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Corneal topography, near work
and eyelid forces
Tobias F. Buehren
Diplom Ingenieur (FH) Augenoptik
A thesis in partial fulfilment of the requirements
for the degree of Doctor of Philosophy
Centre for Eye Research
School of Optometry
Queensland University of Technology
Brisbane, Australia
2003
KEYWORDS
Videokeratoscope, Cornea, Corneal topography, reading, lid forces, aberrations,
refractive error, myopia
ABSTRACT
The cornea is the most powerful refractive component of the eye and as such, subtle
changes in corneal shape can cause substantial changes in the optical characteristics of
the eye. Monocular diplopia has previously been linked to corneal distortion
following near work in various studies but has not been investigated in detail. The
work reported in this thesis has investigated the optical effects of corneal distortions
caused by eyelid forces and demonstrated that several corneal higher and lower order
Zernike wavefront aberrations can change following reading.
Measuring subtle changes in corneal topography requires the highest possible
instrument accuracy, while software analysis tools should be able to detect and
highlight those subtle changes with high reliability. The effect of ocular
microfluctuations on the qualitative and quantitative analysis of corneal topography
was investigated. A technique was developed to measure tilt, displacement, and
cyclotorsion in multiple videokeratographs from the same cornea. This information
was used to reposition each videokeratograph according to the average position of a
sample of multiple measurements. The corneal topography of ten subjects was
measured 20 times each, using videokeratoscopy. The RMSE calculated from
difference between single videokeratographs and the average videokeratograph
decreased by an average of 24.6 % for the ten subjects’ data. The method can improve
the precision performance of videokeratoscopy in multiple measurements of corneal
topography.
I
A study was undertaken, to investigate whether there are significant changes in
corneal topography during accommodation in normal corneas and corneas that are
pathologically thinner due to keratoconus. This was done to eliminate the possibility
that changes in corneal aberrations associated with near work could be at least partly
due to corneal changes caused by the effects of accommodation. A videokeratoscope
was modified to present an accommodation stimulus that was coaxial with the
instrument’s measurement axis. Six subjects with normal corneas and four subjects
with keratoconus were studied. In the initial analysis it was found that a number of the
subjects showed significant changes in corneal topography as accommodation
changed. However further analysis showed a significant group mean excyclotorsion of
the topography maps for both accommodation stimuli compared with the 0 D
stimulus. When the excyclotorsion was accounted for, no clear evidence of
statistically significant changes in corneal topography as a result of accommodation
were found. A small ocular excyclotorsion typically accompanies accommodation and
this changes the relative orientation of the topography of the cornea.
To investigate the effects of eyelid pressure on corneal shape and corneal aberrations
during reading, twenty young subjects with normal ocular health were recruited.
Cornea1 topography of one eye was measured with a videokeratoscope prior to
reading and then again after a 60 minute reading task. Twelve of the twenty corneas
showed significant changes in central topography immediately following reading. The
location of the changes corresponded closely to the position and angle of the subject’s
eyelids during reading. Within the central region of the cornea there were significant
changes in corneal wavefront Zernike coefficients, the root-mean-square error, overall
refractive power and astigmatism. The changes observed in corneal topography
II
appear to be directly related to the force exerted by the eyelids during reading. These
findings may have important implications for the definition of refractive status and
may also aid in the understanding of the relationship between reading and the
development of refractive errors.
To study whether corneal distortions after reading significantly differ between
refractive error groups, corneal aberrations were measured before and after a period of
reading, for a group of ten young progressing myopes and a group of ten young stable
emmetropes. The major difference between the two groups was the location and
magnitude of the corneal distortions, which had a significantly larger effect on central
corneal optics in the myopic group compared to the emmetropic group. A
significantly smaller palpebral aperture for the myopic group in the reading gaze
position was the cause of this difference.
The experiments described in this thesis have shown that numerous corneal
characteristics can change due to eyelid forces during near work. The eye was shown
to undergo a small cyclotorsion during higher levels of accommodation. There was a
shift in direction of against the rule astigmatism of the cornea following reading and a
change was found for primary vertical coma and trefoil. The changes in corneal shape
following reading appear to be different in myope versus emmetropic refractive error
groups. These findings are important for our understanding of the stability of the
refractive error of the eye and could have important implications for refractive error
development.
III
CONTENTS
Abstract I
Contents IV
Statement of Authorship VIII
Acknowledgements X
Chapter 1:
1.1
1.2
1.3
1.4
1.5
Introduction
Videokeratoscopy
1.1.1 Placido-based Instruments
1.1.2 Technical requirements
1.1.3 Corneal topography reconstruction
1.1.4 Topographic displays
1.1.5 Limitations of videokeratoscopes
1.1.6 Accuracy and repeatability
Corneal shape
Corneal mechanics
1.3.1 Hydration effects
1.3.2 Tear instability
1.3.3 Mechanical properties
1.3.4 Stability of corneal shape
1.3.5 Diurnal variations
1.3.6 Corneal epithelia1 cell movement
The effect of lid pressure on corneal topography
1.4.1 Monocular diplopia associated
with near work
Eyelids and blinks
1.5.1 Blinking
1 .5.2 Eyelidpressure
Page
1
3
3
4
7
8
8
11
16
19
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21
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24
25
27
29
34
36
37
IV
1.6
1.7
1.8
Wavefront aberrations of the human eye
1.6.1 Aberroscopy
1.6.2 Measurements of monochromatic
wavefront aberrations
1.6.3 Ocular wavefront aberrations and
accommodation
1.6.4 Cornea1 and total wavefront aberrations
of the eye
1.6.5 Wavefront aberrations and myopia
Myopia and refractive error development
1.7.1 Myopia prevalence
1.7.2 Myopia etiology
1.7.3 Emmetropisation
1.7.4 Near work related myopia studies
in humans
Attempts to prevent myopia progression 1.7.5
Rationale
Chapter 2: Ocular Microfluctuations and
Video kera toscopy
2.1 Introduction
2.2 Methods
2.2.1 Regression plane - to remove tilts
2.2.2 Sphere apex - to remove x,y,z, shifts
2.2.3 Best-fit sphero-cylinder - to remove
cyclo-deviations
2.2.4 Limitations
2.2.5 Protocol
2.3 Results
2.4 Discussion
40
40
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44
46
47
47
49
50
52
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59
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63
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75
V
Chapter 3:
3.1
3.2
3.3
3.4
Chapter 4:
4.1
4.2
4.3
4.4
4.5
Chapter 5:
5.1
5.2
5.4
5.5
Chapter 6:
6.1
6.2
6.3
6.4
6.5
Corneal Topography and
Accommodation
Introduction
Methods
Results
Discussion
Corneal Aberrations and Reading
Introduction
Methods
Analysis
Results
Discussion
Corneal aberrations following reading
in progressing myopes
Introduction
Methods
Results
Discussion
Conclusions
Ocular micro fluctuations
Accommodation and topography
Corneal aberrations, reading and myopia
Future directions
Summary
77
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85
93
97
97
98
100
104
114
120
120
122
128
146
153
153
154
155
160
165
VI
References: 166
Appendix 1: Publications from thesis A
VII
STATEMENT OF ORIGINAL AUTHORSHIP
“The work contained in this thesis has not been previously submitted for a degree or
diploma at 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.”
Signed: ................................................
Date: .........................
VIII
Authorship
AUTHOR’S STATEMENT
The research reported in this thesis was carried out by myself or under my direction.
The development of some techniques described in this thesis has involved
collaboration with other persons.
Chapter 2: Ocular microfluctuations and videokeratoscopy
The development and writing of the fixation error minimization algorithm described
in this thesis primarily involved collaboration of Brenden J. Lee and D. Robert
Iskander. The author was responsible for all other aspects of the study.
Chapter 3: Corneal topography and accommodation
In manufacturing the telescope system to present a target co-axial with the Keratron
videokeratoscope, the collaborator was the physics department at Queensland
University of Technology. Jim Loughridge provided assistance with the data
collection. The author was responsible for all other aspects of the study.
Chapter 4: Corneal aberrations and reading
Brett Davis, D. Robert Iskander and Mark Morelande assisted with the various aspects
of the data analysis. The author was responsible for all other aspects of the study.
Chapter 5: Corneal aberrations following reading in progressing myopes
D. Robert Iskander, Sigfried Mioschek, and Martin Trunk developed the digital image
analysis software. Stephanie Voetz provided assistance with the data collection. The
author was responsible for all other aspects of the study.
ACKNOWLEDGEMENTS
My special thanks go to Michael J. Collins and Leo G. Carney for giving me the
opportunity to do a PhD at Queensland University of Technology and also for their
assistance and encouragement during my studies.
X
CHAPTER 1
Introduction
In the last two decades, the development of new technologies has significantly
enhanced research achievements in the field of visual optics. Today we are able to
measure the optical performance of the human eye to a degree of sophistication that
often exceeds our ability to understand this complex optical system. The questions I
have investigated in this dissertation concern the accurate measurement of corneal
shape and aberrations, its stability and its potential role in the development of
refractive error.
Measurement and understanding of corneal topography has been significantly
improved by the introduction of videokeratoscopy. Information is available on a much
larger area of corneal data compared with keratometry and the ability to measure
small regional changes in corneal topography is enhanced. The term precision of an
instrument refers to the agreement between repeated observations with the given
device. Accuracy of a method refers to how closely a measured value agrees with the
true value. To reliably measure small changes in corneal shape one must understand
the repeatability and accuracy of videokeratoscopes.
While the normal corneal shape resembles an ellipsoid, variations in surface occur and
corneal stability has reported to be affected by various factors. Cornea1 changes can
occur due to a range of effects such as finger pressure, eye position, rubbing, eyelid
position, and eyelid pressure. A number of researchers have identified monocular
1
diplopia as the consequence of lid pressure effects on the cornea1 shape following near
work.
With the introduction of wavefront sensing technology, research in the field of optical
aberrations of the human eye has grown rapidly. Aberrations of the whole eye as well
as for various ocular components and conditions can be measured in detail. These new
techniques have the potential to provide fresh insights regarding the optical
characteristics and also the optical development and function of the human eye.
Within the last two decades of human myopia research interest has shifted towards
retinal image quality and it is now widely believed that emmetropisation is a vision-
dependent phenomenon. It is thought that some form of visual feedback mechanism
regulates retinal image-mediated ocular growth. Within this context, the measurement
of the optical characteristics of the human eye using videokeratoscopy and wavefront-
sensing technologies may provide a significant new insight to this research field.
2
1.1 VIDEOKERATOSCOPY
Since the development of computer-assisted videokeratoscopes in the mid- 1980s,
there has been a rapid increase in technical sophistication and features of the devices.
The Cornea1 Modelling System was the first commercially available
videokeratoscope, and incorporated the colour-coded contour map (Maguire et al.
1987). The basic principle of these instruments involves projection of a target light
source on the cornea and capturing of the reflection of this light from the cornea by a
video camera (Figure 1-1). This information is analysed by software and the data is
displayed in a variety of formats. Earlier forms of corneal measuring devices supplied
significantly less data points than current videokeratoscopes. This allows a much
more detailed description of corneal shape. The number of measurements obtained
from current videokeratoscopes range from 5000 up to more than 8000 discrete points
depending on the instrument.
1.1.1 Placido-based Instruments
Placido-based videokeratoscopes measure the angle of the corneal surface and use this
angular information to compute curvature and height. A conical Placido disc target
projects numerous concentric rings on the cornea and a virtual image located behind
the reflecting surface is detected by a video camera and analysed to determine the size
and shape of the rings (Sanders and Koch 1993). Each of the rings in the virtual image
is analysed at a certain angular interval (often 256 meridians) to allow computation of
topography for a total of many thousand points. On the optic axis of the
videokeratograph is a luminous fixation point that is centred with respect to the
concentric rings comprising the object target. Several algorithms for analysing ring
data are available (Keller and van Saarloos 1997). Local curvature algorithms are
3
based on instantaneous radius of curvature along a particular meridian and essentially
utilises local changes in curvature to generate topography maps. Spherically biased
algorithms for this analysis assume that the cornea is spherical, and small errors are
introduced as a result. The third algorithm used is based on the posterior focal power
of the cornea and is calculated using Snell’s law. After the cornea1 surface is
reconstructed, a graphical picture of the patient’s topography is presented most
commonly in a colour-coded contour map. Other presentation forms include
difference maps, various contact lens fitting presentations, isometric displays, numeric
format, composite plot displays, and meridional displays.
1.1.2 Technical requirements
The improvements of computer hardware and software in terms of storage capacity
and processing speed led to a tremendously increased number of points that can be
analysed. Although many refinements have been made to focus techniques, alignment
systems, target designs, and algorithms, limitations arise from underlying assumptions
and several measurement errors still exist. Bibby described the technical requirements
for reliable topographic measurements as follows; “the instrument must be
independent from the shape being measured and should measure the total area of
shape (Bibby 1976). Furthermore, all information should be acquired simultaneously
with high accuracy and reproducibility.”
4
Placido-rings
Figure 1 - 1 : Simple schematic model of Placido-based computer-assisted videokeratoscope
5
With regards to working distance, two types of instruments can be distinguished.
Image capture can be either achieved by a small faceplate at short working distance
(e.g. Keratron) or a large faceplate at long working distance (e.g. EyeSys). The
smaller target design at short working distance is used to minimise unwanted
reflections of lashes and adnexa in the ring image (Mandell 1996).
These devices are more likely to have an area that is not interrupted by the ocular
adnexa. The instruments allow measurements to extend further into the cornea1
periphery and sometimes to the limbus (Mandell 1996). On the other hand, larger
targets have the advantage of allowing a longer object distance, which will
theoretically cause less error from any unwanted decentration or defocusing of the eye
during the measurement. Thereby long working distance systems should provide
higher reproducibility.
The image of the reflected target, which is located behind the cornea, should lie on a
flat plane however this is not possible for every cornea. Thus the reflected image
commonly lies on a curved image plane, which means that there is only one point of
focus on the flat plane of the photographic film (Dave et al. 1998). Different target
designs have been tested to minimise the problems encountered when focusing on a
curved image plane. Current obtainable faceplate geometry varies in features like
number of rings, their colour, brightness and spacing. Ring mires that are to closely
spaced might blur together when reflected off distorted corneas. Ring mires that are
too small in diameter are difficult to detect due to the limited pixel resolution of the
video camera.
6
Focusing of the Placido-ring target on the cornea can be achieved either manually or
by an automatic focusing system. The image may be captured automatically when the
target disc is positioned in the correct distance from the cornea. In some instruments
automatic focusing systems have a setting, which may be varied to offer easier
capture or a higher accuracy. The automatic focusing systems may compensate focus
errors on actual corneas or use an out of focus detector and make adjustments in the
algorithm (Opticon 1997).
Most commercially available reflective videokeratoscopes are designed such that the
instrument axis is aligned normal to the corneal surface along a direction known as
the vertex normal. For measurements applied to visual problems such as refractive
surgery, the ideal would be a position when the videokeratoscope axis coincides with
the point where the line of sight intersects the cornea (Mandell 1992).
1.1.3 Cornea1 topography reconstructions
Most videokeratoscopes reconstruct the cornea using a two-dimensional coordinate
system known as a plane geometry model. The algorithm, which is spherically biased,
demands that the centre of curvature lies on the videokeratoscope axis. The instrument
has to be centred and placed at the correct focal distance and the algorithm (also
known as the axial solution), calculates corneal power at any point as the power of a
sphere, which would produce the same ring reflection as that of the cornea. This
approximation is accurate for axis-centred spheres only. For non-spherical surfaces,
the centre of curvature actually moves off the optical axis. Another method, the arc-
step algorithm is not spherically biased and reconstructs corneal surface composed of
several multiple arcs. This reconstruction technique can accurately describe aspheric
7
corneal profiles because more peripheral arcs need not be centred on the instrument
axis. The corneal shape is reconstructed by adding adjacent arcs sharing a common
tangent where they meet (Tripoli et al. 1995; Mattioli and Tripoli 1997).
1.1.4 Topographic displays
A range of topographic displays is available to present corneal raw data (i.e. slope or
height data). Topographic displays can be divided into two main categories: corneal
function and corneal shape. The subgroup of corneal shape displays consists of three
different displays, axial curvature, tangential curvature, and surface height. The
refractive power map display is classified as a corneal function map (Roberts 1998).
Many devices supply other features like multiple images, profile plots, difference
maps, or contact lens software, which simulates the fluorescein pattern of rigid lenses
fitted to the corneal topography.
1.1.5 Limitations of videokeratoscopes
Videokeratographs are aligned along an axis that is slightly, but significantly
displaced from the line of sight. The videokeratoscope axis is aligned perpendicular to
the cornea and is thus directed towards the centre of curvature more than the centre of
the entrance pupil. This corneal position is more peripheral than the sighting centre,
which is the intersection of the line of sight with the corneal surface. The patient
views the fixation point inside the target cone while the operator carries out focusing
and alignment. When achieved it gives an individual position of the pupil centre, the
optic axis of the videokeratograph, and its distance from the vertex normal (Mandell
1996).
8
The influence of defocus can have significant effects on corneal height measurement
error. Due to the relatively smaller amount of defocus with long working distance
devices compared to the same amount of defocus with short working distance devices,
the latter are particularly sensitive to this problem. Also an accurate camera to cornea
distance is very important, so that maximum contrast of the camera resolution can be
satisfied. Although Mandell demonstrated that longer working distance systems
provide higher reproducibility, they are more sensitive to shadowing from the
eyelashes and nose at the corneal surface (Mandell 1996).
Generally the corneal surface is described using a set of Cartesian coordinates (x, y,
and z) to define its profile. However the two-dimensional image in videokeratoscopy
has insufficient information on its own to enable a point-by-point localisation in three-
dimensional space. Therefore several assumptions must be made. Dave et al.
described, in general, the assumptions that needed to be made for the various
reconstruction techniques (Dave et al. 1998). The working distance from the target to
the image is a constant. The instrument axis is perpendicular to the corneal surface.
The light from one meridian of the target is reflected in the same meridian in the film
plane. There is no circumferential tilt of the corneal surface although for point targets,
this assumption is not required. The position of the image at the film plane is unique
for a particular surface. The image plane lies on a flat plane.
Incorrect or unsteady fixation of the luminous fixation point is a potential source of
error in videokeratoscopy. This error can become significant if patients have large
refractive error or another source of low visual acuity, which prevent them from
9
maintaining fixation. Fixation errors are most noticeable in the cornea1 periphery and
produce effects similar to instrument misalignment.
Hubbe and Foulks assessed fixation error effects using five subjects who fixated in
certain angles from coaxial with the instrument (Hubbe and Foulks 1994). The I-S
value method was applied to compare the corresponding meridians. The I-S value is
the difference between the inferior (I) and superior (S) powers of the cornea. An I-S
value greater than 1.20 D suggests the presence of keratoconus. The I-S values
increased as fixation angle increased as expected. A mean value of 1.26 D, which is
the value used by Rabinowitz and McDonnell as the limit for early keratoconus
detection, was reached by three out of five normal corneas at 5". At 10" misalignment,
all of them easily reached that value (Rabinowitz and McDonnell 1989).
Using a radially aspheric surface, Roberts investigated the potential spherical bias of
the TMS- 1 (Roberts 1995). The instrument demonstrated increasing error from centre
to periphery for an ellipsoid with 7.5 mm apical radius of curvature and a value of 0.5
of eccentricity. Roberts presented an error of more than 3 D at 4 mm from apex. This
strong spherical bias was found to influence system performance by limiting the
ability of the device to detect subtle shifts in surface curvature. Compared to
misalignment errors, this inherent algorithm error in mapping a radically aspheric
surface was found to be relative high.
Tripoli et al. estimated the accuracy of Keratron's arc-step profile reconstruction
algorithm with four rotationally symmetric, radially aspheric test surfaces (Tripoli et
al. 1995). It was intended to distinguish between error caused by the algorithm and
10
error from other sources. Keratron measurements were compared with the surface
formula and ray-traced simulations of the profile reconstruction algorithm.
Tripoli et al. concluded that Keratron’s arc-step algorithm measured height more
precisely than videokeratoscopes that use spherically biased algorithms.
Belin and Ratliff assessed smoothing functions of raw data acquisition (axial solution)
of seven commercially available videokeratographs (TMS, EyeSys, CAS, Master Vue,
CM-1000, Keratron, and TechnoMed C-Scan) (Belin and Ratliff 1996). Six calibrated
test objects to simulate clinical conditions such as myopic or hyperopic ablation,
simulated central islands and spherical or sphero-cylindrical shapes were used. It was
found that no system accurately measured all objects. Sources of error occurred with
excessive raw data smoothing, loss of accuracy in the periphery, poor central
coverage and the inability to read large transitions.
Mattioli and Tripoli assessed the accuracy of the profile reconstruction algorithm used
by the Keratron videokeratoscope (Mattioli and Tripoli 1997). The height of eight test
surfaces with central astigmatism ranging from 4 D to 16 D was measured. Keratron
measurements were compared with the surface formula and ray-traced simulations of
the profile reconstruction algorithm. The maximum height error ranged from 0.47 %
to 2.9 % of the total height, with the eight test surfaces.
1.1.6 Accuracy and repeatability
Topographers measure corneas less precisely than they measure artificial test surfaces.
Determination of statistically significant differences in corneal topography for clinical
applications demands a large amount of data processing. Regarding corneal
11
topography measurements, videokeratoscopes are the most accurate devices and
collect significantly more data than other instruments such as keratometers. Test
surfaces such as perspex or steel balls of known surface shape determined using
standard surface metrology methods may be measured with videokeratoscopes and the
results compared. This is not possible for measurements of real corneas. To estimate
the accuracy of a videokeratoscope for cornea1 topography measurements it must be
compared with other models of videokeratoscopes taking the instruments’ accuracy
for artificial test surfaces into account.
A comparison of three videokeratoscopes (TMS-1, EyeSys, and the Visioptic EH-
270) in measurement of toric test surfaces was undertaken by Greivenkamp et al.
(Greivenkamp et al. 1996). They used precision diamond-turned toric surfaces, which
were independently measured. The results showed systematic performance differences
among the three instruments. The general characteristics that lead to potential
inaccuracies were overall high frequency noise in the power maps and surface height
maps (TMS-l), discontinuities in the centre of the power maps, and underestimation
of the amount of astigmatism because of excessive data smoothing (EyeSys and
Visioptics).
Dave et al. used 12 perspex convex surfaces of varying eccentricities and different
apical radii to evaluate the accuracy and repeatability of the EyeSys model II (Dave et
al. 1998). The sagittal radius of curvature for both central and peripheral known
points were measured twice on each surface. To evaluate accuracy and repeatability of
the points and the relationship between eccentricities, raw data tables were analysed.
The accuracy of the EyeSys model II decreased slightly as the p-value decreased.
12
Repeatability for the aspheric surfaces was shown to be high (SD f 0.01 mm in all
quadrants).
A study from Hilmantel et al. determined the accuracy of the Tomey, Topographic
Modelling System to measure asymmetric surfaces (Hilmantel et al. 1999). The
characteristics of asymmetric surfaces were created through ellipsoidal test objects
tilted relative to the videokeratoscope axis. A Melles-Griot mini-goniometer was used
to permit accurate rotation of the test objects about its apex. Smooth, mildly
asymmetric surfaces were created with maximum tilts of up to 15". Root mean square
error (RMSE) of surface elevation for all objects at all tilts, varied from a low of
0.69 pm to a high of 11.32 pm. Hilmantel found the TMS-1 to be capable of
measuring with an accuracy of about 1 pm to 10 pm while the degree of asymmetry
did not have a statistically significant effect on accuracy.
Tang et al. investigated accuracy and precision performance of four
videokeratoscopes (Keratron, Medmont, and TMS) and the rasterstereogrammetry
based videokeratoscope (PAR-CTS) in measuring six test surfaces (Tang et al. 2000).
A Talysurf instrument was used to accurately quantify the topography of the test
surfaces that consisted of a sphere, an asphere, a multicurve and three bicurve (5.0,
6.5, and 8.5 mm radius of curvature) surfaces. The elevation errors were calculated by
subtracting the Talysurf readings from the instruments averaged data. The study
showed high accuracy of instruments on some but not all surfaces. Keratron and
Medmont showed the best accuracy on average for the sphere, asphere, and
multicurve followed by TMS, which showed slightly better performance for the 5.0
and 6.5 bicurve surfaces. The PAR-CTS had the poorest performance in precision of
13
the four devices but was more accurate than the other three instruments for the 8.5
bicurve surface.
Jeandervin and Barr compared the accuracy and repeatability of three commercially
available videokeratoscopes for real eye measurements and four calibration spheres
respectively (Jeandervin and Barr 1998). Of the three instruments (Alcon EyMap EH-
290, EyeSys system 2000, Humphrey Mastervue topography system), the EyeSys
system 2000 was found to have best repeatability while the Humphrey Atlas was
shown to be the most accurate instrument based on the measurements of calibration
spheres. Hough and Edwards assessed reproducibility of four EyeSys systems for the
measurement of vertex radius and central topography (Hough and Edwards 1999). In
contrast to Jeandervin and Barr’s data, Hough and Edwards concluded that the EyeSys
system does not provide reproducible values of corneal dimensions at a level that
would normally be acceptable for the specification of rigid lens back surface radii. It
was pointed out that Jeandervin and Barr's results were based on two measurements
of twelve eyes only and therefore may have underestimated the extend of variation.
The Keratron was found to show high repeatability for corneal topography
measurement within the central 4 to 5 mm of the map (Buehren et al. 2001). The
standard deviation within most areas of this region showed *OS0 D of instantaneous
power and *0.25 D of refractive power. However at the edge of an 8 mm diameter,
instantaneous power maps frequently reached more than *1.00 D of standard
deviation.
14
Cho et al. compared the performance of four videokeratoscopes (Humphrey Atlas
991, Orbscan 11, Dicon CT200, Medmont E300) in measuring topography of young
Chinese adults (Cho et al. 2002). Both the Humphrey Atlas and the Medmont
demonstrated high levels of performance, showing good agreement between elevation
values. Of the four videokeratoscopes tested, the Orbscan II showed the poorest
repeatability and reproducibility.
In summary, Placido-based videokeratoscopes provide an important tool for cornea1
topography analysis and diagnosis. Differences in accuracy and precision
performance exist between instruments due to various factors.
15
1.2 CORNEAL SHAPE
Based on early studies using keratometers, a mean value of the central corneal radius
of curvature is 7.85 mm f0.25 mm (Clark 1973) with a difference in curvature
between the flattest and steepest meridian of 0.15 f 0.15 mm in normal Caucasian
populations (Guillon et al. 1986). Curvature usually flattens towards the periphery.
Kiely et al. found that an ellipsoidal surface best describes the asphericity of the
corneal shape (Kiely et al. 1982). The mean and standard deviation of the central
radius of curvature for 176 healthy eyes was 7.72 f 0.27 and the asphericity was
Q = -0.26 f 0.18. Kiely et al. pointed out that the cornea is significantly asymmetric
in both radius of curvature and asphericity (Kiely et al. 1982).
Features of normal corneal topography have been extensively characterized and
classified (Bogan et al. 1990; Rabinowitz et al. 1996). Bogan et al. qualitatively
classified the topography of 399 normal corneas based on computer-assisted
videokeratography (Bogan et al. 1990). They compared their descriptions of
topographic maps and identified five characteristic patterns: round, oval, symmetric
bow tie, asymmetric bow tie and irregular. Rabinowitz et al. divided
videokeratographs into 10 categories and included 10 analysis indices in order to
quantitatively describe phenotypic features (Rabinowitz et al. 1996). Indices provide
an objective measure and reproducibility of videokeratoscope analysis, which can be a
useful tool in the interpretation of pathological conditions such as keratoconus;
contact lens induced corneal warpage, or surgically altered corneas.
Wilson et al. suggested standardisation of colour-coded scales, because the clinical
and research use of the instruments have increased enormously (Wilson et al. 1993). It
16
was claimed that the so-called Klyce-Wilson scale (constant, 1.5 dioptre intervals)
provides the best combination of sensitivity and the best range of coverage on a wide
variety of corneas ranging from normal to surgically altered, and to those affected by
pathology.
Keratoconus is a pathological condition characterised by unusual corneal topography
that has been extensively investigated and a number of videokeratographic methods
for the detection of keratoconus have been developed (Dingeldein et al. 1989;
Rabinowitz and McDonnell 1989; Maeda et al. 1994). Smolek and Klyce proposed a
neural network approach, which was found to outperform several other methods in
distinguishing between keratoconus, keratoconus suspects, and topographies that are
similar to keratoconus (Smolek and Klyce 1997).
Various mathematical techniques have been used to categorize corneal topography.
Schwiegerling et al. presented a method to decompose corneal height data captured
with a videokeratoscope using a set of Zernike polynomials (Schwiegerling et al.
1995). The method provides a sophisticated technique for extracting high-order
corneal height variations such as those arising from disease or refractive surgery.
Decomposition overcomes the drawback that the spherical and cylindrical
components of the cornea obscure small variations in the surface. For applications like
refractive surgery the Zernike polynomials are a useful technique for determining the
shape of the aberrated cornea as well as the ablation pattern to convert the cornea into
an ideal shape (Greivenkamp et al. 1996; Schwiegerling and Greivenkamp 1996;
Schwiegerling et al. 1996; Schwiegerling 1997; Schwiegerling and Greivenkamp
1997; Langenbucher et al. 1999; Langenbucher et al. 1999).
17
Oshika and co-authors applied the Zernike technique to measure corneal aberrations
as a function of aging in a large population of normal subjects (Oshika et al. 1999).
An increase in third order (coma like) cornea1 aberrations with age was found while
spherical-like aberrations did not vary with aging. These results are in agreement with
the results of McLellan et al. on changes in ocular aberrations with age (McLellan et
al. 2001).
In summary, the normal corneal shape resembles an ellipsoid. Using a set of
mathematical functions, corneal height data can be decomposed into distinct surface
components. Small variations in surface height can then be highlighted, which
otherwise would be obscured by spherical and cylindrical components.
18
1.3 CORNEAL MECHANICS
The corneal surface is a dynamic structure affected by various factors such as
hydration, tear characteristics, hypoxia, lid pressure, blinking and external forces.
When determining accuracy and reproducibility of videokeratoscopes these factors
represent a source of variability and are sometimes difficult to quantify. The functions
of tear film, tear flow, tear chemistry, and tear film stability have been researched in
many studies. Much remains unknown about the influence of blink forces, lid
pressure, blink frequency, and tear layer dynamics on corneal topography
measurements.
1.3.1 Hydration effects
A study by Rom et al. describes the relationship between topography and corneal
oedema (Rom et al. 1995). Lack of corneal oxygen supply was created using a
nitrogen chamber goggle for one eye, while the other eye served as control.
Topographic measurement and baseline pachymetry of each eye from 10 subjects
were obtained. Thickness of all corneas exposed to the nitrogen chamber increased
but demonstrated no significant topographic changes, apart from the nasal area where
the corneal power lessened. There was no significant correlation between changes in
corneal topography and corneal thickening in any area measured.
Using de-epithelized eye-bank eyes at various stages of hydration, Ousley and Terry
evaluated hydration effects on the central and paracentral corneal topography (Ousley
and Terry 1996). The average central corneal steepening between pre-and post-
hydration conditions was 0.44 D, while the average paracentral steepening was
0.89 D.
19
1.3.2 Tear instability
Using videokeratoscopy, Pavlopoulos et al. examined the effect of artificial tears
applied to normal and post-keratoplasty eyes (Pavlopoulos et al. 1995). In normal
eyes, the application of artificial tears showed increasing corneal asymmetry and
changes to the location of the steepest point of the cornea. For eyes that had
undergone keratoplasty, the artificial tears created a more regular and symmetric
surface and significantly altered the simulated keratometry values. It was
recommended that corneal topography be performed before the application of
artificial tears.
Novak et al. analysed the effect of six artificial tear preparations on videokeratoscopic
measurements with the EyeSys (Novak et al. 1997). All preparations except two
induced significant, time-dependent changes in mean corneal power in the central
five-millimetre zone compared with baseline measurements. The mean induced
change was less than 0.5 D. When performing repeated measurements, the highest
consistency was achieved when no tears were instilled.
Licznerski et al. introduced a new method for evaluating tear film stability in the
human eye, using the lateral shearing interference technique (Licznerski et al. 1998).
The lateral shearing interferometer allows non-invasive testing of the human tear film
with a high accuracy. They presented sequences of shearing interferograms showing
the development of break-up on the normal eye during the inter-blink period. The tear
layer distribution process was clearly visible through the interference fringes that
become more and more distorted due to the evaporation of the tears and formation of
20
break-up sites. Nemeth et al. used high-speed videokeratography to detect tear film
regularity changes following blinking (Nemeth et al. 2002). It was found that the
corneal surface becomes more regular in the first few seconds after a blink.
In summary it appears unlikely that hydration effects in the in-vivo human cornea
have a significant impact on corneal topography. The tear film represents a significant
source of variability during corneal topography measurements with tear-break-up
being capable of substantially distorting the local surface. Artificial tear preparations
do not appear to be beneficial in improving the videokeratoscope precision
performance. Following a blink, it takes the tear film a few seconds to reach the most
regular and stable state.
1.3.3 Mechanical properties
The mechanical properties of the in vivo human cornea are difficult to determinate. In
materials like metals, the relationship between stress and strain is a simple linear one.
Young’s modulus (E) is the constant parameter, which characterizes the elastic range
of those materials. Biological materials show a more complex behaviour. Constant
increasing stress might be followed by a non-linear decrease of strain, which is known
as ‘stress stiffening.’ Nyquist and Nash et al. have demonstrated that the mechanical
properties of the cornea are viscoelastic (Nyquist 1968; Nash et al. 1982). This means
that additionally to the elastic behaviour, a retarded strain component occurs without
further increasing the stress. This behaviour is called creep. Furthermore the cornea
consists of different layers each showing different mechanical characteristics.
21
Many investigations concerning Young’s modulus of the cornea have been performed
using stress-strain tests on strips of excised cornea (Nyquist 1968; Andreassen et al.
1980; Nash et al. 1982). While Andreassen et al. found differences in stress strain
parameters between normal and keratoconic corneas (Andreassen et al. 1980),
Nash et al. found no correlation between elastic parameters and age, or a measurable
difference in the elastic behaviour of normal and keratoconus corneas under
physiologically relevant stress levels (Nash et al. 1982).
Other researchers used whole eyes in vitro to measure the displacement of mercury
drops that had been placed on the cornea1 surface, while inducing an increase of intra
ocular pressure (Hjortdal and Jensen 1995; Shin et al. 1997). For intra ocular
pressures of physiological relevance, Shin et al. reported small values of average
strain for the central region of the cornea but indicated that the strain distribution
throughout the entire cornea was unexpectedly non-uniform. Wang et al. applied an
ultrasonic technique for the measurement of elastic moduli of the human cornea
(Wang et al. 1996). The results of Young’s moduli (5 to 20 x 106Nm-2) compare with
those testing the stress-strain relationship on strips of cornea (Nyquist 1968;
Andreassen et al. 1980; Nash et al. 1982).
Hjortdal and Jensen studied the regional performance of the cornea and limbus in
vitro by pressure loading of 18 intact human cadaver eyes (epithelium removed)
(Hjortdal and Jensen 1995). Circumferential as well as meridional deformation with
pressure varied between the centre, para-centre, periphery, and limbus. Meridional
strains were smallest at the para-centre and periphery, and largest at the limbus
suggesting reinforcing para-central and peripheral structures in the meridional
22
direction. Circumferentially, strains were smallest at the limbus, suggesting
reinforcing limbal structures in the circumferential direction.
In summary, the mechanical properties of the cornea are viscoelastic. Quantification
of corneal mechanics is a difficult and complex problem. Various techniques have
been applied to measure elastic moduli of the in-vitro cornea and regional differences
in strains of corneal structures have been found.
1.3.4 Stability of corneal shape
Mandell and St Helen investigated the influence eye position, accommodation,
convergence, pupil size, lid position and closure, miotics, and rubbing on stability of
the corneal contour (Mandell and St Helen 1968). Cornea1 curvature was found to
change significantly as a result of digital pressure, lid forces, and rubbing.
In 1972, Carney and Clark investigated experimental deformation of the in vivo
cornea (Carney and Clark 1972). Corneas of two subjects were flattened by pressing a
flat surface against the corneal apex over five different time periods. The recovering
cornea was measured along a horizontal or vertical meridian before and during a 10-
min period after applanation. In the experiment, for the human in vivo cornea, at least
99 % of the central displacement had been recovered within 8 sec after retraction of
the tonometer probe. Carney and Clark therefore concluded that the delayed response
in the recovery of the in vivo cornea from deformation is much faster than expected
compared with previous studies on deformation of post-mortem corneas (Carney and
Clark 1972).
23
Knoll summarized the cause of “unnatural” effects on corneal shape changes, the
magnitude of the effects on the corneal shape, and how quickly the corneal shape is
restored (Knoll 1976). Concentrating on short-term effects, factors such as finger
pressure and tugging on the lids, eye position, rubbing, application of an applanation
tonometer, changes in corneal astigmatism induced by retracted lids and lid pressure
that causes bilateral monocular diplopia following near work were identified.
Studies that have investigated the effect of accommodation on the corneal shape have
been limited by the available technology. Investigations of the more central regions of
the cornea using keratometers (Fairmaid 1959; Lopping and Weale 1965) and
photokeratoscopes (Mandell and St Helen 1968) have created contradictory findings.
Fairmaid showed meridional changes in corneal curvature with convergence but
found no shape changes in the accommodating but non-verging eye (Fairmaid 1959).
Lopping and Weale also reported that significant changes occur in corneal shape
during ocular convergence (Lopping and Weale 1965). Mandell and St Helen did not
find any changes in topography with either convergence or accommodation (Mandell
and St Helen 1968). Using a modified keratometer, Pierscionek et al. found changes
in corneal topography with accommodation in at least one of the principal meridians
for most of the subjects tested (Pierscionek et al. 2001).
1.3.5 Diurnal variation
The cornea has also been observed to have diurnal variations in thickness and
topography (Reynolds and Poynter 1970; Rengstorff 1972; Kiely et al. 1982).
Kiely et al. measured corneal topography and thickness during a period of 12 hr of
one day in hourly intervals (Kiely et al. 1982). Instrumentation comprised an auto-
24
collimating photokeratoscope, a keratometer, and a pachometer attached to a slitlamp.
In agreement with other studies a significant overall steepening of corneal curvature
throughout the day was observed (Reynolds and Poynter 1970; Kiely et al. 1982).
Thickness at five locations was shown to be greatest immediately after awakening and
became thinner at all locations as time during the day elapsed.
1.3.6 Corneal epithelial cell movement
The corneal epithelium consists of five to seven layers of cells and has an overall
thickness of 50 to 52 pm (Smolin and Thoft 1994). It has a complete cell turnover in
5 to 7 days (Hanna and O'Brien 1960). Davanger and Evensen discovered the
migration of epithelial cells from the corneal limbus towards the centre (Davanger and
Evensen 1971). They found evidence that the limbal structure can produce cells that
migrate over the cornea. Corneal epithelial stem cells have shown to be located at the
palisades of Vogt at the limbo-cornea1 junction and have been found to proliferate
epithelium cells from the limbal region (Kinoshita et al. 1982; Schermer et al. 1986;
Kinoshita et al. 2001). Schermer et al. and Cotsarelis et al. confirmed that the source
of cell proliferation and migration is epithelial cells from the sclero-cornea1 limbus
(Schermer et al. 1986; Cotsarelis et al. 1989).
Thoft and Friend proposed the X, Y, Z hypothesis of corneal epithelial maintenance.
It basically expresses the relationship between epithelial cell proliferation and
epithelial cell loss; where X is the proliferation of basal epithelial cells; Y, the
contribution to the cell mass by centripetal movement of peripheral cells; and Z, the
epithelial cell loss from the surface (Thoft and Friend 1983). Hence corneal epithelial
25
maintenance can be defined by the equation: X + Y = Z, which simply states that cell
loss must be balanced by cell replacement.
In summary, various factors affect the stability of the corneal shape. Factors such as
diurnal variations in thickness and cell movements can change the structure and
thereby the shape of the cornea. While various short-term effects such as mechanical
pressure from lids or applanation tonometry can change corneal shape due to
mechanical deformation.
26
1.4 THE EFFECT OF LID PRESSURE ON CORNEAL
TOPOGRAPHY
Several factors indicate that lid forces may be capable of influencing corneal shape.
Grosvenor’s theory of with the rule astigmatism development says that small forces
(long term pressure) of the eyelids, in the area where they cover the corneal surface,
could gradually cause steeping of the superior and inferior regions of the cornea
(Grosvenor 1978). Furthermore indirect evidence comes from case reports of
monocular diplopia (Fincham 1963; Mandell 1966; Knoll 1975; Bowman et al. 1978;
Carney et al. 1981; Kommerell 1993; Ford et al. 1997; Campbell 1998; Golnik and
Eggenberger 2001) associated with near work. In most of these cases the eyelids were
thought to be responsible for the changes in corneal curvature.
Kiely and Carney examined corneal topography in a series of trials involving blinking
and lid retraction (Kiely and Carney 1978). The corneal topography of eight subjects
was monitored with the auto-collimating photokeratoscope of Clark (Clark 1972). The
effect on corneal topography of normal blinking, lid retraction and hard forced
blinking were determined. For each condition, photokeratograms were taken before
and immediately after the trial, while in the case of the forced blink trials,
photokeratograms were taken additionally at two and five minutes after the trial. No
significant changes were found in this study except in one isolated case.
The effect of lifting the lids away from the globe has been shown to change the
measured toricity in the direction of less with the rule astigmatism (Wilson et al.
1982; Grey and Yap 1986). Keratometric measurements served to determine corneal
changes in 36 eyes with normal lid position and after retraction with a lid speculum.
27
The results showed a significant increase of steepness in the horizontal corneal
meridian while the vertical meridian didn’t show significant changes. For high
astigmats the changes were systematically in the direction of less with the rule
astigmatism while low astigmats showed no systematic trends.
Vihlen and Wilson investigated whether the pressure of the eyelids influences corneal
astigmatism (Vihlen and Wilson 1983). Lid tension and corneal curvature of 100
subjects was compared. It was hypothesised that if lid forces are involved in the
shaping of the cornea, then senile changes leading to a decrease of lid tension with
age should be a factor in corneal changes with age. However, there was no
experimental evidence found that lid tension between individuals is responsible for
differences in corneal toricity.
Grey and Yap measured corneal astigmatism in connection with three different
narrowed lid positions (Grey and Yap 1986). They found a statistically significant
increase of corneal with the rule astigmatism when the lid aperture was narrowed to
leave uncovered only a central vertical area of 2.0 to 2.5 mm of the cornea. In this
position, corneal astigmatism changed by about 2 D. Widening of the palpebral
aperture didn’t cause significant change in corneal astigmatism.
Lieberman and Grierson investigated central corneal shape with and without the
eyelids touching the corneal surface using a stereogrammetry based device
(Lieberman and Grierson 2000). Difference maps between the two conditions
revealed significant central corneal distortion with the lids in their normal position
touching the cornea. In a preliminary study leading to this dissertation, Buehren et al.
28
found statistically significant corneal power changes within a few seconds of the post-
blink interval in the upper and lower regions of the topography maps (Buehren et al.
2001). The location of the band-like distortions correlated well with the subjects’
natural position of the eyelids in primary gaze.
In summary, several studies have found short-term effects of eyelid forces on corneal
astigmatism and corneal distortion. However there has been no conclusive evidence
that long-term effect of lid forces are involved in the shaping of the cornea.
1.4.1 Monocular diplopia associated with near work
Morgan first reported a single case of monocular diplopia (i.e. double images in one
eye) and Fincham observed slight doubling of monocular vision by a large proportion
of subjects with good visual acuity (43% of 70 eyes) (Morgan 1955; Fincham 1963).
Usually one image was fainter than the other and hence was often unnoticed.
Frequently only one eye was affected. It was interesting that all these cases were
similar in that the doubling was almost always approximately in the vertical direction
and homonymous. Fincham assumed that refractive index differences in the
crystalline lens are responsible for the diplopia since he didn’t detect any changes in
corneal topography.
Between 1966 and 1992 three case reports of monocular diplopia are noteworthy.
Mandell reported of a single case of monocular diplopia associated with near work.
The patient complained about blur and vertically double images after reading
(Mandell 1966). The pinhole and the stenopaic slit (placed in the horizontal meridian)
were used to test visual acuity and clearly identified the source of diplopia as optical
29
in origin. When placing the stenopaic slit in the vertical meridian the diplopia
persisted. Furthermore, the retinoscopic reflex revealed dark lines approximately in
the horizontal direction that had not been observed when the patient didn’t experience
diplopia. Finally, keratometer readings exhibited mire distortions that occurred just
after reading. Mandell therefore concluded the cause of the monocular diplopia was
due to changes in the corneal contour.
The second case report of Bowman et al. presented quantitative results of corneal
deformation associated with monocular diplopia following near work (Bowman et al.
1978). Using the autocollimating photokeratoscope of Clark, corneal asphericity from
a reference sphere in any number of meridians were calculated. Across an area about
1.5 mm radially from the ophthalmometric axis, a shift in direction of positive
asphericity (more oblate) was measured in the superior temporal, superior and
superior nasal semi-meridians.
The third study by Goss and Criswell concerned a case report of a 36 year old male
with bilateral monocular polyopia following television viewing (Goss and Criswell
1992). Apparently the monocular polyopia resulted from corneal surface changes
induced by narrowing of the lid aperture. This narrowing was associated with the
supine posture, which was used by the patient to watch television. It seemed logical to
assume that it was the upper eyelid that was distorting the cornea in this case, because
of its lowered position associated with the downgaze position. In photokeratograms
taken before watching television, the rings where smooth and regular, while numerous
irregularities were present afterwards.
30
Knoll described his personal experience of bilateral monocular diplopia following
near work (Knoll 1975). Photokeratograms verified that the upper lids were producing
furrows in the corneas near the upper edge of the pupil, since reading with one eye
closed prevented the closed eye from developing diplopia. Knoll also found a
vertically shifted and homonymous ghost image and likened the effect of it to having
a prism placed base down on the upper part of the pupil.
Carney et al. predicted the angular positions of any secondary image resulting from
corneal distortion. Nine subjects viewed monoculary through a microscope while
keeping the other eye forcibly closed (Carney et al. 1981). Five of the subjects
reported the presence of secondary images in the closed eye after 15 min of the task.
Tracing rays from a distant object point through the distorted cornea could plot the
angular displacement of each ray as a function of its distance from the
ophthalmometric axis. The results showed that the predicted angles of the secondary
images correlated well with the measured angular positions.
Based on retinoscopic characteristics, Kommerell described his findings of monocular
diplopia in 20 patients with ghost images as the “Venetian blind phenomenon”
(Kommerell 1993). Abnormal pressure from the upper eyelid was explained to be the
cause for the phenomenon.
Ford et al. investigated monocular diplopia associated with near work and
hypothesized that the corneal alterations are primarily related to the position of the
lids and tear film interaction with the corneal surface (Ford et al. 1997). Six subjects
that complained of monocular diplopia were examined and compared with a control
31
group of 20 patients without such complaints. A preliminary full ophthalmological
examination for each subject was carried out. Before and after a reading task of 30
minutes, videokeratographs were acquired using the Topographic Modeling System 1
(TMS). In addition, the red reflex using direct retinoscopy was observed and the lid
position in relation to the pupil in primary gaze and during the reading task was noted.
Each of the six subjects showed a horizontal band in the red reflex and developed
diplopia, whereas two controls also showed a faint band but did not complain about
optical effects. Further analysis of corneal topography was undertaken using the
difference map. The difference maps of the six subjects showed horizontal bands of
steepening and flattening of approximately 2.5 D of axial power.
More recently Golnik and Eggenberger published a study which investigated
symptomatic corneal topographic changes induced by reading in downgaze (Golnik
and Eggenberger 200 1). Three symptomatic cases of monocular diplopia following
reading and a control group of nine subjects were studied. The three symptomatic
cases showed changes of up to 2.5 D in the topography difference maps following
reading. The non-symptomatic controls also showed central refractive power change
of up to 1.5 D, however they did not experience monocular diplopia following
reading. Golnik and Eggenberger reported that 30 to 60 minutes is needed to resolve
visual symptoms after cessation of reading.
32
Chapter 1
N
Summary of monocular diplopia studies
Method Decay Finding/Conclusion
30 - 60 min
Study
Corneal topographic change
Task Instrument
Fincham (1 963) 70 Illuminated cylinder vessel
Refractive index difference in lens
Mandell (1 966) Keratometer Reading Change in cornea1 shape Pinhole Stenopaic slit Case report
Knoll (1975) Photokeratoscope Reading 30 - 60 Furrows in the cornea min Own experience
Bowman (1 978)
Carney (1 98 1)
Photokeratoscope Reading Microscope (15 min)
Corneal deformation
Corneal distortion
Case report
9 I Case report Cross and
Criswell(l992) Kommerell (1993) 20
Television viewing Photokeratoscope
Retinoscope Abnormal eyelid pressure
Ford (1 997) Videokeratoscope Reading for (30 min)
Horizontal bands of distortion 6 and 20 controls
Golnik and Eggenberger (2001)
3 symptomatic and 9 controls Videokeratoscope Reading
Table 1-1 : Summary of studies reporting monocular diplopia following near work activities, which have been published within the last 40 years.
33
Corneal surface changes
1.5 EYELIDS AND BLINKS
The major tasks of the eyelids are to protect the eye from injury or excessive light by
closure and to spread a film of tears over the cornea by blinking (Wolff 1968). The
upper eyelid is larger and more mobile than the lower eyelid and they meet at the
medial and lateral angles (canthi). The lateral canthus is about 2 to 3 mm higher than
the medial (Dutton 1994; Snell and Lemp 1998). Interpalpebral fissure measures of
the adult range from 8 to 1 1 mm, whereas the horizontal length is 30 to 31 mm (Snell
and Lemp 1998).
There has been conjecture that only a limited area of the conjunctiva of the upper
eyelid is in close contact with the eyeball (Parsons 1904; Ehlers 1965). Kessing, using
tomography, provided the only direct demonstration of the contact of the eyelids with
the ocular surface (Kessing 1967). He concluded that only a marginal area of the
upper eyelid, while in the lower lid the entire tarsal area, is in close contact with the
globe. More recently Korb et al. described the marginal conjunctiva of the upper
eyelid as a wiping surface to spread the tear film over the ocular surface and therefore
named this area the “lid wiper” (Figure 1-2) (Korb et al. 2002). Korb and co-authors
found characteristic staining with fluorescein of that portion of the marginal
conjunctival epithelium in contact lens wearers suffering from dry eye symptoms. The
clinical condition was described as lid-wiper epitheliopathy.
34
Figure 1-2: The area of the lid-wiper starts posterior to the Meibomian glands, where the
stratified squamous epithelium changes from keratinised to non-keratinised tissue, and
extends superiorly to the subtarsal fold (Figure courtesy of Korb et al. 2002).
35
1.5.1 Blinking
King and Michels measured a blink rate of about 12 blinks/min, while Abelson and
Holly reported blink frequencies of 16 to 17 blinks per minute (King and Michels
1957; Abelson and Holly 1977). However substantial differences in blink rate
between individuals have been reported by York et al., Carney and Hill (York et al.
1971; Carney and Hill 1982), who found typical blink rates of 13 blinks per minute
with marked individual variations. Furthermore, a variety of factors have been shown
to influence blink frequency. Decreased blink rates were observed with subjects
during difficult visual tasks (York et al. 1971) and with soft contact lens wearers that
seemed to subconsciously develop a blinking strategy to suppress blinking during
critical tasks (Pointer et al. 1985). In general, anxiety increases the blink rate, while
increased attention decreases the blink rate (King and Michels 1957).
Types of blinks are frequently divided into three categories: spontaneous blinks,
reflex blinks and voluntary blinks (Guitton et al. 1991; Kaneko and Sakamoto 1999).
Abelson and Holly classified spontaneous blinks into three types: twitch blink,
consisting of a small movement of the upper eyelid (-2%) ; incomplete blink, in which
the descending upper eyelid covered less than two third of the cornea (-17%); and
normal complete blinks (-80%); and voluntary or forced blinks that included an
upward movement of the upper lids (Abelson and Holly 1977).
A mean value of maximum velocity for the closing phase of a typical spontaneous
blink of 8 to 10 mm amplitude is 280 mdsec reached within 70 msec (Collewijn et
al. 1985). Total duration of the down phase is -100 to 150 msec. Average values of
maximum velocity for the opening phase corresponds to 150 mm/sec (Guitton et al.
36
1991) with 200 to 300 msec of total blink duration (Collewijn et al. 1985; Guitton et
al. 1991).
1.5.2 Eyelid pressure
A few researchers have attempted to measure eyelid pressure. Moller conducted two
studies in 1954 and 1955 using a modified Hansen manometer, which enabled direct
measurement of the change in pressure that accompanied blinking (Moller 1954;
Moller 1955). The results showed 10, 20 and 50 (mm water) of lid pressure for gentle
(natural closure), full (deliberate blink), and forced (hard squeeze) blinks,
respectively.
Miller developed a scleral lens and balloon system to measure lid pressure (Miller
1967). His results for the different kinds of blink types showed 38 for gentle, 140 for
full and 693 for forced blinks (pressure in mm water), which differed significantly
from the results of Moller. The eyes were first anaesthetised and then a 0.84 mm thick
scleral contact lens was inserted. The scleral lens and lens-balloon combination
measured a total thickness of 2.5 mm at the apex. After insertion, the combination was
attached to a pressure transducer and lid pressure was determined on ten normal
subjects. Because of the unnatural thickness of the lens-balloon system the results
obtained by Miller are questionable.
Lydon and Tait applied a special lens pressure transducer and used a thin (0.1 mm)
modified scleral shell to measure lid pressure (Lydon and Tait 1988). The transducer
was connected via a valve to a manometer. Before insertion of the scleral lens and
performance of blinking manoeuvres, the subjects’ corneas were anaesthetized. The
37
results of lid pressure measurement under normal conditions showed small pressure
values. In cases of forced blinks, a significantly higher pressure was reached.
In order to measure lid tension, Kennard and Smyth glued a perspex saddle to the lid
sulcus from which various weights were hung (Kennard and Smyth 1963). The
tension of the upper lid was found to not be constant. Vihlen and Wilson derived the
passive spring constant of the upper lid by pulling it away from its rest position
(Vihlen and Wilson 1983). The method involved a small clamp, which was attached
to the upper lid and displaced in a direction normal to the cornea. A range of 1.2 to
6.8 g/mm was measured (mean 3.2 g/mm, SD = f 1.1). The results correlated well
with earlier findings (Hung et al. 1977). Evinger et al. applied weight to the eyelid
while attaching a silk suture to the outer surface of the lid so that the suture pulled
almost straight down on the eyelid (Evinger et al. 1984). Applications of weight to the
lid caused a displacement of the lid that was recorded by a lid monitor. Lid tension of
10 g/mm was measured in primary gaze but was only about 2.5 g/mm in a gaze
direction of 40 degree below horizontal.
Bilateral eye globe retraction occurs during blinking (Evinger et al. 1984; Collewijn et
al. 1985; Riggs et al. 1987). The globe retraction occurs due to co-contraction of the
extraocular muscles, rather than lid forces driving the globe back into the orbit. Lydon
and Tait found that the eye retracts about 0.5 mm on normal blinking and twice as
much on forced blinking (Lydon and Tait 1988). The most plausible explanation for
this effect is the co-contraction of the extraocular muscles on normal blinking while
the lids may contribute some additional force under forced blinking conditions.
38
The magnitude of retraction (interquartile range: gentle and full 0.4 - 0.7 mm, forced
0.7 - 1.3 mm) was in agreement with the results of Doane and Riggs et al. (Doane
1980; Riggs et al. 1987).
In summary, the eyelids protect the eye and spread the tear film over the cornea. It has
been shown that just a portion of the upper eyelid, the marginal conjunctival
epithelium, acts as a lid wiper to spread the tear film over the corneal surface. Mean
blink rate is around 12 to 17 blinks per minute, showing large individual variability.
Blink rate is affected by contact lens wear, level of attention, anxiety, and corneal
sensitivity. Characteristics of blinks have been identified, measured, and types of
blinks have been divided into several categories. Eyelid pressure has not been
measured with high reliability. In cases of forced blinks, significantly higher pressures
may be reached compared to normal blinking conditions. Lid tension was found to not
be constant and lower in the direction of downward gaze. A bilateral eye globe
retraction occurs during blinking, which is due to co-contraction of extraocular
muscle rather than eyelid forces.
39
1.6 WAVEFRONT ABERRATIONS OF THE
HUMAN EYE
1.6.1 Aberroscopy
In 1893, using a grid, a blurring lens and a viewing point source, Tscherning
subjectively quantified aberrations and thereby described the first aberroscope
(Tscherning 1893). Howland and Howland later applied the cross cylinder
aberroscope technique invented by Howland to the measurement of monochromatic
aberrations of the human eye (Howland 1968; Howland and Howland 1976; Howland
and Howland 1977). The technique relied on the subject drawing a grid shadow
formed on the retina, which was then analysed to derive a Taylor polynomial to
quantify the aberrations of the eye. In 1984 Walsh et al. presented an objective
technique for the determination of monochromatic aberrations of the human eye
(Walsh et al. 1984). In agreement with previous findings using the subjective method,
Walsh and co-workers confirmed that third order aberrations are typically larger than
fourth order aberrations in the total wavefront error (Walsh et al. 1984).
Almost parallel to Tscherning’s work in the late nineteenth century, Hartmann used
the Scheiner principle to measure the aberrations of mirrors and lenses (Hartmann
1900). A perforated opaque screen was used to isolate numerous light bundles. Any
deviation of the propagating light bundle then can be measured with a sensor. Shack
and Platt improved the idea of the Hartmann screen by using an array of small lenslets
that focuses light into an array of spots (Shack and Platt 1971). Liang and co-authors
first applied the Hartmann-Shack wavefront technology to measure aberrations of
human eyes (Liang et al. 1994). Today the technique represents the most widely used
objective method to assess the aberrations of human eyes.
40
1.6.2 Measurements of monochromatic wavefront aberrations
In order to characterise the wavefront of an eye it is useful to analyse the aberrations
based on a set of mathematical functions. It is possible to describe aberrations with a
Taylor series expansion. Each term represents aberrations of a particular order. Seidel
used a better approximation and derived five components now known as Seidel
aberrations (spherical aberration, coma, astigmatism, Petzval curvature of field and
distortion) (Freeman 1990). Zernike polynomial series offer an advantage due to their
orthogonality for continuous curves. Therefore Zernike polynomials are most suitable
for optical applications and have been used to estimate ocular (Liang et al. 1994) and
cornea1 aberrations (Schwiegerling et al. 1995). Today Zernike polynomials are the
standard method for describing monochromatic aberrations of the human eye.
There are different conventions of Zernike polynomial presentations in use (No11
1976; Kim and Shannon 1980; Tyson 1982; Conforti 1983; Born and Wolf 1985;
Malacara et al. 1990). This has led to difficulties within the vision research
community when comparing the result of ocular aberrations that have used different
Zernike conventions. In response, the OSA (Optical Society of America) taskforce
was formed in 1999 to establish standards for reporting of optical aberrations in visual
optics research and related clinical disciplines (Thibos 2000). In Table 1-2 the first 20
Zernike terms according to the OSA convention are presented. Within this thesis any
presentation of wavefront aberrations with Zernike polynomials uses the OSA
convention.
41
ZERNIKE POLYNOMIALS ACCORDING TO OSA CONVENTION
J N m Orthonormal Zernikes Description
Table 1-2: The first 20 Zernike terms according to the OSA (Optical Society of America)
convention are presented, with Z," (n = order, m = frequency).
42
After Liang et al. first presented aberrations of the human eye using the Hartmann-
Shack wavefiont sensor technology, this research field has grown rapidly (Liang et al.
1994). First results showed large subject-to-subject variations however some
correlation was found between right and left eyes of the same subject (Liang and
Williams 1997). Marcos and Burns found little symmetry between left and right eyes
(Marcos and Burns 2000) however three large population based studies confirmed the
findings (Porter et al. 2001; Castejon-Mochon et al. 2002; Thibos et al. 2002).
Castejon-Mochon et al. reported of a tendency for mirror symmetry between eyes
while Thibos et al. also indicated the presence of significant bilateral symmetry
(Castejon-Mochon et al. 2002; Thibos et al. 2002).
Thibos et al. showed an exponential decline of aberrations with increasing Zernike
order and a linear increase of the wavefiont error with increasing pupil area (Thibos et
al. 2002). Castejon-Mochon et al. found that 99% of the root-mean square wavefront
error is contained in the first four orders of a Zernike expansion (Castejon-Mochon et
al. 2002). Changes in monochromatic aberrations with age have shown that
aberrations of the cornea and eye increase with age (Guirao et al. 2000; McLellan et
al. 2001).
Recently Carkeet et al. presented monochromatic aberration data from a population of
Singaporean school children (Carkeet et al. 2002). The results revealed significant
differences between refractive error groups as well as between racial groups. Chinese
subjects showed significantly higher amounts of aberrations than Malay subjects.
43
1.6.3 Ocular wavefront aberrations and accommodation
Before the introduction of Hartmann-Shack wavefront technology, changes in
spherical aberration with accommodation have been reported (Koomen et al. 1949;
Ivanoff 1956; Jenkins 1963). Eyes generally decrease from positive spherical
aberration and changed to negative values with increasing levels of accommodation.
Atchison et al. first characterized the wave front aberration as a function of
accommodation of the eye in detail (Atchison et al. 1995). It was found that third
order (coma and coma-like) aberrations were dominant for most people which was in
agreement with earlier findings (Howland and Howland 1976; Howland and Howland
1977; Walsh et al. 1984; Walsh and Charman 1985). Also the classical trend towards
negative spherical aberration with increasing accommodation was found for about
half of the subjects. Ninomiya et al. confirmed the change in spherical aberration
towards negative dioptric values in young adults (He et al. 2000; Ninomiya et al.
2002). He et al. found a trend of increasing wavefront aberrations with increasing
levels of accommodation (He et al. 2000).
1.6.4 Corneal and total wavefront aberrations of the eye
The anterior corneal surface is the eyes’ most powerful refractive component and
therefore is a major contributor to the eyes’ total wavefront aberrations.
Videokeratoscopes capture several thousand raw data points from the corneal surface.
In order to investigate individual corneal surface characteristics, the corneal shape can
be decomposed using a set of mathematical functions. Corneal wavefront information
and knowledge about its contribution to the total aberrations of the eye can be
obtained using a ray trace technique.
44
Guiaro and Artal first demonstrated a procedure to calculate the wavefront aberrations
of the human cornea from its surface shape measured by videokeratoscopy (Guirao
and Artal 2000). The method describes the procedure to calculate the wavefront
aberration of a refracting surface from the elevation data. In order to characterise the
exact wavefront aberration values at each point of the surface, it may be fitted with
Zernike polynomials using the same method used for fitting the corneal surface
(Schwiegerling et al. 1995).
Applegate et al. calculated corneal wavefiont variance and compared the results with
various contrast sensitivity and acuity measurements (Applegate et al. 2000).
Wavefiont variance was defined as the difference between a reference wavefront and
the actual corneal wavefront. A statistically significant correlation between visual
performance and corneal wavefront variance was found. Marcos et al. suggested that
corneal irregularities are a major contributor to the variability of monochromatic and
transverse chromatic aberrations of the eye (Marcos et al. 2001).
The amount of total versus corneal wavefront aberrations was found to be larger in the
cornea than for the complete eye, indicating a partial compensation of corneal
aberrations by internal optics of the eye (Artal et al. 2001; Mrochen et al. 2003).
Barbero et al. compared corneal and total optical aberrations in both eyes of a
unilateral aphakic patient (Barbero et al. 2002). Cornea1 wavefiont aberration was
calculated using videokeratoscopic elevation data. The aphakic eye showed a 98.4 %
correspondence between the corneal and total aberrations. For the normal eye, the
corneal spherical aberration was higher than the total spherical aberration indicating a
45
compensatory role of the crystalline lens in total spherical aberration of the normal
eye.
1.6.5 Wavefront aberrations and Myopia
The relationship between monochromatic aberrations and refractive error has also
been investigated. Collins et al. first objectively measured monochromatic aberrations
in the eyes of young myopic and young emmetropic subjects using the modified
Howland and Howland aberroscope technique (Atchison et al. 1995; Collins et al.
1995). Myopes showed higher levels of negative spherical aberration relative to the
emmetropic subjects for both non-accommodated and accommodated conditions. A
high proportion of the aberroscope grids in the myopic eyes were too highly aberrated
to permit analysis indicating higher levels of aberrations in the myopic eyes. Collins
et al. suggested that high amounts of wavefront aberrations might play a role in
myopia development (Collins et al. 1995).
Several studies confirmed that myopes have significantly larger wavefront aberrations
than emmetropes (Cheng et al. 2000; He et al. 2000; Marcos et al. 2000) although
there has been some diversity of findings. Greater root mean square (RMS) errors of
wavefront aberrations have been found for myopes compared with emmetropes
(He et al. 2002). While Marcos et al. found significantly increased 3rd order
components in myopes, He et al. reported of significantly greater 2nd and 4* order
components (He et al. 2000; Marcos et al. 2000). Paquin et al. found a quasi-linear
relationship between increasing aberrations and refractive error (Paquin et al. 2002).
Based on the results found for different racial background and refractive error,
Carkeet et al. found no evidence for aberration-driven form-deprivation as a major
46
mechanism of myopia development (Carkeet et al. 2002). More recently Cheng et al.
found no correlation between total higher order aberrations and refractive error in
myopic and hyperopic eyes but a tendency towards larger higher-order aberrations for
astigmats as compared with non-astigmats (Cheng et al. 2003).
1.7 MYOPIA AND REFRACTIVE ERROR DEVELOPMENT
While there is evidence that refractive error is partly genetically determined, there is a
growing body of evidence that the type of visual tasks undertaken also influence
refractive error development. The observed increase in myopia prevalence over recent
decades has increased debate regarding the relative contribution of environmental and
genetic factors to myopia development. In Singapore, for instance, within a decade the
prevalence of myopia in young adults has increased from 26% to 65% in university
graduates (Tay et al. 1992). Today it is generally accepted that the risk factors for
myopia development are both genetic and environmental (Mutti et al. 1996; Pacella et
al. 1999; Wu and Edwards 1999).
1.7.1 Myopia prevalence
Many Asian populations are reported to have significantly higher rates of myopia than
western populations (Chandran 1972; Lin et al. 1988; McCarty et al. 1997; Wong et
al. 2000). For comparable young age ranges the prevalence of myopia in populations
in Taiwan is 84% (Lin et al. 1995), in Japan 65.6% it is amongst students (Matsumura
and Hiroaki 1999), and it is 50% to 70% in Hong Kong (Lam and Goh 1991). For
Australia a myopia prevalence of 17% has been reported (Wensor et al. 1999). In the
United States myopia prevalence of 25% has been found (Sperduto et al. 1983),
although more recently McCarty et al. reported more than 40% prevalence in the US
47
(McCarty et al. 1997). These differences in myopia prevalence between different
ethnic groups with similar living standards seem to underscore the relevance of
genetic factors in refractive error development.
More evidence to support the importance of genetics in myopia comes from twin
studies (e.g. (Teikari et al. 1989; Hammond et al. 2001) and links between parental
history and the myopia development in children (Gwiazda et al. 1993; Yap et al.
1993; Zadnik et al. 1994; Goss and Jackson 1996; Edwards 1998; Pacella et al. 1999;
Hammond et al. 200 1 ; Lee et al. 200 1). Gwiazda et al. reported a myopia prevalence
of 43% in children with two myopic parents, 22.5% when only one parent is myopic
and 8% with neither parent myopic (Gwiazda et al. 1993). Zadnik and co-workers
found that even before juvenile myopia onset, children of myopic parents have longer
eyes (Zadnik et al. 1994).
On the other hand numerous investigators have noted an association between near
work activities and myopia (Parssinen and Lyyra 1993; Goss and Rainey 1998; Tan et
al. 2000). A number of reports of a high prevalence of myopia among student
populations comes from Norway (Midelfart et al. 1992; Kinge and Midelfart 1999;
Kinge et al. 1999; Kinge et al. 2000), indicating that intensive near work may initiate
or lead to myopia progression in young adults. Other examples reported to show high
myopia prevalence and progression related to intense near work are Orthodox Jewish
male students (Zylbermann et al. 1993), and law students (Zadnik and Mutti 1987;
Loman et al. 2002).
48
Further support for environmental factors playing a role in myopia comes from
studies of some occupational groups. Adams and McBrien reported a prevalence of
refractive errors in a population of clinical microscopists of 71% with 49% reporting
onset or progression of myopia after entry into the profession (Adams and McBrien
1992). The incidence of myopia progression in a follow up study in this occupational
group was 45% (McBrien and Adams 1997).
1.7.2 Myopia etiology
The etiology of myopia is not fully understood, however many theories have been
proposed. The biological theory explains the distribution of refractions with a natural
variation (Gaussian distribution) between individuals in the growth of the eye. This
early theory by Steiger implies that myopia is not preventable (Steiger 19 13).
Use-abuse theories state that intensive near work, such as reading, cause myopia due
to tensing of muscles in or around the eye, which over a period of time makes the eye
permanently more myopic (Angle and Wissmann 1980). Angle and Wissmann
showed an association between education and the tendency of myopia appearance and
progression among 12 to 17 year olds, concluding that at least some of the variance of
myopia can be explained by the use-abuse theory (Angle and Wissmann 1978; Angle
and Wissmann 1980). Van Alphen has supported the theory showing a potential
significance of ciliary muscle tone on choroidal tension and scleral stretch following
inflation of in vitro eyes (van Alphen 1986).
The hypothesis suggesting that emmetropisation is a vision-dependent phenomenon
(Rabin et al. 198 1) has shifted researchers interest towards retina1 image quality rather
49
than tensing of muscles in or around the eye as possible etiological risk factor of
myopia. Goss and Wickham proposed that retinal image-mediated ocular growth is a
possible etiological factor in juvenile-onset myopia (Goss and Wickham 1995). The
hypothesis is consistent with animal models (Wallman et al. 198 1 ; Raviola and
Wiesel 1985; Schaeffel et al. 1988; Wildsoet 1997) and is supported by numerous
human infant refraction data taken early in life (Howland et al. 1978; Ingram and Barr
1979; Atkinson et al. 1980; Howland and Sayles 1984; Ehrlich et al. 1997)
1.7.3 Emmetropisation
Emmetropisation is the process by which the normally distributed refractive error of
infants changes towards a narrower distribution, showing a marked peak about
emmetropia. The proposal finds support from several studies that have reported of
high incidence of astigmatism within the first months after birth followed by a
significant decrease of astigmatism within year one to six (Howland et al. 1978;
Ingram and Barr 1979; Atkinson et al. 1980; Howland and Sayles 1984; Ehrlich et al.
1997). Gwiazda et al. conducted a study of noncycloplegic refractions of 1000
children between the age of 0 to 6 years showing a large reduction in the amount of
cylindrical error accompanied by an astigmatic change from against-the-rule
astigmatism before age 4.5 years to with-the-rule astigmatism thereafter (Gwiazda et
al. 1984).
Hyperopia (Mayer et al. 2001; Pennie et al. 2001) and myopia (Ehrlich et al. 1995)
have also been found to decline significantly with increasing age. Ehrlich et al.
showed significant emmetropisation of the mean spherical equivalent towards low
hyperopia in a group of infant myopes from 8.5 to 38.5 months of age and
50
furthermore found a significant decline for both with-the-rule astigmatism and
against-the-rule astigmatism (Ehrlich et al. 1995).
The most compelling evidence for a process of active emmetropisation comes from
animal studies that have shown compensatory eye growth in response to focusing
errors imposed by lenses (Schaeffel et al. 1988; Troilo and Wallman 1991; Norton
and Siegwart 1995; Wildsoet 1997). Schaeffel et al. raised chickens with defocusing
lenses of different power in front of their eyes (Schaeffel et al. 1988). A consistent
shift in the chickens' refractive state in a direction to compensate for the lens was
found. Schaeffel et al. discuss the findings in the context of a closed-loop feedback
system acting to regulate eye growth (Schaeffel et al. 1988).
Rabin et al. based their suggestion of emmetropisation being a visually dependent
phenomenon, on a retrospective analysis of refractive error among humans subjected
to various ocular anomalies which disrupt vision (Rabin et al. 198 1). A link between
increasing incidence of ametropia and visual anomalies such as ptosis or congenital
aphacic eyes was identified. In human infants, a degradation of retina1 image quality
due to various pathological conditions has been shown to result in high myopia (Robb
1977; O'Leary and Millodot 1979; Hoyt et al. 1981; Nathan et al. 1985; Miller-Meeks
et al. 1990). Several authors have reported an association between congenital ptosis
and increased presence of astigmatism, myopia, or amblyopia (O'Leary and Millodot
1979; Ugurbas and Zilelioglu 1999; Gusek-Schneider and Martus 2000). Temporal
and manifest changes in spectacle or contact lens correction after ptosis surgery has
been found in adults (Cadera et al. 1992; Holck et al. 1998; Brown et al. 1999).
51
1.7.4 Near work related myopia studies in humans
The literature of myopia studies in humans is immense. Within this thesis, just near
work related studies that might be of importance in association with cornea1 distortion
during reading are summarized. Since prolonged near work is thought to be an
environmental risk factor associated with myopia development, one possibility is
related to the accuracy of accommodation during near viewing. A typical
accommodation stimulus-response curve (ASRC) shows a lead of accommodation for
far objects, a crossing point possibly close to the eyes’ tonic level, and
accommodative lag at the near point (Morgan 1944).
A widely discussed hypothesis is that accommodative lag during near work results in
a blurred retinal image (hyperopic defocus), which in turn triggers eye growth. A
large number of studies have investigated whether accommodative stimulus/response
behaviour differs with refractive error (McBrien and Millodot 1986; Rosenfield and
Gilmartin 1988; Gwiazda et al. 1993; Gwiazda et al. 1995; Abbott et al. 1998).
Despite considerable methodological differences, reduced accommodation stimulus
responses in myopes have been reported in many studies (i.e. lags of accommodation
tend to be higher in myopes) (McBrien and Millodot 1986; Rosenfield and Gilmartin
1988; Gwiazda et al. 1993; Gwiazda et al. 1995). Abbott et al. observed a greater lag
of accommodation in progressing myopes compared to those whose myopia was
stable (Abbott et al. 1998). Conflicting reports however have found that an increased
lag of accommodation accompanies rather than precedes the development of myopia
(Rosenfield et al. 2002).
52
A related research area, which has been extensively investigated, is near work induced
transient myopia (NITM), a short-term myopic shift of the far point immediately
following a sustained near visual task (Ong and Ciuffieda 1995). NITM is thought to
be the effect of a prolonged accommodation response time to a far target following
extending near viewing tasks, but has also been found over a range of accommodative
stimulus levels (Owens and Wolf-Kelly 1987) and for the near point of
accommodation value (Fisher et al. 1987). Some researchers have attributed this
refractive shift to an actual change in tonic accommodation (Ehrlich 1987; Owens and
Wolf-Kelly 1987). NITM has shown a dependency of ethnicity (Wolffsohn et al.
2003) and time of the visual near task (Ehrlich 1987; Rosenfield et al. 1992) on decay
characteristics and is manifest during the progressive phase of myopia development
(Vera-Diaz et al. 2002). Since myopes show particularly striking near work after-
effects, it has been speculated that NITM may cause or be a precursor to permanent
myopia or myopic progression (Ciuffieda and Wallis 1998).
Some researchers hypothesized that uncorrected astigmatism may play a role in the
development of school-age myopia (Fulton et al. 1982; Grosvenor and Goss 1998;
Gwiazda et al. 2000) and against-the rule astigmatism has been associated with faster
myopic progression rates in children (Hirsch 1964; Grosvenor et al. 1987; Gwiazda et
al. 1993). Although there is general agreement that axial elongation is the most
obvious cause of school-age myopia progression, myopes have steeper corneas (Scott
and Grosvenor 1993; Carney et al. 1997; Goss et al. 1997) and myopia progression
has been shown to correlate with steepening of the principal meridian nearest to
vertical (Goss and Erickson 1987) (i.e. with-the-rule cornea1 astigmatism).
53
1.7.5 Attempts to prevent myopia progression
Methods that have been used to prevent myopia progression have shown limited
success (Grosvenor 1989). Theories that sustained accommodation promotes myopia
progression in humans have led to the use of bifocal or progressive spectacle lenses in
children to reduce the progression of childhood myopia. Earlier clinical trials with
bifocal lenses have been inconclusive (Goss 1982). More recently, Edwards and co-
workers have found no difference in the increase in myopia between a matched
treatment group wearing progressive lenses and control group (Edwards et al. 2002).
However there are several studies that have noted a link between esophoria and
reduced myopia progression following bifocal lens wear in children (Oakley and
Young 1975; Goss 1986; Fulk et al. 2000; Brown et al. 2002).
Clinical procedures involving the treatment of myopia with cycloplegia such as
atropine, in combination with bifocal lenses appear to be effective in preventing
myopia progression (Bedrossian 1979; McBrien et al. 1993; Chou et al. 1997; Lin et
al. 1999). However myopia progresses when atropine is discontinued and problems of
the treatment comprise various side effects and patients’ compliance (Woo and
Wilson 1990).
There have been a number of studies reporting that rigid contact lenses may slow the
progression of myopia in children (Stone 1976; Grosvenor et al. 1987; Grosvenor et
al. 1989; Khoo et al. 1999). Stone performed the first major clinical study in which a
significant annual reduction of myopia progression in the contact lens wearers
(0.17 D) as compared with the control group (0.38 D) was found (Stone and Powell-
Cullingford 1974). Cornea1 flattening accounted for only about half of the reduction in
54
myopia. Therefore it was concluded that rigid lenses might have an effect on the axial
growth of the eye. A clinical trial, the contact lens and myopia progression (CLAMP)
study, is under way to further clarify the effect of rigid gas-permeable contact lenses
on myopia progression in children (Walline et al. 2001).
In summary, based on numerous studies in the field of myopia prevalence and
progression, the risk factors for myopia development can be broadly divided into a
combination of both genetic and environmental factors. The most widely accepted
theory regarding the etiology of myopia suggests that retinal image quality is an
etiological risk factor in juvenile-onset myopia. The hypothesis is supported by
various animal studies, the process of emmetropisation observed early in life and
pathological conditions that degrade retinal image quality that have been shown to
disrupt infant emmetropisation.
An increased lag of accommodation during near work, which would result in a blurred
retinal image, has been suggested to trigger eye growth. Near work induced transient
myopia (NITM) has been speculated to be a precursor to manifest myopia since it has
been shown to accompany the progression of myopia, while against-the-rule
astigmatism has been associated with faster myopia progression rates. Bifocal lenses
in combination with cycloplegia are effective in preventing the progression of myopia
during the therapy, while rigid contact lenses have shown to slow down myopia
progression in children and have been speculated to have an effect on axial length.
55
1.8 RATIONALE
Videokeratoscopes provide a sophisticated description of the corneal shape. Accuracy
and repeatability of the instruments have been investigated and show that several
sources of error impose limits to corneal topography measurement. There have been
numerous studies concerning the stability of corneal shape and lid force induced
corneal distortions following reading. One of the major environmental risk factors for
myopia development is reading and near work. However the cornea is not thought to
play a major role in refractive error development, maybe because too little is known
about corneal stability during near work and the optical effects of corneal distortions
on visual performance of the eye. In a series of experiments described in this thesis,
several of these issues were addressed, and potential interactions between corneal
optics and refractive error are discussed.
One of the sources of error in videokeratoscope measurement is the stability of the
eye being measured. Chapter 2 describes a method which was developed to minimize
the effect of ocular microfluctuations during videokeratoscopy to improve the
qualitative and quantitative analysis of corneal topography. A technique was
developed to measure tilt, displacement, and cyclotorsion in multiple
videokeratographs from the same cornea. This information was used to reposition
each videokeratograph according to the average position of a sample of multiple
measurements. The method provided an improvement to the precision performance of
videokeratoscopy in multiple measurements of corneal topography.
One factor that could have an effect on the corneal shape during near work is
accommodation. Previous studies regarding the effect of accommodation on corneal
56
curvature on normal corneas have been restricted by the available technology.
Chapter 3 reports a study that was undertaken to determine if there are significant
changes in corneal topography during accommodation in normal corneas and corneas
that are pathologically thinner due to keratoconus. A videokeratoscope was modified
to present an accommodation stimulus that was coaxial with the instrument’s
measurement axis. The effects of ocular micromovements on multiple topography
maps were minimized using the technique described in Chapter 2. Using this
experimental set up, the accuracy of corneal topography measurement should
substantially improve compared with previous studies that have used keratometers or
photokeratoscopes to measure corneal topography during accommodation.
Monocular diplopia has been linked to corneal distortion following near work in
various studies, however the optical cause of the distortions have never been analysed
in detail. To investigate the effects of eyelid pressure on corneal shape and corneal
aberrations during reading, a detailed objective analysis using traditional sphero-
cylinder and corneal higher order aberrations was performed in Chapter 4. Twenty
young subjects with normal ocular health were recruited for the study. The experiment
was conducted early in the morning, with subjects instructed not to perform any
prolonged reading prior to the experiment. Significant changes in corneal root-mean-
square error, overall corneal refractive power, and corneal astigmatism were found
after reading.
Since these findings may have important implications for the relationship between
reading and the development of refractive errors, the question arises whether the
optical characteristics of the cornea following reading differ between different
57
refractive error groups. In the experiment described in Chapter 5, cornea1 distortions
following reading were studied in a group of young progressing myopes and a group
of young stable emmetropes.
58
CHAPTER 2
Ocular Microfluctuations and
Video keratoscopy
2.1 INTRODUCTION
The measurement of subtle changes in corneal topography requires the highest
possible instrument accuracy and also requires software analysis tools that can detect
and highlight those subtle changes with high reliability. The work described in this
chapter addresses the issue of the statistical significance of change in corneal
topography and describes methods to improve the estimation of topography change.
Videokeratoscopes provide sophisticated qualitative and quantitative descriptions of
the cornea. While currently available videokeratoscopes incorporate a number of
important improvements compared to older instruments (Dave 1998), there are still
significant differences between instruments in terms of precision (Binder 1995;
Jeandervin and Barr 1998; Moura et al. 1998; Tang et al. 2000). For all
videokeratoscopes, the precision with inanimate test surfaces (Potvin et al. 1995;
Greivenkamp et al. 1996; Dave et al. 1998; Priest and Munger 1998; Hilmantel et al.
1999; Tang et al. 2000) is expected to be higher than the performance on real eyes
(Wilson et al. 1992; Kanpolat et al. 1997; Jeandervin and Barr 1998; Hough and
Edwards 1999), since natural dynamics of the eye and anterior ocular surface are
likely to decrease the instruments’ precision. Studies on real eyes have found that the
tear layer (Cronje-Dunn and Harris 1996; Licznerski 1998; Thibos and Hong 1999;
59
Nemeth et al. 2001), and lid forces (Wilson et al. 1982; Ford et al. 1997; Lieberman
and Grierson 2000) can contribute to increased topographical variability. It has also
been shown that poor fixation is a potential source of measurement variability (Hubbe
and Foulks 1994; Mandell 1996; Keller et al. 1997; Douthwaite and Pardhan 1998).
Errors may occur in videokeratoscopy as a result of variations in the measurement
axis. Chan and Mandell showed that decentration of the corneal apex can produce
significant videokeratograph errors when using standard alignment, rather than
alignment with the apex (Chan and Mandell 1997). Eccentric subject fixation
produces changes such as corneal asymmetry (Douthwaite and Pardhan 1998) or
irregular astigmatism similar to that seen in cases of keratoconus (Silverman 1994;
Keller et al. 1997). Hubbe and Foulks also observed these pseudokeratoconus patterns
with fixation deviations of less than 5 degrees in some patients with normal corneas
(Hubbe and Foulks 1994).
A normal fixation pattern is characterised by miniature eye movements such as micro-
saccades, drifts, and tremor (Riggs and Ratliff 195 1; Steinman et al. 1973 (28)). These
microfluctuations are typically 5 to 7 minutes of arc in magnitude (Steinman et al.
1973 (28); Tulunay-Keesey 1976 (29); Dell'Osso and Dardoff 1983 (30); Ferman et
al. 1987 (3 1)). Dell'Osso and Dardoff reported that they can range from 1 to 25
minutes of arc (Dell'Osso and Dardoff 1983 (30)), and the direction of eye movements
varies considerably from subject to subject (Steinman et al. 1973(28)). When visual
acuity is diminished through factors such as amblyopia or uncorrected refractive
errors, these microfluctuations are thought to increase in magnitude (Srebro 1983;
Westall and Aslin 1984). More recently Jampel and Shi have measured retina1
60
micromovements of a mean of about 3 minutes of arc, ranging from less than 1 to 24
minutes of arc within 33.3 msec (Jampel and Shi 2000 (34)). A succession of
micromovements caused the visual line to trace a zigzag pathway across the foveola.
Difference maps are useful to investigate changes in corneal topography. Changes can
occur as a consequence of contact lens wear (e.g. orthokeratology), refractive surgery,
or pathological changes. One of the problems associated with interpreting difference
maps is the uncertainty regarding the significance of changes apparent in the
difference map. This problem can be largely overcome by averaging multiple
videokeratographs taken for both the first and second measurement conditions. Such
an approach requires interpolation of the topography data into a common coordinate
system for all points in all of the maps. This allows not only an average
videokeratograph map to be derived for each condition, but also a standard deviation
to be calculated for all points in the map (Buehren et al. 2001).
One of the factors that are likely to make a major contribution to the standard
deviation (variance) associated with multiple videokeratoscope measurements is the
small variation in fixation due to natural microfluctuations in eye position. This
results in the measurement points from two videokeratographs being captured at
slightly different point locations of the cornea relative to the videokeratoscope axis
(VK axis). Thus each measurement is slightly displaced and the corresponding
corneal locations are no longer at the same position relative to the instrument axis.
This displacement decreases precision of repeated videokeratographs and will also
result in errors when two videokeratographs are subtracted from each other (i.e.
difference map).
61
In this study, a technique was developed to use videokeratoscope data to minimise
lateral shifts, tilts and cyclo-deviations caused by fixation errors and cyclo-rotations.
We investigated the apparent amount of these deviations in the data from ten subjects
and calculated the effects of these errors on difference maps and Zernike polynomials
derived from videokeratographs.
2.2 METHODS
The Keratron videokeratoscope, based upon the Placido disk principle, was used for
all corneal topography measurements. Across a range of inanimate test surfaces, the
Keratron has been shown to have an accuracy between < 0.25 and 1 micron centrally,
about 3 to 5 microns at 3.5 mm from centre, and precision of 5 f 1 micron of standard
error (Tripoli et al. 1995; Tang et al. 2000). Before the study, the instrument
calibration was checked according to the manufacturer’s instructions. Twenty
measurements were taken from each subject. Cornea1 height data from the Keratron
software and the corresponding radial data files were exported and then changed into
Cartesian coordinates (the Keratron samples the data at 256 equally spaced semi-
meridians). The videokeratograph that showed the smallest available number of
complete Placido rings, within a sample of twenty videokeratographs captured from
one subject, was used for analysis of all twenty videokeratographs, omitting the
incomplete ring data at the edges of the map. In this way the same corneal diameter
was used for each of the maps during the correlation procedure.
The technique of minimizing fixation errors is based on a number of assumptions that
can be made when taking multiple measurements of the same cornea within a short
time period. If we assume that corneal topography does not change during the
62
measurement period, then within the limitations of the videokeratoscope's precision,
there is only one unique shape for an individual cornea. By extracting some of these
unique characteristics, such as tilt, shift, and cylinder axis, it should be possible to
reposition a single measurement with respect to the average of multiple
measurements of the same cornea. This should not only improve the interpretation of
difference maps but also increase the precision associated with multiple
measurements. The principle of the method we describe here should be applicable to
any cornea1 height data derived from any type of videokeratoscope.
2.2.1 Regression plane - to remove tilts
A two-dimensional regression plane, fitted into a set of three-dimensional data points,
gives a measure of the tilt of this set of data points with respect to the coordinate
system (Figure 2-1). We collect the discrete videokeratoscope height data C(x,, y,) ,
d = 1,. . . , D , into a column vector C, and form a linear regression C=AP, where A is
the column vector of the parameters, P=[X Y I ] is a (D x 3) matrix of the plane, and
D denotes the number of sample points. We use the least squares (LS) method to
estimate the parameters of the fitted plane a= (PTP)-'PTC, and calculate the best
plane fit using eP=h.
The angle of tilt shown by the plane relative to the coordinate system (i.e. VK axis)
represents the sum of the inherent surface tilt due to the surface asymmetry and the
additional tilt induced by fixation errors. The above procedure is applied to all
multiple measurements of the same cornea and an average tilt, eP(+ of the plane is
calculated. Then, every map is rotated into this average tilt. Since the timing of
multiple videokeratoscope measurements is random, there is no way of knowing the
63
true tilt of the corneal surface. However, the greater the number of multiple
measurements, the more likely it becomes that the average tilt is accurate, because
less bias is present.
2.2.2 Sphere apex - to remove x, y, z shifts
In the next step, spheres are fitted to each of the 20 tilt adjusted maps using the LS
method since the corneal apices have moved away from the VK axis following tilt
adjustment. The apices of the fitted spheres are assumed to find corresponding
locations on each surface since there are no more tilts between maps and the sphere
fit is unaffected by potentially inherent cyclo-deviations between measurements.
Now, the apices of the spheres are shifted to the centre of the coordinate system (i.e.
VK axis) as they are assumed to represent the same location on the cornea. These
shifts have no effect on the angles of the regression planes (tilts), which are now also
the same in each map. Hence, the maps are now correlated with respect to map tilts
and surface shifts along the x-, y-, and z-axis. Since the cornea is not perfectly
rotationally symmetric, it can’t be assumed that the new corneal apices are equivalent
to the apices found by the spheres. Hence the corneal apices are yet not shifted into
the mean corneal apex (i.e. VK axis). Subtracting the average amount of shifts that
were applied to a sample of maps from each individual shift of a map achieves this
aim. Now, the sum of all remaining shifts shows the smallest possible amount
relatively to the VK axis. Hence no more bias from the sphere fit is apparent. The
locations of the new corneal apices are now at the mean corneal apex (i.e. VK axis).
64
-4 -4 Y X
Figure 2-1 : 2-D linear regression plane fit to a set of raw data points of cornea1 height
measurement. Cornea1 height data is shown in Placido rings. Scale for x, y, and z is in mm.
65
2.2.3 Best-fit sphero-cylinder - to remove cyclo-deviations
In general, cyclo-deviations are associated with cyclophoria. Wick and Ryan
measured cyclophoria on 100 consecutive non-strabismic patients and found a mean
value of 0.78 degree (Wick and Ryan 1982 (37)). Additional variability is likely to
come from differences in head positioning in the videokeratoscope’s headrest. Ferman
repeatedly measured ocular torsion in four subjects and found deviations of
approximately 1.5 to 5 degrees in static primary positions while the subjects viewed a
central target (Ferman et al. 1987 (3 1)).
Astigmatic corneas will show toric (saddle) shape in the difference map, if a cyclo-
deviation is present between two videokeratographs. To find the best-fit sphero-
cylinder to the corneal surface, the technique proposed by Maloney was applied
(Maloney et al. 1993). This method was used to determinate the orientation of corneal
astigmatism in each videokeratograph (i.e. axis of astigmatism). Then an average
value of the corneal astigmatic axis for the sample of multiple measurements was
calculated and all maps rotated accordingly around the z-axis.
In Figure 2-2 (top) a difference map is shown from two videokeratographs of subject
4. The map indicates asymmetric infero-temporal changes (2-D plot) reaching slightly
more than 5 microns at the edge of a 6 mm zone (profile plot). After the two
videokeratographs were tilt-reduced and apex matched (centre), a toric (saddle) shape
difference comes to light (2-D plot), leaving infero-temporal and supero-nasal
changes of approximately 3 microns in magnitude (profile plot). The RMSE is slightly
decreased from 1.25 microns to 1.02 microns. Figure 2-2 (bottom) shows the result
when the full procedure is applied (i.e. tilt reduced, apex matched, and cyclo-rotation
66
reduced). The RMSE decreased by 45.4 % from the original 1.25 microns to 0.68
microns. The maximum value in the difference map is just slightly above 2 microns
and most data points lie within a difference off 1 micron (profile plot). The 2-D plot
shows a relatively symmetric increase in differences from the centre to the edge of the
map. These differences are now approaching the level of the instrument’s precision
performance for inanimate test surfaces (Tripoli et al. 1996; Tang et al. 2000).
2.2.4 Limitations
The procedure for minimization of fixation errors has been derived with certain
assumptions that ultimately limit the accuracy of the outcomes. Firstly, the technique
does not take into account that, concomitant with slight gaze changes, the area of
measurement also slightly changes. This means that at the edges of the maps, along
the direction of the deviation, slightly more or less data will be captured in the
videokeratograph. No matter which diameter is chosen to correlate a set of multiple
measurements, these data points at the edge of the map represent slightly different
areas between maps. However since the gaze changes and thus the difference between
cornea1 areas are very small (approximately -0.4 %), this problem should have little
effect on the methods’ accuracy. Secondly, the technique cannot exceed the
measurement precision of the instrument itself. This means that measurement errors
other than caused by ocular micromovements (e.g. instrument errors, tear layer
variability, or lid force effects) decrease the accuracy of the regression plane, the
sphere, as well as the cyclo-rotation procedure, in finding the same characteristic from
each videokeratograph.
67
Figure 2-2: Difference map (top) of two successively captured videokeratographs of subject 4
(data untreated). The same difference map after tilt reduction and apex matching (centre) and
additional cyclo-deviation correction (bottom) was applied.
68
Thirdly, the effectiveness of the procedure in fmding the average spatial position of
the cornea is dependent on the number of measurements. In this study we have used
20 measurements as a basis for the mean, however it is obvious that the larger the
sample of measurements, the more reliable the average becomes. Finally, for a
perfectly rotationally symmetric cornea, the technique of fmding the axis of corneal
astigmatism would not apply. However such a cornea would be rare and small
amounts of corneal astigmatism would cause relatively small cyclo-torsional precision
errors.
2.2.5 Protocol
Ten subjects took part in this study. Mean age was 29 years ranging from 22 to 43
years. None of the subjects had significant corneal disease. Three subjects were
emmetropes, two were myopes, and five had myopic astigmatism.
Videokeratographs of all 10 subjects were captured with the instruction to the subjects
to fixate the videokeratoscope target and just prior to image capture, to blink and then
open the eyes wide (i.e. normal image capture procedure). For the 20 measurements
taken from each subject, the root mean square error (RMSE) of corneal height
difference maps between each single videokeratograph and the averaged
videokeratograph of the 20 measurements was compared before and after fixation
error minimization. Cornea1 height data was fitted with the first 11 Zernike
polynomials according to the Zernike convention of No11 (No11 1976). This is
equivalent to taking terms up to the third radial and azimuthal order plus the fourth
order radial term (Thibos et al. 2000). After the data was corrected for fixation errors,
the procedure was repeated, fitting the first 11 Zernike terms. The mean and standard
69
deviation of the two terms was compared for the normal videokeratographs and the
videokeratographs corrected for fixation errors. The analysis for both RMSE
calculation and Zernike polynomial fit was performed in a 5 mm pupil area for all
subjects’ data.
2.3 RESULTS
Across the group, microfluctuations derived from the repositioned videokeratographs
showed an average value of 5.8 minutes of arc f 2.2 (SD), which was in general
agreement with the values reported by studies of these eye movements (Table 2-1).
This corresponds to an average apex shift from the mean of 10 microns f 3.5 SD. This
apex shift was calculated by deriving the hypotenuse of x-shifts and y-shifts, which
were effectively applied to a single videokeratograph after sphere bias correction. To
compare this value with the angles of miniature eye movements reported in the
literature (5 to 7 minutes of arc), it has to be doubled (i.e. 20 microns f 7 SD) and
then the angle between this distance and the centre of eye rotation has to be
calculated. Doubling is necessary because the distance of a single apex from the
average apex represents just half the distance of an equivalent eye movement from a
start point to an end point. Gullstrands’ eye-model was used to determinate the
distance between cornea1 apex and the centre of eye rotation. Subject 2 showed the
largest eye movement of the group with 23 min of arc (apex displacement
82 microns). Cyclo-deviations were estimated to average 2.4 degrees f 1.1 (SD)
between maps, with a maximum value of 4.6 degrees shown by subject 6.
The RMSE shows an average decrease of 24.6% after minimization of fixation errors
ranging from 14.3 % to 43.2 %. In Figure 2-3 the average decrease of the RMSE in
70
percentage for each of the ten subjects are shown. The absolute values appear to be
small in magnitude (all averages less than 1 micron) however this value has to be
analysed with caution. Videokeratoscopes capture several thousand data points on the
cornea, which are unequally distributed within the measurement area (i.e. more data
points are close to the centre). Thus, the amount of the RMSE for the entire map is
biased to the smaller measurement errors occurring in more central areas.
As expected, the standard deviation of the horizontal and vertical prism components
derived from the Zernike polynomial expansion decreased considerably following
minimization of fixation errors. There was an 82.3 % decrease of the 2,' (p, (3)
1 vertical prism term and 73.8 % decrease of 2, (p, 0) horizontal prism term (Figure 2-
4). Also the standard deviation of zi2 (p, primary astigmatism (45 degrees)
decreased substantially by 43.8 %. Since the oblique astigmatism term 2,' (p, is
likely to be the smaller primary astigmatism component for most people, small
cyclotorsional corrections of the cornea are expected to show larger effects on the
standard deviation of this term compared with 2: (p, primary astigmatism
(90 degrees). The remaining Zernike terms showed little decrease of standard
deviations.
71
Ocular Microfluctuations
Average
eye rotation
Average
apex movement
Average
cyclo-deviation
Maximum
eye rotation
Maximum
apex movement
Maximum
cyclo-deviation
This study based on
corneal topography
5.8 min of arc
f 2 (SD)
20 pm f 7 pm
2.4"
f 1.1 (SD)
23 min of arc
82 pm
4.6"
Other studies based on
eye movements
(28 - 31,34,37)
6 min of arc (28,30)
5 min of arc (29)
7 min of arc (3 1)
3 min of arc in
33.3 msec intervals (34)
Range 1.5" to 5" (37)
f 1.2 to f 2.07 (SD)
Range
1-25 min of arc (30)
1-24 min of arc in
33.3 msec intervals (34)
5" (37)
Table 2-1: Comparison of miniature eye movements between measurements based on corneal
topography and conventional measurement techniques.
72
2.4 DISCUSSION
When we compare the eye movements calculated in this study with the values
reported for ocular microfluctuations, the results agree surprisingly well. This
indicates that the technique we have developed to reposition videokeratographs is
capable of detecting the topographical effects of these small eye movements. We have
not analysed the directions of eye movements because the 20 separately captured
videokeratographs did not measure eye movements at specific time intervals. The
videokeratographs were captured at irregular intervals and therefore represent a
random sample of eye movements that have occurred within a longer time period.
The average value for cyclo-deviations lies within the range of deviations reported by
Ferman (Ferman et al. 1987 (3 1)). Our mean value is calculated from 200
measurements that were captured from 10 subjects. Ferman described the range of 88
displacements taken from both eyes of 4 subjects. The maximum cyclo-deviation
measured in this study was 4.6 degrees, which is close to the 5 degrees of Ferman’s
study. These cyclo-deviations contributed significantly to increased variability
between measurements.
Following minimization of the effect of eye movements, the RMSE clearly showed a
decrease of variability between measurements with an average decrease of 24.6 %
across the group. This increase in precision will allow better analysis of the quality of
real changes between measurements, since the color-coding of difference maps is less
biased by differences due to eye movements (e.g. tilts). However, there was still a
significant amount of remaining variability between measurements even after fixation
error minimization. These differences are presumably due to tear layer instability and
75
lid force effects. Variability was also evident in overall curvature (i.e. steeper or
flatter), which probably results from small defocus errors (i.e. instrument to cornea
distance). More sophisticated range finder systems might be able to decrease these
measurement errors resulting from defocus.
Fitting the surface with the Zernike polynomial expansion showed that some terms are
particularly vulnerable to eye movements. The variability of prism terms as well as
astigmatism components could be decreased considerably following minimization of
fixation errors. This will aid procedures that aim to correct refractive errors, based on
corneal or total wavefront information. However, it should be emphasized that the
methodology does not improve the instruments accuracy. It only improves the
instruments precision performance leading to a more reliable estimate of change. For
example in the topographical diagnosis and monitoring of keratoconus, small changes
over time could be measured with greater sensitivity and certainty. Analyses such as
corneal height difference maps from multiple measurements, or changes in Zernike
polynomials between visits could also be evaluated with higher precision.
This study revealed that the precision performance of videokeratoscopes for
measurements of corneal topography could be improved. The RMSE analysis, the
Zernike analysis, and the changes shown in the difference maps, indicate that the
algorithm developed in this study helps to decrease the standard deviation of multiple
measurements from corneal topography.
76
Chapter 3
CHAPTER 3
Cornea1 Topography and Accommodation
3.1 INTRODUCTION
Changes in corneal aberrations associated with near work could not only be due to
corneal distortions caused by eyelid forces (Mandell 1966; Knoll 1975; Bowman et
al. 1978; Carney et al. 198 1 ; Goss and Criswell 1992; Kommerell 1993; Ford et al.
1997; Campbell 1998; Golnik and Eggenberger 2001) but also due to changes in
corneal topography caused by accommodation. The ocular forces generated during
accommodation and convergence can be substantial. It is feasible that forces arising
during accommodation could lead to changes in corneal topography given the
proximity of the ciliary muscle to the limbus and the forces exerted onto the eye
globe by the extraocular muscles during convergence.
The optical characteristics of the human eye change during accommodation. The term
accommodation implies a change in the spherical refractive power of the eye.
Changes in astigmatism with accommodation are known as near, dynamic, or
accidental astigmatism (O'Brien and Bannon 1947; Fletcher 1954; Rabbetts 1972;
Brzezinski 1982; Millodot and Thibault 1985; Ukai and Ichihashi 1991; Byakuno et
al. 1994). It is thought that near astigmatism originates from meridional changes of
the crystalline lens during accommodation. Various studies have shown that the
unaccommodated eye normally has positive spherical aberration, which changes to
become negative spherical aberration as the level of accommodation increases
77
(Koomen et al. 1949; Ivanoff 1956; Jenkins 1963; Lu et al. 1993; Atchison et al.
1995; Collins et al. 1995). There is some evidence to suggest that asymmetric
aberrations of the eye (eg. coma) may also change in type and magnitude as a
function of accommodation (Lu et al. 1993; Atchison et al. 1995; Collins et al. 1995).
It is reasonable to assume that changes in crystalline lens features such as shape,
position or refractive index distribution are the most likely causes of these changes in
monochromatic aberrations associated with accommodation. However as the cornea
is the major refracting surface of the eye, small changes in its topography due to the
forces associated with accommodation could contribute to changes in the optics of the
eye.
Previous studies of the effect of accommodation on the corneal topography of normal
eyes have been limited by the available technology. Studies of the more central
regions of the cornea with keratometers (Fairmaid 1959; Lopping and Weale 1965)
and photokeratoscopes (Mandell and St Helen 1968), have produced contradictory
findings. Fairmaid reported meridional changes in curvature with convergence but
found no corneal shape changes in the accommodating but non-verging eye (Fairmaid
1959). Lopping and Weale also reported that significant changes occur in corneal
topography during ocular convergence (Lopping and Weale 1965). However Mandell
and St Helen did not find any changes in topography with either convergence or
accommodation (Mandell and St Helen 1968). More recently, using a modified
keratometer, Pierscionek et al. found changes in topography with accommodation in
at least one of the principal meridians for most of the subjects tested (Pierscionek et
al. 2001).
78
Chapter 3
The hypothesis that we investigated in this study is that the forces exerted upon the
cornea during accommodation are sufficient to alter the shape of the human cornea.
We measured changes in topography of normal corneas and corneas that were
pathologically thinner due to keratoconus. We reasoned that corneas weakened
through keratoconus might be more susceptible to these potential changes.
Any changes that occur in corneal shape associated with accommodation were
expected to be relatively small, compared to the overall topography. Therefore the
method we employed for the detection of these changes must have the highest
possible accuracy and precision and be statistically verifiable.
3.2 METHODS
The Keratron videokeratoscope was used for all corneal topography measurements.
For normal eyes, the instrument’s standard deviation for the central 4 mm diameter
has shown to be in the order o f f 0.25 D of refractive power ( f 2 microns) (Buehren
et al. 2001). We modified the Keratron to measure the topography of the anterior
corneal surface while accommodation demand was varied. The modification allowed
the accommodation stimulus to be induced coaxially with the instrument’s
measurement axis (Figure 3-1). The amount of accommodation could be varied while
the subject directly fixated the target inside the cone of the instrument. Previous
studies used one or more semi-transparent mirrors in order to align a peripherally
located target with the instrument axis. However great care needs to be taken to
avoid the possibility of alignment errors.
79
Our modification involved the replacement of the standard light emitting diode (LED)
fixation target within the Keratron with a telescope focussing system. The new
fixation target was a black cross hair on a diffuse white background at the end of a
perspex rod. The rod is able to slide within a hollow metal tube, which fits into the
position of the original LED fixation target. The accommodation control system
contained two lenses of appropriate power to allow the fixation cross to be focussed
with a precisely defined accommodation demand. The operator adjusted the required
accommodation demand by moving of the perspex rod within the tube according to
the calibrated dioptric scale etched onto the side of the rod.
Calibration of the rod was checked using an emmetropic subject and cycloplegia was
induced to prevent the subject from accommodating. Lenses of known power were
inserted at the spectacle plane of the observer while the perspex rod was moved until
the black cross was in sharp focus. Vertex distance was taken into account when
calculating the appropriate accommodation stimulus to lens power relationship.
Results showed that the accommodation demand 'error' was within f 0.50 D of the
amount of accommodation 'set' on the fixation tube scale (Figure 3-2). Given the
levels of accommodation tested in the study (0 D, 4 D and 9 D) we considered this
degree of error to be acceptable.
80
Chapter 3
k I I I I
A <AT. I I I I I I I I
1 I
Figure 3-1: Telescope system consisting of a cross-hair target and a two-lens system
projecting the virtual target “2” at distances between -3 D and +9 D of accommodation
demand, coaxially with the videokeratoscope axis.
81
Chapter 3
For the main experiment, ten young subjects were recruited to fulfil the following
criteria. Six were emmetropic to mildly myopic subjects with normal corneas and
four subjects had mild to moderate degrees of keratoconus. The University Human
Research Ethics Committee approved the study and informed consent was obtained
for all subjects. None of the subjects were regular contact lens wearers to avoid
potential confounding effects of the lenses on corneal function. The normal subjects
had no history of significant corneal or ocular pathology. All subjects were able to
achieve sharp focus of the crosshair for maximum amplitudes of accommodation of
up to 9 D. The subjects’ eye that showed the smaller amount of refractive error was
chosen for measurement. Individual variability of refractive errors led to individual
differences in the maximum amplitude of accommodation demand that could be
induced with the telescope system. This resulted in maximum effective
accommodation amplitudes ranging between 6.75 D and 9 D (mean 8 D). For the 4 D
accommodation stimulus, individual refractive errors were taken into account by
changing the tube setting accordingly (e.g. for a -2 D myopic subjects the tube setting
was + 6 D of accommodation stimulus; i.e. - 2 D + 6 D = + 4 D effective
accommodation demand).
Data collection was performed in the following order. Six measurements were
collected for 0 D accommodation demand, then six measurements for 4 D demand,
then again 0 D demand, thereafter 9 D demand, and finally again six measurements
for 0 D demand (i.e. 18 measurements of 0 D accommodation demand and six
measurements for each of the two accommodation stimuli of 4 D and 9 D demand).
Any maps where the lid position was too close to the topography measurement area
were discarded in order to minimize measurement variability from eyelid forces
83
(Buehren et al. 2001). This reduced the total number of measurements per condition
slightly (i.e. 17.2 f 1.7 SD measurements of 0 D accommodation demand and 5.4 f
1.1 SD measurements for each of the two accommodation stimuli of 4 D and 9 D
demand). A one minute break was taken between testing at each accommodation
demand level as a precaution against residual effects.
After collection of the data, each map was exported using the Keratron export utility.
For the different stimulus conditions (i.e. 0 D, 4 D, 9 D), height data maps were
correlated and repositioned to best approximate the average spatial position of the
cornea based on the number of measurements taken for each stimulus level
(Chapter 2). This procedure minimizes the effects of ocular micromovements on
multiple topography maps. The technique is based on the assumption that corneal
topography does not change when taking multiple measurements of the same cornea
within a short time period, provided that the conditions between measurements are
the same. The correlation between maps takes into account corneal tilt, apex
movement, and cyclotorsion, all relative to the average of the set of maps being
correlated.
The average map at each accommodation demand, standard deviation map, and
number of valid measurement points at each point location were calculated. The
average maps of the 4 D and 9 D accommodation stimuli were subtracted from the 0
D accommodation stimulus average. A two-tailed t-test was applied to the differences
at each point location within the maps and p-value maps were plotted along with the
relevant topography difference maps. The diameter of the central corneal area, which
84
Chapter 3
was used for analysis, varied depending on the number of complete Placido-ring data
available from the videokeratoscope measurements (mean 6.2 mm f 0.4 mm).
3.3 RESULTS
Five out of the ten subjects showed areas of significant (p < 0.001) change in corneal
height within the measurement area as a result of changing accommodation. The
subjects showing changes were the four keratoconic subjects as well as one normal
subject. Two keratoconic corneas (subjects 9 and 10) showed local flattening at about
3 mm distance from pupil center. These changes were significant for both the 4 D
accommodation stimulus and the 9 D stimulus. The other two keratoconics also
revealed significant changes in topography with accommodation. Subject 8 showed
corneal elevation changes between -6 and +13 microns with greater changes for the
9 D stimulus (
Figure 3-3). Subject 7 showed smaller areas of change for the 9 D stimulus, but not
for the 4 D stimulus. For the one normal eye (subject 2), the 9 D accommodation
stimulus caused a corneal steepening in some local areas at the edge of a 6 mm pupil.
The remaining five normal eyes mostly showed smaller changes up to f 3 microns,
however none of those changes were statistically significant in the t-test maps. An
example of the height differences for subject 1 is shown in Figure 3-4.
Apart from the changes in the topography difference maps, we also observed changes
in the corneal astigmatic axis in many of the subjects. For the 4 D stimulus, 3 subjects
(subjects 3, 8, and 10) showed significant excyclotorsion of the axis of corneal
astigmatism (p < O.Ol), while subject 7 showed significant incyclotorsion (p < 0.05).
For the 9 D stimulus, five (1,2,3, 8, and 10) out of ten subjects showed significant
85
excyclotorsion (p < 0.05). Furthermore, for the group as a whole there was a
significant shift towards excyclotorsion for both the 4 D stimulus (p = 0.03) and the
9 D stimulus (p = 0.01). The magnitude of cyclotorsion of the axis of corneal
astigmatism was in the order of 1 O to 2" f 2". Cyclotorsion results for individual
subjects are shown in Table 3-1.
In view of the changes in corneal astigmatic axis, we hypothesised that the changes in
the topography difference maps we had observed between the various levels of
accommodation could be due to differences in eye position (cyclotorsion) relative to
the instruments' measurement axis rather than being due to real corneal shape
changes. In order to investigate this hypothesis we reanalysed the data. This time we
applied the fixation error minimization technique based on the grouped average
corneal position for all conditions (i.e. 0 D, 4 D and 9 D demand combined). This
means that the repositioning of each single map was based on the mean corneal
spatial position of all 30 measurements (i.e. 18 measurements for the 0 D demand
plus 6 measurements for each of the 4 D and 9 D accommodation stimuli). We
anticipated that if the accommodation-related changes we found were actually due to
differences in eye rotation, the changes in topography between accommodation levels
should disappear following the procedure. However if the changes were real corneal
shape changes, the fixation error minimization algorithm would not change the
outcomes.
86
The corneal topography height differences associated with accommodation for
subject 8 and subject 1 are shown in Figure 3-3 and Figure 3-4 respectively. The
height difference, the p-value map and profile plot are shown before maps had been
repositioned using the fixation error minimization algorithm. The same data is also
plotted after the corneas were repositioned using the fixation error minimization
algorithm. The normal cornea of subject 1 (Figure 3-4) shows little effect of
accommodation on topography height difference either before or after cyclotorsion
correction. But the cyclotorsion correction for the keratoconic cornea of subject 8
(Figure 3-3) shows much less variation in the height difference map and only very
small regions of significant change within the p-value map. For all four keratoconic
corneas the height differences decreased after cyclotorsion correction and the highly
significant areas within the differences maps disappeared almost entirely. However
subject 2 (normal cornea) who showed corneal steepening for the 9 D stimulus still
showed significant change after fixation error minimization procedure. We decided to
repeat our full protocol with subject 2. When we combined the data from the original
and second trials for subject 2 and reanalysed the effects of accommodation, there
were few areas of significant change apparent in the topography difference maps.
In order to verify the cyclotorsional changes we found in topography, we identified
blood vessels on the conjunctiva in the area surrounding the limbus in our
videokeratographs. We then looked at the angle of a blood vessel relative to the
videokeratoscope axis for each accommodation stimulus level and compared this
angle to that of the corneal astigmatic axis at the same accommodation stimulus level.
The result for subject 8 is presented in Figure 3-5, showing about four degrees of
excyclotorsion for both, cylinder axis (indicated by dark arrow) and blood vessel
88
Chapter 3
(indicated by bright arrow). These results support eye rotation as the primary cause
for the changes in cornea1 shape which we found as a result of different
accommodation demands.
89
Chapter 3 _
90
Figure 3-3: Top panel: Shows the height difference map between 7 D and 0 D of
accommodation stimulus for subject 8 (left), along with the 3-D difference map plot (right)
and the relevant p-value map showing areas of statistical significance (p < 0.001) in black.
Bottom panel: Shows the same height difference map after the maps had been repositioned to
minimize fixation errors. Bottom panel (right): 3-D difference plot and relevant p-value map
(p < 0.001).
Height difference 0D v 7D
Height difference 0D v 7D
Cyclotorsion corrected
P-value map
Height difference 0D v 7D
P-value map
Height difference 0D v 7D
P-value
P-value
Subject 8
Chapter 3
91
Figure 3-4: Top panel: Shows the height difference map between 8.75 D and 0 D of
accommodation stimulus for subject 1 (left), along with the 3-D difference map plot (right)
and the relevant p-value map showing areas of statistical significance (p < 0.001) in black.
Bottom panel: Shows the same height difference map after the maps had been repositioned to
minimize fixation errors. Bottom panel (right): 3-D difference plot and relevant p-value map
(p < 0.001).
Height difference 0D v 8.75D
Cyclotorsion corrected
P-value map
Height difference 0D v 8.75D
P-value map
Height difference 0D v 8.75D
Height difference 0D v 8.75D
P-value
P-value
Subject 1
Chapter 3 _
92
Figure 3-5: Example of refractive power map output for subject 8, for a 0 D accommodation stimulus (left) and a 7 D accommodation stimulus (right).
Differences in corneal astigmatic axis are shown along with the displacement of blood vessels (indicated by arrows; white for blood vessels and grey for
astigmatic axis) relative to the videokeratoscope coordinate system. The magnitudes of both are similar and approximately 4°.
0 D 7 D
Chapter 3
3.4 DISCUSSION
We did not find clear evidence of statistically significant changes in corneal
topography as a result of accommodation in the subjects examined in this study. This
was the case for both the subjects with normal corneas and those with keratoconic
corneas. These results are consistent with previous studies on central regions of the
cornea (Fairmaid 1959; Lopping and Weale 1965; Mandell and St Helen 1968).
We did however find a significant cyclotorsion of corneal topography of many of the
eyes when changing focus from far to near distances and this may explain the
apparently contradictory findings in the literature in this field.
During fixation the amount of torsion is fixed for each eye position (Listing’s law)
(Fetter and Haslwanter 1999). In our study we induced convergence in the presence
of a deliberate head turn and therefore our results may not be directly comparable to
the findings of Fairmaid, or Lopping and Weale on corneal changes associated with
natural convergence (Fairmaid 1959; Lopping and Weale 1965). Fairmaid reported an
increase of curvature in the horizontal meridian and a decrease of curvature in the
vertical meridian while Lopping and Weale found flattening in the horizontal
meridian associated with convergence.
As in our experiment, Pierscionek et al. induced accommodation in the measured eye,
while the other eye was covered (Pierscionek et al. 2001). This produces
asymmetrical convergence (i.e. a different head position relative to normal
convergence). Pierscionek et al. found differences in central corneal curvature in at
least one principal meridian in most of the subjects tested (Pierscionek et al. 2001).
However the results of the study, which also measured accommodation stimuli of up
93
to 9 D, may have been affected by the cyclotorsional variations, which have been
reported by other authors (Allen and Carter 1967; Bannon 1971; Enright 1980) and
which also have been found in our study. Allen and Carter have shown that even with
an experimental procedure that produces asymmetrical convergence, excyclotorsion
can arise in the non-verging eye (Allen and Carter 1967).
The technique, which was used to confirm that cyclotorsional changes had caused the
apparent changes in the topography difference maps was initially developed in order
to remove ocular micromovements during videokeratoscopy (Chapter 2). By applying
the method across all accommodation conditions not only cyclotorsion was corrected
but also lateral shifts and tilts between corneal topography measurements were
minimized. It was previously shown that cyclotorsional fluctuation is a substantial
contributor to micromovements during steady fixation (Chapter 2). The order of
magnitude (2.4" f 1.1) is similar to what was found for the different accommodation
conditions in this study.
In some of my subjects, these ocular microfluctuations may have masked
cyclotorsional changes related to the different accommodation conditions. However,
within the group it still was possible to show statistically significant cyclotorsional
differences between the 0 D demand condition and the 4 D or 9 D demand conditions.
Furthermore, the comparison between the location of limbal blood vessels and the
changes in corneal astigmatic axis also supported the role of ocular cyclotorsion in
causing apparent changes in corneal shape with accommodation.
94
Chapter 3
Along with others (Allen and Carter 1967; Bannon 1971) it was found that
excyclotorsion occurred with accommodation for most of the subjects. When it was
not accounted for cyclotorsional effects, the keratoconic corneas showed the greatest
changes with accommodation due to higher levels of corneal asymmetry. In the case
of a cyclotorsion occurring between far and near viewing conditions, this would
clearly lead to larger differences occurring in keratoconic corneas rather than more
rotationally symmetric “normal” corneas. The two examples shown in
Figure 3-3 and Figure 3-4 confirm this effect. Both eyes show a significant amount of
cyclotorsion between the different accommodation conditions (Table 3-1). The
excyclotorsion in case of the keratoconic cornea of subject 8 (showing 4 D of corneal
astigmatism) caused significant height changes in the difference map. However, the
excyclotorsion in case of the normal cornea of subject 1 (showing only 0.5 D of
corneal astigmatism) did not lead to such significant changes in the difference map.
The rotation of corneal topography during accommodation has significant
implications for the accuracy of results obtained from optometers or wavefront
sensors that measure the optical characteristics of eyes during near versus far viewing
conditions and pre- versus post operative refractive surgery. As a result of
accommodation, small changes in ocular astigmatism may occur and also asymmetric
higher order aberrations such as coma will be affected. For example, ocular
cyclotorsion while fixating a near target during refractive surgery procedures may
contribute to residual astigmatism outcomes. Furthermore, analyses such as
videokeratoscope difference maps and wavefront analyses of pre- versus post-
operative refractive surgery will be affected if the change in the eye’s refractive status
leads to a change in accommodative status during the image capture procedure.
95
In summary it appears unlikely that changes occur in central corneal shape during
accommodation up to a level of 9 D. Therefore, the changes in corneal topography
that have been reported to occur in some individuals following reading can be
ascribed to lid force effects as suggested by most of these authors (Mandell 1966;
Knoll 1975; Bowman et al. 1978; Carney et al. 1981; Goss and Criswell 1992;
Kommerell 1993; Ford et al. 1997; Campbell 1998; Golnik and Eggenberger 200 1)
rather than due to forces caused by accommodation. However, we found a significant
excyclotorsion of the eye globe during accommodation, which in turn caused a
rotation of corneal topography relative to the instrument’s measurement axis. While
the amount of this cyclotorsion is small, it should be taken into account when
considering the optical characteristics of the eye for different levels of
accommodation.
96
Chapter 4
97
CHAPTER 4
Corneal Aberrations and Reading
4.1 INTRODUCTION
The anterior surface of the eye is its most powerful refractive component and as such,
subtle changes in corneal shape can cause substantial changes in its optical
characteristics. Monocular diplopia has been linked to corneal distortion following
near work in various studies dating back over 35 years (Mandell 1966; Knoll 1975;
Bowman et al. 1978; Carney et al. 1981; Goss and Criswell 1992; Kommerell 1993;
Ford et al. 1997; Campbell 1998; Golnik and Eggenberger 2001). The corneal
distortions that have been observed in these studies have been explained by sustained
(Mandell 1966; Knoll 1975; Bowman et al. 1978; Carney et al. 1981) or abnormal lid
pressure (Kommerell 1993), lid position (Goss and Criswell 1992; Ford et al. 1997),
and tear film interactions with the corneal surface during sustained close work (Ford
et al. 1997; Golnik and Eggenberger 2001). During routine topography measurements,
lid pressure effects on corneal topography have been observed in the central and
peripheral corneal shape (Lieberman and Grierson 2000; Buehren et al. 2001).
There has been conjecture that lid pressure may cause corneal astigmatism (Wilson et
al. 1982; Grey and Yap 1986). Vihlen and Wilson found no significant association
between the tension of the eyelids and the amount of corneal toricity (Vihlen and
Wilson 1983). Grey and Yap measured ocular astigmatism in subjects with three
deliberately narrowed lid positions and found a statistically significant increase of
Chapter 4 _
98
ocular with-the-rule astigmatism when the lid aperture was narrowed (Grey and Yap
1986). There is also evidence that astigmatism can be induced by chalazion (Nisted
and Hofstetter 1974; Cosar et al. 2001), lid-loading procedures used in the treatment
of lagophthalmos (Kartush et al. 1990; Brown et al. 1999; Goldhahn et al. 1999), and
after ptosis surgery (Holck et al. 1998).
While studies on monocular diplopia after near work provide useful information about
the subjectively perceived optical effects of corneal distortion, there hasn’t been a
detailed objective analysis regarding the optical characteristics of corneal distortions
following near work. In this study we have investigated the effect of one hour of
reading on corneal topography. The position of eyelids during reading, relative to the
location and size of the pupil, was measured and compared with corneal topography
changes. We have analysed the optical consequences of the changes that were
observed using traditional sphero-cylinder and corneal higher order aberrations.
4.2 METHODS
Twenty subjects (age range 20 to 37 years, mean 27 years) with healthy eyes were
recruited for the experiment, and one eye was randomly chosen for analysis. Informed
consent was obtained for all subjects. The twenty eyes had a range of refractive errors
(mean –1.6 D, range +0.25 to –6.00 D); five were emmetropic (i.e. ≤ 0.5 D in the
worst meridian), five were primarily astigmatic (i.e. ≤ 0.5 D of spherical component
and > 0.5 D of astigmatic component), five had simple myopia (i.e. ≤ 0.5 D of
astigmatism and > 0.5 D of myopic component), and five had myopic astigmatism
(i.e. > 0.5 D of myopic and astigmatic component).
Chapter 4
99
The experiment was always conducted early in the morning, approximately 2-3 hours
after the subjects woke. All subjects were given the instruction not to perform any
sustained reading (e.g. newspaper) prior to the experiment. For each subject, six
baseline videokeratographs were taken prior to reading and six videokeratographs
were again taken immediately after the 60 minutes reading task.
The Keratron videokeratoscope (EyeQuip Division, Alliance Medical Marketing,
Jacksonville, FL) was used for all corneal topography measurements. The Keratron
has been shown to have high accuracy and precision performance for inanimate test
objects (Tripoli et al. 1995; Tang et al. 2000). Prior to the study, the instrument
calibration was checked according to the manufacturer’s instructions. The
videokeratoscope is based on the placido-disk principle and enables the capture of six
consecutive videokeratographs without the requirement for immediate data
processing.
The subjects were seated and asked to read from a novel for 60 minutes. During this
time the subjects were allowed to adopt whatever head posture was comfortable.
Photopic lighting conditions were used during the reading task. The subjects’ pupil
size was measured in the photopic room condition with the subjects focused at a
distance of 33 cm.
Prior to the reading experiment, digital photography was used to document the
external ocular features using a high-resolution digital camera (Kodak DC260).
Photography was conducted with: (1) the eyes in reading gaze posture, and (2) the
subject positioned in a headrest with eyes in primary gaze. A ruler with millimetre
Chapter 4 _
100
increments was placed in the peripheral field of the captured images to allow
calibration of subsequent measurements.
To determine the approximate position of the eyelids during reading in relation to the
corneal topography, we identified iris features in the digital photographs of the eye
taken during both reading and in the headrest. We then assumed that the relative
position of the eye during videokeratoscopy was the same as that photographed when
the subject was in the headrest. This allowed us to superimpose the approximate
position of the eyelids during reading onto the corneal topography measurements
taken after reading (Figure 4-1). In this way, we could investigate the potential
association between lid position during reading and changes in topography.
After 30 minutes of reading, the subjects’ blink frequency was measured over a time
period of 3 minutes and mean blink rate per minute was later calculated. The subjects
were not informed that blink frequency was being monitored, since this may cause a
change in blink characteristics (Zaman and Doughty 1997; Cho et al. 2000).
4.3 ANALYSIS
Corneal instantaneous power, height data, and refractive power were exported from
the videokeratoscope for analysis. The instantaneous power maps were chosen to
compare corneal topography with the subject’s natural lid position during reading,
because the instantaneous power maps are most sensitive to local power changes
caused by slight variations in slope.
Chapter 4
101
To study the potential effect of reading on topography, height difference maps were
calculated. For each set of six baseline measurements and six post-reading
measurements, the effect of ocular microfluctuations were minimized using the
method described in Chapter 2. The methodology repositions a given
videokeratograph map to best approximate an “average” videokeratograph based on a
set of multiple measurements of the same cornea. This procedure involves
interpolating (bilinear) the topography data to a common grid format (256 meridians
and point spacing along the meridian of ~0.15 mm) and subsequent calculation of an
average height map for each set of maps (i.e. before and after reading).
From the six refractive power maps for each condition (i.e. pre- and post-reading) we
calculated the average, standard deviation, and the number of valid measurements at
each grid location within the map. Difference maps of pre- versus post-reading
topography were calculated along with the t-test maps showing significant areas of
change (Buehren et al. 2001). The root mean square error (RMSE) between corneal
refractive power and best-fit sphero-cylinder before and after reading was calculated
and t-tests were applied to measure the significance of changes in refractive power
between the averages of the two conditions.
This was performed for each individual’s photopic pupil size and also for fixed pupil
sizes of 2.5, 3, 4, 5, and 6 mm. For the 4 mm fixed pupil size, power matrices (Harris
2000) were used to average individual best-fit sphero-cylinders for each condition and
again to calculate the corneal changes in sphere, cylinder and astigmatic axis pre
versus post-reading. A multivariate test (Hotelling’s T2) representing a generalisation
Chapter 4 _
102
of the t statistic was used to test the significance of overall change in corneal sphero-
cylinder.
The anterior surface of the cornea was modelled as a single surface optical system in
order to derive the corneal wavefront error using a method similar to that described by
Guirao and Artal (Guirao and Artal 2000). Optical path distance (OPD) for each point
on the surface was calculated using 3-D ray tracing and the wavefront was fitted using
a set Zernike terms of up to the fourth order polynomial expansion according to the
Optical Society of America convention (OSA convention) (Thibos 2000) for pupil
sizes of 2.5 mm, 4 mm, and 6 mm (image plane at circle of least confusion, wavefront
error scaled by λ = 555 nm, refractive index n = 1.376, and midline symmetry taken
into account (Smolek et al. 2002). All wavefront coefficients were normalized to a
unit circle to enable quantitative comparison between different pupil sizes. The
wavefront was centred on the line of sight. To achieve this we calculated the average
pupil offset derived from the pupil detection system provided by the Keratron
videokeratoscope for each subject and used this offset as the new principle axis
reference point. A full 3-D ray-trace technique was applied to calculate the wavefront
error along the line of sight. T-tests were used to identify statistically significant
changes in corneal wavefront Zernike coefficients after reading.
Chapter 4
103
Figure 4-1: Method for overlaying eyelid features onto corneal topography maps. Iris features (indicated by arrows) are used in each of the images to record relative
lid position. Subject 13 (top left), lid position in primary gaze, lid position during reading (bottom left), baseline corneal topography overlaid with lid position in
primary gaze (top right), and post-reading corneal topography overlaid with lid position during reading (bottom right).
Chapter 4 _
104
4.4 RESULTS
In twelve of the twenty subjects we studied, the instantaneous power maps after
reading showed distinct band-like distortions in the superior region of the maps,
which correlated closely with the subject’s natural lid position during reading. In
Figure 4-2, two examples of videokeratograph comparisons before and after reading
for subject 1 and 15 are shown, with the overlay of the subjects’ lid position during
reading. These topography changes were often encroaching within the boundary of
the subjects’ upper pupil margin. Topography changes were also often evident in the
inferior cornea associated with the position of the lower lid margin during reading
(see subject 1, Figure 4-2). However these inferior distorted regions generally did not
encroach within the pupil zone.
Analysis of the corneal wavefronts revealed that seven wavefront coefficients were
significantly changed after one hour of reading (Figure 4-3). The terms that changed
significantly for all pupil sizes were 22Z primary astigmatism (p < 0.05 at 2.5 mm and
p < 0.01 at 4 mm and 6 mm), 13−Z primary vertical coma (p < 0.01 at 2.5 mm and
p < 0.001 at 4 mm and 6 mm), and 33−Z trefoil 30° (p < 0.05 at 6 mm and p < 0.01 at
2.5 mm and 4 mm). The change of the primary astigmatism terms was in the direction
of against-the-rule (i.e. with-the-rule astigmatism decreased or against-the-rule
astigmatism increased).
Chapter 4
105
Figure 4-2: Examples of the effect of lid position during reading upon corneal topography. Subject 1 (left) and subject 15 (right), corneal topography pre-reading
(top) versus pos-reading (bottom) is shown overlaid with the subjects’ lid position in primary gaze and during reading respectively.
Chapter 4 _
106
Other changes in Zernike terms were limited to certain pupil sizes (i.e. corneal
regions). For the 2.5 mm pupil size, the term 13Z primary horizontal coma (p < 0.05)
changed significantly. The defocus term 02Z changed for the 4 mm and 6 mm pupil
sizes (p < 0.01 at 4 mm and 6 mm). The vertical prism term 11−Z changed for the 6
mm pupil size (p < 0.05) and the secondary astigmatism component 24Z changed for
the 4 mm pupil size (p < 0.05).
There was a significant association between changes occurring in the wavefront for
the 13−Z vertical coma and the 3
3−Z trefoil 30° terms after reading. Most subjects (15
of 20) showed positive vertical coma and negative trefoil 30°, or negative vertical
coma and positive trefoil 30° in the baseline (pre-reading) measurements and this
trend was increased after reading (18 of 20). Both of these combinations of coma and
trefoil terms represent a wave-like shape (Figure 4-4 bottom) but they are opposite in
direction. After reading, there was a trend for the vertical coma term to shift in the
negative direction, whereas the trefoil 30° term generally shifted in the positive
direction. The changes in the vertical coma and trefoil 30° coefficients after reading
are shown in Figure 4-4 (top). These wave-like shape changes in the wavefront are
consistent with the changes in instantaneous power maps associated with the effect of
the upper lid margin.
Chapter 4
107
* * ** * * * * *
* * * * *
-0.15
-0.12
-0.09
-0.06
-0.03
0
0.03
0.06
0.09
Zernike Coefficients (OSA convention)
Cha
nge
in W
avef
ront
Err
or C
oeff
icie
nt V
alue
(
)
2.5mm P upil4.0mm P upil6.0mm P upil
1- 1 Z
1 1 Z
-22Z
02Z
22Z
-33Z
-13Z
1 3 Z
3 3 Z
-44Z
-24Z
0 4 Z
24Z
44Z
* = t-test significant at (p < 0.05)
Figure 4-3: The group mean change (±SE) of normalized Zernike wavefront coefficients after reading (post minus pre) for three pupil sizes (2.5 mm, 4 mm, 6 mm) is
shown. The Zernike polynomials are vertical prism 1
1−Z , horizontal prism
11Z , primary astigmatism along 45°
22−Z , defocus
02Z , primary astigmatism
22Z ,
trefoil along 30° 3
3−Z , primary vertical coma
13−Z , primary horizontal coma
13Z , trefoil
33Z , tetrafoil along 22.5°
44−Z , secondary astigmatism along 45°
24−Z ,
spherical aberration 04Z , secondary astigmatism
24Z , and tetrafoil
44Z .
Chapter 4 _
108
Correlation between Change in vertical Coma and Trefoil along 30° after reading
y = -0.8739x - 0.0056R = 0.8121
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04
Change in primary vertical ComaWavefront Coefficient Value (λ)
Cha
ng
e in
Tre
foil
alo
ng
30°
W
ave
fro
nt
Co
eff
icie
nt
Val
ue
()
Negative Coma Positive Trefoil Negative Coma + Positive Trefoil
Figure 4-4: Correlation between change in primary vertical coma and trefoil along 30° (4 mm pupil)
following reading. Bottom panel shows the combination of negative vertical coma and positive trefoil
30° coefficients producing a “wave-like” distortion.
Chapter 4
109
An example of the optical changes in corneal refractive power following reading is
presented for subject 8 in Figure 4-5. In the difference map (pre-versus post-reading
refractive power), the superior semi-meridian shows values of up to -1.34 D change.
These changes are highly statistically significant as shown by the p-values of the t-test
map (Figure 4-5). Within a 4-mm pupil, thirteen of the twenty subjects showed
statistically significant (p < 0.001) areas of change in refractive power (Table 4-1, last
column). These significant regions of change were mostly located in the upper, and/or
the lower pupil areas. Some subjects showed small randomly distributed points of
statistically significant change, however these areas were considered to be non-
systematic and probably related to local tear instabilities rather than true changes in
corneal topography and were not classified as representing statistically significant
change (in Table 4-1, last column).
The group mean RMSE deviation from the best-fit sphero-cylinder was slightly larger
for the post-reading corneas (Table 4-1). This difference was statistically significant
when calculated for the individuals’ photopic pupil size (pre 0.23 D versus post 0.28 D,
p = 0.013) as well as for fixed pupils of 5 mm and 6 mm (pre 0.31 D versus post 0.35
D, p = 0.036 and pre 0.38 D versus post 0.42 D, p = 0.022 respectively). The increased
RMSE was not statistically significant for the 2.5, 3 and 4 mm pupils (p = 0.66, p =
0.28, and p = 0.09 respectively).
In Table 4-1 individual subject data for various refractive power changes following
reading are summarized. This includes the total refractive error, corneal best-fit sphero-
cylinder power pre and post-reading and the change in corneal sphero-cylinder for the
twenty subjects.
Chapter 4 _
110
Across the group, lid fissure width decreased from a mean of 9.4 mm (SD ± 0.9) in
primary gaze to 6.8 mm (SD ± 1.0) in the reading position. Average pupil size of the
subject group during reading in the photopic condition was 3.3 mm (SD ± 0.7). Blink-
frequency showed large variability between individuals, with an average value of 8.3
blinks/minute (range 2 to 26 blinks per minute). There was no significant correlation
between blink rate and corneal RMSE differences (R2 = 0.10).
The changes in corneal aberrations that we measured following reading were clearly
associated with forces applied by the eyelid margin to the surface of the eye. However
the role of eye movements during reading was unknown. To investigate this we
recruited one subject (subject 9) who showed obvious corneal topography changes
following the reading trial. The subject was retested on a separate morning, but this
time the subject had to stare (fixed gaze) at a single word on a page for 60 minutes in
normal reading gaze. The changes in refractive power following the fixed gaze trial
along with the results from the initial reading trial of the same subject are shown in
Figure 4-6. The corneal changes after 60 minutes of staring are less pronounced, with
values approximately half those found after 60 minutes of reading. The locations of
changes shown after both trials indicate that a similar lid position was adopted during
the two experiments. Although it is not clear whether other factors may also have
influenced these two trials, it may be speculated that eye movements during reading
contribute to the forces applied to the cornea.
Chapter 4
111
Corneal Refractive Power Analysis (Subject 8)
Figure 4-5: Average baseline refractive power map (top left) and average post-reading refractive
power map (top right) for a 6-mm pupil zone of subject 8. Bottom left: Refractive power difference
map of post-reading minus baseline refractive power for a 4 mm pupil zone. Bottom right:
Significance map based on t-tests at all points within the map. The regions where p values < 0.001 are
in black, 0.001< p < 0.05 are in grey and p values > 0.05 are in white.
60 Min Read
RMSE = 0.30 D RMSE = 0.42 D
Baseline
Difference in 4 mm Pupil P-values
Chapter 4 _
112
Table 4-1: The changes in corneal refractive power (sph, cyl, and axis) are presented as refractive error, not correction. The RMSE is the difference between the
corneal refractive power and the best-fit corneal sphero-cylinder. The topographic refractive power changes illustrate those subjects where statistically significant
areas of change occurred in refractive power within the central 4 mm of the cornea following reading (see Figure 5 example). Because of potential type 1 errors
associated with repeated statistical testing, we have chosen to highlight only corneal changes where p < 0.001 (i.e. * = p < 0.05; ** = p< 0.01; *** = p < 0.001).
Subject RMSE 4mm (D)
RMSE 4mm (D)
Subjective Refractive Error (Correction)
Corneal Refractive Power Pre-reading
(4mm)
Corneal Refractive Power Post-reading
(4mm)
Changes in Corneal Best-fit Sphero-cylinder
(4mm)
Region/s of Refractive
Power Change (4mm)
Pre-read. Post-read. Sph Cyl Axis Sph Cyl Axis Sph Cyl Axis Sph Cyl Axis
1 0.19 0.29 *** -3.00 -0.25 168° +46.60 +1.40 4° +46.56 +1.34 179° -0.14 +0.23 128° *** ***
2 0.31 0.21 * -4.00 -0.5 178 +46.00 +0.40 6° +46.10 +0.41 7° +0.09 +0.02 33°
3 0.29 0.36 -0.75 -0.75 180° +48.33 +1.50 183° +48.19 +1.52 188° -0.25 +0.25 49° **
4 0.43 0.43 -3.25 -0.25 160° +50.37 +0.98 176° +50.42 +0.80 174° -0.14 +0.20 97°
5 0.12 0.17 0.00 0.00 -- +47.94 +0.15 139° +48.03 +0.18 156° -0.05 +0.10 5° **
6 0.20 0.25 * -2.75 -0.25 20° +48.30 +1.48 169° +48.56 +1.56 169° +0.26 +0.08 167° *** ***
7 0.34 0.26 * 0.00 0.00 -- +47.91 +1.38 173° +48.11 +1.45 173° +0.19 +0.09 150° ** ***
8 0.30 0.42 *** -0.25 -0.75 115° +50.38 +0.33 151° +50.39 +0.28 121° -0.17 +0.30 87° * ***
9 0.22 0.41 *** -0.75 -0.75 20° +47.46 +1.67 180° +47.40 +1.37 181° -0.37 +0.31 90° ** ***
10 0.29 0.28 0.00 0.00 -- +48.38 +0.67 153° +48.41 +0.69 155° +0.02 +0.05 12° ***
11 0.22 0.36 * 0.00 -0.25 180° +47.39 +0.78 173° +47.78 +0.60 166° +0.19 +0.23 99° ***
12 0.18 0.16 -5.00 -1.25 163° +48.70 +1.91 179° +48.75 +2.02 180° +0.04 +0.13 17°
13 0.32 0.48 *** +0.25 -1.25 17° +49.05 +2.20 5° +49.14 +1.85 8° -0.28 +0.41 81° *** ***
14 0.19 0.25 -0.75 -0.75 9° +47.28 +0.89 20° +47.24 +0.92 16° -0.08 +0.11 161°
15 0.22 0.36 *** -0.50 -1.00 6° +49.70 +2.07 1° +49.73 +1.83 4° -0.24 +0.30 73° *** ***
16 0.43 0.40 0.00 -2.25 82° +49.59 +1.90 86° +49.62 +1.82 82° -0.14 +0.28 31° ** ***
17 0.22 0.29 0.00 0.00 -- +49.42 +0.87 9° +49.40 +0.88 11° -0.05 +0.07 53° ***
18 0.32 0.29 -5.25 -0.25 5° +48.26 +1.00 180° +48.34 +1.12 2° +0.06 +0.15 18° ***
19 0.33 0.37 * -6.00 -1.75 35° +47.79 +2.06 8° +47.69 +2.02 10° -0.20 +0.18 61° ** ***
20 0.20 0.32 *** 0.00 -1.25 84° +49.48 +0.30 82° +49.36 +0.66 83° -0.12 +0.36 81° *** ***
Mean 0.27 0.32 ** -1.83 -0.22 20° +48.56 +0.92 91° +48.62 +0.85 92° -0.06 +0.07 74°
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Figure 4-6: Top: Refractive power difference map for an 8 mm pupil zone of subject 9 after 60
minutes of reading. Bottom: Refractive power difference map for a 8 mm pupil zone of subject 9 after
60 minutes of staring (fixed gaze) at a single word on a page for 60 minutes in normal reading gaze.
RMSE = 0.41
RMSE = 0.27
Refractive power difference after 60 min. fixed gaze (Subject 9)
Refractive power difference after 60 min. reading (Subject 9)
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4.5 DISCUSSION
We have shown that some individuals have significant changes in the topographical
and optical characteristics of the cornea following one hour of reading. The
topographical changes showed a clear association with the position of the eyelids
during the reading task. The upper eyelid in particular, caused a wave-like distortion
that was evident in the topography and corneal wavefront post-reading.
Corneal distortions have been previously reported in cases associated with monocular
diplopia following reading (Mandell 1966; Knoll 1975; Bowman et al. 1978; Carney
et al. 1981; Goss and Criswell 1992; Kommerell 1993; Ford et al. 1997; Campbell
1998; Golnik and Eggenberger 2001). Most of these studies have reported that
subjects perceive vertical doubling of images. The wave-like aberration change that
we found in many subjects, related to the vertical coma and trefoil Zernike terms
(Figure 4), is the likely optical explanation for this perception of vertical doubling.
The significant wave-like aberration changes we found following reading were
oriented vertically and would have the effect of blurring the retinal image along the
vertical axis.
The magnitude of change and the time course of remission of corneal changes
following reading are probably influenced by various factors. These may include the
time spent reading, the visual tasks undertaken after reading, the subject’s blink
frequency, individual corneal tissue characteristics, and the effect of age on both lid
tension and corneal tissue characteristics. To gain an impression of this time course,
we continued to measure corneal topography after the 60-minute reading task for one
subject (subject 9). A large proportion of the corneal changes had disappeared at ten
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minutes post-reading, however it required 120 minutes before the topography was
approaching pre-reading shape. Knoll found that the perception of double images
caused by corneal distortions after reading can last several hours, as long as no further
near work is done (Knoll 1975). Golnik have recently reported that 30 to 60 minutes
is needed to resolve visual symptoms after cessation of reading (Golnik and
Eggenberger 2001). Since the time period of the experimental reading task in this
experiment extended over only 60 minutes, longer periods of reading may intensify
the degree of corneal changes that occur and the recovery of normal topography may
take substantial time.
The changes we observed in the corneal topography following reading are probably
the result of displacement of epithelial tissue, although this assumption needs to be
confirmed by pachometry of the epithelium. The magnitude of the height changes
observed in post-reading topography were in the order of 4 microns (range 3 to 7),
which would suggest that only a few superficial epithelial cells would need to be
displaced for this topographical change to occur.
Since reading in some individuals can significantly change the corneal shape, this
raises the question of the true refractive error of these eyes. It could be argued that a
refractive correction for reading/close work might be best derived after a period of
reading in these individuals. In terms of the best-fit sphero-cylinder to corneal
topography, this result changed by up to 0.37 D in spherical component, up to 0.41 D
in cylinder component, and up to 30 degrees in cylinder axis when comparing pre- to
post-reading topography.
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In another scenario, the question of the appropriate refractive correction of an
individual arises in corneal refractive surgery. The appropriate sphero-cylinder
correction in procedures such as laser in situ keratomileusis (LASIK) and
photorefractive keratectomy (PRK) may be altered if the individual has undertaken
significant reading prior to corneal topography measurement. Potentially more
problematic is the case of customized LASIK, where the higher order wavefront
aberrations of the eye are also corrected by a corneal ablation (Alessio et al. 2000;
Knorz and Neuhann 2000; Mrochen et al. 2000). We have shown that a number of
higher order Zernike aberration terms of the corneal wavefront are significantly
changed by 60 minutes of reading.
The anterior corneal surface is the eyes’ most powerful refractive component and
therefore is a major contributor to the eyes’ total wavefront aberrations. In general,
third-order (coma and coma-like) aberrations are the dominant aberrations for most
eyes (Howland and Howland 1977; Liang and Williams 1997). In this study, corneal
coma and trefoil have changed substantially after reading in both magnitude and
direction. Our results suggest that studies of the eyes’ total aberrations should account
for the visual tasks undertaken prior to total wavefront aberration measurement.
Various studies of the eyes’ total wavefront aberrations have found that higher order
aberrations change with increasing levels of accommodation (Atchison et al. 1995; He
et al. 2000). Since the changes we observed in the corneal wavefront following
reading were related to lid position, we expect that previous studies of aberrations and
accommodation have been measuring the effects of changes in the optical
characteristics of the crystalline lens and not the cornea, because wavefront sensors
typically induce accommodation with the subject in primary gaze (not downward
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reading gaze). To fully understand the optical characteristics of the eye during reading
it would be necessary to measure the eye’s total wavefront during reading (or
downgaze).
The results of studies that have measured accommodation (refractive status) of the eye
pre- versus post-reading tasks may have been influenced by the temporary optical
changes that we have found to occur in the corneas of some subjects. The exact effect
of these corneal changes upon total refractive error (accommodative status) is difficult
to predict, but would depend on the method of refractive measurement used by the
optometer (Collins 2001).
It is generally accepted that the risk factors for myopia development can be broadly
classed as genetic and environmental factors (Mutti et al. 1996). One of the major
environmental factors which have been shown to have an association with myopia
development is reading and near work (Adams and McBrien 1992; Goss and Rainey
1998; Hepsen et al. 2001) and there has been considerable speculation about the role
of retinal image quality in myopia development (Rabin et al. 1981). The results of our
study suggest that in some individuals the corneal optics change during reading in a
variety of ways that influence retinal image quality. Corneal sphero-cylinder can
change, individual aberrations change (eg. vertical coma and trefoil) and the total
corneal root-mean-square error (i.e. variation from a perfect sphero-cylinder) can
change.
When we studied the interaction between corneal root-mean-square error (i.e.
variation from a perfect sphero-cylinder) and pupil size, we found that the group mean
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RMSE became significantly higher after reading for pupil sizes of 5 and 6 mm,
showed borderline significance for a 4 mm pupil, and was not statistically significant
for pupil sizes of 2.5 and 3 mm. For many individuals within the group, this increased
RMSE was significant at all pupil sizes and if we analysed the increase in RMSE
post-reading for each individuals’ photopic pupil size, the effect was again significant.
This suggests that there is a small, but significant overall loss in retinal image quality
for some individuals during reading.
Studies of myopia development in various animals show that the overall sign of
defocus can regulate eye growth (Schaeffel et al. 1988; Troilo and Wallman 1991;
Norton and Siegwart 1995). In our subjects, the optical changes induced by the
eyelids during reading did not typically have a rotationally symmetrical form. We
described the most common change in shape of the corneal wavefront as “wave-like”
accompanied by an astigmatic shift in direction of against-the-rule. When we
examined the group mean change in the corneal wavefront defocus, there was a small
change indicating slight central steepening of the cornea for pupil sizes of 4 mm and
6mm.
Lid related forces could play a role in refractive error development. O’Leary and
Millodot reported that subjects with ptosis were more likely to develop myopia and
speculated palpebral aperture may be a factor in the aetiology of myopia (O'Leary and
Millodot 1979). Many Asian populations are reported to have significantly higher
rates of myopia than western populations (Chandran 1972; Lin et al. 1988; McCarty
et al. 1997; Wong et al. 2000). Compared with western populations it is well known
that Asian eyes have smaller vertical palpebral apertures (Lam and Loran 1991) and
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different anatomical characteristics resulting in a thickened upper eyelid and
overlying fold of skin (Doxanas and Anderson 1984), all of which may serve to
increase the optical effects of lid forces during reading. A number of studies have
reported that rigid contact lenses may slow the progression of myopia in some
children (Stone 1976; Grosvenor et al. 1987). We might expect that rigid contact
lenses would absorb much of the force of the eyelids during reading. These potential
interactions are speculative, but we believe are worthy of further investigation.
During reading, corneal topography can change and this effect appears to be directly
related to the force exerted by the eyelids. As a consequence, the optical
characteristics of the eye can be significantly altered during and after reading. This
leads to questions of how we define the refractive status of the cornea and eye, which
may need to be qualified in terms of the visual tasks undertaken prior to the refractive
and corneal topography measurements. These findings may also lead to a better
understanding of the relationship between reading and the development of refractive
errors.
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CHAPTER 5
Corneal aberrations following reading in progressing myopes
5.1 INTRODUCTION
It was shown that the optical characteristics of the cornea can change following reading
(Chapter 4). It was therefore of interest to examine whether corneal distortions after
reading might represent a factor in refractive error development by studying the
response of different refractive error groups.
Studies on monocular diplopia after near work provide useful information about the
subjectively perceived optical effects of corneal distortion. The most common
description is that of monocular vertical doubling (Mandell 1966; Knoll 1975; Bowman
et al. 1978; Carney et al. 1981; Goss and Criswell 1992; Kommerell 1993; Ford et al.
1997; Campbell 1998; Golnik and Eggenberger 2001). In Chapter 4, a detailed objective
analysis of the optical characteristics of corneal distortions after reading has been
performed in which it is shown that several lower and higher order Zernike wavefront
coefficients significantly change.
The introduction of ocular wavefront technology has enabled such detailed analysis of
the eyes’ optical characteristics. Several studies that have measured ocular wavefront
aberrations as a function of refractive error found that myopes have significantly larger
wavefront aberrations than emmetropes (Collins et al. 1995; Cheng et al. 2000; He et al.
Chapter 5 _
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2000; Marcos et al. 2000). Paquin found a quasi-linear relationship between increasing
aberrations and refractive error (Paquin et al. 2002). Collins suggested that high
amounts of wavefront aberrations might play a role in myopia development (Collins et
al. 1995).
The changes of optical characteristics during reading raise the question of how to define
refractive status and, more importantly, whether corneal distortions during reading
might be linked to refractive error development. Based on a retrospective analysis of
refractive error among humans subjected to various ocular anomalies disrupting pattern
vision, Rabin suggested emmetropisation to be a vision-dependent phenomenon (Rabin
et al. 1981). Goss proposed that retinal image-mediated ocular growth is a possible
etiological factor in juvenile-onset myopia (Goss and Wickham 1995). The hypothesis is
consistent with animal models based on various studies (e.g. (Wallman et al. 1981;
Raviola and Wiesel 1985; Schaeffel et al. 1988) and supported by human infant
refraction data taken early in life (Howland et al. 1978; Ingram and Barr 1979; Atkinson
et al. 1980; Howland and Sayles 1984; Ehrlich et al. 1997).
Several authors have reported an association between congenital ptosis and increased
presence of astigmatism, myopia, or amblyopia (O'Leary and Millodot 1979; Ugurbas
and Zilelioglu 1999; Gusek-Schneider and Martus 2000). Experimentally induced
congenital ptosis in chicks produces regional axial myopia (Langford et al. 1998).
Changes in refractive error after ptosis surgery have been found in humans (Cadera et
al. 1992; Holck et al. 1998; Brown et al. 1999). O’Leary pointed out that in the normal
reading posture the palpebral aperture is reduced and that many races prone to myopia
have a narrow palpebral aperture (O'Leary and Millodot 1979).
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In this study we have investigated corneal topography, corneal aberrations, and
palpebral aperture before and after a period of up to two hours of reading, for a group of
young progressing myopes and a group of young stable emmetropes. The aim was to
study whether corneal distortions after reading significantly differ between the two
groups and whether lid position during reading differs between the two groups.
5.2 METHODS
Ten young progressing myopic subjects and ten young emmetropic subjects participated
in the experiment. The subjects were recruited mostly from optometry students at the
Queensland University of Technology. The mean age of the myopic group was 22 years
ranging from 19 to 27 years. Average best sphere refraction was –3.13 D with a range of
–1.00 D to –6.00 D of myopia. The mean cylindrical refraction was –0.30 D ± 0.28 D
(SD). Mean myopia progression rate was -0.6 D over the last two years (varying from
–0.50 to –1.00 D). Subjects who were regular contact lens wearers were asked not wear
the lenses for at least 40 hours prior to the experiment to avoid potential confounding
effects of the lenses on corneal function. There were no rigid gas permeable contact lens
wearers amongst the myopic subjects. As a control group, ten young emmetropic
students were recruited. The mean age was 22 years ranging from 19 to 28 years.
Average best spherical refraction was –0.03 D range +0.25 to –0.25 D. The mean
cylindrical refraction was –0.05 D ± 0.18 D (SD). The emmetropic group did not show
any significant refractive error shift within the last two years (–0.05 D varying from
0.00 to –0.25 D).
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For all subjects the left eye was used for measurements. The subjects had no history of
significant corneal or ocular pathology and achieved 0 logMAR, or better, corrected
vision. The experiment was always conducted in the morning between 9.00 and
12.00 am. All subjects were given the instruction not to perform any significant near
tasks prior to the experiment. Informed consent was obtained for all subjects.
The protocol and data collection procedures were similar to those described in the
“Corneal aberrations and reading” study (Chapter 4). The Keratron videokeratoscope
(EyeQuip Division, Alliance Medical Marketing, Jacksonville, FL) was used for all
corneal topography measurements. Prior to the study, the instrument calibration was
checked according to the manufacturer’s instructions. For both the myopic and
emmetropic groups, six baseline videokeratographs were taken prior to a 1-hour reading
task and again immediately after 1-hour of reading and after a further 1-hour reading
task (i.e. after a total of 2 hours of reading). Reading distance for each individual was
measured at the beginning of the reading trials and compared as a function of refractive
error group.
Digital photography was used to document the external ocular features with the eyes in
reading gaze posture, and also with the subject positioned in a headrest with eyes in
primary gaze focusing on a 5-m distant Bailey-Lovie Chart. For subsequent analysis, a
calibration scale was placed within the frame of the images taken in the headrest with
eyes in primary gaze. The subjects were informed that at some stage during the reading
protocol, a photo of the left eye would be taken. The subjects were instructed, when
approached, not to change their reading posture as a consequence of the photography.
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A software program for digital image processing measurement was used for analysis of
the external eye images (Iskander et al. 2003). Utilising several customised image-
processing techniques the software allowed automatic analysis of the pupil, limbus, and
palpebral fissure parameters. After acquisition of eye biometrics from the photographs
taken in the headrest with eyes in primary gaze, the horizontal limbus diameter was used
as a reference for calibration and subsequent analysis of the digital photographs taken
with the eye in natural reading gaze posture.
Corneal instantaneous power and height data were exported from the videokeratoscope
for analysis. For the instantaneous power maps, the six corneal measurements taken
from each subject for each of the pre- and post-reading conditions were averaged. Then
the individually averaged pre- and post-reading maps were used to calculate the group
mean instantaneous power and standard deviation map for both the emmetropic group
and the myopic group. To study the potential effect of reading on topography, the
average difference map of pre- versus post-reading topography was calculated for each
reading period and refractive error group along with the t-test maps showing significant
areas of change within the maps.
The corneal wavefront was calculated using the same methods as in Chapter 4, but this
time Zernike terms of up to the sixth radial order (OSA convention) were fitted to the
corneal wavefront. For the two post-reading conditions the wavefront was calculated at
the baseline circle of least confusion in order to highlight potential changes in corneal
spherical power. The lower order Zernike wavefront coefficients were used to calculate
corneal sphero-cylinder power (Salmon 1999) at the pre-reading circle of least
confusion before and after reading for pupil sizes of 3, 4, and 5 mm. Power matrices
Chapter 5 _
125
(Harris 2000) were applied to calculate the group mean best-fit sphero-cylinder for each
condition and again to calculate the corneal changes in sphere, cylinder and astigmatic
axis pre versus post-reading. The Hotelling’s T2 multivariate test was used to test the
significance of overall change in corneal sphero-cylinder between the emmetropic and
myopic groups. For the 3, 4, and 5 mm pupil sizes, the group mean corneal wavefront,
root mean square error RMS was calculated as total wavefront RMS change, total higher
order wavefront RMS change, 3rd order, 4th order, 5th order, and 6th order wavefront
RMS change. T-tests were applied to investigate the significance of change of the
various wavefront RMS components between the emmetropic and myopic subjects.
After the subjects had finished the reading experiment, they were asked complete a near
task activity questionnaire (Table 5-1). The questionnaire was based on the
questionnaire reported by Walline, but was adapted for the near work activity of a
university student population (Walline et al. 2001). Questions included the number of
hours per week of university classes, how many hours per week outside of university
classes students do study or read for assignments, use a computer, read for pleasure, and
do intensive near work activities (e.g. model building, sewing etc.).
A point system was developed to characterise the relevance of different visual near task
activities with respect to its potential to affect corneal shape and optics. It has been
shown that different visual near tasks such as computer work, reading, and microscopy
have different effects on the corneas’ optical changes within the central pupil area
(Collins et al. 2003). Furthermore, eye movements during reading appear to play an
important role in intensifying these effects (Chapter 4). Therefore, near tasks that are
usually performed in downward gaze and are accompanied by systematic eye
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movements such as “study or read for assignment” or “reading for pleasure” were
assigned factor 3 = high relevance. Other near work activities that are usually performed
in downward gaze but are not typically associated with systematic eye movements such
as model building were assigned factor 2 = medium relevance, while computer work
was given a factor of 1 = low relevance because of the relatively horizontal gaze
direction during computer work. For the hours of weekly university classes a medium
relevance factor of 2 was assigned. Each subject’s weekly hours for each of the near
work activities were multiplied with its weighting factor and then added to a total value
representing the weekly near work activity as a function of its potential effect corneal on
shape and optics.
Chapter 5 _
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CORNEAL ABERRATIONS FOLLOWING READING REPORT OF NEAR WORK ACTIVITY
Patient Age Gender
Sph Cyl Axis Myopia progression within the last 2 years How many hours per week of university classes do you have?
How many hours per week outside of university classes do you: Study or read for assignments? Hours
Use a computer? Hours Read for pleasure? Hours
Do intensive near work activities (e.g. model building, sewing etc.)
Hours
Table 5-1: Near work activity questionnaire for a university student population. Near work
activities are categorised in relevance levels according to the near task’s potential to change
corneal shape and optics. Study or read for assignment and reading for pleasure = factor 3: high
relevance. Intensive near work activities such as model building and university classes = factor
2: medium relevance, while computer work = factor of 1: low relevance.
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5.3 RESULTS
Both emmetropic and myopic groups showed corneal shape and optics changes
following 1-hour and 2 hours of reading. The main difference between the two groups
was the location and magnitude of the corneal distortions, which had a significantly
larger effect on central corneal optics in the myopic group compared to the emmetropic
group.
The average baseline (pre-reading) corneal instantaneous power maps (Figure 5-1) for
the ten emmetropes (left) and the ten myopes (right) show higher corneal astigmatism in
the myopic group (emmetropes: cyl –0.56 D axis 27º; myopes: cyl –1.03 D axis 3º)
indicating that the higher total astigmatism amongst the myopes is primarily of corneal
origin. The relevant standard deviation maps were calculated at each point of the
average maps for each of the two groups (bottom panel). Particularly in the upper semi-
meridian toward the 12 o’clock position, the myopic group shows increasing standard
deviation indicating larger variability of slope of the myopic “baseline” (pre-reading)
corneas within this region. There is also a small, but less distinctive, increase of the
standard deviation within the emmetropic corneas in this area. After one hour of
reading (Figure 5-2) the corneas of myopes become increasingly asymmetrical due to a
flattening of the central upper semi-meridian, as can be seen in the difference map
(centre right). P-values within the t-test maps (bottom panel) show little to no statistical
significance of the changes.
Chapter 5 _
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BASELINE CORNEAL TOPOGRAPHY
Emmetropes (n = 10) Myopes (n = 10)
Figure 5-1: Average baseline instantaneous power map of emmetropic group (top left) and myopic
group (top right) for a 6 mm pupil zone. Bottom left: Standard deviation map calculated at each point
of the average map based on the emmetropic group (n = 10). Bottom right: Standard deviation map
calculated at each point of the average map based on the myopic group (n = 10).
Instantaneous Power Instantaneous Power
Standard Deviation Standard Deviation
* = t-test significant at (p = 0.05)
Sph +0.32 Cyl –0.56 Axis 27 Sph +0.59 Cyl –1.03 Axis 3
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130
POST-1HR-READING CORNEAL TOPOGRAPHY
Emmetropes (n = 10) Myopes (n = 10)
Figure 5-2: Average post 1-hour reading instantaneous power map of emmetropic group (top left) and
myopic group (top right) for a 6 mm pupil zone. Centre: Instantaneous power difference map of post
reading minus baseline instantaneous power for emmetropic group (center left) and myopic group
(center right). Bottom right: Significance map based on t-tests at all points within the map for
emmetropic group (bottom left) and myopic group (bottom right).
Instantaneous Power Instantaneous Power
Difference Map Difference Map
P-value map P-value map
* = t-test significant at (p = 0.05)
Sph +0.61 Cyl –0.92 Axis 6 Sph +0.31 Cyl –0.63 Axis 29
Chapter 5 _
131
POST-2HR-READING CORNEAL TOPOGRAPHY
Emmetropes (n = 10) Myopes (n = 10)
Figure 5-3: Average post 2-hour reading instantaneous power map of emmetropic group (top left) and
myopic group (top right) for a 6 mm pupil zone. Centre: Instantaneous power difference map of post
reading minus baseline instantaneous power for emmetropic group (center left) and myopic group
(center right). Bottom right: Significance map based on t-tests at all points within the map for
emmetropic group (bottom left) and myopic group (bottom right).
Instantaneous Power Instantaneous Power
Difference Map Difference Map
P-value map P-value map
* = t-test significant at (p = 0.05)
Sph +0.62 Cyl –0.86 Axis 7 Sph +0.25 Cyl –0.57 Axis 28
Chapter 5
132
After two hours of reading (Figure 5-3 top) the mean corneal map of the myopic group
shows a distinct band like distortion at less than 2 mm from the pupil centre. The mean
corneal map of the emmetropes also shows more asymmetry due to distortions in the
upper cornea at about 2.5 mm from the pupil centre. The changes are highlighted in the
difference maps showing a similar but larger and more complex distortion pattern in the
myopic group. The distortions in the myopes are more closely located to the pupil centre
and show higher statistical significance (bottom right) than in case of the emmetropic
group (bottom left).
The change of corneal wavefront RMS error after two hours of reading is shown in
Figure 5-4. What becomes evident from this analysis is that a large proportion of the
increased total wavefront RMS error change in the myopic group comes from the lower
order defocus and primary astigmatism components. In comparison, the emmetropic
group does not show such a distinct difference between total RMS and higher order
RMS changes. For a 5 mm pupil, the amount of the total higher order RMS changes in
both groups are very similar. When the RMS error is analysed in terms of the Zernike
higher order components, a more complex distortion pattern within the myopic group is
indicated by larger 4th order RMS changes and significantly larger 5th order RMS
changes (p = 0.008) in the myopes, while the 3rd order components are larger in the
emmetropes. For the smaller pupil regions of 4 mm and 3 mm, the magnitude of change
in the Zernike 4th, 5th, and 6th order terms became less significant in myopes and
emmetropes. As a consequence, within a 3 mm pupil zone the myopes show increased
higher order RMS changes. In the 3 mm pupil these changes are primarily due to the 3rd
order components in the myopes resulting in a statistically significant increase of the
total wavefront RMS error (p = 0.029) in this pupil size.
Chapter 5 _
133
Analysis of the corneal wavefronts revealed significantly changed wavefront
coefficients for both groups after one and two hours of reading. For a 5 mm pupil the
corneal wavefront coefficients before and after 2 hours of reading for the emmetropic
group and the myopic group are shown in Figure 5-5 and Figure 5-6 respectively. As in
Chapter 4, for the myopic group the changes in primary vertical coma and trefoil along
30º were similar in magnitude and as such that primary vertical coma shifted in negative
direction while the trefoil component shifted in positive direction. Statistical significant
corneal wavefront coefficients for emmetropes and myopes for all pupil sizes are
summarized in Table 5-2.
Chapter 5
134
-0.08
-0.04
0
0.04
0.08
0.12
0.16
0.2
0.24
0.28
0.32
0.36
0.4
0.44
Cha
nge
in W
avef
ront
RM
S V
alue
(mic
rons
)Myopic GroupEmmetropic Group
Figure 5-4: Group mean change (±SD) in wavefront root mean square error (RMS) after 2 hours of reading for myopes and emmetropes for three different
pupil sizes (3, 4, and 5 mm) is shown. Corneal wavefront RMS is presented as total RMS, higher order RMS, 3rd order, 4th order, 5th order, and 6th order RMS
components along with the relevant significance values for the t-test comparison between the change in value for the myopic versus emmetropic groups.
5 mm Pupil 4 mm Pupil 3 mm Pupil
Total RMS
Higher Order
3rd Order
4th Order
5th Order
6th Order
p-Value 0.079
0.726
0.212
0.076
0.008
0.404
p-Value 0.114
0.229
0.633
0.321
0.221
0.488
p-Value 0.029
0.052
0.079
0.083
0.269
0.173
Total RMS
Higher Order
3rd Order
4th Order
5th Order
6th Order
Total RMS
Higher Order
3rd Order
4th Order
5th Order
6th Order
Corneal Wavefront RMS change after 2 hours of Reading (OSA convention)
*
*
Chapter 5 _
135
Figure 5-5: Group mean wavefront coefficients (±SD) of emmetropes before and after 2 hours of reading for a 5 mm pupil sizes is shown. Zernike terms
according to OSA convention of up to the 6th order polynomial expansion are presented. Piston and the prism coefficients are excluded.
-0.5
-0.45
-0.4
-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
Zernike Coefficients (OSA convention)
Cha
nge
in W
avef
ront
Err
or C
oeff
icie
nt V
alue
(mic
rons
)BaselinePost 2-h read
* = t-test significant at (p < 0.05)
13−Z 3
3−Z 4
4−Z 1
3Z
33Z
24Z
04Z
24−Z 4
4Z
55−Z 3
5−Z 1
5−Z 1
5Z 35Z
55Z
66−Z 4
6−Z 2
6−Z 0
6Z
26Z
46Z
66Z
22Z
22−Z 0
2Z
* * *
Emmetrope Group: Baseline and post 2-hours reading Zernike wavefront coefficients (5 mm pupil)
Chapter 5
136
Figure 5-6: Group mean wavefront coefficients (±SD) of myopes before and after 2 hours of reading for a 5 mm pupil sizes is shown. Zernike terms
according to OSA convention of up to the 6th order polynomial expansion are presented. Piston and the prism coefficients are excluded.
-0.5
-0.45
-0.4
-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
Zernike Coefficients (OSA convention)
Cha
nge
in W
avef
ront
Err
or C
oeff
icie
nt V
alue
(mic
rons
)BaselinePost 2-h read
* = t-test significant at (p < 0.05)
13−Z 3
3−Z 4
4−Z 1
3Z
33Z
24Z
04Z
24−Z 4
4Z
55−Z 3
5−Z 1
5−Z 1
5Z 35Z
55Z
66−Z 4
6−Z 2
6−Z 0
6Z
26Z
46Z
66Z
22Z
22−Z 0
2Z
Myopic Group: Baseline and post 2-hours reading Zernike wavefront coefficients (5 mm pupil)
* * * *
* *
Chapter 5 _
137
Summary of significant corneal wavefront changes after 2 hours of reading for various pupil sizes:
Table 5-2: The change of various normalised corneal Zernike wavefront coefficients in microns (OSA convention) along with the relevant p-values for the
emmetropic and myopic group respectively is shown.
Emmetropic Group Myopic Group
Zernike Pupil Pupil Pupil Pupil Pupil Pupil
Microns 3 mm p-value 4 mm p-value 5 mm p-value 3 mm p-value 4 mm p-value 5 mm p-value
11−Z -0.031 0.006 -0.049 0.003 -0.064 0.041 -0.086 0.018 -0.10 0.006 2
2−Z -0.008 0.031 -0.009 0.042 22Z 0.036 0.040 0.039 0.004 3
3−Z 0.020 0.017 0.015 0.017 0.010 0.023
13−Z -0.007 0.010 -0.014 0.010 -0.019 0.003 -0.022 0.020 -0.017 0.002 -0.014 0.012 13Z -0.004 0.047 -0.005 0.011 -0.007 0.027 -0.008 0.018 2
4−Z 0.004 0.049 0.005 0.049
44−Z 0.003 0.044 04Z 0.002 0.036
55−Z -0.002 0.030 0.004 0.035 66Z -0.003 0.039
Chapter 5
138
The difference in corneal wavefront error coefficient changes after two hours of reading
between the myopic and emmetropic groups revealed a significantly larger change of
the 22Z primary astigmatism term in direction of against-the-rule in the myopic group
(p < 0.05 at 5 mm) (Figure 5-7). The 02Z defocus term shifted toward corneal flattening
(hyperopia) in myopes (see Figure 5-6) while emmetropes tended to show slightly
steeper corneas following reading (see Figure 5-5). This led to a significant 02Z defocus
term difference (p < 0.05 at 3, 4, and 5 mm) between emmetropes and myopes. There is
little statistically significant change within the 3rd order terms, however several 4th and
higher order terms changed significantly different, confirming the more complex
distortion pattern of the instantaneous power maps in the myopes.
The effect on corneal higher order RMS of time spent reading revealed a linear trend
towards more significant changes for longer reading periods and larger pupils (4 mm
and 5 mm pupil) within the emmetropic group (Figure 5-8). After one hour of reading
the higher order wavefront RMS values show larger increases in the myopic group,
reaching statistically significant differences compared with the emmetropic group for
the three pupil sizes analysed. After two hours of reading the mean corneal higher order
wavefront RMS for myopes decreases slightly relative to the 1-hour reading trial while
emmetropes continued to increase. However, for the 4 mm and 5 mm pupils the
difference still was significantly larger in myopes. The mean corneal higher order
wavefront RMS in microns for a 3, 4, and 5 mm pupil at the baseline condition was not
significantly higher in the myopic group compared with the emmetropic group
(emmetropes: 0.07 µm, 0.11 µm, and 0.19 µm ; myopes: 0.08 µm, 0.16 µm, and 0.26
µm for a 3, 4, and 5 mm pupil respectively).
Chapter 5 _
139
-0.15
-0.125
-0.1
-0.075
-0.05
-0.025
0
0.025
0.05
0.075
0.1
Zernike Coefficients (OSA convention)
Cha
nge
in W
avef
ront
Err
or C
oeff
icie
nt V
alue
(mic
rons
) 3mm Pupil4mm Pupil5mm Pupil
Figure 5-7: Group mean difference in wavefront coefficient change (±SD) between myopes and emmetropes after 2 hours of reading for three different pupil
sizes (3, 4, and 5 mm) is shown. Zernike terms according to OSA convention of up to the 6th order polynomial expansion are presented. Piston and the prism
coefficients are excluded.
* = t-test significant at (p < 0.05)
13−Z 3
3−Z 4
4−Z 1
3Z
33Z
24Z
04Z
24−Z 4
4Z
55−Z 3
5−Z 1
5−Z 1
5Z 35Z
55Z
66−Z 4
6−Z 2
6−Z 0
6Z
26Z
46Z
66Z
22Z
22−Z 0
2Z
* * * * *
* *
* *
* * *
Corneal wavefront error change after 2 hours of reading (Difference for Myopic minus Emmetropic Group)
Chapter 5
140
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Hig
her
orde
r wav
efro
nt R
MS
(mic
rons
)
Emmetrope
Myope
Figure 5-8: Higher order corneal wavefront RMS (±SD) before and after 1-hour and 2 hours of reading for myopic group and emmetropic group. The increase for various pupil sizes is shown.
pre-read post 1-h post 2-h
pre-read post 1-h post 2-h
pre-read post 1-h post 2-h
3 mm pupil 4 mm pupil 5 mm pupil
*
*
* *
*
* = t-test significant at (p < 0.05)
Chapter 5 _
141
The group mean characteristic shape difference between emmetropes and myopes of the
total corneal wavefront in a 5 mm pupil zone after 2 hours of reading, show increased
differences in the upper region of the wavefront (Figure 5-9 top left). The higher order
Zernike wavefront (top right) as well as 4th and 5th order components (centre right and
bottom left) show the characteristic band like distortion pattern following reading with
the 4th order component (centre right) making up for most (RMS = 0.0595 µm) of the
differences in higher order wavefront error change between the myopes and the
emmetropes.
In Table 5-3 the group mean corneal sphero-cylinder and corneal best sphere lens
(sphero-cyl and BSL measured at pre-reading circle of least confusion) before and after
1 hour and 2 hours of reading are shown along with the differences, and the statistical
significance of the changes (Hoteling T2). For the myopes, within the 3 and 4 mm pupils
the group mean sphere and cylinder after 2 hours of reading show the largest changes
with sph +0.22 (±0.35) and cyl –0.21 (±0.32) for a 3 mm pupil, while for a 4 mm pupil a
change of sph +0.22 (±0.27) and cyl –0.23 (±0.23) is shown. However only within the 3
mm pupil, the sphero-cylinder change at 1 hour after reading in the myopic versus the
emmetropic group is significantly different (Hoteling T2, p = 0.049). The changes in
corneal wavefront RMS are shown in Table 5-2 along with the t-test results for each
group. For both myopic and emmetropic groups there is a trend towards more
significant changes for larger pupils and longer reading periods.
Chapter 5
142
Wavefront Error Difference (Myopic minus Emmetropic Group)
All Coefficients Higher Order
3rd order 4th order
5th order 6th order
Figure 5-9: Group mean difference in wavefront root mean square error (RMS) between myopes
and emmetropes (myopes minus emmetropes) is shown. Corneal wavefront RMS difference is
presented as total RMS (top left) along with the sphero cylinder change, higher order RMS (top
right), 3rd order (centre left), 4th order (centre right), 5th order (bottom left), and 6th order RMS
components (bottom left).
Chapter 5 _
143
Emmetropic and myopic group data of sphero-cylinder changes
Emmetropes (n = 10) Myopes (n = 10)
Pupil 3mm Pupil
3mm
Baseline Sph Cyl A BSL HO RMS Baseline Sph Cyl A BSL HO
RMS Mean
SD 0.32
(±0.19) -0.56
(±0.39) 27 0.040 (±0.07)
0.067 (±0.013)
Mean SD
0.59 (±0.38)
-1.03 (±0.75) 3 0.070
(±0.047) 0.081
(±0.03)
Post1-h read Sph Cyl A BSL HO RMS Post1-h read Sph Cyl A BSL HO
RMS Mean
SD 0.31
(±0.18) -0.63
(±0.39) 29 0.000 (±0.08)
0.071 (±0.012)
Mean SD
0.61 (±0.38)
-0.92 (±0.70) 6 0.148
(±0.184) 0.104
(±0.04) Difference
SD 0.00
(±0.07) -0.09
(±0.07) 46 -0.040 0.004 Difference SD
0.15 (±0.24)
-0.14 (±0.18) 78 +0.079 0.023
T-Test T-Test T-Test T-Test P=0.095 p=0.229
P=0.165 p=0.043
Difference in Sphero-Cylinder change between Emmetropic and Myopic Groups Hoteling T2: p = 0.049
Post2-h read Sph Cyl A BSL HO RMS Post2-h read Sph Cyl A BSL HO
RMS Mean
SD 0.25
(±0.24) -0.57
(±0.38) 28 -0.033 (±0.129)
0.069 (±0.012)
Mean SD
0.62 (±0.34)
-0.86 (±0.71) 7 0.187
(±0.232) 0.099
(±0.05) Difference
SD -0.06
(±0.15) -0.04
(±0.05) 61 -0.07 0.005 Difference SD
0.22 (±0.35)
-0.21 (±0.32) 76 +0.117 0.018
T-Test T-Test T-Test T-Test P=0.126 p=0.365
P=0.115 p=0.356
Difference in Sphero-Cylinder change between Emmetropic and Myopic Groups Hoteling T2: p = 0.165 Pupil 4mm Pupil
4mm
Baseline Sph Cyl A BSL HO RMS Baseline Sph Cyl A BSL HO
RMS Mean
SD 0.36
(±0.19) -0.59
(±0.42) 26 0.068 (±0.051)
0.107 (±0.028)
Mean SD
0.58 (±0.40)
-1.01 (±0.76) 1 0.076
(±0.026) 0.158
(±0.08)
Post1-h read Sph Cyl A BSL HO RMS Post1-h read Sph Cyl A BSL HO
RMS Mean
SD 0.34
(±0.16) -0.63
(±0.38) 27 0.029 (±0.06)
0.120 (±0.028)
Mean SD
0.58 (±0.38)
-0.85 (±0.78) 4 0.15
(±0.14) 0.191
(±0.094) Difference
SD -0.01
(±0.07) -0.06
(±0.06) 46 -0.039 0.012 Difference SD
0.16 (±0.22)
-0.18 (±0.20) 78 +0.076 0.034
T-Test T-Test T-Test T-Test P=0.07 P=0.10
P=0.120 p=0.101
Difference in Sphero-Cylinder change between Emmetropic and Myopic Groups Hoteling T2: p = 0.110
Post2-h read Sph Cyl A BSL HO RMS Post2-h read Sph Cyl A BSL HO
RMS Mean
SD 0.28
(±0.24) -0.62
(±0.41) 27 -0.029 (±0.143)
0.128 (±0.028)
Mean SD
0.59 (±0.37)
-0.81 (±0.78) 5 0.1833
(±0.168) 0.177
(±0.065) Difference
SD -0.08
(±0.17) -0.04
(±0.05) 54 -0.097 0.021 Difference SD
0.22 (±0.27)
-0.23 (±0.23) 77 +0.108 0.019
T-Test T-Test T-Test T-Test P=0.086 p=0.067
p=0.074 p=0.46
Difference in Sphero-Cylinder change between Emmetropic and Myopic Groups Hoteling T2: p = 0.088 Pupil 5mm Pupil
5mm
Baseline Sph Cyl A BSL HO RMS Baseline Sph Cyl A BSL HO
RMS Mean
SD 0.42
(±0.21) -0.61
(±0.43) 25 0.112 (±0.048)
0.186 (±0.05)
Mean SD
0.62 (±0.41)
-1.02 (±0.76) 1 0.112
(±0.029) 0.260
(±0.11)
Post1-h read Sph Cyl A BSL HO RMS Post1-h read Sph Cyl A BSL HO
RMS Mean
SD 0.39
(±0.20) -0.63
(±0.41) 26 0.07 (±0.06)
0.202 (±0.04)
Mean SD
0.60 (±0.39)
-0.91 (±0.78) 2 0.15
(±0.08) 0.314
(±0.12) Difference
SD -0.03
(±0.08) -0.03
(±0.06) 44 -0.04 0.017 Difference SD
0.09 (±0.13)
-0.18 (±0.10) 79 +0.035 0.054
T-Test T-Test T-Test T-Test p=0.076 p=0.112
p=0.246 p=0.005
Difference in Sphero-Cylinder change between Emmetropic and Myopic Groups Hoteling T2: p = 0.167
Post2-h read Sph Cyl A BSL HO RMS Post2-h read Sph Cyl A BSL HO
RMS Mean
SD 0.33
(±0.26) -0.61
(±0.40) 27 0.02 (±0.14)
0.219 (±0.06)
Mean SD
0.615 (±0.39)
-0.86 (±0.74) 3 0.19
(±0.11) 0.30
(±0.10) Difference
SD -0.06
(±0.17) -0.05
(±0.06) 71 -0.09 0.06 Difference SD
0.16 (±0.16)
-0.18 (±0.10) 80 +0.073 0.041
T-Test T-Test T-Test T-Test p=0.106 p=0.048
p=0.073 p=0.049
Difference in Sphero-Cylinder change between Emmetropic and Myopic Groups Hoteling T2: p = 0.054
Table 5-3: The best sphere lens (BSL) change is calculated from the difference between the
baseline corneal wavefront circle of least confusion and post reading circles of least confusion at
various pupil sizes. HO RMS = Higher order wavefront root mean square error.
Chapter 5
144
Analysis of digital image processing measurement revealed a significantly smaller
palpebral aperture for the myopic group in the reading gaze position (emmetropic group
= 8.15 mm (±1.91); myopic group = 6.74 mm (±1.21); p = 0.042) but not in primary
gaze position (emmetropic group = 10.72 mm (±1.44); myopic group = 10.21 mm
(±1.61); p = 0.47). Also the distance from the upper lid margin to the pupil centre in the
myopic group was significantly smaller in reading gaze position (emmetropic group =
3.38 mm (±1.50); myopic group = 2.14 mm (±1.0); p = 0.028) but not in primary gaze
position (emmetropic group = 4.52 mm (±1.04); myopic group = 4.08 mm (±0.73); p =
0.29). No statistical significant difference was found for the distance from the lower lid
margin to the pupil centre either in primary gaze position (emmetropic group = 6.20 mm
(±0.82); myopic group = 6.13 mm (±1.00); p = 0.87) or in reading gaze position
(emmetropic group = 4.77 mm (±1.07); myopic group = 4.6 mm (±0.59); p = 0.63). A
typical example of reading gaze ocular biometrics for an emmetropic subject and a
myopic subject (Figure 5-10) is shown.
Average horizontal limbus diameter was 12.36 mm (±0.48) for the emmetropic group
and for the myopic group 11.97 mm (±0.61) (p = 0.13). The average reading distance
for emmetropes was 42.80 cm ranging from 30 to 52 cm, while myopes showed a mean
reading distance of 36.60 cm ranging from 23 to 48 cm (p = 0.087). Near work activity
scores showed 82 (±26) for the emmetropes and 97 (±31) for the myopes (p = 0.24)
respectively.
Chapter 5 _
145
Figure 5-10: Ocular biometrics data in reading gaze position using automatic image
measurement techniques for an emmetropic subject (left) and a myopic subject (right)
respectively. The information extracted from digital photographs is PUPIL d = pupil diameter,
LIMBUS d = limbus diameter, APERTURE UP = distance from limbus centre to upper lid
margin, and APERTURE DOWN = distance from limbus centre to lower lid margin.
PUPIL d = 4.13 mm LIMBUS d = 12.00 mm Aperture UP = 3.38 mm
Aperture DOWN = 4.89 mm
PUPIL d = 3.79 mm LIMBUS d = 10.79 mm Aperture UP = 2.26 mm
Aperture DOWN = 4.69 mm
Chapter 5
146
5.4 DISCUSSION
The major difference between the two groups of emmetropes and myopes found in this
study was the location and magnitude of corneal distortions following reading. This was
most noticeable in the instantaneous power difference maps and supported by the digital
image analysis of lid position during reading. For the myopic group, the location and
magnitude of distortions caused larger central corneal optical changes as compared with
the emmetropes, which was most clearly highlighted by the total RMS error changes.
Almost all subjects showed some changes in the corneal instantaneous power
topography after two hours of reading. The exception was one emmetropic subject in
whom there was virtually no change in topography apparent after two hours of reading.
This emmetropic subject also showed the largest palpebral aperture in the reading gaze
position (12.3 mm) and this provides a likely explanation for the lack of central (>5mm)
corneal topography changes.
Corneal wavefront RMS analysis revealed that distortions closer to the pupil centre not
only have a larger impact on higher order Zernike term components but also
significantly change the lower order astigmatism and defocus components. Analysis of
corneal wavefront error confirmed several of the previously reported results (Chapter 4),
which were found to be associated with the band like distortions related to lid forces.
For the myopic group an astigmatic shift in the direction of against-the-rule, as well as
significant changes of the primary vertical coma and trefoil along 30° terms were found.
While the link between lid force effects on the cornea and the changes of coma and
trefoil components is interesting, it may not always be a precise description for these
Chapter 5 _
147
corneal distortions. As distortions become more complex, a combination of secondary
astigmatism and tetrafoil components in addition to some 5th and 6th order terms may
provide a more accurate description. For larger pupils in particular, several 5th and 6th
order Zernike coefficients changed significantly in both groups indicating that Zernike
terms up to the 4th order may not always be enough to adequately describe the changes
in the corneal surface associated with lid forces.
Due to the 1 hour and 2 hour time periods the participants spent on reading, it was
possible to gain an impression of the effect of time on distortions, which showed a
group mean increase in magnitude of distortions and optical effects with increasing
time. Some subjects did not show increased higher order aberration changes after 2
hours, but rather showed a slight decrease relative to the 1-hour trial. While there was a
group mean increase in lower order terms, the change in higher order components did
not always lead to an increased higher order wavefront RMS. In one myopic subject the
corneal changes after reading even lead to a decrease in wavefront RMS error compared
with the subject’s baseline RMS. The differences between the 1-hour and 2 hour trial
might also be affected by a change in reading strategy (i.e. a change in body or head
posture or a change in book position) after a certain period of reading. To further
investigate this effect, continuous or periodic digital photos of lid and eye position
during the entire reading period would need to be taken. Reading a book for 2 hours
without any breaks is probably uncommon. In our experiment there was a short break of
just a view minutes between the 1-hour and 2 hour reading trials to collect corneal data
after the first hour of reading.
Chapter 5
148
Averaging of individuals’ corneal instantaneous power maps (Figure 5-1 to Figure 5-3)
may have resulted in distortions being masked due to differences in location on the
corneal surface. However the aim of this analysis was to illustrate the group mean trend
for emmetropes and myopes. A more accurate analysis is provided by the corneal
wavefront Zernike coefficients and RMS data.
The most commonly reported subjective visual observation that has been reported
following reading is monocular vertical doubling (Fincham 1963; Mandell 1966; Knoll
1975; Bowman et al. 1978; Carney et al. 1981; Kommerell 1993; Ford et al. 1997;
Campbell 1998; Golnik and Eggenberger 2001). Some studies have estimated the time
course of remission of distortions after reading based on subjective perception of
remission of the vertical doubling (Knoll 1975; Golnik and Eggenberger 2001). When
objectively measuring the time course of remission of the lid induced changes on the
corneal surface, there appears to be a non-linear decrease in the distortion with a large
proportion of the effect disappearing within a short time period after cessation of
reading, followed by a continuous slowing down of the process that may take more than
120 minutes after 60 minutes of reading (Chapter 4). It has also been shown that lid
related distortions in the periphery of the cornea change within seconds during the post-
blink interval (Buehren et al. 2001).
The optical effects during reading with the eyelids in reading gaze posture are likely to
be larger, taking into account short term changes that have been reported within the
post-blink interval (Buehren et al. 2001). In order to allow individual statistical analysis
to be drawn from our data and to improve accuracy, we have collected six corneal
topography measurements for each subject and each of the pre- and post reading
Chapter 5 _
149
conditions. After reading, several subjects’ data showed a small trend towards
decreasing distortions even within the short time frame it took to capture the six images
(approximately 30 sec). Furthermore, the effect of the tear meniscus at the lid margin in
cases where the upper lid position is near the upper pupil edge could also contribute to
changes in optical characteristics during reading. In order to capture the full magnitude
of the optical changes of eyes during reading it would be necessary to measure the eye’s
corneal and total wavefront aberrations after a period of reading with the eye in the
reading gaze position.
The exact mechanism of how the changes on the corneal surface occur is not clear. The
pattern of remission could indicate cell displacement similar to the mechanism that has
been proposed in orthokeratology (Swarbrick et al. 1998). However this assumption
needs to be confirmed by pachometry of the epithelium.
The likelihood of corneal distortions effecting overall visual performance during the day
will be significantly influenced by the time spent on near work activities. The sample of
myopes in this study reported that they spend about 20 % more time on near work
activities than the sample of emmetropes, although the difference was not statistically
significant. The myopes also used smaller reading distances than emmetropes, which is
likely to have an influence on eye movements during reading.
The issue of labelling subject groups as emmetropic and progressing myopes in this
study is not straightforward. If changes in topography associated with lid forces during
reading lead to myopia progression then the amount of time spent reading is an
important factor influencing myopia progression. It is conceivable that a subject
Chapter 5
150
classified as emmetropic might have significant corneal changes associated with lid
forces following reading. However if this subject performs little habitual reading, then
there would be no stimulus for myopia progression. On the other hand a subject with
lesser lid force, who reads often, could become a progressing myope. Therefore the
possible influence of lid forces during reading on myopia progression cannot be
considered in isolation from the amount of time spend reading.
Prolonged near work, which is a well established environmental risk factor associated
with myopia development (Tan et al. 2000; Hepsen et al. 2001; Saw et al. 2002) has
drawn researchers attention in the field of ocular wavefront aberrations. Changes in
spherical aberration with accommodation have been reported to decrease from positive
spherical aberration and changed to negative values with increasing levels of
accommodation (Koomen et al. 1949; Ivanoff 1956; Jenkins 1963; Atchison et al. 1995;
Ninomiya et al. 2002). Third order (coma and coma-like) aberrations are dominant for
most people (Howland and Howland 1976; Howland and Howland 1977; Walsh et al.
1984; Walsh and Charman 1985) and also have found to change with accommodation
(Atchison et al. 1995; He et al. 2000; Ninomiya et al. 2002).
One of the main interests in the field of myopia research is the mechanism of
accommodation and its possible relationship to myopia development. Using auto-
refractometers, a large number of studies have investigated whether accommodative
stimulus/response behaviour differs with refractive error (McBrien and Millodot 1986;
Rosenfield and Gilmartin 1988; Gwiazda et al. 1993; Gwiazda et al. 1995; Abbott et al.
1998). A common hypothesis is that accommodative lag results in a blurred retinal
image (hyperopic defocus), which in turn triggers eye growth. This is consistent with
Chapter 5 _
151
the results of animal studies (Schaeffel et al. 1988; Wildsoet 1997) that have
demonstrated that in the presence of artificially imposed hyperopic retinal defocus (with
negative lenses), the axial length of the eye increases, presumably to compensate for the
induced retinal defocus, and myopia develops. Reduced accommodation stimulus
responses in myopes have been reported in many studies (i.e. lags of accommodation
tend to be higher in myopes) (McBrien and Millodot 1986; Rosenfield and Gilmartin
1988; Gwiazda et al. 1993; Gwiazda et al. 1995). Conflicting reports have found that an
increased lag of accommodation accompanies rather than precedes the development of
myopia (Rosenfield et al. 2002).
Considering the various factors that can affect visual performance during the reading
process, much remains unknown. The complex optical characteristics shown by corneal
distortions and their interaction with internal ocular aberrations have not been
investigated. Studies that use wavefront sensors to investigate far and near viewing
conditions have the potential to provide more detailed information about the eye’s
optical characteristics during and after reading. While there is ongoing research
concerning the accommodation system, little is known about how corneal distortions
might affect accommodation. Furthermore the question must be raised of how much of
the apparent differences found in accommodation behaviour in myopes might have their
origin in the changes in corneal aberrations associated with reading in downgaze.
The hypothesis that corneal distortions during reading may contribute to juvenile-onset
myopia is consistent with the hypothesis of retinal image-mediated ocular growth.
Congenital ptosis has been associated with higher incidence of refractive error. In this
study it is shown that the optical effects of prolonged narrowing of the palpebral
Chapter 5
152
aperture is likely to compromise retinal image quality during reading and thereby could
have an effect on retinal image-mediated ocular growth. The results of this study have
also shown that the distance from pupil centre significantly influences optical changes
due to corneal distortion. In the group of myopes in this study, corneal distortions
following reading tended to be larger and occur closer to the central corneal area
compared with the emmetropic group.
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