The inclusion of the epithelium in numerical models of the human cornea.

We present a patient-specific finite element model of the human cornea that accounts for the presence of the epithelium. The thin anterior layer that protects the cornea from the external actions has a scant relevance from the mechanical point of view, and it has been neglected in most numerical models of the cornea, which assign to the entire cornea the mechanical properties of the stroma. Yet, modern corneal topographers capture the geometry of the epithelium, which can be naturally included into a patient-specific solid model of the cornea, treated as a multi-layer solid. For numerical applications, the presence of a thin layer on the anterior cornea requires a finer discretization and the definition of two constitutive models (including the corresponding properties) for stroma and epithelium. In this study, we want to assess the relevance of the inclusion of the epithelium in the model of the cornea, by analyzing the effects in terms of uncertainties of the mechanical properties, stress distribution across the thickness, and numerical discretization. We conclude that if the epithelium is modeled as stroma, the material properties should be reduced by 10%. While this choice represents a sufficiently good approximation for the simulation of in vivo mechanical tests, it might result into an under-estimation of the postoperative stress in the simulation of refractive surgery.

Modeling the biomechanics of laser corneal refractive surgery.

We present a finite element model of the human cornea used to simulate corneal refractive surgery according to the three most diffused laser procedures, i. e., photo-refractive keratectomy (PRK), laser in-situ keratomileusis (LASIK) and small incision lenticule extraction (SMILE). The geometry used for the model is patient-specific in terms of anterior and posterior surfaces of the cornea and intrastromal surfaces originated by the planned intervention. The customization of the solid model prior to finite element discretization avoids the struggling difficulties associated with the geometrical modification induced by cutting, incision and thinning. Important features of the model include the identification of the stress-free geometry and an adaptive compliant limbus to account for the surrounding tissues. By the way of simplification, we adopt a Hooke material model extended to the finite kinematics, and consider only the preoperative and short-term postoperative conditions, disregarding the remodeling and material evolution aspects typical of biological tissues. Albeit simple and incomplete, the approach demonstrates that the post-operative biomechanical state of the cornea, after the creation of a flap or the removal of a small lenticule, is strongly modified with respect to the preoperative state and characterized by displacement irregularities and stress localizations.

A 3D fluid-solid interaction model of the air puff test in the human cornea.

We present a numerical model of a contactless test commonly used to assess the biomechanics of the human cornea. The test, consisting in a rapid air jet applied to the anterior surface of the cornea, is controversial. Although the numerous studies documented in the literature have not been able yet to clarify its relevance as a diagnostic tool, the test has the potential to be combined with inverse analysis procedures to characterize the parameters of numerical models of the cornea. With the final goal of employing the air puff test in advanced material identification algorithms, here we propose to model the cornea with standard finite elements and the fluids filling the anterior chamber of the eye with a meshfree discretization. The interaction between moving fluids and deforming cornea is accounted for by modifying the interface boundary conditions of both fluid and solid. The proposed model represents the first fully 3D example of an aqueous-cornea fluid-solid interaction analysis which uses a robust meshfree approach for the fluid. Although we restrict our scope to isotropic nonlinear materials, numerical results confirm the undeniable importance of including internal fluids in the simulation of the air puff test. Thus the proposed approach stands as a procedural paradigm for the identification of the mechanical parameters of the human cornea.

Modelling with a meshfree approach the cornea-aqueous humor interaction during the air puff test.

The air puff test is an in-vivo investigative procedure commonly utilized in ophthalmology to estimate the intraocular pressure. Potentially the test, quick and painless, could be combined with inverse analysis methods to characterize the patient-specific mechanical properties of the human cornea. A rapid localized air jet applied on the anterior surface induces the inward motion of the cornea, that interacts with aqueous humor-the fluid filling the narrow space between cornea and iris-with a strong influence on the dynamics of the cornea. While models of human cornea reproduce accurately patient-specific geometries and have reached a considerable level of complexity in the description of the material, yet scant attention has been paid to the aqueous humor, and no eye models accounting for the physically correct fluid-solid interaction are currently available. The present study addresses this gap by proposing a fluid-structure interaction approach based on a simplified two-dimensional axis-symmetric geometry to simulate the anterior chamber of the eye undergoing the air puff test. We regard the cornea as a membrane described through an analytical model and discretize the fluid with a mesh-free particle approach. The membrane is assumed to be nonlinear elastic and isotropic, and the fluid weakly compressible Newtonian. Numerical analyses reveal a marked influence of the fluid on the dynamics of the cornea. We perform a parametric analysis to assess the quantitative influence of geometrical and material parameters on the mechanical response of the model. Additionally, we investigate the possibility to use the dynamics of the test to estimate the intraocular pressure.