Hyperopia and Presbyopia - part 9 pptx

tion, the surgeon would choose a polymer gel with an appropriate refractive index for thecorrection of the patient’s particular amount of ametropia.The second strategy involves altering

tion, the surgeon would choose a polymer gel with an appropriate refractive index for thecorrection of the patient’s particular amount of ametropia.

The second strategy involves altering the volume of the de novo lens with a view

to altering the anterior and posterior curvatures and thickness By doing so, the power ofthe crystalline lens and hence the total power of the eye can also be altered

This second strategy can be implemented in two ways Firstly the refractive error

of the patient could be measured prior to operation and the appropriate volume for refillingcalculated and used Alternatively, an in-line refractometer could be used to monitor therefractive state of the eye during refilling to provide an endpoint indication to the surgeonwhen the correct volume has been reached

Given the simplicity of these strategies, their applicability and feasibility is worthy

of evaluation

While the concepts relating to these two strategies are relatively simple, there arenumerous difficulties that render the evaluation of the feasibility of these strategies imprac-tical by physical in-surgery means For instance, in order to evaluate the feasibility ofcontrolling refractive index of the refillant, a range of polymers would need to be synthe-sized first Even then, extraneous factors, such as the mechanical properties of the range

of polymer gels, would need to be controlled in order to return valid results

With these constraints, analyses by theoretical modeling provide a good, workable,first approximation as an alternative to evaluation of the feasibility of these strategies Inthe remainder of this chapter, we endeavor to evaluate, by computer-assisted modeling,the feasibility of controlling refractive index and controlling refilled volume as strategiesfor the simultaneous correction of ametropia with Phaco-Ersatz

5 Controlling Refractive Index

As mentioned, this strategy involves the management of the refractive status (or “error”)

of the eye through controlling the power of the de novo lens by controlling its refractiveindex A hint as to the feasibility of this strategy came from early studies in lens refillingthat coincidentally made use of materials of a low refractive index In those studies, theeye with de novo lenses with low refractive index were found to be hypermetropic (17).However, altering the refractive index of the lens has an accompanying effect onthe amplitude of accommodation Hence, while ametropia may be correctable by control-ling the refractive index of the refillant, it is equally important to ensure that the resultantamplitude of accommodation is sufficient for near work Therefore, any analysis of thefeasibility of this strategy must take into account the range of ametropia that is correctable

as well as the impact on the amplitude of accommodation

We reported on such a study (18) in which the feasibility of simultaneous correction

of ametropia with Phaco-Ersatz through controlling the refractive index of the polymergel was analyzed by theoretical modeling (Fig 3)

We analyzed a paraxial [Gullstrand no 1 Schematic Eye (19)] and a finite asphericeye [Navarro aspheric model eye (20)] using paraxial optical equations and computer-assisted optical ray tracing (Zemax version 9, Focus Software Incorporated, AZ) respec-tively Both refractive and axial refractive ametropia were analyzed In each case, therefractive index of the gel varied between 1.34 and 1.49 A backward ray trace (fromretina to air) was conducted to find the corresponding far point of the eye The accommoda-tion state of the model eye was then set to a nominal value of 10 D and the backward ray

trace repeated to find the near point The amount of correctable ametropia was obtainedfrom the first ray trace The difference in results between the second and first ray traceyields the associated amplitude of accommodation.

1 Refractive Error Correction

Using the Gullstrand model eye and a refractive index range of 1.34 to 1.49 for the refillant,the range of correctable refractive ametropia is between ⳮ11.0 D and Ⳮ14.6 D, andⳮ12.6 D and Ⳮ12.4 D for refractive and axial ametropia, respectively (Fig 2) For theNavarro eye, this range is betweenⳮ12.4 D and Ⳮ12.2 D, and ⳮ14.6 D and Ⳮ10.9 Dfor refractive and axial ametropia, respectively

to achieve emmetropia (From Ref 18.)

hypermetropia, respectively, with the Gullstrand eye model, and to 9.7 D and 8.9 D forrefractive and axial hypermetropia, respectively, with the Navarro model The nominalstate of accommodation was equivalent to 10 D in all cases.

3 Discussion

It should be noted that the reported theoretical analysis (18) is based on a key assumptionthat the shape of the refilled lens does not differ significantly from the original naturallens This assumption is probably reasonable given that the shape of the young lens isdetermined largely by the properties of the capsule (21,22) Thus, provided the mechanicalproperties of the polymer gel refillant closely mimic those of the young natural lens, largedepartures from the natural shape are presumed to be unlikely (Fig 3)

The implications of controlling the refractive index of the refillant on correction ofametropia and amplitude of accommodation is shown by combining the data from Figs

2 and 3 (Fig 4) The amplitude of accommodation progressively decreases as we attempt

to correct higher amounts of myopia In the limiting case, the correction of a ⳮ12 Dmyope would result in virtually no accommodation being available At this point, therefractive index of the refillant is almost identical to that of the surrounding ocular mediaand hence, the de novo lens has near zero power and consequently is also incapable ofproviding accommodative power

Figure 3 Amplitude of accommodation resulting from varying the refractive index of the polymergel in Phaco-Ersatz for two model eyes and ametropia types (From Ref 18.)

Figure 4 Relationship between the amplitude of accommodation and the amount of ametropiathat was correctable for two model eyes and ametropia types (From Ref 40.)

A practical limit to the range of ametropia that is correctable may be derived byassuming a required minimum amplitude for accommodation For example, if a standardnear work distance of 40 cm is adopted and assuming that an additional 50% of accommo-dative amplitude is required in reserve at all times for comfortable, prolonged reading(23), we set the acceptable minimum amplitude of accommodation at around 5 D Withthis value, Figure 4 indicates that, for the Gullstrand model eye, myopia greater thanⳮ2.5

D should not be corrected by reducing the refractive index of the refillant According to theNavarro model, no corrections for myopia are acceptable with the assumed requirements

In addition to the limitation on myopic corrections, the following practical issues mayalso impact the feasibility of this strategy These issues are as follows:

The need for a series of polymer gels with a large range of refractive indexes to beavailable for Phaco-Ersatz The synthesis of such a range of polymers with similarmechanical properties and biocompatibility factors poses a daunting technicalchallenge to polymer developers

The accuracy required for correction of ametropia to an accuracy of Ⳳ0.125 Dwould require the refractive index to be controlled to an accuracy ofⳲ0.0008.This accuracy needs to be maintained over its working life despite potentialchanges in hydration and fouling

Correction of ametropia with this strategy is limited to spherical refractive errors.Astigmatic correction is not feasible

Figure 5 Geometrical definitions of the two models for under- and overfilling of the crystallinelens (A) Model 1 describes the “spherization” model The “normal” lens is defined by an ellipsoid

of revolution with major and minor axes a and b (see Table 1) When the lens is under- or overfilled,its major and minor axes are defined by a′ and b′ A scaling factor is used to determine a′ and b′from a and b [Eq (2a) and (2b)] With this set of equations for defining a′ and b′, the effect is that

as the lens volume changes, there is a more rapid accompanying change in the curvature of theanterior than the posterior lens surface (B) Model 2 describes the “proportional expansion” model

In this model, a′ and b′ are set by a scaling factor according to Eqs (3a) to (3c) This model providesfor a more rapid accompanying change in the posterior curvature of the lens surface as lens volume

changes Note that the scaling factor [s in Eqs (2a), (2b), (3b), and (3c)] is used only as a parameter

for computation The relationship between this scaling factor and lens volume is different for thetwo models

Figure 6 The relationship between the equivalent power of the crystalline lens and its thickness,with lens volume according to Models 1 and 2.

Correction of anisometropia is also not feasible, as such an attempt would result inanisoaccommodation Further, the result at near is an induced anisometropia ofthe opposite sign to the original state of anisometropia

A further issue relates to ocular aberrations There is evidence (24–26) that thespherical aberration of the eye changes over the range of accommodation (Figure 5) Ithas been postulated that this change in spherical aberration with accommodation is aneffect of the refractive index gradient of the crystalline lens (27) (Fig 6) When thisgradient is replaced by a uniform refractive index, ocular aberration during near workwith the de novo lens would differ from the natural lens and may affect near visualperformance (Fig 7) Conversely, the greater positive aberration might increase depth offocus and reduce the accommodative demand and, more significantly, permit greater toler-ance in the accuracy of ametropia correction

While a number of limitations have been presented above with respect to the strategyunder discussion, it should be noted that a few of these (e.g., requirement of accuracy ofrefractive index) apply not just to controlling refractive index within Phaco-Ersatz butalso to any nonaccommodating polymer-based intracapsular ametropia correction devices(e.g., injectable IOLs) as well (Fig 8)

While conceptually attractive, it is clear from the foregoing findings and the number ofpotential implementation difficulties that significant challenges will face any attempt tointroduce this strategy as a method for correcting ametropia within Phaco-Ersatz

Figure 7 Refractive and axial ametropia correctable by controlling the refilled volumed of thecrystalline lens in Phaco-Ersatz according to models 1 and 2 using the modified Navarro eye.

Figure 8 Axial positions of the anterior cornea, anterior and posterior crystalline lens surfacesand the lens equator and retina as a function of lens volume for refractive and axial ametropia within

models 1 and 2 The anterior cornea is located at the x⳱0 axial position Note the extreme shallowness

of the anterior chamber and great lens thickness associated with the correction of high amounts ofhypermetropia

3 Controlling Refilled Volume

In this section, we evaluate the feasibility of the second strategy for simultaneous correction

of ametropia within Phaco-Ersatz With this strategy, the interaction of the mechanicaland geometrical properties of the lens and capsule, as well as the influence of the vitreous

on lens position and potentially the shape of the lens, creates a more complex system Anumber of these parameters are unknown, as they have not been measured to any acceptablelevel of accuracy in the living eye For example, it is not known how the vitreous influenceslens position and shape Even more basic parameters, such as the shape of the crystallinelens at various levels of accommodation, have not been measured in a systematic manner.*Due to the lack of detailed, quantitative knowledge about many of the influencingparameters, any theoretical model of this strategy must necessarily require imposition of

a number of assumptions To facilitate our modeling analysis, we adopted the followingassumptions:

1 The position and shape of the lens is not affected by the iris or vitreous regardless

of the volume of refilling

2 The position of the lens is set by its equatorial plane at all volumes of refillingand the position of the equatorial plane is fixed with respect to the eye

4 Eye Models

a Requirements

A suitable model eye for analyzing the optical effect of altering lens volume must possessthe following features:

1 Accurate rendering of lens volume

2 Reasonable anatomical approximation

3 Faithful rendering of the optics of the eye

The first requirement is absolute for the purpose of this study The consequence ofthe second requirement is that the model lens must not only possess similar radii ofcurvature and thickness as the crystalline lens but that it must also have a continuoussurface at the equator

Unfortunately, we have found no eye model in the literature that satisfies all of theabove requirements We therefore set out to develop an eye model for the purpose of thisstudy by combining suitable elements from established eye and lens models

b Modified Navarro Eye

The current model is based on a modification of the Navarro aspheric eye model (20),which represents a de facto standard in finite eye models in terms of its employment andcitation

The crystalline lens component of the Navarro model was replaced by a model lens,which accurately portrayed the lens volume as well as providing a reasonable approxima-

* Good data exist on the thickness, curvatures and optical power of a crystalline lens in the relaxed state (28,29) However, no quantitative data exist relating changes in all of these parameters with accommodation We note that efforts are being made currently to develop measurement systems for quantifying the topography of the anterior and posterior crystalline lens surfaces at various levels of accommodation (30,31) We look forward

to the availability of these data for improving the precision of our model.

Table 1 The Prescription of the Modified Navarro Eye for Modeling the Relationship BetweenRefilled Lens Volume and Ametropia Correction

Surface Radius Thickness Index Diameter Q

of the Navarro eye By setting the length of the major axes (perpendicular to the opticalaxis) of the half-ellipsoids to be identical, the continuity of the lens surface at the equatorwas ensured We chose 200␮L as a reasonable nominal initial volume of the model lens

to simulate the natural human lens (33)

Given the assumed curvatures, equatorial diameter, and lens volume, the asphericityand half-thickness of each half-ellipsoid were calculated employing equations relating tothe apical radius of curvature and shape factors of conic sections (34)

Finally, the model eye was “emmetropized” by adjusting the vitreous chamber depth(distance between posterior lens surface and retina)

The resultant prescription of the modified Navarro model eye for analysis of ling refilled lens volume is given in Table 1 The volume of this lens model is 208␮L.The equatorial diameter of 8.8 mm is slightly less while the thickness of 5.12 mm

control-is slightly greater than the respective parameters for the typical adult lens (28) However,this was necessitated by a compromise in providing reasonable optical and geometricalproperties to the model

c Refilling Model

No information is available in the literature about the quantitative relationship betweenlens curvatures and lens volume Hence, a validated model of the change in lens curvaturewith refilling is not possible at this stage In view of this paucity of information, wedeveloped two simple but plausible mathematical models for lens refilling These were:

1 Model 1: “spherization”

2 Model 2: proportional expansion

These two models (Fig 5) provide contrasting relationships between lens thicknessand curvature with increasing lens volume during refill In general, Model 1 predicts thatthe anterior curvature and half-thickness of the lens will change more quickly than theposterior curvature and half-thickness as the lens refills during Phaco-Ersatz, while Model

2 predicts the converse The intention of testing two such disparate models is to provide

a “bracketing” of the results, such that the actual life situation might lie somewhere inbetween

Model 1: “Spherization.”

This model assumes that as the lens is filled and then overfilled; it converges toward asphere (i.e., the length of the major and minor axes at the endpoint of filling is the same).Hence, the posterior and anterior curvatures would converge with overfilling Given thatthe anterior radius of curvature is greater at the “normal” volume, this model predicts thatwith overfilling, the anterior curvature would change more rapidly than the posteriorcurvature We assumed that the lens equator expands slightly with overfilling

Model 1 is represented mathematically as follows (Fig 5) The anterior and posteriorhalf-lenses are represented by half-ellipsoids of revolution such that their two-dimensionalcross sections may be described by

x2

where x is the distance along the optical axis

y is the distance across the optical axis

a is the half-length of the minor axis representing the half-thickness of the lens-half

at normal volume

b is the half-length of the major axis representing the half-diameter of the lens at

its equator at normal volume

Lens refilling according to Model 1 follows the relationship of

where a′ is the half-thickness of the over-or underfilled half-lens.

b is the half-diameter of the over-or underfilled lens.

beis the radius of the endpoint sphere towards which the shape of an overfilled lenswill converge

s is a scaling factor defining the amount of over-or underfilling (s⳱ 0 is normal

volume of filling, s ⬎ 0 is overfilling, and s ⬍ 0 is underfilling).

Model 2: “Proportional Expansion.”

Model 2 assumes that as the lens is filled and then overfilled, the posterior and anteriorhalf-ellipsoids increase in axial dimensions (i.e., the length of the minor axis) in the sameratio In contrast to Model 1, the posterior curvature in Model 2 would increase morerapidly than the anterior curvature as the lens overfills As in Model 1, we assumed thatthe lens equator expands slightly with overfilling

Model 2 is represented mathematically as follows (Fig 5):

The anterior and posterior half-lenses are again represented by half-ellipsoids ofrevolution according to Eq (1) During lens refilling, Model 2 defines the following changes

to the anterior half-lens; subscript p⳱ values for the posterior half-lens For both models,

we assumed beto be 4.9 mm

a Calculation of Volume of Over-Underfilling

For a lens constructed of two half-ellipsoids of revolution, the volume V can be calculated

as

V⳱2

3 ⳯ ␲ ⳯b

From Eqs (1) through (4) and assigning various values for scaling factor s, we can calculate

the volume of the de novo lens at various amounts of filling

b Calculation of Lens Power

The central radius of curvature r of an ellipse is given by (34)

r⳱ a

and its thickness (34) d by:

From Eqs (1) through (3) and (5a) and (5b), the assigned refractive indices, and assigning

various values for the scaling factor s, the power of the de novo lens can be calculated

at various amounts of filling

c Modeling Correctable Ametropia

Armed with the calculated lens curvatures and thicknesses at different levels of lens ing, it is now possible to calculate the associated amount of ametropia that is correctablewithin the two models using the modified Navarro eye model

refill-One final variable had to be fixed—that of the position of the lens at differentlevels of filling Because of the enormous complexity of the interactions between capsulartension, lens volume, vitreous influence, zonular tension and iris influence as well as thelack of precise, quantitative information in many of these factors, we assumed a simplified

model in which the equatorial plane of the lens remains fixed in the axial (x) direction at

all levels of filling Under this assumption, the anterior and posterior lens surfaces wouldbulge forward and backward, respectively, by an amount equal to the change in the length

of the minor axes of the respective half-ellipsoids

The amount of ametropia correctable was computed in two ways—assuming tive ametropia and assuming axial ametropia

refrac-Paraxial optical equations were used in all calculations Dioptric values of ametropiawere referred to the plane of the cornea on the model eye

6 Results

Figure 6 shows the relationship between the volume of lens refilled (expressed as a age of a lens with normal volume) and equivalent refractive power and thickness of theresultant lens The resultant lens thicknesses are not greatly different for Models 1 and 2

percent-The refractive power of the refilled lens varied slightly more with change in refilled volumefor Model 1 than for Model 2 This suggests that should lens refilling follow the shapeand thickness changes predicted by Model 1, a greater amount of ametropia may becorrectable.

From the results shown in Fig 6, the overall power of the eye with a refilled lens,and hence the amount of ametropia correctable, was computed This is shown in Fig 7,which plots the amount of ametropia that is correctable under Models 1 and 2 for bothaxial and refractive ametropia The maximum ametropia that is correctable occurs usingModel 1 with axial ametropia (approximately Ⳳ4 D) The minimum ametropia that iscorrectable occurs using Model 2 with axial ametropia

7 Discussion

a Eye Model

As noted, the geometrical dimensions of the lens model deviated from typical adult humanlenses in that the equatorial diameter was slightly less and the thickness slightly higher.This compromise was necessary to enable simple ellipsoids of revolutions to be used toconstruct a model lens while maintaining reasonable values for the optics and geometricalparameters A more mathematically sophisticated approach (35) has been developed toprovide an anatomically precise representation of the adult human lens However, thatmodel employed a pair of parametric functions within a system of polar coordinates todescribe the lens Given the parametric nature of the model description, there is no directmethod by which changes in volume and curvature may be modeled without a high level

of mathematical complexity Hence for convenience, we adopted the half-ellipsoids ofrevolution (27,32)

The assumed endpoint diameter of the lens was 8.9 mm, which represents a

0.1-mm increase in the diameter of a lens when overfilled to 200% (double the volume).Should this prove to be an overestimation, there would be an increase in the amount ofametropia that is correctable with controlled lens refilling due to the expected increase incurvatures

This model is able to estimate only the amount of ametropia that is correctable bycontrolling the refilled volume of a lens with Phaco-Ersatz Due to a number of limitationsrelating to quantitative understanding of the influence of lens volume on lens shape duringaccommodation, it is not yet possible to study the effect of over- or underfilling on theamplitude of accommodation, as has been done for the refractive index strategy.Hence, there may be detrimental effects on the amplitude of accommodation in theapplication of this strategy, which are yet to be determined

The critical assumption in our lens model is that the lens capsule has a negligibleeffect on the change in curvature and thickness during refilling Intuitively, this wouldnot be the case, given that there is a difference in thickness between the anterior andposterior capsules (21,36,37), which would influence lens shape and thickness duringrefilling However, we have introduced two contrasting models for refilling with the inten-tion that the actual lens response would lie somewhere within this “bracketing.” We be-lieve, therefore, that the robustness of the predictions within our model should be reasona-ble, especially considering that the two contrasting refilling models returned similarpredictions

Finally, there are effects on aberrations that have not been considered First, thegradient index of the natural lens has been eliminated by Phaco-Ersatz This would alter

the aberration state of the eye at both distance and, as discussed, more critically at near.Further, as the lens shape changes, it is highly likely that its surface asphericity would alsochange, thereby altering the aberrations at different refill volumes These considerations arebeyond the scope of the current model but merit further investigation.

b Correction of Ametropia

If we accept the above assumptions and exceptions discussed, then our theoretical analysiswith the eye model predicts the following:

Even at the highest estimate predicted, the amount of ametropia that is correctable

is too low to be practical (Model 1 and axial ametropia) Therefore controllingthe refilled volume alone during Phaco-Ersatz for correcting ametropia is insuffi-cient to correct any other than low degrees of ametropia

The reciprocal of the average slope of the four curves in Fig 7 indicates that inorder to correct ametropia with an accuracy ofⳲ0.125 D, percentage refillingwould have to be controlled to an accuracy ofⳲ2.3% This equates to an approxi-mate accuracy in volume of Ⳳ5 ␮L This may pose a technical and surgicalchallenge

c Issues of Implementation

There are also issues of implementation relating to this strategy

Figure 8 shows the predicted positions of the lens surfaces and retina with changes

in refilled lens volume assuming a fixed position for the equatorial plane Over the range

of under-to overfilling analyzed (50 to 150%), the lens thickness changes from mately 3.5 mm to approximately 8 mm Even ignoring the effect of the iris and vitreous,

approxi-it is certain that such a range would impose impractical values to the resultant anteriorchamber depth In particular, correction of medium to high hypermetropia would result

in dangerously shallow anterior chambers

In addition to considerations of anterior chamber depth, there are other practicallimits to the amount of over-and underfilling that can be achieved The minimum amount

of underfilling is set by the lowest volume that can still produce an undistorted, opticallyuseful de novo lens Below this limit, prism due to sagging, and distortions due to rippling,warping, or waviness as a result of a lack of sufficient capsule tension may degrade visionbelow acceptable limits

There is also an upper limit on the amount of overfilling Beyond this limit, giventhe finite breaking strain of the capsule (38,39), rupture of the capsule would occur.While reliable data on the limits of optical imperfection with excessive underfillingand capsule rupture with excessive overfilling do not exist, a reasonable estimation may

be assumed on these lower and upper limits Experience in our laboratories, which hasbeen conducting surgical trials of Phaco-Ersatz, suggests that a “safe” limit for over- andunderfilling may beⳲ20% of the normal volume Referring back to Fig 7, introduction

of this limit to the volume of refilling predicts that the range of ametropia that is correctable

is significantly reduced to approximatelyⳲ2 D This is probably not a viable range foruseful correction of ametropia

In addition to the above, other implementation issues relevant to the first strategy

as listed in the previous section also apply These include a limitation in the range ofcorrection to spherical (nonastigmatic) refractive errors

8 Summary

Due to the complexity of the interplay between physiology, mechanics, and optics, wehave been able to test only a simplified model of controlled refilling However, even thisfirst approximation suggests that the range of corrections achievable within this strategywould be small because of the limitations of lens thickness as well as implementationdifficulties

In this chapter, we have analyzed, using theoretical modeling, the feasibility of two gies that are intrinsic to Phaco-Ersatz for simultaneous correction of ametropia It appearsfrom the results and consideration of implementation issues that neither strategy on itsown is sufficient or feasible for simultaneous correction of ametropia within Phaco-Ersatz

strate-We have not investigated the feasibility of a combination of the two strategies.However, in view of the above discussions, it may be expected that those combinationswould also lack sufficient range and accuracy for applicability

We therefore conclude, even in the absence of physical experimental results, thatsimultaneous correction using these two intrinsic strategies would be unattractive andprobably not feasible

However, predictions from models are only as reliable as the assumptions made andthe values for parameters assumed We recognize that there are potential shortcomings inour theoretical analyses, which warrant further research In particular, the lack of reliable,quantitative knowledge of relationships such as lens shape and thickness with differentlevel of refilling—as well as the effect of the capsule thickness, vitreous, and iris on lensshape and position—merits study as well in order to refine our models A number ofstudies are under way in our laboratories seeking to address such issues (13,30,31) Webelieve that researchers in this area should persist in their efforts to understand thoserelationships

REFERENCES

1 US Census Bureau International Program Center International Database (IDB) update May2000

2 Simonet P, Papineau Y, LaPointe R Peripheral power variations in progressive addition lenses

Am J Optom Physiol Opt 1986; 63(11):873–880

3 Sullivan C, Fowler C Progressive addition and variable focus lenses: a review OphthalmPhysiol Opt 1988; 8:402–414

4 Parel J-M, Gelender H, Trefers W, Norton E Phaco-Ersatz: cataract surgery designed topreserve accommodation Graefes Arch Clin Exp Ophthalmol 1986; 224(2):165–173

5 Nishi O, Hara T, Hara T, Hayashi F, Sakka Y, Iwata S Further development of experimentaltechniques for refilling the lens of animal eyes with a balloon J Cataract Refract Surg 1989;15:584–588

6 Hara T, Hara T, Yasuda A, Yamada Y Accommodative intraocular lens with spring action:Part 1 Design and placement in an excised animal eye Ophthalm Surg 1990; 21:128–133

7 Parel JM Phaco-Ersatz 2001: cataract surgery designed to preserve and restore accommodation

An Inst Barraquer 1991; 22:1–20

8 Hettlich HJ, Asiyo-Vogel M Experiments with balloon implantation into the capsular bag as

an accommodative IOL Ophthalmologe 1996; 93:73–75

9 Haefliger E, Parel J-M, Fantes F, Norton E, Anderson D, Forster R, Hernandez E, Feuer WJ.Accommodation of an endocapsular silicone lens (Phaco-Ersatz) in the nonhuman primate.Ophthalmology 1987; 94(4):471–477.

10 Haefliger E, Parel J-M Accommodation of an endocapsular silicone lens (Phaco-Ersatz) inthe aging rhesus monkey J Refract Corneal Surg 1994; 10(5):550–555

11 Parel J-M, Holden B Accommodating intraocular lenses and lens refilling to restore dation (restoring accommodation) In: Azar D, ed Intraocular Lenses in Cataract and RefractiveSurgery Philadelphia: Saunders, 2001

accommo-12 Parel JM, Simon G Phaco-Ersatz 2001: update Ann Inst Barraquer 1995; 25:143–151

13 Tahi H, Fantes F, Hamaoui M, Parel J-M Small peripheral anterior continuous curvilinearcapsulorhexis J Cataract Refract Surg 1999; 25:744–747

14 Tahi H, Chapon P, Parel JM, inventors; CRCERT, assignee Mini capsulorhexis valve (MCV)for crystalline lens refilling and posterior capsule opacification (PCO) prevention procedures.United States patent US60/121,179 (US Patent Appl, 2000) PCT/US00/04339 (InternationalAppl 2000)

15 Wilson S LASIK: management of common complications Laser in situ keratomileusis Cornea1999; 17(5):459–467

16 Price F, Jr, Belin M, Nordan L, McDonnell P, Pop M Epithelial haze, punctate keratopathyand induced hyperopia after photorefractive keratectomy for myopia J Refract Surg 1999;15(3):384–387

17 Kessler J Refilling the rabbit lens Further experiments Arch Ophthalmol 1966; 76(4):596–598

18 Ho A, Erickson P, Manns F, Pham T, Parel J-M Theoretical analysis of accommodationamplitude and ametropia correction by varying refractive index in Phaco-Ersatz Optom VisSci 2001; 78(6):1

19 Gullstrand A Appendix II: Procedure of rays in the eye Imagery—laws of the first order In:Southall J, ed Helmholtz’s Treatise on Physiological Optics 3rd ed Optical Society of Amer-ica, 1909

20 Navarro R, Santamaria J, Bescos J Accommodation-dependent model of the human eye withaspherics J Opt Soc Am A 1985; 2(8):1273–1281

21 Fincham E The mechanism of accommodation Br J Ophthalmol 1937; Monograph SupplVIII:5–80

22 Nishi O, Nishi K, Mano C, Ichihara M, Honda T Controlling the capsular shape in lensrefilling Arch Ophthalmol 1997; 115:507–510

23 Borish IM Clinical Refraction, 3rd ed Chicago: Professional Press, 1970

24 Atchison D, Smith G Continuous gradient index and shell models of human lens Vis Res1995; 35(18):2529–2538

25 He J, Burns S, Marcos S Monochromatic aberrations in the accommodated human eye VisRes 2000; 40:41–48

26 Gray G, Campin J, Liedel K, Pettit G Use of wavefront technology for measuring tion and corresponding changes in higher order aberrations Invest Ophthalmol Vis Sci 2001;42(4):S26

accommoda-27 Smith G, Pierscionek B, Atchison D The optical modelling of the human lens OphthalmPhysiol Opt 1991; 11:359–369

28 Howcroft M, Parker J Aspheric curvatures for the human lens Vis Res 1977; 17:1217–1223

29 Glasser A, Campbell M Biometric, optical and physical changes in the isolated human line lens with age in relation to presbyopia Vis Res 1999; 39:1991–2015

crystal-30 Hamaoui M, Manns F, Ho A, Parel J-M Topographical analysis of ex-vivo human crystallinelens Invest Ophthalmol Vis Sci 2000; 41(4):S428

31 Fernandez V, Manns F, Zipper S, Sandadi S, Minhaj A, Ho A, et al Topography of anteriorand posterior crystalline lens surfaces of human eye-bank eyes Invest Ophthalmol Vis Sci2001; 42(4):S880

32 Popiolek-Masajada A Numerical study of the influence of the shell structure of the crystallinelens on the refractive properties of the human eye Ophthalm Physiol Opt 1999; 19(1):41–49.

33 Koretz J, Cook C, Kaufman P Aging of the human lens: changes in lens shape at zero-diopteraccommodation J Opt Soc Am A 2001; 18(2):265–272

34 Burek H, Douthwaite W Axial-radial interconversion J Br Contact Lens Assoc 1993; 16(1):5–13

35 Kasprzak H New approximation for the whole profile of the human crystalline lens OphthalmPhysiol Opt 2000; 20(1):31–43

36 Salzmann M Anatomy and Histology of the Human Eyeball in the Normal State: Its ment and Senescence Chicago: University of Chicago Press; 1912

Develop-37 Tahi H, Hamaoui M, Parel J-M Human lens-capsule thickness: correlation with lens shapeduring accommodation and practical consequence for cataract surgery designed to restoreaccommodation Invest Ophthalmol Vis Sci 1999; 40:S887

38 Krag S, Andreassen T, Olsen T Elastic Properties of the lens capsule in relation to tion and presbyopia Invest Ophthalmol Vis Sci 1996; 37(3):S163

accommoda-39 Krag S Biomechanical measurements of the lens capsule Acta Ophthalmol Scand 1999; 77(3):364