Vertical Eye Position-Dependence of the Human Vestibuloocular Reflex During Passive and Active Yaw Head Rotations

Matthew J. Thurtell,1,2 Ross A. Black,1 G. Michael Halmagyi,1 Ian S. Curthoys,3 and Swee T. Aw1

 1Eye and Ear Research Unit, Department of Neurology, Royal Prince Alfred Hospital, Camperdown, Sydney, New South Wales 2050; and  2Department of Physiology and  3Department of Psychology, University of Sydney, Sydney, New South Wales 2006, Australia


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

Thurtell, Matthew J., Ross A. Black, G. Michael Halmagyi, Ian S. Curthoys, and Swee T. Aw. Vertical eye position-dependence of the human vestibuloocular reflex during passive and active yaw head rotations. The effect of vertical eye-in-head position on the compensatory eye rotation response to passive and active high acceleration yaw head rotations was examined in eight normal human subjects. The stimuli consisted of brief, low amplitude (15-25°), high acceleration (4,000-6,000°/s2) yaw head rotations with respect to the trunk (peak velocity was 150-350°/s). Eye and head rotations were recorded in three-dimensional space using the magnetic search coil technique. The input-output kinematics of the three-dimensional vestibuloocular reflex (VOR) were assessed by finding the difference between the inverted eye velocity vector and the head velocity vector (both referenced to a head-fixed coordinate system) as a time series. During passive head impulses, the head and eye velocity axes aligned well with each other for the first 47 ms after the onset of the stimulus, regardless of vertical eye-in-head position. After the initial 47-ms period, the degree of alignment of the eye and head velocity axes was modulated by vertical eye-in-head position. When fixation was on a target 20° up, the eye and head velocity axes remained well aligned with each other. However, when fixation was on targets at 0 and 20° down, the eye velocity axis tilted forward relative to the head velocity axis. During active head impulses, the axis tilt became apparent within 5 ms of the onset of the stimulus. When fixation was on a target at 0°, the velocity axes remained well aligned with each other. When fixation was on a target 20° up, the eye velocity axis tilted backward, when fixation was on a target 20° down, the eye velocity axis tilted forward. The findings show that the VOR compensates very well for head motion in the early part of the response to unpredictable high acceleration stimuli---the eye position- dependence of the VOR does not become apparent until 47 ms after the onset of the stimulus. In contrast, the response to active high acceleration stimuli shows eye position-dependence from within 5 ms of the onset of the stimulus. A model using a VOR-Listing's law compromise strategy did not accurately predict the patterns observed in the data, raising questions about how the eye position-dependence of the VOR is generated. We suggest, in view of recent findings, that the phenomenon could arise due to the effects of fibromuscular pulleys on the functional pulling directions of the rectus muscles.


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

For the angular vestibuloocular reflex (VOR) to stabilize an image on the retina, it must generate an eye movement equal in speed but exactly opposite in direction to the head movement stimulus. Hence the eye and head velocity axes must be parallel to one another, and the magnitude of the eye velocity must be equal to that of the head. In many experiments, the three-dimensional VOR in humans has been investigated with the eye initially positioned in the center of the ocular motor range at the onset of the head rotation stimulus. In these experiments, the responses to yaw, pitch, and roll head movements have been investigated, and the eye velocity axis was found to remain approximately parallel with the head velocity axis (Aw et al. 1996; Tweed et al. 1994). Similar observations have been made in monkeys (Crawford and Vilis 1991).

Fetter et al. (1992) investigated the effect of different initial eye-in-head positions on the three-dimensional characteristics of the human VOR during the first 1-2 s of the response to constant velocity (150°/s) rotations of the whole body in yaw, pitch, and roll. They found that the eye velocity output of the VOR systematically depended on eye-in-head position. When the initial eye-in-head position was moved away from the center of the ocular motor range, the eye velocity axis was observed to tilt away from its optimal orientation, thereby compromising retinal image stability.

Misslisch et al. (1994) made similar observations when studying the response to sinusoidal (0.3 Hz) whole-body rotations in yaw, pitch, and roll. Specifically, during yaw rotations, the eye velocity axis was observed to tilt away from its optimal position when the initial eye-in-head position was either up or down. During pitch rotations, the eye velocity axis was observed to tilt away from its optimal position when the initial eye-in-head position was left or right. During roll rotations, the eye velocity axis tilted away from its optimal position when the initial eye-in-head position was up, down, left or right. Misslisch et al. (1994) noted that the axis tilts were such that the foveal image always remained stabilized during the rotations being studied; only peripheral retinal image stability was compromised.

Misslisch et al. (1994) concluded that the axis tilts arose due to a compromise between perfect image stabilization and Listing's law. Listing's law is a constraint on ocular kinematics observed during fixations, saccades and smooth pursuit. The law states that for any eye position, there is an associated plane (the displacement plane) such that the eye assumes only those positions that can be reached from the initial position by a single rotation about an axis in that plane (von Helmholtz 1962). To keep these axes in the displacement plane during an eye movement, the eye velocity vectors must systematically tilt away from the displacement plane (because the time derivative of angular eye position does not equal angular eye velocity) (see Tweed and Vilis 1987). Consequently, the velocity vectors are found to lie in distinct planes (called velocity planes) that have unique orientations depending on eye-in-head position (Tweed and Vilis 1990). Hence, if the VOR does partially obey Listing's law, then, in response to a head rotation stimulus, the eye velocity axis will tilt toward the velocity plane for the current eye-in-head position. One of the models presented by Misslisch et al. (1994) used a VOR-Listing's law compromise strategy, in which the eye velocity vector was positioned exactly halfway between its optimal position and the velocity plane as predicted by Listing's law. As this model could predict, both qualitatively and quantitatively, the mean axis tilts observed in the subjects, Misslisch et al. (1994) concluded that the VOR-Listing's law compromise was responsible for the eye position-dependence of the VOR. The compromise strategy was thought to be neural in origin. There is now evidence that the functional pulling directions of the rectus muscles change with eye-in-head position (Demer et al. 1995). Therefore the observed axis tilts could arise as a result of orbital mechanics.

In all of the previous experiments, the eye position-dependence of the VOR was investigated using predictable, passive, low-frequency, steady-state stimuli. Furthermore, only the spatial characteristics of the eye position-dependence were investigated; the temporal characteristics were not described. Our aim was to measure the effect of vertical eye-in-head position on the response to high acceleration yaw head rotations, which we have called head "impulses" (Halmagyi and Curthoys 1988; Halmagyi et al. 1990). The responses to passive, unpredictable head rotations were contrasted with the responses to active predictable head rotations. To characterize the response to both stimuli, we sought to describe both the spatial and temporal characteristics of any eye position-dependence observed in the responses.


    METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

Paradigms and subjects

We conducted two experiments. In the first, the effect of vertical eye-in-head position on the response to passive yaw head impulses (Halmagyi and Curthoys 1988; Halmagyi et al. 1990) was investigated. The passive yaw head impulse is an unpredictable, low-amplitude (15-25°), high-acceleration (4,000-6,000°/s2) horizontal head rotation. It has a peak velocity of 150-350°/s (the mean head velocities from each of the subjects are plotted in Fig. 1A). During a passive yaw head impulse, the axis of head rotation approximately aligns with the z axis of the head (because the stimulus is delivered manually, there is always a small vertical and torsional component to the head rotation). In the experiment, the vertical position of the fixation target was altered to be either straight ahead (0°), 20° up, or 20° down relative to the subject's left eye. The head and eye rotations were recorded during passive yaw head impulses for each of the different vertical positions of the eye. The paradigm in which passive yaw head impulses were applied with fixation straight ahead (at 0°) was exactly the same as that studied by Aw et al. (1996).



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Fig. 1. A: mean horizontal, vertical, and torsional head velocities from each subject during leftward and rightward passive yaw head impulses. Impulse onset is indicated (arrow). B: mean horizontal, vertical, and torsional head velocities from each subject during active yaw head impulses. Head velocity profiles generated during active head impulses are similar to those generated during passive head impulses.

The second experiment was identical to the first except that the head rotation stimulus used was an active (self-generated) yaw head impulse. The head velocities recorded during the second experiment were similar to those recorded in the first experiment (the mean head velocities from each of the subjects are plotted in Fig. 1B). The use of the active yaw head impulse stimulus has been reported previously (Foster et al. 1997).

In the passive head impulse experiment, eight normal human subjects (26-55 yr, 37 ± 11 yr, mean ± SD) were tested. Eight normal human subjects (21-50 yr, 33 ± 10 yr, mean ± SD) were tested in the active head impulse experiment (6 of these subjects also were tested with the passive head impulse stimuli). None of the subjects had symptoms or signs of vestibular or ocular motor disease, and all were alert at the time of testing. Each subject gave informed consent before each test. The experimental protocols were approved by the Royal Prince Alfred Hospital Human Ethics Committee.

Recording system

Eye and head positions in three-dimensional space were measured using the magnetic search coil technique (Collewijn et al. 1985; Robinson 1963), with the subject seated in the center of 1.9 × 1.9 × 1.9 m magnetic field coils (CNC Engineering, Seattle, WA). Eye position was recorded with a dual search coil (Skalar, Delft, The Netherlands) placed on the left eye. Head position was recorded with a dual search coil secured to the nosepiece of a lightweight spectacle frame. The spectacle frame was strapped very tightly to the subject's head to prevent it from slipping on the head. To confirm that movement of the spectacle frame was coupled tightly to movement of the head, one subject was tested wearing the usual head coil on the spectacle frame and a search coil attached to a bite bar. We assumed that movement of the bite bar was coupled very closely to movement of the head. The difference between the spectacle frame and bite bar coil velocities was very small (see Fig. 2). The vertical components and torsional components of the velocities were virtually identical throughout the data analysis period. We did notice that, as the head approached peak velocity, the horizontal component of the spectacle frame coil velocity was slightly less than that of the bite bar coil. However, the difference between the horizontal components of the spectacle frame and bite bar coil velocities was always <5°/s.



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Fig. 2. Time series of the 3 components of head velocity, as recorded by 2 different search coils, during a passive head impulse. One coil was mounted securely on a spectacle frame, the other on a bite bar. Velocity traces of the coils are almost identical, indicating that movement of the spectacle frame was coupled closely to movement of the head.

The signal from the eye search coil was degraded significantly if the subject blinked during the head impulses. Hence the position of the eyelid in space was recorded with a 2-mm diam, two-dimensional induction coil that was lightly but securely attached to the eyelid to monitor for blinks. Data found to contain blinks were removed from any subsequent analysis.

The four signals from each search coil were recovered by phase detectors (CNC Engineering) and then passed through a custom-made antialiasing filter with a cutoff frequency of 100 Hz (only 2 signals were recovered from the "blink" coil and passed through the filter). The signals were digitized at 1 kHz with a 16-bit analog-digital converter (model AT-MIO-16X, National Instruments, Austin, TX) and then saved to the hard disk of an IBM-compatible PC running under Windows 3.11. Data acquisition programs for the PC were written in LabVIEW (Version 4.1, National Instruments).

Maximum peak-to-peak position noise of the search coil system was <1 min of arc, and maximum peak-to-peak velocity noise was ±3.6°/s. Because of the low system noise, the data did not require smoothing in software.

To preserve the linearity of the magnetic fields, all metallic objects (except those essential for the normal functioning of the system) were removed from the vicinity of the magnetic fields. Previous studies have shown that this search coil system is not sensitive to translations of the magnitude that occur during head impulses (Aw et al. 1996).

A fixation target was provided by a solid-state red laser, which was rear-projected onto a 2 × 1.5 m Plexiglas tangent screen placed exactly 94 cm from the front of the cornea. The laser position was altered by mirror galvanometers driven horizontally and vertically by the PC. The offset of the laser was adjusted so that the fixation spot was positioned in the exact center of the tangent screen (at the level of the subject's left eye).

Calibration procedures

Before each test, the head and eye search coils were calibrated in vitro with a plexiglas Fick gimbal positioned in the exact center of the magnetic fields. During the calibrations, the gimbal was moved between ±20° (in 5° steps) for roll, pitch, and yaw positions (each in a separate calibration). The signals from the search coils were recorded at each calibration position. For the torsional, vertical, and horizontal search coil channels, the signal voltage was plotted against the sine of the calibration angle and an off-line linear regression analysis (in Splus) was used to calculate the search coil gain. The calibration was only considered acceptable if the square of the multiple correlation coefficient (R2) for the linear regression analysis was >0.99. R2 was always >0.9999 in these experiments. It was assumed that the gains and offsets of the search coils were the same in vivo as during the in vitro calibration (Aw et al. 1996; Haslwanter et al. 1996).

Experimental protocols

The subject was seated so that the head was positioned in the exact center of the magnetic fields. The front surface of the cornea of the left eye was positioned exactly 94 cm from the tangent screen.

In vivo calibration data were gathered while the subject was fixating on a target placed in the center of the tangent screen. During this calibration, the subject's head was positioned so that the yaw, pitch, and roll signals from the head search coil were in a software window of ±1° from the zero position of the head. The in vivo calibration was repeated at regular points during each test. The data from the in vivo calibrations were used to correct for the misalignment of the search coil on the eye (as in Tweed et al. 1990).

Listing's plane data were collected at the beginning of each test. The subject was instructed to fixate a number of dots arranged concentrically (from ±20°) on the tangent screen. At least 90 s of data were collected, to calculate the orientation of Listing's plane. During the acquisition of the data, the subject's head was held firmly so that the yaw, pitch, and roll signals from the head search coil were maintained steadily in the ±1° software window.

The head impulse experiments were conducted in soft lighting conditions, with the subject comfortably seated in the center of the magnetic fields. Before the onset of each head impulse (passive or active), the experimenter was required to alter the subject's head position so that the signals from the head search coil were in the ±1° software window. For the passive head impulses, once the head was positioned correctly, the data acquisition system was triggered manually. Subjects were instructed to stare at the fixation target while the head was rotated quickly to the left or the right by the experimenter. Data acquisition ceased a few seconds after the head impulse onset. For the active head impulses, once the head was positioned correctly, the experimenter removed his or her hands from the vicinity of the subject's head. The subject was required to maintain the head position, and, on command, quickly rotate their head to the predetermined side while maintaining fixation on the laser target. Data acquisition commenced ~1 s before the onset of the impulse and ceased a couple of seconds after the onset. Data from subjects who moved their head before the onset of the active head impulse were discarded. The subjects were carefully tutored and given ample time to practice before the search coil was placed on the eye.

Some of the active head impulse experiments were carried out with the subject in complete darkness to investigate whether the response changed when there was no visual input. The laser target was extinguished immediately before the onset of the impulse so that there were no visual cues during the impulse. During these tests, the experimenter wore a virtual reality headset (Virtual i-O, Seattle, WA), enabling them to view the head search coil signals (and therefore position the head so that the coil signals were in the ±1° software window) without compromising the dark environment in which the subject was placed.

Some of the passive and active head impulse tests were carried out on more than one occasion to determine how consistent the responses from a single subject were on repeated testing. In all cases, the data from the initial test were used in the analysis---the data from the repeated tests were only used for comparison with the previously collected data.

Data analysis

All data were analyzed off-line on a DECstation 5000/240 using C and Splus (Becker et al. 1988), under Ultrix. The analysis procedures applied to the data from both experiments were identical.

The horizontal and vertical Fick angles representing eye and head position, with reference to a right-handed space-fixed coordinate system, were calculated from the raw data and the search coil gains using the methods described by Haslwanter (1995). The torsional Fick angle (with reference to a right-handed space-fixed coordinate system) was calculated using the equation from Bruno and van den Berg (1997) to correct for nonorthogonality between the direction and torsion induction coils of the search coil. Nonorthogonality between the induction coils results in pseudotorsion during purely vertical movements of the search coil. The correction proved effective in eliminating the error (see APPENDIX).

The Fick angles were used to calculate the rotation matrices representing the eye and head rotations in three-dimensional space. The in vivo calibration data were used to calculate the offset rotation matrix for both the eye and head in three-dimensional space. Using the methods described by Tweed et al. (1990), the raw eye and head rotation matrices were corrected for any position offset using the offset rotation matrices. From the corrected rotation matrices, the rotation vectors representing head and eye position were calculated (Haslwanter 1995; Haustein 1989). The velocity vectors of the head-in-space, eye-in-space, and eye-in-head were calculated from the corresponding rotation vectors using the equation from Hepp (1990). We calculated head velocity with reference to a head-fixed coordinate frame using the methods of Aw et al. (1996) so that the eye and head velocities were expressed with reference to the same coordinate frame for our analysis. Head velocity with reference to a head-fixed coordinate frame is simply the velocity of the head-in-space expressed with respect to the head-fixed coordinate frame. The concept is illustrated in Fig. 3.



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Fig. 3. Difference between head velocity with reference to the space-fixed coordinate frame and head velocity with reference to the head-fixed coordinate frame is illustrated. Subject is undergoing a clockwise rotation about a nasooccipital axis. Head is pitched 30° up, relative to the zero position of the head in space at the time of the sample. A: head velocity vector is expressed relative to the space-fixed coordinate frame (dark lines) and is found to be rotated 30° up from perfect alignment with the x axis. B: head velocity vector is expressed relative to the head-fixed coordinate frame (dark lines), which moves with the head. Velocity vector is aligned with the x axis (the nasooccipital axis) because the head is rotated 30° up relative to the space-fixed coordinate frame at the time of sampling. Note that the magnitude of the velocity vector is unchanged---only the orientation of the vector is altered when it is described with respect to a different coordinate frame.

Models presented later in the paper require that the orientation of Listing's plane be known for each subject. The 90 s of Listing's plane data were used to fit a plane of best fit, using a singular value decomposition algorithm (Press et al. 1988)
<B>r</B><SUB><IT>x</IT></SUB><IT>=</IT><IT>f</IT><IT>+</IT><IT>f</IT><SUB><IT>v</IT></SUB><B>r</B><SUB><IT>y</IT></SUB><IT>+</IT><IT>f</IT><SUB><IT>h</IT></SUB><B>r</B><SUB><IT>z</IT></SUB>
where rx, ry, and rz are the rotation vectors representing the torsional, vertical, and horizontal components of the rotation and f, fv, and fh are coefficients.

The time of onset of each head impulse was calculated using an algorithm developed by Aw et al. (1996). The analysis of the head-impulse data was restricted to a period of 100 ms, beginning 20 ms before the onset of the head impulse. Thus in the case of the passive head impulses, the effects of non-VOR systems (such as the cervicoocular reflex and smooth pursuit) were excluded because these systems have latencies >90 ms after the onset of head rotation (Bronstein and Hood 1986; Carl and Gellman 1987; Tychsen and Lisberger 1986).

The data were not desaccaded because saccades and quick phases do not normally occur within 100 ms of the onset of passive head impulses (Aw et al. 1996) or, as we discovered, active head impulses. Nevertheless, all head impulse data were inspected visually to check for blinks, search coil slippage, and other artifacts; data that showed such artifacts were not included in the analysis.

The spatial alignment of the head and eye velocity axes (with reference to a head-fixed coordinate frame) was displayed by plotting the head and eye velocity vectors in the pitch (xz) and roll (yz) planes. Data were not plotted in the yaw (xy) plane as these plots did not clearly illustrate the spatial arrangement of the vectors (the head and eye velocity vectors were aligned fairly closely to the z axis of the head, which is coincident with the origin of the yaw plane).

The temporal characteristics of any eye-head axis misalignment cannot be illustrated clearly in the pitch and roll plane plots; a complete three-dimensional VOR performance measure is required. The temporal characteristics of VOR performance initially were measured using the indices (misalignment angle, speed gain, and VOR gain) introduced by Aw et al. (1996). At low eye and head velocities, however, the indices cannot be calculated because of the presence of erratic values introduced by the processing. To overcome this problem, we developed a new performance measure that allowed complete description of the input-output kinematics of the VOR in three dimensions, regardless of eye or head velocity. The performance measure, named the VOR error vector (epsilon ), is simply the difference between the velocity vectors representing the head (omega h) and eye (omega e) rotations with reference to a head-fixed coordinate frame
&egr;=−<IT>ω<SUB>e</SUB>−ω<SUB>h</SUB></IT>
The eye velocity vector is inverted to allow easy comparison with the head-velocity vector. If the head and eye velocity vectors were equal in magnitude and exactly opposite in direction, then epsilon  would be equal to zero and there would be no retinal slip. However, any axis misalignment or "gain" difference between the eye and head velocity vectors would result in epsilon  having a direction and magnitude (see Fig. 4). All three components (torsional, vertical, and horizontal) of epsilon  were calculated and plotted, thereby providing a means of analyzing the input-output kinematics of the VOR in three-dimensions for the entire duration of the analysis period. The error vector calculations assume that fixation was on an object positioned at infinity---because fixation was on a target 94 cm from the eye, it must be noted that the error vector does slightly underestimate the amount of retinal slip.



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Fig. 4. Vestibuloocular reflex (VOR) error vector is the difference between the inverted eye-in-head velocity vector and the head-in-head velocity vector. When the eye-in-head and head-in-head vectors are equal in magnitude and opposite in direction, there is no VOR error vector. However, any difference in magnitude or direction results in the VOR error vector having a direction and magnitude.

For the first experiment (passive yaw head impulses), the analysis also involved the calculation of misalignment angle, speed gain, and VOR gain so that we could directly compare our results with those of Aw et al. (1996). These indices were calculated 80 ms after impulse onset, near the peak head and eye velocities, where the low-velocity artifact would be minimal.

Means ± two-tailed 95% confidence intervals were computed for the epsilon  time series, misalignment angle, speed gain, and VOR gain. At various stages in the data analysis, a standard two-sample t-test was performed to establish the existence of a significant difference or otherwise between two samples. The P value was set at 0.05, and the null hypothesis was that the difference between the means of the two samples was equal to zero.


    RESULTS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

The results from the two experiments are considered separately. There are three categories of analysis for each experiment: position and velocity time series, spatial alignment of the head and eye velocity vectors in three-dimensional space, and three-dimensional analysis of the input-output kinematics of the VOR.

Position and velocity time series for passive head impulses

The horizontal, vertical, and torsional components of the VOR in response to leftward passive yaw head impulses, from one subject, with gaze directed toward each of the three vertical targets are plotted against time in Fig. 5A. Position and velocity data for head-in-space, eye-in-space, and eye-in-head are shown. Head rotation data with reference to a head-fixed coordinate frame are not displayed in this plot.



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Fig. 5. A: horizontal, vertical, and torsional components of the head-in-space (head), eye-in-space (gaze), and eye-in-head (eye) from a normal subject during leftward passive yaw head impulses with fixation on targets 20° up, center (0°), and 20° down. Onset of the impulse is indicated by the small arrow. Note the changes in torsional eye velocity (large arrow). As vertical eye-in-head position moves from 20° up to 20° down, the torsional eye-in-head velocity becomes increasingly counterclockwise with respect to the head-in-space. B: same as A during leftward active yaw head impulses. Eye-in-head response compensates best for the head rotation stimulus when the target is in the center; torsional eye velocity is clockwise relative to the head when fixation is 20° up and counterclockwise relative to the head when fixation is 20° down.

The horizontal and vertical eye-in-head components are the mirror images of the corresponding head-in-space components, regardless of vertical eye-in-head position. Consequently the horizontal and vertical components of gaze remain constant throughout the impulses. The degree to which the eye-in-head torsion component mirrors the head-in-space torsion depends, however, on the vertical eye-in-head position. The effect is most obvious in the velocity traces, when the torsional eye-in-head components 125 ms after head impulse onset (large arrows in Fig. 5A) are compared with each other. The torsional eye-in-head response most closely matches the torsional head-in-space stimulus when the vertical eye-in-head position is 20° up. As the vertical eye-in-head position moves from 20° up to 20° down, the torsional eye-in-head velocity becomes progressively more counterclockwise relative to an ideal torsional eye-in-head response. The eye-in-head torsional responses during rightward yaw head impulses were the opposite of those observed during the leftward yaw head impulses---as vertical eye-in-head position progressively moved from up to down, the eye-in-head velocity became progressively more clockwise relative to an ideal eye-in-head response. Any mismatch between the torsional eye-in-head and head-in-space traces resulted in a subtle torsional gaze offset at the end of the impulse. The torsional gaze offset was least when vertical eye-in-head position was 20° up and became progressively greater when fixation was on targets at 0 and 20° down (see dashed traces in Fig. 5A).

The responses shown in Fig. 5A are representative of the data obtained from the entire group. In each subject, the direction and magnitude of the torsional eye-in-head response was consistent for each vertical fixation position, throughout each test and on repeated testing.

Velocity axis alignment in passive head impulses

Mismatch of the torsional eye-in-head and head-in-space velocities, especially when fixation was on the targets at 0 and 20° down, suggests misalignment of the head and eye velocity axes. To allow the velocities to be compared, both were calculated relative to the same head-fixed coordinate frame. The eye-in-head velocity vector also was inverted to facilitate comparison between the two vectors. The spatial alignment of the mean eye-in-head and head-in-head velocity vectors (averaged across all 8 subjects) for each of the vertical eye-in-head fixation positions is shown in Fig. 6A. In Fig. 6A, the vectors are shown in two planes (pitch and roll) to display the degree of vector alignment in all three dimensions.



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Fig. 6. A: mean head and eye velocity vectors (referenced to a head-fixed coordinate frame), averaged across all 8 subjects, for passive head impulses with fixation 20° up, center (0°), and 20° down. Velocity vectors are plotted in the pitch plane (top) and the roll plane (bottom). Eye velocity vectors have been inverted to aid comparison. Vectors are well aligned in the roll plane for all vertical eye-in-head positions. Misalignment between the vectors in the pitch plane increases as fixation is lowered---the eye velocity vector tilts forward. However, the vectors remain well aligned in the pitch plane at low velocities regardless of vertical eye-in-head position. B: mean head and eye velocity vectors (averaged across all 8 subjects), plotted in both pitch and roll planes, for active head impulses. Vectors are well aligned in the roll plane for all vertical eye-in-head positions. Axis alignment in the pitch plane is best when fixation is on the center target. Eye velocity axis tilts back when fixation is 20° up and tilts forward when fixation is 20° down.

The eye velocity vector most closely aligned with the head velocity vector, in both the pitch and roll planes, when the vertical eye-in-head position was 20° up. The vectors became increasingly misaligned in the pitch plane as the vertical eye-in-head position moved from up to down; the eye velocity vector tilted forward as eye position moved from up to down. Surprisingly, the eye and head velocity vectors remained aligned at low velocities for all vertical eye-in-head positions. The eye position-dependence of the response only became obvious when eye velocity was >75°/s. In contrast, the eye and head velocity vectors remained aligned in the roll plane, regardless of vertical eye-in-head position.

Input-output analysis for passive head impulses

To evaluate how closely eye velocity mirrored head velocity, the VOR error vector (epsilon ) was calculated for each of the three vertical eye-in-head fixation positions. The time series of the horizontal, vertical, and torsional components of epsilon  are plotted for each vertical eye-in-head fixation position (see Fig. 7A).



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Fig. 7. A: group means ± 2-tailed 95% confidence intervals of the magnitudes of the 3 components of the VOR error vector (epsilon ) for each of the fixation conditions during passive head impulses. Responses from right and left impulses are illustrated in different shades to show any left-right asymmetries that may be present in the subject group. Arrow indicates the onset of the head impulse. Torsional component of epsilon  (epsilon x) is clearly dependent of the vertical eye-in-head position. Maximum values of epsilon x are smallest when fixation is on a target 20° up and largest when fixation is on a target 20° down. epsilon x takes a similar course for ~45 ms after the onset of the impulse for each of the vertical eye-in-head positions. No eye position-dependence is obvious in the other components of epsilon . B: group means ± 2-tailed 95% confidence intervals of the magnitudes of the components of epsilon  during active head impulses. epsilon x is, once again, dependent on vertical eye-in-head position. No eye position-dependence is obvious in the other components of epsilon .

When the data from the left and right impulse sets were compared, no large asymmetries were observed. There was a significant difference (P < 0.05) when the left and right horizontal components of epsilon  (epsilon z) in the center (0°) fixation condition were compared at 80 ms after the impulse onset, indicating a small left-right asymmetry in the VOR responses of the subject group (see Fig. 7A). No significant difference was observed for any of the other conditions.

epsilon z was consistently larger than the other epsilon  components (mean maximum values were 20.8°/s for leftward impulses and 33.1°/s for rightward impulses), regardless of the vertical eye-in-head fixation position, in all subjects. Thus horizontal eye velocity did not exactly match the horizontal head velocity in any of the fixation conditions. There was, however, considerable variability in the extent to which the horizontal eye velocity matched horizontal head velocity. No significant differences were observed between epsilon z (at 40 and 80 ms after impulse onset) for each of the vertical eye-in-head fixation positions (P > 0.05), indicating no dependence of epsilon z on vertical eye-in-head position.

There was a small vertical component of epsilon  (epsilon y) in most subjects---mean maximum values were <±10°/s for each of the vertical eye positions. When epsilon y for each of the vertical eye-in-head fixation positions (at 40 and 80 ms after impulse onset) were compared, they were not significantly different (P > 0.05).

In contrast, the torsional component of epsilon  (epsilon x) varied systematically with vertical eye-in-head fixation position: it was consistently small throughout the head impulses when the fixation position was 20° up, it became larger when the fixation position was central and larger again when the fixation position was 20° down. However, for all vertical eye-in-head fixation positions, the magnitude of epsilon x was similar for the first 40 ms after the onset of the head impulse---only in the last 40 ms of the data analysis period did the changes in epsilon x magnitude become apparent. The means ± two-tailed 95% confidence intervals of epsilon x at 40 and 80 ms after the onset of the head impulse, for the responses to both leftward and rightward impulses, are listed in Table 1. When epsilon x for each of the vertical fixation positions was compared 40 ms after impulse onset, the differences were not significant (P > 0.05). However, a significant difference (P < 0.05) was observed 80 ms after the impulse onset. The time at which the vertical eye-in-head position dependence becomes significant (P < 0.05), defined as the point at which epsilon x for the 20° up and 20° down conditions become significantly different, was 47 ms after the onset of the head impulse.


                              
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Table 1. Means ± two-tailed 95% confidence intervals of epsilon x for passive head impulses

Position and velocity time series for active head impulses

The three components of the response to leftward active yaw head impulses, from one subject, with fixation on each of the three vertical targets are plotted in Fig. 5B. For each of the different vertical eye-in-head fixation positions, the horizontal and vertical components of eye in head are, once again, the approximate mirror images of the corresponding components of head in space, and the horizontal and vertical components of gaze remain constant throughout the impulses. The torsional component of eye in head does not mirror the torsional component of head in space in the 20° up and 20° down conditions, but it does when fixation is at 0°. When vertical eye-in-head fixation position is 20° up, the eye-in-head torsion is clockwise relative to an ideal eye-in-head response; when fixation is 20° down, the eye-in-head torsion is relatively counterclockwise. Subsequently, there are torsional gaze offsets at the end of these two impulses, unlike when fixation is on the center target. Once again, the eye-in-head torsional responses during rightward yaw head impulses were the opposite of those observed during the leftward impulses.

The patterns observed in Fig. 5B are representative of the results from the whole subject group in response to leftward active head impulses. For each subject, the direction and magnitude of the response was very consistent for each vertical eye-in-head fixation position throughout the test, on repeated testing, and when tested in complete darkness. The magnitudes of the responses did differ between subjects (as with the passive head impulses).

Velocity axis alignment in active head impulses

The spatial alignment of the mean eye and head velocity vectors (averaged across all 8 subjects) for each of the vertical eye-in-head fixation positions is shown in Fig. 6B. Note that the head velocity profiles for the three vertical eye-in-head fixation positions are similar, indicating that the head rotation stimulus was consistent regardless of eye position.

The head and eye velocity vectors were most closely aligned in the pitch and roll planes when the vertical eye-in-head fixation position was at 0°, although the vectors did not align perfectly at low velocities in the pitch plane. When the vertical eye-in-head fixation position was 20° up or 20° down, the vectors did not align in the pitch plane. The vectors remained well aligned in the roll plane, regardless of vertical eye-in-head position. In general, the eye velocity vectors tilted forward when the vertical eye-in-head position was 20° down, and tilted backward when it was 20° up. It is clear from the pitch plane plots that the eye and head velocity vectors do not necessarily align well at low velocities---the degree of the alignment does show some eye position-dependence. For example, in Fig. 6B, when the vertical eye-in-head position is 20° down, the head and eye velocity vectors do not align well at the low velocities, in contrast with the responses to the passive head impulses (see Fig. 6A).

Input-output analysis for active head impulses

The means ± two-tailed 95% confidence intervals of epsilon x, epsilon y, and epsilon z for the subject group are shown in Fig. 7B with vertical eye-in-head fixation position at 0°, 20° up, and 20° down. The responses from leftward active head impulses are illustrated in black shading, whereas those from the rightward active head impulses are illustrated in gray.

There were no significant left-right asymmetries (P > 0.05). The mean maximum values of epsilon z were 10.6°/s for leftward active head impulses and 15.8°/s for rightward impulses. Thus the horizontal eye velocity did not exactly match the horizontal head velocity in any of the conditions. No significant differences were observed when epsilon z (at 40 and 80 ms after impulse onset) at each of the vertical fixation positions was compared (P > 0.05), indicating no dependence of epsilon z on vertical eye position.

The mean maximum values of epsilon y were < ±10°/s. When epsilon y at each of the fixation positions was compared (at 40 and 80 ms after impulse onset), no significant differences were observed (P > 0.05).

The profile of epsilon x did vary systematically depending on the vertical fixation position: it remained closest to zero throughout the data analysis period when fixation was on the target at 0°. For leftward impulses, it became increasingly negative when fixation was on the 20° up target (indicating that the torsional eye velocity was more clockwise than the ideal response). When fixation was on the 20° down target, it became increasingly positive (indicating that the torsional eye velocity was more counterclockwise than the ideal response). The opposite was observed in the rightward active head impulses. There was considerable intersubject variability in the magnitude of the responses, in particular, when fixation was on the 20° up target. However, the directions of the responses were consistent within the group.

The means ± two-tailed 95% confidence intervals of epsilon x at 40 and 80 ms after active head impulse onset, for the responses to both leftward and rightward impulses, are listed in Table 2. When epsilon x at 40 ms after impulse onset was compared, a significant difference (P < 0.05) was found between the 0° and 20° down fixation positions and the 20° up and 20° down fixation positions. At the 80-ms point, when epsilon x for each of the fixation positions were compared, there was a significant difference (P <=  0.01). epsilon x for the 20° up and 20° down fixation positions became significantly different (P < 0.05) within the first 5 ms after the onset of the active head impulses. Thus epsilon x depends on vertical eye-in-head fixation position from 5 ms after the onset of an active head impulse in contrast with the response to a passive head impulse, which does not become eye position-dependent until 47 ms after onset.


                              
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Table 2. Means ± two-tailed 95% confidence intervals of epsilon x for active head impulses


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

VOR during central fixation

When fixation was on a target at 0° during the passive yaw head impulses, the head and eye velocity axes did not remain perfectly aligned for the duration of the data analysis period, and the horizontal eye velocity was slightly less than that of the head. Aw et al. (1996) made similar observations. They calculated time series of the angle between the eye and head velocity axes (misalignment angle), the speed gain of the response (magnitude of eye velocity divided by magnitude of head velocity), and the VOR gain (speed gain multiplied by the cosine of misalignment angle). To compare our results directly with those of Aw et al. (1996), we calculated the misalignment angle, speed gain, and VOR gain at 80 ms after the head impulse onset. Our calculated values and those reported by Aw et al. (1996) are listed in Table 3. The mean values from the present study lie within the two-tailed 95% confidence intervals reported by Aw et al. (1996).


                              
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Table 3. Means ± two-tailed 95% confidence intervals of misalignment angle, speed gain, and VOR gain

In pilot experiments, we observed that the VOR became less compensatory when head velocity was >350°/s during passive head rotation. Our observation is in agreement with previous findings. Pulaski et al. (1981) found that the VOR compensated well for head velocities up to ~350°/s during both active and passive head rotation, provided there was an attempt to visualize a real or imagined target in space.

We found that the eye and head velocity axes aligned better during the active head impulses with fixation at 0° than during the passive head impulses. Furthermore the horizontal components of eye and head velocity were matched more closely during the active head impulses than during the passive head impulses. epsilon z was significantly smaller at 40 and 80 ms after impulse onset in the active head impulses (P < 0.05). The horizontal head velocities of the two stimuli were similar (see Fig. 1), so differing head rotation kinematics would not explain why there is less horizontal error in response to the active head impulses. We suggest that other neural mechanisms (e.g., horizontal VOR gain enhancement) could be responsible for improving the compensatory eye movement performance during active head impulses in normal subjects.

VOR and vertical eye position

The three-dimensional orientation of the eye velocity axis changed when vertical eye-in-head position was varied during both passive and active head impulses. The shifts in eye velocity axis were most obvious in the pitch plane: when the vertical eye-in-head position was 20° up, the eye velocity axis tilted backward, when the vertical eye-in-head position was 20° down, the eye velocity axis tilted forward. The spatial characteristics and magnitudes of the axis shifts agree with previous findings reported for both passive (Fetter et al. 1992; Frens et al. 1996; Misslisch et al. 1994) and active head rotations (Misslisch 1995).

We found considerable intersubject variability in the magnitudes of the axis shifts. Misslisch (1995), who also observed large intersubject variability, suggested that the variability could be related to the level of alertness of the subject. In our experiments, subjects who were drowsy at the time of testing were noted to have subtle axis tilts compared with when alert. Such a finding would be consistent with the idea of a VOR-Listing's law compromise because Listing's law fails during sleep (Nakayama 1975). However, the level of alertness in the subjects was not objectively measured in the experiments. Therefore it cannot be concluded that differing alertness levels were responsible for the observed variations in the magnitude of axis tilt. To the contrary, the majority of subjects who showed subtle responses during their initial test continued to do so on repeated testing regardless of their apparent alertness level. It appears then that the variation in the axis shift magnitude is more likely due to variations between subjects, rather than to the level of alertness of the subject.

The temporal courses of the axis tilts have not been previously studied. Our measurements of the VOR error vector (epsilon ) show that during passive head impulses, the head and eye velocity vectors show a similar profile of misalignment in the first 47 ms after head impulse onset, regardless of vertical eye-in-head position! It was only after this period that differences appeared in epsilon x for the different vertical fixation positions. Also the head and eye velocity axes were well aligned in the pitch plane at low velocities (<75°/s) regardless of vertical eye-in-head fixation position. Whether the lack of relative misalignment between the different vertical fixation positions is velocity related or due to a latency in the response is unclear. Evidence that suggests that the axis tilt is not velocity related includes the finding that axis shifts are still present for the different vertical eye positions at velocities <50°/s (Misslisch et al. 1994). Therefore it appears that after the onset of a passive yaw head impulse there is a 47-ms delay before the VOR becomes dependent on vertical eye position.

In contrast, after an active yaw head impulse there is <5 ms delay before the VOR becomes dependent on vertical eye position. Therefore the major finding from this study is that there is vertical eye position-dependence in the response to both active and passive high-acceleration head rotations; the eye velocity generated depends on both the head velocity stimulus and the current vertical eye-in-head position. The eye position-dependence is not apparent in response to the passive head impulses until 47 ms after impulse onset, whereas it is apparent within 5 ms of impulse onset when the stimulus is actively generated. The findings are summarized in Fig. 8, which shows the mean misalignment angle between the eye and head velocity axes in the pitch plane as a function of time for both passive and active head impulse stimuli.



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Fig. 8. A: mean pitch misalignment angle (averaged across all subjects) during passive head impulses for the 3 vertical eye-in-head fixation positions. Degree of alignment is similar regardless of vertical eye-in-head position until ~50 ms after head impulse onset. Note that ~20 ms of data close to the head impulse onset are not displayed due to low-velocity artifact (see METHODS). B: mean pitch misalignment angle (averaged across all subjects) for active head impulses. From this figure, it can be concluded that the degree of axis alignment is dependent on vertical eye-in-head position from >= 20 ms after head impulse onset.

Consequences for retinal image stabilization

To investigate the effect of the axis shifts on retinal image stabilization for both sets of head impulse stimuli, a computer simulation was developed. In the simulation, an array of target points on a tangential screen 94 cm from the eye was rotated passively using representative rotation matrices from the eye-in-space position data. The target points were, at each millisecond in time, projected on to the back of a sphere corresponding to the retina of the eye. The dimensions of the sphere and fovea corresponded to anatomic data (Williams et al. 1989). The result of the simulation was a representation of the cumulative slip or smear of the retinal image over the course of each head impulse.

First, we examined how much slip occurred in the first 60 ms of the data analysis period (from 20 ms before impulse onset to 40 ms after impulse onset). In response to the passive head impulses, very little retinal slip was evident. Therefore the VOR is very effective in stabilizing the retinal image in response to very short-duration (<40 ms) high-acceleration yaw head rotations regardless of the initial vertical eye-in-head position. In response to the active head impulses, there was little retinal slip when the vertical eye-in-head position was at 0°. When the vertical eye-in-head fixation position was 20° up and 20° down, there was slippage of the image in the periphery of the retina and over the fovea with the point of maximum stability being near the lower and upper poles of the retina, respectively. It seems then that the response in active head impulses is optimized to stabilize retinal images when the starting eye position is near the center of the ocular motor range.

We also investigated how much retinal slip occurred over the entire duration of the data analysis period. The foveal image was not well stabilized for any of the fixation positions or either of the stimuli. The fact that the horizontal eye velocity did not exactly match the horizontal head velocity resulted in a degree of horizontal image slip over the fovea for each of the vertical eye positions. During the passive head impulses, image stability was best when vertical eye-in-head position was 20° up; during the active head impulses, it was best when vertical eye-in-head position was at 0° (see Fig. 9). For the other vertical eye-in-head positions, there was increased torsional slippage of the retinal image in the periphery, which was combined with the horizontal slippage so that the point of maximal image stability was on the periphery of the retina. The findings contrast with those of Misslisch et al. (1994), who reported that the foveal image was well stabilized, whereas image stability on the periphery was compromised. The argument that the VOR-Listing's law compromise strategy allows efficient stabilization of the foveal image therefore is not supported by the findings from the current experiment.



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Fig. 9. Computer simulation of retinal smear obtained from representative active head impulses (from the same subject as shown in Fig. 5B) during fixation 20° up, in the center, and 20° down. View is anteroposterior, toward the back of the subject's retina. Margin of the fovea is marked in the center of the retina. Image on the fovea is not stabilized in any of the conditions. There is increased torsional image slippage on the retina when the vertical eye-in-head position is 20° up or 20° down. In these 2 conditions, the point of maximum image stability is near the lower pole and upper pole of the retina, respectively. Image slip is almost purely horizontal when the target is in the center. Arrow indicates general direction of image slip.

Possible axis shift mechanisms

The head velocity profiles for the different vertical eye-in-head positions are almost identical. Hence differing inputs from the semicircular canals with the different fixation positions cannot be responsible for the observed axis shifts. In our experiments, the possibility that search coil defects were responsible for the observed patterns was eliminated by the use of an algorithm (Bruno and van den Berg 1997) to correct for the effects of nonorthogonality between the direction and torsion induction coils (see APPENDIX). The mechanism responsible for producing the axis tilts is therefore most likely the same as that responsible for producing the phenomena observed in previous experiments (Fetter et al. 1992; Misslisch et al. 1994).

For each of the vertical eye positions, the eye velocity vectors tilted toward the velocity planes predicted by Listing's law, indicating that the response could be due to a compromise between the ideal eye velocity axis and that predicted by Listing's law. To investigate this possibility, we developed a model similar to that presented by Misslisch et al. (1994). Our model calculated the eye-in-head torsional velocity to be exactly halfway between the optimal eye-in-head torsional velocity, which would stabilize the entire retinal image, and that predicted by Listing's law (calculated from the subjects' Listing's plane data). The eye-in-head velocity vectors predicted by the model, for both passive and active head impulses, are shown in the pitch plane in Fig. 10 along with the actual data for comparison. The model does predict the correct direction for the eye velocity axis shifts, but it does not predict the correct magnitude of the response; it also does not predict the initial good alignment of the head and eye velocity vectors in the passive head impulses, as expected. These findings contrast with those of Misslisch et al. (1994), who reported that the averaged eye velocity responses of their subject group were matched by the output of their model. A simple VOR-Listing's law compromise strategy is therefore inadequate to explain our findings and the mechanism responsible for bringing about the eye position-dependence of the VOR now is called into question.



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Fig. 10. A: comparison of the modeled and actual responses to the passive head impulse stimuli. Data are viewed in the pitch plane. The VOR-Listing's law model does predict the correct direction of axis shift but does not predict the correct magnitude of the axis shift or the initial good alignment of the eye and head velocity axes. B: comparison of the modeled and actual responses to the active head impulse stimuli. Once again, the correct direction of axis shift is predicted by the model. The predicted magnitude does not match the data.

In previous studies (Misslisch 1995; Misslisch et al. 1994), it was concluded that the eye position-dependence of the VOR probably comes about due to neural processing and that ocular motor plant mechanics could not (or at least not solely) be responsible for producing it. Recently, Demer et al. (1995) demonstrated that the tendons of the rectus muscles pass through fibromuscular pulleys near their insertions on eyeball, keeping the paths of the muscle bellies relatively fixed so that the functional pulling directions of the muscles change with different eye-in-head positions. Because the functional pulling directions of the rectus muscles are dependent on eye-in-head position, the pulleys therefore could play a very important role in producing the observed axis tilts.

Using a model-based approach, it has been shown that Listing's law is obeyed when a two-dimensional (yaw-pitch) saccadic pulse is sent to an ocular motor plant that incorporates pulleys (Quaia and Optican 1998; Raphan 1997, 1998). In other words, the systematic tilts of the eye velocity vectors that occur during an eye movement that obeys Listing's law are predicted by models that incorporate pulleys, when the saccadic pulse has only yaw and pitch components! In the case of the VOR, the commands being sent to the eye muscles have three components (yaw, pitch, and roll); this would explain why the VOR does not obey Listing's law when considered in the context of the pulley model. Indeed, Raphan (1997) has shown that after incorporation of the pulley system into a vector-integrator model of ocular motor control, the eye position-dependence of the VOR is predicted when a three-dimensional eye movement command is sent to the eye muscles. To predict the eye position-dependence of the VOR, Tweed also incorporated the pulley effect into his quaternion model of ocular motor control so that "the muscles' pulling directions move when the eye moves, in the same direction but only about half as far" (Tweed 1997).

Although it is likely that the pulleys have a role in bringing about the eye position-dependence of the VOR, there is currently no experimental evidence to support the hypothesis. Therefore a neural mechanism in which the eye movement signal is altered depending on eye-in-head position (as hypothesized by Misslisch et al. 1994) is still a possibility. We are unable to establish which of the proposed mechanisms (if either) is responsible for the eye position-dependence of the VOR based on the results from the current experiment. Indeed, our findings serve more to highlight the complexity of the issue. As discussed earlier, the eye and head velocity axes were aligned better during the active head impulses than during the passive head impulses when fixation was on a target at 0°. If the degree of muscle contraction in the smooth muscle pulleys does not change, the pulleys should exert a constant effect on the eye muscles given a particular eye-in-head position regardless of whether the stimulus was generated passively or actively. Such an argument initially may be considered as evidence that the neural hypothesis is responsible for the observed patterns in axis tilt. The argument is not as convincing as one may think, however. It must be noted that the eye velocity response to the head impulse depends on both the head velocity stimulus and the current eye-in-head position. It is clear, from Figs. 1 and 6, that although the stimuli are similar they are not identical. On average, the head velocity axis tilted back from the roll (yz) plane during the passive head impulses, whereas it tilted forward from the roll plane during the active head impulses. The eye velocity axis was, on average, tilted forward relative to the head velocity axis during the passive head impulses when fixation was on the target at 0°, whereas the averaged head and eye velocity axes remained well aligned during the active head impulses for the same fixation position. Hence it is certainly possible that the differing stimulus profiles partly explain the differences between the responses to passive and active head impulses. We also found that the horizontal eye velocity was a much better match for horizontal head velocity during the active head impulses (resulting in a smaller horizontal error vector component---see Fig. 7). Therefore, at the very least, there is a degree of enhancement of the horizontal VOR gain to reduce horizontal retinal image slip during the active head impulses. The mechanism responsible for the improved performance is unclear, but in any case there has to have been some neural modification of the eye movement command to bring about these changes. Hence for head movements with identical kinematics, the neural commands traveling to the eye muscles probably are altered depending on whether the eye movement is generated in response to a passive or active head impulse. Consequently the differing axis tilt patterns in response to passive and active head impulses do not provide sufficient evidence to rule out the possibility that a pulley system has an effect on the VOR.

The observed latency in the axis shift, after the passive head impulse onset, is difficult to explain in the context of both pulley and neural hypotheses. It is possible that, if the eye position-dependence of the VOR arises primarily due to the effects of the pulleys, the initial alignment of the axes results from some neural effort to improve the early VOR performance. Alternatively, if the eye position-dependence of the VOR arises primarily due to a neural mechanism, the delay before the axis tilt may occur due to some processing delay in the CNS.

In summary, the degree of misalignment between the eye and head velocity axes depends on vertical eye-in-head position during both passive and active yaw head impulses. The initial 47 ms of the response to passive head impulses is not eye position-dependent. The response to the active head impulses is eye position-dependent almost immediately. The findings show that the initial lack of eye position-dependence in the VOR after the onset of an unpredictable head rotation results in almost perfect stabilization of the retinal image during that time. In view of the current evidence, the eye position-dependence of the VOR probably arises due to the effects of fibromuscular pulleys on the pulling directions of the rectus eye muscles.


    APPENDIX
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

Nonorthogonality correction

The algorithm to correct for the nonorthogonality between the direction and torsion induction coils was based on formulae presented in Bruno and van den Berg (1997). To establish that the correction does improve the estimation of the torsional Fick angle, a search coil with nonorthogonal induction coils was placed in the gimbal and moved through a combination of different horizontal, vertical, and torsional angles. Two graphs are presented in Fig. A1: in the first, the torsional Fick angle without the correction for nonorthogonality is plotted; in the second, the torsional Fick angle with the correction for nonorthogonality is plotted. On the x axis, the actual value of the torsional Fick angle, according to the gimbal, is given. It can be seen clearly that the best estimation of the torsional Fick angle is seen when the signal is corrected for the nonorthogonality between the induction coils.



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Fig. A1. Torsional Fick angle is plotted against the true value of the Fick angle (according to the gimbal) while the gimbal is moved through a variety of horizontal, vertical, and torsional angles. Data were obtained from a search coil with nonorthogonal induction coils. The torsional Fick angle is much closer to its true value when the correction is applied. Any remaining error is probably due to imperfections in the gimbal and the fact that the search coil was somewhat deformed.


    ACKNOWLEDGMENTS

The authors thank all of the subjects who participated in the experiments, M. Todd and G. Serdaris for assistance with the engineering aspects of the study, A. Burgess and A. Migliaccio for assistance with the computing aspects of the study, and J. Ramsay for assisting in some of the tests. In addition, the authors acknowledge Prof. A. Sefton, Dr. J. Demer, and Dr. T. Raphan for valuable comments and Dr. D. Tweed for supplying his VOR model.

This work was supported by the Royal Prince Alfred Hospital Department of Neurology Trustees.


    FOOTNOTES

Address for reprint requests: M. J. Thurtell, Eye and Ear Research Unit, Dept. of Neurology, Royal Prince Alfred Hospital, Camperdown, Sydney, NSW 2050, Australia.

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Received 15 June 1998; accepted in final form 25 November 1998.


    REFERENCES
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

0022-3077/99 $5.00 Copyright © 1999 The American Physiological Society