A mathematical model for laser in situ keratomileusis and photorefractive keratectomy

The purpose of ablation refractive surgery is to remove the refractive error from the inherently asymmetric aspheric cornea. Although the technique is gaining wide acceptance and popularity, some patients are left with irregular corneas. Our objective was to develop a methodology to analyze corneal shape, reduce the shape to arcs, modify the local arc value to the desired new arc value, and render a new continuous Euclidean surface without discontinuity.

The method to reconstruct the corneal surface consists of importing scanner output elevation data points into a computer-aided design (CAD) application to form the surface model. The corneal arc measurements are derived at 5 degrees increments and centered about the Gauss point of symmetry. Each arc is manipulated to adjust the corresponding arc on the proposed corneal surface to reflect the new arc value, correcting for the refractive error. The method determines the amount of corneal tilt and ablation depth at a given diameter required for the refractive error with a smooth transition zone to the base cornea.

The case example is a patient who began with a spherical refraction of -8.75 D and after LASIK was emmetropic, but had irregular astigmatism and 20/30 best spectacle-corrected Snellen visual acuity. The proposed mathematical model compares the achieved surface shape to the mathematically planned surface contour. An enhancement procedure to remove the LASIK-induced corneal irregularity was designed.

A mathematical technique to plan myopic ablative surgery to make the corneal surface regular and symmetric is proposed.