Pulse-step models of control strategies for dynamic ocular accommodation and disaccommodation

BCLA CLEAR presbyopia: Mechanism and optics

With over a billion adults worldwide currently affected, presbyopia remains a ubiquitous, global problem. Despite over a century of study, the precise mechanism of ocular accommodation and presbyopia progression remains a topic of debate. Accordingly, this narrative review outlines the lenticular and extralenticular components of accommodation together with the impact of age on the accommodative apparatus, neural control of accommodation, models of accommodation, the impact of presbyopia on retinal image quality, and both historic and contemporary theories of presbyopia.

Seeing the future: Predictive control in neural models of ocular accommodation

Ocular accommodation is the process of adjusting the eye's crystalline lens so as to bring the retinal image into sharp focus. The major stimulus to accommodation is therefore retinal defocus, and in essence, the job of accommodative control is to send a signal to the ciliary muscle which will minimize the magnitude of defocus. In this article, we first provide a tutorial introduction to control theory to aid vision scientists without this background. We then present a unified model of accommodative control that explains properties of the accommodative response for a wide range of accommodative stimuli. Following previous work, we conclude that most aspects of accommodation are well explained by dual integral control, with a “fast” or “phasic” integrator enabling response to rapid changes in demand, which hands over control to a “slow” or “tonic” integrator which maintains the response to steady demand. Control is complicated by the sensorimotor latencies within the system, which delay both information about defocus and the accommodation changes made in response, and by the sluggish response of the motor plant. These can be overcome by incorporating a Smith predictor, whereby the system predicts the delayed sensory consequences of its own motor actions. For the first time, we show that critically-damped dual integral control with a Smith predictor accounts for adaptation effects as well as for the gain and phase for sinusoidal oscillations in demand. In addition, we propose a novel proportional-control signal to account for the power spectrum of accommodative microfluctuations during steady fixation, which may be important in hunting for optimal focus, and for the nonlinear resonance observed for low-amplitude, high-frequency input. Complete Matlab/Simulink code implementing the model is provided at https://doi.org/10.25405/data.ncl.14945550.

Objectively-based vergence and accommodative dynamics in mild traumatic brain injury (mTBI): A mini review

Vergence and accommodation have been critical areas of investigation in those with mild traumatic brain injury (mTBI). In this mini-review, the major laboratory studies in the area using objective assessment of vergence and accommodative dynamics in this population are discussed. These include the basic findings, their diagnostic and therapeutic implications, potential study limitations, and suggested future research directions. All studies provided important new information, and insights, into the area. There were two key outcomes of the reviewed studies common to both the vergence and accommodative systems in those with mTBI. First, most dynamic parameter's responsivity at baseline was abnormal: it was slowed, delayed, and/or inaccurate as compared to the normative control data. Second, most of the abnormal dynamic parameter's responsivity could be remediated, at least in part, following a short period of oculomotor-based vision therapy, thus demonstrating considerable residual neuroplasticity in the damaged, human brain.

Lags and leads of accommodation in humans: Fact or fiction?

The focusing response of the human eye — accommodation — exhibits errors known as lags and leads. Lags occur when the stimulus is near and the eye appears to focus farther than the stimulus. Leads occur with far stimuli where the eye appears to focus nearer than the stimulus. We used objective and subjective measures simultaneously to determine where the eye is best focused. The objective measures were made with a wavefront sensor and an autorefractor, both of which analyze light reflected from the retina. These measures exhibited typical accommodative errors, mostly lags. The subjective measure was visual acuity, which of course depends not only on the eye's optics but also on photoreception and neural processing of the retinal image. The subjective measure revealed much smaller errors. Acuity was maximized at or very close to the distance of the accommodative stimulus. Thus, accommodation is accurate in terms of maximizing visual performance.

The pulse: transient fMRI signal increases in subcortical arousal systems during transitions in attention

Studies of attention emphasize cortical circuits for salience monitoring and top-down control. However, subcortical arousal systems have a major influence on dynamic cortical state. We hypothesize that task-related increases in attention begin with a "pulse" in subcortical arousal and cortical attention networks, which are reflected indirectly through transient fMRI signals. We conducted general linear model and model-free analyses of fMRI data from two cohorts and tasks with mixed block and event-related design. 46 adolescent subjects at our center and 362 normal adults from the Human Connectome Project participated. We identified a core shared network of transient fMRI increases in subcortical arousal and cortical salience/attention networks across cohorts and tasks. Specifically, we observed a transient pulse of fMRI increases both at task block onset and with individual task events in subcortical arousal areas including midbrain tegmentum, thalamus, nucleus basalis and striatum; cortical-subcortical salience network regions including the anterior insula/claustrum and anterior cingulate cortex/supplementary motor area; in dorsal attention network regions including dorsolateral frontal cortex and inferior parietal lobule; as well as in motor regions including cerebellum, and left hemisphere hand primary motor cortex. The transient pulse of fMRI increases in subcortical and cortical arousal and attention networks was consistent across tasks and study populations, whereas sustained activity in these same networks was more variable. The function of the transient pulse in these networks is unknown. However, given its anatomical distribution, it could participate in a neuromodulatory surge of activity in multiple parallel neurotransmitter systems facilitating dynamic changes in conscious attention.

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.

(Disparity-Driven) Accommodation Response Contributes to Perceived Depth

When looking at objects at various distances in the physical space, the accommodation and vergence systems adjust their parameters to provide a single and clear vision of the world. Subtended muscle activity provides oculomotor cues that can contribute to the perception of depth and distance. While several studies have outlined the role of vergence in distance perception, little is known about the contribution of its concommitant accommodation component. It is possible to unravel the role of each of these physiological systems by placing observers in a situation where there is a conflict between accommodation and vergence distances. We thus sought to determine the contribution of each response system to perceived depth by simultaneously measuring vergence and accommodation while participants judged the depth of 3D stimuli. The distance conflict decreased depth constancy for stimulus displayed with negative disparity steps (divergence). Although vergence was unaffected by the stimulus distance, accommodation responses were significantly reduced when the stimulus was displayed with negative disparities. Our results show that biases in perceived depth follow undershoots in the disparity-driven accommodation response. These findings suggest that accommodation responses (i.e., from oculomotor information) can contribute to perceived depth.

Is blur sensitivity altered in children with progressive myopia?

School aged children with progressive myopia show large accommodative lags to blur only cue which is suggestive of a large depth of focus (DOF). While DOF measures are lacking in this age group, their blur detection and discrimination capacities appear to be similar to their non-myopic peers. Accordingly, the current study quantified DOF and blur detection ability in progressive myopic children showing large accommodative lags compared to their non-myopic peers and adults. Blur sensitivity measures were taken from 12 children (8-13 years, 6 myopes and 6 emmetropes) and 6 adults (20-35 years). DOF was quantified using step changes in the lens induced defocus while the subjects viewed a high contrast target through a Badal lens at either 2 or 4D demand. Blur detection thresholds (BDT) were tested using a similar high contrast target in a 2-alternate forced-choice paradigm (2AFC) at both the demands. In addition to the large accommodative lags, micro fluctuations and DOF were significantly larger in myopic children compared to the other groups. However, BDTs were similar across the three groups. When limited to blur cues, the findings of a large DOF coupled with large response lags suggests that myopes are less sensitive to retinal defocus. However, in agreement to a previous study, refractive error had no influence on their BDTs suggesting that the reduced sensitivity to the defocus in a myopic eye appears to be compensated by some form of an adjustment in the higher visual processes to preserve the subjective percept even with a poor retinal image quality.

Are high lags of accommodation in myopic children due to motor deficits?

Children with a progressing myopia exhibit an abnormal pattern of high accommodative lags coupled with high accommodative convergence (AC/A) and high accommodative adaptation. This is not predicted by the current models of accommodation and vergence. Reduced accommodative plant gain and reduced sensitivity to blur have been suggested as potential causes for this abnormal behavior. These etiologies were tested by altering parameters (sensory, controller and plant gains) in the Simulink model of accommodation. Predictions were then compared to the static and dynamic blur accommodation (BA) measures taken using a Badal optical system on 12 children (6 emmetropes and 6 myopes, 8-13years) and 6 adults (20-35years). Other critical parameters such as CA/C, AC/A, and accommodative adaptation were also measured. Usable BA responses were classified as either typical or atypical. Typical accommodation data confirmed the abnormal pattern of myopia along with an unchanged CA/C. Main sequence relationship remained invariant between myopic and nonmyopic children. An overall reduction was noted in the response dynamics such as peak velocity and acceleration with age. Neither a reduced plant gain nor reduced blur sensitivity could predict the abnormal accommodative behavior. A model adjustment reflecting a reduced accommodative sensory gain (ASG) coupled with an increased AC cross-link gain and reduced vergence adaptive gain does predict the empirical findings. Empirical measures also showed a greater frequency of errors in accommodative response generation (atypical responses) in both myopic and control children compared to adults.

Effect of oculomotor rehabilitation on accommodative responsivity in mild traumatic brain injury

Accommodative dysfunction is a common oculomotor sequelae of mild traumatic brain injury (mTBI). This study evaluated a range of dynamic (objective) and static (subjective) measures of accommodation in 12 nonstrabismic individuals with mTBI and near vision-related symptoms before and after oculomotor training (OMT) and placebo (P) training (6 wk, two sessions per week, 3 h of training each). Following OMT, the dynamics of accommodation improved markedly. Clinically, there was a significant increase in the maximum accommodative amplitude both monocularly and binocularly. In addition, the near vision symptoms reduced along with improved visual attention. None of the measures were found to change significantly following P training. These results provide evidence for a significant positive effect of the accommodatively based OMT on accommodative responsivity. Such improvement is suggestive of oculomotor learning, demonstrating considerable residual brain-visual system plasticity in the adult compromised brain.

Revisiting the impact of phenylephrine hydrochloride on static and dynamic accommodation

Purpose:

Phenylephrine hydrochloride (PHCl), a commonly used mydriatic agent, causes a small but significant deterioration of accommodation. The relative roles of pharmacology and optics in this deterioration, however, remain unascertained. The study determined the combined impact of PHCl concentration (pharmacology) and pupil size (optics) on the static and dynamic characteristics of accommodation.

Materials and Methods:

A total of 16 emmetropic Indian adults viewed a high-contrast visual target that switched between 67 and 33 cm viewing distance (1.5D stimulus) with their right eye (left eye occluded using infrared transmitting filter) through natural pupils and through 8, 6, 4, and 1 mm diameter artificial pupils. This protocol was repeated once without PHCl and once each with 2.5%, 5%, and 10% PHCl. Consensual accommodation of the left eye was recorded using infrared photorefraction (60 Hz).

Results:

Relative to no PHCl, the horizontal pupil diameter of left eye was significantly larger (P < 0.001) and the response magnitude and peak velocity of accommodation and disaccommodation were modestly but significantly smaller (P < 0.02 for all) for all concentrations of PHCl tested. There was no significant difference in these parameters across the three drug concentrations (P > 0.4 for all). The response magnitude and peak velocity also decreased significantly with pupil diameter, at similar rates for the no PHCl and the three PHCl conditions (P < 0.001 for all).

Conclusion:

The reduction in accommodative performance with all drug concentrations and with pupil diameter suggests independent roles of pharmacology and optics in determining accommodative performance with PHCl. The reduction in accommodative performance is, however, modest and may be clinically irrelevant in Indian eyes.

Processing blur of conflicting stimuli during the latency and onset of accommodation

The accommodative response (AR) to changes in dioptric accommodative stimulus (AS) during the latency period and onset of accommodation was investigated. Participants monocularly observed one period of a square wave in AS, with a 2-D baseline and mean, and amplitude 1 D or 2 D; the period of the square wave ranged from 0.10 s to 1.00 s; both increases and decreases were used for the first step in AS. At periods of 0.30s and longer, accommodation was found to respond to both levels of the stimulus. Rapid retinal monitoring appeared to be taking place for such stimuli. The amplitudes of peaks in AR did not usually depend on whether a particular level of AS occurred first or second, but for 8/40 conditions, a significant difference was found, with a stronger response when the level of AS occurred second. Null or incorrect responses were also observed in many trials, possibly linked with the natural microfluctuations of accommodation. Minimum response times to the changes in AS were observed, which increased with decreasing period of the AS. The time interval between peaks in the AR decreased with decreasing period of the AS. The findings were consistent with a parallel processing model previously proposed for saccades, where input from a later change in stimulus may enter an element of the control system when that element has finished processing an earlier change. More than one change in stimulus may therefore be passing through the multi-element control system at a time.

Static and dynamic accommodation measured using the WAM-5500 Autorefractor

PURPOSE

This study was undertaken to compare static and dynamic accommodation measurements using the Grand Seiko WR-5500 (WAM) in young, phakic subjects.

METHODS

Fifteen subjects, aged 20 to 28 years (23.8 ± 0.58 years; mean ± SD years) participated. Accommodation was stimulated with printed text presented at various distances. In static mode, three measurements were taken for each stimulus amplitude. In dynamic mode, 5-Hz recordings were started, and subjects alternately looked through a transparent near chart and focused on a letter chart at 6 m for 5 seconds and then focused on the near letter chart for 5 seconds for a total of 30 seconds. After smoothing the raw data, the highest three individual values recorded in each 5-s interval of focusing at near were averaged for each stimulus amplitude. Analysis of variance and Bland-Altman analysis were used to compare the static and dynamic measurements. A calibration was performed with +3.00 to -10.00 D trial lenses behind an infrared filter, in 1.00 D steps in 5 of the 15 subjects.

RESULTS

Stimulus-response graphs from static and dynamic modes were not significantly different in the lower stimulus range (<5.00 D, p = 0.93), but differed significantly for the higher stimulus amplitudes (p = 0.0027). One of the 15 subjects showed a significant difference between the static and dynamic modes. Corresponding pupil diameter could be recorded along with the accommodation responses for the subjects, and pupil diameter decreased with increasing stimulus demand. Calibration curves for static and dynamic measurements were not significantly different from the 1:1 line or from each other (p = 0.32).

CONCLUSIONS

Slight differences between the dynamically and statically recorded response amplitudes were identified. This is attributed to differences in the accommodative responses in this population and not to the instrument performance. Dynamic measurement of accommodation and pupil constriction potentially provides additional useful information on the accommodative response other than simply the response amplitude.

Effect of temporal location of correction of monochromatic aberrations on the dynamic accommodation response

Dynamic correction of monochromatic aberrations of the eye is known to affect the accommodation response to a step change in stimulus vergence. We used an adaptive optics system to determine how the temporal location of the correction affects the response. The system consists of a Shack-Hartmann sensor sampling at 20 Hz and a 37-actuator piezoelectric deformable mirror. An extra sensing channel allows for an independent measure of the accommodation level of the eye. The accommodation response of four subjects was measured during a +/- 0.5 D step change in stimulus vergence whilst aberrations were corrected at various time locations. We found that continued correction of aberrations after the step change decreased the gain for disaccommodation, but increased the gain for accommodation. These results could be explained based on the initial lag of accommodation to the stimulus and changes in the level of aberrations before and after the stimulus step change. Future considerations for investigations of the effect of monochromatic aberrations on the dynamic accommodation response are discussed.

The first and second order dynamics of accommodative convergence and disparity convergence

Main sequences, the function describing the relationship between eye movement amplitude and velocity, have been used extensively in oculomotor research as an indicator of first-order dynamics yet it is difficult to find main sequence analyses for accommodative vergence or for disparity vergence in isolation when all mitigating factors have been well controlled and there are no studies in which accommodative vergence and disparity vergence main sequences have been generated for the same group of subjects. The present study measured main sequences in: (1) accommodative vergence with disparity vergence open loop, (2) disparity vergence with accommodation open loop, and (3) combinations of accommodative and disparity vergence. A dynamic AC/A ratio was defined and was found to be similar to the traditional static AC/A ratio. Vergence acceleration was measured for all conditions. A pulse-step model of accommodation and convergence was constructed to interpret the dynamics of the crosslinked interactions between the two systems. The model supports cross-coupling of both the pulse and step components and simulates the primary empirical findings that: (1) disparity vergence has a higher main sequence slope than accommodative vergence, (2) both accommodative and disparity vergence acceleration increase with response amplitude whereas accommodation acceleration does not.

Adaptive calibration of dynamic accommodation--implications for accommodating intraocular lenses

PURPOSE

When the aging lens is replaced with prosthetic accommodating intraocular lenses (IOLs), with effective viscoelasticities different from those of the natural lens, mismatches could arise between the neural control of accommodation and the biomechanical properties of the new lens. These mismatches could lead to either unstable oscillations or sluggishness of dynamic accommodation. Using computer simulations, we investigated whether optimal accommodative responses could be restored through recalibration of the neural control of accommodation. Using human experiments, we also investigated whether the accommodative system has the capacity for adaptive recalibration in response to changes in lens biomechanics.

METHODS

Dynamic performance of two accommodating IOL prototypes was simulated for a 45-year-old accommodative system, before and after neural recalibration, using a dynamic model of accommodation. Accommodating IOL I, a prototype for an injectable accommodating IOL, was less stiff and less viscous than the natural 45-year-old lens. Accommodating IOL II, a prototype for a translating accommodating IOL, was less stiff and more viscous than the natural 45-year-old lens. Short-term adaptive recalibration of dynamic accommodation was stimulated using a double-step adaptation paradigm that optically induced changes in neuromuscular effort mimicking responses to changes in lens biomechanics.

RESULTS

Model simulations indicate that the unstable oscillations or sluggishness of dynamic accommodation resulting from mismatches between neural control and lens biomechanics might be restored through neural recalibration.

CONCLUSIONS

Empirical measures reveal that the accommodative system is capable of adaptive recalibration in response to optical loads that simulate effects of changing lens biomechanics.

Edinger--Westphal stimulated accommodative dynamics in anesthetized, middle-aged rhesus monkeys

The relationships between peak velocity and amplitude of Edinger-Westphal (EW) stimulated accommodation and disaccommodation were investigated in anesthetized, middle-aged rhesus monkeys. Accommodative responses were recorded at 30Hz with infrared photorefraction. Peak velocity of accommodation and disaccommodation increased linearly with stimulus amplitude. Peak velocities of accommodation continued to increase with stimulus amplitudes greater than required to produce the maximum response. The peak velocity of disaccommodation did not further increase with supramaximal stimulus amplitudes beyond that achieved with maximal stimulus amplitudes. Although maximum accommodative response amplitude is reduced in older rhesus monkeys, within the methodological constraints of this study, older monkeys appear to achieve accommodative and disaccommodative peak velocities similar to adolescent monkeys for the same response amplitudes.

Effects of pharmacologically manipulated amplitude and starting point on edinger-westphal-stimulated accommodative dynamics in rhesus monkeys

PURPOSE

The aim of this study was to determine whether pharmacologically manipulated resting refraction, amplitude, and starting point affect accommodative and disaccommodative dynamics in anesthetized adolescent rhesus monkeys.

METHODS

Pilocarpine and atropine were applied topically to manipulate resting refraction, accommodative amplitude, starting point, and end point in two monkeys with permanent electrodes in the Edinger-Westphal nucleus. Accommodation was centrally stimulated with submaximal and maximal current amplitudes. Dynamic accommodative responses were measured with infrared photorefraction before and during the course of action of the drugs. Accommodative and disaccommodative dynamics were analyzed in terms of peak velocity as a function of amplitude, starting point, and end point.

RESULTS

Pilocarpine caused a myopic shift in resting refraction of 11.62 +/- 1.17 D. Centrally stimulated accommodative amplitude was 10.08 +/- 1.15 D before pilocarpine and 0.68 +/- 0.29 D after pilocarpine. Changes were found in accommodative dynamics as a function of starting point and in disaccommodative dynamics as a function of amplitude and end point. Accommodative amplitude was 11.25 +/- 0.18 D before atropine administration and 0.52 +/- 0.11 D after atropine administration. Accommodative dynamics as a function of amplitude were not substantially altered during the course of pilocarpine-induced accommodation or atropine-induced cycloplegia.

CONCLUSIONS

Accommodative response amplitude is reduced with pilocarpine by shifting the eye to a more myopic state and with atropine by cycloplegia. Pharmacologic manipulations showed that accommodative and disaccommodative dynamics in anesthetized monkeys depend on amplitude, starting point, and end point of the response and on the contributions of neural and receptor activity.

Dynamic performance of accommodating intraocular lenses in a negative feedback control system: a simulation-based study

A dynamic model of ocular accommodation is used to simulate the stability and dynamic performance of accommodating intraocular lenses (A-IOLs) that replace the hardened natural ocular lens that is unable to change focus. Accommodation simulations of an older eye with A-IOL materials having biomechanical properties of a younger eye illustrate overshoots and oscillations resulting from decreased visco-elasticity of the A-IOL. Stable dynamics of an A-IOL are restored by adaptation of phasic and tonic neural-control properties of accommodation. Simulations indicate that neural control must be recalibrated to avoid unstable dynamic accommodation with A-IOLs. An interactive web-model of A-IOL illustrating these properties is available at http://schorlab.berkeley.edu.

Initial destination of the disaccommodation step response

Peak velocity and peak acceleration of disaccommodation step responses remain invariant of response magnitude for a constant starting position and they increase linearly with proximity of starting position. This suggests that disaccommodation response is initiated towards an initial (default) destination and is switched mid-flight to attain the desired final destination. The dioptric location of initial destination was estimated from the x-intercept of regression of peak velocity on response starting position. The x-intercept correlated well with subject's cycloplegic refractive state and poorly with their dark focus of accommodation. Altering the dark focus by inducing fatigue in the accommodative system did not alter the x-intercept. These observations suggest that cycloplegic refractive state is a good behavioral correlate of initial destination of disaccommodation step responses.