Dispersive Mixing in the Posterior Tear Film Under a Soft Contact Lens

Abstract

This paper is a first attempt to model mixing in the tear layer of the eye sandwiched between the cornea and a soft contact lens (i.e., the post-lens tear film or POTF). The proposed driving force for mixing is lateral diffusion enhanced by the periodic lateral (up-down) and squeezing (in-out) motion of the contact lens during blinking. In a mechanism similar to Taylor dispersion, the classical diffusion equation emerges at long times when concentration gradients smooth, but with a mechanical dispersion coefficient, D*, rather than a molecular diffusion coefficient, D. Calculated values of the dispersion coefficient are orders of magnitude larger than molecular diffusivities permitting mixing in the POTF on time scales much shorter than that of pure diffusion, L 2 /D, where L is the lens radius. The dispersive-mixing model is tested against clinical experiments of fluorescein-labeled dextran decay from the POTF on 23 human subjects, each with soft contact lenses of four different diameters. Comparison between theory and experiment for the nonreactive dye is reasonable, especially considering the fact that accurate measurements of several parameters are not available, such as the transverse lens travel and the tear-film thickness. The model captures the essential physics involved in the mixing process but requires modification to improve quantitative prediction. Further, the proposed dispersive-mixing theory for flushing of the POTF serves as a foundation for predicting the mixing behavior of reactive solutes, such as oxygen, carbon dioxide, and bacteria.

Ocular Drug Delivery Role of Contact Lenses

“…2,14,15,16 . While eye drops are comfortable to instill, the low bioavailability of less than 5% is a major drawback.…”

Settling and Deformation of a Thin Elastic Shell on a Thin Fluid Layer Lying on a Solid Surface

“…This gives the first of the two boundary conditions in Eq. [12]. The second boundary condition at the lens center is due to symmetry.…”

“…[11]) are solved subject to the boundary conditions [7] and [12] by finite difference. The term ∂δ/∂t in Eq.…”

“…Contact with draping, however, is of concern because it reduces the superior-inferior motion of the lens (11) and reduces mixing in the post-lens tear film (12). In addition, draping may lead to mechanical interaction between the lens and the cornea, perhaps eventually causing epithelial damage.…”

“…Thus, as in our model of a concave lens, in a human eye too, first contact is expected beyond the limbus. This implies that a lens with edge thickness of about 1.2 times the central thickness is preferable in order to limit the conformity between the lens and the cornea-sclera surface, thereby preventing or at least minimizing adherence and also maximizing tear mixing (12). However, this critical thickness ratio depends on other lens parameters, such as the actual value of central thickness and the lens modulus.…”