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
8
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
theanterior 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
9
1.3.4 Aqueoushumour outflow resistance – – – – 38
1.3.4.1 Resistance in the trabecular meshwork – – – 39
1.3.4.1.1 Aqueous humourresistance 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
3.0The 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
3.2Mathematical 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
10
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 practitionersunderstand the mechanism of sight more and more;
and then find ways to improve the condition of human eye.
15
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
16
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 hyaloids
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
17
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 Califonia, 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 Canninget 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
18
evaporation. Hence temperature increases from outer surface of cornea towards eye
core when ambient temperature is less than 370Cand 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.
19
1.0.2 Fluid Flow through aMesh 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 Adamet 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)
20
outflow pathways for the evacuation of aqueous humour from the eye. (Artur (2003).
Michael et al, (2006). Paul( 2008)).
Fig.1.2Schematic diagram of outflow system of human eye
(adapted from Satish, 2003).
21
Fig 1.3: Scematic diagram of trabecular meshwork
(adaptedZahaila (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; Adamet 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
22
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 trabeculur meshwork thereby increasing the thorough flow of
23
aqueous humour (Canninget 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 resisitance
moiety within the normal human eye as well as the added resistance in eyes with
POAG is not yet known (Patrick, 2006; Adamet 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.
24
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)
25
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 (Canninget 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 temperaturegradient
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
26
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
27
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). Infact, 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 (Adamet 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).
28
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 opticwindow 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
29
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.
30
The human eye can be considered a neurosensory 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
31
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
32
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 Sclerawhich 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 posterioly 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
33
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)
34
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.
· 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.
· 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.
· 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.
· 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
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layer pumps water from the cornea, keeping it clear. If damaged or disease, theses
cells will not regenerate. Descemet’s membrane is about 10μm.
· The corneal endothelium is composed of a single layer of cubiodal cells which
function to keep the cornea dehydrated.
· Tiny vessels at the outmost edge of the cornea provide nourishment, along with the
aqueous and tear film.
· 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.
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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
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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 importantfunction 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
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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.
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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).
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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.
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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 commssure 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 irissphincter 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
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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 occulomotor 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 paravertebral 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 capsular43
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 closerange
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).
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