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.

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.

Modelling drainage of the precorneal tear film after a blink.

We study the drainage of the precorneal tear film in humans. A fluid dynamic model for the drainage of the aqueous layer is developed that includes the effects of evaporation and gravity. The model may be reduced to a single nonlinear partial differential equation for the thickness of the aqueous layer. The equation is solved numerically and accurate times for film rupture are obtained for physically realistic parameters. The results indicate that although gravity and evaporation are not the most dominant effects in some parts of the film, they can nevertheless materially affect the film drainage process and should therefore be included in models for tear film drainage.

Estrous cycle status alters N-methyl-N-nitrosourea (NMU)-induced rat mammary tumor growth and regression.

The relationship between mammary carcinoma growth, ovariectomy-induced regression and estrogen receptor status were determined in Sprague-Dawley rats with 5-day estrous cycles after injection of N-methyl-N-nitrosourea (NMU) on metestrus (ME), diestrus-1 (DE-1), proestrus (PE) or estrus (E). Rats exposed to NMU on PE had a shorter tumor latency than those injected on ME and E, as well as more carcinomas per rat than those exposed on ME and DE-1. Mammary carcinomas grew faster in rats injected on ME (doubling time, 6.4 days) and DE-1 (6.9 days) compared with PE (15.2 days) and E (16.3 days). Tumor regression was also significantly faster in rats injected on ME (time to 50% vol., 5.5 days) and DE-1 (5.3 days) compared with PE (8.2 days) and E (8.5 days) following bilateral-ovariectomy during log phase growth. Significantly, total nuclear estrogen receptor (ERN) content was increased in carcinomas from rats injected on PE compared with DE-1 (70.8 +/- 11.3 vs. 32.9 +/- 7.3 fm/mg DNA) (P less than 0.05) and DE-1 and ME combined (P less than 0.01). These observations generalize the concept that estrous cycle stage at the time of NMU injection alters subsequent mammary carcinoma biology, and represents the first experimental evidence that slower growing and responding estrogen receptor positive rat mammary carcinomas may be associated with an increase in circulating estrogen prior to carcinogen exposure.

Transplacentally acquired caffeine and the occurrence of apnea, bradycardia, and periodic breathing in preterm infants: preliminary communication.

Cord blood caffeine concentrations were measured by high-pressure liquid chromatography in 79 preterm infants. Eleven infants (14%) had detectable caffeine concentrations ranging from 1.1 to 3.7 micrograms/mL (means +/- SD = 2.5 +/- 0.8), and 68 infants had no measurable caffeine. Seven infants with detectable caffeine (group 1) had impedance pneumograms recorded before 2 weeks of age. Each infant in group 1 was matched with two infants without detectable caffeine by birthweight, gestational age, and chronologic age at pneumogram recording to yield a control group (group 2) of 14 infants. Comparison of the groups using quantitative measures of apnea, bradycardia, and periodic breathing obtained from pneumogram analysis and the incidence of monitor alarms on bedside nursing records showed no significant differences. Thus, caffeine was present infrequently and at low concentrations at birth in 79 preterm infants. The amount of apnea, bradycardia, and periodic breathing experienced before 2 weeks of age in 7 preterm infants with detectable cord blood caffeine was not different from that in 14 similar infants without caffeine. Future studies are planned to examine the relationship between postnatal changes in transplacentally acquired methylxanthine concentrations and quantitative measures of apnea, bradycardia, and periodic breathing in a larger number of preterm infants without cardiorespiratory disease.

Replacement of amalgams with crowns: a cost-effectiveness analysis.

No formal analyses comparing the treatment alternatives of replacing a failed amalgam with either another amalgam or crown have been done to determine the optimum treatment strategy based on lifetime costs to the patient. Using decision analysis, a computer model was developed of the lifetime restorative needs of an adult's posterior tooth. A cost-effectiveness analysis of large amalgams vs crowns was then done to determine the optimum strategy. According to the analyses, the optimum treatment decision is to attempt to replace the failed first amalgam with another amalgam, instead of with a crown. When this amalgam restoration fails, then the subsequent replacement may be with a crown. Potential lifetime cost savings were between 11% and 24% if the first replacement was an amalgam. This study concludes that the technique of decision analysis provides the dental community with an effective evaluation tool for the study of clinical decision-making, taking into account all levels of clinical uncertainty.

Estrous cycle modification of rat mammary gland DNA alkylation by N-methyl-N-nitrosourea.

Virgin Sprague-Dawley rats exhibiting regular estrous cycles were used as a model system to determine whether the level of circulating estrogen modifies the alkylation pattern of mammary gland DNA by a direct-acting carcinogen, N-methyl-N-nitrosourea (NMU). The concentration of 7-methylguanine and O6-methylguanine were similar in mammary epithelial DNA 0.25, 0.50, and 1.0 h after i.v. injection of 50 mg/kg body weight NMU on different days of the rat estrous cycle. However, O6-methylguanine was significantly higher in mammary gland DNA 8 and 24 h after a single i.v. dose of carcinogen on proestrus or estrus, compared to rats receiving carcinogen on diestrus. There was no difference in the 7-methylguanine levels at 8 h in any group, but this adduct was higher in estrous-treated rats at 24 h. The ratio of O6-methylguanine to 7-methylguanine was significantly lower at 8 h in mammary gland DNA from diestrous-injected rats, and this difference reflected the lower level of O6-methylguanine adducts in this group. In contrast, O6-methylguanine concentrations in DNA extracted from the liver of the same animals were virtually identical at all time periods examined. 7-Methylguanine levels were higher in the liver at 0.5, 1, 8, and 24 h post-NMU in proestrus as compared with diestrous-injected rats. The observed adduct clearance suggests that rat mammary epithelium may contain repair systems capable of removing O6-methylguanine. These results also suggest that the initial removal of the O6-methylguanine lesions in mammary epithelial DNA (rather than the initial rate of alkylation) is affected by the hormonal environment during carcinogen exposure. This effect may be tissue specific since removal of O6-methylguanine from liver DNA is apparently not altered by the stage of the estrous cycle at which NMU is administered.

Estrous cycle modification of rat uterine DNA alkylation by N-methyl-N-nitrosourea.

The present study was designed to determine whether the stage of the estrous cycle at the time of N-nitroso-N-methylurea (NMU) presentation altered DNA adduct formation and repair in the rat uterus. In uterus the rate of O6-methylguanine (O6-meGua) and 7-methylguanine (7-meGua) formation and the total yield of adducts was estrous cycle dependent. Uterine DNA from rats injected with NMU on diestrus formed O6-meGua and 7-meGua more rapidly and had significantly higher adduct levels than those rats injected on proestrus or estrus. Repair of O6-meGua and 7-meGua was also significantly faster between 1 and 24 h post-NMU in uterine DNA isolated from rats injected on diestrus compared to those injected on proestrus or estrus.