The Journal of Neuroscience, 1999, Vol. 19 RC34 1 of 5

Composition and Decomposition of Internal Models in Motor
Learning under Altered Kinematic and Dynamic Environments
J. Randall Flanagan,1 Eri Nakano,2 Hiroshi Imamizu,3 Rieko Osu,3 Toshinori Yoshioka,3 and Mitsuo Kawato2,3
Department of Psychology, Queen’s University, Kingston, Ontario K7L 3N6, Canada, 2ATR International, Kyoto 6190288, Japan, and 3Kawato Dynamic Brain Project, Exploratory Research for Advanced Technology, Japan Science andTechnology Corporation, Kyoto 619-0288, Japan1

The learning process of reaching movements was examined
under novel environments whose kinematic and dynamic properties were altered. We used a kinematic transformation (visuomotor rotation), a dynamic transformation (viscous curl field),
and a combination of these transformations. When the subjects
learned the combined transformation, reaching errors were
smaller if the subject first learned the separate kinematic anddynamic transformations. Reaching errors under the kinematic(but not the dynamic) transformation were smaller if subjects
first learned the combined transformation. These results suggest that the brain learns multiple internal models to compensate for each transformation and has some ability to combine
and decompose these internal models as called for by theoccasion.
Key words: motor learning; reaching; internal model; visuomotor transformation; force fields; arm movement

Most purposef ul actions, including tool use, involve significant
interactions with the environment. The motor commands required to perform such actions depend not only on the kinematics(Lacquaniti et al., 1995) and dynamics (Kalaska et al., 1989) of
the musculoskeletal system but also on the kinematics and dynamics of manipulated tools and the environment. The ability ofhumans to adapt to a range of environments and to easily switch
between familiar environments indicates that the C NS learns andmaintains internal models of the kinematics and dynamics ofdifferent environments.
A fundamental question related to internal models concerns
their granularity. Here the issue is whether C NS uses a small
number of global internal models or whether it maintains a large
number of internal models or modules for different contexts. Fora global internal model to adapt to different sensorimotor contexts, it must learn the properties of tools and environments
whenever they are altered— even if these properties have beenlearned previously. On the other hand, if the C NS uses multiple
internal models, each model could learn the properties of aparticular environment or tool, and there would be less relearning
involved. Moreover, initial learning of tools and environments
may be facilitated by combining stored modules (Ghahramani and
Wolpert, 1997). The recently proposed multiple internal model
hypothesis (Kawato and Wolpert, 1998; Wolpert and Kawato,
1998; Wolpert et al., 1998) argues for motor control and learning
based on such a modular strategy. This model assumes that
separate internal models are learned for different environments
and also permits mixtures of internal models to cope with a single
environment or task.
Several lines of evidence support the multiple internal model

hypothesis. Brashers-Krug et al. (1996) and Shadmehr andBrashers-Krug (1997) examined adaptations to unusual force
fields in reaching movements. They have shown that subjects areable to learn internal models of multiple force fields, and thatthese models can be successfully recalled, with little decrement in
performance, for up to 5 months and probably longer. Previous
work on learning in reaching tasks has demonstrated that humans
are able to adapt to a wide range of visuomotor (MacGonigle andFlook, 1978; Welch, 1986; Welch et al., 1993; Flanagan and Rao,
1995; Imamizu and Shimojo, 1995; Imamizu et al., 1995; Ghahramani and Wolpert, 1997) and dynamic (Shadmehr and MussaIvaldi, 1994; Brashers-Krug et al., 1996; Conditt et al., 1997;
Flanagan and Wing, 1997; Sheidt et al., 1997) transformations.
However, little is known about how the CNS deals with novel
environments in which the kinematic and dynamic properties arealtered simultaneously.
The first goal of the current study was to test the hypothesisthat the CNS can effectively combine previously learned internal
models when encountering a novel environment in which thepreviously learned sensorimotor transformations are simultaneously presented (combined transformation). The second goal
was to test the related hypothesis that the CNS can decompose
the previously learned combined transformation when encountering the separate (and novel) component transformations. To
evaluate these hypotheses, we used visuomotor (660° rotation)

Received July 8, 1999; revised Aug. 18, 1999; accepted Aug. 20, 1999.
This work was supported by the Human Frontier Science Program, the Japan
Science and Technology Agency, and the Natural Sciences and Engineering Research Council of C anada.
Correspondence should be addressed to J. Randall Flanagan, Department of
Psychology, Queen’s University, Kingston, Ontario, Canada K7L 3N6. E-mail:flanagan@psyc.queensu.ca.
Copyright © 1999 Society for Neuroscience 0270-6474/99/190001-•$05.00/0

This article is published in The Journal of Neuroscience, Rapid
Communications Section, which publishes brief, peerreviewed papers online, not in print. Rapid Communications
are posted online approximately one month earlier than theywould appear if printed. They are listed in the Table ofContents of the next open issue of JNeurosci. Cite this article
as: JNeurosci, 1999, 19:RC34 (1–5). The publication date is
the date of posting online at www.jneurosci.org.
http://www.jneurosci.org/cgi/content/full/3586

2 of 5 J. Neurosci., 1999, Vol. 19

and dynamic (viscous curl fields of opposite sign) transformations
either separately or in combination. In the composition experiment, subjects first learned separate visuomotor and dynamictransformations and then the combined transformation. In thedecomposition experiment, the same subjects first learned the
combined transformation and then the separate transformations.
Transformations of opposite sign were used in the two experiments to guard against transfer of learning, and the two experiments were separated by at least 1 week to guard against interference effects (Shadmehr and Brashers-Krug, 1997).
We hypothesized that performance under the combined transformation would be facilitated by previous learning of the separate transformations. This would indicate that subjects are able toeffectively combine the previously learned visuomotor and dynamic internal models. We also hypothesized that performance
under the separate transformations would be facilitated by previous learning of the combined transformation. This would suggestthat the C NS is able to decompose the combined transformation(or an internal model of the combined transformation) into
separate internal models.

MATERIALS AND METHODS
Subjects. Six males and two females, 21–35 years old, participated inthese experiments after giving informed consent. None of the subjects
reported sensorimotor or neurological problems, and all had correct-fornormal vision. All of the subjects were naive with respect to the hypotheses under study, and none had previously experienced the sensorimotortransformations examined.
Apparatus. Subjects sat on a chair, held the tip of a force-reflecting
manipulandum (Gomi and Kawato, 1996) with the right hand and executed reaching movements in the horizontal plane to visually presented
targets. The arm was supported by either a strap from the ceiling or abrace fixed to the manipulandum. The current hand position (a cursor 0.4
cm in diameter) measured by the manipulandum and the target circle (1cm in diameter) were indicated on a large cathode ray tube (CRT) screen
located 1.6 m in front of the subject. The scales of the CRT coordinatesand hand coordinates were the same. The position of the hand and theforces applied by the hand to the manipulandum were sampled at 500 Hz.
The subject performed the task only by looking at the CRT screen; aboard occluded vision of the arm.
Procedure. Subjects were asked to move the cursor quickly and accurately to a series of targets that appeared in succession on the screen.
Each target served as the start position for the next movement. Targets
were randomly positioned within the work space (14 cm in radius) but
were constrained to be 10 cm from the start position. Each new target waspresented for 600 msec and then extinguished. After a short delay, thenext target appeared. Targets were presented in sets of 10. At the start ofeach set the subject positioned the cursor in the center of the work space.
Each subject completed the composition and decomposition experiments at least 1 week apart with the order counterbalanced acrosssubjects. Both experiments consisted of four transformation conditions:normal, visuomotor, dynamic, and combined (visuomotor and dynamic).
The normal condition was included to familiarize subjects with themanipulandum.
In both experiments, subjects first completed 30 sets of 10 trials in thenormal condition. In the composition experiment they then completed 50
sets of trials in the visuomotor and dynamic conditions (counterbalanced
across subjects) followed by 50 sets of trials in the combined condition. In
the decomposition experiment, subjects completed 50 sets of trials in the
combined condition followed by 50 sets in the visuomotor and dynamic
conditions (again counterbalanced across subjects). The subjects took
brief rests between transformation conditions.
The normal, rotational, and viscous transformations are coded N, R,
and B, respectively and the combined transformation is coded R1B.
Superscripts are used to indicate the perturbation direction (see below).
To guard against practice effects across experiments (i.e., weeks), thedirections of the transformations were reversed for each subject. R9 andB9 denote transformations with signs opposite R and B respectively.
Previous work on adaptation to viscous force fields (Shadmehr andBrashers-Krug, 1997) and visuomotor rotations (E. Nakano, unpublisheddata) has revealed that there are no positive or negative transfer effects

Flanagan et al. • Composition and Decomposition of Internal Models

when the direction of the perturbation is reversed and the perturbations
are delivered .24 hr apart. We assumed that R and R9, B and B9, andR1B and R91B9 were equivalent in terms of difficulty.
Transformation rules. In the rotational transformation, the subjects
controlled the position of the cursor (x, y) which corresponded to theposition of the actual hand ( p, q) rotated about the center of the work
space:SD SD S
x
y

p
5R q

5

cosu
sinu

2sinu
cosu

DS D

p
q .

T wo rotation matrices were used: R 1 where u 5 60° and R 2 whereu 5 260°.
For the viscous transformation, we used the same type of viscous curl
force fields used by Shadmehr and Mussa-Ivaldi (1994). The manipulandum produced forces ( fx, fy) on the subject’s hand that were proportion
to the velocity of the hand (ṗ, ṗ):SD SD Sfxṗf y 5 B q̇

5

a
x

x
2a

DS D

ṗ
.
q̇

T wo viscosity matrices we used: B 1 where a 5 13 N z m 21 z sec 21 andB 2 where a 5 213 N z m 21 z sec 21. x was always 213 N z m 21 z sec 21.
Data anal ysis. The position data were digitally filtered using a fourthorder low-pass Butterworth filter with a cutoff frequency of 20 Hz.
Velocities were computed with a three-point local polynomial approximation. The start and end of each movement were defined as the points
at which the curvature of the two-dimensional path of the hand firstexceeded and then subsequently dropped below 3 mm 21, respectively(Imamizu et al., 1995). Defined in this way, the end of the movement
occurs before small corrective movements often observed near the target.
To quantif y trajectory learning, we computed two measures of performance. The target error was defined as the distance between the target
and end positions. This error has previously been used to study adaptation under rotational transformations (Imamizu et al., 1995). The pathdistance was defined as the length or distance traveled by the hand.
Shadmehr and Mussa-Ivaldi (1994) demonstrated that during adaptation
to viscous force fields, hand paths become less and less curved andeventually become approximately straight. Thus, the path distance decreases with learning. The target errors and path distances were averaged
across the 10 trials within each set. Thus, for each measure, we obtained
30 values in the normal condition and 50 values in the rotational, viscous,and combined conditions. In this paper, we focus on the first 30 sets oftrials in each condition.
Repeated measures ANOVAs were used to assess various experimental effects on the two trajectory measures. A significance level of 5% wasconsidered statistically reliable.

RESULTSWe first provide a brief qualitative description of the results using
single-trial data from a single subject and then present the results,
in quantitative form, using data averaged across subjects.

Single-trial data
Hand paths
Examples of hand paths in early ( gray traces) and later (black
traces) stages of learning are shown in Figure 1 for both thecomposition experiment and the decomposition experiment (datafrom subject R.B.). Under the normal transformation, the handpaths were almost straight, and the target errors were small bothin early and late trial sets. In the early stage of learning in thecomposition experiment, large directional errors in the hand path
were observed under the rotational transformation (R 1), andcurved and misdirected hand paths were also seen under viscoustransformation (B 2). Under the combined transformation (R 1 1
B 2), deviations in the hand paths early in learning were generally
small in comparison with the deviations observed in early learning under the previously encountered rotational and viscous transformations. In the early stage of learning in the decomposition
experiment, large deviations in the hand paths were observed
under the combined transformation (R 2 1 B 1). However, theFlanagan et al. • Composition and Decomposition of Internal Models

J. Neurosci., 1999, Vol. 19 3 of 5

Figure 1. Single hand paths measured under each transformation in the composition (top) and decomposition (bottom) experiments. Hand paths are shown for trials performed in the earlystage of learning (1st set; gray traces) and in the late stage oflearning (30th set; black traces). N, R, B, and R1B denote thenormal, rotational, viscous, and combined transformations withsuperscripts indicating the direction of the transformation. The
initial ( x) hand position and target position ( o) are indicated foreach trial. Data are from subject R.B.

Figure 2. Changes in target error and path distance across trial sets under each transformation
for subject R.B. For the normal ( N), rotational( R), and viscous ( B) transformations, the left
sides show data from the composition experiment(Comp.) in which R and B were tested before the
combined transformation (R1B). The right sides
show data from the decomposition (Dec.) experiment in which R9 and B9 were tested after learning R91B9. For the combined transformation, thelef t and right sides show performance without andwith previous learning of the separate transformations, respectively. E xponential functions
have been fit to each set of data (see Results fordetails).

deviations under the rotational (R 2) and viscous (B 1) transformations, encountered after learning the combined transformation, were relatively small. Under all transformations, nearlystraight hand paths were eventually observed after adaptation.

Learning curves
Figure 2 shows, for subject R.B., target errors and path distances
as a function of trial set for each transformation condition. The
left and right sides of each panel show the errors or distances
obtained without and with previous learning of the complementary transformation(s), respectively. Thus, this subject experienced R and B before R1B (composition experiment) but experienced R9 and B9 after R91B9 (decomposition experiment). For
the normal transformation, the lef t and right sides of the panels
show data obtained in the composition and decomposition experiments, respectively. For illustrative purposes, exponentials of theform k0 1 k1 * exp (2k2 * n), where n denotes the set number andki denotes a constant coefficient, were fit to each set of data.
For this subject, performance under the separate rotational(R9) and viscous (B9) transformations was clearly facilitated byprevious learning of the combined (R91B9) transformation. Sim-ilarly, performance under the combined transformation (R1B)
was facilitated by previous learning of the two separate transformations (R and B). However, transfer of learning was not perfect.
Whereas the initial target errors and path distances were smaller
after previous learning of the complementary transformation(s),they also tended to be greater than the errors and distances
observed at the end of the previous learning.

Averaged data
To characterize performance under each transformation condition, we first computed subject averages, for both target error andpath distance, over the first 10 sets of trials and over sets 21–30.
Thus, we characterized the initial performance under each transformation as well as later performance. We then computed means
and SDs based on the subject averages. Figure 3 shows, for eachtransformation, the mean target errors and path distances during
both early learning (circles) and later performance (squares). The
errors observed with ( filled symbols) and without (open symbols)
previous learning of the complementary transformation(s) are
joined by lines. The stars indicate a reliable difference ( p , 0.05)

4 of 5 J. Neurosci., 1999, Vol. 19

Flanagan et al. • Composition and Decomposition of Internal Models

learning than without (see Fig. 3, Composition benefit). However,
the mean path distances with and without previous learning were
not reliably different (F(1,7) 5 0.81; p 5 0.40). These results
indicate that performance in the combined transformation condition was facilitated by previous learning of the separate visuomotor and viscous transformations. This improvement in performance was reliably observed in the target error.

Transfer of learning in decomposition
To test the decomposition hypothesis, we compared initial performance under the separate transformations with and without
previous learning of the combined transformation. We will firstconsider the rotation transformation. The mean path distance wassignificantly smaller with previous learning than without (F(1,7) 5
8.67; p 5 0.02). Similarly, the mean target error with previous
learning was reliably smaller than without previous learning(F(1,7) 5 6.24; p 5 0.04). Thus, for the visuomotor transformation
condition, the results clearly indicate that previous learning of the
combined transformation facilitated performance (see Fig. 3,
Decomposition benefit). In contrast, such transfer of learning was
not observed under the viscous transformation. Reliable effects ofprevious learning of the combined transformation were not observed on mean initial path distance (F(1,7) 5 1.22; p 5 0.31) ormean initial target error (F(1,7) 5 0.15; p 5 0.71).
Figure 3. Mean target errors (top) and path distances (bottom) duringinitial learning (circles) and later performance (squares) under each of thefour transformation conditions. For the rotational and viscous transformations, the closed and open symbols represent performance with andwithout prior learning of the combined transformation. For the combinedtransformation, the filled and open symbols represent performance withand without prior learning of the separate rotational and viscous transformations. Error bars represent SDs. Stars indicate a statistically significant difference between pairs of transformations with and without priorlearning.

between pairs of transformations (with and without previous
learning), and the error bars represent SDs.
Figure 3 reveals that hand trajectories were clearly alteredduring initial learning by the visuomotor, dynamic, and combinedtransformations. Without previous learning of the complementary transformations (open circles), both targets errors (F(1,7) 539.1; p , 0.001) and path distances (F(1,7) 5 60.2; p , 0.001) werereliably greater under the rotational, viscous, and combinedtransformations (grouped together) than under the normal transformation. Even with previous learning of the complementarytransformations ( filled circles), initial target errors (F(1,7) 5 28.9;
p 5 0.001) and path distances (F(1,7) 5 16.4; p 5 0.005) werereliably greater under the rotational, viscous, and combinedtransformations than under the normal transformation. Overall,initial performance under the non-normal transformations was
better with previous learning (open circles) than without ( filled
circles) both in terms of target error (F(1,7) 5 17.4; p 5 0.004) andpath distance (F(1,7) 5 17.0; p 5 0.004).

Transfer of learning in composition
To assess the composition hypothesis, we compared initial performance under the combined transformation with and without
previous learning of the separate transformations. If previous
learning of the separate transformations facilitates performance
under the combined condition, then the initial performance
should be better than that observed without previous learning.
Repeated measures ANOVA revealed that the mean target error
was significantly smaller (F(1,7) 5 9.05; p 5 0.02) with previous

Order effects
We used viscous force fields and visuomotor rotations of opposite
signs to guard against practice effects across experiments (i.e.,
weeks). Nevertheless, to assess possible effects of practice, we
compared the performance between the second and third transformations in the composition experiment and between the thirdand fourth transformations in the decomposition experiment.
Thus, only the rotation and viscous transformations were considered. In both experiments, half the subjects received the rotationtransformation followed by the viscous transformation, and theother half received the transformations in the opposite order.
Therefore, we were able to assess the effects of order while
counterbalancing across the two types of transformation. Repeated measures ANOVAs were used to assess the effects oforder on target error and path distance in both experiments. Thus
four separate ANOVAs were performed, two for each experiment. No reliable effects of order were observed ( p . 0.20 in allcases). Thus, performance under the second transformation(third or fourth) was not reliably different from performance
under the first (second or third).

DISCUSSION
The present study tested two general hypotheses concerninginternal models of sensorimotor transformations. The composition hypothesis holds that the CNS can effectively combine internal models of two previously learned sensorimotor transformations when dealing with a novel environment in which bothtransformations are present. The decomposition hypothesis holds
that, when encountering a complex environment featuring morethan one sensorimotor transformation, the CNS can effectively
decompose the environment into separate internal models appropriate for the separate transformations.
We found clear support for the composition hypothesis. Movement performance in the combined transformation was superior
if subjects had previously learned the separate transformations. In
particular, target errors were smaller under the combined transformation after exposure to the separate rotational and viscousFlanagan et al. • Composition and Decomposition of Internal Models

transformations. However, transfer of learning to the combinedtransformation was not total. Even if two internal models for the
separate transformations were already perfectly learned in two
anatomically distinct sites in the brain, it is not at all trivial to findthe cascade of these two that can resolve the newly given composition task and to establish f unctional neural connections between the two. Thus, total transfer of learning should not necessarily be expected.
We also found partial support for the decomposition hypothesis. We observed that performance under the rotational transformation was clearly facilitated by previous learning of the combined transformation. Both target errors and path distances werereduced when subjects had previously been exposed to the combined transformation. However, we did not observe a significant
facilitation of performance under the viscous transformation attributable to previous learning of the combined transformation.
Thus, although subjects appeared to be able to learn and thenrecall the visuomotor rotation component of the combined transformation, they were not able to learn and /or recall the dynamic
component of the same transformation.
It is not clear to us why learning of the combined transformation should only have transferred to the visuomotor transformation. However, one possible explanation is that, when learning the
combined transformation, the subject may have adapted primarily
to the visuomotor rotation because of the large target errors
initially caused by this transformation. Note that when subjects
experienced the separate rotational and viscous transformations
before learning the combined transformation, target errors weremuch larger under the rotational transformation. It stands toreason, therefore, that the best way to reduce target errors under
the combined transformation would be to focus on learning thevisuomotor component. The subjects in our experiment experienced 50 sets of 10 trials under the combined transformation fora total of 500 movements. By the end of this period, errors levels
flattened out (Fig. 2) and approached baseline levels (Fig. 3).
Thus, it does not seem likely that f urther training under the
combined transformaton would have led to decreased errors
under the subsequent viscous transformation.
There are two ways in which subjects might acquire internal
models of components of a combined transformation. One possibility is that internal models of the separate transformations (e.g.,
visuomotor and viscous) are acquired simultaneously during adaptation to the combined transformation. Ghahramani and Wolpert(1997) have recently proposed such a mechanism. These authors
argued that a complex visuomotor task can be divided into simpler
subtasks, each learned by a separate module in the brain. Anotherpossibility is that the CNS learns a single internal model of the
combined transformation and only later decomposes it into its
component parts when required. The present results do not enable
us to distinguish between these two alternatives, and further modeling efforts will be required to assess their relative advantages.
Overall, the results of this study are consistent with the generalhypothesis that the CNS maintains multiple internal models ofdifferent environments or sensorimotor transformations. First,
the lack of interference effects between the visuomotor anddynamic transformations (i.e., the absence of order effects) suggests that the C NS learned and maintained distinct internal
models for these two transformations. If the C NS used a single orglobal internal model for both the visuomotor and dynamictransformation, learning of one transformation should interferewith subsequent learning of the other. Further support for thisview comes from the finding that subjects could successfully inte-

J. Neurosci., 1999, Vol. 19 5 of 5

grate previously acquired knowledge of the two separate transformations when faced with a novel, combined transformation.
Support for the multiple internal models hypothesis has recently been provided by imaging studies. Shadmehr and Holcomb(1997) have shown that consolidation of learned internal models
in memory involves changes in ipsilateral anterior cerebellar
cortex. Imamizu et al. (1998) demonstrated that neural activity
can be observed in different parts of the cerebellum corresponding to different kinematic transformations after learning. The
authors suggested that the different regions of activation correspond to distinct internal models for the different kinematictransformations. The present results suggest that the notion ofmultiple internal models can be extended to different classes oftransformations, namely, dynamic and kinematic transformations.

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