DYNAMICAL COMPLEXITY ANALYSIS OF SACCADIC EYE MOVEMENTS IN TWO DIFFERENT PSYCHOLOGICAL CONDITIONS.

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.

EYE MOVEMENT RECORDING AND NONLINEAR DYNAMICS ANALYSIS - THE CASE OF SACCADES.

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.

Applying saccade models to account for oscillations.

Saccadic oscillations are unwanted back-to-back saccades occurring one upon the other that produce a high-frequency oscillation of the eyes (usually 15-30 Hz). These may occur transiently in normal subjects, for example, around the orthogonal axis of a purely horizontal or vertical saccade, during combined saccade-vergence gaze shifts or during blinks. Some subjects may produce saccadic oscillations at will, usually with convergence. Pathological, involuntary saccadic oscillations such as flutter and opsoclonus are prominent in certain diseases. Our recent mathematical model of the premotor circuit for generating saccades includes brainstem burst neurons in the paramedian pontine reticular formation (PPRF), which show the physiological phenomenon of post-inhibitory rebound (PIR). This model makes saccadic oscillations because of the positive feedback among excitatory and inhibitory burst neurons. Here we review our recent findings and hypotheses and show how they may be reproduced using our lumped model of the saccadic premotor circuitry by reducing the inhibitory efficacy of omnipause neurons.

Irregularity distinguishes limb tremor in cervical dystonia from essential tremor.

INTRODUCTION: Patients with cervical dystonia (CD) often have limb tremor that is clinically indistinguishable from essential tremor (ET). Whether a common central mechanism underlies the tremor in these conditions is unknown. We addressed this issue by quantifying limb tremor in 19 patients with CD and 35 patients with ET. METHOD: Postural, resting and kinetic tremors were quantified (amplitude, mean frequency and regularity) using a three-axis accelerometer. RESULTS: The amplitude of limb tremor in ET was significantly higher than in CD, but the mean frequency was not significantly different between the groups. The cycle-to-cycle variability of the frequency (ie the tremor irregularity), however, was significantly greater (approximately 50%) in CD. Analysis of covariance excluded the possibility that the increased irregularity was related to the smaller amplitude of tremor in CD (ANCOVA: p = 0.007, F = 5.31). DISCUSSION: We propose that tremor in CD arises from oscillators with different dynamic characteristics, producing a more irregular output, whereas the tremor in ET arises from oscillators with similar dynamic characteristics, producing a more regular output. We suggest that variability of tremor is an important parameter for distinguishing tremor mechanisms. It is possible that changes in membrane kinetics based on the pattern of ion channel expression underlie the differences in tremor in some diseases.

Age-related differences in visual perception: a PET study.

To assess age-related differences in cortical activation during form perception, two classes of visual textures were shown to young and older subjects undergoing positron emission tomography (PET). Subjects viewed even textures that were rich in rectangular blocks and extended contours and random textures that lacked these organized form elements. Within-group significant increases in regional cerebral blood flow (rCBF) during even stimulation relative to random stimulation in young subjects were seen in occipital, inferior and medial temporal regions, and cerebellum, and in older subjects, in posterior occipital and frontal regions. Group by texture type interactions revealed significantly smaller rCBF increases in older subjects relative to young in occipital and medial temporal regions. These results indicate that young subjects activate the occipitotemporal pathway during form perception, whereas older subjects activate occipital and frontal regions. The between-group differences suggest that age-related reorganization of cortical activation occur during early visual processes in humans.

Extent of compensation for variations in monkey saccadic eye movements.

We investigated and quantified the ability of the primate saccadic system to generate accurate eye movements in spite of naturally occurring variations in saccadic speed and trajectory. We show that the amplitude of a series of saccades directed to the same target is positively correlated to their peak speed, i.e., the faster the saccade, the bigger its amplitude. We demonstrate that this result cannot be simply accounted for by the main sequence, and that on average the saccadic system is able to compensate for only 61% of the variability in speed. Deviations from the average trajectory are also only partially compensated: the underlying mechanism, which tends to bring the eyes back toward the desired trajectory, underperforms for small movements and overperforms for large movements. We also demonstrate that the performance of this compensatory mechanism, and the metrics of saccades in general, do not depend on the presence of visual information during the movement. By showing that deviations from the desired behavior are corrected during the saccade, our results further support the hypothesis that the innervation signal that generates saccadic eye movements is not pre-programmed but rather is dynamically adjusted during the movement. However, the compensation for deviations from the desired behavior is only partial, and the underlying mechanisms have yet to be completely understood. Although none of the current models of the saccadic system can account for our results, some of them, if appropriately modified, probably could.

Striate cortex in humans demonstrates the relationship between activation and variations in visual form.

Electrophysiologic and functional imaging studies have shown that the visual cortex produces differential responses to the presence or absence of structure within visual textures. To further define and characterize regions involved in the analysis of form, functional magnetic resonance imaging (fMRI) was used to detect changes in activation during the viewing of four levels of isodipole textures. The texture levels systematically differed in the density of visual features such as extended contours and blocks of solid color present within the images. A linear relationship between activation level and density of structure was observed in the striate cortex of human subjects. This finding suggests that a special subpopulation of striate cortical neurons participates in the ability to extract and process structural continuity within visual stimuli.

Model of the control of saccades by superior colliculus and cerebellum.

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.

Cortical regions involved in visual texture perception: a fMRI study.

To determine visual areas of the human brain involved in elementary form processing, functional magnetic resonance imaging (fMRI) was used to measure regional responses to two types of achromatic textures. Healthy young adults were presented with 'random' textures which lacked spatial organization of the black and white pixels that make up the image, and 'correlated' textures in which the pixels were ordered to produce extended contours and rectangular blocks at multiple spatial scales. Relative to a fixation condition, random texture stimulation resulted in increased signal intensity primarily in the striate cortex, with slight involvement of the cuneus and middle occipital, lingual and fusiform gyri. Correlated texture stimulation also resulted in activation of these areas, yet the regional extent of this activation was significantly greater than that produced by random textures. Unlike random stimulation, correlated stimulation additionally resulted in middle temporal activation. Direct comparison of the two stimulation conditions revealed significant differences most consistently in the anterior fusiform gyrus, but also in striate, middle occipital, lingual and posterior temporal regions in subjects with robust activation patterns. While both random and correlated stimulation produced activation in similar areas of the occipital lobe, the increase in regional activation during the correlated condition suggests increased recruitment of neuronal populations occurs in response to textures containing visually salient features. This increased recruitment occurs within striate, extrastriate and temporal regions of the brain, also suggesting the presence of receptive field mechanisms in the ventral visual pathway that are sensitive to features produced by higher-order spatial correlations.

PET reveals occipitotemporal pathway activation during elementary form perception in humans.

To define brain regions involved in feature extraction or elementary form perception, regional cerebral blood flow (rCBF) was measured using positron emission tomography (PET) in subjects viewing two classes of achromatic textures. Textures composed of local features (e.g. extended contours and rectangular blocks) produced activation or increased rCBF along the occipitotemporal pathway relative to textures with the same mean luminance, contrast, and spatial-frequency content but lacking organized form elements or local features. Significant activation was observed in striate, extrastriate, lingual, and fusiform cortices as well as the hippocampus and brain stem. On a scan-by-scan basis, increases in rCBF shifted from the occipitotemporal visual cortices to medial temporal (hippocampus) and frontal lobes with increased exposure to only those textures containing local features. These results suggest that local feature extraction occurs throughout the occipitotemporal (ventral) pathway during extended exposure to visually salient stimuli, and may indicate the presence of similar receptive-field mechanisms in both occipital and temporal visual areas of the human brain.

Commutative saccadic generator is sufficient to control a 3-D ocular plant with pulleys.

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.

Reversible inactivation of monkey superior colliculus. II. Maps of saccadic deficits.

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.

Model with distributed vectorial premotor bursters accounts for the component stretching of oblique saccades.

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.

Detection, classification, and superposition resolution of action potentials in multiunit single-channel recordings by an on-line real-time neural network.

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.

Scaling effects in the perception of higher-order spatial correlations.

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.

Involuntary attentional shifts due to orientation differences.

We tested the ability of orientation differences to cause involuntary shifts of visual attention and found that these attentional shifts can occur in response to an orientation "pop-out" display. Texture-like cue stimuli consisting of discrete oriented bars, with either uniform orientation or containing a noninformative orthogonally oriented bar, were presented for a variable duration. Subsequent to or partially coincident with the cue stimulus was the target display of a localization or two-interval forced-choice task, followed by a mask display. Naive subjects consistently showed greater accuracy in trials with the target at the location of the orthogonal orientation compared with trials with uniformly oriented bars, with only 100 msec between the cue and mask onsets. Discriminating these orientations required a stimulus onset asynchrony (SOA) of 50-70 msec. The attentional facilitation is transient, in most cases absent with a cue-mask SOA of 250 msec [corrected]. These results suggest that the preattentive character of some texture discrimination tasks with SOAs of only 100 msec is vitiated by the involuntary attentional shifts that are caused by orientation differences.

Primate striate and prestriate cortical neurons during discrimination. I. simultaneous temporal encoding of information about color and pattern.

1. We recorded the responses of neurons in cortical areas V1, V2, and V4 to a set of 36 colored patterns while monkeys discriminated among the stimuli on the basis of their color or their pattern. In the discrimination task a colored square or a black and white pattern was presented foveally as a cue stimulus. The monkey was required to choose, by making a saccade, which of three peripheral targets had the same property as the cue. One of the peripheral targets was centered on the receptive field of the neuron, and the other two were positioned at equally distant points around the circumference of an imaginary circle centered on the cue and passing through the receptive field. 2. An examination of the responses to the stimuli showed that there was a complex interaction between the effects of color and of pattern on the neuronal responses. Because of these interactions, we tested sensitivity to color and pattern by sorting the responses to all stimuli according to the color or pattern of the stimulus. We found that the number of spikes in the responses was affected by only one or the other of the stimulus parameters, but that the temporal distribution of spikes was affected by both stimulus parameters. We quantified the relative sensitivities of each neuron to color and pattern by dividing the amount of information the neuron transmitted about color by the amount of information the neuron transmitted about pattern. The distributions of information ratios assuming a spike count code were broad, indicating that many neurons were sensitive to only one stimulus parameter or the other. In contrast, the distributions of information ratios assuming a wave-form code were narrow and centered near 1.0, indicating nearly equal sensitivities to both stimulus parameters. 3. In our initial experiments, it appeared that the color or pattern used as the cue for the discrimination task affected the responses of many neurons to stimuli on the receptive field. To determine whether the cue effect was due to simple visual interactions or to the cognitive requirements of the discrimination task, we performed a control experiment in which the cue was turned on 80 ms after the peripheral stimuli. For many of the neurons in the control experiment, an effect related to the cue appeared in the response before the cue had been turned on. Thus the effect we observed must have been due to visual interactions with the distractor targets, even though these were outside the neuron's classically defined receptive field. 4. We compared the rate at which color and pattern information developed in the response over time assuming either a spike count or a waveform code. The spike count code gained more of its information in the first 20ms of the response than did the waveform code, but thereafter the information carried by the spike count code developed more slowly and reached a lower asymptote than did the information carried by the waveform code. 5. The waveform codes carried nearly equal amounts of information about color and pattern, but the messages about these two parameters did not develop at the same rate in all areas. The messages about color and pattern developed at the same rate in area V1, but messages about color developed more slowly than did the messages about pattern in areas V2 and V4. 6. These results offer a neurophysiological basis for both the psychological separateness of color and pattern, and the binding of color and pattern into a unified percept. We propose that the separateness of color and form arises not by virtue of their being encoded by different populations of neurons, but by virtue of their being encoded by separable waveform codes in the responses of single neurons. We propose that the binding of color and form occurs by virtue of their codes being multiplexed on the same neurons.