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1Department of Neurology and 2Department of Neurobiology and Behavior, Columbia University, New York 10032; and 3Center for Neurosciences, Northshore-Long Island Jewish Research Institute, Manhasset, New York 11030 and New York University School of Medicine
Submitted 11 July 2003; accepted in final form 25 September 2003
| ABSTRACT |
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| INTRODUCTION |
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More important, there were marked differences in the effect of target number on the time course and degree of generalization of rotation and gain adaptation. Increasing the number of training directions from one to 8 for rotation proportionately reduced the rate of initial adaptation and adaptation was less complete at the end of the slower phase. Generalization to unexplored directions occurred only with more extended practice in multiple target directions. In contrast, subjects adapted to a new gain at the same rapid rate when training with one or multiple target distances, suggesting acquisition of a scaling factor for the whole workspace. This was supported by the finding that after training to a single target, subjects were able to generalize learning of a new gain to previously unvisited distances and directions.
These psychophysical data raise the possibility of separate anatomical substrates for the storage and processing of directional and extent errors needed for adapting to rotational and gain transformations. Previous work by our group and by others have shown that rotation adaptation activates right posterior parietal cortex (Ghilardi et al. 2000
; Inoue et al. 2000
) and cerebellum (Imamizu et al. 2000
). We are not aware of any imaging studies of gain adaptation for reaching movements. Similarly, the presence of 2 phases of learning suggests differences in the fast and slow processing of directional and extent errors that might be paralleled by differences in brain activation over time. This possibility is supported by imaging studies that have shown modulation and shift in brain regions activated during the time course of motor learning (Inoue et al. 1997
; Sakai et al. 1998
). Such shifts have been proposed to reflect the transitions from learning simple stimulus-response associations to learning of sequences (Sakai et al. 1999
), from novelty to automaticity (Doyon et al. 1996
; Krebs et al. 1998
; Petersen et al. 1998
) or from working memory to consolidation (Shadmehr and Holcomb 1997
).
In this paper we used PET to investigate the brain regions involved in rotation learning and to compare these regions to those involved in gain learning. Additionally, we compared activations associated with the rapid decrement in error during the first phase to more complete adaptation when learning is allowed to proceed through the second phase. To keep subjects in the rapid phase we alternated opposite values of the rotational or gain transformations every 16 movements. Some of these results were published previously in abstract form (Krakauer et al. 2000a
).
| METHODS |
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Twelve neurologically normal right-handed male subjects (ages 24-29 yr) volunteered for the study. All were naïve to the purpose of the experiment, signed an institutionally approved consent form, and were paid to participate. They all underwent MRI imaging to exclude any brain abnormalities.
Apparatus
Subjects underwent brain scanning while performing 2 sets of 5 motor tasks during blocks of 96 movements each. Basic task requirements are described in detail in previous publications (Ghilardi et al. 2000
; Nakamura et al. 2001
). In brief, all tasks required subjects to move a handheld cursor with their right hand on a 18 x 12-in. digitizing tablet (Numonics Corporation, Model 2200), while their hand and target locations were displayed on a 15-in. computer screen. A computer controlled the experiment, generated screen displays, and acquired kinematic data from the digitizing tablet at 200 Hz. On the day before PET scanning, all subjects had a session of training to become familiar with the setup and to achieve stable levels of accuracy (95% hits in 2-cm-diameter targets at a distance of 4.2 cm) in the motor reference task (CONTROL; see following text).
General procedure for motor tasks
For all tasks, subjects were required to move a cursor out and back in one uninterrupted movement from a central starting position to one of 8 radially arrayed circular targets. Targets, displayed on the vertical computer screen, were 45° apart and 4.2 cm from the center. At the start of a trial block, a series of 3 tones were sounded at 1 s intervals to provide the required tempo of the movements to follow. With the 4th and subsequent tones, successive targets turned black every second in synchrony with a tone in a predictable counterclockwise order beginning at the 3 o'clock position. Subjects were instructed to reverse sharply and in synchrony with the tone. Subjects then had to pause briefly in the starting position before moving to the next target. The specific motor tasks were the following. 1) CONTROL. This was the control task as described above with a 1:1 relation between tablet and screen distance and rightward motion of the hand moved the cursor to the right and upward motion of the hand moved the cursor upward on the screen. 2) GAIN. The tablet-to-screen gain was changed to 1:1.5 for one scan and 1:0.5 for the other. The former required subjects to make 2.8 cm movements and the latter 8.4 cm movements to displace the screen cursor 4.2 cm. The order of the 2 GAIN scans was randomized across subjects. These 2 gains were chosen so that the mean gain for the 2 scans combined was 1 as for the 2 control scans. 3) GAINalt. The gain was alternated between 1:1.5 and 1:0.5 every 16 movements. This was done to keep subjects in the rapid phase of gain adaptation throughout the scanning period. 4) ROT. The direction of cursor movement relative to the direction of the hand on the tablet was rotated 30° clockwise (CW) for one scan and 30° counterclockwise (CCW) for the other. The order of the 2 ROT scans was randomized across subjects. CW and CCW rotations were chosen so that the mean angle of rotation for the 2 scans was 0°, as in the 2 control scans. 5) ROTalt. The cursor rotation was alternated between 30°CW and 30°CCW every 16 movements. Because successive opposite rotations interfere with consolidation (Krakauer et al. 1999
), subjects remained in the rapid phase of learning throughout the scan period.
Subjects performed two 96 s scans of each task. The scans were performed in 2 sets of task blocks and the task order within each set was pseudo-random. The 2 ROTalt scans were always performed as the last 2 scans of the 2nd task block for each subject. This was done to prevent practice or interference effects of either of the 2 ROT scans on performance in the 2 ROTalt scans, given that in previous work we showed that a second exposure to the same rotation leads to savings in performance. Savings is prevented, however, if a rotation is followed by a counterrotation (Krakauer et al. 1999
), as was done here. Thus the 2 ROT conditions interfered with each other before the ROTalt conditions were experienced. This precaution was not taken for the GAINalt scans because gain learning is so fast and savings is negligible. Between adaptation conditions, subjects were brought back to baseline performance by doing 96 s of CONTROL.
Psychophysical data analysis
As described in previous publications (Ghilardi et al. 2000
; Nakamura et al. 2001
), for the outward phase of each movement we computed movement time, movement extent, and the directional error. The directional error for each movement was defined as the difference between the direction of the target from the initial hand position and the direction of the position of the hand at the peak outward velocity from the same initial position. Averages and SE values of means were generated for each successive movement across all subjects.
Additionally, mean velocity and mean directional error for each cycle of 8 movements was calculated (mean peak velocity per cycle = Vpk; mean directional error at the peak velocity per cycle = DirErrVpk).
Rotation adaptation was calculated as a percentage
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Gain adaptation was calculated as a percentage (where the error in gain learning would be the expected value of VpkN minus the actual VpkN achieved)
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PET
IMAGE ACQUISITION. PET studies were performed in 3D mode using the GE Advance tomograph at North Shore University Hospital, Manhasset, NY. This 8-ring bismuth germanate scanner provided 35 2D image planes with an axial field of view of 14.5 cm and transaxial resolution of 4.2 mm [full width at half the maximum (FWHM)] in all directions. Ethical permission for these studies was obtained from the Institutional Review Board of North Shore University Hospital. Written consent was obtained from each subject after detailed explanation of the procedures.
In each PET session, subjects were positioned in the scanner using the Laitinen stereoadapter (Hariz and Eriksson 1986
) (Sandstrom Trade and Technology, Welland, Ontario, Canada) with 3D laser alignment with reference to the orbitomeatal line. To minimize repositioning errors, we used identical stereoadapter and laser settings in all imaging sessions. Each subject was scanned in 2 sets of task blocks. Each set consisted of 5 task blocks presented in pseudorandomized order (ROT, ROTalt, GAIN, GAINalt, and CONTROL). The ROTalt condition was always performed last so that the 2 ROT scans had interfered with each other and so neither one could exert a savings effect on ROTalt. Motor tasks were performed with the dominant right arm and an intravenous catheter was placed in the left arm for administration of H215O. Relative cerebral blood flow (rCBF) was estimated using a modification of the slow bolus method of Silbersweig et al. (1993
), in which 10 mCi of H215O in 4 ml saline was injected by automatic pump in 16 s (15 ml/min) followed by a manual 3-ml saline flush. Using this injection protocol, there was a time delay of about 17 s before onset of brain radioactivity, and the time from onset to peak count rate was 45-50 s. PET data acquisition began at the time of radioactivity arrival (about 10 s after the start of the motor task) in the brain and continued for 80 s. The interval between successive H215O administrations was 10 min to allow for the decay of radioactivity.
IMAGE ANALYSIS. Data processing was performed using SPM99 (Wellcome Department of Cognitive Neurology, London, UK) implemented in Matlab (MATLAB6R12, Mathworks, MA).
All the scans were spatially standardized to the PET CBF template provided with SPM99 using the nonlinear spatial standardization facility with 7 x 8 x 7 basis functions and resliced with voxel size 2 x 2 x 2 mm (Ashburner et al. 2000
). All spatially standardized scans were smoothed using a 10-mm FWHM isotropic Gaussian spatial filter before the voxel-wise statistical analysis (Friston et al. 1996
). The 2 repeated scans of each condition were averaged using the Mean Images tool within SPM99, an option that accounts for differences in global activity by proportionally scaling each image to its global mean before averaging the individual voxel activity.
To identify changes in rCBF associated with the main effects of task, we used the SPM99 statistics option Multi-subject: conditions and covariates. The main effect of task was investigated using the contrast [1 -1] for each of the 4 task conditions (ROT, ROTalt, GAIN, GAINalt) with respect to the CONTROL condition. In separate analyses, to identify areas associated with linear increases in rCBF across similar task conditions (Turner et al. 1998
) a linear weighted contrast [-1 0 1] was used. This was done to identify those regions previously identified by the subtraction analysis where the change in blood flow is linearly related to the change in level of adaptation [e.g. (CONTROL, ROT, ROTalt) and (CONTROL, GAIN, GAINalt); see Figs. 5 and 7].
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The anatomical locations of significant clusters represented in the SPM(t) image were determined using the Talairach and Tournoux Atlas (Tailarach and Tournoux 1988
), after converting the calculated SPM99 coordinates into Talairach coordinate space (http://www.mrccbu.cam.ac.uk/Imaging/MNI/Tailarachdifferences).
| RESULTS |
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In the control condition, subjects moved their right hand out and back with straight paths and sharp reversals and both movement segments had unimodal velocity profiles with minima at the outermost point in the paths. These trajectory characteristics were unchanged during the adaptation conditions. Specifically, during both rotation conditions there was no increased curvature or directional updates. In the gain conditions, outward velocity profiles remained unimodal without apparent submovements. The mean movement extent and peak outward velocity were somewhat greater, and movement time smaller (<20% difference) for the 4 adaptation conditions compared with CONTROL (Table 1). However, there was no significant difference in these kinematic parameters across the adaptation conditions (averaged for both scans of each condition). Subjects had 96 learning trials in the ROT and GAIN conditions and, on average, achieved >70% learning.
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Imaging of rotation learning
To identify areas associated with the learning of a rotated reference frame, we subtracted mean ROT images from mean CONTROL images. This revealed significant activations in the right posterior parietal cortex, right ventral premotor (PMv) cortex, and in the left lateral cerebellum (see Fig. 3 and Table 2). To identify areas associated more specifically with the rapid phase of error reduction, we subtracted mean ROTalt from mean CONTROL images (see Fig. 4 and Table 2). This revealed significant activation only in the preSMA. We did not find any significant additional activations within the execution-related mask (see METHODS) even at the lower threshold of P < 0.05 (extent, uncorrected).
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Imaging of gain learning
A preliminary investigation of the data showed that neither GAIN - CONTROL nor the GAINalt - CONTROL subtractions showed significant activation at P < 0.05 (extent, corrected for multiple statistical comparisons), which would seem to indicate that these tasks are using the same regions already activated by the CONTROL task. Support for this possibility comes from a recent PET study investigating the effect of movement velocity on rCBF, which showed activation in a subset of cortical and subcortical regions activated during movement execution (Turner et al. 1998
). Thus given that gain adaptation involves modulating movement velocity to a given target distance, we hypothesized that neural changes may be confined to subregions of the previously identified CONTROL network. To test this hypothesis, we looked for activation only within a CONTROL mask (see METHODS; also see Fukuda et al. 2001
). We found no significant activation inside the mask for the GAIN - CONTROL subtraction. However, the GAINalt - CONTROL subtraction, inside the CONTROL mask, showed significant activations in the left insula/putamen, left medial cerebellum, and right putamen (see Fig. 6 and Table 2). Thus the rapid phase of gain adaptation was associated with activation in a subset of the motor areas activated in the CONTROL task. Subtraction images showed no significant additional activation late in the performance at the new gain, unlike the cortical activation seen in ROT. However, weighted linear contrasts did show that GAIN caused intermediate levels of activation in the medial cerebellum and right putamen (Fig. 7). This supports the idea that the rapid process of gain adaptation occurring throughout GAINalt also occurred at the beginning of the GAIN task.
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| DISCUSSION |
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We sought to determine whether different regions are involved in the early rapid phase of adaptation compared with the later slower phase of adaptation. To maintain subjects in the early rapid phase of adaptation we alternated the rotation or the gain every 2 cycles. This procedure was successful in keeping subjects in the more rapid phase of adaptation for both the gain and rotation transformations throughout the scan. Our previous work and that of others suggests that alternating perturbations should interfere with savings and consolidation of any learning that occurs during the previous 2 cycles (Krakauer et al. 1999
; Wigmore et al. 2002
). This is supported by the psychophysical results in the current study, which did not show improved performance the second time the same rotation or gain was experienced in the alternation tasks (see Figs. 1C and 2C). Thus at each alternation, subjects adapted as though performing the rotation or gain for the first time. In rotation learning, the regions activated were principally cortical for both rapid and slow learning phases. In contrast, we found that the rapid phase of gain learning involves subcortical components of a previously identified motor execution network. Operating at a new gain caused no significant activation outside of the baseline execution network.
The number of individual movements was constant across conditions but there were small but significant differences (up to about 20%) in peak velocity and movement extent in the learning conditions compared with CONTROL (Table 1). Turner et al. (2003
) examined the activation patterns associated with different near constant velocities and different extents using a single degree of freedom tracking task. To keep visual input the same under the different velocity conditions, subjects were adapted to different gains before scanning. The authors found a linear relationship between movement velocity and extent and rCBF in bilateral basal ganglia and the ipsilateral cerebellum. It is unlikely, however, that differences in velocity or movement extent account for our findings: In the 2 gain tasks, a pattern of subcortical activation, somewhat similar to that found by Turner et al. (2003
), was found only in GAINalt, even though the peak velocity was higher in GAIN; the opposite result would have been predicted if the changes were attributed to a dependency on velocity. Moreover, the average movement velocity was almost identical in the rotation and gain conditions, whereas the activation patterns were distinctly different. Thus the activation differences in our study are more likely to reflect processes associated with adaptation. Interestingly, we obtained contralateral rather than ipsilateral cerebellar activation in GAINalt. This is consistent with studies that have shown that gain adaptation generalizes (Bock 1992
; Krakauer et al. 2000b
) and is not specific to the trained limb (Vindras and Viviani 2002
), whereas the control of velocity would be expected to be effector-dependent.
Learning a rotated reference frame
We investigated the rapid phase of rotation adaptation using the ROTalt task, in which the direction of the rotation changed sign every 2 cycles, and found significant activation only in the preSMA. This same area is activated early in motor sequence learning (Hikosaka et al. 1996
, 1998
) and seems to relate to learning visuomotor associations for individual sequence elements (Sakai et al. 1999
). In a previous study of rotation adaptation to 8 targets, we found that for at least the first 18 visits to any particular target the rate of adaptation was the same as training to a single target (Krakauer et al. 2000b
). This suggested that learning of a cursor rotation with multiple targets is target direction-specific in the early phase and generalizes to intermediate directions only in later cycles. It is therefore plausible that alternating the sign of the rotation every 16 movements erased the previously stored elements and prevented target direction-specific responses from being combined into a new spatial map. Recent studies provide evidence for a role of the preSMA in working memory (Petit et al. 1998
) and more specifically in coding a change in direction of an upcoming movement (Matsuzaka and Tanji 1996
). Thus activation of the preSMA seen in our task could reflect the temporary storage of target direction-specific responses during rotation learning.
With more complete adaptation to the rotation, we found significant activation in the right PMv, right posterior parietal cortex, and left inferolateral cerebellum. Although we did not find significant preSMA activation in the ROT-CONTROL contrast, the weighted linear contrast did show that preSMA activation was higher in ROT than in CONTROL. This supports the idea that the preSMA activation reflects the process of rapid error reduction common to both ROTalt and ROT, rather than the process of interference that occurs only in ROTalt. There was less activation of the preSMA during the ROT task because this was dominated by the second slower phase of rotation adaptation.
Thus moving from the early to the late phase of rotation adaptation is associated with a reduction in preSMA activation and a transition to novel areas of activation. A similar shift in areas of brain activation with increasing practice in a task was previously demonstrated in several imaging studies (Doyon et al. 1996
; Inoue et al. 2000
; Krebs et al. 1998
; Petersen et al. 1998
; Sakai et al. 1998
; Shadmehr and Holcomb 1997
; van Mier et al. 1998
). We found significant activation in PMv, an area reported to represent visual targets in arm-centered coordinates (Graziano et al. 1997
). Unexpectedly, the PMv activation was ipsilateral to the moving limb. However, recent studies in monkeys have shown that PMv activation can be effector independent in preparation to reach a target (Hoshi and Tanji 2002
) and for other forms of visuomotor transformation (Fogassi et al. 2001
). The right PMv activation seen in our study could thus have resulted from cortico-cortical input from the activated right posterior parietal cortex.
We also found significant left lateral cerebellar activation, an area connected to right PMv, and close to the posterior superior fissure, an area associated with late learning (hours) of a novel rotational transformation in a recent fMRI study (Imamizu et al. 2000
). Finally, we obtained activation in the right posterior parietal cortex, as previously shown (Ghilardi et al. 2000
; Inoue et al. 1997
, 2000
). Interestingly, of the 3 regions activated during the ROT task only the posterior parietal cortex showed a linear increase in activation from CONTROL to ROTalt to ROT. This may imply that the new map is stored in the cerebellum or premotor cortex and the parietal cortex is involved in a more general visuospatial computation. Such a role for the posterior parietal cortex in integrating sensory information with motor output is supported by other imaging studies that have implicated posterior parietal cortex as a site for the representation of motor sequences (Sakai et al. 1998
) and for internal models of limb dynamics (Shadmehr and Holcomb 1997
). The right-sided posterior parietal activation found in our study contrasts with recent studies that have implicated the left posterior parietal lobe in "on-line" trajectory corrections (Desmurget et al. 1999
, 2001
). The absence of significant left-sided parietal activation and subjects' straight hand paths support the conclusion that such corrections did not play a significant role in the adaptive process studied here.
Further experiments will be required to determine whether the transition from activation in preSMA to 3 anatomically connected areas, previously shown to be involved with visuomotor transformations and storage and retrieval of internal representations, is attributed to a generalization process that combines target direction-specific information into a new rotated reference frame, to consolidation, or to some other process over time.
Interestingly, the cortical activations were ipsilateral and the cerebellar activation contralateral to the right arm. Other studies of motor learning have shown similar activation of regions that are not directly connected to the effector (Imamizu et al. 2000
; Inoue et al. 2000
; van Mier et al. 1998
). A possible concern with these studies is that activations in the contralateral hemisphere may not reach significance because they are already close to maximally active in the control task so that further learning-related increments are small and remain undetected. We do not think this explains the laterality of our activations for 3 reasons: First, we demonstrated increased activation in left-sided structures with sequence learning but not for rotation learning in another PET study that compared these 2 conditions (Ghilardi et al. 2000
). Second, we did not find any additional rotation learning-related activation within the baseline execution-related mask. Third, the literature consistently reports a right hemispheric specialization for computing spatial coordinate relationships (Dong et al. 2000
; Harris et al. 2000
; Vallar et al. 1999
), processes that are likely to be similar to the rotation in extrinsic space required by ROT. Thus we conclude that there is hemispheric specialization for particular aspects of motor learning that is accessible to either arm.
Learning a scaling factor
In the gain conditions of the current study, subjects rescaled their peak velocity within about a cycle after the perturbation. They then maintained the new scaling factor for the remainder of the block. Thus for most of the GAIN task, adaptation was at an asymptotic level, a level also reached by the 2nd cycle of each alternation in GAINalt. This may explain why our initial image analysis did not reveal a significant activation in either of the 2 GAIN tasks, compared with control, because for significant portions of the scans subjects were at a steady gain just as they were in the control task. We therefore hypothesized that gain adaptation may be a process that occurs within regions activated by the CONTROL task and created a mask. Further support for this hypothesis comes from recent studies that show that modulation in the velocity of movements occurs in subregions of the basic motor execution network (Turner et al. 1998
, 2003
).
The GAIN - CONTROL subtraction image showed no significant activations even with a priori defined regions using the mask. However, the GAINalt - CONTROL subtraction showed subcortical activation with significant basal ganglia and cerebellar activation. The basal ganglia activation was in the right posterior putamen and left insula/putamen. The posterior putamen receives input from motor areas (Hoover and Strick 1993
), is somatotopically organized (Crutcher and DeLong 1984
), and contains neurons with visual receptive fields that are in register with their arm tactile receptive fields, coding the adjacent space in hand- and arm-centered coordinates (Graziano and Gross 1993
). Recent animal and imaging studies have implicated the sensorimotor striatum in the later phases of procedural learning when behavior becomes automatic (Doyon et al. 1996
; Jog et al. 1999
; Jueptner et al. 1997a
,b
; Miyachi et al. 1997
). The other subcortical site activated was the left medial cerebellum. Studies have also implicated the cerebellum in late learning and automatization (Doyon et al. 1997
, 1998
; Miyachi et al. 1997
). The amount of error correction in GAINalt was greater than that in ROT (compare Fig. 1D and Fig. 2D) and yet no cortical activation was seen in GAINalt. Thus differences in activation between rotation and gain tasks are not likely to have resulted from differences in the difficulty of learning the 2 types of transformation. Our psychophysical studies show fundamental differences in generalization for these 2 types of transformation (Krakauer et al. 2000b
), suggesting that the activation differences we see are attributable to categorical differences in the way directional and extent errors are processed during adaptation.
A weighted linear contrast analysis revealed that the same areas activated in GAINalt were also activated but to a lesser degree in GAIN, suggesting that these areas reduce their activation as adaptation proceeds. Our results differ from those in the learning studies already cited because we found significant cerebellar and putaminal activation in the early rather than late phases of learning. However, a series of single-unit recording studies in monkeys adapting to a novel gain found that changes in climbing fiber discharge occurred transiently over the period that velocity was rescaled and not once adaptation was complete (Ojakangas and Ebner 1992
, 1994
). The authors concluded that the climbing fiber system is involved in calibration of movement velocity. Thus our finding of subcortical activation early rather than late during gain adaptation may be because recalibration is an overlearned process. In this frame-work, the error induced by the gain change is recognized as a contextual cue that triggers recall of the already acquired calibration process and so activates structures associated with late rather than early learning. A recent model makes just such a distinction between using sensory information for contextual switching of internal models versus using the sensory information to learn a new internal model (Wolpert and Kawato 1998
). This interpretation is also consistent with recent suggestions that the striatum and cerebellum are involved in context switching (Bischoff-Grethe et al. 2002
; Houk and Wise 1995
; Laforce and Doyon 2001
; Peigneux et al. 2000
). Finally, recent studies have implicated the cerebellum (Desmurget et al. 1998
, 2000
) and the basal ganglia (MacAskill et al. 2002
) in a form of saccadic adaptation, analagous to a gain change, suggesting interesting similarities to our results. A tentative scheme might be that the putamen is involved in context switching and the cerebellum is involved in adaptive rescaling of the movement velocity. This division is similar to one proposed for implicit sequence learning (Exner et al. 2002
). The bilateral subcortical activation might help explain why gain adaptation transfers readily across limbs (Vindras and Viviani 2002
).
In conclusion, our PET study provides insight into why gain and rotation adaptation show such distinct differences at the psychophysical level (Krakauer et al. 2000b
). Rotation adaptation involves learning a new reference frame that requires recruitment of novel cortical regions. In contrast, gain adaptation transiently recruits subcortical regions within the motor execution network, consistent with the contextual recall of an already acquired recalibration procedure. The different activations both for initial rapid reductions in direction and extent errors and for later more complete rotation and gain learning imply a separation in the processing of extent and direction errors. This is consistent with vectorial planning for horizontal reaching movements. In addition, the activation differences between the early and later phases provide further imaging evidence that adaptation to new spatial mappings may consist of 2 distinct and successive processes (Desmurget et al. 2000
; Imamizu et al. 2000
; Redding and Wallace 2001
).
| ACKNOWLEDGMENTS |
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GRANTS
This work was supported by National Institute of Neurological Disorders and Stroke Grants NS-K23 02138, NS-K08 01961, NS-R01 22715, and NS-R01 35069.
| FOOTNOTES |
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Address for reprint requests and other correspondence: J. W. Krakauer, Neurological Institute, Columbia University, College of Physicians and Surgeons, 710 West 168th St., Box 214, New York, NY 10032 (E-mail: jwk18{at}columbia.edu).
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