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. Subjects were able to perfectly fuse the vertically disparate target images with respect to the projected Helmholtz point of single binocular vision, independent of the particular location relative to the horizontal plane of regard. Target image fusion was achieved by binocular torsion combined with corrective modulations of the differential half-vergence angles of the eyes in the horizontal plane. Our findings support the notion that oculomotor control combines vergence in the horizontal plane of regard with active torsion in the frontal plane to achieve fusion of the dichoptic binocular target images.

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. The torsion consisted of a coarse, widely varying component of opposite polarity in the two eyes, which contained a more robust, much smaller modulation that sharply increased toward the end of saccades. The reorientation of the eyes in torsion depended on each eye's azimuth, elevation, and target distance. We conclude that refixation saccades are generated by motor commands that control ocular torsion in concert with the saccade generator, which operates in Donders-Listing kinematics underlying Listing's law.

Static and dynamic properties of vergence-induced reduction of ocular counter-roll in near vision.

We have examined the characteristics of vergence-induced reduction of ocular counter-roll in near vision. Monkeys were trained to make convergent and divergent refixations with the head and body either upright or in various roll orientations. During near viewing requiring 17 degrees horizontal vergence, we found that static binocular torsion was suppressed by about 68% (averaged over both eyes, two monkeys and both near target locations). This result is in accordance with a previous study in which binocular torsion was quantified based on the displacement planes of eye positions in far and near viewing. Latency and duration of the change in torsional eye position depended (for each eye differently) on body roll and the depth plane of fixation. For instance, during convergent refixations in left-ear-down orientations, the latencies of the left eye were smaller and the durations were longer than those of the right eye. However, both eyes reached their final positions required to fixate the second visual target at roughly the same time. The different dynamics of the two eyes is explained by the fact that each eye rotated temporally when the eyes converged, a pattern named binocular extension of Listing's law. Coming from or aiming at a common torsional value (normal ocular counter-roll) in convergent or divergent refixations, the required torsion differs in the two eyes. The brain compensates for these differences by adjusting the dynamics of each eye's movement.

Three-dimensional vestibular eye and head reflexes of the chameleon: characteristics of gain and phase and effects of eye position on orientation of ocular rotation axes during stimulation in yaw direction.

We investigated gaze-stabilizing reflexes in the chameleon using the three-dimensional search-coil technique. Animals were rotated sinusoidally around an earth-vertical axis under head-fixed and head-free conditions, in the dark and in the light. Gain, phase and the influence of eye position on vestibulo-ocular reflex rotation axes were studied. During head-restrained stimulation in the dark, vestibulo-ocular reflex gaze gains were low (0.1-0.3) and phase lead decreased with increasing frequencies (from 100 degrees at 0.04 Hz to < 30 degrees at 1 Hz). Gaze gains were larger during stimulation in the light (0.1-0.8) with a smaller phase lead (< 30 degrees) and were close to unity during the head-free conditions (around 0.6 in the dark, around 0.8 in the light) with small phase leads. These results confirm earlier findings that chameleons have a low vestibulo-ocular reflex gain during head-fixed conditions and stimulation in the dark and higher gains during head-free stimulation in the light. Vestibulo-ocular reflex eye rotation axes were roughly aligned with the head's rotation axis and did not systematically tilt when the animals were looking eccentrically, up- or downward (as predicted by Listing's Law). Therefore, vestibulo-ocular reflex responses in the chameleon follow a strategy, which optimally stabilizes the entire retinal images, a result previously found in non-human primates.

Combined influence of vergence and eye position on three-dimensional vestibulo-ocular reflex in the monkey.

This study examined two kinematical features of the rotational vestibulo-ocular reflex (VOR) of the monkey in near vision. First, is there an effect of eye position on the axes of eye rotation during yaw, pitch and roll head rotations when the eyes are converged to fixate near targets? Second, do the three-dimensional positions of the left and right eye during yaw and roll head rotations obey the binocular extension of Listing's law (L2), showing eye position planes that rotate temporally by a quarter as far as the angle of horizontal vergence? Animals fixated near visual targets requiring 17 or 8.5 degrees vergence and placed at straight ahead, 20 degrees up, down, left, or right during yaw, pitch, and roll head rotations at 1 Hz. The 17 degrees vergence experiments were performed both with and without a structured visual background, the 8.5 degrees vergence experiments with a visual background only. A 40 degrees horizontal change in eye position never influenced the axis of eye rotation produced by the VOR during pitch head rotation. Eye position did not affect the VOR eye rotation axes, which stayed aligned with the yaw and roll head rotation axes, when torsional gain was high. If torsional gain was low, eccentric eye positions produced yaw and roll VOR eye rotation axes that tilted somewhat in the directions predicted by Listing's law, i.e., with or opposite to gaze during yaw or roll. These findings were seen in both visual conditions and in both vergence experiments. During yaw and roll head rotations with a 40 degrees vertical change in gaze, torsional eye position followed on average the prediction of L2: the left eye showed counterclockwise (ex-) torsion in down gaze and clockwise (in-) torsion in up gaze and vice versa for the right eye. In other words, the left and right eye's position plane rotated temporally by about a quarter of the horizontal vergence angle. Our results indicate that torsional gain is the central mechanism by which the brain adjusts the retinal image stabilizing function of the VOR both in far and near vision and the three dimensional eye positions during yaw and roll head rotations in near vision follow on average the predictions of L2, a kinematic pattern that is maintained by the saccadic/quick phase system.

Responses of neurons in area VIP to self-induced and external visual motion.

Single-unit recordings were obtained from directionally tuned neurons in area VIP (ventral intraparietal) in two rhesus monkeys under conditions of external (passive) and self-induced (active) visual motion. A large majority of neurons showed significant differences in directional tuning for passive and active visual motion with regard to preferred direction and tuning width. The differences in preferred directions are homogeneously distributed between similar and opposite. Generally, VIP neurons are more broadly tuned to passive than to active visual motion. This is most striking for the group of cells with widely different preferred directions in active and passive conditions. Response amplitudes to passive and active visual motion are not different in general, but are slightly smaller for passive visual motion if the preferred directions differ widely. We conclude that VIP neurons can distinguish between passive and active visual motion.

Temporal properties of optic flow responses in the ventral intraparietal area.

The ventral intraparietal area (VIP) is located at the end of the dorsal stream. Its neurons are known to have receptive-field characteristics similar to those of MT and MST neurons, but little is known about the temporal characteristics of VIP cells' responses. How fast are directionally selective responses evoked in the ventral intraparietal area after viewing optic flow patterns, and what are the temporal properties of these neuronal responses? To examine these questions, we recorded the activity of 37 directionally selective ventral intraparietal area (VIP) neurons in two awake macaque monkeys in response to optic flow stimuli with presentation times ranging from 17 ms to 2000 ms. We found a minimum response latency of 45 ms, and a median latency of 152 ms. Of all neurons, 10% showed early response components only (response latency < 150 ms and no activity in 500-2000 ms interval after stimulus onset), 55% only late response components (response latency >150 ms and sustained activity in 500-2000 ms interval), and 35% both early and late response components. Early responses appeared to very brief stimulus presentations (33-ms duration), while the late responses required longer stimulus durations. The directional selectivity was independent of optic flow duration in all cells. These results suggest that only a subset of neurons in area VIP may contribute to the fast processing of optic flow, while showing that the temporal properties of VIP responses clearly differ from the temporal characteristics of neurons in areas MT and MST.

Geometrical properties of three-dimensional binocular eye position in light sleep.

We examined three-dimensional binocular positions in the alert and sleepy monkeys. In contrast to the tightly yoked eye movements observed in alertness, the eyes were usually converged, vertically misaligned and had a much larger torsional variability during light sleep. While in alertness eye position vectors were confined to fronto-parallel planes, the corresponding planes were rotated temporally (e.g. leftward for the left eye) in light sleep. There was no correlation between temporal rotation of the eye position planes and horizontal vergence. All these observations can be explained by randomly innervated extraocular muscles that are rotating the two eyes about anatomically determined axes.

Neural and mechanical factors in eye control.

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.

Stereopsis outweighs gravity in the control of the eyes.

The eyes are controlled by multiple brain circuits, some phylogenetically old and some new, whose aims may conflict. Old otolith reflexes counterroll the eyes when the head tilts relative to gravity. Newer vergence mechanisms coordinate the eyes to aid stereoptic vision. We show that counterroll hinders stereopsis, weakly when you look into the distance but strongly when you look near. The resolution of this conflict is that counterroll virtually vanishes when monkeys look close, i.e., stereopsis overrides gravity-driven reflexes but only on near gaze. This balance between gyroscopic and stereoptic mechanisms explains many other puzzling features of primate gaze control, such as the weakness of our otolith-ocular reflexes even during far viewing and the strange geometry of the primate counterpitch reflex, which rolls the eyes clockwise when monkeys look leftward while their heads are tipped nose up, but rolls them counterclockwise when the monkeys look rightward, and reverses this pattern when the head is tipped nose down.

Effect of light sleep on three-dimensional eye position in static roll and pitch.

We examined three-dimensional eye positions in alertness and light sleep when monkeys were placed in different roll and pitch body orientations. In alertness, eye positions were confined to a fronto-parallel (Listing's) plane, torsional variability was small and static roll or pitch induced a torsional shift or vertical rotation of these planes. In light sleep, the planes rotated temporally by about 10 degrees, torsional variability increased by a factor of two and the static otolith-ocular reflexes were reduced by about 70%. These data support the importance of a neural control of the thickness and orientation of Listing's plane, and suggest that part of the vestibular input underlying otolith-ocular reflexes depend on polysynaptic neural processing.

Torsional dynamics and cross-coupling in the human vestibulo-ocular reflex during active head rotation.

Six subjects fixated an imagined space-fixed target in darkness, or a visible target against a structured visual background, while rotating their heads actively in yaw, pitch and roll at four different frequencies, from 0.3 to 2.4 Hz. We used search coils to measure the 3-dimensional rotations of the head and eye, and described the relation between them--the input-output function of the rotational vestibulo-ocular reflex (VOR)--using gain matrices. We found consistent cross-coupling in which torsional head rotation evoked horizontal eye rotation. The reason may be that the eyes are above the axis of torsional head rotation, and therefore may translate horizontally during the head motion, so the VOR rotates them horizontally to compensate. Torsional gain was lower than horizontal or vertical, more variable from subject to subject and decreased at low frequencies. One reason for the low gain may be that torsional head rotation produces little retinal slip near the fovea; hence little compensatory eye motion is needed, and so the VOR reduces its torsional gain to save energy or to approximate Listing's law by keeping ocular torsion near zero. In addition, the human VOR has little experience with purely torsional head rotations and so its adaptive networks may be poorly trained for such stimuli. The drop in torsional gain at low frequencies can be explained based on the leak in the neural integrator that helps convert torsional eye-velocity commands into eye-position commands.

Three-dimensional vestibuloocular reflex of the monkey: optimal retinal image stabilization versus listing's law.

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 degrees 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.

Canal-otolith interactions after off-vertical axis rotations I. Spatial reorientation of horizontal vestibuloocular reflex.

We examined the three-dimensional (3-D) spatial orientation of postrotatory eye velocity after horizontal off-vertical axis rotations by varying the final body orientation with respect to gravity. Three rhesus monkeys were oriented in one of two positions before the onset of rotation: pitched 24 degrees nose-up or 90 degrees nose-up (supine) relative to the earth-horizontal plane and rotated at +/-60 degrees /s around the body-longitudinal axis. After 10 turns, the animals were stopped in 1 of 12 final positions separated by 30 degrees. An empirical analysis of the postrotatory responses showed that the resultant response plane remained space-invariant, i.e., accurately represented the actual head tilt plane at rotation stop. The alignment of the response vector with the spatial vertical was less complete. A complementary analysis, based on a 3-D model that implemented the spatial transformation and dynamic interaction of otolith and lateral semicircular canal signals, confirmed the empirical description of the spatial response. In addition, it allowed an estimation of the low-pass filter time constants in central otolith and semicircular canal pathways as well as the weighting ratio between direct and inertially transformed canal signals in the output. Our results support the hypothesis that the central vestibular system represents head velocity in gravity-centered coordinates by sensory integration of otolith and semicircular canal signals.

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.

Interaction of smooth pursuit and the vestibuloocular reflex in three dimensions.

1. What is the neural mechanism of vestibuloocular reflex (VOR) cancellation when a subject fixates a target moving with the head? One theory is that the moving target evokes pursuit eye movements that add to and cancel the VOR. A recent finding with implications for this theory is that eye velocity vectors of both pursuit and the VOR vary with eye position, but in different ways, because pursuit follows Listing's law whereas the VOR obeys a "half-Listing" strategy. As a result, pursuit cannot exactly cancel the VOR in most eye positions, and so the pursuit superposition theory predicts an eye-position-dependent pattern of residual eye velocities during cancellation. To test these predictions, we measured eye velocity vectors in humans during VOR, pursuit, and cancellation in response to torsional, vertical, and horizontal stimuli with the eyes in different positions. 2. For example, if a subject is rolling clockwise (CW, frequency 0.3 Hz, maximum speed 37.5 deg/s) while looking 20 deg up, the VOR generates an eye velocity that is mainly counterclockwise (CCW), but also leftward. If we then turn on a small target light, located 20 deg up and moving with the subject, then pursuit superposition predicts that the CCW component of eye velocity will shrink and the horizontal component will reverse, from leftward to rightward. This pattern was seen in all subjects. 3. Velocities depended on eye position in the predicted way; e.g., when subjects looked 20 deg down, instead of 20 deg up, during CW roll, the reversal of horizontal eye velocity went the other way, from rightward to leftward. And when gaze was 20 deg right or left, analogous reversals occurred in the vertical eye velocity, again as predicted. 4. Analogous predictions for horizontal and vertical stimulation were also borne out by the data. For example, when subjects rotated rightward while looking 20 deg up, the VOR response was leftward and CCW. When the target light switched on, the torsional component of the response reversed, becoming CW. And analogous predictions for other eye positions and for vertical stimulation also held. 5. For all axes of stimulation and all eye positions, eye velocity during cancellation was roughly parallel with the gaze line. This alignment is predicted by pursuit superposition and has the effect of reducing retinal image slip over the fovea. 6. The fact that the complex dependence of eye velocity on the stimulation axis and eye position predicted by pursuit superposition was seen in all subjects and conditions suggests strongly that the VOR indeed is canceled additively by pursuit. However, eye velocities during cancellation were consistently smaller than predicted. This shrinkage indicates that a second mechanism, besides pursuit superposition, attenuates eye velocities during cancellation. The results can be explained if VOR gain is reduced by approximately 30%, and if, in addition, pursuit is driven by retinal slip rather than reconstructed target velocity in space.

Effects of full-field visual input on the three-dimensional properties of the human vestibuloocular reflex.

The three-dimensional (3-D) properties if the vestibuloocular reflex (VOR) were studied in six normal human subjects during passive whole-body rotations in darkness and with full-field visual input in light. Subjects were asked to fixate a point target stationary in space straight ahead or to imagine such a target in darkness. Using a 3-D rotating chair, subjects were rotated sinusoidally (frequency .3 Hz, maximum speed 37.5 degrees/s) about an earth-vertical axis for horizontal stimulation and about an earth-horizontal axis for vertical and torsional stimulation. The subject faced forward for vertical stimulation, 90 degrees to the side for torsional stimulation, or 15 degrees to the right or left side for combined vertical and torsional stimulation. Left eye position was measured using 3-D search coils. The VOR response was quantified using the 3-D analogue of gain, a 3 x 3 matrix where each element describes the dependence of one component--torsional, vertical, or horizontal--of eye velocity on one component of head velocity. Average gain matrices were calculated for three cycles of rotation (10 s). Major findings were: (1) Gain values for the VOR were higher in light than in darkness for all directions. In light, vertical and horizontal responses were fully compensatory in both magnitude and direction, whereas the torsional responses were still weak. (2) Intersubject variability, large in the dark, was very small in the light for the vertical and horizontal responses but still considerable for the torsional.(ABSTRACT TRUNCATED AT 250 WORDS)

The influence of gravity on Donders' law for head movements.

Three-dimensional (3-D) head rotations were examined in seven human subjects when their bodies were inclined +/- 45 degrees in pitch and roll. The selection of 3-D orientations of the head while subjects looked at visual targets was similar to that seen previously for the eye: there was a small static counter pitch and counter roll of approx. 10%. Thus rotations of the head relative to the trunk are largely independent of the trunk's position relative to gravity and the head's torsional orientation is primarily dependent on its horizontal and vertical position relative to the trunk.

Rotational kinematics of the human vestibuloocular reflex. II. Velocity steps.

1. Gain matrices were used to quantify the three-dimensional vestibuloocular reflex (VOR) in five human subjects who were accelerated over 1 s and then spun at a constant 150 degrees/s for 29 s in darkness. Rotations were torsional, vertical and horizontal, about earth-vertical and earth-horizontal axes. 2. Elements on the main diagonal of the gain matrices were much smaller than the optimal value of -1, and torsional gain was weaker than vertical or horizontal. Off-diagonal elements, indicating cross talk, were minimal except for a small but consistent horizontal response to torsional head rotation. 3. Downward slow phases were more than twice as fast as upward at the start of rotation about both earth-vertical and earth-horizontal axes, but the asymmetry vanished later in the rotation. 4. During earth-vertical-axis rotation, all matrix elements decayed to zero. The main-diagonal torsional and vertical gains waned with time constants close to that of the cupula (6.7 and 7.3 s). Velocity storage prolonged the horizontal response to horizontal head rotation (time constant 14.2 s) but not the horizontal response to torsion (7.7 s). A simple explanation is that velocity storage acts on a central estimate of head motion that accurately distinguishes horizontal from torsional and that the inappropriate horizontal eye velocity response to torsion occurs because of cross talk downstream from velocity storage. 5. During earth-horizontal-axis rotation, the torsional, vertical, and horizontal main-diagonal elements declined, with time constants of 7.6, 8.2, and 7.9 s, to maintained nonzero values, all equal to about -0.1. Off-diagonal elements, including the horizontal response to torsion, decayed to zero, so that the otolith-driven reflex, late in the rotation, was equally strong in all dimensions and almost free of detectable cross talk. 6. The difference between gain curves over the course of earth-vertical- and earth-horizontal-axis rotations was not constant but increased with time, suggesting that the VOR response to earth-horizontal-axis rotation is not a simple sum of canal and otolith reflexes.

Rotational kinematics of the human vestibuloocular reflex. I. Gain matrices.

1. This series of three papers aims to describe the three-dimensional, kinematic input-output relations of the rotational vestibuloocular reflex (VOR) in humans, and to identify the functional advantages of these relations. In this first paper the response to sinusoidal rotation in darkness at 0.3 Hz, maximum speed 37.5%/s, was quantified by the use of the three-dimensional analogue of VOR gain: a 3 x 3 matrix where each element describes the dependence of one component (torsional, vertical, or horizontal) of eye velocity on one component of head velocity. 2. The three matrix elements indicating collinear gains (i.e., dependence of torsional eye velocity on torsional head velocity, vertical on vertical, and horizontal on horizontal) were smaller than the -1's required for optimal retinal image stabilization. Of these three the torsional gain was weakest: -0.37 for rotation about an earth-vertical axis, versus -0.73 and -0.64 for vertical and horizontal gains. Matrix elements indicating cross talk were mostly negligible. There was a tendency to leftward eye rotation in response to clockwise head motion, but this was not statistically significant. 3. VOR responses were compared for rotation about earth-vertical and earth-horizontal axes. The varying otolith input due to the rotation of the gravity vector relative to the head during earth-horizontal axis rotation made no difference to the collinear gains. 4. There were no consistent phase leads or lags except for a torsional phase lead of up to 10 degrees, usually more marked for clock-wise head rotation versus counterclockwise, and for oblique axis rotations versus purely torsional. 5. Torsional gain was magnified, averaging -0.52, when the torsional component of head rotation was only a small part of a predominantly vertical or horizontal rotation, i.e., when the axis of head rotation was near the frontal plane. Because most natural head rotations occur about such axes, the torsional VOR is probably somewhat stronger than the response to pure torsion would suggest. 6. The speed of eye rotation in response to a given stimulus varied widely among subjects, but the direction of rotation was much more uniform. For head rotations about oblique axes out of the frontal plane, there was a systematic misalignment of eye and head axes, with eye axes tilted toward the frontal plane. These findings can be explained on the basis of a strategy where the VOR balances the muscular effort of rotating the eyes against the cost of retinal slip.