Corneal Topography and the New Wave

Stephen D. Klyce, Ph.D.

The normal prolate ellipsoidal corneal front surface with its clinical advance had been made since 1880 when Antonio Placido 8–10-␮m thin and optically smooth tear film accounts for about first introduced the Placido disk. When keratorefractive surgery two-thirds of the refractive power of the eye. Disruptions in the made its entrance in the late 1970s, it became clear that a more tear film and induction of irregularity in corneal shape can, there- sensitive and quantitative method for corneal shape analysis was in fore, degrade the optical quality of the eye and reduce visual order. Visual inspection of Placido mires can fail to detect up to 3 acuity. Such distortions in the corneal surface can be so subtle as diopters (D) of corneal cylinder, mild keratoconus, and, in refrac- to escape detection with the usual biomicroscope examination. tive surgery and corneal transplants, the etiology of postoperative Retinoscopy is a subjective diagnostic procedure that can reveal visual distortions. fairly slight distortions in the retinal image that can arise from the One of the most successful analytical approaches to providing cornea. However, retinoscopy does not reveal the nature and/or quantitative measures from photokeratoscopy derived from the locus of the aberrating medium, for corneal back surface, lenticu- work of Doss et al.4 who, in 1981, scanned Corneascope photo- lar, and retinal anomalies can distort vision as well. Twenty-five graphs and proposed a mathematical method for the conversion of years ago, corneal specialists used retinoscopy and photokeratos- mire size and shape to corneal power. These data were presented copy to diagnose mild keratoconus and to manage astigmatism in in the form of a numerical plot. Subsequently in 1984, Klyce5 corneal grafts. Just a few years later, refractive surgery took its proposed a method for reconstructing corneal shape and power by first halting steps into clinical practice; it was this scenario that digitizing mires from NIDEK photokeratoscope photographs. In provided the impetus for the development of improved methods this work, graphical plots using three-dimensional wire mesh mod- for analyzing corneal shape. Corneal topography as a routine clini- els were used to depict corneal topography, as condensing the cal examination was born, and its acceptance can be judged by the thousands of data points collected from the photokeratoscope pho- explosive growth of publications on this subject in the peer- tographs was necessary to permit clinical use. The final graphical reviewed literature (Fig. 1). presentation form of this data, which has become the international standard, was the color-coded contour map of corneal powers presented by Maguire et al.6 in 1987. THE PHOTOKERATOSCOPE Corneal power or curvature had been measured clinically for nearly a century before the advent of corneal topographers. Oph- In the mid 1970s, corneal topography was evaluated with the thalmometers (such as the ophthalmometer Javal and Schioetz in- photokeratoscope, and the two models generally available were the troduced in the 1890s), predecessors to the keratometers, very 1 NIDEK PKS-1000 (NIDEK Corporation, Gamagori, Japan) and accurately measure the curvature of the corneal front surface. They the Corneascope (International Diagnostic Instruments, Tulsa, OK, are calibrated so that a surface with a 7.5-mm radius of curvature 2 U.S.A.). These devices combine an illuminated Placido disk tar- would correspond to 45 D of refractive power. This leads to the ס get and an instant film camera to capture an image of the Placido convenient, but artificial, refractive index gradient of 7.5 × 45 mires reflected from the cornea. Initially, clinicians interpreted 337.5, which is termed the keratometric index. Importantly, this photokeratoscope photographs by visual inspection, recognizing convention yields an accurate measure of the radius of curvature that corneal steepening was represented by minification of the for the front surface of the cornea for contact lens fitting; however, mires, that corneal flattening was represented by a magnification this relation cannot be accurately used to predict corneal refractive of the mires, and that irregular astigmatism was represented by power changes, particularly when only the anterior surface curva- irregularities in the mire pattern. Further, corneal cylinder repre- ture is modified.7,8 Nevertheless, for consistency of clinical inter- sented by elliptically shaped mires and keratoconus often revealed pretation, the keratometric index has been carried over for the itself as pear-shaped mires. Although this technology was useful, expression of corneal power in corneal topographers. On the av- particularly for trying to manage the sizable astigmatism present in erage, normal adult human corneal power is about 43 D with this 3 corneal transplants, it was humbling to realize that no significant convention. For the 43-D cornea, anterior surface curvature, thus, is 7.85 mm (337.5/43). Submitted February 16, 2000. Revision received May 17, 2000. Ac- cepted May 18, 2000. THE COLOR-CODED MAP From the Lions Eye Research Laboratories, LSU Eye Center, Louisiana State University Medical Center School of Medicine, New Orleans, Loui- With the introduction of the color-coded contour map of corneal siana, U.S.A. Address correspondence and reprint requests to Dr. Stephen D. Klyce, powers, the concept of color association conveyed whether corneal LSU Eye Center, 2020 Gravier Street, Suite B, New Orleans, LA 70112, power was higher or lower than the average 43-D norm. A color U.S.A. E-mail: [email protected] spectrum was chosen so that powers near the norm showed as

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normal corneas, contact lens-wearing corneas, early to moderate and advanced keratoconus, penetrating keratoplasties, extracapsu- lar cataract surgery, excimer laser photorefractive keratectomy (PRK), radial keratotomy, aphakic epikeratoplasty, and myopic epikeratoplasty. It was found that the correct interpretation for all cases could be made with the 1.5-D scale without resorting to a 1.0-D or lower interval scale.9 Additionally, the 1.5-D scale proved broad enough to cover the full range of powers encountered in the study. The routine use of a fixed standard scale showing only adequate detail and not redundant information or extraneous measurement noise is essential for efficient and accurate clinical interpretation. It should be noted that the sensitivities and resolutions of corneal topographers varies with design. A scale with a 1.5-D interval was found adequate for the Tomey corneal topographers,9 whereas a 0.5-D interval is generally used on topographers with fewer and FIG. 1. Corneal topography publications per year. The number of broader mires and correspondingly less sensitivity. peer-reviewed publications on corneal topography (MEDLINE) has grown dramatically over the last 25 years since the first radial kera- It has been traditional that videokeratoscopes provide adaptable totomy procedure was performed in the United States in 1979. Since scales that are self-adjusting to the range of powers found for a the color-coded map and commercial corneal topographers became given cornea. The use of such scales runs counter to standardiza- available (1987), the diagnostic procedure has become the standard tion in corneal topography and can be misleading. Such scales can of medical practice for cornea/anterior segment clinicians. make grossly irregular corneas look uncomplicated and quite normal corneas look complex with extensive amounts of irregular green, powers lower than the norm showed as cool colors (blue astigmatism. Such adaptive scales should be avoided except as an hues), and high corneal powers showed as warm colors (red hues). adjunct to examine details of corneal topography. Only a few distinct, recognizable colors were chosen over the Although manufacturers have universally accepted the use of central range of corneal powers so that a specific power range warm colors for high powers and cool colors for low powers, not could be easily identified. Using a contour map allows the asso- all agree that contrasting colors need to be used in the central ciation of certain patterns with different corneal shapes. Hence, range. The use of continuous hues can mask contours that hide pattern recognition permits the identification of naturally occurring irregular astigmatism. Figure 2 compares a version of an American topographies, such as corneal cylinder (bow tie pattern), kerato- National Standards Institute-proposed standard scale to the Klyce- conus (local area of steepening), and pellucid marginal degenera- Wilson scale. Figure 3 shows a commercial implementation of the tion (inferior arcuate steepening), as well as features associated ANSI proposal and compares it to a similar surgical case. The loss with refractive surgery, such as optical zone size, centration, and of topographic information with less contrasting colors reduces (rarely) central islands. clinical use. CORNEAL TOPOGRAPHERS STANDARDIZED SCALES The Corneal Modeling System (Computed Anatomy, New The clinical use of corneal topography depends on how well the York, NY, U.S.A.) was the first of a growing number of devices color-coded maps can be interpreted using color association and for measuring corneal topography and this class of machine em- pattern recognition as mentioned above. The colors and dioptric ploying the videocapture of Placido disk images was known as a intervals originally proposed6 have been modified in a number of videokeratoscope. The Placido disk approach has been the most ways by manufacturers, as efforts to standardize corneal topogra- clinically and commercially successful (Table 1). Some of these phy have not been successful. Because standards are essential for have been validated in terms of accuracy and reproducibility10–17 the comparison and sharing of information, it is important that they as there can be considerable differences between the results ob- be established in corneal topography. The first scale used on a tained with the various machines. Two types of Placido targets commercial topographer was patterned after Maguire et al.6 Called have been used. A large diameter target can be less sensitive to the Absolute Scale, it spanned a range of corneal powers from misalignment due to a long working distance but is subject to data 9–101.5 D, with 1.5 D intervals in the middle of the range and 5 loss by eclipse of the mires by the brow and nose of the patient. A D intervals at each end. Wilson et al.9 introduced a more practical small diameter cone-shaped target does not suffer from peripheral scale (the Klyce/Wilson scale), which ranged 28.0–65.5 D in equal data loss due to shadows, but given their short working distances, 1.5-D intervals. Replacing the 5.0-D intervals at the extremes was these rely on automatic alignment and focus or compensation for particularly important with the advent of refractive surgical pro- misalignment for accuracy. cedures; because, with corrections for high myopia, if irregular The chronologically second technology developed to measure astigmatism occurred in the central, surgically flattened region, it corneal shape is the technique of rasterstereography.18–20 With this could be masked. approach, fluorescein is first instilled in the tear film, and a grid or Even with this improvement, it was often argued that the 1.5-D raster pattern is projected with cobalt blue light onto the anterior interval was so wide that important features in corneal topography surface of the eye. Images are then captured simultaneously from could be hidden between contours. The diagnostic adequacy of the two directions and processed using triangulation methodology to Klyce/Wilson scale was evaluated in a clinical series that included reconstruct the shape of the cornea. This seems to be less sensitive

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captured in something over 1 second, are registered with one an- other and are used to reconstruct a full thickness cornea. Subse- quently, thickness profiles, surface elevation maps, and conven- tional topography maps are calculated and displayed. The accuracy of the scanning slit method for measuring corneal thickness has been questioned22,23 showing a need for independent validation studies. Further, the validity of scanning slit studies reporting keratectasia after LASIK has been challenged on mathematical grounds.24 There may be shortcomings to the scanning slit approach that are difficult to overcome. Because the cornea is in constant motion from fixation drift, muscle tremor, pulse, and nystagmus, correlated measurements must be captured simultaneously or in a minimum time period of 30 ms or less. Simulta- neous data capture was incorporated into optical pachometers and keratometers using the principle of image doubling—using an image splitter to superimpose or line up, for example, the slit image of the endothelium with that of the epithelium. A scanning slit device capturing successive slit images over a long period of time requires either a tracking system (expensive) or an accurate post-

FIG. 2. Color association and corneal power. A: Distinct, identifiable colors in the central part of this color-coded contour map proposed by Maguire et al.6 permit association of a power interval with certain regions on the cornea. B: The use of a progression of hues as currently proposed by an ANSI task force makes knowledge of power interval difficult and reduces contrast. than Placido disk topography; and, this limitation along with the inconvenience of having to instill fluorescein reduces its useful- ness. On the plus side, rasterstereography can measure actual corneal shape directly without the successive approximation method used with Placido disk machines. Hence, there is the potential for greater accuracy in measuring corneal shape when compared to surface power. The use of scanning slit beam technology can provide the opportunity to analyze both the outer and inner surfaces of the cornea and was first introduced in the Corneal Modeling System. Because both of these refracting surfaces—as well as corneal thickness— come into play when calculating total corneal power, measuring the position of the surfaces directly would provide an advantage. Additionally, because each of the surfaces can be measured directly with slit beam technology, no approximation errors should arise as with the Placido disk-based devices. Further, the ability to measure corneal thickness over a broad area would provide valuable guidance to the refractive surgeon, particularly if the sensitivity were great enough to detect the local stromal thinning associated with clinical keratoconus or the keratectasia that is claimed to result when too thin a corneal stromal bed is left after a laser in FIG. 3. Color choices for maps are critical for interpretation. These situ keratomileusis (LASIK) procedure is performed.21 are two different patient corneas, each underwent LASIK and each This technique is currently embodied in the Orbscan II (Bausch lost two or more lines of best spectacle corrected vision. A: The choice of contrast colors easily permits appreciation of the irregular and Lomb, Rochester, NY, U.S.A.; Table 1), which uses a Placido astigmatism within this patient’s entrance pupil. B: In this commercial disk for a traditional measurement of corneal topography and a implementation of the ANSI proposal, lack of contrast hides pupillary scanning slit to obtain 40 slit images of the cornea. These images, irregular astigmatism and the cause of this patient’s reduced acuity.

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TABLE 1. Corneal topographers tometry or “K-Readings.”31 SimK values provide the powers and axes of the steepest and flattest meridians (SimK1 and SimK2, Manufacturer Model(s) Method respectively), similar to values provided by the keratometer. Cyl- Alcon Surgical EyeMap EH-290 Placido inder is often provided as the simple difference between SimK1 Alliance Medical Mkts Keratron CT; Scout Placido Dicon CT-200 Placido and SimK2. On the Tomey topographers, SimK values are calcu- Euclid Systems ET-800 Fluorescein profilometry lated from rings 7–9, approximately corresponding with the posi- EyeSys/Premier EyeSys 2000; Vista Placido tion on the cornea at which keratometer measurements are ob- EYETEK CT2000 Placido Kera Metrics CLAS-1000 Phase modulated laser tained. SimK values correlate well with keratometry values, and all holography corneal topographers provide this measurement. Used for fitting Humphrey Instruments Atlas 991, 992 Placido Medmont E300 Placido contact lenses and refractive surgery calculations, SimK values can Oculus Keratograph Placido be extremely valuable as a beginning point to determine the quan- Bausch & Lomb Surgical Orbscan II 40 Scanned slits & tity and axis of astigmatism during refractions in eyes with irregu- Placido Bausch & Lomb Surgical Orbshot Placido lar corneal shapes. PAR Vision Systems CTS, Accugrid Fluorescein profilometry PAR Vision Systems Intraop. CTS Fluorescein profilometry Sun Contact Lens Co. SK-2000 Placido Technomed Technology C-SCAN Placido Corneal Eccentricity Index Tomey Technology Auto Topographer Placido The Corneal Eccentricity Index (CEI) is a quantitative descrip- Topcon American Corp. CM-1000 Placido tor that indicates the eccentricity of the central cornea.32 CEI is generally calculated by fitting an ellipse to corneal elevation data obtained with the corneal topographer. The CEI for 22 control capture image registration technique (difficult with low contrast corneas was reported to be 0.33 ± 0.26 (SD), which corresponds images) to eliminate significant movement artifact. with the prolate shape of the normal central cornea. This value is Potentially, the most accurate methodology that has been pro- 25 useful in contact lens fitting and for differentiating between normal posed to measure corneal shape is interferometry. Interference prolate corneas and oblate corneas flattened by myopic refractive techniques are used in the optical industry to detect lens and mirror surgery. aberrations of subwavelength dimensions. In essence, a reference surface (or its hologram) is compared to the measured surface (cornea) and interference fringes are produced as a result of dif- Average Corneal Power ferences between the two shapes. With respect to the measurement The Average Corneal Power (ACP) is an area-corrected average of corneal shape, there is such a wide variation in the shapes of of the corneal power before the entrance pupil.33 It is generally corneas, even among those that are normal, that it is difficult for a equal to the keratometric spherical equivalent except for decen- single interference device to represent all variations. Examples of tered refractive surgical procedures. In such cases, ACP may be interference devices include a phase-modulated laser holography- helpful to determine central corneal curvature for intraocular lens based device26,27 (Table 1) and an acoustic holographic tech- power calculations. nique.28 Neither approach has led yet to a clinically accepted diagnostic tool. Belin and Missry29 more completely review the technology used in modern corneal topographers. TOPOGRAPHIC INDEXES AND METHODS FOR MEASURING CORNEAL OPTICAL QUALITY CORNEAL TOPOGRAPHIC INDEXES Surface Regularity Index Although the color-coded map provides a rapid method for The development of corneal topography analysis was acceler- clinical diagnosis and is constructed from quantitative measure- ated with the advent of refractive surgery in the late 1970s as clues ments taken from the corneal surface, such maps do not provide by were sought to complications that could arise from the induction of themselves numerical values that can be used for clinical manage- irregular astigmatism. The first topographic index that measured ment. To this end, a number of indexes were developed to make a irregular astigmatism was the Surface Regularity Index (SRI).34 host of diagnostic uses possible. These might be divided into basic The SRI measured the meridional mire-to-mire changes in power traditional measures used for contact lens fitting, indexes that for the cornea over the apparent entrance pupil of the eye. These could be used to assess the optical quality of the corneal surface, changes were summed to provide the index, SRI. This index was and indexes that could be used in artificial intelligence systems to then correlated to the visual acuity of the patients’ eyes for a group aid in the diagnosis of corneal shape anomalies. For ease of use, of normals as well as patients with keratoconus and corneal trans- most topographic indexes are abbreviated; following are abbrevia- plants. With this correlation, the Potential Visual Acuity (PVA) of tions adopted by the author, but the same, or similar, indexes are the eye could be predicted and was provided in terms of Snellen in common use with different designations as, for example, with 30 lines. the Holladay Diagnostic Summary. A different approach to measuring corneal surface distortion was taken by Maloney et al.35 and Holladay30 who chose to find THE BASIC TOPOGRAPHY INDEXES the best fitting ellipsoid to the central cornea and then to calculate the difference between this semi-ideal surface and the corneal Simulated Keratometry elevation. Using clinical correlations, Holladay presented these The first quantitative descriptor of corneal topography was the distortions in the form of a color-coded map of predicted regional Simulated Keratometry (SimK) that simulated the familiar kera- Snellen acuity as a measure of optical quality.

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Fourier Methods fractive keratotomy [RK], PRK, and LASIK), it is universally seen Fourier series are particularly good at fitting periodic functions that the calculated total corneal aberrations increase significantly and decomposing these into their underlying components through with a 7-mm pupil. This is not surprising because the planned a transform from the spatial domain to the time domain. This optical zone of these procedures varied from <5 mm to 5.5 mm at transformation can provide ACP, amount and axis of regular astig- the most. However, when 3-mm pupils were assessed, the amount matism, and terms that can be summed to provide an estimate of of induced optical aberrations was considerably less (300 times) irregular astigmatism as well.36–38 This approach has been used to than for the 7-mm pupil. Although coma increased slightly with evaluate both regular and irregular corneal astigmatism. the 3-mm pupil, spherical-like aberrations were actually dimin- ished.44 More recent studies with a third generation scanning laser (Model EC-5000; NIDEK) found a statistically significant de- Ray Tracing crease in total aberrations for the 3-mm pupil, a strong indication Although the SRI is a primitive form of ray tracing, a more that refractive surgical procedures are showing significant im- precise and sophisticated approach has been taken by several provement. groups. Using ray tracing techniques, effective spherical aberration was found to be highly correlated with best corrected acuity in 39 patients who had underdone PRK. The TechnoMed C-Scan TOPOGRAPHIC INDEXES FOR CLASSIFICATION (Table 1) uses ray tracing through a Gullstrand Model Eye to AND AUTODIAGNOSIS estimate visual acuity from the minimum resolvable variable. Camp et al.40 and Maguire et al.41 demonstrated a subjective ray Rabinowitz and McDonnell45 developed algorithms for the de- tracing approach by calculating images that would be formed tection of keratoconus that are available on some corneal topog- through individual corneas with irregular astigmatism. raphers. This method is based on three observations regarding keratoconus. First, dioptric power differences are commonly noted Aberration Structures between the superior and inferior paracentral corneal regions in Optical systems have traditionally been studied by evaluating keratoconus. The computation measuring this difference is referred wavefronts, the term used to describe the optical path length of to as the I−S value. Second, central corneal power is usually sig- light rays through a lens system. If the optical path lengths were nificantly higher in keratoconus than normals. Third, there is com- uniform over the pupil of the eye, there would be no aberration of monly a difference in progression of corneal steepening between the wavefront and supernormal vision could be achieved, which is the two eyes of a keratoconus patient. The approach is straight thought to be equivalent to 20/8, the limit imposed by receptor forward and might be used manually on most corneal topogra- diameter in the fovea and diffraction. However, the optics of the phers. The method yields a positive result for keratoconus suspect eye are not ideal, and distortions occur that blur the retinal image. if the central corneal power is >47.2 D. It also yields a positive Even so, most normal eyes achieve 20/20 vision and some can result for keratoconus suspect if the I−S value is >1.4 D. The achieve 20/10 vision unaided. method yields a positive result for clinical keratoconus if the cen- Because the corneal/tear film is the major refracting interface in tral corneal power is >48.7 D or if the I−S value is >1.9 D. the eye and because it is easily accessible, the measurement of the Extending this approach to autodiagnosis, an expert system was 46,47 eye’s aberrations stemming from corneal shape imperfections has developed by Maeda et al. With this method, discriminant received a good deal of attention. Applegate et al.42,43 and others44 analysis is used to produce the keratoconus prediction index. The have applied wavefront analysis to examine the aberration struc- keratoconus prediction index is obtained from topographic indexes ture of the cornea before and after refractive surgery with the aim designed to capture the characteristics seen in keratoconus maps— to understand the impact on visual function. The method is local abnormal elevations in corneal power. These include the straightforward, but elegant. Corneal topography data ordinarily differential sector index, the opposite sector index, and the center/ comprises three-dimensional elements that include position on the surround index. Several other indexes were used as well to in- corneal surface, dioptric power, and elevation (true shape data). To crease the specificity of the method: the surface asymmetry index, determine the aberration structure of a cornea, the elevations of the the irregular astigmatism index, and the percent area analyzed. The presurgical cornea over a specified diameter centered over the output of the discriminant analyzer was fed to a binary decision pupil are matched with the best-fitting sphere. The differences tree to further enhance the method’s performance. between the postoperative corneal elevations and this best-fitting A more sophisticated approach for classification of corneal to- sphere are found and this is called the remainder lens. This struc- pography and detection of topographic abnormalities developed by 48 ture is then fit with a three-dimensional Taylor polynomial equa- Maeda et al. is the neural network model involving artificial tion and is transformed to a Zernike polynomial series to examine intelligence. This method entails automated pattern interpretation tilt or prism, defocus and astigmatism, coma-like aberrations, through the training of a neural network computer program. This 49 spherical-like aberrations, and irregular aberrations. Analyses are approach was extended by Smolek and Klyce to produce a done that compare preoperative corneal aberrations to the same method that obtained 100% accuracy, specificity, and sensitivity in types of aberration after surgery. With this approach one can ex- both the training set as well as, importantly, a test set to which the amine the aberrations for various pupil diameters. This generally is neural network was naive. done with a 3-mm pupil to examine daylight vision and with a 7-mm pupil to evaluate night vision. The Future of Corneal Topography With this approach, a number of both obvious and subtle ob- One year ago our crystal ball was murky. Glimpses toward the servations have been made when analyzing the results of refractive future did not forecast a huge leap forward in technology beyond surgery. First, with all forms of refractive surgery analyzed (re- the production of portable or hand-held topographers that cost very

Cornea, Vol. 19, No. 5, 2000 728 S.D. KLYCE little, took up almost no clinic space, could suggest a diagnosis on learn what the perfect optics are for optimal neuroretinal function. command, and had software for every conceivable application Like Columbus’ findings on the curvature of the Earth, we may from a simple color-coded map of the cornea to contact lens fitting. discover that the perfect wavefront is not flat! Those visions certainly did not look too far ahead, as we have these capabilities today. We also had hopes that the scanning slit tech- Acknowledgments: This work was supported in part by U.S. Public Health Service grants EY03311 and EY02377 from the National Eye In- nology would emerge as the total corneal modeling system Com- stitute, National Institutes of Health, Bethesda, MD, U.S.A. puted Anatomy had so many years ago tried to perfect. 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