Shifts in Listing’s Plane Produced by Vertical Axis Rotation: Sustained Ocular Torsion Due to Semicircular Canal Stimulation

Abstract

purpose. With the head upright and stationary, ocular torsion is confined by Listing’s Law (LL), so that three-dimensional eye rotational axes form Listing’s plane (LP). During head rotation, the vestibulo-ocular reflex violates LL by driving ocular torsion opposite to head torsion, sometimes out of LP. Saccades originating from non-Listing’s initial torsional positions remain in a plane offset from, but parallel to, the original LP. The present study was conducted to determine whether whole-body yaw alters the position and orientation of LP.

methods. Eight normal subjects and six with unilateral vestibular deafferentation (UVD) underwent binocular eye and head movement recordings with 3-D magnetic search coils. Visual fixations were used to define LP, after which subjects underwent whole-body yaw rotation of 30° or 70°, at peak accelerations from 125 deg/s² to 2800 deg/s². Gaze during rotation was either central or 20° up. After rotation, a dynamic LP (DLP) was defined during fixations.

results. Orientation and thickness of the DLP did not vary significantly from the previously defined LP; however, DLP was offset an average of 4° ± 4° (mean ± SD), 87% of head torsion relative to LP. Stimulus intensity, UVD, and starting vertical gaze direction had no effect on DLP offset or orientation. The DLP torsional offset declined toward the original LP with a time constant of approximately 1 minute, suggesting mediation by neural integration.

conclusions. Yaw rotation can cause stable torsional offsets in the location of Listing’s Plane.

The eye can move in three degrees of freedom (DF): pitch, yaw, and torsion. However, when the head is upright and stationary, eye position during pursuit and saccades has only 2 DF: ocular torsion is constrained by Listing’s Law (LL). ^{1 2} The classic description of LL states that ocular torsion is determined as if eye position were reached from the primary position by rotation about a single axis lying in Listing’s plane (LP). ³ Conformity with LL can be directly tested by expressing eye positions as quaternions, which when plotted will lie in LP. ^{4 5 6}  

The VOR is a conspicuous violator of LL, ^{7 8 9} because the VOR must compensate for head rotation about any axis to stabilize images on the retina. Since head motion during ambulation occurs in all three DF, ¹⁰ an ideal VOR would compensate without constraint on ocular torsion. The ideal ocular rotational axis for the VOR is aligned with the head axis. When examined in the position domain, VOR-driven eye positions roughly mirror head rotation about a wide range of axes in both monkeys ¹¹ and humans. ¹²  

Previous studies have explored the relationship between the VOR and LL. Ocular torsion can be driven out of LP by the VOR, ⁹ after which visual saccades can be evoked from a non-LL torsional starting position. ¹³ This situation presents a kinematic dilemma: a saccade returning eye position to the original LP would have to include transient torsion violating LL, and further saccades conforming to LL would necessarily maintain the initial non-LL torsion. In fact, observed saccades initiated from starting positions outside LP do not return to the original LP, but rather maintain the non-LL torsion and remain parallel to the original LP. ¹³  

The VOR is abnormal in subjects with unilateral vestibular deafferentation (UVD). The transient, slow phase VOR is greatly attenuated during ipsilesional head rotation at high acceleration in UVD. ^{14 15 16} The behavior of the VOR with respect to LL is also abnormal after UVD. Although the VOR axis varies by one quarter of eye position in normal subjects, ^{7 8 9 17} when rotating ipsilesionally to UVD, the VOR axis more closely approximates the half-angle dependency on eye position consistent with LL. ¹⁸ It has been supposed that this may be due to supplementation of the deficient slow phase by visual pursuit during ipsilesional rotation. One purpose of the present study was to determine how much ipsilesional rotation can displace ocular torsion out of LP. 

In the present study, we asked whether there are persistent alterations in ocular kinematics after the VOR drives ocular torsion out of LP. Previous work indicates that ocular torsion remains out of LP at least long enough to make a saccade, ¹³ but it is not known whether this is an ephemeral phenomenon. After the eye is driven out of LP by the VOR, do subsequent saccades form another plane; and, if so, what are the characteristics of this plane? One supposition is that the VOR may only transiently shift the eye out of LP, with quick phases spontaneously returning the eye to LP as observed with torsional optokinetic nystagmus ¹⁹ or electrical stimulation. ²⁰ Others have supposed that the VOR may shift LP itself, such that ocular torsion lies in a new, dynamic LP whose long-term position is influenced by the VOR ^{21 22} , although definitive data are lacking. These are fundamental questions that may provide insight into the underlying, yet currently mysterious, purpose of LL. Furthermore, although the existence of LL is most likely due to properties of the extraocular pulley muscles, these properties are proposed to be under active neural control to subserve purposes not yet clear. ^{23 24} In the present study, we probed some of these issues, as well as potentially modifying factors such as velocity of head rotation, ^{25 26} gaze direction, ^{7 8 9 17} and UVD. ¹⁸  

Methods

Subjects

Eight paid, normal adult human volunteers gave written consent to participate in the experiments, according to a protocol approved by the Institutional Review Board of the University of California, Los Angeles, and in conformity with the tenets of the Declaration of Helsinki. Normal subjects consisted of six women and two men of average age 23 ± 4 years (mean ± SD; range 19–29). 

An additional six subjects had well compensated surgical UVD, including four women and two men of average age 56 ± 17 years (mean ± SD; range 25–76). Surgery consisted of labyrinthectomy in five subjects and a suboccipital craniotomy with nerve section in the remaining subject. Surgery was completed 2 to 160 months before testing (mean 60 months). The UVD was on the right in three subjects and on the left in the others. 

All subjects underwent ophthalmic examination to verify that they were free of ocular disease and would be able to see the targets clearly without the aid of corrective lenses. Subjects were monitored during experiments via infrared closed-circuit television and with a duplex intercom. 

Apparatus

Angular binocular eye and head positions were measured with dual winding magnetic search coils, as previously used in the current laboratory. ¹⁴ 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). This configuration placed the center of the cube near eye level. The two vertically oriented coil pairs were driven by 60-kHz sinusoidal currents in phase quadrature. ²⁷ The horizontally oriented coil pair was driven by a 120-kHz sinusoidal current. ²⁸ Dual-winding scleral magnetic search coil annuli (Skalar Medical, Delft, The Netherlands) were placed under topical anesthesia with proparacaine 0.5%. Binocular coils were used in all control subjects, and three subjects with UVD. Head motion was recorded using a pair of orthogonal search coils mounted on a dental mold of the upper teeth. Search coils were connected to detectors (C-N-C Engineering) incorporating single-pole, low-pass filters with a cutoff frequency of 167 Hz. Horizontal angular positions were demodulated by a phase angle method that is linear over a range of ±100°. Search coil signals were demodulated to calculate Fick angles, rotation matricies, and quaternions, as previously described in the current laboratory. ^{9 10}  

Homogeneity of the reference magnetic field was directly verified. Gain calibration curves were constant to ±5% within a central cube 58 cm on each side and ±1.6% within a central cube measuring 11 cm on each side. The measured peak-to-peak position noise level of the search coil system at a bandwidth of 0 to 100 Hz was 2 min arc. The root mean square (RMS) horizontal velocity noise of the system over a bandwidth of 0 to 43 Hz was 30 min arc/s. 

Experimental control and data acquisition were performed by computer (Macintosh; Apple Computer, Cupertino, CA, running the MacEyeball software package). Search coil data (horizontal, vertical, and torsion gazes and head positions) were displayed on a digital polygraph and low-pass filtered over a bandwidth (4-pole Butterworth) of 300 Hz before simultaneous digital sampling with 16-bit precision at 1.2 kHz. 

Subjects were rotated by a 500 N-m stepper motor (Compumotor, Rohnert Park, CA) with a dedicated driver and position feedback digital controller as previously described. ¹⁴ The motor had a resolution of 425,984 steps per revolution and could reliably reproduce the desired head motion. Because the motor’s step resolution was 0.05 min arc, the steps were well below the noise level of the search coil system, making the steps indistinguishable from continuous rotation. Head position was adjusted so that the axis of rotation was located between the external auditory canals, which were approximately 7 cm posterior to the eyes. This axis was chosen to minimize the translational stimulus to the otoliths. Six rotational stimuli were used: 2800 deg/s² acceleration to a peak velocity of 190 deg/s; 2000 deg/s² acceleration to a peak velocity of 140 deg/s; 1000 deg/s² acceleration to a peak velocity of 70 deg/s; 500 deg/s² acceleration to a peak velocity of 35 deg/s; 250 deg/s² acceleration to a peak velocity of 20 deg/s; and 125 deg/s² acceleration to a peak velocity of 10 deg/s. All subjects underwent rotation to 30°, the most commonly used displacement. In two control subjects, rotations of 70° were also used. 

The stimulus for saccades was provided by a red laser spot back projected on a screen located 175 cm anterior to the subject. Target position was controlled via a two-axis mirror galvanometer (General Scanning, Watertown, MA) synchronously controlled by the data acquisition computer. 

Measurement Conditions

During each trial, the subject sat with the head comfortably upright in a hardwood chair fabricated with nonmetallic fasteners, as previously described. ^{9 14} The chair was fit with dense foam cushions. Each subject was secured by lap and chest belts, as well as padded clamps 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 (Confor-foam; EAR Specialty Composites, Newark, DE) to the forehead, vertex, occipital and malar eminences, and mental promontory of the subject’s head. Rotational trials were each preceded by a 2-second calibration recording in which the subject aligned head and eyes toward a centered target 175 cm away. 

In 25-second recordings sampled at 1.2 kHz, a static LP (SLP) was defined for each eye with the head immobile as subjects tracked projected target motion. The target moved over a range of ±30° from the center of the target. When the target reached the center position at the end of a cycle, the direction of motion changed slightly so that the resulting radial pattern covered the field of view. The sinusoidal peak velocity was 60 deg/s. 

Yaw rotation trials consisted of three major types. In type 1 trials, eight directionally randomized, transient 30° yaw rotations (four in each direction) were delivered over a 60- to 70-second period. Subjects were instructed to track the target throughout the trial. At rotation onset, the target was located either straight ahead or 20° up. The target remained in its original position for 1 second after a 30° yaw rotation, then moved 30° to the new straight-ahead position, after which a dynamic LP (DLP) was briefly defined by moving the target for 1 second each to 20° up, 20° down, 20° left, and 20° right. The subject then rotated to the center position before the next trial. 

Type 2 trials consisted of two rotations (one in each direction but in random order) during an approximately 70-second interval. This trial was similar to the type 1 trial except that the target continued to move at 1-second intervals between 20° eccentric positions for 30 seconds. The size setup of the laboratory and the size of the target screen set a practical limit on head rotation of about ±35°. 

Type 3 trials were performed in only two control subjects to examine very large rotations. In these trials, an SLP was defined from a starting position that was 35° left or right of center. The chair then underwent a single 70° rotation and a DLP was defined by multiple visual fixations. During both types of trials, rotation onset was varied randomly by ≤250 ms, to avoid predictive effects. Except for the laser target, which was always visible, the laboratory was dark. 

Each trial type was repeated for the six stimulus motion conditions previously listed. Experiments in each subject were limited to 30 minutes, and so not all stimuli could be tested in every subject. Of the eight control subjects tested, the peak acceleration of 2800 deg/s² was omitted in two subjects, the 500 deg/s² in one subject, and 125 deg/s² in five subjects. 

Data Analysis

Data were analyzed automatically with custom software (written in LabView 7.1; National Instruments, Austin TX, on Macintosh G5 computers; Apple Computer). For each subject, rotational transients were grouped based on direction of rotation, initial direction of gaze, eye, and rotational stimulus. Data defining DLP were removed from analysis if the thickness was greater than 2°, and SLP trials were not considered if more than 3°, which usually indicated a search coil slip or failure. This criterion removed 3.3% of DLP trials and 3.8% of SLP trials from further analysis. However, in the case of SLP trials, coil problems were often evident at the time of the experiment so that the trial could be repeated. 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. ^{6 9 10} Data from LP definition and VOR trials were first corrected for orientation of the coils on the eye in central gaze during the immediately preceding reference trial, as previously described. ¹⁰ The orientation of LP was determined using the best fit to the quaternion eye positions. ²⁹  

Eye and head position relative to LP were determined for each trial for each eye and viewing condition. The head stimulus and ocular response during VOR initiation were converted to quaternions in Listing’s coordinates, allowing the distance from LP for the eye and head to be determined at any point in the time course of the response. Velocity vectors (ω) for the eyes and head were computed from the corrected quaternion position (q) and derivative ((α)), as previously described ^{6 13 30} :  

\[{\omega}\ {=}\ 2\ \frac{{\dot{q}}}{q}.\]

The quaternion derivative (q̇) was calculated from position (q) by taking the derivative of each component of the quaternion and filtering with a third-order Butterworth filter with a cutoff frequency of 50 Hz. The tilt angle of the velocity vector out of LP, φ (in the sagittal plane), was determined using the horizontal (h) and torsional (t) components of velocity, as previously described. ^{13 30} Automated software was used to find and measure the orientation of DLPs. Onset of motor rotation was controlled by a synchronization pulse used in analysis to identify onset of head rotation. ¹⁴ The DLP was analyzed for orientation and thickness in a manner similar to the static LP defined before rotation. 

Because the quaternion coordinate system is not intuitively familiar, we expressed the torsional offset and orientation of LP in degrees, which is problematic, because when eye movements are plotted in the more familiar Fick or Helmholtz coordinate systems, they do not lie in a plane, even when behavior obeys LL. Ideal torsion (ψ_ideal) predicted by LL can be calculated for any eye position in yaw (θ) and pitch (φ) as previously described ⁹ :  

\[{\psi}_{\mathrm{ideal}}\ {=}\ \mathrm{arctan}\left(\frac{\mathrm{sin{\theta}sin{\phi}}}{\mathrm{cos{\theta}\ {+}\ cos{\phi}}}\right).\]

The SD of observed (ψ) minus calculated ideal torsion (ψ_ideal) was used to quantify LP thickness in degrees. Because eye position was in the statically defined LP before any rotation, the position offset of DLP was determined by subtracting ψ from ψ_ideal. A normalized LP offset was calculated by determining the ocular torsion relative to the SLP at the start of DLP definition. The relative torsion through the DLP definition was then divided by this value to yield a normalized DLP offset which was always unity at the start of a trial and would be 0 if ocular torsion returned to the originally defined SLP. These data were averaged, and a best fit was calculated using the equation  

\[{\psi}_{\mathrm{norm}}{=}Ae^{{-}t/{\tau}}\]

where ψ_norm is the normalized ocular torsion, A is a constant, t is time, and τ is the time constant. 

Results

Static Listing’s Plane

Before head rotations, the pitch orientation of SLP relative to earth vertical was not significantly different between the two eyes (P > 0.1) and averaged 5 ± 13° backward (mean ± SD). In yaw, the right eye SLP was oriented 9 ± 2° nasally, and the left eye SLP was orientated 19 ± 10° nasally. The thickness of LP was not significantly different between the two eyes, averaging 1.3 ± 0.7° (mean ± SD). 

Dynamic Listing’s Plane

Data from a typical trial are plotted as Fick angles in Figure 1 , and the same data in quaternions in Figure 2 . Because the SLP was generally tilted relative to the rotational axis (on average tilted 5 ± 13° backward), relative to SLP the head rotational axis was not purely horizontal (yaw) but also contained significant torsion. The average amount of head torsion in an SLP coordinate system was 4 ± 1° (mean ± SD) during 30° yaw rotation. 

The thickness of DLP was 0.80 ± 0.16° (range, 0.54–1.02°) during 5-second definition trials (significantly thinner than the SLP, P < 0.01). When measured over 30 seconds, DLP thickness was 1.10 ± 0.42° (range, 0.64–1.98°), not significantly different from the SLP thickness of 1.7 ± 0.7° (P = 0.04) 

Orientation of the DLP was determined relative to the previously determined SLP for each eye. Differences between the orientations of the SLP and DLP were small in most cases. On average, DLP was aligned with SLP within 4 ± 4° (mean ± SD) in both pitch and yaw. We sought to find a condition that significantly altered DLP orientation. There was no significant variation in mean DLP orientation with eye, direction of gaze at VOR onset, duration of DLP definition, or stimulus used. When data from all control subjects were pooled, there was no significant effect of rotation direction, but this was the result of cancellation of individual effects. However, most individual subjects showed a significant difference in DLP orientation with rotation direction (Fig. 3) . This effect of rotation direction on DLP orientation was unrelated to adduction versus abduction. 

Torsional coil slip around the limbus was a potential artifact of obvious concern when measuring the offset between DLP and SLP. After each DLP was defined, the head was rotated back to the central position. The amount of coil slip was assessed by comparing the ocular torsion before rotation and after return to this initial location. If no slip occurred during the DLP definition, and if the effect of yaw rotation was directionally symmetrical, then the difference between ocular torsion at the beginning and end of the trial should be near 0. However, even in the absence of coil slip, ocular torsion might not return exactly to its initial value if it decays toward 0 during prolonged rest after a transient yaw rotation. Mean ocular torsion changed by 1.4 ± 1.6° (mean ± SD) from the initial baseline on return from prolonged eccentric head positions. The amount of torsion change varied significantly among subjects over the range 0.71 to 3.10°, which probably reflected minor effect of coil slips. Data from the two subjects whose torsion change on return to starting head position averaged >2° were excluded from determination of DLP offset relative to SLP, because coil slips appeared to be frequent in these subjects. 

The major effect of yaw rotation was torsional displacement of DLP relative to SLP. The amount of head torsion relative to Listing’s primary coordinates was largely a function of LP orientation relative to the earth vertical rotational axis, averaging 3.6 ± 1.6° (mean ± SD; range, 2.3–5.0) after a 30° rotation. This was much larger than the average ocular torsion difference between the start and end of each trial which averaged 1.2 ± 1.3° (mean ± SD) in these subjects. Because the head torsion was expressed in coordinates relative to LP, the orientation of LP was a key factor in determining DLP offset. Furthermore, there was no correlation between the torsion difference and the DLP torsional displacement (correlation coefficient = 0.04). Because LP could be tilted either forward or backward with respect to earth vertical, the direction sense of head torsion relative to LP varied with rotation direction. The DLP offset had a strong inverse correlation with head torsion that was statistically significant (P < 0.01, Fig. 4 ). Linear regression of head torsion and DLP offset had a slope of −0.87 with a coefficient of determination of 0.72. Thus, the ocular torsion out of LP averaged 87% of head torsion, and was in the opposite direction. For trials of 70° rotation, there was greater head torsion, averaging 6.8 ± 1.7° (mean ± SD; range, 4.5–7.4). The slope of the relationship between DLP offset and head torsion was not significantly different (P > 0.1) at −0.92 with a coefficient of determination of 0.56. The offset in DLP was generally not the same in right and left eyes; the difference averaged 2.8 ± 2.4° (mean ± SD; range, 0.2–6.4°). The pitch orientation of the DLP after rotation did not vary significantly between the right and left eyes (P > 0.1). Yaw orientation of the DLP after rotation was, on average, 0.9 ± 4.8° (mean ± SD) further left in the left eye relative to the right eye. Although this small trend was significant (P < 0.01), there was considerable individual variation. 

We investigated possible effects of several factors that might influence DLP orientation, including the intensity of rotation and starting gaze position. Six intensities of stimuli were used, ranging from peak acceleration of 2800 deg/s² down to 125 deg/s². All stimuli with the same displacement (30° or 70°) produced similar amounts of LP offset and similar LP orientations. Rotation was imposed for gaze either straight ahead or 20° up. Both of these conditions produced similar DLP offset, orientation, and thickness. 

We examined the DLP over a 30-second interval, seeking evidence of possible drift over time toward SLP. This could have been done by examining ocular torsion in quaternions, but the quaternion coordinate system is not intuitive. Plotting the torsional location in degrees is also problematic because eye positions conforming to LL do not fall in a plane when plotted in a Fick coordinate system. Instead, the theoretical Fick torsion for SLP was subtracted from observed Fick torsion to give the offset of LP (Fig. 5) . In individual trials, LP position varied over several degrees and intertrial variation made it difficult to assess drift in pooled data. To identify potential sources of drift, we averaged 30-second DLP trials across subjects after normalization to the 0 torsion at the end of head rotation. Signs were assigned so that negative was always toward SLP. When averaged over 90 trials, eye position at the end of 30 seconds had drifted an average of 0.43 ± 2.7° (mean ± SD; SE 0.28°) closer to SLP. This drift was small but included all trials, with varying initial torsional differences between the SLP and DLP. A time constant of the return of ocular torsion to the SLP was determined by normalizing each trial by dividing the ocular torsion during the DLP definition by the initial torsional offset of the DLP from SLP when the rotated body position was first reached. To avoid dividing by values close to zero, trials in which the difference between DLP and SLP was less than 0.4° were excluded from this portion of the analysis. Without this exclusion, small coil slips and torsional noise would not have excessively influenced mean results. Normalized data were then averaged (Fig. 6)and used to calculate a time constant of drift. The best fit to the equation ψ_norm=Ae ^−t/τ was with A = 1.02, and τ = 52 s (R² = 0.54). 

Unilateral Vestibular Deafferentation

In subjects with UVD, mean (± SD) SLP orientation was tilted up 13 ± 8° and 8 ± 15° left, similar to the range in the control subjects. SLP thickness was 1.3 ± 0.4° (range, 0.79–1.9°), slightly but not significantly thinner than in control subjects. 

The thickness of DLP after 30° rotation was 0.76 ± 0.19° during 5-second determinations and 0.98 ± 0.20° during 30 seconds determinations. These values were not significantly different from each other (P = 0.12) and were within the range of control values. Similar to the control subjects, orientation of DLP relative to the earlier SLP was not significantly different (P > 0.1 for both pitch and yaw) when the subjects’ data were pooled. However, when DLP orientation was measured relative to SLP orientation, there were differences in individual subjects between right and leftward rotations similar to those in the control subjects (Fig. 3) . When data were grouped into ipsilesional and contralesional directions, there was no significant difference between the groups in either vertical or horizontal orientation (P > 0.1 for both), regardless of the acceleration delivered. 

Average head torsion relative to the SLP was 3.3 ± 0.7° (mean ± SD) in subjects with UVD. The linear regression of head torsion and DLP torsional offset had a slope of −1.12 and a coefficient of determination of 0.58. The offset of DLP averaged 3.6 ± 1.6° during ipsilesional rotation and 3.4 ± 2.2° during contralesional rotation. These values were not significantly different (P > 0.1) from each other. Similar to the control subjects, the DLP in subjects with UVD was not significantly influenced by direction of gaze during whole body motion or the velocity or acceleration of the rotation. 

At the end of 30 seconds trial, average ocular torsion offset of DLP in subjects with UVD drifted by only −0.04 ± 2.1° (mean ± SD, SEM was 0.25°, NS). The torsional drift in LP was fit by parameters A = 1.05 and τ = 94 seconds. Qualitatively the data were similar to Figure 6and are not illustrated. 

Discussion

The orientation of LP is influenced by multiple factors, including vergence ^{17 31 32} and changes in static head orientation relative to gravity. ³³ Eye torsion can be brought out of LP by torsional optokinetic nystagmus and returned by saccades or quick phases. ¹⁹ However, when the transient angular VOR is used to drive eye torsion out of LP, quick phases may be avoided or minimized by selection of experimental conditions so that ocular torsion remains outside of LP. ¹³ Current results demonstrate that subsequent ocular kinematics inscribe a new plane torsionally offset from LP. Except for the initial condition of torsional offset, LL then remains in force after a torsional disturbance by the angular VOR. As measured by LP thickness, LL after a torsional disturbance by the angular VOR has the same precision as before the disturbance. 

LP orientation, however, was not preserved after LL. Significant idiosyncratic individual changes in LP orientation were observed in most subjects after rotation. There was a small difference in LP orientation that depended on the direction of rotation (Fig. 3) , although the direction and magnitude of the difference varied between subjects. The mean DLP differed from the SLP only in that there was a small torsional offset between them. There were no statistical differences in orientation or plane thickness. 

The possibility that some of the observed offset in LP could have been due to an artifact was explored. Artificially adding to observed data coil signal offsets, and multiplying signals by scale factors, caused the resultant LP to be warped and nonplanar. Such artifactitious behavior was not observed in the actual data. Because LL does not correspond to a physical gimbal, it is difficult to imagine electrical artifacts that could cause an offset in LP without also distorting the shape of LP. One artifact that can change the offset of LP without changing its shape is torsional coil slip on the eye. Potential slips were investigated by measuring the ocular torsion before and after head rotation in trials in which the subject viewed a central target before and after rotation. The average difference between these conditions was 1.4 ± 1.6° (mean ± SD), less than half the mean torsional offset of the DLP. Such differences did not correlate with the offset in DLP and on average are not likely to have affected measurement of the mean offset in DLP. After the shift occurred, DLP torsion drifted back toward its original value with a long but not infinite time constant, inconsistent with artifact as the source of the shift. 

VOR’s Influence on the DLP

The main factor influencing the torsional displacement of LP was head rotation about an axis nonparallel to LP. Thus, tilt of LP relative to the head was associated with greater ocular torsion out of LP. The imposed rotational axis was always earth vertical, and so no torsion was imposed in earth coordinates. A coordinate system based on Listing’s primary position was convenient, since it made obvious any tilt or drift of the subsequent DLP. The amount of head torsion relative to LP depended on the orientation of the SLP and the magnitude of the head rotation. This head torsion caused a torsional offset of DLP averaging 4° for 30° rotation and 7° for 70° rotation. Ocular torsion was only slightly less than head torsion in control subjects, and DLP displacement was strongly correlated with head torsion (Fig. 4) . This corresponds to a static torsional VOR gain of 0.87 in normal subjects, and is consistent with a torsional VOR gain slightly less than unity. 

Human VOR performance depends on the type of stimulus delivered. ³⁴ Thus, we anticipated that with very low velocity and acceleration rotation, VOR gain might be lower and ocular displacement out of LP might be less. Such effects were not observed, even with rotation intensity as low as 125 deg/s² acceleration to a peak velocity of 10 deg/s. We conclude that the torsional offset in LP induced by semicircular canal stimulation is not strongly dependent on stimulus intensity. Subjects with UVD are known to have an attenuated slow phase when rotating ipsilesionally at high acceleration. ^{14 15} Catch-up saccades and pursuit ^{35 36} supplement the deficient VOR slow phase in subjects with UVD. In the present study, the displacement of DLP was similar after both ipsilesional and contralesional rotation, perhaps because the torsional component of the evoked VOR was well below the acceleration threshold required to manifest the slow-phase nonlinearity in UVD. ¹⁸  

Temporal Stability of the Dynamic Listing’s Plane

A goal of the present study was to determine how long DLP remained shifted from SLP after yaw rotation. Ocular torsion out of LP was previously assumed to be transient, since such shifts induced by torsional OKN quickly return to LP with eye movements often synchronized with quick phases. ¹⁹ To investigate the possible return of torsion to LP, after transient whole-body rotation, we asked the subjects to remain in the rotated position for 30 seconds while making saccades. Time limitations on the experiment made it impractical to study longer periods. During this 30-second period, a slow torsional drift of LP was observed toward the prerotation SLP. 

It is a mystery why ocular torsion promptly returns to LP during torsional OKN, ¹⁹ yet torsion induced by the VOR in the present study persisted with a long time constant. Torsional OKN has a very low gain, even under optimal conditions ³⁷ and may not be effective in creating a sustained ocular torsion. A more intense torsional VOR stimulus may induce nystagmus, the quick phases of which are programmed in 3D. ^{8 38} We propose that our experimental conditions avoided quick phases altering torsion with respect to LP, because the eye remained within the torsional oculomotor range of up to 11° without quick phases. ³⁹  

The current data provide a novel finding, in that the torsional offset of LP can be persistently influenced by semicircular canal stimulation without a change in head orientation with respect to gravity. One way of describing the current results is that head rotation can be used to drive the eye out of LP, where the eye remains for a prolonged period. However, such a description implies that LP has a fixed location. An alternative concept would be that the VOR influences ocular torsion by constantly modulating the torsional position of LP. This concept is consistent with the notion that the oblique extraocular muscles form a sort of “outer gimbal” for the rectus muscles and their pulleys, which mechanically implement LL as an “inner gimbal.” ²¹  

The rectus pulley array counterrolls in the same direction as ocular counterrolling (OCR) during sustained head roll ⁴⁰ —a reflex presumably driven by otolith inputs and mediated by the torsional neural integrator. ⁴¹ The time constant of the torsional neural integrator in the absence of otolith input in this study was found to be on the order of 1 minute, similar to the more than 20-second time constant of the horizontal velocity to position neural integrator. ⁴² The time constant of the torsional neural integrator during supine rotation has been estimated at 2 seconds. ³⁹ The much shorter time constant found by Seidman et al. ³⁹ may be due to the lack of otolith loading during supine rotation, or possible involvement of the horizontal integrator in our stimulus which was primarily horizontal. Static OCR in the range of 3° to 4° has been reported with binocular disconjugacy averaging 1.5°. ⁴³ The torsional offsets and ocular disconjugacy observed here after semicircular canal stimulation are analogous to static OCR and are similar in both magnitude and disconjugacy. It is intriguing to speculate that the same neural integrator responsible for OCR during otolith stimulation may also be responsible for the sustained torsional offset of LP observed in the present study during semicircular canal stimulation. ²²  

 Supported by National Eye Institute Grant EY-08313 (JLD). JLD is the Leonard Apt Professor of Ophthalmology. BTC was supported by a grant from the Giannini Family Foundation.

 Submitted for publication October 10, 2006; revised December 12, 2006; accepted February 13, 2007.

 Disclosure: B.T. Crane, None; J.-R. Tian, None; J.L. Demer, None

 The publication costs of this article were defrayed in part by page charge payment. This article must therefore be marked “advertisement” in accordance with 18 U.S.C. §1734 solely to indicate this fact.

 

Figure 1.

 

Fick angle recordings during a 67-second trial in which a typical control subject rotated to the left, remained there for 30 seconds while DLP was defined, then briefly returned to the center, and finally rotated to the right and remained there for 30 seconds while another DLP was defined. Black: head position. Red trace: left eye position during the first part of the trial, blue trace: position during the second half of the trial. Green trace: theoretical ocular torsion expected were the eye to remain in the original LP.

Figure 2.

 

Data from Figure 1replotted as quaternions rotated into coordinates of SLP defined before head motion (black). Red trace: left eye position during the first part of the trial, blue trace: left eye position during the second half of the trial. Head position is not shown. DLP shifted along the torsional axis after head rotation.

Figure 3.

 

Dynamic LP orientation after rotation typically changed significantly relative to the previously defined SLP. Angles are given relative to SLP. Each control subject is represented by a unique symbol. Solid symbols: rightward rotation; open symbols: leftward rotation. Error bars, ±1 SEM, and if not shown are smaller than the plot symbol.

Figure 4.

 

Relationship of head torsion and displacement of the dynamic LP relative to the originally defined static LP. Each symbol represents an individual trial, illustrating all trials in which the head rotated 30°.

Figure 5.

 

Torsional offset of DLP in a representative subject diminished slowly over time, but showed variations due to superimposed saccades and eccentric fixations. Data are from the same subject and trial as shown in Figures 1 and 2 . Position of the DLP was calculated by subtracting the ideal torsion necessary to remain in LP from the observed torsion.

Figure 6.

 

The normalized torsional offset of DLP declined slowly over time in control subjects during 30-second intervals after rotation to an eccentric whole-body position. Data were normalized to unity at the end of head movement, relative to the SLP normalized to 0. Thick solid line: the mean; shaded area: ±1 SE. Trials in which DLP was offset from SLP by <0.4° were excluded to minimize noise (<2% of trials). Dashed line: best fit of an exponential decay function that had a time constant of 52 seconds. A total of 79 trials are included.