 |
 Previous Article | Next Article 
The Journal of Neuroscience, October 15, 2000, 20(20):7807-7815
Spatial Generalization from Learning Dynamics of Reaching
Movements
Reza
Shadmehr and
Zahra M. K.
Moussavi
Department of Biomedical Engineering, Johns Hopkins University,
Baltimore, Maryland 21205-2195
 |
ABSTRACT |
When subjects practice reaching movements in a force field, they
learn a new sensorimotor map that associates desired trajectories to
motor commands. The map is formed in the brain with elements that allow
for generalization beyond the region of training. We quantified spatial
generalization properties of these elements by training in one extreme
of the reachable space and testing near another. Training resulted in
rotations in the preferred direction (PD) of activation of some arm
muscles. We designed force fields that maintained a constant rotation
in muscle PDs as the shoulder joint rotated in the horizontal plane. In
such fields, training in a small region resulted in generalization to
near and far work spaces (80 cm). In one such field, the forces on the
hand reversed directions for a given hand velocity with respect to the
location of original training. Despite this, there was generalization.
However, if the field was such that the change in the muscle PDs
reversed as the work spaces changed, then performance was worse than
performance of naive subjects. We suggest that the sensorimotor map of
arm dynamics is represented in the brain by elements that globally
encode the position of the arm but locally encode its velocity. The
elements have preferred directions of movement but are modulated
globally by the position of the shoulder joint. We suggest that tuning
properties of cells in the motor system influence behavior and that
this influence is reflected in the way that we learn dynamics of
reaching movements.
Key words:
motor learning; motor cortex; motor control; electromyography; internal model; computational modeling; human
| |
INTRODUCTION |
Motor commands that generate
reaching movements are constructed by the brain by taking into account
predicted force dynamics of the desired trajectory (Gottlieb, 1994 ;
Shadmehr and Mussa-Ivaldi, 1994). When novel forces are imposed on the
arm, the prediction will be incorrect, and the hand will not follow the
desired trajectory (Lackner and Dizio, 1994; Goodbody and Wolpert,
1998; Flanagan et al., 1999; Krakauer et al., 1999). With practice,
motor commands are modified, and the trajectory converges to the
desired path. The computation being performed during this learning is
analogous to forming a new sensorimotor map: an association between a
desired hand trajectory and the corresponding motor commands. Tests of generalization have demonstrated that the alteration of the motor command is not limited to movements for which examples of the novel
dynamics were provided (Conditt et al., 1997). For example, learning to
compensate for novel forces along one direction of movement results in
a generalization pattern to neighboring directions that decays with
angular distance (Gandolfo et al., 1996; Sainberg et al., 1999; Ghez et
al., 2000).
Using the computational framework of learning that was proposed by
Poggio and Girosi (1990), we have hypothesized that these tests of
generalization are essentially probes regarding the tuning properties
of neurons that are taking part in representing the changing
sensorimotor map. By quantifying how learning in one direction of
movement affects other directions, we have inferred that the map is
being formed with elements that encode hand velocity locally with
nonlinear activation functions that have preferred directions of motion
(Thoroughman and Shadmehr, 2000). We have argued that this property of
the inferred computational elements is not unlike tuning properties of
some cells in the cerebellum and the motor cortex.
Although these results have quantified how the formation of a new
sensorimotor map generalizes in terms of velocity of the hand,
considerably less is known about generalization patterns in position
space. We had noted previously that after training in one region of the
work space, subjects had aftereffects when movements were performed at
a nearby work space (33 cm away) (Shadmehr and Mussa-Ivaldi, 1994).
That is, subjects expected to experience specific forces at the new arm
configuration. The patterns of aftereffects suggested that
generalization was in intrinsic, joint-centered coordinates.
During learning of dynamics of arm movements, a muscle's
activity (quantified as a function of movement direction) changes, and
one way to quantify this change is via rotations in the preferred direction (PD) of activation of each muscle during the initiation of
movement (Thoroughman and Shadmehr, 1999). With training, muscle PDs
may gradually rotate from that observed in the null field (when no
external forces are imposed). However, a muscle's PD may also depend
on the configuration of the arm (Buneo et al., 1997). We thought that
the patterns of spatial generalization of dynamics might be related to
the relative change of muscle PDs that learning of a field
induces. Specifically, learning a field in one work space might
generalize to all other arm configurations if the field was such that
it required a constant relative change in muscle PDs across work
spaces. In these experiments we made such fields and tested this idea.
From the results, we make further inferences regarding the mathematical
properties of the elements that take part in representing the
sensorimotor map for arm dynamics in the brain.
| |
MATERIALS AND METHODS |
Thirty-four healthy right-handed individuals (25 ± 5.7 years old) participated in this study. The study protocol was approved by the Johns Hopkins University Joint Committee on Clinical
Investigation, and all subjects signed a consent form.
Experimental setup. The torque motors of a two-dimensional
robotic manipulandum (Shadmehr and Brashers-Krug, 1997) were programmed to produce forces as a function of the position and velocity of the
robot's handle. When the motors were turned off, the field was null.
Subjects sat on a chair in front of the manipulandum and grasped its
handle, with the right arm being supported by a sling. Figure
1A shows the schematic
of the apparatus. A projector was hung from the ceiling and displayed a
cursor (2 × 2 mm2) representing hand
position and boxes (8 × 8 mm2)
representing targets of reaching movements on a 47 × 32 cm2 horizontal screen positioned directly
above the subject's hand (<1 cm above the robot's handle). To allow
for a comfortable viewing angle, the subject was positioned so that his
or her hand was 10 cm below the configuration in which the arm's
motion is in the horizontal plane. Cursor location was tightly
calibrated to coincide with the position of the handle. Arm link
lengths for each subject were measured, and joint angles were computed
from a simple three-dimensional kinematic model, represented in terms of the Z Y-Z Euler angles (Craig, 1986). Because the arm's plane of
action was only slightly outside the horizontal plane (by ~10°), to
compute two-dimensional force fields we projected the result onto the
horizontal plane.
View larger version (23K):
[in this window]
[in a new window]
|
Figure 1.
Experimental setup. A, Subjects
reached to visual targets while holding the handle of a manipulandum.
The location of their hand was displayed directly above their hand via
a video projector on a horizontal screen that was mounted at <1 cm
above the handle. B, Performance was measured in three
small work spaces, each a semicircle of radius 10 cm. When the hand was
in a given work space, it was initially positioned at the center
target. For odd-numbered movements, targets were chosen randomly from
the marked locations on the circumference of the work space. Targets
for even-numbered targets were always at the center of the work space.
The typical joint angle vector at the left work space
(Left) was ql = (104°,71°), that at the center work space (Center)
was qc = (63°,90°), and that
at the right work space (Right) was
qr = (13°,65°). A typical arm
link length for the upper arm was l1 = 33 cm, and that for the forearm was
l2 = 34 cm.
|
|
The projection of the cursor on top of the hand, rather than on a
computer monitor, allowed the subjects to maintain an angle of gaze
similar to the one that they would use if they were looking directly at
their hand. We found this to be a crucial factor in tests of spatial
generalization in which the configuration of the arm was greatly
changed from one position to another. If the subject did not look at
the hand but looked at a vertical monitor, the angle of gaze at the
right and left work spaces (Fig. 1B, Right, Left) was
not the same as it would be when the subjects were looking at their
hand. This discrepancy caused large errors in perception of target
position with respect to the hand in the off-center locations, but not
at the center location (Fig. 1B, Center).
Therefore, it seemed that a test of spatial generalization that did not
provide a tight coupling between the angle of gaze and the true
position of the hand might introduce a confounding variable. The
current setup was designed in view of this realization.
EMG signals were recorded from biceps, triceps, and anterior and
posterior deltoids by pediatric cardiac electrodes in a bipolar mode.
To reduce motion artifacts, EMG signals were preamplified differentially very near the electrodes (gain of 100) and then bandpass
filtered (fourth-order Butterworth; 25-400 Hz), amplified (gain of
50), and RMS rectified (32 msec window). Hand position and
velocity and the rectified EMG signals were digitized and sampled at
100 Hz.
Learning task. The task was to reach to a displayed target
(displacement of 10 cm) within 500 ± 50 msec. If the target
location was reached too slowly or too quickly, the target turned blue or red, respectively. The target "exploded" when the reach was in
time. The hand was required to remain at the target until the next
target was shown. A target set consisted of 192 targets. In some target
sets, a target had a one-sixth probability of turning the force field
off. These null field targets were catch trials in which we hoped to
measure aftereffects of adaptation.
Movements took place in three arm configurations (Fig.
1B), labeled left, center, and right work spaces
(Left, Center, and Right). The work spaces were selected by
moving the subject's chair while keeping the robot's arm
configuration constant. Because the left and right arm configurations
were near the limits of the reachable space, care was taken to choose
target directions that could be comfortably reached. In the Center and
Left work spaces, the initial target was chosen randomly from 0, 45, 90, or 135°. The next target was always at the center. In the Right work space, the initial target was chosen randomly from 180, 225, 270, and 315°. The next target was always at the center. A target set
consisted of 192 targets. All subjects were familiarized with the task
by performing one target set in the null field in each of the three
work spaces at least 24 hr before the main experiment began.
Force field design. We had observed previously that learning
a force field at a given work space resulted in changes in EMG patterns
from those observed in the null field (Thoroughman and Shadmehr, 1999).
These changes could be quantified as rotations in the PD of each
muscle's spatial tuning function. A tuning function is defined as the
average activity of a muscle during initiation of movement ( 50 to 100 msec) as a function of movement direction. The preferred direction of
this function is the vector sum of the individual activation vectors.
Furthermore, a simple biomechanical model that parceled the joint
torques into muscle forces via a moment arm matrix and assumed a
mathematically reciprocal level of activation between antagonist
muscles was able to predict accurately the magnitude of rotations that
occurred during the learning of a given force field (Thoroughman and
Shadmehr, 1999). The term "relative rotation of the PD vector"
refers to the angular change that occurs at a given arm configuration
to the PD vector between the null field and the learning of the force
field. Our initial goal then was to use this model to design a field
such that training at a given work space would result in muscle PD
rotation that would be conserved across the work spaces; that is, the
relative rotations should remain constant as a function of arm
configuration. A good candidate was a field in which torques depended
on joint angular velocity but were invariant to joint angular position.
One way to design such a field is to produce forces with the robot as a
function of the subject's joint velocities. In practice, this is
difficult because joint velocities of subjects are hard to estimate
on-line. Another approach is to produce a field that depends on hand
velocity and assume that the work space is small enough such that the
relation between hand and joint velocities, called a Jacobian, remains
constant. Although this can be accomplished by limiting training to
only small-amplitude reaching movements (for example, 10 cm), the
Jacobian would still need to be reestimated at each configuration to
make the torques invariant to joint position.
It turns out, however, that there is a special class of force fields
for which the reestimation of the Jacobian is not necessary. In these
fields, the forces on the hand and the torques on the joints are
simultaneously invariant to arm configuration. Because the torques are
invariant, rotations in muscle PDs may remain nearly constant as a
function of arm configuration.
We begin by deriving this class of fields. In our paradigm, the forces
acting on a subject's hand are described by a matrix B and
hand velocity { }. Because we will be using a
number of different force fields in this report, we index B
with integer i:
|
(1)
|
where in our planar movements
Bi is a 2 × 2 matrix. The joint
torques  for the coordinate system shown in Figure
1B can be written as:
|
(2)
|
where qs and
qe are shoulder and elbow joint
angles, J(q) is the Jacobian matrix,
l1 and
l2 are lengths of upper arm and forearm, x is the hand position vector, and T is
the transpose operator. Using the chain rule, we have
{} = J(q){ } and:
|
(3)
|
We observe that if B is skew symmetric, then
matrix:
where = W{}, is independent
of shoulder angle qs. For example,
when B = {0,1;1,0} N.sec/m, we
have:
|
(4)
|
Therefore, if B is skew symmetric, not only are the
forces on the hand invariant to hand position, but the corresponding torques on the joints (in Eq. 3) are also invariant to the position of
the shoulder. Furthermore, if we allow the elbow angle to change, its
effect is merely to scale the W matrix. In other words, if one learns a field represented by a skew-symmetric matrix B
at an elbow angle of 90°, the field is the same at any other arm configuration but simply weaker depending on the position of the elbow
angle. The word "same" in this case means that for this special
field, the forces on the hand and the torques on the joints are
approximately position invariant simultaneously.
Choice of joint coordinates. The representation of the
Jacobian in Equation 2 assumed that the elbow angle
qe was measured relative to the upper
arm (Fig. 1B). This is commonly called a relative joint coordinate system. Representation of
qe in a different way will of course
change the Jacobian. For example, if we choose to represent the elbow
angle with respect to the x-axis (commonly called an
absolute coordinate system) and call this angle
pe, then with respect to our relative
joint angle coordinates, pe = qs + qe and
ps = qs. The Jacobian in this
absolute coordinate system becomes:
and the W matrix now becomes:
Therefore, when the B matrix is skew symmetric, the
corresponding torque field in relative or absolute joint coordinates maintains its characteristic weak dependence to arm configuration.
Pilot study: generalization to a near work space. We
initially asked whether training at either Left or Right work spaces resulted in improved performance (as compared with that of naive subjects) at the Center work space. We recruited eight subjects. No EMG
was recorded from this pilot group. These subjects were trained
initially in the null field in each of the three work spaces. They then
trained in field B1 = {0,13;13,0} N.sec/m at Right (two target sets; total of 384 targets). The force field was present in all movements. After a 5 min
rest, subjects were tested in the same field at Center (a single target
set). In Center we chose 33 random targets and turned off the field to
record aftereffects of adaptation (Shadmehr and Mussa-Ivaldi, 1994). Subjects then returned on a second day. They were trained on a new
force field B2 = B1 at Left and then tested in
B2 at Center. The performance at
Center was compared with the performance of naive subjects in the same
field at Center. This naive group consisted of 21 subjects who only
trained at Center; 14 learned B1,
whereas 7 learned field B2. The data
from this control group come from a previous experiment (Thoroughman
and Shadmehr, 1999). The experiment with group 1 allowed us to ask
whether generalization takes place when the arm's configuration is
changed from the outside (Left or Right) to Center.
Experiment 1: generalization to a far work space. We next
tested the hypothesis that generalization might occur over larger distances in hand position, i.e., from Left to Right and vice versa. We
recruited six new subjects and trained them at Left in
B1 (three target sets) and tested them
at Right in the same field (one target set). Performance at Right was
compared with that of naive individuals (subjects in the pilot study).
Subjects then returned on a subsequent day and trained in
B2 at Right (three target sets) and
were then tested at Left (one target set).
Experiment 2: generalization in intrinsic coordinates. In
Experiment 1 we expected generalization to occur because the field had
torques that were essentially invariant to joint position, resulting in
rotations in muscle PDs that remained constant across the work space.
However, the force field was also invariant to hand position.
Therefore, generalization might have occurred not because muscle PDs
rotated by a constant amount but because forces on the hand were the
same at the two locations. To differentiate between these two
possibilities, we performed an experiment in which the torques were
invariant to joint configuration but forces were not invariant to hand
position. In this field, we expected muscle PDs to rotate by
approximately the same amount at each of the two arm configurations
(Left and Right) but the forces at the hand to be in opposite directions.
The field that we considered was B3 = {11,11;11,11} N.sec/m. This symmetric matrix produces joint
torques that are highly dependent on the configuration of the arm. If
subjects train in B3 at the Left work
space, our task is to find the field at the Right work space that would
preserve the relative rotations in muscle PDs. We did this by
translating B3 from Left to Right so that the relation between joint torques and joint velocities was maintained. The procedure was as follows: In the Left work space where
joint angles are described by vector
ql, the forces imposed on the hand
are F = B3{},
corresponding to joint torques:
When this field is translated in joint coordinates to the Right
work space where joint angles are described by vector
qr, the forces on the hand are:
Plugging in typical values for
ql = (104°,71°) and
qr = (13°,65°) provides the
surprising result that:
This is intriguing because it predicts that the translation of
B3 in joint space results in a field
B3* that in terms of forces on the hand is
very nearly opposite to the one that subjects originally trained in
(correlation between force field generated by
B3* and
B3 is at r = 0.985).
We had observed previously that if subjects trained in field
A and then were presented with field A in the
same work space, performance was much worse than that with naive
individuals (Brashers-Krug et al., 1996; Shadmehr and Brashers-Krug,
1997). The theory now predicted that if we train at Left in
B3 but then change the configuration
of the arm to the Right work space and test in the field
B4 = B3, subjects would demonstrate generalization.
Five subjects were recruited for this experiment. All trained in null
at Right and Left. They then trained in
B3 at Left (three target sets) and
were then tested at Right in B4 = {11,11;11,11} N.sec/m (one target set). Performance at Right was
compared with that of naive subjects (n = 4).
Experiment 3: generalization in extrinsic coordinates. It is
possible that subjects generalized in the above experiments not because
the coordinate systems matched their internal model but because they
simply had become more familiar with the robot and regardless of the
force field would do better than naive individuals would. We performed
a control experiment to test for this possibility.
In this experiment, subjects were tested for generalization in a field
that was translation invariant in hand space but not joint space. They
trained in a field that resulted in the rotation of muscle PDs in one
direction, but for the test of generalization at the new work space
they were given a field that required muscle rotations in the opposite
direction. Therefore, if the internal model generalized in terms of
muscle PDs, then, after subjects trained in Left, performance at Right
should be actually worse than those of naive individuals, despite the
fact that forces remained invariant with respect to hand position.
For this last experiment, 11 new subjects were recruited. All subjects
began by training in the null field in each of the two work spaces.
Next, six subjects trained at Left in
B3 (three target sets) and then were
tested at Right (one target set) in B3. The remaining five subjects were
trained at Right in B3 and then tested
at Left in B3. The performance in the
first set of training of each group of subjects was used as the control
for the test of generalization of the other group.
Data analysis. The onset and termination of a movement were
defined as when the tangential hand velocity crossed a threshold (0.03 m/sec) and remained above or below this level. In all fields, our
measure of movement error was the maximum perpendicular displacement from a straight line to the target.
The method for calculating spatial tuning functions of recorded EMG
signals has been described previously (Thoroughman and Shadmehr, 1999).
Briefly, EMG traces were normalized, and the average value between 50 msec before and 100 msec after the onset of the movement was calculated
for each movement and then averaged across movements for each
direction. For each target set, there were eight scalar values
representing the average EMG activity toward each of the eight
directions. We multiplied each of the eight scalars by a unit vector in
the direction of movement and formed a polar plot representing the
function that mapped target direction into initial EMG activity.
Summing the eight vectors resulted in a vector that represented the
directional bias of the muscle activity, i.e., preferred direction of
the tuning function for that muscle.
To determine whether a muscle's spatial tuning function had a
significant directional bias, we used a nonparametric approach to
estimate the distribution of the length and angle of the PD vector. By
the use of a bootstrapping technique, the 192 vectors representing the
192 EMG values for a given muscle (one for each movement during a
target set) were randomly sampled, with replacement, with uniform
probability to generate 192 new vectors (Efron and Tibshirani, 1993).
As described above, the PD vector was calculated from this resampled
population. This procedure was repeated 200 times to produce a
distribution of the PD vector for that muscle in that target set. From
this distribution the confidence intervals (in terms of SDs)
were estimated for the PD vector. We considered the tuning function to
have a significant directional bias if the magnitude of the PD vector
was >3 SDs larger than zero. Changes in the angle of the directional
PD vector between two conditions were measured only if the tuning
curves had a significant directional bias. Generally, the change in the
PD vector was represented as rotation relative to the PD of that muscle
in the null field.
| |
RESULTS |
Our objective was to test the hypothesis that there is a link
between how a sensorimotor map of arm dynamics generalizes from training in a small work space and the rotations that occur in muscle
PDs. We imagined that learning a field in one work space might
generalize to all other arm configurations if the field was such that
it required a constant relative change in muscle PDs across work
spaces. Data for a typical subject are shown in Figure
2. In Figure 2A, the
subject's arm is in the Left work space, and the EMG from biceps is
illustrated for movements made to the eight directions in the null
field and force field B3 (a symmetric
matrix in which joint torques are highly configuration dependent). The
average EMG during initiation of movements (between 50 and 100 msec),
averaged over all movements to that direction in the target set, is
plotted as a function of movement direction in the center plot. In the
null field condition, biceps has a PD vector that points toward
89 ± 1.9° (mean ± SD). With training in the field, the
EMGs gradually change, resulting in a new PD at 127 ± 2.1°.
The hypothesis predicts that when the arm is tested in another work
space, the brain will expect the field to require the same amount of
rotation in the PD of biceps. If this is the case, then performance
will be better than that of naive individuals. If the field is such
that it requires a rotation of biceps PD at the new configuration
opposite that of the original training, then performance will be worse
than that of naive individuals.
View larger version (43K):
[in this window]
[in a new window]
|
Figure 2.
EMG and kinematic data from a typical subject who
trained for three sets (each set, 192 movements) at Left in field
B3 and was then tested at Right in joint
space translation of that field, named B4.
A, EMG data from biceps during movements in the null
field (solid line) and in the force field
B3 (dashed line). Data are
aligned to the initiation of movement. The arm is in the Left work
space. Each subfigure indicates EMG activity for a
movement toward a target at one of the eight directions. The
solid line is for the null field, and the dashed
line is for the last set of training in field
B3. The center figure is the
spatial tuning function for this muscle in the null and force fields.
The EMG from time 50 to 100 msec for each movement is averaged, and
the mean ± SD over all movements toward each of eight directions
is shown. The preferred direction vector is the sum of the eight
vectors. The means ± SD of the vector's angle and the length are
noted by the gray region. Training in the field is
coincident with a 38° rotation in the preferred direction vector.
B, Magnitude of the hand velocity vector perpendicular
to the direction of the target, averaged for each target set. The
black lines are for training in
B3 at Left (3 target sets). The gray
line is for the test of generalization at Right in
B4 (1 target set). Movement
numbers are indicated. C, Magnitude of
the parallel velocity vector toward targets. Little change is observed.
D, Maximum displacement perpendicular
(Perp.) to the direction of the target. The bin size is
16 movements. Connected lines indicate a target set (192 movements). E, Spatial EMG function for biceps in the
Right work space. Field B4 at Right required
a rotation of 31° in the biceps' preferred direction, similar to
the rotation that field B3 required at Left.
Coincident with this, performance measures indicated generalization.
L, Left; R, Right.
|
|
Performance was measured by how far the force field displaced the hand
from a straight-line path to the target. With training in the Left work
space, the velocity of the hand in a direction perpendicular to that of
the target was significantly reduced (Fig. 2B),
resulting in the convergence of the hand's path to a straight line
(Fig. 2D). The subject was then tested in the Right
work space in field B4. We had
predicted that B4 at Right would
require approximately the same rotations in muscle PDs as B3 at Left. It is worth noting that
although the fields were completely opposed in hand coordinates, they
were very similar in joint coordinates. Performance at Right
demonstrated generalization (Fig. 2B,D). The EMG
tuning function for biceps at the Right work space is shown in Figure
2E; the PD for this muscle was at 178 ± 2.3°
in the null field and rotated to 147 ± 2.8° in field
B4.
Fields that are position invariant in both hand and
joint coordinates
A force field that produces torque on the arm in a way that is
invariant to joint position may produce changes in muscle PDs that are
also invariant to joint position. We began with a special class of such
fields: a field that produced forces on the hand and torques on the
joints that were simultaneously invariant to arm configuration. In this
way we hoped to be able to ask whether there is generalization across
arm configuration without having to specify the coordinate system in
which the generalization might take place. When we found
generalization, we performed further experiments to test between
alternate coordinate systems of representation.
In the pilot study, subjects learned field
B1 (forces and torques invariant to
hand or joint position) at the Right work space and then were tested at
Center on B1. On a separate day they
learned B2 at Left and were tested at
Center on B2. Two separate control groups learned either B1 or
B2 only at Center. Subject performance is shown in Figure 3. Displacement
significantly decreased as subjects learned the field at either Left or
Right. When they were tested at Center, performance was significantly
better than that of controls (p < 0.0001, Left
to Center; p < 0.001, Right to Center), demonstrating
generalization.
View larger version (32K):
[in this window]
[in a new window]
|
Figure 3.
Generalization from Left or Right to Center. The
fields are translation invariant in both hand and joint coordinates.
A, Subjects practiced in the null field, then learned
field B1 at Right, and were then tested at
Center (C) in field B1
(bin size = 64 movements; mean ± SEM). Performance at Center
was significantly better than that of naive controls. B,
Subjects learned field B2 at Left and were
tested at Center on B2. Performance at
Center was significantly better than that of naive controls.
|
|
Although control subjects at Center had to build gradually an internal
model of the field and as a consequence gradually developed aftereffects, subjects that had trained in the field at Left or Right
had significant aftereffects from the onset of testing at Center. On
their very first catch trial (second movement in the field), trained
subjects displayed an aftereffect of 1.59 ± 0.18 and 1.72 ± 0.20 cm for Left-to-Center and Right-to-Center groups, respectively. In
contrast, during the same movements the control subjects had an average
aftereffect size of 0.31 ± 0.2 cm. This suggested that the
training in the small work space at Left (or Right) had resulted in an
internal model that the brain could use to program movements at Center.
To test whether this generalization could be extended over larger
changes in hand position, in Experiment 1 we trained subjects at Left
in B1 and then tested them at Right in
B1. On a separate day, the same
subjects were trained at Right in B2
and then tested at Left in B2. Despite
the fact that work spaces were 80 cm apart, in the test of
generalization there were significant aftereffects present from the
very first catch trial: 1.49 ± 0.32 and 1.09 ± 0.18 cm from
Left to Right and Right to Left, respectively. As predicted,
performances during tests of generalization (Fig. 4) were significantly better than that of
controls (p < 0.05, Left to Right;
p < 0.001, Right to Left).
View larger version (31K):
[in this window]
[in a new window]
|
Figure 4.
Generalization across the work space. The fields
are translation invariant in both hand and joint coordinates.
A, Subjects trained at Left in
B1 and were then tested at Right in
B1 (bin size = 64 movements).
Performance at Right was significantly better than that in controls.
B, Subjects trained at Right in
B2 and were tested at Left in
B2. Performance at Left was significantly
better than that in controls. C, Rotations with respect
to the null field in the preferred direction of EMG tuning functions
during learning of field B1 at Left
(mean ± SE; bin size = 192 movements) and testing in field
B1 at Right are shown. At Right, the
rotation of EMG was similar to the rotation that was recorded at Left.
The field was nearly translation invariant in terms of muscle rotations
(as well as hand forces), coincident with generalization of performance
measures.
|
|
Because fields B1 and
B2 are nearly translation invariant in
joint space, we expected the rotation of muscle PDs to be invariant with respect to the location at which each field was learned. The EMG
rotations are shown in Figure 4C. When subjects learned B1 at Left, the PDs rotated. When the
same field was given at Right, the rotation remained essentially
unchanged for the biceps, triceps, and anterior deltoid and reduced
somewhat in the posterior deltoid. Therefore, generalization occurred
across the work space in a force field that was nearly configuration
independent, simultaneously, with respect to forces on the hand,
torques on the joints, and muscle PDs.
We note, however, that performances during tests of generalization
often declined when compared with the best performance in the original
arm configuration. This may reflect the fact that for field
B2 in the two configurations tested in
Figure 4, there is a small but nonzero dependence on the position of
the elbow angle. The small difference in the angle of the elbow joint
at these two configurations may have played a role in the lack of complete generalization.
Fields that are position invariant in joint but not
hand coordinates
The next step was to remove the position invariance property of
the field in terms of hand forces and to test whether generalization still took place. In Experiment 2, subjects learned field
B3 at Left and were then tested at
Right in B4. The fields were designed to produce similar rotations in muscle PDs at the left and right work
spaces but to have opposite hand forces. Performance at Right as
compared with that of naive controls (Fig.
5A) was significantly better
(p < 0.01). Because the fields were designed to
produce similar torques as a function of arm velocity at the two work spaces, the EMG rotations remained invariant to the configuration of
the arm (Fig. 5B).
View larger version (34K):
[in this window]
[in a new window]
|
Figure 5.
Generalization across the work space. The field is
translation invariant in joint coordinates but not hand coordinates.
A, Subjects trained at Left in
B3 and were then tested at Right in
B4 (bin size = 64 movements).
Performance at Right was significantly better than that in controls.
B, Rotations with respect to the null field in the
preferred direction of EMG tuning functions during learning of field
B3 at Left (bin size = 192 movements)
and testing in field B4 at Right are shown.
EMG rotations remained invariant to changes in arm configuration. Such
invariance is sufficient for generalization of training.
|
|
It is noteworthy that B3 = B4 and that hand forces at Left and
Right are reversed with respect to each other. If two fields with this
property are presented in sequence in the same work space, subjects
demonstrate negative interference, and performance in the second field
is significantly worse than that of naive controls (Shadmehr and
Brashers-Krug, 1997). However, with the change of the work spaces, the
two very different force fields produce similar torque patterns in
joint space, resulting in similar rotations in muscle PDs, and
generalization of learning.
Fields that are position invariant in hand but not
joint coordinates
It is possible that performance of the trained subjects in the
above experiments was better than that of the naive control groups
because they simply had more practice with the robot. A strong
prediction of our hypothesis, however, is that if a field requires a
rotation in muscle PDs at one configuration and that rotation is
opposite that required for movement in a field in another arm
configuration, then performance of the trained subjects should be worse
than that of naive individuals. In other words, generalization would
still occur, but it would impede performance.
Some subjects in Experiment 3 trained in field
B3 at Left and then were tested at
Right in B3. Remaining subjects
were trained in B3 at Right and
then were tested at Left in B3. The
fields at the two work spaces were identical in terms of forces on the hand but very different in terms of torques on the joints. Coincident with the learning of the field at Left was a negative rotation in PDs
of some muscles (Fig.
6B). However, when the
subjects were tested at Right, the movements required a positive
rotation in some muscle PDs. Predictably, performance at Right (Fig.
6A) was now significantly worse than that of naive
subjects (p < 0.01). Similarly, subjects that
trained at Right and were then tested at Left (Fig. 6C)
performed significantly worse than did naive subject
(p < 0.01). The newly formed sensorimotor map
continued to generalize, but now this generalization impeded
performance because the torques in the field did not remain invariant
to joint position.
View larger version (27K):
[in this window]
[in a new window]
|
Figure 6.
Generalization does not occur when the EMG
rotations at one arm configuration do not match the rotations that are
required for movements in another arm configuration. A,
Performance of subjects that trained in B3
at Left and were tested in B3 at Right
(mean ± SE; bin size = 64 movements) is shown. The field was
configuration independent in hand-centered coordinates but not joint
coordinates. Subjects performed significantly
worse than did naive controls. B,
Rotations with respect to the null field in the preferred direction of
EMG tuning functions during learning of B3
at Left and testing in field B3 at Right are
shown. The rotations at Left are opposite the rotations required to
move in the same hand-centered field at Right. When the relative change
in EMG PD angles rotates with arm configuration, training does not
generalize. C, Subjects that learned field
B3 at Right were also significantly worse
than control subjects in their test of generalization at Left.
Disp., Displacement.
|
|
| |
DISCUSSION |
Learning to reach in a novel dynamical environment requires a
change in the association between target directions and motor commands,
i.e., formation of a new sensorimotor map. Previously we had observed
that training in a force field at one arm configuration resulted in a
sensorimotor map that allowed the subjects to generalize to a nearby
arm configuration (Shadmehr and Mussa-Ivaldi, 1994). The generalization
appeared to have a proximal coordinate system associated with it. When
the force field was the same at the two work spaces in terms of a map
that transformed hand velocities to hand forces, subjects performed
poorly in the test of generalization. They performed much better,
however, if the field was a map that transformed joint velocities into
torques on the joints of the arm.
Practicing in a field at a given arm configuration results in a change
in the pattern of muscle activations (or forces) as a function of
movement direction (or desired motor state). The change may be
quantified as a rotation in the spatial tuning curves, or preferred
directions, of EMGs (Thoroughman and Shadmehr, 1999). In this work we
hypothesized that although the PD of each muscle may depend on the
configuration of the arm, learning might generalize as a constant
relative change in muscle PDs across the arm's work space. This would
be consistent with the coordinate system found in our previous study.
To test this idea, we designed force fields such that their learning at
a given work space would result in a constant relative change in muscle
PDs across the work spaces. One of these fields was defined by a
skew-symmetric transformation of hand velocity. This field had the
desirable property that forces on the hand and torques on the joints
were simultaneously invariant to the position of the shoulder joint.
When subjects trained in a small work space in this field, their
performance as compared with that of naive subjects was significantly
better at a work space 80 cm away. Coincident with this was a constant
relative change in the muscle PDs.
We next designed a force field that was dependent on arm configuration
in a way that when the arm moved from one work space to another, the
field nearly reversed directions. We had observed previously that
subjects performed extremely poorly, significantly worse than naive
controls, when they attempted to learn a field that was opposite the
one in which they had just completed practice (Shadmehr and
Brashers-Krug, 1997). In this case the hypothesis predicted that by
changing the configuration of the arm, subjects would actually
generalize to this opposite field. Our data were consistent with this
prediction. Notably, the generalization was coincident with a constant
relative change in muscle PDs. When the field was such that forces on
the hand were invariant to hand position but not joint angles,
coincident with a nonconstant relative change in muscle PDs, subjects
performed worse than did naive controls in the test of generalization.
Therefore, it seems that when the adapted sensorimotor map is asked to
produce motor commands in arm configurations in which it has not been
trained, it produces commands that are invariant to arm configuration
when motor commands are expressed in terms of a relative change in
muscle PDs.
Because the generalization was observed over very large portions of the
shoulder's configuration space, we suggest that the map with which the
brain represents dynamics of the arm is constructed with elements that
do not have spatial tuning functions that locally encode arm
configuration. If the map had such elements, then learning at one arm
configuration would generalize to neighboring work spaces, but not
globally. An example of such spatial locality is found among the cells
in the early visual system of the cortex. If one was to learn a visual
discrimination task with elements that have spatially localized
response characteristics, then there will be little generalization
beyond the region of training (Poggio et al., 1992)a prediction that
agrees with observation (Karni and Sagi, 1990; Ahissar and Hochstein,
1997). In contrast to the visual areas, cells in the primary motor
cortex are generally not tuned to a specific arm configuration, but
their firing is often modulated globally, and sometimes linearly, by
arm configuration (Georgopoulos et al., 1984). Learning dynamics with
elements that behave in this way should generalize globally, in
agreement with what we have found in these experiments.
The spatial generalization observed here was associated with a specific
coordinate system: that of joint torques and muscle PDs. This
coordinate system is in agreement with results reported recently for
learning of inertial fields but stands in sharp contrast to spatial
generalization patterns for learning of kinematic transformations (which generalize in extrinsic coordinates) (Ghez et al., 2000). Are
these observations potentially related to properties of cells in the
motor areas of the brain? One such property is directional tuning
during reaching movements (Caminiti and Johnson, 1992): when neuronal
activity is expressed with respect to the direction of reach, the
tuning function is broad and has a PD. When monkeys learn to reach in
viscous force fields, PDs of some cells in the primary, premotor, and
supplementary motor areas undergo rotations (Benda et al., 1997;
Schioppa et al., 1999). These cells have been called "dynamic"
cells to differentiate them from another group of cells that do not
show changes in their PD ("kinematic" cells). The rotations in the
former group are different among the cells, but as a population, the
average rotation is not unlike the rotations in PDs of some muscles.
However, unlike muscle PDs, many of these cells maintain the change in
their PDs during the washout period after the field returns to null
(Gandolfo et al., 2000). Therefore, these cells are not simply upper
motoneurons but are likely involved in representing the memory of the
novel arm dynamics.
We do not know how PDs of these "memory" cells change as a function
of arm configuration, but other studies suggest that while making
reaches in the null field, the active cells in one work space generally
do not cease to fire in the new work space, and their PDs may rotate
(Caminiti et al., 1990, 1991). The rotation is widely different among
the cells, but as a population, the median change is similar to the
change in the shoulder angle. This observation led Caminiti and
colleagues (Burnod et al., 1992) to suggest that firing rates of some
cells in the motor cortex simultaneously reflect two kinds of signals:
a postural signal encoding the arm's configuration in joint space and
a signal encoding aspects of dynamics of the reach. On the basis of the
generalization patterns reported here, it seems reasonable that
the memory cells reported by Bizzi and colleagues (Gandolfo et al.,
2000) might have PDs that, as a population, rotate with the shoulder
joint. This would be the contribution of a postural signal. The crucial prediction is that after training in a force field, when the arm returns to the null field, these memory cells as a population should
maintain a constant relative change in their PD as the arm moves to
various regions of the work space.
We are not implying, however, that the internal model is represented in
the motor cortex. Clearly, tuning properties similar to those of the
motor cortex have been found in the cerebellum (Fortier et al., 1993),
and learning-related changes in the motor cortex may be caused by
changing inputs from this region (Martin et al., 2000). Our suggestion
is that tuning properties of cells in the motor system must influence
behavior. Quantifying patterns of learning and generalization, as seen
in adaptation to novel dynamics, is one way to visualize this
influence. In further support of this conjecture, note that cells in
the motor cortex and cerebellum are tuned with respect to direction of
movement. This predicts a generalization in velocity space that will be
distinctly different from generalization across arm configurations.
Generalization in velocity space, for example, quantifies how learning
in one direction will affect nearby directions of movement. When
training is confined to a single arm configuration, learning a single
direction of movement generalizes to other target directions as a
function that decays with the angular distance of the targets (Ghez et al., 2000; Thoroughman and Shadmehr, 2000). The shape of this generalization function predicts that learning is with computational elements that have directional tuning characteristics not unlike those
found in the cerebellum and the motor cortex (Thoroughman and Shadmehr,
2000). Taken together, current results from various laboratories on how
humans learn dynamics of reaching movements point to a sensorimotor map
that is composed by the brain with elements that encode arm
configuration globally but arm velocity locally. The output of this map
is force represented in joint- or muscle-based coordinates.
Nevertheless, the elements that are used by the brain to represent a
particular sensorimotor map are likely to also depend on the degree of
difficulty in the task. Studies in visual perceptual learning provide
important clues: when a perceptual discrimination task is very
difficult, learning is specific to the orientation and position of the
stimulus and does not generalize (Karni and Sagi, 1990; Poggio et al.,
1992). This suggests that the map is formed with elements that have the
fine spatial retinotopy exhibited in the early stages of visual
information processing (Poggio, 1990). However, when the perceptual
task is easy, learning generalizes across orientations and retinal
positions, matching the spatial generalization of higher
visual-processing areas (Ahissar and Hochstein, 1997). Taken together,
it seems that the perceptual-learning process in the brain begins by
assembling elements at the highest levels of visual processing first,
which in turn direct learning to their respective lower level inputs if
the condition is hard enough to warrant it (Ahissar and Hochstein,
1997).
In the hierarchy of control in the motor cortical systems, the highest
levels are often associated with pre-SMA, SMA, and the
premotor regions, whereas the lowest level is occupied by the primary
motor cortex. Approximately fitting into this framework is the result
that stimulation generally produces complex multijoint bilateral
movements in the SMA and single-joint unilateral twitch-like movements
in the primary motor cortex. Therefore, the size of the "effective
field" in the SMA is much larger than that of the localized field (in
terms of region of influence in the configuration space of the entire
body) that is evoked from the primary motor cortex stimulation. If one
could learn a motor task with one hand and be able to generalize to
another limb, then the theory predicts that learning had engaged
elements in the higher levels of motor control in which effective
fields are broad. An example of this is our ability to sign our name
with our dominant hand and yet retain much of the stroke
characteristics when the foot is used for the task. Interestingly,
functional imaging shows that regions that are activated in both hand
and foot signing are in the SMA and premotor cortex, and not in the
primary motor cortex or the basal ganglia (Rijntjes et al., 1999).
| |
FOOTNOTES |
Received May 5, 2000; revised July 14, 2000; accepted Aug. 1, 2000.
This work was funded in part by grants from the United States Office of
Naval Research and by the National Institute of Neurological Disorders
and Stroke Grant NS 37422. The work has benefited greatly from our
interactions with K. A. Thoroughman and the other scientists at
the Johns Hopkins University Laboratory for Computational Motor Control.
Correspondence should be addressed to Dr. Reza Shadmehr, Johns Hopkins
School of Medicine, 419 Traylor Building, 720 Rutland Avenue,
Baltimore, MD 21205-2195. E-mail: reza{at}bme.jhu.edu.
Dr. Moussavi's present address: Department of Electrical Engineering,
University of Manitoba, Winnipeg, MB R3T2N2, Canada. E-mail:
mousavi{at}ee.umanitoba.ca.
| |
REFERENCES |
-
Ahissar M,
Hochstein S
(1997)
Task difficulty and the specificity of perceptual learning.
Nature
387:401-405[Medline].
-
Benda BJ,
Gandolfo F,
Li CSR,
Tresch MC,
DiLorenzo D,
Bizzi E
(1997)
Neuronal activities in M1 of a macaque monkey during reaching movements in a viscous force field.
Soc Neurosci Abstr
23:1556.
-
Brashers-Krug T,
Shadmehr R,
Bizzi E
(1996)
Consolidation in human motor memory.
Nature
382:252-255[Medline].
-
Buneo CA,
Soechting JF,
Flanders M
(1997)
Postural dependence of muscle actions: implications for neural control.
J Neurosci
17:2128-2142[Abstract/Free Full Text].
-
Burnod Y,
Grandguillaume P,
Otto I,
Ferraina S,
Johnson PB,
Caminiti R
(1992)
Visuomotor transformations underlying arm movements toward visual targets: a neural network model of cerebral cortical operations.
J Neurosci
12:1435-1453[Abstract].
-
Caminiti R,
Johnson PB
(1992)
Internal representation of movement in the cerebral cortex as revealed by the analysis of reaching.
Cereb Cortex
2:269-276[Free Full Text].
-
Caminiti R,
Johnson PB,
Urbano A
(1990)
Making arm movements within different parts of space: dynamic aspects in the primate motor cortex.
J Neurosci
10:2039-2058[Abstract].
-
Caminiti R,
Johnson PB,
Galli C,
Ferraina S,
Burnod Y
(1991)
Making arm movements within different parts of space: the premotor and motor cortical representation of a coordinate system for reaching to visual targets.
J Neurosci
11:1182-1197[Abstract].
-
Conditt MA,
Gandolfo F,
Mussa-Ivaldi FA
(1997)
The motor system does not learn the dynamics of the arm by rote memorization of past experience.
J Neurophysiol
78:554-560[Abstract/Free Full Text].
-
Craig JJ
(1986)
In: Introduction to robotics: mechanics and control. Reading, MA: Addison-Wesley.
-
Efron B,
Tibshirani RJ
(1993)
In: An introduction to the bootstrap, pp 45-56. New York: Chapman and Hall.
-
Flanagan JR,
Nakano E,
Imamizu H,
Osu R,
Yoshioka T,
Kawato M
(1999)
Composition and decomposition of internal models in motor learning under altered kinematic and dynamic environments.
J Neurosci
19:RC34.
-
Fortier PA,
Smith AM,
Kalaska JF
(1993)
Comparison of cerebellar and motor cortex activity during reaching: directional tuning and response variability.
J Neurophysiol
69:1136-1149[Abstract/Free Full Text].
-
Gandolfo F,
Mussa-Ivaldi FA,
Bizzi E
(1996)
Motor learning by field approximation.
Proc Natl Acad Sci USA
93:3843-3846[Abstract/Free Full Text].
-
Gandolfo F,
Li CR,
Benda BJ,
Schioppa CP,
Bizzi E
(2000)
Cortical correlates of learning in monkeys adapting to a new dynamical environment.
Proc Natl Acad Sci USA
97:2259-2263[Abstract/Free Full Text].
-
Georgopoulos AP,
Caminiti R,
Kalaska JF
(1984)
Static spatial effects in motor cortex and area 5: quantitative relationships in two-dimensional space.
Exp Brain Res
54:446-454[Web of Science][Medline].
-
Ghez C,
Krakauer JW,
Sainburg RL,
Ghilardi MF
(2000)
Spatial representation and internal models of limb dynamics in motor learning.
In: The new cognitive neurosciences (Gazzaniga MS,
ed), pp 501-514. Cambridge, MA: MIT.
-
Goodbody SJ,
Wolpert DM
(1998)
Temporal and amplitude generalization in motor learning.
J Neurophysiol
79:1825-1838[Abstract/Free Full Text].
-
Gottlieb GL
(1994)
The generation of the efferent command and the importance of joint compliance in fast elbow movements.
Exp Brain Res
97:545-550[Web of Science][Medline].
-
Karni A,
Sagi D
(1990)
Where practice makes perfect in texture discrimination: evidence for primary visual cortex plasticity.
Proc Natl Acad Sci USA
88:4966-4970[Abstract/Free Full Text].
-
Krakauer JW,
Ghilardi MF,
Ghez C
(1999)
Independent learning of internal models for kinematic and dynamic control of reaching.
Nat Neurosci
2:1026-1031[Web of Science][Medline].
-
Lackner JR,
Dizio P
(1994)
Rapid adaptation to Coriolis force perturbations of arm trajectory.
J Neurophysiol
72:299-313[Abstract/Free Full Text].
-
Martin JH,
Cooper SE,
Hacking A,
Ghez C
(2000)
Differential effects of deep cerebellar nuclei inactivation on reaching and adaptive control.
J Neurophysiol
83:1886-1899[Abstract/Free Full Text].
-
Poggio T
(1990)
A theory of how the brain might work.
Cold Spring Harb Symp Quant Biol
55:899-910[Abstract/Free Full Text].
-
Poggio T,
Girosi F
(1990)
Theory of networks for learning.
Science
247:978-982[Abstract/Free Full Text].
-
Poggio T,
Fahle M,
Edelman S
(1992)
Fast perceptual learning in visual hyperacuity.
Science
256:1018-1021[Abstract/Free Full Text].
-
Rijntjes M,
Dettmers C,
Buchel C,
Kiebel S,
Frackowiak RSJ,
Weiller C
(1999)
A blueprint for movement: functional and anatomical representations in the human motor system.
J Neurosci
19:8043-8048[Abstract/Free Full Text].
-
Sainberg RL,
Ghez C,
Kalakanis D
(1999)
Intersegmental dynamics are controlled by sequential anticipatory, error correction, and postural mechanisms.
J Neurophysiol
81:1045-1056[Abstract/Free Full Text].
-
Schioppa CP,
Li CSR,
Bizzi E
(1999)
Neural activity in the supplementary and pre-supplementary motor areas of a monkey adapting to a viscous force field.
Soc Neurosci Abstr
25:380.
-
Shadmehr R,
Brashers-Krug T
(1997)
Functional stages in the formation of human long-term motor memory.
J Neurosci
17:409-419[Abstract/Free Full Text].
-
Shadmehr R,
Mussa-Ivaldi FA
(1994)
Adaptive representation of dynamics during learning of a motor task.
J Neurosci
14:3208-3224[Abstract].
-
Thoroughman KA,
Shadmehr R
(1999)
Electromyographic correlates of learning internal models of reaching movements.
J Neurosci
19:8573-8588[Abstract/Free Full Text].
-
Thoroughman KA, Shadmehr R (2000) Learning of action through
adaptive combination of motor primitives. Nature, in
press.
Copyright © 2000 Society for Neuroscience 0270-6474/00/20207807-09$05.00/0
This article has been cited by other articles:
|
|
|
|
 
N. Cothros, J. Wong, and P. L. Gribble
Visual Cues Signaling Object Grasp Reduce Interference in Motor Learning
J Neurophysiol,
October 1, 2009;
102(4):
2112 - 2120.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
A. de Rugy, M. R. Hinder, D. G. Woolley, and R. G. Carson
The Synergistic Organization of Muscle Recruitment Constrains Visuomotor Adaptation
J Neurophysiol,
May 1, 2009;
101(5):
2263 - 2269.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
M. E. Berryhill and H. C. Hughes
On the minimization of task switch costs following long-term training
Atten Percept Psychophys,
April 1, 2009;
71(3):
503 - 514.
[Abstract]
[PDF]
|
|
|
|
|
|
|
K. Rabe, O. Livne, E. R. Gizewski, V. Aurich, A. Beck, D. Timmann, and O. Donchin
Adaptation to Visuomotor Rotation and Force Field Perturbation Is Correlated to Different Brain Areas in Patients With Cerebellar Degeneration
J Neurophysiol,
April 1, 2009;
101(4):
1961 - 1971.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
T. Bhatt and Y. C. Pai
Generalization of Gait Adaptation for Fall Prevention: From Moveable Platform to Slippery Floor
J Neurophysiol,
February 1, 2009;
101(2):
948 - 957.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
J. Kluzik, J. Diedrichsen, R. Shadmehr, and A. J. Bastian
Reach Adaptation: What Determines Whether We Learn an Internal Model of the Tool or Adapt the Model of Our Arm?
J Neurophysiol,
September 1, 2008;
100(3):
1455 - 1464.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
S. Tremblay, G. Houle, and D. J. Ostry
Specificity of Speech Motor Learning
J. Neurosci.,
March 5, 2008;
28(10):
2426 - 2434.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
A. G. Richardson, G. Lassi-Tucci, C. Padoa-Schioppa, and E. Bizzi
Neuronal Activity in the Cingulate Motor Areas During Adaptation to a New Dynamic Environment
J Neurophysiol,
March 1, 2008;
99(3):
1253 - 1266.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
A. A. G. Mattar and D. J. Ostry
Modifiability of Generalization in Dynamics Learning
J Neurophysiol,
December 1, 2007;
98(6):
3321 - 3329.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
K. A. Thoroughman, W. Wang, and D. N. Tomov
Influence of Viscous Loads on Motor Planning
J Neurophysiol,
August 1, 2007;
98(2):
870 - 877.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
J. L. Emken, R. Benitez, A. Sideris, J. E. Bobrow, and D. J. Reinkensmeyer
Motor Adaptation as a Greedy Optimization of Error and Effort
J Neurophysiol,
June 1, 2007;
97(6):
3997 - 4006.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
E. Guigon, P. Baraduc, and M. Desmurget
Computational Motor Control: Redundancy and Invariance
J Neurophysiol,
January 1, 2007;
97(1):
331 - 347.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
A. G. Richardson, S. A. Overduin, A. Valero-Cabre, C. Padoa-Schioppa, A. Pascual-Leone, E. Bizzi, and D. Z. Press
Disruption of Primary Motor Cortex before Learning Impairs Memory of Movement Dynamics
J. Neurosci.,
November 29, 2006;
26(48):
12466 - 12470.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
T. E. Milner and M. R. Hinder
Position Information But Not Force Information Is Used in Adapting to Changes in Environmental Dynamics
J Neurophysiol,
August 1, 2006;
96(2):
526 - 534.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
M. S. Fine and K. A. Thoroughman
Motor Adaptation to Single Force Pulses: Sensitive to Direction but Insensitive to Within-Movement Pulse Placement and Magnitude
J Neurophysiol,
August 1, 2006;
96(2):
710 - 720.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
L. E. Sergio, C. Hamel-Paquet, and J. F. Kalaska
Motor Cortex Neural Correlates of Output Kinematics and Kinetics During Isometric-Force and Arm-Reaching Tasks
J Neurophysiol,
October 1, 2005;
94(4):
2353 - 2378.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
K. A. Thoroughman and J. A. Taylor
Rapid Reshaping of Human Motor Generalization
J. Neurosci.,
September 28, 2005;
25(39):
8948 - 8953.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
N. Malfait, P. L. Gribble, and D. J. Ostry
Generalization of Motor Learning Based on Multiple Field Exposures and Local Adaptation
J Neurophysiol,
June 1, 2005;
93(6):
3327 - 3338.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
S. K. Wainscott, O. Donchin, and R. Shadmehr
Internal Models and Contextual Cues: Encoding Serial Order and Direction of Movement
J Neurophysiol,
February 1, 2005;
93(2):
786 - 800.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
J. J. Marotta, G. P. Keith, and J. D. Crawford
Task-Specific Sensorimotor Adaptation to Reversing Prisms
J Neurophysiol,
February 1, 2005;
93(2):
1104 - 1110.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
T. Lam and V. Dietz
Transfer of Motor Performance in an Obstacle Avoidance Task to Different Walking Conditions
J Neurophysiol,
October 1, 2004;
92(4):
2010 - 2016.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
N. Malfait and D. J. Ostry
Is Interlimb Transfer of Force-Field Adaptation a Cognitive Response to the Sudden Introduction of Load?
J. Neurosci.,
September 15, 2004;
24(37):
8084 - 8089.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
J. Wang and R. L. Sainburg
Interlimb Transfer of Novel Inertial Dynamics Is Asymmetrical
J Neurophysiol,
July 1, 2004;
92(1):
349 - 360.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
B. K. Barry and R. G. Carson
The Consequences of Resistance Training for Movement Control in Older Adults
J. Gerontol. A Biol. Sci. Med. Sci.,
July 1, 2004;
59(7):
M730 - M754.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
R. F. Reynolds and A. M. Bronstein
The Moving Platform Aftereffect: Limited Generalization of a Locomotor Adaptation
J Neurophysiol,
January 1, 2004;
91(1):
92 - 100.
[Abstract]
[Full Text]
|
|
|
|
|
|
|
C. Padoa-Schioppa, C.-S. R. Li, and E. Bizzi
Neuronal Activity in the Supplementary Motor Area of Monkeys Adapting to a New Dynamic Environment
J Neurophysiol,
January 1, 2004;
91(1):
449 - 473.
[Abstract]
[Full Text]
|
|
|
|
|
|
|
O. Donchin, J. T. Francis, and R. Shadmehr
Quantifying Generalization from Trial-by-Trial Behavior of Adaptive Systems that Learn with Basis Functions: Theory and Experiments in Human Motor Control
J. Neurosci.,
October 8, 2003;
23(27):
9032 - 9045.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
C. D. Mah and F. A. Mussa-Ivaldi
Generalization of Object Manipulation Skills Learned without Limb Motion
J. Neurosci.,
June 15, 2003;
23(12):
4821 - 4825.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
L. E. Sergio and J. F. Kalaska
Systematic Changes in Motor Cortex Cell Activity With Arm Posture During Directional Isometric Force Generation
J Neurophysiol,
January 1, 2003;
89(1):
212 - 228.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
M. Flanders, J. M. Hondzinski, J. F. Soechting, and J. C. Jackson
Using Arm Configuration to Learn the Effects of Gyroscopes and Other Devices
J Neurophysiol,
January 1, 2003;
89(1):
450 - 459.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
S. E. Criscimagna-Hemminger, O. Donchin, M. S. Gazzaniga, and R. Shadmehr
Learned Dynamics of Reaching Movements Generalize From Dominant to Nondominant Arm
J Neurophysiol,
January 1, 2003;
89(1):
168 - 176.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
N. Malfait, D. M. Shiller, and D. J. Ostry
Transfer of Motor Learning across Arm Configurations
J. Neurosci.,
November 15, 2002;
22(22):
9656 - 9660.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
O. Donchin, L. Sawaki, G. Madupu, L. G. Cohen, and R. Shadmehr
Mechanisms Influencing Acquisition and Recall of Motor Memories
J Neurophysiol,
October 1, 2002;
88(4):
2114 - 2123.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
J. B. Dingwell, C. D. Mah, and F. A. Mussa-Ivaldi
Manipulating Objects With Internal Degrees of Freedom: Evidence for Model-Based Control
J Neurophysiol,
July 1, 2002;
88(1):
222 - 235.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
D.Y.P. Henriques and J. D. Crawford
Role of Eye, Head, and Shoulder Geometry in the Planning of Accurate Arm Movements
J Neurophysiol,
April 1, 2002;
87(4):
1677 - 1685.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
TOP
ABSTRACT
INTRODUCTION
