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.

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.

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.

Dynamics and function of the tear film in relation to the blink cycle.

Great strides have recently been made in quantitative measurements of tear film thickness and thinning, mathematical modeling thereof and linking these to sensory perception. This paper summarizes recent progress in these areas and reports on new results. The complete blink cycle is used as a framework that attempts to unify the results that are currently available. Understanding of tear film dynamics is aided by combining information from different imaging methods, including fluorescence, retroillumination and a new high-speed stroboscopic imaging system developed for studying the tear film during the blink cycle. During the downstroke of the blink, lipid is compressed as a thick layer just under the upper lid which is often released as a narrow thick band of lipid at the beginning of the upstroke. "Rippling" of the tear film/air interface due to motion of the tear film over the corneal surface, somewhat like the flow of water in a shallow stream over a rocky streambed, was observed during lid motion and treated theoretically here. New mathematical predictions of tear film osmolarity over the exposed ocular surface and in tear breakup are presented; the latter is closely linked to new in vivo observations. Models include the effects of evaporation, osmotic flow through the cornea and conjunctiva, quenching of fluorescence, tangential flow of aqueous tears and diffusion of tear solutes and fluorescein. These and other combinations of experiment and theory increase our understanding of the fluid dynamics of the tear film and its potential impact on the ocular surface.

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.

A MODEL FOR THE TEAR FILM AND OCULAR SURFACE TEMPERATURE FOR PARTIAL BLINKS.

In this paper, we investigate the dynamics of tear film and the associated temperature variation for partial blinks. We investigate the mechanism of fluid supply during partial blink cycles, and compare the film thickness with observation in vivo. We find that varying the thickness of the fluid layer beneath the moving upper lid improves the agreement for the in vivo measurement of tear film thickness after a half blink. By examining the flux of the fluid, we provide an explanation of this assumption. We also investigate the temperature dynamics both at the ocular surface and inside the simulated anterior chamber. Our simulation results suggest that the ocular surface temperature readjusts rapidly to normal temperature distribution after partial blinks.

An overset grid method for the study of reflex tearing.

We present an overset grid method to simulate the evolution of human tear film thickness subject to reflex tearing. The free-surface evolution is governed by a single fourth-order non-linear equation derived from lubrication theory with specified film thickness and volume flux at each end. The model arises from considering the limiting case where the surfactant is strongly affecting the surface tension. In numerical simulations, the overset grid is composed of fine boundary grids near the upper and lower eyelids to capture localized capillary thinning referred to as 'black lines' and a Cartesian grid covers the remaining domain. Numerical studies are performed on a non-linear test problem to confirm the accuracy and convergence of the scheme. The computations on the tear film model show qualitative agreement with in vivo tear film thickness measurements. Furthermore, the role of the black lines in the presence of tear supply from the lid margins, reflex tearing, was found to be more subtle than a barrier to tear fluid flow between the anterior of the eye and the meniscus at the lid margin. During reflex tearing, tears may flow through the region normally containing the black line and drift down over the cornea under the influence of gravity.

Single-equation models for the tear film in a blink cycle: realistic lid motion.

We consider model problems for the tear film over multiple blink cycles that utilize a single equation for the tear film; the single non-linear partial differential equation that governs the film thickness arises from lubrication theory. The two models that we consider arise from considering the absence of naturally occurring surfactant and the case when the surfactant is strongly affecting the surface tension. The film is considered on a time-varying domain length with specified film thickness and volume flux at each end; only one end of the domain is moving, which is analogous to the upper eyelid moving with each blink. Realistic lid motion from observed blinks is included in the model with end fluxes specified to more closely match the blink cycle than those previously reported. Numerical computations show quantitative agreement with in vivo tear film thickness measurements under partial blink conditions. A transition between periodic and non-periodic solutions has been estimated as a function of closure fraction and this may be a criterion for what is effectively a full blink according to fluid dynamics.

The thickness of the human precorneal tear film: evidence from reflection spectra.

PURPOSE: Interferometric methods have considerable potential for studying the thickness of layers of the human tear film and cornea because of their ability to make noninvasive, accurate, and rapid measurements. However, previous interferometric studies by Prydal and Danjo yielded tear thickness values near 40 and 11 microm, respectively, considerably greater than estimates made by invasive methods of 4 to 8 microm. Using a modified version of Danjo's method, interference effects from the tear film and cornea were studied, with the aim of correlation with known structure and optical properties of the cornea and hence determining the most probable value of tear film thickness. METHODS: Reflectance spectra from the human cornea were measured at normal incidence. These spectra show oscillations whose maxima correspond to constructive interference between light reflected from the air surface and from some deeper surface. The frequency of these spectral oscillations is proportional to the thickness of the layer between the air surface and the second surface. Therefore, Fourier analysis of reflectance spectra can be used to determine the thickness of layers of the tear film and cornea. In the main experiment, 36 low-resolution spectra were obtained from six normal eyes for measuring thickness up to 100 microm. Control experiments included measurements of the time course of thickness changes and high-resolution spectra for measuring thickness up to 1000 microm. RESULTS: For the main experiment, in the thickness range 1 to 100 microm, the strongest peak in the Fourier transform was near 3 microm (range, 1.5-4.7 microm) beneath the air surface. In the range 20 to 100 microm, the strongest peak was near 55 microm (range, 50-59 microm) for all 36 spectra; none were in Prydal's range near 40 microm. This 55-microm peak is consistent with a reflection from the basement membrane of the epithelium. Time course measurements after a blink show that the 3-microm peak is not an artifact. High-resolution spectra gave a peak near 510 microm, corresponding to the complete thickness of the cornea (plus tear film). This peak had a contrast similar to that of the 3-microm peak. CONCLUSIONS: These studies did not confirm Prydal's estimate of approximately 40 microm. Nor were there prominent peaks near Danjo's value of approximately 11 microm, except in cases of probable reflex tears. Because the reflection at the aqueous-mucus boundary would be expected to be weaker than that from the epithelial surface, the 3-microm peak is unlikely to correspond to the aqueous layer (rather than the complete tear film). The proposal that the 3-microm peak corresponds to a reflection from the front of the cornea is supported by the demonstration of a peak of similar contrast from the back of the cornea. Thus, the current evidence consistently supports a value of approximately 3 microm for the thickness of the human precorneal tear film.

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.

Interferometric measurement of tear film thickness by use of spectral oscillations.

A method of measuring the tear film thickness is described in which interference causes oscillations in the reflectance spectrum from the tears. Strong oscillations were usually observed when a contact lens was worn. Measurement of modulation and phase of these oscillations confirmed that they were associated with the tear layer in front of the contact lens. Calculated thickness of this layer averaged 2.7 microns. In one out of five subjects, weak oscillations were sometimes observed without a contact lens. These oscillations probably arose from the aqueous layer of the tears with a thickness of approximately 3 microns. The relative merits of three interference methods of measuring the tear film are discussed.

Comparison of red-green, blue-yellow and achromatic losses in glaucoma.

Achromatic losses in glaucoma would be expected to be greater than, or equal to, red-green chromatic losses if the following assumptions are made: (1) the function of the remaining axons is either unchanged or non-selectively reduced; (2) red-green chromatic information is signaled by the midget ganglion cell system; and (3) the function of the magnocellular system is reduced at least as much as that of the midget ganglion cells. This prediction was tested by measuring red-green (along with blue-yellow) mixture thresholds for 1 deg, 0.2 sec test spots presented on a color monitor on a white background of 50 cd/m2. Ellipses were fitted to plots of green contrast as a function of red contrast (or yellow as a function of blue), and major and minor axes of these ellipses were taken as measures of chromatic and achromatic thresholds, respectively. The study population consisted of 29 eyes in 29 patients with early glaucoma; control data were derived from a data bank of 83 normal eyes. Red-green losses were significantly (P < 0.05) greater than achromatic losses in 6 out of the 11 eyes which showed significant losses of either chromatic or achromatic sensitivity (or both). It is concluded that, for these eyes, at least one of the above three assumptions is incorrect.

Principles of an adaptive method for measuring the slope of the psychometric function.

Recent developments in the efficient estimation of threshold are here extended to the problem of how best to estimate the slope of the psychometric function. An adaptive method is described for selecting stimulus intensities that are optimal for slope estimation. A two-dimensional array of probabilities of different thresholds and slopes is used to calculate the stimulus intensity for the next trial; this array is updated after the trial, using Bayes' theorem to incorporate information from the subject's response. The practical implementation and efficiency of the method are demonstrated and discussed.

Efficient and unbiased modifications of the QUEST threshold method: theory, simulations, experimental evaluation and practical implementation.

QUEST [Watson and Pelli, Perception and Psychophysics, 13, 113-120 (1983)] is an efficient method of measuring thresholds which is based on three steps: (1) Specification of prior knowledge and assumptions, including an initial probability density function (p.d.f.) of threshold (i.e. relative probability of different thresholds in the population). (2) A method for choosing the stimulus intensity of any trial. (3) A method for choosing the final threshold estimate. QUEST introduced a Bayesian framework for combining prior knowledge with the results of previous trials to calculate a current p.d.f.; this is then used to implement Steps 2 and 3. While maintaining this Bayesian approach, this paper evaluates whether modifications of the QUEST method (particularly Step 2, but also Steps 1 and 3) can lead to greater precision and reduced bias. Four variations of the QUEST method (differing in Step 2) were evaluated by computer simulations. In addition to the standard method of setting the stimulus intensity to the mode of the current p.d.f. of threshold, the alternatives of using the mean and the median were evaluated. In the fourth variation--the Minimum Variance Method--the next stimulus intensity is chosen to minimize the expected variance at the end of the next trial. An exact enumeration technique with up to 20 trials was used for both yes-no and two-alternative forced-choice (2AFC) experiments. In all cases, using the mean (here called ZEST) provided better precision than using the median which in turn was better than using the mode. The Minimum Variance Method provided slightly better precision than ZEST. The usual threshold criterion--based on the "ideal sweat factor"--may not provide optimum precision; efficiency can generally be improved by optimizing the threshold criterion. We therefore recommend either using ZEST with the optimum threshold criterion or the more complex Minimum Variance Method. A distinction is made between "measurement bias", which is derived from the mean of repeated threshold estimates for a single real threshold, and "interpretation bias", which is derived from the mean of real thresholds yielding a single threshold estimate. If their assumptions are correct, the current methods have no interpretation bias, but they do have measurement bias. Interpretation bias caused by errors in the assumptions used by ZEST is evaluated. The precisions and merits of yes-no and 2AFC techniques are compared.(ABSTRACT TRUNCATED AT 400 WORDS)

Opponent-color detection threshold asymmetries may result from reduction of ganglion cell subpopulations.

Thresholds for psychophysically opposite stimuli--light and dark, or equiluminous red and green, or equiluminous blue and yellow--are usually nearly equal. This color threshold symmetry is sometimes violated in subjects who have optic nerve hypoplasia, a congenital loss of retinal ganglion cells. We describe a subject who has optic nerve hypoplasia, who exhibits large red-green and blue-yellow detection threshold asymmetries for equiluminous spots. Temporal and spatial integration for equiluminous red and green test spots also differed from normal; static perimetric thresholds for equiluminous green, blue, and yellow (but not red) spots lacked the normal "V" shaped minimum at the fovea. These asymmetries may relate to a developmental paucity of some ganglion cell subtypes. Optic nerve hypoplasia may allow the contributions to detection made by individual ganglion cell subtypes to be isolated psychophysically, in analogy to the study of cone spectral sensitivity in dichromats.

Correlation of chromatic, spatial, and temporal sensitivity in optic nerve disease.

Spearman rank-order correlations (R) were made between the color-mixture threshold, spatial contrast sensitivity, and flicker sensitivity measurements of 38 patients with a variety of optic nerve disorders. Patients had to satisfy the following criteria: greater than 0.5 log unit loss of chromatic or achromatic sensitivity (compared to age-matched normals), central fixation, no congenital color defects, and no ocular media abnormalities. The results of the analysis show a significant correlation between selective losses of high spatial frequency sensitivity (relative to low) and selective losses of red/green and blue/yellow sensitivities [R = -0.680 (P less than 0.001) and R = -0.439 (P less than 0.01), respectively]. A mild correlation was found between selective spatial and selective temporal losses [r = -0.399 (P less than 0.05)] (ie, low temporal frequency losses correlate with high spatial frequency losses and vice versa). A stronger correlation was found between selective red/green and selective blue/yellow sensitivity losses [R = 0.657 (P less than 0.001)]. No correlation was found between selective temporal losses and selective chromatic losses. These findings can be explained in terms of differential losses of three types of fibers: (1) fibers that are particularly sensitive to red/green color, high spatial and low temporal frequencies; (2) fibers signalling blue/yellow color; and (3) fibers that are relatively sensitive to high temporal frequencies and low spatial frequencies.

Chromatic, spatial, and temporal losses of sensitivity in multiple sclerosis.

Chromatic, spatial, and temporal losses of sensitivity were measured in 15 eyes of 10 patients with recovered optic neuritis. Chromatic sensitivities (for both red-green and blue-yellow) were measured using color-mixture thresholds; the chromatic sensitivity loss was classified as "selective" if it was significantly greater than the achromatic loss. Spatial and temporal sensitivities were measured with contrast sensitivity functions and flicker modulation sensitivity, respectively; these losses were classified as selective if the losses at high (spatial or temporal) frequencies were significantly greater (or significantly less) than losses at low frequencies. All patients had central fixation and were optically corrected carefully. In 1 eye, selective losses of sensitivity for red-green and blue-yellow were combined with a selective loss of sensitivity at high spatial (but not temporal) frequencies. This type of loss may indicate a selective loss of small axons in the optic nerve. The 8 other eyes that showed significant losses were generally nonselective in their chromatic, spatial, and temporal losses; this may indicate a nonselective loss of small and large axons.

A quantitative scoring technique for panel tests of color vision.

Panel tests of color vision (eg FM100-Hue test) lack a common quantitative method for the scoring of cap arrangements. We describe a scoring method applicable to all panel tests that makes use of a novel technique to analyze test cap data, namely the calculation of a moment of inertia from the Color Difference Vectors (CDVs) of any arrangement pattern. Using the Farnsworth D-15 panel, as an example, we specify how to determine CDVs and demonstrate the benefits of calculating a moment of inertia for the analysis of these vectors. Moment of inertia analysis yields three factors which quantify cap arrangements: the first is the confusion angle which identifies the type of color defect; the second is the Confusion index (C-index) which quantifies the degree of color loss relative to a perfect arrangement of caps; and the third is the Selectivity index (S-index) which quantifies the amount of polarity or lack of randomness in a cap arrangement. A retrospective study on the result of 53 normal and 66 congenitally color defective observers is reported and provides normative data. We show that the technique differentiates between different types of color defect and provides useful clinical information regarding a loss of color vision. Likewise, a similar observation is made on a smaller sample of FM100-Hue results. A BASIC computer program is provided for anyone wishing to use the technique.

Rod and cone ERGs and their oscillatory potentials.

Normal human ERGs were recorded from a dark-adapted subject using white and colored test flashes. Oscillatory potentials (OPs) were studied after high-pass digital filtering. When blue and red responses were compared at equivalent photopic intensities, OPs were visible at much lower intensities for the blue flashes. As the intensity was reduced from maximum, the first (negative) wave for red flashes maintained a latency of 20-25 msec before being lost in noise, whereas the first wave for blue flashes increased its latency progressively from 25 to 60 msec. These differences between photopically matched red and blue responses are interpreted to be due to rod-generated responses. When blue, orange, and white responses were compared at equivalent scotopic intensities, the latency of the largest negative wave was found to be similar for all three colors. The authors interpret this wave to be the beginning of the rod-generated OPs, so that the preceding waves (particularly evident for orange flashes) are cone-generated OPs, and they propose that the existence of separate rod and cone OPs should be borne in mind when investigating clinical changes in OPs.