Corneal Topography and the Morphology of the Palpebral Fissure
Corneal topography and the morphology
of the palpebral fissure.
Scott A. Read
B.App.Sc(Optom) Hons
Institute of Health and Biomedical Innovation
School of Optometry
Queensland University of Technology
Brisbane
Australia
Submitted as part of the requirements for the award of the degree of Doctor of Philosophy Keywords
Keywords
Cornea
Astigmatism
Aberrations
Eyelids
Corneal topography
Videokeratoscopy
Digital imaging
Eyelid morphology
II Abstract
Abstract
The notion that forces from the eyelids can alter the shape of the cornea has been proposed for many years. In recent times, there has been a marked improvement in our ability to measure and define the corneal shape, allowing subtle changes in the cornea to be measured. These improvements have led to the findings that pressure from the eyelids can cause alterations in corneal shape following everyday visual tasks such as reading. There are also theories to suggest that pressure from the eyelids may be involved in the aetiology of corneal astigmatism. In this program of research, a series of experiments were undertaken to investigate the influence of the eyelids on the shape of the cornea.
In the first experiment, an investigation into the diurnal variation of corneal shape was carried out by measuring corneal topography at three different times (approximately 9 am, 1 pm and 5 pm) during the day over three days of the week (Monday, Tuesday and Friday). Highly significant diurnal changes were found to occur in the corneal topography of 15 of the 17 subjects. This change typically consisted of horizontal bands of distortion in the superior, and to a lesser extent, inferior cornea, increasing throughout the day (and returning to baseline the next morning). These changes appeared to be related to forces from the eyelids on the anterior cornea. Some changes were also found in corneal astigmatism. Corneal astigmatism power vector
J0 (astigmatism 90/180°) was found to increase slightly over the course of the week. Whilst the changes in astigmatism were small in magnitude, this
III Abstract result leaves open the possibility that pressure from the eyelid may cause changes in corneal astigmatism. If pressure from the eyelids is involved in the aetiology of corneal astigmatism, then one may expect associations to exist between certain characteristics of the eyelids and corneal shape. An experiment was then undertaken to explore these possible associations.
We defined the average morphology of the palpebral fissure in different angles of vertical gaze for 100 young normal subjects. This was achieved through analysis of digital images that were captured in primary gaze, 20° downgaze and 40° downgaze. Parameters defining the size, position, angle and contour of the eyelids were determined. Highly significant changes were found to occur in the palpebral fissure with downward gaze. The palpebral aperture narrows in downward gaze, and the angle of the eyelids changes from being slightly upward slanted in primary gaze, to being slightly downward slanted in downward gaze. The eyelid margin contour also flattens significantly in downward gaze.
The average topography of the central and peripheral cornea was also defined for this same population. A technique was used that allowed the capture and subsequent combination of topography data from both the central and the peripheral cornea. The use of this technique provided a large corneal topography map, with data extending close to the limbus for each subject. Marked flattening was found to occur in the peripheral cornea and a conic section was found to be a poor descriptor of corneal contour in the periphery (i.e. greater than 6 mm diameter). Corneal astigmatism was also
IV Abstract found on average to reduce in the periphery. However a number of distinct patterns of peripheral corneal astigmatism were noted in the population.
Corneal astigmatism in the peripheral cornea was either found to remain stable (59% of subjects), increase (10% of subjects) or reduce (31% of subjects) in magnitude in comparison to the amount of central corneal astigmatism.
We also investigated associations between the parameters defining the palpebral fissure and parameters describing corneal shape in this population of subjects. A number of highly significant associations were found between the morphology of the palpebral fissure in primary gaze and the shape of the cornea. A general tendency was found for subjects with wider horizontal palpebral fissure widths to exhibit larger corneas and also flatter central corneal powers. There were also highly significant associations found between the angle of the eyelids and the axis of corneal astigmatism, but not the magnitude of corneal astigmatism. The associations found between corneal astigmatism and palpebral fissure morphology is further evidence supporting the hypothesis that pressure from the eyelids is involved in the aetiology of corneal astigmatism.
The results of these investigations have shown that corneal changes as a result of eyelid forces occur in the majority of young subjects tested over the course of a normal working day. The average morphology of the palpebral fissure and topography of the central and peripheral cornea has also been defined in detail for a large population of young subjects. Significant
V Abstract associations were found between corneal astigmatism and the morphology of the palpebral fissure. Whilst these results support a model of corneal astigmatism development based on eyelid morphology, they do not prove causation. Further research including measurement of eyelid pressure and corneal rigidity may aid in understanding the exact aetiology of the magnitude and axis of corneal astigmatism.
VI Contents
Table of Contents
Chapter 1: Literature review
1.1 Introduction 1
1.2 The shape of the cornea 2
1.2.1 Methods for measuring corneal shape 2
1.2.2 Corneal reference points 6
1.2.3 Describing the shape of the cornea 9
1.2.4 Mathematical descriptions the cornea 12
1.3 The normal shape of the cornea 18
1.3.1 Corneal aberrations 22
1.3.2 Influence of age on the normal cornea 24
1.3.3 The association between corneal shape and
refractive error 25
1.3.3.1 The cornea in myopia 26
1.3.3.2 The cornea in hyperopia 29
1.4 Other factors influencing corneal shape 29
1.4.1 The pre-corneal tear film 30
1.4.2 External forces and corneal shape 31
1.4.2.1 Orthokeratology 32
1.4.2.2 The corneal epithelium 34
1.4.2.3 The corneal stroma 36
1.4.3 Accommodation and corneal topography 39
1.4.4 Extraocular muscles and corneal topography 42
VII Contents
1.4.4.1 Extraocular muscle surgery and the cornea 43
1.4.4.2 Corneal topography and nystagmus 44
1.4.5 Corneal topography and eyelid forces 45
1.4.5.1 Eyelid pathology and corneal topography 49
1.4.5.2 Visual tasks and corneal topography 51
1.5 Astigmatism 56
1.5.1 Prevalence and changes of astigmatism with age 59
1.5.1.1 Astigmatism in infants and children 59
1.5.1.2 Astigmatism in adults 61
1.5.2 Javal’s rule 63
Symmetry of axis of astigmatism between right and 1.5.3 left eyes 67
1.5.4 Myopia and astigmatism 68
1.5.5 Genetics and astigmatism 72
1.5.6 Astigmatism in ethnic and disease groups 75
1.5.7 Animal studies and astigmatism 79
1.5.8 Corneal astigmatism and eyelid forces 82
1.6 Rationale 85
Chapter 2: The diurnal variation of corneal topography and aberrations
2.1 Introduction 89
2.2 Methods 93
2.2.1 Subjects and procedures 93
2.2.2 Data analysis 96
VIII Contents
2.3 Results 99
2.4 Discussion 109
2.5 Conclusions 120
Chapter 3: The morphology of the palpebral fissure in different angles of vertical gaze
3.1 Introduction 123
3.2 Methods 127
3.2.1 Subjects and procedures 127
3.2.2 Data analysis 133
3.3 Results 138
3.3.1 Caucasian population 141
3.3.2 Difference associated with gender 146
3.3.3 Difference associated with ethnicity 148
3.4 Discussion 150
3.5 Conclusions 164
Chapter 4: The topography of the central and peripheral cornea
4.1 Introduction 167
4.2 Methods 170
4.2.1 Subjects and procedures 170
4.2.2 Data analysis 183
4.3 Results 190
4.4 Discussion 205
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4.5 Conclusions 213
Chapter 5: The association between the topography of the cornea and the morphology of the palpebral fissure
5.1 Introduction 215
5.2 Methods 219
5.2.1 Subjects and procedures 219
5.2.2 Data analysis 224
5.3 Results 228
5.3.1 Corneal topography and eyelid morphology 228
5.3.2 Corneal diameter and corneal power 238
5.3.3 Eyelid morphology and refractive error 242
5.3.4 Corneal topography and refractive error 243
5.4 Discussion 244
5.5 Conclusions 254
Chapter 6: Conclusions
6.1 Summary and main findings 255
6.1.1 The diurnal variation of corneal topography 255
6.1.2 The association between corneal topography and
eyelid morphology 257
6.2 A possible model of corneal shape and astigmatism
development 261
6.3 Future research directions 269
X Contents
References 271
Appendices
Appendix 1 Ethics 323
Appendix 2 Publications arising from the thesis 327
Figures
Figure 1.1 A typical Placido ring image as captured by the Keratron
videokeratoscope 4
Figure 1.2 Illustration of the different reference axes in
videokeratoscopy. 8
Figure 1.3 An example of a dioptric power map (tangential power)
from the Keratron videokeratoscope. 10
Figure 1.4 Illustration of the type of conic section given by different
values of the asphericity parameter Q. 14
Figure 1.5 Example of corneal topography map following reading.
Note the close correlation between the eyelid position
during reading (top) and the superior band of corneal
steepening in the corneal topography map (bottom). 54
Figure 1.6 Example of a topographical map of an astigmatic cornea. 57
Figure 2.1 Tangential power difference maps (left) and significance
maps (right) for 4 subjects. 101
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Figure 2.2 Mean change in refractive power RMSE difference from
best fit refractive power sphero-cylinder (5.5 mm pupil)
from baseline over the course of the week. 103
Figure 2.3 a) Mean change in sphere power “M” from baseline over
the course of the week (5.5 mm pupil). b) Mean change in
astigmatism 90/180° “J0” from baseline over the course of
the week (5.5 mm pupil). c) Mean change in astigmatism
45/135° “J45” from baseline over the course of the week. 104
Figure 2.4 −3 Mean change in trefoil along 30 degrees ( Z 3 ) and primary
−1 vertical coma ( Z 3 ) from baseline (Monday morning) over
the course of the week (5.5 mm pupil). 108
Figure 2.5 Tangential power maps from subject DK illustrating the
effect of different visual tasks on corneal topography. 117
Figure 3.1 Camera set-up for capturing images of the anterior eye in
three different directions of vertical gaze. 130
Figure 3.2 Palpebral fissure biometric measurements on a typical
digital image. 134
Figure 3.3 Example of polynomial fitting to the eyelid contour. A
second order polynomial of the form Y = AX2 + BX + C is fit
to the central upper and lower eyelid contour. 137
Figure 3.4 Example of the comparison between the two observers for
the analysis of the digital images (comparison for
Theta_HEF measure is shown). 139
XII Contents
Figure 3.5 Diagrammatic representation of the mean biometric
palpebral fissure dimensions for the right eye of the 76
Caucasian subjects (left) and an example of primary gaze,
20° downgaze, and 40° downgaze images from the right
eye of a typical male Caucasian subject (subject 43) (right). 142
Figure 4.1 Example of central and peripheral corneal data and
combined data map (axial curvature maps are shown). 175
Figure 4.2 Example of two subjects’ corneal axial curvature data in
one semi-meridian (the data from the combined map is
shown). 176
Figure 4.3 Example of the comparison between actual and predicted
data for one semi-meridian of central map data for subject
65. 178
Figure 4.4 Average eye movement maps and videokeratoscope
movement maps for the 2 subjects in the control
experiment. 182
Figure 4.5 RMS fit error versus polynomial fit order for different
corneal analysis diameters. 186
Figure 4.6 Illustration of the annulus sphero-cylinder analysis method
used for examining the change in the corneal sphero-
cylinder in the peripheral cornea. 189
Figure 4.7 Frequency distributions for Ro and Q for 6, 8 and 9 mm 193 corneal diameters.
XIII Contents
Figure 4.8 Frequency distribution for corneal power best sphere ‘M’
for corneal diameters 6, 7, 8 and 9 mm (top). Scatter plots
of J45 and J0 for corneal axial power are displayed for 6
mm, 7 mm and 8 mm corneal diameters (bottom). 197
Figure 4.9 Corneal cylinder axis and cylinder power versus annulus
diameter for the 0.5 mm annulus analysis. 200
Figure 4.10 Examples of corneal classification based upon central and
peripheral toricity. 203
th Figure 4.11 Third and 4 order Zernike polynomial coefficients (and
0 term Z 6 ) for 6, 8 and 9 mm corneal diameters. 204
Figure 5.1 Frequency histogram of central corneal cylinder axes (i.e.
minus correcting cylinder) for the 92 subjects with valid
corneal topography data. 227
Figure 5.2 Corneal best sphere ‘M’ for 8 mm analysis diameter versus
primary gaze horizontal palpebral fissure width. 231
Figure 5.3 Corneal J45 for 8 mm analysis diameter versus primary
gaze Theta HEF. 232
Figure 5.4 Example of the correlation between the angle of the
palpebral fissure and the angle of the corneal cylinder axis
for two subjects. 234
Figure 5.5 Scatter plot of corneal J45 versus angle of the palpebral
fissure for subjects exhibiting WTR corneal cylinder axes
and central astigmatism (>0.75DC) that is stable or
increasing in the peripheral cornea. 240
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Figure 6.1 Representation of the proposed model of the cause of
corneal astigmatism. 263
Figure 6.2 Illustration of how passive growth could lead to a reduction
in astigmatism. 265
Tables
Table 1.1 Summary of studies of the best fitting conic section to the
corneal contour. 20
Table 2.1 Group mean change in Zernike coefficients (averaged
over the three days of testing) for 3.5 mm and 5.5 mm
pupil sizes expressed in microns, with results from
repeated measures ANOVA (test of within-subjects
effects). 106
Table 3.1 Definitions of the biometric measures of the palpebral
fissure and anterior eye. 135
Table 3.2 Group mean biometric palpebral fissure measurements. 140
Table 3.3 Results of repeated measures ANOVA. 147
Table 3.4 Summary of previous investigations into biometric
measures of the palpebral fissure. 154
Table 4.1 Average conic fit and polynomial fit data from the corneal
height data averaged across all meridians. 191
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Table 4.2 Group mean conic fit data for the steepest and flattest
corneal meridian. 194
Table 4.3 Group mean axial power corneal sphero-cylinder for 6, 7,
8 and 9 mm corneal diameters. 196
Table 4.4 Group mean axial power corneal sphero-cylinder for 0.5
mm annulus data. 199
Table 5.1 Subjective refraction details of the 100 subjects. 220
Table 5.2 The palpebral fissure and corneal topography parameters
ascertained for each subject. 225
Table 5.3 Results from correlation analysis between corneal axial
power sphero-cylinder data (8 mm) and primary gaze
eyelid morphology parameters (n = 78). 230
Table 5.4 Results from correlation analysis between corneal axial
power sphero-cylinder data (8 mm) and primary gaze
eyelid morphology parameters for subjects exhibiting
WTR central corneal cylinder axis (n = 58). 237
Table 5.5 Results from correlation analysis between corneal axial
power sphero-cylinder data (8 mm) and primary gaze
eyelid morphology parameters for subjects with WTR
corneal cylinder axes and central corneal astigmatism
(<0.75 DC) that was stable or increased in the peripheral
cornea (n = 16). 239
Table 5.6 Results for correlation between corneal diameter and
corneal axial power. 241
XVI Statement of Authorship
Statement of original authorship:
The work contained in this thesis has not been previously submitted for a degree or diploma at this or any other higher education institution. To the best of my knowledge and belief, the thesis contains no material previously published or written by another person except where due reference is made.
Signature: ______
Date: ______
XVII Acknowledgements
Acknowledgements:
I would like to thank my supervisor Associate Professor Michael Collins for his invaluable advice, assistance and support throughout my candidature. I would also like to thank my associate supervisor Professor Leo Carney for all of his assistance and encouragement.
All of the research performed in this thesis was carried out by myself or under my direction. However, a number of the techniques used in this research, both in the collection of data and subsequent analysis were developed by some of my fellow researchers in the Contact Lens and Visual Optics
Laboratory. I would like to acknowledge Mr Brett Davis, Mr Ross Franklin and Dr Robert Iskander for their work in developing these techniques and their advice and assistance throughout my studies.
Thanks also to Claudia Hackl and Wiebke Rohloff for their assistance with the lengthy task of analysing the digital images reported in Chapter 3.
Finally, I would like to thank Gina Correnti for her support, patience and encouragement during my studies.
XVIII Chapter 1
Chapter 1: Literature Review
1.1 Introduction
The cornea (in conjunction with the pre-corneal tear film) represents the eye’s most anterior optical surface. It functions as a refractive surface, and also as a protective barrier for the internal components of the eye. The curvature of the cornea, combined with the large refractive index difference between air and corneal tissue, means that the cornea is the eye’s most powerful refractive surface. Subtle changes in the cornea’s shape therefore have the potential to have considerable effects on vision.
The cornea is a transparent, avascular tissue, consisting of five distinct layers. The anterior epithelium, overlying a basement membrane (Bowman’s layer), the stroma, which consists of a regular arrangement of collagen fibres, and the endothelium which is attached to a basement membrane
(Descemet’s membrane) (Snell and Lemp 1989).
With advances in digital technology, our ability to accurately measure and describe the shape and optical properties of the cornea has improved considerably. These advances mean that subtle corneal changes can now be more easily revealed. Developments in corneal analysis techniques have also markedly improved our ability to characterise and define normal corneal shape and optics.
1 Chapter 1
1.2 The shape of the cornea
The cornea is one of the ocular structures that can be observed and measured readily in a non-invasive manner. The shape and optical properties of the cornea have therefore been studied extensively for many years. Accurate and detailed assessment of corneal shape and optics is required for a number of different clinical and research applications including: contact lens fitting; assessing contact lens induced corneal changes; diagnosis and monitoring of corneal ectatic disorders; laser refractive surgery; corneal grafting; assessing the effects of other ocular surgeries; and assessing and monitoring corneal astigmatism (Seitz et al 1997).
1.2.1 Methods for measuring corneal shape
One of the earliest methods (and still a commonly used clinical technique) developed for measuring corneal shape is keratometry. The keratometer utilises a reflected image formed by the anterior corneal surface (Purkinje image I) to measure the central radius of curvature of the cornea in two perpendicular meridians (Bennett and Rabbetts 1984). As the keratometer measures from only four positions along two meridians of maximum and minimum power in the central cornea, it only provides limited information regarding corneal shape (Klyce and Wilson 1989). The limitations associated with keratometry led to more advanced techniques being developed for evaluating corneal shape.
2 Chapter 1
Photokeratoscopes were subsequently developed based upon the Placido disk principle. These instruments treat the cornea as a convex mirror, and a series of illuminated concentric rings (the Placido disk) are reflected from the corneal surface and the resultant image photographed. Using knowledge of the geometry of the instrument rings and the resultant spacing of the rings in the reflected image, the slope of the corneal surface can be determined at an array of different corneal points (Schwiegerling et al 1995, Seitz et al 1997).
The derivative of the corneal slope provides the corneal curvature, which is directly related to the optical power of the cornea (Schwiegerling et al 1995).
Information from many points across the cornea can thus be used to describe corneal shape. One of the major drawbacks of these instruments was the lengthy computation time required to calculate corneal power.
Advances in digital imaging and computer technology mean that modern instruments based upon the Placido disk principle can quickly capture and assess images and provide corneal shape information from thousands of different points across the cornea. These instruments consist of a Placido disk target, a digital video camera, along with a computer system and are known as “computer-assisted videokeratoscopes”. Figure 1.1 displays a typical image of the Placido rings as captured by the Keratron videokeratoscope (EyeQuip Division, Alliance Medical Marketing,
Jacksonville, FL, USA).
Studies investigating the accuracy and repeatability of modern Placido disk- based videokeratoscopes have generally found most instruments to be highly
3 Chapter 1
Figure 1.1: A typical Placido ring image as captured by the Keratron videokeratoscope.
4 Chapter 1 accurate and repeatable for measuring spherical, aspheric and astigmatic inanimate test objects (Tripoli et al 1995, Tripoli et al 1996, Tang et al 2000).
A number of instruments have also exhibited highly repeatable measures on human corneas (Cho et al 2002). Placido disk-based techniques do have a number of limitations, including difficulties in acquiring adequate data points within the central 2 mm of the cornea and in imaging objects with sudden slope transitions (Belin and Ratlif 1996). Inaccuracies may also occur due to alignment, focusing or centration errors (Seitz et al 1997). Modern instruments tend to incorporate strategies to minimize focusing and centration errors such as the automatic range finding device and misalignment correction system that is incorporated into the Keratron videokeratoscope (Mattioli and Tripoli 1997).
A number of other methods have also been developed to measure corneal shape. In raster stereography, a grid pattern is projected onto the cornea
(e.g. PAR CTS instrument)(PAR vision systems , New Hartford, NY, USA).
Distortions in the grid pattern are then analysed to determine the corneal elevation based on the camera and grid projection angles (Seitz et al 1997).
Optical beam scanning (as used in the Orbscan instrument)(Orbscan, Inc,
Salt Lake City, UT, USA) takes an image of a slit of light intersecting the cornea to give a cross section of the corneal surface (Naufal et al 1997).
This technique also allows other anterior chamber structures to be measured such as posterior corneal curvature, corneal thickness and anterior chamber depth (Seitz et al 1997).
5 Chapter 1
The technique of laser holographic interferometry uses wave interference to measure corneal shape (Naufal et al 1997). A laser beam is reflected off the cornea onto a grid and the optical path difference of the illuminating and reflected beam is measured to determine the corneal elevation (Kasprzak et al 1994).
These other techniques for measuring corneal shape have generally not proved to be as popular as Placido disk-based instruments, particularly in the clinical setting. Placido disk-based computer assisted videokeratoscopes remain the most commonly used in clinical practice.
1.2.2 Corneal reference points
It is important to define a number of key reference points associated with videokeratoscopy and the cornea. When viewing an object, the line from the fixation point to the centre of the eye’s entrance pupil is known as the line of sight (Mandell 1994). The point where the line of sight intersects the corneal surface is often referred to as the ‘corneal sighting centre’. Another important reference point is the corneal geometric centre. The distance from corneal geometric centre to the line of sight differs between individuals. The geometric centre has been shown to be located on average 0.21 ± 0.16 mm temporally to the line of sight in a population of 50 subjects (Pande and
Hillman 1993).
6 Chapter 1
The centre of the videokeratoscope image is located at a point where the optical axis of the instrument is perpendicular to the cornea, known as the
‘vertex normal’ (Mandell, 1994) (Figure 1.2). The ‘vertex normal’ is not coincident with either the corneal sighting centre or the corneal geometric centre. The displacement of the vertex normal from the other two reference points has also been shown to differ between individuals. Mandell et al
(1995) found the vertex normal to be displaced by on average 0.38 ± 0.1 mm from the corneal sighting centre. The displacement between each of these reference points is generally small and will therefore only have a relatively minor effect on corneal power, toricity and axis measures (Mandell et al
1995). However, Salmon and Thibos (2002) suggested that large misalignments between the vertex normal and line of sight may cause significant errors when comparing videokeratoscope data to other measurements of ocular optics (such as higher order aberrations) based upon the line of sight.
The most appropriate corneal reference point to use may depend on the particular application of the corneal data. If one is concerned with the effect of the optics of the cornea on vision, then the most appropriate reference point is the corneal sighting centre. If however one is more concerned with the shape of the cornea (e.g. for contact lens fitting and design) it may be more appropriate to use the corneal geometric centre as the reference.
7 Chapter 1
Figure 1.2: Illustration of the different reference axes in videokeratoscopy.
Note the displacement between the centre of the videokeratoscope image
(the vertex normal) and the corneal sighting centre. (Figure adapted from
Mandell, 1994)
8 Chapter 1
1.2.3 Describing the shape of the cornea
Videokeratoscopes provide topographic information from thousands of corneal locations. This information is often displayed in the form of colour- coded dioptric maps. These maps use a range of colours that correspond to different power ranges, so that the power map represents a contour plot of the corneal dioptric powers (Schwiegerling et al 1995). This allows large amounts of information regarding the corneal shape to be displayed in a manner that is quickly and easily understood. Figure 1.3 displays a typical corneal dioptric power map from the Keratron videokeratoscope. The dioptric topographical map can be checked for asymmetry, asphericity, astigmatism and abnormally steep or flat areas to give an estimate of corneal optical irregularities (Maeda 2002). This qualitative assessment of the cornea allows an estimate of the severity of irregularities to be made as well as allowing the differentiation between normal and abnormal corneas.
In general there are three different dioptric power maps used by videokeratoscopes. These are the axial power map, the tangential (or instantaneous) power map and the refractive power map. To calculate corneal power, the axial map uses the axial distance along the normal to the cornea to the videokeratoscopic axis, the tangential power map uses the radius of curvature calculated from a local region of the cornea while the refractive power map uses the focal length of the cornea (calculated using
Snell’s law for paraxial rays). Bafna et al (1998) suggested that the instantaneous maps more accurately describe subtle localised changes in
9 Chapter 1
Figure 1.3: An example of a dioptric power map (tangential power) from the
Keratron videokeratoscope.
10 Chapter 1 corneal shape, and that the refractive maps may be preferable for understanding the effects of corneal shape on vision.
Some attempts have been made to classify corneal dioptric power maps based upon their qualitative appearance (Bogan et al 1990, Rabinowitz et al
1996). Bogan et al (1990) measured the corneal topography of 212 normal subjects. The corneal power maps were then examined and categorised into one of four groups according to the qualitative appearance of the maps: round (22.6% of subjects), oval (20.8%), symmetric bow tie (17.5%), asymmetric bow tie (32.1%) and irregular (7.1%).
Several authors have attempted to quantitatively estimate the optical qualities of the cornea based on data from videokeratoscopes. A number of different
‘topographic indices’ have been formulated, and whilst each index measures a slightly different parameter, most attempt to give a quantitative assessment
(through calculation of a single numerical index) of the power distribution or degree of irregularity of the cornea (Wilson and Klyce 1991a, Smolek et al
1998, Chastang et al 1999). Two of the more commonly used topographical indices are the Surface Asymmetry Index (a centrally weighted measure of surface asymmetry calculated by summation of the difference in corneal powers for points 180 degrees apart) and the Surface Regularity Index (a measure of localised fluctuations in the power of the central cornea as measured over the central 10 rings) (Wilson and Klyce 1991b).
11 Chapter 1
Corneal height maps can also used to describe corneal topography. By integrating the slope data from a videokeratoscope, the height or sag of the cornea (from a reference plane) can be derived (Schwiegerling et al 1995).
The drawback of using corneal height is that subtle variations in height can be hidden by the pronounced spherical structure of the cornea (Young and
Siegel 1995, Schwiegerling and Greivenkamp 1997). This can be overcome by subtracting a reference surface (corresponding to the general shape of the cornea or best fit sphere) from the height data, which allows subtle changes in height to be revealed (Young and Siegel, 1995, Schwiegerling and
Greivenkamp 1997). Young and Siegel (1995) suggested that these height maps more accurately represent the corneal contour than the traditional power maps as they display the actual corneal topography (rather than surface power).
1.2.4 Mathematical descriptions of the cornea
The simplest way to describe the shape of the central cornea is as a section of a sphere. Keratometry provides a spherical radius as a description of central corneal shape. It is well recognised though, that the cornea departs significantly in shape from a sphere in the periphery.
A common way to describe the aspheric nature of the cornea is as a section of an ellipse (a type of conicoid) rotated (symmetrically) around the Z axis
(the optical axis of the cornea). A general equation for describing a conicoid
2 2 is given by y = 2rox - px (Bennett 1988) where y is the distance from corneal
12 Chapter 1 centre and x is the corneal height and ro is the radius of curvature at the corneal apex. The term “p” is an asphericity parameter which describes the degree to which the corneal surface departs from a sphere. Another commonly used asphericity parameter is termed “Q”. Q is related to p by the equation Q = p – 1.
Q describes the type of conicoid that best fits the central cornea where:
Q = 0 is a sphere,
Q > 0 is an ellipsoid with minor axis along Z axis (an oblate or steepening ellipse),
-1 < Q < 0 is an ellipsoid with major axis along Z axis ( a prolate or flattening ellipse),
Q = -1 is a paraboloid, and
Q < -1 is an hyperboloid.
(Figure 1.4)
Modern videokeratoscopes have revealed that a simple conic section may not adequately describe corneal shape in some cases (particularly for irregularly shaped corneas). Other methods have been developed which describe the cornea with a set of more complex mathematical functions.
Schwiegerling and Greivenkamp (1997) suggested that the shape of the corneal surface can be represented mathematically in a Cartesian coordinate system as a function of the form z = f (x, y). Where z is the height or sag of the surface at a given point (x, y). When the functional form of f (x, y) is
13 Chapter 1
Figure 1.4: Illustration of the type of conic section given by different values of the asphericity parameter Q.
14 Chapter 1 complicated, analysing the surface is simplified by representing the cornea as a linear combination of simpler surfaces (with each simple surface given a weight describing the amount of that surface present in the overall surface).
These simpler surfaces are described mathematically as a set of functions so that the complex shape of the cornea can be related to more familiar optical quantities such as spherical and cylindrical curvature and power. One such set of functions is the Taylor series expansion, which is a polynomial series in two dimensions (Howland and Howland 1977, Oshika et al 1999b). The
Taylor series expansion is non-orthogonal, meaning that the coefficients are interrelated and dependant upon the number of terms in the expansion (i.e. adding or subtracting terms leads to changes in the other terms of the series).
Another set of functions used to describe the corneal surface is the Zernike polynomials. The Zernike polynomials are a set of functions that are orthogonal over the unit circle (i.e. the set of coefficients are independent of one another and independent of the number of terms in the series expansion). The Zernike functions are characterised by a polynomial variation in the radial direction p (for 0 ≤ p ≤ 1) and a sinusoidal variation in the azimuthal direction θ. (Schwiegerling and Greivenkamp 1995). Several different numbering systems have been used to represent the Zernike polynomials. Thibos et al (2002) recommended the use of a double indexing scheme, which allows unambiguous description of each function’s radial order (the subscript) and azimuthal frequency (the superscript).
15 Chapter 1
Several of the lower order Zernike terms represent familiar corneal shapes.
0 1 The function Z 0 describes a surface of constant height. The function Z1
−1 describes a plane tilted about the y axis and Z1 describes a plane tilted
1 0 about the x axis (or Z1 rotated by 90 degrees), Z 2 is a paraboloid and
2 −2 represents an average curvature of the cornea. Z 2 and Z 2 describe corneal astigmatism and are two saddle shaped surfaces rotated 45 degrees with respect to each other (Schwiegerling and Greivenkamp 1995). Higher order
Zernike terms represent more complex corneal shapes including coma, trefoil and spherical aberration. The orthogonal nature of the Zernike polynomials means that adding or subtracting terms does not affect the expansion coefficient values of the other terms (i.e. each term is independent of the other). The variance of the surface is also given by the sum of the squares of the expansion coefficients.
Zernike polynomials have also been used to estimate the optical qualities of the cornea by describing the ‘corneal wavefront aberration’. Hemenger et al
(1995) demonstrated that the optical path length at the entrance pupil, of rays passing through the cornea, can be calculated from the corneal height data
(as provided by the videokeratoscope). The departure from the condition of equal optical path lengths across the pupil provides a measure of the aberrations (i.e. the distortion of the wavefront, or the optical path difference).
The optical path difference thus represents the difference between the actual corneal wavefront and the ideal wavefront. The distribution of optical path lengths across the pupil can then be fitted with a set of Zernike polynomials.
16 Chapter 1
This procedure provides a systematic classification of the optical properties of the cornea.
Thus the properties of the cornea can be described with Zernike polynomials by decomposing the surface of the cornea into a polynomial expansion, or by fitting the optical path length distribution of rays passing through the cornea with a polynomial expansion (corneal wavefront error). Fitting Zernike polynomials to the corneal surface provides corneal shape information, whereas the corneal wavefront error provides information regarding the optical quality of the cornea.
Fourier series harmonic analysis can also be used to mathematically describe corneal topographical data (Hjortdal et al 1995). A Fourier series can be used to transform any periodic function into trigonometric components
(Hjortdal et al 1995, Maeda 2002). Studies have demonstrated that Fourier analysis allows the corneal power data to be decomposed into components that have well known optical meanings (Hjortdal et al 1995, Keller and van
Saarloos 1997). The complex corneal topographical information can thus be broken down into spherical, regular astigmatic and irregular astigmatic components.
Maloney et al (1993) used a slightly different technique for describing the optical quality of the cornea. They mathematically calculated the best fit sphero-cylinder that most closely approximates the corneal topographical data. At each point, the difference between the best fit dioptric power and
17 Chapter 1 the actual corneal dioptric power was calculated. The root mean square of the sum of these differences was calculated to give an overall measure of topographic irregularity (the RMS error).
A number of different methods can be used to describe the optical properties of the cornea. In recent times the use of the Zernike expansion has become the most common method used to investigate the optics of the cornea and the eye as it provides a comprehensive assessment of the eye’s optical properties in terms that are generally familiar to the clinician. The orthogonal nature of the Zernike polynomials allows for more straightforward analysis of individual optical components than other techniques (e.g. the Taylor series expansion) and makes this method ideal for a number of different applications.
1.3 The normal shape of the cornea
Knowledge of the normal corneal shape allows us to more easily diagnose corneas that are abnormal and to understand how these abnormalities may affect vision (Dingeldein and Klyce, 1989). Early studies into the average corneal shape used keratometry and photokeratoscopy to measure the cornea. More recently, computer-assisted videokeratoscopy has become the method of choice for studying corneal shape.
18 Chapter 1
In an early study, Knoll (1961) measured the shape of 67 corneas using photokeratoscopy. In general, corneas were found to be close to spherical centrally and became flatter in radius in the periphery (i.e. a prolate ellipse).
Some variations in central corneal symmetry and the rate of peripheral corneal flattening were noted between subjects. Clark (1974a) also measured the corneal shape of 164 normal subjects with a photokeratoscope. The mean central curvature for all subjects was 7.759 mm. The peripheral cornea showed a prolate shape in 90% of corneal semi- meridians measured. Asymmetry of corneal asphericity was also found to be common, with nasal and superior regions often being more prolate. Clark
(1974b) noted that large variations exist in the corneal topography of normal subjects.
A number of investigators have found the best fitting conic section to the contour of the cornea and reported the average ro and Q-values for the population. Table 1.1 presents a summary of the results of some of these studies.
Kiely et al (1982b) found the mean central radius of curvature to be 7.72 mm and mean asphericity (Q) was –0.26. The majority of eyes exhibited a Q- value between 0 and –0.50 indicating a prolate elliptical shape for most subjects. A slight (but significant) correlation was found between radius of curvature and Q (i.e. a steeper radius was associated with more peripheral flattening). Kiely et al (1982b) also fitted their data with a non-rotationally symmetrical model, which was found to be a better descriptor of corneal
19 Chapter 1
Table 1.1: Summary of studies of the best fitting conic section to the corneal contour. The average data across all corneal meridians is presented.
Method of Corneal Author n Age Mean Ro Mean Q measurement diameter (apical radius) (asphericity)
Photokeratoscope Kiely et al (1982b) 88 16-80 6 mm 7.72 ± 0.3 -0.26 ± 0.2
Photokeratoscope + Guillon et al (1986) 110 17-60 9 mm* 7.78 ± 0.3 -0.15 ± 0.2 Keratometer
Videokeratoscope Eghbali et al (1995) 41 23-61 6 mm 7.67 ± 0.2 -0.18 ± 0.2
Douthwaite et al (1999) 98 20-59 Videokeratoscope 6 mm 7.86 ± 0.2 -0.21 ± 0.1
(*Guillon et al (1986) stated that the photokeratoscope used can measure up to 9 mm diameter, but the actual measured diameter may have been smaller.)
.
20 Chapter 1 shape for most subjects. This suggests an inadequacy of the simple conic section model to fully describe the corneal shape.
Guillon et al (1986) found the mean central corneal curvature to be 7.775 mm. The mean Q-value was found to be -0.17 for the flattest meridian and -
0.19 for the steep meridian. Central and peripheral astigmatism were found to be similar. The authors noted that marked variations were found in the corneal shapes of the normal individuals tested (e.g. some subjects showed no flattening in the periphery and some subjects even displayed a steepening).
Dingeldein and Klyce (1989) measured corneal topography on 22 normal subjects. All subjects exhibited a steeper central cornea with peripheral flattening. The majority of eyes tested showed flattening beginning closer to the nasal side. A considerable similarity was found between the topography of right and left eyes for 18 of the 22 subjects. The topography of one eye was often the mirror image of the other eye.
In a retrospective study, Eghbali et al (1995) calculated the preoperative corneal asphericity for a group of 41 subjects who had undergone radial keratotomy. The mean Q-value was found to be -0.18. Eighty percent of subjects exhibited prolate elliptical corneal shapes.
Douthwaite et al (1999) found a mean apical radius of 7.93 mm horizontally and 7.78 mm vertically. The mean Q-values were -0.24 horizontally and -
21 Chapter 1
0.18 vertically (indicating the corneas flattened slightly more horizontally).
The corneal radii of curvature of male subjects were found to be significantly longer than the female, but there was no gender difference for Q. No significant association was found between the apical radius and asphericity.
In 2000, Cheung et al also calculated shape factor and apical radius for 63
Hong Kong Chinese subjects. They also found males to have longer apical radii than females. The average apical radius was found to be 7.82 mm (in the flattest meridian) and 7.64 mm (in the steepest meridian). The average
Q-value was found to be -0.17 (in the flattest meridian) and -0.22 (in the steepest meridian). The mean apical radius was found to be significantly steeper for the Asian subjects compared to Caucasians, but no significant difference was found in the asphericity (i.e. Asian corneas were steeper, but of the same general shape as Caucasian corneas).
1.3.1 Corneal aberrations
In recent times, as our ability to measure the shape of the cornea has improved, a number of studies have used the more complex mathematical descriptors of the cornea such as Zernike polynomials to investigate the shape and aberrations of the cornea. These studies have attempted to more thoroughly define the complexities of the normal corneal shape in the population.
22 Chapter 1
Studies investigating the average aberrations of the cornea in the population have generally noted that a wide degree of variability exists in the amount of corneal aberrations present between individuals, with some normal subjects exhibiting relatively high amounts of corneal aberrations, particularly for larger pupil sizes (Hemenger et al 1996, Guirao et al 2000, Wang et al
2003b). Hemenger et al (1996) suggested that for sufficiently large pupils, these aberrations were large enough to produce measurable losses in vision.
The group of aberrations making the largest contribution to the total higher order aberrations of the cornea tends to be the 3rd order aberrations
(including coma and trefoil terms) (Artal et al 2001, Wang et al 2003b, Kelly et al 2004). The magnitude of aberrations is generally found to become progressively smaller for the higher order aberration terms (i.e. for the more complex corneal shape descriptors) (Wang et al 2003b, Vinciguerra et al
th 0 2003). The 4 order term Z 4 (the spherical aberration term) also tends to make a large contribution to the overall higher order aberrations of the cornea, with the cornea generally found to exhibit positive spherical aberration (Artal et al 2001, Wang et al 2003b, Kelly et al 2004).
Corneal diseases such as keratoconus cause a marked increase in corneal aberrations, particularly the third order aberrations of coma and trefoil
(Schwiegerling and Grievenkamp 1996, Barbero et al 2002). Surgery on the cornea, including laser refractive surgery procedures, has also been shown to cause a significant increase in corneal higher order aberrations (Oshika et al 1999b, Marcos et al 2001, Nanba et al 2005, Hjortdal et al 2005).
23 Chapter 1
1.3.2 Influence of age on the normal cornea
The normal corneal shape has been shown to change significantly with age.
Friling et al (2004) measured corneal curvature in newborn infants (both premature and full term) and found the cornea of newborns to be steep and to exhibit relatively high amounts of against-the-rule (ATR) astigmatism. The newborns with the lowest birth weight and the youngest post conceptional age exhibited the steepest corneas and the greatest corneal astigmatism.
Asbell et al (1990) measured the corneal shape by keratometry in 110 infant eyes. The steepest corneas were found in the youngest subjects and the flattest in the oldest. Corneal curvature had stabilised and reached adult levels by 54 months of age.
In general, young adult subjects exhibit a predominance of corneal astigmatism with the steepest meridian vertical (with-the-rule (WTR) astigmatism) and peripheral corneal flattening (Hayashi et al 1995, Goto et al
2001). Older subjects (over 60 years) exhibit steepening of the cornea and a shift towards corneal astigmatism with the steepest meridian near horizontal
(ATR) (Hayashi et al 1995, Guirao et al 2000, Goto et al 2001). Older subjects also tend to show an increase in corneal aberrations, particularly in coma-like aberrations (Oshika et al 1999a, Guirao et al 2000). Thus the optical performance of the anterior cornea decreases with age. Goto et al
(2001) found differences in age related corneal changes between males and females. When looking at the changes in astigmatism for older males and females, the males showed a steepening of the horizontal and a flattening of
24 Chapter 1 the vertical meridian, whereas females showed a steepening of both meridians. The authors suggested that these gender differences may relate to differences in sex hormones in older age for males and females.
It is clear from the preceding review that the majority of normal corneas are in the general form of a prolate ellipse (i.e. flattening in the periphery). It is also clear that significant variation in corneal shape occurs between individuals.
The advent of videokeratoscopy has allowed more complex classifications of normal corneal shape based on the appearance of topographical maps.
Most young subjects display WTR corneal astigmatism and with age subjects show a shift towards ATR. Whilst many studies have shown no significant effect of race or gender on corneal shape, females appear to display slightly steeper corneas and males and females appear to show slightly different changes with age. There still does not appear to be a universal method for describing corneal shape, but a conic section is the most widely used method. The increasing use of Zernike polynomials may lead to a more uniform classification system for normal corneas.
1.3.3 The association between corneal shape and refractive error
As the cornea is the eye’s primary refractive element, it follows that a relationship may exist between the shape of the cornea and the development of refractive error. There have been a number of studies investigating the possible influence of corneal shape on refractive error, in particular myopia.
25 Chapter 1
1.3.3.1 The cornea in myopia
A number of studies have reported a weak but significant correlation between central corneal curvature and degree of myopia (Grosvenor and Scott 1994,
Carney et al 1997b, Budak et al 1999), indicating that the more myopic subjects exhibit slightly steeper central corneas. Grosvenor and Scott (1994) suggested that the ratio between the axial length and the corneal radius of curvature (AL/CR ratio) is the most significant determinant of the refractive status of the eye. Grosvenor and Goss (1998) proposed that a high AL/CR ratio (greater than three) was a risk factor for youth-onset myopia.
Goss and Erickson (1987) examined corneal power changes and refractive error change in myopes. Younger myopic children (aged 6-15 years) showed no significant change in corneal power with progression of myopia. However, steepening of the cornea appeared to be responsible for the progression of myopia in the young adult myopes (18 years and older). In contrast to this,
Adams (1987) reported on his own adult-onset myopia and suggested that axial elongation and not corneal curvature change was the cause of his myopia. McBrien and Millodot (1987) also reported no significant difference in corneal curvature between a group of 30 young adult-onset myopes and emmetropes.
Sheridan and Douthwaite (1989) reported their myopic subjects to exhibit significantly steeper corneas than their emmetropic or hyperopic subjects.
26 Chapter 1
However, no difference was found between the corneal asphericity of the different refractive error groups.
In a cross sectional study, Chang et al (2001) measured ocular refraction and corneal curvature on 216 myopic Taiwanese subjects. The central corneal curvature was found to flatten with increasing myopia. Corneal curvature was measured with keratometry and thus there is no information on the asphericity of the cornea from this study. The results of this study (i.e. central corneal curvature flattening with increasing myopia) conflict with many of the other studies mentioned and may represent an ethnic variation in the shape of the cornea in myopia.
Pärssinen (1993) investigated corneal refraction and topography in myopic children. Over the three year study, myopia was found to progress, but no significant change was found in corneal curvature or corneal asphericity.
Axial elongation was noted to be the cause of the myopia progression.
Carkeet et al (2002) also found no significant relationship between corneal asphericity and myopic refractive error in their study into the corneal topography of 268 Singaporean school children.
In their cross sectional study, Carney et al (1997b) examined the relationship between corneal topography and myopia. Corneal topography was measured on 113 eyes and corneal asphericity (Q) calculated. Q was found to be positively correlated with spherical equivalent refractive error (i.e. Q became less negative with increasing myopia). This suggests that myopes
27 Chapter 1 have corneas that flatten less rapidly in the periphery (less prolate). This association was found to be most obvious for myopes over –4.00 D. The authors suggested that the decrease in Q with increasing myopia means that positive spherical aberration of the cornea also increases with increasing myopia.
Horner et al (2000) investigated longitudinal changes in corneal asphericity with myopia in adolescents over a five year period. Over this period, subjects showed an increase in myopia and axial length but no significant changes were found in central corneal curvature. Corneal asphericity did significantly change with Q becoming less negative (i.e. the cornea became less prolate with increasing myopia). Horner et al (2000) also examined their subjects’ initial asphericity and found that subjects who initially had more prolate corneas were more likely to progress in their myopia.
In a study of corneal topographical data on 643 children, Davis et al (2005) found their myopic subjects to have significantly less prolate corneas than their emmetropic and hyperopic subjects. However, in contrast to the results of Horner et al (2000), they found that subjects’ initial corneal asphericity was of little or no value in predicting refractive error progression.
Although there is some conflicting evidence, there does appear to be some association between corneal shape and myopia. In general, myopic subjects are often found to have slightly steeper corneas. There is also some evidence to suggest that myopic subjects exhibit less prolate corneas (i.e.
28 Chapter 1 less peripheral corneal flattening). It is not clear whether these corneal changes are part of the cause of myopia, a corneal response to myopia progression, or simply a consequence of the ocular elongation occurring in myopia.
1.3.3.2 The cornea in hyperopia
Compared to the research involving the cornea in myopia, there have been relatively few studies investigating the cornea in hyperopia. Most studies have found that hyperopes exhibit slightly flatter central corneas than emmetropes or myopes (Sheridan and Douthwaite 1989, Strang et al 1998,
Mainstone et al 1998, Llorente et al 2004). Sheridan and Douthwaite (1989) and Mainstone et al (1998) found no significant relationship between corneal asphericity and hyperopic refractive error. Llorente et al (2004) however, found their hyperopic subjects to display less prolate corneas than their myopic subjects. This result is in contrast to those studies showing myopic subjects to have less prolate corneas (Carney et al 1997b, Davis et al 2005).
1.4 Other factors influencing corneal shape
Besides the influence of age, gender and refractive error, there are a number of other factors that can also impact upon the optics and shape of the cornea.
29 Chapter 1
1.4.1 The pre-corneal tear film
The pre-corneal tear film is a fluid layer that covers the anterior surface of the eye. As the tear film covers the corneal surface, it essentially represents the eye’s most anterior refractive surface. The pre-corneal tear film acts to neutralise the microscopically irregular corneal epithelial surface to create a smooth optical surface. Any changes in the thickness or regularity of the tear film thus have the potential to affect corneal topographical measurements and vision.
Investigators have found that break up of the pre-corneal tear film leads to reductions in retinal image quality and an increase in higher order ocular aberrations as well as reductions in subjective vision measures (Albarran et al 1997, Thibos and Hong 1999, Tutt et al 2000, Koh et al 2002). Corneal topography measurements also show significant increase in irregularity following tear film break-up (Nemeth et al 2001).
A stable, smooth tear film is essential for accurate measurements of the corneal surface. Measurements of corneal aberrations and total eye aberrations should be made soon after a blink and prior to tear film break-up to avoid tear-related artefacts.
30 Chapter 1
1.4.2 External forces and corneal shape
The application of external force to the cornea has the potential to significantly alter its shape and optics. One of the earliest investigations into the effect of external forces on corneal topography was performed by
Mandell and St Helen (1968). Using a photokeratosope, they found that both eye rubbing and digital pressure on the cornea through the eyelids caused significant short term changes (lasting several minutes) in corneal topography.
Carney and Clark (1972) deliberately deformed subjects’ corneas through the use of a modified applanation tonometer. The corneal topography was measured with a photokeratoscope before and after the force was applied.
The applied forces caused significant deformations of the cornea which then recovered quickly. In most cases the corneal irregularity disappeared within
10 minutes.
More recently, Mansour and Haddad (2002) studied the effect of ocular rubbing on corneal topography. Subjects exhibited an increase in corneal distortion following eye rubbing. The eye rubbing also induced a small amount of corneal astigmatism. The corneal changes were found to return to baseline after five minutes. The increase in corneal distortion with eye rubbing was thought to be due to corneal surface deformation and tear film alteration.
31 Chapter 1
There is speculation that persistent application of external force to the eye
(e.g. persistent eye rubbing) may lead to a permanent deformation of corneal shape. The following case reports indicate a possible association between persistent eye rubbing and the development of keratoconus.
Coyle (1984) presented a case of unilateral keratoconus in a patient with a congenital heart defect. To stop persistent tachycardia, the patient would vigorously massage his left eye for 5 to 10 seconds, 10 to 20 times a day for
6 years. Examination revealed unilateral keratoconus in the left eye. Upon cessation of the constant eye rubbing, the corneal changes were found to stabilise. The author suggested that the origin of the patient’s keratoconus may well be mechanical. Lindsay et al (2000) reported on a case of unilateral keratoconus also associated with continual eye rubbing. Due to right congenital punctal agenesis, the patient was constantly wiped and rubbed their right eye. Examination revealed the presence of keratoconus in the right eye only. These cases highlight the possible influence of persistent external pressure on the development of a permanent corneal deformation
(i.e. keratoconus). However, this hypothesis does not account for the characteristic thinning of the cornea associated with keratoconus.
1.4.2.1 Orthokeratology
An example where external forces alter corneal shape is orthokeratology. In orthokeratology, rigid gas permeable contact lenses produce forces which deliberately flatten the curvature of the central cornea to temporarily reduce
32 Chapter 1 myopia. Nichols et al (2000) postulated that the corneal shape changes observed in orthokeratology may be caused by a redistribution of corneal epithelial tissue from the centre to the mid-periphery, thus causing a flattening of the central cornea (i.e. the changes are a result of remodelling the anterior corneal surface and not an overall bending of corneal shape).
Recent research into the cornea following orthokeratology lens wear suggests that the refractive changes seen with modern orthokeratology techniques are caused by a central thinning and a mid-peripheral swelling of the cornea. Alharbi and Swarbrick (2003) noted the central corneal thinning to be due to epithelial changes and the mid-peripheral thickening to be primarily stromal in origin. They concluded that the refractive changes due to orthokeratology are primarily brought about by the changes in the anterior corneal thickness and not by an overall bending of corneal tissue. Significant corneal changes with orthokeratology can occur within as little as 10 minutes of lens wear (Sridharan and Swarbrick 2003).
Wang et al (2003a) measured corneal thickness with optical coherence tomography following orthokeratology lens wear and demonstrated a significant thinning of the central epithelium and thickening of the mid- peripheral epithelial tissue. This highlights the fact that changes in corneal epithelial thickness (particularly localised changes) can have significant effects on corneal shape and optics. Wang et al (2003a) also found that the corneal thickness changes had returned to baseline 3 hours after lens removal, but some reduction in myopia was still present 12 hours after lens removal. This indicates that along with anterior corneal thickness changes,
33 Chapter 1 an overall change in corneal curvature (that does not affect corneal thickness measures) may be occurring with orthokeratology lens wear. Owens et al
(2004) revealed that some changes occurred in the posterior corneal curvature in the early stages of orthokeratology lens wear, also indicating some overall bending of the corneal stroma in this process.
The changes occurring with orthokeratology indicate that corneal shape can be altered with external forces. These changes in corneal shape appear to result (in part) from a redistribution of epithelial tissue but may also involve some overall bending or thickening of corneal tissue (i.e. stromal deformation). Thus forces applied to the cornea may cause changes to the corneal epithelium and/or the stroma which can lead to significant changes in corneal shape and optics. The specific properties of the corneal epithelium and stroma will therefore play an important role in maintaining corneal shape and optics.
1.4.2.2 The corneal epithelium
The corneal epithelium is the most anterior portion of the cornea and acts as a barrier between the stroma and the external environment. The corneal epithelium consists of approximately five layers of regularly arranged cells.
Alterations in the corneal epithelium have the potential to cause changes to corneal shape.
34 Chapter 1
The corneal epithelium is in a state of dynamic equilibrium, with superficial cells shed into the tear film (aided by the process of blinking) and replaced by newly formed cells. This rapid turnover of cells helps to maintain an intact epithelial structure by allowing removal and replacement of infected, injured or transformed cells (Suzuki et al 2003). In order to maintain this turnover of cells and preserve a stable epithelium, a source of new epithelial cells is required (Davanger and Evensen 1971). It is now generally accepted that this source of epithelial cells originates from the limbus, where epithelial stem cells are located (Davanger and Evensen 1971, Gipson 1989, Townsend
1991, Dua and Azuaro-Blanco 2000).
Thoft and Friend (1983) proposed the X, Y, Z hypothesis of corneal epithelial maintenance. They suggested that the normal stability of the corneal epithelium is maintained provided that the proliferation of basal epithelial cells
(X) and centripetal movement of peripheral cells (from the limbus) to the centre of the cornea (Y) is equivalent to the rate of epithelial cell loss from the surface (Z). Thus a stable epithelium requires a balance between the processes of cell proliferation, cell migration (both horizontally and vertically) and cell exfoliation (i.e. X + Y = Z).
The maintenance of a stable corneal epithelial surface is complex and is dependant upon a number of factors. Interactions between the cells and the extracellular matrix as well as the corneal sensory nerves play a role in the maintenance of corneal integrity (Suzuki et al 2003). Growth factors and cytokines also appear to play an important role (Lee et al 2001). The actions
35 Chapter 1 of these growth factors and cytokines may be up- or down-regulated in response to injury (Kinoshito et al 2001). Complex communications also occur between the epithelial cells and the stromal cells and vice versa
(Wilson et al 1999). When the normal balance between epithelial cell degradation and repair is interrupted, changes in corneal thickness and shape can occur. These changes have the potential to significantly affect vision.
Simon et al (1993) investigated the optics of the corneal epithelium. An automated keratometer was used to measure 10 fresh human eye-bank eyes with and without their epithelium intact. The removal of epithelium led to an increase in corneal refractive power in all eyes as well as changes in the axis and degree of corneal astigmatism. These results suggest that the epithelium plays an active role in determining the optical power of the cornea
(by effectively increasing the radius of curvature). It also appears that the epithelium does not form a layer of uniform thickness over Bowman’s layer
(as astigmatism changed with removal of the epithelium). This study indicates that changes in the corneal epithelial thickness and distribution of thickness can result in changes to refractive error and hence vision.
1.4.2.3 The corneal stroma
The corneal stroma consists of collagen fibrils arranged regularly in bundles
(lamellae) (Meek and Boote 2004). This regular arrangement helps to maintain the cornea’s transparency. The specific architecture of collagen
36 Chapter 1 fibrils in the stroma will influence both the shape of the cornea and its biomechanical properties.
There have been a number of investigations into the biomechanical properties of the cornea in-vitro. The elastic properties of the cornea are generally investigated by applying a stress to the cornea (eg increasing intraocular pressure) and measuring the strain response of the tissue.
The cornea has been found exhibit a non-linear strain response, with the cornea found to be stiffer for higher pressures (Hjortdal and Jensen 1995).
The cornea also behaves as a visco-elastic material, so that for a given stress, the strain is dependant upon time. The cornea shows an initial large deformation as stress is first applied followed by a slow deformation as the stress persists (Hjortdal and Jensen 1995). The elastic response of the cornea is also highly dependant upon its level of hydration. Hjortdal (1995) measured corneal strain while maintaining corneal hydration at a normal physiological level. With corneal hydration maintained, the stiffness of the cornea was found to be greater than had been shown in previous studies.
The cornea also appears to exhibit regional differences in its elastic properties. Hjortdal (1996) found meridional strain to be lowest in the paracentral cornea and greatest at the limbus. Circumferential strain varied least, but was largest in the paracentral region. It was concluded that these regional differences most probably relate to differences in the elastic
37 Chapter 1 properties of the collagen fibrils, the degree of reinforcement of the fibrils and variation in the orientation of the fibrils in the corneal stroma (Hjortdal 1996)
Muller et al (2001) also studied the effect of different hydration levels on the cornea. The most anterior portion of the corneal stroma was found to be extremely resistant to swelling. The specific architecture of the anterior stroma (i.e. tightly inter-woven collagen fibrils) was thought to prevent morphological changes to the region, even in the presence of extreme swelling. The authors felt that the rigidity of the anterior stroma plays an important role in maintaining the corneal curvature, particularly in the presence of external stresses.
As well as being important from a biomechanical point of view, the arrangement of the collagen fibrils will also influence corneal shape. Studies using x-ray diffraction techniques have found two orthogonal preferred directions of collagen fibril orientation within the central 7 mm of the cornea
(Daxer and Frazl 1997, Meek et al 2005). These two preferred orientations are in the vertical and horizontal directions. Boote et al (2005) quantified the relative number of stromal collagen fibrils in the vertical and horizontal directions and found that on average the number of fibrils oriented in each of the two orthogonal directions is roughly equal. However, some eyes were found to have as much as 25% more of the collagen fibrils oriented in one direction compared to the other. They suggested that an imbalance in the orientation of collagen fibrils may impact on corneal shape and cause differences in vertical and horizontal corneal radii of curvature (i.e. lead to
38 Chapter 1 corneal astigmatism). The collagen fibrils have been shown to bend and assume a circumferential orientation close to the limbus (Newton and Meek
1998, Meek and Boote 2004). It has been suggested that this change in orientation of fibrils at the limbus is to help to maintain corneal curvature at the corneo-scleral junction (Newton and Meek 1998). In keratoconus, marked changes occur to the normal preferred collagen orientations in the central cornea (Daxer and Frazl 1997, Meek et al 2005).
Thus the regular arrangement of the collagen fibrils helps to maintain corneal transparency, shape and its biomechanical properties. The cornea has been shown to exhibit non-linear visco-elastic properties. These properties display regional differences across the cornea. The elastic properties, and the specific architecture of the cornea, mean that in-vivo, the corneal shape can be deformed with external forces. These same properties also mean that the cornea returns to its normal shape quickly following the application of external forces. Changes in both the corneal epithelium and stroma may cause significant changes in corneal shape.
1.4.3 Accommodation and corneal topography
Whether or not the cornea displays changes in shape as a result of accommodation has been a topic of interest for some years now. It is of importance for our understanding of corneal topography, and for the
39 Chapter 1 techniques required to accurately and reliably measure the topography of the cornea.
Early studies investigating the effects of accommodation on the shape of the cornea indicated that the act of accommodation had no significant effect on corneal curvature (Fairmaid 1959, Lopping and Weale 1965, Mandell and St
Helen 1968). Sun et al (1996) found that pharmacological pupil constriction
(which also causes contraction of the ciliary muscle and hence an increase in accommodation) and dilation (which causes a relaxation of the ciliary muscle and hence accommodation) had no significant effect on corneal topography measurements.
Pierscionek et al (2001) used a keratometer to investigate possible changes in corneal curvature during accommodation, and found that some subjects did appear to exhibit changes in corneal curvature with accommodation. The exact nature of the corneal changes appeared to differ between subjects (i.e. no definite trend was evident in the results of all of the subjects). The authors concluded that the action of the ciliary muscle does cause changes to central corneal curvature. He et al (2003) also studied changes in corneal curvature with accommodation using a videokeratoscope. A flattening of the central cornea and a steepening of the peripheral cornea were noted as a result of accommodation. The authors suggested that the corneal changes found may be due to ciliary muscle contraction or to changes in intraocular pressure accompanying accommodation.
40 Chapter 1
A study into corneal topography and accommodation was performed by
Buehren et al (2003b). Initial data analysis indicated a significant change in corneal topography accompanying accommodation in some subjects.
Further data analysis revealed a significant excyclotorsion of the eyes accompanying accommodation. When this excyclotorsion was taken into account in the data analysis, no statistically significant changes in corneal topography were found as a result of accommodation. Hence the initial changes noted were due to changes in eye position and not to a true change in corneal shape. The authors postulated that the results of many of the earlier studies into corneal topography and accommodation may have been affected by this cyclotorsion effect.
There have been some conflicting results from the various studies into accommodation and corneal shape. The early studies are limited in their ability to accurately and precisely measure corneal topography due to the technology of the time. Obviously highly accurate and precise methods are required to measure subtle corneal topographical changes. Buehren et al
(2003b) have used a videokeratoscope and a sophisticated analysis technique in their study, and appear to have provided the most definitive answer about changes in corneal topography during accommodation (i.e. cyclotorsional eye movements occur during accommodation, but no significant change in corneal topography accompany these changes).
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1.4.4 Extraocular muscles and corneal topography
The effect of extraocular muscle (EOM) tension on corneal topography is a subject that has received relatively limited coverage in the literature. The exact influence that contraction and relaxation of the EOMs has on corneal topography is still not fully understood.
Early research into this topic investigated the changes occurring in corneal curvature during convergence. In 1959, Fairmaid found that the act of convergence caused a slight flattening of the cornea in the horizontal meridian and a slight steepening in the vertical meridian. Fairmaid (1959) concluded that for clinical purposes, the corneal response to convergence was only of slight importance. Lopping and Weale (1965) also found a significant flattening of the cornea (in the horizontal meridian) accompanied convergence (for non presbyopic subjects). For presbyopic subjects, no significant change in corneal curvature was found with convergence. In
1968, Mandell and St Helen reported that no significant changes in corneal curvature (as measured with a photokeratoscope) occurred with convergence or with changes in fixation (i.e. changes in EOM tension did not cause a change in corneal shape). The authors did comment on the possible degree of error involved in their experiments and suggested that some reports of changes in corneal curvature under various conditions may lack appropriate control. All of these studies were limited by the technology of their time and the techniques used may not have provided a sufficiently accurate
42 Chapter 1 assessment of the periphery of the cornea to describe any changes occurring to the cornea during convergence.
1.4.4.1 Extraocular muscle surgery and the cornea
More recent reports of the effect of EOM tension on corneal topography have centred on changes occurring in corneal topography and refraction following
EOM surgery.
Kwitko et al (1991) used a videokeratoscope to investigate changes occurring in the corneal topography of rabbits following EOM surgery. A procedure to reduce tension in the superior rectus muscle was found to cause a significant flattening of the cornea in the superior meridian. However a procedure to increase the tension in the superior rectus caused no significant corneal change. A procedure to excise all of the rectus muscles was also performed (leading to an overall reduction in EOM tension) and was found to cause a generalised flattening of the cornea. This study indicates that changes in EOM tension have the potential to cause changes in corneal topography. It is noted though that anatomical differences between rabbit and human eyes predispose the rabbit eyes to greater corneal changes as a result of EOM tension changes.
There have been a number of reports of changes in human corneal topography and refraction following strabismus surgery. EOM surgery has been shown to cause highly significant changes in astigmatism (Reynolds et
43 Chapter 1 al 1991, Preslan et al 1992, Denis et al 1995a, Killer and Bahler 1999,
Bagheri et al 2003). Surgery on the EOM’s has also been shown to cause significant changes in corneal topography (Kwitko et al 1992a, Nardi et al
1997). However, the exact cause of this change in corneal topography is still not known. Alteration in muscle tension (and subsequent alteration in the force applied by the muscles to the anterior globe) or changes in tractional forces due to surgery have both been suggested as possible causes of these topographical changes (Denis et al 1995a, Bagheri et al 2003). Factors relating to surgical recovery (e.g. inflammation in and around the globe) may also influence the corneal topography following strabismus surgery (Nardi et al 1997). It remains to be seen whether alterations in EOM tension from everyday tasks such as convergence and eye movement also cause significant changes in corneal topography.
1.4.4.2 Corneal topography and nystagmus
Nystagmus is a condition characterised by rapid involuntary oscillatory eye movements. These back and forth eye movements typically occur horizontally. Nystagmus may occur as a physiological phenomenon or be a congenital or acquired defect. Congenital nystagmus can be associated with many different ocular and neurological defects.
Subjects with nystagmus have been shown to display an increased prevalence of high astigmatism (Nathan et al 1986, Ohmi and Reinecke
1993, Sampath and Bedell 2002). The astigmatism in these subjects is
44 Chapter 1 generally WTR in axis and corneal in origin (Dickinson and Abadi 1984,
Wildsoet et al 2000).
It appears that the process of emmetropisation (i.e. the normal process of reduction of neonatal refractive errors with eye growth) is impaired in subjects with nystagmus (Sampath and Bedell 2002). These subjects show a wide spread of refractive errors, with high degrees of WTR corneal astigmatism being particularly common. Whilst the exact cause of the high degrees of astigmatism is not known, mechanical interaction between the eyelids and the cornea (which would be increased as a result of the constant nystagmus eye movement) may play a role (Ohmi and Reinecke 1993,
Wildsoet et al 2000, Sampath and Bedell 2002).
1.4.5 Corneal topography and eyelid forces
Kessing (1967) used x-ray examination to investigate the area of contact between the eyelids and the globe. Only the marginal area of the upper eyelid was found to be in contact with the globe, whereas, the entire tarsal area of the lower eyelid was found to be in contact. Korb et al (2002) termed the area of contact between the upper eyelid and the globe as the ‘lid wiper’.
They suggested that this area of touch extends from just posterior to the
Meibomian gland openings to the subtarsal fold on the upper lid (Korb et al
2002). The function of the ‘lid wiper’ appears to be spreading the tear film over the surface of the eye.
45 Chapter 1
There have been a number of studies which have aimed to measure the pressure that the eyelids exert on the ocular surface. Miller (1967) investigated the pressure from the eyelids occurring during various blinks and eyelid squeezes. A moulded scleral contact lens with a latex rubber balloon and a pressure transducer were used to measure the pressure exerted by the eyelids. The lens/balloon combination measured 2.5 mm thick at the lens apex. The mean lid pressure found for a light blink was 2.8 mmHg and for a deliberate blink was 10.3 mmHg. An average pressure of 51 mmHg was found during a hard, forced squeeze of the eyelids.
Coleman and Trokel (1969) directly measured the IOP of a human subject
(whose eye was to be enucleated). They found that blinking produced pressure increases of 5-10 mmHg. EOM contraction was found to produce
IOP increases of similar magnitude. Forced eyelid closure produced pressures of over 70 mmHg.
Hung et al (1977) measured the dynamics of the human blink by loading the upper eyelid of one subject with various weights (with the subject looking downwards by 45 degrees). The eyelid’s passive spring constant was found to be 1.5 gm/mm (i.e. 1.5 gm of upward loading force was required to displace the lid by 1 mm). They also found that an ordinary blink utilises up to 20 gm driving force but a forced blink can use up to 80 gm of force.
Vihlen and Wilson (1983) used a similar method to measure eyelid tension, on a group of 100 subjects aged 20-80 years. The force exerted by the
46 Chapter 1 upper lid as it was pulled away from its resting place on the eye was measured, with subjects looking straight ahead in primary gaze. They found that the average elastic coefficient of the lid was 3.33 gm/mm (ranging from
1.16-6.78). The tension of the eyelids was found to reduce as a function of subject age.
Evinger et al (1984) measured upper eyelid tension on three human subjects.
They found the average tension of the lids with subjects looking straight ahead to be 10 gm/mm. When subjects looked 40° downwards, the tension of the eyelids reduced to 2.5 gm/mm. The eye movements accompanying a blink were also measured in this study. A significant retraction of the globe was found to accompany the blink. This was thought to be due to co- contraction of the EOMs during the blink.
Lydon and Tait (1988) also investigated the pressure exerted by the eyelids.
They suggested that Miller’s (1967) results may have overestimated the pressure due to the thickness of the measuring system. Lydon and Tait
(1988) measured globe displacement, orbital resistance and eyelid pressure.
They found that a slight globe retraction (approximately 0.5 mm) occurred with gentle and full blinks, which increased with forced blinks. The orbital resistance was found to be 27.9 gm/mm (i.e. the median orbital tension required to produce a globe displacement of 1 mm was 27.9 gm). The eyelid pressure exerted on the eye under normal circumstances was found to be quite small, but significant pressures could be reached with forced blinking.
The authors concluded that under normal circumstances, the pressure
47 Chapter 1 exerted by the eyelids on the globe is small, due to the damping effect when the globe retracts on blinking (i.e. the lid-globe relationship is essentially self compensating and the pressure that the upper lid produces is compensated by the orbital resistance). They suggested that these facts mean that the lids cannot adversely affect the shape and power of the cornea during blinking.
More recently, Ehrmann et al (2001) developed an instrument to objectively measure the passive tension of the eyelids. Using this instrument, no difference was found between the upper eyelid tension of subjects of Asian and Caucasian ethnicity. The subject numbers in this study were small (only four Asian and four Caucasian subjects were tested) and therefore a larger pool of subjects would be required for a more definitive comparison between the eyelid tension of Asian and Caucasian subjects. This same instrument was used to measure the tension of the lower lid in a population of 32 subjects (Francis et al 2005). The tension in the lower eyelid was found to be similar to that previously reported for the upper eyelid. No significant reduction in lower lid tension was found with age in the subjects tested. The authors did however acknowledge that a larger pool of subjects with a wider range of ages would be required to fully investigate the effect of age on lower eyelid tension.
It appears that the lids do exert a small force on the globe which can increase markedly with forced blinking. However the influence of these increased forces on the globe is dampened through a retraction of the globe that occurs in conjunction with blinking. There have been a range of different
48 Chapter 1 measurement techniques used and results reported for the tension exerted by the eyelids on the eye. Early studies (e.g. Miller 1967) were limited by the technology of their times and therefore some questions remain over these results. Recent studies using more sophisticated instrumentation have been limited by the relatively small subject numbers used and the demanding nature of the procedure (Ehrmann 2005). As technology improves, future research will hopefully provide a more conclusive answer as to the exact magnitude and distribution of pressure that the eyelids exert on the cornea.
1.4.5.1 Eyelid pathology and corneal topography
There have been numerous reports of how certain eyelid pathologies can cause corneal distortions and changes in corneal astigmatism. These reports highlight the influence that changes in eyelid pressure can play on corneal topography.
The presence of a chalazion in the eyelid has been shown to cause significant corneal distortions and resultant changes in corneal topography and astigmatism in some patients (Nisted and Hofstetter 1974, Rubin 1975,
Cosar et al 2001). The surgical removal of the chalazion has generally been found to lead to resolution of the corneal changes.
Records (1980) presented various causes of monocular diplopia. He suggested that external irregularities of the cornea and eyelids including
49 Chapter 1 chalazia and unusually tight lids may produce corneal distortions that may lead to monocular diplopia.
Robb (1977) reported on refractive errors in infants with eyelid and orbital hemangiomas. Sixteen of the 37 patients with hemangioma exhibited astigmatic refractive errors. In nearly all cases of astigmatism, the hemangioma appeared to be in a position where it exerted pressure on the eye in a direction perpendicular to the axis of astigmatism. Hence the astigmatism was probably related to the pressure exerted by the lesion on the cornea. Plager et al (1997) reported three cases where the surgical resection of eyelid and orbital capillary hemangiomas in infants caused a resolution of astigmatism. Pressure from the hemangioma on the globe was suggested as the cause of the astigmatism in these infants.
Ptosis and the surgical repair of ptosis have also been implicated in the development of astigmatism. Patients with congenital ptosis have been shown to have a higher degree of corneal topographic assymetry and irregularity, as well as a higher degree of corneal astigmatism (Ugurbas and
Zilelioglu 1999). Astigmatism also appears to change following surgical repair of congenital ptosis (Cadera et al 1992). This was thought to be due to changes in the lid/cornea interaction following surgery.
Blepharoplasty surgery in adult patients has also been shown to cause changes in corneal astigmatism (Holck et al 1998, Brown et al 1999). The changes in astigmatism were typically found to be an increase in WTR
50 Chapter 1 astigmatism. As some of these changes regressed with time after surgery,
Holck et al (1998) concluded that the astigmatic changes may be due to post- surgery eyelid swelling. A recent case report (Kim et al 2000) described superior corneal steepening in a 62 year old man with bilateral blepharoptosis. Repair of the ptosis led to relief of symptoms of monocular diplopia and amelioration of the corneal distortion.
Lid-loading procedures (with metal lid weights) to treat lagophthalmos have also been shown to induce 1-2 D of astigmatism in the vertical meridian in some patients (Goldahn et al 1999). The astigmatism in these cases was attributed to implants that were too heavy or of incorrect radii that caused increased pressure on the cornea.
All of these eyelid pathologies have the effect of increasing the influence of the eyelids on the cornea and have been shown to cause significant changes to the shape of the cornea. Resolution or removal of these pathologies generally leads to a reversal of the corneal changes.
1.4.5.2 Visual tasks and corneal topography
Sustained pressure on the cornea from ‘normal’ eyelids (i.e. with no eyelid pathology) may also lead to corneal changes. A number of reports have appeared in the literature relating episodes of monocular diplopia (caused by corneal distortion) to periods of near work in downward gaze.
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Mandell (1966) reported a case of monocular diplopia occurring in a young female patient following near work. Keratometry following reading revealed corneal distortion. Knoll (1975) noted his own monocular diplopia following reading. The amount of diplopia seemed to be related to the length of time reading and could occur within a matter of minutes. His cornea also showed distortion following reading, and he suggested that the corneal distortions were caused by his upper lids. Stampfer and Tredici (1975) reported on 15 patients complaining of monocular diplopia. Five of these cases were found to exhibit significant corneal irregularities that lead to the diplopia.
Bowman et al (1978) revealed superior corneal distortion occurred in a patient experiencing monocular diplopia following reading. As the corneal irregularity was found to closely follow the position of the upper lid during reading, the authors concluded that sustained pressure from the eyelids on the cornea led to the distortion. Carney et al (1981) deliberately induced corneal distortion in nine subjects. Subjects performed a microscopy task with one eye forcibly closed for fifteen minutes. Five of the nine subjects experienced monocular diplopia along with corneal distortion in the closed eye following the task.
Goss and Criswell (1992) reported a case of bilateral monocular polyopia following television viewing. The subject viewed television in a supine position, which caused a narrowing of the palpebral aperture. Measurement of corneal shape following television viewing demonstrated marked superior corneal distortion, presumably caused by forces from the upper eyelid.
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Ford et al (1997) reported on six subjects complaining of monocular diplopia following reading. These subjects exhibited significant changes in corneal topography following reading, as well as a dark band in the retinoscopic reflex. This band appeared to be directly related to the position of the eyelids when reading. The subjects also exhibited a narrower palpebral aperture when reading, compared to controls. The position of the eyelids appears to have been responsible for the corneal changes. The authors postulated that a focal tear film disturbance which related to the position of the eyelids during reading may have led to the distortion.
Golnik and Eggenberger (2001) examined three subjects reporting monocular blur following reading in downgaze. Corneal topographical changes were found in these subjects after reading. The symptoms were found to cease when the subjects read in primary position. The corneal changes noted were thus attributed to effects from the eyelids and not accommodation, as the symptoms ceased with a change in eye position (and hence lid position) during reading.
A study by Buehren et al (2003a) investigated the effects of reading on corneal topography in 20 young subjects. Twelve of the 20 subjects showed significant changes in central corneal topography immediately following a 60- minute reading task. The change in corneal shape was described as a wave- like distortion which corresponded closely to the position and angle of the lids during reading. Figure 1.5 illustrates this corneal distortion following reading.
The distortion altered a number of the corneal wavefront Zernike coefficients
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Figure 1.5 Example of corneal topographical map following reading. Note the close correlation between the eyelid position during reading (top) and the superior band of corneal steepening in the corneal topographical map
(bottom). (Figure courtesy of Dr. Tobias Buehren).
54 Chapter 1
(in particular primary vertical coma and trefoil). Significant changes were also found in root mean square error, overall corneal refractive power and astigmatism. The change in corneal astigmatism following reading was towards ATR.
Corneal topographical changes (and the time-course of recovery of these changes) following reading in a group of six young subjects were measured by Collins et al (2005b). These subjects displayed distinctive changes due to pressure from the eyelids in the superior and inferior regions of the corneal topographical maps following reading. The magnitude of topographical change and the length of time for recovery were found to be related to the time spent reading. The longer the time spent reading, the higher the magnitude of change and the longer the changes took to recover. Corneal changes were evident after as little as 10 minutes reading. The corneal changes following two hours of reading regressed quickly within the first 10 minutes following reading, but took approximately two hours to fully recover.
The effect of different visual tasks on corneal topography was investigated by
Collins et al (2005a). Corneal topography was measured before and after subjects performed a 60-minute reading task, a microscopy task and a computer task. Eyelid induced corneal topographical changes were evident following each of the different tasks. The reading and microscopy tasks generally resulted in larger, more centrally located corneal topographical changes. The pattern of topographical change observed appeared to be
55 Chapter 1 related to the position of the eyelids (with the magnitude of change being smallest following computer work, where subjects displayed a wider palpebral aperture than in the other two tasks) and the amount of horizontal eye movement involved in the task. With tasks involving more horizontal eye movements (e.g. reading) exhibiting more localised corneal changes.
Evidence to date indicates that sustained pressure from the eyelids on the cornea can result in significant corneal distortions. These distortions, if large enough, can have significant effects on vision and cause a vertical monocular diplopia. With recent developments in corneal topography and improved methods of visualising and analysing the shape of the cornea, more subtle changes in corneal shape due to pressure from the eyelids have become more readily evident.
1.5 Astigmatism
Astigmatism, particularly in low amounts, is one of the most common refractive errors. Ocular astigmatism may occur as a result of unequal corneal curvatures along the two principle meridians, and/or due to asymmetry in the other refractive surfaces of the eye. The astigmatism due to the corneal surface is generally referred to as ‘corneal astigmatism’, and that due to the other refractive surfaces of the eye is known as ‘residual astigmatism’. Figure 1.6 shows an example of a topographical map of an astigmatic cornea. Residual astigmatism may be caused by the posterior
56 Chapter 1
Figure 1.6: Example of a topographical map of an astigmatic cornea. A with- the-rule astigmatic cornea is displayed. Note the greater corneal power in the vertical meridian.
57 Chapter 1 cornea, unequal curvatures of the front and back surfaces of the crystalline lens, decentration or tilting of the crystalline lens or unequal refractive index across the crystalline lens. The sum of the corneal and residual astigmatism gives the total astigmatism of the eye.
Astigmatism is of particular interest to vision researchers due to the fact that the presence of significant astigmatism has the potential to affect normal visual development and lead to amblyopia. Brown et al (2000) found associations between high astigmatism (particularly oblique astigmatism) and the presence of amblyopia in their population of adult subjects (40 years and older). Abrahamsson and Sjostrand (2003) found that the presence of oblique astigmatism, and/or the presence of increasing astigmatism in childhood are significant risk factors for the development of amblyopia.
Dobson et al (2003) investigated a population of preschool children with a high incidence of astigmatism. In this group, astigmatism (≥ 1.50D) was again found to be associated with the presence of amblyopia (i.e. subjects with ≥ 1.50D of astigmatism exhibited worse best corrected visual acuity than non astigmatic subjects). The severity of amblyopia appeared to be associated with the magnitude of astigmatism.
Uncorrected astigmatism causes a form of visual deprivation whereby stimuli of certain orientations are more blurred than others (Charman and Voisin
1993), which may also lead to meridional amblyopia (i.e. where the visual system’s resolution is reduced to targets of certain orientations). Gwiazda et
58 Chapter 1 al (1986) found the presence of significant astigmatism in childhood to be associated with meridional amblyopia. Dobson et al (2003) also found meridional amblyopia to be present in their population of astigmatic children.
1.5.1 Prevalence and changes of astigmatism with age
There have been numerous studies conducted into the prevalence of astigmatism and its change with age. Review of these studies reveals a number of different trends.
1.5.1.1 Astigmatism in infants and children
Atkinson et al (1980) used photo-refraction techniques to measure astigmatism in a population of infants. A high prevalence of astigmatism was found in the early months of life which was found to reduce significantly by 18 months of age.
Gwiazda et al (1984) also found a high incidence of astigmatism in subjects from birth to 2 years. By the age of 4 years, the incidence of significant astigmatism was greatly reduced. Before the age of 4 years, the majority of astigmatism was found to be ATR which shifted to WTR after the age of 4.
The authors postulated that this shift in astigmatic axis from ATR to WTR was due to pressure from the eyelids altering the astigmatic axis over time.
59 Chapter 1
Dobson et al (1984) also found a shift in the axis of astigmatism with age from a predominance of ATR (under the age of 3.5 years) to a predominance of WTR (over the age of 5.5 years). Howland and Sayles (1985) measured both corneal and total astigmatism in infants and confirmed that the changes occurring in astigmatism in infants were due to changes in the cornea.
In a longitudinal study, Abrahamsson et al (1990) investigated a population of
310 children with ≥ 1 D of astigmatism at 1 year of age over a period of three years. The majority of children showed ATR astigmatism at first testing.
Most children exhibited a reduction in the amount of astigmatism over the period of the study. Seven percent of the children at age 4 were found to have amblyopia. This study supports the hypothesis that the presence of astigmatism in infancy can disturb the visual input and thus cause abnormal visual development (i.e. the development of amblyopia).
Ehrlich et al (1997) conducted a longitudinal study on refractive data from
254 normal, healthy children from 9 to 20 months of age. In this study, WTR astigmatism was more common than ATR at initial testing and WTR astigmatism also showed a greater reduction over time. The mean spherical refraction was found to reduce by 30% over the study and the astigmatic error was found to reduce by 59%. The rate of change was highly correlated with the magnitude of the initial refractive error. The change in spherical error appeared to be independent of the rate of change in astigmatic error.
This indicates that the processes underlying emmetropisation of spherical and astigmatic errors may be independent of each other.
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In summary, children have a high incidence of astigmatism at birth. This astigmatism is thought to be corneal in origin, and reduces significantly with age in most children (i.e. most children exhibit an emmetropisation of their astigmatic refractive error). The majority of studies show the axis of astigmatism changing from a predominance of ATR at birth, to a predominance of WTR as children get older (over the age of 4 years). This change in axis may be due to interactions between the eyelids and the cornea.
1.5.1.2 Astigmatism in adults
Anstice (1971) performed a retrospective cross sectional study on refractive data from 621 randomly selected clinical records. Significant changes in total and corneal astigmatism were found with age, but no significant change was found in residual astigmatism. Patients showed a shift in astigmatism from predominantly WTR at young ages (from 5 to 40 years) to predominantly
ATR in older age (over 40 years). The cause of this change in astigmatism was due to change in corneal curvature with age. In another cross sectional study, Saunders (1981) analysed the refractive error data for 2665 patients and also found that astigmatic axis changed from WTR to ATR with increasing age.
Baldwin and Mills (1981) investigated longitudinal changes in corneal and total astigmatism in 34 patients over a 40-year period. In general, a steepening of the cornea was found with aging. Again, an increase in ATR
61 Chapter 1 astigmatism was found in older age. The majority of this change in astigmatism was due to corneal change (i.e. a steepening of the horizontal meridian of the cornea). The authors suggested that this change in corneal curvature may be due to reduction in tension of the lids with age.
Subjective refraction and corneal curvatures were examined by Fledelius and
Stubgaard (1986) in a cross sectional study of 454 subjects. Forty six percent of the total population were found to have astigmatism >0.5 D but only 4.7% had astigmatism >1.5 D. They also found an increase in ATR astigmatism with older age (over 56 years), although WTR astigmatism was the predominant form in all age groups.
Satterfield (1989) collected refractive data from 1112 subjects in a military population. Astigmatism of 0.25 D or greater was found in 63% of the population. Approximately 70% of the astigmatic subjects exhibited 1.0 D or less astigmatism. The majority of cases were either WTR or ATR (in approximately equal frequency) with oblique astigmatism occurring in only
8% of subjects.
In a population of 5308 subjects aged 40 years or older, Katz et al (1997) found the prevalence of astigmatism to increase with age and to be slightly higher for white people compared to black people. The subject’s education level was found to be positively correlated with myopia (and negatively with hyperopia), but no association was found between education level and the prevalence of astigmatism.
62 Chapter 1
Astigmatism (particularly of a low magnitude) is a common refractive error.
Estimates of the prevalence of astigmatism vary between studies due to differences in the populations studied and in the criteria used to define the presence of astigmatism. In general in an adult population, WTR astigmatism is the most common and oblique astigmatism the least common form of astigmatism. After the age of 50, there tends to be a shift in the axis of astigmatism towards ATR astigmatism.
1.5.2 Javal’s Rule.
In 1890, Javal proposed a rule for predicting the total astigmatism of the eye based on the corneal astigmatism (Grosvenor 1978). Javal’s rule states:
At = k + p (Ac)
Where: At is the total astigmatism and Ac is the corneal astigmatism. k and p are constants approximated by 0.5 and 1.25 respectively. This rule relies on the fact that residual astigmatism is thought to be fairly constant and ATR in most people (i.e. -0.50 D ATR). Javal’s rule thus does not apply for oblique astigmatism.
Dunne et al (1994) investigated residual astigmatism in 70 subjects, by measuring the difference between ocular and total astigmatism (by cylindrical decomposition). The average residual astigmatism was found to be –0.46 ×
98.2° for right eyes and –0.50 × 99.4° for left eyes. In approximately two
63 Chapter 1 thirds of eyes, the axis of the residual astigmatism was perpendicular to the axis of corneal astigmatism.
Grosvenor et al (1988) suggested a simplification of Javal’s rule. They measured corneal and total astigmatism in three different clinical populations
(a group of 98 myopic children, a group of 200 patients examined at a university optometry clinic and a group of 493 patients examined in an optometric practice in New Zealand). A regression was performed on these two variables with the slope of this regression line equivalent of the constant p, and the y intercept equivalent to k. For all three populations, the slope of the regression line was found to be slightly less than 1, and the y intercept close to 0.5. The authors thus proposed a simplified Javal’s rule of At = Ac –
0.5. This simplified rule was found to fit the data for the three clinical populations better than the original Javal’s rule.
In a group of 155 eyes with high levels of astigmatism (between 2.25 and 6.5
D), Grosvenor and Ratnakaram (1990) found a slope of 1.25 for the corneal and total astigmatism linear regression. This led them to question whether the relationship between corneal and total astigmatism was in fact linear.
They then reanalysed this high astigmatism population and included data from the three populations tested by Grosvenor et al in 1988. The regression line for this data (which included both high and low levels of astigmatism) had a slope of 1.03 and y intercept of –0.5. This data was also fitted with 3rd and
4th polynomial functions which did not fit the data any better than the simple
64 Chapter 1 linear model. The authors concluded that the relationship between corneal and total astigmatism can be sufficiently characterised by a linear fit.
Keller et al (1996) investigated the relationship between corneal and total astigmatism by measuring corneal astigmatism using computer-assisted videokeratoscopy for 31 subjects. The corneal topographical data was converted into a best fit sphero-cylinder for a number of different pupil sizes
(2, 3, 4, 5, 6 and 7 mm) and subjective refraction was also measured using the same pupil sizes. Corneal astigmatism was plotted against total astigmatism for the different pupil sizes tested. There was no significant difference in the regression lines for the different pupil sizes. Thus the relationship between corneal and total astigmatism was found to be independent of pupil size. The results of this study also support the simplified Javal’s rule of Grosvenor et al (1988) (i.e. a slope of 1 and a y intercept of –0.5).
A vectorial method of analysis of astigmatic data was used by Tong et al
(2001), which allowed WTR, ATR and oblique cylinders to be analysed.
Total astigmatism and corneal astigmatism were measured with autorefraction and autokeratometry for 1004 subjects. Astigmatic errors were broken down into two vectors J0 and J45. Where J0 is a Jackson crossed cylinder with axes 180° and 90° and J45 is a Jackson crossed cylinder with axes 135° and 45°. The corneal astigmatism was plotted against the total astigmatism for vectors J0 and J45. A strong linear association was found
65 Chapter 1 for both J0 and J45. When combined, the two associations could be used to predict the total refractive error astigmatism based on the total corneal astigmatism. This vector based rule provides a more accurate description
(than previous approximations of Javal’s rule) as it allows all subjects with all axes to be included.
Kelly et al (2004) used an instrument that allowed simultaneous capture of corneal and total eye aberrations on a population of 30 young subjects. They found that a number of corneal aberrations are compensated for by the internal optics of the eye, including horizontal/vertical astigmatism, lateral coma and spherical aberration. They suggested that the horizontal/vertical astigmatism compensation is an active process determined through a fine- tuning emmetropisation process. No significant compensation was found for oblique astigmatism in the population.
The compensation of corneal astigmatism by the internal optics of the eye has been known for many years (Grosvenor 1978, Dunne et al 1994, Kelly et al 2004). The numerous studies into Javal’s rule tend to indicate that this compensation is a somewhat passive process (i.e. the majority of the population has approximately 0.5 D ATR of internal astigmatism which compensates for the predominant WTR corneal astigmatism in the population). However some authors (Kelly et al 2004) have suggested the possibility of an active ‘feedback driven’ process to reduce the total astigmatism of the eye (particularly horizontal/vertical astigmatism).
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1.5.3 Symmetry of axis of astigmatism between right and left eyes
There is widespread agreement that some degree of symmetry exists between the refractive error of right and left eyes. It is for this reason that many studies have only used the refractive error from one eye of each subject for their analysis. A number of studies have noted mirror symmetry to occur between the axes of astigmatism of right and left eyes (Dunne et al
1994, Haugen et al 2001b, Garcia et al 2003).
McKendrick and Brennan (1996) measured corneal and ocular refraction
(with autorefraction and autokeratometry) in a group of 198 subjects. The mean (power and axis) and spread of astigmatic errors were similar for right and left eyes. The axes of corneal and total astigmatism were found to be remarkably similar between the two eyes. If one eye showed WTR astigmatism then it was likely that the other eye also exhibited WTR astigmatism (McKendrick and Brennan 1997). Analysis of frequency distributions showed that most eyes displayed either close to mirror or direct symmetry of astigmatic axes. There was however, no predominance of either mirror or direct symmetry of astigmatic axes when analysis was carried out for the population.
Similarities do exist between the axes of astigmatism for right and left eyes.
In a normal population, it appears that mirror or direct symmetry between the
67 Chapter 1 two eyes often occurs. Errors may occur in data analysis if this symmetry between the two eyes is not taken into account (Smolek et al 2002).
1.5.4 Myopia and astigmatism
There is also some evidence to suggest that the presence of astigmatism may influence the development of spherical refractive errors. A number of studies have investigated the impact of astigmatism on the development of myopia.
The relationship between astigmatism and myopia was studied by Fulton et al (1982) in a population of 298 myopic children aged from birth to 10 years.
Subjects with astigmatism (particularly oblique astigmatism) were found to have higher degrees of myopia than non-astigmats. Progression of myopia was also found to be greater in subjects with astigmatic refractive errors.
The authors suggested that uncorrected astigmatic errors influenced the development of myopia and that the optical blur from uncorrected astigmatism may be a trigger for myopia development.
Goss and Erickson (1987) examined the relationship between corneal power changes and refractive error changes of myopes during childhood and young adulthood. They found that an increase in astigmatism in the WTR direction was generally associated with an increase in myopia. In contrast to this,
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Grosvenor et al (1987), in their three year longitudinal study into childhood myopia progression found patients exhibiting WTR astigmatism had significantly lower rates of myopia progression than those having ATR or no astigmatism.
The relationship between childhood myopia progression rates and type of astigmatism was studied by Goss and Shewey (1990). Longitudinal refractive data from 275 myopic subjects (from age 6 to 15) were analysed.
They found no difference in the progression rates among patients with ATR,
WTR or no astigmatism. Goss and Shewey (1990) also reanalysed the data from Grosvenor et al’s (1987) study. The reanalysis of Grosvenor et al’s
(1987) data using the exclusion criteria and data analysis procedures of Goss and Shewey (1990) revealed no significant difference in the progression rates of the different astigmatic categories.
Over a period of three years, Pärssinen (1991) followed changes in astigmatism in a population of myopic children (mean age 10.9 years). The majority of the astigmatism found was ATR. A weak correlation was found between the spherical equivalent and astigmatism at the beginning of the study. Overall, the results of the study indicate that myopic progression is not related to the degree of astigmatism. The author concluded that astigmatism was simply a symptom of refractive deviation from emmetropia.
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In another longitudinal study, Gwiazda et al (2000) followed refractive changes in 245 subjects over a period of 23 years. Almost half of the infants tested (0-6 months) had significant astigmatism (≥ 1D), but the prevalence declined sharply after infancy and reached a minimum of 5% from 6-10 years of age. Children exhibiting significant infantile astigmatism often showed an increase in astigmatism after age 10 (particularly in subjects showing ATR astigmatism). After the age of 7 years, the presence of significant ATR astigmatism was related to higher levels of myopia. In fact the data showed that subjects with ATR astigmatism and myopic refractions in infancy were more likely to become myopic at school age. Astigmatism, including that which is present at infancy, and that which is increasing during the school years (especially ATR), appears to be associated with the development of school age myopia.
Tong et al (2002) performed a cross sectional study of 1028 Singapore school children aged 7 to 9 years. The prevalence of astigmatism (≥ 1 D) was found to be 19% (compared to 32% for myopia ≥0.5 D). The majority of astigmatism was WTR. The presence of myopia was significantly associated with astigmatism. A greater severity of WTR astigmatism was associated with more severe myopia. The presence of a high AC/A ratio was also associated with astigmatism. The severity of astigmatism was also found to be associated with the amount of computer use each day. Longitudinal analysis of data from the same subjects revealed on average only a small amount of astigmatic progression (mean cylinder power changed by 0.09D over the three year study) (Tong et al 2004). The amount of myopia present
70 Chapter 1 at baseline testing and hours of computer use were associated with a greater progression rate of J0 (i.e. increase WTR astigmatism).
A study of 522 Chinese preschool children aged 2-6 years by Fan et al
(2004) revealed a prevalence of astigmatism (≥ 0.50 D) of 55.8%, which was predominantly WTR. One hundred and eight children were examined 5 years later and on average showed a slight reduction in astigmatism. The presence of astigmatism was found to be associated with greater levels of myopia and greater myopic progression. Children with increasing astigmatic errors were found to have higher progression rates of myopia than children with stable or reducing astigmatism.
Ninn-Pedersen (1996) carried out a cross sectional study of 5878 adult eyes examined prior to undergoing cataract surgery. The relationship between astigmatism, corneal shape, axial length, intraocular pressure, gender and age were studied. Eyes with a longer axial length tended to have more WTR astigmatism. Astigmatic errors deviated more from normal for both long and short axial lengths (i.e. as the axial length differed more from the normal, so too did the corneal shape). WTR astigmatism decreased with increasing intraocular pressure. The authors concluded that axial length is related to the direction and amount of astigmatism.
In a large scale study, Fairbrother et al (2004) investigated the relationship between astigmatic axis and spherical refractive error. A significant
71 Chapter 1 association was found between the presence of WTR astigmatism and the presence of high myopia and high hyperopia. Low myopes were found to be more likely to have ATR astigmatism. Heidary et al (2005) also found a high prevalence of astigmatism (particularly WTR astigmatism) in a population of subjects with high myopia. In this study, the severity of myopia was found to be associated with the degree of astigmatism.
Whilst there is some equivocal evidence, there does appear to be an association between astigmatism and the development and progression of myopia. The exact nature of this relationship and the mechanisms underlying it are still not fully understood.
1.5.5 Genetics and astigmatism
While numerous studies have been undertaken, the exact influence of genetics on the development of astigmatism is still not known.
Wixson (1965) investigated the heritability of corneal power by comparing corneal power in a group of parents and children and in a group of husbands and wives. It was concluded that both parents seem to participate in determining the corneal power characteristics of the child. Inheritance of corneal power appeared to be best approximated by an autosomal recessive pattern.
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Studies comparing monozygotic and dizygotic twins have been conducted to investigate the genetic influence on astigmatic refractive errors. In 1989,
Teikari and O’Donnell studied 72 pairs of twins (42 monozygotic and 30 dizygotic) aged 30-31 years. No significant difference was found in the amount of astigmatism between monozygotic twins compared to dizygotic twins. This suggests that the genetic contribution to astigmatism is low, with environmental factors being the major contributor.
Teikari et al (1989) examined 20 pairs of twins (9 monozygotic and 11 dizygotic) with a mean age of 69 years. Refractive error, axial length and total astigmatism were measured on each subject. There was greater intra- pair correlation among monozygotic twins compared to dizygotic twins for both spherical refractive error and axial length, indicating a genetic influence
(at least in part) on these two variables. Total astigmatism, however did not show a significant difference in intra-pair correlation between monozygotic and dizygotic twins. Axis position differed less among monozygotic twins than dizygotic twins. This again indicates only minimal genetic influence on astigmatism.
Valluri et al (1999) studied corneal topography and refractive error in monozygotic and dizygotic twins. Twenty monozygotic and 19 dizygotic twins (aged 12 to 73) had their refractive error, axial length and corneal topography assessed. Spherical refractive error and axial length showed significant differences between monozygotic twins compared to dizygotic
73 Chapter 1 twins, again indicating a strong genetic influence on these factors. There were no significant intra-pair differences between monozygotic and dizygotic twins for magnitude or direction of astigmatism, again indicating minimal genetic influence on astigmatism. Analysis of corneal topographical data also showed very few differences in the intra-pair comparisons. The authors did comment that most of their patients exhibited only low amounts of astigmatism, and thus one may find different results for subjects with higher degrees of astigmatism.
In a large study of twins, Hammond et al (2001) investigated the refractive error of 506 female twins (226 monozygotic and 280 dizygotic). The heritability of astigmatism was lower than that found for spherical refractive errors. Heritability of astigmatism was found to be 50 to 65%. (i.e. 50-65% of the variance in astigmatic refractive error can be attributed to genetic effects).
The authors found that the heritability predominantly involved dominant genetic effects.
Clementi et al (1998) analysed data from 125 families affected by astigmatism. Refractive error and corneal astigmatism were measured with automated techniques for 476 subjects (125 probands and 351 first degree relatives). When the data was analysed for astigmatism simply as a qualitative trait (i.e. affected/unaffected), no definite model of inheritance was found to best fit the data. When the severity of astigmatism was included in the analysis an autosomal dominant model provided the best fit to the data.
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The authors estimated that the frequency of the putative gene was low and that it had more effect on the presence of astigmatism than on its severity
(although an astigmatic subject carrying the putative gene had a higher probability of carrying the severe form). Clementi et al (1998) suggested that bias (in subject selection and analysis) in previous studies may have led to inconsistent results.
The studies into genetics and astigmatism present some conflicting results.
The more recent studies seem to indicate some degree of heritability of astigmatism (particularly in high degrees of astigmatism and where multiple family members are affected). Other studies favour a stronger environmental influence. It would appear that both genetic and environmental factors play some role in the development of astigmatism. The exact nature of these mechanisms is still not fully understood.
1.5.6 Astigmatism in ethnic and disease groups
Studies of astigmatism are often carried out on populations consisting of predominantly young, healthy Caucasian subjects. Studies into populations with different ethnic backgrounds and of those with disease (particularly those with higher incidences of astigmatism) may provide further insight into the aetiology of astigmatism.
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Studies into subjects of Native American ethnic origin have shown a predominance of high levels of astigmatism, particularly WTR (Abraham and
Volovick 1972, Lyle et al 1972, Goss 1989, Dobson et al 1999). It has been shown that this high degree of astigmatism is corneal in origin (Dobson et al
1999) and it has been postulated that these high degrees of WTR astigmatism may relate to heredity or nutritional factors (Abraham and
Volovick 1972, Lyle et al 1972, Goss 1989).
Lyle et al (1972) performed a cross sectional study on a population of 230
Native American children in the Saskatchewan region. Corneal astigmatism was measured and compared to a group of Caucasian children and to a group of Native American children from Brandtford. The Native American children had significantly more corneal astigmatism (predominantly WTR) for all age groups compared to the Caucasian children. The Saskatchewan subjects also had higher degrees of corneal astigmatism than the Brandtford
Native American subjects. This was possibly due to the Brandtford subjects having a lifestyle more similar to the Caucasian population than the
Saskatchewans. The authors suggested that environmental effects are a possible reason for the high degree of corneal astigmatism. An association between poor nutrition (the Saskatchewans appeared to have adopted the worst part of the Caucasian diet), and lower ocular rigidity leading to an increase in astigmatism due to pressure from the upper lids were suggested as a possible mechanism.
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Fuller et al (1995) found a high proportion of WTR astigmatism in a population of 31 Bangladeshi children living in East London.
Kame et al (1993) presented retrospective longitudinal data on changes in corneal astigmatism in a clinical population of 500 Asian subjects. The subjects were primarily Japanese, although some Chinese and Korean subjects were included. They found that subjects under the age of 30 generally showed an increase in WTR astigmatism and subjects over the age of 30 showed a decrease in WTR astigmatism. The rates of change of astigmatism were found to be greater for the Asian subjects studied than for that reported in previous longitudinal studies of Caucasian subjects. Kame et al (1993) suggested that the greater tightness of the Asian eyelids and narrower palpebral apertures led to the greater observed rates of change of astigmatism.
Down’s syndrome has been associated with significant ocular abnormalities.
Da Cunha and de Castro Moreira (1996) noted that 82% of the Down’s syndrome patients studied exhibited up-slanting palpebral fissures (i.e. temporal canthus is higher than nasal canthus) and 60% exhibited astigmatism. Astigmatism (>0.5D) was the most common refractive error found in the population and severe astigmatism (>3D) was found in 20% of the children. Haugen et al (2001b) presented longitudinal data on 60 children with Down’s syndrome. They found 57% of the children to have astigmatism
(the majority being WTR). The reduction in infant astigmatism seen in the first years of life in a normal population was not exhibited by the Down’s
77 Chapter 1 syndrome population (i.e. there was a failure of the emmetropisation process in this population). Eleven children had oblique astigmatism which displayed distinct mirror symmetry of axes between right and left eyes. The authors suggested that this dramatic mirror symmetry for oblique astigmatism may be caused by mechanical factors exerted upon the cornea by the up-slanting of the palpebral fissures (Haugen et al 2001a). Cregg et al (2003) also found a failure of emmetropisation in Down’s syndrome children. Of those children with oblique axes, the majority also showed mirror symmetry of the axes between eyes.
Treacher Collins syndrome is a rare congenital malformation syndrome.
Wang et al (1990) reported on the ocular findings of 14 patients with
Treacher Collins syndrome. The patients were noted to generally exhibit a downward slanting of the palpebral fissure. Corneal astigmatism (>2 D) was present in 5 of the 14 patients. There was an overall correlation between the degree of facial deformity and the presence of astigmatism. The axis of astigmatism was generally in the same quadrant as the horizontal palpebral fissure axis.
Ocular abnormalities are also found in Spina Bifida. Paysse et al (2002) found exaggerated up-slanting of the palpebral fissure to be a common finding in their 73 subjects with Spina Bifida. A high prevalence of oblique astigmatism was also found. The majority of the patients with up slanting palpebral fissures exhibited astigmatism (>0.75 D). Of the patients with astigmatism and upslanting palpebral fissures, the axis of astigmatism
78 Chapter 1 tended to be oriented perpendicular to the angle of the palpebral fissure, similar to the trends reported with Down’s syndrome.
All of the above populations exhibit a high prevalence of astigmatism. It appears that in some cases, the increased astigmatism prevalence and axis of astigmatism can be explained by changes in the mechanical interactions of the eyelids with the cornea. Asymmetric corneal growth is another possible explanation.
1.5.7 Animal studies and astigmatism
Studies with experimental animals have provided further insight into refractive error development. These studies have generally investigated the effects of altering an animal’s normal visual experience. Experiments have shown that form deprivation (through tarssorhaphy, corneal opacification, or with form depriving goggles) causes axial myopia, which recovers upon the removal of the deprivation (Phillips 1990, Troilo 1992, Norton and Siegwart
1995, Wildsoet 1997). This indicates that the image occurring on the retina provides information that is used to control axial elongation (Norton and
Siegwart 1995). Imposing defocus on experimental animals using spherical lenses has also produced changes in ocular growth where the eye grows so as to match both the direction and magnitude of the imposed spherical defocus (Norton and Siegwart 1995, Wildsoet 1997, Smith 1998).
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A number of studies have also been carried out to assess the effect of inducing astigmatic refractive errors in animals. Two animals commonly used in these investigations are chicks and monkeys.
Irving et al (1995) induced astigmatic refractive errors in chick eyes using goggles and found that the chick eyes grew to partially compensate for the induced astigmatic errors. Their results were consistent with the chick compensating towards the best sphere of the inducing lens. However, the authors noted a high degree of variation in response between animals.
Schmid and Wildsoet (1996) also induced astigmatic refractive errors in chick eyes. Whilst they found that the induced astigmatic errors did cause alterations to ocular growth, the changes were not consistent with the chicks compensating for the induced astigmatic errors.
McLean and Wallman (2003) used cross cylinder lenses (which produce blurred retinal images, but have no spherical power) to induce astigmatic blur in chicks. They also found no evidence that the chicks compensated for the imposed astigmatic errors. However, when the cross cylinder lenses were used in conjunction with a spherical lens, the eyes grew to compensate for the spherical lens only. This indicates that large amounts of astigmatic blur do not interfere with the spherical lens compensation in chick eyes which implies that the amount of blur present is less important than the sign of the defocus, and that sharp images are not required for lens compensation.
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There have also been a number of studies investigating the effect of inducing astigmatic refractive errors in monkey eyes. Kee et al (2003) imposed WTR,
ATR and oblique astigmatic refractive errors in monkeys. These animals developed significant amounts of astigmatism (corneal in origin, oblique in axis and bilaterally mirror symmetric), which were reversible upon the removal of the induced refractive errors. The axes of the astigmatism that developed however were not appropriate to compensate for the induced astigmatic errors. These animals also showed changes in spherical refractive errors as a result of the induced astigmatic errors (Kee et al 2004).
Both myopic and hyperopic refractive errors were found to occur as a result of the astigmatic defocus, with the monkeys’ eyes found to grow in compensation to one of the principal meridians of the astigmatic lenses.
Kee et al (2005) investigated changes in astigmatism occurring in monkeys as a result of experimentally induced myopia and hyperopia. Significant amounts of astigmatism were found to occur as a result of inducing both myopia and hyperopia (with spherical adapting lenses). These astigmatic errors were corneal in origin, oblique in axis and bilaterally mirror symmetric.
The authors suggested a possible growth related mechanism related to the development of the spherical refractive errors that leads to the astigmatism.
These astigmatic errors were found to diminish upon reversal of the myopia or hyperopia.
These studies have presented some conflicting results as to the exact end point of emmetropisation when astigmatic refractive errors are induced in
81 Chapter 1 experimental animals. There is only limited evidence to suggest that the eye can grow to compensate for astigmatic refractive errors. It is clear though, that inducing astigmatic errors has the potential to significantly affect normal eye growth in these animals (both axial growth and corneal shape can be altered as a result of induced astigmatic errors).
1.5.8 Corneal astigmatism and eyelid forces
Pressure from the eyelids on the cornea has also been implicated as a possible factor in the development of astigmatism. There have been a number of experiments examining the effect of eyelid forces on corneal astigmatism. Wilson et al (1982) investigated changes in corneal astigmatism brought about by lifting the eyelids. Eighteen subjects had their corneal astigmatism measured (by keratometry) with lids in normal position and with the lids retracted (with a speculum). Subjects with more than 1 D of
WTR astigmatism showed a systematic change in the direction of less WTR astigmatism when the lids were retracted. Those subjects showing changes exhibited a steepening of the horizontal meridian of the cornea, but not a flattening of the vertical meridian as may have been expected. The results of this experiment indicated that the lids have an influence on the degree and direction of corneal astigmatism.
Vihlen and Wilson (1983) found a definite reduction in lid tension with age, and a definite change in corneal toricity towards ATR with age. However, no
82 Chapter 1 association was found between eyelid tension and corneal toricity (i.e. tighter lids did not correlate with more astigmatism).
The influence of lid position on astigmatism was also studied by Grey and
Yap (1986). Ocular astigmatism was measured on patients with three different lid positions, deliberately widened, normal position and deliberately narrowed lids. A significant increase in ocular astigmatism was found for the deliberately narrowed eyelid position. Most subjects showed an increase of
WTR astigmatism in this situation.
Lieberman and Grierson (2000) measured corneal topography in subjects with and without the lids touching the cornea. They found changes in corneal shape when the lids were retracted from the cornea. This further confirms the fact that the lids do influence the shape of the cornea.
Garcia et al (2003) studied a population of 53 children with high astigmatism
(>1.5D). Cycloplegic retinoscopy, corneal topography and palpebral fissure slant were measured. The majority of astigmatism found was WTR. The majority of subjects also displayed an up-slanting of the palpebral fissure. A significantly higher proportion of patients with high corneal and total astigmatism also displayed abnormally slanted palpebral fissures. The axis of astigmatism was found to be significantly correlated with the degree of palpebral fissure slant. The steeper corneal axis was found to be oriented perpendicular to the horizontal axis of the palpebral fissure. Correlations were also found with gender and axis of astigmatism. Males tended to have
83 Chapter 1 more downward fissure slanting and excyclorotated cylinder axes, and females tended to have more up-slanting palpebral fissures and incyclorotated cylinder axes. Garcia et al (2003) suggested two possible mechanisms for the association between palpebral fissure slant and astigmatic axis: developmental factors may lead to correlated growth between the lids and the cornea or the mechanical effects of the slanting eyelid cause alterations in the corneal shape.
Grosvenor (1978) proposed a theory on the aetiology of astigmatism based on pressure from the eyelids. He suggested that the eye could be considered to be a spheroidal vessel filled with fluid and that without any external forces the cornea would assume a spherical shape. The band-like pressure from the upper eyelid on the cornea thus causes the eye to exhibit
WTR astigmatism as it does in the majority of the population. Grosvenor
(1978) suggested that the tightness of the eyelids and the rigidity of the ocular surface interacted to produce corneal astigmatism. This theory was used to explain changes in astigmatic axis with age.
The exact cause of astigmatism is not known. Current research indicates that both genetic and environmental factors are involved. The relative contribution of these two factors is also not known. Interaction between the cornea and the eyelids can be used as an explanation of increased astigmatism in a number of different ethnic and disease groups. Pathologies of the eyelids and pressure from the eyelids during reading have also been shown to produce changes in corneal astigmatism. Recent research into
84 Chapter 1 children with high astigmatism indicates that the eyelids have an influence on the axis and degree of corneal astigmatism. The hypothesis that eyelid pressure is an aetiological factor in the development of corneal astigmatism has been present for over 20 years. However, the exact influence of the eyelids on the nature of astigmatism is still not fully understood.
1.6 Rationale
The cornea is the eye’s most powerful refractive component, and can be readily examined and measured in a non-invasive fashion. For this reason, there have been numerous studies investigating the shape of the cornea in the population. However, in recent times there have been a number of advances in technology, which have improved our ability to measure and define the shape of the cornea. Many subtle corneal changes can now be detected and characterised more readily than has previously been possible.
A large amount of evidence suggests that the eyelids do exert an influence on the shape of the cornea. Early studies show that corneal changes as a result of eyelid pressure can occur as a result of eyelid pathology, or abnormal eyelid position. Improved corneal measurement and analysis techniques have also led to the findings that significant corneal changes can occur as a result of the normal eyelid position during everyday visual tasks such as reading in downward gaze.
85 Chapter 1
Pressure from the eyelids on the cornea has also been implicated as a possible aetiological factor in the development of corneal astigmatism. The tension of the lids, position of the lids, corneal rigidity and corneal epithelial and tear film integrity may all play a role in the interaction between eyelids and cornea. Whilst there is a range of evidence to support a theory of astigmatism development based upon eyelid pressure, the most convincing evidence comes from more recent studies into children with high amounts of astigmatism and studies into subjects with certain diseases and syndromes associated with a high prevalence of astigmatism.
The aim of this project was to further investigate how the eyelids influence corneal topography in the normal population both in the short and longer term. The eyelids have been shown to cause significant short term changes to the cornea as a result of reading in downward gaze. We were interested to investigate whether these short term changes in the cornea lead to significant changes in corneal topography over the course of the normal working day in a group of young subjects. If significant corneal topographical change happened in the short term as a result of eyelid forces in young subjects over the course of the normal working day, we would then explore the possible role of longer term eyelid pressure in the aetiology of corneal astigmatism.
If longer term pressure from the eyelids on the cornea does lead to corneal astigmatism, then it follows that associations may exist between the angle and position of the eyelids and aspects of corneal astigmatism. We
86 Chapter 1 subsequently aimed to investigate the possible influence of the angle and position of the eyelids on corneal astigmatism in a population of young subjects with a range of normal refractive errors. The results of these studies will improve our understanding of corneal topography and the average shape of the cornea, as well as to examine the influence that the eyelids play in determining the normal corneal shape and astigmatism.
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88 Chapter 2
Chapter 2: The diurnal variation of corneal topography and aberrations
2.1 Introduction
It has been shown that periods of reading can cause significant changes to corneal topography, due to interactions between the eyelids and the cornea during reading in downward gaze (Buehren et al 2003a). If reading causes changes in corneal topography, we were interested to observe the extent to which these changes were evident in subjects’ corneas over the course of their normal day. We expect these changes to be more likely seen in subjects routinely performing large amounts of close work. Therefore, to further investigate the significance of these corneal topographical changes due to eyelid forces, we investigated the diurnal variation of corneal topography in a group of young healthy subjects selected from a university population of staff and students.
Numerous ocular parameters show variation across the course of the day.
Intraocular pressure (David et al 1992, Hughes et al 2003, Liu et al 2003), retinal function, (Hankins et al 1998, Otto and Bach 1997), axial length
(Stone et al 2004), pupil size (Wilhelm et al 2001), palpebral fissure width
(Loving et al 1996) and tonic accommodation (Kurtev et al 1990) all exhibit some diurnal variation.
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It is known that corneal thickness undergoes a significant diurnal change, being thickest upon waking and then returning to a baseline level within the first 2 hours after waking (Mertz 1980, Harper et al 1996, Feng et al 2001, Du
Toit et al 2003). This corneal thickening upon waking is thought to be caused by the reduced oxygen supply to the cornea, and changes to the pre-corneal tear film in the closed eye environment (Mertz 1980, Feng et al 2001). Some variability has also been found in corneal thickness throughout the course of the day, which cannot be attributed to the deswelling of the cornea following eye opening (Harper et el 1996, Odenthal et al 1999, DuToit et al 2003).
This variability in corneal thickness is thought to be caused by changes in internal and external environmental factors such as blink rate, tear production, tear evaporation and IOP (Odenthal et al 1999, DuToit et al
2003).
Corneal curvature also appears to exhibit diurnal variation. Most investigators have found the cornea to be at its flattest in the morning, with a slight but significant steepening (of approximately 0.2 D) occurring throughout the day (Reynolds and Poynter 1970, Kiely et al 1982a, Cronje and Harris 1997, Handa et al 2002). However, Rengstorff (1972) found no significant pattern of variation in corneal curvature during the day. All these studies into diurnal variation of corneal curvature have used either keratometry (Reynolds and Poynter 1970, Rengstorff 1972, Cronje and
Harris 1997), photokeratoscopy and keratometry (Kiely et al 1982a) or an average (across all meridians) of videokeratoscope data (Handa et al 2002) to assess corneal curvature. One may expect that regional or more
90 Chapter 2 peripheral changes in corneal topography may not be detected by these methods.
Some patients who have undergone radial keratotomy (RK) exhibit exaggerated diurnal corneal curvature changes, with substantial corneal steepening (and subsequent myopic shift in refractive error) occurring throughout the day (McDonnell et al 1989, Kwitko et al 1992b, McDonnell et al 1996, Kemp et al 1999). These exaggerated diurnal changes are thought to be due to delayed corneal wound healing and reduced corneal tensile strength leading to persistent corneal instability for up to 12 years following surgery (McDonnell et al 1996).
Some conflicting evidence exists as to the effect of the female menstrual cycle on corneal curvature. Some studies have suggested that significant changes in corneal thickness and curvature (due to changing hormone levels) occur over the course of the menstrual cycle (Kiely et al 1983, Handa et al 2002). Conversely, other investigators have found no demonstrable pattern of change in corneal thickness (El Hage and Beaulne 1973) or corneal topography (Oliver et al 1996) across the cycle.
The pre-corneal tear film also varies diurnally. The tear film in the closed eye environment has been found to be significantly different to that in the open eye (Sack et al 1992, Sack et al 1997, Sack et al 1999). A number of different tear proteins and enzymes have been found to be at a maximum concentration in the tear film upon first waking (Huth et al 1981, Fullard and
91 Chapter 2
Carney 1984, Sack et al 1992, Sack et al 1997, Sack et al 1999). These levels then reduce rapidly after waking and remain relatively stable throughout the day (Huth et al 1981, Ng et al, 2001). The tear film stability, and tear evaporation rates vary in a similar fashion (Patel et al 1988,
Tomlinson and Cedarstaff 1991). Tear stability and evaporation rate are at a minimum in the early morning, and then rise to a stable level within the next two hours.
Previous studies into the diurnal change in corneal curvature have not investigated any regional or peripheral change in the cornea. However recent research has shown that significant regional corneal change may occur as a result of eyelid forces during reading. Therefore the aim of this experiment was to investigate the diurnal variation in corneal topography using videokeratoscopy and corneal wavefront error analysis. These techniques may be expected to detect regional and peripheral changes more accurately than previous studies. We measured corneal topography at three times during the day (over an eight hour period) over three days of the week
(Monday, Tuesday and Friday).
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2.2 Methods
2.2.1 Subjects and procedures.
Twenty young subjects were recruited for the experiment. All subjects had normal ocular health, with no history of ocular surgery and none were rigid gas permeable contact lens wearers. Some part-time soft contact lens wearers were included, but these subjects were instructed not to wear contact lenses for the week of the experiment. The subjects were university students, researchers or administrators at the Queensland University of
Technology. Their visual tasks were therefore primarily lecture classes, computer work and reading and were mostly performed indoors. Approval from the university human research ethics committee was obtained prior to commencement of the study and informed consent was obtained from all subjects.
Two of the subjects were excluded from the experiment because of inaccurate corneal topographical results due to poor fixation control, and one subject was excluded as corneal topographical results indicated the presence of previously undiagnosed keratoconus. Of the 17 remaining participants, 8 were female and 9 were male with an age range of 20 to 35 years (mean age
25.8). The 17 subjects exhibited a range of refractive errors. Five subjects were primarily myopic (range -1.25 D to -4.25 D), 2 subjects were primarily astigmatic (-1.5 D) and the remaining 10 subjects were classified as emmetropic (range -0.25 D to +0.50 D). Each subject underwent a
93 Chapter 2 preliminary slit lamp examination to detect any anterior eye disease or tear film abnormalities.
All corneal topography measurements were taken using the Keratron videokeratoscope (EyeQuip Division, Alliance Medical Marketing,
Jacksonville, FL, USA). Images were captured according to manufacturers instructions, with subjects instructed to blink, and the image captured within a few seconds after the blink. The Keratron videokeratoscope is based on the
Placido disk principle and has been shown to exhibit a high degree of accuracy and precision for measuring spherical, aspheric and astigmatic inanimate test objects (Tripoli et al 1995, Tripoli et al 1996, Tang et al 2000).
To reduce focusing and eye positioning errors, this instrument utilises an automatic range finding device, which only captures an image when sharp focus is attained, and a misalignment correction system that corrects for poor centration of the image (Mattioli and Tripoli 1997). The Keratron uses a non- spherically biased, arc-step algorithm to reconstruct the corneal surface, which has been shown to measure height more accurately than videokeratoscopes based on spherically biased algorithms (Tripoli et al
1995).
To avoid confounding factors in the averaging of corneal topographical data, the right eye of all subjects was used for corneal measurements. For each subject, corneal topography measurements were taken at three different times throughout the day on three different days of the week. Measurements were taken in the morning (approximately 9 am), at lunchtime (approximately
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1 pm) and in the afternoon (approximately 5 pm) on Monday, Tuesday and
Friday. Therefore, each subject had a total of 9 measurement sessions. To minimise any possible changes due to the menstrual cycle, each subject’s measurements were taken during the one week.
Twelve corneal topography measurements were taken consecutively for each subject at each measurement session. Subjects were instructed not to perform any significant amounts of reading prior to the morning measurement on each of the three days. Two subjects were unable to attend for measurements on one of their three measurement days. The data from these subjects were excluded from any analyses that examined changes over the entire week.
To determine each subject’s normal eye and eyelid position during different visual tasks, digital photography was performed using a Nikon Coolpix 995
3.34 mega pixel digital camera. The digital images were obtained of each subject with eyes in primary gaze, during reading and during computer work.
During image capture, subjects were instructed to maintain their normal posture used for each visual task and to fixate on the camera’s lens which was positioned approximately 50-60 cm from the subject’s eyes. The camera’s built-in flash was used for each image. Wherever possible, the photographs were taken with the subjects in their normal work environment.
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2.2.2 Data analysis
Following data collection, corneal tangential power, refractive power and corneal height data were exported from the videokeratoscope. Any topographical maps which displayed poor focus or local irregularities (e.g. tear film instability) were discarded. A range of 8 to 12 maps were exported from each session for each subject with the mean number of maps exported being 11.
The corneal topography data were analysed using customized software. For each measurement session, the 8 to 12 individual tangential power maps for each subject were averaged to give an “average tangential power map”. This averaging procedure involves a bilinear interpolation of the data into a square grid format.
To highlight the changes occurring in tangential power throughout the day, difference maps were calculated. This was done by subtracting the average morning tangential power map from the average lunchtime tangential power map and from the average afternoon tangential power map. For each data point on the difference map, a two-tailed paired t-test was performed, thus providing the significance of the differences between the average maps at each point. These data were displayed as a “significance map” with p values at each location in the map.
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Corneal refractive power data were analysed by calculating the best fit sphero-cylinder for each map from each subject for each measurement session (for 3.5 mm and 5.5 mm map diameters). These best fit sphero- cylinders were then converted into the power vectors M (best fit sphere), J0
(representing a Jackson cross-cylinder axis 180° which gives a measure of horizontal/vertical astigmatism) and J45 (representing a Jackson cross- cylinder axis 45° which gives a measure of oblique astigmatism) using the method of Thibos et al (1997). This allowed the average sphero-cylinder for each session to be calculated and for subsequent statistical analysis to be carried out on these data. The Root Mean Square Error (RMSE) between the corneal refractive power and best fit corneal sphero-cylinder were also calculated for each map, and an average calculated for each subject for each measurement session (for 3.5 mm and 5.5 mm map diameters).
To investigate changes over the week of testing, the refractive power sphero- cylinder data and RMSE data were subsequently analysed using a repeated measures analysis of variance (ANOVA) with two within-subject factors (time of day and day of the week). The Greenhouse-Geisser correction of the degrees of freedom was used to reduce the chance of type I errors, where the sphericity assumption was violated. Pair-wise comparisons were then carried out using a Bonferroni adjusted t-test to determine which days and times showed significantly different topography results.
Corneal height data were also averaged to give an average height map for each subject at each session. Three dimensional ray tracing was used to
97 Chapter 2 calculate the optical path differences for each point on the “average height” surface. The wavefront error was then calculated (as the difference between the ideal wavefront and the measured wavefront) and Zernike wavefront coefficients were fitted to the wavefront error (up to and including the 6th radial order). The Zernike wavefront coefficients were expressed using the double index notation (OSA convention) (Thibos et al 2002). The image plane was at the circle of least confusion and the wavelength used was 555 nm. The wavefront was centred on the line of sight. This was achieved by using the average pupil offset value from the pupil detection function in the
Keratron videokeratoscope for each measurement session for each subject, and using this average pupil offset as the new reference axis for the wavefront.
The procedure of converting corneal height data into wavefront error has been shown to be accurate and precise and limited primarily by the accuracy of the videokeratoscope (Guirao and Artal 2000). The wavefront error was calculated for a 3.5 mm and 5.5 mm pupil (one subject did not have complete
Placido ring data out to 5.5 mm in one average map and so was excluded from analysis for the 5.5 mm pupil size). The Zernike wavefront coefficients were then averaged for all subjects at each measurement session to provide a mean corneal wavefront error for each measurement session. To test the adequacy of a 6th order Zernike polynomial fit to the corneal height data, the data from two subjects were fit with higher order terms (up to and including the 8th order). Fitting the corneal height data with these higher order coefficients was found to only contribute 1.6% and 1.9% of the total RMSE
98 Chapter 2 for each subject. We therefore concluded that a 6th order Zernike polynomial fit provided an adequate representation of the height data for our subjects.
The Zernike wavefront coefficients were also subsequently analysed using a repeated measures analysis of variance procedure (as outlined above).
The digital images were analysed to calculate each subject’s vertical palpebral aperture width during the three different visual tasks (primary gaze, reading and computer work). To provide a scale for each of the digital images, a single videokeratoscope image for each subject was analysed using automatic limbus detection software (Morelande et al 2002). This procedure provided a measurement of each subject’s limbus diameter and the distance from the corneal geometric centre, to the videokeratoscope axis.
These values were then used to allow accurate calculation of the vertical palpebral fissure width in each subject’s digital image of the anterior eye (i.e. the vertical distance between the upper and lower eyelid margins), using the videokeratoscope axis as the reference axis for the measurement.
2.3 Results
Examination of the tangential power maps of each subject showed that 15 out of the 17 subjects displayed distinct changes in their corneal topography throughout the day. Subjects exhibited horizontal bands of distortion to differing degrees in the superior and inferior cornea occurring throughout the day. Inspection of the significance maps showed that in most cases these
99 Chapter 2 areas of change were highly statistically significant. It is interesting to note that the two subjects who showed no significant pattern of change in corneal topography throughout the day had the two widest vertical palpebral apertures of 8.7 mm and 10.0 mm while reading. The group mean palpebral aperture in primary gaze was found to be 9.96 mm (range 7.87-11.70 mm), during computer work was 9.20 mm (range 7.24-12.2 mm) and during reading was 6.86 mm (range 4.84-10.04 mm).
The difference maps and significance maps for the Monday morning minus
Monday afternoon condition for four subjects are displayed in Figure 2.1.
These results were representative of the results of the 15 subjects showing distinct changes over the course of the day.
Analysis of the mean RMSE difference from the best fit sphero-cylinder for the corneal refractive power for the 3.5 mm and 5.5 mm pupil sizes both showed the same general trend. The RMSE was lowest for the morning measurement and then gradually increased throughout the day. The RMSE then returned to a similar baseline level for the next morning measurement.
A statistically significant change in RMSE with ‘time of day’ was found for the
5.5 mm pupil size (p= 0.028). The mean RMSE averaged over the three days of testing for the morning measurement (5.5 mm pupil) was 1.121 D and the mean RMSE for both the lunchtime and afternoon measurement was
1.141 D. Pair-wise comparison revealed a significant difference between the morning and lunchtime refractive power RMSE. There was no significant effect of ‘day of the week’ and no significant interaction between ‘day of the
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Figure 2.1: Tangential power difference maps (left) and significance maps
(right) for 4 subjects. Monday morning topography minus Monday afternoon topography condition is shown.
101 Chapter 2 week’ and ‘time of day’. Although the RMSE for the 3.5 mm pupil size exhibited a similar trend, the changes just failed to reach statistical significance (p= 0.056). Figure 2.2 shows the change in mean refractive power RMSE from baseline (Monday morning measurement) over the week for the 5.5 mm pupil size.
The best fit sphero-cylinder from the refractive power data also showed a number of diurnal trends. The group mean corneal refractive power best sphere (power vector M) at baseline (Monday morning measurement) was
49.03 ± 1.9 D and 49.69 ± 1.9 D for the 3.5 mm and 5.5 mm pupil sizes respectively. The best fit sphere exhibited a slight increase over the course of the day of approximately 0.1 D. Repeated measures ANOVA revealed a significant effect of time of day (p= 0.0002 for 3.5 mm and 5.5 mm pupil sizes), but no significant effect of day of the week or day/time interaction.
Pair-wise comparison revealed the lunchtime and afternoon measurements to be significantly different to the morning measurement but no significant difference between the lunchtime and afternoon measurement (i.e. the greatest change in M occurred in the morning). Figure 2.3 (a) displays the change in mean “M” from the baseline measurement (Monday morning) over time for the 5.5 mm pupil size.
The power vector J0 (astigmatism at 90/180°) also exhibited some diurnal variation. The group mean corneal refractive power J0 for the baseline measurement (Monday morning) was found to be 0.37 ± 0.39 D and 0.39 ±
0.38 D for the 3.5 mm and 5.5 mm pupil sizes respectively. Figure 2.3 (b)
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Figure 2.2: Mean change in refractive power RMSE difference from best fit refractive power sphero-cylinder (5.5 mm pupil) from baseline over the course of the week. Error bars indicate the standard errors of the mean change. Repeated measures ANOVA p= 0.028 for ‘time of day’.
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Figure 2.3: a) Mean change in sphere power “M” (repeated measures
ANOVA p= 0.0002 for ‘time of day’) from baseline over the course of the week (5.5 mm pupil). b) Mean change in astigmatism 90/180° “J0” (repeated measures ANOVA p= 0.051 for ‘day of week’) from baseline over the course of the week (5.5 mm pupil). c) Mean change in astigmatism 45/135° “J45”
(repeated measures ANOVA p= 0.006 for ‘time of day’) from baseline over the course of the week (5.5 mm pupil). Error bars indicate the standard errors of the mean change.
104 Chapter 2 demonstrates the change in mean J0 from baseline over time for the 5.5 mm pupil size. A slight trend is observed for a decrease in J0 (i.e. an increase in
ATR astigmatism) throughout the day and an increase in J0 (i.e. an increase in WTR astigmatism) over the week. The change with ‘time of day’ was not statistically significant, and the change in J0 with day of the week bordered upon statistical significance for the 5.5 mm pupil sizes (p= 0.051). Power vector J45 (astigmatism at 45/135°) showed a significant change with time of day (J45 became smaller over the course of the day) (p= 0.044 and p= 0.006 respectively for 3.5 mm and 5.5 mm pupils) but no significant change over the day of the week for both the 3.5 mm and 5.5 mm pupil sizes. The group mean corneal refractive power J45 at the baseline measurement (Monday morning) was 0.06 ± 0.18 D and 0.06 ± 0.20 D for the 3.5 mm and 5.5 mm pupil sizes respectively. The change in mean J45 from baseline over time
(5.5 mm pupil size) is displayed in Figure 2.3 (c).
Analysis of the mean corneal wavefront error revealed significant diurnal changes occurring in a number of Zernike wavefront coefficients. Table 2.1 provides the mean change in aberration averaged over the three days of testing and p values from the repeated measures ANOVA for the wavefront aberrations for both the 3.5 mm and 5.5 mm pupil sizes for the significant
(and near significant) changing Zernike coefficients.
Two of the lower order Zernike coefficients exhibited significant change.
−2 These coefficients were Z 2 (primary astigmatism along 45 degrees) and
2 Z 2 (primary astigmatism along 180 degrees). The changes in these
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Table 2.1: Group mean change in Zernike coefficients (averaged over the three days of testing) for 3.5 mm and 5.5 mm pupil sizes expressed in microns, with results from repeated measures ANOVA (test of within-subjects effects). P-values of the F statistic are displayed. Only coefficients exhibiting significant and near significant change are displayed.
Day * Time Time of Day Effect Day of Week Effect Interaction
3.5 mm 5.5 mm 3.5 mm 5.5 mm 3.5 mm 5.5 mm Change (p-value) Change (p-value) Change (p-value) Change (p-value) (p-value) (p-value)
−2 0.009 (0.087) 0.022 (0.003)** -0.003 (0.297) 0.005 (0.263) (0.685) (0.720) Z2 2 0.000 (0.386) 0.013 (0.108) -0.018 (0.021)* -0.026 (0.018)* (0.360) (0.557) Z 2 −3 0.005 (0.041)* 0.015 (0.019)* -0.001 (0.882) -0.003 (0.682) (0.435) (0.482) Z3 −1 -0.006 (0.120) -0.021 (0.001)** 0.001 (0.658) 0.000 (0.560) (0.368) (0.347) Z3 −4 -0.001 (0.841) 0.002 (0.682) -0.001 (0.170) -0.001 (0.213) (0.081) (0.011)* Z4 −2 0.001 (0.670) -0.002 (0.732) 0.001 (0.356) 0.002 (0.277) (0.004)* (0.178) Z4 2 0.000 (0.863) 0.004 (0.479) 0.002 (0.056) 0.006 (0.137) (0.918) (0.171) Z 4 −5 -0.001 (0.250) 0.004 (0.377) 0.002 (0.058) 0.002 (0.505) (0.435) (0.309) Z 5 5 -0.003 (0.052) -0.007 (0.042)* 0.000 (0.369) -0.003 (0.450) (0.488) (0.463) Z 5
* = Significant p < 0.05
** = Highly Significant p < 0.01
106 Chapter 2 aberrations paralleled those changes observed in the power vectors J45 and
J0 for corneal refractive power. Astigmatism along 45 degrees showed a significant decrease over the course of the day for the 5.5 mm pupil (increase
−2 in Z 2 , p= 0.003 for 5.5 mm pupil) and astigmatism along 180 showed a significant increase over the course of the week for both the 3.5 mm and 5.5
2 mm pupils (decrease in Z 2 , p= 0.021 and p= 0.018 for the 3.5 mm and 5.5 mm pupils respectively). Two higher order wavefront coefficients also displayed a significant change over the course of the day. These coefficients
−3 were Z 3 (trefoil along 30 degrees) which showed a significant change with
−1 time of day for the 3.5 mm and 5.5 mm pupil, and Z 3 (primary vertical coma) which showed significant change with time of day for the 5.5 mm pupil.
−3 −1 Figure 2.4 displays the change in mean Z 3 and Z 3 from baseline
−3 (Monday morning) over time for a 5.5 mm pupil size. Z 3 exhibits a gradual increase over the course of the day (i.e. becomes more positive) whereas
−1 Z 3 exhibits a decrease over the course of the day (i.e. becomes more negative). Comparison of the magnitude of change in aberration with the
−3 magnitude of the aberration at baseline reveals Z 3 to change on average by
−1 48% and Z 3 to change by 13% of its mean baseline level throughout the day for the 5.5 mm pupil size.
The combination of positive trefoil along 30 degrees and negative primary vertical coma represents a wave-like distortion of the corneal wavefront
(Buehren et al 2003a). This result indicates that the wave-like distortion represented by the combination of these two wavefront coefficients increases
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−3 Figure 2.4: Mean change in trefoil along 30 degrees ( Z 3 ) and primary
−1 vertical coma ( Z 3 ) from baseline (Monday morning) over the course of the week (5.5 mm pupil). Error bars represent the standard error of the mean change.
108 Chapter 2 over the course of the day. These two aberrations were also found to be significantly correlated (r2 = 0.722, p < 0.01, for the 5.5 mm pupil size). The horizontal bands of change in tangential power seen in the difference maps of Figure 1 correspond to the wave-like distortion in corneal wavefront
−1 −3 resulting from the combination of Z 3 and Z 3 . A number of other higher order aberrations showed significant or near significant change with time of day or day of week or day/time interaction (Table 2.1).
2.4 Discussion
We have shown that significant diurnal changes can occur in corneal topography over the course of the day. The most significant changes occurred as horizontal areas of ‘wave-like’ distortion in the superior and inferior cornea. These wave-like aberrations appeared to be cyclical in nature, gradually increasing throughout the course of the day and returning back to a baseline level the next morning.
Higher order corneal aberrations are generally of a much smaller magnitude than the lower order aberrations. Of the higher order aberrations, the 3rd order Zernike wavefront coefficients have been shown to make the largest contribution towards the total higher order aberrations (Howland and
Howland, 1977, Guirao et al 2002). We have shown that 2 of these 3rd order aberrations exhibit significant systematic changes throughout the day for a
5.5 mm pupil size. The magnitude of change in these corneal aberrations for
109 Chapter 2 the 3.5 mm pupil size was much smaller and only significant for one of the 3rd
−3 order aberrations ( Z 3 ). Therefore the impact that these topographical changes have upon vision will depend on the size of the natural pupil.
Our results are consistent with previous investigations into diurnal variations of corneal curvature. We found a slight steepening in the corneal refractive power best fit sphere. Earlier investigators have also found a slight steepening of the cornea to occur throughout the day (Reynolds and Poynter
1970, Kiely et al 1982a, Cronje and Harris 1997, Handa et al 2002). Kiely et al (1982a) found a correlation between the change in corneal thickness and the change in horizontal corneal curvature (i.e. the slight corneal steepening throughout the day occurred as a result of the reduction in corneal thickness that occurs in the first few hours following waking). Our results tend to agree with this premise, as the slight steepening in refractive power noted in our study occurred most significantly between the morning and lunchtime measurements. Our morning measurement was taken between 1 and 3 hours after waking and we expected that some subjects may still be exhibiting slight corneal swelling at this first measurement. The wave-like distortions found in the superior and inferior cornea could also potentially cause a steepening of the refractive power best fit sphere over the course of the day.
Upon initial inspection, the group mean change in best fit sphere of approximately 0.1 D over the course of the day appeared to be small and possibly not clinically significant. However, closer scrutiny of the data
110 Chapter 2 revealed that the diurnal variation in the cornea found in this study could significantly affect the clinical measurement of subjective refraction.
Inspection of the individual subjects’ refractive power data revealed that 12 out of the 17 subjects exhibited a steepening of the cornea over the course of the day of >0.125 D on at least one day of testing (for the 3.5 mm pupil size), potentially leading to a subjective change in refraction of 0.25 D. The largest change observed in refractive power best fit sphere was a steepening of 0.37
D over the course of the day on one day for one subject (5.5 mm pupil size).
It should be noted again that the corneal changes were more pronounced for the larger corneal maps. The magnitude of change in the corneal refractive power best fit sphero-cylinder, RMSE and the corneal aberrations were greater for the larger corneal analysis diameters. Therefore any visual effects related to these corneal changes will be more pronounced for subjects with large pupils or in low light conditions. Subjects with smaller pupils (i.e. less than 3.5 mm) may exhibit relatively little subjective visual change due to these diurnal corneal changes.
Intraocular pressure (IOP) is also known to vary diurnally (David et al 1992,
Hughes et al 2003, Liu et al 2003). David et al (1992) found an average variation in IOP of 5 mmHg over the day for normal subjects. If changes in
IOP do affect corneal shape, then one may expect this to be a factor in the diurnal variation of corneal topography. However, Lam and Douthwaite
(1997) found no significant changes in corneal curvature as a result of artificially increasing IOP in subjects by (on average) 6.5 mmHg.
Eysteinsson et al (2002) and Morgan et al (2002) also found no significant
111 Chapter 2 association between IOP and corneal curvature. Whilst there remains a possibility that IOP changes may influence corneal topography, one would expect that these changes would be a generalised steepening or flattening of the cornea and not the more localised changes that we have observed in this study.
A number of the 4th and 5th order corneal aberrations exhibited some variation with time of day and day of the week, of which some were statistically significant while others approached significance. Some of these aberrations represent the higher order form of some of the significantly
2 2 changed lower order aberrations (e.g. Z 2 primary astigmatism and Z 4 secondary astigmatism), while others represent more complex corneal
5 shapes (e.g. Z 5 pentafoil). Changes in some of these more complex aberrations may represent local tear film changes. As the pre-corneal tear film itself undergoes diurnal variation in both composition (Huth et al 1981,
Fullard and Carney 1984, , Sack et al 1992, Sack et al 1997, Sack et al 1999) and stability (Patel et al 1988, Tomlinson and Cedarstaff 1991), and as local tear film disruption has been shown to cause significant changes in corneal topography (Dursun et al 2000, Nemeth et al 2001) and retinal image quality
(Albarran et al, 1997, Thibos and Hong 1999, Tutt et al 2000, Koh et al 2002) some of the changes in higher order aberrations found in our study may be related to these local tear film changes. Tear film changes can explain some of the short-term variability in corneal aberrations observed, but the systematic changes seen in many of the corneal aberrations are not readily explained by alterations in the tear film.
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Cheng et al (2004) recently reported significant variability in Shack-Hartmann wavefront error measurements over different time scales (seconds, hours, days and months). The authors suggested that this variability in wavefront error was due to actual changes in the optical characteristics of the eye as opposed to measurement noise. Accommodation fluctuations, tear film instability and eye movements were all suggested as possible sources of variability. The diurnal variation in corneal aberrations found in our study is likely to be another source of the variability found in total wavefront error over time, since changes in the corneal wavefront directly influence the total wavefront of the eye. Inspection of the standard deviation maps for the average wavefront error for different time scales in Cheng et al’s (2004) study reveals the greatest standard deviations occurring in horizontal bands in the inferior and superior regions of the maps. This is consistent with the changes in corneal aberrations found in our study.
Buehren et al (2003a) found similar wave-like distortion in the superior and inferior cornea in subjects who had performed a one hour reading task. They also found a significant increase in the primary vertical coma and trefoil
(along 30 degrees) following reading (these two aberrations were also found to be significantly correlated). By analysing the position of the eyelids whilst reading (from digital images), Buehren et al (2003a) found a significant association between the position of the eyelids during reading and the position of the corneal distortions. They concluded that these corneal distortions may be related to pressure from the eyelids leading to displacement of epithelial tissue. The changes that we have observed in
113 Chapter 2 corneal topography appear to parallel those observed by Buehren et al
−3 (2003a) and affect the same Zernike wavefront coefficients (in particular Z 3
−1 and Z 3 ). We believe the changes that we have observed also relate to pressure from the eyelids on the anterior cornea.
Previous reports of episodes of corneal distortion and associated monocular diplopia due to pressure from the eyelids have either been isolated case reports, or studies where corneal distortions was deliberately induced through a particular task to produce monocular diplopia (Mandell 1966, Knoll
1975, Stampfer and Tredici 1975, Bowman et al 1978, Carney et al 1981,
Goss and Criswell 1992, Kommerell 1993, Ford et al 1997, Golnik and
Eggenberger 2001). We have shown that more subtle corneal distortions due to eyelid forces are a phenomenon that has occurred in the majority of our subjects over the course of a normal work day.
All of our subjects were routinely performing large amounts of near work and the majority of subjects exhibited corneal topographical changes over the course of the day. It is possible that a correlation would exist between the amount of near work performed and the degree of change in corneal topography over the course of the day. However, this relationship between the amount of near work and degree of corneal change would be expected to be a complex one as corneal hydration, tear film stability, blink frequency, vertical palpebral aperture width and the length of time between near work and corneal measurement may all influence the degree of topographical change observed. The type of near task performed would also be expected
114 Chapter 2 to affect the magnitude of change. Tasks with a narrower palpebral aperture
(e.g. reading which produced a mean vertical palpebral aperture width of
6.86 mm in these subjects) and greater eye movements might be expected to cause greater topographical change than those with a wider palpebral aperture and less eye movements.
As near work and eyelid pressure plays a role in the diurnal corneal variation, it is likely that the diurnal variation in corneal topography may be different if another population of subjects were studied who were not performing significant amounts of close work. However, some of our subjects (in particular those with fairly narrow palpebral apertures in primary gaze) exhibited some degree of wave-like distortion even in their baseline measurements (at around 9 am). These subjects appeared to exhibit changes due to the interaction between the eyelids and the cornea in primary gaze and thus also exhibited changes when they were not performing near tasks. This suggests that some similar diurnal corneal changes may still be observed in other populations.
In orthokeratology, forces are induced by rigid gas-permeable contact lenses to alter corneal shape to reduce myopia. Recent research has indicated that the application of modern ‘reverse-geometry’ orthokeratology contact lenses can cause rapid changes in corneal shape which is possibly caused by a redistribution of epithelial cellular tissue (Alharbi and Swarbrick 2003,
Sridharan and Swarbrick 2003, Wang et al 2003a). Some degree of individual variability in patient’s corneal response to orthokeratology has also
115 Chapter 2 been noted. Individual variations in the degree of corneal change, time course of change and amount of regression of corneal change have all been observed (Mountford 1997, Mountford, 1998). A similar process of corneal epithelial tissue change may be occurring as a result of eyelid forces to cause the corneal distortions found in our study. Variability in subject’s corneal epithelial properties, as well as differences in eyelid tension may be another reason for some of the differences between subjects found in this study.
To further investigate the diurnal corneal topography changes, two subjects were retested on a separate day. On this day of testing, corneal topography measurements were taken at hourly intervals between 9:00 am and 5:00 pm.
An apparent association between the amount of close visual activities and the degree of corneal change was seen from these measurements. The largest corneal changes occurred following large amounts of intense close- work (e.g. concentrated computer work) and regression of most of these changes occurred following a break from these activities (e.g. a lunch or coffee break). Figure 2.5 illustrates this observation with two tangential power maps for subject DK at two separate times of the day. The 11 am measurement followed an hour of concentrated computer work and exhibited a large band of distortion in the superior cornea. The 3 pm measurement followed a late lunch break on the same day and showed significantly less distortion in the superior cornea.
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Figure 2.5: Tangential power maps from subject DK illustrating the effect of different visual tasks on corneal topography. The 11 am measurement followed an hour of intense computer work, whereas the 3 pm measurement followed a lunch break.
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The results of this study have a number of different clinical and research implications. The diurnal variation in the higher order aberrations could potentially impact on the results of wavefront guided refractive surgery. For example, some components of the wavefront error in the morning will be significantly different to the same components wavefront error in the afternoon, so that some aberrations will either be over- or under-corrected depending upon whether the ablation is based on a morning or afternoon measurement of wavefront error. Numerous factors, including the corneal biomechanical response to ablation (Roberts 2002) and corneal epithelial and collagen wound healing (Lipschitz 2002) are currently thought to limit the ability to successfully correct all higher order aberrations. The fact that certain aberrations tend to vary in a cyclical nature adds another factor limiting the effectiveness of wavefront guided refractive surgery. A similar problem would also be encountered for customized contact lens corrections.
Recent research has shown that a reduction in corneal stiffness and corneal biomechanical properties occurs following laser in situ keratomileusis
(LASIK) and photorefractive keratectomy (PRK) refractive surgery procedures (Hjortdal et al 2005, Luce 2005, Schmack et al 20005). A reduction in the biomechanical strength of the cornea may be expected to lead to an increased effect of eyelid forces on the cornea. The diurnal variation in corneal topography and aberrations may therefore be expected to be increased in subjects following these procedures. Studies have noted that exaggerated diurnal variation in corneal curvature occurs following RK
(McDonnell et al 1989, Kwitko et al 1992b, McDonnell et al 1996, Kemp et al
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1999), however Goldberg et al (1997) found no significant diurnal change in corneal curvature following PRK (as measured with keratometry). Further research examining corneal topography and corneal aberrations is required to further explore the possibility that increased diurnal corneal topographical changes occur following LASIK and PRK.
Researchers studying the aberrations of the eye should also be aware of these diurnal changes in corneal wavefront aberrations. These aberrations tend to be at their lowest levels in the early morning (prior to subject’s commencing significant close work). To avoid the diurnal variation confounding results, aberration measurements should be taken in the early morning or at a fixed time of day for all subjects, taking account of prior visual tasks.
Pressure from the eyelids has also been implicated in the aetiology of WTR astigmatism (Grosvenor 1978, Wilson et al 1982, Grey and Yap 1985,
Lieberman and Grierson 2000, Garcia et al 2003). We did find some changes in astigmatism occurring over the course of the day. Astigmatism along 45 degrees appeared to gradually decrease with time of day, but showed no significant change over the week. Astigmatism along 180 degrees showed a slight (but statistically insignificant) reduction over the course of the day and a significant increase over the week. All of these diurnal variations in astigmatism were quite small in magnitude and as such would not be considered clinically significant. Further research is required to fully clarify the influence of eyelid forces on the aetiology of corneal
119 Chapter 2 astigmatism, but the findings of this study leave open the possibility that over many years, the force of the lids could alter corneal astigmatism.
Buehren et al (2003a) speculated that corneal aberrations caused by eyelid forces during reading may be an important factor in refractive error development. We have further shown that changes in corneal aberrations occur in the majority of subjects tested over the course of a normal work day.
There also appeared to be some association between the amount of concentrated near work performed and the amount of corneal distortion occurring. We would expect that these changes would cause a slight degradation of retinal image quality over the course of the day (as indicated by the significant increase in RMSE with time) which would be worse for those subjects performing large amounts of concentrated close work and those with narrow palpebral apertures or tight eyelids. This may prove important in the aetiology of myopia as both retinal image quality and near work are thought to be important factors in myopia development (Troilo 1992,
Norton and Siegwart 1995, Saw et al 1996, Wildsoet 1997, Lam and
Edwards 1999).
2.5 Conclusions
In summary, this study has shown that significant diurnal variation can occur in corneal topography. The most significant change was a wave-like distortion occurring in the superior and inferior cornea increasing over the
120 Chapter 2 course of the day. This distortion appears to be related to pressure from the eyelids on the anterior cornea. These changes occur in a cyclical nature, being at a minimum each morning and gradually increasing throughout the day. This diurnal variation may have important implications for customized refractive corrections (as corneal aberrations are not constant throughout the day) and in refractive error development.
The results of this study confirm that corneal changes as a result of eyelid forces are evident in the majority of subjects tested over the course of a normal day. We have also shown that changes in corneal astigmatism occur over the course of the day and week. Whilst the magnitude of astigmatic change was small, it may be that the changes over the day represent a short term change in corneal astigmatism related to eyelid pressure. The changes over the course of the week (i.e. the slight increase in WTR astigmatism found) may reflect a longer term change in corneal astigmatism as a result of eyelid forces. The small magnitude of change in corneal astigmatism means that no firm conclusions can be drawn regarding this.
If pressure from the eyelids is an aetiological factor in the development of corneal astigmatism, then the angle, position and contour of the eyelids may all be important in determining the normal shape of the cornea. To further investigate the influence of the eyelids on the shape of the cornea an experiment was carried out to define the average eyelid morphology and average corneal topography in a large population of young healthy subjects.
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Chapter 3: The morphology of the palpebral fissure in different angles of vertical gaze
3.1 Introduction
In Chapter 2, we have shown that significant changes can occur in the topography of the cornea over the course of the day, which appears to result from eyelid pressure. As pressure from the eyelids can cause corneal topographical change and could also be an aetiological factor in corneal astigmatism, the position and angle of the eyelids may therefore be an important determinant of the shape of the cornea. If this is the case, then it is important to define the angle, position and contour of the eyelids in the normal population. As corneal changes due to eyelid forces arise following downgaze visual tasks, and as many of our daily visual tasks are performed in downward gaze, we aimed to quantify the changes occurring to the eyelid morphology in downward gaze and to define the average position, angle and contour of the eyelids in downward gaze. To accomplish this, a series of biometric anterior eye measurements were made (through the analysis of digital images) for 100 young subjects in three different directions of vertical gaze (primary gaze, 20° downgaze and 40° downgaze).
Accurate knowledge of the biometric dimensions of the anterior eye and adnexae is important for a variety of other clinical and research applications.
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Some examples of these applications include the diagnosis and management of various ocular pathologies and abnormalities, ocular surgery, the design and fitting of contact lenses and the measurement of eye growth. Age, gender and ethnic background may also influence the expected normal values of these biometric eye measures.
Ethnic background is an important factor in determining the appearance of the palpebral fissure. For example, Asian eyes typically differ in appearance to Caucasian eyes. Anatomical studies of the eyelids have shown Asian eyelids to be thickened (due to extension of orbital fat into the eyelids), with a poorly developed eyelid crease (or in some cases no eyelid crease) in both the upper and lower eyelids compared to Caucasian eyelids (Doxanas and
Anderson 1984, Lim et al 2004). Subjects of Asian ethnic origin have also been shown to exhibit slightly smaller corneas, smaller palpebral apertures and more angled palpebral fissures than those of Caucasian ethnic origin
(Lam and Loran 1991, Hanada et al 2001).
The appearance of the palpebral fissure may also be influenced by age and gender. Significant and complex changes have been found to occur in the palpebral fissure in infancy (Paiva et al 2001). Paiva et al (2001) found rapid changes to occur in palpebral fissure measurements from birth to 48 months of age, with many measurements approaching adult levels within the first 1-2 years of life. In adult subjects, significant changes to the palpebral fissure occur with increasing age. A general increase in the laxity of the eyelids has been found in subjects over the age of 50 (Hill 1975, Vihlen and Wilson 1983,
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Shore 1985). This increased laxity leads to a shortening of the horizontal eyelid fissure (Hill 1975, Van den Bosch et al 1999) and sagging of the lower eyelid (Shore 1985, Van den Bosch et al 1999). Van den Bosch et al (1999) reported their male subjects to exhibit wider horizontal eyelid fissures (by approximately 0.7 mm) than their female subjects.
The accurate assessment of biometric anterior eye measures is important for the diagnosis and management of anterior eye malformations such as microophthalmos, megalocornea and conditions such as congenital glaucoma (Ho and Walton 2004, Bartke et al 2000, Kwok 1990). The diagnosis and appropriate surgical correction of abnormalities of lid position such as eyelid retraction and blepharoptosis also depend upon accurate biometric measures of the eyelids and the relation between the eyelids and the globe (Small and Meyer 2004, Boboridis et al 2001, Souza et al 2000,
Meyer and Rheeman 1995, Cartwright et al 1994, Beard1981). A range of biometric measures such as eyelid position and eyelid contour are also important for assessing post-operative outcomes following eyelid surgery
(Shore 1996). Attaining a “normal” eyelid position, smooth contour and symmetry between the two eyes following surgery are important factors for achieving a good surgical result (Beard 1981, Shore 1996).
Palpebral fissure morphology also has the potential to influence contact lens fitting. Carney et al (1997a) found that the position of the eyelids can influence rigid contact lens centration and stability. The position and angle of the eyelids has also been shown to effect soft toric contact lens orientation
125 Chapter 3 and stability (Waldron 1984, Young et al 2002). Alternating vision bifocal contact lenses rely upon the movement of the lens upwards (in relation to the pupil) in downgaze so that the line of sight is directed through the near segment of the contact lens (Borish and Perrigin 1987, Borish 1988).
Success with these lenses will be influenced by the position of the eyelids and their interaction with the lens in downgaze.
While there is a range of information in the literature about the average biometric measures of the eye and adnexae in primary gaze, there is less information about these dimensions in downward gaze. Stoller and Meyer
(1994) investigated the change in upper eyelid position that occurs in downgaze. A significant reduction in vertical inter-palpebral fissure of approximately 2.3 mm was noted in downgaze. Guimaraes and Cruz (1995) found the vertical palpebral aperture to decrease linearly as a function of downward gaze angle (a decrease of palpebral aperture of 1.36 mm per 10° of downward gaze was reported). These studies have only reported upon the changes in the vertical dimensions of the palpebral fissure with downward gaze.
Further detailed investigation of the palpebral fissure in downward gaze is important since a large proportion of visual tasks occur in varying degrees of downward gaze (e.g. reading, walking, eating, and computer work). The aim of this study was therefore to establish normative data for a range of biometric measures of the anterior eye structures for a population of young
126 Chapter 3 subjects with a normal range of refractive errors in primary gaze, and in two different angles of downward vertical gaze.
3.2 Methods
3.2.1 Subjects and procedures
Digital images of the anterior eye and adnexae from 100 young adult subjects were captured. The subjects ranged in age from 18 to 35 years, with a mean age of 24 years. Fifty nine of the 100 subjects were female. All subjects had normal ocular health, were free of any ocular disease or systemic disease or syndrome that may alter anterior eye appearance, and had no history of any ocular or eyelid surgery. Each subject underwent an initial slit lamp examination to rule out any anterior eye pathology. The subjects had a range of refractive errors, with the mean best sphere refractive error being -1.14 D (range +0.63 D to -8.13 D). No rigid gas permeable contact lens wearers were included in the study because there is evidence that long term rigid contact lens wear can lead to a slight ptosis
(Van den Bosch and Lemij 1992, Fonn et al 1996, Jupiter and Karesh 1999,
Thean and McNabb 2004). Nine of the subjects were occasional soft contact lens wearers.
The subjects also had different ethnic backgrounds. Eighty of the 100 subjects were of Caucasian ethnic background and 20 were of various East
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Asian ethnic backgrounds (including subjects from China, Japan, Korea,
Malaysia and Vietnam). The images from 4 subjects were excluded completely from the analysis, due to poor image quality. Of the 96 subjects included in the final analysis, 76 were of Caucasian ethnic origin and 20 were of East Asian ethnic origin. Approval from the Queensland University of
Technology human research ethics committee was obtained prior to commencement of the study and informed consent was obtained from all of the subjects.
High resolution digital images of the anterior eye were captured using a
Canon 300D 6.3 megapixel Digital SLR Camera (Canon Inc Tokyo, Japan) with a 100 mm macro lens. As a subject’s level of fatigue or alertness may cause variations in eyelid position (Small et al 1989), all digital images were captured in the morning. The digital images were all taken in the same room, with the same ambient room lighting conditions for each subject. The room lighting was provided by standard fluorescent lights giving an approximate illuminance at the plane of the subject’s eye of 300 lux. The camera’s built-in flash was used for all images and the camera was positioned at a distance of approximately 500 mm from the subject. Lam et al (1995) have reported that palpebral fissure asymmetry between the right and left eye is uncommon for subjects in primary gaze. Therefore, only the right eye image of each subject was acquired and analysed.
Prior to the experiment, a pilot study was carried out with 5 subjects to examine the effect of the use of a head rest on palpebral fissure
128 Chapter 3 measurements. Images were taken in primary gaze and in downward gaze with and without the use of a headrest. For primary gaze there was very little difference between the images taken with, and without the headrest. The mean vertical palpebral aperture width in primary gaze was 10.73 mm with the head rest, and 10.81 mm without. In downward gaze, the vertical palpebral aperture widths were found to be narrower in the head rest condition. The mean vertical palpebral aperture width at 40° downgaze was
5.51 mm with a head rest and 7.65 mm without. This difference was due to the slight downward head tilt that subjects naturally adopted in downward gaze (which is prevented through the use of a head rest). On average, the subjects were found to employ a downward head tilt of approximately 15° to view an object 40° below the horizontal.
A camera mount was constructed for capturing the images of the eye in three vertical directions of gaze (0°, 20° and 40° below horizontal). The camera mount consisted of a counter weighted, metal arm attached to a tripod. The camera was fixed to one end of the metal arm. The swivelling tripod head thus allowed the camera to be moved downwards in an arc for capturing the downgaze images. The head of the tripod also had a protractor which allowed for accurate determination of the angle at which the camera was located with respect to horizontal. A calibration cross was attached to the tripod and positioned at the centre of rotation of the tripod head. Figure 3.1 shows the camera apparatus used in the study.
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Figure 3.1: Camera set-up for capturing images of the anterior eye in three different directions of vertical gaze.
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For each subject, digital images were taken in the frontal plane. Images were captured in primary gaze (0°), in 20° downgaze and in 40° downgaze.
Prior to image capture, care was taken to make sure that the camera was level, thus ensuring the accuracy of the angles measured in the digital images. The subject was positioned such that their right eye was directly adjacent to the calibration cross. The camera was then aligned so that its central focus point was directly in line with the subject’s right eye for capture of the primary gaze image. This setup ensured that for the primary gaze image, the subject’s eye was level horizontally with the centre of the camera and the camera was perpendicular to the frontal plane of the eye. To capture the downgaze images, the camera was then moved down in an arc to be at
20° and then 40° below horizontal. As the subject was positioned at the centre of rotation of this arc (i.e. directly adjacent to the calibration cross), the camera maintained the same alignment with the subject in all angles of gaze.
For all images, the subject was instructed to maintain natural posture and to fixate upon the centre of the camera’s lens (i.e. the fixation target for all images was the centre of the camera lens).
In our protocol, we aimed to capture the position of the eye and eyelids that our subjects would naturally assume in a variety of downgaze visual tasks.
We therefore attempted to ensure that the measurement conditions were as natural as possible. To make these conditions as close to the subject’s normal environment, each image was captured in ‘free space’ and subjects were instructed to maintain their natural posture (i.e. we did not use a chin or head rest for capturing the images). Kroemer and Hill (1986) suggested that
131 Chapter 3 subjects achieved downgaze viewing through a combination of eye and head movement. For a 40° downgaze task, they suggest that a head tilt of 10-15° occurs. Hill et al (2005) also found that subjects naturally held a book at approximately 43° below the eyes and tilted their head by approximately 17°, in combination with a downward movement of the eyes to view the book.
Therefore most subjects will naturally tilt their head slightly downward for the
20° and 40° downward gaze conditions. This slight head tilt was confirmed in our pilot study.
Occupational health and safety experts typically recommend the optimum placement of a computer screen to be approximately 15-20° below horizontal
(North 1993, Turville et al 1998). It has also been established that the preferred viewing zone for near tasks typically ranges from 20-60° below the horizontal (i.e. a range from 20-60° below the horizontal, with an average preferred viewing angle of 40° below horizontal) (Kroemer and Hill 1986).
Therefore, to simulate a range of typical downgaze viewing positions, we placed our fixation target (the camera) at 20° and 40° below the horizontal and allowed subjects to assume their natural head and eye position for viewing the target.
To account for any normal variations occurring in the palpebral aperture of each subject, three images were taken for each angle of gaze. A total of 9 images were therefore captured for each subject. After image capture, each image was examined using the camera’s inbuilt liquid crystal display and any image displaying poor focus, or any obvious errors (e.g. a picture that was
132 Chapter 3 captured mid-blink) were discarded. This left a total of 766 images from the
96 subjects included in the analysis (i.e. an average of 2.7 images per angle of gaze for each subject).
3.2.2 Data analysis
Each digital image was analysed using custom written software that provides a range of biometric measures of the anterior eye and adnexae (Iskander et al 2004). This program enables the user to locate the Cartesian coordinates of a number of different anterior eye landmarks including the limbus (16 points), pupil (eight points), temporal and nasal canthi (one point at each canthus) and the upper and lower eyelid contour (eight points along each lid margin). Based upon the coordinates of these locations, the program then calculates a range of palpebral fissure biometric parameters. Figure 3.2 and
Table 3.1 illustrate the range of anterior eye parameters investigated.
A calibration ruler consisting of two crosses separated by 25 mm was included directly beside the eye in all images for scaling purposes. The average scaling factor from all images analysed was 28.1 pixels per mm (i.e. each pixel was 35.6 microns in width).
To quantify the eyelid contour, a second order polynomial function was fitted to the coordinates derived from the upper and lower eyelid margins.
Malbouisson et al (2000) found that a polynomial function of the form
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Figure 3.2: Palpebral fissure biometric measurements on a typical digital image. All measurements are taken in millimetres and all angles are measured in degrees. Parameters are listed in Table 3.1
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Table 3.1: Definitions of the biometric measures of the palpebral fissure and
anterior eye. Abbreviations refer to those used in Figure 3.2.
ABBREVIATION EXPLANATION DEFINITION HEF Horizontal eyelid fissure The horizontal distance between the nasal and temporal canthi. NC_TC Nasal canthus to temporal The vertical distance between the nasal and temporal canthus (Positive value canthus means the nasal canthus is higher than the temporal canthus). PC_TC Pupil centre to temporal The horizontal distance from pupil centre to the temporal canthus. canthus HVID Horizontal visible iris diameter PD Pupil diameter The mean of the major and minor diameters of the ellipse that best fit the pupil outline. LC_PC Limbus centre to pupil centre The horizontal (x) and vertical (y) distance from the centre of the limbus to the centre of the pupil. PC_UL Pupil centre to upper lid The vertical distance from pupil centre to the upper eyelid. PC_LL Pupil centre to lower lid The vertical distance from pupil centre to the lower eyelid. PA Palpebral aperture The vertical distance between the upper and lower lid as measured at pupil centre. INA Inferior nasal aperture Vertical distance from nasal canthus to the lower eyelid. STA Superior temporal aperture Vertical distance from temporal canthus to the upper eyelid. Theta HEF Theta horizontal eyelid fissure The angle between the temporal and nasal canthus (a positive angle indicates the nasal canthus is higher than the temporal canthus). Theta_UL Theta upper lid The angle between the line joining the two points where the upper lid intersects the limbus, and the horizontal (a positive angle indicates that the nasal portion of the central upper eyelid is higher than the temporal portion of the central upper eyelid). Theta_LL Theta lower lid The angle made between the line joining the two points where the lower lid intersects the limbus and the horizontal (positive angle indicates the nasal portion of the central lower eyelid is higher than the temporal portion of the central lower eyelid). Theta_Head Theta horizontal head tilt The angle made between the line joining the nasal canthus of the right eye and the nasal canthus of the left eye and horizontal (a positive angle indicates a head tilt towards the right side and a negative angle indicates a head tilt to the left side).
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Y = AX2 + BX +C provides a reasonable fit to the contour of the upper and lower eyelids in two dimensional images of the frontal view of the eye. They found that fit errors were reduced if only the ciliated portions of the eyelid contour were included in the contour fitting (i.e. when the nasal canthal portion was excluded). Therefore to provide the most accurate fit to the upper and lower eyelid contours in our data, we have only fitted the central portion of the upper and lower eyelid contour (i.e. our fitting excluded the canthal regions). The length of the eyelid margin that was typically fitted extended from approximately 2 mm beyond the width of the HVID nasally and temporally on the upper and lower eyelid. The centre of the coordinate system for this polynomial function was the limbus centre. Figure 3.3 illustrates the eyelid contour fitting and the length of eyelid margin typically fitted in our analysis.
All digital images were analysed by two different observers. The independent results for each anterior eye parameter from each observer were subsequently compared. Any image where the difference between the results of the two observers was three standard deviations away from the mean difference between the two observers was identified as an outlier. All outlying images were then re-analysed by a third observer and the two results (out of the three observers) that were closest to each other were then used for subsequent analysis. The mean of the results from the two observers was then used as the mean measurement for each image. The results from the two observers were found to be correlated very closely.
Linear regression analysis comparing the results of the two observers for all
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Figure 3.3: Example of polynomial fitting to the eyelid contour. A second order polynomial of the form Y = AX2 + BX + C is fitted to the central upper and lower eyelid contour. The centre of the coordinate system for the polynomial is the limbus centre. Each gradation on the horizontal and vertical axes represents one millimetre.
137 Chapter 3 of the biometric measures for all subjects revealed an average coefficient of determination (r2) of 0.91 ± 0.15 and an average linear regression slope of
0.96 ± 0.11. The third observer was used to analyse 13% of the total images. Figure 3.4 illustrates the comparison between the two observers for the Theta_HEF measurement for all images analysed.
This mean measurement for each subject in each angle of gaze was then used to calculate the group mean and standard deviation of each measurement for primary gaze, 20° and 40° downgaze. The group mean data were analysed using a repeated measures analysis of variance, with one within-subject effect (angle of gaze) and two between-subject effects (i.e. gender and ethnicity).
3.3 Results
A number of highly significant changes were found to occur in the biometric measures of the palpebral fissure in downgaze. The group mean and standard deviation values for the various biometric measures in primary gaze and 20° and 40° downgaze for the 76 Caucasian subjects and 20 Asian subjects are displayed in Table 3.2. Repeated measures analysis of variance revealed that the changes occurring with downgaze for all of the measurements (except for the horizontal head tilt measure) in Table 3.2 were highly statistically significant (p<0.001 for the within-subjects effect of angle of gaze). The change in the horizontal head tilt measure (Theta_Head) with
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Figure 3.4: Example of the comparison between the two observers for the analysis of the digital images (comparison for Theta_HEF measure is shown). Graph A shows excellent agreement for the Theta_HEF results between the two observers (r2 = 0.99). Perfect agreement would mean all points lie on the dashed line. Graph B shows the difference between the results of the two observers plotted against the mean of their results. Any images where the agreement between the two observers was outside of three standard deviations of the mean difference between the two observers (outside the dashed line) were analysed by the third observer.
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Table 3.2: Group mean biometric palpebral fissure measurements. All
measurements are for the right eye and are expressed in millimetres and all
angles are expressed in degrees. Repeated measures analysis of variance
showed that all of the measurements exhibited highly significant change as a
function of angle of gaze (all p< 0.001), except for Theta Head (p = 0.012).
CAUCASIAN SUBJECTS (N = 76) ASIAN SUBJECTS (N = 20)
Primary Gaze 20° Downgaze 40° Downgaze Primary Gaze 20° Downgaze 40° Downgaze
Dimension Mean SD Mean SD Mean SD Mean SD Mean SD Mean SD
HEF 27.133 1.508 26.872 1.493 25.621 1.801 24.836 1.746 24.986 1.671 24.005 1.950 NC_TC -1.747 1.813 1.640 1.779 4.008 1.763 -2.547 1.211 0.607 1.637 2.954 2.030 Theta_HEF -3.706 3.850 3.497 3.777 8.912 3.896 -5.821 2.762 1.437 3.829 7.040 4.973 PC_TC 12.075 0.577 11.670 0.619 10.958 0.803 12.225 0.652 12.025 0.757 11.445 0.772 LC_PC x 0.261 0.097 0.269 0.097 0.254 0.103 0.211 0.114 0.233 0.102 0.216 0.094 y 0.097 0.127 0.130 0.114 0.158 0.127 0.142 0.137 0.162 0.123 0.214 0.139 PC_UL 3.536 0.827 3.222 0.878 3.026 0.825 3.169 0.553 2.909 0.606 2.423 0.573 PC_LL -6.132 0.576 -4.711 0.592 -3.388 0.826 -6.309 0.677 -5.085 0.618 -3.861 0.786 PA 9.668 1.180 7.933 1.209 6.415 1.141 9.476 0.884 7.994 0.845 6.284 0.971 INA 2.471 1.057 3.446 1.062 4.174 1.220 1.947 0.621 2.894 0.931 3.769 1.117 STA 5.458 1.128 6.127 1.190 6.250 1.233 4.984 0.763 5.706 0.967 5.469 1.302 A Upper -0.032 0.004 -0.031 0.004 -0.031 0.004 -0.033 0.006 -0.033 0.004 -0.030 0.005 curve B Lid 0.001 0.068 0.100 0.069 0.191 0.067 -0.057 0.056 0.034 0.063 0.114 0.077 tilt C 3.635 0.857 3.329 0.870 3.138 0.793 3.325 0.563 3.067 0.634 2.616 0.596 height A Lower 0.023 0.003 0.021 0.004 0.018 0.005 0.024 0.003 0.022 0.004 0.021 0.005 curve B Lid 0.062 0.057 0.115 0.060 0.166 0.067 0.061 0.056 0.095 0.062 0.137 0.073 Tilt C -6.053 0.566 -4.613 0.590 -3.273 0.793 -6.182 0.697 -4.947 0.626 -3.679 0.742 height
Theta_UL -0.910 3.968 4.729 3.969 9.881 3.739 -4.058 3.365 1.066 3.799 5.738 4.404
Theta_LL 4.234 3.229 7.155 3.311 9.893 3.673 4.008 3.180 5.948 3.479 8.257 4.134
Theta_Head 0.507 2.192 0.773 2.492 1.097 2.762 1.710 1.860 2.352 2.431 2.756 2.924
140 Chapter 3 downgaze also just reached statistical significance (p = 0.012). As the majority of subjects in the study were of Caucasian ethnic origin, the results from these subjects will be presented first, followed by a separate section outlining the differences found between the Asian and Caucasian population.
3.3.1 Caucasian population
The palpebral fissure underwent a number of significant changes in downgaze. Figure 3.5 illustrates diagrammatically, the mean biometric palpebral fissure and anterior eye measures from Table 3.2 for the 76
Caucasian subjects in primary gaze, 20° downgaze and 40° downgaze.
Figure 3.5 also displays the individual primary gaze, 20° and 40° downgaze images from a typical Caucasian subject (Subject 43).
In primary gaze, the mean horizontal fissure length (HEF) was 27.13 ± 1.5 mm, with a mean palpebral fissure angle (Theta_HEF) of -3.71 ± 3.9° indicating on average, a slight up-slanting of the palpebral fissure in primary gaze. Up-slanting means that the temporal canthus is higher than the nasal canthus. In downgaze, the horizontal fissure length (HEF) gradually shortened to a mean of 25.62 ± 1.8 mm and the angle of the fissure changed to a mean of 8.91 ± 3.9° down-slanted for 40° downgaze. As would be expected from these results, the vertical distance between the nasal and temporal canthi (NC_TC) changed from a mean of -1.75 ± 1.8 mm in primary gaze (i.e. temporal canthus was 1.75 mm higher than the nasal canthus in
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Figure 3.5: Diagrammatic representation of the mean biometric palpebral fissure dimensions for the right eye of the 76 Caucasian subjects (left) and an example of primary gaze, 20° downgaze, and 40° downgaze images from the right eye of a typical male Caucasian subject (subject 43) (right).
142 Chapter 3 primary gaze) to a mean of 4.01 ± 1.8 mm (i.e. temporal canthus is 4.01 mm lower than the nasal canthus) in 40° downgaze. The horizontal distance from the pupil centre to the temporal canthus (PC_TC) also slightly shortened from
12.08 ± 0.6 mm in primary gaze to 10.96 ± 0.8 mm in 40° downgaze. The mean horizontal head tilt (Theta_Head) was found to be 0.51 ± 2.1° (i.e. on average subjects tilted their heads very slightly towards the right). In downgaze, the group mean Theta_Head changed slightly to be 1.1 ± 2.8° in
40° downgaze. The average horizontal head tilt was small, but would lead to a slight underestimation of an upward slanting palpebral fissure, and a slight overestimation of a downward slanting palpebral fissure. In primary gaze, the average corrected palpebral fissure angle (i.e. taking into account the slight head tilt) was -4.2° upward slanted. The change in horizontal head tilt in downward gaze accounted for only 4.67% of the total change in the palpebral fissure angle (Theta_HEF) with downgaze.
The vertical palpebral aperture also underwent significant change. In primary gaze the mean vertical distance from pupil centre to upper lid (PC_UL) measured at 3.54 ± 0.8 mm and the mean distance from pupil centre to lower lid (PC_LL) was -6.13 ± 0.6 mm (total PA of 9.67 ± 1.2 mm). In downgaze the upper lid moved downwards slightly with mean PC_UL of 3.22 ± 0.9 mm and 3.03 ± 0.8 mm for the 20° and 40° downgaze positions respectively. A larger movement was found to occur in the lower lid in downgaze with respect to pupil centre, with mean PC_LL of -4.71 ± 0.6 mm and -3.39 ± 0.8 mm for the 20° and 40° downgaze positions respectively. This was a change in upper lid position of 0.5 mm and a change in lower lid position of 2.7 mm
143 Chapter 3 from the primary gaze to the 40° downgaze position. This equated to a total vertical palpebral aperture (PA) reduction from 9.67 mm in primary gaze to
6.41 mm in 40° downgaze.
The inferior nasal aperture (INA) measurement significantly increased from
2.47 ± 1.1 mm in primary gaze, to 4.17 ± 1.2 mm in 40° downgaze. This indicated a lowering of the bottom eyelid in relation to the nasal canthus in downgaze. The superior temporal aperture (STA) measurement also significantly increased in downgaze (from a mean of 5.46 ± 1.1 mm in primary gaze to a mean of 6.25 ± 1.2 mm in 40° downgaze). This suggested that the temporal canthus was moving downwards in relation to the upper lid in downgaze.
The eyelid contour was quantified by fitting a polynomial function of the form
Y = AX2 + BX +C to the contour of the upper and lower eyelid. In this polynomial, the coefficient “A” refers to the curvature of the eyelid
(Malbouisson et al 2000). The larger the magnitude of “A” the steeper the curve of the contour, with the upper lid having a negative curve and the lower lid having a positive curve. The term “B” (slope term) refers to the tilt or angle of the eyelid. The larger the magnitude of “B”, the more angled the lid, with a positive tilt indicating a tilt downward towards the temporal side. The constant term “C” (intercept term) refers to the height of the eyelid above or below the corneal geometric centre.
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The contours of both the upper and lower eyelid were found to undergo significant changes in downgaze. The curvature of the eyelid (term “A”) was found to flatten significantly (reduction in magnitude of term “A”) in downgaze for both the upper and lower eyelids. The angle of the upper lid also changed from being close to horizontal in primary gaze (term “B” = 0.001 ±
0.07) to being angled slightly downward (term “B” = 0.191 ± 0.07 in 40° downgaze) in the downgaze positions. The angle of the lower lid changed similarly, being close to horizontal (“B” = 0.062 ± 0.06) in primary gaze and slightly down-slanted in downgaze (“B” = 0.1661 ± 0.07). The constant term
“C” also changed significantly. The changes in this term revealed the upper lid to move down from 3.64 ± 0.9 mm from limbus centre in primary gaze to
3.14 ± 0.8 mm in 40° downgaze. The lower lid was found to move from -6.05
± 0.6 mm in primary gaze to -3.3 ± 0.8 mm below limbus centre in 40° downgaze. This is a similar change to that observed in the PC_UL and
PC_LL measurements.
The angles of the central upper eyelid (Theta_UL) and the central lower eyelid (Theta_LL) are similar measurements to that given by the eyelid contour term “B” for the upper and lower eyelid. However as Theta_UL and
Theta_LL refer to the angle of the central lid, where the lid intersects the cornea, slight differences were found between the two results. The central upper lid was slightly up-slanted in primary gaze (-0.91 ± 4.0°) and changed to being slightly down-slanted in 40° downgaze (9.88 ± 3.7°). The central lower lid was observed to be slightly down-slanted in primary gaze (4.23 ±
3.2°) and moved to be further down-slanted in 40° downgaze (9.89 ± 3.7°).
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The average horizontal visible iris diameter (HVID) for all Caucasian subjects across all measurement conditions was found to be 11.92 ± 0.4 mm.
3.3.2 Difference associated with gender
The results from the repeated measures ANOVA for between-subject effects and within-subject interactions are shown in Table 3.3.
Male and female subjects were found to exhibit a highly significant difference in only one of the palpebral fissure measures. The horizontal palpebral fissure length (HEF) was significantly larger in male subjects (mean across all conditions of 26.75 ± 1.7 mm) compared to female (25.70 ± 1.9 mm) subjects across all conditions (p = 0.001). The difference between the horizontal head tilt (Theta_Head) between males and females also just reached statistical significance (p = 0.0239), with females exhibiting a slightly greater head tilt to the right side.
There were significant angle of gaze and gender interactions for three measures. These measures were PC_LL, PA and lower eyelid contour term
“C”. These interactions were brought about by the female lower eyelid being slightly further from pupil centre than the male lower eyelid in the 40 degrees downgaze position by approximately 0.1 mm (in the other angles of gaze the male lower eyelid was sightly further from pupil centre than the female lower eyelid by approximately 0.1 mm). In other words, the female lower eyelid
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Table 3.3 Results of repeated measures ANOVA. Between-subject effects
and within-subject interactions are shown. P value of the F statistic is
displayed.
BETWEEN-SUBJECT EFFECTS WITHIN-SUBJECT INTERACTIONS
Downgaze Downgaze Downgaze Angle* Gender* Gender Ethnicity angle* angle* Gender* Ethnicity gender ethnicity Ethnicity
Dimension p-value p-value p-value p-value p-value p-value
HEF 0.001** <0.001 ** 0.178 0.620 0.036* 0.745
NC_TC 0.658 0.021* 0.644 0.415 0.512 0.633
Theta HEF 0.579 0.025* 0.631 0.718 0.816 0.542
HVID 0.404 <0.001** 0.875 0.087 0.472 0.537
PC_TC 0.303 0.016* 0.660 0.536 0.183 0.321
LC_PC X 0.400 0.179 0.220 0.420 0.080 0.105
Y 0.079 0.273 0.248 0.099 0.384 0.123
PC_UL 0.588 0.035* 0.832 0.561 0.069 0.260
PC_LL 0.658 0.039* 1.000 0.016* 0.090 0.800
PA 0.532 0.818 0.887 0.011* 0.272 0.223
INA 0.431 0.033* 0.379 0.439 0.533 0.528
STA 0.517 0.071 0.807 0.561 0.051 0.363 A 0.163 0.643 0.983 0.446 0.002** 0.513 curve B Upper Lid 0.251 <0.001** 0.729 0.528 0.173 0.272 tilt C 0.801 0.063 0.970 0.754 0.131 0.453 height A 0.067 0.142 0.485 0.967 0.005** 0.772 curve B Lower Lid 0.196 0.194 0.552 0.771 0.003** 0.542 tilt C 0.450 0.059 0.821 0.004** 0.144 0.596 height Theta UL 0.278 <0.001** 0.656 0.527 0.194 0.285
Theta LL 0.190 0.168 0.583 0.747 0.006** 0.528
0.241 0.577 0.472 Theta Head 0.024* 0.031* 0.438
** = p < 0.01 * = p < 0.05
147 Chapter 3 showed slightly less change (narrowing) than the male eyelid in the 40° downgaze position.
3.3.3 Difference associated with ethnicity
A number of biometric measures showed significant differences between subjects of Asian and Caucasian ethnic origins (Table 3.3). The main differences found between the two ethnic groups can be summarised by differences in three main areas: the horizontal size of the eye, the vertical palpebral fissure and the angle of the palpebral fissure.
The Asian subjects exhibited significantly smaller horizontal eye measures than the Caucasians. The Asian subject’s horizontal palpebral fissure length
(HEF) (24.61 ± 1.8 mm averaged across all measurement conditions) was significantly smaller than the Caucasian subject’s (26.54 ± 1.7 mm averaged across all measurement conditions, p < 0.001). The horizontal visible iris diameter (HVID) in Asian subjects (11.35 ± 0.3 mm) was also significantly smaller than that of the Caucasian subjects (11.92 ± 0.4 mm, p < 0.001).
The vertical aperture width also differed between the two ethnic groups. The distance from pupil centre to upper lid (PC_UL) was significantly smaller in the Asian subjects (2.83 ± 0.7 mm) compared to the Caucasian subjects
(3.26 ± 0.9 mm, p = 0.04). However, the distance from pupil centre to lower lid (PC_LL) was also significantly larger in the Asian subjects (-5.09 ± 1.2 mm) compared to the Caucasian subjects (-4.74 ± 1.3 mm, p = 0.04). This
148 Chapter 3 led to there being no significant difference in the total vertical palpebral aperture width (PA) between the two ethnic groups (mean Asian 7.90 ± 1.6 mm, mean Caucasian 7.98 ± 1.8 mm, p = 0.84). The inferior nasal aperture
(INA) measure was found to be significantly smaller in the Asian subjects also (mean Asian 2.87 ± 1.2 mm, mean Caucasian 3.36 ± 1.3 mm, p = 0.04), due to the Caucasian palpebral fissure being on average more down-slanted, leading to the lower eyelid sitting further below the nasal canthus in the
Caucasian subjects.
The angle of the palpebral fissure was found to be significantly more up- slanted in the Asian subjects in comparison to the Caucasian subjects across all conditions. This manifested itself as significant differences in the vertical distance from the nasal canthus to the temporal canthus (NC_TC: Asian 0.34
± 2.8 mm, Caucasian 1.30 ± 3.0 mm, p = 0.02), angle of the palpebral fissure
(Theta_HEF: Asian 0.90 ± 6.6°, Caucasian 2.90 ± 6.4°, p = 0.03), upper lid contour term “B” (Asian 0.030 ± 0.1, Caucasian 0.097 ± 0.1, p < 0.001) and the angle of the central upper eyelid (Theta_UL: Asian 0.92 ± 5.6°,
Caucasian 4.57 ± 5.9°, p < 0.001). The Asian eyelids/palpebral fissure on average were more up-slanted in primary gaze (Theta_HEF -5.82 ± 2.8°,
Theta_UL -4.1 ± 3.4° in primary gaze) than the Caucasian eyelids/palpebral fissure (Theta_HEF -3.71 ± 3.9°, Theta_UL -0.91 ± 4.0°), and also remained more up-slanted in downgaze.
The horizontal head tilt (Theta_Head) was also slightly greater in the Asian subjects than the Caucasian subjects (p = 0.031). The Asian subjects
149 Chapter 3 exhibited a slightly greater head tilt to the right than the Caucasian subjects by on average 1.5°. This slight horizontal head tilt to the right also caused a slight underestimation of an upward slanting palpebral fissure angle and a slight overestimation of a downward slanting palpebral fissure. Therefore the corrected Theta_HEF for the Asian subjects in primary gaze (i.e. taking into account the 1.7° head tilt to the right) was -7.53° upward slanting. The change in horizontal head tilt (Theta_Head) with downward gaze accounted for only of 8.13% of the total change in palpebral fissure angle (Theta_HEF) with downgaze.
A number of the anterior eye biometric measures displayed significant ethnicity and angle of gaze interactions. These interactions were brought about by the rates of change in the HEF, the upper and lower eyelid curvature and the lower eyelid angle being slightly greater with downward gaze for the Caucasian subjects (i.e. the Caucasian subjects showed greater change in these measures with downward gaze).
There were no significant gender and ethnicity interactions and also no significant angle of gaze and gender and ethnicity interactions.
3.4 Discussion
We have shown that highly significant changes occur in many of the dimensions of the palpebral fissure in downward gaze. These changes
150 Chapter 3 caused significant alterations to the vertical and horizontal palpebral fissure dimensions, the eyelid contour and the angles of the upper and lower eyelids.
In general, the palpebral fissure narrowed, with the upper lid moving slightly downwards (by 0.5 mm on average) and the lower eyelid moving upwards
(by 2.7 mm on average) in relation to the pupil centre. The angle of the palpebral fissure changes from on average being slightly up-slanted in primary gaze to being slightly down-slanted in downward gaze positions.
In 2003, Cook et al demonstrated that significant changes to the position of the temporal and nasal canthi occur with horizontal gaze shifts (i.e. they showed that the medial and temporal canthi can move). We have similarly shown that significant changes in position of the canthi (and numerous other palpebral landmarks) occur with vertical shifts in gaze. This highlights the fact that the canthi, and in fact the entire palpebral fissure is dynamic and changes significantly with changes in gaze. Our findings further enforce the view that the dynamic changes in the canthi should be taken into account in anterior eye surgery, and also show that the dynamic changes in eyelid position and contour with vertical gaze should also be considered in eyelid surgery. Eyelid surgery should aim to restore normal eyelid position and contour in primary gaze, but should also aim to maintain the normal eyelid position in downward gaze and to preserve the dynamics of the eyelids in different angles and positions of gaze.
Evinger et al (1991) investigated the mechanisms of upper eyelid movement occurring in blinking and with downward gaze. They found that the
151 Chapter 3 downward movement of the upper lid during a blink is caused by contraction of the orbicularis oculi muscle, and relaxation of the levator palpebrae muscle. However, the movement of the upper lid in downward gaze (referred to as a lid saccade) was caused primarily by a relaxation of the levator muscle and passive downward force (i.e. the orbicularis muscle has very little involvement in the movement of the eyelids in downward gaze). Further research is required to fully quantify the changes occurring in eyelid position, angle and contour during blinking, but one may expect that as different muscles are involved in the blink mechanisms, that some subtle differences may be found between the changes occurring in downward gaze and the changes accompanying a normal blink.
There have been a number of previous investigations that have reported population average values for a range of the palpebral fissure dimensions that have been reported in our study. The majority of these studies have investigated subjects of Caucasian ethnic origin in primary gaze and have used a range of different measurement techniques. As the age of subjects may influence the anterior eye dimensions, we have tried where possible to make comparisons with studies that have investigated similar age groups to our study. A summary of the results from previous studies and comparison to our present study is presented in Table 3.4.
A number of studies have measured the horizontal length of the palpebral fissure (HEF) and have presented average results (ranging from 26.1 to 28.4 mm) that are close to our mean value for Caucasian subjects in primary gaze
152 Chapter 3 of 27.1 ± 1.5 mm. The range of values reported in the literature for the angle of the palpebral fissure (Theta_HEF) also closely approximates the measure found in our Caucasian subjects in primary gaze of -3.71 ± 3.9°. The vertical distance between the temporal and nasal canthus (NC_TC) is dependant upon the length of the palpebral fissure (HEF) and the angle of the fissure
(Theta_HEF). Our average value of -1.8 ± 1.8 mm is also similar in magnitude to previous investigations of this measurement. The standard deviations associated with these dimensions of the palpebral fissure indicate that there is a relatively wide range of palpebral fissure lengths and angles in our population (the 95% confidence interval for HEF was 24-30 mm and for
Theta_HEF was +4.0 to -11.4°). Previous investigators have noted that a down-slanting palpebral fissure is rare (Fox 1966, Hanada et al 2001). We also found this to be the case, with only two out of the total 96 subjects exhibiting a down-slanting of the palpebral fissure in primary gaze of greater than 2 mm.
The palpebral fissure in the vertical dimension has also been investigated extensively for subjects in primary gaze as it is an important measure in the diagnosis of eyelid malpositions such as ptosis and lid retraction. Table 3.4 demonstrates that the average total vertical palpebral aperture width (PA) from previous studies ranges from 9.1 mm to 10.8 mm, which compares closely to our average value of 9.7 ± 1.2 mm in primary gaze.
The PA does not provide information regarding the position of the eyelids in relation to the globe. This information is provided by the pupil centre to upper
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Table 3.4: Summary of previous investigations into biometric measures of the palpebral fissure. All of the data presented are from subjects of Caucasian ethnic origin in primary gaze. Ages presented are either the range of ages tested or the mean age of the subject’s tested. If the study presented data from different age groups, then the data presented here is that which is closest in age to our present study. - indicates value not reported in study. * indicates that the average value was not reported, but estimated from a figure in the paper. The Theta_UL and Theta_LL in Young et al’s (2002) study were calculated based upon the angle at which the upper and lower eyelid intersected a contact lens on the eye, as opposed to the limbus as measured in our study.
MEAN BIOMETRIC EYE DIMENSIONS IN PRIMARY GAZE
T Upper Eyelid Lower Eyelid
AUTHORS AGE
A B C A B C L QUE curve tilt height curve tilt height a_ HEF a_UL a_L INA STA Thet Thet MEASUREMEN TECHNI SUBJECT N HEF NC_TC Thet HVID PC_UL PC_LL PA
Fox (1966) Ruler 0-93 1723 28 - - - - - 10 ------Hill (1975) Photograph 18-49 82 27.1 ------3.45 ------Frueh (1984) Ruler 15-44 57 - - - - 3.6 - 9.3 ------Lam and Loran (1991) Ruler 21.2 65 28.4 - - 11.7 - - 9.8 ------Van den Bosch + Lemij (1992) Photograph 35.6 50 - - - - 4.2 -5.8 10 ------Stoller + Meyer (1994) Photograph 24-82 50 - - - - 4.1 -5.8 9.9 ------Guimaraes + Cruz (1995) Ruler 15-76 25 - - - - 3.7 -5.4 9.11 ------Fonn et al (1996) Photograph 19-53 74 ------10.1 ------Cruz et al (1998) Digital Image 5-57 50 26.1 -2.6 -3.2 - 3.6 - - - - -0.035 ------+ Souza et al (2000) Van den Bosch et al (1999) Photograph 20-30 40 27.0 -2 - 11.9 3.8* -5.2* ------Malbouisson et al (2000) Digital Image 10-60 110 ------0.037 - - 0.029 - - - - Hanada et al (2001) Digital Image 14-60 38 - - -4.6 ------Young et al (2002) Digital Image - 42 - - -3 11.6 - - 9.53 2.98 5.45 ------2.7 2.9 Lin et al (2003) Ruler 22.5 41 ------10.8 ------Buehren et al (2005) Digital Image 22.5 40 - - - 12.1 4.2 -6.4 10.4 ------Our Study (2005) Digital Image 18-35 76 27.1 -1.8 -3.7 11.9 3.5 -6.1 9.7 2.5 5.5 -0.032 0.0008 3.63 0.023 0.062 -6.05 -0.9 4.2
154 Chapter 3 lid (PC_UL) and pupil centre to lower lid (PC_LL) measurements. Our group mean measurement for the PC_UL for the Caucasian subjects in primary gaze of 3.5 ± 0.9 mm is fractionally lower than the majority of previous studies. However, this value is still within a half a millimetre of the mean of the majority of other studies and corresponds exactly with the “normal value” of PC_UL of 3.5 mm quoted by Small et al in their 1989 review of palpebral fissure measurements. Our PC_LL measurement is also relatively close to the results from previous studies.
Previous studies have shown a relatively wide range of “normal” average values for palpebral fissure measurements in the vertical dimension, reflecting the range of different measurement techniques used (from the simple measurement with a ruler in front of the eye to more sophisticated digital image analysis techniques), the different ages of subjects tested and experimental protocols used (e.g. head in a head rest, head in ’free space’).
These differences in methodology might be expected to give slightly different measures for the palpebral aperture in the vertical dimension.
One possible confounding factor in the vertical palpebral fissure dimension in our study was the refractive error of the subjects tested. Our population had a range of refractive errors, and to enable an unobstructed and unmagnified view of the palpebral fissure in each image, no refractive correction was worn when the digital images were taken. Therefore, some degree of blur of the fixation target would be present for some subjects (22 of our subjects had greater than -2 D best sphere refractive error). Subjects may therefore have
155 Chapter 3 narrowed their palpebral aperture in an attempt to reduce the blur of the fixation target. If this was happening for a significant number of subjects then one may expect there to be a correlation between the spherical refractive error and the vertical palpebral aperture width (PA). However no significant correlation was found between the PA and the spherical refractive error for any of the downgaze angles.
Some previous studies have defined ptosis as when the upper eyelid is less than 2 mm from the centre of the pupil (Beard 1981, Small et al 1989, Meyer and Rheeman 1995). If we consider the lower 95% confidence interval for the pupil centre to upper lid (PC_UL) measurement in our present study, then
97.5 % of the population would be expected to have a PC_UL measurement of greater than 1.9 mm. If we use this measurement (i.e. PC_UL of less than
1.9 mm) as an approximate definition for ptosis it can be seen that this compares very closely to the definitions of ptosis in the literature.
Whilst the vertical and horizontal measures of the eyelid and palpebral fissure provide information regarding the position of the lids in relation to one another and surrounding structures, they do not provide information regarding the contour of the eyelids. To fully quantify the appearance of the eye and eyelids, an assessment of eyelid contour is required. Previous investigators have also investigated eyelid contour by fitting a polynomial function to the lid. Malbouisson et al (2000) found an average polynomial term “A” of -0.037 and 0.029 for the upper and lower eyelid respectively for their group of 110 subjects. This compared closely to our population
156 Chapter 3 averages for the Caucasian subjects in primary gaze of -0.032 and 0.023.
Any slight differences between the two studies may be due to the different ages of subject’s tested in the two studies (subjects with an age range of 10-
60 years were tested in the Malbouissonn et al study (2000), whereas a range of 18-35 years were tested in our study) or to the slightly different areas of the lid margins fit in the two studies.
The eyelid contour term “A” has previously been shown to be greater in cases of eyelid retraction and lower in blepharoptosis (i.e. the higher the upper lid, the more steeply curved is the eyelid contour and vice versa) (Cruz et al 1998). Our results are consistent with this premise, as we found a significant flattening of the eyelid contour to occur in downward gaze (i.e. as the palpebral aperture narrowed, the contour of the eyelids flattened).
Previous studies into eyelid contour have only presented results for the polynomial term “A”. We have shown that by using a coordinate system for the polynomial function which is centred on a known landmark (e.g. the limbus centre in our study) then the other terms in the polynomial, “B” and “C” take on meaningful values (i.e. the term “B” relates to the tilt of the eyelid, and term “C” relates to the height of the lid above or below the limbus centre). Results for term “B” in primary gaze in the Caucasian subjects indicated that the central upper eyelid was very close to horizontal in primary gaze, and the central lower lid was slightly down-slanted in primary gaze, with both upper and lower eyelid becoming more down-slanted in downward gaze. The results for term “C” for both the upper and lower eyelid equated
157 Chapter 3 closely to the result for PC_UL and PC_LL respectively as would be expected. Young et al (2002) showed that the vertical palpebral aperture width and the angle of the central eyelid were associated with soft toric contact lens orientation and stability. It follows from this that the eyelid contour terms “B” and “C” are also likely to influence toric lens orientation and stability.
Downward movement of the eyes is required for numerous everyday visual tasks such as reading and computer work. Stoller and Meyer (1994) found that the changes in the upper eyelid in downgaze were more pronounced for older subjects, who were found to exhibit a greater downward movement of the upper eyelid in downgaze (possibly due to increased laxity of the upper eyelid, or decreased innervation to the levator muscle with increasing age).
The magnitude of change in upper eyelid position in downgaze in our study
(0.5 mm) was less than the value of 1.0 mm reported by Stoller and Meyer
(1994) which may be partly explained by the different average age of the subjects tested in the two studies (average age of Stoller and Meyer’s (1994) subjects was 55 years and the average age of our subjects was 24 years).
The protocol used to measure eyelid parameters in downgaze will also influence the results and is a likely reason for the differences in results between ours and previous studies. As subjects typically achieve downward gaze through a combination of head and eye movements, in our study, we allowed our subjects to adopt their natural downgaze head and eye positions.
The protocols used by Stoller and Meyer (1994) and Guimaraes and Cruz
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(1999) precluded their subjects from adopting any head tilt in downward gaze, thus shifts in gaze were achieved solely through movement of the eyes. One would expect that in these protocols, a greater movement of the eyelids would be observed in downward gaze than if a combination of eye and head movement is allowed. This was found to be the case, with
Guimaraes and Cruz (1999) reporting an average change in vertical palpebral aperture width of approximately 2 mm more in 40° downgaze than was found in our study (where subjects’ natural downward head tilts were allowed).
Guimaraes and Cruz (1999) found a reduction of vertical palpebral fissure width (PA) of 1.36 mm for every 10° of downward gaze (in their study where all gaze shifts were achieved through eye movement). If we apply this formula to our data (where gaze shifts were achieved through a combination of head and eye movements), then the downward angle of the eyes for our subjects was on average 24.26° for the 40° downgaze condition. It follows from this that on average our subjects were tilting their heads downwards by approximately 15.7°. This amount of head tilt is consistent with that quoted by Kroemer and Hill (1986) and Hill et al (2005), for downgaze tasks.
Previous investigations into the change in the palpebral aperture in downward gaze have only presented measurements for the palpebral fissure in the vertical dimension (Stoller and Meyer 1994, Guimaraes and Cruz
1999). To our knowledge, we are the first to report on the changes in eyelid contour and eyelid angle occurring in downgaze, and to quantify the slight
159 Chapter 3 flattening in the eyelid contour and downward slant of the eyelids that occurs with downgaze eye movements.
Our male and female populations showed only slight differences in their average anterior eye dimensions. In general, many of the measures of palpebral fissure size in the vertical and horizontal dimension were slightly larger for the male than the female population. However the only highly statistically significant difference found between males and females was the horizontal palpebral fissure length (HEF), which was significantly larger in male subjects than in females. Van den Bosch (1999) also made comparisons between their male and female subjects and found the HEF to be significantly larger in their male subjects. This was also the only dimension measured in their study which differed significantly between the two genders.
We found a number of significant differences in anterior eye dimensions between our Asian and Caucasian populations. As our Asian population
(n=20) was much smaller than our Caucasian population (n=76), caution should be taken in making generalisations about the population. To more accurately quantify the differences between the palpebral fissure morphology of Asian and Caucasian subjects, a larger population of Asian subjects would need to be investigated.
Our Asian subjects exhibited significantly smaller corneas in the horizontal dimension (average HVID=11.4 ± 0.3 mm) compared to our Caucasian
160 Chapter 3 population (average HVID =11.9 ± 0.4 mm). This is consistent with previous investigations into the HVID in Asian and Caucasian populations where Asian subjects were reported to have smaller HVIDs (Lam and Loran 1991,
Matsuda et al 1992). The horizontal palpebral fissure length (HEF) was found to be approximately 2 mm smaller in our Asian subjects compared to our Caucasian subjects. Other investigators have also found the HEF to be smaller in Asian populations compared to Caucasians (Lam and Loran 1991,
Le et al 2002).
Previous investigators have found that the total vertical palpebral aperture width (PA) in Asian subjects is slightly smaller than in Caucasian subjects
(Lam and Loran et al 1991, Lin et al 2003). No measure of pupil centre to upper lid and pupil centre to lower lid was provided in these studies. In our study, the mean PA for Caucasian subjects in primary gaze (9.7 ±1.2 mm) was found to be slightly larger than the mean PA in primary gaze for Asian subjects (9.5 ± 0.8 mm) however this difference was not statistically significant. The pupil centre to upper lid (PC_UL) measure was significantly smaller in the Asian subjects (indicating that the Asian eyelid is on average
0.4 mm closer to pupil centre than the Caucasian upper eyelid in primary gaze), and the pupil centre to lower lid (PC_LL) was significantly larger in the
Asian subjects (by approximately 0.2 mm in primary gaze).
The other major difference found between the Asian and Caucasian populations in our study relates to the obliquity of the palpebral fissure.
Hanada et al (2001) investigated the obliquity of the palpebral fissure in a
161 Chapter 3 group of Japanese subjects using digital image analysis and found them to have significantly greater palpebral fissure obliquity (Theta_HEF) than their
Caucasian subjects (mean angle of 9.39° up-slanted for their Asian subjects compared to a mean angle of 4.6° up-slanted for their Caucasian subjects).
We also found our Asian subjects to have significantly more up-slanted palpebral fissures than our Caucasian subjects (Theta_HEF in primary gaze of 5.8° in Asian subjects and 3.7° up-slanted for our Caucasian subjects).
However, the magnitude of palpebral fissure slant in our Asian subjects was slightly less than that reported by Hanada et al (2001). A slight horizontal head tilt of on average 1.7° to the right side was found in our Asian subjects in primary gaze. This slight head tilt to the right led to the palpebral fissure angle (Theta_HEF) measuring slightly less upward slanted. When we took this slight horizontal head tilt into account for our Asian subjects in primary gaze, then we attained a corrected Theta_HEF of 7.53° upward slanting, a value much closer to Hanada et al’s average palpebral fissure slant. Hanada et al’s (2001) population consisted of Japanese Asian subjects whereas our population consisted of subjects from a range of different East Asian countries (Chinese, Japanese, Korean, Malaysian and Vietnamese). Le et al
(2002) found differences in certain anthropometric facial measurements between different Asian ethnicities amongst a population of 60 Chinese, 60
Vietnamese and 60 Thai subjects. Whilst no study has specifically investigated whether different Asian ethnicities exhibit different palpebral aperture characteristics, it is likely.
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The ethnic differences found in this study may have implications for refractive error development. However, it should also be noted that due to the relatively small number of Asian subjects tested, that the ethnic differences found in palpebral fissure morphology should not be considered conclusive.
Buehren et al (2005) hypothesised that corneal distortion following reading may be a factor in myopia development. Many developed East Asian countries exhibit a very high incidence of myopia (Yap et al 1993, Saw 2003,
Edwards and Lam 2004, Lam et al 2004). The results from our study indicate that the Asian upper eyelid is significantly closer to the pupil in all angles of gaze than the Caucasian upper eyelid. Previous anatomical studies, have also shown the Asian eyelids to be thicker (Doxanas and Anderson 1984,
Lim et al 2004). These factors potentially increase the forces of the eyelids on the globe and would locate any corneal optics changes following reading closer to the central cornea and pupil. If corneal distortions due to reading are a factor in myopia development, then the morphology of the Asian eyelid may be one reason for the high prevalence of myopia in these populations.
Previous studies have also shown the angle and position of the eyelids in primary gaze can influence both rigid and soft toric contact lens fitting
(Carney et al 1997a, Young et al 2002). It is therefore likely that the significant changes that occur in the eyelid morphology as a result of downward gaze could also lead to alterations in contact lens stability, position and orientation. Translating rigid bifocal contact lenses rely on the upward movement of the lower lid with respect to the pupil centre (PC_LL) to achieve
‘alternating vision’ in downward gaze. Our data for young subjects suggests
163 Chapter 3 that on average this degree of movement is only 1.42 mm in 20° downward gaze and 2.74 mm in 40° downward gaze, highlighting the difficulty in achieving adequate translation of the near vision segment in the lens.
3.5 Conclusions
The changes in palpebral fissure morphology in downward gaze have the effect of bringing both the upper and lower eyelid closer to pupil centre and corneal geometric centre, as well as significantly altering the angle and contour of the eyelids. Any changes relating to the mechanical effects of the eyelids on the central cornea would therefore be expected to increase in downward gaze as a result of the morphological changes occurring in the eyelids. Corneal distortions as a result of eyelid pressure may also be expected to alter depending upon the gaze angle, since the angle and shape of the eyelid margin changes in different degrees of downward gaze.
The results from this experiment have quantified the highly significant changes that occur in the morphology of the palpebral fissure with shifts in vertical gaze. The average morphology of the palpebral fissure in primary gaze and in two typical angles of downward gaze has also been defined in detail. The angle and position of the eyelids may prove to be a factor in determining the shape of the cornea through mechanical pressure effects. In the next chapter we will report the corneal topography data from this same
164 Chapter 3 population, and then in the subsequent chapter, explore the association between the corneal topography and eyelid fissure morphology.
165 Chapter 3
166 Chapter 4
Chapter 4: The topography of the central and peripheral cornea
4.1 Introduction
In Chapter 3, we have reported on the morphology of the palpebral fissure in a population of young healthy subjects. In this chapter, we will describe the corneal topography of this same population. Due to the position of the eyelids in relation to the centre of the cornea, one may expect that if eyelid pressure influences corneal shape then changes may be more evident in the peripheral cornea. However, if pressure from the eyelids causes an overall bending of corneal tissue (as may be the case if long term eyelid pressure causes corneal astigmatism), then associations may also be evident in the central cornea. When investigating associations between the morphology of the palpebral fissure and the shape of the cornea (which will be addressed in
Chapter 5), it is important to obtain accurate topographical data from both the central and peripheral cornea. A technique has recently been developed that allows measurement of the peripheral cornea and the subsequent combination of central and peripheral corneal topography data to provide a
“total corneal topography” map (Franklin et al 2006). Using this technique we have measured the total corneal topography (i.e. the topography of the central and peripheral cornea) of the right eye of 100 subjects.
167 Chapter 4
The advent of computer-assisted videokeratoscopes has greatly improved our understanding of the cornea’s shape and its optics. The detailed information provided by these instruments is routinely used in the clinical setting for the diagnosis of corneal ectatic disorders such as keratoconus
(Schwiegerling and Grievenkamp 1996), rigid and soft contact lens fitting
(Szczotka 1997, Reddy et al 2000, Szczotka et al 2002), the screening of refractive surgery candidates (Ambrosio et al 2003, Varssano et al 2004), and for customised refractive surgery corrections (Alessio et al 2000, Knorz and Jendritza 2000, Kanjani et al 2004, Kymionis et al 2004).
The area of the cornea measured by videokeratoscopes is much larger than that of the traditional keratometer. However, for videokeratosopes based on the Placido disk principle, corneal coverage is limited by the fact that the instrument is based upon specular reflection from the corneal surface and further limited by obscuration of the ring image by the subjects’ nose, brow and eyelashes (Klein et al 2002). Corneal coverage with Placido-based videokeratoscopes is improved by utilising a small measurement cone, as obscuration by the nose and brow is avoided. Videokeratoscopes based on other principles (such as slit scanning and rasterstereography techniques) have the potential to measure larger corneal areas than Placido-based systems (Mejia-Barbosa and Malacara-Hernandez 2001), although they are still limited by interference from the eyelids and eyelashes. However, these other techniques have generally not been proven to be as precise or accurate in their measurements (Tang et al 2000, Cho et al 2002).
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A number of studies have defined the average shape of the cornea for a normal adult population by deriving the average conic parameters ro and Q
(Kiely et al 1982b, Guillon et al 1986, Eghbali et al 1995, Carney et al 1997b,
Douthwaite et al 1999). These studies have produced average ro values ranging from 7.68 to 7.85 mm and average Q values ranging from -0.33 to
-0.18 (i.e. the vast majority of subjects exhibit corneas with a prolate elliptical shape). Whilst the average results across these studies have been relatively consistent, most investigators noted that large variations in corneal shape existed between normal subjects. Recently, more complex quantitative descriptors of shape such as Fourier series analysis (Keller and Van
Saarloos 1997) and Zernike polynomials (Schwiegerling and Greivenkamp
1997, Guirao and Artal 2000) have been used to describe the shape of the cornea.
The majority of studies of corneal shape have investigated only the central 6 mm of the cornea. Whilst data from the central cornea is obviously the most important for vision, this represents only approximately one quarter of the cornea’s total surface area. Information from the peripheral cornea is particularly important in the fitting of contact lenses.
There have been relatively few studies investigating the shape of the peripheral cornea, outside the central 6 mm diameter. Mandell (1998) used offset fixation points in a videokeratoscope to measure peripheral corneal topography in 11 subjects, and found that for peripheral measurements, an ellipse was a poor descriptor of cornea shape due to increased flattening of
169 Chapter 4 the corneal surface in the periphery. An average tangential radius of 11.29 ±
1.82 mm was found at 4.5 mm from corneal centre for the 11 subjects tested.
Reddy et al (2000) classified subjects’ corneal astigmatism based upon central and peripheral corneal topographical data. However their peripheral corneal measurement was based upon data only 3.5 mm from the corneal centre and data from the superior peripheral cornea was not used for some subjects due to data dropout in the superior portion of the corneal topographical maps.
As there is limited information in the literature regarding the shape of the peripheral cornea, our aim was therefore to provide normative information regarding the shape of the total cornea for a large population of young healthy adult subjects with a range of normal refractive errors.
4.2 Methods
4.2.1 Subjects and procedures
Corneal topography maps were acquired for the right eye of 100 young adult subjects. All subjects had normal ocular health with no history of ocular surgery, trauma or corneal disease. No full-time soft contact lens (SCL) or rigid gas permeable (RGP) contact lens wearers were included in the study.
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Nine part time SCL wearers were included in the study, but were instructed not to wear contact lenses on the day of testing. Approval from the
Queensland University of Technology human research ethics committee was obtained prior to commencement of the study and informed consent was obtained from all of the subjects.
Of the 100 subjects participating, eight subjects were excluded from all analyses due to poor correlation between central and peripheral corneal topography maps (our criterion for exclusion due to poor map correlation is described later). This left a total of 92 subjects in the final data analysis. The subjects’ ages ranged from 18 to 35 years, with a mean age of 24 years. Of the 92 subjects, 54 were female. Eighteen of the 92 subjects were of Asian ethnic origin. The subjects exhibited a range of refractive errors with the group mean best sphere refractive error being -1.1 ± 1.8 D and group mean astigmatic refractive error being -0.32 ± 0.6 D. To rule out any significant anterior eye or tear film abnormalities, each subject underwent a preliminary slit lamp examination.
All corneal topography measurements were taken using the Medmont E300
Videokeratoscope (Medmont Pty. Ltd.,Victoria, Australia). The Medmont
E300 is based on the Placido disk principle and has been shown to have a high degree of accuracy and precision for measuring inanimate test objects
(Tang et al 2000). Tang et al. (2000) found the Medmont E300 to exhibit a mean height error of 2 µm for measuring spherical and aspheric test surfaces. This instrument has also exhibited highly repeatable results for
171 Chapter 4 measurements on corneas in-vivo (Cho et al 2002). Cho et al (2002) found that two repeated measurements were required with the instrument to ensure a precision in corneal elevation data of 2 µm. The Medmont E300 has a sophisticated range finding device that determines the distance from the corneal apex to the instrument’s camera and automatically captures the videokeratoscopic image only when good focus and alignment of the eye are attained.
In Chapter 2 we found that significant diurnal variation can occur in corneal topography which appeared to be due to pressure from the eyelids on the cornea. Corneal topography results may also be influenced by prior visual tasks (Buehren et al 2003a, Collins et al 2005a). To reduce these effects, all measurements were taken in the morning and subjects were advised to refrain from performing significant amounts of close work immediately prior to testing.
The procedure used for measuring the total corneal topography has been previously described in detail (Franklin et al 2006). The corneal topography of one eye was measured while the subject viewed an external fixation target positioned 1.5 metres away from the videokeratoscope with the fellow eye
(through the use of a mirror). The external fixation target has a central target and six peripheral targets in different peripheral angles of gaze (at 0°, 60°,
120°, 180°, 240° and 300° and approximately 30 cm from the central target).
Three videokeratoscope images were captured with the subject fixating on the instrument’s internal central fixation target. The subject was then
172 Chapter 4 instructed to fixate on the external target with the fellow eye, and videokeratoscope images were captured with the subject looking at each of the six peripheral fixation targets in turn. A total of four videokeratoscope images were captured for each of the six peripheral directions of gaze (i.e. three central images and 24 peripheral images were captured).
The corneal height data for each of the videokeratoscope images were exported from the instrument and analysed using custom written software
(Franklin et al 2006). This program examined the correlation between central and peripheral corneal topographical data. The aim of this process was to find the point in the peripheral map corresponding to the centre of the central topography map (the vertex normal). Essentially, it located the point on the peripheral map (defined by the radial distance, azimuthal angle and degree of cyclo-rotation from the centre of the peripheral map) where the sum of squares of differences in the overlapping portions of the central and peripheral corneal topographical maps was minimised.
The central topography map was correlated with each of the four peripheral maps in one direction of peripheral gaze and the peripheral map which gave the best correlation (i.e. the smallest sum of squares difference) with the central map was chosen as the best peripheral map for that direction of gaze.
This procedure was repeated for each of the six directions of peripheral gaze.
The one central map and six peripheral maps were then chosen that gave the overall smallest sum of squares of differences between central and peripheral corneal topographical data.
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Following this map correlation process, the central and peripheral maps were combined. The point of best correlation in each peripheral map was rotated to make this point a normal apex, and the peripheral maps were then combined with the central map. In the combined map, the central 6 mm of the central map was preserved, and the peripheral data were added past this point. The combined map was output in the same format as the standard
Medmont height map except that the combined map has 46 rings of data in
300 semi-meridians (the standard Medmont height map has only 32 rings of data). Combined axial curvature maps were also calculated based upon the combined corneal height maps. Figure 4.1 shows an example of central and peripheral corneal axial curvature maps and a combined data map for one subject.
To assess the accuracy of this process, Franklin et al (2006) compared the original central map data with the rotated peripheral map data. Data from a conic test surface showed less than 0.5 µm difference between central and rotated peripheral data, and data from a real cornea showed errors between the central and rotated peripheral maps of less than 1 µm across the central
7 mm of data.
If central and peripheral maps correlated well, then the combined map exhibited a smooth transition between central data (the central 6 mm diameter) and peripheral data (outside of the central 6 mm diameter). A feature of combined maps with poor correlation was a large change at the junction between the central and peripheral corneal data. Figure 4.2 shows
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Figure 4.1: Example of central and peripheral corneal data and combined data map (axial curvature maps are shown). The map correlation process attempted to find the point in each of the peripheral maps that corresponded to the vertex normal of the central map. Each peripheral map was then rotated and combined with the central map to produce the combined corneal topographical map (right).
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Figure 4.2: Example of two subjects’ corneal axial curvature data in one semi-meridian (the data from the combined map is shown). Subject 60 had a poor correlation between central and peripheral corneal data. Note the large change in axial power at the junction of the central and peripheral zones of the map (at 2.87 mm from corneal centre) for subject 60. Subject 76 had good correlation and exhibited a smooth transition between central and peripheral data. Subject 60 was excluded from analysis due to poor correlation.
176 Chapter 4 an example of a subject with poor (Subject 60), and a subject with excellent
(Subject 76) correlation between central and peripheral corneal data.
To determine what would be an unacceptable difference in axial curvature at the junction between the central and peripheral data, every semi-meridian of axial curvature data from every subject’s standard central map was analysed and a 2nd order polynomial function fit to a small region of data just inside 3 mm from corneal centre for each map. The difference between the actual axial radius and the axial radius predicted by the polynomial fit was then calculated for the point just outside 3 mm from centre for each semi-meridian.
The average and standard deviation of the difference between actual and predicted axial radius was found to be 0.04 ± 0.07 mm, with an outer 95% confidence interval of 0.18 mm. Differences greater than 0.18 mm would therefore reflect an unreasonable amount of change between the central and peripheral axial curvature data, and suggest a poor correlation between the central and peripheral maps. Figure 4.3 illustrates the comparison of actual and predicted data for one semi-meridian of central map data for one subject.
The combined central and peripheral axial radius of curvature maps were analysed in a similar fashion. A polynomial function was fit to the final five central map data points just inside 3 mm from corneal centre and the predicted data then compared to the first two peripheral map data points at
3.13 mm and 3.26 mm from corneal centre. Any maps showing a difference between actual and predicted data of greater than ± 0.2 mm in more than 40 semi-meridians at the junction between central and peripheral data were
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Figure 4.3: Example of the comparison between actual and predicted data for one semi-meridian of central map data for subject 65. The expected data was calculated based upon a 2nd order polynomial fit to the first five data points (red data points) of the actual data. The difference between the actual
(blue data point) and expected data at the final point was calculated for every valid semi-meridian of data for every subject’s central map.
178 Chapter 4 considered to have a poor correlation (one poorly correlated peripheral map would be expected to result in an abrupt boundary change in 50 semi- meridians). Out of the 100 subjects who had corneal topography measurements taken, eight were excluded due to poor correlation between central and peripheral topographical data.
It is possible that changes in EOM tension (as occurs in our protocol for capturing the peripheral topography data) may cause changes in corneal topography (Fairmaid 1959, Lopping and Weale 1965, Kwitko et al 1991). A control experiment was carried out to investigate whether the eye movements (and subsequent changes in EOM tension) used in our protocol to capture the peripheral corneal topography maps had an effect on the peripheral topographical data.
Two normal healthy subjects (one with an astigmatic central cornea and one with a spherical central cornea) had topography measurements taken of their right eye. A central measurement was initially captured for each subject.
The videokeratoscope was then moved by 11 degrees (the equivalent of the amount of eye movement carried out in the original peripheral map capturing protocol) to take measurements of the temporal peripheral cornea (10 measurements were taken). The videokeratoscope was then moved back to the original position and the subject then assumed fixation (with the fellow eye) 11 degrees to their left (10 measurements were taken). This gave one central map and twenty peripheral maps for each of the two subjects (10 peripheral maps achieved through videokeratoscope movement and 10
179 Chapter 4 peripheral maps achieved through eye movement). For each of the peripheral maps, the point of best correlation with the central map was determined, and the central data were combined with the peripheral data for each peripheral map (so each combined map had the same central data and different peripheral data). The 5 maps for each condition (i.e. for the eye movement and the videokeratoscope movement condition) that gave the best correlation (i.e. smallest sum of squares between the central and peripheral data) out of the 10 were then chosen and averaged. This provided an average and a standard deviation map for each condition for each subject.
The peripheral corneal topographical data from the two average maps for each subject were then compared. A two-tailed paired t-test was performed for each peripheral data point to determine if there was any significant difference between the average ‘eye movement’ data and the average
‘videokeratoscope movement’ data. Only small differences were found between the average “eye movement map” and the average
“videokeratoscope movement map” for each subject. The average ± SD difference in axial curvature across all valid peripheral data points between the eye movement data and the videokeratoscope movement data was
-0.05 ± 0.06 mm (range: 0.43 mm to -1.09 mm) for Subject 1 and -0.02 ±
0.05 mm (range: 0.57 to -0.645) for Subject 2. To reduce the chances of a type 1 statistical error, a Bonferroni correction for multiple comparisons was applied to the data (1121 and 1100 comparisons were made for Subject 1 and Subject 2 respectively, which equates to a corrected p-value of 0.00005 for both subjects). For this analysis, none of the peripheral data points
180 Chapter 4 showed any significant difference between the two conditions for either of the two subjects. If we were less conservative with our statistical testing, and did not apply the Bonferroni correction but instead use a significance level of
0.01, then we find that only 8 out of 1121 and only 13 out of 1100 peripheral data points for subject 1 and 2 respectively show a significant difference (i.e. only approximately 1% of data points showed a significant difference between the two conditions). We concluded from this, that the alteration of
EOM tension associated with the change in fixation in our peripheral map capturing protocol (about 11°) was not enough to cause significant changes in the peripheral corneal topography data. Figure 4.4 shows the average combined eye movement and videokeratoscope movement axial curvature maps for the two subjects.
The centre of standard corneal topography maps is located at a point where the optical axis of the videokeratoscope is perpendicular to the cornea, known as the vertex normal (Mandell 1994) (Figure 1.2). The position of the vertex normal relative to the geometric centre of the cornea is known to differ from person to person (Mandell et al 1995). Therefore in order to have each subject’s corneal topography map centred to a common point, each combined map was rotated to corneal geometric centre. The videokeratoscope image from the best central map (as determined through the map correlation process) for each subject was analysed to determine the position of the corneal geometric centre using customised computer software that locates the corneal limbus in the videokeratoscope image (Morelande et al 2002).
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Figure 4.4: Average eye movement maps and videokeratoscope movement maps for the two subjects in the control experiment. The peripheral data is on the temporal side of the map. Note very little difference in the average topographical maps between each subject for each condition.
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4.2.2 Data Analysis
The average sizes of the topographical maps in the vertical and horizontal dimensions for both standard (central fixation) and combined corneal topography were calculated. This was done by finding the shortest complete semi-meridian of data within five meridians (6°) of the horizontal (temporal and nasal) and vertical (superior and inferior) directions. The shortest semi- meridians in the temporal and nasal directions were combined, and the shortest semi-meridians in the superior and inferior directions were also combined. This provided an estimate of the minimum horizontal and vertical map diameters for both the standard topographical and the combined topographical maps. Individual subject data was combined to calculate the group mean map size for each technique.
Each subject’s corneal height data was averaged across all semi-meridians and the average ro and Q values were calculated based upon Baker’s
2 2 equation for conic sections y = 2rox - px where y is the distance from corneal centre and x is the corneal height (Bennett 1988). A linear in parameters least squares fitting was carried out to calculate the ro and p for the averaged semi-meridian data. The asphericity parameter Q is related to p in the following way Q = p-1. The conic parameters ro and Q were calculated for 6, 8, 9 and 10 mm corneal diameters. For this average across all semi-meridians, only subjects with at least 200 semi-meridians of complete data were included in the analysis. Any missing data (even in the combined maps) tends to be in the superior semi-meridians due to
183 Chapter 4 interruptions from the brow and eyelashes, therefore, the larger diameter analyses will be slightly biased towards the horizontal regions. We would expect this bias to have only a slight effect and only on the 9 mm and 10 mm diameter data. The root mean square (RMS) fit error was also calculated for each corneal diameter. A repeated measures analysis of variance (ANOVA) with one within-subject factor (corneal diameter) was used to investigate whether ro and Q changed significantly for the different corneal diameters tested.
The conic fitting was also carried out for the steepest and flattest meridian of corneal data for each subject. The steepest and flattest meridians were calculated based upon the best fit sphero-cylinder to the corneal axial power data for an 8 mm corneal diameter. This provided the axis of the steepest and flattest corneal meridian for each subject. The meridian of data corresponding with the corneal cylinder axis and the two adjacent meridians on either side were averaged to provide the average corneal data along the steepest corneal meridian. The same was carried out for the flattest meridian data. The best fitting ro and Q values were then calculated for each meridian for each subject. To investigate meridional variations in ro and Q, repeated measures ANOVA was carried out with two within-subject factors (corneal diameter and corneal meridian).
Franklin et al (2006) showed that for larger corneal diameters, a polynomial function fit corneal height data better than a conic fit. They found that a 4th order polynomial was required to reasonably fit 7 mm diameter data and that
184 Chapter 4 for a 10.7 mm diameter a 9th order polynomial fit was required. The average corneal height data (averaged across all valid semi-meridians) was also therefore fit with a polynomial function of the form y = Ax + Bx2 + Cx3 +
Dx4….etc (where y is the corneal height and x is the distance from corneal centre). For each subject, the 3rd through to the 9th order polynomial functions were all fit to the corneal height data for 6, 8, 9 and 10 mm diameters. The RMS fit error was also calculated for each of the polynomial orders and for each corneal diameter. For larger corneal diameters, progressively higher order fits were required to adequately fit the corneal height data (Figure 4.5).
For each subject, axial power maps were calculated based upon the combined corneal height data. The axial power data for each subject were analysed to calculate the best fit corneal sphero-cylinder using the method of
Maloney et al (1993). We found these fitting routines to be highly sensitive to any missing data points, therefore only subjects with 300 complete semi- meridians of axial power data to the edge of the outer diameter were included in each of the analyses. The best fit sphero-cylinder data for each subject was converted into the power vectors M (best sphere), J0 (astigmatism
90/180°) and J45 (astigmatism 45/135°) (Thibos et al 1997), to allow the group mean average and standard deviation values to be calculated. The best fit corneal sphero-cylinder was calculated for corneal diameters of 6, 7,
8 and 9 mm. To investigate for significant changes in the corneal sphero- cylinder with increasing diameter, a repeated measures ANOVA was used with one within-subject factor (corneal diameter).
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Figure 4.5: RMS fit error versus polynomial fit order for different corneal analysis diameters. Note that progressively higher polynomial fit orders were required to reduce the RMS fit errors for increasing analysis diameters (i.e. to bring the RMS fit error to a minimum). The smallest number of polynomial terms was used, above which no substantial reduction in RMS fit error occurred (e.g. for an 8 mm diameter a 5th order polynomial was used. Note that only minor improvement in RMS error is achieved by fitting above the 5th order for this data).
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Changes in the corneal sphero-cylinder with increasing corneal diameter gave some indication of variations in the peripheral cornea. However, the large diameter corneal sphero-cylinder fits contained data from both the peripheral and the central cornea. Therefore some changes in the peripheral cornea may be somewhat masked by data from the central cornea. To overcome this, and to further analyse the peripheral cornea, we have broken the cornea down into concentric annuli of data. The best fit sphero-cylinder was then calculated for each annulus of corneal axial power data and again broken down into the power vectors M, J0 and J45. For this analysis, only subjects with complete semi-meridians of axial power data to 8 mm diameter were included.
This analysis was performed for annuli of 2 mm width and for annuli of 0.5 mm width. The 2 mm width analysis provided a measure of the central cornea from the inner annulus (from 0 to 4 mm diameter) and a measure of the peripheral cornea from the outer annulus (from 4 to 8 mm diameter).
This analysis has the advantage that the data in each annulus are mutually exclusive (i.e. the inner annulus provide information about the central cornea only and the outer annulus provides information about the peripheral cornea only). From this analysis we were able to broadly classify each subjects’ central cornea as either Type 1 (spherical central cornea with astigmatism
< 0.75 D) or Type 2 (astigmatic central cornea with astigmatism >0.75 D).
The peripheral cornea was classified as either Type A (peripheral astigmatism stable, changing less than 0.25 D from the central cornea), Type
B (increasing peripheral astigmatism of 0.25 D or more) or Type C (reducing
187 Chapter 4 peripheral astigmatism of 0.25 D or more). Previous investigators have also classified corneas according to central and peripheral astigmatism in a similar fashion (Reddy et al 2000, Szczotka et al 2002).
The 0.5 mm analysis provides a higher resolution investigation of the changes in the corneal sphero-cylinder with increasing distance from corneal centre. Figure 4.6 illustrates the corneal spherocylinder annulus analysis for one subject. To investigate changes in the annulus corneal sphero-cylinder with distance from corneal centre, a repeated measures ANOVA was used with one within-subject factor (corneal annulus diameter) and one between- subjects factor (central corneal type).
To provide a mathematical analysis of the corneal surface shape for each subject, Zernike polynomials were fit to the corneal height data using a least squares fitting method (Iskander et al 2001). Zernike polynomials up to and including the 6th radial order were fit to the corneal height data for 6, 8 and 9 mm corneal diameters. Zernike polynomials were expressed using the double indexed OSA convention (Thibos et al 2002). This fitting routine will also be sensitive to any missing or invalid data. We therefore only included subjects with complete corneal height data to the 9 mm diameter in the analysis. A repeated measures ANOVA was used with one within-subject factor (corneal diameter) to investigate changes in each of the higher order
Zernike polynomials (3rd order and above) with increasing corneal diameter
(6, 8 and 9 mm). The Greenhouse-Geisser correction of the degrees of
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Figure 4.6: Illustration of the annulus sphero-cylinder analysis method used for examining the change in the corneal sphero-cylinder in the peripheral cornea. The best fit sphero-cylinder was calculated for annulus 1 and 2 for the 2mm width analysis (top left) and was calculated in annulus 1-7 for the
0.5 mm width analysis (top right). The sphero-cylinder for each of the annuli is plotted in the bottom maps.
189 Chapter 4 freedom was used to reduce the chance of type I errors, where the sphericity assumption was violated for all ANOVAs carried out.
4.3 Results
The map correlation and combination process provides a much larger corneal coverage than that given by standard topography maps alone. The average diameter of map for the standard corneal topography (central fixation) was 9.2 ± 0.3 mm in the horizontal dimension and 7.2 ± 0.7 mm in the vertical dimension. The average map diameter in the extended corneal topographical maps was 11.4 ± 0.4 mm in the horizontal dimension and 9.8 ±
0.6 mm in the vertical dimension. This represents an increase in the horizontal and vertical map dimensions of 25 % and 36% respectively. The use of the map pasting protocol therefore led to an approximate increase of
68% in corneal topography map area.
The average conic fit parameters (ro and Q), polynomial function and RMS fit errors for the average corneal height data across all meridians is presented in Table 4.1. The average ro for a 6 mm corneal diameter was found to be
7.77 ± 0.2 mm and the average Q value was -0.19 ± 0.1. For a 10 mm corneal diameter, the average ro was 7.72 ± 0.2 mm and Q was -0.36 ± 0.2.
This indicates an increase in the rate of corneal flattening for the peripheral cornea. Repeated measures ANOVA revealed that both ro and Q changed significantly with increasing corneal diameter (p <0.0001 for both ro and Q).
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Table 4.1: Average conic fit and polynomial fit data from the corneal height
data averaged across all meridians
Corneal Diameter
6 mm 8 mm 9 mm 10 mm (n = 92) (n =92) (n = 92) (n = 84)
Conic Fit ro 7.77 ± 0.2 7.76 ± 0.2 7.73 ± 0.2 7.72 ± 0.2
Q -0.19 ± 0.1 -0.23 ± 0.1 -0.30 ± 0.1 -0.36 ± 0.1
RMS Fit Error (microns) 0.79 ± 0.4 4.19 ± 4.4 11.66 ± 7.9 21.18 ± 11.1
-8.815E-05 -2.598E-04 -1.266E-04 -7.276E-06 A
6.467E-02 6.518E-02 6.469E-02 6.381E-02 B
-1.982E-04 -6.910E-04 -8.062E-05 1.812E-03 C
Polynomial Fit 2.760E-04 4.659E-04 1.280E-04 -2.235E-03 D (y = Ax + Bx2 + 3 Cx ...) -2.549E-05 6.001E-05 1.704E-03 E
-8.064E-06 -6.692E-04 F
1.520E-04 G
-1.843E-05 H
9.114E-07 I
RMS Fit Error (microns) 0.03 ± 0.01 0.10 ± 0.2 0.26 ± 0.4 0.28 ± 0.4
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No significant correlation was found between ro and Q (p > 0.05) for any of the corneal analysis diameters. The RMS fit error was found to increase dramatically for larger corneal diameters. For the conic fitting of the corneal data, the RMS fit error increased from a mean value of 0.79 ± 0.4 µm for the
6 mm diameter to 21.18 ± 11.1 µm for the 10 mm corneal diameter. These fit errors highlight the inadequacy of the conic section to describe the peripheral cornea. To reduce the RMS fit error for larger corneal diameters, polynomial fitting to the data was required. For increasing corneal diameters, progressively higher order fits were needed to reasonably fit the data (i.e. to reduce the RMS fit error). For a 6 mm corneal diameter, a 4th order polynomial had an average RMS fit error of 0.03 ± 0.01 µm. For the 10 mm corneal diameter, a 9th order polynomial fit gave an average RMS fit error of
0.28 ± 0.4 µm. Figure 4.7 displays the frequency distribution for ro and Q for the different diameters tested. This figure illustrates the relatively wide range of ro and Q values for the population. The shift in Q to more negative values for the larger corneal diameters is also highlighted in the frequency distribution plots.
The group mean ro and Q values for the steepest and flattest corneal meridians are displayed in Table 4.2. The average ro along the steepest corneal meridian was found to be 7.69 ± 0.2 mm and was 7.83 ± 0.2 mm for the flattest meridian for a 6 mm diameter. The average Q value was -0.21 ±
0.1 along the steepest and -0.17 ± 0.1 along the flattest meridian for the 6mm diameter. Both ro and Q were found to change significantly with increasing corneal diameter (p< 0.001 for ro and Q). This is a similar change to that
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Figure 4.7: Frequency distributions for ro and Q for 6, 8, 9 and 10 mm corneal diameters.
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Table 4.2: Group mean conic fit data for the steepest and flattest corneal
meridians.
Corneal Diameter 6 mm 8 mm 9 mm (n = 92) (n = 86) (n = 64) Steep Flat Steep Flat Steep Flat r 7.69 ± 0.2 7.83 ± 0.2 7.69 ± 0.3 7.83 ± 0.2 7.68 ± 0.3 7.81 ± 0.2 Conic Fit o Q -0.21 ± 0.1 -0.17 ± 0.1 -0.27 ± 0.1 -0.23 ± 0.1 -0.32 ± 0.1 -0.30 ± 0.1 RMS Fit Error (microns) 1.99 ± 1.0 1.40 ± 0.7 5.39 ± 7.2 3.60 ± 1.8 15.59 ± 16.9 10.62 ± 5.8
194 Chapter 4 found for the data averaged across all meridians. The repeated measures
ANOVA also revealed significant meridional variation in ro and Q. As would be expected, the ro values were significantly different between the two meridians (p< 0.0001). The Q values were also significantly different between the steepest and flattest meridians, with Q along the steepest meridian being significantly more negative (p< 0.01). This indicated that the steepest corneal meridian had a slightly greater rate of peripheral flattening.
Both ro and Q showed significant diameter and meridian interactions (p <0.05 for ro and Q).
The group mean best fit sphero-cylinder data for the axial power maps for 6,
7, 8 and 9 mm corneal diameters are presented in Table 4.3. Figure 4.8 displays the frequency distribution for the sphere power M and scatter plots of astigmatism 90/180° (J0) and astigmatism 45/135° (J45). The average M was found to be 48.2 ± 1.5 D, J0 was 0.32 ± 0.4 D and J45 was -0.05 ± 0.2 D for a 6 mm corneal diameter (this equates to an average corneal sphero- cylinder of 48.5 / -0.64 x 176). It is evident from the scatter plots in Figure
4.8 that the majority of subjects exhibited positive values for J0 and relatively small levels of J45. In other words, most subjects exhibited a corneal cylinder axis relatively close to horizontal (i.e. WTR corneal astigmatism).
With increasing corneal diameter the average values of M, J0 and J45 all reduced slightly in magnitude. These changes with increasing corneal diameter were found to be significant (P< 0.0001 for M and J45 and P<0.01 for J0), indicating that the cornea flattened significantly in the periphery and exhibited a slight reduction in its toricity.
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Table 4.3: Group mean ± SD axial power corneal sphero-cylinder for 6, 7, 8 and 9 mm corneal diameters. The power vectors M (best sphere), J0
(astigmatism 90/180) and J45 (astigmatism 45/135) are presented. Only subjects with complete data to 8 mm diameter are presented.
Corneal Diameter 6 mm 7 mm 8 mm 9 mm (n = 78) (n = 78) (n = 78) (n = 38) M (D) 48.2 ± 1.5 48.1 ± 1.5 47.96 ± 1.5 47.28 ± 1.5 J0 (D) 0.32 ± 0.4 0.31 ± 0.4 0.30 ± 0.4 0.26 ± 0.3 J45 (D) -0.05 ± 0.2 -0.04 ± 0.2 - 0.03 ± 0.2 -0.05 ± 0.2
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Figure 4.8: Frequency distribution for corneal power best sphere ‘M’ for corneal diameters 6, 7, 8 and 9 mm (top). Scatter plots of J45 and J0 for corneal axial power are displayed for 6, 7 and 8 mm corneal diameters
(bottom).
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The 2 mm width corneal sphero-cylinder annulus analysis highlighted the changes occurring to the corneal sphero-cylinder in the peripheral cornea.
For the central annulus (0-4mm diameter annulus) the group mean M was
48.3 ± 1.5 D, J0 was 0.32 ± 0.4 D and J45 was -0.07 ± 0.2 D (48.6 / -0.7 x
174). For the peripheral annulus (4-8 mm diameter annulus) the group mean
M was 47.6 ± 1.4 D, J0 was 0.27 ± 0.3 D and J45 was -0.001 ± 0.2 D (47.9 /
-0.5 x 180). The group mean best fit corneal sphero-cylinder data for the 0.5 mm annulus analysis is presented in Table 4.4. This further highlights the changes occurring in the peripheral cornea. The average best sphere M, J0 and J45 all reduced in magnitude with increasing annulus diameter. This manifests itself as a general flattening, a slight change in corneal cylinder axis and a slight reduction in corneal astigmatic power in the more peripheral cornea. Repeated measures ANOVA revealed the changes occurring in M,
J0 and J45 with increasing annulus diameter to be highly significant
(p<0.0001 for M and J45 and p<0.001 for J0).
Based on the classification according to central corneal type there were 42 subjects with a spherical central cornea (Type 1 <0.75 D astigmatism) and 36 subjects with an astigmatic central cornea (Type 2 >0.75 D astigmatism). A significant interaction was found to occur between corneal annulus diameter and central corneal type for the change in J0 (p = 0.0002). This indicates that the reduction occurring in J0 in the peripheral cornea was greater for subjects with greater central corneal astigmatism. Figure 4.9 shows the group mean corneal cylinder power and axis as a function of distance from corneal centre for the 0.5 mm annulus analysis (data for both the central
198 Chapter 4
Table 4.4: Group mean axial power corneal sphero-cylinder for 0.5 mm
annulus data. The power vectors M (best sphere), J0 (astigmatism 90/180)
and J45 (astigmatism 45/135) are presented, for outer annulus diameters
from 2 mm to 8 mm. Only data from subjects with complete data out to 8 mm
are presented.
Outer Annulus Diameter (n = 78) 2mm 3mm 4mm 5mm 6mm 7mm 8mm
M (D) 48.4±1.5 48.3±1.5 48.2±1.5 48.0±1.5 47.8±1.5 47.6±1.4 47.1±1.4 J0 (D) 0.34±0.4 0.32±0.4 0.31±0.4 0.31±0.4 0.28±0.4 0.24±0.3 0.23±0.3 J45 (D) -0.09±0.2 -0.06±0.2 -0.05±0.2 -0.03±0.2 -0.001±0.2 -0.003±0.2 0.03±0.2
199 Chapter 4
Figure 4.9: Corneal cylinder axis and cylinder power versus annulus diameter for the 0.5 mm annulus analysis.
200 Chapter 4 spherical and central astigmatic corneas are shown). From this figure, the change in astigmatic power in the peripheral cornea is much greater for the subjects with astigmatic central corneas (astigmatic subjects showed on average a reduction in cylinder from centre to periphery of 0.43 D whereas spherical subjects showed only a 0.09 D reduction). The average change in cylinder axis in the peripheral cornea was similar between the two groups with both the astigmatic and spherical corneas showing a slight anti- clockwise shift in cylinder axis with increasing distance from corneal centre.
Whilst the annulus analysis data shows the average corneal toricity reducing as a function of distance from corneal centre, examination of individual subject data revealed a number of different individual patterns of corneal topography. Each cornea was classified based upon the amount of central
(Type 1 or 2) and peripheral astigmatism (Type a, b or c). The different patterns of corneal topography found in the 78 subjects with complete data out to an 8 mm diameter in order of most common to least common were:
Type 1, a (central spherical, periphery spherical, n = 30), Type 2, c ( central astigmatic, peripheral astigmatism reducing, n = 17), Type 2, a ( central astigmatic, peripheral astigmatism stable, n = 16), Type 1, c (central spherical, peripheral astigmatism reducing n = 7), Type 1, b (central spherical, peripheral astigmatism increasing n = 5), Type 2, b (central astigmatic, peripheral astigmatism increasing n = 3). The most common peripheral corneal types were peripheral astigmatism stable (n = 40) and peripheral astigmatism reducing (n = 24). Only eight of the 78 subjects exhibited an increase in astigmatism in the peripheral cornea. Figure 4.10
201 Chapter 4 shows examples of axial power maps and corneal cylinder power annulus maps for subjects with the different patterns of corneal astigmatism.
Zernike polynomials up to and including the 6th radial order were fitted to the corneal height data for 6, 8 and 9 mm diameters. Repeated measures
ANOVA revealed a number of the higher order Zernike coefficients to exhibit significant change with increasing corneal diameter.
−1 1 −2 The Zernike polynomial coefficients Z 3 (p = 0.001 ), Z 3 (p = 0.002 ), Z 4 (p
0 4 0 = 0.009), Z 4 (p < 0.0001), Z 4 (p = 0.006 ), and Z 6 (p < 0.0001) all showed highly significant change (p < 0.01) with increasing corneal diameter.
Figure 4.11 shows the group mean 3rd and 4th order corneal surface Zernike
0 th polynomial coefficient values (and Zernike term Z 6 , as this was the only 5 or
6th order term exhibiting highly significant change) for the 6, 8 and 9 mm
th 0 corneal diameters. It is evident from Figure 4.11 that the 4 order term Z 4 was the higher order coefficient of the largest magnitude and exhibits the largest change (and also the most significant) with increasing corneal diameter.
202 Chapter 4
Figure 4.10: Examples of corneal classification based upon central and peripheral toricity. The axial power maps are shown on the left. To highlight the changes in astigmatism, the maps on the right illustrate the cylinder power for the inner and outer annulus (i.e. the best sphere has been removed from the data for each annulus).
203 Chapter 4
Figure 4.11: Third and 4th order Zernike polynomial coefficients (and
0 term Z 6 ) for 6, 8 and 9 mm corneal diameters. * indicates coefficient exhibits highly significant change with increasing corneal diameter (p value < 0.01).
Each error bar represents one standard error of the mean.
204 Chapter 4
4.4 Discussion
We have presented normative data across a range of parameters to describe the topography of the central and peripheral cornea in our large population of young healthy adult subjects. The use of a conic fit as an estimator of corneal shape has been carried out in a number of previous studies on young adult subjects (Kiely et al 1982b, Guillon et al 1986, Eghbali et al 1995,
Carney et al 1997b, Douthwaite et al 1999). This simple fitting method has the advantage that it defines the contour of the cornea with the use of only two parameters. There have been a number of previous studies into the population average ro and Q values (see Chapter 1, Table 1.1 for a summary of these studies) and these studies have used a range of different measurement techniques. In spite of this, our results (for the 6 mm corneal diameter) compared closely to these previous studies, and correlated particularly closely with two more recent studies which have also used a videokeratoscope for corneal measurements (Eghbali et al 1995, Douthwaite et al 1999).
Corneal topography measures have been shown to exhibit a number of changes with subject age (with a shift towards a predominance of ATR corneal astigmatism and slightly steeper, more irregular corneas found after the age of 50) (Hayashi et al 1995, Goto et al 2001). Differences in the age of subjects may therefore be a reason for some of the slight differences in results between our study, and previous studies. Our subjects were all young adults (age range 18-35) whereas most previous studies have
205 Chapter 4 investigated a wider range of ages with many including subjects over the age of 50.
The average Q value for the population in our study (and from previous studies) indicates that the cornea on average is a prolate elliptical shape (i.e. steeper centrally and flattening in the periphery). Some previous investigators have stated that a small subset of normal subjects exhibit an oblate corneal shape (i.e. a cornea that is steeper in the periphery) (Kiely et al 1982b, Guillon et al 1985, Eghbali et al 1995). Eghbali et al (1995) found eight of their 41 subjects to exhibit an oblate corneal profile. In our data only one subject exhibited a positive Q value (oblate cornea) for the 6 mm measurement zone. For corneal diameters larger than 8 mm, all subjects were found to exhibit a prolate elliptical shape.
We found a small but significant meridional variation in the asphericity parameter Q, indicating that the steeper principal corneal meridian flattened at a slightly faster rate than the flattest meridian. Kiely et al (1982b) also investigated for meridional variation in the asphericity of the cornea and could find no specific trend for the Q values to differ from one meridian to the other.
Other investigators have noted some small meridional variations to exist in corneal asphericity (Eghbali et al 1995, Douthwaite et al 1999). Kiely et al’s
(1982b) subjects all had under 2 D of refractive astigmatism. We had only one subject with more than 2 D of refractive astigmatism (Subject 99 had a
2.75 D cylinder refraction). The meridional variation in Q remains significant even if this subject is excluded from analysis (p = 0.01). The difference that
206 Chapter 4 we found between the two principal corneal meridians was quite small in magnitude, but was highly statistically significant. It may be that the meridional differences that exist in corneal asphericity were too small to be accurately ascertained with a photokeratoscope, and were only revealed by using computer-assisted videokeratoscopy.
We have shown that the conic fit parameters ro and Q are highly dependant upon the diameter of cornea measured. With increasing corneal diameter, ro reduces and Q becomes more negative (indicating an increased rate of flattening in the peripheral cornea). With increasing corneal diameter, the
RMS fit error for the conic section also increases markedly. This indicates that although it is convenient and simple to understand, the conic section is a poor estimator of the peripheral cornea. To accurately specify the contour of the peripheral cornea, more complex fitting is required. We found that the use of a 9th order polynomial function provided an excellent fit to the average corneal contour over a 10 mm diameter, producing an RMS fit error 75 times smaller than that given by the simple conic fitting.
The changes occurring in the contour of the cornea in the periphery will have little influence on foveal vision. Peripheral corneal changes do however play a role in off-axis aberrations and vision. It is therefore possible that the changes occurring in the peripheral cornea may be a part of the balancing of the peripheral refraction or aberrations. It is more likely that these changes in shape are occurring for mechanical or anatomical reasons. The marked flattening of the cornea in the periphery is most probably occurring to
207 Chapter 4 produce a smooth transition from the cornea to the flatter scleral surface.
The slight meridional variation in corneal asphericity (i.e. the steeper meridian flattening more rapidly leading to a slight reduction in peripheral corneal toricity) may occur to minimize curvature change at the corneo- scleral limbus, if we assume that the sclera is not toric. The corneal collagen orientation has been found to change in the limbal zone becoming circumferentially oriented in the peripheral cornea (Newton and Meek 1998,
Meek and Boote 2004). This marked change in corneal stromal collagen orientation is the possible anatomical reason for the flattening and reduction in astigmatism found in the peripheral cornea.
We have investigated the average corneal sphero-cylinder based upon the corneal axial power data and found the majority of our subjects exhibited some degree of WTR astigmatism. This is consistent with many previous studies of corneal astigmatism in groups of young healthy adult subjects
(Anstice 1971, Baldwin and Mills 1981, Kiely et al 1982b, Grosvenor and
Ratnakaram 1990, Hayashi et al 1995). The best fit corneal sphero-cylinder was also found to change significantly with increasing distance from corneal centre. On average the best fit sphere became flatter and the amount of corneal astigmatism reduced slightly in the peripheral cornea. This reduction in toricity of the peripheral cornea was consistent with the meridional variation found in the asphericity parameter Q.
Whilst, on average, corneal astigmatism was found to reduce slightly in the periphery, a number of individual patterns of central and peripheral
208 Chapter 4 astigmatism were noted. The majority of subjects exhibited stable peripheral astigmatism (59%) or reducing peripheral astigmatism (30%), with only 10% of subjects exhibiting an increase in corneal astigmatism in the corneal periphery. Guillon et al (1985) noted that the majority of their subjects displayed similar central and peripheral levels of astigmatism, but also noted some individual variations, with some subjects exhibiting a reduction or an increase in peripheral astigmatism. Reddy et al (2000) also classified their subjects’ corneal topography based upon central and peripheral corneal astigmatism. In contrast with our study, Reddy et al (2000) found the most common form of astigmatism to be an increased or irregular astigmatism in the periphery, with stable or reducing corneal astigmatism found to be less common. This difference may be due to the subject selection procedures.
Our study aimed to examine the average corneal topography of normal healthy subjects, whereas Reddy et al’s (2000) study involved subjects who had been fitted with soft toric contact lenses. Thus Reddy et al’s population would be expected to have a much larger proportion of subjects with high degrees of corneal astigmatism (in fact only 6% of their subjects had spherical central corneas). The methods of calculating central and peripheral astigmatism were also different between the two studies. Reddy et al (2000) calculated the central astigmatism based upon the “sim-K” data reported by their videokeratoscope and calculated the peripheral astigmatism based upon four points along the principal meridians 3.5 mm from corneal centre
(the peripheral astigmatism was based upon only three points of peripheral data in cases where there was missing data in the peripheral cornea). In our study central and peripheral astigmatism was calculated based upon all
209 Chapter 4 central (central 4 mm) and peripheral (4 to 8 mm) data points across all semi- meridians (no subjects with any missing data within the central 8 mm corneal diameter were included in analysis) using the methods of Maloney et al
(1993).
The use of Zernike polynomials provides a mathematical description of the entire corneal surface (which does not require averaging across meridians of data as occurs for the conic and polynomial fittings to the average corneal contour). Figure 4.11 shows that the Zernike coefficients that made the greatest contribution to the higher order terms for all corneal diameters were
rd −3 −1 1 th 0 the 3 order Zernike terms ( Z 3 , Z 3 , Z 3 ) and the 4 order term Z 4 . The two terms displaying the most significant change with change in corneal
0 0 diameter were the ‘spherical’ terms Z 4 and Z 6 . The highly significant changes in these terms were due to the significant flattening occurring in the corneal periphery. Other coefficients also exhibited some small, but significant changes. As the corneal topographical maps that we analysed were constructed by combining one central map with six peripheral maps, one may expect that if the central and peripheral data were not correlated well, that significant change may be found in some of the 6th order Zernike
6 −6 terms (e.g. the six lobed terms such as Z 6 or Z 6 ) with increasing corneal diameter. In fact, the 6th order terms were found to be quite small in magnitude and the only term to change significantly with increased diameter
0 was the ‘spherical’ term Z 6 .
210 Chapter 4
Our aim was to investigate the normative shape of the central and peripheral cornea; we therefore chose to fit Zernike polynomials to the corneal surface
(centred on the corneal geometric centre). Whilst this gives us important information regarding the shape of the corneal surface, it is not relevant to vision (particularly for the large corneal diameters that we have analysed it is not practical or realistic to consider the effects of the peripheral cornea on vision). Other investigators, who have been concerned with the central cornea’s effect on vision, have characterised corneal aberrations in terms of
Zernike polynomials fit to smaller diameters of the cornea (which uses ray tracing methods and centring the calculations upon the line of sight, to determine the ‘corneal wavefront error’). It is therefore difficult to make direct comparisons between our study (where we have calculated the Zernike polynomials that best fit the corneal surface) and other studies (who have calculated the Zernike polynomials that fit the aberrations of the corneal surface using ray tracing methods). Studies into corneal aberrations in normal healthy corneas have also found that the 3rd order terms and 4th order
0 spherical aberration term Z 4 to be the ‘dominant’ higher order aberration terms (Artal et al 2001, Wang et al 2003b, Kelly et al 2004). Increasing the corneal diameter over which the corneal aberrations are measured has also been found to cause a general increase in the higher order corneal aberrations, particularly for spherical aberration and coma terms (Oshika et al
1999b, Vinciguerra et al 2003, Nanba et al 2005).
The peripheral cornea will not influence vision significantly, but its shape is of great importance from an anatomical and mechanical point of view. It will be
211 Chapter 4 of particular significance to the design and fitting of contact lenses. Reddy et al (2000) found that the peripheral corneal contour influenced the fitting success of soft toric contact lenses. Improved understanding of the peripheral corneal contour may lead to improvements in the designs or fitting methods with these contact lenses. Many corneal topography systems have the ability to simulate the fitting of RGP contact lenses. Many of these systems use the central corneal curvature combined with a corneal asphericity measurement to calculate the best fitting RGP lens for a particular cornea (Jani and Szczotka 2000). We have shown that significant fitting errors can occur when the peripheral cornea is fitted with a conic section.
These fitting errors to the corneal contour could potentially lead to inaccuracies in the simulated RGP fitting. The use of higher order fits to the peripheral corneal contour may lead to more accurate simulated contact lens fitting programs and may lead to more successful fitting with these programs.
Cho et al (2000) suggested that the fitting of reverse geometry orthokeratology contact lenses requires a higher degree of precision than routine contact lens fitting. Many of these orthokeratology lenses are designed based upon corneal topographical measurements of apical radius and eccentricity (Mountford 1997, Cho et al 2000). Improvements in how we define the shape of the peripheral cornea (i.e. the use of higher order fitting to more accurately quantify the peripheral corneal contour), may improve the accuracy and predictability of current orthokeratology lens designs.
To characterise the shape of the ‘normal’ central and peripheral cornea this study specifically excluded subjects who had corneal disease or who had
212 Chapter 4 undergone corneal surgery. Future research using these techniques to measure the peripheral cornea in subjects undergoing corneal refractive surgery, or orthokeratology may improve our understanding of the changes to the peripheral cornea accompanying these procedures. Investigating the peripheral cornea in subjects with keratoconus or other corneal ectatic disorders may also provide further insight into the aetiology of these corneal diseases.
4.5 Conclusions
In summary, our results for the topography of the central and peripheral cornea have agreed closely with previous investigations. The use of videokeratoscopy with a new measurement technique which allows the combination of central and peripheral corneal topographical data has allowed us to present a highly detailed analysis of the topography of the normal cornea in our large population of young subjects for a larger diameter of the cornea than has previously been reported.
On average, the cornea flattens significantly and becomes slightly less astigmatic in the periphery. However, a number of different “patterns” of central and peripheral astigmatism were found in individual subjects. A conic section was found to be a poor estimator of the corneal shape for the peripheral cornea. Higher order polynomial fits are required to adequately describe the corneal contour in the periphery. The normative values that we
213 Chapter 4 have reported will be of particular relevance for those designing and fitting contact lenses.
214 Chapter 5
Chapter 5: The association between the topography of the cornea and the morphology of the palpebral fissure
5.1 Introduction
In Chapter 2 we have shown that small but significant changes can occur in the shape of the cornea over the course of the day as a result of interactions between the eyelids and the cornea. In Chapter 3 we defined the normal position, angle and shape of the eyelids in three typical angles of vertical gaze in a large population of normal healthy subjects and subsequently reported on the topography of the central and peripheral cornea in this same population in Chapter 4. In this chapter we will explore the association between the shape of the cornea and the morphology of the palpebral fissure in this population of young subjects and investigate how these associations compare with different models of the aetiology of astigmatism.
The concept of eyelid pressure influencing corneal shape is not new.
Reports have appeared since the 1960s relating episodes of monocular diplopia to corneal distortions caused by pressure from the eyelids (Mandell
1966, Knoll 1975). In 1978, Grosvenor proposed a theory on the aetiology of astigmatism whereby pressure from the eyelids causes the cornea to assume it’s typically WTR astigmatic shape. This theory suggests that in the absence
215 Chapter 5 of any external pressure, the cornea would assume a spherical shape, but the pressure from the tarsal plate (in combination with the degree of ocular rigidity) leads to the cornea’s astigmatic shape. Grosvenor (1978) explained that the typical changes in astigmatism with age may be caused by the reduction in eyelid tension with age.
Since Grosvenor’s theory was proposed in 1978 there has been a growing body of evidence to suggest that pressure from the eyelids may indeed play a role in the aetiology of corneal astigmatism. Populations of Native
American and East Asian ethnicity typically show a high prevalence of WTR astigmatism (Abraham and Volovick 1972, Lyle et al 1972, Goss 1989, Kame et al 1993, Dobson et al 1999), and also display characteristic eyelid anatomy/morphology that is different to Caucasian populations. These differences in eyelid anatomy may be expected to increase the pressure of the eyelids on the cornea.
Downs Syndrome, Treacher Collins Syndrome and Spina Bifida are all congenital conditions associated with a high prevalence of astigmatism and a characteristic abnormal slanting of the palpebral fissure (Wang et al 1990, Da
Cunha and de Castro Moreira 1996, Haugen et al 2001a, Paysse et al 2002).
The degree of slanting of the fissure has also been found to be associated with the axis of astigmatism in some cases (Wang et al 1990, Haugen et al
2001a, Paysse et al 2002). Patients with nystagmus also tend to exhibit a high prevalence of WTR corneal astigmatism (Dickinson and Abadi 1984,
Wildsoet et al 2000). It has been hypothesised that the constant eye
216 Chapter 5 movements occurring in nystagmus may lead to increased mechanical force of the eyelids on the cornea, thus leading to the high prevalence of astigmatism often found in these patients (Ohmi and Reinecke 1993,
Wildsoet et al 2000, Sampath and Bedell 2002).
Certain eyelid pathologies which would be expected to increase the normal pressure of the eyelids on the cornea (e.g. chalazia and eyelid capillary hemangiomas) have also been shown to cause significant changes in corneal astigmatism (Nisted and Hofstetter 1974, Robb 1977, Rubin 1975,
Plager et al 1997, Cosar et al 2001). The presence of ptosis and its surgical repair (which again would be expected to alter the mechanical interaction between the eyelids and the cornea) can also cause changes in corneal astigmatism (Cadera et al 1992, Ugurbas and Zilelioglu, 1999).
Studies of subjects with normal lid morphology have also shown that altering the position of the eyelids can cause changes in corneal astigmatism. Lifting the lids has been found to cause significant changes in corneal astigmatism and topography (Wilson et al 1982, Lieberman and Grierson 2000). Grey and Yap (1986) found that narrowing the palpebral aperture caused a significant increase in WTR ocular astigmatism.
A recent study into children with high degrees of WTR astigmatism found a number of associations between the angle of the palpebral fissure and the magnitude and axis of astigmatism (Garcia et al 2004). A significantly higher proportion of the subjects with high corneal astigmatism also displayed
217 Chapter 5 abnormally slanted palpebral fissures. The axis of astigmatism was found to be significantly correlated with the angle of palpebral fissure and the magnitude of corneal astigmatism was found to be significantly correlated with the square of the palpebral fissure angle.
Astigmatism remains one of the most common refractive errors encountered in optometric practice, however its cause remains unknown. Whilst there is some evidence to suggest genetic causes for astigmatism, particularly in cases of high astigmatism where multiple family members are affected
(Clementi et al 1998, Hammond et al 2001), there are also indications to suggest that environmental factors such as eyelid pressure may play a role.
The evidence for eyelid pressure as an aetiological factor in corneal astigmatism is particularly compelling from studies into children with high astigmatism and in certain syndromes and diseases associated with abnormal palpebral fissure morphology and a high prevalence of astigmatism. If eyelid pressure does play a role in corneal astigmatism, then we were interested to investigate whether associations exist between the morphology of the eyelids and the shape of the central and peripheral cornea in a population of young healthy subjects with a range of refractive errors.
218 Chapter 5
5.2 Methods
5.2.1 Subjects and Procedures
One hundred young subjects were recruited for this experiment, primarily from the students and staff of the Queensland University of Technology.
Many of the characteristics of this population have been reported in Chapters
3 and 4. All subjects had normal ocular health, were free of any ocular disease, and had no history of any ocular or eyelid surgery or trauma. None of the subjects were RGP contact lens wearers. Nine of the subjects were part-time soft contact lens wearers and these subjects were requested not to wear their lenses on the day of testing. The subjects’ ages ranged from 18-
35 years with an average age of 24 ± 4 years. Fifty nine of the 100 subjects were female. Eighty of the 100 subjects were of Caucasian ethnic background and 20 were of various East Asian ethnic backgrounds. All subjects had best corrected visual acuity of 6/7.5 or better in their right eye.
Each subject was classified according to their subjective refraction as either: emmetropic (best sphere < +0.75 and > -0.75, cylinder power < 0.75 DC), myopic (best sphere ≤ -0.75 DS, cylinder power < 0.75 DC), myopic astigmatic (cylinder power ≥ 0.75 DC, sphere power ≤ -0.75 DS), or astigmatic (cylinder power ≥ 0.75 DC and sphere power < +0.75 DS and > -
0.75 DS). A detailed description of the 100 subject’s subjective refraction data are presented in Table 5.1. To allow for statistical analysis of the subjective refraction results, each subject’s refractive error was also broken
219 Chapter 5
Table 5.1: Subjective refraction details of the 100 subjects.
Refractive Error Mean Sphere Power ± SD (D) Mean Cylinder Power ± SD (D) n Group (range) (range)
+ 0.05 ± 0.23 -0.04 ± 0.12 Emmetropic 56 (-0.50 to +0.75) (0.0 to -0.50)
-2.56 ± 2.01 -0.21 ± 0.20 Myopic 28 (-0.50 to -7.50) (0.0 to -0.50)
-2.47 ± 1.80 -1.56 ± 0.77 Myopic/Astigmatic 10 (-0.75 to -6.75) (-0.75 to -2.75)
-0.17 ± 0.20 -1.45 ± 0.37 Astigmatic 6 (-0.50 to 0.00) (-0.75 to -1.75)
220 Chapter 5 down into the power vectors M (best sphere), J0 (astigmatism 90/180) and
J45 (astigmatism 45/135) (Thibos et al 1997).
Prior to testing, each subject underwent a slit lamp examination to rule out any anterior eye pathology or tearfilm abnormalities. To reduce the effects of the diurnal variation in corneal topography that was reported in Chapter 2, all measurements were taken in the morning, and subjects were requested to refrain from performing significant amounts of close work prior to testing.
The Medmont E300 videokeratoscope was used for all corneal topographical measurements. The Medmont E300 has been found to give highly accurate and repeatable measurements on inanimate test surfaces (Tang et al 2000) and highly repeatable measurements on human corneas (Cho et al 2002).
Each subject had the corneal topography of their right eye measured using a technique that allows central and peripheral corneal topographical data to be captured and then subsequently combines this data to produce one extended corneal topographical map for each subject. The corneal topographical data from eight subjects was excluded due to poor correlation between central and peripheral topographical data. This method for measuring corneal topography has been described in detail in Chapter 4, and measures a much larger area of the cornea than standard measurements (increase of topographical map dimensions of approximately 30%)
Each extended corneal topography map was rotated to make the corneal geometric centre the reference axis for the maps. A detailed analysis of the
221 Chapter 5 corneal height, axial power and axial radius of curvature was carried out for each subject’s corneal topography data to provide a range of different parameters to describe the corneal topography of the central and peripheral cornea. The best fitting corneal axial power sphero-cylinder (defined by M,
J0 and J45) and the best fitting conic section defined by the apical radius ro and asphericity parameter Q, were all calculated for each subject. Each corneal axial power map was also classified according to the amount of astigmatism in the central 4 mm diameter as either central spherical (<0.75
DC) or central astigmatic (>0.75 DC) and according to the change in astigmatism in the peripheral cornea (stable astigmatism with less than ±0.25
D change, increasing astigmatism by more than 0.25 D and reducing astigmatism by more than 0.25 D). A description of the average corneal topography parameters of the central and peripheral cornea for the population is presented in Chapter 4.
Following the corneal topography measurements, digital images of the right eye in the frontal plane were captured for each subject in primary gaze, 20° downgaze and 40° downgaze. A high resolution Canon 300D 6 mega pixel
Digital SLR camera with a 100 mm macro lens attached to a specially designed camera mount, was used to capture these images. The data from four subjects was excluded due to poor image quality.
Each digital image was analysed using customised software to determine a wide range of biometric measures of the palpebral fissure and anterior eye for each subject in each of the three different angles of vertical gaze. A
222 Chapter 5 detailed description of the method of image capture and analysis is provided in Chapter 3. Measures of the palpebral aperture’s vertical and horizontal dimensions, angle of the palpebral fissure and the contours of the upper and lower eyelids were calculated for each subject. The eyelid contour was quantified by fitting a polynomial function of the form Y = Ax2 +Bx + C to the upper and lower eyelid. In this polynomial, the coefficient “A” refers to the curvature of the eyelid, the term “B” refers to the tilt or angle of the eyelid and the constant term “C” refers to the height of the eyelid above or below the corneal geometric centre. Chapter 3 also details the average morphology of the palpebral fissure for the three different directions of vertical gaze.
Each subject’s central videokeratoscope image was analysed to determine the diameter of the cornea. Customised software was used which allowed the user to locate 16 points at the corneal edge. An ellipse was then fitted to the 16 points defined as the edge of the cornea, using an orthogonal least squares fitting procedure (Ahn et al 2001). This corneal ellipse is defined by its major or longest diameter (diam_A), minor or shortest diameter (diam_B) and theta (i.e. the angle between the major diameter and the horizontal).
The videokeratoscope images were used for this analysis since in these images, subjects have their eyes wide open and thus a large proportion of the edge of the cornea is visible. Correlation analysis was then carried out between the corneal diameter parameters and the corneal topography parameters.
223 Chapter 5
Both corneal topographical and palpebral fissure measures have a tendency to exhibit a high degree of symmetry between right and left eyes (Dingeldein and Klyce 1989, Lam et al 1995, Smolek et al 2002). For this reason, each subject’s right eye only was used for the corneal topographical and palpebral fissure measurements.
5.2.2 Data analysis
For each subject, a range of parameters defining the palpebral fissure morphology and the topography of the cornea were determined. Table 5.2 describes the range of corneal topographical and palpebral fissure morphological parameters that were determined for each subject.
To investigate the associations between the corneal topographical and palpebral fissure morphological measures, correlation analysis was carried out. Each of the corneal topographical parameters (for each of the corneal analysis diameters tested) was compared to each of the palpebral fissure morphological parameters (for each of the vertical angles of gaze measured) and Pearson’s correlation coefficient calculated. The correlation analysis was first carried out for all subjects with valid corneal topographical and eyelid morphological data.
The subjects with central astigmatic corneas (> 0.75 DC, n = 43) and subjects with central spherical corneas (< 0.75 DC, n = 49) were subsequently analysed separately to determine if there were any differences
224 Chapter 5
Table 5.2: The palpebral fissure and corneal topography parameters
ascertained for each subject.
Palpebral Fissure Parameters Corneal Topography Parameters
(0°,20°,40° down gaze)
HEF - Horizontal eyelid fissure width. ro - Corneal Apical Radius
(6 mm, 8 mm 10 mm)
Theta HEF - Angle of the palpebral fissure. Q - Asphericity Parameter
(6 mm, 8 mm, 10 mm)
PC_UL - Vertical distance from upper lid to M - Corneal Best Sphere
pupil centre. ( 4 mm, 6 mm, 8 mm)
PC_LL - Vertical distance from lower lid to J0 - Corneal Astigmatism 90/180
pupil centre (4mm, 6mm, 8 mm)
PA - Vertical distance between upper and J45 - Corneal Astigmatism 45/135
lower lid (4 mm, 6 mm, 8 mm)
Theta Upper Lid - Angle of the upper eyelid Peripheral Corneal M
(4 - 8 mm annulus)
Theta Lower Lid - Angle of the lower eyelid Peripheral Corneal J0
(4 - 8 mm annulus)
Upper eyelid contour polynomial terms A, B Peripheral Corneal J45
and C (4 - 8 mm annulus)
Lower eyelid contour polynomial terms A, B
and C
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To determine if any of the eyelid morphological parameters differed significantly between the astigmatic central corneas and the spherical central corneas, a repeated measures ANOVA was carried out for each of the eyelid morphological parameters with one within-subject factor (angle of gaze) and one between-subjects factor (central corneal astigmatic type).
When the subjects are grouped according to the central corneal cylinder axis
(from the central 4 mm diameter corneal axial power data) as having either
WTR central axis (central corneal cylinder axis 30° - 150°, n = 69), ATR central axis (central corneal cylinder axis 60° - 120°, n = 11) or oblique central axis (OBL, central cylinder axis 30° - 60° or 120° - 150°, n = 12) (Lyle
1991). The most common central corneal cylinder axis was WTR. Figure 5.1 displays a frequency histogram of the subjects’ central corneal cylinder axes.
Only a small number of subjects exhibited ATR or OBL cylinder axes.
Hence, it was difficult to draw any firm conclusions regarding the data from these groups of subjects. The WTR corneal cylinder axis group was therefore analysed separately to determine the association between the corneal topography and eyelid morphology for this group. The WTR subjects were also separated into groups according to their peripheral corneal astigmatism type (i.e. peripheral astigmatism stable, peripheral astigmatism increasing and peripheral astigmatism reducing), and these groups were analysed separately.
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Figure 5.1: Frequency histogram of central corneal cylinder axes (i.e. minus correcting cylinder for right eye) for the 92 subjects with valid corneal topographical data.
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Correlation analysis was also carried out between the corneal diameter parameters and the corneal axial power data. The corneal best fit sphero- cylinder for the 8 mm corneal diameter was compared with the corneal major diameter (diam_A), the toricity of the corneal diameter (“Dtor”, defined as the difference between the major and minor corneal diameters) and corneal diameter theta (i.e. the angle between the diam_A and horizontal).
We also investigated associations between the corneal topographical parameters and the subjective refraction data and between the eyelid morphological data and subjective refraction.
5.3 Results
5.3.1 Corneal topography and eyelid morphology
Correlation analysis revealed a number of highly significant correlations between the eyelid morphological measures and the best fitting corneal axial power sphero-cylinder. Whilst correlations were similar for the different corneal analysis diameters, the strongest and most significant correlations were generally found for the larger corneal analysis diameters (8 mm corneal diameter and peripheral annulus analysis). The correlation between the corneal sphero-cylindrical data and eyelid morphological data was also found to be strongest for the primary gaze eyelid parameters. Correlations became progressively weaker for the 20° and 40° downgaze eyelid parameters.
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Table 5.3 presents the significant correlations (defined by Pearson’s correlation coefficient ‘r’ and p value) between the primary gaze eyelid parameters and the 8 mm corneal axial power sphero-cylinder data. The corneal axial power best sphere “M” showed a highly significant correlation with the horizontal palpebral fissure width (r = -0.428, p <0.001), indicating that the larger the horizontal eyelid dimensions, the flatter the cornea. Figure
5.2 displays a scatter-plot of the corneal best sphere ‘M’ (8 mm diameter) and the horizontal palpebral aperture width measure (HEF, primary gaze).
Corneal J45 was found to exhibit highly significant correlations with the angle of the palpebral fissure in primary gaze. The palpebral fissure angle
(Theta_HEF, r = 0.392, p = <0.001), the angle of the upper lid (Theta_UL, r =
0.232, p = 0.044) and the angle of the lower lid (Theta_LL, r = 0.48 p =
<0.001) all showed significant correlations with corneal J45 (8 mm diameter).
These correlations indicated that subjects with more upward slanting palpebral fissures exhibit more negative J45 (and vice versa). Figure 5.3 illustrates the relationship between corneal J45 (8 mm analysis diameter) and the angle of the palpebral fissure (primary gaze Theta_HEF).
The amount and sign of corneal J45 will determine each subject’s cylinder axis. A positive J45 indicates a cylinder axis between 0° and 90°, and a negative J45 an axis between 90° and 180°. We also examined the correlation between corneal cylinder axis and the angle of the eyelids.
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Table 5.3: Results from correlation analysis between corneal axial power sphero-cylinder data (8 mm) and primary gaze eyelid morphological parameters (n = 78). Note only significant correlations are shown.
PRIMARY GAZE EYELID PARAMETERS HEF Theta PC_UL PC_LL PA Theta_ Theta_ Upper Eyelid Contour Lower Eyelid Contour HEF UL LL Topography A B C A B C measures M r -0.428 -0.249 -0.275 p <0.001 0.03 0.016 J0 r 0.298 0.288 p 0.009 0.012 J45 r 0.392 0.232 0.48 0.246 0.473 p <0.001 0.044 <0.001 0.036 <0.001
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Figure 5.2: Corneal best sphere ‘M’ for 8 mm analysis diameter versus primary gaze horizontal palpebral fissure width (HEF).
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Figure 5.3: Corneal J45 for 8 mm analysis diameter versus primary gaze palpebral fissure angle (Theta_HEF). Note the more up-slanted palpebral fissure is associated with a more negative J45 (indicating a cylinder axis between 90 and 180), and more down-slanting palpebral fissure is associated with a more positive J45 (indicating a cylinder axis between 0 and
90).
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For this analysis, the cylinder axes were transposed so that the horizontal cylinder axes were continuous (i.e. a cylinder axis of 170° was transposed to be -10° so that the axes were continuous around the horizontal). The corneal cylinder axis also showed significant correlations with primary gaze eyelid angles Theta_HEF (r = 0.317, p = 0.005) and the upper (Theta_UL, r =
0.308, p = 0.007) and lower eyelid angles (Theta_LL, r = 0.364, p = 0.001).
The positive correlation between the corneal cylinder axes and the palpebral fissure angles indicated a tendency for the cylinder axis to be at a similar angle to the angle of the palpebral fissure in primary gaze. The correlations between the lid angle and cylinder axis were strongest for the lower eyelid angles, indicating that the steepest corneal meridian had a tendency to be aligned perpendicular to the angle of the lower eyelid. This is evident in
Figure 5.4 which shows the corneal axial power maps for two subjects overlayed with their primary gaze eyelid images.
The best fitting conic section to the corneal height data showed some associations with the eyelid parameters. The apical radius ro (8 mm diameter) was significantly correlated with the primary gaze palpebral fissure width (HEF) exhibiting a correlation coefficient r of 0.449 and p value < 0.001
(i.e. a similar result to the correlation between HEF and corneal best sphere
M, as would be expected). The asphericity parameter Q showed no significant correlation with any of the eyelid parameters for any of the corneal analysis diameters.
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Figure 5.4: Example of the correlation between the angle of the palpebral fissure and the angle of the corneal cylinder axis for two subjects. Subject 62 has a slightly up-slanted palpebral fissure (Theta_HEF of -7°) and a cylinder axis of 173°, subject 91 has a slightly downward slanted palpebral fissure (Theta_HEF of 4.5°) and a cylinder axis of 15°. Note also the tendency for the steepest corneal meridian to align at right angles to the angle of the lower eyelid.
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When the subjects were grouped according to central corneal astigmatism magnitude (i.e. central spherical corneas < 0.75DC or central astigmatic corneas > 0.75DC), correlation analysis between the corneal topographical parameters and the eyelid morphological parameters revealed similar trends to those when all subjects data were analysed as a group. Both groups still exhibited a highly significant correlation between the corneal J45 (8 mm diameter) and primary gaze palpebral fissure angle Theta_HEF (r = 0.41, p =
0.014 for the astigmatic central group, and r = 0.42, p = 0.006 for the spherical central group). The astigmatic central group showed a stronger correlation between the corneal J45 for the lower lid angle (r = 0.511, p = <
0.001) and no significant correlation with the upper lid angle (r = 0.086, p =
0.621). The spherical central group exhibited a stronger correlation between corneal J45 and the upper lid (r = 0.495, p = 0.001) than for the lower lid (r =
0.301, p = 0.056). This suggests that the angle of the lower lid has more influence on the axis of astigmatism for subjects with higher degrees of astigmatism.
Repeated measures ANOVA revealed no significant between-subjects effect due to central corneal astigmatism type for any of the eyelid parameters (i.e. there was no eyelid morphological parameter that was significantly different between the central astigmatic cornea group and the central spherical cornea group).
The correlation analysis was also performed for only those subjects exhibiting WTR central corneal cylinder axes. When all of the WTR subjects
235 Chapter 5 were analysed together, corneal M (8 mm diameter) showed significant correlation with the primary gaze palpebral fissure width (HEF, r = -0.422, p =
0.001). Corneal J0 (8 mm) showed a significant correlation with the curvature of the lower lid in primary gaze (lower lid “A”, r = -0.335, p = 0.001), indicating the subjects with more WTR corneal astigmatism exhibit a flatter curve of their lower eyelid. Corneal J45 (8 mm) showed significant correlation with Theta_HEF (r = 0.374 p = 0.004) and with the angle of the lower eyelid Theta_LL (r = 0.511, p = <0.001) in primary gaze. Table 5.4 shows the correlation coefficients (r) and significance levels (p) for the analysis of all of the WTR subjects.
The WTR subjects data were further classified into different peripheral astigmatism categories (reducing peripheral astigmatism n = 19, stable peripheral astigmatism n = 34 and increasing peripheral astigmatism n = 5).
The subjects with increasing and stable peripheral astigmatism were analysed together (as these subjects represented those with astigmatic peripheral corneas, or who would be expected to have astigmatism from
‘limbus to limbus’). The subjects with stable or increasing peripheral astigmatism exhibited stronger correlations between corneal topographical measures and primary gaze eyelid morphology than those with reducing peripheral astigmatism.
The stable or increasing peripheral astigmatism group exhibited significant correlations between corneal best sphere M (8mm) and HEF (r = -0.562, p <
0.001), corneal J0 (8 mm) and lower lid “A” (r = -0.59, p < 0.001), and
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Table 5.4: Results from correlation analysis between corneal axial power sphero-cylinder data (8 mm) and primary gaze eyelid morphology parameters for subjects exhibiting WTR central corneal cylinder axis (n = 58). Only significant correlations are shown.
PRIMARY GAZE EYELID PARAMETERS HEF Theta PC_UL PC_LL PA Theta_ Theta_ Upper Eyelid Contour Lower Eyelid Contour HEF UL LL Topography A B C A B C measures M r -0.422 p 0.001 J0 r -0.335 p 0.001 J45 r 0.374 0.511 0.503 p 0.004 <0.001 <0.001
237 Chapter 5 corneal J45 (8 mm) and Theta_HEF (r = 0.54, p = 0.001), Theta_UL (r =
0.343, p = 0.038 , and Theta _LL (r = 0.49, p = 0.002). The reducing peripheral astigmatism group only exhibited a significant correlation between corneal J45 (8 mm) and primary gaze Theta_LL (r = 0.562 p = 0.012).
The stable and increasing peripheral WTR astigmatic group were analysed further, by only including the subjects with central corneal astigmatism (>
0.75 DC). When only the WTR subjects with central astigmatism (> 0.75 DC) which was stable or increasing in the periphery were analysed, the correlations between the corneal axial power sphero-cylinder and the primary gaze eyelid morphological parameters were found to be stronger. Table 5.5 shows the results of the correlation analysis for these subjects. Corneal J45 showed highly significant correlation with Theta_HEF (r = 0.718, p = 0.002) and Theta_LL (r = 0.612, p = 0.012). Figure 5.5 shows a scatter-plot of corneal J45 and Theta HEF for these subjects. Corneal J0 showed a significant correlation with lower lid contour term “A” (r = -0.517, p = 0.04).
5.3.2 Corneal diameter and corneal power
Some associations were found between corneal topographical parameters and the corneal diameter. Table 5.6 displays the correlation coefficients r and significance p for the correlations between the corneal topographical parameters (8 mm) and the corneal diameter analysis. The corneal axial power best sphere was found to be significantly correlated with the corneal
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Table 5.5: Results from correlation analysis between corneal axial power sphero-cylinder data (8 mm) and primary gaze eyelid morphology parameters for subjects with WTR corneal cylinder axes and central corneal astigmatism (<0.75 DC) that was stable or increased in the peripheral cornea (n = 16). Only significant correlations are shown.
PRIMARY GAZE EYELID PARAMETERS HEF Theta PC_UL PC_LL PA Theta_ Theta_ Upper Eyelid Contour Lower Eyelid Contour HEF UL LL Topography A B C A B C measures M r -0.573 p 0.02 J0 r -0.517 p 0.04 J45 r 0.718 0.612 0.603 p 0.002 0.012 0.013
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Figure 5.5: Scatter plot of corneal astigmaticsm 45/135° (J45) versus angle of the palpebral fissure (Thete_HEF) for subjects exhibiting WTR corneal cylinder axes and central astigmatism (>0.75DC) that was stable or increasing in the peripheral cornea.
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Table 5.6: Results for correlation between corneal diameter and corneal axial power.
Corneal Topographical Parameter
Axial Power 8mm Diameter
Sphere Cylinder Axis
Diam_A r -0.399
p <0.001
Diameter Toricity r 0.429
p <0.001
Diameter Theta r 0.152
p 0.183
241 Chapter 5 diameter (diam_A) (r = -0.39, p < 0.001), indicating that larger corneas tend to be flatter.
A weak, but significant correlation was found between the magnitude of corneal astigmatism and the toricity of the corneal diameter (r = 0.429, p <
0.001), indicating that subjects with more astigmatic corneas tend to display more toricity of the corneal diameter. No significant relationship was found between the axis of astigmatism and the axis of the corneal diameter ellipse.
Correlation analysis was also carried out between the corneal diameter and the eyelid parameters. In general, only very weak correlations were found between the eyelid parameters and the corneal diameter. The strongest correlation was that between the major diameter (diam_A) and the primary gaze horizontal palpebral fissure width, HEF (r = 0.435, p < 0.001).
5.3.3 Eyelid morphology and refractive error
Some weak but significant correlations were found between the eyelid morphology parameters and the subjective refraction data. Similarly to the corneal data, subjective refraction J45 showed significant correlation with primary gaze Theta_HEF (r = 0.227, p = 0.026) and with lower lid angle
Theta_LL (r = 0.326, p = 0.001).
The subjective refraction best sphere ‘M’ showed a weak but significant correlation with 40° downgaze pupil centre to upper lid measure (r = 0.239, p
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= 0.019), indicating that the more myopic subjects exhibited a lower position of the upper eyelid in 40° downgaze.
5.3.4 Corneal topography and refractive error
Correlation analysis was carried out to investigate if there was any association between the subjective refractive error best sphere and the corneal topographical parameters. For the 8 mm corneal diameter analysis the refractive error best sphere showed a weak but significant correlation with corneal best sphere “M” (r = -0.266, p = 0.019 ), indicating a tendency for the more myopic subjects to exhibit slightly steeper corneas. The best sphere refraction also showed a significant correlation with corneal J0 (r = -0.385, p
= 0.001) and corneal J45 (r = -0.284, p = 0.012), indicating the more myopic subjects also exhibited more astigmatic corneas (particularly WTR astigmatism). The correlation coefficient and significance values were also found to be similar for the 4 mm, 6 mm and peripheral annulus corneal analysis diameters. No significant correlation was found between the asphericity parameter Q and best sphere refractive error in our population for any of the corneal analysis diameters tested (r = 0.102, p = 0.335 for the 8 mm corneal diameter).
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5.4 Discussion
The major finding of this study is that significant correlations exist between certain parameters of the morphology of the eyelids and parameters relating to the topography of the cornea. Significant correlations were found between the spherical corneal power and the eyelid morphology, as well as between corneal astigmatism and certain eyelid parameters. Previous investigators have shown correlations between corneal astigmatism and eyelid parameters in subjects with eyelid pathologies (Robb 1977), in some congenital malformation syndromes associated with abnormal palpebral fissure slanting
(Wang et al 1990, Haugen et al 2001a, Paysse et al 2002) and in children with high degrees of astigmatism (Garcia et al 2004). We have shown that associations between the morphology of the eyelids and the shape of the cornea also occur in a population of normal healthy young adult subjects.
Corneal spherical power tended to correlate with measures of overall eye size (i.e. horizontal palpebral fissure width and corneal diameter). Corneal diameter was significantly correlated with the horizontal palpebral fissure width, and the horizontal palpebral fissure width was significantly correlated with the central corneal best sphere ‘M’. These associations suggest that there are some parallels occurring in the growth of the different anterior eye ocular components as may be expected (i.e. subjects with larger palpebral fissures tend to also have larger corneas and subsequently flatter central corneal curvature). A previous study into foetal facial growth in humans has found significant correlations between many orbito-facial measures (including
244 Chapter 5 the palpebral fissure width) and the diameter of the cornea (Denis et al
1995b). Denis et al (1995b) suggest that horizontal growth of the eye as measured by the corneal diameter is related to that of the face and the body as a whole. Rasooly and Zauberman (1988) also found a significant correlation between corneal curvature and subject height and head diameter in adult subjects (with a larger head diameter being associated with a flatter cornea).
The correlations found between corneal astigmatism and the eyelid parameters indicate that in general, the angle of the eyelids is associated with the axis of corneal astigmatism. These correlations between the palpebral fissure angle and corneal J45 are significant for both subjects with low (< 0.75 DC) degrees and for subjects with higher degrees (> 0.75 DC) of corneal astigmatism. The majority of the correlations between corneal astigmatism and the eyelid parameters relate to the axis of astigmatism as opposed to the magnitude. This indicates that the morphology of the eyelids in this population of normal subjects has a greater association with the axis of astigmatism than with the magnitude of astigmatism. The correlation coefficients (r) between corneal J45 and the different eyelid angles ranged from 0.3 to 0.5. While these correlations are relatively weak, they do indicate that 10 - 25% of the variance in corneal J45 can be accounted for by the eyelid angles. There are obviously a number of other unknown factors that are also contributing to the amount of corneal J45 in these subjects (e.g. eyelid tension, corneal rigidity, or genetic factors associated with corneal shape).
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Whilst significant correlations were found between the eyelid morphological and the corneal topographical parameters when the data from all subjects were analysed together, the strongest associations were found for subjects with WTR central corneal astigmatism (> 0.75 DC) that was stable or increasing in the periphery. The correlation coefficient (r) between corneal
J45 and palpebral fissure angle was found to be 0.72, indicating that 52% of the variability in corneal J45 can be accounted for by the palpebral fissure angle in these subjects. Lesser correlations were found for subjects exhibiting central WTR astigmatism which reduced in the periphery.
Subjects with central astigmatism and stable or increasing peripheral astigmatism have an astigmatic cornea extending into the peripheral cornea to an 8 mm diameter. If the pressure from the eyelids is causing an overall
‘bending’ of the cornea to lead to its astigmatic shape, then one would most probably expect this astigmatism to extend into the peripheral cornea, at least to the position of the eyelids in primary gaze (the average distance from corneal centre to upper lid was 3.6 mm and from corneal centre to lower lid was 6 mm). The pattern of astigmatism shown by these subjects (who exhibited the highest correlations between corneal astigmatism and eyelid angles) is therefore consistent with the corneal shape being altered through mechanical pressure from the eyelids. It is also a possibility that the eyelids were passively following the shape of the peripheral cornea, however the magnitude of change in eyelid position due to this would be expected to be small.
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There was no significant difference between the eyelid morphological parameters of the subjects exhibiting central spherical corneas and the subjects exhibiting central astigmatic corneas. This suggests that the defining reason for the corneas being more astigmatic does not relate directly to the measured eyelid parameters in this study. It is possible that the reason for the presence of the central astigmatism is due to differences in corneal anatomy or physiology (e.g. differences in stromal collagen architecture or corneal rigidity), or perhaps in an eyelid factor that was not measured (e.g. eyelid tension). Therefore while the subjects with astigmatic and spherical central corneas may collectively exhibit similar eyelid morphology, they may differ in their response to eyelid pressure.
There were only small numbers of subjects exhibiting ATR and OBL central corneal cylinder axes. We were therefore unable to draw any reliable conclusions regarding the association between the eyelid parameters and the corneal topography for these subjects. It is difficult to envisage how eyelid morphology or pressure could result in ATR astigmatism. However, the fact that when all subjects are analysed together (i.e. WTR, ATR and OBL included) the correlations between lid angle and corneal astigmatism remain highly significant suggests that the lid angles may play a part in the astigmatism development for the ATR and OBL subjects also. Further research is required investigating a larger population of subjects with ATR and OBL corneal cylinder axes, to confirm this.
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The eyelid morphological parameters relating to the lower eyelid were often found to give stronger correlations with corneal astigmatism than those of the upper lid. This is an interesting finding as it has typically been pressure from the upper eyelid that has been implicated in the cause of astigmatism
(Grosvenor 1978). It is possible that the lower lid does play a more important role in determining corneal shape than has previously been thought. Kessing
(1967) found that the entire tarsal area of the lower lid was in contact with the globe, whereas only the margin of the upper eyelid was in contact with the globe, which suggests that the area over which the lower lid exerts pressure on the globe is greater than the upper lid. However, Doughty et al (2004) noted that Marx’s line (the presumed point of contact between the marginal area of the eyelid and the globe) was present on both the upper and lower lid, suggesting a similar distribution of eyelid pressure between the two eyelids. A significant correlation was found between the magnitude of corneal J0 and the curvature of the lower eyelid for subjects exhibiting WTR corneal astigmatism, with a flatter lower eyelid curvature being associated with greater degrees of WTR astigmatism. It is conceivable that the curve of the eyelid may be related to eyelid tension, if this is the case then one would expect that a tighter lid would be associated with a flatter lower eyelid curve.
Thus the tension in the lower eyelid may be related to the magnitude of WTR astigmatism.
There is limited information regarding the tension of the lower eyelid, as studies into eyelid tension generally concentrated upon the tension in the upper eyelid (Hung et al 1977, Vihlen and Wilson 1983, Evinger et al 1984,
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Ehrmann et al 2001). Francis et al (2005) measured the tension of the lower eyelid and reported a similar level of tension to that previously found for the upper lid. Our results suggest that the angle of the lower eyelid and the curvature of the lower eyelid have an influence on the angle and magnitude of corneal astigmatism in some subjects. Further research on the tension of the lower eyelid and its possible association with astigmatism is needed to fully clarify the reason for the correlations found. Significant changes occur to the position of the lower eyelid over the age of 50, consistent with a reduction in the tension of the lower lid with age (Shore 1985, Van den Bosch et al 1999). However, Francis et al (2005) found no significant change in lower eyelid tension with age (although they suggested that more subjects with a wider range of ages may be required to fully investigate the changes in lower eyelid tension with age). The age-related changes in the lower eyelid may be a factor in the typical shift in corneal astigmatism towards ATR after the age of 50 years.
We found the amount of toricity of the corneal diameter to be significantly correlated with the magnitude of corneal astigmatism. Edmund (1988) also investigated the relationship between corneal diameter and central corneal curvature, and found a similar correlation between central corneal astigmatism and the toricity of the corneal diameter in their normal subjects.
The fact that the magnitude of the corneal astigmatism tends to be associated with the magnitude of toricity of the corneal diameter, suggests that astigmatic subjects have a cornea that has an astigmatic overall form
(i.e. a cornea that is inherently astigmatic). The axis of the astigmatism did
249 Chapter 5 not correlate significantly with the angle of the corneal diameter ellipse, suggesting that other factors may be playing a role in determining the axis of corneal astigmatism (e.g. environmental factors such as eyelid pressure).
A number of our results support a model for corneal astigmatism development based upon mechanical pressure from the eyelids. In this model, we expect that corneal characteristics such as stromal collagen architecture, corneal rigidity and eyelid parameters such as eyelid angles and tension of the eyelids, would be inherited traits and that sustained pressure from the eyelids throughout life could lead to the cornea’s characteristic shape. In this model, one would expect that the angle of the eyelids would be correlated with the axis of astigmatism (as was found in our study). But such a model would also lead to the expectation that the magnitude of corneal astigmatism would be related to eyelid factors, yet this was generally not found to be the case in our subjects. However, the magnitude of astigmatism may be more dependant upon some other characteristics (not related to the angle or position of the eyelids) such as the stromal collagen architecture or the degree of pressure exerted by the lids. We did not assess the tension of the eyelids in our subjects, so there remains a possibility that this factor did play a role in determining the magnitude of astigmatism. It is most likely that multiple factors like the eyelid tension, eyelid position, along with the corneal physiological characteristics (such as stromal collagen orientation and corneal rigidity) all play a role in determining the magnitude of astigmatism.
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Whilst the significant correlations found between the eyelid morphology and corneal astigmatism tend to support an eyelid pressure model of corneal astigmatism development, it does not prove that pressure from the eyelids is causing corneal astigmatism. Another possible reason for the associations found would be a ‘correlated growth model’ of astigmatism development. In this model, we assume that pressure from the eyelids has a negligible effect on corneal shape throughout life. Corneal and eyelid parameters would therefore all be primarily inherited characteristics. For non-causal associations to occur between the eyelid parameters and corneal shape, correlations in the normal growth of these structures would need to occur
(presumably due to a similar genetic influence upon these ocular components). The finding that the corneal best sphere correlated significantly with the horizontal palpebral fissure width tends to support this correlated growth model. However if the eyelids and cornea were growing in a correlated manner so that the axis of corneal astigmatism was consistent with the angle of the eyelids (as our results have shown), then one would also expect that the angle of the corneal diameter ellipse would also correlated with the palpebral fissure angles. However, no significant correlation was found between the eyelid angles and the angle of the corneal diameter ellipse.
Some recent studies with animals have suggested that corneal astigmatism can develop in response to imposed astigmatic defocus (Kee et al 2004). It is therefore also possible that the development of corneal astigmatism in humans may at least partly involve a visual feedback mechanism. In this
251 Chapter 5 model, the corneal growth would be mediated by visual feedback, presumably leading towards emmetropia (i.e. emmetropization). Buehren et al (2003a) found that pressure from the eyelids on the cornea during downgaze reading typically leads to an increase in ATR astigmatism.
Therefore in a model involving a visual feedback mechanism, for a group of subjects typically performing a large amount of closework, the cornea may have a tendency to grow in a WTR direction to compensate for the ATR shift occurring as a result of the corneal changes during reading. If this was true, one would expect the ATR change to be associated with the angle and position of the eyelids in downgaze, and therefore the subsequent WTR compensatory shift would also be expected to be associated with eyelid parameters in downgaze. However, the corneal astigmatism parameters in our subjects showed their strongest correlations with the primary gaze eyelid morphological parameters and not with the downgaze eyelid parameters, as would be predicted by this visual feedback model.
A weak but significant correlation was found between subjective refraction best sphere ‘M’ and the distance from pupil centre to the upper lid in 40° downgaze. Subjects with a lower resting position of the upper eyelid in 40° downgaze exhibited higher degrees of myopia. To provide the clearest view of the palpebral fissure, our subject’s refractive errors were uncorrected for the capturing of the palpebral fissure images. For myopic subjects (> -2.00
D) the fixation target for the capturing of the palpebral fissure images would be expected to be defocused to some degree. Subjects may therefore have narrowed their palpebral aperture in order to see the fixation target more
252 Chapter 5 clearly. This may have led to the myopic subjects exhibiting narrower palpebral apertures than our emmetropic subjects, and may have led to the significant correlation between PC_UL and best sphere refractive error.
However, if the myopic subjects were narrowing their eyelids to see the fixation target during the palpebral aperture image capture, one would expect that the correlation between palpebral aperture width would be significant for all angles of gaze, and for the PC_LL and PA measure. This was not found to be the case.
Buehren et al (2005) found their myopic subjects exhibited significantly greater corneal distortions following reading due to narrower palpebral apertures in downward gaze than their emmetropic subjects. They suggested that the increased corneal distortions following downgaze reading may provide a cue to eye growth in myopia. The significant correlation between subjective refraction ‘M’ and pupil centre to upper eyelid (albeit a very weak one) tends to support this theory as a narrower aperture during reading would tend to increase corneal distortions due to eyelid pressure which may promote more myopia. There is also some recent evidence from studies with monkeys that deprivation of peripheral form vision leads to changes in foveal eye growth and myopia development (Smith et al 2005).
Meyer et al (1993) illustrated that even mild degrees of ptosis can cause significant visual field depression, particularly in the superior hemi-field. A lower upper eyelid position in downward gaze may therefore promote myopic eye growth due to deprivation of peripheral form vision.
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5.5 Conclusions
None of the possible models of astigmatism development that we have discussed exactly matches with our experimental results. It therefore appears that the most likely explanation of our results may be a combination of correlated growth and eyelid morphology. To ascertain which model of corneal astigmatism development is the most appropriate, further research needs to be carried out. Two factors that are likely to be important for further understanding of astigmatism development are an accurate measure of upper and lower eyelid tension, and a measure of the rigidity of the cornea.
In summary, we have shown that a number of parameters relating to the morphology of the palpebral fissure are significantly correlated with parameters relating to the shape of the cornea in a normal population of young subjects. These results add to the body of evidence to suggest that pressure from the eyelids is a significant factor in the cause of corneal astigmatism. However we have not proven that pressure from the eyelids causes corneal astigmatism.
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Chapter 6: Conclusions
6.1 Summary and main findings
6.1.1 The diurnal variation of corneal topography
In our first experiment that examined the diurnal variation of corneal topography, small but highly significant changes were found to occur in the shape of the cornea over the course of the day and week. Many of these changes appear to occur as a result of pressure from the eyelids on the cornea and manifest themselves as band-like areas of corneal distortion in the upper and lower regions of the cornea. Buehren et al (2003a) found similar changes occurring in the cornea as a result of eyelid pressure from reading for 1 hour in downward gaze. As well as these localised corneal changes occurring, some significant changes were also found in corneal astigmatism. A small reduction in corneal J0 was found to occur over the course of the day (i.e. an increase in ATR astigmatism), and a small increase in corneal J0 (i.e. an increase in WTR astigmatism) was found to occur over the course of the week (Monday to Friday).
The results from this study confirm the slight steepening of the cornea throughout the day found by previous investigators, but through the use of videokeratoscopy and modern corneal topographical analysis techniques, we were able to speculate further upon the aetiology of the diurnal corneal
255 Chapter 6 variations found. It appears that pressure from the eyelids on the cornea plays a role in these diurnal corneal changes, including changes in astigmatism. Buehren et al (2003a) found that eyelid induced corneal distortions typically resulted in a change towards an increase in ATR corneal astigmatism. This is the likely cause of the slight shift in J0 that was found over the course of the day. Grosvenor (1978) speculated that the band-like pressure from the eyelids on the cornea caused the cornea to assume its typically WTR shape (i.e. pressure from the eyelids caused the cornea to be steeper in the vertical meridian than the horizontal). It is therefore possible that pressure from the eyelids on the cornea over the week caused the slight increase in J0 over the course of the week. We may have therefore observed short term (resulting in an increase in ATR corneal astigmatism over the course of the day) and longer term corneal changes (resulting in an increase in WTR corneal astigmatism over the course of the week) due to eyelid pressure in this experiment.
Corneal topography in this study was measured on three days of a normal working week (i.e. Monday to Friday). Corneal J0 was found to change by approximately 0.02 D over the week (difference between Monday and Friday group mean J0 measurements for the 5.5 mm analysis diameter). If one assumes that this same magnitude of change in astigmatism occurs every week as a result of eyelid pressure, then this equates to approximately 1 D change in J0 over the course of the year. Obviously this assumes that the subjects would be performing the same type and amount of visual tasks every week and that no regression of these astigmatic changes occurs on
256 Chapter 6 non-working days, which may in fact not be the case. It is likely that on non- working days, most subjects are performing less concentrated work with the eyes. Therefore, we expect that some regression of the changes in corneal astigmatism would occur on those days when subjects are not at work. This regression on non-working days would lead to the total change in corneal astigmatism over a longer period of time being much smaller. Further study measuring corneal topography over a longer time period would be required to clarify the degree of change in corneal astigmatism over time and the amount of any regression of change that occurs on non-working days.
Both the short and long term changes found in corneal astigmatism were very small in magnitude, and would not be expected to have any clinically significant effects on vision. However these results support the hypothesis that pressure from the eyelids is a factor in the aetiology of corneal astigmatism. This led us to begin further investigations into the association between the eyelids and the shape of the cornea.
6.1.2 The association between corneal topography and eyelid
morphology
In Chapters 3, 4 and 5 we further explored the possibility that the eyelids play a part in the aetiology of corneal astigmatism. A comprehensive assessment of the topography of the cornea and the morphology of the palpebral fissure was carried out on a large population of young healthy subjects.
257 Chapter 6
In Chapter 3 we defined the average morphology of the palpebral fissure in this population of young subjects. High resolution digital images were taken of the anterior eye and adnexae in three different directions of vertical gaze using a specially made camera apparatus. Customised software was then used to determine an extensive range of parameters defining the angle, position and contour of the palpebral fissure for each subject. Improvements in digital imaging technology, allowed us to conduct a detailed investigation of the average angle, position, contour of the palpebral fissure. Highly significant changes were found to occur in the palpebral fissure morphology with shifts in vertical gaze. Defining the average morphology of the palpebral fissure in detail is important for a number of clinical applications including the diagnosis of normal and abnormal eyelid position, assessment of eyelid surgery, and contact lens fitting and design.
In Chapter 4 we examined the average topography of the cornea on this same population. By using a technique that allowed the capture and subsequent combination of corneal topography data from the central and peripheral cornea to provide one large extended corneal topography map we have been able to present a detailed assessment of the topography of the cornea in the centre and periphery close to the limbus. In general, corneal astigmatism was found to reduce in magnitude in the peripheral cornea, however, a number of different patterns of peripheral corneal astigmatism were identified (i.e. increasing, reducing or stable peripheral astigmatism). A conic section was found to be a poor descriptor of the corneal contour in the peripheral cornea (i.e. greater than 6 mm diameter). A comprehensive
258 Chapter 6 description of the average topography of the central and peripheral cornea from a large population of young subjects is particularly useful for the design and fitting of contact lenses.
In Chapter 5 we explored the associations between the average corneal topographical measures and the average eyelid morphological parameters.
Highly significant associations were found between certain parameters describing corneal astigmatism and parameters describing the morphology of the palpebral fissure. A general tendency for subjects with larger eyes (i.e. wider horizontal palpebral fissure widths) to exhibit larger corneas (larger corneal diameters) and subsequently display flatter central corneal powers was found. This suggests that there are some parallels in the general growth of the cornea and of the eyelids. Previous studies have also found associations between measures of facial and body size and corneal diameter and curvature (Rasooly and Zauberman 1988, Denis et al 1995b).
There were also highly significant associations found between the angle of the eyelids and the axis of corneal astigmatism. The strongest correlations between corneal astigmatism and the palpebral fissure angle were found for subjects exhibiting WTR corneal astigmatism that was stable or increasing in the peripheral cornea (i.e. subjects with significant amounts of WTR corneal astigmatism that extended to the peripheral cornea). This pattern of astigmatism (i.e. astigmatism in the peripheral cornea) is consistent with an overall bending of the cornea (involving the total corneal thickness) into an
259 Chapter 6 astigmatic shape as may be expected to occur as a result of pressure from the eyelids.
The most significant associations between corneal astigmatism and eyelid morphology were found for the primary gaze eyelid parameters. Weaker correlations were found between corneal astigmatism and the eyelid morphology parameters in down gaze. One would expect that the magnitude and angle at which pressure from the eyelids is exerted on the cornea would be dynamic over time. The pressure would be expected to change depending on the nature of task being performed. For example the angle and position of the lids in relation to the cornea changes significantly with shifts in vertical gaze which would potentially alter the amount and direction of pressure from the lids on the cornea. Also the amount of eye movement and direction of eye movements such as reading involving predominantly horizontal eye movements would be expected to induce different pressures compared to a task involving vertical eye movements or no eye movements.
The magnitude of pressure and angle of the eyelids in relation to the cornea during blinking may also be a factor. To our knowledge there is no specific literature outlining the angle and contour of the eyelids during blinking, and thus further research (using high speed imaging) would be required to investigate this feature of eyelid pressure. Since the pressure from the eyelids on the cornea is influenced by many factors, the shape of the cornea would therefore be expected to be determined as a result of the amount and regional distribution of pressure over time. From our data it appears that the
260 Chapter 6 static images taken of the eye in primary gaze give the best approximation of the average position of the eyelids over time.
The eyelid morphology parameters were found to show significant correlations with the axis of corneal astigmatism and only limited association with the magnitude of corneal astigmatism. It might therefore be possible to predict the axis of astigmatism based upon the angle of the palpebral fissure
(particularly for subjects with central WTR astigmatism that is stable or increasing in the peripheral cornea). However, there is little evidence to suggest that we can predict the magnitude of astigmatism based upon the morphology of the palpebral fissure in our subjects.
Whilst the associations found between corneal astigmatism and eyelid morphology are further evidence to support the theory that pressure from the eyelids is important in the aetiology of corneal astigmatism, they do not prove causation.
6.2 A possible model of corneal shape and astigmatism development
Based upon the associations we found between eyelid morphology and corneal topography, it is possible to formulate a hypothetical model of astigmatism development. This model is based upon the assumption that mechanical interaction between the eyelid and the cornea is having
261 Chapter 6 significant influence on the corneal shape. Figure 6.1 illustrates this proposed model of corneal astigmatism development.
A number of recent studies suggest that genetic factors play an important role in the aetiology of astigmatism (Clementi et al 1998, Hammond et al
2001). We expect that many of the individual characteristics of the cornea and the eyelids would be inherited traits. Corneal characteristics such as the corneal stromal collagen architecture (e.g. the orientation of stromal collagen fibrils and linkages between fibrils), and the thickness and rigidity of the cornea may all be inherited. Eyelid morphology such as the angle, position and contour of the eyelids, along with the tension of the eyelids are also likely to be inherited traits. The characteristics of the cornea would then interact with the characteristics of the eyelids throughout life to lead to the shape of the cornea for each individual. Environmental factors such as types of visual tasks performed, contact lens wear and even general health and nutritional factors may all be expected to play a role in altering the interactions that occur between the corneal and eyelid characteristics to determine corneal shape.
This proposed model can account for a number of the known changes in corneal astigmatism that happen with age. Most studies of corneal shape in newborns and infants have typically shown the cornea to be steep and exhibit a high prevalence of astigmatism (typically ATR) in the months following birth (Howland and Sayles 1985, Asbell et al 1990, Frilling et al
2004). Over the first few years of life, the cornea undergoes significant
262 Chapter 6
Figure 6.1: Representation of the proposed model of the cause of corneal astigmatism. (Corneal cross section diagram from Snell and Lemp (1989)).
References: 1 (Boote et al 2005), 2 (Hartstein and Becker 1970), 3
(Grosvenor 1978), 4 (Fass et al 2004), 5 (Garcia et al 2003), 6 (Read 2006),
7 (Grey and Yap 1986), 8 (Denis et al 1995b), 9 (Rasooly and Zaubeman
1988), 10 (Nisted and Hofstetter 1974), 11 (Robb 1977), 12 (Ugurbus and
Zilelioglu 1999), 13 (Buehren et al 2003a), 14 (Tong et al 2002), 15 (Ing
1976), 16 (Liu and Pflugfelder 2000) and 17 (Lyle 1972).
263 Chapter 6 flattening and becomes less astigmatic as it grows. Typically over the age of
4 years, studies have shown the prevalence of corneal ATR astigmatism reduces, with subjects exhibiting a predominance of (small degrees of) WTR corneal astigmatism (Atkinson et al 1980, Gwiazda et al 1984, Howland and
Sayles 1985). Asbell et al (1990) found that the cornea flattened in curvature significantly over the first months of life and reached adult levels by 54 months.
The general flattening that occurs in the cornea in the first few years of life appears to be correlated with general facial and body growth (i.e. subjects who are larger in general will tend to exhibit larger, flatter corneas) and as such, may be a genetically determined passive growth mechanism (Rasooly and Zauberman 1988, Denis et al 1995b). The changes in astigmatism over the first few years of life may also be in part related to a passive growth mechanism (i.e. as the cornea flattens it becomes less astigmatic) (Figure
6.2) but the shift from ATR to WTR is difficult to explained by this mechanism. The changes occurring in the shape of the cornea in infancy are consistent with pressure from the eyelids moulding the cornea to become steeper in the vertical meridian than the horizontal. It seems likely that over this time of rapid corneal growth, that the adhesions between collagen fibrils may not be as strong as later in life (as fixed collagen fibrils would preclude many of these rapid corneal changes from occurring), and thus the cornea may be more susceptible to pressure from the eyelids. According to this model, passive growth and changes in corneal shape due to eyelid pressure would cause the reduction in astigmatism and flattening of the cornea
264 Chapter 6
Figure 6.2: Illustration of how passive growth could lead to a reduction in astigmatism. Both corneas exhibit a difference in curvature in their principal meridians of 0.2 mm, but due to the overall difference in curvature between the two corneas, cornea 2 displays less astigmatic power.
265 Chapter 6 observed in infancy that leads to the small levels of WTR astigmatism typically found in young children.
After the age of 50 years, significant changes also occur in corneal shape and a shift to a predominance of ATR corneal astigmatism is typically observed (Anstice 1971, Baldwin and Mills 1981, Hayashi et al 1995, Guirao et al 2000, Goto et al 2001). Increasing age causes eyelid tension to reduce, and leads to a number of changes in the position of the eyelids (Hill 1975,
Vihlen and Wilson 1983, Shore 1985, Van den Bosch et al 1999). A reduction in the pressure exerted by the eyelids on the cornea would be expected to lead to a reduction in WTR astigmatism (i.e. an increase in ATR astigmatism). Age-related changes in corneal structure may also play a role in the topographical changes observed.
In some cases the typical emmetropisation of corneal astigmatism in early childhood does not happen and increased corneal astigmatism occurs. In the case of subjects who develop significant amounts of WTR astigmatism, the inherited characteristics of the cornea (e.g. stromal collagen orientation) may lead to the cornea inherently having a more WTR astigmatic shape
(interactions between the eyelids and the cornea would then lead to an increase in the WTR astigmatism and lead to associations between the axis of astigmatism and the angle of the eyelids). It is also possible that the rigidity of the cornea may be lower in these subjects which would in turn lead to pressure from the eyelids causing an increased level of WTR astigmatism.
266 Chapter 6
The other possibility is that these subjects display increased eyelid tension which leads to the increased WTR astigmatism.
In the case of subjects who develop ATR astigmatism, it is likely that these subjects inherit corneal characteristics that lead the cornea to assume its
ATR astigmatic shape. Pressure from the lids would be expected to reduce
ATR astigmatism. For the cornea to continue to exhibit ATR characteristics in the presence of pressure form the eyelids, these subjects may exhibit characteristics that cause the lids to exert less influence on corneal shape
(e.g. more rigid corneas or lower eyelid tension or a combination of these factors). It should of course be noted that ATR astigmatism is not a common finding in young subjects.
There are also a number of environmental factors which may be expected to influence the relationship between the eyelids and the cornea. The type and quantity of different visual tasks performed may lead to differences in the magnitude and direction of the pressure exerted by the eyelids on the cornea which could possibly alter corneal astigmatism. There have been limited associations found between visual tasks and astigmatism, however Tong et al (2002) found a significant association between the magnitude of astigmatism and amount of computer work performed. Certain nutritional or general health factors could potentially cause alterations in corneal function and lead to reduced rigidity of the cornea, making the cornea more susceptible to lid pressure induced shape changes. Other environmental
267 Chapter 6 factors such as contact lens wear could also influence the cornea lid relationship by causing alterations in corneal rigidity.
Whilst this model accounts for a number of our observed associations between eyelid morphology and corneal topography, as well as explaining a number of the well known changes in corneal astigmatism with age, there is a possibility that other mechanisms are involved. Recent animal studies have shown that imposed astigmatic defocus can lead to changes in corneal astigmatism (i.e. alterations in visual experience have the potential to cause changes in corneal shape) (Kee et al 2004). If the cornea can alter its shape in response to changes in visual input, it opens up the possibility that a visual feedback mechanism may be operating in the aetiology of human corneal astigmatism. The associations that have been reported between myopia and astigmatism also tend to suggest that visual feedback may be important in the aetiology of astigmatism (Ninn-Pederson 1996, Gwiazda et al 2000,
Fairbrother et al 2004). We also found a tendency for our more myopic subjects to exhibit corneas with greater WTR astigmatism. There is some evidence to suggest that the position of the eyelids may be a factor in myopia development (O’Leary and Millodot 1979, Langford et al 1998, Buehren et al
2005). If this is the case, and if corneal astigmatism is caused in part by eyelid pressure, then potentially this could mean that some of the factors promoting myopia may also be similar to factors that promote corneal WTR astigmatism.
268 Chapter 6
6.3 Future research directions
The results from this study have shown that highly significant correlations exist between certain eyelid morphological and corneal topographical parameters in a group of young normal subjects. However the exact aetiology of astigmatism is still unclear. The results from our investigations tend to support the notion of eyelid pressure leading to corneal astigmatism, but do not prove this to be the case.
There are a number of potential areas for further research that may help to shed more light on the causes of corneal astigmatism. Two unknown parameters that we were not able to assess in our population that could potentially improve our understanding of the influence of the eyelids on corneal astigmatism are the tension of the eyelids and the rigidity of the cornea. As interactions between the rigidity of the cornea, the tension of the eyelids and the angle and position of the eyelids may all contribute to determining the shape of the cornea, a study which accurately measures all of these factors on a large population of subjects may further our understanding of the causes of astigmatism.
Assessing corneal topography and eyelid parameters in a younger group of normal subjects may also provide insight into the causes of astigmatism. As many of the eyelid parameters and corneal topography parameters are in a state of flux in infancy, it may be that the position of the eyelids may have a closer correlation with corneal parameters than that which is found in young
269 Chapter 6 adults. A study into eyelid position and corneal topography in older subjects may also provide further insight into the reasons for the typical changes in corneal astigmatism in older age. Longitudinal studies into corneal topography and eyelid parameters (particularly in these groups of subjects where corneal and eyelid parameters are known to be changing) may also provide more information regarding the influence of the eyelids on the shape of the cornea.
This research project has shown that highly significant corneal changes can occur over the course of the day due to pressure from the eyelids on the cornea. We have also presented an assessment of the average morphology of the palpebral fissure and the topography of the cornea in a population of young subjects. Improved technology has allowed us to provide a more detailed and extensive description of these parameters than has previously been presented. We have further shown that significant correlations exist between the morphology of the eyelids and the topography of the cornea.
The results from these experiments open up a number of other research questions that if addressed, may help to further elucidate the influence of the eyelids on the shape of the cornea. Whilst we have presented evidence to suggest that pressure from the eyelids does play a role in the development of corneal astigmatism, many unanswered questions remain about the aetiology of astigmatism.
270 References
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322 Appendix 1
Appendices
Appendix 1: Ethics
Following are the research ethics information sheets and consent forms used in each of the experiments.
323 Appendix 1
EYE DYNAMICS
Information Sheet
The Research Team The research team are students and staff of the Centre for Eye Research and School of Mathematics in the Faculties of Health and Science at the Queensland University of Technology.
Program Leader: Dr Michael Collins Ph W 3864 5702 H 3289 3940 Mr Scott Read Ph W 3864 5708
The Project The project we are undertaking is designed to provide us with information regarding the dynamic changes that naturally occur on the surface of the eye (in the tears and cornea) and in the internal structures of the eye. This study aims to investigate the mathematical characteristics of these fluctuations.
You will be required to undergo an initial screening examination of your eyes to determine your suitability for this study. In this study the shape of the front surface of the eye (tears and cornea) will be measured using a videokeratoscope and the internal optics of your eye will be measured with a wavefront sensor. You will be asked to look into a clinical instrument, the videokeratoscope or wavefront sensor, while your optics are measured. The videokeratoscope and wavefront sensors are normal clinical instruments and pose no risk to the health of your eyes. We may also photograph the eye with a digital camera or high speed camera.
We have contacted you as a potential participant in the study after reviewing your clinical record in the Optometry Clinic at QUT.
Expected Benefits Your involvement in this project will not directly benefit you. We are interested in modelling the natural fluctuations which occur in the optics of the human eye. Data collected from this study is expected to improve understanding of this area and aid further research.
324 Appendix 1
Risks There are no greater risks in this study than those associated with your routine eye examinations.
Confidentiality The research data we gather from the experiments will not personally identify you by name, or in any way that allows you to be identified. Any publication of data arising from this research will use a code system which does not identify you personally. The data will be stored securely in the Centre for Eye Research.
Voluntary Participation We have identified you as a potential subject for this study after reviewing your clinical record at the QUT Optometry Clinic. Your participation in this study is entirely voluntary and you can withdraw from the study at any stage without comment or penalty. Your decision not to participate or to withdraw from the study will in no way influence your relationship with QUT (such as your student grades, employment or clinical care).
Questions and further information If you wish to discuss any aspect of this study or have any further enquiries feel free to contact Dr Michael Collins (listed above).
Concerns or complaints You may also contact the Secretary of the University Human Research Ethics Committee on 3864 2902 if you wish to raise any concerns about the conduct of this research.
Feedback We will be happy to discuss your individual results during or after the experiment. We will provide you with a written copy of any reports or publications arising from this research if you so request.
325 Appendix 1
EYE DYNAMICS
RESEARCH CONSENT FORM
Name of Chief Investigator: Dr Michael Collins Ph W 3864 5702 H 3289 3940
Mr Scott Read Ph W 3864 5708
By signing below, you are indicating that:
• The tests and procedures involved in this study have been explained to me,
• I have read the information sheet,
• I have been given the opportunity to ask questions regarding this project and
the tests involved,
• I understand that if I have additional questions I can contact any member of
the research team,
• I have been informed that I am free to withdraw from the study at any time,
without comment or penalty;
• The project is for the purpose of research and not for treatment of my eyes;
• I can contact the Secretary of the University Human Research Ethics
Committee on
3864 2902 if I wish to raise any concerns about the conduct of this research.
• I consent to participate in this project.
Participant's name:...... …
Signature: ...... Date:………………………..
326 Appendix 2
Appendix 2: Publications arising from the thesis
Following are the publications which have arisen from the work in this thesis at the time of submission.
Journal articles
1. Read SA, Collins MJ and Carney LG. The diurnal variation of corneal topography and aberrations. Cornea. 2005; 24: 678-687.
2. Read SA, Collins MJ, Carney LG and Franklin RJ. The topography of the central and peripheral cornea. Invest Ophthalmol Vis Sci. 2006; 47: 1404-
1415
3. Read SA, Collins MJ, Carney LG and Iskander DR. The morphology of the palpebral fissure in different directions of vertical gaze. Optom Vis Sci. 2006;
(In Press)
Published abstracts
1. Read SA, Collins MJ, Carney LG and Iskander DR. The morphology of the anterior eye in three different angles of vertical gaze. (Abstract) Clin Exp
Optom. 2006; 89: 105.
Presented at the 11th Scientific Meeting in Optometry, QUT September 2005.
327 Appendix 2
2. Read SA, Collins MJ, Carney LG and Franklin RJ. The topography of the peripheral cornea. Optom Vis Sci. 2005; 82: E-Abstract 055023.
Presented at the American Academy of Optometry Meeting, San Diego
December 2005.
328