Flow of aqueous humor in the canal of Schlemm

Abstract

A mathematical model is presented for the flow of aqueous humor in Schlemm's canal in the eye. The model introduces a canal segment between two collector channels as a rectangular channel with porous upper wall. Two cases have been considered in the model: (I) the inner porous wall of the canal is rigid; (II) the inner wall is collapsible. Analytical solution of the governing equation in case I is straightforward, whereas the nonlinear equation in case II is solved by an iterative procedure. Aqueous fluid pressure and flow profiles in the proposed model are drawn, and the effects of important parameters on these profiles are brought out and discussed. It is concluded that for case I, resistance to aqueous flow is influenced by the filtration constant of the trabecular and endothelial meshwork and that narrowing of the canal reduces outflow. In case II, an increase in intraocular pressure (IOP) or compliance coefficient of the canal inner wall increases the collapse of the canal, which offers increased resistance to flow resulting in the decreased flow whereas increasing filtration constant facilitates aqueous outflow. These theoretical results suggest that increased IOP or decreased rigidity of the inner wall may contribute to the development of increased resistance as observed in some cases of glaucoma and that increasing values of filtration constant may contribute to the facility of outflow increase.