A ‘tachometer’ feedback model of smooth pursuit eye movements

A new model of smooth pursuit eye movements is presented. We begin by formally analyzing the stability of the proportional-derivative (PD) model of smooth pursuit eye movements using Pontryagin's theory. The PD model is the linearized version of the nonlinear Krauzlis-Lisberger (KL) model. We show that the PD model fails to account for the experimentally observed dependence of the eye velocity damping ratio and the oscillation period on the total delay in the feedback loop. To explain the data, a new `tachometer' feedback model, based on an efference copy signal of eye acceleration, is proposed and analyzed by computer simulation. The model predicts some salient features of monkey pursuit data and suggests a functional role for the extraretinal input to the medial superior temporal area (MST). Received: 9 February 1995 / Accepted in revised form: 13 June 1995     

Association of Neuregulin 1 rs3924999 genotype with antisaccades and smooth pursuit eye movements

Neuregulin 1 (NRG1) has been identified as one of the leading candidate genes for schizophrenia. However, its functional mechanisms and its effects on neurocognition remain unclear. In this study, we used two well‐established oculomotor endophenotypes, the antisaccade (AS) and smooth pursuit eye movement (SPEM) tasks, to investigate the functional mechanisms of a single nucleotide polymorphism (SNP) in NRG1 (rs3924999) at the neurocognitive level in a healthy volunteer sample. A total of 114 healthy Caucasian volunteers completed genotyping for NRG1 rs3924999 and infrared oculographic assessment of AS and SPEM (at target velocities of 12°, 24° and 36° per second). Additionally, self‐report questionnaires of schizotypy, neuroticism, attention deficit hyperactivity and obsessive‐compulsive traits were included. A significant effect of rs3924999 genotype, with gender as a covariate, was found for AS amplitude gain (P < 0.01), with an increasing number of A alleles being associated with increasingly hypermetric performance. No statistically significant associations were found for other AS and SPEM variables or questionnaire scores. These findings indicate that NRG1 rs3924999 affects spatial accuracy on the AS task, suggesting an influence of the gene on the neural mechanisms underlying visuospatial sensorimotor transformations, a mechanism that has been previously found to be impaired in patients with schizophrenia and their relatives.     

A model of visually-guided smooth pursuit eye movements based on behavioral observations

We report a model that reproduces many of the behavioral properties of smooth pursuit eye movements. The model is a negative-feedback system that uses three parallel visual motion pathways to drive pursuit. The three visual pathways process image motion, defined as target motion with respect to the moving eye, and provide signals related to image velocity, image acceleration, and a transient that occurs at the onset of target motion. The three visual motion signals are summed and integrated to produce the eye velocity output of the model. The model reproduces the average eye velocity evoked by steps of target velocity in monkeys and humans and accounts for the variation among individual responses and subjects. When its motor pathways are expanded to include positive feedback of eye velocity and a switch, the model reproduces the exponential decay in eye velocity observed when a moving target stops. Manipulation of this expanded model can mimic the effects of stimulation and lesions in the arcuate pursuit area, the middle temporal visual area (MT), and the medial superior temporal visual area (MST).     

Nonlinear parameter estimation applied to a model of smooth pursuit eye movements

We present a procedure that optimally adjusts specified parameters of a mathematical model to describe a set of measured data. The technique integrates a dynamic systems-simulation language with a robust algorithm for nonlinear parameter estimation, and it can be implemented on a microcomputer. Sensitivity functions are generated that indicate how the operation of the model is affected by each updated parameter. This procedure offers a greater resolution of optimal parameter values than other, less rigorous methods. To illustrate this technique we have applied it to the model of human smooth pursuit eye movements proposed by D.A. Robinson and colleagues (1986).     

Frame of reference transformations in motion perception during smooth pursuit eye movements

Smooth pursuit eye movements change the retinal image velocity of objects in the visual field. In order to change from a retinocentric frame of reference into a head-centric one, the visual system has to take the eye movements into account. Studies on motion perception during smooth pursuit eye movements have measured either perceived speed or perceived direction during smooth pursuit to investigate this frame of reference transformation, but never both at the same time. We devised a new velocity matching task, in which participants matched both perceived speed and direction during fixation to that during pursuit. In Experiment 1, the velocity matches were determined for a range of stimulus directions, with the head-centric stimulus speed kept constant. In Experiment 2, the retinal stimulus speed was kept approximately constant, with the same range of stimulus directions. In both experiments, the velocity matches for all directions were shifted against the pursuit direction, suggesting an incomplete transformation of the frame of reference. The degree of compensation was approximately constant across stimulus direction. We fitted the classical linear model, the model of Turano and Massof (2001) and that of Freeman (2001) to the velocity matches. The model of Turano and Massof fitted the velocity matches best, but the differences between de model fits were quite small. Evaluation of the models and comparison to a few alternatives suggests that further specification of the potential effect of retinal image characteristics on the eye movement signal is needed.     

Contrast dependence of smooth pursuit eye movements following a saccade to superimposed targets

Dorsal stream areas provide motion information used by the oculomotor system to generate pursuit eye movements. Neurons in these areas saturate at low levels of luminance contrast. We therefore hypothesized that during the early phase of pursuit, eye velocity would exhibit an oculomotor gain function that saturates at low luminance contrast. To test this, we recorded eye movements in two macaques trained to saccade to an aperture in which a pattern of dots moved left or right. Shortly after the end of the saccade, the eyes followed the direction of motion with an oculomotor gain that increased with contrast before saturating. The addition of a second pattern of dots, moving in the opposite direction and superimposed on the first, resulted in a rightward shift of the contrast-dependent oculomotor gain function. The magnitude of this shift increased with the contrast of the second pattern of dots. Motion was nulled when the two patterns were equal in contrast. Next, we varied contrast over time. Contrast differences that disappeared before saccade onset biased post-saccadic eye movements at short latency. Changes in contrast occurring during or after saccade termination did not influence eye movements for approximately 150 ms. Earlier studies found that eye movements can be explained by a vector average computation when both targets are equal in contrast. We suggest that this averaging computation may reflect a special case of divisive normalization, yielding saturating contrast response functions that shift to the right with opposed motion, averaging motions when targets are equated in contrast.     

Expansion of direction space around the cardinal axes revealed by smooth pursuit eye movements

It is well established that perceptual direction discrimination shows an oblique effect; thresholds are higher for motion along diagonal directions than for motion along cardinal directions. Here, we compare simultaneous direction judgments and pursuit responses for the same motion stimuli and find that both pursuit and perceptual thresholds show similar anisotropies. The pursuit oblique effect is robust under a wide range of experimental manipulations, being largely resistant to changes in trajectory (radial versus tangential motion), speed (10 versus 25 deg/s), directional uncertainty (blocked versus randomly interleaved), and cognitive state (tracking alone versus concurrent tracking and perceptual tasks). Our data show that the pursuit oblique effect is caused by an effective expansion of direction space surrounding the cardinal directions and the requisite compression of space for other directions. This expansion suggests that the directions around the cardinal directions are in some way overrepresented in the visual cortical pathways that drive both smooth pursuit and perception.     

A model of the smooth pursuit eye movement system

Human, horizontal, smooth-pursuit eye movements were recorded by the search coil method in response to Rashbass step-ramp stimuli of 5 to 30 deg/s. Eye velocity records were analyzed by measuring features such as the time, velocity and acceleration of the point of peak acceleration, the time and velocity of the peaks and troughs of ringing and steady-state velocity. These values were averaged and mean responses reconstructed. Three normal subjects were studied and their responses averaged. All showed a peak acceleration-velocity saturation. All had ringing frequencies near 3.8 Hz and the mean steady-state gain was 0.95.It is argued that a single, linear forward path with any transfer function G(s) and a 100 ms delay (latency) cannot simultaneously simulate the initial rise of acceleration and ring at 3.8 Hz based on a Bode analysis. Also such a simple negative feedback model cannot have a steady-state gain greater than 1.0; a situation that occurs frequently experimentally. L.R. Young's model, which employs internal positive feedback to eliminate the built-in unity negative feedback, was felt necessary to resolve this problem and a modification of that model is proposed which simulates the data base. Acceleration saturation is achieved by borrowing the idea of the local feedback model for saccades so that one nonlinearity can account for the acceleration-velocity saturation: the main sequence for pursuit. Motor plasticity or motor learning, recently demonstrated for pursuit, is also incorporated and simulated.It was noticed that the offset of pursuit did not show the ringing seen in the onset so this was quantified in one subject. Offset velocity could be characterized by a single exponential with a time constant of about 90 ms. This observation suggests that fixation is not pursuit at zero velocity and that the pursuit system is turned on when needed and off during fixation.     

Extra-retinal adaptation of cortical motion-processing areas during pursuit eye movements

Repetitive eye movement produces a compelling motion aftereffect (MAE). One mechanism thought to contribute to the illusory movement is an extra-retinal motion signal generated after adaptation. However, extra-retinal signals are also generated during pursuit. They modulate activity within cortical motion-processing area MST, helping transform retinal motion into motion in the world during an eye movement. Given the evidence that MST plays a key role in generating MAE, it may also become indirectly adapted by prolonged pursuit. To differentiate between these two extra-retinal mechanisms we examined storage of the MAE across a period of darkness. In one condition observers were told to stare at a moving pattern, an instruction that induces a more reflexive type of eye movement. In another they were told to deliberately pursue it. We found equally long MAEs when testing immediately after adaptation but not when the test was delayed by 40 s. In the case of the reflexive eye movement the delay almost completely extinguished the MAE, whereas the illusory motion following pursuit remained intact. This suggests pursuit adapts cortical motion-processing areas whereas unintentional eye movement does not. A second experiment showed that cortical mechanisms cannot be the sole determinant of pursuit-induced MAE. Following oblique pursuit, we found MAE direction changes from oblique to vertical. Perceived MAE direction appears to be influenced by a subcortical mechanism as well, one based on the relative recovery rate of horizontal and vertical eye-movement processes recruited during oblique pursuit.     

Quantitative evaluation of smooth pursuit eye movements by personal computer. I) Normative data and effect of aging

We recorded the smooth pursuit eye movements (SPEM) of 52 healthy subjects by binocular electrooculographic technique. The 52 subjects were homogeneously distributed from the 2nd to the 6th decade. The target moved over 60 deg of amplitude at constant velocity (ramp); different target velocities were used ranging from 10 to 50 deg/sec. All subjects were tested with the same 58 pseudo-random ramp sequence under the control of a Personal Computer (PC). The quantitative analysis of SPEM was carried out by an interactive program implemented on the same PC. Different equations were tested by a multiple regression analysis in order to describe the relationship between SPEM gain values and target velocities; two of these equations were chosen and used in order to find out if SPEM gain was influenced by target direction (the direction effect) and/or by subject age (the age effect). The statistical analyses we performed, demonstrated that SPEM gain values were influenced by aging but not by target direction: SPEM gain decreased as age increased.     

Quantitative analysis of smooth pursuit eye movements by personal computer. II. Evaluation of individual performance and clinical applicability

In a previous report on quantitative analysis of smooth pursuit eye movements (SPEM) we assessed two equations in order to describe the SPEM gain/target velocity relationship, and we demonstrated that this relationship is age-related. This report presents a method to evaluate normality of a single subject SPEM performance. Three points have been considered: 1) The control of gain asymmetries depending on target direction (leftward vs rightward SPEM) 2) The definition of age-related control values 3) The subject vs control values comparison An example to explain how our method actually works and its clinical applicability is shown. Finally, the reasons why no choice has been made between the two equations are discussed.     

The reliability of eye movement quantitative evaluation. II. Smooth pursuit eye movements.

We adopted the estimate of the intraclass coefficient of reliability, R, to evaluate the reliability of smooth pursuit eye movement quantitative analysis. At a one-week interval, we recorded twice smooth pursuit eye movements from fifteen healthy subjects by means of the binocular electrooculographic technique. R was computed for the constant and the slope of the target velocity/gain relationships. R values were rated good for the slope and excellent for the constant. Finally, we computed for each parameter the maximum variability value according to two differing methods; on the basis of the within-subjects mean square values, we defined the normal range of biological test-retest variability for the two parameters.     

New methods for removing saccades in analysis of smooth pursuit eye movement

New computation methods for removing saccades in analysis of smooth pursuit eye movement characteristics were developed. They have removed saccades more completely than previous methods, and were very effective especially for noisy data recorded by the EOG method. The fully developed method was applicable to eye movement data in tracking of pseudo-random target movement as well as deterministic target movement. Furthermore, the methods were also useful for extracting the number and magnitudes of saccades more precisely.     

Cortical mechanisms of smooth eye movements revealed by dynamic covariations of neural and behavioral responses

Neural activity in the frontal eye fields controls smooth pursuit eye movements, but the relationship between single neuron responses, cortical population responses, and eye movements is not well understood. We describe an approach to dynamically link trial-to-trial fluctuations in neural responses to parallel variations in pursuit and demonstrate that individual neurons predict eye velocity fluctuations at particular moments during the course of behavior, while the population of neurons collectively tiles the entire duration of the movement. The analysis also reveals the strength of correlations in the eye movement predictions derived from pairs of simultaneously recorded neurons and suggests a simple model of cortical processing. These findings constrain the primate cortical code for movement, suggesting that either a few neurons are sufficient to drive pursuit at any given time or that many neurons operate collectively at each moment with remarkably little variation added to motor command signals downstream from the cortex.     

Neuregulin 3 does not confer risk for schizophrenia and smooth pursuit eye movement abnormality in a Korean population

Located on chromosome 10q22‐q23, the human neuregulin3 (NRG3) is considered to be a strong positional and functional candidate gene for schizophrenia pathogenesis. Several case–control studies examining the association of polymorphisms in NRG3 with schizophrenia and/or related traits such as delusion have been reported recently in cohorts of Han Chinese, Ashkenazi Jews, Australians and white Americans of Western European ancestry. Thus, this study aimed to comprehensively investigate the association of NRG3 genetic variations with the risk of schizophrenia and smooth pursuit eye movement (SPEM) abnormality in a Korean population. Using TaqMan assay, six single‐nucleotide polymorphisms (SNPs) in the intronic region of NRG3 were genotyped and two major haplotypes were identified in 435 patients with schizophrenia as cases and 393 unrelated healthy individuals as controls. A total of 113 schizophrenia patients underwent an eye tracking task, and degree of SPEM abnormality was measured using the logarithmic values of the signal/noise (Ln S/N) ratio. Differences in frequency distributions were analyzed using logistic and regression models following various modes of genetic inheritance and controlling for age and sex as covariates. Subsequent analysis revealed that the frequency distributions of NRG3 polymorphisms and haplotypes were similar between schizophrenia patients and healthy controls of Korean ethnicity. Furthermore, no significant differences were observed between the genetic variants tested for SPEM abnormality. By elucidating a lack of association in a Korean population, findings from this study may contribute to the understanding of the genetic etiology focusing on the role of NRG3 in schizophrenia pathogenesis.