The "accommodative convergence / accommodation" (CA / A) ratio expresses the amount of convergence that each accommodating diopter induces. In normal individuals or in strabismic individuals with far / near concomitance, this relationship is always the same for a given interpupillary distance. In individuals with far / near incomitance, this ratio is higher than normal, if there is an excess of convergence, and lower, if there is a defect.

We will present this chapter in sections:

• Accommodation.
• Convergence.
• Stimuli for accommodation and convergence.
• AC / A ratio.
• CA / A techniques and notation.
• Importance of the CA / A measure.

ACCOMMODATION

Accommodation is the act by which the individual focuses on the retina the images of objects in close vision. This is achieved through a complex process, of which the fundamental thing is the increase in the refractive power of the lens, achieved by the contraction of the ciliary muscle, which causes an increase in the curvature of the anterior and posterior surfaces of the lens. The mechanism by which this occurs is still a matter of discussion.

Under normal conditions, accommodation is accompanied by miosis, changes in the depth of the anterior chamber (narrowing in the center and an increase in the periphery), slight phacodonesis, intracrystalline structural modifications, which increase the refractive index of the optical area, ocular convergence, etc. . Of these phenomena, the one that interests us is convergence.

An emmetropic eye in accommodative relaxation is focused to infinity; that eye is said to have its remote point at infinity. When the eye makes a maximum effort of accommodation, it is focused to a near point located at the minimum distance at which it is able to see clearly; such a point is the proximal point of that eye. The distance between the remote point and the next is known as the "accommodation path", and the accommodative power required for this path is measured in "diopters", according to the inverse of the focal length in meters: thus, an eye that makes an effort to focus at 25 Cm. (that is, at 24.84 cm, since the measurement starts at the main point of the eye), it is said that it accommodates 4 diopters (that is, 1: 0.25), and another that focuses at 0.20m, that accommodates 5 diopters (that is, 1: 0.20).

The accommodation capacity of an eye gradually decreases over the years according to the following table:

The progressive sclerosis of the lens determines that the effort of the ciliary muscle to achieve the same accommodation increased with age. This led FLIERINGA (1923) to introduce the concept of myo-diopter, the power of ciliary contraction necessary for the lens to accommodate 1 diopter. In children, this is not important, since the accommodation needs are far from their physiological limit, but in adults, especially from the second half of life, the ciliary effort to maintain accommodation becomes greater and can cause headache

Accommodation is more easily done when the eye looks inward, and better still, if it looks down and in, on the contrary, it is more difficult when looking up or to the side. The relationship between the action of the extrinsic oculomotor muscles and the accommodating stimuli was determined by RIPPLE (1952), who observed that in 56 emmetropic individuals their proximal point is closer when looking down and in than in any other position. Alluding to this, GIL del RIO (1957) stated that "if the determinations are made outside the usual reading positions, the results will not be exact. These facts must be taken into account and not directly use the results obtained by means of optotypes. of hand held in an unnatural fixed position, to study the anomalies of the near vision and of the accommodation, but the optotypes for the near vision must be used in the habitual position that is the natural one ”.

It is called "relative accommodation" (MÁRQUEZ RODRÍGUEZ, 1926) that which is more or less than what is necessary for a given convergence. For example, to converge and focus at 33 cm it may be that an individual has to accommodate 4 diopters, being hyperopic of 1 diopter, this person is said to have a positive relative accommodation of 1 diopter If, on the contrary, the individual is myopic of 1 diopter, he focuses at 33 cm with only 2 diopters of accommodation; that person has a negative relative accommodation of 1 diopter In a strabic child, the relative accommodation is usually eliminated by having his ametropia corrected, but this implies certain considerations when measuring convergence, as we will see in the next section.

CONVERGENCE

Ocular convergence is the coordinate movement by which the gaze axes of both eyes are directed to the same near point, so that under normal circumstances both foveas can collect the same image.

To converge, the eyes rotate around a place that is not in the center of the eye, nor is it an immobile and constant point throughout the convergence movement. This center of rotation is somewhat behind the anatomical center; in a normal adult eye with a 25mm axis, it is approximately 16mm behind the anterior pole; in a child eye with a 20mm axis, at 13mm. In myopic patients, the center of rotation is posterior to that of emmetropes.

When the convergence movement is made to fix a point located in the sagittal plane of the patient, both eyes converge in equal measure, this is the normalized position and the one that should be taken as a pattern for exploration in both orthotropic and strabic children. When the fixation point is displaced laterally, the need for convergence of each eye varies, and while in one it decreases, in the other it increases (asymmetric accommodation). When the lateralization of the point is equal to the naso-pupillary distance, one of the eyes remains immobile; when the lateralization of the point is greater than the naso-pupillary distance, one of the eyes even abducts (does not diverge), to maintain convergence.

A certain amount of convergence corresponds to each proximity distance, which is not the same for all cases, but is in relation to the ocular separation; obviously two eyes 4 centimeters apart have to converge less to look at 1 meter, than others 6 centimeters apart.

The convergence of each eye can be measured in sexagesimal degrees or in prismatic diopters. The measurement in sexagesimal degrees (°) expresses in 360ths of circumference the angle between the gaze axis in primary position and the gaze axis in convergence position. The measurement in prismatic diopters (∆) expresses according to the deviation that a light beam would experience that follows the line of sight in primary position, to pass to the line of sight in convergence, considering that 1∆ deflects the beam 1 cm at the distance 1 meter. These measurements are always made on the vertical planes that pass through the gaze axis, in both positions, since if they were made on the isolated axes, the downward rotation of the eyes would have to be considered, and this would introduce a new variant, according to this displacement was greater or lesser. According to the above, a child with an interpupillary distance of 5 centimeters, (mean naso-pupillary distance of 2.5 cm) to converge to 50 cm (that is, approximately 48.7 mm anterior to the anterior surface of the eye, since convergence starts at the center of rotation of the eyeball) it needs to converge 5.7 ° or 10∆ (in each eye 2.9 ° or 5∆.

Often the convergence measurement will be done with the patient corrected for his ametropia, to avoid relative accommodation, and this optical correction will almost always be with glasses, and rarely with contact lenses. When the convergence measurement is made with glasses, if the lenses are centered for the distance gaze, as is the norm, the near gaze will suffer a deviation due to the prismatic effect of the glasses, which will force to increase the convergence if the lenses they are positive, and to decrease it, if they are negative. This prismatic effect of glasses, whose possible clinical repercussion was already indicated by JAVAL in 1865, has been determined in lenses of different powers, material, refractive indices, decentration and oblique incidence of the gaze; It has been seen, as an approximate calculation / that a lens, for each diopter of power and millimeter of decentring, causes 0.1 ° deviation from the gaze axis; thus, a 3mm deviation in a 5 diopter lens causes 1.5 ° (that is, 0.1 x 3 x 5 = 1.5) of gaze deviation.

The measurement of convergence should be made taking the primary gaze as the initial position and the manual work as the final position, that is, with the eyes converging to a point near the sagittal plane (15-25 cm in children and 25- 35 in the adult), located 20-30 ° below the transverse plane of the face that passes through both eyes. The absolute perfection of the measurement would be achieved by making the measurement of the convergence position with the head slightly inclined, so that the proprioception of the cervical muscles provides the same information as in physiological circumstances of near vision. However, in clinical practice, the measurement of convergence is usually made with the head in an upright position and with the nearby fixation point at eye level.

ENCOURAGES FOR CONVERGENCE AND ACCOMMODATION

BEHR (1924) pointed out that there are some eye movements that have a purpose in themselves, and others that are an association induced secondarily to a primary movement. Convergence and accommodation are both of the first type, since they have their own independent stimuli and can be dissociated; for example, it is possible to read closely avoiding convergence with a nasal base prism, but maintaining spontaneous accommodation; as well as it is possible to read closely, avoiding accommodation with positive lenses, but maintaining spontaneous convergence. However, each of these movements (convergence and accommodation) is a reciprocal secondary stimulus for the other, that is, they are mutually of the second type to each other.

The stimuli that cause convergence and accommodation are of three types: specific, common and reciprocal.

Among the specific stimuli that induce convergence, the most important is the disparity of the retinal images of one eye and the other produced by a nearby object, when the eyes are parallel or not converging towards that object; To avoid this disparity and to achieve that the image of the object falls simultaneously in the foveola of both eyes, the convergence movement is triggered. On the other hand, the convergence of one eye induces an equal amount of convergence in the other eye, unless a higher order interferes.

Among the specific stimuli that induce accommodation, the most important is that of the diffusion circles of the defocused retinal images, which cause an accommodative adjustment and readjustment game, until the most contrasted image possible is achieved. The dispersive chromatic halos in the images also seem to stimulate accommodation: objects close to an unaccommodated eye are more focused on the cold band of the dispersive spectrum than on the warm one; this chromatic imbalance induces an accommodation that brings focus to the central band of the spectrum.

Among the common stimuli, which act simultaneously and independently, causing convergence and accommodation, the most important is the awareness that something close is being looked at. It also seems that the incidence in the eye of the light emitted by the object (the rays hit the eye with greater divergence the closer the object is) and its luminosity (with the same ambient light, the object is all the more luminous the closer it is). Furthermore, perhaps the specific stimuli (diffusion circles, dispersive chromatic halos, etc.) initiate a reflex arc whose afferent pathway is unique, but whose efferent pathway is multiple, mobilizing convergence, accommodation, and miosis.

Finally, there are reciprocal stimuli, convergence and accommodation, they stimulate each other. Contraction of the extrinsic eye muscles of the convergence triggers a ciliary contraction reflex, and vice versa.

In the current state of our knowledge, it is not clear to what extent both types of stimulus influence convergence and accommodation, and how they are regulated in normal and abnormal conditions, since the capacity for brain readjustment and adaptation is large and different for diverse individuals and situations. The difficulty in determining how much accommodation influences as a stimulus for convergence, makes clinical practice resort to an experimental exploration, from which conventional conclusions are drawn: to determine what accommodation influences convergence, we do to accommodate one eye in primary position and the convergence it causes in the other is measured, or it is made to accommodate on the sagittal plane (that is, converging) and the other eye is supposed to converge in equal measure; any excess or defect is assumed as a working hypothesis, which is due to the accommodative stimulus.

AC / A RATIO

Due to their specific, common and reciprocal stimuli, there is a clear quantitative relationship between convergence and accommodation movements.

In normal-emmetropic and orthophoric eyes, each amount of convergence corresponds to an appropriate amount of accommodation. With the first, it is achieved that both eyes look at a certain nearby point, so that the rays that come from it are refracted on the foveoles. With the second, that those rays that go to the foveoles form focused images on them.

The amount of accommodation varies according to a single parameter, which is the proximity of the fixation point: the closer it is, the more accommodation. The amount of convergence varies according to two parameters, which are the proximity of the fixation point and the separation of the eyes from each other: the closer the fixation point, and the more interocular separation, the more convergence. Once these variables are known (proximity of the object and interocular separation), constant relationships between accommodation and convergence can be established.

If we neglect the separation between the center of rotation of the eye (which would be the basis for convergence measurements) and the main object point of the eye (which would be the basis for accommodation measurements) as insignificant, we find that, for different separations binoculars, focus distances and accommodations, convergence needs are as listed in the table below:

Table: Normal accommodative convergence expressed in prismatic diopters according to gaze distance and accommodation (in the upper row) and naso-pupillary distance (in the left column). The right column shows the CA / A ratio deduced from each row.

 
From the consideration of this table the following general equation is extracted: "The normal convergence of an eye, expressed in prismatic diopters, is equal to the naso-pupillary distance, expressed in centimeters, multiplied by the accommodation, expressed in spherical diopters".

It is also extracted from the table that the CA / A ratio is linear, that is, for the same naso-pupillary distance, each diopter of accommodation that is added produces an equal increase in convergence. For example, a person with a naso pupillary distance of 2.8 cm. to look at infinity it does not converge; to look at 1 meter (1 accommodation diopter) converge with each eye 2.8∆; to look at 0.5 meters (2D) converge 2 x 2.8∆; to look at 0.33m (3D) converge 3 x 2.8, etc. This linearity has more or less irregular deviations in 20% of the individuals.

Throughout life, an individual's convergence increases as their naso-pupillary distance widens. This causes its CA / A ratio to grow in absolute values, ranging from 2∆ / 1D in children with a naso-pupillary distance of 2 cm to 3.5∆ / 1D in adults with a naso-pupillary distance of 3.5cm.

Cycloplegic drugs (atropine, homatropine, scopolamine, cyclopentolate, tropicamide) increase the CA / A ratio, since the cycloplegic patient sends an over stimulus to his ciliary muscle to achieve accommodation, and this over stimulus is accompanied by an over convergence; This is the reason why the angle of esotropia increases in many children when they are cycloplegic. Miotic drugs (pilocarpine, eserine) hardly modify the CA / A ratio.

EXPLORATION TECHNIQUES OF THE CA / A RELATIONSHIP

The CA / A ratio is explored clinically in two ways:

1. With the fixing eye in the primary position of the gaze.
   
   The strabic child is placed in free space or synoptophore with the fixating eye in primary position looking at a distant object, and the target angle of the strabic eye is determined. The object is then brought closer to the child, so that the child must accommodate to keep it in focus, which induces an increase in the deviation of the strabic eye, which is determined again. The AC / A ratio is the ratio of the magnification of the target angle divided by the diopters required to focus. This way of measuring AC / A is far from the standard situation, since it uses an asymmetric convergence in which the directing eye does not alter its position in front.
   
   Some authors are even further away from reality when, instead of bringing the object closer to the patient, to cause accommodation they keep it away, and force accommodation by placing negative lenses before their directing eye. This way of doing the measurement, which at first glance might seem the most exact, since they almost reduce the stimulus that triggers convergence to accommodation, is nevertheless the furthest from clinical reality since it dispenses with all the common stimuli of accommodation. and convergence.
2. With the fixing eye in a near vision position.
   
   Of the various possible ways, we expose here how the Viso goniometer uses it to execute it. The viso goniometer is a perimeter arc with a 180 ° circumference and a 20cm radius of curvature. In the center of the arc length the zero degree of gaze deviation has been marked, and to the right and left the remaining 90 ° (with their correspondence in prismatic diopters) on each side; extreme degrees may not be marked, as a strabismus will never reach them, but we prefer to maintain an arc length of 180 °, as it facilitates the centering of the patient's head. The 20 cm radius of curvature forces the patient to fix at that distance, making an accommodation of 5 diopters on his position in distance vision: an arc with a radius of 25 cm would force to accommodate 4 diopters, and one of 33 cm, 3 diopters; We prefer the one with a radius of 20cm, because it is a distance that the child uses frequently in his close gaze, and because it causes a convergence five times greater than that which would cause an accommodation of 1 diopter, so that the deviation is better measured and the Small possible errors in the measurement are divided by five when obtaining the final quotient.
   
   To make the initial measurement, the child is placed with the squint eye in the center of curvature of the instrument; The directing eye is therefore off-center for as many centimeters as the patient's interpupillary distance. The child with his directing eye looks at an object 4-6 meters away, keeping his eye in the primary position, that is, with his gaze axis passing over the scanning arc not above zero, but homo- laterally to it, as many centimeters as the patient's interpupillary distance. In this position, the objective angle of the strabic eye is measured, which can be done by alternating occlusion, if the child has central fixation, and by the corneal light reflex, if not. In the first case, a reference object is placed on the exploration arc in the direction of the gaze axis of the strabic eye, and it is moved over the arc, until when the directing eye is occluded, the strabic eye fixes the object without travel. In the second case, a light source is placed outside the perimeter arch, and moved along the arch until it causes a glow in the corneal center or over the pupillary center when the deployed eye, the light and the examiner are in the same line.
   
   To make the final measurement, the child begins to look closely with his directing eye, fixing an object located in his sagittal plane on the exploratory arc (that is, the object will be separated from the zero of the arc by a distance equal to the child's naso-pupillary ). Since the radius of the arc is 20cm, the accommodation of the directing eye to focus at that distance is 5 diopters. This induces a convergence of the other eye, the amount of which is re-measured in the same way as the distance deviation. The increase in deviation is the accommodative convergence that has been caused by the accommodative effort, and other courtship of physiological stimuli (awareness of near vision, divergence of the light emanating from the nearby object, fixation in the sagittal plane, etc.). This increase is the one that is of interest for clinical purposes. The CA / A ratio will be formed with that accommodative convergence as the numerator, and the 5 accommodation diopters as the denominator.

The measurement can be repeated by fixing both eyes, with and without cycloplegia, with and without correction, etc. With this device it is easy to measure the AC / A ratio in asymmetric convergence positions, if you want to determine whether or not there are incomitances in the different vergences. Also, if the bow is tilted, it is possible to measure the deviation in near vision with the eyes converging downward.

When the CA / A ratio is determined to accumulate preoperative information that allows planning the surgical act, the measure must reproduce the circumstances of the fixing eye, correction of ametropia and others that the patient is supposed to have in the postoperative period.

NOTATION

The simplest way to express the AC / A ratio clinically is to relate the accommodative convergence prismatic diopters with the accommodating spherical diopters. To draw conclusions from this notation, it is necessary to add the naso-pupillary distance (or the interpupillary distance, from which dividing by 2 the first will be deduced).

For example, a strabic child who from a distance has an esotropia of 15∆, when looking at 33 cm he becomes 22.8∆ • her CA / A ratio will be 6.8∆ / 3D. But if the naso-pupillary distance is not specified, we will not know if it is an abnormal or normal relationship, since if the naso-pupillary distance is 2.6 cm, the relationship is normal; but if it is 2.1 cm, it is abnormal due to excess convergence. This makes it necessary to add the information on the naso-pupillary distance to the CA / A value.

If the ratio of the CA / A ratio gives a value equal to the naso-pupillary distance, the ratio is normal; if it is higher there is an accommodative hyperconvergence; and if it is less, an accommodative hypoconvergence. For example, a child with a 2.5cm naso pupillary distance, when looking at 20cm (and accommodating 5D) develops 12.5 convergence in each eye. The AC / A ratio of it is 12.5 / 5 = 2.5, which is normal.

Although in the clinical reports and in the relationship with colleagues we use the previous notation because it is the usual one, for our internal information we prefer to divide the CA / A ratio by the naso-pupillary distance, thereby reducing the result to a single number: if this number is 1, the AC / A ratio is normal; if it is greater than 1 there is an excess of convergence, and if less than 1, a defect of convergence. Thus, for example, a child with a naso-pupillary distance of 3 cm has an exotropia of 10∆; when looking at 25 cm (and accommodating 4D), the eyes are parallel. Its CA / A ratio is 10/4 = 2.5, and its final relative value 2.5 / 3 = 0.83. This type of more elaborate notation offers the advantage of its greater ease of use and that when the separation of the patient's eyes increases over the years, it gives an immediate idea about the evolution of the CA / A ratio.

Let's look at several assumptions, an emmetropic, orthotropic and orthophoric child in all positions of the distance gaze, with a naso-pupillary distance of 2.5cm, when looking at 20cm (D = 5, ∆ = 12.5) maintains orthotropy, that is that is, converge 12.5∆ with each eye. The CA / A ratio = 12.5 / 5 = 2.5. The elaborated result would be 2.5 / 2.5 = 1.

Now suppose that the same child, who does not lose near orthotropia, by placing a screen over one of the eyes and dissociating binocularity in near vision, the occluded eye moves 2.5∆more. As a result, its CA / A ratio is 15/5 = 3 (relative value 3: 2.5 = 1.2), from which it follows that it has an excess of convergence whereby, even though it is orthophoric in the gaze from a distance, an endophoria appears in the near look, which under normal conditions does not appear to maintain binocular fusion. This example clearly shows that in non-strabismic children the determination of the CA / A ratio must be done by dissociating the eyes.

It may be that the same child when looking closely, even without instrumentally provoking a binocular dissociation, one of the eyes instead of addressing the fixation object converges 25∆, its CA / A value is 25/5 = 5 (relative value 5 / 2.5 = 2). His diagnosis would be normality in the distant gaze and strabismus in the near gaze due to excess convergence.

Now suppose another child, with the same naso-pupillary distance but who by far has a concomitant strabismus of + 17.5∆. When looking close to 20cm, he happens to have a target angle of deviation of 30∆; the CA / A ratio = 12.5 / 5 = 2.5 and its relative value 2.5 / 2.5 = 1. That is, this child has an absolute concomitant strabismus.

But if that same child, when looking at 20cm, happens to have a deviation of + 40 el in the squint, its CA / A value = 22.5 / 5 = 4.5 (relative value 1.8), that is, that child , which has a concomitant strabismus, nevertheless has a far / near incomitance.

CLINICAL USEFULNESS OF THE CA / A RELATIONSHIP

The CA / A ratio determines whether there is a binocular far / near concomitance. The discovery of far / near incomitances, apart from clarifying the clinical picture of the patient, allows correcting them by surgical methods or compensating them with prism methods. Orthoptic treatment, in the experience of most strabologists and orthoptists, does not appreciably modify the CA / A ratio.

There are non-strabic individuals who are orthophoric from a distance, but develop a heterophoria due to hypo- or hyper-convergence up close. This heterophoria may not become heterotropic due to the fusional reflex, but it occasionally results in asthenopic disorders. If the fusion breaks and the heterophoria transforms into heterotropia, the child, normal in the distance gaze, will have a strabismus that only manifests itself in the close gaze.

Strabismus who have incomitance in the different positions of the distance gaze, usually add incomitance when passing from the distance gaze to near, but this is not always the case. For example, a patient with a naso-pupillary distance of 3cm has a paresis of the external rectus muscle of the right eye that causes a convergent strabismus of + 30∆ in the primary gaze position, which becomes greater in the gaze to the right and minor in the gaze to the left, that is, it has an incomitance in the gaze from afar. Looking closely at 33cm, if the deflection angle goes to + 39∆, the CA / A ratio = 1; it has a far / near concomitance. In the different asymmetric convergences it reappears

an incomitance. The individual of such a theoretical assumption would be said to have distance incomitance, near incomitance, and far / near concomitance.

Individuals who have a concomitant strabismus. for far they may or may not have far / near concomitance. For example, an endotropic child with a naso-pupillary distance of 2cm, which in the distance gaze has a deviation of 25∆ which remains the same in all positions, when looking at 16.6cm (6 accommodation diopters) it happens to have a 37∆ deviation in which case it maintains the concomitance for far near, since its CA / A ratio is 12∆ / 6D = 2, its relative value being 2/2 = 1. If when looking at 16.6cm it converges more or less than 37∆ will have a concomitant strabismus for far with incomitance far / near. The surgical procedure would be different in one case and another.