Numerical modeling of radial, astigmatic, and hexagonal keratotomy

Abstract

Background: A mechanical model of the human cornea is proposed and employed in a finite element formulation for simulating the effects of keratotomy on the cornea.

Methods: The formulation assumes that the structural behavior of the cornea is governed by the properties of the stroma which is modeled as a thick membrane. The tensile forces in the cornea are resisted by the collagen fibrils embedded in the ground substance of the stromal lamellae. When the stromal lamellae are cut, as in keratotomy, it is assumed that they no longer carry any tensile forces, and the forces in the cornea are then resisted only by the remaining uncut lamellae. A constitutive model, which represents the anisotropy and inhomogeneity in the membrane rigidity induced by the incisions, has been employed in a geometrically nonlinear finite element membrane formulation for small strains with moderate rotations. This preliminary model is restricted to linear material behavior with no time dependency.

Results: A number of numerical examples are presented to illustrate the effectiveness of the proposed constitutive model and the finite element formulation for computing the immediate postoperative shift in corneal power resulting from radial, astigmatic, and hexagonal keratotomy. Surgical changes computed using the proposed model compare well with surgical corrections predicted by expert surgeons.

Conclusions: The proposed computational model of the cornea and the effects of surgical procedures on it is based on a number of important simplifying assumptions regarding the mechanical properties and structure of the corneal tissue at the ultrastructure level. The encouraging results found with present model suggest that further development and refinement will be useful.