Lecture Notes in Computer Science
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- Prediction Accuracy.
- 4.2 Identification Results Obtained Using the GMDH
- 4.3 Identification Results Obtained Using the Conventional Neural Network
- 4.4 Companion of the Identification Results
- 5 Conclusion
Fig. 4. Variation of the mean errors(J 1 and J 2 ) and AIC values: (a)mean error J 1 ; (b) mean error J 2 ; (c) AIC values
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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
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0.0005 0.0339 J 2 (Mean Error) 0.0017 0.0679 Prediction Accuracy. The prediction accuracy was evaluated by using the following equation.
∑ = − = 16 9 * 2 8 | | i i i J φ φ (21) where
φ i (i=9,10,…,16) were the actual values at the prediction points and φ i * (i=9,10,…,16) were the predicted values of φ i
Figure 4(b) shows the variation of J 2 in each layer. From this figure, we can see that the values of J 2 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.
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 1 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 2 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.
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
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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 J 1 0.0118 0.0118 0.0118 0.0133 J 2 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 1 (Mean Error) 0.0005 0.0339 0.0118 Maximum Error -0.0020 -0.0955 -0.0258 Prediction J 2 (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.
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. 1 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. 2 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
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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
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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. 3 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 i and O i 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
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1.4 Wrist velocity [m/sec] Time [sec] N C1 O1 C2 O2 C3 O3 C4 O4 (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
i lags behind the other conditions and especially grip aperture of C 4 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 i are almost the same as those of unperturbed grasping. While, the movement times for C i change in the latter half of the movement and especially the movement times of C 3 and C 4 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
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0.8 1 1.2 1.4 N C1 O1 C2 O2 C3 O3 C4 O4 Movement time [sec] Measurement conditions * ** ns ns ns ns ns ns (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 N C 1 O 1 C 2 O 2 C 3 O 3 C 4 O 4 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 ns ** 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 ns * ns ** ns of movement. The finish time of reaching for C i lags behind the other condi- tions and especially the velocity of C 4 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 i are not significantly different with respect to those of N. Reach- ing for C i changes in the latter half of the movement as shown in Figs. 3(d), and especially the movement times of C 3 and C 4 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
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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.
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ns ns ns 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 N C
O 1 C 2 O 2 C 3 O 3 C 4 O 4 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 ns ns ns 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 —– ns ns ns ns ns ns ns ns 900 M. Katayama and H. Katayama 4 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 i , although there was no failure for O i . 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.
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5 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 1 , Yutaka Hirata 2 , Pablo M. Blazquez 1 , and Stephen M. Highstein 1 1
4566 Scott Avenue, St. Louis, MO 63110, USA 2 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. 1 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. 2 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. G 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 cf 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. G 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. A B
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. G cf
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. G 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: dg syn
dt = N i=1 S i · w i (t) · (1 − g syn
) − g
syn · 1 τ (1)
where N , S i , w i 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: I 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: dV dt = −g l · (V (t) − E leak
) − M syn=1 I syn (V (t), t) (3)
where g l 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). G ecopy preF L (s) = (α
e s 2 + β e s + γ e )e −p e s (4) G vestib
preF L (s) = (α
h s 2 + β h s + γ h )e −p h s (5) G visual
preF L (s) = (α
r s 2 + β r s + γ r )e −p r s (6) G postF L
(s) = 1 u e s 2 + v e s + w e e −q e s (7) G vestib
nonF L (s) =
(a h s 2 + b
h s + c
h )e −q h s u h s 2 + v h s + w h (8)
G visual
nonF L (s) =
(a r s 2 + b
r s + c
r )e −q r s u r s 2 + v r s + w r (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 G cf
(s) = (α c s 2 + β
c s + γ
c )e −p c s (10) where α c , β c and γ
c denote the coefficient of acceleration, velocity and position of retinal slip. p c 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 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 i (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. 3 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. 4 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]. References 1. Albus, J.S.: A Theory of Cerebellar Function. Mathematical Biosciences 10, 25–61 (1971)
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