torque; and filled diamonds, 5 - N m torque
516
60
Electromyogram. Figure 11 shows the effect of 5-Nm extensor torque on the averaged biceps E M G of patient
1, for comparison with Fig. 6. Two differences are clearly
observed: (1) the presence of tonic biceps E M G activity
of approximately 10-15 gV before and after the movement, in order to maintain position against the motor
torque; and (2) a dramatically larger first E M G burst
area, to accelerate the limb to the target despite the extensor torque. Of particular interest, but less obvious,
is the decline in agonist activation below the tonic level
following the first burst, which is small in 10 ~ movements
(Fig. 11, top arrow) but more obvious in 30 ~ movements
(bottom arrow). In the Discussion we will argue that
by controlling the magnitude of this "silent period",
the patient gains some control over limb deceleration.
o_
120
>
v
(D
60
bJ
"--
E
O
E~
<
{3
120
Discussion
Strength and sensory differences between patients
and control subjects
60
D
i
0
i
,
i
i
i
i
,
,
,
100 200 300 400 500 600 700 800 900
Time (ms)
Fig. 11. Averaged, rectified EMG recorded from biceps of patient 1
during fast movements of 10~ (top), 20~ (middle), and 30~ (bottom).
Arrows mark relative silent period following first EMG burst
(Fig. 9). The decrease in the decelerative phase was
larger, making patients' acceleration profiles more symmetric and similar to those of fast movements produced
by control subjects (Fig. 2; also Wiegner and Wierzbicka
1992). At the same time, peak velocity, acceleration, and
deceleration were increased (Fig. 10).
The 2.5-Nm torque yielded a clear reduction of movement time in each patient (Fig. 5); in general, the slower
the original movement time, the better the improvement.
Further reduction of the movement time with 5 N m of
torque was small and often not different from that obtained with 2.5 Nm of torque. Figure 5 also includes the
original and follow-up movement time data from patient
7, whose triceps strength recovered to essentially normal
over the course of a year. As it recovered, the patient's
ability to perform our task improved, placing the movement times within the normal range. At that point, providing external torque had no additional effect on the
patient's movement times.
Errors. When external torque was provided, patients
were able to produce more accurate 10 ~ movements, with
constant and variable movement errors statistically similar to those of control subjects (Table 2). In addition,
patients improved consistency of 20 ~ movements as indicated by the decreased variable error which was statistically indistinguishable from the control data at this distance.
In spinal cord injury at the C5 6 motor level, triceps
weakness does not occur in isolation; we should consider
the possible impact of biceps weakness and sensory deficits on our results. Despite the fact that the strength
of patients' biceps muscles was less than " n o r m a l " ,
there was no evidence that biceps strength was a factor
in this study. All patients increased their movement
speed and acceleration when they flexed against the motor torque, suggesting that quadriplegics chronically underutilize their biceps muscles because of the control
problems associated with triceps weakness.
Patients qualified for this study based on their motor
level of injury; their sensory levels were not necessarily
the same. All had some sensation on the skin over the
biceps and triceps, and all could detect changes in the
angle of their elbow joint (joint angle proprioception).
Nevertheless, all or most may have had some loss of
sensory feedback related to elbow flexion, largely from
triceps muscle spindles, although this cannot be quantified clinically. We cannot be sure that this had no effect
on movement accuracy; but the fact that patients, with
the extensor torque turned on, performed as accurately
as control subjects suggests that any proprioceptive deficit did not play a major role in this task.
Effect of missing antagonist on biceps EMG
Our experiments showed that quadriplegic subjects
" p r o g r a m m e d " their first agonist E M G burst in the
same way as control subjects making fast movements.
That is, burst amplitude was approximately scaled with
the target distance, and the width of the burst was maintained at about 100 ms (Fig. 7), in accordance with the
pulse height control strategy (Freund and Budingen
1978; Gordon and Ghez 1987a; Hoffman and Strick
1990) used by normal subjects to scale their responses
with distance. Despite the fact that patients' movements
were much slower than those of the control subjects,
517
they did not show a "slow movement control pattern"
characterized by prolonged activation of the agonist
muscle (Hallett etal. 1975; Gordon and Ghez 1984;
Mustard and Lee 1987). Furthermore, when a second
agonist burst was seen, it occurred at about the time
of peak displacement, as in control subjects. Thus the
two agonist EMG bursts in quadriplegic patients were
usually separated by a longer-than-normal silent interval
(Fig. 8).
The antagonist and movement time
Even though the first agonist burst was of normal duration, the weak or absent antagonist resulted in a substantial prolongation of movement time (Fig. 3). This prolonged movement time could be considerably shortened
by providing a constant extensor torque at the elbow
joint (Fig. 5). These results are consistent with our earlier
hypothesis, based on computer simulations, that the antagonist has a dominant effect on movement time
(Wierzbicka et al. 1986). This idea is further supported
by other investigators who have reported that the area
of the antagonist burst correlates best with the reciprocal
of movement duration/force rise time when subjects perform movements/isometric contractions of different amplitudes at various speeds (Ghez and Gordon 1987;
Hoffman and Strick 1990). The prolonged accelerative
phase of movement in quadriplegics with weak triceps
indicates that the braking torque provided by antagonist
activation contributes to the early termination of the
accelerative phase of movement, as suggested earlier by
Hoffman and Strick (1990).
Patient 7 was fortunate to regain full strength in the
triceps muscle, with no change in the biceps strength,
during the course of this study. As strength was regained,
movement times improved to within the normal range
and the external torque provided no further improvement (Fig. 5), as also seen in normal subjects. These
results provide further assurance that the differences observed in this study are in fact attributable to triceps
weakness, and not to other, unrecognized factors related
to spinal cord injury.
Braking without the antagonist
In this study we demonstrated that human subjects without a physiological antagonist can produce goal-directed
movements which rely on passive viscoelastic torque for
braking, as predicted (Lestienne 1979; Wierzbicka et al.
1986). Passive viscoelasticity provides a variable amount
of braking, depending on the velocity of the movement
and the absolute angle at movement termination (Marsden et al. 1983; Meinck etal. 1984). To minimize the
variability in the elastic component of the passive torque,
which tends to return the elbow to its neutral angle of
107+ 10~ in normal controls (Wiegner and Watts 1986)
but more flexed in patients, all movements in our experiments were terminated at the same final position, 60~
of flexion. In contrast, passive viscous torque would be
Agonist
13-
A
~0
BT
Fig. 12. Schematic illustration of net torque (shaded areas) resulting
from changes in agonist muscle torque (top heavy line) during
movements against a constant braking (extensor) torque, BT (bottom heavy line). Passive torques are not shown. + , net acceleration;
--, net negative acceleration
expected to increase with movement velocity, and our
results showed that peak deceleration did increase, although weakly, with distance and velocity (Fig. 4).
The antagonist and deceleration
Previous studies of fast motor responses of varied amplitudes have showed that the agonist EMG burst increases
in magnitude with movement/contraction amplitude
(Terzuolo et al. 1973; Hallett and Marsden 1979; Brown
and Cooke 1981; Marsden et al. 1983; Ghez and Gordon 1987; Gottlieb et al. 1989). In contrast, the antagonist burst size is not well correlated with the response
amplitude. Some authors observed small changes in the
magnitude of the antagonist burst (Marsden et al. 1983;
Ghez and Gordon 1987; Mustard and Lee 1987; Hoffman and Strick 1990), while others reported no relationship (Hallett and Marsden 1979; Wadman et al. 1979;
Brown and Cooke 1981). However, in general, it has
been observed that larger movements are characterized
by proportionally larger accelerations and decelerations
than smaller movements; therefore it was expected that
larger movements require more braking torque and
should have a larger antagonist burst than smaller movements (Flament et al. 1984; Hoffman and Strick 1986).
The lack of clear scaling of antagonist burst size with
distance, suggesting that torque produced by the antagonist is approximately constant, has been considered paradoxical (Hoffman and Strick 1990).
Our current findings show that, although an "artificial triceps" provided a constant braking torque, deceleration increased with movement amplitude. This was
because net braking torque was not constant, but varied
with changes in agonist (active) torque and viscoelastic
(passive) torque. Time-dependent changes in torque produced by contraction of the agonist include the gradual
decay of torque following the initial activtion of the agonist and the subsequent increase of torque with the next
activation of the agonist. Therefore, in trials with constant external extensor torque, our patients could control the amount of net braking torque (constant braking
torque plus viscoelastic torque minus active biceps
torque) by activation of their biceps.
This is shown schematically in Fig. 12. Prior to movement, tonic activation of the agonist maintains initial
518
position against the extensor torque. Phasic agonist activation provides net acceleration to begin the movement.
Net negative acceleration results from subsequent reduction of agonist torque below the tonic level. Finally,
a second agonist activation produces accelerative torque,
used to stabilize the limb at the target before the agonist
reverts to its final tonic activity. This apparent ability
of the motor system to learn to control negative acceleration is illustrated in Fig. 11. In 30~ movements (bottom
arrow), a substantial "silent period" is often seen following the first agonist burst, during which time the
full 5-Nm extensor torque decelerates the limb. In contrast, the full 5-Nm braking torque is not needed in
10~ movements, so the agonist remains partially active
(top arrow).
Movement kinematics also illustrate this point. We
can estimate deceleration (a) which would result from
constant extensor torque (T) applied to the elbow according to Newton's law:
a= T/I
(1)
where I ~ 0.1 kgm 2 (moment of inertia of arm plus apparatus). Therefore an extensor torque of 2.5 Nm would
produce a maximum deceleration of approximately
1500~ 2, and 5 Nm, 3000~ 2. The measured decelerations were substantially smaller for 10~ and 20 ~ movements and closer to the predicted values for 30~ movements (Fig. 10). These smaller-than-predicted decelerations must have resulted from coactivation of the agonist, as seen in Fig. 11. The modulation of the activation
of the agonist muscle, working against the constant extensor torque, allows for active control of the amount
of net braking torque. Thus it is not necessary for us
to provide a pulsatile deceleration torque, with the attendant problems of determining its timing, amplitude, and
duration for each movement. If we simply provide a
constant torque, the subject learns to control deceleration by modulation of agonist activation.
In light of this analysis, one reason for the weak correlation in normal subjects between antagonist burst size
and kinematic parameters such as peak deceleration is
that actual deceleration during a movement depends not
directly on antagonist activation but on the complex
interaction between torques produced by opposing muscles as well as passive torques. The excess of antagonist
activation above the level necessary only for braking,
reported by Karst and Hasan (1987), may be accounted
for by agonist coactivation and by the use of antagonist
torque for control purposes (regulating movement time
and limb stiffness).
The antagonist and movement accuracy
Small-amplitude movements are the most difficult to
control and are characterized by the largest relative errors, as shown previously (Sanes 1986) and in the control
group of this study (Table 2). Patients with no or weak
antagonist have even greater difficulty controlling the
amplitude of small movements, producing significantly
(P<0.01) larger constant and variable errors (Table 2).
Although errors in 30~ movements were not statistically
different in the patient and control groups, it might be
argued that patients, who moved more slowly, would
be expected to be more accurate than control subjects,
since the trade-off between speed and accuracy is a wellknown phenomenon (e.g., Meyer et al. 1982). When our
control subjects prolonged their movement time to approximate that of the patient group with no external
torque, their constant error in 30~ movements did become significantly smaller (Table 2), but their variable
error was unchanged. Since constant error is biased by
factors such as a subject's interpretation of our instructions, variable error more accurately reflects subjects'
overall control of individual movements. That variable
error of control subjects was not related to movement
speed should not be surprising, because corrective efforts, which can yield greater accuracy in slower movements, were not allowed. Similarly, the speed accuracy
trade-off does not apply to the comparison of patients'
10~ movements, performed both more quickly and more
accurately with external torque than without it, because
of the change in physical conditions in these two experiments.
Gordon and Ghez (1987b) have suggested that very
early error correction of ballistic movements may be incorporated in the generation of the antagonist burst.
If so, this might appear to be an explanation for the
poorer results obtained by our quadriplegic group, in
whom this correction mechanism is lacking. However,
when braking torque was provided by a motor, patients
were able to move faster and with accuracy similar to
that of control subjects (Table 2), even though they still
could not activate their antagonist. It may be that when
sufficient braking torque of any origin is present, accuracy can be obtained by modulating braking torque by
use of the agonist (see The antagonist and deceleration).
Further studies are needed to clarify the interaction of
accuracy, movement time, and braking torque.
In summary, the performance of elbow flexions in
C5-6 quadriplegics clearly demonstrates that the lack
of an antagonist muscle has an important effect on
movement time and accuracy of fast goal-directed movements. The perception of this by our patients is seen
in the comment of one subject, who noted that with
the loss of his triceps came great difficulty in controlling
his arm, even when the arm was used for a task where
the biceps did the work.
Acknowledgements. The authors are indebted to Dr. R.R. Young
for his encouragement and valuable comments on the manuscript.
This research was supported, in part, by a Rehabilitation Research
Fellowship award to Dr. Wierzbicka from the National Institute
on Disability and Rehabilitation Research, United States Department of Education.
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