Computed tear film and osmolarity dynamics on an eye-shaped domain

Abstract

The concentration of ions, or osmolarity, in the tear film is a key variable in understanding dry eye symptoms and disease. In this manuscript, we derive a mathematical model that couples osmolarity (treated as a single solute) and fluid dynamics within the tear film on a 2D eye-shaped domain. The model includes the physical effects of evaporation, surface tension, viscosity, ocular surface wettability, osmolarity, osmosis and tear fluid supply and drainage. The governing system of coupled non-linear partial differential equations is solved using the Overture computational framework, together with a hybrid time-stepping scheme, using a variable step backward differentiation formula and a Runge–Kutta–Chebyshev method that were added to the framework. The results of our numerical simulations provide new insight into the osmolarity distribution over the ocular surface during the interblink.

TFOS DEWS II Tear Film Report

“…Various mathematical models, as summarized and furthered by Braun et al, have stated that the osmolarity across the ocular surface is different to that measured in the tear meniscus [153]. During the blink interval the tear film thins over the cornea, mainly due to evaporation, leading to a hyperosmotic shift [153,154]. The level of hyperosmotic shift depends on the thinning rate, which is driven by the evaporation rate [154].…”

“…During the blink interval the tear film thins over the cornea, mainly due to evaporation, leading to a hyperosmotic shift [153,154]. The level of hyperosmotic shift depends on the thinning rate, which is driven by the evaporation rate [154]. In the event of a low thinning rate, such as 1 μm/min, tear film osmolarity over the ocular surface will increase from 300 mOsm/L to 332 mOsm/L over a 25 s period, but will increase to 1830 mOsm/L in the case of a rapid thinning rate of 20 μm/min [153].…”

Dynamics and function of the tear film in relation to the blink cycle

“…In this section, the diffusivity of salt and fluorescein are assumed equal and to be that of the salt value from Zubkov et al (2012), and the isotonic osmolarity is 302 mOsM. We focus on results for the thickness, osmolarity (Li et al, 2014a) and fluorescence distributions over the exposed ocular surface shown in Figs. 23 and 24.…”

“…The flux of fluid entering the domain is a sum of influx from the lacrimal gland ( lg ) and efflux via the puncta ( p ). They are complicated functions that are given elsewhere (Li et al, 2014a, 2014b). The flux boundary condition is shown at specific times in Fig.…”

Better methods of clinically assessing mucus functions are required

“…Ocular mucus helps maintain the wettability of the ocular surface and provides lubrication for lid movements over it 2 . In the healthy eye, the glycocalyx, which has previously been referred to as the mucus layer, prevents the epithelial surface from dewetting 3 . Consistent with the current understanding of tear function, the fluorescein tear break up time test devised by Norn 4 was originally intended to be used as a measure of mucus efficiency or deficiency.…”