The Significance of Listing’s Law on the Design of Spectacle Lenses

Author(s):  
Frederic Seve ◽  
Rainer G. Dorsch ◽  
Helmut Altheimer ◽  
Peter Baumbach
1992 ◽  
pp. 307-319 ◽  
Author(s):  
K. Hepp ◽  
T. Haslwanter ◽  
D. Straumann ◽  
M.-C. Hepp-Reymond ◽  
V. Henn

1997 ◽  
Vol 77 (2) ◽  
pp. 654-666 ◽  
Author(s):  
Douglas Tweed

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.


2001 ◽  
Vol 86 (4) ◽  
pp. 1877-1883 ◽  
Author(s):  
H. Misslisch ◽  
D. Tweed

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.


1998 ◽  
Vol 80 (5) ◽  
pp. 2274-2294 ◽  
Author(s):  
Eliana M. Klier ◽  
J. Douglas Crawford

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.


2013 ◽  
Vol 109 (1) ◽  
pp. 183-192 ◽  
Author(s):  
Bernhard J. M. Hess

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.


Strabismus ◽  
2000 ◽  
Vol 8 (1) ◽  
pp. 29-32
Author(s):  
K.H. Wassill ◽  
Thomas Kowarsch

1993 ◽  
Vol 33 (5-6) ◽  
pp. 691-708 ◽  
Author(s):  
L.J. Van Run ◽  
A.V. Van Den Berg

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