# Generalized Mathematical Modeling of Aqueous Humour Flow in the Anterior Chamber and Through A Mesh Channel in the Human Eye

Filed in Articles on November 4, 2022

– Generalized Mathematical Modeling of Aqueous Humour Flow in the Anterior Chamber and Through A Mesh Channel in the Human Eye –

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### 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 always 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.

### INTRODUCTION

This research work is based on mathematical models on aqueous humour flow in the interior chamber of the human eye and its exit through the outflow pathways. We shall consider this under two subheadings. A generalized mathematical model of aqueous humour flow driven by temperature gradient and a model on fluid flow through a mesh channel in the human eye. We shall also discuss any other information that may be very necessary for proper understanding of our mathematical models, results and subsequent analysis.

A Generalized Mathematical Model for the Aqueous Humour Flow Driven by Temperature Gradient.

Vision is one of the most important human senses (BO 2009, Umit 2003, Valdivia 2009, Zuhaila 2008). The human eye is one of the most complex organ and complex structure in the biology of man. As a sense organ, the eye is the (optic) window through which man Visualizes his environment and what happens in and around him.

The power of vision and conception all lie in the power of sight enabled by the eye. If the eye is a major vital organ in man, its study is of prominent concern. This is to enable eye health practitioners understand the mechanism of sight more and more; and then find ways to improve the condition of human eye.

### REFERENCES

Adam Villamarin, Sylvain Roy, Reda Hasballa, Orestis Vardoulis, Philippe Reymond and Nikolas Stergiopulos (2012). 3D  Simulation of the  Aqueous Flow in the Human Eye. Medical Engineering and Physics34(2012) 1462 – 1470 lausanne Switzerland.

Ales, M and Jaroslav, P (2000).The Human Iris Structure and its Usages. Acta University Palacki Olomuc, Fac. Rev, NAT Physica 39, 87 – 95.

Alessandro, S., Roddfo, R and Chiara, C., (2007). Eye Rotations Induced  Dynamics of a Newtonian Fluid within the Vitreous Cavity: The effect of the chamber shape. Phys. Med. Biol. 52 2021- 2034.

American Academy of Ophthalmology; Preferred practice pattern (PPP)/Primary Open Angle Glaucoma. Glaucoma panel, Hoskins Center for Duality Eye Care, 2010.

Artur Liobex, Xavier Gasal, Arcadi Gual (2003). Understanding Trabecular Meshwork Physiology: A key to the control of intraocular pressure? American Physiological Society. Vol. 18 no 205-209 Dol: 10. 1152/nips 01443.

Ascher, KW (1942). Aqueous Veins: Physiologic Importance of Visible Elimination of Intraocular Fluid. AMJ Ophthalmol. 25:1174.

CSN Team.