VS 117 (Dr. Schor)
February 24, 1998
by MAC SHUI
Conjugate eye movement: Rotation of the eyes in the same direction.
Disconjugate eye movement: Rotation of the eyes in opposite directions.
This is also referred to as Vergence.

Vergence comes in many forms:

Cyclo-vergence: Both eyes twist nasally or both eyes twist temporally.
Incyclovergence: The upper edges of both cornea are turned inward.
Excyclovergence: The upper edges of both cornea are turned outward.
Vertical vergence: One eye rotates upward; the other eye rotates downward
Horizontal vergence: One eye rotates right; the other eye rotates left.

Quantifying measurements for vergence

MDs like to use "Degrees"
ODs like to use "Prism Diopters" (D)
Prism Diopter of convergence (D) = 100 tan q
where q is the vergence angle x
displacement
q (cm)
100 cm
(Recall that xD prism diopters = x cm displacement from a distance of 100 cm)

PhDs like to use "Meter Angles" (MA)
By definition: MA = 1
viewing distance (m)
By geometry,

q tan q = IPD
viewing viewing distance
distance
(VD) By incorporating this relationship into the equation for
IPD prism diopter, we get:

Prism diopter of convergence (D) = 100 x IPD
VD
then (D) = IPD (cm)
VD (m)

So (D) = MA (m-1) x IPD (cm)

This is very handy in clinical practice. With any given viewing distance and IPD, the amount of convergence needed to center in on the target can be easily calculated.
E.g. Target at viewing distance of 33 cm
Patient with IPD of 60 mm
Calculate: MA = 1 / 0.33m = 3 m-1
IPD = 6 cm
D = 3 x 6 = 18D convergence needed

Technically, MA involves the viewing distance measured from the center of rotation of the eye whereas the accommodative stimulus involves viewing distance as measured from the cornea. However, for viewing distances beyond 20 cm, this difference is negligible.

Maddox components of convergence:
Tonic
Proximal
Fusional
Cross-coupling (Accommodative Vergence) ß Today’s emphasis

Isovergence circle:
If you maintain a fixed vergence distance while varying your version (direction of gaze), the positions of fixation points will lie on an isovergence circle (similar to the Vieth-Muller Circle in VS118)

Accommodative Vergence

When you cover the left eye and present the open right eye with an accommodative demand, the left eye will converge even though it receives no visual stimuli. In fact, convergence will actually begin earlier (i.e. shorter latency period) than accommodation. Accommodation is very sluggish (300-400 msec latency period). Therefore, although the innervation to stimulate accommodation and convergence is simultaneous, the actual responses are not.

Measuring Accommodative Vergence:
An "open-loop" measure is used. An "open-loop" for convergence means that we remove any feedback to the eye regarding vergence (i.e. there is not binocular disparity). We cover one eye and then stimulate accommodation in the open eye. We then observe any coupled vergence response in the covered eye.

Theoretically, to view a target at a distance of 1 m, we would need 1D of accommodation and 6D of convergence (D = 1 m-1 x 6 cm). So ideally, we should get 6D of convergence for every 1D of accommodation. So the Accommodative Convergence / Accommodation (AC/A) Ratio should be 6/1. However, typically AC/A is observed to be lower (~3.5/1 to 4/1).

There are two notations of the AC/A ratio (stimulus and response). The stimulus AC/A ratio has the accommodative stimulus in the denominator while the response AC/A ratio has the accommodative response in the denominator. Since the accommodative response is usually less than its stimulus, the stimulus AC/A ratio is usually greater than the response AC/A ratio.

The lag of accommodation plays a part in making the stimulus AC/A appear lower. Accommodative response (AR) is usually less than the accommodative demand. This lag translates into less stimulation for accommodative convergence. Since it is accommodative demand (not AR) that is used in the stimulus AC/A calculation. Even if the accommodative response is taken into account, the AC/A ratio is lower than the ideal for reasons we do not understand.

Synergies: Two motor responses that are linked to one another
The activation of accommodation stimulates convergence (accommodative convergence).
The activation of convergence stimulates accommodation.(convergence accommodation)

Convergence accommodation

Measuring Convergence accommodation:

"Open-loop" for accommodation. This means we remove feedback (blur) to the eye regarding accommodation. We stimulate convergence binocularly with the accommodative loop opened and then observe any coupled accommodation that is associated with convergence.

How can we create a stimulus for convergence that does not provide a blur stimulus for accommodation?

Pinhole? NO. Pinhole does remove the stimulus for accommodation but it’s too tiny to do retinoscopy to determine accommodative response.

Another option: use a big coarse blurred target line. The blur eliminates high spatial frequency detail so that accommodation is not triggered. Normally blur caused by a lens preserves coarse detail and only reduces contrast of fine detail. We stimulate convergence and then use retinoscopy to measure the associated convergence accommodation.

By measuring the diopters of convergence accommodation achieved through a meter-angle of vergence, we get the CA/C Ratio.

Ideally, CA/C = 1D/1 MA. Whereas actual AC/A is lower than its ideal, the actual CA/C ratio is very close to its ideal. However, after about age 20, CA/C starts to drop due to less amplitude of accommodation.

Distribution of AC/A ratios
Even though an AC/A of 6/1 is ideal, very few people exhibit this. The greatest percentage of subjects had stimulus AC/A ratios of 3.5/1. Therefore, any AC/A within the range of 2/1 to 5/1 would be considered "normal".
Due to the great variation in population AC/As, near phorias among individuals are much more variable than far phorias.

Quantifiying AC/A

There are two measures of AC/A:
1) Calculated measure:
AC/A = IPDcm + (PN - PF) / MA PN is near phoria
PF is far phoria
MA is in reference to near viewing
distance
e.g. Patient with 2 exo at far (-2)
3 eso at near (+3)
IPD = 60 mm = 6 cm
Near viewing distance is 40 cm (MA = 1/0.4m = 2.5)
Calculate AC/A = 6 cm + [+3 - (-2)] / 2.5
AC/A = 8/1

e.g. Patient with 4 eso at far (+4)
2 exo at near (-2)
IPD = 6 cm
Near viewing distance is 33 cm
Calculate: AC/A = 6 cm + [-2 - 4] / 3
AC/A = 4/1

In general, going from far to near,
If there’s more eso(i.e. less exo) at near, then AC/A is higher than ideal
If there’s more exo(i.e. less eso) at near, then AC/A is lower than ideal
In general, most people have more exo at near than at far.

2) Gradient measure
AC/A = Change in near phoria
Change in accommodation stimulus

To determine the gradient measure, we first measure the near phoria. We then place a lens in front of the open eye to stimulate accommodation. We now measure the near phoria again and determine the change in near phoria.

By this method we are stimulating accommodation with a lens. In the calculated measure, we are stimulating accommodation by switching fixation between far and near viewing distances. Proximal convergence is present in the near target response but not the far target response in the calculated AC/A whereas the gradient AC/A measures are all taken at one viewing distance that has the same proximal vergence for all measures of the phoria. Therefore, the changes in phoria with viewing distance are affected more by proximal vergence than the changes in phoria at a fixed viewing distance stimulated by lenses. Therefore, the calculated AC/A ratio tends to be higher than gradient measures.

Linearity of AC/A

In Graph C above, prior to the leveling off of accommodative response, the curve is strikingly straight. The reciprocal of the slope equals the response AC/A. This demonstrates that AC/A is a highly linear function. Beyond the linear portion of the curves, the amplitude of accommodation is reached so accommodative response levels off. However, innervation for accommodative convergence continues as the eye tries really hard to accommodate so converge increases dramatically.

Stability of AC/A
The stability of AC/A is important if we wish to prescribe prisms or lenses (the prescription would be useless if AC/A was constantly changing with time).

AC/A actually only varies up to +0.25 D. Thus, AC/A is a remarkably stable and reliable function.

Cross-links of Accommodation and Convergence
If you understand the cross-links in this diagram, the rest of the lecture will seem easy to understand.. (It’s much easier than it sounded during lecture.) Just keep referring to this diagram:

There are two types of accommodation and convergence:
1) Optical-reflex (fast) accommodation
2) (Slow) Tonic accommodation adaptation

Usually we rely on Tonic accommodation to sustain accommodation with little effort. But if there is a quick change to the accommodative demand, Tonic accommodation is too slow to keep up so we switch over to utilizing Fast accommodation.

Fast accommodation stimulates accommodation in response to blur (as expected). In addition, it also stimulates accommodative convergence (AC). These stimuli can be stored up by the tonic vergence adaptation system so that it can continue stimulating vergence later after tonic accommodation takes over the response from fast optical reflex accommodation.

Tonic accommodation does NOT stimulate accommodative convergence.

Similarly, there are two types of convergence:
1) Fast fusion / disparity vergence
2) (Slow) Tonic vergence adaptation

Again, we usually rely on Tonic vergence to sustain convergence unless changing disparity demands call for a shift to Fast fusion/vergence.

Fast fusion/vergence stimulates vergence (as expected). In addition, it also stimulates convergence accommodation (CA). These stimuli can be stored up by the tonic accommodation adaptation system so that it can continue stimulating accommodation later after slow tonic vergence takes over for fast disparity vergence.

Tonic vergence does NOT stimulate convergence accommodation.

A good understanding of these cross links will help explain the characteristics of accommodative and convergence responses.

e.g. We cover the left eye (open the vergence loop) and suddenly introduce a lens to stimulate accommodation in the open right eye. Fast accommodation kicks in to respond. In the process it also stimulates AC in the covered left eye. Eventually, we discontinue Fast accommodation as Tonic accommodation takes over. Yet, even when Fast accommodation is turned off, the left eye continues to converge … How?? Answer: AC stimulated by Fast accommodation was stored by the Tonic vergence adaptation system. So even when Fast accommodation was turned off, Tonic vergence continued to sustain AC originally stimulated by the accommodative system.

Can we change the AC/A ratio?
Although AC/A is very stable and reliable it can still change if we vary certain parameters.
Factors that affect or change AC/A:

1) Drugs such as cycloplegics (e.g. atropine)
Atropine dilates the pupil and blocks parasympathetic innervation for accommodation.
With accommodation disabled, AC/A shoots up as sky-high as 20/1. It also takes a long time (20hrs!) to return to baseline. In clinic we use Tropicamide which also increases the AC/A temporarily by making it more difficult to accommodate.

2) Velocity of accommodative response
When the eye must accommodate quickly, AC/A is high because the response is controlled mainly by the fast component of accommodation
When the eye must accommodate slowly, AC/A is low because the response is controlled mainly by the slow tonic component of accommodation
e.g. When a target is brought slowly in over 8 sec then slowly back out,
AC/A is essentially zero.

Side note: Similarly, the velocity of convergence affects CA/C.
When the convergence stimulus is changing quickly, CA/C is high

3) Age
As we lose accommodation amplitude with age, AC/A shoots up. As accommodation approaches zero, AC/A approaches infinity. At the same time the CA/C ratio decreases with age because of the onset of presbyopia.

4) Vision training

Telestereoscope: by special orientation of mirrors, this essentially gives you a wider IPD and thus better stereopsis because it exaggerates disparity. It stimulates less accommodation and more convergence. This causes the AC/A ratio to increased to almost double. By wearing this apparatus for just 1 hour, you can increase your AC/A from 4/1 to 7/1.

Lens rock/Prism rock flippers:
Can be used for pediatric patients whose AC/A is abnormally high. Normal people rely on tonic adaptation for accommodation rather than fast accommodation to sustain the near response. But patients with abnormally high AC/A ratios, there is little or no tonic accommodation so that they rely entirely on Fast accommodation to control the optical power of the eye. Excessive Fast accommodation stimulates excessive accommodative convergence, hence causing an abnormally high AC/A. These patients have much greater adaptation of vergence which stores the excessive accommodative convergence. The object of the exercises is to reduce the adaptation of vergence so that the excessive accommodative vergence wont be stored.
Lens rock/Prism rock involves flippers with base out and base in prisms. The eye is stimulated to converge for 1 sec and then diverge for 1 sec. This training will fatigue the tonic vergence adaptation so that it does not store AC signals from Fast accommodation anymore. Ultimately this reduces AC/A.

Patients can also have abnormally low AC/A ratios if they have excessive tonic adaptation of accommodation. The AC/A can be increased to normal values if exercises cause a reduction of tonic adaptable accommodation.
Accommodative rock/flipper exercises which change accommodation from +2 to -2 once every 2 seconds can be used to reduce adaptable accommodation and cause the patient to rely on fast accommodation. This causes the AC/A to increase from a low value to a normal value. This however is not a long lasting solution. After training is discontinued, AC/A returns to baseline.

AC/A and CA/C tend to be reciprocally related.
a) High AC/A is associated with Low CA/C. How? A strong tonic vergence adaptation contributes to increased accommodative convergence. In addition, because there is less reliance on fast fusion (vergence), there is less stimulation of convergence accommodation.

b) Low AC/A is associated with a High CA/C. How? A strong tonic accommodation adaptation contributes to increased convergence accommodation. In addition, because there is less reliance on fast accommodation, there is less stimulus for accommodative convergence.
Etiology of accommodative esotropia (developmental factors that cause the AC/A ratio to increase to abnormal values and cause esotropia.
There are two forms of accommodative esotropia (refractive and non-refractive)
Refractive accommodative esotropia occurs in pediatric patients that have inherited high hyperopia and a normal AC/A ratio.
Non Refractive accommodative esotropia occurs in patients with high AC/
a ratios and normal refractive errors.
The infant that is born with high amounts of hyperopia can compensate for retinal image blur by:

a) Using tonic accommodation adaptation to clear the blur. But without the blur, the developing eye is not stimulated to grow and become emmetropic so it stays abnormally short. As the child grows older, tonic accommodation eventually gives out, resulting in latent hyperopia that is controlled by fast accommodation. (Now it’s blurry but growth has already stopped).
Problem: Latent Hyperopia which stimulates accommodative convergence and esotropia.

b) Suppressing Tonic accommodation adaptation. Blur is sustained to stimulate normal eye growth. However, by suppressing Tonic accommodation adaptation, the child relies predominantly on Fast accommodation. Tonic accommodation remains permanently suppressed. Fast accommodation stimulates Accommodative convergence signals so that AC/A becomes abnormally high and esotropia results.
Problem: AC/A too high

Clinical solution: Prescribe (+) Lenses but undercorrect so that some blur is sustained to stimulate normal eye growth. Then monitor closely and taper off as eye is emmetropizing (becoming more emmetropic). Good because: Eye grows normally, Tonic accommodation is not suppressed so AC/A is normal and there is no latent hyperopia.