High Resolution Images of Human Meibum Spread on Saline.

Purpose: Understanding of the role of the tear film lipid layer (TFLL) in evaporative dry eye requires knowledge of its structure. X-ray studies show 11.1-nm thick lamellae in meibum at tear film temperature (approximately 35°C), whereas below 30°C, 4.

A Perspective on the Use of Fluorescent Imaging to Reveal Mechanisms of Breakup.

Tear film instability, which can lead to rapid tear film breakup (TBU), is considered to be a major etiological factor in dry eye. However, experimental support for many of the proposed theories for TBU mechanisms is relatively scarce. The major aim of this perspective is to show that fluorescence studies of TBU can be used to provide experimental evidence for two proposed underlying mechanisms of TBU, evaporation and divergent flow.

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 where the tear film may fail. The models attempt to identify the important physical processes, and their parameters, governing the tear film in health and disease.

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 is hypothesized to be caused by localized excess lipid, or "globs.

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' tear films. The fitting is done with thin film fluid dynamics models that are nonlinear partial differential equation models for the thickness, osmolarity and fluorescein concentration of the tear film for circular (spot) or linear (streak) tear film breakup.

The influence of a lipid reservoir on the tear film formation.

We present a mathematical model to study the influence of a lipid reservoir, seen experimentally, at the lid margin on the formation and relaxation of the tear film during a partial blink. Applying the lubrication limit, we derive two coupled non-linear partial differential equations characterizing the evolution of the aqueous tear fluid and the covering insoluble lipid concentration. Departing from prior works, we explore a new set of boundary conditions (BCs) enforcing hypothesized lipid concentration dynamics at the lid margins.

Mechanisms, imaging and structure of tear film breakup.

Tear film breakup (BU) is an important aspect of dry eye disease, as a cause of ocular aberrations, irritation and ocular surface inflammation and disorder. Additionally, measurement of breakup time (BUT) is a common clinical test for dry eye. The current definition of BUT is subjective; here, a more objective concept of "touchdown" - the moment when the lipid layer touches down on the corneal surface - is proposed as an aid to understanding processes in early and late stages of BU development.

On tear film breakup (TBU): dynamics and imaging.

We report the results of some recent experiments to visualize tear film dynamics. We then study a mathematical model for tear film thinning and tear film breakup (TBU), a term from the ocular surface literature. The thinning is driven by an imposed tear film thinning rate which is input from in vivo measurements.

Computed tear film and osmolarity dynamics on an eye-shaped domain.

The concentration of ions, or osmolarity, in the tear film is a key variable in understanding dry eye symptoms and disease. In this manuscript, we derive a mathematical model that couples osmolarity (treated as a single solute) and fluid dynamics within the tear film on a 2D eye-shaped domain. The model includes the physical effects of evaporation, surface tension, viscosity, ocular surface wettability, osmolarity, osmosis and tear fluid supply and drainage.

A model for tear film thinning with osmolarity and fluorescein.

Purpose: We developed a mathematical model predicting dynamic changes in fluorescent intensity during tear film thinning in either dilute or quenching regimes and we model concomitant changes in tear film osmolarity.

Methods: We solved a mathematical model for the thickness, osmolarity, fluorescein concentration, and fluorescent intensity as a function of time, assuming a flat and spatially uniform tear film.

Results: The tear film thins to a steady-state value that depends on the relative importance of the rates of evaporation and osmotic supply, and the resulting increase of osmolarity and fluorescein concentrations are calculated.

Four characteristics and a model of an effective tear film lipid layer (TFLL).

It is proposed that a normal, effective tear film lipid layer (TFLL) should have the following four characteristics: 1) high evaporation resistance to prevent water loss and consequent hyperosmolarity; 2) respreadability, so it will return to its original state after the compression-expansion cycle of the blink; 3) fluidity sufficient to avoid blocking secretion from meibomian glands; 4) gel-like and incompressible structure that can resist forces that may tend to disrupt it. These characteristics tend to be incompatible; for example, lipids that form good evaporation barriers tend to be disrupted by compression-expansion cycles. It is noted that clues about the function and organization of the TFLL can be obtained by comparison with other biological lipid layers, such as lung surfactant and the lipid evaporation barrier of the skin.

Tear film images and breakup analyzed using fluorescent quenching.

Purpose: Tear evaporation should increase fluorescein concentration, causing fluorescence dimming from self-quenching for high but not low fluorescein concentration. This prediction was tested and compared to the predicted effect of "tangential flow" that fluorescence dimming should be similar for high and low concentrations.

Methods: A custom optical system was used for video recording of tear film fluorescence in 30 subjects.

Evaporation-driven instability of the precorneal tear film.

Tear-film instability is widely believed to be a signature of eye health. When an interblink is prolonged, randomly distributed ruptures occur in the tear film. "Black spots" and/or "black streaks" appear in 15 to 40 s for normal individuals.

Tear film breakup and structure studied by simultaneous video recording of fluorescence and tear film lipid layer images.

Purpose: The thinning of the precorneal tear film between blinks and tear film breakup can be logically analyzed into contributions from three components: evaporation, flow into the cornea, and tangential flow along the corneal surface. Whereas divergent tangential flow contributes to certain types of breakup, it has been argued that evaporation is the main cause of tear thinning and breakup. Because evaporation is controlled by the tear film lipid layer (TFLL) it should therefore be expected that patterns of breakup should match patterns in the TFLL, and this hypothesis is tested in this study.

High resolution microscopy of the lipid layer of the tear film.

Tear film evaporation is controlled by the lipid layer and is an important factor in dry eye conditions. Because the barrier to evaporation depends on the structure of the lipid layer, a high resolution microscope has been constructed to study the lipid layer in dry and in normal eyes. The microscope incorporates the following features.

Tear film dynamics on an eye-shaped domain I: pressure boundary conditions.

We study the relaxation of a model for the human tear film after a blink on a stationary eye-shaped domain corresponding to a fully open eye using lubrication theory and explore the effects of viscosity, surface tension, gravity and boundary conditions that specify the pressure. The governing non-linear partial differential equation is solved on an overset grid by a method of lines using a finite-difference discretization in space and an adaptive second-order backward-difference formula solver in time. Our 2D simulations are calculated in the Overture computational framework.

A model for wetting and evaporation of a post-blink precorneal tear film.

We examine a fluid dynamic model for the evolution of a precorneal tear film that includes evaporation of the aqueous layer and a wetting corneal surface. Our model extends previous work on the break-up time for a post-blink tear film to include a more realistic model for evaporation. The evaporation model includes the effects of conjoining pressure and predicts the existence of an equilibrium adsorbed fluid layer that serves as a model for a wetting corneal surface/mucin layer.

The contribution of lipid layer movement to tear film thinning and breakup.

Purpose: To investigate whether the tear film thinning between blinks is caused by evaporation or by tangential flow of the tear film along the surface of the cornea. Tangential flow was studied by measuring the movement of the lipid layer.

Methods: Four video recordings of the lipid layer of the tear film were made from 16 normal subjects, with the subjects keeping their eyes open for up to 30 seconds after a blink.

Contributions of evaporation and other mechanisms to tear film thinning and break-up.

Purpose: To evaluate the contribution of three mechanisms-evaporation of the tear film, inward flow of water into the corneal epithelium or contact lens, and "tangential flow" along the surface of epithelium or contact lens-to the thinning of the tear film between blinks and to tear film break-up. In addition to a discussion of relevant studies, some previously unpublished images are presented illustrating aspects of tear film break-up. CONTRIBUTIONS OF THREE MECHANISMS TO TEAR FILM BREAK-UP: Inward flow of water into the epithelium or contact lens is probably unimportant, and a small flow in the opposite direction may actually occur.

Applications of small-world network theory in alcohol epidemiology.

Objective: This study develops a mathematical model of alcohol abuse in structured populations, such as communities and college campuses. The study employs a network model that has the capacity to incorporate a variety of forms of connectivity membership besides personal acquaintance, such as geographic proximity and common organizations. The model also incorporates a resilience dimension that indicates the susceptibility of each individual in a network to alcohol abuse.

Hydrodynamics of a bounded vertical film with nonlinear surface properties.

The drainage of a thin liquid film with an insoluble monolayer down a vertical wall is studied. Lubrication theory is used to develop a model where the film is pinned at the top with a given thickness and the film drains into a bath at the bottom. A nonlinear equation of state is used for the surface tension and the surface viscosity is a nonlinear function of the surfactant concentration; these are appropriate for some aqueous systems.