A model of the oculomotor system addressing both simple and competing target saccades that can reproduce straight-line and curved saccade trajectories. Highly curved saccades are supported with additional hypothetical (not observed neurologically) parallel inputs to saccade burst generators.
Visual input (float array 20x20) - Magnitude of the float at integer-coordinate vertices specifies the saliency of activity at that location
Horizontal SBG Signal (float) - Optional excitatory input to horizontal SBG. Exclusion uses the SC-only version of the model. Inclusion uses the full model.
Vertical SBG Signal (float) - Optional excitatory input to vertical SBG. Exclusion uses the SC-only version of the model. Inclusion uses the full model.
SNr Disinhibition (float array 20x20) - Gaussian-shaped disinhibition of localized regions of the visual field corresponding to saccade targets
Horizontal Eye Position (integer) - Index of the horizontal eye position in the fixed visual field
Vertical Eye Position (integer) - Index of the vertical eye position in the fixed visual field
Synaptic Weights (float) - The weights of the various synapses that are involved in merging SC output with parallel signals during saccade generation, and also those synapses involved in the saccade feedback to the SC.
Figure 1: Saccadic system model for multiple competing visual inputs
The black arrows from the SC model saccade control path supplemented by additional parallel (red outline) inputs to the brainstem SBGs. The SC is a network of units with local excitatory and short-range lateral inhibitory connections. Inputs and outputs from SC are distributed (ribbon arrows). Spatially separated visual inputs excite multiple loci of SC activity. Spatially tuned disinhibition from the SNr interacts with visually activated loci on the SC to generate weighted input to the SBGs. In the model, the SBGs generate vertical and horizontal components of eye movements and include NIs for feedforward connections to the eye plants. Inhibitory eye-displacement signals from resettable NIs (not shown) and eye-velocity feedback to the SC from the SBGs reduce collicular output during saccades
Figure 2: Topologically organized inhibitory input to the SC motor map from the SNr during ﬁxation
The visual ﬁeld is represented by the 20 × 20 unit SC network. The upper ﬂat grid (A) indicates that during ﬁxation each unit in the SC grid receives global and constant inhibition from a distributed SNr input. The Gaussian-shaped bowl (B) indicates that a broadly distributed portion of the SC grid receives a much lower level of inhibition during a saccade. Distributed visual inputs that are located near the center of this bowl are greatly facilitated in comparison with those that appear closer to the edges of the bowl. In the example shown here, the maximum SNr disinhibition (the bottom of the bowl) is located at 10 degrees horizontal and vertical.
Figure 3: Example Model Saccade Activity
Distributed activity in the optimized SC portion of the model for a (20, 45) degree saccade direction up and to the right. Figure A shows the eye movement trajectory for the saccade. Location of the single target in the visual ﬁeld is shown by the red asterisk. Initial ﬁxation location is shown by the small cross. Figure B shows distributed activity in the SC network. Activity at saccade onset is shown at the left and at saccade end at the right. Figure C shows the summed, weighted input from the SC to the horizontal and vertical SBGs. Figure D shows component horizontal and vertical eye velocities produced by the model during the 20 degree saccade (solid curves) compared to average component eye velocities for the same saccade from a single monkey.
Figure 4: Distributed activity in the model SC for a simulated averaging saccade
Figure A shows saccade trajectory. Two visual stimuli (green asterisks) are input at 20 degrees in amplitude and ± 45 degrees in direction. The centers of the basins of disinhibition from the SNr are shown by the green annuli. Because neither stimulus has been selected as the target, the depth of disinhibition is the same at both visual stimulus locations (α = β = 0.5). Inhibition color coded using the color scale from the previous figure. Figure C shows instantaneous direction of the saccade. Figure D shows activity on the model SC map at saccade onset.
Figure 5: Model behavior after decreasing feedforward and feedback weights to match realistic hypermetricity
Figure A shows a spatial plot of a saccade to a single target generated by the colliculus-only model with the reduced feed-forward and feedback weights (left panel) and one produced by the full model including the parallel inputs (right panel). The target (red asterisk) is located at 20 degrees in amplitude and 45 degrees up and to the right in direction. Figure B shows the horizontal and vertical components of the change in eye position during the hypermetric saccade (blue curves), the horizontal and vertical target positions (dashed horizontal lines), and the summed, weighted output from the SC to the horizontal and vertical SBGs (red curves) for the colliculus-only model. Figure C shows the eye-velocity components produced by the colliculus-only model during the hypermetric saccade (solid curves) and those produced by the original full model (dashed curves). Figure D shows the computed horizontal and vertical parallel signals. Figure E shows the horizontal and vertical components of a saccade produced by the full model with parallel signals from Figure D. Figure F shows eye-velocity components produced by full model (solid curves) and those produced by original full model (dashed curves).
Submodules (click to view and edit)
Saccade Burst Generator - Two saccade burst generators (horizontal and vertical control) receive an input target from the SC and generate saccades to the target. This model uses a modified version of the SBG that allows parallel inputs to control the target location. This model comes directly from:
Dean P (1995) Modelling the role of the cerebellar fastigial nuclei in producing accurate saccades: the importance of burst timing. Neuroscience 68:1059–1077
Variable saccade trajectories are produced in visual search paradigms in which multiple potential target stimuli are present. These variable trajectories provide a rich source of information that may lead to a deeper understanding of the basic control mechanisms of the saccadic system. This model uses published behavioral observations and neural recordings in the superior colliculus (SC), gathered in monkeys performing visual search paradigms, to guide the construction of a new distributed model of the saccadic system. The new model can account for many of the variations in saccade trajectory produced by the appearance of multiple visual stimuli in a search paradigm. The model uses distributed feedback about current eye motion from the brainstem to the SC to reduce activity there at physiologically realistic rates during saccades. The long-range lateral inhibitory connections between SC cells used in previous models have been eliminated to match recent physiological evidence. The model features interactions between visually activated multiple populations of cells in the SC and distributed and topologically organized inhibitory input to the SC from the SNr to produce some of the types of variable saccadic trajectories, including slightly curved and averaging saccades, observed in visual search tasks. The distributed perisaccadic disinhibition of SC from the SNr is assumed to have broad spatial tuning. In order to produce the strongly curved saccades occasionally recorded in visual search, the existence of a parallel input to the saccadic burst generators in addition to that provided by the distributed input from the SC is required. The spatiotemporal form of this additional parallel input is computed based on the assumption that the input from the model SC is realistic. In accordance with other recent models, it is assumed that the parallel input comes from the cerebellum, but the model predicts that the parallel input is delayed during highly curved saccadic trajectories.