The Journal of Neuroscience, October 15, 2008 • 28(42):10751–10765 • 10751

Behavioral/Systems/Cognitive

Neural Correlates of Predictive and Postdictive Switching
Mechanisms for Internal Models
Hiroshi Imamizu1,2 and Mitsuo Kawato1
1

Advanced Telecommunications Research Institute International, Computational Neuroscience Laboratories, and 2National Institute of Information andCommunications Technology, Kyoto 619-0288, Japan

Switching of sensorimotor tasks may be classified into predictive switching based on contextual information and postdictive switchingbased on the error between sensorimotor feedback and predictions. We used functional neuroimaging to study the brain regions involvedin each type of switching of internal models for visuomotor rotations (clockwise and counterclockwise rotations of visual feedback). The
color of a cue presented before movement initiation corresponded to direction of rotation of the feedback in an instructed condition, but
not in a noninstructed condition. Switching-related activity was identified as activity that transiently increased after the direction ofrotation was changed. The switching-related activity in cue periods in the instructed condition, when a predictive switch is possible, wasobserved in the superior parietal lobule (SPL). However, the switching-related activity in feedback periods in the noninstructed condition, when prediction error is crucial for the postdictive switch, was observed in the inferior parietal lobule (IPL) and prefrontal cortex.
The functional influence of the SPL on the lateral cerebellum, namely, a possible neural correlate for internal models, increased in the
instructed condition, but the influence of the IPL on the cerebellum was increased in the noninstructed condition. We observed a rapid
activity increase in the instructed condition and a gradual activity increase in the noninstructed condition mainly in the lateral occipitotemporal cortices (LOTC) and supplementary motor cortex (SMA). These results are consistent with separate mechanisms for predictive
and postdictive switches and suggest that the LOTC and SMA receive output signals from appropriate internal models.
Key words: task switching; internal models; visuomotor rotation; contextual information; sensorimotor feedback; functional magnetic
resonance imaging

Introduction
Skilled manipulation of objects, including our own bodies, relieson the brain learning to control the object and predict the consequences of this control. Neural mechanisms that mimic the input– output properties of objects support prediction and control;
these are termed internal models (Kawato et al., 1987; Wolpert etal., 1995). Considerable evidence from behavioral, neurophysiological, and functional imaging studies indicates that the CNS
maintains a number of internal models for different objects andenvironments in a modular manner (Ghahramani and Wolpert,
1997; Flanagan et al., 1999; Krakauer et al., 1999; Gribble andScott, 2002; Imamizu et al., 2003; Yamamoto et al., 2007). Behavioral studies have shown that humans can switch internal models
based on contextual information. For example, an auditory tonecue can induce context-dependent adaptation to prismatic displacement (Kravitz and Yaffe, 1972). Contextual cues, such ascolor, can contribute to simultaneous learning and switching between internal models representing different dynamic environments (Wada et al., 2003; Osu et al., 2004). However, little isReceived March 13, 2008; revised July 26, 2008; accepted Sept. 10, 2008.
We thank K. Kurimoto for technical support and Drs. H. Tanaka and T. Kouchiyama for helpful comments on thismanuscript.
Correspondence should be addressed to Hiroshi Imamizu, National Institute of Information and Communications
Technology, 2-2-2 Hikaridai, Keihanna Science City, Kyoto 619-0288, Japan. E-mail: imamizu@gmail.com.
DOI:10.1523/JNEUROSCI.1106-08.2008
Copyright © 2008 Society for Neuroscience 0270-6474/08/2810751-15$15.00/0

known about the neural mechanisms underlying internal model
switching.
Recent studies have indicated that humans optimally determine their behaviors by combining predictions about environments based on previous knowledge with evidence from sensory
feedback in a manner consistent with a Bayesian process (forreview, see Körding and Wolpert, 2006). Empirically, two typesof information are crucial for the switching of internal models.
For example, when we lift an object, both contextual information, such as color or shape of the objects that can be perceived
before movement execution, and error in the prediction of sensorimotor feedbacks that can be obtained during or after execution, contribute to the switching. Here, the error is a continuous
value reflecting the difference between predicted and actual feedback (prediction error), which can be used to compute likelihood
in a Bayesian process. A computational model for switching internal models, called the modular selection and identification forcontrol (MOSAIC) (Wolpert and Kawato, 1998; Haruno et al.,2001) model, has proposed two separate switching architectures
for each type of information.
In our previous behavioral study (Imamizu et al., 2007b), subjects learned to move their index fingers to targets while visualfeedback of the finger movements was rotated clockwise (CW) or
counterclockwise (CCW) by 40° around the initial position.
When subjects adapted to alternating blocks of opposing rotations, we investigated the effects of contextual information about

10752 • J. Neurosci., October 15, 2008 • 28(42):10751–10765

Imamizu and Kawato • Predictive and Postdictive Switching of Internal Models

forthcoming direction of the rotations on subjects’ performances. Consequently, the contextual information selectively
improved predictive switching performance, but did not affectswitching performance based on prediction errors, suggesting theexistence of two functionally independent mechanisms: a predictive mechanism based on contextual information and a postdictive mechanism based on prediction error.
In the current study, using functional magnetic resonanceimaging (fMRI), we examined whether these two mechanisms
are based on separate neural substrates. After training for the 40°
CW and CCW rotations, activity was measured while the direction of rotation was alternately changed. Subjects could predictively switch their behaviors based on previous contextual information in an instructed condition, but could not do so and reliedon prediction errors in a noninstructed condition. We comparedswitching-related activity in the instructed condition to that in
the noninstructed condition. Furthermore, using functional connectivity analysis, we investigated how information obtained byeach mechanism is combined in the brain.

Materials and Methods
Experimental design

Experiments were designed so as to dissociate brain activity related to
predictive switching based on contextual information from activity related to postdictive switching based on prediction error as follows.
Subjects moved their index fingers from the center start zone toward atarget and back to the start zone (out-and-back pointing movement) ineach trial while lying in the supine position (Fig. 1 A). Subjects’ forearms
were fixed on a platform, and movements of the wrist and the metacarpophalangeal joint of the right index finger were allowed. Surgical tape
fixed the distal and proximal interphalangeal joints of the finger. A
marker of a position recording system (OPTOTRAK; Northern Digital)
was attached to the right index fingertip. A cursor, targets, and the startzone were projected onto a screen, which was viewed by the subjects
through a mirror. The cursor, corresponding to the position of the index
finger tip, was always visible on the screen, and its position was determined by the marker position, which was projected onto a plane parallelto the screen (x–y plane). A target set consisted of eight radially arrayedcircles, separated in direction by 45°, placed on a circle with a radius of 5
cm on the screen (Fig. 1 B, left panel), requiring a 10 cm movement of themarker for subjects to point at the targets. Only one of these targets
appeared in each trial. The subjects were asked to start movements immediately after the target appeared, and to move in a fast and smooth
motion without trajectory correction.
The cursor position was rotated 40° CW or CCW around the center ofthe screen as illustrated in Figure 1C. That is, when subjects moved theirfingers, for example, in the directions indicated by the black arrows, thecursor on the screen moved in the directions indicated by the whitearrows, depending on the direction of rotation. After intensive training
with both CW and CCW rotations, brain activity was measured while thedirection of rotation was alternately changed with pseudorandom timing. Subjects could predictively switch their behaviors under an instructed condition, in which the color of a cue as previous contextual
information presented before the initiation of movement corresponded
to the direction of rotation. However, under a noninstructed condition,in which the color did not correspond to the direction of rotation, subjects relied on prediction errors calculated from sensorimotor feedback.
Many previous studies have investigated the neural mechanisms involved when subjects switched from one arbitrary stimulus–response
relationship (stimulus–response mapping) to another according to contextual information (Dove et al., 2000; Kimberg et al., 2000; Crone et al.,2006) (for review, see Murray et al., 2000; Passingham et al., 2000). For
example, when the color of a contextual cue was green, subjects pressed aleft key if a “⫹” sign was presented on a screen or a right key if a “⫺” sign
was presented. However, when the color was red, the relationship between the sign and the key was reversed (Dove et al., 2000). This paradigm is different from that in the current study, because the task mainly

Figure 1. A, Posture of subjects during experiments both outside and inside the magnetic
resonance (MR) scanner (scanner is not drawn in the figure). B, Positions of the start circle andtargets (T1–T8) on the screen (left panel) and in the hand space (right panel) under 40° clockwise visuomotor rotation. “E” indicates the angular error of a pointing movement. C, Relationship between the direction of finger movements (black arrows) and cursor movements (whitearrows) under 40° CW (left panel) and 40° CCW (right panel) rotations. The numbers indicate
correspondence between black and white arrows.
involves predictive switching of subjects’ responses based on contextual
information. Furthermore, switching is unlikely to be based on continuous prediction error between predicted and actual sensorimotor feedback, because subjects’ responses are simple and stereotyped (namely,
hand movement in the left or right direction). In contrast, the current
experimental design included a noninstructed condition, in which predictive switching was not possible. Error in prediction of sensorimotor
feedback is a continuous value in the above pointing movements, because the cursor can continuously move in any direction within thetwo-dimensional screen space and is not restricted in the two directions.
In our previous study (Imamizu et al., 2004) investigating regional
differences between switching-related activity and internal-modelrelated activity, subjects manipulated three types of computer mousewith different input– output properties. Assuming that switching-related
activity transiently increases after a change in mouse type, and thatinternal-model-related activity shows sustained activity specific to eachmouse type, we investigated the temporal profiles of activity in various
brain regions. Consequently, we identified switching-related activity
mainly in the cerebellum, parietal regions, and Brodmann’s area (BA) 46.
However, the experimental design did not allow us to distinguish activity
related to predictive switching from that related to postdictive switchingfor the following reasons. While subjects tracked a target continuously
moving at high speed on a screen, the mouse type was changed, and,simultaneously, cognitive cues (change of cursor color and letters indicating the mouse type) were presented. In this way, subjects simultaneously obtained cognitive cues for predictive switching and sensorimo-Imamizu and Kawato • Predictive and Postdictive Switching of Internal Models

J. Neurosci., October 15, 2008 • 28(42):10751–10765 • 10753

clockwise condition. Similarly, when you movethe finger straight up, the cursor will move in an
upper-right direction under the clockwise condition, but in an upper-left direction under thecounterclockwise condition, etc.” During the
break, subjects were informed of the rotation
direction in the subsequent session.

Switching sessions in the scanner

A session consisted of 72 trials and lasted ⬃20
min. A total of 12 sessions were conducted on 4
or 5 separate days within a 2 week period. On
each day, subjects underwent two or three sessions without getting out of the scanner. Subjects were repositioned in the scanner at the beginning of the first session of each day. A bitebar molded for each subject was attached to a
fixed position of the head coil so that the subjects’ heads were placed at the same position
relative to the coil across different days. We
carefully adjusted the slice positions of functional images so that the positions did notchange across different days.
Each trial began with the presentation of acolored cue circle (diameter, 1.0 cm) at thescreen center (Fig. 2 A). A white start circle replaced the cue circle after a random delay of
5–10 s, defined as the cue period. Simultaneously, a target appeared in the peripheral areaof the screen, and the cursor appeared at thecenter of the start circle. Subjects were instructed to move the cursor to the target immeFigure 2. A, Timeline in each trial of a switching session. Regions enclosed by green broken lines are magnified in B. B, diately on its appearance, and back to the start
Examples of cursor trajectories (top panels, white dots) and marker trajectories (bottom panels, black dots) from test (left), circle as soon as possible (within 1 s), and thenerror-equalized baseline (middle), and error-zeroed baseline (right) trials. The dots indicate the positions of the cursor or the to maintain the cursor in the start circle. Thecue circle for the next trial replaced the startmarker every 3 ms. The arrows near the trajectories indicate moving direction.
circle after a random delay of 7–12 s from thetarget appearance, defined as an execution/
feedback period. The time intervals (5–10 or
tor feedback for postdictive switching; thus, cue-related activity
7–12
s)
were
inserted
betweenthe events because we used event-related
temporally overlapped feedback-related activity. The current study used
fMRI to distinguish activity related to the cue and activity related to thediscrete pointing movements and event-related fMRI to separate activity
execution/feedback. The cursor was always visible in the execution/feedrelated to presentation of the cognitive cue from that related to sensoriback periods; thus, there was no time interval between execution andmotor feedback.
feedback, because such an interval might degrade subjects’ performanceand learning (Kitazawa et al., 1995). Therefore, instead of separating
Subjects
Fourteen subjects (10 males and four females; 19 – 44 years of age) parfeedback-related activity of interest from execution/feedback-related acticipated in this study. All participants were right-handed according totivity using an event-related design, we measured execution-related acthe Edinburgh Inventory (Oldfield, 1971). A signed informed consent
tivity during baseline periods and subtracted this activity fromform, approved by the institutional ethics committee, was obtained fromexecution/feedback-related activity during the test periods (see below).
each participant.
Within each session, a block was defined as a set of 18 trials. The
direction of rotation did not change within a block, and whether or not it
Familiarization session outside the magnetic resonance scannerchanged between successive blocks was randomly determined. Each
Subjects conducted a familiarization session without the visuomotor roblock consisted of the following: (1) a test period; (2) an error-equalized
tations to become accustomed to pointing while lying in the supine pobaseline period; and (3) an error-zeroed baseline period in this order.
sition. The eight targets were presented randomly in each cycle of eight
Each period consisted of six trials, and six targets that were randomly
trials. One session consisted of 15 cycles (120 trials) and lasted 9 min.
selected from the eight possible targets (Fig. 1 B) appeared in the sequence. The order of the six targets did not change across periods within
Training sessions outside the scannera block; that is, the identical target appeared in the n, (n ⫹ 6), and (n ⫹Several days after the familiarization session, subjects were intensively12)th trials. Sets of six targets were counterbalanced across blocks andtrained to perform pointing movements with 40° CW and CCW rotation
sessions so that each target appeared an equal number of times over all
conditions. The targets and numbers of trials in each training session
sessions.
were the same as in the familiarization session. Subjects underwent 10
In a test period (Fig. 2 B, left panel), subjects conducted pointing
sessions with a 3 min break between each session. The direction of rotamovements under 40° CW or CCW rotation conditions, and cursor tration changed alternately every session, and the order of rotations was
jectories were recorded in a computer memory. In the error-equalizedcounterbalanced between subjects. Before the onset of the first session,baseline period (middle panel), the cursor moved toward a target accordsubjects were given the following instruction about the rotations while
ing to the trajectory recorded in the preceding test period; that is, thebeing shown Figure 1C: “The cursor position will be rotated 40° CW or
cursor movement in the (n ⫺ 6)th trial was replayed on the screen during
CCW around the center of the screen. Thus, when you move your finger
the execution/feedback period. Subjects were instructed to assume thatstraight right, the cursor will move in a lower-right direction under thethe direction of rotation would be the same as that in the preceding test
clockwise condition, but in an upper-right direction under the counter-10754 • J. Neurosci., October 15, 2008 • 28(42):10751–10765

period, and to compensate for the rotation so as to move the cursor
toward the target. The purpose of the error-equalized periods was tomeasure baseline activity related to visual stimuli (for example, target
and motion of the cursor), movement execution, and visual feedback ofperformance error. In the error-zeroed baseline period (right panel), thetask for subjects was the same as that in the error-equalized period.
However, the cursor moved according to the recorded trajectory that was
rotated around the center of the screen beforehand so that the cursor
always moved to a target; that is, the pointing error is constantly zero. The
purpose of the error-zeroed period was to measure baseline activity related to the visual stimuli and movement execution. Before the beginningof the experiment, subjects were informed of the above mechanisms of
cursor movements in the error-equalized and the error-zeroed baseline
periods.
The error-equalized baseline period, which occurred immediately after the test period, is more important than the error-zeroed baseline
period for the following reasons. To identify switching-related brain regions, we looked for brain activity that increased immediately after alteration of rotation direction and decreased as the number of trials increased in the test periods (see below, Imaging data analysis). However,
performance error is also supposed to increase after the alteration ofrotation direction. It is known that this error evokes strong activity inlarge regions in the cerebral cortices and cerebellum (Imamizu et al.,
2000; Diedrichsen et al., 2005). Thus, we measured baseline activity
evoked by errors in the error-equalized period when switching was notneeded and subtracted this activity from activity in the test period.
There were two conditions in the test period according to the existenceof correspondence between the cue color and the direction of rotation. In
the instructed condition, the color was red or blue when the rotation was
40° CW or CCW, respectively. Thus, subjects could know the direction ofrotation in a cue period. However, in the noninstructed condition, thecolor was purple regardless of the rotation direction. In both conditions,the color was orange in the error-equalized baseline period and cyan in
the error-zeroed baseline period.

Magnetic resonance imaging acquisition
A 1.5 T scanner (Shimadzu-Mariconi) was used to obtain blood oxygen
level-dependent (BOLD) contrast functional images. Images weighted
with the apparent transverse relaxation time were obtained with anechoplanar imaging sequence (repetition time, 3.5 s; echo time, 50 ms;
flip angle, 90°). The whole brain was covered in 35 axial slices (3 mmthickness; 1 mm gap), each of which was acquired as a 64 ⫻ 64 matrix(field of view, 192 mm), with a voxel size of 3 ⫻ 3 ⫻ 4 mm. Three
hundred fifty-four volumes were acquired in each session. T1-weighted
structural images were acquired with 1 ⫻ 1 ⫻ 1 mm resolution with agradient echo sequence.

Behavioral data analysis
To gauge performance accuracy, we measured the angular error of the
movement (Fig. 1 B, right panel, “E”). The error was computed in thehand space as the absolute value of angle between the vector fromthe start circle to the target and the vector from the start circle to themarker position at the moment of first maximal velocity. We also investigated spatiotemporal data to examine whether subjects’ performances
differed among the above three periods. Movement initiation was defined as the first time when the tangential velocity of the marker crossed
5% of the maximum velocity of each trial. Movement termination was
the last time the velocity fell ⬍5% of the maximum. We computed reaction time (interval between the target onset and the movement initiation), movement time (interval between the movement initiation and thetermination), and the marker path length from movement initiation to
its termination.

Imaging data analysis
Functional imaging data were analyzed using SPM2 (Wellcome Department of Cognitive Neurology, London, UK; http://www.fil.ion.
ucl.ac.uk/spm). We discarded the first four volumes of images in eachsession to allow for T1 equilibration. For preprocessing, data were temporally realigned to correct for the sequence of slice acquisition and thenspatially aligned to the first volume with a six-parameter rigid-bodyImamizu and Kawato • Predictive and Postdictive Switching of Internal Models

transformation. The data were spatially normalized to the Montreal Neurological Institute (MNI) (Montreal, Quebec, Canada) reference brain
and resliced to a 2 mm isotropic voxel size. Data were smoothed spatiallywith a Gaussian kernel with 12 mm full-width at half-maximum. Because
we were interested in differences in activity in global brain regions rather
than local ones between predictive and postdictive mechanisms, a relatively large size filter was applied to ameliorate differences in intersubject
localization. Data were high-pass filtered with a cutoff frequency of 1/128
s to remove slowly varying trends.
To check the displacement of subjects’ heads that might be caused byrepositioning of subjects in the scanner at the beginning of each day after
the second day (see above, Switching sessions in the scanner), we investigated the six-parameter values for spatial alignment of the first volumeof images from each day with the first volume from the first day. Meanabsolute values across days and subjects for translation (x, y, and z) androtation (pitch, roll, and yaw) were 1.15 (SD, 0.90) mm, 1.30 (0.96) mm,
1.01 (0.91) mm, and 0.86° (0.63°), 0.64° (0.45°), and 0.96° (0.76°), respectively. Thus, the displacement was thought to be well within therange that can be corrected by SPM alignment.
General statistical analyses were performed in two stages. The firststage individual (fixed-effect) analysis was based on an event-related
fMRI design. In this analysis, 72 types of events were defined: 2 (instructed and noninstruction conditions) ⫻ 3 (test, error-equalized baseline and error-zeroed baseline periods) ⫻ 6 (1– 6th trials) ⫻ 2 (cue andexecution/feedback events). The cue or execution/feedback event wasmodeled by an impulse function locked at the onset of the cue or the
execution/feedback period, respectively. The impulse functions wereconvolved with a canonical hemodynamic response function in SPM2 toyield regressors in a general linear model for each voxel as follows:

冘
72

Si ⫽

k⫽1

冘
12

␤ k x ki ⫹

␥ k y ki ⫹ e.

k⫽1Here, Si is the fMRI activity in the ith scan. xs are regressors corresponding to the 72 types of events above explained. ys are regressors of nointerest corresponding to 12 sessions, each of which was assigned 1 in thecorresponding session and 0 otherwise. Regression weights (␤s and ␥s)and the residual (e) were estimated for each voxel by the least-squares
method. The estimated weights of interests (␤s) or contrasts of theweights were carried forward to a second-stage group (random effect)analysis using a one-way ANOVA model with nonsphericity correction
and adjustment for correlated repeated measures. The results were inspected using t contrasts according to the analysis designs explained
below.
To average poststimulus BOLD responses for display purposes, wedefined another model in the first-stage individual analysis using a finite
impulse response (FIR) basis function with a bin width of 3.5 s (therepetition time of scans), modeling a total of six bins from 0 to 21 s after
onset of one of the 72 aforementioned events. The model contains six
regressors for an event of interest and regressors for the other events.
Intuitively, the FIR basis set considers each time bin after stimulus onset
to model the BOLD response that would have been seen in the absence ofother events, and captures any possible shape of hemodynamic response
function up to a given frequency limit. In this model, the estimatedweights for each time bin are directly proportional to the average BOLD
response at that time. This analysis was conducted by using a peristimulus histogram function in SPM2. We obtained the poststimulus responsetime courses for the events in the test trials and the error-equalized baseline trials. We subtracted the average response time course across thebaseline trials from time course in each test trial, and displayed the subtracted time course averaged across subjects (see Fig. 6 B).
(1) Analysis of activity related to cue presentation or execution/feedbackof movements. To confirm whether the above event-related analysis could
dissociate activity related to cue presentation from that related to execution/feedback of pointing movements, we applied the following analysis
1), whichto the estimated ␤ weights for the first trials of test periods (␤test
are expected to be the most important trials for the switching of behav1
iors. We carried images of ␤test
estimates in the first-stage analysis forImamizu and Kawato • Predictive and Postdictive Switching of Internal Models

four events (cue and execution/feedback events by instructed and noninstructed conditions) to the second-stage group analysis, and identified
regions significantly activated by these events using a one-sample t test1
(␤teset⬎ 0) (see Fig. 4 A, B, E, F ). To confirm the subtraction of errorequalized baseline activity from the test activity, we made four contrast
images in the first-stage analysis by subtracting the averaged estimate
within the error-equalized baseline period (␤error-equalized), individually,1from the estimates for the above four events (C1⫽␤test⫺ ␤error-equalized).
Then we carried them into the second-stage analysis to identify regions inwhich C1 is significantly larger than zero (see Fig. 4C, D, G,H ). The
threshold in the second-stage analysis was p ⬍ 0.05 when corrected for
multiple comparisons at cluster level ( p ⬍ 0.001, uncorrected at voxel
level and a cluster size ⬎270). This threshold was low compared withthose used in the imaging analyses described below (2, 4, and 5), because
we intended to confirm at this low threshold if our event-related design
could dissociate activity related to cue presentation from that related to
execution/feedback.
(2) Analysis of activity decreasing as a function of trial numbers after achange in rotation direction. According to behavioral data (described below), the size of angular errors increased immediately after a change inthe direction of rotation and decreased gradually as a function of trial
number. This suggests that adaptive switching processes proceeded gradually, and that activity directly related to these processes decreased gradually. To identify the activity related to switching, we conducted thefollowing analysis. In the first-stage analysis, contrast images were generated by subtracting the averaged ␤ estimate within the error-equalizedbaseline period, individually, from the estimate for the cue or execution/
feedback event in the six test trials. In the second-stage analysis, a onesample t test was applied to the contrast images to identify voxels inwhich the contrast of the ␤ estimates significantly decreased as a functionof test trial number; that is, the weighted sum of the parameters (5 䡠 C1 ⫹3 䡠 C2 ⫹ 1 䡠 C3 ⫺ 1 䡠 C4 ⫺ 3 䡠 C5 ⫺ 5 䡠 C6) is significantly larger than zero.
Here, Ci indicates the contrast of the estimates obtained from the ith test
trial. The second-stage analysis was performed separately for four events(cue and execution/feedback events by instructed and noninstructedconditions). Decreasing activity evoked by cue events in the instructedcondition and by execution/feedback events in the noninstructed condition are of particular interest, because the former activity is likely to berelated to a predictive switch based on contextual information, and thelatter activity is likely to be related to postdictive switching based on theerror in prediction of sensorimotor feedback. The threshold was p ⬍ 0.05
corrected at voxel level and a cluster size ⬎30.
To investigate the actual time courses of the above decreasing activity
across trials, we examined how the value of Ci in individual subjects
changed as a function of test trial numbers (i) in regions identified by thesecond-stage analysis. Ci is a contrast of ␤ estimates as described above.
The magnitude of the estimate is proportional to the maximum height of
the fitted hemodynamic response function and captures the size of theeffect of the event on the hemodynamic response. Therefore, Ci reflects
the effect size in test trials in the absence of the effects that were measured
in the error-equalized baseline trials. The Ci value was divided by themean signal intensity for a given voxel to normalize differences amongvoxels. We named this value “effect size.” The effect size was averaged
across subjects and voxels in a region of interest, and plotted as a functionof test trial number (see Fig. 6C).
The above two types of decreasing activity were mainly observed inadjacent parietal regions [the superior parietal lobule (SPL), the inferiorparietal lobule (IPL), and the precuneus]. To quantify the spatial segregation of the two types of activity, we measured the volume of the overlapping region in which both types of activity were observed, and compared it with the volume of regions in which either type was observed. For
group volumetric analysis, we measured the volume of each type of activity detected and thresholded by the procedure described above. However, for individual analysis, because the above two types of activity wereobtained by two-stage analysis [(1) subtraction of activity in the errorequalized baseline period from activity in the test periods in theindividual-analysis stage, and (2) detection of a decreasing trend in activity with an increase in trial number by using the above contrast (5 䡠 C1
⫹ 3 䡠 C2 ⫹ 1 䡠 C3 ⫺ 1 䡠 C4 ⫺ 3 䡠 C5 ⫺ 5 䡠 C6) in the group analysis stage],

J. Neurosci., October 15, 2008 • 28(42):10751–10765 • 10755

we could not conduct an individual analysis equivalent to the group
analysis. Therefore, in individual volumetric analyses, we looked for activity evoked by cue or execution/feedback events in the first test trial,
which is expected to be the most important trial for the switching of
behaviors. Specifically, we subtracted averaged activity evoked by a cue
event within the error-equalized baseline period from activity evoked bya cue event in the first test trial of the instructed condition, to extract
activity related to a predictive switch. We subtracted averaged activity
evoked by an execution/feedback event within the error-equalized baseline period from activity evoked by an execution/feedback event in thefirst test trial of the noninstructed condition to extract activity related toa postdictive switch. We applied a low threshold ( p ⬍ 0.001, uncorrected) to each extracted activity to avoid underestimation of overlapping volume. We defined parietal regions of interest as the union of the
SPL, IPL, and precuneus based on the Automated Anatomical Labelingmap (Tzourio-Mazoyer et al., 2002) in the WFU PickAtlas toolbox(http://fmri.wfubmc.edu/cms/software) (Maldjian et al., 2003) for
SPM2, and measured the volumes of regions related to either predictive
or postdictive switches, and regions related to both.
(3) Analysis of changes in effective connectivity according to conditions.
Dynamic causal modeling (DCM) is a system identification procedurethat uses Bayesian estimation to make inferences about the effective connectivity between neural systems and how it is affected by experimental
conditions (Friston et al., 2003). Because connectivity in DCM is measured through the coupling of changes in imaging signals, rather thananatomically, a significant unidirectional modularity influence of one
brain region on another does not necessarily reflect the presence of adirect and unidirectional anatomical connection. Instead, the connectivity revealed by DCM reflects the inferred direction of neural influencesthat is specific to the experimental conditions, and that may be mediatedthrough interneurons or brain regions not explicitly included in themodel.
The results of the above analysis (2) suggested that activity in the SPL
is related to predictive switching based on contextual information, andthat activity mainly in the IPL and prefrontal cortex (PFC) is related to
postdictive switching based on prediction error derived from sensorimotor feedback. We investigated how different conditions influenced effective connectivity between these regions and the lateral cerebellum, inwhich many studies have reported activity related to internal models invarious kinds of sensorimotor tasks (Shidara et al., 1993; Shadmehr andHolcomb, 1997; Gomi et al., 1998; Kobayashi et al., 1998; Imamizu et al.,
2000; Blakemore et al., 2001; Miall et al., 2001; Krakauer et al., 2004;
Milner et al., 2007; Yamamoto et al., 2007). Only left cerebral hemisphere
regions and right lateral cerebellar regions were included in our network
to maintain model simplicity. Group maxima of activation were identified in the second-stage analysis described in (2). Then, subject-specificmaxima were determined operationally as the nearest local maxima to
the group maxima in regions significantly activated by any of the four
events (namely, cue or execution/feedback events in the instructed or
noninstructed conditions in the first test trial) in individual analyses( p ⬍ 0.001, uncorrected). Regarding the PFC, we found multiple activation clusters in BAs 10, 11, and 46 in the second-stage group analysis, but
selected the group maximum in BA 46 in which activity related tointernal-model switching was also found in our previous study (Imamizu
et al., 2004). Regarding the cerebellum, because subjects were required tocompensate for the rotations in all trials in the current experiment, thisdesign does not allow us to directly identify internal model activity basedon a contrast between compensation and no-compensation (null) conditions. However, previous studies (Tamada et al., 1999; Imamizu et al.,2000, 2004, 2007a) have reported that internal models for the rotations
are acquired near the posterior superior fissure. Thus, we anatomicallylocated the group maximum around the center of the posterior superior
fissure in the MNI reference brain (x, y, z: 40, ⫺60, ⫺34). Because thelateral cerebellum was included in regions significantly activated by anyof the above four events, we could identify subject-specific maxima in the
cerebellum. Using SPM2, BOLD signal time courses were then extracted
from 8 mm spheres centered on subject-specific maxima, and summarized as the principal eigenvariates of the time courses.
Effective connectivity analysis was performed using the DCM tool in10756 • J. Neurosci., October 15, 2008 • 28(42):10751–10765

Imamizu and Kawato • Predictive and Postdictive Switching of Internal Models

SPM5. According to anatomical studies, mainly
in monkeys, there exists connectivity between
the cerebellum and parietal regions including
the SPL and the IPL (Schmahmann and Pandya, 1989; Stein and Glickstein, 1992; Clower etal., 2001), between the cerebellum and the dorsolateral PFC (Kelly and Strick, 2003), and between the dorsolateral PFC and the parietal regions (Petrides and Pandya, 1999; Marconi etal., 2001). However, the exact connectivity
among these regions in the human brain is unknown. Therefore, subject-specific DCMs were
fully and reciprocally connected with modulatory influences from both conditions specified
on all of the connections. The modulatory influences were modeled in the first test trial tomaintain model simplicity. Input stimuli to the
network were modeled as exerting direct effects
on the SPL and the IPL. The effects of the input
stimuli on the SPL model visual inputs evokedby cue presentation, and are exerted at the onsets of cue periods, whereas their effects on the
IPL model sensorimotor-feedback inputs andare exerted at the onsets of execution/feedback
periods.
The DCM analysis was performed in a twostage procedure similar to the functional image
analysis explained above. The parameters corresponding to the strength of intrinsic or mod- Figure 3. Angular error measured in the hand space. A, Angular error in the familiarization and training sessions before brain
ularity effects obtained from the subject- activity measurement. The curves show the medians of the errors within a cycle (8 trials) averaged across subjects (⫾SD) as a
specific first-level DCM models were taken to a function of cycle number in each session. The horizontal thick lines indicate mean error within each session. B, Angular error insecond between-subjects level analysis. A one- switching sessions inside the MR scanner. The curves show error averaged across sessions and subjects (⫾SD) as a function of trial
sample t test ( p ⬍ 0.05) was used in the second- number after a change in rotation direction. *p ⬍ 0.05, Tukey’s HSD post hoc test.
level analysis. Because it is unknown whether
the DCM parameters were normally distribsize ⬎30 voxels. To investigate actual time courses of activity in regions ofuted, we confirmed that a nonparametric test (Wilcoxon’s signed-rankinterest across trials, we plotted effect size [see above, (2)] calculatedtest) yielded the same results as the t test at the p ⬍ 0.05 level. The
from the values of C cuei and C exei as a function of test trial number (i).
threshold was not corrected for multiple comparisons because connec(5) Analysis of activity related to visual feedback of performance error.
tions of interest were restricted by the results of the analysis (2).
We examined the difference between the error-equalized and the error(4) Analysis of increasing activity as switching process proceeds. To idenzeroed baseline periods to identify activity related to visual feedback oftify brain regions related to the degree of contribution of appropriate
the error. Specifically, in the first-stage analysis, contrast images wereinternal models, we looked for increasing activity as switching process
yielded by subtracting ␤ estimates for the execution/feedback periods ofproceeds. According to our previous behavioral and simulation study
the error-zeroed baseline trials from those for the execution/feedback(Imamizu et al., 2007b), the time courses of signals reflecting the degree
periods of the error-equalized baseline trials. In the second-stage analyof contributions of appropriate internal models during the predictive
sis, a one-sample t test was applied to these images to identify voxels inswitch based on contextual information were markedly different fromwhich the contrast of the estimates was significantly higher than zero.
the time courses during the postdictive switch based on prediction error.
The threshold was p ⬍ 0.05 corrected at the voxel level and cluster size
Specifically, the signal immediately increased after a change in the envi⬎30.
ronment in the predictive switch condition, whereas it gradually increased with trial number in the postdictive switch condition. Based on
Results
this result, we looked for brain activity that increased immediately after a
Behavioral datachange in the direction of rotation in cue periods of the instructed conFigure 3A shows subjects’ performances in the familiarization
dition, but gradually increased in execution/feedback periods of the nonandtraining sessions. The curves show angular error as a function
instructed condition. Specifically, contrast images were yielded for eachof cycles (eight trials) in each session. The ordinate represents thetrial by the same subtraction as described in (2), in the first-stage analysis,
average (⫾SD) across subjects in which the value for each subject
and then a one-sample t test was applied to the images to identify voxels
is the median size of errors within a cycle. The direction of rotain which the weighted sum of contrasts of ␤ estimates was significantly
higher than zero. The weighted sum was defined as follows: 5 䡠 C cue1 ⫹tion did not change within a training session, but alternately
5 䡠 C cue2 ⫹ 5 䡠 C cue3 ⫹ 5 䡠 C cue4 ⫹ 5 䡠 C cue5 ⫹ 5 䡠 C cue6 ⫺ 15 䡠 C exe1 ⫺changed across the sessions. The error markedly increased at the
11 䡠 C exe2 ⫺ 7 䡠 C exe3 ⫺ 3 䡠 C exe4 ⫹ 1 䡠 C exe5 ⫹ 5 䡠 C exe6. Here, C cuei
beginning of each session, but gradually decreased as cycle numindicates a contrast of the estimates corresponding to the ith trial in the
ber increased within the session. The error averaged within eachcue period in the instructed condition (predictive switch). C exei indicatessession (horizontal lines) increased in the second training sesa contrast corresponding to the ith trial in the execution/feedback period
sion, in which subjects experienced the opposing rotation for thein the noninstructed condition (postdictive switch). Weights for the
first time, but decreased as the number of sessions increased. We
C cuei take the highest value (⫽5) from the first trial, and were constantexe
applied a two-way (cycle by session) repeated-measures ANOVA
across trials, but those for C i gradually increased from the lowest
to the medians of errors, and found significant effects of cycle(⫽⫺15 in the first trial) to the highest (⫽5 in the last trial) values as trial(F(14,182) ⫽ 2.71; p ⬍ 0.0001) and session (F(9,117) ⫽ 8.89; p ⬍number (i) increased. These weights were adjusted so that their sum was
0.0001). According to Tukey’s honestly significant difference
zero. The threshold was p ⬍ 0.05, corrected at voxel level and a clusterImamizu and Kawato • Predictive and Postdictive Switching of Internal Models

J. Neurosci., October 15, 2008 • 28(42):10751–10765 • 10757

Figure 4. A–H, Activation evoked by cue presentation (A–D) or execution/feedback of movements (E–H ) in between-subjects analysis. A, B, E, and F show event-related activity in the first trialof test period without subtraction of activity in the error-equalized baseline period ( p ⬍ 0.05, corrected for multiple comparisons at cluster level). C, D, G, and H show activity in the first trial yieldedby the contrast of the test period versus the error-equalized baseline period. The brain projections view the brain from above (transverse), right (sagittal), and behind (coronal). The red circles indicate
the occipital regions related to visual information. The blue circles indicate regions mainly related to motor control (for example, the dorsal premotor regions, the supplementary motor regions, andthe primary sensorimotor regions).

(HSD) post hoc test at p ⬍ 0.05, the size of error averaged acrosssessions and subjects was smaller in the last cycle (7.46°) than thefirst cycle (27.55°), suggesting that error decreased within a session. Furthermore, error averaged across cycles and subjects was
smaller in the last session than the second session, suggesting thatit decreased across sessions after the second session. These results
indicate short-term adaptation within each session as well as
long-term learning of the opposing rotations across sessions after
the second session. These results are consistent with our previous
behavioral experiment investigating adaptation to opposing rotations, in which subjects were instructed about the direction ofrotation when the rotation direction was changed (Imamizu etal., 2007b).
Figure 3B shows subjects’ performances in switching sessions
in the scanner. The ordinate represents angular error averaged
across sessions and subjects (⫾SD). The abscissa represents trial
number after a change in rotation direction. We computed, foreach subject, condition, and trial number after the change, average angular error in the test period across sessions and applied a
two-way (instructed or noninstructed condition by trial number
after the change) repeated-measures ANOVA to the average error. The effect of trial number was significant (F(5,65) ⫽ 88.73; p ⬍0.0001), and the size of error was smaller in the sixth trial than in
the first trial (Tukey’s HSD post hoc test, p ⬍ 0.05). An interaction
between condition and trial number was significant (F(5,65) ⫽2.66; p ⬍ 0.03), suggesting a different condition effect that depended on the trials. When we compared the averaged errors
between conditions for each trial, the error in the first trial was
smaller in the instructed condition (mean ⫾ SD, 36.89 ⫾ 11.43)
than in the noninstructed condition (46.27 ⫾ 12.64) (Tukey’s
HSD post hoc test, p ⬍ 0.05).
The error was almost constant in the error-equalized baseline
period (Fig. 3B, middle) and the error-zeroed baseline period(right). We compared the error in the last trial of the test period asa reference to the errors in every trial of both baseline periods
using Dunnett’s test at the p ⬍ 0.05 level, but could not find any
significant difference. This suggests that the error in the baseline
periods was maintained at the same level as the last trial of the test
period.
Regarding subjects’ performances in addition to error, we
computed reaction time, movement time, and marker path
length averaged across trials, sessions, and conditions for eachsubject and period. We applied one-way (period) repeatedmeasures ANOVA to the averaged values, and found no significant effect of period at p ⬍ 0.05 level (reaction time, F(2,39) ⫽0.032; movement time, F(2,39) ⫽ 0.27; and path length, F(2,39) ⫽0.27). This result indicates that the subjects maintained constantperformance throughout the test and the two baseline periods.
The mean values across periods and subjects were 243.07 ms (SD,Imamizu and Kawato • Predictive and Postdictive Switching of Internal Models

10758 • J. Neurosci., October 15, 2008 • 28(42):10751–10765

30.27) for reaction time, 244.17 ms (33.81)
for movement time, and 22.25 cm (2.29)
for out-and-back path length.
Activity related to cue presentation or
execution/feedback of movements
Figure 4 shows group mean activity
evoked by cue presentation (Fig. 4 A–D) or
execution/feedback of pointing movements (Fig. 4 E–H ). Figure 4, A, B, E, andF, shows the evoked activity in the first trialof test period without subtraction of activity in the error-equalized baseline period[see Materials and Methods, (1)]. Figure 4,
C, D, G, and H, shows activity in the firsttrial yielded by the contrast of the test period versus the error-equalized baseline
period ( p ⬍ 0.05, corrected for multiple
comparisons at cluster level). Activity
evoked by cue presentation was found bilaterally in prefrontal regions, dorsal premotor regions, parietal regions, occipitalregions, and the lateral cerebellum, and in
the left temporal regions (for detailed locations, see supplemental tables, availableat www.jneurosci.org as supplemental material). These regions were activated inboth the instructed and noninstructedconditions, but the activated regions werelarger in the instructed condition (Fig. 4 A)
than in the noninstructed condition (Fig.
4 B). In the comparison of the test period
versus the error-equalized baseline period(Fig. 4C,D), activation in the occipital regions related to visual information processing disappeared relative to the eventrelated activity without subtraction ofactivity in the error-equalized baseline period (red broken circles). Activity evokedby execution/feedback of pointing movements was found bilaterally in dorsal premotor regions, supplementary motor regions, intraparietal regions, and the lateral
cerebellum, as well as in the left primarysensorimotor regions. These regions wereactivated in both the instructed and noninstructed conditions (Fig. 4 E, F ). In thecomparison of test periods versus theerror-equalized baseline period (Fig.
4G,H ), activation in regions mainly related to motor control, namely the dorsal
premotor regions, the supplementary motor regions, and the primary sensorimotor
regions, disappeared (blue broken circles),and restricted regions in the intraparietal
regions and the lateral cerebellum remained. Almost identical activation patterns to those shown in Figure 4, C, D, G,
and H, were obtained when we used datain the error-zeroed baseline period insteadof the error-equalized baseline period.
In the baseline periods, subjects were
instructed to assume that the same direc-

Figure 5. Activity decreases as trial number increases after switching in between-subjects analysis ( p ⬍ 0.05, corrected for
multiple comparisons at voxel level; cluster size, ⬎30 voxels). A, Decreasing activity in cue periods in the instructed condition. The
broken green lines indicate the IPS. The left, middle, and right panels show the brain surface viewed from left, above, and right,
respectively. The circled numbers indicate the local maxima of activation corresponding to the data in Table 1. B, Decreasing
activity in the execution/feedback period in the noninstructed condition.
Table 1. Summary of activations
MNI coordinates
Anatomical regions

x

y

z

Cluster size

T value at peakDecreasing activity in the cue period in the instructed condition
SPL cluster(1) L superior parietal lobule
⫺32
⫺60
54
7.25
(2) R precuneus
12
⫺70
56
6.81
2335
(3) L precuneus
⫺8
⫺68
54
6.80
Decreasing activity in the execution/feedback period in the noninstructed condition
IPL(4) L inferior parietal lobule
⫺48
⫺52
50
918
7.08
(5) R inferior parietal lobule
46
⫺60
50
1182
6.79
Temporal region(6) R inferior temporal gyrus (BA 20)
68
⫺28
⫺22
88
6.46
Prefrontal regions(7) R middle frontal gyrus (BA 11)
36
54
⫺10
67
5.42
(8) L inferior frontal gyrus (BA 46)
⫺46
34
20
51
5.38
(9) L middle frontal gyrus (BA 10)
⫺42
50
⫺4
130
5.31
Activity that was high immediately after the switch in cue periods of the instructed condition and gradually increased in theexecution/feedback periods in the noninstructed condition(10) R LOTC
54
⫺56
⫺2
2354
7.91
(11) L LOTC
⫺52
⫺56
0
93
5.41
(12) R/L SMA/cingulate (BA 6)
⫺6
⫺4
48
1103
6.62
(13) L M1 (BA 4)
⫺32
⫺30
54
203
5.84
(14) L middle temporal gyrus (BA 21)
⫺56
⫺4
⫺14
155
5.62
(15) R dorsal premotor region (BA 6)
52
2
48
86
5.27
Error-equalized baseline ⬎ error-zeroed baseline(16) R angular gyrus (BA 40)
54
⫺50
32
8
10.10
Cluster size is represented by a number of 2 mm isotropic voxels. L, Left; R, right.

Imamizu and Kawato • Predictive and Postdictive Switching of Internal Models

J. Neurosci., October 15, 2008 • 28(42):10751–10765 • 10759

switching is most needed in the first trial
among the test periods and that the necessity for switching gradually decreased toward the sixth trial. Therefore, we looked
for brain activity that decreased from thefirst to the sixth trial.
Activity decreasing as a function of trial
number after a change inrotation direction
The activations shown in Figure 5 wereidentified to decrease in magnitude as thetrial number increased in the group level
analysis ( p ⬍ 0.05, corrected for multiple
comparisons; cluster size, ⬎30 voxels)
when contrast images in individual analyses were yielded by subtraction of activation in the error-equalized baseline periods from that in the test periods [seeMaterials and Methods, (2)]. Figure 5A
shows decreasing activity in cue periods
under the instructed condition, whereas
Figure 5B shows decreasing activity in theexecution/feedback periods under thenoninstructed condition. The locations of
the activations are listed in Table 1. The
decreasing activity in the cue periods of the
instructed condition constituted a large
cluster in the bilateral SPL containing
three activation peaks. The most anterior
peak (1 in Fig. 5A, Table 1) existed in the
medial wall of the left intraparietal sulcus(IPS). The other peaks existed in the precuneus of both hemispheres (2 and 3). In
contrast, the decreasing activity in the execution/feedback periods of the noninstructed condition constituted large clusters in the bilateral IPL (4 and 5 in Fig. 5B,
Table 1) and relatively small clusters in theinferior temporal gyrus (6; BA 20) andprefrontal regions (7–9; BAs 11, 46, andFigure 6. A, Spatial segregation of the two types of activity corresponding to Figure 5, A and B, around the IPS. Activations are 10). Regarding parietal activation, the desuperimposed on transverse (left) and coronal (right) slices from the subjects’ averaged structural images at levels indicated by the creasing activity in cue periods in the inwhite lines in the left panels of Figure 5, A and B. B, Poststimulus hemodynamic responses evoked by cue events in test trials after structed condition (Fig. 6 A, cyan region)
subtraction of responses in error-equalized baseline periods. The vertical axis represents values of parameter estimates (arbitrary existed medially to the IPS (dashed green
units) from an FIR model that includes regressors modeling the response with a bin width of 3.5 s from 0 to 21 s after cue onset (see line), whereas the decreasing activity in the
Materials and Methods). The response time courses were estimated for local maxima in the cyan regions of A and averaged acrossexecution/feedback periods of the noninthe maxima and subjects (⫾SE). C, Time courses for the sizes of the effects (arbitrary units) (see Materials and Methods) of cue or
structed condition (magenta regions) exexecution/feedback events on hemodynamic responses averaged across voxels and subjects (⫾SE) as a function of test trial
number after a change in rotation direction. The left panel shows the size of the effect of the cue events in the cyan region of A. The isted laterally to the IPS. Almost identical
middle panel shows the size of the effect of the execution/feedback events in magenta regions. The right panel shows the size of activation patterns with those shown in
the effect of the execution/feedback events averaged across PFC regions in Figure 5B. **p ⬍ 0.001, *p ⬍ 0.05, ⫹p ⬍ 0.10, Figures 5 and 6 A were obtained when weused data in the error-zeroed baseline peTukey’s post hoc test.
riod instead of the error-equalized baseline period.
tion of rotation as in the preceding test period would be imposed,
The overlapping volume between the cyan and magenta reand to conduct pointing movements so as to compensate for thegions in Figure 6 A was 2.1 cm 3, whereas the volume of eachrotation. Thus, in the comparison of test periods versus the errorregion was 18.7 cm 3 (cyan) or 16.8 cm 3 (magenta). Thus, theoverlap was only 6.3% of the union of the two regions. In indiequalized baseline, the activation related to the compensation
vidual volumetric analysis, we subtracted (1) activity evoked by
was subtracted, and the remaining activation was supposed tocue events in the error-equalized baseline periods from activity
reflect information processing for the switching of internal modevoked by cue events in the first test trial of the instructed condiels. As shown in Figure 3B, left panel, angular error after a changetion, and (2) activity evoked by execution/feedback events in thein rotation direction decreased as trial number increased, anderror-equalized baseline periods from activity evoked by execureached an asymptotic level in the sixth trial, suggesting that

10760 • J. Neurosci., October 15, 2008 • 28(42):10751–10765

tion/feedback events in the first test trial of the noninstructedcondition ( p ⬍ 0.001, uncorrected). Then, we investigated thevolumes of the two types of subtracted activity and the overlap
between them in the parietal regions (see Materials and Methods). The overlapping volume averaged across subjects was 0.3(SE, 0.1) cm 3, whereas the volume of the activity related to predictive or postdictive switches was 5.1 (SE, 1.8) or 8.6 (2.3) cm 3,
respectively. Thus, the overlap was only 2.2% of the union volume of the two types of activity in the individual analysis.
Figure 6 B shows the time course of activity in the cue period of
the test trials in the cyan regions of Figure 6 A. Using the FIRmodel (see Materials and Methods), we estimated BOLD response time courses evoked by cue events in the test trials and theerror-equalized baseline trials at local maxima in the cyan regions(Table 1, 1–3). We subtracted the average time course across thebaseline trials from the time course in each test trial, separately
for each maximum and subject. We plotted the subtracted timecourse averaged across the maxima and subjects (⫾SE) as a function of poststimulus time in Figure 6 B. Activation level gradually
decreased as trial number increased in the instructed condition(solid lines). The level also decreased in the noninstructed condition (broken lines) across trials, but the level was highest in thesecond trial.
To quantitatively capture the above change in activity levelacross trials, we investigated the size of the effect of the cue eventon hemodynamic responses in terms of the magnitude of the ␤estimate in each test trial after subtraction of the estimate averaged across the error-equalized baseline trials [see Materials andMethods, (2)]. Figure 6C, left panel, shows the effect sizes of cue
events averaged across voxels and subjects (⫾SE) in the cyan
regions of Figure 6 A. The solid and broken lines correspond to
the instructed and noninstructed conditions, respectively. We
applied a two-way (condition by trial number) repeatedmeasures ANOVA to the effect size averaged across the voxels foreach subject. An interaction between condition and trial number
was significant (F(5,65) ⫽ 13.92; p ⬍ 0.0001), indicating a different
condition effect that depended on the trials. Specifically, in thefirst trial, the effect size in the instructed condition was greaterthan that in the noninstructed condition (Tukey’s post hoc test,p ⬍ 0.05). However, the opposite was true in the second trial,
reversing again after the third trial.
Figure 6C, middle panel, indicates the time courses for thesizes of the effects of execution/feedback events across subjects
and voxels in the magenta regions in Figure 6 A. The effect sizes
decreased as trial numbers increased in both the instructed andthe noninstructed conditions. However, the interaction between
condition and trial number was significant (F(5,65) ⫽ 6.96; p ⬍0.0001), and the effect size in the noninstructed condition was
significantly greater than that in the instructed condition in thefirst trial (Tukey’s post hoc test, p ⬍ 0.001). Similar profiles wereobserved for the sizes of the effects of execution/feedback events
averaged across subjects and voxels in three prefrontal clusters(BAs 11, 10, and 46) (Fig. 6C, right panel). We investigated thetime courses for each prefrontal cluster, but could not find significant difference among the clusters.
Change in effective connectivity according to conditions
Figure 7A shows subject-specific maxima of activations in the left
SPL, the left IPL, the left PFC, and the right lateral cerebellum(CBL), from which BOLD signal time courses for the DCM analysis were extracted [see Materials and Methods, (3)]. Parameters
corresponding to the magnitude of intrinsic influences (that is,connections that are independent of the condition) among these

Imamizu and Kawato • Predictive and Postdictive Switching of Internal Models

Figure 7. Results of DCM analysis. A, Subject-specific maxima of activations from which
BOLD signal time courses for DCM analysis were extracted. The brain projections view the brain
from left (top) and above (bottom). B, Intrinsic connections. The average parameters corresponding to strength of influences from a region to another across subjects (SD) are presented.
The solid and dashed arrows indicate significant ( p ⬍ 0.05) and nonsignificant influences,respectively. C–F, Modulation effects in the instructed (C, E) and noninstructed (D, F ) conditions. Significant effects are presented in the cue (C, D) and execution/feedback periods (E, F ).
G, Influences that are modulated by the instructed condition significantly more than by thenoninstructed condition in the cue period. H, Influences that are modulated by the noninstructed condition significantly more than by the instructed condition in the execution/feedback period.

regions were derived from the DCM analysis. Figure 7B shows themeans of the parameters across subjects. The solid arrows indicate parameters that were significantly larger than zero ( p ⬍0.05) in the between-subject level analysis. Figure 7, C–F, showsparameters corresponding to the magnitude of the modulation
effect of the instructed (Fig. 7C,E) or noninstructed (Fig. 7 D, F )conditions on the intrinsic influences in the first trial of the test
period during the cue (Fig. 7C,D) or execution/feedback (Fig.
7 E, F ) periods. As shown in these figures, a significant modulation effect of the conditions on the intrinsic influences could be
identified at many connections. To identify an effect of contex-

Imamizu and Kawato • Predictive and Postdictive Switching of Internal Models

J. Neurosci., October 15, 2008 • 28(42):10751–10765 • 10761

number in the execution/feedback periodsin the noninstructed condition. Large activation clusters were found in bilateral
SMA/cingulate regions and the right lateral occipito-temporal cortices (LOTC).
Figure 8 B shows time courses for effectsize [see Materials and Methods, (2)] averaged across subjects and voxels in each region, separately for the cue and the execution/feedback events. Similar time courses
were observed in both regions. We could
confirm that the size of the effect of the cue
event was high in the first trial in the instructed condition (cyan solid line), andthat the size of the effect of the execution/
feedback event gradually increased in thenoninstructed condition (magenta brokenline). The size of the effect of the cue eventin the noninstructed condition (cyan broken line) increased later than that in the
instructed condition (cyan solid line). In
contrast, the size of the effect of the execution/feedback event in the instructed condition (magenta solid line) increased earlier, namely, in the first and the second
trials, than that in the noninstructed condition (magenta broken line). Similar timecourses were observed in the left primary
motor cortex (M1), the left middle temporal gyrus (MTG), and the right dorsal premotor regions (PMd) (Table 1).
The time courses shown in Figure 8 B
are almost mirror patterns of those in FigFigure 8. A, Regions in which activation was high immediately after a change of rotation direction in cue periods in the ure 6C about a horizontal axis for correinstructed condition and gradually increased as trial number increased in execution/feedback periods in the noninstructed con- sponding event and condition, suggesting
dition ( p ⬍ 0.05, corrected at voxel level; cluster size, ⬎30 voxels). The left and right panels show the brain surface viewed from negative correlations. We investigated thethe left and right, respectively. The middle panel shows activation superimposed on a midsagittal slice from the subjects’ averaged relationships between the SPL and either
structural images. B, Time courses of activity measured as the size of the effect of cue (cyan) or execution/feedback (magenta) the SMA or LOTC in terms of effect size
events on hemodynamic responses. Time courses were averaged across subjects and voxels in the SMA/cingulate (left panels) orafter the cue event (Fig. 8C, left two panLOTC (right panels) (⫾SE), and plotted as a function of test trial number. The solid and dashed lines correspond to the instructedels), and those between the IPL and either
and noninstructed conditions, respectively. C, Correlations between the sizes of the effects of cue or execution/feedback events inparietal regions and each of the regions in B. The left two panels show the correlation between the SPL and either the SMA/ the SMA or LOTC in terms of effect size
cingulate or LOTC regarding the cue event. The right two panels show the correlation between the IPL and either the SMA/ after the execution/feedback event (rightcingulate or LOTC regarding the execution/feedback event. Each panel contains 168 points (⫽6 test trials ⫻ 2 conditions ⫻ 14 two panels). Each panel plots effect sizes
subjects). The black lines were fitted to the points in each panel. ***p ⬍ 0.001, **p ⬍ 0.01, and *p ⬍ 0.05 indicate significance (total 168 points) in test trials (6) combinlevels in a one-sample t test with the null hypothesis that the slope of the line would not be lower than zero (Bonferroni’s ing data from the instructed and nonincorrection for multiple comparisons).
structed conditions (⫻2) and subjects(⫻14). The slopes (regression coefficients)
tual information on switching, we examined each connection toof lines fitted to the points were negative, as shown in the panels.
determine whether the parameter values in the instructed condiUsing a one-sample t test, we tested the null hypothesis that thetions were higher than those in the noninstructed condition durslope would not be lower than zero (a one-sided test). The hying the cue periods, and found a significant difference in influpothesis was rejected for every line (t(166) ⬎ 2.33; p ⬍ 0.05 after
Bonferroni’s correction for multiple comparisons), suggesting aence from the SPL to the CBL between conditions (Fig. 7G) ( p ⬍negative correlation between the above regions in terms of their0.05). Regarding an effect of sensorimotor feedback on switching,activity.
we examined whether the values in the noninstructed condition
were higher than those in the instructed condition, and found a
Activity related to visual feedback of performance error
significant difference in influence from the IPL to the SPL and
Figure 9 shows the regions activated more in the error-equalized
CBL between conditions (Fig. 7H ).
baseline period than in the error-zeroed baseline period. We
could not identify an activation cluster exceeding 30 voxels, but
Increasing activity as switching process proceeds
found a small cluster (eight voxels) showing strong activation
Figure 8 A shows the regions found by the analysis (4) (see Mate(peak t value, 10.10) (Table 1) in BA 40 of the angular gyrus. In
rials and Methods) to identify activation that was high immedithe above analyses, we found almost identical results when we
ately after a change in rotation direction in the cue periods in theused data from the error-zeroed baseline period instead of the
instructed condition, and that gradually increased with trial

10762 • J. Neurosci., October 15, 2008 • 28(42):10751–10765

Figure 9. Regions activated significantly more in the error-equalized baseline period thanthe error-zeroed baseline period in the group analysis ( p ⬍ 0.05, corrected at voxel level). AG,
Angular gyrus.

error-equalized baseline period. This is because the difference in
activation between the two baselines was significant, but was restricted to a very small region in the angular gyrus.

Discussion
Activity in the SPL (Fig. 6 A, cyan region) increased immediately
after a change in the direction of rotation and decreased as trial
number increased in the cue periods in the instructed condition.
In the first test trial, the activity in this region, measured as thesize of the effect of the cue event on the hemodynamic response inthis region, was higher in the instructed condition than in thenoninstructed condition (Fig. 6C, left panel), suggesting that thisregion is related to the predictive switch based on contextual
information. Many studies have indicated contribution of the
SPL to the planning of action based on visual information (Medendorp et al., 2005; Culham et al., 2006; Field et al., 2007).
Kimberg et al. (2000) reported that the SPL is related to switching
between different stimulus–response mappings based on contextual information. Our study suggests that the SPL associates contextual information with an appropriate set of relative contribution degrees of internal models for the current context.
It is known that SPL is activated by cues to shift spatial attention in a particular direction (Vandenberghe et al., 2001; Yantis etal., 2002). Our subjects could not know or predict a target position during the cue period as shown in Figure 2 A. Thus, the SPL
activity in the current experiment was unlikely directly related toa shift of attention. However, switching of behaviors often follows shifts of spatial attention; for example, switching between
preparations for forehand and backhand strokes is determinedaccording to spatial information about an approaching ball captured by attention systems. Therefore, shifts of spatial attention
and predictive switching of behaviors and internal models are
related to each other, and we speculate that they are based onneural mechanisms in the SPL regions. However, this may be
dependent on the type of attention, because Pollmann et al.
(2006) reported that the neural correlates of attentional shifts
from one stimulus dimension to another are dissociated fromthose of behavioral changes.
Angular error after a change in rotation direction gradually
decreased as trial number increased (Fig. 3B) even in the instructed condition, suggesting that the switching of internal
models were not completed in the first trial. Therefore, switching
was necessary in the subsequent trails, and both the switchingmechanisms based on contextual information and the mechanism based on prediction error were activated. Consequently, theImamizu and Kawato • Predictive and Postdictive Switching of Internal Models

SPL activity gradually decreased, even in the instructed condition, in proportion to the decrease in the angular error.
Activity in IPL and PFC regions (Figs. 5B; 6 A, magenta region) decreased as trial number increased in the execution/feedback periods in the noninstructed condition. In the first test trial,
the average effect size in these regions was higher in the noninstructed condition than in the instructed condition (Fig. 6C, middle and right panels), suggesting that this region is related to thepostdictive switch. Grefkes et al. (2002) reported a contributionof the IPL to integration between visual and somatosensory information. In the current task, the IPL is expected to integratevisual and proprioceptive feedbacks, to compare them with predictions made by internal models and to calculate prediction
error. We cannot directly measure the prediction error. However,
it is likely to be equal to the angular error between the target
direction and direction of the cursor movements because subjects
were asked to move the cursor toward a target, and, thus, theprediction of the feedback is the cursor movement toward thetarget. The activity measured as the size of the effect of execution/
feedback events in the IPL (Fig. 6C, middle panel) decreased inproportion to the decrease in the angular error in the test period(Fig. 3B, left panel), suggesting that the IPL is related to prediction error. Our previous study (Imamizu et al., 2004) investigatedactivity related to the switching of internal models in a tracking
task using a computer mouse, and found activation in the IPL and
the PFC (BA 46). This suggests that the switching mechanism
investigated in our previous study was mainly based on prediction error.
Diedrichsen et al. (2005) reported that activity related to errors under visuomotor rotation was spread over the precentral
gyrus, the postcentral gyrus, the IPL, and the SPL. Because theirtask allowed corrective movements near a target, on-line correction of movement might evoke large activities. Our results suggest that, among the error-related activities in their study, theactivity in the IPL is related to prediction error derived fromsensorimotor feedback that contributes to the switching of internal models.
In the comparison between the error-equalized and the errorzeroed baseline periods, we found a small but strong activation in
BA 40 (Fig. 9). Because switching of internal models was notneeded in the error-equalized periods, errors contributing toswitching activate large regions in the IPL, but errors that are
unimportant for switching activate a small region in BA 40.
Our connectivity analysis suggested that information flowchanges according to the type of switching. The effect of conditions on the functional influence of the SPL on the lateral cerebellum was higher in the instructed condition than in the noninstructed condition (Fig. 7G). In light of previous studies
suggesting that internal models are acquired in the cerebellum,
top– down information from the SPL to the cerebellum contributes to predictive switching between internal models. In contrast,
the effect of conditions on the influence of the IPL on the lateral
cerebellum and the SPL increased more in the noninstructedcondition than in the instructed condition (Fig. 7H ). Information flow from the IPL to the cerebellum contributes to postdictive switching based on prediction error. The increased influenceof the IPL on the SPL may reflect the flow of information about
the rotation direction that was revealed by the prediction error
and used as contextual information for the predictive switch inthe subsequent trial. The SPL activity (Fig. 6C, left panel, dashedline) increased more in the cue event of the second trial in thenoninstructed condition than in the first trial. The predictive
switching mechanism could not work because the contextual in-Imamizu and Kawato • Predictive and Postdictive Switching of Internal Models

J. Neurosci., October 15, 2008 • 28(42):10751–10765 • 10763

Decreasing activity in the execution/
feedback period in the noninstructed condition was found in BAs 10 and 11 (Fig.
5B). These regions are lateral parts of theorbitofrontal cortex that receives projections from midbrain dopamine neurons
and contribute to learning based on reward (for review, see Schultz, 2004). Successful switching with small performanceerror might be a type of reward for subjects
and that reward learning mechanisms
might be activated.
Figure 10 A illustrates the architectureof a mixture-of-experts model, which was
proposed as a computational model fortask switching. A single switching mechanism (a gating module) determines the degree of contribution of each internal
model to the total output (Jacobs et al.,
1991; Ghahramani and Wolpert, 1997).
However, our current study suggested two
separate mechanisms for predictive andpostdictive switching, consistent with a recently proposed MOSAIC model (WolpFigure 10. Computational models for the switching of internal models. A, Mixture-of-experts model having a single switching ert and Kawato, 1998; Haruno et al., 2001)
mechanism (a gating module). B, MOSAIC model having separate switching mechanisms for predictive switching based on (Fig. 10 B). The SPL is related to the precontextual information and postdictive switching based on the prediction error of sensorimotor feedback. F, Forward internal
dictive mechanism, whereas the IPL andmodels that predict sensorimotor feedback from an efference copy of a motor command. I, Inverse internal models that calculate
the PFC are related to the postdictive
motor commands from intended motion.
mechanism. Output signals from the predictive mechanism correspond to an information was not available in the first trial of the noninstructedcrease in the influence of the SPL on the cerebellum in the incondition, but a predictive switch is possible in the second trial if
structed condition (Fig. 7G), whereas output signals from thethe mechanism can use rotation direction information generated
postdictive mechanism correspond to an increase in the influenceby the IPL in the execution/feedback event of the first trial.
of the IPL on the cerebellum in the noninstructed condition (Fig.
The mechanisms related to the increased influence from the
7H ). As discussed above, the influence of the IPL on the SPL in
IPL on the SPL may be analogous to those underlying behavioral
the noninstructed condition reflects the flow of information
adjustment after conflict or error in cognitive control tasks such
about the direction of rotation (Fig. 10 B, dashed arrow) as reas the Stroop color-naming task. Kerns et al. (2004) found that anvealed by the postdictive mechanism. The output signals from theincrease in activity in the anterior cingulate cortex (ACC) in an
two mechanisms are combined and determine the degree of conerror trial leads to an increase in activity in the PFC (BAs 8 and 9)
tribution of the appropriate internal models to subject behaviors.
in the subsequent trial, and suggested that the ACC monitors the
The regions shown in Figure 8 A are related to the combined
conflict and that the PFC produces behavioral adjustments based
signals or the total output signal (Fig. 10 B, gray regions) (for timeon detection of the conflict. It can be postulated that the IPL iscourses of the signals, see supplemental figure, available at www.
involved in the monitoring of error, and the SPL contributes tojneurosci.org as supplemental material).
subsequent behavioral adjustment by predictive switching beRegarding the regions in Figure 8 A, the LOTC (Bonda et al.,tween internal models.
1996; Iacoboni et al., 2001; Schmid et al., 2001; Kawawaki et al.,The activity in the PFC, including BA 46, increased in the first2006) and the MTG (Rizzolatti et al., 1996) have been reported totrial of the execution/feedback period in the noninstructed concontribute to the prediction and observation of movements. Outdition (Fig. 6C, right panel). Connectivity between the PFC andput signals from forward internal models, which predict sensorithe parietal regions increased in the noninstructed condition
motor feedback from efference copy of motor command, play an(Fig. 7 D, F ) compared with the instructed condition (Fig. 7C,E),
important role in prediction and observation of movements ofalthough the difference did not reach a statistically significant
level. A possible reason for the PFC activity may be the execution
objects and other persons (Frith et al., 2000; Blakemore and Deof behavioral adjustment as suggested by the above study oncety, 2001). Thus, the LOTC and MTG likely receive output sigcognitive control. Another reason specific to the current task isnals from forward models. The other regions in Figure 8 A (SMA/
the reasoning of the rotation direction. Because subjects were
cingulate, M1, and PMd) are related to motor control, and likely
informed of the two types of rotation, subjects could reason thereceive output signals from inverse internal models, which calcucurrent rotation direction based on the result of the first test trial.
late appropriate motor commands from intended motion. If theGoel and Dolan (2004) reported that BA 9, which exists in theregions shown in Figure 8 A receive output signals from internal
dorsolateral PFC adjacent to BA 46, is involved in inductive reamodels, it is reasonable that activation of these regions increases
soning. The activation of the dorsolateral PFC may reflect thewith the number of trials after the change in rotation, and withinductive reasoning based on observation of results, and contribthe degree of contribution of appropriate internal models.
utes to the switching in the next trial.

10764 • J. Neurosci., October 15, 2008 • 28(42):10751–10765

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