Peter Ewen King-Smith

Three interferometric methods for measuring the thickness of layers of the tear film.

The thickness of different layers of the tear film has been measured by three types of interference method, namely, wavelength-dependent fringes (WDFs), thickness-dependent fringes (TDFs), and angle-dependent fringes (ADFs). This review begins with a discussion of characteristics which are common to all these methods--high-, intermediate-, and low-index layers, phase, optical path difference, and contrast. For each of the three methods, we present a figure showing constructive and destructive interference, derive equations for calculating tear layer thickness, describe a typical optical system, and show representative results. The particular advantages and limitations of each method are discussed. Given the clinical importance of the tear film in dry eye syndrome and contact lens wear, it is unfortunate that there are considerable discrepancies among the results of interferometric and other methods for measuring tear film thickness; further development of these noninvasive, interferometric methods should help to provide a clearer picture of the thickness of different layers of the tear film, in normal and dry eyes, and in contact lens wear.

Tear film dynamics on an eye-shaped domain. Part 2. Flux boundary conditions

We model the dynamics of the human tear film during relaxation (after a blink) using lubrication theory and explore the effects of viscosity, surface tension, gravity and boundary conditions that specify the flux of tear fluid into or out of the domain. The governing nonlinear partial differential equation is solved on an overset grid by a method of lines using finite differences in space and an adaptive second-order backward difference formula solver in time. Our simulations in a two-dimensional domain are computed in the Overture computational framework. The flow around the boundary is sensitive to both our choice of flux boundary condition and the presence of gravity. The simulations recover features seen in one-dimensional simulations and capture some experimental observations of tear film dynamics around the lid margins. In some instances, the influx from the lacrimal gland splits with some fluid going along the upper lid towards the nasal canthus and some travelling around the temporal canthus and then along the lower lid. Tear supply can also push through some parts of the black line near the eyelid margins.

Analysis of Comparison of Human Meibomian Lipid Films and Mixtures with Cholesteryl Esters In Vitro Films using High Resolution Color Microscopy.

PURPOSE The lipid layer of the tears has been studied in vivo using high resolution color microscopy (HRCM). The purpose of these experiments was to gain further insight into the structure of the lipid layer by applying HRCM to in vitro meibomian lipid films. METHODS Films of human meibomian lipids, cholesteryl nervonate, cholesteryl palmitate, or their mixtures, were spread on a Langmuir trough. Changes to the films were monitored using HRCM as the films were compressed to different surface pressures. The penetration of albumin into a meibomian lipid film also was studied. RESULTS Small amounts of meibomian lipids at low pressures formed very thin films estimated to be 5.2 nm thick. Compression caused spots to appear in the films. At higher concentrations, micro lenses were a feature of the film. Cholesteryl nervonate formed a multilayered oil slick that did not change with surface pressure. Cholesteryl palmitate formed a stiff film that collapsed at high compression. Mixtures of cholesteryl nervonate and meibomian lipids showed that they mixed to increase surface pressures above that of the individual components. HRCM also allowed albumin to be seen penetrating the meibomian lipid film. CONCLUSIONS HRCM combined with in vitro surface pressure measurements using a Langmuir trough is useful for modeling meibomian lipid films. The films often resemble the appearance of the lipid layer of in vivo films. The data indicate that the lipid layer might be modeled best as a duplex film containing an array of liquid crystals.

Texture based prelens tear film segmentation in interferometry images

Interferometric imaging has been identified as a novel approach to the evaluation of prelens tear film (PLTF) thickness in contact lens patients. In this paper, we present a texture based segmentation approach for the detection of tear film breakup regions on interferometry images. First, the textural information was extracted from the studied images using a bank of Gabor filters. A novel classifier, EM-MDA, which integrates traditional Expectation-Maximization with Multiple Discriminant Analysis, was then trained for the recognition of breakup regions of the PLTF. Experimental results provided a correct classification rate of 91.0% which proved significantly higher compared to traditional EM or well known Linear Discriminant Analysis.

Tear film dynamics with evaporation, wetting, and time-dependent flux boundary condition on an eye-shaped domain

We study tear film dynamics with evaporation on a wettable eye-shaped ocular surface using a lubrication model. The mathematical model has a time-dependent flux boundary condition that models the cycles of tear fluid supply and drainage; it mimics blinks on a stationary eye-shaped domain. We generate computational grids and solve the nonlinear governing equations using the OVERTURE computational framework. In vivo experimental results using fluorescent imaging are used to visualize the influx and redistribution of tears for an open eye. Results from the numerical simulations are compared with the experiment. The model captures the flow around the meniscus and other dynamic features of human tear film observed in vivo.

Computed flow and fluorescence over the ocular surface

Fluorescein is perhaps the most commonly used substance to visualize tear film thickness and dynamics; better understanding of this process aids understanding of dry eye syndrome which afflicts millions of people. We study a mathematical model for tear film flow, evaporation, solutal transport and fluorescence over the exposed ocular surface during the interblink. Transport of the fluorescein ion by fluid flow in the tear film affects the intensity of fluorescence via changes in concentration and tear film thickness. Evaporation causes increased osmolarity and potential irritation over the ocular surface; it also alters fluorescein concentration and thus fluorescence. Using thinning rates from in vivo measurements together with thin film equations for flow and transport of multiple solutes, we compute dynamic results for tear film quantities of interest. We compare our computed fluorescent intensity distributions with in vivo observations. A number of experimental features are recovered by the model.

Duplex Tear Film Evaporation Analysis

Tear film thinning, hyperosmolarity, and breakup can cause irritation and damage to the human eye, and these form an area of active investigation for dry eye syndrome research. Recent research demonstrates that deficiencies in the lipid layer may cause locally increased evaporation, inducing conditions for breakup. In this paper, we explore the conditions for tear film breakup by considering a model for tear film dynamics with two mobile fluid layers, the aqueous and lipid layers. In addition, we include the effects of osmosis, evaporation as modified by the lipid, and the polar portion of the lipid layer. We solve the system numerically for reasonable parameter values and initial conditions and analyze how shifts in these cause changes to the system’s dynamics.

Mathematical modelling of glob-driven tear film breakup

Evaporation is a recognized contributor to tear film thinning and tear breakup (TBU). Recently, a different type of TBU is observed, where TBU happens under or around a thick area of lipid within a second after a blink. The thick lipid corresponds to a glob. Evaporation alone is too slow to offer a complete explanation of this breakup. It has been argued that the major reason of this rapid tear film thinning is divergent flow driven by a lower surface tension of the glob (via the Marangoni effect). We examine the glob-driven TBU hypothesis in a 1D streak model and axisymmetric spot model. In the model, the streak or spot glob has a localized high surfactant concentration, which is assumed to lower the tear/air surface tension and also to have a fixed size. Both streak and spot models show that the Marangoni effect can lead to strong tangential flow away from the glob and may cause TBU. The models predict that smaller globs or thinner films will decrease TBU time (TBUT). TBU is located underneath small globs, but may occur outside larger globs. In addition to tangential flow, evaporation can also contribute to TBU. This study provides insights about mechanism of rapid thinning and TBU which occurs very rapidly after a blink and how the properties of the globs affect the TBUT.

Dynamics of Fluorescent Imaging for Rapid Tear Thinning

A previous mathematical model has successfully simulated the rapid tear thinning caused by glob (thicker lipid) in the lipid layer. It captured a fast spreading of polar lipid and a corresponding strong tangential flow in the aqueous layer. With the simulated strong tangential flow, we now extend the model by adding equations for conservation of solutes, for osmolarity and fluorescein, in order to study their dynamics. We then compare our computed results for the resulting intensity distribution with fluorescence experiments on the tear film. We conclude that in rapid thinning, the fluorescent intensity can linearly approximate the tear film thickness well, when the initial fluorescein concentration is small. Thus, a dilute fluorescein is recommended for visualizing the rapid tear thinning during fluorescent imaging.