Latitude and longitude vertical disparities

The literature on vertical disparity is complicated by the fact that several different definitions of the term "vertical disparity" are in common use, often without a clear statement about which is intended or a widespread appreciation of the properties of the different definitions. Here, we examine two definitions of retinal vertical disparity: elevation-latitude and elevation-longitude disparities. Near the fixation point, these definitions become equivalent, but in general, they have quite different dependences on object distance and binocular eye posture, which have not previously been spelt out. We present analytical approximations for each type of vertical disparity, valid for more general conditions than previous derivations in the literature: we do not restrict ourselves to objects near the fixation point or near the plane of regard, and we allow for non-zero torsion, cyclovergence, and vertical misalignments of the eyes. We use these expressions to derive estimates of the latitude and longitude vertical disparities expected at each point in the visual field, averaged over all natural viewing. Finally, we present analytical expressions showing how binocular eye position-gaze direction, convergence, torsion, cyclovergence, and vertical misalignment-can be derived from the vertical disparity field and its derivatives at the fovea.

No oculomotor plant, no final common path

The assumption that there is an oculomotor plant, a fixed relationship between motoneuron firing rate and eye position, is disproved by brainstem recording studies showing that this relationship depends on which supernuclear subsystem determines firing rate. But it remains possible that there is a final common path (FCP), a fixed relationship between firing rate and muscle force. But then, brainstem recording studies predict that lateral rectus (LR) forces (and probably medial rectus (MR) forces, as well) will be higher in converged than in unconverged gaze for a given eye position. We recently measured these forces and found that they are slightly lower in convergence, disproving the FCP hypothesis. Thus, even the relationship between motoneuron firing rate and muscle force is under supernuclear control. What peripheral oculomotor articulations could vary the relationship of firing rate to muscle force?: (1) Actively movable EOM pulleys could alter oculorotary muscle force for a given oculorotory innervation by altering muscle lengths. (2) 'Outer' motoneurons may function as gamma efferents in conjunction with palisade endings and non-twitch global EOM fibers. (3) Complex nonlinear interactions likely arise among both parallel and serially connected muscle fibers.

Vergence Dynamics and Variability of Fixation Disparity in Children and Adults

With dichoptic nonius lines presented repetitively on a computer monitor for only short moments in time (e.g., 80 ms), temporal aspects of vergence can be assessed: the variability of fixation disparity with a stationary central fusion stimulus and the velocity of convergence or divergence changes. Results and test-retest correlations of these psychophysical vergence measures are shown for children and adults. In most children older than about 7 years, the estimation of vergence velocity turned out as well as in adults in terms of amount and reliability.

Eye-Movement Responses to Disparity Vergence Stimuli with Artificial Monocular Scotomas

The effects of artificial monocular scotomas on eye-movement responses to horizontal disparity vergence stimuli were studied in six subjects with normal binocular vision. Subjects viewed stereoscopic 1.5 degrees horizontal step disparity vergence stimuli through liquid crystal shutter glasses. The central portion of the stimulus presented to the right eye was removed to simulate monocular artificial scotomas of variable diameters (2 degrees to 10 degrees ). Eye movements were recorded with a binocular head-mounted eye tracker. Responses included pure vergence, vergence followed by saccades, and pure saccadic eye movements. The rate of responses with saccadic eye movements increased with the diameter of the artificial scotoma (p < 0.0001); there was an increase in the rate of responses starting with saccades (p < 0.0001), as well as an increase in the rate of saccades after initial vergence responses (p < 0.01). The probability of saccades after initial vergence responses was affected by the open-loop gain of the vergence response (p < 0.001). The open-loop gain decreased with increased diameters of the artificial scotomas (p < 0.0001). As the diameter of the artificial scotomas increased, the amplitude of the initial vergence eye-movement responses decreased, and the prevalence of saccadic eye movements and asymmetric vergence increased. The effects of the diameter of artificial monocular scotomas on eye-movement responses in subjects with normal binocular vision are consistent with the effects of diameter of suppression scotomas on eye-movement responses to disparity vergence stimuli in patients with infantile esotropia.

Acute superior oblique palsy in the monkey: effects of viewing conditions on ocular alignment and modelling of the ocular motor plant

We investigated the immediate and long-term changes in static eye alignment with acute superior oblique palsy (SOP) in the monkey. When the paretic eye was patched immediately after the lesion for 6-9 days, vertical alignment slowly improved. When the patch was removed and binocular viewing was allowed, alignment slowly worsened. In contrast when a monkey was not patched immediately after the lesion vertical alignment did not improve. We also show that a model of the eye plant can reproduce the observed acute deficit induced by SOP, but only by abandoning Robinson's symmetric simplification of the reciprocal innervation relationship within pairs of agonist-antagonist muscles. The model also demonstrated that physiologic variability in orbital geometry can have a large impact on SOP deficits.

Measuring fixation disparity with infrared eye-trackers

Fixation disparity, that is, misalignment of the gaze direction of both eyes, may be observed in static conditions (through standard optometric evaluation) and dynamic conditions (through eye movement recording). A computation method is presented to determine vergence angles and fixation disparity from gaze positions as commonly recorded by infrared eye-trackers when a participant looks at a personal computer (PC) screen. Eye-tracking devices provide gaze position in coordinates relative to the bidimensional screen surface. From these data, vergence angles can be calculated by trigonometric triangulations; fixation disparity is then calculated from the vergence angles. The application of the procedure to the recordings of one participant is described. To control for the effective alignment of the two eyes on the target during binocular calibration, a procedure based on the dichoptic presentation of nonius lines was used. The recordings confirm that computation and the dichoptic calibration procedures ensure reliable measures of vergence and fixation disparity. The usefulness of this approach with infrared recording of eye position is discussed.

Cyclopean geometry of binocular vision

The geometry of binocular projection is analyzed in relation to the primate visual system. An oculomotor parameterization that includes the classical vergence and version angles is defined. It is shown that the epipolar geometry of the system is constrained by binocular coordination of the eyes. A local model of the scene is adopted in which depth is measured relative to a plane containing the fixation point. These constructions lead to an explicit parameterization of the binocular disparity field involving the gaze angles as well as the scene structure. The representation of visual direction and depth is discussed with reference to the relevant psychophysical and neurophysiological literature.

The use of cues to convergence and accommodation in naïve, uninstructed participants

A remote haploscopic video refractor was used to assess vergence and accommodation responses in a group of 32 emmetropic, orthophoric, symptom free, young adults naïve to vision experiments in a minimally instructed setting. Picture targets were presented at four positions between 2 m and 33 cm. Blur, disparity and looming cues were presented in combination or separately to asses their contributions to the total near response in a within-subjects design. Response gain for both vergence and accommodation reduced markedly whenever disparity was excluded, with much smaller effects when blur and proximity were excluded. Despite the clinical homogeneity of the participant group there were also some individual differences.

The prescribing of prisms in clinical practice

The use of prisms in cases of decompensated heterophoria is an established treatment modality. The clinical literature lacks consensus upon the appropriate use of prisms, and fails to provide the necessary evidence base. While the experimental literature can guide the practitioner, the lack of double-blind, placebo-controlled clinical studies needs to be addressed.

Role of ocular convergence in the Romberg quotient

The Romberg test generally shows that postural stability is better with eyes open than eyes closed; the Romberg quotient (RQ) is generally 2.5. This study examines the possible role of vergence angle on the RQ. Eighteen young (25.3+/-2.7 years) and 17 old (61.6+/-4.4 years) subjects were required to fixate a target at 40 cm or at 200 cm inducing different vergence angle (i.e. 8.6 degrees and 1.7 degrees, respectively) either with eyes open or closed. Postural stability of subjects was measured with force platform (TechnoConcept). The RQ was about 2 at 40 cm but dropped to 1 at 200 cm. In a second experiment, 15 subjects (26.7+/-5.5 years) run the Romberg test with eye movement measures (Chronos). Subjects were required to fixate a target placed at 20 cm, 40 cm, 90 cm, 200 cm or 350 cm either in light or in dark. The RQ at 20 cm and 40 cm was close to 2 and dropped to 1 at 90 cm and beyond. In parallel, the vergence angle at 20 cm and 40 cm changed significantly between light and dark, while at 90 cm and beyond it was stable (about 2 degrees both in light and dark). The distance had a significant effect on the co-variance between the RQ based on the anterior-posterior sway, and the change of vergence angle. We suggest different ways of control of posture according to the viewing distance: at near distance and in the light, the CNS uses vision coupled with oculo-motor convergence signals (efferent and afferent) leading to high RQ; at intermediate and far distances, it would use mostly internal signals (vestibular, proprioceptive, somatosensory), and similarly in the light and in the dark.

The forced vergence cover test and phoria adaptation

Phoria adaptation (PA) provides innervation to help maintain the correct vergence posture for binocularly viewing objects. Once fusion is disrupted, such as is required for measuring a (dissociated) phoria, this innervation is slowly depleted. Thus, extended periods of monocular occlusion can be required to dissipate PA and reveal the full extent of the phoria. Two versions of a forced vergence modification of the alternating cover test (CT) have been proposed to rapidly show the full phoria. We evaluated the ability of these forced vergence CTs (FVCT-1 and FVCT-2) to deplete the PA induced by a 15 min adaptation period to base out prism. In both experiments, the CT followed by the FVCT was performed before and after the adaptation period. In Experiment 1 (n = 13), the FVCT-1 was evaluated at 40 cm. Experiment 2 (n = 32) evaluated the FVCT-2 at 4 m. In Experiments 1 and 2, the difference between pre- and post-adaptation CTs showed significant PA occurred during the adaptation period (7.8(Delta), p < 0.0005, and 5.4(Delta), p < 0.0005 respectively). In Experiment 1, the FVCT-1 did not reveal a larger phoria than the CT before (mean difference: 0.4(Delta), p = 0.34) or after (no difference for all subjects) the adaptation period. Thus, the FVCT-1 did not alter PA. In Experiment 2, the FVCT-2 did show a shift in the phoria compared to the CT. However, this shift was found to be equivalent before and after the adaptation period (mean difference in shift: 0.22(Delta), 95% CI: -0.52 to 0.96(Delta)). Thus, the FVCT-2 shifts the phoria a constant amount independent of the amount of PA present. We conclude that neither FVCT's behaviour is dependent on the PA present. Thus, these procedures are unlikely to be effective clinical procedures for revealing the full magnitude of the phoria.

Cross-coupling between accommodation and convergence is optimized for a broad range of directions and distances of gaze

Accommodation and convergence systems are cross-coupled so that stimulation of one system produces responses by both systems. Ideally, the cross-coupled responses of accommodation and convergence match their respective stimuli. When expressed in diopters and meter angles, respectively, stimuli for accommodation and convergence are equal in the mid-sagittal plane when viewed with symmetrical convergence, where historically, the gains of the cross coupling (AC/A and CA/C ratios) have been quantified. However, targets at non-zero azimuth angles, when viewed with asymmetric convergence, present unequal stimuli for accommodation and convergence. Are the cross-links between the two systems calibrated to compensate for stimulus mismatches that increase with gaze-azimuth? We measured the response AC/A and stimulus CA/C ratios at zero azimuth, 17.5 and 30 deg of rightward gaze eccentricities with a Badal Optometer and Wheatstone-mirror haploscope. AC/A ratios were measured under open-loop convergence conditions along the iso-accommodation circle (locus of points that stimulate approximately equal amounts of accommodation to the two eyes at all azimuth angles). CA/C ratios were measured under open-loop accommodation conditions along the iso-vergence circle (locus of points that stimulate constant convergence at all azimuth angles). Our results show that the gain of accommodative-convergence (AC/A ratio) decreased and the bias of convergence-accommodation increased at the 30 deg gaze eccentricity. These changes are in directions that compensate for stimulus mismatches caused by spatial-viewing geometry during asymmetric convergence.

Response pattern asymmetry of binocular vision vertical fusion amplitudes in a normal population

PURPOSE

To compare the maximum vertical fusion amplitudes in vertical directions (response pattern by respective higher eye), to investigate for possible asymmetry.

METHODS

Vertical fusion amplitude (VFA) was measured in one hundred normal adults with normal single binocular vision using a computer based device that produced a gradually increasing, but optically distant test distance, Vertical fusion amplitudes in the vertical left- over-right (L/R, elevation of the left eye above the right eye) pattern direction were compared to the vertical fusion amplitudes in the vertical right-over-left direction pattern(R/L).

RESULTS

The mean VFA was 4.08 +/-1.01 prism diopters, with vertical fusion amplitudes of 4.40 +/-1.44 prism diopters in the L/R direction and 3.75 +/-1.19 prism diopters in the R/L direction. There was no association between ocular dominance and the direction of greater VFA. Asymmetry in the vertical fusion response was found, with 77/100 subjects showing greater than a 10% difference between the means of the L/R and R/L measurements. The group with asymmetry had 17% greater mean VFA than the symmetric group.

CONCLUSION

Normal adults frequently have asymmetric directional vertical fusion amplitudes. The asymmetry appears to be due to the contribution of the direction with the greater VFA, rather than the result of both alternatives. These results are intriguing and bear further investigation. Possible explanations my be asymmetry of orbital anatomy or functional asymmetry of either muscular or neuronal origin. They do not appear to be due to the relative ocular dominance. Inherent VFA asymmetry should therefore be considered in all forms of vergence testing in the vertical direction.

Involvement of the cerebellar dorsal vermis in vergence eye movements in monkeys

Frontal-eyed primates use both smooth pursuit in frontoparallel planes (frontal pursuit) and pursuit-in-depth (vergence pursuit) to track objects moving slowly in 3-dimensional (3D) space. To understand how 3D-pursuit signals represented in frontal eye fields are processed further by downstream pathways, monkeys were trained to pursue a spot moving in 3D virtual space. We characterized pursuit signals in Purkinje (P) cells in the cerebellar dorsal vermis and their discharge during vergence pursuit. In 41% of pursuit P-cells, 3D-pursuit signals were observed. However, the majority of vermal-pursuit P-cells (59%) discharged either for vergence pursuit (43%) or for frontal pursuit (16%). Moreover, the majority (74%) of vergence-related P-cells carried convergence signals, displaying both vergence eye position and velocity sensitivity during sinusoidal and step vergence eye movements. Preferred frontal-pursuit directions of vergence + frontal-pursuit P-cells were distributed in all directions. Most pursuit P-cells (73%) discharged before the onset of vergence eye movements; the median lead time was 16 ms. Muscimol infusion into the sites where convergence P-cells were recorded resulted in a reduction of peak convergence eye velocity, of initial convergence eye acceleration, and of frontal-pursuit eye velocity. These results suggest involvement of the dorsal vermis in conversion of 3D-pursuit signals and in convergence eye movements.

The vergence eye movements induced by radial optic flow: some fundamental properties of the underlying local-motion detectors

Radial optic flow applied to large random dot patterns is known to elicit horizontal vergence eye movements at short latency, expansion causing convergence and contraction causing divergence: the Radial Flow Vergence Response (RFVR). We elicited RFVRs in human subjects by applying radial motion to concentric circular patterns whose radial luminance modulation was that of a square wave lacking the fundamental: the missing fundamental (mf) stimulus. The radial motion consisted of successive 1/4-wavelength steps, so that the overall pattern and the 4n+1 harmonics (where n=integer) underwent radial expansion (or contraction), whereas the 4n-1 harmonics--including the strongest Fourier component (the 3rd harmonic)--underwent the opposite radial motion. Radial motion commenced only after the subject had fixated the center of the pattern. The initial RFVRs were always in the direction of the 3rd harmonic, e.g., expansion of the mf pattern causing divergence. Thus, the earliest RFVRs were strongly dependent on the motion of the major Fourier component, consistent with early spatio-temporal filtering prior to motion detection, as in the well-known energy model of motion analysis. If the radial mf stimulus was reduced to just two competing harmonics--the 3rd and 5th--the initial RFVRs showed a nonlinear dependence on their relative contrasts: when the two harmonics differed in contrast by more than about an octave then the one with the higher contrast completely dominated the RFVRs and the one with lower contrast lost its influence: winner-take-all. We suggest that these nonlinear interactions result from mutual inhibition between the mechanisms sensing the motion of the different competing harmonics. If single radial-flow steps were used, a brief inter-stimulus interval resulted in reversed RFVRs, consistent with the idea that the motion detectors mediating these responses receive a visual input whose temporal impulse response function is strongly biphasic. Lastly, all of these characteristics of the RFVR, which we attribute to the early cortical processing of visual motion, are known to be shared by the Ocular Following Response (OFR)--a conjugate tracking (version) response elicited at short-latency by linear motion-and even the quantitative details are generally very similar. Thus, although the RFVR and OFR respond to very different patterns of global motion-radial vs. linear-they have very similar local spatiotemporal properties as though mediated by the same low-level, local-motion detectors, which we suggest are in the striate cortex.

Postural control in dyslexic and non-dyslexic children

Postural control relies to visual-motion processing (afferent or efferent) and this is thought to be deficient in dyslexics. There is a controversy between clinic and fundamental studies as to the presence of posture abnormalities in dyslexics. To explore further this issue, this study examines posture stability in quite stance in 13 dyslexics (mean age: 13.5 years) and in 13 non-dyslexics (mean age: 13 years). Experiment 1 shows that, similarly to adults and elderly, all children (dyslexics and non-dyslexics), present better stability at near distance (i.e. smaller surface area of the COP, smaller lateral and antero-posterior oscillations). This could be due to reduced angular size of retinal motion signals at far, but also to convergence relaxation. Importantly, the surface area of the COP, lateral and antero-posterior oscillations are significantly higher in dyslexics. Experiment 2 examines posture stability while subjects make active vergence movements between a far and a near target. For many dyslexics, moving the eyes back and forth in depth rather improved postural stability. The only significant difference was that the lateral oscillations were still higher in dyslexics. Experiment 3 uses eye movement recordings (video-oculography) and demonstrates that dyslexics have problems with maintaining stable the angle of vergence for a prolonged period. We conclude that mild postural instability may exist in dyslexics but it could be improved by oculomotor and attention processes.

Stereoacuity and binocular visual acuity in prism-induced exodeviation

BACKGROUND

Intermittent exotropia may be controlled by accommodative or motor convergence. Previous studies have reported that reduced binocular visual acuity in intermittent exotropia is due to the accommodation required to control the deviation. To test this hypothesis, we simulated convergence stress by inducing exodeviations in normal volunteers to investigate whether the transition from nonfused to fused is associated with a gradual or immediate transition in stereoacuity and binocular visual acuity.

METHODS

Convergence stress was induced in 25 visually normal adults with 40(Delta) base-out prism and reduced stepwise in increments of 5(Delta) until 20(Delta), and 2(Delta) thereafter. Stereoacuity (Frisby Davis Distance [FD2] and the Distance Randot [DR]) and binocular visual acuity were measured at each step. For each subject, the recovery of fine stereoacuity (< or =60 arcsec) was categorized as immediate (nil to fine) or gradual (nil to moderate to fine).

RESULTS

Twenty-four of 25 (96%) showed gradual recovery of fine stereoacuity on either FD2 or DR. Median binocular visual acuity at baseline, first level of fusion, and subsequent levels was 20/15.

CONCLUSIONS

Under convergence stress, the transition from nonfused to fused is accompanied by a gradual recovery of fine stereoacuity in most individuals, consistent with some studies of patients with intermittent exotropia. Nevertheless, this degradation of stereoacuity was not associated with decreased binocular visual acuity, suggesting that accommodative convergence may not be recruited to restore and maintain binocularity under conditions of convergence stress.

Dry dissection of disparity divergence eye movements using independent component analysis

Dry dissection, a concept developed by Lawrence Stark, includes a variety of techniques designed to isolate internal neural control components by using cleverly designed stimulus or measurement protocols. As envisioned by Stark, the concept applies only to motor systems that have multiple stimulus inputs and/or response behaviors. A new application of independent component analysis (ICA) can be used to extend the dry dissection concept to identify motor components from a single, isolated response. It is only necessary that multiple responses can be obtained to the same stimulus. This "ensemble ICA" technique is well suited to analyze various eye movement behaviors as even isolated motor systems often include multiple control processes. Here we apply ensemble ICA to vergence eye movements: the inward (convergence) or outward (divergence) turning of the eyes that allows us to view images at various distances. Previous studies concerning the dynamics of convergence and divergence eye movements have produced varied, sometimes contradictory, results: most studies report that convergence is considerably faster than divergence, but opposite results have also been reported. Experimental results have shown that the dynamics of divergence movements depend on the initial vergence position while those of convergence do not: divergence eye movements in response to targets initially near to the subject can attain peak velocities twice that of those driven by more distant targets. To determine the underlying cause of this behavior, ensemble ICA was applied to divergence responses. Results show that both convergence and divergence contain a sustained (step-like) and a transient (pulse-like) control component, but the amplitude of the transient component in divergence is dependent on initial stimulus position.

An investigation into the mechanisms causing antipodean strabismus

BACKGROUND

Antipodean strabismus is a rare clinical entity in which a patient manifests an esotropia when fixating with one eye and an exotropia when fixating with the other eye. It has been described in the settings of marked uncorrected anisometropia, dissociated strabismus or combinations of paresis, and mechanical restriction of eye movement.

METHODS

A retrospective review of four patients with antipodean strabismus.

RESULTS

All patients demonstrated a unique and uncommon pattern in which there was esotropia with one eye fixating and exotropia with the other eye fixating. None of the patients demonstrated anisometropia or signs of dissociated horizontal deviation. One patient developed antipodean strabismus after prior surgery to correct a traumatic sixth nerve palsy. Another patient had an associated pseudotumor cerebri. The other two patients had no pertinent medical history and, on clinical examination, demonstrated markedly asymmetric accommodative convergence/accommodation (AC/A) ratios.

CONCLUSIONS

Antipodean strabismus is an atypical heterotropia, which can be associated with a variety of clinical findings. This article demonstrates the uniqueness of this clinical entity and illustrates the first association of this pattern with a markedly asymmetric AC/A ratio.

Variation of binocular-vertical fusion amplitude with convergence

PURPOSE

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.

METHODS

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.

RESULTS

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.

CONCLUSIONS

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.