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The Journal of Neuroscience, February 1, 2002, 22(3):1108-1113
Kinematics and Dynamics Are Not Represented Independently in
Motor Working Memory: Evidence from an Interference Study
Christine
Tong1,
Daniel
M.
Wolpert2, and
J. Randall
Flanagan1
1 Department of Psychology and Centre for Neuroscience
Studies, Queen's University, Kingston, Ontario, K7L 3N6, Canada, and
2 Sobell Department of Neurophysiology, Institute of
Neurology, University College London, London, WC1N 3BG, United
Kingdom
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ABSTRACT |
Our capacity to learn multiple dynamic and visuomotor tasks is
limited by the time between the presentations of the tasks. When
subjects are required to adapt to equal and opposite position-dependent visuomotor rotations (Krakauer et al., 1999
) or velocity-dependent force fields (Brashers-Krug et al., 1996) in quick succession, interference occurs that prevents the first task from being
consolidated in memory. In contrast, such interference is not
observed between learning a position-dependent visuomotor rotation and
an acceleration-dependent force field. On the basis of this finding, it
has been argued that internal models of kinematic and dynamic
sensorimotor transformations are learned independently (Krakauer et
al., 1999). However, these findings are also consistent with the
perturbations interfering only if they depend on the same kinematic
variable. We evaluated this hypothesis using kinematic and dynamic
transformations matched in terms of the kinematic variable on which
they depend. Subjects adapted to a position-dependent visuomotor
rotation followed 5 min later by a position-dependent rotary force
field either with or without visual feedback of arm position. The force
field tended to rotate the hand in the direction opposite to the
visuomotor rotation. To assess learning, all subjects were retested 24 hr later on the visuomotor rotation, and their performance was compared with a control group exposed only to the visuomotor rotation on both
days. Adapting to the position-dependent force field, both with and
without visual feedback, impaired learning of the visuomotor rotation.
Thus, interference between our kinematic and dynamic transformations
was observed, suggesting that the key determinant of interference is
the kinematic variable on which the transformation depends.
Key words:
motor learning; internal models; arm movement; visuomotor
rotation; force field; motor memory
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INTRODUCTION |
The problem of motor learning is one
of mastering novel sensorimotor transformations that relate motor
commands to sensory outcomes. Such learning involves the acquisition of
internal models that capture these sensorimotor transformations and
enable the CNS to accurately estimate the motor commands required to
achieve desired outcomes and to predict the consequences of actions
(Johansson and Cole, 1992; Miall et al., 1993; Shadmehr and
Mussa-Ivaldi, 1994; Wolpert et al., 1995; Conditt et al., 1997;
Flanagan and Wing, 1997; Kawato, 1999; Wolpert and Ghahramani, 2000).
Two classes of sensorimotor transformations have been widely used in
motor control research: kinematic and dynamic. Kinematic
transformations are mappings between different geometric variables (and
their derivatives) and, importantly, do not depend on the dynamic
properties of the system. In contrast, dynamic transformations relate
motor commands to the motion of the system; therefore, they do depend on dynamic properties such as inertia and viscosity. Thus, for example,
to control a computer mouse, we must learn the kinematic transformation
that relates mouse motion to cursor motion and the dynamic
transformation that relates the forces applied to the mouse to its
resultant motion, a mapping that will depend on the inertia of the
mouse and the friction between the mouse and the mouse pad.
Brashers-Krug et al. (1996) have shown that learning internal models of
novel dynamics involves a period of consolidation, during which motor
memory is susceptible to disruption. If people adapt to two equal and
opposite viscous force fields in quick succession, performance on the
second is impaired (anterograde interference) and the memory of the
first is overwritten (retrograde interference). Similar interference
effects are observed when learning opposing visuomotor rotations
(Krakauer et al., 1999; Wigmore et al., 2001).
Although opposing kinematic and opposing dynamic transformations
interfere with each other, Krakauer et al. (1999) observed independent
learning of internal models for novel kinematic and dynamic
transformations. They showed that learning a visuomotor rotation is not
affected by adaptation to an inertial load presented either
simultaneously or 5 min later. Similarly, a recent study shows lack of
anterograde interference between a visuomotor rotation and a viscous
force field (Flanagan et al., 1999).
In summary, these studies of motor interference have shown interference
between two position-dependent visuomotor mappings and interference
between two velocity-dependent force fields but no interference between
a position-dependent visuomotor rotation and either an
acceleration-dependent or velocity-dependent force field. Based on
these results, Krakauer et al. (1999) concluded that internal models of
kinematic and dynamic transformations are stored in distinct systems of
working memory. An alternative hypothesis is that transformations that
depend on different kinematic parameters do not interfere, but those
that depend on similar kinematic parameters do interfere. We tested
this hypothesis using kinematic and dynamic transformations matched by
the kinematic parameter on which they depend. In particular, we used a
position-dependent visuomotor rotation and a position-dependent rotary
force field. The hypothesis that kinematic and dynamic learning are
independent predicts that adapting to the force field soon after
adapting to the visuomotor rotation should not interfere with
consolidation of the former. The hypothesis that transformations that
depend on the same kinematic parameter interfere with one another
predicts the opposite finding (i.e., that dynamic learning should
interfere with the consolidation of kinematic learning).
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MATERIALS AND METHODS |
Subjects. After providing written informed
consent, 26 subjects (15 women and 9 men) between the ages of 17 and 45 participated. A local ethics committee approved the experimental
protocol. All subjects were right-handed and had normal vision or
vision that was corrected for normal. Subjects were assigned to one of
three groups. Subjects in the control group (n = 10)
were presented with a visuomotor rotation session on successive days.
Subjects in the visual-feedback group (n = 8) were
presented with a visuomotor rotation session followed 5 min later by a
force field learning session on day 1; they were then presented with
the visuomotor rotation again on day 2. The visuomotor transformation
was turned off during adaptation to the force field. Subjects in the
no-visual-feedback group (n = 8) were presented with
the same sequence of tasks as subjects in the visual-feedback group,
except that they did not receive visual feedback of the hand position
during presentation of the force field. The control group contained 10 subjects because 2 subjects, originally scheduled for inclusion in
another group, did not have time to complete two tasks on day 1.
Apparatus. While seated, subjects grasped a
lightweight, force-reflecting manipulandum (Phantom Haptic
Interface 3.0; Sensable Technologies, Woburn, MA) that they
moved to targets located in a horizontal plane. The targets and the
position of the hand were represented as virtual spheres using a
three-dimensional projection system with shutter glasses [for full
details of the setup, see Goodbody and Wolpert (1998); subjects could
not see their hand or arm (Fig. 1)]. The
spheres representing targets (green) and the position
of the hand (white) were 2 cm in diameter. The
three-dimensional force exerted by the manipulandum on the hand was
servo-controlled at 1 kHz to create a position-dependent rotary force
field in the horizontal plane (see below). Under the null force field, subjects experienced small forces associated with the passive mechanics
of the manipulandum.
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Figure 1.
Experimental setup. Subjects moved a
force-reflecting manipulandum between targets in a horizontal plane.
The targets were virtual spheres presented using a three-dimensional
projection system with shutter glasses. The force exerted by the
manipulandum was servo-controlled to create a position-dependent rotary
force field, and visual feedback was altered to create a
position-dependent visuomotor rotation.
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Procedure. Subjects made out-and-back movements to one of
eight targets from a central starting position (or target) located ~10 cm below shoulder level and in the subject's midsagittal plane. The targets were located radially about the starting position and in
the same horizontal plane. All targets were located 15 cm from the
starting position. Participants were instructed to move their hand out
to the target and back to the starting position in a single, quick,
continuous motion; they were asked not to make corrective adjustments
during the movement. Under the visuomotor rotation, the position of the
hand sphere was rotated 30° counterclockwise about the starting
position in the horizontal plane. Following the procedure used by
Krakauer et al. (1999), targets were presented in a constant sequence,
starting at 0° (directly away from the subject) and continuing in
positive, counterclockwise increments of 45°. A cycle was
defined as eight successive trials from 0° to 315°. Each session
consisted of 30 cycles (i.e., 240 movements). To avoid fatigue,
subjects were given a brief 1 min rest every five cycles (i.e., every
40 trials).
To begin each trial, subjects had to position the sphere representing
their hands at the starting position. The trial was initiated only when
the hand was within the starting area for a full second. At the start
of the trial, one of the targets was presented and the subjects had to
move out to the target and back to the starting position, which
remained visible. To ensure that the participants were able to return
to the starting position when visual feedback was not provided during
the movement, we illuminated the cursor if the hand was off the
starting location at the end of their out-and-back movement but within
5 cm of the starting location. Visual feedback of the position of the
cursor was turned off at the start of the trials. To control movement time, a counter was started as soon as the hand moved 2 cm away from
the starting position. After 450 msec, an auditory signal was provided
and the starting position flashed red for 100 msec. The subjects' task
was to arrive back at the starting position at the same time that these
auditory and visual cues were turned on. Thus, the subject was
encouraged to complete the out-and-back movement in 450 msec.
Transformations. Under the position-dependent visuomotor
transformation, the position of the hand was rotated about the starting position (origin) in the horizontal plane using the following rotation
matrix:
where x and y are the coordinates of the
hand in the horizontal plane relative to its starting location (Fig.
1), 
equals 30°, and p and q are the
coordinates of the new, rotated "hand" position. Note that when the
hand is located at the starting position (x = 0, y = 0), the locations of the actual and visually
perceived hand are identical.
Under the position-dependent rotary force field, the force applied to
the hand by the manipulandum handle was proportional to the
displacement of the hand away from the starting position and directed
perpendicular to the hand displacement vector, such that the force
tended to rotate the hand clockwise (in the direction opposite to the
visuomotor rotation). The following equation was used to compute the
force to be applied:
where x and y are the coordinates of the
hand in the horizontal plane relative to the starting location,
Fx and
Fy are forces acting in the horizontal
plane, k equals 60 N/m, and equals 
90°.
Analysis. The three-dimensional position of the hand (center
of the manipulandum handle) was recorded at 200 Hz using the encoders
of the Phantom. To compute the velocity of the hand, these position
data were first digitally filtered using a low-pass second-order
Butterworth filter with a cutoff frequency of 14 Hz. A three-point
central difference equation was then applied to compute the velocities
in three dimensions. The tangential velocity of the hand in the
horizontal plane was computed as the resultant of the velocities in the
x and y directions.
To quantify the learning of the position-dependent visuomotor rotation,
we first computed movement direction defined as the instantaneous
direction of cursor movement 150 msec after the start of the movement.
We then computed the angle between the direction of movement and the
target direction (the direction of the vector from the start position
to the target). We measured movement direction 150 msec after the start
of the movement so that our measure would not be affected by
significant on-line corrections based on visual feedback of cursor
position. The start of the movement was taken as the point at which the
tangential velocity of the hand (in the horizontal plane) last exceeded
0.02 m/sec before reaching a speed of 0.2 m/sec.
To quantify learning of the position-dependent rotary force field, we
computed the normalized path length in the horizontal plane.
Specifically, we divided the integrated path length by twice the
maximum hand displacement from the starting position; in other words,
we normalized the path length by the minimum possible path length given
the displacement of the hand away from the starting position. This
normalization procedure was used because, under the condition of no
visual feedback, subjects could produce movements that either overshot
or undershot the visual target. In such cases, the path length, without
normalization, would be influenced by movement amplitude independently
of path curvature.
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RESULTS |
Hand paths at the start and end of adaptation
Subjects in all three experimental groups were first exposed to
the position-dependent visuomotor rotation, in which a cursor that
represents the position of the hand was rotated 30° from the position
of the hand. Figure 2a shows
individual cursor paths to each of the eight targets for a single
subject in the first and last (30th) cycles. As expected, in the first
cycle, the paths were rotated counterclockwise with respect to the
target direction (straight lines). However, after 30 cycles,
the subject adapted and produced paths that were directed toward the
targets.
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Figure 2.
Performance in the first and last cycles under the
visuomotor rotation (a) and elastic force field
with visual feedback (b). The gray
curves show the individual paths of the cursor representing
hand position for a single subject (different subjects are shown in
a and b). The straight solid
lines indicate the direction and extent of the corresponding
targets. For the first cycle, two movement paths (directed to opposing
targets) are shown in each plot. For the last cycle, all eight paths
are shown in one plot. Because the force field was presented after
adaptation to the visuomotor rotation, subjects initially directed
their movements 30° clockwise to the targets. These rotated
directions are indicated by the straight dashed lines in
b. In the first cycle, large errors were observed under
both transformations. However, after 30 cycles, these errors were
greatly reduced.
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After adapting to the position-dependent visuomotor rotation, subjects
in two of the three groups were exposed to a position-dependent rotary
force field, either with vision, in which case the visuomotor transformation was turned off, or without vision. Figure 2b
shows individual hand paths to each of the targets in the first and last cycles for a single subject in the visual-feedback group. Because
the subjects had just adapted to the visuomotor rotation, they made
direction errors in the first cycle. In particular, they directed their
hand movements 30° clockwise from the targets. (The targets are
indicated by solid straight lines and the rotated targets are indicated by dashed lines.) In addition, in the
first cycle, the rotary force field gave rise to large loops in the hand path. At the start of each movement, the hand paths were directed
toward the rotated targets, but they then veered clockwise as
the hand was displaced from the origin and the rotary force increased.
After 30 cycles, the subject once again adapted so as to produce
relatively straight hand paths to the targets. This involved both an
unlearning of the visuomotor rotation and an adaptation to the rotary
force field.
Interference between kinematic and dynamic learning
Figure 3 shows learning curves under
the visuomotor rotation on day 1 (solid curves) and day 2 (dashed curves) for each of the three experimental groups.
To construct these curves, we first computed the mean directional error
for each subject and cycle (averaging across the eight movements within
each cycle) and then computed the average directional error across
subjects for each cycle. The height of the gray area
represents 1 SE. Figure 3a shows the results for the control
group subjects, who were exposed to the 30° visuomotor rotation on
day 1 and then retested on day 2. On day 1, the subjects initially
produced directional errors close to 30°. After 30 cycles (or 240 movements), their errors were greatly reduced. When the same subjects
were retested 24 hr later, the initial directional errors were much
smaller, indicating substantial retention of learning. Note that even
at the end of day 2 there was a small directional bias of ~5°,
which is consistent with previous reports (Krakauer et al., 1999;
Wigmore et al., 2001).
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Figure 3.
Adaptation to the visuomotor rotation. Curves show
mean angular error (between movement and target directions) as a
function of cycle on day 1 (solid lines) and day 2 (dashed lines). The height of the gray
area represents ±1 SE. a shows results for the
control group, who adapted only to the visuomotor rotation on day 1. b and c show results from two groups, who
on day 1 adapted to the visuomotor rotation and 5 min later adapted to
the position-dependent rotary force field either with
(a) or without (b) visual
feedback. The two groups exposed to the force field on day 1 exhibited
greater directional errors at the start of day 2 than did the control
group.
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Figure 3, b and c, shows the results for the two
groups of subjects exposed to the position-dependent force field 5 min
after adapting to the position-dependent visuomotor rotation on day 1. The data shown in Figure 3b are for the group who received visual feedback of the cursor position during adaptation to the force
field; the data in Figure 3c are for the group who did not receive visual feedback. There was a small improvement in performance from day 1 to day 2 in both groups. However, in comparison with the
control group (Fig. 3a), it is apparent that adapting to the force field on day 1 interfered dramatically with the retention of the
visuomotor rotation that would otherwise be expected.
In all of the curves shown in Figure 3, small peaks can be observed
every five cycles. These are the cycles that followed the 2 min rest
breaks. Although the rest breaks resulted in transient increases in
direction error for a single cycle, these increases did not appear to
affect the shape of the learning curve otherwise. Note that the
decrease in direction error from the cycle immediately after the break
(i.e., the cycle exhibiting the peak in error) to the next cycle tended
to be large. Thus, qualitatively, subjects appeared to recover rapidly
after the break and stay on course in terms of adaptation.
To quantify the learning curves shown in Figure 3, we adopted the
procedure used by Krakauer et al. (1999). Specifically, for each
subject we computed the average directional error over the second and
third cycles as well as the average directional error over the last two
cycles (cycles 29 and 30). We then averaged these errors across
subjects to obtain mean values. The bar graphs in Figure
4 depict the mean directional errors over
the second and third cycles for each experimental group and for day 1 (solid bars) and day 2 (dashed bars). The
inner gray bars represent the corresponding directional
errors over the last two cycles.
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Figure 4.
Initial and final angular errors under the
visuomotor rotation. The height of each white bar
represents the angular error averaged over the second and third cycles;
the height of each gray bar represents the corresponding
angular error averaged over the 29th and 30th cycles. The bars outlined
with solid and dashed lines represent days 1 and 2, respectively. Separate means are reported for each of the three
experimental groups. Vertical lines represent the
SE.
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To test our main hypotheses, we performed two comparisons involving
orthogonal partial interactions between day and group with the
directional error over the second and third cycles as the dependent
variable. First, to assess the overall effect of dynamic learning
(independent of visual feedback conditions) we examined the interaction
between day and group while combining groups 2 and 3. A highly reliable
effect was observed (F(1,24) = 26.76;
p < 0.001), indicating that dynamic learning
interfered with kinematic learning. To test whether this effect was
mediated by visual feedback conditions, we assessed the orthogonal
interaction between day and group in which only groups 2 and 3 were
included in the analysis. In this case, a significant interaction was
not found (F(1,16) = 0.41;
p = 0.531). Thus, we found no evidence that the level
of interference observed between dynamic and kinematic learning depends
on whether subjects received visual feedback during dynamic learning.
Exposure to the position-dependent rotary force field clearly
interfered with retention of the position-dependent visuomotor rotation. However, limited retention of the latter was observed. When
combining the two groups exposed to the force field (groups 2 and 3),
the initial directional error (in the second and third cycles) was
19.4° on day 1 and 13.2° on day 2, an improvement of 6.2°.
Although this level of retention was markedly smaller than the level
observed for the control group (a difference across days of 15.8°),
it was nevertheless reliable (F(1,16) = 38.41; p < 0.001). Thus, dynamic learning did not
result in a complete absence of consolidation of kinematic learning.
Adaptation to the position-dependent force field
Our finding that exposure to the position-dependent rotary force
field interferes with kinematic learning suggests that subjects did in
fact adapt to and learn the force field. Figure
5 shows that this was indeed the case.
The curves in Figure 5a show normalized path length (a
measure of the curvature of the hand path) as a function of the
cycle for both the visual-feedback group (dashed line) and
the no-visual-feedback group (solid line). Each point on the
curve represents the mean of subject means, each averaged across the
eight movements within a cycle. In both groups of subjects, the
normalized path length decreased markedly over the first 10 cycles or
so and then decreased more gradually thereafter. After 30 cycles, the
normalized path length approached 1.1 for both groups; a perfectly
straight path out to and back from the target would result in a
normalized path length of 1.
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Figure 5.
Adaptation to the elastic rotary force field.
a, Distance traveled by the hand as a function of cycle
(normalized for maximum displacement of the hand). The
dashed and solid lines represent mean
distances for the visual feedback and no-visual-feedback groups,
respectively. The height of the gray area around the
dashed curve and the gray line
around the solid curve represent ±1 SE.
b, Corresponding mean angular errors for the two groups.
For both groups, the magnitude of the angular error decreased as the
visuomotor rotation previously adapted to was gradually unlearned
during adaptation to the force field.
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While adapting to the position-dependent rotary force field, subjects
also unlearned the visuomotor rotation they learned before they were
exposed to the force field. This "de-adaptation" is evident in
Figure 5b, which shows mean directional error (averaged across subjects and based on subject means) as a function of cycle. As
can be appreciated visually, the rate of de-adaptation (or re-adaptation to the 0° rotation) was slightly faster when visual feedback of the cursor position was provided. Moreover, the absolute directional error after 30 cycles was slightly smaller in the visual-feedback group. However, the differences between the two curves
are small, and it is striking how quickly subjects in the no-visual-feedback group unlearned the visuomotor rotation, presumably by comparing visual information about the target with proprioceptive information related to arm position.
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DISCUSSION |
We have demonstrated clear interference between kinematic and
dynamic learning. First, we showed that when subjects adapted to a
position-dependent visuomotor rotation and were tested on the same
visuomotor rotation a day later, their performance was greatly
improved. This result is consistent with previous studies (Krakauer et
al., 1999; Wigmore et al., 2001); it indicates that the knowledge of
the visuomotor rotation was consolidated in long-term memory. Second,
we demonstrated that when subjects successively adapted to a
position-dependent visuomotor rotation and then to a position-dependent
rotary force field, retention of the visuomotor rotation was
significantly impaired when performance was tested the next day. This
retrograde interference indicates that learning and consolidation of
the visuomotor rotation was disrupted by adaptation to the rotary force field.
Previous work has demonstrated retrograde interference between opposing
kinematic (Krakauer et al., 1999) and opposing dynamic (Brashers-Krug
et al., 1996) sensorimotor transformations that are presented close
together in time. Thus, when subjects adapt to two opposing visuomotor
rotations presented 5 min apart, there is no improvement in performance
on the first rotation when tested a day later (Krakauer et al., 1999).
Similarly, when subjects adapt to a velocity-dependent force field that
generates rotary forces in one direction and then adapt 5 min later to
a field that generates rotary forces in the opposite direction,
performance on the first force field is not improved when evaluated the
next day (Brashers-Krug et al., 1996). In contrast, Brashers-Krug et al. (1996) have shown that when the two opposing force fields are
presented ~6 hr apart, retrograde interference is no longer observed.
That is, subjects exhibit normal retention on the first force field
when retested a day later. These authors also found that anterograde
interference (i.e., a deficit in performance on the second force field
attributable to prior learning of the first) decreased over this period
[but see Bock et al. (2001) for an example of long-lasting anterograde
interference]. Based on these results, Brashers-Krug et al.
(1996) argued that motor learning involves a two-step process in
which knowledge acquired during practice is initially stored as an
internal model in working memory and then gradually consolidated in
long-term memory. The internal model in working memory is fragile and
can be interfered with by new learning that competes for the same
resources. In contrast, once consolidated in long-term memory, the
internal model is stable and is not susceptible to retrograde
interference by new learning (Brashers-Krug et al., 1996; Shadmehr and
Brashers-Krug, 1997). The results presented here indicate that
position-dependent and rotational kinematic and dynamic transformations
compete for common resources in motor working memory and argue against
the idea that separate working-memory systems underlie kinematic and dynamic learning (Krakauer et al., 1999).
Our results appear to be in direct disagreement with those of Krakauer
et al. (1999), who found independent learning of kinematic and dynamic
transformations. They showed that when subjects successively adapt to a
visuomotor rotation and then to an inertial load, adaptation to the
inertial load does not interfere with learning and retention of the
visuomotor rotation. We believe that the difference between the two
sets of results is best explained in terms of the nature of the
kinematic and dynamic transformations used. Krakauer et al.
(1999) used transformations that depended on different kinematic parameters, namely a position-dependent visuomotor rotation and an
inertial or acceleration-dependent load. In contrast, we used two
transformations that were equal in terms of the kinematic parameters on
which they depended. Thus, our results suggest that separate motor
working-memory resources may be used when learning transformations that
depend on different kinematic parameters. Note that this hypothesis is
not jeopardized by the results of Flanagan et al. (1999), who found
that there is no transfer of learning when subjects successively adapt
to a position-dependent visuomotor rotation and a velocity-dependent
rotary force field. Although this lack of transfer supports the idea
that kinematic and dynamic learning are independent, the
transformations involved depended on different kinematic parameters.
Although we have argued that the key difference between our study and
the study by Krakauer et al. (1999) is whether the transformations involved depend on the same or different kinematic parameters, there
are several other differences between the two studies that may have
contributed to the difference in results. In our experiment, forces
under the dynamic transformation were applied through the hand, whereas
in the study by Krakauer et al. (1999), forces were applied via
a support attached to the forearm. It might be argued that the dynamic
transformation used by Krakauer et al. (1999) is learned in
intrinsic coordinates related to the sensors and muscles of the arm,
whereas the dynamic transformation we used is learned in extrinsic
coordinates related to the position of the hand in space. Because
visuomotor rotations appear to be learned in extrinsic coordinates
(Krakauer et al., 2000), the difference between our results and those
obtained by Krakauer et al. (1999) may relate to the coordinate systems
in which the transformations are learned. However, previous work on
motor adaptation to dynamic perturbations indicates that force fields
applied to the hand are represented in intrinsic coordinates (Shadmehr
and Mussa-Ivaldi, 1994; Gandolfo et al., 1996).
Another important difference between our study and that of Krakauer et
al. (1999) concerns the properties of the sensory error signals and
motor adjustments brought about by the kinematic and dynamic
transformations. The two transformations used in our study produced
rotary errors in opposite directions and, likewise, required opposing
motor adjustments. Under the visuomotor rotation, subjects had to
generate commands that would send their arm to the right of the visual
target, whereas under the elastic force field, they had to generate
commands that would send their arm to the left of the visual target. In
contrast, the dynamic perturbation used by Krakauer et al. (1999) did
not appear to rotate the position of the hand away from the target
significantly. Thus, the kinematic and dynamic transformations produced
sensory errors and required motor adjustments that were neither both
rotational nor both opposite. It may be that the interference we
observed between kinematic and dynamic learning is related to the fact
that our transformations required somewhat opposing motor adjustments.
Indeed, previous work has shown that two kinematic tasks that depend on
the same dependent variable interfere with one another only when the
transformations involve conflict (Bock et al., 2001).
We observed statistically equivalent interference effects regardless of
whether or not subjects received visual feedback of the cursor position
while adapting to the rotary force field. Thus, the interference we
observed between kinematic and dynamic learning does not depend on
receiving sensory feedback in the same (visual) modality. Moreover,
receiving somewhat opposing visual feedback when adapting to the
kinematic and dynamic transformations does not increase the magnitude
of the interference. To the extent that opposing sensory errors might
be responsible for the observed interference, our results suggest that
these errors may be represented in a common coordinate system in motor
working memory.
In summary, we have shown that kinematic and dynamic transformations
are not learned independently when the transformations are both rotary
and position-dependent. We hypothesize that the kinematic parameter on
which a transformation depends is a key factor mediating the allocation
of resources in motor working memory. Thus, if two transformations
depend on the same kinematic parameter and also require opposing
sensorimotor adjustments, they should interfere with one another. The
strong prediction from this hypothesis is that two dynamic or two
kinematic transformations should not interfere with one another if they
depend on different kinematic parameters.
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FOOTNOTES |
Received Aug. 27, 2001; revised Oct. 31, 2001; accepted Nov. 12, 2001.
This work was supported by the Natural Sciences and Engineering
Research Council of Canada, the Wellcome Trust, and the Human Frontier
Science Program.
Correspondence should be addressed to J. Randall Flanagan, Department
of Psychology, Queen's University, Kingston, ON K7L 3N6, Canada.
E-mail: flanagan{at}psyc.queensu.ca.
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ABSTRACT
INTRODUCTION
