Corneal Tomography in Clinical Practice (Pentacam System) [4 ed.] 1787791610, 9781787791619

Table of contents :
Contents
Abbreviations
SECTION 1 : Introduction
CHAPTER 1 : Corneal Optics and Geometry
CHAPTER 2 : Measuring Corneal Geometry
CHAPTER 3 : Screening Guidelines
SECTION 2 : Tomographic Maps and Profiles
CHAPTER 4 : Overview
CHAPTER 5 : Corneal Power Maps
CHAPTER 6 : Elevation Maps
CHAPTER 7 : Belin/Ambrósio Enhanced Ectasia
CHAPTER 8 : Corneal Thickness Maps and Profiles
CHAPTER 9 : Geometric Tomography and Corneal Topometry
SECTION 3 : Understanding Corneal Refraction
CHAPTER 10 : Astigmatism
CHAPTER 11 : Objective Corneal Dioptric Power
CHAPTER 12 : Astigmatic Disparity
SECTION 4 : Wavefront Science
CHAPTER 13 : Basics of Wavefront Analysis and Measurements
CHAPTER 14 : Zernike Analysis
CHAPTER 15 : Fourier Analysis
CHAPTER 16 : Corneal Asphericity and Related Functions
SECTION 5 : The Systematic Interpretation of Corneal Tomography
CHAPTER 17 : Factors of False Findings
CHAPTER 18 : Enantiomorphism
CHAPTER 19 : The Practical Subjective Scoring System (PS3)
CHAPTER 20 : The Practical Subjective IOL Selection Algorithm
SECTION 6 : Corneal Tomography inEctatic Corneal Diseases
CHAPTER 21 : Tomographic Characteristics of Ectatic Corneal Diseases
CHAPTER 22 : Grading Systems of Ectatic Corneal Diseases
CHAPTER 23 : Progression Criteria
CHAPTER 24 : Entities Misdiagnosed as Ectasia
SECTION 7 : Miscellaneous
CHAPTER 25 : The Holladay Report
CHAPTER 26 : Corneal Tomography in Cataract Surgery
Index

Citation preview

CORNEAL TOMOGRAPHY IN CLINICAL PRACTICE

(PENTACAM SYSTEM) Basics and Clinical Interpretation

NOTIFICATION • The information provided via this book is intended for general information purposes. • The information provided via this book is published to assist you, but it is not to be relied upon as authoritative. • The author accepts no liability whatsoever for any direct or consequential loss arising from any use of the information contained in this book.

CORNEAL TOMOGRAPHY IN CLINICAL PRACTICE

(PENTACAM SYSTEM) Basics and Clinical Interpretation Fourth Edition

Mazen M Sinjab  MD MSc ABOphth PhD FRCOphth (Hons) CertLRS (London)

Professor of Ophthalmology, Damascus University, Syria Visiting Professor, Hassan II University, Casablanca, Morocco Consultant Ophthalmic Surgeon Phaco-Refractive Surgeon Dr Mazen Sinjab Eye Clinic, Dubai, UAE Al Zahra Eye Center, Damascus, Syria

London • New Delhi

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Website: www.jaypeebrothers.com Website: www.jaypeedigital.com © 2021, Jaypee Brothers Medical Publishers The views and opinions expressed in this book are solely those of the original contributor(s)/author(s) and do not necessarily represent those of editor(s) of the book. All rights reserved. No part of this publication may be reproduced, stored or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission in writing of the publishers. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. Medical knowledge and practice change constantly. This book is designed to provide accurate, authoritative information about the subject matter in question. However, readers are advised to check the most current information available on procedures included and check information from the manufacturer of each product to be administered, to verify the recommended dose, formula, method and duration of administration, adverse effects and contra indications. It is the responsibility of the practitioner to take all appropriate safety precautions. Neither the publisher nor the author(s)/editor(s) assume any liability for any injury and/or damage to persons or property arising from or related to use of material in this book. This book is sold on the understanding that the publisher is not engaged in providing professional medical services. If such advice or services are required, the services of a competent medical professional should be sought. Every effort has been made where necessary to contact holders of copyright to obtain permission to reproduce copyright material. If any have been inadvertently overlooked, the publisher will be pleased to make the necessary arrangements at the first opportunity. Inquiries for bulk sales may be solicited at: [email protected]

Corneal Tomography in Clinical Practice (Pentacam System): Basics and Clinical Interpretation First Edition: 2009 Second Edition: 2012 Third Edition: 2019 Fourth Edition: 2021 ISBN: 978-1-78779-161-9 Printed at:

Dedicated to My dear Father Mohamad (may God rest his soul), who implanted in my soul the love of excellence I will mention his name with my name all my life My Mother Almasah (may God rest her soul), who implanted in my heart the love of the poor and helping others My Wife Ruba (may God save her), For the unwavering support that was critical for all my success

Mazen Mohamad Sinjab

A Message from the Other World Man is born and has been granted “The Life” To live is an only one chance that cannot be repeated We have been created without our choice, and we are going to die without our choice as well, but to make our life is our choice Success does not need to be created, it just needs to be made Making success needs five tools, sincerity, honest, humility, persistence and patience But, to deliver success to others, an additional tool is essential; it is loving others “Make your success and deliver it to others; life is very short”

Mazen Mohamad Sinjab

Preface to the Fourth Edition Since launching the 3rd edition, new concepts and applications of corneal tomography have risen. That made it necessary to write the 4th edition to stay up-to-date and allow the readers to catch up with the latest technology. Why this edition? Because it helps better understanding of concepts and adds new applications of topography, tomography, and aberrometry in refractive surgery, cataract surgery, and keratoconus management. This edition has two new chapters. It is divided into seven sections and 26 chapters, discussing in detail the basics and principles, guidelines of screening and validating the data, maps and profiles, wavefront analysis, factors of false findings, ectatic corneal diseases, and much more. As always committed to simplifying the information and consolidating the concepts in a systematic step-by-step method, I keep on creating new methods to present the best for my readers.

Mazen M Sinjab

Preface to the First Edition Taking the right decision in laser refractive surgery depends to a great extent on good reading of corneal topography and its clinical interpretation. This is very important for having the aimed results and avoiding postoperative complications. The data in this book were obtained and gathered from the user manual of the Pentacam, international conferences, refractive journals, personal contacts with many refractive professors and of course self-experience. The strategy in compiling this little book is combining excellence in pictorial quality with a concise but ordered text. I have aimed the book at all those who need some initial assistance in reading and clinical interpretation of corneal topography. As the ophthalmology editor, I take full responsibility for any error and look forward to being further educated.

Mazen M Sinjab

Acknowledgments I would like to acknowledge my wife Ruba and my daughter Reem for the kind assistance in designing the cover of this book.

Contents SECTION 1: Introduction 1. Corneal Optics and Geometry................................................................................................ 3 The Optical System of the Human Eye  3 Corneal Geometry  5

2. Measuring Corneal Geometry................................................................................................ 8 Curvature-based Devices (Topographers)  8 Elevation-based Tomographers  10 OCT-based Tomographers  11 Topography versus Tomography  11 Systems Available in the Market  13

3. Screening Guidelines............................................................................................................ 14 The Four-Composite Map  14 General Settings  14 Main Color Bar Settings  16 Maps Overlay  17 Specific Settings for Holladay Report  20 Image Quality Control  20

SECTION 2: Tomographic Maps and Profiles 4. Overview................................................................................................................................ 29 Corneal Parameters  29

5. Corneal Power Maps............................................................................................................. 32 Factors Affecting Corneal Power Measurement  32 Maps Measuring Corneal Power  32 Patterns of Corneal Curvature  37 Clinical Differences between the Sagittal and Tangential Curvature Maps  42

6. Elevation Maps...................................................................................................................... 45 Principle of the Elevation Maps  45 The Reference Surface  45 Patterns of Elevation Maps  49

7. Belin/Ambrósio Enhanced Ectasia....................................................................................... 54 The Belin/Ambrósio Ectasia Display  54 Pachymetric Data  55 Numeric Values  60 Clinical Applications of Belin/Ambrósio Enhanced Ectasia  60

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Corneal Tomography in Clinical Practice (Pentacam System): Basics and Clinical Interpretation

8. Corneal Thickness Maps and Profiles.................................................................................. 64 Corneal Thickness Map (Pachymetry Map)  64 Corneal Thickness Spatial Profile and Percentage Thickness Increase   66 Pachymetric Progression Index  67 The Relative Pachymetry  70

9. Geometric Tomography and Corneal Topometry............................................................... 75 Corneal Toricity  75 Corneal Asphericity  75 Corneal Asymmetry  76

SECTION 3: Understanding Corneal Refraction 10. Astigmatism.......................................................................................................................... 83 Definitions and Classifications of Astigmatism  83 Types of Astigmatism  83 Etiology of Irregular Astigmatism  86 Evaluation of Irregular Astigmatism  90

11. Objective Corneal Dioptric Power....................................................................................... 95 Calculating Objective Corneal Dioptric Power  95 Clinical Examples  96

12. Astigmatic Disparity............................................................................................................. 99 Etiology  99 Types of Astigmatic Disparity  100 Management of Astigmatic Disparity  100

SECTION 4: Wavefront Science 13. Basics of Wavefront Analysis and Measurements............................................................ 105 Principles of Wavefront and Wavefront Analysis  105 Classification of Aberrations  105 Measurement of Aberrations  105 Analytic Systems  108 Changes of Aberrations with Age  109 Clinical Application of Wavefront Technology  109

14. Zernike Analysis.................................................................................................................. 111 Understanding Zernike Polynomials  112 Correlation between Zernike Polynomials and Irregular Astigmatism Types  112 Description of Zernike Polynomials  115

15. Fourier Analysis................................................................................................................... 123 Fourier Analysis of Corneal Wavefront  124

Contents

16. Corneal Asphericity and Related Functions...................................................................... 127 Corneal Shapes related to Asphericity  127 Q-Value and Corneal Asphericity  128 Corneal and Ocular Spherical Aberration   128 Visual Function and Spherical Aberration  132 Depth of Focus   132 Ocular Spherical Aberration and Neural Adaptation  135 The Effect of Corneal Asphericity on Measuring Refraction  137 The Effect of Corneal Asphericity on Vision  139

SECTION 5: The Systematic Interpretation of Corneal Tomography 17. Factors of False Findings.................................................................................................... 143 Contact Lenses  143 Misalignment  143 Large Angle Kappa or Lambda  146 Tear Film Disturbance  146 Corneal Opacities and Pathologies  148 Previous Corneal Surgeries  148 Inadequate Exposure to the Camera  149 Pregnancy  149

18. Enantiomorphism............................................................................................................... 152 19. The Practical Subjective Scoring System.......................................................................... 157 The Practical Subjective Scoring System (PS3)  157 Application of the PS3 in Laser-based Refractive Surgery  162 Regularity versus Risk Scoring  163

20. The Practical Subjective IOL Selection Algorithm............................................................ 169

SECTION 6: Corneal Tomography in Ectatic Corneal Diseases 21. Tomographic Characteristics of Ectatic Corneal Diseases............................................... 173 Tomographic Definition of ECDs  173

22. Grading Systems of Ectatic Corneal Diseases................................................................... 180 Amsler–Krumeich Classification  180 Alio–Shabayek Modification  180 Modification of Ishii and Associates  180 Belin “ABCD” Grading System  180

23. Progression Criteria............................................................................................................ 184 Parameters of Progression  184 Observing Progression  187 To Crosslink or not to Crosslink  188 Observation after Corneal Crosslinking  188

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Corneal Tomography in Clinical Practice (Pentacam System): Basics and Clinical Interpretation

24. Entities Misdiagnosed as Ectasia....................................................................................... 189 Source  189 Patterns  189

SECTION 7: Miscellaneous 25. The Holladay Report........................................................................................................... 205 Holladay Report  205 Holladay Detailed EKR Report  207 Clinical Examples  209

26. Corneal Tomography in Cataract Surgery......................................................................... 218 Preoperative Screening Process  218 Preoperative Planning Process  219 Postoperative Planning Process  222

Bibliography................................................................................................................................................................225 Index..............................................................................................................................................................................235

Abbreviations AB Asymmetric bowtie AB/IS Asymmetric bowtie inferior steep AB/Srax Asymmetric bowtie with skewed radial axis index AB/SS Asymmetric bowtie superior steep AC Anterior chamber ACA Anterior chamber angle ACD Anterior chamber depth ACV Anterior chamber volume AK Astigmatic keratotomy AS-OCT Anterior segment-optical coherence tomography ATR Against-the-rule AZ Ablation zone BAD Belin/Ambrósio Ectasia Display BFS Best fit sphere BFTE Best-fit-toric ellipsoid BVD Back vertex distance CAD Central ablation depth CCT Central corneal thickness CDVA Corrected distance visual acuity CI Confidence interval CL Contact lens CLE Clear lens extraction CLVC Customized laser vision correction CP Corneal periphery CR Cycloplegic refraction CTSP Corneal thickness spatial profile CXL Corneal crosslinking D Diopter DED Dry eye disease DOF Depth of focus EBMD Epithelial basement membrane dystrophy ECDs Ectatic corneal diseases EDOF Extended depth of focus EKR Equivalent K-reading ELP Effective lens position EME Entities misdiagnosed as ectasia EOZ Efficient optical zone EP Entrance pupil Epi-LASIK Epipolis laser in situ keratomileusis Femto-LASIK Femtosecond laser in situ keratomileusis FFKC Forme fruste keratoconus

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Corneal Tomography in Clinical Practice (Pentacam System): Basics and Clinical Interpretation

FT Flap thickness HOAs Higher-order aberrations HSTS Horizontal sulcus-to-sulcus HWTW Horizontal white-to-white I Inferior ICRs Intracorneal rings IOL Intraocular lens IS Inferior steep K1 Flat K-reading K2 Steep K-reading KC Keratoconus KCS Keratoconus suspect KG Keratoglobus Km Mean K-reading Kmax Maximum K-reading Kref Reference K-reading LASEK Laser subepithelial keratomileusis LASIK Laser in situ keratomileusis LKP Lamellar keratoplasty LOAs Lower-order aberrations LOS Line of sight LRIs Limbal relaxing incisions LVC Laser vision correction MA Manifest astigmatism MTF Modulation transfer function NAR Neural adaptation range OA Optical axis OD Right eye ODP Objective spherocylindric dioptric power ODP-t Translated objective spherocylindric dioptric power OS Left eye OSD Ocular surface disease OTF Optical transfer function OZ Optical zone PA Pupillary axis PHT Pin hole test PIOL Phakic intraocular lens PKP Penetrating keratoplasty PLK Pellucid-like keratoconus PMD Pellucid marginal degeneration PMT Postmydriatic test PPI Pachymetric progression index PRK Photorefractive keratectomy PS3 The Practical Subjective Scoring System PSF Point spread function PSIS The Practical Subjective IOL Selection PTA Percent of tissue altered PTF Phase transfer function

Abbreviations

PTI Percentage thickness increase PVA Potential visual acuity Qs Quality specifications RGP Rigid gas permeable RI Refractive index RK Radial keratotomy RLE Refractive lens exchange RMS Root mean square RS Reference surface S Superior SA Spherical aberration SB Symmetric bowtie SB/SRAX Symmetric bowtie with skewed radial axis index SBK Sub-Bowman keratomileusis SD Standard deviation SE Spherical equivalent SIA Surgically induced astigmatism Sim K Simulated keratometry SMILE Small incision lenticule extraction SR Strehl ratio SRAX Skewed radial axis index SS Superior steep TA Tomographic astigmatism TCRP Total corneal refractive power TCT Thinnest corneal thickness TL Thinnest location TNP True net power TR Total refraction TransPRK Transepithelial photorefractive keratectomy TZ Treated zone UDVA Uncorrected distance visual acuity VA Visual axis VK Vertex keratoscope WFG Wavefront-guided WFO Wavefront-optimized WTR With-the-rule ZC Zernike coefficient

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SECTION

1 Introduction ◆ Corneal Optics and Geometry ◆ Measuring Corneal Geometry

◆ Screening Guidelines

CHAPTER

Corneal Optics and Geometry THE OPTICAL SYSTEM OF THE HUMAN EYE The optical system of the human eye is composed of: • Four main noncoaxial optical elements: The anterior and posterior corneal and lens surfaces. • The pupil. • The retina. It is aplanatic to compensate for the native spherical aberration (SA) and coma through its nonplanar geometry. The optical surfaces are aligned almost coaxially, but the deviations from a perfect optical alignment result in a range of axes and their inter-relationships (Fig. 1). That guides us to the following definitions: • The visual axis (VA): It is the line connecting the fixation point with the foveola, passing through the two nodal points of the eye, but not necessarily through the pupil center. • The optical axis (OA): It is the axis connecting the center of curvatures of the optical surfaces of the eye. It can be recognized by the Purkinje images I, II, III, and IV, namely of the outer corneal surface (I), inner corneal surface (II),

•

•

• •

•

1

anterior surface of the lens (III), and the posterior surface of the lens (IV). If the ocular optical surfaces were perfectly coaxial, these four images would be coaxial, but seldom observed. The principle line of sight (LOS): It is the ray from the fixation point reaching the foveola via the center of the entrance pupil (EP). The pupillary axis (PA): It is the normal line to the corneal surface that passes through the center of the EP and the center of curvature of the anterior corneal surface. The achromatic axis: It is defined as the axis connecting the EP center with the nodal points. The vertex keratoscope (VK) normal: It is the axis that is perpendicular to the plane of the capturing machine (original the keratoscope) and intersecting with the anterior corneal surface at the corneal apex (corneal vertex). Therefore, corneal apex is not necessarily the highest point of anterior corneal slope and not necessarily the anatomical center of the cornea. Angle kappa (measured in degrees): It is the angle between PA and VA. Angle kappa may be a source of false findings and should be differentiated from

Fig. 1: Optical system of the eye (superior view of the right eye): Surfaces, angles, and axes. (EP: entrance pupil [the opening within the dotted line]; F: foveola; FP: focal point; LOS: line of sight; N: nodular point; OA: optical axis; PA: pupillary axis; VK: video keratoscope axis; VA: visual axis).

4

Section 1: Introduction

misalignment (Chapter 17). It also affects the decision and the plan for laser-based and lens-based refractive surgery. In laser-based refractive surgery, angle kappa should be compensated for by recentration of the laser profile and the flap cut, particularly in hyperopic treatment (hyperopia, hyperopic astigmatism, and mixed astigmatism), and in myopic astigmatic treatment when the myopic astigmatic magnitude is ≥1.5 diopters (D). In lens-based refractive surgery, premium IOL implantation is contraindicated when angle kappa is >400 µm to avoid the risk of postoperative intractable dysphotopsia.  Normal distribution of angle kappa was studied by using Orbscan II (Placido-based) and the Synoptophore. It was found that values of angle kappa measured by the Orbscan II were almost as twice as when measured by the Synoptophore. Based on Orbscan II, Hashemi and associates determined an average value of angle kappa of 5.46 ± 1.33° in Iranian adults with an insignificant intergender difference. In another study, Gharaee H and associates determined average value of 4.96 ± 1.38° in total, average horizontal angle kappa of −0.02 ± 0.49 mm, and average vertical angle kappa of −0.09 ± 0.32 mm. In addition, studies reporting normative angle kappa values in different conditions found that angle kappa was significantly higher in exotropes than in esotropes or controls, and tended to be larger in the left eye than in the right eye. Moreover, there was a positive correlation between angle kappa and positive refractive errors, which can be explained by the negative correlation with the axial length of the globe.



Unlike Placido-based topographers, Scheimpflug-based tomographers cannot measure angle kappa directly. Therefore, the Pentacam cannot measure angle kappa directly. There are two methods to estimate the angle by the Pentacam, chord m in the Holladay report (Fig. 2), and considering half the values of X and Y coordinates of pupil center if Holladay report is not available. Chord m is the chord distance from vertex normal (assumed to be the visual axis) and the EP. On the Pentacam, the normal value is 0.20 ± 0.11 mm, so values above 0.42 mm (highlighted in yellow) would be highly unusual. Figure 3 shows the X and Y coordinates of the pupil center. In this example, angle kappa is estimated to be (−0.10, +0.02) in OD and (−0.02, −0.05) in OS. • Angle alpha (measured in degrees): The angle formed at the first nodal point by OA and VA. • Angle lambda (measured in degrees): The angle between PA and LOS. • Chord m (measured in mm): As mentioned above, it is the chord distance from vertex normal (assumed to be the visual axis) and the EP. The refractive power of the human eye comes mainly from the cornea and the crystal lens. In emmetropia, corneal power ranges from 39 to 48 D (average 43.05 D), while the power of the crystalline lens ranges from 15 to 24 D (average 19.11 D). The refractive media in the human eye is: tear film (n = 1.336), cornea (n = 1.376), aqueous humor (n = 1.336), crystalline lens (n = 1.406), and vitreous humor (1.336); where “n” is the refractive index (RI) of the media measured relatively to air (n = 1.000). The dioptric power of the media

Fig. 2: Estimation of angle kappa in the Pentacam by the Holladay report.

Chapter 1: Corneal Optics and Geometry

Fig. 3: Estimation of angle kappa in the Pentacam by the pupil center coordinates.

is determined by the radius of curvature, the RI, and the distance amongst various interfaces.

CORNEAL GEOMETRY The cornea has two surfaces separated by corneal substance. The anterior surface is coated with the tear film, and they form one refractive surface separating air from the corneal substance. The posterior surface separates corneal substance from aqueous humor. The cornea is not a part of a perfect sphere. The shape of both surfaces is defined as an aspheric prolate, toric, asymmetric conoidal shape (Figs. 4 and 5). Each of the previous expressions is explained in detail in the following paragraphs.

Fig. 4: Corneal geometry of the right eye (OD). (T: temporal; N: nasal; Ra: radius of curvature of the anterior corneal surface; Rp: radius of curvature of the posterior corneal surface; n: refractive index).

Corneal Dimensions Corneal dimensions include diameters, meridians, radii of curvature, corneal zones, corneal thickness, corneal shape, and corneal power.

Diameters The sclerocorneal junction (base of the cornea) is an ellipse. The vertical corneal diameter is 10.6 mm on average, whereas the average horizontal corneal diameter is 11.7 mm.

Meridians The normal cornea in the adults has two meridians that are 90° apart. Due to the elliptical base of the cornea at the sclerocorneal junction, the vertical diameter is generally shorter than the horizontal one, meaning that the vertical meridian is steeper (smaller radius of curvature) than the horizontal one (greater radius of curvature). Due to this difference, corneal shape is considered as toric. This toricity is responsible for corneal astigmatism. In younger eyes, this toricity is represented as with-the-rule (WTR) astigmatism, where the vertical meridian is steeper than the horizontal one. This steepness reverses with age, leading to againstthe-rule (ATR) astigmatism.

Fig. 5: Corneal shape of the left eye. The normal human cornea has a conoidal shape.

Radius of Curvature The cornea has two surfaces, anterior with an approximate radius of 7.8 mm and posterior with an approximate radius of 6.5 mm. These two radii are for the central (axial) zone of the cornea. The radii increase while moving to the periphery, indicating a flatter corneal periphery. The normal cornea flattens progressively from center to periphery by 2–4 D, with the nasal area flattening more than the temporal area; this is shown on the curvature map as the nasal side becoming blue (flat)

5

6

Section 1: Introduction

more quickly (Fig. 6). The normal average anterior/ posterior radii ratio is 1.21 in virgin nonoperated corneas. This ratio is altered by keratorefractive surgeries, which is a leading source of wrong IOL measurements.

Corneal Thickness Due to the difference in radius between the two corneal surfaces, the cornea is thinner in its central zone than at its periphery. There are two important values in corneal thickness, the central corneal thickness (CCT) and thinnest corneal thickness (TCT). Both are discussed later in this chapter.

Corneal Zones Clinically, the cornea is divided into zones that surround fixation (corneal vertex or apex) and blend into one another: • The central zone (central 3 mm): It overlies the pupil and is responsible for high definition vision. The central part is almost spherical and is also called the apical or axial zone. • The paracentral zone (3–6 mm): It has a doughnut shape with an outer diameter of 6 mm. It represents an area of progressive flattening toward the third zone. • The peripheral zone (6–9 mm): It is also known as the transitional zone. This zone is asymmetrically flatter than the central zone. The nasal and superior segments are flatter than the temporal and inferior ones. • The limbal zone (>9 mm): It is adjacent to the sclera and is the area where the cornea steepens before merging with the sclera at the limbal sulcus.  The central and paracentral zones are responsible for the refractive power of the cornea, and they are in charge of contact lens fitting. Being steeper in the center and

Fig. 6: Nasal, temporal asymmetry in a normal cornea.

flatter at the periphery gives the cornea what is known as a “prolate” aspheric shape.

Corneal Shape The corneal shape is “Conoidal” (Fig. 5). It is a composition of toricity, asphericity, and asymmetry. From a meridional viewpoint, the cornea is “Toric,” which is the source of corneal astigmatism. From the zonal viewpoint, the cornea is “aspheric” because the radius of curvature differs from the center toward the periphery. From a sectorial viewpoint, the cornea is asymmetric because the nasal sector is usually flatter than the temporal sector as shown in Figure 6. Corneal asphericity is represented by some of values, such as Q-value, p-value, E-value, and eccentricity. The most popular one is the Q-value, which represents the ratio between the central and the peripheral radii of curvature. The relationship between corneal shape, Q-value, corneal SA, depth of focus, and contrast sensitivity is discussed in detail in Chapter 16.

Corneal Power The anterior corneal surface with its associated tear film layer plays a role of a convex refractive surface. Due to both its convexity and separation between two different media: air (smaller RI; n = 1.000) and corneal substance (larger RI; n = 1.376), it is the most powerful refractive surface in the optical system of the eye. The refractive power of the central (apical or axial) zone of the anterior corneal surface is approximately 49 D. On the other hand, although the posterior surface of the cornea is convex, it acts as a negative concave surface because it separates corneal substance (larger RI; n = 1.376) from aqueous humor (smaller RI; n = 1.336). The refractive power of the posterior corneal surface is approximately −6 D. Moreover, corneal epithelium has an impact on corneal power. The shape of the epithelial layer is responsible for about 0.40 D of astigmatism. The mean Q-value is −0.20 ± 0.13 (0.06 to −0.60) with the epithelium and −0.26 ± 0.23 (0.07 to −1.51) without the epithelium. In other words, the cornea is more prolate without the epithelium, which means that the epithelial layer forms a negative lens (thinner in the center) as shown in Figure 7. This fact has a clinical

Fig. 7: The effect of corneal epithelium on the corneal shape. The cornea is more prolate without the epithelium.

Chapter 1: Corneal Optics and Geometry

Fig. 8: The remodeling characteristic of the epithelium. It reduces corneal irregularities.

Fig. 9: The remodeling effect in postmyopic and posthyperopic laser ablations.

impact on laser-based procedures, especially in surface ablation techniques. This fact is more important in the case of irregular corneal surface because the epithelium has a remodeling (filling) feature, which masks the real corneal power and a significant portion of the underlying corneal irregularities as shown in Figure 8. Moreover, the remodeling feature of the epithelium affects the outcomes

of laser-based procedures, characterized by a partial loss of effect after both myopic and hyperopic corrections. The epithelium forms a positive convex lens after myopic ablation and a negative concave lens after hyperopic correction (Fig. 9). Corneal power methods of measurements and their clinical applications are discussed in Chapter 5.

7

CHAPTER

Measuring Corneal Geometry

2

Corneal geometry is measured by “topography” and “tomography.” Topography is a term given to the data generated from the anterior corneal surface by the curvature-based devices (topographers). At the same time, tomography is a term given to the data generated from both corneal surfaces in addition to corneal thickness mapping by using the elevation-based devices (tomographers) or the optical coherence tomographers (OCT-based).

The accuracy of the keratometry measurement is affected by eye movement, misalignment, and tear film disturbance. Video keratograph can freeze the reflected corneal image, and perform the measurements once the image is captured on the video or computer screen, allowing better precision.

CURVATURE-BASED DEVICES (TOPOGRAPHERS)

The keratometer can obtain measurements from only a small central area (approximately 6%) of the anterior corneal surface and, therefore, does not show anterior surface shape. The photokeratoscope (illuminated kerato­ scope) was developed to generate qualitative information about the shape of most of the anterior surface of the cornea. It is a qualitative reflection-based device that is based on Placido disk, consisting of series of concentric rings (10 or 12 rings) or a cone with illuminated rings lining the internal surface of the instrument (Fig. 2). It obtains information from almost 60–70% of the total anterior corneal surface. Depending on the shape of the reflected rings and the spaces in between, the shape of the anterior surface of the cornea can be predicted; for instance, small,

The anterior surface acts as a transparent convex mirror; it reflects part of the incident light. Many devices have been developed to assess the anterior surface by measuring the reflected light. These noncontact devices use a light target (in different shapes) and a microscope or other optical systems. The instruments are either quantitative or qualitative and are either reflection-based or projectionbased.

Keratometry

Photokeratoscopy

Keratometry is a quantitative reflection-based measurement. The keratometer measures corneal radius on a ring at 15° around the corneal apex. It uses the keratometric formula and the keratometric refractive index (1.3375) to measure the keratometric curvature power at the 3.2 mm central circle of the anterior corneal surface as shown in Figure 1.

Fig. 1: The Sim-K measurement.

Fig. 2: The Placido disk.

Chapter 2: Measuring Corneal Geometry

A

B

Figs. 3A and B: The reflection of Placido mires from the anterior tear film layer. (A) A regular cornea; (B) An irregular cornea; the red arrow points at a steep area where the mires are crowded, while the white arrow points at a flat area where the mires are separated by wide intervals.

narrow, and closely spaced rings suggest steep regions with small radius of curvature (Figs. 3A and B). The use of the photokeratoscope was replaced by modern topographers.

Computerized Videokeratoscopy The principle is similar to photokeratoscopy. It is a photokeratoscope provided with a central video camera that captures the reflected rings from the tear film layer, and software to analyze the data. The computer numerically evaluates the distance between the concentric rings (dark and light areas) and calculates the power accordingly. The shorter the distance, the higher the power, and vice versa. The computer displays the results as a color-coded map as shown in Figure 4. The Placido cone may be large or small, according to the manufacturer. The larger the cone, the more the rings and the larger the evaluated area. The mires of most systems do not cover the very central cornea and paralimbal area as shown in Figures 3A and B. The reproducibility and validity of videokeratoscopy measurements mainly depend on the accuracy of manual adjustment in the focal plane.

Maps Generated by Topographers Topographers generate three types of maps: the sagittal (axial) curvature map, the tangential (instantaneous or local) curvature map, and the elevation map, but all are for the anterior corneal surface. The topographer directly measures the anterior curvature maps, from which it indirectly calculates (reconstruct) the anterior

Fig. 4: The interpretation of Placido mires’ shape into a color-coded map. Hot colors indicate a steep area, while cold colors indicate flat areas.

elevation map. The principle of these maps is discussed in detail in Section 2.

Limitations of Curvature-based Topography Data obtained by the Placido-based devices has the following limitations: • They provide information about the first layer over the cornea, namely the tear film layer. That is why tear film

9

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Section 1: Introduction

The tomographers obtain information from both corneal surfaces in addition to corneal thickness. There are three types of elevation-based tomographers with three different principles: 1. Slit-scanning devices: The slit-scanning technology uses two parallel vertical white, flash slit-lights to perform parallel vertical scans through the projection of a number of optical slits, nasal and temporal, onto the cornea at a fixed angle (45°) to the instrument axis (Fig. 5). Afterward, the digital confront video camera

captures the slits. Their anterior and posterior edges are subsequently analyzed and reconstructed to generate data from anterior and posterior corneal surfaces, corneal thickness, the anterior chamber, and part of the crystalline lens, depending on the size of the pupil. 2. Scheimpflug-based devices: They use the Scheimpflug camera, which is based on the Scheimpflug principle by which an obliquely tilted object can be placed in a maximum depth of focus with a minimal image distortion (Fig. 6). The Scheimpflug system consists of a rotational central blue (UV free) slit-light that coincides with a fixation target, and a lateral rotational Scheimpflug camera (Fig. 7). The rotational measuring procedure generates Scheimpflug images in three dimensions. The difference between the Scheimpflug camera and the conventional camera is in three planes (the picture plane, the objective plane, and the film plane). The planes are parallel in the conventional camera (Fig. 8), while they are not parallel, but they intersect in one line or one point in the Scheimpflug camera (Fig. 6) to get a higher depth of focus and a sharp picture but distorted. The collected data are analyzed and reconstructed to generate data from anterior and posterior corneal surfaces, corneal thickness maps and profiles, the anterior chamber, and part of the crystalline lens, depending on the size of the pupil. 3. LED-based devices: This technology is color lightemitting diode tomography that uses a multicolor (red, yellow, and green) spot pattern, which analyses the specular reflection using 679 light-emitting diodes (LED) spots superimposed on the cornea (Fig. 9). Each LED is positioned with its neighbors in a matrix pattern to give GPS-like coordination. This ray tracing technology, combined with the second-Purkinje imaging technology, measures the relative position of

Fig. 5: The principle of the slit-scanning technology.

Fig. 6: The principle of the Scheimpflug camera.

•

• •

•

disturbance, ocular surface diseases (OSDs), and the chronic use of topical medications, such as antiglaucoma, alter the tear film and, to some extent, the epithelium, leading to variable and unreliable measurements. They provide no information about the posterior corneal surface. Therefore, early ectatic changes cannot be detected. They provide no information about corneal thickness profiles. Apart from the very central blind spot that corresponds to the location of the camera, the evaluated area is almost the central 60–70% of the anterior corneal surface. Therefore, peripheral pathologies are missing, such as pellucid marginal degeneration (PMD), peripheral keratoconus (KC), and peripheral scars. The elevation map is calculated (reconstructed) from the curvature map. Any errors in measuring the latter affect the former. Moreover, the sagittal map is based on a reference axis known as videokeratoscopic (VK) normal (Chapter 1). It is a misleading axis in the case of large angle kappa and misalignment. The tangential map has a deferent principle and is less affected (Chapter 5).

ELEVATION-BASED TOMOGRAPHERS

Chapter 2: Measuring Corneal Geometry

Fig. 7: The principle of the Scheimpflug-based technology. Lateral rotating Scheimpflug camera, central rotating UV-free slit-light, and central fixation target.

Fig. 8: The principle of imaging in the conventional camera.

Fig. 9: The LED-based ray-tracing imaging device.

Fig. 10: The principle of the LED-based ray-tracing imaging technology.

each point, i.e., elevation increases the distance between points while depression decreases the distance (Fig. 10), and to calculate the power accordingly. This technology provides information from corneal surfaces in addition to corneal thickness, but not from the anterior chamber or the crystalline lens.

OCT-BASED TOMOGRAPHERS This type of tomographers is based on high-resolution anterior segment OCT (Fig. 11). Devices differ according

to the range of specifications and the maps and profiles they provide. The ideal device provides noninvasive tear film analysis, epithelial and stromal mapping, in addition to power, elevation, and thickness maps and profiles.

TOPOGRAPHY VERSUS TOMOGRAPHY Table 1 is a comparison of the three technologies. In summary: • The topography provides information from the anterior corneal surface, while the tomography measures both.

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Section 1: Introduction

Fig. 11: The anterior segment OCT-based tomography.

Table 1: Comparison topography and tomography. Specifications

Topography

Elevation-based tomography

OCT-based tomography

Coverage

Central 60–70%

Limited limbus-to-limbus

Limbus-to-limbus

Central blind spot



X

X

Evaluated surface

Anterior surface

Both surfaces

Both surfaces

Posterior surface

X



Better

Total corneal power

X



Better

Ray tracing for IOL

X



Better

Pachymetry map and thickness profiles

X



Better

Epithelial and stromal map

X

X



Angle kappa measurements

Directly

Indirectly

Indirectly

Tear film disturbance or OSD

Significantly affected

Less affected

Less affected

Tear film analysis

Some devices

X



Affection by angle kappa







Affection by misalignment







(IOL: intraocular lens; OCT: optical coherence tomography; OSD: ocular surface disease)

• The posterior corneal surface is measured and evaluated by the tomographers. The OCT-based tomography is much more accurate than Scheimpflug because it is much less affected by stromal haze and scarring. • The tomographers measure total corneal power with the OCT-based being much more accurate because they are much less affected by stromal haze and scarring. • Ray tracing for IOL calculation is measured by the tomographers with the OCT-based being much more accurate because they are much less affected by stromal haze and scarring. • The corneal thickness map and profiles are not obtained by the topography. • The epithelial map is obtained by the OCT-based tomography.

• Since the Placido-based technology is reflection-based, it is much more accurate than the elevation-based tomography in describing the anterior corneal surface in the case of scars and stromal haze. In the elevation-based tomography, light suffers from scattering and provides misleading information. That makes the topography more accurate in the topography-guided customized laser vision correction. On the other hand, the OCTbased tomographers are superior in the case of haze and scars because the wavelength of the light used in the OCT is much shorter than that used in the elevation-based tomographers. • The angles kappa, alpha, and lambda are measured directly by the topographers and indirectly by the tomographers.

Chapter 2: Measuring Corneal Geometry

• The topography is significantly affected by tear film disturbance and OSDs, while the tomography is less affected. • Tear film analysis is provided by the OCT-based tomographers and some topographers. • The maps generated by the three technologies are affected by abnormal angle kappa and misalignment while capturing the cornea; therefore, they need skillful interpretation.

Elevation-based Tomographers

SYSTEMS AVAILABLE IN THE MARKET

Hybrid Devices

Several systems are available in the market with different specifications.

Topographers • The OCULUS Keratograph ®   5M (Oculus, Wetzlar, Germany). • The CSO ANTARES® and MODI’ 02 (CSO, Costruzione Strumenti Oftalmici, Italy). • The Topcon CA-800 ® corneal analyzer (Topcon Corporation, Japan). • The TOMEY TMS-4® Topographer (Tomey Corporation, Japan).

The Pentacam® (Oculus, Wetzlar, Germany) is the only pure Scheimpflug-based tomographer available in the market. Other Scheimpflug-based tomographers are combined with Placido.

LED-based Tomographers The Cassini® (i-optics, The Hague, Netherlands) is the only pure LED-based tomographer available in the market.

Some devices implement more than one technology to gain more advantages and overcome some disadvantages. • The Orbscan® (Bausch & Lomb Surgical, Inc) combines slit-scanning with Placido. • The SIRIUS® (CSO, Italy) combines Scheimpflug with Placido. • The Galilei ® (Ziemer Ophthalmic Systems AG, Switzerland) combines double Scheimpflug with Placido. • The Tomey TMS-5 ® (Tomey Corporation, Japan) combines Scheimpflug with Placido. • The CSO MS-39® (CSO, Italy) combines anterior segment OCT with Placido. • The Tomey CASIA2® (Tomey, Japan) combines anterior segment OCT with Placido.

13

CHAPTER

Screening Guidelines

The device settings should be adjusted based on international guidelines to: • Display the captures in a standard form to make it easy to compare with other visits and other centers using the same device. • Validate the capture systematically. • Avoid false findings and, therefore, over- and underestimation. Screening guidelines are related to display and validation.

3

THE FOUR-COMPOSITE MAP The four-composite map is the main map to be studied. There are different types of this map as shown in Figure 1. The standard map in clinical practice is the “Four Maps Refractive” (Fig. 2).

GENERAL SETTINGS (FIG. 3) • Radius of curvature: Select horizontal/vertical (Rh and Rv) rather than flat/steep. That makes it easier

Fig. 1: List of maps and displays in the Pentacam HR.

Chapter 3: Screening Guidelines

Fig. 2: The “4 Maps Refractive” display. It is the standard map in clinical practice.

Fig. 3: The recommended general settings in the Pentacam HR.

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Section 1: Introduction

•

• • •

•

•

•

•

to recognize with-the-rule (WTR) astigmatism (vertical Rv in red) from against-the-rule (ATR) astigmatism (vertical Rv in blue). Axis of astigmatism: Select the flat (blue) rather than the steep (red) because the flat axis is the axis of the correcting minus cylindrical lens, which makes it easy to compare it with the manifest astigmatism in the minus cylindrical equation. The box of “Show sign of Astigmatism” should be left blank because, in many instances, the sign is misleading. The option “Store 9 mm Zone setting” is discussed below in the “Maps Overlay.” The “Shape factor presentation”: Select Asphericity (Q-value). Q-value is the standard expression used to describe the overall slope of the cornea in the selected zone. The “Eccentricity Calculation Zone”: It is measured in the 6-mm ring when the “peripheral mm-Rings” option is selected, or in the 20°-ring when the “Sagittal Angle” option is selected; however, both are the same. The 6-mm (or the 20°) ring is the standard one because it is the functional optical zone of the cornea. In the “Elevation Reference Shape,” select the Sphere, Float, and Optimize Shift mode with a Manual Calculation Diameter of 8 mm. This is discussed below in “Reference Shape.” The “Anterior Chamber Depth Range”: Select the “Internal (Endothelium)” to measure the anterior chamber depth (ACD) from corneal endothelium to the anterior surface of the crystalline lens. In the “External (Epithelium)” option, corneal thickness is included. The external ACD is used for Phakic IOL (PIOL) calculations, while the internal ACD is considered for glaucoma workup and to indicate or contraindicate PIOL implantation. In the “Color Map Appearance,” select the Black Dots option rather than White Area option because missing

Fig. 4: The curvature map in the 0.25 D color scale. This scale is very fine and exaggerates the colors but not the values.

data can easily be recognized in the former display. This is discussed below in “Maps Overlay.”

MAIN COLOR BAR SETTINGS There are two types of the color scale, the normalized and the absolute types. In the normalized scale, the computer provides color contour maps based on the average dioptric value of the measured cornea. The disadvantage is that the color of two maps cannot be compared directly and have to be interpreted based on the values. In the absolute (standardized) scale, the computer displays all corneas on the same scale, making a comparison between corneas possible. Additionally, the color increments of the curvature map can be chosen to be in 0.25, 0.5, 1 or 1.5 D scales. In general, using finer scales exaggerate irregularities while using coarser scales may hide them, as shown in Figures 4 to 6. It is recommended to use the 1 D scale with

Fig. 5: The curvature map in the 0.5 D color scale. This scale is fine and exaggerates the colors but not the values.

Fig. 6: The curvature map in the 1.00 D color scale. This scale is neutral, i.e., neither coarse to hide nor fine to exaggerate the details.

Chapter 3: Screening Guidelines

the sagittal map and the 1.5 D scale with the tangential map to avoid over- and underestimation. The same can be said for elevation and pachymetry maps. For the elevation maps and pachymetry map, it is recommended to use the 5-mm and the 10-mm scales, respectively (Fig. 7). Additionally, there are different sets of color scales in the Pentacam software, Oculus, Holladay Primary, American Style, Atlas (fixed), Belin Intuitive, Smolek/Klyce USS, Ambrosio2, and TMS. These sets of colors differ in

color coding but not in the displayed values. Professors Michael Belin and Renato Ambrosia recommend using Belin Intuitive for the curvature map and the elevation maps, and Ambrosio2 for the pachymetry map. However, readers are free to choose the color set that they are satisfied with, but in all cases, it is strongly advised to use the absolute color scale, the 1 D scale for the curvature map, the 1.5 D scale for the tangential map (Smolek/Klyce scale), the 5-mm scale for the pachymetry map, the 10-mm scale for the elevation maps, and the 61 colors option.

MAPS OVERLAY Map overlay consists of the components that should appear on the map for the complementary study.

Curvature Map Overlay

Fig. 7: Color scales for the curvature, pachymetry, and elevation maps.

Figure 8 shows the overlay of the curvature map. • Apex position: It is the position of the cornea vertex. • Thinnest location. • Minimum radius position front: It is the position of the maximum K-readings (Kmax) on the anterior corneal surface. It is usually encountered in the center of an island of high K-readings known as “hot spot” (Fig. 9; red arrow). If it is very peripheral, it might be an artifact due to a peripheral scar, lid interference of the capture, or tear film disturbance (Fig. 10). • Pupil center and pupil edge are essential to check for misalignment. Pupil edge is important to study power

Fig. 8: Overlay for the anterior sagittal curvature map.

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Section 1: Introduction

Fig. 9: Kmax symbol within the center of the hot spot.

Fig. 10: A very peripheral Kmax symbol, indicating an artifact. The capture should be repeated.

Fig. 11: Extrapolated data displayed as black-dotted areas at the corneal periphery.

Fig. 12: Extrapolated data displayed as a blank white area at the corneal periphery.

gradient along the pupil in customized laser vision correction. • Nasal/temporal and OD/OS. • Maximum diameter 9 mm: The 9-mm display is important to check the quality of the capture. In the case of missing data, the computer will extrapolate the areas of missing data either in black dots (Fig. 11) or white blank areas (Fig. 12). As mentioned above in the general settings, extrapolation is easier to be recognized with the “black dot” option. If there were extrapolated areas on the full diameter map (Fig. 11), and they do not disappear

on the 9-mm magnified display (Fig. 13; blue arrows), the capture cannot be accepted. Figures 14 and 15 represent a case of extrapolation that disappears on the 9-mm magnified display. • N u m e r i c v a l u e s a n d m i n i m u m / m a x i m u m values: The distribution of keratometric power of the anterior sagittal map as blue (flat) and red (steep) segments (semimeridians). This option is important for predicting corneal irregularities and studying and classifying the patterns, as discussed in Chapter 5 in detail.

Chapter 3: Screening Guidelines

Fig. 13: Extrapolated data in the 9-mm display (red circle).

Fig. 14: Mild peripheral extrapolation on the full display. It disappears on the 9-mm display in the next figure.

Fig. 15: Disappearance of extrapolation on the 9-mm display. See the previous figure.

Fig. 16: Overlay for the elevation maps.

Elevation Maps Overlay Figure 16 shows the overlay of the elevation maps displayed in the best fit sphere (BFS) and the best fit toric ellipsoid (BFTE) modes (see Reference Shape below). • The symbol of the thinnest location (red arrows) is important to study the corresponding values on the elevation maps (Chapter 6). • Nasal/temporal and OD/OS.

• Maximum diameter 9 mm. • Full numeric values should be displayed (blue arrow).

Thickness Map Overlay Figure 17 shows the overlay of the thickness map. • Thinnest location. • Nasal/temporal and OD/OS.

19

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Section 1: Introduction

Fig. 17: Overlay for the corneal thickness map.

Fig. 18: The standard 8-mm zonal diameter for the BFS reference surface.

• Maximum diameter 9 mm. • Full numeric values should be displayed.

Reference Body Shape There are five types of reference body in the Pentacam. The standard types are the BFS and the BFTE. Both should be displayed in optimize shift float mode and 8 mm in diameter, as shown in Figure 18. The display and the values are very affected by the diameter. Using a smaller diameter underestimates irregularities (false negatives), while using a larger diameter overestimates (false positives) irregularities. Figures 19 to 21 show how the elevation map differs when adjusted in different diameters.

SPECIFIC SETTINGS FOR HOLLADAY REPORT Figure 22 shows the general settings for Holladay report. These settings are automatically set by default. Figure 23 is the corneal thickness map overlay. Figure 24 is the overly for the rest five maps.

IMAGE QUALITY CONTROL Purpose Obtaining reliable and repeatable images is important for the following reasons: • Candidate selection for refractive surgery. • Postoperative follow-up.

Chapter 3: Screening Guidelines

Fig. 19: Posterior elevation map with the standard 8-mm BFS.

Fig. 20: The same posterior elevation map with a 5-mm BFS. Values are underestimated.

• If the patient is pregnant, refractive surgery is not recommended, and corneal evaluation will not be accurate. • Recommend the patient to bring all reports and tests if there were previous corneal or ocular surgeries or comorbidity.

Capturing the Cornea

Fig. 21: The same posterior elevation map with a 10-mm BFS. Values are overestimated.

• Evaluation of ectatic corneal diseases (ECDs). • Observing the progression of ECDs. • Research and studies.

Before the Appointment Obtaining good quality of captures starts from the first call for an appointment. Before arranging an appointment, the call center should explain the following: • Using contact lenses should be stopped at least 1 week before the visit.

Some factors produce false findings (false positives and false negatives). The sources of these factors should be avoided before capturing the cornea and should be recognized after the capture to avoid misinterpretation. The sources are discussed in detail in Chapter 17. • Before capturing the eye, the technician should: – Be sure that contact lenses were stopped for at least 1 week. – Explain to the patient the proper method of fixation to avoid misalignment. – Take into consideration any anatomical features that may interfere with full eye exposure to the camera. – Be sure that any head cover, including head scarfs, should be aside from the camera pathway. – Alert the physician if the patient is pregnant, has dry eye symptoms, had a history of eye infection (source of corneal scars or opacities), or had a history of previous corneal surgery. • While taking the capture, the technician: – Should align the device properly. – Should monitor the eye continuously. – Must not use anesthesia drops. If the technician finds the patient blinking frequently, dry eye is suspected.

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Section 1: Introduction

Fig. 22: General settings for the Holladay report.

Fig. 23: Overlay for the corneal thickness map in the Holladay report.

Anesthesia drops are forbidden because they alter the integrity of the epithelium, tear film, and corneal surface. – Should not be using lubricant drops immediately before the capture. Dry eye disease should sufficiently be treated before the examination.

Validating the Quality of the Capture After taking the capture, there are two steps for validating the quality of the captures. The first step is performed by the

Fig. 24: Overlay for the other five maps, in the Holladay report.

technician before printing the examination, and the second step is performed by the physician when they receive the printed examination.

Technician Step Before printing the capture and sending it to the physician, the technician should validate the capture by the following steps: • Quality specification (Qs): It should be white “OK.” If it is not white OK, repeat the capture. In the case of repeatable bad QS, such as in corneal opacities, very

Chapter 3: Screening Guidelines

•

•

•

•

distorted corneas in ECDs, or after operations, do the following: – Click on the QS box to display the items (Fig. 25). – Select the captures with the least extrapolation and data gaps. – Write a note to the physician explaining that. No extrapolated area in the 9-mm display. If there is extrapolation, as in Figure 13, the capture should be repeated. Km: Three captures should be taken in the session. The Km (mean K reading on the anterior corneal surface) is compared. If >0.3 D difference is found between the captures, they should be repeated. If the difference is insignificant, the capture with the median number is reliable. Example 1: three captures with Km 45.3 D, 45.8 D, and 45 D, the captures should be repeated. Example 2: three captures with Km 43.4 D, 43.7 D, and 43.5 D, the captures are accepted, and the median one (43.5 D) is reliable as the main capture for this visit. That is important, especially in observing the progression of ectatic corneal diseases (ECDs) and comparing pre- with postoperative results. Please note that the variation in Km is high in ectatic eyes, hence needing to be patient while taking the captures. Kmax: Check the symbol of the maximum K-reading (Kmax) on the anterior sagittal map. If it is very peripheral, as in Figure 10, recapture the cornea; if it is repeatedly peripheral, check lid position on Scheimpflug images; if there is no lid interference, tell the physician to check tear film and look for blepharitis, inferior punctate epithelial erosions, or corneal scars. Misalignment: To rule out misalignment and differentiate it from large angle kappa, compare X and Y coordinates of pupil center between the two eyes. Usually, the sign of X is –ve in the right eye and +ve in the left eye, and vice versa in case of negative angle Kappa (e.g., high axial myopia).

Fig. 25: The detailed report of quality specification (Qs) of the capture.

On the other hand, the sign of Y should be similar in both eyes, i.e., both –ve or both +ve. To check misalignment, calculate X + X and Y − Y. If X + X and/or Y − Y > 0.2 mm (>200 mm), there is misalignment (Fig. 26; red arrows), and the capture should be repeated. On the other hand, angle kappa is symmetric in both eyes regardless of its value. Figure 27 is an example of a large angle kappa. In the case of large angle kappa, an abnormal skewed radial axis index (SRAX) can be considered insignificant and can be neglected. Fundamentally, the Pentacam does not measure angle kappa directly. There are two methods to estimate the angle by the Pentacam, chord m in the Holladay report, and considering half the values of X and Y coordinates of pupil center, if Holladay report is not available. Figure 28 is the Holladay report measuring chord m (red ellipse). It is the chord distance from vertex normal (assumed to be the visual axis) and the pupil center. On the Pentacam, the normal value is 0.20 ± 0.11 mm, so values above 0.42 mm (highlighted in yellow) would be highly unusual. Chapter 24 is devoted to Holladay report. Figure 29 shows the X and Y coordinates of the pupil center. In this example, angle kappa is roughly around (–0.10, +0.02) in OD and (–0.02, –0.05) in OS.

Physician Step The physician should check the followings before accepting the capture: • Check Qs. Qs should be white OK. • Check if any extrapolated area in the 9-mm display, as mentioned above.

Fig. 26: Misalignment. A significant difference in the pupil-center Y-coordinate between the two eyes.

23

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Section 1: Introduction

• Check misalignment, as described above. • Check astigmatic disparity. Compare tomographic astigmatism (TA) with the subjective manifest astigmatism (MA). The accurate method to measure TA is the total corneal refractive power (TCRP) at the 3-mm ring centered with the apex (Fig. 30). If that is not available, it can be calculated roughly by deducting posterior astigmatism from anterior astigmatism (Fig. 31) and using the flat anterior axis. Please note that the sign of astigmatism should not be displayed to avoid confusion. In Figure 31, the anterior astigmatism is 4.7 D, and the posterior astigmatism is 0.9 D. Therefore, TA = 4.7 − 0.9 = 3.8 D × 3.3° (the flat axis of anterior astigmatism). This TA should be compared with the MA using the absolute value at the flat axis.

Fig. 27: Large angle kappa. Intereye symmetric coordinates of the pupil center.

A difference between the TA and MA of ≥1 D in magnitude or ≥10° in axis is considered abnormal, and the capture should be repeated. If the disparity continues to appear in the following captures, exclude early cataract, corneal opacities, and other sources of false findings.

Fig. 28: The Holladay report. The red ellipse indicates chord m, which is an approximation of angle kappa.

Chapter 3: Screening Guidelines

Fig. 29: The pupil center coordinates relative to the corneal apex.

Fig. 30: The total corneal refractive power (TCRP) in the power display. The red arrows indicate the standard settings: ring/apex. The red ellipse indicates the true total corneal astigmatism measured by the TCRP at 3-mm ring/apex.

25

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Section 1: Introduction

Fig. 31: Estimating tomographic astigmatism by subtracting the absolute values of the posterior from the anterior astigmatism and using the flat axis of the anterior astigmatism.

SECTION

2 Tomographic Maps and Profiles ◆ Overview

◆ Corneal Thickness Maps and Profiles

◆ Corneal Power Maps

◆ Geometric Tomography and

◆ Elevation Maps ◆ Belin/Ambrósio Enhanced Ectasia

Corneal Topometry

CHAPTER

Overview

4

The four-composite refractive map consists of corneal parameters, displayed on the left side, and four maps displayed on the right side of the display. Corneal parameters are cornea front (anterior corneal surface), cornea back (posterior corneal surface), landmarks, and miscellaneous. The four maps on the right side are anterior sagittal curvature map, anterior and posterior elevation maps, and the pachymetry (thickness) map. Both eyes should be studied for accurate decisions.

CORNEAL PARAMETERS (FIG. 1) Cornea Front (Anterior Surface) • Qs: Quality specification. It specifies the quality of the tomographic capture; it should be white “OK”; otherwise, there is missing information that was extrapolated, and the capture should be repeated. However, in some instances, there is misalignment despite good white Qs (Chapter 17). • Q-val: It represents the asphericity of the anterior surface of the cornea. It should be adjusted to display the 6 mm zone. • K1: The anterior flat simulated keratometer (Sim-K1) on a 15°-ring (at 3.2 mm) around the corneal apex. • Rh: Horizontal radius of anterior corneal curvature of the central Sim-Ks. If it is in blue, the cornea has withthe-rule (WTR) astigmatism. If it is in red, the cornea has against-the-rule (ATR) astigmatism. • K2: The anterior steep simulated keratometer (Sim-K2) on a 15°-ring (at 3.2 mm) around the corneal apex. • Rv: Vertical radius of anterior corneal curvature of the central Sim-Ks. If it is in red, the cornea has WTR astigmatism. If it is in blue, the cornea has ATR astigmatism. • Km: The anterior Km is the arithmetic mean (average) of the central Sim-Ks of the anterior surface. In the normal population, it is I. Since most of the devices do not show the

Chapter 5: Corneal Power Maps

Fig. 13: Patterns of the anterior sagittal curvature map.

Fig. 14: Horizontal bowtie indicating against-the-rule astigmatism.

difference in this way, and to simplify the method of reading, the difference between the inferior and the superior values on the vertical meridian on the second circle of numbers can be considered (Fig. 23).

Fig. 15: Oblique symmetric bowtie indicating oblique astigmatism.

Group C (Angulated Patterns) It consists of two patterns: symmetric bowtie with skewed radial axis index (SB/SRAX) (Fig. 24) and asymmetric bowtie with skewed radial axis index (AB/SRAX) (Fig. 25).

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Section 2: Tomographic Maps and Profiles

A

B

C

Figs. 16A to C: Sectors defining the orientation of corneal astigmatism. (A) With-the-rule (WTR); (B) Against-the-rule (ATR); and (C) Oblique.

Fig. 17: Asymmetric bowtie inferior steep.

Fig. 18: Asymmetric bowtie superior steep.

Fig. 19: Inferior steep.

Fig. 20: Superior steep.

Chapter 5: Corneal Power Maps

Fig. 21: Principle of calculating the inferior, superior (IS) index based on the Rabinowitz method.

Fig. 22: The inferior, superior (IS) index on the topometry display.

Group C is considered abnormal when the angle between the axes of the superior and inferior segments in the innermost circle (3 mm) is >21° AND the Sim-K astigmatism is significant (≥1 D). In the case of insignificant astigmatism, any SRAX can be ignored (Fig. 26).

Group D (Special Shapes) It consists of crab-claw (Fig. 27), butterfly (Fig. 28), vertical D (Fig. 29), clown face (Fig. 30), vortex (Fig. 31), and unspecific irregular patterns. The unspecific irregular pattern is found in 7% of the normal population. The other five patterns in this group are always abnormal.

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Section 2: Tomographic Maps and Profiles

Fig. 23: The approximate estimation of the inferior, superior (IS) index.

Fig. 24: Symmetric bowtie with skewed radial axis index.

Fig. 25: Asymmetric bowtie with skewed radial axis index.

Fig. 26: Insignificant skewed radial axis index.

CLINICAL DIFFERENCES BETWEEN THE SAGITTAL AND TANGENTIAL CURVATURE MAPS • The tangential map is more susceptible to local curvature changes because it depends on circles. Therefore, it is more capable of revealing corneal irregularities.

That is clear when comparing the sagittal (A) with the tangential (B) in Figures 32A and B; both are for the same cornea. • The tangential map is better in describing the contour of zones. Therefore, it is better used for cone description in ECDs, and in describing operated corneas (Chapter 24).

Chapter 5: Corneal Power Maps

Fig. 27: Crab claw.

Fig. 28: Butterfly.

Fig. 29: Vertical D.

Fig. 30: Clown face.

• Each point on the tangential map is calculated independently, i.e., there is no reference axis. Therefore, it is, to some extent, less affected by misalignment during acquisitions.

• K-readings obtained by the tangential map are higher than when obtained by the sagittal map. Therefore, the tangential map K-readings cannot be used in IOLcalculation formulas.

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Fig. 31: Vortex pattern.

A

B Figs. 32A and B: Comparison between the anterior sagittal map and the anterior tangential map for the same cornea.

CHAPTER

Elevation Maps PRINCIPLE OF THE ELEVATION MAPS The surface of the cornea is mostly similar to the surface of the Earth in terms of elevations and depressions. The main difference between the Earth and the cornea is that the former has a reference surface (RS), namely the sea level, to which all elevations (mountains) and depressions (valleys) are related. Because the cornea has no similar natural RS, it is imperative to create an artificial one based on the mean central radii of the examined surface.

6

main positions of the RS, the float and the nonfloat modes (Fig. 5). In the float mode, the computer adjusts the position of the RS based on the average radii of the central zone of the cornea. To make it easy to understand, it applies the a + b = c principle, as shown in Figure 5, to adjust the RS in a neutral

THE REFERENCE SURFACE Principle The software creates an RS for each surface being captured (Fig. 1). It considers all points above the RS as elevations, displayed in positive values and given hot colors, and considers all points below the RS as depressions, displayed in negative values and given cold colors; all values are in microns. The coincidence points between the RS and the measured surface are displayed as zeros, i.e., exactly like the sea level (Fig. 2). Figure 3 is an elevation map generated by the software for the anterior corneal surface of the left eye. The shape of the elevation map depends on four factors related to the position, steepness, diameter, and shape of the RS.

Fig. 2: The principle of measurement and the color scale of the elevation maps.

Position of the Reference Surface Figure 4 represents different positions of the same RS in relation to the same corneal surface. Obviously, the values differ according to the position. In general, there are two

Fig. 1: The principle of the elevation maps.

Fig. 3: An example of the elevation map of the anterior corneal surface.

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position where all elevations are equal to all depressions. In the nonfloat mode, the RS touches the apex of the cornea regardless of the elevations and depressions. Figures 6A and B represent the float (right image) and the nonfloat (left image) of the same corneal surface. Interestingly, the float mode may touch the apex of the cornea when the cornea is very regular and symmetric, as in Figure 7. The standard position of the RS that should be used as a default is the float mode.

Parameters

Fig. 4: Position effect.

Each RS is specified by two parameters, the radius (blue ellipse) and the diameter (red ellipse), as shown in Figure 8. The software chooses the radius of the RS based on the mean radii of the central corneal surface. The diameter is the diameter of the used zone of this specific RS. Figure 9 is an illustration of this concept. In this figure, a spherical RS is demonstrated. As shown in this figure, same corneal surface and same RS in A and B (RS radius = 7.81 mm), but the difference is in the diameter of the studied zone; 8 mm

Fig. 5: A schematic view of the float mode and nonfloat mode.

A

B Figs. 6A and B: The elevation map in the float (A) and the nonfloat (B) mode for the same corneal surface.

Chapter 6: Elevation Maps

in A and 10 mm in B. As mentioned before, the software in the float mode adjusts the position of the RS based on the principle a + b = c. Due to this principle, the corneal surface takes a more prominent position in larger diameters and vice versa. Choosing a larger diameter causes false positives because of increased sensitivity and reduced specificity while choosing smaller diameters causes false negatives (hides the cone) due to reduced sensitivity and increased specificity, as shown in Figures 10A and B. In this figure, the diameter on the left (A) is 10 mm and 5 mm on the right (B). Notice the difference in the presentation of the center of the same corneal surface. The standard diameter that should be used as a default is 8 mm.

Types There are two standard shapes of the RS: the sphere and the toric ellipsoid (Fig. 11).

Best Fit Sphere Fig. 7: The regular, symmetric hourglass shape on the elevation map, indicating regular corneal astigmatism.

This shape is recommended by Michael Belin and Renato Ambrosio as the standard RS to display the elevation data.

Fig. 8: The parameters of a reference surface.

Fig. 9: A schematic view illustrating the principle of reference surface diameter.

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A

B

Figs. 10A and B: Two different elevation maps for the same corneal surface. The difference comes from different diameters.

Fig. 11: The two standard shapes of the reference surface.

Since the shape of the cornea is conoidal (aspherictoric-asymmetric), the Best fit sphere (BFS) RS highlights corneal astigmatism and can describe elevation patterns (see below). Based on the 8-mm BFS, Khachikian, Belin, and Ambrosio determined the cutoff values of elevations at the points corresponding to the thinnest location (Fig. 12). Tables 1 and 2 show the normative data for the Pentacam in myopic and hyperopic populations, respectively, in 1 standard deviation (SD), 2 SD, and 3 SD matrix. The 3 SD cut-off values are used by default for quantification. Figure 13 is an example of abnormal elevation maps using the standard BFS RS. Moreover, the posterior elevation map with the BFS is the best map to classify cone location in ectatic corneal

diseases (ECDs), as shown in Figure 14. The cone is considered central, paracentral, or peripheral when its apex is within the central 3-mm zone, between 3 and 5 mm central zones, or outside the 5-mm central zone, respectively.

Best Fit Toric Ellipsoid (BFTE) This shape is recommended by Jack Holladay to display the elevation data (Fig. 15). It is rotationally symmetrical according to three different axes (Fig. 11). Because it is the closest RS to corneal shape, this RS fits well to a normal astigmatic cornea to display the remaining irregularities and the related higher-order aberrations (HOAs). This RS is used in Holladay report to detect early keratoconus (Chapter 25).

Chapter 6: Elevation Maps

Fig. 12: Evaluating the elevation maps with the best-fit-sphere reference surface. Normal elevation maps.

Table 1: Cut-off elevation values for myopic patients.

Table 2: Cut-off elevation values for hyperopic patients.

Location

1 SD

2 SD

3 SD

Location

1 SD

2 SD

3 SD

Anterior

+3.7

+5.7

+7.7

Anterior

+2.1

+4.3

+6.5

Posterior

+8.3

+13

+17.7

Posterior

+16.3

+22.1

+27.8

(SD: standard deviation)

(SD: standard deviation)

Fig. 13: Evaluating the elevation maps with the best-fit-sphere reference surface. Abnormal elevation maps.

According to Holladay, the elevation map is considered abnormal if any value within the central 5-mm zone is >12 mm for the anterior or >15 mm for the posterior elevation maps (Fig. 16).

PATTERNS OF ELEVATION MAPS Elevation patterns should be studied by using the 8-mm BFS float optimize-shift mode. The patterns can be classified

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Fig. 14: Classification of cone location based on the posterior elevation map with the best-fit-sphere reference surface.

Fig. 15: Evaluating the elevation maps with the best-fit-toric-ellipsoid reference surface. Normal elevation maps.

Fig. 16: Evaluating the elevation maps with the best-fit-toric-ellipsoid reference surface. Abnormal elevation maps.

Chapter 6: Elevation Maps

into group A (symmetric patterns) and group B (asymmetric patterns). • Group A: Regular patterns (Figs. 17A and B). They are symmetric hourglass and central island. – Symmetric hourglass: In regular corneal astigmatism, there are two cardinal perpendicular meridians, steep and flat. When the cornea is symmetrical and regular, the float BFS RS fits the center of the cornea, generating what is known by symmetric hourglass pattern, as in Figure 7. In this pattern, the steep meridian is above the RS, while the flat meridian is below (Fig. 18). That displays the steep meridian in cold colors and minus values and the flat meridian in hot colors and plus values. The hourglass pattern reflects significant (≥1 D) corneal astigmatism on the measured surface. The hourglass is oriented

A

vertically in with-the-rule (WTR) astigmatism (Figs. 19A and B), horizon­tally in against-the-rule (ATR) astigmatism (Figs. 20A and B), and obliquely in oblique astigmatism (Figs. 21A and B). – Central island is found when the measured corneal surface has insignificant astigmatism (1 mm in size and has a relatively different steepness from the surrounding by >1 D in power and does not extend to the periphery. It may be flatter (Fig. 7) or steeper (Fig. 8) than the periphery. In both cases, it results in night glare if it is smaller than the mesopic pupil. The etiology is multifactorial, including the wound healing process, pupil size, amount of correction, ablation diameter and profile, quality of the ablation, and quality of the flap. Central island induces positive spherical aberration if it is flat, and negative spherical aberration if it is steep. • Micro-irregular pattern: It is defined as discrete irregularities described by poorly defined steep and flat areas. This pattern may resemble paraectasia pattern (Chapter 21); therefore, history taking is essential. Moreover, corneal irregularities induced by LVC can be graded into four grades based on their clinical impact. Table 1 represents Jorge Alio’s clinical grading of corneal irregularities induced by LVC. • Keratoplasty: – Penetrating keratoplasty (PKP): PKP induces irregular astigmatism due to the following determinants: ◆ Preoperative determinants: Donor age, size of recipient’s cornea, and pathologic properties of the recipient’s cornea, such as peripheral thinning

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Fig. 7: Central flat island.

Fig. 8: Central steep island.

Table 1: Grading of post-LVC* corneal irregularities. Grade

Signs and symptoms

1

• Mild symptoms at night or daylight conditions • Loss of 1–2 lines of BCVA: Useful vision for reading, driving and walking • No disability for normal life, but with discomfort • No monocular diplopia • Ray tracing abnormal. Distortion = 2–8 μm • Aberrometry: RMS = 2–3 μm

2

• Moderate disability • Loss of 3–4 lines of BCVA • Reading and driving partially affected, especially in dim-light conditions • Some patients prefer not to use the eye • Moderate monocular diplopia • Ray tracing affected. Distortion = 8–14 μm • Aberrometry: RMS = 3–6 μm

3

• Severe disability • Eye not useful for visual performance • Loss of >5 lines of BCVA: Patients prefer not to use the eye • Reading and driving affected at light conditions • Severe monocular diplopia or polyopia • Ray-tracing disaster. Distortion >14 μm • Aberrometry: RMS >6 μm

4

• Eye not useful, legally blind • BCVA = 20/200 or less • Aberrometry, ray tracing, and topography not possible to capture due to the severity of irregularities

*LVC: laser vision correction (BCVA: best corrected visual acuity; RMS: root mean square)

Chapter 10: Astigmatism

or ectasia, focal edema or scar, defects of Bowman’s layer, degree of vascularization, and previous PKP or other corneal surgeries. ◆ Intraoperative determinants: Decentration of donor and/or recipient trephination; “Vertical tilt” due to discrepancies of wound configuration, application of different trephination techniques in donor and recipient, tilt of the trephine away from the optical axis, limbal plane not horizontal, creation of steps due to change of trephination direction, high/low intraocular/intracameral pressure, and overlap of dehiscence due to vertical cut incongruence; “Horizontal torsion” due to asymmetrical placement of second cardinal suture and unfavorable alignment of the graft due to horizontal shape incongruence; excessive over/ undersizing of the donor; distortion and squeezing of the cornea (for example, dull trephine); traumatizing of the cornea by surgical instruments; suture-related factors such as suture material, suture technique (single, running, double running, combined), suture length, suture angle relative to graft-host-junction, suture tension and “depth disparity;” simultaneous intraocular interventions (triple procedures, IOL exchange, …, etc.); fixation rings and lid specula; and surgeon’s experience. ◆ Postoperative determinants: Suture-related factors such as “cheese wiring” of sutures, suture loosening, suture adjustment/selective suture removal, the timing of suture removal and sequential or all-ata-time suture removal; wound healing processes including wound dehiscence, retrocorneal membrane, incarceration of overlapping cut edges and focal vascularization; medication (for example, corticosteroids); and postoperative trauma. In addition, trephination can either be mechanical or nonmechanical (Femtosecond Laser). The latter is superior to the former in avoiding trauma to intraocular tissues, avoiding radial and tangential forces affecting tissue “squeezing,” reducing horizontal torsion “Erlangen orientation teeth,” reducing vertical tilt “perfect” congruent cut surfaces of donor and recipient, and reducing recipient, donor decentration. • Lamellar keratoplasty (LKP): What has been mentioned in PKP can be applied to LKP. However, some of the intraoperative determinants may have less impact in LKP in comparison with PKP. Both PKP and LKP induce corneal irregularities. That can be due to sutures, especially if they were asymmetric, or even after suture removal if it was uncontrolled by tomography. Figure 9 shows the orientation of corneal astigmatism on a corneal graft before suture removal. It shows a steep 120° meridian with high astigmatism.

Figure 10 shows the new orientation of astigmatism after removal of the 120° sutures. • Traumatic: Corneal trauma may result in irregular astigmatism relative to the type of trauma and the surgical technique used in the initial approach. Corneal wounds affect vision by two mechanisms: scars across the visual axis and/or scars inducing irregular astigmatism. The location, size, texture, and depth of the scar are critical to the patient’s visual potential. Tomographic features of corneal scars differ according to their size, location, and density. In general, small scars cannot be detected by the quality specification (QS) of the tomographer because the area of the scar may be extrapolated (Figs. 11 and 12). However, corneal scars are characterized by the following tomographic features: • True flattening over the area of the scar • A corresponding false overestimated thinning: There might be some thinning due to stromal contracture, but due to light scattering, the tomographer cannot obtain a real measurement of thickness through the scar, as was mentioned in Chapter 8 (see Figures 7 to 12 of Chapter 8). • A corresponding false overestimated bulging in the posterior elevation map: There might be abnormal posterior elevation due to stromal contracture, but due to light scattering, the tomographer cannot obtain a real measurement of posterior elevation through the scar. The above three criteria differentiate the tomography of the scar from the tomography of an ECD, as the latter is described by a steepening of the anterior curvature map rather than flattening in addition to abnormal posterior elevation. This is described in detail in Chapters 21 and 24. Please note that OCT-based tomographers are superior to Scheimpflug-based tomographers in the case of corneal scars and opacities. • Pathologic: Any corneal disease, inflammation, infection, dystrophy, or degeneration that alters corneal structure can potentially cause irregular astigmatism. The ocular surface disease is a significant source of irregular astigmatism. In general, dry eye, contact lens warpage, pterygium, and herpetic disease are the most common causes of induced astigmatism in nonectatic corneas. – Dry eye affects the accuracy of K-readings and induces focal irregularities, most commonly central or inferior steepening, which may mimic an early ECD (Fig. 13). Epithelial mapping, which is not available in the Pentacam, is fundamental for differentiation. In ECDs, the epithelium shows thinning and asymmetry while in the dry eye disease, it shows thickening or diffuse irregularity.

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Fig. 9: Corneal graft before suture removal.

– Extended wear of contact lenses usually induces false corneal steepening due to epithelial hypertrophy, as shown in Figure 14. OCT-based tomography is fundamental for differentiating the false steep­ ness due to contact lens wear and the true steepness associated with ECDs. The average time required for these changes to resolve after discontinuing the contact lenses depends on how often the contact lenses are used. Patients are advised to remove the contact lenses at least 1 week before any test. – Pterygium usually causes irregular WTR astigmatism (Figs. 15 and 16). Several mechanisms were suggested: obscuration of the underlying corneal tissue, leading to extrapolated data; pooling of tear at the apex of the pterygium; compression of the underlying stroma; and asymmetric contraction along the semimeridian of the pterygium. The magnitude of

the induced astigmatism is related to the size of the pterygium. – The herpetic disease may be complicated by linear dendritic and/or spot scars. Tomographic features of the traumatic scars apply here. Scars induced by other infections are usually more severe and diffuse, giving the tomographic pattern of unspecific micro-irregular astigmatism.

EVALUATION OF IRREGULAR ASTIGMATISM Both qualification and quantification of irregular astigmatism are essential. Qualification is performed objectively, while quantification is performed subjectively and objectively.

Chapter 10: Astigmatism

Fig. 10: Corneal graft after removal of the 120° sutures.

Subjective Evaluation of Irregular Astigmatism Subjective evaluation starts with suspicion, followed by a thorough examination.

Suspicion of Irregular Astigmatism Irregular astigmatism is suspected in the following cases: • Symptoms: Patients complain of low quality of vision due to shadows, glare, starbursts, ghost images, distortion of images, and monocular diplopia. • A positive family history of an ECD • Unusual manifest astigmatism (MA): Some physicians consider the MA suspicious when it is WTR >3 D, ATR >1.5 D, and oblique >2 D. • Irregular reflex on retinoscopy: Retinoscopy is a part of the subjective refraction. Irregular reflex is known as

scissoring reflex, which is the earliest sign of a subclinical ECD but can be seen in all cases of irregular astigmatism and media opacities. • Nonoptimum spectacle-corrected distance visual acuity (CDVA), but with optimum potential visual acuity (PVA). PVA is visual acuity measured with spectacles and pinhole test (PHT) or with rigid gas permeable (RGP) contact lenses. The PHT reduces the area of irregularity and enhances visual acuity, while the RGP lens creates a perfect artificial surface over the cornea and negates the irregularities. • Difficulty in determining the axis of the MA: When the patient hesitates and gives different answers for different axes, or when they cannot give a final answer when using the astigmatic fan and the astigmatic dial. • Disparity between MA and objective astigmatism (Chapter 12).

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Fig. 11: Peripheral corneal scar (black arrows). Data are extrapolated and overlooked by the QS (red arrow).

Fig. 12: Peripheral corneal scar (black arrow). Slit-lamp view of the same previous figure.

Fig. 13: Hot spot caused by dry eye.

Chapter 10: Astigmatism

Fig. 14: Hot spot caused by prolonged use of a soft contact lens.

Fig. 15: Bilateral pterygium. Slit-lamp view.

Fig. 16: Bilateral pterygium. The four-composite refractive map for the same previous figure.

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Fig. 17: Anisometropia on the horizontal meridian.

Fig. 18: Anisometropia on an oblique meridian.

• Anisometropia: It is defined by a significant difference in refractive error between the two eyes of >1 D at any meridian. Figure 17 is an example of anisometropia on the horizontal meridian. In the case of oblique astigmatism in one eye (Fig. 18), the refraction on the vertical and horizontal meridians should be calculated for comparison by the following formula:

but not for customized LVC or the workup for intracorneal ring implantation.

Fθ = (Fcyl) sin2 θ

where “Fθ” is the power in the vertical meridian, “Fcyl” is the power in the oblique meridian, and “θ” is the angle between the vertical meridian and the correcting cylinder axis.

Subjective Refraction Subjective refraction consists of MR, cycloplegic refraction (CR), and postmydriatic test (PMT). In mild cases of irregular astigmatism, determination of the MR is straight forward, while in moderate cases, it becomes a challenge, and becomes impossible in severe cases. However, all subjective measures should be tried to obtain an accurate MR, such as the astigmatic dial, astigmatism fan, crosscylinder, and over-refraction techniques. Although there are manipulations to be used in binocular balance, they are important only for the prescription of glasses,

Cycloplegic refraction is indicated in the following cases: • Nonoptimum CDVA, but with optimum PVA. • Difficulty in determining the axis of the MA. • Disparity between MA and objective astigmatism. • Anisometropia. • Disparity between the “corrected” MR and corneal refraction (Chapter 11). PMT is important to refine the results after CR, and performed after the effect of cycloplegia has resolved, usually after 3 days.

Objective Evaluation of Irregular Astigmatism Irregular astigmatism is objectively evaluated by corneal tomography/topography and wavefront analysis. • Corneal tomography and topography: Normal and abnormal tomographic patterns were discussed in Chapters 5 to 8. • Wavefront analysis: Analyzing HOAs is fundamental in decision-making for both laser-based and lens-based refractive surgery. Chapters 13 to 15 are devoted to wavefront analysis.

CHAPTER

Objective Corneal Dioptric Power

Objective corneal refraction is a term given to the calculated spherocylindric dioptric power of the cornea. Corneal power is usually measured and expressed in keratometric dioptric power (K-readings) rather than a spherocylindric dioptric power. Measuring the objective spherocylindric dioptric power (ODP) of the cornea is important for the following reasons: • Evaluating the refraction in the situations wherein manifest refraction (MR) is not applicable such as in young children and toddlers, patients with neurological deficits whose subjective responses are not reliable, and ocular media obstructions, such as cataracts, vitreous hemorrhage, and hyphema. • In the case of a significant difference between the ODP and the MR, other factors that affect the MR should be investigated, such as the accommodative spasm, abnormal depth of anterior chamber (deep or shallow), and abnormal axial length. • Measuring ODP is very helpful in ectatic corneal diseases (ECDs) and irregular corneas wherein the determination of MR may be difficult or even confusing, especially in moderate and severe cases. • The ODP can explain how the topography-guided software calculates the spherocylindric power (sphere, cylinder, and axis) in irregular and ectatic corneas. To understand how ODP is calculated, maps measuring keratometric corneal power should first be reviewed in Chapter 5.

CALCULATING OBJECTIVE CORNEAL DIOPTRIC POWER Since the total corneal refractive power (TCRP) uses ray tracing to calculate keratometric corneal power, K-readings obtained by this method are most reliable. However, capturing an accurate tomography is not always possible in uncooperative patients. In such cases, the keratometric readings can be used.

11

The ODP is calculated in the plus cylindrical equation by: • Considering the K-readings (K1 and K2) obtained from the TCRP map at 3 mm ring/apex, as mentioned in Chapter 3. • Referencing the TCRP Ks to the average K-reading found in the normal population (Kref ). The Kref differs depending on the method used to measure it and the studied population. The Kref = 43 D will be used in the calculations because the average normal corneal power is 43.05 D, as mentioned in Chapter 1. After calculating the ODP, it should be translated to the plane of spectacles because the ODP is at the plan of the cornea. Therefore, the equivalent power should be calculated at the plane of spectacles to compare it with the MR. The equivalent power is calculated by translating the ODP to the plane of spectacles after considering the back vertex distance (BVD). It is very similar to translating contact lens power backward into spectacle power. The ODP-t term refers to the translated ODP at the plane of spectacle. The following are the five-practical steps in calculating the ODP, translating it to spectacle power, and comparing it with the MR. However, since translating the power from the corneal plain to the spectacles plain (steps 4 and 5) is sophisticated, readers can follow only steps 1 to 3 and compare the ODP-t with the MR. Step 1: Obtain K-readings (K1 and K2) from the TCRP map at the 3-mm ring/apex. Step 2: Calculate the ODP astigmatism. The magnitude = K2 − K1 and the axis is the axis of K2. Step 3: Calculate the magnitude of the sphere by Kref − K2. Step 4: Calculate the ODP-t by using the following equation: ODP-t = ODP/(1 + d × ODP). Where ODP is corneal power at corneal plane, ODP-t is corneal power at spectacle plane, and “d” is back vertex distance (BVD) in meters (usually 0.012 m or 0.015 m).

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The equation should be applied to meridional power in the following steps: • The ODP is projected as the meridian of maximum power and the meridian of minimum power. • The meridian of minimum power (lowest plus or highest minus) is translated by the above-mentioned equation and is given the term ODP-t1. • The meridian of maximum power (highest plus or lowest minus) is translated by the above-mentioned equation and is given the term ODP-t2. • The ODP-t sphere = ODP-t of minimum power • The ODP-t astigmatism = ODP-t of maximum − ODP-t of minimum power. The ODP-t astigmatic axis is the meridian of the minimum power.

Step 4: The ODP is +3 D sph/+2.5 D cyl × 90°. At this point, the readers can compare the ODP-t with the MR. However, the ODP-t is calculated as follows: • The meridional power of the ODP is shown in Figure 2. • ODP-t1 = +3/(1 + 0.015 × 3) = +2.87 D@ 90°. This is the meridian of the minimum power. • ODP-t2 = +5.5/(1 + 0.015 × 5.5) = +5.08 D@ 180°. This is the meridian of the maximum power. • The ODP-t sphere = +2.87 D sph • The ODP-t astigmatism = 5.08 − 2.87 = +2.21 D × 90°

Step 5: Compare ODP-t with MR.

Example 2

CLINICAL EXAMPLES In the following examples, the easy (steps 1 to 3) and the sophisticated (steps 1 to 5) will be shown.

Example 1 A patient with right eye MR = +4 D sph/+3 D cyl × 90° for BVD = 15 mm. Figure 1 shows the two corneal meridians (K1 and K2), and shows the position of the Kref value. Step 1: TCRP K1 = 37.5 D × 180° and K2 = 40 D × 90°. This is with-the-rule (WTR) astigmatism. Step 2: ODP astigmatism = 40 − 37.5 = +2.5 D cyl × 90°. Step 3: ODP sphere = 43 − 40 = +3 D sph.

Fig. 1: The meridional power of the cornea.

Step 5: The ODP-t = +2.87 D sph/+2.21 D cyl × 90°. The MR = +4 D sph/+3 D cyl × 90°. There is no significant difference between the MR and the ODP-t.

A patient with left eye MR = −1.5 D Cyl × 90° for BVD = 12 mm. Figure 3 shows the two corneal meridians (K1 and K2), and shows the position of the Kref value. Step 1: TCRP K1 = 44 D × 90° and K2 = 47 D × 180°. This is against-the-rule (ATR) astigmatism. Step 2: ODP astigmatism = 47 − 44 = +3 D cyl × 180°. Step 3: ODP sphere = 43 − 47 = −4 D sph. Step 4: The ODP is −4 D sph/+3 D cyl × 180°. At this point, the readers can compare the ODP-t with the MR. However, the ODP-t is calculated as follows: • The meridional power of the ODP is shown in Figure 4. • ODP-t1 = −1/(1 + 0.012 × −1) = −1.01 D @ 90°. This is the meridian of the maximum power. • ODP-t2 = −4/(1 + 0.012 × −4) = −3.82 D @ 180°. This is the meridian of the minimum power.

Fig. 2: The meridional power of the objective dioptric power (ODP).

Chapter 11: Objective Corneal Dioptric Power

Fig. 3: The meridional power of the cornea.

Fig. 4: The meridional power of the objective dioptric power (ODP).

• The ODP-t sphere = −3.82 D sph. • The ODP-t astigmatism = −1.01 − (−3.82) = +2.81 D × 180°. Step 5: The ODP-t = −3.82 D sph/+2.81 D × 180°. The MR = −1.5 D sph/+1.5 D cyl × 180°. There is a significant difference between the MR and the ODP-t. Causes should be investigated.

Example 3 A patient with keratoconus with right eye UDVA = 0.3 decimal, spectacle CDVA = 0.7 decimal, and MR = −3 D sph/−3 D cyl × 75° for BVD = 12 mm. Figure 5 is the fourcomposite refractive map of his right eye. Figure 6 is the power distribution map. Step 1: TCRP K1 = 43.9 D × 54° and K2 = 47.6 D × 144°. This is oblique astigmatism.

Step 2: ODP astigmatism = 47.6 − 43.9 = +3.7 D cyl × 144°. Step 3: ODP sphere = 43 − 47.6 = −4.6 D sph. Step 4: The ODP is −4.6 D sph/+3.7 D cyl × 144°. At this point, the readers can compare the ODP-t with the MR. However, the ODP-t is calculated as follows: • The meridional power of the ODP is shown in Figure 7. • ODP-t1 = −0.9/(1 + 0.012 × −0.9) = −0.89 D @ 54°. This is the meridian of the maximum power. • ODP-t2 = −4.6/(1 + 0.012 × −4.6) = −4.36 D @ 144°. This is the meridian of the minimum power. • The ODP-t sphere = −4.36 D sph. • The ODP-t astigmatism = −0.89 − (−4.36) = +3.47 D × 144°. Step 5: The ODP-t = −4.36 D sph/+3.47 D × 144°. The MR = −6 D sph/+3 D cyl × 165. There is a significant difference between the MR and the ODP-t. Causes should be investigated.

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Fig. 5: The four-composite refractive map of the right eye. A keratoconus case.

Fig. 6: The power distribution display.

Fig. 7: The meridional power of the objective dioptric power (ODP).

CHAPTER

Astigmatic Disparity

Clinical manifest astigmatism (MA) is measured by subjective refraction, while tomographic astigmatism (TA) is objectively obtained from the total corneal refractive power (TCRP) at 3 mm ring/apex (see Figure 30 of Chapter 3). However, in daily practice, the TCRP is usually not printed. In such cases, the TA can be calculated roughly by deducting the posterior astigmatism from the anterior astigmatism (see Figure 29 of Chapter 3) and using the flat anterior axis, as mentioned in Chapter 3. MA occasionally differs from the TA. This is called astigmatic disparity. It may either be in values or in axes or both. It is considered significant if there is ≥1 D and/or ≥10° difference between MA and TA. The importance of astigmatic disparity comes from its impact on decisionmaking in refractive surgery. For instance, in laser vision correction (LVC), if MA is not consistent with the TA, there is a risk of flipping the axis of corneal astigmatism, creating irregular astigmatism, and inducing higher-order aberrations (HOAs).

12

ETIOLOGY Sources of astigmatic disparity are as follows: • Irregular astigmatism. • Use of contact lenses. • Misalignment during the capture. • Large angle kappa. • Tear film disturbance. • Corneal opacities. • Previous corneal surgeries. • Lenticular astigmatism. • Lens subluxation. • IOL tilt, dislocation, or subluxation. • Cataract: All types of cataract cause astigmatic disparity. An early cataract may be skipped by the initial slit-lamp biomicroscopy examination. Therefore, in all cases of astigmatic disparity, careful dilated examination and Scheimpflug imaging are fundamental. Figure 1 is a Scheimpflug image showing an early cataract.

Fig. 1: Scheimpflug image showing an early cataract resulting in astigmatic disparity.

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• Ocular pathologies affecting the media. • Inadequate exposure to the camera because of anatomical factors, such as prominent eyebrows, small eyes, deep-set eyes, nasal bridge or long lashes, or tight headscarves. • Pregnancy.

NB: The astigmatism is considered as WTR when the steep axis is 90° ± 15°, as ATR when the steep axis is 180° ± 15°, and as oblique if otherwise. Table 1 represents the nine probabilities.

TYPES OF ASTIGMATIC DISPARITY

In refractive lens exchange (clear lens extraction) and cataract surgery, the TA is considered because the lenticular component will be removed. In phakic IOL (PIOL) implantation, the MA should be considered regardless of the TA because the operation is not on corneal plane. In laser-based refractive surgery, the operation is on corneal plane; therefore, there are general rules that should be followed to avoid or reduce surprises as much as possible. The general rules are: • If MA > TA, avoid flipping the WTR TA into ATR TA. • If MA > TA, try reducing the difference in magnitude by compensating with the spherical equivalent (SE) without affecting the corrected distance visual acuity (CDVA). • If MR is modified, plan for enhancement.

There are nine probabilities of astigmatic disparity, depending on the difference in the magnitude and axis of astigmatism. 1. TA and MA are with-the-rule (WTR), and the magnitude of the former is more than the latter. 2. TA and MA are WTR, and the magnitude of the former is less than the latter. 3. TA and MA are against-the-rule (ATR), and the magnitude of the former is more than the latter. 4. TA and MA are ATR, and the magnitude of the former is less than the latter. 5. TA is WTR and MA is ATR, and the magnitude of the former is more than the latter. 6. TA is WTR and MA is ATR, and the magnitude of the former is less than the latter. 7. TA is ATR and MA is WTR, and the magnitude of the former is more than the latter. 8. TA is ATR and MA is WTR, and the magnitude of the former is less than the latter. 9. TA and/or MA are oblique with >15° difference between their axes.

MANAGEMENT OF ASTIGMATIC DISPARITY

Table 2 summarizes management recommendations in correlation with the probabilities mentioned in Table 1. The following are clinical examples. Example 1: MR = −1.00 D sph/−2.75 D cyl × 180 TA = −2.25 D cyl × 170 Recommended correction: −1.25 D sph/−2.00 D cyl × 180. NB: The patient may need enhancement.

Table 1: Probabilities of astigmatic disparity. Examples Probability

MA

TA

Magnitude

Number

MA

TA

1

WTR

WTR

MA > TA

1

−2.75 × 180

−2.25 × 170

2

WTR

WTR

MA < TA

2

−1.75 × 10

−2.50 × 180

3

ATR

ATR

MA > TA

3A

−2.00 × 80

−1.25 × 95

ATR

ATR

MA > TA

3B

−2.75 × 80

−1.25 × 95

4

ATR

ATR

MA < TA

4

−2.50 × 100

−3.00 × 95

5

ATR

WTR

MA > TA

5

−1.25 × 85

−0.50 × 165

6

ATR

WTR

MA < TA

6

−1.00 × 80

−1.75 × 180

7

WTR

ATR

MA > TA

7

−1.25 × 175

−0.25 × 90

8

WTR

ATR

MA < TA

8

−0.50 × 180

−0.75 × 85

9

MA, TA, or both are oblique Regardless

9

−0.75 × 55

−1.00 × 95

(ATR: against the rule; WTR: with the rule; MA: manifest astigmatism; TA: tomographic astigmatism)

Chapter 12: Astigmatic Disparity

Table 2: Management recommendations in astigmatic disparity. Probability

Treatment rules

Example a

1

Correct the magnitude of TA on the MA axis and compensate with the SE

1

2

Correct the MA

2

3 4 5 6

MA–TA ≤1 D: Correct the MA

a

3A

MA–TA >1 D: Correct the magnitude of TA on the MA axis +1 D and compensate for the residual by SEa

3B

Correct the MA

4 a

5

a

6

Recheck refraction, use the least possible amount of MA, and compensate by SE Recheck refraction, use the least possible amount of MA, and compensate by SE

7

a

Recheck refraction, use the least possible amount of MA, and compensate by SE

7

8

Recheck refraction, use the least possible amount of MA, and compensate by SEa

8

9

Correct the MA

a

9

(MA: manifest astigmatism; SE: spherical equivalent; TA: tomographic astigmatism) a Plan for enhancement

Example 2: MR = −0.50 D sph/−1.75 D cyl × 10 TA = −2.50 D cyl × 180 Recommended correction: −0.50 D sph/−1.75 D cyl × 10 Example 3A: MR = −0.50 D sph/−2.00 D cyl × 80 TA = −1.25 D cyl × 95 Recommended correction: −0.50 D sph/−2.00 D cyl × 80 NB: The patient may need enhancement. Example 3B: MR = −0.50 D sph/−2.75 D cyl × 80 TA = −1.25 D cyl × 95 Recommended correction: −0.75 D sph/−2.25 D cyl × 80 NB: The patient may need enhancement. Example 4: MR = −1.00 D sph/−2.50 D cyl × 100 TA = −3.00 D cyl × 95 Recommended correction: −1.00 D sph/−2.50 D cyl × 100 Example 5: MR = +0.75 D sph/−1.25 D cyl × 85 TA = −0.50 D cyl × 165 Recommended correction: Recheck, use the least magnitude of astigmatism, and compensate with the SE; e.g., +0.50 D sph/−0.75 D cyl × 85 NB: The patient may need enhancement.

Example 6: MR = −1.50 D sph/−1.00 D cyl × 80 TA = −1.75 D cyl × 180 Recommended correction: Recheck, use the least magnitude of astigmatism, and compensate with the SE, e.g., −1.75 D sph/−0.50 D cyl × 80 NB: The patient may need enhancement. Example 7: MR = +0.50 D sph/−1.25 D cyl × 170 TA = −0.25 D cyl × 90 Recommended correction: Recheck, use the least magnitude of astigmatism, and compensate with the SE; e.g., +0.25 D sph/−0.75 D cyl × 170 NB: The patient may need enhancement. Example 8: MR = −3.00 D sph/−0.50 D cyl × 180 TA = −0.75 D cyl × 85 Recommended correction: Recheck, use the least magnitude of astigmatism, and compensate with the SE; e.g., −3.25 D sph NB: The patient may need enhancement. Example 9: MR = −4.00 D sph/−0.75 D cyl × 55 TA = −1.00 D cyl × 95 Recommended correction: MR = −4.00 D sph/−0.75 D cyl × 55 NB: The patient may need enhancement.

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SECTION

4 Wavefront Science ◆ Basics of Wavefront Analysis and Measurements

◆ Zernike Analysis

◆ Fourier Analysis ◆ Corneal Asphericity and Related Functions

CHAPTER

Basics of Wavefront Analysis and Measurements PRINCIPLES OF WAVEFRONT AND WAVEFRONT ANALYSIS The parallel light rays coming from infinity are composed of sinusoidal oscillations. Locations of equal phase within the entire array of sinusoidal oscillations form planar wavefronts. A wavefront is a constant phase that is normal to the light rays (Fig. 1). When the parallel light rays pass through a perfect refractive surface, they (and the wavefronts) meet precisely at a point known as the focal point “F.” Practically, the ideal situation is never encountered because real wavefronts show deviations from a perfect plain after passing through the refractive surface, leading to what is known as “wavefront aberrations.” The shape of a wavefront passing through a theoretically perfect eye with no aberrations is a flat plain known as “piston”. The difference (deviation) between the actual wavefront shape and the ideal flat shape represents the amount of aberration in the wavefront, as shown in Figure 2. The smaller the deviation/aberration, the higher the quality of the optical system.

Fig. 1: The wavefront principle.

13

CLASSIFICATION OF ABERRATIONS • Based on the origin, aberrations are classified into corneal, internal (mainly lenticular), and ocular or total. • Based on the composition, the aberrations can either be polychromatic or monochromatic. The former is a function of the refractive indices of colors, while the latter is a function of the profile of the refractive surfaces. • Based on the order and degree of complexity, Fritz Zernike classifies the monochromatic aberrations into constant, lower-order aberrations (LOAs), and higherorder aberrations (HOAs), as shown in Figure 3. The LOAs result from spherocylindrical refractive errors, i.e., myopia, hyperopia, and astigmatism, while the HOAs result from irregularity and/or asymmetry in refractive surfaces. The next chapter is devoted to terminology and description of this classification.

MEASUREMENT OF ABERRATIONS Higher-order aberrations (HOAs) can be measured subjectively and objectively. Subjective measurement is

Fig. 2: Root mean square measurement of aberrations.

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Fig. 3: Zernike pyramid.

difficult, time-consuming, and affected by the patient’s perception. Corneal aberrations are objectively measured by corneal tomography, while ocular aberrations are objectively measured by aberrometers. The internal (lenticular) aberrations are a mathematical subtraction of the corneal from the ocular aberrations.

Corneal Tomography All technologies of corneal tomography calculate corneal aberrations from the elevation maps (indirect measurement).

Aberrometers Aberrometers measure ocular aberrations depending on ray tracing technology. Based on the technique used, there are three types of aberrometer: 1. Outgoing reflective aberrometry: Used by the Hartmann– Shack wavefront sensor. 2. Ingoing reflective aberrometry: Used by the Tscherning aberroscope, cross-cylinder aberroscope, and the sequential ray-tracing technique. 3. The ingoing feedback aberrometry: Used in the spatially resolved refractometer. A variant of this technique is the optical path difference method.

Factors Affecting Measurements Several factors affect both human-eye aberrations and their measurement. These factors are: • Pupil size: Pupil size affects the measurement of ocular aberrations. The corneal aberrations are not affected

•

• •

•

by pupil size. The best functional pupil diameter is 3–3.2 mm; the larger the pupil, the more disturbing the aberrations; at the same time, smaller pupils (0.35 μm, otherwise it is normal.

Lower-order Aberrations

Constant Aberrations Constant aberrations exist in all optical systems. They occupy the zero order and the first order of the Zernike pyramid. • Zero order: It is known as Piston or Reference point (Fig. 6). It is given the symbol Z(0,0), which means no meridians and no slopes; it is just a planner pattern. • First order: It is known as Tilt or Prism. It is a flat deviation in the direction that a beam of light propagates. It is caused by decentered optics. It is given the symbol Z(1,−1) for vertical and Z(1,1) for horizontal (Fig. 7).

Lower-order aberrations (LOAs) are aberrations that occupy the second order of the pyramid. They include two components of astigmatism and a spherical blur component or defocus. LOAs are usually associated with the spherocylindrical refractive errors and can be corrected with glasses. In the general population, LOAs constitute approximately 80–90% of all aberrations. • Second order: Defocus and astigmatic aberration. – Defocus: It is the translation along the optical axis away from the plane or surface of the best focus. In general, defocus reduces the sharpness and contrast of the image (Fig. 8). In the human eye, spherical refractive errors are associated with defocus; in myopia, the focal point lies in front of the retina, whereas in hyperopia, it lies behind it. Defocus is a circular LOA and given the symbol Z(2,0), which means no meridians but two slopes along any direction (Fig. 5). Defocus increases with larger pupil size, as shown in Figure 8.

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Fig. 6: The piston.

Fig. 7: The tilt or prism.

Chapter 14: Zernike Analysis

– Astigmatic aberration: In the human eye, regular astigmatism is associated with lower-order astigmatic aberration. It is a periodic LOA and given the symbol Z(2,−2) for vertical and Z(2,2) for horizontal, which means two meridians with two slopes on each of them (Fig. 9).

Fig. 8: The defocus. The relationship between the defocus and the pupil size.

Higher-order Aberrations Higher-order aberrations (HOAs) constitute about 15% of the total aberrations. They have more complex geometrical forms and start at the third order in Zernike polynomials. They may or may not be associated with refractive errors. However, they affect the objective and subjective measurements of refractive errors (LOAs); for example, coma affects astigmatism, and SA affects the sphere. HOAs cannot be corrected with conventional optics. They can be treated by customized laser vision ablation. The impact of HOAs on vision quality depends on various factors, including the underlying cause, amount and type of HOAs, pupil size, and light conditions. They usually cause haloes (Fig. 10A), glare (Fig. 10B), ghost images (Fig. 10C), starburst (Fig. 10D), and monocular diplopia, especially in low lighting conditions and during night driving. People with larger pupil sizes generally may have more visual symptoms related to HOAs, particularly in low lighting conditions. However, even people with small or moderate pupils can have significant visual symptoms when HOAs are caused by conditions such as corneal scars or cataracts. Also, specific types and orientation of

Fig. 9: The astigmatic lower-order aberration.

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A

B

C

D Figs. 10A to D: Visual symptoms related to higher-order aberrations.

HOAs have been found in some studies to affect vision quality of eyes with smaller pupils. Large amounts of certain HOA can have a severe, even disabling, impact on vision quality. Some of the HOAs have terms such as coma, trefoil, and SA, but many more of them are identified only by mathematical expressions to have an order. Order refers to the complexity of the shape of the wavefront emerging through the pupil; the more complex the shape, the higher the order of aberration. However, in clinical practice, optical analysis is only considered important to the sixth order, and by some researchers up to the fourth-order. • Third-order aberrations: They are trefoil and coma. – Trefoil (Fig. 11): It is a periodic HOA. It is also known as triangular astigmatism. The term came from the Trifolium plant (Clover) that has compound trifoliate leaflets. The eye with a trefoil aberration receives a point of light like a Mercedes-Benz symbol (Fig. 12). Peripheral vision is usually affected more than central vision. Additionally, the trefoil affects both sphere and astigmatism measurements. In Zernike polynomials, trefoil is given the symbol Z(3,−3) for vertical and Z(3,3) for horizontal, which means three meridians with three slopes on each of them.

– Coma (Fig. 13): It is a nonperiodic HOA. It is the most HOA affecting central vision. It is defined as a variation of refractive power along one meridian over the entrance pupil. Coma causes the light source to be seen like a comet (has a tail), as shown in Figure 14. The coma results from central and paracentral asymmetry in ocular optical components, affecting central vision, such as in keratoconus, decentered laser-ablated zone, and decentered IOL. Additionally, coma affects the measurement of astigmatism. In Zernike polynomials, coma is given the symbol Z(3,−1) for vertical and Z(3,1) for horizontal, which means one meridian with three slopes on it. • Fourth order aberrations: They are SA, secondary astigmatism, and tetrafoil. – SA (Fig. 15): SA results from abnormal Q-value. It usually affects peripheral vision, affects measure­ ments of the sphere, and results in halos around oncoming lights. Figure 16 is a simulation of the scene of light source seen by an eye with SA. In Zernike polynomials, SA is a circular HOA and given the symbol Z(4,0). Chapter 16 is devoted to SA and its correlation with corneal shape.

Chapter 14: Zernike Analysis

Fig. 11: The trefoil.

Fig. 12: The Mercedes-Benz image resulting from the trefoil.

– Secondary astigmatism (Fig. 17): It is a periodic HOA and given the symbol Z(4,−2) for the vertical and Z(4,2) for the horizontal subtypes. It has two regular irregular meridians with four slopes on each meridian. This aberration affects mid-peripheral vision and measurements of astigmatism.

– Tetrafoil (Fig. 18): It is a periodic HOA and given the symbol given Z(4,−4) and Z(4,4) for the vertical and horizontal subtypes, respectively. It has four regular irregular meridians with four slopes on each meridian. This aberration affects peripheral vision and measurements of both sphere and astigmatism.

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Fig. 13: The coma.

Fig. 14: The comet resulting from the coma.

• Fifth order and higher: Starting from the fifth order and descending progressively in the analysis of the aberrations in the pyramid, each of the above aberrations presents its secondary, tertiary, quarterly,…, component, which is a variation in shape of the primary based on number of meridians and number

of slopes. However, the rate of the fifth and the higher levels is usually low, and their role in the visual performance degradation is usually small but can become significant in some special conditions such as irregular scarring, incisional surgery, and penetrating keratoplasty.

Chapter 14: Zernike Analysis

Fig. 15: The spherical aberration.

Fig. 16: Different types of halos resulting from spherical aberration.

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Fig. 17: The secondary astigmatism higher-order aberration.

Fig. 18: The tetrafoil.

CHAPTER

Fourier Analysis INTRODUCTION Fourier analysis is a mathematical method alternative to Zernike polynomials used to analyze and reconstruct the wavefront of the visual system. It is also known as Fourier

15

transform and is named after the French mathematician Joseph Fourier. It is the analysis of a periodic function into its simple sinusoidal or harmonic components. It is mostly used to deconstruct corneal wavefront into the following components (Fig. 1): spherical component

Fig. 1: The Fourier analysis of corneal wavefront. An example of a keratoconus case.

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Figure 1 represents Fourier analysis of corneal wavefront into four components. A case of keratoconus was selected to highlight the importance of the analysis.

• Spherical component (Fig. 2): This map represents the potential sphere of the cornea. Objective corneal dioptric power (ODP) is discussed in Chapter 11. When comparing the central K in this map with the Kref = 43 D, the reader can imagine the potential spherical power of this cornea. In our example, the difference is 43 − 58.3 = −15.3 D. There are two boxes at the bottom of the map: Spherical Rmin, representing the steepest radius of curvature in this map, and spherical ecc, representing the mean numerical eccentricity of the spherical component. From the latter, the reader can calculate corneal asphericity based on this map. Q = −e2, so in our example, Q = −(1.28)2 = −1.64, which means that the cornea is hyperprolate. • Decentration (Fig. 3): This map represents decentration of corneal optics, which is translated as coma, secondary coma, tertiary coma,…, etc. The important clinical application of this map is in topography-guided laser treatment. • Regular astigmatism (Fig. 4): This map represents regular astigmatism component. There are two boxes at the bottom of the map: astigmatism center, showing the amount and axis of corneal astigmatism within the central 3-mm zone, and astigmatism periph, showing the amount and axis between 6- and 9-mm zones. There are two clinical applications of this map which are as follows: 1. The central astigmatism in this map is usually more consistent with the subjective refraction than

Fig. 2: The spherical component.

Fig. 3: The decentration component.

(corneal sphere), decentration (corneal coma), regular astigmatism (corneal astigmatism), and irregularities (residual higher-order aberrations (HOAs). Fourier analysis is superior to Zernike polynomials because the polynomials have the following limitations: • They can be used only in circular patterns, such as circular pupils. If the pupil is elliptical, the data outside the circle are not valid. • They approximate the wavefront error of the eye/ cornea by averaging and smoothening. They limit the data resolution in eyes with high amounts of irregular astigmatism. However, Zernike smoothing of the data could be beneficial on occasion, especially where variable data could be artifactual, e.g., due to dry eye rather than the physical corneal shape. • The data lose fidelity beyond the 9th order and more, and noise rather than information is introduced beyond the 10th order. • They cannot describe the aberrations generated by straight-line irregularities, such as those resulting from flap striae and cap amputations.

FOURIER ANALYSIS OF CORNEAL WAVEFRONT

Chapter 15: Fourier Analysis

Fig. 4: The regular astigmatism component.

the Sim-K astigmatism. In other words, in distorted corneas and nonoptimal corrected vision, the amount and axis of astigmatism in this map can be considered an initial step in subjective refraction, just like when considering corneal astigmatism of total corneal refractive power as discussed in Chapter 11. 2. Whenever there is a disparity in the axis between central and peripheral astigmatism, a significant higher-order astigmatism exists, such as astigmatism from the order of secondary, tertiary, quarterly, …, etc. In our case, there is a significant dissociation, which can be identified by three elements:

Fig. 5: The irregularity component.

1. A difference between central and peripheral axes >15°. 2. The vortex distribution of the circles on the map (red and blue arrows). 3. The astigmatic pattern of the map shows peri­ pheral steep and flat areas that do not correspond to the central symmetric bowtie (white arrows). • Irregularity (Fig. 5): This map represents other HOAs from the Foil family (trefoil, tetrafoil, pentafoil, hexafoil,…, etc.). Figure 6 is Fourier analysis of a normal cornea for comparison.

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Fig. 6: An example of the Fourier analysis of a normal cornea.

CHAPTER

Corneal Asphericity and Related Functions

The normal cornea is aspheric, as mentioned in Chapter 1. Corneal asphericity results from the difference in radii of curvature among corneal zones, as shown in Figure 1 of Chapter 9. Different mathematical expressions represent corneal asphericity, namely are Q-value, p-value, shape factor E, and eccentricity. Q-value is a unitless value and the most commonly used one. Corneal asphericity is the source of corneal spherical aberration (SA), which is correlated to what is known as depth of focus (DOF). SA affects the quality of vision, and, when severe, affects the quantity as well. All these points will be discussed in this chapter.

16

• Positive prolate: The central cornea is slightly steeper than the peripheral cornea (Fig. 3). Although the radii of curvature of the central cornea are slightly smaller than those of the peripheral cornea, the peripheral rays are refracted slightly more than the paraxial ones. • Parabola (perfect prolate): The central cornea is perfectly steeper than the peripheral cornea (Fig. 4) to make all rays focus on one focal point.

CORNEAL SHAPES RELATED TO ASPHERICITY Based on corneal asphericity, the cornea can be: • Oblate: The central cornea is flatter than the peripheral cornea (Fig. 1), which means that the radii of curvature decrease toward the periphery. The peripheral rays are refracted more than the paraxial ones. This cornea is usually encountered after myopic ablation. • Spheric: The shape is a part of a sphere (Fig. 2). Although the radii of curvature are equal all over the cornea, the peripheral rays are refracted more than the paraxial ones.

Fig. 2: The spherical corneal shape.

Fig. 1: An oblate corneal shape.

Fig. 3: A positive prolate corneal shape.

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Fig. 4: The parabolic corneal shape.

Fig. 5: A negative prolate corneal shape.

Fig. 6: A hyperprolate corneal shape.

Fig. 7: The range and the average of Q-value in the normal population.

• Negative prolate: The central cornea is moderately steeper than the peripheral cornea (Fig. 5). The radii of curvature of the central cornea are moderately smaller than those of the peripheral cornea. As a result, the paraxial rays are refracted more than the peripheral ones. • Hyperprolate: The central cornea is significantly steeper than the peripheral cornea (Fig. 6). The radii of curvature of the central cornea are significantly smaller than those of the peripheral cornea. Consequently, the paraxial rays are refracted significantly more than the peripheral ones. This type is usually encountered in keratoconus and after ablating the cornea to correct >+3.0 D.

• Q is negative: The center is steeper than the periphery. That means the center is steeper than the spheric. Corneal shape is positive prolate, parabola (perfect prolate), negative prolate, or hyperprolate.

Q-VALUE AND CORNEAL ASPHERICITY As mentioned above, the Q-value is a unitless expression of corneal asphericity. Very simply, it is the ratio between peripheral and axial radii of curvature. In general, when Q = 0, the shape is spheric. The Q-value takes +ve and –ve values when the shape deviates from the spheric. Accordingly: • Q = 0: Corneal shape is spheric. • Q is +ve: The center is flatter than the periphery. That means the center is flatter than the spheric. Corneal shape is oblate.

The range of Q-value in the normal population is +0.4 to −0.8, with an average of −0.26 (Fig. 7). There are specific values of Q correlated with the types of corneal asphericity: • Oblate shape: Q > 0 (+ve), as in Figure 1. • Spheric shape: Q = 0, as in Figure 2. • Positive prolate: Q < 0 and >−0.53, as in Figure 3. • Parabola (perfect prolate): Q = −0.53, as in Figure 4. • Negative prolate: Q −1, as in Figure 5. • Hyperprolate: Q ≤−1, as in Figure 6.

CORNEAL AND OCULAR SPHERICAL ABERRATION Spherical aberration (SA) occurs when the power of the symmetric refractive surface differs, in a symmetric and gradual manner, between the center and the periphery of the refractive surface (Fig. 8).

Chapter 16: Corneal Asphericity and Related Functions

Fig. 8: A schematic view of the spherical aberration.

• Positive prolate cornea produces slight +ve SA, as shown in Figure 12. • Parabola or perfect prolate cornea produces no SA, as shown in Figure 13. • Negative prolate cornea produces slight –ve SA, as shown in Figure 14. • Hyperprolate cornea produces moderate-to-high –ve SA according to how much negative is Q-value, as shown in Figure 15.

Fig. 9: Types of the spherical aberration.

There are two types of SA (Fig. 9): 1. Positive (+ve) SA: It is generated when the peripheral rays are refracted more than the paraxial rays. 2. Negative (-ve) SA: It is generated when the paraxial rays are refracted more than the peripheral rays. Based on the above: • Oblate cornea produces high +ve SA, as shown in Figure 10. • Spheric cornea produces moderate +ve SA, as shown in Figure 11.

Figure 16 illustrates the relationship between Q-value, corneal asphericity shapes, and SA. The normal nonoperated cornea has +ve SA. Corneal SA in the normal population ranges between +0.1 µm and +0.55 µm with an average of +0.27 µm, as shown in Figure 17. Corneal SA is not only a factor of Q-value, but of K-readings (radius of curvature) as well. In general, SA is proportional to the Q-value and inversely proportional to the third power of the corneal radius (1/r3). That explains how the normal cornea has +ve SA, although the range of Q-value in the normal population is +0.4 to −0.8 (Fig. 7). The +ve corneal SA of the normal nonoperated cornea is compensated by the –ve SA generated by the crystalline lens. The resultant ocular SA is around +0.1 µm at age 19 years (Fig. 18), which has been found the best age in terms of quality of vision. As the crystalline lens ages, it generates more +ve SA, and the resultant ocular SA becomes more +ve, as shown in Figure 19. Corneal SA, and therefore ocular SA, is changed by laser-based refractive surgery. Myopic ablation pushes the cornea to more +ve SA (Fig. 20), while hyperopic ablation pushes the cornea to less +ve SA, zero SA, or even convert it to –ve SA in high hyperopic ablations (Fig. 21).

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Fig. 10: Positive spherical aberration induced by an oblate cornea.

Fig. 11: Positive spherical aberration induced by a spherical cornea.

Fig. 12: Positive spherical aberration induced by a positive-prolate cornea.

Chapter 16: Corneal Asphericity and Related Functions

Fig. 13: A parabolic cornea inducing no spherical aberration.

Fig. 14: Negative spherical aberration induced by a negative-prolate cornea.

Fig. 15: Negative spherical aberration induced by a hyperprolate cornea.

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Fig. 16: The relationship between Q-value, corneal shapes, and spherical aberration.

There is an inversely proportional relationship between SA and contrast sensitivity; the higher the SA, the lower the contrast sensitivity and the lower the quality of vision (Fig. 22). It is a fact regardless of whether the SA is +ve or –ve, although the quality of vision is slightly better with the –ve SA compared with the same amount of +ve SA. In other words, if two different eyes, one has ocular SA = −0.25 µm and the other has ocular SA = +0.25 µm, the former has a better quality of vision than the latter. The exception is when ocular SA = +0.1 µm, the quality of vision is optimum.

DEPTH OF FOCUS

Fig. 17: The range of the spherical aberration in the normal population.

In other words, the eye has more +ve SA after myopic ablation and less +ve SA or even –ve SA after hyperopic ablation.

VISUAL FUNCTION AND SPHERICAL ABERRATION In general, spherical aberration (SA) affects the clarity (quality) of vision because it affects contrast sensitivity.

Although ocular SA affects the quality of vision, it has the advantage of increasing the DOF. DOF is the ability to move (displace) the seen object closer and farther to the eye and keep it in focus (see it clearly) for the same amount of accommodation. For example, an eye with no accommodation uses the +3.00 D lens to see an object at 33 cm. If the eye has no depth of focus (DOF), any displacement of the object will let it be out of focus and blurred. If the eye has DOF, there is a field of focus rather than a single point of focus, and the object will stay clear or relatively clear as long as it moves within the field of focus. There is a correlation between DOF, corneal asphericity, and SA: • An oblate cornea produces high +ve SA and high +ve DOF, as shown in Figure 23. • The spherical cornea produces moderate +ve SA and moderate +ve DOF, as shown in Figure 24.

Chapter 16: Corneal Asphericity and Related Functions

Fig. 18: The range of the corneal and ocular spherical aberration (SA) in the normal young eye.

Fig. 19: The range of the corneal and ocular spherical aberration (SA) in the normal aged eye.

Fig. 20: The corneal spherical aberration after myopic ablation.

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Fig. 21: The corneal spherical aberration after hyperopic ablation.

Fig. 22: The relationship between the spherical aberration (SA) and the contrast sensitivity.

Fig. 23: The depth of focus (DOF) in an oblate cornea.

Fig. 24: The depth of focus (DOF) in the spherical cornea.

• A positive-prolate cornea produces slight +ve SA and slight +ve DOF, as shown in Figure 25.

• A negative-prolate cornea produces slight –ve SA and slight –ve DOF, as shown in Figure 27. • A hyperprolate cornea produces moderate-to-high –ve SA and –ve DOF according to how much negative is the Q-value, as shown in Figure 28.

• The parabolic cornea produces no SA and no DOF, as shown in Figure 26.

Chapter 16: Corneal Asphericity and Related Functions

Fig. 25: The depth of focus (DOF) in a positive-prolate cornea.

Fig. 26: The depth of focus (DOF) in the parabolic cornea.

Fig. 27: The depth of focus (DOF) in a negative-prolate cornea.

Fig. 28: The depth of focus (DOF) in a hyperprolate cornea.

As shown in the previous figures, when there is SA, there is a field of focus rather than a single point of focus.

is no DOF, and the image is blurred on the retina and in the brain, as shown in Figure 31. 2. Tolerable SA: When SA ranges between 0 µm and 0.35 µm in both directions (+ve and –ve), there is DOF, as shown in Figure 32. The image is blurred on the retina but is adjusted by the brain by neural adaptation. If the object moves within the DOF, it stays clear in the brain (Fig. 32), but blurs when it moves beyond, as shown in Figure 33. 3. Nontoxic SA: The SA is above the threshold (>0.35 µm) up to 0.60 µm in both directions. Although the image is blurred on the retina, it is much less blurred in the brain, as shown in Figure 34. The advantage of the nontoxic SA is the wide DOF but on account of the quality of vision.

OCULAR SPHERICAL ABERRATION AND NEURAL ADAPTATION The clarity of the near object depends not only on DOF but also on the capability of the brain to perform neural adaptation. To understand the relationship between ocular SA, DOF, neural adaptation, and clarity of the image, ocular SA is classified into four categories (Fig. 29): 1. No SA: Theoretically, when the SA = 0, the image on the retina is very sharp, as shown in Figure 30. If the seen object moves, image quality drops down because there

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Fig. 29: Classification of the spherical aberration (SA) based on severity.

Fig. 30: A schematic view of image clarity in the case of absent spherical aberration. The image is in focus.

Fig. 31: A schematic view of image clarity in the case of absent spherical aberration. The image is out of focus.

Chapter 16: Corneal Asphericity and Related Functions

Fig. 32: A schematic view of image clarity in the case of tolerable spherical aberration. The image is in focus.

Fig. 33: A schematic view of image clarity in the case of tolerable spherical aberration. The image is out of focus.

4. Toxic SA: The SA is >0.60 µm in both directions. The image is significantly blurred on the retina and in the brain, as shown in Figure 35. The brain cannot adapt, and the DOF is useless. Figure 36 summarizes the relationship between SA, DOF, and quality of vision (contrast sensitivity).

THE EFFECT OF CORNEAL ASPHERICITY ON MEASURING REFRACTION Corneal asphericity affects cycloplegic refraction when refracting the patient by retinoscopy. Due to the difference

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Fig. 34: A schematic view of image clarity in the case of nontoxic spherical aberration.

Fig. 35: A schematic view of image clarity in the case of toxic spherical aberration.

in power between central and peripheral cornea, the light reflex through the dilated pupil shows a paradoxical movement, e.g., the central segment of the light reflex moves in the same direction of the streak while the

peripheral segments move to the opposite direction. That can be misinterpreted as scissoring reflex. Therefore, it is recommended to focus on and consider the central light movement only.

Chapter 16: Corneal Asphericity and Related Functions

Fig. 36: The relationship between spherical aberration (SA), contrast sensitivity, and depth of focus (DOF).

THE EFFECT OF CORNEAL ASPHERICITY ON VISION The effect of corneal asphericity on vision differs according to the status of refraction: • Corneal asphericity in emmetropia: – If Q >−0.53 (more positive), positive SA is present. When the eye is refracted in dim light (larger pupil size), it shows an amount of hyperopia. – If Q = −0.53, no SA is present. The eye is emmetropic in both scotopic and photopic light conditions. – If Q < −0.53 (more negative), negative SA is present. When the eye is refracted in dim light (larger pupil size), it shows an amount of myopia. This explains why some people suffer from myopia at night. • Corneal asphericity in myopia: – If Q >−0.53 (more positive), positive SA is present. When the eye is refracted in dim light (larger pupil size), it shows less myopia (hyperopic shift).

– If Q = −0.53, no SA is present. The eye has the same amount of myopia in both scotopic and photopic light conditions. – If Q −0.53 (more positive), positive SA is present. When the eye is refracted in dim light (larger pupil size), it shows a larger amount of hyperopia (hyperopic shift). – If Q = −0.53, no SA is present. The eye has the same amount of hyperopia in both scotopic and photopic light conditions. – If Q 3.5 D.

MISALIGNMENT Loss of fixation or misalignment during capturing the cornea is one of the main factors for false findings.

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Fig. 1: Hot spot pattern on the anterior curvature map induced by prolonged use of a soft contact lens.

Both patient and examiner may be responsible for misalignment. Misalignment may cause false positives and false negatives.

four-composite map of the same eye after teaching the patient the proper fixation. Notice how misalignment can be responsible for false keratoconus features.

Types of Misalignment

Changes in the Curvature Maps

• Patient’s error misalignment: This occurs when the patient does not fixate appropriately on the target. This error is called misalignment by rotation. Of course, this appears clearly to the examiner, but instead of asking the patient to refixate and align properly, the examiner tries to overcome this problem by realigning the camera on the displaced pupil! • Examiner’s error misalignment: The patient here aligns properly on the fixation point, but the examiner does not adjust the camera properly on the patient’s pupil. This error is called misalignment by translation.

Effect of Misalignment All tomographic maps are affected by misalignment. Figure  3 is a four-composite map of an eye that was fixating downward during the capture. Figure 4 is the

Figures 5 and 6 are illustrations of changes occurring in the symmetric bowtie (SB) due to misalignment. The bowtie pattern changes according to the direction of gaze. Therefore, not every asymmetric bowtie (AB) or skewed pattern (SRAX) is abnormal; it may result from misalignment. That is called “false positives.” Figure 7 is an example of a false negative. The real pattern is SB/SRAX. Assuming that this is the left eye and the patient is fixating temporally, the pattern appears as an SB. Besides, if the SRAX of the real SB/SRAX is insignificant (3.5 D over the 16 days.

Based on the above illustrations, the reader can imagine how other patterns can change, generating a variety of classified and unclassified patterns that can be misinterpreted. 

Changes in the Elevation Maps Similar to the curvature maps, symmetric patterns on the elevation maps convert into asymmetric patterns and vice versa. In addition, normal values usually convert to abnormal values. This is obvious in Figures 3 and 4.

Changes in the Thickness Map The normal concentric shape changes into the dome pattern or horizontal displacement pattern. X and Y coordinates of the thinnest location (TL) show abnormal values in case of false positives or normal values in case of false negatives. This can be seen clearly in Figures 3 and 4.

Changes in the Spatial Thickness Profile Misalignment can affect the average progression more than the pattern of the red curve. Figure 8 is the spatial profile in the misalignment situation, while Figure 9 is in the appropriately fixation position. Notice the change in average.

Clues of Misalignment The following are the clues of misalignment. These clues are part of the validation steps and are discussed in detail in Chapter 3. • Quality specification (QS): Checking QS is the first step in validating the captures. The QS should be “white OK.” However, being white OK is not a clue of a good capture. Look at Figure 3, there is a gross misalignment while the QS is white OK!

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Fig. 3: Misalignment. The four-composite refractive map of an eye fixating downward during capturing the cornea.

• Comparison of pupil center coordinates: This is the second step in validating the captures. If X–X or Y+Y is >200 µm (>0.20 mm), misalignment is suspected. • Km repeatability: Usually, three captures should be taken in a session. The three captures should be compared in terms of the Km of the anterior corneal surface. There is usually 1.0 D in the magni­ tude or >10° in the axis difference between the manifest astigmatism (MA) and the TA obtained from the total corneal refractive power (TCRP) at 3 mm ring/apex. • Asymmetric patterns on the curvature, elevation, or pachymetry maps. If any of the above clues exists, the captures should be repeated.

LARGE ANGLE KAPPA OR LAMBDA The definition of these two angles is mentioned in Chapter 1. The effect of large angles is similar to misalignment. The difference between large angles

and misalignment is that in the former X+X and Y–Y are ≤200 µm (≤0.20 mm).

TEAR FILM DISTURBANCE Dry Eye Disease Dry eye disease and ocular surface diseases affect the integrity of the tear film and corneal epithelium, which leads to surface irregularities, changes in K-readings, and hot spot formation, as shown in Figure 10. These changes improve or disappear after proper management (Fig. 11). Changes are more prominent in topographers rather than tomographers because the formers are reflection-based and obtain data from the tear film and the anterior corneal surface.

Excess Tear Film Excessive tear film meniscus is a factor of false hot spot formation. The excessive tear meniscus on the lower lid margin takes a concave shape, followed by an upper convex corneal surface (Fig. 12). That would be interpreted by the

Chapter 17: Factors of False Findings

Fig. 4: Misalignment. The four-composite refractive map of the same eye in Figure 3 after realignment.

Fig. 5: The effect of misalignment and large angle kappa on the presentation of a true vertical symmetric bowtie (SB).

Fig. 6: The effect of misalignment and large angle kappa on the presentation of a true horizontal symmetric bowtie (SB).

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Fig. 7: The effect of misalignment and large angle kappa on the presentation of a true vertical symmetric bowtie with skewed radial axis index (SB/SRAX).

computer as a hot spot, as shown in Figure 13A. Figure 13B is the same cornea after wiping; notice that the hot spot has disappeared.

Fig. 8: Misalignment. The thickness profiles of the same eye in Figure 3 in misalignment situation.

CORNEAL OPACITIES AND PATHOLOGIES Corneal opacities, haze, degenerations, and dystrophies are sources of corneal irregularities, hot spot formation, and false findings (see Figures 7 to 12 of Chapter 8).

PREVIOUS CORNEAL SURGERIES Corneal surgeries are: • Laser vision correction (LVC). • Cataract surgeries. • Corneal grafts. • Radial keratotomy (RK). • Astigmatic keratotomy (AK) and limbal relaxing incisions (LRIs). Careful history taking is a critical step in the workup for refractive surgery. Previous corneal surgeries are sources of corneal irregularities, hot spot formation, and false findings. They affect by the following mechanisms: • Tear film disturbance. • Distortion due to sutures. • Distortion due to postoperative flap complications. • Light scattering due to interface complications or corneal haze.

Fig. 9: Misalignment. The thickness profiles of the same eye in Figure 3 in realignment situation.

Chapter 17: Factors of False Findings

Fig. 10: Dry eye. The four-composite refractive map before treatment.

• Irregular RK incisions and incisions extending into the optical zone. • Irregular or asymmetric AK incisions or LRIs. • Corneal instability due to RK. • Abnormal corneal response, leading to decentered, irregular, or small postoperative optical zones. These may occur due to improper laser ablation as well. • Postoperative ectasia.

INADEQUATE EXPOSURE TO THE CAMERA During taking the capture, the eye should properly be exposed to the camera to avoid any missing data and, therefore, extrapolation. Inadequate exposure to the camera can result from anatomical features, patient noncooperation, or tight headscarves.

These features can be overcome by adjusting the head in compensating positions. For example, if the cause was a prominent nasal bridge, the face should be turned to the left to capture the right eye and vice versa.

Patient Noncooperation Frequent blinking, moving the eyes, and following the camera are frequently encountered in noncooperative patients. Proper patient education would overcome this. It is also essential to treat the causes of frequent blinking, such as dry eye disease. It is strongly recommended to avoid using anesthesia drops to overcome frequent blinking.

Tight Headscarves Headscarves may obscure the camera, especially from the temporal sides.

Anatomical Features

PREGNANCY

They include prominent eyebrows, small palpebral fissures, small eyes, deep-set eyes, nasal bridge, and long lashes.

During pregnancy, a temporary increase in corneal curvature and corneal thickness is usually encountered.

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Fig. 11: Dry eye. The four-composite refractive map after treatment.

Fig. 12: The effect of excess tears on tomography.

Chapter 17: Factors of False Findings

A

B Figs. 13A and B: Excess tears. A false hot spot in excess tear status (A); (B) is after wiping the ocular surface.

They are related to hormonal changes. That explains why a pregnant woman is not the right candidate for refractive surgery, especially that the hormonal changes lead to an unpredictable corneal response to refractive surgery. Physicians should be reluctant to perform refractive surgery during or directly after pregnancy and should wait until the

cornea is back to normal. Moreover, when a keratoconic female becomes pregnant, there is a risk of progression, and hence there is a need for follow-up. Chapter 23 is devoted to the progression criteria of ECDs. Progression criteria may be masked by the changes in curvature and thickness during pregnancy.

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CHAPTER

Enantiomorphism

Enantiomorphism is the phenomenon of mirror shape intereye symmetry. In this phenomenon, the right eye is a mirror shape of the left eye in both tomographic patterns and values. Figures 1 and 2 are the four-composite maps of the right eye (OD) and the left eye (OS), respectively, of a refractive surgery candidate. The reader can notice how OD

18

is a mirror shape of OS. Figures 3 to 6 demonstrate single map comparisons. This phenomenon was studied to differentiate normal from keratoconic corneas by establishing a numeric scoring system that outlines the normal range of asymmetry between right and left eyes.

Fig. 1: Enantiomorphism. The right eye of a refractive-surgery candidate. It is a mirror shape of the left eye in Figure 2.

Chapter 18: Enantiomorphism

Fig. 2: Enantiomorphism. The left eye of a refractive-surgery candidate. It is a mirror shape of the right eye in Figure 1.

Fig. 3: Enantiomorphism on the curvature maps.

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Fig. 4: Enantiomorphism on the anterior elevation maps.

Fig. 5: Enantiomorphism on the posterior elevation maps.

Chapter 18: Enantiomorphism

Fig. 6: Enantiomorphism on the thickness maps.

Table 1: Intereye corneal asymmetry score.* Scoring criteria

Positive (+1 point) if intereye difference

Mean anterior keratometry (Km anterior)

≥0.3 D

Mean posterior keratometry (Km posterior)

≥0.1 D

Thinnest pachymetry

≥12 µm

Front elevation at thinnest location

≥2 µm

Back elevation at thinnest location

≥5 µm

*Score of 3 is observed in up to 6–11% of healthy patients, whereas a score of 4 is found in 50 a

TCT (µm)

470–500

Sb • S–I ≥2.5 D if S > Ib

• SRAX ≥ 22°c • Butterfly, crab claw, vertical D, and clown face

Elevation maps based on BFS

–

• ≥+8 µm anterior or ≥+18 µm posterior in emmetropia and myopia • ≥+7 µm anterior or ≥+28 µm posterior in hyperopia and mixed astigmatism

Elevation maps based on BFTE –

>+12 µm anterior or >+15 µm posterior, regardless of refraction

Corneal thickness map

Dome and droplet

Bell and globus

Thickness profiles

• Normal slope but average ≥1.20d • S shape after 6 mm

• Quick slope • S shape before 6 mm • Inverted slope

Relative thickness map

500 µm. – Moderate risk: 470–500 µm. – High risk: I, as in Figure 5. ◆ Low risk: I–S −8

>3.5 to ≤4.5

No central scars

>2.5 to ≤3.5

No central scars

1.5–2.5

No central scars

Myopia, induced astigmatism or both 2

>48 to ≤53

401–500

(−5,−8) Myopia, induced astigmatism or both

1

≤48

>500

5.90 mm

>490 µm

= 20/20

–

>5.70 mm

>450 µm

>5.15 mm

>400 µm

(7.05 mm

(= 1.0)

(6.35 mm >6.15 mm 55.0 D)

300 µm

(51 D. • Corneal thickness map: This map is important to study the patterns. There are five landmarks on this map. – The dashed black circle is the border of the pupil. – The brackets indicate the center of the limbus, which is considered the Optical Center of the cornea. The center of the limbus is always temporal and inferior to the vertex normal (average is 0.38 ± 0.22 mm temporal and 0.01 ± 0.14 mm inferior). It is important to know that the implanted IOL will naturally center in the bag at the optical center, rather than the pupil center or the visual axis. – The white circle with a central black dot indicates the Corneal Apex, which is known as Vertex Normal. – Angle alpha is the angle or the chord distance between the optical center (the center of the limbus) and the corneal apex (considered as the visual axis). – The small black circle is the location of thinnest corneal thickness (Pachy thin). It is usually temporal and inferior to the apex. – The black cross is the centroid of the pupil. It is usually less temporal and less inferior to the apex.

Chapter 25: The Holladay Report

• Elevation maps: In the Holladay report, the elevation maps are in BFTE float mode. As mentioned in Chapter 6, Holladay believes that BFTE is better to study corneal shape because the cornea is toric ellipsoid. Therefore, matching the cornea with a reference surface that is similar to its shape excludes the effect of corneal astigmatism and highlights corneal irregularities. • Within the central 5 mm zone, the highest plus value is suspicious or abnormal if it is >+12 µm or >+15 µm on the anterior or posterior elevation maps, respectively. • Relative pachymetry map: The minimum relative pachymetry value (%) is suspicious or abnormal if it is