A mathematical model for solute coupled water transport in the production of aqueous humor

A simple mathematical model for the transport of solute and water in the production of aqueous humor by ciliary epithelium in the eye has been developed. The model introduces the intercellular channel, caped with a leaky (porous) tight junction between the layers of non-pigmented ciliary epithelium, as a bisectional channel which consists of two sections: one representing the tight junction which constitutes the blood-aqueous barrier and the other intercellular space with the active solute transport pumps on its lateral surfaces near the junction. The intercellular space and porous tight junction are modeled as electroneutral, uniform, semi-permeable channels of unequal cross-sectional area. Both the cylindrical pore- and rectangular-slit models for the transport through the channels are simultaneously introduced. The approximate analytical solutions to the governing non-linear coupled equations are obtained in normalized forms by employing Segal’s “Isotonic Convection Approximation”. The computational results for the scaled variables are presented through the graphs. The effects of important parameters on the flow/transport produced by (1) the hydrostatic pressure difference alone, (2) the concentration difference alone, and (3) the active transport alone, are examined and discussed. The results of the model may contribute to the present understanding of the mechanisms governing transport processes involved in the aqueous production.