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Direction selective neurons in macaque primary visual cortex are narrowly tuned for orientation, and are thus afflicted by the aperture problem. At the next stage of motion processing, in the middle temporal (MT) area, some cells appear to solve this problem, responding to the pattern motion direction of plaids. Models have been proposed to account for this computation, but they do not replicate the diversity of responses observed in MT. We recorded from 386 cells in area MT of two male macaques, while presenting a wide range of random-line stimuli and their compositions into noise plaids. As we broadened the range of stimuli used to probe the cells, yielding ever more challenging conditions for extracting pattern motion, the diversity of the responses observed increased, and the fraction of cells that faithfully encoded pattern motion direction shrank. However, we show here that a pattern motion signal is present at the population level. We identified four mechanisms, one never proposed before, that together might account for the observed diversity in single-cell responses. Pattern motion is thus extracted in area MT, but it is encoded across the population, and not in a small subset of pattern neurons.SIGNIFICANCE STATEMENTSome neurons in the middle temporal area of macaques solve the aperture problem, signaling the direction of motion of complex patterns. As the number of pattern types used to probe this mechanism is increased, fewer and fewer cells retain this capability. We show here that different cells fail in different ways, and that simply summing their responses averages away their failures, yielding a clear pattern motion signal. Similar encodings, which unequivocally violate the “neuron as a feature detector” hypothesis that has dominated sensory processing theories for the past 50 years, might apply throughout the brain.

Natural images are typically broadband, whereas detectors in early visual processing are selective for narrow ranges of spatial frequency. White noise patterns are widely used in laboratory settings to investigate how responses are derived from Fourier components in the image. Here, we report disparity vergence responses (DVRs) to white noise stimuli in human subjects and compare these with responses to white noise patterns filtered with bandpass filters and notch filters and to sinusoidal gratings. Although the contribution of these short-latency eye movements to the overall vergence response to a given stimulus is generally small, they have proven to be a valuable tool for the study of the early mechanisms that process disparity stimuli in human subjects. Removing lower spatial frequency (SF) components reduced DVR amplitude, whereas removing higher SF components led to an increase in DVR amplitude. For larger disparities, the transition occurred at lower SFs. All of these effects were quantitatively well described by a model that combined two factors: (a) an excitatory drive determined by a weighted sum of stimulus Fourier components, which was scaled by (b) a contrast normalization mechanism.

Ocular following eye movements have provided insights into how the visual system of humans and monkeys processes motion. Recently, it has been shown that they also reliably reveal stereoanomalies, and, thus, might have clinical applications. Their translation from research to clinical setting has however been hindered by their small size, which makes them difficult to record, and by a lack of data about their properties in sizable populations. Notably, they have so far only been recorded in adults. We recorded ocular following responses (OFRs)–defined as the change in eye position in the 80–160 ms time window following the motion onset of a large textured stimulus–in 14 school-age children (6 to 13 years old, 9 males and 5 females), under recording conditions that closely mimic a clinical setting. The OFRs were acquired non-invasively by a custom developed high-resolution video-oculography system, described in this study. With the developed system we were able to non-invasively detect OFRs in all children in short recording sessions. Across subjects, we observed a large variability in the magnitude of the movements (by a factor of 4); OFR magnitude was however not correlated with age. A power analysis indicates that even considerably smaller movements could be detected. We conclude that the ocular following system is well developed by age six, and OFRs can be recorded non-invasively in young children in a clinical setting.

Direction selective neurons in primary visual cortex (area V1) are affected by the aperture problem, i.e., they are only sensitive to motion orthogonal to their preferred orientation. A solution to this problem first emerges in the middle temporal (MT) area, where a subset of neurons (called pattern cells) combine motion information across multiple orientations and directions, becoming sensitive to pattern motion direction. These cells are expected to play a prominent role in subsequent neural processing, but they are intermixed with cells that behave like V1 cells (component cells), and others that do not clearly fall in either group. The picture is further complicated by the finding that cells that behave like pattern cells with one type of pattern, might behave like component cells for another.We recorded from macaque MT neurons using multi-contact electrodes while presenting both type I and unikinetic plaids, in which the components were 1D noise patterns. We found that the indices that have been used in the past to classify neurons as pattern or component cells work poorly when the properties of the stimulus are not optimized for the cell being recorded, as is always the case with multi-contact arrays. We thus propose alternative measures, which considerably ameliorate the problem, and allow us to gain insights in the signals carried by individual MT neurons.We conclude that arranging cells along a component-to-pattern continuum is an oversimplification, and that the signals carried by individual cells only make sense when embodied in larger populations.

Purpose Stereoscopic vision, by detecting interocular correlations, enhances depth perception. Stereodeficiencies often emerge during the first months of life, and left untreated can lead to severe loss of visual acuity in one eye and/or strabismus. Early treatment results in much better outcomes, yet diagnostic tests for infants are cumbersome and not widely available. We asked whether reflexive eye movements, which in principle can be recorded even in infants, can be used to identify stereodeficiencies. Methods Reflexive ocular following eye movements induced by fast drifting noise stimuli were recorded in 10 adult human participants (5 with normal stereoacuity, 5 stereodeficient). To manipulate interocular correlation, the stimuli shown to the two eyes were either identical, different, or had opposite contrast. Monocular presentations were also interleaved. The participants were asked to passively fixate the screen. Results In the participants with normal stereoacuity, the responses to binocular identical stimuli were significantly larger than those induced by binocular opposite stimuli. In the stereodeficient participants the responses were indistinguishable. Despite the small size of ocular following responses, 40 trials, corresponding to less than 2 minutes of testing, were sufficient to reliably differentiate normal from stereodeficient participants. Conclusions Ocular-following eye movements, because of their reliance on cortical neurons sensitive to interocular correlations, are affected by stereodeficiencies. Because these eye movements can be recorded noninvasively and with minimal participant cooperation, they can potentially be measured even in infants and might thus provide an useful screening tool for this currently underserved population.

Sensory neurons are activated by a range of stimuli to which they are said to be tuned. Usually, they are also suppressed by another set of stimuli that have little effect when presented in isolation. The interactions between preferred and suppressive stimuli are often quite complex and vary across neurons, even within a single area, making it difficult to infer their collective effect on behavioral responses mediated by activity across populations of neurons. Here, we investigated this issue by measuring, in human subjects (three males), the suppressive effect of static masks on the ocular following responses induced by moving stimuli. We found a wide range of effects, which depend in a nonlinear and nonseparable manner on the spatial frequency, contrast, and spatial location of both stimulus and mask. Under some conditions, the presence of the mask can be seen as scaling the contrast of the driving stimulus. Under other conditions, the effect is more complex, involving also a direct scaling of the behavioral response. All of this complexity at the behavioral level can be captured by a simple model in which stimulus and mask interact nonlinearly at two stages, one monocular and one binocular. The nature of the interactions is compatible with those observed at the level of single neurons in primates, usually broadly described as divisive normalization, without having to invoke any scaling mechanism.SIGNIFICANCE STATEMENTThe response of sensory neurons to their preferred stimulus is often modulated by stimuli that are not effective when presented alone. Individual neurons can exhibit multiple modulatory effects, with considerable variability across neurons even in a single area. Such diversity has made it difficult to infer the impact of these modulatory mechanisms on behavioral responses. Here, we report the effects of a stationary mask on the reflexive eye movements induced by a moving stimulus. A model with two stages, each incorporating a divisive modulatory mechanism, reproduces our experimental results and suggests that qualitative variability of masking effects in cortical neurons might arise from differences in the extent to which such effects are inherited from earlier stages.

From a mathematical point of view, extracting motion and disparity signals from a binocular visual stream requires very similar operations, applied over time for motion and across eyes for disparity. This similarity is reflected in the theories that have been proposed to describe the neural mechanisms used by the brain to extract these signals. At the behavioral level there are, however, several differences in how humans react to these stimuli, which presumably reflect differences in how these signals are processed by the brain. Here we highlight three such differences: the degree to which different axes of motion/disparity are treated isotropically, the importance of reference signals, and the rules that underlie the combination of 1D signals to extract 2D signals.

Neuronal and psychophysical responses to a visual stimulus are known to depend on the preceding history of visual stimulation, but the effect of stimulation history on reflexive eye movements has received less attention. Here, we quantify these effects using short-latency ocular following responses (OFRs), a valuable tool for studying early motion processing. We recorded, in human subjects, the horizontal OFRs induced by drifting vertical 1D pink noise. The stimulus was preceded by 600 to 1000 ms of maintained fixation (on a visible cross), and we explored the effect of different stimuli ("fixation patterns") presented during the fixation period. We found that any temporal modulation present during the fixation period reduced the magnitude of the subsequent OFRs. Even changes in the overall luminance during the fixation period induced significant suppression. The magnitude of the effect was a function of both spatial and temporal structure of the fixation pattern. Suppression that was selective for both relative orientation and relative spatial frequency accounted for a considerable fraction of total suppression. Finally, changes in stimulus temporal structure alone (i.e. "flicker" versus "transparent motion") led to changes in the spatial frequency tuning of suppression. In the time domain, the suppression developed quickly: 100 ms of temporal modulation in the fixation pattern produced up to 80% of maximal suppression. Recovery from suppression was instead more gradual, taking up to several seconds. By presenting transparent motion during the fixation period, with opposite motion signals having different spatial frequency content, we also discovered a direction-selective component of suppression, which depended on both the frequency and the direction of the moving stimulus.

From a mathematical point of view, extracting motion and disparity signals from a binocular visual stream requires very similar operations, applied over time for motion and across eyes for disparity. This similarity is reflected in the theories that have been proposed to describe the neural mechanisms used by the brain to extract these signals. At the behavioral level there are, however, several differences in how humans react to these stimuli, which presumably reflect differences in how these signals are processed by the brain. Here we highlight three such differences: the degree to which different axes of motion/disparity are treated isotropically, the importance of reference signals, and the rules that underlie the combination of 1D signals to extract 2D signals.

Using sinusoidal gratings we show that an increase in stimulus size confined to the dimension orthogonal to the axis of motion leads to stronger Ocular Following Responses (OFRs) up to a certain optimal size. An increase beyond this optimum produces smaller responses, indicating suppressive interactions. In sharp contrast, when the stimulus growth occurs parallel to the axis of motion OFR magnitudes increase monotonically both for horizontal and vertical directions of motion. Similar results are obtained with 1D white noise patterns. However, the OFR spatial anisotropy is minimal with 2D white noise patterns, revealing a pivotal role of orientation-selective (i.e., cortical) mechanisms in mediating this phenomenon. The lack of anisotropy for 2D patterns suggests that directional signals alone are not sufficient to elicit this suppression. The OFR spatial anisotropy is potentiated if a stationary grating is presented for 600–1000ms before its motion commences, further emphasizing the importance of static orientation signals. These results suggest that the strength of cortical spatial interactions is asymmetric—i.e., larger in the direction of the ends than the flanks of an orientation-selective receptive field—which corroborates the existing neurophysiological evidence.

We recorded horizontal ocular-following responses to pairs of superimposed vertical sine wave gratings moving in opposite directions in human subjects. This configuration elicits a nonlinear interaction: when the relative contrast of the gratings is changed, the response transitions abruptly between the responses elicited by either grating alone. We explore this interaction in pairs of gratings that differ in spatial and temporal frequency and show that all cases can be described as a weighted sum of the responses to each grating presented alone, where the weights are a nonlinear function of stimulus contrast: a nonlinear weighed summation model. The weights depended on the spatial and temporal frequency of the component grating. In many cases the dominant component was not the one that produced the strongest response when presented alone, implying that the neuronal circuits assigning weights precede the stages at which motor responses to visual motion are generated. When the stimulus area was reduced, the relationship between spatial frequency and weight shifted to higher frequencies. This finding may reflect a contribution from surround suppression. The nonlinear interaction is strongest when the two components have similar spatial frequencies, suggesting that the nonlinearity may reflect interactions within single spatial frequency channels. This framework can be extended to stimuli composed of more than two components: our model was able to predict the responses to stimuli composed of three gratings. That this relatively simple model successfully captures the ocular-following responses over a wide range of spatial/temporal frequency and contrast parameters suggests that these interactions reflect a simple mechanism.

Ocular following responses (OFRs) are the initial tracking eye movements elicited at ultra-short latency by sudden motion of a textured pattern. We wished to evaluate quantitatively the impact that subcortical stages of visual processing might have on the OFRs. In three experiments we recorded the OFRs of human subjects to brief horizontal motion of 1D vertical sine-wave gratings restricted to an elongated horizontal aperture. Gratings were composed of a variable number of abutting horizontal strips where alternate strips were in counterphase. In one of the experiments we also utilized gratings occupying a variable number of horizontal strips separated vertically by mean-luminance gaps. We modeled retinal center/surround receptive fields as a difference of two 2-D Gaussian functions. When the characteristics of such local filters were selected in accord with the known properties of primate retinal ganglion cells, a single-layer model was capable to quantitatively account for the observed changes in the OFR amplitude for stimuli composed of counterphase strips of different heights (Experiment 1), for a wide range of stimulus contrasts (Experiment 2) and spatial frequencies (Experiment 3). A similar model using oriented filters that resemble cortical simple cells was also able to account for these data. Since similar filters can be constructed from the linear summation of retinal filters, and these filters alone can explain the data, we conclude that retinal processing determines the response to these stimuli. Thus, with appropriately chosen stimuli, OFRs can be used to study visual spatial integration processes as early as in the retina.

In the context of motion detection, the endings (or terminators) of 1-D features can be detected as 2-D features, affecting the perceived direction of motion of the 1-D features (the barber-pole illusion) and the direction of tracking eye movements. In the realm of binocular disparity processing, an equivalent role for the disparity of terminators has not been established. Here we explore the stereo analogy of the barber-pole stimulus, applying disparity to a 1-D noise stimulus seen through an elongated, zero-disparity, aperture. We found that, in human subjects, these stimuli induce robust short-latency reflexive vergence eye movements, initially in the direction orthogonal to the 1-D features, but shortly thereafter in the direction predicted by the disparity of the terminators. In addition, these same stimuli induce vivid depth percepts, which can only be attributed to the disparity of line terminators. When the 1-D noise patterns are given opposite contrast in the two eyes (anticorrelation), both components of the vergence response reverse sign. Finally, terminators drive vergence even when the aperture is defined by a texture (as opposed to a contrast) boundary. These findings prove that terminators contribute to stereo matching, and constrain the type of neuronal mechanisms that might be responsible for the detection of terminator disparity.

Stereo matching, i.e., the matching by the visual system of corresponding parts of the images seen by the two eyes, is inherently a 2D problem. To gain insights into how this operation is carried out by the visual system, we measured, in human subjects, the reflexive vergence eye movements elicited by the sudden presentation of stereo plaids. We found compelling evidence that the 2D pattern disparity is computed by combining disparities first extracted within orientation selective channels. This neural computation takes 10–15 ms, and is carried out even when subjects perceive not a single plaid but rather two gratings in different depth planes (transparency). However, we found that 1D disparities are not always effectively combined: When spatial frequency and contrast of the gratings are sufficiently different pattern disparity is not computed, a result that cannot be simply attributed to the transparency of such stimuli. Based on our results, we propose that a narrow-band implementation of the IOC (Intersection of Constraints) rule ([Fennema and Thompson, 1979][1]; [Adelson and Movshon, 1982][2]), preceded by cross-orientation suppression, underlies the extraction of pattern disparity. [1]: #ref-23 [2]: #ref-1

We studied human short-latency vergence eye movements to a novel stimulus that produces interocular velocity differences without a changing disparity signal. Sinusoidal luminance gratings moved in opposite directions (left vs. right; up vs. down) in the two eyes. The grating seen by each eye underwent ¼-wavelength shifts with each image update. This arrangement eliminated changing disparity cues, since the phase difference between the eyes alternated between 0° and 180°. We nevertheless observed robust short-latency vergence responses (VRs), whose sign was consistent with the interocular velocity differences (IOVDs), indicating that the IOVD cue in isolation can evoke short-latency VRs. The IOVD cue was effective only when the images seen by the two eyes overlapped in space. We observed equally robust VRs for opposite horizontal motions (left in one eye, right in the other) and opposite vertical motions (up in one eye, down in the other). Whereas the former are naturally generated by objects moving in depth, the latter are not part of our normal experience. To our knowledge, this is the first demonstration of a behavioral consequence of vertical IOVD. This may reflect the fact that some neurons in area MT are sensitive to these motion signals (Czuba, Huk, Cormack, & Kohn, 2014). VRs were the strongest for spatial frequencies in the range of 0.35-1 c/°, much higher than the optimal spatial frequencies for evoking ocular-following responses observed during frontoparallel motion. This suggests that the two motion signals are detected by different neuronal populations. We also produced IOVD using moving uncorrelated one-dimensional white-noise stimuli. In this case the most effective stimuli have low speed, as predicted if the drive originates in neurons tuned to high spatial frequencies (Sheliga, Quaia, FitzGibbon, & Cumming, 2016).

Passive extraocular muscles (EOMs), like most biological tissues, are hyperelastic, that is, their stiffness increases as they are stretched. It has always been assumed, and in a few occasions argued, that this is their only nonlinearity and that it can be ignored in central gaze. However, using novel measurement techniques in anesthetized paralyzed monkeys, we have recently demonstrated that EOMs are characterized by another prominent nonlinearity: the forces induced by sequences of stretches do not sum. Thus, superposition, a central tenet of linear and quasi-linear models, does not hold in passive EOMs. Here, we outline the implications of this finding, especially in light of the common assumption that it is easier for the brain to control a linear than a nonlinear plant. We argue against this common belief: the specific nonlinearity of passive EOMs may actually make it easier for the brain to control the plant than if muscles were linear.

Psychophysical studies and our own subjective experience suggest that, in natural viewing conditions (i.e., at medium to high contrasts), monocularly and binocularly viewed scenes appear very similar, with the exception of the improved depth perception provided by stereopsis. This phenomenon is usually described as a lack of binocular summation. We show here that there is an exception to this rule: Ocular following eye movements induced by the sudden motion of a large stimulus, which we recorded from three human subjects, are much larger when both eyes see the moving stimulus, than when only one eye does. We further discovered that this binocular advantage is a function of the interocular correlation between the two monocular images: It is maximal when they are identical, and reduced when the two eyes are presented with different images. This is possible only if the neurons that underlie ocular following are sensitive to binocular disparity.

Since the discovery of neurons selective for pattern motion direction in primate middle temporal area MT (Albright, 1984; Movshon et al., 1985), the neural computation of this signal has been the subject of intense study. The bulk of this work has explored responses to plaids obtained by summing two drifting sinusoidal gratings. Unfortunately, with these stimuli, many different mechanisms are similarly effective at extracting pattern motion. We devised a new set of stimuli, obtained by summing two random line stimuli with different orientations. This allowed several novel manipulations, including generating plaids that do not contain rigid 2D motion. Importantly, these stimuli do not engage most of the previously proposed mechanisms. We then recorded the ocular following responses that such stimuli induce in human subjects. We found that pattern motion is computed even with stimuli that do not cohere perceptually, including those without rigid motion, and even when the two gratings are presented separately to the two eyes. Moderate temporal and/or spatial separation of the gratings impairs the computation. We show that, of the models proposed so far, only those based on the intersection-of-constraints rule, embedding a motion-from-form mechanism (in which orientation signals are used in the computation of motion direction signals), can account for our results. At least for the eye movements reported here, a motion-from-form mechanism is thus involved in one of the most basic functions of the visual motion system: extracting motion direction from complex scenes.SIGNIFICANCE STATEMENTAnatomical considerations led to the proposal that visual function is organized in separate processing streams: one (ventral) devoted to form and one (dorsal) devoted to motion. Several experimental results have challenged this view, arguing in favor of a more integrated view of visual processing. Here we add to this body of work, supporting a role for form information even in a function—extracting pattern motion direction from complex scenes—for which decisive evidence for the involvement of form signals has been lacking.

Models of the oculomotor plant (globe, muscles, pulleys, and orbital tissues) fall into three categories: 1). one-dimensional dynamic with lumped plant elements, 2). three-dimensional dynamic with lumped plant elements, or 3). three-dimensional static with distinct plant elements. The second class of models is most often used when studying the neural control of 3-D eye movement, because they best represent the plant dynamics. However, they are often faulted because they make two unrealistic assumptions: 1). muscle pairs act along the three orthogonal axes (symmetry assumption); and 2). the force generated by the muscles depends only on their innervation (force assumption). It turns out that the symmetry assumption is quite benign, because in a realistic model of the plant the deviations from orthogonal axes can be easily accounted for by simple adjustments to the innervation. In contrast, the force assumption introduces some serious problems. In the present paper, the authors show that a realistic, dynamic model of the geometry of the orbit, with independent muscles, makes different predictions than a similar model with lumped muscles. This difference arises because muscle force is a function of both innervation and muscle length.

At least under some conditions, plaid stimuli are processed by combining information first extracted in orientation and scale-selective channels. The rules that govern this combination across channels are only partially understood. Although the available data suggests that only components having similar spatial frequency and contrast are combined, the extent to which this holds has not been firmly established. To address this question, we measured, in human subjects, the short-latency reflexive vergence eye movements induced by stereo plaids in which spatial frequency and contrast of the components are independently varied. We found that, although similarity in component spatial frequency and contrast matter, they interact in a nonseparable way. One way in which this relationship might arise is if the internal estimate of contrast is not a faithful representation of stimulus contrast but is instead spatial frequency-dependent (with higher spatial frequencies being boosted). We propose that such weighting might have been put in place by a mechanism that, in an effort of achieve contrast constancy and/or coding efficiency, regulates the gain of detectors in early visual cortex to equalize their long-term average response to natural images.

Single-unit discharges were recorded in the medial superior temporal area (MST) of five behaving monkeys. Brief (230-ms) horizontal disparity steps were applied to large correlated or anticorrelated random-dot patterns (in which the dots had the same or opposite contrast, respectively, at the two eyes), eliciting vergence eye movements at short latencies [65.8 ± 4.5 (SD) ms]. Disparity tuning curves, describing the dependence of the initial vergence responses (measured over the period 50–110 ms after the step) on the magnitude of the steps, resembled the derivative of a Gaussian, the curves obtained with correlated and anticorrelated patterns having opposite sign. Cells with disparity-related activity were isolated using correlated stimuli, and disparity tuning curves describing the dependence of these initial neuronal responses (measured over the period of 40–100 ms) on the magnitude of the disparity step were constructed ( n = 102 cells). Using objective criteria and the fuzzy c-means clustering algorithm, disparity tuning curves were sorted into four groups based on their shapes. A post hoc comparison indicated that these four groups had features in common with four of the classes of disparity-selective neurons in striate cortex, but three of the four groups appeared to be part of a continuum. Most of the data were obtained from two monkeys, and when the disparity tuning curves of all the individual neurons recorded from either monkey were summed together, they fitted the disparity tuning curve for that same animal's vergence responses remarkably well ( r 2: 0.93, 0.98). Fifty-six of the neurons recorded from these two monkeys were also tested with anticorrelated patterns, and all showed significant modulation of their activity ( P < 0.005, 1-way ANOVA). Further, when all of the disparity tuning curves obtained with these patterns from either monkey were summed together, they too fitted the disparity tuning curve for that same animal's vergence responses very well ( r 2: 0.95, 0.96). Indeed, the summed activity even reproduced idiosyncratic differences in the vergence responses of the two monkeys. Based on these and other observations on the temporal coding of events, we hypothesize that the magnitude, direction, and time course of the initial vergence velocity responses associated with disparity steps applied to large patterns are all encoded in the summed activity of the disparity-sensitive cells in MST. Latency data suggest that this activity in MST occurs early enough to play an active role in the generation of vergence eye movements at short latencies.

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.

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.

Quaia, Christian and Lance M. Optican. Commutative saccadic generator is sufficient to control a 3-D ocular plant with pulleys. J. Neurophysiol. 79: 3197–3215, 1998. 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.

Quaia, Christian, Hiroshi Aizawa, Lance M. Optican, and Robert H. Wurtz. Reversible inactivation of monkey superior colliculus. II. Maps of saccadic deficits. J. Neurophysiol. 79: 2097–2110, 1998. 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.

Ocular following responses (OFRs) are tracking eye movements elicited at ultrashort latency by the sudden movement of a textured pattern. Here we report the results of our study of their dependency on the spatial arrangement of the motion stimulus. Unlike previous studies that looked at the effect of stimulus size, we investigated the impact of stimulus location and how two distinct stimuli, presented together, collectively determine the OFR. We used as stimuli vertical gratings that moved in the horizontal direction and that were confined to either one or two 0.58° high strips, spanning the width of the screen. We found that the response to individual strips varied as a function of the location and spatial frequency (SF) of the stimulus. The response decreased as the stimulus eccentricity increased, but this relationship was more accentuated at high than at low spatial frequencies. We also found that when pairs of stimuli were presented, nearby stimuli interacted strongly, so that the response to the pair was barely larger than the response to a single strip in the pair. This suppressive effect faded away as the separation between the strips increased. The variation of the suppressive interaction with strip separation, paired with the dependency on eccentricity of the responses to single strips, caused the peak response for strip pairs to be achieved at a specific separation, which varied as a function of SF.

Ocular following responses (OFRs) are the initial tracking eye movements that can be elicited at ultra-short latency by sudden motion of a textured pattern. The OFR magnitude depends upon stimulus size, and also upon the spatial frequency (SF) of sine-wave gratings. Here we investigate the interaction of size and SF. We recorded initial OFRs in human subjects when 1D vertical sine-wave gratings were subject to horizontal motion. Gratings were restricted to elongated horizontal apertures—“strips”—aligned with the axis of motion. In Experiment 1 the SF and the height of a single strip was manipulated. The magnitude of the OFR increased with strip height up to some optimum value, while strip heights greater than this optimum produced smaller responses. This effect was strongly dependent on SF: the optimum strip height was smaller for higher SFs. In order to explore the underlying mechanism, Experiment 2 measured OFRs to stimuli composed of two thin horizontal strips—one in the upper visual field, the other in the lower visual field—whose vertical separation varied 32-fold. Stimuli of different sizes can be reconstructed from the sum of such horizontal strips. We found that the OFRs in Experiment 1 were smaller than the sum of the responses to the component stimuli, but greater than the average of those responses. We defined an averaging coefficient that described whether a given response was closer to the sum or to the average. For any one SF, the averaging coefficients were similar over a wide range of stimulus sizes, while they varied considerably (7-fold) for stimuli of different SFs.

We investigated the immediate and long-term changes in static eye alignment with acute superior oblique palsy (SOP) in the monkey. When the paretic eye was patched immediately after the lesion for 6-9 days, vertical alignment slowly improved. When the patch was removed and binocular viewing was allowed, alignment slowly worsened. In contrast when a monkey was not patched immediately after the lesion vertical alignment did not improve. We also show that a model of the eye plant can reproduce the observed acute deficit induced by SOP, but only by abandoning Robinson's symmetric simplification of the reciprocal innervation relationship within pairs of agonist-antagonist muscles. The model also demonstrated that physiologic variability in orbital geometry can have a large impact on SOP deficits.

Superior oblique.palsy (SOP) is a common cause of cyclo-vertical strabismus. The primary action of the superior oblique muscle is intorsion, and its secondary action is depression. Consequently, the paretic eye of a patient with a weakness of the SO muscle is elevated and extorted relative to the normal eye. The diagnosis of SOP often rests on the results of the Bielschowsky head-tilt test: In SOP, the vertical deviation increases when the head is tilted toward the side of the paretic eye. This response is due to the vestibulo-ocular reflex induced by a static roll tilt of the head. Normally, when the head is tilted laterally, the superior rectus (SR) muscle and SO muscles cooperate to intort the lower eye.1 When the head is tilted toward the side of an SOP, however, the upward action of the SR muscle is unopposed by the (paretic) SO muscle, leading to an increased vertical deviation. As part of a study of the ocular motor signature of acquired SOP in monkeys,2–4 we sought to assay the function of the SO muscle by measuring the torsional response to an optokinetic stimulus that rotated around the line of sight (tOKN). By eliciting torsional nystagmus, we could examine the effect of the SOP on the primary action of the SO muscle. In addition, we asked if examining the changes in the dynamic characteristics of eye movements during tOKN might give information complementary to that from the Bielschowsky head-tilt test. Both monkeys also received corrective strabismus procedures (a weakening procedure of the ipsilateral inferior oblique [IO] muscle in both animals and a subsequent weakening procedure of the contralateral inferior rectus [IR] muscle in one animal). This gave us the opportunity to examine the effects of weakening of muscles with different primary muscle actions on the response to tOKN.

We investigated the immediate and long-term changes in static eye alignment with acute superior oblique palsy (SOP) in the monkey. When the paretic eye was patched immediately after the lesion for 6–9 days, vertical alignment slowly improved. When the patch was removed and binocular viewing was allowed, alignment slowly worsened. In contrast when a monkey was not patched immediately after the lesion vertical alignment did not improve. We also show that a model of the eye plant can reproduce the observed acute deficit induced by SOP, but only by abandoning Robinson's symmetric simplification of the reciprocal innervation relationship within pairs of agonist–antagonist muscles. The model also demonstrated that physiologic variability in orbital geometry can have a large impact on SOP deficits.

PURPOSE To investigate the three-dimensional orientation of the eye and its relationship to Listing's Law in monkeys with acute acquired superior oblique palsy (SOP). METHODS The trochlear nerve was severed intracranially in two rhesus monkeys. Three-axis eye movements (horizontal, vertical, and torsion) were measured with binocular, dual search coils during fixation of targets in a 40 degrees x 40 degrees grid. Rotation vectors were calculated, and Listing's plane (LP) was determined by a least-squares planar fit of eye torsion as a function of horizontal and vertical position. RESULTS The main findings were: (1) In the paretic eye, there was an immediate and sustained rotation of the orientation plane by approximately 25 degrees in the temporal direction; (2) the thickness of LP, defined as the torsional standard deviation (SD), increased little (by 0.13 degrees in M1 and 0.08 degrees in M2) after SOP, and (3) the SD of intrasaccadic torsion was slightly greater than that during fixation, but there was no change after SOP. CONCLUSIONS Acute SOP in rhesus monkeys leads to a temporal rotation of LP. This is consistent with a relatively increased extorsion in down gaze due to a loss of normal intorsion by the superior oblique muscle. The SD of torsion increased by only a small amount, implying that the validity of Listing's Law is not affected much by complete SOP, despite the large change in the orientation of LP.

PURPOSE To investigate vertical and torsional eye motion during and immediately after vertical saccades with acute acquired superior oblique palsy (SOP) in monkeys. METHODS The trochlear nerve was severed intracranially in two rhesus monkeys. After surgery, the paretic eye was patched for 6 to 9 days, and then binocular viewing was allowed. Three-axis eye movements (horizontal, vertical, and torsion) were measured with binocular, dual search coils. Eye movements were recorded before surgery and then beginning 2 to 3 days after surgery during 20 degrees vertical saccades over a +/-20 degrees horizontal and vertical range. RESULTS The main findings were: (1) Saccade amplitude in the paretic eye (PE) was smaller than that of the normal eye (NE), especially for downward saccades with the PE in adduction; (2) vertical drift was backward after upward saccades with the PE in adduction or abduction, onward after downward saccades with the PE in adduction, but backward for downward saccades with the PE in abduction, drift time constants averaged 35 ms; (3) peak dynamic blip intrasaccadic torsion increased (relative extorsion), the most for upward saccades with the PE in abduction; (4) postsaccadic torsional drift increased (relative intorsion), the most for downward saccades with the PE in adduction; and (5) the peak velocity-amplitude relationship in vertical saccades was little affected, but the ratio between the peak velocity of the two eyes was a consistent indicator of the palsy. CONCLUSIONS Rhesus monkeys with acute acquired SOP show characteristic changes in vertical and torsional movements during and immediately after vertical saccades that help define the ocular motor signature of denervation of the SO muscle. These dynamic changes were largely unrelated to the changes in static alignment over time, suggesting that static and dynamic disturbances in SOP are influenced by separate central mechanisms.

We investigate the role that superior colliculus (SC) and cerebellum (CBLM) might play in controlling saccadic eye movements. Even though strong experimental evidence argues for an important role for the CBLM, the most recent models of the saccadic system have relied mostly on the SC for the dynamic control of saccades. In this study, we propose that saccades are controlled by two parallel pathways, one including the SC and the other including the CBLM. In this model, both SC and CBLM provide part of the drive to the saccade. Furthermore, the CBLM receives direct feedback from the brain stem and keeps track of the residual motor error, so that it can issue appropriate commands to compensate for incorrect heading and to end the movement when the target has been foveated. We present here a distributed model that produces realistic saccades and accounts for a great deal of neurophysiological data.

Humans and monkeys can direct their eyes to the spatial location of briefly flashed targets even when a saccade intervenes between the stimulus flash and the saccade to acquire its location. It had been proposed that the oculomotor system performs this task by resorting to a supraretinal representation of space. In this paper we review neurophysiological and clinical data suggesting that the brain can use a different strategy that does not require an explicit supraretinal representation of targets. We propose and implement a simple neural model that can keep track continuously of the location of saccade targets in eye-centered coordinates. Finally, based on recent data, we argue that such a neural mechanism is in fact used to keep track not only of saccade targets but of the location of salient areas of the visual scene in general.

Disparity steps applied to large patterns elicit vergence eye movements at ultrashort latencies. Disparity tuning curves, describing the dependence of the amplitude of the initial vergence responses on the amplitude of the disparity steps, resemble the derivative of a gaussian and indicate that appropriate servo-like behavior occurs only with small disparity steps (

How does the brain tell the eye where to go? Classical models of rapid eye movements are lumped control systems that compute analogs of physical signals such as desired eye displacement, instantaneous error, and motor drive. Components of these lumped models do not correspond well with anatomical and physiological data. We have developed a more brain-like, distributed model (called a neuromimetic model), in which the superior colliculus (SC) and cerebellum (CB) play novel roles, using information about the desired target and the movement context to generate saccades. It suggests that the SC is neither sensory nor motor; rather it encodes the desired sensory consequence of the saccade in retinotopic coordinates. It also suggests a non-computational scheme for motor control by the cerebellum, based on context learning and a novel spatial mechanism, the pilot map. The CB learns to use contextual information to initialize the pilot signal that will guide the saccade to its goal. The CB monitors feedback information to steer and stop the saccade, and thus replaces the classical notion of a displacement integrator. One consequence of this model is that no desired eye movement signal is encoded explicitly in the brain; rather it is distributed across activity in both the SC and CB. Another is that the transformation from spatially coded sensory information to temporally coded motor information is implicit in the velocity feedback loop around the CB. No explicit spatial-to-temporal transformation with a normalization step is needed.