corneal topography and the new wave · the corneal modeling system (computed anatomy, new york, ny,...

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Corneal Topography and the New Wave Stephen D. Klyce, Ph.D. The normal prolate ellipsoidal corneal front surface with its 8–10-m thin and optically smooth tear film accounts for about two-thirds of the refractive power of the eye. Disruptions in the tear film and induction of irregularity in corneal shape can, there- fore, degrade the optical quality of the eye and reduce visual acuity. Such distortions in the corneal surface can be so subtle as to escape detection with the usual biomicroscope examination. Retinoscopy is a subjective diagnostic procedure that can reveal fairly slight distortions in the retinal image that can arise from the cornea. However, retinoscopy does not reveal the nature and/or locus of the aberrating medium, for corneal back surface, lenticu- lar, and retinal anomalies can distort vision as well. Twenty-five years ago, corneal specialists used retinoscopy and photokeratos- copy to diagnose mild keratoconus and to manage astigmatism in corneal grafts. Just a few years later, refractive surgery took its first halting steps into clinical practice; it was this scenario that provided the impetus for the development of improved methods for analyzing corneal shape. Corneal topography as a routine clini- cal examination was born, and its acceptance can be judged by the explosive growth of publications on this subject in the peer- reviewed literature (Fig. 1). THE PHOTOKERATOSCOPE In the mid 1970s, corneal topography was evaluated with the photokeratoscope, and the two models generally available were the NIDEK PKS-1000 1 (NIDEK Corporation, Gamagori, Japan) and the Corneascope (International Diagnostic Instruments, Tulsa, OK, U.S.A.). 2 These devices combine an illuminated Placido disk tar- get and an instant film camera to capture an image of the Placido mires reflected from the cornea. Initially, clinicians interpreted photokeratoscope photographs by visual inspection, recognizing that corneal steepening was represented by minification of the mires, that corneal flattening was represented by a magnification of the mires, and that irregular astigmatism was represented by irregularities in the mire pattern. Further, corneal cylinder repre- sented by elliptically shaped mires and keratoconus often revealed itself as pear-shaped mires. Although this technology was useful, particularly for trying to manage the sizable astigmatism present in corneal transplants, 3 it was humbling to realize that no significant clinical advance had been made since 1880 when Antonio Placido first introduced the Placido disk. When keratorefractive surgery made its entrance in the late 1970s, it became clear that a more sensitive and quantitative method for corneal shape analysis was in order. Visual inspection of Placido mires can fail to detect up to 3 diopters (D) of corneal cylinder, mild keratoconus, and, in refrac- tive surgery and corneal transplants, the etiology of postoperative visual distortions. One of the most successful analytical approaches to providing quantitative measures from photokeratoscopy derived from the work of Doss et al. 4 who, in 1981, scanned Corneascope photo- graphs and proposed a mathematical method for the conversion of mire size and shape to corneal power. These data were presented in the form of a numerical plot. Subsequently in 1984, Klyce 5 proposed a method for reconstructing corneal shape and power by digitizing mires from NIDEK photokeratoscope photographs. In this work, graphical plots using three-dimensional wire mesh mod- els were used to depict corneal topography, as condensing the thousands of data points collected from the photokeratoscope pho- tographs was necessary to permit clinical use. The final graphical presentation form of this data, which has become the international standard, was the color-coded contour map of corneal powers pre- sented by Maguire et al. 6 in 1987. Corneal power or curvature had been measured clinically for nearly a century before the advent of corneal topographers. Oph- thalmometers (such as the ophthalmometer Javal and Schioetz in- troduced in the 1890s), predecessors to the keratometers, very accurately measure the curvature of the corneal front surface. They are calibrated so that a surface with a 7.5-mm radius of curvature would correspond to 45 D of refractive power. This leads to the convenient, but artificial, refractive index gradient of 7.5 × 45 337.5, which is termed the keratometric index. Importantly, this convention yields an accurate measure of the radius of curvature for the front surface of the cornea for contact lens fitting; however, this relation cannot be accurately used to predict corneal refractive power changes, particularly when only the anterior surface curva- ture is modified. 7,8 Nevertheless, for consistency of clinical inter- pretation, the keratometric index has been carried over for the expression of corneal power in corneal topographers. On the av- erage, normal adult human corneal power is about 43 D with this convention. For the 43-D cornea, anterior surface curvature, thus, is 7.85 mm (337.5/43). THE COLOR-CODED MAP With the introduction of the color-coded contour map of corneal powers, the concept of color association conveyed whether corneal power was higher or lower than the average 43-D norm. A color spectrum was chosen so that powers near the norm showed as Submitted February 16, 2000. Revision received May 17, 2000. Ac- cepted May 18, 2000. From the Lions Eye Research Laboratories, LSU Eye Center, Louisiana State University Medical Center School of Medicine, New Orleans, Loui- siana, U.S.A. Address correspondence and reprint requests to Dr. Stephen D. Klyce, LSU Eye Center, 2020 Gravier Street, Suite B, New Orleans, LA 70112, U.S.A. E-mail: [email protected] Cornea 19(5): 723–729, 2000. © 2000 Lippincott Williams & Wilkins, Inc., Philadelphia 723

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Page 1: Corneal Topography and the New Wave · The Corneal Modeling System (Computed Anatomy, New York, NY, U.S.A.) was the first of a growing number of devices for measuring corneal topography

Corneal Topography and the New Wave

Stephen D. Klyce, Ph.D.

The normal prolate ellipsoidal corneal front surface with its8–10-�m thin and optically smooth tear film accounts for abouttwo-thirds of the refractive power of the eye. Disruptions in thetear film and induction of irregularity in corneal shape can, there-fore, degrade the optical quality of the eye and reduce visualacuity. Such distortions in the corneal surface can be so subtle asto escape detection with the usual biomicroscope examination.Retinoscopy is a subjective diagnostic procedure that can revealfairly slight distortions in the retinal image that can arise from thecornea. However, retinoscopy does not reveal the nature and/orlocus of the aberrating medium, for corneal back surface, lenticu-lar, and retinal anomalies can distort vision as well. Twenty-fiveyears ago, corneal specialists used retinoscopy and photokeratos-copy to diagnose mild keratoconus and to manage astigmatism incorneal grafts. Just a few years later, refractive surgery took itsfirst halting steps into clinical practice; it was this scenario thatprovided the impetus for the development of improved methodsfor analyzing corneal shape. Corneal topography as a routine clini-cal examination was born, and its acceptance can be judged by theexplosive growth of publications on this subject in the peer-reviewed literature (Fig. 1).

THE PHOTOKERATOSCOPE

In the mid 1970s, corneal topography was evaluated with thephotokeratoscope, and the two models generally available were theNIDEK PKS-10001 (NIDEK Corporation, Gamagori, Japan) andthe Corneascope (International Diagnostic Instruments, Tulsa, OK,U.S.A.).2 These devices combine an illuminated Placido disk tar-get and an instant film camera to capture an image of the Placidomires reflected from the cornea. Initially, clinicians interpretedphotokeratoscope photographs by visual inspection, recognizingthat corneal steepening was represented by minification of themires, that corneal flattening was represented by a magnificationof the mires, and that irregular astigmatism was represented byirregularities in the mire pattern. Further, corneal cylinder repre-sented by elliptically shaped mires and keratoconus often revealeditself as pear-shaped mires. Although this technology was useful,particularly for trying to manage the sizable astigmatism present incorneal transplants,3 it was humbling to realize that no significant

clinical advance had been made since 1880 when Antonio Placidofirst introduced the Placido disk. When keratorefractive surgerymade its entrance in the late 1970s, it became clear that a moresensitive and quantitative method for corneal shape analysis was inorder. Visual inspection of Placido mires can fail to detect up to 3diopters (D) of corneal cylinder, mild keratoconus, and, in refrac-tive surgery and corneal transplants, the etiology of postoperativevisual distortions.

One of the most successful analytical approaches to providingquantitative measures from photokeratoscopy derived from thework of Doss et al.4 who, in 1981, scanned Corneascope photo-graphs and proposed a mathematical method for the conversion ofmire size and shape to corneal power. These data were presentedin the form of a numerical plot. Subsequently in 1984, Klyce5

proposed a method for reconstructing corneal shape and power bydigitizing mires from NIDEK photokeratoscope photographs. Inthis work, graphical plots using three-dimensional wire mesh mod-els were used to depict corneal topography, as condensing thethousands of data points collected from the photokeratoscope pho-tographs was necessary to permit clinical use. The final graphicalpresentation form of this data, which has become the internationalstandard, was the color-coded contour map of corneal powers pre-sented by Maguire et al.6 in 1987.

Corneal power or curvature had been measured clinically fornearly a century before the advent of corneal topographers. Oph-thalmometers (such as the ophthalmometer Javal and Schioetz in-troduced in the 1890s), predecessors to the keratometers, veryaccurately measure the curvature of the corneal front surface. Theyare calibrated so that a surface with a 7.5-mm radius of curvaturewould correspond to 45 D of refractive power. This leads to theconvenient, but artificial, refractive index gradient of 7.5 × 45 �337.5, which is termed the keratometric index. Importantly, thisconvention yields an accurate measure of the radius of curvaturefor the front surface of the cornea for contact lens fitting; however,this relation cannot be accurately used to predict corneal refractivepower changes, particularly when only the anterior surface curva-ture is modified.7,8 Nevertheless, for consistency of clinical inter-pretation, the keratometric index has been carried over for theexpression of corneal power in corneal topographers. On the av-erage, normal adult human corneal power is about 43 D with thisconvention. For the 43-D cornea, anterior surface curvature, thus,is 7.85 mm (337.5/43).

THE COLOR-CODED MAP

With the introduction of the color-coded contour map of cornealpowers, the concept of color association conveyed whether cornealpower was higher or lower than the average 43-D norm. A colorspectrum was chosen so that powers near the norm showed as

Submitted February 16, 2000. Revision received May 17, 2000. Ac-cepted May 18, 2000.

From the Lions Eye Research Laboratories, LSU Eye Center, LouisianaState University Medical Center School of Medicine, New Orleans, Loui-siana, U.S.A.

Address correspondence and reprint requests to Dr. Stephen D. Klyce,LSU Eye Center, 2020 Gravier Street, Suite B, New Orleans, LA 70112,U.S.A. E-mail: [email protected]

Cornea 19(5): 723–729, 2000. © 2000 Lippincott Williams & Wilkins, Inc., Philadelphia

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green, powers lower than the norm showed as cool colors (bluehues), and high corneal powers showed as warm colors (red hues).Only a few distinct, recognizable colors were chosen over thecentral range of corneal powers so that a specific power rangecould be easily identified. Using a contour map allows the asso-ciation of certain patterns with different corneal shapes. Hence,pattern recognition permits the identification of naturally occurringtopographies, such as corneal cylinder (bow tie pattern), kerato-conus (local area of steepening), and pellucid marginal degenera-tion (inferior arcuate steepening), as well as features associatedwith refractive surgery, such as optical zone size, centration, and(rarely) central islands.

STANDARDIZED SCALES

The clinical use of corneal topography depends on how well thecolor-coded maps can be interpreted using color association andpattern recognition as mentioned above. The colors and dioptricintervals originally proposed6 have been modified in a number ofways by manufacturers, as efforts to standardize corneal topogra-phy have not been successful. Because standards are essential forthe comparison and sharing of information, it is important that theybe established in corneal topography. The first scale used on acommercial topographer was patterned after Maguire et al.6 Calledthe Absolute Scale, it spanned a range of corneal powers from9–101.5 D, with 1.5 D intervals in the middle of the range and 5D intervals at each end. Wilson et al.9 introduced a more practicalscale (the Klyce/Wilson scale), which ranged 28.0–65.5 D in equal1.5-D intervals. Replacing the 5.0-D intervals at the extremes wasparticularly important with the advent of refractive surgical pro-cedures; because, with corrections for high myopia, if irregularastigmatism occurred in the central, surgically flattened region, itcould be masked.

Even with this improvement, it was often argued that the 1.5-Dinterval was so wide that important features in corneal topographycould be hidden between contours. The diagnostic adequacy of theKlyce/Wilson scale was evaluated in a clinical series that included

normal corneas, contact lens-wearing corneas, early to moderateand advanced keratoconus, penetrating keratoplasties, extracapsu-lar cataract surgery, excimer laser photorefractive keratectomy(PRK), radial keratotomy, aphakic epikeratoplasty, and myopicepikeratoplasty. It was found that the correct interpretation for allcases could be made with the 1.5-D scale without resorting to a1.0-D or lower interval scale.9 Additionally, the 1.5-D scaleproved broad enough to cover the full range of powers encounteredin the study. The routine use of a fixed standard scale showing onlyadequate detail and not redundant information or extraneous mea-surement noise is essential for efficient and accurate clinical in-terpretation.

It should be noted that the sensitivities and resolutions of cor-neal topographers varies with design. A scale with a 1.5-D intervalwas found adequate for the Tomey corneal topographers,9 whereasa 0.5-D interval is generally used on topographers with fewer andbroader mires and correspondingly less sensitivity.

It has been traditional that videokeratoscopes provide adaptablescales that are self-adjusting to the range of powers found for agiven cornea. The use of such scales runs counter to standardiza-tion in corneal topography and can be misleading. Such scales canmake grossly irregular corneas look uncomplicated and quite nor-mal corneas look complex with extensive amounts of irregularastigmatism. Such adaptive scales should be avoided except as anadjunct to examine details of corneal topography.

Although manufacturers have universally accepted the use ofwarm colors for high powers and cool colors for low powers, notall agree that contrasting colors need to be used in the centralrange. The use of continuous hues can mask contours that hideirregular astigmatism. Figure 2 compares a version of an AmericanNational Standards Institute-proposed standard scale to the Klyce-Wilson scale. Figure 3 shows a commercial implementation of theANSI proposal and compares it to a similar surgical case. The lossof topographic information with less contrasting colors reducesclinical use.

CORNEAL TOPOGRAPHERSThe Corneal Modeling System (Computed Anatomy, New

York, NY, U.S.A.) was the first of a growing number of devicesfor measuring corneal topography and this class of machine em-ploying the videocapture of Placido disk images was known as avideokeratoscope. The Placido disk approach has been the mostclinically and commercially successful (Table 1). Some of thesehave been validated in terms of accuracy and reproducibility10–17

as there can be considerable differences between the results ob-tained with the various machines. Two types of Placido targetshave been used. A large diameter target can be less sensitive tomisalignment due to a long working distance but is subject to dataloss by eclipse of the mires by the brow and nose of the patient. Asmall diameter cone-shaped target does not suffer from peripheraldata loss due to shadows, but given their short working distances,these rely on automatic alignment and focus or compensation formisalignment for accuracy.

The chronologically second technology developed to measurecorneal shape is the technique of rasterstereography.18–20 With thisapproach, fluorescein is first instilled in the tear film, and a grid orraster pattern is projected with cobalt blue light onto the anteriorsurface of the eye. Images are then captured simultaneously fromtwo directions and processed using triangulation methodology toreconstruct the shape of the cornea. This seems to be less sensitive

FIG. 1. Corneal topography publications per year. The number ofpeer-reviewed publications on corneal topography (MEDLINE) hasgrown dramatically over the last 25 years since the first radial kera-totomy procedure was performed in the United States in 1979. Sincethe color-coded map and commercial corneal topographers becameavailable (1987), the diagnostic procedure has become the standardof medical practice for cornea/anterior segment clinicians.

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than Placido disk topography; and, this limitation along with theinconvenience of having to instill fluorescein reduces its useful-ness. On the plus side, rasterstereography can measure actual cor-neal shape directly without the successive approximation methodused with Placido disk machines. Hence, there is the potential forgreater accuracy in measuring corneal shape when compared tosurface power.

The use of scanning slit beam technology can provide the op-portunity to analyze both the outer and inner surfaces of the corneaand was first introduced in the Corneal Modeling System. Becauseboth of these refracting surfaces—as well as corneal thickness—come into play when calculating total corneal power, measuringthe position of the surfaces directly would provide an advantage.Additionally, because each of the surfaces can be measured di-rectly with slit beam technology, no approximation errors shouldarise as with the Placido disk-based devices. Further, the ability tomeasure corneal thickness over a broad area would provide valu-able guidance to the refractive surgeon, particularly if the sensi-tivity were great enough to detect the local stromal thinning asso-ciated with clinical keratoconus or the keratectasia that is claimedto result when too thin a corneal stromal bed is left after a laser insitu keratomileusis (LASIK) procedure is performed.21

This technique is currently embodied in the Orbscan II (Bauschand Lomb, Rochester, NY, U.S.A.; Table 1), which uses a Placidodisk for a traditional measurement of corneal topography and ascanning slit to obtain 40 slit images of the cornea. These images,

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 cornealthickness has been questioned22,23 showing a need for independentvalidation studies. Further, the validity of scanning slit studiesreporting keratectasia after LASIK has been challenged on math-ematical grounds.24 There may be shortcomings to the scanningslit approach that are difficult to overcome. Because the cornea isin constant motion from fixation drift, muscle tremor, pulse, andnystagmus, correlated measurements must be captured simulta-neously or in a minimum time period of 30 ms or less. Simulta-neous data capture was incorporated into optical pachometers andkeratometers using the principle of image doubling—using an im-age splitter to superimpose or line up, for example, the slit imageof the endothelium with that of the epithelium. A scanning slitdevice capturing successive slit images over a long period of timerequires either a tracking system (expensive) or an accurate post-

FIG. 3. Color choices for maps are critical for interpretation. Theseare two different patient corneas, each underwent LASIK and eachlost two or more lines of best spectacle corrected vision. A: Thechoice of contrast colors easily permits appreciation of the irregularastigmatism within this patient’s entrance pupil. B: In this commercialimplementation of the ANSI proposal, lack of contrast hides pupillaryirregular astigmatism and the cause of this patient’s reduced acuity.

FIG. 2. Color association and corneal power. A: Distinct, identifiablecolors in the central part of this color-coded contour map proposedby Maguire et al.6 permit association of a power interval with certainregions on the cornea. B: The use of a progression of hues ascurrently proposed by an ANSI task force makes knowledge ofpower interval difficult and reduces contrast.

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capture image registration technique (difficult with low contrastimages) to eliminate significant movement artifact.

Potentially, the most accurate methodology that has been pro-posed to measure corneal shape is interferometry.25 Interferencetechniques are used in the optical industry to detect lens and mirroraberrations of subwavelength dimensions. In essence, a referencesurface (or its hologram) is compared to the measured surface(cornea) and interference fringes are produced as a result of dif-ferences between the two shapes. With respect to the measurementof corneal shape, there is such a wide variation in the shapes ofcorneas, even among those that are normal, that it is difficult for asingle interference device to represent all variations. Examples ofinterference devices include a phase-modulated laser holography-based device26,27 (Table 1) and an acoustic holographic tech-nique.28 Neither approach has led yet to a clinically accepted di-agnostic tool. Belin and Missry29 more completely review thetechnology used in modern corneal topographers.

CORNEAL TOPOGRAPHIC INDEXES

Although the color-coded map provides a rapid method forclinical diagnosis and is constructed from quantitative measure-ments taken from the corneal surface, such maps do not provide bythemselves numerical values that can be used for clinical manage-ment. To this end, a number of indexes were developed to make ahost of diagnostic uses possible. These might be divided into basictraditional measures used for contact lens fitting, indexes thatcould be used to assess the optical quality of the corneal surface,and indexes that could be used in artificial intelligence systems toaid in the diagnosis of corneal shape anomalies. For ease of use,most topographic indexes are abbreviated; following are abbrevia-tions adopted by the author, but the same, or similar, indexes arein common use with different designations as, for example, withthe Holladay Diagnostic Summary.30

THE BASIC TOPOGRAPHY INDEXES

Simulated KeratometryThe first quantitative descriptor of corneal topography was the

Simulated Keratometry (SimK) that simulated the familiar kera-

tometry or “K-Readings.”31 SimK values provide the powers andaxes of the steepest and flattest meridians (SimK1 and SimK2,respectively), similar to values provided by the keratometer. Cyl-inder is often provided as the simple difference between SimK1and SimK2. On the Tomey topographers, SimK values are calcu-lated from rings 7–9, approximately corresponding with the posi-tion on the cornea at which keratometer measurements are ob-tained. SimK values correlate well with keratometry values, and allcorneal topographers provide this measurement. Used for fittingcontact lenses and refractive surgery calculations, SimK values canbe extremely valuable as a beginning point to determine the quan-tity and axis of astigmatism during refractions in eyes with irregu-lar corneal shapes.

Corneal Eccentricity IndexThe Corneal Eccentricity Index (CEI) is a quantitative descrip-

tor that indicates the eccentricity of the central cornea.32 CEI isgenerally calculated by fitting an ellipse to corneal elevation dataobtained with the corneal topographer. The CEI for 22 controlcorneas was reported to be 0.33 ± 0.26 (SD), which correspondswith the prolate shape of the normal central cornea. This value isuseful in contact lens fitting and for differentiating between normalprolate corneas and oblate corneas flattened by myopic refractivesurgery.

Average Corneal PowerThe Average Corneal Power (ACP) is an area-corrected average

of the corneal power before the entrance pupil.33 It is generallyequal to the keratometric spherical equivalent except for decen-tered refractive surgical procedures. In such cases, ACP may behelpful to determine central corneal curvature for intraocular lenspower calculations.

TOPOGRAPHIC INDEXES AND METHODS FORMEASURING CORNEAL OPTICAL QUALITY

Surface Regularity IndexThe development of corneal topography analysis was acceler-

ated with the advent of refractive surgery in the late 1970s as clueswere sought to complications that could arise from the induction ofirregular astigmatism. The first topographic index that measuredirregular astigmatism was the Surface Regularity Index (SRI).34

The SRI measured the meridional mire-to-mire changes in powerfor the cornea over the apparent entrance pupil of the eye. Thesechanges were summed to provide the index, SRI. This index wasthen correlated to the visual acuity of the patients’ eyes for a groupof normals as well as patients with keratoconus and corneal trans-plants. With this correlation, the Potential Visual Acuity (PVA) ofthe eye could be predicted and was provided in terms of Snellenlines.

A different approach to measuring corneal surface distortionwas taken by Maloney et al.35 and Holladay30 who chose to findthe best fitting ellipsoid to the central cornea and then to calculatethe difference between this semi-ideal surface and the cornealelevation. Using clinical correlations, Holladay presented thesedistortions in the form of a color-coded map of predicted regionalSnellen acuity as a measure of optical quality.

TABLE 1. Corneal topographers

Manufacturer Model(s) Method

Alcon Surgical EyeMap EH-290 PlacidoAlliance Medical Mkts Keratron CT; Scout PlacidoDicon CT-200 PlacidoEuclid Systems ET-800 Fluorescein profilometryEyeSys/Premier EyeSys 2000; Vista PlacidoEYETEK CT2000 PlacidoKera Metrics CLAS-1000 Phase modulated laser

holographyHumphrey Instruments Atlas 991, 992 PlacidoMedmont E300 PlacidoOculus Keratograph PlacidoBausch & Lomb Surgical Orbscan II 40 Scanned slits &

PlacidoBausch & Lomb Surgical Orbshot PlacidoPAR Vision Systems CTS, Accugrid Fluorescein profilometryPAR Vision Systems Intraop. CTS Fluorescein profilometrySun Contact Lens Co. SK-2000 PlacidoTechnomed Technology C-SCAN PlacidoTomey Technology Auto Topographer PlacidoTopcon American Corp. CM-1000 Placido

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Fourier MethodsFourier series are particularly good at fitting periodic functions

and decomposing these into their underlying components througha transform from the spatial domain to the time domain. Thistransformation can provide ACP, amount and axis of regular astig-matism, and terms that can be summed to provide an estimate ofirregular astigmatism as well.36–38 This approach has been used toevaluate both regular and irregular corneal astigmatism.

Ray TracingAlthough the SRI is a primitive form of ray tracing, a more

precise and sophisticated approach has been taken by severalgroups. Using ray tracing techniques, effective spherical aberrationwas found to be highly correlated with best corrected acuity inpatients who had underdone PRK.39 The TechnoMed C-Scan(Table 1) uses ray tracing through a Gullstrand Model Eye toestimate visual acuity from the minimum resolvable variable.Camp et al.40 and Maguire et al.41 demonstrated a subjective raytracing approach by calculating images that would be formedthrough individual corneas with irregular astigmatism.

Aberration StructuresOptical systems have traditionally been studied by evaluating

wavefronts, the term used to describe the optical path length oflight rays through a lens system. If the optical path lengths wereuniform over the pupil of the eye, there would be no aberration ofthe wavefront and supernormal vision could be achieved, which isthought to be equivalent to 20/8, the limit imposed by receptordiameter in the fovea and diffraction. However, the optics of theeye are not ideal, and distortions occur that blur the retinal image.Even so, most normal eyes achieve 20/20 vision and some canachieve 20/10 vision unaided.

Because the corneal/tear film is the major refracting interface inthe eye and because it is easily accessible, the measurement of theeye’s aberrations stemming from corneal shape imperfections hasreceived a good deal of attention. Applegate et al.42,43 and others44

have applied wavefront analysis to examine the aberration struc-ture of the cornea before and after refractive surgery with the aimto understand the impact on visual function. The method isstraightforward, but elegant. Corneal topography data ordinarilycomprises three-dimensional elements that include position on thecorneal surface, dioptric power, and elevation (true shape data). Todetermine the aberration structure of a cornea, the elevations of thepresurgical cornea over a specified diameter centered over thepupil are matched with the best-fitting sphere. The differencesbetween the postoperative corneal elevations and this best-fittingsphere are found and this is called the remainder lens. This struc-ture is then fit with a three-dimensional Taylor polynomial equa-tion and is transformed to a Zernike polynomial series to examinetilt or prism, defocus and astigmatism, coma-like aberrations,spherical-like aberrations, and irregular aberrations. Analyses aredone that compare preoperative corneal aberrations to the sametypes of aberration after surgery. With this approach one can ex-amine the aberrations for various pupil diameters. This generally isdone with a 3-mm pupil to examine daylight vision and with a7-mm pupil to evaluate night vision.

With this approach, a number of both obvious and subtle ob-servations have been made when analyzing the results of refractivesurgery. First, with all forms of refractive surgery analyzed (re-

fractive keratotomy [RK], PRK, and LASIK), it is universally seenthat the calculated total corneal aberrations increase significantlywith a 7-mm pupil. This is not surprising because the plannedoptical zone of these procedures varied from <5 mm to 5.5 mm atthe most. However, when 3-mm pupils were assessed, the amountof induced optical aberrations was considerably less (300 times)than for the 7-mm pupil. Although coma increased slightly withthe 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-crease in total aberrations for the 3-mm pupil, a strong indicationthat refractive surgical procedures are showing significant im-provement.

TOPOGRAPHIC INDEXES FOR CLASSIFICATIONAND AUTODIAGNOSIS

Rabinowitz and McDonnell45 developed algorithms for the de-tection of keratoconus that are available on some corneal topog-raphers. This method is based on three observations regardingkeratoconus. First, dioptric power differences are commonly notedbetween the superior and inferior paracentral corneal regions inkeratoconus. The computation measuring this difference is referredto as the I−S value. Second, central corneal power is usually sig-nificantly higher in keratoconus than normals. Third, there is com-monly a difference in progression of corneal steepening betweenthe two eyes of a keratoconus patient. The approach is straightforward and might be used manually on most corneal topogra-phers. The method yields a positive result for keratoconus suspectif the central corneal power is >47.2 D. It also yields a positiveresult for keratoconus suspect if the I−S value is >1.4 D. Themethod yields a positive result for clinical keratoconus if the cen-tral corneal power is >48.7 D or if the I−S value is >1.9 D.

Extending this approach to autodiagnosis, an expert system wasdeveloped by Maeda et al.46,47 With this method, discriminantanalysis is used to produce the keratoconus prediction index. Thekeratoconus prediction index is obtained from topographic indexesdesigned to capture the characteristics seen in keratoconus maps—local abnormal elevations in corneal power. These include thedifferential sector index, the opposite sector index, and the center/surround index. Several other indexes were used as well to in-crease the specificity of the method: the surface asymmetry index,the irregular astigmatism index, and the percent area analyzed. Theoutput of the discriminant analyzer was fed to a binary decisiontree to further enhance the method’s performance.

A more sophisticated approach for classification of corneal to-pography and detection of topographic abnormalities developed byMaeda et al.48 is the neural network model involving artificialintelligence. This method entails automated pattern interpretationthrough the training of a neural network computer program. Thisapproach was extended by Smolek and Klyce49 to produce amethod that obtained 100% accuracy, specificity, and sensitivity inboth the training set as well as, importantly, a test set to which theneural network was naive.

The Future of Corneal TopographyOne year ago our crystal ball was murky. Glimpses toward the

future did not forecast a huge leap forward in technology beyondthe production of portable or hand-held topographers that cost very

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little, took up almost no clinic space, could suggest a diagnosis oncommand, and had software for every conceivable applicationfrom a simple color-coded map of the cornea to contact lens fitting.Those visions certainly did not look too far ahead, as we have thesecapabilities today. We also had hopes that the scanning slit tech-nology would emerge as the total corneal modeling system Com-puted Anatomy had so many years ago tried to perfect. We lookedfor the development of an accurate intraoperative topography sys-tem to guide the tensioning of sutures at the close of a cornealtransplant or a cataract procedure to further diminish induced cyl-inder. These latter two goals have yet to be met, but meanwhile,there has been an enormous resurgence of interest in an old tech-nology: spatially resolved refractometry, which Thompson et al.introduced to ophthalmology a decade ago.50

WAVEFRONT SENSING

As discussed above, determination of the aberration structure ofthe cornea from topography data can help to understand the opticalquality of the corneal surface after refractive surgery. However,although keratorefractive surgery is performed on (PRK) andwithin (LASIK) the cornea to correct ametropias, the goal of theprocedure is to correct the refractive error of the whole eye. Mostrefractive surgical procedures correct vision just as spectacles dowith an attempted spherocylindrical change. However, as excimerlasers become more sophisticated, it is becoming possible to makecomplex shape changes on the corneal surface. Examples of suchcommercial products include the “custom cornea” feature of theSummit/Autonomous Technologies (Orlando, FL, U.S.A.)LadarVision flying spot excimer laser, the VISX excimer laserwith its Custom Ablation Pattern (VISX Corporation, Sunnyvale,CA, U.S.A.), and the ARK-10000/EC-5000 from NIDEK Corpo-ration. With the capability to custom carve the corneal surfacecame the realization that correcting the corneal’s irregular astig-matism, as with phototherapeutic keratectomy, was a good firststep to improving visual acuity. But as Keith Thompson and othersrealized so many years ago, if we could measure the optical ab-errations of the whole eye on a point-by-point basis, then onemight be able to use a scanning laser to modify the cornea tocorrect total optical aberrations. As a result, the Hartmann-Shackaberrometer was hauled unceremoniously out of the astronomer’slaboratory and was transformed to the task of wavefront sensing bySummit/Autonomous Technologies. Other approaches to measurewavefronts include ray tracing with a scanning laser beam (Tracey;Tracey Technologies, Houston, TX, U.S.A.) and a scanning devicebased on the principle of skiascopy (ARK-10000; NIDEK).

Wavefront sensors are now becoming front ends to excimerlasers used in refractive surgery and there is the glib notion thatsuch devices will obsolete corneal topographers. One needs to bereminded that to alter the refractive properties of the cornea, oneneeds to know the initial corneal topography. Additionally, at thismoment in time, the spatial resolution of wave sensing technologyis inadequate to detect the finer details of corneal irregular astig-matism. Finally, the detection of corneal pathology such as mildkeratoconus could be confounded by aberrations elsewhere in theeye.

The goal of refractive surgery has been to correct ametropias.Currently, the goal is to eliminate all of the eye’s aberrations tocreate super-vision. This is perhaps a wonderful opportunity to

learn what the perfect optics are for optimal neuroretinal function.Like Columbus’ findings on the curvature of the Earth, we maydiscover that the perfect wavefront is not flat!

Acknowledgments: This work was supported in part by U.S. PublicHealth Service grants EY03311 and EY02377 from the National Eye In-stitute, National Institutes of Health, Bethesda, MD, U.S.A.

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