Dissertation Defense - Mazen Althobaiti, PhD Mathematical Sciences

Candidate: Mazen Althobaiti

Program: PhD Mathematical Sciences

Date: Thursday, June 11, 2026

Time: 9:00am

Place: Exploratory Hall, room 4301

Title: Computational Models for Pre-Lens Tear Film Drug Concentration Dynamics with Drug Supply from a Contact Lens and Drug Exchange during Blinking.

Abstract: We investigated the dynamics of the pre-lens tear film (PrLTF) and the transport of drug released from a drug-eluting contact lens under both blinking and non-blinking conditions. To capture the factors governing tear film thinning and drug transport, we developed a mathematical model that incorporates evaporation, pressure, and drug diffusion within the tear film. Under blinking conditions, the motion of the upper eyelid was incorporated through a time-dependent moving boundary formulation together with a domain-mapping approach that transforms the physical domain into a fixed computational domain. The resulting nonlinear system of partial differential equations was solved numerically using the method of lines together with MATLAB’s differential-algebraic equation solver ode15i. The numerical framework was validated through comparisons with results reported in previous studies and problems involving higher-order linear partial differential equations with periodic boundary conditions.

Both blinking and non-blinking models were analyzed, as blinking refreshes the PrLTF, which, in our study, contains the drug concentration. Several boundary conditions were considered, including no-flux and non-zero-flux conditions at the eyelid boundaries. In particular, the effects of different concentration conditions beneath the upper eyelid during blinking were investigated. Simulations of four blinks were also performed to study tear film thickness and cumulative drug transport behavior. Numerical results demonstrated that blinking alters the spatial and temporal evolution of drug concentration within the PrLTF while simultaneously refreshing the tear film. An interpolation strategy was implemented to reuse tear film solutions during one complete blink for solving the drug transport equation over multiple blinks, on the order of hours. The simulations revealed that the tear film behavior remains nearly periodic across blink cycles under selected parameters, whereas the drug concentration evolves over time. The study also identified numerical challenges associated with long time simulations (>10 blinks). Overall, this work provides a mathematical and computational framework for analyzing tear film dynamics and ocular drug delivery from contact lenses under physiologically relevant blinking conditions.

Committee chair: 

Prof. Daniel M. Anderson (Co-chair)

Prof. Rayanne A. Luke (Co-chair)

Committee members:

Prof. Padmanabhan Seshaiyer

Prof. Kara Maki