Saccadic eye movements minimize the consequences of motor noise

The durations and trajectories of our saccadic eye movements are remarkably stereotyped. We have no voluntary control over these properties but they are determined by the movement amplitude and, to a smaller extent, also by the movement direction and initial eye orientation. Here we show that the stereotyped durations and trajectories are optimal for minimizing the variability in saccade endpoints that is caused by motor noise. The optimal duration can be understood from the nature of the motor noise, which is a combination of signal-dependent noise favoring long durations, and constant noise, which prefers short durations. The different durations of horizontal vs. vertical and of centripetal vs. centrifugal saccades, and the somewhat surprising properties of saccades in oblique directions are also accurately predicted by the principle of minimizing movement variability. The simple and sensible principle of minimizing the consequences of motor noise thus explains the full stereotypy of saccadic eye movements. This suggests that saccades are so stereotyped because that is the best strategy to minimize movement errors for an open-loop motor system.     

Frequency characteristics of the saccadic eye movement

Using a piecewise linear approach, individual saccadic eye movements have been Fourier decomposed in an attempt to determine the effect of saccadic amplitude on frequency characteristics. These characteristics were plotted in the traditional Bode plot form, showing gain and phase as a function of frequency for various eye movement amplitudes. Up to about one octave beyond the -3 db gain frequency, the limiting system dynamics represented by the saccadic trajectory of a given amplitude may be considered linear and second order. The -3 db gain frequency was used as a measure of bandwidth, and the -90 degrees phase crossover frequency was used as a measure of undamped natural frequency. These two quantities were used to calculate the damping factor. Both bandwidth and undamped natural frequency decrease with increasing saccadic eye movement amplitude. The damping factor shows no trend with amplitude and indicates approximate critical damping. When compared with the normal variation of characteristics for a given movement, the frequency characteristics of fixed-amplitude saccades showed no generalized trends with changes in direction or DC operating level of movement.     

Probability of Seeing Increases Saccadic Readiness

Associating movement directions or endpoints with monetary rewards or costs influences movement parameters in humans, and associating movement directions or endpoints with food reward influences movement parameters in non-human primates. Rewarded movements are facilitated relative to non-rewarded movements. The present study examined to what extent successful foveation facilitated saccadic eye movement behavior, with the hypothesis that foveation may constitute an informational reward. Human adults performed saccades to peripheral targets that either remained visible after saccade completion or were extinguished, preventing visual feedback. Saccades to targets that were systematically extinguished were slower and easier to inhibit than saccades to targets that afforded successful foveation, and this effect was modulated by the probability of successful foveation. These results suggest that successful foveation facilitates behavior, and that obtaining the expected sensory consequences of a saccadic eye movement may serve as a reward for the oculomotor system.     

The saccadic and neurological deficits in type 3 Gaucher disease

Our objective was to characterize the saccadic eye movements in patients with type 3 Gaucher disease (chronic neuronopathic) in relationship to neurological and neurophysiological abnormalities. For approximately 4 years, we prospectively followed a cohort of 15 patients with Gaucher type 3, ages 8-28 years, by measuring saccadic eye movements using the scleral search coil method. We found that patients with type 3 Gaucher disease had a significantly higher regression slope of duration vs amplitude and peak duration vs amplitude compared to healthy controls for both horizontal and vertical saccades. Saccadic latency was significantly increased for horizontal saccades only. Downward saccades were more affected than upward saccades. Saccade abnormalities increased over time in some patients reflecting the slowly progressive nature of the disease. Phase plane plots showed individually characteristic patterns of abnormal saccade trajectories. Oculo-manual dexterity scores on the Purdue Pegboard test were low in virtually all patients, even in those with normal cognitive function. Vertical saccade peak duration vs amplitude slope significantly correlated with IQ and with the performance on the Purdue Pegboard but not with the brainstem and somatosensory evoked potentials. We conclude that, in patients with Gaucher disease type 3, saccadic eye movements and oculo-manual dexterity are representative neurological functions for longitudinal studies and can probably be used as endpoints for therapeutic clinical trials. TRIAL REGISTRATION: ClinicalTrials.gov NCT00001289.     

Blink Perturbation Effects on Saccades Evoked by Microstimulation of the Superior Colliculus

Current knowledge of saccade-blink interactions suggests that blinks have paradoxical effects on saccade generation. Blinks suppress saccade generation by attenuating the oculomotor drive command in structures like the superior colliculus (SC), but they also disinhibit the saccadic system by removing the potent inhibition of pontine omnipause neurons (OPNs). To better characterize these effects, we evoked the trigeminal blink reflex by delivering an air puff to one eye as saccades were evoked by sub-optimal stimulation of the SC. For every stimulation site, the peak and average velocities of stimulation with blink movements (SwBMs) were lower than stimulation-only saccades (SoMs), supporting the notion that the oculomotor drive is weakened in the presence of a blink. In contrast, the duration of the SwBMs was longer, consistent with the hypothesis that the blink-induced inhibition of the OPNs could prolong the window of time available for oculomotor commands to drive an eye movement. The amplitude of the SwBM could also be larger than the SoM amplitude obtained from the same site, particularly for cases in which blink-associated eye movements exhibited the slowest kinematics. The results are interpreted in terms of neural signatures of saccade-blink interactions.     

Different programming modes of human saccadic eye movements as a function of stimulus eccentricity: Indications of a functional subdivision of the visual field

1. Voluntary saccadic eye movements were made toward flashes of light on the horizontal meridian, whose duration and distance from the point of fixation were varied; eye movements were measured using d.c.-electrooculography.—2. Targets within 10°–15° eccentricity are usually reached by one saccadic eye movement. When the eyes turn toward targets of more than 10°–15° eccentricity, the first saccadic eye movement falls short of the target by an angle usually not exceeding 10°. The presence of the image of the target off the fovea (visual error signal) subsequent to such an undershoot elicits, after a short interval, corrective saccades (usually one) which place the image of the target on the fovea. In the absence of a visual error signal, the probability of occurrence of corrective saccades is low, but it increases with greater target eccentricities. These observations suggest that there are different, eccentricity-dependent modes of programming saccadic eye movements.—3. Saccadic eye movements appear to be programmed in retinal coordinates. This conclusion is based on the observations that, irrespective of the initial position of the eyes in the orbit, a) there are different programming modes for eye movements to targets within and beyond 10°–15° from the fixation point, and b_ the maximum velocity of saccadic eye movements is always reached at 25° to 30° target eccentricity. —4. Distributions of latency and intersaccadic interval (ISI) are frequently multimodal, with a separation between modes of 30 to 40 msec. These observations suggest that saccadic eye movements are produced by mechanisms which, at a frequency of 30 Hz, process visual information. —5. Corrective saccades may occur after extremely short intervals (30 to 60 msec) regardless of whether or not a visual error signal is present; the eyes may not even come to a complete stop during these very short intersaccadic intervals. It is suggested that these corrective saccades are triggered by errors in the programming of the initial saccadic eye movements, and not by a visual error signal. —6. The exitence of different, eccentricity-dependent programming modes of saccadic eye movements, is further supported by anatomical, physiological, psychophysical, and neuropathological observations that suggest a dissociation of visual functions dependent on retinal eccentricity. Saccadic eye movements to targets more eccentric than 10°–15° appear to be executed by a mechanism involving the superior colliculus (perhaps independent of the visual cortex), whereas saccadic eye movements to less eccentric targets appear to depend on a mechanism involving the geniculo-cortical pathway (perhaps in collaboration with the superior colliculus).     

A Mathematical Model of Optimal Saccadic Eye Movement by a Pair of Muscles

This paper presents a model of saccadic eye movements. Eye movements are considered as being ballistic, since saccades (rapid concurrent movements of both eyes) occur several hundred thousand times per day; visual perception of the environment is interrupted by a saccade. The optimal control was constructed for the motion considered in three consecutively refined assumptions. The controls included in the time-optimal problem were the resultant moment of force exerted by the extraocular muscles, individual moments of force exerted by either muscle of the agonist–antagonist pair, and finally, the rate of change of these moments. This approach is consistent with the view that is currently upheld by physiologists, who believe that a saccade is programmed by the central nervous system before the beginning of an eye movement and is scarcely adjusted during the movement itself. The solution of the optimal control problem and the results obtained by subsequent numerical modeling of saccadic trajectories were compared with the published experimental data. The saccadic trajectories were compared based on the main sequence, the known consistent relationship between saccade amplitude and duration, which is the most widely applied and commonly accepted way of describing saccade data. The main sequence of saccades obtained from the solution of the optimal control problem formulated in the most complete form agreed well with published experimental results.     

Both Lexical and Non-Lexical Characters Are Processed during Saccadic Eye Movements

On average our eyes make 3–5 saccadic movements per second when we read, although their neural mechanism is still unclear. It is generally thought that saccades help redirect the retinal fovea to specific characters and words but that actual discrimination of information only occurs during periods of fixation. Indeed, it has been proposed that there is active and selective suppression of information processing during saccades to avoid experience of blurring due to the high-speed movement. Here, using a paradigm where a string of either lexical (Chinese) or non-lexical (alphabetic) characters are triggered by saccadic eye movements, we show that subjects can discriminate both while making saccadic eye movement. Moreover, discrimination accuracy is significantly better for characters scanned during the saccadic movement to a fixation point than those not scanned beyond it. Our results showed that character information can be processed during the saccade, therefore saccades during reading not only function to redirect the fovea to fixate the next character or word but allow pre-processing of information from the ones adjacent to the fixation locations to help target the next most salient one. In this way saccades can not only promote continuity in reading words but also actively facilitate reading comprehension.     

On identification of saccades from sinusoidal eye movement signals

Sinusoidal eye movements and potential saccadic eye movements are examined using the syntactic pattern recognition method presented previously. A few computer tests are presented for the verification of potential saccades from signals of sinusoidal eye movements. The technique was developed and tested with electro-oculographic signals. The verification of saccades consists of three tests: the estimation of average noise peaks in an eye movement signal; an angular velocity threshold; and the comparison between a sinusoidal eye movement signal and the corresponding stimulus signal. The technique is also efficient for noisy signals of eye movements, which were stimulated by both predictive and non-predictive sinusoidal stimulus movements.     

The Fixation and Saccade P3

Although most instances of object recognition during natural viewing occur in the presence of saccades, the neural correlates of objection recognition have almost exclusively been examined during fixation. Recent studies have indicated that there are post-saccadic modulations of neural activity immediately following eye movement landing; however, whether post-saccadic modulations affect relatively late occurring cognitive components such as the P3 has not been explored. The P3 as conventionally measured at fixation is commonly used in brain computer interfaces, hence characterizing the post-saccadic P3 could aid in the development of improved brain computer interfaces that allow for eye movements. In this study, the P3 observed after saccadic landing was compared to the P3 measured at fixation. No significant differences in P3 start time, temporal persistence, or amplitude were found between fixation and saccade trials. Importantly, sensory neural responses canceled in the target minus distracter comparisons used to identify the P3. Our results indicate that relatively late occurring cognitive neural components such as the P3 are likely less sensitive to post saccadic modulations than sensory neural components and other neural activity occurring shortly after eye movement landing. Furthermore, due to the similarity of the fixation and saccade P3, we conclude that the P3 following saccadic landing could possibly be used as a viable signal in brain computer interfaces allowing for eye movements.     

Looking for Discriminating Is Different from Looking for Looking’s Sake

Recent studies provide evidence for task-specific influences on saccadic eye movements. For instance, saccades exhibit higher peak velocity when the task requires coordinating eye and hand movements. The current study shows that the need to process task-relevant visual information at the saccade endpoint can be, in itself, sufficient to cause such effects. In this study, participants performed a visual discrimination task which required a saccade for successful completion. We compared the characteristics of these task-related saccades to those of classical target-elicited saccades, which required participants to fixate a visual target without performing a discrimination task. The results show that task-related saccades are faster and initiated earlier than target-elicited saccades. Differences between both saccade types are also noted in their saccade reaction time distributions and their main sequences, i.e., the relationship between saccade velocity, duration, and amplitude.     

Cortical mechanisms for trans-saccadic memory and integration of multiple object features

Constructing an internal representation of the world from successive visual fixations, i.e. separated by saccadic eye movements, is known as trans-saccadic perception. Research on trans-saccadic perception (TSP) has been traditionally aimed at resolving the problems of memory capacity and visual integration across saccades. In this paper, we review this literature on TSP with a focus on research showing that egocentric measures of the saccadic eye movement can be used to integrate simple object features across saccades, and that the memory capacity for items retained across saccades, like visual working memory, is restricted to about three to four items. We also review recent transcranial magnetic stimulation experiments which suggest that the right parietal eye field and frontal eye fields play a key functional role in spatial updating of objects in TSP. We conclude by speculating on possible cortical mechanisms for governing egocentric spatial updating of multiple objects in TSP.     

Influence of Retinal Image Shifts and Extra-Retinal Eye Movement Signals on Binocular Rivalry Alternations

Previous studies have indicated that saccadic eye movements correlate positively with perceptual alternations in binocular rivalry, presumably because the foveal image changes resulting from saccades, rather than the eye movement themselves, cause switches in awareness. Recently, however, we found evidence that retinal image shifts elicit so-called onset rivalry and not percept switches as such. These findings raise the interesting question whether onset rivalry may account for correlations between saccades and percept switches.We therefore studied binocular rivalry when subjects made eye movements across a visual stimulus and compared it with the rivalry in a ‘replay’ condition in which subjects maintained fixation while the same retinal displacements were reproduced by stimulus displacements on the screen. We used dichoptic random-dot motion stimuli viewed through a stereoscope, and measured eye and eyelid movements with scleral search-coils.Positive correlations between retinal image shifts and perceptual switches were observed for both saccades and stimulus jumps, but only for switches towards the subjects'' preferred eye at stimulus onset. A similar asymmetry was observed for blink-induced stimulus interruptions. Moreover, for saccades, amplitude appeared crucial as the positive correlation persisted for small stimulus jumps, but not for small saccades (amplitudes < 1°). These findings corroborate our tenet that saccades elicit a form of onset rivalry, and that rivalry is modulated by extra-retinal eye movement signals.     

A competitive integration model of exogenous and endogenous eye movements

We present a model of the eye movement system in which the programming of an eye movement is the result of the competitive integration of information in the superior colliculi (SC). This brain area receives input from occipital cortex, the frontal eye fields, and the dorsolateral prefrontal cortex, on the basis of which it computes the location of the next saccadic target. Two critical assumptions in the model are that cortical inputs are not only excitatory, but can also inhibit saccades to specific locations, and that the SC continue to influence the trajectory of a saccade while it is being executed. With these assumptions, we account for many neurophysiological and behavioral findings from eye movement research. Interactions within the saccade map are shown to account for effects of distractors on saccadic reaction time (SRT) and saccade trajectory, including the global effect and oculomotor capture. In addition, the model accounts for express saccades, the gap effect, saccadic reaction times for antisaccades, and recorded responses from neurons in the SC and frontal eye fields in these tasks.     

A model that integrates eye velocity commands to keep track of smooth eye displacements

Past results have reported conflicting findings on the oculomotor system’s ability to keep track of smooth eye movements in darkness. Whereas some results indicate that saccades cannot compensate for smooth eye displacements, others report that memory-guided saccades during smooth pursuit are spatially correct. Recently, it was shown that the amount of time before the saccade made a difference: short-latency saccades were retinotopically coded, whereas long-latency saccades were spatially coded. Here, we propose a model of the saccadic system that can explain the available experimental data. The novel part of this model consists of a delayed integration of efferent smooth eye velocity commands. Two alternative physiologically realistic neural mechanisms for this integration stage are proposed. Model simulations accurately reproduced prior findings. Thus, this model reconciles the earlier contradictory reports from the literature about compensation for smooth eye movements before saccades because it involves a slow integration process. Action Editor: Jonathan D. Victor     

Evidence for the lateral intraparietal area as the parietal eye field.

It has long been appreciated that the posterior parietal cortex plays a role in the processing of saccadic eye movements. Only recently has it been discovered that a small cortical area, the lateral intraparietal area, within this much larger area appears to be specialized for saccadic eye movements. Unlike other cortical areas in the posterior parietal cortex, the lateral intraparietal area has strong anatomical connections to other saccade centers, and its cells have saccade-related responses that begin before the saccades. The lateral intraparietal area appears to be neither a strictly visual nor strictly motor structure; rather it performs visuomotor integration functions including determining the spatial location of saccade targets and forming plans to make eye movements.     

Cursive writing with smooth pursuit eye movements

The eyes never cease to move: ballistic saccades quickly turn the gaze toward peripheral targets, whereas smooth pursuit maintains moving targets on the fovea where visual acuity is best. Despite the oculomotor system being endowed with exquisite motor abilities, any attempt to generate smooth eye movements against a static background results in saccadic eye movements [1, 2]. Although exceptions to this rule have been reported [3-5], volitional control over smooth eye movements is at best rudimentary. Here, I introduce a novel, temporally modulated visual display, which, although static, sustains smooth eye movements in arbitrary directions. After brief training, participants gain volitional control over smooth pursuit eye movements and can generate digits, letters, words, or drawings at will. For persons deprived of limb movement, this offers a fast, creative, and personal means of linguistic and emotional expression.     

Saccadic adaptation to moving targets

Saccades are so called ballistic movements which are executed without online visual feedback. After each saccade the saccadic motor plan is modified in response to post-saccadic feedback with the mechanism of saccadic adaptation. The post-saccadic feedback is provided by the retinal position of the target after the saccade. If the target moves after the saccade, gaze may follow the moving target. In that case, the eyes are controlled by the pursuit system, a system that controls smooth eye movements. Although these two systems have in the past been considered as mostly independent, recent lines of research point towards many interactions between them. We were interested in the question if saccade amplitude adaptation is induced when the target moves smoothly after the saccade. Prior studies of saccadic adaptation have considered intra-saccadic target steps as learning signals. In the present study, the intra-saccadic target step of the McLaughlin paradigm of saccadic adaptation was replaced by target movement, and a post-saccadic pursuit of the target. We found that saccadic adaptation occurred in this situation, a further indication of an interaction of the saccadic system and the pursuit system with the aim of optimized eye movements.     

Attention governs action in the primate frontal eye field

While the motor and attentional roles of the frontal eye field (FEF) are well documented, the relationship between them is unknown. We exploited the known influence of visual motion on the apparent positions of targets, and measured how this illusion affects saccadic eye movements during FEF microstimulation. Without microstimulation, saccades to a moving grating are biased in the direction of motion, consistent with the apparent position illusion. Here we show that microstimulation of spatially aligned FEF representations increases the influence of this illusion on saccades. Rather than simply impose a fixed-vector signal, subthreshold stimulation directed saccades away from the FEF movement field, and instead more strongly in the direction of visual motion. These results demonstrate that the attentional effects of FEF stimulation govern visually guided saccades, and suggest that the two roles of the FEF work together to select both the features of a target and the appropriate movement to foveate it.     

Open-loop simulations of the primate saccadic system using burst cell discharge from the superior colliculus

 Saccade-related burst neurons (SRBNs) in the monkey superior colliculus (SC) have been hypothesized to provide the brainstem saccadic burst generator with the dynamic error signal and the movement initiating trigger signal. To test this claim, we performed two sets of open-loop simulations on a burst generator model with the local feedback disconnected using experimentally obtained SRBN activity as both the driving and trigger signal inputs to the model. First, using neural data obtained from cells located near the middle of the rostral to caudal extent of the SC, the internal parameters of the model were optimized by means of a stochastic hill-climbing algorithm to produce an intermediate-sized saccade. The parameter values obtained from the optimization were then fixed and additional simulations were done using the experimental data from rostral collicular neurons (small saccades) and from more caudal neurons (large saccades); the model generated realistic saccades, matching both position and velocity profiles of real saccades to the centers of the movement fields of all these cells. Second, the model was driven by SRBN activity affiliated with interrupted saccades, the resumed eye movements observed following electrical stimulation of the omnipause region. Once again, the model produced eye movements that closely resembled the interrupted saccades produced by such simulations, but minor readjustment of parameters reflecting the weight of the projection of the trigger signal was required. Our study demonstrates that a model of the burst generator produces reasonably realistic saccades when driven with actual samples of SRBN discharges. Received: 25 October 1994/Accepted in revised form: 20 June 1995