Visually Evoked Cyclovergence and Extended Listing's Law

Ignace Th. C. Hooge and A. V. van den Berg

Department of Physiology, Helmholtz School for Autonomous Systems Research, Erasmus University Rotterdam, NL-3000 DR Rotterdam, The Netherlands


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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.


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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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Fig. 1. Helmholtz coordinate system. Orientations of the 2 eyes relative to the ego-center (E) expressed in Helmholtz angles. x axis is chosen such that it coincides with the version primary direction. theta  denotes vertical version, alpha  denotes horizontal version, and nu  denotes horizontal vergence. Helmholtz coordinate system has 2 eye-fixed rotation axes (the vertical and the torsion axis) and 1 head-fixed axis (horizontal). In this coordinate system, torsion (psi , not drawn) is about the line of sight.

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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Fig. 2. Helmholtz torsion of the 2 eyes as a function of µ and vertical version. In this example, horizontal version (alpha ) equals 0, horizontal vergence is negative (fixation of a near target), vertical version (theta ) is either negative, 0 or positive. A: torsion angles predicted by L2 with µ <0.25, B: torsion angles predicted by L2 with µ = 0.25. C: torsion angles predicted by L2 with µ > 0.25. Upward gaze is associated with extorsion for µ < 0.25, no cyclovergence for µ = 0.25 and intorsion for µ > 0.25.

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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Fig. 3. Cyclodisparities during head translations. A1-C1: head translation above a table while the eyes fixate a cross on this table. A2-C2: vertical version and vergence required to fixate the cross on the table. L, left eye; r, right eye; c, ego center; F, fixation point. Version primary direction (- - -) intersects the table in p. Angle lfr, horizontal vergence; angle fcp, vertical version. A3-C3: perspective projections of the cross in the left and right eye socket during the head movement of A1-C1. As indicated by the arrows, the movement from A to C causes an intorsion of the vertical lines. Minimization of whole-field cyclodisparity would require intorsion of the eyes by half the amount of the intorsion of the vertical lines.

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.


    METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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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Fig. 4. Offset-compensated and -corrected signals. A: output of the offset compensator. Two-channel offset compensator was fed with the torsion signal (0.150 V/°) of the left and right eye. Offset compensator resets a signal within 2 ms to 0 V if its magnitude exceeds 1.0 V. This corresponds to ±6.67° (±1.0/0.150). Thus if the absolute value of the torsion signal exceeds 6.67°, it is reset to 0°. We added the offset of the original torsion signal to the corrected signal because the offset compensated signal lacks an overall offset. B: torsion signal after offset correction.

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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Fig. 5. From coil voltages to Listing's and Helmholtz coordinates. Each experimental session contained 3 types of trials. Signals from the primary direction measurement and the calibration were used to transform the cyclovergence measurement signals from coil voltages to Listing's and Helmholtz coordinates (fat arrow). Signals from all measurements were transformed to Fick angles (A), linearized (C), and corrected for the nonorthogonality of the direction and the torsion coils (D). We used the offset compensator in the cyclovergence trials. Before linearization and correction for nonorthogonality, we corrected the torsion signals of the cyclovergence trial for the effects of the offset compensator (B). Calibration trial was used to determine the coil misalignment (E). Signals of the primary direction measurement and the cyclovergence measurement were corrected for coil misalignment (F) using the correction factors (D). From the signals of the primary direction measurement, we determined the version primary direction (G). Version primary direction was used to transform the signal of the cyclovergence measurements to Listing's coordinates (H). Subsequently, these signals were transformed to Helmholtz angles (I).

In the primary direction trial, we determined the primary direction from the version component of the eyes. Version was computed by averaging the rotation vectors of the left and the right eye. Fitting a plane to the collection of averaged rotation vectors, we determined the version primary direction (Bruno and van den Berg 1997a). We also fitted planes to the rotation vectors of each eye (displacement planes) and computed primary directions from those fits using the same procedure. The versional primary direction was used to transform the rotation vectors of each eye to a new basis that is aligned with the (versional) primary direction (Haslwanter 1995). The reference direction is then aligned with the primary direction instead of the x axis of the coil frame. We refer to such rotation vectors as expressed in "Listing coordinates." The data also were expressed as Helmholtz angles. This was done by a transformation from Listing's coordinates to Fick angles (Bruno and van den Berg 1997a), followed by a transformation from Fick coordinates to Helmholtz coordinates (Lemij 1990).

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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Fig. 6. Stimulus. A-C: top, side, and front view of the stimulus. In experiment 1, we varied the radius of the stimulus, the distance of the simulated bunch of lines (horizontal vergence angle), the simulated cyclovergence amplitude, number of lines, depth in the stimulus, and size of the fixation marker.

Stimuli were back-projected (Sony VPH 1270QM projection television, only the red and green tubes were used) on a translucent screen (distance 1.0 m, size 75 × 75°). Otherwise, the experimental room was completely dark. Left and right eye images were separated by using red and green filters in front of the tubes of the projection television and in front of the subject's eyes. Frame rate was 120 Hz (60 Hz/eye).

To evoke visually driven cyclovergence, we used a method called "simulated cyclovergence." Our simulations on the screen of a 3D scene allowed us to rotate each eye's image about any axis. In most conditions, a fixation point was shown. If so, simulated cyclovergence consisted of rotation of the simulated scene about an axis through the fixation point and the center of rotation of that eye as determined before the experiment. The direction of this torsion movement was opposite for the two eyes. If no fixation point was shown, the axis of rotation cut through the center of each eye's image. This method in a number of respects is a generalization of the stimuli used by Howard and Zacher (1991) and van Rijn et al. (1992, 1994a). First, the torsion axis can have any orientation relative to the screen. Thus visually evoked cyclovergence for horizontally converged eyes can be studied. Second, we can make the torsion axis dynamic, i.e., the cyclovergence can be presented to horizontally and/or vertically moving eyes. Finally, the simulated cyclovergence method also allows us to use 3D stimuli [instead of the flat stimuli used by Howard and Zacher (1991) and van Rijn et al. (1992, 1994a)].

The experiment was divided in three parts, which are described in the following text.

Experiment 1. Visually evoked cyclovergence during fixation. The first experiment was designed to replicate parts of the results of Howard and Zacher (1991) and van Rijn et al. (1992, 1994a). We wondered whether our stimuli would be as effective as in those of the previous studies in which slide projectors were used to present the stimuli. Howard and Zacher (1991) and van Rijn et al. (1992, 1994a) reported the highest gains and lowest phase lags for rotation frequencies of respectively used 0.05 and 0.0625 Hz. We took a frequency of 0.125 Hz to limit trial duration. Presentation time of each stimulus was 32 s. Thus each trial contained four periods of simulated cyclovergence. Amplitude of the cyclorotation per image was 1, 2, 3, or 4°. This caused simulated cyclovergence of 2, 4, 6, or 8°. As a control, we varied the diameter of the stimulus because in experiment 3 the whole stimulus moved with respect to the observer. This movement caused variation of the size of the stimulus on the screen. Diameter of the stimulus was 52, 56, 60, 64, or 70°. Number of lines in the stimulus was 400, 600, 800, or 1,000. As an extension of the previous studies, we also investigated the effects of the horizontal vergence angle and depth in the stimulus. To do so, the distance at which the stimulus was presented was varied. These distances corresponded to horizontal vergence angles of -0.2, -4, -8, -12, and -16°. Because of the convention for angles (vergence equals left eye angle minus right eye angle and left, down and clockwise are positive), fixations of points nearer than infinity result in negative horizontal vergence angles. Moreover we varied the size of the fixation point to check whether this has an effect on visually evoked cyclovergence gains because van Rijn et al. (1992) suggested (but did not formally report) that selective focal attention to such a point may cause a reduction in gain (their page 1877). The diameter of the fixation marker was 0.85, 0.42, or 0.21°. The size of the stimuli in the direction of the x axis (depth) varied from 1 to 75% of the distance between the subject and the fixation marker.

Depth and eye vergence factors were added to the experiment because the ability to cycloverge in response to a visual stimulus is possibly better developed for near than for far stimuli. After all, the cyclodisparity of a fixated line that is slanted in depth increases as the line is placed nearer to the eyes.

In each trial, one of the six parameters was varied relative to a default stimulus. The specifications of the default stimulus were: simulated cyclovergence amplitude = 4°, radius = 35°, density = 400 lines, fixation marker = 0.85°, horizontal vergence = -2°, and depth was 1% of the distance between the observers eyes and the far-end of the stimulus (the plane in which the fixation marker was located).

Stimulus presentation was started by the experimenter, but the subject indicated with a mouse click that he was ready. Sampling was not started immediately after the mouse click though but postponed until the next positive zero crossing of the simulated cyclovergence stimulus. This ensured that signal recording always started at the same stimulus phase.

The next two experiments were designed to investigate visually driven and L2-related components of cyclovergence during pursuit eye movements. We attempted to separate these components in the cyclovergence response by subtraction of responses in carefully matched trials in which the presence and phase of the visually driven cyclovergence was varied. Experiments 2 and 3 investigated the effects of pursuit during simulated target movement and simulated self-movement respectively.

Experiment 2. Visually evoked cyclovergence during pursuit in a static environment. In the second experiment, subjects were asked to follow a moving dot (diameter, 1°) by eye. This dot traveled through the visual pyramid (Fig. 7A). All other objects in view had a fixed location with respect to the subject's head. The dot either could move from far down to near up (horizontal vergence and vertical version in phase: middle point of the trajectory was at a distance of 0.66 m, z amplitude = 0.25 m, x amplitude = 0.25 m), near down to far up (horizontal vergence and vertical version 180° out of phase; same movement parameters as previous movement), along a vertical at 2 distances (x = 0.33 m, z amplitude = 0.125 m; x = 0.66 m, z amplitude = 0.25 m), or it could move along a horizontal track in depth (middle point of the trajectory was at eye height at a distance of 0.66 m, x amplitude = 0.25 m). Only during the horizontal movement the stimulus was a ground plane consisting of randomly oriented lines. Finally the target moved on a circular trajectory (i.e., horizontal vergence and vertical version were 90° out of phase, amplitudes and middle point of the trajectory as in the diagonal stimulus). The frequency of the target movement was 0.125 Hz in all cases. These target movements in the midsagittal plane were chosen to evoke eye movements with various amounts of horizontal vergence and vertical version and with several different phase relations. As mentioned before, according to the extension of Listing's law, the product of HH horizontal vergence and HH vertical version is proportional to the amount of cyclovergence (rotation vectors). Notice that because of this nonlinear interaction between horizontal vergence and vertical version, the cyclovergence associated with L2 will in general not be a pure sinusoidal movement. We hoped to obtain a fairly complete sample of cyclovergence eye movements during pursuit by using the various amplitude relations and phase relations between vertical version and horizontal vergence in our set of stimuli.



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Fig. 7. Stimulus of experiment 2 (A) and experiment 3 (B). A: in experiment 2, the fixation marker traveled through a bunch of lines [vertical near, diagonal (from near down to far up), horizontal (above a ground plane), vertical far, diagonal (from near up to far down) and circular]. B: in experiment 3, we used the same 6 movements (shown are 3 movements). Now the bunch of lines was attached to the moving fixation marker. Whole stimulus translated (it did not rotate) through space. In the horizontal movement stimulus the stimulus consisted of a bunch of lines (instead of the ground plane of experiment 2).

Each of the above conditions was presented three times with different levels of superimposed cyclovergence. In trials in which superimposed cyclovergence was absent only the target dot moved (0trials). In the first and last trial of each triple, the same target movement was accompanied by simulated cyclovergence of the background. The simulated cyclovergence in the first trial of each triple started with an in-torsion rotation of the images of the scene (+trial). In the last trial of the triple, the simulated cyclovergence was opposite and this -trial started with an extorsion. Depending on the subject's µ (see INTRODUCTION), visually driven cyclovergence (in Helmholtz coordinates) is in either the same or the opposite direction as the cyclovergence caused by L2.

The intermediate 0trial of a triple did not contain simulated cyclovergence and was used in the analysis to find out which fraction of the cyclovergence was caused by L2 and which fraction was visually driven. This was done by subtracting the cyclovergence response of the intermediate 0trial from the cyclovergence response of the -trial and +trial. The residue represents the fraction of the cyclovergence that is related to the counter rotation of the half-images. Amplitude of the cyclorotations was 2° per eye, which equals simulated cyclovergence amplitude of 4°. The diameter of the circular stimulus was 70°. The number of lines in the stimulus was 400.

Experiment 3. Visually evoked cyclovergence during pursuit in a moving stimulus (simulated head movement). In the third experiment, we simulated self-motion, i.e., the motion sequence that was shown to each eye represented the image viewed by an eye that translates through the simulated 3D scene. The simulated trajectory of the eyes through the scene was determined by the interocular distance and the simulated movement of the head through the 3D scene. The graphics computer performed all the 3D and perspective transformations required for the two eyes on a frame-by-frame basis.

Each image contained a fixation dot that was at a fixed location in the 3D scene (Fig. 7B). As the dot moved on the screen, the visual environment moved along with the dot. Thus the motion of the fixation dot always was accompanied with motion of the background. Subjects had a vivid self-motion percept when they tracked the dot.

The simulated self-motion trajectories were comparable with the pursuit trajectories of experiment 2. On the screen, the dot could move from far down to near up, near down to far up, pure vertical (at two distances), pure horizontal, or circular. As in the second experiment, each trial was presented three times. In the first and last trial of each triple, rotation of the background motion about the visual axis was added to the simulated self-motion. Thus the image motion was now consistent with a simulated self-motion superimposed on a simulated cyclovergence of the eyes. The simulated cyclovergence in the first trial of each triple was opposite to the simulated cyclovergence of the last trial. Similarly, as in experiment 2, the cyclovergence response of the intermediate trial was used to find out which fraction of the cyclovergence was caused by L2 and which fraction was visually driven. Frequency of the cyclorotation was 0.125 Hz and presentation time was 32 s. Amplitude of the cyclorotation was 2° per eye, which equals simulated cyclovergence amplitude of 4°.

The maximum diameter of the stimulus was 70°. When the stimulus moved away from the observer it shrank. The number of lines in the stimulus was 400. Stimulus presentation and sampling were started using the same procedure as for experiment 2.

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 -trial of each triple to obtain the visually driven cyclovergence. We averaged (after inversion of the corrected responses derived from the -trial, see Fig. 8) the cyclovergence responses from these trials and computed gain and phase lag of this averaged visually driven cyclovergence component using Fourier analysis as previously described for experiment 1.

Cyclovergence obtained in the 0trial enabled us to check whether cyclovergence follows L2 during pursuit of a fixation marker that travels in 3D through (experiment 2) or together with a rich visual environment (experiment 3). We refer to this signal as L2-related cyclovergence. We compared the cyclovergence responses of the 0trial to the responses simulated by the LRB model. This analysis was done using Listing's coordinates and Helmholtz angles. The LRB model is fed with the HH vertical version and HH horizontal vergence and predicts rotation vector components. The LRB model is a special formulation of L2 (Mok et al. 1992; Tweed 1997) having a µ of 0.5 (see INTRODUCTION). This method enabled us to estimate µ from pursuit in the midsagittal plane without the need to sample pursuit on a large sector of an iso-vergence surface. If the cyclovergence (in Listing's coordinates) of a subject fits the LRB model, we conclude that µ = 0.5 for this subject. If, for example, the cyclovergence fits half the cyclovergence predicted by the LRB model, we conclude µ = 0.25. If the cyclovergence response does not fit the LRB model altogether, pursuit does not obey the extension of Listing's law.

In the LRB model, it is assumed that the Listing's planes of the two eyes are parallel when the lines of sight are parallel. We observed that this assumption often was violated (this phenomenon also has been described by Bruno and van den Berg 1997a; Haslwanter et al. 1994; Mikhael et al. 1995; Mok et al. 1992). Therefore we did a second analysis. Cyclovergence angles were compared with predictions of a model that incorporates nonparallel Listing's planes when looking at infinity (van den Berg et al. 1995). We refer to this model as the LBR model. The LBR model was developed to explain the excess cyclovergence of patients with intermittent exotropia. This model interprets the nonparallel Listing planes for fixation of distant targets as indicating that a convergence effort is being made already to obtain parallel lines of sight. This convergence effort results in a cyclovergence of the eyes similar to that found when normal subjects are actually converging. Thus predicted cyclovergence according to the LBR model depends on the angle of convergence added to the angle between the Listing planes for fixation of distant targets.

To check the assumption of superposition further, we averaged the cyclovergence responses of the +trial and the -trial of each triple (Fig. 8). In this way we should end up with a signal that equals the L2 part of cyclovergence because the simulated cyclovergence was opposite in the +trial and the -trial. This "reconstructed" L2 part was subtracted of the cyclovergence in the corresponding 0trial. We called this signal the residual cyclovergence.



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Fig. 8. Subtraction method: determination of the visually driven cyclovergence gains during pursuit. Thin lines denote real cyclovergence signals. Fat line denotes the simulated cyclovergence. A-C: cyclovergence signals of a +trial, a 0trial, and a -trial. D: if L2-related cyclovergence is equal for the +trial, the 0trial, and the -trial, the residual cyclovergence should equal 0. E: we computed (+trial - -trial)/2 to determine the visually driven cyclovergence gains


    RESULTS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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 <= 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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Fig. 9. Orientation of the version Listing's plane with respect to the coil frame and the orientation of the left and right eye Listing's plane in Listing's coordinates. Clockwise rotation about the y axis (A) and z axis (B) are denoted with a negative angles. C and D: orientation of the version Listing's plane with respect to the coil frame. Light bars represent rotations of the version Listings plane about the z axis of the coil frame. Dark bars represent the rotation of Listing's plane about the y axis of the coil frame. E: alpha [the angle between the left and right eye Listing plane (Listing's coordinates)]. Alpha is negative in this illustration. F: alpha obtained from experiment 2 (black bars) and experiment 3 (white bars)

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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Fig. 10. Visually driven cyclovergence signal vs. time. This figure shows data of subject MF. Stimulus was flat and had a radius of 35°. Number of lines in the stimulus was 400 and vergence angle was 12°. Cyclovergence signal was corrected for drift and offset. Both the simulated cyclovergence and visually driven cyclovergence are expressed in Helmholtz angles. Thus the angles represent the difference in rotations about the lines of sight. Positive angles correspond to intorsion. Amplitude of the visually driven cyclovergence is smaller than the amplitude of the simulated cyclovergence. In this condition, the cyclovergence response has a phase lag of ~30°.



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Fig. 11. Cyclovergence gains of experiment 1. In each trial, 1 of the 6 parameters was varied relative to a default stimulus. Specifications of the default stimulus were: simulated cyclovergence amplitude = 4°, radius = 35°, density = 400 lines, fixation marker = 0.85°, horizontal vergence = -2°, and depth (the linear dimension of the stimulus along the x axis) was 1% of the distance between the observers eyes and the far-end of the stimulus (the plane in which the fixation marker was located).

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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Fig. 12. Phase lag of visually driven cyclovergence of experiment 1. In each trial 1 of the 6 parameters was varied relative to a default stimulus. Specifications of the default stimulus were: simulated cyclovergence amplitude = 4°, radius = 35°, density = 400 lines, fixation marker = 0.85°, horizontal vergence = -2°, and depth was 1% of the distance between the observers eyes and the far-end of the stimulus (the plane in which the fixation marker was located).

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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Fig. 13. Examples of pursuit (experiment 3). Subjects followed the fixation dot perfectly in the majority of the trials. However, A shows an example of vergence drop. This is data of subject MF (experiment 3, diagonal movement from far down to near up). MF does not follow the dot in the intervals between the dashed lines. B: example of subject MF. In this trial (experiment 3, circular movement, no simulated cyclovergence (0trial)). MF made many small saccades (little arrows). Other subjects followed the dot more smoothly. 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 ranges between -1.5 and 2° for this huge vertical version movement.

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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Fig. 14. Vertical vergence, vertical version, horizontal vergence, cyclovergence, and predicted cyclovergence (LRB) against time. Numbers on the y axis are the tangent of half the rotation vector component. These numbers roughly correspond to the angle in degrees divided by 100.

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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Fig. 15. L2-related cyclovergence. µ represents the prediction of the LRB model. µ-corrected represents the prediction of the LBR model. Predicted cyclovergence according to the LBR model depends on the angle of convergence added to the angle between the Listing planes for fixation of distant targets. A: µ (LRB) averaged over trials for 6 subjects., B: µ (LBR) averaged over trials for 6 subjects. C: µ (LBR) averaged over subjects for 6 different stimuli. Light bars represent results from experiment 2. Dark bars represent results from experiment 3. Error bars denote standard error of the mean.

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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Fig. 16. Visually driven cyclovergence. A: gains of the visually driven cyclovergence vs. whole-field cyclodisparity caused by both imperfect L2 (µ not equal  0.25) and simulated cyclovergence. B: visually driven cyclovergence gains relative to L2 averaged over trials for 6 subjects. C: visually driven cyclovergence gains relative to L2 averaged over subjects for 6 different stimuli. D: phase lags of the visually driven cyclovergence relative to L2 averaged over trials for 6 subjects. E: phase lags of the visually driven cyclovergence relative to L2 averaged over subjects for 6 different stimuli. White bars represent results from experiment 2. Black bars represent results from experiment 3. Dashed bars represent results of experiments 2 and 3 averaged. Error bars denote standard error of the mean.

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 LRB - 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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Fig. 17. Standard deviation of the HH cyclovergence and visual gain against |µ LRB - 0.25|. A: standard deviation of the HH cyclovergence against |µLRB - 0.25|. Each data point represents 1 trial of experiments 2 or 3. B: visually driven cyclovergence gain vs. |µLRB - 0.25|. Each data point represents 1 trial of experiment 2 or 3.

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.


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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.


    ACKNOWLEDGMENTS

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).


    FOOTNOTES

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.


    REFERENCES
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
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