The Kinetics of Lid Motion and its Effects on the Tear Film

Berke, Allison P.; Mueller, Stefan C.

doi:10.1007/978-1-4615-5359-5_58

Cited by 14 publications

(13 citation statements)

References 1 publication

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“…The comparison with our computations for full blinks with FPLM boundary conditions is shown in figure 18. We note that our function X t (x) (adapted for incomplete closure from Berke & Mueller (1998)) is more symmetric than that measured by Wong et al, and this is reflected in the values we compute from their formula. We find that at smaller S values, our computed results are thinner, while those at larger S are thicker.…”

Section: Comparison With Wong Fatt and Radkementioning

confidence: 68%

“…The ratio of the length 5 scales, ǫ = d ′ /L ′ is the small parameter for lubrication theory; for the above scales, ǫ ≈ 10 −3 . The velocity scale along the film is the maximum or mean blink closing speed, U m = 10-30cm/s for the maximum speed case (Doane, 1980;Berke & Mueller, 1998). ǫU m is the characteristic speed across the film.…”

Section: Formulationmentioning

confidence: 99%

“…The location of the upper lid is specified by X ′ (t ′ ) (prime indicates dimensional quantity); the lower lid is always at L ′ = 5mm. A mathematical fit to the lid position at the center of the palpebral fissure (eye opening) was obtained by Berke & Mueller (1998) for the data in Berke & Mueller (1996); comparison was made with similar data of Doane (1980). Blink data was also measured and fit by Jones et al (2005).…”

Section: Lid Motionmentioning

confidence: 99%

“…The relations given by Berke & Mueller (1998) are repeated below in terms of the coordinate system of our previous work (Braun, 2006;Braun & King-Smith, 2006) where the origin is the middle of the fully open domain (when X ′ (t ′ ) = −L ′ ). Thus, the domain at any time is given by…”

Section: Full Lid Closurementioning

confidence: 99%

“…In this work, we incorporate realistic lid motion functions that fit observed lid motion data (Doane, 1980;Berke & Mueller, 1998) into two fluid dynamic models for the tear film, and do this for multiple blink cycles. We generalize the flux boundary conditions developed by Jones et al (2005) as an initial step toward implementing the theory of tear film drainage proposed by Doane (1981) for the blink cycle.…”

Section: Introductionmentioning

confidence: 99%

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

Heryudono

Braun

Driscoll

et al. 2007

Mathematical Medicine and Biology

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We consider model problems for the tear film over multiple blink cycles that utilize a single equation for the tear film; the single nonlinear partial differential equation (PDE) that governs the film thickness arises from lubrication theory. The two models that we consider arise from considering the absence of naturally occuring 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 nonperiodic 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.

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Section: Comparison With Wong Fatt and Radkementioning

confidence: 68%

Section: Formulationmentioning

confidence: 99%

Section: Lid Motionmentioning

confidence: 99%

Section: Full Lid Closurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Heryudono

Braun

Driscoll

et al. 2007

Mathematical Medicine and Biology

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Contact lens fitting and changes in the tear film dynamics: mathematical and computational models review

Ramasubramanian,

Hernández-Verdejo,

López-Alonso

2024

Graefes Arch Clin Exp Ophthalmol

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Purpose This review explores mathematical models, blinking characterization, and non-invasive techniques to enhance understanding and refine clinical interventions for ocular conditions, particularly for contact lens wear. Methods The review evaluates mathematical models in tear film dynamics and their limitations, discusses contact lens wear models, and highlights computational mechanical models. It also explores computational techniques, customization of models based on individual blinking dynamics, and non-invasive diagnostic tools like high-speed cameras and advanced imaging technologies. Results Mathematical models provide insights into tear film dynamics but face challenges due to simplifications. Contact lens wear models reveal complex ocular physiology and design aspects, aiding in lens development. Computational mechanical models explore eye biomechanics, often integrating tear film dynamics into a Multiphysics framework. While different computational techniques have their advantages and disadvantages, non-invasive tools like OCT and thermal imaging play a crucial role in customizing these Multiphysics models, particularly for contact lens wearers. Conclusion Recent advancements in mathematical modeling and non-invasive tools have revolutionized ocular health research, enabling personalized approaches. The review underscores the importance of interdisciplinary exploration in the Multiphysics approach involving tear film dynamics and biomechanics for contact lens wearers, promoting advancements in eye care and broader ocular health research.

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Simulation of parabolic flow on an eye-shaped domain with moving boundary

2018

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During the upstroke of a normal eye blink, the upper lid moves and paints a thin tear film over the exposed corneal and conjunctival surfaces. This thin tear film may be modeled by a nonlinear fourth-order PDE derived from lubrication theory. A challenge in the numerical simulation of this model is to include both the geometry of the eye and the movement of the eyelid. A pair of orthogonal and conformal maps transform a square into an approximate representation of the exposed ocular surface of a human eye. A spectral collocation method on the square produces relatively efficient solutions on the eye-shaped domain via these maps. The method is demonstrated on linear and nonlinear second-order diffusion equations and shown to have excellent accuracy as measured pointwise or by conservation checks. Future work will use the method for thin-film equations on the same type of domain.

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The Kinetics of Lid Motion and its Effects on the Tear Film

Cited by 14 publications

References 1 publication

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

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

Contact lens fitting and changes in the tear film dynamics: mathematical and computational models review

Simulation of parabolic flow on an eye-shaped domain with moving boundary

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