J.A.M. Van Gisbergen

Collicular ensemble coding of saccades based on vector summation

The superior colliculus in the monkey contains a topographically organized representation of the target in its upper layers and saccade-related activity in its deeper layers. Since collicular movement fields are quite large, a considerable region of the colliculus is active whenever a saccade is made. We have modelled the collicular role in saccade generation based on the idea, proposed earlier in the literature, that each movement cell causes a movement tendency in the direction of the external world point which it represents in the collicular map. The model is organized as follows: An anisotropic logarithmic mapping transforms retinal coordinates into collicular coordinates. A two-dimensional Gaussian function describes the spatial extent of the movement-related activity in the deeper layers. An efferent mapping function specifies how the direction and the size of the movement contribution of each colliculus neuron depends on its location and its firing rate. The total saccade is the vector sum of the individual cell contributions. This very simple model (seven fixed parameters) has been used to simulate metrical properties of saccades: in response to visual targets; in response to electrical stimulation in one colliculus, and after a colliculus lesion. Model performance appears to be remarkably realistic but cannot account for some border effects and responses to double stimulation. Suggestions on how the model can be improved and extended will be presented.

A parametric analysis of human saccades in different experimental paradigms.

In this paper we report on human saccade dynamics in three different experimental paradigms: visual target, remembered target and anti-saccade task. We found that saccades to remembered targets and anti-saccades have strongly reduced peak velocities coupled with markedly increased durations. In addition we observed a considerable degree of asymmetry in the velocity profiles of these saccades. By using gamma functions to describe the shape of the velocity profiles a parameter characterizing the degree of asymmetry (skewness) was computed: it was found that skewness increases with saccade amplitude. Due to the large variability in saccade durations for any given amplitude in our data we could confirm the recent claim, based on pharmacologically induced slow saccades, that skewness is more tightly related to duration than to amplitude. The duration/skewness relationship appeared to be nearly invariant with saccade type. We conclude that the commonly used main-sequence description of saccades is incomplete and can be extended usefully by including skewness. The possible neural basis of the task-related differences in saccade properties and their implications for models of the saccadic system are discussed. It is suggested that the marked differences in dynamic properties among different saccade types may reflect processes in the visuomotor rather than in the motor system.

Coordination of fast eye and arm movements in a tracking task.

SummaryEye and arm movements to single and double-step target displacements were studied to investigate whether or not the motor systems of the eye and arm share common command signals from the internal representation, which specify a) when a movement is initiated and b) the end position of a movement. The correlation between the time of onset of eye and arm movements was significant for single-step and double-step target displacements into the same direction. However, it was small and not significant for double-step target displacements into opposite directions if the time interval between first and second target displacement was 75 or 100 ms. This indicates that the command signal which specifies when a movement is started is different for both systems. However, the reconstructed signal in the internal representation, which specifies the end position of movements, is rather similar for eye and arm movements which seems to point to a common command signal. This result was corroborated by experiments in which eye and arm were found to jump always to the same target in the condition that two different targets were presented simultaneously.

Scatter in the metrics of saccades and properties of the collicular motor map

Abstract Saccades, elicited by an identical visual stimulus in repeated trials, exhibit a certain amount of amplitude and direction scatter. The present paper illustrates how this scatter may be used to discern various properties of the subsystem that determines the metrics of a saccade. It is found in humans that scatter along the eccentricity axis is consistently more pronounced than along the direction axis. The ratio of amplitude scatter and direction scatter is approximately constant for all target positions tested. In addition, the absolute amount of scatter increases roughly linearly with target eccentricity but does not depend on target direction. We have explored whether these findings may reflect noisy variations in the neural representation of the saccade vector at the level of the collicular motor map. There are good reasons to assume that the motor map, at least in the monkey (1) is organized in polar coordinates (2) has a nonhomogeneous (roughly logarithmic) representation of saccade amplitude (3) is anisotropic in nature ( Robinson, 1972 ; Ottes, Van Gisbergen & Eggermont, 1986 ; Van Gisbergen, Van Opstal & Tax, 1987 ). To account for the intertrial variability in saccades, we have slightly extended an existing model for the collicular role in the coding of saccade metrics (Van Gisbergen et al., 1987) by allowing small variations in both the total amount and the location of the collicular population activity. We discuss how such noisy variations at the level of the motor map would be expressed in the metrics of saccadic responses and consider alternative models which could explain our data.

Skewness of saccadic velocity profiles: A unifying parameter for normal and slow saccades

It has become customary to make use of so-called main sequence plots to characterize the dynamic properties of saccades. However, such a description does not account for the fact that the ratio between the accelerating and the decelerating fraction of the eye movement is not constant for all saccades. In this paper we introduce a new parameter, skewness, that characterizes this much neglected aspect of the saccade velocity profile. Human saccade data in this report demonstrate a clear relation between saccade duration (D) and skewness (S). When saccadic eye movements become extremely slow, due to fatigue or diazepam, the main sequence relation breaks down, while the S-D relation still holds. Despite large differences in amplitude, saccades of a fixed duration appear to have the same shape of velocity profile. A unifying equation relating the saccade parameters amplitude, maximum velocity and skewness, which is valid for both normal and slow saccades, is proposed.

A short-latency transition in saccade dynamics during square-wave tracking and its significance for the differentiation of visually-guided and predictive saccades

SummarySeveral recent studies indicate that saccades elicited in the absence of a visual target are slower than visually-guided movements of the same size. In addition, we have shown earlier that the slower saccades observed in two different paradigms had more asymmetrical (skewed) velocity profiles. Recently, it has been reported that predictive saccades are also slower. An interesting question, which arises if predictive and visually-guided saccades do have different velocity profiles, is whether the time when the transition occurs can be determined from their dynamic characteristics (peak velocity and skewness) and whether this transition latency can serve as a plausible criterion for distinguishing predictive and visually-guided saccades. To investigate this problem, visually-guided and predictive saccades were elicited by various experimental paradigms in six normal human subjects. Eye movements were measured using the double-magnetic induction method. We found that scatter plots of normalized peak velocity against latency showed an abrupt, small (10–20%) increase at a surprisingly short latency (about 30–70 ms). Furthermore, skewness of the saccadic velocity profile showed a significant drop at comparable latencies. There was a tight correlation between the peak velocity and skewness transition latencies of each subject. Considering the shape of the latency histograms in this and earlier studies, as well as other data, it appears unlikely that these very short transition latencies demarcate the distinction between predictive and fully visually-guided saccades. Instead, we suggest the possibility that the visual stimulus can speed up saccades at an earlier time than it can initiate and guide them. If this is the case, the very short transition latencies (mean: about 50 ms) probably represent the sum of afferent and efferent pure time delays in the system and do not include the time needed for the computation of saccade metrical properties.

Experimental test of two models for the generation of oblique saccades

SummaryIn this paper, we report a detailed study of the dynamic properties of horizontal, vertical and oblique saccades. These eye movements were measured with an improved version of the double-magnetic induction method in two rhesus monkeys. We found that onsets of orthogonal components of oblique saccades are so well synchronized in the monkey that a common initiation system seems likely. Saccade vectors obeyed a nonlinear peakvelocity/amplitude relationship in all directions. The peak-velocity/duration/amplitude relationship for components was not fixed, but depended on the relative size of the orthogonal component: for a component with a given size, its duration increased and its peak velocity decreased, as the saccade vector to which it contributed turned away from the component direction under consideration. This stretching effect, which reflects a nonlinearity in the system, was negligible for small saccade vectors but became very pronounced in large oblique saccades. These experimental data were confronted with quantitative predictions derived from two different models for the generation of saccades in two dimensions. It appears that a model which assumes the existence of synchronized, but otherwise independent, pulse generators for horizontal and vertical components must be rejected. An alternative model, featuring a nonlinear vectorial pulse generator followed by a decomposition stage which generates component velocity command signals from the vectorial eye velocity signal, provides good fit with the data. According to this common-source model, the two nonlinear phenomena observed, viz., the curvilinear peak-velocity/amplitude relationship of saccades in all directions and component stretching in large oblique saccades, are due to a single nonlinearity in the proposed vectorial pulse generator. A possible neural basis for the common-source model is discussed.

Collicular involvement in a saccadic colour discrimination task

SummaryWe have recorded the neural activity of single superior colliculus (SC) neurons in monkeys engaged in a saccadic target/nontarget discrimination task based on a colour cue. Since correct execution of this task probably depends on cortical signal processing, our experiments are of interest for getting a better insight in the problem of how cortical and subcortical signals, relevant for the visual guidance of saccades, are combined. The experiments were designed to distinguish between two extreme possibilities: 1) The crucial cortical signal affects the saccadic system at or above the level of the SC movement-related cells (serial hypothesis); 2) The colour-based target information bypasses the motor colliculus and affects the saccadic system at a level more downstream (bypass hypothesis). Under conditions where the saccadic system had to select a green target stimulus and to ignore the red nontarget spot, the saccade-related activity in SC visuomotor neurons remained as tightly coupled to the metrics of the saccade as it was in a simple spot-detection task. Since the saccade-related activity of these cells appeared to be based on colour information, we conclude that our data corroborate the serial hypothesis. The initial activity after stimulus onset appeared to be colour nonopponent in all neurons. In some cells the neural activity was quantitatively slightly different for the green target and the red nontarget. Since these minor differences were colour rather than motor response dependent, they were probably not part of the target-selection process. These data suggest the possibility that the decision as to which saccade should be made was largely imposed upon the SC visuomotor cells by an external source. We discuss various possibilities for the origin of the putative intervening signal which orders a saccade by causing a burst in the appropriate SC visuomotor neurons.

Role of monkey superior colliculus in saccade averaging.

SummaryWe have investigated the involvement of collicular movement cells in the monkey in the execution of averaging saccades, elicited by a visual double-step stimulus. We found that, qualitatively, most (12/14) movement cells were recruited during averaging saccades in roughly the same way as for comparable visually-elicited saccades to single targets (V-saccades). However, movement-cell responses during averaging saccades in trials where the target suddenly changed direction were often less intense than for a comparable V-saccade. In these cases, the averaging responses were observed to be also slower than V-saccades of the same amplitude. Firing rate and double-step saccade dynamics were found to be significantly correlated in 9/14 cells tested. Several hypotheses for the collicular role in the generation of averaging saccades are discussed.

Comparison of saccades evoked by visual stimulation and collicular electrical stimulation in the alert monkey

SummaryIn the alert monkey we have compared the properties of saccades elicited by a visual stimulus (V-saccades) with those generated by electrical stimulation in the superior colliculus (E-saccades). We found that whereas there exists a graded relation betweenE-saccade amplitude and current strength,E-saccade direction is remarkably independent of electrical stimulation parameters. At sufficiently high current strengths (about 20 μA),E-saccades are consistently directed toward the center of the movement field of nearby cells, except when stimulation is performed at sites near the collicular borders. Further interesting differences between the amplitude and direction behaviour were observed when the variability inE-saccade vectors, obtained with fixed stimulation parameters, was analyzed. In all cases,E-saccade amplitude scatter exceeds direction scatter, suggesting the possibility of a polar coordinate organization for the coding of saccade metrics. These data are compared withV-saccade scatter data, recently obtained in the human (Van Opstal and Van Gisbergen 1989 c). Finally, an analysis of saccade dynamics shows thatE-saccades can reachV-saccadic velocities at higher current strengths. However, at near-threshold current strengths, whereE-saccade amplitude decreases (see above), we found at most stimulation sites (22/37) thatE-saccades are consistently slower thanV-saccades of the same amplitude. Possible mechanisms underlying the collicular role in saccade generation are discussed.