1Departamento de Fisiologia e Biofísica, Universidade Estadual de Campinas, Cidade Universitaria Zeferino Vaz., CEP 13.081-970 Campinas, SP Brazil; 2School of Kinesiology (M/C 194) and 3Department of Psychology, University of Illinois at Chicago, Chicago 60680; 4Department of Neurological Sciences, Rush Medical College, Chicago 60612; and 5College of Health and Human Development Sciences, University of Illinois at Chicago (MC 898), Chicago, Illinois 60612-7251
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ABSTRACT |
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Almeida, Gil Lúcio, Daniel M. Corcos, and Ziaul Hasan. Horizontal-Plane Arm Movements With Direction Reversals Performed by Normal Individuals and Individuals With Down Syndrome. J. Neurophysiol. 84: 1949-1960, 2000. We examined the systematic variation in shoulder and elbow torque, as well as movement kinematics, for horizontal-plane arm movements with direction reversals performed by normal individuals and individuals with Down syndrome. Eight neurologically normal individuals and eight individuals with Down syndrome performed horizontal, planar reversal movements to four different target locations. The four locations of the targets were chosen such that there is a systematic increase in elbow interaction torque for each of the four different target locations. This systematic increase in interaction torque has previously been shown to lead to progressively larger movement reversal errors, and trajectories that do not show a sharp reversal of direction, for movements to and from the target in patients who have proprioceptive abnormalities. We computed joint torques at the elbow and shoulder and found a high correlation between elbow and shoulder torque for the neurologically normal subjects. The ratio of joint torques varied systematically with target location. These findings extend previously reported findings of a linear synergy between shoulder and elbow joints for a variety of point-to-point movements. There was also a correlation between elbow and shoulder torque in individuals with Down syndrome, but the magnitude of the correlation was less. The ratio of joint torques changed systematically with target direction in individuals with Down syndrome but was slightly different from the ratio observed for neurologically normal individuals. The difference in the ratio was caused by the generation of proportionately more elbow torque than shoulder torque. The fingertip path of individuals with Down syndrome showed a sharp reversal in moving toward and then away from the target. In this respect, they were similar to neurologically normal individuals but dissimilar to individuals with proprioceptive deficits. Finally, we observed that individuals with Down syndrome spend proportionately more time in the vicinity of the target than normal individuals. Collectively these results show that there is a systematic relationship between joint torques at the elbow and shoulder. This relationship is present for reversal movements and is also present in individuals with Down syndrome.
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INTRODUCTION |
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The control of voluntary
movement to different regions of the workspace requires the
coordination of multiple limb segments. For example, touching one's
nose requires flexion movements of the shoulder, elbow, and wrist. The
rules that describe how muscle torques are coordinated to generate such
movements have not been extensively studied, although several
hypotheses have been advanced for how multi-degree of freedom movements
are coordinated. One hypothesis is that movement trajectories are
planned in terms of the kinematic features of the movement. Support for
this hypothesis comes from a series of studies that show that reaching
movements have certain kinematic invariances. For example, certain
types of movement have been shown to have relatively straight paths and
bell-shaped velocity profiles (Morasso 1981) despite the
fact that joint rotation varies considerably when movements are made to
different targets. These kinematic features have been accounted for by
the minimum jerk hypothesis (Flash and Hogan 1985
).
According to some models, muscle activation patterns and muscle torques are consequences of shifts in the equilibrium point of the limb to a
target (Bizzi et al. 1984
; Feldman and Levine
1995
) and are not explicitly represented in the CNS.
In contrast to hypotheses that are based on kinematic properties of
movements, it has also been proposed that movements are planned in
terms of movement kinetics. Patterns of neural excitation are planned
that produce muscle torques that generate movement (Buneo et al.
1995; Gottlieb et al. 1996a
). For example,
Gottlieb and colleagues have shown that there is a high linear
relationship between torques at the shoulder and elbow joints when the
time series of the torques at each joint are correlated. They have shown this to be the case for a variety of movements that they have
studied in the vertical plane and have referred to the linear relationship between the muscle torques of two joints as "linear synergy" (Gottlieb et al. 1996a
,b
). A close temporal
pattern for the muscle torques at the shoulder and the elbow has also
been shown by Topka et al. (1998)
for both normal
individuals and, surprisingly, for patients with cerebellar ataxia.
Gottlieb and colleagues (1997)
have also shown that the
ratio of joint torques differs systematically for movements to
different directions. To date, however, the generalizability of the
linear relationship between joint torques has not been explored for
movements performed in the horizontal plane nor has it been explored in
movements to and from a target ("reversal movements").
Individuals with Down syndrome are characterized as hypotonic, slow,
and clumsy (Anson 1992; Latash 1992
).
Muscle hypotonia is easily recognized in the first few months of life,
but no studies have related muscle hypotonia to impaired motor
performance. The fact that individuals with Down syndrome are slow has
been reported in a wide variety of cognitive and motor tasks, but no
mechanisms have been identified that explain the reasons for movement
slowness and clumsiness (Almeida et al. 2000
). One
possible explanation for the fact that they are clumsy is that they
have abnormalities in the timing of muscle activation. Whereas
neurologically normal individuals tend to activate proximal muscles
prior to distal muscles (Karst and Hasan 1991
),
individuals with Down syndrome have much greater variability in the
timing of the onset of muscle activation such that distal muscle
activation often precedes proximal muscle activation (Anson and
Mawston 2000
). A deficit in the timing of muscle activation
could lead to movements in which there is not a linear relationship
between the joint torques. A second possible explanation is that they
have a deficit in proprioception that could lead to movement
trajectories that are abnormal when individuals are asked to make
horizontal reversal movements to a target. For example, Sainburg
et al. (1995)
have observed that whereas in neurologically
normal subjects the path to a target is virtually identical to the path
back from the target when performing a reversal movement, patients with
impaired proprioception exhibit consistently different paths to and
from the target. Sainburg and colleagues attribute the "reversal
error" made by the patients in the vicinity of the target to their
inability to account for the "interaction torque" at the elbow
produced by the motion of the upper arm, whose effect is particularly
prominent near the reversal point. Bastian and colleagues
(1996)
have developed the same argument to explain why patients
with cerebellar ataxia do not follow relatively straight paths when
making pointing movements to a target.
To study the rules by which healthy individuals and individuals with
Down syndrome make reversal movements in the horizontal plane, we
analyzed a set of movements performed to four different target
locations. The movements were similar to those studied by
Sainburg and colleagues (1995) in that they were
designed to have a similar elbow excursion but a different shoulder
excursion for all four target directions; we did not, however, provide
a template for the path. First, we determined whether individuals with
Down syndrome would perform the movements with the same type of
movement path observed for patients with impaired proprioception (Ghez et al. 1990
; Sainburg et al. 1995
).
We hypothesized that instead of showing a sharp reversal of the path in
the vicinity of the target, as neurologically normal subjects do,
individuals with Down syndrome would follow a rounded path, which
results from uncompensated interaction torque, as has been observed in the case of patients with impaired proprioception. If, however, a sharp
reversal of the path was observed contrary to the hypothesis, this
would still not rule out the possibility of uncompensated interaction
torque because a nearly normal spatial path could arise from adopting
an abnormal temporal pattern that reduces the interaction torque near
the reversal point. Our second hypothesis tested this possibility.
Based on an observation by Henderson, Morris, and Frith
(1981)
that individuals with Down syndrome had difficulty
reversing direction when performing a sinusoidal tracking task, we
hypothesized that individuals with Down syndrome would pause in the
region of the target, thereby reducing the interaction torque near the
reversal point. Third, we determined whether the linear relationship
that has been observed between shoulder torque and elbow torque in
vertical plane, point-to-point movements is observed in horizontal
plane reversal movements. We hypothesized that the shoulder and elbow
torque profiles would be related linearly for individuals who are
neurologically normal but that the high degree of linearity would be
reduced in individuals with Down syndrome.
Contrary to our first hypothesis, we found that in the vicinity of the reversal point the path to the target is quite similar to the path away from the target and is characterized by a sharp reversal in direction. Also, contrary to our second hypothesis, there was no evidence of long pauses in the region of the target although individuals with Down syndrome did take longer in the target region. In support of our third hypothesis, there is a linear relationship between shoulder torque and elbow torque in neurologically normal individuals but this relationship is weaker for individuals with Down syndrome in selected regions of the workspace.
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METHODS |
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Subjects
Eight individuals with Down syndrome (DS) and eight neurologically normal (NN) individuals (4 males and 4 females in each group) were tested after giving informed consent according to Institutional Review Board protocols approved by the University of Illinois at Chicago. The two groups were matched by age and gender. The gender, age, weight, height, and the segment length of the upper-arm, forearm, and hand for each subject are presented in Table 1.
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Apparatus and task
The subjects sat in a chair positioned close to a table. The right upper arm and forearm of the subject were positioned on the table such that the right upper arm was horizontal and facing forward (adducted horizontally by 90°) as illustrated in Fig. 1. The right forearm was flexed 90° with respect to the right upper arm as illustrated in the shaded part of Fig. 1.
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In the initial position shown in Fig. 1, subjects kept their fingers extended. A metal plate was placed under their fingers at the initial position. The forearm was pronated. The wrist and the hand were immobilized with a thermoplastic splint (Aquaplast). This immobilization was necessary to match the equations used to calculate muscle torque. The trunk of the subjects was strapped in a chair to restrain movement, and the height of the chair was adjusted to keep the upper limb 10 cm above the top of the table. Even though the chair was adjusted to keep the upper limb 10 cm above the top of the table, the movement was not constrained to the horizontal plane. During the movement, the subjects had to hold their limb above the table with just the tip of the fingertip resting in the home plate. In front of the subject a target was placed in one of four different positions, all in the horizontal plane passing through the initial fingertip position. The target was made of cotton that the subjects could touch easily without any resistance. These positions were determined as follows. Four different lines were drawn through the initial starting position of the fingertip at angles of 45°. These are referred to as 135, 90, 45, and 0° in Fig. 1. Along each line, the hand of the subject was passively moved by the experimenter, until the elbow extended from the initial 90° to an angle of 135°; a small rectangular target was placed at the fingertip position. Thus movements to any of the four targets required 45° of elbow excursion into extension from the initial angle of 90°. Different target directions, however, required different amounts of shoulder excursion. We will use the terms shoulder flexion and extension as synonyms for horizontal adduction and horizontal abduction. Movements to the 135° target required shoulder flexion, movements to 90° required virtually no shoulder excursion, and movements to 45 and 0° required shoulder extension.
The subjects were instructed to position their right arm in the initial position holding the tip of the fingers in contact with the metal plate. They were then instructed to move to the target and return to the initial position "as fast as possible" on hearing a computer-generated sound along with the experimenter's command to go. As the subject's finger tip moved out of the home plate, a light was turned on at the target and stayed on until the subject had returned and touched the home plate again. Neither reaction time nor accuracy was stressed. The subjects performed movements in blocks of five trials to each target from 0 to 135°.
For the targets at 45 and 0°, the subjects were also asked to move in a time that was specified by the experimenter. The motivation for this experimental manipulation was to be able to determine whether any differences observed between individuals with DS and NN individuals were consequences of differences in movement speed. This is because it is quite possible that there is a higher correlation between shoulder torque and elbow torque for faster movements since the kinematic variables that are used to calculate the torques are larger and less influenced by noise. Subjects were instructed to move in 1.2 and 1.0 s, respectively, for the 0 and 45° target locations. For these trials, subjects were provided with movement time feedback after every trial. The feedback was based on an auditory tone that was activated when the movement was initiated and terminated when the subject reached the home plate. Subjects were told if they had reached the home plate at the correct time, too early or too late. We recorded five trials that were performed in the required movement time. Prior to data collection, subjects practiced movements in all four movement directions. The subjects had five practice trials for each target direction performed in reverse order, from 135 to 0°. They also had three to four practice trials for the controlled movement time experiments.
Kinematic recording and quantification
A two-camera Selspot motion-analysis system was used for
kinematic recording. Pairs of active markers (infrared light emitting diodes) were fixed with tape on the upper arm and forearm aligned along
the long axis of each segment. The proximal marker on the upper arm was
placed as closely as possible to the glenohumeral joint center.
Three-dimensional position data were collected for each marker at a
rate of 200 samples/s for a duration of 2 s. From these data the
orientations of the two segments were calculated off-line. Upper and
forearm orientations with respect to the mediolateral axis (Fig. 1,
x axis) in the horizontal plane are denoted by
1 and
2,
respectively, defined as positive in the counterclockwise direction.
The difference between the two angles represents the elbow angle. The
position, as well as orientation values, were smoothed in a two-step
procedure: at each sample time, a cubic polynomial was fitted to the
sample value and the two neighboring samples on each side, and the
value of the polynomial was calculated and, subsequently, each value
was replaced by the average over a 7-point window extending over three
adjacent points on each side. For each time derivative, the slope of
the cubic polynomial was calculated and was then smoothed over a
7-point window.
With the knowledge of the measured distance between the tip of the middle finger and the distal marker on the forearm, the position of this marker and the orientation of the forearm at each sample time were used to calculate the position of the fingertip. The velocity of the fingertip was calculated likewise from the derivatives of the marker position and forearm orientation. Thus we could determine the path of the tip, as well as its tangential speed, the latter being the magnitude of the velocity. Peak tangential speed of the fingertip was determined visually from a display using a cursor; two peak values were identified, one during the motion toward the target and the other during the return to the initial position. The root mean square (RMS) departure from the mean was calculated for the fingertip in the vertical (z) direction to provide an estimate of how much motion was occurring outside of the horizontal plane. We also calculated the time taken in the region of the target ("target time"). The target time was calculated from the time when the tangential speed of the finger tip dropped to 10% of its first peak to the time when it rose to 10% of the second peak. The target time can be seen in Fig. 3A.
Kinetic computation
We estimated the inertial parameters for the proximal segment
(upper arm) and for the distal segment (forearm plus hand) based on
measured values of the subject's weight and segment lengths, using the
gender-dependent anthropometric parameters provided by
Plagenhoef and colleagues (1983) and also cited by
Kreighbaum and Barthels (1996)
. The anthropometric
measures provided by Plagenhoef and colleagues (1983)
are based on NN individuals. It is well known that the morphology of
individuals with DS is different to that of NN individuals. They tend
to be heavier (Block 1991
) and shorter. However, the
ratio of limb segment lengths is the same in both normal individuals
and in individuals with DS. Paired t-tests showed that there
is no difference between the two groups of individuals for the ratio of
the upper arm length to the forearm length, t (14) = 0.581, P = 0.578, and for the ratio of the upper arm
length to the hand length, t (14) =
1.378,
P = 0.2105. The lengths of the limb segments are
presented in Table 1.
In addition to the measured lengths of the proximal and distal segments (L1 and L2 respectively, as can be seen in Fig. 1), the following inertial parameters were estimated: the masses of the segments (m1, m2), the distances from the proximal end of the segment to its center of mass (c1, c2), and the moments of inertia about the center of mass (I1, I2). Given the similarity in relative segment lengths and given that our estimates of the inertial parameters were based on actual segment lengths, we believe that the estimates are valid for both groups of individuals. Even if there are differences in density between the two groups of subjects that affect the estimates of the inertial parameters, the relative torques calculated at the shoulder and elbow would not be affected.
At each moment of time and for each segment, given the current coordinates of one of the markers fixed to the segment and the orientation of the segment, the known distance of the marker from the center of mass was used to determine the coordinates of the center of mass. The center of mass coordinates are denoted by (x1, y1) for the proximal segment and (x2, y2) for the distal segment.
The equations of motion, derived from first principles, relating the
torque at each joint to kinematic variables and inertial parameters,
are as follows. T1 and
T2 represent, respectively, the
"muscle" torques (defined as positive when flexor) at the shoulder
and elbow joints. Some authors refer to this as the "generalized muscle torque (moment)" (Schneider et al. 1989, 1990
)
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(1) |
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(2) |
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Interaction torque was calculated as the difference between the muscle
torque at the joint and the "self torque," the latter being the
product of the second derivative of the joint angle and the moment of
inertia of the segment about its proximal end. Using the sign
convention of Sainburg et al. (1995), according to which
a positive value provides angular acceleration in the flexion
direction, the interaction torque at the elbow was defined as
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(3) |
Statistical analysis
We used factorial ANOVA with repeated measures and post hoc comparisons (Fisher's protected least significant difference) to determine the effect of subject group and target direction on both kinematic and kinetic parameters. We also used t-tests to determine whether there were differences in movement time between NN individuals and individuals with DS in the experiment in which movement time was controlled by the experimenter.
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RESULTS |
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Individuals with DS reverse movement direction normally
The data in Fig. 2 depict the finger-tip paths for one NN individual (A) and one individual with DS (B) for movements performed as fast as possible to all four targets and then back to the initial starting position. It is important to note that at the 135° target location both groups of subjects moved toward the right of the target. Subjects did this to avoid contacting the metal plate with their thumb when the hand left the target (see Fig. 1). As such, subjects on average moved to "targets" at about 115°. All subjects displayed this constant directional error. This constant directional error does not influence our results or conclusions. Although the target was placed to restrain elbow excursion to 45° in extension at the location of each target, the path of the movement to each target was not specified.
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The key point to stress about Fig. 2 is that although there are
differences in the path to and from the target, there is a sharp
reversal in direction for both subjects. Also, these differences are
small in comparison with the differences that Sainburg et al.
(1995) observed in individuals who have a proprioceptive
abnormality. This was the case for all eight subjects in the two
groups, and for all four target locations.
Movements of individuals with DS are slower and show more fluctuations
Figure 3 shows time series data for kinematic variables (finger-tip tangential speed in A, shoulder and elbow excursion in B and C) as well as kinetic variables (shoulder and elbow muscle torque in D and E). The data were obtained from one movement trial to the 0° target location performed by one NN individual (broken line) and one subject with DS (solid line). The data are representative for both groups of subjects. There are both similarities and differences in the way the movements are performed by the two groups of subjects. The following similarities can be observed. The tangential speed of the finger tip exhibits two approximately bell-shaped curves, corresponding to the motions toward the target and back from the target. The angular excursions of the elbow and shoulder joint are approximately similar. Also, the shoulder and the elbow muscle torques are composed of three phases (see METHODS). Despite these similarities there are differences in the movement profiles between the two subjects. First, both peaks of tangential speed are smaller for the individual with DS, and his deceleration time for the first peak is prolonged in comparison to the acceleration time. Second, the excursion of the elbow angle is larger for the individual with DS. Third, the pattern of muscle torque has three clear phases for the NN subject, but this pattern is much less evident for the individuals with DS. Fourth, there are more fluctuations in the shape of the elbow and shoulder muscle torque profiles of the individual with DS. This is a reflection of a less smooth shoulder and elbow excursion profile and can also be observed in the finger-tip tangential speed. Fifth, the muscle torque is smaller for the individuals with DS for both joints. These differences were discernible in all eight individuals with DS.
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As the target was moved from 135 to 0°, the linear distance increased. Peak tangential speed increased with respect to target location for both groups of subjects as can be seen in Fig. 4A (see Table 2 for the statistical analysis). There was an interaction between groups (NN vs. DS subjects) and target location such that NN individuals displayed a greater increase in speed with respect to changes in target location than did individuals with DS. Post hoc analysis showed that at the 135° target location the peak tangential speed was similar for both groups. Individuals with DS moved more slowly to the three other target locations than did NN individuals. Identical findings were made for the second peak of tangential speed (see Fig. 4B and Table 2), except for the 90° target location where the difference between the groups was 44.6 cm/s, but the required critical difference for statistical significance was set at 46.5 cm/s.
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Individuals with DS spend more time in the region of the target
The data in Fig. 4C show the "target time," i.e., the time spent in the region of the target, as defined in the methods section. Individuals with DS spent more time (182 ms on average) in the target region in comparison to the NN subjects (15 ms on average). There was no effect of target location on target time (see Table 2). It is important to note that at the 135° target location, despite moving at the same speed to and from the target, individuals with DS spent more time in the region of the target than did NN individuals. Therefore the longer time they spend in the region of the target is not simply a consequence of their slower movement speed. Instead there was a proportionately greater increase in deceleration time than acceleration time for individuals with DS for the movement toward the target (see Table 2). For NN individuals, the ratio of acceleration time to deceleration time was 1.08. For individuals with DS, it was 0.68. It is also important to note that if the complete movement to the 0° target is considered, NN individuals spent 47% of the time moving to the target, 3.59% of the time at the target and 49.25% of the time returning from the target. In contrast, individuals with DS spent 40.50% of the time moving to the target, 14.1% of the time at the target and 45.3% of the time returning from the target.
Shoulder and elbow torque impulses
Figure 5 depicts the averaged
muscle torque impulses for the three phases of the movement at the
shoulder (left) and elbow (right) joints for the
DS () and NN (- - -) groups as functions of target location. In
phase I, which corresponds to the initial part of the movement, the
shoulder impulse was positive into flexion for the 135° target but
was into extension for the other three target locations, whereas the
initial elbow impulse was always into extension. The first muscle
impulse (phase I) accelerated the limb toward the target location, and
its action ended at approximately the time of the first finger-tip peak
speed. The second impulse (phase II) initially decelerated the movement
toward the target location and then accelerated the limb back toward
the initial position. The end of the second muscle impulse was
approximately around the second peak of the finger-tip speed. The third
impulse (phase III) helped to brake the movement back toward the
initial position. The shoulder muscle impulse during the three movement phases increased as the target changed from 135 to 0° for both groups
of subjects (see ANOVA results in Table 2). There was a statistically
significant interaction between subject group and target location for
all three phases. Post hoc comparison showed that the shoulder impulse
between NN individuals and individuals with DS differed just for the 45 and 0° target locations. Note that at the 90° target location the
shoulder impulse was close to zero for both groups of individuals in
all three phases.
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For phases I and III, there was no significant group difference for the elbow impulse. There was a significant effect of target location and no interaction. Elbow impulse increased with target location. For phase II, there was not only a similar significant effect of target location, but there was also an interaction between group and target location showing that the elbow impulse was significantly smaller for the DS group only for the 45 and 0° target location.
Covariation of shoulder and elbow torques
We plotted the time-series data for shoulder muscle torque
against elbow muscle torque and calculated the linear regression for
each trial for each subject. Typical trials for a NN individual and an
individual with DS are shown in Fig.
6A for movements to the 0°
target. The slope obtained from this linear regression is plotted for
both subject groups against the four target locations in Fig.
6B. The open symbols depict the data for the movements performed as fast as possible. For the 45 and 0° target locations, we
also plotted the slope obtained from movements performed in an
experimenter controlled movement time ( and
). The rationale for
testing both groups in an experimenter controlled movement time was to
test whether speed differences might be related to coordination
differences. Both groups of subjects had to slow down movement speed to
accomplish the controlled movement time task. There was no
statistically significant difference in movement time for the 45°
target location, t (14) =
0.46, P = 0.66 [average movement time for DS = 1,052 ± 21 (SD) ms;
average movement time for NN = 1,045 ± 30 ms]. There was
also no statistically significant difference in movement time for the
0° target location, t (14) =
1.23,
P = 0.24 (average movement time for DS = 1,261 ± 18 ms; average movement time for NN = 1,246 ± 31). In these trials in which the movement time was controlled by the
experimenter, for the NN subjects the first peak of the finger-tip
tangential speed was 58 and 69% of the speed presented in Fig.
4A for 45 and 0° target locations. For the DS subjects,
this tangential speed was 89 and 88% of the speed presented in Fig.
4A for 45 and 0° target locations. We will first discuss
movements to the 0°and 45° target location since these movements
were made with both speed instructions. We will then discuss the
movements to 90 and 135°.
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We used two three-way mixed model ANOVAs to test the effect of movement time instruction (as fast as possible vs. controlled movement time), target location (45 vs. 0°) and subject group (DS vs. NN) on the slope of shoulder torque versus elbow torque. The results showed that the speed instruction had no effect on the slope, F(1, 14) = 0.69, P = 0.42. There was a difference due to group, F(1, 14) = 15.64, P < 0.0001, such that the slope was larger for the NN subjects than it was for the individuals with DS. In other words, the DS subjects produced relatively less shoulder torque in relation to elbow torque, compared with the NN subjects. There was also an effect of target location F(1, 14) = 88.45, P < 0.001, such that the slope was larger for movements to 0° as opposed to 45°. None of the interactions were significant. The ANOVA results for the correlation coefficient |r| only showed an effect of subject group, F(1, 14) = 8.41, P < 0.01, the correlation being smaller for the individuals with DS.
At 90° there was no group difference in the slope of the regression between shoulder and elbow muscle torques, which was close to zero. At 135° the slope was negative for the NN subjects (Fig. 6B), because their shoulder and elbow muscle torques were into opposite directions (Fig. 7A), but the slope was close to zero for the DS group (Fig. 6B). This may appear to contradict the observation that at the 135° target location, there were no group difference in shoulder and elbow muscle impulse in each of the three phases (Fig. 5). The fact that the slope of the shoulder-elbow muscle torque relationship is close to zero for individuals with DS (Fig. 6B) shows that, averaged over all three phases, there is little correlation between them. This does not, however, imply that the shoulder torque did not vary in each of the three phases and therefore does not contradict the existence of nonzero impulses in the different phases. The near-zero slope for the individuals with DS for the 135° target location is consistent with the following observations. First, individuals with DS had even more fluctuation in the shoulder muscle torque profile at this target location (compare Fig. 7, A with B). Second, there was more variability in the time in which the shoulder and the elbow muscle torque changed direction at this target location.
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Interaction torque
Peak elbow interaction torque did scale systematically with target location from 135 to 0° in both groups of subjects, F(3, 42) = 31.54, P < 0.0001 as would be expected since the targets were placed such that shoulder excursion changed systematically. There was no effect of group, F(1, 14) = 2.21, P = 0.16, and there was no interaction between group and target location, F(3, 42) = 2.05, P = 0.121). These data are shown in Fig. 8.
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Assumptions underlying the kinetic analysis
The equations of motion that we present in Eqs. 1 and 2 are predicated on several considerations that can influence the validity and generalizability of the kinetic calculations. The first is that the so-called "muscle torque" that is calculated is due not only to muscle but is in fact the torque produced about the joint by muscles as well as passive tissues and, as such, it is influenced by any factor that affects the joint. This includes properties of tendons, ligaments and cartilage. (Differences in the properties of joints between NN individuals and those with DS are addressed in the discussion.) Second, the torque we calculate is that related to motion in the horizontal plane because it was calculated only about the vertical axis. We investigated motion in the vertical plane. We found no statistically significant difference between the two groups in the RMS value of the fingertip motion in the vertical plane, F(1, 14) = 0.91, P = 0.35. There was a statistically significant effect of target orientation, F(3, 42) = 10.9, P < 0.0001. There was greater vertical motion for the target at 0° (Fisher's protected least significant test) than the other three locations but this motion only amounted to 1.8 cm. There was no interaction between subject group and target location, F(3, 42) = 1.56, P = 0.21. Third, because our estimates of the inertial parameters are based on cadaver data obtained from NN individuals, our estimates of the torque magnitudes could be in error if the inertial parameters were significantly different for individuals with DS. We know of no reason to believe, however, that the relative masses of the forearm and upper arm segments, for example, are different in individuals with DS compared with individuals who are NN. Therefore the relative torques at the two joints, and thus the slope relating them, should not be in error for the DS individuals. Fourth we splinted the wrist and hand, asked subjects to keep their arms above the table and did not allow any impact with the target so that the equations of motion would not be compromised by unaccounted for joint motion, friction and impact.
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DISCUSSION |
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The data we have presented extend previous findings of a linear relationship between elbow torque and shoulder torque to horizontal, planar reversal movements. The strength of this linear synergy is less in individuals with DS, and the slope of the relationship between elbow torque and shoulder torque is also different in individuals with DS for some target directions. The data also show that individuals with DS spend more time in the vicinity of the target. Finally, we found that the hand path of individuals with DS is similar to and from the target in the vicinity of the reversal point. We will discuss each of these issues in turn.
Linear synergy in reversal movements
As has previously been reported, we also find that the dynamic
muscle torques of horizontal, reversal movements are triphasic (Gottlieb 1998; Sainburg et al. 1995
;
Schmidt et al. 1988
; Sherwood et al.
1988
). The first muscle impulse accelerates the limb toward the
target location. The second impulse initially decelerates the movement
toward the target location and then accelerates the limb back toward
the initial position. The third impulse terminates the movement at the
initial position. The elbow and shoulder muscle torques that generate
these impulses are qualitatively very similar and are closely
synchronized temporally in NN individuals.
Gottlieb and colleagues (1996a) have shown that in
normal subjects the shoulder and elbow torques follow a coordination
rule, termed "linear synergy," for the performance of a variety of
different movements. The CNS sends a common temporal pattern to
activate the muscles of the two joints, leading to muscle torque
profiles of similar shapes at each joint. These muscle torques are then scaled in amplitude to the demands of the task. In other words, the
elbow and shoulder muscle torques are related by a scaling constant.
They pass through extremes and zero crossings almost simultaneously for
a variety of different movements as has also been shown by Topka
et al. (1998)
. When an individual is explicitly instructed to
use an unusual hand-path, the linear synergy rule does not apply
(Gottlieb et al. 1996a
), and therefore this rule is not
an obligatory feature of the mechanics of the movement. This linear
synergy between muscle torques can be found in sagittal planar
movements during pointing (Gottlieb et al. 1996a
),
reaching movements in different directions (Gottlieb et al.
1997
) and in the data reported by Bock (1994)
and Buneo and colleagues (1995)
.
In the present data set, we show that linear synergy is also observed
for unconstrained horizontal plane reversal movements, which require
the coordination of elbow and shoulder torques. The ratio between the
torques varies with target location as shown for pointing movements
performed against gravity in the saggital plane (Gottlieb et al.
1997). We also confirm the observation of Gottlieb and
colleagues (1996b)
that the ratio of the muscle torques does
not depend on movement speed. When the subjects were asked to move to
the 45 or 0° target locations at different speeds, they used the same
ratio between elbow and shoulder muscle torque independently of speed
(Fig. 6B).
We found that, in general, both NN individuals and individuals with DS use linear synergy to perform reversal movements. However, there were subtle differences in the generation of shoulder and elbow torques by DS individuals that may account for certain differences in their movement performance. One such difference is that there is more fluctuation in the muscle torque for the movements of DS individuals (Figs. 3, D and E, and 7B). This decrement in the smoothness of the movements of individuals with DS may well explain the reduction in the strength of the linear relationship between elbow and shoulder torque observed in the individuals with DS. The ratio of the torques determines movement direction, whereas the magnitude of the torques determines movement speed. We will now address the question of how differences in the magnitude and ratio of the torques can explain the characteristics of the movements of individuals with DS.
Movement trajectory
We observed no major differences in the trajectories of the
individuals with DS in comparison with the NN individuals. They made
movements both to and from the target following a similar path to that
of the NN individuals (Fig. 2). This is in sharp contrast to the
movements described for deafferented subjects in which the movement
path to and from the target was very different, especially in the
vicinity of the reversal point, despite the fact that, unlike in our
study, the subjects were given a straight line to follow
(Sainburg et al. 1995). As such the data do not support
our first hypothesis that individuals with DS may exhibit a pronounced
difference in movement paths during reversal of movement akin to what
has been reported for individuals with impaired proprioception.
The argument has been made that certain neurological deficits may give
rise to an inability to "control interaction torque" (Bastian et al. 1996; Sainburg et al.
1995
). The rationale for this argument is based on the
assumption that individuals with a loss of proprioception or with a
lesion of the cerebellum do not have an appropriate model of limb
dynamics to account for interaction torques using a feedforward
mechanism. In our experimental design, as in that of Sainburg
and colleagues (1995)
, the magnitude of peak interaction torque
at the elbow systematically increased with targets requiring greater
shoulder extension. As such, if individuals with DS did not have an
appropriate model of limb dynamics, the reversal of movement in the
vicinity of the 0° target, when the interaction torque is greatest,
should have exhibited a rounded path rather than a sharp turnaround. It
did not. We failed to identify any kind of pattern for the interaction
torque that discriminated between normal individuals and the
individuals with DS.
Movement speed and target time
As has been observed in several previous studies (Almeida
et al. 1994; Aruin and Almeida 1997
;
Aruin et al. 1996
), the movements of individuals with DS
are slower when compared with NN subjects [cf. a review by
Anson (1992)
]. They move slowly because they generate
smaller muscle torques. The only exception was for the 135° target
location (Fig. 4). At this target location, the muscle torque impulses
were comparable across groups and so was the movement speed (Fig. 4,
A and B). Note that even though elbow and
shoulder muscle torques were not temporally correlated for the 135°
target location for the individuals with DS (Fig. 7B), the
magnitude of the torque impulses were similar across subject groups
(Fig. 5).
The time in the vicinity of the target was disproportionally longer for
individuals with DS for all target locations (Fig. 4C). This
longer time in the target region is consistent with a study by
Henderson et al. (1981) in which children with DS were asked to track a moving sinusoidal template. The children with DS could
track the sine wave quite well when the movement was slow and even draw
it from memory on stationary paper. However, they failed to track the
moving sinusoidal template when it moved quickly, especially as it
reversed direction. They made a series of straight, discrete movements
instead. A pause separating the movements to and from the point of
reversal would also seem consistent with an attempt to reduce the
interaction torque, which would otherwise impart an unwanted motion to
the elbow. Based on these considerations, we had hypothesized that to
produce a sharp reversal in the spatial path, individuals with DS would
move to the target, stop, and then return. In other words, they would
perform the task as two discrete movements. This was clearly not the
case because if they had paused at the target location, their
finger-tip speed would have remained zero during the target time, and
this is not what we observed (Fig. 3). This observation rules out the possibility that they could have forgotten for a brief time to return
to the initial position and therefore treated the reversal movement as
two separate movements. This is because simple reaction time has been
reported to be 150 ms for control subjects and more than 300 ms for
individuals with DS (Berkson and Baumeister 1967
). The
average target time for the individuals with DS was around 182 ms,
which is considerably less than the time one would expect if the return
movement was a new movement. Furthermore the longer reversal time for
the DS subjects did not result in an appreciable reduction in the peak
interaction torque (Fig. 8), which contradicts the idea that the
altered temporal pattern exhibited by DS subjects is an adaptation for
an inability to account for interaction torques in movement planning.
The increased time in the vicinity of the target (Fig. 4C)
also cannot be attributed to differences in movement speed between the
two groups of subjects. This is because at the 135° target location
both groups of individuals moved at comparable speeds but the time in
the vicinity of the target of the individuals with DS was about 150 ms
longer. The longer time in the vicinity of the target can be
attributed, in part, to a prolongation of the deceleration phase toward
the target, which we observed. Although Almeida and colleagues
(1994) have shown that DS individuals exhibit symmetry between
the acceleration and deceleration phases for elbow flexion movements,
the symmetry may be compromised in the case of reversal movements.
Alternatively, it may be the case that deceleration time may be
prolonged in individuals with DS for movements that require close
monitoring of visual feedback. Charlton, Insen, and Lavelle
(2000)
have also shown that individuals with DS spend a greater
proportion of time in the deceleration phase of the movement than the
acceleration phase in comparison with older and younger control
children when performing reaching movements that also involved grasping
an object.
Neurobiological basis of motor difficulties in DS
The results that we have presented are important for two reasons.
On the one hand, they suggest that linear synergy is a fundamental feature of the control of movement that is not degraded even in the
presence of a genetically abnormal sensori-motor, musculo-skeletal system (Chiarenza and Stagi 2000). On the other hand,
the neurological and biomechanical differences in individuals with DS
may well explain the differences in movement speed and time spent in
the region of the target that are observed between the two groups of
individuals. For example, pyramidal cell abnormalities have been
identified in the motor cortex of a child with DS (Marin-Padilla 1976
), and the weight of the cerebellum has been reported to be reduced (Crome et al. 1966
). In addition, there is
evidence of axonal degeneration from the study of peripheral and CNS
conduction parameters (Mackenzie et al. 1983
).
Individuals with DS may also have differences in bone density and
cartilage hypoplasia and possibly alterations in the biomechanical
properties of ligaments, although the evidence for differences in the
biomechanical properties of ligaments has been questioned
(Cremers and Beijer 1993
; Stein et al.
1991
). These differences might influence the ability to generate joint torque, especially since individuals with DS do generate
reduced levels of force when generating isokinetic contractions (Cioni et al. 1994
). It is also possible that
differences in movement speed and time spent in the region of the
target are indirect consequences of mental retardation and not due to
the above-mentioned reasons. Future studies are required that use a
control group matched for differences in intelligence to determine
whether the differences that we have documented are due to altered
central processing or due to alterations in the sensorimotor system.
Conclusion
The results that we have presented show that linear synergy occurs in horizontal plane reversal movements to a target. These results confirm and extend previous findings concerning the linear relationship between joint torques. Linear synergy also occurs in individuals with DS. They do have the ability to specify different ratios of torques at the shoulder and elbow joints to move to selected targets, although they do generate more elbow torque in relation to the shoulder torque as compared with NN individuals. The movement path, however, is sufficiently similar to that of normals to suggest that their abnormality is not akin to the abnormality observed in patients with proprioceptive deficits. Individuals with DS differ from normal individuals mainly in that they produce less muscle force, and thus their movements are slower, but they slow down in the vicinity of a reversal point disproportionately more than what may be expected on the basis of their lower speed. This somewhat altered speed profile, however, does not result in an appreciable reduction in the peak interaction torque. In addition, their muscle torque profiles show greater fluctuations. The results suggest that future research on the motor ability of individuals with DS should focus on the precise timing and sequencing of muscle activation for movements in different directions.
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ACKNOWLEDGMENTS |
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We acknowledge the valuable comments and suggestions of Dr. Gerald Gottlieb.
This study was supported in part by National Institutes of Health Grants R01-AR-33189, K04-NS-01508, R01-NS-28127, and RO1-NS-19407 and by Fundação de Amparo À Pesquisa do Estado de São Paulo (FAPESP) Brazil Grant 95/9608-1.
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FOOTNOTES |
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Address for reprint requests: D. Corcos, School of Kinesiology (M/C 194), University of Illinois at Chicago, 901 W. Roosevelt Rd., Chicago, IL 60608 (E-mail: dcorcos{at}uic.edu).
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 30 March 1999; accepted in final form 5 July 2000.
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REFERENCES |
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