A mathematical model for laser in situ keratomileusis and photorefractive keratectomy

PURPOSE: The purpose of ablation refractive surgery is to remove the refrac tive error from the inherently asymmetric aspheric cornea. Although the tec hnique is gaining wide acceptance and popularity, some patients are left wi th irregular corneas, Our objective was to develop a methodology to analyze corneal shape, reduce the shape to arcs, modify the local are value to the desired new are value, and render a new continuous Euclidean surface witho ut discontinuity. METHODS: The method to reconstruct the corneal surface consists of importin g scanner output elevation data points into,a computer-aided design (CAD) a pplication to form the surface model, The corneal are measurements are deri ved at 5 degrees increments and centered about the Gauss point of symmetry. Each are is manipulated to adjust the corresponding are on the proposed co rneal surface to reflect the new are value, correcting for the refractive e rror, The method determines the amount of corneal tilt and ablation depth a t a given diameter required for the refractive error with a smooth transiti on zone to the base cornea, RESULTS: The case example is a patient who began with a spherical refractio n of -8.75 D and after LASIK was emmetropic, but had irregular astigmatism and 20/30 best spectacle-corrected Snellen visual acuity. The proposed math ematical model compares the achieved surface shape to the mathematically pl anned surface contour. An enhancement procedure to remove the LASIK-induced corneal irregularity was designed. CONCLUSION: A mathematical technique to plan myopic ablative surgery to mak e the corneal surface regular and symmetric is proposed.