A closed shell structured eyeball model with application to radial keratotomy

A closed shell structured eyeball model was developed for predicting the displacements and curvatures in an eyeball due to radial keratotomy. Both the cornea and sclera are modeled as an ellipsoidal cap, and the two caps are connected at the limbus to form a closed shell. The analysis of the number of corneal collagen laminae required for the tissue to be theoretically transversely isotropic was presented. The cornea, as well as the limbus and sclera, is considered as macroscopically homogeneous and isotropic in this study. A procedure to obtain the principal curvature at a point on the exterior surface was established. In the basic formulation, large displacements are contemplated. However, the FORTRAN computer program that was prepared to implement the procedure considers small displacements, and the resulting equations are linear. Although the results from this shell structured eyeball model are fairly good quantitatively, they do show vividly the following qualitative corneal behavior after the operation is performed: The opening of an incision has a V-shape, the radial displacements through the corneal thickness are nearly the same, and the largest in-plane displacement is only one-tenth of the largest radial displacement.