Characterization of prediction in the primate visual smooth pursuit system

Cerebellar Role in Predictive Control of Eye Velocity Initiation and Termination

Predictive motor control is essential to achieve rapid and precise motor action in all vertebrates. Visuomotor transformations have been a popular model system to study the underlying neural mechanisms, in particular, the role of the cerebellum in both predictive and gain adaptations. In all species, large-field visual motion produces an involuntary conjugate ocular movement facilitating gaze stabilization called the optokinetic response. Gain adaptation can be induced by prolonged optokinetic visual stimulation; and if the visual stimulation is temporally periodic, predictive behavior emerges. Two predictive timing components were identifiable in this behavior. The first was prediction of stimulus initiation (when to move) and the other was stimulus termination (when to stop). We designed visual training that allowed us to evaluate initiation and termination independently that included the recording of cerebellar activity followed by acute and chronic cerebellar removal in goldfish of both sexes. We found that initiation and termination predictions were present in the cerebellum and more robust than conflicting visual sensory signals. Each prediction could be acquired independently, and both the acquisition and maintenance of each component were cerebellar-dependent. Subsequent analysis of the neuronal connectivity strongly supports the hypothesis that the acquired eye velocity behaviors were dependent on feedforward velocity buildup signals from the brainstem, but the adaptive timing mechanism itself originates within the circuitry of the cerebellum.SIGNIFICANCE STATEMENT Predictive and rapid motor control is essential in our daily life, such as in the playing of musical instruments or sports. The current work evaluates timing of a visuomotor behavior shown to be similar in humans as well as goldfish. Given the latter species' known brainstem cerebellar neuronal connectivity and experimental advantage, it was possible to demonstrate the cerebellum to be necessary for acquisition and maintenance of both the initiation and termination components of when to move and to stop. All evidence in this study points to the adaptive predictive control site to lie within the cerebellar circuitry.

Synchronizing the tracking eye movements with the motion of a visual target: Basic neural processes

In primates, the appearance of an object moving in the peripheral visual field elicits an interceptive saccade that brings the target image onto the foveae. This foveation is then maintained more or less efficiently by slow pursuit eye movements and subsequent catch-up saccades. Sometimes, the tracking is such that the gaze direction looks spatiotemporally locked onto the moving object. Such a spatial synchronism is quite spectacular when one considers that the target-related signals are transmitted to the motor neurons through multiple parallel channels connecting separate neural populations with different conduction speeds and delays. Because of the delays between the changes of retinal activity and the changes of extraocular muscle tension, the maintenance of the target image onto the fovea cannot be driven by the current retinal signals as they correspond to past positions of the target. Yet, the spatiotemporal coincidence observed during pursuit suggests that the oculomotor system is driven by a command estimating continuously the current location of the target, i.e., where it is here and now. This inference is also supported by experimental perturbation studies: when the trajectory of an interceptive saccade is experimentally perturbed, a correction saccade is produced in flight or after a short delay, and brings the gaze next to the location where unperturbed saccades would have landed at about the same time, in the absence of visual feedback. In this chapter, we explain how such correction can be supported by previous visual signals without assuming "predictive" signals encoding future target locations. We also describe the basic neural processes which gradually yield the synchronization of eye movements with the target motion. When the process fails, the gaze is driven by signals related to past locations of the target, not by estimates to its upcoming locations, and a catch-up is made to reinitiate the synchronization.

Gain Control in Predictive Smooth Pursuit Eye Movements: Evidence for an Acceleration-Based Predictive Mechanism

The smooth pursuit eye movement system incorporates various control features enabling adaptation to specific tracking situations. In this work, we analyzed the interplay between two of these mechanisms: gain control and predictive pursuit. We tested human responses to high-frequency perturbations during step-ramp pursuit, as well as the pursuit of a periodically moving target. For the latter task, we found a nonlinear interaction between perturbation response and carrier acceleration. Responses to perturbations where the initial perturbation acceleration was contradirectional to carrier acceleration increased with carrier velocity, in a manner similar to that observed during step-ramp pursuit. In contrast, responses to perturbations with ipsidirectional initial perturbation and carrier acceleration were large for all carrier velocities. Modeling the pursuit system suggests that gain control and short-term prediction are separable elements. The observed effect may be explained by combining the standard gain control mechanism with a derivative-based short-term predictive mechanism. The nonlinear interaction between perturbation and carrier acceleration can be reproduced by assuming a signal saturation, which is acting on the derivative of the target velocity signal. Our results therefore argue for the existence of an internal estimate of target acceleration as a basis for a simple yet efficient short-term predictive mechanism.

Learning the trajectory of a moving visual target and evolution of its tracking in the monkey

An object moving in the visual field triggers a saccade that brings its image onto the fovea. It is followed by a combination of slow eye movements and catch-up saccades that try to keep the target image on the fovea as long as possible. The accuracy of this ability to track the "here-and-now" location of a visual target contrasts with the spatiotemporally distributed nature of its encoding in the brain. We show in six experimentally naive monkeys how this performance is acquired and gradually evolves during successive daily sessions. During the early exposure, the tracking is mostly saltatory, made of relatively large saccades separated by low eye velocity episodes, demonstrating that accurate (here and now) pursuit is not spontaneous and that gaze direction lags behind its location most of the time. Over the sessions, while the pursuit velocity is enhanced, the gaze is more frequently directed toward the current target location as a consequence of a 25% reduction in the number of catch-up saccades and a 37% reduction in size (for the first saccade). This smoothing is observed at several scales: during the course of single trials, across the set of trials within a session, and over successive sessions. We explain the neurophysiological processes responsible for this combined evolution of saccades and pursuit in the absence of stringent training constraints. More generally, our study shows that the oculomotor system can be used to discover the neural mechanisms underlying the ability to synchronize a motor effector with a dynamic external event.

Active inference and oculomotor pursuit: the dynamic causal modelling of eye movements

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We use a normative (Bayes optimal) model of oculomotor pursuit.

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We average the empirical responses of subjects performing a pursuit paradigm.

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We invert these responses using the pursuit model and dynamic causal modelling.

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We thereby estimate the precision of subjects’ Bayesian beliefs from their pursuit.

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This could be used to quantify abnormal precision encoding in schizophrenia.

Background

This paper introduces a new paradigm that allows one to quantify the Bayesian beliefs evidenced by subjects during oculomotor pursuit. Subjects’ eye tracking responses to a partially occluded sinusoidal target were recorded non-invasively and averaged. These response averages were then analysed using dynamic causal modelling (DCM). In DCM, observed responses are modelled using biologically plausible generative or forward models – usually biophysical models of neuronal activity.

New method

Our key innovation is to use a generative model based on a normative (Bayes-optimal) model of active inference to model oculomotor pursuit in terms of subjects’ beliefs about how visual targets move and how their oculomotor system responds. Our aim here is to establish the face validity of the approach, by manipulating the content and precision of sensory information – and examining the ensuing changes in the subjects’ implicit beliefs. These beliefs are inferred from their eye movements using the normative model.

Results

We show that on average, subjects respond to an increase in the ‘noise’ of target motion by increasing sensory precision in their models of the target trajectory. In other words, they attend more to the sensory attributes of a noisier stimulus. Conversely, subjects only change kinetic parameters in their model but not precision, in response to increased target speed.

Conclusions

Using this technique one can estimate the precisions of subjects’ hierarchical Bayesian beliefs about target motion. We hope to apply this paradigm to subjects with schizophrenia, whose pursuit abnormalities may result from the abnormal encoding of precision.

Cognitive processes involved in smooth pursuit eye movements: behavioral evidence, neural substrate and clinical correlation

Smooth-pursuit eye movements allow primates to track moving objects. Efficient pursuit requires appropriate target selection and predictive compensation for inherent processing delays. Prediction depends on expectation of future object motion, storage of motion information and use of extra-retinal mechanisms in addition to visual feedback. We present behavioral evidence of how cognitive processes are involved in predictive pursuit in normal humans and then describe neuronal responses in monkeys and behavioral responses in patients using a new technique to test these cognitive controls. The new technique examines the neural substrate of working memory and movement preparation for predictive pursuit by using a memory-based task in macaque monkeys trained to pursue (go) or not pursue (no-go) according to a go/no-go cue, in a direction based on memory of a previously presented visual motion display. Single-unit task-related neuronal activity was examined in medial superior temporal cortex (MST), supplementary eye fields (SEF), caudal frontal eye fields (FEF), cerebellar dorsal vermis lobules VI–VII, caudal fastigial nuclei (cFN), and floccular region. Neuronal activity reflecting working memory of visual motion direction and go/no-go selection was found predominantly in SEF, cerebellar dorsal vermis and cFN, whereas movement preparation related signals were found predominantly in caudal FEF and the same cerebellar areas. Chemical inactivation produced effects consistent with differences in signals represented in each area. When applied to patients with Parkinson's disease (PD), the task revealed deficits in movement preparation but not working memory. In contrast, patients with frontal cortical or cerebellar dysfunction had high error rates, suggesting impaired working memory. We show how neuronal activity may be explained by models of retinal and extra-retinal interaction in target selection and predictive control and thus aid understanding of underlying pathophysiology.

Emulation as an integrating principle for cognition

Emulations, defined as ongoing internal representations of potential actions and the futures those actions are expected to produce, play a critical role in directing human bodily activities. Studies of gross motor behavior, perception, allocation of attention, response to errors, interoception, and homeostatic activities, and higher cognitive reasoning suggest that the proper execution of all these functions relies on emulations. Further evidence supports the notion that reinforcement learning in humans is aimed at updating emulations, and that action selection occurs via the advancement of preferred emulations toward realization of their action and environmental prediction. Emulations are hypothesized to exist as distributed active networks of neurons in cortical and sub-cortical structures. This manuscript ties together previously unrelated theories of the role of prediction in different aspects of human information processing to create an integrated framework for cognition.

The influence of cues and stimulus history on the non-linear frequency characteristics of the pursuit response to randomized target motion

When humans pursue motion stimuli composed of alternating constant velocity segments of randomised duration (RD), they nevertheless initiate anticipatory eye deceleration before stimulus direction changes at a pre-programmed time based on averaging prior stimulus timing. We investigated, in both the time and frequency domains, how averaging interacts with deceleration cues by comparing responses to stimuli composed of segments that were either constant-velocity ramps or half-cycle sinusoids. RDs were randomized within 6 ranges, each comprising 8 RDs and having differing mean RD. In sine responses, deceleration cues could be used to modulate eye velocity for long-range stimuli (RD = 840-1,200 ms) but in the shortest range (RD = 240-660 ms) cues became ineffective, so that sine responses resembled ramp responses, and anticipatory timing was primarily dependent on averaging. Additionally, inclusion of short duration (240 ms) segments reduced peak eye velocity for all RDs within a range, even when longer RDs in the range (up to 1,080 ms) would normally elicit much higher velocities. These effects could be attributed to antagonistic interactions between visually driven pursuit components and pre-programmed anticipatory deceleration components. In the frequency domain, the changes in peak velocity and anticipatory timing with RD range were translated into non-linear gain and phase characteristics similar to those evoked by sum-of-sines stimuli. Notably, a reduction in pursuit gain occurred when high-frequency components associated with short duration segments were present. Results appear consistent with an adapted pursuit model, in which pre-programmed timing information derived from an internally reconstructed stimulus signal is stored in short-term memory and controls the initiation of predictive responses.

Incorporating prediction in models for two-dimensional smooth pursuit

A predictive component can contribute to the command signal for smooth pursuit. This is readily demonstrated by the fact that low frequency sinusoidal target motion can be tracked with zero time delay or even with a small lead. The objective of this study was to characterize the predictive contributions to pursuit tracking more precisely by developing analytical models for predictive smooth pursuit. Subjects tracked a small target moving in two dimensions. In the simplest case, the periodic target motion was composed of the sums of two sinusoidal motions (SS), along both the horizontal and the vertical axes. Motions following the same or similar paths, but having a richer spectral composition, were produced by having the target follow the same path but at a constant speed (CS), and by combining the horizontal SS velocity with the vertical CS velocity and vice versa. Several different quantitative models were evaluated. The predictive contribution to the eye tracking command signal could be modeled as a low-pass filtered target acceleration signal with a time delay. This predictive signal, when combined with retinal image velocity at the same time delay, as in classical models for the initiation of pursuit, gave a good fit to the data. The weighting of the predictive acceleration component was different in different experimental conditions, being largest when target motion was simplest, following the SS velocity profiles.

Oculomotor prediction of accelerative target motion during occlusion: long-term and short-term effects

The present study examined the influence of long-term (i.e., between-trial) and short-term (i.e., within-trial) predictive mechanisms on ocular pursuit during transient occlusion. To this end, we compared ocular pursuit of accelerative and decelerative target motion in trials that were presented in random or blocked-order. Catch trials in which target acceleration was unexpectedly modified were randomly interleaved in blocked-order trials. Irrespective of trial order, eye velocity decayed following target occlusion and then recovered towards the different levels of target velocity at reappearance. However, the recovery was better scaled in blocked-order trials than random-order trials. In blocked-order trials only, the reduced gain of smooth pursuit during occlusion was compensated by a change in saccade amplitude and resulted in total eye displacement (TED) that was well matched to target displacement. Subsidiary analysis indicated that three repeats of blocked-order trials was sufficient for participants to modify eye displacement compared to that exhibited in random-order trials, although more trials were required before end-occlusion eye velocity was better scaled. Finally, we found that participants exhibited evidence of a scaled response to an unexpected change in target acceleration (i.e., catch trials), although there were also transfer effects from the preceding blocked-order trials. These findings are consistent with the suggestion that on-the-fly prediction (short-term effect) is combined with memorized information from previous trials (long-term effect) to generate a persistent and veridical prediction of occluded target motion.

Dynamics of smooth pursuit maintenance

Smooth pursuit eye movements allow the approximate stabilization of a moving visual target on the retina. To study the dynamics of smooth pursuit, we measured eye velocity during the visual tracking of a Gabor target moving at a constant velocity plus a noisy perturbation term. The optimal linear filter linking fluctuations in target velocity to evoked fluctuations in eye velocity was computed. These filters predicted eye velocity to novel stimuli in the 0- to 15-Hz band with good accuracy, showing that pursuit maintenance is approximately linear under these conditions. The shape of the filters were indicative of fast dynamics, with pure delays of merely approximately 67 ms, times-to-peak of approximately 115 ms, and effective integration times of approximately 45 ms. The gain of the system, reflected in the amplitude of the filters, was inversely proportional to the size of the velocity fluctuations and independent of the target mean speed. A modest slow-down of the dynamics was observed as the contrast of the target decreased. Finally, the temporal filters recovered during fixation and pursuit were similar in shape, supporting the notion that they might share a common underlying circuitry. These findings show that the visual tracking of moving objects by the human eye includes a reflexive-like pathway with high contrast sensitivity and fast dynamics.

Anticipatory models in gaze control: a developmental model

Infants gradually learn to predict the motion of moving targets and change from a strategy that mainly depends on saccades to one that depends on anticipatory control of smooth pursuit. A model is described that combines three types of mechanisms for gaze control that develops in a way similar to infants. Initially, gaze control is purely reactive, but as the anticipatory models become more accurate, the gain of the pursuit will increase and lead to a larger fraction of smooth eye movements. Finally, a third system learns to predict changes in target motion, which will lead to fast retuning of the parameters in the anticipatory model.

Smooth pursuit of nonvisual motion

Unlike saccades, smooth pursuit eye movements (SPEMs) are not under voluntary control and their initiation generally requires a moving visual target. However, there are various reports of limited smooth pursuit of the motion of a subject's own finger in total darkness (pursuit based on proprioceptive feedback) and to the combination of proprioception and tactile motion as an unseen finger was moved voluntarily over a smooth surface. In contrast, SPEMs to auditory motion are not distinguishable from pursuit of imagined motion. These reports of smooth pursuit of nonvisual motion cues used a variety of paradigms and different stimuli. In addition, the results have often relied primarily on qualitative descriptions of the smooth pursuit. Here, we directly compare measurements of smooth pursuit gain (eye velocity/stimulus velocity) to visual, auditory, proprioceptive, tactile, and combined tactile + proprioceptive motion stimuli. The results demonstrate high gains for visual pursuit, low gains for auditory pursuit, and intermediate, statistically indistinguishable gains for tactile, proprioceptive, and proprioceptive + tactile pursuit.

Temporal evolution of 2-dimensional direction signals used to guide eye movements

The smooth pursuit system must integrate many local motion measurements into a coherent estimate of target velocity. Several laboratories have studied this integration process using eye movements elicited by targets, such as tilted bars, containing conflicts between local motion signals measured along contours [one dimensional (1D)] and those measured at the bar's endpoints, or terminators [two dimensional (2D)]. The general finding is that 1D signals dominate early responses, whereas later components of the behavior are determined by 2D signals. We studied the dynamics of the integration process in macaque monkeys by systematically varying the relative proportions of 1D and 2D signals and the retinal eccentricities at which they appeared. Predictably, longer bars produced greater and longer-lasting contour-induced deviations. The evolution of the 2D response occurred over a period of 50-400 ms, depending on the relative proportions of 1D and 2D signals. As contours were displaced from the fovea the deviation decreased but much less so for early (1st 40 ms) than for late (subsequent 40 ms) pursuit initiation. These bottom-up effects could be overcome to a limited extent by the top-down influence of predictability. Finally, we observed that when animals were free to track any part of the bar, they spontaneously made short-latency saccades to the terminators on most trials, especially when the bars were tilted. This suggests an increased saliency of moving terminators, particularly when discrepancies exist among local motion signals.

Oculomotor responses to gradual changes in target direction

Smooth pursuit tracking of targets moving linearly (in one dimension) is well characterized by a model where retinal image motion drives eye acceleration. However, previous findings suggest that this model cannot be simply extended to two-dimensional (2D) tracking. To examine 2D pursuit, in the present study, human subjects tracked a target that moved linearly and then followed the arc of a circle. The subjects' gaze angular velocity accurately matched target angular velocity, but the direction of smooth pursuit always lagged behind the current target direction. Pursuit speed slowly declined after the onset of the curve (for about 500 ms), even though the target speed was constant. In a second experiment, brief perturbations were presented immediately prior to the beginning of the change in direction. The subjects' responses to these perturbations consisted of two components: (1) a response specific to the parameters of the perturbation and (2) a nonspecific response that always consisted of a transient decrease in gaze velocity. With the exception of this nonspecific response, pursuit behavior in response to the gradual changes in direction and to the perturbations could be explained by using retinal slip (image velocity) as the input signal. The retinal slip was parallel and perpendicular to the instantaneous direction of pursuit ultimately resulted in changes in gaze velocity (via gaze acceleration). Perhaps due to the subjects' expectations that the target will curve, the sensitivity to the image motion in the direction of pursuit was not as strong as the sensitivity to image motion perpendicular to gaze velocity.

Commentary: smooth pursuit eye movements: from low-level to high-level vision

If an object of great interest moves in our environment, we are able to elicit smooth pursuit eye movements that keep the image of the moving object stationary on our fovea. The processing of visual motion underlying the execution of smooth pursuit eye movements is very similar to the processing underlying the perception of visual motion. During initiation of smooth pursuit, an averaging across all available motion information occurs. Cognitive factors including attention, prediction and learning are able to influence the execution of smooth pursuit. The pursuit target trajectory in space is represented in the discharge rates of neurons in the posterior parietal cortex of rhesus monkeys.

Ocular pursuit responses to repeated, single-cycle sinusoids reveal behavior compatible with predictive pursuit

The link between anticipatory smooth eye movements and prediction in sinusoidal pursuit was investigated by presentation of series of identical, single-cycle, sinusoidal target motion stimuli. Stimuli occurred at randomized intervals (1.2-2.8 s) but were preceded by an audio warning cue 480 ms before each presentation. Cycle period (T) varied from 0.64 to 2.56 s and target displacement from 4 to 20 degrees in separate series. For T </= 1.28 s, responses to the first stimulus of each series exhibited a time delay across the whole cycle (mean = 121 ms for T = 0.8 s). But, in the second and subsequent (steady-state) presentations, anticipatory movements, proportional to target velocity, were made and time delay was significantly reduced (mean = 43 ms for T = 0.8 s). Steady-state time delays were comparable to those evoked during continuous sinusoidal pursuit and less than pursuit reaction time. Even when subjects did not follow the target in the first presentation, they responded to the second presentation with reduced time delay. Throughout the experiments, three types of catch trial (A-C) were introduced. In A, the target failed to appear as expected after the warning cue. Anticipatory smooth movements were initiated, reaching a peak velocity proportional to prior target velocity around 200 ms after expected target onset. In B, the target stopped midway through the cycle. Even if the target remained on and was stationary, the eye movement continued to be driven away from the stationary target with a velocity similar to that of prior responses, reaching a peak velocity that was again proportional to expected target velocity after >/=205 ms. In C, the amplitude of the single sinusoid was unexpectedly increased or decreased. When it decreased, eye velocity throughout the first half-cycle of the response was close to that executed in response to prior stimuli of higher velocity and did not return to an appropriate level for 382-549 ms. Conversely, when amplitude increased, eye velocity remained inappropriately low for the first half-cycle. Results of A and C indicate that subjects are able to use velocity information stored from prior presentations to initiate an oculomotor drive that predominates over visual feedback for the first half-cycle. Results of B indicate that the second part of the cycle is also preprogrammed because it continued despite efforts to suppress it by fixation. The results suggest that initial retinal velocity error information can be sampled, stored, and subsequently replayed as a bi-directional anticipatory pattern of movement that reduces temporal delay and could account for predictive control during sinusoidal pursuit.

Cerebellar flocculus and paraflocculus Purkinje cell activity during circular pursuit in monkey

Responses from 69 Purkinje cells in the flocculus and paraflocculus of two rhesus monkeys were studied during smooth pursuit of targets moving along circular trajectories and compared with responses during sinusoidal pursuit and fixation. A variety of interesting responses was observed during circular pursuit. Although some neurons fired most strongly in a single preferred direction during clockwise (CW) and counterclockwise (CCW) pursuit, others had directional preferences that changed with rotation direction. Some of these neurons showed similar modulation amplitudes during CW and CCW pursuit, whereas other neurons showed a preference for a particular rotation direction. Response specificity also was observed during sinusoidal pursuit. Some neurons showed responses that were much stronger during centrifugal pursuit, others showed a preference for centripetal pursuit, and still others showed responses during both centripetal and centrifugal motion. Differences in preferred response direction were sometimes observed for centripetal versus centrifugal pursuit. CW/CCW and centrifugal/centripetal preferences were not explained by a breakdown in component additivity. That is, modulations in firing rate during pursuit along a circular trajectory equaled the sum of modulations during horizontal and vertical sinusoidal components as well as for diagonal components. Instead all responses were well fit by a model that expressed the instantaneous firing rate of each neuron as a multilinear function of the two-dimensional position and velocity of the eye. This model generalized well to performance at different sinusoidal frequencies. It did somewhat less well for responses during fixation, suggesting some separation in the neural mechanisms of dynamic and static positioning. The model indicates that position sensitivity accounted for approximately 36% of the modulation during circular pursuit, and velocity sensitivity accounted for approximately 64%. When position and velocity sensitivity vectors were aligned, responses were simpler and modulations were similar during CW versus CCW pursuit. In contrast, when these vectors pointed in different directions, response complexity increased. Nonaligned position and velocity influences tended to reinforce during circular pursuit in one direction and to cancel each other during pursuit in the opposite direction. They also tended to produce response differences during centripetal versus centrifugal sinusoidal pursuit. The distinct roles played by position and velocity in shaping Purkinje cell responses are compatible with the control signals required to generate smooth pursuit along circular and other two-dimensional trajectories.

Slow eye movements

Monkeys and humans are able to perform different types of slow eye movements. The analysis of the eye movement parameters, as well as the investigation of the neuronal activity underlying the execution of slow eye movements, offer an excellent opportunity to study higher brain functions such as motion processing, sensorimotor integration, and predictive mechanisms as well as neuronal plasticity and motor learning. As an example, since there exists a tight connection between the execution of slow eye movements and the processing of any kind of motion, these eye movements can be used as a biological, behavioural probe for the neuronal processing of motion. Global visual motion elicits optokinetic nystagmus, acting as a visual gaze stabilization system. The underlying neuronal substrate consists mainly of the cortico-pretecto-olivo-cerebellar pathway. Additionally, another gaze stabilization system depends on the vestibular input known as the vestibulo-ocular reflex. The interactions between the visual and vestibular stabilization system are essential to fulfil the plasticity of the vestibulo-ocular reflex representing a simple form of learning. Local visual motion is a necessary prerequisite for the execution of smooth pursuit eye movements which depend on the cortico-pontino-cerebellar pathway. In the wake of saccades, short-latency eye movements can be elicited by brief movements of the visual scene. Finally, eye movements directed to objects in different planes of depth consist of slow movements also. Although there is some overlap in the neuronal substrates underlying these different types of slow eye movements, there are brain areas whose activity can be associated exclusively with the execution of a special type of slow eye movement.

Single-neuron activity in the dorsomedial frontal cortex during smooth-pursuit eye movements to predictable target motion

A region of dorsomedial frontal cortex (DMFC) has been implicated in planning and executing saccadic eye movements; hence it has been referred to as a supplementary eye field (SEF). Recently, activity related to executing smooth-pursuit eye movements has been recorded from the DMFC, and microstimulation here has been shown to evoke smooth eye movements. This report documents neuronal activity present in smooth-pursuit tasks where the predictability of target motion was manipulated. The activity of many neurons in the DMFC reached a peak when a predictable change in target motion occurred. Furthermore, the peak activity of some cells was systematically shifted by manipulating the duration of the target event, indicating that the network these neurons were in could learn the temporal characteristics of new target motion. Finally, the activity of most neurons tested was greater when target motion was predictable than when it was unpredictable. The results suggest that the DMFC participates in planning smooth-pursuit eye movements based on past stimulus history.

Predictive smooth pursuit of complex two-dimensional trajectories demonstrated by perturbation responses in monkeys

Two-dimensional sum-of-sines waveforms were pursued by the eye with very small phase delays compared with visual feedback delays estimated in the same monkeys. Processing delays in making smooth corrections averaged 90 msec after infrequent right-angle perturbations from a circular trajectory. These feedback delays were much larger than component phase delays during pursuit that averaged: 10 msec for sinusoids, 3 msec for circles, 20 msec for sum-of-two-sines trajectories, and 19 msec for sum-of-three-sines trajectories. This suggests that predictive control can play a strong role during tracking for a variety of simple and complex target trajectories.

Prediction of complex two-dimensional trajectories by a cerebellar model of smooth pursuit eye movement

A neural network model based on the anatomy and physiology of the cerebellum is presented that can generate both simple and complex predictive pursuit, while also responding in a feedback mode to visual perturbations from an ongoing trajectory. The model allows the prediction of complex movements by adding two features that are not present in other pursuit models: an array of inputs distributed over a range of physiologically justified delays, and a novel, biologically plausible learning rule that generated changes in synaptic strengths in response to retinal slip errors that arrive after long delays. To directly test the model, its output was compared with the behavior of monkeys tracking the same trajectories. There was a close correspondence between model and monkey performance. Complex target trajectories were created by summing two or three sinusoidal components of different frequencies along horizontal and/or vertical axes. Both the model and the monkeys were able to track these complex sum-of-sines trajectories with small phase delays that averaged 8 and 20 ms in magnitude, respectively. Both the model and the monkeys showed a consistent relationship between the high- and low-frequency components of pursuit: high-frequency components were tracked with small phase lags, whereas low-frequency components were tracked with phase leads. The model was also trained to track targets moving along a circular trajectory with infrequent right-angle perturbations that moved the target along a circle meridian. Before the perturbation, the model tracked the target with very small phase differences that averaged 5 ms. After the perturbation, the model overshot the target while continuing along the expected nonperturbed circular trajectory for 80 ms, before it moved toward the new perturbed trajectory. Monkeys showed similar behaviors with an average phase difference of 3 ms during circular pursuit, followed by a perturbation response after 90 ms. In both cases, the delays required to process visual information were much longer than delays associated with nonperturbed circular and sum-of-sines pursuit. This suggests that both the model and the eye make short-term predictions about future events to compensate for visual feedback delays in receiving information about the direction of a target moving along a changing trajectory. In addition, both the eye and the model can adjust to abrupt changes in target direction on the basis of visual feedback, but do so after significant processing delays.