Modular organization of internal models of tools in
the human cerebellum
Hiroshi Imamizu*†, Tomoe Kuroda‡, Satoru Miyauchi§, Toshinori Yoshioka*, and Mitsuo Kawato**Advanced Telecommunications Research Institute, Human Information Science Laboratories, 2-2-2 Hikaridai, Seika, Soraku, Kyoto 619-0288, Japan;‡Japan Science and Technology Corporation兾Exploratory Research for Advanced Technology Kawato Dynamic Brain Project, 2-2-2 Hikaridai, Seika,
Soraku, Kyoto 619-0288, Japan; and §Communications Research Laboratory, 588-2, Iwaoka, Nishi-ku, Kobe, Hyogo 651-2401, Japan
Edited by Leslie G. Ungerleider, National Institutes of Health, Bethesda, MD, and approved February 26, 2003 (received for review September 20, 2002)

S

tructural and functional modularity is an important key tounderstanding brain and mind mechanisms. Much is known
about the modular architecture in the primary cerebral cortex.
Somatotopic organization in the sensory-motor cortices is a wellknown modular feature (1). Regarding the cerebellum, Snider
and Eldred (2) recorded surface potentials evoked by peripheral
stimuli and presented somatotopic maps in cats and monkeys,
where one map lay in the anterior lobe and the other lay in theintermediate parts of the posterior lobe (Fig. 1). Recently, byusing functional MRI (fMRI), Grodd et al. (3) investigatedactivation patterns in the human cerebellum during motor tasks
and found two homunculoid representations similar to thosefound by Snider and Eldred (2). These somatotopic maps show
modularity on a relatively large scale. Functional modularity ona fine scale has also been studied in these regions. Regarding
parallel fiber inputs, somatotopic maps have been identified in
the cerebellar cortex, but the map is fractured, that is, each small
area of body surface is represented multiple times by spatiallyseparated clusters of cells (4, 5). Microzones, as long as several
centimeters along the longitudinal axis of the cerebellar folia andas wide as 0.2 mm, have been identified for climbing fiber inputs
as functional units (6).
The above cerebellar modularity has been demonstrated only
for motor and somatosensory functions. In the past decade, agrowing number of studies revealed that the cerebellum contributes to higher cognitive functions. One of the first examples
during a clearly cognitive task came from studies of language
processing and reported activation in the right lateral cerebellum(7, 8). Since then, other studies (for reviews, see refs. 9 and 10)
have also pointed to cerebellar involvement in cognitive tasks
such as working memory (11), problem solving (12, 13), andvisual attention (14). Many studies (11, 14, 15) demonstrated
that cognitive and motor (somatosensory) processing independently activate distinct cerebellar regions: the former activates
www.pnas.org兾cgi兾doi兾10.1073兾pnas.0835746100

Fig. 1. Flattened view of cerebellar surface illustrating that anterior lobe
and intermediate parts of posterior lobe are related to ‘‘motor and somatosensory functions,’’ whereas lateral posterior cerebellum is related to ‘‘cognitive functions.’’ (a) Arrows indicate difference between ‘‘motor’’ and ‘‘cognition’’ found in previous neuroimaging studies. (b) Arrows indicate
modularity within lateral posterior cerebellum for two different cognitive
functions. Illustrations were modified from refs. 39 and 40.

the lateral part of the posterior lobe, and the latter activates theanterior lobe and the intermediate parts of the posterior lobe,
where the homunculoid representations lie (Fig. 1a, arrows).
Although this dichotomy is not deterministic, convergent evidence in functional imaging studies suggests that the lateral partof the posterior lobe is closely related to the cognitive functions.
Regarding cognitive functions in the lateral cerebellum, studies performing metaanalysis of published data suggested that
there is anatomical distribution of activity related to different
tasks (10, 16). However, it has not been resolved whether eacharea might uniquely contribute to a distinct cognitive function.
Hence, modularity has yet to be experimentally demonstrated
for the ‘‘cognitive’’ cerebellum (Fig. 1b, arrows).
Recent computational models such as MOdular Selection
And Identification Controller (MOSAIC) (17–20) suggest thatmultiple internal models reside in the cerebellum. Internal
models are neural mechanisms that can mimic the input–output
properties of motor apparatuses or their inverses (21–23). This
motor control theory can be extended to a cognitive domain, i.e.,use of tools, by simply extending the object of internal model
learning from motor apparatuses (objects of motor control) to a
general object in the external world. In our previous study, we
found that an internal model for a novel tool is acquired in the
cerebellar cortex while human subjects learn to use the tool (24).
Here, we investigate modularity and multiplicity of internal
models in cerebellar cortex after subjects learn to switch between
two different novel tools.
Methods
Subjects. Seven neurologically normal subjects (21–32 years ofage; five females and two males) participated in the experiments.

This paper was submitted directly (Track II) to the PNAS office.
Abbreviation: fMRI, functional MRI.
†To whom correspondence should be addressed. E-mail: imamizu@atr.co.jp.

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Human capabilities in dexterously manipulating many different
tools suggest modular neural organization at functional levels, butanatomical modularity underlying the capabilities has yet to be
demonstrated. Although modularity in phylogenetically older
parts of the cerebellum is well known, comparable modularity inthe lateral cerebellum for cognitive functions remains unknown.
We investigated these issues by functional MRI (fMRI) based on ourprevious findings of a cerebellar internal model of a tool. After
subjects intensively learned to manipulate two novel tools (therotated mouse whose cursor appeared at a rotated position, andthe velocity mouse whose cursor velocity was proportional to themouse position), they could easily switch between the two. The
lateral and posterior cerebellar activities for the two different tools
were spatially segregated, and their overlaps were <10%, even at
low statistical thresholds. Activities of the rotated mouse weremore anterior and lateral than the velocity mouse activities. These
results were consistent with predictions by the MOdular Selection
And Identification Controller (MOSAIC) model that multiple internal models compete to partition sensory-motor experiences andtheir outputs are linearly combined for a particular context.

All subjects were right-handed except for one left-handed participant (25). Informed written consent was obtained from eachparticipant. The protocol was approved by the ethics committeesof Communications Research Laboratory and Advanced Telecommunications Research Institute.
Tasks. All subjects, including the one left-handed subject, ma-nipulated a computer mouse with the right hand to track arandomly moving target on a screen with a cursor (a trackingtask). By changing the transformation, i.e., from mouse movement to cursor movement, we generated two novel tools: therotated mouse and the velocity mouse. The relationship between
the cursor position and the mouse position was

冉冊 冉

xc
cos120°⫽⫺sin120°yc

sin120°cos120°

冊冉 冊
xm
ym

for the rotated mouse, where (xc, yc) denotes the cursor’s screen
coordinates (visual angle, °), and (xm, ym) denotes the mouse兾
hand coordinates (centimeters). In contrast, the cursor’s velocity(ẋ c, ẏ c) (°兾second) was determined by the mouse position for thevelocity mouse:

冉冊

冉 冊

ẋ c
xm
⫽ 8.76.
ẏ cym

Equalization of Tracking Error. In our previous study (24), two typesof activity related to the learning were observed in the cerebellum. One reflected the error signals guiding the learning acquisition of the internal models, and the other reflected an acquired
internal model. The former activity was very strong and distributed over the cerebellum and also blurred the latter activity.
Following a procedure used in the previous study, tracking error
during manipulation of one mouse was equalized to another byusing a linear relationship between a tracking error and a target
velocity. This procedure allowed us to distinguish internal model
activity for the novel tools from activity reflecting the error
signal.
Before the functional imaging, the subjects performed thetracking task by using each mouse (the normal, the rotated, orthe velocity mouse) at various target velocities for 15 min. A
linear relationship was derived by the least-squares method. In
the first scanning experiment, the target velocity was increasedin the baseline period by using this relationship, so that thebaseline error was equal to the mean error in the preceding test
period. In the supplementary experiment, the order of the tools
was 1. rotated 2. normal 3. velocity or 1. velocity 2. normal 3.
rotated, and the errors for the second and third tools werematched to the mean error for the first tool. The details of thismethod are described in ref. 24.
MRI Acquisition. MRI scanners (1.5 T) were used to obtain blood

A projector controlled by a personal computer displayed thetarget and the cursor. A small white square target was presented
on a dark background. The x and y components of the target path
were each sums of sinusoids whose amplitude and frequency
were randomly determined. The subjects moved a small crosshair cursor on the screen with the mouse.
The subjects were given detailed verbal instructions about thetransformation. The color of the cursor (red, violet, or green)
and text presented on the screen (‘‘rotate,’’ ‘‘velocity,’’ or‘‘normal’’) indicated the current tool.

oxygen level-dependent contrast functional images. Images
weighted with the apparent transverse relaxation time wereobtained with an echo-planar imaging sequence (repetition time,
5.4 s; echo time, 66 ms; flip angle, 90°; field of view, 256 ⫻ 256
mm; matrix size, 64 ⫻ 64). Twenty-two axial slices (thickness, 4mm) encompassing the cerebellum were selected. One hundred
twenty-eight or 192 functional images were scanned for eachslice during one session in the first or the supplementary
experiment, respectively. High-resolution anatomical images
were obtained for these slices with a T1 weighted sequence.

Training Sessions. Seven subjects performed 18 training sessions

Analysis of Behavior Data. The cursor and the target positions were

before fMRI scanning. The sessions were divided into 2 days (14sessions on Day 1). The tasks were performed outside of the
MRI scanner, but the subjects lay as in the scanner. In eachsession, the subjects performed the tracking task by using the twonovel mice and a normal mouse, six times each in blocks of 43.2 s.
The order of the mice (1. rotated 2. normal 3. velocity or 1.
velocity 2. normal 3. rotated) was counterbalanced between
sessions. The subjects had a rest period in every fourth block,which also lasted 43.2 s. Therefore, a training session lasted 17.28
min [ ⫽ 43.2 s ⫻ 6 repetitions ⫻ (three tools ⫹ rest)].

Scanning Sessions. All subjects underwent four fMRI scanningsessions after the training sessions. Each session comprised 16
alternating blocks (one block, 43.2 s) of test and baseline
periods and lasted 11 min and 31 s (⫽ 43.2 s ⫻ eight
repetitions ⫻ two tools). In two of the four sessions, thesubjects manipulated the rotated mouse during the test periods
and the normal mouse during the baseline periods (‘‘rotatedsession’’). In the other two sessions, the subjects manipulated
the velocity mouse during the test periods and the normalmouse during the baseline periods (‘‘velocity session’’). The
session order was counterbalanced between subjects. By increasing the target velocity during the baseline periods, theerrors during the baseline periods were matched to thoseduring the test periods according to the methods explained
below (see Equalization of Tracking Error). Five of the sevensubjects performed the supplementary scanning experiment inwhich they manipulated the three kinds of mice in a single
session. Each session was the same as the training session
except that the error was equalized (see below).
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sampled at 60 Hz. Mouse positions were reconstructed from thecursor positions afterward. Each subject’s performance wasmeasured by the tracking errors, i.e., the average distance
between the cursor and the target. The distance between the
cursor and the target at each sampling point was accumulated
over 5.4 s (position tracking error). The mouse velocity or thetarget velocity was also accumulated over 5.4 s, and this was used
as an explanatory variable in the regression analysis of the brain
activity.

MRI Analysis. Motion artifacts were removed by using AUTO-

MATED IMAGE REGISTRATION (http:兾兾bishopw.loni.ucla.edu兾
AIR3). We used SPM99 (www.fil.ion.ucl.ac.uk兾spm) for further
analysis. The functional images of each subject’s cerebellum weretransformed to the Montreal Neurological Institute’s (MNI;
Montreal, Canada) reference brain. The data were spatiallysmoothed with a Gaussian kernel with an 8-mm full width at half
maximum (FWHM). The voxel time series were temporallysmoothed with a Gaussian filter (FWHM of 4 s).

A Model for Simple Subtraction Analysis. For the comparison
between each novel mouse and the normal mouse, conditionspecific effects were estimated with a linear model:

S ik ⫽ ␣ i t ik ⫹ ␤ i u ik ⫹ ␥ i v ik ⫹ e i .
Here, Sik denotes the fMRI signal at the ith voxel in the kth scan.
t, u, and v were explanatory variables representing the type ofmouse used (t, rotation, u, velocity; and v, normal). Each was astep function assigned 1 if the scan corresponded to its mouse
Imamizu et al.

Fig. 2. (a) Tracking errors (across-subjects, mean ⫾ SD) when subjects manipulate rotated mouse (orange line), velocity mouse (blue line), and normal mouse(black line) in training sessions. (b) Time course of errors (across-subjects, mean ⫾ SD) in last five training sessions aligned on switching of tools. Broken line with
open circles indicates time course obtained from a control experiment, in which the cursor position was reset to center but the tool did not change and was always
the normal mouse. (c) Tracking errors (across-subjects, mean ⫹ SD) when cerebellar activity was scanned in the first experiment. Error during manipulation ofrotated mouse or velocity mouse was matched by changing target velocity during manipulation of normal mouse (baseline). Baseline error matched to rotatedmouse was significantly larger than corresponding test error [F(1, 6) ⫽ 15.52, P ⬍ 0.01]. There was no significant difference in errors between velocity mouseand corresponding baseline [F(1, 6) ⫽ 0.45]. (d) Tracking errors (across-subjects, mean ⫹ SD) in the first and the supplementary scanning experiments. There wasno significant difference between any pair of mean values according to Tukey’s honestly significant difference method (at P ⬍ 0.05 level).

A Model for Multiple Regression Analysis. We also conducted amultiple regression analysis including explanatory variables corresponding to various behavioral factors. The linear model was:

S ik ⫽ ␣ i t ik ⫹ ␤ i u ik ⫹ ␥ i v ik ⫹ ␦ i w ik ⫹ ␧ i x ik ⫹ ␨ i y ik ⫹ ␩ i z ik ⫹ e i .
As described above, the first three variables were step functionsof the mouse type. w represented switching of a mouse and was
assigned 1 in the scan immediately after the mouse type changed
and 0 otherwise. x, y, and z were the mouse velocity, tracking
error, and target velocity, respectively. They were recorded
during the scans and averaged over a scan interval (5.4 s). Mouse
velocity is related to mouse and兾or hand movements, and thetarget velocity is related to visual motion information andattention. Activations related to the rotation and the velocity
mice were specified by the statistical comparisons: ␣ ⬎ ␥ and ␤ ⬎␥. Activations related to the last four variables were specified byfinding regions where the estimated parameters (␦, ␧, ␨, and ␩)
were significantly larger than zero.
We used the effective degree of freedom adjusted for analysis
of fMRI (26). In assessing statistical significance, we made acorrection for multiple comparisons based on the theory of
random Gaussian fields. This correction was made for the entire
volume of the cerebellum.
Results
Behavioral Results During Training Sessions. For the rotated andvelocity mice, the tracking errors decreased significantly as thenumber of sessions increased (Fig. 2a, orange or blue line),suggesting that learning occurred. A repeated-measures
ANOVA on the errors indicated a significant effect of sessions
for the rotated mouse [F(17, 102) ⫽ 21.32, P ⬍ 0.0001] and forthe velocity mouse [(F(17, 102) ⫽ 14.90, P ⬍ 0.0001]. In contrast,
for the normal mouse, the errors were small and constant (blackline). There was no significant effect of sessions for the normalmouse [F(17, 102) ⫽ 0.53].
The tracking errors aligned on the switching of the tools (Fig. 2b),
averaged over the subjects and the last five sessions, were almost
constant after the switching, indicating that the subjects rapidly
Imamizu et al.

switched internal models appropriate for the different tools. Although a repeated-measures ANOVA on the errors indicated asignificant effect of the time after the switching for the rotatedmouse [F(7, 42) ⫽ 17.45, P ⬍ 0.0001] and the normal mouse [F(7,42) ⫽ 20.24, P ⬍ 0.0001], only the error during the first 5.4 s after
the switching was significantly larger than the other errors (at theP ⬍ 0.05 level by Tukey’s honestly significant difference method).
The transient error increase was most probably induced by reset ofthe cursor position to the center of the screen when a tool changed.
We conducted a control experiment where the cursor was reset tothe center but the tool did not change and found a very similar timecourse of the error (the broken line with open circles in Fig. 2b). The
behavioral data strongly suggest that internal models are acquired
as separate functional modules.
Comparison of Activation Patterns Between Each Novel Mouse and theNormal Mouse. The colored regions in Fig. 3a (subject 1) and Fig.

3b (subject 2) indicate regions significantly more activatedduring the test periods than the baseline periods [t (236) ⬎ 4.1,
fixed effect model, P ⬍ 0.05 corrected]. The orange and blue
regions indicate activity for the rotated mouse and the velocity
mouse, respectively. Fig. 3c shows the four local maxima with thehighest activity for each subject [t maps; t (236) ⬎ 3.1, P ⬍ 0.001
not corrected] derived from a comparison of the test periods withthe baseline periods for all subjects. Here, the colors indicate thetools (orange ⫽ rotated, blue ⫽ velocity), and the numbers
indicate subjects. The rotated mouse activations tend to belocated more anteriorly and laterally than the velocity mouse
activations. A multivariate ANOVA on the 3D positions of thelocal maxima (anterior–posterior, inferior–superior, and lateral–
medial) revealed this significant positional difference [F(2, 41) ⫽3.54, P ⬍ 0.05]. Significant increase in activity in the test periods
cannot be attributed to the tracking error, the mouse兾hand
movements, the visual target velocity, attention, or effort, because the magnitudes of these factors in the baseline periods
were larger than those in the test periods as described below.
Fig. 2c shows the tracking errors averaged across the subjects.
In the rotated session, the baseline error was significantly larger
than the test error [F(1, 6) ⫽ 15.52, P ⬍ 0.01], whereas in thevelocity session, there was no significant difference between thetest and the baseline errors [F(1, 6) ⫽ 0.45]. These results suggestthat the above activation revealed by the test minus the baseline
contrast does not reflect error signals.
To check whether the activation was evoked by behavioral factors
other than the error, we investigated the kinematics (velocity and
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type and 0 otherwise. e is a residual error. Session-specific effects
were also modeled as effects of no interest. Activations related
to the rotated mouse and the velocity mouse were specified bystatistical comparisons of the estimated parameters (␣ ⬎ ␥ forrotation and ␤ ⬎ ␥ for velocity) by using t statistics (StatisticalParametric Mapping{t}).

reported that they needed more effort and attention in the baseline
periods than in the test periods because of the increased target
velocity. Thus, the activation increase in the test periods cannot be
attributed to the mouse兾hand movements, the visual motion, theeye movements, attention, or effort. The most plausible explanationis that the activity increase in the test periods reflects the acquired
internal model for the novel tools.
Table 1 shows a summary of activation. The activated volume wasmeasured in each subject’s activity map and then averaged. The
overlapping region is only 2.1% of the total activated volume byusing a moderate threshold (P ⬍ 0.05 corrected) and 6.3% even ata considerably lower threshold (P ⬍ 0.001 uncorrected). The sizesof the orange (57.5%) and blue (40.4%) regions are comparable atthe moderate threshold. The different tools evoked activities indistinct locations with small overlap, demonstrating the modularityand multiplicity of internal models for tools.
We also measured activated volume (P ⬍ 0.05 corrected) inthe left and the right sides of the cerebellum for each subject. The
averaged volume was 5.76 cm3 in the left side and 3.79 cm3 in theright side for the rotated mouse, whereas it was 3.24 and 3.56 cm3for the velocity mouse. Activation was bilateral in general, but apreference for the left side was observed in the rotated-mouse
activity.

Fig. 3. (a and b) Cerebellar activity of two typical subjects in transverse
sections. Colored regions were significantly more activated in test periods
than in baseline periods (P ⬍ 0.05 corrected for multiple comparisons in the
cerebellum). Orange and blue regions were activated in rotated and velocity
sessions, respectively. Overlap between orange and blue was activated in bothsessions. Numbers in bottom left corners of images indicate superior–inferior(z) positions in Montreal Neurological Institute’s coordinates (see Methods).
(c) Distributions of four local maxima with highest activity (P ⬍ 0.001 notcorrected) for each subject. Orange and blue numbers indicate maxima inrotated sessions and velocity sessions, respectively. Positions of maxima andnormalized anatomical images are projected onto transverse, coronal andsagittal sections. Numbers correspond to different subjects.

acceleration) of the cursor and the mouse兾hand movements (seealso Supporting Text and Table 2, which are published as supporting
information on the PNAS web site, www.pnas.org). In any comparison between the test and baseline periods, the velocity andacceleration in the baseline periods were significantly larger thanthose in the test periods [F(1, 6) ⬎ 63.7, P ⬍ 0.0002; about 1.5-foldfor velocity and 2-fold for acceleration]. Because the force is
proportional to the acceleration, dynamic factors in the baseline
periods are also expected to be larger than those in the test periods.
The target velocity and acceleration are closely related to visualmotion and eye movements. They were large in the baseline periodsin comparison to those in the test periods [F(1, 6) ⬎ 22.4, P ⬍ 0.003],
suggesting that the magnitudes of the visual motion and eye
movements were larger in the baseline periods. All of the subjects

Results of Multiple Regression Analysis. As described above, theactivation increase in the test periods cannot be attributed tobehavioral factors (i.e., tracking error, mouse兾hand movements,
visual motion, eye movements, attention, or effort). However, wehave to justify our assumption that the difference in activation
patterns obtained from the simple subtraction analyses solely
reflects the regional differences in the internal models. This isbecause the error-equalization procedure inevitably increases
the magnitudes of the behavioral factors in the baseline periods,
and the level of this increase depends on the tracking error
during use of the novel mice. Use of the normal mouse at different
levels of these factors may change the baseline activation patterns
and may affect the results of the subtraction analysis.
Because it is impossible to simultaneously equalize every
aspect of a subject’s behavior, we decided to conduct an additional analysis by using a multiple regression technique toremove possible factors that may affect the cerebellar activity,
i.e., tool switching, hand兾mouse movements, tracking error,
visual motion, and eye movements (see Methods). Using a linear
model of brain activity including these factors and the type ofmouse as explanatory variables, we can estimate the unadulterated effect associated with the use of each mouse. Large
variability and a large data set are necessary for a reliablemultiple regression analysis. Thus, we conducted a supplementary experiment with a different design from the previous one(see Methods) and then combined the data from the previous andthe supplementary experiments.
There was no significant difference in the tracking error
among the mice, as shown in Fig. 2d (at P ⬍ 0.05 level by Tukey’s
honestly significant difference method), because the tracking
errors for the three kinds of mice were equalized by changing thetarget velocity.

Table 1. Percentage of activated volume to total activated volume (%) and absolute activated volume (cm3, inparentheses) averaged over all subjects
Region*Color codes in Figs. 3 and 4

R-(R 艚 V) orange

V-(R 艚 V) blue

R 艚 V overlap

ThresholdP ⬍ 0.001 corrected (t ⬎ 5.0)
P ⬍ 0.05 corrected (t ⬎ 4.1)
P ⬍ 0.001 uncorrected (t ⬎ 3.1)

75.7 (6.36)
57.5 (9.22)
45.4 (13.82)

24.1 (2.03)
40.4 (6.46)
48.3 (14.70)

0.2 (0.02)
2.1 (0.34)
6.3 (1.9)*R-(R 艚 V) or V-(R 艚 V) was activated only when subjects manipulated rotated mouse or velocity mouse, respectively. R 艚 V was activatedwhen subjects manipulated either rotated mouse or velocity mouse.
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Imamizu et al.

common cerebellar areas are allocated for each tool across all
subjects, although there exist large interindividual differences atexact locations (Fig. 3c).
Discussion

To specify the activation related to use of the novel tools, byusing t statistics, we compared the parameters estimated for theabove explanatory variables corresponding to mouse type. Theorange (or the blue) regions in Fig. 4 indicate voxels where theparameter for the rotated mouse (or the velocity mouse) was
significantly larger than the parameter for the normal mouse[t(7,113) ⬎ 5.23, fixed effect model, P ⬍ 0.001 corrected; see also
Movies 1–8, which are published as supporting information on
the PNAS web site]. The relative locations of the two tools
averaged across subjects (i.e., anterior and lateral for rotatedmouse) were very similar to those in Fig. 3 for individual subjects.
Activations related to the other explanatory variables were
specified by finding regions where the estimated parameters
were significantly larger than zero (the same threshold as above).
Activations correlated with tool switching were in bilateralsuperior parts of the cerebellum (anterior lobule). The peaks ofswitching activation in Montreal Neurological Institute’s space(x, y, z, respectively) and their t values were (⫺22, ⫺82, ⫺18; t ⫽15.16) in the left hemisphere and (28, ⫺74, ⫺18; t ⫽ 10.92) inthe right hemisphere. Activations correlated with the mouseaverage velocity, that is, directly correlated with movement
control, were in the anterior lobule (24, ⫺54, ⫺28; t ⫽ 13.52) andthe biventer lobule (24, ⫺60, ⫺56; t ⫽ 7.52) ipsilateral to thehand that was used. This is consistent with the previous study (3)indicating somatotopic organization for sensory-motor functions. Only weak activity related to the tracking error wasobserved in the lateral parts of the cerebellum at low thresholds(P ⬍ 0.05 not corrected; ⫺50, ⫺68, ⫺26; t ⫽ 1.66), because thetracking error was constant by experimental design (Fig. 2d).
Activity related to the average target velocity (visual motion
information and eye movements) did not reach significant levelsin the cerebellum even with a low threshold.
The error-equalization procedure increased magnitudes ofhand兾mouse movements and other behavioral factors in thebaseline periods and may have affected the activation patterns in
the previous analysis. However, the multiple regression analysisof the combined data from the previous and supplementary
experiments demonstrated similar activation patterns to theprevious analysis even when several possible factors were taken
into account. These results together demonstrate that somewhat
Imamizu et al.

Number of Microzones Contributing to Internal Models of the Novel
Tools. Each forward or inverse model may correspond to a

microzone from a neurophysiological viewpoint. Using two
different methods, we estimated the number of microzones that
constitute internal models of the novel mice. In the first simple
method, we estimated the activated microzones based on theratio of the activated volume to the cerebellar volume and thenumbers of microzones contained in the human cerebellum.
According to Table 1, the mean activated volume is 9.22 cm3 forthe rotated mouse only and 6.46 cm3 for the velocity mouse onlyat the medium threshold (P ⬍ 0.05 corrected). Human cerebellar
volume of healthy adults is about 130 cm3 (27), which contains
5,000–10,000 microzones (28). Thus, the estimated numbers are
355–709 (⫽ 5,000 or 10,000 ⫻ 9.22兾130) for the rotated mouseand 298–497 (⫽ 5,000 or 10,000 ⫻ 6.46兾130) for the velocity
mouse. This estimation gives the upper bounds, because we
assume that microzones are densely packed into fMRI voxels
and neglects any blurring effects by the spatial smoothing filter
used in the analysis.
The other, more reasonable, method is based on the anatomical
size of the microzone and considers how a microzone’s activity was
blurred by our imaging resolution and the smoothing filter. The sizeof the microzone along the cerebellar folia ranges between 5 and 12
mm in humans (3), with a width of 0.2 mm (6) and a cortical
thickness of 1 mm (29). Accounting for our imaging resolution(4-mm isotropic voxels), one microzone activates three voxels(length ⫻ width ⫻ thickness: 3 ⫻ 1 ⫻ 1 voxels). Because we spatiallysmoothed the image with a Gaussian filter having an 8-mm full
width at half maximum, the activity could spread maximally over
the adjacent 14 voxels. As mentioned above, the mean activatedvolume was 9.22 cm3 for the rotated mouse and 6.46 cm3 for the
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Fig. 4. Regions related to manipulation of the novel tools as revealed bymultiple regression analysis. Regions are shown in superior–posterior–lateralview (Center), lateral view from right side (Left), superior view (Bottom), andposterior (Right) view. Orange and blue colors indicate regions where activation was more highly and positively correlated with manipulation of rotatedor velocity mouse, respectively, than manipulation of normal mouse. Statistical thresholds are P ⬍ 0.001 corrected.

Integration of Multiple Internal Models. The MOSAIC theory (17)proposes that multiple pairs of controllers (inverse internal
models) and predictors (forward internal models) are tightly
coupled as functional units. They contribute to the selection of
appropriate modules for the current behavioral situation. The
key feature is a ‘‘responsibility signal’’ calculated for each
module. The forward model generates a prediction of theoutcome of the motor commands being issued. The prediction is
confirmed by the sensory consequences. The smaller the prediction error, the more likely that the pair of forward and inverse
models must have been appropriate for the current situation, andhence the higher the module’s responsibility. The responsibility
signals determine the degree of each module’s contribution to
the total output from the cerebellum. Because each responsibility signal is an analog value, the linear combination of multiple
modules’ outputs is possible. By modulating and combining theoutput, an enormous repertoire of behaviors can be generated
even if the number of modules is limited (20). Many situations
that we encounter may be derived from a combination ofpreviously experienced situations, that is, the same modules may
be activated in different situations.
Our results were consistent with the theory in two points. First,
activation related to a specific novel tool was observed in multiple
regions (Figs. 3 and 4), which suggests that multiple modules are
combined to cope with the tool. Second, small but significant
common regions were activated by different tools (Table 1). Thissuggests that the internal models acquired in these regions represent
common properties with the novel mice. It is not likely that they
were related to the hand movements or the normal mouse because
they were found by subtraction of the activation for the normalmouse from the activation for the novel mouse.

velocity mouse at the medium threshold. The volumes of 3 and 17
voxels are 0.192 cm3 and 1.088 cm3. We estimated the number ofmicrozones by dividing the activated volume by the volume corresponding to one microzone, i.e., 9 (⫽ 9.22兾1.088) ⫺ 48 (⫽ 9.22兾
0.192) for the rotated mouse, and 6 (⫽ 6.46兾1.088) ⫺ 34 (⫽6.46兾0.192) for the velocity mouse.
This estimation assumes that microzones related to a similarfunction are sparsely distributed. If these microzones are densely
packed in each voxel, the estimated number of microzones
increases. However, it is unlikely that neighboring microzones
behave similarly, which is against the definition of a microzone(i.e., different climbing fiber inputs and hence different functions). Although there is a large variability in the estimatednumbers, a small portion of all microzones (about 10% at
maximum) is related to each novel mouse.
Multiple Internal Models for Cognitive Functions. For the following

reasons, we believe that internal models acquired in the current
experiment are for cognitive functions rather than basic sensorymotor transformations. First, the acquired internal models inthese experiments are expected to represent the relationshipbetween the cursor movement and the ‘‘mouse’’ movement
rather than the ‘‘hand’’ movement. This is because our previous
behavioral study (30) found that the learning effects in this task
are not specific to the hand, that is, the effects acquired during
practice by using one hand can be easily carried over to performance by using the other hand. Second, the bilateral activity may
indicate that activated regions acquire internal models forcognitive functions independent of the ipsilateral correspondence between the motor apparatus and the cerebellum (e.g.,
refs. 11, 13–15, 31). Regarding the rotated-mouse activation, apreference for the left side, i.e., contralateral to the performing
hand, was observed and agrees with activity related to cognitive
spatial operations (e.g., maze learning, ref. 15).
Anatomical and physiological studies in monkeys demonstrated connectivity between the lateral cerebellum and thefrontal and parietal cortices (32–34). Our previous study (35)
investigated the entire brain activity when human subjects
learned to use the rotated mouse. We revealed that functional
connectivity between the loci of the lateral cerebellum examinedin this study and the ventral premotor cortex (especially the right
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