(Investigative Ophthalmology and Visual Science. 2001;42:1479-1486.)
© 2001
by The Association for Research in Vision and Ophthalmology, Inc.
Adaptive Changes in Dynamic Properties of Human Disparity-Induced Vergence
Mineo Takagi1,2,
Hiroshi Oyamada3,
Haruki Abe1,
David S. Zee4,
Hiruma Hasebe1,
Atsushi Miki1,
Tomoaki Usui1,
Shigeru Hasegawa1 and
Takehiko Bando2,3
From the
1 Department of Ophthalmology and
3 Physiology, Niigata University School of Medicine, Japan;
2 Core Research for Evolutional Science and Technology, Japan Science and Technology, Saitama, Japan; and the
4 Department of Neurology, The Johns Hopkins Hospital, Baltimore, Maryland.
 |
Abstract
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PURPOSE. Vergence eye movements undergo adaptive recalibration in response to a
training stimulus in which the initial disparity is changed just after
vergence begins (the double-step paradigm). In the present study the
changes in the dynamic properties of convergence, speed and
acceleration, were examined by using this double-step paradigm, before
and after adaptation.
METHODS. Four normal subjects participated. Three-dimensional visual stimuli
were provided by a head-mounted display with two liquid crystal diode
(LCD) panels. To induce adaptation, a double step of disparity was
used: an initial step from distances of 2 to 1 m was followed by a
second step to distances of 0.7 m ("increasing paradigm") or
1.4 m ("decreasing paradigm") after a constant period of 0.2
seconds. The dynamic properties of vergence were compared before and
after 30 minutes of training with these paradigms.
RESULTS. Peak velocity of convergence became significantly greater (increasing
paradigm) or smaller (decreasing paradigm) after 30 minutes’ training.
Changes in the dynamic properties of convergence were also obvious in
phase–plane (velocity versus position) and main sequence (peak
velocity versus amplitude) plots. Further analysis revealed that
adaptive increases in vergence velocity were accomplished by an
increase in the duration of the acceleration period, whereas adaptive
decreases were induced by a decrease in the maximum value of
acceleration.
CONCLUSIONS. The pattern of change in the dynamic characteristics of vergence after
adaptation was similar to that of saccades and the initiation of
pursuit eye movements, suggesting common neural mechanisms for adaptive
changes in the open-loop control of eye
movements.
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Introduction
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The response of the vergence system to a disparity stimulus
has been characterized as a closed-loop feedback control system in
which motor performance is modified on-line on the basis of visual
information.1
Recently, however, it has been suggested
that the initial portion of the vergence response is controlled by a
different mechanism, because it is open-loop—that is, not subject to
immediate feedback control because of the inherent delay imposed by the
time to process new visual information. Jones2
suggested
that the vergence response was under control of two different processes
that mediate transient and sustained components. Semmlow et
al.3
proposed a dual-mode theory, in which the dynamic
properties of vergence eye movements are described by a two-component
control system. The initial component is not controlled by immediate,
continuous visual feedback. Rather, it is preprogrammed after being
activated in response to an abrupt change in disparity produced by a
rapidly moving target. The slow component is mediated by a visual
feedback control system. It tracks slowly moving targets and corrects
for errors that follow the initial vergence response. If the initial
component cannot be under continuous visual control, then adaptive
modification of the underlying premotor control processes, driven by
some form of error information, might be expected.
This is just the case for the other ocular motor subsystems, such as
saccades4
and the initial portion of smooth
pursuit,5
in which visual feedback, because of obligatory,
inherent delays in visual processing, is too slow to provide immediate
corrective error information to modify the initial motor command.
Consequently, there is a need for adaptive modification of saccades and
the initial component of pursuit. Adaptation of saccade and pursuit
accuracy takes place as a form of motor learning and depends on the
dorsal cerebellar vermis (e.g., Takagi et al.6
7
)
Adaptation of vergence, too, has been demonstrated.8
9
10
11
Herein, we report further studies of vergence adaptation using a
double-step stimulus, similar to that used to elicit saccade and
pursuit adaptation. Preliminary aspects of this work have been
previously reported in a single experimental subject.12
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Methods
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Subjects
Four normal subjects (30–38 years old) participated. They had
normal corrected vision, eye motility, and stereoacuity. Subjects 1, 2,
3, and 4 had interpupillary distances of 64, 59, 65, and 64 mm and
phorias at a viewing distance of 5 m of -6, -4, +1, and -4
prism diopters, respectively (exodeviations are negative). The head was
immobilized with a dental bite bar. Viewing was always binocular, and
refractive error was corrected with lenses. Subjects were told to
maintain a gaze on the visual target. Each subject gave informed
consent before the experiments. The research followed the tenets of the
Declaration of Helsinki (1964) and was approved by the human
experimentation committee of the Niigata University School of Medicine.
Visual Stimulation
Disparity stimuli were presented on a head-mounted display with
two liquid crystal display (LCD) panels (viewing angle 30° x 22°;
Sony, Tokyo, Japan).13
The image to stimulate each
eye was drawn in either an even or odd field of the image board
(CT-9800B; Cybertec, Osaka, Japan) with the aid of a personal computer.
The visual target was a black cross (0.63° x 1.2°), surrounded by
a bright rectangle (0.84° x 1.6°) and presented against a dark
background.
Experimental Paradigm
A protocol was designed to provide repeated exposure to the
training stimulus. An experimental run comprised three sessions: a
preadaptation session, an adaptation session, and a postadaptation
session. The preadaptation session (single-step paradigm) consisted of
21 sequential responses to a single step of disparity, in which the
target jumped from 2 to 1 m, eliciting convergence. The adaptation
session consisted of a double-step stimulus: an initial convergence
step from distances of 2 to 1 m, followed by a second step to a
distance of 0.7 m ("increasing paradigm") or 1.4 m
("decreasing paradigm"), after a constant period of 0.2 seconds
(Fig. 1)
. This stimulus was designed to induce a large error in the initial
open-loop vergence response by stepping the target backward or forward.
For an interpupillary separation of 64 mm, a target distance of 2.0,
1.4, 1.0, and 0.7 m called for 1.8°, 2.6°, 3.7°, and 5.2°
of vergence angle, respectively.
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Figure 1. Schematic illustration of the paradigm using a double step of
disparity. Dashed line: target movement in depth. First
the target jumped from distances of 2 to 1 m, but after 0.2
seconds, to a distance of 0.7 m (in the increasing paradigm) or to
1.4 m distance (in the decreasing paradigm). In both cases the
target stayed at its final position for 1.5 seconds. The intertrial
interval was randomized.
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Throughout the training period, the time interval between trials was
randomized between 1.5 and 3.5 seconds to eliminate predictive
responses, although the target always stayed in the first position for
0.2 seconds, and the second position for 1.5 seconds. Twelve
subsessions were presented, each consisting of 21 trials, with a brief
interval of approximately 1 minute between each subsession. The total
testing period was approximately 30 minutes. The postadaptation session
consisted of the same 21 single-step stimuli as were presented in the
preadaptation session. The two types of training paradigms, increasing
gain and decreasing gain, were tested on separate days.
Eye Movement Recording and Data Analysis
An infrared limbus tracker (Handaya, Osaka, Japan), which
provides a resolution of approximately 0.1°, was used to monitor the
horizontal position of both eyes. The sensors of the device were
attached to a glass frame, which was fitted to the head-mounted
device.14
Eye position was sampled at 500 Hz and stored on
a computer for later off-line analysis. A calibration procedure was
performed before and after the experiment, in which the subject was
required to fix on targets at left 5°, center, and right 5°, to
confirm that the calibration did not change during the experiment.
Trials in which the subject blinked during the initiation of the
vergence response were eliminated from further analysis (<5%). The
vergence angle was obtained by subtracting the position of the left eye
from that of the right. The vergence angle was then filtered with a
single-pole analog filter with a cutoff frequency of 15 Hz and then
differentiated with a two-point difference algorithm to get vergence
velocity. To calculate vergence latencies, a velocity criterion of 1.5
deg/sec was used. The correctness of the choice of the computer
algorithm was verified for each individual trial by the experimenter.
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Results
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Representative traces from the pre- and postadaptation sessions
are shown in Figure 2
. The vergence responses were markedly stereotyped during a subsession,
which enabled us to compare vergence dynamics using average traces. The
latencies of vergence responses were consistent from trial to trial
(
150 msec), which means that the second step of disparity, after the
constant period of 0.2 seconds, occurred within the open-loop period of
the vergence response. There was not a statistically significant change
in latency either after adaptation or in the final vergence angle of
the response (measured at 1 second). However, after the subject was
trained with the increasing paradigm, the slope of the initial
convergence response, which reflects vergence velocity, became steeper.
Similarly, after the subject was trained with the decreasing paradigm,
the slope became shallower. Thus, the velocity during the initiation of
vergence changed as dictated by the adaptive stimulus.
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Figure 2. Representative traces from subject 2 to show the effect of
training with the double-step paradigm. Pre, preadaptation session;
post, postadaptation session. Twenty-one traces are aligned with
reference to the onset of the step of disparity (time 0 indicates
target onset). The y-axis indicates the vergence angle
(downward deflection indicates convergence). The same disparity step
(from 2 to 1 m) was presented to the subject. The slope of a line
approximating the initial vergence response changed before and after
training. In the increasing paradigm, the line was steeper and in the
decreasing paradigm, the line was shallower (arrows).
Reprinted in modified form, with permission from Elsevier Science, from
Takagi M, Trillenberg P, Zee DS. Adaptive control of eye movements in
humans: control of smooth pursuit, vergence and eye torsion.
Vision Res. In press.
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Figure 3
shows a comparison of the average of 21 velocity traces in the pre- and
the postadaptation sessions. With the increasing paradigm (Fig. 3A)
,
peak average values increased by 57%, 65%, 40%, and 20% in subjects
1, 2, 3, and 4, respectively. These changes were significant in all
subjects, when the difference between peak velocities was tested with
the Mann-Whitney rank sum test. With the decreasing paradigm (Fig. 3B)
,
the peak average values decreased to 68%, 76%, 93%, and 58% in
subjects 1, 2, 3, and 4, respectively. These changes were significant
in subjects 1, 2, and 4.
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Figure 3. Comparison of velocity profiles between pre- and postadaptation
responses for all four subjects: (A) increasing adaptation,
(B) decreasing adaptation. Thick line: average
velocity of 21 traces; thin lines: one SD. The
x-axis indicates the time after the first target jump; the
y-axis indicates the vergence velocity (downward deflection
indicates convergence). After training, peak velocity increased
(A) or decreased (B). The significance of
differences of peak velocities between pre- and postadaptation were
tested using the Mann-Whitney rank sum test. n.s.: P >
0.05; *0.05 > P > 0.01; **P < 0.01.
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In a further analysis of the dynamic properties of the response, we
used phase–plane plots (eye position versus eye velocity). An example
of an average trace from subject 2 is shown in the upper panel of
Figure 4
. Solid vertical arrows indicate 150 msec after the onset of the
vergence response and thus identify the open-loop portion. Curved
dotted arrows indicate the direction of eye motion relative to time.
Several observations were notable: First, the very initial portion of
the response was unchanged; the pre- and postadaptation responses
overlapped in the initial approximately 0.2° of movement. Secondly,
in the increasing paradigm, peak velocity of convergence was increased
and shifted to a later portion of the convergence response. Thirdly,
also in the increasing paradigm, the peak velocity relative to the
vergence amplitude reached at the end of the open-loop period (150 msec
after the onset of eye movement) was much larger after adaptation.
To evaluate these last two points quantitatively, two further analyses
were performed. First, pre- and postadaptation values for peak velocity
and those for vergence amplitude at peak velocity were compared, by
using the Mann-Whitney rank sum test (Fig. 4 , middle and lower panels).
In the increasing paradigm, peak velocity increased significantly in
all cases, and the point at which peak velocity was reached was shifted
to a later portion of the convergence response in three of four
subjects. With the decreasing paradigm, peak velocity decreased
significantly in three subjects, but there was little change in the
point in the trial when peak velocity was reached.
Secondly, a main sequence analysis was used, in which peak vergence
velocity during the first 150 msec of the vergence movement (the
open-loop period) was compared with the vergence amplitude 150 msec
after the onset of vergence. This is shown for pre- and postadaptation
values in Figure 5
. A linear regression line, passing through the origin, was fitted to
the data points using a least-squares technique, and in all cases the
significance of the correlation was at P < 0.0001. A
main sequence ratio15
was calculated as the peak velocity
within 150 msec divided by the vergence amplitude at 150 msec, and then
the difference between pre- and postadaptation values was tested with
the Mann-Whitney rank sum test. Significant changes in the main
sequence relationships were seen in three of four subjects for
increasing adaptation (subjects 1, 2, and 3), but only in one subject
(number 1) for decreasing adaptation. Thus, with the increasing
paradigm in particular, the results suggest that vergence adaptation
induced not only a change in the amplitude of response in the open-loop
period to a given disparity but also in the relationship of peak
vergence velocity to a given vergence amplitude.
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Figure 5. Main sequence analysis of pre- and postadaptive vergence response in
the four subjects. (A) Increasing paradigm; (B)
decreasing paradigm. The x-axis indicates the vergence
amplitude 150 msec after vergence onset and the y-axis the
maximum vergence velocity during the first 150 msec after vergence
onset. ( ) Preadaptation responses; (•) postadaptation responses.
Linear regression lines, which pass through the origin, are also shown
in each panel. Solid line: preadaptation response;
dashed line: postadaptation response. A main sequence ratio
was calculated as peal velocity within the first 150 msec of vergence
response divided by the vergence amplitude at 150 msec. Statistical
differences were tested using the Mann-Whitney rank sum test.
Statistical differences are given in each panel. n.s.:
P > 0.05, *0.05 > P > 0.01,
**P < 0.01.
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We also noted the slope of the initial vergence velocity response to
assess changes in vergence acceleration. For the increasing paradigm
(Fig. 3A)
, the initial slope of the velocity trace, which reflects the
amplitude of acceleration, did not change, but the duration of the
acceleration period, as reflected in the length of the slope, was
longer after adaptation. In contrast, in the decreasing paradigm (Fig. 3B)
, the slope of the velocity trace decreased with training,
indicating that the amplitude of acceleration decreased. Figure 6
shows the average acceleration traces from subject 2. Although the
traces are noisy, the increase in the duration of acceleration with the
increasing paradigm and the decrease in the amplitude of acceleration
with the decreasing paradigm are seen clearly.
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Figure 6. Change in average vergence acceleration traces with the increasing
paradigm (left) and the decreasing paradigm
(right) in subject 2. Thin line:
preadaptation; thick line: postadaptation. Downward
defection indicates convergence. With the increasing paradigm, the
duration of acceleration was extended as indicated by the
vertical arrows; with the decreasing paradigm, the
amplitude of acceleration was diminished as indicated by the
horizontal arrows. Reprinted in modified form, with
permission from Elsevier Science, from Takagi M, Trillenberg P, Zee DS.
Adaptive control of eye movements in humans: control of smooth
pursuit, vergence and eye torsion. Vision Res. In
press.
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Figure 7A
shows the progressive change in the velocity profile in subject 2
during a training session. At the beginning of the training period with
the increasing paradigm, individual peaks were seen both at the first
(1 m) and the second (0.7 m) target steps. The first peak increased to
approximately 13 deg/sec by the third subsession and subsequently
changed little, indicating that a large part of the adaptive change in
peak velocity was completed in the first 10 minutes of training. The
second peak showed little change, but the two peaks gradually fused
into one. Figure 7B
shows the change in the velocity profile during
decreasing training from the same subject. At the beginning, a
double-peaked response, first convergence and then divergence, was
seen. During training, the second divergence peak disappeared and the
first convergence peak became smaller.
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Figure 7. Change in the velocity profile during the adaptation session from
subject 2: (A) increasing paradigm; (B)
decreasing paradigm. Each panel shows average (thick line)
and one SD (thin line) of 21 trials in each subsession. The
x-axis indicates time after target jump; y-axis
indicates vergence velocity (downward defection indicates convergence).
The number at the top of each panel indicates the subsession
during the adaptation session. The double-peaked response gradually
fused to one greater or smaller peak as adaptation progressed during
the increasing or decreasing training paradigm, respectively.
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We can also see in these traces differences in the initial acceleration
between the increasing and decreasing paradigms. With the increasing
adaptation paradigm the initial slope of the vergence velocity trace
did not change but the duration of acceleration (as reflected in the
duration of the slope) increased after training. With the decreasing
adaptation paradigm, the slope of the initial response became smaller.
We further analyzed the changes in initial acceleration by obtaining
the value of vergence velocity at every 10 msec from the average trace
of each subsession and calculating a correlation coefficient between
the value of the vergence velocity in each epoch and the progress of
adaptation training (1st to 12th subsessions). In Figure 8
, the correlation coefficients are plotted for each time epoch of the
convergence response. In general, during the open-loop period, the
correlation coefficients with the decreasing paradigm were larger
approximately 30 to 40 msec earlier than those with the increasing
paradigm. In other words, for adaptation in the decreasing paradigm,
the very early part of the vergence response showed a positive
correlation, whereas for adaptation in the increasing paradigm,
adaptation was better correlated with a later portion of the response
but still within the open-loop period. (Because subject 4 did not show
a robust adaptation in the increasing paradigm, there was not a
significant negative correlation in lower right panel.)
This result is consistent with the idea that for increasing adaptation,
the duration of acceleration becomes longer, but for decreasing
adaptation the peak amplitude of acceleration becomes smaller. To
exclude the possibility that these correlations were due to a change in
vergence latency, we examined the relationship between latency and
progression of training in a similar way and found no significant
correlation.
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Discussion
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The capability of the vergence system to undergo an adaptive
modification of its initial response to a given change in disparity has
been demonstrated previously by changing the disparity just after the
eye has begun moving in response to the initial disparity8
or by using a step-ramp stimulus, in which case the disparity continues
to increase after the initial step change in
disparity.11
We have replicated this capability for
vergence adaptation in this study, also using the double-step stimulus.
In our study, as previously reported in other studies of vergence
adaptation,8
10
11
14
adaptation was exceedingly rapid,
with the major change requiring only approximately 100 trials, which
took just 10 minutes of training. As also reported previously, the
adaptive changes in the vergence response were relatively large
compared with saccade and pursuit adaptation in similar types of
training paradigms.4
16
Our study, however, added new
qualitative and quantitative information about the adaptive response,
which also allowed us to compare the mechanisms of vergence, saccade,
and pursuit adaptation. In particular, we scrutinized the adapted
responses by using a phase–plane analysis,17
a main
sequence analysis,18
and an interval-by-interval
correlation analysis.
The main sequence analysis allowed us to look for changes in the
dynamic properties of the vergence response after adaptation by
comparing pre- and postadaptation values for the peak vergence velocity
within the open-loop period with a given-sized vergence amplitude at
the end of the open-loop period. By confining the analysis to the first
150 msec of vergence tracking we could largely exclude effects of
visual feedback on the initial response. In the increasing paradigm we
found significant changes in the main sequence for vergence eye
movements in three of four cases, supporting the idea that adaptation
to an increasing stimulus is accompanied by a change in the dynamic
properties of the vergence response and not just a change in the
mapping of the amplitude of the preprogrammed movement to the amplitude
of a given disparity. On the contrary, with the decreasing paradigm, we
found significant changes in the main sequence in only one of four
subjects.
The phase–plane and correlation analyses confirmed several features of
the adaptive response that could also be appreciated in the time plots.
First, for the responses with the increasing paradigm, the point when
peak velocity was reached occurred later in the trial. This finding is
compatible with the idea that adaptation to a stimulus calling for an
increased response is accomplished by an increase in the duration, not
by the maximum value of eye acceleration. For the responses in the
decreasing paradigm, there was little change in the point in the trial
when peak velocity was reached. This finding is compatible with the
idea that adaptation to a stimulus calling for a decreased response is
accomplished, at least in part, by a decrease in the maximum value of
eye acceleration. This interpretation was also supported by the results
of the correlation analysis between the value of the vergence velocity
in each epoch and the progress of adaptation training (Fig. 8)
. They
showed that vergence eye velocity within an individual trial changed
earlier in the decreasing than in the increasing paradigms.
Our present findings are in many ways analogous to those reported for
adaptation of saccades and the open-loop portion of pursuit. For
pursuit, adaptation in paradigms calling for an increased response is
accomplished by an increase in the duration of the acceleration period,
whereas adaptation in paradigms calling for a decreased response is
largely accomplished by a decrease in the maximum value of eye
acceleration in the open-loop period.7
Saccade peak
velocity approaches a saturation for large-amplitude saccades, and,
when adaptation to muscle weakness is required, increases in the size
of larger saccades are probably accomplished by an increase in the
duration, rather than by an increase in the maximum value of the
saccade velocity command.19
20
In vergence (and presumably
saccades and pursuit), the maximum value of eye acceleration during the
open-loop period may be relatively limited, necessitating an increase
in the duration of the period during which peak eye acceleration is
maintained when vergence innervation must be increased further.
The site of vergence adaptation in the central nervous system is not
known. One mechanism may be a higher level cognitive adjustment in
vergence innervation, because the visual stimulus was repetitive and
called for the same change in amplitude. However, even when single- or
double-step stimuli were presented so that the net vergence response
should have been the same, motor modifications still appeared after
double-step training, excluding a pure cognitive effect.8
Similarly, in our paradigm the time of occurrence of the initial target
step was randomized, eliminating prediction in the initial vergence
response. Changes in attention level or fatigue21
also
could be factors. However, the same pattern of trial and rest periods
in the different training paradigms caused significantly different
modifications in the dynamic pattern of responses. Alternatively,
adaptation may reflect changes in the lower-level motor machinery that
generates premotor vergence commands and may be related to the function
of the cerebellum.
Many data suggest that in the cases of saccades and the open-loop
portion of pursuit, the posterior vermis of the cerebellum and the
underlying fastigial oculomotor region are involved in mediating
adaptive changes in similar double-step
paradigms.6
7
20
22
23
In the posterior vermis there are
cells sensitive to disparity,24
and vergence-related
activity is also found in the portions of the pons that relay
information to the dorsal cerebellar vermis.25
These
findings suggest that the posterior vermis could also be involved in
the adaptive control of the open-loop portion of vergence eye
movements. Neurophysiological investigation is needed to help settle
this question.
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Footnotes
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Supported by Grant-in-Aid for Scientific Research 11671727 from the Japan Ministry of Education, Science, Sports and Culture (MT), by grants from the Mechanical Social System Foundation and the Electronic Industries Association of Japan, and by the Japan Keirin Association. DSZ was supported by National Institutes of Health Grant R01-EY01849.
Submitted for publication August 3, 2000; revised February 2, 2001; accepted February 16, 2001.
Commercial relationships policy: N.
The publication costs of this article were defrayed in part by page charge payment. This article must therefore be marked "advertisement" in accordance with 18 U.S.C. 
1734 solely to indicate this fact.
Corresponding author: Mineo Takagi, Department of Ophthalmology, Niigata University School of Medicine, 1 Asahimachi, Niigata-City, 951-8510 Japan. mtakagi{at}med.niigata-u.ac.jp
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Top
Abstract
Introduction
) postadaptation responses. The
significance of differences for peak velocity and vergence amplitude
was tested with the Mann-Whitney rank sum test and is indicated along
the vertical and horizontal arrows, respectively.
n.s: P > 0.05; *0.05 > P >
0.01, **P < 0.01.
) Increasing paradigm; (
) decreasing paradigm. A
positive correlation coefficient indicates a decrease in vergence
velocity and a negative correlation coefficient an increase.
Dashed horizontal lines (from top to
bottom): r = 1, r = 0.71
(P = 0.01), r = 0.58
(P = 0.05), r = -0.58
(P = -0.05), r = -0.71
(P = -0.01), and r = -1.