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1 From the Department of Ophthalmology, University of Heidelberg, Germany; and the 2 Departments of Neurology and Ophthalmology, the Johns Hopkins Hospital, Baltimore, Maryland.
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Abstract |
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METHODS. Six normal subjects were required to fixate on a 3 x 3 array (40° on a side) of light-emitting diodes arranged on a flat screen 124 cm from the subject. Disparity-induced vergence was elicited with a horizontal Fresnel prism (30 cm/m, ~17°) placed in front of one eye. In four subjects accommodative vergence (10° to 15°) was produced by placing a minus spherical lens in front of one eye while the other eye was covered. Eye position was measured binocularly using three-axis search coils. Control data were collected without prisms during monocular and binocular viewing. For all data a planar regression was used to fit torsional eye position as a function of horizontal and vertical position to calculate the horizontal and vertical primary positions that define the orientation of Listing’s plane.
RESULTS. In the prism experiment, the horizontal primary position of the eye not wearing the prism rotated temporally by 3.9° ± 1.7° compared with the both eyes viewing control condition. The rotation of the prism eye was in a similar range (3.4° ± 2.0°). With accommodation, the horizontal primary position of the viewing eye rotated temporally by 4.4° ± 1.4° compared with the monocular viewing control. In both the accommodation and the prism paradigms there was usually a rotation of vertical primary position downward.
CONCLUSIONS. Vergence-induced changes in Listing’s plane can be independent of changes in orbital position associated with vergence. This finding supports a role for changes in central innervation in the elaboration of Listing’s law.
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Introduction |
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TopAbstractIntroductionMethodsResultsDiscussionReferences |
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In these recent reports the vergence stimulus caused both eyes to change their orbital position.1 2 3 4 5 6 7 Thus, a potential confounding influence on the orientation of Listing’s plane–the change in the horizontal position of the eyes in the orbit associated with the change in vergence–was not considered. Here, we asked whether or not "position-independent" vergence leads to a similar rotation of Listing’s plane. For example, with both eyes viewing, does vergence induced by placing a laterally-displacing prism in front of just one eye affect the Listing’s plane of the other eye? Similarly, does vergence induced by accommodation during monocular viewing affect the Listing’s plane of the viewing eye? In both examples, only 1 eye undergoes a change in its position in association with the change in vergence, although both eyes may receive a convergence command. The main result of this study is that the rotation of Listing’s plane with convergence is independent of any vergence-induced change in eye position.
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Methods |
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Visual Stimuli
Fixation points consisted of nine light-emitting diodes (LEDs),
placed on a flat screen, 124 cm in front of the subject’s eye. They
were arranged in a 3 x 3 array, 40° on a side, with the center
LED (0,0) located at the straight-ahead reference position. For the
accommodation paradigm (see below), small numbers, which could only be
discerned with a visual acuity of at least 20/25, were placed just
under each LED to provide an accommodative target. The room lights
remained on during all experiments.
Recording of Eye Movements and Calibration Procedure
Movements of both eyes were recorded around all three axes of
rotation (horizontal, vertical, and torsional) using the magnetic field
search coil method with dual annuli. The output signals from the
frequency detectors were filtered with a bandwidth of 0 to 90 Hz and
sampled with a digital computer at 500 Hz with 12-bit resolution. The
accuracy of the measurements was to at least 0.1° with noise levels
less than 0.05°. Data were stored on disc for later off-line analysis
using Matlab (Mathworks). Further details of the calibration and
recording procedures can be found in Straumann et al.8
The annuli were placed on each eye after administration of a topical anesthetic (proparacaine HCl 0.5%, Alcaine). The subject’s head (orbits) was precisely centered in the field coils using space-fixed horizontally and vertically-oriented laser beams emanating from immediately next to the center LED. The head was immobilized with a bite-bar made of dental impression material. The head orientation in the field coil system was not explicitly measured, but in most subjects in our setup the head is oriented such that Reid’s line makes an angle of 20° upward.
Experimental Protocol
Two types of stimuli were used to elicit vergence: a Fresnel prism
oriented horizontally in front of 1 eye, to elicit disparity-linked
convergence, and a negative diopter spherical lens placed in front of
one eye (the other eye was covered) to elicit accommodative-linked
convergence. The Fresnel prisms were pasted onto a pair of spectacles
that contained plano lenses. The spectacles were entirely made of
nonmetal material and therefore did not affect the coil signals.
The general pattern of presentation of target stimuli was as follows. After initial fixation at the center LED (0,0), LEDs at the eight eccentric positions were lit consecutively in the counterclockwise direction. Before the appearance of the LED at each eccentric stimulus, however, the center LED was illuminated, so that subjects always made consecutive centrifugal and centripetal shifts of eye position. Each LED position was illuminated for 3 seconds. The entire series of eight eccentric LED fixations was usually repeated three times. We verified for every fixation point that the horizontal and vertical positions were correct for that LED.
Prism-Induced Vergence Paradigm.
The prism-induced vergence paradigms were performed on all six
subjects. First, control data were collected with both eyes viewing
without prisms (Fig. 1A
). Then the same paradigm was performed with both eyes viewing but with
a horizontal Fresnel prism placed base out (30 cm/m = ~17.1°)
in front of the right eye (Fig. 1B) . The left eye wore no prism.
Subjects were asked to fuse the images of the LED. The vergence angle
was calculated and displayed. Next, there was a second control
experiment with both eyes viewing without prisms
(BE2 paradigm). Then the prism was positioned in
front of the left eye (BELP paradigm). Finally,
another set of data with both eyes viewing without prisms was collected
(BE3 paradigm). To summarize, the disparity
paradigm order was as follows: BE1 (both eyes
viewing, no prisms, first control), BERP (both
eyes viewing, right eye wearing prism), BE2 (both
eyes viewing, no prisms, second control), BELP
(both eyes viewing, left eye wearing prism), and
BE3 (both eyes viewing, no prisms, third
control).
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Because of the depth of their globes in the orbits and the relative location of their nasal bridges, four subjects could not reliably see the targets with the eye with the prism, when the targets were located in some of the nasal positions, which corresponded to the most temporal positions of the nonprism eye. Because fusion was lost in these positions, they were not used for analysis of either eye. Accordingly, analysis of the nonprism eye was based on the six nasal positions, and analysis of the prism eye on the six temporal-most positions, in which fusion was maintained by all subjects at all times. However, because of the change in orbital position of the prism eye during convergence, temporal positions with the prism in place were approximately 15° more nasal than the temporal positions of the control paradigm. Therefore, calculations of Listing’s plane in the control paradigm were based on the six nasal positions for all eyes.
In the binocular and monocular control paradigms, in which all subjects could see all nine LEDs, we determined the effects of choosing a subset of points (relatively nasal or temporal) on the calculated orientation of Listing’s plane. There was a small but consistent apparent "temporal rotation" (mean 2.4° ± 0.6° RE- and LE-paradigm, mean 2.0° ± 0.8° in the BE1-paradigm) of the horizontal primary position, when the six nasal-most LEDs were selected instead of all nine LEDs. Selecting the six temporal-most LEDs for the calculation (instead of all nine LEDs) led to an apparent "nasal rotation" of the horizontal primary position of a similar magnitude (mean 1.7° ± 0.9° in the RE- and LE-paradigms, mean 1.9° ± 0.5° in the BE1-paradigm). Thus, there is a small but consistent influence on the calculation of horizontal primary position, which depends on the LEDs selected; using relatively nasal eye positions leads to more temporal rotation of the primary position, and vice versa. Our data, as has been reported previously,9 indicate that Listing’s "plane" is not a true plane but is curved and that the departures from a planar surface may be greater for more eccentric eye positions. This feature emphasizes the importance of matching, as closely as possible, the orbital positions used to calculate Listing’s planes in the corresponding control and vergence paradigms.
Accommodation-Vergence Paradigm.
Four of the subjects underwent the accommodation-vergence paradigm. Two
presbyopic subjects were excluded. For this paradigm the subjects were
encouraged to look at the small numbers placed next to the LEDs. The
pattern of target presentation was otherwise as above. The subjects
looked at the targets under monocular viewing conditions, first without
and then with a minus lens of -5.0 D that called for accommodation
(Fig. 1C)
. To summarize, the accommodation paradigm order was as
follows: RE, monocular, right eye viewing with no minus lens (left eye
covered); REL, monocular, right eye viewing with
minus lens (left eye covered); LE, monocular, left eye viewing with no
minus lens (right eye covered); and LEL,
monocular, left eye viewing with minus lens (right eye covered).
Data Analysis
The three-dimensional angular eye positions, relative to the fixed
coil frame and hence to the immobilized head, were analyzed as rotation
vectors and converted to gaze positions.10
Vergence angles
were calculated as the difference in the horizontal gaze positions of
the 2 eyes, with convergence being positive.
All trials were visualized offline. For the analysis, all data points during an eccentric fixation period of 250 msec immediately before the return to the straight-ahead (0,0) reference position were taken. Thus, there was plenty of time for each subject to acquire the peripheral target, and the accuracy of fixation was also verified. Both the torsion value of each eye and the vergence angle were calculated for this period of fixation. Because each eccentric trial was both preceded and followed by a return to the reference position, any coil slip (as reflected in a sudden jump in the torsional eye signal) could be detected and corrected for by updating the reference position. This was not possible for the eye wearing the prism. When coil slips were observed in prism eyes, the affected data were excluded from the analysis. This occurred in 3 eyes of two subjects in which consistent coil slip happened in some positions of gaze. Overall, less than 5% of data points had to be deleted because of blinks or subjects not looking at the target.
Fixation data were combined from circling the entire array three times. A regression was used to fit the data points to a plane. The goodness of the fit was expressed as the standard deviation of the torsional eye positions, the so-called "thickness of the plane." From each planar fit, horizontal and vertical primary positions were calculated.11 The shift in primary position was calculated as the difference between the primary position during vergence and the primary position during the corresponding control condition. For the prism experiment, data were compared to the immediately preceding control (i.e., BERP to BE1 and BELP to BE2). Likewise, primary positions during accommodation were compared with those of the immediately preceding monocular control. For convenience and to facilitate pooling of data, horizontal primary positions of the left eye were mirrored to the right by reversing the sign of the left eye value: Positive values describe upward and temporal rotations of either eye.
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Results |
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The mean horizontal primary position (hPP) was 4.80° ± 5.13° for the right eye and 4.91° ± 6.58° for the left eye. Vertical primary positions (vPP) were 8.54° ± 5.94° for the right eye and 8.63° ± 5.82° for the left eye. Thus, although there was a wide variation, on average the hPPs were temporal to and the vPPs above the straight-ahead reference position. These findings are similar to those reported by previous investigators.1 2 3 4 5 6 7
Shift of Horizontal Primary Position.
We next analyzed the effects of prism-induced vergence on the
orientation of Listing’s plane. We verified that the subjects were
fusing the targets by monitoring the horizontal vergence angle. The
values were in the 15° to 16° range as predicted from the power of
the prism, except for the one subject (SA) who wore his spectacles. For
this subject the vergence angle was several degrees smaller and
commensurate with the minus power (about -3.0 D) of his spectacles.
Figure 2A
demonstrates the shift of the horizontal primary position of the eye
not wearing the prism (nonprism eye) for all subjects. Although
individual hPPs varied across subjects, the shift of the hPP showed a
uniform pattern. The hPP of the left eye (BERP
paradigm) shifted temporally by 3.4° ± 2.1° (P =
0.01, paired t-test), and the hPP of the right eye
(BELP paradigm) shifted temporally by 4.1° ±
1.3° (P < 0.01, paired t-test). The
difference between the two eyes was not significant (P = 0.08). Combining right and left eyes, the average temporal rotation
of the hPP was 3.9° ± 1.7°.
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A "gain" for vergence-induced changes in primary position can be calculated by dividing the shift of hPP by the amount of prism-induced change in horizontal vergence. For the right eye in the BELP paradigm the calculated gain was 0.23 ± 0.16 and for the left eye (BERP paradigm) the gain was 0.29 ± 0.13. The gains of the converging eyes were similar, 0.22 ± 0.14 for the right eye (BERP paradigm) and 0.26 ± 0.22 for the left eye (BELP paradigm).
Shift of Vertical Primary Position.
The shift of the vPP of the nonprism eye is depicted in Figure 2B . For
most subjects, the vPP was displaced downward. In one subject (DZ),
there was a slight upward shift of the vPP of whichever eye was the
nonprism eye. In another subject (LG), the vPP of one eye did not
change and the other shifted downward. On average, for all subjects,
there was a downward shift of the vPP in both the nonprism and prism
eyes. The mean shift for the nonprism eye was -3.18° ± 3.84°
(P < 0.01) and for the prism eye -5.19° ± 5.37°
(P < 0.01). As for the temporal rotation of the hPP,
no difference was observed in the shift of vPP of an individual eye,
whether it was the one looking through the prism or not
(P = 0.44). Likewise, no significant difference was
found in the change of vPP between the prism eye and its fellow eye
(P = 0.34). There was also no significant correlation
between temporal shifts of hPP and downward shifts of the vPP for
either the nonprism eyes (correlation coefficient = 0.29) or the
prism eyes (correlation coefficient = 0.05).
Accommodation-Induced Vergence
In a second set of experiments, which was possible in the four
subjects without presbyopia, we used accommodation and accommodative
vergence as the stimulus for a rotation of Listing’s plane. We used
the amount of convergence of the covered eye in the monocular viewing
condition as a rough measure of accommodation. During the monocular
viewing paradigm with the minus lens in front of the viewing eye the
mean values of the associated change in vergence ranged from 9.9° to
15.4°. These values are reasonable for accommodative vergence; they
correspond to AC/A ratios ranging from 1.9 to 3.1, which is
within the range of normal.12
As for the both eye viewing paradigms, there was a large intersubject variability in the hPP and vPP in the accommodation paradigms. However, accommodation consistently led to a temporal rotation of the hPP and to a downward rotation of the vPP. Figure 3 demonstrates the changes of the horizontal and vertical primary positions associated with accommodation-induced vergence. Only 7 eyes (instead of 8) are shown, because 1 subject (SA) developed an "accommodative spasm" after accommodating with the left eye and could not "relax" for the subsequent control paradigm. The mean temporal shift of the hPP was 4.4° ± 1.4°. Based on the accommodation-induced vergence change of the covered eye, the mean gain for the temporal rotation of the hPP associated with accommodation was 0.35 ± 0.13 was for all 7 eyes.
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Discussion |
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Our study showed no consistent difference in the magnitude of hPP shift between the converging and nonconverging eye. Recently, Porrill et al.,13 recording smooth tracking in-depth with the target aligned along the visual axis of one eye, found a greater change in relative torsion on up versus down gaze in the eye that was converging. The discrepancy between our study and theirs remains unexplained, although the experimental stimuli and the method of analyzing eye movements were different.
In another recent study, Kapoula et al.14 showed that not only the vergence itself but also the stimulus driving the vergence influence the amount of rotation of Listing’s plane associated with near viewing. Although disparity-driven vergence alone led to a strong temporal rotation of Listing’s plane in both eyes, albeit sometimes asymmetrical, accommodation-induced vergence led to variable results, with no apparent correlation between the tilt in Listing’s plane and the change of vergence. In our study, however, the effects of vergence on the shift of primary position induced by disparity or by blur were similar, perhaps reflecting the facts that the visual stimuli used in our study were simpler than those used by Kapoula et al.14 and also that there was no associated disparity with our accommodative stimulus. Nevertheless, the results of Kapoula et al. argue for a "sensory" as well a "motor" component to the shift of Listing’s plane produced by near viewing.
The rotation of vertical primary position downward was a consistent finding in our paradigms but showed no difference between the prism and the nonprism eye.
Perhaps, because near viewing is usually associated with down gaze, there might be an advantage in rotating Listing’s plane in the same direction to which both the eyes themselves rotate. On the other hand, the explanation may lie in the proposed changes in the innervation to the superior oblique muscle that accompany changes in vergence, as discussed below.
Listing’s Law and the Ocular Motor Periphery
A controversial issue in ocular motor physiology is the role of
peripheral versus central factors in the elaboration of Listing’s
law.16
The discovery of ocular motor "pulleys" in the
orbital periphery, which could in themselves constrain eye rotations to
a specific plane, has focused interest on the contributions of orbital
mechanics to Listing’s law and has challenged prior assumptions about
the nature of the central contribution to the elaboration of Listing’s
law.17
18
Although vergence has been long known to produce
changes in the orientation of Listing’s plane,1
2
3
4
5
6
7
our
experimental paradigms removed one potentially confounding factor in
the studies of the effect of convergence on Listing’s law: the
interaction between the position of the eye in the orbit and the
changing command for convergence. The horizontal and vertical orbital
positions of the nonprism and the accommodating eyes were unaltered by
the change in vergence state, whether accommodative- or
disparity-induced. The finding of a rotation of Listing’s plane in the
nonprism or in the accommodating eye in our paradigm thus provides even
stronger evidence for a central contribution to Listing’s law.
There are at least two mechanisms by which vergence might induce a change in the orientation of Listing’s plane. First, it is possible that a change in the central innervation to the smooth muscle of the orbital pulleys under conditions of convergence might lead to a change in the way that the pulleys alter the axis of eye rotation. It seems unlikely, however, that simply altering smooth muscle tone could lead to such precise and consistent changes in the axis of eye rotation associated with disparity- or accommodative-induced convergence. Alternatively, and more likely, convergence might lead to a change in the central pattern of innervation to the ocular muscles that would alter the axis around which the eyes rotates.
The reasons for rotation of Listing’s plane with convergence have been argued extensively; both motor and sensory explanations have been invoked.18 The changes in primary position with convergence are similar to those that occur with a paralysis of the superior oblique muscle (producing a gradation of relative extorsion increasing from up to down gaze and a relative shift of the vertical primary position of the paretic eye downward).19 These changes may relate to relaxation of the superior oblique muscle during convergence. This is supported by the finding that trochlear motor unit activity decreases with convergence to a greater degree than with an equivalent conjugate adduction.20 Relaxation of the superior oblique during convergence might facilitate adduction by decreasing its presumed tertiary action, abduction.20 Alternatively, the horizontal consequences of superior oblique relaxation might not be a direct effect but rather due to changes in the pulling directions of other muscles in the setting of excyclotorsion.21 A greater degree of excyclotorsion in down gaze, and thus a temporal rotation of Listing’s plane, is consistent with the finding of increased trochlear unit sensitivity to convergence with decreasing elevation.20
In our experiments of asymmetrical prism-induced vergence, the amount of temporal rotation of Listing’s plane was the same in the prism and nonprism eyes, even though only the prism eye was adducted. This suggests that an equal "convergence signal," including perhaps superior oblique relaxation, is sent to the two eyes, even when convergence is asymmetrical. A superimposed versional command could correct the horizontal position of the nonprism eye, while maintaining excyclotorsion, consistent with the limited effect of horizontal version (relative to vergence) on trochlear unit activity.20
In conclusion, our results using an asymmetrical convergence paradigm argue for a central contribution to the convergence-evoked rotation of Listing’s plane. Furthermore, the finding that there was no difference in the amount of rotation of the horizontal primary position of the prism and the nonprism eye suggests that convergence commands are distributed symmetrically between the two eyes even in asymmetrical stimulus conditions.
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Acknowledgements |
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Footnotes |
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Submitted for publication July 14, 1999; revised October 20, 1999; accepted October 27, 1999.
Commercial relationships policy: N.
Corresponding author: David S. Zee, Pathology 2-210, Johns Hopkins Hospital, 600 North Wolfe Street, Baltimore, MD 21287-6921. dzee{at}dizzy.med.jhu.edu
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hPP).
(B) Shift of vertical primary position (