Evolution of control system models of ocular accommodation, vergence and their interaction

Success rates, near-response patterns, and learning trends with free-fusion stereograms

Free-fusion stereograms are routinely used for demonstrating various stereoscopic effects. Yet, untrained observers find it challenging to perform this task. This study showed that only less than 1/3rd of sixty-one pre-presbyopic adults with normal binocular vision could successfully free-fuse random-dot image pairs and identify the stereoscopic shapes embedded in these patterns. Another one-third of participants performed the task with poor success rates, while the remaining could not perform the task. There was a clear dissociation of vergence and accommodative responses in participants who were successful with free-fusion, as recorded using a dynamic infrared eye tracker and photorefractor. Those in the unsuccessful cluster either showed strong vergence and accommodation or weak vergence and strong accommodation during the task. These response patterns, however, were specific to the free-fusion task because all these participants generated good convergence/accommodation to real-world targets and to conflicting vergence and accommodative demands stimulated with prisms or lenses. Task performance of the unsuccessful cluster also improved significantly following pharmacological paralysis of accommodation and reached the performance levels of the successful cluster. A minority of participants also appeared to progressively learn to dissociate one of the two directions of their vergence and accommodation crosslinks with repeated free-fusion trials. These results suggest that successful free-fusion might depend upon how well participants generate a combination of volitional and reflex vergence responses to large differences in disparity with conflicting static accommodative demands. Such responses would require that only one direction of the vergence-accommodation crosslinks be active at any given time. The sequence of near-responses could also be learnt through repeated trials to optimize task performance.

Recent understanding of binocular vision in the natural environment with clinical implications

Technological advances in recent decades have allowed us to measure both the information available to the visual system in the natural environment and the rich array of behaviors that the visual system supports. This review highlights the tasks undertaken by the binocular visual system in particular and how, for much of human activity, these tasks differ from those considered when an observer fixates a static target on the midline. The everyday motor and perceptual challenges involved in generating a stable, useful binocular percept of the environment are discussed, together with how these challenges are but minimally addressed by much of current clinical interpretation of binocular function. The implications for new technology, such as virtual reality, are also highlighted in terms of clinical and basic research application.

A covered eye fails to follow an object moving in depth

To clearly view approaching objects, the eyes rotate inward (vergence), and the intraocular lenses focus (accommodation). Current ocular control models assume both eyes are driven by unitary vergence and unitary accommodation commands that causally interact. The models typically describe discrete gaze shifts to non-accommodative targets performed under laboratory conditions. We probe these unitary signals using a physical stimulus moving in depth on the midline while recording vergence and accommodation simultaneously from both eyes in normal observers. Using monocular viewing, retinal disparity is removed, leaving only monocular cues for interpreting the object's motion in depth. The viewing eye always followed the target's motion. However, the occluded eye did not follow the target, and surprisingly, rotated out of phase with it. In contrast, accommodation in both eyes was synchronized with the target under monocular viewing. The results challenge existing unitary vergence command theories, and causal accommodation-vergence linkage.

Spasm of Near Reflex: Objective Assessment of the Near-Triad

Purpose

To characterize binocular steady-state accommodation, pupil and convergence responses (near triad) in spasm of near reflex (SNR) before and after optical and pharmacological intervention. To identify the putative source of SNR in the neural control schema of accommodation-vergence interaction using controls-engineering modeling.

Methods

Near-triad of 15 patients with SNR (9 to 23 years) was recorded using an infrared photorefractor at 2m viewing distance for 120s during clinical presentation, after optical fogging intended to relieve spasm, with cycloplegia, post-cycloplegia and long-term follow-up visits. Data were also collected without cycloplegia in 15 age-matched controls. Schor (1999) model was used to computationally simulate accommodation and vergence responses of controls and SNR.

Results

Both eyes of SNR exhibited significant myopia and refraction fluctuations (<1.0Hz) during clinical presentation [median (25^th to 75^th IQR) refraction: −1.7D (−3.2 to −0.8D); root mean squared (RMS) deviation: 1.1D (0.5 to 1.5D)], relative to controls [0.8D (−0.03 to 1.4D); 0.2D (0.1 to 0.3D)] (p < 0.001). These decreased after optical fogging, largely eliminated with cycloplegia and partially re-appeared in the post-cycloplegia and follow-up visits. SNR responses could be modeled by increasing the gain and decay time of tonic accommodation, vis-à-vis, controls. Pupil and convergence responses in SNR were similar to controls at all visits (p > 0.1).

Conclusions

Exaggerated fluctuations of steady-state accommodation may be a signature feature of SNR, even while their pupil and convergence responses may remain unaffected. These fluctuations may arise from the tonic accommodation controller, the properties of which could be potentially altered after optical fogging to relieve the disorder.

Ocular Focusing Behavior of the One-Eyed Child

PURPOSE

To compare the accommodative gain and pupil miosis of children with only one functional eye with the binocular and monocular accommodative and pupil responses of typically developing age-matched controls.

METHODS

Forty-one uniocular cases and 43 controls (3-14 years for both cohorts) watched a cartoon movie on an LCD screen that ramped between 90 and 30 cm, with a stable period of 4 seconds at both viewing distances. Cases performed the task with their only functional eye whereas controls performed the task binocularly and monocularly. A subset of subjects also repeated the task while reading 20/40-sized letters on the LCD screen. Accommodative and pupil responses were recorded using the Plusoptix PowerRef3 photorefractor.

RESULTS

Accommodative gain of cases [median (25th-75th IQR): 0.73 (0.60-0.85)] was larger than the monocular gain of controls [0.56 (0.47-0.79)] (P = .03). Both responses were lower than the binocular gain of controls [0.95 (0.81-1.11)] (P < .001). Uniocular pupil miosis of cases [0.14 mm (0.06-0.24 mm)] were similar to monocular [0.12 mm (0.05-0.29 mm)] (P = .69) and smaller than binocular [0.23 mm (0.14-0.34 mm)] (P < .001) responses of controls. The increase in accommodative gain from movie watching to reading was significant only for controls (P = .02) but not for cases (P = .15). Age and time of visual deficit were poorly correlated with accommodative gain and pupil miosis of cases (r ≤ 0.25; P ≥ .1 for all). Age was also poorly correlated with the binocular and monocular accommodative and pupil performance of controls (r ≤ -0.3; P = .33).

CONCLUSIONS

The accommodative gain of children with permanent loss of binocularity is in between the binocular and monocular gains of typically developing children. Their accommodative gains do not show any significant increase with a cognitively demanding task even while such a behavior is observed in controls. Pupil responses of uniocular children are similar to the monocular responses of age-matched controls.

Stereoscopic 3D Visual Discomfort Prediction: A Dynamic Accommodation and Vergence Interaction Model

The human visual system perceives 3D depth following sensing via its binocular optical system, a series of massively parallel processing units, and a feedback system that controls the mechanical dynamics of eye movements and the crystalline lens. The process of accommodation (focusing of the crystalline lens) and binocular vergence is controlled simultaneously and symbiotically via cross-coupled communication between the two critical depth computation modalities. The output responses of these two subsystems, which are induced by oculomotor control, are used in the computation of a clear and stable cyclopean 3D image from the input stimuli. These subsystems operate in smooth synchronicity when one is viewing the natural world; however, conflicting responses can occur when viewing stereoscopic 3D (S3D) content on fixed displays, causing physiological discomfort. If such occurrences could be predicted, then they might also be avoided (by modifying the acquisition process) or ameliorated (by changing the relative scene depth). Toward this end, we have developed a dynamic accommodation and vergence interaction (DAVI) model that successfully predicts visual discomfort on S3D images. The DAVI model is based on the phasic and reflex responses of the fast fusional vergence mechanism. Quantitative models of accommodation and vergence mismatches are used to conduct visual discomfort prediction. Other 3D perceptual elements are included in the proposed method, including sharpness limits imposed by the depth of focus and fusion limits implied by Panum's fusional area. The DAVI predictor is created by training a support vector machine on features derived from the proposed model and on recorded subjective assessment results. The experimental results are shown to produce accurate predictions of experienced visual discomfort.

Transfer Function Model of Physiological Mechanisms Underlying Temporal Visual Discomfort Experienced When Viewing Stereoscopic 3D Images

When viewing 3D images, a sense of visual comfort (or lack of) is developed in the brain over time as a function of binocular disparity and other 3D factors. We have developed a unique temporal visual discomfort model (TVDM) that we use to automatically predict the degree of discomfort felt when viewing stereoscopic 3D (S3D) images. This model is based on physiological mechanisms. In particular, TVDM is defined as a second-order system capturing relevant neuronal elements of the visual pathway from the eyes and through the brain. The experimental results demonstrate that the TVDM transfer function model produces predictions that correlate highly with the subjective visual discomfort scores contained in the large public databases. The transfer function analysis also yields insights into the perceptual processes that yield a stable S3D image.

Stereo vision and strabismus

Binocular stereopsis, or stereo vision, is the ability to derive information about how far away objects are, based solely on the relative positions of the object in the two eyes. It depends on both sensory and motor abilities. In this review, I briefly outline some of the neuronal mechanisms supporting stereo vision, and discuss how these are disrupted in strabismus. I explain, in some detail, current methods of assessing stereo vision and their pros and cons. Finally, I review the evidence supporting the clinical importance of such measurements.

Short exposure to telestereoscope affects the oculomotor system

Under natural viewing conditions, the accommodation and vergence systems adjust the focus and the binocular alignment of the eyes in response to changes in viewing distance. The two responses are linked via cross-coupling and proceed almost simultaneously. Some optical devices, such as virtual reality or helmet mounted displays, create an oculomotor conflict by modifying demands on both vergence and accommodation. Previous studies extensively investigated the effect of such a conflict on the cross-coupling between vergence and accommodation, but little is known about the plasticity of the whole oculomotor system. In the present study, an oculomotor conflict was induced by a telestereoscope which magnified the standard inter-pupillary separation threefold and thus increased the convergence demand while accommodation remained almost unchanged. The effect of a 10 min exposure was assessed via a series of optometric parameters selected on the basis of existing oculomotor models. Associated with subject's visual complaints, most of the oculomotor parameters tested were modified: there was (1) deterioration of stereoscopic threshold; (2) increase in AC/A ratio; (3) increase in near and far phorias; and (4) shift of the zone of clear and single binocular vision towards convergence. These results showed a change in gain of accommodative vergence and a shift of vergence reserves towards convergence in response to telestereoscopic viewing. The subject's binocular behaviour tended towards esophoria with convergence excess as confirmed by Sheard's and Percival's criteria. Such changes in oculomotor parameters support adaptive behaviour linked with telestereoscopic viewing.

Objective vs subjective measures of fixation disparity for short and long fixation periods

PURPOSE

Fixation disparity, i.e. the vergence error for stationary fusion stimuli, can be measured objectively with eye trackers and subjectively with nonius lines. Between these two measures, previous studies found differences that tended to be proportional to the amount of forced vergence, i.e. the discrepancy between vergence and accommodative stimulus. We investigate whether objective and subjective fixation disparity might be similar without forced vergence.

METHOD

We simultaneously measured fixation disparity with the EyeLink II system and with flashed dichoptic nonius lines in 17 subjects who observed targets at a vergence stimulus of 6 deg in an haploscope with 60 cm viewing distance.

RESULTS

We found individual differences in objective fixation disparity in a range of about 20 (eso) to -60 (exo) min arc which was considerably larger than the range of subjective fixation disparity. Results were similar for long fixation periods (about 15 s) and short fixation periods (about 1.5 s) between 5 deg saccadic gaze shifts. Further, objective fixation disparity was correlated with objective heterophoria, i.e. the vergence state without a fusion stimulus (r = 0.8, p < 0.001).

CONCLUSION

Subjective fixation disparity explained only about 25% of the inter-individual variability in objective fixation disparity. The discrepancy between these two measures might be explained by sensory shifts in retinal correspondence, also in the present condition without forced vergence.

Cues for the control of ocular accommodation and vergence during postnatal human development

Accommodation and vergence help maintain single and focused visual experience while an object moves in depth. The relative importance of retinal blur and disparity, the primary sensory cues to accommodation and vergence, is largely unknown during development; a period when growth of the eye and head necessitate continual recalibration of egocentric space. Here we measured the developmental importance of retinal disparity in 192 typically developing subjects (1.9 months to 46 years). Subjects viewed high-contrast cartoon targets with naturalistic spatial frequency spectra while their accommodation and vergence responses were measured from both eyes using a PowerRefractor. Accommodative gain was reduced during monocular viewing relative to full binocular viewing, even though the fixating eye generated comparable tracking eye movements in the two conditions. This result was consistent across three forms of monocular occlusion. The accommodative gain was lowest in infants and only reached adult levels by 7 to 10 years of age. As expected, the gain of vergence was also reduced in monocular conditions. When 4- to 6-year-old children read 20/40-sized letters, their monocular accommodative gain reached adult-like levels. In summary, binocular viewing appears necessary under naturalistic viewing conditions to generate full accommodation and vergence responses in typically developing humans.

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.

Accommodation and vergence latencies in human infants

PURPOSE

Achieving simultaneous single and clear visual experience during postnatal development depends on the temporal relationship between accommodation and vergence, in addition to their accuracies. This study was designed to examine one component of the dynamic relationship, the latencies of the responses.

METHODS

Infants and adults were tested in three conditions (i) binocular viewing of a target moving in depth at 5 cm/s (closed loop) (ii) monocular viewing of the same target (vergence open loop) (iii) binocular viewing of a low spatial frequency Difference of Gaussian target during a prism induced step change in retinal disparity (accommodation open loop).

RESULTS

There was a significant correlation between accommodation and vergence latencies in binocular conditions for infants from 7 to 23 weeks of age. Some of the infants, as young as 7 or 8 weeks, generated adult-like latencies of less than 0.5 s. Latencies in the vergence open loop and accommodation open loop conditions tended to be shorter for the stimulated system than the open loop system in both cases, and all latencies were typically less than 2 s across the infant age range.

CONCLUSIONS

Many infants between 7 and 23 weeks of age were able to generate accommodation and vergence responses with latencies of less than a second in full binocular closed loop conditions. The correlation between the latencies in the two systems suggests that they are limited by related factors from the earliest ages tested.

From biological models to the evolution of robot control systems

Attempts to formulate realistic models of the development of the human oculomotor control system have led to the conclusion that evolutionary factors play a crucial role. Moreover, even rather coarse simulations of the biological evolutionary processes result in adaptable control systems that are considerably more efficient than those designed by human researchers. In this paper I shall describe some of the aspects of these biological models that are likely to be useful for building robot control systems. In particular, I shall consider the evolution of appropriate innate starting points for learning/adaptation, patterns of learning rates that vary across different system components, learning rates that vary during the system's lifetime, and the relevance of individual differences across the evolved populations.

Neural network control systems that learn to perform appropriately

Setting up a neural network with a learning algorithm that determines how it can best operate is an efficient way to formulate control systems for many engineering applications, and is often much more feasible than direct programming. This paper examines three important aspects of this approach: the details of the cost function that is used with the gradient descent learning algorithm, how the resulting system depends on the initial pre-learning connection weights, and how the resulting system depends on the pattern of learning rates chosen for the different components of the system. We explore these issues by explicit simulations of a toy model that is a simplified abstraction of part of the human oculomotor control system. This allows us to compare our system with that produced by human evolution and development. We can then go on to consider how we might improve on the human system and apply what we have learnt to control systems that have no human analogue.

Gaze-shift dynamics in subjects with and without symptoms of convergence insufficiency: influence of monocular preference and the effect of training

We studied gaze-shift dynamics during several gaze-shift tasks and during reading, in five subjects with convergence insufficiency (C.I., a diminished ability to converge), and in ten subjects without C.I. Furthermore, we studied the effect of vergence training in order to verify previous claims that orthoptic exercises can improve vergence performance. We recorded binocular eye movements with the scleral coil technique. Subjects switched fixation between nearby and distant light emitting diodes (LEDs) arranged in isovergence arrays (distances 35 and 130 cm) in a dimly lit room. In both the C.I. and non-C.I. group, two classes of subjects occurred: vergence responders and saccadic responders. During pure vergence tasks, saccadic responders made saccades with no or little vergence; vergence responders made vergence movements with no or small saccadic components. In saccadic responders, fixation of nearby targets was monocular. Subjects with a preferred eye, according to our determination, used the preferred eye. The five C.I. subjects showed idiosyncratic responses with insufficient vergence during most trials. They all had a tendency to alternate fixation between the left and right eye. Vergence-version tasks always elicited larger vergence components than pure vergence tasks. During a reading task, vergence angles were more accurate than during gaze-shifts between LEDs. After the pre-training sessions, nine subjects (one of which had C.I.) practised a pure vergence task three times a day for at least 2 weeks. Vergence amplitudes of four of these subjects were larger after training. We conclude that vergence training can change oculomotor performance. Although C.I. is often associated with abnormal vergence dynamics, there are no typical C.I. vergence dynamics. Unstable monocular preferences may play a role in the aetiology of C.I.

Dynamics of horizontal vergence movements: interaction with horizontal and vertical saccades and relation with monocular preferences

We studied the dynamics of pure vergence shifts and vergence shifts combined with vertical and horizontal saccades. It is known from earlier studies that horizontal saccades accelerate horizontal vergence. We wanted to obtain a more complete picture of the interactions between version and vergence. Therefore we studied pure version (horizontal and vertical), pure vergence (divergence and convergence) and combinations of both in five adult subjects with normal binocular vision and little phoria (< 5 degrees). The visual targets were LED's in isovergence arrays presented at two distances (35 and 130 cm) in a dimly lit room. Two targets were continuously lit during each trial and gaze-shifts were paced by a metronome. The two subjects with a strong monocular preference made vergence eye movements together with small horizontal saccades during pure vergence tasks. The other subjects, who did not have a strong monocular preference, made pure vergence movements (without saccades). These findings, suggest that monocular preferences influence the oculomotor strategy during vergence tasks. Vergence was facilitated by both horizontal and vertical saccades but vergence peak-velocity during horizontal saccades was higher than during vertical saccades.