Listing's Law Research Articles

Commutative saccadic generator is sufficient to control a 3-D ocular plant with pulleys.

One-dimensional models of oculomotor control rely on the fact that, when rotations around only one axis are considered, angular velocity is the derivative of orientation. However, when rotations around arbitrary axes [3-dimensional (3-D) rotations] are considered, this property does not hold, because 3-D rotations are noncommutative. The noncommutativity of rotations has prompted a long debate over whether or not the oculomotor system has to account for this property of rotations by employing noncommutative operators. Recently, Raphan presented a model of the ocular plant that incorporates the orbital pulleys discovered, and qualitatively modeled, by Miller and colleagues. Using one simulation, Raphan showed that the pulley model could produce realistic saccades even when the neural controller is commutative. However, no proof was offered that the good behavior of the Raphan-Miller pulley model holds for saccades different from those simulated. We demonstrate mathematically that the Raphan-Miller pulley model always produces movements that have an accurate dynamic behavior. This is possible because, if the pulleys are properly placed, the oculomotor plant (extraocular muscles, orbital pulleys, and eyeball) in a sense appears commutative to the neural controller. We demonstrate this finding by studying the effect that the pulleys have on the different components of the innervation signal provided by the brain to the extraocular muscles. Because the pulleys make the axes of action of the extraocular muscles dependent on eye orientation, the effect of the innervation signals varies correspondingly as a function of eye orientation. In particular, the Pulse of innervation, which in classical models of the saccadic system encoded eye velocity, here encodes a different signal, which is very close to the derivative of eye orientation. In contrast, the Step of innervation always encodes orientation, whether or not the plant contains pulleys. Thus the Step can be produced by simply integrating the Pulse. Particular care will be given to describing how the pulleys can have this differential effect on the Pulse and the Step. We will show that, if orbital pulleys are properly located, the neural control of saccades can be greatly simplified. Furthermore, the neural implementation of Listing's Law is simplified: eye orientation will lie in Listing's Plane as long as the Pulse is generated in that plane. These results also have implications for the surgical treatment of strabismus.

Modeling control of eye orientation in three dimensions. I. Role of muscle pulleys in determining saccadic trajectory.

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.

Visual test of Listing's law during vergence.

A simple visual test was used to measure how much Listing's plane rotates as a function of the vergence angle. This test measured the elevation-dependent torsional disparity of horizontal and vertical lines during three tasks: vergence on a near target, vergence through prisms that remained fixed, and through prisms that rotated with eye elevation. Consistent with our previous search-coil measurements, the results here suggest that the angle between the Listing's planes of the two eyes is somewhat less than the vergence angle.

Neural Constraints on Eye Motion in Human Eye-Head Saccades

We examined two ways in which the neural control system for eye-head saccades constrains the motion of the eye in the head. The first constraint involves Listing's law, which holds ocular torsion at zero during head-fixed saccades. During eye-head saccades, does this law govern the eye's motion in space or in the head? Our subjects, instructed to saccade between space-fixed targets with the head held still in different positions, systematically violated Listing's law of the eye in space in a way that approximately, but not perfectly, preserved Listing's law of the eye in head. This finding implies that the brain does not compute desired eye position based on the desired gaze direction alone but also considers head position. The second constraint we studied was saturation, the process where desired-eye-position commands in the brain are "clipped" to keep them within an effective oculomotor range (EOMR), which is smaller than the mechanical range of eye motion. We studied the adaptability of the EOMR by asking subjects to make head-only saccades. As predicted by current eye-head models, subjects failed to hold their eyes still in their orbits. Unexpectedly, though, the range of eye-in-head motion in the horizontal-vertical plane was on average 31% smaller in area than during normal eye-head saccades, suggesting that the EOMR had been reduced by effort of will. Larger reductions were possible with altered visual input: when subjects donned pinhole glasses, the EOMR immediately shrank by 80%. But even with its reduced EOMR, the eye still moved into the "blind" region beyond the pinhole aperture during eye-head saccades. Then, as the head movement brought the saccade target toward the pinhole, the eyes reversed their motion, anticipating or roughly matching the target's motion even though it was still outside the pinhole and therefore invisible. This finding shows that the backward rotation of the eye is timed by internal computations, not by vision. When subjects wore slit glasses, their EOMRs shrank mostly in the direction perpendicular to the slit, showing that altered vision can change the shape as well as the size of the EOMR. A recent, three-dimensional model of eye-head coordination can explain all these findings if we add to it a mechanism for adjusting the EOMR.

Visual-motor transformations required for accurate and kinematically correct saccades.

The goal of this study was to identify and model the three-dimensional (3-D) geometric transformations required for accurate saccades to distant visual targets from arbitrary initial eye positions. In abstract 2-D models, target displacement in space, retinal error (RE), and saccade vectors are trivially interchangeable. However, in real 3-D space, RE is a nontrivial function of objective target displacement and 3-D eye position. To determine the physiological implications of this, a visuomotor "lookup table" was modeled by mapping the horizontal/vertical components of RE onto the corresponding vector components of eye displacement in Listing's plane. This provided the motor error (ME) command for a 3-D displacement-feedback loop. The output of this loop controlled an oculomotor plant that mechanically implemented the position-dependent saccade axis tilts required for Listing's law. This model correctly maintained Listing's law but was unable to correct torsional position deviations from Listing' s plane. Moreover, the model also generated systematic errors in saccade direction (as a function of eye position components orthogonal to RE), predicting errors in final gaze direction of up to 25 degrees in the oculomotor range. Plant modifications could not solve these problems, because the intrisic oculomotor input-output geometry forced a fixed visuomotor mapping to choose between either accuracy or Listing's law. This was reflected internally by a sensorimotor divergence between input-defined visual displacement signals (inherently 2-D and defined in reference to the eye) and output-defined motor displacement signals (inherently 3-D and defined in reference to the head). These problems were solved by rotating RE by estimated 3-D eye position (i.e., a reference frame transformation), inputting the result into a 2-D-to-3-D "Listing's law operator," and then finally subtracting initial 3-D eye position to yield the correct ME. This model was accurate and upheld Listing's law from all initial positions. Moreover, it suggested specific experiments to invasively distinguish visual and motor displacement codes, predicting a systematic position dependence in the directional tuning of RE versus a fixed-vector tuning in ME. We conclude that visual and motor displacement spaces are geometrically distinct such that a fixed visual-motor mapping will produce systematic and measurable behavioral errors. To avoid these errors, the brain would need to implement both a 3-D position-dependent reference frame transformation and nontrivial 2-D-to-3-D transformation. Furthermore, our simulations provide new experimental paradigms to invasively identify the physiological progression of these spatial transformations by reexamining the position-dependent geometry of displacement code directions in the superior colliculus, cerebellum, and various cortical visuomotor areas.

Visual-motor optimization in binocular control

When we view objects at various depths, the 3-D rotations of our two eyes are neurally yoked in accordance with a recently discovered geometric rule, here called the binocular extension of Listing's law, or L2. This paper examines the visual and motor consequences of this rule. Although L2 is a generalization of Listing's original, monocular law, it does not follow from current theories of the latter's function, which involve minimizing muscle work or optimizing certain aspects of retinal image flow. This study shows that a new optimization strategy that combines stereo vision with motor efficiency does explain L2, and describes the predictions of this new theory. Contrary to recent suggestions in the literature, L2 does not ensure single vision of lines orthogonal to the visual plane, but rather reduces cyclodisparity of the visual plane itself; and L2 does not arise because a single, conjugate angular velocity command is sent to both eyes, but actually requires that the two eyes rotate with different speeds and axes when scanning an isovergence surface. This study shows that L2 is compatible with a 1-D control system for vergence alone (because horizontal and torsional vergence are yoked) and a 3-D system for combined, head-fixed saccades and vergence.

Listing's plane dependence on alternating fixation in a strabismus patient

Listing's law of the eye is one of the best studied findings in motor control, but its functional meaning is still incompletely understood and its status in neurological disorders and in strabismus is almost entirely unknown. We investigated the mechanisms underlying Listing's law and its possible clinical relevance. The dual magnetic search coil technique was used to record three-dimensional binocular eye movements in a stereoblind strabismic patient with good visual acuity in both eyes and capable of voluntarily alternating fixation. This technique yielded an accurate, objective and simultaneous measure of ocular misalignment in three dimensions and showed that the squint angle depended on which eye was fixating. Saccadic eye movement data throughout the oculomotor range were used to fit Listing's plane. Listing's primary position and the thickness of the plane for each eye were calculated for three different fixation conditions. For comparison, control measurements were taken from four normals. In the patient, no large deviations from normal values for the thickness of Listing's plane and the confidence limits of the Listing primary position were found. The most remarkable abnormality was that the orientation of Listing's plane depended on which eye was fixating. Both the change in ocular misalignment and the shift of Listing's primary positions observed when changing fixation are probably linked to accommodation-related vergence. Despite repeated surgery at early age, the patient had well-defined Listing planes for both eyes, but their alignment during left-eye fixation was abnormal. The obedience to Listing's law may reflect a strategy which minimizes muscular effort in each eye separately. The abnormal fixation-condition dependence is probably due to an aberrant coupling with vergence.

Pathological torsional eye deviation during voluntary saccades: a violation of Listing's law.

BACKGROUND: Under normal conditions, there are no torsional eye movements during voluntary saccades when the head is stationary (Listing's law). METHODS AND RESULTS: Using dual search coils for three dimensional...

Three-dimensional model of the human eye-head saccadic system.

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 degrees 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.

システムニューロサイエンス教教育講座 ７． なぜ今Ｌｉｓｔｉｎｇなのか？

The anatomical configuration of the eye ball in the orbit is similar to that of a ball-and-socket joint, and the arrangement of extra-ocular muscles gives the globe three rotational degrees of freedom (DOF). If one describes a three-dimensional (3D) eye position using three consecutive rotations about the horizontal, vertical, and torsional eye-fixed axes, the value of torsion, so-called false torsion, depends on the order of rotation. This is a result of the non-commutativity of rotatory movements. The problem of false torsion can be avoided by representing a 3D eye position by a single axis rotation from a chosen reference position to the current eye position, e. g. rotation vectors (Haustein, 1989).According to Listing's law, all axes about which the eye rotates from the reference position to other positions lie in a plane, so-called Listing's plane, provided the head is erect and stationary (Helmholtz, 1867). If the reference position coincides with the primary position, Listing's plane is perpendicular to the direction of gaze in primary position. Listing's law is a remarkable example, of how a motor system reduces DOF (from 3 to 2) to simplify multidimensional motor control.Characteristic changes in the orientation of Listing's plane have been reported under several conditions: Static tilts in the frontal plane of the head induce ocular counterrolling, i.e. parallel shifts of Listing's plane along the torsional axis. Static tilts in the sagittal plane counter-rotate Listing's plane about the vertical axis. Convergence leads to a temporal rotation of Listing's plane about the horizontal axis. During sleep, Listing's plane is not preserved, which implies neural implementation of Listing's law.

1514 Torsional eye movements during drowsy periods in monkeys

In five normal subjects, we analyzed uncalled for torsion (blips) during and after horizontal and vertical saccades. Torsion was defined as movement out of Listing's plane. During horizontal saccades in downward gaze the abducting eye extorted and the adducting eye intorted. The direction of the blips reversed in upward gaze. Peak torsional amplitudes (up to 1–2 deg) were always reached during saccades; drifts back to Listing's plane outlasted the saccades. Torsion of the extorting eye was larger than that of the intorting eye, producing a transient positive cyclovergence. Torsion and cyclovergence evoked by vertical saccades were also stereotyped in each eye, but showed idiosyncratic differences among subjects. We conclude that Listing's law is violated during saccades. Transient saccade-evoked torsion might reflect properties of the three-dimensional velocity-to-position integrator and/or the ocular plant.

Validity of Listing's law during fixations, saccades, smooth pursuit eye movements, and blinks.

In its original formulation, Listing's law referred only to eye positions during steady fixation. In recent years, however, several studies have suggested that Listing's law can be extended to the movements of the eyes, including during saccades and smooth pursuit. A major problem in deciding whether or not Listing's law is obeyed during eye movements is the influence of any spontaneous fluctuations in torsional eye position. To try to settle this question, the three-dimensional position of the eyes (around the three axes: horizontal, vertical, and torsional) was recorded with dual search coils in five normal subjects during fixations, 20 degrees saccades, blinks, and 20 degrees pursuit movements with a 20 degrees/s stimulus velocity. Eye movements across a wide range of horizontal positions were measured at different elevations of gaze during 11 min. Variability (as reflected in the standard deviation of torsional eye position) was used as a measure of the validity of Listing's law. After linear detrending single trials, each lasting 21.5 s, to remove the effects of drift over minutes, the reduction in the standard deviation of torsional position in tertiary eye positions was 54% assuming a planar and 58% assuming a second-order curved Listing's surface. We attributed this long-term fluctuation of the torsional signal to slippage of the coil on the eye. The remaining variability was mainly due to short-term fluctuation of eye torsion over seconds. The impact of hysteresis, associated with consecutive centrifugal-centripetal horizontal movements, on the variability of torsional eye position appeared negligible. Peak increases in the standard deviation from the fixation baseline after fitting individual Listing's planes for each trial were 348% during blinks, 141% during saccades, and 72% during pursuit movements (median value of five subjects). In conclusion, Listing's law during blinks, saccades, and pursuit is less valid than during fixations, which raises doubts about the existence of an internal "Listing's law operator" for eye movements. Possibly, central eye velocity commands do not comply with Listing's law.

Theoretical explanations of Listing's law and their implication for binocular vision

We shall discuss three theoretical explanations of Listing's law for conjugate eye movements with the head fixed: the original argument by Helmholtz, which is “sensorimotor” in its attempt to optimize vision by using internal feedback from the oculomotor system, and two comparatively simple recent explanations based on either visual or oculomotor performance. These geometrical demonstrations shed some light on recent generalizations of Listing's law to vergent eye movements.

Transient torsion during and after saccades

In five normal subjects, we analyzed uncalled for torsion (blips) during and after horizontal and vertical saccades. Torsion was defined as movement out of Listing's plane. During horizontal saccades in downward gaze the abducting eye extorted and the adducting eye intorted. The direction of the blips reversed in upward gaze. Peak torsional amplitudes (up to 1–2 deg) were always reached during saccades; drifts back to Listing's plane outlasted the saccades. Torsion of the extorting eye was larger than that of the intorting eye, producing a transient positive cyclovergence. Torsion and cyclovergence evoked by vertical saccades were also stereotyped in each eye, but showed idiosyncratic differences among subjects. We conclude that Listing's law is violated during saccades. Transient saccade-evoked torsion might reflect properties of the three-dimensional velocity-to-position integrator and/or the ocular plant.

Excess cyclovergence in patients with intermittent exotropia

Recently, we developed a model of binocular fixation. This model predicts the amount of cyclovergence as a function of target elevation and horizontal target vergence. The prediction derives from the assumption that version and vergence add linearly and that the eye positions are constrained in three respects: (1) the foveae of the two eyes are directed towards the target, (2) the version component follows Listing's law, i.e. cycloversion, and horizontal and vertical version are not independent, (3) the vergence component is restricted to a plane approximately perpendicular to Listing's plane, i.e. horizontal, vertical and torsional vergence are not independent. The version and the vergence components are characterized by a common primary direction for the two eyes. We applied this model to data of patients with intermittent exotropia. In two patients with an amblyopic eye we found that the common primary direction rotates towards the amblyopic eye. In the third patient, not suffering from amblyopia, the common primary direction was practically straight ahead. In all three patients, cyclovergence angles were larger than those found in normal subjects. We found that the increased cyclovergence was compatible with our model for normal subjects if an offset on the horizontal vergence was given. This offset represents the additional convergence effort required in these patients to overcome the exodeviation of the eyes. According to our model the increased horizontal vergence effort results in excess cyclovergence. The relation between horizontal vergence and cyclovergence offers a new method for measuring the angle of exotropia.

Analysis of saccadic short-term plasticity in three dimensions

The capacity for short-term adaptation is a well-established property of the horizontal (H) and vertical (V) components of saccades. It allows these directional components, which clearly serve the goal of foveation, to maintain their precision even under changing circumstances. Torsional (T) saccade components, on the other hand, which deal with the orientation of the target on the fovea, have hardly been investigated in adaptation experiments. They appear to be severely restricted by Listing's law during fixations and saccades. The main purpose of Listing's law is far from obvious but could be visual or oculomotor. Better knowledge of the adaptive capacity of the saccadic system in the torsional direction could throw new light on the functional significance of this interesting neural strategy. To study short-term plasticity in the torsional components of saccades, binocular 3D-eye positions were measured, using magnetic search foils. Five normal human subjects were instructed to make uni-directional refixation saccades, while they viewed a large visual scene. To induce a change in the torsional component, the complete stimulus was rapidly rotated during these saccades. We thoroughly investigated the torsional responses of the saccadic system, to see if any short-term adaptive response in torsional direction was induced, in which case the notion of a visual purpose for Listing's law would be strengthened. In none of our experiments, however, did we find any clear adaptive response in torsional direction. To further investigate the reliability of this result and to ascertain that our experimental conditions allowed classical gain adaptation, we also did experiments designed to achieve a combination of torsional adaptation and classic gain shortening in one of the directional components. While gain adaptation was very obvious, none of the experiments provided evidence for a short-term effect in torsion. We conclude that our experiments do not support a purely visual basis for Listing's law.

How do Motor Systems Deal with the Problems of Controlling Three-Dimensional Rotations?

Abstract Rotations are fundamental to motor control, not only for orienting to stimuli but also in the joint articulations that underlie translational movements. Studying three-dimensional (3-D) rotations of the simplest joint system, the eye, has provided general insights into the neural control of movement. First, in selecting one 3-D eye orientation for each two-dimensional (2-D) gaze direction, the oculomotor system generates a behavior called Listing's law that constrains eye position to a 2-D plane, Listing's plane. This selection is made internally by an inverse kinematic transformation called the Listing's law operator. Second, the oculomotor system incorporates the inherent multiplicative relationship between rotational velocity and position to generate the 3-D movement and position commands required by Listing's law. Finally, the coordinate systems for these commands appear to align with Listing's plane rather than with anatomic structures. Recent investigations have revealed similar behavioral ...

Three-dimensional eye, head, and chest orientations after large gaze shifts and the underlying neural strategies

1. The fixation orientations adopted by the eye, head, and chest were examined when all three were allowed to participate in gaze shifts to visual targets. The objective was to discover whether there are invariant, neurally determined laws governing these orientations that might provide clues to the processes of perception and motor control. This is an extension of the classical studies of eye-only saccades that determined that there is only one eye orientation for each gaze direction (Donders' law) and that the rotations necessary to take the eye from a reference orientation to all other orientations adopted are about axes that lie in a plane (Listing's law). 2. The three-dimensional orientations of the static eyes, head, and chest were measured after each gaze shift to a visual target, the targets having been fixed at positions ranging from 0 to 135 degrees to the left and right of center and 45 degrees up and down. These measurements were taken of seven human subjects by means of the search coil technique with coils attached to the sternum, head, and right eye. Orientations were plotted as quaternion vectors so that those orientations obeying Donders' law formed a surface and those obeying Listing's law formed a plane. 3. The orientations adopted by the eye, head, and chest were found to be a small subset of those possible under the biomechanical and task-imposed constraints. Thus there is a neurally implemented restriction, specifically of the rotation of the eye relative to space (i.e., the orientation variable es) and to the head (eh); also of the rotation of the head relative to space (hs) and to the chest (hc), and the rotation of the chest relative to space (cs). Plotted as quaternion vectors, the data for each orientation variable formed a characteristic surfacelike shape. In the case of es, hs, and hc these were twisted surfaces, whereas for eh the surface was planar and for cs it was nearly linear. Thus to a first approximation each of the orientation variables conformed to Donders' law. 4. The eye adopted a pointing (gaze) direction that has the ratio of vertical to horizontal components generally greater than one when fixating each of the corner targets. The chest, by contrast, moved almost entirely in the horizontal direction, whereas the head performed an intermediate role. 5. The es-, hs-, and hc-fitted surfaces and cs-fitted lines were titled remarkably little from the vertical axis (i.e., the gravity direction) despite larger tilts being possible.(ABSTRACT TRUNCATED AT 400 WORDS)

Rotational kinematics of the human vestibuloocular reflex. III. Listing's law

1. Do slow phase eye velocities generated by the vestibuloocular reflex (VOR) depend on eye position? If the purpose of the VOR is simply to stabilize the retinal image, there can be no such dependence, because eye velocity must always be equal and opposite to head velocity. But if the VOR tolerates some retinal slip to achieve other goals, such as reducing eye velocity or following Listing's law, then one should see specific patterns of dependence. We examined VOR responses of human subjects to yaw, pitch, and roll rotation looking in various directions to quantify how the input-output properties of the VOR vary with eye position. 2. Eye rotation axes during yaw and pitch tilted in the same direction as the gaze line but only one-quarter as far on average. Thus, during yaw head rotation, the axis of eye rotation was roughly aligned with the head axis when the subject looked straight ahead, but tilted up when the gaze direction was up, and down when gaze was down. The amount of tilt varied between subjects, but on average a 30 degrees change in eye position caused a 7.5 degrees tilt in the eye rotation axis. During pitch, the eye axis tilted right when gaze was right and left when gaze was left, also moving 7.5 degrees on average for a 30 degrees change in the gaze direction. 3. During roll stimulation, the axis of eye rotation tilted in the opposite direction to the gaze line, and about one-half as far. On average, when the gaze line moved 30 degrees down, the eye rotation axis tilted 12.0 degrees up; when the gaze moved 30 degrees left, the eye axis tilted 15.3 degrees right. 4. It is often argued that the torsional VOR is weak because head rotation about the line of sight causes little image displacement on the fovea. But the line of sight is collinear with the torsional axis only when the subject looks straight ahead. Does the "weak axis" of the VOR stay collinear with the gaze line when the subject looks eccentrically? We calculated the axis of head rotation for which the VOR response is weakest and found that it does vary with eye position, but does not stay parallel with the gaze direction. When subjects looked straight ahead, the weak axis was roughly collinear with the gaze line; when gaze shifted eccentrically, the weak axis shifted in the same direction but only about one-half as far.(ABSTRACT TRUNCATED AT 400 WORDS)

Three-dimensional human eye movements are organized differently for the different oculomotor subsystems

Three-dimensional (3-D) eye movements during steady fixation, saccades and smooth pursuit are governed by a powerful strategy restricting eye position to 2 degrees of freedom by keeping the torsional component close to o (Listing's law). To test if Listing's law is also obeyed during optokinetic and vestibular stimulation, the study compares 3-D eye movements in humans during pursuit, optokinetic and vestibular activation using similar gaze trajectories. The optokinetic and vestibuloocular reflexes deviate from Listing's law showing a strategy lying about halfway between optimal full-field retinal image stabilization and Listing's law. The fact that for similar gaze trajectories the brain can choose between different 3-D movement strategies depending on the oculomotor subsystem currently in action (supposedly to optimize for the specific requirements of a particular oculomotor subsystem) suggests that Listing's law is due to a neurally-im-posed constraint on the oculomotor output.