A Mathematical Model of the Biofluidmechanics of the Non-Newtonian Mucus Layer of the Tear Film in the Human Eye PDF Download
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Author: Douglas M. Platt
Publisher:
ISBN:
Category : Biomechanics
Languages : en
Pages : 0
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Author: Douglas M. Platt
Publisher:
ISBN:
Category : Biomechanics
Languages : en
Pages : 0
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Author: Dieter W. Liepsch
Publisher: Springer Science & Business Media
ISBN: 3642523382
Category : Science
Languages : en
Pages : 546
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Proceedings of the 2nd International Symposium Biofluid Mechanics and Biorheology. June 25-28, 1989, Munich
Author: Colin Cerretani
Publisher:
ISBN:
Category :
Languages : en
Pages : 344
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Book Description
The increasing global prevalence of dry-eye disease has spurred clinical and research interest in understanding this condition. Most cases of dry eye are attributed to increased tear-evaporation rates. The current paradigm holds that a dysfunctional tear-film lipid layer (TFLL) leads to an increased tear-evaporation rate from the exposed ocular surface, which causes elevated tear salinity (hyperosmolarity). Chronic tear hyperosmolarity then triggers an inflammatory cascade that leads to clinical dry-eye disease. However, a limited fundamental understanding of the role of the TFLL in dry eye impedes progress in developing care strategies. In an effort to advance knowledge in the field, this thesis focuses on tear evaporation in dry eye, on the structure and physical properties of tear lipid, and on the role of duplex-oil films in water-evaporation reduction. First, a compartmental tear-dynamics model is presented that predicts the role of various tear flows on relevant tear parameters such as tear osmolarity and volume. The tears are compartmentalized based on physiology, and tear physics is described over an entire blink cycle. Coupled water- and salt-conservation equations govern the dynamics within each compartment. Tear-supply and tear-evaporation rates are varied to investigate tear behavior in normal and dry-eye conditions. Model predictions match clinical measurements over a wide range of tear-supply and tear-evaporation rates. The tear-evaporation rate is the strongest driver of tear osmolarity. Inclusion of osmotic water flow through the cornea and conjunctiva enables better matching to clinical data than previous models. Additionally, osmotic water flow is found to contribute significantly to tear flow, especially in dry-eye conditions. Despite substantial knowledge of the chemical composition of the secreted lipid, called meibum, little is known of its structure or bulk properties. We investigate the physical and structural properties of collected bulk samples of human and bovine meibum utilizing rheology, calorimetry, and x-ray scattering. Steady and oscillatory shear rheology demonstrate both human and bovine meibum to be remarkably viscoelastic and shear-thinning even at elevated temperatures. Small- and wide-angle x-ray scattering (SAXS and WAXS) confirm the presence of structured crystalline domains at physiological temperature that dissipate with increasing temperature. The melting of crystalline structures near eye temperature measured by SAXS and differential scanning calorimetry (DSC) corresponds to a decrease in meibum viscosity and elasticity over the same temperature range. Meibum viscoelasticity persists even after crystal structures liquefy in SAXS experiments. Thus, our proposed structure for the TFLL at physiologic temperature is a highly viscoelastic, shear-thinning liquid suspension consisting of lipid lamellar-crystallite particulates immersed in a continuous liquid phase. This new paradigm for viewing the lipid layer contrasts with the current picture of several layers of stacked lipids. Finally, we measure water-evaporation reduction by duplex-oil films at thicknesses from 100 nm and 100 μm. Water-evaporation rates are measured gravimetrically with a newly constructed apparatus under controlled gas-phase mass transfer and environmental conditions. White-light interferometry permits continuous visualization of the deposited oil layers to monitor film uniformity. Duplex-film spreading and dewetting are identified as key challenges to obtaining reliable water-evaporation reduction. Duplex-oil films of oxidized mineral oil, bovine meibum, and human meibum reduce evaporation by a proposed dissolution-diffusion mechanism. The data are fitted to dissolution-diffusion theory to yield the water permeability of the duplex-oil film, Dk, which is a material property of the oil. Measured film permeabilities of oxidized mineral oil agree with those reported in literature. Bovine and human meibum, however, do not reduce water-evaporation rates significantly at thicknesses near 100 nm. These findings appear to contradict in-vivo tear-evaporation measurements performed clinically. However, clinical evaporation measurements lack calibration and gas-phase mass-transfer characterization. Consequently, more experiments are needed to clear up this apparent contradiction and to discern the true role of the TFLL in evaporation reduction.
Author: M.W. Collins
Publisher: WIT Press
ISBN: 1853128996
Category : Blood
Languages : en
Pages : 205
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Book Description
All fluid flow problems in the human body involve interaction with the vessel wall. This volume presents a number of studies where primarily mathematical modelling has been applied to a variety of medical wall-fluid interaction problems. The medical applications discussed are highly varied, while some key clinical areas are also addressed. Unusually, a number of important medical challenges involving fluid flow are considered in combination with the relevant solid mechanics. The complexity of addressing combined fluid flow and solid behaviour is viewed positively by the book’s distinguished contributors. For the researcher it offers new scope for developing and demonstrating a mastery of the scientific principles involved.
Author: Emily Kiesel
Publisher:
ISBN:
Category : Eye
Languages : en
Pages : 35
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"The study of the tear film of the eye is important for understanding the causes of dye eye syndrome, a disease causing damage to the ocular surface resulting in discomfort for many people. A popular mathematical model describing the evolution of the tear film thickness over time is a fourth-order nonlinear partial differential equation (PDE). This model has been formulated two different ways to facilitate numerical approximations. The first way is just one PDE including a fourth derivative along with the boundary and initial conditions that is solved for the tear film thickness. The second is a system of coupled second-order PDEs, with the analogous boundary and initial conditions, describing the tear film thickness and pressure. Typically, the second formulation is used when computing the solution as the first poses challenges. These challenges are generally attributed to approximating a scaled fourth derivative and specifying a third derivative for one of the boundary conditions. In this thesis, I explore the computational differences between the two formulations of the tear film model in one spatial dimension. Both formulations are approximated by implementing a method of lines approach where spatial derivatives are approximated with second-order centered finite differences, and then the system of differential equations are integrated forward in time using a backward Euler method. The stability of each numerical method is proven analytically with von Neumann analysis, and the usefulness of each formulation is characterized by studying the condition number of each discretization for different parameters and boundary conditions. In particular, I examine the implications of the relationship between the lid function and boundary conditions. Lastly, a comparison is made with results from the two-dimensional equivalent model on a realistic blinking eye-shaped domain."--Abstract.
Author:
Publisher:
ISBN: 9781109386684
Category : Cornea
Languages : en
Pages :
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The two self-contained parts of this thesis each investigate a challenging phenomenon using scientific computing. In the powerful technique of scientific computing, mathematical models are first developed, and then analyzed and solved through the construction of numerical algorithms. In Part I, we study the stability of Gaussian elimination with partial pivoting via experiments on random matrices. In Part II, we investigate the dynamics of the human tear film subject to reflex tearing, and the tear flow on the eye-shaped geometry subject to different boundary conditions. The growth factor of an n x n matrix quantifies the amount of potential error growth when a linear system is solved by Gaussian elimination with partial pivoting. It has long been know that there exists matrices with growth factors up to 2 n -1, and therefore, Gaussian elimination with partial pivoting is theoretically unstable. However, years of experience and analysis suggest that these matrices with exponentially large growth factors are exceedingly rare. In Part I, we build upon the work of Trefethen and Bau [84] to explore the tails of growth factor probability distributions with a multicanonical Monte Carlo method. Our results suggest that the occurrence of an 8 x 8 matrix with a growth factor of 40 is on the order if a once-in-the-age-of-the-universe event. The human tear film is a complicated multilayer thin film on the surface of the eye that plays an essential role in the health and protection of the eye. In Part II, we focus on modeling the relaxation of the tear film after a blink (i.e., the period when the lids remain open) and explore the effects of viscosity, surface tension, gravity, evaporation, and different boundary conditions. The governing nonlinear partial differential equation derived using an lubrication theory is numerically solved on an overset grid by an implementation of the method of lines with a finite difference discretization in space and an adaptive backward difference formula solver in time. The choice to use an overset grid is motivated by our desire to simulate the tear film dynamics on a blinking domain. The OVERTURE framework is used in two dimensions, because it has many functions needed for interpolation, data handling, and so forth, required for this complex domain. Chapter 5 investigates the phenomenon of reflex tearing along a single line down the center of the cornea. The computations of our tear film model show qualitative agreement with in vivo tear film thickness measurements illustrating the effects of reflex tearing. Furthermore, the role of the black lines in the presence of tear supply from the lid margins was found to be more subtle than as a barrier to tear fluid flow between the anterior of the eye and the meniscus at the lid margin. In Chapters 6 and 7, we focus our efforts on simulating the tear flow on an eye-shaped domain subject to different pressure and flux boundary conditions. The computed flows show sensitivity to both our choice of boundary condition and to the presence of gravity. Moreover, the simulations recover features seen in one-dimensional simulations and capture some experimental observations including hydraulic connectivity between the menisci by the upper and lower lids.
Author: Robert Montes-Mico
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Lan Zhong
Publisher:
ISBN: 9780438595811
Category :
Languages : en
Pages : 139
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Book Description
Rapid tear film thinning has been frequently observed in vivo. The tear film can thin dramatically within one second. However, the dominant mechanisms are unknown. There are different arguments why rapid tear film thinning occurs. In this dissertation, we hypothesized that a non-uniform lipid layer drives tear film thinning; thicker lipid (glob) spreads to its surrounding thinner region, which induces a strong tangential flow and thins the aqueous layer. To test this hypothesis, we built lipid-driven thin film models using lubrication theory. The models successfully captured a very strong tangential flow as well as the short time scale. One successful prediction is that tear film breakup (TBU) occurs beneath a small glob and around the edge of a large glob; these match well with in vivo experimental results. ☐ We then adapted our lipid-driven model by adding equations for solute (salt ions and fluorescein) transport to investigate osmolarity and fluorescein concentration distribution. In rapid thinning, osmolarity and fluorescein concentration remains approximately constant. With the computed fluorescein concentration and aqueous layer thickness, we estimated fluorescein intensity, which is often used to visualize the tear thinning in clinical settings. Fluorescein intensity is proportional to aqueous layer thickness if tear film breakup time (TBUT) is less than 4 seconds. For tear film breakup (TBU) longer than 4 seconds, an initial fluorescein concentration less than about 0.2% can capture rapid tear thinning accurately. We made a close comparison between our simulation results (predicted fluorescein intensity) with in vivo experimental results, and the simulation matches the time scale and physical dimensions very well. ☐ Evaporation has been believed to be a major mechanism of TBU that develops over long times; our mathematical models in this thesis showed that the lipid layer can play an essential role in rapid TBU. This additional understanding of TBU provides insights about better imaging methods and treatment of lipid-driven TBU. ☐ To date, processing experimental images has been a very labor intense task. Thousands of high resolution microscopic images of the lipid layers of several thousand subjects were taken by a research group from The Ohio State University to study lipid layer structure. However, most of these images share limited and similar patterns. To better analyze these images, we built a classification model under the framework of Bag of Features using a small portion of the whole dataset. The classification model is then utilized to classify the remaining images. The model achieved an accuracy of 0.82 on the test dataset and highly reduced the workload of analyzing lipid layer images.
Author: Kaveh Azartash
Publisher:
ISBN: 9781124186795
Category :
Languages : en
Pages : 150
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Book Description
Tear film stability and its interaction with the corneal surface play an important role in maintaining ocular surface integrity and quality of vision. Dry Eye Syndrome (DES) refers to abnormalities of tear film secretion and/or stability diagnosed by conventional methods such as the Schirmer test and tear break-up time (TBUT). Several different physical methods have been developed to measure non-invasively the structure and function of the tear film including high-speed videokeratography and dynamic wavefront aberrometry. Interferometry and optical coherence tomography are amongst new proposed methods to measure tear film thickness that have remained in research phase due to their complex, bulky and expensive instrumentation. Here we present Fluctuation Analysis of Spatial Image Correlation (FASIC), a non-invasive method for evaluating the complex dynamics of the tear film surface by spatial correlation analysis. With this technology, a series of images are obtained using a laser illumination and a cMOS camera. The spatial auto-correlation is calculated for every frame. We have developed a mathematical model to obtain the thickness of the tear film from the sinusoidal background which appears in the spatial auto-correlation image. The model includes the macroscopic dynamics of small lipid droplets in the tear film. Consistent data with live animal model and human clinical study has been obtained.
Author: Abraham Kayal
Publisher:
ISBN:
Category : Electronic books
Languages : en
Pages : 0
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Book Description
The precorneal tear film is a thin layer, about 2,Äì5.5¬†Œom thick, which overlays the corneal and conjunctival epithelium. It functions to lubricate and protect the corneal and eyelid interface from environmental and immunological factors as well as provide an optical medium. The tear film is depicted as a three-layered structure: lipid, aqueous, and mucous layers. Within each layer possesses a different composition which dictates its function. In common between the three layers are their homeostatic process of evaporation and drainage. Any dysfunction in either of the layers can result in Dry Eye Syndrome (DES). The composition, regulation, and pathology of tear film will be discussed in this chapter.
