Abstract
purpose. To describe adaptive changes in torsional alignment that follow
sustained cyclovergence in healthy humans.
methods. Eye movements were recorded binocularly from four healthy subjects
using dual-coil scleral annuli. Cyclovergence movements were evoked
over periods of 30 to 150 seconds using a stereoscopic display,
presenting gratings of lines arranged horizontally, vertically, or at
45°, subtending angles of up to 48°. In- and excyclodisparities of
5° were introduced and removed in a single-step fashion. After
stimulation, the time course and magnitude of the decay in
cyclovergence was compared with the subject either in darkness or
viewing a baseline stimulus of zero cyclodisparity.
results. As reported previously, the cyclovergence response to
incyclodisparities was greater than to excyclodisparities. After
sustained excyclovergence, however, in all subjects and in response to
all orientations of the gratings, the decay in darkness was incomplete,
implying an adaptive change in torsional alignment. In response to the
horizontal gratings, for incyclovergence there was also an incomplete
decay in darkness but to a lesser degree than in response to
excyclovergence, and in only three of four subjects. The
incyclovergence evoked by the oblique and vertical gratings was of
small magnitude, and its decay was unaffected by the presence or
absence of a visual stimulus.
conclusions. After sustained cyclovergence, its decay in the absence of a visual
stimulus may be incomplete. The residual component may be interpreted,
by analogy with horizontal and vertical vergence, as reflecting
so-called phoria adaptation for torsional
alignment.
The torsional orientation of the eye is usually determined solely
by the position of the eye in its horizontal and vertical dimensions:
Listing’s law constrains the degrees of freedom of movement of the
eyes to two. Exclusively torsional movements, however, can be elicited
in certain circumstances. In 1861, Nagel
1 first proposed
that disjunctive torsional movement around the visual axis,
cyclovergence, takes place when horizontal lines, observed in the
stereoscope, are rotated in opposite directions. There was much
controversy about the existence of these movements because subjective
methods, none of which was entirely satisfactory,
2 had to
be used to imply the presence of cyclovergence. It was not until 1975
that Crone and Everhard–Halm
3 demonstrated the existence
of cyclovergence objectively using a photographic technique. Since
then, cyclovergence has been well characterized (see Howard and
Rogers
2 for a recent review). Many of its dynamic
characteristics are qualitatively similar to those of horizontal and
vertical vergence
4 5 6 7 although cyclovergence, similar to
vertical vergence, is much slower than horizontal
vergence
8 9 and usually
10 is not under
voluntary control.
Horizontal vergence can be elicited by horizontal disparity between the
images on the retinas. If this retinal disparity signal is removed,
either by occluding one eye
11 or by placing the subject in
darkness,
8 the eyes return to their initial, resting
horizontal position. The time taken for this decay is greater than the
rise time in response to a disparity,
8 11 and if
horizontal disparity vergence is maintained for periods of hours, then
the decay on removal of retinal disparity is incomplete for several
hours or until binocular fixation is reinstated.
12 The
portion of the vergence response that is sustained after removal of the
disparity stimulus has been attributed to the output of a slow fusional
vergence response that leads to so-called prism or phoria
adaptation.
13 It can be observed after exposure to
disparities for periods as brief as 30 seconds. A similar phenomenon
may be observed after exposure to vertical
disparity.
14 15 16
Investigation of the behavior of the cyclovergence system, by
using subjective methods of estimating cyclovergence, suggests that, as
is the case for the horizontal vergence system, the return to the
initial alignment occurs more slowly in the dark than if a zero
disparity stimulus is provided. In contrast to the horizontal system,
the decay of torsion to its initial alignment is reportedly almost
complete, even after prolonged (tens of minutes
17 )
exposure. Van Rijn et al.
18 reported a systematic
difference in cyclovergence, measured using an objective technique,
while a subject fixed on a dot with or without a structured background.
This difference implies cyclophoria in the absence of disparity cues.
Adaptation of cyclophoria, related to head roll, has been described
recently in abstract form.
19
In the present study, using an objective technique to measure the
torsional position of the eye, the time course of decay of
cyclovergence after a sustained exposure to cyclodisparity is
described. The present study also provides an objective demonstration
of rapid phoria adaptation in the cyclovergence system.
Subjects were seated in the dark, their heads stabilized by a bite
bar. Stimuli were presented dichoptically using a virtual-reality
display mounted on the head (ProView 60; Kaiser Electro-optics,
Carlsbad, CA), with a display brightness of 25 foot lamberts and
display area of 36° (V) × 48° (H), composed of 480 ×
640 pixels, the boundary of which was visible during display. This
display was calibrated using a small video camera mounted on a
calibrated gimbal to determine the angle subtended between lines
forming a grid of known pixel spacing. The virtual-reality display was
shown in preliminary experiments not to confound the measures of eye
position. Recorded eye position was unaffected by whether the video
display was on or off, and translation of the headset over many
centimeters caused a variation in recorded eye position of, at most,±
0.16°. In the experiments, any headset movement was minimized by
supports for the eyepieces that were fixed to the bite bar, and the
head itself was stabilized with the bite bar.
Three kinds of stimuli were used, all light-on-dark gratings rendered
with antialiasing (3D Studio, Autodesk, San Rafael, CA).
Horizontal gratings were used in all subjects: subtending 48°
horizontally and 36° vertically, composed of eight equidistant
horizontal, parallel lines, each subtending 0.4°, and a central
fixation spot (a disc subtending 0.7°), located between the parallel
lines. The horizontal disparity of the central fixation spot was such
that 1.0° of vergence was required for binocular fixation. This was
determined by comparing the vergence angle during viewing of the
display and during viewing a distant target (124 cm) outside the
display. The orientation of the grating presented to each eye could be
altered independently, to allow control of cyclodisparity—defined as
the relative orientation of the dichoptic images designated positive or
negative according to whether the images are rotated top toward (in-)
or top away (ex-), respectively, from each other.
In additional experiments performed in two of the subjects, circular
gratings of diameter 34°, composed of 10 equally spaced parallel
lines of width 0.3°, with the lines either lying vertically or
obliquely (running from left inferior to right superior, forming an
angle of 45° to the vertical) were used.
In each trial, the subject was initially presented with a
stimulus at zero cyclodisparity. After a period of 10 seconds, the
stimulus was stepped to a 5° cyclodisparity, either in- or ex-, which
was maintained for 30 seconds. At the end of this period the stimulus
either returned to zero cyclodisparity (baseline response), or was
extinguished so that the subject was in darkness without any disparity
cues (open-loop response) for 40 seconds before reappearance of the
target at zero cyclodisparity. Thus, there were four permutations (two
cyclodisparities × two final states). Subjects were presented
with the four-permutation sequence of (short) trials three times, with
brief breaks approximately every 5 to 8 minutes. Pairs of (long) trials
(one cyclodisparity × two final states) in which the
cyclodisparity was maintained for 150 seconds were interleaved between
the three shorter sequences: incyclodisparity trials first,
excyclodisparity second.
At the start (twice) and the end (once) of the experiment, subjects
were shown the stimulus at zero cyclodisparity for 60 seconds,
interrupted at 20 seconds by 40 seconds of darkness, to allow
assessment of baseline cyclophoria.
Two subjects also performed trials with two other designs using
the horizontal gratings. In the first, after 10 seconds of zero
cyclodisparity, the 5° cyclodisparity (either in- or ex-) was
maintained for 30 seconds, after which the targets were extinguished
for only 5 seconds before reappearing at zero cyclodisparity. In the
second, 10 seconds of zero cyclodisparity was followed by periods of
cyclodisparity (either in- or ex-) lasting in sequence, 5, 10, 30, and
60 seconds, separated from one another by 10-second periods of
darkness, finishing with 10 seconds of darkness followed by
target reappearance at zero cyclodisparity.
Auditory cues were used to provide a 5-second warning period before
changes in cyclodisparity. During this period, the subject was
encouraged to blink gently to reduce the necessity for blinking in the
period subsequent to the change in stimulus. Subjects could identify
the onset of fusion and periods of diplopia by pressing a button.
Cyclovergence was calculated by subtracting the torsional position
of the right eye from that of the left. Therefore, a relative
incyclovergence is positive and a relative excyclovergence, negative.
Vergence in horizontal and vertical axes was calculated similarly.
Version was taken as the average of the positions of the two eyes. The
eye position was sampled at 500 Hz, and commercial software (Matlab,
The Mathworks, Natick, MA; Excel, Microsoft, Redmond, WA) used for
analysis. The magnitude of the cyclovergence response to the 5°
cyclodisparity was calculated by the difference between mean
cyclovergence in the 100-msec period just before the offset of
cyclodisparity and in a 100-msec period 5 seconds later in the period
of exposure to the zero cyclodisparity stimulus (when cyclovergence had
returned its baseline value). If the latter period was unrepresentative
(e.g., a blink obscured the eye position measures) then the first
preceding 100-msec window without artifact was used. The use of this
method, rather than simply comparing the initial and final eye
positions in the period of cyclodisparity, has the advantage of a
briefer time between compared positions and thus less likelihood that
coil slip would have occurred in the interim (as described earlier).
A measure of adaptation was calculated, using a similar method, by
recording the residual cyclovergence after 5 seconds in darkness and
expressing this as a proportion of the magnitude of cyclovergence in
the baseline condition. Thus, if the cyclovergence decayed equally in
darkness and with the target present, it would have a residual of zero;
if it did not decay at all, a residual of 1; and if some part of the
cyclovergence response were sustained in darkness, it would have a
residual between zero and 1. Because the decay of cyclovergence may not
be complete within this 5-second period, this method may tend to
overestimate the degree of adaptation, but other measures (see the
Results section) support the idea that much of the sustained response
after 5 seconds in darkness is due to adaptation.
For clarity of presentation only, in
Figures 1 2 and 3 relative cyclovergence is shown, in that the value of cyclovergence at
the disappearance of the stimulus is offset so that the value in
response to a zero cyclodisparity stimulus tends to zero over time.
Likewise, the cyclovergence at time 0 is equal for open-loop (dark) and
baseline conditions. For display of the data in the figures, eye
position data were filtered digitally with a 3-dB point of 12.5 Hz.
Results are means ± SE. Subjects MT, DZ, and VJ showed
similar magnitudes of response to the cyclodisparity stimuli. Subject
SA showed a qualitatively similar pattern, although the amplitude of
responses was usually less than 1.0°. For subjects MT, DZ, and VJ,
both individually and as a group, the magnitude of the cyclovergence
responses to the horizontal gratings was significantly greater
(
P < 0.05, two-tailed
t-test) for
incyclodisparity (2.65 ± 0.20°) than for excyclodisparity
(1.70 ± 0.25°; also, see
Fig. 4 ). For subject MT, the magnitude of the incyclovergence response to the
horizontal grating (2.27 ± 0.35°) was significantly greater
than to either oblique (1.24 ± 0.08°) or vertical (0.70 ±
0.12°) gratings (
P < 0.05, Bonferroni
t-test), but there were no significant differences among the
magnitudes of excyclovergence. For subject DZ, the magnitude of
incyclovergence to the horizontal grating (2.60 ± 0.25°) was
significantly greater than that to the vertical (1.05 ± 0.19°;
P < 0.05, Bonferroni), but not the oblique (1.70 ± 0.23°).
For the horizontal gratings, all subjects were able to fuse the images
when either the in- or the excyclodisparity was maintained for 150
seconds. Failure to fuse the excyclodisparity within the shorter
30-second exposure occurred on one (subjects MT and VJ), two (subject
DZ), and six (subject SA) of eight occasions. Subjects MT, DZ, and VJ
were also able to fuse the short incyclodisparity, but subject SA
failed to fuse the short incyclodisparity on seven of eight occasions.
When fusion occurred, the time taken to fuse the images was in each
subject significantly less for incyclodisparities than for
excyclodisparities (Bonferroni t-test, P <
0.05). Overall, the fusion times for the horizontal gratings were for
incyclodisparities, 12.4 ± 1.0 seconds and for
excyclodisparities, 25.8 ± 1.6 seconds. The vertical and oblique
stimuli were fused readily by both subjects in whom they were used.
The main finding of this investigation is the persistence, in
darkness, of some of the change in cyclovergence induced by a preceding
short period of sustained exposure to a cyclodisparity. This is a form
of phoria adaptation for the torsional orientation of the eyes. In this
section, we review the features of the initial cyclovergence response
to the cyclodisparity, the subsequent change in cyclophoria, and the
potential functional and clinical implications of cyclophoria
adaptation.
For the horizontal gratings, the amplitude and the asymmetry (being
higher for incyclodisparity) of the cyclovergence response to the
cyclodisparity observed here are in accord with responses to similar
stimuli reported previously.
9 17 25 The time to fusion was
also less, by approximately 50% on average, for the incyclodisparity
stimuli, perhaps reflecting the larger motor response, and consequent
smaller residual disparity, in this direction. We could not directly
compare the responses to the three different orientations of the
gratings, because the field of view of the vertical and oblique
gratings was slightly smaller than that of the horizontal gratings, but
the finding of a lower amplitude of response to the
vertical
26 and oblique stimuli, given their reduced
vertical-shear component,
27 and also the smaller angle
they subtended,
28 29 are compatible with that described in
the literature. The decay of cyclovergence on return to the zero
cyclodisparity stimulus was also similar to that seen previously, with
the return from both incyclovergence and excyclovergence being
initially rapid and decreasing in velocity asymptotically as the eyes
approached the position of rest.
9 17
A detailed analysis of the decay of cyclovergence in darkness after
sustained cyclovergence stimulation has not been reported previously
using an objective method. Previous investigators, using subjective
methods to assess retained cyclovergence at discrete times, reported
that after long (30 minutes) exposure to cyclodisparity, decay was
slower in open-loop (absence of disparity cues) than in baseline (zero
cyclodisparity stimulus present) conditions, but still almost
complete.
17 For all excyclovergence stimuli presented
here, some cyclovergence persisted in open-loop (dark) conditions until
the visual stimulus was restored. We observed a variable response for
incyclovergence, however. In some circumstances its decay in open-loop
(dark) and baseline (zero disparity) conditions was equal in both
extent and rapidity, whereas in others its decay in darkness was
slower. These differences between the pattern of decay in darkness of
the responses to excyclovergence and incyclovergence could not be
explained solely by any preexisting cyclophoria, which was much smaller
than the changes in cyclovergence measured in darkness after the
sustained exposure to the cyclodisparity stimulus. It is certainly
possible, however, that any inherent cyclophoria may influence the
relative response to in- and excyclodisparities in a given subject.
Nevertheless, it can be speculated that the more persistent
cyclovergence aftereffect in darkness after sustained ex- rather than
incyclovergence could supplement the relatively less robust immediate,
visually driven cyclovergence response to ex- compared with
incyclodisparities.
In the horizontal vergence system, incomplete decay of vergence in
open-loop conditions after prolonged vergence has been attributed to a
slow fusional vergence system, producing phoria or prism adaptation,
and may be conceptualized as a slow integral controller in parallel
with the output of a fast fusional controller.
30 It would
be attractive by analogy to consider a similar model for the control of
the cyclovergence system, but any satisfactory model of the
cyclovergence system would also have to explain the dependence of gain
on amplitude
5 and the marked asymmetry between
incyclovergence and excyclovergence, seen not only in the amplitude at
onset,
9 but also, as described here, in their decay in the
dark.
The presence of phoria adaptation in the cyclovergence system is
consistent with the finding that cyclovergence is tightly controlled in
normal subjects.
18 Although torsional diplopia—which has
little influence on foveal function—does not present the same degree
of subjective disturbance of binocular vision as does horizontal or
vertical diplopia, torsional misalignment still can have perceptual
consequences for the localization and orientation of objects (e.g., the
perception of slant).
There are also findings in the clinical literature relevant to
maintaining torsional alignment. Acquired cyclotropia, for example, due
to fourth nerve palsy, presents the retinas with disparate images of
the world. Such patients exhibit adaptive responses to cyclotropia,
although the responses are variable in nature and
extent.
31 Torsional diplopia in casual viewing is
far less frequent than that which can be elicited with Maddox
Rods,
32 which in turn underestimates the presence of
anatomic cyclotropia.
33 34 Much of the relief from
torsional diplopia is achieved by sensory mechanisms.
31 32 Patients may retain a disparity-driven cyclovergence
response,
35 yet it is reported that on monocular occlusion
in the clinic setting, no decay of any adaptive cyclovergence is
observed, whether on fixation photographs obtained with either eye
fixating, or during scotometry.
31 Preoperative monocular
occlusion maintained over days, however, may reveal some decay of a
corrective cyclovergence.
36
In summary, we have shown that phoria adaptation occurs to help sustain
changes in torsional alignment just as it does for vertical and
horizontal alignment. The error signal or signals that drive torsional
phoria adaptation (cyclodisparity, monitoring of cyclovergence, or
both), its relationship to vertical phoria adaptation, and its anatomic
and physiological substrate remain to be determined.
Supported by National Institutes of Health Grant EY-01849 and the Kass Foundation.
Submitted for publication April 20, 1999; revised September 22 and November 2, 1999; accepted November 30, 1999.
Commercial relationships policy: N.
Corresponding author: David S. Zee, Pathology 2-210, Johns Hopkins Hospital, 600 North Wolfe Street, Baltimore, MD 21287.
dzee@dizzy.med.jhu.edu
Table 1. Cyclophoria Adaptation in Four Subjects
Table 1. Cyclophoria Adaptation in Four Subjects
| DZ | MT | VJ | SA |
| Horizontal | | | | |
| IN | 0.04 ± 0.13* , † | 0.34 ± 0.08* | 0.41 ± 0.12 | 0.67 ± 1.7 |
| EX | 0.70 ± 0.16* , † | 0.44 ± 0.09* | 0.35 ± 0.22 | 1.0 ± 0.21 |
| Oblique | | | | |
| IN | −0.01 ± 0.11 | 0.12 ± 0.22 | — | — |
| EX | 0.78 ± 0.25 | 0.65 ± 0.11 | — | — |
| Vertical | | | | |
| IN | −0.33 ± 0.35 | −0.25 ± 0.48 | — | — |
| EX | 1.44 ± 0.32 | 0.78 ± 0.08 | — | — |
Table 2. Baseline Cyclophoria, Horizontal Vergence, and Vertical Version in Four
Subjects
Table 2. Baseline Cyclophoria, Horizontal Vergence, and Vertical Version in Four
Subjects
| DZ | MT | VJ | SA |
| Cyclovergence | −1.59 | 0.03 | 0.39 | −0.17 |
| Horizontal vergence | −2.1 | 0.91 | 1.43 | 0.44 |
| Vertical version | −8.01 | −1.73 | 4.03 | −2.52 |
The authors thank Heimo Steffen, who participated in preliminary
aspects of these experiments.
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