Mathematical models of water transport across ocular epithelial layers

Abstract

Fluid transport underpins many of the key physiological processes that occur in the eye. As a consequence, disorders of these transport processes account for much of the observed ocular pathology. The eyeball itself can be compared to a bicycle tire that needs to be pumped up (by the production of the aqueous humor) in order to maintain its shape. The retina is separated by a potential space from its underlying retinal pigment epithelium (RPE) and only remains attached due to the pumping of fluid out of the subretinal space by the aforementioned RPE. Equally, the cornea has to be kept relatively dehydrated in order to be transparent. Failure of these active fluid flows, generated by the ciliary epithelium (CE), RPE, and corneal endothelium, will result, respectively, in collapse of the eyeball (phthisis bulbi), retinal detachment, and corneal edema; common ocular disorders. In this chapter, we review the physical mechanisms responsible for fluid transport across epithelial layers, focusing on ocular tissues. These mechanisms include oncotic, osmotic, and mechanical pressure differences across the layer, electroosmosis along the clefts separating adjacent cells and local osmosis. The relative importance of these processes depends on the particular epithelium. Understanding the functioning of epithelial pumping is important to develop strategies for manipulating the flow, which is often necessary to treat pathologic conditions. For instance, reduction of aqueous production by the CE is one option for treating glaucoma and increase of RPE pumping helps deal with fluid accumulation in the subretinal space, associated with macula edema. Mathematical modeling has proven to be a useful tool to understand fluid transport across epithelial layers and to single out the role of specific mechanisms. We will first discuss how the earlier-mentioned effects can be described making use of mathematical approaches with the appropriate degree of complexity. Since each epithelium requires a specific modeling approach, based on its physiology and on the effects that need to be accounted for, we will review mathematical models of three ocular cell layers: the CE, the corneal endothelium, and the RPE.