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

Heryudono, Alfa; Braun, Richard; Driscoll, Tobin A.; Maki, Kara L.; Cook, L. Pamela; King‐Smith, P. Ewen

doi:10.1093/imammb/dqm004

Cited by 52 publications

(70 citation statements)

References 41 publications

(88 reference statements)

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“…As done in other studies [11,12,7,13,3,4], for computations it is convenient to map the problem onto a fixed computational domain using the change of variables x = L(t)η, with 0 ≤ η ≤ 1 and the normalized film thickness h(x, t) = HH(η, t), yielding the governing equation…”

Section: Acknowledgmentsmentioning

confidence: 99%

“…Tear films are have previously been modelled as a thin film of Newtonian liquid moving over a solid surface. The aspect ratio of the problem is used to reduce the Navier-Stokes equations to the equations of lubrication theory [2,3,7,11,12,26].…”

Section: Introductionmentioning

confidence: 99%

“…They conclude that the model reproduces tear film profiles measured in vivo for half blinks. This work is extended in Heryudono et al [7] to incorporate a more realistic eyelid velocity and flux under both eyelids to take account of supply from the lacrimal gland and drainage due to the puncta. The model is solved in the two cases described in [4] and compared with the solution of previous models and with experiments.…”

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confidence: 99%

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The Effect of Polar Lipids on Tear Film Dynamics

2010

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In this paper we present a mathematical model describing the effect of polar lipids on the evolution of a precorneal tear film, with the aim of explaining the interesting experimentally observed phenomenon that the tear film continues to move upwards even after the upper eyelid has become stationary. The polar lipid is an insoluble surface species that locally alters the surface tension of the tear film. In the lubrication limit, the model reduces to two coupled nonlinear partial differential equations for the film thickness and the concentration of lipid. We solve the system numerically and observe that the presence of the lipid causes an increase in flow of liquid up the eye. We further exploit the size of the parameters in the problem to explain the initial evolution of the system.

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Section: Acknowledgmentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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The Effect of Polar Lipids on Tear Film Dynamics

2010

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“…Without a sufficient tear film, eye irritation may occur and can lead to more severe damage of the corneal surface. The understanding of diseases such as dry eye syndrome has led to a growing interest in the applied mathematics and fluid dynamics community in developing models that allow for quantitative prediction of tear film thinning and rupture addressing issues such as aqueous layer stability (Sharma and Ruckenstein [8]), the dynamics of tear deposition and thinning due to lid motion (Wong, Fatt, and Radke [9]), mucus layer stability (Sharma, Khanna, and Reiter [1]), non-Newtonian rheology of the tear film (Zhang, Matar, and Craster [2]), evaporation and gravitational drainage (Braun and Fitt [3]), evaporation and corneal surface wetting (Winter, Anderson, and Braun [10]), dynamics during blink cycles (Heryudono et al [11], Braun and King-Smith [12]), reflex tearing (Maki et al [13]) and two-dimensional eye-shaped domains (Maki et al [14,15]). …”

mentioning

confidence: 99%

“…In this section we outline the results of lubrication theory applied to the problem described in the main text with the tangentially immobile boundary condition u ·t = 0 in place of the boundary condition (11). For completeness we present results for both the Beavers-Joseph slip condition as well as the Le Bars-Worster slip condition.…”

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confidence: 99%

Thin Film Evolution over a Thin Porous Layer: Modeling a Tear Film on a Contact Lens

Nong¹,

Anderson²

2010

SIAM J. Appl. Math.

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Abstract.We examine a mathematical model describing the behavior of the precontact lens tear film of a human eye. Our work examines the effect of contact lens thickness and lens permeability on the film dynamics. Also investigated are gravitational effects and the effects of different slip models at the fluid-lens interface. A mathematical model for the evolution of the tear film is derived using a lubrication approximation applied to the hydrodynamic equations of motion in the fluid film and the porous layer. The model is a nonlinear fourth-order partial differential equation subject to boundary conditions and an initial condition for post-blink film evolution. The evolution equation is solved numerically, and the effects of various parameters on the rupture of the thin film are studied. We find that increasing the lens thickness, permeability, and slip all contribute to an increase in the film thinning rate, although for parameter values typical for contact lens wear, these modifications are minor. Gravity plays a role similar to that for tear films in the absence of a contact lens. The presence of the contact lens does, however, fundamentally change the nature of the rupture dynamics as the inclusion of the porous lens leads to rupture in finite time rather than infinite time. [5], and Cher [6]) suggest a somewhat more complex system. In particular, the current view replaces the mucus and aqueous layers with a mucoaqueous layer in which mucins secreted from goblet cells are distributed throughout the bulk of the tear film and epithelial mucins form a complex barrier at the corneal surface. Measurements of the overall thickness of a human tear film range from a few microns to as many as 40 (see the review by Bron et al. [5]). The corneal surface itself has 100-nm-scale microbumps and rod-like mucins of length 200-500 nm that extend into the tear film [4]. These mucins have multiple functions ranging from cleanup and removal of debris from the tear film, stabilization of the tear film, and, with particular attention to the membrane-associated mucins, maintaining wettability at the corneal surface. The lipid layer, whose thickness has been estimated to range between 13-100 nm, serves to further stabilize the film and to slow evaporative mass loss (Bron et al. [5]).Dry eye syndrome is a common disorder of the human tear film that results from decreased tear production, excessive tear evaporation, and/or an abnormality in the

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