letters to natureThis work was supported by grants from the Training and Mobility of Researchers
programme of the European Commission to M.J.S., and the National Science Foundation
to M.S.S.
Correspondence and requests for materials should be addressed to M.J.S.
(e-mail: Michael_J_Stanhope@sbphrd.com) or M.S.S. (e-mail: mark.springer@ucr.edu).

Initialstage

a.................................................................

Hiroshi Imamizu*, Satoru Miyauchi², Tomoe Tamada*, Yuka Sasaki²³,
Ryousuke Takino§, Benno PuÈtz*³, Toshinori Yoshioka*& Mitsuo Kawato*k* JST/ERATO Kawato Dynamic Brain Project, 2-2 Hikaridai, Seika-cho,
Soraku-gun, Kyoto 619-0288, Japan² Communications Research Laboratory, 588-2, Iwaoka, Nishi-ku, Kobe,
Hyogo 651-2401, Japan§ Shiraume Gakuen College, 1-830, Ogawa-cho, Kodaira-shi, Tokyo 1878570,
Japan
k ATR Human Information Processing Research Laboratories, 2-2 Hikaridai,
Seika-cho, Soraku-gun, Kyoto 619-0288, Japan..............................................................................................................................................

Theories of motor control postulate that the brain uses internal
models of the body to control movements accurately. Internal
models are neural representations of how, for instance, the arm
would respond to a neural command, given its current positionand velocity1±6. Previous studies have shown that the cerebellar
cortex can acquire internal models through motor learning7±11.
Because the human cerebellum is involved in higher cognitive
function12±15 as well as in motor control, we propose a coherent
computational theory in which the phylogenetically newer part ofthe cerebellum similarly acquires internal models of objects in theexternal world. While human subjects learned to use a new tool (acomputer mouse with a novel rotational transformation), cere³ Present addresses: Massachusetts General Hospital NMR Center, 149, 13th Street, Charlestown,
Massachusetts 02129, USA (Y.S.); Kernspintomographie, Max-Planck-Institut fur Psychiatrie, Kraepelinstrasse 10, 80804 Muenchen, Germany (B.P.).

192

Error signal

Learning trialsb

Initial stage

Late stage
Error signals

Input signals
to be transformed

Human cerebellar activity
re¯ecting an acquired internal modelof a new tool

Late
stage

MR signal
increase from baseline

Acknowledgements

bellar activity was measured by functional magnetic resonanceimaging. As predicted by our theory, two types of activity wereobserved. One was spread over wide areas of the cerebellum andwas precisely proportional to the error signal that guides theacquisition of internal models during learning. The other was
con®ned to the area near the posterior superior ®ssure andremained even after learning, when the error levels had beenequalized, thus probably re¯ecting an acquired internal model ofthe new tool.
Most neuroimaging studies have found that the regional blood¯ow in the human cerebellum increases signi®cantly at the beginning of learning for a new motor or cognitive task and decreases as
the learning proceeds16±19. These results are often interpreted asmeaning that the cerebellum is involved only in the early phase oflearning and is not a memory site, that is, it does not store internal
models. Here we present a different interpretation (see also ref. 15)
based on our computational theory and experimental results.
Previous cerebellar learning theories20±22 make no speci®c predictions about the activity of internal models (see Supplementary
Information for details). We have proposed that multiple internal
models exist and that they compete to learn new environments andtools23. During the learning, all of these multiple internal models
receive a copy of the error signal and only one or a few learn the newtransformation, thereby reducing the error signal and localizing the
new activity to a distinct region of the cerebellum. The two types of

Improper outputsc

MR signal
increase from baseline

13. Miller, G. S. The families and genera of bats. Bull. US Natl Mus. 57, 1±282 (1907).
14. Novacek, M. J. & Wyss, A. R. Higher-level relationships of the recent eutherian orders: morphologicalevidence. Cladistics 2, 257±287 (1986).
15. Beard, K. C. in Primates and their relatives in phylogenetic perspective (ed. MacPhee, R. D. E.) 63±90(Plenum, New York, 1993).
16. Rayner, J. M. V. The cost of being a bat. Nature 350, 383±384 (1991).
17. Gould, E. Evidence for echolocation in the Tenrecidae of Madagascar. Proc. Am. Phil. Soc. 109, 352±
360 (1965).
18. Tomasi, T. E. Echolocation by the short-tailed shrew Blarina brevicauda. J. Mammal. 60, 751±759(1979).
19. Forsman, K. A. & Malmquist, M. G. Evidence for echolocation in the common shrew, Sorex araneus.
J. Zool. Lond. 216, 655±662 (1988).
20. Speakman, J. R & Racey P. A. No cost of echolocation for bats in ¯ight. Nature 350, 421±423 (1991).
21. Kalko, E. K. V. Coupling of sound emission and wing-beat in naturally foraging European pipistrelle(Microchiroptera: Vespertilionidae). Folia Zool. 43, 363±376 (1994).
22. Springer, M. S. et al. Endemic African mammals shake the phylogenetic tree. Nature 388, 61±64(1997).
23. Stanhope, M. J. et al. Molecular evidence for multiple origins of Insectivora and for a new order ofendemic African insectivore mammals. Proc. Natl Acad. Sci. USA 95, 9967±9972 (1998).
24. Kishino, H. & Hasegawa, M. Evaluation of the maximum likelihood estimate of the evolutionary tree
topologies from DNA sequence data, and the branching order within Hominoidea. J. Mol. Evol. 29,
170±179.
25. Templeton, A. R. Phylogenetic inference from restriction endonuclease cleavage site maps withparticular reference to the evolution of humans and the apes. Evolution 37, 221±244 (1983).
26. Lyons-Weiler, J., Hoelzer, G. A. & Tausch, R. J. Relative Apparent Synapomorphy Analysis (RASA) I:
the statistical measurement of phylogenetic signal. Mol. Biol. Evol. 13, 749±757 (1996).

Proper outputs

Internal
model

Error signal

Learning trials
Figure 1 Changes in cerebellar activity predicted by the learning theory of internal
models. a, Signal intensity change caused by error signals (red curve). b, Activity maps ofthe initial and late stages of learning. Each small square represents a unit of multiple
internal models. Orange squares indicate regions where the internal model is acquired.
c, Signal intensity change in the regions where the internal model is acquired. Orange
curve indicates activity in the orange squares (the sum of activity re¯ecting error signals(red curve) and that re¯ecting the acquired internal model (cyan curve)).

© 2000 Macmillan Magazines Ltd

NATURE | VOL 403 | 13 JANUARY 2000 | www.nature.com

letters to nature

Tracking error on
screen (º)

a

25

a

120°
BaselinecursorTargetCentres

Hand
space

b

Mouse
positiondcSlice 1
(superior)2

3

4(inferior)
Right
CC
0.3

Left
CC
1.0

Figure 2 Visuomotor learning task and cerebellar activity. a, Rule for changing therelationship between mouse and cursor positions. A cross cursor coloured red or green
appears on the screen in the test periods or baseline periods, respectively. The open
circles indicate the centres of the screen and the hand space. b, Cerebellar activity of atypical subject in the ®rst training session. The colour-coded regions were signi®cantly
activated in the test periods (CC . 0:3). The broken lines indicate the posterior superior®ssure. c, Cerebellar activity of the same subject in the last training session. d, Regionsthat were more active during the tracking task (cursor position was not rotated) thanduring the task of pursuing the moving target with the eyes but without hand/mouse
movements. These active regions are apparently different from those in b and c and arelocated in the superior anterior and inferior anterior parts of the cerebellum on the rightside, ipsilateral to the hand that was performing the task.

b

All subjects averaged

Test

ScreenTest cursor

n.s.

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10
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7>8 t value

Figure 3 The two types of cerebellar activity. a, Activity that decreased with learning
progress. Top, tracking error (mean 6 s:d:) in the training sessions. Bottom, activation
maps showing the regions that were signi®cantly activated in the test periods incomparison to those in the baseline periods (P , 0:05 corrected). The slice position was
NATURE | VOL 403 | 13 JANUARY 2000 | www.nature.com

Tracking error on
screen (º)

cerebellar activity representing the error signals and the internal
model are predicted to occur in speci®c spatio-temporal patterns(Fig. 1). Large error signals are fed into broad regions for all possible
internal model candidates at the initial learning stage (red andorange in Fig. 1b). Because the subject's performance improves andthe error signals decrease with learning, activity re¯ecting the error
signals also decreases with learning (Fig. 1a). This prediction agrees
with previous imaging data. However, signals representing theacquired internal model must increase (cyan curve in Fig. 1c) andremain even at the late stages of learning only in the limited region(orange in Fig. 1b). This region contains a group of the mostaccurate internal models. Even in this region, total activity is
expected to decrease (orange curve in Fig. 1c) because the observed
activity is the sum of the error signal (broken red curve) and theinternal model (cyan curve). However, signi®cant activity mustremain even after the learning is complete. In our interpretation, theactivity re¯ecting the learned model is smeared by the strong
activity re¯ecting the error signal and, therefore, was not detectedin previous imaging studies. In our present study, however, wefound internal model activity by equalizing the errors under thebaseline condition to those under the test condition. Furthermore,
the time course of the internal-model activity (cyan curve in Fig. 1c)
was estimated by subtracting the error signal activity (red curve)
from the total activity (orange curve).
The task for the subjects was to manipulate a computer mouse sothat the corresponding cursor followed a randomly moving target
on a screen (Fig. 2a; a tracking task). Seven subjects performed thetask for eleven sessions (training sessions). We used functional
magnetic resonance imaging (fMRI) to scan the cerebellum in the
odd-numbered sessions. Each session lasted 9 min and 23 s andcomprised eight alternating blocks of test and baseline periods.
During the test periods, the cursor appeared in a position rotated1208 around the centre of the screen to necessitate subject learning(novel mouse); during the baseline periods, it was not rotated(ordinary mouse). In the ®rst session (Fig. 2b), large regions near
the posterior superior ®ssure in the lateral cerebellum were signi®cantly more active during the test periods than the baseline
periods (correlation coef®cient CC . 0:3); in the last session(Fig. 2c), only restricted subregions were activated. We con®rmedthat this activity cannot be attributed to larger hand movements(Fig. 2d) or larger eye movements in the test than in the baseline
periods by showing that hand-movement or eye-movement activity
is different from the activity shown in Fig. 2b and c (see also
Supplementary Information).

0
Test Baseline(error-equalized)

approximately the same as slice 2 in Fig. 2. b, The activity that remained when the
tracking error was equalized. Top, tracking error (mean 6 s:d:) in the error-equalized
session. n.s.: not signi®cant (F 1; 6  4:52). Bottom, activation map.

© 2000 Macmillan Magazines Ltd

193

letters to nature

1.0
0.8

250

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Tracking error increase
from baseline (%)

a
MR signal increase
from baseline (%)

The subjects' performances were measured by tracking errors (thedistance between the cursor and the target; see Methods). The errors
in the test periods decreased signi®cantly as the number of sessions
increased, whereas the errors in the baseline periods were constant(upper panel in Fig. 3a). A repeated-measures analysis of variance(ANOVA) on the errors indicated a signi®cant effect of the sessions
in the test periods (F 10; 60  10:60, P , 0:001) but no signi®canteffect in the baseline periods F 10; 60  0:67. Activation maps
(P , 0:05, corrected for multiple comparisons) derived from data
across all subjects (Fig. 3a) indicated that the activity in the lateral
cerebellum became smaller as learning progressed (see Methods).
The learning during the test periods was suf®cient for there to be
no signi®cant difference in the tracking error between any pairs of
the last three sessions according to the post hoc test (at P , 0:001
level by Tukey's honestly signi®cant difference method). Thus, thecerebellar activation observed in the late stage of learning should
include the activity of the acquired internal model. However, wecannot conclude that the activation solely re¯ects the internal
model because the test error was close to, but signi®cantly larger

Errorequalized

b

c
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Figure 4 Cerebellar activity related to error signals and activity related to the acquired
internal model. a, Activity change (red circles) in the red and orange regions in b incomparison to the decrease in tracking error (black circles). Each curve indicates the
exponential function ®tted to the circles. b, Activity in the red and orange regions was
signi®cantly (P , 0:05) correlated with the tracking error in the training sessions. Activity
in the blue and orange regions was correlated with a step function representing theinternal-model activity in the error-equalized session. c, Activity change in the blue andorange regions (blue circle ®lled by orange). The cyan circle indicates the subtraction of
the activity in the red region from that in the blue and orange regions. The black circles
and solid curve indicate the tracking error increase (as in a). The red broken curve is a
duplication of the red curve in a.
194

than, the baseline error (for example, F 1; 6  28:52, P , 0:005 on
the error in the last training session across all subjects). That is, theactivation may partly re¯ect error signals.
To evaluate this possibility, all of the subjects underwent an`error-equalized' experiment: the target velocity in the baseline
periods was increased so that the baseline error was equal to thetest error. Here, we used the linear relationship between error andtarget velocity (see Methods). As result, there was no signi®cantdifference between the test and the baseline errors (Fig. 3b, top).
However, regions near the posterior superior ®ssure were signi®cantly more active during the test periods than during the baseline
periods (Fig. 3b, bottom). This activity cannot be related tothe tracking error. Moreover, the amount of mouse movement(measured by the cursor trajectory length) and the target velocity
in the baseline periods were signi®cantly larger than those in thetest periods (F 1; 6  38:16, P , 0:001, on average 2.38-fold, andF 1; 6  156:63, P , 0:001, on average 2.71-fold, respectively). Allof the subjects reported that more effort and attention were neededin the baseline periods than in the test periods. Thus, the signi®cant
activity increase in the test period cannot be attributed to themouse/hand movements, the visual target velocity, attention oreffort. The most plausible explanation is that the remaining activity
in Fig. 3b re¯ects the acquired internal models, whereas the decreasein activity as learning progresses (Fig. 3a) may largely re¯ect theerror signals.
To strengthen the above conclusion quantitatively, we examined
the time courses of gross signal intensity during all sessions averaged
over two regions of interest. First, the error-related region (red andorange in Fig. 4b) was de®ned as voxels whose signal intensity
during all the training sessions was signi®cantly and positively
correlated with the tracking error (that is, the estimated regression
coef®cient was signi®cantly larger than zero, t 5276 . 2:33,
P , 0:05 corrected). Second, the internal-model-related region(blue and orange in Fig. 4b) was de®ned as voxels whose signal
intensity during the error-equalized session was signi®cantly andpositively correlated with the explanatory variable which takes 1 in
the test period scans and 0 in the baseline period scans, and thus
represents internal-model activity (t 874 . 2:33, P , 0:05 corrected). Orange voxels were correlated with both the tracking
error and the internal model activity. The error-related region is
widely spread over the lateral cerebellum, whereas the internal
model seems to be acquired only in the restricted subregions.
The relative activity in the red and orange regions (per cent ofmean signal increase from the baseline periods, all subjects averaged) decreased as the session number increased (red curve in
Fig. 4a) and was highly correlated with the tracking error (per centof increase from the baseline) indicated by the black curve(r 2  0:82 for all sessions, F 1; 5  22:87, P , 0:005). In contrast,
the activity in the blue and orange regions did not markedly
decrease (orange curve in Fig. 4c), and its correlation with theerror was low (r 2  0:25, F 1; 5  1:68). The signal increase in theblue and orange regions was signi®cantly larger than that in the redand orange regions (F 1; 6  7:38, P , 0:05). These data indicatethat the activity in the blue and orange regions may include
components that cannot be explained solely by the error. The
cyan curve in Fig. 4c shows the subtraction of the red curve fromthe orange curve, and represents the internal model activity according to our theory. This activity increased at the initial phase oflearning and remained high even in the late learning stage where theerror was equalized (Fig. 4c, right).
The acquired internal models in these experiments are expected
to represent the altered relationship between the cursor movement
and the mouse movement (forward and/or inverse kinematics
models of the novel tool). We believe that these internal models
were stored in different regions from those for an ordinary mouse,as no signi®cant activity was observed near the posterior superior®ssure when the subjects used an ordinary mouse in the test periods© 2000 Macmillan Magazines Ltd

NATURE | VOL 403 | 13 JANUARY 2000 | www.nature.com

letters to natureand pursued the moving target with the eyes but without hand/mouse movements in the baseline periods (see Fig. 2d and Supplementary Information). According to an electrophysiological study
in monkeys24, regions near this ®ssure receive parallel ®bre inputs
from the premotor and parietal association cortex, and are thus
suitable to represent kinematic models of tools. The bilateral
activity (see ref. 25 for related bilateral activity) may indicate that
activated regions acquire internal models for cognitive function
independent of the ipsilateral correspondence between the motor
apparatus and the cerebellum. Whereas previous neurophysiological experiments indicated that internal models for the motor
apparatus are present in phylogenetically older parts of the cerebellum (such as the ventral para¯occulus, vermis and intermediateparts)8±11, internal models of objects and tools in the external world
seem to reside in newer parts. We further speculate that the
cerebellum assists information processing in cerebral areas byproviding general internal models of extended controlled objects
in the external world such as concepts, symbols and languages. M

Methods
Task
The subjects moved a computer mouse (PocketEgg, Elecom) using the right hand whilelying in an MRI scanner. Head movements were restrained by a bite bar. They used a tilted
mirror to view a rear-projection screen outside the scanner. A colour projector (VPH1272OJ LCD; Sony) controlled by a computer (PC-9821 AP2; NEC) displayed the target
and the cursor on the screen. During the tracking task, a small white square target waspresented on a dark background. The x and y components of the target path were eachsums of sinusoids whose amplitude and frequency were pseudorandomly determined. The
subjects moved a small cross-hair cursor on the screen with the mouse. The cursor
position was sampled at 60 Hz. The distance between the cursor and the target at eachsampling point was accumulated over 4.4 s (tracking error).

Subjects
Ten neurologically normal subjects (20±34 years of age; ®ve females and ®ve males)
participated in the experiments. Each participant gave informed written consent. Seven of
the subjects (®ve right-handed and two left-handed26) underwent the training sessions andthe error-equalized experiment. The other three subjects (two right-handed and one lefthanded) underwent the training sessions and control experiments. In the control
experiments, we con®rmed that the activity observed in the above seven subjects could not
be attributed to differences in hand or eye movements (see Fig. 2d and Supplementary
Information).

MRI acquisition
A 1.5-T MRI scanner (Magnetom Vision; Siemens) was used to obtain blood oxygen leveldependent contrast functional images. Images weighted with the apparent transverse
relaxation time (T*2) were obtained with an echo-planar imaging sequence (repetition time(TR) 4.4 s, echo time (TE) 66 ms, ¯ip angle (FA 908, ®eld of view (FoV)
240 mm 3 240 mm, matrix size 128 3 128). We selected ten axial slices (thickness 7 mm,
slice gap 0.21 mm) encompassing the cerebellum. We scanned 128 functional images foreach slice during one session. Anatomical images for these slices were obtained with a T1
weighted sequence (TR 350 ms, TE 6 ms, FA 908, FoV 240 mm 3 240 mm, matrix size
256 3 256).

MRI analysis
Motion artefacts in all functional images were removed by using Automated Image
Registration (AIR) version 3.0 (ref. 27). We used two approaches to analyse the functional
images: a correlation analysis on a pixel-by-pixel basis28 and an analysis based on thegeneral linear model as implemented in SPM99b (Wellcome Department of Cognitive
Neurology). Details of the correlation analysis have been reported in ref. 29. To analysegroup data, functional images of each subject's cerebellum were stereotactically transformed to a standard template in SPM, and were smoothed with a gaussian kernel 4 mm
full width at half maximum (FWHM). In the activation analyses shown in Fig. 3,
condition-speci®c effects were estimated with the linear model with a boxcar wave form.
Areas of signi®cant change in brain activity were speci®ed by linear contrasts of thecondition-speci®c effects and determined using the t-statistics (SPM{t}). Results were
thresholded at t-value 2.33. In assessing the statistical signi®cance of each cluster, we
corrected for multiple comparisons based on random gaussian ®eld theory in terms ofspatial extent and/or peak height (P , 0:05). Voxel time series were temporally smoothedwith a gaussian ®lter (FWHM of 4 s). We used the effective degree of freedom adjusted foranalysis of fMRI time-series30. In the activation analyses shown in Fig. 4b, the explanatory
variable of main interest was either the tracking error or the internal model activity.

Equalization of the tracking error according to the relationship between theerror and the target velocity
The subjects performed the tracking task under various target velocities for about 15 min.
The cursor position was not rotated during this task. The averaged target velocity
NATURE | VOL 403 | 13 JANUARY 2000 | www.nature.com(21:308 s 2 1 ) used in the training sessions was multiplied by a value ranging from 1.0 to 5.0
at intervals of 0.2. Therefore, the target moved at 21 different averaged velocities in
random order. Then, the relationship was estimated linearly by the least-squares method.
The effect of the velocity on the error was signi®cant (r2 . 0:70, F 1; 19 . 45:27,
P , 0:0001) for each subject. When the cerebellar activity was scanned, the target velocity
was increased in the baseline period using this relationship, so that the baseline error was
equal to the mean error in the preceding test period.
Received 12 July; accepted 14 October 1999.
1. Kawato, M., Furukawa, K. & Suzuki, R. A hierarchical neural-network model for control and learningof voluntary movement. Biol. Cybern. 57, 169±185 (1987).
2. Lackner, J. R. & Dizio, P. Rapid adaptation to Coriolis force perturbations of arm trajectory.
J. Neurophysiol. 72, 299±313 (1994).
3. Shadmehr, R. & Mussa-Ivaldi, F. A. Adaptive representation of dynamics during learning of a motor
task. J. Neurosci. 14, 3208±3224 (1994).
4. Wolpert, D. M., Ghahramani, Z. & Jordan, M. I. An internal model for sensorimotor integration.
Science 269, 1880±1882 (1995).
5. Imamizu, H., Uno, Y. & Kawato, M. Internal representations of the motor apparatus: implications
from generalization in visuomotor learning. J. Exp. Psychol. Hum. Percept. Perform. 21, 1174±1198(1995).
6. Gomi, H. & Kawato, M. Equilibrium-point control hypothesis examined by measured arm stiffness
during multijoint movement. Science 272, 117±120 (1996).
7. Kawato, M. & Gomi, H. A computational model of four regions of the cerebellum based on feedbackerror learning. Biol. Cybern. 68, 95±103 (1992).
8. Shidara, M., Kawano, K., Gomi, H. & Kawato, M. Inverse-dynamics model of eye movement control
by Purkinje cells in the cerebellum. Nature 365, 50±52 (1993).
9. Gomi, H. et al. Temporal ®ring patterns of Purkinje cells in the cerebellar ventral para¯occulus duringocular following responses in monkeys I. Simple spikes. J. Neurophysiol. 80, 818±831 (1998).
10. Kobayashi, Y. et al. Temporal ®ring patterns of Purkinje cells in the cerebellar ventral para¯occulus
during ocular following responses in monkeys II. Complex spikes. J. Neurophysiol. 80, 832±848(1998).
11. Kitazawa, S., Kimura, T. & Yin, P. B. Cerebellar complex spikes encode both destinations and errors inarm movements. Nature 392, 494±497 (1998).
12. Raichle, M. E. et al. Practice-related changes in human brain functional anatomy during nonmotor
learning. Cereb. Cortex 4, 8±26 (1994).
13. Kim, S. G., Ugurbil, K. & Strick, P. L. Activation of a cerebellar output nucleus during cognitive
processing. Science 265, 949±951 (1994).
14. Allen, G., Buxton, R. B., Wong, E. C. & Courchesne, E. Attentional activation of the cerebellum
independent of motor involvement. Science 275, 1940±1943 (1997).
15. Thach, W. T. On the speci®c role of the cerebellum in motor learning and cognition: Clues from PET
activation and lesion studies in man. Behav. Brain Sci. 19, 411±431 (1996).
16. Friston, K. J., Frith, C. D., Passingham, R. E., Liddle, P. F. & Frackowiak, R. S. Motor practice andneurophysiological adaptation in the cerebellum: a positron tomography study. Proc. R. Soc. Lond. B
Biol. Sci. 248, 223±228 (1992).
17. Grafton, S. T., Woods, R. P. & Tyszka, M. Functional imaging of procedural motor learning: relating
cerebral blood ¯ow with individual subject performance. Hum. Brain Mapp. 1, 221±234 (1994).
18. Seitz, R. J. et al. Successive roles of the cerebellum and premotor cortices in trajectorial learning.
NeuroReport 5, 2541±2544 (1994).
19. Flament, D., Ellermann, J. M., Kim, S. G., Ugurbil, K. & Ebner, T. J. Functional magnetic resonanceimaging of cerebellar activation during the learning of a visuomotor dissociation task. Hum. Brain
Mapp. 4, 210±226 (1996).
20. Marr, D. A theory of cerebellar cortex. J. Physiol. (Lond.) 202, 437±470 (1969).
21. Albus, J. S. A theory of cerebellar function. Math. Biosci. 10, 25±61 (1971).
22. Ito, M. Cerebellar control of the vestibulo-ocular re¯exÐaround the ¯occulus hypothesis. Annu. Rev.
Neurosci. 5, 275±296 (1982).
23. Wolpert, D. M. & Kawato, M. Multiple paired forward and inverse models for motor control. NeuralNetw. 11, 1317±1329 (1998).
24. Sasaki, K. et al. Mossy ®bre and climbing ®bre responses produced in the cerebellar cortex bystimulation of the cerebral cortex in monkeys. Exp. Brain Res. 29, 419±428 (1977).
25. Roland, P. E., Eriksson, L., Widen, L. & Stone-Elander, S. Changes in regional cerebral oxidative
metabolism induced by tactile learning and recognition in man. Eur. J. Neurosci. 1, 3±18 (1988).
26. Old®eld, R. C. The assessment and analysis of handedness: the Edinburgh inventory. Neuropsychologia
9, 97±113 (1971).
27. Woods, R. P., Grafton, S. T., Holmes, C. J., Cherry, S. R. & Mazziotta, J. C. Automated image
registration: I. General methods and intrasubject, intramodality validation. J. Comput. Assist. Tomogr.
22, 139±152 (1998).
28. Bandettini, P. A., Jesmanowicz, A., Wong, E. C. & Hyde, J. S. Processing strategies for time-course data
sets in functional MRI of the human brain. Magn. Reson. Med. 30, 161±173 (1993).
29. Tamada, T., Miyauchi, S., Imamizu, H., Yoshioka, T. & Kawato, M. Cerebro-cerebellar functional
connectivity revealed by the laterality index in tool-use learning. NeuroReport 10, 325±331 (1999).
30. Worsley, K. J. & Friston, K. J. Analysis of fMRI time-series revisitedÐagain. Neuroimage 2, 173±181(1995).

Supplementary information is available on Nature's World-Wide Web site (http://
www.nature.com) or as paper copy from the London editorial of®ces of Nature.

Acknowledgements
We thank D. Wolpert, C. Miall, M. Honda, K. Sakai and S. Kitazawa for comments on the
manuscript. Supported by Human Frontier Science Projects, and Special Coordination
Fund to Brain Science.
Correspondence and requests for materials should be addressed to H.I.
(e-mail: imamizu@erato.atr.co.jp).

© 2000 Macmillan Magazines Ltd

195news and views
a

O

E

b

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c

E

Figure 2 Fish braincases in lateral view, showing
the eyestalk, or its base or site of attachment (allmarked as E; see also Fig. 2 on page 186). The
eyestalk is a diagnostic feature that was thought
to be unique to chondrichthyans andplacoderms, but is evident in Basden andcolleagues’ fish1. a, Chlamydoselachus(chondrichthyan), a recent shark5. b, Jagorina,
a placoderm6. c, Brindabellaspis, a placoderm1.
O, the opening for the optic nerve.

matching the condition in Jagorina. So there
is no doubt that AMF101607 had an eyestalk.
In consequence, eyestalks can no longer beconsidered to be unique to chondrichthyans
and placoderms.
This is not a trivial point. Changing
knowledge about the distribution of key
characteristics often radically alters ourunderstanding of the evolutionary relationships of their bearers. Take feathers, forexample — as soon as it was found thattheropod dinosaurs possessed them, feathers could no longer be regarded as unique tobirds. The revelation that the new fish from
Australia had an eyestalk has similar significance (if less public appeal).
Based on the cranial features of AMF101607 and of examples of other groups in
the evolutionary tree constructed by Zhu etal.2, and using a computer program called
PAUP, Basden et al. produced several alternative positions of their fish and Psarolepis
in the tree (see Fig. 3 on page 187). Theirpreference is for one with the new form at thebase of the bony fishes and Psarolepis at thebase of the lobe-finned fishes.
Uncertainty about the positions of thetwo forms in Basden and colleagues’ tree
arises mainly from insufficient information.
Specimen AMF101607 is very similar to thetwo Late Devonian ray-finned fishes, so weought to compare them more thoroughly.
The eyestalk-attachment area in AMF101607 seems to occupy exactly the same
position as the opening for the optic nervein Mimia and Moythomasia (and is almost
NATURE | VOL 403 | 13 JANUARY 2000 | www.nature.com

the same shape and size), so it could be thatthese fishes also had an eyestalk. Comparison of the new form with Mimia andMoythomasia will help to identify the closest
relative of bony fishes, and may even tell us
something about the evolution of jawedvertebrates as a whole.
Other new knowledge also has to be taken
into account. The characters previously held
to be unique to osteichthyans have recently
been identified in a chondrichthyan from
Bolivia8, and a molecular study places the
cartilaginous fishes within the bony-fish
evolutionary tree9. All of these developments
challenge our understanding of the relationships among the major groups of primitive
back-boned animals and demand a profound change of conventional wisdom. The
new form reported by Basden et al. is awelcome addition to the list of candidates
for the position of ‘ancestor’ of the bony
fishes. But whether it will be elected remains
to be seen.
■
Meemann Chang is at the Institute of Vertebrate
Paleontology and Paleoanthropology, PO Box 643,
100044 Beijing, China.
e-mail zhangmm@public.bta.net.cn
1. Basden, A. M., Young, G. C., Coates, M. I. & Ritchie, A.
Nature 403, 185–188 (2000).
2. Zhu, M., Yu, X. & Janvier, P. Nature 397, 607–610(1999).
3. Yu, X. J. Vert. Paleontol. 18, 261–274 (1998).
4. Gardiner, B. G. Bull. Brit. Mus. Nat. Hist. (Geol.) 37, 173–428(1984).
5. Allis, E. P. Acta Zool. 4, 123–221 (1923).
6. Stensiö, E. in Traité de Paléontologie IV, Vol. 2 (ed. Piveteau, J.)
71–692 (Masson, Paris, 1969).
7. Young, G. Palaeontolgraphica 167A, 10–76 (1980).
8. Janvier, P. Trends Ecol. Evol. 14, 298–299 (1999).
9. Rasmussen, A.-S. & Arnason, U. J. Mol. Evol. 48, 118–123(1999).

Neurobiology

Internal model visualized
Masao Itoow can we instantly recognize a familiar object? Probably because, in thebrain, we already have a model of that
object which is activated through vision.
Similarly, we can quickly comprehend what
we hear because the brain is likely to containa model representing the meanings of thesounds we encounter. And we can probably
carry out complex movements so easily andaccurately because the cerebellum provides amodel of what is to be moved. Such internal
models provide an attractive explanation
for the brain’s subtle cognitive and control
mechanisms, but there has been no way
to investigate them experimentally. Now,
however, on page 192 of this issue, Imamizu
et al.1 report a set of brain-imaging data thatH

provide the first evidence for such a model
being formed in the cerebellum.
The basis of the work done by Imamizu
et al. is the unique theory2 of the adaptivecontrol system with two degrees of freedom(Fig. 1). It works like this. When we move a
hand, a desirable movement worked out
somewhere in the brain is conveyed as an
instruction to the motor area and its related
regions in the cerebral cortex. These areas inturn generate command signals, which act
on the hand/arm system to carry out the
movement. Information about the realized
movement is conveyed through the visualsystem back to the motor and related areas,and compared with the movement received
as an instruction. This feedback ensures that

Feedforward
motor
commandInverse modelin cerebellum

Error
Hand/arm
systemCerebralcortexDesiredmovement

Feedback
motor
commandMotorcommand

Realized
movement

Figure 1 Block diagram of the two degrees of freedom adaptive-control system with feedback-error
learning mechanism. This system combines a feedback control by the cerebral cortex and afeedforward control by the cerebellum. The cerebral cortex compares the instructed, desired
movement with a realized movement by sensory feedback, whereas the cerebellum receives only the
instruction. To realize a desired movement without feedback of the realized movement, thecerebellum needs to form an inverse model of the hand/arm system, as visualized by Imamizu et al.1
using brain-imaging data. (Modified from ref. 2.)© 2000 Macmillan Magazines Ltd

153news and views
PurkinjecellPurkinje
cell

Cerebellar
cortexLTD
Granulecell

Climbing
fibre
Inferior
olive

Mossy
fibre

Error
signal–Input+

Cerebellar
nucleus

OutputFigure 2 Basic structure of the neuronal circuitry
in the cerebellum. A single functional ‘unit’ isshown. Mossy-fibre signals provide inputs tothe unit and neurons in the cerebellar nucleus
generate outputs. Climbing-fibre signals
represent errors, reorganizing internal
connections within the unit to modify its
input–output relationship. LTD, long-term
depression. (Adapted from ref. 3.)

the realized movement is similar to the‘instruction’ movement. The instruction
may also be converted to command signals
by the cerebellum, instead of by the cerebral
cortex.
Even without such feedback, this pathway could produce a movement that closely
matches the movement received as an
instruction. For this to happen, however,the cerebellum would need to contain the
inverse of the dynamics or kinematics of thehand/arm system — in other words, thecerebellum would need to contain an inverse
model of the hand/arm system. The model isformed and updated through learning, byreferring to the errors between the intended
and performed movements, as detected by
the motor and related areas of the cerebral
cortex (feedback-error learning)2.
To test this hypothetical prediction,
Imamizu et al.1 asked a human subject lying
in a functional magnetic resonance imaging(fMRI) scanner to manipulate a computer
mouse. During the so-called ‘baseline’ period,
the subject followed a moving square
target with a cross-hair cursor on a screen.
Then, during the test, the position of the
cursor was rotated 120° around the centre of
the screen to provide a new mouse ‘condition’. At first, during the test period, large
regions of the cerebellum were significantly
activated compared with their activity during the baseline period. But this activation
decreased after repeated test trials, in parallelwith a reduction of the tracking errors. However, certain restricted sub-regions of thebrain (near the posterior superior fissure)continued to be activated. The authors propose that this remaining activity represents
an internal model that is formed during therepeated test trials. This model defines the154

new relationship between movement of the
cursor and of the mouse.
The internal-model concept for motor
learning is reasonable if we consider the
known cellular mechanisms of the cerebellum. The cerebellum has a compartmentalized structure that consists of numerous
small, functional units, each of which contains a neuronal network, composed of
Purkinje and other neurons, organized in ageometrically beautiful way (Fig. 2). Each
unit can change its input–output relationship through learning, which is driven byerror signals conveyed to the Purkinje cellsby a unique input structure, the climbing
fibres. Climbing-fibre signals induce longterm depression (LTD) of transmission froma major input to the Purkinje cells, via themossy fibre–parallel fibre pathway3. LTD
depresses those synapses between the parallel fibres and Purkinje cells that are involvedin making errors, thereby reorganizing internal connections towards a reduction of theerrors. Through this learning mechanism
a cerebellar unit could modify its input–
output relationship until it represents themodel required for precise control.
A crucial question is whether an increasein local blood flow in the cerebellum, asdetected by fMRI, really represents the formation and maintenance of an internal
model. If LTD is the only synaptic plasticity
that underlies the learning mechanism of thecerebellar circuitry, the learning is unlikely tobe accompanied by an increase in electric
impulse discharges (which may be reflected
as increased local blood flow). So the authors
assume that excitatory and inhibitory synaptic transmissions to the Purkinje cells
are facilitated, and that electric-impulse
discharges of the Purkinje cells increase.
But in the complex neuronal circuitry of
the brain there may be other possibilities. For
example, many chemical reactions underlie
the induction of LTD, including the release of
nitric oxide, which has a well-known actionof relaxing blood capillaries. The next question to address experimentally is how not only
the electric-impulse discharges, but also thecomplex chemical processes, contribute toincreases in local blood flow in the cerebellum.
As neuroscientists strive to understandthe molecular and cellular events that occur
in neurons, effective technologies andmethodologies for experimentally investigating computational and cognitive principles of the brain are still in short supply. The
success of Imamizu et al.1 in visualizing aninternal model in the cerebellum should
therefore provide tremendous encouragement for other researchers in the field.
■
Masao Ito is at the Brain Science Institute, RIKEN,
Wako, Saitama 351-0198, Japan.
e-mail: masao@mailsv.brain.riken.go.jp
1. Imamizu, H. et al. Nature 403, 192–195 (2000).
2. Kawato, M. & Gomi, H. Biol. Cybern. 68, 95–103 (1992).

Daedalus

Coal, air, fire and water
Coal-mining is a costly, labour-intensive
activity. Many attempts have been made to
extract at least some of the energy of coalin situ, by underground gasification.
Daedalus is now updating this idea.
A coal mine, he points out, fills withwater unless constantly pumped out. In aflooded mine the water is underhydrostatic pressure. At the bottom of amine more than about 2.2 km deep, it
would reach supercritical pressure.
Heated, it could not boil, but would go tosupercritical water — a powerful solvent
and reaction medium. If it contained
dissolved oxygen, organic materials
including coal would burn spontaneously
in it. So, says Daedalus, drill two holes
down to a sufficiently deep coal seam,
lower some sort of robot borer to drill atunnel connecting the two holes, and fill
the whole thing with water. Ignite the coalelectrically or pyrotechnically, and pumpaerated water down one shaft and up theother. The water flow will then deliver the
products to the surface.
What will those products be? In thepresence of excess fuel — such as a vast coalseam — supercritical combustion is a very
partial business. Toluene, for example,
burns in limited oxygen to benzoic acid.
Coal will go to big aromatic or quinonoid
molecules, with enough oxygen in them todissolve in the water. The upcoming streamof hot water will boil as the hydrostaticpressure lessens. The steam will containthe more volatile organics, easily separable
by fractionation, ideally by stepwise
expansion in a steam engine. Bigger
molecules will stay in the water; some will
crystallize out as it cools. So the mine will
yield steam power, plus a stream of useful
fuels and chemical feedstocks. Sulphur
dioxide in the water will be processed to
useful sulphuric acid, and solid ash will
mainly stay underground.
A supercritical mine will access a vast
amount of coal. The initial narrow tunnel
will soon widen laterally as it eats the seamaway from between the rocky strata aboveand below it. As it widens, the tunnel willslowly collapse in the middle bysubsidence, giving two tunnels. These will
gradually move apart through the seam,scouring it out as subsidence propels themsideways. The vast coal reserves more than
2.2 km down, too deep for normal mining,
will be accessible at last.
David Jones
The Further Inventions of Daedalus (Oxford
University Press), 148 past Daedalus columns
expanded and illustrated, is now on sale.
Special Nature offer: m.curtis@nature.com

3. Ito, M. Trends Cog. Sci. 2, 313–321 (1998).

© 2000 Macmillan Magazines Ltd

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