A van Zyl Thesis

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THE EFFECTS OF RIBOFLAVIN UV CROSSLINKING ON KERATOMETRIC BEHAVIOUR IN

KERATOCONUS: A SIX-MONTH FOLLOW-UP STUDY

by

AME van Zyl

Thesis

Submitted in fulfilment of the requirements of the degree

Magister Philosophiae

in

Optometry

in the

FACULTY OF HEALTH SCIENCES

at the

UNIVERSITY OF JOHANNESBURG

SUPERVISOR: PROFESSOR WDH GILLAN

2015

i

ABSTRACT

Ultraviolet riboflavin crosslinking (CXL) for keratoconus is a relatively new procedure done

by ophthalmologists. It seems to be the only form of treatment available at present to stop

the progression of keratoconus. As the progression of keratoconus results in a decrease of

vision as well as the inability of vision to be adequately restored with spectacles or soft

contact lenses, it is important to do the procedure as early as possible. Early CXL treatment

seems to preserve the patient’s vision at a better level, it should only be done if progressive

keratoconus has been established and if the cornea is not thinner than 400 µm. It has been

found that keratometric measurements (K-readings) flatten or stabilise, or that the cornea

tends to take on a more symmetric form after CXL. In a few rare cases a steepening of K-

readings might be found. The aim of this study was to analyse the change in K-readings

(which are related to the shape or topography) of the cornea following CXL of keratoconic

corneas over a six-month period.

Participants undergoing CXL were examined to ensure that they qualify for the study. In the

treatment group, fourteen eyes of eleven subjects were analysed. Fifty consecutive K-

readings were done with an autokeratometer before the procedure, at one week post-

operatively, one month post-operatively and at six months post-operatively.

Two keratoconic eyes in the keratoconic control group and twelve eyes (of six subjects) in

the non-keratoconic control group were analysed. Both these groups underwent the same

measurements on the same time line as the treatment group. A test eye was also analysed

during the study period. The test eye was used to assess the accuracy and repeatability of

the autokeratometer used in this study.

Keratometric measurements were converted into a symmetric dioptric power matrix before

analysing the data. The converted measurements were used to produce clusters of data

points including their respective distribution ellipsoids to represent each of the

measurement sessions on a stereo-pair scatter plot in three dimensional dioptric power

space for each eye. The changes in keratometric measurements over the six-month follow-

up period are presented using appropriate tables, graphical and statistical methods. The

ii

analysis and representation of the data presented in this thesis provides a complete

mathematical and statistical indication of the keratometric behaviour exhibited in the

cornea. As far as we know, it is the first time that these methods of analysis are used in a

CXL study, making this study a unique addition to CXL research. This study will provide a

more complete understanding of corneal change induced by CXL.

The keratometric behaviour of all three subject groups (treatment, keratoconic control and

non-keratoconic control) is considered in group form and then compared to each other.

The results of the study can be summarised as follows:

• A general trend is seen in the keratometric behaviour of the eyes included in the

treatment group. The CXL procedure appears to produce a change in the

keratometric behaviour of the majority of treatment subjects. The character of the

change was most distinctly different at the one-week measurement session where

increased variation was seen between the fifty measurements taken at this session

when compared to the other measurement sessions for a particular eye, and the

largest antistigmatic (For/J and Fob/K) changes were noted at the one-week

measurement session. From the one-month to the six-month measurement session

the keratometric behaviour of the treatment subject’s corneas demonstrated a slow

but continuous return towards the pre-operative corneal form, with a decrease in

variation among the fifty measurements taken at the six-month measurement

session. The decreased variation between the measurements at the six-month

measurement session could be interpreted as a stabilisation of the keratometric

behaviour and a possible regulation of the corneal curvature induced by the CXL

procedure.

• Out of the fourteen eyes that were included in the treatment group, seven

demonstrated a stigmatic (Fst/I) flattening six months after the CXL procedure and

the remaining seven eyes included in the treatment group demonstrated a stigmatic

steepening of curvature six months post-operatively. The difference in corneal

curvature over the six-month post-CXL period was dissimilar when comparing the

iii

differences of the fourteen eyes of the treatment group to each other, indicating

that the CXL procedure induces a contrasting effect on treated eyes six months post-

operatively. The mean change seen in the treatment group as a whole consisted of a

minimal stigmatic flattening combined with a minimal antistigmatic (For/J and Fob/K)

corneal curvature change.

• In general the non-keratoconic control group, consisting of twelve eyes, displayed

very little change in keratometric behaviour over the six-month follow-up period.

The mean change seen for each of the twelve non-keratoconic control eyes were

comparable and the mean difference in curvature seen over the six-month follow-up

period for the entire non-keratoconic control group was small, indicating the stability

in curvature seen over the six-month period of time within each non-keratoconic

control eye and in the non-keratoconic control group as a whole.

• Large amounts of variation were detected between the fifty keratometric

measurements of a single measurement session in the treatment group, whereas the

variation seen between the fifty measurements of each measurement session taken

of the non-keratoconic control eyes was, comparably, largely reduced. The variation

between the measurements of each measurement session (including the before

measurement session) in the treatment group could indicate that the irregular form

caused by keratoconus in these corneas causes the variation seen between the

measurements.

• In the treatment group the mean difference (change) between the before and six-

month measurement session for the stigmatic (Fst/I) component was 0.17 D and

for the antistigmatic (For/J and Fob/K) components 0.07 D and 0.30 D respectively.

The mean difference in the non-keratoconic control group for the stigmatic

component was 0.00 D and for the antistigmatic components 0.02 D and 0.02 D

respectively.

• The CXL procedure did induce changes in the keratometric behaviour of the treated

corneas in the treatment group, but the overall mean change seen in the treatment

iv

and non-keratoconic groups were comparable. The minimal overall change seen in

the treatment group six months following the CXL procedure, and specifically the

mean flattening seen in the stigmatic (Fst/I) component for the group as a whole,

seems to indicate that the procedure was successful at stopping the keratometric

change (increase in stigmatic curvature) expected from keratoconic progression.

• The specific autokeratometer utilised in the study is accurate and produces

repeatable measurements, indicated by the test eye measurements, so the

variations measured in the three subject groups included in the study are probably

not induced by the measuring instrument.

v

DEDICATION

To my stepdad, Eduard Sevenster, I would like to extend my deepest gratitude for his

ongoing support, encouragement and motivation throughout my optometric career and for

always pushing me to do more than I think is possible. He selflessly provided me with the

opportunity and time to pursue this degree. His unquenchable thirst for knowledge, his

willingness to share his knowledge and his passion for life is an inspiration to me.

vi

ACKNOWLEDGMENTS

Firstly, I would like to thank God for guiding me through this challenging project and time

and for surrounding me with extraordinary people.

I would like to thank my mom for her understanding, love, support and encouragement

throughout the last few years and my whole life. She was in the end what made me

complete this thesis.

I wish to express my sincere thanks to my supervisor, Wayne Gillan, for the support,

patience, sharing his expertise and valuable guidance that he extended to me throughout

the course of this study. I consider it an honour to have worked with him.

Gratitude also goes to the two ophthalmologists and their staff that gave me access to the

potential subjects, without your support it would not have been possible to conduct this

research. Thank you also to the subjects that willingly gave of their time to participated in

this study.

Last but not least, I would like to thank my family, friends and colleagues for their patience,

support and understanding throughout the writing of this thesis.

vii

CONTENTS

PAGE

ABSTRACT i

DEDICATION v

ACKNOWLEDGMENTS vi

1) INTRODUCTION 1

2) LITERATURE REVIEW 4

2.1 Introduction 5

2.2 Keratoconus 5

2.3 Riboflavin collagen crosslinking for keratoconus 7

2.3.1 The biochemistry of riboflavin UV crosslinking 8

2.3.2 Surgical techniques 8

2.3.3 Changes after CXL 9

2.3.4 Possible prognostic factors 12

2.3.5 Complications 13

2.4 Other uses of crosslinking 14

2.5 New developments 14

2.6 Autokeratometers 17

3) OVERVIEW OF METHODS OF ANALYSIS 19

3.1 Introduction 20

3.2 The dioptric power matrix 20

3.3 Graphical representation of dioptric power in Euclidean 3-space 22

3.3.1 Stereo-pair scatter plots 23

3.3.2 Distribution ellipsoids 25

3.4 Statistical characteristics of dioptric power 26

3.4.1 The mean 27

3.4.2 Variance-covariance matrix 27

3.4.3 Hypothesis testing 29

3.5. Multivariate normality assumption/underlying assumptions 32

viii

3.6 Possible outliers 33

4) EXPERIMENTAL METHOD 36

4.1 Introduction 37

4.2 Study protocol 38

4.3 Measurement protocol 39

4.4 Measurement groups 40

5) RESULTS 42

5.1 Introduction 43

5.1.1 Stereo-pair scatter plots 43

5.1.2 Hypothesis tests 44

5.1.3 Outliers 44

5.1.4 Mean differences 45 5.2 Test eye 46 5.3 Treatment group 51

5.3.1 Subject 1 left eye 53

5.3.2 Subject 2 right eye 58














5.3.16 Mean differences 120

5.3.17 Discussion of differences 124

ix

5.4 Keratoconic control group 126

5.4.1 Keratoconic control Subject 4 right eye 127

5.4.2 Keratoconic control Subject 7 left eye 131



5.4.5 Discussion of differences 138

5.5 Non-keratoconic control group 140

5.5.1 Non-keratoconic control Subject 1 right eye 141

5.5.2 Non-keratoconic control Subject 1 left eye 144













5.5.15 Discussion of the differences 185

5.6 Comparison of the differences seen in the three subject categories 187

5.6.1 Discussion of the differences in the three subject groups 189

6) DISCUSSION 192

6.1 General trends seen in the keratrometric behaviour of the treatment,

keratoconic control and non-keratoconic control groups 193

6.2 Limitations of the study 198

6.2.1 Eligibility of subjects require referral from ophthalmologist 198

6.2.2 Time constraints 199

6.2.3 Instrument constraints 199

x

6.2.4 Variation of keratometric behaviour of the cornea 200

6.2.5 Keratoconic control subjects 201

6.2.6 Analysis limitations 202

6.2.7 Procedure done by multiple specialists 203

6.3 Relevance of study 203

6.4 Suggestions for future research 204

6.4.1 Corneal variation 204

6.4.2 Longer follow-up period 204

6.4.3 Larger sample size 205

6.4.4 Classification of progression 205

7) CONCLUSION 207

8) REFERENCES 211

APPENDICES 222

Appendix A: Ophthalmologist consent form 223

Appendix B: Subject information letter 224

Appendix C: Subject consent form 225

Appendix D: Rotated scatter plots 226

D 1 Test Eye 229

D 2 Treatment group 230

D 2.1 Subject 1 left eye 230

D 2.2 Subject 2 right eye 231











xi



D 2.15 Differences of treatment group 249

D 3 Keratoconic control group 250

D 3.1 Keratoconic control Subject 4 right eye 250

D 3.2 Keratoconic control Subject 7 left eye 251

D 3.3 Differences of keratoconic control group 252

D 4 Non-keratoconic control group 253

D 4.1 Non-keratoconic control Subject 1 right eye 253

D 4.2 Non-keratoconic control Subject 1 left eye 254











D 4.13 Differences of non-keratoconic control group 266

D 5 Differences of the treatment group, keratoconic control

group and non-keratoconic control group 267

Appendix E: Publication 268

1

CHAPTER 1

INTRODUCTION

2

Keratoconus is a degenerative, mostly bilateral ectasia of the cornea that causes distorted

and decreased vision (Rabinowitz, 1998). The onset of keratoconus is typically between the

age of ten and twenty (Pouliquen, 1987) thereafter the keratoconus progresses

continuously causing thinning, irregular astigmatism, progressive myopia, protrusion and

scarring of the cornea (Rabinowitz, 1998). The progression generally halts in the third to

fourth decade of life, which is generally attributed to natural crosslinking taking place in the

cornea (Grewal et al 2009; Rabinowitz, 1998; Wollensak, 2006). The riboflavin UV

crosslinking procedure was developed in an attempt to replicate the crosslinking effect seen

with corneal aging by inducing crosslinks between the collagen fibrils in the cornea by way

of a biochemical reaction using riboflavin and UVA light. The riboflavin UV crosslinking

procedure (CXL) is considered successful at stopping progressive keratoconus (Agrawal,

2009; Caporossi et al, 2010; Coskunseven et al, 2009; El-Raggal, 2009; Hersh et al, 2011;

Raiskup-Wolf et al, 2008; Raiskup et al, 2015; Toprak et al, 2013; Wollensak et al, 2003,

2004; Wollensak, 2006) and is currently globally accepted as the treatment for progressive

keratoconus.

The aim of the study was to evaluate the effect of the crosslinking procedure on the shape

of a keratoconic cornea in the first six months post-operatively by taking fifty keratometric

measurements by means of an autokeratometer on the shape of the cornea before the

procedure, one week after the procedure, one month after the procedure and six months

after the procedure. Fourteen eyes of eleven subjects were included in the treatment

group. Two control groups were included in the study and went through the same

sequence of measurement sessions. Two subjects from the treatment group had their

contralateral untreated keratoconic eyes included in the keratoconic control group and

twelve eyes of six subjects were included in the non-keratoconic control group.

The keratometric measurement data was converted to the component form of dioptric

power where after the measurement data was analysed. The three subject groups were

first examined independently. Each eye was analysed separately and thereafter the three

groups were compared to one another. The measurements collected at each measurement

session of each eye were presented on a stereo-pair scatter plot, the before measurement

session in black, the one-week session in red, the one-month session in green and the six-

3

month measurement session in blue. The mean of each measurement session as well as the

variance-covariance of each measurement session was calculated and presented.

Multivariate statistical analysis was conducted making use of a hypothesis test to compare

the means (all three components of the means) of each measurement session for a single

eye to each other, as well as a separate hypothesis test comparing the multivariate

variance-covariances of each measurement session to each other. The overall difference in

the shape of the cornea six months after surgery was calculated by only making use of the

measurements taken at the before and six-month measurement sessions. The means,

variance-covariances, hypothesis tests and differences are discussed for each of the three

subject groups separately and later the differences seen in the three groups were

compared.

Chapter 2 presents a summary of the relevant literature related to keratoconus and

riboflavin collagen crosslinking, referring to the biochemistry, surgical techniques, variation

seen after CXL, possible prognostic factors, complications and new developments associated

with CXL, as well as information regarding the autokeratometer. Chapter 3 gives an

overview of the methods of analysis utilised in this study, introducing the concept of the

dioptric power matrix, representation of dioptric power in dioptric power space by way of a

stereo-pair scatter plot, multivariate statistical analysis of dioptric powers and the concept

of possible outliers. In Chapter 4 the experimental method employed is presented. The

results are reported in Chapter 5 for the test eye, treatment group consisting of eleven

subjects (fourteen eyes are included), the keratoconic control group consisting of two

subjects (two eyes are included) and the non-keratoconic control group consisting of six

subjects (twelve eyes are included). Chapter 6 contains the discussion of the keratometric

behaviour reported on in the results (Chapter 5), looks at limitations that were present in

the study, the relevance of the study and suggestions for future research. The conclusion is

presented in Chapter 7. Chapter 8 lists the references referred to in the text. Lastly, the

appendices are attached consisting of the ophthalmologist consent form, the subject

information letter, subject consent form, rotated stereo-pair scatter plots related to the

results found in Chapter 5 and lastly an article written in preparation for this thesis.

4

CHAPTER 2

LITERATURE REVIEW

5

2.1 INTRODUCTION

Numerous studies have been done to examine the effect of riboflavin UV crosslinking (CXL)

of the cornea in subjects presenting with progressive keratoconus. The literature review

will contain information pertaining to keratoconus, riboflavin UV crosslinking and

autokeratometers. In the section dealing with CXL the biochemistry of riboflavin

crosslinking, the surgical techniques, the changes in parameters seen after CXL, possible

prognostic factors, complications associated with CXL and new developments in the CXL

field are presented.

2.2 KERATOCONUS

Keratoconus is a degenerative, usually bilateral ectasia of the cornea that results in

distorted and decreased vision due to progressive thinning, irregular astigmatism,

progressive myopia, protrusion and scarring of the cornea (Galvis et al, 2015; Rabinowitz,

1998; Raiskup-Wolf et al, 2008). It is not predisposed to race or gender (Rabinowitz, 1998).

The cause and pathogenesis of keratoconus is still unclear, however, aspects like eye

rubbing, decreased ocular rigidity, abnormalities of connective tissue, the role of

degradative enzymes, protein inhibitors and genetics are considered important (Galvis et al,

2015; Krachmer et al, 1984; Rabinowitz, 1998). Keratoconus has recently been called a

quasi-inflammatory or inflammatory-related disease rather than a non-inflammatory

disease (Galvis et al, 2015; McMonnies, 2015). Keratoconus is commonly seen as an

isolated disorder yet has been found in conjunction with mitral valve prolapse (Sharif et al,

1992), Down’s syndrome, Leber’s congenital amaurosis, atopic disease and connective

tissue diseases (Krachmer et al, 1984; Rabinowitz, 1998).

In general, keratoconus arises between ten and twenty years of age (Pouliquen, 1987). The

treatment options for keratoconus depend on the stage of the disease. Initially, spectacles

and/or soft contact lenses may be used to improve vision. As the irregular astigmatism

increases, vision will deteriorate and hard contact lenses, scleral lenses, hybrid contact

lenses, intra-corneal rings or photorefractive keratectomy (PRK) will be the next options.

These treatment options are aimed at compensating for the refractive error induced by the

6

keratoconus and cannot halt the progression (Raiskup-Wolf et al, 2008; Wollensak, 2006).

With further progression the cornea becomes too thin or scarred, resulting in the need for

corneal transplantation (penetrating or lamellar keratoplasty depending on the damage to

the cornea (Raiskup-Wolf et al, 2008; Raiskup et al, 2015)).

The progression of keratoconus normally stops in the third or fourth decade of life and is

due to corneal ageing where natural crosslinking causes spontaneous biomechanical and

biochemical stability of the disease (Grewal et al, 2009; Rabinowitz, 1998; Wollensak, 2006).

The progression of keratoconus is extremely variable differing from patient to patient as

well as between the two eyes of one patient. A patient with keratoconus is fortunate if the

keratoconic progression halts spontaneously before the integrity of the cornea or the vision

is severely compromised. A number of keratoconic patients do progress to the point where

drastic intervention in the form of a corneal transplant might be necessary to restore the

patient’s sight.

Different classification systems for keratoconus exist and are regularly expanded to

categorise the severity of keratoconus. Probably the most famous is the Amsler-Krumeich

system. Others have seen the need to redefine, refine and expand this system because of

intersection that might be present between the categories, advanced knowledge on the

biochemistry and biomechanics of the cornea and the increased volumes of information

derived from modern highly sensitive topographers and other instruments (Belin et al, 2012;

Kanellopoulos and Asimellis, 2013; Sinjab, 2012).

The diagnosis of keratoconus in its early stages is difficult. One of the reasons is that visual

acuity (VA) is often not effected before the keratoconus has progressed to a more advanced

stage and the diminished VA is usually the first reason for a patient to seek medical or

optometric assistance. Another reason is the inconspicuous changes seen in the cornea in

the early stages of keratoconus. A large number of practitioners in clinical practice would

not identify these changes as significant, as a degree of variation in the refraction and

curvature of the cornea is seen as normal, thus not warranting further investigation. With

progression, characteristic signs and symptoms of keratoconus become more apparent,

7

leading to detailed examination of the cornea in question and consequently, diagnosis or

possible referral to a specialist.

In general, the eyes of a patient are similar and can be described as mirror images of each

other. The similarity is called enantiomorphism (Kanellopoulos and Asimellis, 2013) which is

no longer present in keratoconic patients as keratoconus is usually an asymmetrical bilateral

condition, where one eye has a more advanced stage of keratoconus than the other. In

some cases the patient will only notice the decrease in VA, and thus hindrance in their

everyday life, once the second (or better eye) is affected, leaving the other eye at a fairly

advanced stage of keratoconus before seeking intervention.

2.3 RIBOFLAVIN COLLAGEN CROSSLINKING FOR KERATOCONUS

In the 1990’s, corneal collagen crosslinking with riboflavin and UVA radiation was

developed in Germany at the Dresden Technical University and in 1998 the first patient

with keratoconus was treated with the procedure (Raiskup-Wolf et al, 2008; Vinciguerra et

al, 2009b).

The stabilising effects of natural collagen crosslinking seen in the keratoconic cornea

because of aging suggest that the riboflavin ultraviolet crosslinking (CXL) procedure, which

induces crosslinks between the collagen fibrils of the cornea, may be the best way to

reduce or eliminate the progression of keratoconus remembering, however, that

keratoconus is not yet curable (Raiskup-Wolf et al, 2008).

The aim of CXL is to stop the progression of keratoconus (Agrawal, 2009; Caporossi et al,

2006; Spoerl et al, 1998; Vinciguerra et al, 2009a; Wittig-Silva et al, 2014; Wollensak et al,

2003), and is used to alter the stromal composition of the cornea by inducing crosslinks

between the collagen fibrils that may increase the tensile strength of the cornea, thereby

stopping thinning and thus the progression of keratoconus (Doors et al, 2009). CXL is still

regarded as a relatively new procedure even though it is now widely used across the globe.

8

2.3.1 THE BIOCHEMISTRY OF RIBOFLAVIN UV CROSSLINKING

Riboflavin acts as a photo-sensitizer when combined with UVA light. In the case of the

cornea, approximately 95% of the UV radiation is absorbed in the stroma (Kymionis et al,

2009). The biochemical process that takes place in the cornea because of the combination

of riboflavin and UVA-light causes increased covalent bonds to form between amino groups

of the collagen fibrils in the stoma. These covalent bonds then change tissue properties and

stabilise the collagen scaffold which results in an increase in rigidity (Spoerl et al, 1998;

Wollensak, 2006). The biochemical effect of crosslinking mainly occurs in the anterior 200-

300 µm of the cornea (Doors et al, 2009; Kohlhaas et al, 2006; Koller et al, 2009a;

Wollensak, 2006), which is seen by an increase in collagen fibre diameter (Wollensak, 2006)

and is due to the high levels of absorption of UVA radiation in this area (Goldich et al, 2009;

Kohlhaas et al, 2006). The crosslinking effect only occurring in the anterior part of the

cornea ensures that more posterior structures are not adversely affected by the UVA light

(Kohlhaas et al, 2006; Spoerl et al, 1998; Wollensak, 2006). An absolute minimum corneal

thickness of 400 µm is required to diminish the potential for damage (Caporossi et al, 2006;

Wollensak, 2006). Using the protocol specified above, the treatment is seen to be as safe

(Doors et al, 2009; Koller et al, 2009b; Kymionis et al, 2009; Spoerl et al, 1998, 2007;

Vinciguerra et al, 2009b; Wollensak, 2006), or safer than corneal transplantation (Spoerl et

al, 1998).

2.3.2 SURGICAL TECHNIQUES

The CXL procedure is done by ophthalmologists on an outpatient basis in a sterile

environment. Topical anaesthesia is administered to the eye, the lids are separated by a lid

speculum and epithelial tissue is removed. Riboflavin solution is applied before and during

irradiation every 1-5 minutes (Daxer et al, 1998; Greenstein et al, 2012; Hersh et al, 2011;

Jankov et al, 2010; Koller et al, 2011; Kránitz et al, 2014; Kymionis et al, 2009; Raiskup-Wolf

et al, 2008; Spoerl et al, 1998; Toprak et al, 2013; Vinciguerra et al, 2009a; Wisse et al, 2014;

Wollensak et al, 2003; Wollensak, 2006), starting 5-40 minutes before irradiation (Caporossi

et al, 2006; Greenstein et al, 2012; Hersh et al, 2011; Kohlhaas et al, 2006; Koller et al, 2011;

Kránitz et al, 2014; Kymionis et al, 2009; Raiskup-Wolf et al, 2008; Spoerl et al, 1998; Toprak

9

et al, 2013; Vinciguerra et al, 2009a; Wisse et al, 2014; Wollensak et al, 2003; Wollensak,

2006). The eye is examined under a slit lamp to ensure full corneal penetration of the

riboflavin (riboflavin needs to be seen in the anterior chamber) (Greenstein et al, 2012;

Hersh et al, 2011; Jankov et al 2010; Koller et al, 2011; Toprak et al, 2013; Vinciguerra et al,

2009a). Irradiation is performed at a distance of 1-6 cm (Jankov et al, 2010; Kohlhaas et al,

2006; Kránitz et al, 2014; Kymionis et al, 2009; Spoerl et al, 2007; Wollensak et al, 2003;

Wollensak, 2006) from the eye for 30 minutes using a UVA light source at 365 ± 10 nm with

irradiance of 3 mW/cm2 (which is equal to a dose of 5.4 J/cm2) (Caporossi et al, 2006; El-

Raggal, 2009; Greenstein et al, 2012; Hersh et al, 2011; Jankov et al, 2010; Kohlhaas et al,

2006; Koller et al, 2009b, 2011; Kránitz et al, 2014; Kymionis et al, 2009; Spoerl et al, 1998,

2007; Toprak et al, 2013; Vinciguerra et al, 2009a, 2009b; Wollensak et al, 2003; Wollensak,

2006). A bandage contact lens is usually placed on the cornea post-operatively (El-Raggal,

2009; Greenstein et al, 2012; Hersh et al, 2011; Jankov et al, 2010; Mazzotta et al, 2008;

Toprak et al, 2013; Vinciguerra et al, 2009a; Wisse et al, 2014) until re-epithelialization is

complete (Greenstein et al, 2012; Hafezi et al, 2007; Toprak et al, 2013; Vinciguerra et al,

2009a).

2.3.3 CHANGES AFTER CXL

Following CXL it has been found that K-readings have flattened (Agrawal, 2009; Caporossi et

al, 2010; Coskunseven et al, 2009; El-Raggal, 2009; Hersh et al, 2011; Kránitz et al, 2014;

Raiskup-Wolf et al, 2008; Raiskup et al, 2015; Tomkins et al, 2008; Toprak et al, 2013;

Vinciguerra et al, 2009a, 2009b; Wollensak et al; 2003, 2004; Wollensak, 2006), stabilised

(Razmjoo et al, 2015; Spoerl et al, 1998; Wollensak et al, 2003; Wollensak, 2006) or that the

cornea had a tendency to take on a more symmetric form (Arbelaez et al, 2009; Caporossi et

al, 2006; Caporossi et al, 2010; Raiskup-Wolf et al, 2008; Raiskup et al, 2015; Spoerl et al,

1998; Toprak et al, 2013; Vinciguerra et al, 2009a, 2009b; Wollensak et al, 2003). In some

studies, a lowering of specifically corneal astigmatism was mentioned as opposed to or in

combination with the cornea being more regular (Raiskup-Wolf et al, 2008; Raiskup et al,

2015). Rarely steepening of K-readings were found (Caporossi et al, 2011; Koller et al,

2009b; Raiskup et al, 2009, 2015; Wollensak et al, 2003). It is important to realise that a

flattening effect of a keratoconic cornea has never before been documented before the CXL

10

procedure was introduced and that control groups of keratoconic eyes showed progression

or increase in K-readings (Vinciguerra et al, 2009a, 2009b; Wollensak et al, 2003). The

flattening effect of CXL has been called post-operative regression which was found in 70% of

CXL patients in one study (Wollensak et al, 2003).

The flattening of K-readings consequently had a positive effect on the visual acuity of the

concerned eyes. Uncorrected visual acuity, referring to the level of vision achieved without

the aid of spectacle or contact lenses (Greenstein et al, 2012; Vinciguerra et al, 2009a,

2009b) and best spectacle corrected visual acuity (BSCVA) had a significant improvement in

some cases (El-Raggal, 2009; Greenstein et al, 2012; Raiskup et al, 2015; Spoerl et al, 2007;

Toprak et al, 2013; Vinciguerra et al, 2009a; Wollensak et al, 2003; Wollensak, 2006). A slow

but significant improvement in refractive error (Caporossi et al, 2006; Doors et al, 2009; El-

Raggal, 2009; Grewal et al, 2009; Kymionis et al, 2009; Spoerl et al, 1998; Vinciguerra et al,

2009a, 2009b; Wollensak et al, 2003) and cylindrical refractive error (Vinciguerra et al,

2009a; Caporossi et al; 2006) was seen in as little as three months post-operatively when

compared to mean pre-operative values. However, two studies (El-Raggal, 2009;

Vinciguerra et al, 2009a) found an astigmatic axis shift post-operatively. It has been

suggested that minor changes in the topography of the cornea is seen for years after CXL

treatment was administered (Agrawal, 2013; Raiskup-Wolf et al, 2008).

Doors et al (2009) found that the shape of the corneas treated with the CXL procedure

became steeper when measuring both maximum and central K-readings one month post-

operatively, but these returned to their pre-operative levels three months post-operatively

and remained stable at a six and twelve-month post-operative follow-up. The increase in K-

readings one month post-operatively coincides with a significant decrease in best spectacle

corrected visual acuity (BSCVA) which also returned to pre-operative values three months

post-operatively and remained stable. It was noted that 50% of the eyes treated gained at

least one Snellen line at the six-month follow-up. The increase in K-readings and

subsequent decrease in BSCVA at one month was attributed to the remodelling process

taking place in the cornea in the first month after crosslinking.

A one-year follow-up study by Vinciguerra et al (2009a), produced similar results to Doors et

al (2009). Mean pre-operative flattest meridian keratometry, steepest meridian

11

keratometry, average keratometry and simulated keratometry cylinder were determined

before crosslinking and one, three, six and twelve months post-operatively. An initial

increase was seen in all these parameters at the one-month follow-up (seeming to be

caused by the epithelial debridement) thereafter all the parameters displayed a slow

decrease when compared to the pre-operative measurements. The improvement was

attributed to re-epithelialization initially and thereafter to the crosslinking effect. The

conclusion was reached that the CXL procedure causes a flattened and more regular cornea,

which lead to an improvement of visual acuity post-operatively. It seems that the

improvement in visual acuity takes place in the first three to twelve months post-operatively

and then remains unchanged.

A follow-up study by Raiskup-Wolf et al (2008), ranging from one to six years post-CXL,

which started with 142 eyes and ended with only five eyes at six years, reported a

statistically significant decrease in astigmatism and K-values at one year post-operatively

which also remained stable throughout the study. A decrease of 0.50 D or more was seen in

the maximum K-reading, K-reading of the apex and astigmatism in all the patients.

As far as we know the longest follow-up study to date was recently published (Raiskup et al,

2015). In Raiskup et al’s study a statistically significant decrease in mean apical keratometry

and mean maximum and minimum K-values was evident as well as an increase in corrected

distance visual acuity (CDVA). Pre-operative data was subtracted from post-operative data

to come to the above conclusions. Since this seems to be the longest CXL follow-up study to

date, it is suggested that the CXL procedure is successful at stabilising the progression of

keratoconus for at least ten years post-operatively.

The methods used by many of the authors to determine the refractive change varied from

subtracting data collected at follow-up examinations from data collected on the day of the

procedure (Raiskup-Wolf et al, 2008) to converting the data into vectors and then

calculating the change found on follow-up visits when comparing data to the data collected

on the day of the procedure (Doors et al, 2009). Mostly curvature parameters compared in

previous studies were limited to mean, maximum and minimum keratometry

measurements (Raiskup-Wolf et al, 2008; Raiskup et al, 2015; Vinciguerra et al, 2009a).

12

2.3.4 POSSIBLE PROGNOSTIC FACTORS

It is clear that the CXL procedure induces different types of changes in different patients and

between the eyes of a single patient. As the CXL treatment protocols are constantly

improving and becoming more useful in the clinical setting, it is also becoming more

important for practitioners to be able to give their patients a better estimation of the

outcome of the procedure. Clinicians have found that in some patients the progression of

keratoconus proceeds unhindered in spite of them receiving the CXL treatment (Wisse et al,

2014). Age, CDVA, cone location and maximum keratometry before treatment have been

identified as the main prognostic factors for avoiding complications and getting the best

results from the CXL procedure (Greenstein et al, 2012; Koller et al, 2009b, 2011). Age over

thirty-five years and CDVA of 20/25 or better pre-operatively were identified as factors that

increased the risk of complications post-operatively and a maximum keratometry reading of

above 58.00 D was an indicator for an increased possibility that the procedure would not be

effective in stopping, or reversing, the progression of the keratoconus (Koller et al, 2009b).

More recently it was found that a pre-operative maximum keratometry reading of more

than 54.00 D was an indicator that it was more likely for the eye to have a statistically

significant flattening of more than 1 D in the first year post-operatively (Koller et al, 2011).

Thus it seems that when regarding keratometry readings alone, we can expect the best

outcome for patients with K-readings between 54.00 and 58.00 D pre-operatively. It was

found that cone positioning could possibly predict the outcome of keratometry readings

twelve months post-operatively, where corneas with more centrally located cones exhibited

more flattening twelve months post-operatively than corneas with peripherally located

cones (Greenstein et al, 2012; Wisse et al, 2014). Centrally located cones tend to have

greater maximum keratometry readings than peripherally located cones, hence it is possible

that the location of the cone is not as important as the actual maximum K-reading is

(Greenstein et al, 2012).

Raiskup-Wolf et al (2008) reported on two patients with neurodermatitis where the

progression of their keratoconus was halted for eighteen and twenty-one months

respectively after CXL. However, as their neurodermatitis got worse, they also displayed a

13

progression of their keratoconus. The CXL procedure was repeated in both cases but no

feedback was given on the progression after the second CXL procedure in either case.

A study by Caporossi et al (2011), where patients were divided into groups according to age,

found a more positive functional outcome after CXL treatment in patients under twenty-six

years of age. The lower functional response in patients over the age of twenty-seven is

attributed to a reduction in the ability to mold the cornea in older patients.

2.3.5 COMPLICATIONS

The most common complication seen following the CXL procedure is haze (Koller et al,

2009b; Mazzotta et al, 2007; Razmjoo et al, 2014; Vinciguerra et al, 2009a). Some patients

complained of haloes and night glare for the first three months post-operatively

(Vinciguerra et al, 2009a). Sterile infiltrates and stromal scars have been noted in a small

number of cases (Koller et al, 2009b).

Additional complications were post-operative herpetic keratitis with iritis in a patient with

no history of herpetic disease (Kymionis et al, 2007a) and diffuse lamellar keratitis in a

patient treated with CXL for post-laser in situ keratomileusis (Kymionis et al, 2007b).

In a study by Koller et al (2009b), three of the 105 eyes that were included in the study lost

two Snellen lines of CDVA in the first year post-CXL, which was seen as a complication.

Failure of the CXL treatment was defined as an increase in maximum K-reading of 1.00 D or

more in the first post-operative year which was seen in 8 of the 105 eyes included in the

study.

More serious complications noted are corneal scarring with permanent reduction of vision,

possible corneal melting and perforation being mentioned (Raiskup et al, 2015). The cornea

is more vulnerable to infection and melting during the re-epithelialization process (Koller et

al, 2009b).

14

2.4 OTHER USES OF CROSSLINKING

CXL was developed to stop the progression of keratoconus but with time it has become

useful for a number of other problems. CXL is currently also successfully used to stop the

progression of iatrogenic keratectasia after excimer laser ablation (Wollensak et al, 2009)

and to partly reverse the keratectasia in these patients (Hafezi et al, 2007), although the

flattening effect seen in keratoconus patients post-CXL is bigger than what is seen in post-

laser-assisted in situ keratomileusis (LASIK) post-CXL (Hersh et al, 2011).

The CXL procedure has been indicated as a method of treating infectious keratitis and

corneal melts (Schnitzler et al, 2000) and as a method to reduce corneal edema in bullous

keratopathy and even to postpone an impending corneal transplant (Wollensak et al, 2009).

CXL is useful when utilised in combination with procedures that reshape the cornea (in an

attempt to increase the patient’s vision) to try and stabilise the flattening or more regular

shape that has been induced (Wollensak et al, 2009). These include topography-guided

photorefractive keratectomy (PRK) and the implantation of intra-corneal rings. The

combination of these procedures with CXL causes a greater improvement of the corneal

curvature than CXL alone (Wollensak et al, 2009). In the instances where the CXL procedure

is combined with PRK, the patient has the benefit of only having their epithelium abraded

once, thus inducing less pain than abrading the cornea for each procedure separately (Koller

et al, 2011).

2.5 NEW DEVELOPMENTS

The standard method of CXL has evolved in many different ways to include more patients

and make the procedure less painful for the patient (Jankov et al, 2010).

The standard method of CXL involves the removal of the corneal epithelium. The removal is

done to ensure the complete absorption of riboflavin into the deeper layers of the cornea,

which is necessary to protect the underlying structures such as the endothelium, lens and

retina from the potentially harmful UV radiation (Spoerl et al, 1998). The tight junctions

15

between the epithelial cells hinder the penetration of the riboflavin into the cornea, thus

the epithelium is removed in an area with a diameter of 7-9 mm (Jankov et al, 2010; Koller

et al, 2009b; Wollensak et al, 2003). The patient experiences intense pain because of the

absence of the epithelium and the likelihood of getting an infection is increased until re-

epithelialization is complete.

Riboflavin solutions containing substances like benzalkonium chloride (a preservative

regularly used in ophthalmic medication) have been used to loosen the junctions between

the epithelial cells before administrating the riboflavin to the eye pre-operatively to aid in

the penetration of the riboflavin into the stroma (Jankov et al, 2010). In other cases only

partial grid-pattern removal of the epithelium was done; this facilitated the penetration of

riboflavin into the stroma, but the penetration is irregular, which could influence the effect

the CXL procedure has on the cornea (Jankov et al, 2010).

Treatment with hypo-osmolar riboflavin solution in thin corneas was developed after

researchers established a link between subjects presenting with permanent haze following

the CXL procedure and high keratometric values and thin corneas pre-CXL (Raiskup et al,

2009), which are associated with advanced keratoconus. Several factors could cause the

cornea to become thinner during the CXL procedure. Foremost the cornea is thinner after

epithelial debridement (Hovakimyan et al, 2012; Raiskup et al, 2011) and thinning could be

caused by possible dehydration of the cornea induced by isotonic riboflavin solution and/or

the eye being opened for a prolonged time with a lid speculum prior to epithelial removal.

When using the original protocol, a minimum corneal thickness of 400 µm is necessary to

ensure that the procedure is safe, which could be a problem as dehydration could lead to

thin corneas becoming dangerously thin when administering the CXL treatment (Doors et al,

2009; Koller et al, 2009b; Kymionis et al, 2009; Spoerl et al, 1998, 2007; Vinciguerra et al,

2009b; Wollensak, 2006). As a result of the safety concern for thin corneas, a different

method of swelling the cornea with hypo-osmolar solution prior to CXL was developed. In

this procedure the epithelium is abraded and hypo-osmolar riboflavin solution (0.1% hypo-

osmolar riboflavin) is instilled in the eye without holding the lids open with a lid speculum,

preventing dehydration during the procedure and simultaneously swelling the cornea. The

cornea was only irradiated once a thickness of 400 µm or more was measured. The

16

installation of the hypo-osmolar solution was repeated throughout the procedure. Raiskup

et al (2011) administered the modified technique to thirty-two eyes whereafter no

permanent haze was noted and the progression was stable one year post-operatively. The

modified technique broadened the inclusion criteria for patients needing CXL as thinner

corneas could now be treated and corneal transplantation could be avoided or delayed in

keratoconic patients with thin corneas.

Epithelial removal not only reduces the thickness of the cornea but is also associated with a

bigger risk of infection, severe pain and photophobia until re-epithelialization is complete

(Hovakimyan et al, 2012; Nawaz et al, 2015). For this reason an alternative to the

epithelium off (epi-off) CXL (or conventional CXL protocol) was created, called trans-

epithelial (TE-CXL) (or epithelium on (epi-on) CXL). The corneal epithelium halts the

penetration of riboflavin into the cornea but does not diminish the UVA irradiance (Bottós

et al, 2011). To overcome the riboflavin penetration problem a solution was formulated

with two enhancers (trometamol (tris-hydroxymethyl aminomethane) and EDTA

(ethylenediaminetetraacetic acid) sodium salt) that assists the riboflavin to saturate the

cornea through the epithelium (Filippello et al, 2012). Filippello et al (2012) concluded that

the epi-on CXL procedure was effective in stopping the progression of keratoconus and

concurrently found an improvement in corneal topographic parameters post-operatively.

The epi-on procedure used was described as safe and it was proposed that it should be used

in pediatric cases, uncooperative patients and thin corneas. Filippello et al (2012) stated

that the epi-on CXL procedure does not have to be performed in a sterile environment

which makes it possible for the procedure to be performed in an office setting and thus for

the procedure to be more readily available which would particularly benefit third world

countries like South Africa, especially because of a lack of donor corneas and

ophthalmological surgical theaters. It was concluded that the epi-on procedure is effective

in stopping the progression of keratoconus (Amin et al, 2014; De Barnardo et al, 2014;

Nawaz et al, 2015). Hafez (2014) believes that the conventional protocol CXL procedure is

superior to the epi-on procedure, because of the exceeding improvement and stabilisation

of VA. Similarly, Razmjoo et al (2014) found that the original protocol resulted in a superior

improvement in maximum keratometric values and the cornea was more symmetric when

compared to the outcome of epi-off CXL.

17

It is important to note that, because CXL can stop or delay the progression of keratoconus it

can reduce the need for penetrating (and lamellar) keratoplasty (Raiskup et al, 2015;

Wollensak et al, 2003). In young patients presenting with keratoconus this is especially

important, as the corneas of younger patients are more pliable and more time is potentially

available for the keratoconus to progress before natural crosslinking takes place, making it

more likely for these young patients to need keratoplasty in future. The conventional epi-

off CXL protocol is the treatment of choice for patients younger than twenty-six with

corneas of a thickness of at least 400 µm (Caporossi et al, 2011).

CXL is presently the only form of treatment available to stop the progression of keratoconus

and consequently preserve the patient’s vision. CXL is a relatively new procedure and

longer follow-up studies, with larger subject populations, are necessary, especially because

the durability of the crosslinking effect is unknown after ten years and a repeated procedure

may be necessary. CXL is a relatively simple, minimally invasive (Raiskup et al, 2015;

Wollensak et al, 2009) and low cost procedure (Wollensak et al, 2003) with a short recovery

time. It is currently the globally recognised treatment for progressive keratoconus (Raiskup

et al, 2015).

CXL is considered successful at stopping the progression of keratoconus (Agrawal, 2009;

Caporossi et al, 2010; Coskunseven et al, 2009; El-Raggal, 2009; Hersh et al, 2011; Raiskup-

Wolf et al, 2008; Raiskup et al, 2015; Tomkins et al, 2008; Toprak et al, 2013; Wollensak et

al, 2003, 2004; Wollensak, 2006).

2.6 AUTOKERATOMETERS

The function of the keratometer is to measure the radius of curvature of the anterior

corneal surface, determining the shape of the cornea (Cronje et al, 1997). The keratometer

uses the reflective properties of the cornea to measure the radius of curvature and the

quantity and direction of corneal astigmatism. The measurement takes place in a 3.0 mm

diameter area of the central cornea (Gutmark and Guyton, 2010).

18

Keratometric measurements are objective readings as no feedback is necessary from a

patient, this makes it an ideal tool for most patients including children. The

autokeratometer is a keratometer which makes use of computer based calculations to

deliver quick keratometer readings.

The NIDEK TONOREF II Auto Refractor/Keratometer/Non-Contact Tonometer utilised in this

study can in fact perform all three of these functions. Specifically, the keratometry readings

will be regarded in this study. Only one specific instrument was used throughout the study,

to limit instrument variation.

It is possible to program the autokeratometer in such a way that measurements are taken

by manually focusing the mires seen on the corneal surface and pressing a button to take

the measurements, as well as using it in automatic mode where the instrument

automatically focusses the mires on the front surface of the cornea. In both the manual and

automatic mode, the instrument takes a set of three measurements and averages these to

form a reading.

It has been suggested that the autokeratometer is more accurate than the manual

keratometer as it produces less variation when measuring a steel ball as well as an eye

(Cronje-Dunn, 1995).

In the case where corneal astigmatism is measured the autokeratometer has been found

very comparable to the manual keratometer and can be used interchangeably (Lee et al,

2012). Autokeratometers show good repeatability in their measurements (Chang et al,

2012; Kobashi et al, 2012), produce accurate results (Hammack, 1997) and are thus seen as

reliable in clinical practice.

The keratometer is the most frequently used instrument to estimate corneal curvature in

clinical practise because of its ease of use, speed, accurate measurements and being non-

invasive to the patient, as no direct contact is made with the eye to take the measurement

(Chang et al, 2012; Gutmark and Guyton, 2010); as far as we are aware it possesses no risk

to the eye being measured.

19

CHAPTER 3

OVERVIEW OF METHODS OF ANALYSIS

20

3.1 INTRODUCTION

In the optometric and ophthalmological fields it is important to use the correct form of the

refractive power of the eye when doing calculations. The standard or clinical form of

dioptric power utilised in practice is ineffective in mathematical and statistical calculations.

Fortunately, methods to transform the clinical form of dioptric power into a 2 2 dioptric

power matrix have been developed by researchers such as Harris, Thibos, Keating and

Saunders. The dioptric power matrix makes it possible to work with refractive power as a

holistic concept, opening the door to an array of mathematical calculations and multivariate

statistical analysis methods, allowing for the correct, and complete, analysis and

manipulation of refractive power data. This method of analysis was utilized in previous

keratometric research by among others Chetty et al (2010) and Cronje-Dunn (1995).

3.2 THE DIOPTRIC POWER MATRIX

Dioptric power (or refractive power) is a single concept, although it is multivariate and

represented by three numbers. In the clinical form the three numbers are the power of the

sphere (from here on symbolized by ), the power of the cylinder ( ), and the axis ( )

which is the direction of the cylinder measured from a reference meridian (usually 180⁰)

(Harris, 1988, 1989a, 1989b). and are measured in diopters (D or m-1) and is

measured in degrees (Harris, 1988).

The clinical or conventional form of refractive power is written as follows:

(3.1)

When scientifically analysing dioptric power, it is necessary for us to convert the clinical or

conventional form of dioptric power into a matrix. The conversion enables us to use

mathematical properties that are already known regarding matrices in this process (Harris,

2001). The concept of the dioptric power matrix was credited to WF Long (1976) by Harris

(1988) and later modified and simplified by Keating and Harris (Harris, 1988; Keating, 1980,

1981, 1982, 1986).

21

The dioptric power matrix (Long, 1976), in general form looks as follows:

F = (3.2)

In this dioptric power matrix F, the principal diagonal elements are and , and the off-

diagonal elements are and .

The dioptric power matrix is a 2 2 matrix which is said to be symmetric, because the two

off-diagonal elements are always the same. Thus there are three numbers of interest in the

dioptric power matrix. In the case of the dioptric power matrix, all the elements in the

matrix have diopters (D) as units (Harris 1988, 1989b, 1990b).

Determination of the individual entries of the matrix is done using:

f11 Fs Fc sin2 a (3.3)

f12 F21 Fc sin a cos a (3.4)

f22 Fs Fc cos2 a (3.5)

The element relates to the curvital power in the horizontal meridian and to the

curvital power in the vertical meridian of refractive power. The elements and (that

are equal) link back to the torsional power component of refractive power (Keating, 1986).

If necessary, it is possible to convert back to conventional notation from matrix

representation by the following (Keating, 1980, 1981):

(3.6)

(3.7)

(3.8)

22

In the equations above is the trace (used in 3.6 and 3.7) and is the determinant (3.6) of

the F matrix.

(3.9)

Thus trace is the sum of the diagonal elements and

(3.10)

The determinant is found by taking the product of the two diagonal elements and then

subtracting the product of the off-diagonal elements.

By using the dioptric power matrix we can now, with clarity, use calculations on refractive

powers. Before this method of conversion from the clinical form to matrix representation,

mathematical and statistical calculations were used in an unscientific and incomplete way

(Harris, 1988, 1989a, 1989b, 1990b).

3.3 GRAPHICAL REPRESENTATION OF DIOPTRIC POWER IN EUCLIDEAN 3-SPACE

Graphically dioptric power is found in a three dimensional space and is comprised of three

distinct parts, these being Fst (the stigmatic/scalar coefficient), For (the ortho antistigmatic

coefficient) and Fob (the oblique antistigmatic coefficient) (Harris, 2001).

F FstI ForJ FobK (3.11)

this can also be written as

F Fst For Fob (3.12)

The stigmatic, ortho antistigmatic and oblique antistigmatic coeffecients are derived by the

following equations with elements defined in Section 3.2:

Fst 0.5 (f11 f22) Fs ½Fc

(3.13)

For 0.5 (f11 – f22) ½ Fc cos 2a (3.14)

Fob 0.5 (f21 f12) ½ Fc sin 2a (3.15)

It is important to remember that we are working exclusively with sphero-cylinder powers

represented in symmetric dioptric power space. Symmetric dioptric power space is three

dimensional and is also called Euclidean 3-space (Harris, 1991; 1997; 2001). Three mutually

23

orthogonal axes are utilised to graphically represent the relevant data. These axes are I, J

and K.

Consider the equation 3.11 which can be written as a coordinate vector:

v (3.16)

In this space v is a three-dimensional generalised vector, which is formed by I, J and K and is

used to represent the keratometric measurements taken on each subject. These

components in the matrix give us Fst (FstI) which is the spherical or stigmatic part of the

power and is plotted on the I-axis, For (ForJ) is the ortho antistigmatic power, which is

plotted on the J-axis and has principal meridians along 0⁰ and 180⁰ and then lastly Fob (FobK)

is the oblique antistigmatic power found on axis K which has principal meridians along 45⁰

and 135⁰.

3.3.1 STEREO-PAIR SCATTER PLOTS

Stereo-pair scatter plots can be used to graphically represent keratometric measurements.

As Euclidean space is three dimensional, these scatter plots are specifically set up to

illustrate this dimensional view. The three dimensional effect of the stereo-pairs can be

seen by converging the eyes to form one three dimensional representation. Converging the

eyes is done by focusing on a point in front of the paper plane in line with a point between

the stereo-pair scatter plots. In the background the plots should move until a three

dimensional image is perceived. Some readers might find this difficult and for that reason

the scatter plots in the text are rotated in space and provided in Appendix D. The rotation

helps us to visualise the distribution of the data easier and make all data points visible as

some could be obscured by other data points in the foreground.

A computer program was developed by Harris and Malan and then modified by Rubin which

works specifically with optometric data (Malan, 1993). In this study, keratometric readings

taken by an autokeratometer, in radii of curvature along principal meridians, were entered

into the program. The program converted the data from radii of curvature into diopters

24

along principal meridians (Harris, 1992a; Malan, 1993), allowing multivariate statistical

analysis of the data and the graphical representation of the measurement data on stereo-

pair scatter plots. A refractive index of 1.3375 was utilised by the program as the nominal

refractive index.

The data from the measurements is graphically represented by converting the data into the

component form (I, J, K) and then plotting the corresponding data points on stereo-pair

scatter plots in Euclidean 3-space, as example refer to Figure 3.3.1.1. Each data point on the

scatter plots represents a single keratometric measurement. At each of the four

measurement sessions, fifty keratometric readings were taken, therefore each

measurement session is represented by fifty data points. Each of the measurement sessions

is presented in a different colour (black representing the before measurement session, red

the one-week, green the one-month and blue the six-month measurement session) on the

scatter plots.

Figure 3.3.1.1 shows the data collected, presented in the “usual” or ”conventional”

orientation. Figure 3.3.1.2 shows the same data as that seen in Figure 3.3.1.1 but with the

plot rotated so that the data can be visualized along the antistigmatic, J-K plane.

Visualization of the data, looking down the stigmatic (I) axis, can be appreciated in Figure

3.3.1.3.

Each eye included in the study will have a stereo-pair scatter plot related to Figure 3.3.1.1

presented in Chapter 5 (Results) as well as stereo-pair scatter plots related to Figure 3.3.1.2

and Figure 3.3.1.3 in Appendix D to facilitate clarity and ease of interpretation of the data.

25

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

Figure 3.3.1.1 Stereo-pair scatter plot representing clusters of measurements of Subject 1. The before measurement session (black), one-week (red), one-month (green) and six-month measurement session (blue) are shown. The 95% distribution ellipsoid for each session is included. The axis origin is at 52.5 I D. Axis length is 3 D and tick interval is set at 1 D.

Figure 3.3.1.2 Stereo-pair scatter plot representing the same data as Figure 3.3.1.1 rotated in Euclidean 3-space to look along the J-K plane. The axis origin is 52.5 I D.

Figure 3.3.1.3 Stereo-pair scatter plot representing the same data as Figure 3.3.1.2 rotated in Euclidean 3-space to look along the I-axis. The axis origin is 52.5 I D.

3.3.2 DISTRIBUTION ELLIPSOIDS

Also termed ellipsoids of constant probability density. As explained in Section 3.3.1,

collected data can be graphically represented by scatter plots. Each data point on a scatter

plot represents a single measurement taken. When making use of distribution ellipsoids,

each data point still represents one measurement, but ellipsoids are calculated based on

these measurements and added together with the data points on the plot. The distribution

ellipsoids in this study were all chosen at a 95% constant probability density, meaning it is

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

26

anticipated that 95% of measurements taken from the population from which the sample

comes from, will be found within the 95% distribution ellipsoid.

The geographical center of the ellipsoid is the mean of the sample. No definite mark

represents the mean but it is seen on the plot where the major and minor axes of the

ellipsoid intersect. The size of the distribution ellipsoid indicates the level (or amount) of

variation seen between measurements in a sample. If the distribution ellipsoid is small, it is

seen as a sample with little variation in its measurements and the measurements can be

seen as a tight cluster. The opposite is true for a large distribution ellipsoid which is derived

from a loose cluster of measurements representing more variation between the

measurements.

The size, shape and the orientation of the ellipsoids in Euclidean 3-space are used to make

conclusions about the measurements taken (Rubin, 1993b). See Section 5 (Results) for an

in-depth description of the distribution ellipsoids formed for each subject in this study.

3.4 STATISTICAL CHARACTERISTICS OF DIOPTRIC POWER

In the past, before it was possible to convert refractive power from clinical form to the

dioptric power matrix, calculations were used in an incomplete way (Harris, 1988, 1989a,

1989b, 1990a, 1992b). The refractive power was broken down into various parts, looking at

Fs and Fc and a separately or at the nearest equivalent sphere (practically ignoring a).

Another way was that the average refractive error was calculated by introspection or a

naïve method (Harris, 1988, 1990b, 1990c, 1992b).

As stated earlier Fs, Fc and a are not separate entities, but together form a single concept

(Harris, 1990a). The relationship between these entities is crucial when we look at averages

of refractive errors and when using a whole array of mathematical and statistical

calculations. Following the advances made as a consequence of being able to use dioptric

power in a matrix form, multivariate statistical analysis is now applied to data processing in

our field. If dioptric power is not used in its matrix form, and thus not used correctly,

conclusions made from the data at hand could be misinterpreted or important information

27

can be completely missing (Harris, 1989b, 1990b, 1990c). At present research is still done

and conclusions drawn from refractive data in its clinical form which is of importance, but

more comprehensive, scientifically correct conclusions could be drawn from research

analysed by working with dioptric power in component form.

For clarity of the naïve mean, mean by introspection and why it is incorrect, the interested

reader is referred elsewhere (see Harris, 1989b, 1990b).

3.4.1 THE MEAN

In 1983, Keating (1983) was the first person to determine the mean of a sample of refractive

powers by using the dioptric power matrix.

The sample mean of refractive powers, , , … is calculated by (Harris, 1989b,

1992b):

( … ) (3.17)

Or (3.18)

The calculation of the mean when using refractive errors in matrix form is relatively easy.

The matrices are simply added together (making use of conventional methods) and the sum

is then divided by the number of refractive errors ( ) that the mean is calculated for. For

each measurement session a mean of the fifty keratometric measurements taken is

determined. At the end of the six-month follow-up period the means for all four visits are

compared to see if any significant change in keratometric behaviour took place.

3.4.2 VARIANCE-COVARIANCE MATRIX

The variance is a measurement of the grouping of data points of a sample around the mean,

it indicates the variation of dioptric power in a sample. Harris (1988, 1990b, 1990c) regards

28

the mean and variance of a sample as critical tools to make meaningful conclusions about

the data in question.

To find the variance of a set of data, one must be able to square the data. Saunders (1985)

suggested that dioptric power, except for pure spheres, could not be squared and therefore

it was not possible to work out the variance for dioptric power. It was a problem for

researchers working with dioptric power, since without a variance for a set of data, the

statistical description of the data was incomplete and consequently incomplete conclusions

were made (Harris, 1988, 1990b, 1990c).

Harris (1990a, 1990c) revealed that it was possible to square dioptric power when using it in

its matrix form and, as a result, that it was possible to determine the variance of a sample of

dioptric powers. Thus it was the first time that the variance of a dioptric power was

calculated using the dioptric power as a multivariate, holistic concept (Harris, 1990a). When

calculating the variance of this multivariate concept, the variance of all the elements is

found, as well as the covariance between these elements. It gives us a complete variance

for a set of dioptric power data, if it is normally distributed.

The variance-covariance matrix ( ) is calculated using the following equation where the

vector (equation 3.17) represents the mean of the sample (Harris, 1990c):

(3.19)

Which could also be written as

(3.20)

29

The 3 x 3 variance-covariance matrix is symmetric, with the unit D2 and looks as follows:

D2 (3.21)

where

s12 = s21, s13 = s31 and s23 = s32

(3.22)

s11, s22 and s33 are the diagonal entries.

Equation 3.19 can be simplified, when using dots to imply symmetry (Harris, 1990a):

D2

Since it is a symmetric matrix, only six of the values in this matrix are important (Harris,

1990a). The elements along the diagonal of the matrix represent the variances, and have

been called pure variances of the components of the dioptric power matrix (Harris, 1990c).

The variance is the variance of Fst, is the variance of For and is the variance of Fob.

The off-diagonal elements represent the covariances of the components of the dioptric

power matrix. Then is the covariance of Fst and For, is the covariance of For and Fob

and is the covariance of Fst and Fob. Covariance is not easily understood, but if explained

very basically, it is the change that takes place between a pair of variances in a multivariate

sample.

To clarify the explanation above, if all six relevant numbers in the variance-covariance

matrix were equal to 0 D2, no variation would exist between the measurements, meaning

that all the measurements would be exactly the same and, when looking at the graphical

representation of the sample, only one data point would be visible because all the data

points would be superimposed on the graph (Rubin et al, 1994).

3.4.3 HYPOTHESIS TESTING

After Harris (1990a, 1990c) demonstrated that it was possible to square a dioptric power

(see Section 3.3.2), statistical analysis by way of hypothesis testing was made possible when

utilising dioptric power. The goal of performing hypothesis tests is to establish if the

30

changes found between certain aspects of the compared samples are in fact significant

changes or if the changes can be attributed to random fluctuations in the data. In the cases

where the null hypothesis is accepted, it indicates that there are no significant changes or

differences between the aspects compared in the samples. If the null hypothesis is rejected

the alternate hypothesis is accepted, indicating that the changes or differences seen

between the samples are statistically significant. Ultimately hypothesis testing gives the

researcher more confidence in conclusions made from the data.

The null hypothesis, the alternate hypothesis and test statistic for multivariate inference are

respectively defined as (Harris, 1990c, 1992b):

Null hypothesis:

HO : µv µv0

Alternate hypothesis:

H1 : µv µv0

µv symbolizing the mean of the sample.

And the test statistic is represented as:

w µv0 ’ µv

0

(3.23)

The null hypothesis (H0) is rejected and the alternate hypothesis accepted when the test

statistic (w) is equal to or bigger than the critical value, given by

w

F relates to the F-distribution, is the level of significance and m is the degree of freedom in

the numerator and the degree of freedom in the denominator. These are read from

Snedecor’s F- distribution table (Harris, 1992b). In research, it is common practice to take

as 0.05; consequently the level of confidence is 0.95 and henceforth it is expressed as a

95% confidence interval (Harris, 1990c).

The null hypothesis for variance-covariance is:

: 0

31

The alternate hypothesis is

: 0

The test statistic is calculated by

Σ0 0-1 (3.24)

The alternate hypothesis is accepted and the null hypothesis is rejected if

The Chi-square table is used to find .

In this study, hypothesis testing was done on the means and variance-covariances for each

of the four follow-up visits of each subject (keratoconic controls, non-keratoconic controls

and test eye included). When looking at real-world data it seems logical that there are

always random fluctuations present. In this case the fluctuations could, among other things,

have been caused by either the subject or refractionist involved (Harris, 1992b).

Two types of errors are defined for hypothesis testing. A Type I error stipulates that a

significant result is found, but actually no effect is present and a Type II error, where a

significant result is present, but the researcher fails to see it as significant.

Certain assumptions are made when using statistical equations on dioptric power. We

assume that we are working with a population with a multivariate normal distribution and

that the sample variance-covariance is the same for each sample. For a dioptric power with

cylinder and axis the data is often not normally distributed (Harris, 1992b). Caution should

be taken when these assumptions are not met, as conclusions made when they are not met

may not be reliable (Harris, 1990b, 1992b). It is very useful and seems necessary to also

have the graphical representation of the data in Euclidean space to aid and reinforce

conclusions derived from the data and to minimise the risk of making a Type I or II error.

32

3.5 MULTIVARIATE NORMALITY ASSUMPTION/UNDERLYING ASSUMPTIONS

Assumptions are made when utilising multivariate statistics. When working with several

multivariate populations of dioptric powers, we assume that the populations have

multivariate normal distributions (Harris, 1992b). In dioptric power this is regularly not the

case and is often visible when analysing scatter plots (Harris, 1992b). The central limit

theorem has been mentioned concerning this problem (Harris, 1990c). In very basic terms,

the central limit theorem claims that any distribution of a population will be normally

distributed if sufficiently large quantities of data are collected from the population. As an

alternative, models of robustness could be investigated. We will not be exploring any of

these.

When using hypothesis testing on the means of several populations, one assumes that the

variance-covariance of the populations are the same. If the assumption is not met, it

becomes one of the multivariate Behrens-Fisher type problems (Harris, 1992b). There are

proposed solutions available for this problem, but none of them are regarded as being

reasonable and exact (Krishnamoorthy et al, 2004). No attempt was made in this study to

establish whether the data used was normally distributed or if the variance-covariance of

the populations were the same.

When populations have different variance-covariances and/or are not normally distributed,

it is necessary to proceed with caution when using the normal methods, as it increases the

odds of coming to wrongful conclusions (Harris, 1992b); in such cases it is imperative to use

the graphical representation of the data to aid with the interpretation thereof.

It is easier to interpret the dioptric power data from the graphical representation than the

numerical representation thereof, but both these methods should ideally be used in

conjunction with each other to ensure that the most reliable conclusions are drawn (Gillan,

1998; Harris, 1990c; Malan, 1993).

33

3.6 POSSIBLE OUTLIERS

Outliers are data points that are significantly different from the rest of the data points in a

sample. The outliers in a set of data are not necessarily wrong measurements and could

very well be true data points, thus we deliberately refer to these points as possible outliers.

If a study involves large quantities of data, it is much easier to identify possible outliers by

looking at the graphical representation of the data, than looking at the raw data; even more

so in the cases where the data consists of multivariate concepts. Possible outliers could be

present for a number of different reasons and should not necessarily be interpreted as

negative. They could make the researcher aware of measurements that were not entered

accurately. Possible outliers make it necessary for the researcher to recheck all the data in

that sample.

Possible outliers could also be caused by the tear film, blinking of the eye, instrumentation

errors or errors made by the operator of the instrument used for capturing the

measurements (Rubin et al, 1995). Depending on the research and data at hand, outliers

could be very interesting.

If the raw data includes a possible outlier, one should be wary of its influence on the

sample. One or two possible outliers could notably change the statistical conclusion derived

from the sample (Rubin et al, 1995). Since the data point is present in the measurements,

we cannot simply remove it, but it is sensible to represent the data with and without the

possible outliers present. In this way the impact of the possible outliers on the set of data

can be established. The presence of possible outliers could have a significant impact on the

conclusions drawn from a study as it could vastly affect the spread of the data and the

orientation of the concerned distribution ellipsoid.

Possible outliers in this study are seen as data points (representing measurements) that are

very different from the other data points of the sample represented on a stereo-pair scatter

plot. The data point is far removed from the cluster of data points in the sample, and can

easily be singled out if it is not too diverse, or if the scale of the graph allows it.

34

Figure 3.6.1 is a stereo-pair scatter plot presenting the measurement of Subject 2’s right

eye. Two green data points, representing measurements taken at the one-month

measurement session, are far removed from the cluster of green data points, and were

identified as possible outliers. The two possible outliers were removed from the data set

and the stereo-pair scatter plot reconstructed in Figure 3.6.2 using the altered data set.

Note that the scale used in Figure 3.6.2 is three times smaller than the scale used in Figure

3.6.1, as the possible outliers could not be identified on a scatter plot with the same scale as

Figure 3.6.2. The green (one-month) distribution ellipsoid in Figure 3.6.1 seems much larger

than the other ellipsoids on the same scatter plot, but in Figure 3.6.2 the green (one-month)

ellipsoid produced by the altered data set (data set without the two possible outliers) is

more similar to the other ellipsoids on the same scatter plot even though the green ellipsoid

still seems to be the largest on the scatter plot. Removing the two possible outliers from

the data set resulted in a change in the spread of the data points, which resulted in a

smaller green (one-month) distribution ellipsoid in Figure 3.6.2 when compared to the green

(one-month) ellipsoid in Figure 3.6.1.

In the treatment group both eyes of Subject 2, the right eye of Subject 5, the left eyes of

Subjects 8 and 9 and in the non-keratoconic control group the left eye of non-keratoconic

control Subject 5, possible outliers were identified. The means and variance-covariances

were recalculated for the concerned measurement sessions and the scatter plots were

reproduced without these possible outliers.

Figure 3.6.1 Presenting the measurement data of the four measurement sessions of the right eye of Subject 2. The before measurements are presented in black, one-week measurements in red, one-month measurements in green and the six-month measurement session in blue. Axis length is 9 D and the tick interval is set at 3 D. Origin is set at 47.5 I D

9 I

9 K

9 J

9 I

9 K

9 J

9 I

9 K

9 J

9 I

9 K

9 J

9 I

9 K

9 J

9 I

9 K

9 J

9 I

9 K

9 J

9 I

9 K

9 J

35

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

Figure 3.6.2 Stereo-pair scatter plot presenting the measurement data of Subject 2’s right eye after the removal of two possible outliers from the one-month measurement data. Axis length is 3 D and the tick interval is set at 1 D. The origin is set at 47.5 I D.

36

CHAPTER 4

EXPERIMENTAL METHOD

37

4.1 INTRODUCTION

Subjects were recruited from the patient base of ophthalmologists in private practices.

Prior to the start of the study, each ophthalmologist was approached, the study was

explained and permission was requested to discuss the study with potential subjects and to

gain access to the ophthalmologist’s medical records of the subject (if applicable) by signing

a consent form (see Appendix A). Only subjects that consulted the ophthalmologist for

consideration for CXL and who complied with the necessary requirements by the

ophthalmologist, for CXL, were considered for participation in this study. The CXL

procedure, risks, contra-indications, expectations, benefits and consent for the CXL surgical

procedure were discussed and obtained by the relevant ophthalmologist as per usual

protocol before a CXL procedure is performed by a surgeon.

Before patients were accepted as subjects in this study:

• The patient was invited to take part in the study.

• The study was explained to the potential subject.

• An information letter explaining the study was given to the subject (see Appendix B).

• The potential subject had to sign a consent form (see Appendix C). A copy of the

signed consent form (with follow-up examination dates confirmed with the potential

subject) was also given.

Exclusion criteria:

• Subjects older than thirty-five years of age at the time of the CXL procedure were

excluded from the study, as the risk of post-operative complications increases

after thirty five-years of age (Koller et al, 2009b).

• If any systemic or hereditary diseases or syndromes were present, the subject was

excluded from the study as these could influence the study’s outcome in ways that

we might not understand.

• Any previous corneal surgery excluded a potential subject from the study.

• Acute hydrops and corneal scarring excluded potential subjects.

38

Participation was voluntary and it was made clear to all potential subjects that they could

withdraw from the study at any time, but that we would appreciate notification of this

intention. A total of eleven subjects were enrolled in the treatment group for the study. It

was envisaged that a minimum of ten subjects would complete the six-month follow-up

period. Time constraints were a factor in the number of subjects who would be able to

complete the six-month follow-up. In this study the subjects needed to come in for two

extra follow-up examinations, over and above the normal follow-up examinations required

by the ophthalmologist.

A consent form (see Appendix C) had to be signed by the subject before being enrolled in

the study. The consent form allowed us to use all information related to the subjects in the

study and to ensure that they understood the nature of the study and what it entailed. An

information letter about the study (see Appendix B) as well as a copy of the subject’s signed

consent form was given to the subject on the day of enrolment.

4.2 STUDY PROTOCOL

All measurements were taken in the private practice of one specific ophthalmologist

partaking in the study. Only one autokeratometer, kept in a separate room, was used in the

study in an attempt to limit instrument variation and to try to ensure constant ambient

illumination for each measuring session. It was not necessary to change any light bulbs

within the two-and-a-half-year period in which the data collection of the study took place.

Fifty K-readings were taken from each subject at the pre-operative and follow-up visits. The

acquisition of K-readings was done using a NIDEK TONOREF II Autorefractor / Keratometer /

Non-Contact Tonometer, which is non-invasive and poses no known risk to the subject. The

study was pre-approved by the Ethics Committee of the Faculty of Health Science,

University of Johannesburg.

39

The sequence of procedures occurred as follows:

• The study was explained and the consent form signed. The first fifty

keratometric measurements were taken of the eye undergoing the procedure.

CXL procedure was undertaken.

• One week following CXL procedure: Fifty K- readings were taken.

• One month following CXL procedure: Fifty K-readings were taken.

• Six months after CXL procedure: Fifty K-readings were taken.

4.3 MEASUREMENT PROTOCOL

While taking the keratometry measurements of each subject, the subject was positioned on

a chair in front of the autokeratometer, the height of the hydraulic table upon which the

keratometer is placed was adjusted for the patient’s comfort. The instrument was set on

manual and programmed to take only autokeratometric readings as opposed to

autorefractive and tonometry readings. Each subject was instructed to place their chin in

the chinrest of the instrument and press their forehead onto the forehead stabilisation and

positioning bracket; the chinrest was adjusted until the subject confirmed a comfortable

position. The subject was instructed to keep their head still, refrain from talking and to

fixate on the internal target of the instrument before and while measurements were taken.

The instrument was refocused by pulling back the joy-stick to defocus the image seen on the

screen after every measurement. A button on the joy-stick was pressed to induce the

instrument to take a measurement. With every press of the button, three keratometric

readings were taken and a mean of the three recorded; after the completion of all three

readings the mean was printed. In some cases the instrument couldn’t take all three

readings with one press of the button and the button had to be pressed again, in all cases

the measurement was only used when all three readings were present to ensure

consistency throughout the measuring process. After printing the tenth successive set of

measurements, each subject was instructed to sit back and blink a few times. The rest

period lasted only a few seconds. Thereafter, four more measurement sessions were

completed. On average it took approximately fifteen minutes to complete an entire

40

measuring session on an eye. In the cases where both eyes of a subject were measured it

was done in one sitting.

4.4 MEASUREMENT GROUPS

Each of the fifty autokeratometry measurements taken, at each consultation, was entered

into custom-developed software developed by WF Harris and DJ Malan and modified by

A Rubin (Malan, 1993). The program converted K-readings into conventional (sphere,

cylinder and axis) and component (Fst, Fob, For) form. The conversion of the K-readings to a

dioptric power matrix expressed in component form makes it possible to use a host of

multivariate statistical methods to analyze the data. (Multivariate statistical analysis of

dioptric power is seen as significant as well as thorough and facilitates meaningful

conclusions derived from the data. It also made it possible to graphically represent each

measurement taken, on a stereo-pair scatter plot in three dimensional dioptric power

space.) For each eye all fifty measurements, for each consultation, are displayed in different

colours on the same scatter plot. The representation makes the data more comprehensible

and more accessible, giving more insight into the changes that might have taken place

between consultations. The means and variance-covariance matrices for each consultation

were derived and hypothesis tests on the means and variances were calculated for each

eye. Lastly, the differences between the first and the last measurement session for each

eye were computed. Hypothesis testing was done on the mean difference calculated for

each eye by comparing them with each other. The group of subjects was labeled the

treatment group and comprised of fourteen keratoconic eyes.

Subjects 4 and 7 were included in the treatment group, however but their contralateral eyes

were not treated and were included in the keratoconic control group. The measurements

on both keratoconic control eyes were taken at the same time as the contralateral treated

eye. The data was analysed in the same way as the data in the treatment group.

In the case of the non-keratoconic control eyes the measurements were taken at a first

measuring session (simulating the “before CXL” measurement session), second

measurements session a week after the first session, the third session a month after the first

41

and the last session six months later. From the treatment group Subjects 2 and 5 could not

attend the one-month and the one-week measurements sessions respectively, resulting in

only three measuring sessions for these eyes. In the non-keratoconic control group, control

Subject 6 was unavailable for the one-month measurement session in both eyes, giving us

three sessions for each eye.

A non-keratoconic control group, consisting of twelve eyes of six subjects, underwent the

same consent and measuring procedure as the treatment group over a six-month follow-up

period, but did not undergo the CXL procedure and none of these subjects had keratoconus.

The data from this group was again analysed with multivariate statistics and made it

possible to construct scatter plots, do hypothesis tests on the means and variance-

covariance matrices and calculate the difference for each eye from before to after the six-

month follow-up period and lastly to perform hypothesis testing on the means seen for each

eye.

A calibration eye (test eye) was included in the study. The measuring sessions on this eye

were done at random times throughout the two and a half years that data was gathered for

the other subjects. The test eye was measured in an attempt to ensure consistent

measurement variation within the instrument throughout the study. The K-readings for the

test eye were analysed and measured in the same fashion as the other three groups of

subjects.

Lastly, the mean differences for each eye seen in three of the categories (treatment,

keratoconic control and non-keratoconic control) were graphically represented on the same

scatter plot to compare changes seen in the keratometric behaviour of the individual eyes in

group form.

42

CHAPTER 5

RESULTS

43

5.1 INTRODUCTION

The twenty-nine “eyes” involved in the study were divided into four categories: one test

eye, the treatment group (fourteen eyes), the keratoconic control group (two eyes) and the

non-keratoconic control group (twelve eyes). The four categories, as well as each eye within

the distinctive categories, are first considered separately. The mean dioptric power of the

fifty measurements taken at each measurement session is represented in a table in both

conventional and component notation and the variance-covariances for each measuring

session are given in a second table.

5.1.1 STEREO-PAIR SCATTER PLOTS

The measurements are represented on stereo-pair scatter plots in three-dimensional

dioptric power space. Graphical representation makes it easier to visually assess

information about the data and to better understand and appreciate the changes seen from

one measurement session to the next. Each data point on a scatter plot represents one

keratometric measurement and the data points include an ellipsoidal surface of constant

probability density set at a 95% level of confidence on the figures. Each set of fifty

measurements are colour coded to ease the differentiation of the various measurement

times on the scatter plots. The pre-operative data is displayed in black, the one-week data

in red, the one-month in green and the six-month data in blue.

Each subject eye has three stereo-pair scatter plots (see Section 3.3.1) representing the

same data, but have been rotated in three-dimensional space to facilitate ease of discerning

any changes in measurements seen at the different measurement sessions. The original

stereo-pair scatter plot for each eye is found in the body of the text (refer to Figure 5.3.1.1

as an example), whereas the other two are included in Appendix D. The origin of each

scatter plot is set at a value related to the mean of each set of measurements for the

specific eye. The origin of the scatter plots varies from one subject to the next, hence the

origin is stated in the figure caption for each figure. All the scatter plots have an axis length

of 3 D with tick intervals of 1 D on each axis. Keeping the scale of the scatter plots constant

throughout the study puts the relevant changes seen for each eye into perspective. The test

44

eye results include a further set of three scatter plots, over and above the regular scale, with

an axis length of 0.1 D, to provide the means to distinguish between measurements and

emphasize the reduced magnitude of the measurements relative to measurements

obtained from living eyes.

5.1.2 HYPOTHESIS TESTS

For each eye hypothesis tests (see Section 3.4.3) were carried out on the means and

variance-covariances of each set of measurements; comparing the means and variance-

covariance of the measurement sessions respectively with each other for the full follow-up

period. The null hypothesis states: no statistically significant change took place between the

means or variance-covariances within the specific eye over the six-month follow-up period.

If the null hypothesis was accepted, it meant that any changes in the curvature of the eye

were not statistically significant. Alternatively, if the null hypothesis is rejected, it means

that statistically significant change did take place between the means and variance-

covariances of an eye over the completed follow-up period. In the treatment group the

change could be attributed to the CXL procedure, whereas for the keratoconic control eyes

the change could be attributed to progression of keratoconus. If the null hypothesis is

rejected for an eye in any of the control groups, it would indicate that ordinary day to day

fluctuation in keratometric behaviour by itself could be enough to give a statistically

significant change in curvature.

5.1.3 OUTLIERS

Possible outliers were identified in both the treatment and control groups. In the treatment

group, the right eye of Subjects 2, 5 and 8, as well as the left eye of Subjects 2 and 9

presented with possible outliers. In the non-keratoconic control group only the right eye of

non-keratoconic control Subject 5 showed a potential outlier. Possible outliers were

removed from the corresponding data sets and the means, variance-covariance and critical

values for hypothesis testing were recalculated and the figures reconstructed (for more

information and an example refer to Section 3.6). The changes seen in each eye regarding

45

the possible outliers are discussed after the presentation of results and discussion of the

corresponding original data set.

5.1.4 MEAN DIFFERENCES

The mean overall difference in corneal curvature between the first (or pre-operative)

measuring session and the last measuring session is of importance to obtain the overall

change present at the end of the follow-up period. To investigate this overall change for an

eye, the fifty measurements of the first measuring session was subtracted from the fifty

measurements of the last session, this was done pairwise for the fifty measurements. The

mean change for each eye was calculated from the fifty differences and reported in a table

which is presented at the end of each category (test eye in Table 5.2.5, the fourteen eyes

included in the treatment group in Table 5.3.16.1, the two eyes included in the keratoconic

control group in Table 5.4.4.1 and the twelve eyes included in the non-keratoconic control

group in Table 5.5.14.1). The mean difference represents the total change in keratometric

behaviour seen at the end of the study for each subject eye and does not consider any

change in curvature during this time period.

In Section 5.6.1 the four categories of eyes included in the study are compared to each

other. The mean difference and variance-covariance within each category as a whole

(except for the test eye) is presented in Table 5.6.1 and Table 5.6.2 respectively. The mean

differences of the eyes within each category (except for the test eye) are presented in a

scatter plot (see Figure 5.6.1) together for ease of comparison.

46

5.2 TEST EYE

The test eye is the calibration tool used for most autorefractors and autokeratometers. It

comprises of a curved piece of glass housed in a plastic bracket, which can be attached to

the chin rest of the machine to enable the operator of the machine to take measurements

of the curvature of the glass surface. It is accompanied with the exact curvature value of

the surface as well as the dioptric power of the surface in conventional notation.

The test eye was used in this study to make sure that the autokeratometer remains

calibrated throughout the duration of the study and to establish what degree of variation

this static surface would yield. Any spread of the measurements in one measuring session

would probably not be caused by a change in the surface of the test eye, as expected in live

corneal tissue, but would be attributed to the measuring instrument itself

(autokeratometer) or the operator of the keratometer.

Fifty measurements were taken of the test eye on four different occasions, as was the case

with all the eyes included in the study. The main difference was that the measurement

sessions were not taken on the same timeline as the other eyes, but were taken at random

times throughout the two and a half years that formed the measuring component of the

study.

Statistical analysis of the data obtained from the test eye is provided in Tables 5.2.1 and

5.2.2. Table 5.2.1 presents the mean for each measurement session in both conventional

and component notation. The means seem to be closely related to each other. Little

oblique antistigmatic or ortho antistigmatic power is measured in the curvature of the test

eye in any of the measurement sessions. The stigmatic components of dioptric power seem

to be related to each other. Table 5.2.2 displays the variance-covariance data extracted

from the variance-covariance matrix calculated for each measuring session. The values in

Table 5.2.2 are extremely small; they were not rounded off to three decimals as seen in the

variance-covariance data tables in the rest of the chapter to ensure that most values were

not reported as zero.

47

The measurements of each of the four measurement sessions are graphically presented in

Figure 5.2.1 (and in Appendix D 1 (a) and (b) in different orientations) on a scatter plot with

an axis length of 3 D and a tick interval of 1 D, which is the scale that is used throughout the

study, except where stated otherwise. It is difficult to distinguish between the

measurements in the scatter plot presenting the measurements taken on the test eye

(Figure 5.2.1, Appendix D 1 (a) and (b)), as the data points are situated close to each other.

The scatter plot was reconstructed with a greatly reduced scale in Figure 5.2.2 (Appendix D

1 (c) and (d)) on a scatter plot with an axis length of 0.05 D. Only three data points, two

blue and one green, are distinguishable in Figure 5.2.2 (Appendix D 1 (c) and (d)) even

though two hundred measurements are represented on the scatter plot. The other

measurements can’t be seen as all two hundred measurements are superimposed on each

other, giving us only the three data points representing the two hundred measurements.

This attests to the accuracy of the autokeratometer and the operator of the instrument.

Table 5.2.1 The means of the fifty autokeratometry readings of the test eye for each of the four measurement sessions are shown. Means are presented in both conventional and component notation. In conventional notation the sphere and cylinder are measured in diopters (D) and the axis in degrees, whereas in component notation all the components are measured in diopters (D).

DIOPTRIC POWER

MEASUREMENT

SESSION

CONVENTIONAL NOTATION COMPONENT NOTATION

SPHERE CYLINDER AXIS Fst/I For/J Fob/K

First 42.23 0.01 90.0 42.23 0.00 0.00

Second 42.24 0.02 90.0 42.23 0.01 0.00

Third 42.23 0.01 90.0 42.22 0.00 0.00

Fourth 42.24 0.01 90.0 42.23 0.00 0.00

48

Table 5.2.2 The variance-covariance of the test eye for the follow-up period are shown. Variance-covariance has units of diopters squared (D2).

VARIANCE-COVARIANCE DATA

MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

First 0.00040 0.00009 0.00000 0.00005 0.00000 0.00000

Second 0.00026 0.00016 0.00000 0.00013 0.00000 0.00000

Third 0.00051 0.00010 0.00000 0.00004 0.00000 0.00000

Fourth 0.00010 0.00010 0.00000 0.00010 0.00000 0.00000

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

Figure 5.2.1 Scatter plot illustrating the measurements taken on the test eye. The measurements were taken at four different occasions, which are represented with different colours on the graph. The first measurement session is shown in black, the second in red, the third in green and the fourth measurement session in blue, but the colours are superimposed making only the blue data point visible on the graph. Origin is at 42.20 I D. Axis length is 3 D and tick interval is set at 1 D on each axis.

0.05 I

0.05 K

0.05 J

0.05 I

0.05 K

0.05 J

0.05 I

0.05 K

0.05 J

0.05 I

0.05 K

0.05 J

0.05 I

0.05 K

0.05 J

0.05 I

0.05 K

0.05 J

0.05 I

0.05 K

0.05 J

0.05 I

0.05 K

0.05 J

Figure 5.2.2 Illustrates the same measurements seen in Figure 5.2.1, but for clarity the scale of the scatter plot was greatly decreased to emphasize the similarity between the measurements and to provide the means to distinguish between the measurements on the scatter plot. The origin is at 42.20 I D and the axis length is 0.05 D on each axis.

49

Two hypothesis tests were done, one comparing the means of the four measurement

sessions in component notation (data presented in Table 5.2.1) and the other on the

variance-covariance of the four measurement sessions (data presented in Table 5.2.2). The

reason for this is to establish whether the means and variance-covariances of the four

different measurement sessions are significantly different or not when each is compared to

the other by multivariate analysis. In the hypothesis tests for both the means and variance-

covariance, the null hypothesis is rejected if the test statistic is greater than the critical

value. If the null hypothesis is rejected, it implies that the means and variance-covariances

respectively of the four measurement sessions are statistically significantly different from

each other at a 95% level of confidence. The null hypothesis for the means (Table 5.2.3) and

the null hypothesis for the variance-covariances (Table 5.2.4) of the test eye were rejected.

Even though the means and variance-covariances for the four measurement sessions

respectively were found to be statistically significantly different, the differences are

probably not clinically significant. The small differences seen in the means presented in

Table 5.2.1 and the variance-covariances in Table 5.2.2 would not have an influence on the

dioptric power in a clinical setting, as dioptric power is customarily measured in 0.25 D steps

(a small number of practitioners use 0.12 D steps) and would be negligibly small in clinical

practice.

The difference between the first and last measurement sessions is calculated by subtracting

the fifty measurements from the last measurement session from the fifty measurements of

the first measurement session whereafter a mean difference and a mean variance-

covariance difference is calculated from the resulting fifty measurements. The mean

difference for the test eye is presented in Table 5.2.5 and the mean variance-covariance

difference in Table 5.2.6 which, in both cases, were found to be insignificant in clinical

practice. The mean difference of the test eye in Table 5.2.5 is presented to the fourth

decimal (whereas the mean difference of the other eyes included in the study are given to

the second decimal), and the mean variance-covariance difference in Table 5.2.6 is

presented to the fifth decimal (in contrast to the mean variance-covariance difference of the

other eyes included in the study which is given till the third decimal), this is an indication of

how small the differences seen in the test eye within the six-month follow-up period is,

especially when compared to the mean difference seen in the treatment group in

50

Table 5.3.16.3 and the mean variance-covariance difference of the treatment group in

Table 5.3.16.4.

Table 5.2.3 The critical value and test statistic for the hypothesis test done on the means of the four measurement sessions of the test eye are shown. The null hypothesis was rejected if the test statistic (theta) was bigger than or equal to the critical value.

TEST STATISTIC CRITICAL VALUE

SUBJECT THETA

Test eye 0.071 0.066

Table 5.2.4 The critical value and test statistic for hypothesis test done on the variance-covariance of the four measurement sessions of the test eye. The null hypothesis was rejected if the test statistic (µ) was bigger than or equal to the critical value ( ).


SUBJECT µ

Test eye 2698.718 28.869

Table 5.2.5 Presents the mean difference between the first and the last measurement sessions of the test eye. Means are presented in both conventional and component notation. In conventional notation the sphere and cylinder are measured in diopters (D) and the axis in degrees, whereas in component notation all the components are measured in diopters (D).

DIOPTRIC POWER

SUBJECT CONVENTIONAL NOTATION COMPONENT NOTATION


Test eye 0.0084 0.0011 90 0.0079 0.0005 0.0000

Table 5.2.6 The mean variance-covariance derived from the difference between the first and last measurement sessions for the test eye. Variance-covariance has units of diopters squared (D2).


SUBJECT VARIANCE COVARIANCE

I J K I-J J-K I-K

Test eye 0.00041 0.00013 0.00000 0.00008 0.00000 0.00000

51

5.3 TREATMENT GROUP

The treatment group consists of fourteen eyes of eleven subjects. Each eye in this group

underwent the crosslinking procedure and will be regarded separately. The keratometric

behaviour of each eye is provided in two tables, one presenting the mean dioptric power for

each measurement session in both conventional and component notation and the second

table the variance-covariance matrix data for each session. A scatter plot allows graphical

representation of the fifty measurements taken for each measurement session. Each

measurement session is presented in a different colour assisting with the understanding of

the changes taking place. The measurement data from the pre-operative or before

measurement session is presented in black, the one-week post-operative measurement

session in red, the one-month post-operative session in green and the six-month post-

operative measurement session in blue.

The fifty data points representing the fifty measurements taken at each measurement

session present as clusters (of different colours) on the stereo-pair scatter plots (see Figure

5.3.1.1 for an example). When one or more of the data points are markedly removed from

the cluster, resulting in a noticeably larger distribution ellipsoid (when compared to the

distribution ellipsoids representing the other measurement sessions on the scatter plot as

seen with the red data in Figure 5.3.3.1), the detached data points could be regarded as

possible outliers. The concept of a possible outlier is discussed in Section 3.6. Possible

outliers were identified in the right eyes of treatment Subjects 2, 5 and 8 and in the left eyes

of treatment Subjects 2 and 9 and are elaborated on in the discussions on each of these

eyes. Where possible outliers were identified, abnormal measurements were removed

from the data set and the data reanalyzed. An altered mean and variance-covariance was

calculated for the corresponding altered data set and the scatter plots reconstructed with

the altered data. The likely influence of the removed data points is discussed for the

concerned eyes

Similar to the test eye (Section 5.2), two multivariate hypothesis tests were done on the

means and variance-covariances respectively for all four measurement sessions for each

eye. The discussion of each eye in the treatment group includes two tables on the

52

hypothesis tests, one presenting the critical value and test statistic of the means and the

other for the critical value and test statistic of the variance-covariance of the relevant eye.

Section 5.3.15 provides a summary of the hypothesis tests done on all fourteen eyes in the

treatment group.

The difference between the means and variance-covariances of the before and six-month

measurement sessions were calculated to attain the amount of change that transpired in

the six-month follow up period. At the end of the discussion of each of the fourteen eyes a

table is provided with the difference in means and another table presenting the difference

in variance-covariances. An analysis and stereo-pair scatter plot of all the differences in

means and variance-covariances of all fourteen eyes together is provided in Section 5.3.16.

53

5.3.1 SUBJECT 1 LEFT EYE

Only the left eye of Subject 1 was included in the study. In Figure 5.3.1.1 the measurement

data of each of the four measurement sessions are presented in clusters of data points

including their corresponding 95% distribution ellipsoids in different colours, black (before),

red (one-week), green (one-month) and blue (six-month measurements). See Appendix D

2.1 (a) and (b) for the rotated scatter plots of the same data presented in Figure 5.3.1.1. See

Section 3.3.1 for a review of stereo-pair scatter plots. In Figure 5.3.1.1 the cluster of red

data points (one-week measurements) seems unusual in size and orientation when

compared to the other clusters on the scatter plot. In Figure 5.3.1.1 (Appendix D 2.1 (a) and

(b)) it seems that the red (one-week) distribution ellipsoid is the biggest in size and the black

(before), green (one-month) and blue (six-month) distribution ellipsoids are comparable in

size each containing a tight cluster of data points. In Appendix D 2.1 (b) it seems that the

red (one-week) cluster is the only cluster that orientates along the K-axis whereas the other

three clusters appear to lie along the I-J plane. In Figure 5.3.1.1 (and more so in Appendix D

2.1 (a)) the red cluster (one-week measurements) appears to be the highest and the blue

cluster (six-month measurements) the lowest on the I-axis

In Tables 5.3.1.1 and 5.3.1.2 the one-week data seems different and the before, one-month

and six-month data for the means and variance-covariance seem more similar. Considering

Table 5.3.1.1 the stigmatic component (Fst/I) increased one week after the CXL procedure,

at the one-month measurement session the stigmatic component decreased and then

decreased more at the six-month measurement session which presents with the lowest

stigmatic value for the entire six-month follow-up period. From the changes in the stigmatic

component seen in Table 5.3.1.1, the curvature of the cornea became steeper one week

after the CXL procedure, while one month post-operatively the cornea is flatter. At six

months post-operatively the cornea was at its flattest. Comparing the antistigmatic

components (For/J and Fob/K) of the four measurement sessions in Table 5.3.1.1, the

antistigmatic component of the one-week measurement session is abnormal when

compared to the other measurement sessions, which correlates with the orientation change

of the red (one-week) ellipsoid seen in Appendix D 2.1 (b). In Table 5.3.1.2, the variance

data of the one-week session is the largest in magnitude and again stands out, the variance-

54

covariance correlates with the spread of the data, meaning that the most variation was seen

between the fifty measurements taken at the one-week measurement session. This links

back to the red (one-week) distribution ellipsoid being the largest on the scatter plots in

Figure 5.3.1.1 (Appendix D 2.1 (a) and (b)). The one-week measurements presenting with

the highest level of variation in the six-month follow-up could indicate that the cornea was

more unstable one week post-operatively. It seems that the shape of the cornea changed

and is less stable after the CXL procedure which is demonstrated by the increase in stigmatic

and antistigmatic components (seen in Table 5.3.1.1) and increase in variation (seen in Table

5.3.1.2) measured at the one-week measurement session; thereafter the shape of the

cornea gradually returned to its pre-operative shape over the six-month follow-up period,

indicated by the decrease measured in both dioptric power (Table 5.3.1.1) and variance-

covariance (Table 5.3.1.2) measured at the one-month measurement session and the

further decrease in dioptric power (Table 5.3.1.1) and variance-covariance (Table 5.3.1.2)

measured at the six-month measurement session.

Table 5.3.1.1 The means of the four measurement sessions expressed in both conventional and component notation. In conventional notation the sphere and cylinder are measured in diopters (D) and the axis in degrees, whereas in component notation all the components are measured in diopters (D).

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 53.72 2.38 177.82 52.53 1.19 0.09

One-week 53.83 1.40 29.51 53.13 0.36 0.60

One-month 54.41 2.94 179.62 52.94 1.47 0.02

Six-month 53.59 3.35 2.74 51.91 1.66 0.16

55

Table 5.3.1.2 Variance-covariance for each of the four measurement sessions. Variance-covariance has units of diopters squared (D2).


MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

Before 0.019 0.014 0.010 0.006 0.002 0.003

One-week 0.021 0.035 0.061 0.005 0.005 0.010

One-month 0.013 0.016 0.005 0.006 0.002 0.002

Six-month 0.014 0.010 0.006 0.007 0.000 0.002

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

Figure 5.3.1.1 Stereo-pair scatter plot representing clusters of measurements of Subject 1. The before measurement session (black), one-week (red), one-month (green) and six-month measurement session (blue). The 95% distribution ellipsoid for each session is included. Origin is at 52.5 I D. Axis length is 3 D and tick interval is set at 1 D on each axis.

The hypothesis test conducted on the means of the four measurement sessions suggests

that the null hypothesis cannot be accepted (see Table 5.3.1.3). This result indicates that

the means for the four measurement sessions are significantly different.

Table 5.3.1.3 Critical value and test statistic for hypothesis test of the means of the four measurement sessions of Subject 1. The null hypothesis is rejected if the test statistic is bigger than or equal to the critical value.


SUBJECT THETA

Subject 1 OS 0.948 0.066

56

Table 5.3.1.4 Presenting the critical value and test statistic for hypothesis test done on the variance-covariance of the four measurement sessions of Subject 1


SUBJECT µ

Subject 1 OS 155.449 28.869

To establish the degree of change that took place at the end of the six-month follow-up, the

mean difference between the measurements of the before and last measurement sessions

was calculated. Table 5.3.1.5 presents the mean dioptric power difference that took place

at the end of the six-month follow-up period. The difference seen in the stigmatic

component is negative indicating that the cornea became flatter six months post-

operatively and corresponds to the blue (six-month) ellipsoid being lower on the I-axis when

compared to the black (before) ellipsoid in Appendix D 2.1 (a); a change has also taken place

in the antistigmatic components.

Table 5.3.1.5 Presents the mean difference between the first and the last measurement sessions of the left eye of Subject 1. Means are presented in both conventional and component notation. In conventional notation the sphere and cylinder are measured in diopters (D) and the axis in degrees, whereas in component notation all the components are measured in diopters (D).

DIOPTRIC POWER



Subject 1 OS 0.08 1.08 13.82 0.62 0.48 0.25

Table 5.3.1.6 The mean variance-covariance derived from the difference between the first and last measurement session for the left eye of Subject 1. Variance-covariance has units of diopters squared (D2).



I J K I-J J-K I-K

Subject 1 OS 0.036 0.028 0.014 0.018 0.000 0.003

57

In summary, Figure 5.3.1.1 gives a visual exposition of how the data sets varied over the six-

month follow-up period. The black data set (before) gives a visual indication of the

curvature of the cornea before CXL was performed. The red data set (one-week) shows how

the cornea steepened and that the measurements became more variable. The green (one-

month) and blue (six-month) data sets show how the cornea recovered over six months

following surgery, with a final flattening of the cornea indicated by the blue (six-month) data

set.

58

5.3.2 SUBJECT 2 RIGHT EYE

Both eyes of Subject 2 are included in the study; this is also the case with Subjects 4, 5, 7, 8

and 9. As keratoconus is usually a bilateral phenomenon, with time both eyes frequently

undergo the CXL procedure. In Figure 5.3.2.1 (Appendix D 2.2 (a) and (b)) each of the four

measurement sessions (displayed in different colours) are represented by a cluster of data

points and a 95% distribution ellipsoid. The green cluster (one-month measurements)

seems more spread out, resulting in a large green ellipsoid which stands out compared to

the other three ellipsoids which contain tighter clusters of data points. Most of the red

(one-week) data points appear the highest on the I-axis in the orientation of Figure 5.3.2.1

and Appendix D 2.2 (a) with the black (before) and blue (six-month) data points

simultaneously appearing the lowest on the I-axis. The black (before) and blue (six-month)

ellipsoids lie along the I-axis and seem similar in orientation, the green (one-month) and red

(one-week) ellipsoids seem more slanted toward the I-J plane where the orientation of the

red (one-week) ellipsoid seems to differ the most from the other ellipsoids in Figure 5.3.2.1

and Appendix D 2.2 (a).

Regarding the component notation data in Table 5.3.2.1, the mean of the one-week data

deviates the most from the means of the other measurement sessions and the mean of the

before and six-month data are similar. The stigmatic component (Fst/I) is the largest at the

one-week follow-up session, followed with a lesser value for the stigmatic component at the

one-month session and the lowest stigmatic value is seen at six months, suggesting that the

cornea become steeper one-week post-operatively, became slightly flatter one-month post-

operatively and continued to flatten until it was slightly flatter at the six-month post-

operative measurement session when compared to the pre-operative (before)

measurement session, which compares well with the changes seen in Subject 1 (Section

5.3.1). In Table 5.3.2.1 the one-week mean demonstrates the largest change in

antistigmatic power (For/J and Fob/K), which is graphically suggested in Figure 5.3.2.1

(Appendix D 2.2 (a) and (b)) by the orientation of the red (one-week) ellipsoid that deviates

the most when comparing all four ellipsoids. Comparing the variance-covariance data in

Table 5.3.2.2, the mean of the one-month measurements session is abnormally large, the

variance-covariance data relates to the spread or variation seen between the fifty

59

measurements in a measurement session and indicates that the largest variation between

measurements presented at the one-month measurement session and correlates with the

size of the green (one-month) ellipsoid being the largest in Figure 5.3.2.1 (Appendix D 2.2 (a)

and (b)). In Table 5.3.2.1 presenting the dioptric power means and Table 5.3.2.2 presenting

the variance-covariances of all four measurement sessions the before and six-month after

measurement sessions are similar. In Figure 5.3.2.1, Appendix D 2.2 (a) and (b) the black

(before) data points and blue (six-month) data points and their corresponding ellipsoids

resemble each other in size, shape and orientation and a large part of each of the ellipsoids

intersect. The conclusion from these similarities is that the shape of the cornea seems not

to have changed a great deal following surgery (at six months post-operatively).

Table 5.3.2.1 The dioptric power means in component and conventional form for each of the four measurement sessions of the right eye of Subject 2.

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 48.85 4.82 125.57 46.44 0.78 2.28

One-week 52.97 6.74 113.51 49.60 2.30 2.47

One-month 50.69 4.65 117.62 48.36 1.32 1.91

Six-month 48.55 4.80 123.20 46.14 0.96 2.20

60

Table 5.3.2.2 The variance-covariance data for the entire six-month follow-up period.


MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

Before 0.130 0.053 0.014 0.067 0.022 0.024

One-week 0.093 0.092 0.028 0.075 0.351 0.032

One-month 2.099 0.616 0.369 0.805 0.026 0.159

Six-month 0.128 0.076 0.016 0.081 0.024 0.024

Figure 5.3.2.1 Stereo-pair scatter plot presenting the measurement data of Subject 2’s right eye. The measurement sessions are colour coded as follows: the pre-operative measurements (black), one-week (red), one-month (green) and six-month measurements (blue). Axis length is 3 D and tick interval is set at 1 D. Origin is set at 47.5 I D.

Figure 5.3.2.2 Presenting the measurement data of the four measurement sessions of the right eye of Subject 2. The before measurements are presented in black, one-week measurements in red, one-month measurements in green and the six-month measurement session in blue. Axis length is 9 D and the tick interval is set at 3 D. Origin is set at 47.5 I D

9 I

9 K

9 J

9 I

9 K

9 J

9 I

9 K

9 J

9 I

9 K

9 J

9 I

9 K

9 J

9 I

9 K

9 J

9 I

9 K

9 J

9 I

9 K

9 J

3 I

3 K

3 J

3 I

3 K3 J

3 I

3 K

3 J

3 I

3 K3 J

3 I

3 K

3 J

3 I

3 K3 J

3 I

3 K

3 J

3 I

3 K3 J

61

In Figure 5.3.2.1 the green (one-month) distribution ellipsoid is substantially larger than the

other distribution ellipsoids on the scatter plot. The green (one-month) data points visible

on the scatter plot are roughly grouped in the center of the distribution ellipsoid, suggesting

that other data points not visible on the scatter plot (the general scaling used throughout

the study was utilised in Figure 5.3.2.1, Appendix D 2.2 (a) and (b) to ease the comparison of

the different graphical presentations in the study) are influencing the size of the ellipsoid.

One of these seemingly abnormal data points is visible on the scatterplot rotated to look

down the I-axis (Appendix D 2.2 (b)). Figure 5.3.2.2 was constructed to represent the same

measurement data shown in Figure 5.3.2.1, Appendix D 2.2 (a) and (b) but on a much larger

scale (axis length is 9 D with a tick interval set at 3 D on each axis). The abnormal

measurements are seen as two green (one-month) data points positioned on either side of

the I-axis in the orientation in Figure 5.3.2.2. Examining the fifty measurements of the raw

one-month follow-up data set two seemingly abnormal measurements were identified and

were regarded as possible outliers. The two possible outliers were removed from the raw

one-month data set and the mean and variance-covariance were recalculated and all scatter

plots for the right eye of Subject 2 were reconstructed. Comparing the altered green (one-

month) ellipsoid in each of the reconstructed scatter plots in Figure 5.3.2.3, Appendix D 2.2

(c) and (d) to the original green (one-month) ellipsoid in Figure 5.3.2.1, Appendix D 2.2 (a)

and (b), the altered green (one-month) ellipsoid is similar to the original green (one-month)

distribution ellipsoid in orientation, but is much smaller. Table 5.3.2.3 presents the means

and Table 5.3.2.4 the variance-covariance of both the original one-month data set and the

altered one-month data sets respectively. Removing the possible outliers did not change

the means of the one-month data set by a large amount (as the means in Table 5.3.2.3 are

similar); on the contrary the possible outliers did influence the variance-covariance data

presented in Table 5.3.2.4 as the variance-covariance of the altered data set is distinctively

smaller than the variance-covariance of the original data set. The smaller variance-

covariance of the altered data set in Table 5.3.2.4 correlates with the smaller size of the

altered green (one-month) ellipsoid in Figure 5.3.2.3 and suggests that the variation in the

measurements of the one-month measurement set is smaller when the possible outliers are

removed.

62

Table 5.3.2.3 The original mean and altered mean (mean after removal of two possible outliers) for the one-month measurement session.

DIOPTRIC POWER

MEASUREMENT

SESSION



One-month 50.69 4.65 117.62 48.36 1.32 1.91

Altered one-

month 50.36 4.45 118.96 48.14 1.18 1.88

Table 5.3.2.4 Variance-covariance of the one-month measurement session with and without two possible outliers


MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

One-month 2.099 0.616 0.369 0.805 0.026 0.159

Altered one-

month 0.877 0.075 0.144 0.009 0.036 0.303

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

Figure 5.3.2.3 Stereopair scatter plot presenting the measurement data of Subject 2’s right eye after the removal of two possible outliers from the one-month measurement data. The origin is set at 47.5 I D.

From Table 5.3.2.5 and Table 5.3.2.6 both hypothesis tests on the different multivariate

components present in the means and variance-covariance data of all four measurement

63

sessions were rejected, which indicates that the difference in means and variance-

covariance for the four measurement sessions were found to be statistically significantly

different.

Table 5.3.2.5 Hypothesis test data for the means of the four measurement sessions of Subject 2’s right eye.


SUBJECT THETA

Subject 2 OD 0.781 0.066

Table 5.3.2.6 The critical value and test statistic for the hypothesis test done on the variance-covariance of the four measurement sessions of the right eye of Subject 2.


SUBJECT µ

Subject 2 OD 627.870 28.869

The difference between the means of the pre-operative (before) and six-month

measurement sessions were calculated (presented in Table 5.3.2.7) as well as the difference

between the means in variance-covariance of the before and six-month follow-up sessions

(seen in Table 5.3.2.8). The stigmatic component of the mean difference seen in Table

5.3.2.7 was minimal but negative, implying that the cornea became slightly flatter six

months post-operatively.

Table 5.3.2.7 Presents the mean difference between the first and the last measurement sessions of the right eye of Subject 2. Means are presented in both conventional and component notation. In conventional notation the sphere and cylinder are measured in diopters (D) and the axis in degrees, whereas in component notation all the components are measured in diopters (D).

DIOPTRIC POWER



Subject 2 OD 0.10 0.40 78.26 0.30 0.18 0.08

64

Table 5.3.2.8 The mean variance-covariance derived from the difference between the first and last measurement session for the right eye of Subject 2. Variance-covariance has units of diopters squared (D2).



I J K I-J J-K I-K

Subject 2 OD 0.187 0.126 0.030 0.113 0.048 0.045

In brief, Figure 5.3.2.3 presents a visual account of how the data sets varied over the six-

month follow-up period. The black (before) data set represents the curvature of the cornea

before CXL. The red (one-week) data set shows that the cornea became steeper and the

green (one-month) data set suggests that the cornea became flatter and that the

measurements were more varied at this stage. The blue (six-month) data set resembles the

black (before) data set which indicates that the curvature of the cornea returned to its pre-

operative curvature six months after CXL.


Data from only three measurement sessions were obtained as Subject 2 was unable to

attend the measurement session scheduled one month after undergoing CXL on his left eye.

We will only consider the data at hand and not speculate over the missing data. As a result

of the missed one-month measurement session the scatter plots presenting the

measurements of Subject 2’s left eye in Figure 5.3.3.1, Appendix D 2.3 (a) and (b) only

display three clusters of data points, the first representing the pre-operative (before)

measurement session in black, red for the one-month session and blue for the six-month

measurement session together with their corresponding 95% distribution ellipsoids. In

Figure 5.3.3.1, Appendix D 2.3 (a) and (b), the red (one-week) ellipsoid seems to stands out

because of its bigger size whereas the black (before) and blue (six-month) ellipsoids are

smaller and similar in size. The majority of the red (one-week) data points in Figure 5.3.3.1

and Appendix D 2.3 (a) are situated above the black (before) and blue (six-month) data

points in this orientation. The orientation of all three ellipsoids are comparable in Figure

5.3.3.1, Appendix D 2.3 (a) and (b) and lie mostly along the I-axis.

65

Similar to Subject 1 (Table 5.3.1.1) and the right eye of Subject 2 (Table 5.3.2.1) the one-

week measurement session has the largest stigmatic component (Fst/I in Table 5.3.3.1) over

the six-month follow up period correlating with the majority of the red (one-week) data

points seen higher on the I-axis on the stereo-pair scatter plots in Figure 5.3.3.1 and

Appendix D 2.3 (a) compared to the black (before) and blue (six-month) data points. It

seems to indicate that the cornea was the steepest at the one-week measurement session,

but then returned to a flatter form more similar to the pre-operative measurements.

In Figure 5.3.3.1, Appendix D 2.3 (a) and (b), the cluster of black (before) and blue (six-

month) data points look similar in size and orientation and seem to roughly superimpose on

each other. This observation suggests that the measurements taken at the before and six-

month measurement sessions are similar. Additionally, the variance-covariance of the

before and six-month measurement sessions in Table 5.3.3.2 are similar and the variance-

covariance of the one-week measurement session is higher. It correlates with the red (one-

week) cluster of data points being more spread out in Figure 5.3.3.1, Appendix D 2.3 (a) and

(b), indicating that the measurements of the one-week measurement session were more

varied than the measurements in the before and six-month sessions.

Table 5.3.3.1 The means of each of the three measurement sessions. Means are presented in both conventional and component notation. In conventional notation the sphere and cylinder are measured in diopters (D) and the axis in degrees, whereas in component notation all the components are measured in diopters (D).

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 44.79 1.91 34.8 43.83 0.33 0.90

One-week 45.64 1.73 46.1 44.77 0.03 0.86

Six-month 45.14 2.02 44.2 44.13 0.03 1.01

66

Table 5.3.3.2 The variance-covariance for all three measurement sessions. Variance-covariance has units of diopters squared (D2).


MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

Before 0.022 0.008 0.005 0.011 0.004 0.008

One-week 0.160 0.154 0.030 0.126 0.031 0.021

Six-month 0.024 0.009 0.006 0.010 0.005 0.011

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

Figure 5.3.3.1 Scatter plot presenting the measurement sessions of Subject 2’s left eye. The measurements were taken at three different occasions, which are represented with different colours on the graph. The graph shows the pre-operative measurements (black), one-week follow-up (red ellipsoid) and six-month measurement session (blue). Origin is at 44 I D. Axis length is 3 D and tick interval is set at 1 D on each axis.

The size of the red (one-week) distribution ellipsoid is large in comparison to the black

(before) and blue (six-month) ellipsoids in Figure 5.3.3.1 and Appendix D 2.3 (a) and (b). The

three red (one-week) data points visible outside the red (one-week) distribution ellipsoids in

Figure 5.3.3.1 and Appendix D 2.3 (a) and (b), were identified as possible outliers and were

removed from the data set of fifty measurements of the one-week measurement session.

Thereafter, the means and variance-covariance were recalculated for the one-week

measurement session and scatter plots reconstructed with the altered data. The

orientation of the altered red (one-week) ellipsoid in Figure 5.3.3.2 and Appendix D 2.3 (c) is

similar to the original red (one-week) ellipsoid in Figure 5.3.3.1 and Appendix D 2.3 (a), but

the size is smaller and the related variance-covariance for the altered one-week

measurement session (seen in Table 5.3.3.4) is less. It indicates that there is less variation

67

present in the measurements in the altered data set compared to the original one-week

data set.

Table 5.3.3.3. Table presenting the original mean and the altered mean (after removing three possible outliers) from the one-week measurement session.

DIOPTRIC POWER

MEASUREMENT

SESSION



One-week 45.64 1.73 46.1 44.77 0.03 0.86

Altered one-

week 45.60 1.77 45.4 44.72 0.01 0.88

Table 5.3.3.4 The original variance-covariance data for the one-week measurement session as well as after the removal of three possible outliers.


MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

One-week 0.160 0.154 0.030 0.126 0.031 0.021

Altered one-

week 0.057 0.062 0.016 0.033 0.012 0.010

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

Figure 5.3.3.2 Scatter plot presenting the measurements of all three measurement sessions of Subject 2’s left eye after three possible outliers were removed from the one-week data set. The pre-operative measurements are presented in black, the altered one-week measurements in red and the six-month measurements in blue. The origin is set at 44 I D.

68

In Table 5.3.3.5 and Table 5.3.3.6 we can see that the null hypothesis was rejected for both

the means and variance-covariance of the three measurement sessions. Thus the difference

in means and variance-covariance for the three measurement sessions were found to be

statistically significantly different from each other.

Table 5.3.3.5 The statistical data for the hypothesis test done on the means of the three measurement sessions of the left eye of Subject 2.


SUBJECT THETA

Subject 2 OS 0.797 0.074

Table 5.3.3.6 The critical value and test statistic for hypothesis test done on the variance-covariance of the three measurement sessions of the left eye of Subject 2.


SUBJECT µ

Subject 2 OS 316.706 21.026

The difference in means (Table 5.3.3.7) and variance-covariances (Table 5.3.3.8) between

the before and six-month measuring sessions were calculated. The stigmatic component of

the difference seen in Table 5.3.3.7 is minimal and positive indicating that a slight

steepening took place in this cornea six months post-operatively. This finding is supported

visually by the positioning of the blue (six-month) data set slightly above the black (before)

data set in Figure 5.3.3.2.

69

Table 5.3.3.7 Presents the mean difference between the first and the last measurement sessions of the left eye of Subject 2. Means are presented in both conventional and component notation. In conventional notation the sphere and cylinder are measured in diopters (D) and the axis in degrees, whereas in component notation all the components are measured in diopters (D).

DIOPTRIC POWER



Subject 2 OS 0.62 0.65 79.96 0.30 0.31 0.11

Table 5.3.3.8 The mean variance-covariance derived from the difference between the first and last measurement sessions for the left eye of Subject 2. Variance-covariance has units of diopters squared (D2).



I J K I-J J-K I-K

Subject 2 OS 0.052 0.016 0.012 0.023 0.010 0.020

In short, the visual representation of the three measurement sessions seen in Figure 5.3.3.5,

the black data set represents the curvature of the cornea before the CXL procedure, the red

(one-week) data set indicates that the cornea became steeper at this time and that the

measurements were more varied. The blue (six-month) data set is very similar to the black

(before) data set suggesting that the curvature of the cornea at the end of the six-month

follow-up resembles the pre-operative shape.

70


Only the right eye of Subject 3 is included in the study. The graphical representation of the

keratometric measurements for Subject 3 seem to differ compared to the previous two

subjects, as all four ellipsoids on the scatter plots in Figure 5.3.4.1, Appendix D 2.4 (a) and

(b), look similar in shape, size and orientation. In Figure 5.3.4.1, Appendix D 2.4 (a) and (b)

the black (before), red (one-week), green (one-month) and blue (six-month) distribution

ellipsoids seem to orientate along the I-axis and the data points are mostly spread out along

the I-axis (seen in Figure 5.3.4.1 and Appendix D 2.4 (a)) with little spread present across the

J-K plane (seen in Appendix D 2.4 (b)). The black (before) and red (one-week) ellipsoids are

situated higher up on the I-axis whereas the green (one-month) and blue (six-month)

ellipsoids are slightly lower on the I-axis. A large amount of stigmatic variation is seen for

each data collection session. The stigmatic variation seen here is in contrast to the

character of the variation seen in Subjects 1 and 2.

The stigmatic component (Fst/I) of the dioptric power in Table 5.3.4.1 for the before and

one-week measurement sessions seem similar. After the one-week measurement session

the stigmatic component seems to decrease and then appears to stabilise at the one-month

measurement session, resulting in the stigmatic components of the one-month and six-

month measurement sessions being similar. Little change took place in the antistigmatic

component over the full six-month follow-up period (seen in Table 5.3.4.1). It correlates

with all four measurement sessions presenting as tight clusters which seem to mostly

intersect with each other on the rotated scatter plot in Appendix D 2.4 (b). In Table 5.3.4.2

the variance-covariance data for the antistigmatic components (For/J and Fob/K) seem

minimal when compared to the stigmatic component (Fst/I) of the measurement sessions in

the same table. It corresponds with the spread of all the ellipsoids in Figure 5.2.4.1 and

Appendix D 2.4 (a) being greater along the I-axis

71

Table 5.3.4.1 Presenting the means of each of the four measurement sessions.

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 52.37 3.16 107.3 50.79 1.30 0.90

One-week 52.55 3.55 103.3 50.77 1.59 0.79

One-month 51.36 2.83 105.3 49.94 1.22 0.72

Six-month 51.56 3.22 107.0 49.95 1.33 0.90

Table 5.3.4.2 The variance-covariance for all four measurement sessions.


MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

Before 0.739 0.040 0.016 0.041 0.009 0.012

One-week 0.588 0.015 0.008 0.035 0.001 0.010

One-month 0.591 0.048 0.029 0.027 0.031 0.043

Six-month 0.484 0.039 0.016 0.064 0.021 0.039

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

Figure 5.3.4.1 Scatter plot presenting the measurement data for the right eye of Subject 3. The before measurement session (black), one-week (red), one-month (green) and six-month measurement session (blue) each with their 95% distribution ellipsoid included. Origin is at 50.0 I D.

72

Table 5.3.4.3 and Table 5.3.4.4 present the test statistic and critical value for the hypothesis

tests done on the means and variance-covariance respectively. The hypothesis tests were

done to establish if the means of the different measurement sessions (Table 5.3.4.1) and

variance-covariances (Table 5.3.4.2) present in each measurement session were significantly

different. The null hypothesis was rejected concerning the means (Table 5.3.4.3) and

variance-covariance (Table 5.3.4.4) indicating that the means and variance-covariance of the

different sessions were significantly different.

Table 5.3.4.3 Presenting the data for the hypothesis test conducted on the means of the right eye of Subject 3.


SUBJECT THETA

Subject 3 OD 0.976 0.066

Table 5.3.4.4 The critical value and test statistic for hypothesis test done on the variance-covariance of the four measurement sessions of the right eye of Subject 3.


SUBJECT µ

Subject 3 OD 75.126 28.869

It is of importance to know what effect, if any, was induced by CXL at the end of the six-

month follow-up period. The difference in means is shown in Table 5.3.4.5 indicating that a

change was induced in the stigmatic component, but little change in the antistigmatic

components, was present six months after the surgery. The negative stigmatic value for the

component notation in Table 5.3.4.5 implies that the cornea became flatter six months post-

operatively, other than the stigmatic flattening, the CXL procedure did not seem to induce

much change in this cornea. This is supported by the visual impression indicated in Figure

5.3.4.1.

73

Table 5.3.4.5 Presents the mean difference of Subject 3’s right eye.

DIOPTRIC POWER



Subject 3 OD 0.81 0.06 94.43 0.84 0.03 0.05




I J K I-J J-K I-K

Subject 3 OD 1.183 0.067 0.021 0.134 0.022 0.050

In summary, Figure 5.3.4.1 provides a visual account of the changes in curvature seen in the

cornea within the six-month follow-up period. All four data sets show lots of stigmatic

variation, but the means are not very different, indicating that little change in curvature

occurred in this cornea in the six months following the CXL procedure.

74


Subject 4’s left eye is included in the treatment group whereas the right eye is included in

the keratoconic control group (see Section 5.4.1). Similar to the left eyes of Subjects 1 and

2, the red (one-week) distribution ellipsoid seems to be the largest in Figure 5.3.5.1,

Appendix D 2.5 (a) and (b). All four clusters of measurements representing the four

measurement sessions appear to be similar in shape, size and orientation and intersect each

other.

The means of each measurement session in component notation are presented in Table

5.3.5.1. The means of all four measurement sessions seem similar in all three components

and correlate with the similarity of the clusters of measurements seen in Figure 5.3.1,

Appendix D 2.5 (a) and (b). In Table 5.3.5.2 the variance-covariance data of the one-week

measurement session stands out compared to the variance-covariance of the before, one-

month and six-month measurement sessions. (which have smaller values and appear more

equal). The left eye of Subject 4 seems similar to Subject 3 in the sense that the CXL

procedure didn’t induce much change in the curvature of the cornea in the six-month

follow-up period, which can be appreciated visually by the superimposition of all the data

sets (see Figure 5.3.5.1, Appendix D 2.5 (a) and (b)).

Table 5.3.5.1 Reporting the means of the four measurement sessions for the left eye of Subject 4 in both conventional and component notation.

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 53.81 3.33 74.7 52.15 1.43 0.85

One-week 53.27 3.07 80.2 51.73 1.45 0.52

One-month 53.40 3.02 76.1 51.89 1.34 0.70

Six-month 53.17 2.83 70.7 51.75 1.10 0.88

75

Table 5.3.5.2 The means of variance-covariance for each of four measurement sessions.


MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

Before 0.008 0.005 0.007 0.002 0.001 0.001

One-week 0.028 0.010 0.042 0.006 0.001 0.020

One-month 0.003 0.009 0.006 0.000 0.002 0.000

Six-month 0.013 0.003 0.004 0.001 0.000 0.002

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

Figure 5.3.5.1 Scatter plot representing the measurement sessions for the left eye of Subject 4. The pre-operative measurements (black), one-week (red), one-month (green) and six-month (blue) measurement sessions are represented by clusters of data points including their corresponding 95% distribution ellipsoids. Origin is at 52.5 I D. Axis length is 3 D and tick interval is set at 1 D on each axis.

A hypothesis test was done on the means (see Table 5.3.5.1) and another on the means of

the variance-covariance of each measurement session in (see Table 5.3.5.2). The null

hypothesis was rejected if the test statistic was bigger than or equal to the critical value.

From Table 5.3.5.3 and Table 5.3.5.4 it is clear that the null hypothesis was rejected for the

means and variance-covariance of Subject 4’s left eye, implying that the differences seen

between the four measurement sessions in mean and variance-covariance was statistically

significant.

76

Table 5.3.5.3 Presenting the critical value and test statistic for hypothesis test done on the means of the left eye of Subject 4.


SUBJECT THETA

Subject 4 OS 0.810 0.066

Table 5.3.5.4 The critical value and test statistic for hypothesis test done on the variance-covariance of the four measurement sessions.


SUBJECT µ

Subject 4 OS 186.795 28.869

Comparing the before and six-month measurements with each other gives us the difference

seen at the end of the six-month follow-up period. The difference is an indication of the

change induced by the CXL procedure on the cornea six months post-operatively. Table

5.3.5.5 presents the difference of the means in both conventional and component notation,

the stigmatic component of the difference in means has a small negative value indicating

that a minimal amount of flattening took place in the cornea six months post-operatively.

The eye seemed flatter and more stable indicated by a tighter cluster of measurements at

the six-month follow up (See Figure 5.3.5.1, Appendix D 2.5 (a) and (b)).

Table 5.3.5.5 Presents the mean difference between the first and the last measurement sessions of the left eye of Subject 4.

DIOPTRIC POWER



Subject 4 OS 0.07 0.66 3.05 0.40 0.33 0.04

77

Table 5.3.5.6 The mean variance-covariance of the difference seen in the left eye of Subject 4. Variance-covariance has units of diopters squared (D2).



I J K I-J J-K I-K

Subject 4 OS 0.027 0.008 0.009 0.004 0.001 0.002

In short, Figure 5.3.5.1 is a visual representation of the curvature changes that took place in

this cornea in the six months following CXL. The black (before) data gives an indication of

the curvature of the cornea before the procedure, the red (one-week), green (one-month)

and blue (six-month) data sets seem similar to the black (before) data set, indicating that

very little change in curvature took place in this cornea in the six months following the CXL

procedure.

78


Both eyes of Subject 5 were included in the study. In Figure 5.3.6.1, Appendix D 2.6 (a) and

(b), the black (before) distribution ellipsoid stands out because of its increased size

compared to the other ellipsoids on the scatter plots. The spread of the black data points

(representing the before measurements) seems to form two clusters within the black

(before) distribution ellipsoid making it a binomial data set. All the measurement sessions

have fairly large distribution ellipsoids when examining the scatter plots in Figure 5.3.6.1,

Appendix D 2.6 (a) and (b). The orientation of the green (one-month) distribution ellipsoids

in Figure 5.3.6.1 and Appendix D 2.6 (b) is mostly along the K-axis which seems abnormal

when compared to the other ellipsoids that orientate mostly across the I-J plane. The size of

the distribution ellipsoids seem to decrease in sequence starting with the black (before)

ellipsoid that seems to be the biggest and ending with the blue (six-month) ellipsoid that

appears to be the smallest in Figure 5.3.6.1, Appendix D 2.6 (a) and (b).

Looking at the component notation in Table 5.3.6.1 the stigmatic component (Fst/I) became

larger at the one-week measurement session and mostly remained stable thereafter,

whereas a change in both antistigmatic components (For/J and Fob/K) was measured at the

one-month measurement session and again at the six-month measurement session. In

Table 5.3.6.2, representing the variance-covariance data of the four measurement sessions,

we see mostly large numbers indicating that there was lots of variation of the

measurements taken within each measurement session which seems to diminish

consecutively throughout the six-month follow-up period, this correlates with the

distribution ellipsoids decreasing in size in the same fashion. The seemingly large

antistigmatic variance-covariance seen in Table 5.3.6.2 is out of the ordinary when

compared to the antistigmatic variance-covariance data of Subjects 1 to 4.

79

Table 5.3.6.1 Presenting the means of each of the four measurements sessions.

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 53.21 4.95 72.6 50.73 2.03 1.41

One-week 55.84 5.95 69.1 52.87 2.22 1.98

One-month 56.50 7.81 71.1 52.59 3.09 2.39

Six-month 55.65 7.02 60.6 52.14 1.82 3.00

Table 5.3.6.2 The variance-covariance for the entire six-month follow-up period. Variance-covariance has units of diopters squared (D2).

VARIANCE COVARIANCE DATA

MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

Before 0.961 0.625 0.358 0.715 0.312 0.501

One-week 0.072 0.507 0.148 0.067 0.014 0.067

One-month 0.048 0.069 0.206 0.002 0.046 0.083

Six-month 0.082 0.147 0.061 0.032 0.037 0.049

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

Figure 5.3.6.1 Scatter plot presenting the measurement data of the four measurement sessions of Subject 5’s right eye. Origin is at 52.0 I D. Axis length is 3 D and tick interval is set at 1 D on each axis.

80

In Figure 5.3.6.1 one red (one-week) and one blue (six-month) data point is seen on the

lower half of the scatter plot outside of their relative ellipsoids, both seem to be far

removed from their respective clusters. These two measurements could be seen as possible

outliers and were identified in their corresponding original measurement data sets and

removed. Thereafter the means and variance-covariance of both altered measurement sets

involved were recalculated and scatter plots reconstructed to conclude what influence the

possible outliers could have on the data. Both altered data sets created tighter clusters of

measurements (see Figure 5.3.6.4, Appendix D 2.6 (c) and (d)) which seemed to be caused

by the large decrease in variance-covariance (Table 5.3.6.4) of the antistigmatic components

of the altered measurement sets. The removal of the possible outlier from the one-week

data set seemed to induce greater change than the removal of the possible blue (six-month)

outlier, specifically seen by the reduction in size and change in orientation of the red (one-

week) ellipsoid (best seen comparing the scatter plots in Appendix D 2.6 (b) and (d) with

each other). Overall the possible outliers had a negligible influence on the means (Table

5.3.6.3) but a definite effect on the variance-covariance (Table 5.3.6.4) of the respective

measurement sessions. It indicates less variation being present between the measurements

of the one-week and six-month measurement sessions after the removal of the possible

outliers.

Table 5.3.6.3 One possible outlier was removed from the data set of both the one-week and six-month measurement sets. The table presents the original mean and the altered mean for the respective measurement sessions.

DIOPTRIC POWER

MEASUREMENT

SESSION



One-week 55.84 5.95 69.1 52.87 2.22 1.98

Altered one-

week 55.94 6.11 70.0 52.88 2.31 2.00

Six-month 55.65 7.02 60.6 52.14 1.82 3.00

Altered six-

month 55.69 7.05 60.9 52.16 1.86 3.00

81

Table 5.3.6.4 After removal of two possible outliers, one at one week and the other at six months, the variance-covariance for the respective measuring sessions are compared in the table below.


MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

One-week 0.072 0.507 0.148 0.067 0.014 0.067

Altered one-

week 0.062 0.103 0.137 0.001 0.062 0.056

Six-month 0.082 0.147 0.061 0.032 0.037 0.049

Altered six-

month 0.069 0.071 0.061 0.002 0.029 0.054

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

Figure 5.3.6.4 Scatter plot of the measurement data for the right eye of Subject 5 after a possible outlier was removed from the one-week (red) measurement session and one from the one-month (green) measurement session. Origin is at 52.0 I D. Axis length is 3 D and tick interval is set at 1 D on each axis.

Hypothesis tests were conducted on the means and variance-covariances and are presented

in Table 5.3.6.2 and Table 5.3.6.6 respectively. Similar to the previous eyes included in the

treatment group, the null hypothesis was rejected on both occasions.

82

Table 5.3.6.5 The critical value and test statistic for hypothesis test done on the means of the four measurement sessions of the right eye of Subject 5.


SUBJECT THETA

Subject 5 OD 0.856 0.066

Table 5.3.6.6 The critical value and test statistic for hypothesis test done on the variance-covariance of the four measurement sessions of the right eye of Subject 5. The null hypothesis was rejected if the test statistic (µ) was bigger than or equal to the critical value ( ).


SUBJECT µ

Subject 5 OD 347.888 28.869

The difference seen between the before and six-month measurement sessions was

calculated for both the means (Table 5.3.6.7) and variance-covariance (Table 5.3.6.8) to

establish what change was induced by the CXL procedure six months post-operatively.

Regarding Table 5.3.6.7 the stigmatic component of the difference is quite large compared

to the stigmatic change seen in the previous eyes. It indicates that the cornea became

steeper six months post-operatively and a change was seen in the antistigmatic component

of the cornea. The variation in the measurements of the six-month measurement session is

much lower than the variation seen in the before measurements (Table 5.3.6.8). It could

indicate that the CXL procedure induced a noteworthy change in the shape of the cornea

together with the shape becoming more stable after six months.

Table 5.3.6.7 Presents the difference between the first and the last measurement sessions of the right eye of Subject 5.

DIOPTRIC POWER



Subject 5 OD 3.02 3.21 41.13 1.41 0.22 1.59

83

Table 5.3.6.8 The mean variance-covariance derived from the difference between the first and last measurement session.



I J K I-J J-K I-K

Subject 5 OD 0.762 0.697 0.290 0.606 0.194 0.369

In summary, Figure 5.3.6.4 is a visual presentation of the curvature changes seen in the

cornea over the six-month follow-up period. The black (before) data set represents the

curvature of the cornea pre-CXL. The black (before) data set displays the most variation

between measurements, the red (one-week) data set and green (one-month) data set are

displayed by tighter clusters of data points and the blue (six-month) data set presents with

the tightest cluster of data points. The size of the clusters indicate that the measurements

taken after the CXL procedure were less varied than the measurements taken before the

procedure and the measurements were most stable six months post-operatively, even

though the cornea became slightly steeper.


Subject 5 was not able to attend the one-week measurement session scheduled for his left

eye. Similar to the left eye of Subject 2 (missed one-month measurement session), we will

only consider the data at hand. As a result of the missed one-week measurement session

the scatter plots in Figure 5.3.7.1, Appendix D 2.7 (a) and (b), only display three clusters of

data, the black (before) cluster, green (one-month) and blue (six-month) cluster of data

points. When considering each of the three scatter plots (Figure 5.3.7.1, Appendix D 2.7 (a)

and (b)) individually, the three distribution ellipsoids seem to orientate in roughly the same

direction and intersect each other. The size of the ellipsoids seems to change depending on

what scatter plot is analysed, except for the green (one-month) ellipsoid which appears to

remain the smallest throughout.

84

Compared to the previous subjects in the treatment group (Subjects 1, 2 both eyes, 3, 4)

both eyes of Subject 5 seem to display large amounts of antistigmatic power (For/J and

Fob/K) with the antistigmatic components (Table 5.3.7.1) of the left eye being the highest in

the study so far. Similar to the right eye of Subject 3 and the left eye of Subject 4, not much

change was induced by the CXL procedure in this eye.

Table 5.3.7.1 Displaying the means of the pre-operative (before) measurement session, one-month and six-month measurement sessions. Means are presented in both conventional notation and component notation.

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 54.60 9.31 73.2 49.94 3.88 2.58

One-month 55.27 10.29 72.7 50.12 4.23 2.93

Six-month 54.69 9.31 72.1 50.04 3.78 2.72

Table 5.3.7.2 The variance-covariance of the three measurement sessions of the left eye of Subject 5. Variance-covariance has units of diopters squared (D2).


MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

Before 0.131 0.240 0.058 0.129 0.105 0.053

One-month 0.090 0.114 0.038 0.083 0.043 0.017

Six-month 0.281 0.103 0.015 0.105 0.020 0.020

85

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

Figure 5.3.7.1 Scatter plot presenting the measurement data for the pre-operative (black) measurement session, one-month (green) and six-month (blue) measurement sessions, each including their corresponding 95% distribution ellipsoid. Origin is at 49.5 I D. Axis length is 3 D and tick interval is set at 1 D on each axis.

Similar to the previous treated eyes included in the study the null hypothesis was rejected

for both means (Table 5.3.7.3) and variance-covariance (Table 5.3.7.4) indicating that the

differences between the three measurement sessions, when comparing the means (see

component notation in Table 5.3.7.1) and variance-covariance (Table 5.3.7.2), were found to

be statistically significantly different.

Table 5.3.7.3 Presents the critical value and test statistic for the hypothesis test done on the means of the left eye of Subject 5. The null hypothesis was rejected if the test statistic (theta) was bigger than or equal to the critical value.


SUBJECT THETA

Subject 5 OS 0.759 0.074

Table 5.3.7.4 Presents the information regarding the hypothesis test done on variance-covariance for the left eye of Subject 5.


SUBJECT µ

Subject 5 OS 87.057 21.026

The difference seen between the before and six-month measurement sessions is provided in

Table 5.3.7.5 for the means and Table 5.3.7.6 for the variance-covariance data of Subject 5’s

left eye. From Table 5.3.7.5 we conclude that a small amount of steepening took place six

86

months post-operatively. It is assumed that the CXL procedure did not have a clinical

influence on the shape of the cornea as the change is clinically insignificant.

Table 5.3.7.5 Presents the mean difference between the first and the last measurement sessions of the left eye of Subject 5.

DIOPTRIC POWER



Subject 5 OS 0.27 0.35 27.51 0.10 0.10 0.14

Table 5.3.7.6 The difference in variance-covariance between the first and last measurement sessions for the left eye of Subject 5.



I J K I-J J-K I-K

Subject 5 OS 0.393 0.346 0.047 0.235 0.098 0.070

Figure 5.3.7.1 is a visual representation of the curvature change that took place in the

cornea over the six-month follow-up period. The black data set represents the curvature of

the cornea before the CXL procedure. The green (one-month) and blue (six-month) data

sets represent the curvature of the cornea after the procedure and seem very similar to the

black (before) data set except that the measurements are less variable after the CXL

procedure and the cornea became slightly steeper.

87


Only the right eye of Subject 6 was included in the study. The red (one-week) ellipsoid

seems to be the biggest in Figure 5.3.8.1, Appendix D 2.8 (a) and (b), followed by the black

(before) ellipsoid whereas the green (one-month) and blue (six-month) ellipsoids appear to

be smaller and equivalent in size. The right eye of Subject 6 can be compared to the left

eyes of Subjects 1, 2 and 4 because of the size of the red (one-week) ellipsoid being the

biggest in the scatter plots representing the subjects. All four ellipsoids in Figure 5.3.8.1

seem to orientate roughly along the I-axis and appear to intersect with each other in Figure

5.3.8.1, Appendix D 2.8 (a) and (b). Consecutive ellipsoids tend to move back to the general

position of the black (pre-operative) data set.

In Table 5.3.8.1, when looking at the component notation, the one-week measurements had

the highest values for each component. The variance-covariance seen in Table 5.3.8.2

increased at the one-week measurement session, but decreased from the one-month

measurement session onwards, ending up with the lowest variance-covariance data seen at

the six-month follow-up. The variance-covariance changes correlate with the scatter plot in

Figure 5.3.8.3 where the red (one-week) ellipsoid seems bigger in size compared to the

black (before) ellipsoid with the green (one-month) ellipsoid appearing smaller and the blue

(six-month) ellipsoid being the smallest. The decreasing variance-covariance data (Table

5.3.8.1) indicates that less variation was apparent in the measurements, chronologically,

from the one-week measurement session onwards, suggesting some form of improved

stability in the cornea taking place one week after the CXL procedure. Six months post-

operatively the cornea had undergone steepening in terms of the stigmatic component

(Fst/I) while, antistigmatically (For/J and Fob/K) little change had occurred.

88

Table 5.3.8.1 Showing the means for the pre-operative (before) measurement session, one-week, one-month and six-month measurement session.

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 46.14 2.64 91.8 44.82 1.32 0.08

One-week 47.76 4.46 82.6 45.53 2.16 0.57

One-month 46.67 2.95 80.8 45.20 1.40 0.47

Six-month 46.58 2.62 87.7 45.27 1.31 0.11

Table 5.3.8.2 Providing the variance-covariance data for the entire six-month follow-up period.


MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

Before 0.097 0.072 0.057 0.068 0.017 0.004

One-week 0.190 0.110 0.027 0.082 0.013 0.016

One-month 0.048 0.043 0.015 0.036 0.011 0.013

Six-month 0.041 0.013 0.012 0.011 0.004 0.009

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

Figure 5.3.8.1 Presenting the measurement data of Subject 6 on a stereo-pair scatter plot. Origin is at 45.0 I D.

89

Hypothesis tests were conducted on the multivariate components of both the means and

variance-covariance of the four measurement sessions (see Table 5.3.8.3 and Table 5.3.8.4).

Similar to all the eyes included in the treatment group thus far, both null hypotheses were

rejected.

Table 5.3.8.3 The critical value and test statistic for the means of the right eye of Subject 6. The null hypothesis was rejected if the test statistic (theta) was bigger than or equal to the critical value.


SUBJECT THETA

Subject 6 OD 0.823 0.066

Table 5.3.8.4 Hypothesis test data for the variance-covariance of the four measurement sessions of the right eye of Subject 6.


SUBJECT µ

Subject 6 OD 175.516 28.869

The mean change that took place throughout the six-month follow-up was calculated by

comparing the six-month measurement session and before measurement session to each

other for both the means and variance-covariance. The mean difference (Table 5.3.8.5)

indicates that an increase took place in the stigmatic component (Fst/I) suggesting that the

cornea became steeper six months post-operatively.

Table 5.3.8.5 Presents the difference between the means of the first and the last measurement sessions of the right eye of Subject 6.

DIOPTRIC POWER



Subject 6 OD 0.64 0.38 43.21 0.45 0.01 0.19

90

Table 5.3.8.6 The mean variance-covariance derived from the difference.



I J K I-J J-K I-K

Subject 6 OD 0.116 0.087 0.072 0.066 0.007 0.009

Essentially, Figure 5.3.8.1 gives a representation of the change seen in the curvature of the

cornea in the six-month follow-up period. The black (before) data set represents the

curvature of the cornea pre-operatively. The red (one-week) data set demonstrates that the

cornea became steeper at this time and the green (one-month) and blue (six-month) data

sets indicate that the curvature of the cornea became flatter post-operatively from one

month onwards, eventhough ultimately the cornea is steeper six months post-operatively

than it was pre-operatively. The measurements became less variable at the one-month

measurement session and even more so at the six-month follow-up.

91


The right eye of Subject 7 is included in the treatment group and the left eye in the

keratoconic control group (Section 5.4.2). In Figure 5.3.9.1, Appendix D 2.9 (a) and (b)

presenting the measurement data for the four measurement sessions the red (one-week)

ellipsoid seems to be the biggest, which correlates with the red (one-week) ellipsoids of the

right eye of Subject 6 and the left eyes of Subjects 1, 2 and 4. All four distribution ellipsoids

seem to orientate along the I-axis and seem to mostly deviate from each other by their

position related to the I-axis in Figure 5.3.9.1 and Appendix D 2.9 (a). All four ellipsoids

seem to intersect each other and little variation is seen in the J-K plane looking down the I-

axis in Appendix D 2.9 (b).

Overall the right eye of Subject 7 seems to display mainly stigmatic variation within each

measurement session with regards to the variance-covariance data (Table5.3.9.2) as well as

between the means of each measurement session (Table 5.3.9.1 component notation). The

antistigmatic components of the one-week measurement session seems the most different

compared to the other measurement sessions and links to the deviation in orientation of

the red (one-week) ellipsoid compared to the other ellipsoids in Figure 5.3.9.1 and Appendix

D 2.9 (a). The cornea seemed flatter and more regular after the one-week measurement

session. At the six-month measurement session the cornea had the lowest stigmatic

component (see Fst/I in Table 5.3.9.1) indicating that the cornea was flattest at the six-

month follow-up; this coincides with the six-month measurement sessions of the right eyes

of Subjects 2 and 6 and the left eye of Subject 1. The six-month measurement session also

presented with the smallest amount of variance-covariance.

92

Table 5.3.9.1 The means for each of the four measuring sessions.

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 55.00 4.76 102 52.62 2.18 0.97

One-week 54.91 5.13 98.5 52.34 2.45 0.75

One-month 53.87 4.30 99.4 51.71 2.04 0.69

Six-month 52.77 4.29 102.9 50.62 1.93 0.93

Table 5.3.9.2 The variance-covariances for the entire six-month follow-up period. Variance-covariances have units of diopters squared (D2).


MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

Before 0.135 0.025 0.033 0.035 0.006 0.021

One-week 0.158 0.071 0.046 0.073 0.031 0.015

One-month 0.116 0.036 0.014 0.028 0.005 0.000

Six-month 0.090 0.017 0.006 0.022 0.007 0.007

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

Figure 5.3.9.1 Scatter plot presenting the four measurement sessions of Subject 7’s right eye including their respective 95% distribution ellipsoids. The pre-operative measurements are presented in black, the one-week measurements in red, the one-month in green and the six-month measurements in blue. Origin is at 51.5 I D.

93

Hypothesis tests were done respectively on the means in Table 5.3.9.1 and the means in

variance-covariance in Table 5.3.9.1 to establish whether statistically significant change took

place between the multivariate components of the measurement sessions when comparing

them to each other. The null hypothesis was rejected if the test statistic (theta) was bigger

than or equal to the critical value. From Table 5.3.9.3 and Table 5.3.9.4 we derive that the

null hypothesis was rejected in both cases, leading us to believe that statistically significant

change did take place between the follow-up sessions.

Table 5.3.9.3 Presents the critical value and test statistic for the means.


SUBJECT THETA

Subject 7 OD 0.847 0.066

Table 5.3.9.4 Presents the statistical data for the hypothesis test on the variance-covariance.


SUBJECT µ

Subject 7 OD 127.836 28.869

The difference seen in the shape of the cornea was calculated by only looking at the before

and six-month measurements. In Table 5.3.9.5 the stigmatic component is large when

compared to the previous eyes that were included in the treatment group. A negative

stigmatic component indicates that the cornea became notably flatter six months post-

operatively.

94

Table 5.3.9.5 Displaying the mean difference six months post-operatively for the right eye of Subject 7. Means are presented in both conventional and component notation. In conventional notation the sphere and cylinder are measured in diopters (D) and the axis in degrees, whereas in component notation all the components are measured in diopters (D).

DIOPTRIC POWER



Subject 7 OD 1.75 0.50 4.10 2.00 0.25 0.04

Table 5.3.9.6 The mean variance-covariance of the difference between the first and last measurement session for the right eye of Subject 7. Variance-covariance has units of diopters squared (D2).



I J K I-J J-K I-K

Subject 7 OD 0.158 0.037 0.037 0.047 0.005 0.021

In summary, when evaluating the change in curvature that took place in this cornea,

represented in Figure 5.3.9.1, the black data set represents the pre-operative shape of the

cornea, the red (one-week) data set indicates that the measurements were more variable at

this stage, the green (one-month) data set indicates that the measurements are less varied

and the cornea is flatter at this follow-up session and the blue (six-month) data set indicates

that the curvature of the cornea is the flattest at this stage and that less variation is present

between the measurements in this session, which could indicate improved stability of the

cornea six months post-operatively.

95


The right eye of Subject 8 was included in the study. There seems to be a binomial pattern

in the distribution of the black (before) and in a lesser degree in the red (one-week)

measurement data, which is the easiest to see in Appendix D 2.10 (a) where the scatter plot

is rotated to look down the J-K plane. The same binomial pattern was previously noticed in

the distribution of the black (before) measurement data of the right eye of Subject 5. In

Figure 5.3.10.1 and Appendix 2.10 (a) the red (one-week) ellipsoid seems to have the largest

size and seems to be abnormally large in Appendix D 2.10 (b). In Figure 5.3.10.1 and

Appendix D 2.10 (a) all four of the ellipsoids seem to orientate along the I-axis.

In Table 5.3.10.1 the means seem to all differ from each other in the stigmatic (Fst/I) and

both antistigmatic components (For/J and Fob/K). The stigmatic component showed a

marked increased at the one-week measurement session. It increased a bit more at the

one-month session and then a marked decrease was seen at the six-month measurement

session. This results in the lowest stigmatic value for the entire follow-up. The change in

the antistigmatic components was most noticeable at the one-week measurement session

which is related to deviation in orientation seen by the red ellipsoid when comparing it to

the other ellipsoids in Figure 5.3.10.1 and Appendix D 2.10 (a). The six-month

measurements had the least variation (Table 5.3.10.1) in the measurement set which

correlates with the right eyes of Subjects 6 and 7. The six-month measurement session also

presented with the lowest stigmatic component in Table 5.3.10.2, hence the cornea was the

flattest at this time. It coincides with the right eye of Subjects 2 and 7 and the left eye of

Subject 1.

96

Table 5.3.10.1 The means of all four measurement sessions of Subject 8.

Table 5.3.10.2 The variance-covariance for the entire six-month follow-up period.


MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

Before 0.522 0.081 0.046 0.031 0.003 0.009

One-week 0.745 1.123 0.388 0.069 0.572 0.149

One-month 0.167 0.119 0.026 0.007 0.013 0.011

Six-month 0.017 0.017 0.016 0.001 0.004 0.001

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

Figure 5.3.10.1 Presenting the four measurement sessions of Subject 8’s right eye. Origin is at 53.5 I D.

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 57.96 9.52 105.2 53.20 4.10 2.42

One-week 58.39 7.29 105.3 54.74 3.14 1.86

One-month 59.79 9.50 105.7 55.04 4.05 2.48

Six-month 56.81 8.44 104.4 52.59 3.70 2.03

97

There are possible outliers present in the one-week readings for this subject. The red

ellipsoid is notably larger especially in Appendix D 2.10 (b). The red data point on the

bottom of Figure 5.3.10.1 could be seen as a possible outlier and was identified and

removed from the one-week measurement data set, thereafter the means and variance-

covariance were recalculated and scatter plots reconstructed for the altered data set. The

red ellipsoids representing the altered one-week measurement session in Figure 5.3.10.2,

Appendix D 2.10 (c) and (d) is notably smaller especially looking down the I-axis in Appendix

D 2.10 (d) as the removal of the possible outlier had a large effect on the variance-

covariance of the one-week data set. The mean of the altered one-week measurement

session is very similar to the original mean and seems to indicate that the removal of the

possible outlier did not influence the mean of the one-week measurement session.

Table 5.3.10.3 One possible outlier was removed from the data set of the one-week measurements. The table presents the original mean and the altered mean for the one-week measurement set. In conventional notation the sphere and cylinder are measured in diopters (D) and the axis in degrees, whereas in component notation all the components are measured in diopters (D).

DIOPTRIC POWER

MEASUREMENT

SESSION



One-week 58.39 7.29 105.3 54.74 3.14 1.86

Altered one-

week 58.56 7.62 105.3 54.75 3.28 1.94

98

Table 5.3.10.4 Presenting the variance-covariance data of the one-week measurement session with and without a possible outlier removed.


MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

One-week 0.745 1.123 0.388 0.069 0.572 0.149

Altered one-

week 0.754 0.097 0.068 0.012 0.003 0.199

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

Figure 5.3.10.2 Scatter plot illustrating the measurement data for all four measurement sessions of Subject 8’s right eye after one possible outlier was removed from the red cluster of measurements representing the one-week measurement session. The measurements are represented with different colours., the pre-operative measurements in black, the altered one-week measurement session in red, the one-month in green and the six-month session in blue. Origin is set at 53.5 I D.

Similar to all the previous eyes in the treatment group, hypothesis tests were conducted on

the means and variance-covariance (both consisting of multivariate data) of all the

measurement sessions and were rejected as concluded by the test statistic being bigger

than the critical value in Table 5.3.10.5 for the means and Table 5.3.10.6 for the variance-

covariance.

99

Table 5.3.10.5 The critical value and test statistic for hypothesis test done on the means of the four measurement sessions of the right eye of Subject 8. The null hypothesis was rejected if the test statistic (theta) was bigger than or equal to the critical value.


SUBJECT THETA

Subject 8 OD 0.785 0.066

Table 5.3.10.6 The critical value and test statistic for hypothesis test done on the variance-covariance of the four measurement sessions of the right eye of Subject 8. The null hypothesis was rejected if the test statistic (µ) was bigger than or equal to the critical value ( ).


SUBJECT µ

Subject 8 OD 448.721 28.869

Table 5.3.10.7 presents the difference in means and Table 5.3.10.8 of the variance-

covariance of the before and six-month measurement sessions. The differences in Table

5.3.10.7 and Table 5.3.10.8 express the mean change in the shape of the cornea seen after

the six-month follow-up. The negative stigmatic value (Fst/I) in Table 5.3.10.7 indicates that

the cornea was flatter six months post-operatively.

Table 5.3.10.7 Presents the mean difference between the first and the last measurement sessions of the right eye of Subject 8.

DIOPTRIC POWER



Subject 8 OD 0.06 1.11 21.74 0.61 0.40 0.38

100




I J K I-J J-K I-K

Subject 8 OD 0.544 0.085 0.064 0.040 0.004 0.017

To give an outline of the curvature change that took place in the right eye of Subject 8, refer

to Figure 5.3.10.2 which gives a visual description of the change over the six-month follow-

up. The black data set represents the curvature of the cornea before CXL, the red data set

shows how the cornea became steeper and the measurements more variable one week

post-CXL. The green data set indicates that the cornea became even steeper one month

post-CXL, but that the measurements were less variable. The blue data set shows that the

cornea became flatter and improved stability is present in the cornea six months after CXL.

101


Both eyes of Subject 9 were included in the study. In Figure 5.3.11.1, Appendix D 2.11 (a)

and (b) the blue (six-month) ellipsoid seems to be the largest in size and the red (one-week)

ellipsoid the smallest. The red (one-week) ellipsoid seems to orientate along the K-axis

deviating from the other ellipsoids that seem to orientate along the I-axis. All the ellipsoids

except for the red (one-week) ellipsoid intersect in Appendix D 2.11 (b).

The stigmatic component (Fst/I) of the before measurement session in Table 5.3.11.1 is the

lowest indicating that the cornea of this patient was flatter before the CXL procedure than

any recorded time after. Marked changes were seen in the measurements of the one-week

measurement session, this is clear from the variation in the antistigmatic components (For/J

and Fob/K) in Table 5.3.11.2 and relates to only the red (one-week) ellipsoid not intersecting

with the other ellipsoids on the scatter plot in Appendix D 2.11 (b). For the other

measurement sessions, the most notable changes were seen in the stigmatic component in

Table 5.3.11.1 correlating with the variation in position related to the I-axis of the black

(before), green (one-month) and blue (six-month) ellipsoids in Figure 5.3.11.1. From Table

5.3.11.2 we conclude that the most variation was present between the measurements of

the six-month measurement session.

Table 5.3.11.1 The means of the four measurement sessions.

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 55.34 4.50 109.2 53.09 1.76 1.40

One-week 57.06 5.96 94.2 54.08 2.95 0.43

One-month 57.40 5.19 108.8 54.80 2.06 1.58

Six-month 56.15 3.86 106.7 54.22 1.61 1.06

102



MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

Before 0.085 0.030 0.014 0.009 0.004 0.016

One-week 0.018 0.014 0.027 0.008 0.011 0.002

One-month 0.074 0.026 0.018 0.005 0.009 0.013

Six-month 0.179 0.034 0.031 0.026 0.002 0.013

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J Figure 5.3.11.1 Scatter plot presenting the measurements for all four measurement sessions including their 95% distribution ellipsoids of Subject 9’s right eye. Origin is at 53.5 I D. Axis length is 3 D and tick interval is set at 1 D on each axis.

The hypothesis data for the means are depicted in Table 5.3.11.3 and the means in variance-

covariance in Table 5.3.11.4, the null hypothesis was rejected in both cases which correlates

with all the other eyes in the treatment group thus far.

Table 5.3.11.3 The critical value and test statistic for hypothesis test done on the means of the four measurement sessions of the right eye of Subject 9. The null hypothesis was rejected if the test statistic (theta) was bigger than or equal to the critical value.


SUBJECT THETA

Subject 9 OD 0.942 0.066

103

Table 5.3.11.4 The critical value and test statistic for hypothesis test done on the variance-covariance of the four measurement sessions of the right eye of Subject 9


SUBJECT µ

Subject 9 OD 136.163 28.869

Table 5.3.11.5 and Table 5.3.11.6 depict the difference in mean and variance-covariance of

the full follow-up period by only comparing the before and six-month measurement

sessions to each other. The positive value for the stigmatic component (Fst/I) in Table

5.3.11.5 indicates that the cornea became steeper six months post-operatively.

Table 5.3.11.5 Presents the mean difference for the right eye of Subject 9.

DIOPTRIC POWER



Subject 9 OD 1.51 0.74 32.80 1.14 0.15 0.34




I J K I-J J-K I-K

Subject 9 OD 0.252 0.076 0.051 0.036 0.008 0.012

To summarise, see Figure 5.3.11.1 which is an illustration of the change seen in the

curvature of the right eye of Subject 9’s cornea. The black data set depicts the shape of the

cornea before the CXL procedure. The red data set indicates that the cornea became

steeper one week post-operatively and that less variation was present between the

measurements. The green data set shows that the cornea became steeper one month post-

CXL and the blue data set indicates that the cornea became flatter six months post-

104

operatively, but increased variation is present between the measurements. The cornea

became steeper six months post-CXL and was less stable.


In Figure 5.3.12.1 the black (before) ellipsoid seems larger than the other ellipsoids on the

scatter plot; this corresponds with the right eye of Subject 5. The black (before) ellipsoid

demonstrated the same binomial appearance seen in the right eyes of Subjects 5 and 8 and

this subject’s other eye. The scatter plots in Figure 5.3.12.1, Appendix D 2.12 (a) and (b)

seem to display a lot of variance in both the J and K components which is easier to see in

Appendix D 2.12 (b) when the scatter plot is rotated to look down the I-axis as the ellipsoids

seem large from this angle. The only other eye in the treatment group thus far that

presented with the same amount of variation across the J-K plane, is the left eye of Subject

5, and to a smaller degree the right eyes of Subjects 2 and 6. All four the ellipsoids seem

very different in size and orientation in Figure 5.3.12.1, Appendix D 2.12 (a) and (b), but the

red (one-week), green (one-month) and blue (six-month) ellipsoids seem to intersect in all

of the scatter plots.

The stigmatic component (Fst/I) seemed to decrease after the CXL procedure and was the

lowest at the one-week measurement session (see the component notation in Table

5.3.12.1). In Table 5.3.12.2 the variance seems to be the lowest at the six-month follow-up

session.

105

Table 5.3.12.1 The means of the measurements taken at the four measurement sessions presented in both conventional notation and component notation.

Table 5.3.12.2 Presenting the mean variance-covariance for the four measurement sessions for the left eye of Subject 9.


MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

Before 0.041 0.173 0.669 0.068 0.263 0.100

One-week 0.197 0.097 0.063 0.087 0.021 0.003

One-month 0.027 0.325 0.070 0.026 0.117 0.002

Six-month 0.060 0.020 0.073 0.009 0.019 0.003

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

Figure 5.3.12.1 Scatter plot illustrating the measurement sessions of Subject 9’s left eye. Origin is at 55.0 I D.

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 58.51 4.17 93.7 56.43 2.07 0.27

One-week 56.63 3.74 77.7 54.77 1.70 0.78

One-month 57.69 4.99 85.0 55.19 2.46 0.44

Six-month 56.86 3.48 87.3 55.13 1.73 0.16

106

In Figure 5.3.12.1 and Appendix D 2.12 (b) one red (one-week) and one green (one-month)

data point appear to be removed from their corresponding ellipsoids and could be seen as

possible outliers. Each of these possible outliers were identified in their corresponding

measurement data sets (by seeming abnormal when correlated with the other data in each

set) and removed, thereafter the means and variance-covariance for the one-week and one-

month measurement sessions were recalculated and scatter plots reconstructed. From

Table 5.3.12.3 the original and altered means for both the one-week and one-month

measurement sessions seem very similar, which correlates with the similarity in position of

the altered red (one-week) and green (one-month) ellipsoids in Figure 5.3.12.2, Appendix D

2.12 (c) and (d) compared to the same ellipsoids in Figure 5.3.12.1, Appendix D 2.12 (a) and

(b). In Table 5.3.12.4 presenting the variance-covariance data of the original and altered

data sets the one-week data seems very similar, but the altered one-month variance-

covariance has a notable decrease and correlates with the green ellipsoid in Appendix D

2.12 (d) which seems much smaller than the corresponding green (one-month) ellipsoid in

Appendix D 2.12 (b).

Table 5.3.12.3 Presenting the original and altered means of the one-week and one-month measurement sessions after the removal of possible outliers. In conventional notation the sphere and cylinder are measured in diopters (D) and the axis in degrees, whereas in component notation all the components are measured in diopters (D).

DIOPTRIC POWER

MEASUREMENT

SESSION



One-week 56.63 3.74 77.7 54.77 1.70 0.78

Altered one-

week 56.65 3.79 77.5 54.76 1.72 0.80

One-month 57.69 4.99 85.0 55.19 2.46 0.44

Altered one-

month 57.77 5.14 85.5 55.20 2.54 0.41

107

Table 5.3.12.4 Providing the original and altered variance-covariance for the one-week and one-month measurement sessions. Variance-covariance has units of diopters squared (D2).


MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

One-week 0.197 0.097 0.063 0.087 0.021 0.003

Altered one-

week 0.199 0.084 0.037 0.094 0.001 0.003

One-month 0.027 0.325 0.070 0.026 0.117 0.002

Altered one-

month 0.027 0.012 0.023 0.009 0.006 0.009

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

Figure 5.3.12.2 Presenting the measurements of the four measurement sessions of Subject 9’s left eye, the one-week and one-month measurement sessions were provided without possible outliers. The original before measurements are provided in black, the altered one-week measurements in red, the altered one-month measurements in green and the original six-month measurements in blue. Each of the measurement sessions includes their 95% distribution ellipsoids. Origin is at 55.0 I D. Axis length is 3 D and tick interval is set at 1 D on each axis.

Similar to all the other eyes that have been included in the treatment group hypothesis tests

were conducted on the means and variance-covariance of this eye (statistical data provided

in Table 5.3.12.5 and Table 5.3.12.6) and was rejected in both cases.

108

Table 5.3.12.5 The critical value and test statistic for hypothesis test done on the means of the four measurement sessions of the left eye of Subject 9. The null hypothesis was rejected if the test statistic (theta) was bigger than or equal to the critical value.


SUBJECT THETA

Subject 9 OS 0.858 0.066

Table 5.3.12.6 The critical value and test statistic for hypothesis test done on the variance-covariance of the four measurement sessions of the left eye of Subject 9. The null hypothesis was rejected if the test statistic (µ) was bigger than or equal to the critical value ( ).


SUBJECT µ

Subject 9 OS 371.516 28.869

The difference between the before and six-month measurements were calculated for both

means and variance-covariance and are presented in Table 5.3.12.7 and Table 5.3.12.8

respectively. Table 5.3.12.7 indicates that a notable decrease took place in the stigmatic

component (Fst/I) and could be interpreted as a notable flattening of the cornea six months

post-operatively.

Table 5.3.12.7 Presents the mean difference between the first and the last measurement sessions.

DIOPTRIC POWER



Subject 9 OS 0.75 1.10 25.96 1.30 0.34 0.43

109

Table 5.3.12.8 The mean variance-covariance derived from the difference between the first and last measurement session for the left eye of Subject 9.



I J K I-J J-K I-K

Subject 9 OS 0.036 0.028 0.014 0.018 0.000 0.003

To sum up, Figure 5.3.12.2 shows the change in curvature seen over the six-month follow-up

period. The black data set portrays the shape of the cornea pre-CXL which indicates that the

measurements were variable at this stage. The red data shows how the cornea flattened

and that the measurements became less variable. The green data set shows more stability

in the measurements and steepening of the cornea, whereas the blue data set indicates that

the cornea ultimately became flatter six months after the CXL treatment and that the

measurements were less variable.

110


Only the left eye of Subject 10 was included in this study. In Figure 5.3.13.1, Appendix D

2.13 (a) and (b) all four measurement sessions produced tight clusters of data points closely

positioned to each other as well as the origin of the scatter plot (42.5 I).

In Table 5.3.13.1 the stigmatic component (Fst/I) increased at the one-week measurement

session. Thereafter it decreases to a level similar to the before measurement session at the

six-month follow-up. Likewise, a change was seen at the one-week measurement session in

the antistigmatic components (For/J and Fob/K) but ended up at a level similar to the before

measurements. The antistigmatic components for all the measurement sessions are low in

Table 5.3.13.1 which links to the measurement clusters being close to the origin of the

scatter plots in Figure 5.3.13.1, Appendix D 2.13 (a) and (b). From Table 5.3.13.2 little

change is seen throughout the six-month follow-up period correlating with the

measurement clusters that seem equal in size in Figure 5.3.13.1. It seems that the

procedure did not induce much change in this eye which corresponds to the right eye of

Subject 3 and the left eyes of Subjects 4 and 5.

Table 5.3.13.1 Provides means of each of the four measurement sessions of Subject 10.

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 43.00 0.87 6.0 42.56 0.42 0.09

One-week 43.89 1.39 175.8 43.20 0.69 0.10

One-month 43.37 0.94 10.4 42.90 0.44 0.17

Six-month 43.00 0.79 13.2 42.60 0.35 0.18

111



MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

Before 0.009 0.008 0.006 0.004 0.002 0.002

One-week 0.006 0.017 0.003 0.001 0.003 0.002

One-month 0.024 0.014 0.005 0.014 0.005 0.008

Six-month 0.005 0.001 0.004 0.001 0.000 0.003

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

Figure 5.3.13.1 Scatter plot illustrating each of the four measurement sessions including their respective 95% distribution ellipsoids for Subject 10’s left eye. Origin is at 42.5 I D. Hypothesis tests were done to establish whether the changes in the components of each

measurement session significantly changed when comparing all four measurement sessions

to each other. Table 5.3.13.3 and Table 5.3.13.4 present the statistical data for the

hypothesis tests between the means and variance-covariance respectively. In both cases

the null hypothesis was rejected which corresponds to all the other eyes included in the

treatment group thus far.



SUBJECT THETA

Subject 10 OS 0.926 0.066

112

Table 5.3.13.4 The critical value and test statistic for hypothesis test done on the variance-covariance of the four measurement sessions of the left eye of Subject 10.


SUBJECT µ

Subject 10 OS 212.496 28.869

Table 5.3.13.5 and Table 5.3.13.6 provide the difference in means and variance-covariance

respectively from the before to the six-month measurement session. The amount of change

seen for the means in Table 5.3.13.5 is minimal meaning that the CXL produced a negligibly

small change in the shape of this cornea six months post-operatively.

Table 5.3.13.5 Presents the mean difference between the first and the last measurement sessions in both conventional and component notation.

DIOPTRIC POWER



Subject 10 OS 0.15 0.22 64.51 0.04 0.07 0.09




I J K I-J J-K I-K

Subject 10 OS 0.012 0.010 0.007 0.002 0.001 0.003

Briefly, Figure 5.3.13.1 presents the change in corneal curvature seen in the first six months

following CXL. The black data set represents the curvature of the cornea pre-operatively,

the red data set shows that the cornea steepened one week post-CXL. The green and blue

data sets indicate that the cornea recovered to the pre-operative shape six month after CXL.

113


Only the left eye of Subject 11 was included in this study. In Figure 5.3.14.1, Appendix D

2.14 (a) and (b) the data points in the scatter plots seem abnormal as they present in a

strange pattern of vertical lines within each of the ellipsoids; these lines are artefacts of the

software used in this study. In Figure 5.3.14.1 and Appendix D 2.14 (a) the red (one-week)

ellipsoid seems to stand out as it is the largest as well as highest and seems to be the only

ellipsoid that orientates along the I-axis whereas the other ellipsoids seem to orientate

along the K-axis. The black (before) and blue (six-month) ellipsoids seem the most similar

when comparing positioning and size on the scatter plots in Figure 5.3.14.1, Appendix D 2.14

(a) and (b). Compared to the other eyes in the treatment group, the ellipsoids are situated

abnormally far from the origin in Appendix D 2.14 (b) when looking down the I-axis.

Looking at the stigmatic components (Fst/I) of the four measurement sessions in Table

5.3.14.1, an increase is seen in the one-week measurement session followed by an ongoing

decrease at the one-month and six-month measurement sessions. Not much change was

seen between the measurement sessions in the antistigmatic components (see For/J and

Fob/K in Table 5.3.14.1) but the antistigmatic components in Subject 11 are large when

compared to the same components in the other subjects in the treatment group. In Table

5.3.14.2 the variance-covariance data seemed to change between the measurement

sessions but returned to values similar to the before measurement session at the end of the

six-month follow-up.

114

Table 5.3.14.1 The means of each of the four measuring sessions. Means are presented in both conventional notation and component notation

Table 5.3.14.2 The variance-covariance data for Subject 11.

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J Figure 5.3.14.1 Presenting four measurement sessions and their corresponding 95% distribution ellipsoids for Subject 11’s left eye. Origin is at 55.0 I D. Axis length is 3 D and tick interval is set at 1 D on each axis.

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 58.86 8.54 96.2 54.59 4.17 0.91

One-week 61.45 10.79 96.2 56.05 5.27 1.16

One-month 60.36 9.92 97.0 55.40 4.81 1.21

Six-month 59.79 9.80 93.0 54.89 4.87 0.51


MEASUREMENT

SESSION

VARIANCE COVARIANCES

I J K I-J J-K I-K

Before 0.031 0.010 0.064 0.013 0.002 0.028

One-week 0.094 0.013 0.035 0.026 0.007 0.022

One-month 0.016 0.008 0.027 0.007 0.006 0.007

Six-month 0.021 0.019 0.060 0.008 0.011 0.008

115

Hypothesis test were conducted on the means and variance-covariance of the four

measurements and, similar to the other thirteen eyes in the treatment group, both were

rejected (statistical data for the means are presented in Table 5.3.14.3 and variance-

covariance in Table 5.3.13.4).



SUBJECT THETA

Subject 11 OS 0.929 0.066

Table 5.3.14.4 The critical value and test statistic for hypothesis test done on the variance-covariance of the four measurement sessions of the left eye of Subject 11. The null hypothesis was rejected if the test statistic (µ) was bigger than or equal to the critical value ( ).


SUBJECT µ

Subject 11 OS 148.865 28.869

Table 5.3.14.5 and Table 5.3.14.6 present the difference between only the before and six-

month measurement sessions for the means and the variance-covariance respectively.

Viewing the component notation in Table 5.3.14.5, a change is seen in both the stigmatic

and antistigmatic components, the positive value of the stigmatic component indicates that

the cornea became slightly steeper six months post-operatively

Table 5.3.14.5 Presents the mean difference between the first and last measurement sessions of Subject 11. Means are presented in both conventional and component notation.

DIOPTRIC POWER



Subject 11 OS 1.11 1.60 75.20 0.30 0.70 0.40

116

Table 5.3.14.6 The mean variance-covariance of the difference between the first and last measurement session.



I J K I-J J-K I-K

Subject 11 OS 0.067 0.037 0.141 0.029 0.018 0.016

In short, Figure 5.3.14.1 depicts the change in curvature of the cornea seen over the six-

month post-operative follow-up. The black data set represents the curvature of the cornea

pre-CXL, the red data set (one-week) illustrates how the cornea became steeper. The green

data set shows how the cornea became flatter and the measurements became less variable

one month post-operatively and the blue data set indicates that the shape mostly recovered

to the pre-operative shape but is steeper six months post-operatively.


When the null hypothesis is accepted, it suggests that no statistically significant curvature

change took place in the corneas of the eyes included in the study over a six-month follow-

up period. The null hypothesis was tested by comparing the mean found at each

measurement session with the other means from the various measurement sessions for

each eye. The critical values and test statistics for the means of the fourteen eyes included

in the treatment group are displayed in Table 5.3.15.1. The null hypothesis was rejected if

the test statistic (theta) was larger than or equal to the critical value of the involved eye

(refer to Section 3.4.3). The critical value for the hypothesis test involving the means was

found to be 0.066 from Heck tables for most of the eyes in this category, except for the left

eyes of Subjects 2 and 5 where the critical value differs because the related eyes only

attended three of the four measurement sessions giving a critical value of 0.74. The null

hypothesis was rejected for all the eyes in the experimenta subject group.

Thereafter, hypothesis testing was done comparing the variance-covariance of each

measurement session for a specific eye. The null hypothesis in this case states that no

117

statistically significant change in variance-covariance took place between the four

measurement sessions (three in the left eyes of Subjects 2 and 5). The test statistic (µ) and

the corresponding critical value ( ) found on the Chi-square table is set out in Table

5.3.15.2. The null hypothesis is rejected if the test statistic (µ) value was greater or equal to

the critical value on the Chi-square table. The critical value was 28.869, for the majority of

eyes included in the treated eye category, except for left eyes of Subjects 2 and 5 with

critical values of 21.026. The null hypothesis is rejected for all fourteen eyes.

The rejection of the null hypothesis indicates that the changes seen in the curvature of the

cornea over the six-month follow-up period cannot be attributed to random fluctuations

alone, thus the hypothesis tests here suggest that the changes seen in the keratometric

behaviour of these eyes respectively are induced by the CXL procedure.

118

Table 5.3.15.1 Critical values and test statistics for the means of the four measurement sessions done on the majority of subjects, except for the left eyes of Subjects 2 and 5, which only had three follow-up visits. Hypothesis tests were done on the means; the null hypothesis is rejected if the test statistic (theta) is greater than or equal to the critical value. An asterisk (*) indicates statistically different changes.


SUBJECT THETA

Subject 1 OS 0.948* 0.066

Subject 2 OD 0.781* 0.066

Subject 2 OS 0.797* 0.074

Subject 3 OD 0.976* 0.066

Subject 4 OS 0.810* 0.066

Subject 5 OD 0.856* 0.066

Subject 5 OS 0.759* 0.074

Subject 6 OD 0.823* 0.066

Subject 7 OD 0.847* 0.066

Subject 8 OD 0.785* 0.066

Subject 9 OD 0.942* 0.066

Subject 9 OS 0.858* 0.066

Subject 10 OS 0.926* 0.066

Subject 11 OS 0.929* 0.066

119

Table 5.3.15.2 Critical values and test statistics for the variance-covariance of the four measuring sessions done on the majority of subjects, except for the left eyes of Subjects 2 and 5, which had three visits each. Hypothesis tests were done on the variance-covariance and the null hypothesis rejected if the test statistic (µ) is greater than or equal to the critical value ( An asterisk (*) indicates statistically different changes.


SUBJECT µ

Subject 1 OS 155.449* 28.869

Subject 2 OD 627.870* 28.869

Subject 2 OS 316.706* 21.026

Subject 3 OD 75.126* 28.869

Subject 4 OS 186.795* 28.869

Subject 5 OD 347.888* 28.869

Subject 5 OS 87.057* 21.026

Subject 6 OD 175.516* 28.869

Subject 7 OD 127.836* 28.869

Subject 8 OD 448.721* 28.869

Subject 9 OD 136.163* 28.869

Subject 9 OS 371.516* 28.869

Subject 10 OS 212.496* 28.869

Subject 11 OS 148.865* 28.869

120


It is important to know if meaningful change had occurred in the mean corneal curvature six

months after CXL when compared with the initial corneal curvature before the CXL

procedure was administered. The measurements of the first and last measurement sessions

for each eye were utilized to calculate the difference seen over the six-month period. The

difference was calculated by subtracting each of the fifty measurements of the first (before)

measurement session from the fifty measurements of the six-month post-operative

measurement session. A mean and mean variance-covariance was derived from the

resulting dataset of fifty differences for each eye and is provided in Table 5.3.16.1 and Table

5.3.16.2 respectively. The differences in Table 5.3.16.1 represent the curvature change that

took place in each eye in the six-month follow-up period. The variance-covariance is

provided in Table 5.3.16.2 and is related to the spread of the measurements in the data set.

The values in Table 5.3.16.1 are presented in Figure 5.3.16.1. Each data point symbolises

the difference seen for one of the subjects.

121

Table 5.3.16.1 Presents the differences between the means of the first and the last measurement sessions. Differences are presented in both conventional and component notation.

DIOPTRIC POWER



Subject 1 OS 0.08 1.08 13.82 0.62 0.48 0.25

Subject 2 OD 0.10 0.40 78.26 0.30 0.18 0.08

Subject 2 OS 0.62 0.65 79.96 0.30 0.31 0.11

Subject 3 OD 0.81 0.06 94.43 0.84 0.03 0.05

Subject 4 OS 0.07 0.66 3.05 0.40 0.33 0.04

Subject 5 OD 3.02 3.21 41.13 1.41 0.22 1.59

Subject 5 OS 0.27 0.35 27.51 0.10 0.10 0.14

Subject 6 OD 0.64 0.38 43.21 0.45 0.01 0.19

Subject 7 OD 1.75 0.50 4.10 2.00 0.25 0.04

Subject 8 OD 0.06 1.11 21.74 0.61 0.40 0.38

Subject 9 OD 1.51 0.74 32.80 1.14 0.15 0.34

Subject 9 OS 0.75 1.10 25.96 1.30 0.34 0.43

Subject 10 OS 0.15 0.22 64.51 0.04 0.07 0.09

Subject 11 OS 1.11 1.60 75.20 0.30 0.70 0.40

122

Table 5.3.16.2 The variance-covariance derived from the difference data set for each eye. Variance-covariance has units of diopters squared (D2).



I J K I-J J-K I-K

Subject 1 OS 0.036 0.028 0.014 0.018 0.000 0.003

Subject 2 OD 0.187 0.126 0.030 0.113 0.048 0.045

Subject 2 OS 0.052 0.016 0.012 0.023 0.010 0.020

Subject 3 OD 1.183 0.067 0.021 0.134 0.022 0.050

Subject 4 OS 0.027 0.008 0.009 0.004 0.001 0.002

Subject 5 OD 0.762 0.697 0.290 0.606 0.194 0.369

Subject 5 OS 0.393 0.346 0.047 0.235 0.098 0.070

Subject 6 OD 0.116 0.087 0.072 0.066 0.007 0.009

Subject 7 OD 0.158 0.037 0.037 0.047 0.005 0.021

Subject 8 OD 0.544 0.085 0.064 0.040 0.004 0.017

Subject 9 OD 0.252 0.076 0.051 0.036 0.008 0.012

Subject 9 OS 0.144 0.168 0.725 0.103 0.213 0.223

Subject 10 OS 0.012 0.010 0.007 0.002 0.001 0.003

Subject 11 OS 0.067 0.037 0.141 0.029 0.018 0.016

3 I

3 K

3 J

3 I

3 K

3 J

Figure 5.3.16.1 Presents the differences (Table 5.3.16.1) seen in each of the fourteen eyes included in the treatment group as data points. Origin is at plano or 0.00 I D. Axis length is 3 D and tick interval is set at 1 D on each axis.

123

Table 5.3.16.3 presents the mean difference of the means of the fourteen eyes included in

the treatment group, and Table 5.3.16.4 presents the overall variance-covariance difference

of the treatment group. Although the fourteen differences of the means seen over the six-

month follow-up period in the treatment group were inconsistent, the mean difference of

means in the group is small looking at the component values in Table 5.3.16.3 indicating

that not much change took place in the overall shape of the eyes included in the treatment

group six months post-operatively.

Table 5.3.16.3 Presents the mean of the differences between the first and the last measurement sessions for all fourteen eyes in the treatment group. The mean is presented in both conventional and component notation.

DIOPTRIC POWER



Treatment

Group 0.13 0.60 38.17 0.17 0.07 0.29

Table 5.3.16.4 The variance-covariance derived from the difference data set for each eye. Variance-covariance has units of diopters squared (D2).



I J K I-J J-K I-K

Treatment

Group 0.82 0.101 0.162 0.090 0.018 0.193

124

5.3.17 DISCUSSSION OF DIFFERENCES

The differences seen in Table 5.3.16.1 represent the keratometric behaviour seen in each of

the fourteen eyes included in the treatment group of subjects when only looking at the

before and six-month post-CXL measurement sessions. The stigmatic component of dioptric

power for each of the fourteen eyes in Table 5.3.16.1 covers a range from as little as 0.04 D

to 2.00 D giving us an indication of the diverse reactions induced by the CXL procedure six

months post-operatively. Looking at the variation in the stigmatic component the largest

amount of steepening that took place is 1.41 D (Subject 5 right eye) and the maximum

amount of flattening seen is 2.00 D (Subject 7 right eye). The CXL procedure induced the

least amount of change in the left eye of Subject 10 which had a change of only 0.04 D

steepening in the stigmatic component. The ortho antistigmatic component (For/J in Table

5.3.16.1) mostly decreased in size with the biggest reduction being 0.70 D (Subject 11 left

eye) and a maximum increase of 0.48 D (Subject 1 left eye). In the oblique antistigmatic

component (Fob/K in Table 5.3.16.1) the only decrease seen was 0.05 D in the right eye of

Subject 3 and a maximum increase of 1.59 D was seen in the right eye of Subject 5; the

magnitude of the change in the oblique antistigmatic power seen in Subject 5 was much

larger than what was seen in any of the other subjects in the treatment group. The

maximum increase in stigmatic and oblique antistigmatic components for this group are

both found in the right eye of Subject 5.

From the stigmatic components (seen in Table 5.3.16.1) for the fourteen eyes included in

the treatment group, seven eyes became flatter (the right eyes of Subjects 2, 3, 7 and 8 and

the left eyes of Subjects 1, 4 and 9) and the remaining seven eyes became steeper (the right

eyes of Subjects 5, 6 and 9 and the left eyes of Subjects 2, 5, 10 and 11). When considering

the stigmatic components of Subjects 2, 5 and 9 (Table 5.3.16.1), where both eyes were

included in the study, only the eyes of Subject 5 reacted the same by both becoming steeper

following the CXL procedure even though the magnitude of the change is very different

(0.10 and 1.41 D). Only the right eyes of Subjects 5 and 7 and both eyes of Subject 9 had a

change in any of the three components of dioptric power with a magnitude larger than

125

1.00 D. Table 5.3.16.2 presents the variance-covariance seen in the differences of the

fourteen eyes included in the treatment group.

Table 5.3.16.3 presents the mean of the fourteen differences from Table 5.3.16.1

representing the mean difference seen in the entire treatment group indicating that overall

change was seen in all three of the components, the stigmatic component of the group is

negative indicating that a decrease of 0.17 D took place in the stigmatic component

whereas an overall increase took place in the antistigmatic components. A small change of

0.07 D was effected in the ortho antistigmatic power and a change of 0.29 D in the oblique

antistigmatic component. The mean difference in Table 5.3.16.3 seems to suggest that not

much change takes place in the cornea when considering the change seen in the fourteen

eyes included in the treatment group which indicates that the procedure overall seems to

only alter the form of the cornea slightly. Table 5.3.16.4 presents the overall difference

seen in the variance-covariance of the fourteen eyes in the treatment group indicating that

the biggest change within the treatment group was seen in the variation of the stigmatic

components of each of the differences in Table 5.3.16.1. It is confirmed in Figure 5.3.16.1

presenting the differences seen in each of the eyes in the treatment group where the

biggest variation between the difference is seen along the stigmatic or I-axis causing the

included 95% distribution ellipsoid to orientated mainly along the stigmatic or I-axis. As far

as we know, no other research has mentioned the change in the antistigmatic components

of power following the CXL procedure.

126

5.4 KERATOCONIC CONTROL GROUP

The keratoconic control group consists of Subject 4’s right eye and Subject 7’s left eye. Both

eyes were diagnosed with keratoconus but did not receive crosslinking treatment for

various reasons. Each eye will be regarded separately, in the same pattern and concerning

the same information as the fourteen eyes included in the treatment group. The

measurement sessions for each of the two eyes in the keratoconic control group directly

followed the measurement of the specific subject’s contralateral eye, which was included in

the treatment group, for this reason the measurement sessions are similarly referred to as

before, one-week, one-month and six-month measurement sessions as the same timeline

was followed. In the graphical representation the pre-operative (before) measurement

session is again presented in black, the one-week measurement session in red, the one-

month session in green and the six-month post-operative measurement session in blue.

127

5.4.1 KERATOCONIC CONTROL SUBJECT 4 RIGHT EYE

The measurement data of the four measurement sessions of the right eye of Subject 4 are

represented in Figure 5.4.1.1, Appendix D 3.1 (a) and (b) as tight clusters that seem

superimposed and are similar in size.

The mean values of each of the four measurement sessions presented in Table 5.4.1.1 are

comparable, which correlates with the clusters of measurements being superimposed in

Figure 5.4.1.1, Appendix D 3.1 (a) and (b). In Table 5.4.1.2 the variance-covariance of the

four sessions resemble each other, implying that the fifty measurements taken within each

session are similar and the four sessions correlate with each other, giving rise to the tight

clusters of measurements in Figure 5.4.1.1 and Appendix D 3.1 (a) and (b).

When comparing Subject 4’s left eye (see Section 5.3.5), which was included in the

treatment group, with Subject 4’s right eye, the keratometric behaviour seems similar even

though the left eye received the CXL treatment. The similarity seen in and between the

measurements of the four measurement sessions in Subject 4’s right eye is comparable to

the right eye of Subject 3 and the left eyes of Subjects 4, 5 and 10, in the sense that not

much change took place in the eye over the six-month follow-up period.

Table 5.4.1.1 Presenting the dioptric power means of the four measurement sessions. Means are presented in both conventional and component notation.

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 49.53 4.20 113.3 47.43 1.45 1.53

One-week 49.74 4.30 111.6 47.59 1.57 1.48

One-month 49.58 3.98 112.8 47.59 1.39 1.42

Six-month 49.84 4.33 112.0 47.67 1.56 1.50

128

Table 5.4.1.2 Presenting the variance-covariance data for the entire six-month follow-up period. Variance-covariance has units of diopters squared (D2).


MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

Before 0.018 0.025 0.014 0.010 0.011 0.005

One-week 0.009 0.017 0.005 0.011 0.007 0.004

One-month 0.008 0.017 0.006 0.007 0.009 0.003

Six-month 0.011 0.009 0.003 0.006 0.001 0.001

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

Figure 5.4.1.1 Scatter plot illustrating the measurement data of the right eye of Subject 4. The first (before) measurements in black, one-week in red, one-month in green and six-month measurement session in blue. The origin is at 47.5 I D. Axis length is 3 D and tick interval is set at 1 D on each axis.

Hypothesis tests were conducted on the means and variance-covariance of the four

measurements and the hypotheses were rejected in both cases. The statistical data for the

means are presented in Table 5.4.1.3 and variance-covariance in Table 5.4.1.4.

Table 5.4.1.3 The critical value and test statistic for hypothesis test done on the means of the four measurement sessions. The null hypothesis was rejected if the test statistic (theta) was bigger than or equal to the critical value.


SUBJECT THETA

Subject 4 OD 0.726607 0.066

129

Table 5.4.1.4 Presenting the critical value and test statistic for hypothesis test on the variance-covariance of the four measurement sessions of the right eye of Subject 4. The null hypothesis was rejected if the test statistic (µ) was bigger than or equal to the critical value ( ).


SUBJECT µ

Subject 4 OD 115.035828 28.869

The difference between the first and six-month measurement sessions was calculated for

the means (Table 5.4.1.5) and variance-covariance (Table 5.4.1.6). In Table 5.4.1.5 the

difference in the stigmatic component indicates that the cornea became slightly steeper in

the six-month follow-up period which can be seen in Figure 5.4.1.1 and Appendix D 3.1 (a)

where the blue data is slightly above the other data on the I-axis. The variance-covariance

in Table 5.4.1.6 is minimal, indicating that little variation is found between the first and last

measurement sessions.

Table 5.4.1.5 Presents the mean difference between the first and last measurement sessions of Subject 4’s right eye. Means are presented in both conventional and component notation.

DIOPTRIC POWER



Subject 4 OD 0.36 0.23 83.92 0.24 0.11 0.024




I J K I-J J-K I-K

Subject 4 OD 0.030 0.037 0.017 0.018 0.012 0.004

130

To conclude, the data in Figure 5.4.1.1 illustrates the change in curvature of the cornea over

a six-month follow-up period. The black data represents the cornea at the first

measurement session; the red (one-week), green (one-month) and blue (six-month) data

sets are all superimposed showing us that little change took place in the form of this cornea

over the six-month period, although the blue data set indicates that the cornea became

slightly steeper after six months.

131

5.4.2 KERATOCONIC CONTROL SUBJECT 7 LEFT EYE

In Figure 5.4.2.1, Appendix D 3.2 (a) and (b), presenting the measurement data of all four

measurement sessions the red (one-week) distribution ellipsoid appears to be the biggest in

size and the smallest ellipsoids seen are the green (one-month) and blue (six-month)

ellipsoids which seem very similar in size.

From Table 5.4.2.1 we find that the stigmatic component (Fst/I) increased at the one-week

measurement session followed by a continuous decrease in the stigmatic component ending

at six months with a stigmatic component less than was measured at the first (before)

measurement session. The finding indicates that the cornea was the flattest at the six-

month follow-up measurement session which is similar to the right eyes of Subjects 2 and 7

and the left eye of Subject 1. Table 5.4.2.2 indicates that a larger amount of variation was

present between the measurements of the before and one-week measurement sessions

and at the one-month measurement session the variation reduced and remained at a similar

level at the six-month follow-up.

Table 5.4.2.1 The means of the autokeratometry readings for each of the four measurement sessions presented in both conventional and component notation.

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 52.90 5.65 65.2 50.07 1.83 2.15

One-week 54.63 6.18 51.1 51.54 0.65 3.02

One-month 52.05 5.34 58.3 49.38 1.19 2.39

Six-month 50.02 4.36 59.7 47.84 1.90 1.90

132



MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

Before 0.130 0.032 0.022 0.005 0.010 0.030

One-week 0.074 0.041 0.076 0.001 0.006 0.024

One-month 0.016 0.004 0.011 0.004 0.003 0.005

Six-month 0.014 0.012 0.009 0.007 0.001 0.003

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

Figure 5.4.2.1 Scatter plot illustrating the measurement data of Subject 7’s left eye. The measurements were taken at four different occasions, which are represented with different colours on the graph. The before measurements (black ellipsoid), one-week follow-up (red ellipsoid), one-month follow-up (green ellipsoid) and six-month follow-up measurement session (blue ellipsoid). The origin is at 50.0 I D. Axis length is 3 D and tick interval is set at 1 D on each axis.

Similar to all the eyes in the treatment group and the other eye in the keratoconic control

group, multivariate hypothesis tests were performed on the means and variance-covariance

data of the four measurement sessions respectively and were rejected in both cases (see

Table 5.4.2.3 and Table 5.4.2.4).

133

Table 5.4.2.3 The critical value and test statistic for hypothesis test done on the means of the four measurement sessions.


SUBJECT THETA

Subject 7 OS 0.976 0.066

Table 5.4.2.4 Presenting the critical value and test statistic for hypothesis test on the variance-covariance of the four measurement sessions of the left eye of Subject 7.


SUBJECT µ

Subject 7 OS 289.185 28.869

The means and variance-covariance differences between the first and six-month

measurement sessions were calculated and presented in Table 5.4.2.5 and Table 5.4.1.6

correspondingly. The stigmatic component In Table 5.4.2.5 indicates that the cornea

became flatter at the end of the six-month follow-up period and that this keratoconic

cornea had not progressed but regressed in the six-month follow-up period.

Table 5.4.2.5 Presents the mean difference of the first and last measurement sessions.

DIOPTRIC POWER



Subject 7 OS 1.43 1.61 170.87 2.24 0.76 0.25




I J K I-J J-K I-K

Subject 7 OS 0.157 0.052 0.018 0.004 0.004 0.022

134

In summary, Figure 5.4.2.1 shows a visual representation of the change seen between the

data sets over the six-month follow-up period. The black data set gives a visual indication of

the initial curvature of the cornea at the first measurement session. The red data set

indicates how the cornea steepened one week later. The green data set shows how the

cornea became flatter and the measurements became less variable one month later and the

blue data set illustrates how the cornea became even flatter and more stable at the six-

month measurement session.


The null hypothesis states that no statistically significant curvature change took place in the

corneas of the two eyes included in the keratoconic control group over a six-month follow-

up period. The null hypothesis was tested in the right eye of Subject 4 by comparing the

means (Table 5.4.1.1) of the four measurement sessions in component notation to each

other; likewise, the hypothesis test was also performed on Subject 7’s left eye by comparing

the four means (Table 5.4.12.1) to each other. The critical value and test statistic for the

means of the right eye of Subject 4 and the left eye of Subject 7 are displayed in Table

5.4.3.1. The null hypothesis was rejected if the test statistic (theta) was bigger than or equal

to the critical value ( ) of the involved eye. The critical value was found to be 0.066 for

both subjects, thus the null hypothesis is rejected in both cases.

Hypothesis testing was done on the variance-covariance for the respective measurement

session for each of the two keratoconic controls. The null hypothesis in this case, states that

no statistically significant variance-covariance change took place between the four

measurement sessions when comparing the variance-covariance found in the variance-

covariance matrix for each measurement session. The test statistic (µ) and the

corresponding critical value ( ) found on the Chi-square table are set out in Table 5.4.3.2.

The null hypothesis is rejected if the test statistic (µ) value was bigger or equal to the critical

value on the Chi-square table. The critical value, 28.869, is the same for both keratoconic

control eyes, and since the test statistics are larger, the null hypothesis is rejected in both

cases.

135

Table 5.4.3.1 Test statistics and critical values for the means of all four of the measurement sessions for Subject 4 (right eye) and Subject 7 (left eye).


SUBJECT THETA

Subject 4 OD 0.727 0.066

Subject 7 OS 0.976 0.066

Table 5.4.3.2 The critical values and test statistic for the hypothesis test done on the variance-covariance of the four measuring sessions done on the right eye of Subject 4 and the left eye of Subject 7.


SUBJECT µ

Subject 4 OD 115.036 28.869

Subject 7 OS 289.185 28.869


The difference between the first and last measurement session was calculated by

subtracting each of the fifty measurements of the first session from the fifty measurements

in the six-month follow-up session. From the resulting fifty measurements of the difference,

a mean was calculated as well as a variance-covariance matrix, revealed respectively in

Table 5.4.4.1 and Table 5.4.4.2.

The differences for each subject indicated the amount of change that took place in the six-

month follow-up period. In the cornea of the right eye of Subject 4, it is evident that the

cornea became slightly steeper, but looking at the relatively small differences in variance-

covariance for each component, the spread of the data remained mostly stable. In Subject

7’s left eye the values reveal a relatively large amount of flattening after the six-month

follow-up and the variance-covariance difference indicates a tighter cluster of

measurements.

136

In Figure 5.4.4.1 the full set of fifty differences seen in each of the keratoconic control eyes

are presented as data points with their corresponding 95% distribution ellipsoids, the black

measurements represent the right eye of Subject 4 and the red measurements present the

left eye of Subject 7. The black (Subject 4 right eye) ellipsoid seems to center around the

origin (0.00 I D) of the scatter plot in Figure 5.4.4.1, indicating a small change between the

data points of the difference set and thus measurements of the before and six-month

measurement sessions. The red (Subject 7 left eye) ellipsoid seems the largest in Figure

5.4.4.1, indicating that more variation was seen between the data points in the difference

data set for the left eye of Subject 7 and is confirmed by the larger variance-covariance seen

in Table 5.4.4.2 for Subject 7’s left eye; the red (Subject 7 left eye) ellipsoid is lower than the

origin on the I-axis revealing that the cornea became flatter. The distribution ellipsoids are

relatively far from each other and do not intersect, giving us an indication of how

inconsistent the change seen over the six-month follow-up is when comparing the two eyes

of the keratoconic control group. The mean difference seen in the right eye of Subject 4 is

presented as a single black data point and the mean difference in the left eye of Subject 7 as

a single red data point in Figure 5.4.4.2.

Table 5.4.4.1 The means of the differences between the first and the last measurement sessions.

DIOPTRIC POWER


SUBJECT SPHERE CYLINDER AXIS Fst/I For/J Fob/K

Subject 4 OD 0.36 0.23 84.0 0.24 0.11 0.02

Subject 7 OS 1.43 1.61 170.9 2.24 0.76 0.25

137



VARIANCE COVARIANCE

SUBJECT I J K I-J J-K I-K

Subject 4 OD 0.030 0.037 0.017 0.018 0.012 0.004

Subject 7 OS 0.157 0.052 0.018 0.004 0.004 0.022

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

Figure 5.4.4.1 Each data point represents the measurement difference between the first and last measurement sessions for the two keratoconic controls. The black 95% distribution ellipsoid and dots represent the right eye of Subject 4 and the red the left eye of Subject 7. The origin is at plano or 0.00 I D.

Figure 5.4.4.2 The black data point represents the mean difference of the right eye of keratoconic control Subject 4 and the red data point represents the mean difference seen in the left eye of keratoconic control Subject 7. The origin is at plano or 0.00 I D.

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

138

Table 5.4.4.3 Presents the mean of the differences between the first and the last measurement sessions for the two eyes in the keratoconic control group. Means are presented in both conventional and component notation.

DIOPTRIC POWER



Keratoconic

Control Group 0.54 0.92 127.45 1.00 0.33 0.12

Table 5.4.4.4 The mean variance-covariance derived from the difference data sets of the two eyes in the keratoconic control group. Variance-covariance has units of diopters squared (D2).



I J K I-J J-K I-K

Keratoconic

Control Group 0.094 0.045 0.018 0.011 0.008 0.013

5.4.5 DISCUSSION OF DIFFERENCES

The large discrepancy in measurement variation and thus cluster size is to be expected from

an irregular keratoconic cornea. The steepening seen in the right eye of Subject 4 is normal

as a slow progression of keratoconus is expected in a non-crosslinked eye of a patient in the

inclusion age group. What is surprizing is the rather large amount of flattening seen in the

left eye of Subject 7. Flattening in contralateral keratoconic control eyes of CXL subjects

has, as far as we know, not been documented before. Subject 7 suffers severe eczema and

a link between keratoconus and atopic disease has been established (Rahi et al, 1977). The

subject was questioned regarding his improved appearance at a follow-up session, as

marked eczema was seen on his face pre-CXL, which had to clear up before CXL was

administered. A homeopathic treatment regime for the eczema was revealed as well as a

daily overdose of vitamin C. The flattening seen in this eye coincided with a flattening and

stabilisation effect seen in the treated eye (in Section 5.3.9), the contralateral treated eye

139

was the eye that exhibited the largest amount of flattening seen in the treatment group.

The flattening could have been caused by a more stable tear layer forming over a possible

healthier epithelial layer because of the eczema being under control.

140

5.5 NON-KERATOCONIC CONTROL GROUP

Some fluctuation is expected in all living organisms, including the keratometric behaviour of

the normal eye (Kanellopoulos and Asimellis, 2013). To estimate how much variation is

seen in normal eyes, twelve eyes of six non-keratoconic control subjects were included in

the study. These subjects were all under the age of 35, none had previous eye surgery or

procedures done and all six control subjects did not have keratoconus. The measurement

sessions of the non-keratoconic control group were conducted on the same timeline as the

treatment and keratoconic control groups and for simplicity the first measurement session

will similarly be referred to as the before measurement session even though the eyes in this

group did not undergo crosslinking. Non-keratoconic control Subject 6 was the only subject

with an incomplete follow-up history in the non-keratoconic control group, only three of the

four measurement sessions were attended as the one-month measurement session could

not be attended.

Each eye will be regarded separately. The keratometric behaviour of each eye is provided in

two tables, one presenting the dioptric power of the mean for each measurement session in

both conventional and component notation and the second the variance-covariance data

for each session. A scatter plot presents the measurements for each measurement session

in a different colour. If possible outliers seemed to be present, tables with the altered

means and variance-covariance were provided for the changed data sets as well as a scatter

plot representing the altered data set. Hypothesis testing was done on the means and

variance-covariance seen in each eye and presented in two tables respectively, thereafter

the difference from the first to six-month measurement sessions for each eye is presented

in a table.

In general the non-keratoconic control group presented with flatter corneas when

compared to the treatment and keratoconic control groups and only a minimal amount of

the antistigmatic component. Lastly, a summary of the hypothesis tests and differences of

the twelve eyes in the non-keratoconic control group is presented together and discussed.

141

5.5.1 NON-KERATOCONIC CONTROL SUBJECT 1 RIGHT EYE

Very little variation is seen throughout the six-month follow-up period in the right eye of

non-keratoconic control Subject 1. In Figure 5.5.1.1, Appendix D 4.1 (a) and (b) the

measurements of all four measurement sessions seem very similar presenting as tight

clusters of different colours that are superimposed. Table 5.5.1.1 presents the means and

Table 5.5.1.2 the variance-covariance of the four measurement sessions which respectively

seem similar; the small magnitude of the variance-covariance is related to the spread of the

measurements indicating very little deviation of the measurements in each session and the

similarity of the means caused the clusters representing the measurement sessions to be

mostly superimposed. From Table 5.5.1.1 we gather that a minimal amount of antistigmatic

power is present in this eye

The black (before) data point seen deviating from the superimposed clusters in Figure

5.5.1.1, Appendix D 4.1 (a) and (b) could be a possible outlier but, since the variance in each

component seen in Table 5.5.1.2 for the first measurement session is relatively small, it was

not removed from the data set, as it was not believed to have a big influence in skewing the

means derived from this measurement session.

Table 5.5.1.1 The means of each of the four measurement sessions starting from the first (before) and ending at the six-month visit.

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 41.15 0.43 123.7 40.94 0.08 0.20

One-week 40.99 0.29 130.9 40.85 0.02 0.14

One-month 40.92 0.37 132.0 40.74 0.02 0.18

Six-month 40.97 0.38 130.3 40.78 0.03 0.19

142



MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

Before 0.009 0.003 0.005 0.002 0.000 0.004

One-week 0.004 0.005 0.003 0.002 0.001 0.001

One-month 0.006 0.005 0.002 0.001 0.000 0.001

Six-month 0.004 0.002 0.001 0.001 0.001 0.001

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

Figure 5.5.1.1 Scatter plot illustrating the measurement data of the right eye of non-keratoconic control Subject 1. The first measurement session is presented in black, one-week in red, one-month in green and the six-month measurements in blue. Origin is at 40.5 I D.

The statistical data related to the hypothesis test on the means is presented in Table 5.5.1.3

and on the variance-covariance of the four measurement sessions in Table 5.5.1.3. In both

cases the null hypothesis was rejected. Although the means and variance-covariances of the

four measurement sessions were found to be statistically different, the difference between

these sessions are not clinically significant.

143

Table 5.5.1.3 The critical value and test statistic for hypothesis test done on the means of the four measurement sessions of the right eye of non-keratoconic control Subject 1. The null hypothesis was rejected if the test statistic (theta) was bigger than or equal to the critical value.


SUBJECT THETA

Control Subject 1 OD 0.524 0.066

Table 5.5.1.4 The critical value and test statistic for hypothesis test done on the variance-covariance of the four measurement sessions of the right eye of non-keratoconic control Subject 1. The null hypothesis was rejected if the test statistic (µ) was bigger than or equal to the critical value ( ).


SUBJECT µ


Table 5.5.1.5 presents the overall difference that took place between the first and last

measurement sessions, the stigmatic component seemed to become slightly flatter, but the

difference in curvature in the follow-up period was not clinically significantly different.

Table 5.5.1.6 presents the difference between the variance-covariance of the first and last

measurement sessions and again the values are minimal making the difference seen

clinically insignificant.

Table 5.5.1.5 Presents the mean difference between the first and last measurement sessions of non-keratoconic control Subject 1. Means are presented in both conventional and component notation.

DIOPTRIC POWER



Control

Subject 1 OD 0.12 0.10 6.03 0.16 0.05 0.01

144




I J K I-J J-K I-K

Control

Subject 1 OD 0.012 0.005 0.007 0.002 0.001 0.002

5.5.2 NON-KERATOCONIC CONTROL SUBJECT 1 LEFT EYE

The two eyes of non-keratoconic control Subject 1 are very similar, not only in form, but in

the keratometric behaviour demonstrated over the six months monitored. In Figure 5.5.2.1,

Appendix D 4.2 (a) and (b) the four clusters of measurements representing the four

measurement sessions are tight and superimposed as was seen in the contralateral eye.

The means of the four measurement sessions in Table 5.5.2.1 are similar as well as the

variance-covariance of the four sessions in Table 5.5.2.2.

Table 5.5.2.1 Presents the means of the autokeratometer readings for each of the four measurement sessions.

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 41.64 0.92 75.9 41.19 0.40 0.22

One-week 41.56 0.92 78.1 41.10 0.42 0.18

One-month 41.28 0.74 79.7 40.90 0.35 0.13

Six-month 41.37 0.90 74.4 40.91 0.39 0.23

145



MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

Before 0.009 0.005 0.002 0.001 0.001 0.001

One-week 0.010 0.004 0.001 0.001 0.001 0.001

One-month 0.007 0.002 0.014 0.001 0.000 0.000

Six-month 0.008 0.007 0.004 0.001 0.004 0.000

3 I

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Figure 5.5.2.1 Stereo-pair scatter plot presenting the measurement data of all four measurement sessions for the left eye of non-keratoconic control Subject 1. The measurements are presented in black (before), red (one-week), green (one-month) and blue (six-month). Origin is at 40.5 I D.

Hypothesis testing on the means (Table 5.5.2.3) and variance-covariance (Table 5.5.2.4) of

the four measurement sessions were both rejected as the test statistic was bigger than the

critical value in both cases. Although the means and variance-covariance of the four

measurement sessions were found to be statistically different, the difference between the

measurement sessions are not clinically significant.

146

Table 5.5.2.3 The critical value and test statistic for hypothesis test done on the means of the four measurement sessions of the left eye of non-keratoconic control Subject 1. The null hypothesis was rejected if the test statistic (theta) was bigger than or equal to the critical value.


SUBJECT THETA

Control Subject 1 OS 0.667 0.066

Table 5.5.2.4 The critical value and test statistic for hypothesis test done on the variance-covariance of the four measurement sessions of the left eye of non-keratoconic control Subject 1. The null hypothesis was rejected if the test statistic (µ) was bigger than or equal to the critical value ( ).


SUBJECT µ


The mean difference in form over the six-month follow-up period was calculated by

subtracting the data from the last measurement session from the data of the first

measurement session. The difference in mean is presented in Table 5.5.2.5 and the

difference in variance-covariance in Table 5.5.2.6, a slight flattening was seen in the

stigmatic component but little other change in the six months.


DIOPTRIC POWER



Subject 1 OS 0.25 0.45 22.05 0.27 0.02 0.02

147




I J K I-J J-K I-K

Subject 1 OS 0.021 0.010 0.007 0.003 0.004 0.000

148


The right eye of non-keratoconic control Subject 2 is very similar to both eyes of non-

keratoconic control Subject 1. In Figure 5.5.3.1 the measurement sessions are presented in

tight clusters and are again superimposed. The means of the four measurement sessions in

Table 5.5.3.1 are very similar and the mean variance-covariance of the four sessions in Table

5.5.3.2 is similar.

Table 5.5.3.1 The means of the autokeratometer readings for each of the four measurement sessions starting from the first (before) and ending at the six-month follow-up.

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 45.39 0.80 80.3 44.99 0.38 0.13

One-week 45.54 0.90 89.2 45.09 0.45 0.01

One-month 45.44 0.85 84.5 45.02 0.42 0.08

Six-month 45.42 0.80 82.3 45.02 0.40 0.11

Table 5.5.3.2 Presents the variance-covariance for the entire six-month follow-up period.


MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

Before 0.003 0.001 0.001 0.001 0.000 0.001

One-week 0.004 0.001 0.001 0.000 0.000 0.000

One-month 0.003 0.001 0.001 0.000 0.000 0.000

Six-month 0.003 0.003 0.001 0.000 0.000 0.000

149

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Figure 5.5.3.1 Scatter plot presenting the measurement data for all four measurement sessions of the right eye of non-keratoconic control Subject 2. Origin is at 44.5 I D.

Table 5.5.3.3 and Table 5.5.3.4 present the statistical data for the hypothesis tests

conducted on the right eye of non-keratoconic control Subject 2, both were rejected.



SUBJECT THETA




SUBJECT µ


The difference data in Table 5.5.3.5 represents the difference seen between the means of

the first and last measurement sessions and Table 5.5.3.6 the difference between the

variance-covariance of the two sessions. From both we gather that the change seen in the

six-month follow-up period was clinically insignificant.

150


DIOPTRIC POWER



Control

Subject 2 OD 0.06 0.06 124.99 0.03 0.01 0.03




I J K I-J J-K I-K

Control

Subject 2 OD 0.005 0.005 0.003 0.000 0.001 0.000


The eyes of non-keratoconic control Subject 2 are very comparable in form and

keratometric behaviour throughout the six-month follow-up period indicated by the

similarity of the data in Table 5.5.4.1 and Table 5.5.4.2 respectively as well as the tight,

superimposed clusters seen in Figure 5.5.4.1, Appendix D 4.4 (a) and (b).

151

Table 5.5.4.1 The means of the four measurement sessions. Means are presented in both conventional notation and component notation.

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 45.26 0.78 85.3 44.88 0.38 0.06

One-week 45.32 0.89 87.0 44.87 0.45 0.05

One-month 45.44 0.85 84.5 45.02 0.42 0.08

Six-month 45.34 0.99 83.9 44.84 0.48 0.10



MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

Before 0.002 0.002 0.002 0.000 0.000 0.000

One-week 0.003 0.001 0.001 0.001 0.000 0.000

One-month 0.003 0.001 0.001 0.000 0.001 0.000

Six-month 0.003 0.001 0.002 0.000 0.002 0.001

3 I

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3 I

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Figure 5.5.4.1 Scatter plot illustrating measurement data for the left eye of non-keratoconic control Subject 2. The first measurements are presented in black, one-week in red, one-month in green and the six-month measurement session in blue. Origin is at 44.5 I D.

152

Table 5.5.4.3 and Table 5.5.4.4 present the statistical data for the hypothesis tests on the

means and variance-covariance of the four measurement sessions respectively, in both

cases the null hypothesis was rejected. Even though the changes seen between the means

and variance-covariances of the four measurement sessions were statistically significant, the

change seen is not clinically significant.



SUBJECT THETA




SUBJECT µ


Table 5.5.4.5 presents the mean difference and Table 5.5.4.5 the mean difference in

variance-covariance of the first and the last measurement sessions, and were small in both

cases indicating that little change took place in the six-month follow-up period.

153


DIOPTRIC POWER



Control

Subject 2 OS 0.08 0.22 78.83 0.03 0.10 0.04




I J K I-J J-K I-K

Control

Subject 2 OS 0.004 0.003 0.004 0.001 0.000 0.001

154


The right eye of non-keratoconic control Subject 3 appears to have the most variation

between measurements within measurement sessions for the non-keratoconic control

group when examining Figure 5.5.5.1. The clusters are still superimposed as seen in both

eyes of non-keratoconic control Subjects 1 and 2, but especially the red (one-week)

distribution ellipsoid seems to be larger. This is substantiated by the higher variance-

covariance seen in Table 5.5.5.2 although the means are still comparable in Table 5.5.5.1.

Table 5.5.5.1 Presenting the means for all four measurement sessions.

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 43.03 0.66 97.0 42.71 0.32 0.08

One-week 42.87 0.47 88.1 42.64 0.23 0.02

One-month 42.96 0.55 91.2 42.69 0.27 0.01

Six-month 43.16 0.86 94.7 42.73 0.43 0.07



MEASUREMENT

SESSION

VARIANCES COVARIANCES

I J K I-J J-K I-K

Before 0.014 0.009 0.003 0.000 0.001 0.001

One-week 0.031 0.045 0.005 0.016 0.003 0.002

One-month 0.007 0.010 0.001 0.003 0.001 0.000

Six-month 0.010 0.012 0.002 0.004 0.001 0.002

155

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Figure 5.5.5.1 Scatter plot illustrating the four measurement sessions being the first measurements (black), one-week (red), one-month (green) and six-month measurements (blue). Origin is at 42.5 I D. Axis length is 3 D and tick interval is set at 1 D on each axis.

The null hypothesis was rejected where the means of the four measurement sessions were

compared and where the four variance-covariances were compared. The statistical data is

presented in Table 5.5.5.3 and Table 5.5.5.4. The changes were statistically significant but

clinically insignificant.



SUBJECT THETA




SUBJECT µ


The difference in means (Table 5.5.5.5) and variance-covariance (Table 5.5.5.6) of the first

and the last measurement sessions are minimal indicating that the change seen in the six-

month follow-up period was clinically insignificant.

156


DIOPTRIC POWER



Control

Subject 3 OD 0.13 0.22 87.65 0.02 0.11 0.01




I J K I-J J-K I-K

Control

Subject 3 OD 0.015 0.019 0.005 0.002 0.000 0.002


The left eye of non-keratoconic control Subject 3 was similar to all the previous non-

keratoconic control eyes in form and keratometric behaviour over the full six-month follow

up period, as is seen in the scatter plots in Figure 5.5.6.1, Appendix D 4.6 (a) and (b) and

from the mean data in Table 5.5.6.1 and the mean variance-covariance data in Table 5.5.6.2.

157

Table 5.5.6.1 The means of the autokeratometer readings for each of the four measurement sessions starting from the first (before) and ending at the six-month measurement session.

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 42.95 0.67 80.2 42.62 0.31 0.11

One-week 42.76 0.50 77.0 42.52 0.22 0.11

One-month 42.87 0.48 76.5 42.64 0.21 0.11

Six-month 43.03 0.83 77.9 42.62 0.38 0.17



MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

Before 0.010 0.013 0.002 0.003 0.001 0.000

One-week 0.009 0.009 0.003 0.001 0.003 0.001

One-month 0.015 0.015 0.005 0.008 0.006 0.002

Six-month 0.009 0.013 0.004 0.006 0.004 0.002

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Figure 5.5.6.1 Scatter plot illustrating the measurement data of the left eye of non-keratoconic control Subject 3. The measurements were taken at four different occasions, the first measurements (black), one-week (red), one-month (green) and six-month (blue) measurement sessions. Origin is at 42.5 I D.

158

Hypothesis testing on the means and variance-covariance of the four measurement sessions

for this eye resulted in the null hypothesis being rejected in both cases, which was similar to

the previous five eyes included in the non-keratometric control group.



SUBJECT THETA




SUBJECT µ


The difference in means of the first and last measurement session was calculated and

presented in Table 5.5.6.5 and the variance-covariance in Table 5.5.6.6. In both cases the

means are small, indicating the stability of the cornea throughout the six-month follow-

up period.

Table 5.5.6.5 Presents the mean difference between the first and last measurement

sessions of non-keratoconic control Subject 3. Means are presented in both

conventional and component notation.

DIOPTRIC POWER



Control

Subject 3 OS 0.09 0.18 69.05 0.00 0.07 0.06

159




I J K I-J J-K I-K

Control

Subject 3 OS 0.020 0.024 0.007 0.007 0.006 0.003

160


The right eye of non-keratoconic control Subject 4 exhibited only slight variation between

the measurements in each measurement session concluded from the small amounts of

variance-covariance seen in Table 5.5.7.2, and the means of the four measurement sessions

in Table 5.5.7.1 are comparable, exhibiting similar keratometric behaviour as the other eyes

in the non-keratoconic control group.

A red measurement from the one-week measurement session is different to the rest of the

measurements seen in Figure 5.5.7.1, Appendix D 4.7 (a) and (b) and could be a possible

outlier. The deviating measurement was not removed from the data set as the variation

that it causes in the one-week mean and variance-covariance data, seen in Table 5.5.7.1 and

Table 5.5.7.2, doesn’t indicate departure from normality when comparing the one-week

information to the other measurement sessions for this eye.

Table 5.5.7.1 Presenting the means of the autokeratometer readings for each of the four measurement sessions starting from the first (before) and ending at the six-month visit.

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 44.32 0.60 78.13 44.02 0.28 0.12

One-week 44.21 0.56 76.13 43.93 0.25 0.13

One-month 44.23 0.60 68.87 43.93 0.22 0.20

Six-month 44.33 0.43 55.35 44.11 0.08 0.20

161



MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

Before 0.002 0.002 0.003 0.001 0.001 0.001

One-week 0.006 0.009 0.012 0.000 0.004 0.001

One-month 0.006 0.009 0.004 0.001 0.001 0.001

Six-month 0.002 0.006 0.002 0.002 0.000 0.000

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Figure 5.5.7.1 Scatter plot presenting the measurement data of the right eye of non-keratoconic control Subject 4. The before measurements are presented in black, one-week in red, one-month in green and the six-month measurements in blue. Origin is at 43.5 I D.

Multivariate statistical analysis was done by comparing the means in component notation

from Table 5.5.7.1 of all four measurement sessions and the test statistic and critical value

are presented in Table 5.5.7.3, and similarly multivariate analysis was done on the means of

the variance-covariance in Table 5.5.7.2 and presented in Table 5.5.7.4, in both tests the null

hypothesis was rejected as the test statistic is higher than the critical value.



SUBJECT THETA


162



SUBJECT µ


The difference was calculated by only considering the first and the last measurement

sessions for the means in Table 5.5.7.5 and for the means in variance-covariance in Table

5.5.7.6 in both cases the difference is small indicating that a clinically insignificant change

took place in this eye over the six-month period and compares to the other eyes in the non-

keratometric control group.

Table 5.5.7.5 Presents the mean difference between the first and last measurement sessions of non-keratoconic control Subject 4.

DIOPTRIC POWER



Control

Subject 4 OD 0.03 0.43 11.05 0.10 0.20 0.08




I J K I-J J-K I-K

Control

Subject 4 OD 0.004 0.009 0.005 0.003 0.002 0.005

163


Three of the keratometric measurements (two black (before) data points and one blue (six-

month) data point) presented in Figure 5.5.8.1 and Appendix D 4.8 (a) seem removed from

their respected measurement clusters. These measurements could be possible outliers, but

similar to this subject’s right eye, they do not seem to have an influence on the means and

variance-covariance in Table 5.5.8.1 and Table 5.5.8.2, as all the means in the respective

tables are comparable. This eye is related to the other eyes in the non-keratoconic control

group as the form of the cornea was stable throughout the six-month follow-up.

Table 5.5.8.1 Presenting the means of each of the four measurement sessions.

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 44.42 0.58 102.94 44.13 0.26 0.13

One-week 44.29 0.48 103.28 44.05 0.21 0.11

One-month 44.19 0.61 84.09 43.89 0.30 0.06

Six-month 44.63 0.40 123.57 44.43 0.08 0.18

Table 5.5.8.2 Presents the variance-covariance for each of the four measurement sessions.


MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

Before 0.020 0.015 0.007 0.012 0.003 0.004

One-week 0.008 0.009 0.003 0.001 0.001 0.001

One-month 0.002 0.003 0.001 0.002 0.001 0.001

Six-month 0.007 0.004 0.003 0.002 0.001 0.001

164

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3 I

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Figure 5.5.8.1 Scatter plot illustrating the measurements for the left eye of non-keratoconic control Subject 4. Each measurement session is presented in a different colour, the first measurement session in black, one-week in red, one-month in green and the six-month measurement session in blue. Origin is at 43.5 I D

Multivariate hypothesis tests were carried out on the means in component notation of all

four measurement sessions and the statistical data presented in Table 5.5.8.3. Multivariate

hypothesis tests were also done on the means in variance-covariance of the four

measurement sessions and presented in Table 5.5.8.4. Coinciding with the other eyes in the

non-keratoconic control group, the null hypothesis was rejected in both cases.

Table 5.5.8.3 The critical value and test statistic for hypothesis test done on the means of the four measurement sessions of the left eye of non-keratoconic control Subject 4.


SUBJECT THETA


Table 5.5.8.4 The critical value and test statistic for hypothesis test done on the variance-covariance of the four measurement sessions of the left eye of non-keratoconic control Subject 4.


SUBJECT µ


The differences in mean (Table 5.5.8.5) and mean variance-covariance (Table 5.5.8.6) of the

first and last measurement session in both cases are very small, indicating that little change

took place over the six-month follow-up period.

165


DIOPTRIC POWER



Control

Subject 4 OS 0.49 0.38 171.44 0.30 0.18 0.06




I J K I-J J-K I-K

Control

Subject 4 OS 0.018 0.019 0.009 0.010 0.005 0.004

166


Little change was exhibited over the six-month period. All four clusters representing the

four measurement sessions seem small and are superimposed in Figure 5.5.9.1 Appendix D

4.9 (a) and (b) and the means of the four measurement sessions in Table 5.5.9.1 and four

mean variance-covariance measurements are very similar respectively.

Table 5.5.9.1 Presents the mean of each of the measurement sessions. Means are presented in both conventional notation and component notation.

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 44.14 0.56 89.51 43.85 0.28 0.00

One-week 44.18 0.60 85.61 43.88 0.30 0.05

One-month 44.19 0.61 84.09 43.89 0.30 0.06

Six-month 44.22 0.62 80.78 43.91 0.29 0.10

Table 5.5.9.2 The variance-covariance for the four measurement sessions.


MEASUREMENT

SESSION

VARIANCES COVARIANCES

I J K I-J J-K I-K

Before 0.001 0.001 0.001 0.000 0.000 0.001

One-week 0.002 0.001 0.001 0.000 0.000 0.000

One-month 0.002 0.003 0.001 0.002 0.001 0.001

Six-month 0.002 0.001 0.001 0.001 0.000 0.000

167

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Figure 5.5.9.1 Scatter plot illustrating the measurement of the four measurement sessions of the right eye of non-keratoconic control Subject 5. The first measurement session is presented in black, one-week in red, one-month in green and six-month measurement session in blue. Origin is at 43.5 I D.

Corresponding to the other eyes included in the non-keratoconic control group the null

hypothesis was rejected when comparing the means of the four measurement sessions as

well as where the variance-covariance of the four sessions were compared.



SUBJECT THETA


Table 5.5.9.4 The critical value and test statistic for hypothesis test done on the variance-covariance of the four measurement sessions of the right eye of non-keratoconic control Subject 5.


SUBJECT µ


The differences for the means and variance-covariance of the first and last measurement

sessions (Table 5.5.9.5 and Table 5.5.9.6) indicated that little change took place over the six-

month period.

168

Table 5.5.9.5 Presents the mean difference between the first and last measurement sessions of non-keratoconic control Subject 5 right eye.

DIOPTRIC POWER



Control

Subject 5 OD 0.15 0.19 48.84 0.06 0.01 0.09




I J K I-J J-K I-K

Control

Subject 5 OD 0.003 0.002 0.002 0.000 0.000 0.002


Similar to the previous eyes included in the non-keratoconic control group, the clusters

representing the four measurement sessions are tight and superimposed in Figure 5.5.10.1,

Appendix D 4.10 (a) and (b) except for one black (before) data point. The means of the four

measurement sessions in Table 5.5.10.1 are comparable. The means of variance-covariance

presented in Table 5.5.10.2 are also comparable except for the before measurement session

that seems much bigger than the three variance-covariance means of the other three

measurement sessions. The black data point that seems to deviate from the other data

points in Figure 5.5.10.1, Appendix D 4.10 (a) and (b), represents a measurement from the

first measurement session and was identified as a possible outlier. It was removed from the

data set of the first measurement session. The mean and variance-covariance of the first

measurement session were then recalculated from the altered data set and the scatter plot

reconstructed to establish the influence of this possible outlier.

169

Table 5.5.10.1 The means of the autokeratometer readings for each of the four measurement sessions starting from the first (before) and ending at the six-month visit.

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 44.32 0.68 98.57 43.98 0.32 0.10

One-week 44.29 0.65 95.28 43.97 0.32 0.06

One-month 44.32 0.68 95.21 43.98 0.34 0.06

Six-month 44.29 0.60 97.55 43.99 0.29 0.08

Table 5.5.10.2 Presenting the variance-covariance of the four measurement sessions in the six-month follow-up period.


MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

Before 0.025 0.039 0.014 0.029 0.019 0.016

One-week 0.002 0.001 0.002 0.000 0.000 0.000

One-month 0.002 0.002 0.000 0.001 0.000 0.000

Six-month 0.002 0.002 0.001 0.001 0.000 0.000

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Figure 5.5.10.1 Scatter plot presenting the measurements for the left eye of non-keratoconic control Subject 5. Each data point represents a single measurement. The first measurements are presented in black, one-week in red, one-month in green and six-month measurements in blue. Origin is at 43.5 I D. Axis length is 3 D and tick interval is set at 1 D on each axis.

170

The original and altered means and variance-covariance of the first measurement session is

presented in Table 5.5.10.3 and Table 5.5.10.4. The possible outlier did not have a

noteworthy influence on the mean of the first measurement session as the means in Table

5.5.10.3 are comparable. In Table 5.5.10.4 the removal of the possible outlier from the data

set of the first measurement session caused a decrease in the variance-covariance of each

component, the altered variance-covariance in accordance with the variance-covariance

data of the one-week, one-month and six-month measurement sessions in Table 5.5.10.2.

In Figure 5.5.10.2 the measurements of the altered data set are presented in black, together

with the measurement of the other three measurement sessions. The altered data set

presents the same as the original data set, only without the one deviating black data point

and gave rise to a smaller cluster of measurements that no longer stands out.

Table 5.5.10.3 One possible outlier was removed from the data set of the first measurements. Consequently the mean for the new data set changed. The table presents the original mean and the altered mean for the first measurement session.

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 44.32 0.68 98.57 43.98 0.32 0.10

Altered before 44.37 0.72 96.87 44.00 0.35 0.09

Table 5.5.10.4 After removal of one possible outlier the variance-covariance for the one-week measurement session changed and can be compared in this table.


MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

Before 0.025 0.039 0.014 0.029 0.019 0.016

Altered before 0.003 0.002 0.004 0.000 0.000 0.001

171

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Figure 5.5.10.2 Scatter plot illustrating measurements of the left eye of non-keratoconic control Subject 5 after a possible outlier was removed from the one-week measurement data. Origin is at 43.5 I D. Axis length is 3 D and tick interval is set at 1 D on each axis.

Hypothesis testing was done on the means in Table 5.5.10.1 by comparing all four

measurement sessions in component notation and the null hypothesis rejected according to

the statistical data in Table 5.5.10.5. Similarly, hypothesis testing was done on the variance-

covariance means of the four measurement sessions found in Table 5.5.10.2 and presented

in Table 5.5.10.6 where the null hypothesis is again rejected, indicating that the change in

curvature seen between the different components of the four measurement sessions were

statistically significantly different; since the values are small, little change took place

showing the stability of the corneal curvature over the six-month follow-up period making

the change clinically insignificant.



SUBJECT THETA




SUBJECT µ


172

The differences were calculated from the first and last measurement sessions. The

difference in mean presented in Table 5.5.10.7 indicates that little change took place. The

difference in variance-covariance presented in Table 5.5.10.8 is higher than seen in the

other eyes included in the non-keratoconic control group. The higher variance-covariance is

caused by the presence of the possible outlier in the data set the difference was calculated

from.


DIOPTRIC POWER



Control

Subject 5 OS 0.05 0.08 16.12 0.01 0.03 0.02




I J K I-J J-K I-K

Control

Subject 5 OS 0.032 0.047 0.012 0.035 0.019 0.015

173


Non-keratoconic control Subject 6 was not able to attend his one-month measurement

session. As a result, only the before, one-week and six-month measurement sessions are

presented. The keratometric behaviour of this eye is related to the other non-keratoconic

controls in this category, indicated by the tight, superimposed clusters of measurements in

Figure 5.5.11.1, Appendix D 4.11 (a) and (b), the similarity in the means of the three

measurement sessions in Table 5.5.11.1 as well as the variance-covariance of the three

measurement sessions in Table 5.5.11.2.

Table 5.5.11.1 The means of the measurements of the three measurement sessions (no one-month measurement data is available for this patient).

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 45.28 0.76 116.63 44.90 0.23 0.31

One-week 45.20 0.69 117.49 44.86 0.20 0.28

Six-month 45.10 0.62 118.94 44.79 0.16 0.26

Table 5.5.11.2 Presenting the variance-covariance for before, one-week and six-month measurement sessions. Variance-covariance has units of diopters squared (D2).


MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

Before 0.007 0.009 0.004 0.001 0.001 0.002

One-week 0.025 0.014 0.007 0.004 0.000 0.001

Six-month 0.010 0.004 0.005 0.000 0.001 0.001

174

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

Figure 5.5.11.1 Scatter plot illustrating the measurements of the right eye of non-keratoconic control Subject 6. The measurements were taken at three different occasions, which are represented with different colours on the graph. The first measurements (black), one-week (red) and six-month measurement session (blue). Origin is at 44.5 I D

Multivariate hypothesis tests were conducted on the means of the three measurement

sessions (in component notation) as well as a separate multivariate hypothesis test on the

variance covariance of the three measurement session. The statistical data is presented in

Table 5.5.11.3 for the means and Table 5.5.11.4 for the variance-covariance and in both

cases the null hypothesis was rejected which correlated with the other eyes in the non-

keratoconic control group. The means and variance-covariances were found to be

statistically significant, nonetheless the magnitude of the changes between the different

measurement sessions are too small to be clinically significant.

Table 5.5.11.3 The critical value and test statistic for hypothesis test done on the means of the three measurement sessions of the right eye of non-keratoconic control Subject 6. The null hypothesis was rejected if the test statistic (theta) was bigger than or equal to the critical value.


SUBJECT THETA


Table 5.5.11.4 The critical value and test statistic for hypothesis test done on the variance-covariance of the three measurement sessions of the right eye of non-keratoconic control Subject 6. The null hypothesis was rejected if the test statistic (µ) was bigger than or equal to the critical value ( ).


SUBJECT µ


175

The differences were calculated looking at only the first and the last measurement sessions.

The difference in means (Table 5.5.11.5) as well as the difference in variance-covariance

(Table 5.5.11.6) are very small indicating that the change seen in the six-month follow-up

period was not clinically significant and that the corneal curvature was stable over the six-

month period.


DIOPTRIC POWER



Control

Subject 6 OD 0.03 0.16 17.37 0.11 0.06 0.04




I J K I-J J-K I-K

Control

Subject 6 OD 0.003 0.011 0.011 0.000 0.003 0.003


Similar to the right eye of non-keratoconic control Subject 6, the left eye does not have

measurement data for the one-month measurement session. In Figure 5.5.12.1 the clusters

of measurements were superimposed and more spread out when compared to the other

eleven eyes in the non-keratoconic control group. One red (one-week) data point seems to

deviate from the rest of the data points and was identified as a possible outlier but was not

removed from the one-week data set because the means of the three measurement

sessions in Table 5.5.12.1 presented very similar. The variance-covariance of all three

176

measurement sessions in Table 5.5.12.2 seem to be larger when compared to the other eyes

included in the non-keratoconic control group.

Table 5.5.12.1 Presents the means of the autokeratometer readings for each of the three measuring sessions.

DIOPTRIC POWER

MEASUREMENT

SESSION



Before 44.98 0.66 50.56 44.64 0.06 0.33

One-week 44.93 0.53 47.19 44.67 0.02 0.26

Six-month 44.99 0.64 48.68 44.67 0.41 0.32

Table 5.5.12.2 Presents the variance-covariance for the first, one-week and six-month measurement sessions.


MEASUREMENT

SESSION

VARIANCE COVARIANCE

I J K I-J J-K I-K

Before 0.019 0.009 0.017 0.001 0.003 0.003

One-week 0.047 0.009 0.036 0.003 0.001 0.032

Six-month 0.023 0.026 0.015 0.008 0.000 0.005

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J Figure 5.5.12.1 Scatter plot presenting the measurements for the left eye of non-keratoconic control Subject 6. The first measurements are presented in black, the one-week in red and the six-month measurement session in blue. Origin is at 44.5 I D.

177

The multivariate hypothesis tests on the means and variance-covariance of the three

measurement sessions resulted in the null hypothesis being accepted for the means and

rejected for the variance-covariance. This is the only null hypothesis that was accepted in

this study.

Table 5.5.12.3 The critical value and test statistic for hypothesis test done on the means of the three measurement sessions of the left eye of non-keratoconic control Subject 6. The null hypothesis was rejected if the test statistic (theta) was bigger than or equal to the critical value.


SUBJECT THETA




SUBJECT µ


The difference between the first and last measurement sessions of the means and variance-

covariance were calculated respectively. The difference in means Table 5.5.12.5 attests to

the minimal change seen over the six-month period where as the difference in variance-

covariance was larger than seen in most of the other non-keratoconic control eyes, but still

the differences seen in the non-keratoconic control eyes are all clinically insignificant as the

corneal curvatures remained stable throughout the entire six-month period.

178

Table 5.5.12.5 Presents the mean difference between the first and last measurement sessions of non-keratoconic control Subject 6.

DIOPTRIC POWER



Control

Subject 6 OS 0.05 0.05 171.93 0.02 0.02 0.01




I J K I-J J-K I-K

Control

Subject 6 OD 0.052 0.031 0.022 0.019 0.002 0.008


Similar to the test eye, treatment group and the keratoconic control group multivariate

statistical analysis was performed by comparing the means of the four measurement

sessions per eye (three measurement sessions for non-keratoconic control Subject 6) in

component notation with each other by utilizing a hypothesis test. Similarly, multivariate

statistical analysis by way of a hypothesis test was done on the variance-covariance of the

four measurement sessions per eye (three measurement sessions for Subject 6). The null

hypothesis states that no statistically significant curvature change took place in the cornea

of the specific eye considered (included over a six-month follow-up period). The critical

value and test statistic for the means of all twelve non-keratoconic control eyes are

displayed in Table 5.5.13.1. The null hypothesis was rejected if the test statistic (theta) was

bigger than or equal to the critical value ( ) of the involved eye. The critical value was

found to be 0.066 for non-keratoconic control Subjects 1 to 5 and 0.074 for non-keratoconic

control Subject 6 (only patient that had only three measurement sessions) thus the null

179

hypothesis is rejected for all the eyes in this category, except for the left eye of non-

keratoconic control Subject 6, where the null hypothesis is accepted.

Thereafter hypothesis testing was done on the variance-covariance of the respective

measurement sessions for each eye of non-keratoconic control Subjects 1 to 6. The null

hypothesis in this case states that no statistically significant variance-covariance change

took place between the four measurement sessions (three in the case of non-keratoconic

control Subject 6), when comparing the variance-covariance found in the variance-

covariance matrix for each measurement session. The test statistic (µ) and the

corresponding critical value ( ) found on the Chi-square table are set out in Table 5.5.13.2.

The null hypothesis was rejected if the test statistic (µ) value was bigger or equal to the

critical value on the Chi-square table. The critical value was 28.869 for each eye of non-

keratoconic control Subjects 1 to 5, and 21.026 for both eyes of non-keratoconic control

Subject 6. As the test statistic seen for each of the non-keratoconic control eyes in Table

5.5.13.2 was larger than the corresponding critical value the null hypothesis is rejected for

all twelve eyes in the non-keratoconic control group.

The hypothesis tests imply that the changes seen between the components of the means

and variance-covariance of the four measurement (three for Subject 6) sessions were

statistically significantly different, although this is the case the changes were minimal which

makes the changes clinically insignificant and the cornea is regarded as stable throughout

the six-month follow-up period. In the left eye of non-keratoconic control Subject 6, the null

hypothesis was accepted when testing the means of the three measurement sessions,

indicating that the components of all three means for this eye were statistically and clinically

significantly similar.

180

Table 5.5.13.1 Critical values and test statistics for the means of the four measuring sessions done on non-keratoconic control Subjects 1 to 5 and the three measuring sessions on non-keratoconic control Subject 6. An asterisk (*) indicates a significant difference between means.


NON-KERATOCONIC

CONTROL GROUP

THETA

Control Subject 1 OD 0.524* 0.066

Control Subject 1 OS 0.667* 0.066











181

Table 5.5.13.2 Critical values and test statistics for the variance-covariance of the four measurement sessions done on non-keratoconic control Subjects 1 to 5 and the three measuring sessions on non-keratoconic control Subject 6. An asterisk (*) indicates significant difference.


NON-KERATOCONIC

CONTROL GROUP

µ














It is of value to know what the overall change in corneal curvature for each of the twelve

eyes that were included in the non-keratoconic control group was to establish what change

in corneal curvature takes place in a normal cornea over six months. For each of the twelve

eyes in the non-keratoconic control group, a difference of means was calculated by

subtracting each of the fifty keratometric measurements of the first measurement session

from the fifty keratometric measurements of the six-month measurement session of the

involved eye, resulting in a data set of fifty difference measurements. From this difference

data set the mean was calculated (mean difference) as well as the variance-covariance

182

(mean difference variance-covariance) and are respectively presented in Table 5.5.14.1 and

Table 5.5.14.2.

The differences of means listed in Table 5.5.14.1 represent the amount of change that took

place in the shape of each of the twelve eyes included in the non-keratoconic control group

over the six-month follow-up period. The mean variance-covariance differences listed in

Table 5.5.14.2 represent the spread of the fifty measurements calculated for each of the

twelve eyes in the non-keratoconic control group.

The twelve differences of means (Table 5.5.14.1) of the non-keratoconic control group are

presented in Figure 5.5.14.1 as twelve red data points that form a tight cluster around the

origin of the scatter plot (0.00 I D), indicating the similarity of the twelve differences of

means and the small magnitude of these differences, suggesting that the change seen in the

non-keratoconic group as a whole was very minimal.

The overall mean of the differences seen in the twelve eyes of the non-keratoconic control

group is presented in Table 5.5.14.3 and the overall mean difference in variance-covariance

is presented in Table 5.5.14.4.

183

Table 5.5.14.1 The differences of means between the first and the last measurement session of twelve eyes included in the non-keratoconic control group. Means are presented in both conventional and component notation.

DIOPTRIC POWER

NON-

KERATOCONIC

CONTROL

GROUP



Control 1 OD 0.12 0.10 6.03 0.16 0.05 0.01

Control 1 OS 0.25 0.45 22.05 0.27 0.02 0.02

Control 2 OD 0.06 0.06 124.99 0.03 0.01 0.03

Control 2 OS 0.08 0.22 78.83 0.03 0.10 0.04

Control 3 OD 0.13 0.22 87.65 0.02 0.11 0.01

Control 3 OS 0.09 0.18 69.05 0.00 0.07 0.06

Control 4 OD 0.03 0.43 11.05 0.10 0.20 0.08

Control 4 OS 0.49 0.38 171.44 0.30 0.18 0.06

Control 5 OD 0.15 0.19 48.84 0.06 0.01 0.09

Control 5 OS 0.05 0.08 16.12 0.01 0.03 0.02

Control 6 OD 0.03 0.16 17.37 0.11 0.06 0.04

Control 6 OS 0.05 0.05 171.93 0.02 0.02 0.01

184

Table 5.5.14.2 The mean difference in variance-covariance for each of the eyes in the non-keratoconic control group.


NON-

KERATOCONIC

CONTROL

GROUP

VARIANCE COVARIANCE

I J K I-J J-K I-K

Control 1 OD 0.012 0.005 0.007 0.002 0.001 0.002

Control 1 OS 0.021 0.010 0.007 0.003 0.004 0.000

Control 2 OD 0.005 0.005 0.003 0.000 0.001 0.000

Control 2 OS 0.004 0.003 0.004 0.001 0.000 0.001

Control 3 OD 0.015 0.019 0.005 0.002 0.000 0.002

Control 3 OS 0.020 0.024 0.007 0.007 0.006 0.003

Control 4 OD 0.004 0.009 0.005 0.003 0.002 0.005

Control 4 OS 0.018 0.019 0.009 0.010 0.005 0.004

Control 5 OD 0.003 0.002 0.002 0.000 0.000 0.002

Control 5 OS 0.032 0.047 0.012 0.035 0.019 0.015

Control 6 OD 0.003 0.011 0.011 0.000 0.003 0.003

Control 6 OS 0.052 0.031 0.022 0.019 0.002 0.008

3 I

3 K

3 J

3 I

3 K

3 J

Figure 5.5.14.1 Presents the mean differences of the twelve eyes in the non-keratoconic control group together as a cluster of data points. The 95% distribution ellipsoid is included. The origin is set at plano or 0.00 I D.

185

Table 5.5.14.3 Presents the mean difference of the entire non-keratoconic control group.

DIOPTRIC POWER



Non-

keratoconic

Control Group 0.03 0.07 23.1 0.00 0.02 0.02

Table 5.5.14.4 The mean variance-covariance difference of the whole non-keratoconic control group.


VARIANCE COVARIANCE

GROUP I J K I-J J-K I-K

Non-

keratoconic

Control Group 0.020 0.009 0.002 0.005 0.001 0.001

5.5.15 DISCUSSION OF THE DIFFERENCES

In Table 5.5.14.1 looking at the stigmatic (Fst/I) component of the differences in the twelve

eyes of the non-keratoconic control group, a negative value indicates a flattening of the

cornea and a positive value a steepening. Four eyes became steeper in the six-month

follow-up period (both eyes of non-keratoconic control Subject 1, the left eye of non-

keratoconic control Subject 2 and the right eye of non-keratoconic control Subject 6)

whereas the other eight eyes in the non-keratoconic control group became steeper (it

seems that the left eye of non-keratometric control Subject 3 displayed no change in the

Fst/I component, but this is due to round off as a small amount of steepening did take

place). The values in Table 5.5.14.1 are small, ranging from 0.27 D to 0.30 D which

indicate that only small amounts of corneal curvature change took place in the eyes of the

non-keratoconic control group over the six-month follow-up period. Looking at the

stigmatic component of the differences in Table 5.5.14.1, we see that the largest amount of

186

flattening was 0.27 D and took place in the left eye of non-keratoconic control Subject 1.

The largest amount of steepening was 0.30 D and took place in the left eye of non-

keratoconic control Subject 4. The change seen in the stigmatic component of these two

eyes could be seen as clinically significant (as it is higher than 0.25 D which is the lowest

dioptric power that is generally prescribed) whereas the other ten eyes in the non-

keratoconic control group displayed clinically insignificant amounts of change. The

relatively larger amounts of change seen in the left eyes of non-keratoconic control Subjects

1 and 4 could be attributed to a possible unstable tear film in both cases. The antistigmatic

components of the differences in Table 5.5.14.1 are small, with non-keratoconic control

Subject 4 presenting with the biggest change seen in For/J in the right eye with 0.20 D and

the left eye with 0.18 D.

The mean difference and mean variance-covariance of the differences of the entire non-

keratoconic control group are presented in Table 5.5.14.3 and Table 5.5.14.4 respectively.

The low values of the components of the mean difference indicate the minimal change that

was seen between the first and six-month measurement sessions of the group as a whole

and the mean variance-covariance of the differences of the group indicate the stability of

the measurements taken at the first and last measurement sessions when compared to

each other. Considering the values in Table 5.5.14.3 and Table 5.5.14.4, the overall change

seen in the non-keratoconic control group was clinically insignificant, as essentially no

difference was seen in the corneal curvature of the twelve eyes included in the non-

keratoconic control group.

Figure 5.5.14.1 presents the differences for each of the twelve eyes in the non-keratoconic

control eyes as red data points which are centered around the origin (0.00 I D) and forming

a tight cluster, again suggesting the similarity of the change seen in the non-keratoconic

control group as a whole.

187

5.6 COMPARISON OF THE MEAN DIFFERENCES SEEN IN THE THREE GROUPS

The mean difference seen in the entire treatment group of fourteen subjects, the mean

difference of the two subjects in the keratoconic control group and the twelve eyes of the

non-keratoconic control group are displayed in Table 5.6.1 and the mean difference in

variance-covariances of each of the three subject groups respectively in Table 5.6.2.

For graphical comparison of the differences seen in each of the three subject groups, the

data points from Figure 5.3.15.1, Figure 5.4.4.2 and Figure 5.5.14.1 were combined in Figure

5.6.1 (different orientations of the scatter plot is seen in Appendix D 5 (a) and (b)). In Figure

5.6.1 (Appendix d 5 (a) and (b)) the mean differences of the treatment group are presented

as black data points, the mean differences of the two eyes of the keratoconic control group

as green data points and the mean differences non-keratoconic control group as red data

points. The 95% distribution ellipsoids are included for the treatment group and the non-

keratoconic control group, but the distribution ellipsoid for the two eyes included in the

keratoconic control group was not included as the sample size of this group is small. The

two green data points in Figure 5.6.1 that represent the differences of the two eyes included

in the keratoconic control group could be difficult to identify; please refer to Figure 5.4.4.2

where only the differences of the two eyes included in the keratoconic control group are

presented on the scatter plot (in Figure 5.4.4.2 the mean difference seen in the right eye of

Subject 4 is presented as a single black data point and the mean difference seen in the left

eye of Subject 7 as a single red data point). The test eye was not included in this

comparison of the three subject groups because it was mainly used as a calibration tool for

the autokeratometer and in Figure 5.6.1 the data point representing the mean difference

for the test eye would have been close to the origin and would be lost due to the other data

points super imposing the reading.

188

Table 5.6.1 The means of the differences between the first and the last measurement sessions for the treatment and control groups. The means are presented in both conventional and component notation. In conventional notation the sphere and cylinder are measured in diopters (D) and the axis in degrees, whereas in component notation all the components are measured in diopters (D).

DIOPTRIC POWER

GROUP CONVENTIONAL NOTATION COMPONENT NOTATION


Treatment 0.13 0.60 38.2 0.17 0.07 0.30

Keratoconic

Control 0.54 0.92 127.45 1.00 0.33 0.12

Non-keratoconic

Control 0.03 0.07 23.1 0.00 0.02 0.02

Table 5.6.2 The variance-covariance for the mean differences seen in the treatment and non-keratoconic control groups. Variance-covariance has units of diopters squared (D2).


VARIANCE COVARIANCE

GROUP I J K I-J J-K I-K

Treatment 0.821 0.101 0.162 0.090 0.018 0.193

Keratoconic

Control 0.094 0.045 0.018 0.011 0.008 0.013

Non-keratoconic

Control 0.020 0.009 0.002 0.005 0.001 0.001

189

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

3 I

3 K

3 J

Figure 5.6.1 Presents the difference measurements seen in the treatment group in black, the keratoconic control group in green and the non-keratoconic control group in red. The 95% distribution ellipsoids for the black (treatment group) and red (non-keratoconic control group) data points are included. The origin is set at plano or 0.00 I D.

5.6.1 DISCUSSION OF THE DIFFERENCES IN THE THREE SUBJECT GROUPS

The mean differences in each of the three subject groups seen in Table 5.6.1 are important

as they relate to the overall change seen in the curvature of keratoconic corneas treated

with CXL, untreated keratoconic corneas and non-keratoconic corneas over a six-month

follow-up period. In Table 5.6.1 the mean difference for the keratoconic control group

seems higher than the mean differences of the other two subject groups. The large mean

difference indicating a flattening of 1.00 D in the stigmatic component testifies to the

large variation in keratoconic behaviour measured over the six-month follow-up period

when comparing the two eyes in the keratoconic control group with each other. Since the

keratoconic control group only comprised of two eyes, not much emphasis is placed on the

large mean difference seen in the keratoconic control group. The overall mean difference in

the non-keratoconic control group presented in Table 5.6.1 is close to zero, the stigmatic

component is displayed as 0.00 D because of round off, which indicates that the mean

change seen in the twelve eyes of the non-keratoconic control group was minimal and the

curvature of non-keratoconic control eyes are stable over a six-month follow-up period. The

mean difference seen in Table 5.6.1 for the treatment group is larger compared to the mean

difference seen in the non-keratoconic control group. Considering the stigmatic (Fst/I)

component, the eyes in the treatment group as a whole seemed to become 0.17 D flatter

six months after the CXL procedure was performed. Note that a change of 0.30 D was seen

in the Fob/K component indicating that the CXL procedure had an influence on the

antistigmatic power of the corneas of the treatment group six months post-operatively. The

190

mean changes seen in both the treatment and non-keratoconic control groups in Table 5.6.1

indicate that a minimal amount of change took place in both groups over the six-month

follow-up period.

In Table 5.6.2 the mean variance-covariance difference for each of the three subject groups

is presented; a large discrepancy is seen between the readings of the control groups and the

treatment group. The mean variance-covariance difference seen in Table 5.6.2 for the

keratoconic control group is more comparable to the mean variance-covariance of the non-

keratoconic control group in the same table, but since the sample size of the keratoconic

control group was much smaller than the other subject groups, not much emphasis will be

placed on these readings. The non-keratoconic control group presented with minimal

difference in variance-covariance (seen in Table 5.6.2), implying that the difference seen

between the first and last measurement sessions of the twelve eyes included in the non-

keratoconic control group were similar. The mean difference in variance-covariance of the

treatment group in Table 5.6.2 is notably large when compared to the other groups in the

same table, the large variance-covariance indicates that the mean differences of the

fourteen eyes in the treatment group are mismatched, implying that the keratometric

behaviour induced by the CXL procedure in the fourteen eyes of the treatment group is

inconsistent. The mean difference in variance-covariance seen in Table 5.6.2 for the

treatment group seems to be the largest along the I-axis, implying that the discrepancy of

the keratometric behaviour of the fourteen eyes included in the treatment group was

mostly in the stigmatic components.

The black ellipsoid in Figure 5.6.1 (Appendix D 5 (a) and (b)) seems large as the fourteen

black data points representing the mean differences of the fourteen eyes in the treatment

group are spread out, which indicates that the differences seen in the fourteen eyes are

mostly unrelated to each other. In Figure 5.6.1 (Appendix D 5 (a) and (b)) the twelve red

data points representing the mean differences seen in the non-keratoconic control group

seem to form a tight cluster which seems centered around the origin of the graph, indicating

that the differences seen in the twelve eyes of the non-keratoconic control group were

more related to one another and minimal as the origin is set at 0.00 I D.

191

In Figure 5.6.1 (Appendix D 5 (a) and (b)) the tight red cluster of data points (representing

the differences of the non-keratoconic control group) and the loose cluster of black data

points (representing the mean differences of the treated eyes) represent the mismatch seen

in the keratometric behaviour that took place in the shape of the treatment group and the

non-keratoconic control group over the six-month follow-up period. The non-keratoconic

control subjects as a group demonstrated a higher degree of conformity in keratoconic

behaviour overall.

In Figure 5.6.1 (Appendix D 5 (a)), seven of the treated subjects show progression (in

variable degrees) of their keratoconus six months after undergoing the CXL procedure which

could indicate that a repeated CXL procedure should be done on these eyes; a repeat of the

CXL procedure has been found to stop continuous progression after the first CXL procedure

failed (Raiskup et al, 2015).

192

CHAPTER 6

DISCUSSION

193

6.1 GENERAL TRENDS SEEN IN THE KERATOMETRIC BEHAVIOUR OF THE TREATMENT, KERATOCONIC CONTROL AND NON-KERATOCONIC CONTROL GROUPS

The treatment group consisted of eleven patients that were diagnosed with keratoconus;

from these patients, fourteen eyes were included in the study. The riboflavin UVA

crosslinking (CXL) procedure was performed on all the eyes included in the treatment group

and each of the fourteen eyes had follow-up sessions for a six-month period post-

operatively. In the six months the patients whose eyes were included in the study came in

for four measurement sessions (three measurement sessions for the left eyes of Subjects 2

and 5) where fifty autokeratometry measurements were taken in each measurement

session.

When analyzing the scatter plots of the fourteen subjects in the treatment group, there

seems to be a tendency for the treated eyes to display the largest deviation in keratometric

behaviour at the one-week post-CXL measurement session. When looking at the scatter

plots in Section 5.3, the red (one-week) data points and corresponding red distribution

ellipsoids seemed to stand out from the other colours of data points representing the other

measurement sessions, either because of the difference seen in the spread of the red data

points or the orientation of the red ellipsoid compared to the other follow-up measurement

sessions presented for each particular eye. The right eye of Subject 3 did not present with

this trend as all four measurement sessions for this eye produced clusters of data points

that were similar, as seen in Figure 5.3.4.1, Appendix D 2.4 (a) and (b). The trend was

likewise not seen in the left eye of Subject 5, as the one-week measurement session was not

attended and subsequently no red data points are presented in Figure 5.3.7.1, Appendix D

2.7 (a) and (b). The deviation seen in the one-week measurement session compared to the

other measurement sessions for each eye could be attributed to an unstable tear film or

corneal edema caused by the epithelial debridement during the CXL procedure and the

consequent re-epithelialization taking place in the first week post-operatively. It is possible

that the eye could be sensitive, irritated and photophobic in the first week post-operatively

causing reflex tears or an unusual blinking pattern which could influence the measurements

taken with the autokeratometer (Cronje-Dunn, 1995).

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Considering the scatter plots of each of the treated subjects in Section 5.3, the data overall

seems to show an increase in variation and magnitude of components after the CXL

procedure which slowly and continuously seems to return to the character of the pre-CXL

measurements in the six months after the procedure. Similar variation or spread of the

measurements is seen when comparing the pre-CXL and six-month post-operative data for

Subject 1 (Figure 5.3.1.1, Appendix D 2.1 (a) and (b)), both eyes of Subject 2 (in Figure

5.3.2.1, Appendix D 2.2 (a) and (b) for the right eye and Figure 5.3.3.1, Appendix D 2.3 (a)

and (b) for the left eye), and the left eye of Subject 5 (Figure 5.3.7.1, Appendix D 2.7 (a) and

(b)). Comparing the six-month measurement sessions to their corresponding before

measurement sessions, the right eye of Subjects 5, 6, 7 and 8 (Subject 5 right eye in Figure

5.3.6.1, Appendix D 2.6 (a) and (b), Subject 6 right eye in Figure 5.3.8.1, Appendix D 2.8 (a)

and (b), Subject 7 right eye in Figure 5.3.9.1, Appendix D 2.9 (a) and (b) and the right eye of

Subject 8 in Figure 5.3.10.1, Appendix D 2.10 (a) and (b)) and the left eyes of Subject 9 and

10 (Subject 9 left eye in Figure 5.3.12.1, Appendix D 2.12 (a) and (b) and Subject 10 left eye

in Figure 5.3.13.1, Appendix D 2.13 (a) and (b)) exhibit less variation at the six-month

measurement session than in the pre-CXL measurements. Subject 3 seems to have a tighter

cluster of measurements at the six-month measurement session, but because of all the

distribution ellipsoids on the scatter plots in Figure 5.3.4.1, Appendix D 2.4 (a) and (b) being

similar, it is difficult to see this from the graphic representation alone. It is confirmed that

there is less variation between the measurements of the six-month measurement session in

Table 5.3.4.2 looking at the mean variance-covariance for the measurement sessions. In

contrast the right eye of Subject 9 presents with a more spread out cluster of blue (six-

month) data points in Figure 5.3.11.1, Appendix D 2.11 (a) and (b), and the left eye of

Subject 9 presented with a red (one-week) ellipsoid lower on the I-axis than the black

(before) ellipsoid in Figure 5.3.12.1 and Appendix D 2.12 (a), indicating a decrease in the

stigmatic component of power or flattening in the curvature of the cornea post-CXL at the

first week measurement session, but also seems to follow with the trend of the data points

(measurements) of each sequential measurement session more closely resembling the

spread of the black (pre-operative) cluster of data points after the one-week measurement

session.

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The rough correlation of change seen in the treatment group suggests that the keratometric

behaviour of the cornea is disturbed by the CXL procedure causing more variation or spread

between the measurements taken at the one-week post-operative measurement session

and mostly an increase in curvature of the cornea looking at the three components of

dioptric power measured at the one-week measurement session (which could be called a

steepening when increase is seen in the stigmatic or Fst/I component). These values are

presented in a table of means for each eye included in the discussion of the treatment

group in Section 5.3. After the one-week post-operative measurement sessions, a slow

return is seen in the character of the keratometric behaviour, in most cases from the one-

month follow-up onwards. This trend coincides with a study by Vinciguerra et al (2009a),

where the parameters measured (mean pre-operative flattest meridian keratometry,

steepest meridian keratometry, average keratometry and simulated keratometry cylinder)

seemed to worsen one month after the CXL procedure, the corneas became slightly flatter

and exhibited a more regular form from three months post-operatively and all parameters

seemed improved at the one-year follow-up session. Doors et al (2009) similarly found that

the crosslinked corneas in their study initially became steeper and thereafter mostly

recovered to their pre-operative shape six months post-operatively. In this study, the

treated corneas displayed a steepening in shape (measuring maximum and central K-

readings) of the corneas one month post-CXL, but consequently recovered to the pre-CXL

shape three months post-operatively and remained stable at the six and twelve-month

follow-up sessions. The increased/steepening of the keratometric measurements one

month post-operatively were attributed to the restructuring process taking place in the

cornea in the first month post-CXL. Interestingly, Vinciguerra et al (2009b) noted a

steepening of the simulated keratometry measurements (flattest meridian, steepest

meridian, average and cylinder) analysed at the one-month measurement session when

compared to the pre-CXL measurements while the epithelium was still on, whereas the

keratometry measurements one month post-CXL were flatter when compared to the

keratometry measurements pre-CXL after the epithelium was removed. Vinciguerra et al

(2009b) points out that the initial steepening of the cornea post-CXL is caused by the

removal of the epithelium, thereafter re-epithelialization takes place and the flattening and

regularization of the shape of the cornea caused by CXL is only apparent six months post-

operatively.

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In a study by Greenstein et al (2012), crosslinked corneas included in the study became

continuously thinner from one to three months post-operatively, but seemed to become

thicker when measured between the three to twelve months post-operatively. It is possible

that the mechanism causing the variation in thickness, as well as keratocyte apoptosis seen

post-CXL (Caporossi et al, 2006; Koller et al, 2011; Wollensak et al, 2004) might have an

influence on the keratometric behaviour observed in the treatment group.

The keratoconic control group (Section 5.4) comprised of two subjects that were diagnosed

with keratoconus in both eyes. Only one eye of each of the subjects was included in the

keratoconic control group and did not undergo the CXL treatment, the contralateral eye of

each of the two subjects were included in the treatment group and did receive the CXL

treatment. The right eye of Subject 4 seen in Figure 5.4.1.1 and Appendix D.3.1 (a) and (b)

did not display much change over the six-month follow-up period. The left eye of Subject 7

seen in Figure 5.4.2.1 and Appendix D 3.2 (a) and (b) displayed the same general trend as

seen in the treatment group where the red (one-week) measurements were more varied

from each other and formed a loosely spread cluster of data points. After this, the green

(one-month) cluster and blue (six-month) cluster of data points displayed less variation

between measurements, indicating that the cornea possibly became more stable at the one-

month measurement session. The keratoconic behaviour displayed by the two eyes in the

keratoconic control group were very different and since the sample size was so small, not

much emphasis will be placed on the results seen in this group.

In comparison to the treatment group and one eye of the keratoconic control group, the

non-keratoconic control group presented in Section 5.4 exhibited minimal amounts of

change throughout the entire six-month follow-up period.

The difference in keratometric behaviour was calculated by subtracting the fifty

keratometry measurements of the six-month measurement session from the fifty

keratometry measurements of the first measurement session for each eye included in the

study, and then calculating the mean difference and mean difference in variance-covariance

for each eye. The mean differences of the fourteen eyes in the treatment group are listed in

Table 5.3.16.1. When considering the stigmatic component (Fst/I) of dioptric power seven

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of the eyes became flatter and seven of the eyes became steeper at the six-month follow-up

measurement session. The mean differences of the two eyes included in the keratoconic

control group are presented in Table 5.4.4.1. Looking at the stigmatic component (Fst/I) of

dioptric power, one eye became steeper and the other flatter. The mean differences of the

twelve eyes included in the non-keratoconic control group is given in Table 5.5.14.1 and

again looking at the stigmatic component (Fst/I) of dioptric power four of the eyes became

flatter and eight became steeper. The overall mean difference and mean variance-

covariance difference was calculated for each subject group and is presented in Table 5.6.1

and Table 5.6.2 respectively. The difference seen in the treatment group as a whole is

higher, indicating a flattening by means of a decrease in the stigmatic component (Fst/I) and

an increase in the antistigmatic components, than seen in the non-keratoconic control

group although the mean differences are comparable. The mean variance-covariance

differences of the treatment and non-keratoconic control groups in Table 5.6.1 seem very

different. The treatment group had much more variation between the fourteen mean

differences seen in this group than were observed between the twelve mean differences of

the non-keratoconic control group. Even though the mean differences of the treatment and

non-keratoconic control groups are similar, the character of the differences seen within the

two groups was very different indicated in Figure 5.6.1 by comparing the spread of the black

data points (representing the treatment group) and the red data points (representing the

non-keratoconic control group) and their corresponding 95% distribution ellipsoids with

each other. In Figure 5.6.1 the cluster of black data points representing the differences of

the eyes included in the treatment group are spread loosely and resulted in a black

distribution ellipsoid that seems much larger than the red distribution ellipsoid produced

from the tight cluster of red data points representing the non-keratoconic control group.

The spacial orientation of the tight cluster of red data points indicates that the differences

of the twelve eyes of the non-keratoconic control group were similar when comparing the

stigmatic (Fst/I), ortho antistigmatic (For/J) and oblique antistigmatic (Fob/K) components of

each difference to the corresponding component of the other differences in the group. In

contrast to the similarity of the twelve differences of the non-keratoconic control group, the

differences of the fourteen eyes included in the treatment group were different and

presented with variation in the stigmatic (Fst/I), ortho antistigmatic (For/J) and oblique

antistigmatic (Fob/K) components when comparing the corresponding components to each

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other. In Figure 5.6.1 the black distribution ellipsoid is orientated mostly along the I-axis

indicating that the largest deviation was seen in the stigmatic (Fst/I) component of the

differences of the eyes included in the treatment group, suggesting that the fourteen eyes

included in the treatment group mainly varied in their reaction to the CXL treatment

regarding the stigmatic component of power at the six-month measurement session. The

mean change calculated for the treatment group as a whole was minimal and similar to the

mean change seen in the non-keratoconic control group, but the mean variance-covariance

of the treatment group was significantly higher than that seen in the non-keratoconic

control group, implying that the CXL treatment induces very different keratoconic behaviour

in eyes treated. Interestingly the oblique antistigmatic (Fob/K) component of dioptric power

presented with the largest difference in the treatment group indicating the importance of

using the diopter power of the eye in its component form in order to derive more

comprehensive and scientific conclusions from the data at hand.

6.2 LIMITATIONS OF THE STUDY

6.2.1 ELIGIBILITY OF SUBJECTS REQUIRED REFERRAL FROM OPHTHALMOLOGIST

Of the 23 ophthalmologists who were approached to partake in the study, seven signed the

consent form, but only two sent patients for possible enrollment in the study. Only patients

that were going to have the CXL procedure done and who gave consent could be

approached. This could only be done after the relevant ophthalmologist’s administrative

staff alerted us to a specific patient. As this study was done on a part-time basis, the

researcher was not available at all times to approach these patients to enroll them as

subjects, leading to some potential subjects being lost.

It was noticed that Subject 10’s left eye presented with K-readings and low astigmatism that

seems to fall within normal limits (non-keratoconic) even though this eye had undergone

treatment and was included in the keratoconic treatment group. The eligibility of the

subjects was decided on by the treating ophthalmologist and not speculated on by the

researcher and thus this eye was included in the study.

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6.2.2 TIME CONSTRAINTS

The subjects had to come in for four measurement sessions in a six-month follow-up period.

Although a longer follow-up period would have been desirable, the six-month follow-up

schedule already turned out to be more troublesome than expected. Ten potential subjects

could no longer commit to the six-month follow-up period after the one-week or one-month

follow-up measurement session was concluded and had to be completely dismissed from

the study.

In the treatment group, Subject 2 was unable to attend the one-month measurement

session scheduled for the left eye and Subject 5 was unable to attend the one-week

measurement session scheduled for the left eye. In the non-keratoconic control group,

Subject 6 was unable to attend the one-month measurement session scheduled for both

eyes. These three subjects (four eyes) were still included in the study as only one

measurement session was missed per eye and the before and six-month measurement

sessions, which were seen as the most important measurement sessions, were completed in

all four eyes.

6.2.3 INSTRUMENT CONSTRAINTS

All the keratometry readings were taken on a specific autokeratometer (NIDEK TONOREF II

Auto Refractor/Keratometer/Non-Contact Tonometer) to limit instrument variation. The

autokeratometer was calibrated with the test eye at four intervals throughout the two-and-

a-half-year period that the measurements were taken. The measurements on the test eye

displayed very little variation as described in Section 5.2. This makes us confident in

assuming that the variation seen in the keratometric behaviour of the eyes included in the

study was not linked to the instrument itself but predominantly to variation that occurred in

the eyes. In a previous study, the advantage of being able to program the instrument to

take measurements at specific intervals and the instrument having the memory capability to

save a larger amount of K-readings at a time was noted (Rubin, 1993a). The use of a

programmable autokeratometer would have been preferable in this study to eliminate

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discrepancies that could be present in the data, because of different time lapse periods in

between each of the fifty measurements recorded in a measurement session.

6.2.4 VARIATION OF KERATOMETRIC BEHAVIOUR OF THE CORNEA

A multitude of studies have recorded diurnal variation seen in normal eyes (Cronje and

Harris, 1997; Cronje-Dunn, 1995; Rubin, 1993b). A degree of variation is expected in living

organisms and therefore it is not surprising to see more variation in the non-keratometric

control subjects than in the manufactured test eye. Diurnal variation seems to cause the

normal cornea to become slightly steeper later in the day (Cronje and Harris, 1997) and a

slight steepening is even apparent in the normal control eyes enrolled in another study as

little as three hours after the initial measuring session (Chetty and Gillan, 2010).

In a study using the same multivariate methods of analysis that were utilised in this study,

the author reported on corneal curvature variation within one subject at two measuring

sessions in one day and the magnitude of variation in keratometric readings varied from

subject to subject as well. It was noted that even physical activity might have a short term

steepening effect on the corneal curvature (Cronje and Harris, 1997).

The keratometric variation induced by a fluid layer over a steel ball was analysed in a study

and it was found that the presence of the fluid layer induced much bigger variation in the

measurements of the surface of the steel ball, than was noted when measuring the dry

surface of the steel ball (Cronje-Dunn, 1995). This suggests that the tear layer might play an

important role in the variation seen in the normal eye (or any living human eye), especially

because of the continuous nature of tear secretion and blinking of the eye.

The variation induced by the tear layer would also have an influence on the keratometric

measurements of a keratoconic eye, probably to a larger extent because of the irregular

surface of the cornea with keratoconus that needs to be coated by the tear layer. The

protruding cone could possibly create an area on the surface of the eye were the tear layer

is thinner when compared to the rest of the surface of the eye, or where the tears break up

first.

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The tear layer could be influenced by irritation of the eye, unnatural blinking patterns

because of forced blinking or less regular blinking by the subjects included in the study while

taking the fifty keratometry measurements at each session.

The tear layer could also possibly induce different variation patterns in eyes with meibomian

gland dysfunction, evaporative dry eye, transient irritation or tired eyes to name a few. As

twelve non-keratoconic control eyes were monitored as well as the two keratoconic control

eyes and the fourteen treated eyes, from our results it does seem that the main differences

in variation of measurements are still induced by the keratoconus and CXL procedure itself.

Taking all these seemingly normal variations in the cornea into account it is important to

compare these to any variations seen in a treatment group. In Section 5 the variations

noted in the control eyes are minimal compared to the variations seen in the enrolled

keratoconic eyes in both the keratoconic and treatment group, giving us a clear indication

that the changes seen in the keratoconic groups cannot be attributed to normal

fluctuations. It would be ideal to have a reference of what level of variation to expect in the

keratoconic cornea, this proves to be very difficult because of the multiple parameters

involved in classifying the severity of keratoconus, the age of the subject and genetics

among others probably all having an interrelated influence on the variation. The study

including these factors would require a very large sample, more time and a team of

researchers.

6.2.5 KERATOCONIC CONTROL SUBJECTS

The subjects included in the treatment group would have undergone the CXL procedure

whether they were enrolled in our study or not. We only approached the subjects after the

decision was made that the patient would undergo the CXL procedure. The standard

protocol for admission to a surgical procedure was done by the ophthalmologists’ practice.

We could not ask the ophthalmologist to keep the contralateral eye as a keratoconic control

since we did not influence any of the treatment decisions. In Subjects 4 and 7 we were

fortunate enough to have keratoconic contralateral eyes that had no exclusion criteria

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present, that we included in the keratoconic control group discussed in Section 5.3. In

Subjects 1, 3, 6, 10 and 11 only one eye per subject was included as the other eye had either

already been crosslinked prior to our study, had undergone corneal transplantation or was

compromised and soon to undergo corneal transplantation. It would have been ideal to

enroll one eye per subject in the treatment group and the other in the keratoconic control

group, because of ethical considerations when delaying the crosslinking of an eye with

progressive keratoconus for documentation purposes, especially since most research found

that CXL was successful at stopping the progression of the keratoconus (Agrawal, 2009;

Caporossi et al, 2010; Coskunseven et al, 2009; El-Raggal, 2009; Hersh et al, 2011; Raiskup-

Wolf et al, 2008; Raiskup et al, 2015; Tomkins and Garzozi, 2008; Toprak and Yildirim, 2013;

Wollensak et al; 2003, 2004; Wollensak, 2006). A study by Raiskup-Wolf et al (2008)

specifically mentioned that the enrollment of a keratoconic control group would be ethically

unacceptable, because of the positive results of the CXL treatment. In comparison a study

by Vinciguerra et al (2009b) included the contralateral eyes of 28 keratoconic subjects

undergoing CXL as controls, the contralateral eyes all presented with a slow progression of

keratoconus.

For that reason, a group of normal eyes were enrolled as controls to show the normal effect

of a six-month follow up on keratometric behaviour as presented in Section 5.3.

6.2.6 ANALYSIS LIMITATIONS

Fourteen eyes of eleven subjects were included in the treatment group, two eyes of two

subjects in the keratoconic control group and twelve eyes of six subjects in the non-

keratoconic control group. Each eye included in the study was regarded separately,

whereafter the subject group was examined as an entity and then compared to the other

subject groups in the study. Both eyes of Subjects 2, 5 and 9 were included in the treatment

group, both eyes of non-keratoconic control Subjects 1, 2, 3, 4, 5, and 6 were included in the

study and Subject 4’s right eye was included in the keratoconic control group and left eye in

the treatment group and Subject 7’s right eye was included in the treatment group and left

eye in the keratoconic control group. As some variables are considered dependent to an

individual, it might have been beneficial to analyse subjects with both eyes included in the

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study in a different way to relate the data of the two eyes of a subject to each other.

Raiskup et al (2015) mentioned the same limitation in their ten year CXL follow-up study.

6.2.7 PROCEDURE DONE BY MULTIPLE SPECIALISTS

The patients of two ophthalmologists were included in the study. The specific technique

used by each of the ophthalmologists when performing the CXL procedure could vary

slightly which could possibly have influenced the keratometric behaviour of the eyes

included in the treatment group in ways that we do not understand.

6.3 RELEVANCE OF THE STUDY

As explained in Section 3, it is important to regard the curvature of the cornea as a whole.

The curvature of the cornea was examined in the component form of dioptric power,

comprising of three mutually dependent components (stigmatic (Fst/I), ortho antistigmatic

(For/J) and oblique antistigmatic (Fob/K) components) that should not be regarded as

separate entities, but holistically to ensure meaningful, comprehensive conclusions could be

drawn from the data. As far as we know all previous research done on the keratometric

behaviour of the cornea following CXL treatment was done by analysing the dioptric power

of the eye by converting the dioptric power in conventional form to a single concept

(equivalent sphere) or the dioptric power was analysed by making a distinction between the

spherical and cylindrical parts of the power to allow simplified calculation with the data; in

both instances valuable information is lost as the complete data set is not considered.

Analysing the scatter plots (Section 5 and Appendix D) presenting the keratometric

measurements of the eyes included in the study, it becomes clear that the shape of a

keratoconic cornea cannot be fully comprehended by taking one keratometric

measurement. The spread of the measurements in a single measurement session for most

of the eyes included in the treatment group indicate that a high level of variation was

present between the fifty measurements taken at each measurement session in these

irregular corneas. Multiple measurements are crucial when attempting to understand the

shape of an irregular cornea.

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Caution must be taken when making conclusions from the multivariate statistics utilised in

this study as the underlying assumption that the data displayed multivariate normal

distribution was not met. As a result, it was important to rely on the graphical

representation of the data as well.

As CXL is still a relatively new procedure, research on the effects induced by CXL is crucial

not only to keep the patients safe but to give the ophthalmologists a better understanding

of the changes that are induced in the corneas of patients that undergo the CXL treatment.

The multivariate analysis of dioptric power in component form utilised in this study aims to

give a more scientific, comprehensive analysis of the keratometric behaviour that might be

induced by the CXL procedure.

6.4 SUGGESTIONS FOR FUTURE RESEARCH

6.3.1 CORNEAL VARIATION

All measurement sessions should be scheduled for the same time of day for all eyes

included in the study and an effort could be made to restrict the subjects from doing any

strenuous physical activity within a number of hours before presenting for their

measurement sessions (Cronje and Harris, 1997). Diurnal variation seems to cause the

normal cornea to become slightly steeper later in the day (Cronje and Harris, 1997) and a

slight steepening is even apparent in the normal control eyes enrolled in another study as

little as three hours after the initial measuring session (Chetty and Gillan, 2010).

6.3.2 LONGER FOLLOW-UP PERIOD

A longer follow-up period post-operatively would be preferable, as keratometric behaviour

could possibly still be unstable six months after CXL, even though it has been indicated that

parameters are stable following the six-month post-CXL follow-up (Kránitz et al, 2014).

Since the CXL procedure is still relatively new, there is still no certainty of the long term

effects that it might induce. A ten-year follow-up study by Raiskup et al (2015) is the longest

follow-up to date, two of the twenty-four subjects in this study had to undergo a repeated

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CXL procedure to successfully stabilise the progression of keratoconus in these eyes

following the first CXL treatment. This information is important as it gives us an indication

that a minimal amount of patients have continuous keratoconic progression in spite of the

CXL procedure as well as the indication that the progression can be halted by a second CXL

procedure. Patients in clinical practice should be warned about this late onset of continued

progression of keratoconus after CXL, a yearly check-up by their ophthalmologist should be

compulsory after CXL to monitor for progression and thus initiate intervention as soon as

possible.

6.3.3 LARGER SAMPLE SIZE

A larger sample of a population would inherently give a better representation of the

population as a whole, leading to increased validity of conclusions derived from a study. It

would, most importantly, be beneficial to include more subjects in the treatment group as

well as the keratoconic control group, because of the considerable inconsistency seen in the

keratometric behaviour of the eyes included in these groups.

6.3.4 CLASSIFICATION OF PROGRESSION

The respective ophthalmologist of each subject was responsible for deciding whether

progression of the keratoconus was present or not. The lack of specific classification of

progression of keratoconus in this study could have an influence on the outcomes of the CXL

procedure. In a recent study reporting on a ten-year follow-up after CXL, only patients with

a classified rate of progression of keratoconus underwent the CXL procedure. The

progression was defined as an increase of at least 1.00 D in apical keratometry value

measured by a corneal topographer within six to twelve months pre-operatively (Raiskup et

al, 2015). In two other studies (Koller et al, 2007; Raiskup-Wolf et al, 2008) progression was

similarly defined as an increase in K-readings of 1.00 D or more within twelve months before

considering CXL. Koller et al (2007) additionally only included subjects with mild to

moderate keratoconus and Raiskup et al (2008) added a decrease in VA and the necessity of

a contact lens refit within two years pre-operatively to their list of progression criteria.

Progression, and possibly the rate of progression, should be established prior to a study

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monitoring the keratometric behaviour of the cornea after the CXL procedure, as the rate of

progression pre-CXL could have a significant influence on the change initiated by the CXL

procedure in the keratometric behaviour post-CXL.

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CHAPTER 7

CONCLUSION

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By utilizing the dioptric power matrix as representation of the corneal curvature, possible

patterns might be identified when examining the keratometric behaviour of keratoconic

progression in the keratoconic cornea, which might in turn give us additional indications for

the classification of keratoconus regarding, specifically, the progression thereof. A narrower

classification system regarding progression might, in turn, produce narrower sub-sets of

subjects to examine after the CXL procedure and hopefully a pattern might be seen in the

response of the keratometric behaviour induced by the procedure. This would make it

possible for ophthalmologists to establish the best time to utilize the CXL procedure on a

specific patient, as well as providing a better indication of the prognosis expected in

individual patients. Keratoconus classification tweaking would enhance the usage of CXL on

its own or combined with a host of other procedures or the procedures on their own.

At present if keratoconic progression is identified within a keratoconic cornea, the next step

would be to undergo CXL to stabilise the keratoconus as soon as possible in an attempt to

conserve the vision of the patient at the best possible level. But it seems that this is not

always the case because of the varied response to the procedure. In future the mindset of

progression immediately indicating the need for CXL might shift to a mindset of performing

CXL at the opportune time within the progression time frame to ensure the most optimum

prognosis for the patient.

SUMMARY OF CONCLUSIONS

• A general trend is seen in the keratometric behaviour of the eyes included in the

treatment group. The CXL procedure appears to produce a change in the

keratometric behaviour of the majority of treated eyes. The character of the change

was most different at the one-week measurement session where increased variation

was seen between the fifty measurements taken at this session when compared to

the other measurement sessions for a particular eye and the largest antistigmatic

changes were noted at the one-week measurement session. From the one-month to

the six-month measurement session the keratometric behaviour of the treated

subject’s corneas demonstrated a slow but continuous return towards the pre-

operative corneal form, with a decrease in variation among the fifty measurements

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taken at the six-month measurement session. The decreased variation between the

measurements at the six-month measurement session could be interpreted as a

stabilisation of the keratometric behaviour and a possible regulation of the corneal

curvature induced by the CXL procedure.

• Of the fourteen eyes that were included in the treatment group, seven

demonstrated a stigmatic flattening six months after the CXL procedure and the

remaining seven eyes included in the treatment group demonstrated a stigmatic

steepening of curvature six months post-operatively. The difference in corneal

curvature over the six-month post-CXL period was dissimilar when comparing the

differences of the fourteen eyes of the treatment group to each other, indicating

that the CXL procedure induces a contrasting effect on treated eyes six months post-

operatively. The mean change seen in the treatment group as a whole consisted of a

minimal stigmatic (Fst/I) flattening of 0.17 D combined with a minimal

antistigmatic (For/J and Fob/K) corneal curvature change of 0.07 D and 0.30 D

respectively.

• In general, the non-keratoconic control group, consisting of twelve eyes, displayed

very little change in keratometric behaviour over the six-month follow-up period.

The mean change seen for each of the twelve non-keratoconic control eyes was

comparable and the mean difference in curvature seen over the six-month follow-up

period for the entire non-keratoconic control group was 0.00 D of stigmatic (Fst/I)

variation and for the antistigmatic (For/J and Fob/K) components 0.02 D and 0.02 D

respectively indicating the stability in curvature seen over the six-month period of

time within each non-keratoconic control eye and in the non-keratoconic control

group as a whole.

• Large amounts of variation were detected between the fifty keratometric

measurements of a single measurement session in the treatment group, whereas the

variation seen between the fifty measurements of each measurement session taken

of the non-keratoconic control group were comparable. The variation between the

measurements of each measurement session (including the before measurement

210

session) in the treatment group could indicate that the irregular form caused by

keratoconus in these corneas causes the variation seen between the measurements.

• The CXL procedure did induce changes in the keratometric behaviour of the eyes

included in the treatment group, but the overall mean change seen in the treatment

and non-keratoconic subject groups were comparable. In conclusion to the small

overall change seen in the treatment group six months following the CXL procedure,

it seems that the procedure did not induce much change in the corneas of the

treated group of eyes which could indicate that the procedure was successful at

stopping the keratometric change (increase in stigmatic curvature) expected from

keratoconic progression.

• The specific autokeratometer utilised in the study as measuring instrument is

accurate, as displayed by data from the test eye, so the variations measured in the

three subject groups included in the study are not induced by the measuring

instrument.

211

CHAPTER 8

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222

APPENDICES

Appendix A: Ophthalmologist consent form

Appendix B: Subject information letter

Appendix C: Subject consent form

Appendix D: Rotated scatter plots

223

APPENDIX A

Consent form Date: ___/___/20___ University of Johannesburg Participation in research project towards a Masters degree in Optometry The effects of Riboflavin UV crosslinking on keratometric behaviour in keratoconus: a six-month follow-up study. I __________________________________________________ HPCSA _____________________,

(Name of ophthalmologist) accept the invitation to participate in this research project and as far as possible to help identify potential participants without the specified exclusion criteria as stated below. Exclusion criteria:

• Patients older than 35 years of age. • Presence of any systemic or hereditary diseases or syndromes. • Any previous corneal surgery. • Acute hydrops and corneal scarring.

In addition, I give the researcher permission to discuss the research project to the potential participant and invite them to take part in the study. The researcher will have access to the medical records of the potential participants under my supervision. I am aware that the researcher will see the participant for 2-3 extra follow-up visits over and above my consultations. These visits will be at no cost to the participant. I also give voluntary consent for the collection and analysis of all information gathered in this study to be used and distributed as the researcher sees fit. I am aware that my patient and I will stay anonymous throughout the entire study. In the case where the researcher observes any change in the health status of the participant’s eyes the researcher will immediately refer the participant back to me, except in emergency cases where I am not available, the participant will be referred to the doctor on call. I am aware that I can withdraw from this study at any time. My signature below acknowledges that I have read this consent form and understand what this entails and that I have received the information letter given to the participants on the study. Dated at Pretoria on this _________________ day of _________________________ 20____ _____________________ Researcher _______________________________ Ophthalmologist _____________________ Witness Researcher Contact Details: Annelize van Zyl Contact number: (012) 3438021 (8:00-16:30) [email protected]

224

APPENDIX B

Information letter

University of Johannesburg – Research Project towards a Masters degree in Optometry

The effects of Riboflavin UV crosslinking on keratometric behaviour in keratoconus: a six-month follow-up study.

This study will look at the changes in the form/roundness of the cornea induced by the UV crosslinking procedure over a six-month period. UV crosslinking is a relatively new procedure and as far as we know the data collected about changes in the form of the cornea have not been analysed previously making use of our methods of analysis. Hopefully the study will provide us with a more complete understanding of corneal changes induced by the UV crosslinking procedure.

This study requires you to come in to the practice three times in six months following the procedure, to undergo measurements. The eye will be examined and fifty measurements with an autokeratometer will be taken before doing the UV crosslinking procedure and at every follow-up visit.

As a patient undergoing UV crosslinking, you will have to see the involved ophthalmologist for two follow-ups after the procedure has been completed (this is the normal protocol for all CXL patients); on these occasions you will also be seen by the researcher. If enrolled in this study you will be asked to come in to the practice on two more occasions, this is for study-specific K-readings to be obtained and will be at no charge to you. On these occasions you will not be examined by the ophthalmologist involved but only by the researcher.

Schedule for appointments and procedures to be done: • Research study explained and consent form signed. Fifty K-readings are taken of

the eye before the UV crosslinking procedure.• One week following procedure: Eye is examined. Fifty K- readings will be taken.• One month following procedure: Eye is examined. Fifty K-readings are taken.• Six months after procedure: Eye is examined. Fifty K-readings are taken.

If any complications are seen in the follow-up examinations, you will be referred back to the involved ophthalmologist and be excluded from the study.

As a participant you can request copies of any publications (results) that may be produced as a result of this research.

Researcher Contact Details: Annelize van Zyl Contact number: (012) 3438021 (8:00-16:30) [email protected]

225

APPENDIX C

Consent form Date: ___/___/20___ University of Johannesburg Enrolment in research project for a Master’s degree in Optometry

The effects of Riboflavin UV crosslinking on keratometric behaviour in keratoconus: a six-month follow-up study. I __________________________________________________ID number _____________________, (Name of subject) the undersigned, accept the invitation to partake in this study and hereby give voluntary consent for the collection and analysis of all information gathered in this study to be used and distributed as the researcher sees fit. I am aware that I will stay anonymous throughout the entire study. I also give consent for my medical records to be used to determine the presence of exclusion criteria. Such access to my records will be under the supervision of my ophthalmologist. Examination schedule:

1. Pre-operative examination ________________________ 2. One-week post-operative examination ________________________ 3. One-month post-operative examination ________________________ 4. Six-month post-operative examination ________________________

I do realise that this follow-up schedule includes two examinations in excess of the normal follow-up schedule for the ophthalmologist involved. If there is a change in the health status of my eye or if I will not be able to attend a follow-up examination because of unforeseen circumstances, I will inform the researcher as soon as possible. I understand what is being researched and have had an opportunity to ask the researcher questions about this study and the procedure involved. I am aware that I can withdraw from this study at any time with no disadvantage to me. An information letter was given to me and the study explained. My/my guardian’s (in case of a minor) signature below acknowledges that I have read this consent form and understand what this entails and that I have received the information letter on the study. Dated at Pretoria on this _________________ day of _________________________ 20____ _______________________________ _____________________________ Researcher Signature of Patient/Guardian _______________________________ _____________________________ Witness Capacity Researcher Contact Details: Annelize van Zyl Contact number: (012) 3438021 (8:00-16:30) [email protected]

226

APPENDIX D

Appendix D presents scatter plots corresponding to the scatter plots in Chapter 5 (Results).

The scatter plots in Appendix D were constructed from the same data as their related

scatter plots in the main text, but have been rotated in three dimensional dioptric space to

present the data on scatter plots with different orientations compared with the scatter plots

in Chapter 5. The purpose of presenting the data on scatter plots with different orientations

is to uncover data points that might have been obscured by other data points in the

foreground in a certain orientation, but might be visible in another orientation of the scatter

plot. Rotated scatter plots for the test eye, the fourteen eyes included in the treatment

group, the two eyes in the keratoconic control group and the twelve eyes in the non-

keratoconic control group are presented in Appendix D. As well as rotated scatter plots for

the differences seen in each of the four groups and the differences found in the treatment

group, the keratoconic control group and the non-keratoconic control group presented on

the same scatter plots.

Data for all four measurement sessions are presented on each scatter plot for the eyes

included in the study, except for left eye of Subject 2 in the treatment group (no data is

available for the one-month measurement session), the left eye of Subject 5 in the

treatment group (no data is available for the one-week measurement session) and non-

keratokonic control Subject 6 (no data is available for the one-month measurement session

for both eyes). In the (a) and (b) scatter plots in sub-sections D 2.15, D 3.3, D 4.13 only the

data presenting the differences in each group are presented and Section D 5 which

graphically presents the differences of the treatment group, the keratoconic control group

and the non-keratoconic control group on the same scatter plots. The measurements from

the first measurement session are presented in black, the second in red, the third in green

and the fourth measurement session in blue. In the corresponding sub-sections the (a)

scatter plots are rotated in such a way that the reader is looking along the J-K plane, in sub-

section (b) the scatter plots are rotated to look down the I-axis. In the measurement data of

the treatment group and non-keratoconic control group where possible outliers were

present these were removed and the corresponding scatter plots reconstructed in sub-

section (c) where the scatter plot is rotated so that the reader looks along the J-K plane and

227

sub-section (d) where the rotation makes it possible to look down the I-axis. The axis length

in all the scatter plots (a), (b), (c) and (d) are 3 D and the tick interval is set at 1 D, except for

the scatter plots in D 1 (c) and (d) where the axis length is set at 0.05 D.

In Section D 1 the measurement data of all four measurement sessions of the test eye are

presented on each of the four scatter plots. The scatter plots (a) and (c) are rotated in three

dimensional dioptric space and shown in an orientation where the reader is looking along

the J-K plane. Scatter plots (b) and (d) are rotated in such a way that the reader is looking

down the I-axis. The axis length in scatter plots (a) and (b) are 3 D and the tick interval is set

at 1 D. The data points representing the measurements on scatter plots (a) and (b) are very

close to the origin and present as only one data point. In scatter plot (c) and (d) the scale of

the plot was greatly decreased to an axis length of 0.05 D to enable the reader to distinguish

between the different data points on the scatter plots. Only 3 data points are visible on the

scatter plots in (c) and (d), one of the dots are green and the other two are blue. This

indicates that the measurement data representing the first measurement session (black)

and the second measurement session (red) are superimposed by the measurements from

the third measurement session (green) and the fourth measurement session (blue), refer to

Section 5.2.

In Section D 2 the rotated scatter plots for all fourteen eyes included in the treatment group

are presented. The right eyes of Subjects 2, 5, and 8 in the treatment group as well as the

left eyes of Subjects 2 and 9 in the treatment group have additional scatter plots (c) and (d)

which represent the measurement data without possible outliers. The differences in each

of the fourteen eyes are represented in D 2.15 (a) and (b) in black.

Section D 3 represents the rotated scatter plots for the two eyes in the keratoconic control

group. Section D 3.3 represents the differences of both of the keratoconic control subjects

with a green dot.

All twelve eyes included in the non-keratoconic control group are presented in Section D 4,

only the left eye of non-keratoconic control Subject 5 includes scatter plots (c) and (d)

representing the measurement data without possible outliers. D 4.13 displays the

228

differences seen in each of the twelve eyes in the non-keratoconic control group as red

dots.

Lastly in Section D 5 the differences of the treatment group from D 2.15 (black), the

keratoconic control group from D 3.3 (green) and the non-keratoconic control group of

subjects from D 4.13 (red) are presented on the same scatter plots.

229

D 1 TEST EYE

Rotated scatter plots for the test eye. The origin is 0.00 I D.

(a)

(b)

(c)

(d)

0.05 I 0.05 K

0.05 J

0.05 I 0.05 K

0.05 J

0.05 I 0.05 K

0.05 J

0.05 I 0.05 K

0.05 J

0.05 I 0.05 K

0.05 J

0.05 I 0.05 K

0.05 J

0.05 I 0.05 K

0.05 J

0.05 I 0.05 K

0.05 J

0.05 I

0.05 K0.05 J

0.05 I

0.05 K0.05 J

0.05 I

0.05 K0.05 J

0.05 I

0.05 K0.05 J

0.05 I

0.05 K0.05 J

0.05 I

0.05 K0.05 J

0.05 I

0.05 K0.05 J

0.05 I

0.05 K0.05 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

230

D 2 TREATMENT GROUP

D 2.1 SUBJECT 1 LEFT EYE

Rotated scatter plots for Subject 1 left eye. The origin is 52.5 I D.

(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

231

D 2.2 SUBJECT 2 RIGHT EYE

Rotated scatter plots for Subject 2 right eye. The origin is 47.5 I D.

(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

232

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

(c) SUBJECT 2 RIGHT EYE POSSIBLE OUTLIERS REMOVED

(d) SUBJECT 2 RIGHT EYE POSSIBLE OUTLIERS REMOVED

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

233



(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

234

(c) SUBJECT 2 LEFT EYE POSSIBLE OUTLIERS REMOVED

(d) SUBJECT 2 LEFT EYE POSSIBLE OUTLIERS REMOVED

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

235



(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

236



(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

237



(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

238



3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

239



(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

240



(a)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

(b)

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

241



(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

242



(a)

(b)

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

243



3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

244



(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

245



(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

246

(c) SUBJECT 9 LEFT EYE POSSIBLE OUTLIERS REMOVED

(d) SUBJECT 9 LEFT EYE POSSIBLE OUTLIERS REMOVED

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

247



(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

248



(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

249

D 2.15 DIFFERENCES OF TREATMENT GROUP

Rotated scatter plots for differences of treatment group. The origin is 0.0 I D.

(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

250

D 3 KERATOCONIC CONTROL GROUP

D 3.1 KERATOCONIC CONTROL SUBJECT 4 RIGHT EYE

Rotated scatter plots for keratoconic control Subject 4 right eye. The origin is 47.5 I D.

(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

251

D 3.2 KERATOCONIC CONTROL SUBJECT 7 LEFT EYE

Rotated scatter plots for keratoconic control Subject 7 left eye. The origin is 50.0 I D.

(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

252

D 3.3 DIFFERENCES OF KERATOCONIC CONTROL GROUP

Rotated scatter plots for differences of keratoconic control group. The origin is 0.0 I D.

(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

253

D.4 NON-KERATOCONIC CONTROL GROUP

D 4.1 NON-KERATOCONIC CONTROL SUBJECT 1 RIGHT EYE

Rotated scatter plots for non-keratoconic control Subject 1 right eye. The origin is 40.5 I D.

(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

254

D 4.2 NON-KERATOCONIC CONTROL SUBJECT 1 LEFT EYE

Rotated scatter plots for non-keratoconic control Subject 1 left eye. The origin is 40.5 I D.

(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

255



(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

256



(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

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257



(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

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258

D. 4.6 NON-KERATOCONIC CONTROL SUBJECT 3 LEFT EYE


(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

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3 J

3 I 3 K

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259



(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

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260



(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

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3 J

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261



(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

262



(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

263

(c) NON-KERATOCONIC CONTROL SUBJECT 5 LEFT EYE POSSIBLE OUTLIERS REMOVED

(d) NON-KERATOCONIC CONTROL SUBJECT 5 LEFT EYE POSSIBLE OUTLIERS REMOVED

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

264



(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

265



(a)

(b)

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I 3 K

3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

266

D 4.13 DIFFERENCES OF NON-KERATOCONIC CONTROL GROUP

Rotated scatter plots for differences of non-keratoconic control group. The origin is 0.0 I D.

(a)

(b)

3 I

3 K3 J

3 I

3 K3 J

3 I 3 K

3 J

3 I 3 K

3 J

267

D 5 DIFFERENCES OF THE TREATMENT GROUP, KERATOCONIC CONTROL GROUP AND

NON-KERATOCONIC CONTROL GROUP

Rotated scatter plots for differences of the treatment group, keratoconic control group and

non-keratoconic control group. The origin is 0.0 I D.

(a)

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

3 I

3 K3 J

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APPENDIX E PUBLICATION

S Afr Optom 2012 71(4) 188-193

The South African Optometrist ISSN 0378-9411 188

Riboflavin and Ultraviolet A radiation cross-link-ing for keratoconus management: a review*AME van Zyla andWDH Gillanb

Department of Optometry, University of Johannesburg, PO Box 524, Auckland Park, 2006 South Africa

<[email protected]>

Received 17 January 2011; revised version accepted 31 October 2012

aBOptom(UJ)bDip Optom DPhil(RAU) CAS(NewEnCO) FAAO FIACLE

*This article results from preliminary research towards a Masters degree undertaken by A van Zyl with the supervision of Professor WDH Gillan at the University of Johannesburg

Introduction

Keratoconus is a non-inflammatory ectasia that results in distorted and decreased vision due to pro-gressive thinning, protrusion and scarring of the cornea1. Keratoconus is not predisposed to race or gender and is found in approximately one in 2000 members of the general population2. The cause and pathogenesis of keratoconus is still unclear, howev-er, aspects like eye rubbing, decreased ocular rigid-ity, abnormalities of connective tissue, the role of degradative enzymes and protein inhibitors, genet-ics as well as the possible role of interleukin 1 are considered important1, 2. Keratoconus is commonly seen as an isolated disorder yet has been found in conjunction with mitral valve prolapse3, Down’s syndrome, Leber’s congenital amaurosis, atopic dis-ease and connective tissue diseases1, 2. The treat-ment options for keratoconus depend on the stage of the disease. Initially spectacles and soft contact lenses may be used to improve vision. As the ir-regular astigmatism increases, however, vision will no longer be good enough and hard contact lenses, scleral lenses or hybrid lenses will be the next op-tions. With further progression the cornea becomes too thin or scarred resulting in the need for corneal transplant as a last resort (this could be penetrating or lamellar depending on the damage to the cornea). The progression of keratoconus normally stops in the third or fourth decade of life and is due to cor-neal ageing where natural cross-linking causes spon-taneous biomechanical and biochemical stability of

the disease2, 4, 5. In diabetic patients keratoconus is very rarely found because of possible advanced gly-cation end products causing natural cross-linking, which increases corneal rigidity5, 6. The effects of ageing and diabetes on the cornea suggest that ribo-flavin ultraviolet cross-linking (CXL) may be the best way to stop the progression of keratoconus, remem-bering however that keratoconus is not yet curable7. The aim of CXL is to alter the stromal composition by inducing cross-links between the collagen fibrils that may increase the tensile strength of the cornea, and stop thinning and thus the progression of keratoco-nus7, 8. In the 1990’s the technique for corneal colla-gen cross-linking with Riboflavin and UVA radiation was developed in Germany at the Dresden Technical University and in 1998 the first patient with keratoco-nus was treated with the procedure7, 9.

Procedure of CXL

The procedure is done on an outpatient basis. Topi-cal anesthesia is administered to the eye and thereafter epithelial tissue is mechanically removed with a blunt instrument in a 7-9 mm6, 7, 9-18 diameter zone (the epithelium can be debrided with a variety of tools: a Beaver blade6, Amoil brush9, 10, rotating soft brush13, blunt spatula11, 14, 15, 18, 19, blunt hockey knife20, a blunt crescent knife21 or a blunt knife12, 16). The epithelium is a diffusion barrier to the cornea which needs to be removed to aid the penetration of riboflavin, which is water soluble22, into the cornea. Riboflavin solution is applied before and during irradiation every 3-5

S Afr Optom 2012 71(4) 188-193 AME van Zyl and WDH Gillan-Riboflavin and Ultraviolet A radiation cross-linking for keratoconus management

The South African Optometrist ISSN 0378-9411189

and stabilize the collagen scaffold. This results in an increase in rigidity of the cornea, increased resist-ance against proteolytic enzymes7 and a significant increase in the diameter of collagen fibers5.

Safety concerns on UVA radiation

The cross-linking effect only occurs in the ante-rior 200-300 µm of the cornea8, 11, 20 which is due to the high levels of absorption of UVA radiation in this area24. This ensures that more posterior structures (for example, the endothelium, lens and retina) are not adversely affected, however, an absolute mini-mal corneal thickness of 400 µm is required to di-minish potential for damage3, 5, 7,12, 19. If this value is not respected the treatment may induce cataracts or even retinal damage. Damage could also arise when a patient does not maintain fixation on the focus point resulting in the limbus being irradiated. In these low-compliance patients a poly-methyl methacrylate ring can be placed over the limbus to ensure limbal pro-tection. Under normal conditions (adequate fixation) the limbus is not exposed to the effects of UVA radia-tion. Less than 20 µm lateral diffusion (from the edge of the abraded area) of radiation effects occur. The protection is provided by the presence of the epithe-lium11.

Wollensak et al20 measured the cytotoxicity of dif-ferent irradiance levels of UVA, different concentra-tions of riboflavin and the combination of one con-centration of riboflavin and different UVA irradiance levels. No cytotoxicity was found for riboflavin alone. The cytotoxicity level for UVA in combination with riboflavin was found to be 10 times lower than with UVA alone. This level of cytotoxic effect did happen gradually but at a distinct threshold of irradiance lev-el. The cytotoxicity is caused by the oxidant effect of UVA radiation. In human corneas the cytotoxic effect on keratocytes reaches approximately 300 µm deep into the cornea when the proposed protocol is used21,

20. When using the protocol specified and threshold minimal thickness is adhered to, the treatment is seen as safe5, 6, 8, 11, 18, 19 and safer than corneal transplant6.

Keratocytes

In a normal cornea the distribution of keratocytes is denser in the anterior cornea decreasing in density

minutes6, 13, 15, 19, 23, starting 5-40 minutes before irra-diation6, 7, 11-13, 19, 23. The eye is examined under a slit-lamp using blue light to look for yellow colouring of the aqueous which ensures full penetration of ribofla-vin into the anterior chamber. The lids are then sepa-rated with a lid speculum. Irradiation is performed6, 7,

9-15, 18, 19, 23 at a distance of 1-5 cm18, 19, 23 from the eye for 30 minutes using a UVA double diode at 370 nm and an irradiance of 3 mW/cm2. A bandage contact lens is usually placed on the cornea post-operatively9,

16, mostly for three to five days6, 11, 14, 18, 23, or until reepithelialization is complete10, 13, 15. Reepitheliali-zation can take anything from one to four days4, 10, 12. No persistent epithelial deficit has been found post-operatively12, 13, 16, 18.

Alternative protocols have been used. In three studies9-11 pilocarpine drops were instilled to reduce the amount of UVA light entering the eye and protect the ocular lens. Caporossi et al14 used a procedure that was unique. They interrupted application of radiation every five minutes by turning the diodes off, instilling riboflavin in the eye, and then continuing. What is important is to ensure full penetration of the cornea with riboflavin. The UVA source must be used with a potentiometric voltage regulator and the device must be properly calibrated with a UVA power meter prior to every patient being radiated. This will ensure that every patient receives5, 15 a uniform homogeneous level of UVA radiation of 370 nm with irradiance of 3 mW/cm2.

Generally, UV radiation represents a danger to the eye but this is mostly true for UVB radiation (290-320 nm).12 UVA radiation (320-400 nm) alone has a damage threshold value of 4 mW/cm2 at the cor-nea16. When riboflavin is instilled into the cornea the damage threshold drops to 0.35 mW/cm2 12. During cross-linking UVA radiation at 370 nm is used as this wavelength is optimally absorbed by riboflavin thus ensuring that approximately 95% of the UV radiation is absorbed in the cornea7, 19.

Riboflavin acts as a photo-sensitizer when com-bined with UVA light7, 10. Riboflavin is excited into its triplet state generating reactive oxygen species (ROS), comprised of singlet oxygen and a few su-peroxide anion radicals. These ROS react with mol-ecules in the cornea causing increased covalent bonds to form between amino groups of collagen fibrils5. These covalent bonds then change tissue properties



towards the posterior cornea13. Removing the epithe-lial layer results in keratocyte apoptosis (the process of programmed cell death) in the anterior 50 µm of the cornea18, 21. One month post-operatively kerato-cyte apoptosis was noted to a corneal depth of ap-proximately 300-350 µm13, 15, 18. Repopulation of keratocytes was found to occur in the anterior cornea and mid-stroma in the following few months and was associated with corneal edema8, 10, 13, 18. It has been shown that the repopulation of keratocytes is initiat-ed from activated keratocytes in deeper layers of the stroma18. Stroma deeper than approximately 350 µm showed an increased density of keratocytes in the first and third post-operative months13. Stromal repopula-tion was almost complete within six months15, 18.

Stromal density is increased after CXL is performed because well-structured compact collagen lamellae are produced after repopulation of keratocytes, which is seen as haze11. Even though cross-linking does in-duce cellular apoptosis, the regeneration processes of these cells result in normal tissue histology8.

Stromal thickness

Numerous studies have reported on a decrease in corneal thickness one year after CXL9, 10, 16, 17 while others6, 19, 21 have found that corneal thickness does not change post-operatively. Optical Coher-ence Tomography (OCT) has been used to show a significant increase in corneal thickness six months post-operatively. It is believed that this increase is caused by keratocytes producing new proteoglycans. The increase can be seen as an indication that the de-crease in corneal thickness after one year is not an indication of progression of keratoconus, as the nor-mal progression of keratoconus is not linked with a period of increased thickness but only thinning16. Alternatively the early increase of stromal thickness could be a measurement artifact seen in most patients post-operatively because of haze. This artifact is not present one year post-operatively, because of the dis-appearance of haze, seen with slit-lamp observation17.

Corneal transparency and endotheliumIn two studies10, 11 11-12.6% of the eyes treated

developed corneal haze which was successfully man-aged with a regimen of topical steroids. El-Ragga16 observed faint diffuse haze post-operatively, in all his

subjects, that spontaneously disappeared within one month. One eye, however, was left with a faint su-perficial corneal scar. The post-operative haze seems to be more prevalent in subjects with more advanced keratoconus18. In other studies11, 25 hyperactivated keratocyte nuclei in the anterior stroma (to a depth of 80 µm), and reticular patterned dark microstriae (with or without Vogt’s striae) were identified as possible risk factors for corneal opacity when observed pre-operatively. The haze seemed to not decrease these patients vision. The risk factors are important as these patients are more likely to not only develop haze but late stromal scarring post-operatively as well.

Post-operatively few clinical changes17, 18, 25 morpho-logical changes13, 14 or changes in cell count have been noted in the endothelium following CXL9, 10, 12, 14. In one study16, one out of 29 eyes treated presented with endothelial irregularities one month post-operatively. These irregularities disappeared two months later with-out any visual hindrance. The most important factor in reducing radiation and thus cytotoxic effects on the en-dothelium is to ensure a minimal inclusion thickness of 400 µm for all CXL patients7.

Regression of keratometric (K)-readings

Progression of keratoconus can be established by the ongoing steepening of the K-values of the cor-nea. After CXL it has been found that K-readings flattened9, 10, 17 or stabilized6, 7 and that the cornea had a tendency to take on a more symmetric form6, 13, 14. In a few rare cases a steepening of K-readings was found. Wollensak et al12 observed a minimal increase in one out of 23 eyes examined. It is important to realize that a flattening effect of a keratoconic cornea has never before been documented and that control groups of keratoconic eyes showed definite progres-sion. This flattening has been called post-operative re-gression which was found in 70 % of CXL patients12.

Stromal demarcation lineChanges in the corneal microstructure do not occur

throughout the entire cornea. The transition between the treated zone and untreated zone of the cornea is rapid18, 22 and is normally less than 350 µm into the cornea. Initially the anterior stroma shows edema and hypo-reflectivity while the posterior stroma is nor-mal. The transition can be seen as an opaque/whit-



ish line when using an OCT for instance, because of the rapid change between the two zones. Generally, the demarcation line disappears within three months post-operatively16, 22. The average depth of this line is approximately 313 µm16, 17. From the third to sixth months post-operatively the reflectivity of the anterior area changes from hypo- to hyper-reflectivity because of increased density in this part of the cornea. The line between the normal density cornea and the hyper reflective area is now called the late demarcation line. This late demarcation line can be detected for up to three years post-operatively when using confocal la-ser scanning microscopy11.

Subepithelial plexus

One month post-operatively there is an absence of the subepithelial nerve plexus in the treatment area when observed with a confocal microscope11, 13. Re-generation starts within the next few months. The nerves grow from the surrounding area that had not been irradiated. The anterior midstromal nerve fibers are also absent post-operatively but these are regener-ated from the deep stromal nerve plexus13. After six months the cornea’s sensitivity is restored to normal and reinnervation is nearly complete. Only two years after CXL does the nerve plexus fully resemble the pre-operative structure11.

Intra Ocular Pressure

Several studies have shown that no statistically sig-nificant changes take place in intra ocular pressure (IOP) measurements following CXL7, 12, 14, 16, 19. Gol-dich et al23, however, showed an increase in post-oper-ative IOP using contact and noncontact IOP measure-ment techniques. It could not be concluded, however, whether it was a true elevation in IOP or an increase due to the stiffening effect caused by CXL.

Visual Acuity

Uncorrected visual acuity (UCVA) was statisti-cally significantly improved by approximately 1-1.3 lines6, 10, 14, best corrected visual acuity (BCVA) had a statistically significant increase of approximately 1.26 lines8, 12 and best corrected spherical visual acuity (BCSVA) remained stable14, 16 when compar-

ing pre- and post-operative values. Interestingly, Doors et al16 found a significant de-

crease in BCSVA one month post-operatively but at three, six and 12 months post-operatively the BSCVA was stable compared to pre-operative val-ues. The decrease at one month was attributed to the remodeling process taking place in the cornea. It seems that the improvement in VA happens in the first three to 12 months post-operatively and then remains unchanged7, 10. The methods used to meas-ure these changes varied, in one study snellen charts were used14 in others logMAR charts6, 7, 10 and one study measured visual acuity with a snellen chart, but converted the data into logMAR for comparison of data22.

Refractive status after procedure

A slow but significant improvement in spherical re-fractive error6, 9, 12, 14, 16, 19 and cylindrical refractive error9, 10, 14 was seen in as little as three months post-operatively when compared to mean pre-operative values. However two studies9, 10 found an axis shift post-operatively. The methods of determining the re-fractive change varied from subtracting data collected at follow-up examinations from data collected on the day of the procedure7 to converting the data into vec-tors and then calculating the change found on follow-up visits when comparing data to the data collected on the day of the procedure16.

Complications of CXL

The most common complication evaluated was haze6, 10, 11, 18, 25 and some patients complained of ha-loes and night glare for the first three months post-operatively10. Additional complications were post-operative herpetic keratitis with iritis in a patient with no history of herpetic disease26 and diffuse lamellar keratitis in a patient treated with CXL for post-laser in situ keratomileusis27.

Conclusion

CXL seems to be the only form of treatment availa-ble to stop the progression of keratoconus. As the pro-gression of keratoconus leads to a decrease of vision and inability of vision to be adequately restored with



spectacles and soft contact lenses, it is important to do the procedure as soon as keratoconus is diagnosed12,

16 and before the cornea thins too much. Computer-assisted videokeratoscopes are the most sophisticated and sensitive devices for diagnosing irregular astig-matism which is the hallmark sign of keratoconus2. Early CXL treatment will preserve the patient’s vision at a better level12, 16. This procedure should only be done if progressive keratoconus has been established, and if the cornea is not thinner than 400 µm5, 6, 8, 11, 14. Most keratoconic patients over the age of 35 years no longer have progression of keratoconus thus patient selection is very important.

There is a debate between ophthalmologists wheth-er to remove the epithelium or not when doing the procedure because of the pain that patients have for approximately a day post-operatively. It has been concluded that removal of the epithelium is necessary for the absorption of riboflavin by the stroma11.

The main aim of the procedure initially was to stabilize the keratoconic cornea. Stabilization was achieved with extra benefits like more symmetric corneas, which not only increased VA but made the cornea easier to fit with contact lenses. It is reported that the cornea still tolerates contact lenses after the procedure12. Some investigations indicate that Kera-toconus leads to keratoplasty in approximately 20% of patients2, 5, 10, 22. CXL will significantly decrease the need for keratoplasty1, 7, 18, 19, 23, 24 or at least delay the need for it, which is especially important in third world countries where donor corneas are not easy to come by. CXL is still a new procedure and longer follow-up studies with bigger population groups are necessary, especially because the durability of the cross-linking effect is unknown and a repeated proce-dure may be necessary.

CXL is a simple and low cost procedure12 with a short recovery time and when looking at the research comparing the positive and negative aspects it seems that it should be the first line of action for any patient with keratoconus.

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Krachmer JH, Feder RS, Belin MW. Keratoconus and re-lated noninflammatory corneal thinning disorders. Surv Ophthalmol 1984 28 293-322.Rabinowits YS. Keratoconus. Surv Ophthalmol 1998 42 297-319.Sharif KW, Casey TA, Coltart J. Prevalence of mitral valve

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A van Zyl Thesis

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