Sensitivity of corneal biomechanical and optical behavior to material parameters using design of experiments method

Abstract

The optical performance of the human cornea under intraocular pressure (IOP) is the result of complex material properties and their interactions. The measurement of the numerous material parameters that define this material behavior may be key in the refinement of patient-specific models. The goal of this study was to investigate the relative contribution of these parameters to the biomechanical and optical responses of human cornea predicted by a widely accepted anisotropic hyperelastic finite element model, with regional variations in the alignment of fibers. Design of experiments methods were used to quantify the relative importance of material properties including matrix stiffness, fiber stiffness, fiber nonlinearity and fiber dispersion under physiological IOP. Our sensitivity results showed that corneal apical displacement was influenced nearly evenly by matrix stiffness, fiber stiffness and nonlinearity. However, the variations in corneal optical aberrations (refractive power and spherical aberration) were primarily dependent on the value of the matrix stiffness. The optical aberrations predicted by variations in this material parameter were sufficiently large to predict clinically important changes in retinal image quality. Therefore, well-characterized individual variations in matrix stiffness could be critical in cornea modeling in order to reliably predict optical behavior under different IOPs or after corneal surgery.

Individualized Characterization of the Distribution of Collagen Fibril Dispersion Using Optical Aberrations of the Cornea for Biomechanical Models

“…Second, we did not consider the contribution of the interaction effects between important biomechanical parameters (geometry, matrix stiffness, and fibril dispersion) on the IOP-induced changes in corneal wavefront aberrations. Our previous sensitivity study 19 showed that the interaction between the matrix stiffness and fibril dispersion had an impact on the IOP-induced changes in corneal optical aberrations, but the effects of interactions among geometry, matrix stiffness, and fibril dispersion have not yet been clearly quantified. Neglecting these interaction effects may also affect estimation of collagen fibril dispersion.…”

“…The 3D anisotropic hyperelastic corneal models in this study were all developed using FE software (Abaqus Unified FEA; Dassault Systèmes Simulia Corp., Johnston, RI, USA) as described in our previous study 19 and shown in Figure 1 . An improved strain energy function from the original Gasser–Holzapfel–Ogden model 34 with pre-integrated fibril distribution was adopted to describe the microstructure of the cornea.…”

“…The total changes in corneal wavefront aberrations induced by IOP elevation, W (ρ, θ) , have five contributing biomechanical parameters, as indicated in Equation 1 : where the subscripts geometry , C 10 , κ(ρ, θ), k 1 , and k 2 represent the aberration changes due to those parameters. Because variations in fiber stiffness ( k 1 ) and fiber nonlinearity ( k 2 ) between the eyes have nearly negligible impact on the optical aberrations, 19 Equation 1 can be approximately simplified as: …”

“… 3 Our previous sensitivity study identified fibril dispersion as an important material parameter that influences corneal aberrations induced by IOP elevation. 19 The spatial distribution of fibril dispersion may also vary among individual healthy corneas and between healthy and diseased corneas, such as keratoconus. 15 , 20 , 21 Although biomechanical models accounting for the details of collagen fibril structure have been proposed in several studies, 2 , 3 , 22 inter-subject variations in fibril dispersion have not been studied yet.…”

Theoretical Analysis of Wave-Front Aberrations Induced from Conventional Laser Refractive Surgery in a Biomechanical Finite Element Model

“…Our analysis also found that the material parameters of the corneal and scleral tissues played an important role in their biomechanical and optical behavior. 28 The material parameters of the cornea significantly affect the displacement of the anterior and posterior corneal surfaces. Moreover, once the scleral elasticity maintained a constant, with the increase of corneal elasticity, the maximum stress and maximum displacement moved toward the edge of the cornea.…”