The oculomotor system--simulation of physiologic and pathologic horizontal saccadic eye movements

Horizontal saccadic eye movements were analyzed by way of the input- and output-functions of the oculomotor system. On the basis of the parameters of the model, it was possible to simulate both physiological and pathological saccades. In this paper we present the results of simulation experiments that were performed to study the influence of various ocular motor disorders. The parameters of the model proved a useful diagnostic aid.     

Neural network simulations of the primate oculomotor system IV. A distributed bilateral stochastic model of the neural integrator of the vertical saccadic system

 The present report examines the performance of a distributed bi-directional neural network that simulates the vertical velocity to position integrator of the primate brain. Consistent with anatomy and physiology, its units receive stochastically weighted input from vertical medium-lead burst neurons. Also consistent with anatomy, units belonging to integrators with opposite on-directions (up or down) are interconnected via the posterior commissure (again in a stochastically weighted manner) and they can be excitatory or inhibitory. To demonstrate that integration can be a one-step process, the output of model units was routed directly to vertical motoneurons. Model units replicate the wide range of saccade-related discharge patterns encountered in the portion of the primate brain that is thought to house the vertical neural integrator (the interstitial nucleus of Cajal) while “lesions” of model units and/or their interconnections replicate the symptoms which follow insults to this brain area. Received: 20 June 2000 / Accepted in revised form: 17 July 2001     

Neuronal activity of the external oculomotor nucleus during saccadic eye movement in the waking cat

The activity of antidromically identified abducens nucleus motoneurons and inter-nuclear neurons has been recorded during saccadic eye movements in the alert cat. The activity of these neurons has been demonstrated to be the sum of a velocity component proportional to eye velocity plus a position component proportional to instantaneous eye position during the movement. Results are discussed in relation to proposed models about the generation of saccadic eye movements.     

Vision as oculomotor reward: cognitive contributions to the dynamic control of saccadic eye movements

Humans and other primates are equipped with a foveated visual system. As a consequence, we reorient our fovea to objects and targets in the visual field that are conspicuous or that we consider relevant or worth looking at. These reorientations are achieved by means of saccadic eye movements. Where we saccade to depends on various low-level factors such as a targets’ luminance but also crucially on high-level factors like the expected reward or a targets’ relevance for perception and subsequent behavior. Here, we review recent findings how the control of saccadic eye movements is influenced by higher-level cognitive processes. We first describe the pathways by which cognitive contributions can influence the neural oculomotor circuit. Second, we summarize what saccade parameters reveal about cognitive mechanisms, particularly saccade latencies, saccade kinematics and changes in saccade gain. Finally, we review findings on what renders a saccade target valuable, as reflected in oculomotor behavior. We emphasize that foveal vision of the target after the saccade can constitute an internal reward for the visual system and that this is reflected in oculomotor dynamics that serve to quickly and accurately provide detailed foveal vision of relevant targets in the visual field.     

Directional prediction by the saccadic system

One popular and fruitful approach to understanding what influences the decision of where to look next has been to present targets in a series of trials either to the right or left of a central fixation point and examine sequential effects on saccadic latency. However, there is a problem with this paradigm: Every saccade to a target is necessarily followed by an equal and opposite movement back to the center, yet the potentially confounding influence of this refixation saccade is rarely considered. Here, we introduce a novel random-walk paradigm that eliminates this difficulty. Each successive target appears to the left or right of the previous one, allowing us to study long sequences of saccades uncontaminated by refixations. This exposes a new stimulus-history effect, which is remarkably prolonged and relates primarily to movement direction: A saccade reduces the latency for subsequent movements made in the same direction and retards those in the opposite direction. Although in conventional refixation paradigms this effect cancels out, it is of particular significance in the real world--where our fixation point shifts constantly with the object of interest--and reflects a prediction of the way that real objects typically move.     

Models of the saccadic eye movement control system

1. A sequence of four models is proposed for the saccadic eye movement control system. The models become increasingly complex as they are made to respond to increasingly more complicated target movements in accordance with experimental results. Compatibility with neurological structure and function is stressed in the formation of the models. In each case, the elements of the models are constructed to conform as closely as possible to neuroanatomical structures and behave in a way that has been established or suggested by neurophysiology.
2. The dynamic behavior of the mechanics of the extraocular muscles and eyeball suspensory tissues has been established by recording from oculomotoneurons in alert monkeys. The transfer function of this mechanical system is used in these models.
3. Recent experiments on the neural circuits in the brain stem that are responsible for saccadic eye movements suggest an arrangement of the premotor circuitry that contains two principal neural networks; an integrator and a pulse generator. This circuitry is used in the models.
4. When the above modifications are made to existing models of the saccadic system, they remove the necessity of supposing that the visual information is sampled by the nervous system. The models do not include a sampler although the saccadic pulse generator still makes the overall system behavior similar to that of a sampled-data system.
5. The basic model is modified to make its behavior agree with experimental eye movement responses to target ramps and step-ramps. This is done by using error and its rate of change to estimate the error that will exist one reaction time in the future.
6. Parallel processing of data is a well recognized property of the nervous system. By utilizing it in combination with a random decision threshold, the model is extended to produce results in agreement with experiments for double-step target movements in which the second step occurs less than 0.2 sec after the first.
7. Finally, a model is presented which incorporates a continuum of parallel processing to represent the retinotopic spatial organization of the visual system and the tecto-bulbar motor commands. The model is conceptual; it was not constructed or tested but is used to discuss more complex eye movement phenomena such as those that appear to occur when the decision process must shift between hemispheres and how the system might produce quick correcting saccades with latencies as short as 85 msec.

     

A model of the saccadic sensorimotor system of salamanders

A model of the saccadic system of salamanders on the basis of electrophysiological and anatomical results is presented. The model includes centers found to be significant for the guidance of saccades in these comparatively simple vertebrates. In particular, these are the optic tectum, the bulbar reticular formation and the motor system. The latter consists of two pairs of neck-muscles, an epaxial and a hypaxial one driven by their respective motoneurons. The model includes a visual, a sensori-motor, and a motor level. At the sensory level, the retinal coordinates are transferred to the optic tectum to establish an orthogonal map of visual angles. A secondary visual map of the ipsilateral eye with a pointsymmetrical organization exists in addition. The premotor system of the tectum was modelled according to an ensemble-coding principle. Thus, local activation of the visual map results in recruitment of an appropriate number of tectal premotor units. Simulation of the model reproduces correct metric properties of salamander saccades under varying stimulus presentations.     

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.     

The knowledge base of the oculomotor system.

In everyday life, eye movements enable the eyes to gather the information required for motor actions. They are thus proactive, anticipating actions rather than just responding to stimuli. This means that the oculomotor system needs to know where to look and what to look for. Using examples from table tennis, driving and music reading we show that the information the eye movement system requires is very varied in origin and highly task specific, and it is suggested that the control program or schema for a particular action must include directions for the oculomotor and visual processing systems. In many activities (reading text and music, typing, steering) processed information is held in a memory buffer for a period of about a second. This permits a match between the discontinuous input from the eyes and continuous motor output, and in particular allows the eyes to be involved in more than one task.     

The oculomotor system of Daphnia magna

Summary The highly mobile cyclopic compound eye of Daphnia magna is rotated by six muscles arranged as three bilateral pairs. The three muscles on each side of the head share a common origin on the carapace and insert dorsally, laterally and ventrally on the eye. The dorsal and ventral muscles are each composed of two muscle fibers and the lateral muscle is composed of from two to five fibers, with three the most common number. Individual muscle fibers are spindle-shaped mononucleated cells with organized bundles of myofilaments. Lateral eye-muscle fibers are thinner than those of the other muscles but are otherwise similar in ultrastructure. Two motor neurons innervate each dorsal and each ventral muscle and one motor neuron innervates each lateral muscle. The cell bodies of the motor neurons are situated dorsally in the supraesophageal ganglion (SEG) and are ipsilateral to the muscles they innervate. The dendritic fields of the dorsal-muscle motor neurons are ipsilateral to their cell bodies; those of the ventral-muscle motor neurons are bilateral though predominantly contralateral. The central projections of the lateral-muscle motor neurons are unknown. In the dorsal and ventral muscles one motor axon synapses principally with one muscle fiber; in each lateral muscle the single motor axon branches to, and forms synapses with, all the fibers. The neuromuscular junctions, characterized by pre- and postsynaptic densities and clear vesicles, are similar in all the eye muscles.     

A neurological integrator for the oculomotor control system

This paper describes a mathematical model of a neurological integrator that has been developed to provide the very long leakage time constant required of the intgrator in the oculomotor system. The Gaussian distribution of cell thresholds and the eye-position- related discharge of the individual cells of the integrator model, and the highly specialized short-duration, high-frequency burst required of the input, have been modeled after the single-cell behavior actually observed in the oculomotor control areas of the brain stem of an alert primate.     

A proposed neural network for the integrator of the oculomotor system

Single-unit recordings, stimulation studies, and eye movement measurements all indicate that the firing patterns of many oculomotor neurons in the brain stem encode eye-velocity commands in premotor circuits while the firing patterns of extraocular motoneurons contain both eye-velocity and eye-position components. It is necessary to propose that the eye-position component is generated from the eye-velocity signal by a leaky hold element or temporal integrator. Prior models of this integrator suffer from two important problems. Since cells appear to have a steady, background signal when eye position and velocity are zero, how does the integrator avoid integrating this background rate? Most models employ some form of lumped, oositive feedback the gain of which must be kept within totally unreasonable limits for proper operation. We propose a lateral inhibitory network of homogeneous neurons as a model for the neural integrator that solves both problems. Parameter sensitivity studies and lesion simulations are presented to demonstrate robustness of the model with respect to both the choice of parameter values and the consequences of pathological changes in a portion of the neural integrator pool.     

Reflex actions of the functional divisions in the crayfish oculomotor system

Summary The electrical responses of motor neurons in different anatomical subdivisions of the crayfish oculomotor system were examined during various kinds of experimentally manipulated sensory stimulation. Geotactic reflexes are effected by neurons in the anterior motor cluster and the medulla terminalis. Optokinetic and proprioceptive nystagmus are generated by neurons in the lateral motor cluster. This functional diversity in the major subdivisions contrasts with an intradivisional homogeneity of function, in that the different motor neurons of each all contribute to reflexes initiated by different kinds of sensory input.This research was supported by USPHS Research Grant NS 04989.     

A learning network model of the neural integrator of the oculomotor system

Certain premotor neurons of the oculomotor system fire at a rate proportional to desired eye velocity. Their output is integrated by a network of neurons to supply an eye positon command to the motoneurons of the extraocular muscles. This network, known as the neural integrator, is calibrated during infancy and then maintained through development and trauma with remarkable precision. We have modeled this system with a self-organizing neural network that learns to integrate vestibular velocity commands to generate appropriate eye movements. It learns by using current eye movement on any given trial to calculate the amount of retinal image slip and this is used as the error signal. The synaptic weights are then changed using a straightforward algorithm that is independent of the network configuration and does not necessitate backwards propagation of information. Minimization of the error in this fashion causes the network to develop multiple positive feedback loops that enable it to integrate a push-pull signal without integrating the background rate on which it rides. The network is also capable of recovering from various lesions and of generating more complicated signals to simulate induced postsaccadic drift and compensation for eye muscle mechanics.     

Learning in the oculomotor system: from molecules to behavior

A combination of system-level and cellular—molecular approaches is moving studies of oculomotor learning rapidly toward the goal of linking synaptic plasticity at specific sites in oculomotor circuits with changes in the signal-processing functions of those circuits, and, ultimately, with changes in eye movement behavior. Recent studies of saccadic adaptation illustrate how careful behavioral analysis can provide constraints on the neural loci of plasticity. Studies of vestibulo-ocular adaptation are beginning to examine the molecular pathways contributing to this form of cerebellum-dependent learning.     

Modelling of congenital nystagmus waveforms produced by saccadic system abnormalities

 Models of the mechanisms of normal eye movements are typically described in terms of the block diagrams which are used in control theory. An alternative approach to understanding the mechanisms of normal eye movements involves describing the eye movement behaviour in terms of smooth changes in state variables. The latter approach captures the burst cell firing against motor error (difference between target gaze angle and current gaze angle) phase plane behaviour which is found experimentally and facilitates the modelling of variations in burst cell behaviour. A novel explanation of several types of congenital nystagmus waveforms is given in terms of a saccadic termination abnormality. Received: 12 May 1999 / Accepted in revised form: 19 November 1999     

Unequal saccades generated by velocity interactions in the peripheral oculomotor system

Experiments with precision eye movement recordings show binocularly unequal saccades to be present under several stimulus conditions having as a common theme ongoing low velocities at the times of the saccades. Simulations using a model of eye muscles and eyeball dynamics reproduce these unequal saccades in quantitative agreement with the experimental findings. The model uses equal innervation for the saccades, and demonstrates a peripheral interaction between the muscle forces and the eye velocities to be the cause of the large inequality of the simulated binocular saccades. Thus, the simulations provide evidence that Hering's law continues to describe the innervation patterns to corresponding muscles producing these binocularly unequal saccades found in the experimental situation.     

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