Central Representation of Dynamics When
Manipulating Handheld Objects

Theodore E. Milner, David W. Franklin, Hiroshi Imamizu and Mitsuo Kawato
J Neurophysiol 95:893-901, 2006. First published Oct 26, 2005; doi:10.1152/jn.00198.2005
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J Neurophysiol 95: 893–901, 2006.
First published October 26, 2005; doi:10.1152/jn.00198.2005.

Central Representation of Dynamics When Manipulating Handheld Objects
Theodore E. Milner,1,2 David W. Franklin,1,2 Hiroshi Imamizu,1 and Mitsuo Kawato1
1

Computational Neuroscience Laboratories, ATR, Kyoto, Japan; and 2School of Kinesiology, Simon Fraser University, Burnaby, Canada

Submitted 24 February 2005; accepted in final form 21 October 2005

The stability of dynamic interactions between humans andcommon implements that we employ as tools and instruments
can vary widely. Our ability to use implements effectively
requires that we be able to adapt to differences in dynamics.
With experience we can quickly change patterns of muscle
activation to adjust to differences in mass, moment of inertia,
rigidity, or other mechanical properties. This ability is thought
to depend on a central representation (internal model) of the
dynamics of the interaction between the human subject and themanipulated object (Kawato 1999), which we will henceforthrefer to as manipulation dynamics. In the context of this study,
an internal dynamics model comprises neural mechanisms that
represent the transformation from neural command to movement of a handheld object or the inverse transformation.
The cerebellum and primary motor cortex appear to be theregions of the brain most directly implicated in the formationand implementation of internal dynamics models. In particular,
the ipsilateral cerebellum shows changes in regional cerebral
blood flow during adaptation to novel manipulation dynamics

that appear to be related to changes in motor error (Nezafat etal. 2001). Furthermore, individuals with cerebellar atrophy areless able to adapt to novel manipulation dynamics than control
subjects (Maschke et al. 2004), and individuals with cerebellar
lesions do not update motor commands based on past error(Smith and Shadmehr 2005) unlike control subjects. Other
evidence from fMRI studies suggests that the cerebellum is
involved in forming and implementing representations of noveltransformations between hand and cursor motion (Imamizu etal. 2000, 2003). Evidence for involvement of primary motor
cortex is based primarily on single unit recordings from nonhuman primates. Studies of changes in manipulation dynamics
with non-human primates have reported shifts in the preferred
directions of neurons in primary motor area (M1) (Li et al.
2001) and to a lesser extent in supplementary motor area
(SMA) (Padoa-Schioppa et al. 2004) that develop during adaptation and are retained after washout. However, there aremajor outputs from the cerebellum to M1 and minor outputs to
SMA (Sakai et al. 2002), so it is possible that underlying
changes in cerebellar activity may be responsible for theobserved changes in M1 and SMA.
In fact, there are reciprocal or recurrent pathways between
the cerebellum and primary motor cortex (Holdefer et al. 2000;
Middleton and Strick 2000) that appear to be functionallyorganized such that the regions in each structure that represent
the same anatomical region are connected. The pathway fromthe cortex to the cerebellum is believed to provide the cerebellum with a copy of the motor command being sent to themuscles through the mossy fiber input (efference copy). The
climbing fiber input to the cerebellum is thought to provide a
training signal related to error, which leads to adaptive changes
in the output of the cerebellum. There are several models for
how this takes place. One that has received much attention isfeedback error learning, which asserts that the climbing fibers
provide a feedback error representing error in the motor command that is used to form an internal dynamics model by an
iterative corrective process (Kawato 1990). However, thisconcept has recently been questioned on the grounds thatclimbing fibers are primarily activated by sensory inputs, so analternative model of cerebellar adaptation has been proposed
based on recurrent cerebellar connectivity (Porrill et al. 2004).
To test the hypothesis that cerebellar activity more closely
represents implementation of an internal model than does
activity in primary motor cortex, we designed an fMRI experiment in which subjects balanced similar objects that differedmarkedly in their dynamic behavior. We varied the complexityof the manipulation dynamics by altering the mechanical stability and the flexibility of the objects to vary the extent toAddress for reprint requests and other correspondence: T. E. Milner, Schoolof Kinesiology, Simon Fraser University, Burnaby, B.C. V5A 1S6, Canada(E-mail: tmilner@sfu.ca).

The costs of publication of this article were defrayed in part by the paymentof page charges. The article must therefore be hereby marked “advertisement”
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

INTRODUCTION

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Milner, Theodore E., David W. Franklin, Hiroshi Imamizu, andMitsuo Kawato. Central representation of dynamics when manipulating handheld objects. J Neurophysiol 95: 893–901, 2006. First
published October 26, 2005; doi:10.1152/jn.00198.2005. To explore
the neural mechanisms related to representation of the manipulation
dynamics of objects, we performed whole-brain fMRI while subjects
balanced an object in stable and highly unstable states and while theybalanced a rigid object and a flexible object in the same unstable state,in all cases without vision. In this way, we varied the extent to which
an internal model of the manipulation dynamics was required in the
moment-to-moment control of the object’s orientation. We hypothesized that activity in primary motor cortex would reflect the amount ofmuscle activation under each condition. In contrast, we hypothesizedthat cerebellar activity would be more strongly related to the stability
and complexity of the manipulation dynamics because the cerebellum
has been implicated in internal model-based control. As hypothesized,
the dynamics-related activation of the cerebellum was quite different
from that of the primary motor cortex. Changes in cerebellar activity
were much greater than would have been predicted from differencesin muscle activation when the stability and complexity of the manipulation dynamics were contrasted. On the other hand, the activity ofthe primary motor cortex more closely resembled the mean motor
output necessary to execute the task. We also discovered a small
region near the anterior edge of the ipsilateral (right) inferior parietal
lobule where activity was modulated with the complexity of themanipulation dynamics. We suggest that this is related to imagining
the location and motion of an object with complex manipulation
dynamics.

894

T. E. MILNER, D. W. FRANKLIN, H. IMAMIZU, AND M. KAWATO

which an internal model of the manipulation dynamics was
required in the moment-to-moment control of the object’s
orientation. We compared manipulation of the same object in astable state and a highly unstable state as well as comparing
manipulation of a rigid object and a flexible object in the same
unstable state. From earlier studies, we expected that activity inboth primary motor cortex and cerebellum, relative to restingbaseline, would increase in proportion to muscle activation(Dai et al. 2001; Dettmers et al. 1996; Ehrsson et al. 2001;
Kuhtz-Buschbeck et al. 2001; Thickbroom et al. 1998). However, we predicted that for similar levels of muscle activation
we would find little or no difference in primary motor cortex
activity but marked differences in activation of the cerebellum
because of its involvement in internal model-based control. We
conducted whole-brain fMRI to test this prediction. Although
we were not able to match the level of muscle activation acrossconditions, we did find dramatic differences in cerebellar
activation that appeared to be more closely linked to manipulation dynamics than muscle activation.

Subjects and general procedure
Nineteen neurologically normal subjects participated in the fMRI
experiment. Nine of these subjects and three additional subjects
participated in a second psychophysical experiment. Five of thesesubjects and six additional subjects participated in a third experimentto estimate grip force. All subjects gave informed consent to theprocedures that were approved by the institutional ethics board andconformed to the Declaration of Helsinki. Subjects performed an
object manipulation task while lying in the supine position. All
subjects performed the task with the right hand. The conditions
consisted of holding a flexible object in a stable equilibrium position(stable), balancing a rigid object at an unstable equilibrium position(unstable 䡠 r), balancing the flexible object at an unstable equilibrium
position (unstable 䡠 f) and relaxing (rest). The condition changed every
30 s.

ProtocolIn the fMRI experiment, there was a 6-s interval between conditions
during which the experimenter prepared the subject for the next
condition. The subject went through the conditions five times in one
order and then five times in the reverse order. The condition order wasvaried randomly among subjects. The experimenter stood at the
subject’s side throughout the recording session and placed the object
in the subject’s hand prior to the start of each 30-s scan. At the end of
the scan, the current object was removed from the subject’s hand andreoriented or replaced according to the condition order.
Because of the position of the subject’s head in the gantry of thescanner, the subject could not see the objects. Therefore the task was
performed using only somatosensory feedback. When holding an
object, subjects rested their forearm on a soft support surface, although the wrist remained unsupported. The flexible object consistedof a thin plastic ruler with two 130-g weights centered 25 cm from thecenter of the grip position (Fig. 1). The rigid object was a rectangularpiece of wood of the same length and width as the plastic ruler, but
considerably thicker, with identical weights positioned at the same
distance from the center of the grip position. Thin wooden blocks
were attached to either side of the plastic ruler with double-sided tape
to serve as grip surfaces. The blocks allowed texture, friction, andthickness of the grip surfaces to be matched across conditions. Wheneither object was gripped below the weight, it was in a mechanicallyunstable state. When the ruler was inverted with the weight below thehand, it was in a mechanically stable state. Subjects held the object ina pinch grip between the thumb and two or three fingers. They were
instructed to maintain the weight directly above the hand under theunstable conditions, i.e., not to allow it to deviate from vertical. Theirtask under the stable condition was to hold the flexible ruler with agrip force that they perceived as matching their grip force under theunstable condition. We wish to emphasize that although the difficulty
varied greatly between controlling the orientation under the stableversus the unstable conditions, extensive training was not required toperform the task successfully. All subjects were given sufficient
practice with each condition prior to the experiment to master thecontrol of each object. Furthermore, the majority of the subjects had
previously participated in an experiment, which involved controllingthe orientation of the flexible object under identical conditions.

Psychophysical experiment
For eight subjects, the motion of the object being held was tracked
using an OPTOTRAK system (Northern Digital) while they performed the task in the MRI scanner. Infrared light emitting diodes(IREDs) were mounted at the center of each grip surface and at thecenter of the weight on each object. We discovered later that activation of the IREDs introduced noise into the MRI signal. Consequently,
we had these subjects repeat the experiment a second time without
motion tracking, although the original OPTOTRAK recordings were
included in the analysis described in the following text.
In the psychophysical experiment, 12 subjects performed four
repetitions of the four conditions outside of the scanner. The condition
order was randomized and also performed in the reverse order as in
the scanner. Subjects reclined on a mat, adopting the same body
posture as during the brain imaging. Their right arm was similarly
supported, and subjects again received no vision of their hand or theobject while performing the task. As well as tracking the motion of theobject with the OPTOTRAK system at 300 Hz, EMG was recordedwith surface electrodes placed over the flexor pollicis brevis, firstdorsal interosseus, biceps brachii, flexor carpi radialis, pronator teres,
extensor carpi ulnaris, and extensor carpi radialis longus muscles of
the right hand. Because flexor pollicis brevis is relatively small, theelectrode overlying the muscle may have also picked up activity fromthe adductor pollicis muscle. The EMG was recorded using a Delsys
Bagnoli 16 system, which amplified and band-pass filtered the signals
between 20 Hz (high-pass) and 450 Hz (low-pass). EMG signals werethen sampled at 2 kHz and stored for later analysis. Torque about thecenter of the grip position was computed from the position of thecenter of the weight relative to the center of the grip position. The
absolute value of the torque was integrated over time and its meanvalue and variance were computed for comparison across conditions
using repeated-measures ANOVA. Because the center of the weight
was at a fixed distance from the center of the grip position for the two

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METHODS

FIG. 1. Objects are shown in the orientation in which subjects were instructed to hold them. The grip position on each object is indicated. The objects
under the stable and unstable 䡠 f conditions differed only in orientation.

CENTRAL REPRESENTATION OF DYNAMICS

unstable objects, mean torque is equivalent to average inclination of
the object relative to vertical, whereas torque variance is equivalent toposition variance of the center of the weight. The root mean square(rms) EMG for each muscle was also computed for comparison acrossconditions. After subtracting the rms EMG of the relaxed state (restcondition), statistical comparisons were made using repeated-measures ANOVA. Significant effects were then examined using Scheffe’s post hoc test to look at differences across conditions.

Grip force experimentregions in which the local maxima were located. Further analysis was
restricted to these ROIs to increase sensitivity. Three ROIs wereidentified, namely the ipsilateral cerebellar hemisphere, contralateral
M1 (Brodmann area 4) and a region in the ipsilateral inferior parietal
lobule that included the postcentral gyrus, inferior parietal gyri andsuperior parietal gyrus. The random effects analysis was then repeatedwith the correction for multiple comparisons restricted to the smaller
volume of the ROIs (Worsely et al. 1996). Figure 2 shows thethree-dimensional projections of these ROIs onto the sagittal, coronaland transverse planes.
Because the degree of difficulty in performing the task varied considerably between the stable and unstable conditions, we wanted to ensurethat the amount of head movement did not vary with the stability of theobject. We estimated the amount of head movement from post hoc

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A miniature load cell (LM-2KA-P, Kyowa) sandwiched between
two thin wooden surfaces was used to measure the maximum grip
force of 11 subjects. The load cell apparatus was then attached inplace of one of the grip surfaces on each object, and the subject
performed the same manipulation task as in the fMRI experiment,
under the three stability conditions. Grip force was first recorded forthree maximal efforts. The subject then performed the manipulation
task under each condition for 30 s and the mean grip force over thelast 20 s was computed. Each condition was repeated twice. The mean
grip force for each condition was expressed as a percentage of thesubject’s maximum grip force.

895

Brain imaging
The 1.5 T MRI scanner (Shimadzu-Marconi) in the ATR Brain
Activity Imaging Center was used to obtain blood-oxygenation-leveldependent (BOLD) contrast functional images. High-resolution anatomical (structural) images were obtained with a T1-weighted sequence for each subject. Functional images weighted with the apparent transverse relaxation time (T2*) were obtained with an echoplanar imaging sequence (repetition time ⫽ 5.4 s, echo time ⫽ 65 ms,
flip angle ⫽ 90°). 92 sequential whole brain volumes (64 ⫻ 64 ⫻ 50
voxels at 3 mm isotropic resolution) were acquired in each session.
We used SPM 99 software (http://www.fil.ion.ucl.ac.uk/spm/) toanalyze the images. The first two image volumes were discarded toallow for T1 equilibration. The remaining 90 image volumes wererealigned to the first volume and normalized to the Montreal Neurological Institute (MNI; Montreal, Canada) reference brain. The data
were spatially smoothed with a Gaussian kernel with 6-mm full widthat half-maximum (FWHM). The voxel time series were temporallysmoothed with a Gaussian filter (FWHM of 4 s). Anatomical regions
were identified from normalized T1 structural images averaged
across subjects, using the Automated Anatomical Labeling method ofTzourio-Mazoyer et al. (2002), and functional anatomy was determined from the Brodmann map as implemented in the FWU pick atlas(Maldjian et al. 2003, 2004).

Statistical analysis
Statistical parametric maps of t-statistics were calculated for condition specific effects (stable, unstable 䡠 r, unstable 䡠 f, and rest) withina general linear model. We computed the statistical images corresponding to the contrasts: (unstable 䡠 f-stable), (unstable 䡠 r-stable),(unstable 䡠 f-unstable 䡠 r) and each manipulation task minus the restingbaseline (level 1). The contrast images obtained from level 1 wereentered into a second level t-test to create an SPM {t} map and wereanalyzed using a random effects model to accommodate intersubject
variability in group analysis (Penny and Holmes 2003; Schmitz et al.
2005). A one-sample t-test was used (18 df). Voxels were identified at
P ⬍ 0.05 after correction for multiple comparisons. The condition
specific effects were first tested for significance for every voxel fromthe brain. Linear contrasts between conditions were used to create
activation maps. From these activation maps we determined thelocations of local maxima of activity for which t(18) ⬎ 7.64 (P ⬍ 0.05
when corrected for multiple comparisons for the whole brain volume).
Region of interest (ROI) masks were created for the anatomical

FIG. 2. Planar projections of the 3 region of interest (ROI) masks The redarrows indicate the location of the origin of the Montreal Neurological Institute(MNI) coordinate system.

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896
TABLE 1.

T. E. MILNER, D. W. FRANKLIN, H. IMAMIZU, AND M. KAWATO

Manipulation tasks versus baseline
MNI Coordinates
Anatomical Region

Stable versus baseline
Left primary motor cortex (M1)
Unstable-r versus baseline
Left primary motor cortex (M1)
Right cerebellum (lobule V/VI lateral)
Right cerebellum (lobule V/VI medial)
Unstable-f versus baseline
Left primary motor cortex (M1)
Right cerebellum (lobule V/VI lateral)
Right cerebellum (lobule V/VI medial)
Right cerebellum (lobule VIIIB/IX)

x

y

z

Peak zScore

ClusterSize†*P Value†

⫺48

⫺14

56

4.42

4‡

0.013

⫺36
22
4

⫺18
⫺50
⫺66

50
⫺26
⫺14

5.02
5.35
4.65

194‡
89
6

0.001
0.001
0.018

⫺38
16
4
14

⫺18
⫺52
⫺68
⫺64

52
⫺22
⫺16
⫺50

5.68
5.59
4.87
4.64

350
244
13
7

⬍0.001⬍0.0010.007
0.019*Number of 8 mm3 voxels in cluster, †Corrected P values using a small volume correction, ‡Cluster was not contiguous.

RESULTS

Brain activation: all manipulation conditions minus rest
We identified three ROIs from the whole brain analysis (Fig.
2). These were the only regions in which a significance level ofP ⬍ 0.05 (corrected for multiple comparisons) was reached inany of the contrasts. Using the ROI masks, we then located the
local maxima of voxel clusters. The anatomical locations ofthese maxima are listed in Table 1. The contrasts with respect
to the resting baseline revealed several important features of
the task-related brain activation. First, there was a relatively
large region near the border of the anterior and superior
posterior lobes of the ipsilateral cerebellum, lateral to themidline, and a much smaller region closer to the midline where
activity was statistically significant under both unstable conditions. In contrast, there was no statistically significant activity
anywhere in the cerebellum under the stable condition. Second,
there was a small focus of activation in the ipsilateral biventer
lobule under the unstable 䡠 f condition. Third, the total activatedvolume of the contralateral M1 was almost two orders ofmagnitude greater under either unstable condition than under
the stable condition. Finally, activity in the ipsilateral inferiorparietal lobule was not statistically significant for any of theconditions relative to the resting baseline.
Table 2 compares the number of activated voxels in contralateral M1 and ipsilateral cerebellum for P ⬍ 0.001 (uncorrected). These results are included for comparison with thestudies of Thickbroom et al. (1998) and Dai et al. (2001) toassess whether changes in activation of M1 and cerebellum
with the stability condition might simply be related to changes
in grip force or muscle activation.
Brain activation: stability contrasts
The principal objective of this study was to compare activation in M1 and cerebellum for (unstable 䡠f-stable), (unstable 䡠

r-stable), and (unstable䡠f-unstable 䡠r) contrasts. For completeness, we also examined the reverse contrasts, but these showedno statistically significant activity anywhere in the brain. For
the unstable 䡠f-stable contrast, we found that a small region in
the contralateral M1 and a much larger region near the borderof the anterior and superior posterior lobes of the ipsilateral
cerebellum were activated as well as a small region near theanterior edge of the ipsilateral inferior parietal lobule (Fig. 3).
The regions in M1 and cerebellum were located in areas
previously shown to be activated during finger, hand, andelbow movements (Grodd et al. 2001; Kawashima et al. 1995).
Of particular interest, is that the region in the cerebellum had
two foci, separated by ⬃12 mm (Fig. 3). When we contrasted
unstable 䡠r-stable, we found that the only activated region wasin M1 and that it comprised a small fraction (⬃8%) of theactivated region identified in the unstable䡠f-stable contrast. On
the other hand, for the unstable 䡠f– unstable 䡠r contrast there wasno significant activation in M1, but a significant portion of thecerebellar region identified in the unstable 䡠f–stable contrast
was activated (⬃30%). However, there was only one focus ofactivation in the cerebellum that was ⬃4.5 mm from the morelateral focus of activation in the unstable䡠f-stable contrast.
There was again a focus of activation in the ipsilateral inferiorparietal lobule which was shifted ⬃14 mm inferior to that of
the unstable 䡠f-stable contrast. The anatomical locations of all
maxima are listed in Table 3.
Psychophysical results
To confirm that learning did not play a part in the observed
differences in BOLD signals, we compared the mean torque
TABLE 2. Comparison of number of activated voxels in M1
and cerebellum
Anatomical Region
Stable versus baseline
Left primary motor cortex (M1)
Right cerebellum
Unstable-r versus baseline
Left primary motor cortex (M1)
Right cerebellum
Unstable-f versus baseline
Left primary motor cortex (M1)
Right cerebellum

Number of Voxels

P Value*

162
24

0.001
0.001

696
652

0.001
0.001

851
1057

0.001
0.001

*Not corrected for multiple comparisons as in Thickbroom et al. (1998).

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realignment of MR images and compared the maximum absolute difference in head position and orientation for rest, stable, unstable䡠r, andunstable䡠f conditions. The absolute difference in each coordinate wasaveraged across repetitions of the epoch for each subject. The averaged
differences (19 subjects ⫻ 4 condition ⫻ 6 coordinates) were analyzed bya two-way (condition ⫻ coordinate) ANOVA. There was no significant
effect of the condition [F(3,432) ⫽ 1.55, P ⬎ 0.201]. Furthermore, themean of the maximum head displacement over the 30-s intervals did notexceed 0.1 mm in any direction.

CENTRAL REPRESENTATION OF DYNAMICS

897

and torque variance between the first and last two 30-s blocks
in the case of the unstable conditions for the eight subjects forwhom we had OPTOTRAK data in the MRI scanner. Note thatthese measures are equivalent to the average inclination and theposition variance of the object, respectively. We found no
TABLE 3.

significant difference in either the absolute torque (P ⫽ 0.41
for unstable䡠r, P ⫽ 0.31 for unstable䡠f) or the torque variance(P ⫽ 0.34 for unstable䡠r, P ⫽ 0.66 for unstable䡠f). Thus
subjects’ performance, as represented by their ability to maintain the object in a vertical position or by the amount that the

Task specific activations
MNI Coordinates
Anatomical Region

Unstable-r versus stable
Left primary motor cortex (M1)
Unstable-f versus stable
Left primary motor cortex (M1)
Right cerebellum (lobule V/VI lateral)
Right inferior parietal lobule
Unstable-f versus unstable-r
Right cerebellum (lobule V/VI lateral)
Right inferior parietal lobule

x

y

z

Peak zScore

ClusterSize*

P Value†

⫺36

⫺18

46

4.08

1

0.038

⫺42
26
16
44

⫺18
⫺50
⫺54
⫺36

54
⫺26
⫺20
52

4.21
4.82
4.74
5.95

12
80
19

0.024
0.009
0.013
⬍0.001

30
40

⫺50
⫺30

⫺28
38

5.46
4.21

25
1

⬍0.001
0.048*Number of 8 mm3 voxels in cluster, †corrected P values using a small volume correction.
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FIG. 3. ROI masks (blue and green regions) and foci of activity for the unstable 䡠 f-stable contrast (top), the unstable 䡠 r-stable contrast (middle), and theunstable 䡠 f-unstable 䡠 r contrast (bottom). Asterisks (ⴱ) indicate that there was no significant activation in the corresponding region. Anatomical images werenormalized and averaged across subjects. Transverse slices corresponding to locations of local maxima are shown for M1 and inferior parietal lobule; coronalslices are shown for cerebellum. Coordinates of local maxima shown below each slice correspond to those listed in Table 3.

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T. E. MILNER, D. W. FRANKLIN, H. IMAMIZU, AND M. KAWATO

and it was significantly higher under both unstable conditions
than under the stable condition (P ⬍ 0.05). The rms EMG offirst dorsal interosseus was significantly higher under the unstable conditions than the stable condition (P ⬍ 0.05). This
would suggest that the grip force was lowest in the stablecondition, higher in the unstable 䡠 r condition, and highest in
the unstable 䡠f condition. However, the grip force experimentsuggested that there was relatively little difference among
stability conditions. The mean values across subjects ranged
from ⬃10% of maximum grip force for the stable andunstable 䡠r condition to 12% for the unstable䡠f condition, although these differences were not statistically significant (P ⬎0.28).
The variation in muscle activation with the stability of themanipulation dynamics introduced a potential confounding
factor that we will consider now. Three previous studies were
specifically designed to examine how the fMRI signal varies
with hand force and muscle activation. The first of these(Dettmers et al. 1996) focused on a single slice through M1 andposterior supplementary area and found that signal intensity
increased in a logarithmic fashion for index finger forces
between ⬃5 and 40% of maximum force. The second study(Thickbroom et al. 1998) examined the entire contralateral
primary sensorimotor cortex and found that there was a relatively greater increase in voxel number than mean signal per
voxel for finger flexion forces between 5 and 50% of maximum. The third study (Dai et al. 2001) examined multiple
motor-related areas of the brain in a power grip task, but overa different force range (20 – 80% of maximum). The ROIs
included those relevant to our study, namely contralateral M1
and cerebellum, although the entire cerebellum was treated as
one region of interest. They showed that both the averageintensity and the number of activated pixels increased in a
linear or less than linear fashion with grip force and withrectified averaged surface EMG of the long finger flexor andextensor muscles. All of these studies suggest that the numberof activated voxels should increase monotonically but not morethan linearly with grip force or EMG if the activation of aregion simply reflects the amount of muscle activation needed
to perform the task.

FIG. 4. A: mean torque and torque variance under stable (S), unstable 䡠 r (R), andunstable 䡠 f (F) conditions with SEs (n ⫽ 16).
B: mean root mean square (rms) EMG withstandard errors (n ⫽ 12) for flexor pollicis
brevis (FPB), 1st dorsal interosseus (1DI),
biceps brachii (BB), flexor carpi radialis(FCR), pronator teres (PT), extensor carpi
ulnaris (ECU), and extensor carpi radialis
longus (ECRL) muscles. *, statistically significant differences (P ⬍ 0.05).

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object moved, did not change significantly over the course of
the experiment, providing evidence that learning did not occur.
There was no significant difference in the mean absolute
torque between the two unstable conditions (Fig. 4A). However, the mean absolute torque was lower under the stablecondition (P ⬍ 0.05). Note that because subjects did not
maintain the object in an orientation that was exactly vertical or
perfectly stationary, the mean absolute torque was not zero,even under the stable condition. The torque variance washigher under the unstable䡠 f condition than under the stable orunstable䡠r conditions, suggesting that flexibility made the object more difficult to control. This was also confirmed fromanalysis of the object movement for the eight subjects noted in
the preceding text. We computed an average magnitude for the
angular velocity of the object from the variation in the orientation of the object, which was 0.058 ⫾ 0.017 (SD) rad/s under
the unstable䡠f condition compared with 0.023 ⫾ 0.012 rad/s
under the unstable䡠r condition and 0.022 ⫾ 0.018 rad/s under
the stable condition. The angular velocity was quite small
under all conditions, i.e., movement of the hand was generally
not noticeable. However, although there was no difference inthe movement of the object under the unstable䡠 r and stableconditions (P ⫽ 0.89), there was significantly more movement
under the unstable䡠f condition than either the unstable䡠r (P ⬍0.0001) or stable condition (P ⫽ 0.0012).
There was no difference in the rms EMG of the more
proximally acting muscles (prontator teres and biceps brachii)
between conditions. However, there were significant differences for wrist and finger muscles (Fig. 4B). In the case of thewrist, the rms EMG of the wrist flexor (flexor carpi radialis)and extensor muscles (extensor carpi radialis longus and extensor carpi ulnaris) under the unstable䡠 f condition was significantly higher than under the stable condition (P ⬍ 0.05),
indicating that wrist stiffness was increased by muscle cocontraction. Wrist stiffness was likely also higher under theunstable䡠f condition than under the unstable 䡠r condition since
the rms EMG of the wrist extensor muscles was significantly
higher (P ⬍ 0.05). In the case of the finger muscles, the rms
EMG of flexor pollicis brevis was significantly higher under
the unstable䡠 f condition than under the unstable 䡠 r condition

CENTRAL REPRESENTATION OF DYNAMICS

Because grip force did not vary by ⬎20% across stability
conditions based on our estimates, changes in grip force could
not account for changes in activation of any of the activatedbrain structures. Activity of hand and wrist muscles, however,increased by as much as 200 –300% between the stable andunstable䡠f conditions (Fig. 4). A 300% increase in muscle
activation could account for at least half the increase inactivated voxels in M1 between the stable and unstable 䡠fconditions assuming a linear relation between EMG and voxel
number (Table 2). On the other hand, it would not account for⬎7% of the increase in activated voxels in the cerebellum.
There was a much smaller increase in the number of activatedvoxels in both M1 and cerebellum between unstable䡠r andunstable䡠f conditions, similar to the difference in muscle activation between the two conditions.

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cortex that were activated in relation to different aspects ofmanipulation with precision grip. The study by Kuhtz-Buschbeck et al. (2001) was the most similar to our study in that
subjects continuously maintained the same grip force for ⬃40s, although grip initiation, lifting of the object, setting theobject down, and releasing the grip were also part of the task.
When subjects used a firm grip, the contralateral primarysensorimotor areas, premotor areas (PMd and PMv) and Brodmann area 7 were activated along with Brodmann area 40
bilaterally. The cerebellum, however, was outside the field ofview. The principal difference with our study is that we did not
find significant activation of contralateral premotor areas orcontralateral areas 7 and 40. The main reason for this may bethat their task would have involved decision and planningphases for initiating and releasing the grip, which were absent
in our task.

DISCUSSION

Condition-dependent differences in muscle activation
The experiment was designed to match muscle activity
under the unstable and stable conditions by instructing subjects
to exert excessive grip force in the stable condition. However,the EMG records clearly indicate that despite this explicit
instruction, muscle activation was modulated with the stabilityof the manipulation dynamics. Torque was required to movethe weight to the upright position whenever it deviated or tomaintain the weight at a deviated position when the subject
failed to perceive that it had drifted from upright. The object
was moved principally by “rolling” action of the thumb andfingers. Consequently the activity of thumb and finger muscles
served both to grip and apply torque to the object. To keep thewrist stationary, the activity of wrist muscles had to be modulated to balance torque arising from thumb and finger muscles
crossing the wrist and to increase joint stiffness for stability.
The variation in the rms EMG of finger and wrist muscles withthe stability of the manipulation dynamics can be explained by
the differences in the mean absolute torque and the torquevariance, which created demands for muscle activation in
addition to those required for grip force. Thus mean grip force
may have been the same across stability conditions, but muscle
activation increased as stability decreased and control became
more complex.
Previous fMRI studies of manipulation
Ehrsson et al. (2001, 2003) and Kuhtz-Buschbeck et al.
(2001) identified a number of regions in frontal and parietal

Activity in cerebellum and primary motor cortex
Based on the analysis of number of activated voxels in Table
2, it appears that activity in the cerebellum represents thestability of the manipulation dynamics, although it does notprovide a clear indication that complexity of the manipulation
dynamics (unstable䡠f vs. unstable䡠r) is independently represented. The stability contrasts (Table 3), on the other hand,suggest that both stability and complexity of the dynamics are
represented in the cerebellum as opposed to M1. The differences in activation of contralateral M1 seen in the stability
contrasts were similar to the differences in mean absolute
torque but not to the differences in torque variance under thethree stability conditions. The case was reversed for the ipsilateral cerebellum. We found no significant difference in themean absolute torque between the two unstable conditions,whereas it was significantly less under the stable condition thanunder either of the unstable conditions. Correspondingly, we
found no significant activation of contralateral M1 for theunstable 䡠f– unstable 䡠r contrast and significant activation forboth the unstable 䡠f–stable and unstable 䡠r–stable contrasts. This
would suggest that changes in activation of M1 with themanipulation dynamics primarily reflect changes in mean levels of muscle activation.
In the case of the torque variance, we found no significant
difference under the stable and unstable䡠r conditions but amarked increase under the unstable 䡠f condition relative to theother two conditions. This corresponds with the finding that
there was no significant activation of the ipsilateral cerebellum
for the unstable 䡠r-stable contrast and significant activation forboth the unstable 䡠f–stable and unstable 䡠f– unstable 䡠r contrasts.
The torque variance reflects changes in torque over timerequired to correct for deviation of the object from a verticalorientation. Therefore it can be thought of as a measure of the
moment-to-moment changes in muscle activation needed tocontrol the orientation of the object. The cerebellum has been
implicated in both feedback and feedforward control of movement. In the one case, it regulates feedback gains (MacKay andMurphy 1979) and in the other it represents the system dynamics (Nezafat et al. 2001). That there was no activation of thecerebellum under the stable condition compared with the resting baseline could be interpreted as indicating that in the stablestate the object is balanced with little feedback regulation andwithout the need for representation of the manipulation dynam-

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As we hypothesized, when the brain activity under the stablecondition was subtracted from that under the unstable conditions, it became evident that the dynamics-related activation of
the cerebellum was quite different from that of the primary
motor cortex. In the discussion that follows, we propose that
cerebellar activity was indicative of moment-to-moment predictive control derived from an internal dynamics model,
whereas the activity of the primary motor cortex more closely
resembled the mean motor output necessary to execute thetask. Somewhat unexpectedly, we found an ipsilateral region
near the anterior edge of the inferior parietal lobule where
activity was also modulated with the stability of the manipulation dynamics. This region appears to be important in complex hand manipulation.

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T. E. MILNER, D. W. FRANKLIN, H. IMAMIZU, AND M. KAWATO

Cerebellum and internal models
Imamizu et al. (2000) found a region of the cerebellum thatwas selectively activated when subjects were required to makea visuomotor transformation to track a moving target. The
region was bilateral and extended toward the lateral boundariesof the cerebellum. They later showed that different regions
were activated when the visuomotor transformations weredifferent, although there was some overlap (Imamizu et al.
2003). They interpreted their results in terms of separate
internal representations or models for different transformations. Kawato et al. (2003) argued that the contralateral cerebellum was the site of such an internal model for the coordination of grip force with load force during object transport,
although they did identify another candidate region in theipsilateral cerebellum close to the activated regions under theunstable 䡠r and unstable䡠f conditions of our study. It is possiblethat a portion of the activated region under the unstable䡠r
condition represents implementation of an internal model ofthe manipulation dynamics of a rigid inverted pendulum andthat the expansion of this region or the appearance of a second
focus of activation under the unstable䡠 f condition represents
the added complexity of manipulating an inverted pendulumwith a flexible shaft.
Inferior parietal lobule
The activated region that we identified near the anterior edgeof the ipsilateral inferior parietal lobule showed statisticallysignificant activation under the unstable 䡠 f condition relative tothe two other conditions but not relative to the resting baseline.
Because it was not activated under the unstable 䡠r condition
relative to the stable condition, its activity would appear to berelated principally to the complexity of the manipulation rather
than to its stability. Bilateral activation of this general region of
the brain has been linked to three-dimensional object featuresthat are related to aspects of visually guided grasping, such as

hand shape, aperture, or orientation (Binkofski et al. 1999).
However, this region has also been shown to be activatedbilaterally during exploration of complex shapes in the absenceof vision (Jäncke et al. 2001). In these previous studies, thisregion was referred to as the anterior intraparietal area (AIP),
although it is not clear yet whether it is analogous to AIP in themonkey. The most surprising finding in our study was that it
was activated only on the ipsilateral (right) side, although thiswould be consistent with the spatial function of the righthemisphere because our task was purely spatial. The need to
involve parietal cortex was likely related to imagining theposition and motion of the flexible ruler while controlling it
without vision. Because the exploration task of Jäncke et al.
(2001) also had a verbal component, i.e., subjects manipulated
shapes that could be named (hammer, bag, cup, umbrella, car)and the purpose of the manipulation was to identify the shapes,
subjects in their study also activated the left hemisphere.
In summary, our results indicate that the cerebellum isdifferentially activated for manipulation of an object that ismechanically unstable compared with one that is mechanicallystable. In addition, cerebellar activation appears to discriminate
features of the manipulation dynamics that are not represented
in M1. We, therefore propose that the cerebellar activity
represents the implementation of an internal dynamics modelof the object manipulation that is necessary for feedback
control. We also found differential activation of a region near
the anterior edge of the inferior parietal lobule of the righthemisphere in relation to the complexity of the manipulation
dynamics. This is likely related to having to imagine thelocation and motion of an object with complex manipulation
dynamics when controlling it without vision.
ACKNOWLEDGMENTS

We thank G. Liaw for assisting in the second experiment.
GRANTSThis work was supported by National Institute of Information and Communications Technology and National Sciences and Engineering ResearchCouncil.
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