Computer Simulation of Arcuate Keratotomy for Astigmatism

Abstract

The development of refractive corneal surgery involves numerous attempts to isolate the effect of individual factors on surgical outcome. Computer simulation of refractive keratotomy allows the surgeon to alter variables of the technique and to isolate the effect of specific factors independent of other factors, something that cannot easily be done in any of the currently available experimental models. We used the finite element numerical method to construct a mathematical model of the eye. The model analyzed stress-strain relationships in the normal corneoscleral shell and after astigmatic surgery. The model made the following assumptions: an axisymmetric eye, an idealized aspheric anterior corneal surface, transversal isotropy of the cornea, nonlinear strain tensor for large displacements, and near incompressibility of the corneoscleral shell. The eye was assumed to be fixed at the level of the optic nerve. The model described the acute elastic response of the eye to corneal surgery. We analyzed the effect of paired transverse arcuate corneal incisions for the correction of astigmatism. We evaluated the following incision variables and their effect on change in curvature of the incised and unincised meridians: length (longer, more steepening of unincised meridian), distance from the center of the cornea (farther, less flattening of incised meridian), depth (deeper, more effect), and the initial amount of astigmatism (small effect). Our finite element computer model gives reasonably accurate information about the relative effects of different surgical variables, and demonstrates the feasibility of using nonlinear, anisotropic assumptions in the construction of such a computer model. Comparison of these computer-generated results to clinically achieved results may help refine the computer model.