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Saccadic eye movements of a normal subject were assessed through semi-quantitative analysis algorithms based on linear and non-linear test application in order to highlight the dynamics type characterizing saccadic neural system behavior. These movements were recorded during a simple visually-guided saccade test and one with a cognitive load involving button pressing to show a decision. Following the application of specific computational tests, chaotic dynamical trend dominancy was mostly revealed with some differences between the two saccade recording conditions: auto-correlation time was increased from 170 to 240 by cognitive task superposition and the Hurst exponent was enhanced from 0.52 to 0.76, denoting more persistence in the dynamics of saccadic system during increased neural activity related to cognitive task.

Evidence of a chaotic behavioral trend in eye movement dynamics was examined in the case of a saccadic temporal series collected from a healthy human subject. Saccades are highvelocity eye movements of very short duration, their recording being relatively accessible, so that the resulting data series could be studied computationally for understanding the neural processing in a motor system. The aim of this study was to assess the complexity degree in the eye movement dynamics. To do this we analyzed the saccadic temporal series recorded with an infrared camera eye tracker from a healthy human subject in a special experimental arrangement which provides continuous records of eye position, both saccades (eye shifting movements) and fixations (focusing over regions of interest, with rapid, small fluctuations). The semi-quantitative approach used in this paper in studying the eye functioning from the viewpoint of non-linear dynamics was accomplished by some computational tests (power spectrum, portrait in the state space and its fractal dimension, Hurst exponent and largest Lyapunov exponent) derived from chaos theory. A high complexity dynamical trend was found. Lyapunov largest exponent test suggested bi-stability of cellular membrane resting potential during saccadic experiment.

Experimental evidence indicates that the superior colliculus (SC) is important but neither necessary nor sufficient to produce accurate saccadic eye movements. Furthermore both clinical and experimental evidence points to the cerebellum as an indispensable component of the saccadic system. Accordingly, we have devised a new model of the saccadic system in which the characteristics of saccades are determined by the cooperation of two pathways, one through the SC and the other through the cerebellum. Both pathways are influenced by feedback information: the feedback determines the decay of activity for collicular neurons and the timing of the activation for cerebellar neurons. We have modeled three types of cells (burst, buildup, and fixation neurons) found in the intermediate layers of the superior colliculus. We propose that, from the point of view of motor execution, the burst neurons and the buildup neurons are not functionally distinct with both providing a directional drive to the brain stem circuitry. The fixation neurons determine the onset of the saccade by disfacilitating the omnipause neurons in the brain stem. Excluding noise-related variations, the ratio of the horizontal to the vertical components of the collicular drive is fixed throughout the saccade (i.e., its direction is fixed); the duration of the drive is such that it always would produce hypermetric movements. The cerebellum plays three roles: first, it provides an additional directional drive, which improves the acceleration of the eyes; second, it keeps track of the progress of the saccade toward the target; and third, it ends the saccade by choking off the collicular drive. The drive provided by the cerebellum can be adjusted in direction to exert a directional control over the saccadic trajectory. We propose here a control mechanism that incorporates a spatial displacement integrator in the cerebellum; under such conditions, we show that a partial directional control arises automatically. Our scheme preserves the advantages of several previous models of the saccadic system (e.g., the lack of a spatial-to-temporal transformation between the SC and the brain stem; the use of efference copy feedback to control the saccade), without incurring many of their drawbacks, and it accounts for a large amount of experimental data.

One-dimensional models of oculomotor control rely on the fact that, when rotations around only one axis are considered, angular velocity is the derivative of orientation. However, when rotations around arbitrary axes [3-dimensional (3-D) rotations] are considered, this property does not hold, because 3-D rotations are noncommutative. The noncommutativity of rotations has prompted a long debate over whether or not the oculomotor system has to account for this property of rotations by employing noncommutative operators. Recently, Raphan presented a model of the ocular plant that incorporates the orbital pulleys discovered, and qualitatively modeled, by Miller and colleagues. Using one simulation, Raphan showed that the pulley model could produce realistic saccades even when the neural controller is commutative. However, no proof was offered that the good behavior of the Raphan-Miller pulley model holds for saccades different from those simulated. We demonstrate mathematically that the Raphan-Miller pulley model always produces movements that have an accurate dynamic behavior. This is possible because, if the pulleys are properly placed, the oculomotor plant (extraocular muscles, orbital pulleys, and eyeball) in a sense appears commutative to the neural controller. We demonstrate this finding by studying the effect that the pulleys have on the different components of the innervation signal provided by the brain to the extraocular muscles. Because the pulleys make the axes of action of the extraocular muscles dependent on eye orientation, the effect of the innervation signals varies correspondingly as a function of eye orientation. In particular, the Pulse of innervation, which in classical models of the saccadic system encoded eye velocity, here encodes a different signal, which is very close to the derivative of eye orientation. In contrast, the Step of innervation always encodes orientation, whether or not the plant contains pulleys. Thus the Step can be produced by simply integrating the Pulse. Particular care will be given to describing how the pulleys can have this differential effect on the Pulse and the Step. We will show that, if orbital pulleys are properly located, the neural control of saccades can be greatly simplified. Furthermore, the neural implementation of Listing's Law is simplified: eye orientation will lie in Listing's Plane as long as the Pulse is generated in that plane. These results also have implications for the surgical treatment of strabismus.

Neurons in the superior colliculus (SC) are organized as maps of visual and motor space. The companion paper showed that muscimol injections into intermediate layers of the SC alter the trajectory of the movement and confirmed previously reported effects on latency, amplitude, and speed of saccades. In this paper we analyze the pattern of these deficits across the visual field by systematically comparing the magnitude of each deficit throughout a grid of targets covering a large fraction of the visual field. We also translate these deficits onto the SC map of the visual/movement fields to obtain a qualitative estimate of the extent of the deficit in the SC. We found a consistent pattern of substantially increased saccadic latency to targets in the contralateral visual hemifield, accompanied by slight and inconsistent increases and decreases for saccades to the ipsilateral hemifield. The initial and peak speed of saccades was reduced after the injection. The postinjection amplitude of the saccades were either hypometric or normometric, but rarely hypermetric. Although errors in the initial direction of the postinjection saccades were small, they consistently formed a simple pattern: an initial direction with minimal errors (a null direction) separating regions with clockwise and counterclockwise rotations of the initial direction. However, the null direction did not go through the center of the inactivated zone, as would be expected if the SC alone were determining saccade direction, e.g., with a population code. One hypothesis that can explain the misalignment of the null direction with the lesion site is that another system, acting in parallel with the SC, contributes to the determination of saccadic trajectory.

Human texture discrimination depends both on spatial-frequency content and on higher-order or multi-point correlations. Spatial-frequency discrimination exhibits a high degree of scale invariance over a range of several octaves, but the scaling behavior of sensitivity to higher-order correlation structure is unknown. We explored the scale dependence of texture discrimination for image ensembles which shared the same power spectrum, but differed in their higher-order correlations. Literally scaling the ensembles so that they occupy larger retinal regions results in discrimination performance that is largely independent of scale over a 3 octave range. Holding the display size constant and scaling the texture being sampled within the display over the same range produces performance that varies with scale appreciably. The ideal observer performance is computed, and the absolute efficiency is seen to be quite small, on the order of 10(-2)-10(-1). As the texture is scaled down, increasing the number of checks within the fixed display size, performance increases while the efficiency decreases. These dependencies remain when the stimulus onset asynchrony is increased from 50 to 500 msec. We created sets of textures which varied both in check number and correlation strength, for which ideal observer performance was equated. For the human observers, efficiency was significantly higher for textures with higher correlation strength, but fewer checks. These results are consistent with a model in which a fixed number of checks is processed in a scale-invariant manner, while the remainder of the display is processed much less efficiently.

During oblique saccades, the durations of the horizontal and vertical components are stretched until they are approximately equal. Models of the saccadic system have been proposed that provide a mechanism for that stretching. However, they fail to simulate the pattern of activity recorded from premotor medium lead burst neurons (MLBNs) in the brain stem. A new model of the saccadic system is proposed that accounts for both the component stretching of oblique movements and the pattern of activity recorded in MLBNs. MLBNs that project to horizontal (or vertical) motoneurons actually have a wide span of on-directions (the direction associated with the largest discharge) around the cardinal direction. We infer from the wide span of their on-directions that, at the level of individual MLBNs, the vectorial signal present in spatially organized structures (e.g., the superior colliculus) is not decomposed into the separate horizontal and vertical components represented by the motoneurons. Nonetheless, all prior models of the saccadic system have decomposed the vectorial premotor command into horizontal and vertical commands at the level of the MLBNs. That decomposition was explicit, because individual MLBNs, with a sine- or cosine-shaped directional tuning curve, were used. We propose here that the decomposition into horizontal and vertical commands is carried out only at the level of the motoneurons. This decomposition is implicit, because no single MLBN encodes the horizontal or vertical command; the command only exists implicitly in the activity of the population of MLBNs. The new vectorial burster model correctly simulates the pattern of activity recorded in primate MLBNs, and the components of its oblique saccades are stretched. Two mechanisms contribute to this stretching: the distribution of MLBN tuning curves and the inhibition exerted by the contralateral population of MLBNs. In contrast, feedback control of the saccade contributes negligibly to the stretching. Even though the vectorial burster model predicts a component stretching, it is not constrained to produce perfectly straight oblique saccades because no trajectory control is implemented. The amount of curvature depends on the similarity of the horizontal and vertical systems (both neural and mechanical). In this model, stretching is interpreted simply as a side effect of the properties of the MLBNs' tuning curves. The distributed MLBNs of the vectorial burster model forces the general organization of the saccadic system to be reconsidered. We propose that a distributed architecture in which several different neural systems cooperate is needed.

Determination of single-unit spike trains from multiunit recordings obtained during extracellular recording has been the focus of many studies over the last two decades. In multiunit recordings, superpositions can occur with high frequency if the firing rates of the neurons are high or correlated, making superposition resolution imperative for accurate spike train determination. In this work, a connectionist neural network (NN) was applied to the spike sorting challenge. A novel training scheme was developed which enabled the NN to resolve some superpositions using single-channel recordings. Simulated multiunit spike trains were constructed from templates and noise segments that were extracted from real extracellular recordings. The simulations were used to determine the performances of the NN and a simple matched template filter (MTF), which was used as a basis for comparison. The network performed as well as the MTF in identifying nonoverlapping spikes, and was significantly better in resolving superpositions and rejecting noise. An on-line, real-time implementation of the NN discriminator, using a high-speed digital signal processor mounted inside an IBM-PC, is now in use in six laboratories.

Recent models have placed the superior colliculus inside the local feedback loop that generates the pulse of innervation needed to make a saccade. Such closed-loop models need to take into account the different coordinate systems of visual and motor signals. This paper presents a computational model showing how the superior colliculus can bring the visual and motor information together in a common reference frame.

The intrinsic neuronal code that carries visual information and the perceptual mechanism for decoding that information are not known. However, multivariate statistics and information theory show that neurons in four visual areas simultaneously carry multiple, stimulus-related messages by utilizing multiplexed temporal codes. The complexity of these temporal messages increases progressively across the visual system, yet the temporal codes overlap in time. Thus, visual perception may depend on the concurrent processing of multiplexed temporal messages from all visual areas.

Vergence-induced accommodation (V-A) and accommodation-induced vergence (A-V) were measured in human subjects before and after they had worn various optical devices for 30 min. Laterally displacing periscopic spectacles, which increase the required change in vergence per unit change in accommodation, caused decreases and increases in the gain of V-A and A-V responses, respectively. These observations are consistent with the view that the gain of the neural cross-linkages between vergence and accommodation are subject to adaptive regulation. However, there were strong asymmetries: Medially displacing periscopes (cyclopean spectacles), which reduce the required change in vergence per unit change in accommodation to zero, were almost totally without effect. Base-out prisms, which increase the required convergence by an amount that is constant for all viewing distances, caused downward and upward shifts in the V-A and A-V response curves, respectively. Base-in prisms, which reduce the required convergence by a constant amount for all viewing distances, caused downward shifts of A-V curves but had no significant effect on V-A curves. These effects of prisms are in essential agreement with the work of others and confirm the existence of adaptive elements that regulate the bias in the vergence and/or accommodation control systems. Secondary effects of wearing periscopes and prisms indicated a certain lack of specificity in the sensing of gain and bias errors: vertical shifts of V-A and A-V curves (resembling those seen with base-out prisms) often occurred with the laterally displacing periscopes, and gain changes (generally resembling those seen with laterally displacing periscopes) often occurred with the base-out prisms.

The authors investigated the mechanisms underlying the head shaking shown by some patients with congenital nystagmus (CN). In order to improve visual function by head shaking, a patient with CN must have some visual acuity loss due to retinal image motion created by the nystagmus; an abnormal vestibulo-ocular reflex (VOR); and the head shaking must be correlated with the nystagmus. The authors measured the VOR gain (eye velocity/head velocity) and examined eye-head coordination in five patients with CN with various combinations of these three factors. One patient met all three criteria and was able to increase his acuity by shaking his head. Other patients who shook their heads either had no loss of visual acuity due to the nystagmus or had a normal VOR. In either case, head shaking was of no apparent visual benefit and may represent, instead, an associated pathologic tremor in the cephalomotor control system.

The vestibulo-ocular reflex (VOR) is under long-term adaptive regulation to minimize retinal image slip during head movement; normally this process keeps VOR gain (eye velocity divided by head velocity) near 1.0. It has been common to think of the adaptive mechanism as a single pure gain element, although some properties of the system (e.g., frequency-selective changes in the gain of the VOR) argue that it must be more complex. We now report new observations on the frequency selectivity of the adaptive mechanism. Our data suggest a new model in which the VOR operates as a series of parallel, temporal frequency channels, each of which has an independently adjustable gain element. Adaptive changes were produced by oscillating monkeys sinusoidally at a single temporal frequency (0.2 or 2.0 Hz) in visual conditions that cause either increases (toward two) or decreases (toward zero) in VOR gain. When tested in darkness at the adapting frequency, the VOR showed large changes in gain and little or no change in phase. When tested at frequencies other than the adapting frequency, the VOR showed less pronounced changes in gain and unexpected changes in phase. The phase changes were orderly but depended in a complex way on adapting frequency, testing frequency, and VOR gain. We have tested the channels concept by calculating the response properties of a mathematical model that processed its inputs in parallel pathways. The model reproduced our data when we assumed that the vestibular primary afferents were distributed in an orderly way to parallel brain channels that had differing dynamics: vestibular inputs with more phase lead projected to higher frequency channels, which themselves had faster dynamics than their low frequency counterparts. Such an organization, when regulated by an adaptive controller that can selectively alter the gain of one channel, could play a key role in establishing and maintaining the frequency-independent performance seen in the adult VOR.