December 2007
Volume 48, Issue 12
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Eye Movements, Strabismus, Amblyopia and Neuro-ophthalmology  |   December 2007
Unilateral Deafferentation and Eye Position Misdirect the Initial Vestibulo-ocular Reflex: A Model-Based Study
Author Affiliations
  • Benjamin T. Crane
    From the Department of Surgery (Division of Otolaryngology/Head and Neck Surgery), the
    Department of Ophthalmology and Jules Stein Institute, and
  • Junru Tian
    Department of Ophthalmology and Jules Stein Institute, and
  • Akira Ishiyama
    From the Department of Surgery (Division of Otolaryngology/Head and Neck Surgery), the
  • Joseph L. Demer
    Department of Ophthalmology and Jules Stein Institute, and
    Departments of Neurology,
    Bioengineering, and
    Neuroscience Interdepartmental Programs, University of California, Los Angeles, California.
Investigative Ophthalmology & Visual Science December 2007, Vol.48, 5512-5522. doi:10.1167/iovs.07-0784
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      Benjamin T. Crane, Junru Tian, Akira Ishiyama, Joseph L. Demer; Unilateral Deafferentation and Eye Position Misdirect the Initial Vestibulo-ocular Reflex: A Model-Based Study. Invest. Ophthalmol. Vis. Sci. 2007;48(12):5512-5522. doi: 10.1167/iovs.07-0784.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

purpose. Orbital eye position and vestibular sensitivity have both been postulated to influence vestibulo-ocular reflex (VOR) axis direction. The interaction of these factors in unilateral vestibular deafferentation (UVD) was examined.

methods. Initial VOR direction and magnitude were examined in six normal human subjects and five with UVD during transient whole-body yaw at 2800 deg/s2. The effect of eye position was evaluated by computing the tilt angle ratio (TAR), the ratio of change in VOR axis orientation relative to change in target direction for targets 20° up or down.

results. Gain during the initial 50 ms in UVD subjects was 0.66 ± 0.13 (mean ± SD) during contralesional, and 0.30 ± 0.16 during ipsilesional rotation, but 0.87 ± 0.02 in normal control subjects. In control subjects VOR axis direction was independent of stimulus direction. During ipsilesional rotation, subjects with UVD had a significant (P < 0.01) initial forward VOR axis tilt relative to contralesional rotation averaging 9.5 ± 4.9°, which was evident 20 ms after rotation. Initial TAR was 0.18 ± 0.08 in control subjects and 0.32 ± 0.08 in subjects with UVD. Since Listing’s Law (LL) requires 0.5 TAR, whereas a VOR axis perfectly aligned with head axis requires 0, the observed intermediate TAR implies a compromise between the two criteria. In the interval 150 to 200 ms after rotation onset, subjects with UVD had 0.21 ± 0.06 TAR during contralesional rotation and 0.50 ± 0.11 during ipsilesional rotation, suggesting late synergy between the VOR and visual pursuit.

conclusions. A vector-based model accounts for observed axis tilt based on semicircular canal directional sensitivity and response saturation. Overall, the deviating effect of eye position on VOR axis is not influenced by UVD, but canal nonlinearity and geometric orientation account for the additional VOR axis error.

Performance of the vestibulo-ocular reflex (VOR) has classically been characterized by its gain: evoked eye velocity divided by the stimulus head velocity. 1 2 3 Measurement of VOR gain in response to a rapid yaw head rotation has proven valuable for diagnosis of vestibular lesions, whether the stimulus is delivered manually 3 or mechanically. 2 4 Gain is nevertheless a one-dimensional parameter that incompletely describes the VOR. Although two-dimensional (2-D) eye rotations suffice to stabilize an image on the fovea, to do so over the entire retina requires a VOR accurate in all three angular dimensions (3-D). 5 6  
In normal subjects viewing straight ahead, the VOR axis closely aligns with the axis of sinusoidal head rotation in monkeys 7 and humans. 6 Axis alignment within 5° has also been demonstrated during manually delivered head rotations at accelerations up to 4000 deg/s2 in normal humans. 5 However, significant axis shifts are observed after unilateral deafferentation (UVD) with high-acceleration stimuli. 8 After UVD the VOR axes were not reported to differ significantly between ipsi- and contralesional rotation for the initial 50 ms of the VOR in response to transient, manually delivered head rotation, but later the axis shifted forward so that misalignment from the head axis during ipsilesional rotation approached 70° by 100 ms. 8 It is puzzling that the VOR axis did not depend on the direction of rotation during the first 50 ms, since VOR gain asymmetry after UVD is evident within the initial 10 ms. 2 Manually delivered head rotations typically have small amplitude. The large axis shifts that occurred 80 ms and more after small, manually delivered head rotations are difficult to extrapolate to larger amplitude rotations. For example, persistent misalignment of eye and head axes of 70° would result, after only a short time, in extreme gaze errors or corrective saccades. Prior manually delivered yaw VOR axis determinations may have been confounded by introduction of concurrent pitch and roll due to neck mechanics, unintended otolith stimulation, and variability in head rotations. 9 10  
When the head is upright and stationary, eye movements are governed by Listings Law (LL), which constrains ocular torsion to a unique value for each combination of horizontal and vertical eye position. 11 12 The familiar position domain formulation of LL states that any eye position may be reached from a primary position by rotation about a single axis located in Listing’s plane (LP). A second, equivalent formulation of LL is expressed in the velocity domain and requires that the ocular velocity axis change by half the angle of eye position change. 13 The VOR is a notable violator of LL, since head rotation is not constrained to any particular axis, and ocular rotation ideally must parallel the axis of head rotation in 3-D to stabilize images on the retina. 7 14  
Even though matching of the VOR axis to the axis of head rotation would be visually optimal, several studies have reported that the normal human angular VOR compromises between LL and the axis of head rotation. 9 10 15 16 17 18 The general finding has been that regardless of the orientation of the head axis relative to LP, the VOR velocity axis is influenced by eye position in the orbit. The change in VOR velocity axis is less than half the change in ocular angle dictated by LL, motivating description of the VOR as observing a “half-Listing’s strategy” or “quarter angle” rule. 9 10 16 17 18 Contradictory reports have claimed that the normal VOR closely follows the head axis, 5 6 although these reports deal with nearly central eye positions for which minimal axis tilt is predicted. 
Despite the controversies, it appears that at least two factors affect the VOR axis: peripheral vestibular lesions, 8 and eye position in the orbit. 9 10 17 18 Possible interaction of these factors in UVD has not been explored. 
To clarify this question, we used a whole-body, mechanical rotation to avoid the potentially confounding effects of otolith stimulation and neck mechanics in studying the effects of ocular position and UVD on VOR axis. We developed an analytic model to explain the origin and variation in the VOR axis after UVD, and its interaction with eye position in the orbit. 
Methods
Subjects
Subjects were paid volunteers who consented to the experiments, according to a protocol approved by the local institutional review board in conformity with the tenets of the Declaration of Helsinki. Subjects underwent ophthalmic examination to verify that they were free of ocular disease and would be able to focus targets clearly, with corrective lenses as necessary. Subjects were monitored during experiments via infrared closed-circuit television and with a duplex intercom. 
The control group consisted of six healthy women (average age, 23 ± 3 years [mean ± SD]; range, 21–29). The group with UVD consisted of two men and three women (average age, 54 ± 14 years; range, 35–74). Deafferentation affected the left side in three subjects and the right side in the other two. Labyrinthectomy was performed in four of the subjects (two during acoustic neuroma resection and two for Ménière’s disease). The remaining subject had a right acoustic neuroma resected via a suboccipital approach involving sacrifice of the eighth cranial nerve. All subjects with UVD had absent ipsilesional caloric responses. Vestibular deafferentation was completed an average of 6 ± 4 years (range, 5 months to 12 years) before testing. 
Apparatus
Binocular eye and head angular positions were measured with dual winding scleral magnetic search coils (Skalar Medical, Delft, The Netherlands), 19 as used by other investigators 20 and in the current laboratory. 2 Reference magnetic fields were generated by three pairs of solenoid coils, each 2 m in diameter, and arranged to form the sides of a cube (C-N-C Engineering, Seattle, WA) with its center near eye level. The two vertically oriented coil pairs were driven by 60-kHz sinusoidal currents in phase quadrature. 19 The horizontally oriented coil pair was driven by a 120-kHz sinusoidal current. 21 Dual-winding scleral magnetic search coil annuli were placed on both eyes of every control subject and of three of the five subjects with UVD. The remaining two subjects with UVD wore a dual-winding scleral coil on only one eye. All coils were placed under topical anesthesia with proparacaine 0.5%. Angular head position was measured via dual search coils mounted on a bite bar molded to the upper teeth so that they were rigidly coupled to skull motion. Search coils were connected to external detectors (C-N-C Engineering, Seattle, WA). Horizontal, vertical, and torsional gaze and head positions were displayed on a digital polygraph and low-pass filtered over a 300-Hz bandwidth (4-pole Butterworth) before digital sampling with 16-bit precision at 1.2 kHz. Subjects were rotated by a 500 N-m stepper motor (Compumotor, Rohnert Park, CA), as previously described. 2  
Measurement Conditions
During each trial, subjects sat with the head comfortably upright in nonmetallic chair as previously described. 2 The chair was fitted with dense foam cushions. Lap and chest belts, as well as padded clamps secured each subject over the knees and feet to prevent decoupled body motion. The head was held firmly within a nonmetallic head holder that provided adjustable pressure support via foam-padded clamps to the forehead, vertex, occiput, malar eminences, and mental promontory. Every rotational trial was preceded by a 2-second baseline determination recording in which the stationary subject looked directly at centered target 175 cm away. In 60 seconds recordings LP was defined for each eye as subjects tracked the movements of a laser target on a tangent screen 175 cm away. During such recordings the laser spot moved radially with a sinusoidal velocity peaking at 60 deg/s and an amplitude of 30° relative to central position. 
The angular VOR was tested during 50-second trials that included 20 directionally unpredictable transient yaw rotations (10 in each direction). During each trial, subjects viewed a target located at eye level, ∼20° up, or ∼20° down. Each target consisted of a laser dot against a dark background in an otherwise dark room. Subjects were instructed to maintain gaze on the target at all times. Rotation onsets varied randomly from periodic by ≤250 ms, and stimulus direction was randomized to avoid prediction. Subjects returned to center after each rotation. 
Head position was adjusted so that the rotational axis was midway between the external auditory canals, which were ∼7 cm posterior to the eyes. This axis was chosen to minimize the translational stimulus to the otoliths. Rotations had a peak acceleration of 2800 deg/s2 to a velocity of 190 deg/s, moving the head 40° in 250 ms, which was the time peak velocity occurred. At 300 ms, the velocity averaged 150 deg/s. The head moved to its maximum offset of 55° after 550 ms. 
Data Analysis
Data were analyzed automatically (LabView ver. 7.1; National Instruments, Austin, TX on a Macintosh G5; Apple, Cupertino, CA). For each subject, rotational transients were grouped based on direction of rotation and starting eye position. Transient rotations in which eye position varied by >0.2° in the 80 ms before rotation were discarded as failures of fixation. For study of the early slow phase VOR, events were also discarded when there were saccades or blink artifact within 70 ms of the onset of head rotation. Less than 10% of trials had to be removed because of such artifacts, and most trials from all 11 subjects could be analyzed during this early period. All subjects with UVD and several control subjects typically introduced a saccade 80 to 200 ms after rotation onset. 
Sampled search coil voltages were corrected for misalignment of the sine nonlinearity in the pitch axis of the search coil system. Fick angles were converted to rotation matrices, as previously described. 14 22 Data from LP definition and VOR trials were first corrected for presumed imperfect alignment of coils on the eye using central eye position data collected in the immediately preceding reference trial, as previously described. 18 Eye position data were then expressed as quaternions in a coordinate system aligned to LP. 
Velocity vectors for eye and head were computed from quaternion positions (q) and derivatives (dq/dt) as previously described. 17 18 22 23 Eye and head rotations were also examined in the velocity domain. The tilt angle of the velocity vector out of LP, φ (in the approximately sagittal plane perpendicular to LP), was determined using the horizontal (h) and torsional (t) components of velocity, as previously described. 17 18  
Linear regression was used to calculate the tilt of the velocity axis in the sagittal plane, φ, relative to vertical eye position. Linear regression was performed on data sets obtained from three similar testing conditions: when starting eye position was central, up, and down. Each regression was repeated every 800 μs from 40 ms before the onset of head motion to 400 ms after the onset of head rotation. In previous analysis of this type, data points were removed when more than 2 SD from the initial fit. 18 This exclusion was unnecessary for the current data, as accurate slopes could be calculated in all but one subject using entire data sets. Because of an unusual noise artifact precluding accurate regression in one subject with UVD, regression data for this subject was excluded from analysis. 
Gain of the VOR was determined in the velocity domain by dividing eye by head velocity during only the first 60 ms of head rotation. Gain calculated after this time is often confounded by abrupt decelerations and rapid eye movements, such as catch-up saccades. 
Model
A model of VOR velocity axis tilt was developed by using vectors to represent eye and head velocities. 24 An orientation of the labyrinth in Fick pitch (φ), yaw (θ), and roll (ψ) was assumed and used to create a rotation matrix, as previously described 14 :  
\[{[}\ \begin{array}{cc}\mathrm{cos}({\phi})\mathrm{cos}({\theta})&\mathrm{{-}cos}({\psi})\mathrm{sin}({\theta}){+}\mathrm{sin}({\psi})\mathrm{sin}({\phi})\mathrm{cos}({\theta})\\\mathrm{cos}({\phi})\mathrm{sin}({\theta})&\mathrm{cos}({\psi})\mathrm{cos}({\theta}){+}\mathrm{sin}({\psi})\mathrm{sin}({\phi})\mathrm{cos}({\theta})\\\mathrm{{-}sin}({\phi})&\mathrm{sin}({\psi})\mathrm{cos}({\phi})\end{array}\ \begin{array}{c}\mathrm{sin}({\psi})\mathrm{sin}({\theta}){+}\mathrm{cos}({\psi})\mathrm{sin}({\phi})\mathrm{cos}({\theta})\\\mathrm{{-}sin}({\psi})\mathrm{cos}({\theta}){+}\mathrm{cos}({\psi})\mathrm{sin}({\phi})\mathrm{sin}({\theta})\\\mathrm{cos}({\psi})\mathrm{cos}({\phi})\end{array}{]}.\]
 
Because an earth vertical yaw axis was used, the last column of the rotation matrix can be taken as a vector describing the fraction of the stimulus projected onto each of the three semicircular canals. Torsional orientation of the labyrinth in the skull (ψ) was assumed to be 0, and the three semicircular canals of each labyrinth orthogonal to each other, consistent with anatomic data. 25 26 Making these assumptions, equation 1simplifies to:  
\[{[}\ \begin{array}{ccc}\mathrm{cos}({\phi})\mathrm{cos}({\theta})&\mathrm{{-}sin}({\theta})&\mathrm{sin}({\phi})\mathrm{cos}({\theta})\\\mathrm{cos}({\phi})\mathrm{sin}({\theta})&\mathrm{cos}({\theta})&\mathrm{sin}({\phi})\mathrm{sin}({\theta})\\\mathrm{{-}sin}({\phi})&0&\mathrm{cos}({\phi})\end{array}{]}.\]
We can then multiply equation 2by the head-velocity vector to yield the head velocity in each of the canal planes:  
\[{[}\ \begin{array}{c}{\dot{H}}_{t}\\{\dot{H}}_{h}\\{\dot{H}}_{v}\end{array}{]}\ {[}\ \begin{array}{ccc}\mathrm{cos}({\phi})\mathrm{cos}({\theta})&\mathrm{{-}sin}({\theta})&\mathrm{sin}({\phi})\mathrm{cos}({\theta})\\\mathrm{cos}({\phi})\mathrm{sin}({\theta})&\mathrm{cos}({\theta})&\mathrm{sin}({\phi})\mathrm{sin}({\theta})\\\mathrm{{-}sin}({\phi})&0&\mathrm{cos}({\phi})\end{array}{]}.\]
The head-velocity vector has components in each of three axes. Because the stimulus in the current experiment was purely yaw, the head-velocity vector has only one nonzero component corresponding to the vertical axis, v , whereas torsional ( t ) and horizontal ( h ) components remain zero. Because the labyrinth is fixed in the head, the-velocity vector experienced by the canals (Ċ) must be the same as that of the head (), except that a different coordinate system is used to reflect the labyrinth orientation in the head. Canal velocity (Ċ) can be expressed as three orthogonal components responding to the horizontal (Ċ HC ), superior (Ċ SC ), and posterior (Ċ PC ) canals. 24 When the head rotates about a vertical axis at an angular velocity v , the velocity reported by each canal is given by:  
\[{[}\ \begin{array}{c}{\dot{C}}_{SC}\\{\dot{C}}_{PC}\\{\dot{C}}_{HC}\end{array}{]}{=}{[}\ \begin{array}{c}0\\0\\{\dot{H}}_{v}\end{array}{]}\ {[}\ \begin{array}{ccc}\mathrm{cos}({\phi})\mathrm{cos}({\theta})&\mathrm{{-}sin}({\theta})&\mathrm{sin}({\phi})\mathrm{cos}({\theta})\\\mathrm{cos}({\phi})\mathrm{sin}({\theta})&\mathrm{cos}({\theta})&\mathrm{sin}({\phi})\mathrm{sin}({\theta})\\\mathrm{{-}sin}({\phi})&0&\mathrm{cos}({\phi})\end{array}{]}{=}{[}\ \begin{array}{c}{\dot{H}}_{v}\mathrm{sin}({\phi})\mathrm{cos}({\theta})\\{\dot{H}}_{v}\mathrm{sin}({\phi})\mathrm{sin}({\theta})\\{\dot{H}}_{v}\mathrm{cos}({\phi})\end{array}{]}.\]
 
The head-velocity vector reported by the labyrinths combines orthogonal components corresponding to each semicircular canal. The compensatory eye-velocity vector that could be generated by an ideal VOR is equal and opposite the head-velocity vector, as sensed by the canals. 
In normal subjects, it is assumed that the velocity encoded by each canal is proportional to the head velocity projected onto the plane of that canal. Left and right canals are oriented into nearly coplanar pairs projecting centrally in push–pull fashion. If each canal could accurately encode its rotation, eye velocity could be neurally commanded to be opposite head velocity, and the VOR would be ideal, or could be commanded to vary from an ideal direction as a function of eye position, for example. However, after UVD, the remaining canals exhibit nonlinear inhibitory saturation during ipsilesional rotation (Ewald’s second law), and thus fail to encode accurately the high ipsilesional head velocity. 3 To model this effect ,we specified a maximum angular velocity Ċmax that can be encoded by each canal. The component of rotation velocity in each canal plane (Ċ HC , Ċ SC , and Ċ PC ) is calculated as shown in equation 4 . If any component exceeds Ċmax, it is replaced with Ċmax. We assumed that the V max for each canal (Ċmax) is the same as VOR slow-phase velocity recorded during ipsilesional yaw. The simulated VOR eye-velocity vector was calculated by negating the clipped canal components (since the ideal eye velocity is equal and opposite to head velocity sensed by the canals) and transferring them back into head coordinates. 
Experimental data from subjects with UVD were fitted to the model by using the observed VOR gain and ocular axis tilt in central eye position. Gain asymmetry was calculated by dividing gain during ipsilesional rotation by gain during contralesional rotation. The observed gain asymmetry and direction specific ocular axis tilts were used to fit the experimental data to the model. The Ċmax was varied as a percentage of head velocity until a single labyrinth orientation was found that best accounted for observed gain asymmetry and ocular axis tilt. 
Results
Listing’s Plane
Orientation and thickness of LP were measured in each subject by recording eye positions as quaternions during 60 seconds of visual pursuit that covered ±30° horizontal and vertical range in a systematic raster. Orientation of LP varied between eyes of individual subjects and among subjects. The top of LP was tilted 6 ± 6° backward relative to earth vertical in the right eye and −4 ± 12° in the left (mean ± SD) in normal subjects. In subjects with UVD, the top of LP was tilted backward 11 ± 8° in the right eye and 9 ± 11° in the left eye. In control subjects, LP was inclined nasally 8 ± 5° in the right and 26 ± 14° in the left eye. In subjects with UVD, LP was inclined nasally 17 ± 5° in the right eye and 18 ± 5° in the left eye. Control and UVD groups had significantly different LP orientations (P < 0.01) only for the right eye in yaw and left eye in pitch. The thickness of LP was similar in both groups: 1.3 ± 0.5° in control subjects and 1.5 ± 0.6° in subjects with UVD (P = 0.45). 
VOR Gain
Yaw components of eye and head velocity were evaluated quantitatively. In normal subjects, there was no significant directional asymmetry in the VOR. In subjects with UVD, eye velocity in response to ipsilesional rotation was significantly decreased compared with the response to contralesional rotation (Fig. 1) . Because the eye and head velocity varied with time, performance was quantified over an interval as a scalar VOR gain (yaw component eye velocity/yaw component of head velocity). In subjects with UVD, there were rapid eye movements such as abrupt decelerations and catch-up saccades evident as early as 60 ms after the onset of head rotation, but more commonly in the 80 to 120 ms interval. To avoid including these rapid eye movements in gain calculation, analysis of VOR gain was limited to the initial 50 ms of the VOR (Fig. 2) . Gain during these first 50 ms remained approximately constant in control subjects at 0.87 ± 0.02 (mean ± SD, range 0.85–0.90). In subjects with UVD, gain varied more, averaging 0.66 ± 0.13 (range, 0.48–0.83) during contralesional rotation, and significantly lower at 0.30 ± 0.16 (range, 0.06–0.43) during ipsilesional rotation. Mean gain was significantly subnormal in subjects with UVD for both ipsi- and contralesional rotation (P < 0.01). 
VOR Axis Shift Due to Vestibular Deafferentation
Orientation of the ocular velocity axis was determined every 800 μs throughout each response after digitally low-pass filtering the data at 40 Hz. In subjects with UVD, the VOR axis during the first 50 ms of the rotation was tilted top end forward during ipsilesional rotation relative to the axis during contralesional rotation (Fig. 3) . The VOR rotational axis is only definable when the eye is rotating at a speed significantly exceeding measurement noise. Thus, VOR axis was undefined before 10 ms from onset of head rotation, the latency of the first VOR eye movement. However, by 20 ms the VOR exhibited a well-defined axis that was significantly different during ipsi- versus contralesional rotation (Fig. 3C) . After 60 ms, there were quick phase eye movements that often altered the VOR axis. These later effects are beyond the scope of the current analysis, so discussion of the axis tilt is limited to the first 50 ms of the VOR. In control subjects, the axes of the eye and head aligned within a few degrees, and did not depend significantly on direction of rotation (P > 0.1). During the first 50 ms of the VOR, the difference in VOR axis tilt between right and left rotations was near zero, with an absolute difference of 1.9 ± 1.7° (mean ± SD; range, 0.2–4.9; Fig. 4 ). However, all subjects with UVD had a significant forward tilt in the ocular axis during ipsilesional rotation averaging 9.5 ± 4.9° (mean ± SD; range, 2.7–13.7, P < 0.01; Fig. 4 ) relative to contralesional rotation. 
VOR Axis Shift with Eccentric Eye Positions
The VOR was examined in three eye positions: straight ahead (0°), 20° up, and 20° down. Ocular velocity axis orientation was calculated as a function of time as described in the Methods section (Fig. 5) . The VOR axis was similarly influenced by eye position in control subjects and subjects with UVD. In all subjects, the VOR axis shifted backward in up gaze and forward in down gaze. The forward tilt of the VOR axis during ipsilesional rotation in subjects with UVD was maintained in eccentric vertical eye positions and was superimposed on a eye-position–dependent axis tilt (Fig. 5)
The tilt angle ratio (TAR) was quantified for each subject by examining VOR axis orientation as a function of vertical eye position for the three targets (Fig. 6) . A major advantage of the mechanically delivered stimulus was high repeatability of the imposed head motion. The TAR was calculated at 800-μs intervals throughout the rotation. By performing linear regressions for each sampled time point in multiple rotations for each individual subject, a coefficient of determination could be calculated that was associated with the TAR value at each time point as an indication of the TAR value’s reliability and that represented the fraction of axis direction variability attributable to orbital eye position (Fig. 7) . Coefficients of determination were low early in the response, reflecting greater uncertainty in VOR axis orientation, but these coefficients increased later due to greater head and eye velocities. In one subject with UVD, the TAR could not be accurately determined during ipsilesional rotation, although during contralesional rotation, the TAR was similar to that of other subjects with UVD. The indeterminate TAR during ipsilesional rotation in this subject reflected low VOR gain, giving a low-amplitude slow phase whose rotational axis was indeterminate. Data from this subject were excluded from this portion of the analysis. 
One purpose of this study was to determine whether the TAR differed during ipsi- versus contralesional rotation. In individual subjects with UVD, there were often short periods when the TAR appeared to depend on the direction of rotation, although these tended to be early in the response when the coefficient of determination was low (Fig. 7) . This question was addressed further by examining aggregate data from all subjects. The data was grouped into three periods: an initial response in the first 50 ms, 50 to 100 ms, and 150 to 200 ms (Fig. 8)
During the initial 50 ms, the mean TAR of control subjects was 0.18 ± 0.08 (mean ± SD; range, 0.08–0.27; Fig. 8A ) with no significant effect of rotation direction (P > 0.05). During this same period, the TAR of subjects with UVD was 0.34 ± 0.08 (range, 0.24–0.41) for ipsilesional and 0.30 ± 0.07 for contralesional rotation (range, 0.20–0.36). The TARs for ipsi- and contralesional rotation were not significantly different during the initial 50 ms (P > 0.10), nor were differences from control values significant (P = 0.06). 
During the later 50- to 100-ms epoch, the mean TAR of control subjects was 0.32 ± 0.08 (range, 0.18–0.38), irrespective of rotation direction (P > 0.10), but significantly greater than the TAR observed during the first 50 ms (P < 0.01). During the 50- to 100-ms epoch, subjects with UVD also demonstrated a significant (P < 0.01) increase in the TAR to 0.45 ± 0.09 (range, 0.41–0.51), with no significant effect of rotation direction (P > 0.1). 
The final epoch of 150–200 ms demonstrated the most variable responses. The mean TAR of control subjects was 0.38 ± 0.10 (range, 0.25–0.49), with individual values tending to cluster near the high and low ends of the range (Fig. 8E) , and again no significant effect of rotation direction. During the final epoch, the TAR of subjects with UVD was 0.21 ± 0.06 (mean ± SD, range 0.13–0.27) for contralesional rotation, significantly less (P < 0.01) than the mean TAR of 0.50 ± 0.11 for ipsilesional rotation (Fig. 8F)
Each epoch was evaluated to determine whether there was any difference in TAR between right versus left eye, or adduction for abduction for aggregate data in control subjects. No significant difference was found (P > 0.05 for each condition). In UVD this relationship was difficult to evaluate, because in several subjects only monocular recordings could be made. 
Discussion
Orbital eye position and vestibular sensitivity have both been postulated to influence VOR axis direction. This study examined the interaction of these factors, using UVD as a model incorporating selectively reduced vestibular sensitivity under some but not all rotational conditions in which orbital eye position could be identically varied. Although the absent caloric vestibular responses recorded in the current subjects do not by themselves assure complete absence of vestibular input at high frequencies and accelerations, 27 absent calorics in the setting of known surgical deafferentation may be regarded as reliable indicators of complete UVD. 
VOR Gain
It is widely recognized that in UVD, the VOR is more severely impaired during high acceleration in ipsilesional than in contralesional head rotation. 2 3 4 8 The present study confirmed this asymmetry, but further demonstrated an approximately 25% reduction in contralesional VOR gain compared with the current younger control subjects and a 15% reduction compared with similarly aged, normal elderly subjects tested by Tian et al. 28 using the identical stimulus. 28 This finding suggests that UVD significantly impairs the VOR even for contralesional rotation. 
Early VOR gain varied only approximately 5% among control subjects during the initial 50 ms. Subjects with chronic, uncomplicated surgical UVD exhibited much wider variation in initial VOR gain. These results suggest that the VOR gain of normal subjects is adapted to an optimal value unattainable in UVD, even for contralesional rotation, perhaps due to ablated sensory input 4 or compensatory mechanisms. 14  
VOR Axis Shift Due to Vestibular Deafferentation
Current methods were sensitive to subtle changes in early VOR axis. The whole-body rotator attained high stimulus repeatability about a fixed axis, avoiding variations in head axis due to neck mechanics and proprioception. 2 Multiple trials were averaged without additional stimulus variability and were analyzed with precise time alignment for various viewing and rotational conditions. 
Forward shift in VOR axis during ipsilesional rotation has been reported by Aw et al. 8 in human UVD during manually delivered head-on-body rotation with 3000 to 4000 deg/s2 peak acceleration, 200 deg/s peak velocity, and 10 to 20° displacement. 8 Although stimulus intensity was comparable to the present study, Aw et al. 8 observed abnormal VOR axis behavior only 50 or more ms after head rotation onset. The present study found abnormal VOR axis during ipsilesional rotation in UVD as early as 10 ms after head rotation onset in some subjects (Fig. 3A) , significant over all subjects by 20 ms (Figs. 3B 3C) . This time is similar to the latency of ipsi- versus contralesional gain differences in UVD, 2 and basic VOR latency itself. 29 30 In UVD, VOR gain and axis direction might be expected to covary. The different finding of Aw et al. 8 may arise from a poorly defined VOR axis direction in the first milliseconds when eye and head rotations are small relative to measurement noise. This problem may have been compounded by manually delivered head rotation, which typically includes unintended torsion due to neck mechanics. 10  
In the current study, we found a <15° VOR axis shift in every subject with UVD during the initial 50 ms of rotation (Fig. 4)and the maximum shift within 60 ms. We observed no examples of larger VOR axis misalignments up to 75° reported 100 ms or more after the onset of manually delivered head on neck rotations. Perhaps these large shifts were not observed in the present study because feedback from the continuously visible target corrected the late VOR axis. 8 The angular displacement used in the present study was also much larger than is possible for head-on-body rotation. Within the oculomotor range, large axis shifts may be physically possible only for small rotations, where the kinematic consequences would remain small. 
Ocular Axis with Eccentric Eye Positions
During pursuit and saccades with the head upright and stationary, ocular axis depends on orbital eye position as specified by LL, which dictates that the ocular velocity axis shifts by half the angle of eye position. 13 During the present study, conformity to LL was established in all subjects by measuring the thickness of LP, which was similar in control and subjects with UVD. Theoretically, optimal VOR performance requires that the ocular axis match the head axis. 7 The VOR generally violates LL in a compromise between LL and the visually optimal performance of colinear eye and head axes. Observed VOR velocity axis varies by roughly a quarter of the orbital eye position change. 9 17 18  
A current goal was to determine whether quarter-angle VOR axis dependence occurs in UVD and whether it interacts with ipsi- versus contralesional VOR axis shifts. Eye movements conforming to LL would have a TAR of 0.5, 18 but an optimal VOR would have 0 TAR. The TAR in control subjects and in those with UVD was similar, within the range previously observed during high-acceleration whole-body 18 and manual head rotations 9 15 and less than 0.5. The VOR’s dependence on orbital eye position in UVD is thus normal. 
The time course of the VOR axis dependency on eye position has been inconsistently reported for manual head-on-neck rotations, with studies showing 0-angle behavior during the first 47 ms, 9 quarter angle after 40 ms, 15 or quarter angle behavior limited to lower velocity head thrusts. 10 During high-acceleration, whole-body rotation, results have been more consistent, with the latency of the eye position axis dependence near the 10 ms latency of the VOR itself. 18 Although low initial VOR amplitude in UVD precluded determination of the exact latency of VOR axis shift, latency was less than 50 ms. 
Direction of the VOR axis varied with time in both control subjects and subjects with UVD. Unlike control subjects, however, subjects with UVD exhibited a late VOR axis dependence consistent with LL, 31 rather than the quarter-angle dependence 16 maintained by normal subjects. During the period 50 to 100 ms from head rotation onset, control subject TAR averaged 0.32, but 0.45 in subjects with UVD. Conformity with LL during the later VOR may have been due to substitution of compensatory, nonvestibular rapid eye movements, such as saccades or abrupt decelerations that altered the ocular rotational axis. 
Since a large-amplitude stimulus was used, the present study could examine the TAR 150 to 200 ms after rotation onset. During this time, the target remained visible so that eye movement could be controlled by either the VOR, or visually guided eye movements such as pursuit and saccades. The late TAR was variable, consistent with strategic alternation between VOR and LL kinematics. Among control subjects, two had TAR consistent with quarter angle VOR behavior, whereas others exhibited half-angle behavior consistent with pursuit (Fig. 8E) . Perhaps either pursuit or VOR could suffice to stabilize images in control subjects, with one or the other elected strategically. In UVD, the late TAR was directionally dependent. During ipsilesional rotation when the VOR gain in UVD was most impaired, TAR averaged 0.5 consistent with LL, suggesting that visual tracking dominated. During contralesional rotation, when VOR performance was nearly normal, TAR was a significantly lower, indicating that pursuit plays only a lesser role supplementing a more effective VOR. 
We propose that examination of the TAR can generally provide insight into the origins of slow-phase eye movements. Eye movements associated with a TAR near 0.25 are likely to be of vestibular origin, whereas those associated with a TAR near 0.50 are likely to be of nonvestibular origin. This kinematic criterion may be useful in studying combined visual and vestibular eye movements during high-velocity stimulation, where saccade and slow-phase velocity ranges overlap. 
Model of Ocular Velocity Axis
The VOR velocity axis was modeled using a two-stage vector summation approach. In the first stage, individual canal contributions are considered as a sensory contribution. In the second and presumably motor stage, the resulting VOR axis is influenced by orbital eye position (Fig. 9) . The idea of modeling the VOR based on transforming the head velocity into canal coordinates originated with Robinson. 24 The Robinson model used matrices that can be multiplied by head or canal-velocity vectors to demonstrate the effects of isolated canal lesions. The current model is in one respect a simplification of the Robinson model, since the current model does not represent the ocular motor plant as a separate matrix, or attempt to describe effects of plasticity. The Robinson vector and matrix approach does not model nonlinear phenomena such as canal saturation in UVD. The current model implements nonlinearity by saturations on components of the canal-velocity vector, and incorporates an effect of eye position on VOR velocity axis. Central and peripheral nonlinearities in the steady state yaw VOR have elsewhere been modeled in one dimension. 32  
Components of head velocity rotated by nonlinearities in individual semicircular canals were computed as described in the Methods section, to derive reported 3-D head velocity. Because yaw rotation was delivered, most of the stimulus was sensed by the horizontal canal (HC). Thus, the HC was most susceptible to inhibitory saturation predicted by Ewald’s second law, 3 whereas less intensely stimulated vertical canals were more likely to encode their head velocity components accurately. Labyrinth orientation was not determined in the current subjects, but in normal subjects, the HC is tilted posteriorly with respect to Frankfort’s plane by 20 ± 7°. 25 When an HC reaches the inhibitory cutoff, the resultant VOR-velocity vector is predicted to be hypometric (low gain) and tilted anteriorly (Fig. 9)
The vector addition model can predict the VOR axis. Inhibitory cutoff of the human labyrinth is probably not a hard-velocity saturation, and while the precise nonlinearity is unknown, there is clearly an inhibitory asymmetry. 2 3 In the present study, control VOR gain tightly clustered around 0.87 without asymmetry. In subjects with UVD, ipsilesional gain averaged 0.30 with a broader range. Ipsilesional gain was 43% ± 22% (mean ± SD, range 12%–67%) of contralesional gain. This implies that the labyrinth encodes an average of 43% of velocity in the inhibitory direction that it can in the excitatory direction (Fig. 10)
Vestibular physiology is more complex than modeled. The model assumes that the three canals of each labyrinth are mutually orthogonal and that the superior canal (SC) and posterior canal (PC) are oriented at a 45° angle from the midsagittal plane such that the ipsilateral SC is coplanar with the contralateral PC. Normative radiographic data from a large sample of humans supports these assumptions. 25 The model also assumes that inhibitory nonlinearities for the SC and PC are similar to that of the HC, that ideal VOR gain is unity and that gain is measured in the direction of eye motion rather than in a head- or space-fixed coordinate system. Subunity gain was observed in both control subjects and subjects with UVD. To account for this, gains were compared with model predictions using the ratio of ipsi- to contralesional gain. The basis of VOR axis dependency on eye position is unknown, but single-unit recordings in alert monkeys suggest that it is not mediated by commands to cyclovertical extraocular muscles carried by oculomotor and trochlear motoneurons. 33 There must be some neural mediation, however, since the VOR’s TAR of approximately 0.25 is different from that of 0.50 for pursuit and saccades. The model implements VOR axis on orbital eye position as a presumably motor phenomenon downstream of the sensory effect of canal components. The eye position effect is modeled by a rotation of the canal estimate of the head velocity axis by the product of eccentric eye position and the TAR. 
The model makes emergent predictions about the VOR in UVD. First, in primary gaze when the horizontal canal (HC) is perpendicular to the head-velocity axis, the VOR axis can be perfectly aligned to the head axis, albeit at minimal VOR gain, because of absence of stimulus velocity in the SC and PC planes that would otherwise be informative that head velocity exceeds that reported by the saturated HC (Fig. 10) . As the head velocity axis becomes oblique to the HC plane, the model initially predicts both increased VOR gain, and VOR axis misalignment from the head axis. These effects are predicted to increase until the SC and PC ultimately also saturate (Fig. 10) . For four of five subjects with UVD (GP, MU, VK, and KM), the model fits best for an HC orientation near 30°, similar to the orientation found radiographically in humans. 25 In the remaining subject with UVD (PL), the VOR axis was closely aligned with the head despite a significant directional asymmetry in gain. An HC plane lying nearly perpendicular to the head velocity axis may explain this. Although the three semicircular canals within individual labyrinths are consistently orthogonal, recent magnetic resonance imaging indicates that labyrinth orientation may vary up to 25° from the plane of the horizontal rectus extraocular muscles in individual subjects. 26 Although it seems reasonable that the subject’s head positioning relative to the rotator axis may introduce a further 10° in labyrinth orientation relative to the head velocity axis, additional factors including limitations in actuation of ocular torsion, 34 may also contribute to VOR axis direction. 
The second stage of the model (Fig. 9 , right side) accounts for the effect of eye position on VOR axis direction and thus the TAR. During the first 50 ms of the VOR slow phase, the TAR was similar for ipsi- versus contralesional rotation (Fig. 8B) , and did not differ significantly between control subjects and subjects with UVD. Thus, a simple summation effect of eccentric eye position multiplied by the TAR explains the final VOR axis. This idea is consistent with the suggestion that the VOR TAR of <0.5 is due to relatively low torsional VOR gain. 34  
The vector model explains the major findings of the present study: The VOR axis during ipsilesional rotation is rotated forward and gain is decreased. The model explains how the range of ipsilesional VOR gain and axis orientation may be related by labyrinth orientation and variation in physiology. Other investigators have reported minimal early VOR axis tilt, but very large later tilts, not observed here, approaching 80°. 8 Tilts exceeding 45° are inconsistent with the current model, because the tilt is limited by canal saturation. Nearly orthogonal tilts reported elsewhere are most likely due to nonlinear effects not predicted by the model, such as quick phases, or artifacts due to difficulty controlling or determining axes during manual head-on-body rotation. 
Although the experiment used yaw rotation, the physiological principles underlying the model should be applicable to head rotation about any axis in UVD, including pitch and roll. In each case, inhibitory rotation in the maximum sensitivity direction of a unilaterally intact labyrinth’s semicircular canal is predicted to evoke relatively low VOR gain but with axis aligned to the head except for quarter-angle dependency on orbital eye position. Inhibitory rotation up to 45° oblique to the labyrinth’s maximum sensitivity directions is predicted to increase VOR gain at the expense of introducing error in axis direction. 
The VOR’s goal can be considered twofold: appropriate magnitude of compensatory eye movement (gain) during rotation about an axis closely aligned with that of the head. The normal VOR attains both goals, probably due to constant VOR gain adjustment. After UVD, these goals may be unattainable due to inhibitory saturation of individual semicircular canals encoding directional components of head rotation. The vector model demonstrates that VOR axis alignment to the stimulus in UVD comes at the expense of VOR gain. One compensatory strategy is limitation of voluntary head motion to subsaturation velocity. 14 However, a low-velocity strategy is impossible during externally imposed motion. During human ambulation, the highest-frequency head rotation occurs in pitch, with a lower frequency but significant amplitude in yaw. 14 20 Labyrinth orientation itself may be compensatory, because the pitch axis is reflected nearly equally by the PC and SC, whereas the HC is oriented 20° on average behind the yaw axis relative to Frankfort’s plane. 25 Thus, labyrinth misalignment with the head-rotation axes most common during ambulation may serve as a compromise to increase VOR gain at the expense of VOR axis accuracy in labyrinthine disease. 
 
Figure 1.
 
Asymmetry in ipsi- versus contralesional VOR in a representative subject with left UVD. The right eye VOR slow phase is directed opposite the head and plotted as negative, and eye responses for both ipsi- and contralesional rotation are plotted as positive for comparison. Thick lines: average of 10 trials in each direction with a centered target; thin lines: ±1 SD.
Figure 1.
 
Asymmetry in ipsi- versus contralesional VOR in a representative subject with left UVD. The right eye VOR slow phase is directed opposite the head and plotted as negative, and eye responses for both ipsi- and contralesional rotation are plotted as positive for comparison. Thick lines: average of 10 trials in each direction with a centered target; thin lines: ±1 SD.
Figure 2.
 
VOR gain during the first 50 ms of head rotation in control and subjects with UVD. Error bars represent the ±1 SD. In control subjects (A) gain did not depend on the direction of rotation. In subjects with UVD (B), gain was significantly lower during ipsilesional rotation (P < 0.01).
Figure 2.
 
VOR gain during the first 50 ms of head rotation in control and subjects with UVD. Error bars represent the ±1 SD. In control subjects (A) gain did not depend on the direction of rotation. In subjects with UVD (B), gain was significantly lower during ipsilesional rotation (P < 0.01).
Figure 3.
 
Dependence of VOR velocity axis on stimulus direction in subjects with UVD. (A) Contra- minus ipsilesional rotation in the example subject with UVD shown in Figure 1 . Positive values indicate forward axis shift during ipsilesional rotation (leftward) relative to the VOR axis during contralesional (rightward) rotation. Data are averaged from 10 trials in each direction with a centered target. (B) Contra- minus ipsilesional axis tilt averaged across all subjects with UVD (solid line) ±1 SE. Dashed lines: SE. (C) Probabilities calculated with paired t-tests comparing ipsi- versus contralesional rotation at each time point. Differences in axis tilts between ipsi- and contralesional rotations became significant after 20 ms.
Figure 3.
 
Dependence of VOR velocity axis on stimulus direction in subjects with UVD. (A) Contra- minus ipsilesional rotation in the example subject with UVD shown in Figure 1 . Positive values indicate forward axis shift during ipsilesional rotation (leftward) relative to the VOR axis during contralesional (rightward) rotation. Data are averaged from 10 trials in each direction with a centered target. (B) Contra- minus ipsilesional axis tilt averaged across all subjects with UVD (solid line) ±1 SE. Dashed lines: SE. (C) Probabilities calculated with paired t-tests comparing ipsi- versus contralesional rotation at each time point. Differences in axis tilts between ipsi- and contralesional rotations became significant after 20 ms.
Figure 4.
 
Directional dependence of the VOR axis during the initial 50 ms of rotation in control subjects and those with UVD. Positive values indicate a relative forward tilt of the top end of velocity axes during leftward head rotation. Negative values indicate relative forward tilt during rightward rotation.
Figure 4.
 
Directional dependence of the VOR axis during the initial 50 ms of rotation in control subjects and those with UVD. Positive values indicate a relative forward tilt of the top end of velocity axes during leftward head rotation. Negative values indicate relative forward tilt during rightward rotation.
Figure 5.
 
Effect of eye position on VOR axis tilt relative to the earth–vertical axis of head rotation in a representative subject with UVD. Negative values indicate forward tilt and positive values backward tilt of the top ends of velocity axes.
Figure 5.
 
Effect of eye position on VOR axis tilt relative to the earth–vertical axis of head rotation in a representative subject with UVD. Negative values indicate forward tilt and positive values backward tilt of the top ends of velocity axes.
Figure 6.
 
Calculation of TAR 45 ms after the onset of contralesional head rotation in the single subject whose data are illustrated in Figure 5 . Linear regression has a slope (TAR) of 0.22, with a coefficient of determination of 0.19.
Figure 6.
 
Calculation of TAR 45 ms after the onset of contralesional head rotation in the single subject whose data are illustrated in Figure 5 . Linear regression has a slope (TAR) of 0.22, with a coefficient of determination of 0.19.
Figure 7.
 
Left: TAR for a single subject calculated at 800-μs time intervals by the linear regression method shown in Figure 6 . Right: the coefficient of determination (R 2) represents the quality of the linear regression performed at each data point shown.
Figure 7.
 
Left: TAR for a single subject calculated at 800-μs time intervals by the linear regression method shown in Figure 6 . Right: the coefficient of determination (R 2) represents the quality of the linear regression performed at each data point shown.
Figure 8.
 
Average TAR in epochs after the onset of head rotation for control (top row) and subjects with UVD (bottom row). Error bars: ±1 SD. *Significant differences.
Figure 8.
 
Average TAR in epochs after the onset of head rotation for control (top row) and subjects with UVD (bottom row). Error bars: ±1 SD. *Significant differences.
Figure 9.
 
Graphic representation of the model explaining observed VOR axis shifts in UVD. First, vector addition of canal components yields an initial estimate of the head-velocity vector. The activities in the HC, SC, and PC are shown. The model includes two stages: The canals first encode the head-velocity axis, which is then modified by eye position. Top (normal or contralesional rotation): Components of the head-velocity vector are accurately represented in each canal plane. The resultant eye-velocity vector (right) matches the head-velocity vector both in magnitude and direction. Bottom (ipsilesional): Components of the head-velocity vector as represented by canal afferents. Although the PC and SC are represented accurately, the HC (white arrow) saturates and reports a low lower magnitude than is appropriate for the head rotation. When canal vectors are summed, the result is smaller and tilted forward relative to normal. Right (eye position): In central eye position, the head-velocity vector represented by the labyrinth correctly specifies the ocular velocity axis. In an upward eye position (exaggerated for clarity), the head-velocity vector (light gray) is rotated by vertical eye position eccentricity multiplied by the TAR (black arrowhead) to yield the final ocular-velocity vector.
Figure 9.
 
Graphic representation of the model explaining observed VOR axis shifts in UVD. First, vector addition of canal components yields an initial estimate of the head-velocity vector. The activities in the HC, SC, and PC are shown. The model includes two stages: The canals first encode the head-velocity axis, which is then modified by eye position. Top (normal or contralesional rotation): Components of the head-velocity vector are accurately represented in each canal plane. The resultant eye-velocity vector (right) matches the head-velocity vector both in magnitude and direction. Bottom (ipsilesional): Components of the head-velocity vector as represented by canal afferents. Although the PC and SC are represented accurately, the HC (white arrow) saturates and reports a low lower magnitude than is appropriate for the head rotation. When canal vectors are summed, the result is smaller and tilted forward relative to normal. Right (eye position): In central eye position, the head-velocity vector represented by the labyrinth correctly specifies the ocular velocity axis. In an upward eye position (exaggerated for clarity), the head-velocity vector (light gray) is rotated by vertical eye position eccentricity multiplied by the TAR (black arrowhead) to yield the final ocular-velocity vector.
Figure 10.
 
Quantitative model predictions of yaw VOR axis tilt and gain as functions of horizontal canal orientation, for central eye position. Filled gray circles: data from individual subjects are superimposed. The model assumes the SC and PC are mutually orthogonal and offset 45° from midsagittal that so they sense equal amounts of head rotation. Lines represent model predictions when each canal of a single labyrinth encodes 8%, 22%, 43%, or 47% of ipsilesional head velocity (bottom) before saturating at that maximum, while encoding 100% of contralesional velocity. Positive values indicate the effect of backward rotation of the labyrinth (x-axis, top and bottom) or forward rotation of the ocular axis relative to the head (y-axis, top). Subject data are derived from that shown in Figures 2 and 4 . Top: Predicted VOR axis tilt as a function of canal orientation. VOR axis tilt initially increases with labyrinth pitch, becoming maximum as the vertical canals also enter inhibitory cutoff. The model predicts 45° maximum ocular axis tilt even when two canals encode only a minimal fraction of actual head rotation due to saturation. Bottom: Gain is minimized when the head velocity axis is aligned directly with the horizontal canal. As the vertical canals reflect more of the stimulus, their contributions increase VOR gain; this effect increases until the vertical canals also reach saturation, above which VOR gain saturates.
Figure 10.
 
Quantitative model predictions of yaw VOR axis tilt and gain as functions of horizontal canal orientation, for central eye position. Filled gray circles: data from individual subjects are superimposed. The model assumes the SC and PC are mutually orthogonal and offset 45° from midsagittal that so they sense equal amounts of head rotation. Lines represent model predictions when each canal of a single labyrinth encodes 8%, 22%, 43%, or 47% of ipsilesional head velocity (bottom) before saturating at that maximum, while encoding 100% of contralesional velocity. Positive values indicate the effect of backward rotation of the labyrinth (x-axis, top and bottom) or forward rotation of the ocular axis relative to the head (y-axis, top). Subject data are derived from that shown in Figures 2 and 4 . Top: Predicted VOR axis tilt as a function of canal orientation. VOR axis tilt initially increases with labyrinth pitch, becoming maximum as the vertical canals also enter inhibitory cutoff. The model predicts 45° maximum ocular axis tilt even when two canals encode only a minimal fraction of actual head rotation due to saturation. Bottom: Gain is minimized when the head velocity axis is aligned directly with the horizontal canal. As the vertical canals reflect more of the stimulus, their contributions increase VOR gain; this effect increases until the vertical canals also reach saturation, above which VOR gain saturates.
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Figure 1.
 
Asymmetry in ipsi- versus contralesional VOR in a representative subject with left UVD. The right eye VOR slow phase is directed opposite the head and plotted as negative, and eye responses for both ipsi- and contralesional rotation are plotted as positive for comparison. Thick lines: average of 10 trials in each direction with a centered target; thin lines: ±1 SD.
Figure 1.
 
Asymmetry in ipsi- versus contralesional VOR in a representative subject with left UVD. The right eye VOR slow phase is directed opposite the head and plotted as negative, and eye responses for both ipsi- and contralesional rotation are plotted as positive for comparison. Thick lines: average of 10 trials in each direction with a centered target; thin lines: ±1 SD.
Figure 2.
 
VOR gain during the first 50 ms of head rotation in control and subjects with UVD. Error bars represent the ±1 SD. In control subjects (A) gain did not depend on the direction of rotation. In subjects with UVD (B), gain was significantly lower during ipsilesional rotation (P < 0.01).
Figure 2.
 
VOR gain during the first 50 ms of head rotation in control and subjects with UVD. Error bars represent the ±1 SD. In control subjects (A) gain did not depend on the direction of rotation. In subjects with UVD (B), gain was significantly lower during ipsilesional rotation (P < 0.01).
Figure 3.
 
Dependence of VOR velocity axis on stimulus direction in subjects with UVD. (A) Contra- minus ipsilesional rotation in the example subject with UVD shown in Figure 1 . Positive values indicate forward axis shift during ipsilesional rotation (leftward) relative to the VOR axis during contralesional (rightward) rotation. Data are averaged from 10 trials in each direction with a centered target. (B) Contra- minus ipsilesional axis tilt averaged across all subjects with UVD (solid line) ±1 SE. Dashed lines: SE. (C) Probabilities calculated with paired t-tests comparing ipsi- versus contralesional rotation at each time point. Differences in axis tilts between ipsi- and contralesional rotations became significant after 20 ms.
Figure 3.
 
Dependence of VOR velocity axis on stimulus direction in subjects with UVD. (A) Contra- minus ipsilesional rotation in the example subject with UVD shown in Figure 1 . Positive values indicate forward axis shift during ipsilesional rotation (leftward) relative to the VOR axis during contralesional (rightward) rotation. Data are averaged from 10 trials in each direction with a centered target. (B) Contra- minus ipsilesional axis tilt averaged across all subjects with UVD (solid line) ±1 SE. Dashed lines: SE. (C) Probabilities calculated with paired t-tests comparing ipsi- versus contralesional rotation at each time point. Differences in axis tilts between ipsi- and contralesional rotations became significant after 20 ms.
Figure 4.
 
Directional dependence of the VOR axis during the initial 50 ms of rotation in control subjects and those with UVD. Positive values indicate a relative forward tilt of the top end of velocity axes during leftward head rotation. Negative values indicate relative forward tilt during rightward rotation.
Figure 4.
 
Directional dependence of the VOR axis during the initial 50 ms of rotation in control subjects and those with UVD. Positive values indicate a relative forward tilt of the top end of velocity axes during leftward head rotation. Negative values indicate relative forward tilt during rightward rotation.
Figure 5.
 
Effect of eye position on VOR axis tilt relative to the earth–vertical axis of head rotation in a representative subject with UVD. Negative values indicate forward tilt and positive values backward tilt of the top ends of velocity axes.
Figure 5.
 
Effect of eye position on VOR axis tilt relative to the earth–vertical axis of head rotation in a representative subject with UVD. Negative values indicate forward tilt and positive values backward tilt of the top ends of velocity axes.
Figure 6.
 
Calculation of TAR 45 ms after the onset of contralesional head rotation in the single subject whose data are illustrated in Figure 5 . Linear regression has a slope (TAR) of 0.22, with a coefficient of determination of 0.19.
Figure 6.
 
Calculation of TAR 45 ms after the onset of contralesional head rotation in the single subject whose data are illustrated in Figure 5 . Linear regression has a slope (TAR) of 0.22, with a coefficient of determination of 0.19.
Figure 7.
 
Left: TAR for a single subject calculated at 800-μs time intervals by the linear regression method shown in Figure 6 . Right: the coefficient of determination (R 2) represents the quality of the linear regression performed at each data point shown.
Figure 7.
 
Left: TAR for a single subject calculated at 800-μs time intervals by the linear regression method shown in Figure 6 . Right: the coefficient of determination (R 2) represents the quality of the linear regression performed at each data point shown.
Figure 8.
 
Average TAR in epochs after the onset of head rotation for control (top row) and subjects with UVD (bottom row). Error bars: ±1 SD. *Significant differences.
Figure 8.
 
Average TAR in epochs after the onset of head rotation for control (top row) and subjects with UVD (bottom row). Error bars: ±1 SD. *Significant differences.
Figure 9.
 
Graphic representation of the model explaining observed VOR axis shifts in UVD. First, vector addition of canal components yields an initial estimate of the head-velocity vector. The activities in the HC, SC, and PC are shown. The model includes two stages: The canals first encode the head-velocity axis, which is then modified by eye position. Top (normal or contralesional rotation): Components of the head-velocity vector are accurately represented in each canal plane. The resultant eye-velocity vector (right) matches the head-velocity vector both in magnitude and direction. Bottom (ipsilesional): Components of the head-velocity vector as represented by canal afferents. Although the PC and SC are represented accurately, the HC (white arrow) saturates and reports a low lower magnitude than is appropriate for the head rotation. When canal vectors are summed, the result is smaller and tilted forward relative to normal. Right (eye position): In central eye position, the head-velocity vector represented by the labyrinth correctly specifies the ocular velocity axis. In an upward eye position (exaggerated for clarity), the head-velocity vector (light gray) is rotated by vertical eye position eccentricity multiplied by the TAR (black arrowhead) to yield the final ocular-velocity vector.
Figure 9.
 
Graphic representation of the model explaining observed VOR axis shifts in UVD. First, vector addition of canal components yields an initial estimate of the head-velocity vector. The activities in the HC, SC, and PC are shown. The model includes two stages: The canals first encode the head-velocity axis, which is then modified by eye position. Top (normal or contralesional rotation): Components of the head-velocity vector are accurately represented in each canal plane. The resultant eye-velocity vector (right) matches the head-velocity vector both in magnitude and direction. Bottom (ipsilesional): Components of the head-velocity vector as represented by canal afferents. Although the PC and SC are represented accurately, the HC (white arrow) saturates and reports a low lower magnitude than is appropriate for the head rotation. When canal vectors are summed, the result is smaller and tilted forward relative to normal. Right (eye position): In central eye position, the head-velocity vector represented by the labyrinth correctly specifies the ocular velocity axis. In an upward eye position (exaggerated for clarity), the head-velocity vector (light gray) is rotated by vertical eye position eccentricity multiplied by the TAR (black arrowhead) to yield the final ocular-velocity vector.
Figure 10.
 
Quantitative model predictions of yaw VOR axis tilt and gain as functions of horizontal canal orientation, for central eye position. Filled gray circles: data from individual subjects are superimposed. The model assumes the SC and PC are mutually orthogonal and offset 45° from midsagittal that so they sense equal amounts of head rotation. Lines represent model predictions when each canal of a single labyrinth encodes 8%, 22%, 43%, or 47% of ipsilesional head velocity (bottom) before saturating at that maximum, while encoding 100% of contralesional velocity. Positive values indicate the effect of backward rotation of the labyrinth (x-axis, top and bottom) or forward rotation of the ocular axis relative to the head (y-axis, top). Subject data are derived from that shown in Figures 2 and 4 . Top: Predicted VOR axis tilt as a function of canal orientation. VOR axis tilt initially increases with labyrinth pitch, becoming maximum as the vertical canals also enter inhibitory cutoff. The model predicts 45° maximum ocular axis tilt even when two canals encode only a minimal fraction of actual head rotation due to saturation. Bottom: Gain is minimized when the head velocity axis is aligned directly with the horizontal canal. As the vertical canals reflect more of the stimulus, their contributions increase VOR gain; this effect increases until the vertical canals also reach saturation, above which VOR gain saturates.
Figure 10.
 
Quantitative model predictions of yaw VOR axis tilt and gain as functions of horizontal canal orientation, for central eye position. Filled gray circles: data from individual subjects are superimposed. The model assumes the SC and PC are mutually orthogonal and offset 45° from midsagittal that so they sense equal amounts of head rotation. Lines represent model predictions when each canal of a single labyrinth encodes 8%, 22%, 43%, or 47% of ipsilesional head velocity (bottom) before saturating at that maximum, while encoding 100% of contralesional velocity. Positive values indicate the effect of backward rotation of the labyrinth (x-axis, top and bottom) or forward rotation of the ocular axis relative to the head (y-axis, top). Subject data are derived from that shown in Figures 2 and 4 . Top: Predicted VOR axis tilt as a function of canal orientation. VOR axis tilt initially increases with labyrinth pitch, becoming maximum as the vertical canals also enter inhibitory cutoff. The model predicts 45° maximum ocular axis tilt even when two canals encode only a minimal fraction of actual head rotation due to saturation. Bottom: Gain is minimized when the head velocity axis is aligned directly with the horizontal canal. As the vertical canals reflect more of the stimulus, their contributions increase VOR gain; this effect increases until the vertical canals also reach saturation, above which VOR gain saturates.
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