Interaction of Disparity and Accommodative Vergence
Michele L. Kung1, Tara L. Alvarez1, John L. Semmlow2,3
1
Department of Biomedical Engineering, New Jersey Institute of Technology, Newark, NJ
Department of Biomedical Engineering, Rutgers University, 3Department of Surgery, Bioengineering,
Robert Wood Johnson Medical School – UMDNJ, New Brunswick, NJ
2
Abstract – To fixate on a target that moves from far to near, two
systems become activated; accommodation and disparity
vergence. The goal of this study is to investigate how these
systems interact through a new signal-processing algorithm
known as independent component analysis. Preliminary data
suggest that three underlying neural subcomponents are present
where the two components of disparity vergence initiate the
movement and the accommodative portion is activated to
facilitate the steady state portion of the response.
I. INTRODUCTION
A vergence eye movement is defined as the inward or
outward turning of the eyes. Disparity vergence occurs when
images fall on opposite sides of the fovea (part of retina),
causing diplopia (double vision). The eyes rotate inward or
outward to place the image on the fovea, which fuses the two
images into one. This retinal disparity is one of the key
inputs into the disparity vergence control system.
Accommodative vergence is driven by blur to change the
shape of the lens in the eye.
We are studying the interaction between the disparity and
accommodative vergence systems. This will lead to further
insight of how the two systems interact. This information can
be used to help people with accommodative and disparity
dysfunction.
Disparity vergence uses dual control to obtain both speed
and accuracy. The disparity vergence system has been
modeled using the Dual Mode Theory as a two-component
system, an initiating and a sustaining component. The
initiating component is a feed forward, open loop control
system, which depicts the system’s speed. The sustaining
component is a feedback, closed-loop control system, which
depicts the system’s accuracy. This model has been validated
by neurophysiological data, which shows burst and tonic cells
exist in the vergence neural circuit [1-2]. The burst cells
correlate to the feed forward or pulse portion of the vergence
model and the tonic cells correlate to the feedback or step
portion of the vergence model. It is hypothesized that there is
a third feedback driven component from the accommodative
vergence system.
Our study builds upon the work of Hung and colleagues
where they studied the difference between disparity vergence
with constant accommodation and disparity vergence with a
change in accommodation [3]. This group studied variance
and showed that a significant amount of variance existed
during the transient phase after response latency, which
corresponds to the two components, found in disparity
vergence. However, their key finding was in comparing
disparity vergence with constant accommodation vs. disparity
vergence with a change in accommodation. More variance
was found in the later part of the disparity vergence with a
change in accommodation compared to disparity vergence
with
constant
accommodation
suggesting
that
accommodation is present during the later steady state portion
of the response.
II. METHODOLOGY
The convergence movements made by the eyes were
measured using the Skalar Iris model 6500, an infrared
limbus-tracking device that was placed on the subject’s head.
These movements were recorded at a rate of 200 Hz. The
resolution of the eye movement monitor was 2 minute arc
with a linearity of ± 25 degrees. Throughout the experiment,
the data was collected from each eye independently.
A five point calibration was performed by illuminating the
targets (either light emitting diodes (LEDs), or the reflected
oscilloscope lines) in a sequence and recording the voltage
value at each position, then doing a regression analysis to
determine a linear equation for the conversion.
After calibration, subjects would push a trigger button to
initiate an experiment and a random time delay occurred
(either LEDs or oscilloscopes) to remove anticipation by the
subject. Furthermore, the four and six degree steps were
randomly selected by the computer to avoid subject
prediction. These responses were recorded for three seconds
and experiments occur in complete darkness where the
subject only observed the presence of the targets.
The apparatus for the oscilloscope set up (haploscope) is
shown in Figure 1a. It consists of two partially reflective
mirrors positioned 45 degrees to the subject’s line of sight,
two oscilloscopes that provide the step stimulus, and a
limbic tracking system, which collects the eye movements.
Each oscilloscope emits a line stimulus towards the
mirrors, which in effect produce two lines that the subject
would fuse into single line. After the subject pushed the
trigger, the two lines would move in a step manner. The
subject would follow the stimulus and would once again fuse
the lines. The oscilloscopes project targets at a constant
focal length from the subject to stimulate disparity vergence
while keeping accommodation constant.
2 Mirrors
Oscilloscope 2
Oscilloscope 1
Left Eye
Right Eye
Figure 1a – Haploscope Set up
Initial Target
A
A
4 Degree Final Target
B
6 Degree Final Target
Left Eye
S.C
S.C
Right Eye
Figure 1b – 3D Target Set up
For the 3D Target Set-Up shown in Figure 1b, the stimulus
always began at the same initial position using an illuminated
LED. The computer initiated the shutting off of the initial
LED and the lighting of the next LED where subjects were
asked to track the new target positioned along the midline of
the subject as shown in Figure 1b. The LED’s provided real
targets in 3-D space, which stimulates disparity vergence
with a change in accommodation.
PCA analysis has shown that two components account for
more than 90% of the variability in convergence eye
movements. Therefore, Independent Component Analysis
(ICA) was run with two components. ICA is a more
advanced signal processing technique compared to the one
used by Hung et al. It is a linear transformation method in
which the statistical dependence of the components is
minimized. ICA was used as a blind source separation
method, to separate the components of the response [4].
I.C.
I.C.
C
D
S.C
I.C.
S.C
I.C.
X = As
Where X is the response, A is the unmixing matrix, and S
is the two components found in disparity vergence. This
analysis used the “Fast ICA” program developed by the ICA
group at the Helsinki University [5].
III. RESULTS
Vergence data is the plotted as difference between the left
eye and the right eye movements.
Figure 4 ICA on haploscope (A,B) and led (C,D) vergence data shown
for 4(A,C) and 6 (B,D) degree. S.C. (sustaining component), and I.C.
(initiating component) labeled.
Figure 4 shows the ICA of haploscope (top) and led (bottom)
vergence data shown for 4 degree (left) and 6 degree (right).
The labels S.C. (sustaining component), and I.C. (initiating
component) represent the two components found in the
disparity system.
IV. DISCUSSION
Preliminary data suggest the steady state response to be from
one second to two seconds. We see in the figure 4 A, B
(haploscope), the sustaining component for the disparity
vergence response with constant accommodation maintains a
flat step response during the steady state portion of the
response. The step component for the disparity vergence
response with non-constant accommodation does not
maintain a flat step response during the steady state portion of
Figure 2. haploscope vergence data. 4 degree and 6 degree shown.
the response but instead decays as indicated by arrows
Figure 2 is haploscope vergence data, which is disparity (shown in figure 4 C, D). Based on this preliminary data we
speculate this deviation may be a result of the
vergence with constant accommodation
accommodative vergence response.
REFERENCES
Figure 3. LED vergence data. 4 degree and 6 degree shown.
Figure 3 is LED vergence data, which is disparity vergence
with a change in accommodation.
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[5] http://www.cis.hut.fi/projects/ica/fastica/fp.html