Richard J Braun, Tobin A Driscoll, Carolyn G Begley, P Ewen King-Smith, Javed I Siddique
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引用次数: 21
Abstract
We report the results of some recent experiments to visualize tear film dynamics. We then study a mathematical model for tear film thinning and tear film breakup (TBU), a term from the ocular surface literature. The thinning is driven by an imposed tear film thinning rate which is input from in vivo measurements. Solutes representing osmolarity and fluorescein are included in the model. Osmolarity causes osmosis from the model ocular surface, and the fluorescein is used to compute the intensity corresponding closely to in vivo observations. The imposed thinning can be either one-dimensional or axisymmetric, leading to streaks or spots of TBU, respectively. For a spatially-uniform (flat) film, osmosis would cease thinning and balance mass lost due to evaporation; for these space-dependent evaporation profiles TBU does occur because osmolarity diffuses out of the TBU into the surrounding tear film, in agreement with previous results. The intensity pattern predicted based on the fluorescein concentration is compared with the computed thickness profiles; this comparison is important for interpreting in vivo observations. The non-dimensionalization introduced leads to insight about the relative importance of the competing processes; it leads to a classification of large vs small TBU regions in which different physical effects are dominant. Many regions of TBU may be considered small, revealing that the flow inside the film has an appreciable influence on fluorescence imaging of the tear film.
期刊介绍:
Formerly the IMA Journal of Mathematics Applied in Medicine and Biology.
Mathematical Medicine and Biology publishes original articles with a significant mathematical content addressing topics in medicine and biology. Papers exploiting modern developments in applied mathematics are particularly welcome. The biomedical relevance of mathematical models should be demonstrated clearly and validation by comparison against experiment is strongly encouraged.
The journal welcomes contributions relevant to any area of the life sciences including:
-biomechanics-
biophysics-
cell biology-
developmental biology-
ecology and the environment-
epidemiology-
immunology-
infectious diseases-
neuroscience-
pharmacology-
physiology-
population biology