Ординатура / Офтальмология / Английские материалы / Hyperopia and Presbyopia_Tsubota, Boxer Wachler, Azar_2003
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tion is occurring throughout the developed countries. Therefore, increasing emphasis will be placed on the provision of near vision aids to this sector of the world’s population.
1. Background to Presbyopia Restoration
Unfortunately, currently available devices for near vision assistance—which we may call the “conventional” presbyopia options—suffer from a number of optical and practical disadvantages. Devices such as bifocal spectacles, diffractive intraocular lenses (IOLs), and monovision compromise the position of gaze, field of view, image contrast, or stereopsis because of the method by which they provide near focusing power. More critically, these conventional options do not recreate the continuous focusing ability of the natural young eye. Of the conventional options available, the progressive aspheric spectacle lens (PAL) most closely approaches the ideal of providing continuous near focal distance. However, the continuous focus facility of PALs compromises the position of gaze and field of view within which the required power may be used and introduces often significant optical distortions due to the need to employ sophisticated aspheric surfaces in the design (2,3).
Clearly, none of the conventional options can provide a continuous near focus, full aperture, and field optical system for the presbyope.
Given the deficiencies of the conventional options, many workers have been engaged in the development of strategies seeking to truly restore accommodative function to the presbyopic eye (4–8).
2. Phaco-Ersatz
The strategy of Phaco-Ersatz (4,7,9–11) is to restore accommodation to the presbyopic eye. In this method (Fig. 1), the contents of the presbyopic crystalline lens is extracted
Figure 1 The procedure of Phaco-Ersatz for restoring accommodation. (A) A corneal incision is made followed by a very small diameter ( 1 mm) capsulorhexis. The lens nucleus, cortex, and epithelial cells are extracted through the minicapsulorhexis, leaving an intact lens capsule (B). Using a fine cannula, a polymer gel with the appropriate properties is injected into the lens capsule (C), reproducing a soft, flexible de novo lens (D). The two controllable variables in this approach, which forms the basis of the strategies discussed in this chapter, are the refractive index of the polymer gel and the refilled volume of the de novo lens.
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through a small (around 1 mm in diameter) capsulorhexis and is replaced with a soft polymer gel that is injected into the intact lens capsule. Accommodation is restored by replacing the hardened lens with a polymer gel that recreates the flexibility of the young lens.
Phaco-Ersatz can restore up to 4 D of accommodation in the senile nonhuman primate when a silicone gel is used as the lens refillant (9,10). The most recent developments have refined Phaco-Ersatz by using more sophisticated polymer gels that do not leak out of the capsule and by improving the delivery of the surgery (11–14).
Modern Phaco-Ersatz has reached a sufficiently advanced stage that our attention may now be extended to address other patient-related issues. Certainly with the PhacoErsatz method, it is possible for the patient to employ any of the conventional options for correcting static refractive error such as spectacles and contact lenses. However, patients strongly prefer to avoid any form of ophthalmic appliance. This is evident by the increasing development in and popularity of refractive surgery. Hence, an ability to simultaneously correct refractive error while restoring accommodation would significantly enhance the attractiveness and acceptability of any such procedure for presbyopia correction.
3. Simultaneous Correction of Ametropia
Surgical vision correction options such as radial keratotomy (RK), photo-refractive keratectomy (PRK), laser-assisted in situ keratomileusis (LASIK), keratoprostheses (e.g., corneal inlays) and phakic IOLs may also be used with Phaco-Ersatz. Together, these would restore accommodation as well as correct the ametropic patient.
However, there are advantages in providing a Phaco-Ersatz procedure that can, by itself, simultaneously correct ametropia. For example, there would be reduced risk because only one instead of two surgical procedures is required. Further, the disadvantages [e.g., postsurgical corneal haze and discomfort in PRK and LASIK (15,16)] of some of the aforementioned vision correction options may be obviated.
The purpose of this chapter is to investigate the feasibility of strategies intrinsic to the Phaco-Ersatz procedure that could simultaneously correct ametropia while restoring accommodation.
4. Two Intrinsic Approaches
As the Phaco-Ersatz procedure can principally modify the crystalline lens physical parameters, we are limited to two intrinsic strategies by which ametropia may be corrected simultaneously:
1.controlling the refractive index of the refillant
2.controlling the refilled volume of the de novo lens
The first strategy relies on controlling the power of the de novo lens by increasing or decreasing the refractive index of the polymer gel used for refilling. Assuming that the other properties such as curvature and thickness are not altered, this strategy is conceptually relatively straightforward. Using a polymer gel with a lower refractive index would reduce the power of the crystalline lens, thereby reducing the power of the total eye. This could be used to correct myopia. Conversely, polymer gel with a higher refractive index would increase the power of the eye and be useful for correcting hypermetropia.
The implementation of this first strategy requires polymer gels with a range of refractive indices to be synthesised and made available for Phaco-Ersatz. During the opera-
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tion, the surgeon would choose a polymer gel with an appropriate refractive index for the correction 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 of the 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 refilling calculated and used. Alternatively, an in-line refractometer could be used to monitor the refractive state of the eye during refilling to provide an endpoint indication to the surgeon when 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 are numerous difficulties that render the evaluation of the feasibility of these strategies impractical by physical in-surgery means. For instance, in order to evaluate the feasibility of controlling refractive index of the refillant, a range of polymers would need to be synthesized 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. In the remainder of this chapter, we endeavor to evaluate, by computer-assisted modeling, the feasibility of controlling refractive index and controlling refilled volume as strategies for 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 refractive index. A hint as to the feasibility of this strategy came from early studies in lens refilling that coincidentally made use of materials of a low refractive index. In those studies, the eye 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 on the amplitude of accommodation. Hence, while ametropia may be correctable by controlling the refractive index of the refillant, it is equally important to ensure that the resultant amplitude of accommodation is sufficient for near work. Therefore, any analysis of the feasibility 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 polymer gel was analyzed by theoretical modeling (Fig. 3).
We analyzed a paraxial [Gullstrand no 1 Schematic Eye (19)] and a finite aspheric eye [Navarro aspheric model eye (20)] using paraxial optical equations and computerassisted optical ray tracing (Zemax version 9, Focus Software Incorporated, AZ) respectively. Both refractive and axial refractive ametropia were analyzed. In each case, the refractive index of the gel varied between 1.34 and 1.49. A backward ray trace (from retina to air) was conducted to find the corresponding far point of the eye. The accommodation state of the model eye was then set to a nominal value of 10 D and the backward ray
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trace repeated to find the near point. The amount of correctable ametropia was obtained from the first ray trace. The difference in results between the second and first ray trace yields the associated amplitude of accommodation.
B. RESULTS
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 11.0 D and 14.6 D, and12.6 D and 12.4 D for refractive and axial ametropia, respectively (Fig. 2). For the Navarro eye, this range is between 12.4 D and 12.2 D, and 14.6 D and 10.9 D for refractive and axial ametropia, respectively.
2. Amplitude of Accommodation
When the refractive index of the refillant ranges from 1.34 to 1.49, the amplitude of accommodation ranges from near zero to 14.6 D and 13.4 D for refractive and axial
Figure 2 Refractive and axial ametropia correctable by varying the refractive index of the polymer gel in Phaco-Ersatz for two model eyes. Interpolation of the Gullstrand results indicates that the lens cortex and nucleus may be replaced by an equivalent single uniform refractive index of 1.409 to achieve emmetropia. (From Ref. 18.)
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hypermetropia, respectively, with the Gullstrand eye model, and to 9.7 D and 8.9 D for refractive and axial hypermetropia, respectively, with the Navarro model. The nominal state 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 assumption that the shape of the refilled lens does not differ significantly from the original natural lens. This assumption is probably reasonable given that the shape of the young lens is determined largely by the properties of the capsule (21,22). Thus, provided the mechanical properties of the polymer gel refillant closely mimic those of the young natural lens, large departures from the natural shape are presumed to be unlikely (Fig. 3).
The implications of controlling the refractive index of the refillant on correction of ametropia 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 12 D myope would result in virtually no accommodation being available. At this point, the refractive index of the refillant is almost identical to that of the surrounding ocular media and hence, the de novo lens has near zero power and consequently is also incapable of providing accommodative power.
Figure 3 Amplitude of accommodation resulting from varying the refractive index of the polymer gel in Phaco-Ersatz for two model eyes and ametropia types. (From Ref. 18.)
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Figure 4 Relationship between the amplitude of accommodation and the amount of ametropia that 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 by assuming a required minimum amplitude for accommodation. For example, if a standard near work distance of 40 cm is adopted and assuming that an additional 50% of accommodative 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. With this value, Figure 4 indicates that, for the Gullstrand model eye, myopia greater than 2.5 D should not be corrected by reducing the refractive index of the refillant. According to the Navarro model, no corrections for myopia are acceptable with the assumed requirements. In addition to the limitation on myopic corrections, the following practical issues may also 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 be available for Phaco-Ersatz. The synthesis of such a range of polymers with similar mechanical properties and biocompatibility factors poses a daunting technical challenge to polymer developers.
The accuracy required for correction of ametropia to an accuracy of 0.125 D would require the refractive index to be controlled to an accuracy of 0.0008. This accuracy needs to be maintained over its working life despite potential changes in hydration and fouling.
Correction of ametropia with this strategy is limited to spherical refractive errors. Astigmatic correction is not feasible.
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Figure 5 Geometrical definitions of the two models for underand overfilling of the crystalline lens. (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 underor 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 the anterior 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 provides for 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 the two models.
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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 in anisoaccommodation. Further, the result at near is an induced anisometropia of the opposite sign to the original state of anisometropia.
A further issue relates to ocular aberrations. There is evidence (24–26) that the spherical aberration of the eye changes over the range of accommodation (Figure 5). It has been postulated that this change in spherical aberration with accommodation is an effect of the refractive index gradient of the crystalline lens (27) (Fig. 6). When this gradient is replaced by a uniform refractive index, ocular aberration during near work with the de novo lens would differ from the natural lens and may affect near visual performance (Fig. 7). Conversely, the greater positive aberration might increase depth of focus and reduce the accommodative demand and, more significantly, permit greater tolerance in the accuracy of ametropia correction.
While a number of limitations have been presented above with respect to the strategy under discussion, it should be noted that a few of these (e.g., requirement of accuracy of refractive index) apply not just to controlling refractive index within Phaco-Ersatz but also to any nonaccommodating polymer-based intracapsular ametropia correction devices (e.g., injectable IOLs) as well (Fig. 8).
4. Summary
While conceptually attractive, it is clear from the foregoing findings and the number of potential implementation difficulties that significant challenges will face any attempt to introduce this strategy as a method for correcting ametropia within Phaco-Ersatz.
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Figure 7 Refractive and axial ametropia correctable by controlling the refilled volumed of the crystalline 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 surfaces and 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 x 0 axial position. Note the extreme shallowness of the anterior chamber and great lens thickness associated with the correction of high amounts of hypermetropia.
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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 mechanical and 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. A number of these parameters are unknown, as they have not been measured to any acceptable level of accuracy in the living eye. For example, it is not known how the vitreous influences lens position and shape. Even more basic parameters, such as the shape of the crystalline lens 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 influencing parameters, any theoretical model of this strategy must necessarily require imposition of a number of assumptions. To facilitate our modeling analysis, we adopted the following assumptions:
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 refilling and 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 possess the 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 of the second requirement is that the model lens must not only possess similar radii of curvature and thickness as the crystalline lens but that it must also have a continuous surface at the equator.
Unfortunately, we have found no eye model in the literature that satisfies all of the above requirements. We therefore set out to develop an eye model for the purpose of this study 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 and citation.
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.