A model of the saccade-generating system that accounts for trajectory variations produced by competing visual stimuli

Variable saccade trajectories are produced in visual search paradigms in which multiple potential target stimuli are present. These variable trajectories provide a rich source of information that may lead to a deeper understanding of the basic control mechanisms of the saccadic system. We have used published behavioral observations and neural recordings in the superior colliculus (SC), gathered in monkeys performing visual search paradigms, to guide the construction of a new distributed model of the saccadic system. The new model can account for many of the variations in saccade trajectory produced by the appearance of multiple visual stimuli in a search paradigm. The model uses distributed feedback about current eye motion from the brainstem to the SC to reduce activity there at physiologically realistic rates during saccades. The long-range lateral inhibitory connections between SC cells used in previous models have been eliminated to match recent physiological evidence. The model features interactions between visually activated multiple populations of cells in the SC and distributed and topologically organized inhibitory input to the SC from the SNr to produce some of the types of variable saccadic trajectories, including slightly curved and averaging saccades, observed in visual search tasks. The distributed perisaccadic disinhibition of SC from the substantia nigra (SNr) is assumed to have broad spatial tuning. In order to produce the strongly curved saccades occasionally recorded in visual search, the existence of a parallel input to the saccadic burst generators in addition to that provided by the distributed input from the SC is required. The spatiotemporal form of this additional parallel input is computed based on the assumption that the input from the model SC is realistic. In accordance with other recent models, it is assumed that the parallel input comes from the cerebellum, but our model predicts that the parallel input is delayed during highly curved saccadic trajectories.     

Neural network simulations of the primate oculomotor system

The performance of a neural network that simulates the vertical saccade-generating portion of the primate brain is evaluated. Consistent with presently available anatomical evidence, the model makes use of an eye displacement signal for its feedback. Its major features include a simple mechanism for resetting its integrator at the end of each saccade, the ability to generate staircases of saccades in response to stimulation of the superior colliculus, and the ability to account for the monotonic relation between motor error and the instantaneous discharge of presaccadic neurons of the superior colliculus without placing the latter within the local feedback loop. Several experimentally testable predictions about the effects of stimulation or lesion of saccaderelated areas of the primate brain are made on the basis of model output in response to “stimulation” or “lesion” of model elements.     

A two dimensional model for saccade generation

A model for the generation of oblique saccades is constructed by extending and modifying the one dimensional local feedback model. It is proposed that the visual system stores target location in inertial coordinates, but that the feedback loop which guides saccades works in retinotopic coordinates. To achieve straight trajectories for centripetal and centrifugal saccades in all meridians, a comparator computes motor error as a vector and uses the vectorial error signal to drive two orthogonally-acting burst generators. The generation of straight saccade trajectories when the extraocular muscles are of unequal strengths requires the introduction of a burst-tonic cell input to motor neurons. The model accounts for the results of two-site stimulation of the superior colliculus and frontal eye fields by allowing simultaneous activation of more than one comparator. The postulated existence of multiple comparators suggests that motor error may be computed topographically.     

The Mechanism of Saccade Motor Pattern Generation Investigated by a Large-Scale Spiking Neuron Model of the Superior Colliculus

The subcortical saccade-generating system consists of the retina, superior colliculus, cerebellum and brainstem motoneuron areas. The superior colliculus is the site of sensory-motor convergence within this basic visuomotor loop preserved throughout the vertebrates. While the system has been extensively studied, there are still several outstanding questions regarding how and where the saccade eye movement profile is generated and the contribution of respective parts within this system. Here we construct a spiking neuron model of the whole intermediate layer of the superior colliculus based on the latest anatomy and physiology data. The model consists of conductance-based spiking neurons with quasi-visual, burst, buildup, local inhibitory, and deep layer inhibitory neurons. The visual input is given from the superficial superior colliculus and the burst neurons send the output to the brainstem oculomotor nuclei. Gating input from the basal ganglia and an integral feedback from the reticular formation are also included.We implement the model in the NEST simulator and show that the activity profile of bursting neurons can be reproduced by a combination of NMDA-type and cholinergic excitatory synaptic inputs and integrative inhibitory feedback. The model shows that the spreading neural activity observed in vivo can keep track of the collicular output over time and reset the system at the end of a saccade through activation of deep layer inhibitory neurons. We identify the model parameters according to neural recording data and show that the resulting model recreates the saccade size-velocity curves known as the saccadic main sequence in behavioral studies. The present model is consistent with theories that the superior colliculus takes a principal role in generating the temporal profiles of saccadic eye movements, rather than just specifying the end points of eye movements.     

Saccade-related remapping of target representations between topographic maps: a neural network study

The goal of this study was to explore how a neural network could solve the updating task associated with the double-saccade paradigm, where two targets are flashed in succession and the subject must make saccades to the remembered locations of both targets. Because of the eye rotation of the saccade to the first target, the remembered retinal position of the second target must be updated if an accurate saccade to that target is to be made. We trained a three-layer, feed-forward neural network to solve this updating task using back-propagation. The network's inputs were the initial retinal position of the second target represented by a hill of activation in a 2D topographic array of units, as well as the initial eye orientation and the motor error of the saccade to the first target, each represented as 3D vectors in brainstem coordinates. The output of the network was the updated retinal position of the second target, also represented in a 2D topographic array of units. The network was trained to perform this updating using the full 3D geometry of eye rotations, and was able to produce the updated second-target position to within a 1 degrees RMS accuracy for a set of test points that included saccades of up to 70 degrees . Emergent properties in the network's hidden layer included sigmoidal receptive fields whose orientations formed distinct clusters, and predictive remapping similar to that seen in brain areas associated with saccade generation. Networks with the larger numbers of hidden-layer units developed two distinct types of units with different transformation properties: units that preferentially performed the linear remapping of vector subtraction, and units that performed the nonlinear elements of remapping that arise from initial eye orientation.     

A spiking neural network model of the midbrain superior colliculus that generates saccadic motor commands

Single-unit recordings suggest that the midbrain superior colliculus (SC) acts as an optimal controller for saccadic gaze shifts. The SC is proposed to be the site within the visuomotor system where the nonlinear spatial-to-temporal transformation is carried out: the population encodes the intended saccade vector by its location in the motor map (spatial), and its trajectory and velocity by the distribution of firing rates (temporal). The neurons’ burst profiles vary systematically with their anatomical positions and intended saccade vectors, to account for the nonlinear main-sequence kinematics of saccades. Yet, the underlying collicular mechanisms that could result in these firing patterns are inaccessible to current neurobiological techniques. Here, we propose a simple spiking neural network model that reproduces the spike trains of saccade-related cells in the intermediate and deep SC layers during saccades. The model assumes that SC neurons have distinct biophysical properties for spike generation that depend on their anatomical position in combination with a center–surround lateral connectivity. Both factors are needed to account for the observed firing patterns. Our model offers a basis for neuronal algorithms for spatiotemporal transformations and bio-inspired optimal controllers.     

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.     

Self-Organizing Task Modules and Explicit Coordinate Systems in a Neural Network Model for 3-D Saccades

The goal of this study was to train an artificial neural network to generate accurate saccades in Listing's plane and then determine how the hidden units performed the visuomotor transformation. A three-layer neural network was successfully trained, using back-prop, to take in oculocentric retinal error vectors and three-dimensional eye orientation and to generate the correct head-centric motor error vector within Listing's plane. Analysis of the hidden layer of trained networks showed that explicit representations of desired target direction and eye orientation were not employed. Instead, the hidden-layer units consistently divided themselves into four parallel modules: a dominant "vector-propagation" class (approximately 50% of units) with similar visual and motor tuning but negligible position sensitivity and three classes with specific spatial relations between position, visual, and motor tuning. Surprisingly, the vector-propagation units, and only these, formed a highly precise and consistent orthogonal coordinate system aligned with Listing's plane. Selective "lesions" confirmed that the vector-propagation module provided the main drive for saccade magnitude and direction, whereas a balance between activity in the other modules was required for the correct eye-position modulation. Thus, contrary to popular expectation, error-driven learning in itself was sufficient to produce a "neural" algorithm with discrete functional modules and explicit coordinate systems, much like those observed in the real saccade generator.     

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.     

Functional organization within a neural network trained to update target representations across 3-D saccades

The goal of this study was to understand how neural networks solve the 3-D aspects of updating in the double-saccade task, where subjects make sequential saccades to the remembered locations of two targets. We trained a 3-layer, feed-forward neural network, using back-propagation, to calculate the 3-D motor error the second saccade. Network inputs were a 2-D topographic map of the direction of the second target in retinal coordinates, and 3-D vector representations of initial eye orientation and motor error of the first saccade in head-fixed coordinates. The network learned to account for all 3-D aspects of updating. Hidden-layer units (HLUs) showed retinal-coordinate visual receptive fields that were remapped across the first saccade. Two classes of HLUs emerged from the training, one class primarily implementing the linear aspects of updating using vector subtraction, the second class implementing the eye-orientation-dependent, non-linear aspects of updating. These mechanisms interacted at the unit level through gain-field-like input summations, and through the parallel "tweaking" of optimally-tuned HLU contributions to the output that shifted the overall population output vector to the correct second-saccade motor error. These observations may provide clues for the biological implementation of updating.     

Neural network simulations of the primate oculomotor system III. An one-dimensional, one-directional model of the superior colliculus

This report evaluates the performance of a biologically motivated neural network model of the primate superior colliculus (SC). Consistent with known anatomy and physiology, its major features include excitatory connections between its output elements, nigral gating mechanisms, and an eye displacement feedback of reticular origin to recalculate the metrics of saccades to memorized targets in retinotopic coordinates. Despite the fact that it makes no use of eye position or eye velocity information, the model can account for the accuracy of saccades in double step stimulation experiments. Further, the model accounts for the effects of focal SC lesions. Finally, it accounts for the properties of saccades evoked in response to the electrical stimulation of the SC. These include the approximate size constancy of evoked saccades despite increases of stimulus intensity, the fact that the size of evoked saccades depends on the time that has elapsed from a previous saccade, the fact that staircases of saccades are evoked in response to prolonged stimuli, and the fact that the size of saccades evoked in response to the simultaneous stimulation of two SC sites is the average of the saccades that are evoked when the two sites are separately stimulated. Received: 3 November 1997 / Accepted in revised form: 30 June 1998     

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.     

On your mark, get set: brainstem circuitry underlying saccadic initiation

Saccades are rapid eye movements that are used to move the visual axis toward targets of interest in the visual field. The time to initiate a saccade is dependent upon many factors. Here we review some of the recent advances in our understanding of the these processes in primates. Neurons in the superior colliculus and brainstem reticular formation are organised into a network to control saccades. Some neurons are active during visual fixation, while others are active during the preparation and execution of saccades. Several factors can influence the excitability levels of these neurons prior to the appearance of a new saccadic target. These pre-target changes in excitability are correlated to subsequent changes in behavioural performance. Our results show how neuronal signals in the superior colliculus and brainstem reticular formation can be shaped by contextual factors and demonstrate how situational experience can expedite motor behaviour via the advanced preparation of motor programs.     

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     

A nonlinear model for collicular spatial interactions underlying the metrical properties of electrically elicited saccades

An earlier model for the collicular role in the generation of saccades (Van Gisbergen et al. 1987), based on ensemble coding and linear vector addition of movement contributions from independent movement cells, yields normometric saccades in all directions over a considerable range of amplitudes. The model, however, cannot account for two nonlinear phenomena which are known from collicular electrical stimulation experiments: 1) saccade amplitude has a roughly sigmoid dependence upon current strength and 2) two electrical stimuli applied simultaneously at different sites yield a response that resembles a weighted average of the individual responses. In the present paper we propose an intracollicular mechanism which, based on lateral spatial interactions in the deeper layers of the colliculus, results in nearby excitation and remote inhibition when current is applied. Both nonlinear phenomena can thus be explained. The possibility of excitatory and inhibitory collicular interactions is supported by recent evidence in the literature. The nonlinearity in the model, essential to explain the electrical stimulation findings, resides in the input-output characteristic of the deeper layer movement cells. The results, obtained by quantitative simulations with the model, are discussed together with possible alternative explanations.     

Saccadic command signals in the superior colliculus: implications for sensorimotor transformations

Recent findings concerning the anatomical and functional organization of the deep division of the primate superior colliculus are summarized. These data are interpreted as supporting the hypothesis that the deeper layers of the superior colliculus are organized in motor, rather than sensory, coordinates. According to this hypothesis, a dynamic remapping of sensory signals is required for interfacing with the map of motor error space contained in the superior colliculus.     

A novel interpretation for the collicular role in saccade generation

Recently, we found evidence that the activity of neurons in the deep layers of the monkey superior colliculus (SC) is modulated by initial eye position (gain fields). In this paper, we propose a quantitative model of the motor SC which incorporates these new findings. Inputs to the motor map represent the desired eye displacement vector (motor error), as well as initial eye position. A unit's activity in the motor map is described by multiplying a weak linear eye position sensitivity with a gaussian tuning to motor error. The motor map projects to several sets of output neurons, representing the coordinates of the desired eye displacement vector, the desired eye position in the head, and the three-dimensional ocular rotation axis for saccades in Listing's plane, respectively. All these signals have been hypothesized in the literature to drive the saccade burst generator. We show that these signals can be extracted from the motor map by a linear weighting of the population activity. The saccadic system may employ all coding strategies in parallel to ensure high spatial accuracy in many complex sensorimotor tasks, such as orienting to multimodal stimuli.     

Frontal eye field inactivation alters the readout of superior colliculus activity for saccade generation in a task-dependent manner

Saccades require a spatiotemporal transformation of activity between the intermediate layers of the superior colliculus (iSC) and downstream brainstem burst generator. The dynamic linear ensemble-coding model (Goossens and Van Opstal 2006) proposes that each iSC spike contributes a fixed mini-vector to saccade displacement. Although biologically-plausible, this model assumes cortical areas like the frontal eye fields (FEF) simply provide the saccadic goal to be executed by the iSC and brainstem burst generator. However, the FEF and iSC operate in unison during saccades, and a pathway from the FEF to the brainstem burst generator that bypasses the iSC exists. Here, we investigate the impact of large yet reversible inactivation of the FEF on iSC activity in the context of the model across four saccade tasks. We exploit the overlap of saccade vectors generated when the FEF is inactivated or not, comparing the number of iSC spikes for metrically-matched saccades. We found that the iSC emits fewer spikes for metrically-matched saccades during FEF inactivation. The decrease in spike count is task-dependent, with a greater decrease accompanying more cognitively-demanding saccades. Our results show that FEF integrity influences the readout of iSC activity in a task-dependent manner. We propose that the dynamic linear ensemble-coding model be modified so that FEF inactivation increases the gain of a readout parameter, effectively increasing the influence of a single iSC spike. We speculate that this modification could be instantiated by FEF and iSC pathways to the cerebellum that could modulate the excitability of the brainstem burst generator.

     

Error Correcting Mechanisms during Antisaccades: Contribution of Online Control during Primary Saccades and Offline Control via Secondary Saccades

Errors in eye movements can be corrected during the ongoing saccade through in-flight modifications (i.e., online control), or by programming a secondary eye movement (i.e., offline control). In a reflexive saccade task, the oculomotor system can use extraretinal information (i.e., efference copy) online to correct errors in the primary saccade, and offline retinal information to generate a secondary corrective saccade. The purpose of this study was to examine the error correction mechanisms in the antisaccade task. The roles of extraretinal and retinal feedback in maintaining eye movement accuracy were investigated by presenting visual feedback at the spatial goal of the antisaccade. We found that online control for antisaccade is not affected by the presence of visual feedback; that is whether visual feedback is present or not, the duration of the deceleration interval was extended and significantly correlated with reduced antisaccade endpoint error. We postulate that the extended duration of deceleration is a feature of online control during volitional saccades to improve their endpoint accuracy. We found that secondary saccades were generated more frequently in the antisaccade task compared to the reflexive saccade task. Furthermore, we found evidence for a greater contribution from extraretinal sources of feedback in programming the secondary “corrective” saccades in the antisaccade task. Nonetheless, secondary saccades were more corrective for the remaining antisaccade amplitude error in the presence of visual feedback of the target. Taken together, our results reveal a distinctive online error control strategy through an extension of the deceleration interval in the antisaccade task. Target feedback does not improve online control, rather it improves the accuracy of secondary saccades in the antisaccade task.     

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.