Ординатура / Офтальмология / Английские материалы / Hyperopia and Presbyopia_Tsubota, Boxer Wachler, Azar_2003

error and the axial length of the globe (r2 0.611, p 0.0001) (14). There was also a weak but significant correlation between mean corneal radius and mean refractive error (r2 0.128, p 0.009). Grosvenor also found that hyperopic eyes were smaller and tended to have flatter corneas than emmetropic eyes (15).

G. OPTICS OF THE CRYSTALLINE LENS

The lens has an average index of refraction that higher than the index of corneal stroma (1.427 vs. 1.376) (16). However, the contribution of the lens to the total power of the eye is about half that of the anterior corneal surface, because the lens is surrounded by fluid with an index near 1.336, whereas the cornea is exposed to air with an index of 1.0, which greatly increases its refractivity. While a single index of refraction of the lens is useful for simple calculations, in reality, the lens cannot be defined by a single value. Mapping the gradient index of the lens has proved difficult. Simple models using concentric shells of varying index gradients do not yield accurate ray-tracing results, and the models do not agree with refractive index measurements made by tissue probes (17). It is interesting to find that significant levels of transient hyperopia have been attributed entirely to changes in the refractive index of the lens. Saito and coworkers noted hyperopia peaking between 1 to 2 weeks after abrupt decreases in plasma glucose and attributed this effect to water influx into the lens (18). Okamoto et al. also noted hyperopia after treatment for hyperglycemia and found no changes in lens thickness or anterior chamber depth, thus implicating a change entirely due to the refractive index of the lens (19).

Although the lens is the primary component associated with accommodation for near vision, the contribution of depth of focus of the eye should not be discounted, particularly in presbyopic eyes. Brighter viewing conditions or the use of miotics that constrict the pupil increase the depth of focus and help to extend the effective range of accommodation.

H. OPTICAL ABERRATIONS

The shape of the gradient index profile across the lens as well as shape changes due to accommodation alter not only effective power but also the spherical aberration of the eye (20). By accommodating to approximately 3 D (a 33-cm viewing distance), the negative spherical aberration of the lens corrects for much of the positive spherical aberration induced by the cornea (21). Further accommodation tends to give the eye an overall negative spherical aberration, but the exact amount varies among individuals (22). In general, near accommodation tends to increase the monochromatic wavefront aberrations of the eye (23). Fourth-order aberrations can either increase or decrease with increasing accommodation, but higher-order aberrations tend to increase (22). It has been suggested that there is no correlation between the change in aberration during accommodation and the total amount of aberration for the relaxed eye (22). It can be concluded that any clarity of vision provided by refractive surgery must diminish by a measurable extent with accommodation, but certainly more work needs to be done to ascertain the significance of aberration change on visual performance.

REFERENCES

1.Donders FC. On the Anomalies of Accommodation and Refraction of the Eye. London, 1864.

2.Duane A. Normal values of accommodation at all ages. JAMA 1912; 59:1010–1013.

3.Moore B, Lyons SA, Walline J. A clinical review of hyperopia in young children. The Hyperopic Infants’ Study Group, THIS Group. J Am Optom Assoc 1999; 70:215–224.

4.Applegate RA, Howland HC. Magnification and visual acuity in refractive surgery. Arch Ophthalmol 1993; 111:1335–1342.

5.Slataper FJ. Age norms of refraction and vision. Arch Ophthalmol 1950; 43:466–481.

6.Wang Q, Klein BEK, Klein R, Moss SE. Refractive status in the Beaver Dam Eye Study. Invest Ophthalmol Vis Sci 1994; 35:4344–4347.

7.Brown NP, Koretz JF, Bron AJ. The development and maintenance of emmetropia. Eye 1999; 13:83–92.

8.Hayashi K, Hayashi H, Hayashi F. Topographic analysis of the changes in corneal shape due to aging. Cornea 1995; 14:527–532.

9.Goto T, Klyce SD, Zheng X, Maeda N, Kuroda T, Ide C. Gender and age related differences in corneal topography. Cornea 2001; 20:270–276.

10.van Alphen GWHM. On emmetropia and ametropia. Ophthalmologica Suppl 1961; 142:1–92.

11.Zadnik K, Mutti DO, Fusaro RE, Adams AJ. Longitudinal evidence of crystalline lens thinning in children. Invest Ophthalmol Vis Sci 1995; 36:182–187.

12.Sorsby A, Benjamin B, Sheridan M. Refraction and Its Components During the Growth of the Eye from the Age of Three. MRC special report series no. 301. London: Her Majesty’s Stationery Office, 1961.

13.Cheng H-M, Singh OS, Kwong KK, Xiong J, Woods BT, Brady TJ. Shape of the myopic eye as seen with high-resolution magnetic resonance imaging. Optom Vis Sci 1992; 69:698–701.

14.Strang NC, Schmid KL, Carney LG. Hyperopia is predominantly axial in nature. Curr Eye Res 1998; 17:380–383.

15.Grosvenor T. High axial length/corneal radius ratio as a risk factor in the development of myopia. Am J Opt Physiol Opt 1988; 65:689–696.

16.Mutti DO, Zadnik K, Adams AJ. The equivalent refractive index of the crystalline lens in childhood. Vis Res 1995; 35:1565–1573.

17.Pierscionek BK. Refractive index contours in the human lens. Exp Eye Res 1997; 64:887–893.

18.Saito Y, Ohmi G, Kinoshita S, Nakamura Y, Ogawa K, Harino S, Okada M. Transient hyperopia with lens swelling at initial therapy in diabetes. Br J Ophthalmol 1993; 77:145–148.

19.Okamoto F, Sone H, Nonoyama T, Hommura S. Refractive changes in diabetic patients during intensive glycaemic control. Br J Ophthalmol 2000; 84:1097–1102.

20.Smith G, Pierscionek BK, Atchison DA. The optical modelling of the human lens. Ophthalmic Physiol Opt 1991; 11:359–369.

21.Koomen MJ, Tousey R, Scolnik R. The spherical aberration of the eye. J Opt Soc Am 1949; 39:370–376.

22.He JC, Burns SA, Marcos S. Monochromatic aberrations in the accommodated human eye. Vis Res 2000; 40:41–48.

23.He JC, Marcos S, Webb RH, Burns SA. Measurement of the wave-front aberration of the eye by a fast psychophysical procedure. J Opt Soc Am A Opt Image Sci Vis 1998; 15:2449–2456.

Figure 1 Hermann Ludwig Ferdinand von Helmholtz (b, 1821; d, 1894) was not the first to describe the accommodative mechanism of the human eye, but he provided the first comprehensive and most accurate description based on the experiments he had performed and on the work done by many preceding him. Helmholtz succeeded where others had failed at providing a consistent and harmonious description of how accommodation occurs. Although the description that Helmholtz provided was largely accurate, subsequent experimental studies have shown that some aspects of the accommodative mechanism are not as Helmholtz described. For example, Helmholtz believed that the posterior surface of the lens did not move with accommodation and that the iris played an important role in mediating the accommodative changes in the lens.

the gross anatomy of the accommodative apparatus, in general there is a consensus, and has been for some time (2). The primary accommodative structures of the eye consist of the ciliary body, the ciliary muscle, the posterior and anterior zonular fibers, the lens capsule, and the lens substance.

C. THE CILIARY MUSCLE

The ciliary muscle consists of three subgroups of muscle fiber cells differentiated by their positions and orientations within the ciliary body (3). The muscle fibers group are (1) the longitudinal fibers, sometimes referred to as meridional fibers or Bru¨cke’s muscle (4); (2) the radial or reticular fibers; and (3) the equatorial or circular fibers. The longitudinal fibers are located most peripherally in the eye, just inside the sclera at the ciliary region. Inward of the longitudinal fibers and closer to the vitreous are the radial fibers, and inside these are the circular fibers, located most anteriorly in the ciliary body and closest to the lens (5). The ciliary muscle is located within the ciliary body, bounded externally by the

sclera of the eye and the collagen fibers, fibroblasts, and melanocytes of the outer surface of the ciliary body (3). The inner surface of the ciliary muscle is bounded anteriorly by the pars plicata and posteriorly by the pars plana of the ciliary body. Anteriorly, the ciliary muscle inserts into the scleral spur and the trabecular meshwork, which serve as a relatively fixed anterior anchor point against which the ciliary muscle contracts (3). Posteriorly, the ciliary muscle attaches via the elastic tendons to the stroma of the choroid.

D. THE ZONULAR FIBERS

The zonular fibers of the eye can broadly be broken down into two subgroups. The posterior zonular fibers or the pars plana zonule and the anterior zonular fibers. The pars plana zonule extends from the posterior insertion of the zonule at the posterior attachment of the ciliary muscle near the ora serrata of the retina to the ciliary processes.(6) The anterior zonular fibers span the circumlental space between the ciliary processes and the equatorial region of the lens (Fig. 2). From their posterior origin, the posterior zonular fibers extend longitudinally toward the pars plicata of the ciliary body as a mat or meshwork of interlacing fibers, following a straight path toward the tips of the ciliary processes (7). The majority of the posterior zonular fibers course forward to the pars plicata region of the ciliary body and enter the valleys between the ciliary processes, inserting into the walls of the valleys of the ciliary processes (8). The pars plicata region of the ciliary body separates the

Figure 2 Early anatomists had an excellent knowledge of the anatomy of the crystalline lens (A) and the ciliary region of the eye. The lens is composed of lens fiber cells arranged in concentric layers. New lens fibers develop from the germinative zone at the anterior equatorial region of the lens. The lens capsule surrounds the lens. The anterior surface of the lens is to the left. (From Ref. 2.) (B) Similarly, investigators whose work preceded that of Helmholtz (1) had already provided excellent anatomical information on the structure and relationships of various elements of the accommodative apparatus to each other. In particular, the arrangement of the zonular fibers passing from the ciliary body to the lens equator shows a picture remarkably consistent with subsequent descriptions of this tissue, but quite unlike that postulated in recent controversial and anatomically inaccurate theories (i.e., Refs. 9 and 43). (From Ref. 2.)

posterior zonule from the anterior zonule (8). Some zonular fibers pass from the pars plana through the valleys between the ciliary processes and on toward the lens (6,8). A spanning or tension fiber system of many finer strands forms the zonular plexus, which attach the zonule to the ciliary epithelium in the valleys of the ciliary processes (6). This serves to anchor the anterior and pars plana zonule to the ciliary epithelium of the ciliary body. As the anterior zonular fibers near the lens equator, they fan out to insert into the lens capsule around the equatorial region of the lens. The individual zonular fibers terminate within zonular lamellae of the lens capsule (6). No discrete zonular fiber bundles can be seen to selectively insert specifically to the lens anterior, equatorial, and posterior surfaces, as suggested by Schachar (9); instead, the zonular fibers form a uniform distribution or meshwork of fibers inserting all around the equatorial region of the lens (10,11).

E. THE LENS AND CAPSULE

The lens capsule is a thin, acellular, elastic membrane surrounding the lens. It is principally composed of type IV collagen with some glycosaminoglycans (12). The capsule is not of uniform thickness. Fincham, in 1937, found it to be thickest at the peripheral anterior surface and thinner toward the lens equatorial region. On the lens posterior surface, the capsule is thinnest at the region of the posterior pole of the lens but thicker toward the periphery (13).

The lens consists of a monolayer of epithelial cells on the anterior surface beneath the capsule, with elongated lens epithelial cells at various stages of maturation. The lens fiber cells are arranged in layers to form the younger peripheral cortex and the more mature central lens cortex (Fig. 2). The human lens does not shed any of its cells and grows throughout life by adding lens fibers at its outer equatorial zone. Isolated lenses show a linear increase in mass with age (14–16). The axial thickness of the lens increases with increasing age. Its axial thickness can readily be measured in vivo in the living eye with A-scan ultrasound or Schiempflug (17–19). Since the lens thickness increases with accommodation, it is important to measure this dimension in unaccommodated eyes to draw conclusions about changes due to aging. As the lens grows, there is an increase in the anterior and posterior surface curvatures of the unaccommodated lens as measured with Schiempflug slit-lamp photography (20,21). While the axial thickness and surface curvatures of the lens can readily be measured in the living eye, lens diameter, until recently, could not. Based on the observation that the diameter of lenses removed from postmortem human eyes increases with increasing age (22), it has been suggested that there is a growth-related increase in the lens equatorial diameter throughout life (23–25). However, Smith (22) recognized that his measurements of isolated lenses did not reflect a growth-related increase in diameter. When lenses are removed from the eye, the outwarddirected zonular tension on the lens equator is removed. Isolated lenses are therefore in an accommodated form, rather more so for the younger than the older lenses (3). Advances in magnetic resonance imaging (MRI) have recently allowed lens diameter to be measured in the living eye. The MRI measurements do not show an increase in lens diameter with age (26).

F. OPTICAL CHANGES WITH ACCOMMODATION

1. Increased Optical Power of the Eye

Accommodation is defined as a dioptric change in power of the eye (27). The increase in refractive power or the change in refractive state of the eye is the predominant optical

change of accommodation and is readily measured. The cornea, the anterior and posterior lens surfaces, and the lens gradient refractive index provide optical refractive power to the eye. In the unaccommodated, emmetropic eye, the optical refracting power allows the image of a distant object to be focused on the retina. In this case, parallel rays of light from the distant object enter the eye and become convergent to focus the image on the retina. A near object, closer to the eye than optical infinity, however, has diverging light rays entering the cornea. In order for the divergent rays to be drawn to a focus on the retina, the optical power of the eye must increase. During accommodation, this is accomplished primarily by an increase in curvature of the anterior and posterior lens surfaces. In addition, lens thickness increases and anterior chamber depth and, to a lesser degree, vitreous chamber depth decreases during accommodation. All these changes contribute to an increase in optical refracting power. If the optical power or the refraction of a young eye is measured with an objective refractometer during accommodation, it is clear that the optical power increases, resulting in a myopic shift in the refraction.

2. Depth of Field

The accommodative triad describes the neuronally coupled accommodation, convergence, and pupil constriction that occur with an accommodative effort. Both accommodation and pupil constriction contribute to near visual acuity. Depth of field is the distance an object can be moved in object space without appreciably altering image focus or, in the case of the eye, without appreciably altering the eye’s visual acuity. This plays an important role in the perception of a sharply focused image on the retina. An eye with a large pupil diameter has a small depth of field. This means that the eye can detect a change in focus of the retinal image with small movements of the object toward or away from the eye. An eye with a small pupil diameter has a large depth of field. In this case, the object can be moved a greater distance toward or away from the eye without appreciably altering the retinal image focus. The pupillary constriction that occurs with accommodation results in an increased depth of field, which also contributes to maintaining a clear image of a near object on the retina. Pupillary constriction can also occur without accommodation, as with increased illumination. This too improves depth of field and hence near reading ability, but without accommodation. Pupillary constriction and increased depth of field are important for improving near reading ability but are very different from the refractive change that accompanies accommodation.

3. Aberrations of the Eye

The imperfect optics of the eye mean that the eye suffers from optical aberrations. The low-order aberrations, such as defocus and astigmatism, can be corrected with optical prescriptions, but higher-order aberrations cannot. These higher-order aberrations include spherical aberration and coma, for example. While the presence of aberrations in the eye reduces retinal image quality, they also have important implications for accommodation. Ocular aberrations result in decreased retinal image quality and contribute to a larger depth of field of the eye due to its inability to detect small changes in image focus as an object is moved closer or further from the optimal point of focus. Before the accommodative mechanism was fully understood, Sturm (2) proposed that astigmatism could explain how the eye could see at different distances. An optical system with astigmatism has two line foci at orthogonal meridians separated by a distance called the interval of Sturm. No perfect image focus is attained anywhere between the two line foci, so if an object is

moved such that the interval of Sturm remains on the retina, only a modest change in image quality occurs, but without a distinct perception of a change in focus. Thus subjective accommodation testing may suggest the presence of accommodation in an individual with ocular aberrations even when no functional accommodation occurs. This illustrates the importance of considering of the optical aberrations of the eye—how they can contribute to near vision but yet are clearly distinct from active accommodation.

G. THE HELMHOLTZ DESCRIPTION OF ACCOMMODATION

Helmholtz (2) provided the first accurate description of the eye’s accommodative anatomy and mechanism. He described that in the unaccommodated state, resting tension on the

Figure 3 Sections of the (A) unaccommodated and (B) accommodated ciliary muscle. Eyes were placed in a fixative after maximal contraction of the ciliary muscle with eserine or maximum relaxation of the ciliary muscle with atropine. These histological diagrams illustrate that the inner apex of the ciliary body moves forward and toward the axis of the eye with accommodation. Notice that in the unaccommodated state, the inner apex of the ciliary muscle resides behind the scleral spur; but in the maximally accommodated state, this portion of the ciliary muscle has moved forward of the scleral spur. (From Ref. 2.) (C) The Helmholtz accommodative mechanism. In the left half of the diagram, the eye is shown in the unaccommodated state, focused for far (F), and the right half, in the accommodated state, focused for near (N). A contraction of the ciliary muscle moves the ciliary body closer to the lens equator. Resting zonular tension is released. The anterior lens surface is shown to move forward with accommodation and the posterior lens position to remain unchanged. (From Ref. 2.)

zonular fibers at the lens equator pull and hold the lens in a flattened and unaccommodated state. The zonular fibers extend from the ciliary processes to their insertion on the lens capsule at the lens equatorial region. When the ciliary muscle contracts with an accommodative effort, it undergoes a forward redistribution of its center of mass (Fig. 3). This moves the anterior-inward apex of the ciliary body toward the lens equator to release the resting zonular tension. When the zonular tension is released, the elastic lens capsule molds the lens to decrease equatorial diameter, increase thickness, and allow the lens anterior and posterior surfaces to undergo an increase in curvature (Fig. 3).

H. TSCHERNING’S THEORY OF ACCOMMODATION

Tscherning (28) challenged the Helmholtz theory of accommodation, believing that with accommodation there is an increase in traction of the zonular fibers at the lens equator and that the curvatures of the central lens increase while those at the periphery flatten on account of the greater resistance and steeper curvatures of the lens nucleus (Fig. 4). In other words, with a traction of the zonular fibers, the softer cortex is molded around the harder nucleus, so that the central lens surface curvatures more closely resemble the steeper central curvatures of the lens nuclear surface. Tscherning also believed that the vitreous provided a force on the lens posterior surface to aid in the accommodative mechanism. Tschering’s accommodative mechanism required no significant modification of the anatomy of the accommodative apparatus as Helmholtz had described it.

Figure 4 Tscherning (Ref. 28.) proposed an alternative mechanism of lenticular accommodation.

(A) The unaccommodated lens is shown as a solid line with the accommodated lens superimposed as a dashed line. Tscherning believed that the accommodative change in the form of the lens occurred as a consequence of an increase in traction of the zonular fibers at the lens equator. Thus, as depicted by Tscherning, the unaccommodated lens has a larger diameter, but the lens undergoes no change in axial thickness. The anterior surface of the lens is to the left. (B) Tscherning believed this change in form of the lens occurred as a consequence of the relatively softer cortex being molded around the relatively hardened nucleus. He believed the surfaces of the nucleus to be more steeply curved than the surfaces of the lens. With an increase in traction of the zonular fibers at the lens equator the peripheral lens surfaces are flattened while at the middle of the lens the curvatures increase. The cornea and anterior lens surface are on the left of the diagram. (From Ref. 28.)

I. SCHACHAR’S THEORY OF ACCOMMODATION

Schachar too has proposed that accommodation occurs through an increase in zonular tension, essentially restating Tscherning’s theory. Unlike Tscherning’s theory, however, Schachar’s theory requires significant modification of the accommodative anatomy. Schachar requires that the zonular fibers insert into the anterior face of the ciliary muscle, which Schachar believes moves backward in the eye with an accommodative effort. Schachar’s theory also requires that separate and discrete zonular fiber bundles insert to that lens anterior, equatorial, and posterior surfaces and that the tension on these discrete subgroups be differentially adjusted with accommodation. Like Tscherning, Schachar proposes that when the ciliary muscle contracts with accommodation, there is an increase in zonular tension at the lens equator, but that the tension of the zonular fibers on the lens anterior and posterior surfaces relax during accommodation. Schachar believes that the increased zonular tension at the lens equator results in an increase in lens equatorial diameter, but that the release of zonular tension on the lens anterior and posterior surfaces results in a flattening of lens peripheral surfaces and an increase in curvature at the center of the lens.

J. DEBATE OVER THE ACCOMMODATIVE MECHANISM

Central to the debate over the Helmholtz and Schachar theories of accommodation is the mechanism by which the ciliary muscle/zonular complex acts on the lens. Cramer (29), by observing minification of Purkinje images reflected off the anterior lens surface with accommodation, first unequivocally demonstrated that the crystalline lens anterior surface undergoes an increase in curvature with accommodation (see appendix in Ref. 29). Cramer’s belief that this was mediated by a contraction of the iris sphincter was later disproved by von Graefe (31), who observed that an aniridic patient had normal accommodation. Helmholtz, apparently unaware of Cramer’s work, subsequently and independently also observed minification of Purkinje images of the anterior lens surface with accommodation. It is beyond debate that for accommodation to occur, the lens power must increase, and that this is accomplished in part through an increase in the lens anterior surface curvature. However, the Helmholtz accommodative mechanism on the one hand and the Tscherning/ Schachar theories on the other are at odds as to how this occurs.

K. TSCHERNING’S STUDIES

Young (32) stated that the amplitude of accommodation diminishes toward the periphery of the pupil. Tscherning observed in his own eye that, with accommodation, the refraction at the center of his pupil increased more than the refraction at the periphery. Tscherning arrived at this conclusion from observations of the change in the appearance of the pointspread of his eye and by positioning Young’s double-slit optometer in the center and toward the periphery of his pupil during accommodation. Tscherning believed the Helmholtz accommodative mechanism to be incorrect because it provided no obvious explanation for this observation. Tscherning believed that this could be explained only by a steepening of the central lens and a flattening of the peripheral lens.