Three-Dimensional Kinematics of Ocular Drift in Humans With Cerebellar Atrophy

2000 ◽  
Vol 83 (3) ◽  
pp. 1125-1140 ◽  
Author(s):  
D. Straumann ◽  
D. S. Zee ◽  
D. Solomon
Keyword(s):  
Vertical Velocity ◽  
Three Dimensional ◽  
Cerebellar Atrophy ◽  
Eye Position ◽  
Downbeat Nystagmus ◽  
Ocular Motor ◽  
Listing's Law ◽  
Listing’S Law ◽  
Horizontal Gaze ◽  
Velocity Bias

One of the signs of the cerebellar ocular motor syndrome is the inability to maintain horizontal and vertical fixation. Typically, in the presence of cerebellar atrophy, the eyes show horizontal gaze-evoked and vertical downbeat nystagmus. We investigated whether or not the cerebellar ocular motor syndrome also includes a torsional drift and, specifically, if it is independent from the drift in the horizontal-vertical plane. The existence of such a torsional drift would suggest that the cerebellum is critically involved in maintaining the eyes in Listing's plane. Eighteen patients with cerebellar atrophy (diagnosis confirmed by magnetic resonance imaging) were tested and compared with a group of normal subjects. Three-dimensional eye movements (horizontal, vertical, and torsional) during attempted fixations of targets at different horizontal and vertical eccentricities were recorded by dual search coils in a three-field magnetic frame. The overall ocular drift was composed of an upward drift that increased during lateral gaze, a horizontal centripetal drift that appeared during lateral gaze, and a torsional drift that depended on horizontal eye position. The vertical drift consisted of two subcomponents: a vertical gaze-evoked drift and a constant vertical velocity bias. The increase of upward drift velocity with eccentric horizontal gaze was caused by an increase of the vertical velocity bias; this component did not comply with Listing's law. The horizontal-eye-position–dependent torsional drift was intorsional in abduction and extorsional in adduction, which led to an additional violation of Listing's law. The existence of torsional drift that is eye-position–dependent suggests that the cerebellum is critically involved in the implementation of Listing's law, perhaps by mapping a tonic torsional signal that depends on the direction of the line of sight. The magnitude of this signal might reflect the difference in torsional eye position between the torsional resting position determined by the mechanics of the eye plant and the torsional position required by Listing's law.

Three-dimensional visuo-motor control of saccades

2013 ◽  
Vol 109 (1) ◽  
pp. 183-192 ◽  
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.

Three-Dimensional Vestibuloocular Reflex of the Monkey: Optimal Retinal Image Stabilization Versus Listing's Law

2000 ◽  
Vol 83 (6) ◽  
pp. 3264-3276 ◽  
Author(s):  
Hubert Misslisch ◽  
Bernhard J. M. Hess
Keyword(s):  
Retinal Image ◽  
Three Dimensional ◽  
Oculomotor Control ◽  
Slow Phase ◽  
Eye Position ◽  
Vestibuloocular Reflex ◽  
Image Stabilization ◽  
Listing's Law ◽  
Listing’S Law ◽  
Visual Background

If the rotational vestibuloocular reflex (VOR) were to achieve optimal retinal image stabilization during head rotations in three-dimensional space, it must turn the eye around the same axis as the head, with equal velocity but in the opposite direction. This optimal VOR strategy implies that the position of the eye in the orbit must not affect the VOR. However, if the VOR were to follow Listing's law, then the slow-phase eye rotation axis should tilt as a function of current eye position. We trained animals to fixate visual targets placed straight ahead or 20° up, down, left or right while being oscillated in yaw, pitch, and roll at 0.5–4 Hz, either with or without a full-field visual background. Our main result was that the visually assisted VOR of normal monkeys invariantly rotated the eye around the same axis as the head during yaw, pitch, and roll (optimal VOR). In the absence of a visual background, eccentric eye positions evoked small axis tilts of slow phases in normal animals. Under the same visual condition, a prominent effect of eye position was found during roll but not during pitch or yaw in animals with low torsional and vertical gains following plugging of the vertical semicircular canals. This result was in accordance with a model incorporating a specific compromise between an optimal VOR and a VOR that perfectly obeys Listing's law. We conclude that the visually assisted VOR of the normal monkey optimally stabilizes foveal as well as peripheral retinal images. The finding of optimal VOR performance challenges a dominant role of plant mechanics and supports the notion of noncommutative operations in the oculomotor control system.

Implications of rotational kinematics for the oculomotor system in three dimensions

1987 ◽  
Vol 58 (4) ◽  
pp. 832-849 ◽  
Author(s):  
D. Tweed ◽  
T. Vilis
Keyword(s):  
Three Dimensional ◽  
Oculomotor System ◽  
Three Dimensions ◽  
Eye Position ◽  
Head Velocity ◽  
Listing’S Law ◽  
Indirect Path ◽  
Dimensional Models ◽  
Three Dimensional Models ◽  
Eye Velocity

1. This paper develops three-dimensional models for the vestibuloocular reflex (VOR) and the internal feedback loop of the saccadic system. The models differ qualitatively from previous, one-dimensional versions, because the commutative algebra used in previous models does not apply to the three-dimensional rotations of the eye. 2. The hypothesis that eye position signals are generated by an eye velocity integrator in the indirect path of the VOR must be rejected because in three dimensions the integral of angular velocity does not specify angular position. Computer simulations using eye velocity integrators show large, cumulative gaze errors and post-VOR drift. We describe a simple velocity to position transformation that works in three dimensions. 3. In the feedback control of saccades, eye position error is not the vector difference between actual and desired eye positions. Subtractive feedback models must continuously adjust the axis of rotation throughout a saccade, and they generate meandering, dysmetric gaze saccades. We describe a multiplicative feedback system that solves these problems and generates fixed-axis saccades that accord with Listing's law. 4. We show that Listing's law requires that most saccades have their axes out of Listing's plane. A corollary is that if three pools of short-lead burst neurons code the eye velocity command during saccades, the three pools are not yoked, but function independently during visually triggered saccades. 5. In our three-dimensional models, we represent eye position using four-component rotational operators called quaternions. This is not the only algebraic system for describing rotations, but it is the one that best fits the needs of the oculomotor system, and it yields much simpler models than do rotation matrix or other representations. 6. Quaternion models predict that eye position is represented on four channels in the oculomotor system: three for the vector components of eye position and one inversely related to gaze eccentricity and torsion. 7. Many testable predictions made by quaternion models also turn up in models based on other mathematics. These predictions are therefore more fundamental than the specific models that generate them. Among these predictions are 1) to compute eye position in the indirect path of the VOR, eye or head velocity signals are multiplied by eye position feedback and then integrated; consequently 2) eye position signals and eye or head velocity signals converge on vestibular neurons, and their interaction is multiplicative.(ABSTRACT TRUNCATED AT 400 WORDS)

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

1997 ◽  
Vol 77 (2) ◽  
pp. 654-666 ◽  
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.

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

1998 ◽  
Vol 80 (5) ◽  
pp. 2274-2294 ◽  
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.

scholarly journals Three-Dimensional Eye-Head Coordination Is Implemented Downstream From the Superior Colliculus

2003 ◽  
Vol 89 (5) ◽  
pp. 2839-2853 ◽  
Author(s):  
Eliana M. Klier ◽  
Hongying Wang ◽  
J. Douglas Crawford
Keyword(s):  
Superior Colliculus ◽  
Three Dimensional ◽  
Slow Phase ◽  
Neural Basis ◽  
Gaze Shift ◽  
The Gaze ◽  
Listing's Law ◽  
Listing’S Law ◽  
Normal Behavior ◽  
The Brain

How the brain transforms two-dimensional visual signals into multi-dimensional motor commands, and subsequently how it constrains the redundant degrees of freedom, are fundamental problems in sensorimotor control. During fixations between gaze shifts, the redundant torsional degree of freedom is determined by various neural constraints. For example, the eye- and head-in-space are constrained by Donders' law, whereas the eye-in-head obeys Listing's law. However, where and how the brain implements these laws is not yet known. In this study, we show that eye and head movements, elicited by unilateral microstimulations of the superior colliculus (SC) in head-free monkeys, obey the same Donders' strategies observed in normal behavior (i.e., Listing's law for final eye positions and the Fick strategy for the head). Moreover, these evoked movements showed a pattern of three-dimensional eye-head coordination, consistent with normal behavior, where the eye is driven purposely out of Listing's plane during the saccade portion of the gaze shift in opposition to a subsequent torsional vestibuloocular reflex slow phase, such that the final net torsion at the end of each head-free gaze shift is zero. The required amount of saccade-related torsion was highly variable, depending on the initial position of the eye and head prior to a gaze shift and the size of the gaze shift, pointing to a neural basis of torsional control. Because these variable, context-appropriate torsional saccades were correctly elicited by fixed SC commands during head-free stimulations, this shows that the SC only encodes the horizontal and vertical components of gaze, leaving the complexity of torsional organization to downstream control systems. Thus we conclude that Listing's and Donders' laws of the eyes and head, and their three-dimensional coordination mechanisms, must be implemented after the SC.

scholarly journals Chameleon eye position obeys Listing's law

2001 ◽  
Vol 41 (17) ◽  
pp. 2245-2251 ◽  
Author(s):  
Peter S Sándor ◽  
Maarten A Frens ◽  
Volker Henn
Keyword(s):  
Eye Position ◽  
Listing's Law ◽  
Listing’S Law

scholarly journals V1 neurons encode the perceptual compensation of “false torsion” arising from Listing’s law

2018 ◽  
Author(s):  
Mohammad Farhan Khazali ◽  
Peter Thier
Keyword(s):  
Eye Movements ◽  
Visual System ◽  
Eye Position ◽  
V1 Neurons ◽  
Listing's Law ◽  
Listing’S Law ◽  
Torsional Component

AbstractWe try to deploy the retinal fovea to optimally scrutinize an object of interest by directing our eyes to it. Horizontal and vertical components of these fixation eye movements are determined by the object’s location. However, fixation eye movements also involve a torsional component, which according to Listing’s law is fully determined by the 2D eye position acquired. According to Von Helmholtz knowledge of the torsion provided by this law alleviates the perceptual interpretation of the image tilt that changes with fixation, a view supported by psychophysical experiments he pioneered. We address the question where and how Listing’s law is implemented in the visual system and we show that neurons in monkey area V1 use knowledge of torsion to compensate the image tilt associated with specific eye positions as set by Listing’s law.

scholarly journals Kinematic Strategies for Upper Arm–Forearm Coordination in Three Dimensions

2000 ◽  
Vol 84 (5) ◽  
pp. 2302-2316 ◽  
Author(s):  
W. P. Medendorp ◽  
J. D. Crawford ◽  
D.Y.P. Henriques ◽  
J.A.M. Van Gisbergen ◽  
C.C.A.M. Gielen
Keyword(s):  
Three Dimensional ◽  
Vertical Plane ◽  
Elbow Flexion ◽  
Three Dimensions ◽  
Upper Arm ◽  
Elbow Angle ◽  
Listing's Law ◽  
Listing’S Law ◽  
Governing Principle ◽  
The Cost

This study addressed the question of how the three-dimensional (3-D) control strategy for the upper arm depends on what the forearm is doing. Subjects were instructed to point a laser—attached in line with the upper arm—toward various visual targets, such that two-dimensional (2-D) pointing directions of the upper arm were held constant across different tasks. For each such task, subjects maintained one of several static upper arm–forearm configurations, i.e., each with a set elbow angle and forearm orientation. Upper arm, forearm, and eye orientations were measured with the use of 3-D search coils. The results confirmed that Donders' law (a behavioral restriction of 3-D orientation vectors to a 2-D “surface”) does not hold across all pointing tasks, i.e., for a given pointing target, upper arm torsion varied widely. However, for any one static elbow configuration, torsional variance was considerably reduced and was independent of previous arm position, resulting in a thin, Donders-like surface of orientation vectors. More importantly, the shape of this surface (which describes upper arm torsion as a function of its 2-D pointing direction) depended on both elbow angle and forearm orientation. For pointing with the arm fully extended or with the elbow flexed in the horizontal plane, a Listing's-law-like strategy was observed, minimizing shoulder rotations to and from center at the cost of position-dependent tilts in the forearm. In contrast, when the arm was bent in the vertical plane, the surface of best fit showed a Fick-like twist that increased continuously as a function of static elbow flexion, thereby reducing position-dependent tilts of the forearm with respect to gravity. In each case, the torsional variance from these surfaces remained constant, suggesting that Donders' law was obeyed equally well for each task condition. Further experiments established that these kinematic rules were independent of gaze direction and eye orientation, suggesting that Donders' law of the arm does not coordinate with Listing's law for the eye. These results revive the idea that Donders' law is an important governing principle for the control of arm movements but also suggest that its various forms may only be limited manifestations of a more general set of context-dependent kinematic rules. We propose that these rules are implemented by neural velocity commands arising as a function of initial arm orientation and desired pointing direction, calculated such that the torsional orientation of the upper arm is implicitly coordinated with desired forearm posture.

scholarly journals Revealing the Kinematics of the Oculomotor Plant With Tertiary Eye Positions and Ocular Counterroll

2011 ◽  
Vol 105 (2) ◽  
pp. 640-649 ◽  
Author(s):  
Eliana M. Klier ◽  
Hui Meng ◽  
Dora E. Angelaki
Keyword(s):  
Eye Movements ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Abducens Nerve ◽  
Oculomotor System ◽  
Primary Position ◽  
Listing's Law ◽  
Listing’S Law ◽  
Ocular Counterroll ◽  
Half Angle

Retinal information is two-dimensional, whereas eye movements are three-dimensional. The oculomotor system solves this degrees-of-freedom problem by constraining eye positions to zero torsion (Listing's law) and determining how eye velocities change with eye position (half-angle rule). Here we test whether the oculomotor plant, in the absence of well-defined neural commands, can implement these constrains mechanically, not just in a primary position but for all eye and head orientations. We stimulated the abducens nerve at tertiary eye positions and when ocular counterroll was induced at tilted head orientations. Stimulation-induced eye velocities follow the half-angle rule, even for tertiary eye positions, and microstimulation at tilted head orientations elicits eye positions that adhere to torsionally shifted planes, similar to naturally occurring eye movements. These results support the notion that oculomotor plant can continuously apply these three-dimensional rules correctly and appropriately for all eye and head orientations that obey Listing's law, demonstrating a major role of peripheral biomechanics in motor control.

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