A Neural Model of Spatio Temporal Coordination in Prehension

A Neural Model of Spatio Temporal Coordination in Prehension Javier Molina-Vilaplana, Jorge Feliu Batlle, and Juan López Coronado Departamento de Ingeniería de Sistemas y Automática. Universidad Politécnica de Cartagena. Campus Muralla del Mar. C/ Dr Fleming S/N. 30202. Cartagena. Murcia. Spain. {Javi.Molina, Jorge.Feliu, Jl.Coronado}@upct.es

Abstract. The question of how the transport and grasp components in prehension are spatio–temporally coordinated is addressed in this paper. Based upon previous works by Castiello [1] we hypothesize that this coordination is carried out by neural networks in basal ganglia that exert a sophisticated gating / modulatory function over the two visuomotor channels that according to Jeannerod [2] and Arbib [3] are involved in prehension movement. Spatial dimension and temporal phasing of the movement are understood in terms of basic motor programs that are re–scaled both temporally and spatially by neural activity in basal ganglia thalamocortical loops. A computational model has been developed to accommodate all these assumptions. The model proposes an interaction between the two channels, that allows a distribution of cortical information related with arm transport channel, to the grasp channel. Computer simulations of the model reproduce basic kinematic features of prehension movement.

1 Introduction Prehension is usually divided into two distinct components: hand transport and grip aperture control. The transport component is related with the movement of the wrist from an initial position to a final position that is close to the object to be grasped. The grip aperture component is related to the opening of the hand to a maximum peak aperture and then, with fingers closing until they contact the object. There is a parallel evolution of reaching and hand preshaping processes, both of them initiating and finishing nearly simultaneously. Temporal invariances exist in prehension, in terms of a constant relative timing between some parameters of the transport and grasp components. For instance, the time to maximum grip aperture occurs between 60–70% of movement duration despite large variations in movement amplitude, speed, and different initial postures of the fingers [2], [4], [5]. Time of maximum grip aperture is also well correlated with time of maximum deceleration of the transport component [6]. Jeannerod [2] and Arbib [3] suggest that the transport and hand preshaping components evolve independently trough two segregated visuomotor channels, coordinated by a central timing mechanism. This timing mechanism ensures the temporal alignment of key moments in the evolution of the two components. In this way, Jeannerod [2] suggests that the central timing mechanism operates such that peak hand aperture is reached at

J.R. Dorronsoro (Ed.): ICANN 2002, LNCS 2415, pp. 9–14, 2002. © Springer-Verlag Berlin Heidelberg 2002

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the moment of peak deceleration of the reaching component. Castiello et al [1] in reach to grasp perturbation experiments with Parkinson’s disease subjects, conclude that there are indications that the basal ganglia might be seen in the context of the neural networks that actively gate the information to and between the channels, needed for the coordination in time of the two components in prehension movement. Haggard and Wing [7] proposed a model of coordination during prehension movement. This model is based on coupled position feedback between the transport and grasp components. Hoff and Arbib [8] proposed a model for temporal coordination during prehension movement based on constant enclosed time. In this paper, a neural model of prehension movement coordination is proposed. Vector Integration To Endpoint (VITE) [9] dynamics is used to model the grasp and transport channels. Movement execution is modulated by a basal ganglia neural network model that exerts a sophisticated gating function [10] over these channels.

2 Neural Model of Reach to Grasp Coordination The visuomotor channels related with transport and grasp components have been simulated using the VITE model of Bullock and Grossberg [9]. VITE gradually integrates the difference between the desired target finger aperture (T) and the actual finger aperture (P) to obtain a difference vector (V). For transport component, (T) models the wrist desired final position near the object to be grasped and (P) the actual wrist position. The difference vectors code information about the amplitude and direction of the desired movement. These vectors are modulated by time-varying G(t) gating signals from basal ganglia neural networks [10], producing desired grip aperture velocity and wrist velocity commands (V*G(t)). Temporal dynamics of (V) and (P) vectors are described by equations (1) – (2). dV/dt = 30.(-V + T - P) dP/dt = G(t). V

(1) (2)

According to Jeannerod [2], we propose a biphasic programming of the grasp component; therefore the motor program for the movement of fingers has been modeled as consisting of two sequential subprograms (G1, G2), where G1 is related to the maximum grip aperture and G2 equals the object size. VITE model has been modified in the grasp channel to account for the apparent gradual specification of target amplitude [11]. The model shown in Figure 1 (this figure only shows the structure of one of the two visuomotor channels) assumes that the target aperture is not fully programmed before movement initiation; rather, it is postulated that target acquisition neuron (T) in grasp channel, sequentially and gradually specify, in a first phase the desired maximum grip aperture (G1), and in a second phase the aperture corresponding to the object size (G2). Dynamics of the target acquisition neuron in grasp channel is described by equation (3): dT/dt = a. (G – T)

(3)

In this model, time of peak deceleration (Tpdec, the instant when the acceleration in the transport channel is minimum) triggers the read-in of G2 by the target

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acquisition neuron in grasp channel. In principle, proprioceptive information could be used by CNS to derive tpdec or a related measurement [12]. Tpdec detection generates a signal in a SMA (Supplementary Motor Area) cortical neuron (Fig1). This neuron projects its activity to the putamen neurons in the grasp channel triggering the modulation of the final enclosing phase. No other interactions between transport and grasp components were assumed.

Fig. 1. Schematic diagram of the computational structure of the model. Movement execution is modeled by VITE dynamics (left part of Figure 1). Modulatory gating functions over movement execution is carried out by basal ganglia neural networks (Right part of Figure 1). Inhibitory projection activity from striatum to GPi and GPe is affected by dopamine levels (see text for details). Arrows finishing with + / - symbol, mean excitatory / inhibitory connections respectively. Connections from VLo to P in both channels are multiplicative gating connections.

Neural circuits of basal ganglia depicted in Figure 1 have been modeled (like in previous models [10], [13]), with, non linear, ordinary differential equations. Dynamics of basal ganglia neurons are described by equations (4) - (5): dSk/dt = bk[ - Ak Sk + (Bk – Sk)Ek – (Dk + Sk)Ik ] J

dNJ/dt = b(BNJ(D) – NJ) – cS 1NJ

(4) (5)

where Sk represents neural population activity of Putamen (k=1), internal globus pallidus (GPi, k=2), external globus pallidus (GPe, k=3), subthalamic nucleus (STN, k=4) and VLo (k=5). Appendix A shows the numerical values of the parameters used in our simulations and an extended mathematical description of the model. Thalamus (VLo) neuronal activity is identified with G(t) gating signals of the VITE model. Dopamine appears as an explicit parameter (D), modulating the functioning of basal ganglia thalamocortical loops. In equation (5), NJ models the amount of available neurotransmitter in direct (J=1) and indirect pathway (J=2) (GABA/ Substance P in direct pathway, GABA/Enkephalin in indirect pathway). Maximum level of available neurotransmitter (BNJ ) is a function of dopamine level (BNJ(D) =1 for D = 1 and J=1,2).

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3 Simulation Results Two different simulated experiments were performed. In first of them, ‘subjects’ carried out single reach to grasp movements of different width objects placed at he same distance (Experiment 1). In the second simulated experience, ‘subjects’ had to move to different amplitudes from initial wrist position to final wrist placement in order to grasp an object (Experiment 2). Experiment 1: In these simulations, transport motor program was named as T and set to 30 cm. G1 = [35, 75] mm and G2 = [10 , 50 ] mm were the biphasic motor programs used to simulate prehension of [small , big] object. Experiment 2: In these simulations, grasping motor program was set to G1 = 75 mm / G2 = 50 mm. Transport motor programs were T = [20, 30, 40]cm.

Fig. 2. Wrist velocity and aperture profiles for grasping as a function of distances and object size. Experiment 1 (Left) simulates a ‘subject’ that reaches out to grasp two different width objects at the same distance away. No difference is seen in wrist velocity profiles but differences appear in grip aperture profiles. Experiment 2 (Right) simulates a ‘subject’ that reaches out to grasp an object of constant size at three different distances away. The velocity profile shows a systematic increase with distance but no difference is seen in the grip aperure. Abcisas represents normalized movement time. Wrist velocity (cm/s) in dashed lines. Finger aperture (mm) in solid lines.

In all simulations initial finger aperture and initial wrist position was set to zero. The biphasic motor program in the grasp channel (G1,G2) was designed taking into account the fact that the amplitude of maximum grip aperture covaries linearly with object size. Transport velocity exhibits a bell shaped but asymmetrical velocity profile typical of point to point arm movements [9]. The plot of hand aperture shows the opening of the hand until it gets to maximum peak aperture, then it shows a decreasing of grip aperture until it reaches object size. As seen in Figure 2, the distance of the object away from the subject affects the transport component (peak velocity increases with the distance to be moved) but not the grasping component (Experiment 2). Figure 2 also shows how the object size affects the grasping component (maximum aperture covaries linearly with object size), while the transport component remains unaltered (Experiment 1).

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4 Discussion The question of how the transport and grasp components in prehension are spatio– temporally coordinated is addressed in this paper. In the proposed model this coordination is carried out by neural networks in basal ganglia that exert a sophisticated gating/modulatory function over the two visuomotor channels that are involved in the reach to grasp movement. Simulation results show how the model is able to address temporal equifinality of both channels (i.e. wrist transport and grip closure finishing simultaneously) and how it reproduces basic kinematic features of single prehension movements. One advantage of the model is the explicit inclusion of a parameter such like dopamine level (D) which affects whole model performance, allowing us to simulate prehension tasks under simulated Parkinson Disease (PD) symptoms. These symptoms are characterized by dopamine level depletions (D