Key words: accommodation, convergence, adaptation, gradient, calculated, tonic, phasic

Outline
XII. Near Response: Pupil constriction, Accommodation and Vergence. 

Part III: Cross-coupling (of accommodation and convergence)

• Introduction (Examples of cross-coupling)
  cyclotorsion and convergence, AC/A, CA/C, cross-axis VOR, VOR gain & vergence, compensation for noncomitance
   
• Measurement of AC/A Ratio
  Gradient- stimulus and response measures
  Calculated
   
• Linearity
   
• Stability
  age affects
  drug affects
  Adpatation
   
• Dynamics
  Phasic stimulation
  interactions with tonic adaptation
   
• Innervation of convergence and accommodation
   

Introduction
Frequently many motor responses occur simultaneously when we perform complex tasks such as seeing. We need to aim the eyes in the direction of the target to permit foveation, converge correctly to align targets on corresponding retinal points, control the focus to sharpen the foveal image, control pupil size to adjust luminance, and compensate for head and body movements during fixation. All of these tasks are performed simultaneously whenever we change fixation from one object to another. To help coordinate these motor responses, the brain stem has many associated reflexes such that stimulation of just one of these motor activities causes the others to respond appropriately as though they had been stimulated directly. Generally these cross-coupled responses serve to make coarse adjustments in associated gaze shifts and then retinotopic cues are used to refine the response.

The most well known of the visual cross-coupling responses is the near triad whereby stimulation of either convergence or accommodation causes changes in convergence, accommodation and pupil size. This association is called a synkinesis. This is not the only synkinesis in the visual system. Also the VOR gain is related to the state of convergence. As you translate your head laterally, the amount your eyes need to counter rotate to maintain exact fixation increases as viewing distance decreases. The VOR automatically increases with convergence.  Another cross-coupling response occurs between cyclovergence and eye elevation. When we look down at the ground plane our eyes automatically excycloverge and when we look up they automatically incycloverge. This helps us fuse the ground and ceiling planes which are declinated and inclinated with respect to the visual axes in these vertical positions. Another example is the counter roll of the eyes when the head rolls to one side, stimulating the otoliths. Clearly there are many other examples outside of vision that involve coordination of heart contraction, digestion, and postural control.

In Optometry, we are primarily concerned with the cross-coupling between accommodation and convergence. When accommodation is stimulated alone by occluding one eye, the covered eye still converges via a coupling referred to as the AC/A ratio. Similarly, if we converge with pinhole pupils we stimulate vergence but accommodation also responds. This cross-link is referred to as the CA/C ratio. These ratios are normally tuned to be very accurate and appropriate for the geometry of our eye separation, but occasionally something goes wrong and the ratios are either too high or too low. This causes imbalance of convergence and accommodation such that we may over-converge when we accommodate because of a high AC/A ratio. This induces an esophoria. If we are also hyperopic, it may induce an esotropia. When this occurs one of the main treatments is to prescribe bifocals to reduce the accommodative stimulus and the resulting esophoria. However many surgeons, particularly in Europe, like to do surgery on these patients. The result is that they create exotropes at far after they diverge the eyes because the eyes are too divergent when accommodation is not stimulated. It is very important to understand the source of the esotropia in a child to avoid making this mistake. Now letís look at the normal status of the AC/A.

Measuring Amplitude of the AC/A
The AC/A ratio is measured by two techniques called the calculated AC/A and the gradient AC/A. The gradient AC/A is measured by occluding one eye, placing a minus one lenses over the open eye and measuring the change in phoria as shown by deviation of the covered eye. This can be done by alternate cover test or a diplopia test such as red lens or Maddox rod. The resulting change in convergence stimulated by the change of accommodation quantifies the gradient AC/A ratio.

The calculated AC/A ratio is measured by comparing the near and far phorias using the equation:
calculated AC/A ratio =IPD + (near phoria - far phoria)/MA
 
IPD is the interpupillary distance measured in centimeters. Phoria is measured in prism diopters. MA (meter angles) = 1/near target distance measured in meters. Ideally, the phoria is zero at all distances. In the ideal case, the calculated AC/A = IPD in centimeters. For example if you converge to 1 meter, your eyes form an angle of convergence of 6 prism diopters (assuming an IPD of 60mm) or whatever your IPD is in prism diopters. If you are more eso at near than far, the ideal AC/A is increased by the additional change in phoria between the far and near test distances divided by the change in accommodative stimulus from far to near. Generally, the calculated AC/A is slightly higher than the gradient because of the addition of proximal convergence to the measurement of the phoria.

The gradient AC/A can be specified as the ratio of the change in phoria divided by the accommodative stimulus, in which case it is called the stimulus gradient AC/A ratio, or by the ratio of the change in phoria divided by the accommodative response, in which case it is called the response AC/A ratio. The normal value of the stimulus ratio is 3.6 prism diopters/D accommodation and the normal response AC/A ratio is 4.0 prism diopters/D. The difference between stimulus and response AC/A is due to the lazy lag of accommodation which reduces the denominator of the response ratio.

If both CA/C ratio and AC/A ratios are velocity sensitive, you may wonder what keeps the AC and CA active during steady fixation when there are no changes in stimuli to accommodation or convergence. Focus and eye alignment are maintained by an adaptation response of both systems. The accommodative system adapts to replace CA and convergence adapts to replace AC. This is shown in the cross-link block diagram. An imbalance of adaptablilty of accommodation and convergence can lead to abnormally large and small cross-link ratios that interfere with normal binocular vision.

Abnormal values of CA/C ratio and AC/A ratios tend to be reciprocally related. A person with a high AC/A usually has a low CA/C. This reciprocal relationship is due to a single causal factor which is an imbalance of tonic adaptation of accommodation and convergence. For example, assume that accommodation is highly adaptable but convergence is not. This means that CA will build up a tonic aftereffect of accommodation but AC will not build up a tonic aftereffect of convergence. In addition, due to the lack of adaptation of convergence, the phasic component of vergence must always be active and this causes more than normal stimulation of CA. The result is a very high CA/C ratio and very low AC/A ratio.

Similarly, if vergence is very adaptable and accommodation is not, the lack of accommodation adaptation causes phasic accommodation to be overly active and cause excess innervation of AC. This is exacerbated by the robust adaptation of convergence that enhances the already large AC. The highly adaptable convergence will lower phasic vergence and reduce the CA to below-normal values. One treatment is to perform eye exercises to enhance the weakened adapter so that it matches the strength of the stronger adapter and balances the interactions between accommodation and convergence.

Innervation of Convergence
Both convergence and accommodation are stimulated by the oculomotor nucleus. This nucleus receives pre-motor inputs from a variety of supranuclear regions of the brainstem and cerebellum. It used to be thought there was a convergence center called the nucleus of Perlia near the Edigner Westfall nucleus but this has not been verified. Instead there is a main source of innervation from a region dorsal to the III in the mesencephalon called the supraoculomotor nucleus. This nucleus contains cells for convergence and accommodation that are homologous to the pause, burst and tonic cells described earlier for saccades. Burst cells encode vergence velocity and tonic cells code vergence amplitude or position. There are both convergence and divergence burst neurons but convergent cells are more abundant. The tonic cells have firing rates that vary with vergence amplitude. The firing rate is related only to vergence response and not to right or left eye version position, nor to vertical eye position. The response of a given cell is plotted as a function of vergence angle. It shows that each cell has a slope or sensitivity and threshold. The thresholds are all within a few degrees of orthophoria and the slopes are all very similar. Presumably the tonic cells represent the neural integration of the burst cells. Some of these tonic cells exhibit prism adaptation aftereffects. They continue to respond when the disparity stimulus had been removed by covering one eye and at the same time there is a convergence aftereffect. Some cells respond to disparity, others to accommodation and some to both. These cells represent the final common pathway for all vergence responses to disparity, accommodation, and probably proximity and tonicity.
Two other regions have also been found with cells that are responsive during accommodation and vergence. On is in the posterior interposed nucleus of the cerebellum (one of the deep cerebellar nuclei) and the other is in the NRTP, nucleus reticularis tegminti pontis. Not much else is known about them.

Clinical Application of Maddox Components
Chapter 22 describes how the various Maddox components are measured and plotted on a single graph to illustrate their additivity. The graph is used to determine how a given patient utilizes the various components of convergence to obtain clear single binocular vision. The figure below is a graph showing a plot of convergence on the horizontal axis and accommodation on the vertical axis. The circles represent the limit of clear single vision and the squares represent an extension of the range of single vision by exerting accommodative vergence. The result is a greater range of singleness, but with blurred vision.

Review Questions:

1.How are the gradient and calculated AC/A ratios computed and how do they differ in amplitude ?
2.What are the stimulus and response AC/A ratios.
3.How does the CA/C ratio change with age?
4.What is the effect of a parasympatholytic drug on the AC/A ratio?

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