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.     

Saccadic Momentum and Facilitation of Return Saccades Contribute to an Optimal Foraging Strategy

The interest in saccadic IOR is funneled by the hypothesis that it serves a clear functional purpose in the selection of fixation points: the facilitation of foraging. In this study, we arrive at a different interpretation of saccadic IOR. First, we find that return saccades are performed much more often than expected from the statistical properties of saccades and saccade pairs. Second, we find that fixation durations before a saccade are modulated by the relative angle of the saccade, but return saccades show no sign of an additional temporal inhibition. Thus, we do not find temporal saccadic inhibition of return. Interestingly, we find that return locations are more salient, according to empirically measured saliency (locations that are fixated by many observers) as well as stimulus dependent saliency (defined by image features), than regular fixation locations. These results and the finding that return saccades increase the match of individual trajectories with a grand total priority map evidences the return saccades being part of a fixation selection strategy that trades off exploration and exploitation.     

Human fast negative EEG potentials before express saccades

Fast negative EEG potentials preceding fast regular saccades and express saccades were studied by the method of backward averaging under conditions of monocular stimulation of the right and left eye. "Step" and "gap" experimental paradigms were used for visual stimulation. Analysis of parameters of potentials and their spatiotemporal dynamics suggests that, under conditions of the increased attention and optimal readiness of the neural structures, express saccades appear when the previously chosen program of the future eye movement coincides with the actual target coordinates. We assumed that the saccade latency decreases at the expense of the involvement of the main oculomotor areas of motor and saccadic planning in its initiation; an express saccade can be initiated also by means of direct transmission of the signal from the cortex to the brainstem saccadic generator passing by the superior colliculus. Moreover, anticipating release from the central fixation and attention distraction are necessary for the successful initiation of an express saccade.     

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.     

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.     

Binocular coordination of the eyes during reading

Saccadic eye movements and fixations are the behavioral means by which we visually sample text during reading. Human oculomotor control is governed by a complex neurophysiological system involving the brain stem, superior colliculus, and several cortical areas. A very widely held belief among researchers investigating primate vision is that the oculomotor system serves to orient the visual axes of both eyes to fixate the same target point in space. It is argued that such precise positioning of the eyes is necessary to place images on corresponding retinal locations, such that on each fixation a single, nondiplopic, visual representation is perceived. Vision works actively through a continual sampling process involving saccades and fixations. Here we report that during normal reading, the eyes do not always fixate the same letter within a word. We also demonstrate that saccadic targeting is yoked and based on a unified cyclopean percept of a whole word since it is unaffected if different word parts are delivered exclusively to each eye via a dichoptic presentation technique. These two findings together suggest that the visual signal from each eye is fused at a very early stage in the visual pathway, even when the fixation disparity is greater than one character (0.29 deg), and that saccade metrics for each eye are computed on the basis of that fused signal.     

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).     

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.     

Effect of dopamine deficiency on the preparation of visually guided saccadic eye movements

Parameters of saccadic eye movements were studied in patients with Parkinson's disease and control subjects. In parkinsonian patients, the number of slow regular saccades was shown to be increased, and the number of express saccades was shown to be decreased. As a result the mean of saccade latency in patients was longer than in the control group. Moreover, the percentage of multistep saccades in patients with Parkinson's disease. In this case, not one but two or three saccades were performed with smaller amplitude to the target. We point, that the multistep saccades occurred mainly among the express saccades. Obviously, the dopamine deficiency distinguishing parkinsonian patients takes the primary part in the development of saccadic disorders. Degeneration of the nigrostriatal dopamine pathway results in imbalance in activity of the direct and indirect output pathways of the striatum. We suppose that this leads to inhibition of neurons activity in the superior colliculus during the saccade performance, which results in the early saccade interruption. In support of this reasoning, the mean of saccade latency and the percentage of the multistep saccades decreased in patients with Parkinson's disease after dopamine D2/D3 agonist (piribedil) treatment, due to activity restoration of the indirect pathway.     

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.     

The effect of illumination on involuntary eye saccades]

A study was made of the influence of sudden illumination micromovements of the eyes. Sudden contour illumination of the eye by a 15 degrees field with a crossing in the centre and a brightness of 100 nit reduced the amplitude of involuntary saccades and their frequency. The effect was particularly distinct with preliminary recording of the eye micromovement in complete darkness without a fixation point. In the case of fixation of a stationary point with one eye and of illumination of the other, the effect was also manifest, but it was less pronounced. During illumination of the eye with diffused light (through spectacles with frosted glasses) the effect of diminution of the saccade amplitude was smaller, though the brightness remained unchanged. A decrease in the saccade amplitude was practically not observed when the point was fixed at diffuse illumination. It has also been shown that with greater brightness of the fixation point (0.3; 25; 92 and 1000 nit), the amplitude and frequency of involuntary saccades diminish. The results attest that in choosing the conditions of work of the saccadic system two factors should be taken into consideration: the presence of the contours of the visible object and its brightness, the latter by itself having a lesser effect than the former.     

Natural and drug-induced variations of velocity and duration of human saccadic eye movements: Evidence for a control of the neural pulse generator by local feedback

The present report considers goal directed human saccadic eye movements. It addresses the question how a given perceived target excentricity is transformed into the innervation pattern that creates the saccade to the target. More specifically, it investigates whether this pattern is an appropriately selected preprogram or whether it is continuously controlled by a local feedback loop that compares a non-visual eye position signal to the perceived target excentricity (a visual signal would be too slow). To this end, the relation between the accuracy of saccades aimed at a given target and their velocity and duration was examined. Duration and velocity were found to vary by as much as 60% while the amplitude showed no related variation and had an almost constant accuracy of about 90%. By administrating diazepam, the variability of saccade duration and velocity could be further increased, but still the amplitude remained almost constant. These results favour the hypothesis that saccadic innervation is controlled by a local feedback loop.This investigation was supported by Deutsche Forschungsgemeinschaft, SFB 70, Gruppe Ulm     

Sensory processing of motor inaccuracy depends on previously performed movement and on subsequent motor corrections: a study of the saccadic system

When goal-directed movements are inaccurate, two responses are generated by the brain: a fast motor correction toward the target and an adaptive motor recalibration developing progressively across subsequent trials. For the saccadic system, there is a clear dissociation between the fast motor correction (corrective saccade production) and the adaptive motor recalibration (primary saccade modification). Error signals used to trigger corrective saccades and to induce adaptation are based on post-saccadic visual feedback. The goal of this study was to determine if similar or different error signals are involved in saccadic adaptation and in corrective saccade generation. Saccadic accuracy was experimentally altered by systematically displacing the visual target during motor execution. Post-saccadic error signals were studied by manipulating visual information in two ways. First, the duration of the displaced target after primary saccade termination was set at 15, 50, 100 or 800 ms in different adaptation sessions. Second, in some sessions, the displaced target was followed by a visual mask that interfered with visual processing. Because they rely on different mechanisms, the adaptation of reactive saccades and the adaptation of voluntary saccades were both evaluated. We found that saccadic adaptation and corrective saccade production were both affected by the manipulations of post-saccadic visual information, but in different ways. This first finding suggests that different types of error signal processing are involved in the induction of these two motor corrections. Interestingly, voluntary saccades required a longer duration of post-saccadic target presentation to reach the same amount of adaptation as reactive saccades. Finally, the visual mask interfered with the production of corrective saccades only during the voluntary saccades adaptation task. These last observations suggest that post-saccadic perception depends on the previously performed action and that the differences between saccade categories of motor correction and adaptation occur at an early level of visual processing.     

Saccades during Attempted Fixation in Parkinsonian Disorders and Recessive Ataxia: From Microsaccades to Square-Wave Jerks

During attempted visual fixation, saccades of a range of sizes occur. These “fixational saccades” include microsaccades, which are not apparent in regular clinical tests, and “saccadic intrusions”, predominantly horizontal saccades that interrupt accurate fixation. Square-wave jerks (SWJs), the most common type of saccadic intrusion, consist of an initial saccade away from the target followed, after a short delay, by a “return saccade” that brings the eye back onto target. SWJs are present in most human subjects, but are prominent by their increased frequency and size in certain parkinsonian disorders and in recessive, hereditary spinocerebellar ataxias. Here we asked whether fixational saccades showed distinctive features in various parkinsonian disorders and in recessive ataxia. Although some saccadic properties differed between patient groups, in all conditions larger saccades were more likely to form SWJs, and the intervals between the first and second saccade of SWJs were similar. These findings support the proposal of a common oculomotor mechanism that generates all fixational saccades, including microsaccades and SWJs. The same mechanism also explains how the return saccade in SWJs is triggered by the position error that occurs when the first saccadic component is large, both in the healthy brain and in neurological disease.     

Dysfunctional mode switching between fixation and saccades: collaborative insights into two unusual clinical disorders

Voluntary rapid eye movements (saccades) redirect the fovea toward objects of visual interest. The saccadic system can be considered as a dual-mode system: in one mode the eye is fixating, in the other it is making a saccade. In this review, we consider two examples of dysfunctional saccades, interrupted saccades in late-onset Tay-Sachs disease and gaze-position dependent opsoclonus after concussion, which fail to properly shift between fixation and saccade modes. Insights and benefits gained from bi-directional collaborative exchange between clinical and basic scientists are emphasized. In the case of interrupted saccades, existing mathematical models were sufficiently detailed to provide support for the cause of interrupted saccades. In the case of gaze-position dependent opsoclonus, existing models could not explain the behavior, but further development provided a reasonable hypothesis for the mechanism underlying the behavior. Collaboration between clinical and basic science is a rich source of progress for developing biologically plausible models and understanding neurological disease. Approaching a clinical problem with a specific hypothesis (model) in mind often prompts new experimental tests and provides insights into basic mechanisms.

     

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.     

The three-loop model: a neural network for the generation of saccadic reaction times

This paper presents a computer simulation of the three-loop model for the temporal aspects of the generation of visually guided saccadic eye movements. The intention is to reproduce complex experimental reaction time distributions by a simple neural network. The operating elements are artificial but realistic neurones. Four modules are constructed, each consisting of 16 neural elements. Within each module, the elements are connected in an all-to-all manner. The modules are working parallel and serial according to the anatomically and physiologically identified visuomotor pathways including the superior colliculus, the frontal eye fields, and the parietal cortex. Two transient-sustained input lines drive the network: one represents the visual activity produced by the onset of the saccade target, the other represents a central activity controlling the preparation of saccades, e.g. the end of active fixation. The model works completely deterministically; its stochastic output is a consequence of the stochastic properties of the input only. Simulations show how multimodal distributions of saccadic reaction times are produced as a natural consequence of the model structure. The gap effect on saccadic reaction times is correctly produced by the model: depending only on the gap duration (all model parameters unchanged) express, fast-regular, and slow-regular saccades are obtained in different numbers. In agreement with the experiments, bi- or trimodal distributions are produced only for medium gap durations (around 200 ms), while for shorter or longer gaps the express mode disappears and the distributions turn bi- or even unimodal. The effect of varying the strength of the transient-sustained components and the ongoing activity driving the hierarchically highest module are considered to account for the interindividual variability of the latency distributions obtained from different subjects, effects of different instructions to the same subject, and the observation of express makers (subjects who produce exclusively express saccades). How the model can be extended to describe the spatial aspects of the saccade system will be discussed as well as the effects of training and/or rapid adaptation to experimental conditions.     

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.     

Age-related changes in saccadic eye movements in healthy subjects and patients with Parkinson's disease

Age-related changes in characteristics of saccadic eye movements (latency, duration and percentage of multistep saccades) in healthy subjects and patients with Parkinson's disease were evaluated. Healthy volunteers were divided into 6 age groups (17-20 years, 21-30 years, 31-40 years, 41-50 years, 51-60 years, 61-75 years), parkinsonian patients into 3 age groups (41-50 years, 51-60 years, 61-75 years). According to our data, saccade characteristics depend upon age in both healthy subjects and parkinsonian patients. In healthy volunteers the percentage of multistep saccades and the mean saccade latency increase significantly after the age of 60. Values of these characteristics in patients with Parkinson's disease significantly exceed the values in the corresponding age groups of healthy subjects. The "disease" factor (MANOVA) has a greater influence on saccade latency and percentage of multistep saccades then the "age" factor. The duration of single saccades depends on age to a smaller extent and does not change in patients with Parkinson's disease. The peculiarities of neurodegenerative processes during normal aging and aging with Parkinson's disease are discussed.     

Craniotopic updating of visual space across saccades in the human posterior parietal cortex

The neural mechanisms underlying the craniotopic updating of visual space across saccadic eye movements are poorly understood. Previous single-unit recording studies in primates and clinical studies in brain-damaged patients have shown that the posterior parietal cortex (PPC) has a key role in this process. In the present study, we used single-pulse transcranial magnetic stimulation (TMS) to disrupt the processing within the PPC during a task that requires craniotopic updating: double saccades. In this task, two targets are presented in quick succession and the subject is required to make a saccade to each location as accurately as possible. We show here that TMS delivered to the PPC just prior to the second saccade effectively disrupts the craniotopic coding normally observed in this task. This causes subjects to revert to saccades more consistent with a representation of the targets based on their positions relative to one another. By contrast, stimulation at earlier times between the two saccades did not disrupt performance. These results suggest that extraretinal information generated during the first perisaccadic period is not put into functional use until just prior to the second saccade.