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

14

Corneal Surface Profile After

Hyperopia Surgery

DAMIEN GATINEL

Fondation Ophthalomogique Adolphe de Rothschild and Bichat Claude Bernard Hospital, Paris, France

The desired change in corneal curvature to correct for hyperopia with current excimer laser systems is based on principles of geometric optics and the precise interaction of the excimer radiation with the corneal tissue. In comparison to myopic correction in which the goal is to flatten the central cornea, in hyperopia the central corneal area must be steepened to increase its optical power. This central steepening makes the planned correction of the hyperopic eye more difficult because the steepened central corneal portion has to join the peripheral unablated area of lower curvature via a transition area. These represent the important special features of the correction of hyperopic errors, which are emphasized in this chapter.

A. CORRECTION OF PURE SPHERICAL HYPEROPIC ERRORS

The profile of ablation to correct for spherical hyperopia is radially symmetrical and predominates in the periphery in an annular fashion. A subtraction shape model based on geometric optics allowed Munnerlyn et al., in 1988, to announce the principles of laserguided photoablation in the central corneal area (effective optical zone) (1). The modifications of the corneal profile are analyzed separately below for the optical zone and for the transition zone.

1. Optical Zone Design

Conforming to the pioneering work of Munnerlyn et al., the change in paraxial corneal power can be predicted by considering the initial unablated and the final ablated corneal

141

When we address theoretical considerations on the different approaches to blend a steepened optical zone to the untouched peripheral cornea, some constraints had be taken into consideration (2). Should this be done by a noncontinuous constant curvature profile, avoiding the induction of a continuous negative curvature, or by minimizing the slope of the transition zone with a continuous change in its curvature but inducing negative curvature (Fig. 2)? Because the patterns of ablation for the hyperopic transition zone are proprietary, it is difficult to find confirmations of the use and interest of any of the transition zone profile design characteristics. It seems, however, reasonable to postulate that any profile of ablation should be “smooth” in a mathematical sense—i.e., avoiding local discontinuities to prevent epithelial hyperplasia. A continuous profile of ablation with a very gradual change in its curvature seems a better option to correct for hyperopia while limiting regression. This pattern implies the need of two points of inflexion (inversion of the sign of the local curvature) to prevent the occurrence of discontinuities (Fig. 2).

Some publications have emphasized on the need for a large transition zone outer diameter in order to improve biological tolerance and minimize regression (3–5). Conversely, enlarging the optical zone diameter, although desirable to preserve the quality of vision and reduce the risk of decentration, represents a limiting factor, since the depth per diopter at the edge of the optical zone will increase with the square of the optical zone diameter. This could account for the low success rate observed for corrections over 5 or 6 D of hyperopia. The determination of the diameter of the ablation zone should logically

Figure 2 Profile of ablation for the spherical hyperopic error. O, ablation center; OZ, optical zone; TZ, transition zone; dotted black line, preoperative corneal profile; full black line, postoperative corneal profile; blue line, postoperative profile over the transition zone with no local curvature discontinuities but negative slope between the points of inflexion T and N; red line, postoperative transitional profile having a constant positive slope, but with a noncontinuous junction with the edge of the optical zone.

depend on the diameter of the optical zone. For example, a planned optical zone of 6.0 mm would require an ablation zone of 8.5 to 9.0 mm. Otherwise, effective optical zone diameters might be diminished by epithelial filling of the peripheral ring of ablation in case of high-magnitude of treatment. In LASIK, the corneal flap covering of the ablation zone minimizes the epithelial healing response (6). This might account for the better reported results of this technique over photorefractive keratectomy (PRK).

Because the total ablation zone diameter is equal to the outer diameter of the transition zone, it is mandatory to obtain large flap sizes for hyperopic LASIK procedures (7).

B. CORRECTION OF PURE CYLINDRICAL HYPEROPIC ERRORS

1. Optical Zone Design

The principles of the Munnerlyn pattern can be extended to the correction of astigmatism by taking into consideration the meridional variations in corneal apical power. In the case of pure hyperopic astigmatism, a “cylindrical profile of ablation” can be generated, which aims to selectively steepen the initial flatter principal meridian. This pattern has no center but there is axis symmetry along each of the principal meridians. A three-dimensional representation of the etched corneal lenticule for such correction over a circular optical zone is depicted in Figure 3. The depth of ablation is maximal at the edge of the optical zone along the flat meridian, while the steep meridian is untreated by the laser.

2. Transition Zone Design

The shape of the transition zone is dictated by the features of the optical zone. As for the optical zone, the central symmetry is broken. The step in tissue height is maximal at the boundary of the optical zone along the flat meridian. This discontinuity then tapers slowly and becomes null along the untreated steep meridian. To alleviate this variation, the diameter of the transition zone should be longer along the flat meridian and minimal (equal to

Figure 3 Schematic representation of the lenticule corresponding to the correction of a pure hyperopic astigmatism. Its thickness is null along the steep meridian (S) and maximal in the periphery along the flat meridian (F). The profile of ablation along the flat meridian is underlined in green.

1.The positive-cylinder approach (ablating the cylinder along the flattest meridian and then treating the residual spherical component)

2.The negative-cylinder approach (ablating the cylinder along the steepest meridian and then treating the residual spherical component)

3.The cross-cylinder approach (ablating half of the power of the cylinder along the steepest meridian and the remaining half along the flattest meridian before the residual spherical equivalent is treated)

Even if the optical result may be the same, these strategies may result in different amount and depths of tissue ablation. The increasing number of reports of corneal ectasia following LASIK suggests that the strategies that remove less of the corneal tissue should be preferred for the treatment of any compound astigmatism. Recently Azar et al. compared the theoretical ablation profiles and depths of tissue removal in the treatment of compound hyperopic astigmatism and of mixed astigmatism (8). They found that strategies combining the use of hyperopic spherical and myopic cylindrical corrections incur the greatest amount of corneal tissue ablation.

Three-dimensional drawings were generated to depict the theoretical shapes of the volumes of corneal tissue ablated to treat similar amounts of compound astigmatic hyperopic errors (Fig. 5A–C). These images can be interpreted more easily and quickly than abstract mathematical functions. The shapes and volumes of the corresponding lenticules can be analyzed for different strategies of ablation, and this makes if possible to estimate the theoretical differences in the amount of ablated corneal volume.

In compound hyperopic astigmatism, all the corneal meridians have excessive flattening. The negative cylinder and the cross cylinder approaches both imply an additional flattening that will cause redundant ablation by necessary additional positive spherical treatment.

Figure 5 Schematic representation of the lenticules ablated for the correction of compound hyperopic astigmatism for three different strategies to treat the same refraction: 3 ( 2 0 degrees). The optical zone diameter is identical for each of the depicted strategies. (A) Positive-cylinder approach. The positive cylinder (2 0 degrees) ablated lenticule is represented above, with its section along the flat axis outlined in light green. The spherical ablated lenticule ( 3) is represented below, with two meridian outlined in dark green.

ablation profile for patients with hyperopic errors but rather induce radially asymmetrical variations in the peripheral “step” at the edge of the optical zone. The transition zone pattern will have to take this variability in account and its optimized slope will have to be determined to ensure the stability of the induced changes over the optical zone.

E. CONCLUSION

For several reasons, the correction of hyperopia with PRK or LASIK is more difficult than for myopia. The patterns of the profiles of ablation to steepen the cornea might account for the limited success in excimer laser surgery for hyperopia. Refinements based on simple geometrical considerations and the incorporation of customized data might improve the results of such surgery.

APPENDIX 1

To correct for a spherical hyperopic error, Munnerlyn et al., by considering the initial unablated and the final ablated corneal surface as two spherical surfaces with a single but different radius of curvature (Fig. 6), proposed the following formula for the ablation profile over the optical zone:

t(y) R2 R1 R 21 y2 R 22 y2

where t(y) expresses the depth of tissue removal as a function of the distance y from the center of an optical zone diameter of S when R1 and R2 are the initial and final corneal anterior radii of curvature, respectively. The power of the removed lenticule (D) corresponds to the intended refractive change and is related to R1, R2, and the index of refraction (n) as follows:

Figure 6 Schematic representation of the profile of ablation for spherical hyperopia along a corneal meridian. Both initial and final surfaces are assumed to be spherical of radius R1 and R2 respectively. The gray portion corresponds to the material to be removed to steepen the anterior part of the cornea over an optical zone diameter of S mm.

D (n 1) R12 R11

where R2 R1 for hyperopic ablations

The maximal depth occurs at the edge of the optical zone of diameter S and is equal

to:

t(S/2) R2 R1 R 21 (S/2)2 R 222 (S/2)2

APPENDIX 2

To generate a conceptual graphic representation of theoretical shapes of the lenticules ablated during LASIK treatments of similar amounts of spherical and cylindrical treatment, we used a digital modeling software that makes it possible to visualize the results of Boolean operation on orientated three-dimensional surfaces (Bryce 3D, Metacreation Corp. Dublin, Ireland). Using these Boolean operations (subtraction of one object from another) on geometrical primitives such as spheres, cylinders, or toroidal ellipsoids, three-dimen- sional representations of the theoretical ablated volumes were generated (Fig. 7).

The optical zone was circular and the final corneal surface was spherical in all cases. For spherical corrections, the initial and final corneal surfaces were modeled as two spherical surfaces of different radii of curvature (the latter being flatter for myopic spherical corrections and steeper for hyperopic correction). For pure cylindrical corrections, the initial corneal surface was modeled as a spherocylinder with two major apical radii of curvature along the principal meridians, the final surface being spherical. In cases of myopic cylindrical correction, one of the principal radii of curvature of the initial surface was shorter, the other being equal to that of the final corneal surface. In the case of hyperopic cylindrical corrections, one of the principal radii of curvature of the initial surface was longer, the other being equal to that of the final corneal surface. The three-

Figure 7 Model of the ablated lenticule for the correction of pure hyperopic astigmatism. This volume is generated by boolean operation on primitive figures such as sphere, ellipsoid, cylinder, in accordance with assumptions regarding subtraction shape models.