C. Prablanc, D. Pélisson and Y. Rossetti (Eds.)
Progress in Brain Research, Vol. 142© 2003 Elsevier Science B.V. All rights reserved

CHAPTER 11

Internal forward models in the cerebellum: fMRI study on
grip force and load force coupling
Mitsuo Kawato 1,∗ , Tomoe Kuroda 2 , Hiroshi Imamizu 1 , Eri Nakano 1 ,Satoru Miyauchi 3 and Toshinori Yoshioka 1

1

ATR Human Information Science Laboratories, 2-2-2, Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-0288, Japan
JST/ERATO Kawato Dynamic Brain Project, 2-2-2, Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-0288, Japan
3
Communications Research Laboratory, 588-2, Iwaoka, Iwaoka-cho, Nishi-ku, Kobe, Hyogo 651-2492, Japan

2

Abstract: Internal models are neural mechanisms that can mimic the input–output or output–input properties of the motor
apparatus and external objects. Forward internal models predict sensory consequences from efference copies of motor
commands. There is growing acceptance of the idea that forward models are important in sensorimotor integration as
well as in higher cognitive function, but their anatomical loci and neural mechanisms are still largely unknown. Someof the most convincing evidence that the central nervous system (CNS) makes use of forward models in sensory motor
control comes from studies on grip force–load force coupling. We first present a brief review of recent computational andbehavioral studies that provide decisive evidence for the utilization of forward models in grip force–load force couplingtasks. Then, we used functional magnetic resonance imaging (fMRI) to measure the brain activity related to this couplingand demonstrate that the cerebellum is the most likely site for forward models to be stored.

Introduction
Internal models are neural mechanisms located inside the brain that can mimic the input–output properties of the motor apparatus and external objects(located outside the brain), or their inverse transformations. Forward internal models predict sensory
consequences of executed movements from information on efference copies of motor commands,
whereas inverse internal models determine the appropriate motor commands from information on the∗ Correspondence

to: Mitsuo Kawato, ATR Human Information Science Laboratories, 2-2-2, Hikaridai, Seikacho, Soraku-gun, Kyoto 619-0288, Japan. Tel.: +81-77495-1058; Fax: +81-774-95-2647;
E-mail: kawato@atr.co.jp

desired motor consequences. Several computational
theories have proposed that forward and/or inverse
models are learned in the cerebellum (Kawato et al.,
1987; Kawato and Gomi, 1992; Miall et al., 1993;
Wolpert et al., 1998; Kawato, 1999).
We have accumulated quite convincing data fromboth electrophysiological studies (Shidara et al.,
1993; Gomi et al., 1998; Kitazawa et al., 1998;
Kobayashi et al., 1998; Takemura et al., 2001; Yamamoto et al., 2002) and human imaging studies(Imamizu et al., 2000) demonstrating that inverse
models are acquired through motor learning basedon Purkinje cell synaptic plasticity and stored in
the cerebellum. Even though many behavioral (Miall et al., 1993; Wolpert et al., 1995; Flanagan andWing, 1997; Scarchilli and Vercher, 1999; Mehta
and Schaal, 2002) and theoretical studies (Kawato
et al., 1987; Jordan and Rumelhert, 1992; Miall et

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al., 1993; Wolpert and Kawato, 1998; Kawato, 1999)
have suggested that forward models are functionallyand computationally critical for a broad repertoireof behaviors ranging from sensorimotor integration
to higher cognitive function, the anatomical lociand neural mechanisms of forward models are stilllargely unknown. In addition to their use in sensory–
motor control, Blakemore et al. (1998, 1999, 2001))
demonstrated that forward models are used for cancellation of sensory inputs generated by one’s own
movements; in this series of elegant perceptual studies, they suggested that the forward models are located in the cerebellum (see also Vercher et al., 2003,
this volume).
Some of the most convincing evidence showing that the CNS makes use of forward models in
sensory–motor control comes from studies on grip
force–load force coupling. Grip force–load force
coupling is a common phenomenon that has been
observed in the following situation. When an object
is held in a precision grip (e.g. a grasp between
the tips of the thumb and forefinger) and moved byvoluntary movements (e.g. arm movements), the grip
force perpendicular to the contact surfaces changes
in phase with, and in a similar temporal waveform to,
the load force induced by the movements (Johansson
and Westling, 1984; Flanagan and Tresilian, 1994;
Johansson, 1996). The coupling between the twoforces prevents the object from slipping while using
the minimal grip force. This grip force modulation
is anticipatory in the sense that changes in the grip
force occur at the same time as, or even prior to,changes in the load force.
Previously we proposed computational models
that explain grip force–load force coupling with forward models (Kawato, 1999), and their predictions
have been confirmed by recent behavioral studies(Flanagan and Wing, 1996; Vetter et al., 2002). Here,
we summarize these previous computational and behavioral studies that demonstrate the utilization of
forward models in grip force–load force coupling.
Then, we present a functional magnetic resonanceimaging (fMRI) experiment that investigates the possible brain loci of the forward models used for the
coupling and suggest that the cerebellum is the likeliest site.

Computational models and behavioral
experiments that support the use of forward
models in grip force–load force coupling
We first briefly explain a simple example of grip
force–load force coupling to facilitate clear understanding of the phenomenon. In preparation for thefMRI experiment, we measured grip force and load
force outside the MRI scanner to confirm that thetwo forces were coupled in the current task paradigm(Fig. 1). A subject lay down in a supine position andmade cyclic up-and-down arm movements paced bybeep sounds (2 Hz) while holding a ping-pong ballbetween the tips of the thumb and forefinger. At each
beep, the subject made a set of up and down strokes
above the abdomen. The LED marker of a position
recording system (OPTOTRAK, Northern Digital,
Inc., Canada) was mounted on top of the object.
The marker’s vertical position was sampled at 500
Hz. We obtained the object’s acceleration due to arm
movement by twice differentiating the time seriesof the position data. Load force was then calculated
as the absolute value of the product of the object’s
acceleration and mass (0.015 kg), where acceleration
was the sum of the acceleration due to movement
and gravitational acceleration. Grip force was measured by small and light pressure gauges (PS-10KA,
Kyowa Electronic Instruments Co., Japan) attachedto the contact surfaces. The amplitude of the arm
movements was 30–40 cm. Because grip force iscoupled with the absolute value of load force, it
had two peaks coinciding with the acceleration anddeceleration peaks of the arm movement within one
cycle. Thus with a 2 Hz movement, the primary
frequency of the grip force (solid line in Fig. 1B)and load force modulation was 4 Hz (dotted line in
Fig. 1B). As has been reported in numerous studies(Johansson and Westling, 1984; Flanagan and Tresilian, 1994; Johansson, 1996), the grip force wastemporally coupled with the load force during movement, and a cross-correlation analysis indicated thatthe phase of the grip force preceded that of the load
force by approximately 15 ms with a correlation coefficient of 0.88. These values are in close agreementwith previously reported values for cyclic movement(Flanagan and Wing, 1995).
Previous studies on grip force–load force coupling have suggested that both feedback (Johansson

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Fig. 1. (A) Experimental setup of grip force–load force coupling in our fMRI study. A subject lay down in a supine position and madecyclic up-and-down arm movements above the abdomen while holding a ping-pong ball between the tips of the thumb and forefinger. (B)A subject’s sample record of the temporal pattern of grip force (solid line), load force (dotted line) and vertical position (broken line) of
the grasped object. Grip force and load force coupling were observed while transporting a ping-pong ball.

and Westling, 1984) and feedforward (Flanagan andTresilian, 1994) components are necessary for controlling grip force. Feedback control is important forestablishing a stable grip force/load force ratio andfor responding to unexpected disturbances, while
feedforward control is important for rapid, predictive
and accurate coupling of grip force to load force
during movement. The fact that the change in grip
force precedes the change in load force suggests thatpure sensory feedback, which has large (70 ms) timedelays, cannot be the sole source of grip force modulation. Therefore the CNS predicts changes in load
force to modulate grip force.
There may be a number of computational andneural models that can explain the observed grip
force–load force coupling. However, because of theabove mentioned predictive nature of grip force modulation, we can assume that either forward or inverse
models, or a combination of the two, are utilized
in grip–load coupling. Accordingly, there are threemodels that can potentially explain the observed
grip force–load force coupling (Fig. 2). The firstmodel (Fig. 2A) consists of a single inverse dynamics model (IDM) of the combined arm, handand object dynamics. The combined IDM generates

the arm motor command as well as the hand motor
command. For generation of hand motor commands,
this model is not computationally attractive since theentire IDM must be relearned every time a different hand grasping posture is taken and a different
object is manipulated. In other words, this modelhas the least structural and functional modularity
with respect to separation of object manipulation,
hand posture control and arm movement control.
This model is the least economically compatible interms of the number of modules required when it iscombined with the MOSAIC structure, that contains
multiple models (Wolpert and Kawato, 1998). The
second model shown in Fig. 2B has modularity between arm and hand control. The IDM of the armand object generates the motor command for the arm
while receiving the desired trajectory information.
The object’s IDM predicts the load force necessary
to transport the object along the desired trajectory.
This load force information is fed to the grip force
controller, which generates the hand motor commands required for the grip force that is proportional
to the predicted load force. Specifically, the futureload force is computed by the object’s IDM, which
is divided by a friction coefficient and multiplied by

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Fig. 2. Three different computational models, A, B, and C, of grip force–load force coupling (left) and their predictions on the auto-correlation and cross-correlation of load(L) and grip (G) forces (right). Only the third model shown in C utilizes the forward model.

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a safety factor to derive an appropriate future grip
force. Finally, this necessary force is realized in a
predictive manner by the grip force controller.
Kawato (1999) proposed the computational modelof grip force–load force coupling shown in Fig. 2C.
In this framework, the IDM of the combined dynamics of the arm, hand, and object calculates theappropriate arm motor commands from the desired
trajectory of the arm. This command is sent to thearm muscles as well as to the forward model of the
combined dynamics of the arm, hand, and object
as an efference copy (see also Flanagan and Wing,
1997). The forward model predicts the arm trajectory
50 to 100 ms in the future. From this predicted arm
trajectory, a hand motor command is generated in
the same way as for the model shown in B. The thirdmodel has the largest modularity and utilizes bothforward and inverse models of the arm and object.
Its extension to multiple models in the frameworkof MOSAIC (Wolpert and Kawato, 1998) was also
proposed by Kawato (1999) so that multiple-object
manipulation could be easily switched. Even in themodels of B and C, the IDM of the combined armand object should be relearned or switched every
time when a new object is grasped. However, thiscombined IDM is used for only arm control in B
and C, and arm motor commands are less influenced
by different object characteristics than hand motor
commands, while hand motor command should bedrastically altered for different objects. The MOSAIC architecture is best suited for the computational model C, because both the forward and inverse
models are utilized, and the learning of object IDM
for hand motor command generation is decoupledfrom learning of arm dynamics.
From the viewpoint of grasp control, the essential difference between models B and C is that theformer uses the desired arm trajectory in computing
the necessary grip force while the latter uses thearm trajectory estimated by the forward model. If
the environment is a well-learned one, the desired
arm trajectory is accurately realized and should be
similar to the estimated trajectory. Therefore, the behaviors of the two kinds of models are similar andcannot be discriminated between. However, for novel
environments that are not well controlled, the desired
trajectory and the predicted trajectory could be very
different, allowing us to discriminate between thethree models. In particular, if one assumes that theforward model is learned more rapidly than the inverse model, an idea consistent with the MOSAIC
model, then one would expect good coupling between grip force and load force before good control
over the movement trajectory is established.
The right side of Fig. 2 shows predictions of thethree models in terms of how three different correlations — involving grip and load forces — willchange when learning to manipulate an object withnovel dynamics. These correlations are the correlation between load force in a given trial with load
force after adaptation (LL), the correlation between
grip force in a given trial and grip force after adaptation (GG), and the correlation between the grip force
and load force in a given trial. By definition, both
LL and GG start from a low value and increase to
1 as learning progresses. From previous studies ongrip force–load force coupling, we know that GL
takes a high value in the late stages of learning whensubjects are well experienced at manipulating theobjects (Flanagan and Wing, 1997).
For the single IDM of model A, LL, GG and GL,
as shown in the right side of Fig. 2A, should all havea similar rate of increase because a single common
neural network generates both hand and arm motor
commands as a single unit. If the load dynamics arehighly altered, compared with objects subjects arefamiliar with, the novel dynamics alter the realized
trajectory, and induce different acceleration patterns,
thus altering the load-force time course while thegrip-force time course is inappropriate for the new
object and starts from the old pattern for a familiar
object. Therefore, at the early stage of learning, GL
is low, but as learning progresses both the arm andhand motor commands become appropriate for the
new object dynamics, and GL approaches a highvalue.
Quantitative details of predictions made by model
B depend on the relative lengths of the learning time
constants of the combined object and arm IDM andthe object IDM. The LL-increase time course is determined solely by the learning rate of the combined
IDM of arm and object (τ1 ), while the GG-increasetime course is determined solely by the learning rateof the object IDM (τ2 ). At the early phase of learning, after a new object dynamic is imposed, GL islow because the load-force time course is altered,

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as in A. As learning progresses, both the combined
IDM and object IDM become better models of thecontrolled objects, and GL increases for two reasons.
First, due to combined IDM learning, the desired
arm trajectory is better realized and the load force
approaches that predicted from the desired trajectory.
Secondly, the predicted grip force becomes closer tothat required with the new dynamics for the actual
arm trajectory because the object IDM improves,and the final realized trajectory approaches the desired trajectory. Consequently, the time course of
GL-increase is governed by both of the two time
constants of the two IDM learning rates (τ1 andτ2 ). This can also be seen from the block diagramof model B, since GL is the correlation computed
through the cascade of the two IDMs (Fig. 2B).
For the third model, C, GL is determined by thethird time constant (τ3 ) of the forward model of thearm and object as well as the object IDM because thepredicted arm trajectory can be close to the actual
trajectory even if it is greatly distorted only if theforward model is good. On the other hand, GG isgoverned by both the third time constant (τ3 ) and thefirst time constant (τ1 ), because the grip-force timecourse is determined by the cascade of all four elements in C (combined IDM and FDM, object IDM,
and grip controller). Quantitative details of the timecourses of LL, GG and GL differ depending on relative lengths of the learning time constants of each of
the different elements within these models. However,regardless of this we can make some qualitative predictions. For the model A, the GL rise rate is exactly
the same as those of GG and LL. For the model
B, the GL rise rate is not larger than that of either
LL or GG. Only model C can have a GL rise rate
higher than that of LL. This will occur if the learning
rate of the combined IDM (τ1 ) is slower than that of
the forward model (τ3 ). As described below, recent
experimental data unequivocally support model C’s
predictions, and the utilization of forward models isstrongly supported.
Behavioral studies done by Flanagan and Wing
(1996, 1997) supported model C. In their experiments, they changed the dynamics of manipulated
objects by using a one-degree-of-freedom robotic
manipulator. This alternation of the object’s dynamics significantly disrupted both the hand trajectory
and the grip force–load force coupling. Even inthese novel situations generated by inertia, viscous,or spring force, grip and load forces became closely
coupled after a relatively small number of learning
trials, whereas the learning of the hand trajectory
was much slower. In other words, during early learning trials, good grip force–load force coupling wasquickly acquired even though the arm velocity profile was irregular and poorly controlled. One of thelimitations of these studies is that grip–load correlations were examined across learning trials where theload force waveform was changing. Recently, Vetter
et al. (2002) dealt with this potential confound byhaving subjects produce trajectories — after having
adapted to the novel load — that were similar to
those observed in early learning. They found that after some four learning trials, subjects generated grip–
load coupling that was similar to that observed after
adaptation and for similar movements (and henceload force waveforms). Consequently, utilization of
forward models in grip force–load force coupling iswell established. Based on this, we have exploredthe possible sites of forward models through fMRI
experiments.
Materials and methods
Subjects
Three females (ranging in age from 25 to 31) andthree males (from 27 to 43) participated in the experiment after giving written informed consent. The
protocol was approved by the ethics committee of
CRL. All subjects were right-handed.
Task and procedure
The transporting task shown in Fig. 1A includes
three components: arm movement control, grip force
modulation, and coordination of arm movement andgrip force. Therefore, if we remove the first twocomponents, we can extract the brain activity exclusively related to coordination or, more specifically,
to forward models. We used a 2 by 2 factorial designof tasks to compare neural activity under conditions
with and without arm movement and with and without grip force modulation (Fig. 3). Accordingly, theexperimental tasks were (A) transporting an object,(B) loaded arm movement, (C) grip force modula-

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Fig. 3. A 2 × 2 factorial design (with/without arm movement/grip force modulation) of four tasks in the fMRI experiment. The
solid lines in the inset boxes depict temporal patterns of grip force, and the dotted lines depict temporal patterns of load force. These
measurements were made during behavioral experiments performed outside of the MRI scanner under similar experimental conditions(see section ‘Materials and methods’).

tion, and (D) rest. In all four tasks, the subjects wore
a glove. In the transport and loaded arm movementtasks, movement amplitude was 20–25 cm becauseof the limited workspace in the gantry. The glove did
not alter the basic coupling between grip force andload force (compare Fig. 1 and the inset of Fig. 3A).
The loaded arm movement task was similar to thetransport task except that the object was attached at
the tips of the thumb and forefinger by removableadhesive tape. In this case, grip force modulation is

not necessary, and the actual grip force modulation
was very small as shown by the solid line in theinset of Fig. 3B. In retrospective inquiries, subjects
reported that they were not conscious about the absence of grip force modulation in the loaded arm
movement task. Thus, it is unlikely that some kindsof voluntary suppression of grip force in the loadedarm movement condition took place, and this factor
influenced brain imaging data. The pressure gauges
were attached to the glove underneath the adhesive

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tape rather than on the ping-pong ball to avoid any
artifact caused by the adhesive tape. During the grip
force modulation condition, the subjects held the object in the same grip as in the transport task andperiodically changed the grip force voluntarily at 4
Hz (see the inset of Fig. 3C). They were instructed to
produce a larger grip force than in the transport task.
In the rest period, they made no overt movements.
For brevity, the three task conditions A, B and C
will be called transport, arm and grasp movements,
respectively.
The dynamics of both arm movement and handconfiguration were similar in the two arm-movementtasks (A and B) because the object was attached to
the fingers during loaded arm movement. Thus, arm
motor commands, hand motor commands for handand finger postural maintenance, and the proprioceptive feedback would also be expected to be similar inthese two tasks. Furthermore, the preliminary measurement outside the scanner confirmed that grip
force changes that occurred during the grip force
modulation task were as large as, or larger than,changes during the transport task (compare the insets
of Fig. 3A and 3C). Consequently, finger tactile feedbacks due to modulation of grip forces perpendicular
to contact surfaces would be expected to be similar inthese two tasks (A and C). Because volitional controlof grip force in the grip force modulation task (C)may be more demanding than automatic adjustmentof the force in the transport task (A), the subtractionof the signal values in the grasping task from thosein the transport task could cause an underestimationof the brain activity related to components other than
the grasping component in the transport. However,more importantly it is unlikely that such activation
was overestimated.
Each subject performed the tasks with her or his
dominant, right arm and hand. Their heads were
fixed by using individually molded bite bars. An
experimental session consisted of four blocks; ineach block, and for all subjects, each of the four task
periods occurred for 35.2 s in the fixed order of A,
B, C and D as shown in Fig. 3. The subjects prepared
for the task during the first 4.4 s of each task period,and performed the task for the successive 30.8 s.
Eight functional image volumes of the whole brain
were acquired in each task period. Thus, total 128
volumes were acquired in each session.

Brain imaging
A 1.5 T Magnetom Vision system (Siemens, Erlangen) was used to acquire both sixteen axial gradient-echo, echo-planar T2* weighted image volumes[TR = 4.4 s, TE = 66 ms, flip angle = 90°, thickness= 7 mm, slice gap = 2.8 mm, in-plane resolution =2 mm × 2 mm] and T1 weighted structural image
volumes for anatomical co-registration [TR = 560
ms, TE = 6 ms, flip angle = 90°, thickness = 7 mm,
slice gap = 2.8 mm, in-plane resolution = 1 mm
× 1 mm]. Each session began with two ‘dummy’scans, the data of which were discarded to allow forT1 equilibration effects. Each subject participated insix separate sessions of functional imaging. All themultiple session data were analyzed at once in thefollowing two methods. Session-specific effects weremodeled and removed as confounding effects in thegeneral linear model explained below.
Analyses
We used SPM99 [http://www.fil.ion.ucl.ac.uk/spm]
for all of the preprocessing and statistical inference procedures except motion correction. To remove motion artifacts, all volumes of each functional
imaging session were realigned to the reference,
the 65th volume, by using AIR3.08 [http://bishopw.
loni.ucla.edu/AIR3]. After that, they were stereotactically normalized using affine and nonlinear transformation and then resampled using sinc interpolation into the space of a standard brain. The volumes
were then smoothed with a Gaussian kernel of 4 mm
full-width half-maximum (FWHM). The first two
image volumes of each task period were regarded asa preparation phase and discarded in order to avoid
the effects of task transition, and six other volumes
were regarded as a test phase. High-frequency noises
were removed with a Gaussian filter (FWHM = 4
s).
Condition and session effects were estimated according to the general linear model at each and every
voxel with delayed boxcar waveforms. To investigate regionally specific condition effects of interest,
the estimated coefficients were compared using appropriately weighted linear contrasts (Friston et al.,1995). In the first half of the analyses to obtaintransport > rest, grasp > rest, and arm > rest con-

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Fig. 4. Statistical parametrical maps (SPMt) illustrating activation loci of transport > rest (A), grasp > rest (B) and arm > rest (C).
Topography of brain regions related to transport movements (A), grasp movements (B) and loaded arm movements (C) are expected tobe revealed by these contrasts. (D) The numbers of voxels.

trasts (Fig. 4) and transport > arm and transport> grasp contrasts (Figs. 5 and 6), a conjunction
analysis across subjects (Friston et al., 1999) wasapplied to find common activation to the subjects atthe threshold of 5% corrected for multiple comparisons.
In the latter half of the analysis, the so-calledfactorial analysis was carried out to identify co-

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Fig. 5. Statistical parametrical maps (SPMt) illustrating activation loci of the transport > arm (A) and transport > grasp (B).

ordination-related brain regions (Fig. 8A). Namely,
coordination-related areas were investigated in termsof the interaction between arm movement and grip
force modulation effects: (a-b)–(c-d) (a, transport;b, loaded arm; c, grip force modulation; and d,rest). The resulting set of voxel values for each contrast constitutes a statistical parametric map of the tstatistic, SPMt. Here, conjunction analysis was not
utilized, and SPM99b was used.
Results
Fig. 4A–C shows the topography of brain regions
related to object transport, grip force modulation andloaded arm movement, respectively. More specifically, they show statistical parametric maps (SPMt)
illustrating the activation loci of transport > rest (A),grasp > rest (B), and arm > rest (C). The main
effect of transport movement (Fig. 4A) was observedin many cerebral cortical areas including the bilateral sensory–motor cortices, bilateral premotor cortices, bilateral SMA, bilateral inferior frontal gyri,
left middle frontal gyrus, bilateral cingulate gyri,bilateral inferior parietal lobules, right intraparietal
sulcus, and bilateral insula (Table 1). The activity
was also observed in the bilateral thalamus, basal
ganglia, and cerebellum. In cerebral cortical areas,
the thalamus and in the basal ganglia, activity wasstronger in the contralateral (left) hemispheres to theusing hand. This was not the case in the parietal
cortex. However, the cerebellum had much stronger
ipsilateral activation (Table 1). The main effect ofgrip force modulation (Fig. 4B) revealed activity inthe left primary sensorimotor cortex, left premotor
cortex, left SMA, left insula, and right anterior cerebellum, which are mainly small subsets of brain lociactivated during transport movements. The primaryeffect of loaded arm movement (Fig. 4C) revealed
activity in a wide range of regions including theleft primary motor cortex, left premotor cortex, left
SMA, bilateral postcentral gyri, inferior and middle
frontal gyri, left cingulate gyrus, bilateral inferiorparietal lobules, bilateral insula, bilateral thalamus,
left basal ganglia, and the right anterior cerebellum,
which are mainly large subsets of brain loci activatedduring transport movements.
Fig. 4D shows the numbers of activated voxels
examined in the above three SPM contrasts in theformat of the Venn diagram. One might first notethat the number of activated voxels for transport
movement was by far the largest, that for the loadedarm movement was medium, and that for the grasp
was the smallest. A large portion (79%) of the arm-activated voxels was also activated in transport
movement. Similarly, a large portion (71%) of thegrasp-activated voxels was also activated in transport

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Fig. 6. One slice with z = −20 mm in MNI coordinates showing a region of (transport > grasp) and (transport > arm) in the rightanterior cerebellum. The open area shows the voxels that were more activated in transport than in grasp. The filled area shows the voxelsthat were more activated in transport than in arm. The mosaic area shows the conjunction of these two areas.

movement. On the other hand, a large portion (54%)
of the transport-activated voxels was not activated ineither arm or grasp movement.
Fig. 5 shows voxels that were more activated intransport than in loaded arm movement and thosethat were more activated in transport than in grasp
movement, respectively. As expected from the results of Fig. 4, only the left primary motor cortex,
right postcentral gyrus, and right anterior cerebellum

were more activated in transport movements than inarm movements (Fig. 5A and Table 2). On the other
hand, many brain loci, including the left primary motor cortex, left premotor cortex, left SMA, bilateral
postcentral gyri, right inferior frontal gyrus, left cingulate gyrus, bilateral inferior parietal lobules, leftthalamus, bilateral basal ganglia, and right anterior
cerebellum, were more activated in transport than ingrasp movements (Fig. 5B and Table 2).

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TABLE 1
Principal areas of activation related to three movement tasks compared with the rest condition
Transport > rest

Grasp > rest

MNI coordinates
L. BA4
R. BA4
L. BA6
R. BA6
L. SMA
R. SMA
L. postcentral gyrus
R. postcentral gyrus
L. inferior frontal gyrus
R. inferior frontal gyrus
L. middle frontal gyrus
L. cingulate gyrus
R. cingulate gyrus
L. inferior parietal lobule
R. inferior parietal lobule
R. intraparietal sulcus
L. insula
R. insula
L. thalamus
R. thalamus
L. basal ganglia
R. basal ganglia
R. cerebellum
L. cerebellum

Arm > restt value

MNI coordinates

t value

MNI coordinates

−28
38
−22
8
−4
10
−54
58
−52

−22
−6
−16
2
−8
−2
−24
−24
−2

54
48
72
72
56
54
18
16
8

10.24
2.13
4.06
2.68
6.00
1.54
3.41
1.80
2.73

−38

−18

44

5.00

−24

−26

52

9.03

t value

−10

0

72

1.59

−22

−16

70

7.03

−2

−4

54

1.64

−4

−10

52

5.17

−58

−18

22

1.78

−40
−22
14
−52
52
26
−40
46
−18
14
−28
14
14
−24

48
−10
10
−34
−28
−56
2
4
−22
−8
−14
0
−50
−42

0
42
46
48
20
26
16
−2
12
20
6
16
−16
−24

1.96
1.64
1.61
2.40
2.79
1.56
3.25
2.61
4.18
2.16
3.84
1.63
10.35
1.98

−58
48
−60
60
−38
−18

−18
−26
4
4
34
−10

24
22
28
4
20
40

3.60
3.21
2.04
1.66
1.73
1.68

−46
56

−34
−26

28
26

3.59
1.60

−38

0

16

1.63

−44
46
−18
14
−32

−4
2
−12
−28
−6

4
−4
14
0
−2

1.77
2.72
1.56
1.57
3.06

16

−54

−18

3.76

6

−58

−12

7.85

p < 0.05, corrected. Activation peaks are reported in MNI coordinates. The MNI coordinates and t scores (degrees of freedom = 4481)
for maxima of activations are presented. R and L indicate the right hemisphere and left hemisphere, respectively.

TABLE 2
Principal activations related to the transport task compared with two other movement tasks
Transport > arm

L. BA4
L. BA6
L. SMA
L. postcentral gyrus
R. postcentral gyrus
R. inferior frontal gyrus
L. cingulate gyrus
L. inferior parietal lobule
R. inferior parietal lobule
L. thalamus
L. basal ganglia
R. basal ganglia
R. cerebellum

Transport > grasp

MNI coordinates

t value

MNI coordinates

t value

−40

−20

48

2.24

38

−28

40

1.86

12

−54

−16

3.44

−26
−18
−2
−56
50
60
−16
−40
44
−22
−30
12
2

−26
−16
−8
−26
−28
20
−24
−26
−32
−4
−14
0
−58

54
72
60
20
22
16
44
28
50
20
2
18
−12

6.32
3.65
1.98
2.59
2.00
1.91
2.54
2.26
1.76
2.43
3.59
2.04
7.84

p < 0.05, corrected. Activation peaks are reported in MNI coordinates.

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When we consider the conjunction of Fig. 5, thenactivated voxels were found only in the right anteriorand superior cerebellum. That is, voxels that were
simultaneously more activated in transport than ingrasp movements, and more activated in transport
than in arm movements were only found to exist in
the cerebellum. Fig. 6 shows these activated voxels
in the cerebellum at the slice of z = −20 mm of MNI
coordinates. Here, the open areas show the voxelsthat were more activated in transport than in grasp.
The filled areas show the voxels that were more
activated in transport than in arm movement. The
mosaic areas show the conjunction of these two areasand indicate the voxels that were simultaneously
more activated in transport than in grasp and more
activated in transport than in arm movement. The
number of these conjointly activated voxels was 37.
The region of interest was defined as the above
conjointly activated areas (mosaic, 37 voxels), andthe relative blood oxygen level dependent (BOLD)
signal increase compared with the rest condition was
averaged over all voxels across all subjects. Fig. 7
shows that the BOLD signal increase was the largest
for transport movements, slightly smaller for arm
movements, and the smallest for grasp movements.
Finally, the coordination-related area was identified by the factorial analysis, which was explained inFig. 7. Relative signal increase averaged across subjects in common regions of transport > grasp and transport > arm. Error
bars show standard deviations between subjects.

the latter half of the method. As shown in Fig. 8, theleft biventer in the cerebellum was the only region
identified as having a statistically significant relation to coordination (uncorrected p < 10−4 for eachvoxel, larger than 62 voxels for cluster, correctedp < 0.05).
Fig. 8B shows the relative BOLD signal in thisregion of interest (ROI). As shown in Fig. 8B, themean BOLD signal in the ROI was higher under the
rest condition (d) than under the other three conditions (a, b, and c); i.e. this region was deactivatedby all movement tasks. The amount of deactivation
by transporting task (a from d) was much smaller
than the combined amount of deactivation by arm
movement (b from d) and grip force modulation (cfrom d) tasks.
Discussion
Most regions related to arm movement and grip force
modulation corresponded to those that were reported
in many previous studies on simple hand or arm
movement tasks (e.g. Fink et al., 1997). In particular,
the coordinate of the peak t-score in grip force modulation (x, y, z in MNI coordinates: −38, −18, 44) inthe primary sensorimotor cortex was located inferiorly and laterally to that found with arm movements(−24, −26, 52). This different location of peaks
is congruent with the somatotopic organization of
the hand and arm (Penfield and Rasmussen, 1950).
Furthermore, in the anterior cerebellum the peak ingrip force modulation (16, −54, −18) was locatedlaterally to that found with arm movements (6, −58,
−12). This difference in peak location is also congruent with previous findings that distal parts of the
body are represented more laterally in the anterior
cerebellum than more proximal parts of the body
(Snider and Eldred, 1952; Grodd et al., 2001).
According to the computational model of grip
force–load force coupling shown in Fig. 2C, the four
different task conditions of Fig. 3 are expected toactivate the three computational elements, the inverse model, the forward model and the grip force
controller differently. None of the three elements isutilized in the rest condition. Only the grip force controller is activated for grip force modulation (grasp),
and only the inverse model is activated for loadedarm movements (arm). On the other hand, all three

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Fig. 8. Coordination-related activation superimposed on an anatomical coronal slice of a subject normalized to the MNI space. Only
voxels with t-scores above 3.09 ( p < 10−4 , uncorrected) were analyzed. We only found an active cluster of voxels in the left biventer ofthe cerebellum ( p < 0.05, corrected on the basis of the random field theory). The MNI coordinates and t-score (df = 4481) for maxima
of activations were −17, −58, −54 and 5.01. Adjusted BOLD contrast signals relative to the fitted mean in the cerebellar ROI related tocoordination.

elements are utilized simultaneously for transport ofthe object. Consequently, with the transport > rest
contrast shown in Fig. 4A, we expected to observe
union of the activities of the three elements. For thegrasp > rest contrast of Fig. 4B, activated voxels
were assumed to contain activity of the grip force
controller of Fig. 2C. Similarly, for the arm > rest
contrast of Fig. 4C, we expected to observe activity
related to the inverse model for arm. As Fig. 4D
demonstrated, more than half of the activated voxels
for the transport > rest contrast were not significantly more activated during either arm or grasp
compared with the rest. Therefore, these voxels may
contain activity of the forward model.

To further explore this possibility, the two contrasts
transport > arm and transport > grasp were examined in Fig. 5. According to the computational modelof Fig. 2C, the former contrast may reveal activityof the grip force controller and the forward model,
while the latter may show activity of the inverse
model and the forward model. Logically, the conjunction of the grip controller or the forward modeland the inverse model or the forward model should
reveal the locus of the forward model, and the conjunction of these is shown in Fig. 6. Only the small
number of voxels in the right, anterior and superior
cerebellum showed statistical significance, and may
correspond to the forward model locus. The BOLDCICERO/GALAYAA B.V. / Prablanc 11: pp. 171-188

185

signal increase for this ROI (Fig. 7) is compatible
with the hypothesis that the ROI contains the forward
model used for grip force–load force coupling.
If one simply assumes that the BOLD signal increases induced by activation in the three elementsof Fig. 2C are linearly added to each other, the transport signal increase would have to be larger than
the summation of the grasp increase and the arm
increase because the forward model increase mustalso be added. However, this simple expectation wasapparently not met, as shown by the BOLD signal of
the right anterior cerebellum in Fig. 7. Consequently,
in parallel to the above conjunction analysis, we further explored the possible forward model locus by
the factorial analysis (a-b)–(c-d), based on this linear
addition assumption (a = transport; b = loaded arm;c = grip force modulation; and d = rest). With thelinear addition assumption, (a-b)–(c-d) should reveal
only the forward model activation. Using these assumptions, multiple regression analysis showed thatthe left biventer in the cerebellum could be the only
statistically significantly activated region involved inarm movement–grip force coordination. The previous conjunction analysis did not show this second
ROI because it was deactivated by all movementtasks. This deactivation is consistent with the results of previous research that reported that hand
movement could deactivate the cerebellum contralateral to the employed hand (Allison et al., 2000).
The amount of deactivation by the transporting task
was much smaller than the amount of summation ofdeactivation by the two simple movement tasks. Furthermore, the second ROI was more activated in thetransporting task than in the arm movement or grip
force modulation task. Therefore, according to thelinear addition assumption, this ROI can be regarded
as a potential coordination-related region.
The finding that the second ROI was in the left,
i.e. contralateral, cerebellum strengthens the argument that this increased activation is related tocoordination per se and not to grip force or arm
movement control itself, since simple movementsof a motor effector activate the anterior cerebellum
ipsilaterally (Nitschke et al., 1996). Because mostcorticopontine projections and almost all cerebellar
projections to the cerebral cortex are contralateral(Middleton and Strick, 1998), this activity in the left
cerebellum during transport with the right hand iscongruent with previous findings that lesions of theright cerebral cortex are often associated with ipsilateral impairments of complex sensorimotor tasks(Winstein and Pohl, 1995). More recently, Ehrsson
et al. (2000) conducted an fMRI study with normal
human subjects and found that the right cerebral
cortex was engaged in a precision grip task performed with the right hand, although muscles ofthe left hand did not show reliable electromyogram(EMG) activity. Furthermore, Ehrsson et al. (2001)
found that the right intraparietal cortex was more
activated when subjects generate small grip forces
than when they employ large grip forces. The small
grip forces were representative of the forces thatare typically used when manipulating small objects
with precision grips in everyday situations. Thus,
the left cerebellum together with the right cerebral
cortex may be recruited in tasks more demanding
than simple movement, in this case, coordination
between the right arm and hand. Independently tothe current work, Ehrsson et al. (2002) conducted aclosely related fMRI experiment to examine cortical representations of coordinated grip and lift force
control. Although their motivation was very similar
to ours, the actual experimental paradigm was different. Their task was purely isometric and did not
involve arm movement. The caudal two thirds of thecerebellum were not covered (z > −22 in the MNI
standard space). They did not find any cerebellar
activity in the coordination task compared with theother two tasks. They instead found that the coordination was specifically associated with activation ofa posterior section of the right intraparietal cortex.
The left biventar lobule activation, which we found,
was outside their coverage, and might have anatomical connection with their right intraparietal cortex.
Different experimental paradigms or different scanning coverage may explain the different results onright anterior cerebellum activity.
In summary, the same data were analyzed twice,in ways that are both expected to detect the additional activation due to coupled arm and grip action compared to either alone. The two analyses
give different results, most spectacularly in that the
cerebellar activation site shifts from right anterior
cerebellum to left posterior. The different results obtained are due to different assumptions made in thetwo different analyses. In the first analysis, simple

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overlap between arm and grasp conditions was assumed small, which was quantitatively supported by
Fig. 4D. In the second analysis, linear summation
assumption of BOLD signals corresponding to different brain functions was made, which should bewrong in general. However, as Fig. 8B shows, theleft biventar activation was certainly larger duringtransport than arm or grip, thus the analysis wasvalidated. Consequently, our data and the two analysis methods suggested that the right, anterior andsuperior cerebellum and/or biventer in the left cerebellum were the only regions related to grip force–load force coupling.
We hypothesized that the coordination-related regions include the neural substrate of the internal
forward model. The present results suggest that theright anterior and superior cerebellum and/or the leftbiventer may contain such forward models. This supports the prediction by previous computational theories (Kawato et al., 1987; Kawato and Gomi, 1992;
Miall et al., 1993; Wolpert et al., 1998; Kawato, 1999)
that forward models are located in the cerebellum.
Finally, we compared the locations of the first
and the second ROIs revealed in our study with the
cerebellar locations of interests, which are related
to forward models (Blakemore et al., 2001; Miall etal., 2001). The first ROI in the right, anterior andsuperior cerebellum is located approximately 25 mm
medial and 20 mm superior to the right superior
cerebellar locus, which was found to be significantly
correlated with the delay in the self-tickling taskof Blakemore et al. (2001). Both studies involved
right arm and hand movement, but ours involved
grip force modulation while theirs involved perceptual modulation due to forward model prediction.
Since cancellation of tactile sensation due to selfmovement is thought to be more cognitive than grip
force–load force coupling as motor coordination, themore lateral and inferior location of more cognitive
forward models is not surprising. The second ROI,in the left biventar location in our study is about
15 mm medial and 20 mm inferior to the locus thatwas found to be correlated with asynchrony and independence of eye–hand coordination by Miall et al.
(2001). Both studies involved right hand movements,
but ours dealt with arm–hand coordination while
theirs dealt with eye–hand coordination. Physically,
the arm and hand are coupled more closely, and thegrip force–load force coupling tasks may be interpreted as a more basic form of motor coordination.
Thus, it was not surprising to find the more sophisticated eye–hand coordination induced more lateraland more superior activation near the bottom of theleft cerebellum.
In the current behavioral paradigm, the forward
model predicts future arm movement and load force
from the efference copy of the arm motor command. Recent studies have rigorously demonstrated
that the cerebellum plays an essential role in thecoordination of movements with multiple degrees
of freedom (Bastian et al., 1996). In this study, we
supported a specific computational model of coordination as shown in Fig. 2C. That is, we explained
the coupling of grip force and load force by themechanism where the forward model in the cerebellum predicts a trajectory of one motor effector (arm)and this prediction is used to control another motor effector (hand). Apparently, this computationalframework can be generalized to arbitrary pairs of
motor effectors such as eye and hand (Scarchilli and
Vercher, 1999; Miall et al., 2000, 2001) and rightand left hands; moreover, the framework might beconsidered a general principle of coordination.
Conclusions
The present experiment adopted a factorial deconvolution of the transporting task when subjects transported an object with a precision grip using theright arm and hand. The obtained imaging data suggested that the right, anterior and superior cerebellum and/or biventer in the left cerebellum were theonly regions related to grip force–load force coupling. This agrees with previous findings that theright cerebral cortex is involved in more complex
precision grip tasks than simple motor control while
using the right hand. Furthermore, from a computational viewpoint, these cerebellar regions might
contain forward models of arm movements.
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QUERIES:?#1: Please check the word ‘sinc’. (page 178)?#2: Submitted to which journal? (page 188)

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