Department of Physiology, Helmholtz School for Autonomous Systems Research, Erasmus University Rotterdam, NL-3000 DR Rotterdam, The Netherlands
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ABSTRACT |
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Hooge, Ignace Th. C. and A. V. van den Berg. Visually Evoked Cyclovergence and Extended Listing's Law. J. Neurophysiol. 83: 2757-2775, 2000. Cyclovergence is a simultaneously occurring cyclorotation of the two eyes in opposite directions. Cyclovergence can be elicited visually by opposite cyclorotation of the two eyes' images. It also can occur in conjunction with horizontal vergence and vertical version in a stereotyped manner as described by the extended Listing's law (or L2). We manipulated L2-related and visually evoked cyclovergence independently, using stereoscopic images of three-dimensional (3D) scenes. During pursuit in the midsagittal plane, cyclovergence followed L2. The amount of L2-related cyclovergence during pursuit varied between subjects. Each pursuit trial was repeated three times. Two of the three trials had additional image rotation to visually evoke cyclovergence. We could separate the L2-related and visual components of cyclovergence by subtraction of the cyclovergence response in matched trials that differed only in the image rotation that was applied during pursuit. This indicates that visual and L2-related contributions to cyclovergence add linearly, suggesting the presence of two independent systems. Visually evoked cyclovergence gains were characteristic for a given subject, little affected by visual stimulus parameters, and usually low (0.1-0.5) when a static target was fixated. Gain and phase lag of the visually evoked cyclovergence during vertical pursuit was comparable with that during fixation of a static target. The binocular orientations are in better agreement to orientations predicted by L2 then would be predicted by nulling of the cyclodisparities. On the basis of our results, we suggest that visually driven and L2-related cyclovergence are independent of each other and superimpose linearly.
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INTRODUCTION |
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How are the eyes oriented when we look around in a
rich visual environment? Images can be fused only within a certain
range of retinal disparities (angular difference between the left and right eyes' image-locations of a single target). Thus when we like to
inspect a small object, the lines of sight of both eyes are made to
intersect in this object by a horizontal vergence eye movement. Even if
the two lines of sight intersect, both eyes still can be rotated about
their lines of sight; in opposite directions (cyclovergence) or in the
same direction (cycloversion). This affects the horizontal and vertical
disparities of the more eccentric parts of the fixated object as well
as its background. Cyclovergence is known to promote retinal
correspondence (Howard and Zacher 1991; van Rijn
et al. 1992
, 1994a
) for nearly parallel gaze lines when visual
stimuli are rotated in opposite directions about the eyes' lines of
sight. This type of cyclovergence, to which we refer as visually driven
cyclovergence, is slow and related to vertical shear and
cyclodisparities (Howard and Kaneko 1994
). Cyclovergence
movements also occur when the eyes converge. These cyclovergence eye
movements obey the extended Listing's law (L2) and are virtually
independent of the visual environment (Minken and van Gisbergen
1994
; van den Berg et al. 1997
). L2 has been studied mainly with sparse visual stimuli and for fixation. Our study
deals with the possible interaction between L2-related and visually
driven cyclovergence during pursuit in a rich visual environment.
Before we further explain L2, we briefly introduce the relation between
viewing direction and torsion that is known as Listing's law.
According to Listing's law, the torsion component of the eye
orientation is constrained as follows: all axes about which the eye can
rotate from a single reference orientation to any other orientation lie
in a plane. Such a plane is called a velocity or displacement plane
(Tweed and Vilis 1990). The unique reference direction
that is normal to the displacement plane is called the primary
direction. The matching displacement plane is called Listing's plane.
Modern studies use the rotation vector format (Haustein 1989
) for the description of eye rotation. Briefly, the format specifies the axis direction and the amount of rotation about that axis
that is required to carry the eye from the reference orientation into
the specified eye orientation. In this format Listing's law
corresponds to: rx = 0; i.e., there is no component of
rotation about the axis perpendicular to Listing's plane.
Unfortunately this description ignores the complications that arise for
nonparallel gaze directions that occur during fixation of nearby
targets (Donders 1869; Nakayama 1983
). We
need to take into account this complexity when we ask whether the
torsion eye movements promote retinal correspondence in near vision.
Recently Listing's law has been extended to describe the
three-dimensional orientations of the two eyes (Minken and van
Gisbergen 1994
; Mok et al. 1992
; van Rijn
and van den Berg 1993
) in such conditions. The extended
Listing's law or L2 states that: the displacement plane of each eye
turns by an amount µ * D when the eyes are converged D (Mok et al. 1992
). As Tweed
(1997)
writes: "this means that when you converge your eyes
so that the angle between your lines of sight is 40°, the planes
swing out like saloon doors, pivoting µ * 40° about the ocular centers."
This intuitively appealing description does not specify explicitly how
the eyes are oriented toward a particular target because it is not
immediately clear to which pair of points in the rotated Listing's
planes this fixation corresponds (this pair can be found, however, by a
geometric construction). van Rijn and van den Berg (1993) formulated the extended Listing's law in another way
(LRB model) that provides such an explicit description. The LRB model is fed with Helmholtz angles (Fig. 1)
that specify the target position, and it produces two rotation vectors
(one for each eye). The LRB model states that the torsional difference
between the rotation vectors of left and right eye (cyclovergence) is
proportional to the product of the Helmholtz elevation of- and the
Helmholtz horizontal vergence within the plane of regard. The plane of
regard is the plane that contains the two lines of sight (of the left and the right eye). This form of L2 is practical for researchers who
describe their stimuli in a Helmholtz coordinate system, as commonly
used in the field of stereovision.
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The LRB model and L2 are related. The LRB model predicts that the rotation vectors of left and right eyes are located in planes when the targets are configured on an iso-vergence surface. These planes are not parallel. The angle between them corresponds to L2 with µ = 0.5. Both models predict that when we look upward (negative vertical version) to a target that is nearer than infinity (negative horizontal vergence), the cyclovergence part of the rotation vector is positive (intorsion). When we look down, the cyclovergence is negative (extorsion). The amount of cyclovergence increases in proportion to the horizontal vergence angle.
The description of eye orientation in terms of rotation vectors is efficient. For the description of retinal disparities, however, it is useful to describe L2 in terms of Helmholtz angles. In this coordinate system, torsion is a rotation about the line of sight rather than about an axis fixed in the head as for the rotation vectors. If µ is between 0.0 and 0.25, Helmholtz (HH) cyclovergence is positive when one looks down while converging and is negative when one looks up (Fig. 2A). If µ = 0.25, HH cyclovergence does not differ much from zero (Fig. 2B). In this case, targets in the plane of regard always stimulate corresponding retinal meridia, irrespective of the fixated location. Finally, if µ > 0.25, HH cyclovergence is negative when one looks down while converging, and cyclovergence is positive when one looks up (Fig. 2C). Thus whereas different levels of µ correspond to qualitatively similar patterns of cyclovergence for near vision when expressed in rotation vectors, this is not the case when cyclovergence is expressed in Helmholtz coordinates. Because Helmholtz torsion of the two eyes bear a direct relation to retinal disparity, keeping in mind this difference is important for the analysis of the potential visual benefit of L2.
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The reason for Listing's law (as well its recent extension) has
remained a mystery. It has been proposed that for µ = 0.25, L2
helps to keep in register the images of the local surface around the
fixation point that is perpendicular to the plane of regard (van
Rijn and van den Berg 1993). Tweed (1997)
pointed out, however, that this cannot be true because vertical
meridians are not aligned when the horizontal meridians of the eyes are
located in a single plane (Helmholtz 1867
; Ogle
1950
). Hence a vertical line on that perpendicular surface is
not imaged on corresponding points when horizontal lines are. Second,
L2 by itself cannot always bring the eye's images (i.e., local patches
around the fixation point) in register in dynamical situations. Let us
consider the following example. An observer is looking down at a table
(Fig. 3A1). If he moves his
head forward and maintains fixation at a point on the table (Fig. 3,
B1 and C1), the eyes need to move downward while
converging (Fig. 3, A2-C2). Depending on the µ of this
observer, the eyes will show HH extorsion (µ > 0.25), no HH
cyclovergence (µ = 0.25), or HH intorsion (µ < 0.25). In Fig.
3C, 1-3, it is analyzed what kind of
cyclovergence would help to reduce the cyclodisparity of the table's
top surface. Shown are projections of the cross on the table on the eye
sockets at the three instants during the head translation as depicted
in Fig. 3A. Because of perspective, the projections of the
cross are sheared horizontally relative to each other during the head
translation. The intorsion of the eyes if µ < 0.25 would help
to decrease the large cyclodisparity of the vertical lines at the
expense of an increase of the cyclodisparity of the horizontal lines
(Fig. 2A). Yet such an eye movement will maintain both the
horizontal and the vertical line within the fusion range for a longer
period. In contrast, the extorsion that would occur if µ > 0.25 would increase the cyclodisparity of both lines. Thus certain
combinations of µ and slant may reduce cyclodisparity, whereas other
combinations may increase cyclodisparities during forward motion.
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This begs the question to what extent cyclovergence is evoked visually
in situations in which L2 does not reduce cyclodisparity (as pointed
out in Fig. 3, when L2 is not perfect). To answer that question one
needs to know whether L2 that was described for fixation (Minken
and van Gisbergen 1994; Mok et al. 1992
; van Rijn and van den Berg 1993
) holds for pursuit and
whether visual stimuli during pursuit are as effective in evoking
cyclovergence as during fixation (Howard and Zacher
1991
; van Rijn et al. 1992
, 1994a
).
Specifically, we investigated visually driven cyclovergence during
fixation (as in the Howard and Zacher experiment) and during pursuit in
a static or moving environment. The latter case consists of a simulated
head movement, in which the images show the changing perspective of an
eye that is moving through space. Our study thus aims to further probe
the conditions under which L2 is valid and how visual and L2-related
cyclovergence combine.
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METHODS |
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Subjects
Six male subjects (age 24-32 yr, subject IH is the first author) participated in the experiments. Subjects IH, JB, MF, and HW were experienced in wearing scleral coils for eye movement recording. Subjects EP and JR were naive paid subjects and had no experience with the dual search-coil method. After the experiments, we found that subject EP showed different behavior than the other subjects. Therefore we sent him to the eye hospital for investigation. His stereopsis was optimal (Titmus stereo test). The vertical fusion range was normal. EP had a small exophoria (<5°) at near. In the midsagittal plane, EP had hypertropia (the right eye has an negative vertical offset relative to the right eye). The inferior oblique of the left eye showed under action.
Eye-orientation measurements
Three-dimensional (3D) eye orientations were measured with the
dual search-coil technique (Skalar Eye position meter 3020, Delft, The
Netherlands) (Collewijn et al. 1975, 1985
;
Robinson 1963
). Horizontal, vertical, and torsion eye
orientations were measured at a sampling rate of 125 Hz. To investigate
the torsion signal at high resolution, it was split into two signals.
The first signal was amplified four times and fed through an
offset-compensator (Collewijn 1977
). The
offset-compensator resets a signal to 0.0 V within a period of two ms
if it exceeds 1.0 V or
1.0 V (Fig. 4).
Before digitization, the eight signals (horizontal, vertical, torsion,
and amplified "offset compensated" torsion of the 2 eyes), were fed
through a low-pass analogue filter with a cutoff frequency of 62.5 Hz.
The offset-compensated signal (which lacks information about the
offset) and the offset of the original torsion signal were used to
reconstruct the torsion eye position signal off-line. As a result of
this manipulation, the resolution of the torsion signal (600 mV/°)
was 4.0 times higher than the resolution of both the horizontal (150 mV/°) and the vertical signals. By this method, we measured with a
standard 12 bits analogue AD converter both large shifts and very slow
small changes in torsion eye orientation. This was necessary due to L2
and coil misalignment; torsion angles of an individual eye ranged
between
20 and +20°. Data were stored on disk for off-line
analysis.
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Procedure
To prevent the subject from making head movements, an adjustable
(3 axes) bite-board was used. Each experimental session started with
careful positioning of the subject's head. We asked the subject to
position the head in such a way that the interocular axis was horizontal and approximately parallel to the screen. This was checked
with two horizontally placed hairlines on each side of the magnetic
field cubicle. We were satisfied when for each eye in a side view, the
two hairlines were aligned and cut right through the pupil. The 3D
location of the center of rotation of each eye relative to the screen
then was measured by a computerized trigonometric method (van
den Berg 1996).
Experiments were done on three different days because the scleral coil method limits the duration of experimental sessions to ~30 min. To position the subject's head in the same position and orientation in subsequent sessions, we used a laser pointer attached to the bite-board. We inspected the torsion signal while we placed the coils on the subject's eyes. To this end we used a plastic suction device to avoid distortion of the magnetic field. Subjects were instructed to look straight ahead during the placement of the coils to limit torsion offset due to L2.
The experiment contained three types of trials, cyclovergence trials (trial duration: 32 s), primary direction trials (duration: 32 s), and calibrations (duration: 2 s). Each experimental session consisted of 19 (experiment 1), 18 (experiment 2), or 24 cyclovergence trials (experiment 3).
In cyclovergence trials, subjects fixated or made various pursuit eye movements, and cyclovergence occurred as a result of L2, was evoked visually, or was evoked by both methods at the same time.
During a primary direction trial, subjects were asked to fixate at their own pace nine dots of a rectangular grid in random order (20 × 20°). The pattern was presented dichoptically at a simulated distance of 19 m (see STIMULI). In this way, we measured the orientation of the Listing's planes of the two eyes with almost parallel gaze.
During calibration, the subject gazed at a single target at simulated distance of 19 m straight ahead, i.e., in the direction perpendicular to the revolving magnetic field. This allows one to measure the horizontal, vertical and torsion offset angles. This coil misalignment could change over time due to coil slippage. Therefore each primary direction measurement and each cyclovergence trial was preceded by a calibration trial.
Data analysis
GENERAL DATA ANALYSIS: FROM COIL VOLTAGES TO LISTING'S COORDINATES
AND HELMHOLTZ ANGLES.
The Skalar eye position meter provides coil voltages. Figure
5 shows a diagram of the transformations
and manipulations, which were used to transform coil voltages to
Helmholtz angles and Listing's coordinates. We need both Helmholtz
angles and rotation vectors (Listing's coordinates) because we use the
LRB scheme to estimate µ. Preceding each experiment, the coils were
calibrated to determine the sensitivity of and the relative orientation
between the direction and the torsion coils (Bruno and van den
Berg 1997b). Coil voltages were transformed to Fick angles by a
linearization and a correction for coil nonorthogonality. This
nonorthogonality error correction was done by the method described in
Bruno and van den Berg (1997a)
. Subsequently the Fick
angles were transformed to rotation vectors (Haustein
1989
). By a 3D counter rotation (Haslwanter
1995
), the rotation vectors were corrected for the coil
misalignment, which was determined in the preceding calibration trial.
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STIMULI. Stimuli were generated by a Graphics workstation (SGI ONYX). The computer presented the perspective view appropriate for each eye of a simulated 3D scene. The locations of the eyes relative to the screen as determined directly before the experiment were used to compute these images. The scene consisted of line objects of random orientation, length, and position. These objects were located within a cone-like volume, of which the apex was located at the ego-center of the subject. Thus a circular part of the screen was filled with a bunch of lines, that could recede in depth (Fig. 6, A-C). We varied the diameter of the ground plane of the cone, its height (= simulated depth), the number of lines, and the distance between the lines and the subject.
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SPECIFIC DATA ANALYSIS. Experiment 1. Coil voltages were off-line transformed to Helmholtz angles using the procedure described in the general data analysis (Fig. 5). Eye orientations were expressed in HH coordinates. Thus the cyclovergence was simulated around the line of sight. A computer program removed blinks and saccades based on velocity (10°/s) and duration criteria (>12 ms). Gaps in the cyclovergence signals were interpolated using a second-order interpolation. All trials also were inspected by eye. Linear regression analysis of the cyclovergence response was used to correct it for drift and offset. Subsequently the cyclovergence response was transformed by a fast Fourier routine. We computed the visually evoked cyclovergence gains and phase lag from the component that was related to the stimulus frequency of 0.125 Hz.
Experiments 2 and 3. In experiments 2 and 3, the analysis was designed to separate the contributions of L2 and visual stimuli to cyclovergence. We subtracted the 0trial (no simulated cyclovergence) from the cyclovergence responses of the +trial and the
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RESULTS |
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Calibrations
Each cyclovergence or Listing's plane (or primary direction)
measurement was preceded by a calibration. The calibration was used to
compensate for coil misalignment due to slip and offset. Despite the
careful placement of the coils, offsets often remain. How stable was
the coil attached to the eye? In general, the standard deviation of the
torsion component of all calibration trials of an experimental session
was lower than 2°. Torsion offsets ranged from 18 to 22°. In the
majority of the trials, we found offsets that ranged from
10 to
10°. The time interval between two calibrations was ~50 s (8 s to
accustom the subject to the new stimulus, 32-s trial duration and 10-s
between a trial and the subsequent calibration). Inspection of the
calibration trials showed that the torsion offset is stable over time.
Thus the coils were well attached to the eye.
Listing's planes
From our binocular data, we determined the orientations of the displacement planes for each eye separately and the displacement plane of the averaged rotation vectors: the versional displacement plane. We started by extracting the primary directions from the version signals and proceeded with reporting the differences in orientation between the primary directions of the two eyes.
The interocular axis of the subject was positioned approximately
parallel to the y axis of the coil frame. Figure
9, C and D, shows
the orientations of the version Listing's plane with respect to the
Skalar coil frame. Rotations about the z axis ranged (Fig.
9B) from 2.5 to +7.0° in experiment 2 and from
3 to +3° in experiment 3. Within subjects, differences
between experiments 2 and 3 were <1° for four
subjects (MF, JB, HW, and IH) and ~5° for two
subjects (EP and JR). Large upward rotations of
the versional primary position (Fig. 9A) were found for
subjects MF (
23° for experiment 2 and
20°
for experiment 3) and HW (
17° for
experiment 2). Rotation about the y axis ranged
from
4 to +5° for the other four subjects. Within subjects,
differences between experiments 2 and 3 were
largest for subjects HW (10°) and JR (4°) and
3° for subjects MF, JB, EP, and IH. In
summary, orientations of version Listing's plane varied between
subjects and experiments. Between subjects, we found a large variation
in rotation about the y axis. Variation in rotation about
the z axis was much smaller.
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In some previous studies in our laboratory (Bruno and van den
Berg 1997a, normal subjects; van de Berg and van Rijn
1995
, patients), it was found that the primary directions of
the two eyes are not parallel when looking at targets at optical
infinity. We confirm this observation. Figure 9F shows the
angle (alpha) between the left and right eye's Listing planes (these
planes are normal to the primary directions) when looking at infinity. Alpha is negative when the left-eye plane is rotated counter clockwise and the right plane is rotated clockwise (in a top view as in Fig.
9E). There were large differences between subjects.
Subject EP and HW had the largest values for
alpha (
12 to
18°), corresponding to excess cyclovergence [even
with respect to van Rijn and van den Berg's (1993)
model for the actual amount of horizontal convergence]. Alpha's of
the other subjects ranged from
6 to +3°. Also Listing's planes
measured on different days could vary in relative orientation. The
modified model (van den Berg et al. 1995
), to which we
will refer as LBR, compensates for nonparallel Listing's planes. In the paragraph describing the results of experiments 2 and
3, we will estimate µ by both the LRB and the LBR model.
Experiment 1. Visually driven cyclovergence during fixation
We had a number of reasons to do this experiment. First, we wished
to check whether our stimuli were as effective as described previously
(Howard and Zacher 1991; van Rijn et al. 1992
,
1994a
). Second, we wished to explore further the stimulus
factors that may affect the cyclovergence in response to changing
cyclodisparities. This could help us understand the dichotomy between
the results of Howard and Zacher and van Rijn et al. Finally, we wished
to explore the effect of a factor that was not controlled for
explicitly in those older studies: the horizontal vergence angle of the eyes.
Whole-field opposite cyclorotations of left and right eye images are
known to evoke the percept of a slanted stimulus (Collewijn et
al. 1991; Howard and Kaneko 1994
) if a visual
reference like an object placed before the screen is visible. In the
absence of a visual reference, the stimulus cyclovergence goes
unnoticed and no changes in slant are perceived. In the visual
periphery, the borders of the coil frame were dimly visible, but except
for JB subjects reported that they perceived a stable
vertically oriented stimulus. Subject JB sometimes became
aware that the slant of the stimulus had changed but never did he
perceive rotation of the stimulus about a horizontal axis. Thus we
conclude that perceived slant was stable across conditions and was not
related to the eye movements reported in the following text.
A typical example of the cyclovergence response to simulated
cyclovergence is shown in Fig. 10.
Amplitude of the simulated cyclovergence is defined as the peak-to-peak
value divided by 2 [note: Howard and Zacher (1991)
report the peak-to-peak value]. Figure
11A shows visually driven
cyclovergence gains as a function of simulated cyclovergence amplitude.
Gains ranged from 0.08 (IH) to 0.70 (MF). Varying the amplitude of the
simulated cyclovergence had a large effect for subjects MF
and HW and a small effect for subjects IH and
JB. Gains decreased with increasing amplitude of the
simulated cyclovergence. In general, MF has the highest and
IH has the lowest gains. If the radius of the stimulus
increases from 28 to 32°, the area of the stimulus increases with a
factor of 1.5. This has no effect on the visually driven cyclovergence gains (Fig. 11B). Except for MF (radius 30°)
gains ranged from 0.12 (IH) to 0.41 (MF). Again
MF has the highest and IH has the lowest gains.
This result is in agreement with results of Kertesz and Sullivan
(1978)
and Howard et al. (1994)
. In their
experiments, gain began to fall off for stimuli that had a radius
<20°. The same holds for the "number of lines in the stimulus"
and "the size of the fixation marker" conditions (Fig. 11,
C and D). These two parameters did not affect
visually driven cyclovergence.
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In the experiments of Howard and Zacher (1991) and
van Rijn et al. (1992
, 1994a
), the horizontal vergence
angle was unspecified. It seems likely that the experiments were done
with almost parallel gaze. We systematically varied the horizontal
vergence angle by shifting the fixation target in depth within the
stimulus. All subjects produced the demanded vergence angle. As Fig.
11F shows, horizontal vergence angle does not affect the
cyclovergence gain at all in one subject (IH). For the other
three subjects, there is a slight trend discernable for the
cyclovergence gain to increase for larger convergence.
Figure 11E depicts cyclovergence gain versus depth in the stimulus. Nearby lines cause huge horizontal and vertical disparities, yet varying depth in the stimulus does not affect the cyclovergence gains systematically.
Figure 12 depicts the phase lag as a function of amplitude, radius, number of lines, size of the fixation marker, horizontal vergence angle and depth. In general phase lag ranged from 22 to 57°. The majority of the phase lags are ~40°. Except for the amplitude condition, none the varied parameters had any systematic effect on the phase lags. The phase lag of subject MF decreases as rotation amplitude increases.
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To prevent the effect of a stationary frame on cyclovergence we used a circular aperture. However, the frame of the almost invisible Skalar box was very dimly visible
To examine for the possible effect of the almost invisible skalar box (because the subjects wore red green anaglyphes) on the cyclovergence gains, each experiment included a control trial. The visual stimulus of the control trial was similar to the other stimuli except for its shape on the screen. The outline of the control stimulus was rectangular. The outline was fixed to the screen so the stimulus looked like a large bunch of lines seen through a rectangular aperture. If the dimly visible skalar box was affecting the cyclovergence gains, the less eccentric and sharp borders of the control stimulus should have reduced the gain even more. Gains of the visually evoked cyclovergence were 0.22 (HW), 0.16 (IH), 0.25 (JB), and 0.48 (MF). These gains are comparable with the gains found for all other stimuli in experiment 1 (Fig. 11). Apparently the sharp stationary borders of the control stimulus did not act as a visual reference. Thus we think that the dimly visible skalar box did not affect cyclovergence gains at all. Perhaps this is not convincing for subjects with a low gain, it is for subject MF.
Summarizing, except for simulated cyclovergence amplitude and less so horizontal vergence angle, none of the varied parameters had a systematic influence on cyclovergence gain. The most important observations are 1) that cyclovergence gains are as low as in the experiment of van Rijn et al. If a subject has a low gain, he has a low gain in all conditions (IH). The order of the subjects with respect to their gains is almost the same in each figure; 2) that the cyclovergence gains are subject dependent; and 3) that phase lags were nearly constant at a level of 40° at 0.125 Hz.
Experiments 2 and 3
SLANT PERCEPTS. Trials having simulated cyclovergence and trials without were mixed. After the last experimental session, we asked each subject whether he had been aware of torsional motion of the images in two-thirds of the trials. None of the subjects had noticed the difference between zero-condition trials and simulated cyclovergence trials. None of the subjects reported changes in perceived slant of the stimulus during the experiment.
L2 during smooth pursuit in depth
The target motion through a 3D scene evoked smooth-pursuit eye
movements often with large changes in elevation and horizontal vergence. We start with a description of the cyclovergence evoked in
0trials in which no cyclovergence of the images
was presented. The visual environment (a bunch of lines) was fixed with
respect to the head (experiment 2) or with respect to the
moving fixation dot (experiment 3). Pursuit was usually
smooth and accurate, but this did not always prevent loss of fusion.
During trials A (nearby target, pure vertical movement),
C (diagonal movement), D (horizontal), and
E (diagonal movement), some subjects complained that they occasionally lost fusion. Figure 13
shows a typical example of a trial in which subject MF lost
fusion (experiment 3, diagonal movement from far down to
near up). HH horizontal vergence dropped when the HH horizontal
vergence of the target was large (about 5 to
6°). This occurred
in each period of the diagonal movement. The majority of the subjects
followed the dot smoothly. However, MF made many small
saccades (Fig. 13B, little arrows). Because of L2, the
vertical saccades affected cyclovergence. During the first saccade
(down), the eyes make an intorsion movement. During the second saccade
(up), the eyes make an extorsion movement. This relation holds for all
other saccades in the figure. Notice that HH cyclovergence ranged
between
1.5 and 2° for this huge vertical version movement.
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Figure 14A shows eye orientations (Listing's coordinates) of subject EP while following a dot that moved vertically with an amplitude of 0.125 m at a simulated distance 0.33 m in front of his head. This movement evoked nearly 30° of vertical version and 4° changes in horizontal vergence. The cyclovergence panel of Fig. 14A contains two lines. The thin line represents the measured cyclovergence, which is not corrected for offset or drift. The fat line represents cyclovergence predicted (LRB) based on the vertical version and the horizontal vergence. The shape of the measured cyclovergence signal corresponds to the predicted cyclovergence signal, but the amplitude is smaller. Figure 14B shows an example of pursuit by subject JB. In this trial, JB followed a dot that was moving diagonally with an amplitude of 0.35 m from up near to far down. The middle point of the trajectory was at eye height at a distance of 0.66 m in front of the subject. In this trial cyclovergence and predicted cyclovergence matched perfectly. Halfway through the trial subject JB blinks. The blink affects all eye-movement signals. After the blink, the eyes make an intorsion movement and return within 2 s to orientations comparable with these of the previous and the following period. In Fig. 14, both A and B, we observe a small periodical vertical vergence movement with an amplitude of ~0.6° (EP) and 0.25° (JB). These vertical vergence angles correspond to a relative difference between the vertical components of the left and right eye of ~3% (EP) and 1% (JB). The 1% difference of JB may be due to gain differences between the left and the right version channels. The 3% difference of EP may be related to the hypertropia (see Subjects).
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We computed µ for each stimulus using the cyclovergence signal and the LRB model prediction. Because the computation of µ essentially involves a division by the average cyclovergence predicted by the model, this computation was sensible only when the predicted cyclovergence was larger than the noise. To determine whether a trial was suitable, we therefore adopted the criterion that the LRB model should predict cyclovergence angles that were three times larger than the standard deviation of the cyclovergence signal of a calibration trial. Sixty two of the 83 0trials passed this criterion. There were no consistent effects of the pursuit trajectory on µ across subjects. Figure 15 therefore depicts µ averaged over trials per subject. There was a large variation in µ between subjects. For subjects MF, HW, and EP, we find high values for µ. Moreover, µ varied between experiments 2 and 3 in some subjects (MF and HW).
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We wondered to what extent this variation in µ was correlated to the variation across subjects of the relative orientation of the Listing planes of the two eyes. In the LRB model, it is assumed that Listing's planes are parallel when looking at infinity. Figure 9 shows that this is usually not the case. The LBR model compensates for nonparallel Listing's planes when looking at infinity. Essentially, µ of this model describes how much cyclovergence changes when fixation changes from distant to nearby viewing without the requirement that Listing planes should be parallel for parallel gaze. Figure 15B depicts µ (LBR) averaged over trials per subject. Now the variation in µ is much smaller.
Finally, Fig. 15C depicts µ (LBR) averaged over trials. We did not find a significant effect of stimulus on µ. The exception is stimulus D (pure horizontal vergence movement). In this case, only one measurement passed the noise criterion.
Visually driven cyclovergence gains
As explained in METHODS, we isolated the visually evoked cyclovergence by subtraction of trials that only differed in imposed visually driven cyclovergence. The assumptions are that L2-related cyclovergence matched in these trials and that the imposed cyclovergence consisted of a rotation about the visual axis. We could not control the latter directly (this would have required feedback of eye orientation to the stimulus generator). Because we simulated rotation about the axis through the eye and the fixation dot on the screen, we had to rely on correct pursuit of the dot. We investigated the validity of both assumptions.
First, we determined in (Helmholtz angles) the error of pursuit during each trial. Trials that had an average unsigned-difference between viewing direction and target direction larger than 2.5° were excluded from the analysis. This occurred in 13 of 246 trials. After removing these trials, average fixation error over all subjects and trials was smaller than 1.0°. We found this an acceptable deviation because the diameter of the fixation marker was 0.85°. Thus in the majority of the measurements pursuit was sufficiently accurate.
The residual cyclovergence provides a measure of the match of the
L2-related cyclovergence in each triple of trials (Fig. 8). Ideally,
the average of the cyclovergence of the +trial
and the trial equals the cyclovergence of the
0trial, and residual cyclovergence is zero.
However, there was always some residual cyclovergence due to variations
in pursuit and variation in the cyclovergence signal. We found that the
amplitude of the averaged, visually driven cyclovergence
[(+trial
trial)/2] was three or more times larger than
the amplitude of the residual cyclovergence
[(+trial +
trial)/2
0trial] at the stimulus frequency (0.125 Hz)
in 52 of 83 triples. In those 52 triples, the visually driven
cyclovergence was on average 6.2 times higher than the residual
cyclovergence. Thus in the majority of trials we could reliably measure
the visually driven cyclovergence during smooth pursuit in 3D.
Either the simulated cyclovergence can be in the same direction as or
opposite to L2-related cyclovergence (depending on the µ). Thus we
checked whether the direction of the simulated cyclovergence relative
to L2-related cyclovergence affected the visual gains. In the analysis
we determined the amplitude of the L2-related HH cyclovergence (from
the 0trial). This component was added to the
amplitude (4°) of the simulated cyclovergence (present in both
+trial and trial).
Depending on the value for µ, the amplitude of the changing whole
field cyclodisparities (caused by L2 and simulated cyclovergence) could
be larger or smaller than 4°. The visual gain was determined by
dividing the visually driven cyclovergence by the amplitude of the
changing whole field cyclodisparities (due to L2 and simulated cyclovergence). The visually driven cyclovergence is defined by the
difference between the cyclovergence signals of the
+trial or
trial and the
0trial. Figure
16A shows that the amplitude
of the changing whole field cyclodisparity does not affect the gain of
the visually evoked cyclovergence. This implies that the relative
direction between L2-related and visually driven cyclovergence does not affect the visual gains. Based on this observation we further computed
the gains of the visually driven cyclovergence as shown in Fig. 8 and
described in Specific data analysis, experiments 2 and 3.
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There was no systematic effect across subjects of the pursuit trajectory on the gain of the visually driven cyclovergence. Figure 16B shows gains of the visually driven cyclovergence averaged over trials for each subject. Visual cyclovergence gains ranged from 0.1 to 0.3. Similar to the gains for L2-related cyclovergence, gains of the visually driven cyclovergence did not depend on the stimulus (Fig. 16C). Again, we find low gains for the pure horizontal vergence stimulus. We also find low gains for stimulus B (vertical movement while converging). We do not see a systematic difference between experiments 2 and 3. Figure 16, D and E, shows the phase lags, which ranged from 30 to 50°. The majority of the subjects have a phase lag of ~40°. In summary, visually driven cyclovergence gains are low (~0.2) and phase lags are ~40°.
µ and Helmholtz cyclovergence
Tweed (1997) and van Rijn and van den Berg
(1993)
showed that if µ = 0.25, cyclovergence in
Helmholtz angles should be close to zero. If µ has a larger or
smaller value, HH cyclovergence should deviate from zero. To provide
insight in how µ is related to HH cyclovergence angles, we plotted
the standard deviation of the Helmholtz cyclovergence signals versus
|µLRB
0.25| (Fig. 17A) for the
0trials. We ask if the standard deviation of the
HH cyclovergence increases with |µLRB
0.25| increasingly different from zero. Figure 17A shows
indeed, that there is a linear relation between |µLRB
0.25| and the deviation of the HH
cyclovergence. In the majority of the conditions, the standard
deviation of the cyclovergence is small (<2°). The standard
deviation of the cyclovergence measured during fixation (van
Rijn et al. 1994b
) is represented by - - -. Thus the standard
deviation of the HH cyclovergence during fixation is much smaller than
during pursuit.
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L2 and visual gains
If visually driven cyclovergence has to keep the two eyes' images
in register in situations were L2 cannot, we may find a relation
between the magnitude of |µLRB 0.25|
(causing an increased deviation of the HH cyclovergence; Fig.
17A), and visually driven cyclovergence gains. Figure
17B shows visually driven cyclovergence gains against
|µLRB
0.25|. Data for individual
subjects have been plotted separately. We do not see a relation between
|µLRB
0.25| and the visual gains. This
means that subject EP (who has large µ's), does not
compensate large deviations from 0° HH cyclovergence with visually
driven cyclovergence.
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DISCUSSION |
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In this study, we investigated whether it is possible to describe the three dimensional orientations of the two eyes during pursuit in 3D as the sum of L2 and visually evoked cyclovergence. We examined visually driven cyclovergence during fixation and the combination of visually driven and L2-related cyclovergence during pursuit in the midsagittal plane. We varied both eye movement parameters (static vergence in experiment 1 and different combinations of vertical version and horizontal vergence in experiments 2 and 3) and parameters of the visual stimulus (amplitude of the simulated cyclovergence, depth, size of the stimulus, size of the fixation marker and line density in experiment 1 and different changing disparity fields during similar eye movements in experiments 2 and 3). The analysis of the cyclovergence was done in terms of Listing's coordinates (estimation of µ) and Helmholtz angles (determination of the gain of the visually driven cyclovergence). To transform coil voltages to these coordinates, we also measured the version primary-direction before each experimental session.
Listing's planes when fixating distant targets
Mikhael et al. (1995) reported that subjects
spontaneously positioned their heads in such a way that the vertical
primary gaze direction was close to the central target (2.1 ± 2.7°). This suggests that when subjects are asked to position their
head vertically, they set their version primary direction horizontal.
With the exception of MF (experiments 2 and
3) and HW (experiment 2), our subjects
set their version primary direction approximately horizontal although
the range of deviations was larger than reported by Mikhael (
7 to
+7°) when asked to orient their heads parallel to the screen. However, the primary directions of MF (about
20°,
experiments 2 and 3) and HW (
17°,
experiment 2) were rotated upward considerably. Our
subjects' choices were probably more constrained than in Mikhael's study because a comfortable position of the head in the cubicle was
aimed for. To find a comfortable position on the bite-board may have
invited subjects MF and HW to tilt their heads
backward despite its adjustability.
The eyes' primary directions when looking at a target at 19 m
were not parallel. Nonparallel Listing's planes for fixation at a
distant target have been reported by Bruno and van den Berg (1997a), Haslwanter et al. (1994)
,
Mikhael et al. (1995)
, and Mok et al.
(1992)
. Bruno and van den Berg (1997a)
investigated the yaw angle of Listing planes when looking at different
distances. The yaw angle describes the rotation about the vertical
axis. Alpha reported in this study corresponds to the yaw tilt
difference (YTD) reported in Bruno and van den Berg
(1997a)
. For distant targets, they reported an average YTD of
4°. Variation between subjects was not very large. YTD angles
ranged from
3 to
6°. JB was a subject in both studies.
YTD of JB in Bruno and van den Berg (1997a)
was
6°. In the present study, his YTD was
3.5° (experiment 3) and almost 0° (experiment 2).
With the exception of subjects HW and EP, YTD
(alpha) ranged from 6 to +3°. For EP and HW, we
found YTDs that ranged from
12 to
18°. Only Haslwanter et
al. (1994)
reported a larger value (YTD = 28°). Bruno
and van den Berg did not report positive values for YTD. Mok et
al. (1992)
and Mikhael et al. (1995)
reported
negative and positive YTDs. YTD reported in the present study cover
almost the whole range of YTD reported in the literature.
We cannot rule out the possibility that YTD angles may vary over time as we found different YTDs in some subjects for experiments 2 and 3, which were done on different days.
Visually driven cyclovergence superimposes on L2-related cyclovergence
During fixation, we measured low visually driven cyclovergence
gains. These gains were subject dependent and ranged between 0.1 and
0.5. The simulated cyclovergence method enabled us to evoke
cyclovergence movements using three-dimensional stimuli. These 3D
stimuli were as effective as flat stimuli. We varied the properties of
the visual stimuli and static vergence and found that besides rotation
amplitude of the simulated cyclovergence, varying the number of lines,
size of the stimulus, the size of the fixation marker, and the amount
of depth in the stimulus did not have a systematic effect on the
cyclovergence gains. Our results were comparable with the results of
van Rijn et al. (1992, 1994a
). From these findings we
suggest that the differences between the result of Howard and
Zacher (1991
; high gains) and van Rijn et al. (1992
,
1994a
; lower gains) are likely due to individual differences between subjects rather than differences between the set-up and stimuli. Data of Howard and Zacher (1991)
and
Howard, Ohmi, and Sun (1993)
are also in agreement with
this suggestion. They found large differences between their three
subjects. Their youngest subject (JZ) had gains of 0.9 (Howard
and Zacher 1991
) and 0.7 (Howard et al. 1993
),
whereas the other two subjects had had gains ranging from 0.16 to 0.42 (Howard et al. 1993
). In the present experiment, phase
lags were ~40°. These phase lags are in agreement with the data of
both Howard and Zacher (1991)
and van Rijn et al.
(1992
, 1994a
). Static horizontal vergence slightly affected the
gains for three of four subjects. This observation raised the question
whether dynamic changes in vergence would alter gains of the visually
driven cyclovergence.
During pursuit of a target moving in depth and vertically, the eyes make in- and extorsional movements. We simulated additional cyclovergence movement in the image to investigate the potential effects of a changing vergence on visually evoked cyclovergence gain. We used a subtraction technique to separate the L2-related and visually evoked components of cyclovergence (Fig. 8). In the majority of trials, the residual cyclovergence was small, showing that L2-related cyclovergence in general reproduced well across the triplet of trials. Apparently, the visually evoked cyclovergence did not alter the L2-related cyclovergence. Thus we felt confident that in these trials the separation was valid. Visually driven cyclovergence gains measured during pursuit (gain = 0.2) seem lower than those measured during fixation (gain = 0.3). This difference is mainly due to the high gains of subject MF in experiment 1. Except for MF the gains of the visually evoked cyclovergence were not different for fixation and pursuit conditions. Cyclovergence phase lags were comparable with these measured during fixation (~40°). Thus the on-going cyclovergence due to L2 probably affected the gain but not the phase lag of responses to whole-field cyclodisparities. We cannot exclude the possibility that the subtraction technique affected the gains of the visually driven cyclovergence. On the basis of our results, we suggest that visually driven and L2-related cyclovergence are independent of each other and superimpose linearly.
L2-related cyclovergence
In the present experiment, we used a new technique to measure µ during pursuit in a rich visual environment. Subjects were asked to follow by eye a dot that moved in the midsagittal plane. µ was estimated using the LRB and LBR model. These models produce cyclovergence angles as a function of vertical version and horizontal vergence (LRB) or horizontal vergence effort (LBR) and thus make it possible to estimate µ during pursuit in the midsagittal plane.
In experiment 2, the visual stimulus was fixed to the world.
In experiment 3, it was attached to the moving fixation
marker. Stimuli of experiments 2 and 3 thus
presented different changing disparity fields during similar eye
movements. µ estimated during experiments 2 and
3 did not differ, suggesting that the visual environment
does not play an important role in L2. This is in agreement with
results of Minken and van Gisbergen (1994). In their
experiment, subjects were asked to make vergence eye movements at
various levels of elevation. The experiment was carried out both in the
dark (eye movements to remembered locations) and with visible stimuli.
In both conditions they found similar cyclovergence components. Our
finding is also in agreement with van den Berg et al.
(1997)
. van den Berg et al. (1997)
repeated
their experiment with light on and this did not affect cyclovergence.
Our experiments also provide an opportunity to comment on the dichotomy
on the value of µ, which is ~0.4 according to van Rijn and
van den Berg (1992), ~0.18 according to Mok et al.
(1992)
, and ~0.25 according to Minken and van
Gisbergen (1994)
. Estimations of µ produced by the LRB model
ranged from 0.12 to 2.5. If we correct for nonparallel Listing's
planes at infinity (LBR model), estimations become 0.1-0.75. If we
exclude EP (see Subjects) from the analysis, µ ranged from
0.1 to 0.45. These values cover the whole range of µ's reported by
the latter authors. Therefore the main conclusion is that L2 holds
during pursuit in a rich visual 3D environment and that µ is subject
dependent rather than stimulus dependent.
Relation between visually and L2-related cyclovergence
In the INTRODUCTION we hypothesized that visually driven cyclovergence may help to decrease cyclodisparities caused by L2 and slanted objects (Figs. 2 and 3). In this study, we did not find evidence that this may be the case during pursuit. If µ is much smaller or larger than 0.25, HH cyclovergence deviates from zero. HH cyclovergence that deviates from zero causes whole-field cyclodisparities, suggesting that there is a role for visually driven cyclovergence to help to bring the two eyes' images in register. Figure 17A shows that large µ's correlate with large standard deviations of the HH-cyclovergence. However, Fig. 17B showed that subjects having a large µ do not have large visually driven cyclovergence gains, indicating that they do not respond more strongly to whole-field cyclodisparities.
Can visually driven cyclovergence help to bring the two eyes images in
register in situations in which L2 cannot? Because of L2, large and
fast changes of cyclovergence during pursuit movements can occur (for
example, if the target moves from near down to far up). In contrast,
the visually driven cyclovergence system is slow (Howard and
Zacher 1991; van Rijn et al. 1992
, 1994a
).
Although this would seem to rule out an important role for
cyclovergence to reduce or stabilize cyclodisparity during pursuit,
this conclusion would be premature. Changing horizontal vergence and
L2-related cyclovergence might boost the visually driven cyclovergence
system. We report here that this is not the case because pursuit does
not reduce the phase lag of the visually driven cyclovergence. Thus
during pursuit of a target that is moving sinusoidally with a frequency
0.125 Hz, it is conceivable that visually driven cyclovergence
accidentally increases whole-field cyclodisparities due to its sloppy
response. In that respect, the reduced gain for higher frequency and
amplitudes of cyclodisparity appears to be an asset, preventing
inadvertent increases of cyclodisparity at high pursuit speeds in depth
and or vertically. We suggest then that visually driven cyclovergence
does not help to decrease whole field disparities during tasks
involving fast changes of cyclovergence. However, we have an open mind
about the possibility that during tasks in which long-lasting fixation
of a static object is involved, visually driven cyclovergence helps to
reduce cyclodisparities (caused by L2) to within the fusion range (as
in Howard and Kaneko 1994
).
Conclusions
We replicated L2 during pursuit in a rich visual environment. Values of µ varied between subjects and covered the whole range of µ's reported in the literature. We did not find different µ's during pursuit in a static environment and during a simulated head translation. Thus the visual environment does not play an important role in L2. Gains of visual driven cyclovergence were the comparable in the fixation, pursuit and simulated head movement conditions. Thus it is possible to describe the 3D orientations of the two eyes during pursuit in 3D as the sum of L2 and visually evoked cyclovergence.
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ACKNOWLEDGMENTS |
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We thank E. van Wijk for writing the software for eye-movement measurements, R. Grund for assisting with the UNIX-work stations, J. Beintema for critically viewing the stimulus software, and two anonymous referees for providing helpful comments.
I. Hooge was supported by the Human Frontiers Science Program (RG 34/96B).
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FOOTNOTES |
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Present address and address for reprint requests: I.T.C. Hooge, Dept. of Comparative Physiology, Utrecht University, PO Box 80085, 3508 TB Utrecht,The Netherlands.
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 19 January 1999; accepted in final form 18 January 2000.
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REFERENCES |
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