Christian Quaia

Distributed model of control of saccades by superior colliculus and cerebellum

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.

The maintenance of spatial accuracy by the periasaccadic remapping of visual receptive fields

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.

Extent of compensation for variations in monkey saccadic eye movements

Abstract. 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.

Dynamic eye plant models and the control of eye movements

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.

Eye movement sequence generation in humans: Motor or goal updating?

Saccadic eye movements are often grouped in pre-programmed sequences. The mechanism underlying the generation of each saccade in a sequence is currently poorly understood. Broadly speaking, two alternative schemes are possible: first, after each saccade the retinotopic location of the next target could be estimated, and an appropriate saccade could be generated. We call this the goal updating hypothesis. Alternatively, multiple motor plans could be pre-computed, and they could then be updated after each movement. We call this the motor updating hypothesis. We used McLaughlins intra-saccadic step paradigm to artificially create a condition under which these two hypotheses make discriminable predictions. We found that in human subjects, when sequences of two saccades are planned, the motor updating hypothesis predicts the landing position of the second saccade in two-saccade sequences much better than the goal updating hypothesis. This finding suggests that the human saccadic system is capable of executing sequences of saccades to multiple targets by planning multiple motor commands, which are then updated by serial subtraction of ongoing motor output.

The viscoelastic properties of passive eye muscle in primates. I: static forces and step responses.

The viscoelastic properties of passive eye muscles are prime determinants of the deficits observed following eye muscle paralysis, the root cause of several types of strabismus. Our limited knowledge about such properties is hindering the ability of eye plant models to assist in formulating a patients diagnosis and prognosis. To investigate these properties we conducted an extensive in vivo study of the mechanics of passive eye muscles in deeply anesthetized and paralyzed monkeys. We describe here the static length-tension relationship and the transient forces elicited by small step-like elongations. We found that the static force increases nonlinearly with length, as previously shown. As expected, an elongation step induces a fast rise in force, followed by a prolonged decay. The time course of the decay is however considerably more complex than previously thought, indicating the presence of several relaxation processes, with time constants ranging from 1 ms to at least 40 s. The mechanical properties of passive eye muscles are thus similar to those of many other biological passive tissues. Eye plant models, which for lack of data had to rely on (erroneous) assumptions, will have to be updated to incorporate these properties.

The Viscoelastic Properties of Passive Eye Muscle in Primates. III: Force Elicited by Natural Elongations

We have recently shown that in monkey passive extraocular muscles the force induced by a stretch does not depend on the entire length history, but to a great extent is only a function of the last elongation applied. This led us to conclude that Fungs quasi-linear viscoelastic (QLV) model, and more general nonlinear models based on a single convolution integral, cannot faithfully mimic passive eye muscles. Here we present additional data about the mechanical properties of passive eye muscles in deeply anesthetized monkeys. We show that, in addition to the aforementioned failures, previous models also grossly overestimate the force exerted by passive eye muscles during smooth elongations similar to those experienced during normal eye movements. Importantly, we also show that the force exerted by a muscle following an elongation is largely independent of the elongation itself, and it is mostly determined by the final muscle length. These additional findings conclusively rule out the use of classical viscoelastic models to mimic the mechanical properties of passive eye muscles. We describe here a new model that extends previous ones using principles derived from research on thixotropic materials. This model is able to account reasonably well for our data, and could thus be incorporated into models of the eye plant.

Ocular following in humans: Spatial properties

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.

Population coding in cortical area MST.

Abstract: 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 (<1 degree). Lesion data from monkeys suggest that these vergence responses are mediated, at least in part, by neurons in the medial superior temporal area of the cerebral cortex, and we here review a recent study of the associated single unit activity in that area. Few medial superior temporal neurons have disparity tuning curves whose shapes resemble the tuning curve for vergence. Yet, when the disparity tuning curves for all of the disparity‐sensitive cells recorded from a given monkey are summed together, they match the tuning curves for the vergence responses of that monkey very closely, even reproducing that animals idiosyncracies. When all of the spike trains elicited by a given disparity step are summed together to give an average discharge profile for the whole population of recorded cells, many are noisy, but others that are less so match the temporal profile of the motor response, vergence velocity, quite well. We conclude that the discharges of the disparity‐sensitive cells in the medial superior temporal area each represent only a very limited aspect of the sensory stimulus (and/or associated motor response?), but when pooled together, they provide a complete description of the vergence velocity motor response: population coding.

The viscoelastic properties of passive eye muscle in primates. II: testing the quasi-linear theory.

We have extensively investigated the mechanical properties of passive eye muscles, in vivo, in anesthetized and paralyzed monkeys. The complexity inherent in rheological measurements makes it desirable to present the results in terms of a mathematical model. Because Fungs quasi-linear viscoelastic (QLV) model has been particularly successful in capturing the viscoelastic properties of passive biological tissues, here we analyze this dataset within the framework of Fungs theory. We found that the basic properties assumed under the QLV theory (separability and superposition) are not typical of passive eye muscles. We show that some recent extensions of Fungs model can deal successfully with the lack of separability, but fail to reproduce the deviation from superposition. While appealing for their elegance, the QLV model and its descendants are not able to capture the complex mechanical properties of passive eye muscles. In particular, our measurements suggest that in a passive extraocular muscle the force does not depend on the entire length history, but to a great extent is only a function of the last elongation to which it has been subjected. It is currently unknown whether other passive biological tissues behave similarly.