George K. Hung

A Dual-Mode Dynamic Model of the Vergence Eye Movement System

The disparity vergence eye movement system, long thought to be a simple continuous feedback system, has recently been shown to exhibit more complex dual-mode slow and fast responses. A model has been developed which simulates this behavior. The slow component accounts for the smooth following of slowly moving stimuli. The fast component has samnpling and prediction mechanisms which account for the staircase-like step responses to fast ramp stimuli. Model simulation responses to pulse, step, step-pulse, ramp, and sinusoidal stimuli show good fit to these diverse experimental results. This robust and comprehensive model forms the basis for further understanding of the dynamic controlling mechanisms of the vergence system.

Proximal contribution to a linear static model of accommodation and vergence.

To determine the influence of target proximity on accommodation and vergence under both open- (OL) and closed-loop (CL) viewing conditions, a static interactive feedback model, which included proximal accommodation (PA) and proximal vergence (PV) inputs, was developed and analysed quantitatively. It was based on an earlier static dual-interactive feedback model of accommodation and vergence. The proximal inputs were added to both the accommodative and vergence loops at the output of the respective controllers. The values of the PA and PV gains were obtained from experimental dual-OL data. The model equations were analysed over a stimulus range of 1 to 6 D (or MA). It was found that under the dual-OL condition, the contribution of PA to the overall accommodative output ranged from 42.5 to 81.6%, whereas the contribution of PV to the overall vergence output ranged from 56.1 to 88.5%. In contrast, under all other stimulus conditions, with the exception of the PA contribution to the accommodative output under the Aol, Vcl condition (26.5-41.0%), the relative contributions were much smaller, ranging from 0.04 to approximately 7.0%. In particular, under the dual-CL condition, representing the normal binocular visual feedback condition, the relative contributions were only 4.0 and 0.04% for PA and PV, respectively. Thus, although the relative contributions of PA and PV were large under the dual-OL condition, they were generally very small under the various CL conditions that simulated more naturalistic viewing situations. Nevertheless, proximity may still play an important role by providing cues for attaining coordinated and harmonious motor responses under specific viewing conditions.

Convergence and divergence exhibit different response characteristics to symmetric stimuli

The dynamic characteristics of horizontal convergence and divergence eye movement responses to symmetric stimuli were examined. Binocular eye movements were recorded in five, visually normal adult subjects using the infrared reflection technique for symmetric convergent and divergent blur-free, disparity-only, step stimuli of 2, 4, 8, 12, and 16 deg. The main sequence as well as other temporal parameters including latency, time-to-peak velocity, time constant, and total duration were analyzed. A number of fundamental differences in the response characteristics were found between convergence and divergence. First, the slope of the peak velocity vs amplitude curve was approximately twice as high for convergence than divergence. The results are consistent with neurophysiological findings in monkeys and most findings in humans. Second, the initial fast component for convergence exhibited a larger amplitude than for divergence. This may reflect differences in central neural gain for convergence and divergence. And, third, all temporally related components were shorter for convergence than divergence. These findings provide an overall framework for vergence control and suggest fundamental differences in neural processing delays and neural controller pathways for convergence and divergence.

Accommodative stimulus/response function in human amblyopia

Three parameters are essential to describe static accommodative behavior in a comprehensive, quantitative manner: the slope of the stimulus/response curve, the depth of focus, and the tonic response. These parameters were obtained in amblyopes, former amblyopes, strabismics without amblyopia, and normals. Results showed that the accommodative response in the amblyopic eye was characterized by a reduction in the slope of the stimulus/response curve and increased depth of focus. Similar abnormalities but of lesser magnitude were found in the non-dominant eye of some former amblyopes and some strabismics without amblyopia. Orthoptic therapy always increased the slope of the stimulus/response curve in the amblyopic eye. We believe that the reduced accommodative responses found in amblyopic eyes reflect a primary sensory loss over the central retinal region that occurs as a result of prolonged, early, abnormal visual experience associated with the presence of strabismus and/or anisometropia.

Adaptation model of accommodation and vergence

Both accommodation and vergence have been shown to exhibit adaptation after extended near viewing. Normally, when the stimulus to accommodation is removed, the accommodation system returns rapidly towards its ionic position. However, if the stimulus is removed after an extended focusing effort, the decay is much slower. A similar effect can be observed in the vergence system. After prolonged wearing of horizontal prisms, blockage of one eye results in a much slower decay of the vergence output towards its tonic value. No previous models have been shown to simulate quantitatively these effects. An interactive dual‐feedback model of accommodation and vergence was developed to simulate the adaptive behaviour found experimentally. The unique feature of the model is that the output of each controller drives a dynamic adaptive component whose output governs the time constant of the controller. The model was able to simulate the rapid and slow decays following short and long viewing intervals m each of the accommodative and vergence systems. It also simulated adaptation during alternate binocular and monocular viewing under the accommodation closed‐loop condition. Thus, this model can serve as the basis for detailed quantitative evaluation of adaptive behaviour in the accommodation and vergence systems.

Tonic accommodation: a review I. Basic aspects

In the absence of an adequate visual stimulus, accommodation adopts an intermediate position of ∼ I D. Since this position was believed to reflect the level of tonic innervation to the ciliary muscle, this response has been termed tonic accommodation (TA). Part 1 of this review will consider various aspects of this parameter, including its reference to closed‐loop accommodative function and autonomic physiology. In addition, both the methods of measurement and appropriate terminology for this function will be discussed. It is concluded that the response, which becomes apparent under so‐called ‘stimulus‐free’ conditions, in fact probably represents an aggregate response resulting from multiple, non‐optical stimuli. Thus the designation tonic accommodation may not be appropriate, since it fails to describe accurately the heterogeneous composition of the stimulus‐free accommodative response. An associated paper (to be published as part II of this review) will examine accommodative adaptation and both clinical aspects of TA and adaptation of TA.

Initial control component in disparity vergence eye movements

Recent experimental evidence indicates that a portion of the oculomotor response to disparity stimulation is functionally open‐loop; that is, the response occurs without the aid of visual feedback. To investigate the stimulus features that elicit or influence this dynamic movement, convergence responses to a step, a step followed by target disappearance, and a pulse followed by target disappearance were obtained from four subjects using infrared oculography. The target was a thin vertical line (0.25) either 2 or 10 in height. Stimuli having different amplitudes (1. 2, 4 and 8) and disappearance times (50. 100 and 200ms) were selected randomly along with occasional divergent stimuli to minimize prediction and voluntary vergence. Experiments showed that the dynamic characteristics of the initial portion of the response were essentially the same, even when the target disappeared before the movement took place. The magnitude of the initial response depended on the stimulus amplitude, but was not influenced by either stimulus duration or target height. For example, stimulus durations as short as 50 ms elicited responses similar to those caused by standard steps. The initial response was shown to be active over a well‐defined time period of about 200 ms. after which the response appears to be mediated by a visually‐guided control component. These results support the recently developed dual‐mode theory of vergence control in which an initial preprogrammed (open‐loop) control component is followed by a feedback (closed‐loop) controlled component which reduces any remaining disparity.

Tonic accommodation: a review. II. Accommodative adaptation and clinical aspects.

Part I of this review considered basic aspects of tonic accommodation (TA). i.e. the accommodative response observed under degraded stimulus conditions. Part II considers accommodative adaptation, i.e. the apparent change in TA following periods of sustained fixation, and clinical aspects of both baseline TA and accommodative adaptation. It is suggested that the apparent post‐task shift in TA reflects the slow rate of decay of the stimulus‐mediated adaptive accommodative response, while the actual level of tonic innervation to the ciliary muscle remains relatively constant. The clinical implications of both TA and accommodative adaptation are discussed with regard to night, space and instrument myopia and refractive error development, notably nearwork‐induced myopia. It is concluded that the evidence for any association between this form of myopia and either TA or accommodative adaptation is equivocal, and furthermore it seems likely that TA plays only a minor role in influencing the closed‐loop steady‐state accommodative response.

Dynamics of the human eyeblink.

&NA; High‐speed photography of eyeblinks in 4 subjects provided displacement and velocity time functions. The results from dynamic measurements made with a mechanical transducer connected physically to the upper eyelid gave estimates of the passive spring constant (Kp = 1.5 gmf/mm) and the passive viscosity (Bp = 0.09 gmf ‐ sec/mm) of the eyelid. Noting the similarity between the reciprocal‐innervation mechanisms in the eyelid and the eye‐movement systems, a mathematical eyelid model was derived based on the well‐known eye‐movement model and using similar ideal mechanical‐element representations. The model‐simulation time course shows the essential characteristics of an eyeblink and suggests that the force program consists of reciprocally acting pulse forces during the downblink, and pulsestep forces during the upblink. When 1 mm of lid displacement is equated with 5 deg of eyeball rotation and when the main sequences for lid movements and for time‐optimal saccadic eye movements are compared, the eyeblinks are not found to be time optimal for their various amplitudes.

Static vergence and accommodation: population norms and orthoptics effects

The steady-state characteristics of the accommodation and vergence systems can be described by a model with six major oculomotor parameters. These include the system biases (tonic vergence and accommodation) and forward-loop gains (vergence and accommodative gains), as well as the interactive system gains (AC/A and CA/C ratios). We investigated these parameters in two populations: (1) 22 visually-normal asymptomatic individuals, and (2) 21 visually-abnormal symptomatic individuals before and after conventional orthoptic therapy. Two parameters related to system gain differentiated between the symptomatic and asymptomatic individuals: the slope of the fixation disparity curve with accommodation open-looped and the slope of the accommodative response/stimulus curve. Following orthoptic therapy, 4 static model parameters and 1 dynamic clinical parameter showed changes toward the normal mean; this included tonic accommodation, slope of the fixation disparity curve with accommodation closed-loop (2.5D), slope of the accommodative response/stimulus curve, the CA/C ratio, and the ± 2D monocular accommodative flipper rate.