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