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1 From the Departments of Neurology and 2 Ophthalmology, The Johns Hopkins Hospital, Pathology, Baltimore, Maryland.
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Abstract |
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METHODS. Four normal subjects (age range, 24–37 years) wore Fresnel prisms of
increasing power for 72 hours to produce a final left-over-right
disparity (range, 7–11 prism diopters [
3.9–6.2°]) that was
still fusible. Eye movements were measured binocularly, using
three-axis search coils, as subjects fixed on an array of
light-emitting diodes (LEDs) arranged on a flat screen, 124 cm away. A
regression was used to fit the data points to a plane (Listing’s
plane) during monocular and binocular viewing. From each planar fit,
the horizontal and vertical components of primary position (the
direction of gaze that is perpendicular to Listing’s plane) were
calculated. Baseline data were collected in the unadapted state, either
just before or at least 4 days after wearing the prisms.
RESULTS. After the period of viewing through the prisms, there was a change in vertical phoria (prism adaptation) ranging from 1.6° to 3.3°. There was a significant (P < 0.01) shift of the relative orientation of the vertical component of primary position between the two eyes of 6.3 ± 1.7° (right eye value minus left eye, up being positive, each measured during monocular viewing). There was no consistent pattern of change in the horizontal component of primary position.
CONCLUSIONS. Prolonged fusion of a vertical disparity is associated with a change in the orientation of Listing’s plane that persists under monocular viewing. Possible mechanisms include phoria adaptation, the prolonged fusional effort itself, and the residual disparity that must be overcome by sensory mechanisms.
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Introduction |
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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 eyes. 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. The room
lights remained on during all experiments.
Recording of Eye Movements and Calibration Procedure
Three-dimensional eye movements were recorded using the magnetic
field search coil method with dual-coil annuli.8
9
The
field coil system consisted of a cubic coil frame producing three
orthogonal magnetic fields (frequencies: 55.5, 83.3, 42.6 kHz;
intensity: 0.088 Gauss). The dual search coils (Skalar, Delft,
The Netherlands) yielded two sensitivity vectors, each being
characterized by voltages induced in one of the two coils by the three
orthogonal fields. An in vitro calibration was performed before each
experiment, in which voltage offsets were nullified by placing the
coils into a metallic tube that completely shielded the coil from the
magnetic fields. The coil then was placed on a gimbal system that was
in the center of the magnetic coil frame. Coil gains were determined by
aligning the sensitivity vectors of each coil with each of the three
magnetic fields. The output signals of the experiment were filtered
with a bandwidth of 0 to 90 Hz and sampled at 500 Hz with 12-bit
resolution. System noise was less than 0.1°. Data were stored on disc
for later off-line analysis on computer (Matlab; Mathworks, Inc.,
Natick, MA). Further details of the calibration and recording
procedures can be found in Bergamin et al.10
The annuli were placed on each eye after administration of a topical anesthetic (proparacaine HCl 0.5%, Alcaine; Alcon Laboratories, Fort Worth, TX). The subject’s head was precisely centered in the field coils so that the center of the interpupillary line coincided with the center of the frame, and the interpupillary line was parallel to earth horizontal. This was accomplished by using space-fixed, horizontally and vertically oriented laser beams emanating from the location of the zero-position LED. The head was immobilized with an earth-horizontal bite bar made of dental impression material.
Experimental Protocol
A vertical disparity was introduced by placing vertically
oriented prisms in front of one eye (one subject) or both eyes (three
subjects). The Fresnel prisms were pasted on a pair of spectacles that
contained plano lenses (subjects HS and MS) or on the fully corrected,
habitually worn refraction (subjects NH and VP). Spectacle frames
contained no metal. The prisms were always placed base-up in front of
the right eye and base-down in front of the left eye, thus inducing a
left-over-right disparity in all subjects. The prisms were oriented as
close as possible to vertical. Measures of horizontal eye position
indicated that no more than 0.2° of horizontal disparity could have
been introduced with the prism. The power of the prisms was gradually
increased over a period of 3 days, depending on whether fusion occurred
without asthenopia. For the 10 hours preceding the postadaptation
recordings, the power of the vertical prisms was constant. All subjects
performed their natural daily activities, including, for example,
working in front of a computer for at least several hours a day.
The final power of the vertical prisms in each subject is indicated in Table 1 . Recordings were made in two separate sessions: (1) in the unadapted state, just before (subjects NH, VP, and HS) or 4 days after wearing the prisms (subject MS) and (2) in the adapted state after wearing the prisms for 72 hours (all subjects). Data in the adapted state were collected with the prisms in place.
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The order of the paradigms in the unadapted state (without prisms) was monocular right-eye viewing, monocular left-eye viewing, and both eyes viewing. In the adapted state (with prisms on) the order was both eyes viewing, monocular right-eye viewing, and monocular left-eye viewing. The reason for starting the protocol with a both-eyes-viewing condition in the adapted state was to minimize deadaptation during the recording sessions.
Data Analysis
Coil signals were used to calculate rotation
vectors11
representing three-dimensional angular eye
position relative to the fixed coil frame and thus to the immobilized
head. Rotation vectors were converted to degrees and expressed with the
following convention: Positive values describe upward, rightward, and
clockwise rotations from the subject’s viewpoint. A first-order linear
regression was used to fit data points to a plane. The goodness of the
fit was expressed as the SD of the torsional eye positions—the
so-called thickness of the plane. From each planar fit, we computed
directly the horizontal and vertical component of primary position in
degrees from the slopes of the regression,10
11
recalling
that the primary position is defined when the line of sight is along an
axis that is perpendicular to Listing’s plane.
All trials were visualized off-line. For the analysis, all data points during a fixation period of 250 ms immediately before the switch from the reference position 0,0 to an eccentric position or back from the eccentric position to the reference position were taken. Both the torsional position of each eye and the vergence angle were calculated for this period of fixation. Less than 10% of data points had to be deleted due to blinks or loss of fixation.
From the fixation data, the alignment of the eyes was calculated in the different viewing conditions. In the adapted state, the alignment was measured with the prisms on. The vertical phoria is defined as the right eye-minus-left eye vertical position (up is positive) during monocular viewing of the straight-ahead LED. The vertical tropia is defined as the right eye-minus-left eye vertical position during binocular viewing. For the phoria, the mean and the SD were calculated from a total of 20 values obtained from each return to the straight-ahead position from each eccentric position, with 10 values for left-eye viewing and 10 values for right-eye viewing.
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Results |
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phoria), which ranged from -1.6° to -3.3°. The phoria in the adapted state only partially compensated for the prism-induced disparity. The residual disparity (dispres) is the disparity that drives vertical fusion in the adapted state and is the difference between the power of the prisms and the phoria in the adapted state (phoriaa).
Effect of Prolonged Vertical Fusion on the Thickness and
Orientation of Listing’s Plane
We examined the effect of prolonged fusion on the thickness of
Listing’s plane, as reflected in the SD of torsional eye position.
Looking at all subjects and all eyes and across all monocular viewing
paradigms, the mean thickness (i.e., the mean of the SDs) in the
unadapted state was 0.75 ± 0.22° (SD). In the prism-adapted
state the mean thickness was 0.90 ± 0.39°. The thicknesses of
the planes in the unadapted and the prism-adapted states were not
statistically different (P = 0.15, paired
t-test).
After prolonged vertical fusion, there was a relatively consistent pattern of shift of the vertical component of primary position (vPP; Fig. 1A ). As measured during monocular viewing, the vPP of the right eye moved down in all subjects a mean of 4.3 ± 2.9° (P = 0.02, paired t-test). The vPP of the left eye moved up in three subjects and down in one subject (Fig. 1B , HS filled squares) a mean of 2.0 ± 2.8° (P = 0.12).
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Control Experiments for the Changes in vPP
In the adapted state, vPP and, consequently,
vPPdiff were calculated using eye positions that
were from 2.5° to 4.0° different from those used to calculate vPP
in the unadapted state, because of the prisms. To exclude any artifact
from using slightly different eye positions to calculate Listing’s
planes, we performed a control experiment in subject HS. During
monocular viewing, primary positions were measured first with the usual
LED display and then compared with those obtained when looking through
a vertical prism of 4 prism diopters, base-up or base-down. The shift
of the vPPdiff using these two displays was
-1.2°, with the prism base-up in front of the right eye and
base-down in front of the left eye. With the prisms reversed (base-down
in front of the right eye and base-up in front of the left eye) the
vPPdiff shifted by 0.4°. These shifts in
primary position were much less than the shift of the
vPPdiff of approximately 8° measured in HS
after prolonged wearing of the prism. Thus, it is unlikely that the
relatively small difference in fixation positions used to compare
primary positions in the unadapted and adapted states were responsible
for the shifts in the orientation of Listing’s plane after prolonged
wearing of the prism.
We also considered that the changes in Listing’s plane associated with wearing a prism for 3 days may reflect day-to-day fluctuations in the orientation of Listing’s plane. In three of our subjects (NH, HS, MS) we had measures of Listing’s plane at least several months apart. The differences between the values of vPPdiff measured on those two occasions were 2.1°, 1.5°, and 0.6°, respectively, which in each case was less than the shift associated with wearing the prism. The differences between the values of hPPdiff measured on two different occasions were 2.4°, 2.9°, and 0.6°, respectively.
Effect of Vertical Fusion on Listing’s Plane after Adaptation
So far, we have considered the orientation of Listing’s planes
obtained under monocular viewing conditions, before and after
adaptation. There is also a question of whether vertical fusion
influences the orientation of Listing’s plane when changing from
monocular to binocular viewing. After 3 days of sustained vertical
fusion, the phoria adaptation of our subjects was incomplete. During
viewing with both eyes, however, some of the residual prism-induced
disparity was removed with the motor component of the fusional process.
We therefore compared primary positions under monocular viewing (one
eye on target, no fusion) and binocular viewing (both eyes on target
during fusion) in the adapted state. We found no significant changes in
the vPPs of individual eyes with fusion (P = 0.40,
paired t-test), although there was a trend for the relative
orientation of the vPPs to change with fusion (-4.3 ± 4.4°,
P = 0.07). We found no significant shifts of either the
hPP of each eye (P = 0.19, paired t-test) or
of the hPPdiff between the two eyes
(P = 0.28, paired t-test). It must be
remembered that the absolute values of the motor responses to the
vertical dispres in our subjects were relatively
small, with mean values ranging from 1.7° to 2.9°, when looking at
the straight-ahead LED. In the unadapted state, without prisms (i.e.,
with no imposed vertical disparity to fuse) neither hPP nor vPP changed
significantly when comparing monocular and binocular viewing conditions
(for the hPPdiff P = 0.29; for
the vPPdiff P = 0.20, paired
t-test).
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Discussion |
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Shift of Primary Position Associated with Fusion of a Prism-Induced
Vertical Disparity: Comparison with Previous Studies
Our results are consistent with a previous study by Mikhael et
al.5
in which prism-induced vertical vergence was
associated with a shift of the vPP in the same direction as the verging
eye (e.g., a base-up prism induces a downward movement of the eye and a
downward shift of the vPP). Their results were based on data from five
normal subjects who wore vertical prisms in a range of 1.5 to 7 prism
diopters in front of each eye. Overall, they found that, during fusion,
the vPP of either eye rotated by approximately 2.7° per degree of
vertical vergence. Because in the their study, training sessions of 30
to 60 minutes were necessary for the subjects to fuse the induced
vertical disparity, it is not clear whether the shift of the vPP was
entirely related to the reflexive vergence that immediately followed
the disparity demand or to any phoria adaptation that may have taken
place during the training sessions, as a delayed adaptive response.
Furthermore, they did not report values for primary position during
monocular viewing, and we therefore do not know whether there were any
non–disparity-driven changes in the orientation of Listing’s plane.
Indeed, the major finding of our study is that after wearing of the
prism for several days, there was a consistent pattern of long-term
change in the vertical component of primary position, independent of
any immediate attempt to fuse disparity.
The effect of wearing vertical prisms on Listing’s plane was also studied by Straumann and Müller.6 They tested three subjects in whom vertical fusion was elicited after a brief period of wearing vertical prisms with an overall power of 1.5 prism diopters. They found a small tendency for inward (nasal) rotation of Listing’s plane associated with vertical fusion and no change in the plane’s vertical orientation. Mikhael et al.5 also reported changes in the horizontal component of primary position; a temporal rotation with the prism base-up and a nasal rotation with the prism base-down. We found no consistent direction of a shift of the horizontal component of primary position, either after adaptation or during vertical fusion in the adapted state. However, we found a large shift of the horizontal component of primary position in two subjects after adaptation, although in opposite directions. The reason for this striking variability among our subjects is unclear. There was no change in the horizontal phoria in any of our subjects after wearing the vertical prisms. The different patterns of change in the horizontal component of primary position, however, imply different patterns and different degrees of change in the gradient of torsion along the vertical meridian. The direction of torsion that occurs with the vertical vergence associated with vertical fusion is known to be idiosyncratic from person to person.12 If this were reflected in a variable pattern of change in torsion with up-and-down gaze, it might contribute to the variable pattern of change in the horizontal component of primary position. Overall, the reason for the discrepancies among the results of Mikhael et al.,5 Straumann and Müller,6 and ourselves is unknown, although the experimental protocols were quite different.
Functional Implications of a Shift in vPP
Our results seemingly agree with a prediction of the visual-motor
theory of Tweed13
about the changes in torsion associated
with optimal binocular control. Tweed relates the behavior of
Listing’s plane under binocular viewing conditions to preventing
changes in cyclodisparity that would otherwise complicate neural
processing of visual information. His theory includes the prediction
that the direction of the tilt of Listing’s plane during vertical
vergence would be in the same direction as the movement of the verging
eye, whereas the tilt of the plane during horizontal vergence would be
in the opposite direction of the movement of the verging eye. These
tilts of Listing’s plane would minimize changes in cyclodisparity by
equalizing the torsional orientation of both eyes in the visual plane
(defined as the plane containing the gaze lines of both eyes).
In our experiments, the vertical vergence was induced by optical means, so that if vertical eye alignment were readjusted to meet the demands of the prism without a superimposed change in torsion, there would be no change in cyclodisparity and hence no visual drive to alter torsion. However, because primary position is not normally coincident with straight ahead gaze, there could be a change in torsional disparity with vertical realignment of the eyes, which might serve as a stimulus to torsional phoria adaptation,14 as well as to a change in the orientation of Listing’s plane. These considerations, along with the discrepancies between the results of our study and those of previous investigators, raise the issue of a potential role of vertical and torsional phoria adaptation in the elaboration of Listing’s law. Sensory factors related to mechanisms underlying the sensory components of vertical and cyclofusion or changes in the sense of visual direction (which could be altered by prolonged viewing through a prism) may be important. Clearly, more subjects and recordings at more frequent intervals and after complete phoria adaptation are necessary to determine the relationship between phoria adaptation, sensory factors, and the shifts in the orientation of Listing’s plane.
Regardless of the actual mechanisms, our results indicate that Listing’s law is mutable. Schor et al.15 also have shown recently that the orientation of Listing’s plane can be modified by altering cyclofusional demands. A capability for modifying Listing’s plane could help to optimize binocular function in the setting of strabismus and its surgical or optical correction. What parts of the brain mediate the adaptability of Listing’s law and how it is elaborated (through central or peripheral factors) still remain to be discovered.
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Acknowledgements |
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Footnotes |
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Submitted for publication May 24, 2001; revised August 29, 2001; accepted October 23, 2001.
Commercial relationships policy: N.
The publication costs of this article were defrayed in part by page
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"advertisement" in accordance with 18 U.S.C. 
1734
solely to indicate this fact.
Corresponding author: Heimo Steffen, Department of Ophthalmology, University of Heidelberg, Im Neuenheimer Feld 400, D-69120 Heidelberg, Germany; heimo_steffen{at}med.uni-heidelberg.de
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) HS, (
) VP, and (
)
NH. Dashed line: mean value. The vPP of the right eye moved
down in all subjects, the vPP of the left eye moved up in three
subjects.