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 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. 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).

TABLE OF CONTENTS

Title page – – – – – – – – – – i
Approval page – – – – – – – – – ii
Certification- – – – – – – – – – iii
Dedication – – – – – – – – – – iv
Acknowledgement – – – – – – – – v
Table of contents- – – – – – – – – – vii
Abstract – – – – – – – – – – – xi
List of Figures – – – – – – – – – xii
CHAPTER ONE
INTRODUCTION – – – – – – – – – 1
1.0.1 A generalized mathematical model for the aqueous
humour flow driven by temperature gradient – – – 1
1.0.2 Fluid flow through a mesh channel in the human eye – – 6
1.1 Motivation for these models- – – – – – – 11
1.1.1 A generalized mathematical model for the aqueous
humour flow driven by temperature gradient – – – 11
1.1.2 Fluid flow through a mesh channel in the human eye – – 12
1.2 Objectives of the research or study – – – – – 14
1.3 Anatomy and physiology of the eye – – – – – 14
1.3.1 The human eye – – – – – – – 14
1.3.1.1Structure of the eye – – – – – – 17
1.3.1.2 Cornea – – – – – – – – 19
1.3.1.2.1 Layers of the cornea – – – – – 20
1.3.1.3 Sclera – – – — – – – – – 21
1.3.1.4 Iris – – – – – – – – 22
1.3.1.5 Pupil – – – – – – – – 25
1.3.1.6 Lens – – – – – – – – 28
1.3.2 Aqueous humour flow in the anterior chamber – – – 30
1.3.2.1 Functions of Aqueous humour – – – – – 31
1.3.2.2 The physical mechanisms responsible for causing flow in the anterior chamber of the human eye – – 32
1.3.2.3 Importance of flow in the anterior chamber of the eye 32
1.3.3 Mechanism of aqueous humour flow in the anterior chamber 33
1.3.3.1The aqueous humour outflow pathway – – – 33
1.3.3.1.1 The conventional outflow route (Trabecular) and related
Structures – – – – – – – – 33
1.3.3.1.1.1 Uveal and corneoscleral meshwork – – – – 34
1.3.3.1.1.2 The Juxtacanalicular connective tissue (JCT) – 35
1.3.3.1.2 Schlemm’s canal and inner wall endothelia cell – 35
1.3.3.1.3 Collector channels and aqueous veins – – – 36
1.3.3.1.4 Aqueous pump mechanism – – – – – 37
1.3.3.2 Unconventional outflow route – – – – – 37
1.3.4 Aqueous humour outflow resistance – – – – 38
1.3.4.1 Resistance in the trabecular meshwork – – – 39
1.3.4.1.1 Aqueous humour resistance within the uveal and corneoscleral meshwork – – – – – 39
1.3.4.1.2 Aqueous humour resistance within the JCT – – 40
1.3.5 Primary open angle glaucoma as cause of vision loss – – 40
CHAPTER TWO
LITERATURE REVIEW – – — – – – – 43
CHAPTER THREE
MODEL FORMULATION AND SOLUTION – – – – 57
3.0 The models – – – – – – – – – – 57
3.1 A Model for Thermally driven flow in the anterior chamber of the eye – – – – – – – – – – 58
3.1.1 Schematic Diagram of the Anterior Chamber of the Eye – – 58
3.1.2 Reasons for changing the model – – – – – – 58
3.1.3 The modified model – – – – – – – 59
3.1.4 Non-dimensionalization of the resulting equations- – 62
3.1.5 Solution of the model – – – – – – – – 65
3.2 Mathematical formulation of the model on the fluid flow through a mesh channel in the human eye – – – – – – 70
3.2.1 Preambles and the Model Equations – – – – – 70
3.2.2 Solution of the Model Equations in 3.6 – – – – – 75

CHAPTER ONE

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.

1.0.1 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.

The eye as an organ does a variety of functions other than sense of sight. It also tells to some extent some disease conditions. Such diseases produce some changes that are observable in the eye (Smith, 2008). Human eye function is more sophisticated than any man-made optical device (Valdivia, 2009). The eyes are often called the windows to the soul; we communicate and express emotion with our eyes in ways that defy words. When we are shocked or surprised, our eyes open wide. If we are confused, our eyes squint; angry, they appear to narrow; excited, they brighten (Valdivia, 2009).

The eyes are responsible for four-fifth of all the information sent and processed in the Brain. Also eighty percent of learning occurs through the visual pathways (Smith, 2008).

Vision is considered to be the most desirable of all human senses. Without it, a person’s relationship to the surrounding world and the ability to interact with the environment is considered seriously diminished. The visual system also helps to maintain balance and posture in human beings (Wikipedia; free encyclopedia).

In humans, sight mechanisms are also complex, its complexity, in addition to that of the eye, makes its study complex as well. This study has been a major challenge to researches in this field for some time now. Though a great deal has been achieved, a lot still need to be done. This includes understanding the relationship between the sight mechanisms and the fluid in the eye.

The human eye is made up of different fluids. These include the aqueous humour, the vitreous humour and the tear film. The aqueous humour lies in the anterior and posterior chambers of the globe whereas the vitreous humour occupies the posterior segment of the globe (fig.1). The anterior chamber lies between the iris and the cornea and the posterior chamber is the region behind the Iris and anterior to the hyaloid membrane. Thus, understanding the complex mechanisms that regulate aqueous humour circulation is essential for management/treatment of some eye diseases (Adam et al, 2012). Of course, the secretion of aqueous humour and regulation of its outflow are physiological important processes for the normal function of the eye (Jeffrey et al 2002). We seek to know whether significant thermally driven natural convection exists within the anterior chamber when the ambient temperature is higher than the core body temperature.

Generally, the flow in the anterior chamber is thought of to be driven by temperature gradient. Hence, the general idea of anterior chamber convection appears to have been adapted although attempts are still being made to actually understand the driving force for the fluid flow in the eye. Other researchers believed that flow in the anterior chamber appears to take place in a single convection cell, rising (that is, opposing gravity) near to the back of the chamber and falling towards the front. It is believed that there is little or no lateral motion of the fluid (Canning et al 2002).

Even though the thickness of the cornea is assumed to insulate the content of the anterior chamber (fluid) from fluctuations, in areas where the ambient (room) temperature is in excess of the body temperature 370C, wefind that this insulation action may not be true and thus the ambient (room) temperature may not be constant. This is mostly the case as found in the desert and equatorial regions of the world (for example in Africa, Nigeria and Niger in Particular) where most of the parts has room or ambient temperature greater than 400C(for example, recorded temperature extremes of 56.70C in Death valley California, USA (1913).55.00C in Kebili Tunisia (1931) and 46.40C in Yola Nigeria (2010)) (Wikipedia, the free encyclopedia). yet there is aqueous flow. Thus, the modeled equations by Canning et al (2002). Gabriel & Alisteir (2002). Brain & Fitt (2003). Jeffrey and Barocas (2002) and Gonzalez and Fitt (2006) Adam et al (2012).Zuhaila (2013). Crowder & Ervin (2013). may not appropriately take care of this peculiar situation. This is what inspired this work. As a result, we propose a modification of the temperature gradient for the thermally-driving flow in the anterior chamber of the eye.

The major change in the existing model is in the equation and this is to take care of the situation where the ambient (room) temperature is more than the body temperature which is 370C.

In human eye, heat gain occurs through conduction, perfusion, metabolism, blinking, tear flow, evaporation, and convection, but heat loss occurs only through conduction, evaporation, convection and radiation. More factors are involved in heating eye components than cooling. Hence, the human eye is more vulnerable when it is exposed to high temperatures (high ambient temperatures, hyperthermia treatment, laser surgery etc) than low temperatures (low ambient temperatures, cryosurgery treatment etc). At the cornea, heat loss from the eye occurs through convection, radiation, and tear evaporation. Hence temperature increases from outer surface of cornea towards eye core when ambient temperature is less than 370^oC and vice versa. Due to convective heat transport of the blood vessels, the blood picks up energy from hot areas and deposits this at cooler areas or vice versa. The temperature inside the human body depends on the degree of temperature, duration of exposure and the environment conditions which
cause heat gain/loss from tissues (Gokul et al 2013).

Thus we develop a model that takes care of the case where normal room or ambient temperature is more than the body temperature which is 370C which is a more general case.

1.0.2 Fluid Flow through a Mesh Channel in the Human Eye

The trabecular meshwork is a tissue located in the anterior chamber angle (the angle structure include: the outermost part of the iris, the front of the ciliary body, the trabecular meshwork and the canal of Schlemm) of the eye,(Artur et al, 2003; Satish, 2003; Fitt, 2010 and Adam et al,2012). The trabecular meshwork is a wedge shaped lattice, spongy tissue composed of 12 – 30 trabecular layers posteriorly and 3 – 5 layers anteriorly at its apex near the cornea (Patrick, 2006 and Mark, 2006). It is one of the Fig. 1.1: The anterior chamber of the eye Adapted from canning et al (2002) outflow pathways for the evacuation of aqueous humour from the eye. (Artur (2003). Michael et al, (2006). Paul( 2008)).

Fig.1.2 Schematic diagram of outflow system of human eye (adapted from Satish, 2003).

Fig 1.3: Schematic diagram of trabecular meshwork (adapted Zahaila (2013)).

The aqueous humour is a colourless intraocular fluid that is secreted by the ciliary epithelium. It flows in the posterior chamber bathing the lens, through the iris, in the anterior chamber providing a transparent medium, nutrients, means for metabolic waste removal to the avascular tissues, and pressuring the eye and then drains into the episcleral venous system through the trabecular meshwork and the canal of Schlemm.

(Artur et al,2003; Patrick , 2006; Satish, 2003; Adam et al, 2012 and Ram et al, 2014).

As such, disrupting the delicate balance between aqueous humour inflow and outflow may lead to elevation of intraocular pressure (IOP). a known risk factor for primary open angle glaucoma (POAG) (Michael, 1999; Chimdi &Umeh, 2000 and Patrick, 2006).

We find that particulates substances of different sizes, shapes and traits circulate inside the anterior chamber. These particulates such as the red blood cells, white blood cells and other particulates detachment from the eye eventually flow out of the anterior chamber by squeezing themselves through the trabecular meshwork (channel). We shall note that this mesh channel can be reduced in diameter or otherwise depending on the size of these particulates substances. Thus, if we consider this as a non uniform channel whose whole diameter depends on the nature of the ciliary muscles and its own contractile and volume – regulatory properties, we can see that the particulates can obstruct the channel so that we can consider this as flow through a cylindrical channel which is easily described by the Naiver – stokes equations. Again, because the size of the particles are relatively large compared to the diameter of the trabecular meshwork, we can consider the flow of this fluid and the particulates as a bi – layer flow described also by the Naiver – Stokes equations. Hence the action of the ciliary muscles (force) on the trabecular meshwork can be likened to fat deposit in the flow channel regarded as the stenosis. Here we consider multiple stenoses with the effects of slip condition on the flow of aqueous humour in the mesh channel. When this ciliary muscles contract, it is likened to clearance of the stenosis because this forces the ciliary muscles to mechanically stretch the trabecular meshwork thereby increasing the thorough flow of aqueous humour (Canning et al, 2002). If it relaxes, it do contract the meshwork by reducing the diameter and so making it difficult for thorough flow of the particles. The presence of multiple stenoses or constrictions in the mesh channel can lead to increased resistance to outflow with undesirable consequences. This can create an imbalance in the production and drainage of aqueous humour. The intraocular pressure within the eye builds up which might lead to primary open angle glaucoma.

Primary open angle glaucoma (POAG) is the second leading cause of blindness worldwide after cataracts (Fitt, 2010 and Zuhaila, 2013). It is also known as chronic glaucoma or “the silent thief of sight” because of the lack of early symptoms. Most patients with POAG are not aware that they have the disease until significant vision loss occurred.

Interestingly, the human eye appear to be particularly vulnerable to POAG when compared to eyes of non – human species. The reasons for this high susceptibility remains unknown (Patrick, 2006). Also the definite locus for the primary resistance moiety within the normal human eye as well as the added resistance in eyes with POAG is not yet known (Patrick, 2006; Adam et al,2012 and Ezell Research Symposium, 2013). Unfortunately, this lack of fundamental knowledge has prevented the development of an effective anti – glaucoma therapy that could be used to selectively target and weaken the primary resistive moiety to allow for decreased outflow resistance in the trabecular meshwork.

The aim of this study is to investigate the mechanism in the trabecular meshwork responsible for the generation of aqueous humour resistance in the human eye with the hope that specific outflow resistance profile might be identified as this will help in understanding the mechanisms involved in regulating aqueous humour outflow resistance in glaucomatous human eyes.

A mathematical model is presented for the flow of aqueous humour through the trabecular meshwork with multiple stenoses in order to predict changes in intraocular pressure (IOP). The governing equations have been adapted from Gurju and Radhakrishnamacharya (2013) and Gurju et al (2014).

Table 1: Standard Parameter Values for an Adult Human Eye.

Physical Quantity Typical Values

Radius of anterior chamber ı (m) 5.5×10-3

Total width of anterior chamberı(m) 11×10-3

Coefficient of linear expansion of aqueous humour ∝ (k) 3.0×10-4

Gravitational acceleration ı (m/s2) 2.75×10-3

Height of anterior chamber ıı (m) 1.0×10-3

Dynamic viscosity m of aqueous humour (Pa s) 1.0×103

Density Po of aqueous humour (Kg/m3) 1.0×103

Adapted from Fitt & Gonzalez (2006)

1.1 MOTIVATION FOR THESE MODELS

1.1.1 A Generalized Mathematical Model For The Aqueous Humour Flow Driven By Temperature Gradient.

We saw that the models already built on aqueous flow in the eye (Canning et al 2002; Jeffery & Borocas, 2002; Satish, 2003;Gabriela & Alistair, 2002; Braun & Fitt, 2003; Jeffrey & Gonzalez, 2004; Gonzalez & Fitt, 2006; Zuhaila & Fitt, 2008; Adam et al 2012; Zuhaila, 2013 andCrowder & Ervin, 2013) were based on temperature gradient where the inner body temperature was assumed to be higher than the ambient temperature. It is this temperature gradient that caused the outflow of the aqueous through the iris to the outer cornea.

However, through research, we discovered that the normal human body temperature is about 370C and that the consideration of the authors were based on external temperature being less than this 370C, in particular in Europe where temperatures are far less than this body temperature most of the time. In the light of this we see that this model may not have promptly taken care of situations where the external temperature is greater than 370C or even close to 370C. Our question then was, whether there is still aqueous flow in people’s eyes in such regions or places where such temperatures does not subsist. A close observation shows that there is still aqueous flow in people of such regions like in Africa, Malaysia and other Asian or temperate countries of the world. This then means that the existing aqueous flow models may not have promptly represented this very case. Hence, our desire to remodel aqueous flow in human eyes taking into account the various temperature differences in different regions of the world where people live.

1.1.2 Fluid Flow through A Mesh Channel in the Human Eye

Available statistics from the Federal Ministry of Health on the 2014 World Sight Day (9/10/2014) as published in the editorial of the Sun Newspaper of 8th November, 2014 show that Nigeria is one of the countries with the highest blind people. Over 1 million Nigerians are blind with over 3 million being visually impaired. Also 42 out of every 100 adults above the age of 40 are visually impaired. 2 out of every 3 blind Nigerians lost their sight to preventable causes. In addition, Nigerians account for 1 in every 5 blind Africans. Globally, over 45 million people are blind while 135 million have severe visual impairment.

Glaucoma is the second (the first is cataracts) leading cause of blindness globally as well as in most regions including Nigeria. It generally results from an outflow resistance of aqueous humour. When the drainage channel becomes clogged, aqueous fluid cannot leave the eye as fast as it is produced, causing the fluid to accumulate.

This accumulated fluid leads to an increase in intraocular pressure (IOP). As a consequence, the retina ganglion cells progressively suffer irreversible damages that lead to visual field reduction and eventually to blindness, (Artur 2012). This condition is more worrisome as glaucoma can only be stemmed; it cannot be cured (Chimdi and Umeh 2002). Glaucoma presents an even greater public health challenge than cataracts because the blindness it causes is irreversible (Nosiri et al 2009). In fact, vision loss from glaucoma is silent, slow, progressive, irreversible but treatable (Robert, 2008).

However, a conclusive determination of where in the outflow pathways this elevated outflow resistance is generated has been elusive. Also, the locus of aqueous outflow resistance in the normal eye has not been equivocally determined (2013 Ezell Research Symposium). Again, the fluid dynamics of the aqueous humour and the role of the outflow channels is not fully understood (Adam et al 2012). This fact is also evidenced by the great number of drugs used for the treatment of primary open angle glaucoma. The drugs most commonly used either decrease the production of aqueous humour in the ciliary body or increase the uveoscleral (unconventional) outflow.Drugs acting directly on the trabecular meshwork have not yet been developed (Artur et al 2003, Patrick 2006,Zuhaila 2013). However, due to the quantitative significance of the trabecular meshwork in the drainage of aqueous humour, there is need for a tissue
specific anti – glaucoma therapy.

Consequently, we model the fluid flow in the trabecular meshwork by considering the slip condition and multiple constrictions or stenoses in the graded flow channel and its influence on primary open angle glaucoma (P O A G).

1.2 OBJECTIVES OF THE STUDY

This study is undertaken on generalized mathematical modeling of aqueous humour flow in the anterior chamber and through a mesh channel in the human eye. The objectives of the study are to:

1. formulate a mathematical model that describes the fluid flow in the human eye when ambient temperature is higher than core body temperature,

2. investigate the dynamics of the model and compare with that of existing models,

3. describe the pressure and flow velocity in a healthy/glaucomatous eye,

4. describe the velocity streamlines and pressure contours in healthy/glaucomatous eye and

5. analyze the effect of resistance of the drainage system on the flow distribution and intraocular pressure (IOP).

1.3 Anatomy and Physiology of the Eye

1.3.1 The Human Eye

The eye is a special ball- like structure situated at the face of human beings. As a sense organ, the eye is the optic window through which man visualizes his environment and what happens around him. Human memory and mental process rely heavily on sight (Encyclopedia of Nursing and Allied Health). There are more neurons in the nervous system dedicated to vision than any other of the five senses indicating how important vision is.The human eye is not only the organ with the most intricate anatomy, but also the most delicate. It has complicated structures and sophisticated functions (Brubakar, 1982).

The efficiency and completeness of our eyes and brain is unparallel in comparison with any piece of apparatus or instrumentation ever invented. The eye can automatically focus objects as far away as infinity and as near as 10cm. It has a wide field of view of about 160° in the horizontal and about 120° in the vertical. It can smoothly track fast moving objects. It can perceive colors in visual wavelengths. It can efficiently process and analyze images of high resolution. These functions are performed by a normal healthy human eye. The degrees of functionality may differ
among individuals. (Jayoung, 2007).

The human eye can also be considered as a biological system. Tear films, cornea, iris, crystalline lens, anterior and vitreous humor and retina are all incorporated into the eye ball. Each is well structured with living cells and is well coordinated to make objects visible. The eye grows with age and loses or diminishes in functionality for various health reasons. All of the characteristics differ among individuals. The recent developments in cornea surgery and the use of intraocular lens add more variation to the already existing biological divergence.

The human eye can be considered a Neuro sensory system which begins with the transmitting of light energy into changes of membrane potential of the photoreceptors on the retina. The neural images made by the architecture of the photoreceptors are delivered from the eye to the brain through the optic nerve. Since the photoreceptors outnumber the fibers inside the eye, there is a significant degree of image compression between them. Various combinations of the fibers inside the optic nerve with the photoreceptors explain visual perceptions such as color and motion and the visually controlled behaviors such as accommodation and eye movements.

The eyes are responsible for 5-4 (four-fifth) of information sent and processed in the Brain. Also, 80% of learning occurs through the visual pathways (Herbert (2008)).

The eye as an organ does Variety of functions other than sense of sight. It also tells to some extent some disease conditions that produce some observable changes in the eye (Umit, 2003).

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.

In human, sight mechanisms are also complex. Its complexity, in addition to that of the eye makes its study complex as well. This study has been a major challenge to researchers in this field for some time now. Though a great deal has been achieved, a lot still has to be done.

1.3.1.1 Structure of the Eye

The eye is the sense organ for seeing. The human eye is composed of the eyeball and some accessory structures that serve to protect, moisten, lubricate, and move the eyeball.

The eyeball or bulb fits into and is protected by the bones of the orbit and by a thick layer of fascia and fat in which it is embedded. The anterior surface, not surrounded by bone, is protected by the eyelids which are capable of instantaneous closure to exclude foreign objects or too much light or heat.

The upper and lower eyelids are composed of loose connective tissue covered by a thin skin and supported posteriorly by the tarsal plates of dense connective tissue. These plates are provided with complex sebaceous glands called tarsal glands. The skin turns inward at the edges of the eyelids, lining them with a mucous membrane – the conjunctiva. This conjunctiva, at the base of the lids, is reflected back over the anterior surface of the eyeball as a transparent layer, consisting only of stratified epithelium.

Along the edges of the eyelids are the ciliary glands. Their secretions moisten the eyelids and may keep them from adhering to each other. The lacrimal apparatus consists of lacrimal glands, ducts, sacs and nasolacrimal ducts. The lacrimal gland lies hidden from view, in the upper lateral side of the orbit. It produces secretions that move over the anterior surface of the eyeball and drain into a tiny hole or punctum at the medial end of each eyelid. Each punctum leads into a lacrimal duct, which joins it to form the lacrimal sac at the medial side of the orbit. The lacrimal Sac, in turn empties through the nasolacrimal duct into the nasal cavity.

The eyeball is a sphere about one inch in diameter (Crouch, 1982). Its walls are composed of three layers, the outer-most of which is leathery and relatively thick, the Sclera which forms anteriorly a transparent rounded bulge, the cornea. The middle layer, the pigmented Choroid Coat, contains blood vessels for and reduces reflection of the light within the eyeball. Anteriorly at the edge of the cornea, the Choroid Coat thickens to form a ciliary body, which contains smooth muscle, fibers.

Around the anterior edge of the ciliary body is a thin muscular diaphragm, the iris with a hole in the center called the pupil. The middle layer is also made up of the transparent, crystalline lens, held directly behind the pupil by a suspensory ligament that extends inward from the ciliary body. The remaining and inner most coat of the eyeball is the retina, which contains the receptors for light and colour, the rods and cones. The retina is continuous posteriorly with the optic nerve. It diminishes in thickness and in complexity. Posterior part of the retina is a depression in which the retina is exceedingly thin and where the light and colour receptor alone, called cone cells are present in great numbers about 146000 per mm2 (Wilson, 1979). This area is known as the fovea centralis and is the point of greatest visual acuity. Just to the nasal side of the fovea is the place where the optic nerve leaves the eye, the optic disc. Since there are no light receptors on the optic disc, it is often called the blind
spot.

1.3.1.2 Cornea

The cornea is the transparent, dome-shaped window covering the front of the eye. It is a powerful refracting surface, providing 2/3 of the eye’s focusing power. Like the crystal on a watch, it gives us a clear window to look through. The cornea is responsible for focusing light rays to the back of the eye. Cornea is 78% water. (Umit, 2003)

Because there are no blood vessels in the cornea, it is normally clear and has a shiny surface. The cornea is extremely sensitive – there are more nerve endings in the cornea than anywhere else in the body. The reactions of the cornea are quite important in disease processes. It is vascular and therefore reacts differently from those tissues that have a blood supply. Bowman’s layer has little resistance to any pathologic process because of that it is easily destroyed and never generates. Descemet’s membrane, on the other hand, is highly resistant and elastic and may remain in the form of a bulging balloon-like structure, called a “descemetocele,” after all the other layers of the cornea are destroyed (Umit, 2003)

1.3.1.2.1 The Layers of the Cornea

The adult cornea is only about 0.5 mm thick and is comprised of 5 layers: epithelium, Bowman’s membrane, stroma, Descemet’s membrane and the endothelium.

1. The epithelium is layer of cells that cover the surface of the cornea. The epithelium is about 10% of the total thickness of the cornea. It is only about 5-6 cell layers thick., about 50 μ.m (Davson, 1990) and quickly regenerates when the cornea is injured. If the injury penetrates more deeply into the cornea, it may leave a scar. Scars leave opaque areas, causing the corneal to lose its clarity and luster.

2. Bowman’s membrane lies just beneath the epithelium. Because this layer is very tough and difficult to penetrate, it protects the cornea from injury. Bowman’s layer is a sheet of transparent collagen 12 μm thick.

3. The corneal stroma represents certainly one of the most typical examples of highly specialized connective tissue. Its functional efficiency is transparency. The stroma is the thickness layer and lies just beneath Bowmans, it represents some 90 percent of the corneal thickness. The stroma consists normally of about 7 percent of water (values of up to 85 percent are given in the literature). It is composed of densely packed collagen fibrils that run parallel to each other. This special organization of the collagen fibrils gives the cornea its clarity.

4. Descemet’s membrane lies between the stroma and the endothelium. The endothelium is just underneath descemet’s and is only one cell layer thick. This layer pumps water from the cornea, keeping it clear. If damaged or disease, theses cells will not regenerate. Descemet’s membrane is about 10μm.

5. The corneal endothelium is composed of a single layer of cubiodal cells which function to keep the cornea dehydrated.

6. Tiny vessels at the outmost edge of the cornea provide nourishment, along with the aqueous and tear film.

7. Functionally, the most important elements of the cornea are the substantial propria (stoma) and its two limiting cellular membranes, the epithelium and endothelium; damage to the cells of the two membranes, whether mechanical or by interference with metabolism, causes the stroma to lose its transparency as a result, apparently, of the imbibitions of water.

1.3.1.3 The Sclera

The sclera is a thick, opaque white tissue that covers 95% of the surface area of the eye. It is approximately 530 microns (μm) in thickness at the timbus, thining to about 390 μm near the equator of the globe and then thickening to near 1mm (0.04 in) at the optic nerve. At the posterior aspect of the eye, sclera forms a netlike structure or “lamina cribroga” through which the optic nerve passes. The sclera also serves as the anchor tissue for the extraocular muscles.

The cornea and sclera together form the outer-most covering of the eye and withstand both the internal and external force of the eye to maintain the shape of the eyeball and to protect the contents from mechanical injury.

In children, the sclera is thinner and more translucent, allowing the underlying tissue to show through and giving it a bluish cast. As we age, the sclera tends to become more yellow. The sclera becomes transparent when dried. This is assumed to be the result of the concentration of the ground substance so that its refractive index becomes close to that of the collagen. As this happens when the tissue is nearly dry, it acquires a uniform refractive index (Umit(2003)).

The differences between the compositions of the various types of connective tissues, for instance cornea and sclera are more often quantitative than qualitative. The water content of cornea is somewhat higher than that of sclera. The cornea and sclera together form the tough tunic of the eye, which withstands the intra-ocular pressure from within
and protects the contents from mechanical injury from without.

1.3.1.4 The Iris

The iris is a protected internal organ of the eye, located behind the cornea and the aqueous humor, but in front of the lens. A visible property of the iris and the fingerprint is the random Morphogenesis of their Minutiae. The phenotypic expression even of two irises with the same genetic genotype (as in identical twins, or the pair possessed by one individual) have uncorrelated minutiae. (Ales et al, 2000).

This is the part of eye that gives the eye its color (i.e blue, green, brown) (Umit, 2003). The opening in the center of the iris is the pupil. The iris act like a camera shutter and controls the amount of light that enters the eye. It behaves as a diaphragm, modifying the amount of light entering the eye.

The tissue of the iris consists of two main layers, or laminae, separated by a much less dense zone (the cleft of sucks). The posterior lamina contains the muscles of the iris, and is covered posteriorly by two layers of densely pigmented cells, the innermost (nearest the aqueous humour) being the posterior epithelium of the iris, which is continuous with the inner layer of the ciliary epithelium (Umit, 2003).

The most important function of the iris is in controlling the size of the pupil.

Illumination, which enters the pupil and falls on the retina of the eye, is controlled by muscles of the iris. They regulate the size of the pupil and this is what permits the iris to control the amount of light entering the pupil. The change in the size results from involuntary reflexes and is not under conscious control. The tissue of the iris is soft and loosely woven and called stroma.

The layers of the iris have both ectodermal and mesodermal embryological origin. The visible one is the anterior layer, which bears the gaily – coloured relief and it is very lightly pigmented due to genetically determined density of Melanin pigment granules. The invisible one is the posterior layer, which is very darkly pigmented contrary to the anterior layer. The surface of this layer is finely radiantly and concentrically furrowed with dark brown colour. Muscles and the vascularised stroma are found between these layers from back to front. Pigment frill is the boundary between the pupils and the human iris and is a visible section of the posterior layer and looks like a curling edge of the pupil. The whole anterior layer consists of the papillary area and the ciliary area and their boundary is called collavette. The ciliary area is divided into the inner area which is relatively smooth and bears radial furrows, the middle area, heavily furrowed in all directions and with pigment piles on the ridges, and the outer marginal area bearing numerous periphery crypts.

Among the pigment related features are the crypts and the pigment spots. The crypts are the areas when the iris is relatively thin. They have very dark colour due to dark colour of the posterior layer. They appear near the collavette, or on the periphery of the iris. They look like sharply demarcated excavations. The pigment spots are random concentrations of pigment cells in the visible surface of the iris and generally appear in the ciliary area. They are known as moles and freckles with nearly black colour (Ales et al2000).

Features controlling the size of the pupil are radial and concentric furrows.

They are called contraction furrows and control the size of the pupil. Extending radially, in relation to the center of the pupil are radial furrows that are increased in the anterior layer of the iris from which loose tissue may bulge outward and this is what permits iris to change the size of the pupil (Ales et al2000). The concentric furrows are generally circular and concentric with the pupil. They typically appear in the ciliary area, near the periphery of the iris and permit to bulge the loose tissue outward in different direction than the radial furrows. The collarete is a sinuous line which forms an elevated ridge running parallel with the margin of the pupil. The collarette is the thickest part of the human iris.

1.3.1.5 The Pupil

The pupil is the circular aperture of the iris, a contractile diaphragm which helps to regulate the amount of light entering the eye. It aids to increase the depth of focus for near vision (Ravindran, 2001). When maximally dilated, the diameter of the human pupil may be less than lmm; when maximally contracted, it may be more than 9mm. The fibres of the sphincter and dilator muscles of the iris are intimately connected with the iris stroma and areresponsible for the constriction of the pupil even after sphincterotomy or sector iridectomy. Normally, the pupil is placed slightly
nasally and inferiorly. The normal diameter of thepupil is about 2mm to 4mm. The size of the pupil varies with age. The pupilary size and reactivityare a function of parasympathetic and sympathetic tone (Ravindran,2001).

A number of physical and physiological factors also affect the size of the normal pupil including light intensity, light adaptation, refractive status, emotional factors and age. The pupil tend to be larger in the myopic eye and also in youth and adolescence but then become steadily smaller until about age 60.

The pupil during sleep is contracted rather than dilated. Two mechanisms are responsible for the miosis of the pupil during sleep: diminution of tonus of the sympathetically innervated dilator muscle; and diminution of inhibitory impulses from the contex to the constrictor centre. Loss of this cortical inhibition during sleep allows the sub cortical oculomotor centre to act freely.

About one fifth of the normal population has a difference of 0.4 mm in papillary diameter between the two eyes. While the subject is alert, the pupil dilates. But when tired, the pupils gradually become smaller.

The Anatomical path ways controlling the papillary reaction is given below: When light is shown in one eye, there is ipsilateral constriction of the pupil (direct light response). At the same time, there is constriction of the contralateral pupil(consensual light response). The neural pathway for this reflex from a three neuron are: the afferent neurons from retinal ganglion cells to the pretectal area; an intercalated neuron from the pretectal complex to the parasympathetic nucleus; parasympathetic outflow with the oculomotor nerve to the ciliary ganglion and from there to pupillary sphincter.

The afferent limb of the pupillary light reflex begins in the retina with axons from retinal ganglion cells. The fibres destined for mid brain connections separate from the optic tract and enter the midbrain via the brachium of the superior colliculus to reach the pretectal region. The intercalated neurons from the pretectal nuclei hemidecussate through the posterior commissure and synapse in the Edinger-Westphal nucleus. As a result of this mid brain decussation the Edingerwestphal nucleus receives equal drive from both optic nerves. The efferent fibres from the Edinger-westphal are carried in the superficial layer of the oculomotor nerve and eventually ends in its inferior division. It then passes through the superior orbital fissure and synapses in the ciliary ganglion.

Post ganglion fibres which enter the lobe near the optic nerve to supply the ciliary muscles are composed of smooth muscle fibres and have acetylcholine receptors. There is a disparity in the number of cells which innervate the iris-sphincter and those which innervate the ciliary muscle for every axon which leaves the ciliary ganglion to supply the light responses, thirty axons serve the near response (Ravindran, 2001). The latent period of light reaction of the pupil is 0.2 seconds in the bright light and up to 0.5 seconds in dim light.

Dilatation of pupil: Dilatation of the pupil is mediated mainly through the sympathetic nervous system producing contraction of the dilator muscle fibres of the iris. The efferent pathway is more complicated than that of light reflex. Two neural mechanisms are involved one active and the other passive. The active component results from contraction of the radially arranged fibres of the dilator muscle via the cervical sympathetic pathway. The passive component results from relaxation of sphincter muscles caused by inhibition of visceral oculomotor nuclei. In terms of the sympathetic pathway, the dilator fibres pass from the sympathetic centres of the hypothalamus downwards with partial decussation in the midbrain. It then passes through the medulla oblongata into the lateral columns of the cord. The descending fibres, considered to be the first order preganglionic neuron synapses in the intermediolateral portion of the spiral cord known as the cilio-spinal centre of budge.

Next, second order pregangloinic fibres exit the cord primary with the first ventral thoracic root. The fibres then enter the para-vertebral sympathetic chain which is closely related to the pleura of the apex of thelung. Then they ascend up without synapsing through the inferior and middle cervical ganglion to terminate in the superior cervical
ganglion.

1.3.1.6 Lens

The crystalline lens is located just behind the iris. The purpose is to focus light onto the retina (Umit 2003)). The lens in the human eye is avascular even at birth and has no innervation. Molecular make up is unique and it has 2/3 water and 1/3 protein. The percentage of water decreases with aging. It has high Refractive index (RI) because of high protein content and the high RI helps to focus light. Lens does not shed cells and so increases in weight throughout life (Ravindran, 2001).The lens is encased in a capsular like bag and suspended within the -eye by tiny “guy wires” called zonules from ciliary body which are inserted into the equatorial zone and gives rise to epithelial cells that form long fibres reaching anterior posterior poles of lens. With further cell division, the lens fibres are pushed to centre and from necleus. Other cells in the outer region form the cortex surrounded by acellular capsule.

In young people, the lens changes shape to adjust for close or distance vision. This is called accommodation, but with age the lens gradually hardens, diminishing the ability to accommodate.

Accommodation is a procedure that changes the focusing distance of the lens. The lens thickens, increasing its ability to focus at near objects. A young person’s ability – to accommodate allows him or her to see clearly far away and up close. At about the age of 40, the lens becomes less flexible and accommodation is gradually lost, making close range work increasingly difficult. This is known as presbyopia (Umit, 2003).

As noted earlier, the lens continue to grow throughout life. The thickness of human lens increases by 0.02 mm each year. Antero-posterior diameter of lens is about 3.5 to 5 mm and equatorial diameter ranges from 6.5- 9 mm. The anterior surface of the lens is more curved than posterior surface. The radius of curvature anteriorly is 8 – 14mm and radius of curvature posteriorly is 4.5 to 7.5 mm. the refractive power of lens depends on the curvature of anterior and posterior surface and RI of lens material. The average RI of lens is 1.420 (Ravindran 2001).