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

dimensional representation of a lenticule was obtained by first subtracting the volume of the primitive modeling of the final theoretical corneal surface from the primitive volume modeling of the initial corneal surface. These primitives were aligned and centered on the Z axis. The ablated lenticule for the correction of pure cylindrical myopic astigmatism was generated by adjusting the distance between the apex of each surface so that they would intersect along the steep meridian within a predetermined circular optical zone. The difference between each of the radii of curvature was exaggerated as compared to the clinical and surgical range to facilitate the spatial visualization of the contour features of the generated lenticules. However, in comparing different strategies, the initial and final surfaces were identical and were rescaled to the same ratio for purposes of comparison. This made it possible to estimate the theoretical differences in the amount of ablated corneal volume by the different available strategies that combine the ablation of these elementary lenticules to correct for a given compound hyperopic astigmatic refractive error.

The transition zone was modeled as a spherical (constant positive curvature) surface encompassing the circular inferior edge of the ablated lenticule and joining the peripheral unablated cornea.

To facilitate the visualization and the distinction of the shapes of the ablated lenticules, cross-sectional color outlines were added along the principal meridians.

REFERENCES

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2.Dierick HG, Missoten L. Corneal ablation profiles for correction of hyperopia with the excimer laser. J Refract Surg, 1996; 12:767–773.

3.Chayet AS, Assil KK, Montes M, Castellanos A. Laser in situ keratomileusis for hyperopia: new software. J Refract Surg 1997; 13(suppl):S434–S435.

4.Arbelaez MC, Knorz MC. Laser in situ keratomileusis for hyperopia and hyperopic astigmatism. J Refract Surg 1999; 15:406–414.

5.Ditzen K, Huschka H, Pieger S. Laser in situ keratomileusis for hyperopia. J Cataract Refract Surg 1998; 24:42–47.

6.Pallikaris IG, Siganos DS. Excimer laser in situ keratomileusis and photorefractive keratectomy for correction of high myopia. J Refract Corneal Surg 1994; 10:498–510.

7.Rashad KM. Laser in situ keratomileusis for the correction of hyperopia from 1.25 to 5.00 diopters with the Technolas Keracor 117C laser. J Refract Surg 2001; 17:113–122.

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Figure 1 The Shack-Hartmann wavefront sensor forms a regular lattice of image points for a perfect plane wave front of light.

They are responsible for approximately 15% of the average wavefront error. For coma, the wavefront is asymmetrical about the perfectly spherical wavefront, producing a cometshaped pattern on the emmetropic plane. For spherical aberration, the converging wavefront looks spherical near the center of the pupil but changes its curvature toward the edge of the pupil. This aberration gives a continuum of foci and results in point images with halos. Other terms of higher order aberrations are a group of all other deviations of the converging wavefront from perfect sphericity.

3. Chromatic Aberrations

Chromatic aberrations are errors that result of dispersion in optical elements of the eye. Refractive surgery techniques cannot correct chromatic aberration, since this error is inherent to the properties of the ocular materials and not to the shape of the ocular components (11).

Figure 2 The Shack-Hartmann wavefront sensor forms an irregular lattice of image points for an aberrated wavefront of light.

Figure 3 Three-dimensional pictorial directory of Zernike modes 0 to 20.

Aberrations are also classified in terms of orders using Zernike polynomials (12). The wavefront error (difference in shape between the aberrated wavefront and the ideal wavefront) for myopia, hyperopia, and astigmatism is well represented by a polynomial of second order. These aberrations are therefore called second-order aberrations. Following the same principle, coma is a third-order aberration and spherical aberration a fourth-order aberration (Fig. 3).

Laser surgery [photorefractive keratectomy (PRK) and laser-assisted in situ keratomileusis (LASIK)] increases high-order optical aberrations in human eyes, especially spherical aberration and coma (13,14). This increase in high-order optical aberrations after corneal laser surgery is correlated with a significant decrease in quality of vision, especially under scotopic conditions (15).

4. Detection of Wave Aberration: History of Shack-Hartmann

Most of the methods of wave aberration detection and reconstruction have been based on ray tracing. These methods were first described in1900 by Hartmann. About 5 years earlier, Tscherning constructed an aberroscope: a grid superimposed on a 5-D spherical lens where a subject could see a shadow image of the grid on the retina. From the distortions of the grid, one could infer the aberrations of the eye. Over 70 years later, Howland invented the crossed cylinder aberroscope. Instead of using a spherical lens, he used a crossed cylinder lens of 5 D with the negative axis at 45 degrees (16,17).

In 1961, Smirnov developed another method where a grid is viewed by the entire aperture of the eye minus a single central intersection, which is viewed through a small

aperture made to scan the entire pupil sequentially. In 1998, Webb and coauthors made a modern implementation of Smirnov’s method that computes the wave aberration and reduces it to Zernike polynomials.

Last, the Shack-Hartmann sensor was developed in 1970 by Shack in order to improve the images of satellites taken from earth. The first practical application was in 1984 by Wilson to test large telescopes. In 1989, Bille was the first to publish using the ShackHartmann in ophthalmology to measure the profile of the cornea and in 1997 he became the first to project a source onto the retina and use the Shack-Hartmann sensor to measure aberrations of the eye. In the same year, Williams became the first to use the ShackHartmann sensor with adaptative optics to measure and correct aberrations of the eye (18).

5. Principles of Shack-Hartmann

The Shack-Hartmann aberrometer has an objective lens that is actually an array of tiny lenses. With this kind of lens the reflected light is broken into many individual beams, thereby producing multiple images of the same retinal spot of light. For a perfect eye, the reflected plane wave will be focused into a perfect lattice of point images, each image falling on the optical axis of the corresponding lenslet. By contrast, the aberrated eye reflects a distorted wavefront. By measuring the displacement of each spot from its corresponding lenslet axis, we can deduce the slope of the aberrated wavefront when it entered the corresponding lenslet. The wavefront should be analyzed as soon as it passes through the eye’s pupil (19,20).

B. WAVEFRONT OF HYPEROPIC TREATMENT

1. Profile of Hyperopic Correction

In 1988 Munnerlyn and coworkers described the equations that served as a starting point for developing current ablation algorithms. For a hyperopic ablation, the preoperative cornea is modeled as a sphere of lesser curvature than the desired postoperative cornea, which is also modeled as a sphere. Tissue is removed from the peripheral area, flattening this region and producing increased postoperative corneal curvature as a final result. This concept is referred to as the shape-subtraction model of refractive surgery; it permeates current thinking in refractive surgery and forms the basis for both topography and wave- front-guided procedures (21).

2.Wavefront Measurements and Aberration Changes Before and After Conventional Hyperopic LASIK

In our service, we use the Alcon LADARWave Device (Orlando, FL) to study visual aberrations. The LADARWave Device makes detailed measurements of the aberrations present using the Shack-Hartmann principles. We can measure defocus, astigmatism, and higher-order aberration that can be decomposed into coma, spherical aberrations, and other terms of higher order aberrations (Fig. 4).

If we imagine a normal cornea with its normal prolate shape without any kind of surgery done, we will find higher-order aberrations but in low amounts. The pattern of each higher-order aberration is well defined: coma has a comet-shaped pattern with an elevated area (semicircle of hyperopia) just next to a depressed area (semicircle of myopia) in the same meridian (Fig. 5). Spherical aberration has a central elevated area (focus of

Figure 6 Spherical aberration pattern in a normal eye (LADARWave).

hyperopia) surrounded by a depressed circle (annulus of myopia) and with normalization in the far periphery (resembling a flat sombrero) (Fig. 6).

Other terms such as trefoil, quadrafoil, and secondary astigmatism generally have lower values (Fig. 7A and B).

Patients that underwent hyperopic treatments have an accentuated prolate corneal pattern (Fig. 8) (22,23).

When we analyze the spherical aberration pattern of these eyes, we can notice a decrease in the magnitude of spherical aberration and an inversion in the shape pattern. This is because the waves that come from the peripheral ablated zone converge less, so this area looks like a peripheral elevated red ring (annulus of relative hyperopia) and the central rays converge more, giving a central depressed area (focus of relative myopia). We call this pattern a flipped over sombrero hat, which is the opposite pattern of myopic treated eyes (Fig. 9).

C.COMPARISON OF HYPEROPIC VERSUS MYOPIC TREATMENT WAVEFRONT

1. Profile of Myopic Correction

As described by Munnerlyn in 1988, for a myopic ablation, the preoperative cornea is modeled as a sphere of greater curvature than the desired postoperative cornea, which is also modeled as a sphere within the treated zone. The apex of the desired postoperative cornea is displaced from the preoperative cornea by the maximal ablation depth, which is determined by the ablation zone size. The intervening tissue is simply removed or “subtracted” to produce the final result.

A

B

Figure 7 (A) Trefoil pattern. (B) Quadrafoil pattern.

Figure 10 LADARWave device showing defocus, astigmatism, and higher-order aberrations in a myopic patient.

Patients who have undergone myopic treatments have an oblate corneal pattern (Fig. 10) (24). The wavefront pattern shows a flattening or concavity to the otherwise bowlshaped wavefront of myopia.

Analyzing the wavefront of these myopic treatments, we notice that the spherical aberration increases in number and size, with the depressed and elevated areas being accentuated. We describe this kind of pattern as a sombrero hat (Fig. 11).

2. Comparison of Aberration Changes in Hyperopia Versus Myopia

In a study of 113 candidates for LASIK surgery, analyzing all aberrations, defocus and astigmatism were dominant. When analyzing only higher-order terms, coma and spherical aberrations were the most significant.

Another study described the pre-and postwavefront measurements of patients submitted to LASIK for myopia or hyperopia and myopic PRK. It was found that, for LASIK, postoperative total error was significantly smaller for myopes than hyperopes (p 0.05). Both myopic and hyperopic LASIK patients exhibit modest regression in defocus. In analyzing higher-order aberrations, it was noticed that spherical aberration decreased in hyperopic treatments and increased in myopic corrections. All other higher-order terms increased after either type of correction. In the postoperative interval, coma was the most dynamic higher-order aberration, with an overall decrease over time until 6-months postoperatively.