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Generalized FEM to study localized material property changes in human cornea

Elizabeth Bueno Diaz, PhD Qualifying Exam, Advised by Professors Paul Funkenbusch and Amy Lerner

Wednesday, January 6, 2021
1 p.m.

The cornea is composed of collagen fibrils embedded in a rich proteoglycan matrix. This structure confers complex properties to cornea tissue such as inhomogeneity, nonlinearity, anisotropy, viscoelasticity, and near incompressibility. Corneal biomechanics and individual geometry dictate corneal topography and optical performance.  Changes in cornea shape are known to alter vision. Some vision correction procedures take advantage of this to correct refractive errors. Alternatively, differences/changes in mechanical properties can also influence cornea shape and, thus, optical performance. Photorefractive induced crosslinking (Phi-CXL) alters cornea structure, creating new bonds between the collagen fibrils that cause the cornea to stiffen. Phi-CXL can be used to control ectatic disorders and recently has been found promising to achieve refractive correction in a minimally invasive manner. Nonetheless, the procedure still needs refinement for researchers to accurately predict the outcome and plan the treatments.

In the proposed work, finite element modeling (FEM) will be used to predict surface topography changes associated with material changes. Challenges related to the FEM are the many choices needed to build the model, such as material properties and geometry characterization, among others.  Individualized models1, are expensive and not always feasible. Therefore, the goal of the proposed work is to generalize a subject-specific approach to a 3-D cornea model while also assessing the cost of measuring the input parameters and their impact on the prediction results. As a specific demonstration of this approach, we plan to model the effect of CXL on material properties in non-keratoconic eyes based on the changes observed in optical aberrations.

Preliminary work has focused on understanding the role of the boundary conditions, type of model, geometry, and the possible impact of localized material changes (reflecting the impact of CXL) on the cornea model. The proposed work is divided into three aims. Aim 1 is focused on generalizing the Holzapfel model while reducing cost. To fulfill this aim, an analysis based on statistical methods (ANOVA) to identify key variables, studying the impact of the asymmetric variables, and the reduction of the range of values of the variables is proposed. This knowledge will be combined with a cost assessment to understand the cost-quality tradeoff. Aim 2 is devoted to understanding the effect of CXL on material properties. It will focus on C10 (a parameter that reflects matrix stiffness) to model the changes associated with CXL including the depth-dependence of this property. Finally, aim 3 is focused on modeling custom CXL pattern to explore its potential for refractive errors correction as well as the impact of treatment characteristics (size, axial location, etc.) on the predicted changes.

  1. Xu M. Investigation of Corneal Biomechanical and Optical Behaviors by Developing Individualized Finite Element Model in Mechanical Engineering. 2019, University of Rochester.