Hyperopia and Presbyopia - part 2 pot

The primary accommodative structures of the eye consist ofthe ciliary body, the ciliary muscle, the posterior and anterior zonular fibers, the lenscapsule, and the lens substance.. The p

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 somedistance

The closer an object is to the cornea, the greater the divergence of light entering the eyeand the greater the need for more plus power to make the near object conjugate with theretina In youth, accommodation allows viewing at a variety of distances from infinity tovery near targets As a person ages, however, the accommodative ability decreases, andthe near point moves away from the eye Because uncorrected hyperopes often use aportion of their accommodative ability to correct their refractive error for distance, thenear point is located farther from the eye; therefore hyperopes often experience near visionproblems at an earlier age than myopes or emmetropes It should be noted that somemyopes may not experience any near vision problems in the uncorrected state if theirrefractive error maintains a clear image within a comfortable working distance that isneither too close nor too far from their eyes

It is important to appreciate that there is a limited and diminishing amount of modation available at any given age and that the amount available depends in part onwhether accommodation is being used to correct for a hyperopic error This amount of

accom-accommodation in play is specified by the amplitude of accom-accommodation, which is defined

as the vergence difference between the far point and the near point The relationshipbetween age and accommodative amplitude was established by Donders (1) and laterrefined by Duane (2), who presented what has since become the classic representation ofaccommodative amplitude as a function of age (Fig 2) Duane’s data show that accommo-dation begins to decrease in early adulthood, well before the decline is noticed duringthe performance of near vision tasks, such as reading For adolescents, accommodativeamplitude is approximately 14 D, which corresponds to a near point of approximately 7

20 Smolek and Klyce

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 andresults in at best a 25-cm near point distance for that same emmetrope Normal readingdistance is considered to be around 15 in or 37 cm, which is still within the range of aperson in his or her mid- to late forties However, it must be remembered that a continuousand excessive need to accommodate can be tiring and uncomfortable, so the decline inaccommodative amplitude will be noticed by many subjects who are only in their mid-forties and who still have a fair amount of accommodative amplitude in reserve

If the eye has insufficient accommodative amplitude, which normally occurs withadvancing 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 particularpatient 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, andmay do so at an earlier age Children do not normally experience vision problemsfrom mild amounts of hyperopia because their accommodative reserve is large However,those with moderate to high levels of hyperopia may experience visual problemsranging from mild eyestrain and headaches after near work to more severe problemssuch as strabismus and amblyopia (3) Some of these complaints are associated specifi-cally with the ability of the two eyes to fuse images binocularly, because the accommoda-tive 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 veryclose to the eye The myope’s range of accommodation is thus very limited, whereasprepresbyopic low hyperopes may have a range that allows vision to infinity, just as inemmetropia (Fig 3)

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 hyperopewho uses accommodation to self-correct for distance vision Consequently, refractions areseparated into two basic types—manifest and latent refractions—which can give differentrefraction 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 knownamount 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 thelocation of the far point Of course, once the myopia-shifted far point is measured, theadded vergence power is subtracted to provide the true far point location

While fogging a patient removes the manifest portion of the total accommodationthat may be in play, it does not necessarily remove the latent or hidden portion of accommo-dation that may still exist Latent accommodation is that part which cannot be relaxed due

to excessive, spastic tonicity of the ciliary apparatus controlling accommodation

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 theeye, but objects at optical infinity cannot be seen clearly (C) In hyperopia, objects at optical infinitycan 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 constantlydemanding additional plus power from the lens for both near and far tasks, and this effortbuilds up a constant level of spastic tonicity in the ciliary muscle Therefore a cycloplegicdrug is used to completely relax the spastic tonicity of the ciliary muscle, after which arefraction is performed to determine the full latent refractive error Typically, the latentaccommodation may account for approximately 1 D of total accommodation, so the differ-ence between manifest and latent refractions may be clinically significant

A refractive error can be fully corrected and image blur eliminated, but the retinal imagemay 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 aⳭ5 D correction in a spectacle plane 1.2 cm from the cornea Theapparent 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 spectaclecorrection is increased toⳭ10 D, the amount of minification for a corneal plane correctionlikewise doubles to 12% The general rule of thumb is that spectacle magnification inpercent equals the power of the spectacle lens in diopters multiplied by the distancebetween 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 changeexperienced by the subject, distances are considered positive when measured from thecornea 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 thehyperope causes magnification of the retinal image, and the further the spectacle plane isfrom 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 physicallysmaller in the hyperope Therefore, Snellen letters subtend a relatively smaller angle inthe visual field and appear smaller to the patient and harder to distinguish The oppositerelationship holds true for the myope; moving the correction from the spectacle plane tothe cornea causes Snellen letters to appear slightly larger to the myope corrected byrefractive surgery or a contact lens

Applegate and Howland calculated the effects of magnification on Snellen visualacuity and, as expected, showed that the effective change in acuity was nonlinear andgreater for myopes than for hyperopes (4) Whereas myopes had a positive effect ofgaining more letters of visual acuity, hyperopes lost letters of acuity For example, aⳭ5

Table 1 Magnification Effect of Moving a Correction from the Spectacle Plane to the CorneaSpectacle Spectacle plane Spectacle Loss of letters for Snellenpower (D) distance (cm) magnification (%) distance visual acuity

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 onthe exact distance of the spectacle plane from the cornea (Table 1)

Based on spherical equivalent data obtained during cycloplegic refractions, the averageeye is hyperopic through most of life (Fig 4) The average refraction is approximatelyⳭ2.25 D at birth and reaches a hyperopic peak around 8 years of age, after which therefraction becomes increasingly less hyperopic during adolescence and comes close tobeing 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%, respec-

tively, p⳱ 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 refractiontends to drift back toward myopia with very advanced age (5) The hyperopic shiftfor older adults between the ages of 45 and 65 has been attributed to reductions inthe 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 ofcurvature of the cornea, which leads to a higher corneal power (8) This effect occurspredominantly in females (9)

Passive growth of the eye during childhood tends to be a correlated, uniform sion of ocular dimensions (7,10) By “correlated” we mean that as eye growth causes theretina to recede from the optical elements of the eye, we also see changes in the lens andcornea that ideally allow emmetropia to be achieved if the eye is hyperopic or retained

expan-if the eye is already emmetropic Furthermore, it must be remembered that as axial lengthincreases, 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 theerror tends to be hyperopic throughout life and relatively stable from young adulthood to middle

age N⳱ 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 corneoscleralshell (11) In addition, the anterior chamber depth decreases, which reduces the effectivepower 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 thinsfrom an average of 3.6 mm at age 6 to about 3.4 mm at age 10, after which thinningessentially halts (11) The overall lens thinning can be attributed to a compression ofthe 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 runawayincrease in axial length, which is often seen with myopia; but the active growth mechanismdoes 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 sions into adulthood Hyperopic eyes tend to be smaller in all dimensions (not just in axiallength) compared to corresponding age-matched emmetropic eyes Using high-resolutionmagnetic resonance imaging to measure dimensions in the major axes of the eye, Chengand coworkers found that, on average, the hyperopic eye is consistently smaller overallthan 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

dimen-of up toⳭ10 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 hyperopiceyes smaller than eyes with no refractive error The differences in globe dimension between hyperopicand myopic eyes are significant

error and the axial length of the globe (r2⳱ 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)

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 fluidwith an index near 1.336, whereas the cornea is exposed to air with an index of 1.0, whichgreatly increases its refractivity While a single index of refraction of the lens is usefulfor simple calculations, in reality, the lens cannot be defined by a single value Mappingthe 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 donot 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 waterinflux into the lens (18) Okamoto et al also noted hyperopia after treatment for hyperglyce-mia 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 nearvision, the contribution of depth of focus of the eye should not be discounted, particularly inpresbyopic eyes Brighter viewing conditions or the use of miotics that constrict the pupilincrease the depth of focus and help to extend the effective range of accommodation

The shape of the gradient index profile across the lens as well as shape changes due toaccommodation 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 negativespherical aberration of the lens corrects for much of the positive spherical aberrationinduced by the cornea (21) Further accommodation tends to give the eye an overallnegative spherical aberration, but the exact amount varies among individuals (22) Ingeneral, near accommodation tends to increase the monochromatic wavefront aberrations

of the eye (23) Fourth-order aberrations can either increase or decrease with increasingaccommodation, but higher-order aberrations tend to increase (22) It has been suggestedthat there is no correlation between the change in aberration during accommodation andthe total amount of aberration for the relaxed eye (22) It can be concluded that anyclarity of vision provided by refractive surgery must diminish by a measurable extent withaccommodation, 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

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

Hyper-4 Applegate RA, Howland HC Magnification and visual acuity in refractive surgery ArchOphthalmol 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 ofthe Eye from the Age of Three MRC special report series no 301 London: Her Majesty’sStationery 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 EyeRes 1998; 17:380–383

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

16 Mutti DO, Zadnik K, Adams AJ The equivalent refractive index of the crystalline lens inchildhood 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 hyperopiawith 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 duringintensive glycaemic control Br J Ophthalmol 2000; 84:1097–1102

20 Smith G, Pierscionek BK, Atchison DA The optical modelling of the human lens OphthalmicPhysiol 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

The Helmholtz Mechanism of

Accommodation

ADRIAN GLASSER

College of Optometry, University of Houston, Houston, Texas, U.S.A.

“There is no other portion of physiological optics where one finds so many differing andcontradictory ideas as concerns the accommodation of the eye, where only in the mostrecent time have we actually made observations where previously everything was left to theplay of hypotheses.”

H Von Helmholtz (1909)

In 1853 Hermann von Helmholtz described the mechanism of accommodation of thehuman eye This was not the first description of how the human eye accommodates Manydescriptions of and much research on accommodation preceded the work of Helmholtz(1), yet the accommodative mechanism of the human eye is still generally referred to asthe “classic Helmholtz accommodative mechanism.” Helmholtz succeeded where othershad failed at providing a comprehensive and consistent explanation of how accommodationoccurs It was comprehensive in that he described the functions of all of the major elements

of the accommodative apparatus, and it was consistent in that it required no significantmodifications of what was known with certainty at the time regarding how accommodationoccurs

In order to understand how accommodation occurs, it is necessary to have a clear standing of the accommodative apparatus and the relationships of the accommodativestructures to each other While in recent years there has been some limited debate over

under-27

28 Glasser

Figure 1 Hermann Ludwig Ferdinand von Helmholtz (b, 1821; d, 1894) was not the first todescribe the accommodative mechanism of the human eye, but he provided the first comprehensiveand 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 andharmonious description of how accommodation occurs Although the description that Helmholtzprovided was largely accurate, subsequent experimental studies have shown that some aspects ofthe accommodative mechanism are not as Helmholtz described For example, Helmholtz believedthat the posterior surface of the lens did not move with accommodation and that the iris played animportant role in mediating the accommodative changes in the lens

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

The ciliary muscle consists of three subgroups of muscle fiber cells differentiated by theirpositions and orientations within the ciliary body (3) The muscle fibers group are (1) thelongitudinal 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 longitudinalfibers 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 insidethese are the circular fibers, located most anteriorly in the ciliary body and closest to thelens (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

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 equatorialregion 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

interlac-ing fibers, followinterlac-ing 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 concentriclayers New lens fibers develop from the germinative zone at the anterior equatorial region of thelens 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 providedexcellent anatomical information on the structure and relationships of various elements of the accom-modative apparatus to each other In particular, the arrangement of the zonular fibers passing from theciliary body to the lens equator shows a picture remarkably consistent with subsequent descriptions ofthis tissue, but quite unlike that postulated in recent controversial and anatomically inaccurate theories(i.e., Refs 9 and 43) (From Ref 2.)

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 thelens capsule around the equatorial region of the lens The individual zonular fibers termi-nate 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 posteriorsurfaces, as suggested by Schachar (9); instead, the zonular fibers form a uniform distribu-tion or meshwork of fibers inserting all around the equatorial region of the lens (10,11)

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

The lens consists of a monolayer of epithelial cells on the anterior surface beneaththe capsule, with elongated lens epithelial cells at various stages of maturation The lensfiber cells are arranged in layers to form the younger peripheral cortex and the moremature central lens cortex (Fig 2) The human lens does not shed any of its cells andgrows throughout life by adding lens fibers at its outer equatorial zone Isolated lensesshow 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 withaccommodation, it is important to measure this dimension in unaccommodated eyes todraw conclusions about changes due to aging As the lens grows, there is an increase inthe anterior and posterior surface curvatures of the unaccommodated lens as measuredwith Schiempflug slit-lamp photography (20,21) While the axial thickness and surfacecurvatures of the lens can readily be measured in the living eye, lens diameter, untilrecently, could not Based on the observation that the diameter of lenses removed frompostmortem human eyes increases with increasing age (22), it has been suggested thatthere 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 directed zonular tension on the lens equator is removed Isolated lenses are therefore in

outward-an accommodated form, rather more so for the younger thoutward-an the older lenses (3) Advoutward-ances

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 withage (26)

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 posteriorlens surfaces, and the lens gradient refractive index provide optical refractive power tothe eye In the unaccommodated, emmetropic eye, the optical refracting power allows theimage of a distant object to be focused on the retina In this case, parallel rays of lightfrom the distant object enter the eye and become convergent to focus the image on theretina A near object, closer to the eye than optical infinity, however, has diverging lightrays 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 accomplishedprimarily 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 cham-ber 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 measuredwith an objective refractometer during accommodation, it is clear that the optical powerincreases, 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 ofthe 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 pupildiameter 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 alteringthe 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 anear object on the retina Pupillary constriction can also occur without accommodation,

as with increased illumination This too improves depth of field and hence near readingability, but without accommodation Pupillary constriction and increased depth of fieldare important for improving near reading ability but are very different from the refractivechange that accompanies accommodation

3 Aberrations of the Eye

The imperfect optics of the eye mean that the eye suffers from optical aberrations Thelow-order aberrations, such as defocus and astigmatism, can be corrected with opticalprescriptions, but higher-order aberrations cannot These higher-order aberrations includespherical aberration and coma, for example While the presence of aberrations in the eyereduces 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 accommodativemechanism was fully understood, Sturm (2) proposed that astigmatism could explain howthe 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

32 Glasser

moved such that the interval of Sturm remains on the retina, only a modest change inimage quality occurs, but without a distinct perception of a change in focus Thus subjectiveaccommodation testing may suggest the presence of accommodation in an individual withocular aberrations even when no functional accommodation occurs This illustrates theimportance of considering of the optical aberrations of the eye—how they can contribute

to near vision but yet are clearly distinct from active accommodation

Helmholtz (2) provided the first accurate description of the eye’s accommodative anatomyand 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 wereplaced in a fixative after maximal contraction of the ciliary muscle with eserine or maximumrelaxation of the ciliary muscle with atropine These histological diagrams illustrate that the innerapex of the ciliary body moves forward and toward the axis of the eye with accommodation Noticethat in the unaccommodated state, the inner apex of the ciliary muscle resides behind the scleralspur; 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 righthalf, in the accommodated state, focused for near (N) A contraction of the ciliary muscle movesthe ciliary body closer to the lens equator Resting zonular tension is released The anterior lenssurface is shown to move forward with accommodation and the posterior lens position to remainunchanged (From Ref 2.)

zonular fibers at the lens equator pull and hold the lens in a flattened and unaccommodatedstate The zonular fibers extend from the ciliary processes to their insertion on the lenscapsule at the lens equatorial region When the ciliary muscle contracts with an accom-modative 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 torelease the resting zonular tension When the zonular tension is released, the elasticlens capsule molds the lens to decrease equatorial diameter, increase thickness, andallow the lens anterior and posterior surfaces to undergo an increase in curvature (Fig 3).

Tscherning (28) challenged the Helmholtz theory of accommodation, believing that withaccommodation there is an increase in traction of the zonular fibers at the lens equatorand that the curvatures of the central lens increase while those at the periphery flatten onaccount of the greater resistance and steeper curvatures of the lens nucleus (Fig 4) Inother words, with a traction of the zonular fibers, the softer cortex is molded aroundthe harder nucleus, so that the central lens surface curvatures more closely resemblethe steeper central curvatures of the lens nuclear surface Tscherning also believedthat the vitreous provided a force on the lens posterior surface to aid in the accom-modative mechanism Tschering’s accommodative mechanism required no significantmodification of the anatomy of the accommodative apparatus as Helmholtz had de-scribed 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 aroundthe relatively hardened nucleus He believed the surfaces of the nucleus to be more steeply curvedthan the surfaces of the lens With an increase in traction of the zonular fibers at the lens equatorthe 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.)

34 Glasser

Schachar too has proposed that accommodation occurs through an increase in zonulartension, essentially restating Tscherning’s theory Unlike Tscherning’s theory, however,Schachar’s theory requires significant modification of the accommodative anatomy Scha-char 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 Scha-char’s theory also requires that separate and discrete zonular fiber bundles insert to thatlens anterior, equatorial, and posterior surfaces and that the tension on these discretesubgroups be differentially adjusted with accommodation Like Tscherning, Schachar pro-

poses 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 lensanterior and posterior surfaces relax during accommodation Schachar believes that theincreased zonular tension at the lens equator results in an increase in lens equatorialdiameter, but that the release of zonular tension on the lens anterior and posterior surfacesresults in a flattening of lens peripheral surfaces and an increase in curvature at the center

of the lens

Central to the debate over the Helmholtz and Schachar theories of accommodation is themechanism 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 withaccommodation, first unequivocally demonstrated that the crystalline lens anterior surfaceundergoes an increase in curvature with accommodation (see appendix in Ref 29) Cram-er’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 alsoobserved 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, andthat 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

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 Tscherningarrived at this conclusion from observations of the change in the appearance of the point-spread of his eye and by positioning Young’s double-slit optometer in the center and towardthe periphery of his pupil during accommodation Tscherning believed the Helmholtzaccommodative mechanism to be incorrect because it provided no obvious explanationfor this observation Tscherning believed that this could be explained only by a steepening

of the central lens and a flattening of the peripheral lens

In an attempt to prove his accommodative mechanism, Tscherning studied the ior of bovine lenses (Fig 5) He observed that when inward pressure was applied at thelens equator, the anterior and posterior surface curvatures flattened; but when outwardzonular tension was applied at the lens equator, the anterior surface curvature increased.Schachar also performed similar experiments on bovine lenses to provide experimental

behav-support for his accommodative mechanism and recorded an increase in optical power of

the lens with outward-directed zonular tension at the lens equator (33) The bovine eyeand lens bear little resemblance to that of the primate The bovine eye is unlikely toaccommodate, since it has a diminutive ciliary muscle (34) and a lens that is considerablythicker, more spherical, and harder than the primate lens The paradoxical optical resultsthat Tscherning and Schachar et al (28,35) observed from tests on bovine lenses may bedue to the fact that the bovine lens is structurally and functionally quite different from theprimate lens It is inappropriate to draw conclusions on the accommodative performance ofthe primate lens or on the primate accommodative mechanism from observations of the

Figure 5 Tscherning (Ref 28.), like Schachar et al (33), performed experiments on bovine lenses.(A) When Tscherning applied a squeezing force to the equator of the bovine lens, a peripheralflattening and central steepening resulted (solid line) relative to unstressed lens (dashed line) (B)Tscherning believed that the nucleus was harder and had steeper curvatures than the surfaces of thelens and so provided a resistive force around which the cortex is molded (C) When Tscherningapplied a stretching tension to the lens equator (solid line), the softer lens cortex was molded aroundthe hardened nucleus such that there is an increase in curvature at the center of the lens relative tothe unstretched lens (dashed line) Note that there is no change in thickness of the lens with eithersqueezing or stretching While this may be an accurate depiction of the behavior of the bovine lens,this lens is harder and more spherical than that of the primate lens and is from an animal thatprobably has no accommodation Results from studies on bovine lenses cannot be extrapolated toprove anything about the accommodative performance of the human lens or the accommodativemechanism of the human eye It is well established, for example, that there is an increase in axialthickness of the human lens during accommodation (From Ref 28.)