Skills (7)
Publications (17) View all
-
Article: Elastohydrodynamics of the eyelid wiper.
[show abstract] [hide abstract]
ABSTRACT: This paper presents an elastohydrodynamic model of the human eyelid wiper. Standard lubrication theory is applied to the fluid layer between the eyelid wiper and ocular surface. The role of the lubrication film is to reduce the shear stresses by preventing solid to solid contact between the eyelid wiper and ocular surface. For the lubrication film to be effective, it is required that the orientation of the eyelid wiper changes between the opening and closing phases of a blink. In order to model this, the hydrodynamic model is coupled with an elastic mattress model for the soft tissue of the eyelid wiper and ocular surface. This leads to a one-dimensional non-linear partial differential equation governing the fluid pressure in the lubrication film. In order to solve the differential equation, a loading condition or constraint equation must be specified. The resulting system is then solved numerically. The model allows predictions of the tear film flux from under the upper eyelid, as well as normal and shear stresses acting on the ocular surface. These factors are important in relation to dry eye syndrome, deformation of the cornea and contact lens design. It is found that the pressure and shear stress under the eyelid act across a length of approximately 0.1 mm which is consistent with clinical observations. It order to achieve a flow of tears from under the upper eyelid during a blink, the model requires that the normal force the eyelid applies to the ocular surface during the closing phase of the blink is significantly higher than during the opening phase of the blink.Bulletin of Mathematical Biology 03/2008; 70(2):323-43. · 1.85 Impact Factor -
Article: The effect of the lipid layer on tear film behaviour.
[show abstract] [hide abstract]
ABSTRACT: This paper investigates the effect of surfactants during tear film deposition and subsequent thinning. The surfactants occur naturally on the surface of the tear film in the form of a lipid layer. A lubrication model is developed that describes lipid spreading and film height evolution. It is shown that lipids may play an important role in drawing the tear film up the cornea during the opening phase of the blink. Further, nonuniform distributions of lipids may lead to a rapid thinning of the tear film behind the advancing lipid front (shock). Experiments using a fluorescein dye technique and using a tearscope were undertaken in order to visualise the motion of the lipid layer and any associated shocks immediately after a blink. It is found that the lipid layer continues to spread upwards on the cornea after the opening phase of the blink, in agreement with the model. Using the experimental data, lipid particles were tracked in order to determine the surface velocity and these results are compared to the model predictions.Bulletin of Mathematical Biology 09/2006; 68(6):1355-81. · 1.85 Impact Factor -
Article: Dynamics of tear film deposition and draining.
[show abstract] [hide abstract]
ABSTRACT: This paper investigates the deposition of the tear film on the cornea of the human eye. The tear film is laid down by the motion of the upper eyelid and then subsequently flows and thins. Of particular interest is the stability of the tear layer and the development of dry patches on the cornea. While there has been significant research on the behaviour of tear films between blinks, this paper focuses on understanding the mechanisms which control the shape and thickness of the deposited film and how this affects the subsequent film behaviour. Numerical and analytical methods are applied to a lubrication model which includes the effects of surface tension, viscosity, gravity and evaporation. The model reveals the importance of the eyelid velocity, motion of the surface lipid layer and the storage of tear film between blinks.Mathematical Medicine and Biology 10/2005; 22(3):265-88. · 1.82 Impact Factor -
Article: The metapopulation dynamics of an infectious disease: tuberculosis in possums.
[show abstract] [hide abstract]
ABSTRACT: An SEI metapopulation model is developed for the spread of an infectious agent by migration. The model portrays two age classes on a number of patches connected by migration routes which are used as host animals mature. A feature of this model is that the basic reproduction ratio may be computed directly, using a scheme that separates topography, demography, and epidemiology. We also provide formulas for individual patch basic reproduction numbers and discuss their connection with the basic reproduction ratio for the system. The model is applied to the problem of spatial spread of bovine tuberculosis in a possum population. The temporal dynamics of infection are investigated for some generic networks of migration links, and the basic reproduction ratio is computed-its value is not greatly different from that for a homogeneous model. Three scenarios are considered for the control of bovine tuberculosis in possums where the spatial aspect is shown to be crucial for the design of disease management operations.Theoretical Population Biology 03/2002; 61(1):15-29. · 1.65 Impact Factor -
Article: Periodic triggering of an inducible gene for control of a wild population.
[show abstract] [hide abstract]
ABSTRACT: A possible method of control for the management of wild populations consists of continual introgression of an inducible transgene by releasing transgenic individuals, with periodic exposure of the population to a trigger. Exposure to the trigger causes death or sterility in carriers of the transgene, but is otherwise benign. We investigate the effectiveness of various strategies for control. We show that suppression of the population density below any pre-specified level is possible using this technique. At the same time we show that too frequent or too efficient exposure to the trigger can select for non-transgenic genotypes at an intensity such that the population density will be largely unaffected by the trigger. Choices for management parameters can ensure that the latter scenario is avoided. We show that releasing individuals carrying the transgene at more than one locus facilitates density control.Theoretical Population Biology 10/2000; 58(2):95-106. · 1.65 Impact Factor
