A 2-D finite element model of the cornea is developed to simulate corneal reshaping and the resulting deformation induced by refractive surgery. In the numerical simulations, linear and nonlinear elastic models are applied when stiffness inhomogeneities varying with depth are considered. Multiple simulations are created that employ different geometric configurations for the removal of the corneal tissue. Side-by-side comparisons of the different constitutive laws are also performed. To facilitate the comparison, the material property constants are identified from the same experimental data, which are obtained from mechanical tests on corneal strips and membrane inflation experiments. We then validate the resulting models by comparing computed refractive power changes with clinical results. Tissue deformations created by simulated corneal tissue removal using finite elements are consistent with clinically observed postsurgical results. The model developed provides a much more predictable refractive outcome when the stiffness inhomogeneities of the cornea and nonlinearities of the deformations are included in the simulations. Finite element analysis is a useful tool for modeling surgical effects on the cornea and developing a better understanding of the biomechanics of the cornea. The creation of patient-specific simulations would allow surgical outcomes to be predicted based on individualized finite element models.

A biomechanical model of the human cornea is employed in a finite element formulation for simulating the effects of Ultrafast Laser-Lamellar Keratoplasty. Several computer simulations were conducted to study curvature changes of the central corneal zone under various physiological and surgical factors. These factors included the combined effect of corneal flap and residual stromal bed thickness on corneal curvature; the effect of the shape of the lenticle on the surgical procedure outcomes and the effect of flap thickness on stress distribution in the cornea. The results were validated by comparing computed refractive power changes with clinical results. The effect of flap thickness on the amount of central flattening indicates that for flap thickness values 28% over the corneal thickness, central corneal flattening decreases. Moreover, the change in corneal curvature induced by subtraction of a plano-convex lenticle under a uniform flap, naturally imply a smaller change in the structure of the anterior layers of the cornea, but a bigger deformation in the structure of the posterior layers that are left behind the resection of the lenticle. In addition, the model also verified that the corneal curvature increased peripherally with simultaneous thinning centrally after subtraction of corneal tissue. This result shows that not only the treated zone is affected by the surgery, indicating the important role of the biomechanical response of the corneal tissue to refractive surgery, which is unaccounted for in current ablation algorithms. The results illustrate the potentialities of finite element modeling as an aid to the surgeon in evaluating variables.

A finite element method was used to study the biomechanical behavior of the cornea and its response to refractive surgery when stiffness inhomogeneities varying with depth are considered.Side-by-side comparisons of different constitutive laws that have been commonly used to model refractive surgery were also performed. To facilitate the comparison, the material property constants were identified from the same experimental data, which were obtained from mechanical tests on corneal strips and membrane inflation experiments. We then validated the resulting model by comparing computed refractive power changes with clinical results.The model developed provides a much more predictable refractive outcome when the stiffness inhomogeneities of the cornea and nonlinearities of the deformations are included in the finite element simulations. Thus, it can be stated that the inhomogeneous model is a more accurate representation of the corneal material properties in order to model the biomechanical effects of refractive surgery. The simulations also revealed that the para-central and peripheral parts of the cornea deformed less in response to pressure loading compared to the central cornea and the limbus. Furthermore, the deformations in response to pressure loading predicted by the non-homogeneous and nonlinear model, showed that the para-central region is mechanically enhanced in the meridional direction. This result is in agreement with the experimentally documented regional differences reported in the literature by other investigators.

PURPOSE: Refractive consequences of corneal transplants are analyzed using corneal biomechanical models assuming homogeneous and in homogeneous stiffness distributions across the cornea. Additionally, refractive effects of grafts combined with volume removal procedures are also evaluated to develop methods to reduce postoperative refractive management of patients. METHODS: Refinements of a two-dimensional finite element model are applied to simulate the biomechanical and refractive effects of different corneal transplant procedures: anterior lamellar keratoplasty, posterior lamellar keratoplasty, and penetrating keratoplasty. The models are based on a nonlinearly elastic, isotropic formulation. Predictions are compared with published clinical data. RESULTS: The model simulating the penetrating keratoplasty procedure predicts more change in the postoperative corneal curvature than models simulating anterior lamellar keratoplasty or posterior lamellar keratoplasty procedures. When a lenticle-shaped tissue with a central thickness of 50 microns and a diameter of 4 mm is removed from the anterior corneal surface along with the anterior lamellar keratoplasty or posterior lamellar keratoplasty, the models predict a refractive correction of-8.6and -8.9 diopters, respectively. CONCLUSIONS: Simulations indicate that a posterior lamellar keratoplasty procedure is preferable for obtaining a better corneal curvature profile, eliminating the need for specific secondary treatments. [J Refract Surg. 2006;22:293-302.]

The collapse of Hartford Civic Center Coliseum in 1978 and Minneapolis Metrodome arena roof are two incidents that demonstrate the importance of stability considerations in design and construction of arched structural systems. These type of structures usually host various social events and sports games where frequently thousands of spectators attend. design flaws, construction errors, and/or overloading may bring about structural failure of these structures with catastrophic consequences. Developing a reliable structural model to capture salient characteristics of arched structures is a challenging task facing forensic engineers investigating collapse of such structures. In this paper, buckling behavior of shallow and deep arches are studied and the associated failure modes are predicted using non-linear Finite Element Analysis (FEA). FEA results are compared to those obtained from theoretical methods of analysis for shallow arches using energy methods and for high arches through solution of classical differential equations conditions. This paper indicates that the forensic engineer should be competent in understanding and assessing possible buckling behavior of arched structures. In design projects with possible catastrophic buckling collapse, professional engineers should be aware of various buckling analyses that may need to be further examined to ensure the design adequacy of new or non-traditional designs against possible buckling failure.