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Dynamics and mechanisms for tear breakup (TBU) on the ocular surface

The human tear film is rapidly established after each blink, and is essential for clear vision and eye health. This paper reviews mathematical models and theories for the human tear film on the ocular surface, with an emphasis on localized flows …

Automatic detection of the cornea location in video captures of fluorescence

Purpose: Fluorescence imaging is a valuable tool for studying tear film dynamics andcorneal staining. Automating the quantification of fluorescence images is a challenging necessary step for making connections to mathematical models. A significant …

Parameter estimation for mixed-mechanism tear film thinning

Etiologies of tear breakup include evaporation-driven, divergent flow-driven, and a combination of these two. A mathematical model incorporating evaporation and lipid-driven tangential flow is fit to fluorescence imaging data. The lipid-driven motion …

Parameter estimation for evaporation-driven tear film thinning

Many parameters affect tear film thickness and fluorescent intensity distributions over time; exact values or ranges for some are not well known. We conduct parameter estimation by fitting to fluorescent intensity data recorded from normal subjects’ …

Preconditioned nonlinear iterations for overlapping Chebyshev discretizations with independent grids

The additive Schwarz method is usually presented as a preconditioner for a PDE linearization based on overlapping subsets of nodes from a global discretization. It has previously been shown how to apply Schwarz preconditioning to a nonlinear problem. …

ComplexRegions.jl: A Julia package for regions in the complex plane

A model for tear film dynamics during a realistic blink

An Adaptive Partition of Unity Method for Multivariate Chebyshev Polynomial Approximations

An adaptive partition of unity method for Chebyshev polynomial interpolation

Simulation of parabolic flow on an eye-shaped domain with moving boundary