Abstract

Myopia is one of the most common ocular disorders, and is expected to affect approximately five billion people worldwide by 2050. One treatment currently available for myopia is soft contact lenses. In general, about one in ten Americans wear contact lenses, however one in three will stop wearing them due to discomfort. The goal of this dissertation is to develop a mathematical model that predicts the mechanical interactions between the contact lens and the ocular surface. Assuming the ocular tissue is a linear elastic material, we first develop a mathematical model to predict ocular deformation that is anatomically accurate in accounting for the effects of intraocular pressure (IOP). We solve the model weakly using finite elements in the software FreeFem++. An individual’s ocular tissue is always deformed by IOP, but our model is defined on the unstressed eye shape, i.e. the shape of the eye without IOP. Thus, we present an iterative algorithm that predicts this reference configuration, given the desired stressed shape of the eye. We perform analyses of the reference configuration algorithm (RCA) to understand its accuracy and stability. After coupling the RCA to the ocular deformation and contact lens models, we present results of the stresses and strains felt by the ocular surface due to both IOP and a contact lens. We present the contact lens suction pressure model originally published by Maki et al, and we couple it with the ocular deformation model in a staggered numerical algorithm. We then extend the ocular deformation model to be more biologically accurate by modeling the ocular tissue as a poro-elastic material, rather than linear elastic. We present the new governing equations, their weak formulations, and the numerical algorithm we use to approximate the system. Finally, we present preliminary results on ocular deformation and effective stress due to IOP to verify the poro-elastic model. In future work, the poro-elastic ocular deformation model will be coupled to the RCA and contact lens models.

Publication Date

5-2026

Document Type

Dissertation

Student Type

Graduate

Degree Name

Mathematical Modeling (Ph.D)

Department, Program, or Center

Mathematics and Statistics, School of

College

College of Science

Advisor

Lucia Carichino

Advisor/Committee Member

Kara L. Maki

Campus

RIT – Main Campus

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