Hyperopia and Presbyopia - part 9 pptx

262 Ho et al. 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 imprac- tical 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 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. 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 control- ling 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 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, 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 accommoda- tion state of the model eye was then set to a nominal value of 10 D and the backward ray 263Phaco-Ersatz 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 מ11.0 D and ם14.6 D, and מ12.6 D and ם12.4 D for refractive and axial ametropia, respectively (Fig. 2). For the Navarro eye, this range is between מ12.4 D and ם12.2 D, and מ14.6 D and ם10.9 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.) 264 Ho et al. 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 מ12 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.) 265Phaco-Ersatz 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 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. With this value, Figure 4 indicates that, for the Gullstrand model eye, myopia greater than מ2.5 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 ע0.125 D would require the refractive index to be controlled to an accuracy of ע0.0008. 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. 266 Ho et al. Figure 5 Geometrical definitions of the two models for under- and 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 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 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. 267Phaco-Ersatz 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 toler- ance 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. 268 Ho et al. 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 xס0 axial position. Note the extreme shallowness of the anterior chamber and great lens thickness associated with the correction of high amounts of hypermetropia. 269Phaco-Ersatz 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. 270 Ho et al. Table 1 The Prescription of the Modified Navarro Eye for Modeling the Relationship Between Refilled Lens Volume and Ametropia Correction Surface Radius Thickness Index Diameter Q Cornea anterior 7.72 0.55 1.376 – Ϫ0.26 Cornea posterior 6.50 3.05 1.3374 – 0.00 Lens anterior 10.20 1.898 1.42 – 4.3740 Lens equator – 3.227 1.42 8.8 – Lens posterior Ϫ6.00 15.672 1.336 – 0.8595 tion to the anatomical and geometrical parameters of the crystalline lens. This lens model was based on combining two half-ellipsoids of revolution, as employed by past workers (27,32). The anterior and posterior radii of curvature of the lens were the same as those of the Navarro eye. By setting the length of the major axes (perpendicular to the optical axis) of the half-ellipsoids to be identical, the continuity of the lens surface at the equator was 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 asphericity and half-thickness of each half-ellipsoid were calculated employing equations relating to the 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 control- 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 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 geometrical properties to the model. c. Refilling Model No information is available in the literature about the quantitative relationship between lens curvatures and lens volume. Hence, a validated model of the change in lens curvature with refilling is not possible at this stage. In view of this paucity of information, we developed 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 thickness and curvature with increasing lens volume during refill. In general, Model 1 predicts that the anterior curvature and half-thickness of the lens will change more quickly than the posterior 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 in between. 271Phaco-Ersatz Model 1: “Spherization.” This model assumes that as the lens is filled and then overfilled; it converges toward a sphere (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 that the anterior radius of curvature is greater at the “normal” volume, this model predicts that with overfilling, the anterior curvature would change more rapidly than the posterior curvature. We assumed that the lens equator expands slightly with overfilling. Model 1 is represented mathematically as follows (Fig. 5). The anterior and posterior half-lenses are represented by half-ellipsoids of revolution such that their two-dimensional cross sections may be described by x 2 a 2 ם y 2 b 2 ס 1 (1) 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 a′ ס s ן (b e מ a) ם a (2a) b′ ס s ן (b e מ b) ם b (2b) where a′ is the half-thickness of the over-or underfilled half-lens. b is the half-diameter of the over-or underfilled lens. b e is the radius of the endpoint sphere towards which the shape of an overfilled lens will converge. s is a scaling factor defining the amount of over-or underfilling (s ס 0 is normal volume of filling, s Ͼ 0 is overfilling, and s Ͻ 0 is underfilling). Model 2: “Proportional Expansion.” Model 2 assumes that as the lens is filled and then overfilled, the posterior and anterior half-ellipsoids increase in axial dimensions (i.e., the length of the minor axis) in the same ratio. In contrast to Model 1, the posterior curvature in Model 2 would increase more rapidly than the anterior curvature as the lens overfills. As in Model 1, we assumed that the 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 of revolution according to Eq (1). During lens refilling, Model 2 defines the following changes in lens shape: a′ a ס (a′ p ן a a )/a p (3a) a′ p ס s ן (b e מ a p ) ם a p (3b) b′ ס s ן (b e מ b) ם b (3c) where nomenclatures are as for the previous equations and subscript a ס values pertaining [...]... follow-up (months) Study Year No of eyes Technique and microkeratome used O’Brart (12) 199 7 43 6 Daya (3) 199 7 25 6 Jackson (4) 199 8 65 14 VISX Star Excimer Laser 9. 0-mm peripheral zone/ 5.0-mm optical zone Williams (5) 2000 41 12 VISX Star Excimer Laser 9. 0-mm peripheral zone/ 5.0-mm optical zone El-Agha (9) 2000 22 12 Haw (10) 2000 18 24 VISX Star S2 Excimer Laser 8. 8- to 9. 0-mm ablation diameter/5.0-mm... human lens Ophthalm Physiol Opt 199 1; 11:3 59 3 69 28 Howcroft M, Parker J Aspheric curvatures for the human lens Vis Res 197 7; 17:1217–1223 29 Glasser A, Campbell M Biometric, optical and physical changes in the isolated human crystalline lens with age in relation to presbyopia Vis Res 199 9; 39: 199 1–2015 30 Hamaoui M, Manns F, Ho A, Parel J-M Topographical analysis of ex-vivo human crystalline lens Invest... Design and placement in an excised animal eye Ophthalm Surg 199 0; 21:128–133 7 Parel JM Phaco-Ersatz 2001: cataract surgery designed to preserve and restore accommodation An Inst Barraquer 199 1; 22:1–20 8 Hettlich HJ, Asiyo-Vogel M Experiments with balloon implantation into the capsular bag as an accommodative IOL Ophthalmologe 199 6; 93 :73–75 276 Ho et al 9 Haefliger E, Parel J-M, Fantes F, Norton E, Anderson... Press; 191 2 37 Tahi H, Hamaoui M, Parel J-M Human lens-capsule thickness: correlation with lens shape during accommodation and practical consequence for cataract surgery designed to restore accommodation Invest Ophthalmol Vis Sci 199 9; 40:S887 38 Krag S, Andreassen T, Olsen T Elastic Properties of the lens capsule in relation to accommodation and presbyopia Invest Ophthalmol Vis Sci 199 6; 37(3):S163 39 Krag... photorefractive keratectomy for myopia J Refract Surg 199 9; 15(3):384–387 17 Kessler J Refilling the rabbit lens Further experiments Arch Ophthalmol 196 6; 76(4): 596 – 598 18 Ho A, Erickson P, Manns F, Pham T, Parel J-M Theoretical analysis of accommodation amplitude and ametropia correction by varying refractive index in Phaco-Ersatz Optom Vis Sci 2001; 78(6):1 19 Gullstrand A Appendix II: Procedure of rays in the... capsule Acta Ophthalmol Scand 199 9; 77(3): 364 25 Accommodating and Adjustable IOLs SANDEEP JAIN, DIMITRI T AZAR, and RASIK B VAJPAYEE Corneal and Refractive Surgery Service, Massachusetts Eye and Ear Infirmary, Schepens Eye Research Institute, and Harvard Medical School, Boston, Massachusetts, U.S.A A INTRODUCTION This chapter focuses on recent developments of accommodating and adjustable intraocular... Fernandez V, Manns F, Zipper S, Sandadi S, Minhaj A, Ho A, et al Topography of anterior and posterior crystalline lens surfaces of human eye-bank eyes Invest Ophthalmol Vis Sci 2001; 42(4):S880 Phaco-Ersatz 277 32 Popiolek-Masajada A Numerical study of the influence of the shell structure of the crystalline lens on the refractive properties of the human eye Ophthalm Physiol Opt 199 9; 19( 1):41– 49 33... Optom Vis Sci 199 6; 73:382–388 5 Mathews S Scleral expansion surgery does not restore accommodation in human presbyopia Ophthalmology 199 9; 106:873–877 6 Gray GP, Campin JA, Pettit GH, Liedel KK Use of wavefront technology for measuring accommodation and corresponding changes in higher order aberrations (abstr) Invest Ophthalmol Vis Sci 2001; 42:S26 27 Complications of Hyperopia and Presbyopia Surgery... Anderson D, Forster R, Hernandez E, Feuer WJ Accommodation of an endocapsular silicone lens (Phaco-Ersatz) in the nonhuman primate Ophthalmology 198 7; 94 (4):471–477 10 Haefliger E, Parel J-M Accommodation of an endocapsular silicone lens (Phaco-Ersatz) in the aging rhesus monkey J Refract Corneal Surg 199 4; 10(5):550–555 11 Parel J-M, Holden B Accommodating intraocular lenses and lens refilling to restore... diameter/5.0-mm optical zone Summit Apex Plus Excimer Laser, Combining an Erodible mask and an Axicon system 9. 4-mm peripheral zone/6.5-mm optical zone Summit Apex Plus Laser, combining an erodible mask and an Axicon system 9. 5-mm peripheral zone/6.5-mm optical zone Chiron Keracor 116 Excimer Laser 8.5-mm peripheral zone/5.0-mm optical zone Complications Loss of best corrected visual acuity (BCVA) • 21% subepithelial . the isolated human crystal- line lens with age in relation to presbyopia. Vis Res 199 9; 39: 199 1–2015. 30. Hamaoui M, Manns F, Ho A, Parel J-M. Topographical analysis of ex-vivo human crystalline lens Sci 199 9; 40:S887. 38. Krag S, Andreassen T, Olsen T. Elastic Properties of the lens capsule in relation to accommoda- tion and presbyopia. Invest Ophthalmol Vis Sci 199 6; 37(3):S163. 39. Krag. Ophthalmol Scand 199 9; 77(3): 364. 25 Accommodating and Adjustable IOLs SANDEEP JAIN, DIMITRI T. AZAR, and RASIK B. VAJPAYEE Corneal and Refractive Surgery Service, Massachusetts Eye and Ear Infirmary, Schepens