Download Identification of accommodative vergence contribution to the near

Identification of Accommodative Vergence
Contribution to the Near Response
Using Response Variance
George K. Hung,* John L. Semmlow,* and Kenneth J. Guffredaf
An experimental method was developed to isolate accommodative and disparity vergence contributions
to coordinated near vergence motor responses. The variability normally associated with the neural
control signal was used as an identifying marker or tag. Using this approach, the results showed an
increased variability associated with the blur-driven, accommodative vergence component that is
particularly noticeable during the latter half of the movement. This indicated that accommodative
vergence provides a moderate contribution to the near vergence response primarily in the late and
post-transient period when the movement is essentially complete. Presence of this accommodative
contribution lends further support to the "dual interactive model" of near triad control. Invest Ophthalmol Vis Sci 24:772-777, 1983
namic vergence responses to both combined disparity-blur stimulation and disparity-only (ie, without
blur) stimulation. They concluded that accommodative vergence contributed only to the latter half of
the transient response. Difference curves (combined
disparity-blur minus disparity-only responses) were
calculated and presumably reflected the dynamic accommodative vergence contribution. These difference curves indicated that accommodative vergence
played a minor role in near vergence responses. However, implicit in this interpretation is the assumption
that the disparity component is the same under both
stimulus conditions; that is, the presence of blur stimulation and its associated accommodative convergence do not modify the disparity-driven component.
Yet disparity vergence operates within a feedback
control system, and any additional vergence motor
drive (eg, from accommodative vergence) would
modify the disparity component. The addition of blur
stimulation and the associated accommodative vergence should lead to a compensatory reduction of the
disparity component, and, thus, a simple comparison
of external responses would erroneously indicate only
a small contribution from accommodative vergence.
A similar compensatory disparity vergence mechanism was evident in binocular accommodative vergence responses8 (although, instead of combined dynamic stimulation, disparity stimulation was held
constant).
Thus, to determine the role of accommodative
vergence in the combined near vergence response requires a measurement reflecting the internal state of
accommodative vergence during these responses. One
The contribution of accommodative vergence to
the total vergence response during a change in binocular fixation has been of considerable interest to
oculomotor physiologists. Maddox1 was the first to
define the components of vergence. He believed that
blur-driven accommodative vergence was primary,
with disparity (fusional) vergence serving only a supplemental role in the attainment of precise binocular
fixation. Recently, a qualitative model having such
a hierarchical structure was proposed.2 In contrast,
Fincham and Walton,3 after carefully collecting static
measurements of accommodation and vergence,
theorized that disparity provided the dominant vergence drive. Disparity-driven accommodation (vergence accommodation) was found to be nearly sufficient for the target distance, thus necessitating only
"fine-tuning" by blur-driven accommodation. Finally, a recent quantitative theory4"6 provided for significant contributions to vergence drive from both
major stimuli.
Resolution of this long-standing question of stimulus dominance is essential to the development of a
comprehensive theory for the coordinated oculomotor activity seen in the binocular near response.
Recent experiments specifically addressed this question. Semmlow and Wetzel7 compared average dyFrom Rutgers, the State University of New Jersey,* and the State
College of Optometry, State University of New York, New York.f
Supported in part by NIH grants EY 03709 and EY 03541.
Submitted for publication October 20, 1981.
Reprint requests: George K. Hung, PhD, College of Engineering,
Rutgers University, Box 909, Piscataway, NJ 08854.
0146-0404/83/0600/772/$ 1.10 © Association for Research in Vision and Ophthalmology
772
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ACCOMMODATIVE VERGENCE IN NEAR RESPONSE / Hung er ol.
parameter uniquely related to accommodative vergence is the response variability associated with this
component. As in most physiologic processes, the
specific time course of accommodative vergence varies slightly from response to response even though the
driving stimulus is unchanging. Through appropriate
data analysis, which we term ensemble variability
analysis, accommodative vergence variability can be
isolated from the variability inherent in other motor
components. Ensemble variance, which is calculated
from a large number of individual responses, is a
measure of this change in dynamic character of a
movement from response to response. Although feedback compensation occurs within each response, it
does not affect the change in dynamic character of
a component from response to response. If response
variation is assumed to be Gaussian, variabilities
from different motor componets are additive. Hence,
ensemble variability analysis coupled with a simple
subtraction procedure can be used to extract the variability due to accommodative vergence in the binocular near vergence response. This accommodative
variability, in turn, provides information on the relative amount of accommodative vergence contribution to the near response. Further, if variance of responses to different stimulus levels were calibrated,
quantitative information can be obtained.
The purpose of this investigation was to determine
the time course of the accommodative vergence contribution to the total vergence response using ensemble variability analysis. Vergence responses were
measured under three viewing conditions: (a) disparity-only stimulation, (b) combined disparity-blur
stimulation, and (c) blur-only* stimulation. Average
vergence response and variance of vergence responses
were constructed to isolate the accommodative vergence contribution. Response and ensemble variance
curves from blur-only stimulation were used for comparison with the components isolated by the difference curves.
Materials and Methods
Experiments
Binocular stimulation with disparity-only or combined disparity-blur stimuli required a versatile device capable of generating combinations of binocular
stimuli. The dynamic binocular stimulator (DBS)8
was used since it is capable of producing these stimuli.
A target, consisting of 1 ° green circle and positioned
* While the DBS eliminates major cues to accommodation,
other subtle cues may indeed be present. Thus, the use of the term
"blur-only" is a concise way of saying that there is no disparity
stimulation.
773
by means of motor control in a Badal optical system,
served as the stimulus to accommodation. Motor
driven translatin^'rotating mirrors in front of both
eyes provided disparity stimulation. Interaction of
accommodative feedback on disparity9 could be eliminated by reducing the effective entrance pupil to less
than 1 mm,| thus providing disparity-only stimulus.
Blur-only stimulation was produced by blocking the
optical pathway to one eye.
For each of three subjects the vergence response
was measured for three stimulus conditions: (a) 0 to
3 meter angles (MA) disparity-only step stimulus, (b)
0 to 3 MA and 0 to 3 diopters (D) combined disparity
and blur step stimuli, and (c) 0 to 3 D blur-only step
stimulus. Each step stimulus presentation was initiated manually by the experimenter, permitting randomization of stimulus onset time. The stimulus trigger signal was used to mark stimulus onset. After the
completion of each response, a saccadic eye movement of known amplitude was used to calibrate the
response magnitude. Only convergence responses
were analyzed. To avoid adaptation effects,10 the subject was required tofixatea far target in the laboratory
for 10 sec after every 10 records.
Movements of both eyes were measured using the
infrared limbus reflection technique," and data were
transferred directly to an online computer (PDP 11/
40). All three subjects had normal visual-motor function, although two subjects with refractive errors were
corrected by means of lenses added to the DBS optical
system.
Data Analysis
Because of vergence response variability, the vergence time course was obtained by means of ensemble
averaging-^ Usually, the number of individual responses required for accurate representation was determined empirically; however, as the ensemble variability itself is of interest here, a more quantitative
approach was used. Specifically, we needed to determine when our limited sample estimate of the ensemble variance approached the true ensemble variance. In other words, how many individual responses
were required before our estimate of ensemble varif Measurements in the DBS using a Hartinger coincidence optometer show that there is very little change in static accommodative response to different accommodative stimuli under pinhole
viewing conditions.
X Given two time series of equal number of data points, the
ensemble average is obtained as the point for point average between
the two time series, resulting in an averaged time series. An ensemble variance time series can be similarly constructed. This ensemble approach generalizes to any number of time series records
with equal number of points.
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INVESTIGATIVE OPHTHALMOLOGY & VISUAL SCIENCE / June 1983
2 7
6
10
15
20
25
30
35
40
45
NUMBER OF RESPONSE RECORDS
50
55
60
Fig. 1. Average of ensemble variance of the vergence responses
as a function of the number of individual responses. This curve
was used to estimate the number of individual responses required
for an accurate average. As number of responses in the average
increased, the average ensemble variance became smaller, approaching an asymptote at around 40 responses. Data shown is for
subject K.C; those from other subjects were similar.
ance was only slightly improved by additional responses? To answer this, the ensemble variance calculated from individual disparity vergence responses
was averaged over the transient portion of the response (first 3 sec), and this average plotted as a function of number of responses§ (see Fig. 1). Note that
the ensemble variance, as represented by this average
is only slightly modified by additional responses after
about 40 individual responses. This feature was consistent for other vergence responses and other subjects; hence, ensembles of 40 or more individual responses was considered sufficient for accurate estimation of response variance.
Preliminary analysis was applied to some of the
data to determine the influence of response latency
on the variance time course. These responses, initially
synchronized to the stimulus signal, were shifted using an interactive graphical display program to align
§ The measure of interest is the average of the variance of all
the points in the ensemble variance time series given by:
1
Avg.Var.N = -
Z
where
x = vergence response value
M = the number of points in the data array
i = the ith data point in the response; i.e., the time index
N = number of trials
j = the j l h trial.
The change in average ensemble variance with the addition of each
new individual response will converge towards zero as the estimated ensemble variance approaches the true variance.
Vol. 24
the transient onset of each response. This provided
compensation for latency variations so that influences
on the variability calculation could be isolated. Since
our preliminary analysis showed that this factor did
not significantly affect the interpretation of results
(see Results section), latency compensation was not
generally used. Responses containing artifacts such
as eye blinks or saccades were discarded.
After the completion of the ensemble analysis procedure, the ensemble average vergence response time
course and the associated ensemble variance time
course were plotted. Additionally, the average of the
ensemble variance as a function of the number of
individual responses was also calculated. Finally, the
difference in the ensemble variance of responses obtained with combined disparity-blur stimulation and
disparity-only stimulation were calculated and plotted. This procedure was repeated for each subject.
Results
Ensemble average, ensemble variance, and difference in ensemble variance of vergence responses with
and without accommodative stimulation" are presented in Figure 2 for the three subjects. Average vergence response curves (Fig. 2, top row) show slight
differences in dynamic behavior under combined and
disparity-only stimulation. Variance curves show the
time course of response variation (Fig. 2, 2nd row),
while curves of difference in vergence response variance (Fig. 2, 3rd row) isolate the added variability
due to the addition of blur stimulation. Since this
added variability is not influenced by disparity feedback, it represents the actual accommodative vergence contribution to a near response. Accommodative vergence variance curves (Fig. 2, bottom row)
show the general dynamic features of this component's variability and confirms the origin of variability isolated by the difference curves (Fig. 2, 3rd row).
Evident in comparing variance difference curves
(Fig. 2, 3rd row) is the significant contribution of the
accommodative component following an initial artifactual peak in all three subjects. The most likely
origin of this initial peak, which corresponds in time
to the disparity component, is a slight increase in
disparity vergence variability during combined stimulation. The second peak is due to the accommodative contribution as can be seen by matching this
peak with the transient portion of the accommodative
vergence variance curves (Fig. 2, bottom row).
As a preliminary check on our analysis procedure,
11
Responses without accommodative stimulation employed pinhole viewing so that the accommodative system is inactivated
(open-looped).
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ACCOMMODATIVE VERGENCE IN NEAR RESPONSE / Hung er ol.
No. 6
GH
JS
775
KC
Fig. 2. Composite figure
showing in the top row the
ensemble average vergence
response to 3 MA disparityonly stimulus (interrupted
curves) and combined 3
MA/3D disparity-blur stimulus (solid curves). Ensemble variance curves for 3
MA disparity-only (interrupted curves) and combined 3 MA/3D disparityblur (solid curves) stimulation are shown in the second
row. Difference in ensemble
variance curves shown in
third row were obtained by
subtracting ensemble variance curves, (combined disparity-blur variance minus
disparity-only variance) of
the second row. Ensemble
variance of accommodative
vergence is shown in the
bottom row. Figures are for
subjects GH, JS and KC,
left to right columns, respectively.
we also investigated the effect of latency variation on
the ensemble variance curve. The slight reduction in
amplitude of the variance curve with latency compensation (Fig. 3) indicated that the effect of latency
variation is small when compared to variation in
other components of the vergence system.
Discussion
Statistical Isolation of Motor Components
As both blur and disparity stimulation are generated by a near target, and as both separately evoke
a vergence response, the normal binocular vergence
response must be driven by some combination of
these two inputs12 (along with possible contributions
from proximal and related higher level compo-
nents13). Were it not for disparity feedback, the various component contributions could be isolated easily. For example, a direct comparison of vergence
response driven by combined disparity-blur and disparity-only stimulation would identify the blur-driven
contribution. Such a comparison7 would suggest that
accommodative vergence contributes only slightly to
the combined response. It is certainly possible that
accommodative vergence is not a major component
mediating binocular vergence, but it is just as likely,
based solely on a comparison of individual or averaged responses, that the external appearance of a
strong accommodative vergence component is diminished by the compensatory action of disparity
feedback.
Neurophysiologic techniques, probing the appro-
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INVESTIGATIVE OPHTHALMOLOGY & VISUAL SCIENCE / June 1983
<
>
o
or
IMA2
TIME, SEC
Fig. 3. Ensemble variance for disparity-only stimulation for analysis procedures of no-latency compensation (solid curve) and latency compensation (interrupted curve) showing minor reduction
in ensemble variance amplitude due to latency compensation.
priate neural pathways,1415 might resolve this question, but our lack of detailed knowledge concerning
the anatomical location of these pathways, especially
in humans, makes this approach unattractive. As the
resolution of component contribution is central to
any theory of near triad control,4"6 we have developed
a "dry dissection" technique,16 using the variability
associated with the neural signals as a "tag" for a
specific neural control component. Since ensemble
variance is independent of the feedback mechanism,
this technique provides a potentially powerful tool
for isolating control components in a complex motor
response.
Accommodative Contribution to Binocular Vergence
Comparison of the 2nd peak of the variance difference curves (Fig. 2, 3rd row) and the peaks of response difference curves (by calculating differences
seen in Fig. 2, top row) shows the accommodative
contribution occurs later than that indicated by the
vergence response difference approach.7 Also, evaluation of the variance difference curves indicates a
larger accommodative contribution than suggested by
differences in vergence responses. Indeed, the responses of subject KC would indicate a large negative
contribution from accommodative vergence in the
combined-stimulus condition.
The absence Of accommodative vergence component from the initial transient portion is explained
easily: the latency associated with blur-driven components is substantially longer (by about 100-200
Vol. 24
msec) than the latency seen in disparity-driven components.17 Thus, under simultaneous disparity-blur
stimulation, disparity-driven components are well
under way before blur-driven components begin to
have a motor influence. Additionally, the blur-driven
signal has a complex dynamic input due to the effect
of the ongoing vergence response in bringing an eccentric target towards central fixation. The effect of
nonfoveal stimulation is to reduce the effectiveness
of target blur in driving accommodative vergence.1819
However, as convergence continues and the target
approaches the fovea, the accommodative and associated accommodative vergence contribution would
increase progressively. Meanwhile, convergence accommodation would initiate a lens response that
could offset to some extent the increase in blur-driven
accommodative stimulation. The presence of accommodative vergence in the late and post-transient portion of the response as suggested by the variance
curves, but not in the response difference curves, may
be explained by these interaction between vergence
and accommodative components.
It has long been known that the binocular vergence
response is not the summation of the disparity and
blur-driven components to the same response.7 This
is comforting, since in most individuals simple addition of disparity and accommodative vergence
would result in substantial diplopia. In a study comparing combined disparity/blur and disparity-only
stimulation, Semmlow and Wetzel7 proposed that
reduction in the late transient "apparent" accommodative vergence could be due to compensation in
either the disparity or accommodative control system.
They further pointed out the relationship between
these alternative compensatory mechanisms and two
classical views of binocular vergence control: the
Maddox hierarchy1 and the theory of Fincham and
Walton.3 Essentially, these views are divided on the
question of stimulus dominance. Maddox's theory
assumes blur-driven dominance (and vergence compensation). Fincham and Walton's theory assumes
disparity-driven dominance (and accommodative
compensation).5'6 A more recent theory, based on
static quantitative representation of the major feedback systems, allows for interactive control by both
components and provides for some degree of both
disparity and accommodative compensation.4 Simulation of this static model had offered quantification
of the relative dominance of disparity and blur components.20 Essentially, dominance goes to the system
with the largest interactive influence (AC/A or CA/
C ratio) with some favoritism towards the disparity
system due to its higher internal gain. It is interesting
to note that even in the limited sample of subjects
used in our study, there appears to be a link between
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ACCOMMODATIVE VERGENCE IN NEAR RESPONSE / Hung er ol.
the static measure of AC/A (subj. GH 8 A/D; subj.
JS 6 A/D; and subj. KC 7 A/D) and the amplitude
of the dynamic accommodative contribution (subj.
GH .08 MA2; subj. JS .03 MA2; and subj. KC .06
MA2) during combined disparity-blur stimulation
(Fig. 2, 3rd row). Applying ensemble variability analysis on a larger sample of subjects and over a larger
range of AC/A ratios may further elucidate this correlation.
Key words: accommodative vergence, disparity vergence,
accommodation, response variance, Maddox hierarchy,
Fincham-Walton model, neurological control
References
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