Elsevier

Neural Networks

Volume 18, Issue 3, April 2005, Pages 213-224
Neural Networks

A model of smooth pursuit in primates based on learning the target dynamics

https://doi.org/10.1016/j.neunet.2005.01.001Get rights and content

Abstract

While the predictive nature of the primate smooth pursuit system has been evident through several behavioural and neurophysiological experiments, few models have attempted to explain these results comprehensively. The model we propose in this paper in line with previous models employing optimal control theory; however, we hypothesize two new issues: (1) the medical superior temporal (MST) area in the cerebral cortex implements a recurrent neural network (RNN) in order to predict the current or future target velocity, and (2) a forward model of the target motion is acquired by on-line learning. We use stimulation studies to demonstrate how our new model supports these hypotheses.

Introduction

Due to their narrow foveal vision, which has a viewing angle of only a few degrees, primates have to move their eyes to acquire accurate information on small moving targets in the environment. Smooth pursuit eye movements (SPEMs) perform this function and can achieve remarkable performance. For example, humans can maintain a velocity gain, i.e. the ratio of eye velocity to target velocity, of one up to a target speed of about 20°/s, while monkeys have been reported to even exceed this value. The accuracy of smooth pursuit is not only confined to constant velocity targets but has also been observed in periodic motion such as sinusoidal signals with frequencies of less than about 1 Hz (Dallos and Jones, 1963, Stark et al., 1962, Westheimer, 1954). Even a phase lead of the eyes can sometimes be observed in such experiments. Due to the information processing delays (e.g. 80–130 ms for human brain) in the visual pathways, the experimentally observed high performance of the smooth pursuit system cannot be achieved solely with standard negative feedback methods based on visual error signals. Under such delayed information processing, simple feedback control has a significant phase shift to the target signal, and thus some form of predictive control must take place (Pavel, 1990).

Several experimental results have been reported that also shed some light on the predictive nature of the smooth pursuit system. Morris and Lisberger, 1983, Morris and Lisberger, 1987 demonstrated that monkeys were able to execute smooth pursuit with zero retinal slip by using a special target presentation technique called ‘target stabilization’. It is also known that monkeys can maintain smooth pursuit during blink periods, i.e. a sudden disappearance of the target for a brief moment (Churchland and Lisberger, 2000, Kawano et al., 1994, Newsome et al., 1988, Pola and Wyatt, 1997, Sakata et al., 1983). Such predictive compensation has been observed both in constant velocity and sinusoidally moving targets (Becker and Fuchs, 1985, Fukushima et al., 2002, Whittaker and Eaholtz, 1982).

Therefore, it seems clear that SPEMs are a key to uncovering mechanisms for predicting the external world in the primate brain. In place of previous models, this article develops a SPEM model that employs a compact representation of the target motion that can be quickly learned in an on-line fashion based on visual error signals. By taking neuroanatomical findings into account, our model further suggests that the medial superior temporal (MST) area has the possibility of predicting target velocity using only signals that originate from visual information, without relying on efference copies of the oculomotor command or proprioceptive feedback.

Section snippets

Previous models

Pioneering computational models for SPEMs (Robinson et al., 1986, Yasui and Young, 1975) attempted to cancel out the feedback signal in order to enable high velocity gain; their model works as a feedforward controller. Fig. 1 describes the essence of Robinson's model. In this model, the feedback signal with a delay Δ1 is precisely canceled out by a positive feedback loop with the delay Δ1+Δ3. However, their feedforward pathway still contains a significant delay determined by Δ2 and τ such that

Simulation setup

In order to verify that our model can achieve smooth pursuit with gain one and zero-latency, we conducted two evaluations by simulation. In one setup, the input was a ramp input with a constant velocity of 0.5 rad/s, and in the other setup, a sinusoidal input was chosen with a frequency of 1.0 Hz. Note that the dynamics of these inputs is a second-order linear system, which guarantees that the current target velocity can be predicted by the past target state, i.e. position and velocity.

Fig. 3 is

Discussion

We have presented a computational model employing a predictive controller with fast learning of the target dynamics enables zero-lag SPEMs. In our model, the representation of the target motion is much simpler than the memory-based model, and learning proceeds quickly, decreasing the retinal slip without waiting for one period of the target motion. Our model can also maintain SPEMs during the target blinking. We have also demonstrated that the learning predictor of target motion can be realized

References (63)

  • W. Becker et al.

    Prediction in the oculomotor system: smooth pursuit

    Experimental Brain Research

    (1985)
  • G. Bi et al.

    Synaptic modifications in cultured hippocampal neurons: Dependence on spike timing, synaptic strength, and postsynaptic cell type

    Journal of Neuroscience

    (1998)
  • G. Bi et al.

    Distributed synaptic modification in neural networks induced by patterned stimulation

    Nature

    (1999)
  • P. Burgi et al.

    Probabilistic motion estimation based on temporal coherence

    Neural Computation

    (2000)
  • M. Churchland et al.

    Apparent motion produce multiple deficits in visually guided smooth pursuit eye movements of monkeys

    Journal of Neurophysiology

    (2000)
  • P. Dallos et al.

    Learning behaviour of the eye fixation control system

    IEEE Transactions on Automatic Control

    (1963)
  • J. DeSouza et al.

    Eye position signals modulate early dorsal and ventral visual areas

    Cerebral Cortex

    (2002)
  • M. Dürsteler et al.

    Pursuit and optokinetic deficits following chemical lesions of cortical areas MT and MST

    Journal of Neurophysiology

    (1988)
  • M. Dürsteler et al.

    Directional pursuit deficits following lesions of the foveal representation within the superior temporal sulcus of the macaque monkey

    Journal of Neurophysiology

    (1987)
  • S. Eifuku et al.

    Response to motion in extrastriate area MSTI: Centresurround interactions

    Journal of Neurophysiology

    (1998)
  • R. Erickson et al.

    A neuronal correlate of spatial stability during periods of self-induced visual motion

    Experimental Brain Research

    (1991)
  • K. Fukushima et al.

    Predictive responses of periarcuate pursuit neurons to visual target motion

    Experimental Brain Research

    (2002)
  • K. Fukushima et al.

    Coding of smooth eye movements in three-dimensional space by frontal cortex

    Nature

    (2002)
  • A. Georgopoulos et al.

    Neuronal population coding of movement direction

    Science

    (1986)
  • J. Gottlieb et al.

    Neural responses related to smooth-pursuit eye movements and their correspondence with electrically elicited smooth eye movements in the primate frontal eye field

    Jouranl of Neurophysiology

    (1994)
  • J. Houk et al.

    Neutral networks for control, chapter 13 an adaptive sensorimotor network inspired by the anatomy and physiology of the cerebellum

    (1990)
  • K. Kawano et al.

    Response properties of neurons in posterior parietal cortex of monkey during visual-vestibular stimulation. I. Visual tracking neurons

    Journal of Neurophysiology

    (1984)
  • M. Kawano et al.

    Neural activity in cortical area MST of alert monkey during ocular following responses

    Journal of Neurophysiology

    (1994)
  • H. Komatsu et al.

    Relation of cortical areas MT and MST to pursuit eye movements. I. Localization and visual properties of neurons

    Journal of Neurophysiology

    (1988)
  • H. Komatsu et al.

    Relation of cortical areas MT and MST to pursuit eye movements. III. Interaction with full-field visual stimulation

    Journal of Neurophysiology

    (1988)
  • H. Komatsu et al.

    Modualtion of pursuit eye movements by stimulation of cortical areas MT and MST

    Journal of Neurophysiology

    (1989)
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