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Lan Zhong, Richard J Braun, Peter Ewen King-Smith, Carolyn G Begley; Dynamics of Fluorescent Imaging in Glob-Driven Breakup. Invest. Ophthalmol. Vis. Sci. 2017;58(8):2613.
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© ARVO (1962-2015); The Authors (2016-present)
A previous mathematical model (ARVO 2016 abstract, L. Zhong et al, IOVS 57(12):6171) has successfully simulated the immediate breakup due to glob (thicker lipid) in the lipid layer. It captured a fast spreading of polar lipid and a corresponding strong tangential flow in aqueous layer. We now extend the model by adding equations for conservation of solutes, for osmolarity and fluorescein, in order to study their dynamics. We then compare our computed results for the resulting intensity distribution with fluorescence experiments on the tear film.
We extended our previous mathematical model by adding two equations that govern the dynamics of osmolarity and fluorescein. The model also includes an osmotic flow across corneal/aqueous interface. The coupled equations are solved by a custom MATLAB program where we vary the evaporation distributions, glob sizes (xI) and initial concentrations of fluorescein (f0).
We computed results of tear film thickness (h), polar lipid concentration (G), osmolarity (c) and fluorescein concentration (f). The fluorescent intensity (I) is evaluated via Nichols et al (IOVS, 2012, 53:5426). Under all evaporation distributions we used, if TBU occurs in a second or less, the concentration of solutes remained unchanged. If TBU occurs in a longer time, the effect of evaporation becomes more significant (Figure 1). The concentration of both solutes increases and the peak c is lower than for f due to its faster diffusion. Figure 2 shows that the intensity I approximated the thickness of the tear film well only when TBU occurred immediately and f0 is small (dilute case).
In this type of rapid thinning, we found that the fluorescent intensity can approximate the tear film thickness well when the initial f is small and TBU occurred in 1s. Evaporation accelerates TBU but can’t increase the concentration of solutes when the TBUT is short. The osmotic flow across the corneal surface occurs in the model but it is too weak to stop the rapid thinning caused by glob.
This is an abstract that was submitted for the 2017 ARVO Annual Meeting, held in Baltimore, MD, May 7-11, 2017.
Figure 1: Left: TBU occurs in 1.25s when XIis 0.3 (dimensionless). Here c and f are unchanged. Right: XI is 1.2, and TBUT is 5.12s; evaporation is elevated within the glob width and we find increased c and f in TBU region.
Figure2: The upper left plot is the only case where either I or √I closely approximates the thickness; there I is determined by h because f is constant in that case and the glob is small.
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