Publisher Correction: On the role of ocular torsion in binocular visual matching.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

On the retinal correspondences across the binocular visual field.

We have recently reported that objects seen at near distances require adjustments of the relative torsion of the eyes to avoid blurred binocular images or double vision and ultimately to allow binocular fusion. The reason underlying these rotational adjustments is that converging eye movements undo the eyes' torsional alignment, generating disparate binocular images of objects outside the horizontal plane of regard. We show mathematically that it is the distance between the two eyes, their relative orientation in the frontal plane and the distances from each eye to the binocularly intended visual target, that determine the binocular alignment of the lines of sight.

On the role of ocular torsion in binocular visual matching.

When an observer scans the visual surround, the images cast on the two retinae are slightly different due to the different viewpoints of the two eyes. Objects in the horizontal plane of regard can be seen single by aligning the lines of sight without changing the torsional stance of the eyes. Due to the peculiar ocular kinematics this is not possible for objects above or below the horizontal plane of regard.

Three-dimensional ocular kinematics underlying binocular single vision.

We have analyzed the binocular coordination of the eyes during far-to-near refixation saccades based on the evaluation of distance ratios and angular directions of the projected target images relative to the eyes' rotation centers. By defining the geometric point of binocular single vision, called Helmholtz point, we found that disparities during fixations of targets at near distances were limited in the subject's three-dimensional visual field to the vertical and forward directions. These disparities collapsed to simple vertical disparities in the projective binocular image plane.

Transmitter inputs to different motoneuron subgroups in the oculomotor and trochlear nucleus in monkey.

In all vertebrates the eyes are moved by six pairs of extraocular muscles enabling horizontal, vertical and rotatory movements. Recent work showed that each extraocular muscle is controlled by two motoneuronal groups: (1) Motoneurons of singly-innervated muscle fibers (SIF) that lie within the boundaries of motonuclei mediating a fast muscle contraction; and (2) motoneurons of multiply-innervated muscle fibers (MIF) in the periphery of motonuclei mediating a tonic muscle contraction. Currently only limited data about the transmitter inputs to the SIF and MIF motoneurons are available.

The kinematics of far-near re-fixation saccades.

We have analyzed the three-dimensional spatiotemporal characteristics of saccadic refixations between far and near targets in three behaviorally trained rhesus monkeys. The kinematics underlying these rapid eye movements can be accurately described by rotations of the eyes in four different planes, namely, first disconjugate rotations in the horizontal plane of regard converging the eyes toward the near target, followed by rotations in each eye's vertical direction plane, and finally, disconjugate rotations in a common frontoparallel plane. This compounded rotation of the eye was underlying an initially fast-rising variable torsion that typically overshot the final torsion, which the eyes attained at the time of target acquisition.

Kinematics of visually-guided eye movements.

One of the hallmarks of an eye movement that follows Listing's law is the half-angle rule that says that the angular velocity of the eye tilts by half the angle of eccentricity of the line of sight relative to primary eye position. Since all visually-guided eye movements in the regime of far viewing follow Listing's law (with the head still and upright), the question about its origin is of considerable importance. Here, we provide theoretical and experimental evidence that Listing's law results from a unique motor strategy that allows minimizing ocular torsion while smoothly tracking objects of interest along any path in visual space.

Three-dimensional visuo-motor control of saccades.

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.

Quick phases control ocular torsion during smooth pursuit.

One of the open questions in oculomotor control of visually guided eye movements is whether it is possible to smoothly track a target along a curvilinear path across the visual field without changing the torsional stance of the eye. We show in an experimental study of three-dimensional eye movements in subhuman primates (Macaca mulatta) that although the pursuit system is able to smoothly change the orbital orientation of the eye's rotation axis, the smooth ocular motion was interrupted every few hundred milliseconds by a small quick phase with amplitude <1.5° while the animal tracked a target along a circle or ellipse.

Processing of angular motion and gravity information through an internal model.

The vestibular organs in the base of the skull provide important information about head orientation and motion in space. Previous studies have suggested that both angular velocity information from the semicircular canals and information about head orientation and translation from the otolith organs are centrally processed in an internal model of head motion, using the principles of optimal estimation. This concept has been successfully applied to model behavioral responses to classical vestibular motion paradigms.

Decoding 3D search coil signals in a non-homogeneous magnetic field.

We present a method for recording eye-head movements with the magnetic search coil technique in a small external magnetic field. Since magnetic fields are typically non-linear, except in a relative small region in the center small field frames have not been used for head-unrestrained experiments in oculomotor studies. Here we present a method for recording 3D eye movements by accounting for the magnetic non-linearities using the Biot-Savart law.

Geometrical considerations on canal-otolith interactions during OVAR and Bayesian modelling.

During constant-velocity rotation about a tilted axis (OVAR), the VOR and the rotation perception last indefinitely, but show a striking dependency on tilt angle. We show that, during OVAR, a variety of motions can account for the head motion relative to gravity. Some of these are in conflict with canal signals, but correspond to a lower angular velocity; we suggest that the brain performs a trade-off in order to select the best motion.

Control of ocular torsion in the rotational vestibulo-ocular reflexes.

Visual stabilization of the retina during rotational head movements requires that in far vision the eyes rotate about the same axis as the head but in opposite direction with a gain close to unity (optimal strategy). To achieve this goal the vestibulo-oculomotor system must be able to independently control all three rotational degrees of freedom of the eye. Studies of the human rotational vestibulo-ocular reflexes (VOR) have shown that its spatial characteristics are best explained by a strategy that lies halfway between the optimal image stabilization and perfect compliance with Listing's law.

Dynamic effects on the subjective visual vertical after roll rotation.

We investigated in normal human subjects how semicircular canal and otolith signals interact in the estimation of the subjective visual vertical after constant velocity or constant acceleration roll tilt. In the constant velocity paradigm, subjects were rotated in darkness at +/-60 degrees/s for five complete cycles before being stopped in one of seven orientations ranging from 0 to +/-90 degrees (right/left ear down). In the constant acceleration paradigm, subjects were rotated with an acceleration of +30 or -30 degrees/s2 to the same seven end positions between -90 and +90 degrees , by way of passing once through the upside-down position.

Human visuospatial updating after passive translations in three-dimensional space.

To maintain a stable representation of the visual environment as we move, the brain must update the locations of targets in space using extra-retinal signals. Humans can accurately update after intervening active whole-body translations. But can they also update for passive translations (i.

Noncommutative control in the rotational vestibuloocular reflex.

To investigate the role of noncommutative computations in the oculomotor system, three-dimensional (3D) eye movements were measured in seven healthy subjects using a memory-contingent vestibulooculomotor paradigm. Subjects had to fixate a luminous point target that appeared briefly at an eccentricity of 20 degrees in one of four diagonal directions in otherwise complete darkness. After a fixation period of approximately 1 s, the subject was moved through a sequence of two rotations about mutually orthogonal axes in one of two orders (30 degrees yaw followed by 30 degrees pitch and vice versa in upright and 30 degrees yaw followed by 20 degrees roll and vice versa in both upright and supine orientations).

Human visuospatial updating after noncommutative rotations.

As we move our bodies in space, we often undergo head and body rotations about different axes-yaw, pitch, and roll. The order in which we rotate about these axes is an important factor in determining the final position of our bodies in space because rotations, unlike translations, do not commute. Does our brain keep track of the noncommutativity of rotations when computing changes in head and body orientation and then use this information when planning subsequent motor commands? We used a visuospatial updating task to investigate whether saccades to remembered visual targets are accurate after intervening, whole-body rotational sequences.

Differences in the accuracy of human visuospatial memory after yaw and roll rotations.

Our ability to keep track of objects in the environment, even as we move, has been attributed to various cues including efference copies, vestibular signals, proprioception, and gravitational cues. However, the presence of some cues, such as gravity, may not be used to the same extent by different axes of motion (e.g.

Self-motion-induced eye movements: effects on visual acuity and navigation.

Self-motion disturbs the stability of retinal images by inducing optic flow. Objects of interest need to be fixated or tracked, yet these eye movements can infringe on the experienced retinal flow that is important for visual navigation. Separating the components of optic flow caused by an eye movement from those due to self-motion, as well as using optic flow for visual navigation while simultaneously maintaining visual acuity on near targets, represent key challenges for the visual system.

Roles of gravitational cues and efference copy signals in the rotational updating of memory saccades.

Primates are able to localize a briefly flashed target despite intervening movements of the eyes, head, or body. This ability, often referred to as updating, requires extraretinal signals related to the intervening movement. With active roll rotations of the head from an upright position it has been shown that the updating mechanism is 3-dimensional, robust, and geometrically sophisticated.

Canal-otolith interactions after off-vertical axis rotations. II. Spatiotemporal properties of roll and pitch postrotatory vestibuloocular reflexes.

We have examined the spatiotemporal characteristics of postrotatory eye velocity after roll and pitch off-vertical axis rotations (OVAR). Three rhesus monkeys were placed in one of 3 orientations on a 3-dimensional (3D) turntable: upright (90 degrees roll or pitch OVAR), 45 degrees nose-up (45 degrees roll OVAR), and 45 degrees left ear-down (45 degrees pitch OVAR). Subjects were then rotated at +/-60 degrees /s around the naso-occipital or interaural axis and stopped after 10 turns, in one of 7 final head orientations, each separated by 30 degrees .

Control of eye orientation: where does the brain's role end and the muscle's begin?

Our understanding of how the brain controls eye movements has benefited enormously from the comparison of neuronal activity with eye movements and the quantification of these relationships with mathematical models. Although these early studies focused on horizontal and vertical eye movements, recent behavioural and modelling studies have illustrated the importance, but also the complexity, of extending previous conclusions to the problems of controlling eye and head orientation in three dimensions (3-D). An important facet in understanding 3-D eye orientation and movement has been the discovery of mobile, soft-tissue sheaths or 'pulleys' in the orbit which might influence the pulling direction of extraocular muscles.

Dynamic modulation of ocular orientation during visually guided saccades and smooth-pursuit eye movements.

Rotational disturbances of the head about an off-vertical yaw axis induce a complex vestibuloocular reflex pattern that reflects the brain's estimate of head angular velocity as well as its estimate of instantaneous head orientation (at a reduced scale) in space coordinates. We show that semicircular canal and otolith inputs modulate torsional and, to a certain extent, also vertical ocular orientation of visually guided saccades and smooth-pursuit eye movements in a similar manner as during off-vertical axis rotations in complete darkness. It is suggested that this graviceptive control of eye orientation facilitates rapid visual spatial orientation during motion.

Gravity modulates Listing's plane orientation during both pursuit and saccades.

Previous studies have shown that the spatial organization of all eye orientations during visually guided saccadic eye movements (Listing's plane) varies systematically as a function of static and dynamic head orientation in space. Here we tested if a similar organization also applies to the spatial orientation of eye positions during smooth pursuit eye movements. Specifically, we characterized the three-dimensional distribution of eye positions during horizontal and vertical pursuit (0.

Vestibular contributions to gaze stability during transient forward and backward motion.

The accuracy with which the vestibular system anticipates and compensates for the visual consequences of translation during forward and backward movements was investigated with transient motion profiles in rhesus monkeys trained to fixate targets on an isovergence screen. Early during motion when visuomotor reflexes remain relatively ineffective and vestibular-driven mechanisms have an important role for controlling the movement of the eyes, a large asymmetry was observed for forward and backward heading directions. During forward motion, ocular velocity gains increased steeply and reached near unity gains as early as 40-50 ms after motion onset.