Ординатура / Офтальмология / Английские материалы / Hyperopia and Presbyopia_Tsubota, Boxer Wachler, Azar_2003
.pdfIntroduction |
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49.Geerling G, Koop N, Brinkmann R, Tunglar A, Wirbelauer C, Birngruber R, Laqua H. Continu- ous-wave diode laser thermokeratoplasty: first clinical experience in blind human eyes. J Cataract Refract Surg 1999; 25:32–40.
50.Schanzlin DJ. Studies of intrastromal corneal ring segments for the correction of low to moderate myopic refractive errors. Trans Am Ophthalmol Soc 1999; 97:815–890.
51.Cochener B, Savary-LeFloch G, Colin J. Effect of intrastromal corneal ring segment shift on clinical outcome: one year results for low myopia. J Cataract Refract Surg 2000; 26:978–986.
52.Asbell PA, Ucakhan OO, Durrie DS, Lindstrom RL. Adjustability of refractive effect for corneal ring segments. J Refract Surg 1999; 5:627–631.
53.Lindstrom R. Small diameter intracorneal inlay lens for the correction of presbyopia. In: Sher N, ed. Surgery for Hyperopia and Presbyopia. Baltimore: Williams & Wilkins. 1997:195–199.
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71.Mathews S. Scleral expansion surgery does not restore accommodation in human presbyopia. Ophthalmology 1999; 106:873–877.
2
Basic Optics of Hyperopia and
Presbyopia
MICHAEL K. SMOLEK and STEPHEN D. KLYCE
Louisiana State University Health Sciences Center, New Orleans, Louisiana, U.S.A.
A. INTRODUCTION
It normally comes as a surprise that there are more hyperopes than myopes in the general population. The reason for this is that hyperopes can hide behind their accommodative capacity until at least age 40, when the aging process takes away the ability to alter the power of the natural lens. In this chapter, we examine the optical basis and interrelationships between hyperopia and presbyopia.
B. FAR POINT
The simplest and preferred clinical method of determining the refraction of the eye is still the far point method, in which the patient subjectively determines the furthest distance at which he or she can clearly see a target without using any accommodation. The far point location of the eye can also be determined objectively by an examiner using a retinoscope, an automated refractor, or similar method. By definition, the far point is the focal point in object space that is conjugate to the focus at the retina and is, therefore, seen clearly by the subject. Again, because of the spherical aberration (multifocality) of the eye’s optics and the physical size of the pupil, there may actually be a distance range that appears to be in focus simultaneously (i.e., a depth-of-field effect), but a single far point is specified. The far point of the eye is distinct from the near point of the eye, which is the location at which one can maximally accommodate in order to clearly see the closest possible target to the eye.
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For the emmetrope, the far point is located at optical infinity, and no power correction is needed to image a distant target onto the retina (Fig. 1). In myopia, the far point lies close to and a finite distance in front of the eye, so that light from the far point target enters the eye with a certain amount of negative vergence. The amount of negative vergence cancels the excess power inherent within the myopic eye, and the light comes to a focus at the retina. The specific location of the far point for the “nearsighted” myope depends on the level of myopic error; the higher the error, the nearer the far point will be to the eye. In order for the myope to clearly see a target located at optical infinity, negative power must be added to reduce the vergence of the distant light to a negative amount before it enters the eye; otherwise the excessive power of the eye’s optics must be reduced, as through flattening of the cornea by laser surgery. Myopic error is always expressed with a negative sign indicative of the negative power that must be added to achieve correction for viewing distant targets.
In hyperopia, the far point is commonly said to exist “beyond infinity,” because only converging rays can be brought to a focus onto the retina in the uncorrected hyperope (Fig. 1). Actually, it is more accurate to say that the far point of the hyperope is a virtual object that is located a finite distance behind the retina. The far point of the hyperope can be found by noting the location where the converging rays entering the eye would come to a focus if the eye were not present to intercept the light.
Because hyperopic eyes have insufficient plus power to see targets clearly at infinity, positive vergence must be added to the light entering the eye and the refraction is signified by a plus sign. Plus power can be added to the light entering the eye or the eye itself can be made to have relatively more power by making the cornea steeper through laser surgery. However, many young to middle-aged hyperopes can fully correct their distance vision error by adding enough plus power through accommodation to shift the far point to infinity. This ability to self-correct their refractive error gives these hyperopes a distinct advantage over myopes, who cannot “disaccommodate” to move the far point away from the eye. It also explains why these hyperopes can be considered to be farsighted, because they in fact become self-corrected for far vision. Unfortunately, as hyperopes age, the ability to
Figure 1 Far point location specified for three refractive states. R is the location of the far point, defined as the most remote distance at which the unaccommodated eye can see clearly. R’ is the conjugate focus of the far point, which is always located at the retina. D refers to the vergence power entering the eye to bring light to a focus on the retina: zero for emmetropia, negative for myopia, and positive for hyperopia.
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Figure 2 Graphic representation of the decline in accommodative amplitude with age (2).
accommodate diminishes (Fig. 2); thus they lose their ability to see clearly at any distance, while older myopes still retain at least a portion of their ability to see clearly at some distance.
C. ACCOMMODATION FOR NEAR VISION
The closer an object is to the cornea, the greater the divergence of light entering the eye and the greater the need for more plus power to make the near object conjugate with the retina. In youth, accommodation allows viewing at a variety of distances from infinity to very near targets. As a person ages, however, the accommodative ability decreases, and the near point moves away from the eye. Because uncorrected hyperopes often use a portion of their accommodative ability to correct their refractive error for distance, the near point is located farther from the eye; therefore hyperopes often experience near vision problems at an earlier age than myopes or emmetropes. It should be noted that some myopes may not experience any near vision problems in the uncorrected state if their refractive error maintains a clear image within a comfortable working distance that is neither too close nor too far from their eyes.
It is important to appreciate that there is a limited and diminishing amount of accommodation available at any given age and that the amount available depends in part on whether accommodation is being used to correct for a hyperopic error. This amount of accommodation in play is specified by the amplitude of accommodation, which is defined as the vergence difference between the far point and the near point. The relationship between age and accommodative amplitude was established by Donders (1) and later refined by Duane (2), who presented what has since become the classic representation of accommodative amplitude as a function of age (Fig. 2). Duane’s data show that accommodation begins to decrease in early adulthood, well before the decline is noticed during the performance of near vision tasks, such as reading. For adolescents, accommodative amplitude is approximately 14 D, which corresponds to a near point of approximately 7
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cm for an emmetrope. By age 45, this accommodative amplitude drops, due to changes in the accommodative apparatus controlling the crystalline lens power, to about 4 D and results in at best a 25-cm near point distance for that same emmetrope. Normal reading distance is considered to be around 15 in. or 37 cm, which is still within the range of a person in his or her midto late forties. However, it must be remembered that a continuous and excessive need to accommodate can be tiring and uncomfortable, so the decline in accommodative amplitude will be noticed by many subjects who are only in their midforties and who still have a fair amount of accommodative amplitude in reserve.
If the eye has insufficient accommodative amplitude, which normally occurs with advancing age and requires a plus lens addition for comfortable near vision, the condition is called presbyopia. There are no specific values that define the absolute onset of presbyopia, because its effects are dependent on a number of factors including the refractive error, age, amplitude of accommodation, and the near vision tasks and lifestyle of a particular patient. Because using accommodation to correct for distance vision is often tiring in itself, the hyperope will be more likely to complain of tired eyes, eyestrain, and diplopia, and may do so at an earlier age. Children do not normally experience vision problems from mild amounts of hyperopia because their accommodative reserve is large. However, those with moderate to high levels of hyperopia may experience visual problems ranging from mild eyestrain and headaches after near work to more severe problems such as strabismus and amblyopia (3). Some of these complaints are associated specifically with the ability of the two eyes to fuse images binocularly, because the accommodative process is neurologically tied to the convergence of the eyes.
There is a clinical distinction made between accommodative amplitude, which is the optical difference between the near and far point measured in diopters, and the range of accommodation, which is the linear difference between the far point and the near point in terms of physical distance. In the uncorrected myope, the far point may be located very close to the eye. The myope’s range of accommodation is thus very limited, whereas prepresbyopic low hyperopes may have a range that allows vision to infinity, just as in emmetropia (Fig. 3).
D. MANIFEST VERSUS LATENT HYPEROPIA
The refractive state of the eye is measured at rest with respect to the far point, but achieving a totally unaccommodated state can be problematic, especially in the uncorrected hyperope who uses accommodation to self-correct for distance vision. Consequently, refractions are separated into two basic types—manifest and latent refractions—which can give different refraction values for the same eye. A manifest refraction is the obvious, nonhidden part of the refraction that is based on the elimination of any natural stimulus to accommodate. Generally this is best accomplished by providing additional positive vergence of a known amount to the incoming light to the extent that the eye is made artificially myopic. The process is referred to as fogging. The far point thus moves to a finite distance in front of the eye, which in itself is beneficial with respect to interacting with and measuring the location of the far point. Of course, once the myopia-shifted far point is measured, the added vergence power is subtracted to provide the true far point location.
While fogging a patient removes the manifest portion of the total accommodation that may be in play, it does not necessarily remove the latent or hidden portion of accommodation that may still exist. Latent accommodation is that part which cannot be relaxed due to excessive, spastic tonicity of the ciliary apparatus controlling accommodation. Self-
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A
B
C
Figure 3 Example of the possible range of accommodation for three refractive states at three different ages. R is the far point and P is the near point. The dark line refers to the theoretical region in which unaided clear vision is possible. (A) In emmetropia, objects at optical infinity can be seen at any age. (B) In myopia, objects seen clearly are always located a finite distance in front of the eye, but objects at optical infinity cannot be seen clearly. (C) In hyperopia, objects at optical infinity can usually be seen clearly in youth and middle age; by the time late presbyopia occurs, however, no objects can be seen clearly at any distance unless the hyperopic error is corrected.
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correcting hyperopes tend to be prone to accommodative excess because they are constantly demanding additional plus power from the lens for both near and far tasks, and this effort builds up a constant level of spastic tonicity in the ciliary muscle. Therefore a cycloplegic drug is used to completely relax the spastic tonicity of the ciliary muscle, after which a refraction is performed to determine the full latent refractive error. Typically, the latent accommodation may account for approximately 1 D of total accommodation, so the difference between manifest and latent refractions may be clinically significant.
E. MAGNIFICATION AND VISUAL ACUITY
A refractive error can be fully corrected and image blur eliminated, but the retinal image may be smaller or larger than it would be in the uncorrected state; therefore the ability to resolve details in the image may be harder or easier to accomplish. Suppose we have a hyperope with a 5 D correction in a spectacle plane 1.2 cm from the cornea. The apparent image size will be reduced by 6% if the correction is moved to the corneal plane, as in the case of laser refractive surgery or contact lens wear (Table 1). If the spectacle correction is increased to 10 D, the amount of minification for a corneal plane correction likewise doubles to 12%. The general rule of thumb is that spectacle magnification in percent equals the power of the spectacle lens in diopters multiplied by the distance between the spectacle plane and the cornea in centimeters. Because we are considering an image projected from the eye in order to assess the apparent visual angle change experienced by the subject, distances are considered positive when measured from the cornea to the spectacle plane and negative when moving from the spectacle plane back to the cornea. Thus, moving a correction from the cornea to a spectacle plane in the hyperope causes magnification of the retinal image, and the further the spectacle plane is from the eye, the greater the change in the magnification. However, when the correction is moved from the spectacle plane back to the cornea, the retinal image becomes physically smaller in the hyperope. Therefore, Snellen letters subtend a relatively smaller angle in the visual field and appear smaller to the patient and harder to distinguish. The opposite relationship holds true for the myope; moving the correction from the spectacle plane to the cornea causes Snellen letters to appear slightly larger to the myope corrected by refractive surgery or a contact lens.
Applegate and Howland calculated the effects of magnification on Snellen visual acuity and, as expected, showed that the effective change in acuity was nonlinear and greater for myopes than for hyperopes (4). Whereas myopes had a positive effect of gaining more letters of visual acuity, hyperopes lost letters of acuity. For example, a 5
Table 1 Magnification Effect of Moving a Correction from the Spectacle Plane to the Cornea
Spectacle |
Spectacle plane |
Spectacle |
Loss of letters for Snellen |
power (D) |
distance (cm) |
magnification (%) |
distance visual acuity |
|
|
|
|
2 |
1.2 |
2.4 |
1 |
2 |
1.5 |
3.0 |
1 |
5 |
1.2 |
6.0 |
2 |
5 |
1.5 |
7.5 |
2 |
10 |
1.2 |
12.0 |
3 |
|
|
|
|
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D hyperope wearing glasses who has successful refractive surgery is expected to lose two to four letters of acuity as a result of moving the correction to the cornea, depending on the exact distance of the spectacle plane from the cornea (Table 1).
F. HYPEROPIA AND BIOMETRIC CHANGES DURING LIFE
Based on spherical equivalent data obtained during cycloplegic refractions, the average eye is hyperopic through most of life (Fig. 4). The average refraction is approximately2.25 D at birth and reaches a hyperopic peak around 8 years of age, after which the refraction becomes increasingly less hyperopic during adolescence and comes close to being emmetropic during early adulthood (5). In the Beaver Dam Eye Study of adults, hyperopia was more prevalent than myopia in age-matched subjects (49 vs 26.2%, respectively, p 0.0001) (6). Hyperopia increases in later adulthood from 22.1% between ages 43 and 54 to 68.5% at age 75 and above; however, Slataper noted that the refraction tends to drift back toward myopia with very advanced age (5). The hyperopic shift for older adults between the ages of 45 and 65 has been attributed to reductions in the axial length of the eye and changes in the focal power of the lens (7). The cause of the myopic drift in advanced age may be attributed to a shrinking radius of curvature of the cornea, which leads to a higher corneal power (8). This effect occurs predominantly in females (9).
Passive growth of the eye during childhood tends to be a correlated, uniform expansion of ocular dimensions (7,10). By “correlated” we mean that as eye growth causes the retina to recede from the optical elements of the eye, we also see changes in the lens and cornea that ideally allow emmetropia to be achieved if the eye is hyperopic or retained if the eye is already emmetropic. Furthermore, it must be remembered that as axial length increases, there is a reduction in the vergence power required to focus an image on the
Figure 4 Graph based on Slataper’s data (5) of average refractive error during life. Note that the error tends to be hyperopic throughout life and relatively stable from young adulthood to middle age. N 34,570 eyes assessed by cycloplegic refractions.
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retina. During childhood, corneal power decreases by about 2 D because the radius of curvature of the cornea increases as part of the expansive growth of the corneoscleral shell (11). In addition, the anterior chamber depth decreases, which reduces the effective power of the lens, and the lens itself decreases in power as the radius of curvature of the front and back surfaces increases by up to 1 mm (11). Sorsby noted lens power to be on average 23 D at age 3 and only 20 D at age 14 (12). The lens also thins from an average of 3.6 mm at age 6 to about 3.4 mm at age 10, after which thinning essentially halts (11). The overall lens thinning can be attributed to a compression of the nucleus, even though the cortex grows and thickens at this time.
There appears to be an active growth mechanism that uses feedback from the blur of the retinal image to make corrective growth changes to the ocular component dimensions (7,10). A defect in an active growth feedback pathway might be responsible for a runaway increase in axial length, which is often seen with myopia; but the active growth mechanism does not adequately explain hyperopic error. Hyperopia seems more likely to be a failure of the passive growth mechanism, such that the eye retains slightly immature globe dimensions into adulthood. Hyperopic eyes tend to be smaller in all dimensions (not just in axial length) compared to corresponding age-matched emmetropic eyes. Using high-resolution magnetic resonance imaging to measure dimensions in the major axes of the eye, Cheng and coworkers found that, on average, the hyperopic eye is consistently smaller overall than the mean emmetropic eye and significantly smaller than the mean myopic eye (Fig. 5) (13). Strang et al. used biometric data from 53 human subjects with refractive errors of up to 10 D and found that there was a strong correlation between the mean hyperopic
Figure 5 Data based on the findings of Cheng et al. (13) of eye size relative to refractive error. Error bars indicate standard deviations. The general trend is that myopic eyes are larger and hyperopic eyes smaller than eyes with no refractive error. The differences in globe dimension between hyperopic and myopic eyes are significant.