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.

Isospectral shapes with Neumann and alternating boundary conditions.

The isospectrality of a well-known pair of shapes constructed from two arrangements of seven congruent right isosceles triangles with the Neumann boundary condition is verified numerically to high precision. Equally strong numerical evidence for isospectrality is presented for the eigenvalues of this standard pair in new boundary configurations with alternating Dirichlet and Neumann boundary conditions along successive edges. Good agreement with theory is obtained for the corresponding spectral staircase functions. Strong numerical evidence is also presented for isospectrality in an example of a different pair of shapes whose basic building-block triangle is not isosceles. Some possible confirmatory experiments involving fluids are suggested.

Ceramide generation by two distinct pathways in tumor necrosis factor alpha-induced cell death.

Ceramide accumulation in the cell can occur from either hydrolysis of sphingomyelin or by de novo synthesis. In this study, we found that blocking de novo ceramide synthesis significantly inhibits ceramide accumulation and subsequent cell death in response to tumor necrosis factor alpha. When cells were pre-treated with glutathione, a proposed cellular regulator of neutral sphingomyelinase, inhibition of ceramide accumulation at early time points was achieved with attenuation of cell death. Inhibition of both pathways achieved near-complete inhibition of ceramide accumulation and cell death indicating that both pathways of ceramide generation are stimulated. This illustrates the complexity of ceramide generation in cytokine action.

Regulation of membrane release in apoptosis.

Apoptosis is a fundamental process of cell regulation whereby cells execute one or more biochemical programs leading to cell death. Several mechanisms have been evaluated and suggested to play roles in the regulation of apoptosis, including the activation of phospholipase A2 (PLA2), usually measured as release of 3H-labelled arachidonic acid (AA) from prelabelled cells. The current study was aimed at examining the role of PLA2 in regulating apoptosis in response to several inducers (such as vincristine and etoposide) in lymphoid cell lines. Cells were labelled with [3H]fatty acids and the released radioactivity was characterized. These studies indicated that the AA release assay did not reflect release of non-esterified fatty acid via activation of the PLA2 pathway. Rather, studies using TLC and electron microscopy showed that AA release reflected a previously unsuspected shedding of a heterogeneous population of membrane vesicles and fragments, probably as components of apoptotic bodies. Further studies demonstrated that this process is an integral part of apoptosis. Overexpression of Bcl-2 or the addition of caspase peptide inhibitor benzyloxycarbonyl-Asp-Glu-Val-Asp-fluoromethane prevented the characteristic morphological changes of cell death, and completely inhibited the release of membrane vesicles and fragments. On the other hand, release of membrane vesicles and fragments was caused by various inducers of apoptosis, as measured by release of either 3H-labelled AA or palmitic acid. Thus the present study demonstrates that the release of membrane lipids during apoptosis defines a new assay for apoptosis and has allowed the investigation of the mechanisms regulating formation of apoptotic bodies.

Hydrodynamic stability without eigenvalues.

Fluid flows that are smooth at low speeds become unstable and then turbulent at higher speeds. This phenomenon has traditionally been investigated by linearizing the equations of flow and testing for unstable eigenvalues of the linearized problem, but the results of such investigations agree poorly in many cases with experiments. Nevertheless, linear effects play a central role in hydrodynamic instability. A reconciliation of these findings with the traditional analysis is presented based on the "pseudospectra" of the linearized problem, which imply that small perturbations to the smooth flow may be amplified by factors on the order of 10(5) by a linear mechanism even though all the eigenmodes decay monotonically. The methods suggested here apply also to other problems in the mathematical sciences that involve nonorthogonal eigenfunctions.