Vertical Vergence Research Articles

Human vergence eye movements to oblique disparity stimuli: Evidence for an anisotropy favoring horizontal disparities

Binocular disparities applied to large-field patterns elicit vergence eye movements at ultra-short latencies. We used the electromagnetic search coil technique to record the horizontal and vertical positions of both eyes while subjects briefly viewed (150 ms) large patterns that were identical at the two eyes except for a difference in position (binocular disparity) that was varied in direction from trial to trial. For accurate alignment with the stimuli, the horizontal and vertical disparity vergence responses (HDVRs, VDVRs) should vary as the sine and cosine, respectively, of the direction of the disparity stimulus vector. In a first experiment, using random-dots patterns (RDs) with a binocular disparity of 0.2°, this was indeed the case. In a second experiment, using 1-D sine-wave gratings with a binocular phase difference (disparity) of 1/4-wavelength, it was not the case: HDVRs were maximal when the grating was vertical and showed little decrement until the grating was oriented more than ∼65° away from vertical, whereas VDVRs were maximal when the grating was horizontal and began to decrement roughly linearly when the grating was oriented away from the horizontal. We attribute these complex directional dependencies with gratings to the aperture problem, and the HDVR data strongly resemble the stereothresholds for 1-D gratings, which are minimal when the gratings are vertical and remain constant for orientations up to ∼80° away from the vertical when expressed as spatial phase disparities [Morgan, M. J., & Castet, E. (1997). The aperture problem in stereopsis. Vision Research, 37, 2737–2744.]. To explain this constancy of stereothresholds, Morgan and Castet (1997) postulated detectors sensitive to the phase disparity of the gratings seen by the two eyes (rather than their linear separation along some fixed axis, such as the horizontal). However, because (1) our VDVR data with gratings did not show this constancy and (2) the available evidence strongly suggests that there are no major differences in the disparity detectors mediating the initial HDVR and VDVR, we sought an alternative explanation for our data. We show that the dependence of the initial HDVR and VDVR on grating orientation can be successfully modeled by a bias in the number and/or efficacy of the detectors that favors horizontal disparities.

Relationships between versional and vergent quick phases of the involuntary version-vergence nystagmus

We used ground-plane motion stimuli displayed on a computer monitor positioned below eye level to induce involuntary version-vergence nystagmus (VVN). The VVN was recorded with a search coil system. It was shown that the VVN had both vertical versional and horizontal vergence components. The VVN induced by backward motion (toward subjects) had upward versional and divergence quick phases, whereas those induced by forward motion (away from subjects) had downward and biphasic divergence-convergence quick phases. The versional and vergence components of the VVN quick phases were analyzed. A temporal dissociation of about 20 ms between version velocity peak and convergence velocity peak was revealed, which supported a modified saccade-related vergence burst neuron (SVBN) model. We suggest that the temporal dissociation may be partly because of a lower-level OKN control mechanism. Vergence peak time was dependent on version peak time. Linear relationships between vergence peak velocity and versional saccadic peak velocity were demonstrated, which was in line with the new multiplicative model. Our data support the hypothesis that the vergence system and the saccadic system can act separately but interact with each other whenever their movements occur simultaneously.

Acquired Vertical Accommodative Vergence

Vertical accommodative vergence is an unusual synkinesis in which vertical vergence is modulated together with accommodation. It results from a supranuclear miswiring of the network normally conveying accommodative convergence. So far, it is unknown whether this condition is congenital or acquired. We identified an otherwise healthy girl who gradually developed vertical accommodative vergence between five to 13 years of age. Change of accommodation by 3 diopters induced a vertical vergence of 10 degrees. This observation proves that the miswiring responsible for vertical accommodative vergence must not necessarily be congenital, but can be acquired. The cause and the mechanism leading to vertical accommodative vergence are yet unknown.

Vertical imbalance induced by prism‐ballasted soft toric contact lenses fitted unilaterally

Fitting a prism-ballasted soft toric contact lens unilaterally may potentially induce a vergence error that the subject cannot compensate. In the present study, a prism-ballasted (1.5Delta base down) soft toric contact lens was fitted in the right eye only of 10 subjects with normal binocular vision. The effect on binocular vision was evaluated by measuring vertical phoria adaptation and vertical fixation disparity adaptation. The results show that the vertical vergence error induced was well compensated and fully adapted to. However, care might be needed when fitting these lenses unilaterally in subjects with vertical phoria-related problems.

Variation of Binocular-Vertical Fusion Amplitude with Convergence

The maximum binocular vertical disparity that can be fused with disparity vergence (vertical-fusion amplitude or VFA), varies with convergence angle. VFA is larger for convergence responses to near than to far viewing distances; however, the clinical norms for changes in VFA with convergence have not been established. VFA at several convergence angles was measured to obtain a quantitative description of the changes in VFA with convergence. Fifty-six adults took part in the study. Horizontal and vertical disparity stimuli were presented on a computer monitor by using the red-green anaglyphic technique. Stimulus to convergence was altered either by changing horizontal disparity on the computer monitor (experiment I: nine horizontal disparities: 1.2-22.5 PD [Delta]) or by changing the binocular viewing distance (experiment II: five viewing distances: 25-300 cm). Convergence was held constant during an experimental session, while vertical disparity was incremented in steps of 0.05 Delta after a subjective report of fusion, until the subject reported diplopia. The maximum vertical disparity that could be fused was defined as the VFA. VFA increased linearly over the range of convergence stimuli (y = 0.10x + 1.62) and intersubject variability of VFA increased marginally with the amount of convergence. Linear regression equations with similar slopes and y-intercepts were observed in experiments I and II. The results of the experiments provide a quantitative description of a linear relationship between VFA and convergence. The linear regression equation could be used in a clinical setting to establish norms and to screen for vertical vergence abnormalities.

Vergence nystagmus induced by motion in the ground plane: Normal response characteristics

We displayed backward/forward motion on a computer monitor in the ground plane. Subjects looked at the center of a moving pattern and eye movements of both eyes were recorded with a search coil system. Involuntary nystagmus including vertical version (VV) and horizontal vergence (HV) was recorded. Dynamics of the nystagmus showed that the slow and quick phase of VV and HV were always associated with each other while the monocular horizontal eye movements composed of HV were either symmetrical or asymmetrical. Peak velocity, amplitudes and frequency of the VV and HV responses were quantified. The results suggest that involuntary HV nystagmus can be induced by simple motion from simulated optic flow in the ground plane and the HV nystagmus helps moving subjects to stabilize their gazes on the object of interest.

Human vergence eye movements initiated by competing disparities: Evidence for a winner-take-all mechanism

Vergence eye movements were elicited in human subjects at short latencies (∼70 ms) by applying binocular disparities briefly (200 ms) to large grating patterns (46° wide, 35° high). The positions of both eyes were recorded with the electromagnetic search coil technique. Using a dichoptic viewing arrangement (Wheatstone stereoscope), each eye viewed two overlapping 1-D sine waves that had the same orientation but different spatial frequencies. These two sine waves each had a binocular disparity that was 1/4 of its wavelength and the effect of varying their relative contrasts was examined (15 contrast ratios ranging from 0.125 to 8). The first experiment used horizontal gratings and recorded the vertical vergence responses when the two sine waves had spatial frequencies in the ratio 3:5 and vertical disparities of opposite sign. Initial vergence responses showed a highly nonlinear dependence on the contrast ratio. On average, when the contrast of one sine wave exceeded that of the other by a factor of >2.2, the sine wave with the higher contrast dominated responses and the sine wave with the lower contrast had almost no influence: winner-take-all. A second experiment, which used vertical gratings and recorded the horizontal vergence responses when the two sine waves had spatial frequencies in the ratio 3:5 and horizontal disparities of opposite sign, also uncovered nonlinear interactions but these were much more variable from one subject to another and, on average, one sine wave did not achieve complete dominance until its contrast exceeded that of the other by a factor of >4.5. When these two experiments were repeated with grating patterns in which the two sine waves had spatial frequencies in the ratio 3:7 and disparities of the same sign, similar nonlinear interactions were apparent. We attribute the nonlinear dependence on relative contrast to mutual inhibition between the neural elements processing the disparities of the two sine waves. We further suggest that this interaction will help to maintain binocular alignment on the objects in the plane of regard because the retinal images of those objects will tend to be better focused—and hence tend to have higher contrasts—than the images of objects in other depth planes.

Short-latency disparity vergence eye movements: A response to disparity energy

Vergence eye movements were elicited in human subjects by applying disparities to square-wave gratings lacking the fundamental (“missing fundamental”, mf). Using a dichoptic arrangement, subjects viewed gratings that were identical at the two eyes except for a phase difference of 1/4 wavelength so that, based on the nearest-neighbor matches, the features and the 4 n + 1 harmonics (5th, 9th, etc.) all had binocular disparities of one sign, whereas the 4 n − 1 harmonics (3rd, 7th, etc.) all had disparities of the opposite sign. Further, the amplitude of the ith harmonic was proportional to 1/ i. Using the electromagnetic search coil technique to record the positions of both eyes indicated that the earliest vergence eye movements elicited by these disparity stimuli had ultra-short latencies (minimum, <65 ms) and were always in the direction of the most prominent harmonic, the 3rd, but their magnitudes fell short of those elicited when the same disparities were applied to pure sinusoids whose spatial frequency and contrast matched those of the 3rd harmonic. This shortfall was evident in both the horizontal vergence responses recorded with vertical grating stimuli and the vertical vergence responses recorded with horizontal grating stimuli. When the next most prominent harmonic, the 5th, was removed from the mf stimulus (creating the “ mf-5” stimulus) the vertical vergence responses showed almost no shortfall—indicating that it had been almost entirely due to that 5th harmonic—but the horizontal vergence responses still showed a small shortfall, at least with higher contrast stimuli. This small shortfall might represent a very minor contribution from higher harmonics and/or distortion products and/or a feature-based mechanism. We conclude that the earliest disparity vergence responses—especially vertical—were strongly dependent on the major Fourier components of the binocular images, consistent with early spatial filtering of the monocular visual inputs prior to their binocular combination as in the disparity-energy model of complex cells in striate cortex [Ohzawa, I., DeAngelis, G. C., & Freeman, R. D. (1990). Stereoscopic depth discrimination in the visual cortex: neurons ideally suited as disparity detectors. Science, 249, 1037–1041].

Cerebellar skew deviation and the torsional vestibuloocular reflex

Skew deviation is typically caused by brainstem damage, and has not been identified with focal cerebellar lesions. This vertical strabismus has been attributed to asymmetric disruption of vestibuloocular reflex (VOR) projections from otolithic receptors of the utricle to ocular motoneurons, but asymmetry of the utriculo-ocular counter-roll reflex has not been detected. Lesions localized to the cerebellum were identified by MRI in five patients with vertical strabismus. Their skew deviation was measured by prism cover tests in all patients and by search coils in three patients. The angular VOR was tested in patients and 10 controls during sinusoidal +/- 10 degree torsional, vertical, and horizontal head-on-body rotations at 0.5, 1, and 2 Hz. Static torsional VOR gain was measured by the change in torsional eye position divided by change in head position during maintained head tilt. Static torsional VOR gains were asymmetric in each patient. Three patterns of asymmetry were identified: 1) decreased static gain in one eye in both directions; 2) decreased gains in both eyes in one direction; and 3) asymmetric gain in one direction in one eye alone. Dynamic torsional VOR gains were symmetrically reduced in both directions in both eyes in all patients. Focal cerebellar lesions can cause skew deviation. The static torsional vestibuloocular reflex (VOR) is linked to cerebellar control of vertical vergence. Asymmetry between the eyes or in direction of the static torsional VOR provides evidence that monocular or binocular imbalance of the utriculo-ocular reflex leads to cerebellar skew deviation.

Horizontal and vertical prism adaptation are different mechanisms

As part of a study on subjects with convergence insufficiency (CI), their vertical and horizontal vergence adaptation was assessed and compared with age matched controls in order to investigate whether the horizontal adaptation system can be regarded as being independent of the vertical adaptation system. Using a flashed Maddox rod technique horizontal vergence adaptation was found to be reduced in CI subjects whereas no difference could be found in vertical adaptation. These results confirm that the vertical and horizontal adaptation systems can be treated as independent mechanisms.

Das Kopfneigephänomen bei einseitigen und beidseitig symmetrischen Trochlearisparesen

The head-tilt phenomenon (difference between the vertical deviations with an ipsilateral and contralateral head-tilt by 45 deg. each) occurring in patients with a superior oblique palsy has traditionally been explained by the lacking contraction of the superior oblique muscle within the synkinetic movement of ocular counterrolling. However, using a computer model, Robinson showed that the superior oblique palsy itself causes only a relatively small head-tilt phenomenon. Adaptive mechanisms amplifying the otolith reflex were suggested to explain the increase of the head-tilt phenomenon in the course of time. In order to reduce the abnormal head posture required for binocular vision, the otolith reflex would be amplified, accepting the greater vertical deviation when the head is tilted to the paretic side . If the head-tilt phenomenon were solely caused by the lacking contraction of the superior oblique muscle, it should be greater in bilateral than in unilateral superior oblique palsies. If an adaptive mechanism were acting to reduce the abnormal head posture, the head-tilt phenomenon should not be greater, and could even be smaller in bilateral than in unilateral superior oblique palsy, because in bilateral (symmetric) trochlear nerve palsies the vertical deviation at straight gaze is already small or absent without adaptation. We have carried out a retrospective comparison of 10 patients with bilateral symmetric superior oblique palsies and 10 patients with unilateral superior oblique palsy. In all cases, the palsy was acquired and had been present for at least 1 year. The patients with bilateral superior oblique palsy had a head-tilt phenomenon ranging from 0 to 7 degrees (median, 2 deg.). The patients with unilateral superior oblique palsy had a head-tilt phenomenon between 2 and 13 degrees (median, 8 deg.). The difference was significant (p = 0.0117). The head-tilt phenomenon is smaller in long-standing bilateral symmetric superior oblique palsies than in long-standing unilateral superior oblique palsy. This finding supports the hypothesis that in unilateral superior oblique palsy, an adaptive mechanism augments the head-tilt phenomenon by an amplification of the otolith reflex. However, we presume that the amplification of the otolith reflex is only a side effect of the adaptive change of the vertical fusional vergence tonus and thus the price of the improved vertical fusion, rather than a compensatory mechanism.

Illusory depth perception of oblique lines produced by overlaid vertical disparity

Our visual system matches images from both eyes to establish a single view and stereo depth even when they contain a certain amount of vertical disparity. This paper demonstrates a new stereo effect showing an aspect of vertical disparity processing. When oblique lines without disparity are overlaid with sparse random dots with vertical disparity, the lines look closer or farther in depth. The characteristics of this stereo illusion were experimentally investigated. The results showed that the sign of the perceived depth of the oblique lines depended on the combination of the line orientation and the vertical disparity sign, and that the amount of perceived depth became larger as the line orientation became more horizontal. The depth illusion robustly existed even under conditions that ruled out eye movements (i.e., vertical vergence and cyclovergence) by local-parallel or brief presentations of the stereo figures. This phenomenon suggests that the visual system locally measures vertical disparity and is not simply tolerating a small amount of vertical disparity. Stereo capture of vertical disparity and horizontal matching after vertical image shifts were proposed as possible explanations for the depth illusion.

Symmetrical horizontal vergence contributes to the asymmetrical pursuit of targets in depth

When a target travels slowly and smoothly along the line of sight of one eye, the eye that is aligned with the target remains stationary while the other eye adducts. The mechanism that is commonly invoked is that commands signaling conjugate pursuit and symmetrical vergence are combined. The two signals are in the same direction in the adducting eye but are in the opposite direction in the stationary eye and, so, cancel. Recent data have challenged this view and the idea that the two eyes are controlled independently has been resurrected. Pursuit and vergence movements are difficult to separate when they occur together because they have similar latencies and dynamics. We have developed a method where horizontal vergence is “tagged” by training it to have a vertical vergence component that can then be identified in combined pursuit–vergence movements. Four subjects trained eye movements to have a vertical vergence component by fusing vertical disparities that varied in association with horizontal convergence. Following training, the vertical vergence aftereffect was found whenever horizontal vergence was stimulated regardless of whether the horizontal vergence resulted from movement of the target in the midsagittal plane (symmetrical vergence) or from movement of the target along the line of sight of one eye (asymmetrical vergence). The vertical vergence aftereffect was never observed in association with conjugate movements indicating that asymmetrical slow eye movements are not controlled monocularly but contain a vergence component along with symmetrical smooth pursuit.

Influence of viewing distance on vertical strabismus.

Vertical strabismus can be modulated by the viewing distance. We report on 19 patients with this disorder. The following squint angles were measured by the alternate prism and cover test at a viewing distance of 5 m. At 0.3 m, measurements were taken with and without an addition of 3.0 D to the corrected refraction. Cases of a dissociated vertical deviation were excluded. Fifteen patients underwent surgery. They were reexamined 3 months later. At a viewing distance of 5 m, the vertical deviation ranged from 0 degrees to 16 degrees (median 7 degrees ). At 0.3 m, the deviation increased by 2 degrees -15 degrees (median 7 degrees ) in 15 patients and decreased by 3.5 degrees -8 degrees (median 4.5 degrees ) in 4 patients. Eleven patients had a strabismus sursoadductorius and one had a strabismus deorsoadductorius. Eye muscle surgery reduced both the vertical deviation for distance fixation to 0 degrees -14 degrees (median 2 degrees ) and the difference between the deviations for distance and proximal fixation to 1 degrees -6 degrees (median 3 degrees ). In certain cases, vertical strabismus can be modulated by convergence and accommodation. This condition is frequently associated with an incomitance of the vertical deviation in side gaze. The baseline deviation can be reduced by appropriate eye muscle surgery. In cases of vertical accommodative vergence, bifocal glasses can be helpful.

Torsional and vertical eye movements during head tilt dynamic characteristics.

As the first response to a Bielschowsky head tilt test (BHTT), a fast transient torsional eye movement in the same direction as the head tilt has been shown with the three-dimensional (3D)-video oculography (3D-VOG) technique, and this movement is paralleled by a transient vertical vergence shift inducing a physiological skew deviation. The purpose of the present study was to investigate these dynamic eye movements further in response to a BHTT paradigm with the magnetic search coil technique. Ten healthy subjects performed a BHTT (15 degrees, 30 degrees, and 45 degrees) toward each shoulder while (search coil) the monocular eye and head positions were recorded. The same head tilt paradigm was repeated in a second test while (3D-VOG) the binocular eye position was recorded. Subsequent to the initiation of the head tilt (latency, approximately 160 ms) a rapid torsional eye movement (mean peak velocity: 40 deg/s; mean amplitude: 4 degrees) was seen in the same direction as the head movement, followed by a somewhat slower return movement. This torsion was synchronous with a vertical vergence eye movement (mean amplitude 3 degrees). The vertical vergence was always with left eye over right eye in the rightward head tilt and in head straightening from the left shoulder. In the left head tilt and in the head straightening from the right shoulder, this movement was always with the right eye over the left eye. A torsional and vertical vergence back-and-forth eye movement induced by a BHTT was confirmed with the search coil technique. Utricular inertia due to an interaural head translation, combined with a stimulation of the vertical semicircular canals, seems to be a plausible explanation for these eye movements.

Vertical vergence adaptation does improve with practice.

To investigate the effect of repeated testing on adaptation to a 2 Delta vertical prism in subjects with normal binocular single vision. Subjects were required to have good visual acuity and normal binocular single vision. The residual deviation was measured after a 1-min period of adaptation to a 2 Delta vertical prism using a modified Maddox Rod technique. This measurement was repeated 10 times, with a 5-min rest period between each trial. For eight young adult subjects, the mean residual deviation at 1 min reduced with consecutive trials, and this effect was statistically significant (p < 0.0001). No significant correlation was present between the amplitude of vertical vergence and the increase in adaptation with repeated demand. A practice effect for vertical vergence adaptation appears to be present in young adult subjects with normal binocular single vision.

Short-latency disparity-vergence eye movements in humans: sensitivity to simulated orthogonal tropias

Small disparity stimuli applied to large random-dot patterns elicit machine-like vergence eye movements at short latency. We have examined the sensitivity of these eye movements to simulated orthogonal tropias in three normal subjects by recording (1) the effects of vertical disparities on the initial horizontal vergence responses elicited by 2° crossed and uncrossed (horizontal) disparity stimuli, and (2) the effects of horizontal disparities on the initial vertical vergence responses elicited by 1.2° left-hyper and 0.8° right-hyper (vertical) disparity stimuli. Initial vergence responses were strongest when the orthogonal disparity was close to zero, and decreased to zero as the orthogonal disparity increased to 3°–5°, i.e., there was only a limited tolerance for orthogonal disparity. Tuning curves describing the dependence of the initial change in the vergence angle on the orthogonal disparity were well fit by a Gaussian function. An additional subject, who had an esotropia of ∼10° in our experimental setup, showed almost no horizontal vergence responses but did show vertical vergence responses to vertical disparity stimuli at short latency (albeit slightly longer than normal) despite the fact that her esotropia resulted in uncrossed disparities that would have totally disabled the vertical vergence mechanism of a normal subject, cf., anomalous retinal correspondence.

The plasticity of vertical motor and sensory fusion in normal subjects

Purpose It is generally agreed that vertical prism bar training can increase vertical fusion amplitude. However, little is known as to whether the increased vertical fusion amplitude following vergence exercise is due to improvement of the sensory or the motor system or both. The main aim of the present study was to determine the effect of vertical prism bar training on the motor and sensory components of vertical fusion. Methods Fifty normal subjects between 17 and 25 years of age were given vertical prism bar training to improve their vertical fusion amplitude. Vertical vergence eye movements were recorded using an infrared reflectance eye tracker system. The sensory component was assessed using a Sheedy disparometer. Results The findings of the present study showed that the average increase in vertical motor fusion was approximately 30% following vertical prism bar training. The maximum magnitude of VFD remained unchanged in the majority (73%) of subjects. Conclusions The increase in the vertical fusion amplitude following vertical prism bar training is largely due to improvements in the vertical motor fusion. The prism training has little effect on the sensory component.

Vertical Vergence Adaptation in Cases of Superior Oblique Palsy

To investigate the characteristics of vertical adaptation (VA) in superior oblique muscle palsy (SOP). VA was examined in 15 patients with unilateral congenital SOP, 7 patients with unilateral acquired SOP, and 35 normal volunteers. An adaptive change in the fusion-free ocular alignment, VA, was measured with a computer-aided mirror haploscope. The fusion-free ocular alignment was measured before inserting a 3 prismdiopter vertical prism, immediately after inserting the prism, and at 10 minutes and 30 minutes after insertion. We investigated VA gain, age, vertical fusional range, response of prism adaptation test (PAT), and superior oblique muscle atrophy in magnetic resonance imaging (MRI). The VA gain (mean +/- standard deviation, %) at 30 minutes in congenital, acquired, and normal groups was 86 +/- 53, 34 +/- 23 and 58 +/- 16, respectively. The mean of the VA gains at 30 minutes in the congenital group was greatest, and that in the acquired group was least(p < 0.01). In the congenital group there was a correlation between VA gain and response of PAT (p = 0.02, r = 0.60). The VA gain did not significantly correlate with age, vertical fusional range, or muscle atrophy. The VA gain observed in congenital SOP was greater than that of acquired SOP, and affected the response of PAT.

Contribution of vergence adaptation to difference in vertical deviation between distance and near viewing in patients with superior oblique palsy

PURPOSE: To evaluate the adaptive vertical vergence aftereffect and determine whether it contributes to a difference of vertical deviation with respect to gaze distance in patients with vertical strabismus. DESIGN: Prospective noncomparative studies. METHODS: Eighty-four patients with unilateral superior oblique palsies were enrolled and classified into three types—A, B, and C—based on the difference in vertical deviation between distant and near viewing. The prism adaptation test was performed for 2 to 3 hours to correct vertical deviation and the response of vertical deviation to the prism adaptation test was compared among the three types. RESULTS: Adaptive vertical vergence aftereffect, defined as an increase of deviation by 5 prism diopters or more with the prism adaptation test, was identified in 13 patients (16%) at distance and in 23 patients (27%) at near viewing. Among the three types, the adaptive vergence aftereffect contributed mostly to the type B, in which distance deviation exceeds near deviation. Nine patients (39%) of type B changed to type A category with the prism adaptation test; and of these, 7 increased near deviation so that the deviation difference between distant and near viewing decreased. CONCLUSION: The adaptive vertical vergence aftereffect contributes to a difference in vertical deviation between distant and near viewing. The vertical prism adaptation test is specifically useful to determine the extent of surgery by breaking fusional vergence in patients with hypertropia in whom deviation differs with respect to viewing distance.