Lecture Notes in Computer Science

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Fig. 4. Variation of the mean errors(J

and J

) and AIC values: (a)mean error J

; (b) mean error

; (c) AIC values

-50

Layer

AIC

ooo

(c)

Nonlinear Pattern Identification by Multi-layered GMDH-Type Neural Network

889

Table 1. Errors of GMDH-type neural network and the GMDH

Estimation Error

Prediction Error

Data Actual GMDH-NN GMDH

No. value (Error) (Error)

Data Actual GMDH-NN GMDH

No. value (Error) (Error)

1 0.1 0.0000 -0.0069 9

0.9 -0.0069 -0.1533

0.9 -0.0020 -0.0127

0.9 0.0011 0.0832

0.1 0.0000 -0.0067

11 0.1 0.0001 0.0212

0.9 0.0012 0.0842 12 0.9 -0.0057

-0.2594

0.1 0.0002 0.0513

0.1 0.0000

-0.0068

0.1 0.0000 -0.0069

0.1 0.0000 -0.0068

0.9

0.0007

-0.0955

0.1

0.0000 -0.0059

0.1

0.0000

-0.0067

0.1

0.0000 -0.0069

Maximum Error -0.0020 -0.0955 Maximum Error -0.0069 -0.2595

1

(Mean Error)

0.0005 0.0339 J

(Mean Error) 0.0017 0.0679

Prediction Accuracy. The prediction accuracy was evaluated by using the following

equation.

∑

−

i

i

i

J

(21)

where

(i=9,10,…,16) were the actual values at the prediction points and

(i=9,10,…,16) were the predicted values of

i

by the GMDH-type neural network.

Figure 4(b) shows the variation of J

in each layer. From this figure, we can see that

the values of J

were decreased gradually and converged at the tenth layer. The predic-

tion error obtained by the GMDH-type neural network is shown in Table 1. From this

table, the maximum prediction error is -0.0069 and so we can see that the prediction

errors are very small and the GMDH-type neural network has good generalization

ability.

4.2 Identification Results Obtained Using the GMDH

The same input variables as the GMDH-type neural network, which are the x, y and z

co-ordinates, are used. The number of input variables is three. Three intermediate

variables are selected in each layer. The optimum partial polynomials are automati-

cally selected using the prediction error criterion defined as AIC. The calculation of

the GMDH was terminated in the tenth layer. The estimation accuracy was evaluated

by Eq.(20). The variation of J

in each layer is shown in Fig.4(a). The estimation

errors obtained using GMDH are shown in Table 1. The prediction accuracy was

evaluated by using Eq.(21). The variation of J

in each layer is shown in Fig 4(b). The

prediction errors obtained by the GMDH is shown in Table 1. We can see that the

estimation and prediction errors are greater than those of the GMDH-type neural

network.

4.3 Identification Results Obtained Using the Conventional Neural Network

The nonlinear pattern was identified by using the conventional neural network. The

x, y and z co-ordinates are used as the input variables of the conventional neural

890 T.

Kondo

network. The number of input variables is three. The neural network has three layered

architecture. The conventional neural network has not the ability of self-selecting

optimum neural network architecture. The numbers of the neurons in the hidden layer

were set to 5, 10, 15 and 20. The identification accuracy was checked for each neural

network architectures. The weights of the neural network are learned using the back

propagation algorithm. The learning of the weights are repeated 10,000 times per each

point. The estimation accuracy was evaluated by using Eq.(20) and shown in Table 2.The

prediction accuracy was evaluated by using Eq.(21) and shown in Table 2.

Table 2. Estimation and prediction accuracy of the conventional neural network

Mean Error Number of neurons in hidden layer

5 10 15 20

0.0118 0.0118 0.0118 0.0133

0.0358 0.0385 0.0435 0.0444

4.4 Companion of the Identification Results

In both the GMDH-type neural network and the GMDH algorithm, the estimation and

prediction errors were decreased gradually and converged at the tenth layer. Table 3

shows the comparison between the GMDH-type neural network, the GMDH and the

conventional neural network in the estimation and prediction accuracy. The GMDH-

type neural network is most accurate in three networks both the estimation and predic-

tion accuracy and the maximum values of the estimation and prediction errors of the

GMDH-type neural network are very small compared with the GMDH and the con-

ventional neural network. So we can see that the GMDH-type neural network is very

accurate identification method and they have a good generalization ability.

Table 3. Comparison of the GMDH-type neural network, the GMDH and the conventional

neural network

Error GMDH-NN GMDH NN

Estimation J

(Mean Error) 0.0005 0.0339 0.0118

Maximum Error -0.0020 -0.0955 -0.0258

Prediction J

(Mean Error) 0.0017 0.0679 0.0358

Maximum Error -0.0069 -0.2595 -0.0751

5 Conclusion

The GMDH-type neural network can automatically organize the optimal neural net-

work architecture using the heuristic self-organization method. The optimum neural

network architectures is automatically organized using the neurons whose architec-

tures are selected from three kinds of neuron architectures so as to minimize AIC.

Therefore, it is very easy to apply this algorithm to the identification problems of the

practical complex systems.

Nonlinear Pattern Identification by Multi-layered GMDH-Type Neural Network

891

In this paper, the GMDH neural network was applied to the identification problem

of the nonlinear pattern. The GMDH-type neural network was compared with the

GMDH and the conventional neural network. It was shown that the GMDH-type

neural network was accurate and very useful for the nonlinear pattern identification.

References

1. Farlow, S.J. (ed.): Self-organizing Methods in Modeling, GMDH-type Algorithms. Marcel

Dekker, Inc., New York (1984)

2. Ivakhnenko, A.G.: Heuristic self-organization in problems of engineering cybernetics.

Automatica 6(2), 207–219 (1970)

3. Kondo, T., Pandya, A.S., Zurada, J.M.: GMDH-type Neural Networks and their Application

to the Medical Image Recognition of the lungs. In: Proceedings of the 38th SICE Annual

Conference International Session Papers, pp. 1181–1186 (1999)

4. Kondo, T., Pandya, A.S.: GMDH-type Neural Networks with Radial Basis Functions and

their Application to Medical Image Recognition of the Brain. In: Proceedings of the 39th

SICE Annual Conference International Session Papers, vol. 331A-2, pp. 1–6 (2000)

5. Akaike, H.: A new look at the statistical model identification. IEEE Trans. Automatic Con-

trol AC-19(6), 716–723 (1974)

6. Tamura, H., Kondo, T.: Heuristics free group method of data handling algorithm of generat-

ing optimal partial polynomials with application to air pollution prediction. INT. J. SYS-

TEMS SCI. 11(9), 1095–1111 (1980)

7. Draper, N.R., Smith, H.: Applied Regression Analysis. John Wiley and Sons, New York

(1981)

Coordinated Control of Reaching and Grasping

During Prehension Movement

Masazumi Katayama and Hirokazu Katayama

Department of Human and Artiﬁcial Intelligent Systems,

University of Fukui, Japan

katayama@h.his.fukui-u.ac.jp

Abstract. In this paper, we investigate coordinated control of human

reaching and grasping during the prehension movements. The interac-

tion between reaching and grasping has been investigated by using vi-

sual perturbations that unexpectedly change size or position of an object

when executing the movement. Those studies have reported that both

of reaching and grasping interact each other. However, the interaction

may include some properties in visual information processing for physical

properties of an target object. Thus, the interaction should be examined

without the visual perturbations because the detail of the interaction

between reaching and grasping is still unclear. From this point of view,

the inﬂuence from reaching to grasping have been directly investigated

by using mechanical perturbations. While, the inﬂuence from grasping to

reaching have never been examined. In this study, we examined the inﬂu-

ence that grasping aﬀects reaching by giving mechanical perturbations

to the ﬁnger tips during the movement. As a result, we found that hu-

mans adjust the speed of reaching based on the changes in grasping per-

turbed by the mechanical perturbations. Moreover, both the movement

times of grasping and reaching are highly correlated even when grasp-

ing was perturbed by the perturbations. Consequently, we conﬁrmed the

temporally-coordinated adjustment from grasping to reaching during the

prehension movement. This result indicates that the previously proposed

control schemes can not explain our ﬁndings. This ﬁnding is quite im-

portant for building a computational model of the coordinated control

of human reaching and grasping.

Keywords: Human Coordinated Control, Reaching, Grasping, Prehen-

sion Movement.

Introduction

We skillfully manipulate various tools with our own arm and hand in daily life.

In the arm and hand movements, the prehension movement when reaching out

a hand to an object plays an important role in order to achieve skillful object

manipulation. From this point of view, a lot of researchers have investigated for

coordinated control mechanisms between reaching and grasping during the move-

ment. For example, Jeannerod [1] observed “preshaping” from the viewpoint in

M. Ishikawa et al. (Eds.): ICONIP 2007, Part I, LNCS 4984, pp. 892–901, 2008.

c Springer-Verlag Berlin Heidelberg 2008

Coordinated Control of Reaching and Grasping

893

behavioral psychology, that we gradually generate a hand shape to grasp before

our hand reaches a target object. From this observation, Arbib [2] have proposed

a control scheme which explains the preshaping. The scheme makes the basic as-

sumptions that each control of reaching and grasping is executed independently

and in parallel, and also the synchronization signal to start grasping an object is

sent from the control system of reaching to the control system of grasping. The

biological plausibility of the scheme have been investigated by abruptly changing

position or size of an object, that is a visual perturbation (e.g., [3,4,5,6,7,8,9]).

For instance, Paulignan et al. [3] and Gentilucci et al. [4] examined the inﬂu-

ence from reaching to grasping by unexpectedly changing object position. They

have reported that the changing aﬀects drastically not only reaching but also

grasping during the movement, and grasping temporally and spatially changes

depending on changes in reaching. On the other hand, Paulignan et al. [5] exam-

ined the inﬂuence from grasping to reaching by unexpectedly changing object

size when executing the movement. They have reported that the unpredictable

perturbation aﬀects reaching.

As a consequence, for the prehension movement, reaching aﬀects largely grasp-

ing and grasping aﬀects also reaching slightly. Therefore, although the Arbib’s

scheme seems to be plausible, strictly speaking, these results reject the Arbib’s

hypothesis. However, some researchers have reported that the inﬂuence from

grasping to reaching during the movement is negligible small. Thus, the inﬂu-

ence from grasping to reaching is quite diﬀerent for each measurement condition.

These complicated results indicate that it is really diﬃcult to generate pure vi-

sual perturbations that directly aﬀect one control mechanism and that do not

aﬀect the other, by using the visual perturbations. This is because these results

include the inﬂuence of the visual information processing for object size that is

unexpectedly changed when executing the movement. Thus, these studies with

visual perturbations did not investigate directly the coordinated control mecha-

nism of grasping and reaching during the movement. The detail of the inﬂuence

remains to be still unclear. Therefore, we emphasize that the coordinated control

mechanism should be investigated directly without visual manipulation.

From the above points of view, Haggard and Wing [10] examined the inﬂu-

ence from reaching to grasping by giving mechanical perturbations to subject’s

arm when executing the prehension movement. They have reported that pull-

perturbations produce temporal reversals of grip aperture. These results clearly

show that there is a temporal and spacial inﬂuence from reaching to grasping.

However, the inﬂuence from grasping to reaching have never been investigated by

using physical perturbations. Therefore, in this study, we investigate directly the

inﬂuence by giving mechanical perturbations to the ﬁnger tips when executing

the movement.

Measurement Experiments

Five right-handed subjects (males, 22 - 24 years old) participated in the present

experiments. They were completely naive with regard to its speciﬁc purpose.

894

M. Katayama and H. Katayama

PHANToM

OPTOTRAK

Marker

Object

Fig. 1. Experimental environment

PHANToM1

PHANToM2

Object

Start position

30[cm]

10[cm]

15[cm]

20[cm]

25[cm]

Fig. 2. Each position of mechanical

perturbations given to the ﬁnger tips

Before measurement experiments, we instructed the subjects to give unpre-

dictable perturbations to both the ﬁnger tips when executing the movement.

They were given informed consent to the current experiment.

In order to give mechanical perturbations to both the ﬁnger tips of thumb and

index ﬁnger when executing the prehension movement, we built a measurement

system that examines the inﬂuence from grasping to reaching (see Fig. 1). This

measurement system consists of two haptic interface devices (PHANToM 151AG,

SensAble Technologies Inc.) and a three dimensional motion measurement device

(OPTOTRAK 3020, Northern Digital Inc.).

A movement task in this study was to reach toward an object, to grasp it and

to lift up it. The movement distance was 30 [cm] as shown in Fig. 2. The target

object to grasp was a cylinder that is placed at the position of 30 [cm] from the

start position. The height of the object was 10 [cm] and the diameter is 3.3 [cm].

Each subject was seated in a dark room. Each gimbal of two haptic interface

devices was attached to each ﬁnger tip and an infrared maker of the motion mea-

surement device was attached to subject’s wrist joint. The haptic interface devices

was used to give mechanical perturbations to both the ﬁnger tips when executing

the prehension movement and moreover were used to measure movement trajecto-

ries of both the ﬁnger tips at sampling frequency 1[kHz]. The motion measurement

device was used to measure wrist-joint trajectories at 500 [Hz].

The mechanical perturbations given to the ﬁnger tips were selected so as to

reduce the inﬂuence that the perturbation directly aﬀects reaching movements,

by testing various amplitudes and directions of external force as a perturbation.

The amplitude was 2 [N], the duration was for 0.1 [sec] and these perturbations

were given at each position of 10, 15, 20 or 25 [cm] from the start position at

random and at a rate of 30 [%] of the total trials . Moreover, the direction of

the perturbations were two types that grip aperture of the ﬁnger tips opened or

Coordinated Control of Reaching and Grasping

895

closed. In this experiment, 400 trials were measured and the perturbations were

given for 120 trials within the whole trials.

The prehension movements were measured under the two conditions:

Normal condition. Subjects perform the above task.

Without grasping. Subjects only reach to the position of the object and do

not grasp the object. The objective of this condition is to examine the inﬂu-

ence that the perturbations may directly aﬀect reaching.

Subject repeated the task for ten minutes so as to execute the movements

at almost constant movement time before the measurement experiment. The

measurement procedure was as follows:

1. The right hand of subject was placed at the start position in front of the

body.

2. After a beep, subject started the movement task. After the object was lifted

up, the subject maintained his arm posture.

3. After a beep, the right hand was returned to the start position again.

Results

3.1

Movement Time of Grasping and Reaching

Measured data were ﬁltered with a second-order Butterworth dual pass ﬁlter

(cutoﬀ frequency: 15 [Hz]). A few data out of

±3σ and the few trials that failed

to grasp the object were excepted in the below analysis. We show the typical

results or the average of all subjects below because the results of all subjects

have similar characteristics,

Figs. 3(a) and 3(b) show the paths of the ﬁnger tips of thumb and index ﬁn-

ger and the paths of wrist-joint, respectively. Figs. 3(c) and 3(d) show the grip

aperture that is the distance between both the ﬁnger tips and the velocity of

wrist-joint trajectory, respectively. In these ﬁgures, N expresses the condition of

unperturbed trials. C

and O

express the types of the perturbation that grip

aperture closes or opens, respectively. i expresses each position of the pertur-

bations: 1, 2, 3 and 4 correspond to 10, 15, 20 and 25 [cm], respectively (see

Fig. 2). In the below analysis, we deﬁned each movement time of grasping and

reaching. The start time of grasping is when tangential velocity of the center

between the ﬁnger tips becomes larger than a threshold, 0.01 [m/sec], and the

ﬁnish time is when the rate of grip aperture becomes smaller than 0.05 [m/sec].

For the condition without grasping, the ﬁnish time is when the center position

of the ﬁnger tips reaches to the target object. For reaching, the start time is the

same as timing of grasping and the ﬁnish time is when the velocity of wrist-joint

becomes smaller than 0.01 [m/sec].

Grasping movements. Each spatial path of the ﬁnger tips is drastically per-

turbed by the external forces, as shown in Fig. 3(a). For the unperturbed case

(solid line) of Fig. 3(c), the grip aperture increases gradually from about 0.2

896

M. Katayama and H. Katayama

-0.2

-0.15

-0.1

-0.05

0.05

0.1

0.15

0.2

-0.2 -0.15 -0.1 -0.05

0.05 0.1 0.15 0.2

y [m]

x [m]

C1

O1

(a) Paths of the ﬁnger tips

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0.05

0.1

-0.2 -0.15 -0.1 -0.05

0.05 0.1 0.15 0.2

y [m]

x [m]

C1

O1

(b) Paths of the wrist joint

0.02

0.04

0.06

0.08

0.1

0.12

0.2

0.4

0.6

0.8

1.2

1.4

Grip aperture [m]

Time [sec]

-0.2

0

0.2

0.4

0.6

0.8

0.2

0.4

0.6

0.8

1.2

1.4

Wrist velocity [m/sec]

Time [sec]

(d) Velocity of reaching (wrist-joint)

Fig. 3. Paths and trajectories of reaching and grasping when perturbing to the ﬁnger

tips for a typical subject (TA) for the normal condition (solid line: average of unper-

turbed trails, the other lines: average of perturbed trails at each condition)

[sec] after movement onset and becomes the maximum value at about 0.5 [sec].

The grasping movements ﬁnish at about 0.8 [sec]. For the perturbed cases (dot-

ted and dashed lines) of Fig. 3(c), although the grip apertures are drastically

increased or decreased by the external forces, the perturbed movements tend to

return to the same proﬁle as the unperturbed proﬁle except for the conditions

of C

i

. The ﬁnish time of grasping for C

lags behind the other conditions and

especially grip aperture of C

changes drastically.

The movement times of grasping are shown in Fig. 4(a). The movement times

of grasping perturbed by the external forces of O

are almost the same as those

of unperturbed grasping. While, the movement times for C

change in the latter

half of the movement and especially the movement times of C

and C

for all

the subjects are signiﬁcantly diﬀerent with respect to the control group (N).

Reaching movements. The spatial paths of the wrist joint under all the con-

ditions are almost straight, and these paths are invariant, as shown in Fig. 3(b).

It seems that reaching is not aﬀected by the perturbations because their pro-

ﬁles are almost invariant even when the ﬁnger tips are perturbed. These results

indicate that the Arbib’s hypothesis may be plausible. However, as shown in

Fig. 3(d), the velocities are slightly diﬀerent for each condition at the latter half

Coordinated Control of Reaching and Grasping

897

0.6

0.8

1.2

1.4

Movement time [sec]

Measurement conditions

(a) Grasping

0.6

0.8

1.2

1.4

Movement time [sec]

Measurement conditions

(b) Reaching

Fig. 4. Averaged movement times in the normal condition for all subjects (Dunnet

multiple comparison with respect to the control group (N), **: p < 0.01, *: 0.01

≤

p < 0.05, ns: not signiﬁcant, and vertical bars express standard deviation of movement

times)

Table 1. Averaged movement times in the normal condition for all subjects. Upper

values are movement times [sec], middle values are standard deviations [sec], bottom

descriptions are the results of Dunnet multiple comparison with respect to the control

group, N, (**: p < 0.01, *: 0.01

≤ p < 0.05, ns: not signiﬁcant).

Conditions

Grasping 0.811 0.829 0.833 0.847 0.809 0.859 0.815 0.934 0.826

0.111 0.130 0.123 0.127 0.113 0.118 0.122 0.124 0.127

—–

ns

ns

Reaching 0.862 0.877 0.889 0.897 0.860 0.904 0.861 0.999 0.876

0.131 0.146 0.138 0.147 0.127 0.145 0.141 0.153 0.144

—–

ns

ns

of movement. The ﬁnish time of reaching for C

lags behind the other condi-

tions and especially the velocity of C

changes drastically. Therefore, perturbed

grasping may aﬀect reaching during the prehension movement.

Fig. 4(b) shows the movement times of reaching for each condition. The move-

ment times of O

are not signiﬁcantly diﬀerent with respect to those of N. Reach-

ing for C

changes in the latter half of the movement as shown in Figs. 3(d),

and especially the movement times of C

and C

for all subjects are signiﬁcantly

diﬀerent with respect to the control group (N).

Relationship between grasping and reaching. As described in the above

sections, both the movement times of grasping and reaching have the similar

characteristics. Fig. 5 shows a relationship between both the movement times

for all the conditions. Moreover, Table 2 shows the correlation coeﬃcients be-

tween both the movement times. Both the movement times are highly correlated.

These results show that the movement time of reaching is accurately adjusted

depending on the changes in the movement time of grasping. Thus, in human

motor control for reaching and grasping, there is a temporal coordination from

898

M. Katayama and H. Katayama

0.7

0.8

0.9

1.0

1.1

0.7

0.8

0.9

1.0

1.1

Movement time of reaching [sec]

Movement time of grasping [sec]

(a) A typical subject (TA)

0.4

0.6

0.8

1.0

1.2

1.4

0.4

0.6

0.8

1.0

1.2

1.4

Movement time of reaching [sec]

Movement time of grasping [sec]

(b) All subjects

Fig. 5. Linear relation between both the movement times of grasping and reaching

Table 2. Correlation coeﬃcient between both the movement times of grasping and

reaching

Subjects

Average

Correlation coeﬃcients

0.86

0.92

0.82

0.83

0. 87

grasping to reaching. This ﬁnding is really important because computational

models proposed previously do not include the adjustment.

3.2

Reaching without Grasping an Object

As described in Section 2, the mechanical perturbations given to the ﬁnger tips

might directly cause the changes of the movement times of reaching. In this

experiment, the perturbations were selected so as to reduce the inﬂuence that

the perturbation directly aﬀects the motor behavior of reaching. Moreover, in

order to conﬁrm whether the inﬂuence is negligible small or not, we measured

the movement times for reaching without grasping although the perturbations

are given to the ﬁnger tips at the same conditions as the above experiments. If

the perturbations directly aﬀect motor behavior of reaching, the movement time

of reaching should be changed even in this condition without grasping.

Figs. 6(a) and 6(b) show the grip aperture that is the distance between both

the ﬁnger tips and the velocity of wrist-joint trajectory, respectively. Although

these perturbed grip apertures change drastically, the velocities of wrist-joint

are almost invariant for all the conditions. The movement times for all subjects

are shown in Fig. 7. As a result, the inﬂuence is negligible small because all

the movement times of each condition are not signiﬁcantly diﬀerent. Thus, we

ascertained that the mechanical perturbations given to the ﬁnger tips do not

cause directly the changes of the movement times of reaching. Here, we would like

to emphasize again that the movement-time adjustment of reaching described

in the above sections is performed by a coordinated control mechanism for the

prehension movement.

Coordinated Control of Reaching and Grasping

899

0.02

0.04

0.06

0.08

0.1

0.12

0.2

0.4

0.6

0.8

1.2

1.4

Grip aperture [m]

Time [sec]

(a) Grip apertures

-0.2

0

0.2

0.4

0.6

0.8

0.2

0.4

0.6

0.8

1.2

1.4

Wrist velocity [m/sec]

Time [sec]

(b) Velocity of reaching (wrist-joint)

Fig. 6. Paths and trajectories of reaching and grasping for a typical subject (TA)

without grasping an object (solid line: average of unperturbed trails, the other lines:

average of perturbed trails at each condition)

0.4

0.6

0.8

1.2

Movement time [sec]

Measurement conditions

ns

ns

(a) Grasping

0.4

0.6

0.8

1.2

Movement time [sec]

Measurement conditions

ns

ns

(b) Reaching

Fig. 7. Movement times of grasping and reaching for all subjects without grasping an

object (Dunnet multiple comparison with respect to the control group (N), ns: not

signiﬁcant, and vertical bars express standard deviation of movement times)

Table 3. Averaged movement times of reaching for all subjects without grasping an

object (upper values are movement times [sec], middle values are standard deviations

[sec], bottom descriptions are the results of Dunnet multiple comparison with respect

to the control group (N), ns: not signiﬁcant)

Conditions

C

1

Grasping

0.693 0.703 0.657 0.681 0.676 0.703 0.684 0.708 0.688

0.193 0.187 0.184 0.194 0.200 0.192 0.177 0.203 0.191

—–

ns

ns

Reaching

0.777 0.787 0.744 0.765 0.768 0.792 0.783 0.795 0.785

0.146 0.134 0.133 0.137 0.155 0.151 0.146 0.169 0.155

—–

900

M. Katayama and H. Katayama

Discussion

4.1

Coordinated Mechanism between Reaching and Grasping

Haggard et al. [10] examined the detail of the inﬂuence from reaching to grasping

by giving mechanical perturbations to subject’s arm when executing the prehen-

sion movements. These results clearly show that grasping is skillfully adjusted

depending on reaching. In this study, by using mechanical perturbations to the

ﬁnger tips when executing the movement, we directly investigated the inﬂuence

from grasping to reaching. As a result, we found the temporal adjustment that

the movement time of reaching is accurately adjusted so as to ﬁt to the timing

when grasping ﬁnishes because both of the movement times are highly correlated.

There are two possibilities to explain the temporal adjustment: automatic

adjustment such as a spinal reﬂex and voluntary adjustment with a trans-cortical

loop. Moreover, the adjustment may be aﬀected by learning eﬀect through the

iterative trials of the movement task. In this experiment, it seems that there

is no remarkable learning eﬀect, although the variance of the movements in the

beginning of the trials are relatively large. However, there were some failure trials

in grasping for only C

, although there was no failure for O

. It seems that the

lengthened duration of movement time of reaching depends on the number of the

trials that subject failed to grasp the object. From this observation, the temporal

adjustment may be caused by voluntary adjustment and/or its learning. Thus,

there is a possibility that in the human brain the movement time of reaching

is planned by an internal simulation of the movement that grasps an object.

Moreover, the movement time of reaching may be adjusted automatically. The

adjustment can be investigated by detecting the duration between the timing

of the perturbation and the time when reaching is adjusted. From this point of

view, we would like to investigate the temporal adjustment mechanism.

4.2

Biological Plausibility of Computational Models

From computational point of view, computational models that explain the coor-

dinated control mechanism between reaching and grasping during the prehension

movement have been proposed [10,11,12]. For example, Haggard et al. [10] have

proposed a simple computational model with automatic adjustment that reach-

ing and grasping are coupled strongly . Moreover, base on the Arbib’s scheme,

Hoﬀ and Arbib [11] have built a computational model that independently calcu-

lated each trajectory of reaching and grasping and the Hoﬀ-Arbib model explains

motor behavior for unpredictable changing of object position and size and for the

speed-accuracy trade-oﬀ. Bullock et al. have proposed a computational model

based on the VITE model (see [12]). However, those computational models are

not plausible biologically because those models do not include the temporal ad-

justment that grasping aﬀects reaching during the movement. Therefore, those

computational models should be extended so as to explain the temporal adjust-

ment we found.

Coordinated Control of Reaching and Grasping

901

Conclusion

In this paper, by giving the mechanical perturbations to the ﬁnger tips when

executing the prehension movement, we examined the inﬂuence from grasping to

reaching in order to investigate the coordinated control system of human reaching

and grasping movements. As a result, we found the temporal adjustment that the

movement time of reaching is accurately adjusted so as to ﬁt to the timing when

grasping ﬁnishes because both of the movement times are highly correlated. This

ﬁnding is really important for building a computational model of coordinated

control of human reaching and grasping.

References

1. Jeannerod, M.: Intersegmental coordination during reaching at natural visual ob-

jects. In: Long, J., Baddeley, A. (eds.) Attention and Performance IX, pp. 153–168.

ErIbaum, Hillsdale, Nj (1981)

2. Arbib, M., Iberall, T., Lyons, D.: Coodinated control programs for control of the

hands. Experimental Brain Research, Supplement 10, 111–129 (1985)

3. Paulignan, Y., MacKenzie, C.L., Marteniuk, R.G., Jeannerod, M.: Selective per-

turbation of visual input during prehension movements. 1. the eﬀects of changing

object position. Experimental Brain Research 83, 502–512 (1991)

4. Gentilucci, M., Chieﬃ, S., Scarpa, M., Castiello, U.: Temporal coupling between

transport grasp components during prehension movements: Eﬀects of visual per-

turbation. Behavioural Brain Research 47, 71–82 (1992)

5. Paulignan, Y., Jeannerod, M., MacKenzie, C.L., Marteniuk, R.G.: Selective per-

turbation of visual input during prehension movements. 2. the eﬀects of changing

object size. Experimental Brain Research 87, 407–420 (1991)

6. Gentilucci, M., Castiello, U., Corradini, M.L., Scarpa, M., Umilta, C., Rizzolatti,

G.: Inﬂuence of diﬀerent types of grasping on the transport component of prehen-

sion movements. Neuropsychologia 29, 361–378 (1991)

7. Chieﬃ, S., Fogassi, L., Gallese, V., Gentilucci, M.: Prehension movements directed

to approaching objects: Inﬂuence of stimulus velocity on the transport the grasp

components. Neuropsychologia 30, 877–897 (1992)

8. Marteniuk, R.G., Leavitt, J.L., MacKenzie, C.L., Athenes, S.: Functional relation-

ships between grasp transport components in a prehension task. Human Movement

Science 9, 149–176 (1990)

9. Zaal, F., Bootsma, R., van Wieringen, P.: Coordination in prehension. information-

based coupling of reaching and grasping. Experimental Brain Research 119, 427–

435 (1998)

10. Haggard, P., Wing, A.: Coordinated responses following mechanical perturbation

of the arm during prehension. Experimental Brain Research 102, 483–494 (1995)

11. Hoﬀ, B., Arbib, M.: Models of trajectory formation and temporal interaction of

reach grasp. Journal of Motor Behavior 25(3), 175–192 (1993)

12. Ulloa, A., Bullock, D.: A neural network simulating human reach-grasp coordina-

tion by continuous updating of vector positioning commands. Neural Networks 16,

1141–1160 (2003)

Computer Simulation of Vestibuloocular Reﬂex

Motor Learning Using a Realistic Cerebellar

Cortical Neuronal Network Model

Kayichiro Inagaki

, Yutaka Hirata

Pablo M. Blazquez

, and Stephen M. Highstein

1

Washington University School of Medicine, Dept. Otolaryngology,

4566 Scott Avenue, St. Louis, MO 63110, USA

Chubu University, Dept. Computer Science,

1200 Matsumoto Kasugai, Aichi, Japan

Abstract. The vestibuloocular reﬂex (VOR) is under adaptive control

to stabilize our vision during head movements. It has been suggested that

the acute VOR motor learning requires long-term depression (LTD) and

potentiation (LTP) at the parallel ﬁber – Purkinje cell synapses in the

cerebellar ﬂocculus. We simulated the VOR motor learning basing upon

the LTD and LTP using a realistic cerebellar cortical neuronal network

model. In this model, LTD and LTP were induced at the parallel ﬁber

– Purkinje cell synapses by the spike timing dependent plasticity rule,

which considers the timing of the spike occurrence in the climbing ﬁber

and the parallel ﬁbers innervating the same Purkinje cell. The model

was successful to reproduce the changes in eye movement and Purkinje

cell simple spike ﬁring modulation during VOR in the dark after low and

high gain VOR motor learning.

Keywords: VOR motor learning, Spike neuron model, Spike timing de-

pendent plasticity, Long-term depression, Long-term potentiation.

Introduction

The vestibuloocular reﬂex (VOR) stabilizes retinal image during head motion

by counter-rotating the eyes in the orbit. The VOR is under adaptive control

which maintains the compensatory eye movements under the situation where

growth, aging, injury, etc, may cause changes in oculomotor plant dynamics.

The adaptive control of the VOR requires the cerebellar ﬂocculus. Inactivation

of ﬂocculus precludes further VOR motor learning [23] and eliminates the short

term memory of VOR [19]. It is widely accepted that cerebellar long term de-

pression (LTD) or the combination of LTD and long-term potentiation (LTP) at

the parallel ﬁber – Purkinje cell synapses are the underlying mechanisms for the

VOR motor learning [3],[11]. However, how the synaptic plasticity modiﬁes the

signal processing in the cerebellar cortical neuronal network to achieve VOR mo-

tor learning is still unclear. It has been shown that the parallel ﬁber – Purkinje

cell LTD and LTP were induced depending on the input timing of the parallel

M. Ishikawa et al. (Eds.): ICONIP 2007, Part I, LNCS 4984, pp. 902–912, 2008.

c Springer-Verlag Berlin Heidelberg 2008

Computer Simulation of Vestibuloocular Reﬂex Motor Learning

903

ﬁber and the climbing ﬁber [25] innervating the same Purkinje cell. The parallel

ﬁber inputs evoke simple spike (SS) on Purkinje cells at about a hundred Hertz,

whereas the climbing ﬁber input evokes complex spike (CS) in Purkinje cells at

ultra-low frequency (

∼ 5 Hz). In cerebellar computational theories, CSs code an

error signal which is the diﬀerence between intended and actual movements, and

SSs learn to modulate their ﬁring patterns to minimize the error [26]. To date,

several computational models have been proposed to simulate VOR motor learn-

ing (e.g. [7],[16],[27]). These models were conﬁgured by using transfer functions

which process neural ﬁring rate and do not take spike occurrence timing into

consideration to describe the signal processing in VOR neuronal circuitry, thus

cannot evaluate the roles of the spike-timing dependent LTD and LTP in VOR

motor learning. In our previous work [10], we constructed a VOR model in which

the cerebellar cortical neuronal network is explicitly described by integrate-and-

ﬁre neurons based upon the known anatomy and physiology [11]. Presently we

embedded a cerebellar motor learning algorithm in this model based on the par-

allel ﬁber – Purkinje cell LTD and LTP. Simulations conﬁrmed that the model

can successfully reproduce changes in eye movements and Purkinje cell SS ﬁring

modulation after VOR motor learning in squirrel monkeys.

Model

2.1

Structure

Figure 1A illustrates the structure of the model. The model consists of 8 sub-

systems one of which is a cerebellar ﬂocculus cortical neuronal network com-

posed of spiking neurons. Other subsystems are described as transfer functions.

ecopy

preF L

, G

visual

preF L

and G

vestib

preF L

describe characteristics of pre-ﬂocculus pathway

each of which processes the eﬀerence copy, visual, and vestibular signal, respec-

tively. G

preF L

describes characteristics of another pre-ﬂoccular pathway includ-

ing lateral terminal nucleus – inferior olive – Purkinje cell which processes the

visual signal (retinal slip). G

postF L

describes characteristics of post-ﬂoccular

pathway which converts Purkinje cell SS outputs to a part of the motor output.

vestib

nonF L

and G

visual

nonF L

describe characteristics of non-ﬂoccular vestibular pathway

and non-ﬂoccular visual pathway, respectively. The ﬂocculus neuronal network

model consists of 20 Purkinje, 900 Golgi, 60 Basket, and 10000 granule cells

(Figure 1B). Synaptic connections among these cell types are similar to those in

the cerebellar cortical model for eye blink conditioning conﬁgured by Medina et

al.[18]. Namely, each granule cell receives 6 excitatory mossy ﬁber inputs and 3

inhibitory Golgi cell inputs. Each Golgi cell receives 20 excitatory mossy ﬁbers

and 100 granule cell inputs. Each basket cell receives excitatory synaptic inputs

from 250 granule cells. Each Purkinje cell receives excitatory inputs from 10000

granule cells and a single climbing ﬁber as well as inhibitory inputs from 10 bas-

ket cells. In scaling down the cerebellar cortical network to a computationally

feasible dimension, it was suggested that the convergence / divergence ratios

were more important than the cell ratios [18]. Consequently, the model is scaled

down basing upon maintaining the convergence / divergence ratio.

904

K. Inagaki et al.

B

Fig. 1. Structure of the proposed VOR motor learning model. A: entire model struc-

ture. B: structure of the cerebellar cortical neuronal network. In A, the VOR model

consists of 8 subsystems each of which represents diﬀerent anatomical pathways pro-

cessing diﬀerent modality of signals[9]. G

ecopy

preF L

, G

visual

preF L

and G

vestib

preF L

are pre-ﬂoccular

subsystems each of which corresponds to a transfer function of pre-ﬂoccular eﬀer-

ence copy pathway, visual (retinal slip) pathway and vestibular pathway, respectively.

cf

preF L

represents a transfer function of climbing ﬁber pathway, which transfers visual

signal to Purkinje cell CS activity. G

postF L

is a transfer function of post-ﬂoccular path-

way, which transfers the Purkinje cell SS activity to a part of the motor command.

visual

nonF L

and G

vestib

nonF L

represent transfer functions of non-ﬂoccular visual and vestibu-

lar pathway, respectively. In B, the ﬂocculus is explicitly described by spike neuron

model to evaluate the cerebellar motor learning in terms of the spike timing dependent

plasticity. The organization of the ﬂocculus neuronal network and each of synaptic

connections were determined by the anatomical and physiological evidence.

Computer Simulation of Vestibuloocular Reﬂex Motor Learning

905

2.2

Description of Subsystems

Neurons in the ﬂocculus are described as conductance based spike neuron models.

Synaptic conductance g

syn

in the model is calculated as follows:

syn

i=1

· w

(t)

· (1 − g

syn

)

− g

syn

(1)

where N , S

, w

and τ denote the number of the pre-synaptic cells, spike input

from the i-th pre-synaptic cell (0 or 1), synaptic weight, and synaptic decay time

constant, respectively. The synaptic current I

syn

is computed by:

syn

(V (t), t) = g

syn

· g

syn

· (V (t) − P SP

max

)

(2)

where g

syn

and P SP

max

are respectively the scaling coeﬃcient of synaptic

strength and the constant of the post synaptic potential whose sign determines

if the synaptic current is excitatory or inhibitory. Synaptic decay time constant

and post synaptic potential for each cell type are same as those used in previous

report [10]. The membrane potential V is given by:

−g

· (V (t) − E

leak

)

−

syn=1

syn

(V (t), t)

(3)

where g

and E

leak

represent the leak coeﬃcient and leak potential of the post

synaptic cell, respectively. M denotes the number of synapse type connected to a

post synaptic cell. Each cell ﬁres a spike immediately when their membrane po-

tential exceeds the threshold set for individual cell type [10]. Then membrane po-

tential is reset to 0 after the cell ﬁring. Other subsystems are described as transfer

functions modiﬁed from our previous VOR system model [9] as in eq.(4) – (9).

ecopy

preF L

(s) = (α

+ β

s + γ

−p

(4)

vestib

preF L

(s) = (α

+ β

s + γ

−p

(5)

visual

preF L

(s) = (α

+ β

s + γ

−p

(6)

postF L

(s) =

+ v

s + w

−q

(7)

vestib

nonF L

(s) =

+ b

s + c

−q

+ v

s + w

(8)

visual

nonF L

(s) =

+ b

s + c

−q

+ v

s + w

(9)

In each equation, α , β and γ denote the coeﬃcient of acceleration, velocity and

position of eye movement (e), retinal slip (r) and head movement (h). Also u, v

and w are the coeﬃcient of acceleration, velocity and position of eye movement.

q and p are latencies of Purkinje cell SS ﬁring in response to input signal to

906

K. Inagaki et al.

each subsystem. The subsystem for another pre-ﬂoccular pathway representing

lateral terminal nucleus – inferior olive – Purkinje cell pathway is given by

cf

preF L

(s) = (α

+ β

s + γ

−p

(10)

where α

, β

and γ

denote the coeﬃcient of acceleration, velocity and position

of retinal slip. p

is time delay constant. The output of this transfer function

cf (t) is saturated by a sigmoid function before innervating a Purkinje cell.

CF (t) =

1 + exp(κ(cf (t)

− ξ))

(11)

where κ and ξ are free parameters. CF (t) is integrated and CS ﬁres immedi-

ately when the membrane potential exceeds its threshold level. Parameters in the

cerebellar spike neuron network model were ﬁrst pre-adjusted so that the model

approximates experimental Purkinje cell ﬁring patterns during optokinetic re-

sponse (OKR) and VORd (see 2.4). At this point, same parameter values of the

previous VOR model [9] were used for those in the transfer function models.

Then, parameters in the transfer function models were ﬁne-tuned together with

those in the spike neuron model so that the model reproduces both eye veloc-

ities and Purkinje cell ﬁring patterns during OKR and VORd. We then tested

this model by predicting eye velocities and Purkinje cell ﬁring patterns dur-

ing VOR enhancement (VORe) and VOR suppression (VORs) paradigms (see

Experimental paradigm below).

2.3

Description of Learning Rule

The parallel ﬁber – Purkinje cell LTD is induced when a glutamate input from

a parallel ﬁber to a Purkinje cell is followed by an elevation of the calcium ion

level elicited by climbing ﬁber input [25]. On the other hand, LTP is induced

by a glutamate input without an elevation of the calcium ion level [6]. In the

model, these LTD and LTP are represented as changes in synaptic weight (δw)

between the parallel ﬁbers and the Purkinje cell which are described by following

equation.

δw = δ

LT D

· GR(t) · winCF (t) + δ

LT P

· GR(t) · (1 − winCF (t))

(12)

where GR(t) is an input from a granule cell to a Purkinje cell conveyed via

a parallel ﬁber. If the granule cell ﬁres a spike, GR(t) is 1. winCF (t) is the

window function that describes the time window of an elevation of the calcium

ion level in a Purkinje cell. It is 1 for 35msec after a ﬁring of climbing ﬁber and 0

otherwise. δ

LT D

and δ

LT P

are the rate of the change in synaptic weight by LTD

and LTP, respectively. With the learning rule, the synaptic weight (w

(t)) in eq.

(1) between a granule cell and a Purkinje cell is updated so that it decreases

if the granule cell ﬁres within the 35msec window after the ﬁring of climbing

ﬁber (LTD), or increases if the granule cell ﬁres outside the time window (LTP)

[6],[25].

Computer Simulation of Vestibuloocular Reﬂex Motor Learning

907

2.4

Experimental Paradigms

Detailed experimental procedures were mentioned elsewhere [7]. Brieﬂy, squir-

rel monkeys were employed for recording of ﬂocculus Purkinje cells and eye

movements during various visual-vestibular interaction paradigms (see below).

Animals were seated in a primate chair with their head ﬁxated. The chair was

rotated by a servo motor around monkey’s inter-aural axis to produce a vertical

VOR. Black random dots were projected on the cylindrical screen coaxially sur-

rounding the rotation axis of the servo motor. This is the optokinetic stimulus

(OKS). OKR is induced by applying OKS with the monkey’s head stationary,

while in VORd the chair rotates in the dark (no OKS). In VORs, the chair ro-

tates in phase with the OKS, while in VORe the chair and OKS rotate out of

phase. All paradigms consist of sinusoidal chair rotation and/or OKS (frequency

0.5Hz, amplitude 40deg/s). VORs and VORe were utilized for high and low gain

training. Animals were trained toward high or low gain for 3-7h a day. Vertical

and horizontal eye position, chair velocity and OKS velocity were continuously

recorded at a sampling frequency of 200Hz with the use of Power1401 interface

(Cambridge Electronic Design) for display and storage using Spike2 program.

Floccular and ventral paraﬂoccular Purkinje cells were identiﬁed by the ﬁring

of CS and their SS discharge patterns. After a unit was isolated, OKR, VORd,

VORs and VORe paradigms were applied. All these experiments and surgical

procedures were approved by the Animal Welfare and Use Committee of Wash-

ington University.

Results

3.1

Simple and Complex Spike Firing Before Learning

Figure 2 illustrates the simulated Purkinje cell SS and CS ﬁring during VORe,

VORs and VOR in the light (VORl) averaged over 30 stimulus cycles. According

to the experimental evidence [15], CS ﬁring modulates out of phase with SS ﬁring

pattern. Furthermore, SS ﬁring pattern modulates in-phase with head rotation

during VORe and out of phase with head rotation during VORs [2],[7]. In our

model simulation, these SS modulation are well reproduced in both VORe (A,

D, G) and VORs (B, E, H) paradigms, and CS ﬁring rate in these paradigms

are out of phase with the SS ﬁring modulation. During VORl simulation(C, F,

I), the SS slightly modulated in-phase with head rotation [21], whereas the CS

did not signiﬁcantly modulate.

3.2

Simulation of VOR Motor Learning

It has been reported that the gain of VOR can be acutely increased or decreased

by the continuous application of VORe or VORs, respectively in squirrel monkeys

and other animal species [14],[22],[24]. We simulated VOR motor learning in our

model by using VORe and VORs paradigm. In each training paradigm, vestibular

and optokinetic stimuli were applied for 45 stimulus cycles. To quantify the

908

K. Inagaki et al.

Fig. 2. SS and CS of the ﬂoccular Purkinje cell during VORe (A, D, G), VORs (B, E,

H), and VORl (C, F, I) in the computational simulation. Each panel shows: Top, mean

ﬁring rate of a SS, middle, mean ﬁring rate of a CS, bottom, head velocity (solid black

line) and OKS (dashed gray line). Mean ﬁring rate of SS and CS were determined as

an average over 30 stimulus cycles.

Fig. 3. Adaptive gain change during VORe training (ﬁlled circle), VORs training (ﬁlled

square) and VORl (ﬁlled triangle) in the simulation. The gain of VOR increased 0.51

(from 0.79 to 1.30) after VORe training, and decreased 0.30 (from 0.79 to 0.49) after

VORs training. During VORl, the gain of VOR did not change.

Computer Simulation of Vestibuloocular Reﬂex Motor Learning

909

Fig. 4. Purkinje cell SS ﬁring modulation in the experiment using a squirrel monkey

[7] (A, B, C), and in our simulation (D, E, F) during VORd before and after VOR

motor learning (A and D: VORs training, C and F: VORe training). In each panel,

top, Purkinje cell SS response, bottom, eye (solid line) and head velocity (dashed line).

newly acquired VOR memory, we measured gain of VORd every 15 stimulus

cycles. Figure 3 illustrates adaptive gain change in eye movement during VORe

training (ﬁlled circle), VORs training (ﬁlled square) and VORl (ﬁlled triangle).

The model simulation demonstrated that the gain of VOR changed from 0.79

to 1.30 (+0.51) after VORe training and from 0.79 to 0.49 (-0.30) after VORs

training. After VORl training, the gain of VOR did not change. These changes

in gain of VOR after VORe, VORs and VORl training are comparable to those

demonstrated experimentally in monkeys [14]. Figure 4 illustrates Purkinje cell

SS ﬁring modulation in an experiment using squirrel monkey [7](A, B, C) and in

our simulation (D, E, F) during VORd before and after VOR motor learning(A

and D: VORs training, C and F: VORe training). It has been shown that Purkinje

cell SS changes ﬁring modulation during VORd after motor learning [2],[7]. In the

experiment, before any training, Purkinje cell SS during VORd hardly modulate

(Fig.4 B). After VORs training (Fig.4 A), SS slightly modulated out of phase

with the head rotation. After VORe training (Fig.4 C), SS modulated in phase

with the head rotation. In agreement with these experimental ﬁndings, our model

reproduced these changes in the Purkinje cell SS modulation during VORd after

VORs and VORe training.

Discussion and Conclusion

Conceptual theory of cerebellar motor learning was proposed by Marr[17], Albus[1]

and Ito[11]. The cerebellar Purkinje cells receive parallel ﬁber and climbing ﬁber

input. The parallel ﬁbers send vestibular, visual and eﬀerence copy of motor output

to the Purkinje cell and evoke SS, whereas the climbing ﬁber sends error signal to

910

K. Inagaki et al.

the same Purkinje cell and evokes CS. In the conceptual theory, the SS activities en-

code motor performance in their ﬁring rate, while the CS activities reﬂect an error

onto the Purkinje cell to guide motor learning and change SS activity. It has been

suggested that cerebellar motor learning is induced by LTD and LTP [3],[27] and

also shown that LTD or LTP is evoked depending on the input timing of a parallel

ﬁber and a climbing ﬁber [25]. Presently, we simulated VOR motor learning using

the realistic cerebellar cortical neuronal network model with spike timing depen-

dent learning rule for the LTD and the LTP. The model successfully demonstrated

the ﬁring relation between Purkinje cell SS and CS, the adaptive changes in the mo-

tor performance and SS activity. Our principal ﬁnding is that VOR motor learning

is induced when the Purkinje CS is modulated (during VORe and VORs), and is

not induced when the CS hardly modulates (during VORl). In our model, CS ﬁring

modulation reﬂects retinal slip information which is one of the error signal candi-

dates in VOR motor learning, and the modulation of the CS changes the Purkinje

SS ﬁring pattern to guide VOR motor learning. The CS modulates out of phase

with the SS during VORe (Fig.2, D) and in phase with the SS during VORs (Fig.2,

E). During VORl, the CS does not modulate signiﬁcantly (Fig.2, F). Our simula-

tion showed that these CS modulations can change the balance of LTD and LTP at

the synapses between parallel ﬁbers and a Purkinje cell, and guide the motor per-

formance toward respective goals: high, low or normal gain. This consideration,

revealing from our computational simulation, consistents with the theory of CS

guided motor learning [4],[20].

Several types of plasticity in the cerebellum have been reported in in vitro studies

(e.g. [5],[13]). In contrast, we could account for VOR motor learning solely by the

parallel ﬁber – Purkinje cell LTD and LTP. However, the other type of synaptic

plasticity [5],[13] might be required in the complex VOR motor learning: up - down

or left - right asymmetric VOR motor learning [8],[28].

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