Effect of Horizontal Vergence on the Motor and Sensory Components of Vertical Fusion

Naoto Hara,1'2 Heimo Steffen23 Dale C Roberts2 and David S. Zee2

PURPOSE. TO compare motor and sensory capabilities for fusion of vertical disparities at different angles of horizontal vergence in healthy humans. METHODS. Eye movements were recorded from both eyes of 12 healthy subjects using three-axis search coils. The stimulus was a cross (+) (3.4 X 3.2°, vertically and horizontally, respectively) presented to each eye with a stereoscopic display. Vertical disparities were introduced by adjusting the vertical position of the cross in front of one eye. The disparity was increased in small increments (0.08°) every 8 seconds. Viewing was denned as "near" if there was a horizontal disparity that elicited 6° to 15° convergence, depending on the subject's capability for horizontal fusion; viewing was denned as "far" at 1° convergence. Maximum motor (measured), sensory (stimulus minus motor), and total (motor plus sensory) vertical fusion were compared. RESULTS. In 9 (75%) of 12 subjects the maximum total vertical fusion was more in near than in far viewing. The three who did not show this effect had relatively weak horizontal fusion. For the entire group, the motor component differed significantly between far (mean, 1.42°) and near (mean, 2.13°). Total vertical fusion capability (motor plus sensory) also differed significantly between far (mean, 1.68°) and near (mean, 2.39°). For the sensory component there was no difference between between far (mean, 0.268°) and near (mean, 0.270°). As vertical disparity increased in a single trial, however, there was a small gradual increase of the contribution of the sensory component to vertical fusion. CONCLUSIONS. Vertical fusion capability usually increases with convergence. This increase is caused primarily by an increase in the motor component. There is a gradual but small increase in the sensory component as target disparity slowly increases. (Invest Ophthalmol Vis Set. 1998;39: 2268-2276)

he capability for fusion of vertical disparities is much when viewing at 6 m or 25 cm. Eye movements were measured less robust than that for horizontal disparities.1'5 If the in neither of these stvidies, and the relative contributions of vertical disparity is introduced gradually, a larger value motor and sensory mechanisms to vertical fusion for near T 6 of vertical disparity can be fused. Training has been shown to versus far targets are therefore unknown. We examined the improve vertical fusion capability,7"10 and larger than normal effect of convergence on the motor and the sensory compo- vertical fusion capabilities have been shown in patients with nents of vertical fusion. vertical strabismus."12 There is also evidence of a sensory component of the fusion response, but the motor component l3>14 (vertical vergence) dominates the vertical fusion response. METHODS The influence of the fixation distance on the capability of vertical fusion has been largely neglected, although Grafe15 Subjects reported, in examining himself, that near viewing considerably Twelve people (seven men and fivewomen , aged 27-37 years) increased the capability of vertical fusion. The amplitude of participated in this study. All provided their informed written vertical fusion, viewing at 10 cm, was larger (6°) than viewing consent according to a protocol conforming to the Declaration 1 at 6 m (3°). In contrast, Berens et al. studied 218 men and of Helsinki and approved by the Johns Hopkins Joint Commit- found no difference in vertical fusion capability (mean, —2.5°) tee on Clinical Investigation. Four subjects had myopia to a maximum of -5.00 diopters. They wore their full spectacle correction. None had anisometropia greater than 1.50 D. All 'From the Department of Ophthalmology, Kitasato University, had normal stereoscopic vision, determined by the Titmus test. School of Medicine, Kanagawa, Japan; the departments of Neurology and Ophthalmology, The Johns Hopkins Hospital, Baltimore, Maryland; Visual Stimuli 'Department of Ophthalmology, University of Heidelberg, Germany. Supported in part by Grant RO1 EYO-1849 from the National The stimulus was a cross, with a bar thickness of 0.16°, sub- Institutes of Health, Bethesda, Maryland and Deutsche Forschungsge- tending 3-4 X 3.2° vertically and horizontally, respectively. It meinschaft DFG STE 860/2-1. was generated with a virtual-reality stereoscopic display, with Submitted for publication January 31, 1997; revised June 5, 1998; a field of view of 19° horizontally and 16° vertically. The accepted July 2, 1998. stereoscopic display was calibrated by having a subject super- Proprietary interest category: N. Reprint requests: David S. Zee, Johns Hopkins Hospital, 600 North impose the stimulus generated by the virtual-reality display on Wolfe Street, Baltimore, MD 21287-6921. a calibrated array of light-emitting diodes, while viewing with

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3.5

0 O Disparity 3 Sensory Component Motor Component 2.5

1.5 Right minus left (cleg)

0.5

-0.5 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 Target Disparity (cleg)

-1

-2 Right minus left (cleg) .3

-5 O Disparity o Sensory Component — Motor Component

-1 12 3 4 B Target Disparity (deg)

FIGURE 1. Vertical vergence responses from one subject. Vertical stimulus disparity (i.e., target disparity) in degrees is on the abscissa, and the motor and sensory components of fusion in degrees are on the ordinate (right eye minus left eye). The (o) indicates the vertical disparity. The solid line represents the mean amplitude of the motor component, with the SD (error bars) calculated over 21 points in a period of 2 seconds (every 10th sample) during stable fixation at each target disparity. The arrows indicate the point just before fusion was lost. (A) Response to stimulus R/L-r in far viewing; (B) response to stimulus L/R-r in near viewing. Note the gradual increase in the sensory and motor components.

first one eye, then the other. The apparent distance of the coils annuli (horizontal, vertical, and torsional).1617 An accu- virtual image from the observer was the same for both viewing rate calibration was ensured by calibrating the dual coils in distances (4 m); therefore, there was no call tor a change in vitro as described by Straumann et al.18 The annuli were then accommodation. placed on each eye after administration of a topical anesthetic (proparacaine HC1 0.5%, Ophthetic; Allergan, Irvine, CA). Sub- Recording of Eye Movements and Calibration jects sat with the head at the center of the magnetic fieldan d Procedure immobilized with a bite bar. The output signals from the phase Horizontal, vertical, and torsional eye movements were re- detectors were filtered with a bandwidth of 0 Hz to 90 Hz and corded using the magnetic field search coil method with dual sampled by a digital computer at 100 Hz with 12-bit resolution.

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6 6 6

5 5 5 / 4 4 4 / 3 3 deg3 deg deg

2 2 2

1 1 1

0 0 'far' 'near' 'far' 'near' 'far' near' viewing viewing viewing viewing viewing viewing FIGURE 2. A comparison of the capability of vertical fusion in far and near viewing in each subject. Left: Total fusion; center: the motor component; right: the sensory component. There were significant differences between far and near viewing in the mean values of the total and the motor components of vertical fusion (see Results).

System noise limited resolution to approximately 0.05°. Data Experimental Protocol were stored to disc for later off-line analysis using commercial At the beginning of each trial the crosses were adjusted to zero software (MATLAB; Math works). The positions of the eyes vertical disparity, as described. The alignment of both eyes was were calculated in rotation vectors. Because we were primarily interested in the vertical and torsional response to vertical recorded during a period of 10 seconds with zero disparity. disparity, we expressed eye movement data in a Fick coordi- The disparity was then changed by increments of 0.08° every nate reference frame.19 For subjects who wore their corrective 8 seconds. Subjects were instructed to attempt to maintain spectacles during testing (subjects 1, 2, 6, and 12), the stimulus single vision and to report when images became persistently disparity was scaled according to the magnification factor of double. At the end of each paradigm, the crosses were read- the spectacles that was determined behaviorally during refix- justed to zero disparity. When fixation was stable, the horizon- ations around an array of light-emitting diodes. To describe tal, vertical, and torsional positions of the eyes were checked torsion, we adopted the convention that positive torsion refers to look for coil slippage. This paradigm was performed at two to excyclorotation of the right eye (RE) and incyclorotation of vergence angles ("far" and "near") with four stimulus patterns the left eye (LE), that is, clockwise in relation to the subject. presented in the same order:

0.8 0.7 0.6 0.5 0.4 0.3 .-•JV^ 0.2 -V 0.1 0 -0.1 1 2 3 -0.2 J 12 3 4 5 6 Target Disparity (deg) Target Disparity (deg)

FIGURE 3. The change of the sensory component during individual trials. Vertical stimulus disparity (i.e., target disparity) in degrees is on the abscissa, and the sensory component of fusion in degrees is on the ordinate. The closed circles indicate the size of the sensory component at each stimulus disparity. These are data from subject 3. (A) Response in far viewing; (B) response in near viewing. Lines indicate linear regression fits to the data.

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TABLE 1. The Change in Size of the Sensory Component Far Viewing Near Viewing

Subjects Slope r n* P Slope r n* P

1 0.294 0.95 26 <0.001 0.247 0.95 34 <0.001 2 0.273 0.87 14 <0.001 0.065 0.67t 23 0.180 3 0.075 0.75 43 <0.001 0.170 0.87 67 <0.001 4 0.542 0.94 11 <0.001 0.137 0.72 19 <0.001 5 0.256 0.98 27 <0.001 0.221 0.86 25 <0.001 6 0.160 0.93 8 <0.0l4 0.329 0.94 43 <0.001 7 0.299 0.58f 10 0.084 0.182 0.64 21 <0.001 8 0.199 0.68 20 <0.004 0.037 -0.20f 14 0.470 9 0.207 0.82 25 <0.001 0.227 0.72 23 <0.001 10 0.186 0.86 14 <0.001 0.060 0.53 24 0.011 11 0.264 0.98 22 <0.001 0.119 0.49t 11 0.116 12 0.112 0.90 43 <0.001 0.062 0.86 63 <0.001 * The number of the sensory component at each stimulus disparity in one trial, f Not significant; Spearman's rank correlation test.

1. Right over left (R/L-r): The stimulus for the RE was RESULTS moved up. 2. Right over left (R/L-l): The stimulus for the LE was Vertical Fusion Responses moved down. A typical vertical fusion response for one subject in far viewing 3. Left over right (L/R-r): The stimulus for the RE was is shown in Figure 1A. The total fusion response, determined moved down. by the target disparity immediately before the perception of 4. Left over right (L/R-l): The stimulus for the LE was moved diplopia, was 3.36°, consisting of a motor component of 3-27° up. and a sensory component of 0.09°. The response of the same subject in near viewing, with 10° of convergence is shown in At far viewing, the eyes had a convergence angle of 1°. Figure IB. The total vertical fusion was 5.36°, with a motor At near viewing, a symmetrical horizontal convergence an- component of 5.04° and a sensory component of 0.32°. This gle of 15° was elicited. If necessary, the horizontal disparity subject had a particularly robust response. was reduced to 6° to 14° depending on the person's ability to maintain horizontal fusion. This vergence angle was used Correlation between Vertical Fusion and the for the near viewing experiment. Trials lasted from 4 to 9 Motor and Sensory Components minutes depending on the fusion capability. Subjects rested The total, motor, and sensory components of the maximum for at least 1 minute between trials to minimize any phoria fusion responses for each individual in far viewing and in adaptation. One trial was obtained for each of the four near viewing are shown (Fig. 2A, 2B, 2C, respectively). In 8 stimulus conditions. of 12 subjects, vertical fusion capability was better in near viewing. In one subject there was little difference, and in Data Analysis three subjects vertical fusion capability was worse in near viewing. These four subjects had a relatively weak capability The relative vertical alignment or vertical vergence was calcu- for horizontal fusion. The convergence position in near lated by subtracting the vertical position of the LE from the RE. viewing was 10°, 7°, and 10° in the three subjects, with a Horizontal and torsional alignments were calculated in a similar better response at distance and 6° in the subject who manner. We selected the largest vertical fusion response from showed little difference between near and far viewing. The each subject across all stimulus combinations for each viewing mean values among subjects for total vertical fusion (Fig. distance. Sensory fusion was denned as the difference between 2A) were significantly different (1.68° in far viewing, and the total vertical fusion response (determined by the size of the 2.39° in near viewing; P = 0.045; Wilcoxon signed rank target disparity) and the motor component (vertical vergence). test). Similarly, the mean readings for the motor component A 2-second epoch of stable fixation was selected just before the (Fig. 2B) were significantly different (1.42° in far viewing next disparity was imposed, and eye position was sampled and 2.13° in near viewing; P = 0.015). For the sensory every 100 msec during this 2-second period. The amounts of component, however, there was no significant difference vertical and torsional eye movement were measured relative to between the means (0.268° in far viewing, and 0.270° in the zero position of each eye before any disparity was intro- near viewing; P = 0.754). Note also the relatively small duced and the position of the eyes immediately before fusion range of values for the sensory component among subjects. was lost. The maximum responses in far and near viewing in all The motor component compensated for 62% to 99% (0.44°- subjects were compared using the Wilcoxon signed rank test, 3.30°) of the disparity in far viewing and 76% to 98% (0.68°- and correlations were calculated using Spearman's rank corre- 5.04°) in near viewing. Consequently, the range of the lation test. sensory component in all subjects was from 1% to 38% of the

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0.2 0.4 0.6 0.8 1 1.2 1.4 0.5 1 1.5 2 2.5 3.5 Target Disparity (deg) Target Disparity (deg)

4. 4. Vertical Vergence + + Vertical Version

+ + + + ++ + *

+ Vertical Vergence + Vertical Version 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1. 2 n 0 0.5 1.5 2 2.5 3.5 A Target Disparity (deg) B Target Disparity (deg)

+ + Right Eye x x Left Eye

0.5 1 1.5 2 2.5 0 0.2 0.4 0.6 0.8 1 1.2 1.6 1. Target Disparity (deg) Target Disparity (deg)

Vertical Vergence + + Vertical Vergence Vertical Version . + + Vertical Version + + + + + + + + + + + + + +

0.5 1 1.5 2 2.5 3 0.2 0.4 0.6 0.8 1 1.2 1.6 Target Disparity (deg) D° Target Disparity (deg)

FIGURE 4. The patterns of eye movement response to the asymmetrical disparity stimulus. The top figure in each pair shows the responses of each eye. The broken line indicates the stationary target, and the solid line indicates the changing target position. The bottom figure shows the vertical vergence (motor components) and vertical version (conjugate [average] component). With this target configuration the change in vertical version should be one half the target disparity. (A) Version type, (B) monocular type, (C) pure vergence type, (D) fluctuating type. The arrows in (A) and (D) indicate when both eyes are off target. Note that there is an inappropriate vertical version superimposed on the vertical vergence but that the motor component of the fusion response remains appropriate. The stimulus direction is (A) L/R-l, (B) R/L-r, (C) R/L-r, and (D) L/R-l.

overall vertical fusion in far viewing and 2% to 24% in near Pattern of Vertical Eye Movement viewing. These results led to the general conclusion that the The four patterns of eye movements that were made in re- increase in the value for maximum vertical fusion associated sponse to a vertical disparity imposed by moving the target in with convergence was primarily caused by an increase in front of one eye only are shown in Figure 4. In the version type the motor component. (Fig- 4A) both eyes moved, showing a conjugate and a discon- During the individual trials, as vertical disparity was grad- jugate response. This was the most common pattern (six sub- ually increased, there was also an increase in the sensory jects in far viewing and seven in near viewing). In the monoc- component. This change in the sensory component in one ular type (Fig. 4B), only the eye exposed to the target that subject who had a particularly large capability of vertical fusion changed position moved; the fellow eye remained stationary. is shown in Figure 3- The correlation in all subjects between This pattern was seen in four subjects in far viewing and in two target disparity and the sensory component of vertical fusion is subjects in near viewing. In the pure vergence type (Fig. 4C), listed in Table 1. In almost all subjects there was a strong both eyes moved in opposite directions. Only one subject, in correlation between target disparity and the sensory compo- far and near viewing, showed this pattern. In the fluctuating nent of vertical fusion. In each subject, however, there were type (Fig. 4D), the response in a given trial could not be easily no significant differences (P = 0.077; Wilcoxon signed rank classified and was variable. Two subjects in far viewing and test) between the slopes (vertical disparity versus sensory com- two subjects in near viewing showed this pattern. Five subjects ponent) in far and near viewing. showed the same pattern of response in far and near viewing

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(four with the version pattern and one with the fluctuating 0.4

pattern). 0.2 The left-over-right (L/R stimulus) disparity produced maximum total fusion in 9 (75%) of 12 subjects in far viewing and 0 in 8 (67%) in near viewing. These percentages were not sig- -0.2 nificantly different from that expected in a random occurrence (P > 0.5; Fisher's exact test). Six subjects, however, showed -0.4 the maximum response to the same disparity direction in the -0.6 + same eye at both distances. Eight responded best to the target + + moving in the same eye between far and near viewing. In seven -0.8 20 subjects we determined the dominant eye by a pointing test -1 *• and found no correlation between the results of that test and the eye that remained closest to the target. -1.2 Vertical Vergence -1.4 Cyclovergence Pattern of Torsional Eye Movement Cycloversion -1.6 We also examined the correlation between the direction of 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 vertical fusion and cyclovergence or cycloversion. Torsional Target Disparity (deg) eye movements were measured relative to a reference position 1.5 (zero) of each eye (before any disparity was introduced). In + + Vertical Vergence x x Cyclovergence four subjects at both distances, there appeared to be torsional + + Cycloversion coil slippage during the stimulus presentation, because the zero position changed before and after the stimulus presentation. The change in torsion coil position was greater than one 0.5 SD, which ranged from 0.78° to 1.25° in all subjects, depending on the viewing distance and stimulus configuration. We + * + + * + + excluded data from these four subjects. Illustrated in Figure 5 are the torsional eye movements that occurred in response to the L/R disparity in a subject in far viewing (Fig. 5A) and in a -0.5 subject in near viewing (Fig. 5B). Although the direction of the vertical disparity was the same, the pattern of change in cycloversion was opposite. In Figure 5C, data are shown from the same trial as data shown in Figure 4C. This subject had the pure .-15 vergence type of response. Cycloversion showed only a small D 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 counterclockwise change (in relation to the subject) toward Target Disparity (deg) the end of the trial. Neither the amount of cyclovergence (Fig. 2 5 6A) nor cycloversion (Fig. 6B) was correlated with the motor -1- Vertical Vergence 2 x Cyclovergence component of vertical fusion in the eight subjects without + Cycloversion +-

slippage of the coil. All correlations are shown in Table 2. 1.5 +

+ 1 + +

DISCUSSION 0.5 + + + + + + ^ + The main finding of this study is that when the eyes converged, 0 x x + x the capability for vertical fusion was increased. We showed x x x + + x further that the increased capability for vertical fusion in near -0.5 viewing was primarily caused by an increase in the motor + + -1 component of fusion; the sensory component changes little. +++ + + * +

The subjects who had the largest capability of vertical fusion in -1.5 + + far viewing tended to have a larger capability in near viewing. + - Finally, we showed that during an individual trial, the sensory -2 0.5 1 1.5 2.5 component of vertical fusion gradually increased with increas- Target Disparity (deg) ing vertical disparity. FIGURE 5. The correlations between the vertical vergence and Comparison with Previous Data on Vertical torsional eye movements. (A) Indicates that the left-over-right Fusion (L/R-l) stimulus induced counterclockwise torsional eye movement in both eyes (cycloversion), that is, rotation of both The values for vertical fusion that we found here are similar to 4 upper poles toward the left shoulder and (B) indicates that the those reported previously. Yamamoto and Arai, using a syn- same direction of disparity could induce clockwise cyclover- optophore, studied the amplitude of vertical fusion using a sion. In (C) little change is seen in cycloversion in association stimulus pattern subtending approximately 2° of visual angle. with vertical vergence. Note that positive cycloversion refers They found values of 1.4° ± 0.4° in 20 healthy subjects. Sharma to both eyes rotating clockwise in relation to the subject and and Abdul-Rahim5 found that the mean vertical fusion ampli- that positive cyclovergence refers to excylovergence. tude using a vertical prism bar was 2.66° in 60 healthy subjects

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A EX (deg) 2 -r CD 1.5 -• 1 -• * 0.5 -• L/R o _Q . R/L (deg) -2 o -1 •• O-1.5 -• -2 • IN B (:W (deg) 1 5 -. • 1 • • 0 0 5 - r\ l i o O^ 1I ° L/R i- U 'A R/L (deg) -2 -1 ^ -0.5 [ I 1 ± 2 3

-1 • o •

-1 5 • ccw FIGURE 6. Correlation between vertical vergence and cyclovergence in (A) or cycloversion in (B). The circle indicates the size of each movement in far viewing in each subject, and the triangle indicates the size in near viewing. EX, excyclovergence; IN, incyclovergence, CCW, counterclockwise torsion in both eyes (i.e., rotation of both upper poles toward the left shoulder); CW, clockwise torsion.

between the ages of 18 and 63 years. In these studies, how- ent from the ones used in our study. If we had used larger ever, no objective measurement of vertical fusion was per- stimuli that extended into the periphery, or stimuli with dif- formed. Perlmutter and Kertesz,13 used a dichoptic stimulus ferent contrasts, or if there had been an accommodation com- consisting of a single horizontal line subtending 8.5°. They ponent to the near stimulus, we might have seen different reported that the maximum fusible vertical disparity was less vertical vergence capabilities and a different effect of horizon- than 1°. The motor component of total fusion was 80% to 85% tal vergence angle. of the imposed disparity. A somewhat smaller sensory component to vertical fusion has been reported by Duwaer.21 Re- Vertical Sensory Component cently, Howard et al.22 used a sinusoidally oscillating disparity In our experiments, in near and far viewing, the sensory com- stimulus in which the target changed position in front of one ponent of vertical fusion increased in proportion to disparity as eye. They reported a range of vertical vergence capabilities the trial progressed. This finding suggests that there may be among their four subjects similar to the range observed in ours. dynamic changes in Panum's fusion area, perhaps as a function They found values of the motor component from 1.25° to 2.8° of vertical disparity. Others have previously shown that Pa- for a 4° disparity presented at a distance of 57 cm. Our stimulus num's fusion area may change with the characteristics of the and responses were similar to those of Perlmutter and stimulus.23'24 In our experiments, the changes in the sensory Kertesz/314 but in addition we have shown that convergence component could be a function of the relatively slow change in enhances vertical fusion. This findingagree s with the previous disparity and/or the relatively long duration of the motor re- subjective report of Grafe15 but not with that of Berens et al.1 sponse, perhaps inducing some type of sensory adaptation. In both reports, however, the visual stimuli were much differ- These potential factors require further investigation. In con-

TABLE 2. Correlation between the Motor Component ()f Vertical Fusion and Torsion 'Far' Viewing 'Near' Viewing

r* P n r* P 00

Cyclovergence (n == 8) -0.357 0.353 00 0.381 0.321 Cycloversion (n = 8) -0.381 0.321 -0.500 0.182

* Spearman's rank correlation test.

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trast, we found that the horizontal vergence angle had little the head and off to the side. Viewing targets at distance does effect on the maximum value of the sensory component of not require a vertical fusion response. Some of the vertical vertical fusion or on the slopes of the correlation between the realignment that must occur when refixating between laterally sensory component of vertical fusion and disparity. The sen- located targets seems to be independent of an immediate effect sory component of vertical fusion seems to be independent of of disparity, because a vertical realignment occurs in the dark the apparent distance of the stimulus. when making saccades between the imagined locations of near targets or when the images seen by the two eyes are dissoci- Pattern of Vertical Eye Movements ated.31"34 This ability to preprogram vertical realignment inde- 14 22 pendent of visual cues may be related to central mechanisms As others have found, ' our subjects showed variability in 31 35 39 the overall pattern of the vertical eye movement response to a that are under adaptive control ' " and to orbital factors related to changes in pulling directions of vertical muscles vertical disparity. This has been reported with symmetrical and 26 40 asymmetrical (as we used) vertical disparity stimuli. We found associated with changes in horizontal position. ' Presum- various combinations of conjugate (vertical version) and dis- ably, however, in near viewing, disparity-driven vertical fusion conjugate (vertical vergence) responses. Remarkable, how- capability would still be necessary to supplement any prepro- ever, was the consistency and the appropriateness of the mo- grammed mechanism and to fine-tune vertical alignment. tor component of the vertical fusion response. Although both eyes might have drifted away from the center of the target, References causing the images to be located away from the center of the fovea, the absolute difference between the positions of the 1. Berens C, Losey RR, Hardy LH. Routine examination of the ocular eyes remained appropriate for the disparity of the stimulus. muscles and nonoperative treatment. Am JOphthalmol. 1927;10: This finding is confirmation of the well-known fact that extrafo- 910-918. 2. Takao S. Vertical fusion amplitude. J Jpn Ophthalmol Soc. 1936; veal disparity can drive fusion responses. Because our stimulus 40:245-251. did not require visual discrimination at the center of the stim- 3. Veronneau-Troutman S. Fresnel prism membrane in acquired ex- ulus, it is not surprising that relatively small drifts of the eyes traocular muscle palsy. Am OrthoptJ. 1974;24:91-97. away from the target were well tolerated. A conjugate compo- 4. Yamamoto H, Arai M. Study on vertical and cyclofusional ampli- nent might also have appeared if there had been a superposi- tude in human. Jpn Rev Clin Ophthalmol. 1975;69:1382-1384. tion of a conjugate eye movement (pursuit) on a disjunctive 5. Sharma K, Abdul-Rahim AS. Vertical fusion amplitude in normal movement. Such a mechanism has been suggested for the adults. Am] Ophthalmol 1992;ll4:636-637. 6. Ellerbrock VJ. Experimental investigation of vertical fusional move- monocular pattern of response to a slowly changing asymmet- 25 ments. Am] Optom. 1949;26:327-335. rical (monocular) disparity stimulus. We also studied the 7. Robertson KM, Kuhn L. Effect of visual training on the vertical responses to symmetrical stimuli in a few subjects and found vergence amplitude. Am J Optom Physiol Opt. 1985:62:10:659- no differences in their patterns of response compared with 668. those for asymmetrical stimuli. 8. Rutstein RP. Vertical vergence adaptation for normal and hyper- phoric patients. Optom Vis Sci. 1992;69:289-293- 9. Rutstein RP, Daum K, Cho M, Eskridge JB. Horizontal and vertical Pattern of Torsional Eye Movements vergence training and its effect on vergences, fixation disparity Previous workers have suggested that certain patterns of tor- curves, and prism adaptation, II: Vertical data. Am J Optom Physiol Opt. 1988;65:8-13. sional eye movements are associated with vertical vergence. 26 27 10. Green JF. Plasticity of the vergence system. Transactions of the Enright and van Rijn et al. reported that disparity-induced VHth international Orthoptic Congress. 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IEEE Trans Biomed Eng. 1983:30:246-250. usually smaller, and the rate of change of disparity was slower. 15. Grafe, A. Ueber die Fusionsbewegungen der Augen beim Pris- The duration of the stimulus presentation and the eye move- maversuche. Graefes Arch Ophthalmol. 1891;37:243-257. ment response was much longer. Thus, the chance for coil 16. Collewijn H, Van der Mark F, Jansen TC. Precise recording of human eye movements. Vision Res. 1975;15:447-450. slippage in our experiments was increased. Although we 17. Ferman L, Collewijn H, Jansen TC, Van den Berg AV. Human gaze looked carefully for slippage of the annulus and eliminated data stability in the horizontal, vertical and torsional direction during when it appeared to happen, small amounts could have gone voluntary head movements, evaluated with a three-dimensional undetected. Cycloversion is also known to undergo spontane- scleral induction coil technique. 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