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Departments of Ophthalmology and Neurology, University of California, Los Angeles, California 90095-7002
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ABSTRACT |
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 Abstract
 Introduction
Methods
Results
Discussion
References
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Crane, Benjamin T. and Joseph L. Demer. Human gaze stabilization during natural activities: translation, rotation, magnification, and target distance effects. J. Neurophysiol. 78: 2129-2144, 1997. Stability of images on the retina was determined in 14 normal humans in response to rotational and translational perturbations during self-generated pitch and yaw, standing, walking, and running on a treadmill. The effects on image stability of target distance, vision, and spectacle magnification were examined. During locomotion the horizontal and vertical velocity of images on the retina was <4°/s for a visible target located beyond 4 m. Image velocity significantly increased to >4°/s during self-generated motion. For all conditions of standing and locomotion, angular vestibulo-ocular reflex (AVOR) gain was less than unity and varied significantly by activity, by target distance, and among subjects. There was no significant correlation(P > 0.05) between AVOR gain and image stability during standing and walking despite significant variation among subjects. This lack of correlation is likely due to translation of the orbit. The degree of orbital translation and rotation varied significantly with activity and viewing condition in a manner suggesting an active role in gaze stabilization. Orbital translation was consistently antiphase with rotation at predominant frequencies <4 Hz. When orbital translation was neglected in computing gaze, computed image velocities increased. The compensatory effect of orbital translation allows gaze stabilization despite subunity AVOR gain during natural activities. Orbital translation decreased during close target viewing, whereas orbital rotation decreased while wearing telescopic spectacles. As the earth fixed target was moved closer, image velocity on the retina significantly increased (P < 0.05) for all activities except standing. Latency of the AVOR increased slightly with decreasing target distance but remained <10 ms for even the closest target. This latency was similar in darkness or light, indicating that the visual pursuit tracking is probably not important in gaze stabilization. Trials with a distant target were repeated while subjects wore telescopic spectacles that magnified vision by 1.9 or 4 times. Gain of the AVOR was enhanced by magnified vision during all activities, but always to a value less than spectacle magnification. Gain enhancement was greatest during self-generated sinusoidal motion at 0.8 Hz and was less during standing, walking, and running. Image slip velocity on the retina increased with increasing magnification. During natural activities, slip velocity with telescopes increased most during running and least during standing. Latency of the visually enhanced AVOR significantly increased with magnification (P < 0.05), probably reflecting a contribution of the visual pursuit system. The oculomotor estimate of target distance was inferred by measuring binocular convergence, as well as from monocular parallax during head translation. In darkness, target distance estimates obtained by both techniques were less accurate than in light, consistently overestimating for near and underestimating for far targets.
The ability of the vestibulo-ocular reflex (VOR) to stabilize images frequently has been tested by having subjects either voluntarily move their heads in a steady state sinusoidal pattern or by passively rotating the subjects in such a pattern. Significant retinal image motion occurs in humans during self-generated head movement (Steinman and Collewijn 1980 Subjects
Fourteen normal paid volunteers gave written consent to participate in this study according to a protocol approved by the Human Subject Protection Committee in conformity with the tenets of the Declaration of Helsinki. There were five women and nine men of average age 27 ± 7 yr (mean ± SD, range 19-44). Subjects underwent ophthalmologic examination to verify that they were free of disease and would be able to converge and focus the targets clearly. Each subject stood on a motorized treadmill (1.1 kW) throughout the experiment, although the tread was moving only during selected trials. Subjects were monitored via closed-circuit television and intercom.
Apparatus
Angular eye and head positions were measured with magnetic search coils as employed by other investigators (Grossman and Leigh 1990 Measurement conditions
The activities tested consisted of quiet standing, walking, running, and self-generated angular head movements, each in epochs of 10 s. Each trial in which there was no magnification of vision was performed in the light and repeated immediately afterward in darkness with the subject asked to remember the earth-fixed target in the location where it had been previously visible. When vision was magnified with telescopic spectacles, trials were done only in the light because previous studies have shown that telescopes have no effect in darkness (Crane et al. 1996 Data analysis
Data were analyzed automatically using custom software written using the LabView package (National Instruments) running on a Power Macintosh compatible computer. Data collected during calibration trials were averaged and used to define a rotation matrix giving the central (0) position for gaze and angular head position (see APPENDIX). The data in test trials were rotated by these calibration matrices so as to place search coil and FGM data in a common coordinate system (see APPENDIX). For binocular recording, a separate rotation matrix was calculated for the left eye assuming that the vertical component of the eye position was 0° and the horizontal component was the inverse tangent of the interpupillary distance divided by the distance to the target. This assumes the subject was foveating the target during the calibration trial, a capability verified by clinical examination of each subject. The purpose of this calibration was to eliminate errors introduced by possible misalignment or slippage of the search coil on the eye or the head band on the head.
Using three-dimensional translational and rotational measurements, it was possible to determine the position of the target image on the retina during unrestrained head movements (Fig. 1, top). Image position always underwent small perturbations associated with head and eye motions in all 6 df. For example, with a distant target viewed with unmagnified vision, retinal position error as measured by standard deviation was
Head translation and rotation
All subjects exhibited a phase-locked relationship between orbit translation and head rotation at the peak frequency of head motion during standing, walking, and running in both the horizontal and vertical directions (Fig. 1, bottom). As the orbit translated upward, it rotated downward and vise versa. Likewise, as the orbit translated laterally, it rotated medially. This relationship between orbital translation and rotation had a stabilizing effect on retinal images. We investigated a possible frequency dependence of this antiphase behavior using Fourier cross spectral analysis. In spectral analyses over the range 0-20 Hz for each trial, we determined those frequencies where orbit translation and head rotation were antiphase (180 ± 45°). The brief duration of each trial imposed a limited precision in determination of phase at any given frequency, and phase only could be determined at those frequencies where the spectrum of head motion contained significant amplitude. Antiphase behavior was observed only at predominate frequencies <4 Hz and not observed when predominate frequencies exceeded 4 Hz (Fig. 3). Because only the lower frequency data were informative, Fig. 3 plots the range 0-10 Hz. No effect of target distance or visual feedback was detected in head-movement spectra. In the horizontal plane, head rotation and translation usually occurred with the same peak frequency (Table 1, Fig. 3, D and E). In the vertical plane, the peak frequency was often lower for head rotation than for head translation due to slow drift in head position that often occurred during the course of a trial. However, there was also significant spectral content at higher frequency; this matched the predominate head translation frequency (Fig. 3A). Spectral analysis of gaze position exhibited a number of frequencies <3 Hz with significant amplitude (Fig. 3, C and F). In darkness, the peak frequency of gaze was usually much lower because gaze error was dominated by the slow drift in the absence of visual feedback. The predominate frequency in the presence of visual feedback was <1 Hz in all conditions except during running, where it was ~2.5 Hz in the vertical direction. When translation was neglected in gaze calculations, retinal image slip velocity appeared greater than when translation was considered, as shown in Fig. 4. Effects on head motion of target location and activity are considered in detail below.
Stability of gaze during various activities
Despite attainment of retinal image stability under all conditions, AVOR gain varied significantly according to activity (ANOVA P < 0.05), approximating unity only during self-generated head motion. During the natural activities of standing, walking, and running, gains were significantly less than unity (Fig. 5), occasionally as low as 0.55. Gains differed significantly among activities. Clarification of this apparent paradox is provided by examination of the relationship of orbital translation to rotation (Fig. 6). For self-generated pitch, the ratio of RMS translational velocity (bandwidth 0-8 Hz) to rotational velocity was 0.021 ± 0.001 cm·s
Individual variation
Under identical testing conditions, AVOR gain values varied significantly among subjects during natural activities. During walking while viewing the distant target with unaided vision, gain values varied by subject from 0.73 to 0.95 (mean 0.86) in pitch and from 0.56 to 0.93 (mean 0.77) in yaw (Fig. 8, C and D). Similar variation in AVOR gain also was observed during other conditions. The degree of gaze stabilization during this same set of tests was also variable among subjects. Vertical RMS image slip velocity (0-8 Hz) varied from 0.95 to 6.5°/s (mean 2.7°/s) and horizontal image slip varied from 1.3 to 6.6°/s (mean 2.9°/s). We plotted AVOR gain and image slip velocity for individual trials in Fig. 8. Surprisingly, a lower image slip velocity did not correspond to higher AVOR gain for natural viewing conditions except with the extremely low gains seen during running (Figs. 8, C-F). Although much smaller variations in gain occurred during self-generated movements, only for self-generated yaw was there a significant inverse correlation between gain and image slip velocity (R2 for linear fit = 0.87, Fig. 8B).
Effects of target distance
The distance to the target varied continuously because subjects moved about. Mean distance from the far target to the eye was 441.3 ± 0.6 cm (mean ± SE). Mean distance of the intermediate target averaged 89.0 ± 0.5 cm, whereas mean near target distance was 40.6 ± 0.5 cm.
Effects of visual feedback
In general, gaze position was controlled more precisely in light than in darkness. The type of activity did not significantly influence the dispersion of horizontal gaze position. Vertical gaze dispersion was significantly greater during running. However, the percent increase in gaze dispersion in darkness as compared with lit conditions remained similar across natural activities. Averaging across all activities with a far target for the unmagnified viewing condition, the dispersion (SD) of horizontal gaze position was 2.4 ± 0.2 times greater and vertical gaze position 2.5 ± 0.4 times greater in darkness as compared with light (Fig. 2, C, D, G, and H). Much of the increase in gaze dispersion can be explained by slow drift observed in all subjects. Gaze velocity error varied less between darkness and light than did gaze position error, but did vary by activity (Fig. 2, A, B, E, and F). For the unmagnified distant viewing condition, the presence of vision had no significant effect on image slip velocity during standing (P > 0.1). However, there were significant effects during walking where slip velocity was 1.4 ± 0.1 times greater in darkness and during running when slip was found to be greater by a factor of 1.6 ± 0.1. Gain of the AVOR tended to be greater for visible as compared with remembered targets, but this difference was only significant(P < 0.05) during active pitch and yaw movements in their respective axes and walking in pitch (Fig. 5).
Magnified vision
Telescopic spectacles magnify the visual consequences of angular head movements. Retinal image slip velocity was increased with telescopic spectacles under all conditions tested (Fig. 9, E and F). Although significant increases in VVOR gain were observed with magnified vision during all activities, this gain increase did not match the telescopic magnification (Fig. 13). Gain enhancements were larger for voluntary head rotation than during natural activities. During voluntary movements, VVOR gain was not significantly less than unity during unmagnified vision. In pitch, VVOR gain during voluntary rotation was increased to 1.51 ± 0.05 with ×1.9 magnification and to 2.2 ± 0.2 with ×4 magnification (Fig. 13A). Even greater gain enhancement was achieved during voluntary yaw at 1.60 ± 0.08 for ×1.9 and 3.2 ± 0.2 for ×4 telescopes (Fig. 13B). More modest VVOR gain increases were observed under natural motion conditions. During walking, pitch VVOR gain increased from 0.86 ± 0.02 with unmagnified vision to 1.06 ± 0.03 and 1.25 ± 0.08 with ×1.9 and ×4 magnification, respectively (Fig. 13A). Similarly, yaw VVOR gains during walking were 0.77 ± 0.02, 0.99 ± 0.04, and 1.27 ± 0.09 for unmagnified, ×1.9, and ×4 conditions, respectively (Fig. 13B).
By simultaneously accounting for both ocular translation and rotation, images of a remote target on the retina were found to be stabilized during natural activities to <4°/s, a value that would permit clear vision. The evidence here suggests that stabilization of gaze is achieved by a precise dynamic interplay among orbit rotation, orbit translation, and eye rotation. Orbit translation is an important factor in gaze stabilization because neglecting it significantly exaggerates slip velocity (Fig. 4). Although substantial loss of visual acuity is likely for motion >4°/s, some loss of visual acuity is likely to occur with motion as slow as 2°/s (Demer and Amjadi 1993 Gaze stabilization during natural movements
Function of the AVOR traditionally has been described in terms of gain Eye movement recording techniques
All results presented were calculated from data collected with dual winding ocular search coils able to record all three rotational degrees of freedom (Tweed and Vilis 1990 Gaze stabilization during active movements
During self-generated sinusoidal head movements, position and velocity stabilization of images on the retina were worse than for head movements under natural motion conditions. This was true regardless of viewing distance, presence of visual feedback, or magnification of vision. This finding is consistent with previous work showing AVOR gain to be less than unity for either self-generated (Hine and Thorn 1987 Different effects of magnification and target distance
At a superficial level, the effects of magnification with telescopic spectacles are similar to those observed with target proximity. As shown in Fig. 9, increased retinal image slip during natural activities occurs with both near targets and with magnification. Because telescopes were put on immediately before trials, there was no time for the VOR to adapt to a higher gain. This put the burden on the visual pursuit system to stabilize gaze. Pursuit has a latency of 80-120 ms (Bronstein and Gresty 1988 Internal target distance estimates
Because appropriate image stabilization depends on target distance, the gaze stabilization system must estimate distance. The brain probably uses multiple cues such as vergence angle, accommodation, object size, and relationship to the surroundings to determine a single estimate of target distance. The angle of binocular convergence could be used as an estimate of target distance (Paige 1991
INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References
). Evidence suggests that human visual acuity is tolerant of retinal image motion of 
2-4°/s (Barnes and Smith 1981; Demer et al. 1994) although during vigorous voluntary head rotations, image slip can be as much as 70°/s (Grossman et al. 1989). Retinal slip computed from angular measurements during unconstrained, natural movements was found by Grossman et al. (1989) to be <4°/s during standing and walking and ~9°/s during running. However, Grossman et al. did not consider eye translation because the target was at optical infinity.
; Snyder and King 1992; Takeda et al. 1991; Viirre et al. 1986). Because significant ocular translation occurs during locomotion (Bloomberg et al. 1992; Demer and Viirre 1996; Pozzo et al. 1990), the VOR probably must correct for both translational and rotational movement.
; Schwarz et al. 1989) and humans (Bronstein and Gresty 1988; Paige 1991), as well as for combined linear and angular stimulation during rotation about an eccentric axis (Crane et al. 1997; Snyder and King 1992; Viirre et al. 1986). Target distance is thought to influence the linear (otolithic) component of the VOR, such that the response is approximately inversely proportional to target distance (Crane et al. 1997; Paige 1989; Viirre et al. 1986). However, some evidence suggests that, additionally, the angular (semicircular canal) component of the VOR (AVOR) may depend on target distance (Snyder and King 1992). The enhancement of AVOR gain seen with near targets does not depend directly on visual tracking (Crane et al. 1997; McCrea et al. 1996; Viirre and Demer 1996). The binocular vergence angle has been shown to be correlated strongly with the linear VOR response under some conditions (Paige 1991), but not in all subjects (Schwarz and Miles 1991) and not during voluntary convergence (Shirado et al. 1997). In addition to vergence, other cues such as accommodation and the size and context of a visual target, have been suggested as influential on the linear VOR (Busettini et al. 1994). The factors that determine the oculomotor response to target distance are controversial.
). Boyle et al. found that externally applied head or whole-body perturbations were encoded by these neurons but self-generated movements were not. During rotation of the body beneath the fixed head, no significant vestibular response was observed, indicating a lack of contribution from neck proprioception. Motor efference copy and other factors depending on volitional state have a large role in the second-order vestibular unit response during self-generated head movement (McCrea et al. 1996). This physiology is supported by neuroanatomic studies showing that second-order vestibular neurons receive inputs from the vestibulocerebellum, fastigial nucleus, reticular formation, and cervical spinal cord(Büttner-Ennever 1992) in addition to input from the vestibular nerve. Head movements occurring during standing, walking, and running do not squarely fall into either the realm of self-generated movements or passive movements. It is therefore difficult to draw conclusions about VOR function during locomotion based on studies made of the VOR during purely active or passive head movements.
found that during locomotion, the human head translates up as it rotates down and vice versa. They found a similar relationship in the horizontal plane. It also has been observed that the ratio of head translation to rotation decreases when visual targets are moved closer and that vertical reversing prisms change this ratio (Bloomberg et al. 1992). These findings suggest that head translation may play an active role in gaze stabilization rather than being a simple mechanical effect of the linkage between the head and the body. Although this pattern of head motion would seem to stabilize gaze, image motion on the retina has yet to be quantitatively examined. Only after translation is taken into account can it be known how adequately images are stabilized during locomotion.
) and during sinusoidal head motion (Demer et al. 1990). Although VVOR gain increased with magnification under these conditions, the degree of gain enhancement was inadequate to stabilize images on the retina. The effect of translation on retinal image stability with spectacle magnifiers has not previously been studied.
METHODS
Abstract
Introduction
Methods
Results
Discussion
References
; Grossman et al. 1989). 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 for subjects standing in the center. The two vertically oriented coil pairs were driven by 120 kHz sinusoidal currents in phase quadrature (Collewijn et al. 1975). The horizontally oriented coil pair was driven by a 60 kHz sinusoidal current (Robinson 1963). Dual-winding scleral magnetic search coil annuli were placed on each eye in six subjects, and on one eye only in eight subjects, to measure three-dimensional angular position of the eyes in space. Three-dimensional angular head position was measured with a pair of orthogonal search coils mounted on a head band. The ocular coils were embedded in an annular suction contact lens (Skalar Medical, Delft, The Netherlands) that adhered to the eye under topical anesthesia with proparacaine 0.5% (Collewijn et al. 1975). Search coils were connected to external detectors (C-N-C Engineering). Horizontal positions were demodulated by a phase angle method that is linear over a range of ±100°.
) within which the subject's head was located throughout the experiment. The homogeneity of the reference magnetic field was verified directly. 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. During experiments, subjects' heads always remained within the larger region. The measured peak-to-peak position noise level of the search coil system at a bandwidth of 0-100 Hz was 2 min arc. The root-mean-square (RMS) horizontal velocity noise of the system over a bandwidth of 0-43 Hz was 30 min-arc/s. The presence of the treadmill did not have a detectable effect on search coil measurements.
). Standing trials were done with a subject's feet together without external support. Walking trials were done on the treadmill at 0.9 m/s; running trials were done at 1.4 m/s with the subject employing a jogging gait. Although the treadmill provided the feel of running and walking, no attempt was made to simulate optic flow. For safety reasons, locomotion in darkness was done with subjects grasping a hand rail. A safety interlock stopped the treadmill if the subject did not maintain the pace. Trials conducted in the light were done both with and without the subject grasping the rail to determine any effects of touching a stationary object during locomotion. Subjects were trained to make self-generated head movements in pitch or yaw at an amplitude of 5-15° in synchrony with a sinusoidal tone modulated at 0.8 Hz. Mean rotation frequency achieved was0.797 ± 0.005 Hz (mean ± SE) with a range from 0.66 to0.88 Hz.
).
1.0 cm. Values of target distance were constrained to positions in front of the eyes and closer than 10 m. The final trace of target distance estimates was low-pass filtered (0-2 Hz).
175 ms (eye lag). For each of these fits, the mean standard error was calculated. The time offset minimizing mean standard error was taken as AVOR latency. Eye and head velocities then were low-pass filtered (0-20 Hz). After latency correction, another linear regression of eye velocity against head velocity was obtained, and data points found to lie >2 SD from this fit were excluded as quick phases or noise (Demer 1992). The regression and exclusion of outlying points was iterated three additional times after which the slope was taken to be AVOR gain. Coefficients of determination (R2) were calculated for the regressions in each axis after statistical outliers were removed. When the R2 value was 0.7, the corresponding gain was considered reliable.
). Results were considered to be significant for P < 0.05.
RESULTS
Abstract
Introduction
Methods
Results
Discussion
References
0.5° and RMS retinal velocity error was <4°/s for running, walking, and standing (Fig. 2). By both measures, gaze instability was greater under conditions of active head movements, closer targets, magnified vision, and darkness. Effects of these factors are considered in detail below. We repeated our analysis ignoring the eye torsion data and found no significant differences in any of the values. This indicates that two-dimensional eye position measurements would have sufficed.
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FIG. 1.
Stabilization of gaze position of representative subject in light (A) and darkness (B). Subject walked on a treadmill at 0.9 m/s with a target located 150 cm from flux gate magnetometer sensor (FGM) transmitter (~90 cm from eye). Polar plots (top) show 400-Hz time sampled gaze position in target plane calibrated in units of retinal angle. Time plots (below) show position in each of 6 df. Note inverse phase behavior between angular eye position and linear orbit position. Inverse phase behavior also was observed between angular head position and linear head position.
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FIG. 2.
Stabilization of gaze velocity (A, B, E, and F) and image position on the retina (C, D, G, and H). Data shown for all activities and target distances with unaided vision averaged over 14 subjects. A-D: recorded with target visible. E-H: recorded in darkness immediately after corresponding trials on left. Active trials refer to self-generated 0.8-Hz sinusoidal motion in either horizontal or vertical plane, as stated. Velocities are root-mean-square (RMS) values over the range 0-8 Hz. Far target was located 500 cm from FGM, intermediate target located 150 cm from FGM, and near target was located 100 cm from FGM. Error bars ± SE. A: horizontal gaze velocity in light. Minimum image slip velocity occurred for natural activities with far target. Active movements produced greater image motion as compared with natural movements at every target distance. B: vertical gaze velocity in light. As with horizontal axis, lowest image slip occurred for far target. Greater image slip velocities were observed during running with near target when compared with active condition and with running in horizontal axis. C: horizontal gaze position dispersion in light. Standard deviation of gaze position was least for most distant targets. Gaze position was less localized for self generated motion than natural movements. D: vertical gaze position dispersion in light. As with image slip velocity, standard deviation of gaze position was higher in the vertical plane. Running produced greater errors than self-generated head rotation. E: horizontal gaze velocity in darkness. Same trends as seen during lit conditions, except image slip velocities were higher for each condition. F: vertical gaze velocity in darkness. Similar to trend seen with visible target except image slip velocities were greater for each condition. G: horizontal gaze position in darkness. Gaze position was less localized than in light. There was a disproportionately large increase during self-generated head rotation in comparison with natural activities. H: horizontal gaze position in darkness. Standard deviation of gaze position increased in darkness. Increase with active movement was similar to that with natural activities.
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FIG. 3.
Frequency domain analysis of a subject walking while viewing a target at intermediate distance. Same trial shown in Fig. 1A. 
, amplitude spectrum; 
, frequencies with antiphase relationship (180 ± 45°) between head rotation and translation of the eye in corresponding plane. A-C: represent vertical head rotation, eye translation, and angular gaze position. D-F: represent horizontal head rotation, eye translation, and angular gaze position.
View this table:
TABLE 1.
Mean peak frequencies of head movement
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FIG. 4.
Effect of translation on gaze stabilization for 3 target distances. Open symbols represent complete calculations considering eye translation. Solid symbols represent the same data but assume that the eye remains fixed in space 60 cm from the FGM. Data averaged across all 6 subjects where binocular search coils were used. Standing data are omitted for clarity because it shows no significant trend with either target distance or translation consideration. Error bars ± SE. A: vertical, B: horizontal.
1 per deg·s1 (mean ± SE) in the vertical plane. Similarly during active yaw movements the ratio was 0.108 ± 0.005 cm·s1 per deg·s1. These figures indicate negligible orbital translation in comparison with the large rotation, making a gain near unity ideal for self-generated motion. The ratios of translation to rotation velocity were significantly higher during the natural activities of standing, walking, and running in both the pitch and yaw axes (Fig. 6). During standing, consideration of translation in gaze computations was found to have no significant effect or to slightly increase retinal slip velocity. However, orbital translation played a key role in image stabilization during running and walking, as demonstrated by significant drops in image slip velocity when translation is considered for these activities (Fig. 4). Vertical translation, as indicated by the standard deviation of orbit position, ranged from means of 1.2 to 3.2 cm between subjects during running.
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FIG. 5.
Effects of activity on mean angular vestibulo-ocular reflex (AVOR) and visually enhanced VOR (VVOR) gain of 14 subjects. Near target (100 cm from FGM) data are shown by darkest bar, intermediate target (150 cm from FGM) by lightly shaded bar, and far target (500 cm from FGM) by unshaded bar. "Active" represents self-generated 0.8-Hz sinusoidal head movement. For trials in darkness (C and D), subjects remembered the previously visible target. No data shown for conditions where adequate data existed for <2 subjects. Error bars ± SE. A: pitch gain with visible target. Near unity gains occurred only with active head movements. B: yaw gain with visible target. As with pitch axis, near unity gain occurred only with active movement. C: pitch gain in darkness. A decrease in gain was observed as compared with lit conditions across all activities and target distances. D: yaw gain in darkness. When compared with lit conditions, a decrease in gain was observed during active head rotation. During natural movements, no clear trend was present.
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FIG. 6.
Mean ratios of orbital translation to rotation in 14 subjects. Ratio of RMS velocity of orbital translation (cm/s) to RMS velocity of head rotation (deg/s) is plotted on the ordinate. Active refers to self-generated movement in either the vertical ( 
) or horizontal plane (
). Data collected with a lit target located 500 cm from FGM. Error bars ± SE.
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FIG. 7.
Effect on horizontal head motion and yaw AVOR gain of tactile reference as compared with free movement. Data shown for horizontal plane. Error bars ± SE. A: effects of tactile reference on eye translation velocity. During free movement, translation velocities were greater for both modes of locomotion and at all target distances when compared with tactile reference. B: effects of tactile reference on yaw velocity. Velocity of head rotation was greater during free movements than with tactile reference. Although this trend was observed across all conditions, it was only significant for near target conditions. C: effects of tactile reference on yaw AVOR gain. AVOR gain was higher with tactile reference under all conditions, although this difference was only significant for near targets while running and at the intermediate target distance while walking.
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FIG. 8.
Weak relationship between AVOR gain and image slip velocity. Each data point represents an individual trial. Data shown from every trial in 14 subjects. Data were collected with visible target located 500 cm from FGM. More data points are present for walking and running (C-F) because these trials were done in duplicate with and without tactile reference. A: self-generated movements in pitch. Although there were outlying points, a decrease in image slip velocity was observed for gains closest to unity. Gain varied by only 0.07. R2 for linear fit = 0.05. B: self-generated movements in yaw. As with self-generated movement in pitch, velocity of image slip decreased as gain approached unity. Gains varied over narrow range. R2 for linear fit = 0.87. C: vertical data for walking. Gains were more variable than during active head movements. No significant relationship between gain and gaze velocity was observed. R2 for linear fit = 0.04. D: horizontal data for walking. Gain values clustered near 0.8 with many outliers. Significant increase in image slip velocity occurred with higher gain values. R2 for linear fit = 0.16. E: vertical data for running. Gains varied over an octave, yet no correlation between gain and gaze stability was observed, except for increased slip velocity for very low AVOR gains. R2 for linear fit = 0.31. F: horizontal data for running. Despite large variation in gain there was no relationship between AVOR gain and gaze stability. R2 for linear fit = 0.01.
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FIG. 9.
Effects of target distance and magnification on image slip velocity and VVOR latency. Average data from 14 subjects shown during standing, walking, and running. Only points where data from multiple subjects was available are shown. Error bars ± SE. A: vertical image slip velocity increased with closer targets most prominently during running. B: horizontal image slip velocity increased with closer targets mainly during walking and running. C: vertical angular VVOR latency was <10 ms. D: horizontal angular VVOR latency. Lead observed while standing and regarding distant targets. Lag was <10 ms. E: velocity of vertical image slip with ×1.9 and ×4 telescope spectacles increased most during running and walking. F: velocity of horizontal image slip with ×1.9 and ×4 telescopic spectacles was less than vertical for each activity. G: pitch VVOR latency increased with telescopic magnification of vision. Latency was greater during conditions where image slip velocity was lower. H: angular VVOR latency was greater in yaw than it pitch (G) and increased with telescope magnification.
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FIG. 10.
Mean RMS translational and rotational head velocities during natural movements with visible target. Data are shown for distant (500 cm from FGM) and near (100 cm from FGM) targets with unaided vision and distant target while wearing ×4 telescopic spectacles. For each condition and type of motion, velocities decreased from running to walking to standing. Bandwidth was 0-8 Hz, error bars ± SE. A: antero-posterior translation velocity. During running, translation velocity decreased with closer targets and magnification. B: medial-lateral translation velocity. As with anterior-posterior direction, RMS velocity decreased for near targets and with magnification. C: dorsal-ventral translation velocity. Translation velocity decreased with near targets for all activities. Decrease with magnification occurred only during running. D: yaw head velocity increased with near targets. Yaw velocity was less with telescopic spectacles than for viewing of unmagnified, distant target. E: pitch head velocity was similar for near and distant targets. With magnified target, there was a significant decrease in pitch velocity during running.
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FIG. 11.
Changes in oculomotor estimate of target distance during course of representative 10-s trial. Subject walked at 0.9 m/s while viewing target located 150 cm from FGM. Actual target distance as measured from eye (- - -) varied between 80 and 90 cm. Data in left column were collected in light with target visible. Data on right were collected in darkness immediately after trial shown on left. Top: parallax estimate of target distance ( ) as implied from right eye position (for clarity, left eye is not shown but was similar). Notice that parallax target distance varied more from actual target distance in darkness. Bottom: vergence estimate of target distance () as calculated from binocular eye positions. Data filtered to 0-2 Hz.
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FIG. 12.
Estimated target distances derived from parallax and convergence techniques. Parallax data ( 
) averaged over 14 subjects. Convergence data (
) averaged from a subset of 6 subjects who wore binocular search coils. Targets were located 100, 150, or 500 cm away from FGM transmitter located ~60 cm behind subject's eye. Error bars represent ± SE but are smaller than plotting symbols for actual target distance.
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FIG. 13.
Effects of telescopic spectacle magnification on mean VVOR gain of 14 subjects during several activities. Dark shaded bars, unaided (×1) magnified vision; lightly shaded bars, ×1.9 magnifying spectacles worn; unshaded bars, ×4 magnifying telescopic spectacles worn. Data omitted for conditions where fewer than 2 subjects met inclusion criteria. Gain enhancement with magnification was greatest during self-generated (active) head movement. Error bars ± SE. A, pitch; B, yaw.
DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References
; Demer et al. 1994). Some of our subjects did limit far target image motion to <2°/s during walking and even running, but the mean value was 2-4°/s. Targets used in this experiment were large, making them easy to view even with less than optimal visual acuity. This may have affected the cognitive state of some of the subjects, causing them not to attain maximum image stabilization potential (Crane and Demer 1997). For targets closer than 100 cm from the eye, retinal slip frequently exceeded 4°/s, consistent with oscillopsia reported at these distances.
defined as angular eye velocity divided by angular head velocity. However, both eye translation and target distance are required to determine ideal AVOR gain (Crane et al. 1997; Viirre and Demer 1996; Viirre et al. 1986). Gain of the AVOR is informative only when head movement and eye movement are considered in a single plane. This simplification is reasonable under many laboratory conditions when a subject is rotated about a fixed axis or accelerated along a track. However, under natural conditions, head movement is multiplanar. The AVOR gain still can be calculated by arbitrarily choosing planes with respect to which gains can be determined.
4 m with a high degree of visual acuity.
). However, these coils also present a disadvantage in that they are bulkier and more expensive than single winding coils. For small eye movements, the direction of gaze can be approximated closely without taking eye torsion into account. We repeated our analysis ignoring eye torsion and found no significant differences in any of the values. This suggests that future experiments done with a similar protocol need not employ three-dimensional ocular recording.
; Steinman and Collewijn 1980) or passive (Demer 1992; Gresty et al. 1987) sinusoidal rotation. Based on studies made during self-generated rotation about these fixed axes, it might have been anticipated that large values of retinal slip also would occur during natural movements. This has proven not to be the case. There are several possible explanations for this observation. There is plasticity in the VOR such that its gain can be modified during extended periods of training (Demer et al. 1989; Lisberger and Fuchs 1978; Paige and Sargent 1991; Tiliket et al. 1993). During natural movement, as the orbit translates in one direction it rotates in the other so that a lower AVOR gain is needed than would be required for a purely rotational movement (Demer and Viirre 1996). The AVOR might adapt to this lower level of gain during everyday movements. When self-generated, sinusoidal motion is undertaken, the VOR may continue to use this lower gain. A second hypothesis is that the behavioral context during running, walking, and standing also may enhance image stabilization. This idea is supported by recent single-unit recordings made in the vestibular nuclei that show different neuron firing patterns depending on whether a head movement was self-generated or externally applied (McCrea et al. 1996). During standing, walking, and running, gaze stabilization occurred seemingly unconsciously in all subjects, although the degree of gaze stabilization often varied between subjects and even within the same subject. This variation may have been due to the level of concentration subjects had on the target (Collewijn 1989a,b).
; Carl and Gellman 1987; Lisberger 1990), much longer than that of the VOR. When vision was magnified, the latency of the VVOR was prolonged (Fig. 9, G and H), consistent with a linear interaction of the VOR and pursuit systems (Demer 1992). There also may be a role for visual pursuit without magnification at close target distances, but the phase lag effect was more subtle. This varied pursuit contribution may be due to inherent differences between viewing a close target and viewing a magnified distant target. While viewing a near target, translation of the viewer is the primary factor destabilizing images. For a near target, effects of rotation are no greater in terms of angle on the retina than they would be with a distant target. However, both rotational and translational errors are multiplied by the telescopes and hence become key sources of image motion.
) as well as to help correct for errors caused by near targets and inverting spectacles (Bloomberg et al. 1992). We also found that orbit translation velocity decreased concurrent with an increase in rotational velocity for more proximal targets. Although this strategy is appropriate for stabilizing gaze on near targets, it would be a poor one during magnified vision due to increased sensitivity to orbit rotation. With magnified vision, both orbit rotation and translation decreased. This seems to indicate a dynamic adjustment of strategy coordinating translation and rotation according to environmental circumstances. The reduction of orbit translation with magnification does help stabilize gaze, but to no greater degree than it would with unmagnified vision. Further evidence that head movement strategy is the result of neural mechanisms and not just the result of mechanical linkage of the head to the trunk, is provided by the frequency spectra (Fig. 3), which show that antiphase head translation-rotation behavior only occurs at the peak frequency and some local maxima <4 Hz.
; Snyder et al. 1992). However, in darkness, convergence is often not maintained although the low-frequency VOR gain required for a specific target distance is maintained (Viirre and Demer 1996). It is also likely that other cues such as accommodation, image size, and context contribute to estimation of target distance (Busettini et al. 1994). Vergence measured here in six subjects correlated very well with actual target distance in the light (Fig. 12). In darkness, the far and intermediate target distances were underestimated by vergence, whereas the nearest target distance was overestimated.
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ACKNOWLEDGEMENTS |
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This work was supported by United States Public Health Service, National Institutes of Health grants EY-08656 and DC-02952. B. Crane was supported by a National Institute of Health Medical Scientist Training Program Grant.
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APPENDIX |
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Coordinate system corrections
Experimental data were sampled from search coils on eyes and head as well as from the FGM sensor. Search coils were approximately centered on the eyes, and the head coil and flux sensor were mounted relative to the same axes. However, geometric corrections were made for possible coil slippage and alignment error in the coordinate systems of the sensors. To find central gaze position, calibration trials were executed repeatedly throughout the experiment. During calibration trials, the subject was asked to remain still and look directly at the target mounted at eye level. Measurements of three-dimensional angular positions of the eyes and head were taken using both the FGM sensor and the coil system with respect to the right-handed coordinate system with the z axis positive downward, the y axis positive to the subject's right, and the x axis positive forward. Angular eye position recorded by the search coils was used to calculate the following rotation matrix (Haslwanter 1995)
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(A1) |
, H, and F to indicate the values of these parameters during central gaze. For the sake of further analysis, we transform the data to a coordinate system where at central gaze, 
, 
, and 
are all zero. When data are given in this coordinate system, we denote it by E°, H°, and F°. If we take the inverse of the central gaze matrix (which for a rotation matrix is also the transpose) and multiply the rotation matrices of data collected during trial by it, the data then will be in relationship to the axes defined by central gaze
Thus the eye position in the transformed coordinate system is
(A2)
and head position in the transformed coordinate system is
(A3)
We do not assume the FGM coordinate system is the same as the search coil system because the transmitter or receiver could be misaligned slightly relative to the magnetic search coil system. Ideally the FGM and the head coils should give the same values for any position of the head. Creating a separate rotation matrix ensures that this will be the case
(A4)
Rotation matrices also can be used to correct for translation in space. We define two vectors: er, the vector from the FGM receiver to the eye, necessary to obtain orbital translation, and et, the vector from the FGM transmitter (defined as the origin of our coordinate system) to the eye. The vector from the transmitter to the receiver is r. The vector is measured in the coordinate system defined by the orientation of the FGM sensor relative to the head. This vector is converted to the coordinate system defined by central gaze using
(A5)
(A6)
(A7)
In the subsequent derivation, positions will be given without superscripts and should be assumed to be in reference to the axes defined by central gaze, with the origin being the position of the FGM transmitter.
(A8)
Calculation of gaze position First we will define a unit vector, n, that is parallel to the line of gaze
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. The unit vector normal to the screen is given by
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(A11) |
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(A14) |
Parallax method We can calculate the oculomotor estimate of target distance based on two lines of gaze as shown in Fig. 14. These lines of gaze can be determined by measuring the positions and angles of both eyes simultaneously or the position and angles of one eye at different times. Although ideally these two lines of gaze should intersect at the target, in fact real lines never exactly intersect in three-dimensional space. To avoid this problem, we assume that the intended position of gaze is at the segment defining the shortest distance between these two lines. We define the two lines of gaze in parametric form as follows
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(A15) |
a1, b1, c1
and a2, b2, c2. The shortest distance between two lines is along a segment perpendicular to both lines. We can find a vector perpendicular to both lines by taking the cross product of the two gaze vectors
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(A16) |
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(A17) |
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(A18) |
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(A19) |
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(A20) |
![<IT>d</IT><SUB>1</SUB>= {(<IT>a</IT><SUB>1</SUB><IT>b</IT><SUB>2</SUB><IT>− b</IT><SUB>1</SUB><IT>a</IT><SUB>2</SUB>)[<IT>a</IT><SUB>2</SUB>(<IT>y</IT><SUB>1</SUB><IT>− y</IT><SUB>2</SUB>) + <IT>b</IT><SUB>2</SUB>(<IT>x</IT><SUB>2</SUB><IT>− x</IT><SUB>1</SUB>)]](/content/vol78/issue4/fulltext/2129/img033.gif)
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![+ (<IT>c</IT><SUB>1</SUB><IT>a</IT><SUB>2</SUB><IT>− a</IT><SUB>1</SUB><IT>c</IT><SUB>2</SUB>)[<IT>a</IT><SUB>2</SUB>(<IT>z</IT><SUB>2</SUB><IT>− z</IT><SUB>1</SUB>) + <IT>c</IT><SUB>2</SUB>(<IT>x</IT><SUB>1</SUB><IT>− x</IT><SUB>2</SUB>)]](/content/vol78/issue4/fulltext/2129/img034.gif)
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![+ (<IT>b</IT><SUB>1</SUB><IT>c</IT><SUB>2</SUB><IT>− c</IT><SUB>1</SUB><IT>b</IT><SUB>2</SUB>)[<IT>b</IT><SUB>2</SUB>(<IT>z</IT><SUB>1</SUB><IT>− z</IT><SUB>2</SUB>) + <IT>c</IT><SUB>2</SUB>(<IT>y</IT><SUB>2</SUB><IT>− y</IT><SUB>1</SUB>)]}/[(<IT>a</IT><SUB>1</SUB><IT>b</IT><SUB>2</SUB><IT>− b</IT><SUB>1</SUB><IT>a</IT><SUB>2</SUB>)<SUP>2</SUP>](/content/vol78/issue4/fulltext/2129/img035.gif)
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![+ (<IT>c</IT><SUB>1</SUB><IT>a</IT><SUB>2</SUB><IT>− a</IT><SUB>1</SUB><IT>c</IT><SUB>2</SUB>)<SUP>2</SUP>+ (<IT>b</IT><SUB>1</SUB><IT>c</IT><SUB>2</SUB><IT>− c</IT><SUB>1</SUB><IT>b</IT><SUB>2</SUB>)<SUP>2</SUP>]](/content/vol78/issue4/fulltext/2129/img036.gif)
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(A21) |
d2.
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FOOTNOTES |
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Address for reprint requests: J. L. Demer, Jules Stein Eye Institute, 100 Stein Plaza, UCLA, Los Angeles, CA 90095-7002.
Received 4 February 1997; accepted in final form 10 June 1997.
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REFERENCES |
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Abstract
Introduction
Methods
Results
Discussion
References
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