ACCOMMODATIVE LAG, PERIPHERAL ABERRATIONS, AND MYOPIA IN CHILDREN
DISSERTATION
Presented in Partial Fulfillment of the Requirements for
the Degree Doctor of Philosophy in the Graduate
School of The Ohio State University
By
David A. Berntsen, O.D., M.S.
* * * * *
The Ohio State University 2009
Dissertation Committee: Approved by Karla Zadnik, O.D., Ph.D., Advisor
Donald O. Mutti, O.D., Ph.D., Co-Advisor ______Nicklaus Fogt, O.D., Ph.D. Advisor Vision Science Graduate Program
ABSTRACT
The Study of Theories about Myopia Progression (STAMP) is a two-year, double- masked, randomized clinical trial of myopic children 6 to 11 years old. STAMP uses progressive addition lenses (PALs) to evaluate two theories of juvenile-onset myopia progression. Eligible children have a high accommodative lag and either: (1) low myopia
(less myopic than –2.25 D spherical equivalent) or (2) high myopia (more myopic that –
2.25 D spherical equivalent) with esophoria at near. The accommodative lag theory hypothesizes that hyperopic retinal blur drives myopia progression. The mechanical tension theory hypothesizes that ciliary-choroidal tension created by the ocular components restricts equatorial expansion and causes axial elongation in people with factors that produce a large globe. To test between these theories, children were randomly assigned to wear either PALs with a +2.00-D add or single vision lenses (SVLs) for one year to achieve a reduction in myopia progression in the PAL group relative to the SVL group. All children then wear SVLs for the second year to evaluate the permanence of the treatment effect; a maintained treatment effect supports the lag theory, while a rebound supports mechanical tension. The primary outcome in STAMP is central cycloplegic autorefraction. Complete ocular biometric data are being collected at six-month intervals.
Over 17 months, 192 children were screened, and 85 (44%) were deemed eligible and enrolled. Of the children, 44 (52%) were female. The mean age (± SD) was 9.3 ± 1.4 ii years. The mean accommodative lag was 1.71 ± 0.37 D. The mean cycloplegic spherical equivalent refractive error was –1.95 ± 0.78 D, and the mean axial length was 24.17 ±
0.80 mm. Of those enrolled, 54 (64%) were esophoric at near. Complete baseline characteristics of the children enrolled in STAMP are described. Because the clinical trial is still in progress, the study-related findings are confidential.
Central and peripheral aberrometry is performed at each visit. Results validating aberrometry-based relative peripheral refraction (RPR) measurements against measurements made with an autorefractor are presented. A method of analyzing peripheral aberration data collected from a dilated pupil is discussed and validated. A single-valued metric of image quality was calculated to describe retinal image quality at five retinal locations, centrally and in four peripheral retinal locations. When including only higher-order aberrations, image quality was best centrally and decreased in the periphery. When relative peripheral refractive error was included along with higher-order aberrations, more significant reductions in peripheral retinal image quality were present, and the greatest reductions were in the temporal and superior retina where greater amounts of astigmatism were also measured.
Baseline and six-month accommodative lag data from children enrolled in
STAMP were analyzed. Children in STAMP still had a significant lag of accommodation for a 4-D stimulus when tested wearing a +2.00 D bifocal add. No evidence of an effect of bifocal adaptation on accommodative lag was found. Children with greater myopia
iii progression over the previous six months exhibited higher accommodative lags when tested with their full manifest correction. Myopia progression had no effect on accommodative lag when testing was performed with the child’s habitual correction.
These data suggest that a child’s accommodative lag should be measured with both the full manifest and habitual corrections if attempting to relate the retinal blur experienced by the child to his or her myopia progression.
iv
Dedicated to my wife and children
“…find the perfect future in the present.”
-Nathaniel Hawthorne
v ACKNOWLEDGMENTS
First and foremost, I would like to thank my wife Monique. Her encouragement throughout my PhD work has been unconditional, even when late nights were required to see study patients. She has been a pillar of support through both the good times and the bad. I would not be where I am today without her personal sacrifices for both me and our family. Although life has thrown us several curves along the journey, they have only made our love stronger.
I am fortunate to have had the opportunity to train with my co-advisors, Karla
Zadnik and Don Mutti. Their friendships both professionally and personally have meant so much to me and have been instrumental in my professional development. They both share a love and compassion for optometric research that has been truly inspiring. There is no way to repay them for all of their time, thoughts, guidance, and encouragement along the way. Thank you for all that you have done!
STAMP would not have been possible without the help of many fantastic people serving in a variety of roles. I owe an enormous “thank you” to everyone who has helped with STAMP: Masked Examiners (Bradley Dougherty, Kerri McTigue, Kathryn
Richdale, Eric Ritchey, and Aaron Zimmerman), STAMP Opticians (Melissa Button,
Aaron Chapman, Melissa Hill, Brandy Knight, Scott Motley, and Jeff Rohlf), Optometry
Coordinating Center (Lisa Jones, G. Lynn Mitchell, Linda Barrett, Melanie Schray, and
vi Austen Tanner), and Data and Safety Monitoring Committee (Mark Bullimore, Leslie
Hyman, Stephen Mandel, and Mel Moeschberger). Thanks are also owed to Jeff Walline for sharing his clinical trials knowledge and to Larry Thibos and the Indiana University
Visual Optics Group for all of their help with advanced optics and aberrations.
I would also like to thank the members of my dissertation committee (Karla
Zadnik, Don Mutti, and Nick Fogt) for their contributions and guidance during the development of this dissertation.
Thanks are in order for Michael Twa and Melissa Bailey, my first officemates as a PhD student, for providing guidance as I set out on this journey. I also thank Eric
Ritchey and Kathryn Richdale for their invaluable friendships throughout the moments of serenity and insanity as both Cornea and Contact Lens Fellows and PhD students.
Finally, I would like to thank my parents and brother for their encouragement and support through four degrees, including two doctorates. Words cannot express my appreciation of their unconditional support of my education.
This research was supported by the National Eye Institute (K12-EY015447 &
T32-EY013359), Essilor of America, and two American Optometric Foundation (AOF)
William C. Ezell Fellowships sponsored by the AOF Presidents Circle and the American
Academy of Optometry Section on Cornea and Contact Lenses.
vii
VITA
September 1, 1977 Born – Houston, Texas
2000 Bachelor of Science, Optometry The Honors College University of Houston
2002 Doctor of Optometry University of Houston College of Optometry
2002-2004 Fellowship, Cornea and Contact Lenses Graduate Teaching and Research Associate The Ohio State University College of Optometry
2004 Master of Science, Vision Science The Ohio State University College of Optometry
2004-2005 Fellowship, Clinical Research The Ohio State University College of Optometry College of Medicine and Public Health
2005 Postdoctoral Fellow The Ohio State University College of Optometry
2005 – present Senior Research Associate The Ohio State University College of Optometry
viii PUBLICATIONS
Peer-Reviewed Publications
1. Jones LA, Walline JJ, Gaume A, Rah MJ, Manny RE, Berntsen DA, Chitkara M, Kim A, Quinn N, CLIP Study Group. Purchase of contact lenses and contact-lenses-related symptoms following the Contact Lenses in Pediatrics (CLIP) Study. Cont Lens Anterior Eye. (In Press)
2. Lehman BM, Berntsen DA, Bailey MD, Zadnik K. Validation of OCT-based Crystalline Lens Thickness Measurements in Children. Optom Vis Sci. 2009;86:181- 187.
3. Walline JJ, Jones LA, Sinnott L, Chitkara M, Coffey B, Jackson JM, Manny RE, Rah MJ, Prinstein MJ, ACHIEVE Study Group. Randomized trial of the effect of contact lens wear on self-perception in children. Optom Vis Sci. 2009 Mar;86:222-232. (member of the study group)
4. Correction of Myopia Evaluation Trial 2 Study Group for the Pediatric Eye Disease Investigator Group, Manny RE, Chandler DL, Scheiman MM, Gwiazda JE, Cotter SA, Everett DF, Holmes JM, Hyman LG, Kulp MT, Lyon DW, Marsh-Tootle W, Matta N, Melia BM, Norton TT, Repka MX, Silbert DI, Weissberg EM. Accommodative lag by autorefraction and two dynamic retinoscopy methods. Optom Vis Sci. 2009 Mar;86(3):233-43. (member of the study group)
5. Berntsen DA, Merchea MM, Richdale K, Mack CJ, Barr JT. Higher-Order Aberrations when wearing Sphere and Toric Soft Contact Lenses. Optom Vis Sci. 2009;86:115-122.
6. Berntsen DA, Mutti DO, Zadnik K. Validation of Aberrometry-Based Relative Peripheral Refraction Measurements. Ophthal Physiol Opt. 2008; 28:83-90.
7. Walline JJ,Gaume A, Jones LA, Rah MJ, Manny RE, Berntsen DA, Chitkara M, Kim A, Quinn N, CLIP Study Group. Benefits of Contact Lens Wear for Children and Teens. Eye Contact Lens. 2007;33(6, Part 1 of 2):317-321.
8. Richdale K, Berntsen DA, Mack CJ, Merchea MM, Barr JT. Visual Acuity with Spherical and Toric Soft Contact Lenses. Optom Vis Sci. 2007;84:969-975.
9. Walline JJ, Jones LA, Rah MJ, Manny RE, Berntsen DA, Chitkara M, Gaume A, Kim A, Quinn N, CLIP Study Group. Contact Lenses In Pediatrics (CLIP) Study: Chair Time and Ocular Health. Optom Vis Sci. 2007;84:896-902.
10. Berntsen, DA, Mitchell GL, Nichols JJ. Reliability of Grading Lissamine Green Conjunctival Staining. Cornea. 2006;25:695-700. ix
11. Berntsen, DA, Mitchell GL, Barr JT. The Effect of Overnight Contact Lens Corneal Reshaping on Refractive Error-Specific Quality of Life. Optom Vis Sci. 2006;83:354- 359.
12. Berntsen DA, Barr JT, Mitchell GL. The Effect of Overnight Contact Lens Corneal Reshaping on Higher-Order Aberrations and Best Corrected Visual Acuity. Optom Vis Sci. 2005;82:490-497.
13. Nichols JJ, Berntsen DA, Mitchell GL, Nichols KK. An Assessment of Grading Scales for Meibography Images. Cornea. 2005; 24(4):382-388.
14. Nichols, JJ, Berntsen, DA. The Assessment of Automated Measures of Hydrogel Contact Lens Refractive Index. Ophthal Physiol Opt. 2003; 23:517-525.
FIELD OF STUDY
Major Field: Vision Science
x TABLE OF CONTENTS
Page Abstract ...... ii Dedication ...... v Acknowledgments ...... vi Vita ...... viii List of Tables...... xiv List of Figures ...... xvii
Chapters:
1. Introduction ...... 1
1.1 Public Health Significance ...... 1 1.2 Models of Juvenile-Onset Myopia ...... 2 1.3 Accommodative Lag Theory ...... 4 1.3.1 Animal Myopia Literature ...... 5 1.3.2 Human Myopia Literature ...... 7 1.3.3 Accommodative Lag before Myopia Onset ...... 9 1.3.4 Accommodative Lag and Myopia Progression...... 11 1.4 Mechanical Tension Theory ...... 12 1.4.1 Crystalline Lens ...... 14 1.4.2 Peripheral Refraction (Retinal Shape) ...... 15 1.4.3 COMET 3- and 5-Year Results ...... 16 1.4.4 Potential Sources of Ciliary-Choroidal Tension ...... 17 1.5 Limitations of Previous Bifocal/PAL Studies...... 18 1.6 Peripheral Image Quality ...... 21 1.6.1 Predicting the Effect of Aberrations on Visual Quality ...... 23 1.7 Dissertation Goals ...... 24
2. Study of Theories about Myopia Progression (STAMP) ...... 26
2.1 Study Design ...... 26 2.1.1 Expected Outcomes ...... 28 2.1.2 STAMP Enrollment Criteria and Randomization ...... 36 2.1.3 Sample Size Considerations ...... 38 2.1.4 Recruitment and Retention ...... 40 2.1.5 Masking, Crossovers, and Data Entry ...... 41 2.1.6 Spectacles ...... 42 xi 2.1.7 Data and Safety Monitoring Committee ...... 43 2.1.8 Planned Data Analysis (Year 1 and Year 2 Data) ...... 43 2.2 Measurement Methods ...... 45 2.2.1 Autorefraction ...... 45 2.2.2 Cycloplegia and Pupillary Dilation ...... 45 2.2.3 Phoria ...... 46 2.2.4 Accommodative Lag and Response AC/A Ratio ...... 46 2.2.5 Corneal Topography / Pachymetry ...... 47 2.2.6 Tonometry ...... 48 2.2.7 Central and Peripheral Aberrometry...... 48 2.2.8 Relative Peripheral Refraction ...... 49 2.2.9 Video Phakometry ...... 49 2.2.10 A-scan Ultrasonography ...... 50 2.2.11 Interferometry...... 50 2.2.12 Near Work and Outdoor Activity Assessment ...... 51 2.2.13 Parental History of Myopia ...... 51 2.2.14 Non-Outcome Measurements/Procedures ...... 52 2.3 Baseline Characteristics...... 52 2.3.1 Baseline Data Statistical Methods ...... 52 2.3.2 Baseline Characteristics ...... 53 2.4 Discussion ...... 60
3. Validation of Aberrometry-Based Relative Peripheral Refraction (RPR) ...... 64
3.1 Introduction ...... 64 3.2 Methods ...... 65 3.3 Results ...... 67 3.4 Discussion ...... 72
4. Peripheral Aberrations in Myopic Children ...... 80
4.1 Introduction ...... 80 4.2 Validation of a Method of Analyzing Aberration Data from an Oval Pupil ... 83 4.2.1 Methods ...... 85 4.2.2 Results ...... 88 4.2.3 Conclusions ...... 93 4.3 Baseline Central and Peripheral Retinal Image Quality in STAMP ...... 93 4.3.1 Methods ...... 93 4.3.2 Results ...... 97 4.4 Discussion ...... 105 xii
5. The Effect of Bifocal Spectacle Add and Correction Type on Accommodative Lag ...... 109
5.1 Introduction ...... 109 5.2 Methods ...... 112 5.3 Results ...... 114 5.3.1 Accommodative lag and bifocal adaptation ...... 114 5.3.2 Accommodative lag at the baseline and 6-month visits ...... 115 5.3.3 Accommodative lag and undercorrection at baseline ...... 116 5.3.4 Accommodative lag and undercorrection (myopia progression) at 6 months ...... 119 5.4 Discussion ...... 124
6. Conclusions ...... 131
List of References ...... 135 Appendix A: STAMP Manual of Procedures ...... 149 Appendix B: STAMP Data Collection Forms ...... 238
xiii LIST OF TABLES
Table Page
2.1 STAMP secondary outcome measures ...... 29
2.2 Expected outcomes for the accommodative lag theory and the mechanical tension theory...... 31
2.3 Study enrollment criteria ...... 37
2.4 Race and ethnicity distribution of children enrolled in STAMP...... 55
2.5 Summary statistics for primary and secondary outcomes at baseline...... 56
2.6 Mean (± SD) baseline characteristics stratified by treatment group...... 57
2.7 Mean (± SD) baseline characteristics for near work and outdoor activity survey stratified by treatment group...... 59
2.8 Number of myopic parents by treatment group. Percentages indicate proportion within each number of myopic parent category...... 60
2.9 Comparisons of age and spherical equivalent refractive error between children for whom the number of myopic parents is known versus not known...... 60
3.1 Mean ± standard deviation for nasal and temporal relative peripheral refraction (RPR) values are shown for all subjects by instrument. There was not a significant difference between relative peripheral refraction measurements made with the COAS and Grand Seiko autorefractor (p = 0.34)...... 68
3.2 Average refractive error values in diopters (mean ± SD) by instrument and retinal location for sphere only, spherical equivalent (M), J 0, and J 45 . With the exception of J 45 (oblique astigmatism), refractive error differences due to the direction of gaze did not depend on which instrument was used. The average difference between the instruments is also shown...... 70
xiv 3.3 Statistically significant differences in refractive error measurement by direction of gaze are shown. Differences presented in the table were significant at a simultaneous alpha level of 0.05 using Tukey’s HSD test. Oblique astigmatism (J 45 ) is not included in the table because the average difference in J 45 between directions of gaze depended on the instrument used (i.e., there was a significant instrument x gaze interaction)...... 70
4.1 Table of mean differences between RMS wavefront error and individual Zernike terms for the COAS and CLAS-2D methods of analyzing aberration data from an oval pupil. Spearman’s rho was calculated to determine whether a correlation existed between the difference and mean values...... 90
4.2 Table of mean differences between metrics of image quality calculated using Zernike coefficients generated from the COAS and CLAS-2D methods of analyzing data from an oval pupil. Spearman’s rho was calculated to determine whether a correlation existed between the difference and mean values...... 92
4.3 Means (± SD) for the magnitude by location of each relative peripheral refractive error component (M, cylinder, J 0, and J 45 ) included in the HOAs + RPR metric calculations. Considering each component separately, retinal locations that do not have a symbol, uppercase letter, lowercase letter, or number in common are significantly different from each other at an alpha < 0.05 level by Tukey’s HSD...... 104
4.4 Pearson correlation coefficients (r) by retinal location between the magnitude of the natural log of each relative peripheral refractive error component [ln(M), ln(cylinder), ln(J 0), and ln(J 45 )] included in the HOAs + RPR metric calculations and the un-normalized VSOTF image quality metric calculated with HOAs + RPR...... 105
5.1 Accommodative response testing conditions by study visit. By study design, the manifest conditions at the baseline visit are the same as the habitual lens conditions at the six-month visit (indicated by the arrows)...... 113
5.2 Mean (± SD) accommodative lag at the baseline and 6-month visits by correction type and treatment assignment. SVL = single vision lenses; PAL = progressive addition lenses ...... 115
xv 5.3 Mean difference in accommodative lag by correction type at the baseline visit evaluated at three amounts of undercorrection to demonstrate the interaction present between correction type and undercorrection. Differences are obtained from the modeled data...... 118
5.4 Mean difference in accommodative lag by correction type at the six- month visit evaluated at two amounts of undercorrection (i.e., myopia progression during the previous 6 months) to demonstrate the interaction present between correction type and undercorrection. Differences are obtained from the modeled data...... 120
xvi LIST OF FIGURES
Figure Page
1.1 Accommodative lag and mechanical tension theories of myopia progression ...... 3
2.1 Hypothesized progression of myopia based on the mechanical tension theory and the accommodative lag theory...... 30
2.2 Expected retinal shape outcomes for the accommodative lag theory of myopia progression. Solid lines represent the vertical retinal image shell. Dashed lines represent relative peripheral refraction in the vertical meridian...... 34
2.3 Expected retinal shape outcomes for the mechanical tension theory of myopia progression. Dashed lines represent relative peripheral refraction in the horizontal meridian...... 34
2.4 Flowchart of STAMP visits and randomization...... 53
2.5 Mean (± SD) relative peripheral refraction (RPR) at baseline for all children...... 58
3.1 Difference versus mean plots for nasal (3.1a) and temporal (3.1b) relative peripheral refraction (RPR). Neither of the mean differences (solid lines) were significantly different than zero. The dotted lines represent the 95% limits of agreement for nasal RPR and temporal RPR, which were –1.38 D to +1.02 D and –1.89 D to +1.76 D, respectively...... 69
3.2 Linear regression analysis showing that subjects with more myopia had greater relative peripheral hyperopia when examining both nasal retina (figure 3.2a; R 2 = 0.23, slope = –0.21, p = 0.001) and temporal retina (figure 3.2b; R 2 = 0.10, slope = –0.20, p = 0.018)...... 73
3.3 Linear regression showing that nasal-temporal RPR differences are not related to refractive error (p = 0.81). The nasal-temporal RPR differences in this study were consistent across refractive errors...... 73
xvii 4.1 Graphic representation of an oval pupil with an analysis diameter equal to the major axis of the oval pupil data (a). After reconstructing the wavefront using the Zernike coefficients calculated, there is extrapolation outside of the original oval data (b), which makes it necessary to apply a mask with the shape of the original oval pupil (c)...... 82
4.2 Example of using an analysis circle equal in diameter to the major axis of the non-dilated pupil (6 mm) within the dilated pupil...... 84
4.3 Method of analyzing dilated oval pupil data in CLAS-2D software. First, an oval mask with major axis equal to the non-dilated pupil diameter is applied. Next, an analysis circle with diameter equal to the major axis of the non-dilated pupil is used to fit the Zernike polynomials (Wei and Thibos 2008; Shen and Thibos 2009)...... 87
4.4 Point spread functions for a single child calculated for five retinal locations using only higher-order aberrations...... 98
4.5 Point spread functions for a single child calculated for five retinal locations using higher-order aberrations and relative peripheral refractive error (HOAs + RPR). VSOTF = normalized visual Strehl ratio ...... 99
4.6 Histograms and means (± SD) of the un-normalized visual Strehl ratio (e.g., the volume under the neural weighted OTF) calculated with higher- order aberrations only by retinal location. Retinal locations that do not have a letter in common are significantly different from each other at an alpha < 0.05 level by Tukey’s HSD...... 101
4.7 Histograms and means (± SD) of the un-normalized visual Strehl ratio (e.g., the volume under the neural weighted OTF) calculated with higher- order aberrations plus relative peripheral refraction (RPR) by retinal location. Retinal locations that do not have a letter in common are significantly different from each other at an alpha < 0.05 level by Tukey’s HSD...... 102
5.1 Mean accommodative lag at the baseline and six-month visits by correction type. Error bars represent standard error of the mean...... 116
xviii 5.2 Accommodative lag versus the difference between the manifest and habitual prescription (i.e., spherical undercorrection) at the baseline visit. The difference in accommodative lag between the correction types depends on the amount of undercorrection...... 118
5.3 Accommodative lag versus the difference between the manifest and habitual sphere at the six-month visit (i.e., myopia progression in the past six months). The difference in accommodative lag between the correction types depends on the amount of myopia progression in the previous 6 months...... 120
5.4 Relationship between accommodative lag measured with the manifest correction and the reduction in accommodative lag when a +2.00 D bifocal add was introduced. Black circles represent children whose myopia progression over the prior six months was 0.50 D or more. Open diamonds represent children whose myopia progression over the prior six months was less than 0.50 D...... 123
5.5 Relationship between accommodative lag measured with the habitual correction and the reduction in accommodative lag when a +2.00 D bifocal add was introduced. Black circles represent children whose myopia progression over the prior six months was 0.50 D or more. Open diamonds represent children whose myopia progression over the prior six months was less than 0.50 D...... 124
xix
CHAPTER 1
INTRODUCTION
1.1 Public Health Significance
Approximately 33% of adults in the United States are myopic (Vitale et al. 2008).
While less than 2% of children are myopic at age five years when entering school, 15% of children are myopic at age 12 or 13 years when they finish grade school (Blum et al.
1959; Mutti et al. 1996). The mean rate of myopia progression is –0.50 D per year (Fulk et al. 2000; Gwiazda et al. 2003) with an average age of progression cessation of 15 years in females and 16 years in males (Goss and Winkler 1983).
Myopia is associated with an increased risk of chorioretinal degeneration, retinal detachment, open-angle glaucoma, and cataract formation with degenerative myopia the primary cause of roughly 8% of blindness (Perkins 1979). Eyes with low myopia (–1.00
D to –3.00 D) have a fourfold greater chance of having a retinal detachment than non- myopic eyes. The risk increases to tenfold when an eye is more myopic than –3.00 D, and nearly 55% of non-traumatic retinal detachments can be related to myopia (The Eye
Disease Case-Control Study Group 1993). Myopia has been estimated to cost $4.6 billion annually in the United States for eye examinations and correction (Javitt and Chiang
1994). Determining the mechanism responsible for juvenile-onset myopia progression
1 has the potential to reduce the risk of ocular complications and to relieve health care costs if it is used to design more effective treatments.
1.2 Models of Juvenile-Onset Myopia
In order to develop effective treatments to reduce or prevent the progression of juvenile onset myopia, the mechanism responsible for myopic progression must be better understood. Two of the theoretical models of juvenile-onset myopia progression rely on different mechanisms (Figure 1.1). Each theory points to a different therapeutic approach; therefore, identifying the proper model may lead to new and more effective strategies to reduce myopia progression.
The first theory, currently the predominant one in the myopia literature, is based on the idea that hyperopic retinal blur caused by a high lag of accommodation during near work activities induces abnormal axial growth of the eye (Goss et al. 1988; Charman
1999; Goss and Rainey 1999); however, issues exist with this theory. A recent major bifocal study has shown that the majority of the treatment effect produced by reducing hyperopic retinal blur inexplicably occurs during the first year of treatment (Gwiazda et al. 2003). The accommodative lag theory predicts an accumulating benefit over time. In animal models of myopia, brief periods of clear vision completely negate the grow signal produced by otherwise constant hyperopic retinal blur (Schmid and Wildsoet 1996;
Shaikh et al. 1999; Zhu et al. 2003; Norton et al. 2006), questioning the importance of transient hyperopic retinal defocus due to accommodative lag during near work.
Pharmaceuticals that increase accommodative lag also decrease the rate of myopia
2 progression (Siatkowski et al. 2004; Chua et al. 2006; Siatkowski et al. 2008). Finally, there are controversies over whether accommodative lag is elevated prior to the onset of myopia (Gwiazda et al. 2005; Mutti et al. 2006) and whether accommodative lag is associated with myopic progression (Rosenfield et al. 2002; Allen and O'Leary 2006;
Weizhong et al. 2008). These issues will be dealt with in detail later.
Mechanical Accommodative Tension Theory Lag Theory
Factors result in High lag of larger eye size accommodation
Hyperopic Increased ciliary- retinal defocus choroidal tension
Axial elongation High Mechanical accom lag restriction to results equatorial growth Myopia progression
Accelerated axial Lack of lenticular elongation resulting in compensation for prolate globe shape axial ↑
Myopia progression
Figure 1.1: Accommodative lag and mechanical tension theories of myopia progression
The second theory asserts that mechanical tension created by the ocular components restricts equatorial ocular expansion and causes accelerated axial elongation
3 in people with factors resulting in a larger than normal globe (Mutti et al. 2006). In the mechanical tension theory, high accommodative lag is a by-product of myopia and is thus correlated with, but does not cause, myopic progression.
Recent clinical trials have focused on whether treatments such as bifocals (Fulk et al. 2000; Edwards et al. 2002; Gwiazda et al. 2003; Hasebe et al. 2008), rigid contact lenses (Katz et al. 2003; Walline et al. 2004), and pharmaceutical agents (Siatkowski et al. 2004; Tan et al. 2005; Siatkowski et al. 2008) reduce myopia progression; however, because the studies were designed to determine the effectiveness of the intervention, they lack the biometric measurements necessary to describe fully the changes in the ocular components that are needed to explain the treatment’s underlying mechanism. There are also inadequate data describing treatment effect permanence; therefore, the prevention versus simple delay of myopia progression cannot be distinguished from one another.
1.3 Accommodative Lag Theory
The accommodative lag theory is based on the concept that chronic hyperopic retinal blur will drive axial elongation to compensate for the blur stimulus. The observation that myopes have a reduced accommodative response compared to emmetropes (McBrien and Millodot 1986; Bullimore et al. 1992; Gwiazda et al. 1993b;
Abbott et al. 1998), and thus an insufficient accommodative response to blur, lends support to this theory. Research showing that the amount of accommodative lag increases as myopia progresses in children has also been suggested as evidence that blur drives myopia progression (Gwiazda et al. 1995). Data showing that myopia progresses more
4 slowly during the summer when children are not in school also provide additional support for an association between retinal blur and myopia progression due to increased near work (Fulk et al. 2002a). The Correction of Myopia Evaluation Trial (COMET) finding that progressive addition lenses (PALs) are more effective at slowing myopia progression in children with a high accommodative lag also supports this theory (Gwiazda et al.
2004).
1.3.1 Animal Myopia Literature
The lag theory suggests that hyperopic blur is capable of causing axial elongation.
Extensive literature involving multiple animal models indicates that the coordinated ocular growth that occurs during emmetropization is guided by visual input. In general, form-deprivation in young animals using either lid-suture or diffusing lenses has been shown to result in axial elongation and the development of myopia in the chick (Wallman et al. 1978), tree shrew (Sherman et al. 1977; Siegwart and Norton 1998), marmoset
(Troilo and Judge 1993), and rhesus monkey (von Noorden and Crawford 1978; Raviola and Wiesel 1985; Smith et al. 1987). In monkeys, the amount of form-deprivation myopia that develops is proportional to the amount of image degradation (Smith and Hung 2000).
In most young animals, recovery from form-deprivation myopia occurs once they are allowed unrestricted vision (Troilo and Wallman 1991; Siegwart and Norton 1998), provided that the animal is young enough that ocular components of the eye have not already finished growing (Qiao-Grider et al. 2004). There is also evidence that recovery from form-deprivation myopia can be prevented if the induced myopia is optically
5 corrected, supporting the hypothesis that recovery is also visually guided (McBrien et al.
1999).
Lens-induced defocus has also been shown to predictably change eye growth in young animals with negative lenses resulting in longer, myopic eyes and positive lenses resulting in shorter, hyperopic eyes. Refractive error and axial length compensation for lens-induced defocus have been shown in chicks (Schaeffel et al. 1988; Wallman et al.
1995), marmosets (Whatham and Judge 2001), tree shrews (Shaikh et al. 1999), and monkeys (Hung et al. 1995; Smith and Hung 1999); however, while chicks can reliably compensate for defocus as high as +/-15 diopters (D) (Wildsoet and Wallman 1995; Kee et al. 2001), monkeys have a comparatively limited range (less than +/-6 D) for which they can accurately compensate (Hung et al. 1995).
Although form-deprivation and constant defocus disrupt emmetropization in animals, there is significant evidence that visual “stop” signals are vastly more potent than the “grow” signals that result in ocular elongation and myopia. The effects of form- deprivation have been shown to be almost completely negated by two hours and four hours of constant unrestricted vision in chicks and monkeys, respectively (Napper et al.
1995; Smith et al. 2002). Similarly, brief periods of exposure to either plus lenses or unrestricted vision have been shown to prevent axial elongation in response to an otherwise constant stimulus to grow from a minus lens (Schmid and Wildsoet 1996;
Shaikh et al. 1999; Zhu et al. 2003; Norton et al. 2006). These results show that visual stimuli are not simply time-averaged and that stimuli signaling the eye to stop growing are given much greater weight.
6
Interestingly, dividing a constant block of unrestricted vision into multiple smaller periods throughout the day of the same total duration has been shown to be more effective at preventing form-deprivation myopia in chicks than the original constant block of unrestricted vision, suggesting additive effects of neural activity associated with the beginning of a period of unrestricted clear vision (Napper et al. 1997). Likewise, in monkeys, four 15-minute periods per day of unrestricted vision were able to negate the growth stimulus of otherwise constant lens-induced hyperopic defocus (Kee et al. 2007).
Collectively, the animal literature findings cast doubt upon the ability of small, transient amounts of hyperopic foveal blur during near work to cause juvenile-onset myopia and provide insight into the reason why attempts to prevent myopia progression in children with bifocal spectacles have not resulted in clinically meaningful effects
(Edwards et al. 2002; Fulk et al. 2002b; Gwiazda et al. 2003; Hasebe et al. 2008). In addition, it has been suggested that the sensitive period for deprivation myopia in animal models appears to be too early and the amount of deprivation too severe to be able to explain juvenile myopia onset in school-aged children (Zadnik and Mutti 1995).
1.3.2 Human Myopia Literature
Because the accommodative lag theory proposes that sustained hyperopic retinal blur due to high accommodative lag causes myopia progression, increased higher-order aberrations in myopic eyes (He et al. 2002) and increased levels of near work have been suggested as risk factors for juvenile-onset myopia (Gwiazda et al. 1993b). Aberrations have been shown to increase with accommodation (He et al. 2000), but this change does not explain why the increase in higher-order aberrations due to accommodation would 7 trigger myopia only in certain individuals. Near work has long been studied as a risk factor for juvenile myopia progression; however, studies in the US have shown that parental myopia is a more influential factor in juvenile myopia than near work (Mutti et al. 2002), and that children with a parental history of myopia tend to have longer eyes before the onset of myopia (Zadnik et al. 1994). Longitudinal data have also shown that the prevalence of myopia in children increases with the number of myopic parents, again emphasizing the importance of heredity over hyperopic blur in myopia progression
(Gwiazda et al. 1993a; Mutti et al. 2002).
Questions about the accommodative lag theory also arise from recent results of
COMET in which myopic children were randomized to either PALs or single vision lenses and followed for three years to determine the effect of using bifocals to reduce hyperopic blur associated with near work. While there was a significant three-year treatment effect (0.20 D-difference between the treatment and control groups), all of the treatment effect occurred during the first year and then was maintained with no additional gains in years two and three (Gwiazda et al. 2003). If hyperopic blur were the driving force behind progression, the effect should have increased throughout the three years of
PAL wear. Additionally, a similar trial in Hong Kong examining the effect of PALs on juvenile myopia progression found no significant treatment effect, suggesting the PAL treatment effect is not robust (Edwards et al. 2002).
The success of both atropine ophthalmic drops and pirenzepine ophthalmic gel in slowing the progression of myopia in children also limits the applicability of the accommodative lag theory (Shih et al. 2001; Tan et al. 2005; Chua et al. 2006;
Siatkowski et al. 2008). Pirenzepine preferentially blocks M1 receptors and thus causes 8 much less mydriasis and cycloplegia than atropine, which blocks both M 1 and M 3 receptors. A recent US study of 2% pirenzepine found a significant 0.27-D treatment effect after the first year and a 0.41-D treatment effect after the second year (Siatkowski et al. 2004; Siatkowski et al. 2008), which is greater than the effect of PALs, even though pirenzepine may increase accommodative lag due to cycloplegia (Siatkowski et al. 2004).
In two pirenzepine studies, subjects assigned to the active treatment reported significantly more accommodative issues, such as blurred near vision, than placebo-treated children
(Tan et al. 2005; Siatkowski et al. 2008), suggesting an increased lag of accommodation.
In the Atropine in the Treatment of Myopia Study, only one eye of each child in the treatment group received 1% atropine and no bifocal spectacles were given. Even though the atropine treated eye always experienced a significant amount of hyperopic retinal blur during near work, a 0.92-D treatment effect was found after two years (Chua et al. 2006).
Because both pirenzepine and atropine have been shown to reduce myopia progression while increasing accommodative lag, the role of hyperopic blur as a causative factor for myopia progression may be questioned. A better model may be needed to explain the presence of increased accommodative lag in myopic children.
1.3.3 Accommodative Lag before Myopia Onset
There are conflicting reports concerning whether accommodative lag is elevated before the onset of juvenile myopia. Gwiazda et al. reported elevated lag in pre-myopic children two years before myopia onset (Gwiazda et al. 2005); however, the increase was not statistically significant one year before myopia onset, possibly due to low statistical power (n = 80). Data from the Collaborative Longitudinal Evaluation of Ethnicity and 9
Refractive Error (CLEERE) Study (n = 1,107) indicate that accommodative lag in children is not elevated until the onset of myopia (Mutti et al. 2006), which suggests that increased hyperopic blur is a consequence of myopia onset rather than a causative factor.
A study of young adults who became myopic found that they had a lower accommodative lag for a 4-D stimulus than those who were emmetropic or were already myopic
(Rosenfield et al. 2002).
Important accommodative lag measurement differences exist between the
Gwiazda et al. and Mutti et al. papers (Gwiazda et al. 2005; Mutti et al. 2006). Gwiazda et al.’s method of measuring accommodative lag required the child to do a Maddox rod alignment task while also keeping the accommodative target clear. In contrast, the
CLEERE method only required the child to keep the accommodative target clear. The
Gwiazda et al. (2005) method has been shown to result in dioptrically greater accommodative lags than the CLEERE method, possibly because of subject distraction during measurement due to the additional Maddox rod task (Omodio et al. 2005). All children were also tested with full correction in place by Gwiazda et al., even if the child was pre-myopic and did not normally wear correction, while children in CLEERE were tested with their habitual correction. This also may have elevated the amount of lag found by Gwiazda et al. Overall, there does not seem to be conclusive evidence that lag is elevated prior to the onset of myopia considering the disagreement between studies and the lack of temporal robustness of the only positive result across the pre-myopic time period. At the very least, a major discrepancy exists in the literature on this topic.
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1.3.4 Accommodative Lag and Myopia Progression
While there is no consensus regarding whether accommodative lag is elevated prior to the onset of myopia, the literature is rather clear that accommodative response is reduced after the onset of myopia (McBrien and Millodot 1986; Bullimore et al. 1992;
Gwiazda et al. 1993b; Abbott et al. 1998). There are a limited number of studies that report on the association between accommodative lag and the progression of myopia, and the results are conflicting; two report no association in children (Berntsen et al. 2007;
Weizhong et al. 2008), one reports that elevated accommodative lag is associated with myopia progression in adults (Allen and O'Leary 2006), and one reports that lower accommodative lag is associated with myopia progression in adults (Rosenfield et al.
2002).
Weizhong et al. followed 62 7- to 13-year-old myopic children in China for one year and found no correlation between either the initial accommodative lag and myopia progression or the average of the initial and final accommodative lag values and myopia progression (Weizhong et al. 2008). A similar analysis by the CLEERE Study of 534 children in grades one through eight followed over multiple years also found no association between accommodative lag and juvenile-onset myopia progression (Berntsen et al. 2007).
Rosenfield et al. also published a study examining the relationship between accommodative lag and myopia progression in adults age 21 to 27 years (Rosenfield et al.
2002). They reported a significant relationship between accommodative lag and myopia progression (R 2 = 0.25); however, the subjects with the greatest myopia progression were
11 those with the lowest accommodative lag. This result contradicts the conventional hypothesis of hyperopic retinal blur causing myopia progression.
Contrary to the results in children, Allen and O’Leary (2006) reported an association between accommodative lag and myopia progression in adults 18 to 22 years old (R 2= 0.13); however, examination of their myopia progression and accommodative lag data, estimated from Figure 3 of their manuscript (Allen and O'Leary 2006), suggests that the data do not meet the normality assumption of parametric statistical tests. If the data are log-transformed to meet this assumption, the association is no longer statistically significant (p = 0.08). The non-parametric Spearman correlation coefficient on the untransformed data does not corroborate a statistically significant correlation between myopia progression and accommodative lag (p = 0.20). Additionally, the parametric association they report appears to be driven by one outlying data point representing the subject with both the largest lag and the greatest progression. If the data are reanalyzed excluding this one subject, even using a parametric test, there is no longer a statistically significant association (p = 0.25).
1.4 Mechanical Tension Theory
The foundation for the mechanical tension theory is that there are factors that produce a larger than normal eye size in children at risk for myopia (Figure 1.1). In this theory, ciliary-choroidal tension in the anterior portion of the globe reaches a critical point when it can no longer expand with eye growth. When this critical point is reached, ciliary-choroidal resistance restricts growth in the equatorial dimension of the eye, and
12 the tension results in an increase in the amount of effort required to accommodate, thereby producing an increased accommodative lag (Figure 1.2). With equatorial growth restricted, there is accelerated axial growth that results in myopia because the crystalline lens can no longer decrease in power to compensate because equatorial growth is now restricted preventing further thinning and stretching of the lens (Mutti et al. 2000b). This critical point, when ciliary-choroidal tension restricts equatorial growth, may be the trigger for myopia onset and may also explain the observation that high accommodative lag accompanies, rather than precedes, the onset of myopia (Mutti et al. 2006).
A B C
Figure 1.2: The mechanical tension theory of myopia onset. Dashed lines represent the image shell of the corrected eye. A) Normal ocular growth with oblate globe shape and peripheral myopia. B) Increased ciliary-choroidal tension restricts equatorial growth. C) With equatorial growth restricted, axial growth continues and myopia develops. The myopic eye becomes relatively prolate shaped with peripheral hyperopia.
The increase in prevalence of myopia in children as the number of myopic parents increases suggests a genetic component (Gwiazda et al. 1993a; Wu and Edwards 1999;
Mutti et al. 2002). Genome-based evaluations have found chromosomal loci linked to familial high myopia (Young et al. 1998a; Young et al. 1998b; Naiglin et al. 2002; Paluru
13 et al. 2003); however some of these loci do not seem to play a role in developing lower amounts of myopia (Ibay et al. 2004). A study examining twins found a gene linked to myopia development (Hammond et al. 2004), while a study including low myopes also reported a susceptible locus (Stambolian et al. 2004). These results provide further evidence for models involving a hereditary predisposition to a large globe.
1.4.1 Crystalline Lens
A link between equatorial stretching and axial growth has been proposed as the cause of the decrease in crystalline lens power during ocular development (van Alphen
1961). Longitudinal data examining the crystalline lens in children indicate physical lens changes consistent with the changes described in the proposed mechanical tension model.
Video phakometry and ultrasonography performed on the crystalline lens of children participating in the Orinda Longitudinal Study of Myopia (OLSM) showed that the lens concurrently thins and flattens over time, suggesting that the lens is being stretched by equatorial ocular growth (Zadnik et al. 1995; Mutti et al. 1998). An increased response
AC/A ratio was also found in myopic children and was associated with flatter crystalline lens shapes (Mutti et al. 2000a). The mechanical tension theory suggests that the higher
AC/A ratio is due to ciliary-choroidal tension increasing the effort required to accommodate in eyes that are anatomically large and restricted from additional growth in the equatorial dimension. This hypothesis is supported by the previously mentioned finding that before the onset of juvenile myopia, children with myopic parents have longer eyes (Zadnik et al. 1994).
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1.4.2 Peripheral Refraction (Retinal Shape)
Peripheral refractive error has been described frequently in the literature as a surrogate for characterizing ocular shape (Ferree and Rand 1933; Millodot 1981; Mutti et al. 2000b; Seidemann et al. 2002; Logan et al. 2004), and it provides additional information supporting the mechanical tension theory of myopia onset and progression.
The comparison of the spherical equivalent refractive error of a peripheral retinal location to the central spherical equivalent refractive error can be used to make inferences about the relative shape of the globe. Several reports have been published that have examined peripheral refraction and its association with refractive error, particularly myopia
(Hoogerheide et al. 1971; Mutti et al. 2000b; Seidemann et al. 2002; Schmid 2003; Logan et al. 2004; Stone and Flitcroft 2004; Mutti et al. 2007) .
Peripheral autorefraction in adults has consistently shown that myopic eyes are relatively more hyperopic in the periphery of the horizontal meridian of the eye when compared to the fovea (Figure 1.2C), suggesting that the retina has a more prolate or less oblate shape in the horizontal meridian (Millodot 1981; Seidemann et al. 2002; Logan et al. 2004; Atchison et al. 2006). Adult hyperopic eyes have been found to be more myopic in the peripheral retina relative to the fovea (Figure 1.2A), indicating that hyperopic eyes have a relatively more oblate retinal shape. This suggests that different factors influence equatorial and axial growth. A decrease in the oblate shape of the horizontal meridian of the globe (or increase in relative prolate shape) as myopia increases has also been evident in MRI data (Atchison et al. 2005).
The finding of relative peripheral hyperopia in the horizontal meridian of myopic eyes (a more prolate shape) versus relative peripheral myopia in hyperopic eyes (a more 15 oblate shape) has been confirmed in children (Mutti et al. 2000b; Schmid 2003; Mutti et al. 2007). There was also an association between thinner crystalline lenses and more hyperopic relative peripheral refractions in children (Mutti et al. 2000b), providing support for the hypothesis that ciliary-choroidal tension causes restricted equatorial growth with accelerated axial growth. This type of growth would lead to the prolate eye shape of myopes. It was recently reported that children who will become myopic have a significant increase in relative peripheral hyperopia two years prior to the onset of their myopia when compared to emmetropic children and that the increased relative peripheral hyperopia remained stable after myopia onset (Mutti et al. 2007). The change in ocular shape to a relatively more prolate shape prior to myopia onset could be explained by slowed equatorial expansion due to increasing ciliary-choroidal tension that has not yet reached the critical point where equatorial expansion is no longer possible (Figure 1.2B).
The finding that accommodation causes the eye to become more prolate, with the relaxation of accommodation returning the eye to a more oblate shape, provides additional evidence that ciliary-choroidal tension is capable of influencing ocular shape
(Walker and Mutti 2002).
1.4.3 COMET 3- and 5-Year Results
The mechanical tension theory may also provide insight into the three-year findings of the COMET study in which all of the 0.20-D treatment effect of PALs appeared to occur during the first year of wear (Gwiazda et al. 2003). After the first year
PAL treatment effect, myopia appeared to progress equally in years two and three in the
PAL and single vision lens groups. Because PALs reduce accommodative effort at near, 16 it is possible that this temporarily released ciliary-choroidal tension and allowed additional equatorial growth before tension once again reached a critical point that again halted growth of the globe except in the axial direction. By adding “slack” to the system,
PALs may delay the progression of myopia by allowing additional equatorial growth until the slack is taken up and ciliary-choroidal tension once again restricts equatorial growth. This could also explain the finding that the treatment effect was greater in children with a high accommodative lag and esophoria at near (Gwiazda et al. 2004) because a higher lag would indicate more ciliary-choroidal tension.
Recent five-year COMET results, in which the original 469 children were followed in their original randomization arms, are also inconsistent with the accommodative lag theory (Gwiazda et al. 2006). Five-year COMET findings indicate that the three-year significant PAL treatment effect of 0.20 D decreased to a non- statistically significant 0.13 D at year five. The PAL treatment effect for esophores with high accommodative lags decreased from 0.64 D at year three to 0.49 D at year five. The loss of treatment effect with time can potentially be explained by the mechanical tension theory, but is certainly inconsistent with the accommodative lag theory. Overall, the mechanical tension model appears to be a plausible alternative that is consistent with ocular biometric findings and the results of myopia prevention studies.
1.4.4 Potential Sources of Ciliary-Choroidal Tension
If ciliary-choroidal tension in fact restricts equatorial growth of the eye in myopic children, then differences in the ocular component responsible for the tension differences between emmetropic and myopic eyes should be detectable. Although tension on the 17 crystalline lens as measured by post-saccadic lens oscillation has been shown to increase with age, it is not related to refractive error in children (Bailey et al. 2006; Bailey et al.
2008a). This suggests that the crystalline lens is not the source of restricted equatorial growth in myopic children. Recent work has shown that structural differences in the ciliary body are related to refractive error (Bailey et al. 2008b). Bailey at al. (2008b) recently reported that a thicker ciliary body is associated with more myopia and longer axial length in children. This relationship has also been reported in adult eyes with low to moderate myopia, although high myopes (more myopic than roughly –5.00 D) did not show this association (Ernst et al. 2008), which may be because the mechanism leading to pathological myopia is different than the mechanism that produces juvenile-onset myopia. These data provide evidence that hypertrophy of the smooth muscle that makes up the ciliary body could lead to a restriction of equatorial ocular expansion. Further work is necessary to explore whether the changes in ciliary body thickness are related to differences seen in accommodative lag in children.
1.5 Limitations of Previous Bifocal/PAL Studies
Previous studies using either bifocal spectacles or PALs to reduce the progression of myopia share similar limitations in their ability to evaluate the mechanism of myopia progression. Because the purpose of these studies was to determine the efficacy of bifocals as a myopia intervention, cycloplegic autorefraction and axial length measured by ultrasonography were the primary and secondary outcome measures in three randomized clinical trials of bifocal spectacles (Fulk et al. 2000; Edwards et al. 2002;
Gwiazda et al. 2003). The Edwards et al. Hong Kong PAL study found a two-year 0.14-D 18 effect of PAL wear on myopia progression that was not statistically significant; they also found no significant difference in axial length (Edwards et al. 2002). Axial length and central cycloplegic autorefraction were the only ocular measurements, preventing a detailed comparison of ocular changes between the groups. A study that used bifocal spectacles and followed myopic children with esophoria for 30 months found a significant treatment effect of 0.25 D (Fulk et al. 2000); however, insight into the mechanism behind myopia progression was again limited by a lack of ocular component measurements other than cycloplegic autorefraction and A-scan ultrasonography. The most recent PAL study measured cycloplegic autorefraction; however, axial length was only measured in the second half of the study (Hasebe et al. 2008). As discussed earlier,
COMET found a significant, 0.20-D treatment effect with PALs over three years that mainly occurred during the first year of wear; however, while lens thickness measurements were made using ultrasonography, no measurements of lens power, lens curvature, and ocular shape were made. Subgroup analyses of the COMET data found a significant, 0.64-D treatment effect in children with high accommodative lag and near esophoria (Gwiazda et al. 2004); however, without complete ocular biometry, the changes in the ocular components were not described fully. Without these data, it is impossible to thoroughly explain why the treatment is more effective in this subgroup.
Additionally, measurements of accommodative lag through the bifocal add were not made, preventing an analysis to accurately determine the reduction in accommodative lag caused by the PALs.
The small treatment effects, the COMET finding that the treatment effect occurs mainly during the first year of PAL wear (Gwiazda et al. 2003), and the recent COMET 19 report that the PAL treatment effect diminishes with time, even in esophores with high accommodative lags still wearing PALs (Gwiazda et al. 2006), suggest that the benefit of
PALs as a treatment to reduce myopia progression may be due to a mechanism other than accommodative lag. In order to thoroughly interpret the data, additional measurements are needed. Crystalline lens phakometry (Mutti et al. 1992) and peripheral refraction would allow for a full description of thickness and curvature changes of the lens as well as changes in retinal shape. The importance of peripheral image quality in the emmetropization process has been recently demonstrated in animal models (Smith et al.
2005; Smith et al. 2007), suggesting that it is also important to measure peripheral aberrations and the image shell induced by spectacle lenses (see section 1.7). When these measurements are combined with central cycloplegic autorefraction, axial length, anterior and vitreous chamber depth, and corneal shape and thickness, the data necessary to describe fully the changes in the eye will be available and will help determine the most appropriate model of juvenile myopia progression. Another major limitation of all of the above studies is that the permanence of the treatment effect was never measured on a suitably large, randomized sample; therefore, the long-term efficacy of bifocals is still poorly understood. Following children after removing the PAL treatment will evaluate the permanence of the treatment effect. These data will provide additional information concerning the mechanism driving myopia progression and will determine whether myopia progression is being truly prevented or merely delayed.
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1.6 Peripheral Image Quality
Although it is well established that emmetropization is visually guided, it has long been assumed that manipulations of central vision are responsible for the effects observed because resolution acuity is generally highest at the fovea and decreases in the periphery
(Stone and Flitcroft 2004). It is also known that resolution acuity in tree shrews is much lower than in humans (Petry et al. 1984), yet they can still accurately respond to defocus during emmetropization (Norton and Siegwart 1995). A role for peripheral guidance in emmetropization is supported by the observation that detection acuity in humans remains relatively high in the periphery even though resolution acuity decreases rapidly when moving from the fovea to the peripheral retina (Wang et al. 1997). Wang et al. showed that detection acuity in the periphery is rapidly decreased by small amounts of blur while resolution acuity is mainly limited by aliasing. Because detection acuity is limited by the contrast-transferring properties described by the modulation transfer function, which remains rather high in the periphery if refractive error is corrected (Artal et al. 1995;
Williams et al. 1996), detection acuity could potentially provide visual feedback regarding the location of the retina relative to the local image plane for peripheral locations of the eye.
The finding that local retinal regions respond to local visual manipulation in chicks (Wallman et al. 1987; Diether and Schaeffel 1997), tree shrews (Norton and
Siegwart 1995), and monkeys (Smith et al. 2008) also provides support for peripheral guidance of eye growth during emmetropization. A study showing that chicks raised in low-ceiling environments, causing inferior retinal hyperopic defocus, became more myopic in the upper visual field provides further evidence for the influence of local 21 defocus on emmetropization (Miles and Wallman 1990). Additional support for a role of the peripheral retina comes from a retrospective study of children with ocular-disease associated degradation of vision. Nathan et al. found that children with diseases that impaired peripheral vision or peripheral and central vision were associated with myopic refractive errors while diseases that impaired foveal vision were associated with mildly hyperopic refractive errors (Nathan et al. 1985).
Recent work involving peripheral visual manipulation in infant rhesus monkeys provides the most convincing evidence for a significant role of the peripheral visual experience in emmetropization. Smith et al. have shown that monkeys reared wearing helmets holding bilateral spectacle lenses that form-deprived the peripheral retina while allowing clear central vision through either a 4- or 8-mm aperture generally developed form-deprivation myopia (Smith et al. 2005). This suggests that central vision alone may not be adequate for emmetropization. Smith et al. also showed that the same monkeys’ eyes were still able to emmetropize after the lenses were removed and the macula ablated using an argon laser (Smith et al. 2005). This demonstrates that, at least in the absence of a functional macula, peripheral vision can guide recovery from form-deprivation.
In a subsequent experiment, it was shown that infant monkeys with the macula of one eye ablated by argon laser were able to emmetropize normally if the eye was allowed unrestricted vision or developed form-deprivation myopia if the eye was form deprived
(Smith et al. 2007). This again supports that, at least in the absence of a functioning macula, peripheral vision can guide eye growth, whether normal during emmetropization or abnormal during form deprivation. Although the visual manipulations in these experiments were during the initial emmetropization process, they suggest the importance 22 of evaluating peripheral refractive error and image quality in children with juvenile-onset myopia.
1.6.1 Predicting the Effect of Aberrations on Visual Quality
The effect of an increase in higher-order aberrations on visual quality is dependent on several factors. Applegate et al. examined the effect of fixed amounts of
RMS wavefront error on visual acuity. They found that for equal amounts of RMS error, individual Zernike coefficients did not result in equivalent losses in high- and low- contrast visual acuity (Applegate et al. 2002; Applegate et al. 2003). Additionally, they found that equal amounts of RMS error from modes near the center of the Zernike-mode pyramid resulted in greater visual reduction than modes near the edge of the pyramid.
Interestingly, some Zernike modes were found to interact with other modes in a positive manner resulting in better visual acuity than other coefficient combinations with the same total RMS error. The more substantial effect of some aberrations on visual acuity and the potential positive and negative interactions among aberrations make it difficult to predict the effect that a given amount of RMS error has on visual acuity. Additionally, higher- order aberrations have been shown to have a much greater influence on retinal image quality and visual performance as pupil size increases (Liang and Williams 1997;
Applegate 2004).
Because RMS error is a poor predictor of visual acuity and does not allow for comparisons across different pupil sizes, 33 metrics have been developed that assign a single value to image quality and can be classified into metrics of the pupil plane and metrics of the image plane. The pupil plane metrics are based upon the shape of the 23 wavefront at the plane of the pupil. The image plane metrics are composed of metrics that are based upon either the point spread function or the optical transfer function, both of which are calculated from the Zernike coefficients that describe the wavefront (Thibos et al. 2004). Several of these metrics have been reported to correlate well with high-contrast visual acuity performance (Marsack et al. 2004) and subjective judgement of best focus
(Cheng et al. 2004). The metrics of retinal image quality have also been shown to correlate best with low-contrast, mesopic visual acuity (Pesudovs et al. 2004; Applegate et al. 2006), especially in subjects with better than 20/17 Snellen visual acuity. These metrics provide a method of describing visual quality across the retina under varying pupil sizes.
1.7 Dissertation Goals
The Study of Theories about Myopia Progression (STAMP) is a two-year, double- masked, randomized clinical trial designed to evaluate the accommodative lag and mechanical tension theories of juvenile-onset myopia progression. Although clinical trials traditionally determine the efficacy of a treatment, the study design is being used in this case to allow the examination of two current theories of myopia progression. The goals of this dissertation are as follows:
1. To describe the STAMP study design and baseline characteristics of the
children enrolled;
2. To demonstrate the validity of the aberrometry-based relative peripheral
refraction measurements made in STAMP;
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3. To describe central and peripheral retinal image quality in children using a
single-valued metric; and
4. To determine the effect of bifocal add on accommodative lag.
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CHAPTER 2
STUDY OF THEORIES ABOUT MYOPIA PROGRESSION (STAMP)
2.1 Study Design
A double-masked, randomized clinical trial is being conducted to test whether high accommodative lag or mechanical tension in the ocular components is associated with myopia progression. For the first year of this two-year study, children were randomized to wear either single vision lenses (SVLs) or progressive addition lenses
(PALs) with a +2.00-D add. After the first year, all children wear SVLs for the second year of the study to determine the permanence of the PAL treatment effect and the structural changes present when accommodative effort returns to its normal state. A total of 85 children were enrolled with high accommodative lag and either: (1) low myopia (–
2.25 D spherical equivalent or less) or (2) high myopia (more myopic that –2.25 D spherical equivalent) with esophoria at near. These subgroups of myopic children have been shown to have the greatest treatment effects with PALs after one year of wear after controlling for factors that included lag, phoria, baseline myopia, treatment, gender, and age (Gwiazda et al. 2004).
Eligible children were enrolled, randomized, and are being followed at six-month intervals for two years with all children wearing SVLs for the second year. At each visit, complete measurements of the ocular components are being made to determine the 26 mechanism responsible for the PAL treatment effect and why it occurs mainly during the first year of bifocal wear (Gwiazda et al. 2003). Refractive error, axial length, peripheral ocular shape, central and peripheral higher-order aberrations, near work, accommodation, corneal shape, anterior chamber depth, crystalline lens thickness and curvatures, and phoria are being measured at six-month intervals.
Alternative study designs were considered before deciding on this clinical trial. In order to determine if a treatment effect was achieved and whether a rebound of the treatment effect occurred after switching from PALs to SVLs, a control group was necessary. An alternative clinical trial design was one in which both groups of children wore PALs for the first year before one group was switched to SVLs in the second year; however, this design would not have been adequate. First, there would be no group showing normal myopia progression to which other groups could be compared. If the group that was switched from PALs to SVLs during year two did not show an accelerated rate of myopia progression during the second year compared to the group still in PALs, it would not be possible to determine whether this occurred because a significant PAL treatment effect was not achieved in year one or because there was truly no rebound effect after switching to SVLs. Additionally, a significant rebound of the treatment effect could also be masked by a reduction in the efficacy of PALs during the second year of the study in the PAL group (i.e., a reduced treatment effect during the second year of
PAL wear resulting in an increased rate of progression in the PAL group in year two), thus making it more difficult to detect a rebound of myopia without a much larger sample size. Because the PAL treatment effect found in the COMET subgroup analysis has not
27 been replicated and because of the potential for reduced PAL efficacy during year two, this design is inefficient.
These problems are avoided with the chosen study design. By randomizing children to either SVLs or PALs during the first year, it will be possible to detect the presence of the PAL treatment effect during year one of the study. By then having all children wear SVLs in the second year, any significant rebound of the PAL treatment effect can be detected.
2.1.1 Expected Outcomes
The primary outcome measure of STAMP is central cycloplegic autorefraction as measured by the Grand Seiko WR 5100K. Cycloplegic autorefraction is measured at the baseline visit and every six months for two years. The secondary outcome measures of
STAMP are also measured every six months for two years and include complete biometric data of the human eye. The secondary outcome measures are listed in Table
2.1.
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• Phoria • Accommodative Lag • AC/A Ratio • Corneal Curvature • Corneal Thickness • Anterior Chamber Depth and Vitreous Chamber Depth • Intraocular Pressure • Crystalline Lens Curvature • Crystalline Lens Thickness • Crystalline Lens Power • Retinal Shape via Peripheral Autorefraction • Central and Peripheral Aberrations • Axial Length • Near Work • Outdoor Activity
Table 2.1: STAMP secondary outcome measures
A reduction in myopia progression is expected in the PAL group after year one based on both progression models (Figure 2.1). During year two when both groups wear
SVLs, the accommodative lag theory predicts equal rates of myopia progression (i.e., no loss of the treatment effect) for both the PAL and SVL groups. The mechanical tension theory predicts a loss of the treatment effect in the PAL group after being switched to
SVLs (i.e., a greater progression rate in the PAL group than in the SVL group during the second year). A loss of treatment effect would suggest that an increase in ciliary- choroidal tension was present once accommodative effort was restored to its normal state when the PALs were removed; however, to understand fully whether mechanical tension or hyperopic defocus due to accommodative lag drives myopia progression, the ocular component measurements must be considered.
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-1.50 SVLs only
-1.25 PALs to SVLs- Tension Theory -1.00 PALs to SVLs- Lag Theory -0.75
-0.50
-0.25
0.00 Myopia ProgressionMyopiain Diopters
0.25 Baseline Year 1 Year 2
Figure 2.1: Hypothesized progression of myopia based on the mechanical tension theory and the accommodative lag theory.
The expected outcomes after the first year of randomization to either SVLs or
PALs and after the second year, when all subjects wear SVLs, are listed in Table 2.2 for each theory of juvenile myopia progression. Both models predict that axial length will increase less in the PAL group compared to the SVL group after one year, consistent with previous studies (Gwiazda et al. 2003). During year two when both groups will wear
SVLs, the accommodative lag theory predicts equal amounts of axial length growth (i.e., no loss of the treatment effect) for both the PAL and SVL groups. Because accommodative lag returns to normal after being switched from PALs to SVLs, there is no reason to expect the original PAL group to accelerate axial growth to a rate that is greater than that of the SVL group. The mechanical tension theory predicts a loss of the treatment effect in the PAL group after being switched to SVLs (i.e., a greater axial length growth in the PAL group during the second year).
30
Control Experimental Group Year 1 Experimental Group Year 2 Group (PALs for 1 st year) (PALs to SVLs at start of year 2) (SVLs only) Outcome* SVL group Tension Theory Lag Theory Tension Theory Lag Theory at year 1 vs. PALs at 1 year PALs at 1 PAL group now PAL group itself at vs. SVLs at 1 year vs. in SVLs vs. now in SVLs baseline year SVLs at 1 SVL control vs. SVL year group control group Refractive error Normal Reduced Reduced Accelerated Same rate as (cycloplegic progression increase control autorefraction) (Rebound) (No rebound) Axial length Increase Less increase Less increase Accelerated Same rate as increase control (Rebound) (No rebound) Retinal Shape Prolate Less prolate Superior / Prolate Same as (Relative inferior (More prolate control or peripheral asymmetry compared to reduced autorefraction) self at end of superior / year 1) inferior asymmetry AC/A with High but Lower Same as Same as control Same as distance stable with control (Increase control correction time compared to self at end of year 1) Phakometry No change Slightly flatter Same as Slightly flatter Same as lens control (No change control compared to self at end of year 1) Lens thickness No change Slightly thinner Same as Slightly thinner Same as lens control (No change control compared to self at end of year 1) *Primary and secondary outcome measures are included. Other measurements that will be made but are not included in this table are corneal shape, central and peripheral aberrations, IOP, anterior and vitreous chamber depth, crystalline lens power, and accommodative lag. These measurements are included for completeness of the biometric data.
Table 2.2: Expected outcomes for the accommodative lag theory and the mechanical tension theory.
Retinal shape measurements combined with phakometry and lens thickness measurements will determine if there is a decrease in mechanical tension when PALs are worn and if this mechanical tension increases after the PAL group is switched to SVLs 31 during year two of the study. In the accommodative lag theory, no symmetric changes in retinal shape or any differences in crystalline lens thickness or curvature are expected in the PAL group compared to the SVL group because the theory is based on hyperopic blur driving myopia progression. In the mechanical tension theory, changes in these ocular components due to tension changes are expected in the PAL group compared to the SVL group.
In the mechanical tension theory, because PALs decrease accommodative effort, ciliary-choroidal tension created by accommodation will be decreased. If the source of equatorial restriction is primarily from ciliary-choroidal tension, the crystalline lens should be able to stretch as the equator expands, causing flattening and thinning of the lens at the end of year one in the PAL group. In this case, the crystalline lens would remain thinner and flatter at the end of year two in the PAL group after being switched to
SVLs because of the additional equatorial expansion during the first year of the study.
The outcomes in Table 2.2 show possible changes in the crystalline lens based on the assumption that the source of tension is primarily the ciliary muscle; however, because
COMET did not find a significant change in crystalline lens thickness during myopia progression in either SVLs or PALs (Gwiazda et al. 2003), it is possible that either the mechanical tension theory is wrong, or that lens thickness changes, if they exist, are below the repeatability of A-scan ultrasonography. Therefore, it will be important to also evaluate other biometric measurements, such as retinal shape, that can aid in the determination of whether mechanical tension or retinal blur cause the PAL treatment effect.
32
Expected retinal shape changes differ between the two theories. In the accommodative lag theory, either no change in retinal shape will be found throughout the study in the PAL group compared to the SVL group, or there will be a superior/inferior refraction asymmetry. Chicks reared in environments with a low ceiling, resulting in differences in superior/inferior retinal blur, have been shown to have superior/inferior asymmetric retinal growth (Miles and Wallman 1990). Regional lens-induced defocus in monkeys has also recently been shown to result in regional retinal growth (Hung et al.
2009). Therefore, if hyperopic retinal blur induces elongation as proposed in the lag theory, it may also be possible to detect less relative myopia in the superior retina compared to the inferior retina in the PAL group, because the add on the inferior part of the PAL reduces hyperopic defocus on the superior retina (Figure 2.2). This type of asymmetry would support the lag theory. In the mechanical tension theory, relieving accommodative effort with a PAL is expected to result in less restriction to equatorial growth and to create a relatively more oblate shape when compared to the control group after the first year of PAL wear (Figure 2.3). Once the PAL group is switched to SVLs, this theory predicts a relative increase in the prolate shape of the retina because restoring accommodative effort will again result in equatorial restriction to growth.
33
While wearing PALs After switching back to Baseline image (Year 1) SVLs (Year 2) shells (solid line) Superior/inferior asymmetry Same as control or reduced by correction type superior/inferior asymmetry
SVL
-Black dashed line -Black dashed line PAL represents relative represents relative peripheral refraction peripheral refraction
Figure 2.2: Expected retinal shape outcomes for the accommodative lag theory of myopia progression. Solid lines represent the vertical retinal image shell. Dashed lines represent relative peripheral refraction in the vertical meridian.
While wearing PALs After switching back to SVLs (Year 1) (Year 2) Relatively more oblate Relatively more prolate Baseline (reduced peripheral hyperopia) (increased peripheral hyperopia)
Figure 2.3: Expected retinal shape outcomes for the mechanical tension theory of myopia progression. Dashed lines represent relative peripheral refraction in the horizontal meridian.
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The AC/A ratio can also differentiate between these models of myopia progression. The accommodative lag theory does not predict a change in the AC/A ratio with PAL wear because this theory is not based on structural changes in the globe. The mechanical tension theory predicts a relative decrease in the AC/A ratio in the PAL group after year one relative to the control group because relieving ocular tension should reduce the stress on accommodative convergence. After the PAL group is switched to SVLs in year two, the tension theory would predict a relative increase in the AC/A ratio compared to the year of PAL wear because mechanical tension would again result in more ciliary- choroidal tension.
A reduction in optical quality due to higher-order aberrations has been suggested as possible support for the lag theory because myopic eyes have greater higher-order aberrations (He et al. 2002). Research showing that higher-order aberrations increase with accommodation has also been cited as support for the lag theory because bifocal wearers would be exposed to lower levels of aberrations and optical degradation when focusing at near (He et al. 2000); however, it is unclear why accommodation-induced aberrations would only cause myopia in some children. There are currently no studies that have examined peripheral aberrations in children. Central and peripheral aberration data will be collected at each six-month visit in STAMP. Using metrics of retinal image quality that have been shown to predict visual performance (Marsack et al. 2004;
Applegate et al. 2006), higher-order aberrations will be examined to determine if retinal image quality differences exist between the PAL and SVL groups.
Ultimately, the complete biometric data collected over the course of this two-year clinical trial will differentiate between the mechanisms resulting in myopia progression. 35
While no single measurement will provide conclusive support for either theory, the combined results from the measurements discussed will allow us to determine which model best explains the changes in the ocular components.
2.1.2 STAMP Enrollment Criteria and Randomization
The STAMP enrollment criteria are listed in Table 2.3. Children were between the ages of 6 and 11 years at the time of enrollment to ensure that at the end of the study they are still younger than the average age at which myopia progression has been reported to cease (Goss and Winkler 1983). Children with a high accommodative lag had the greatest
PAL treatment effect in COMET (Gwiazda et al. 2004). For study entry, high accommodative lag was defined as “greater than a median split” of data from the
CLEERE Study, the same criterion used to define high accommodative lag in COMET.
COMET defined high accommodative lag as anything greater than the median split of their lag data ( ≥0.43 D) for a 3-D accommodative target at enrollment (Gwiazda et al.
2004). When examining accommodative lag data from 312 myopic children in the
CLEERE Study measured with the Grand Seiko WR 5100K autorefractor, the same instrument being used in this study, the median split lag for a 4-D accommodative demand was 1.30 D. The median COMET lag is most likely less than the CLEERE median lag due to variations in technique and instrumentation as described earlier in section 1.3.3 (Omodio et al. 2005). Because the CLEERE protocol will be used to measure lag in this study, the definition of high accommodative lag was set using the
CLEERE median split for a 4-D accommodative stimulus.
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• 6 to 11 years of age • ≥ 1.30 D accommodative lag (4D stimulus) without correction for lens effectivity • Esophoria at near if more than –2.25 D spherical equivalent (high myopia) • At least –0.75 D myopia in each meridian measured with cycloplegic autorefraction but not more than –4.50 D in each meridian in each eye • Astigmatism < 2.00 DC in each eye • Anisometropia < 2.00 D • No strabismus • No history of contact lens wear • No previous bifocal wear • Best corrected VA of at least 20/32 logMAR equivalent • Birth weight > 1250g by parental report • No diabetes mellitus
Table 2.3: Study enrollment criteria
Myopic children with a high accommodative lag and near esophoria had the greatest three-year treatment effect in COMET (0.64 D). Children with high accommodative lag and low myopia (–2.25 D or less spherical equivalent myopia) had a three-year treatment effect of 0.48 D (Gwiazda et al. 2004). These two subgroups also had the greatest statistically significant one-year PAL treatment effects of 0.39 D and
0.28 D respectively after controlling for age, gender, ethnicity, baseline myopia, phoria, treatment, and lag. By only including these two subgroups of myopic children, the PAL treatment effect will be enhanced. CLEERE data show that the prevalence of children with accommodative lag greater than the median split for a 4.00-D stimulus and either low myopia or high myopia with esophoria at near is 44%.
All myopia measures are based on cycloplegic autorefraction. The upper limit of myopia was set at –4.50 D in each meridian to prevent inclusion of children with high, progressive myopia, which has different genetic markers than common myopia (Ibay et al. 2004). The lower limit of myopia was set at –0.75 D in each meridian to ensure that 37 the child’s uncorrected visual acuity was reduced enough to promote full-time spectacle wear. Up to two diopters of astigmatism and anisometropia were allowed to make the study results more generalizable to myopic children. There is no evidence that the amounts of astigmatism and anisometropia selected have any effect on the amount of myopia progression.
Prior to determining eligibility, parents provided informed consent and children provided verbal assent. The protocol was approved by the Biomedical Sciences
Institutional Review Board at The Ohio State University. All children who met the eligibility criteria were enrolled in the study and randomized to a treatment group after the baseline examination was completed. A web portal was used to administer the randomization, and the group assignment was not accessible until after key examination information confirming eligibility was entered via the web portal. Block randomization using random, even block sizes ensured that an equal number of children were randomized to each group while preventing the examiner from predicting the next assignment. After randomization, all outcome data are collected by an examiner masked to the treatment assignment.
2.1.3 Sample Size Considerations
A PAL treatment effect in year one of the study is necessary in order to test for the primary outcome in year two, which is whether a significant rebound of the treatment effect occurs after switching the PAL group to SVLs as measured by cycloplegic autorefraction. Achieving a PAL treatment effect in year one can reasonably be expected based on the COMET result. In general, myopia in children progresses at an average rate 38 of –0.50 D per year (Goss and Winkler 1983; Fulk et al. 2000; Gwiazda et al. 2003) with a standard deviation of ±0.25 D (Goss and Winkler 1983; Goss and Cox 1985; Goss
1986); however, the mean one-year progression rate reported for the subgroup of children in COMET who wore SVLs and had a high accommodative lag with either low myopia or high myopia with esophoria at near was higher than the typically reported rate of myopic progression. In this subgroup, COMET reported an average one-year progression rate of –0.69 D in the SVL group and –0.38 D in the PAL group, a 0.31-D treatment effect (Gwiazda et al. 2004). Although the standard deviation of the one-year progression rate of –0.69 D for children wearing SVLs in this subgroup was not reported, it can be reasonably estimated by proportionally scaling other known one-year standard deviations of progression.
Using the classically reported yearly progression rate of –0.50 D ± 0.25 D described above, the standard deviation of 0.25 D can be proportionally increased to estimate the standard deviation for a progression rate of –0.69 D, which is 38% greater than –0.50 D. By doing so, the estimated one-year standard deviation for a rate of progression of –0.69 D is 0.35 D. The same answer can also be found by proportionally scaling a one-year standard deviation of progression for children with a higher rate of myopia progression. Children wearing soft contact lenses in the Contact Lens and
Myopia Progression (CLAMP) Study had a rate of myopia progression higher than the traditionally reported rate. Although only the three-year rates of myopia progression were published (Walline et al. 2004), the one-year rate of progression of the 57 children randomized to wear soft contact lenses during the first year of the study was calculated to be –1.19 D ± 0.63 D (Walline and Jones, personal communication). A progression rate of 39
–0.69 D is 58% of –1.19 D; therefore, the CLAMP standard deviation of 0.63 D can be proportionally scaled down to give a standard deviation of 0.37 D, which is similar to the estimated standard deviation of 0.35 D.
COMET found a 0.31-D (45%) one-year PAL treatment effect in children with high accommodative lag and either low myopia or high myopia with esophoria at near
(Gwiazda et al. 2004). A sample size of 36 children per group is sufficient to detect a clinically significant PAL treatment effect in year one and a rebound in year two of 0.25
D with 80% power and α=0.05 based on an average progression rate of –0.69 D ± 0.37 D per year. After adjusting for an estimated loss to follow-up of 15%, it was necessary to enroll a total of 84 children. Based on the CLEERE Study prevalence of 44% for children with high accommodative lag and either low myopia or high myopia with esophoria at near, 190 children needed to be screened.
2.1.4 Recruitment and Retention
Many methods were utilized to recruit myopic children. Letters were sent to all elementary schools, public and private, in the Columbus area. The letters were sent home addressed to the parents of children who wear spectacles. Although this method identifies a few high hyperopes and high astigmats, most of the school-aged children wearing glasses are, in fact, myopes. Telephone screening of respondents was used to minimize the in-person screening of non-myopes.
In addition, children who met the age requirement and were coded as myopes during their visit to The Ohio State University Optometry Clinics one year prior to the start of enrollment and each month thereafter during enrollment were sent a letter with
40 information about the study. Information was also placed in the local area home school network newsletters, and advertisements were placed in local community newspapers.
Pamphlets were given to new subjects when they came in to be screened to distribute to their friends with children. Recruitment posters were also posted in area libraries and community recreation centers.
To minimize subject loss throughout the course of the study, birthday cards containing a gift card are sent to the enrolled children on their birthday. Snacks and other small trinkets are given out at each visit as well.
2.1.5 Masking, Crossovers, and Data Entry
Examiners collecting outcome data are masked to the children’s treatment group assignments. Masked examiners are required to read the STAMP Manual of Operations that outlines the protocol for each test, show proficiency in each test, and be certified before seeing study patients.
The examiner enrolling children (Dr. Berntsen) is not masked to the randomization assignment so that he is able to interact fully with the children and their parents to address problems throughout the study such as lost or broken spectacles and problems adapting to PALs. Before any patient sees the masked examiner, the unmasked examiner stresses the importance of not discussing the glasses the child currently wears or previously wore with the masked examiner. Examiners are trained to avoid asking questions that may unmask a child’s treatment and to notify Dr. Berntsen immediately if a child’s treatment is inadvertently revealed. To statistically evaluate whether masking
41 was successful, examination forms have a question at the end for the examiner to guess which modality the child was wearing and the level of certainty of the guess.
Strict protocols are established in the STAMP Manual of Operations. The Data and Safety Monitoring Committee (DSMC) must be consulted before allowing a child to change treatment assignments for any reason, such as binocular vision problems. The
DSMC makes the final decision on any changes allowed. All data analyses will occur according to the original treatment assignments.
Data entry is performed by personnel in the Optometry Coordinating Center
(OCC) at The Ohio State University College of Optometry. A database was created for this project. All data are dual entered to ensure accuracy, and matching entries are required before the data can be analyzed.
2.1.6 Spectacles
Once randomly assigned to wear either SVLs or PALs, each child was provided with a pair of spectacle lenses manufactured in polycarbonate material and a spectacle frame. PAL lenses with a +2.00-D add were chosen because the COMET Study found a significant treatment effect with this add power (Gwiazda et al. 2003). Another study showed a +2.00-D add to be more effective than a +1.50-D add in slowing myopia progression (Leung and Brown 1999). PALs were fitted with the top of the PAL corridor at least 2.0 mm above the pupil to promote the use of the bifocal portion of the lenses.
Children and parents were required to agree that the study glasses would be worn at all times. Should the study glasses be lost or broken, parents were instructed to contact the
STAMP coordinator’s office immediately for replacement of the spectacles. 42
2.1.7 Data and Safety Monitoring Committee
The Data and Safety Monitoring Committee consists of four members with clinical trial experience, all external to the project. The DSMC is chaired by Mark
Bullimore, MCOptom PhD from The Ohio State University College of Optometry. The other DSMC members are Leslie Hyman, PhD from SUNY Stony Brook, Mel
Moeschberger, PhD, Professor Emeritus in Ohio State’s College of Public Health, and
Stephen Mandel, a Senior Statistical Data Analyst from the Washington University in St.
Louis Division of Biostatistics. The DSMC monitors study outcomes and provides recommendations about subject safety and data analysis issues.
2.1.8 Planned Data Analysis (Year 1 and Year 2 Data)
A traditional intent-to-treat analysis in which all subjects are analyzed in their original treatment group will be performed. The primary outcome is whether a rebound of the PAL treatment effect in year two is detected as measured by cycloplegic autorefraction. A repeated-measures analysis of variance (ANOVA) will be used to determine if there are differences in myopia progression rates between the two groups after years one and two of the study. Significant differences will be evaluated using appropriate post hoc t-tests. This analysis will show whether a treatment effect is present after year one and will determine if a rebound is present during year two when each model of myopia predicts a different outcome. Analysis of myopia progression as a function of the secondary outcome variables will determine which variables are related to the treatment effect. By determining which ocular component changes are related to the 43 treatment effect, the accommodative lag theory and the mechanical tension theory can be evaluated to determine which myopia progression model is better.
Using univariate regression analyses, myopia progression will be modeled as a function of each potential covariate (i.e., near work, outdoor activity, age, gender, and initial refractive error) and each ocular biometric factor. This will determine which variables explain the variance in the data and therefore should be included in the next step of data analysis. Regression models will be created using the myopia progression rate for the first year, the progression rate for the second year, and the difference between the progression rates for the first and second years.
Attention will be given to the ocular biometric values of peripheral refraction and accommodative lag because they are central to the two models of myopia progression being evaluated. Because peripheral refraction describes retinal shape and ocular tension, this ocular component variable will allow us to evaluate the mechanical tension theory.
Because accommodative lag describes the amount of hyperopic retinal blur, this variable will allow us to evaluate the accommodative lag theory.
After determining the covariates and ocular biometric factors that explain a significant amount of the variance of myopia progression, multivariate regression models will be built to determine the confounding effects of any ocular component measures. We will evaluate whether a factor is confounded by evaluating if a factor that was significant in the univariate analysis loses its ability to explain the data variance or loses statistical significance when other factors are added to the model. In this way, we will allow lag of accommodation and retinal shape to “compete” to determine which model of myopia progression best explains the changes found in myopia progression. 44
2.2 Measurement Methods
A brief description of the methods used to measure each outcome listed in Table
2.1 is provided below. For a detailed description of the measurement protocols, the
STAMP Manual of Procedures can be found in Appendix A. Study forms used during data collection can be found in Appendix B.
2.2.1 Autorefraction
Central spherical equivalent refractive error measured with autorefraction under cycloplegia is the primary outcome in STAMP. Autorefraction is performed using the
Grand Seiko WR 5100K autorefractor 30 minutes after instilling the first drop of 1% tropicamide. To ensure that accommodation is not stimulated, a 6-D Badal lens is used to simulate distance viewing. A reduced Snellen chart is moved inward from beyond the far point until the top line is clear. Ten valid autorefractor readings are obtained after eliminating spurious readings. Spurious readings are those in which the reading differs
±5.00 D or more from the mode sphere value or by 1.00 D or more than the mode cylinder value. The readings are averaged using the Thibos power vector method (Thibos et al. 1997).
2.2.2 Cycloplegia and Pupillary Dilation
Cycloplegia with 1% tropicamide is used due to its short duration of action and low side effect profile. Although tropicamide provides poorer cycloplegia after 30 minutes than cyclopentolate after 60 minutes, using tropicamide has a minimal effect on 45 the measurement of distance refractive error and the ocular components (Mutti et al.
1994).
2.2.3 Phoria
Because studies have found the intra- and inter-examiner repeatability of the modified Thorington method to be superior to the objective cover test for measuring phoria (Rainey et al. 1998; Reuter et al. 1999), the modified Thorington method is used to assess phoria in this study. To check for a tropia, unilateral cover test is performed at distance with best-correction in place and at near with best correction with and without a
+2.00-D add.
2.2.4 Accommodative Lag and Response AC/A Ratio
Measurements of accommodative response (lag of accommodation) are made monocularly using the Grand Seiko WR 5100K autorefractor. At each visit, accommodative response of the right eye through the habitual correction is measured at three stimulus levels: 0.00 D, 2.00 D and 4.00 D. The child fixates the letter target viewed through a 6-D Badal lens with the right eye while the left eye is occluded with an infrared lens. The letter target is moved to the appropriate location on the Badal track for each demand level, and five readings are made at each accommodative demand. The position of the left eye is measured simultaneously through an accessory camera mounted onto the Grand Seiko. This camera photographs the positions of Purkinje images I and IV as a measure of eye position at the three levels of accommodation. The change in accommodative response per unit change in eye position yields the AC/A ratio. Each 46 subject is calibrated by measuring the change in the positions of these images for a 10° eye movement prior to measurement.
In addition to the accommodative response measurements made through the habitual correction at each visit, accommodative response for a 4.00-D Badal stimulus is also measured through other correction types. At the baseline visit, additional measurements of accommodative response are made through the manifest refraction determined at that visit and through the manifest refraction with a +2.00 D add. At the 6- month and 12-month visits, additional accommodative response measurements are made through both the child’s habitual correction with a +2.00 D add as well as the manifest refraction and the manifest refraction with a +2.00 D add. Measurements during the first year are made with and without the +2.00 D add in order to preserve masking of the examiner. At the 18-month and 24-month visits, accommodative response is measured through the habitual and manifest corrections only (i.e., no measurements with a +2.00 D add are performed at these visits).
2.2.5 Corneal Topography / Pachymetry
The Humphrey Atlas Corneal Topography System Model 993 (Carl Zeiss Meditech,
Dublin, CA) is being used to measure corneal topographical data. Atlas topography measurements have been shown to be accurate and repeatable in children (Jeandervin and
Barr 1998; Chui and Cho 2005). The Visante anterior segment Optical Coherence
Tomographer (Carl Zeiss Meditech, Dublin, CA) measures full corneal pachymetry.
Pachymetry measurements with this instrument have good repeatability (Mohamed et al.
2007). 47
2.2.6 Tonometry
Intraocular pressure (IOP) is measured using a hand-held Tonopen applanation tonometer. The tip of the device is covered by a latex cover and applanates the anesthetized cornea. The tonometer calibration is checked daily. Children fixate on a target across the room after being anesthetized with 0.5% proparacaine.
2.2.7 Central and Peripheral Aberrometry
The Complete Ophthalmic Analysis System for Vision Research (COAS-VR;
AMO WaveFront Sciences, Albuquerque, NM) is an open field aberrometer, and it is used to measure central and peripheral higher-order aberrations. The COAS is a validated
Shack-Hartmann aberrometer (Cheng et al. 2003). Before dilation drops are instilled, a measurement of the child’s photopic pupil size is made using the COAS. All central and peripheral aberrometry measurements are made after cycloplegia. Nine central measurements of the right eye are made while the child views a fixation target. The child then turns his or her head to view fixation targets located 30°nasally and 30° temporally.
The child turns his or her eye to view targets located 30º superiorly and 20°inferiorly.
Zernike coefficients are calculated following ANSI Z80.28 standards (American National
Standards Institute 2004). At all visits after randomization, regional aberrometry measurements of the child’s right spectacle lens are made at locations on the lens corresponding to each of the five retinal points measured by cycloplegic aberrometry.
The spectacles are mounted in front of a model eye for these measurements.
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2.2.8 Relative Peripheral Refraction
Central and peripheral cycloplegic autorefraction values are obtained from each child’s cycloplegic COAS measurements described above. Retinal shape is determined by calculating the difference in spherical equivalent refractive error between the central and the peripheral spherical equivalent. The COAS has been shown to perform as a repeatable and accurate autorefractor (Salmon et al. 2003), and relative peripheral refraction measurements with the COAS have been validated again those determined by autorefraction (Berntsen et al. 2008). Regional aberrometry measurements of each child’s spectacle lens are combined with the child’s cycloplegic aberrometry measurements to determine the relative peripheral refraction experienced by the child when wearing his or her STAMP glasses.
2.2.9 Video Phakometry
Video phakometry is measured using a custom system (Mutti et al. 1992). The size of a reflected LED image is proportional to the radius of curvature of the reflecting surface. To measure lens radii of curvature, a comparison of the separations of pairs of
Purkinje images I (cornea), III (anterior lens surface), and IV (posterior lens surface) to values from calibration on steel balls of known radius yields radii of curvature in air for each of these surfaces. Calculations transform these raw values in air to radii of curvature in the eye. Additionally, the calculations yield an individual equivalent index of refraction for the crystalline lens.
This measurement is made after cycloplegia with 1% tropicamide. One eye is occluded while the other fixates a red LED. Video recordings of these images are 49 digitized by frame-grabbing software and image processing software determines the distance between each of the Purkinje images. This technique of measuring lens curvature is more repeatable and valid than methods utilizing still photography or indirect calculations (Mutti et al. 1992). Tropicamide has been shown to provide adequate cycloplegia for this measurement (Mutti et al. 1994).
2.2.10 A-scan Ultrasonography
Crystalline lens thickness is measured using A-scan ultrasonography, which has good repeatability (Zadnik et al. 1992). This procedure requires corneal anesthesia, cycloplegia, and mydriasis for accurate measurement. The procedure is performed after cycloplegia with 1% tropicamide and corneal anesthesia with 0.5% proparacaine. Five readings are collected and averaged.
2.2.11 Interferometry
Partial coherence interferometry will be performed using the Zeiss IOLMaster
(Carl Zeiss Meditech, Dublin, CA ) to measure the anterior chamber depth and axial length of the eye. The IOLMaster was chosen because it is more repeatable than A-scan ultrasonography (Carkeet et al. 2004; Sheng et al. 2004). Because the cornea is not applanated in this procedure, axial length measurements are not altered during the measurement. Five measurements will be made using the instrument.
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2.2.12 Near Work and Outdoor Activity Assessment
A determination of the amount of near work and outdoor activity that each child typically does is assessed at each visit using a modified version of the near work questionnaire utilized in the CLEERE Study. The survey is completed by the parent or guardian accompanying the child at the visit. A copy of the survey can be found in
Appendix B. Diopter hours is a composite variable that weights near activities by the assumed accommodative demand for the task. Diopter hours is calculated as follows: 3 x
(hours studying + hours reading for pleasure + hours playing handheld electronic games)
+ 2 x (hours playing video games + computer hours) + (hours watching television).
2.2.13 Parental History of Myopia
Parental history of myopia was assessed using a survey at the baseline visit using previously validated methods (Walline et al. 1996). The parent present was asked to answer questions about each of the child’s biological parents that included the parent’s year of birth, if the parent wears glasses, when the parent first started wearing glasses, if the glasses are bifocals, and whether the glasses are needed for distance work, near work, or both. Using these answers, the number of myopic parents was calculated. A parent was considered myopic if glasses were reported to be primarily for distance work or if glasses were reported to be equally important for both distance and near work and were first prescribed before the age of 17 years.
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2.2.14 Non-Outcome Measurements/Procedures
To provide comprehensive eye care, a complete case history, visual fields, near point of convergence, extraocular motilities, phorometry, and pupillary testing are performed annually. Snellen visual acuity is performed at each visit. An examiner performs a standardized, most plus to maximum visual acuity manifest refraction including a binocular balance at each visit to determine the child’s glasses prescription. A comprehensive slit lamp and internal ocular health examination is performed annually.
The standard of care is followed to manage pertinent findings.
2.3 Baseline Characteristics
STAMP is currently ongoing and is due to be completed in the summer of 2010.
Because data collection for the clinical trial is still in progress, outcome data are not included, and all study-related findings are confidential. Baseline characteristics of the children enrolled in STAMP are reported in this dissertation.
2.3.1 Baseline Data Statistical Methods
Statistical analyses were performed using STATA 9.2 (StataCorp; College
Station, TX) and SPSS 16.0 (SPSS, Inc.; Chicago, IL). Comparisons between children in the PAL and SVL treatment groups were performed using two-sample t-tests, chi-square tests, and F-tests.
52
2.3.2 Baseline Characteristics
Enrollment began in December 2007 and was completed in May 2008. Over 17 months, 192 children were screened, and 85 (44%) were eligible and enrolled (Figure
2.4). Of the children enrolled, 42 were randomly assigned to wear PALs and 43 were assigned to wear SVLs.
Screening/Baseline Visit (n=192)
Randomization (n=85)
Progressive Addition Lenses Single Vision Lenses (PALs) (SVLs) (n=42) (n=43)
6-Month Visit 6-Month Visit
12-Month Visit 12-Month Visit
All wear SVLs during year 2
18-Month Visit
24-Month Visit
Figure 2.4: Flowchart of STAMP visits and randomization. 53
The age of children at the enrollment visit ranged from 6 to 11 years with a mean
(± SD) of 9.3 ± 1.4 years, and 44 (52%) were female. The mean cycloplegic spherical equivalent refractive error was –1.97 ± 0.79 D, and the mean axial length was 24.17 ±
0.80 mm. The mean (± SD) accommodative lag for a 4-D Badal stimulus measured with full manifest correction was 1.71 ± 0.37 D and ranged from 1.18 D to 2.85 D.
Accommodative lag values were not corrected for lens effectivity when determining eligibility; therefore, the minimum effectivity-corrected lag value is less than 1.30 D. Of the 85 children enrolled, 10 (11.8 %) children had an accommodative lag value that is less than 1.30 D after correcting for lens effectivity, and the ten children are split equally between the treatment groups (i.e., 5 in the PAL group and 5 in the SVL group). The lowest amount of accommodative lag for a 4-D stimulus at baseline (1.18 D) is markedly greater than the definition of high accommodative lag in the COMET study ( ≥ 0.43 D) for a 3-D stimulus (Gwiazda et al. 2004).
Of the children enrolled, 54 (64%) were esophoric at near at the baseline visit.
Randomization was stratified by whether the child was esophoric at near. Of the 54 children with esophoria at near, 28 were randomly assigned to wear single vision lenses and 26 were assigned to wear PALs. Of the 31 children who were not esophoric at near,
15 were randomly assigned to wear single vision lenses and 16 were assigned to wear
PALs. There was no imbalance between treatment groups in the number of children with and without esophoria at near (p = 0.76; chi-square test). The race and ethnicity distribution of the children is shown in Table 2.4.
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Race (Ethnicity) Number of Children (Percent) African American (Hispanic) 1 (1.2%) Caucasian (Hispanic) 3 (3.5%) Other (Hispanic) 1 (1.2%) African American (Not Hispanic) 18 (21.2%) Asian (Not Hispanic) 6 (7.1%) Caucasian (Not Hispanic) 53 (62.4%) Other (Not Hispanic) 3 (3.5%)
Table 2.4: Race and ethnicity distribution of children enrolled in STAMP.
With the exception of aberrometry and survey outcomes, summary statistics for the primary and secondary outcomes at baseline are shown in Table 2.5, and baseline characteristics stratified by treatment group are shown in Table 2.6. Aberrometry-based outcomes can be found in Chapter 4. Balance between the treatment groups was determined using t-tests, chi-square tests, and F-tests, where appropriate. There was no imbalance between the treatment groups for the primary outcome variable (central cycloplegic spherical equivalent refractive error; p = 0.38). Imbalance between treatment groups was present for axial length (p = 0.019) and steep corneal keratometry (p =
0.038). The mean axial length of children in the SVL group at baseline was longer and the mean steep keratometric value was flatter than children in the PAL treatment group.
These variables will be controlled for in all outcome analyses.
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Mean ±±± SD Minimum Maximum OD M (Spherical Equivalent) -1.95 D ± 0.78 D -4.02 D -0.83 D OD J 0 +0.08 D ± 0.21 D -0.42 D 0.89 D OD J 45 -0.14 D ± 0.16 D -0.51 D +0.23 D OS M (Spherical Equivalent) -1.99 D ± 0.78 D -4.20 D -0.91 D OS J 0 +0.10 D ± 0.20 D -0.40 D +0.85 D OS J 45 -0.17 D ± 0.18 D -0.60 D +0.19 D Accommodative Lag 1.71 D ± 0.37 D 1.18 D 2.85 D (4-D Stim w/ full Manifest) Axial Length OD (mm) 24.17 ± 0.80 22.36 27.36 Near Phoria ( ∆; + = eso) 0.72 ± 4.23 -16 17 AC/A^ 8.83 ± 3.41 3.12 19.40 Flat Keratometry 43.45 D ± 1.61 D 39.69 D 47.16 D Steep Keratometry 44.20 D ± 1.61 D 39.90 D 47.56 D Intraocular pressure (mmHg) 16.9 ± 2.9 11 24 Corneal pachymetry ( µm) 536.3 ± 31.3 446.3 622.7 Crystalline lens φ Thickness (mm) 3.34 ± 0.20 2.08 3.71 Index of refraction 1.428 ± 0.008 1.414 1.450 Radius of curvature Anterior (mm) 12.28 ± 1.17 9.31 14.87 Posterior (mm) 6.44 ± 0.54 5.37 7.96 Relative peripheral refraction 30º nasal retina +0.56 D ± 0.59 D -0.48 D +2.20 D 30º temporal retina +0.61 D ± 0.77 D -1.53 D +2.98 D 30º superior retina -0.36 D ± 0.92 D -1.99 D +2.39 D 20º inferior retina -0.48 D ± 0.84 D -3.14 D +2.04 D ^ AC/A values filtered if accommodative response is less than 1 diopter for a 4-D stimulus and if AC/A is greater than 20 (n = 69) φ Phakometry data missing on two children due to error with data recording tape (n = 83)
Table 2.5: Summary statistics for primary and secondary outcomes at baseline.
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SVL Group (n=43) PAL Group (n=42) p-value* Age (years) 9.49 ± 1.45 9.10 ± 1.23 0.18 Male (# children) 22 19 0.59 Female (# children) 21 23 OD M (Spherical Equivalent) -2.03 D ± 0.89 D -1.88 D ± 0.66 D 0.38 OD J 0 +0.09 D ± 0.20 D +0.07 D ± 0.21 D 0.61 OD J 45 -0.13 D ± 0.18 D -0.15 D ± 0.13 D 0.56 OS M (Spherical Equivalent) -2.04 D ± 0.91 D -1.95 D ± 0.64 D 0.57 OS J 0 +0.13 D ± 0.22 D +0.08 D ± 0.18 D 0.27 OS J 45 -0.18 D ± 0.16 D -0.16 D ± 0.20 D 0.66 Accommodative Lag 1.65 D ± 0.35 D 1.77 D ± 0.40 D 0.17 (4-D Stim w/ full Manifest) Axial Length OD (mm) 24.37 ± 0.88 23.96 ± 0.66 0.019 Near Phoria ( ∆; + = eso) 0.86 ± 3.55 0.57 ± 4.86 0.75 AC/A^ 9.59 ± 3.79 (n=34) 8.10 ± 2.86 (n=35) 0.07 Flat Keratometry 43.12 D ± 1.62 D 43.79 D ± 1.55 D 0.06 Steep Keratometry 43.84 D ± 1.67 D 44.56 D ± 1.48 D 0.038 Intraocular pressure (mmHg) 16.9 ± 3.0 16.9 ± 2.8 0.97 Corneal pachymetry ( µm) 530.9 ± 33.5 541.8 ± 28.3 0.11 Crystalline lens φ Thickness (mm) 3.33 ± 0.25 3.35 ± 0.14 0.64 Index of refraction 1.43 ± 0.01 (n=42) 1.43 ± 0.01 (n=41) 0.33 Radius of curvature Anterior (mm) 12.27 ± 1.16 (n=42) 12.28 ± 1.19 (n=41) 0.96 Posterior (mm) 6.53 ± 0.58 (n=42) 6.34 ± 0.48 (n=41) 0.10 Relative peripheral refraction 30º nasal retina +0.56 D ± 0.61 D +0.56 D ± 0.57 D 30º temporal retina +0.64 D ± 0.74 D +0.58 D ± 0.80 D 0.92 30º superior retina -0.40 D ± 0.92 D -0.31 D ± 0.93 D 20º inferior retina -0.45 D ± 0.79 D -0.52 D ± 0.89 D * All p-values obtained from t-tests, chi-square tests, or F-tests, where appropriate. ^ AC/A values filtered if accommodative response is less than 1 diopter for a 4-D stimulus and if AC/A is greater than 20. φ Phakometry data missing on two children due to error with data recording tape
Table 2.6: Mean (± SD) baseline characteristics stratified by treatment group.
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Relative peripheral refraction differed by retinal location (p < 0.001); however, the differences by retinal location did not depend on the treatment group (p = 0.75). The mean relative peripheral refraction values for all children are shown in Figure 2.5. There were no asymmetries in relative peripheral refraction in the vertical meridian (superior and inferior retina) or in the horizontal meridian (nasal and temporal retina) (all p > 0.05;
Tukey’s HSD); however, relative peripheral refraction values in the horizontal meridian were more hyperopic than in the vertical meridian (all p < 0.05; Tukey’s HSD). In the horizontal meridian, eyes of myopic children on average had relative peripheral hyperopia (i.e., a relatively more prolate shape). In the vertical meridian, eyes had relative peripheral myopia (i.e., a relatively more oblate shape).
30° Superior Retina RPR -0.36 ±±± 0.92 D
Central 30° Temporal 30° Nasal Spherical Equivalent Retina RPR Retina RPR Refractive Error +0.61 ±±± 0.77 D +0.56 ±±± 0.59 D –1.97 ± 0.79 D
20° Inferior Retina RPR -0.48 ±±± 0.83 D
Figure 2.5: Mean (± SD) relative peripheral refraction (RPR) at baseline for all children.
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Baseline characteristics for the near work and outdoor activity survey stratified by treatment group are shown in Table 2.7. There was no imbalance between the treatment groups for each near work variable or for diopter hours. At baseline, children in the PAL group were reported to engage in outdoor activities 2.76 hours more per week than children in the single vision lens group (p = 0.046). Outdoor activity will be controlled for in all outcome analyses.
Hours per week SVL Group PAL Group p-value* outside of school (n=43) (n=42) Studies or reads for school 5.27 ± 6.01 6.85 ± 12.46 0.45 Reads for pleasure 4.32 ± 5.02 4.47 ± 3.96 0.88 Watches television 9.38 ± 7.84 9.24 ± 5.62 0.92 Uses a computer 4.49 ± 5.01 3.75 ± 2.90 0.41 Plays video games 2.66 ± 3.63 1.99 ± 2.95 0.35 Plays handheld electronic games 1.98 ± 2.72 1.87 ± 2.74 0.86 Diopter hours 58.26 ± 38.89 60.30 ± 40.57 0.81 (near work composite) Engages in outdoor activities 7.57 ± 5.44 10.33 ± 7.07 0.046 * All p-values obtained from t-tests.
Table 2.7: Mean (± SD) baseline characteristics for near work and outdoor activity survey stratified by treatment group.
Of the 85 children enrolled, the number of myopic parents could be determined for 68 (80%) children based on the answers provided. Reasons why the number of myopic parents could not be determined for both biological parents included the child being adopted, the child’s parents being separated, and the child living with relatives other than his or her parents. The number of myopic parents and the number of children where parental history of myopia could not be determined was balanced between the
59 treatment groups (Table 2.8). There was no difference in either age or spherical equivalent refractive error between children for whom the number of myopic parents is known versus not known (Table 2.9).
p = 0.83* Number of Myopic Parents Unknown 0 1 2 Total 7 5 16 15 43 SVL (41.2%) (50%) (55.2%) (51.7%) (50.6%) 10 5 13 14 42 PAL (58.8%) (50%) (44.8%) (48.3) (49.4%) 17 10 29 29 85 Total Treatment Group (100%) (100%) (100%) (100%) (100%) *p-value obtained from chi-square test
Table 2.8: Number of myopic parents by treatment group. Percentages indicate proportion within each number of myopic parent category.
Number of Myopic Parents Known (n = 68) Not Known (n = 17) p-value* Age (years) 9.34 ± 1.28 9.12 ± 1.65 0.55 OD M (Spherical Equivalent) -1.95 D ± 0.77 D -1.97 D ± 0.84 D 0.94 *p-values obtained from t-tests
Table 2.9: Comparisons of age and spherical equivalent refractive error between children for whom the number of myopic parents is known versus not known.
2.4 Discussion
Baseline characteristics of the 85 children enrolled in STAMP have been presented. The mean age (9.3 years), spherical equivalent amount of myopia (-1.95 D),
60 and axial length (24.17 mm) reflect the enrollment criteria for STAMP. The mean lag of accommodation for a 4-D stimulus (1.71 D) reflects the eligibility criteria that children have a high lag of accommodation.
The baseline characteristics of children in STAMP are similar to the baseline characteristics of children who participated in the COMET Study. In COMET, the mean
(± SD) age was 9.3 ± 1.3 years (Gwiazda et al. 2003), spherical equivalent refractive error was -2.38 ± 0.81 D, and axial length was 24.1 ± 0.7 mm (Gwiazda et al. 2002). The baseline refractive error in STAMP was slightly less myopic than in COMET, which likely reflects the requirement that children with higher myopia in STAMP also be esophoric at near. Overall, the children in STAMP appear to be similar to those enrolled in COMET.
The STAMP baseline relative peripheral refraction findings are of particular interest. The majority of studies that have measured relative peripheral refraction have done so in the horizontal meridian of the eye and found that myopic eyes of both adults and children have relative peripheral hyperopia (i.e., a relative more prolate ocular shape)
(Millodot 1981; Mutti et al. 2000b; Seidemann et al. 2002; Schmid 2003; Logan et al.
2004; Atchison et al. 2006; Mutti et al. 2007). Consistent with other reports in the literature, relative peripheral hyperopia in the horizontal meridian was also found in the myopic children enrolled in STAMP; however, relative peripheral myopia was found in the vertical meridian. Two other studies have reported relative peripheral refraction in the vertical meridian of adult eyes. The finding of relative peripheral myopia in the vertical meridian of myopic eyes is consistent with the results of another study that also reported relative peripheral myopia across all refractive errors when measuring the superior and 61 inferior retina of 43 hyperopic, emmetropic, and myopic adult eyes (Atchison et al.
2006). Another study of 18 myopic adult eyes also found relative peripheral myopia in the superior retina; however, relative peripheral hyperopia was reported in the inferior retina (Seidemann et al. 2002).
It was recently reported that local retinal regions respond to local defocus in emmetropizing monkeys (Hung et al. 2009), and it is well established across animal models that brief periods of exposure to either plus lenses or unrestricted vision prevent axial elongation in response to an otherwise constant stimulus to grow from a minus lens
(Schmid and Wildsoet 1996; Shaikh et al. 1999; Zhu et al. 2003; Norton et al. 2006).
Given these results, the STAMP finding of relative peripheral myopia in the vertical meridian of the eye in myopic children casts doubt on whether peripheral retinal defocus guides juvenile-onset myopia progression because myopic defocus in the vertical meridian of the eye should act as a potent “stop” signal to growth. The longitudinal relative peripheral refraction data collected in STAMP will allow for an evaluation of the effects of both horizontal and vertical retinal defocus on myopia progression. Because regional lensometry with each child’s spectacle correction is being performed at locations on the spectacle lens that correspond to the location of each relative peripheral refraction measurement, it will be possible to determine the image shell experienced by each child when wearing his or her spectacles. These data will be used to determine whether the image shells induced by single vision and progressive addition lenses result in corresponding changes in relative peripheral refraction, as described in section 2.1.1.
In conclusion, complete ocular biometric data are being collected in STAMP to determine whether the accommodative lag theory or the mechanical tension theory better 62 explains the reduction in myopia progression observed when children wear PALs. The baseline data will be used to determine whether a PAL treatment effect is present after the first year of the study. STAMP will then determine whether a treatment effect rebound is present after the second year of the study when all children wear single vision lenses. Particular attention will be given to changes in relative peripheral refraction by treatment group to determine whether either defocus or tension-related changes occur.
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CHAPTER 3
VALIDATION OF ABERROMETRY-BASED RELATIVE PERIPHERAL REFRACTION (RPR)
3.1 Introduction
Given the interest in retinal shape and peripheral image quality (sections 1.4.2 and
1.6), the ability to simultaneously collect peripheral refraction and peripheral aberration data would be useful in studies examining mechanisms of myopia development and progression. The Complete Ophthalmic Analysis System G200 (COAS; AMO Wavefront
Sciences, Albuquerque, NM) is a clinical Shack-Hartmann wavefront sensor that provides accurate and reliable autorefractor data when measuring central refractive error in adults (Salmon et al. 2003) and children (Martinez et al. 2006). Higher-order aberration measurements made with the COAS have also been validated (Cheng et al.
2003). The purpose of this study was to validate aberrometry-based relative peripheral refraction measurements and to determine whether differences in relative peripheral refraction exist in the horizontal visual field in adults. This study was completed in preparation for STAMP, and the results have been published (Berntsen et al. 2008).
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3.2 Methods
Thirty healthy, right eyes of thirty subjects were measured in random order with both the Grand Seiko WR-5100K autorefractor (Grand Seiko Co., Ltd.; Hiroshima,
Japan) and with the COAS. The study protocol was approved by The Ohio State
University’s Biomedical Institutional Review Board, in accordance with the Declaration of Helsinki. Subjects were educated on the purpose of the study, and each subject signed an informed consent document before beginning the study. Subjects were recruited using e-mail announcements sent to the faculty, staff, and students at The Ohio State University
College of Optometry. All subjects had to be free of ocular disease, be at least 18 years of age, and be correctable to at least 20/25 Snellen visual acuity in their right eye. A sample size of 21 subjects would provide adequate power to detect a difference of 0.25 D between the instruments assuming a standard deviation of 0.35 D, α = 0.05, and β = 0.10.
Cycloplegia and pupillary dilation were achieved using two drops of 1% tropicamide separated by five minutes (Egashira et al. 1993; Mutti et al. 1994; Manny et al. 2001). Measurements were made 30 minutes after the first drop of tropicamide was instilled. Ten measurements were made in each of three directions of gaze along the horizontal meridian. Measurements were made centrally (along the line of sight), 30 ° nasal from the line of sight (nasal retina), and 30° temporal from the line of sight
(temporal retina). The subject’s head was rotated while keeping the eye in primary gaze for all measurements to prevent any potential changes in ocular shape resulting from tension from the extraocular muscles (Ferree et al. 1931; MacFadden et al. 2007), although others have recently reported that this step was not necessary (Radhakrishnan and Charman 2008; Mathur et al. 2009). 65
During all measurements, the left eye was covered with an eye patch. When making central COAS measurements, subjects viewed the standard internal target within the instrument, which is optically fogged to help control accommodation. When making peripheral measurements with the COAS, subjects viewed a red light-emitting diode
(LED) on the instrument. The instrument was refocused between each measurement and bracketing was used to ensure the best focus was obtained before each measurement.
When making central and peripheral measurements with the Grand Seiko autorefractor, subjects viewed a red LED mounted on the wall across the room 1.75 meters from the instrument. In all cases, subjects were instructed not to try to focus on the LED or to make the LED clear.
The COAS software configuration settings used in this study were based on the findings of a study that validated COAS aberrometry-based refractive error values with those of an autorefractor (Salmon et al. 2003). The COAS default (non-Seidel) method of determining sphere, cylinder, and axis was used instead of the Seidel method because
Salmon et al. reported slightly better repeatability with the default method than with the
Seidel method, which includes higher-order aberration terms in the calculation of refractive error. The chromatic aberration correction setting was turned on and set to 555 nm. The pupil analysis diameter used for the analyses presented was 2 mm because this most closely approximated the size of the measurement beam used by the Grand Seiko
WR-5100K autorefractor (Bailey et al. 2005). Both the COAS and the Grand Seiko autorefractor reference refractive error measurements to the corneal plane.
Relative peripheral refraction (RPR) was calculated by finding the difference between the average nasal or temporal spherical equivalent and the central spherical 66 equivalent. A repeated measures analysis of variance (ANOVA) was used to test for RPR measurement differences by instrument (Grand Seiko or COAS) and retinal location
(nasal RPR or temporal RPR). Bland-Altman difference versus mean plots were created for the nasal RPR and temporal RPR data (Bland and Altman 1986).
Refractive error was converted to power vectors using the method described by
Thibos (Thibos et al. 1997). Repeated measures ANOVAs were performed to test spherical refractive error, M (spherical equivalent), J 0 (with- and against-the-rule astigmatism), and J 45 (oblique astigmatism) for differences by instrument and by direction of gaze (central, nasal, or temporal). Appropriate post hoc t-test comparisons were performed using the method described by Tukey and the appropriate mean square error from the analysis of variance. Statistical significance for all testing was set at an alpha level of 0.05.
Linear regression models were used to determine the relationship between relative peripheral refraction and central spherical equivalent refractive error. A linear regression model was also used to assess the relationship between nasal-temporal relative peripheral refraction differences and central spherical equivalent refractive error. All regression models took into account the correlation due to repeated subjects.
3.3 Results
The mean age (± SD ) of the 30 subjects participating in this study was 31.0 ± 6.7 years and ranged from 23 to 45 years. The mean spherical equivalent refractive error of
67 the sample, as measured by the Grand Seiko autorefractor, was –2.63 D ± 2.05 D and ranged from +0.63 D to –8.41 D.
Average RPR values by instrument are shown in Table 3.1. There was no significant difference in RPR measurements between the COAS and Grand Seiko autorefractor (p = 0.34). Difference versus mean plots are shown for nasal RPR and temporal RPR in Figures 3.1a and 3.1b, respectively. The outlier on each figure represents the same subject. The outlier’s data were verified and in both instances, the
COAS measured less minus (more plus) on peripheral measurements that the Grand
Seiko autorefractor.
Grand Seiko COAS Difference (Grand Seiko – COAS) Nasal RPR +0.43 D ± 1.02 D +0.61 D ± 1.22 D –0.18 D ± 0.60 D Temporal RPR +0.04 D ± 1.27 D +0.10 D ± 1.55 D –0.06 D ± 0.91 D Difference +0.39 D ± 0.99 D +0.51 D ± 1.10 D –0.12 D ± 0.69 D (Nasal – Temporal RPR)
Table 3.1: Mean ± standard deviation for nasal and temporal relative peripheral refraction (RPR) values are shown for all subjects by instrument. There was not a significant difference between relative peripheral refraction measurements made with the COAS and Grand Seiko autorefractor (p = 0.34).
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4.00 4.00 3.00 a 3.00 b 2.00 2.00 1.00 1.00 0.00 0.00 -1.00 -1.00 -2.00 -2.00 -3.00 -3.00 Difference (Grand Seiko -Seiko (Grand Difference COAS) Difference (Grand Seiko -Seiko (Grand Difference COAS) -4.00 -4.00 -3.50 -2.50 -1.50 -0.50 0.50 1.50 2.50 3.50 -3.50 -2.50 -1.50 -0.50 0.50 1.50 2.50 3.50 Mean Nasal Relative Peripheral Refractive Error Mean Temporal Relative Peripheral Refractive Error
Figure 3.1: Difference versus mean plots for nasal (3.1a) and temporal (3.1b) relative peripheral refraction (RPR). Neither of the mean differences (solid lines) were significantly different than zero. The dotted lines represent the 95% limits of agreement for nasal RPR and temporal RPR, which were –1.38 D to +1.02 D and –1.89 D to +1.76 D, respectively.
Descriptive statistics of refractive error by instrument (COAS and Grand Seiko) and retinal location (central, nasal, and temporal) are shown in Table 3.2 for refractive sphere, spherical equivalent (M), with- and against-the-rule astigmatism (J 0), and oblique astigmatism (J 45 ). When examining only the sphere component of the refractive error, measurements made by the COAS were more myopic than those made by the Grand
Seiko autorefractor (mean ± SD = –0.38 D ± 0.61 D; p<0.0001), regardless of the direction of gaze (p=0.38). For both instruments, measurements of spherical refractive error were affected by the direction of gaze (p<0.0001). Post hoc testing revealed that both nasal and temporal spherical refractive error was more hyperopic than central spherical refractive error (p<0.05 Tukey’s HSD; Table 3.3).
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Instrument Central 30° Nasal 30° Temporal (line of sight) Retina Retina Sphere Grand Seiko –2.31 ± 2.09 –1.62 ± 2.02 –1.32 ± 2.09 Only COAS –2.77 ± 2.32 –1.90 ± 2.11 –1.73 ± 2.19 Difference † +0.46 ± 0.29 +0.28 ± 0.69 +0.41 ± 0.74 M Grand Seiko –2.63 ± 2.05 –2.20 ± 1.94 –2.59 ± 2.13 (Spherical COAS –3.12 ± 2.24 –2.51 ± 1.96 –3.02 ± 2.21 equivalent) Difference † +0.49 ± 0.25 +0.31 ± 0.56 +0.43 ± 0.86
J0 Grand Seiko +0.04 ± 0.30 –0.37 ± 0.35 –1.08 ± 0.41 COAS +0.03 ± 0.32 –0.34 ± 0.45 –1.12 ± 0.53 Difference † +0.01 ± 0.16 –0.02 ± 0.31 +0.04 ± 0.51
J45 Grand Seiko +0.11 ± 0.30 –0.20 ± 0.31 +0.42 ± 0.51 COAS +0.09 ± 0.31 –0.10 ± 0.36 +0.27 ± 0.53 Difference † +0.02 ± 0.11 –0.10 ± 0.19 +0.14 ± 0.20 † Difference = Grand Seiko – COAS
Table 3.2: Average refractive error values in diopters (mean ± SD) by instrument and retinal location for sphere only, spherical equivalent (M), J 0, and J 45 . With the exception of J 45 (oblique astigmatism), refractive error differences due to the direction of gaze did not depend on which instrument was used. The average difference between the instruments is also shown.
Nasal – Central Temporal – Central Nasal – Temporal Sphere Only +0.78 D ± 1.17 D +1.01 D ± 1.28 D ∗ M (Spherical +0.52 D ± 1.12 D ∗ ∗ equivalent) J0 –0.39 D ± 0.42 D –1.14 D ± 0.49 D +0.75 D ±0.41 D ∗ No significant difference was found.
Table 3.3: Statistically significant differences in refractive error measurement by direction of gaze are shown. Differences presented in the table were significant at a simultaneous alpha level of 0.05 using Tukey’s HSD test. Oblique astigmatism (J 45 ) is not included in the table because the average difference in J 45 between directions of gaze depended on the instrument used (i.e., there was a significant instrument x gaze interaction).
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Spherical equivalent refractive error was also more myopic when measured by the
COAS (mean ± SD = –0.41 D ± 0.61 D; p<0.0001) regardless of the direction of gaze
(p=0.38). As expected, direction of gaze affected the spherical equivalent refractive error
(p=0.04), regardless of the instrument used. Post hoc testing revealed that nasal spherical equivalent refractive error measurements were more hyperopic on average than central measurements (Table 3.3; p<0.05 Tukey’s HSD). The nasal RPR was significantly different from zero and was significantly more hyperopic than the temporal RPR (nasal
RPR – temporal RPR mean ± SD = +0.45 D ± 1.04 D; p = 0.02), indicating a relatively prolate ocular shape for the nasal retina. No other significant post hoc differences existed between directions of gaze for spherical equivalent refractive error. Temporal RPR was also not significantly different from zero, indicating a more spherical shape for the temporal retina.
Measurements of with- and against-the-rule astigmatism (J 0) obtained in each direction of gaze did not depend on the instrument used (p=0.67). There were no significant differences between instruments in the amount of J 0 measured (p=0.88); however, the measured amount of J 0 depended on the gaze in which it was measured
(p<0.0001). Post hoc testing revealed that J 0 was greatest temporally, followed by nasally, and was least centrally (Table 3.3; all p<0.05 Tukey’s HSD).
Measurements of oblique astigmatism (J 45 ) obtained in each direction of gaze depended on the instrument used (p=0.0001). The average values of J 45 by instrument and direction of gaze are presented in Table 3.2. In central gaze, there was no difference in J 45 between the instruments (p>0.05 Tukey’s HSD). When measuring the magnitude of J 45 for the nasal retina, the Grand Seiko autorefractor measured more oblique astigmatism 71
(J 45 ) than the COAS (mean ± SD = 0.10 D ± 0.19 D; p<0.05 Tukey’s HSD). Similarly, when measuring the magnitude of J 45 for temporal retina, the Grand Seiko autorefractor again measured more oblique astigmatism than the COAS (mean ± SD = 0.14 D ± 0.20
D; p<0.05 Tukey’s HSD).
Linear regression showed that both nasal and temporal relative peripheral refraction is related to central spherical equivalent refractive error (Figures 3.2a and 3.2b, respectively). In both cases, eyes with more myopia had more relative peripheral hyperopia, indicating a more prolate shape in eyes with higher myopia (Nasal RPR: slope
= –0.22 D, R 2 = 0.23, p = 0.001; Temporal RPR: slope = –0.20 D, R 2 = 0.10, p = 0.018).
Linear regression showed that there was not a significant relationship between nasal- temporal RPR differences and central spherical equivalent refractive error (slope = –0.02
D, R 2 = 0.02, p = 0.81). This indicates that nasal-temporal asymmetries were constant across refractive errors (Figure 3.3).
3.4 Discussion
The ability to use an aberrometer to simultaneously measure peripheral aberrations and peripheral refractive error is attractive in clinical vision research. Any time that a single instrument can be used to collect multiple pieces of data, valuable research time can be saved. The validation of aberrometry-based relative peripheral refraction measurements made by the COAS will allow researchers to collect data about peripheral optical quality while simultaneously collecting peripheral refraction data that can be used as a surrogate for ocular shape.
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5 5
4 a 4 b
3 3
2 2
1 1
0 0
Nasal RPR RPR Nasal(D) -1 -1 Temporal RPR RPR (D) Temporal -2 -2
-3 -3
-4 -4 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 Central Spherical Equivalent Refractive Error (D) Central Spherical Equivalent Refractive Error (D)
Figure 3.2: Linear regression analysis showing that subjects with more myopia had greater relative peripheral hyperopia when examining both nasal retina (figure 3.2a; R 2 = 0.23, slope = –0.21, p = 0.001) and temporal retina (figure 3.2b; R 2 = 0.10, slope = –0.20, p = 0.018).
3
2
1
0
-1
-2 Nasal RPR NasalRPR -RPR Temporal
-3 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 Central Spherical Equivalent Refractive Error
Figure 3.3: Linear regression showing that nasal-temporal RPR differences are not related to refractive error (p = 0.81). The nasal-temporal RPR differences in this study were consistent across refractive errors.
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This study had adequate power to detect a 0.25-D difference in relative peripheral refraction measurements between the Grand Seiko autorefractor and the COAS. A limitation of this study is that it was not designed with adequate power to examine differences in relative peripheral refraction after stratifying by the subject’s type of refractive error (i.e., myopia, emmetropia, or hyperopia); however, the linear regression analyses show that the data are in agreement with previously published peripheral refraction data in adults and children that indicate more myopic eyes have greater relative peripheral hyperopia (Millodot 1981; Mutti et al. 2000b; Seidemann et al. 2002; Mutti et al. 2007). The lack of bias in RPR between the two instruments was consistent across the range of refractive errors. In both the nasal and temporal retina, as the amount of central myopia increased, relative peripheral hyperopia increased (Figures 3.2a and 3.2b).
Therefore, this paper focuses on the cohort as a whole.
This study showed that COAS aberrometry-based relative peripheral refraction measurements were equivalent to measurements made using the Grand Seiko autorefractor. The COAS measured more myopia in all directions of gaze than the Grand
Seiko autorefractor; however, because relative peripheral refraction is the difference between spherical equivalent refractive error centrally and peripherally, the uniformly higher amount of myopia measured by the COAS had no effect on the overall relative peripheral refraction value calculated.
The finding that the COAS measured more minus power than the Grand Seiko autorefractor is consistent with other reports in the literature. Studies have reported that
COAS spherical equivalent (M) values were similar to autorefraction measurements
(within 0.25 D) made with the Canon RK-F1 (Martinez et al. 2006) and with the Nidek 74
ARK-2000 (Salmon et al. 2003). Gwiazda and Weber compared autorefraction measurements between three autorefractors and reported that the mean spherical equivalent refractive error (M) measured by the Grand Seiko autorefractor was 0.43 D more hyperopic than the Canon R-1 and 0.65 D more hyperopic than the Nidek ARK
700-A (Gwiazda and Weber 2004). Therefore, our finding that that the Grand Seiko measured 0.41 D more plus power than the COAS when measuring spherical equivalent under cycloplegic conditions is consistent with other reports in the literature. Potential reasons for the difference found could include differences in manufacturer calibration or differences in the fundamental operating principles between the aberrometer and the autorefractor.
It could be argued that the location of the peripheral LED targets used when making measurements with the COAS led to small amounts of residual accommodation even though the subjects were cyclopleged; however, the central COAS measurements were made using the internal COAS target, which is optically fogged. In addition, the extra minus power measured by the COAS was uniform across all directions of gaze.
Therefore, it is unlikely that excess accommodation due to the proximity of the LED targets used for peripheral COAS measurements was the cause of the more minus COAS measurements.
On both difference versus mean plots presented (Figures 3.1a and 3.1b), the same subject was the outlier. The raw Hartmann-Shack data images from the COAS were inspected, and their clarity and centration were verified. In both cases, the COAS measured more plus power than the Grand Seiko. One could argue that alignment errors contributed to the more plus COAS measurement; however, a study validating the COAS 75 found that small lateral or axial displacements had little effect on refractive error measurements and did not induce significant coma (Cheng et al. 2003). Martinez et al. compared central refractive error measurements made with the COAS and Canon RK-F1 autorefractor (Canon, Inc.; Tokyo, Japan) in children (Martinez et al. 2006). They also found a few occasions when the COAS disagreed with the autorefractor; however, the
COAS measured more minus power than the Canon autorefractor.
It is important to note that the refractive error values used when validating the
COAS aberrometry-based relative peripheral refraction measurements were calculated using a 2-mm circular analysis diameter, the same diameter as the infrared beam used by the Grand Seiko autorefractor (Bailey et al. 2005). When the COAS analysis diameter was increased to 6 mm, the aberrometry-based relative peripheral refraction values were no longer equivalent to the Grand Seiko autorefractor. This is most likely because of the increased influence of higher-order aberrations on the COAS-calculated refraction as pupil size increases. It has been reported that higher-order aberrations do not have a large effect on image quality and visual acuity when the pupil is small but do have a large effect on image quality and visual acuity when the pupil is large (Liang and Williams
1997; Berntsen et al. 2005). Additionally, one study of postoperative refractive surgery patients reported that an autorefractor that used a small infrared beam measured less myopia than one with a large measurement beam (Bailey et al. 2005). These findings support the method of matching the COAS analysis diameter to the Grand Seiko infrared measurement beam.
Asymmetry between nasal and temporal relative peripheral refraction was observed. On average, nasal relative peripheral refraction was 0.45 D more hyperopic 76 than temporal relative peripheral refraction. These findings are consistent with nasal- temporal asymmetries in peripheral refraction measurements that have been reported in other studies (Ferree et al. 1932; Rempt et al. 1971; Millodot 1981; Atchison et al. 2006).
The current data also show that the nasal-temporal asymmetry found did not depend on central refractive error (Figure 3.3). This finding indicates that, in this reported cohort, the asymmetry that is present between the nasal and temporal retina is consistent across refractive errors.
The nasal-temporal asymmetry appears to be driven mainly by differences in J 0 astigmatism. Although the COAS on average read more minus than the Grand Seiko autorefractor, there was not a significant difference between the nasal and temporal average sphere values measured; however, when examining J 0 astigmatism, both instruments measured significantly more astigmatism temporally (–1.10 D) than nasally
(–0.35 D) and measured the least amount of J 0 astigmatism centrally (+0.04 D). This finding of higher amounts of astigmatism when measuring temporal retina compared to nasal retina is consistent with other reports in the literature (Millodot 1981; Seidemann et al. 2002; Atchison et al. 2006). Although the Grand Seiko autorefractor measured significantly higher magnitudes of J 45 astigmatism than the COAS nasally and temporally, the magnitude of J 45 astigmatism was nearly 2.5 times less nasally and 3.25 times less temporally than J 0 astigmatism. Therefore, the asymmetry in spherical equivalent refractive error in our sample was mainly driven by the increased J 0 astigmatism in our sample when measuring peripheral retinal locations.
One possible explanation for the greater amount of J 0 astigmatism temporally compared to nasally involves angle lambda. Angle lambda is the angle between the 77 pupillary axis and the line of sight and occurs because the fovea is slightly displaced temporally on the retina compared to the eye’s pupillary axis (Bennett 1998). Because subjects in this study fixated on a target, central measurements were made along the line of sight, which is temporal on the retina compared to the pupillary axis. Therefore, when measuring 30º temporal on the retina from the line of sight, measurements were made more than 30º from the pupillary axis by angle lambda. When measuring 30º nasal on the retina from the line of sight, measurements were made less than 30º from the pupillary axis by angle lambda. Because temporal measurements were made farther from the pupillary axis than nasal measurements, this could explain why more J 0 astigmatism was measured in the temporal retina measurements compared to the nasal retina measurements.
Because the goal of this study was to determine whether the COAS aberrometer could be used to simultaneously collect peripheral refraction data and aberration data, it is important to note that the raw COAS data file (*.bx) must be saved when measuring a patient. Because the refractive error data used to validate the relative peripheral refraction measurements were determined for a 2-mm analysis diameter, it was necessary to reanalyze all of the raw aberration data to obtain the refraction values. Saving the raw data is also necessary in order to retrieve the higher-order aberration information from the measurement, which requires different pupil sizes and shapes due to the oval-shaped pupil that is obtained when making off-axis measurements. Methods of handling the oval-shaped pupil when examining off-axis aberration measurements have been reported and require manipulation of the raw data outside the COAS software (Atchison and Scott
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2002; Atchison et al. 2003; Wei and Thibos 2006; Atchison et al. 2007; Wei and Thibos
2008).
In summary, aberrometry-based relative peripheral refraction measurements made using the COAS are feasible and equivalent to those made with the Grand Seiko autorefractor.
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CHAPTER 4
PERIPHERAL ABERRATIONS IN MYOPIC CHILDREN
4.1 Introduction
The importance of the peripheral retina in the emmetropization process has been demonstrated in animal models, suggesting that it is important to measure peripheral aberrations in studies of human refractive error development (section 1.6). Increased aberrations in the periphery and greater aberrations temporally on the retina (nasal visual field) have been reported in the literature (Navarro et al. 1998; Atchison and Scott 2002).
As described in section 1.6.1, single-value metrics of optical quality have been developed that are calculated using the aberration coefficients of a Zernike expansion used to fit the wavefront of interest (Thibos et al. 2004); however, Zernike polynomials are orthogonal functions that must be fitted in a unit circle. When a peripheral aberration measurement is made, the circular pupil appears oval. Because most aberrometry software only fits circles with diameter equal to the minor axis of an oval pupil, data within the major axis but outside this circle will not be analyzed, and will be “missing.” To properly assess the contributions of peripheral optics, additional processing is needed to utilize all data from peripheral measurements. Several methods of handling wavefront data from an oval pupil have been reported (Navarro et al. 1998; Atchison and Scott 2002; Wei and Thibos 2006;
Wei and Thibos 2008).
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Two methods proposed to deal with data from an oval pupil take very different approaches. The first proposed method involves stretching data from an oval pupil into a circular shape. After determining the centroid locations from a Hartmann-Shack image, the location of the centroids are mathematically stretched from an oval shape into a circular shape by correcting the centroid coordinate locations along the minor axis of the oval by 1/cos θ, where θ is the angle of rotation of the eye (Atchison and Scott 2002). As with all Hartmann-Shack aberrometers, the slopes of the wavefront are determined by comparing each stretched centroid location to its stretched reference location. Because the wavefront is now circular, Zernike polynomials can be fitted to the wavefront slopes; however, Zernike coefficients from one angle of rotation cannot be directly compared to
Zernike coefficients from other angles of rotation because the coefficients are normalized to the edges of the particular oval pupil shape rather than to a unit circle. After reconstructing the wavefront using the Zernike coefficients, the wavefront must be reverted back to its original oval shape.
The second method of analyzing data from an oval pupil does not involve mathematical manipulation of the centroid data and avoids the interpretation issues of the previous method. In this method, an analysis circle with diameter equal to the major axis of the oval pupil is used to analyze the wavefront data (Wei and Thibos 2008; Shen and
Thibos 2009). Because there are no data in the area outside of the oval pupil, these areas are treated as missing data and do not influence the Zernike fit (Figure 4.1). If aberration measurements are made with the Complete Ophthalmic Analysis System (COAS; AMO
Wavefront Sciences, Albuquerque, NM), this analysis procedure can be implemented in the company’s commercially available Complete Light Analysis System software 81
(CLAS-2D). After reconstructing the wavefront using the Zernike coefficients, the wavefront will be circular, with diameter equal to the analysis diameter; however, the wavefront will be extrapolated beyond the area of the original wavefront data. A mask with the same shape as the original oval pupil must be applied so that the extrapolated portions of the wavefront are removed. The oval wavefront can then be used to calculate metrics of image quality. This method assumes that the analysis of all data from the oval pupil is desired; however, this may not be the case if the pupil was dilated before making measurements and the habitual pupil size is of interest is smaller.
a) Oval pupil
Missing data (gray areas)
Analysis circle
b) Reconstructed c) Wavefront wavefront masked with original pupil shape
Figure 4.1: Graphic representation of an oval pupil with an analysis diameter equal to the major axis of the oval pupil data (a). After reconstructing the wavefront using the Zernike coefficients calculated, there is extrapolation outside of the original oval data (b), which makes it necessary to apply a mask with the shape of the original oval pupil (c). 82
The disadvantage of both of these methods is that they require processing of the raw aberrometry data outside of the aberrometer’s normal software, which is less efficient. Both of these methods of analyzing peripheral aberration data from an oval pupil are based on the need to obtain the complete wavefront for the measured pupil; however, if the wavefront for a non-dilated pupil is desired and the pupil was dilated before making the measurement, it would only be necessary to obtain a portion of the wavefront from the dilated pupil measurement. In this case, if an analysis circle with diameter equal to the major axis of the non-dilated pupil can be fitted within the data obtained from a dilated pupil, it may be possible to analyze the data more efficiently with the aberrometer’s standard software. Validation of such a method was necessary before implementation.
The purposes of this chapter are as follows:
1. To validate a method of analyzing aberration data from an oval pupil
for the purpose of calculating metrics of retinal image quality; and
2. To describe peripheral aberrations in myopic children using a metric of
retinal image quality.
4.2 Validation of a Method of Analyzing Aberration Data from an Oval Pupil
If peripheral aberrations are measured after dilating the pupil, a third analysis option may exist if the non-dilated pupil size was measured and if the intent is to only use the coefficients from the Zernike fit to calculate metrics of image quality for the non- dilated pupil. Most aberrometry software will not allow the analysis diameter to be larger than the minor axis of an oval pupil; however, if the minor axis of a dilated oval pupil is 83 at least as large as the major axis of the non-dilated oval pupil of interest, then it is possible to use the software to analyze the data using an analysis circle equal in diameter to the major axis of the non-dilated oval pupil (Figure 4.2). Although this method allows small amounts of data outside of the non-dilated oval pupil of interest to be included in the Zernike fit, these portions of the wavefront will be masked off before calculating metrics of image quality.
Pupil dilated to 8mm viewed 6mm non-dilated pupil at 30 degrees (non-dilated viewed at 30 degrees pupil size superimposed) (habitual pupil size)
6mm 8mm
6mm Analysis diameter
Figure 4.2: Example of using an analysis circle equal in diameter to the major axis of the non-dilated pupil (6 mm) within the dilated pupil.
Because aberration data in STAMP are being collected with a dilated pupil, the method of analyzing data from a dilated oval pupil that is shown in Figure 4.2 can be implemented with the COAS software; however, the method had to be validated because additional data outside the oval pupil of interest are included in the Zernike fit and could potentially influence the fit of the Zernike polynomials. The advantage of fitting an 84 analysis circle equal in diameter to the major axis of the non-dilated oval pupil is that this technique can easily be implemented with the aberrometer’s normal software. In contrast, to implement the method described by Shen and Thibos (2009) when measurements were made after dilating the pupil, it would be necessary to apply an oval mask with dimensions equal to the habitual pupil size prior to fitting Zernike polynomials. The application of a mask before fitting Zernike polynomials must be done by hand in the
CLAS-2D software and is time consuming and increases the chance of alignment errors.
Analyses were performed to validate the analysis method using the COAS software (i.e., a Zernike fit with diameter equal to the major axis of the oval pupil of interest) against the method using the CLAS-2D software (i.e., an oval mask the size of the habitual pupil is applied and then a Zernike fit is performed). With both methods, an oval mask must be applied to the reconstructed wavefront before calculating metrics of image quality.
4.2.1 Methods
A peripheral measurement 30º nasal on the retina from the line of sight was made through the dilated pupil of the right eye of 20 healthy subjects using the Complete
Ophthalmic Analysis System G200 (COAS; AMO WaveFront Sciences; Albuquerque,
NM). Each subject signed an informed consent document after all study procedures were explained. The measurement of lower- and higher-order aberrations with the COAS aberometer has been previously validated (Cheng et al. 2003). Cycloplegia and pupillary dilation were obtained using two drops of 1% tropicamide separated by five minutes.
When peripheral measurements were made with the COAS, subjects viewed a red light- emitting diode (LED). These data were obtained from a subset of the adults described in 85
Chapter 3. Subjects included in the analysis ranged in age from 23 to 45 years (mean ±
SD = 31.3 ± 5.9 years), and central spherical equivalent refractive error ranged from
+0.63 to –8.41 D (mean ± SD = –3.02 D ± 2.21 D).
To implement the first analysis method, a 6-mm analysis diameter within the minor axis of the oval pupil was used to analyze the data with the COAS software, as shown in Figure 4.2 (i.e., a Zernike fit with diameter equal to the major axis of the oval pupil of interest without masking first). Zernike polynomials through the sixth order were fitted. This method included small amounts of data outside the oval pupil size of interest in the Zernike fit. To implement the second analysis method, the raw data were then imported into the CLAS-2D software (i.e., an oval mask the size of the habitual pupil is applied and then a Zernike fit is performed). An oval mask with a major axis diameter of
6 mm and minor axis diameter of 5.20 mm was applied to the raw data from the dilated pupil (Figure 4.3). The minor axis of the oval mask was calculated by multiplying the major axis diameter (6 mm) by the cosine of the angle of rotation, which was 30°. After applying the oval mask, an analysis circle equal in diameter to the major axis of the oval
(6 mm) was used to fit Zernike polynomials through the sixth order, allowing areas of missing data to be included in the Zernike fit as described earlier (Wei and Thibos 2008;
Shen and Thibos 2009). All masks were centered over the same location on the wavefront in the CLAS-2D software as used by the COAS software.
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Dilated pupil Data after applying habitual oval pupil mask Non-dilated Zernike analysis circle oval pupil mask with diameter of major axis of oval pupil
Figure 4.3: Method of analyzing dilated oval pupil data in CLAS-2D software. First, an oval mask with major axis equal to the non-dilated pupil diameter is applied. Next, an analysis circle with diameter equal to the major axis of the non-dilated pupil is used to fit the Zernike polynomials (Wei and Thibos 2008; Shen and Thibos 2009).
Because the CLAS-2D software does not have a chromatic aberration correction option built into the software, the Chromatic Aberration Correction option was turned off in the COAS software. The wavelength in the CLAS-2D software was set to 840 nm, which is the wavelength of the super luminescent diode used by the COAS. Zernike coefficients were converted to comply with ANSI Z80.28 standards (American National
Standards Institute 2004). Root mean squared (RMS) wavefront error was calculated using second through sixth order terms (Total RMS) and again for higher-order aberrations only (HO-RMS; third through sixth order terms).
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The Zernike coefficients obtained from each method were used to calculate the ten metrics of retinal image quality that have been reported to best predict logMAR acuity (Applegate et al. 2006). Calculation of the metrics is described in the literature
(Thibos et al. 2004). After reconstructing each wavefront using the Zernike coefficients, the wavefront was masked with the shape of the oval pupil before calculating metrics or retinal image quality. The metrics were calculated at a wavelength of 840 nm using all aberrations (first through sixth order) and again after zeroing the second-order terms
-1 1 (lower-order aberrations). The prism terms (Z 1 and Z 1 ) were included in all calculations to ensure complete accuracy of the metric calculations.
Paired t-tests were used to compare the RMS wavefront errors, selected Zernike coefficients, and metrics of retinal image quality calculated using the COAS and CLAS-
2D methods. The individual Zernike terms compared were the three second-order terms
-2 0 2 -1 1 (Z 2 , Z 2 , Z 2 ), the two third-order coma terms (Z 3 , Z 3 ), and the fourth-order spherical
0 aberration term (Z 4 ). Because of the limited number of subjects and the presence of outliers, Spearman’s rho was calculated to determine whether a correlation existed between the difference between the COAS and CLAS-2D methods and the mean of the two methods. Statistical significance at the alpha < 0.05 level was determined after correcting for multiple comparisons using the method described by Benjamini and
Hochberg (Benjamini and Hochberg 1995).
4.2.2 Results
The mean differences between the COAS and CLAS-2D methods are shown in
Table 4.1. After correction for multiple comparisons, the Zernike mode for oblique 88
-2 astigmatism (Z 2 ) was the only mode where a significant bias was found between the
COAS and CLAS-2D methods (p < 0.0001); however the difference of –0.0285 microns for a 6-mm pupil is equivalent to only –0.015 D of cylindrical defocus, which is not clinically meaningful. Although the unadjusted p-values for the differences in total RMS
2 and the Zernike mode representing with- and against-the-rule astigmatism (Z 2 ) were less than 0.05, they were not significant after correcting for multiple comparisons; however, if they had been statistically significant, they are equivalent to only 0.001 D of spherical defocus and 0.007 diopters of cylindrical defocus, respectively. None of the Spearman correlations between the difference between methods and the mean of the two methods were significant after correction for multiple comparisons. A statistically significant correlation would have indicated that the difference between the two methods was related to the magnitude of the coefficient.
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Mean p-value 95% Limits of Spearman’s p-value° Difference ± SD^ Agreement rho for diff (microns) vs. mean Total RMS 0.0017 ± 0.0036 0.043 -0.005 to 0.009 0.069 0.77 HO RMS 0.0015 ± 0.0048 0.18 -0.008 to 0.011 0.349 0.13 Z(2,-2) -0.0285 ± 0.0172 <0.0001* -0.063 to 0.006 -0.179 0.45 Z(2,0) 0.0023 ± 0.0127 0.44 -0.023 to 0.028 -0.014 0.95 Z(2,2) 0.0122 ± 0.0204 0.015 -0.029 to 0.053 0.520 0.019 Z(3,-1) -0.0017 ± 0.0062 0.24 -0.014 to 0.011 0.453 0.045 Z(3,1) -0.0013 ± 0.0255 0.82 -0.052 to 0.050 0.454 0.044 Z(4,0) 0.0015 ± 0.0098 0.51 -0.018 to 0.021 0.408 0.07 ^Difference calculated as CLAS-2D method minus COAS method *Significant at the alpha < 0.05 level after correcting for multiple comparisons using Benjamini-Hochberg method °No Spearman correlations were significant at the alpha < 0.05 level after correcting for multiple comparisons using the Benjamini-Hochberg method
Table 4.1: Table of mean differences between RMS wavefront error and individual Zernike terms for the COAS and CLAS-2D methods of analyzing aberration data from an oval pupil. Spearman’s rho was calculated to determine whether a correlation existed between the difference and mean values.
Given that several of the correlations approached significance, differences in the metrics of image quality calculated using the Zernike coefficients from the COAS and
CLAS-2D methods were considered. Because Zernike modes interact when producing an overall effect on visual quality (Applegate et al. 2002) and differ in their individual effect on visual acuity (Applegate et al. 2003), it is difficult to predict whether a significant correlation found for individual Zernike modes translates into a similar range effect for the metrics of image quality. Ultimately, the goal of these analyses is to determine whether there is systematic bias between the two methods of calculating metrics of retinal image quality and whether differences between the methods depend on the magnitude of the metric.
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The mean differences in retinal image quality using Zernike coefficients calculated using the COAS and CLAS-2D methods are shown in Table 4.2. There was no difference between the top ten metrics of retinal image quality calculated with either method for higher-order aberrations and total aberrations (all p > 0.11). After correcting for multiple comparisons, none of the Spearman correlations between the difference between methods and the mean of the two methods were statistically significant, indicating that differences between the COAS and CLAS-2D methods do not depend on the value of the magnitude metric. Although not statistically significant after correction for multiple comparisons, the Spearman correlation for the visual Strehl ratio calculated using the optical transfer function (VSOTF) had a p-value of 0.008. The slope of a line fitted to the VSOTF difference versus mean data using a least squares regression is -0.30; therefore, given that the range of mean VSOTF metric values was from 0.014 to 0.121, the overall change in differences between the COAS and CLAS-2D methods across the range of metric values in this sample would correspond to a -0.03 change in VSOTF. A change in VSOTF of 0.10 has been reported to correspond to between roughly a 0.04 and
0.10 change in logMAR visual acuity (Marsack et al. 2004; Applegate et al. 2006); therefore, the -0.03 change in difference between the COAS and CLAS-2D methods across the range of metric values would correspond to a 0.001 to 0.03 logMAR reduction in image quality at most (0 to 1.5 letters), which is not clinically meaningful.
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Image Mean p-value 95% Limits of Spearman’s p-value° Quality Difference ± SD^ Agreement rho for Metric* Diff vs. Mean Higher-order aberrations (third through sixth order) PFSc -0.0016 ± 0.0222 0.75 -0.046 to 0.043 0.002 0.99 Area OTF -0.0011 ± 0.0098 0.64 -0.021 to 0.019 -0.314 0.18 SFcOTF -0.2922 ± 2.1221 0.55 -4.536 to 3.952 -0.181 0.45 PFSt -0.0002 ± 0.0083 0.92 -0.017 to 0.016 -0.184 0.44 VSOTF -0.0024 ± 0.0120 0.39 -0.026 to 0.022 -0.576 0.008 SRMTF -0.0008 ± 0.0028 0.22 -0.006 to 0.005 -0.188 0.43 STD -0.0003 ± 0.0052 0.79 -0.011 to 0.010 -0.290 0.21 VSMTF -0.0063 ± 0.0521 0.60 -0.110 to 0.098 -0.242 0.30 NS -0.0029 ± 0.0183 0.49 -0.039 to 0.034 -0.114 0.63 RMSw -0.0130 ± 0.1220 0.64 -0.257 to 0.231 -0.329 0.16 Lower- and higher-order aberrations (second through sixth order) PFSc 0.0002 ± 0.0017 0.68 -0.003 to 0.003 -0.107 0.65 Area OTF -0.0000 ± 0.0019 0.93 -0.004 to 0.004 0.108 0.65 SFcOTF -0.4383 ± 2.2450 0.39 -4.928 to 4.052 0.034 0.89 PFSt -0.0001 ± 0.0004 0.48 -0.001 to 0.001 -0.293 0.21 VSOTF -0.0003 ± 0.0014 0.29 -0.003 to 0.002 -0.427 0.06 SRMTF 0.0004 ± 0.0012 0.11 -0.002 to 0.003 0.429 0.06 STD 0.0005 ± 0.0021 0.26 -0.004 to 0.005 0.141 0.55 VSMTF -0.0090 ± 0.0258 0.14 -0.061 to 0.043 -0.298 0.20 NS 0.0006 ± 0.0060 0.64 -0.011 to 0.013 0.290 0.21 RMSw -0.0122 ± 0.0642 0.41 -0.141 to 0.116 0.041 0.87 *Top ten retinal image quality metrics for predicting logMAR visual acuity reported by Applegate et al. 2006 and defined by Thibos et al. 2004 ^Difference calculated as CLAS-2D method minus COAS method °No Spearman correlations were significant at the alpha < 0.05 level after correcting for multiple comparisons using the Benjamini-Hochberg method
Table 4.2: Table of mean differences between metrics of image quality calculated using Zernike coefficients generated from the COAS and CLAS-2D methods of analyzing data from an oval pupil. Spearman’s rho was calculated to determine whether a correlation existed between the difference and mean values.
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4.2.3 Conclusions
Based on these data, metrics of retinal image quality calculated using Zernike polynomials fitted using COAS software are valid compared to metrics calculated using
Zernike polynomials fitted using CLAS-2D software. If the pupil is dilated and an analysis circle with diameter equal to the major axis of the oval pupil of interest will fit within the minor axis of the dilated pupil, this more efficient approach can be utilized.
4.3 Baseline Central and Peripheral Retinal Image Quality in STAMP
4.3.1 Methods
Baseline data from the 85 children enrolled in STAMP were used for these analyses. Characteristics of these children can be found in Chapter 2. Before dilating the pupil, each child’s habitual right pupil’s size was measured under photopic illumination
(75 to 120 cd/m 2) using the COAS aberrometer. Pupil dilation and cycloplegia were achieved with two drops of 1% tropicamide separated by five minutes. As described earlier (Chapter 2), all testing in STAMP that required cycloplegia began 30 minutes after the first drop of tropicamide was instilled.
Aberrations were measured using the COAS G200-VR aberrometer, which is an open field version of the COAS. Nine wavefront measurements of the right eye were captured and averaged in each of the following directions of gaze: centrally, 30º nasal on the retina, 30º temporal on the retina, 30º superior on the retina, and 20º inferior on the retina. With the exception of the inferior retinal measurement, children viewed either an
“x” or a flashing LED mounted on the wall. For the inferior retinal measurement,
93 children viewed a white painted target that was attached to the COAS specifically for that measurement. Although testing was done under cycloplegia, children were still instructed that the target would be blurry and that they should not try to make the target look clear.
The child’s head was turned to point at the target for nasal and temporal retinal measurements, and the child was asked to turn his or her eye to look at the targets for the superior and inferior retinal measurements. The effect of turning the eye versus the head is inconsequential (Radhakrishnan and Charman 2008; Mathur et al. 2009). All aberration data were analyzed at each child’s habitual pupil size. The raw Hartmann-Shack images were visually inspected, and any images with distortions within the analysis circle were excluded. All Zernike coefficients were calculated at a wavelength of 555 nm and were converted to comply with ANSI Z80.28 standards (American National Standards Institute
2004).
Although Zernike coefficients can only be compared across pupils if they are calculated over the same pupil size, metrics of retinal image quality are single value metrics that have already taken the pupil size into account during the calculation. The visual Strehl ratio computed in the frequency domain using the optical transfer function
(OTF) was selected for all metric analyses because it consistently predicts visual acuity and subjective best focus well (Cheng et al. 2004; Marsack et al. 2004; Applegate et al.
2006). The visual Strehl ratio is calculated as the ratio of the volume under the neural weighted OTF divided by the volume under the neural weighted diffraction limited case
(Thibos et al. 2004). VSOTF can range from zero (bad image quality) to one (perfect image quality). The neural weighting in this metric is achieved by multiplying the OTF by the neural contrast sensitivity function (CSF N), which emphasizes frequencies near the 94 peak of the CSF and filters those above the cut-off spatial frequency. The equation is as follows: