The particular orientation of Listing's plane in the head depends on head posture relative to gravity. The spatial orientation of slow phase rotation axes changes smoothly as a function of head orientation. This becomes obvious when plotting torsional versus vertical slow phases of nystagmus at different head orientations. The instantaneous head orientation relative to gravity determined the torsional stance of the eye at any instant of time as a function of momentary gaze direction. The spatial orientation of fast phase rotation axes as a function of horizontal and vertical gaze depended on instantaneous head orientation relative to gravity in a similar way as that of slow phases. The important point here is that, similarly as in the static situation, there is a direction of minimal torsion which changes dynamically its orientation in space as a function of head orientation relative to gravity.

The large capacity of the vestibulo-ocular reflexes (VOR) to change response amplitude and temporal properties adaptively either to short or long-term alterations in the visual environment has been repeatedly demonstrated in a number of species. The recovery of horizontal VOR after inactivation of the lateral semicircular canals was frequency-specific. Selective inactivation of semicircular canals altered the three-dimensional spatiotemporal tuning of the VOR in a characteristic way. The spatial organization of the VOR was investigated by repositioning the animals relative to the axis of rotation and oscillating about different head axes. Similarly to the strongly frequency-specific recovery of horizontal VOR during yaw oscillations, a very short horizontal per- and postrotatory nystagmus was elicited by steps of constant velocity rotation several weeks after lateral canal plugging. The recovery of horizontal VOR, for example, is at least partly due to signals originating from the remaining intact vertical canals.

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

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. Here we performed a quantitative study on the transmitter inputs to SIF and MIF motoneurons of individual muscles in the oculomotor and trochlear nucleus in monkey. Pre-labeled motoneurons were immunostained for GABA, glutamate decarboxylase, GABA-A receptor, glycine transporter 2, glycine receptor 1, and vesicular glutamate transporters 1 and 2. The main findings were: (1) the inhibitory control of SIF motoneurons for horizontal and vertical eye movements differs. Unlike in previous primate studies a considerable GABAergic input was found to all SIF motoneuronal groups, whereas a glycinergic input was confined to motoneurons of the medial rectus (MR) muscle mediating horizontal eye movements and to those of the levator palpebrae (LP) muscle elevating the upper eyelid. Whereas SIF and MIF motoneurons of individual eye muscles do not differ numerically in their GABAergic, glycinergic and vGlut2 input, vGlut1 containing terminals densely covered the supraoculomotor area (SOA) targeting MR MIF motoneurons. It is reasonable to assume that the vGlut1 input affects the near response system in the SOA, which houses the preganglionic neurons mediating pupillary constriction and accommodation and the MR MIF motoneurones involved in vergence.

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. Specifically, during circular pursuit of targets moving at different angular eccentricities (5°, 10°, and 15°) relative to straight ahead at spatial frequencies of 0.067 and 0.1 Hz, the torsional amplitude of the intervening quick phases was typically around 1° or smaller and changed direction for clockwise vs. counterclockwise tracking. Reverse computations of the eye rotation based on the recorded angular eye velocity showed that the quick phases facilitate the overall control of ocular orientation in the roll plane, thereby minimizing torsional disturbances of the visual field. On the basis of a detailed kinematic analysis, we suggest that quick phases during curvilinear smooth tracking serve to minimize deviations from Donders' law, which are inevitable due to the spherical configuration space of smooth eye movements.

Oscillating an animal out-of-phase simultaneously about the roll and pitch axes ("wobble") changes continuously the orientation of the head relative to gravity. For example, it may gradually change from nose-up, to ear-down, nose-down, ear-down, and back to nose-up. Rotations about the longitudinal axis ("spin") can change the orientation of the head relative to gravity in the same way, provided the axis is tilted from vertical. During both maneuvers, the otolith organs in the inner ear detect the change in head orientation relative to gravity, whereas the semicircular canals will only detect oscillations in velocity (wobble), but not any rotation at constant velocity (spin). Geometrically, the whole motion can be computed based on information about head orientation relative to gravity and the wobble velocity. We subjected monkeys (Macaca mulatta) to combinations of spin and wobble and found that the animals were always able to correctly estimate their spin velocity. Simulations of these results with an optimal Bayesian model of vestibular information processing suggest that the brain integrates gravity and velocity information based on a geometrically coherent three-dimensional representation of head-in-space motion.

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. This study measured the dynamic of the vestibuloocular reflex during postrotatory tilt, tilt during the optokinetic afternystagmus, and off-vertical axis rotation. The influence of otolith signal on the VOR was systematically varied by using a series of tilt angles. We found that the time constants of responses varied almost identically as a function of gravity in these paradigms. We show that Bayesian modeling could predict the experimental results in an accurate and consistent manner. In contrast to other approaches, the Bayesian model also provides a plausible explanation of why these vestibulooculo motor responses occur as a consequence of an internal process of optimal motion estimation.

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. We show that the recording errors can be significantly reduced by monitoring current head position and thereby taking the location of the eye in the external magnetic field into account.

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. We show that this theory explains the effect of tilt angle on velocity estimation during OVAR.

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.e., without efference copy signals of an outgoing motor command)? We asked six head-fixed subjects to remember the location of a briefly flashed target (five possible targets were located at depths of 23, 33, 43, 63, and 150 cm in front of the cyclopean eye) as they moved 10 cm left, right, up, down, forward, or backward while fixating a head-fixed target at 53 cm. After the movement, the subjects made a saccade to the remembered location of the flash with a combination of version and vergence eye movements. We computed an updating ratio where 0 indicates no updating and 1 indicates perfect updating. For lateral and vertical whole-body motion, where updating performance is judged by the size of the version movement, the updating ratios were similar for leftward and rightward translations, averaging 0.84 +/- 0.28 (mean +/- SD) as compared with 0.51 +/- 0.33 for downward and 1.05 +/- 0.50 for upward translations. For forward/backward movements, where updating performance is judged by the size of the vergence movement, the average updating ratio was 1.12 +/- 0.45. Updating ratios tended to be larger for far targets than near targets, although both intra- and intersubject variabilities were smallest for near targets. Thus in addition to self-generated movements, extra-retinal signals involving otolith and proprioceptive cues can also be used for spatial constancy.

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. Here we argue that these spatial characteristics are fully compatible with an optimal strategy under the condition of a restrained gain of the torsional velocity-to-position integration. One implication of this finding is that the rotational VORs must override the default operation mode of the ocular plant that, according to recent findings, mechanically favours movements obeying Listing's law.

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. The sequences were reversed, either yaw then roll or roll then yaw, such that the final required eye movements to reach the same space-fixed target were different in each case. While each subject performed consistently irrespective of target location and rotational combination, we found great intersubject variability in their capacity to update. The distance between the noncommutative endpoints was, on average, half of that predicted by perfect noncommutativity. Nevertheless, most subjects did make eye movements to distinct final endpoint locations and not to one unique location in space as predicted by a commutative model. In addition, their noncommutative performance significantly improved when their less than ideal updating performance was taken into account. Thus the brain can produce movements that are consistent with the processing of noncommutative rotations, although it is often poor in using internal estimates of rotation for updating.

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). We found that the change in ocular torsion induced by consecutive rotations about the yaw and the pitch axis depended on the order of rotations as predicted by 3D rotation kinematics. Similarly, after rotations about the yaw and roll axis, torsion depended on the order of rotations but now due to the change in final head orientation relative to gravity. Quantitative analyses of these ocular responses revealed that the rotational vestibuloocular reflexes (VORs) in far vision closely matched the predictions of 3D rotation kinematics. We conclude that the brain uses an optimal VOR strategy with the restriction of a reduced torsional position gain. This restriction implies a limited oculomotor range in torsion and systematic tilts of the angular eye velocity as a function of gaze direction.

Key Points Short-latency eye movements, triggered by visual (ocular following reflex; OFR) and vestibular (translational vestibulo-ocular reflex; TVOR) mechanisms, compensate for the retinal image slip that is experienced during translational self-motion. These eye movements are predominantly conjugate during lateral motion when gaze and travel directions are approximately orthogonal to each other. Motion in a forward direction generates combinations of conjugate and vergence eye movements. Owing to the geometry of the translation-induced flow patterns, the OFR and the TVOR can reduce retinal image slip only locally to maintain foveal visual acuity. Foveal image stabilization is preferred at the cost of peripheral vision even when spatial attention is allocated to a peripheral target. A major challenge for the brain is estimation of target distance, which is necessary to adjust the amplitude of compensatory eye movements. For the OFR, this selection is driven by disparity- and motion parallax-sensitive mechanisms, whereas for the TVOR, target distance is solely computed on the basis of motor cues, primarily vergence angle and accommodation. The OFR is generated using visual motion signals in the medial superior temporal cortex, which projects to the paraflocculus of the cerebellum via the pontine nuclei. Purkinje cells in the ventral paraflocculus are thought to encode a motor command for the OFR. Neural processing underlying the generation of TVOR involves the vestibulo-cerebellum and the vestibular nuclei. Compensation of retinal image slip during translation involves eye movements that, in turn, modify the pattern of optic flow experienced by the moving observer. The mathematical analysis suggests that this interaction does not interfere with the use of optic flow information for visual navigation.

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., yaw vs. roll). We tested whether changes in gravitational cues can be used to improve visuospatial updating performance for yaw rotations as previously shown for roll. We found differences in updating for yaw and roll rotations in that yaw updating is not only associated with larger systematic errors but is also not facilitated by gravity in the same way as roll updating.