The role of torsional viscosity in saccadic listing's law

J. Porrill; P. A. Warren; P. Dean

doi:10.1167/3.9.430

Modeling Control of Eye Orientation in Three Dimensions. I. Role of Muscle Pulleys in Determining Saccadic Trajectory

Journal of Neurophysiology ◽

10.1152/jn.1998.79.5.2653 ◽

1998 ◽

Vol 79 (5) ◽

pp. 2653-2667 ◽

Cited By ~ 110

Author(s):

Theodore Raphan

Keyword(s):

Three Dimensions ◽

Muscle Torque ◽

Listing's Law ◽

Listing’S Law ◽

Eye Rotation ◽

Simple Implementation ◽

Kinematic Transformations ◽

Reported Data ◽

Integrator Model

Raphan, Theodore. Modeling control of eye orientation in three dimensions. I. Role of muscle pulleys in determining saccadic trajectory. J. Neurophysiol. 79: 2653–2667, 1998. This study evaluates the effects of muscle axis shifts on the performance of a vector velocity-position integrator in the CNS. Earlier models of the oculomotor plant assumed that the muscle axes remained fixed relative to the head as the eye rotated into secondary and tertiary eye positions. Under this assumption, the vector integrator model generates torsional transients as the eye moves from secondary to tertiary positions of fixation. The torsional transient represents an eye movement response to a spatial mismatch between the torque axes that remain fixed in the head and the displacement plane that changes by half the angle of the change in eye orientation. When muscle axis shifts were incorporated into the model, the torque axes were closer to the displacement plane at each eye orientation throughout the trajectory, and torsional transients were reduced dramatically. Their size and dynamics were close to reported data. It was also shown that when the muscle torque axes were rotated by 50% of the eye rotation, there was no torsional transient and Listing's law was perfectly obeyed. When muscle torque axes rotated >50%, torsional transients reversed direction compared with what occurred for muscle axis shifts of <50%. The model indicates that Listing's law is implemented by the oculomotor plant subject to a two-dimensional command signal that is confined to the pitch-yaw plane, having zero torsion. Saccades that bring the eye to orientations outside Listing's plane could easily be corrected by a roll pulse that resets the roll state of the velocity-position integrator to zero. This would be a simple implementation of the corrective controller suggested by Van Opstal and colleagues. The model further indicates that muscle axis shifts together with the torque orientation relationship for tissue surrounding the eye and Newton's laws of motion form a sufficient plant model to explain saccadic trajectories and periods of fixation when driven by a vector command confined to the pitch-yaw plane. This implies that the velocity-position integrator is probably realized as a subtractive feedback vector integrator and not as a quaternion-based integrator that implements kinematic transformations to orient the eye.

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The Control of Arm-, Gaze-, and Head-Movements by Listing’s Law

Control of Arm Movement in Space ◽

10.1007/978-3-642-77235-1_16 ◽

1992 ◽

pp. 307-319 ◽

Cited By ~ 2

Author(s):

K. Hepp ◽

T. Haslwanter ◽

D. Straumann ◽

M.-C. Hepp-Reymond ◽

V. Henn

Keyword(s):

Head Movements ◽

Listing's Law ◽

Listing’S Law

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Listing's Law

Wolfram Demonstrations Project ◽

10.3840/002339 ◽

2007 ◽

Keyword(s):

Listing's Law ◽

Listing’S Law

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Three-Dimensional Model of the Human Eye-Head Saccadic System

Journal of Neurophysiology ◽

10.1152/jn.1997.77.2.654 ◽

1997 ◽

Vol 77 (2) ◽

pp. 654-666 ◽

Cited By ~ 52

Author(s):

Douglas Tweed

Keyword(s):

Three Dimensional ◽

Head Movements ◽

Dimensional Model ◽

Three Dimensional Model ◽

Gaze Shifts ◽

One Dimensional ◽

Human Eye ◽

Saccadic System ◽

Listing's Law ◽

Listing’S Law

Tweed, Douglas. Three-dimensional model of the human eye-head saccadic system. J. Neurophysiol. 77: 654–666, 1997. Current theories of eye-head gaze shifts deal only with one-dimensional motion, and do not touch on three-dimensional (3-D) issues such as curvature and Donders' laws. I show that recent 3-D data can be explained by a model based on ideas that are well established from one-dimensional studies, with just one new assumption: that the eye is driven toward a 3-D orientation in space that has been chosen so that Listing's law of the eye in head will hold when the eye-head movement is complete. As in previous, one-dimensional models, the eye and head are feedback-guided and the commands specifying desired eye position eye pass through a neural “saturation” so as to stay within the effective oculomotor range. The model correctly predicts the complex, 3-D trajectories of the head, eye in space, and eye in head in a variety of saccade tasks. And when it moves repeatedly to the same target, varying the contributions of eye and head, the model lands in different eye-in-space positions, but these positions differ only in their cyclotorsion about the line of sight, so they all point that line at the target—a behavior also seen in real eye-head saccades. Between movements the model obeys Listing's law of the eye in head and Donders' law of the head on torso, but during certain gaze shifts involving large torsional head movements, it shows marked, 8° deviations from Listing's law. These deviations are the most important untested predictions of the theory. Their experimental refutation would sink the model, whereas confirmation would strongly support its central claim that the eye moves toward a 3-D position in space chosen to obey Listing's law and, therefore, that a Listing operator exists upstream from the eye pulse generator.

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Neural and Mechanical Factors in Eye Control

Journal of Neurophysiology ◽

10.1152/jn.2001.86.4.1877 ◽

2001 ◽

Vol 86 (4) ◽

pp. 1877-1883 ◽

Cited By ~ 28

Author(s):

H. Misslisch ◽

D. Tweed

Keyword(s):

Soft Tissue ◽

Single Mode ◽

Vestibuloocular Reflex ◽

Neural Processing ◽

Ocular Torsion ◽

Eye Muscles ◽

Kinematic Pattern ◽

Listing's Law ◽

Listing’S Law ◽

Mechanical Factors

Soft tissue “pulleys” in the orbit alter the paths of the eye muscles in a way that may simplify the brain's work in implementing Listing's law, i.e., in holding ocular torsion at zero. But Listing's law does not apply to some oculomotor systems, such as the vestibuloocular reflex (VOR), which shows a different kinematic pattern. To explain this different pattern, some authors have assumed that the pulleys must adopt a different configuration, retracting along their muscles when the eye switches from Listing's law to VOR mode. The proposed retraction has not so far been observed, although the pulleys do move in other ways. We show that the hypothetical retraction of the pulleys would not in fact explain the full kinematic pattern seen in the VOR. But this pattern can be explained entirely on the basis of pulley positions and motions that have actually been observed. If one takes into account the neural processing within the VOR, specifically the fact that the reflex is weak in the torsional dimension, then a single mode of pulley action can serve both vestibuloocular kinematics and Listing's law.

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Human Oculomotor System Accounts for 3-D Eye Orientation in the Visual-Motor Transformation for Saccades

Journal of Neurophysiology ◽

10.1152/jn.1998.80.5.2274 ◽

1998 ◽

Vol 80 (5) ◽

pp. 2274-2294 ◽

Cited By ~ 45

Author(s):

Eliana M. Klier ◽

J. Douglas Crawford

Keyword(s):

Reference Frame ◽

Oculomotor System ◽

Gaze Direction ◽

Eye Position ◽

Look Up Table ◽

Listing's Law ◽

Listing’S Law ◽

Reference Frame Transformation ◽

Visual Motor ◽

Frame Transformation

Klier, Eliana M. and J. Douglas Crawford. Human oculomotor system accounts for 3-D eye orientation in the visual-motor transformation for saccades. J. Neurophysiol. 80: 2274–2294, 1998. A recent theoretical investigation has demonstrated that three-dimensional (3-D) eye position dependencies in the geometry of retinal stimulation must be accounted for neurally (i.e., in a visuomotor reference frame transformation) if saccades are to be both accurate and obey Listing's law from all initial eye positions. Our goal was to determine whether the human saccade generator correctly implements this eye-to-head reference frame transformation (RFT), or if it approximates this function with a visuomotor look-up table (LT). Six head-fixed subjects participated in three experiments in complete darkness. We recorded 60° horizontal saccades between five parallel pairs of lights, over a vertical range of ±40° ( experiment 1), and 30° radial saccades from a central target, with the head upright or tilted 45° clockwise/counterclockwise to induce torsional ocular counterroll, under both binocular and monocular viewing conditions ( experiments 2 and 3). 3-D eye orientation and oculocentric target direction (i.e., retinal error) were computed from search coil signals in the right eye. Experiment 1: as predicted, retinal error was a nontrivial function of both target displacement in space and 3-D eye orientation (e.g., horizontally displaced targets could induce horizontal or oblique retinal errors, depending on eye position). These data were input to a 3-D visuomotor LT model, which implemented Listing's law, but predicted position-dependent errors in final gaze direction of up to 19.8°. Actual saccades obeyed Listing's law but did not show the predicted pattern of inaccuracies in final gaze direction, i.e., the slope of actual error, as a function of predicted error, was only −0.01 ± 0.14 (compared with 0 for RFT model and 1.0 for LT model), suggesting near-perfect compensation for eye position. Experiments 2 and 3: actual directional errors from initial torsional eye positions were only a fraction of those predicted by the LT model (e.g., 32% for clockwise and 33% for counterclockwise counterroll during binocular viewing). Furthermore, any residual errors were immediately reduced when visual feedback was provided during saccades. Thus, other than sporadic miscalibrations for torsion, saccades were accurate from all 3-D eye positions. We conclude that 1) the hypothesis of a visuomotor look-up table for saccades fails to account even for saccades made directly toward visual targets, but rather, 2) the oculomotor system takes 3-D eye orientation into account in a visuomotor reference frame transformation. This transformation is probably implemented physiologically between retinotopically organized saccade centers (in cortex and superior colliculus) and the brain stem burst generator.

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Three-dimensional visuo-motor control of saccades

Journal of Neurophysiology ◽

10.1152/jn.00513.2012 ◽

2013 ◽

Vol 109 (1) ◽

pp. 183-192 ◽

Cited By ~ 5

Author(s):

Bernhard J. M. Hess

Keyword(s):

Motor Control ◽

Reverse Engineering ◽

Visual Information ◽

Three Dimensional ◽

Engineering Problem ◽

Line Of Sight ◽

Eye Position ◽

Listing's Law ◽

Saccade Onset ◽

Listing’S Law

Although the motion of the line of sight is a straightforward consequence of a particular rotation of the eye, it is much trickier to predict the rotation underlying a particular motion of the line of sight in accordance with Listing's law. Helmholtz's notion of the direction-circle together with the notion of primary and secondary reference directions in visual space provide an elegant solution to this reverse engineering problem, which the brain is faced with whenever generating a saccade. To test whether these notions indeed apply for saccades, we analyzed three-dimensional eye movements recorded in four rhesus monkeys. We found that on average saccade trajectories closely matched with the associated direction-circles. Torsional, vertical, and horizontal eye position of saccades scattered around the position predicted by the associated direction-circles with standard deviations of 0.5°, 0.3°, and 0.4°, respectively. Comparison of saccade trajectories with the likewise predicted fixed-axis rotations yielded mean coefficients of determinations (±SD) of 0.72 (±0.26) for torsion, 0.97 (±0.10) for vertical, and 0.96 (±0.11) for horizontal eye position. Reverse engineering of three-dimensional saccadic rotations based on visual information suggests that motor control of saccades, compatible with Listing's law, not only uses information on the fixation directions at saccade onset and offset but also relies on the computation of secondary reference positions that vary from saccade to saccade.

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