Sobell Department of Neurophysiology, Institute of Neurology, London WC1N 3BG United Kingdom
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ABSTRACT |
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Vetter, Philipp, Susan J. Goodbody, and Daniel M. Wolpert. Evidence for an eye-centered spherical representation of the visuomotor map. During visually guided movement, visual coordinates of target location must be transformed into coordinates appropriate for movement. To investigate the representation of this visuomotor coordinate transformation, we examined changes in pointing behavior induced by a local visuomotor remapping. The visual feedback of finger position was limited to one location within the workspace, at which a discrepancy was introduced between the actual and visually perceived finger position. This remapping induced a change in pointing that extended over the entire workspace and was best captured by a spherical coordinate system centered near the eyes.
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INTRODUCTION |
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To reach a visually perceived target, the CNS must
transform visual information into appropriate motor commands
(Andersen et al. 1985; Flanders et al.
1992
; Ghilardi et al. 1995
; Kalaska and
Crammond 1992
; Soechting and Flanders 1989
).
This transformation from visual to motor coordinates is known as the
visuomotor map. Plasticity of the visuomotor map is essential, as
sensorimotor discrepancies inevitably arise throughout life, for
instance due to body growth (Held 1965
; Howard
1982
). This plasticity has been studied extensively,
demonstrating the remarkable ability of the visuomotor map to adapt, at
least partially, to a wide variety of stable remappings (for a review,
see Welch 1986
).
To assess the natural coordinate system of the visuomotor map, we have used a paradigm in which subjects were exposed to a single novel visuomotor (visuoproprioceptive) pairing. Such a single-point remapping can be captured by a shift in almost any coordinate system. However, the pattern of generalization, that is the change in pointing at other points in the workspace, will be determined by the particular coordinate system in which the visuomotor map is represented. In contrast, previous studies of visuomotor adaptation generally have used prisms to alter the visuomotor map over a large region of the workspace. This is equivalent to providing a set of training data in the form of many visuoproprioceptive pairs. From such studies it is difficult to infer the natural coordinate system of the map as the set of visuoproprioceptive pairs experienced may be in conflict with the visuomotor map's natural coordinate system, leading to an ambiguous adaptation.
We compared predicted and actual changes in pointing after such a
single-point remapping based on five a priori hypotheses of the
coordinate system of the visuomotor map: Cartesian coordinates based at
the shoulder and eye, and spherical coordinates based on both shoulder
and eye and joint-based coordinates. This work builds on previous
studies of spatial generalization in one (Bedford 1989,
1993b
) and two dimensions (Ghahramani et al.
1996
), suggesting a Cartesian coordinate system, and
generalization in the velocity domain suggesting a decay of adaptation
at novel velocities (Kitazawa et al. 1997
). The present
study used pointing in three-dimensional space, which allowed natural
pointing movements and joint angle measurements.
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METHODS |
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Subjects
Eight right-handed subjects (5 men; 3 women; ages 21-33) gave their informed consent and participated in the study. Subjects were naive to the purpose of the experiment. They participated in a remapping and a control session on separate days in a balanced order. Control sessions were identical to the remapping session except that no visuomotor remapping was introduced.
Apparatus
A schematic of the setup is shown in Fig.
1. The subject's arm position was
monitored with infrared emitting diodes (IREDs) the positions of which
were detected by an Optotrak 3020 motion analysis system (Northern
Digital, Waterloo, Ontario) at 90 Hz. 18 IREDs were mounted on three
rigid bodies (RB) placed on the subject's fingertip (8), forearm (6),
and upper arm (4). To measure joint angles, the center of the shoulder
rotation (shoulder position) was determined by pivoting the elbow
around a fixed shoulder and calculating the point relative to the upper
arm RB whose positional variance in Cartesian space was minimal. The
elbow position was determined by rotating the upper arm and forearm and
calculating the point relative to the upper arm RB whose positional
variance relative to the forearm RB was minimal, that is, the elbow's
center of rotation. Joint angles were calculated from the two 4 × 4 homogeneous transformation matrices, which define the position and
orientation of the upper arm and forearm RBs. From the orientation of
the upper RB, the joint angles ,
,
, which represent
successive rotations of the upper arm about fixed Cartesian x,
y, and z axes, respectively, were calculated (see Fig.
1). The zero angular position for the upper arm was taken as the upper
arm pointing downward aligned with the vertical z axis and
the forearm pointing along the positive y axis when the
elbow was bent to 90°. The elbow angle
was the angle between the
forearm and the upper arm and was calculated from the relative
orientations of the upper arm and forearm RBs.
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A three-dimensional virtual visual feedback setup was used to overlay
images on to the arm's workspace (for details of this setup, see
Goodbody and Wolpert 1998). The images were generated with the OpenGL graphics package, which uses projective geometry to
adjust the size of the image appropriately with its distance and angle
from the eye. Therefore the subject sees a perspective view in which
the size of the object on the retina reduces as the object moves
further away. The system was calibrated for each subject as the
perspective algorithm depends on the subject's interocular distance.
Subjects could not see their arm but were shown their finger location
as a 1 cm green cube. A computer controlled discrepancy between the
finger and cube position could be introduced. Targets were displayed as
red, 4 mm radius spheres.
Procedure
Each session had four phasesfamiliarization, preexposure,
exposure, and postexposure
interspersed with rest periods every 50 movements. Pointing movements were made to 36 targets in the three-dimensional workspace. One of these targets was the exposure target, at which the visuomotor remapping was introduced (Fig. 1).
Each trial consisted of a pointing movement to one of the targets. The trial started when the finger moved behind a notional fronto-parallel plane 12.2 cm in front of the eyes, at which time a target appeared. Subjects were asked to assume a similar starting position with the finger close to their midline.
In the familiarization phase, subjects pointed to targets with continuous veridical feedback of their finger position. The exposure target was presented 12 times, and all the other targets were presented twice in a pseudorandom order. In the preexposure phase, subjects' pointing errors were assessed before the remapping. Subjects pointed to targets without visual feedback of their finger location. The exposure target was presented 18 times and all other targets 3 times in a pseudorandom order. Each trial ended when the subject's finger velocity dropped below 1 cm/s.
In the exposure phase, subjects repeatedly pointed to the exposure
target (x = 8.1 cm, y = 36.2 cm,
z = 27.6 cm; origin between the eyes) 50 times.
During this phase, a visuomotor remapping was introduced, tailored for
each subject based on their average preexposure pointing position at
the exposure target. This ensured a similar remapping for all subjects
independent of their preexposure pointing biases. The remapping
required subjects to point 6 cm to the right (positive x) of this
average position to perceive their finger on target. The location and
direction of the remapping were chosen so as to maximize the
differences in the predictions of the hypotheses tested. To limit the
visuoproprioceptive exposure, visual feedback of finger position (green
cube) was only displayed when subjects were within 3 cm of the target.
The trial ended when subjects had held their finger on target
continuously for 2 s. The remapping was introduced gradually in
the exposure phase, incrementing on each trial so that the full
perturbation was present on trial 17. In the control condition,
visual feedback was altered so that subjects had to point to their
average preexposure position to see their finger on target.
In the postexposure phase, the changes in pointing due to the exposure phase was assessed. As in the preexposure phase, subjects pointed to the targets without visual feedback. The exposure target was presented 18 times and all other targets 3 times in a pseudorandom order. To prevent any decay of learning, an exposure trial was presented after every three trials.
Analysis
For each subject and target, average pre- and postexposure
pointing positions were calculated. The difference between pre- and
postexposure represented the generalization of the remapping over the
workspace. These changes were compared with predictions based on the
five hypotheses about the natural coordinate system of the visuomotor
map. The first was a Cartesian coordinate system with a fixed origin
between the eyes. Second, a Cartesian coordinate system with origin at
the shoulder was considered. This coordinate system differs from the
eye-centered system as the eye is fixed in external space whereas the
shoulder is free to move by several cm. Thus the Cartesian shoulder
coordinate system represents the finger position relative to the
shoulder. Third, a spherical coordinate system centered about the eyes
(r, ,
) was tested, in which r,
, and
represent distance, azimuth, and elevation, respectively. Fourth, a
spherical coordinate system with the origin at the average shoulder
position was considered. Finally a joint-based coordinate system was
examined (see Apparatus for joint-angle definition).
For each point, a vector was calculated representing the
location of the finger in a particular coordinate system. For each
hypothesis, the observed change at the exposure target is
d
=
postexposure
preexposure. For each hypothesis and
nonexposure target, predictions were made by adding d
to
the preexposure pointing coordinates:
prediction =
preexposure + d
and
then transforming all the predictions into Cartesian space. Thus the
change in pointing at the exposure target created a single, global
offset in the coordinate system (e.g., d
= (dr, d
, d
) in spherical coordinates). In other words,
to predict the change in pointing, the offset calculated from the
exposure target was added to all preexposure pointing coordinates. For
spherical coordinates, we also examined the possibility that the
distance r was altered by a gain (k) change
mechanism, such that rprediction = k × rpreexposure.
The prediction error for each target was calculated as the magnitude of the vector difference between the predicted and actual changes in pointing. Average preexposure and postexposure positions were used to calculate the actual change in pointing. A repeated measure analysis of variance was performed on the prediction errors as a function of hypothesis and target number.
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RESULTS |
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Changes in pointing between the pre- and postexposure phases in the control condition were not significant along any of the Cartesian coordinate axes (Fig. 2A). However, remapping of a single point in space induced significant changes in pointing over the whole workspace (Fig. 2B). The changes were significant along the x and y but not the z axis (2-tailed t-test; P values = x: 0.0001, y: 0.0011, z: 0.41). On questioning, only one subject suspected a remapping during the experimental condition. The pattern of generalization resembled a colinear shift in the coronal plane (xz), whereas in the horizontal plane (xy) changes looked rotational. The average magnitude of change in pointing was 4.54 ± 0.32 cm (mean ± SE) and did not decay significantly with distance from the exposure point (Fig. 3A).
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The actual changes in pointing were best predicted by spherical coordinates centered around the eyes (Fig. 3B). These predictions were significantly better than spherical coordinates about the shoulder (P < 0.05), joint angles (P < 0.05), and Cartesian coordinates (P < 0.001) as well as the hypothesis that there is no generalization (P < 0.05). The absolute prediction errors for each subject and hypothesis are summarized in Table 1. This shows that spherical coordinates about the eye produced the best prediction for five of the eight subjects and produced the second best prediction for the three remaining subjects. As shown in Fig. 3C, spherical coordinates about the eyes captured the pattern of changes in the pointing observed. An analysis of the prediction errors for the spherical coordinate system about the eyes (that is the vector differences between the black and gray arrows of Fig. 3C) showed no obvious trends and in particular showed no correlation along any of the Cartesian axes (P > 0.05). The predictions made by the hypothesis of a scaling of the distance (r) component of the spherical coordinate, as opposed to a single offset, were systematically worse than for the single offset hypothesis (data not shown).
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DISCUSSION |
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A three-dimensional virtual reality setup was used to expose subjects to a highly localized remapping between actual and displayed finger position. This induced significant changes in subjects' pointing behavior over the entire workspace which did not decay significantly with distance from the remapped location. Several hypotheses as to the natural coordinate system of the visuomotor map were tested by comparing predicted changes in pointing with actual changes. The hypothesis of spherical coordinates with the origin at the eyes best captured the observed changes. These predictions were significantly better than those based on spherical coordinates about the shoulder, joint angle coordinates, or Cartesian coordinates.
Our results are consistent with Bedford's (1989,
1993a
,b
) findings that changes in pointing did not decay with
distance from the remapping and were approximately linear along a fixed
radius of arc. Ghahramani et al. (1996)
found a decaying
pattern of generalization in their planar two-dimensional study. Their
study was limited in two important respects that could account for
these differences. First they had no control over the starting position
of the hand, a factor that is thought to exert an influence over the
visuomotor remapping. In our study, subjects were confined to executing
movements from a limited region of space in front of their body.
Second, the nature of their apparatus constrained the subject to make unnatural pointing movements, forcing subjects to point at the height
of their shoulder.
Previous generalization studies focusing on movement dynamics have
found joint-based generalization (Shadmehr and Mussa-Ivaldi 1994). However, we show in this study that for the visuomotor map, the natural coordinate system is not joint-based. Imamizu et al. (1995)
examined pointing behavior with a 75° rotatory
remapping and, consistent with our data, showed that subjects learned
the rotation for movements in one direction and generalized this to movements in other directions.
Flanders et al. (1992) had subjects perform targeted arm
movements to remembered positions of virtual targets in
three-dimensional space. They suggested that retinocentric coordinates
gradually evolve through head-centered to become shoulder-centered
coordinates (Flanders et al. 1992
; Soechting et
al. 1990
). McIntyre et al. (1997)
found evidence
for an eye-centered frame of reference by analyzing variable errors and
constant errors in a three-dimensional pointing task to remembered
positions with visual feedback of the finger position. This finding was
independent of the hand used, its starting position, and head
orientation. In a pointing task without visual feedback of finger
position, Baud-Bovy and Viviani (1998)
found evidence
for a representation in spherical coordinates by analyzing the variable
errors. Our results show that the process of visuomotor learning also
has a natural coordinate system based on spherical coordinates centered
near the eyes.
A neurophysiological study in monkey by Lacquaniti et al.
(1995) suggests that the superior parietal lobule (Brodmann
area 5) might represent a neural substrate for an ego-centric spherical representation of reaching to a visual target. Analysis of electrical discharge of parietal neurons during three-dimensional reaching revealed a specific neural tuning along the distance, azimuth, and
elevation axes. Both shoulder- and eye-centered spherical frames fit
the neural data, but the eye-centered frame fitted slightly better.
In conclusion, by studying a highly limited visuomotor remapping, we could examine the natural coordinate system of the visuomotor map under natural pointing movements in three-dimensional space. On the basis of a comparison of the prediction of several a priori hypotheses, we have determined that the pattern of generalization seen is best captured by a spherical coordinate system centered near the eyes.
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ACKNOWLEDGMENTS |
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This project was supported by the Wellcome Trust, the Biotechnology and Biological Sciences Research Council, and the Royal Society. P. Vetter is funded by the Wellcome four-year PhD Program in Neuroscience at University College London.
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FOOTNOTES |
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Address for reprint requests: D. M. Wolpert, Sobell Dept. of Neurophysiology, Institute of Neurology, Queen Square, London WC1N 3BG, UK.
1 The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 20 July, 1998; accepted in final form 3 November 1998.
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REFERENCES |
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