Finite element methods for simulating refractive surgical procedures on the human cornea

Refractive surgical procedures attempt to correct refractive defects of the eye by altering the corneal shape using corneal implants, or by excimer laser photoablation or by incising the cornea as in keratotomy. This work presents the finite element technology necessary for determining the corneal constitutive parameters and for modeling refractive surgical procedures.; Finite element corneal models, specially designed to simulate in vivo experiments on the human cornea, are developed, which, in conjunction with the experimental data, can be used to determine the in vivo corneal constitutive parameters. Finite element models, based on a hierarchy of assumptions regarding corneal micromechanics, are also developed for simulating refractive surgical procedures; each level of hierarchy results in a distinct model. At the first level of hierarchy, it is argued that due to the low shear modulus of the ground substance, stromal lamellae which are cut, achieve and maintain a stress-free configuration. The membrane forces in the stroma are then resisted only by the uncut stromal lamellae. At the second level of hierarchy, the cut lamellae are assumed to get stressed, and as a result, they now resist membrane forces, but not to the same extent as the uncut ones. In both these models, geometric arguments lead to quantitative representations for the anisotropy and inhomogeneity in the corneal membrane rigidity. These constitutive models are then employed in geometrically nonlinear membrane and three-dimensional finite element formulations. At the third level of hierarchy, it is assumed that the cut and uncut lamellae are identically able to resist membrane forces, and the corneal incisions are represented explicitly as cleavages in a three-dimensional setting.; For modeling the corneal tissue, a 27-node stabilized nonlinear three-dimensional finite element is developed such that it retains its accuracy in thin and incompressible limits. This element is essentially reduced integrated, and the stiffness emanating from the linear part of the Green-Lagrange strain is stabilized in a mixed framework, while keeping the contribution from the nonlinear part underintegrated. This element can also be used for analyzing other soft tissues and organs such as the heart, lungs, skin, brain and muscles.