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The Journal of Neuroscience, October 15, 1998, 18(20):8423-8435
Short-Term Memory for Reaching to Visual Targets: Psychophysical
Evidence for Body-Centered Reference Frames
J.
McIntyre,
F.
Stratta, and
F.
Lacquaniti
Human Physiology Section, Scientific Institute Santa Lucia,
National Research Council and the University of Tor Vergata, 00179 Rome, Italy
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ABSTRACT |
Pointing to a remembered visual target involves the transformation
of visual information into an appropriate motor output, with a passage
through short-term memory storage. In an attempt to identify the
reference frames used to represent the target position during the
memory period, we measured errors in pointing to remembered
three-dimensional (3D) targets.
Subjects pointed after a fixed delay to remembered targets distributed
within a 22 mm radius volume. Conditions varied in terms of lighting
(dim light or total darkness), delay duration (0.5, 5.0, and 8.0 sec),
effector hand (left or right), and workspace location. Pointing errors
were quantified by 3D constant and variable errors and by a novel
measure of local distortion in the mapping from target to endpoint
positions.
The orientation of variable errors differed significantly between light
and dark conditions. Increasing the memory delay in darkness evoked a
reorientation of variable errors, whereas in the light, the
viewer-centered variability changed only in magnitude. Local distortion
measurements revealed an anisotropic contraction of endpoint positions
toward an "average" response along an axis that points between the
eyes and the effector arm. This local contraction was present in both
lighting conditions. The magnitude of the contraction remained constant
for the two memory delays in the light but increased significantly for
the longer delays in darkness. These data argue for the separate
storage of distance and direction information within short-term memory,
in a reference frame tied to the eyes and the effector arm.
Key words:
sensorimotor transformations; reference frames; short-term memory; reaching; constant error; variable error; local
distortion
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INTRODUCTION |
When reaching to a remembered
target, how does the CNS specify the endpoint of the intended movement?
It appears that the CNS does not specify all three spatial dimensions
together. Instead, movement parameters are parcellated into distance
and directional components (Rosenbaum, 1980 ; Georgopoulos, 1991;
Flanders et al., 1992; Fu et al., 1993; Gordon et al., 1994), but the
question remains regarding the origin to which the distance and
direction are referred. Greater variability of final positions in the
direction of movement versus along an orthogonal axis (Gordon et al.,
1994; Desmurget et al., 1997; Messier and Kalaska, 1997), accumulation of errors for sequential movements (Bock and Eckmiller, 1986), and
different central processing times for direction and extent (Rosenbaum,
1980) all suggest that the upcoming movement is planned in terms of the
displacement from the initial posture. In other studies, however,
viewer-centered (Soechting et al., 1990; McIntyre et al., 1997) or
shoulder-centered (Soechting and Flanders, 1989a,b; Berkinblit et al.,
1995) distributions of errors indicate an internal specification of the
final intended position, as opposed to the movement direction and
extent. Differences among these various findings might be explained by
the likely dependence of the reference frame on both task requirements
and available sensory cues (Desmurget et al., 1997; Lacquaniti, 1997;
Messier and Kalaska, 1997).
Additional insight into the encoding schemes used by the CNS can be
gained by imposing a controlled time delay between the target
presentation and the movement. Using this paradigm, characteristics of
internal storage mechanisms can be distinguished from effects of noise
in the sensory input or motor output. Furthermore, the evolution of
errors as the memory delay increases may reveal the reference frames
inherent in the neural circuits that encode the remembered target
position. With this in mind, we performed a series of psychophysical
studies of errors made when pointing to remembered targets presented
visually in three-dimensional (3D) space. We compared performance under
two lighting conditions and three different memory delays. We developed
3D statistical tools used to identify sources of noise, bias, and local
distortion in the transformation from target to pointing position.
Using this approach we have characterized the acquisition,
transformation, and memory storage of sensorimotor information for an
arm-reaching task. We conclude that short-term memory mechanisms store
distance and direction separately in an arm-centered reference frame,
with a faster rate of decay for distance information in the dark. When vision of the hand is permitted, a viewer-centered memory of the target
position can be used to reduce variability and distortions at the
output.
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MATERIALS AND METHODS |
Analyses of constant and variable pointing
errors have been used in the past to identify the sources of
information that contribute to the internal representation of a
memorized target position (Foley and Held, 1972; Prablanc et al., 1979;
Poulton, 1981; Soechting and Flanders, 1989a; Darling and Miller, 1993;
Berkinblit et al., 1995; Desmurget et al., 1997; McIntyre et al.,
1997). Constant error refers to bias in the mean response
for repeated trials to a given target, and variable error
describes the variability of individual responses, as quantified by the
variance or SD about the mean. Three-dimensional variable error is
represented as a 3 × 3 covariance matrix, where the eigenvalues
of this matrix describe the magnitude of the variability. In this paper
we introduce a third measure of error, which we call the local
distortion. Local distortion describes the mapping of spatial
relationships between nearby points as data are processed through the
sensorimotor pathways.
Constant error, variable error, and local distortion provide three
complementary measures of the characteristics of a sensorimotor pathway. Specific workspace-related patterns in any one of these three
measures can provide evidence for the internal structure of a
sensorimotor process. In the following experiments we have used all
three measures of pointing error to characterize the acquisition,
transformation, and storage of sensorimotor information within the
nervous system.
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Experimental protocols |
The experimental apparatus was identical to that described by
McIntyre et al. (1997). Subjects sat on a 45-cm-high straight-back chair facing a table measuring 150 cm wide × 54.5 cm deep at a height of 69 cm. To the opposite edge of the table was fixed an upright, flat backboard measuring 130 cm wide × 85 cm high.
Subjects were seated ~20 cm from the front edge of the table (75 cm
from the backboard). A headrest helped the subject maintain a constant head position throughout the experiment, although the head was free to
turn.
A red, 5-mm-diameter light-emitting diode (LED) was presented to the
subject by a robot, in the region between the subject and the
backboard. The subject placed the index finger of the hand (left or
right, depending on the specific protocol) on one of two starting
positions, located on the table top 10 cm from the front edge of the
table and 20 cm to the right or left of the midline (depending on the
experiment variant; see below). The starting position was an upraised
bump (2.5-mm-radius hemisphere) on the table surface that could be
located by touch.
At the beginning of a trial, a green fixation LED was illuminated,
located on the surface of the backboard at the midline, 13 cm above the
tabletop. One second later an audible attention signal sounded. After a
random delay of 1.2-2.4 sec, the fixation light was extinguished, and
the red target LED was lighted at the target position for a period of
1.4 sec, then extinguished, and quickly removed. After a memory delay
that followed the extinction of the target LED (0.5, 5.0, or 8.0 sec,
depending on the specific protocol described below), a second audible
tone sounded, indicating that the subject should initiate the pointing
movement. Subjects were instructed to place the tip of the index finger
so as to touch the remembered location of the target LED and to attempt to maintain fixation of the remembered target position during the
memory delay period. The subject had 2 sec to perform the movement and
hold at the remembered target position.
Visual conditions
The board, the rod carrying the LED, and the top surface of the
table were painted black. During target presentation, the room was
dimly illuminated with indirect lighting coming from behind the
backboard. Under these conditions, no discernible visual points could
be seen directly behind the presented target. For a gaze fixated on the
center of the backboard, the visual field was uniform over a range of
±40° horizontally and ±30° vertically. Robot motion occurred only
with the LED turned off and thus could not be seen.
The actual pointing movements were performed under two different
illuminations: dim light and total darkness. In the dim light condition, illumination was held constant as described above throughout the target presentation, memory delay, and pointing periods. The finger
was dimly visible (0.0029 cd/m2) against the black
background (0.0010 cd/m2). For trials conducted in
total darkness, the dim room lights were extinguished at the same
moment as the target LED and remained off during the memory delay and
movement.
Positions and movements were measured by a three-dimensional infrared
tracking system (Elite System, BTS, Milan, Italy). During the
experiment, the movement was measured by means of a reflective marker
attached to the fingertip (McIntyre et al., 1997). The marker position
was sampled at a rate of 100 Hz. A second marker attached to the
forehead 2 cm above the midpoint between the eyes was also tracked
during each trial. To measure the actual location of each target
position, the subjects performed a set of 10 control trials before
starting the experiment in which they moved the index finger to touch
the actual LED situated at each of the target positions.
The three-dimensional trajectory of the finger-tip marker was computed
for each trial. We calculated the initial and final position of each
movement as the mean position computed over the first and last 10 samples, respectively, of the 2 sec movement recording. A threshold
based on the SD for these mean positions was used to reject trials in
which the final endpoint position was not stable. Fewer than 2% of
trials were rejected on this basis. A measured 0.16 mm average SD of
the endpoint during the final hold period gives an estimate of the
resolution of our measurements of the endpoint position, taking into
account measurement noise and the stability of the finger at the
endpoint. Variability of the starting position was <2.5 mm (SD) in all
three directions, as noted previously (McIntyre et al., 1997).
Target configurations
Trials were performed in blocks of 60 or 90, with one block of
trials lasting ~15 min. Within a single block of trials, target locations were restricted to a relatively small volume in
three-dimensional space. Three different regions of the workspace were
measured in separate blocks, all located ~10 cm above the shoulder
(35 cm above the table): (1) the middle region, located 60 cm directly in front of the subject, (2) the left region, 60 cm in front of the subject and 38 cm to the left of the midline, and
(3) the right region, 60 cm in front of the subject and 38 cm to the right. For a single workspace region, eight targets were
distributed uniformly on the surface of a sphere of 22 mm radius, with
a ninth target located at the center. This configuration is equivalent to points on the corners of a cube. The cube was tilted such that two
opposite corners and the center formed a vertical line, and rotated to
be symmetric across the midline. Subjects performed a total of 180 test
trials to targets within a single condition and workspace region (20 trials per target).
Protocols
Two sets of experiments were performed: one to identify the
effects of visual conditions and memory delay period on pointing errors
to remembered targets, and the other to clarify the organization of
pointing errors when the hand cannot be seen during the pointing task.
All subjects were right-handed and were naive to the hypotheses being
tested in these experiments.
Lighting and delay. To compare effects of lighting
conditions and memory delay, subjects performed a set of pointing
experiments using the right hand from the right starting position. Six
subjects used the right hand to perform pointing movements in the dim
light conditions, with a 0.5 sec memory delay
(light-short), to all three workspaces regions (left,
middle, and right, in separate blocks). Five of these six subjects
repeated the experiment with pointing movements performed in total
darkness after a 0.5 sec memory delay (dark-short). These
same five subjects performed the pointing task in darkness after a 5.0 sec memory delay (dark-long). Two subjects performed the
task in dim light with a 5.0 sec delay only (light-long) to
the three workspace regions. In a separate experiment, six subjects
pointed to targets in the middle workspace region, with two memory
delays (0.5 and 8.0 sec) mixed within the same block of trials.
Effector arm and starting position. We tested for a
center of rotation for observed effects in darkness by testing two
different starting positions and both arms. Results from the
dark-long protocol provided data for pointing with the
right arm from the right side (right-right). Five subjects
pointed in darkness after a 5.0 sec delay to the left, middle, and
right workspace regions with the right arm, starting from the left
position (right-left). Eight subjects performed the same
protocol to the left and right workspace regions only using the left
arm and starting from the left position (left-left).
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Analysis |
Constant error vectors, computed as the average error over all
nine targets within a single workspace region, were calculated for each
workspace region as described in McIntyre et al. (1997):
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(1)
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where ti is the 3D vector location
of target i, pj i is the final
pointing position for trial j to target i, and
ni and n are the number of
valid trials to target i, and the total number of valid
trials to all nine targets, respectively. The 3D covariance estimated
from data over all k = 9 targets is computed by
Morrison (1990):
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(2)
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where the deviation  ji = pji   i for trial j to target
i is computed relative to the mean
i of trials to target
i, not to the overall mean for all targets. The 3D
covariance matrix S can be scaled to compute the matrix describing the 95% tolerance ellipsoid, based on the total number of
trials n:
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(3)
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where q = 3 is the dimensionality of the
Cartesian vector space and k = 9 is the number of
targets.
Local distortion
Consider a circular array of targets as shown in Figure
1a (open circles). The mean
position of repeated movements to each target creates an array of final
pointing positions (filled circles). The measurement of local
distortion refers to the fidelity with which the relative spatial
organization of the targets is maintained in the configuration of final
pointing positions. If the constant error in the mapping from target to
endpoint position is approximately the same for all eight targets, the
array of final pointing positions will be an undistorted replica of the
target array, despite the overall displacement from the center (Fig.
1b). On the other hand, differences in the mapping of
individual targets can result in a distorted representation of the
target array within the pattern of final pointing positions. This
distortion can manifest itself as an expansion or contraction of the
local space (Fig. 1c,d). The expansion or contraction may be
unequal for different dimensions, resulting in an anisotropic
distortion of the target array (Fig. 1e,f). The
transformation from target to endpoint position might also include a
rotation of the local space, or reflections through the center
position, either alone or in combination with a local expansion or
contraction (data not shown).
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Figure 1.
Definition of local distortion. a,
When pointing accurately, the endpoint positions ( ) reproduce the
spatial organization of the target locations ( ). b,
Transformation from target to endpoint positions with a large constant
error but no local distortion. c-f, Types of local
distortion that can be introduced by a linear transformation, excluding
rotations: local expansion (c), local contraction
(d), anisotropic expansion, and contraction
aligned with two different axes (e, f).
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The transformation from target to final pointing position in general
will be a nonlinear process in which the binocularly acquired target
position is transformed into an appropriate joint posture. For a small
area of the workspace, however, one would expect the transformation to
be continuous and smooth. In this case, local distortions of the
spatial organization of the targets can be approximated by a linear
transformation from target to endpoint position. Such linear
approximations can be represented by a transformation matrix, which in
turn can be presented graphically as an oriented ellipse (ellipsoid in
3D). Note that rotations or mirror reflections within the local
transformation are lost when the transformation is represented
graphically in this manner. However, such reflections and rotations can
be extracted from the local transformation estimate and represented
separately (see below). Figures 1c-f shows the
representation of each type of distortion as a two-dimensional
ellipse.
We therefore wished to find the 3 × 3 transformation matrix that
maps target positions (relative to the average target position) onto
the corresponding endpoint positions (relative to the overall average
endpoint position for all trials). We computed the estimated transformation matrix M as the local linear relationship
that best describes the transformation between targets and endpoints using standard least-squares estimation.
The linear estimation of the local transformation may contain rotation
or reflections as well as a local expansion and/or contraction. A
reflection through the center position would mean, for example, that
for a target located to the left of center, the subject consistently
pointed to the right, and vice versa. Such reflections would be
indicated by negative eigenvalues for the transformation matrix
M. Because no such reflections were observed in the measured
data, the overall local transformation can be represented as the
cascade of two components: a symmetric matrix A,
representing the local distortion, and a rotation matrix R:
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(4)
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The symmetric component A was computed from the
eigenvectors and eigenvalues of the quantity
MTM as follows:
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(5)
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where:
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(6)
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and the columns of W are thus eigenvectors for the
matrix MTM. The orthogonal
matrix R represents a rotation of  degrees around a
single axis  R. For A nonsingular, the matrix
R is given by:
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(7)
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For a 3 × 3 rotation matrix R:
![&thgr;=<UP>cos</UP><SUP><UP>−</UP>1</SUP><FENCE><FR><NU>[<IT>trace</IT>(R)−1]</NU><DE>2</DE></FR></FENCE>,](/content/vol18/issue20/fulltext/8423/img008.gif)
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(8)
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(9)
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The symmetric local distortion matrix A can be
plotted as an oriented 3D ellipsoid, where the major and minor axes
indicate the directions of maximal and minimal expansion.
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Ensemble averages |
Directional data computed from the constant error vectors, the
covariance matrices, and the transformation matrices varied between
subjects. Two different methods were used to compute the average
responses across subjects. In the first method, the average constant
error vectors, covariance matrices, or transformation matrices were
computed by pooling individual trial data from all subjects. The second
method consisted of computing the direction vectors for each subject
and type of measurement and then computing the spherical mean of these
individual vectors (Mardia, 1972). Averages of directional data provide
meaningful information only when the individual eigenvectors are
clustered around a common direction. Clustering can be measured as the
length of the average resultant vector  (Mardia,
1972). Figure 2 shows typical intersubject variability for the dark-short and dark-long pointing conditions. Distributions of constant error directions varied too
widely in our experiment to allow for the computation of a preferred
axis. Similarly, the variability of axes of rotation within the local
transformation matrix did not indicate a preferred axis of rotation. On
the other hand, the directions of maximum variation (first eigenvector
of the covariance matrix) and distortion (third eigenvector of the
local distortion matrix) did cluster significantly across subjects. The
two methods of computing the ensemble averages produced very similar
results for these two measures. In the Results section, 3D figures were
generated from the average constant error vector, average variable
error matrices, and average local distortion matrices, as computed by
method 1. Statistical analyses of directional data were based on
direction vectors computed for individual subjects.
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Figure 2.
Intersubject variability and the computation of
ensemble averages. Each panel represents an equal-area projection of
direction vectors into the horizontal plane, for trials to the
mid-target region in the dark-short (A) and
dark-long (B) conditions. Each filled
circle represents the average response for a single subject for
(1) the constant error, (2) variable error (first eigenvector
indicating the direction of maximum variability), (3) local distortion
(third eigenvector indicating the axis of maximum contraction), and (4)
rotation axis within the local transformation. Points near the center
of each panel represent upward pointing vectors, whereas points near
the edge of the bounding circle indicate forward, backward, leftward,
or rightward directions for the top, bottom, left, and right edges,
respectively. Direction vectors are clustered for the variable error
and local distortion vectors but not for the constant error directions
or rotation axes. Open circles indicate the average of
the individual direction vectors for the distributions showing
significant clustering. The symbol X indicates the direction
vector computed from the corresponding ensemble covariance or local
transformation matrix.
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RESULTS |
Variable error
Clear differences emerged in the patterns of variable errors for
movements in the light versus dark. Movements performed in the light
produced axes of maximum variability (Fig.
3, dark bars) that converge
toward the head, indicating a viewer-centered reference frame for the
endpoints of these movements. In contrast, variable error eigenvectors
for movements in the dark do not converge toward a unique origin.
Viewed from the side (Fig. 3B), the major eigenvectors in
the dark tend to point upward, above the head, with a greater such
tendency for movements performed after a long (5 sec) delay. Viewed
from above (Fig. 3A), the major eigenvectors appear to be
parallel for the short memory delay in the dark, whereas for the long
delay, the vectors rotate from left to right around a body axis.
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Figure 3.
Average variable errors across subjects for two
lighting conditions and two delays, viewed from above
(A), from the right side
(B), and perpendicular to the plane of movement
(C). Ellipsoids represent the tolerance region
containing 95% of responses (see Materials and Methods). Dark
line segments indicate the direction of the major eigenvector
computed for the tolerance ellipsoid. For movements in the dark, a
pattern of major eigenvector rotations upward and away from the
starting position emerges in the ensemble averages, in comparison to
head-centered eigenvector directions seen in the light.
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An interesting pattern for variable errors for long delays in the dark
becomes apparent when the data are viewed from a direction orthogonal
to the movement plane (the plane containing the centers of the three
workspace regions and the hand starting position), as shown in Figure
3C. Under these conditions, the direction of maximum
variability changed for different workspace regions. The major
eigenvector rotates more and more counterclockwise in this plane as one
moves from the right to the left workspace regions. Such an effect was
not readily discernible for movements performed with the lights on
(McIntyre et al., 1997).
The bottom row of Figure 4 shows that for
movements performed in the dark with a 5 sec delay, the direction of
greatest variability was affected more by the starting position of the
hand than by the choice of hand used to perform the task. In the plane
of movement (Fig. 4, bottom row), the major eigenvector of
the variable error ellipsoid tilts closer to the horizontal as the
workspace region moves laterally away from the starting position.
Furthermore, transferring the starting position across the midline for
the same set of targets produced roughly a mirror image of the
eigenvector rotation pattern (Fig. 4, center vs right
column, bottom row). The effect of starting position on the
orientation of the variable error within the movement plane was highly
significant (F(1,8) = 17.98, p < 0.0028). Changing the effector hand had little visible effect on the
orientation of the major eigenvector (Fig. 4, left vs
center column), although the difference is statistically
significant (F(1,11) = 5.775, p < 0.035).
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Figure 4.
Variable errors for two different starting
positions and two different effector hands, averaged across subjects,
for pointing in the dark with a 5.0 sec delay. The orientation of the
variable error ellipsoid is affected by the relative starting position
of the hand but not by the hand used to perform the pointing. Note the
change of scale for ellipsoids viewed in the plane of movement.
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Changing the starting position can change the final configuration of an
arm having redundant degrees of freedom when pointing to the same
endpoint (Soechting et al., 1995). One must consider whether the
observed changes in variable error tied to the starting position stem
from different endpoint arm configurations rather than from different
movement directions. The orientation of the plane containing the wrist,
the elbow, and the shoulder provides a measure of the configuration of
the arm for a given endpoint position. Soechting and colleagues found
variations of the order of 10-15° for pointing with the same arm to
a single target. However, a simple observation of the left and right
arms held at the right target region shows a much larger (90°)
difference between the planar orientations of the two arms. Yet,
changing the effector arm had little influence on the orientation of
the variable error. Thus, it seems that the starting-position effect is
most likely related to the direction of movement, rather than to
changes in arm configurations. Note, however, that although variable
error was affected by the starting position, the axis of maximum
variability did not align with the direction of the pointing movements.
In fact, when viewed from the side (Fig. 3B), the major
eigenvectors for movements in the dark are almost perpendicular to the
direction of movement.
Constant error
As was seen for pointing in the light (McIntyre et al., 1997),
subjects performing movements in the dark did not show a single pattern
of constant errors for either short (0.5 sec) or long (5.0 sec) memory
delays. Both overshoots and undershoots with respect to the subject's
body were observed. For the five subjects who performed the experiment
under three conditions (light-short, dark-short, and dark-long),
there was no significant effect on distance error (overshoot or
undershoot) of either lighting conditions (p > 0.15) or memory delay (p > 0.50) as
within-subjects factors. Final pointing positions were located both
above and below the actual target position for both memory delay
conditions. There was no strict correlation between errors performed by
a given subject for the two different memory delays, and no clear
pattern of constant error emerged for these subjects.
Nevertheless, constant errors did tend to be biased toward the body.
When measured over all subjects, including subjects who used the left
hand or the left starting position, a detectable bias in distance error
emerges, changing from an average of +2.6 mm (overshoot) to 29.3 mm
(undershoot) as a function of memory delay (comparison of mean
overshoot for 0.5 and 5.0 sec delays; F(1,30) = 9.13, p < 0.006). In Figure
5, there appears to be an effect of hand
starting position on the average constant errors shown, although the
vectors do not align with the movement axis. No statistically
significant effect of starting position (F(1,8) = 2.051, p < 0.19), workspace region
(F(1,11), p < 0.91), or
effector arm (F(1,11) = 0.60, p < 0.46) was measured for constant error directions.
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Figure 5.
Constant errors for two different starting
positions and two different effector hands, averaged across subjects,
for pointing in the dark with a 5.0 sec memory delay. Dark
bars indicate the direction and extent of the average constant
error vector (magnified 5× for visibility), pointing away from the
target position indicated by the small sphere. Note the
change of scale for data viewed in the plane of movement.
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Local distortions
Measurements of the local distortion reveal the most consistent
pattern of errors across subjects. Figure
6 shows the average local distortion
ellipsoids for the two lighting and two delay conditions. The
eigenvectors corresponding to the smallest eigenvalue of the local
distortion (Fig. 6, dark bars), indicating the axes of
maximum contraction, point toward the subject for all workspace regions, intersecting the plane of the body at a height that varies between the level of the eyes and the shoulder. In Figure 6 this pattern of distortion is apparent for both memory delays and both lighting conditions.
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Figure 6.
Average local transformation ellipsoids for two
lighting conditions and two delays. Ellipsoids indicate the local
distortions induced by the sensorimotor transformation, as estimated by
a linear approximation to the local transformation (see Materials and
Methods). The unit sphere indicates the ellipsoid corresponding to an
ideal, distortion-free local transformation. Dark bars
indicate the direction of the third (minor) eigenvector, indicating the
axis of maximum local contraction. Under all lighting conditions, axes
of maximal contraction point toward the subject.
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Although the orientations of the local distortions were similar for all
conditions, lengthening the time delay had a differential effect on the
magnitude of the distortion, depending on lighting conditions (Fig.
7). Because the contraction was limited
to a single axis (the first and second eigenvalues are approximately equal), the relative contraction along the axis is described by the
ratio of the third (smallest) eigenvalue to the average of the other
two. Both lighting conditions showed comparable levels of contraction
for a 0.5 sec delay (0.58 and 0.60 for light and dark, respectively).
However, although contraction increased only insignificantly to 0.50 in
the light (F(1,5) = 3.55, p > 0.1), contraction increased significantly (ratio decreases) to 0.36 in
the dark (F(1,4)=23.56, p < 0.0083). Note that for the statistical tests reported here, the two
memory delays for trials performed in the light were mixed within the
same block of trials, whereas in the dark, the two memory delays were
tested in different blocks on different days. Nevertheless, two
subjects who performed reaching movements in the light to targets with
only a single 5.0 sec memory delay showed a contraction ratio of 0.54, on average. This confirms that the lack of contraction change in the
light was independent of whether memory delays were tested separately
or together within the same block of trials.
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Figure 7.
Eigenvalues of the local transformation estimate.
Eigenvalues are unitless gains indicating spatial expansion or
contraction in 3D target-to-endpoint mappings. Eigenvalues >1 indicate
magnification of the local space along the corresponding eigenvector,
whereas eigenvalues <1 indicate spatial contraction. First and second
eigenvalues are averaged (left column) and compared with
the third eigenvalue (center column) representing the
amount of maximal contraction along the corresponding eigenvector. The
right column shows the ratio of the third eigenvalue over the average
of the first and second, indicating the amount of distortion introduced
in the visuomotor transformation. Contraction is relatively constant in
the light, whereas contraction increases with memory delay duration in
the dark.
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Figure 8 shows the effects of starting
position and workspace region on the orientation of the local
distortion for movements in the dark with a 5 sec delay. The azimuth of
the axis of maximal contraction changes significantly between the left
and right workspace regions (F(1,8) = 12.582, p < 0.0075). Changing the starting position of the
hand (right hand, left start vs right hand, right start) had little
effect on the orientation of the transformation matrix when projected
into the horizontal plane (F(1,8) = 0.648, p < 0.442). No consistent pattern is apparent in the
distortion when viewed in the movement plane (bottom row).
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Figure 8.
Effects of workspace region and movement starting
position on estimates of the local transformation. Axes of maximum
contraction are biased slightly toward the side of the effector hand,
independent of the starting hand position.
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The eigenvectors of maximum contraction did not point unambiguously
toward the head/body midline or toward the shoulder. However, changing
the effector hand did have a measurable effect on the orientation of
the distortion matrix. The eigenvectors in Figure 8 are biased toward
the left side for pointing with the left hand, and toward the right
side for pointing with the right hand. Local distortion eigenvectors
were biased to the right side for pointing with the right hand from
either starting position. Changing the effector arm had a significant
effect on local transformation azimuth (F(1,11) = 5.46, p < 0.039). Minor axes of the distortion ellipsoids were generally tilted outward, away from the zero
(straight-ahead direction) for both the left and right workspace
regions. The tilt away from straight ahead for the ipsilateral side was
0.83± 6.43° (mean ± SE), which is not statistically different
from zero at the p = 0.05 confidence level. In
contrast, the tilt away from straight ahead for the contralateral side
(15.39°± 2.69°) was in fact statistically significant at
p < 0.01. The amount of tilt away from zero is
significantly greater for movements to the contralateral workspace
region (F(1,17) = 4.77, p < 0.043), consistent with a rotation of the distortion around an axis
related to the effector arm.
In the current study, the observed contractions in measurements of
local distortion were relatively independent of the observed constant
errors. There was no correlation between the amount of undershoot and
the magnitude of the local contraction (r = 0.047).
Rotations within the estimates of local transformations were in general
relatively small over all workspace regions and starting hand locations
in the dark. The median value of rotation was 10.3°, with 95% of all
values falling between 3.6 and 28.8° (rotation magnitudes are not
normally distributed). Because the axes of rotation varied widely
between subjects, the mean amplitude of rotation is not meaningful.
Because no obvious patterns emerged in the direction of the axes of
rotation across different conditions, we will not discuss further
rotations within the local transformations.
Transformed variable error
When viewed in the horizontal plane, variable errors were greater
in distance from the subject for movements in the light, but greater in
the lateral direction for movements in the dark (Fig. 3). This can be
explained by the compression inherent in the local distortion (Fig. 6).
If a distorted transformation compresses positions along a given axis,
variables errors arising from noise before the distortion will also be
compressed along the same axis. However, the measured local distortion
was independent of the starting hand position. Therefore, the
distortion of viewer-centered noise cannot explain the dependence of
the direction of maximum variability on the starting hand position
(Fig. 4). Thus, although some of the difference in variable errors
observed for movement in the dark versus the light can be attributed to
distortions introduced in the overall transformation, an additional
source of noise is required to fully account for the dependence of
variable error orientation on the starting point of the movement.
| |
DISCUSSION |
In these experiments we observed both nonisotropic variable errors
and local distortions that were aligned in two different egocentric
reference frames. The observed variable errors pointing toward the eyes
might indicate a viewer-centered representation of the target position,
but these errors might also arise from anisotropic sensitivity to noise
in retinal or oculomotor signals mapped onto an otherwise uniform
representation (McIntyre et al., 1997). However, the distortions of
local spatial relationships along axes pointing between the head and
shoulder cannot be explained by anisotropic sensitivity to noise, and
thus more clearly indicate a transformation through a body-centered
coordinate system.
In the dark, local contraction increased for longer delays along an
axis that points between the head and the shoulder (hereafter referred
to as the head/shoulder axis). This argues for a separation of target
distance and direction within short-term memory. Note that although
local contraction is apparent both in light and darkness, this
distortion did not increase for longer memory delays in the light.
Thus, additional information about the target position in a
viewer-centered reference frame may be used to correct the final
pointing position when vision of the fingertip is allowed.
Combined viewer-centered and arm-centered reference frames
Our measurements of local distortion point to an origin between
the eyes and shoulder for movements in the dark. Soechting and Flanders
and colleagues (Soechting et al., 1990; Flanders et al., 1992) have
similarly identified an intermediate reference frame that is related to
both the visual target and the effector arm. Simulations show how the
cascading effects of two transformations, one centered at the eyes, the
other centered at the shoulder, can predict the intermediate reference
frame seen in the data (J. McIntyre, unpublished observations). The
combination of two effects, each tied to a specific anatomical
reference, provides a parsimonious description of the underlying
phenomenon.
Although our methods for documenting distortions in 3D are novel,
evidence for contractions along the sight-line has been reported
previously for visual estimates of target distance. Foley (1980) found
that the slope of perceived versus actual target distance is
consistently less than unity for various different estimation tasks.
Gogel (1969, 1973) proposed that the CNS computes target distance as a
weighted sum of different inputs (stereodisparity, vergence,
accommodation, etc.), including a "specific distance" toward which
the estimate is biased in the absence of adequate sensory cues.
Contractions of pointing positions may reflect the bias toward the
specific distance postulated by Gogel. In three dimensions, however,
there is a greater bias toward a specific distance than toward a
"specific direction," reinforcing the conclusion that the CNS
parcellates the representation of target location into separate
distance and directional components.
In the current experiment, local distortion was uncorrelated with the
magnitude of constant errors. Thus, local distortion is not simply the
product of a global underestimation of egocentric target distance, nor
can the contraction be accounted for by a consistent underestimation in
the mapping between a desired 3D displacement of the hand onto a
corresponding change of joint angles. The magnitude of radial
contraction was similar for movements directed to the same target,
starting from the left or right, yet the change in elbow angle was
quite different in these two cases. Local distortion is thus not the
product of an inaccurate global transformation that is consistently
present across subjects. One might argue that the CNS operates locally
when transforming spatial information about nearby objects (Lacquaniti,
1997). In visual tasks, subjects produce large errors in estimates of
absolute target distances but much better estimates of relative
distances once a local reference frame is established (Gogel, 1961;
Foley, 1980). Such local frames of reference could explain the
conflicting results observed for measurements of constant errors in
different experiments (Foley and Held, 1972; Soechting and Flanders,
1989a; Berkinblit et al., 1995; McIntyre et al., 1997). Measurements of
distortion reported here indicate nonetheless that the reference frame
for the local transformation is linked to the effector arm.
Local distortion increased with lengthening memory delays. The memory
of the target position apparently decays toward an "average" central response. Bias toward an average response value can also be
seen when subjects are forced to respond to a set of stimuli without
sufficient time to adequately prepare the movement (Hening et al.,
1988). In our experiment, the contraction toward the central value is
greater along a head/shoulder-centered axis, arguing once again for an
egocentric reference frame for the representation of the remembered
target position.
A hand-centered reference frame?
Gordon et al. (1994) have argued that increased variability along
the line of movement indicates an internal representation of the hand
displacement in terms of direction and extent from the starting
position. In the current study, ensemble averages of variable errors
were affected by the starting point of the hand, although the axes of
maximum variability did not align with the movement direction. The
effects of starting position are most likely related to the direction
of movement and not to differences in arm configuration, as
demonstrated by the minimal change in variable errors induced by
changing the effector arm. However, the effects of starting position
were not seen in measurements of local distortion, nor can they be
predicted by the distorted transformation of viewer-centered input
noise. If information indeed passes serially through a hand-centered
movement representation, our data indicate that the transformation into
this hypothetical representation is undistorted.
Noise related to movement direction does not necessarily imply a serial
passage of information into a hand-centered reference frame. Additive
noise is also consistent with parallel, convergent processes. Noise
related to movement direction might result from dynamic components of
the motor command added to a static specification of final equilibrium
position (Feldman, 1966a,b; Hogan, 1985; Bizzi et al., 1992; McIntyre
and Bizzi, 1993; Shadmehr et al., 1993). An overestimation or
underestimation of the required dynamic command could cause an
overshoot or undershoot along the movement axis and would thus add
variability in this direction. The effects of variability in a dynamic
motor command would interact with the nonisotropic limb stiffness,
viscosity, and inertia (Hogan, 1985; Shadmehr et al., 1993) and would
not necessarily align precisely with the movement axis. Friction would
increase the likelihood that dynamic overshoot or undershoot would
persist in the steady-state final position, which might explain why
movements against a constraining surface show higher levels of
variability related to the movement direction (Desmurget et al.,
1997).
A conceptual model
Our observations of 3D pointing errors lead us to propose the
schematic description of the pointing task illustrated by Figure 9. Retinal and extra-retinal cues combine
to form a viewer-centered representation of the target location. This
representation is transformed into a reference frame linked to the
effector arm. Finally, noise related to the movement direction is added
to the endpoint position, either by a distortion-free transformation through a representation of hand displacement (Fig. 9B) or
by the parallel addition of dynamic components to the motor command (Fig. 9C). In either case, the increase of the
head/shoulder-centered local contraction for greater delays indicates
that memory storage of the intended endpoint is held within the
viewer-centered and arm-centered representations and not in terms of a
hand-centered displacement. When vision is permitted, the final
fingertip location may be compared with stored visual information of
the target position, reducing the local distortion at the output.
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Figure 9.
Summary of results regarding the sensorimotor
chain for pointing to remembered targets. A,
Viewer-centered visual inputs are passed through internal
transformations that compress the target position along a body-centered
axis as a function of memory delay and then transformed into a motor
command. Ellipsoids marked with red bars indicate
variable errors, for which the red bar indicates the
direction of maximum variability. Ellipsoids marked with blue
bars indicate estimates of local distortion, and the
corresponding axis of maximum contraction. B, C, In the
schematic diagrams of the sensorimotor processes used in pointing to
remembered targets, circles depict data representations
within a specific reference frame, whereas squares
indicate transformations between coordinate systems. Two models can
capture the observed behavior. In both models, binocular visual inputs
are transformed into a viewer-centered visual reference frame, with
contraction of data along the sight line. Data are then transformed
into a motor reference frame linked to the effector arm, with
additional contraction along a shoulder-centered axis. In
B the final output stage includes a distortionless
transformation through a hand-centered reference frame. In
C, a parallel, dynamic component is added to the
remembered endpoint position to generate the final motor command. In
both cases, if vision of the hand is permitted during the pointing
movement, the observed final finger position is compared with the
visual memory of the target to reduce errors at the output.
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Neural substrates
The cascade combination of viewer-centered and arm-centered
representations we have hypothesized here could be mediated by the
combinatorial properties of cortical networks along the dorsal occipito-parieto-frontal stream (cf. Wise et al., 1997; Lacquaniti and
Caminiti, 1998). In the monkey, gaze-position signals modulate the
visual receptive fields in several of these areas. Retinal and
extraretinal signals combine with arm position signals at early stages
of the network, namely in superior parietal areas (areas 7m and V6A) of
the mesial cortex (Ferraina et al., 1997a; Galletti et al., 1997;
Lacquaniti and Caminiti, 1998). Cells in these areas discharge during
instructed-delay tasks before and during arm movements to a
visual target (Ferraina et al., 1997b). Area 7m is connected with area
5 in the superior parietal lobule, as well as with dorsal premotor
cortex (PMd) and primary motor cortex (M1).
Many cells in these areas discharge in a manner correlated with the
direction and extent of the upcoming movement (Georgopoulos et al.,
1982; Kalaska et al., 1983; Schwartz et al., 1988; Fu et al., 1993).
Other cells fire more consistently with respect to the intended
movement endpoint (Hocherman and Wise, 1991; Lacquaniti et al., 1995).
The anisotropic evolution of final pointing errors for different delays
suggests that target memory could be implemented by egocentric
endpoint-position neurons. Many neurons in dorsal area 5 are best tuned
to either the azimuth, elevation, or distance of the endpoint relative
to the body (Lacquaniti et al., 1995). Furthermore, the tuning curves
of area 5 neurons that encode distance exhibit a body-centered
contraction reminiscent of the radial contraction described here.
Cells that indicate the upcoming hand displacement are nevertheless
active during memory delay periods (Smyrnis et al., 1992). We suggest
that these cells may be involved in the computation of dynamic motor
commands. The CNS might reasonably precompute and continually update
the dynamic command, as evidenced by priming experiments (Rosenbaum,
1980). This update processing would be visible in the cell populations
during the delay. In fact, neurons in motor and premotor areas that
encode movement direction and extent appear also to be sensitive to
dynamic parameters such as applied forces (Kalaska et al., 1989) and
instantaneous speed (Schwartz, 1994), and many such neurons are
modulated by changing limb configurations for the same hand
displacement (Caminiti et al., 1991; Scott and Kalaska, 1997). Note
that the population vector in M1 predicts the direction of dynamic
force impulses but not static force biases (Georgopoulos et al.,
1992).
Conclusions
Based on studies of psychophysics and cortical electrophysiology,
different theories have recently emerged that argue for the
representation of hand movements in terms of viewer-centered or
arm-centered reference frames for the intended final position or in
terms of a hand-centered representation of the impending displacement
vector. In an analysis of 3D pointing errors to memorized targets, we
found evidence that might support all three representations. However,
we argue that short-term memory stores the endpoint position in a
viewer-centered and/or shoulder-centered reference frame that
differentiates between parameters of distance and direction.
| |
FOOTNOTES |
Received March 10, 1998; revised July 7, 1998; accepted July 31, 1998.
This work was supported in part by grants from the Italian Health
Ministry, the Italian Space Agency, the Ministero della Universita e
Ricerca Scientifica e Tecnologica, and the Human Frontiers
Science Program. We thank J. Droulez, G. Baud-Bovy, and D. Morrison for
comments on the mathematics and statistics, and M. Carrozzo and L. Bianchi for valuable assistance in the performance of these
studies.
Correspondence should be addressed to Joseph McIntyre, Sezione
di Ricerche Fisiologia Umana, IRCCS Clinica Santa
Lucia, via Ardeatina, 306, 00179 Rome, Italy.
| |
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Top
Abstract
Introduction
