GENERALIZED MATHEMATICAL MODELING OF AQUEOUS HUMOUR FLOW IN THE ANTERIOR CHAMBER AND THROUGH A MESH CHANNEL IN THE HUMAN EYE

GENERALIZED MATHEMATICAL MODELING OF AQUEOUS HUMOUR FLOW IN THE ANTERIOR CHAMBER AND THROUGH A MESH CHANNEL IN THE HUMAN EYE

ABSTRACT

In this work, we propose mathematical models for the processes that take place in the human eye and how they contribute to the development of pathological states. We considered and studied two related dynamics processes that take place in the eye. Firstly, a generalized mathematical model of aqueous humour flow driven by temperature gradient in the anterior chamber is presented. This predicts the flow behavior when the ambient temperature is higher than the core body temperature. The purpose of these models is to predict flow behavior in the presence of high ambient temperatures. Secondly, we consider the aqueous humour flow through a trabecular mesh channel in the presence of multiple constrictions or stenoses. A two dimensional model for the fluid in the mesh channel with couple stress fluid in the core region and Newtonian fluid in the peripheral region is developed. The purpose of these models is to examine the flow behavior and investigate how this influences primary open angle glaucoma (POAG). The models are solved analytically. The result obtained showed that buoyant convective flow would alwarys arise from the temperature gradient that is present across the anterior chamber of the eye. Also, as the cornea height and temperature increases, the fluid velocity decreases. It is observed that resistance to flow and wall shear stress increased with the height of the stenoses. The result equally indicated that intraocular pressure (IOP) increased with the wall shear stress as a result of the multiple stenoses that narrows the trabecular mesh channel. The channel becomes progressively less porous, this might lead to primary open angle glaucoma (POAG).